index int64 0 1,000k | blob_id stringlengths 40 40 | code stringlengths 7 10.4M |
|---|---|---|
996,000 | 1279209d055bb6083db67eebe18954aab648fa90 | # -*- coding: utf-8 -*-
# Generated by Django 1.11.3 on 2017-08-01 21:13
from __future__ import unicode_literals
import datetime
from django.db import migrations, models
import django.db.models.deletion
class Migration(migrations.Migration):
dependencies = [
('outros', '0005_auto_20170801_1355'),
]
operations = [
migrations.CreateModel(
name='item',
fields=[
('id', models.AutoField(primary_key=True, serialize=False)),
('qnt', models.IntegerField()),
('obs', models.CharField(blank=True, max_length=200, null=True)),
('produto1', models.ForeignKey(on_delete=django.db.models.deletion.CASCADE, to='outros.produto')),
],
),
migrations.AlterField(
model_name='comanda',
name='data',
field=models.DateTimeField(default=datetime.datetime(2017, 8, 1, 17, 13, 46, 319845)),
),
migrations.AlterField(
model_name='comanda',
name='produtos',
field=models.ManyToManyField(to='outros.item'),
),
]
|
996,001 | 6173362d4f04d3e63df4f709da495559fc2fd72b | import pickle
import six
import warnings
from functools import partial
import paddle.fluid as fluid
def load_dygraph(model_path, keep_name_table=False):
"""
To load python2 saved models in python3.
"""
try:
para_dict, opti_dict = fluid.load_dygraph(model_path, keep_name_table)
return para_dict, opti_dict
except UnicodeDecodeError:
warnings.warn(
"An UnicodeDecodeError is catched, which might be caused by loading "
"a python2 saved model. Encoding of pickle.load would be set and "
"load again automatically.")
if six.PY3:
load_bak = pickle.load
pickle.load = partial(load_bak, encoding="latin1")
para_dict, opti_dict = fluid.load_dygraph(model_path, keep_name_table)
pickle.load = load_bak
return para_dict, opti_dict
|
996,002 | 678e671846b511dd34bcc5e317ada4d89786a572 | from pyrave.base import BaseRaveAPI
from pyrave.encryption import RaveEncryption
class Preauth(BaseRaveAPI):
"""
Preauthorization Class
"""
def __init__(self):
super(Preauth, self).__init__()
self.rave_enc = RaveEncryption()
def preauthorise_card(self, log_url=False, **kwargs):
"""
:param log_url:
:param client:
:param algo:
:return:
"""
encrypted_data = self.rave_enc.encrypt(preauthorised=True, **kwargs)
if not encrypted_data:
return encrypted_data
request_data = {
"PBFPubKey": self.secret_key,
"client": encrypted_data[1],
"algo": encrypted_data[2]
}
url = self.rave_url_map.get("payment_endpoint") + "charge"
return self._exec_request("POST", url, request_data, log_url=log_url)
def capture_preauthorised_transaction(self, transaction_reference, log_url=False):
"""
:param log_url:
:param transaction_reference:
:return:
"""
request_data = {
"SECKEY": self.secret_key,
"flwRef": transaction_reference,
}
url = self.rave_url_map.get("payment_endpoint") + "capture"
return self._exec_request("POST", url, request_data, log_url=log_url)
def refund_or_void_transaction(self, action, reference_id, log_url=False):
"""
:param log_url:
:param action:
:param reference_id:
:return:
"""
request_data = {
"ref": reference_id,
"action": action,
"SECKEY": self.secret_key
}
url = self.rave_url_map.get("payment_endpoint") + "refundorvoid"
return self._exec_request("POST", url, request_data, log_url=log_url)
def refund(self, reference_id, log_url=False):
request_data = {
"ref": reference_id,
"seckey": self.secret_key
}
url = self.rave_url_map.get("merchant_refund_endpoint")
return self._exec_request("POST", url, request_data, log_url=log_url)
|
996,003 | 2328d7a645a6a15b7df2d0bf56fa06631ea2f455 | listone = list(input("Enter a sequence of comma separated values: ").split(","))
listtwo = list(input("Enter a sequence of comma separated values: ").split(","))
print("First List ", listone)
print("Second List ", listtwo)
thirdList = []
for num in listone:
i = int(num)
if (i % 2 != 0):
thirdList.append(i)
for num in listtwo:
i = int(num)
if (i % 2 == 0):
thirdList.append(i)
# Print result
print("result List is:")
print(thirdList) |
996,004 | 414115bfbf03095646f07e245c24a4976724e117 | import asyncio
import time
import requests
import socket
def ddos(addr):
TCPClient = socket.socket(socket.AF_INET, socket.SOCK_STREAM)
TCPClient.connect(addr) #连接服务器
TCPClient.send('0x00'.encode())
#@asyncio.coroutine
def main():
tasks = []
result = []
for site in sites:
#tasks.append(loop.run_in_executor(None, requests.head, site))
tasks.append(loop.run_in_executor(None, ddos, (site,23151)))
for task in tasks:
#print(time.time())
r = yield from task
result.append(r)
for s in result:
print(r)
now =time.time()
lenth = 10
sites = ['127.0.0.1']*lenth
loop = asyncio.get_event_loop()
loop.run_until_complete(main())
print(time.time()-now)
class QAsyncThread(QThread):
"""
使用异步方式,只支持py3.4以上
还没写完，异步理论上来说会比多线程更快，
但是实际测试中会因为并发太高而导致网站中断连接
"""
signal = pyqtSignal(bool)
def __init__(self):
QThread.__init__(self)
self.Queue = []
self.threads = 10
self.timeout = 10
self.event = None
self.FLAG = True #stop
self.STAT = False #pause
def stop(self):
self.FLAG = False
self.STAT = False
def pause(self):
self.STAT = not self.STAT
def setup(self,**kwargs):
for k,v in kwargs.items():
setattr(self,k,v)
def run(self):
while self.FLAG:
__ = []
if self.STAT:
self.sleep(1)
continue
for _ in range(self.threads):
task = []
result = []
try:
data = next(self.Queue)
except StopIteration:
self.FLAG = False
break
tasks.append(loop.run_in_executor(None, self.__get_status, data))
for task in tasks:
r = yield from task
result.append(r)
for req in result:
self.signal.emit(req,data)
def __get_status(self,url):
pass |
996,005 | 4f886187559336acf27f9cbc1a0406bd20a6721e | #! python3
# -*- encoding: utf-8 -*-
'''
Current module: tests.test_AppiumJs
Rough version history:
v1.0 Original version to use
********************************************************************
@AUTHOR: Administrator-Bruce Luo(罗科峰)
MAIL: luokefeng@163.com
RCS: tests.test_AppiumJs, v1.0 2018年9月7日
FROM: 2018年9月7日
********************************************************************
======================================================================
Provide a function for the automation test
'''
import unittest,os,time
from appuidriver.remote.AppiumJs import AppiumJs
from webuidriver.remote.SeleniumJar import SeleniumJar
class TestAppiumJs(unittest.TestCase):
@classmethod
def setUpClass(cls):
cls.server = AppiumJs(port = 4723)
def tearDown(self):
self.server.stop_server()
def test_AppiumJs_bind_device_1(self):
# device is connected
self.server.bind_device(device_id = "127.0.0.1:6555")
self.server.start_server()
self.assertEqual(self.server.is_runnnig(), True)
self.server.re_start_server()
self.assertEqual(self.server.is_runnnig(), True)
def test_AppiumJs_bind_device_2(self):
# device is not connected
self.server.bind_device(device_id = "rock test")
self.server.start_server()
self.assertEqual(self.server.is_runnnig(), True)
self.server.re_start_server()
self.assertEqual(self.server.is_runnnig(), True)
def test_AppiumJs_node(self):
jar_path = r'C:\d_disk\auto\buffer\test\tools\seleniumjar\selenium-server-standalone-3.14.0.jar'
java_path = "java"
hub = SeleniumJar(jar_path, java_path).hub(4444)
hub.start_server()
self.assertEqual(hub.is_runnnig(), True)
self.server.bind_device(device_id = "127.0.0.1:6555", platform_version = "4.4.4").node("localhost", hub_address=("localhost", 4444))
self.assertTrue(os.path.isfile('nodeconfig.json'))
self.assertEqual(self.server._cap.get('udid'), "127.0.0.1:6555")
self.assertEqual(self.server._cap.get('udversion'), "4.4.4")
self.server.start_server()
self.assertEqual(self.server.is_runnnig(), True)
self.server.re_start_server()
self.assertEqual(self.server.is_runnnig(), True)
hub.stop_server()
if __name__ == "__main__":
unittest.main()
|
996,006 | b6f52454683ea74895e241cd3b7a04ceeeffbaef | #!/usr/bin/env python
# -*- coding: utf-8 -*-
# import functions for opencv
from __future__ import print_function
from collections import deque
from imutils.video import VideoStream
import numpy as np
import cv2
import imutils
import time
from dronekit import connect, VehicleMode, LocationGlobal, LocationGlobalRelative
from pymavlink import mavutil # Needed for command message definitions
import math
# variables for camera/gimbal settings
x_max = 600 # width of pi camera image
y_max = 450 # height of pi camera image
x_center = x_max / 2 # center value used for readability/ease of editing
y_center = y_max / 2 # center value used for readability/ease of editing
gimbal_y_pos = -45 # goes from -90 to 0
pix_per_deg = 40 # used to adjust movement sensitivity
def mapObjectPosition(x, y):
# print object coordinates
print("[INFO] Object Center coordinates at X0 = {0} and Y0 = {1}".format(x, y))
greenLower = (29, 86, 6) # define lower boundaries of green
greenUpper = (64, 255, 255) # define upper boundaries of green
pts = deque(maxlen=64) # list of tracked points
# load the webcam video stream
vs = VideoStream(usePiCamera=True).start()
# serial connection for pixhawk
connection_string = '/dev/serial/by-id/usb-ArduPilot_fmuv2_1C0034000951353332373834-if00'
print('Connecting to vehicle on: %s' % connection_string)
vehicle = connect(connection_string, wait_ready=True) # Connect to the Vehicle
vehicle.flush() # send a "clear all" type message
# keep looping
while True:
# grab the current frame
frame = vs.read()
# handle the frame from VideoCapture or VideoStream
frame = frame[1] if args.get("video", False) else frame
# resize the frame
frame = imutils.resize(frame, width=600)
# blur it
blurred = cv2.GaussianBlur(frame, (11, 11), 0)
# convert to HSV color space
hsv = cv2.cvtColor(blurred, cv2.COLOR_BGR2HSV)
# construct a mask for the color "green"
mask = cv2.inRange(hsv, greenLower, greenUpper)
# filter false positives
mask = cv2.erode(mask, None, iterations=2)
#filter false negatives
mask = cv2.dilate(mask, None, iterations=2)
# find contours in the mask and initialize the current
# (x, y) center of the ball
cnts = cv2.findContours(mask.copy(), cv2.RETR_EXTERNAL,
cv2.CHAIN_APPROX_SIMPLE)
cnts = imutils.grab_contours(cnts)
center = None
# only proceed if at least one contour was found
if len(cnts) > 0:
# find the largest contour in the mask
c = max(cnts, key=cv2.contourArea)
# compute the minimum enclosing circle
((x, y), radius) = cv2.minEnclosingCircle(c)
M = cv2.moments(c) # find centroid
center = (int(M["m10"] / M["m00"]), int(M["m01"] / M["m00"]))
# only proceed if the radius meets a minimum size
if radius > 10:
# draw the circle
cv2.circle(frame, (int(x), int(y)), int(radius),
(0, 255, 255), 2)
# draw the centroid
cv2.circle(frame, center, 5, (0, 0, 255), -1)
# update the list of tracked points
mapObjectPosition(int(x), int(y))
x = x_max - x # flip so zero = left
y = y_max - y # flip so zero = bottom
# adjust gimbal to follow y centroid
if (y > (y_center + pix_per_deg)):
print("above")
gimbal_y_pos = gimbal_y_pos + (y - y_center)/pix_per_deg
elif (y < (y_center - pix_per_deg)):
print("below")
gimbal_y_pos = gimbal_y_pos - (y_center - y)/pix_per_deg
if gimbal_y_pos > 0:
gimbal_y_pos = 0
elif gimbal_y_pos < -90:
gimbal_y_pos = -90
vehicle.gimbal.rotate(int(gimbal_y_pos), 0, 0)
# update the points queue
pts.appendleft(center)
# loop over the set of tracked points
for i in range(1, len(pts)):
# ignore non-valid points
if pts[i - 1] is None or pts[i] is None:
continue
# Compute thickness of line
thickness = int(np.sqrt(64 / float(i + 1)) * 2.5)
# draw the connecting lines
cv2.line(frame, pts[i - 1], pts[i], (0, 0, 255), thickness)
# show the frame to our screen
cv2.imshow("Frame", frame)
key = cv2.waitKey(1) & 0xFF
# if the 'q' key is pressed, stop the loop
if key == ord("q"):
break
# Close vehicle object
print("Close vehicle object")
vehicle.close()
# stop the camera video stream
vs.stop()
print("Completed") |
996,007 | fbd0fef9e825f19c23fbd65dd316f8e9b903fe52 | import threading
from smbus2 import SMBusWrapper
import time
import sys
#from clean_print import Cprint
import math
import numpy as np
#from read_magneto_data import readData as read_magnet
import motor
#length = 455 cm
#width = 149 cm
#data :: R, F, L, B
# 1, 2, 4, 3
d_format = {'fwd' : 1, 'bkwd' : 3, 'left' : 2, 'right' : 0}
address = 0x05
length = 455
width = 149
pos = {'x':0, 'y':0}
magnet_data = None
exitFlag = 0
pos_matrix = np.zeros(625).reshape(25, 25)
pos['x'] = 2
pos['y'] = 2
pos_matrix[2, 2] = 1
# class magReadThread (threading.Thread):
# def __init__(self, threadID, name):
# threading.Thread.__init__(self)
# self.threadID = threadID
# self.name = name
# def run(self):
# readMagneto(self.name)
#
# def readMagneto(name):
# global magnet_data
# while True:
# if exitFlag:
# print('Thread exit ', name)
# name.exit()
#
# magnet_data = read_magnet()
# time.sleep(0.01)
class magReadThread (threading.Thread):
def __init__(self, threadID, name):
threading.Thread.__init__(self)
self.threadID = threadID
self.name = name
def run(self):
readMagneto(self.name)
def readMagneto(name):
#global magnet_data
while True:
motor.send(1)
time.sleep(0.2)
def readData():
with SMBusWrapper(1) as bus:
try:
block = bus.read_i2c_block_data(address, 0, 8)
except:
print("I2C ERROR while reading")
return None
for b in block:
if b & 0xFF == 0xFF:
return None
data = []
data.append(block[0] << 8 | block[1])
data.append(block[2] << 8 | block[3])
data.append(block[4] << 8 | block[5])
data.append(block[6] << 8 | block[7])
return data
#def calculate_position(data):
if __name__ == '__main__':
thread1 = magReadThread(1, 'Thread-1')
try:
thread1.start();
except KeyboardInterrupt:
exitFlag = 1
while True:
data = readData()
if data == None:
continue
data = [d * 0.042857 for d in data]
print("%.0f, %.0f, %.0f, %.0f" % (data[d_format['fwd']], data[d_format['bkwd']], data[d_format['left']], data[d_format['right']]))
# if magnet_data:
# print(magnet_data)
_x = int(data[d_format['bkwd']] / 20)
_y = int(data[d_format['left']] / 20)
if _x < 625 and _x >= 0:
pos['x'] = _x
if _y < 625 and _y >= 0:
pos['y'] = _y
pos_matrix.fill(0)
pos_matrix[pos['x'], pos['y']] = 1
#print(pos_matrix)
print('+++++++++++++++++++++++++')
for i in range(25):
for j in range(25):
if pos_matrix[i, j] == 0:
print(' .', end='')
else:
print(' #', end='')
print('')
print('+++++++++++++++++++++++++')
time.sleep(0.1)
exitFlag = 1
thread1.join()
print('Exiting main thread')
|
996,008 | 8774f627f22f42d01edebb95fb14ce609dd73ad9 | import os
import sys
import glob
import argparse
import pandas as pd
import numpy as np
import mdtraj as md
import prody
import variables as vrb
def open_structure_from_dataframe(csv_file, path_to_simulations, path_to_clusters=vrb.PATH_PATTER_TO_CLUSTERS_FROM_SIMS,
file_column="file_from", separator=";", read_xtc=False):
files_to_analyze = []
dataframe = pd.read_csv(csv_file, sep=separator)
if not read_xtc:
for index, row in dataframe.iterrows():
file_to_analyse = row[file_column]
compound_name = os.path.basename(csv_file).split(".")[0]
path_to_file = os.path.join(path_to_simulations, compound_name, compound_name, path_to_clusters, "{}.*".format(file_to_analyse))
file_in = glob.glob(path_to_file)[0]
files_to_analyze.append(file_in)
return files_to_analyze
else:
for index, row in dataframe.iterrows():
file_to_analyse = row[file_column]
print(files_to_analyze)
file_in = glob.glob(file_to_analyse)[0]
if not file_in in files_to_analyze:
files_to_analyze.append(file_in)
return files_to_analyze
def read_structure_pdb(file_path):
molecule = prody.parsePDB(file_path)
return molecule
def read_structure_xtc(file_path, topology_file_path=None, pdb=False):
if not pdb:
trajectory = md.load(file_path, top=topology_file_path)
else:
trajectory = md.load(file_path)
return trajectory
def select_atom_pair_from_ligand_and_residue_mdtraj(trajectory, resid, name_residue, name_ligand,
ligand_resname="LIG"):
topology = trajectory.topology
selection_string_residue = "resSeq {} and name {}".format(resid, name_residue)
selection_string_ligand = "resname {} and name {}".format(ligand_resname, name_ligand)
selection_residue = topology.select(selection_string_residue)
selection_ligand = topology.select(selection_string_ligand)
return selection_ligand, selection_residue
def select_atom_pair_from_ligand_and_residue(pdb_file, resid, name_residue, name_ligand, ligand_chain="L"):
molecule = read_structure_pdb(pdb_file)
selection_ligand = molecule.select("chain {} and name {}".format(ligand_chain, name_ligand))
selection_residue = molecule.select("resid {} and name {}".format(resid, name_residue))
return selection_ligand, selection_residue
def select_ligand_mdtraj(trajectory, ligand_resname="LIG", heavy=True):
topology = trajectory.topology
if heavy:
selection_string_ligand = "resname '{}' and (not type H)".format(ligand_resname)
else:
selection_string_ligand = "resname '{}'".format(ligand_resname)
selection_ligand = topology.select(selection_string_ligand)
return selection_ligand
def select_ligand_and_residues(trajectory, list_of_residues_ids, ligand_resname="LIG", heavy=True):
topology = trajectory.topology
if heavy:
selection_string = "(resname '{}' or resSeq {}) and (not type H)".format(ligand_resname, list_of_residues_ids)
else:
selection_string = "resname '{}' or resSeq {}".format(ligand_resname, list_of_residues_ids)
selection_ligand_and_residues = topology.select(selection_string)
return selection_ligand_and_residues
|
996,009 | 3c3f46273413abfaf293da8d715d1e99d9668b89 | def Simulate_Network_modified( Ni, Npc, v, PFcent, L, IntNoise):
from brian import *
# This function uses slightly different parameters to Simulate_Network.m, and was used for the majority of simulations
# Note: Npc must be an integer multiple of Ni
# Parameters of integrate and fire neuron
tauI = 40 * msecond # membrane time constant, needs to be quite long to get theta spiking from dc input
tauPC = 20 * msecond # very variable estimates in the literature...
Vt = -50 * mvolt # spike threshold
Vr = -70 * mvolt # reset value (includes AHP)
El = -65 * mvolt # resting potential (same as the reset)
CmPC = 155*pfarad # place cell capacitance
CmI = 200*pfarad # interneuron capacitance
# Synapse time constants
taue = 2 * msecond
taui = 10 * msecond
# Synapse reversal potentials
Ee = 0 * mV
Ei = -70 * mV
# Other parameters
f_th = 8*Hz # septal theta frequency
sigma = 40 * cm # place field gaussian width (subthreshold field is larger than spiking field)
Twidth = sigma / v # place field width in time
Trun = L/v # time to run along track
# Place cell equations
Idc_extPC = (1.1 + 0.005 * v / (cm / second)) * (10 ** -4) * uamp # input current to E cells, Gaussian amplitude
sigma_nE = (1.75 - 0.025* (v / (cm/second))) * mV
eqsPC=('''
dVPC/dt = -(VPC - El)/tauPC - gi*(VPC - Ei)/CmPC + Idc/CmPC + sigma_nE * xi / tauPC**.5: volt
dgi/dt = -gi/taui : uS
Idc = Idc_extPC* PF * second : amp
PF = exp(-(t-Tcent)**2/(2*Twidth**2)) * Hz : Hz
Tcent : second
''')
# Interneuron equations
Idc_MS = 0.065 * v / (cm/second) * (10 ** -6) * uamp
Idc0I = (7.95 + 0.0027 * v / (cm/second)) * (10 ** -5) * uamp
eqsI=Equations('''
dVI/dt = -(VI - El )/tauI - ge*(VI - Ee)/CmI + Idc/CmI + sigma_n * xi / tauI**.5: volt
dge/dt = -ge/taue : uS
Idc = Idc0I - Idc_MS * cos(2*pi*f_th * t) : amp
sigma_n = IntNoise * volt : volt
''')
# Define cell groups
PC = NeuronGroup(N=Npc, model = eqsPC,
threshold=Vt, reset=Vr )
for i in range(Npc):
PC.Tcent[i] = float(PFcent[i]) / v
I = NeuronGroup(N=Ni, model = eqsI,
threshold=Vt, reset=Vr )
# Define connections between cell groups
we = 0.0005*uS
wi = 0.025*uS # set this so as to get realistic membrane oscillations outside place field
CE = Connection(PC,I,'ge')
CI = Connection(I,PC,'gi')
# define E-I connections
for j in range(Ni):
CE[:,j] = 0*we/(Npc*10) # all to all component
CE[(Npc/Ni*j):(Npc/Ni*(j+1)), j] = we # phase precessing component
# define I-E connections
for j in range(Ni):
CI[j, :] = 0*wi/(Ni*5) # all to all component
CI[j, (Npc/Ni*j):(Npc/Ni*(j+1))] = wi # phase precessing component
# Monitor state variables
HPC = StateMonitor(PC, 'VPC', record=True)
HI = StateMonitor(I, 'VI', record=True)
SPC = SpikeCounter(PC)
SI = SpikeCounter(I)
MI = SpikeMonitor(I)
MPC = SpikeMonitor(PC)
# Simulate
PC.VPC = Vr # intial membrane is at resting
I.VI = Vr # intial membrane is at resting
run(Trun)
return (HPC, HI, SPC, SI, MI, MPC)
|
996,010 | cf6a26189ed2d8621c3a67bc4c862f7de013d4bf | # Generated by Django 3.2.4 on 2021-06-06 17:36
from django.db import migrations, models
class Migration(migrations.Migration):
dependencies = [
('products', '0008_auto_20210606_2246'),
]
operations = [
migrations.AddField(
model_name='product',
name='keywords',
field=models.CharField(default=1, max_length=250),
preserve_default=False,
),
]
|
996,011 | 7a6aea46d05ffc224cf1487ee0d61b16f9e1b3f5 | class Animation:
def __init__(self):
self.playList = []
self.loop = False
self.step = 0
def addAction(self, action):
self.playList.append(action)
def play(self):
if len(self.playList) <= self.step:
return;
action = self.playList[self.step]
playOver = action.play()
if playOver:
self.step = self.step + 1
|
996,012 | 04ebe8f52cfd4c0332286daf5c10b6c75812f79b | from machine import Pin, I2C
class PCA9685:
"""
16 units PWM output
"""
min_values = [0 for i in range(16)]
max_values = [4095 for i in range(16)]
max_angles = [360 for i in range(16)]
def _writeByte(self, register, value):
self.i2c.writeto_mem(self.address, register, int(value).to_bytes(1, 'little'))
def _writeRange(self, unit, on, off):
self.i2c.writeto_mem(self.address, 4 * unit + 6, int(on).to_bytes(2, 'little') + int(off).to_bytes(2, 'little'))
def __init__(self, i2c=None, address=0x40, reference_clock_speed=25000000):
if i2c is None:
i2c = I2C(scl=Pin(5), sda=Pin(4), freq=100000)
self.i2c = i2c
self.address = address
self.reference_clock_speed = reference_clock_speed
self.reset()
def reset(self):
"""Reset the chip."""
self.mode1_reg = b'\x20'
@property
def mode1_reg(self):
return self.i2c.readfrom_mem(self.address, 0x00, 1)
@mode1_reg.setter
def mode1_reg(self, value):
return self.i2c.writeto_mem(self.address, 0x00, value)
@property
def prescale_reg(self):
return self.i2c.readfrom_mem(self.address, 0xfe, 1)
@prescale_reg.setter
def prescale_reg(self, value):
# not supported
return
@property
def frequency(self):
"""The overall PWM frequency in Hertz."""
return self.reference_clock_speed / 4096 / self.prescale_reg
@frequency.setter
def frequency(self, freq):
prescale = int(self.reference_clock_speed / 4096.0 / freq + 0.5)
if prescale < 3:
raise ValueError("PCA9685 cannot output at the given frequency")
old_mode = self.mode1_reg # Mode 1
self.mode1_reg = (old_mode & 0x7F) | 0x10 # Mode 1, sleep
self._writeByte(0xfe, prescale) # Prescale
self.mode1_reg = old_mode # Mode 1
time.sleep(0.005)
self.mode1_reg = old_mode | 0xA1 # Mode 1, autoincrement on
def set_pwm(self, unit, on, off):
self._writeRange(unit, on, off)
def init_servo(self, unit, min_val, max_val, max_angle):
if unit < 0 or unit > 15:
return
if min_val < 0 or min_val > 4094:
self.min_values[unit] = 0
else:
self.min_values[unit] = min_val
if max_val <= self.min_values[unit] or max_val > 4095:
self.max_values[unit] = 4095
else:
self.max_values[unit] = max_val
if max_angle < 10:
max_angle = 10
if max_angle > 360:
max_angle = 360
self.max_angles[unit] = max_angle
def set_angle(self, unit, angle):
if unit < 0 or unit > 15:
return
if angle < 0:
angle = 0
if angle > self.max_angles[unit]:
angle = self.max_angles[unit]
switchpoint = self.min_values[unit] + (self.max_values[unit]-self.min_values[unit])*(float(angle)/self.max_angles[unit])
# print(str(int(switchpoint))+' ', end='')
self.set_pwm(unit, 0, int(switchpoint))
def deinit(self):
"""Stop using the pca9685."""
self.reset() |
996,013 | 8f1275f062088f3b6f2b113e085ec4b7899f79e3 | #EXTRACT IMPORTANT INFO FROM OSM FILE
import xml.etree.ElementTree as ET
from neo4j.v1 import GraphDatabase
print("Reading XML")
osmFile = ET.parse("wyandotte.osm")
print("Done parsing...")
root = osmFile.getroot()
# Look for all roads in osm file
print("Collecting roads...")
roads = []
for way in root.findall('way'):
# Check to see if way describes a road or something else
isRoad = False
for tag in way.findall('tag'):
if tag.attrib['k'] == 'name':
isRoad = True
name = tag.attrib['v']
if tag.attrib['k'] == 'railway' or tag.attrib['k'] == 'cuisine' or \
tag.attrib['k'] == 'building' or tag.attrib['k'] == 'landuse' or \
tag.attrib['k'] == 'leisure' or tag.attrib['k'] == 'aeroway' or \
tag.attrib['k'] == 'power' or tag.attrib['v'] == 'boundary' or \
tag.attrib['k'] == 'place':
isRoad = False
break
if not isRoad:
continue
# Collect points that make up roads
points = []
for point in way.findall('nd'):
points.append(point.attrib['ref'])
newRoad = {"name": name, "points": points}
roads.append(newRoad)
# Look through nodes and grab ones that make up roads
print("Collecting points...")
node_num = 1
nodes = {}
for node in root.findall('node'):
node_num += 1
for road in roads:
for point in road['points']:
if node.attrib['id'] == point:
if node.attrib['id'] in nodes:
if road["name"] not in nodes[node.attrib['id']]["road"]:
nodes[node.attrib['id']]["road"].append(road["name"])
else:
nodes[node.attrib['id']] = {"road": [road["name"]], \
"id": point, "lat": node.attrib['lat'], "lon": node.attrib['lon']}
continue
# Input the points into the graph database and connect them
uri = "bolt://localhost:7687"
user = "neo4j"
password = "wyanOSM"
driver = GraphDatabase.driver(uri, auth=(user, password))
# Adds road point as node in graph
def _add_point(tx, node_key):
return tx.run("CREATE (a:MapPoint {id: $node_key, latitude: " + \
nodes[key]['lat'] + ", longitude: " + nodes[key]['lon'] + ", roads: \"" + \
' and '.join(nodes[key]['road']) + "\"}) RETURN a", node_key=node_key)
# Creates relationship between nodes
def _connect_road(tx, road):
for i in range(len(road["points"])-1):
result = tx.run("MATCH (a:MapPoint), (b:MapPoint) "
"WHERE a.id = \"" + str(road["points"][i]) +
"\" AND b.id = \"" + str(road["points"][i+1]) + "\" "
"CREATE (a)-[r:NEXT]->(b) "
"WITH r, point({x: a.longitude, y: a.latitude, crs: 'cartesian'}) AS p1, "
"point({x: b.longitude, y: b.latitude, crs: 'cartesian'}) AS p2 "
"SET r.distance = distance(p1, p2) "
"RETURN type(r);", road=road)
return "All roads connected"
def test_graph(testid):
with driver.session() as session:
return session.run("MATCH (n) "
"RETURN n "
"LIMIT $testid;", testid=testid)
with driver.session() as session:
print("Testing")
test_graph(10)
print("Adding points...")
for key in nodes.keys():
session.write_transaction(_add_point, key)
print("Connecting roads...")
for road in roads:
session.write_transaction(_connect_road, road)
driver.close()
|
996,014 | 83ff18ad213b36ff7b54715f8870eda045967f6f | from orator.migrations import Migration
class CreatePrestamosTable(Migration):
def up(self):
"""
Run the migrations.
"""
with self.schema.create('prestamos') as table:
table.increments('id')
table.integer('user_id').unsigned()
table.foreign('user_id').references('id').on('users')
table.integer('libros_id').unsigned()
table.foreign('libros_id').references('id').on('libros')
table.date('prestado_on')
table.integer('bibliotecas_id').unsigned()
table.foreign('bibliotecas_id').references('id').on('bibliotecas')
table.timestamps()
def down(self):
"""
Revert the migrations.
"""
self.schema.drop('prestamos')
|
996,015 | 7d547d3496b09fd9e989e9e1155c6b8db1bc123b | import logging
import os
from utils.file_names_builder import get_model_filename
from utils.database_handler import DatabaseHandler
from utils.logger import create_loggers_helper
from configuration.configuration_constants import limit_date, excluded_values, \
validation_split_value, verbose_value, epochs_value, current_bucket, model_overwrite, \
train_model_with_price_parameters
from neural_network_model import Model
from utils.plots import draw_plots
from utils.prices_mapping import parcel_prices_mapping
def create_logger():
_logger = logging.getLogger(__name__)
_logger.setLevel(logging.DEBUG)
return create_loggers_helper(_logger)
logger = create_logger()
def train_model_decorator():
def decorator(func):
def func_wrapper(*args, **kwargs):
model_filename = get_model_filename()
if os.path.exists(model_filename) and not model_overwrite:
logger.error('Model exists. To overwrite set model_overwrite constant to True '
'in configuration_constants.py')
return 0
trained_model = func(*args, **kwargs)
return trained_model
return func_wrapper
return decorator
@train_model_decorator()
def train_model(database_handler):
logger.info('Creation of model.')
neural_network_model = Model()
neural_network_model.create_model()
neural_network_model.save_callback()
if train_model_with_price_parameters:
procedure = 'GetDateToTrainModel'
else:
procedure = 'GetDateToTrainModelWithoutPriceParameters'
# Type: dataframe
data_to_train_model = database_handler.execute_query("EXEC dbo.{} "
"@LimitDate = {}, "
"@BucketType={}, "
"@ExcludedList='{}'"
.format(procedure,
limit_date,
parcel_prices_mapping[current_bucket],
excluded_values))
# Pandas DataFrame.shape return a tuple representing the dimensionality of the DataFrame
data_size = data_to_train_model.shape[1]
# Split into X set and Y set
# Take all columns except the first one - OBJECID and the last one - Sale_Amount
x = data_to_train_model.iloc[:, 1: data_size - 1]
y = data_to_train_model.iloc[:, data_size - 1]
results = neural_network_model.fit_model(training_x_values=x.values, training_y_values=y.values,
batch_size=len(x.values), epochs=epochs_value,
validation_split=validation_split_value, verbose=verbose_value)
logging.info('Model summary:')
neural_network_model.model.summary()
draw_plots(history_object=results)
neural_network_model.save_model()
return neural_network_model.model
def main():
database_handler = DatabaseHandler()
try:
train_model(database_handler=database_handler)
finally:
database_handler.close_connection()
if __name__ == '__main__':
main()
|
996,016 | ea4571ce1bdaa585ad067c69eb97dc4087edb695 | ## @file EventCount_jobOptions.py
## @brief JobOptions: Defaults.
## @author Jack Cranshaw (Jack.Cranshaw@cern.ch)
## $Id: EventCount_jobOptions.py,v 1.6 2007-10-18 13:46:20 gemmeren Exp $
#--------------------------------------------------------------
# Event related parameters
#--------------------------------------------------------------
## get a handle on the ServiceManager
from AthenaCommon.AppMgr import ServiceMgr
from CLIDComps.CLIDCompsConf import ClassIDSvc
svcMgr += ClassIDSvc()
from AthenaCommon.Constants import INFO
from AthenaCommon.AlgSequence import AlgSequence
topSequence = AlgSequence()
from xAODEventInfoCnv.xAODEventInfoCnvConf import xAODMaker__EventInfoCnvAlg
alg = xAODMaker__EventInfoCnvAlg()
topSequence += alg
from AthenaPoolTools.AthenaPoolToolsConf import EventCount
topSequence += EventCount( OutputLevel = INFO,
Dump = True )
#==============================================================
#
# End of job options file
#
###############################################################
|
996,017 | 468f2a1b09e40336dfbb2118e7427a17e1da5ea4 | import torch
class AttentionBase(torch.nn.Module):
def __init__(self, attentionName, attentionScope, featuresNumber, cudaFlag):
self.attentionName, self.attentionScope, self.cudaFlag = attentionName, attentionScope, cudaFlag
super(AttentionBase, self).__init__()
if attentionName == 'StandardAttention':
self.attentionWeightLayer = torch.nn.Linear(in_features=featuresNumber, out_features=1)
if attentionName == 'LocalAttention':
self.attentionWeightLayer = torch.nn.Linear(in_features=featuresNumber * attentionScope, out_features=1)
if self.attentionName == 'ComponentAttention':
self.attentionWeightLayer = torch.nn.Conv2d(
in_channels=1, out_channels=featuresNumber, kernel_size=[attentionScope, featuresNumber], stride=[1, 1],
padding_mode='VALID')
if self.attentionName == 'MonotonicAttention':
self.sumKernel = torch.ones(size=[1, 1, self.attentionScope])
self.attentionWeightNumeratorLayer = torch.nn.Linear(in_features=featuresNumber, out_features=1)
self.attentionWeightDenominatorLayer = torch.nn.Linear(in_features=featuresNumber, out_features=1)
def ApplyAttention(self, dataInput, attentionName, inputSeqLen, hiddenNoduleNumbers):
if attentionName == 'StandardAttention':
return self.StandardAttention(
dataInput=dataInput, seqInput=inputSeqLen, hiddenNoduleNumbers=hiddenNoduleNumbers)
if attentionName == 'LocalAttention':
return self.LocalAttention(
dataInput=dataInput, seqInput=inputSeqLen, hiddenNoduleNumbers=hiddenNoduleNumbers)
if attentionName == 'ComponentAttention':
return self.ComponentAttention(
dataInput=dataInput, seqInput=inputSeqLen, hiddenNoduleNumbers=hiddenNoduleNumbers)
if attentionName == 'MonotonicAttention':
return self.MonotonicAttention(
dataInput=dataInput, seqInput=inputSeqLen, hiddenNoduleNumbers=hiddenNoduleNumbers)
def AttentionMask(self, seqInput):
returnTensor = torch.cat(
[torch.cat([torch.ones(v), torch.ones(torch.max(seqInput) - v) * -1]).view([1, -1]) for v in seqInput])
if self.cudaFlag:
return returnTensor.cuda() * 9999
else:
return returnTensor * 9999
def StandardAttention(self, dataInput, seqInput, hiddenNoduleNumbers):
attentionOriginWeight = self.attentionWeightLayer(input=dataInput.reshape([-1, hiddenNoduleNumbers]))
attentionOriginWeight = attentionOriginWeight.view([dataInput.size()[0], dataInput.size()[1]])
if seqInput is not None:
attentionMaskWeight = attentionOriginWeight.min(self.AttentionMask(seqInput=seqInput))
else:
attentionMaskWeight = attentionOriginWeight
attentionWeight = torch.nn.functional.softmax(attentionMaskWeight, dim=-1).view([len(dataInput), -1, 1])
attentionSupplementWeight = attentionWeight.repeat([1, 1, hiddenNoduleNumbers])
attentionSeparateResult = torch.mul(dataInput, attentionSupplementWeight)
attentionResult = attentionSeparateResult.sum(dim=1)
return attentionResult, attentionWeight
def LocalAttention(self, dataInput, seqInput, hiddenNoduleNumbers):
dataInputPaddingPart = torch.zeros(size=[dataInput.size()[0], self.attentionScope, dataInput.size()[2]])
if self.cudaFlag:
dataInputPaddingPart = dataInputPaddingPart.cuda()
dataInputSupplement = torch.cat([dataInput, dataInputPaddingPart], dim=1)
dataInputExtension = torch.cat(
[dataInputSupplement[:, v:dataInput.size()[1] + v, :] for v in range(self.attentionScope)], dim=-1)
attentionOriginWeight = self.attentionWeightLayer(
input=dataInputExtension.view([-1, hiddenNoduleNumbers * self.attentionScope])).view(
[dataInput.size()[0], -1])
#########################################################
if seqInput is not None:
attentionMaskWeight = attentionOriginWeight.min(self.AttentionMask(seqInput=seqInput))
else:
attentionMaskWeight = attentionOriginWeight
attentionWeight = torch.nn.functional.softmax(attentionMaskWeight, dim=-1).view([len(dataInput), -1, 1])
attentionSupplementWeight = attentionWeight.repeat([1, 1, hiddenNoduleNumbers])
attentionSeparateResult = torch.mul(dataInput, attentionSupplementWeight)
attentionResult = attentionSeparateResult.sum(dim=1)
return attentionResult, attentionWeight
def ComponentAttention(self, dataInput, seqInput, hiddenNoduleNumbers):
dataInputPaddingPart = torch.zeros(size=[dataInput.size()[0], self.attentionScope - 1, dataInput.size()[2]])
if self.cudaFlag:
dataInputPaddingPart = dataInputPaddingPart.cuda()
dataInputSupplement = torch.cat([dataInput, dataInputPaddingPart], dim=1)
dataInputSupplement = dataInputSupplement.unsqueeze(1)
attentionOriginWeight = self.attentionWeightLayer(input=dataInputSupplement).squeeze()
if len(attentionOriginWeight.size()) == 2: attentionOriginWeight = attentionOriginWeight.unsqueeze(0)
attentionOriginWeight = attentionOriginWeight.permute(0, 2, 1)
if seqInput is not None:
attentionMask = self.AttentionMask(seqInput=seqInput).unsqueeze(-1).repeat([1, 1, hiddenNoduleNumbers])
attentionMaskWeight = attentionOriginWeight.min(attentionMask)
else:
attentionMaskWeight = attentionOriginWeight
attentionWeight = torch.nn.functional.softmax(attentionMaskWeight, dim=1)
attentionSeparateResult = torch.mul(dataInput, attentionWeight)
attentionResult = attentionSeparateResult.sum(dim=1)
return attentionResult, attentionWeight
def MonotonicAttention(self, dataInput, seqInput, hiddenNoduleNumbers):
attentionNumeratorWeight = self.attentionWeightNumeratorLayer(input=dataInput).tanh()
attentionDenominatorRawWeight = self.attentionWeightDenominatorLayer(input=dataInput).exp()
padDenominatorZero = torch.zeros(size=[attentionDenominatorRawWeight.size()[0], self.attentionScope - 1,
attentionDenominatorRawWeight.size()[2]])
if self.cudaFlag:
padDenominatorZero = padDenominatorZero.cuda()
self.sumKernel = self.sumKernel.float().cuda()
attentionDenominatorSupplementWeight = torch.cat([padDenominatorZero, attentionDenominatorRawWeight], dim=1)
attentionDenominatorWeight = torch.conv1d(input=attentionDenominatorSupplementWeight.permute(0, 2, 1),
weight=self.sumKernel, stride=1)
attentionOriginWeight = torch.div(attentionNumeratorWeight.squeeze(), attentionDenominatorWeight.squeeze())
#########################################################
if seqInput is not None:
attentionMaskWeight = attentionOriginWeight.min(self.AttentionMask(seqInput=seqInput))
else:
attentionMaskWeight = attentionOriginWeight
attentionWeight = torch.nn.functional.softmax(attentionMaskWeight, dim=-1).view([len(dataInput), -1, 1])
attentionSupplementWeight = attentionWeight.repeat([1, 1, hiddenNoduleNumbers])
attentionSeparateResult = torch.mul(dataInput, attentionSupplementWeight)
attentionResult = attentionSeparateResult.sum(dim=1)
return attentionResult, attentionWeight
|
996,018 | b72d9092c65950318d497000a5610307dbfb9cfc | import django_filters
CHOICES = [
["name", "По алфавиту"],
["cheaper_price", "Дешевые сверху"],
["-cheaper_price", "Дорогие сверху"],
["-sale", "Найбольшая скидка"],
["sale", "Найменьшая скидка"],
]
class ProductFilter(django_filters.FilterSet):
ordering = django_filters.OrderingFilter(choices=CHOICES, required=True, empty_label="Выберете тип", )
ProductFilter.base_filters['ordering'].label = 'Сортировать как'
|
996,019 | a7415ab2d91f7d1db7bd8df433c96194ac9a0845 | import image_search
import numpy as np
import random
import Image
# btm_file_path = "/home/bkko/ml_study/fddb/FDDB-folds/rectbtm-1.txt"
# btm_file_path = "/home/bkko/ml_study/week7/ofile_12net/o_annot.txt"
btm_file_path = "/home/bkko/ml_study/week7/ofile_12net/o_annot_10.txt"
top_file_path = "/home/bkko/ml_study/week7/Figure9/fold-10-out.txt"
fddb_path = "/home/bkko/ml_study/fddb"
btm_file = open(btm_file_path, 'r' ).readlines()
top_file = open(top_file_path, 'w' )
btm_file_index = 0
tmp_annot = np.zeros([5]).astype(np.float)
while 1 :
if btm_file_index == len(btm_file) :
break
tmp_line = btm_file[btm_file_index].rstrip()
btm_file_index = btm_file_index + 1
cond_newimg, cond_numface, cond_annot, cond_eof = image_search.decoding_annot(tmp_line )
if cond_eof :
break
if cond_newimg :
tmp_img_path = tmp_line.rstrip()
tmp_img = Image.open("%s/%s.jpg"%(fddb_path, tmp_img_path) )
img_size = tmp_img.size
elif cond_numface :
tmp_numface = int( tmp_line.rstrip() )
tmp_annot_list = np.zeros([tmp_numface,5]).astype(np.float32)
annot_cnt = 0
elif cond_annot :
tmp_annot[0:4] = np.array( tmp_line.split()[0:4] ).astype(np.int16)
# logit_value = random.randint(0,255)/255.
logit_value = tmp_line.split()[4]
left = int(tmp_annot[0] )
btm = int(tmp_annot[1] )
width = int(tmp_annot[2] )
height = int(tmp_annot[3] )
# if left < 0 :
# width = width + left
# left = 0
# if btm < 0 :
# height = height + btm
# btm = 0
# right = left + width
# if right >= img_size[0] :
# right = img_size[0] -1
top = btm + height
# if top >= img_size[1] :
# top = img_size[1] -1
# width = right -left
# height = top -btm
tmp_annot_list[annot_cnt] = [left, btm, width, height, logit_value]
# tmp_annot_list[annot_cnt] = tmp_annot
annot_cnt = annot_cnt + 1
if annot_cnt == tmp_numface :
top_file.write("%s\n" %tmp_img_path)
top_file.write("%d\n" %tmp_numface)
for k in xrange( len(tmp_annot_list) ) :
top_file.write("%s %s %s %s %s\n" %( int(tmp_annot_list[k][0]), int(tmp_annot_list[k][1]), int(tmp_annot_list[k][2]), int(tmp_annot_list[k][3]), tmp_annot_list[k][4]) )
|
996,020 | 6307e7d2e4d4a563e89744b78cd94f2f29f2f9e1 |
#calss header
class _BRAKING():
def __init__(self,):
self.name = "BRAKING"
self.definitions = brake
self.parents = []
self.childen = []
self.properties = []
self.jsondata = {}
self.basic = ['brake']
|
996,021 | ac3dce3b0e3cc07b57252f2ce92591d67459d4c4 | from django.db import models
# Create your models here.
class AdminProfile(models.Model):
phone = models.BigIntegerField()
photo = models.ImageField()
email = models.EmailField()
name = models.CharField(max_length=30) |
996,022 | d82891ff87724ded88e98f6b1321c56be2164738 | import time
import os
from astropy import wcs
import numpy as np
from astropy.io import fits
import scipy
import argparse
import sys
import jwst
from gwcs import wcstools
from jwst import datamodels
from . import auxiliary_functions as auxfunc
from astropy.visualization import (ImageNormalize, AsinhStretch)
import matplotlib
import matplotlib.pyplot as plt
"""
This script tests the FS pipeline pathloss step output for a Point Source.
"""
# HEADER
__author__ = "T King"
__version__ = "1.2"
# HISTORY
# October 19, 2019 - Version 1.0: initial version started
# February 5, 2020 - Version 1.1: Tests pass
# February 26, 2020 - Version 1.2: Mostly pep8 compliant
def get_ps_uni_extensions(fits_file_name, is_point_source):
"""
This functions obtains all the point source or uniform source
extensions in the given file
Args:
fits_file_name: str, name of the fits file of interest
is_point_source: boolean, true if point source; false if uniform source
Returns:
sci_list: list of the numbers of the science extensions
"""
hdulist = fits.open(fits_file_name)
ps_dict = {}
uni_dict = {}
s = 0
for ext, hdu in enumerate(hdulist):
if hdu.name == "PS":
try:
sltname = hdu.header["APERTURE"]
ps_dict[sltname] = ext
except KeyError:
sltname = "Slit_"+repr(s+1)
ps_dict[sltname] = ext
if hdu.name == "UNI":
try:
sltname = hdu.header["APERTURE"]
uni_dict[sltname] = ext
except KeyError:
sltname = "Slit_"+repr(s+1)
uni_dict[sltname] = ext
return ps_dict, uni_dict
def pathtest(step_input_filename, reffile, comparison_filename, writefile=True, show_figs=True,
save_figs=False, plot_name=None, threshold_diff=1e-7,
debug=False):
"""
This function calculates the difference between the pipeline and the
calculated pathloss values. The functions use the output of the
compute_world_coordinates.py script.
Args:
step_input_filename: str, name of the output fits file from the
source type step (with full path)
reffile: str, path to the pathloss FS reference fits file
comparison_filename: str, path to comparison pipeline pathloss file
writefile: boolean, if True writes the fits files of the calculated
pathloss and difference image.
show_figs: boolean, whether to show plots or not
save_figs: boolean, save the plots (the 3 plots can be saved or not
independently with the function call)
plot_name: string, desired name (if name is not given, the plot
function will name the plot by default)
threshold_diff: float, threshold difference between pipeline output
and ESA file
debug: boolean, if true a series of print statements will show
on-screen
Returns:
- 1 plot, if told to save and/or show them.
- median_diff: Boolean, True if smaller or equal to threshold.
- log_msgs: list, all print statements are captured in this variable
"""
log_msgs = []
# start the timer
pathtest_start_time = time.time()
# get info from the rate file header
det = fits.getval(step_input_filename, "DETECTOR", 0)
msg = 'step_input_filename='+step_input_filename
print(msg)
log_msgs.append(msg)
exptype = fits.getval(step_input_filename, "EXP_TYPE", 0)
grat = fits.getval(step_input_filename, "GRATING", 0)
filt = fits.getval(step_input_filename, "FILTER", 0)
msg = "path_loss_file --> Grating:"+grat+" Filter:"+filt+" EXP_TYPE:"+exptype
print(msg)
log_msgs.append(msg)
msg = "Using reference file: "+reffile
print(msg)
log_msgs.append(msg)
is_point_source = True
# get the datamodel from the assign_wcs output file
extract2d_wcs_file = step_input_filename.replace("srctype.fits", "extract_2d.fits")
model = datamodels.MultiSlitModel(extract2d_wcs_file)
if writefile:
# create the fits list to hold the calculated pathloss values for
# each slit
hdu0 = fits.PrimaryHDU()
outfile = fits.HDUList()
outfile.append(hdu0)
# create the fits list to hold the image of pipeline-calculated
# difference values
hdu0 = fits.PrimaryHDU()
compfile = fits.HDUList()
compfile.append(hdu0)
# list to determine if pytest is passed or not
total_test_result = []
# loop over the slits
sltname_list = ["S200A1", "S200A2", "S400A1", "S1600A1"]
msg = "Now looping through the slits. This may take a while... "
print(msg)
log_msgs.append(msg)
if det == "NRS2":
sltname_list.append("S200B1")
# but check if data is BOTS
if fits.getval(step_input_filename, "EXP_TYPE", 0) == "NRS_BRIGHTOBJ":
sltname_list = ["S1600A1"]
# get all the science extensions
ps_uni_ext_list = get_ps_uni_extensions(reffile, is_point_source)
# get files
print("""Checking if files exist & obtaining datamodels.
This takes a few minutes...""")
if os.path.isfile(comparison_filename):
if debug:
print('Comparison file does exist.')
else:
result_msg = 'Comparison file does NOT exist. Skipping pathloss test.'
print(result_msg)
log_msgs.append(result_msg)
result = 'skip'
return result, result_msg, log_msgs
# get the comparison data model
pathloss_pipe = datamodels.open(comparison_filename)
if debug:
print('got comparison datamodel!')
if os.path.isfile(step_input_filename):
if debug:
print('Input file does exist.')
else:
result_msg = 'Input file does NOT exist. Skipping pathloss test.'
log_msgs.append(result_msg)
result = 'skip'
return result, result_msg, log_msgs
# get the input data model
pl = datamodels.open(step_input_filename)
if debug:
print('got input datamodel!')
# loop through the wavelengths
msg = "Looping through the wavelengths... " # SLITS?
print(msg)
log_msgs.append(msg)
slit_val = 0
for slit, pipe_slit in zip(pl.slits, pathloss_pipe.slits):
slit_val = slit_val+1
# only testing S400A1 in this script
if slit_val == 1:
continue
if slit_val == 2:
continue
if slit_val == 4:
continue
slit_id = pipe_slit.name
print('Working with slitlet ', slit_id)
if slit.name == slit_id:
msg = """Slitlet name in fits file previous to pathloss
and in pathloss output file are the same.
"""
log_msgs.append(msg)
print(msg)
else:
msg = """* Missmatch of slitlet names in fits file previous to
pathloss and in pathloss output file. Skipping test.
"""
result = 'skip'
log_msgs.append(msg)
return result, msg, log_msgs
mode = "FS"
if debug:
print("grat = ", grat)
continue_pl_test = False
if fits.getval(step_input_filename, "EXP_TYPE", 0) == "NRS_BRIGHTOBJ":
slit = model
continue_pl_test = True
else:
for slit_in_MultiSlitModel in pl.slits:
if slit_in_MultiSlitModel.name == slit_id:
slit = slit_in_MultiSlitModel
continue_pl_test = True
break
if not continue_pl_test:
continue
else:
try:
if is_point_source is True:
ext = ps_uni_ext_list[0][slit_id]
print("Retrieved point source extension")
elif is_point_source is False:
ext = ps_uni_ext_list[1][slit_id]
print("WARNING: Retrieved uniform source extension")
except KeyError:
ext = sltname_list.index(slit_id)
print("Unable to retrieve extension.")
wcs_obj = slit.meta.wcs
# get the wavelength
x, y = wcstools.grid_from_bounding_box(wcs_obj.bounding_box, step=(1, 1), center=True)
ra, dec, wave = wcs_obj(x, y) # wave is in microns
wave_sci = wave * 10**(-6) # microns --> meters
# get positions of source in file:
slit_x = slit.source_xpos
slit_y = slit.source_ypos
if debug:
print("slit_x, slit_y", slit_x, slit_y)
reffile = 'wst_nirspec_pathloss_0001.fits'
if slit_val == 3:
if is_point_source:
ext = 1
else:
ext = 3
reffile = "jwst-nirspec-a400.plrf.fits"
plcor_ref_ext = fits.getdata(reffile, ext)
if debug:
print("ext:", ext)
hdul = fits.open(reffile)
plcor_ref = hdul[1].data
w = wcs.WCS(hdul[1].header)
# make cube
w1, y1, x1 = np.mgrid[:plcor_ref.shape[0], : plcor_ref.shape[1],
:plcor_ref.shape[2]]
slitx_ref, slity_ref, wave_ref = w.all_pix2world(x1, y1, w1, 0)
previous_sci = slit.data
# print("Test for srctype == extract 2d:", previous_sci == extract_sci)
# print("any differences:", np.where(previous_sci != extract_sci))
pipe_correction = pipe_slit.pathloss
# SET UP MANUALLY TO TEST CORRECTION AT NONZERO POINT
# slit_x = 0.2
# slit_y = 0.2
# if debug:
# print("""WARNING: Using manually set slit_x and slit_y!
# The pipeline correction will not use manually set values and
# thus the residuals will change
# """)
correction_array = np.array([])
lambda_array = np.array([])
wave_sci_flat = wave_sci.reshape(wave_sci.size)
wave_ref_flat = wave_ref.reshape(wave_ref.size)
ref_xy = np.column_stack((slitx_ref.reshape(slitx_ref.size), slity_ref.reshape(slitx_ref.size)))
# loop through slices in lambda from reference file
shape = 0
for lambda_val in wave_ref_flat:
# loop through every lambda value
# flattened so that looping works smoothly
shape = shape + 1
index = np.where(wave_ref[:, 0, 0] == lambda_val)
# index of closest lambda value in reffile to given sci lambda
# took index of only the first slice of wave_ref because
# the others were repetitive & we got extra indices
# take slice where lambda=index:
plcor_slice = plcor_ref_ext[index[0][0]].reshape(plcor_ref_ext[index[0][0]].size)
# do 2d interpolation to get a single correction factor for each slice
corr_val = scipy.interpolate.griddata(ref_xy[:plcor_slice.size], plcor_slice,
np.asarray([slit_x, slit_y]),
method='linear')
# append values from loop to create a vector of correction factors
correction_array = np.append(correction_array, corr_val[0])
# map to array with corresponding lambda
lambda_array = np.append(lambda_array, lambda_val)
# get correction value for each pixel
corr_vals = np.interp(wave_sci_flat, lambda_array, correction_array)
corr_vals = corr_vals.reshape(wave_sci.shape)
corrected_array = previous_sci/corr_vals
# set up generals for all the plots
font = {'weight': 'normal',
'size': 7}
matplotlib.rc('font', **font)
# Plots:
# my correction values
fig = plt.figure()
plt.subplot(221)
norm = ImageNormalize(corr_vals)
plt.imshow(corr_vals, norm = norm, aspect = 10.0, origin='lower', cmap='viridis')
plt.xlabel('dispersion in pixels')
plt.ylabel('y in pixels')
plt.title('Calculated Correction')
plt.colorbar()
# pipe correction
plt.subplot(222)
norm = ImageNormalize(pipe_correction)
plt.imshow(pipe_correction, norm=norm, aspect=10.0, origin='lower',
cmap='viridis')
plt.title("Pipeline Correction")
plt.xlabel('dispersion in pixels')
plt.ylabel('y in pixels')
plt.colorbar()
# residuals
corr_residuals = pipe_correction - corr_vals
plt.subplot(223)
norm = ImageNormalize(corr_residuals)
plt.imshow(corr_residuals, norm=norm, aspect=10.0, origin='lower',
cmap='viridis')
plt.xlabel('dispersion in pixels')
plt.ylabel('y in pixels')
plt.title('Correction residuals')
plt.colorbar()
# my science data after
plt.subplot(224)
norm = ImageNormalize(corrected_array)
plt.imshow(corrected_array, norm=norm, aspect=10.0, origin='lower',
cmap='viridis')
plt.title('Calculated after pathloss data')
plt.xlabel('dispersion in pixels')
plt.ylabel('y in pixels')
plt.colorbar()
fig.suptitle("FS PS Pathloss Correction Test for slit " + str(slit_id))
if save_figs:
plt_name = step_input_filename + "_Pathloss_test_slitlet_"+str(mode) + "_" + str(slit_id) + "_" + str(slit_val) + ".png"
plt.savefig(plt_name)
print('Figure saved as: ', plt_name)
if show_figs:
plt.show()
plt.clf()
# create fits file to hold the calculated pathloss for each slit
if writefile:
msg = "Saving the fits files with the calculated pathloss for each slit..."
print(msg)
log_msgs.append(msg)
# this is the file to hold the image of pipeline-calculated difference values
outfile_ext = fits.ImageHDU(corr_vals, name=slit_id)
outfile.append(outfile_ext)
# this is the file to hold the image of pipeline-calculated difference values
compfile_ext = fits.ImageHDU(corr_residuals, name=slit_id)
compfile.append(compfile_ext)
if debug:
if corr_residuals[~np.isnan(corr_residuals)].size == 0:
msg1 = " * Unable to calculate statistics because difference array has all values as NaN. Test will be set to FAILED."
print(msg1)
log_msgs.append(msg1)
test_result = "FAILED"
else:
msg = "Calculating statistics... "
print(msg)
log_msgs.append(msg)
corr_residuals = corr_residuals[np.where((corr_residuals != 999.0) & (corr_residuals < 0.1) & (corr_residuals > -0.1))] # ignore outliers
if corr_residuals.size == 0:
msg1 = " * Unable to calculate statistics because difference array has all outlier values. Test will be set to FAILED."
print(msg1)
log_msgs.append(msg1)
test_result = "FAILED"
else:
stats_and_strings = auxfunc.print_stats(corr_residuals, "Difference", float(threshold_diff), abs=True)
stats, stats_print_strings = stats_and_strings
corr_residuals_mean, corr_residuals_median, corr_residuals_std = stats
for msg in stats_print_strings:
log_msgs.append(msg)
# This is the key argument for the assert pytest function
median_diff = False
if abs(corr_residuals_median) <= float(threshold_diff):
median_diff = True
if median_diff:
test_result = "PASSED"
else:
test_result = "FAILED"
msg = " *** Result of the test: "+test_result+"\n"
print(msg)
log_msgs.append(msg)
total_test_result.append(test_result)
if writefile:
outfile_name = step_input_filename.replace("srctype", "_calcuated_FS_PS_pathloss")
compfile_name = step_input_filename.replace("srctype", "_comparison_FS_PS_pathloss")
# create the fits list to hold the calculated flat values for each slit
outfile.writeto(outfile_name, overwrite=True)
# this is the file to hold the image of pipeline-calculated difference values
compfile.writeto(compfile_name, overwrite=True)
msg = "\nFits file with calculated pathloss values of each slit saved as: "
print(msg)
log_msgs.append(msg)
print(outfile_name)
log_msgs.append(outfile_name)
msg = "Fits file with comparison (pipeline pathloss - calculated pathloss) saved as: "
print(msg)
log_msgs.append(msg)
print(compfile_name)
log_msgs.append(compfile_name)
# If all tests passed then pytest is marked as PASSED, else it is FAILED
FINAL_TEST_RESULT = False
for t in total_test_result:
if t == "FAILED":
FINAL_TEST_RESULT = False
break
else:
FINAL_TEST_RESULT = True
if FINAL_TEST_RESULT:
msg = "\n *** Final pathloss test result reported as PASSED *** \n"
print(msg)
log_msgs.append(msg)
result_msg = "All slits PASSED path_loss test."
else:
msg = "\n *** Final pathloss test result reported as FAILED *** \n"
print(msg)
log_msgs.append(msg)
result_msg = "One or more slits FAILED path_loss test."
# end the timer
pathloss_end_time = time.time() - pathtest_start_time
if pathloss_end_time > 60.0:
pathloss_end_time = pathloss_end_time/60.0 # in minutes
pathloss_tot_time = "* Script FS_PS.py took ", repr(pathloss_end_time) + " minutes to finish."
if pathloss_end_time > 60.0:
pathloss_end_time = pathloss_end_time/60. # in hours
pathloss_tot_time = "* Script FS_PS.py took ", repr(pathloss_end_time) + " hours to finish."
else:
pathloss_tot_time = "* Script FS_PS.py took ", repr(pathloss_end_time) + " seconds to finish."
print(pathloss_tot_time)
log_msgs.append(pathloss_tot_time)
return FINAL_TEST_RESULT, result_msg, log_msgs
if __name__ == '__main__':
print("\n ** using pipeline version: ", jwst.__version__, "** \n")
# input parameters that the script expects
step_input_filename = 'final_output_caldet1_NRS1_srctype.fits'
reffile = 'jwst_nirspec_pathloss_0001.fits'
comparison_filename = 'final_output_caldet1_NRS1_pathloss.fits'
# name of the output images
writefile = True
# set the names of the resulting plots
plot_name = None # "FS_pathtest_histogram.png"
# Run the principal function of the script
median_diff = pathtest(step_input_filename, reffile, comparison_filename, writefile=writefile,
show_figs=False, save_figs=False,
plot_name=plot_name, threshold_diff=1.0e-7,
debug=True)
|
996,023 | 6615dc687e28638fc2365883d4ba7d7781fff4a2 | arr = []
for i in range(0,10):
num = int(input())
arr.append(num%42)
print(len(set(arr))) |
996,024 | 0232555471dc9aaf993f180e6e4139cdca90d9fe | # -*- coding: utf-8 -*-
"""
Created on Sat Feb 11 19:24:59 2017
@author: weilun
"""
import re
import urllib
def getHtml(url):
page=urllib.urlopen(url)
html=page.read()
return html
def getFolder(html):
r=r'href=".*/"'
re_folder=re.compile(r)
folderList=re.findall(re_folder,html)
return folderList
def getMp4(url,folderlist):
r=r'href=".*a\.mp4"'
for folder in folderlist[1:]:
page=urllib.urlopen(url+folder[6:-1])
htmll=page.read()
re_mp4=re.compile(r)
mp4List=re.findall(re_mp4,htmll)
for mp4url in mp4List:
urllib.urlretrieve(url+folder[6:-1]+mp4url[6:-1],"%s" %(mp4url[6:-1]))
print 'file "%s"' %(mp4url[6:-1])
#The url line below specifies the URL link for Aphasia group video, for Control group video the url below should be 'http://talkbank.org/media/AphasiaBank/English/Control/'
url='http://talkbank.org/media/AphasiaBank/English/Aphasia/'
html=getHtml(url)
folderList=getFolder(html)
getMp4(url,folderList)
|
996,025 | 1ab9a69264b05394e7e810d01024c0fdbc2b0b2b | from rest_framework.views import APIView
from rest_framework.generics import GenericAPIView
from rest_framework.response import Response
from rest_framework import permissions
from django.contrib.auth import login, logout, authenticate
from django.http.response import HttpResponseNotAllowed, HttpResponse
from django.contrib.auth import get_user_model
from .serializers import LoginSerializer, UserSerializer, MenuSerializer
from .models import MenuModel
from rest_framework import exceptions
from django.utils.translation import gettext as _
from rest_framework import viewsets
class LoginAPIView(APIView):
def post(self, request, *args, **kwargs):
serializer = LoginSerializer(data=request.data)
serializer.is_valid(True)
user = authenticate(request, **serializer.validated_data)
if user is None:
raise exceptions.ValidationError(_("invalid username or password"))
login(request, user)
return Response(UserSerializer(user).data)
class UserDetail(APIView):
permission_classes = [permissions.IsAuthenticated]
def get(self, request, *args, **kwargs):
user = request.user
return Response(UserSerializer(user).data)
class MenuAPIView(viewsets.ModelViewSet):
serializer_class = MenuSerializer
queryset = MenuModel.objects.all()
#
# def django_login(request):
# username = request.POST['username']
# password = request.POST['password']
# user = authenticate(request, username=username, password=password)
# if user is None:
# return HttpResponse('error username or password', status=401)
# login(request, user)
# return HttpResponse('login success')
#
# def django_true_login(request):
# username = request.POST['username']
# password = request.POST['password']
# login()
#
# def django_is_login(request):
# print(request.user) # 如果没有登录的话，那么输出AnonymousUser
# # 还有其他的一些有用的属性
# # request.user.is_superuser
# request.user.is_authenticated
# if request.user.is_authenticated:
# return HttpResponse('is logined')
# return HttpResponse('not login', status=401)
#
# def django_register(request):
# email = request.POST['email']
# username = request.POST['username']
# password = request.POST['password']
# User = get_user_model()
# field_meta = User._meta.get_field('username')
# max_length = field_meta.max_length
#
# user = User()
# setattr(user, 'username', username)
# setattr(user, 'email', email)
# user.set_password(password)
# user.save()
# return HttpResponse('register success')
|
996,026 | 9dea10c491c35d8da2cb5d22e1e57fb5c432e145 | '''
Given an array of strings strs, group the anagrams together. You can return the answer in any order.
An Anagram is a word or phrase formed by rearranging the letters of a different word or phrase,
typically using all the original letters exactly once.
Input: strs = ["eat","tea","tan","ate","nat","bat"]
Output: [["bat"],["nat","tan"],["ate","eat","tea"]]
Solution Approach:
1. Make a hashmap to store
ld150@ntrs.com
'''
def groupAnagrams(words):
anagrams = {}
for word in words:
sortedWord = ''.join(sorted(word))
if sortedWord in anagrams:
anagrams[sortedWord].append(word)
else:
anagrams[sortedWord] = [word]
return list(anagrams.values())
print(groupAnagrams(["yo", "act", "flop", "tac", "foo", "cat", "oy", "olfp"]))
|
996,027 | 3e8cab01c3d42f20d926bd76820867796da0d0f6 | import jinja2
import webapp2
import datetime
from utils import time_sec, valid_user, valid_password, valid_verify, valid_email, make_pw_hash, match_pw, front_articles
from handlers import FrontPage, NewPost, Flush, BlogPost, Signup, Welcome, Login, Logout, JsonBlogPost, JsonFront
from db import Blog, User
app = webapp2.WSGIApplication([('/', FrontPage),('/newpost', NewPost),
('/flush', Flush),('/blog/([0-9]+)', BlogPost),
('/blog/([0-9]+).json', JsonBlogPost),('/.json', JsonFront),
('/signup', Signup), ('/welcome', Welcome),
('/login', Login),('/logout', Logout)], debug = True)
|
996,028 | 100c3a755921adaa48d6010dc87bee001d26cc5d | from django.contrib import admin
from .models import LinkedInPost
# Register your models here.
admin.site.register(LinkedInPost)
|
996,029 | 15af0cad8f8b132569cb26a5491ea96ccdb92c46 | import math
import random
class Organism:
fitness = None
data = None
def __init__(self, data):
self.data = data
def mutate(self, mutate_func):
self.data = mutate_func(self.data)
def reproduce(self, reproduce_func, other):
return Organism(reproduce_func(self.data, other.data))
def score(self, fitness_func):
self.fitness = fitness_func(self.data)
class GenerationStats:
raw = []
def __init__(self, population):
self.raw = map(lambda o: o.fitness, population.organisms)
def percentile(self, p):
return self.raw[int((len(self.raw)-1)/100*p)]
class Population:
generate_func = None
mutate_func = None
reproduce_func = None
fitness_func = None
organisms = []
state = None
generation_data = []
def __init__(self, generate_func, mutate_func, reproduce_func, fitness_func, size):
self.generate_func = generate_func
self.mutate_func = mutate_func
self.reproduce_func = reproduce_func
self.fitness_func = fitness_func
for i in range(0, size):
self.organisms += [Organism(generate_func())]
def step(self):
# Score all organisms.
for org in self.organisms:
org.score(self.fitness_func)
# Sort by fitness.
self.organisms.sort(key=lambda o: o.fitness)
# Record generation info.
self.generation_data.append(GenerationStats(self))
# Kill with gradient.
population_size = len(self.organisms)
for i, org in enumerate(self.organisms):
if random.randrange(population_size) < i:
self.organisms[i] = None
# Replace missing in population with new.
org_copy = self.organisms[:]
for i, org in enumerate(self.organisms):
if org is None:
mom = None
dad = None
while True:
mom = self.organisms[random.randrange(population_size)]
if mom is not None:
break;
while True:
dad = self.organisms[random.randrange(population_size)]
if dad is not None:
break;
org_copy[i] = dad.reproduce(self.reproduce_func, mom)
org_copy[i].mutate(self.mutate_func)
self.organisms = org_copy[:]
def has_converged(self):
top = self.generation_data[-1].percentile(0)
median = self.generation_data[-1].percentile(50)
# < 1% difference between top and median in population
return abs((top-median)/top) < 0.01
|
996,030 | e0e9247461d3b1c39b0d35cc9963fa9a7fd50c10 | import math
def countValleys(A=[]):
if len(A) < 2:
return 0,0
tree = A.copy()
tree.insert(0, math.inf)
tree.append(math.inf)
oddValleys = 0
evenValleys = 0
even = True
for i in range(1, len(tree) - 1):
if tree[i - 1] > tree[i] and tree[i] < tree[i + 1]:
if (even):
evenValleys += 1
else:
oddValleys += 1
even = not even
return evenValleys, oddValleys
def solution(A):
n = len(A)
if n < 2:
return 0
if n == 2:
if A[0] != A[1]:
return 0
else:
return 1
evenValleys, oddValleys = countValleys(A)
evenCuts = math.ceil(n/2.0) - evenValleys
oddCuts = math.floor(n/2.0) - oddValleys
return min([evenCuts, oddCuts])
# Algorithm
# O ( N )
# The optimal solution we are looking for has either:
#
# valleys in all even i:
#
# \ / \ / \ /
# 1 9 2 8 3
#
# or valleys in all odd i:
#
# / \ / \ / \
# 9 1 8 2 3
#
# No other solution exists.
#
# Thus, we count the currently existing valleys
# and measure the distance to arrive in either of those
# options.
#
# \0/1\2/
# Number of cuts for even-valleys solution:
# evenCuts = ceil(N/2) - evenValleys
#
# /0\1/2\
# Number of cuts for odd-valleys solution:
# oddCuts = floor(N/2) - oddValleys
# |
996,031 | 8f163fea901e825132012623ad2a3eb94d97dba5 | #!/usr/bin/python3
import unittest
from models.engine.file_storage import FileStorage
class TestFileStorage(unittest.TestCase):
""" test engine: file storage """
def setUp(self):
""" standard setUp() """
self.file_storage = FileStorage()
def test_public_attr(self):
""" test if attributes exist """
self.assertFalse(hasattr(self.file_storage, "foo.json"))
""" def test_all(self):
def test_new(self):
def test_save(self):
def test_reload(self): """
if "__main__" == __name__:
unittest.main()
|
996,032 | 9ccb1180b7fb933894cc2bc98cf148862d78cd14 | from collections import defaultdict
count = defaultdict(int)
print(count[8])
|
996,033 | 02ffaf51c723b71cb377cf272342c44e7a2165fb | # -*- coding: UTF-8 -*-
from playwright import sync_playwright
def run(playwright):
browser = playwright.chromium.launch(headless=False)
context = browser.newContext()
# Open new page
page = context.newPage()
# Go to https://mail.qq.com/
page.goto("https://mail.qq.com/")
# Click input[name="u"]
page.frame(url="https://xui.ptlogin2.qq.com/cgi-bin/xlogin?target=self&appid=522005705&daid=4&s_url=https://mail.qq.com/cgi-bin/readtemplate?check=false%26t=loginpage_new_jump%26vt=passport%26vm=wpt%26ft=loginpage%26target=&style=25&low_login=1&proxy_url=https://mail.qq.com/proxy.html&need_qr=0&hide_border=1&border_radius=0&self_regurl=http://zc.qq.com/chs/index.html?type=1&app_id=11005?t=regist&pt_feedback_link=http://support.qq.com/discuss/350_1.shtml&css=https://res.mail.qq.com/zh_CN/htmledition/style/ptlogin_input_for_xmail51328e.css").click("input[name=\"u\"]")
# Fill input[name="u"]
page.frame(url="https://xui.ptlogin2.qq.com/cgi-bin/xlogin?target=self&appid=522005705&daid=4&s_url=https://mail.qq.com/cgi-bin/readtemplate?check=false%26t=loginpage_new_jump%26vt=passport%26vm=wpt%26ft=loginpage%26target=&style=25&low_login=1&proxy_url=https://mail.qq.com/proxy.html&need_qr=0&hide_border=1&border_radius=0&self_regurl=http://zc.qq.com/chs/index.html?type=1&app_id=11005?t=regist&pt_feedback_link=http://support.qq.com/discuss/350_1.shtml&css=https://res.mail.qq.com/zh_CN/htmledition/style/ptlogin_input_for_xmail51328e.css").fill("input[name=\"u\"]", "1479524067")
# Fill input[name="p"]
page.frame(url="https://xui.ptlogin2.qq.com/cgi-bin/xlogin?target=self&appid=522005705&daid=4&s_url=https://mail.qq.com/cgi-bin/readtemplate?check=false%26t=loginpage_new_jump%26vt=passport%26vm=wpt%26ft=loginpage%26target=&style=25&low_login=1&proxy_url=https://mail.qq.com/proxy.html&need_qr=0&hide_border=1&border_radius=0&self_regurl=http://zc.qq.com/chs/index.html?type=1&app_id=11005?t=regist&pt_feedback_link=http://support.qq.com/discuss/350_1.shtml&css=https://res.mail.qq.com/zh_CN/htmledition/style/ptlogin_input_for_xmail51328e.css").fill("input[name=\"p\"]", "Lyy5201314Lhf.")
# Go to https://mail.qq.com/cgi-bin/frame_html?sid=nX6IdcvM58g8WQFe&r=483fe9cfcd5f9af16141b193a98bb53b
page.goto("https://mail.qq.com/cgi-bin/frame_html?sid=nX6IdcvM58g8WQFe&r=483fe9cfcd5f9af16141b193a98bb53b")
# Close page
page.close()
# ---------------------
context.close()
browser.close()
with sync_playwright() as playwright:
run(playwright) |
996,034 | 9e0901e6379bf3268a8dab55955b793051de0491 | import numpy as np
from tensorflow.keras.layers import Activation
from tensorflow.keras.layers import Dense
from tensorflow.keras.layers import Input
from tensorflow.keras.models import Model
from tensorflow.keras.optimizers import Adam
class Actor(Model):
def __init__(self, num_observations: int, num_actions: int, learning_rate: float):
super().__init__()
self.num_observations = num_observations
self.num_actions = num_actions
self.learning_rate = learning_rate
self.internal_model = self.build_model()
def build_model(self) -> Model:
actor_in = Input(shape=self.num_observations)
x = Dense(units=24)(actor_in)
x = Activation("relu")(x)
x = Dense(self.num_actions)(x)
actor_out = Activation("softmax")(x)
model = Model(
inputs=actor_in,
outputs=actor_out
)
model.compile(
loss="categorical_crossentropy",
optimizer=Adam(learning_rate=self.learning_rate)
)
return model
def call(self, states: np.ndarray) -> np.ndarray:
return self.internal_model(states).numpy()
def fit(self, states: np.ndarray, actions: np.ndarray):
self.internal_model.fit(x=states, y=actions, verbose=0)
def update_model(self, other_model: Model):
self.internal_model.set_weights(other_model.get_weights())
def load_model(self, path: str):
self.internal_model.load_weights(path)
def save_model(self, path: str):
self.internal_model.save_weights(path)
class Critic(Model):
def __init__(self, num_observations: int, num_values: int, learning_rate: float):
super().__init__()
self.num_observations = num_observations
self.num_values = num_values
self.learning_rate = learning_rate
self.internal_model = self.build_model()
def build_model(self) -> Model:
critic_in = Input(shape=self.num_observations)
x = Dense(units=24)(critic_in)
x = Activation("relu")(x)
critic_out = Dense(self.num_values)(x)
model = Model(
inputs=critic_in,
outputs=critic_out
)
model.compile(
loss="mse",
optimizer=Adam(learning_rate=self.learning_rate)
)
return model
def call(self, states: np.ndarray) -> np.ndarray:
return self.internal_model(states).numpy()
def fit(self, states: np.ndarray, values: np.ndarray):
self.internal_model.fit(x=states, y=values, verbose=0)
def update_model(self, other_model: Model):
self.internal_model.set_weights(other_model.get_weights())
def load_model(self, path: str):
self.internal_model.load_weights(path)
def save_model(self, path: str):
self.internal_model.save_weights(path)
if __name__ == "__main__":
actor = Actor(
num_observations=4,
num_actions=2,
learning_rate=0.001
)
actor.internal_model.summary()
critic = Critic(
num_observations=4,
num_values=1,
learning_rate=0.005
)
critic.internal_model.summary()
|
996,035 | 86b3517b277730e0d53dcd0eebc6bf56625b50de |
class GameController:
"""Maintains the state of the game."""
def __init__(self, WIDTH, HEIGHT):
self.WIDTH = WIDTH
self.HEIGHT = HEIGHT
self.player_wins = False
self.pinky_wins = False
def update(self):
"""Carries out necessary actions if pinky or player wins"""
if self.pinky_wins:
fill(1)
textSize(50)
text("PINKY WINS", self.WIDTH/2 - 140, self.HEIGHT/2)
if self.player_wins:
fill(1)
textSize(50)
text("YOU WIN!!!", self.WIDTH/2 - 140, self.HEIGHT/2)
|
996,036 | f5d58f11240e193918f4d8ba6398230ef077e765 | a = [int(s) for s in input().split()]
b = []
if len(a) % 2 == 0:
for i in range (0, len(a), 2):
b += a[i+1], a[i]
else:
for i in range (0, len(a)-1, 2):
b += a[i+1], a[i]
b.append(a[-1])
print(' '.join([str(i) for i in b]))
|
996,037 | 4390274faa3d2fc15541ec060e2210ec6a60afcd | #!/usr/bin/env python
"""
Extract Wikipedia article-term count matrix from KOPI plain text dump.
"""
import logging
from reader import KopiReader
from sklearn.feature_extraction.text import CountVectorizer
from writer import Writer
MAX_DF = 1.0
logging.basicConfig(format='%(asctime)s %(message)s')
log = logging.getLogger()
log.setLevel(logging.INFO) # DEBUG, INFO, WARN, ERROR, CRITICAL
def build(args):
"Build article-term vectors."
kr = KopiReader(args.root, args.date, args.lang)
log.info('Reader:\n{}'.format(kr))
v = CountVectorizer(max_df=args.max_df)
log.info('Vectorizer:\n{}'.format(v))
log.info('Building..')
X = v.fit_transform(kr())
log.info('..done {}.'.format(X.get_shape()))
return kr.y, X, v.get_feature_names()
if __name__ == '__main__':
import argparse
p = argparse.ArgumentParser(description='Extract term matrix from kopiwiki')
p.add_argument('root', help='Path to KOPI Wikipedia root')
p.add_argument('date', help='KOPI extraction date')
p.add_argument('lang', help='KOPI extraction language')
p.add_argument('--max_df', help='Remove frequent', type=float,
default=MAX_DF)
args = p.parse_args()
y, X, vocab = build(args)
Writer(y, X, vocab)()
|
996,038 | d1312a4a5525f0fd7dcc9c6bcce257c043034a60 |
"""
Implementation of a Connect-4 Board class
Author: RR
"""
class Board:
"""A type for representing the state and behavior of a Connect-4 board
Attributes:
width - an integer denoting the number of columns in the board
height - an integer denoting the number of rows in the board
data - a 2D array (i.e. nested list) of characters (strings of length
1) representing the current state of each cell of the board.
The only permitted values for each entry are ' ' (for an
unoccupied cell), 'X' (denoting a peg belonging to player 1),
and 'O' (denoting a peg belonging to player 2).
"""
INVALID_MOVE = -1
def __init__(self, width, height):
"""Constructs an empty board of the specified width and height.
Parameters:
width - the number of columns in the board (an int >= 1)
height - the number of rows in the board (an int >= 1)
Returns:
None.
"""
self.width = width
self.height = height
self.data = []
for i in range(height):
row = []
for j in range(width):
row.append(' ')
self.data.append(row)
def __str__(self):
"""Generates and returns a string representation of this board object
Returns:
A string containing an ASCII representation of the current
state of this Connect-4 board.
"""
data_string = ""
for i in range(self.height):
row = ""
for j in range(self.width):
row += "|" + self.data[i][j]
row += "|\n"
data_string += row
data_string += "-" * (2 * self.width + 1)
data_string += "\n"
# Column numbers are labeled modulo 10 to keep the characters
# aligned correctly
for i in range(self.width):
data_string += " " + str(i % 10)
return data_string
def add_move(self, column, side):
"""Adds a peg of the specified type to the indicated column
This method mutates the given Board object, by adding a peg
to the given column, for the specified player (either 'X' or 'O').
Due to the action of gravity, the peg "drops" from the top of the
column to come to rest at the first vacant cell in this column.
Note that this method performs no bounds-checking to ensure that
'column' is indeed a valid move.
Args:
column - the column number to which we wish to add a peg (an int)
side - the side making this move (either an 'X' or an 'O')
Returns:
None.
"""
row = 0
# Find the first occupied cell in this column
while (row < self.height and self.data[row][column] == " "):
row = row + 1
# Now add the new peg to the row above it
row = row - 1
self.data[row][column] = side
def clear(self):
"""Resets this board object so it's once again empty
Returns:
None.
"""
for i in range(self.height):
for j in range(self.width):
self.data[i][j] = " "
def set_board(self, move_string):
"""Accepts a string of column numbers and places alternating pegs in
them.
For example, b.set_board('012345') would place alternating
'X's and 'O's on the bottom-most row (starting with an 'X').
Parameters:
move_string - a string containing a sequence of moves to play (a
sequence of integers)
Returns:
None.
"""
next_side = "X"
for col_string in move_string:
col = int(col_string)
if col >= 0 and col <= self.width:
self.add_move(col, next_side)
if next_side == "X":
next_side = "O"
else:
next_side = "X"
def allows_move(self, column):
"""Returns whether a legal move may be made in the specified column
of this board.
The move is legal if and only if the specified column index falls
within the width of the board and the column is not already full.
Parameters:
column - the column number in which we wish to place a peg (an int)
Returns:
A boolean value indicating whether 'column' constitutes a legal
move on the given board
"""
return ( (column >= 0)
and (column < self.width)
and (self.data[0][column] == " "))
def is_full(self):
"""Returns whether the current board is completely filled up
Returns:
A boolean value indicating whether every column in the calling
Board object has been filled up
"""
# If at least one of the columns permits a move, then the board is
# not full
for i in range(self.width):
if self.allows_move(i):
return False
return True
def delete_move(self, column):
"""Removes the top-most peg from the specified column
If the specified column is empty, then this method has no effect.
Note that no bounds-checking is performed to ensure that column
is indeed a valid move.
Parameters:
column - the column index from which to remove a peg (an int)
Returns:
None.
"""
row = 0
# Find the first non-empty cell in the specified column
while (row < self.height and self.data[row][column] == " "):
row = row + 1
# If the column is not empty, remove the top peg
if (row != self.height):
self.data[row][column] = " "
def win_for(self, side):
"""Returns whether the current board position represents a win for
the specified side
A player wins by getting four-of-a-kind of their own peg type in a
row. This can happen either horizontally, vertically or diagonally.
This method checks whether any of these conditions has been met.
Parameters:
side - the player for whom we wish to test for wins ('X' or 'O')
Returns:
A boolean value indicating whether the specified player has won
"""
# Testing rows
for row in range(self.height):
for col in range(self.width - 3):
if ( self.data[row][col] == side
and self.data[row][col+1] == side
and self.data[row][col+2] == side
and self.data[row][col+3] == side):
return True
# Testing columns
for col in range(self.width):
for row in range(self.height - 3):
if ( self.data[row][col] == side
and self.data[row+1][col] == side
and self.data[row+2][col] == side
and self.data[row+3][col] == side):
return True
# Testing left diagonal
for row in range(self.height - 3):
for col in range(self.width - 3):
if ( self.data[row][col] == side
and self.data[row+1][col+1] == side
and self.data[row+2][col+2] == side
and self.data[row+3][col+3] == side):
return True
# Testing right diagonal
for row in range(self.height - 3):
for col in range(3, self.width):
if ( self.data[row][col] == side
and self.data[row+1][col-1] == side
and self.data[row+2][col-2] == side
and self.data[row+3][col-3] == side):
return True
return False
def host_game(self):
"""Wrapper method that runs a complete game of Connect-4
This method "hosts" a game of Connect-4 by gluing together all the
other methods. Player 'X' gets to go first. The user is prompted
to enter moves via the terminal, which are then played on the board.
User input is validated to ensure that only valid column numbers are
accepted. When the game terminates, the final state of the board
is printed along with a message indicating which player won (or if
the game ended in a tie).
Returns:
None.
"""
current_side = "X"
while ( (not self.win_for("X"))
and (not self.win_for("O"))
and (not self.is_full())):
print()
print(self)
print()
move = Board.INVALID_MOVE
while not self.allows_move(move):
move = int(input(current_side + "'s move: "))
self.add_move(move, current_side)
if current_side == "X":
current_side = "O"
else:
current_side = "X"
if self.win_for("X"):
print("X wins --- congratulations!\n")
elif self.win_for("O"):
print("O wins --- congratulations!\n")
else:
print("Tied game!\n")
print()
print(self)
def play_game(self, x_player, o_player):
"""Modified wrapper method that manages a game of Connect-4 between two
players, each of whom can either be an AI or a human
This is a modified version of the host_game method that allows for
one or both of the players to be AI agents (i.e., instances of the
Player class). When an AI agent is chosen, then that agent's next_move
method is used to generate moves for that player. When a human player
is chosen, the terminal is used to solicit moves. To set a certain
player to be an AI player, pass in a Player instance for that
parameter; to make a player a human, pass in the string 'human' for
that parameter.
Args:
x_player, o_player - the type of the 'X'/'O' player (either a Player
object or the string 'human')
Returns:
Nothing
"""
#from connectfour import Player #either from connect4_player or connectfour
current_side = "X"
players = {"X": x_player, "O": o_player}
while ((not self.win_for("X")) and
(not self.win_for("O")) and
(not self.is_full())):
print()
print(self)
print()
move = Board.INVALID_MOVE
while not self.allows_move(move):
if players[current_side] == "human":
move = int(input(current_side + "'s move: "))
else:
move = players[current_side].next_move(self)
print("Computer playing for " + current_side +
" plays at " + str(move))
self.add_move(move, current_side)
if current_side == "X":
current_side = "O"
else:
current_side = "X"
if self.win_for("X"):
print("X wins --- congratulations!\n")
elif self.win_for("O"):
print("O wins --- congratulations!\n")
else:
print("Tied game!\n")
print()
print(self)
def main():
"""Tester function"""
myDic = {"x": 'X', "X": 'X', "o": 'O', 'O': 'O'}
player1 = raw_input("Do you want to play as 'x' or 'o'? ")
difficulty = int(raw_input("How hard do you want the AI to be? Choose a level 1-4. Levels 5 and above have slow response times: "))
b = Board(7, 6)
#px = 'human'
from Player import Player;
if myDic[player1] == 'X':
po = Player('O', difficulty, True) #AI player is X
px = 'human'
else:
po = 'human'
px = Player('X', difficulty, True) #AI player is O
b.play_game(px, po)
#used pass here as an attempt to get rid of runtime error
if __name__ == "__main__":
main()
|
996,039 | b0b83f29854b231d0170288538cf64b1d42ba6d3 | import os
from os.path import basename
from gc3libs import Application
from gc3libs.quantity import GB
class GrayscaleApp(Application):
"""Convert an image file to grayscale."""
def __init__(self, img):
inp = basename(img)
out = "gray-" + inp
Application.__init__(
self,
arguments=[
"convert", inp, "-colorspace", "gray", out],
inputs=[img],
outputs=[out],
output_dir="grayscale.d",
stdout="stdout.txt",
stderr="stderr.txt",
# this is needed to circumvent GC3Pie issue #559, see
# <https://github.com/uzh/gc3pie/issues/559>
requested_memory=1*GB)
|
996,040 | a1475fb980a5ac85345c2ec26a1ccaf1e2c549b2 | #!/usr/bin/env python
from herepy import (
MapTileApi,
MapTileApiType,
BaseMapTileResourceType,
TrafficMapTileResourceType,
)
map_tile_api = MapTileApi(api_key="api_key")
# Returns a map tile
map_tile = map_tile_api.get_maptile(latitude=52.525439, longitude=13.38727, zoom=12)
print(map_tile)
# Returns map tile of traffic Map Tile API
map_tile = map_tile_api.get_maptile(
latitude=52.525439,
longitude=13.38727,
zoom=12,
api_type=MapTileApiType.traffic,
resource_type=TrafficMapTileResourceType.flowlabeltile,
)
print(map_tile)
# Returns a map tile of Aerial API using different parameters
map_tile = map_tile_api.get_maptile(
latitude=52.525439,
longitude=13.38727,
zoom=12,
api_type=MapTileApiType.aerial,
scheme="terrain.day",
size=256,
tile_format="png",
)
print(map_tile)
# ppi specifies 320 ppi which corresponds with Hi-Res.
map_tile = map_tile_api.get_maptile(
latitude=52.525439,
longitude=13.38727,
zoom=12,
api_type=MapTileApiType.base,
resource_type=BaseMapTileResourceType.basetile,
scheme="normal.day",
size=256,
tile_format="png8",
query_parameters={"ppi": 320},
)
print(map_tile)
|
996,041 | be4f47fdea628a8b32eb4986b694549773ed61d6 | import os
import sys
# The config system depends on the `ply` parser generator. On Android, this may
# come as a prebuilt, but may _not_ automatically be added to PYTHONPATH. If
# we're on Android (tested by checking for `envsetup.mk`), then add the `ply`
# prebuilt to `sys.path`:
if os.path.isfile("build/make/core/envsetup.mk"):
if os.path.isdir("external/ply/ply"):
sys.path.insert(0, "external/ply/ply")
from .general import (
can_enable,
get_config_bool,
get_config_int,
get_config_string,
get_options_depending_on,
get_options_selecting,
get_warning,
init_config,
read_config,
set_config,
) # nopep8: E402 module level import not at top of file
from .data import (
get_config,
get_config_list,
get_mconfig_dir,
) # nopep8: E402 module level import not at top of file
from .expr import (
format_dependency_list,
) # nopep8: E402 module level import not at top of file
|
996,042 | c40978b9c318b2dbbbf52e2b93a96c4afce04d08 | import pygame
import random
import math
pygame.init()
click ="right"
X=800
Y=600
#print("helo")
screen = pygame.display.set_mode((X,Y))
pygame.display.set_caption("Skier")
img= pygame.image.load("ski.png")
pygame.display.set_icon(img)
#---------------------player------------------->
playerimg=pygame.image.load("snowboard.png")
playerimgL=pygame.transform.flip(playerimg, True, False)
playerX=370
playerY=80
change =0
def player(x):
screen.blit(playerimg,(x,playerY))
def turn():
screen.blit(playerimgL,(playerX,playerY))
#pygame.display.update()
#----------------------Flags--------------------->
flagimg =pygame.image.load("flag.png")
flagX = random.randint(0,740)
flagY = 600 #random.randint(100,650)
changeflag =-0.7
dist=140 #distnace between flags
flag_state="makaynch"
def flags(x,y):
global flag_state
flag_state="kayn"
screen.blit(pygame.transform.flip(flagimg, True, False),(x,y))
screen.blit(flagimg,(x+dist,y))
#----------------------pinetree---------------->
pinetreeimg=[]
pinetreeX=[]
pinetreeY= []
changetree = []
pine_state =[]
num_trees=15
for i in range(num_trees):
pinetreeimg.append(pygame.image.load("winter.png"))
pinetreeX.append(random.randint(0,740))
pinetreeY.append(random.randint(600,1050))
changetree.append(-0.7)
pine_state.append("makaynch")
def pine_generate(x,y,i):
#global pine_state
#pine_state[i] ="kayn"
screen.blit(pinetreeimg[i],(x,y))
#--------- collision---------------->
def isCol2(playerX,playerY,flagX,flagY):
distance =math.sqrt((math.pow(playerX-((flagX+70)),2))+(math.pow(playerY-flagY,2)))
if distance < 50 :
return True
else: return False
def isCol(playerX,playerY,pinetreeX,pinetreeY):
distance =math.sqrt((math.pow(playerX-pinetreeX,2))+(math.pow(playerY-pinetreeY,2)))
if distance < 30:
return True
else: return False
#--------------------Score----------------->
score_val=0
font=pygame.font.Font('freesansbold.ttf', 20)
textX=10
textY=10
def score(x,y):
score=font.render("Score : "+str(int(score_val)), True, (200,60,40))
screen.blit(score,(x,y))
#------------gameover----------->
over_font=pygame.font.Font('freesansbold.ttf', 60)
def game_over():
gameover=over_font.render("Game Over", True, (250,0,0))
rect=gameover.get_rect()
rect.center=((X/2),(Y/2))
screen.blit(gameover,rect)
#------------------------------------------mainLoop--------------------------------->
test=True
while test:
screen.fill((229,255,255))
for event in pygame.event.get():
if event.type== pygame.QUIT:
test=False
if event.type == pygame.KEYDOWN:
if event.key == pygame.K_LEFT:
change = -0.6
click="left"
if event.key == pygame.K_RIGHT:
change = 0.6
click="right"
if event.type == pygame.KEYUP:
if event.key == pygame.K_LEFT or event.key == pygame.K_RIGHT:
change = 0
click="front"
#--------------------------player--------------->
if playerX >= 740:
playerX = 740
if playerX <= 0:
playerX = 0
if click is "left":
turn()
else:
player(playerX)
playerX += change
#-----------------------flag----------->
if flagX >= 640:
flagX = 640
if flagX <= 0:
flagX = 0
if flagY <= 0:
flag_state="makaynch"
flagY=600
if flag_state is "makaynch":
flagX= random.randint(0,640)
flags(flagX,flagY)
if flag_state is "kayn":
flags(flagX,flagY)
flagY += changeflag
col1 = isCol2(playerX, playerY, flagX, flagY)
if col1:
score_val += 0.01
#-------------------------generate trees--------->
for i in range(num_trees):
pinetreeY[i] += changetree[i]
if pinetreeX[i] >= 740:
pinetreeX[i] = 740
if pinetreeX[i] <= 0:
pinetreeX[i] = 0
if pinetreeX[i] >= flagX-10 and pinetreeX[i] <= flagX+dist+46*2 :
if pinetreeY[i] >= flagY-30 and pinetreeY[i] <= flagY+40:
pinetreeX[i]=random.randint(0,740)
pinetreeY[i]=random.randint(600,1050)
if pinetreeY[i] <= -200:
pinetreeY[i]=random.randint(600,1050)
pinetreeX[i]=random.randint(0,740)
pinetreeY[i] += changetree[i]
pine_generate(pinetreeX[i],pinetreeY[i],i)
#--------------collison--------------->
col= isCol(playerX,playerY,pinetreeX[i],pinetreeY[i])
if col:
#for i in range(6):
# score=0
game_over()
test=False
#score_val += 0.01
score(textX,textY)
pygame.display.update() |
996,043 | dacc1709f85a62521d42aba4fba09c0c72f83961 | import sys
import nltk
from nltk import word_tokenize,sent_tokenize
import re
import keras
from keras.layers.embeddings import Embedding
from keras.layers import Dense, Dropout, RepeatVector,Merge
from keras.layers import LSTM
from keras.layers import recurrent
from keras.models import Sequential
from keras.preprocessing.sequence import pad_sequences
from collections import OrderedDict
from keras.models import model_from_json
import h5py
import numpy as np
from keras.models import load_model
import itertools
from sklearn import metrics
import warnings
warnings.filterwarnings('ignore')
from imblearn.over_sampling import SMOTE
from sklearn.neural_network import MLPClassifier
from sklearn.metrics import confusion_matrix
from sklearn.metrics import accuracy_score
from sklearn.metrics import classification_report
import gensim
from gensim.models import word2vec
import sys, os
os.system
import subprocess
from subprocess import Popen, PIPE
import re
corpus=[]
def tokenize(sent):
sent=sent_tokenize(sent)
#print(sent)
return(sent)
def Extracting_Data(lines):
data = []
for i,line in enumerate(lines):
#print(line,i)
#print("\n")
information=[]
question=[]
line=line.strip().split("\t")
sent=sent_tokenize(line[0])
answer=line[1]
for i,sn in enumerate(sent):
if(re.search('\?' , sn)):
question.append(word_tokenize(sn))
else:
information.append(word_tokenize(sn))
information=list(itertools.chain(*information))
question=list(itertools.chain(*question))
#print("information: ",information)
#print("question: ",question)
#print("\n")
corpus.append([information,question])
data.append((information,question,answer))
return data
def get_Data(f):
data = Extracting_Data(f.readlines())
return data
train = get_Data(open('/home/priyanka/Desktop/Final_NLP_Codes/Final_codes__/stanford-parser-full-2018-10-17/DATA/train_New.txt', 'r'))
test = get_Data(open("/home/priyanka/Desktop/Final_NLP_Codes/Final_codes__/stanford-parser-full-2018-10-17/DATA/test_New.txt", 'r'))
import itertools
corpus=list(itertools.chain(*corpus))
model=word2vec.Word2Vec(corpus,min_count=1,size=100)
def vectorize_Data(data, word_idx, word_idx_answer, story_maxlen, query_maxlen):
X = []
Xq = []
Y = []
for story, query, answer in data:
x = [word_idx[w] for w in story]
xq = [word_idx[w] for w in query]
y = np.zeros(len(word_idx_answer))
for item in answer.split():
if re.search('\+|\-|\*|/', item):
y[word_idx_answer[item]] = 1
X.append(x)
Xq.append(xq)
Y.append(y)
return pad_sequences(X, maxlen=story_maxlen), pad_sequences(Xq, maxlen=query_maxlen), np.array(Y)
################# Loading Dataset ###################
train = get_Data(open('/home/priyanka/Desktop/Final_NLP_Codes/Final_codes__/stanford-parser-full-2018-10-17/DATA/train_New.txt', 'r'))
test = get_Data(open("/home/priyanka/Desktop/Final_NLP_Codes/Final_codes__/stanford-parser-full-2018-10-17/DATA/test_New.txt", 'r'))
#test = get_Data(open("DATA/test2.txt", 'r'))
######################## Vocab & word index Formation ##############
vocab = sorted(reduce(lambda x, y: x | y,(set(story + q + [answer]) for story, q, answer in train + test)))
vocab_size = len(vocab) + 1
vocab_answer_set = set()
for story, q, answer in train + test:
for item in answer.split():
if re.search('\+|\-|\*|/', item):
vocab_answer_set.add(item)
vocab_answer = list(vocab_answer_set)
vocab_answer_size = len(vocab_answer)
word_idx = OrderedDict((c, i + 1) for i, c in enumerate(vocab))
word_idx_answer = OrderedDict((c, i) for i, c in enumerate(vocab_answer))
word_idx_operator_reverse = OrderedDict((i, c) for i, c in enumerate(vocab_answer))
story_maxlen = max(map(len, (x for x, _, _ in train + test)))
query_maxlen = max(map(len, (x for _, x, _ in train+ test)))
query_maxlen=story_maxlen # TAKING SAME DIMENSION FOR STORY AND QUESTION....
def get_word2vec(data, word_idx, word_idx_answer, story_maxlen, query_maxlen):
X = []
Xq = []
Y = []
print("length of data")
print(len(data))
for story, query, answer in data:
x = [model[w] for w in story]
xq = [model[w] for w in query]
y = np.zeros(len(word_idx_answer))
for item in answer.split():
if re.search('\+|\-|\*|/', item):
y[word_idx_answer[item]] = 1
x=list(itertools.chain(*x))
xq=list(itertools.chain(*xq))
X.append(x)
Xq.append(xq)
Y.append(y)
return pad_sequences(X, maxlen=story_maxlen), pad_sequences(Xq, maxlen=query_maxlen), np.array(Y)
################## Word2Vector Representation ##############################
'''
X, Xq, Y = get_word2vec(train, word_idx, word_idx_answer, story_maxlen, query_maxlen)
tX, tXq, tY = vectorize_Data(test, word_idx, word_idx_answer, story_maxlen, query_maxlen)
expected_T=[np.argmax(le) for le in Y] #train class labels
print("\n------------------------------------------\n")
print('X.shape = {}'.format(X.shape))
print('Xq.shape = {}'.format(Xq.shape))
print('Y.shape = {}'.format(Y.shape))
print('tX.shape = {}'.format(tX.shape))
print('tXq.shape = {}'.format(tXq.shape))
print('tY.shape = {}'.format(tY.shape))
print('story_maxlen, query_maxlen = {}, {}'.format(story_maxlen, query_maxlen))
print("\n---------------------------------------------\n")
'''
############################## word Index Vector Representation #########################
X, Xq, Y = vectorize_Data(train, word_idx, word_idx_answer, story_maxlen, query_maxlen)
tX, tXq, tY = vectorize_Data(test, word_idx, word_idx_answer, story_maxlen, query_maxlen)
expected_T=[np.argmax(le) for le in Y] #train class labels
print("\n------------------------------------------\n")
print('X.shape = {}'.format(X.shape))
print('Xq.shape = {}'.format(Xq.shape))
print('Y.shape = {}'.format(Y.shape))
print('tX.shape = {}'.format(tX.shape))
print('tXq.shape = {}'.format(tXq.shape))
print('tY.shape = {}'.format(tY.shape))
print('story_maxlen, query_maxlen = {}, {}'.format(story_maxlen, query_maxlen))
print("\n")
############################ Schema Identification ###########################
print("\n--------------------- Schema Identification ---------------------------\n")
print('Build model ...')
print("\n")
print("MultiLayer Perceptron Classifier ...\n\n")
X_new=X+Xq
tX_new=tX+tXq
clf = MLPClassifier(solver='lbfgs', alpha=1e-5, hidden_layer_sizes=(350, 220,50), random_state=1)
clf.fit(X_new, expected_T)
pred=clf.predict(tX_new)
pred_T=clf.predict(X_new)
#print("expected_labels: ",expected_T)
print("Predicted labels: ",pred)
print("\n")
target_names=["+","*","-","/"]
expected=[np.argmax(le) for le in tY]
#predicted=[np.argmax(le) for le in pred] #we dont require one-hot vector
predicted=pred
print("\n Train matrix : \n----------------------------------\n")
print(classification_report(expected_T, pred_T, target_names=target_names))
print("\n Test Matrix : \n----------------------------------\n")
print(classification_report(expected, predicted, target_names=target_names))
print("\n----------------------------------\n")
print("MLP Classifier Train Accuracy: ",accuracy_score(expected_T, pred_T)*100)
print("\n---------------------------------\n")
print("MLP Classifier Test Accuracy: ",accuracy_score(expected, predicted)*100)
print("\n---------------------------------\n")
print("\n")
############################### Seq2Seq Model Classifier ###########################
print("\n ################## Seq2Seq Model Classifier ################\n")
from loading_Model_file import labels_test
print("Predicted_Test LAbel: ",labels_test)
print("****************")
expected=[np.argmax(le) for le in tY]
print("\n---------------------------------\n")
print("seq2seq Classifier Test Accuracy: ",accuracy_score(expected, labels_test)*100)
print("\n------------------------------------------------------------------\n")
print("\n\n")
########################### SMOTE: OVerSampling ##########################
print("################## SMOTE: OVerSampling ##############\n")
print("Before OVer Sampling train data : ",len(X_new),X_new.shape)
sm = SMOTE(random_state=9)
X_new, expected_T = sm.fit_sample(X_new, np.array(expected_T).ravel())
clf = MLPClassifier(solver='adam', alpha=1e-5, hidden_layer_sizes=(350, 220,50), random_state=1)##relu,lbfgs,adam
clf.fit(X_new, expected_T)
pred=clf.predict(tX_new)
pred_T=clf.predict(X_new)
target_names=["+","*","-","/"]
expected=[np.argmax(le) for le in tY]
#predicted=[np.argmax(le) for le in pred] #we dont require one-hot vector
predicted=pred
print("\n Train matrix : \n----------------------------------\n")
print(classification_report(expected_T, pred_T, target_names=target_names))
print("\n Test Matrix : \n----------------------------------\n")
print(classification_report(expected, predicted, target_names=target_names))
print("\n----------------------------------\n")
print("MLP Classifier Train Accuracy: ",accuracy_score(expected_T, pred_T)*100)
print("\n---------------------------------\n")
print("MLP Classifier Test Accuracy: ",accuracy_score(expected, predicted)*100)
print("\n---------------------------------\n")
print("\n")
####################################### Modules for Pre-Processing ################################
print("\n********************** Equation- Answer Generation **************************\n\n\n")
#####Module1 Resolve_Currency#############
def Resolve_Currency(inf):
print ("Sent received at Currency module is:\n",inf)
word_token = inf.split(" ")
mod_sentence=""
for token_curr in word_token:
if(re.search(r"\$",token_curr)):
mod_sentence=mod_sentence+" "+token_curr[1:]+" "+"dollars"
else:
mod_sentence=mod_sentence+" "+token_curr
return(mod_sentence[1:])
def Resolve_Conjunctions(inf,i):
###Applying POS tagging before splitting the sentence#####
word_token = inf.split(" ")
word_token = [X for X in word_token if X!=""]
#print("Word Tokens ", word_token)
pos_tags_sent=[]
temp=nltk.pos_tag(word_token)
pos_tags_sent.append(temp)
#print("\n\n")
#print(pos_tags_sent)
#print("\n\n")
resolve_pos_dict=dict(pos_tags_sent[0])
CC_resolve_pos_dict[i]=resolve_pos_dict
CC_resolve_pos_dict[i+1]=resolve_pos_dict
new_sent=re.split(r"(?:\band\b|\bif\b|\bbut\b|\bso\b)", inf)
#print("CC Resolve sent is ", new_sent)
print("\n")
mod_sentence=''
for sent in new_sent:
mod_sentence+=sent+'.'
return mod_sentence[:-2]
Owner_Entity_dict={}
def Extract_Roles_entities(processed_information,CC_resolve_pos_dict,conjunction_index):
dict_cc_resolve={}
####Word Tokenizing the information sentences####
tokens=[word_tokenize(new_sent_sample) for new_sent_sample in processed_information]
"""print("\n----------------tokens -------------------\n")
print("tokens:",tokens)
print("\n\n-------------- POS tags ----------------\n")"""
#iterate over the all sentences:
#verb=[]
Entity_Values=[]
irrelevent=0
FlagMod=0
for i,sent in enumerate(tokens):
temp={}
verb=[]
mod_I=i
for j,w in enumerate(sent):
Entities=[]
if(CC_resolve_pos_dict[i][w] in verb_tags):
Owners1=[]
Owners2=[]
#print("IN IF")
verb=[w]
if(j!=0):
pre_verb=sent[:j]
pre_verb_tags = [CC_resolve_pos_dict[i][w] for w in sent[:j]]
#print("PREverb is" , pre_verb)
for o,tag in enumerate(pre_verb_tags):
#print("PREverb is" , pre_verb, tag)
if (tag in Noun_tags or tag == "EX"):
#print("In Noun tags ",sent[:j],sent[o])
Owners1.append(sent[o])
#print("Owners1 is ", Owners1)
if (tag in pronoun_tags):
#print("In Pronoun Tag")
if("Owners1" in dict_cc_resolve[mod_I-1].keys() and mod_I!=0):
Curr_Owners=dict_cc_resolve[mod_I-1]["Owners1"]
#print("***************",mod_I, Curr_Owners)
pre_verb=dict_cc_resolve[mod_I-1]["pre_verb"]
Owners1.append(Curr_Owners[0])
#print("Owners1 2nd Prp is ", Owners1)
elif (Owners1==[] and mod_I!=0):
if("Owners1" in dict_cc_resolve[mod_I-1].keys()):
Curr_Owners=dict_cc_resolve[mod_I-1]["Owners1"]
Owners1.append(Curr_Owners[0])
#if (pre_verb in
else:
#print("In else")
if(mod_I!=0):
if("Owners1" in dict_cc_resolve[mod_I-1].keys()):
pre_verb = dict_cc_resolve[mod_I-1]["pre_verb"]
Owners1 = dict_cc_resolve[mod_I-1]["Owners1"]
else:
pre_verb=None
after_verb_tags=[CC_resolve_pos_dict[i][w] for w in sent[j+1:]]
Averb=[]
prp_verb=[]
Prp_verb_Tags=[]
#####Storing the entity vlues:
for k,tag in enumerate(after_verb_tags):
#print("Tag is ", tag)
if (tag in object_tag):
Entities.append(sent[j+1+k])
if (tag == "NNP"):
#print("In Owner2 tags", sent[j+k+1])
Owners2.append(sent[j+k+1])
if(tag =="CD"):
#temp[Entity_value_Tag] = sent[j+k+1]
Entity_Values.append(sent[j+k+1])
if not (tag in Prep_tags):
Averb.append(sent[j+1+k])
else:
prp_verb=sent[j+1+k:]
Prp_verb_Tags=[CC_resolve_pos_dict[i][w] for w in sent[j+1+k:]]
break
for o2,tag in enumerate(Prp_verb_Tags):
if (tag in object_tag):
Entities.append(prp_verb[o2])
if(tag =="CD"):
Entity_Values.append(prp_verb[o2])
if (tag == "NNP"):
Owners2.append(prp_verb[o2])
if (Entities==[] and mod_I!=0):
if("Entities" in dict_cc_resolve[mod_I-1].keys()):
Entities = dict_cc_resolve[mod_I-1]["Entities"]
after_verb=Averb
else:
if(j==len(sent)-1 and mod_I==0 and verb==[]):
#print ("First Sentence , no verb", sent)
pre_verb = sent
if(j==len(sent)-1 and mod_I!=0 and verb==[]):
#print("###########Verb is not in the sentence#############: \n")
#print("prev_sent,Current_sent : ", i , tokens[i-1],sent)
#print("\n")
#print("Dict is ", dict_cc_resolve[i-1], j)
if("pre_verb" in dict_cc_resolve[mod_I-1].keys()):
pre_verb = dict_cc_resolve[mod_I-1]["pre_verb"]
#print("**********Owners1", pre_verb)
if("Owners1" in dict_cc_resolve[mod_I-1].keys()):
Owners1= dict_cc_resolve[mod_I-1]["Owners1"]
if("verb" in dict_cc_resolve[mod_I-1].keys()):
verb= dict_cc_resolve[mod_I-1]["verb"]
after_verb_tags=[CC_resolve_pos_dict[i][w] for w in sent]
Averb=[]
prp_verb=[]
Prp_verb_Tags=[]
for k,tag in enumerate(after_verb_tags):
if (tag in object_tag):
Entities.append(sent[k])
if(tag =="CD"):
Entity_Values.append(sent[k])
if not (tag in Prep_tags):
Averb.append(sent[k])
else:
prp_verb=sent[k:]
Prp_verb_Tags=[CC_resolve_pos_dict[i][w] for w in sent[k:]]
break
for o2,tag in enumerate(Prp_verb_Tags):
if (tag in object_tag):
Entities.append(prp_verb[o2])
if(tag =="CD"):
Entity_Values.append(prp_verb[o2])
if (tag == "NNP"):
Owners2.append(prp_verb[o2])
if (Entities==[]):
if("Entities" in dict_cc_resolve[mod_I-1].keys()):
Entities = dict_cc_resolve[i-1]["Entities"]
after_verb=Averb
temp["verb"]=verb
temp["pre_verb"]=pre_verb
if("after_verb" in temp.keys()):
temp["after_verb"]=after_verb
if("prp_verb" in temp.keys()):
temp["prp_verb"]=prp_verb
if("Entities" in temp.keys()):
temp["Entities"]=Entities
if("Owners1" in temp.keys()):
temp["Owners1"]=Owners1
if("Owners2" in temp.keys()):
temp["Owners2"]=Owners2
if("Entity_Values" in temp.keys()):
temp["Entity_Values"]=Entity_Values
dict_cc_resolve[mod_I]=temp
i=mod_I
return(dict_cc_resolve)
def addition(numbers):
print("Schema Identified :", " Addition ")
result=sum((numbers))
ans=result
return ans
def multiplication(numbers):
print("schema Identified: "," Multiplication ...")
ans=1
for num in numbers:
ans*=num
print("answer: ",ans)
return ans
def substraction(numbers):
print("schema Identified: "," Substraction")
ans=abs(numbers[0]-numbers[1])
print("answer: ",ans)
return ans
def division(numbers):
print("schema Identified: "," Division")
if(numbers[1]>numbers[0]):
ans=numbers[1]/numbers[0]
else:
ans=numbers[0]/numbers[1]
print("answer: ",ans)
return ans
def Generate_Answer(i, values):
print("Test sample, Predicted_class: ",i+1,pred[i])
if(pred[i]==0):
ans=addition(values)
if(pred[i]==2):
ans=substraction(values)
if(pred[i]==3):
ans=division(values)
if(pred[i]==1):
ans=multiplication(values)
return ans
print("\n----------------------------------------\n")
##########Processing the Question#################
test = open("/home/priyanka/Desktop/Final_NLP_Codes/Final_codes__/stanford-parser-full-2018-10-17/DATA/test_New_wt_Values.txt", 'r')
#test = open("DATA/test.txt", 'r')
conjunction_keywords=["and","but","if","then"]
currency_keywords=["$"]
verb_tags=['VBD','VBZ','VBP','VBN','VBG','VB']
Noun_tags=['NNP','NN',"NNS"]
Prep_tags=['IN','TO']
object_tag=['NNS','NNPS']
pronoun_tags=['PRP','PRP$']
conjunction_index=99 # number of sentences not exceeding 99 bcz of CC resolve
for test_sample_index,sample in enumerate(test):
sample= sample.split("\t")
sample = sample[0]
print("\n======================================================================================================================\n")
print("test_sample: ",sample)
print("\n")
conjunction_index=99 # number of sentences not exceeding 99 bcz of CC resolve
sentences=sent_tokenize(sample)
###Dividing input into Information and Question####
information=[]
questions=[]
for i,sn in enumerate(sentences):
if(re.search('\?' , sn)):
questions.append(sn)
else:
information.append(sn)
CC_resolve_pos_dict={}
Original_pos_dict={}
processed_information=[]
ind_mod=0
for i , inf in enumerate(information):
cc_flag=0
if(re.search(r"[\$]" , inf)):
new_curr_sent = Resolve_Currency(inf)
inf = new_curr_sent
#################POS Tagging of INFORMTION SENTENCE##############
word_token = inf.split(" ")
word_token = [X for X in word_token if X!=""]
temp=nltk.pos_tag(word_token)
resolve_pos_dict=dict(temp)
CC_resolve_pos_dict[ind_mod]=resolve_pos_dict
Original_pos_dict[ind_mod]=resolve_pos_dict
#"""print("CC_resolve_pos_dict is ", CC_resolve_pos_dict)
#print("\n\n")"""
#Original_pos_dict = dict(map(reversed, CC_resolve_pos_dict.items()))
#print("Original_resolve_pos_dict is ", Original_pos_dict)
############################END OF POS TAGGING###############
if (re.search(r"\band\b|\bif\b|\bbut\b|\bso\b", inf)):
#print("Going to CC_Resolve module:",cc_flag)
#print("CC resolve is " , CC_resolve_pos_dict)
new_cc_sent = Resolve_Conjunctions(inf,ind_mod)
conjunction_index=i
ind_mod=ind_mod+1
inf = new_cc_sent
inf=inf.split(".")
cc_flag=1
if(cc_flag==1):
for line in inf:
processed_information.append(line)
else:
processed_information.append(inf)
ind_mod=ind_mod+1
word_token = questions[0].split(" ")
temp=nltk.pos_tag(word_token)
CC_resolve_pos_dict[len(CC_resolve_pos_dict)]=dict(temp)
processed_input=processed_information+questions
Roles_Entities= Extract_Roles_entities(processed_input,CC_resolve_pos_dict,conjunction_index)
#print("\n\n")
#print("processed_information: ",processed_information)
#print("\n\n")
print ("Roles and Entities Dictionary" , Roles_Entities)
Getting_values=Roles_Entities[len(Roles_Entities)-1]['Entity_Values']
entity_name=Roles_Entities[len(Roles_Entities)-1]['Entities']
#print("\n--------------------------------------------------\n")
Getting_values = map(int, Getting_values)
print("\n******** Answer Generation ***********\n")
OUTPUT=Generate_Answer(test_sample_index, Getting_values)
stanford_file_test=open("/home/priyanka/Desktop/Final_NLP_Codes/Final_codes__/stanford-parser-full-2018-10-17/TEST_DATA.txt","w")
sample=sample.split("\t")
stanford_file_test.write(str(sample[0]))
stanford_file_test.close()
frr=open("/home/priyanka/Desktop/Final_NLP_Codes/Final_codes__/stanford-parser-full-2018-10-17/TEST_DATA.txt","r")
print("\n\n")
################ Stanford parsing Retrieving ##############
filen="/home/priyanka/Desktop/Final_NLP_Codes/Final_codes__/stanford-parser-full-2018-10-17/TEST_DATA.txt"
res=subprocess.Popen(['bash','lexparser.sh',filen],stdout=subprocess.PIPE)
#print("res:",res)
out, err = res.communicate()
#print("\n\n")
#print(out)
#print("\n-------------------------------------------\n")
sent_parse_dict={}
for i,test_input in enumerate(out.split("\n\n")):
if(test_input!=''):
elements=test_input.strip().split("\n")
elements= [re.sub('[()]', "\t",s) for s in elements]
temp={}
for ele in elements:
ele=ele.split("\t")
key=ele[0]
value=ele[1]
value=value.split(",")
value=[re.sub('-.*',"",e) for e in value]
temp[key]=value
sent_parse_dict[i]=temp
question_parse=sent_parse_dict[len(sent_parse_dict)-1]
#print("question_parse: ",question_parse)
#print("\n")
print("\n\n\nNATURAL LANGUAGE ANSWER GENERATION \n*********************\n")
action=question_parse['root'][1]
print("entity_name: ",entity_name)
if('nsubj' in question_parse.keys()):
subj=question_parse['nsubj'][1]
if('amod' in question_parse.keys()):
entity_name=question_parse['amod'][0]
print(subj,action,OUTPUT,entity_name)
print("\n======================================================================================================================\n")
|
996,044 | fadfce915292be575cecf3c4f2fafe1fdce15327 | def solve_for_coefficients_natural(n, r):
if n == 2:
return natural_interpolate_2(r)
elif n == 3:
return natural_interpolate_3(r)
elif n == 4:
return natural_interpolate_4(r)
elif n == 5:
return natural_interpolate_5(r)
elif n == 6:
return natural_interpolate_6(r)
elif n == 7:
return natural_interpolate_7(r)
elif n == 8:
return natural_interpolate_8(r)
elif n == 9:
return natural_interpolate_9(r)
elif n == 10:
return natural_interpolate_10(r)
elif n == 11:
return natural_interpolate_11(r)
elif n == 12:
return natural_interpolate_12(r)
elif n == 13:
return natural_interpolate_13(r)
elif n == 14:
return natural_interpolate_14(r)
elif n == 15:
return natural_interpolate_15(r)
elif n == 16:
return natural_interpolate_16(r)
elif n == 17:
return natural_interpolate_17(r)
elif n == 18:
return natural_interpolate_18(r)
elif n == 19:
return natural_interpolate_19(r)
elif n == 20:
return natural_interpolate_20(r)
elif n == 21:
return natural_interpolate_21(r)
elif n == 22:
return natural_interpolate_22(r)
elif n == 23:
return natural_interpolate_23(r)
elif n == 24:
return natural_interpolate_24(r)
elif n == 25:
return natural_interpolate_25(r)
elif n == 26:
return natural_interpolate_26(r)
elif n == 27:
return natural_interpolate_27(r)
elif n == 28:
return natural_interpolate_28(r)
elif n == 29:
return natural_interpolate_29(r)
elif n == 30:
return natural_interpolate_30(r)
else:
raise ValueError("Toom-{} is not implemented".format(n))
def natural_interpolate_2(r):
r0 = r[0]
r2 = r['infinity']
r1 = [r[1][i] - r0[i] - r2[i] for i in range(len(r0))]
return (r0, r1, r2)
def natural_interpolate_3(r):
r0 = r[0]
r4 = r['infinity']
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
) // 2 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4)
def natural_interpolate_4(r):
r0 = r[0]
r6 = r['infinity']
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
) // 2 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6)
def natural_interpolate_5(r):
r0 = r[0]
r8 = r['infinity']
r6 = [(15*(r[1][i] + r[-1][i])
- 6*(r[2][i] + r[-2][i])
+ (r[3][i] + r[-3][i])
- 20*r0[i]
- 10080*r8[i]
) // 720 for i in range(len(r0))]
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
- 504*r8[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
- 2*r8[i]
) // 2 for i in range(len(r0))]
r7 = [(-14*r[1][i]
+ 14*r[2][i]
- 6*r[3][i]
+ r[4][i]
+ 5*r0[i]
- 4*r2[i]
+ 20*r4[i]
- 604*r6[i]
- 29740*r8[i]
) // 5040 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
- 1680*r7[i]
- 5542*r8[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
- 126*r7[i]
- 254*r8[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
- r7[i]
- r8[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6, r7, r8)
def natural_interpolate_6(r):
r0 = r[0]
r10 = r['infinity']
r8 = [(-56*(r[1][i] + r[-1][i])
+ 28*(r[2][i] + r[-2][i])
- 8*(r[3][i] + r[-3][i])
+ (r[4][i] + r[-4][i])
+ 70*r0[i]
- 1209600*r10[i]
) // 40320 for i in range(len(r0))]
r6 = [(15*(r[1][i] + r[-1][i])
- 6*(r[2][i] + r[-2][i])
+ (r[3][i] + r[-3][i])
- 20*r0[i]
- 10080*r8[i]
- 105840*r10[i]
) // 720 for i in range(len(r0))]
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
- 504*r8[i]
- 2040*r10[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
- 2*r8[i]
- 2*r10[i]
) // 2 for i in range(len(r0))]
r9 = [(42*r[1][i]
- 48*r[2][i]
+ 27*r[3][i]
- 8*r[4][i]
+ r[5][i]
- 14*r0[i]
+ 10*r2[i]
- 38*r4[i]
+ 490*r6[i]
- 31238*r8[i]
- 2922230*r10[i]
) // 362880 for i in range(len(r0))]
r7 = [(-14*r[1][i]
+ 14*r[2][i]
- 6*r[3][i]
+ r[4][i]
+ 5*r0[i]
- 4*r2[i]
+ 20*r4[i]
- 604*r6[i]
- 29740*r8[i]
- 151200*r9[i]
- 708604*r10[i]
) // 5040 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
- 1680*r7[i]
- 5542*r8[i]
- 17640*r9[i]
- 54958*r10[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
- 126*r7[i]
- 254*r8[i]
- 510*r9[i]
- 1022*r10[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
- r7[i]
- r8[i]
- r9[i]
- r10[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10)
def natural_interpolate_7(r):
r0 = r[0]
r12 = r['infinity']
r10 = [(210*(r[1][i] + r[-1][i])
- 120*(r[2][i] + r[-2][i])
+ 45*(r[3][i] + r[-3][i])
- 10*(r[4][i] + r[-4][i])
+ (r[5][i] + r[-5][i])
- 252*r0[i]
- 199584000*r12[i]
) // 3628800 for i in range(len(r0))]
r8 = [(-56*(r[1][i] + r[-1][i])
+ 28*(r[2][i] + r[-2][i])
- 8*(r[3][i] + r[-3][i])
+ (r[4][i] + r[-4][i])
+ 70*r0[i]
- 1209600*r10[i]
- 25280640*r12[i]
) // 40320 for i in range(len(r0))]
r6 = [(15*(r[1][i] + r[-1][i])
- 6*(r[2][i] + r[-2][i])
+ (r[3][i] + r[-3][i])
- 20*r0[i]
- 10080*r8[i]
- 105840*r10[i]
- 1013760*r12[i]
) // 720 for i in range(len(r0))]
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
- 504*r8[i]
- 2040*r10[i]
- 8184*r12[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
- 2*r8[i]
- 2*r10[i]
- 2*r12[i]
) // 2 for i in range(len(r0))]
r11 = [(-132*r[1][i]
+ 165*r[2][i]
- 110*r[3][i]
+ 44*r[4][i]
- 10*r[5][i]
+ r[6][i]
+ 42*r0[i]
- 28*r2[i]
+ 92*r4[i]
- 868*r6[i]
+ 22652*r8[i]
- 2620708*r10[i]
- 415790788*r12[i]
) // 39916800 for i in range(len(r0))]
r9 = [(42*r[1][i]
- 48*r[2][i]
+ 27*r[3][i]
- 8*r[4][i]
+ r[5][i]
- 14*r0[i]
+ 10*r2[i]
- 38*r4[i]
+ 490*r6[i]
- 31238*r8[i]
- 2922230*r10[i]
- 19958400*r11[i]
- 124075238*r12[i]
) // 362880 for i in range(len(r0))]
r7 = [(-14*r[1][i]
+ 14*r[2][i]
- 6*r[3][i]
+ r[4][i]
+ 5*r0[i]
- 4*r2[i]
+ 20*r4[i]
- 604*r6[i]
- 29740*r8[i]
- 151200*r9[i]
- 708604*r10[i]
- 3160080*r11[i]
- 13645900*r12[i]
) // 5040 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
- 1680*r7[i]
- 5542*r8[i]
- 17640*r9[i]
- 54958*r10[i]
- 168960*r11[i]
- 515062*r12[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
- 126*r7[i]
- 254*r8[i]
- 510*r9[i]
- 1022*r10[i]
- 2046*r11[i]
- 4094*r12[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
- r7[i]
- r8[i]
- r9[i]
- r10[i]
- r11[i]
- r12[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12)
def natural_interpolate_8(r):
r0 = r[0]
r14 = r['infinity']
r12 = [(-792*(r[1][i] + r[-1][i])
+ 495*(r[2][i] + r[-2][i])
- 220*(r[3][i] + r[-3][i])
+ 66*(r[4][i] + r[-4][i])
- 12*(r[5][i] + r[-5][i])
+ (r[6][i] + r[-6][i])
+ 924*r0[i]
- 43589145600*r14[i]
) // 479001600 for i in range(len(r0))]
r10 = [(210*(r[1][i] + r[-1][i])
- 120*(r[2][i] + r[-2][i])
+ 45*(r[3][i] + r[-3][i])
- 10*(r[4][i] + r[-4][i])
+ (r[5][i] + r[-5][i])
- 252*r0[i]
- 199584000*r12[i]
- 7264857600*r14[i]
) // 3628800 for i in range(len(r0))]
r8 = [(-56*(r[1][i] + r[-1][i])
+ 28*(r[2][i] + r[-2][i])
- 8*(r[3][i] + r[-3][i])
+ (r[4][i] + r[-4][i])
+ 70*r0[i]
- 1209600*r10[i]
- 25280640*r12[i]
- 461260800*r14[i]
) // 40320 for i in range(len(r0))]
r6 = [(15*(r[1][i] + r[-1][i])
- 6*(r[2][i] + r[-2][i])
+ (r[3][i] + r[-3][i])
- 20*r0[i]
- 10080*r8[i]
- 105840*r10[i]
- 1013760*r12[i]
- 9369360*r14[i]
) // 720 for i in range(len(r0))]
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
- 504*r8[i]
- 2040*r10[i]
- 8184*r12[i]
- 32760*r14[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
- 2*r8[i]
- 2*r10[i]
- 2*r12[i]
- 2*r14[i]
) // 2 for i in range(len(r0))]
r13 = [(429*r[1][i]
- 572*r[2][i]
+ 429*r[3][i]
- 208*r[4][i]
+ 65*r[5][i]
- 12*r[6][i]
+ r[7][i]
- 132*r0[i]
+ 84*r2[i]
- 252*r4[i]
+ 2004*r6[i]
- 37212*r8[i]
+ 1710324*r10[i]
- 325024572*r12[i]
- 80789566956*r14[i]
) // 6227020800 for i in range(len(r0))]
r11 = [(-132*r[1][i]
+ 165*r[2][i]
- 110*r[3][i]
+ 44*r[4][i]
- 10*r[5][i]
+ r[6][i]
+ 42*r0[i]
- 28*r2[i]
+ 92*r4[i]
- 868*r6[i]
+ 22652*r8[i]
- 2620708*r10[i]
- 415790788*r12[i]
- 3632428800*r13[i]
- 28616744548*r14[i]
) // 39916800 for i in range(len(r0))]
r9 = [(42*r[1][i]
- 48*r[2][i]
+ 27*r[3][i]
- 8*r[4][i]
+ r[5][i]
- 14*r0[i]
+ 10*r2[i]
- 38*r4[i]
+ 490*r6[i]
- 31238*r8[i]
- 2922230*r10[i]
- 19958400*r11[i]
- 124075238*r12[i]
- 726485760*r13[i]
- 4084385750*r14[i]
) // 362880 for i in range(len(r0))]
r7 = [(-14*r[1][i]
+ 14*r[2][i]
- 6*r[3][i]
+ r[4][i]
+ 5*r0[i]
- 4*r2[i]
+ 20*r4[i]
- 604*r6[i]
- 29740*r8[i]
- 151200*r9[i]
- 708604*r10[i]
- 3160080*r11[i]
- 13645900*r12[i]
- 57657600*r13[i]
- 239967004*r14[i]
) // 5040 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
- 1680*r7[i]
- 5542*r8[i]
- 17640*r9[i]
- 54958*r10[i]
- 168960*r11[i]
- 515062*r12[i]
- 1561560*r13[i]
- 4717438*r14[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
- 126*r7[i]
- 254*r8[i]
- 510*r9[i]
- 1022*r10[i]
- 2046*r11[i]
- 4094*r12[i]
- 8190*r13[i]
- 16382*r14[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
- r7[i]
- r8[i]
- r9[i]
- r10[i]
- r11[i]
- r12[i]
- r13[i]
- r14[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14)
def natural_interpolate_9(r):
r0 = r[0]
r16 = r['infinity']
r14 = [(3003*(r[1][i] + r[-1][i])
- 2002*(r[2][i] + r[-2][i])
+ 1001*(r[3][i] + r[-3][i])
- 364*(r[4][i] + r[-4][i])
+ 91*(r[5][i] + r[-5][i])
- 14*(r[6][i] + r[-6][i])
+ (r[7][i] + r[-7][i])
- 3432*r0[i]
- 12204960768000*r16[i]
) // 87178291200 for i in range(len(r0))]
r12 = [(-792*(r[1][i] + r[-1][i])
+ 495*(r[2][i] + r[-2][i])
- 220*(r[3][i] + r[-3][i])
+ 66*(r[4][i] + r[-4][i])
- 12*(r[5][i] + r[-5][i])
+ (r[6][i] + r[-6][i])
+ 924*r0[i]
- 43589145600*r14[i]
- 2528170444800*r16[i]
) // 479001600 for i in range(len(r0))]
r10 = [(210*(r[1][i] + r[-1][i])
- 120*(r[2][i] + r[-2][i])
+ 45*(r[3][i] + r[-3][i])
- 10*(r[4][i] + r[-4][i])
+ (r[5][i] + r[-5][i])
- 252*r0[i]
- 199584000*r12[i]
- 7264857600*r14[i]
- 223134912000*r16[i]
) // 3628800 for i in range(len(r0))]
r8 = [(-56*(r[1][i] + r[-1][i])
+ 28*(r[2][i] + r[-2][i])
- 8*(r[3][i] + r[-3][i])
+ (r[4][i] + r[-4][i])
+ 70*r0[i]
- 1209600*r10[i]
- 25280640*r12[i]
- 461260800*r14[i]
- 7904856960*r16[i]
) // 40320 for i in range(len(r0))]
r6 = [(15*(r[1][i] + r[-1][i])
- 6*(r[2][i] + r[-2][i])
+ (r[3][i] + r[-3][i])
- 20*r0[i]
- 10080*r8[i]
- 105840*r10[i]
- 1013760*r12[i]
- 9369360*r14[i]
- 85307040*r16[i]
) // 720 for i in range(len(r0))]
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
- 504*r8[i]
- 2040*r10[i]
- 8184*r12[i]
- 32760*r14[i]
- 131064*r16[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
- 2*r8[i]
- 2*r10[i]
- 2*r12[i]
- 2*r14[i]
- 2*r16[i]
) // 2 for i in range(len(r0))]
r15 = [(-1430*r[1][i]
+ 2002*r[2][i]
- 1638*r[3][i]
+ 910*r[4][i]
- 350*r[5][i]
+ 90*r[6][i]
- 14*r[7][i]
+ r[8][i]
+ 429*r0[i]
- 264*r2[i]
+ 744*r4[i]
- 5304*r6[i]
+ 81384*r8[i]
- 2605944*r10[i]
+ 192387624*r12[i]
- 55942352184*r14[i]
- 20546119600536*r16[i]
) // 1307674368000 for i in range(len(r0))]
r13 = [(429*r[1][i]
- 572*r[2][i]
+ 429*r[3][i]
- 208*r[4][i]
+ 65*r[5][i]
- 12*r[6][i]
+ r[7][i]
- 132*r0[i]
+ 84*r2[i]
- 252*r4[i]
+ 2004*r6[i]
- 37212*r8[i]
+ 1710324*r10[i]
- 325024572*r12[i]
- 80789566956*r14[i]
- 871782912000*r15[i]
- 8422900930332*r16[i]
) // 6227020800 for i in range(len(r0))]
r11 = [(-132*r[1][i]
+ 165*r[2][i]
- 110*r[3][i]
+ 44*r[4][i]
- 10*r[5][i]
+ r[6][i]
+ 42*r0[i]
- 28*r2[i]
+ 92*r4[i]
- 868*r6[i]
+ 22652*r8[i]
- 2620708*r10[i]
- 415790788*r12[i]
- 3632428800*r13[i]
- 28616744548*r14[i]
- 210680870400*r15[i]
- 1479485236228*r16[i]
) // 39916800 for i in range(len(r0))]
r9 = [(42*r[1][i]
- 48*r[2][i]
+ 27*r[3][i]
- 8*r[4][i]
+ r[5][i]
- 14*r0[i]
+ 10*r2[i]
- 38*r4[i]
+ 490*r6[i]
- 31238*r8[i]
- 2922230*r10[i]
- 19958400*r11[i]
- 124075238*r12[i]
- 726485760*r13[i]
- 4084385750*r14[i]
- 22313491200*r15[i]
- 119387268038*r16[i]
) // 362880 for i in range(len(r0))]
r7 = [(-14*r[1][i]
+ 14*r[2][i]
- 6*r[3][i]
+ r[4][i]
+ 5*r0[i]
- 4*r2[i]
+ 20*r4[i]
- 604*r6[i]
- 29740*r8[i]
- 151200*r9[i]
- 708604*r10[i]
- 3160080*r11[i]
- 13645900*r12[i]
- 57657600*r13[i]
- 239967004*r14[i]
- 988107120*r15[i]
- 4037604460*r16[i]
) // 5040 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
- 1680*r7[i]
- 5542*r8[i]
- 17640*r9[i]
- 54958*r10[i]
- 168960*r11[i]
- 515062*r12[i]
- 1561560*r13[i]
- 4717438*r14[i]
- 14217840*r15[i]
- 42784582*r16[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
- 126*r7[i]
- 254*r8[i]
- 510*r9[i]
- 1022*r10[i]
- 2046*r11[i]
- 4094*r12[i]
- 8190*r13[i]
- 16382*r14[i]
- 32766*r15[i]
- 65534*r16[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
- r7[i]
- r8[i]
- r9[i]
- r10[i]
- r11[i]
- r12[i]
- r13[i]
- r14[i]
- r15[i]
- r16[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16)
def natural_interpolate_10(r):
r0 = r[0]
r18 = r['infinity']
r16 = [(-11440*(r[1][i] + r[-1][i])
+ 8008*(r[2][i] + r[-2][i])
- 4368*(r[3][i] + r[-3][i])
+ 1820*(r[4][i] + r[-4][i])
- 560*(r[5][i] + r[-5][i])
+ 120*(r[6][i] + r[-6][i])
- 16*(r[7][i] + r[-7][i])
+ (r[8][i] + r[-8][i])
+ 12870*r0[i]
- 4268249137152000*r18[i]
) // 20922789888000 for i in range(len(r0))]
r14 = [(3003*(r[1][i] + r[-1][i])
- 2002*(r[2][i] + r[-2][i])
+ 1001*(r[3][i] + r[-3][i])
- 364*(r[4][i] + r[-4][i])
+ 91*(r[5][i] + r[-5][i])
- 14*(r[6][i] + r[-6][i])
+ (r[7][i] + r[-7][i])
- 3432*r0[i]
- 12204960768000*r16[i]
- 1058170098585600*r18[i]
) // 87178291200 for i in range(len(r0))]
r12 = [(-792*(r[1][i] + r[-1][i])
+ 495*(r[2][i] + r[-2][i])
- 220*(r[3][i] + r[-3][i])
+ 66*(r[4][i] + r[-4][i])
- 12*(r[5][i] + r[-5][i])
+ (r[6][i] + r[-6][i])
+ 924*r0[i]
- 43589145600*r14[i]
- 2528170444800*r16[i]
- 120467944396800*r18[i]
) // 479001600 for i in range(len(r0))]
r10 = [(210*(r[1][i] + r[-1][i])
- 120*(r[2][i] + r[-2][i])
+ 45*(r[3][i] + r[-3][i])
- 10*(r[4][i] + r[-4][i])
+ (r[5][i] + r[-5][i])
- 252*r0[i]
- 199584000*r12[i]
- 7264857600*r14[i]
- 223134912000*r16[i]
- 6289809926400*r18[i]
) // 3628800 for i in range(len(r0))]
r8 = [(-56*(r[1][i] + r[-1][i])
+ 28*(r[2][i] + r[-2][i])
- 8*(r[3][i] + r[-3][i])
+ (r[4][i] + r[-4][i])
+ 70*r0[i]
- 1209600*r10[i]
- 25280640*r12[i]
- 461260800*r14[i]
- 7904856960*r16[i]
- 131254905600*r18[i]
) // 40320 for i in range(len(r0))]
r6 = [(15*(r[1][i] + r[-1][i])
- 6*(r[2][i] + r[-2][i])
+ (r[3][i] + r[-3][i])
- 20*r0[i]
- 10080*r8[i]
- 105840*r10[i]
- 1013760*r12[i]
- 9369360*r14[i]
- 85307040*r16[i]
- 771695280*r18[i]
) // 720 for i in range(len(r0))]
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
- 504*r8[i]
- 2040*r10[i]
- 8184*r12[i]
- 32760*r14[i]
- 131064*r16[i]
- 524280*r18[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
- 2*r8[i]
- 2*r10[i]
- 2*r12[i]
- 2*r14[i]
- 2*r16[i]
- 2*r18[i]
) // 2 for i in range(len(r0))]
r17 = [(4862*r[1][i]
- 7072*r[2][i]
+ 6188*r[3][i]
- 3808*r[4][i]
+ 1700*r[5][i]
- 544*r[6][i]
+ 119*r[7][i]
- 16*r[8][i]
+ r[9][i]
- 1430*r0[i]
+ 858*r2[i]
- 2310*r4[i]
+ 15258*r6[i]
- 206790*r8[i]
+ 5386458*r10[i]
- 272513670*r12[i]
+ 30255826458*r14[i]
- 12765597850950*r16[i]
- 6622557957272742*r18[i]
) // 355687428096000 for i in range(len(r0))]
r15 = [(-1430*r[1][i]
+ 2002*r[2][i]
- 1638*r[3][i]
+ 910*r[4][i]
- 350*r[5][i]
+ 90*r[6][i]
- 14*r[7][i]
+ r[8][i]
+ 429*r0[i]
- 264*r2[i]
+ 744*r4[i]
- 5304*r6[i]
+ 81384*r8[i]
- 2605944*r10[i]
+ 192387624*r12[i]
- 55942352184*r14[i]
- 20546119600536*r16[i]
- 266765571072000*r17[i]
- 3083760849804024*r18[i]
) // 1307674368000 for i in range(len(r0))]
r13 = [(429*r[1][i]
- 572*r[2][i]
+ 429*r[3][i]
- 208*r[4][i]
+ 65*r[5][i]
- 12*r[6][i]
+ r[7][i]
- 132*r0[i]
+ 84*r2[i]
- 252*r4[i]
+ 2004*r6[i]
- 37212*r8[i]
+ 1710324*r10[i]
- 325024572*r12[i]
- 80789566956*r14[i]
- 871782912000*r15[i]
- 8422900930332*r16[i]
- 75583578470400*r17[i]
- 643521842437836*r18[i]
) // 6227020800 for i in range(len(r0))]
r11 = [(-132*r[1][i]
+ 165*r[2][i]
- 110*r[3][i]
+ 44*r[4][i]
- 10*r[5][i]
+ r[6][i]
+ 42*r0[i]
- 28*r2[i]
+ 92*r4[i]
- 868*r6[i]
+ 22652*r8[i]
- 2620708*r10[i]
- 415790788*r12[i]
- 3632428800*r13[i]
- 28616744548*r14[i]
- 210680870400*r15[i]
- 1479485236228*r16[i]
- 10038995366400*r17[i]
- 66394067988388*r18[i]
) // 39916800 for i in range(len(r0))]
r9 = [(42*r[1][i]
- 48*r[2][i]
+ 27*r[3][i]
- 8*r[4][i]
+ r[5][i]
- 14*r0[i]
+ 10*r2[i]
- 38*r4[i]
+ 490*r6[i]
- 31238*r8[i]
- 2922230*r10[i]
- 19958400*r11[i]
- 124075238*r12[i]
- 726485760*r13[i]
- 4084385750*r14[i]
- 22313491200*r15[i]
- 119387268038*r16[i]
- 628980992640*r17[i]
- 3275389222070*r18[i]
) // 362880 for i in range(len(r0))]
r7 = [(-14*r[1][i]
+ 14*r[2][i]
- 6*r[3][i]
+ r[4][i]
+ 5*r0[i]
- 4*r2[i]
+ 20*r4[i]
- 604*r6[i]
- 29740*r8[i]
- 151200*r9[i]
- 708604*r10[i]
- 3160080*r11[i]
- 13645900*r12[i]
- 57657600*r13[i]
- 239967004*r14[i]
- 988107120*r15[i]
- 4037604460*r16[i]
- 16406863200*r17[i]
- 66398623804*r18[i]
) // 5040 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
- 1680*r7[i]
- 5542*r8[i]
- 17640*r9[i]
- 54958*r10[i]
- 168960*r11[i]
- 515062*r12[i]
- 1561560*r13[i]
- 4717438*r14[i]
- 14217840*r15[i]
- 42784582*r16[i]
- 128615880*r17[i]
- 386371918*r18[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
- 126*r7[i]
- 254*r8[i]
- 510*r9[i]
- 1022*r10[i]
- 2046*r11[i]
- 4094*r12[i]
- 8190*r13[i]
- 16382*r14[i]
- 32766*r15[i]
- 65534*r16[i]
- 131070*r17[i]
- 262142*r18[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
- r7[i]
- r8[i]
- r9[i]
- r10[i]
- r11[i]
- r12[i]
- r13[i]
- r14[i]
- r15[i]
- r16[i]
- r17[i]
- r18[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18)
def natural_interpolate_11(r):
r0 = r[0]
r20 = r['infinity']
r18 = [(43758*(r[1][i] + r[-1][i])
- 31824*(r[2][i] + r[-2][i])
+ 18564*(r[3][i] + r[-3][i])
- 8568*(r[4][i] + r[-4][i])
+ 3060*(r[5][i] + r[-5][i])
- 816*(r[6][i] + r[-6][i])
+ 153*(r[7][i] + r[-7][i])
- 18*(r[8][i] + r[-8][i])
+ (r[9][i] + r[-9][i])
- 48620*r0[i]
- 1824676506132480000*r20[i]
) // 6402373705728000 for i in range(len(r0))]
r16 = [(-11440*(r[1][i] + r[-1][i])
+ 8008*(r[2][i] + r[-2][i])
- 4368*(r[3][i] + r[-3][i])
+ 1820*(r[4][i] + r[-4][i])
- 560*(r[5][i] + r[-5][i])
+ 120*(r[6][i] + r[-6][i])
- 16*(r[7][i] + r[-7][i])
+ (r[8][i] + r[-8][i])
+ 12870*r0[i]
- 4268249137152000*r18[i]
- 527128768438272000*r20[i]
) // 20922789888000 for i in range(len(r0))]
r14 = [(3003*(r[1][i] + r[-1][i])
- 2002*(r[2][i] + r[-2][i])
+ 1001*(r[3][i] + r[-3][i])
- 364*(r[4][i] + r[-4][i])
+ 91*(r[5][i] + r[-5][i])
- 14*(r[6][i] + r[-6][i])
+ (r[7][i] + r[-7][i])
- 3432*r0[i]
- 12204960768000*r16[i]
- 1058170098585600*r18[i]
- 73775500710912000*r20[i]
) // 87178291200 for i in range(len(r0))]
r12 = [(-792*(r[1][i] + r[-1][i])
+ 495*(r[2][i] + r[-2][i])
- 220*(r[3][i] + r[-3][i])
+ 66*(r[4][i] + r[-4][i])
- 12*(r[5][i] + r[-5][i])
+ (r[6][i] + r[-6][i])
+ 924*r0[i]
- 43589145600*r14[i]
- 2528170444800*r16[i]
- 120467944396800*r18[i]
- 5167100908569600*r20[i]
) // 479001600 for i in range(len(r0))]
r10 = [(210*(r[1][i] + r[-1][i])
- 120*(r[2][i] + r[-2][i])
+ 45*(r[3][i] + r[-3][i])
- 10*(r[4][i] + r[-4][i])
+ (r[5][i] + r[-5][i])
- 252*r0[i]
- 199584000*r12[i]
- 7264857600*r14[i]
- 223134912000*r16[i]
- 6289809926400*r18[i]
- 169058189664000*r20[i]
) // 3628800 for i in range(len(r0))]
r8 = [(-56*(r[1][i] + r[-1][i])
+ 28*(r[2][i] + r[-2][i])
- 8*(r[3][i] + r[-3][i])
+ (r[4][i] + r[-4][i])
+ 70*r0[i]
- 1209600*r10[i]
- 25280640*r12[i]
- 461260800*r14[i]
- 7904856960*r16[i]
- 131254905600*r18[i]
- 2143293425280*r20[i]
) // 40320 for i in range(len(r0))]
r6 = [(15*(r[1][i] + r[-1][i])
- 6*(r[2][i] + r[-2][i])
+ (r[3][i] + r[-3][i])
- 20*r0[i]
- 10080*r8[i]
- 105840*r10[i]
- 1013760*r12[i]
- 9369360*r14[i]
- 85307040*r16[i]
- 771695280*r18[i]
- 6960985920*r20[i]
) // 720 for i in range(len(r0))]
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
- 504*r8[i]
- 2040*r10[i]
- 8184*r12[i]
- 32760*r14[i]
- 131064*r16[i]
- 524280*r18[i]
- 2097144*r20[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
- 2*r8[i]
- 2*r10[i]
- 2*r12[i]
- 2*r14[i]
- 2*r16[i]
- 2*r18[i]
- 2*r20[i]
) // 2 for i in range(len(r0))]
r19 = [(-16796*r[1][i]
+ 25194*r[2][i]
- 23256*r[3][i]
+ 15504*r[4][i]
- 7752*r[5][i]
+ 2907*r[6][i]
- 798*r[7][i]
+ 152*r[8][i]
- 18*r[9][i]
+ r[10][i]
+ 4862*r0[i]
- 2860*r2[i]
+ 7436*r4[i]
- 46420*r6[i]
+ 576236*r8[i]
- 13098580*r10[i]
+ 532310636*r12[i]
- 39968611540*r14[i]
+ 6350631494636*r16[i]
- 3730771315561300*r18[i]
- 2637991952943407764*r20[i]
) // 121645100408832000 for i in range(len(r0))]
r17 = [(4862*r[1][i]
- 7072*r[2][i]
+ 6188*r[3][i]
- 3808*r[4][i]
+ 1700*r[5][i]
- 544*r[6][i]
+ 119*r[7][i]
- 16*r[8][i]
+ r[9][i]
- 1430*r0[i]
+ 858*r2[i]
- 2310*r4[i]
+ 15258*r6[i]
- 206790*r8[i]
+ 5386458*r10[i]
- 272513670*r12[i]
+ 30255826458*r14[i]
- 12765597850950*r16[i]
- 6622557957272742*r18[i]
- 101370917007360000*r19[i]
- 1375210145685786630*r20[i]
) // 355687428096000 for i in range(len(r0))]
r15 = [(-1430*r[1][i]
+ 2002*r[2][i]
- 1638*r[3][i]
+ 910*r[4][i]
- 350*r[5][i]
+ 90*r[6][i]
- 14*r[7][i]
+ r[8][i]
+ 429*r0[i]
- 264*r2[i]
+ 744*r4[i]
- 5304*r6[i]
+ 81384*r8[i]
- 2605944*r10[i]
+ 192387624*r12[i]
- 55942352184*r14[i]
- 20546119600536*r16[i]
- 266765571072000*r17[i]
- 3083760849804024*r18[i]
- 32945548027392000*r19[i]
- 332500281299403096*r20[i]
) // 1307674368000 for i in range(len(r0))]
r13 = [(429*r[1][i]
- 572*r[2][i]
+ 429*r[3][i]
- 208*r[4][i]
+ 65*r[5][i]
- 12*r[6][i]
+ r[7][i]
- 132*r0[i]
+ 84*r2[i]
- 252*r4[i]
+ 2004*r6[i]
- 37212*r8[i]
+ 1710324*r10[i]
- 325024572*r12[i]
- 80789566956*r14[i]
- 871782912000*r15[i]
- 8422900930332*r16[i]
- 75583578470400*r17[i]
- 643521842437836*r18[i]
- 5269678622208000*r19[i]
- 41890044885642492*r20[i]
) // 6227020800 for i in range(len(r0))]
r11 = [(-132*r[1][i]
+ 165*r[2][i]
- 110*r[3][i]
+ 44*r[4][i]
- 10*r[5][i]
+ r[6][i]
+ 42*r0[i]
- 28*r2[i]
+ 92*r4[i]
- 868*r6[i]
+ 22652*r8[i]
- 2620708*r10[i]
- 415790788*r12[i]
- 3632428800*r13[i]
- 28616744548*r14[i]
- 210680870400*r15[i]
- 1479485236228*r16[i]
- 10038995366400*r17[i]
- 66394067988388*r18[i]
- 430591742380800*r19[i]
- 2750479262009668*r20[i]
) // 39916800 for i in range(len(r0))]
r9 = [(42*r[1][i]
- 48*r[2][i]
+ 27*r[3][i]
- 8*r[4][i]
+ r[5][i]
- 14*r0[i]
+ 10*r2[i]
- 38*r4[i]
+ 490*r6[i]
- 31238*r8[i]
- 2922230*r10[i]
- 19958400*r11[i]
- 124075238*r12[i]
- 726485760*r13[i]
- 4084385750*r14[i]
- 22313491200*r15[i]
- 119387268038*r16[i]
- 628980992640*r17[i]
- 3275389222070*r18[i]
- 16905818966400*r19[i]
- 86665431465638*r20[i]
) // 362880 for i in range(len(r0))]
r7 = [(-14*r[1][i]
+ 14*r[2][i]
- 6*r[3][i]
+ r[4][i]
+ 5*r0[i]
- 4*r2[i]
+ 20*r4[i]
- 604*r6[i]
- 29740*r8[i]
- 151200*r9[i]
- 708604*r10[i]
- 3160080*r11[i]
- 13645900*r12[i]
- 57657600*r13[i]
- 239967004*r14[i]
- 988107120*r15[i]
- 4037604460*r16[i]
- 16406863200*r17[i]
- 66398623804*r18[i]
- 267911678160*r19[i]
- 1078605601420*r20[i]
) // 5040 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
- 1680*r7[i]
- 5542*r8[i]
- 17640*r9[i]
- 54958*r10[i]
- 168960*r11[i]
- 515062*r12[i]
- 1561560*r13[i]
- 4717438*r14[i]
- 14217840*r15[i]
- 42784582*r16[i]
- 128615880*r17[i]
- 386371918*r18[i]
- 1160164320*r19[i]
- 3482590102*r20[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
- 126*r7[i]
- 254*r8[i]
- 510*r9[i]
- 1022*r10[i]
- 2046*r11[i]
- 4094*r12[i]
- 8190*r13[i]
- 16382*r14[i]
- 32766*r15[i]
- 65534*r16[i]
- 131070*r17[i]
- 262142*r18[i]
- 524286*r19[i]
- 1048574*r20[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
- r7[i]
- r8[i]
- r9[i]
- r10[i]
- r11[i]
- r12[i]
- r13[i]
- r14[i]
- r15[i]
- r16[i]
- r17[i]
- r18[i]
- r19[i]
- r20[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20)
def natural_interpolate_12(r):
r0 = r[0]
r22 = r['infinity']
r20 = [(-167960*(r[1][i] + r[-1][i])
+ 125970*(r[2][i] + r[-2][i])
- 77520*(r[3][i] + r[-3][i])
+ 38760*(r[4][i] + r[-4][i])
- 15504*(r[5][i] + r[-5][i])
+ 4845*(r[6][i] + r[-6][i])
- 1140*(r[7][i] + r[-7][i])
+ 190*(r[8][i] + r[-8][i])
- 20*(r[9][i] + r[-9][i])
+ (r[10][i] + r[-10][i])
+ 184756*r0[i]
- 936667273148006400000*r22[i]
) // 2432902008176640000 for i in range(len(r0))]
r18 = [(43758*(r[1][i] + r[-1][i])
- 31824*(r[2][i] + r[-2][i])
+ 18564*(r[3][i] + r[-3][i])
- 8568*(r[4][i] + r[-4][i])
+ 3060*(r[5][i] + r[-5][i])
- 816*(r[6][i] + r[-6][i])
+ 153*(r[7][i] + r[-7][i])
- 18*(r[8][i] + r[-8][i])
+ (r[9][i] + r[-9][i])
- 48620*r0[i]
- 1824676506132480000*r20[i]
- 309100200138842112000*r22[i]
) // 6402373705728000 for i in range(len(r0))]
r16 = [(-11440*(r[1][i] + r[-1][i])
+ 8008*(r[2][i] + r[-2][i])
- 4368*(r[3][i] + r[-3][i])
+ 1820*(r[4][i] + r[-4][i])
- 560*(r[5][i] + r[-5][i])
+ 120*(r[6][i] + r[-6][i])
- 16*(r[7][i] + r[-7][i])
+ (r[8][i] + r[-8][i])
+ 12870*r0[i]
- 4268249137152000*r18[i]
- 527128768438272000*r20[i]
- 51442361350668288000*r22[i]
) // 20922789888000 for i in range(len(r0))]
r14 = [(3003*(r[1][i] + r[-1][i])
- 2002*(r[2][i] + r[-2][i])
+ 1001*(r[3][i] + r[-3][i])
- 364*(r[4][i] + r[-4][i])
+ 91*(r[5][i] + r[-5][i])
- 14*(r[6][i] + r[-6][i])
+ (r[7][i] + r[-7][i])
- 3432*r0[i]
- 12204960768000*r16[i]
- 1058170098585600*r18[i]
- 73775500710912000*r20[i]
- 4555411900194355200*r22[i]
) // 87178291200 for i in range(len(r0))]
r12 = [(-792*(r[1][i] + r[-1][i])
+ 495*(r[2][i] + r[-2][i])
- 220*(r[3][i] + r[-3][i])
+ 66*(r[4][i] + r[-4][i])
- 12*(r[5][i] + r[-5][i])
+ (r[6][i] + r[-6][i])
+ 924*r0[i]
- 43589145600*r14[i]
- 2528170444800*r16[i]
- 120467944396800*r18[i]
- 5167100908569600*r20[i]
- 208331313744153600*r22[i]
) // 479001600 for i in range(len(r0))]
r10 = [(210*(r[1][i] + r[-1][i])
- 120*(r[2][i] + r[-2][i])
+ 45*(r[3][i] + r[-3][i])
- 10*(r[4][i] + r[-4][i])
+ (r[5][i] + r[-5][i])
- 252*r0[i]
- 199584000*r12[i]
- 7264857600*r14[i]
- 223134912000*r16[i]
- 6289809926400*r18[i]
- 169058189664000*r20[i]
- 4419351149875200*r22[i]
) // 3628800 for i in range(len(r0))]
r8 = [(-56*(r[1][i] + r[-1][i])
+ 28*(r[2][i] + r[-2][i])
- 8*(r[3][i] + r[-3][i])
+ (r[4][i] + r[-4][i])
+ 70*r0[i]
- 1209600*r10[i]
- 25280640*r12[i]
- 461260800*r14[i]
- 7904856960*r16[i]
- 131254905600*r18[i]
- 2143293425280*r20[i]
- 34682510016000*r22[i]
) // 40320 for i in range(len(r0))]
r6 = [(15*(r[1][i] + r[-1][i])
- 6*(r[2][i] + r[-2][i])
+ (r[3][i] + r[-3][i])
- 20*r0[i]
- 10080*r8[i]
- 105840*r10[i]
- 1013760*r12[i]
- 9369360*r14[i]
- 85307040*r16[i]
- 771695280*r18[i]
- 6960985920*r20[i]
- 62711787600*r22[i]
) // 720 for i in range(len(r0))]
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
- 504*r8[i]
- 2040*r10[i]
- 8184*r12[i]
- 32760*r14[i]
- 131064*r16[i]
- 524280*r18[i]
- 2097144*r20[i]
- 8388600*r22[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
- 2*r8[i]
- 2*r10[i]
- 2*r12[i]
- 2*r14[i]
- 2*r16[i]
- 2*r18[i]
- 2*r20[i]
- 2*r22[i]
) // 2 for i in range(len(r0))]
r21 = [(58786*r[1][i]
- 90440*r[2][i]
+ 87210*r[3][i]
- 62016*r[4][i]
+ 33915*r[5][i]
- 14364*r[6][i]
+ 4655*r[7][i]
- 1120*r[8][i]
+ 189*r[9][i]
- 20*r[10][i]
+ r[11][i]
- 16796*r0[i]
+ 9724*r2[i]
- 24596*r4[i]
+ 147004*r6[i]
- 1708916*r8[i]
+ 35240284*r10[i]
- 1237329236*r12[i]
+ 73853629564*r14[i]
- 7850527669556*r16[i]
+ 1717351379730844*r18[i]
- 1359124435588313876*r20[i]
- 1272410676942417239876*r22[i]
) // 51090942171709440000 for i in range(len(r0))]
r19 = [(-16796*r[1][i]
+ 25194*r[2][i]
- 23256*r[3][i]
+ 15504*r[4][i]
- 7752*r[5][i]
+ 2907*r[6][i]
- 798*r[7][i]
+ 152*r[8][i]
- 18*r[9][i]
+ r[10][i]
+ 4862*r0[i]
- 2860*r2[i]
+ 7436*r4[i]
- 46420*r6[i]
+ 576236*r8[i]
- 13098580*r10[i]
+ 532310636*r12[i]
- 39968611540*r14[i]
+ 6350631494636*r16[i]
- 3730771315561300*r18[i]
- 2637991952943407764*r20[i]
- 46833363657400320000*r21[i]
- 734121065118879803860*r22[i]
) // 121645100408832000 for i in range(len(r0))]
r17 = [(4862*r[1][i]
- 7072*r[2][i]
+ 6188*r[3][i]
- 3808*r[4][i]
+ 1700*r[5][i]
- 544*r[6][i]
+ 119*r[7][i]
- 16*r[8][i]
+ r[9][i]
- 1430*r0[i]
+ 858*r2[i]
- 2310*r4[i]
+ 15258*r6[i]
- 206790*r8[i]
+ 5386458*r10[i]
- 272513670*r12[i]
+ 30255826458*r14[i]
- 12765597850950*r16[i]
- 6622557957272742*r18[i]
- 101370917007360000*r19[i]
- 1375210145685786630*r20[i]
- 17172233341046784000*r21[i]
- 201832098313986359142*r22[i]
) // 355687428096000 for i in range(len(r0))]
r15 = [(-1430*r[1][i]
+ 2002*r[2][i]
- 1638*r[3][i]
+ 910*r[4][i]
- 350*r[5][i]
+ 90*r[6][i]
- 14*r[7][i]
+ r[8][i]
+ 429*r0[i]
- 264*r2[i]
+ 744*r4[i]
- 5304*r6[i]
+ 81384*r8[i]
- 2605944*r10[i]
+ 192387624*r12[i]
- 55942352184*r14[i]
- 20546119600536*r16[i]
- 266765571072000*r17[i]
- 3083760849804024*r18[i]
- 32945548027392000*r19[i]
- 332500281299403096*r20[i]
- 3215147584416768000*r21[i]
- 30076927429146721464*r22[i]
) // 1307674368000 for i in range(len(r0))]
r13 = [(429*r[1][i]
- 572*r[2][i]
+ 429*r[3][i]
- 208*r[4][i]
+ 65*r[5][i]
- 12*r[6][i]
+ r[7][i]
- 132*r0[i]
+ 84*r2[i]
- 252*r4[i]
+ 2004*r6[i]
- 37212*r8[i]
+ 1710324*r10[i]
- 325024572*r12[i]
- 80789566956*r14[i]
- 871782912000*r15[i]
- 8422900930332*r16[i]
- 75583578470400*r17[i]
- 643521842437836*r18[i]
- 5269678622208000*r19[i]
- 41890044885642492*r20[i]
- 325386564299596800*r21[i]
- 2481686964269990316*r22[i]
) // 6227020800 for i in range(len(r0))]
r11 = [(-132*r[1][i]
+ 165*r[2][i]
- 110*r[3][i]
+ 44*r[4][i]
- 10*r[5][i]
+ r[6][i]
+ 42*r0[i]
- 28*r2[i]
+ 92*r4[i]
- 868*r6[i]
+ 22652*r8[i]
- 2620708*r10[i]
- 415790788*r12[i]
- 3632428800*r13[i]
- 28616744548*r14[i]
- 210680870400*r15[i]
- 1479485236228*r16[i]
- 10038995366400*r17[i]
- 66394067988388*r18[i]
- 430591742380800*r19[i]
- 2750479262009668*r20[i]
- 17360942812012800*r21[i]
- 108550450893568228*r22[i]
) // 39916800 for i in range(len(r0))]
r9 = [(42*r[1][i]
- 48*r[2][i]
+ 27*r[3][i]
- 8*r[4][i]
+ r[5][i]
- 14*r0[i]
+ 10*r2[i]
- 38*r4[i]
+ 490*r6[i]
- 31238*r8[i]
- 2922230*r10[i]
- 19958400*r11[i]
- 124075238*r12[i]
- 726485760*r13[i]
- 4084385750*r14[i]
- 22313491200*r15[i]
- 119387268038*r16[i]
- 628980992640*r17[i]
- 3275389222070*r18[i]
- 16905818966400*r19[i]
- 86665431465638*r20[i]
- 441935114987520*r21[i]
- 2244295389943190*r22[i]
) // 362880 for i in range(len(r0))]
r7 = [(-14*r[1][i]
+ 14*r[2][i]
- 6*r[3][i]
+ r[4][i]
+ 5*r0[i]
- 4*r2[i]
+ 20*r4[i]
- 604*r6[i]
- 29740*r8[i]
- 151200*r9[i]
- 708604*r10[i]
- 3160080*r11[i]
- 13645900*r12[i]
- 57657600*r13[i]
- 239967004*r14[i]
- 988107120*r15[i]
- 4037604460*r16[i]
- 16406863200*r17[i]
- 66398623804*r18[i]
- 267911678160*r19[i]
- 1078605601420*r20[i]
- 4335313752000*r21[i]
- 17403958407004*r22[i]
) // 5040 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
- 1680*r7[i]
- 5542*r8[i]
- 17640*r9[i]
- 54958*r10[i]
- 168960*r11[i]
- 515062*r12[i]
- 1561560*r13[i]
- 4717438*r14[i]
- 14217840*r15[i]
- 42784582*r16[i]
- 128615880*r17[i]
- 386371918*r18[i]
- 1160164320*r19[i]
- 3482590102*r20[i]
- 10451964600*r21[i]
- 31364282398*r22[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
- 126*r7[i]
- 254*r8[i]
- 510*r9[i]
- 1022*r10[i]
- 2046*r11[i]
- 4094*r12[i]
- 8190*r13[i]
- 16382*r14[i]
- 32766*r15[i]
- 65534*r16[i]
- 131070*r17[i]
- 262142*r18[i]
- 524286*r19[i]
- 1048574*r20[i]
- 2097150*r21[i]
- 4194302*r22[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
- r7[i]
- r8[i]
- r9[i]
- r10[i]
- r11[i]
- r12[i]
- r13[i]
- r14[i]
- r15[i]
- r16[i]
- r17[i]
- r18[i]
- r19[i]
- r20[i]
- r21[i]
- r22[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22)
def natural_interpolate_13(r):
r0 = r[0]
r24 = r['infinity']
r22 = [(646646*(r[1][i] + r[-1][i])
- 497420*(r[2][i] + r[-2][i])
+ 319770*(r[3][i] + r[-3][i])
- 170544*(r[4][i] + r[-4][i])
+ 74613*(r[5][i] + r[-5][i])
- 26334*(r[6][i] + r[-6][i])
+ 7315*(r[7][i] + r[-7][i])
- 1540*(r[8][i] + r[-8][i])
+ 231*(r[9][i] + r[-9][i])
- 22*(r[10][i] + r[-10][i])
+ (r[11][i] + r[-11][i])
- 705432*r0[i]
- 568744368255469486080000*r24[i]
) // 1124000727777607680000 for i in range(len(r0))]
r20 = [(-167960*(r[1][i] + r[-1][i])
+ 125970*(r[2][i] + r[-2][i])
- 77520*(r[3][i] + r[-3][i])
+ 38760*(r[4][i] + r[-4][i])
- 15504*(r[5][i] + r[-5][i])
+ 4845*(r[6][i] + r[-6][i])
- 1140*(r[7][i] + r[-7][i])
+ 190*(r[8][i] + r[-8][i])
- 20*(r[9][i] + r[-9][i])
+ (r[10][i] + r[-10][i])
+ 184756*r0[i]
- 936667273148006400000*r22[i]
- 211124803367560642560000*r24[i]
) // 2432902008176640000 for i in range(len(r0))]
r18 = [(43758*(r[1][i] + r[-1][i])
- 31824*(r[2][i] + r[-2][i])
+ 18564*(r[3][i] + r[-3][i])
- 8568*(r[4][i] + r[-4][i])
+ 3060*(r[5][i] + r[-5][i])
- 816*(r[6][i] + r[-6][i])
+ 153*(r[7][i] + r[-7][i])
- 18*(r[8][i] + r[-8][i])
+ (r[9][i] + r[-9][i])
- 48620*r0[i]
- 1824676506132480000*r20[i]
- 309100200138842112000*r22[i]
- 40778478784550707200000*r24[i]
) // 6402373705728000 for i in range(len(r0))]
r16 = [(-11440*(r[1][i] + r[-1][i])
+ 8008*(r[2][i] + r[-2][i])
- 4368*(r[3][i] + r[-3][i])
+ 1820*(r[4][i] + r[-4][i])
- 560*(r[5][i] + r[-5][i])
+ 120*(r[6][i] + r[-6][i])
- 16*(r[7][i] + r[-7][i])
+ (r[8][i] + r[-8][i])
+ 12870*r0[i]
- 4268249137152000*r18[i]
- 527128768438272000*r20[i]
- 51442361350668288000*r22[i]
- 4385609982489415680000*r24[i]
) // 20922789888000 for i in range(len(r0))]
r14 = [(3003*(r[1][i] + r[-1][i])
- 2002*(r[2][i] + r[-2][i])
+ 1001*(r[3][i] + r[-3][i])
- 364*(r[4][i] + r[-4][i])
+ 91*(r[5][i] + r[-5][i])
- 14*(r[6][i] + r[-6][i])
+ (r[7][i] + r[-7][i])
- 3432*r0[i]
- 12204960768000*r16[i]
- 1058170098585600*r18[i]
- 73775500710912000*r20[i]
- 4555411900194355200*r22[i]
- 261131482210959360000*r24[i]
) // 87178291200 for i in range(len(r0))]
r12 = [(-792*(r[1][i] + r[-1][i])
+ 495*(r[2][i] + r[-2][i])
- 220*(r[3][i] + r[-3][i])
+ 66*(r[4][i] + r[-4][i])
- 12*(r[5][i] + r[-5][i])
+ (r[6][i] + r[-6][i])
+ 924*r0[i]
- 43589145600*r14[i]
- 2528170444800*r16[i]
- 120467944396800*r18[i]
- 5167100908569600*r20[i]
- 208331313744153600*r22[i]
- 8083281646573056000*r24[i]
) // 479001600 for i in range(len(r0))]
r10 = [(210*(r[1][i] + r[-1][i])
- 120*(r[2][i] + r[-2][i])
+ 45*(r[3][i] + r[-3][i])
- 10*(r[4][i] + r[-4][i])
+ (r[5][i] + r[-5][i])
- 252*r0[i]
- 199584000*r12[i]
- 7264857600*r14[i]
- 223134912000*r16[i]
- 6289809926400*r18[i]
- 169058189664000*r20[i]
- 4419351149875200*r22[i]
- 113605204648320000*r24[i]
) // 3628800 for i in range(len(r0))]
r8 = [(-56*(r[1][i] + r[-1][i])
+ 28*(r[2][i] + r[-2][i])
- 8*(r[3][i] + r[-3][i])
+ (r[4][i] + r[-4][i])
+ 70*r0[i]
- 1209600*r10[i]
- 25280640*r12[i]
- 461260800*r14[i]
- 7904856960*r16[i]
- 131254905600*r18[i]
- 2143293425280*r20[i]
- 34682510016000*r22[i]
- 558432020361600*r24[i]
) // 40320 for i in range(len(r0))]
r6 = [(15*(r[1][i] + r[-1][i])
- 6*(r[2][i] + r[-2][i])
+ (r[3][i] + r[-3][i])
- 20*r0[i]
- 10080*r8[i]
- 105840*r10[i]
- 1013760*r12[i]
- 9369360*r14[i]
- 85307040*r16[i]
- 771695280*r18[i]
- 6960985920*r20[i]
- 62711787600*r22[i]
- 564657746400*r24[i]
) // 720 for i in range(len(r0))]
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
- 504*r8[i]
- 2040*r10[i]
- 8184*r12[i]
- 32760*r14[i]
- 131064*r16[i]
- 524280*r18[i]
- 2097144*r20[i]
- 8388600*r22[i]
- 33554424*r24[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
- 2*r8[i]
- 2*r10[i]
- 2*r12[i]
- 2*r14[i]
- 2*r16[i]
- 2*r18[i]
- 2*r20[i]
- 2*r22[i]
- 2*r24[i]
) // 2 for i in range(len(r0))]
r23 = [(-208012*r[1][i]
+ 326876*r[2][i]
- 326876*r[3][i]
+ 245157*r[4][i]
- 144210*r[5][i]
+ 67298*r[6][i]
- 24794*r[7][i]
+ 7084*r[8][i]
- 1518*r[9][i]
+ 230*r[10][i]
- 22*r[11][i]
+ r[12][i]
+ 58786*r0[i]
- 33592*r2[i]
+ 83096*r4[i]
- 479752*r6[i]
+ 5299736*r8[i]
- 101549512*r10[i]
+ 3208453976*r12[i]
- 164071220872*r14[i]
+ 13743680753816*r16[i]
- 1993276972245832*r18[i]
+ 581947914140407256*r20[i]
- 603916464771468176392*r22[i]
- 730803773459954540777704*r24[i]
) // 25852016738884976640000 for i in range(len(r0))]
r21 = [(58786*r[1][i]
- 90440*r[2][i]
+ 87210*r[3][i]
- 62016*r[4][i]
+ 33915*r[5][i]
- 14364*r[6][i]
+ 4655*r[7][i]
- 1120*r[8][i]
+ 189*r[9][i]
- 20*r[10][i]
+ r[11][i]
- 16796*r0[i]
+ 9724*r2[i]
- 24596*r4[i]
+ 147004*r6[i]
- 1708916*r8[i]
+ 35240284*r10[i]
- 1237329236*r12[i]
+ 73853629564*r14[i]
- 7850527669556*r16[i]
+ 1717351379730844*r18[i]
- 1359124435588313876*r20[i]
- 1272410676942417239876*r22[i]
- 25852016738884976640000*r23[i]
- 462292539259962003646196*r24[i]
) // 51090942171709440000 for i in range(len(r0))]
r19 = [(-16796*r[1][i]
+ 25194*r[2][i]
- 23256*r[3][i]
+ 15504*r[4][i]
- 7752*r[5][i]
+ 2907*r[6][i]
- 798*r[7][i]
+ 152*r[8][i]
- 18*r[9][i]
+ r[10][i]
+ 4862*r0[i]
- 2860*r2[i]
+ 7436*r4[i]
- 46420*r6[i]
+ 576236*r8[i]
- 13098580*r10[i]
+ 532310636*r12[i]
- 39968611540*r14[i]
+ 6350631494636*r16[i]
- 3730771315561300*r18[i]
- 2637991952943407764*r20[i]
- 46833363657400320000*r21[i]
- 734121065118879803860*r22[i]
- 10556240168378032128000*r23[i]
- 142438684135271315212564*r24[i]
) // 121645100408832000 for i in range(len(r0))]
r17 = [(4862*r[1][i]
- 7072*r[2][i]
+ 6188*r[3][i]
- 3808*r[4][i]
+ 1700*r[5][i]
- 544*r[6][i]
+ 119*r[7][i]
- 16*r[8][i]
+ r[9][i]
- 1430*r0[i]
+ 858*r2[i]
- 2310*r4[i]
+ 15258*r6[i]
- 206790*r8[i]
+ 5386458*r10[i]
- 272513670*r12[i]
+ 30255826458*r14[i]
- 12765597850950*r16[i]
- 6622557957272742*r18[i]
- 101370917007360000*r19[i]
- 1375210145685786630*r20[i]
- 17172233341046784000*r21[i]
- 201832098313986359142*r22[i]
- 2265471043586150400000*r23[i]
- 24529324224160803328710*r24[i]
) // 355687428096000 for i in range(len(r0))]
r15 = [(-1430*r[1][i]
+ 2002*r[2][i]
- 1638*r[3][i]
+ 910*r[4][i]
- 350*r[5][i]
+ 90*r[6][i]
- 14*r[7][i]
+ r[8][i]
+ 429*r0[i]
- 264*r2[i]
+ 744*r4[i]
- 5304*r6[i]
+ 81384*r8[i]
- 2605944*r10[i]
+ 192387624*r12[i]
- 55942352184*r14[i]
- 20546119600536*r16[i]
- 266765571072000*r17[i]
- 3083760849804024*r18[i]
- 32945548027392000*r19[i]
- 332500281299403096*r20[i]
- 3215147584416768000*r21[i]
- 30076927429146721464*r22[i]
- 274100623905588480000*r23[i]
- 2446077617962088140056*r24[i]
) // 1307674368000 for i in range(len(r0))]
r13 = [(429*r[1][i]
- 572*r[2][i]
+ 429*r[3][i]
- 208*r[4][i]
+ 65*r[5][i]
- 12*r[6][i]
+ r[7][i]
- 132*r0[i]
+ 84*r2[i]
- 252*r4[i]
+ 2004*r6[i]
- 37212*r8[i]
+ 1710324*r10[i]
- 325024572*r12[i]
- 80789566956*r14[i]
- 871782912000*r15[i]
- 8422900930332*r16[i]
- 75583578470400*r17[i]
- 643521842437836*r18[i]
- 5269678622208000*r19[i]
- 41890044885642492*r20[i]
- 325386564299596800*r21[i]
- 2481686964269990316*r22[i]
- 18652248729354240000*r23[i]
- 138536531588626169052*r24[i]
) // 6227020800 for i in range(len(r0))]
r11 = [(-132*r[1][i]
+ 165*r[2][i]
- 110*r[3][i]
+ 44*r[4][i]
- 10*r[5][i]
+ r[6][i]
+ 42*r0[i]
- 28*r2[i]
+ 92*r4[i]
- 868*r6[i]
+ 22652*r8[i]
- 2620708*r10[i]
- 415790788*r12[i]
- 3632428800*r13[i]
- 28616744548*r14[i]
- 210680870400*r15[i]
- 1479485236228*r16[i]
- 10038995366400*r17[i]
- 66394067988388*r18[i]
- 430591742380800*r19[i]
- 2750479262009668*r20[i]
- 17360942812012800*r21[i]
- 108550450893568228*r22[i]
- 673606803881088000*r23[i]
- 4154688725062207108*r24[i]
) // 39916800 for i in range(len(r0))]
r9 = [(42*r[1][i]
- 48*r[2][i]
+ 27*r[3][i]
- 8*r[4][i]
+ r[5][i]
- 14*r0[i]
+ 10*r2[i]
- 38*r4[i]
+ 490*r6[i]
- 31238*r8[i]
- 2922230*r10[i]
- 19958400*r11[i]
- 124075238*r12[i]
- 726485760*r13[i]
- 4084385750*r14[i]
- 22313491200*r15[i]
- 119387268038*r16[i]
- 628980992640*r17[i]
- 3275389222070*r18[i]
- 16905818966400*r19[i]
- 86665431465638*r20[i]
- 441935114987520*r21[i]
- 2244295389943190*r22[i]
- 11360520464832000*r23[i]
- 57360469753884038*r24[i]
) // 362880 for i in range(len(r0))]
r7 = [(-14*r[1][i]
+ 14*r[2][i]
- 6*r[3][i]
+ r[4][i]
+ 5*r0[i]
- 4*r2[i]
+ 20*r4[i]
- 604*r6[i]
- 29740*r8[i]
- 151200*r9[i]
- 708604*r10[i]
- 3160080*r11[i]
- 13645900*r12[i]
- 57657600*r13[i]
- 239967004*r14[i]
- 988107120*r15[i]
- 4037604460*r16[i]
- 16406863200*r17[i]
- 66398623804*r18[i]
- 267911678160*r19[i]
- 1078605601420*r20[i]
- 4335313752000*r21[i]
- 17403958407004*r22[i]
- 69804002545200*r23[i]
- 279780634372780*r24[i]
) // 5040 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
- 1680*r7[i]
- 5542*r8[i]
- 17640*r9[i]
- 54958*r10[i]
- 168960*r11[i]
- 515062*r12[i]
- 1561560*r13[i]
- 4717438*r14[i]
- 14217840*r15[i]
- 42784582*r16[i]
- 128615880*r17[i]
- 386371918*r18[i]
- 1160164320*r19[i]
- 3482590102*r20[i]
- 10451964600*r21[i]
- 31364282398*r22[i]
- 94109624400*r23[i]
- 282362427622*r24[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
- 126*r7[i]
- 254*r8[i]
- 510*r9[i]
- 1022*r10[i]
- 2046*r11[i]
- 4094*r12[i]
- 8190*r13[i]
- 16382*r14[i]
- 32766*r15[i]
- 65534*r16[i]
- 131070*r17[i]
- 262142*r18[i]
- 524286*r19[i]
- 1048574*r20[i]
- 2097150*r21[i]
- 4194302*r22[i]
- 8388606*r23[i]
- 16777214*r24[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
- r7[i]
- r8[i]
- r9[i]
- r10[i]
- r11[i]
- r12[i]
- r13[i]
- r14[i]
- r15[i]
- r16[i]
- r17[i]
- r18[i]
- r19[i]
- r20[i]
- r21[i]
- r22[i]
- r23[i]
- r24[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24)
def natural_interpolate_14(r):
r0 = r[0]
r26 = r['infinity']
r24 = [(-2496144*(r[1][i] + r[-1][i])
+ 1961256*(r[2][i] + r[-2][i])
- 1307504*(r[3][i] + r[-3][i])
+ 735471*(r[4][i] + r[-4][i])
- 346104*(r[5][i] + r[-5][i])
+ 134596*(r[6][i] + r[-6][i])
- 42504*(r[7][i] + r[-7][i])
+ 10626*(r[8][i] + r[-8][i])
- 2024*(r[9][i] + r[-9][i])
+ 276*(r[10][i] + r[-10][i])
- 24*(r[11][i] + r[-11][i])
+ (r[12][i] + r[-12][i])
+ 2704156*r0[i]
- 403291461126605635584000000*r26[i]
) // 620448401733239439360000 for i in range(len(r0))]
r22 = [(646646*(r[1][i] + r[-1][i])
- 497420*(r[2][i] + r[-2][i])
+ 319770*(r[3][i] + r[-3][i])
- 170544*(r[4][i] + r[-4][i])
+ 74613*(r[5][i] + r[-5][i])
- 26334*(r[6][i] + r[-6][i])
+ 7315*(r[7][i] + r[-7][i])
- 1540*(r[8][i] + r[-8][i])
+ 231*(r[9][i] + r[-9][i])
- 22*(r[10][i] + r[-10][i])
+ (r[11][i] + r[-11][i])
- 705432*r0[i]
- 568744368255469486080000*r24[i]
- 166357727714724824678400000*r26[i]
) // 1124000727777607680000 for i in range(len(r0))]
r20 = [(-167960*(r[1][i] + r[-1][i])
+ 125970*(r[2][i] + r[-2][i])
- 77520*(r[3][i] + r[-3][i])
+ 38760*(r[4][i] + r[-4][i])
- 15504*(r[5][i] + r[-5][i])
+ 4845*(r[6][i] + r[-6][i])
- 1140*(r[7][i] + r[-7][i])
+ 190*(r[8][i] + r[-8][i])
- 20*(r[9][i] + r[-9][i])
+ (r[10][i] + r[-10][i])
+ 184756*r0[i]
- 936667273148006400000*r22[i]
- 211124803367560642560000*r24[i]
- 36608302274885332992000000*r26[i]
) // 2432902008176640000 for i in range(len(r0))]
r18 = [(43758*(r[1][i] + r[-1][i])
- 31824*(r[2][i] + r[-2][i])
+ 18564*(r[3][i] + r[-3][i])
- 8568*(r[4][i] + r[-4][i])
+ 3060*(r[5][i] + r[-5][i])
- 816*(r[6][i] + r[-6][i])
+ 153*(r[7][i] + r[-7][i])
- 18*(r[8][i] + r[-8][i])
+ (r[9][i] + r[-9][i])
- 48620*r0[i]
- 1824676506132480000*r20[i]
- 309100200138842112000*r22[i]
- 40778478784550707200000*r24[i]
- 4645053436190368481280000*r26[i]
) // 6402373705728000 for i in range(len(r0))]
r16 = [(-11440*(r[1][i] + r[-1][i])
+ 8008*(r[2][i] + r[-2][i])
- 4368*(r[3][i] + r[-3][i])
+ 1820*(r[4][i] + r[-4][i])
- 560*(r[5][i] + r[-5][i])
+ 120*(r[6][i] + r[-6][i])
- 16*(r[7][i] + r[-7][i])
+ (r[8][i] + r[-8][i])
+ 12870*r0[i]
- 4268249137152000*r18[i]
- 527128768438272000*r20[i]
- 51442361350668288000*r22[i]
- 4385609982489415680000*r24[i]
- 343350594609952849920000*r26[i]
) // 20922789888000 for i in range(len(r0))]
r14 = [(3003*(r[1][i] + r[-1][i])
- 2002*(r[2][i] + r[-2][i])
+ 1001*(r[3][i] + r[-3][i])
- 364*(r[4][i] + r[-4][i])
+ 91*(r[5][i] + r[-5][i])
- 14*(r[6][i] + r[-6][i])
+ (r[7][i] + r[-7][i])
- 3432*r0[i]
- 12204960768000*r16[i]
- 1058170098585600*r18[i]
- 73775500710912000*r20[i]
- 4555411900194355200*r22[i]
- 261131482210959360000*r24[i]
- 14266599888013304832000*r26[i]
) // 87178291200 for i in range(len(r0))]
r12 = [(-792*(r[1][i] + r[-1][i])
+ 495*(r[2][i] + r[-2][i])
- 220*(r[3][i] + r[-3][i])
+ 66*(r[4][i] + r[-4][i])
- 12*(r[5][i] + r[-5][i])
+ (r[6][i] + r[-6][i])
+ 924*r0[i]
- 43589145600*r14[i]
- 2528170444800*r16[i]
- 120467944396800*r18[i]
- 5167100908569600*r20[i]
- 208331313744153600*r22[i]
- 8083281646573056000*r24[i]
- 305994026290208256000*r26[i]
) // 479001600 for i in range(len(r0))]
r10 = [(210*(r[1][i] + r[-1][i])
- 120*(r[2][i] + r[-2][i])
+ 45*(r[3][i] + r[-3][i])
- 10*(r[4][i] + r[-4][i])
+ (r[5][i] + r[-5][i])
- 252*r0[i]
- 199584000*r12[i]
- 7264857600*r14[i]
- 223134912000*r16[i]
- 6289809926400*r18[i]
- 169058189664000*r20[i]
- 4419351149875200*r22[i]
- 113605204648320000*r24[i]
- 2890388998040544000*r26[i]
) // 3628800 for i in range(len(r0))]
r8 = [(-56*(r[1][i] + r[-1][i])
+ 28*(r[2][i] + r[-2][i])
- 8*(r[3][i] + r[-3][i])
+ (r[4][i] + r[-4][i])
+ 70*r0[i]
- 1209600*r10[i]
- 25280640*r12[i]
- 461260800*r14[i]
- 7904856960*r16[i]
- 131254905600*r18[i]
- 2143293425280*r20[i]
- 34682510016000*r22[i]
- 558432020361600*r24[i]
- 8966533159584000*r26[i]
) // 40320 for i in range(len(r0))]
r6 = [(15*(r[1][i] + r[-1][i])
- 6*(r[2][i] + r[-2][i])
+ (r[3][i] + r[-3][i])
- 20*r0[i]
- 10080*r8[i]
- 105840*r10[i]
- 1013760*r12[i]
- 9369360*r14[i]
- 85307040*r16[i]
- 771695280*r18[i]
- 6960985920*r20[i]
- 62711787600*r22[i]
- 564657746400*r24[i]
- 5082926350320*r26[i]
) // 720 for i in range(len(r0))]
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
- 504*r8[i]
- 2040*r10[i]
- 8184*r12[i]
- 32760*r14[i]
- 131064*r16[i]
- 524280*r18[i]
- 2097144*r20[i]
- 8388600*r22[i]
- 33554424*r24[i]
- 134217720*r26[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
- 2*r8[i]
- 2*r10[i]
- 2*r12[i]
- 2*r14[i]
- 2*r16[i]
- 2*r18[i]
- 2*r20[i]
- 2*r22[i]
- 2*r24[i]
- 2*r26[i]
) // 2 for i in range(len(r0))]
r25 = [(742900*r[1][i]
- 1188640*r[2][i]
+ 1225785*r[3][i]
- 961400*r[4][i]
+ 600875*r[5][i]
- 303600*r[6][i]
+ 123970*r[7][i]
- 40480*r[8][i]
+ 10350*r[9][i]
- 2000*r[10][i]
+ 275*r[11][i]
- 24*r[12][i]
+ r[13][i]
- 208012*r0[i]
+ 117572*r2[i]
- 285532*r4[i]
+ 1602692*r6[i]
- 16996252*r8[i]
+ 307475012*r10[i]
- 8966430172*r12[i]
+ 409745686532*r14[i]
- 29195711499292*r16[i]
+ 3312133208909252*r18[i]
- 636215671041835612*r20[i]
+ 241648300078174135172*r22[i]
- 321511316149669476991132*r24[i]
- 492817676505266866078123708*r26[i]
) // 15511210043330985984000000 for i in range(len(r0))]
r23 = [(-208012*r[1][i]
+ 326876*r[2][i]
- 326876*r[3][i]
+ 245157*r[4][i]
- 144210*r[5][i]
+ 67298*r[6][i]
- 24794*r[7][i]
+ 7084*r[8][i]
- 1518*r[9][i]
+ 230*r[10][i]
- 22*r[11][i]
+ r[12][i]
+ 58786*r0[i]
- 33592*r2[i]
+ 83096*r4[i]
- 479752*r6[i]
+ 5299736*r8[i]
- 101549512*r10[i]
+ 3208453976*r12[i]
- 164071220872*r14[i]
+ 13743680753816*r16[i]
- 1993276972245832*r18[i]
+ 581947914140407256*r20[i]
- 603916464771468176392*r22[i]
- 730803773459954540777704*r24[i]
- 16803810880275234816000000*r25[i]
- 339155768243774227716964552*r26[i]
) // 25852016738884976640000 for i in range(len(r0))]
r21 = [(58786*r[1][i]
- 90440*r[2][i]
+ 87210*r[3][i]
- 62016*r[4][i]
+ 33915*r[5][i]
- 14364*r[6][i]
+ 4655*r[7][i]
- 1120*r[8][i]
+ 189*r[9][i]
- 20*r[10][i]
+ r[11][i]
- 16796*r0[i]
+ 9724*r2[i]
- 24596*r4[i]
+ 147004*r6[i]
- 1708916*r8[i]
+ 35240284*r10[i]
- 1237329236*r12[i]
+ 73853629564*r14[i]
- 7850527669556*r16[i]
+ 1717351379730844*r18[i]
- 1359124435588313876*r20[i]
- 1272410676942417239876*r22[i]
- 25852016738884976640000*r23[i]
- 462292539259962003646196*r24[i]
- 7561714896123855667200000*r25[i]
- 115761644587269354830466596*r26[i]
) // 51090942171709440000 for i in range(len(r0))]
r19 = [(-16796*r[1][i]
+ 25194*r[2][i]
- 23256*r[3][i]
+ 15504*r[4][i]
- 7752*r[5][i]
+ 2907*r[6][i]
- 798*r[7][i]
+ 152*r[8][i]
- 18*r[9][i]
+ r[10][i]
+ 4862*r0[i]
- 2860*r2[i]
+ 7436*r4[i]
- 46420*r6[i]
+ 576236*r8[i]
- 13098580*r10[i]
+ 532310636*r12[i]
- 39968611540*r14[i]
+ 6350631494636*r16[i]
- 3730771315561300*r18[i]
- 2637991952943407764*r20[i]
- 46833363657400320000*r21[i]
- 734121065118879803860*r22[i]
- 10556240168378032128000*r23[i]
- 142438684135271315212564*r24[i]
- 1830415113744266649600000*r25[i]
- 22632897298190126259675220*r26[i]
) // 121645100408832000 for i in range(len(r0))]
r17 = [(4862*r[1][i]
- 7072*r[2][i]
+ 6188*r[3][i]
- 3808*r[4][i]
+ 1700*r[5][i]
- 544*r[6][i]
+ 119*r[7][i]
- 16*r[8][i]
+ r[9][i]
- 1430*r0[i]
+ 858*r2[i]
- 2310*r4[i]
+ 15258*r6[i]
- 206790*r8[i]
+ 5386458*r10[i]
- 272513670*r12[i]
+ 30255826458*r14[i]
- 12765597850950*r16[i]
- 6622557957272742*r18[i]
- 101370917007360000*r19[i]
- 1375210145685786630*r20[i]
- 17172233341046784000*r21[i]
- 201832098313986359142*r22[i]
- 2265471043586150400000*r23[i]
- 24529324224160803328710*r24[i]
- 258058524232798248960000*r25[i]
- 2652208374242713043720742*r26[i]
) // 355687428096000 for i in range(len(r0))]
r15 = [(-1430*r[1][i]
+ 2002*r[2][i]
- 1638*r[3][i]
+ 910*r[4][i]
- 350*r[5][i]
+ 90*r[6][i]
- 14*r[7][i]
+ r[8][i]
+ 429*r0[i]
- 264*r2[i]
+ 744*r4[i]
- 5304*r6[i]
+ 81384*r8[i]
- 2605944*r10[i]
+ 192387624*r12[i]
- 55942352184*r14[i]
- 20546119600536*r16[i]
- 266765571072000*r17[i]
- 3083760849804024*r18[i]
- 32945548027392000*r19[i]
- 332500281299403096*r20[i]
- 3215147584416768000*r21[i]
- 30076927429146721464*r22[i]
- 274100623905588480000*r23[i]
- 2446077617962088140056*r24[i]
- 21459412163122053120000*r25[i]
- 185641639183185136464504*r26[i]
) // 1307674368000 for i in range(len(r0))]
r13 = [(429*r[1][i]
- 572*r[2][i]
+ 429*r[3][i]
- 208*r[4][i]
+ 65*r[5][i]
- 12*r[6][i]
+ r[7][i]
- 132*r0[i]
+ 84*r2[i]
- 252*r4[i]
+ 2004*r6[i]
- 37212*r8[i]
+ 1710324*r10[i]
- 325024572*r12[i]
- 80789566956*r14[i]
- 871782912000*r15[i]
- 8422900930332*r16[i]
- 75583578470400*r17[i]
- 643521842437836*r18[i]
- 5269678622208000*r19[i]
- 41890044885642492*r20[i]
- 325386564299596800*r21[i]
- 2481686964269990316*r22[i]
- 18652248729354240000*r23[i]
- 138536531588626169052*r24[i]
- 1019042849143807488000*r25[i]
- 7436421488952386592396*r26[i]
) // 6227020800 for i in range(len(r0))]
r11 = [(-132*r[1][i]
+ 165*r[2][i]
- 110*r[3][i]
+ 44*r[4][i]
- 10*r[5][i]
+ r[6][i]
+ 42*r0[i]
- 28*r2[i]
+ 92*r4[i]
- 868*r6[i]
+ 22652*r8[i]
- 2620708*r10[i]
- 415790788*r12[i]
- 3632428800*r13[i]
- 28616744548*r14[i]
- 210680870400*r15[i]
- 1479485236228*r16[i]
- 10038995366400*r17[i]
- 66394067988388*r18[i]
- 430591742380800*r19[i]
- 2750479262009668*r20[i]
- 17360942812012800*r21[i]
- 108550450893568228*r22[i]
- 673606803881088000*r23[i]
- 4154688725062207108*r24[i]
- 25499502190850688000*r25[i]
- 155878445775166700068*r26[i]
) // 39916800 for i in range(len(r0))]
r9 = [(42*r[1][i]
- 48*r[2][i]
+ 27*r[3][i]
- 8*r[4][i]
+ r[5][i]
- 14*r0[i]
+ 10*r2[i]
- 38*r4[i]
+ 490*r6[i]
- 31238*r8[i]
- 2922230*r10[i]
- 19958400*r11[i]
- 124075238*r12[i]
- 726485760*r13[i]
- 4084385750*r14[i]
- 22313491200*r15[i]
- 119387268038*r16[i]
- 628980992640*r17[i]
- 3275389222070*r18[i]
- 16905818966400*r19[i]
- 86665431465638*r20[i]
- 441935114987520*r21[i]
- 2244295389943190*r22[i]
- 11360520464832000*r23[i]
- 57360469753884038*r24[i]
- 289038899804054400*r25[i]
- 1454155949521941110*r26[i]
) // 362880 for i in range(len(r0))]
r7 = [(-14*r[1][i]
+ 14*r[2][i]
- 6*r[3][i]
+ r[4][i]
+ 5*r0[i]
- 4*r2[i]
+ 20*r4[i]
- 604*r6[i]
- 29740*r8[i]
- 151200*r9[i]
- 708604*r10[i]
- 3160080*r11[i]
- 13645900*r12[i]
- 57657600*r13[i]
- 239967004*r14[i]
- 988107120*r15[i]
- 4037604460*r16[i]
- 16406863200*r17[i]
- 66398623804*r18[i]
- 267911678160*r19[i]
- 1078605601420*r20[i]
- 4335313752000*r21[i]
- 17403958407004*r22[i]
- 69804002545200*r23[i]
- 279780634372780*r24[i]
- 1120816644948000*r25[i]
- 4488349371924604*r26[i]
) // 5040 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
- 1680*r7[i]
- 5542*r8[i]
- 17640*r9[i]
- 54958*r10[i]
- 168960*r11[i]
- 515062*r12[i]
- 1561560*r13[i]
- 4717438*r14[i]
- 14217840*r15[i]
- 42784582*r16[i]
- 128615880*r17[i]
- 386371918*r18[i]
- 1160164320*r19[i]
- 3482590102*r20[i]
- 10451964600*r21[i]
- 31364282398*r22[i]
- 94109624400*r23[i]
- 282362427622*r24[i]
- 847154391720*r25[i]
- 2541597392878*r26[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
- 126*r7[i]
- 254*r8[i]
- 510*r9[i]
- 1022*r10[i]
- 2046*r11[i]
- 4094*r12[i]
- 8190*r13[i]
- 16382*r14[i]
- 32766*r15[i]
- 65534*r16[i]
- 131070*r17[i]
- 262142*r18[i]
- 524286*r19[i]
- 1048574*r20[i]
- 2097150*r21[i]
- 4194302*r22[i]
- 8388606*r23[i]
- 16777214*r24[i]
- 33554430*r25[i]
- 67108862*r26[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
- r7[i]
- r8[i]
- r9[i]
- r10[i]
- r11[i]
- r12[i]
- r13[i]
- r14[i]
- r15[i]
- r16[i]
- r17[i]
- r18[i]
- r19[i]
- r20[i]
- r21[i]
- r22[i]
- r23[i]
- r24[i]
- r25[i]
- r26[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26)
def natural_interpolate_15(r):
r0 = r[0]
r28 = r['infinity']
r26 = [(9657700*(r[1][i] + r[-1][i])
- 7726160*(r[2][i] + r[-2][i])
+ 5311735*(r[3][i] + r[-3][i])
- 3124550*(r[4][i] + r[-4][i])
+ 1562275*(r[5][i] + r[-5][i])
- 657800*(r[6][i] + r[-6][i])
+ 230230*(r[7][i] + r[-7][i])
- 65780*(r[8][i] + r[-8][i])
+ 14950*(r[9][i] + r[-9][i])
- 2600*(r[10][i] + r[-10][i])
+ 325*(r[11][i] + r[-11][i])
- 26*(r[12][i] + r[-12][i])
+ (r[13][i] + r[-13][i])
- 10400600*r0[i]
- 330295706662690015543296000000*r28[i]
) // 403291461126605635584000000 for i in range(len(r0))]
r24 = [(-2496144*(r[1][i] + r[-1][i])
+ 1961256*(r[2][i] + r[-2][i])
- 1307504*(r[3][i] + r[-3][i])
+ 735471*(r[4][i] + r[-4][i])
- 346104*(r[5][i] + r[-5][i])
+ 134596*(r[6][i] + r[-6][i])
- 42504*(r[7][i] + r[-7][i])
+ 10626*(r[8][i] + r[-8][i])
- 2024*(r[9][i] + r[-9][i])
+ 276*(r[10][i] + r[-10][i])
- 24*(r[11][i] + r[-11][i])
+ (r[12][i] + r[-12][i])
+ 2704156*r0[i]
- 403291461126605635584000000*r26[i]
- 149903436100759314746572800000*r28[i]
) // 620448401733239439360000 for i in range(len(r0))]
r22 = [(646646*(r[1][i] + r[-1][i])
- 497420*(r[2][i] + r[-2][i])
+ 319770*(r[3][i] + r[-3][i])
- 170544*(r[4][i] + r[-4][i])
+ 74613*(r[5][i] + r[-5][i])
- 26334*(r[6][i] + r[-6][i])
+ 7315*(r[7][i] + r[-7][i])
- 1540*(r[8][i] + r[-8][i])
+ 231*(r[9][i] + r[-9][i])
- 22*(r[10][i] + r[-10][i])
+ (r[11][i] + r[-11][i])
- 705432*r0[i]
- 568744368255469486080000*r24[i]
- 166357727714724824678400000*r26[i]
- 37042320704478727628390400000*r28[i]
) // 1124000727777607680000 for i in range(len(r0))]
r20 = [(-167960*(r[1][i] + r[-1][i])
+ 125970*(r[2][i] + r[-2][i])
- 77520*(r[3][i] + r[-3][i])
+ 38760*(r[4][i] + r[-4][i])
- 15504*(r[5][i] + r[-5][i])
+ 4845*(r[6][i] + r[-6][i])
- 1140*(r[7][i] + r[-7][i])
+ 190*(r[8][i] + r[-8][i])
- 20*(r[9][i] + r[-9][i])
+ (r[10][i] + r[-10][i])
+ 184756*r0[i]
- 936667273148006400000*r22[i]
- 211124803367560642560000*r24[i]
- 36608302274885332992000000*r26[i]
- 5425950533240873322086400000*r28[i]
) // 2432902008176640000 for i in range(len(r0))]
r18 = [(43758*(r[1][i] + r[-1][i])
- 31824*(r[2][i] + r[-2][i])
+ 18564*(r[3][i] + r[-3][i])
- 8568*(r[4][i] + r[-4][i])
+ 3060*(r[5][i] + r[-5][i])
- 816*(r[6][i] + r[-6][i])
+ 153*(r[7][i] + r[-7][i])
- 18*(r[8][i] + r[-8][i])
+ (r[9][i] + r[-9][i])
- 48620*r0[i]
- 1824676506132480000*r20[i]
- 309100200138842112000*r22[i]
- 40778478784550707200000*r24[i]
- 4645053436190368481280000*r26[i]
- 481314610282065419059200000*r28[i]
) // 6402373705728000 for i in range(len(r0))]
r16 = [(-11440*(r[1][i] + r[-1][i])
+ 8008*(r[2][i] + r[-2][i])
- 4368*(r[3][i] + r[-3][i])
+ 1820*(r[4][i] + r[-4][i])
- 560*(r[5][i] + r[-5][i])
+ 120*(r[6][i] + r[-6][i])
- 16*(r[7][i] + r[-7][i])
+ (r[8][i] + r[-8][i])
+ 12870*r0[i]
- 4268249137152000*r18[i]
- 527128768438272000*r20[i]
- 51442361350668288000*r22[i]
- 4385609982489415680000*r24[i]
- 343350594609952849920000*r26[i]
- 25398422028160175554560000*r28[i]
) // 20922789888000 for i in range(len(r0))]
r14 = [(3003*(r[1][i] + r[-1][i])
- 2002*(r[2][i] + r[-2][i])
+ 1001*(r[3][i] + r[-3][i])
- 364*(r[4][i] + r[-4][i])
+ 91*(r[5][i] + r[-5][i])
- 14*(r[6][i] + r[-6][i])
+ (r[7][i] + r[-7][i])
- 3432*r0[i]
- 12204960768000*r16[i]
- 1058170098585600*r18[i]
- 73775500710912000*r20[i]
- 4555411900194355200*r22[i]
- 261131482210959360000*r24[i]
- 14266599888013304832000*r26[i]
- 754754307297469839360000*r28[i]
) // 87178291200 for i in range(len(r0))]
r12 = [(-792*(r[1][i] + r[-1][i])
+ 495*(r[2][i] + r[-2][i])
- 220*(r[3][i] + r[-3][i])
+ 66*(r[4][i] + r[-4][i])
- 12*(r[5][i] + r[-5][i])
+ (r[6][i] + r[-6][i])
+ 924*r0[i]
- 43589145600*r14[i]
- 2528170444800*r16[i]
- 120467944396800*r18[i]
- 5167100908569600*r20[i]
- 208331313744153600*r22[i]
- 8083281646573056000*r24[i]
- 305994026290208256000*r26[i]
- 11397316294188849024000*r28[i]
) // 479001600 for i in range(len(r0))]
r10 = [(210*(r[1][i] + r[-1][i])
- 120*(r[2][i] + r[-2][i])
+ 45*(r[3][i] + r[-3][i])
- 10*(r[4][i] + r[-4][i])
+ (r[5][i] + r[-5][i])
- 252*r0[i]
- 199584000*r12[i]
- 7264857600*r14[i]
- 223134912000*r16[i]
- 6289809926400*r18[i]
- 169058189664000*r20[i]
- 4419351149875200*r22[i]
- 113605204648320000*r24[i]
- 2890388998040544000*r26[i]
- 73066712935376160000*r28[i]
) // 3628800 for i in range(len(r0))]
r8 = [(-56*(r[1][i] + r[-1][i])
+ 28*(r[2][i] + r[-2][i])
- 8*(r[3][i] + r[-3][i])
+ (r[4][i] + r[-4][i])
+ 70*r0[i]
- 1209600*r10[i]
- 25280640*r12[i]
- 461260800*r14[i]
- 7904856960*r16[i]
- 131254905600*r18[i]
- 2143293425280*r20[i]
- 34682510016000*r22[i]
- 558432020361600*r24[i]
- 8966533159584000*r26[i]
- 143749174428961920*r28[i]
) // 40320 for i in range(len(r0))]
r6 = [(15*(r[1][i] + r[-1][i])
- 6*(r[2][i] + r[-2][i])
+ (r[3][i] + r[-3][i])
- 20*r0[i]
- 10080*r8[i]
- 105840*r10[i]
- 1013760*r12[i]
- 9369360*r14[i]
- 85307040*r16[i]
- 771695280*r18[i]
- 6960985920*r20[i]
- 62711787600*r22[i]
- 564657746400*r24[i]
- 5082926350320*r26[i]
- 45750363684480*r28[i]
) // 720 for i in range(len(r0))]
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
- 504*r8[i]
- 2040*r10[i]
- 8184*r12[i]
- 32760*r14[i]
- 131064*r16[i]
- 524280*r18[i]
- 2097144*r20[i]
- 8388600*r22[i]
- 33554424*r24[i]
- 134217720*r26[i]
- 536870904*r28[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
- 2*r8[i]
- 2*r10[i]
- 2*r12[i]
- 2*r14[i]
- 2*r16[i]
- 2*r18[i]
- 2*r20[i]
- 2*r22[i]
- 2*r24[i]
- 2*r26[i]
- 2*r28[i]
) // 2 for i in range(len(r0))]
r27 = [(-2674440*r[1][i]
+ 4345965*r[2][i]
- 4601610*r[3][i]
+ 3749460*r[4][i]
- 2466750*r[5][i]
+ 1332045*r[6][i]
- 592020*r[7][i]
+ 215280*r[8][i]
- 63180*r[9][i]
+ 14625*r[10][i]
- 2574*r[11][i]
+ 324*r[12][i]
- 26*r[13][i]
+ r[14][i]
+ 742900*r0[i]
- 416024*r2[i]
+ 994840*r4[i]
- 5454824*r6[i]
+ 55944280*r8[i]
- 966290024*r10[i]
+ 26454613720*r12[i]
- 1109329691624*r14[i]
+ 70212852387160*r16[i]
- 6733670404619624*r18[i]
+ 1005318113348848600*r20[i]
- 249581050854994274024*r22[i]
+ 120719220687299365182040*r24[i]
- 202039976682357297272094824*r26[i]
- 385557844336439370252173428520*r28[i]
) // 10888869450418352160768000000 for i in range(len(r0))]
r25 = [(742900*r[1][i]
- 1188640*r[2][i]
+ 1225785*r[3][i]
- 961400*r[4][i]
+ 600875*r[5][i]
- 303600*r[6][i]
+ 123970*r[7][i]
- 40480*r[8][i]
+ 10350*r[9][i]
- 2000*r[10][i]
+ 275*r[11][i]
- 24*r[12][i]
+ r[13][i]
- 208012*r0[i]
+ 117572*r2[i]
- 285532*r4[i]
+ 1602692*r6[i]
- 16996252*r8[i]
+ 307475012*r10[i]
- 8966430172*r12[i]
+ 409745686532*r14[i]
- 29195711499292*r16[i]
+ 3312133208909252*r18[i]
- 636215671041835612*r20[i]
+ 241648300078174135172*r22[i]
- 321511316149669476991132*r24[i]
- 492817676505266866078123708*r26[i]
- 12703681025488077520896000000*r27[i]
- 286779648275654636997381637852*r28[i]
) // 15511210043330985984000000 for i in range(len(r0))]
r23 = [(-208012*r[1][i]
+ 326876*r[2][i]
- 326876*r[3][i]
+ 245157*r[4][i]
- 144210*r[5][i]
+ 67298*r[6][i]
- 24794*r[7][i]
+ 7084*r[8][i]
- 1518*r[9][i]
+ 230*r[10][i]
- 22*r[11][i]
+ r[12][i]
+ 58786*r0[i]
- 33592*r2[i]
+ 83096*r4[i]
- 479752*r6[i]
+ 5299736*r8[i]
- 101549512*r10[i]
+ 3208453976*r12[i]
- 164071220872*r14[i]
+ 13743680753816*r16[i]
- 1993276972245832*r18[i]
+ 581947914140407256*r20[i]
- 603916464771468176392*r22[i]
- 730803773459954540777704*r24[i]
- 16803810880275234816000000*r25[i]
- 339155768243774227716964552*r26[i]
- 6245976504198304781107200000*r27[i]
- 107413822788261782335458993064*r28[i]
) // 25852016738884976640000 for i in range(len(r0))]
r21 = [(58786*r[1][i]
- 90440*r[2][i]
+ 87210*r[3][i]
- 62016*r[4][i]
+ 33915*r[5][i]
- 14364*r[6][i]
+ 4655*r[7][i]
- 1120*r[8][i]
+ 189*r[9][i]
- 20*r[10][i]
+ r[11][i]
- 16796*r0[i]
+ 9724*r2[i]
- 24596*r4[i]
+ 147004*r6[i]
- 1708916*r8[i]
+ 35240284*r10[i]
- 1237329236*r12[i]
+ 73853629564*r14[i]
- 7850527669556*r16[i]
+ 1717351379730844*r18[i]
- 1359124435588313876*r20[i]
- 1272410676942417239876*r22[i]
- 25852016738884976640000*r23[i]
- 462292539259962003646196*r24[i]
- 7561714896123855667200000*r25[i]
- 115761644587269354830466596*r26[i]
- 1683741850203578528563200000*r27[i]
- 23512975860299444963550050516*r28[i]
) // 51090942171709440000 for i in range(len(r0))]
r19 = [(-16796*r[1][i]
+ 25194*r[2][i]
- 23256*r[3][i]
+ 15504*r[4][i]
- 7752*r[5][i]
+ 2907*r[6][i]
- 798*r[7][i]
+ 152*r[8][i]
- 18*r[9][i]
+ r[10][i]
+ 4862*r0[i]
- 2860*r2[i]
+ 7436*r4[i]
- 46420*r6[i]
+ 576236*r8[i]
- 13098580*r10[i]
+ 532310636*r12[i]
- 39968611540*r14[i]
+ 6350631494636*r16[i]
- 3730771315561300*r18[i]
- 2637991952943407764*r20[i]
- 46833363657400320000*r21[i]
- 734121065118879803860*r22[i]
- 10556240168378032128000*r23[i]
- 142438684135271315212564*r24[i]
- 1830415113744266649600000*r25[i]
- 22632897298190126259675220*r26[i]
- 271297526662043666104320000*r27[i]
- 3170344993810020486920015764*r28[i]
) // 121645100408832000 for i in range(len(r0))]
r17 = [(4862*r[1][i]
- 7072*r[2][i]
+ 6188*r[3][i]
- 3808*r[4][i]
+ 1700*r[5][i]
- 544*r[6][i]
+ 119*r[7][i]
- 16*r[8][i]
+ r[9][i]
- 1430*r0[i]
+ 858*r2[i]
- 2310*r4[i]
+ 15258*r6[i]
- 206790*r8[i]
+ 5386458*r10[i]
- 272513670*r12[i]
+ 30255826458*r14[i]
- 12765597850950*r16[i]
- 6622557957272742*r18[i]
- 101370917007360000*r19[i]
- 1375210145685786630*r20[i]
- 17172233341046784000*r21[i]
- 201832098313986359142*r22[i]
- 2265471043586150400000*r23[i]
- 24529324224160803328710*r24[i]
- 258058524232798248960000*r25[i]
- 2652208374242713043720742*r26[i]
- 26739700571225856614400000*r27[i]
- 265323404171486113659725190*r28[i]
) // 355687428096000 for i in range(len(r0))]
r15 = [(-1430*r[1][i]
+ 2002*r[2][i]
- 1638*r[3][i]
+ 910*r[4][i]
- 350*r[5][i]
+ 90*r[6][i]
- 14*r[7][i]
+ r[8][i]
+ 429*r0[i]
- 264*r2[i]
+ 744*r4[i]
- 5304*r6[i]
+ 81384*r8[i]
- 2605944*r10[i]
+ 192387624*r12[i]
- 55942352184*r14[i]
- 20546119600536*r16[i]
- 266765571072000*r17[i]
- 3083760849804024*r18[i]
- 32945548027392000*r19[i]
- 332500281299403096*r20[i]
- 3215147584416768000*r21[i]
- 30076927429146721464*r22[i]
- 274100623905588480000*r23[i]
- 2446077617962088140056*r24[i]
- 21459412163122053120000*r25[i]
- 185641639183185136464504*r26[i]
- 1587401376760010972160000*r27[i]
- 13442713420403849918131416*r28[i]
) // 1307674368000 for i in range(len(r0))]
r13 = [(429*r[1][i]
- 572*r[2][i]
+ 429*r[3][i]
- 208*r[4][i]
+ 65*r[5][i]
- 12*r[6][i]
+ r[7][i]
- 132*r0[i]
+ 84*r2[i]
- 252*r4[i]
+ 2004*r6[i]
- 37212*r8[i]
+ 1710324*r10[i]
- 325024572*r12[i]
- 80789566956*r14[i]
- 871782912000*r15[i]
- 8422900930332*r16[i]
- 75583578470400*r17[i]
- 643521842437836*r18[i]
- 5269678622208000*r19[i]
- 41890044885642492*r20[i]
- 325386564299596800*r21[i]
- 2481686964269990316*r22[i]
- 18652248729354240000*r23[i]
- 138536531588626169052*r24[i]
- 1019042849143807488000*r25[i]
- 7436421488952386592396*r26[i]
- 53911021949819274240000*r27[i]
- 388701690499592948238012*r28[i]
) // 6227020800 for i in range(len(r0))]
r11 = [(-132*r[1][i]
+ 165*r[2][i]
- 110*r[3][i]
+ 44*r[4][i]
- 10*r[5][i]
+ r[6][i]
+ 42*r0[i]
- 28*r2[i]
+ 92*r4[i]
- 868*r6[i]
+ 22652*r8[i]
- 2620708*r10[i]
- 415790788*r12[i]
- 3632428800*r13[i]
- 28616744548*r14[i]
- 210680870400*r15[i]
- 1479485236228*r16[i]
- 10038995366400*r17[i]
- 66394067988388*r18[i]
- 430591742380800*r19[i]
- 2750479262009668*r20[i]
- 17360942812012800*r21[i]
- 108550450893568228*r22[i]
- 673606803881088000*r23[i]
- 4154688725062207108*r24[i]
- 25499502190850688000*r25[i]
- 155878445775166700068*r26[i]
- 949776357849070752000*r27[i]
- 5771581202353414724548*r28[i]
) // 39916800 for i in range(len(r0))]
r9 = [(42*r[1][i]
- 48*r[2][i]
+ 27*r[3][i]
- 8*r[4][i]
+ r[5][i]
- 14*r0[i]
+ 10*r2[i]
- 38*r4[i]
+ 490*r6[i]
- 31238*r8[i]
- 2922230*r10[i]
- 19958400*r11[i]
- 124075238*r12[i]
- 726485760*r13[i]
- 4084385750*r14[i]
- 22313491200*r15[i]
- 119387268038*r16[i]
- 628980992640*r17[i]
- 3275389222070*r18[i]
- 16905818966400*r19[i]
- 86665431465638*r20[i]
- 441935114987520*r21[i]
- 2244295389943190*r22[i]
- 11360520464832000*r23[i]
- 57360469753884038*r24[i]
- 289038899804054400*r25[i]
- 1454155949521941110*r26[i]
- 7306671293537616000*r27[i]
- 36677059892827099238*r28[i]
) // 362880 for i in range(len(r0))]
r7 = [(-14*r[1][i]
+ 14*r[2][i]
- 6*r[3][i]
+ r[4][i]
+ 5*r0[i]
- 4*r2[i]
+ 20*r4[i]
- 604*r6[i]
- 29740*r8[i]
- 151200*r9[i]
- 708604*r10[i]
- 3160080*r11[i]
- 13645900*r12[i]
- 57657600*r13[i]
- 239967004*r14[i]
- 988107120*r15[i]
- 4037604460*r16[i]
- 16406863200*r17[i]
- 66398623804*r18[i]
- 267911678160*r19[i]
- 1078605601420*r20[i]
- 4335313752000*r21[i]
- 17403958407004*r22[i]
- 69804002545200*r23[i]
- 279780634372780*r24[i]
- 1120816644948000*r25[i]
- 4488349371924604*r26[i]
- 17968646803620240*r27[i]
- 71920337041294540*r28[i]
) // 5040 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
- 1680*r7[i]
- 5542*r8[i]
- 17640*r9[i]
- 54958*r10[i]
- 168960*r11[i]
- 515062*r12[i]
- 1561560*r13[i]
- 4717438*r14[i]
- 14217840*r15[i]
- 42784582*r16[i]
- 128615880*r17[i]
- 386371918*r18[i]
- 1160164320*r19[i]
- 3482590102*r20[i]
- 10451964600*r21[i]
- 31364282398*r22[i]
- 94109624400*r23[i]
- 282362427622*r24[i]
- 847154391720*r25[i]
- 2541597392878*r26[i]
- 7625060614080*r27[i]
- 22875718713142*r28[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
- 126*r7[i]
- 254*r8[i]
- 510*r9[i]
- 1022*r10[i]
- 2046*r11[i]
- 4094*r12[i]
- 8190*r13[i]
- 16382*r14[i]
- 32766*r15[i]
- 65534*r16[i]
- 131070*r17[i]
- 262142*r18[i]
- 524286*r19[i]
- 1048574*r20[i]
- 2097150*r21[i]
- 4194302*r22[i]
- 8388606*r23[i]
- 16777214*r24[i]
- 33554430*r25[i]
- 67108862*r26[i]
- 134217726*r27[i]
- 268435454*r28[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
- r7[i]
- r8[i]
- r9[i]
- r10[i]
- r11[i]
- r12[i]
- r13[i]
- r14[i]
- r15[i]
- r16[i]
- r17[i]
- r18[i]
- r19[i]
- r20[i]
- r21[i]
- r22[i]
- r23[i]
- r24[i]
- r25[i]
- r26[i]
- r27[i]
- r28[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28)
def natural_interpolate_16(r):
r0 = r[0]
r30 = r['infinity']
r28 = [(-37442160*(r[1][i] + r[-1][i])
+ 30421755*(r[2][i] + r[-2][i])
- 21474180*(r[3][i] + r[-3][i])
+ 13123110*(r[4][i] + r[-4][i])
- 6906900*(r[5][i] + r[-5][i])
+ 3108105*(r[6][i] + r[-6][i])
- 1184040*(r[7][i] + r[-7][i])
+ 376740*(r[8][i] + r[-8][i])
- 98280*(r[9][i] + r[-9][i])
+ 20475*(r[10][i] + r[-10][i])
- 3276*(r[11][i] + r[-11][i])
+ 378*(r[12][i] + r[-12][i])
- 28*(r[13][i] + r[-13][i])
+ (r[14][i] + r[-14][i])
+ 40116600*r0[i]
- 309461669780889568409026560000000*r30[i]
) // 304888344611713860501504000000 for i in range(len(r0))]
r26 = [(9657700*(r[1][i] + r[-1][i])
- 7726160*(r[2][i] + r[-2][i])
+ 5311735*(r[3][i] + r[-3][i])
- 3124550*(r[4][i] + r[-4][i])
+ 1562275*(r[5][i] + r[-5][i])
- 657800*(r[6][i] + r[-6][i])
+ 230230*(r[7][i] + r[-7][i])
- 65780*(r[8][i] + r[-8][i])
+ 14950*(r[9][i] + r[-9][i])
- 2600*(r[10][i] + r[-10][i])
+ 325*(r[11][i] + r[-11][i])
- 26*(r[12][i] + r[-12][i])
+ (r[13][i] + r[-13][i])
- 10400600*r0[i]
- 330295706662690015543296000000*r28[i]
- 153257207891488167212089344000000*r30[i]
) // 403291461126605635584000000 for i in range(len(r0))]
r24 = [(-2496144*(r[1][i] + r[-1][i])
+ 1961256*(r[2][i] + r[-2][i])
- 1307504*(r[3][i] + r[-3][i])
+ 735471*(r[4][i] + r[-4][i])
- 346104*(r[5][i] + r[-5][i])
+ 134596*(r[6][i] + r[-6][i])
- 42504*(r[7][i] + r[-7][i])
+ 10626*(r[8][i] + r[-8][i])
- 2024*(r[9][i] + r[-9][i])
+ 276*(r[10][i] + r[-10][i])
- 24*(r[11][i] + r[-11][i])
+ (r[12][i] + r[-12][i])
+ 2704156*r0[i]
- 403291461126605635584000000*r26[i]
- 149903436100759314746572800000*r28[i]
- 42033455827381598974377984000000*r30[i]
) // 620448401733239439360000 for i in range(len(r0))]
r22 = [(646646*(r[1][i] + r[-1][i])
- 497420*(r[2][i] + r[-2][i])
+ 319770*(r[3][i] + r[-3][i])
- 170544*(r[4][i] + r[-4][i])
+ 74613*(r[5][i] + r[-5][i])
- 26334*(r[6][i] + r[-6][i])
+ 7315*(r[7][i] + r[-7][i])
- 1540*(r[8][i] + r[-8][i])
+ 231*(r[9][i] + r[-9][i])
- 22*(r[10][i] + r[-10][i])
+ (r[11][i] + r[-11][i])
- 705432*r0[i]
- 568744368255469486080000*r24[i]
- 166357727714724824678400000*r26[i]
- 37042320704478727628390400000*r28[i]
- 6988909951599209517839155200000*r30[i]
) // 1124000727777607680000 for i in range(len(r0))]
r20 = [(-167960*(r[1][i] + r[-1][i])
+ 125970*(r[2][i] + r[-2][i])
- 77520*(r[3][i] + r[-3][i])
+ 38760*(r[4][i] + r[-4][i])
- 15504*(r[5][i] + r[-5][i])
+ 4845*(r[6][i] + r[-6][i])
- 1140*(r[7][i] + r[-7][i])
+ 190*(r[8][i] + r[-8][i])
- 20*(r[9][i] + r[-9][i])
+ (r[10][i] + r[-10][i])
+ 184756*r0[i]
- 936667273148006400000*r22[i]
- 211124803367560642560000*r24[i]
- 36608302274885332992000000*r26[i]
- 5425950533240873322086400000*r28[i]
- 725494605231272191451136000000*r30[i]
) // 2432902008176640000 for i in range(len(r0))]
r18 = [(43758*(r[1][i] + r[-1][i])
- 31824*(r[2][i] + r[-2][i])
+ 18564*(r[3][i] + r[-3][i])
- 8568*(r[4][i] + r[-4][i])
+ 3060*(r[5][i] + r[-5][i])
- 816*(r[6][i] + r[-6][i])
+ 153*(r[7][i] + r[-7][i])
- 18*(r[8][i] + r[-8][i])
+ (r[9][i] + r[-9][i])
- 48620*r0[i]
- 1824676506132480000*r20[i]
- 309100200138842112000*r22[i]
- 40778478784550707200000*r24[i]
- 4645053436190368481280000*r26[i]
- 481314610282065419059200000*r28[i]
- 46758400573464312663490560000*r30[i]
) // 6402373705728000 for i in range(len(r0))]
r16 = [(-11440*(r[1][i] + r[-1][i])
+ 8008*(r[2][i] + r[-2][i])
- 4368*(r[3][i] + r[-3][i])
+ 1820*(r[4][i] + r[-4][i])
- 560*(r[5][i] + r[-5][i])
+ 120*(r[6][i] + r[-6][i])
- 16*(r[7][i] + r[-7][i])
+ (r[8][i] + r[-8][i])
+ 12870*r0[i]
- 4268249137152000*r18[i]
- 527128768438272000*r20[i]
- 51442361350668288000*r22[i]
- 4385609982489415680000*r24[i]
- 343350594609952849920000*r26[i]
- 25398422028160175554560000*r28[i]
- 1806640043553643996938240000*r30[i]
) // 20922789888000 for i in range(len(r0))]
r14 = [(3003*(r[1][i] + r[-1][i])
- 2002*(r[2][i] + r[-2][i])
+ 1001*(r[3][i] + r[-3][i])
- 364*(r[4][i] + r[-4][i])
+ 91*(r[5][i] + r[-5][i])
- 14*(r[6][i] + r[-6][i])
+ (r[7][i] + r[-7][i])
- 3432*r0[i]
- 12204960768000*r16[i]
- 1058170098585600*r18[i]
- 73775500710912000*r20[i]
- 4555411900194355200*r22[i]
- 261131482210959360000*r24[i]
- 14266599888013304832000*r26[i]
- 754754307297469839360000*r28[i]
- 39057272623118392651008000*r30[i]
) // 87178291200 for i in range(len(r0))]
r12 = [(-792*(r[1][i] + r[-1][i])
+ 495*(r[2][i] + r[-2][i])
- 220*(r[3][i] + r[-3][i])
+ 66*(r[4][i] + r[-4][i])
- 12*(r[5][i] + r[-5][i])
+ (r[6][i] + r[-6][i])
+ 924*r0[i]
- 43589145600*r14[i]
- 2528170444800*r16[i]
- 120467944396800*r18[i]
- 5167100908569600*r20[i]
- 208331313744153600*r22[i]
- 8083281646573056000*r24[i]
- 305994026290208256000*r26[i]
- 11397316294188849024000*r28[i]
- 419948192698268217984000*r30[i]
) // 479001600 for i in range(len(r0))]
r10 = [(210*(r[1][i] + r[-1][i])
- 120*(r[2][i] + r[-2][i])
+ 45*(r[3][i] + r[-3][i])
- 10*(r[4][i] + r[-4][i])
+ (r[5][i] + r[-5][i])
- 252*r0[i]
- 199584000*r12[i]
- 7264857600*r14[i]
- 223134912000*r16[i]
- 6289809926400*r18[i]
- 169058189664000*r20[i]
- 4419351149875200*r22[i]
- 113605204648320000*r24[i]
- 2890388998040544000*r26[i]
- 73066712935376160000*r28[i]
- 1839605249083010572800*r30[i]
) // 3628800 for i in range(len(r0))]
r8 = [(-56*(r[1][i] + r[-1][i])
+ 28*(r[2][i] + r[-2][i])
- 8*(r[3][i] + r[-3][i])
+ (r[4][i] + r[-4][i])
+ 70*r0[i]
- 1209600*r10[i]
- 25280640*r12[i]
- 461260800*r14[i]
- 7904856960*r16[i]
- 131254905600*r18[i]
- 2143293425280*r20[i]
- 34682510016000*r22[i]
- 558432020361600*r24[i]
- 8966533159584000*r26[i]
- 143749174428961920*r28[i]
- 2302548811229721600*r30[i]
) // 40320 for i in range(len(r0))]
r6 = [(15*(r[1][i] + r[-1][i])
- 6*(r[2][i] + r[-2][i])
+ (r[3][i] + r[-3][i])
- 20*r0[i]
- 10080*r8[i]
- 105840*r10[i]
- 1013760*r12[i]
- 9369360*r14[i]
- 85307040*r16[i]
- 771695280*r18[i]
- 6960985920*r20[i]
- 62711787600*r22[i]
- 564657746400*r24[i]
- 5082926350320*r26[i]
- 45750363684480*r28[i]
- 411769379287440*r30[i]
) // 720 for i in range(len(r0))]
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
- 504*r8[i]
- 2040*r10[i]
- 8184*r12[i]
- 32760*r14[i]
- 131064*r16[i]
- 524280*r18[i]
- 2097144*r20[i]
- 8388600*r22[i]
- 33554424*r24[i]
- 134217720*r26[i]
- 536870904*r28[i]
- 2147483640*r30[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
- 2*r8[i]
- 2*r10[i]
- 2*r12[i]
- 2*r14[i]
- 2*r16[i]
- 2*r18[i]
- 2*r20[i]
- 2*r22[i]
- 2*r24[i]
- 2*r26[i]
- 2*r28[i]
- 2*r30[i]
) // 2 for i in range(len(r0))]
r29 = [(9694845*r[1][i]
- 15967980*r[2][i]
+ 17298645*r[3][i]
- 14567280*r[4][i]
+ 10015005*r[5][i]
- 5722860*r[6][i]
+ 2731365*r[7][i]
- 1085760*r[8][i]
+ 356265*r[9][i]
- 95004*r[10][i]
+ 20097*r[11][i]
- 3248*r[12][i]
+ 377*r[13][i]
- 28*r[14][i]
+ r[15][i]
- 2674440*r0[i]
+ 1485800*r2[i]
- 3506488*r4[i]
+ 18850280*r6[i]
- 188004088*r8[i]
+ 3125835560*r10[i]
- 81314498488*r12[i]
+ 3185384180840*r14[i]
- 184064268909688*r16[i]
+ 15598375633694120*r18[i]
- 1958105850969957688*r20[i]
+ 375744491571024583400*r22[i]
- 118117302690774819242488*r24[i]
+ 71447614092662750198256680*r26[i]
- 147980747895225006590333244088*r28[i]
- 346368637877614395127589803878040*r30[i]
) // 8841761993739701954543616000000 for i in range(len(r0))]
r27 = [(-2674440*r[1][i]
+ 4345965*r[2][i]
- 4601610*r[3][i]
+ 3749460*r[4][i]
- 2466750*r[5][i]
+ 1332045*r[6][i]
- 592020*r[7][i]
+ 215280*r[8][i]
- 63180*r[9][i]
+ 14625*r[10][i]
- 2574*r[11][i]
+ 324*r[12][i]
- 26*r[13][i]
+ r[14][i]
+ 742900*r0[i]
- 416024*r2[i]
+ 994840*r4[i]
- 5454824*r6[i]
+ 55944280*r8[i]
- 966290024*r10[i]
+ 26454613720*r12[i]
- 1109329691624*r14[i]
+ 70212852387160*r16[i]
- 6733670404619624*r18[i]
+ 1005318113348848600*r20[i]
- 249581050854994274024*r22[i]
+ 120719220687299365182040*r24[i]
- 202039976682357297272094824*r26[i]
- 385557844336439370252173428520*r28[i]
- 11052202492174627443179520000000*r29[i]
- 276888650579451671741587901762024*r30[i]
) // 10888869450418352160768000000 for i in range(len(r0))]
r25 = [(742900*r[1][i]
- 1188640*r[2][i]
+ 1225785*r[3][i]
- 961400*r[4][i]
+ 600875*r[5][i]
- 303600*r[6][i]
+ 123970*r[7][i]
- 40480*r[8][i]
+ 10350*r[9][i]
- 2000*r[10][i]
+ 275*r[11][i]
- 24*r[12][i]
+ r[13][i]
- 208012*r0[i]
+ 117572*r2[i]
- 285532*r4[i]
+ 1602692*r6[i]
- 16996252*r8[i]
+ 307475012*r10[i]
- 8966430172*r12[i]
+ 409745686532*r14[i]
- 29195711499292*r16[i]
+ 3312133208909252*r18[i]
- 636215671041835612*r20[i]
+ 241648300078174135172*r22[i]
- 321511316149669476991132*r24[i]
- 492817676505266866078123708*r26[i]
- 12703681025488077520896000000*r27[i]
- 286779648275654636997381637852*r28[i]
- 5894507995826467969695744000000*r29[i]
- 112914054231542703053832892635388*r30[i]
) // 15511210043330985984000000 for i in range(len(r0))]
r23 = [(-208012*r[1][i]
+ 326876*r[2][i]
- 326876*r[3][i]
+ 245157*r[4][i]
- 144210*r[5][i]
+ 67298*r[6][i]
- 24794*r[7][i]
+ 7084*r[8][i]
- 1518*r[9][i]
+ 230*r[10][i]
- 22*r[11][i]
+ r[12][i]
+ 58786*r0[i]
- 33592*r2[i]
+ 83096*r4[i]
- 479752*r6[i]
+ 5299736*r8[i]
- 101549512*r10[i]
+ 3208453976*r12[i]
- 164071220872*r14[i]
+ 13743680753816*r16[i]
- 1993276972245832*r18[i]
+ 581947914140407256*r20[i]
- 603916464771468176392*r22[i]
- 730803773459954540777704*r24[i]
- 16803810880275234816000000*r25[i]
- 339155768243774227716964552*r26[i]
- 6245976504198304781107200000*r27[i]
- 107413822788261782335458993064*r28[i]
- 1751393992807566623932416000000*r29[i]
- 27365156266821215807862420562312*r30[i]
) // 25852016738884976640000 for i in range(len(r0))]
r21 = [(58786*r[1][i]
- 90440*r[2][i]
+ 87210*r[3][i]
- 62016*r[4][i]
+ 33915*r[5][i]
- 14364*r[6][i]
+ 4655*r[7][i]
- 1120*r[8][i]
+ 189*r[9][i]
- 20*r[10][i]
+ r[11][i]
- 16796*r0[i]
+ 9724*r2[i]
- 24596*r4[i]
+ 147004*r6[i]
- 1708916*r8[i]
+ 35240284*r10[i]
- 1237329236*r12[i]
+ 73853629564*r14[i]
- 7850527669556*r16[i]
+ 1717351379730844*r18[i]
- 1359124435588313876*r20[i]
- 1272410676942417239876*r22[i]
- 25852016738884976640000*r23[i]
- 462292539259962003646196*r24[i]
- 7561714896123855667200000*r25[i]
- 115761644587269354830466596*r26[i]
- 1683741850203578528563200000*r27[i]
- 23512975860299444963550050516*r28[i]
- 317677725072691341719961600000*r29[i]
- 4176614976496441445095962733316*r30[i]
) // 51090942171709440000 for i in range(len(r0))]
r19 = [(-16796*r[1][i]
+ 25194*r[2][i]
- 23256*r[3][i]
+ 15504*r[4][i]
- 7752*r[5][i]
+ 2907*r[6][i]
- 798*r[7][i]
+ 152*r[8][i]
- 18*r[9][i]
+ r[10][i]
+ 4862*r0[i]
- 2860*r2[i]
+ 7436*r4[i]
- 46420*r6[i]
+ 576236*r8[i]
- 13098580*r10[i]
+ 532310636*r12[i]
- 39968611540*r14[i]
+ 6350631494636*r16[i]
- 3730771315561300*r18[i]
- 2637991952943407764*r20[i]
- 46833363657400320000*r21[i]
- 734121065118879803860*r22[i]
- 10556240168378032128000*r23[i]
- 142438684135271315212564*r24[i]
- 1830415113744266649600000*r25[i]
- 22632897298190126259675220*r26[i]
- 271297526662043666104320000*r27[i]
- 3170344993810020486920015764*r28[i]
- 36274730261563609572556800000*r29[i]
- 407775103607650299563627591380*r30[i]
) // 121645100408832000 for i in range(len(r0))]
r17 = [(4862*r[1][i]
- 7072*r[2][i]
+ 6188*r[3][i]
- 3808*r[4][i]
+ 1700*r[5][i]
- 544*r[6][i]
+ 119*r[7][i]
- 16*r[8][i]
+ r[9][i]
- 1430*r0[i]
+ 858*r2[i]
- 2310*r4[i]
+ 15258*r6[i]
- 206790*r8[i]
+ 5386458*r10[i]
- 272513670*r12[i]
+ 30255826458*r14[i]
- 12765597850950*r16[i]
- 6622557957272742*r18[i]
- 101370917007360000*r19[i]
- 1375210145685786630*r20[i]
- 17172233341046784000*r21[i]
- 201832098313986359142*r22[i]
- 2265471043586150400000*r23[i]
- 24529324224160803328710*r24[i]
- 258058524232798248960000*r25[i]
- 2652208374242713043720742*r26[i]
- 26739700571225856614400000*r27[i]
- 265323404171486113659725190*r28[i]
- 2597688920748017370193920000*r29[i]
- 25147613788240222384169485542*r30[i]
) // 355687428096000 for i in range(len(r0))]
r15 = [(-1430*r[1][i]
+ 2002*r[2][i]
- 1638*r[3][i]
+ 910*r[4][i]
- 350*r[5][i]
+ 90*r[6][i]
- 14*r[7][i]
+ r[8][i]
+ 429*r0[i]
- 264*r2[i]
+ 744*r4[i]
- 5304*r6[i]
+ 81384*r8[i]
- 2605944*r10[i]
+ 192387624*r12[i]
- 55942352184*r14[i]
- 20546119600536*r16[i]
- 266765571072000*r17[i]
- 3083760849804024*r18[i]
- 32945548027392000*r19[i]
- 332500281299403096*r20[i]
- 3215147584416768000*r21[i]
- 30076927429146721464*r22[i]
- 274100623905588480000*r23[i]
- 2446077617962088140056*r24[i]
- 21459412163122053120000*r25[i]
- 185641639183185136464504*r26[i]
- 1587401376760010972160000*r27[i]
- 13442713420403849918131416*r28[i]
- 112915002722102749808640000*r29[i]
- 941961013910760913890393144*r30[i]
) // 1307674368000 for i in range(len(r0))]
r13 = [(429*r[1][i]
- 572*r[2][i]
+ 429*r[3][i]
- 208*r[4][i]
+ 65*r[5][i]
- 12*r[6][i]
+ r[7][i]
- 132*r0[i]
+ 84*r2[i]
- 252*r4[i]
+ 2004*r6[i]
- 37212*r8[i]
+ 1710324*r10[i]
- 325024572*r12[i]
- 80789566956*r14[i]
- 871782912000*r15[i]
- 8422900930332*r16[i]
- 75583578470400*r17[i]
- 643521842437836*r18[i]
- 5269678622208000*r19[i]
- 41890044885642492*r20[i]
- 325386564299596800*r21[i]
- 2481686964269990316*r22[i]
- 18652248729354240000*r23[i]
- 138536531588626169052*r24[i]
- 1019042849143807488000*r25[i]
- 7436421488952386592396*r26[i]
- 53911021949819274240000*r27[i]
- 388701690499592948238012*r28[i]
- 2789805187365599475072000*r29[i]
- 19946749502047187160692076*r30[i]
) // 6227020800 for i in range(len(r0))]
r11 = [(-132*r[1][i]
+ 165*r[2][i]
- 110*r[3][i]
+ 44*r[4][i]
- 10*r[5][i]
+ r[6][i]
+ 42*r0[i]
- 28*r2[i]
+ 92*r4[i]
- 868*r6[i]
+ 22652*r8[i]
- 2620708*r10[i]
- 415790788*r12[i]
- 3632428800*r13[i]
- 28616744548*r14[i]
- 210680870400*r15[i]
- 1479485236228*r16[i]
- 10038995366400*r17[i]
- 66394067988388*r18[i]
- 430591742380800*r19[i]
- 2750479262009668*r20[i]
- 17360942812012800*r21[i]
- 108550450893568228*r22[i]
- 673606803881088000*r23[i]
- 4154688725062207108*r24[i]
- 25499502190850688000*r25[i]
- 155878445775166700068*r26[i]
- 949776357849070752000*r27[i]
- 5771581202353414724548*r28[i]
- 34995682724855684832000*r29[i]
- 211811399872933910999908*r30[i]
) // 39916800 for i in range(len(r0))]
r9 = [(42*r[1][i]
- 48*r[2][i]
+ 27*r[3][i]
- 8*r[4][i]
+ r[5][i]
- 14*r0[i]
+ 10*r2[i]
- 38*r4[i]
+ 490*r6[i]
- 31238*r8[i]
- 2922230*r10[i]
- 19958400*r11[i]
- 124075238*r12[i]
- 726485760*r13[i]
- 4084385750*r14[i]
- 22313491200*r15[i]
- 119387268038*r16[i]
- 628980992640*r17[i]
- 3275389222070*r18[i]
- 16905818966400*r19[i]
- 86665431465638*r20[i]
- 441935114987520*r21[i]
- 2244295389943190*r22[i]
- 11360520464832000*r23[i]
- 57360469753884038*r24[i]
- 289038899804054400*r25[i]
- 1454155949521941110*r26[i]
- 7306671293537616000*r27[i]
- 36677059892827099238*r28[i]
- 183960524908301057280*r29[i]
- 922104761587650687830*r30[i]
) // 362880 for i in range(len(r0))]
r7 = [(-14*r[1][i]
+ 14*r[2][i]
- 6*r[3][i]
+ r[4][i]
+ 5*r0[i]
- 4*r2[i]
+ 20*r4[i]
- 604*r6[i]
- 29740*r8[i]
- 151200*r9[i]
- 708604*r10[i]
- 3160080*r11[i]
- 13645900*r12[i]
- 57657600*r13[i]
- 239967004*r14[i]
- 988107120*r15[i]
- 4037604460*r16[i]
- 16406863200*r17[i]
- 66398623804*r18[i]
- 267911678160*r19[i]
- 1078605601420*r20[i]
- 4335313752000*r21[i]
- 17403958407004*r22[i]
- 69804002545200*r23[i]
- 279780634372780*r24[i]
- 1120816644948000*r25[i]
- 4488349371924604*r26[i]
- 17968646803620240*r27[i]
- 71920337041294540*r28[i]
- 287818601403715200*r29[i]
- 1151686172846664604*r30[i]
) // 5040 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
- 1680*r7[i]
- 5542*r8[i]
- 17640*r9[i]
- 54958*r10[i]
- 168960*r11[i]
- 515062*r12[i]
- 1561560*r13[i]
- 4717438*r14[i]
- 14217840*r15[i]
- 42784582*r16[i]
- 128615880*r17[i]
- 386371918*r18[i]
- 1160164320*r19[i]
- 3482590102*r20[i]
- 10451964600*r21[i]
- 31364282398*r22[i]
- 94109624400*r23[i]
- 282362427622*r24[i]
- 847154391720*r25[i]
- 2541597392878*r26[i]
- 7625060614080*r27[i]
- 22875718713142*r28[i]
- 68628229881240*r29[i]
- 205886837127358*r30[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
- 126*r7[i]
- 254*r8[i]
- 510*r9[i]
- 1022*r10[i]
- 2046*r11[i]
- 4094*r12[i]
- 8190*r13[i]
- 16382*r14[i]
- 32766*r15[i]
- 65534*r16[i]
- 131070*r17[i]
- 262142*r18[i]
- 524286*r19[i]
- 1048574*r20[i]
- 2097150*r21[i]
- 4194302*r22[i]
- 8388606*r23[i]
- 16777214*r24[i]
- 33554430*r25[i]
- 67108862*r26[i]
- 134217726*r27[i]
- 268435454*r28[i]
- 536870910*r29[i]
- 1073741822*r30[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
- r7[i]
- r8[i]
- r9[i]
- r10[i]
- r11[i]
- r12[i]
- r13[i]
- r14[i]
- r15[i]
- r16[i]
- r17[i]
- r18[i]
- r19[i]
- r20[i]
- r21[i]
- r22[i]
- r23[i]
- r24[i]
- r25[i]
- r26[i]
- r27[i]
- r28[i]
- r29[i]
- r30[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30)
def natural_interpolate_17(r):
r0 = r[0]
r32 = r['infinity']
r30 = [(145422675*(r[1][i] + r[-1][i])
- 119759850*(r[2][i] + r[-2][i])
+ 86493225*(r[3][i] + r[-3][i])
- 54627300*(r[4][i] + r[-4][i])
+ 30045015*(r[5][i] + r[-5][i])
- 14307150*(r[6][i] + r[-6][i])
+ 5852925*(r[7][i] + r[-7][i])
- 2035800*(r[8][i] + r[-8][i])
+ 593775*(r[9][i] + r[-9][i])
- 142506*(r[10][i] + r[-10][i])
+ 27405*(r[11][i] + r[-11][i])
- 4060*(r[12][i] + r[-12][i])
+ 435*(r[13][i] + r[-13][i])
- 30*(r[14][i] + r[-14][i])
+ (r[15][i] + r[-15][i])
- 155117520*r0[i]
- 328913546167116912709022515200000000*r32[i]
) // 265252859812191058636308480000000 for i in range(len(r0))]
r28 = [(-37442160*(r[1][i] + r[-1][i])
+ 30421755*(r[2][i] + r[-2][i])
- 21474180*(r[3][i] + r[-3][i])
+ 13123110*(r[4][i] + r[-4][i])
- 6906900*(r[5][i] + r[-5][i])
+ 3108105*(r[6][i] + r[-6][i])
- 1184040*(r[7][i] + r[-7][i])
+ 376740*(r[8][i] + r[-8][i])
- 98280*(r[9][i] + r[-9][i])
+ 20475*(r[10][i] + r[-10][i])
- 3276*(r[11][i] + r[-11][i])
+ 378*(r[12][i] + r[-12][i])
- 28*(r[13][i] + r[-13][i])
+ (r[14][i] + r[-14][i])
+ 40116600*r0[i]
- 309461669780889568409026560000000*r30[i]
- 176516936443019409820508749824000000*r32[i]
) // 304888344611713860501504000000 for i in range(len(r0))]
r26 = [(9657700*(r[1][i] + r[-1][i])
- 7726160*(r[2][i] + r[-2][i])
+ 5311735*(r[3][i] + r[-3][i])
- 3124550*(r[4][i] + r[-4][i])
+ 1562275*(r[5][i] + r[-5][i])
- 657800*(r[6][i] + r[-6][i])
+ 230230*(r[7][i] + r[-7][i])
- 65780*(r[8][i] + r[-8][i])
+ 14950*(r[9][i] + r[-9][i])
- 2600*(r[10][i] + r[-10][i])
+ 325*(r[11][i] + r[-11][i])
- 26*(r[12][i] + r[-12][i])
+ (r[13][i] + r[-13][i])
- 10400600*r0[i]
- 330295706662690015543296000000*r28[i]
- 153257207891488167212089344000000*r30[i]
- 53222214421459539592188788736000000*r32[i]
) // 403291461126605635584000000 for i in range(len(r0))]
r24 = [(-2496144*(r[1][i] + r[-1][i])
+ 1961256*(r[2][i] + r[-2][i])
- 1307504*(r[3][i] + r[-3][i])
+ 735471*(r[4][i] + r[-4][i])
- 346104*(r[5][i] + r[-5][i])
+ 134596*(r[6][i] + r[-6][i])
- 42504*(r[7][i] + r[-7][i])
+ 10626*(r[8][i] + r[-8][i])
- 2024*(r[9][i] + r[-9][i])
+ 276*(r[10][i] + r[-10][i])
- 24*(r[11][i] + r[-11][i])
+ (r[12][i] + r[-12][i])
+ 2704156*r0[i]
- 403291461126605635584000000*r26[i]
- 149903436100759314746572800000*r28[i]
- 42033455827381598974377984000000*r30[i]
- 9910695932425713906157643366400000*r32[i]
) // 620448401733239439360000 for i in range(len(r0))]
r22 = [(646646*(r[1][i] + r[-1][i])
- 497420*(r[2][i] + r[-2][i])
+ 319770*(r[3][i] + r[-3][i])
- 170544*(r[4][i] + r[-4][i])
+ 74613*(r[5][i] + r[-5][i])
- 26334*(r[6][i] + r[-6][i])
+ 7315*(r[7][i] + r[-7][i])
- 1540*(r[8][i] + r[-8][i])
+ 231*(r[9][i] + r[-9][i])
- 22*(r[10][i] + r[-10][i])
+ (r[11][i] + r[-11][i])
- 705432*r0[i]
- 568744368255469486080000*r24[i]
- 166357727714724824678400000*r26[i]
- 37042320704478727628390400000*r28[i]
- 6988909951599209517839155200000*r30[i]
- 1180836611760352104108962611200000*r32[i]
) // 1124000727777607680000 for i in range(len(r0))]
r20 = [(-167960*(r[1][i] + r[-1][i])
+ 125970*(r[2][i] + r[-2][i])
- 77520*(r[3][i] + r[-3][i])
+ 38760*(r[4][i] + r[-4][i])
- 15504*(r[5][i] + r[-5][i])
+ 4845*(r[6][i] + r[-6][i])
- 1140*(r[7][i] + r[-7][i])
+ 190*(r[8][i] + r[-8][i])
- 20*(r[9][i] + r[-9][i])
+ (r[10][i] + r[-10][i])
+ 184756*r0[i]
- 936667273148006400000*r22[i]
- 211124803367560642560000*r24[i]
- 36608302274885332992000000*r26[i]
- 5425950533240873322086400000*r28[i]
- 725494605231272191451136000000*r30[i]
- 90317652741043657957240012800000*r32[i]
) // 2432902008176640000 for i in range(len(r0))]
r18 = [(43758*(r[1][i] + r[-1][i])
- 31824*(r[2][i] + r[-2][i])
+ 18564*(r[3][i] + r[-3][i])
- 8568*(r[4][i] + r[-4][i])
+ 3060*(r[5][i] + r[-5][i])
- 816*(r[6][i] + r[-6][i])
+ 153*(r[7][i] + r[-7][i])
- 18*(r[8][i] + r[-8][i])
+ (r[9][i] + r[-9][i])
- 48620*r0[i]
- 1824676506132480000*r20[i]
- 309100200138842112000*r22[i]
- 40778478784550707200000*r24[i]
- 4645053436190368481280000*r26[i]
- 481314610282065419059200000*r28[i]
- 46758400573464312663490560000*r30[i]
- 4340262299778024388805836800000*r32[i]
) // 6402373705728000 for i in range(len(r0))]
r16 = [(-11440*(r[1][i] + r[-1][i])
+ 8008*(r[2][i] + r[-2][i])
- 4368*(r[3][i] + r[-3][i])
+ 1820*(r[4][i] + r[-4][i])
- 560*(r[5][i] + r[-5][i])
+ 120*(r[6][i] + r[-6][i])
- 16*(r[7][i] + r[-7][i])
+ (r[8][i] + r[-8][i])
+ 12870*r0[i]
- 4268249137152000*r18[i]
- 527128768438272000*r20[i]
- 51442361350668288000*r22[i]
- 4385609982489415680000*r24[i]
- 343350594609952849920000*r26[i]
- 25398422028160175554560000*r28[i]
- 1806640043553643996938240000*r30[i]
- 124998708216981630040289280000*r32[i]
) // 20922789888000 for i in range(len(r0))]
r14 = [(3003*(r[1][i] + r[-1][i])
- 2002*(r[2][i] + r[-2][i])
+ 1001*(r[3][i] + r[-3][i])
- 364*(r[4][i] + r[-4][i])
+ 91*(r[5][i] + r[-5][i])
- 14*(r[6][i] + r[-6][i])
+ (r[7][i] + r[-7][i])
- 3432*r0[i]
- 12204960768000*r16[i]
- 1058170098585600*r18[i]
- 73775500710912000*r20[i]
- 4555411900194355200*r22[i]
- 261131482210959360000*r24[i]
- 14266599888013304832000*r26[i]
- 754754307297469839360000*r28[i]
- 39057272623118392651008000*r30[i]
- 1990236929603886055572480000*r32[i]
) // 87178291200 for i in range(len(r0))]
r12 = [(-792*(r[1][i] + r[-1][i])
+ 495*(r[2][i] + r[-2][i])
- 220*(r[3][i] + r[-3][i])
+ 66*(r[4][i] + r[-4][i])
- 12*(r[5][i] + r[-5][i])
+ (r[6][i] + r[-6][i])
+ 924*r0[i]
- 43589145600*r14[i]
- 2528170444800*r16[i]
- 120467944396800*r18[i]
- 5167100908569600*r20[i]
- 208331313744153600*r22[i]
- 8083281646573056000*r24[i]
- 305994026290208256000*r26[i]
- 11397316294188849024000*r28[i]
- 419948192698268217984000*r30[i]
- 15360962830016613243033600*r32[i]
) // 479001600 for i in range(len(r0))]
r10 = [(210*(r[1][i] + r[-1][i])
- 120*(r[2][i] + r[-2][i])
+ 45*(r[3][i] + r[-3][i])
- 10*(r[4][i] + r[-4][i])
+ (r[5][i] + r[-5][i])
- 252*r0[i]
- 199584000*r12[i]
- 7264857600*r14[i]
- 223134912000*r16[i]
- 6289809926400*r18[i]
- 169058189664000*r20[i]
- 4419351149875200*r22[i]
- 113605204648320000*r24[i]
- 2890388998040544000*r26[i]
- 73066712935376160000*r28[i]
- 1839605249083010572800*r30[i]
- 46197360620085939264000*r32[i]
) // 3628800 for i in range(len(r0))]
r8 = [(-56*(r[1][i] + r[-1][i])
+ 28*(r[2][i] + r[-2][i])
- 8*(r[3][i] + r[-3][i])
+ (r[4][i] + r[-4][i])
+ 70*r0[i]
- 1209600*r10[i]
- 25280640*r12[i]
- 461260800*r14[i]
- 7904856960*r16[i]
- 131254905600*r18[i]
- 2143293425280*r20[i]
- 34682510016000*r22[i]
- 558432020361600*r24[i]
- 8966533159584000*r26[i]
- 143749174428961920*r28[i]
- 2302548811229721600*r30[i]
- 36863840064915642240*r32[i]
) // 40320 for i in range(len(r0))]
r6 = [(15*(r[1][i] + r[-1][i])
- 6*(r[2][i] + r[-2][i])
+ (r[3][i] + r[-3][i])
- 20*r0[i]
- 10080*r8[i]
- 105840*r10[i]
- 1013760*r12[i]
- 9369360*r14[i]
- 85307040*r16[i]
- 771695280*r18[i]
- 6960985920*r20[i]
- 62711787600*r22[i]
- 564657746400*r24[i]
- 5082926350320*r26[i]
- 45750363684480*r28[i]
- 411769379287440*r30[i]
- 3705988838096160*r32[i]
) // 720 for i in range(len(r0))]
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
- 504*r8[i]
- 2040*r10[i]
- 8184*r12[i]
- 32760*r14[i]
- 131064*r16[i]
- 524280*r18[i]
- 2097144*r20[i]
- 8388600*r22[i]
- 33554424*r24[i]
- 134217720*r26[i]
- 536870904*r28[i]
- 2147483640*r30[i]
- 8589934584*r32[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
- 2*r8[i]
- 2*r10[i]
- 2*r12[i]
- 2*r14[i]
- 2*r16[i]
- 2*r18[i]
- 2*r20[i]
- 2*r22[i]
- 2*r24[i]
- 2*r26[i]
- 2*r28[i]
- 2*r30[i]
- 2*r32[i]
) // 2 for i in range(len(r0))]
r31 = [(-35357670*r[1][i]
+ 58929450*r[2][i]
- 65132550*r[3][i]
+ 56448210*r[4][i]
- 40320150*r[5][i]
+ 24192090*r[6][i]
- 12271350*r[7][i]
+ 5259150*r[8][i]
- 1893294*r[9][i]
+ 566370*r[10][i]
- 138446*r[11][i]
+ 26970*r[12][i]
- 4030*r[13][i]
+ 434*r[14][i]
- 30*r[15][i]
+ r[16][i]
+ 9694845*r0[i]
- 5348880*r2[i]
+ 12480720*r4[i]
- 65969520*r6[i]
+ 642563280*r8[i]
- 10347602160*r10[i]
+ 258040917840*r12[i]
- 9564008626800*r14[i]
+ 514021079720400*r16[i]
- 39590373677587440*r18[i]
+ 4371353677873146960*r20[i]
- 701971899866535028080*r22[i]
+ 169737570795219895373520*r24[i]
- 66396273378844288679892720*r26[i]
+ 49448835121192219782326176080*r28[i]
- 124963193751534047864734415925360*r30[i]
- 354113410826574103722030528083469360*r32[i]
) // 8222838654177922817725562880000000 for i in range(len(r0))]
r29 = [(9694845*r[1][i]
- 15967980*r[2][i]
+ 17298645*r[3][i]
- 14567280*r[4][i]
+ 10015005*r[5][i]
- 5722860*r[6][i]
+ 2731365*r[7][i]
- 1085760*r[8][i]
+ 356265*r[9][i]
- 95004*r[10][i]
+ 20097*r[11][i]
- 3248*r[12][i]
+ 377*r[13][i]
- 28*r[14][i]
+ r[15][i]
- 2674440*r0[i]
+ 1485800*r2[i]
- 3506488*r4[i]
+ 18850280*r6[i]
- 188004088*r8[i]
+ 3125835560*r10[i]
- 81314498488*r12[i]
+ 3185384180840*r14[i]
- 184064268909688*r16[i]
+ 15598375633694120*r18[i]
- 1958105850969957688*r20[i]
+ 375744491571024583400*r22[i]
- 118117302690774819242488*r24[i]
+ 71447614092662750198256680*r26[i]
- 147980747895225006590333244088*r28[i]
- 346368637877614395127589803878040*r30[i]
- 10963784872237230423634083840000000*r31[i]
- 302766527792977996357877082103322488*r32[i]
) // 8841761993739701954543616000000 for i in range(len(r0))]
r27 = [(-2674440*r[1][i]
+ 4345965*r[2][i]
- 4601610*r[3][i]
+ 3749460*r[4][i]
- 2466750*r[5][i]
+ 1332045*r[6][i]
- 592020*r[7][i]
+ 215280*r[8][i]
- 63180*r[9][i]
+ 14625*r[10][i]
- 2574*r[11][i]
+ 324*r[12][i]
- 26*r[13][i]
+ r[14][i]
+ 742900*r0[i]
- 416024*r2[i]
+ 994840*r4[i]
- 5454824*r6[i]
+ 55944280*r8[i]
- 966290024*r10[i]
+ 26454613720*r12[i]
- 1109329691624*r14[i]
+ 70212852387160*r16[i]
- 6733670404619624*r18[i]
+ 1005318113348848600*r20[i]
- 249581050854994274024*r22[i]
+ 120719220687299365182040*r24[i]
- 202039976682357297272094824*r26[i]
- 385557844336439370252173428520*r28[i]
- 11052202492174627443179520000000*r29[i]
- 276888650579451671741587901762024*r30[i]
- 6304176301536407493589598208000000*r31[i]
- 133535841584115505205141919375399080*r32[i]
) // 10888869450418352160768000000 for i in range(len(r0))]
r25 = [(742900*r[1][i]
- 1188640*r[2][i]
+ 1225785*r[3][i]
- 961400*r[4][i]
+ 600875*r[5][i]
- 303600*r[6][i]
+ 123970*r[7][i]
- 40480*r[8][i]
+ 10350*r[9][i]
- 2000*r[10][i]
+ 275*r[11][i]
- 24*r[12][i]
+ r[13][i]
- 208012*r0[i]
+ 117572*r2[i]
- 285532*r4[i]
+ 1602692*r6[i]
- 16996252*r8[i]
+ 307475012*r10[i]
- 8966430172*r12[i]
+ 409745686532*r14[i]
- 29195711499292*r16[i]
+ 3312133208909252*r18[i]
- 636215671041835612*r20[i]
+ 241648300078174135172*r22[i]
- 321511316149669476991132*r24[i]
- 492817676505266866078123708*r26[i]
- 12703681025488077520896000000*r27[i]
- 286779648275654636997381637852*r28[i]
- 5894507995826467969695744000000*r29[i]
- 112914054231542703053832892635388*r30[i]
- 2047008246979213061238030336000000*r31[i]
- 35501568925223446300815211192767772*r32[i]
) // 15511210043330985984000000 for i in range(len(r0))]
r23 = [(-208012*r[1][i]
+ 326876*r[2][i]
- 326876*r[3][i]
+ 245157*r[4][i]
- 144210*r[5][i]
+ 67298*r[6][i]
- 24794*r[7][i]
+ 7084*r[8][i]
- 1518*r[9][i]
+ 230*r[10][i]
- 22*r[11][i]
+ r[12][i]
+ 58786*r0[i]
- 33592*r2[i]
+ 83096*r4[i]
- 479752*r6[i]
+ 5299736*r8[i]
- 101549512*r10[i]
+ 3208453976*r12[i]
- 164071220872*r14[i]
+ 13743680753816*r16[i]
- 1993276972245832*r18[i]
+ 581947914140407256*r20[i]
- 603916464771468176392*r22[i]
- 730803773459954540777704*r24[i]
- 16803810880275234816000000*r25[i]
- 339155768243774227716964552*r26[i]
- 6245976504198304781107200000*r27[i]
- 107413822788261782335458993064*r28[i]
- 1751393992807566623932416000000*r29[i]
- 27365156266821215807862420562312*r30[i]
- 412945663851071412756568473600000*r31[i]
- 6053949680529454447550745704030824*r32[i]
) // 25852016738884976640000 for i in range(len(r0))]
r21 = [(58786*r[1][i]
- 90440*r[2][i]
+ 87210*r[3][i]
- 62016*r[4][i]
+ 33915*r[5][i]
- 14364*r[6][i]
+ 4655*r[7][i]
- 1120*r[8][i]
+ 189*r[9][i]
- 20*r[10][i]
+ r[11][i]
- 16796*r0[i]
+ 9724*r2[i]
- 24596*r4[i]
+ 147004*r6[i]
- 1708916*r8[i]
+ 35240284*r10[i]
- 1237329236*r12[i]
+ 73853629564*r14[i]
- 7850527669556*r16[i]
+ 1717351379730844*r18[i]
- 1359124435588313876*r20[i]
- 1272410676942417239876*r22[i]
- 25852016738884976640000*r23[i]
- 462292539259962003646196*r24[i]
- 7561714896123855667200000*r25[i]
- 115761644587269354830466596*r26[i]
- 1683741850203578528563200000*r27[i]
- 23512975860299444963550050516*r28[i]
- 317677725072691341719961600000*r29[i]
- 4176614976496441445095962733316*r30[i]
- 53674391443652368368589209600000*r31[i]
- 676635955671282540673335079110836*r32[i]
) // 51090942171709440000 for i in range(len(r0))]
r19 = [(-16796*r[1][i]
+ 25194*r[2][i]
- 23256*r[3][i]
+ 15504*r[4][i]
- 7752*r[5][i]
+ 2907*r[6][i]
- 798*r[7][i]
+ 152*r[8][i]
- 18*r[9][i]
+ r[10][i]
+ 4862*r0[i]
- 2860*r2[i]
+ 7436*r4[i]
- 46420*r6[i]
+ 576236*r8[i]
- 13098580*r10[i]
+ 532310636*r12[i]
- 39968611540*r14[i]
+ 6350631494636*r16[i]
- 3730771315561300*r18[i]
- 2637991952943407764*r20[i]
- 46833363657400320000*r21[i]
- 734121065118879803860*r22[i]
- 10556240168378032128000*r23[i]
- 142438684135271315212564*r24[i]
- 1830415113744266649600000*r25[i]
- 22632897298190126259675220*r26[i]
- 271297526662043666104320000*r27[i]
- 3170344993810020486920015764*r28[i]
- 36274730261563609572556800000*r29[i]
- 407775103607650299563627591380*r30[i]
- 4515882637052182897862000640000*r31[i]
- 49377994276343186011748723193364*r32[i]
) // 121645100408832000 for i in range(len(r0))]
r17 = [(4862*r[1][i]
- 7072*r[2][i]
+ 6188*r[3][i]
- 3808*r[4][i]
+ 1700*r[5][i]
- 544*r[6][i]
+ 119*r[7][i]
- 16*r[8][i]
+ r[9][i]
- 1430*r0[i]
+ 858*r2[i]
- 2310*r4[i]
+ 15258*r6[i]
- 206790*r8[i]
+ 5386458*r10[i]
- 272513670*r12[i]
+ 30255826458*r14[i]
- 12765597850950*r16[i]
- 6622557957272742*r18[i]
- 101370917007360000*r19[i]
- 1375210145685786630*r20[i]
- 17172233341046784000*r21[i]
- 201832098313986359142*r22[i]
- 2265471043586150400000*r23[i]
- 24529324224160803328710*r24[i]
- 258058524232798248960000*r25[i]
- 2652208374242713043720742*r26[i]
- 26739700571225856614400000*r27[i]
- 265323404171486113659725190*r28[i]
- 2597688920748017370193920000*r29[i]
- 25147613788240222384169485542*r30[i]
- 241125683321001354933657600000*r31[i]
- 2293170112631184981695915264070*r32[i]
) // 355687428096000 for i in range(len(r0))]
r15 = [(-1430*r[1][i]
+ 2002*r[2][i]
- 1638*r[3][i]
+ 910*r[4][i]
- 350*r[5][i]
+ 90*r[6][i]
- 14*r[7][i]
+ r[8][i]
+ 429*r0[i]
- 264*r2[i]
+ 744*r4[i]
- 5304*r6[i]
+ 81384*r8[i]
- 2605944*r10[i]
+ 192387624*r12[i]
- 55942352184*r14[i]
- 20546119600536*r16[i]
- 266765571072000*r17[i]
- 3083760849804024*r18[i]
- 32945548027392000*r19[i]
- 332500281299403096*r20[i]
- 3215147584416768000*r21[i]
- 30076927429146721464*r22[i]
- 274100623905588480000*r23[i]
- 2446077617962088140056*r24[i]
- 21459412163122053120000*r25[i]
- 185641639183185136464504*r26[i]
- 1587401376760010972160000*r27[i]
- 13442713420403849918131416*r28[i]
- 112915002722102749808640000*r29[i]
- 941961013910760913890393144*r30[i]
- 7812419263561351877518080000*r31[i]
- 64474322285718607792730497176*r32[i]
) // 1307674368000 for i in range(len(r0))]
r13 = [(429*r[1][i]
- 572*r[2][i]
+ 429*r[3][i]
- 208*r[4][i]
+ 65*r[5][i]
- 12*r[6][i]
+ r[7][i]
- 132*r0[i]
+ 84*r2[i]
- 252*r4[i]
+ 2004*r6[i]
- 37212*r8[i]
+ 1710324*r10[i]
- 325024572*r12[i]
- 80789566956*r14[i]
- 871782912000*r15[i]
- 8422900930332*r16[i]
- 75583578470400*r17[i]
- 643521842437836*r18[i]
- 5269678622208000*r19[i]
- 41890044885642492*r20[i]
- 325386564299596800*r21[i]
- 2481686964269990316*r22[i]
- 18652248729354240000*r23[i]
- 138536531588626169052*r24[i]
- 1019042849143807488000*r25[i]
- 7436421488952386592396*r26[i]
- 53911021949819274240000*r27[i]
- 388701690499592948238012*r28[i]
- 2789805187365599475072000*r29[i]
- 19946749502047187160692076*r30[i]
- 142159780685991861112320000*r31[i]
- 1010433303980489860989897372*r32[i]
) // 6227020800 for i in range(len(r0))]
r11 = [(-132*r[1][i]
+ 165*r[2][i]
- 110*r[3][i]
+ 44*r[4][i]
- 10*r[5][i]
+ r[6][i]
+ 42*r0[i]
- 28*r2[i]
+ 92*r4[i]
- 868*r6[i]
+ 22652*r8[i]
- 2620708*r10[i]
- 415790788*r12[i]
- 3632428800*r13[i]
- 28616744548*r14[i]
- 210680870400*r15[i]
- 1479485236228*r16[i]
- 10038995366400*r17[i]
- 66394067988388*r18[i]
- 430591742380800*r19[i]
- 2750479262009668*r20[i]
- 17360942812012800*r21[i]
- 108550450893568228*r22[i]
- 673606803881088000*r23[i]
- 4154688725062207108*r24[i]
- 25499502190850688000*r25[i]
- 155878445775166700068*r26[i]
- 949776357849070752000*r27[i]
- 5771581202353414724548*r28[i]
- 34995682724855684832000*r29[i]
- 211811399872933910999908*r30[i]
- 1280080235834717770252800*r31[i]
- 7726641919200262371657988*r32[i]
) // 39916800 for i in range(len(r0))]
r9 = [(42*r[1][i]
- 48*r[2][i]
+ 27*r[3][i]
- 8*r[4][i]
+ r[5][i]
- 14*r0[i]
+ 10*r2[i]
- 38*r4[i]
+ 490*r6[i]
- 31238*r8[i]
- 2922230*r10[i]
- 19958400*r11[i]
- 124075238*r12[i]
- 726485760*r13[i]
- 4084385750*r14[i]
- 22313491200*r15[i]
- 119387268038*r16[i]
- 628980992640*r17[i]
- 3275389222070*r18[i]
- 16905818966400*r19[i]
- 86665431465638*r20[i]
- 441935114987520*r21[i]
- 2244295389943190*r22[i]
- 11360520464832000*r23[i]
- 57360469753884038*r24[i]
- 289038899804054400*r25[i]
- 1454155949521941110*r26[i]
- 7306671293537616000*r27[i]
- 36677059892827099238*r28[i]
- 183960524908301057280*r29[i]
- 922104761587650687830*r30[i]
- 4619736062008593926400*r31[i]
- 23135540444136227047238*r32[i]
) // 362880 for i in range(len(r0))]
r7 = [(-14*r[1][i]
+ 14*r[2][i]
- 6*r[3][i]
+ r[4][i]
+ 5*r0[i]
- 4*r2[i]
+ 20*r4[i]
- 604*r6[i]
- 29740*r8[i]
- 151200*r9[i]
- 708604*r10[i]
- 3160080*r11[i]
- 13645900*r12[i]
- 57657600*r13[i]
- 239967004*r14[i]
- 988107120*r15[i]
- 4037604460*r16[i]
- 16406863200*r17[i]
- 66398623804*r18[i]
- 267911678160*r19[i]
- 1078605601420*r20[i]
- 4335313752000*r21[i]
- 17403958407004*r22[i]
- 69804002545200*r23[i]
- 279780634372780*r24[i]
- 1120816644948000*r25[i]
- 4488349371924604*r26[i]
- 17968646803620240*r27[i]
- 71920337041294540*r28[i]
- 287818601403715200*r29[i]
- 1151686172846664604*r30[i]
- 4607980008114455280*r31[i]
- 18435626012705982700*r32[i]
) // 5040 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
- 1680*r7[i]
- 5542*r8[i]
- 17640*r9[i]
- 54958*r10[i]
- 168960*r11[i]
- 515062*r12[i]
- 1561560*r13[i]
- 4717438*r14[i]
- 14217840*r15[i]
- 42784582*r16[i]
- 128615880*r17[i]
- 386371918*r18[i]
- 1160164320*r19[i]
- 3482590102*r20[i]
- 10451964600*r21[i]
- 31364282398*r22[i]
- 94109624400*r23[i]
- 282362427622*r24[i]
- 847154391720*r25[i]
- 2541597392878*r26[i]
- 7625060614080*r27[i]
- 22875718713142*r28[i]
- 68628229881240*r29[i]
- 205886837127358*r30[i]
- 617664806349360*r31[i]
- 1853003008982662*r32[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
- 126*r7[i]
- 254*r8[i]
- 510*r9[i]
- 1022*r10[i]
- 2046*r11[i]
- 4094*r12[i]
- 8190*r13[i]
- 16382*r14[i]
- 32766*r15[i]
- 65534*r16[i]
- 131070*r17[i]
- 262142*r18[i]
- 524286*r19[i]
- 1048574*r20[i]
- 2097150*r21[i]
- 4194302*r22[i]
- 8388606*r23[i]
- 16777214*r24[i]
- 33554430*r25[i]
- 67108862*r26[i]
- 134217726*r27[i]
- 268435454*r28[i]
- 536870910*r29[i]
- 1073741822*r30[i]
- 2147483646*r31[i]
- 4294967294*r32[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
- r7[i]
- r8[i]
- r9[i]
- r10[i]
- r11[i]
- r12[i]
- r13[i]
- r14[i]
- r15[i]
- r16[i]
- r17[i]
- r18[i]
- r19[i]
- r20[i]
- r21[i]
- r22[i]
- r23[i]
- r24[i]
- r25[i]
- r26[i]
- r27[i]
- r28[i]
- r29[i]
- r30[i]
- r31[i]
- r32[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32)
def natural_interpolate_18(r):
r0 = r[0]
r34 = r['infinity']
r32 = [(-565722720*(r[1][i] + r[-1][i])
+ 471435600*(r[2][i] + r[-2][i])
- 347373600*(r[3][i] + r[-3][i])
+ 225792840*(r[4][i] + r[-4][i])
- 129024480*(r[5][i] + r[-5][i])
+ 64512240*(r[6][i] + r[-6][i])
- 28048800*(r[7][i] + r[-7][i])
+ 10518300*(r[8][i] + r[-8][i])
- 3365856*(r[9][i] + r[-9][i])
+ 906192*(r[10][i] + r[-10][i])
- 201376*(r[11][i] + r[-11][i])
+ 35960*(r[12][i] + r[-12][i])
- 4960*(r[13][i] + r[-13][i])
+ 496*(r[14][i] + r[-14][i])
- 32*(r[15][i] + r[-15][i])
+ (r[16][i] + r[-16][i])
+ 601080390*r0[i]
- 393643732052805521130158146191360000000*r34[i]
) // 263130836933693530167218012160000000 for i in range(len(r0))]
r30 = [(145422675*(r[1][i] + r[-1][i])
- 119759850*(r[2][i] + r[-2][i])
+ 86493225*(r[3][i] + r[-3][i])
- 54627300*(r[4][i] + r[-4][i])
+ 30045015*(r[5][i] + r[-5][i])
- 14307150*(r[6][i] + r[-6][i])
+ 5852925*(r[7][i] + r[-7][i])
- 2035800*(r[8][i] + r[-8][i])
+ 593775*(r[9][i] + r[-9][i])
- 142506*(r[10][i] + r[-10][i])
+ 27405*(r[11][i] + r[-11][i])
- 4060*(r[12][i] + r[-12][i])
+ 435*(r[13][i] + r[-13][i])
- 30*(r[14][i] + r[-14][i])
+ (r[15][i] + r[-15][i])
- 155117520*r0[i]
- 328913546167116912709022515200000000*r32[i]
- 227575282593028191903372678266880000000*r34[i]
) // 265252859812191058636308480000000 for i in range(len(r0))]
r28 = [(-37442160*(r[1][i] + r[-1][i])
+ 30421755*(r[2][i] + r[-2][i])
- 21474180*(r[3][i] + r[-3][i])
+ 13123110*(r[4][i] + r[-4][i])
- 6906900*(r[5][i] + r[-5][i])
+ 3108105*(r[6][i] + r[-6][i])
- 1184040*(r[7][i] + r[-7][i])
+ 376740*(r[8][i] + r[-8][i])
- 98280*(r[9][i] + r[-9][i])
+ 20475*(r[10][i] + r[-10][i])
- 3276*(r[11][i] + r[-11][i])
+ 378*(r[12][i] + r[-12][i])
- 28*(r[13][i] + r[-13][i])
+ (r[14][i] + r[-14][i])
+ 40116600*r0[i]
- 309461669780889568409026560000000*r30[i]
- 176516936443019409820508749824000000*r32[i]
- 74833313645455216256514439249920000000*r34[i]
) // 304888344611713860501504000000 for i in range(len(r0))]
r26 = [(9657700*(r[1][i] + r[-1][i])
- 7726160*(r[2][i] + r[-2][i])
+ 5311735*(r[3][i] + r[-3][i])
- 3124550*(r[4][i] + r[-4][i])
+ 1562275*(r[5][i] + r[-5][i])
- 657800*(r[6][i] + r[-6][i])
+ 230230*(r[7][i] + r[-7][i])
- 65780*(r[8][i] + r[-8][i])
+ 14950*(r[9][i] + r[-9][i])
- 2600*(r[10][i] + r[-10][i])
+ 325*(r[11][i] + r[-11][i])
- 26*(r[12][i] + r[-12][i])
+ (r[13][i] + r[-13][i])
- 10400600*r0[i]
- 330295706662690015543296000000*r28[i]
- 153257207891488167212089344000000*r30[i]
- 53222214421459539592188788736000000*r32[i]
- 15436506593303376230082373484544000000*r34[i]
) // 403291461126605635584000000 for i in range(len(r0))]
r24 = [(-2496144*(r[1][i] + r[-1][i])
+ 1961256*(r[2][i] + r[-2][i])
- 1307504*(r[3][i] + r[-3][i])
+ 735471*(r[4][i] + r[-4][i])
- 346104*(r[5][i] + r[-5][i])
+ 134596*(r[6][i] + r[-6][i])
- 42504*(r[7][i] + r[-7][i])
+ 10626*(r[8][i] + r[-8][i])
- 2024*(r[9][i] + r[-9][i])
+ 276*(r[10][i] + r[-10][i])
- 24*(r[11][i] + r[-11][i])
+ (r[12][i] + r[-12][i])
+ 2704156*r0[i]
- 403291461126605635584000000*r26[i]
- 149903436100759314746572800000*r28[i]
- 42033455827381598974377984000000*r30[i]
- 9910695932425713906157643366400000*r32[i]
- 2078962023961017163954848006144000000*r34[i]
) // 620448401733239439360000 for i in range(len(r0))]
r22 = [(646646*(r[1][i] + r[-1][i])
- 497420*(r[2][i] + r[-2][i])
+ 319770*(r[3][i] + r[-3][i])
- 170544*(r[4][i] + r[-4][i])
+ 74613*(r[5][i] + r[-5][i])
- 26334*(r[6][i] + r[-6][i])
+ 7315*(r[7][i] + r[-7][i])
- 1540*(r[8][i] + r[-8][i])
+ 231*(r[9][i] + r[-9][i])
- 22*(r[10][i] + r[-10][i])
+ (r[11][i] + r[-11][i])
- 705432*r0[i]
- 568744368255469486080000*r24[i]
- 166357727714724824678400000*r26[i]
- 37042320704478727628390400000*r28[i]
- 6988909951599209517839155200000*r30[i]
- 1180836611760352104108962611200000*r32[i]
- 184607985589364774573429361868800000*r34[i]
) // 1124000727777607680000 for i in range(len(r0))]
r20 = [(-167960*(r[1][i] + r[-1][i])
+ 125970*(r[2][i] + r[-2][i])
- 77520*(r[3][i] + r[-3][i])
+ 38760*(r[4][i] + r[-4][i])
- 15504*(r[5][i] + r[-5][i])
+ 4845*(r[6][i] + r[-6][i])
- 1140*(r[7][i] + r[-7][i])
+ 190*(r[8][i] + r[-8][i])
- 20*(r[9][i] + r[-9][i])
+ (r[10][i] + r[-10][i])
+ 184756*r0[i]
- 936667273148006400000*r22[i]
- 211124803367560642560000*r24[i]
- 36608302274885332992000000*r26[i]
- 5425950533240873322086400000*r28[i]
- 725494605231272191451136000000*r30[i]
- 90317652741043657957240012800000*r32[i]
- 10681064948020015063470219264000000*r34[i]
) // 2432902008176640000 for i in range(len(r0))]
r18 = [(43758*(r[1][i] + r[-1][i])
- 31824*(r[2][i] + r[-2][i])
+ 18564*(r[3][i] + r[-3][i])
- 8568*(r[4][i] + r[-4][i])
+ 3060*(r[5][i] + r[-5][i])
- 816*(r[6][i] + r[-6][i])
+ 153*(r[7][i] + r[-7][i])
- 18*(r[8][i] + r[-8][i])
+ (r[9][i] + r[-9][i])
- 48620*r0[i]
- 1824676506132480000*r20[i]
- 309100200138842112000*r22[i]
- 40778478784550707200000*r24[i]
- 4645053436190368481280000*r26[i]
- 481314610282065419059200000*r28[i]
- 46758400573464312663490560000*r30[i]
- 4340262299778024388805836800000*r32[i]
- 389810850996416354285601300480000*r34[i]
) // 6402373705728000 for i in range(len(r0))]
r16 = [(-11440*(r[1][i] + r[-1][i])
+ 8008*(r[2][i] + r[-2][i])
- 4368*(r[3][i] + r[-3][i])
+ 1820*(r[4][i] + r[-4][i])
- 560*(r[5][i] + r[-5][i])
+ 120*(r[6][i] + r[-6][i])
- 16*(r[7][i] + r[-7][i])
+ (r[8][i] + r[-8][i])
+ 12870*r0[i]
- 4268249137152000*r18[i]
- 527128768438272000*r20[i]
- 51442361350668288000*r22[i]
- 4385609982489415680000*r24[i]
- 343350594609952849920000*r26[i]
- 25398422028160175554560000*r28[i]
- 1806640043553643996938240000*r30[i]
- 124998708216981630040289280000*r32[i]
- 8477574188991756975915909120000*r34[i]
) // 20922789888000 for i in range(len(r0))]
r14 = [(3003*(r[1][i] + r[-1][i])
- 2002*(r[2][i] + r[-2][i])
+ 1001*(r[3][i] + r[-3][i])
- 364*(r[4][i] + r[-4][i])
+ 91*(r[5][i] + r[-5][i])
- 14*(r[6][i] + r[-6][i])
+ (r[7][i] + r[-7][i])
- 3432*r0[i]
- 12204960768000*r16[i]
- 1058170098585600*r18[i]
- 73775500710912000*r20[i]
- 4555411900194355200*r22[i]
- 261131482210959360000*r24[i]
- 14266599888013304832000*r26[i]
- 754754307297469839360000*r28[i]
- 39057272623118392651008000*r30[i]
- 1990236929603886055572480000*r32[i]
- 100317304785653440333283635200*r34[i]
) // 87178291200 for i in range(len(r0))]
r12 = [(-792*(r[1][i] + r[-1][i])
+ 495*(r[2][i] + r[-2][i])
- 220*(r[3][i] + r[-3][i])
+ 66*(r[4][i] + r[-4][i])
- 12*(r[5][i] + r[-5][i])
+ (r[6][i] + r[-6][i])
+ 924*r0[i]
- 43589145600*r14[i]
- 2528170444800*r16[i]
- 120467944396800*r18[i]
- 5167100908569600*r20[i]
- 208331313744153600*r22[i]
- 8083281646573056000*r24[i]
- 305994026290208256000*r26[i]
- 11397316294188849024000*r28[i]
- 419948192698268217984000*r30[i]
- 15360962830016613243033600*r32[i]
- 559092713482449420732057600*r34[i]
) // 479001600 for i in range(len(r0))]
r10 = [(210*(r[1][i] + r[-1][i])
- 120*(r[2][i] + r[-2][i])
+ 45*(r[3][i] + r[-3][i])
- 10*(r[4][i] + r[-4][i])
+ (r[5][i] + r[-5][i])
- 252*r0[i]
- 199584000*r12[i]
- 7264857600*r14[i]
- 223134912000*r16[i]
- 6289809926400*r18[i]
- 169058189664000*r20[i]
- 4419351149875200*r22[i]
- 113605204648320000*r24[i]
- 2890388998040544000*r26[i]
- 73066712935376160000*r28[i]
- 1839605249083010572800*r30[i]
- 46197360620085939264000*r32[i]
- 1158251761107990889401600*r34[i]
) // 3628800 for i in range(len(r0))]
r8 = [(-56*(r[1][i] + r[-1][i])
+ 28*(r[2][i] + r[-2][i])
- 8*(r[3][i] + r[-3][i])
+ (r[4][i] + r[-4][i])
+ 70*r0[i]
- 1209600*r10[i]
- 25280640*r12[i]
- 461260800*r14[i]
- 7904856960*r16[i]
- 131254905600*r18[i]
- 2143293425280*r20[i]
- 34682510016000*r22[i]
- 558432020361600*r24[i]
- 8966533159584000*r26[i]
- 143749174428961920*r28[i]
- 2302548811229721600*r30[i]
- 36863840064915642240*r32[i]
- 590028976413583660800*r34[i]
) // 40320 for i in range(len(r0))]
r6 = [(15*(r[1][i] + r[-1][i])
- 6*(r[2][i] + r[-2][i])
+ (r[3][i] + r[-3][i])
- 20*r0[i]
- 10080*r8[i]
- 105840*r10[i]
- 1013760*r12[i]
- 9369360*r14[i]
- 85307040*r16[i]
- 771695280*r18[i]
- 6960985920*r20[i]
- 62711787600*r22[i]
- 564657746400*r24[i]
- 5082926350320*r26[i]
- 45750363684480*r28[i]
- 411769379287440*r30[i]
- 3705988838096160*r32[i]
- 33354157240902960*r34[i]
) // 720 for i in range(len(r0))]
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
- 504*r8[i]
- 2040*r10[i]
- 8184*r12[i]
- 32760*r14[i]
- 131064*r16[i]
- 524280*r18[i]
- 2097144*r20[i]
- 8388600*r22[i]
- 33554424*r24[i]
- 134217720*r26[i]
- 536870904*r28[i]
- 2147483640*r30[i]
- 8589934584*r32[i]
- 34359738360*r34[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
- 2*r8[i]
- 2*r10[i]
- 2*r12[i]
- 2*r14[i]
- 2*r16[i]
- 2*r18[i]
- 2*r20[i]
- 2*r22[i]
- 2*r24[i]
- 2*r26[i]
- 2*r28[i]
- 2*r30[i]
- 2*r32[i]
- 2*r34[i]
) // 2 for i in range(len(r0))]
r33 = [(129644790*r[1][i]
- 218349120*r[2][i]
+ 245642760*r[3][i]
- 218349120*r[4][i]
+ 161280600*r[5][i]
- 100975680*r[6][i]
+ 53993940*r[7][i]
- 24682944*r[8][i]
+ 9612108*r[9][i]
- 3164480*r[10][i]
+ 870232*r[11][i]
- 196416*r[12][i]
+ 35464*r[13][i]
- 4928*r[14][i]
+ 495*r[15][i]
- 32*r[16][i]
+ r[17][i]
- 35357670*r0[i]
+ 19389690*r2[i]
- 44796870*r4[i]
+ 233344890*r6[i]
- 2227139910*r8[i]
+ 34903389690*r10[i]
- 839988260550*r12[i]
+ 29734601940090*r14[i]
- 1506293149214790*r16[i]
+ 107487540061668090*r18[i]
- 10743535525710258630*r20[i]
+ 1511267716903778445690*r22[i]
- 304525956073869018848070*r24[i]
+ 91234873454404063067344890*r26[i]
- 43747586259736794619504039110*r28[i]
+ 39574917458915050445099774637690*r30[i]
- 120523981455993504966525708346887750*r32[i]
- 408775192473644376465790167368394203910*r34[i]
) // 8683317618811886495518194401280000000 for i in range(len(r0))]
r31 = [(-35357670*r[1][i]
+ 58929450*r[2][i]
- 65132550*r[3][i]
+ 56448210*r[4][i]
- 40320150*r[5][i]
+ 24192090*r[6][i]
- 12271350*r[7][i]
+ 5259150*r[8][i]
- 1893294*r[9][i]
+ 566370*r[10][i]
- 138446*r[11][i]
+ 26970*r[12][i]
- 4030*r[13][i]
+ 434*r[14][i]
- 30*r[15][i]
+ r[16][i]
+ 9694845*r0[i]
- 5348880*r2[i]
+ 12480720*r4[i]
- 65969520*r6[i]
+ 642563280*r8[i]
- 10347602160*r10[i]
+ 258040917840*r12[i]
- 9564008626800*r14[i]
+ 514021079720400*r16[i]
- 39590373677587440*r18[i]
+ 4371353677873146960*r20[i]
- 701971899866535028080*r22[i]
+ 169737570795219895373520*r24[i]
- 66396273378844288679892720*r26[i]
+ 49448835121192219782326176080*r28[i]
- 124963193751534047864734415925360*r30[i]
- 354113410826574103722030528083469360*r32[i]
- 12301366626650172535317442068480000000*r33[i]
- 372225904019072507165665501545458070000*r34[i]
) // 8222838654177922817725562880000000 for i in range(len(r0))]
r29 = [(9694845*r[1][i]
- 15967980*r[2][i]
+ 17298645*r[3][i]
- 14567280*r[4][i]
+ 10015005*r[5][i]
- 5722860*r[6][i]
+ 2731365*r[7][i]
- 1085760*r[8][i]
+ 356265*r[9][i]
- 95004*r[10][i]
+ 20097*r[11][i]
- 3248*r[12][i]
+ 377*r[13][i]
- 28*r[14][i]
+ r[15][i]
- 2674440*r0[i]
+ 1485800*r2[i]
- 3506488*r4[i]
+ 18850280*r6[i]
- 188004088*r8[i]
+ 3125835560*r10[i]
- 81314498488*r12[i]
+ 3185384180840*r14[i]
- 184064268909688*r16[i]
+ 15598375633694120*r18[i]
- 1958105850969957688*r20[i]
+ 375744491571024583400*r22[i]
- 118117302690774819242488*r24[i]
+ 71447614092662750198256680*r26[i]
- 147980747895225006590333244088*r28[i]
- 346368637877614395127589803878040*r30[i]
- 10963784872237230423634083840000000*r31[i]
- 302766527792977996357877082103322488*r32[i]
- 7585842753100939730112422608896000000*r33[i]
- 176553572119721839407097582006071612760*r34[i]
) // 8841761993739701954543616000000 for i in range(len(r0))]
r27 = [(-2674440*r[1][i]
+ 4345965*r[2][i]
- 4601610*r[3][i]
+ 3749460*r[4][i]
- 2466750*r[5][i]
+ 1332045*r[6][i]
- 592020*r[7][i]
+ 215280*r[8][i]
- 63180*r[9][i]
+ 14625*r[10][i]
- 2574*r[11][i]
+ 324*r[12][i]
- 26*r[13][i]
+ r[14][i]
+ 742900*r0[i]
- 416024*r2[i]
+ 994840*r4[i]
- 5454824*r6[i]
+ 55944280*r8[i]
- 966290024*r10[i]
+ 26454613720*r12[i]
- 1109329691624*r14[i]
+ 70212852387160*r16[i]
- 6733670404619624*r18[i]
+ 1005318113348848600*r20[i]
- 249581050854994274024*r22[i]
+ 120719220687299365182040*r24[i]
- 202039976682357297272094824*r26[i]
- 385557844336439370252173428520*r28[i]
- 11052202492174627443179520000000*r29[i]
- 276888650579451671741587901762024*r30[i]
- 6304176301536407493589598208000000*r31[i]
- 133535841584115505205141919375399080*r32[i]
- 2672618344480543437732658544640000000*r33[i]
- 51095126335993498323380094454901195624*r34[i]
) // 10888869450418352160768000000 for i in range(len(r0))]
r25 = [(742900*r[1][i]
- 1188640*r[2][i]
+ 1225785*r[3][i]
- 961400*r[4][i]
+ 600875*r[5][i]
- 303600*r[6][i]
+ 123970*r[7][i]
- 40480*r[8][i]
+ 10350*r[9][i]
- 2000*r[10][i]
+ 275*r[11][i]
- 24*r[12][i]
+ r[13][i]
- 208012*r0[i]
+ 117572*r2[i]
- 285532*r4[i]
+ 1602692*r6[i]
- 16996252*r8[i]
+ 307475012*r10[i]
- 8966430172*r12[i]
+ 409745686532*r14[i]
- 29195711499292*r16[i]
+ 3312133208909252*r18[i]
- 636215671041835612*r20[i]
+ 241648300078174135172*r22[i]
- 321511316149669476991132*r24[i]
- 492817676505266866078123708*r26[i]
- 12703681025488077520896000000*r27[i]
- 286779648275654636997381637852*r28[i]
- 5894507995826467969695744000000*r29[i]
- 112914054231542703053832892635388*r30[i]
- 2047008246979213061238030336000000*r31[i]
- 35501568925223446300815211192767772*r32[i]
- 593711792050129855003168210944000000*r33[i]
- 9632134956680435093368218113996247868*r34[i]
) // 15511210043330985984000000 for i in range(len(r0))]
r23 = [(-208012*r[1][i]
+ 326876*r[2][i]
- 326876*r[3][i]
+ 245157*r[4][i]
- 144210*r[5][i]
+ 67298*r[6][i]
- 24794*r[7][i]
+ 7084*r[8][i]
- 1518*r[9][i]
+ 230*r[10][i]
- 22*r[11][i]
+ r[12][i]
+ 58786*r0[i]
- 33592*r2[i]
+ 83096*r4[i]
- 479752*r6[i]
+ 5299736*r8[i]
- 101549512*r10[i]
+ 3208453976*r12[i]
- 164071220872*r14[i]
+ 13743680753816*r16[i]
- 1993276972245832*r18[i]
+ 581947914140407256*r20[i]
- 603916464771468176392*r22[i]
- 730803773459954540777704*r24[i]
- 16803810880275234816000000*r25[i]
- 339155768243774227716964552*r26[i]
- 6245976504198304781107200000*r27[i]
- 107413822788261782335458993064*r28[i]
- 1751393992807566623932416000000*r29[i]
- 27365156266821215807862420562312*r30[i]
- 412945663851071412756568473600000*r31[i]
- 6053949680529454447550745704030824*r32[i]
- 86623417665042381831452000256000000*r33[i]
- 1214146547565910406028014931410521672*r34[i]
) // 25852016738884976640000 for i in range(len(r0))]
r21 = [(58786*r[1][i]
- 90440*r[2][i]
+ 87210*r[3][i]
- 62016*r[4][i]
+ 33915*r[5][i]
- 14364*r[6][i]
+ 4655*r[7][i]
- 1120*r[8][i]
+ 189*r[9][i]
- 20*r[10][i]
+ r[11][i]
- 16796*r0[i]
+ 9724*r2[i]
- 24596*r4[i]
+ 147004*r6[i]
- 1708916*r8[i]
+ 35240284*r10[i]
- 1237329236*r12[i]
+ 73853629564*r14[i]
- 7850527669556*r16[i]
+ 1717351379730844*r18[i]
- 1359124435588313876*r20[i]
- 1272410676942417239876*r22[i]
- 25852016738884976640000*r23[i]
- 462292539259962003646196*r24[i]
- 7561714896123855667200000*r25[i]
- 115761644587269354830466596*r26[i]
- 1683741850203578528563200000*r27[i]
- 23512975860299444963550050516*r28[i]
- 317677725072691341719961600000*r29[i]
- 4176614976496441445095962733316*r30[i]
- 53674391443652368368589209600000*r31[i]
- 676635955671282540673335079110836*r32[i]
- 8391272072243853389701334630400000*r33[i]
- 102611708232289325546408008313624036*r34[i]
) // 51090942171709440000 for i in range(len(r0))]
r19 = [(-16796*r[1][i]
+ 25194*r[2][i]
- 23256*r[3][i]
+ 15504*r[4][i]
- 7752*r[5][i]
+ 2907*r[6][i]
- 798*r[7][i]
+ 152*r[8][i]
- 18*r[9][i]
+ r[10][i]
+ 4862*r0[i]
- 2860*r2[i]
+ 7436*r4[i]
- 46420*r6[i]
+ 576236*r8[i]
- 13098580*r10[i]
+ 532310636*r12[i]
- 39968611540*r14[i]
+ 6350631494636*r16[i]
- 3730771315561300*r18[i]
- 2637991952943407764*r20[i]
- 46833363657400320000*r21[i]
- 734121065118879803860*r22[i]
- 10556240168378032128000*r23[i]
- 142438684135271315212564*r24[i]
- 1830415113744266649600000*r25[i]
- 22632897298190126259675220*r26[i]
- 271297526662043666104320000*r27[i]
- 3170344993810020486920015764*r28[i]
- 36274730261563609572556800000*r29[i]
- 407775103607650299563627591380*r30[i]
- 4515882637052182897862000640000*r31[i]
- 49377994276343186011748723193364*r32[i]
- 534053247401000753173510963200000*r33[i]
- 5722063606154183864914875339648340*r34[i]
) // 121645100408832000 for i in range(len(r0))]
r17 = [(4862*r[1][i]
- 7072*r[2][i]
+ 6188*r[3][i]
- 3808*r[4][i]
+ 1700*r[5][i]
- 544*r[6][i]
+ 119*r[7][i]
- 16*r[8][i]
+ r[9][i]
- 1430*r0[i]
+ 858*r2[i]
- 2310*r4[i]
+ 15258*r6[i]
- 206790*r8[i]
+ 5386458*r10[i]
- 272513670*r12[i]
+ 30255826458*r14[i]
- 12765597850950*r16[i]
- 6622557957272742*r18[i]
- 101370917007360000*r19[i]
- 1375210145685786630*r20[i]
- 17172233341046784000*r21[i]
- 201832098313986359142*r22[i]
- 2265471043586150400000*r23[i]
- 24529324224160803328710*r24[i]
- 258058524232798248960000*r25[i]
- 2652208374242713043720742*r26[i]
- 26739700571225856614400000*r27[i]
- 265323404171486113659725190*r28[i]
- 2597688920748017370193920000*r29[i]
- 25147613788240222384169485542*r30[i]
- 241125683321001354933657600000*r31[i]
- 2293170112631184981695915264070*r32[i]
- 21656158388689797460311183360000*r33[i]
- 203283794784841444836991831621542*r34[i]
) // 355687428096000 for i in range(len(r0))]
r15 = [(-1430*r[1][i]
+ 2002*r[2][i]
- 1638*r[3][i]
+ 910*r[4][i]
- 350*r[5][i]
+ 90*r[6][i]
- 14*r[7][i]
+ r[8][i]
+ 429*r0[i]
- 264*r2[i]
+ 744*r4[i]
- 5304*r6[i]
+ 81384*r8[i]
- 2605944*r10[i]
+ 192387624*r12[i]
- 55942352184*r14[i]
- 20546119600536*r16[i]
- 266765571072000*r17[i]
- 3083760849804024*r18[i]
- 32945548027392000*r19[i]
- 332500281299403096*r20[i]
- 3215147584416768000*r21[i]
- 30076927429146721464*r22[i]
- 274100623905588480000*r23[i]
- 2446077617962088140056*r24[i]
- 21459412163122053120000*r25[i]
- 185641639183185136464504*r26[i]
- 1587401376760010972160000*r27[i]
- 13442713420403849918131416*r28[i]
- 112915002722102749808640000*r29[i]
- 941961013910760913890393144*r30[i]
- 7812419263561351877518080000*r31[i]
- 64474322285718607792730497176*r32[i]
- 529848386811984810994744320000*r33[i]
- 4338547620121893769542630267384*r34[i]
) // 1307674368000 for i in range(len(r0))]
r13 = [(429*r[1][i]
- 572*r[2][i]
+ 429*r[3][i]
- 208*r[4][i]
+ 65*r[5][i]
- 12*r[6][i]
+ r[7][i]
- 132*r0[i]
+ 84*r2[i]
- 252*r4[i]
+ 2004*r6[i]
- 37212*r8[i]
+ 1710324*r10[i]
- 325024572*r12[i]
- 80789566956*r14[i]
- 871782912000*r15[i]
- 8422900930332*r16[i]
- 75583578470400*r17[i]
- 643521842437836*r18[i]
- 5269678622208000*r19[i]
- 41890044885642492*r20[i]
- 325386564299596800*r21[i]
- 2481686964269990316*r22[i]
- 18652248729354240000*r23[i]
- 138536531588626169052*r24[i]
- 1019042849143807488000*r25[i]
- 7436421488952386592396*r26[i]
- 53911021949819274240000*r27[i]
- 388701690499592948238012*r28[i]
- 2789805187365599475072000*r29[i]
- 19946749502047187160692076*r30[i]
- 142159780685991861112320000*r31[i]
- 1010433303980489860989897372*r32[i]
- 7165521770403817166663116800*r33[i]
- 50716588034439244118483617356*r34[i]
) // 6227020800 for i in range(len(r0))]
r11 = [(-132*r[1][i]
+ 165*r[2][i]
- 110*r[3][i]
+ 44*r[4][i]
- 10*r[5][i]
+ r[6][i]
+ 42*r0[i]
- 28*r2[i]
+ 92*r4[i]
- 868*r6[i]
+ 22652*r8[i]
- 2620708*r10[i]
- 415790788*r12[i]
- 3632428800*r13[i]
- 28616744548*r14[i]
- 210680870400*r15[i]
- 1479485236228*r16[i]
- 10038995366400*r17[i]
- 66394067988388*r18[i]
- 430591742380800*r19[i]
- 2750479262009668*r20[i]
- 17360942812012800*r21[i]
- 108550450893568228*r22[i]
- 673606803881088000*r23[i]
- 4154688725062207108*r24[i]
- 25499502190850688000*r25[i]
- 155878445775166700068*r26[i]
- 949776357849070752000*r27[i]
- 5771581202353414724548*r28[i]
- 34995682724855684832000*r29[i]
- 211811399872933910999908*r30[i]
- 1280080235834717770252800*r31[i]
- 7726641919200262371657988*r32[i]
- 46591059456870785061004800*r33[i]
- 280704018540064430354883748*r34[i]
) // 39916800 for i in range(len(r0))]
r9 = [(42*r[1][i]
- 48*r[2][i]
+ 27*r[3][i]
- 8*r[4][i]
+ r[5][i]
- 14*r0[i]
+ 10*r2[i]
- 38*r4[i]
+ 490*r6[i]
- 31238*r8[i]
- 2922230*r10[i]
- 19958400*r11[i]
- 124075238*r12[i]
- 726485760*r13[i]
- 4084385750*r14[i]
- 22313491200*r15[i]
- 119387268038*r16[i]
- 628980992640*r17[i]
- 3275389222070*r18[i]
- 16905818966400*r19[i]
- 86665431465638*r20[i]
- 441935114987520*r21[i]
- 2244295389943190*r22[i]
- 11360520464832000*r23[i]
- 57360469753884038*r24[i]
- 289038899804054400*r25[i]
- 1454155949521941110*r26[i]
- 7306671293537616000*r27[i]
- 36677059892827099238*r28[i]
- 183960524908301057280*r29[i]
- 922104761587650687830*r30[i]
- 4619736062008593926400*r31[i]
- 23135540444136227047238*r32[i]
- 115825176110799088940160*r33[i]
- 579715876176320506935350*r34[i]
) // 362880 for i in range(len(r0))]
r7 = [(-14*r[1][i]
+ 14*r[2][i]
- 6*r[3][i]
+ r[4][i]
+ 5*r0[i]
- 4*r2[i]
+ 20*r4[i]
- 604*r6[i]
- 29740*r8[i]
- 151200*r9[i]
- 708604*r10[i]
- 3160080*r11[i]
- 13645900*r12[i]
- 57657600*r13[i]
- 239967004*r14[i]
- 988107120*r15[i]
- 4037604460*r16[i]
- 16406863200*r17[i]
- 66398623804*r18[i]
- 267911678160*r19[i]
- 1078605601420*r20[i]
- 4335313752000*r21[i]
- 17403958407004*r22[i]
- 69804002545200*r23[i]
- 279780634372780*r24[i]
- 1120816644948000*r25[i]
- 4488349371924604*r26[i]
- 17968646803620240*r27[i]
- 71920337041294540*r28[i]
- 287818601403715200*r29[i]
- 1151686172846664604*r30[i]
- 4607980008114455280*r31[i]
- 18435626012705982700*r32[i]
- 73753622051697957600*r33[i]
- 295047842329672995004*r34[i]
) // 5040 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
- 1680*r7[i]
- 5542*r8[i]
- 17640*r9[i]
- 54958*r10[i]
- 168960*r11[i]
- 515062*r12[i]
- 1561560*r13[i]
- 4717438*r14[i]
- 14217840*r15[i]
- 42784582*r16[i]
- 128615880*r17[i]
- 386371918*r18[i]
- 1160164320*r19[i]
- 3482590102*r20[i]
- 10451964600*r21[i]
- 31364282398*r22[i]
- 94109624400*r23[i]
- 282362427622*r24[i]
- 847154391720*r25[i]
- 2541597392878*r26[i]
- 7625060614080*r27[i]
- 22875718713142*r28[i]
- 68628229881240*r29[i]
- 205886837127358*r30[i]
- 617664806349360*r31[i]
- 1853003008982662*r32[i]
- 5559026206817160*r33[i]
- 16677112980189838*r34[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
- 126*r7[i]
- 254*r8[i]
- 510*r9[i]
- 1022*r10[i]
- 2046*r11[i]
- 4094*r12[i]
- 8190*r13[i]
- 16382*r14[i]
- 32766*r15[i]
- 65534*r16[i]
- 131070*r17[i]
- 262142*r18[i]
- 524286*r19[i]
- 1048574*r20[i]
- 2097150*r21[i]
- 4194302*r22[i]
- 8388606*r23[i]
- 16777214*r24[i]
- 33554430*r25[i]
- 67108862*r26[i]
- 134217726*r27[i]
- 268435454*r28[i]
- 536870910*r29[i]
- 1073741822*r30[i]
- 2147483646*r31[i]
- 4294967294*r32[i]
- 8589934590*r33[i]
- 17179869182*r34[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
- r7[i]
- r8[i]
- r9[i]
- r10[i]
- r11[i]
- r12[i]
- r13[i]
- r14[i]
- r15[i]
- r16[i]
- r17[i]
- r18[i]
- r19[i]
- r20[i]
- r21[i]
- r22[i]
- r23[i]
- r24[i]
- r25[i]
- r26[i]
- r27[i]
- r28[i]
- r29[i]
- r30[i]
- r31[i]
- r32[i]
- r33[i]
- r34[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34)
def natural_interpolate_19(r):
r0 = r[0]
r36 = r['infinity']
r34 = [(2203961430*(r[1][i] + r[-1][i])
- 1855967520*(r[2][i] + r[-2][i])
+ 1391975640*(r[3][i] + r[-3][i])
- 927983760*(r[4][i] + r[-4][i])
+ 548354040*(r[5][i] + r[-5][i])
- 286097760*(r[6][i] + r[-6][i])
+ 131128140*(r[7][i] + r[-7][i])
- 52451256*(r[8][i] + r[-8][i])
+ 18156204*(r[9][i] + r[-9][i])
- 5379616*(r[10][i] + r[-10][i])
+ 1344904*(r[11][i] + r[-11][i])
- 278256*(r[12][i] + r[-12][i])
+ 46376*(r[13][i] + r[-13][i])
- 5984*(r[14][i] + r[-14][i])
+ 561*(r[15][i] + r[-15][i])
- 34*(r[16][i] + r[-16][i])
+ (r[17][i] + r[-17][i])
- 2333606220*r0[i]
- 526990546285693391412999218213683200000000*r36[i]
) // 295232799039604140847618609643520000000 for i in range(len(r0))]
r32 = [(-565722720*(r[1][i] + r[-1][i])
+ 471435600*(r[2][i] + r[-2][i])
- 347373600*(r[3][i] + r[-3][i])
+ 225792840*(r[4][i] + r[-4][i])
- 129024480*(r[5][i] + r[-5][i])
+ 64512240*(r[6][i] + r[-6][i])
- 28048800*(r[7][i] + r[-7][i])
+ 10518300*(r[8][i] + r[-8][i])
- 3365856*(r[9][i] + r[-9][i])
+ 906192*(r[10][i] + r[-10][i])
- 201376*(r[11][i] + r[-11][i])
+ 35960*(r[12][i] + r[-12][i])
- 4960*(r[13][i] + r[-13][i])
+ 496*(r[14][i] + r[-14][i])
- 32*(r[15][i] + r[-15][i])
+ (r[16][i] + r[-16][i])
+ 601080390*r0[i]
- 393643732052805521130158146191360000000*r34[i]
- 326527475737802179777466182265733120000000*r36[i]
) // 263130836933693530167218012160000000 for i in range(len(r0))]
r30 = [(145422675*(r[1][i] + r[-1][i])
- 119759850*(r[2][i] + r[-2][i])
+ 86493225*(r[3][i] + r[-3][i])
- 54627300*(r[4][i] + r[-4][i])
+ 30045015*(r[5][i] + r[-5][i])
- 14307150*(r[6][i] + r[-6][i])
+ 5852925*(r[7][i] + r[-7][i])
- 2035800*(r[8][i] + r[-8][i])
+ 593775*(r[9][i] + r[-9][i])
- 142506*(r[10][i] + r[-10][i])
+ 27405*(r[11][i] + r[-11][i])
- 4060*(r[12][i] + r[-12][i])
+ 435*(r[13][i] + r[-13][i])
- 30*(r[14][i] + r[-14][i])
+ (r[15][i] + r[-15][i])
- 155117520*r0[i]
- 328913546167116912709022515200000000*r32[i]
- 227575282593028191903372678266880000000*r34[i]
- 116309421454977381321426414757478400000000*r36[i]
) // 265252859812191058636308480000000 for i in range(len(r0))]
r28 = [(-37442160*(r[1][i] + r[-1][i])
+ 30421755*(r[2][i] + r[-2][i])
- 21474180*(r[3][i] + r[-3][i])
+ 13123110*(r[4][i] + r[-4][i])
- 6906900*(r[5][i] + r[-5][i])
+ 3108105*(r[6][i] + r[-6][i])
- 1184040*(r[7][i] + r[-7][i])
+ 376740*(r[8][i] + r[-8][i])
- 98280*(r[9][i] + r[-9][i])
+ 20475*(r[10][i] + r[-10][i])
- 3276*(r[11][i] + r[-11][i])
+ 378*(r[12][i] + r[-12][i])
- 28*(r[13][i] + r[-13][i])
+ (r[14][i] + r[-14][i])
+ 40116600*r0[i]
- 309461669780889568409026560000000*r30[i]
- 176516936443019409820508749824000000*r32[i]
- 74833313645455216256514439249920000000*r34[i]
- 26337328459046574816219104447299584000000*r36[i]
) // 304888344611713860501504000000 for i in range(len(r0))]
r26 = [(9657700*(r[1][i] + r[-1][i])
- 7726160*(r[2][i] + r[-2][i])
+ 5311735*(r[3][i] + r[-3][i])
- 3124550*(r[4][i] + r[-4][i])
+ 1562275*(r[5][i] + r[-5][i])
- 657800*(r[6][i] + r[-6][i])
+ 230230*(r[7][i] + r[-7][i])
- 65780*(r[8][i] + r[-8][i])
+ 14950*(r[9][i] + r[-9][i])
- 2600*(r[10][i] + r[-10][i])
+ 325*(r[11][i] + r[-11][i])
- 26*(r[12][i] + r[-12][i])
+ (r[13][i] + r[-13][i])
- 10400600*r0[i]
- 330295706662690015543296000000*r28[i]
- 153257207891488167212089344000000*r30[i]
- 53222214421459539592188788736000000*r32[i]
- 15436506593303376230082373484544000000*r34[i]
- 3960094929842931739454572322881536000000*r36[i]
) // 403291461126605635584000000 for i in range(len(r0))]
r24 = [(-2496144*(r[1][i] + r[-1][i])
+ 1961256*(r[2][i] + r[-2][i])
- 1307504*(r[3][i] + r[-3][i])
+ 735471*(r[4][i] + r[-4][i])
- 346104*(r[5][i] + r[-5][i])
+ 134596*(r[6][i] + r[-6][i])
- 42504*(r[7][i] + r[-7][i])
+ 10626*(r[8][i] + r[-8][i])
- 2024*(r[9][i] + r[-9][i])
+ 276*(r[10][i] + r[-10][i])
- 24*(r[11][i] + r[-11][i])
+ (r[12][i] + r[-12][i])
+ 2704156*r0[i]
- 403291461126605635584000000*r26[i]
- 149903436100759314746572800000*r28[i]
- 42033455827381598974377984000000*r30[i]
- 9910695932425713906157643366400000*r32[i]
- 2078962023961017163954848006144000000*r34[i]
- 401274139495715827174031120636313600000*r36[i]
) // 620448401733239439360000 for i in range(len(r0))]
r22 = [(646646*(r[1][i] + r[-1][i])
- 497420*(r[2][i] + r[-2][i])
+ 319770*(r[3][i] + r[-3][i])
- 170544*(r[4][i] + r[-4][i])
+ 74613*(r[5][i] + r[-5][i])
- 26334*(r[6][i] + r[-6][i])
+ 7315*(r[7][i] + r[-7][i])
- 1540*(r[8][i] + r[-8][i])
+ 231*(r[9][i] + r[-9][i])
- 22*(r[10][i] + r[-10][i])
+ (r[11][i] + r[-11][i])
- 705432*r0[i]
- 568744368255469486080000*r24[i]
- 166357727714724824678400000*r26[i]
- 37042320704478727628390400000*r28[i]
- 6988909951599209517839155200000*r30[i]
- 1180836611760352104108962611200000*r32[i]
- 184607985589364774573429361868800000*r34[i]
- 27272218262298384682708194086092800000*r36[i]
) // 1124000727777607680000 for i in range(len(r0))]
r20 = [(-167960*(r[1][i] + r[-1][i])
+ 125970*(r[2][i] + r[-2][i])
- 77520*(r[3][i] + r[-3][i])
+ 38760*(r[4][i] + r[-4][i])
- 15504*(r[5][i] + r[-5][i])
+ 4845*(r[6][i] + r[-6][i])
- 1140*(r[7][i] + r[-7][i])
+ 190*(r[8][i] + r[-8][i])
- 20*(r[9][i] + r[-9][i])
+ (r[10][i] + r[-10][i])
+ 184756*r0[i]
- 936667273148006400000*r22[i]
- 211124803367560642560000*r24[i]
- 36608302274885332992000000*r26[i]
- 5425950533240873322086400000*r28[i]
- 725494605231272191451136000000*r30[i]
- 90317652741043657957240012800000*r32[i]
- 10681064948020015063470219264000000*r34[i]
- 1216234618180639720975550420582400000*r36[i]
) // 2432902008176640000 for i in range(len(r0))]
r18 = [(43758*(r[1][i] + r[-1][i])
- 31824*(r[2][i] + r[-2][i])
+ 18564*(r[3][i] + r[-3][i])
- 8568*(r[4][i] + r[-4][i])
+ 3060*(r[5][i] + r[-5][i])
- 816*(r[6][i] + r[-6][i])
+ 153*(r[7][i] + r[-7][i])
- 18*(r[8][i] + r[-8][i])
+ (r[9][i] + r[-9][i])
- 48620*r0[i]
- 1824676506132480000*r20[i]
- 309100200138842112000*r22[i]
- 40778478784550707200000*r24[i]
- 4645053436190368481280000*r26[i]
- 481314610282065419059200000*r28[i]
- 46758400573464312663490560000*r30[i]
- 4340262299778024388805836800000*r32[i]
- 389810850996416354285601300480000*r34[i]
- 34168816632541202331763973529600000*r36[i]
) // 6402373705728000 for i in range(len(r0))]
r16 = [(-11440*(r[1][i] + r[-1][i])
+ 8008*(r[2][i] + r[-2][i])
- 4368*(r[3][i] + r[-3][i])
+ 1820*(r[4][i] + r[-4][i])
- 560*(r[5][i] + r[-5][i])
+ 120*(r[6][i] + r[-6][i])
- 16*(r[7][i] + r[-7][i])
+ (r[8][i] + r[-8][i])
+ 12870*r0[i]
- 4268249137152000*r18[i]
- 527128768438272000*r20[i]
- 51442361350668288000*r22[i]
- 4385609982489415680000*r24[i]
- 343350594609952849920000*r26[i]
- 25398422028160175554560000*r28[i]
- 1806640043553643996938240000*r30[i]
- 124998708216981630040289280000*r32[i]
- 8477574188991756975915909120000*r34[i]
- 566640901244029272138606256128000*r36[i]
) // 20922789888000 for i in range(len(r0))]
r14 = [(3003*(r[1][i] + r[-1][i])
- 2002*(r[2][i] + r[-2][i])
+ 1001*(r[3][i] + r[-3][i])
- 364*(r[4][i] + r[-4][i])
+ 91*(r[5][i] + r[-5][i])
- 14*(r[6][i] + r[-6][i])
+ (r[7][i] + r[-7][i])
- 3432*r0[i]
- 12204960768000*r16[i]
- 1058170098585600*r18[i]
- 73775500710912000*r20[i]
- 4555411900194355200*r22[i]
- 261131482210959360000*r24[i]
- 14266599888013304832000*r26[i]
- 754754307297469839360000*r28[i]
- 39057272623118392651008000*r30[i]
- 1990236929603886055572480000*r32[i]
- 100317304785653440333283635200*r34[i]
- 5017302808350824370904132608000*r36[i]
) // 87178291200 for i in range(len(r0))]
r12 = [(-792*(r[1][i] + r[-1][i])
+ 495*(r[2][i] + r[-2][i])
- 220*(r[3][i] + r[-3][i])
+ 66*(r[4][i] + r[-4][i])
- 12*(r[5][i] + r[-5][i])
+ (r[6][i] + r[-6][i])
+ 924*r0[i]
- 43589145600*r14[i]
- 2528170444800*r16[i]
- 120467944396800*r18[i]
- 5167100908569600*r20[i]
- 208331313744153600*r22[i]
- 8083281646573056000*r24[i]
- 305994026290208256000*r26[i]
- 11397316294188849024000*r28[i]
- 419948192698268217984000*r30[i]
- 15360962830016613243033600*r32[i]
- 559092713482449420732057600*r34[i]
- 20280226917834433943755084800*r36[i]
) // 479001600 for i in range(len(r0))]
r10 = [(210*(r[1][i] + r[-1][i])
- 120*(r[2][i] + r[-2][i])
+ 45*(r[3][i] + r[-3][i])
- 10*(r[4][i] + r[-4][i])
+ (r[5][i] + r[-5][i])
- 252*r0[i]
- 199584000*r12[i]
- 7264857600*r14[i]
- 223134912000*r16[i]
- 6289809926400*r18[i]
- 169058189664000*r20[i]
- 4419351149875200*r22[i]
- 113605204648320000*r24[i]
- 2890388998040544000*r26[i]
- 73066712935376160000*r28[i]
- 1839605249083010572800*r30[i]
- 46197360620085939264000*r32[i]
- 1158251761107990889401600*r34[i]
- 29009396635576994764512000*r36[i]
) // 3628800 for i in range(len(r0))]
r8 = [(-56*(r[1][i] + r[-1][i])
+ 28*(r[2][i] + r[-2][i])
- 8*(r[3][i] + r[-3][i])
+ (r[4][i] + r[-4][i])
+ 70*r0[i]
- 1209600*r10[i]
- 25280640*r12[i]
- 461260800*r14[i]
- 7904856960*r16[i]
- 131254905600*r18[i]
- 2143293425280*r20[i]
- 34682510016000*r22[i]
- 558432020361600*r24[i]
- 8966533159584000*r26[i]
- 143749174428961920*r28[i]
- 2302548811229721600*r30[i]
- 36863840064915642240*r32[i]
- 590028976413583660800*r34[i]
- 9442331455422829138560*r36[i]
) // 40320 for i in range(len(r0))]
r6 = [(15*(r[1][i] + r[-1][i])
- 6*(r[2][i] + r[-2][i])
+ (r[3][i] + r[-3][i])
- 20*r0[i]
- 10080*r8[i]
- 105840*r10[i]
- 1013760*r12[i]
- 9369360*r14[i]
- 85307040*r16[i]
- 771695280*r18[i]
- 6960985920*r20[i]
- 62711787600*r22[i]
- 564657746400*r24[i]
- 5082926350320*r26[i]
- 45750363684480*r28[i]
- 411769379287440*r30[i]
- 3705988838096160*r32[i]
- 33354157240902960*r34[i]
- 300188445960277440*r36[i]
) // 720 for i in range(len(r0))]
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
- 504*r8[i]
- 2040*r10[i]
- 8184*r12[i]
- 32760*r14[i]
- 131064*r16[i]
- 524280*r18[i]
- 2097144*r20[i]
- 8388600*r22[i]
- 33554424*r24[i]
- 134217720*r26[i]
- 536870904*r28[i]
- 2147483640*r30[i]
- 8589934584*r32[i]
- 34359738360*r34[i]
- 137438953464*r36[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
- 2*r8[i]
- 2*r10[i]
- 2*r12[i]
- 2*r14[i]
- 2*r16[i]
- 2*r18[i]
- 2*r20[i]
- 2*r22[i]
- 2*r24[i]
- 2*r26[i]
- 2*r28[i]
- 2*r30[i]
- 2*r32[i]
- 2*r34[i]
- 2*r36[i]
) // 2 for i in range(len(r0))]
r35 = [(-477638700*r[1][i]
+ 811985790*r[2][i]
- 927983760*r[3][i]
+ 843621600*r[4][i]
- 641886000*r[5][i]
+ 417225900*r[6][i]
- 233646504*r[7][i]
+ 112971936*r[8][i]
- 47071640*r[9][i]
+ 16811300*r[10][i]
- 5101360*r[11][i]
+ 1298528*r[12][i]
- 272272*r[13][i]
+ 45815*r[14][i]
- 5950*r[15][i]
+ 560*r[16][i]
- 34*r[17][i]
+ r[18][i]
+ 129644790*r0[i]
- 70715340*r2[i]
+ 161960940*r4[i]
- 832930740*r6[i]
+ 7810859340*r8[i]
- 119578066740*r10[i]
+ 2791740107340*r12[i]
- 95062235276340*r14[i]
+ 4584012079172940*r16[i]
- 307268933913567540*r18[i]
+ 28355038085389144140*r20[i]
- 3597774935929125068340*r22[i]
+ 632729503874459828228940*r24[i]
- 157381528472579148083026740*r26[i]
+ 57577884185625191071239755340*r28[i]
- 33404393172944223690128125810740*r30[i]
+ 36271128388074981554067219056171340*r32[i]
- 131671692334895976886647813958596908340*r34[i]
- 529104107360143104505564190890974500955060*r36[i]
) // 10333147966386144929666651337523200000000 for i in range(len(r0))]
r33 = [(129644790*r[1][i]
- 218349120*r[2][i]
+ 245642760*r[3][i]
- 218349120*r[4][i]
+ 161280600*r[5][i]
- 100975680*r[6][i]
+ 53993940*r[7][i]
- 24682944*r[8][i]
+ 9612108*r[9][i]
- 3164480*r[10][i]
+ 870232*r[11][i]
- 196416*r[12][i]
+ 35464*r[13][i]
- 4928*r[14][i]
+ 495*r[15][i]
- 32*r[16][i]
+ r[17][i]
- 35357670*r0[i]
+ 19389690*r2[i]
- 44796870*r4[i]
+ 233344890*r6[i]
- 2227139910*r8[i]
+ 34903389690*r10[i]
- 839988260550*r12[i]
+ 29734601940090*r14[i]
- 1506293149214790*r16[i]
+ 107487540061668090*r18[i]
- 10743535525710258630*r20[i]
+ 1511267716903778445690*r22[i]
- 304525956073869018848070*r24[i]
+ 91234873454404063067344890*r26[i]
- 43747586259736794619504039110*r28[i]
+ 39574917458915050445099774637690*r30[i]
- 120523981455993504966525708346887750*r32[i]
- 408775192473644376465790167368394203910*r34[i]
- 15499721949579217394499977006284800000000*r35[i]
- 511206585269023792365556128001469646849990*r36[i]
) // 8683317618811886495518194401280000000 for i in range(len(r0))]
r31 = [(-35357670*r[1][i]
+ 58929450*r[2][i]
- 65132550*r[3][i]
+ 56448210*r[4][i]
- 40320150*r[5][i]
+ 24192090*r[6][i]
- 12271350*r[7][i]
+ 5259150*r[8][i]
- 1893294*r[9][i]
+ 566370*r[10][i]
- 138446*r[11][i]
+ 26970*r[12][i]
- 4030*r[13][i]
+ 434*r[14][i]
- 30*r[15][i]
+ r[16][i]
+ 9694845*r0[i]
- 5348880*r2[i]
+ 12480720*r4[i]
- 65969520*r6[i]
+ 642563280*r8[i]
- 10347602160*r10[i]
+ 258040917840*r12[i]
- 9564008626800*r14[i]
+ 514021079720400*r16[i]
- 39590373677587440*r18[i]
+ 4371353677873146960*r20[i]
- 701971899866535028080*r22[i]
+ 169737570795219895373520*r24[i]
- 66396273378844288679892720*r26[i]
+ 49448835121192219782326176080*r28[i]
- 124963193751534047864734415925360*r30[i]
- 354113410826574103722030528083469360*r32[i]
- 12301366626650172535317442068480000000*r33[i]
- 372225904019072507165665501545458070000*r34[i]
- 10203983616806318118045818195804160000000*r35[i]
- 259484653500223872483011119661283865786800*r36[i]
) // 8222838654177922817725562880000000 for i in range(len(r0))]
r29 = [(9694845*r[1][i]
- 15967980*r[2][i]
+ 17298645*r[3][i]
- 14567280*r[4][i]
+ 10015005*r[5][i]
- 5722860*r[6][i]
+ 2731365*r[7][i]
- 1085760*r[8][i]
+ 356265*r[9][i]
- 95004*r[10][i]
+ 20097*r[11][i]
- 3248*r[12][i]
+ 377*r[13][i]
- 28*r[14][i]
+ r[15][i]
- 2674440*r0[i]
+ 1485800*r2[i]
- 3506488*r4[i]
+ 18850280*r6[i]
- 188004088*r8[i]
+ 3125835560*r10[i]
- 81314498488*r12[i]
+ 3185384180840*r14[i]
- 184064268909688*r16[i]
+ 15598375633694120*r18[i]
- 1958105850969957688*r20[i]
+ 375744491571024583400*r22[i]
- 118117302690774819242488*r24[i]
+ 71447614092662750198256680*r26[i]
- 147980747895225006590333244088*r28[i]
- 346368637877614395127589803878040*r30[i]
- 10963784872237230423634083840000000*r31[i]
- 302766527792977996357877082103322488*r32[i]
- 7585842753100939730112422608896000000*r33[i]
- 176553572119721839407097582006071612760*r34[i]
- 3876980715165912710714213825249280000000*r35[i]
- 81213796311764134505181592648745883717688*r36[i]
) // 8841761993739701954543616000000 for i in range(len(r0))]
r27 = [(-2674440*r[1][i]
+ 4345965*r[2][i]
- 4601610*r[3][i]
+ 3749460*r[4][i]
- 2466750*r[5][i]
+ 1332045*r[6][i]
- 592020*r[7][i]
+ 215280*r[8][i]
- 63180*r[9][i]
+ 14625*r[10][i]
- 2574*r[11][i]
+ 324*r[12][i]
- 26*r[13][i]
+ r[14][i]
+ 742900*r0[i]
- 416024*r2[i]
+ 994840*r4[i]
- 5454824*r6[i]
+ 55944280*r8[i]
- 966290024*r10[i]
+ 26454613720*r12[i]
- 1109329691624*r14[i]
+ 70212852387160*r16[i]
- 6733670404619624*r18[i]
+ 1005318113348848600*r20[i]
- 249581050854994274024*r22[i]
+ 120719220687299365182040*r24[i]
- 202039976682357297272094824*r26[i]
- 385557844336439370252173428520*r28[i]
- 11052202492174627443179520000000*r29[i]
- 276888650579451671741587901762024*r30[i]
- 6304176301536407493589598208000000*r31[i]
- 133535841584115505205141919375399080*r32[i]
- 2672618344480543437732658544640000000*r33[i]
- 51095126335993498323380094454901195624*r34[i]
- 940618873537377672007825158832128000000*r35[i]
- 16776403501444391106926987629186000345640*r36[i]
) // 10888869450418352160768000000 for i in range(len(r0))]
r25 = [(742900*r[1][i]
- 1188640*r[2][i]
+ 1225785*r[3][i]
- 961400*r[4][i]
+ 600875*r[5][i]
- 303600*r[6][i]
+ 123970*r[7][i]
- 40480*r[8][i]
+ 10350*r[9][i]
- 2000*r[10][i]
+ 275*r[11][i]
- 24*r[12][i]
+ r[13][i]
- 208012*r0[i]
+ 117572*r2[i]
- 285532*r4[i]
+ 1602692*r6[i]
- 16996252*r8[i]
+ 307475012*r10[i]
- 8966430172*r12[i]
+ 409745686532*r14[i]
- 29195711499292*r16[i]
+ 3312133208909252*r18[i]
- 636215671041835612*r20[i]
+ 241648300078174135172*r22[i]
- 321511316149669476991132*r24[i]
- 492817676505266866078123708*r26[i]
- 12703681025488077520896000000*r27[i]
- 286779648275654636997381637852*r28[i]
- 5894507995826467969695744000000*r29[i]
- 112914054231542703053832892635388*r30[i]
- 2047008246979213061238030336000000*r31[i]
- 35501568925223446300815211192767772*r32[i]
- 593711792050129855003168210944000000*r33[i]
- 9632134956680435093368218113996247868*r34[i]
- 152311343455497374594406627803136000000*r35[i]
- 2356318736218539774396037820111678892892*r36[i]
) // 15511210043330985984000000 for i in range(len(r0))]
r23 = [(-208012*r[1][i]
+ 326876*r[2][i]
- 326876*r[3][i]
+ 245157*r[4][i]
- 144210*r[5][i]
+ 67298*r[6][i]
- 24794*r[7][i]
+ 7084*r[8][i]
- 1518*r[9][i]
+ 230*r[10][i]
- 22*r[11][i]
+ r[12][i]
+ 58786*r0[i]
- 33592*r2[i]
+ 83096*r4[i]
- 479752*r6[i]
+ 5299736*r8[i]
- 101549512*r10[i]
+ 3208453976*r12[i]
- 164071220872*r14[i]
+ 13743680753816*r16[i]
- 1993276972245832*r18[i]
+ 581947914140407256*r20[i]
- 603916464771468176392*r22[i]
- 730803773459954540777704*r24[i]
- 16803810880275234816000000*r25[i]
- 339155768243774227716964552*r26[i]
- 6245976504198304781107200000*r27[i]
- 107413822788261782335458993064*r28[i]
- 1751393992807566623932416000000*r29[i]
- 27365156266821215807862420562312*r30[i]
- 412945663851071412756568473600000*r31[i]
- 6053949680529454447550745704030824*r32[i]
- 86623417665042381831452000256000000*r33[i]
- 1214146547565910406028014931410521672*r34[i]
- 16719755812321492798917963359846400000*r35[i]
- 226758627215029497194516602329808882984*r36[i]
) // 25852016738884976640000 for i in range(len(r0))]
r21 = [(58786*r[1][i]
- 90440*r[2][i]
+ 87210*r[3][i]
- 62016*r[4][i]
+ 33915*r[5][i]
- 14364*r[6][i]
+ 4655*r[7][i]
- 1120*r[8][i]
+ 189*r[9][i]
- 20*r[10][i]
+ r[11][i]
- 16796*r0[i]
+ 9724*r2[i]
- 24596*r4[i]
+ 147004*r6[i]
- 1708916*r8[i]
+ 35240284*r10[i]
- 1237329236*r12[i]
+ 73853629564*r14[i]
- 7850527669556*r16[i]
+ 1717351379730844*r18[i]
- 1359124435588313876*r20[i]
- 1272410676942417239876*r22[i]
- 25852016738884976640000*r23[i]
- 462292539259962003646196*r24[i]
- 7561714896123855667200000*r25[i]
- 115761644587269354830466596*r26[i]
- 1683741850203578528563200000*r27[i]
- 23512975860299444963550050516*r28[i]
- 317677725072691341719961600000*r29[i]
- 4176614976496441445095962733316*r30[i]
- 53674391443652368368589209600000*r31[i]
- 676635955671282540673335079110836*r32[i]
- 8391272072243853389701334630400000*r33[i]
- 102611708232289325546408008313624036*r34[i]
- 1239646284649926576486736094822400000*r35[i]
- 14819283410691765614379616648600811156*r36[i]
) // 51090942171709440000 for i in range(len(r0))]
r19 = [(-16796*r[1][i]
+ 25194*r[2][i]
- 23256*r[3][i]
+ 15504*r[4][i]
- 7752*r[5][i]
+ 2907*r[6][i]
- 798*r[7][i]
+ 152*r[8][i]
- 18*r[9][i]
+ r[10][i]
+ 4862*r0[i]
- 2860*r2[i]
+ 7436*r4[i]
- 46420*r6[i]
+ 576236*r8[i]
- 13098580*r10[i]
+ 532310636*r12[i]
- 39968611540*r14[i]
+ 6350631494636*r16[i]
- 3730771315561300*r18[i]
- 2637991952943407764*r20[i]
- 46833363657400320000*r21[i]
- 734121065118879803860*r22[i]
- 10556240168378032128000*r23[i]
- 142438684135271315212564*r24[i]
- 1830415113744266649600000*r25[i]
- 22632897298190126259675220*r26[i]
- 271297526662043666104320000*r27[i]
- 3170344993810020486920015764*r28[i]
- 36274730261563609572556800000*r29[i]
- 407775103607650299563627591380*r30[i]
- 4515882637052182897862000640000*r31[i]
- 49377994276343186011748723193364*r32[i]
- 534053247401000753173510963200000*r33[i]
- 5722063606154183864914875339648340*r34[i]
- 60811730909031986048777521029120000*r35[i]
- 641729418431834160625738740379401364*r36[i]
) // 121645100408832000 for i in range(len(r0))]
r17 = [(4862*r[1][i]
- 7072*r[2][i]
+ 6188*r[3][i]
- 3808*r[4][i]
+ 1700*r[5][i]
- 544*r[6][i]
+ 119*r[7][i]
- 16*r[8][i]
+ r[9][i]
- 1430*r0[i]
+ 858*r2[i]
- 2310*r4[i]
+ 15258*r6[i]
- 206790*r8[i]
+ 5386458*r10[i]
- 272513670*r12[i]
+ 30255826458*r14[i]
- 12765597850950*r16[i]
- 6622557957272742*r18[i]
- 101370917007360000*r19[i]
- 1375210145685786630*r20[i]
- 17172233341046784000*r21[i]
- 201832098313986359142*r22[i]
- 2265471043586150400000*r23[i]
- 24529324224160803328710*r24[i]
- 258058524232798248960000*r25[i]
- 2652208374242713043720742*r26[i]
- 26739700571225856614400000*r27[i]
- 265323404171486113659725190*r28[i]
- 2597688920748017370193920000*r29[i]
- 25147613788240222384169485542*r30[i]
- 241125683321001354933657600000*r31[i]
- 2293170112631184981695915264070*r32[i]
- 21656158388689797460311183360000*r33[i]
- 203283794784841444836991831621542*r34[i]
- 1898267590696733462875776307200000*r35[i]
- 17646072330245312137111933794073350*r36[i]
) // 355687428096000 for i in range(len(r0))]
r15 = [(-1430*r[1][i]
+ 2002*r[2][i]
- 1638*r[3][i]
+ 910*r[4][i]
- 350*r[5][i]
+ 90*r[6][i]
- 14*r[7][i]
+ r[8][i]
+ 429*r0[i]
- 264*r2[i]
+ 744*r4[i]
- 5304*r6[i]
+ 81384*r8[i]
- 2605944*r10[i]
+ 192387624*r12[i]
- 55942352184*r14[i]
- 20546119600536*r16[i]
- 266765571072000*r17[i]
- 3083760849804024*r18[i]
- 32945548027392000*r19[i]
- 332500281299403096*r20[i]
- 3215147584416768000*r21[i]
- 30076927429146721464*r22[i]
- 274100623905588480000*r23[i]
- 2446077617962088140056*r24[i]
- 21459412163122053120000*r25[i]
- 185641639183185136464504*r26[i]
- 1587401376760010972160000*r27[i]
- 13442713420403849918131416*r28[i]
- 112915002722102749808640000*r29[i]
- 941961013910760913890393144*r30[i]
- 7812419263561351877518080000*r31[i]
- 64474322285718607792730497176*r32[i]
- 529848386811984810994744320000*r33[i]
- 4338547620121893769542630267384*r34[i]
- 35415056327751829508662891008000*r35[i]
- 288317531175033442515609896757336*r36[i]
) // 1307674368000 for i in range(len(r0))]
r13 = [(429*r[1][i]
- 572*r[2][i]
+ 429*r[3][i]
- 208*r[4][i]
+ 65*r[5][i]
- 12*r[6][i]
+ r[7][i]
- 132*r0[i]
+ 84*r2[i]
- 252*r4[i]
+ 2004*r6[i]
- 37212*r8[i]
+ 1710324*r10[i]
- 325024572*r12[i]
- 80789566956*r14[i]
- 871782912000*r15[i]
- 8422900930332*r16[i]
- 75583578470400*r17[i]
- 643521842437836*r18[i]
- 5269678622208000*r19[i]
- 41890044885642492*r20[i]
- 325386564299596800*r21[i]
- 2481686964269990316*r22[i]
- 18652248729354240000*r23[i]
- 138536531588626169052*r24[i]
- 1019042849143807488000*r25[i]
- 7436421488952386592396*r26[i]
- 53911021949819274240000*r27[i]
- 388701690499592948238012*r28[i]
- 2789805187365599475072000*r29[i]
- 19946749502047187160692076*r30[i]
- 142159780685991861112320000*r31[i]
- 1010433303980489860989897372*r32[i]
- 7165521770403817166663116800*r33[i]
- 50716588034439244118483617356*r34[i]
- 358378772025058883636009472000*r35[i]
- 2528902640579773012941059115132*r36[i]
) // 6227020800 for i in range(len(r0))]
r11 = [(-132*r[1][i]
+ 165*r[2][i]
- 110*r[3][i]
+ 44*r[4][i]
- 10*r[5][i]
+ r[6][i]
+ 42*r0[i]
- 28*r2[i]
+ 92*r4[i]
- 868*r6[i]
+ 22652*r8[i]
- 2620708*r10[i]
- 415790788*r12[i]
- 3632428800*r13[i]
- 28616744548*r14[i]
- 210680870400*r15[i]
- 1479485236228*r16[i]
- 10038995366400*r17[i]
- 66394067988388*r18[i]
- 430591742380800*r19[i]
- 2750479262009668*r20[i]
- 17360942812012800*r21[i]
- 108550450893568228*r22[i]
- 673606803881088000*r23[i]
- 4154688725062207108*r24[i]
- 25499502190850688000*r25[i]
- 155878445775166700068*r26[i]
- 949776357849070752000*r27[i]
- 5771581202353414724548*r28[i]
- 34995682724855684832000*r29[i]
- 211811399872933910999908*r30[i]
- 1280080235834717770252800*r31[i]
- 7726641919200262371657988*r32[i]
- 46591059456870785061004800*r33[i]
- 280704018540064430354883748*r34[i]
- 1690018909819536161979590400*r35[i]
- 10169113413821714748538703428*r36[i]
) // 39916800 for i in range(len(r0))]
r9 = [(42*r[1][i]
- 48*r[2][i]
+ 27*r[3][i]
- 8*r[4][i]
+ r[5][i]
- 14*r0[i]
+ 10*r2[i]
- 38*r4[i]
+ 490*r6[i]
- 31238*r8[i]
- 2922230*r10[i]
- 19958400*r11[i]
- 124075238*r12[i]
- 726485760*r13[i]
- 4084385750*r14[i]
- 22313491200*r15[i]
- 119387268038*r16[i]
- 628980992640*r17[i]
- 3275389222070*r18[i]
- 16905818966400*r19[i]
- 86665431465638*r20[i]
- 441935114987520*r21[i]
- 2244295389943190*r22[i]
- 11360520464832000*r23[i]
- 57360469753884038*r24[i]
- 289038899804054400*r25[i]
- 1454155949521941110*r26[i]
- 7306671293537616000*r27[i]
- 36677059892827099238*r28[i]
- 183960524908301057280*r29[i]
- 922104761587650687830*r30[i]
- 4619736062008593926400*r31[i]
- 23135540444136227047238*r32[i]
- 115825176110799088940160*r33[i]
- 579715876176320506935350*r34[i]
- 2900939663557699476451200*r35[i]
- 14514140349055749129024038*r36[i]
) // 362880 for i in range(len(r0))]
r7 = [(-14*r[1][i]
+ 14*r[2][i]
- 6*r[3][i]
+ r[4][i]
+ 5*r0[i]
- 4*r2[i]
+ 20*r4[i]
- 604*r6[i]
- 29740*r8[i]
- 151200*r9[i]
- 708604*r10[i]
- 3160080*r11[i]
- 13645900*r12[i]
- 57657600*r13[i]
- 239967004*r14[i]
- 988107120*r15[i]
- 4037604460*r16[i]
- 16406863200*r17[i]
- 66398623804*r18[i]
- 267911678160*r19[i]
- 1078605601420*r20[i]
- 4335313752000*r21[i]
- 17403958407004*r22[i]
- 69804002545200*r23[i]
- 279780634372780*r24[i]
- 1120816644948000*r25[i]
- 4488349371924604*r26[i]
- 17968646803620240*r27[i]
- 71920337041294540*r28[i]
- 287818601403715200*r29[i]
- 1151686172846664604*r30[i]
- 4607980008114455280*r31[i]
- 18435626012705982700*r32[i]
- 73753622051697957600*r33[i]
- 295047842329672995004*r34[i]
- 1180291431927853642320*r35[i]
- 4721465916019935893260*r36[i]
) // 5040 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
- 1680*r7[i]
- 5542*r8[i]
- 17640*r9[i]
- 54958*r10[i]
- 168960*r11[i]
- 515062*r12[i]
- 1561560*r13[i]
- 4717438*r14[i]
- 14217840*r15[i]
- 42784582*r16[i]
- 128615880*r17[i]
- 386371918*r18[i]
- 1160164320*r19[i]
- 3482590102*r20[i]
- 10451964600*r21[i]
- 31364282398*r22[i]
- 94109624400*r23[i]
- 282362427622*r24[i]
- 847154391720*r25[i]
- 2541597392878*r26[i]
- 7625060614080*r27[i]
- 22875718713142*r28[i]
- 68628229881240*r29[i]
- 205886837127358*r30[i]
- 617664806349360*r31[i]
- 1853003008982662*r32[i]
- 5559026206817160*r33[i]
- 16677112980189838*r34[i]
- 50031407660046240*r35[i]
- 150094360419092182*r36[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
- 126*r7[i]
- 254*r8[i]
- 510*r9[i]
- 1022*r10[i]
- 2046*r11[i]
- 4094*r12[i]
- 8190*r13[i]
- 16382*r14[i]
- 32766*r15[i]
- 65534*r16[i]
- 131070*r17[i]
- 262142*r18[i]
- 524286*r19[i]
- 1048574*r20[i]
- 2097150*r21[i]
- 4194302*r22[i]
- 8388606*r23[i]
- 16777214*r24[i]
- 33554430*r25[i]
- 67108862*r26[i]
- 134217726*r27[i]
- 268435454*r28[i]
- 536870910*r29[i]
- 1073741822*r30[i]
- 2147483646*r31[i]
- 4294967294*r32[i]
- 8589934590*r33[i]
- 17179869182*r34[i]
- 34359738366*r35[i]
- 68719476734*r36[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
- r7[i]
- r8[i]
- r9[i]
- r10[i]
- r11[i]
- r12[i]
- r13[i]
- r14[i]
- r15[i]
- r16[i]
- r17[i]
- r18[i]
- r19[i]
- r20[i]
- r21[i]
- r22[i]
- r23[i]
- r24[i]
- r25[i]
- r26[i]
- r27[i]
- r28[i]
- r29[i]
- r30[i]
- r31[i]
- r32[i]
- r33[i]
- r34[i]
- r35[i]
- r36[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36)
def natural_interpolate_20(r):
r0 = r[0]
r38 = r['infinity']
r36 = [(-8597496600*(r[1][i] + r[-1][i])
+ 7307872110*(r[2][i] + r[-2][i])
- 5567902560*(r[3][i] + r[-3][i])
+ 3796297200*(r[4][i] + r[-4][i])
- 2310789600*(r[5][i] + r[-5][i])
+ 1251677700*(r[6][i] + r[-6][i])
- 600805296*(r[7][i] + r[-7][i])
+ 254186856*(r[8][i] + r[-8][i])
- 94143280*(r[9][i] + r[-9][i])
+ 30260340*(r[10][i] + r[-10][i])
- 8347680*(r[11][i] + r[-11][i])
+ 1947792*(r[12][i] + r[-12][i])
- 376992*(r[13][i] + r[-13][i])
+ 58905*(r[14][i] + r[-14][i])
- 7140*(r[15][i] + r[-15][i])
+ 630*(r[16][i] + r[-16][i])
- 36*(r[17][i] + r[-17][i])
+ (r[18][i] + r[-18][i])
+ 9075135300*r0[i]
- 784533926199901667640010836150111436800000000*r38[i]
) // 371993326789901217467999448150835200000000 for i in range(len(r0))]
r34 = [(2203961430*(r[1][i] + r[-1][i])
- 1855967520*(r[2][i] + r[-2][i])
+ 1391975640*(r[3][i] + r[-3][i])
- 927983760*(r[4][i] + r[-4][i])
+ 548354040*(r[5][i] + r[-5][i])
- 286097760*(r[6][i] + r[-6][i])
+ 131128140*(r[7][i] + r[-7][i])
- 52451256*(r[8][i] + r[-8][i])
+ 18156204*(r[9][i] + r[-9][i])
- 5379616*(r[10][i] + r[-10][i])
+ 1344904*(r[11][i] + r[-11][i])
- 278256*(r[12][i] + r[-12][i])
+ 46376*(r[13][i] + r[-13][i])
- 5984*(r[14][i] + r[-14][i])
+ 561*(r[15][i] + r[-15][i])
- 34*(r[16][i] + r[-16][i])
+ (r[17][i] + r[-17][i])
- 2333606220*r0[i]
- 526990546285693391412999218213683200000000*r36[i]
- 518664095654379435828673830565907005440000000*r38[i]
) // 295232799039604140847618609643520000000 for i in range(len(r0))]
r32 = [(-565722720*(r[1][i] + r[-1][i])
+ 471435600*(r[2][i] + r[-2][i])
- 347373600*(r[3][i] + r[-3][i])
+ 225792840*(r[4][i] + r[-4][i])
- 129024480*(r[5][i] + r[-5][i])
+ 64512240*(r[6][i] + r[-6][i])
- 28048800*(r[7][i] + r[-7][i])
+ 10518300*(r[8][i] + r[-8][i])
- 3365856*(r[9][i] + r[-9][i])
+ 906192*(r[10][i] + r[-10][i])
- 201376*(r[11][i] + r[-11][i])
+ 35960*(r[12][i] + r[-12][i])
- 4960*(r[13][i] + r[-13][i])
+ 496*(r[14][i] + r[-14][i])
- 32*(r[15][i] + r[-15][i])
+ (r[16][i] + r[-16][i])
+ 601080390*r0[i]
- 393643732052805521130158146191360000000*r34[i]
- 326527475737802179777466182265733120000000*r36[i]
- 198969979872214920293886346099446251520000000*r38[i]
) // 263130836933693530167218012160000000 for i in range(len(r0))]
r30 = [(145422675*(r[1][i] + r[-1][i])
- 119759850*(r[2][i] + r[-2][i])
+ 86493225*(r[3][i] + r[-3][i])
- 54627300*(r[4][i] + r[-4][i])
+ 30045015*(r[5][i] + r[-5][i])
- 14307150*(r[6][i] + r[-6][i])
+ 5852925*(r[7][i] + r[-7][i])
- 2035800*(r[8][i] + r[-8][i])
+ 593775*(r[9][i] + r[-9][i])
- 142506*(r[10][i] + r[-10][i])
+ 27405*(r[11][i] + r[-11][i])
- 4060*(r[12][i] + r[-12][i])
+ 435*(r[13][i] + r[-13][i])
- 30*(r[14][i] + r[-14][i])
+ (r[15][i] + r[-15][i])
- 155117520*r0[i]
- 328913546167116912709022515200000000*r32[i]
- 227575282593028191903372678266880000000*r34[i]
- 116309421454977381321426414757478400000000*r36[i]
- 49083095586740430887431564189583278080000000*r38[i]
) // 265252859812191058636308480000000 for i in range(len(r0))]
r28 = [(-37442160*(r[1][i] + r[-1][i])
+ 30421755*(r[2][i] + r[-2][i])
- 21474180*(r[3][i] + r[-3][i])
+ 13123110*(r[4][i] + r[-4][i])
- 6906900*(r[5][i] + r[-5][i])
+ 3108105*(r[6][i] + r[-6][i])
- 1184040*(r[7][i] + r[-7][i])
+ 376740*(r[8][i] + r[-8][i])
- 98280*(r[9][i] + r[-9][i])
+ 20475*(r[10][i] + r[-10][i])
- 3276*(r[11][i] + r[-11][i])
+ 378*(r[12][i] + r[-12][i])
- 28*(r[13][i] + r[-13][i])
+ (r[14][i] + r[-14][i])
+ 40116600*r0[i]
- 309461669780889568409026560000000*r30[i]
- 176516936443019409820508749824000000*r32[i]
- 74833313645455216256514439249920000000*r34[i]
- 26337328459046574816219104447299584000000*r36[i]
- 8155948144934385059006601147769159680000000*r38[i]
) // 304888344611713860501504000000 for i in range(len(r0))]
r26 = [(9657700*(r[1][i] + r[-1][i])
- 7726160*(r[2][i] + r[-2][i])
+ 5311735*(r[3][i] + r[-3][i])
- 3124550*(r[4][i] + r[-4][i])
+ 1562275*(r[5][i] + r[-5][i])
- 657800*(r[6][i] + r[-6][i])
+ 230230*(r[7][i] + r[-7][i])
- 65780*(r[8][i] + r[-8][i])
+ 14950*(r[9][i] + r[-9][i])
- 2600*(r[10][i] + r[-10][i])
+ 325*(r[11][i] + r[-11][i])
- 26*(r[12][i] + r[-12][i])
+ (r[13][i] + r[-13][i])
- 10400600*r0[i]
- 330295706662690015543296000000*r28[i]
- 153257207891488167212089344000000*r30[i]
- 53222214421459539592188788736000000*r32[i]
- 15436506593303376230082373484544000000*r34[i]
- 3960094929842931739454572322881536000000*r36[i]
- 930084233815670751630942950980583424000000*r38[i]
) // 403291461126605635584000000 for i in range(len(r0))]
r24 = [(-2496144*(r[1][i] + r[-1][i])
+ 1961256*(r[2][i] + r[-2][i])
- 1307504*(r[3][i] + r[-3][i])
+ 735471*(r[4][i] + r[-4][i])
- 346104*(r[5][i] + r[-5][i])
+ 134596*(r[6][i] + r[-6][i])
- 42504*(r[7][i] + r[-7][i])
+ 10626*(r[8][i] + r[-8][i])
- 2024*(r[9][i] + r[-9][i])
+ 276*(r[10][i] + r[-10][i])
- 24*(r[11][i] + r[-11][i])
+ (r[12][i] + r[-12][i])
+ 2704156*r0[i]
- 403291461126605635584000000*r26[i]
- 149903436100759314746572800000*r28[i]
- 42033455827381598974377984000000*r30[i]
- 9910695932425713906157643366400000*r32[i]
- 2078962023961017163954848006144000000*r34[i]
- 401274139495715827174031120636313600000*r36[i]
- 72837740568171787457915404507152384000000*r38[i]
) // 620448401733239439360000 for i in range(len(r0))]
r22 = [(646646*(r[1][i] + r[-1][i])
- 497420*(r[2][i] + r[-2][i])
+ 319770*(r[3][i] + r[-3][i])
- 170544*(r[4][i] + r[-4][i])
+ 74613*(r[5][i] + r[-5][i])
- 26334*(r[6][i] + r[-6][i])
+ 7315*(r[7][i] + r[-7][i])
- 1540*(r[8][i] + r[-8][i])
+ 231*(r[9][i] + r[-9][i])
- 22*(r[10][i] + r[-10][i])
+ (r[11][i] + r[-11][i])
- 705432*r0[i]
- 568744368255469486080000*r24[i]
- 166357727714724824678400000*r26[i]
- 37042320704478727628390400000*r28[i]
- 6988909951599209517839155200000*r30[i]
- 1180836611760352104108962611200000*r32[i]
- 184607985589364774573429361868800000*r34[i]
- 27272218262298384682708194086092800000*r36[i]
- 3861838803337560097698395778726297600000*r38[i]
) // 1124000727777607680000 for i in range(len(r0))]
r20 = [(-167960*(r[1][i] + r[-1][i])
+ 125970*(r[2][i] + r[-2][i])
- 77520*(r[3][i] + r[-3][i])
+ 38760*(r[4][i] + r[-4][i])
- 15504*(r[5][i] + r[-5][i])
+ 4845*(r[6][i] + r[-6][i])
- 1140*(r[7][i] + r[-7][i])
+ 190*(r[8][i] + r[-8][i])
- 20*(r[9][i] + r[-9][i])
+ (r[10][i] + r[-10][i])
+ 184756*r0[i]
- 936667273148006400000*r22[i]
- 211124803367560642560000*r24[i]
- 36608302274885332992000000*r26[i]
- 5425950533240873322086400000*r28[i]
- 725494605231272191451136000000*r30[i]
- 90317652741043657957240012800000*r32[i]
- 10681064948020015063470219264000000*r34[i]
- 1216234618180639720975550420582400000*r36[i]
- 134607612138429628983625351999488000000*r38[i]
) // 2432902008176640000 for i in range(len(r0))]
r18 = [(43758*(r[1][i] + r[-1][i])
- 31824*(r[2][i] + r[-2][i])
+ 18564*(r[3][i] + r[-3][i])
- 8568*(r[4][i] + r[-4][i])
+ 3060*(r[5][i] + r[-5][i])
- 816*(r[6][i] + r[-6][i])
+ 153*(r[7][i] + r[-7][i])
- 18*(r[8][i] + r[-8][i])
+ (r[9][i] + r[-9][i])
- 48620*r0[i]
- 1824676506132480000*r20[i]
- 309100200138842112000*r22[i]
- 40778478784550707200000*r24[i]
- 4645053436190368481280000*r26[i]
- 481314610282065419059200000*r28[i]
- 46758400573464312663490560000*r30[i]
- 4340262299778024388805836800000*r32[i]
- 389810850996416354285601300480000*r34[i]
- 34168816632541202331763973529600000*r36[i]
- 2941066263016510346147295370272768000*r38[i]
) // 6402373705728000 for i in range(len(r0))]
r16 = [(-11440*(r[1][i] + r[-1][i])
+ 8008*(r[2][i] + r[-2][i])
- 4368*(r[3][i] + r[-3][i])
+ 1820*(r[4][i] + r[-4][i])
- 560*(r[5][i] + r[-5][i])
+ 120*(r[6][i] + r[-6][i])
- 16*(r[7][i] + r[-7][i])
+ (r[8][i] + r[-8][i])
+ 12870*r0[i]
- 4268249137152000*r18[i]
- 527128768438272000*r20[i]
- 51442361350668288000*r22[i]
- 4385609982489415680000*r24[i]
- 343350594609952849920000*r26[i]
- 25398422028160175554560000*r28[i]
- 1806640043553643996938240000*r30[i]
- 124998708216981630040289280000*r32[i]
- 8477574188991756975915909120000*r34[i]
- 566640901244029272138606256128000*r36[i]
- 37469170353622071265887792218112000*r38[i]
) // 20922789888000 for i in range(len(r0))]
r14 = [(3003*(r[1][i] + r[-1][i])
- 2002*(r[2][i] + r[-2][i])
+ 1001*(r[3][i] + r[-3][i])
- 364*(r[4][i] + r[-4][i])
+ 91*(r[5][i] + r[-5][i])
- 14*(r[6][i] + r[-6][i])
+ (r[7][i] + r[-7][i])
- 3432*r0[i]
- 12204960768000*r16[i]
- 1058170098585600*r18[i]
- 73775500710912000*r20[i]
- 4555411900194355200*r22[i]
- 261131482210959360000*r24[i]
- 14266599888013304832000*r26[i]
- 754754307297469839360000*r28[i]
- 39057272623118392651008000*r30[i]
- 1990236929603886055572480000*r32[i]
- 100317304785653440333283635200*r34[i]
- 5017302808350824370904132608000*r36[i]
- 249538838908236261152065923225600*r38[i]
) // 87178291200 for i in range(len(r0))]
r12 = [(-792*(r[1][i] + r[-1][i])
+ 495*(r[2][i] + r[-2][i])
- 220*(r[3][i] + r[-3][i])
+ 66*(r[4][i] + r[-4][i])
- 12*(r[5][i] + r[-5][i])
+ (r[6][i] + r[-6][i])
+ 924*r0[i]
- 43589145600*r14[i]
- 2528170444800*r16[i]
- 120467944396800*r18[i]
- 5167100908569600*r20[i]
- 208331313744153600*r22[i]
- 8083281646573056000*r24[i]
- 305994026290208256000*r26[i]
- 11397316294188849024000*r28[i]
- 419948192698268217984000*r30[i]
- 15360962830016613243033600*r32[i]
- 559092713482449420732057600*r34[i]
- 20280226917834433943755084800*r36[i]
- 733917409397935785284098636800*r38[i]
) // 479001600 for i in range(len(r0))]
r10 = [(210*(r[1][i] + r[-1][i])
- 120*(r[2][i] + r[-2][i])
+ 45*(r[3][i] + r[-3][i])
- 10*(r[4][i] + r[-4][i])
+ (r[5][i] + r[-5][i])
- 252*r0[i]
- 199584000*r12[i]
- 7264857600*r14[i]
- 223134912000*r16[i]
- 6289809926400*r18[i]
- 169058189664000*r20[i]
- 4419351149875200*r22[i]
- 113605204648320000*r24[i]
- 2890388998040544000*r26[i]
- 73066712935376160000*r28[i]
- 1839605249083010572800*r30[i]
- 46197360620085939264000*r32[i]
- 1158251761107990889401600*r34[i]
- 29009396635576994764512000*r36[i]
- 726084725720412923735270400*r38[i]
) // 3628800 for i in range(len(r0))]
r8 = [(-56*(r[1][i] + r[-1][i])
+ 28*(r[2][i] + r[-2][i])
- 8*(r[3][i] + r[-3][i])
+ (r[4][i] + r[-4][i])
+ 70*r0[i]
- 1209600*r10[i]
- 25280640*r12[i]
- 461260800*r14[i]
- 7904856960*r16[i]
- 131254905600*r18[i]
- 2143293425280*r20[i]
- 34682510016000*r22[i]
- 558432020361600*r24[i]
- 8966533159584000*r26[i]
- 143749174428961920*r28[i]
- 2302548811229721600*r30[i]
- 36863840064915642240*r32[i]
- 590028976413583660800*r34[i]
- 9442331455422829138560*r36[i]
- 151094113839739041753600*r38[i]
) // 40320 for i in range(len(r0))]
r6 = [(15*(r[1][i] + r[-1][i])
- 6*(r[2][i] + r[-2][i])
+ (r[3][i] + r[-3][i])
- 20*r0[i]
- 10080*r8[i]
- 105840*r10[i]
- 1013760*r12[i]
- 9369360*r14[i]
- 85307040*r16[i]
- 771695280*r18[i]
- 6960985920*r20[i]
- 62711787600*r22[i]
- 564657746400*r24[i]
- 5082926350320*r26[i]
- 45750363684480*r28[i]
- 411769379287440*r30[i]
- 3705988838096160*r32[i]
- 33354157240902960*r34[i]
- 300188445960277440*r36[i]
- 2701700136811100880*r38[i]
) // 720 for i in range(len(r0))]
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
- 504*r8[i]
- 2040*r10[i]
- 8184*r12[i]
- 32760*r14[i]
- 131064*r16[i]
- 524280*r18[i]
- 2097144*r20[i]
- 8388600*r22[i]
- 33554424*r24[i]
- 134217720*r26[i]
- 536870904*r28[i]
- 2147483640*r30[i]
- 8589934584*r32[i]
- 34359738360*r34[i]
- 137438953464*r36[i]
- 549755813880*r38[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
- 2*r8[i]
- 2*r10[i]
- 2*r12[i]
- 2*r14[i]
- 2*r16[i]
- 2*r18[i]
- 2*r20[i]
- 2*r22[i]
- 2*r24[i]
- 2*r26[i]
- 2*r28[i]
- 2*r30[i]
- 2*r32[i]
- 2*r34[i]
- 2*r36[i]
- 2*r38[i]
) // 2 for i in range(len(r0))]
r37 = [(1767263190*r[1][i]
- 3029594040*r[2][i]
+ 3511574910*r[3][i]
- 3257112960*r[4][i]
+ 2544619500*r[5][i]
- 1709984304*r[6][i]
+ 997490844*r[7][i]
- 506662016*r[8][i]
+ 223926516*r[9][i]
- 85795600*r[10][i]
+ 28312548*r[11][i]
- 7970688*r[12][i]
+ 1888887*r[13][i]
- 369852*r[14][i]
+ 58275*r[15][i]
- 7104*r[16][i]
+ 629*r[17][i]
- 36*r[18][i]
+ r[19][i]
- 477638700*r0[i]
+ 259289580*r2[i]
- 589294500*r4[i]
+ 2996657580*r6[i]
- 27670359300*r8[i]
+ 415064933580*r10[i]
- 9439543875300*r12[i]
+ 310922483993580*r14[i]
- 14379880666402500*r16[i]
+ 914767168887053580*r18[i]
- 79051272004645620900*r20[i]
+ 9231401536061270849580*r22[i]
- 1459700260139475814330500*r24[i]
+ 315843905250429722227637580*r26[i]
- 95612546130070295522414451300*r28[i]
+ 42177612582297377823299737193580*r30[i]
- 29268533564152352561039458453023300*r32[i]
+ 37747202396256876155482291281278813580*r34[i]
- 161759954125032708920885781040309430206500*r36[i]
- 763162014442847423121851269222329739576686420*r38[i]
) // 13763753091226345046315979581580902400000000 for i in range(len(r0))]
r35 = [(-477638700*r[1][i]
+ 811985790*r[2][i]
- 927983760*r[3][i]
+ 843621600*r[4][i]
- 641886000*r[5][i]
+ 417225900*r[6][i]
- 233646504*r[7][i]
+ 112971936*r[8][i]
- 47071640*r[9][i]
+ 16811300*r[10][i]
- 5101360*r[11][i]
+ 1298528*r[12][i]
- 272272*r[13][i]
+ 45815*r[14][i]
- 5950*r[15][i]
+ 560*r[16][i]
- 34*r[17][i]
+ r[18][i]
+ 129644790*r0[i]
- 70715340*r2[i]
+ 161960940*r4[i]
- 832930740*r6[i]
+ 7810859340*r8[i]
- 119578066740*r10[i]
+ 2791740107340*r12[i]
- 95062235276340*r14[i]
+ 4584012079172940*r16[i]
- 307268933913567540*r18[i]
+ 28355038085389144140*r20[i]
- 3597774935929125068340*r22[i]
+ 632729503874459828228940*r24[i]
- 157381528472579148083026740*r26[i]
+ 57577884185625191071239755340*r28[i]
- 33404393172944223690128125810740*r30[i]
+ 36271128388074981554067219056171340*r32[i]
- 131671692334895976886647813958596908340*r34[i]
- 529104107360143104505564190890974500955060*r36[i]
- 21792609061108379656666967670836428800000000*r37[i]
- 779765567254824678774814590170424618060927540*r38[i]
) // 10333147966386144929666651337523200000000 for i in range(len(r0))]
r33 = [(129644790*r[1][i]
- 218349120*r[2][i]
+ 245642760*r[3][i]
- 218349120*r[4][i]
+ 161280600*r[5][i]
- 100975680*r[6][i]
+ 53993940*r[7][i]
- 24682944*r[8][i]
+ 9612108*r[9][i]
- 3164480*r[10][i]
+ 870232*r[11][i]
- 196416*r[12][i]
+ 35464*r[13][i]
- 4928*r[14][i]
+ 495*r[15][i]
- 32*r[16][i]
+ r[17][i]
- 35357670*r0[i]
+ 19389690*r2[i]
- 44796870*r4[i]
+ 233344890*r6[i]
- 2227139910*r8[i]
+ 34903389690*r10[i]
- 839988260550*r12[i]
+ 29734601940090*r14[i]
- 1506293149214790*r16[i]
+ 107487540061668090*r18[i]
- 10743535525710258630*r20[i]
+ 1511267716903778445690*r22[i]
- 304525956073869018848070*r24[i]
+ 91234873454404063067344890*r26[i]
- 43747586259736794619504039110*r28[i]
+ 39574917458915050445099774637690*r30[i]
- 120523981455993504966525708346887750*r32[i]
- 408775192473644376465790167368394203910*r34[i]
- 15499721949579217394499977006284800000000*r35[i]
- 511206585269023792365556128001469646849990*r36[i]
- 15254826342775865759666877369585500160000000*r37[i]
- 421754497238984285335705463354740490210507910*r38[i]
) // 8683317618811886495518194401280000000 for i in range(len(r0))]
r31 = [(-35357670*r[1][i]
+ 58929450*r[2][i]
- 65132550*r[3][i]
+ 56448210*r[4][i]
- 40320150*r[5][i]
+ 24192090*r[6][i]
- 12271350*r[7][i]
+ 5259150*r[8][i]
- 1893294*r[9][i]
+ 566370*r[10][i]
- 138446*r[11][i]
+ 26970*r[12][i]
- 4030*r[13][i]
+ 434*r[14][i]
- 30*r[15][i]
+ r[16][i]
+ 9694845*r0[i]
- 5348880*r2[i]
+ 12480720*r4[i]
- 65969520*r6[i]
+ 642563280*r8[i]
- 10347602160*r10[i]
+ 258040917840*r12[i]
- 9564008626800*r14[i]
+ 514021079720400*r16[i]
- 39590373677587440*r18[i]
+ 4371353677873146960*r20[i]
- 701971899866535028080*r22[i]
+ 169737570795219895373520*r24[i]
- 66396273378844288679892720*r26[i]
+ 49448835121192219782326176080*r28[i]
- 124963193751534047864734415925360*r30[i]
- 354113410826574103722030528083469360*r32[i]
- 12301366626650172535317442068480000000*r33[i]
- 372225904019072507165665501545458070000*r34[i]
- 10203983616806318118045818195804160000000*r35[i]
- 259484653500223872483011119661283865786800*r36[i]
- 6217811871006716259183948315607695360000000*r37[i]
- 141956901865997956445469727796622341498870640*r38[i]
) // 8222838654177922817725562880000000 for i in range(len(r0))]
r29 = [(9694845*r[1][i]
- 15967980*r[2][i]
+ 17298645*r[3][i]
- 14567280*r[4][i]
+ 10015005*r[5][i]
- 5722860*r[6][i]
+ 2731365*r[7][i]
- 1085760*r[8][i]
+ 356265*r[9][i]
- 95004*r[10][i]
+ 20097*r[11][i]
- 3248*r[12][i]
+ 377*r[13][i]
- 28*r[14][i]
+ r[15][i]
- 2674440*r0[i]
+ 1485800*r2[i]
- 3506488*r4[i]
+ 18850280*r6[i]
- 188004088*r8[i]
+ 3125835560*r10[i]
- 81314498488*r12[i]
+ 3185384180840*r14[i]
- 184064268909688*r16[i]
+ 15598375633694120*r18[i]
- 1958105850969957688*r20[i]
+ 375744491571024583400*r22[i]
- 118117302690774819242488*r24[i]
+ 71447614092662750198256680*r26[i]
- 147980747895225006590333244088*r28[i]
- 346368637877614395127589803878040*r30[i]
- 10963784872237230423634083840000000*r31[i]
- 302766527792977996357877082103322488*r32[i]
- 7585842753100939730112422608896000000*r33[i]
- 176553572119721839407097582006071612760*r34[i]
- 3876980715165912710714213825249280000000*r35[i]
- 81213796311764134505181592648745883717688*r36[i]
- 1636103186224681029581052139652775936000000*r37[i]
- 31895543813319775842490572300866856117139480*r38[i]
) // 8841761993739701954543616000000 for i in range(len(r0))]
r27 = [(-2674440*r[1][i]
+ 4345965*r[2][i]
- 4601610*r[3][i]
+ 3749460*r[4][i]
- 2466750*r[5][i]
+ 1332045*r[6][i]
- 592020*r[7][i]
+ 215280*r[8][i]
- 63180*r[9][i]
+ 14625*r[10][i]
- 2574*r[11][i]
+ 324*r[12][i]
- 26*r[13][i]
+ r[14][i]
+ 742900*r0[i]
- 416024*r2[i]
+ 994840*r4[i]
- 5454824*r6[i]
+ 55944280*r8[i]
- 966290024*r10[i]
+ 26454613720*r12[i]
- 1109329691624*r14[i]
+ 70212852387160*r16[i]
- 6733670404619624*r18[i]
+ 1005318113348848600*r20[i]
- 249581050854994274024*r22[i]
+ 120719220687299365182040*r24[i]
- 202039976682357297272094824*r26[i]
- 385557844336439370252173428520*r28[i]
- 11052202492174627443179520000000*r29[i]
- 276888650579451671741587901762024*r30[i]
- 6304176301536407493589598208000000*r31[i]
- 133535841584115505205141919375399080*r32[i]
- 2672618344480543437732658544640000000*r33[i]
- 51095126335993498323380094454901195624*r34[i]
- 940618873537377672007825158832128000000*r35[i]
- 16776403501444391106926987629186000345640*r36[i]
- 291283862319085180678807183848898560000000*r37[i]
- 4942310839108515578583708125038854650555624*r38[i]
) // 10888869450418352160768000000 for i in range(len(r0))]
r25 = [(742900*r[1][i]
- 1188640*r[2][i]
+ 1225785*r[3][i]
- 961400*r[4][i]
+ 600875*r[5][i]
- 303600*r[6][i]
+ 123970*r[7][i]
- 40480*r[8][i]
+ 10350*r[9][i]
- 2000*r[10][i]
+ 275*r[11][i]
- 24*r[12][i]
+ r[13][i]
- 208012*r0[i]
+ 117572*r2[i]
- 285532*r4[i]
+ 1602692*r6[i]
- 16996252*r8[i]
+ 307475012*r10[i]
- 8966430172*r12[i]
+ 409745686532*r14[i]
- 29195711499292*r16[i]
+ 3312133208909252*r18[i]
- 636215671041835612*r20[i]
+ 241648300078174135172*r22[i]
- 321511316149669476991132*r24[i]
- 492817676505266866078123708*r26[i]
- 12703681025488077520896000000*r27[i]
- 286779648275654636997381637852*r28[i]
- 5894507995826467969695744000000*r29[i]
- 112914054231542703053832892635388*r30[i]
- 2047008246979213061238030336000000*r31[i]
- 35501568925223446300815211192767772*r32[i]
- 593711792050129855003168210944000000*r33[i]
- 9632134956680435093368218113996247868*r34[i]
- 152311343455497374594406627803136000000*r35[i]
- 2356318736218539774396037820111678892892*r36[i]
- 35772470531371951985805498114637824000000*r37[i]
- 534273042749950920189640352996759062689148*r38[i]
) // 15511210043330985984000000 for i in range(len(r0))]
r23 = [(-208012*r[1][i]
+ 326876*r[2][i]
- 326876*r[3][i]
+ 245157*r[4][i]
- 144210*r[5][i]
+ 67298*r[6][i]
- 24794*r[7][i]
+ 7084*r[8][i]
- 1518*r[9][i]
+ 230*r[10][i]
- 22*r[11][i]
+ r[12][i]
+ 58786*r0[i]
- 33592*r2[i]
+ 83096*r4[i]
- 479752*r6[i]
+ 5299736*r8[i]
- 101549512*r10[i]
+ 3208453976*r12[i]
- 164071220872*r14[i]
+ 13743680753816*r16[i]
- 1993276972245832*r18[i]
+ 581947914140407256*r20[i]
- 603916464771468176392*r22[i]
- 730803773459954540777704*r24[i]
- 16803810880275234816000000*r25[i]
- 339155768243774227716964552*r26[i]
- 6245976504198304781107200000*r27[i]
- 107413822788261782335458993064*r28[i]
- 1751393992807566623932416000000*r29[i]
- 27365156266821215807862420562312*r30[i]
- 412945663851071412756568473600000*r31[i]
- 6053949680529454447550745704030824*r32[i]
- 86623417665042381831452000256000000*r33[i]
- 1214146547565910406028014931410521672*r34[i]
- 16719755812321492798917963359846400000*r35[i]
- 226758627215029497194516602329808882984*r36[i]
- 3034905857007157810746475187798016000000*r37[i]
- 40151799724774280996886476759684489594632*r38[i]
) // 25852016738884976640000 for i in range(len(r0))]
r21 = [(58786*r[1][i]
- 90440*r[2][i]
+ 87210*r[3][i]
- 62016*r[4][i]
+ 33915*r[5][i]
- 14364*r[6][i]
+ 4655*r[7][i]
- 1120*r[8][i]
+ 189*r[9][i]
- 20*r[10][i]
+ r[11][i]
- 16796*r0[i]
+ 9724*r2[i]
- 24596*r4[i]
+ 147004*r6[i]
- 1708916*r8[i]
+ 35240284*r10[i]
- 1237329236*r12[i]
+ 73853629564*r14[i]
- 7850527669556*r16[i]
+ 1717351379730844*r18[i]
- 1359124435588313876*r20[i]
- 1272410676942417239876*r22[i]
- 25852016738884976640000*r23[i]
- 462292539259962003646196*r24[i]
- 7561714896123855667200000*r25[i]
- 115761644587269354830466596*r26[i]
- 1683741850203578528563200000*r27[i]
- 23512975860299444963550050516*r28[i]
- 317677725072691341719961600000*r29[i]
- 4176614976496441445095962733316*r30[i]
- 53674391443652368368589209600000*r31[i]
- 676635955671282540673335079110836*r32[i]
- 8391272072243853389701334630400000*r33[i]
- 102611708232289325546408008313624036*r34[i]
- 1239646284649926576486736094822400000*r35[i]
- 14819283410691765614379616648600811156*r36[i]
- 175538127424434549895381626305740800000*r37[i]
- 2062659648435073986802743885440046722756*r38[i]
) // 51090942171709440000 for i in range(len(r0))]
r19 = [(-16796*r[1][i]
+ 25194*r[2][i]
- 23256*r[3][i]
+ 15504*r[4][i]
- 7752*r[5][i]
+ 2907*r[6][i]
- 798*r[7][i]
+ 152*r[8][i]
- 18*r[9][i]
+ r[10][i]
+ 4862*r0[i]
- 2860*r2[i]
+ 7436*r4[i]
- 46420*r6[i]
+ 576236*r8[i]
- 13098580*r10[i]
+ 532310636*r12[i]
- 39968611540*r14[i]
+ 6350631494636*r16[i]
- 3730771315561300*r18[i]
- 2637991952943407764*r20[i]
- 46833363657400320000*r21[i]
- 734121065118879803860*r22[i]
- 10556240168378032128000*r23[i]
- 142438684135271315212564*r24[i]
- 1830415113744266649600000*r25[i]
- 22632897298190126259675220*r26[i]
- 271297526662043666104320000*r27[i]
- 3170344993810020486920015764*r28[i]
- 36274730261563609572556800000*r29[i]
- 407775103607650299563627591380*r30[i]
- 4515882637052182897862000640000*r31[i]
- 49377994276343186011748723193364*r32[i]
- 534053247401000753173510963200000*r33[i]
- 5722063606154183864914875339648340*r34[i]
- 60811730909031986048777521029120000*r35[i]
- 641729418431834160625738740379401364*r36[i]
- 6730380606921481449181267599974400000*r37[i]
- 70207898580127312813466155395513222100*r38[i]
) // 121645100408832000 for i in range(len(r0))]
r17 = [(4862*r[1][i]
- 7072*r[2][i]
+ 6188*r[3][i]
- 3808*r[4][i]
+ 1700*r[5][i]
- 544*r[6][i]
+ 119*r[7][i]
- 16*r[8][i]
+ r[9][i]
- 1430*r0[i]
+ 858*r2[i]
- 2310*r4[i]
+ 15258*r6[i]
- 206790*r8[i]
+ 5386458*r10[i]
- 272513670*r12[i]
+ 30255826458*r14[i]
- 12765597850950*r16[i]
- 6622557957272742*r18[i]
- 101370917007360000*r19[i]
- 1375210145685786630*r20[i]
- 17172233341046784000*r21[i]
- 201832098313986359142*r22[i]
- 2265471043586150400000*r23[i]
- 24529324224160803328710*r24[i]
- 258058524232798248960000*r25[i]
- 2652208374242713043720742*r26[i]
- 26739700571225856614400000*r27[i]
- 265323404171486113659725190*r28[i]
- 2597688920748017370193920000*r29[i]
- 25147613788240222384169485542*r30[i]
- 241125683321001354933657600000*r31[i]
- 2293170112631184981695915264070*r32[i]
- 21656158388689797460311183360000*r33[i]
- 203283794784841444836991831621542*r34[i]
- 1898267590696733462875776307200000*r35[i]
- 17646072330245312137111933794073350*r36[i]
- 163392570167583908119294187237376000*r37[i]
- 1507754227229479379470312529237936742*r38[i]
) // 355687428096000 for i in range(len(r0))]
r15 = [(-1430*r[1][i]
+ 2002*r[2][i]
- 1638*r[3][i]
+ 910*r[4][i]
- 350*r[5][i]
+ 90*r[6][i]
- 14*r[7][i]
+ r[8][i]
+ 429*r0[i]
- 264*r2[i]
+ 744*r4[i]
- 5304*r6[i]
+ 81384*r8[i]
- 2605944*r10[i]
+ 192387624*r12[i]
- 55942352184*r14[i]
- 20546119600536*r16[i]
- 266765571072000*r17[i]
- 3083760849804024*r18[i]
- 32945548027392000*r19[i]
- 332500281299403096*r20[i]
- 3215147584416768000*r21[i]
- 30076927429146721464*r22[i]
- 274100623905588480000*r23[i]
- 2446077617962088140056*r24[i]
- 21459412163122053120000*r25[i]
- 185641639183185136464504*r26[i]
- 1587401376760010972160000*r27[i]
- 13442713420403849918131416*r28[i]
- 112915002722102749808640000*r29[i]
- 941961013910760913890393144*r30[i]
- 7812419263561351877518080000*r31[i]
- 64474322285718607792730497176*r32[i]
- 529848386811984810994744320000*r33[i]
- 4338547620121893769542630267384*r34[i]
- 35415056327751829508662891008000*r35[i]
- 288317531175033442515609896757336*r36[i]
- 2341823147101379454117987013632000*r37[i]
- 18983391549723892653716655806647224*r38[i]
) // 1307674368000 for i in range(len(r0))]
r13 = [(429*r[1][i]
- 572*r[2][i]
+ 429*r[3][i]
- 208*r[4][i]
+ 65*r[5][i]
- 12*r[6][i]
+ r[7][i]
- 132*r0[i]
+ 84*r2[i]
- 252*r4[i]
+ 2004*r6[i]
- 37212*r8[i]
+ 1710324*r10[i]
- 325024572*r12[i]
- 80789566956*r14[i]
- 871782912000*r15[i]
- 8422900930332*r16[i]
- 75583578470400*r17[i]
- 643521842437836*r18[i]
- 5269678622208000*r19[i]
- 41890044885642492*r20[i]
- 325386564299596800*r21[i]
- 2481686964269990316*r22[i]
- 18652248729354240000*r23[i]
- 138536531588626169052*r24[i]
- 1019042849143807488000*r25[i]
- 7436421488952386592396*r26[i]
- 53911021949819274240000*r27[i]
- 388701690499592948238012*r28[i]
- 2789805187365599475072000*r29[i]
- 19946749502047187160692076*r30[i]
- 142159780685991861112320000*r31[i]
- 1010433303980489860989897372*r32[i]
- 7165521770403817166663116800*r33[i]
- 50716588034439244118483617356*r34[i]
- 358378772025058883636009472000*r35[i]
- 2528902640579773012941059115132*r36[i]
- 17824202779159732939433280230400*r37[i]
- 125502611080965065134883934376236*r38[i]
) // 6227020800 for i in range(len(r0))]
r11 = [(-132*r[1][i]
+ 165*r[2][i]
- 110*r[3][i]
+ 44*r[4][i]
- 10*r[5][i]
+ r[6][i]
+ 42*r0[i]
- 28*r2[i]
+ 92*r4[i]
- 868*r6[i]
+ 22652*r8[i]
- 2620708*r10[i]
- 415790788*r12[i]
- 3632428800*r13[i]
- 28616744548*r14[i]
- 210680870400*r15[i]
- 1479485236228*r16[i]
- 10038995366400*r17[i]
- 66394067988388*r18[i]
- 430591742380800*r19[i]
- 2750479262009668*r20[i]
- 17360942812012800*r21[i]
- 108550450893568228*r22[i]
- 673606803881088000*r23[i]
- 4154688725062207108*r24[i]
- 25499502190850688000*r25[i]
- 155878445775166700068*r26[i]
- 949776357849070752000*r27[i]
- 5771581202353414724548*r28[i]
- 34995682724855684832000*r29[i]
- 211811399872933910999908*r30[i]
- 1280080235834717770252800*r31[i]
- 7726641919200262371657988*r32[i]
- 46591059456870785061004800*r33[i]
- 280704018540064430354883748*r34[i]
- 1690018909819536161979590400*r35[i]
- 10169113413821714748538703428*r36[i]
- 61159784116494648773674886400*r37[i]
- 367684638335977863351585967588*r38[i]
) // 39916800 for i in range(len(r0))]
r9 = [(42*r[1][i]
- 48*r[2][i]
+ 27*r[3][i]
- 8*r[4][i]
+ r[5][i]
- 14*r0[i]
+ 10*r2[i]
- 38*r4[i]
+ 490*r6[i]
- 31238*r8[i]
- 2922230*r10[i]
- 19958400*r11[i]
- 124075238*r12[i]
- 726485760*r13[i]
- 4084385750*r14[i]
- 22313491200*r15[i]
- 119387268038*r16[i]
- 628980992640*r17[i]
- 3275389222070*r18[i]
- 16905818966400*r19[i]
- 86665431465638*r20[i]
- 441935114987520*r21[i]
- 2244295389943190*r22[i]
- 11360520464832000*r23[i]
- 57360469753884038*r24[i]
- 289038899804054400*r25[i]
- 1454155949521941110*r26[i]
- 7306671293537616000*r27[i]
- 36677059892827099238*r28[i]
- 183960524908301057280*r29[i]
- 922104761587650687830*r30[i]
- 4619736062008593926400*r31[i]
- 23135540444136227047238*r32[i]
- 115825176110799088940160*r33[i]
- 579715876176320506935350*r34[i]
- 2900939663557699476451200*r35[i]
- 14514140349055749129024038*r36[i]
- 72608472572041292373527040*r37[i]
- 363193454272347163609915670*r38[i]
) // 362880 for i in range(len(r0))]
r7 = [(-14*r[1][i]
+ 14*r[2][i]
- 6*r[3][i]
+ r[4][i]
+ 5*r0[i]
- 4*r2[i]
+ 20*r4[i]
- 604*r6[i]
- 29740*r8[i]
- 151200*r9[i]
- 708604*r10[i]
- 3160080*r11[i]
- 13645900*r12[i]
- 57657600*r13[i]
- 239967004*r14[i]
- 988107120*r15[i]
- 4037604460*r16[i]
- 16406863200*r17[i]
- 66398623804*r18[i]
- 267911678160*r19[i]
- 1078605601420*r20[i]
- 4335313752000*r21[i]
- 17403958407004*r22[i]
- 69804002545200*r23[i]
- 279780634372780*r24[i]
- 1120816644948000*r25[i]
- 4488349371924604*r26[i]
- 17968646803620240*r27[i]
- 71920337041294540*r28[i]
- 287818601403715200*r29[i]
- 1151686172846664604*r30[i]
- 4607980008114455280*r31[i]
- 18435626012705982700*r32[i]
- 73753622051697957600*r33[i]
- 295047842329672995004*r34[i]
- 1180291431927853642320*r35[i]
- 4721465916019935893260*r36[i]
- 18886764229967380219200*r37[i]
- 75549758619456576163804*r38[i]
) // 5040 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
- 1680*r7[i]
- 5542*r8[i]
- 17640*r9[i]
- 54958*r10[i]
- 168960*r11[i]
- 515062*r12[i]
- 1561560*r13[i]
- 4717438*r14[i]
- 14217840*r15[i]
- 42784582*r16[i]
- 128615880*r17[i]
- 386371918*r18[i]
- 1160164320*r19[i]
- 3482590102*r20[i]
- 10451964600*r21[i]
- 31364282398*r22[i]
- 94109624400*r23[i]
- 282362427622*r24[i]
- 847154391720*r25[i]
- 2541597392878*r26[i]
- 7625060614080*r27[i]
- 22875718713142*r28[i]
- 68628229881240*r29[i]
- 205886837127358*r30[i]
- 617664806349360*r31[i]
- 1853003008982662*r32[i]
- 5559026206817160*r33[i]
- 16677112980189838*r34[i]
- 50031407660046240*r35[i]
- 150094360419092182*r36[i]
- 450283356135183480*r37[i]
- 1350850618161364318*r38[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
- 126*r7[i]
- 254*r8[i]
- 510*r9[i]
- 1022*r10[i]
- 2046*r11[i]
- 4094*r12[i]
- 8190*r13[i]
- 16382*r14[i]
- 32766*r15[i]
- 65534*r16[i]
- 131070*r17[i]
- 262142*r18[i]
- 524286*r19[i]
- 1048574*r20[i]
- 2097150*r21[i]
- 4194302*r22[i]
- 8388606*r23[i]
- 16777214*r24[i]
- 33554430*r25[i]
- 67108862*r26[i]
- 134217726*r27[i]
- 268435454*r28[i]
- 536870910*r29[i]
- 1073741822*r30[i]
- 2147483646*r31[i]
- 4294967294*r32[i]
- 8589934590*r33[i]
- 17179869182*r34[i]
- 34359738366*r35[i]
- 68719476734*r36[i]
- 137438953470*r37[i]
- 274877906942*r38[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
- r7[i]
- r8[i]
- r9[i]
- r10[i]
- r11[i]
- r12[i]
- r13[i]
- r14[i]
- r15[i]
- r16[i]
- r17[i]
- r18[i]
- r19[i]
- r20[i]
- r21[i]
- r22[i]
- r23[i]
- r24[i]
- r25[i]
- r26[i]
- r27[i]
- r28[i]
- r29[i]
- r30[i]
- r31[i]
- r32[i]
- r33[i]
- r34[i]
- r35[i]
- r36[i]
- r37[i]
- r38[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38)
def natural_interpolate_21(r):
r0 = r[0]
r40 = r['infinity']
r38 = [(33578000610*(r[1][i] + r[-1][i])
- 28781143380*(r[2][i] + r[-2][i])
+ 22239974430*(r[3][i] + r[-3][i])
- 15471286560*(r[4][i] + r[-4][i])
+ 9669554100*(r[5][i] + r[-5][i])
- 5414950296*(r[6][i] + r[-6][i])
+ 2707475148*(r[7][i] + r[-7][i])
- 1203322288*(r[8][i] + r[-8][i])
+ 472733756*(r[9][i] + r[-9][i])
- 163011640*(r[10][i] + r[-10][i])
+ 48903492*(r[11][i] + r[-11][i])
- 12620256*(r[12][i] + r[-12][i])
+ 2760681*(r[13][i] + r[-13][i])
- 501942*(r[14][i] + r[-14][i])
+ 73815*(r[15][i] + r[-15][i])
- 8436*(r[16][i] + r[-16][i])
+ 703*(r[17][i] + r[-17][i])
- 38*(r[18][i] + r[-18][i])
+ (r[19][i] + r[-19][i])
- 35345263800*r0[i]
- 1291865865142504746047217843527183499264000000000*r40[i]
) // 523022617466601111760007224100074291200000000 for i in range(len(r0))]
r36 = [(-8597496600*(r[1][i] + r[-1][i])
+ 7307872110*(r[2][i] + r[-2][i])
- 5567902560*(r[3][i] + r[-3][i])
+ 3796297200*(r[4][i] + r[-4][i])
- 2310789600*(r[5][i] + r[-5][i])
+ 1251677700*(r[6][i] + r[-6][i])
- 600805296*(r[7][i] + r[-7][i])
+ 254186856*(r[8][i] + r[-8][i])
- 94143280*(r[9][i] + r[-9][i])
+ 30260340*(r[10][i] + r[-10][i])
- 8347680*(r[11][i] + r[-11][i])
+ 1947792*(r[12][i] + r[-12][i])
- 376992*(r[13][i] + r[-13][i])
+ 58905*(r[14][i] + r[-14][i])
- 7140*(r[15][i] + r[-15][i])
+ 630*(r[16][i] + r[-16][i])
- 36*(r[17][i] + r[-17][i])
+ (r[18][i] + r[-18][i])
+ 9075135300*r0[i]
- 784533926199901667640010836150111436800000000*r38[i]
- 907705752613286229459492537425678932377600000000*r40[i]
) // 371993326789901217467999448150835200000000 for i in range(len(r0))]
r34 = [(2203961430*(r[1][i] + r[-1][i])
- 1855967520*(r[2][i] + r[-2][i])
+ 1391975640*(r[3][i] + r[-3][i])
- 927983760*(r[4][i] + r[-4][i])
+ 548354040*(r[5][i] + r[-5][i])
- 286097760*(r[6][i] + r[-6][i])
+ 131128140*(r[7][i] + r[-7][i])
- 52451256*(r[8][i] + r[-8][i])
+ 18156204*(r[9][i] + r[-9][i])
- 5379616*(r[10][i] + r[-10][i])
+ 1344904*(r[11][i] + r[-11][i])
- 278256*(r[12][i] + r[-12][i])
+ 46376*(r[13][i] + r[-13][i])
- 5984*(r[14][i] + r[-14][i])
+ 561*(r[15][i] + r[-15][i])
- 34*(r[16][i] + r[-16][i])
+ (r[17][i] + r[-17][i])
- 2333606220*r0[i]
- 526990546285693391412999218213683200000000*r36[i]
- 518664095654379435828673830565907005440000000*r38[i]
- 373138241060740797524227217357125818777600000000*r40[i]
) // 295232799039604140847618609643520000000 for i in range(len(r0))]
r32 = [(-565722720*(r[1][i] + r[-1][i])
+ 471435600*(r[2][i] + r[-2][i])
- 347373600*(r[3][i] + r[-3][i])
+ 225792840*(r[4][i] + r[-4][i])
- 129024480*(r[5][i] + r[-5][i])
+ 64512240*(r[6][i] + r[-6][i])
- 28048800*(r[7][i] + r[-7][i])
+ 10518300*(r[8][i] + r[-8][i])
- 3365856*(r[9][i] + r[-9][i])
+ 906192*(r[10][i] + r[-10][i])
- 201376*(r[11][i] + r[-11][i])
+ 35960*(r[12][i] + r[-12][i])
- 4960*(r[13][i] + r[-13][i])
+ 496*(r[14][i] + r[-14][i])
- 32*(r[15][i] + r[-15][i])
+ (r[16][i] + r[-16][i])
+ 601080390*r0[i]
- 393643732052805521130158146191360000000*r34[i]
- 326527475737802179777466182265733120000000*r36[i]
- 198969979872214920293886346099446251520000000*r38[i]
- 99626745669333527035567016277524852244480000000*r40[i]
) // 263130836933693530167218012160000000 for i in range(len(r0))]
r30 = [(145422675*(r[1][i] + r[-1][i])
- 119759850*(r[2][i] + r[-2][i])
+ 86493225*(r[3][i] + r[-3][i])
- 54627300*(r[4][i] + r[-4][i])
+ 30045015*(r[5][i] + r[-5][i])
- 14307150*(r[6][i] + r[-6][i])
+ 5852925*(r[7][i] + r[-7][i])
- 2035800*(r[8][i] + r[-8][i])
+ 593775*(r[9][i] + r[-9][i])
- 142506*(r[10][i] + r[-10][i])
+ 27405*(r[11][i] + r[-11][i])
- 4060*(r[12][i] + r[-12][i])
+ 435*(r[13][i] + r[-13][i])
- 30*(r[14][i] + r[-14][i])
+ (r[15][i] + r[-15][i])
- 155117520*r0[i]
- 328913546167116912709022515200000000*r32[i]
- 227575282593028191903372678266880000000*r34[i]
- 116309421454977381321426414757478400000000*r36[i]
- 49083095586740430887431564189583278080000000*r38[i]
- 18139371393109511951007844941215406489600000000*r40[i]
) // 265252859812191058636308480000000 for i in range(len(r0))]
r28 = [(-37442160*(r[1][i] + r[-1][i])
+ 30421755*(r[2][i] + r[-2][i])
- 21474180*(r[3][i] + r[-3][i])
+ 13123110*(r[4][i] + r[-4][i])
- 6906900*(r[5][i] + r[-5][i])
+ 3108105*(r[6][i] + r[-6][i])
- 1184040*(r[7][i] + r[-7][i])
+ 376740*(r[8][i] + r[-8][i])
- 98280*(r[9][i] + r[-9][i])
+ 20475*(r[10][i] + r[-10][i])
- 3276*(r[11][i] + r[-11][i])
+ 378*(r[12][i] + r[-12][i])
- 28*(r[13][i] + r[-13][i])
+ (r[14][i] + r[-14][i])
+ 40116600*r0[i]
- 309461669780889568409026560000000*r30[i]
- 176516936443019409820508749824000000*r32[i]
- 74833313645455216256514439249920000000*r34[i]
- 26337328459046574816219104447299584000000*r36[i]
- 8155948144934385059006601147769159680000000*r38[i]
- 2301709517171786559798286695904076365824000000*r40[i]
) // 304888344611713860501504000000 for i in range(len(r0))]
r26 = [(9657700*(r[1][i] + r[-1][i])
- 7726160*(r[2][i] + r[-2][i])
+ 5311735*(r[3][i] + r[-3][i])
- 3124550*(r[4][i] + r[-4][i])
+ 1562275*(r[5][i] + r[-5][i])
- 657800*(r[6][i] + r[-6][i])
+ 230230*(r[7][i] + r[-7][i])
- 65780*(r[8][i] + r[-8][i])
+ 14950*(r[9][i] + r[-9][i])
- 2600*(r[10][i] + r[-10][i])
+ 325*(r[11][i] + r[-11][i])
- 26*(r[12][i] + r[-12][i])
+ (r[13][i] + r[-13][i])
- 10400600*r0[i]
- 330295706662690015543296000000*r28[i]
- 153257207891488167212089344000000*r30[i]
- 53222214421459539592188788736000000*r32[i]
- 15436506593303376230082373484544000000*r34[i]
- 3960094929842931739454572322881536000000*r36[i]
- 930084233815670751630942950980583424000000*r38[i]
- 204528766884160018873274371645367648256000000*r40[i]
) // 403291461126605635584000000 for i in range(len(r0))]
r24 = [(-2496144*(r[1][i] + r[-1][i])
+ 1961256*(r[2][i] + r[-2][i])
- 1307504*(r[3][i] + r[-3][i])
+ 735471*(r[4][i] + r[-4][i])
- 346104*(r[5][i] + r[-5][i])
+ 134596*(r[6][i] + r[-6][i])
- 42504*(r[7][i] + r[-7][i])
+ 10626*(r[8][i] + r[-8][i])
- 2024*(r[9][i] + r[-9][i])
+ 276*(r[10][i] + r[-10][i])
- 24*(r[11][i] + r[-11][i])
+ (r[12][i] + r[-12][i])
+ 2704156*r0[i]
- 403291461126605635584000000*r26[i]
- 149903436100759314746572800000*r28[i]
- 42033455827381598974377984000000*r30[i]
- 9910695932425713906157643366400000*r32[i]
- 2078962023961017163954848006144000000*r34[i]
- 401274139495715827174031120636313600000*r36[i]
- 72837740568171787457915404507152384000000*r38[i]
- 12620369661259070567869332718886859571200000*r40[i]
) // 620448401733239439360000 for i in range(len(r0))]
r22 = [(646646*(r[1][i] + r[-1][i])
- 497420*(r[2][i] + r[-2][i])
+ 319770*(r[3][i] + r[-3][i])
- 170544*(r[4][i] + r[-4][i])
+ 74613*(r[5][i] + r[-5][i])
- 26334*(r[6][i] + r[-6][i])
+ 7315*(r[7][i] + r[-7][i])
- 1540*(r[8][i] + r[-8][i])
+ 231*(r[9][i] + r[-9][i])
- 22*(r[10][i] + r[-10][i])
+ (r[11][i] + r[-11][i])
- 705432*r0[i]
- 568744368255469486080000*r24[i]
- 166357727714724824678400000*r26[i]
- 37042320704478727628390400000*r28[i]
- 6988909951599209517839155200000*r30[i]
- 1180836611760352104108962611200000*r32[i]
- 184607985589364774573429361868800000*r34[i]
- 27272218262298384682708194086092800000*r36[i]
- 3861838803337560097698395778726297600000*r38[i]
- 529471212011799260411940801849645465600000*r40[i]
) // 1124000727777607680000 for i in range(len(r0))]
r20 = [(-167960*(r[1][i] + r[-1][i])
+ 125970*(r[2][i] + r[-2][i])
- 77520*(r[3][i] + r[-3][i])
+ 38760*(r[4][i] + r[-4][i])
- 15504*(r[5][i] + r[-5][i])
+ 4845*(r[6][i] + r[-6][i])
- 1140*(r[7][i] + r[-7][i])
+ 190*(r[8][i] + r[-8][i])
- 20*(r[9][i] + r[-9][i])
+ (r[10][i] + r[-10][i])
+ 184756*r0[i]
- 936667273148006400000*r22[i]
- 211124803367560642560000*r24[i]
- 36608302274885332992000000*r26[i]
- 5425950533240873322086400000*r28[i]
- 725494605231272191451136000000*r30[i]
- 90317652741043657957240012800000*r32[i]
- 10681064948020015063470219264000000*r34[i]
- 1216234618180639720975550420582400000*r36[i]
- 134607612138429628983625351999488000000*r38[i]
- 14578366393789236829898507440652451840000*r40[i]
) // 2432902008176640000 for i in range(len(r0))]
r18 = [(43758*(r[1][i] + r[-1][i])
- 31824*(r[2][i] + r[-2][i])
+ 18564*(r[3][i] + r[-3][i])
- 8568*(r[4][i] + r[-4][i])
+ 3060*(r[5][i] + r[-5][i])
- 816*(r[6][i] + r[-6][i])
+ 153*(r[7][i] + r[-7][i])
- 18*(r[8][i] + r[-8][i])
+ (r[9][i] + r[-9][i])
- 48620*r0[i]
- 1824676506132480000*r20[i]
- 309100200138842112000*r22[i]
- 40778478784550707200000*r24[i]
- 4645053436190368481280000*r26[i]
- 481314610282065419059200000*r28[i]
- 46758400573464312663490560000*r30[i]
- 4340262299778024388805836800000*r32[i]
- 389810850996416354285601300480000*r34[i]
- 34168816632541202331763973529600000*r36[i]
- 2941066263016510346147295370272768000*r38[i]
- 249691933432545691845292589410836480000*r40[i]
) // 6402373705728000 for i in range(len(r0))]
r16 = [(-11440*(r[1][i] + r[-1][i])
+ 8008*(r[2][i] + r[-2][i])
- 4368*(r[3][i] + r[-3][i])
+ 1820*(r[4][i] + r[-4][i])
- 560*(r[5][i] + r[-5][i])
+ 120*(r[6][i] + r[-6][i])
- 16*(r[7][i] + r[-7][i])
+ (r[8][i] + r[-8][i])
+ 12870*r0[i]
- 4268249137152000*r18[i]
- 527128768438272000*r20[i]
- 51442361350668288000*r22[i]
- 4385609982489415680000*r24[i]
- 343350594609952849920000*r26[i]
- 25398422028160175554560000*r28[i]
- 1806640043553643996938240000*r30[i]
- 124998708216981630040289280000*r32[i]
- 8477574188991756975915909120000*r34[i]
- 566640901244029272138606256128000*r36[i]
- 37469170353622071265887792218112000*r38[i]
- 2457916223969789263693314523533312000*r40[i]
) // 20922789888000 for i in range(len(r0))]
r14 = [(3003*(r[1][i] + r[-1][i])
- 2002*(r[2][i] + r[-2][i])
+ 1001*(r[3][i] + r[-3][i])
- 364*(r[4][i] + r[-4][i])
+ 91*(r[5][i] + r[-5][i])
- 14*(r[6][i] + r[-6][i])
+ (r[7][i] + r[-7][i])
- 3432*r0[i]
- 12204960768000*r16[i]
- 1058170098585600*r18[i]
- 73775500710912000*r20[i]
- 4555411900194355200*r22[i]
- 261131482210959360000*r24[i]
- 14266599888013304832000*r26[i]
- 754754307297469839360000*r28[i]
- 39057272623118392651008000*r30[i]
- 1990236929603886055572480000*r32[i]
- 100317304785653440333283635200*r34[i]
- 5017302808350824370904132608000*r36[i]
- 249538838908236261152065923225600*r38[i]
- 12360976075014001109372936189952000*r40[i]
) // 87178291200 for i in range(len(r0))]
r12 = [(-792*(r[1][i] + r[-1][i])
+ 495*(r[2][i] + r[-2][i])
- 220*(r[3][i] + r[-3][i])
+ 66*(r[4][i] + r[-4][i])
- 12*(r[5][i] + r[-5][i])
+ (r[6][i] + r[-6][i])
+ 924*r0[i]
- 43589145600*r14[i]
- 2528170444800*r16[i]
- 120467944396800*r18[i]
- 5167100908569600*r20[i]
- 208331313744153600*r22[i]
- 8083281646573056000*r24[i]
- 305994026290208256000*r26[i]
- 11397316294188849024000*r28[i]
- 419948192698268217984000*r30[i]
- 15360962830016613243033600*r32[i]
- 559092713482449420732057600*r34[i]
- 20280226917834433943755084800*r36[i]
- 733917409397935785284098636800*r38[i]
- 26516869922120782776160606617600*r40[i]
) // 479001600 for i in range(len(r0))]
r10 = [(210*(r[1][i] + r[-1][i])
- 120*(r[2][i] + r[-2][i])
+ 45*(r[3][i] + r[-3][i])
- 10*(r[4][i] + r[-4][i])
+ (r[5][i] + r[-5][i])
- 252*r0[i]
- 199584000*r12[i]
- 7264857600*r14[i]
- 223134912000*r16[i]
- 6289809926400*r18[i]
- 169058189664000*r20[i]
- 4419351149875200*r22[i]
- 113605204648320000*r24[i]
- 2890388998040544000*r26[i]
- 73066712935376160000*r28[i]
- 1839605249083010572800*r30[i]
- 46197360620085939264000*r32[i]
- 1158251761107990889401600*r34[i]
- 29009396635576994764512000*r36[i]
- 726084725720412923735270400*r38[i]
- 18165716613255899607139584000*r40[i]
) // 3628800 for i in range(len(r0))]
r8 = [(-56*(r[1][i] + r[-1][i])
+ 28*(r[2][i] + r[-2][i])
- 8*(r[3][i] + r[-3][i])
+ (r[4][i] + r[-4][i])
+ 70*r0[i]
- 1209600*r10[i]
- 25280640*r12[i]
- 461260800*r14[i]
- 7904856960*r16[i]
- 131254905600*r18[i]
- 2143293425280*r20[i]
- 34682510016000*r22[i]
- 558432020361600*r24[i]
- 8966533159584000*r26[i]
- 143749174428961920*r28[i]
- 2302548811229721600*r30[i]
- 36863840064915642240*r32[i]
- 590028976413583660800*r34[i]
- 9442331455422829138560*r36[i]
- 151094113839739041753600*r38[i]
- 2417657116643486089706880*r40[i]
) // 40320 for i in range(len(r0))]
r6 = [(15*(r[1][i] + r[-1][i])
- 6*(r[2][i] + r[-2][i])
+ (r[3][i] + r[-3][i])
- 20*r0[i]
- 10080*r8[i]
- 105840*r10[i]
- 1013760*r12[i]
- 9369360*r14[i]
- 85307040*r16[i]
- 771695280*r18[i]
- 6960985920*r20[i]
- 62711787600*r22[i]
- 564657746400*r24[i]
- 5082926350320*r26[i]
- 45750363684480*r28[i]
- 411769379287440*r30[i]
- 3705988838096160*r32[i]
- 33354157240902960*r34[i]
- 300188445960277440*r36[i]
- 2701700136811100880*r38[i]
- 24315317723974324320*r40[i]
) // 720 for i in range(len(r0))]
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
- 504*r8[i]
- 2040*r10[i]
- 8184*r12[i]
- 32760*r14[i]
- 131064*r16[i]
- 524280*r18[i]
- 2097144*r20[i]
- 8388600*r22[i]
- 33554424*r24[i]
- 134217720*r26[i]
- 536870904*r28[i]
- 2147483640*r30[i]
- 8589934584*r32[i]
- 34359738360*r34[i]
- 137438953464*r36[i]
- 549755813880*r38[i]
- 2199023255544*r40[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
- 2*r8[i]
- 2*r10[i]
- 2*r12[i]
- 2*r14[i]
- 2*r16[i]
- 2*r18[i]
- 2*r20[i]
- 2*r22[i]
- 2*r24[i]
- 2*r26[i]
- 2*r28[i]
- 2*r30[i]
- 2*r32[i]
- 2*r34[i]
- 2*r36[i]
- 2*r38[i]
- 2*r40[i]
) // 2 for i in range(len(r0))]
r39 = [(-6564120420*r[1][i]
+ 11338026180*r[2][i]
- 13309856820*r[3][i]
+ 12570420330*r[4][i]
- 10056336264*r[5][i]
+ 6962078952*r[6][i]
- 4211628008*r[7][i]
+ 2234741392*r[8][i]
- 1040310648*r[9][i]
+ 423830264*r[10][i]
- 150391384*r[11][i]
+ 46142811*r[12][i]
- 12118314*r[13][i]
+ 2686866*r[14][i]
- 493506*r[15][i]
+ 73112*r[16][i]
- 8398*r[17][i]
+ 702*r[18][i]
- 38*r[19][i]
+ r[20][i]
+ 1767263190*r0[i]
- 955277400*r2[i]
+ 2156197560*r4[i]
- 10855425000*r6[i]
+ 98876533560*r8[i]
- 1456859058600*r10[i]
+ 32382608125560*r12[i]
- 1036360772970600*r14[i]
+ 46242812090245560*r16[i]
- 2813858311510281000*r18[i]
+ 230141619686501005560*r20[i]
- 25097337236284407949800*r22[i]
+ 3642002181929040219157560*r24[i]
- 706474912755087069174777000*r26[i]
+ 185490702479102020671448093560*r28[i]
- 67501512373123369695638979402600*r30[i]
+ 35506616897715366055874618759845560*r32[i]
- 29173319982987640073110629923442306600*r34[i]
+ 44272025958057634433180503709478279085560*r36[i]
- 222019441630075420847480526017947263931809000*r38[i]
- 1219813882056330049405575791394671579625372874440*r40[i]
) // 20397882081197443358640281739902897356800000000 for i in range(len(r0))]
r37 = [(1767263190*r[1][i]
- 3029594040*r[2][i]
+ 3511574910*r[3][i]
- 3257112960*r[4][i]
+ 2544619500*r[5][i]
- 1709984304*r[6][i]
+ 997490844*r[7][i]
- 506662016*r[8][i]
+ 223926516*r[9][i]
- 85795600*r[10][i]
+ 28312548*r[11][i]
- 7970688*r[12][i]
+ 1888887*r[13][i]
- 369852*r[14][i]
+ 58275*r[15][i]
- 7104*r[16][i]
+ 629*r[17][i]
- 36*r[18][i]
+ r[19][i]
- 477638700*r0[i]
+ 259289580*r2[i]
- 589294500*r4[i]
+ 2996657580*r6[i]
- 27670359300*r8[i]
+ 415064933580*r10[i]
- 9439543875300*r12[i]
+ 310922483993580*r14[i]
- 14379880666402500*r16[i]
+ 914767168887053580*r18[i]
- 79051272004645620900*r20[i]
+ 9231401536061270849580*r22[i]
- 1459700260139475814330500*r24[i]
+ 315843905250429722227637580*r26[i]
- 95612546130070295522414451300*r28[i]
+ 42177612582297377823299737193580*r30[i]
- 29268533564152352561039458453023300*r32[i]
+ 37747202396256876155482291281278813580*r34[i]
- 161759954125032708920885781040309430206500*r36[i]
- 763162014442847423121851269222329739576686420*r38[i]
- 33996470135329072264400469566504828928000000000*r39[i]
- 1314149222797294391875041342296266627244339280900*r40[i]
) // 13763753091226345046315979581580902400000000 for i in range(len(r0))]
r35 = [(-477638700*r[1][i]
+ 811985790*r[2][i]
- 927983760*r[3][i]
+ 843621600*r[4][i]
- 641886000*r[5][i]
+ 417225900*r[6][i]
- 233646504*r[7][i]
+ 112971936*r[8][i]
- 47071640*r[9][i]
+ 16811300*r[10][i]
- 5101360*r[11][i]
+ 1298528*r[12][i]
- 272272*r[13][i]
+ 45815*r[14][i]
- 5950*r[15][i]
+ 560*r[16][i]
- 34*r[17][i]
+ r[18][i]
+ 129644790*r0[i]
- 70715340*r2[i]
+ 161960940*r4[i]
- 832930740*r6[i]
+ 7810859340*r8[i]
- 119578066740*r10[i]
+ 2791740107340*r12[i]
- 95062235276340*r14[i]
+ 4584012079172940*r16[i]
- 307268933913567540*r18[i]
+ 28355038085389144140*r20[i]
- 3597774935929125068340*r22[i]
+ 632729503874459828228940*r24[i]
- 157381528472579148083026740*r26[i]
+ 57577884185625191071239755340*r28[i]
- 33404393172944223690128125810740*r30[i]
+ 36271128388074981554067219056171340*r32[i]
- 131671692334895976886647813958596908340*r34[i]
- 529104107360143104505564190890974500955060*r36[i]
- 21792609061108379656666967670836428800000000*r37[i]
- 779765567254824678774814590170424618060927540*r38[i]
- 25214048683702395262763681595157748121600000000*r39[i]
- 754531895504954495472529428607358759602244935860*r40[i]
) // 10333147966386144929666651337523200000000 for i in range(len(r0))]
r33 = [(129644790*r[1][i]
- 218349120*r[2][i]
+ 245642760*r[3][i]
- 218349120*r[4][i]
+ 161280600*r[5][i]
- 100975680*r[6][i]
+ 53993940*r[7][i]
- 24682944*r[8][i]
+ 9612108*r[9][i]
- 3164480*r[10][i]
+ 870232*r[11][i]
- 196416*r[12][i]
+ 35464*r[13][i]
- 4928*r[14][i]
+ 495*r[15][i]
- 32*r[16][i]
+ r[17][i]
- 35357670*r0[i]
+ 19389690*r2[i]
- 44796870*r4[i]
+ 233344890*r6[i]
- 2227139910*r8[i]
+ 34903389690*r10[i]
- 839988260550*r12[i]
+ 29734601940090*r14[i]
- 1506293149214790*r16[i]
+ 107487540061668090*r18[i]
- 10743535525710258630*r20[i]
+ 1511267716903778445690*r22[i]
- 304525956073869018848070*r24[i]
+ 91234873454404063067344890*r26[i]
- 43747586259736794619504039110*r28[i]
+ 39574917458915050445099774637690*r30[i]
- 120523981455993504966525708346887750*r32[i]
- 408775192473644376465790167368394203910*r34[i]
- 15499721949579217394499977006284800000000*r35[i]
- 511206585269023792365556128001469646849990*r36[i]
- 15254826342775865759666877369585500160000000*r37[i]
- 421754497238984285335705463354740490210507910*r38[i]
- 10974654148845317574241976981091935846400000000*r39[i]
- 271793538072560300468434911462753194293644181830*r40[i]
) // 8683317618811886495518194401280000000 for i in range(len(r0))]
r31 = [(-35357670*r[1][i]
+ 58929450*r[2][i]
- 65132550*r[3][i]
+ 56448210*r[4][i]
- 40320150*r[5][i]
+ 24192090*r[6][i]
- 12271350*r[7][i]
+ 5259150*r[8][i]
- 1893294*r[9][i]
+ 566370*r[10][i]
- 138446*r[11][i]
+ 26970*r[12][i]
- 4030*r[13][i]
+ 434*r[14][i]
- 30*r[15][i]
+ r[16][i]
+ 9694845*r0[i]
- 5348880*r2[i]
+ 12480720*r4[i]
- 65969520*r6[i]
+ 642563280*r8[i]
- 10347602160*r10[i]
+ 258040917840*r12[i]
- 9564008626800*r14[i]
+ 514021079720400*r16[i]
- 39590373677587440*r18[i]
+ 4371353677873146960*r20[i]
- 701971899866535028080*r22[i]
+ 169737570795219895373520*r24[i]
- 66396273378844288679892720*r26[i]
+ 49448835121192219782326176080*r28[i]
- 124963193751534047864734415925360*r30[i]
- 354113410826574103722030528083469360*r32[i]
- 12301366626650172535317442068480000000*r33[i]
- 372225904019072507165665501545458070000*r34[i]
- 10203983616806318118045818195804160000000*r35[i]
- 259484653500223872483011119661283865786800*r36[i]
- 6217811871006716259183948315607695360000000*r37[i]
- 141956901865997956445469727796622341498870640*r38[i]
- 3113335802166672719861469258672651632640000000*r39[i]
- 66003822624082868383556482555741495612650600240*r40[i]
) // 8222838654177922817725562880000000 for i in range(len(r0))]
r29 = [(9694845*r[1][i]
- 15967980*r[2][i]
+ 17298645*r[3][i]
- 14567280*r[4][i]
+ 10015005*r[5][i]
- 5722860*r[6][i]
+ 2731365*r[7][i]
- 1085760*r[8][i]
+ 356265*r[9][i]
- 95004*r[10][i]
+ 20097*r[11][i]
- 3248*r[12][i]
+ 377*r[13][i]
- 28*r[14][i]
+ r[15][i]
- 2674440*r0[i]
+ 1485800*r2[i]
- 3506488*r4[i]
+ 18850280*r6[i]
- 188004088*r8[i]
+ 3125835560*r10[i]
- 81314498488*r12[i]
+ 3185384180840*r14[i]
- 184064268909688*r16[i]
+ 15598375633694120*r18[i]
- 1958105850969957688*r20[i]
+ 375744491571024583400*r22[i]
- 118117302690774819242488*r24[i]
+ 71447614092662750198256680*r26[i]
- 147980747895225006590333244088*r28[i]
- 346368637877614395127589803878040*r30[i]
- 10963784872237230423634083840000000*r31[i]
- 302766527792977996357877082103322488*r32[i]
- 7585842753100939730112422608896000000*r33[i]
- 176553572119721839407097582006071612760*r34[i]
- 3876980715165912710714213825249280000000*r35[i]
- 81213796311764134505181592648745883717688*r36[i]
- 1636103186224681029581052139652775936000000*r37[i]
- 31895543813319775842490572300866856117139480*r38[i]
- 604645713103650398366928164707180216320000000*r39[i]
- 11189653759353064214370349765226592602607549688*r40[i]
) // 8841761993739701954543616000000 for i in range(len(r0))]
r27 = [(-2674440*r[1][i]
+ 4345965*r[2][i]
- 4601610*r[3][i]
+ 3749460*r[4][i]
- 2466750*r[5][i]
+ 1332045*r[6][i]
- 592020*r[7][i]
+ 215280*r[8][i]
- 63180*r[9][i]
+ 14625*r[10][i]
- 2574*r[11][i]
+ 324*r[12][i]
- 26*r[13][i]
+ r[14][i]
+ 742900*r0[i]
- 416024*r2[i]
+ 994840*r4[i]
- 5454824*r6[i]
+ 55944280*r8[i]
- 966290024*r10[i]
+ 26454613720*r12[i]
- 1109329691624*r14[i]
+ 70212852387160*r16[i]
- 6733670404619624*r18[i]
+ 1005318113348848600*r20[i]
- 249581050854994274024*r22[i]
+ 120719220687299365182040*r24[i]
- 202039976682357297272094824*r26[i]
- 385557844336439370252173428520*r28[i]
- 11052202492174627443179520000000*r29[i]
- 276888650579451671741587901762024*r30[i]
- 6304176301536407493589598208000000*r31[i]
- 133535841584115505205141919375399080*r32[i]
- 2672618344480543437732658544640000000*r33[i]
- 51095126335993498323380094454901195624*r34[i]
- 940618873537377672007825158832128000000*r35[i]
- 16776403501444391106926987629186000345640*r36[i]
- 291283862319085180678807183848898560000000*r37[i]
- 4942310839108515578583708125038854650555624*r38[i]
- 82203911327563805707081667710859870208000000*r39[i]
- 1343752600475734599375534320311340373516684200*r40[i]
) // 10888869450418352160768000000 for i in range(len(r0))]
r25 = [(742900*r[1][i]
- 1188640*r[2][i]
+ 1225785*r[3][i]
- 961400*r[4][i]
+ 600875*r[5][i]
- 303600*r[6][i]
+ 123970*r[7][i]
- 40480*r[8][i]
+ 10350*r[9][i]
- 2000*r[10][i]
+ 275*r[11][i]
- 24*r[12][i]
+ r[13][i]
- 208012*r0[i]
+ 117572*r2[i]
- 285532*r4[i]
+ 1602692*r6[i]
- 16996252*r8[i]
+ 307475012*r10[i]
- 8966430172*r12[i]
+ 409745686532*r14[i]
- 29195711499292*r16[i]
+ 3312133208909252*r18[i]
- 636215671041835612*r20[i]
+ 241648300078174135172*r22[i]
- 321511316149669476991132*r24[i]
- 492817676505266866078123708*r26[i]
- 12703681025488077520896000000*r27[i]
- 286779648275654636997381637852*r28[i]
- 5894507995826467969695744000000*r29[i]
- 112914054231542703053832892635388*r30[i]
- 2047008246979213061238030336000000*r31[i]
- 35501568925223446300815211192767772*r32[i]
- 593711792050129855003168210944000000*r33[i]
- 9632134956680435093368218113996247868*r34[i]
- 152311343455497374594406627803136000000*r35[i]
- 2356318736218539774396037820111678892892*r36[i]
- 35772470531371951985805498114637824000000*r37[i]
- 534273042749950920189640352996759062689148*r38[i]
- 7866491034006154572049014294052601856000000*r39[i]
- 114383224059606274110181105712262975351245212*r40[i]
) // 15511210043330985984000000 for i in range(len(r0))]
r23 = [(-208012*r[1][i]
+ 326876*r[2][i]
- 326876*r[3][i]
+ 245157*r[4][i]
- 144210*r[5][i]
+ 67298*r[6][i]
- 24794*r[7][i]
+ 7084*r[8][i]
- 1518*r[9][i]
+ 230*r[10][i]
- 22*r[11][i]
+ r[12][i]
+ 58786*r0[i]
- 33592*r2[i]
+ 83096*r4[i]
- 479752*r6[i]
+ 5299736*r8[i]
- 101549512*r10[i]
+ 3208453976*r12[i]
- 164071220872*r14[i]
+ 13743680753816*r16[i]
- 1993276972245832*r18[i]
+ 581947914140407256*r20[i]
- 603916464771468176392*r22[i]
- 730803773459954540777704*r24[i]
- 16803810880275234816000000*r25[i]
- 339155768243774227716964552*r26[i]
- 6245976504198304781107200000*r27[i]
- 107413822788261782335458993064*r28[i]
- 1751393992807566623932416000000*r29[i]
- 27365156266821215807862420562312*r30[i]
- 412945663851071412756568473600000*r31[i]
- 6053949680529454447550745704030824*r32[i]
- 86623417665042381831452000256000000*r33[i]
- 1214146547565910406028014931410521672*r34[i]
- 16719755812321492798917963359846400000*r35[i]
- 226758627215029497194516602329808882984*r36[i]
- 3034905857007157810746475187798016000000*r37[i]
- 40151799724774280996886476759684489594632*r38[i]
- 525848735885794606994555529953619148800000*r39[i]
- 6825564942475643900873841059427230143341544*r40[i]
) // 25852016738884976640000 for i in range(len(r0))]
r21 = [(58786*r[1][i]
- 90440*r[2][i]
+ 87210*r[3][i]
- 62016*r[4][i]
+ 33915*r[5][i]
- 14364*r[6][i]
+ 4655*r[7][i]
- 1120*r[8][i]
+ 189*r[9][i]
- 20*r[10][i]
+ r[11][i]
- 16796*r0[i]
+ 9724*r2[i]
- 24596*r4[i]
+ 147004*r6[i]
- 1708916*r8[i]
+ 35240284*r10[i]
- 1237329236*r12[i]
+ 73853629564*r14[i]
- 7850527669556*r16[i]
+ 1717351379730844*r18[i]
- 1359124435588313876*r20[i]
- 1272410676942417239876*r22[i]
- 25852016738884976640000*r23[i]
- 462292539259962003646196*r24[i]
- 7561714896123855667200000*r25[i]
- 115761644587269354830466596*r26[i]
- 1683741850203578528563200000*r27[i]
- 23512975860299444963550050516*r28[i]
- 317677725072691341719961600000*r29[i]
- 4176614976496441445095962733316*r30[i]
- 53674391443652368368589209600000*r31[i]
- 676635955671282540673335079110836*r32[i]
- 8391272072243853389701334630400000*r33[i]
- 102611708232289325546408008313624036*r34[i]
- 1239646284649926576486736094822400000*r35[i]
- 14819283410691765614379616648600811156*r36[i]
- 175538127424434549895381626305740800000*r37[i]
- 2062659648435073986802743885440046722756*r38[i]
- 24066873273263602745997309174983884800000*r39[i]
- 279069134864297423784787795404361206735476*r40[i]
) // 51090942171709440000 for i in range(len(r0))]
r19 = [(-16796*r[1][i]
+ 25194*r[2][i]
- 23256*r[3][i]
+ 15504*r[4][i]
- 7752*r[5][i]
+ 2907*r[6][i]
- 798*r[7][i]
+ 152*r[8][i]
- 18*r[9][i]
+ r[10][i]
+ 4862*r0[i]
- 2860*r2[i]
+ 7436*r4[i]
- 46420*r6[i]
+ 576236*r8[i]
- 13098580*r10[i]
+ 532310636*r12[i]
- 39968611540*r14[i]
+ 6350631494636*r16[i]
- 3730771315561300*r18[i]
- 2637991952943407764*r20[i]
- 46833363657400320000*r21[i]
- 734121065118879803860*r22[i]
- 10556240168378032128000*r23[i]
- 142438684135271315212564*r24[i]
- 1830415113744266649600000*r25[i]
- 22632897298190126259675220*r26[i]
- 271297526662043666104320000*r27[i]
- 3170344993810020486920015764*r28[i]
- 36274730261563609572556800000*r29[i]
- 407775103607650299563627591380*r30[i]
- 4515882637052182897862000640000*r31[i]
- 49377994276343186011748723193364*r32[i]
- 534053247401000753173510963200000*r33[i]
- 5722063606154183864914875339648340*r34[i]
- 60811730909031986048777521029120000*r35[i]
- 641729418431834160625738740379401364*r36[i]
- 6730380606921481449181267599974400000*r37[i]
- 70207898580127312813466155395513222100*r38[i]
- 728918319689461841494925372032622592000*r39[i]
- 7536441803725213229125462424550696575764*r40[i]
) // 121645100408832000 for i in range(len(r0))]
r17 = [(4862*r[1][i]
- 7072*r[2][i]
+ 6188*r[3][i]
- 3808*r[4][i]
+ 1700*r[5][i]
- 544*r[6][i]
+ 119*r[7][i]
- 16*r[8][i]
+ r[9][i]
- 1430*r0[i]
+ 858*r2[i]
- 2310*r4[i]
+ 15258*r6[i]
- 206790*r8[i]
+ 5386458*r10[i]
- 272513670*r12[i]
+ 30255826458*r14[i]
- 12765597850950*r16[i]
- 6622557957272742*r18[i]
- 101370917007360000*r19[i]
- 1375210145685786630*r20[i]
- 17172233341046784000*r21[i]
- 201832098313986359142*r22[i]
- 2265471043586150400000*r23[i]
- 24529324224160803328710*r24[i]
- 258058524232798248960000*r25[i]
- 2652208374242713043720742*r26[i]
- 26739700571225856614400000*r27[i]
- 265323404171486113659725190*r28[i]
- 2597688920748017370193920000*r29[i]
- 25147613788240222384169485542*r30[i]
- 241125683321001354933657600000*r31[i]
- 2293170112631184981695915264070*r32[i]
- 21656158388689797460311183360000*r33[i]
- 203283794784841444836991831621542*r34[i]
- 1898267590696733462875776307200000*r35[i]
- 17646072330245312137111933794073350*r36[i]
- 163392570167583908119294187237376000*r37[i]
- 1507754227229479379470312529237936742*r38[i]
- 13871774079585871769182921633935360000*r39[i]
- 127291574907112728538906245247680921030*r40[i]
) // 355687428096000 for i in range(len(r0))]
r15 = [(-1430*r[1][i]
+ 2002*r[2][i]
- 1638*r[3][i]
+ 910*r[4][i]
- 350*r[5][i]
+ 90*r[6][i]
- 14*r[7][i]
+ r[8][i]
+ 429*r0[i]
- 264*r2[i]
+ 744*r4[i]
- 5304*r6[i]
+ 81384*r8[i]
- 2605944*r10[i]
+ 192387624*r12[i]
- 55942352184*r14[i]
- 20546119600536*r16[i]
- 266765571072000*r17[i]
- 3083760849804024*r18[i]
- 32945548027392000*r19[i]
- 332500281299403096*r20[i]
- 3215147584416768000*r21[i]
- 30076927429146721464*r22[i]
- 274100623905588480000*r23[i]
- 2446077617962088140056*r24[i]
- 21459412163122053120000*r25[i]
- 185641639183185136464504*r26[i]
- 1587401376760010972160000*r27[i]
- 13442713420403849918131416*r28[i]
- 112915002722102749808640000*r29[i]
- 941961013910760913890393144*r30[i]
- 7812419263561351877518080000*r31[i]
- 64474322285718607792730497176*r32[i]
- 529848386811984810994744320000*r33[i]
- 4338547620121893769542630267384*r34[i]
- 35415056327751829508662891008000*r35[i]
- 288317531175033442515609896757336*r36[i]
- 2341823147101379454117987013632000*r37[i]
- 18983391549723892653716655806647224*r38[i]
- 153619763998111828980832157720832000*r39[i]
- 1241292607509331793516191597844431896*r40[i]
) // 1307674368000 for i in range(len(r0))]
r13 = [(429*r[1][i]
- 572*r[2][i]
+ 429*r[3][i]
- 208*r[4][i]
+ 65*r[5][i]
- 12*r[6][i]
+ r[7][i]
- 132*r0[i]
+ 84*r2[i]
- 252*r4[i]
+ 2004*r6[i]
- 37212*r8[i]
+ 1710324*r10[i]
- 325024572*r12[i]
- 80789566956*r14[i]
- 871782912000*r15[i]
- 8422900930332*r16[i]
- 75583578470400*r17[i]
- 643521842437836*r18[i]
- 5269678622208000*r19[i]
- 41890044885642492*r20[i]
- 325386564299596800*r21[i]
- 2481686964269990316*r22[i]
- 18652248729354240000*r23[i]
- 138536531588626169052*r24[i]
- 1019042849143807488000*r25[i]
- 7436421488952386592396*r26[i]
- 53911021949819274240000*r27[i]
- 388701690499592948238012*r28[i]
- 2789805187365599475072000*r29[i]
- 19946749502047187160692076*r30[i]
- 142159780685991861112320000*r31[i]
- 1010433303980489860989897372*r32[i]
- 7165521770403817166663116800*r33[i]
- 50716588034439244118483617356*r34[i]
- 358378772025058883636009472000*r35[i]
- 2528902640579773012941059115132*r36[i]
- 17824202779159732939433280230400*r37[i]
- 125502611080965065134883934376236*r38[i]
- 882926862501000079240924013568000*r39[i]
- 6206986746547700738292160195379292*r40[i]
) // 6227020800 for i in range(len(r0))]
r11 = [(-132*r[1][i]
+ 165*r[2][i]
- 110*r[3][i]
+ 44*r[4][i]
- 10*r[5][i]
+ r[6][i]
+ 42*r0[i]
- 28*r2[i]
+ 92*r4[i]
- 868*r6[i]
+ 22652*r8[i]
- 2620708*r10[i]
- 415790788*r12[i]
- 3632428800*r13[i]
- 28616744548*r14[i]
- 210680870400*r15[i]
- 1479485236228*r16[i]
- 10038995366400*r17[i]
- 66394067988388*r18[i]
- 430591742380800*r19[i]
- 2750479262009668*r20[i]
- 17360942812012800*r21[i]
- 108550450893568228*r22[i]
- 673606803881088000*r23[i]
- 4154688725062207108*r24[i]
- 25499502190850688000*r25[i]
- 155878445775166700068*r26[i]
- 949776357849070752000*r27[i]
- 5771581202353414724548*r28[i]
- 34995682724855684832000*r29[i]
- 211811399872933910999908*r30[i]
- 1280080235834717770252800*r31[i]
- 7726641919200262371657988*r32[i]
- 46591059456870785061004800*r33[i]
- 280704018540064430354883748*r34[i]
- 1690018909819536161979590400*r35[i]
- 10169113413821714748538703428*r36[i]
- 61159784116494648773674886400*r37[i]
- 367684638335977863351585967588*r38[i]
- 2209739160176731898013383884800*r39[i]
- 13276598260065161268654185556868*r40[i]
) // 39916800 for i in range(len(r0))]
r9 = [(42*r[1][i]
- 48*r[2][i]
+ 27*r[3][i]
- 8*r[4][i]
+ r[5][i]
- 14*r0[i]
+ 10*r2[i]
- 38*r4[i]
+ 490*r6[i]
- 31238*r8[i]
- 2922230*r10[i]
- 19958400*r11[i]
- 124075238*r12[i]
- 726485760*r13[i]
- 4084385750*r14[i]
- 22313491200*r15[i]
- 119387268038*r16[i]
- 628980992640*r17[i]
- 3275389222070*r18[i]
- 16905818966400*r19[i]
- 86665431465638*r20[i]
- 441935114987520*r21[i]
- 2244295389943190*r22[i]
- 11360520464832000*r23[i]
- 57360469753884038*r24[i]
- 289038899804054400*r25[i]
- 1454155949521941110*r26[i]
- 7306671293537616000*r27[i]
- 36677059892827099238*r28[i]
- 183960524908301057280*r29[i]
- 922104761587650687830*r30[i]
- 4619736062008593926400*r31[i]
- 23135540444136227047238*r32[i]
- 115825176110799088940160*r33[i]
- 579715876176320506935350*r34[i]
- 2900939663557699476451200*r35[i]
- 14514140349055749129024038*r36[i]
- 72608472572041292373527040*r37[i]
- 363193454272347163609915670*r38[i]
- 1816571661325589960713958400*r39[i]
- 9085275939429279963731685638*r40[i]
) // 362880 for i in range(len(r0))]
r7 = [(-14*r[1][i]
+ 14*r[2][i]
- 6*r[3][i]
+ r[4][i]
+ 5*r0[i]
- 4*r2[i]
+ 20*r4[i]
- 604*r6[i]
- 29740*r8[i]
- 151200*r9[i]
- 708604*r10[i]
- 3160080*r11[i]
- 13645900*r12[i]
- 57657600*r13[i]
- 239967004*r14[i]
- 988107120*r15[i]
- 4037604460*r16[i]
- 16406863200*r17[i]
- 66398623804*r18[i]
- 267911678160*r19[i]
- 1078605601420*r20[i]
- 4335313752000*r21[i]
- 17403958407004*r22[i]
- 69804002545200*r23[i]
- 279780634372780*r24[i]
- 1120816644948000*r25[i]
- 4488349371924604*r26[i]
- 17968646803620240*r27[i]
- 71920337041294540*r28[i]
- 287818601403715200*r29[i]
- 1151686172846664604*r30[i]
- 4607980008114455280*r31[i]
- 18435626012705982700*r32[i]
- 73753622051697957600*r33[i]
- 295047842329672995004*r34[i]
- 1180291431927853642320*r35[i]
- 4721465916019935893260*r36[i]
- 18886764229967380219200*r37[i]
- 75549758619456576163804*r38[i]
- 302207139580435761213360*r39[i]
- 1208852873637267995922220*r40[i]
) // 5040 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
- 1680*r7[i]
- 5542*r8[i]
- 17640*r9[i]
- 54958*r10[i]
- 168960*r11[i]
- 515062*r12[i]
- 1561560*r13[i]
- 4717438*r14[i]
- 14217840*r15[i]
- 42784582*r16[i]
- 128615880*r17[i]
- 386371918*r18[i]
- 1160164320*r19[i]
- 3482590102*r20[i]
- 10451964600*r21[i]
- 31364282398*r22[i]
- 94109624400*r23[i]
- 282362427622*r24[i]
- 847154391720*r25[i]
- 2541597392878*r26[i]
- 7625060614080*r27[i]
- 22875718713142*r28[i]
- 68628229881240*r29[i]
- 205886837127358*r30[i]
- 617664806349360*r31[i]
- 1853003008982662*r32[i]
- 5559026206817160*r33[i]
- 16677112980189838*r34[i]
- 50031407660046240*r35[i]
- 150094360419092182*r36[i]
- 450283356135183480*r37[i]
- 1350850618161364318*r38[i]
- 4052552953995720720*r39[i]
- 12157661061010417702*r40[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
- 126*r7[i]
- 254*r8[i]
- 510*r9[i]
- 1022*r10[i]
- 2046*r11[i]
- 4094*r12[i]
- 8190*r13[i]
- 16382*r14[i]
- 32766*r15[i]
- 65534*r16[i]
- 131070*r17[i]
- 262142*r18[i]
- 524286*r19[i]
- 1048574*r20[i]
- 2097150*r21[i]
- 4194302*r22[i]
- 8388606*r23[i]
- 16777214*r24[i]
- 33554430*r25[i]
- 67108862*r26[i]
- 134217726*r27[i]
- 268435454*r28[i]
- 536870910*r29[i]
- 1073741822*r30[i]
- 2147483646*r31[i]
- 4294967294*r32[i]
- 8589934590*r33[i]
- 17179869182*r34[i]
- 34359738366*r35[i]
- 68719476734*r36[i]
- 137438953470*r37[i]
- 274877906942*r38[i]
- 549755813886*r39[i]
- 1099511627774*r40[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
- r7[i]
- r8[i]
- r9[i]
- r10[i]
- r11[i]
- r12[i]
- r13[i]
- r14[i]
- r15[i]
- r16[i]
- r17[i]
- r18[i]
- r19[i]
- r20[i]
- r21[i]
- r22[i]
- r23[i]
- r24[i]
- r25[i]
- r26[i]
- r27[i]
- r28[i]
- r29[i]
- r30[i]
- r31[i]
- r32[i]
- r33[i]
- r34[i]
- r35[i]
- r36[i]
- r37[i]
- r38[i]
- r39[i]
- r40[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40)
def natural_interpolate_22(r):
r0 = r[0]
r42 = r['infinity']
r40 = [(-131282408400*(r[1][i] + r[-1][i])
+ 113380261800*(r[2][i] + r[-2][i])
- 88732378800*(r[3][i] + r[-3][i])
+ 62852101650*(r[4][i] + r[-4][i])
- 40225345056*(r[5][i] + r[-5][i])
+ 23206929840*(r[6][i] + r[-6][i])
- 12033222880*(r[7][i] + r[-7][i])
+ 5586853480*(r[8][i] + r[-8][i])
- 2311801440*(r[9][i] + r[-9][i])
+ 847660528*(r[10][i] + r[-10][i])
- 273438880*(r[11][i] + r[-11][i])
+ 76904685*(r[12][i] + r[-12][i])
- 18643560*(r[13][i] + r[-13][i])
+ 3838380*(r[14][i] + r[-14][i])
- 658008*(r[15][i] + r[-15][i])
+ 91390*(r[16][i] + r[-16][i])
- 9880*(r[17][i] + r[-17][i])
+ 780*(r[18][i] + r[-18][i])
- 40*(r[19][i] + r[-19][i])
+ (r[20][i] + r[-20][i])
+ 137846528820*r0[i]
- 2341676862921466497571904343740852616560640000000000*r42[i]
) // 815915283247897734345611269596115894272000000000 for i in range(len(r0))]
r38 = [(33578000610*(r[1][i] + r[-1][i])
- 28781143380*(r[2][i] + r[-2][i])
+ 22239974430*(r[3][i] + r[-3][i])
- 15471286560*(r[4][i] + r[-4][i])
+ 9669554100*(r[5][i] + r[-5][i])
- 5414950296*(r[6][i] + r[-6][i])
+ 2707475148*(r[7][i] + r[-7][i])
- 1203322288*(r[8][i] + r[-8][i])
+ 472733756*(r[9][i] + r[-9][i])
- 163011640*(r[10][i] + r[-10][i])
+ 48903492*(r[11][i] + r[-11][i])
- 12620256*(r[12][i] + r[-12][i])
+ 2760681*(r[13][i] + r[-13][i])
- 501942*(r[14][i] + r[-14][i])
+ 73815*(r[15][i] + r[-15][i])
- 8436*(r[16][i] + r[-16][i])
+ 703*(r[17][i] + r[-17][i])
- 38*(r[18][i] + r[-18][i])
+ (r[19][i] + r[-19][i])
- 35345263800*r0[i]
- 1291865865142504746047217843527183499264000000000*r40[i]
- 1742597865490724651943092149133817822157209600000000*r42[i]
) // 523022617466601111760007224100074291200000000 for i in range(len(r0))]
r36 = [(-8597496600*(r[1][i] + r[-1][i])
+ 7307872110*(r[2][i] + r[-2][i])
- 5567902560*(r[3][i] + r[-3][i])
+ 3796297200*(r[4][i] + r[-4][i])
- 2310789600*(r[5][i] + r[-5][i])
+ 1251677700*(r[6][i] + r[-6][i])
- 600805296*(r[7][i] + r[-7][i])
+ 254186856*(r[8][i] + r[-8][i])
- 94143280*(r[9][i] + r[-9][i])
+ 30260340*(r[10][i] + r[-10][i])
- 8347680*(r[11][i] + r[-11][i])
+ 1947792*(r[12][i] + r[-12][i])
- 376992*(r[13][i] + r[-13][i])
+ 58905*(r[14][i] + r[-14][i])
- 7140*(r[15][i] + r[-15][i])
+ 630*(r[16][i] + r[-16][i])
- 36*(r[17][i] + r[-17][i])
+ (r[18][i] + r[-18][i])
+ 9075135300*r0[i]
- 784533926199901667640010836150111436800000000*r38[i]
- 907705752613286229459492537425678932377600000000*r40[i]
- 764250847583238143225401875995898505750118400000000*r42[i]
) // 371993326789901217467999448150835200000000 for i in range(len(r0))]
r34 = [(2203961430*(r[1][i] + r[-1][i])
- 1855967520*(r[2][i] + r[-2][i])
+ 1391975640*(r[3][i] + r[-3][i])
- 927983760*(r[4][i] + r[-4][i])
+ 548354040*(r[5][i] + r[-5][i])
- 286097760*(r[6][i] + r[-6][i])
+ 131128140*(r[7][i] + r[-7][i])
- 52451256*(r[8][i] + r[-8][i])
+ 18156204*(r[9][i] + r[-9][i])
- 5379616*(r[10][i] + r[-10][i])
+ 1344904*(r[11][i] + r[-11][i])
- 278256*(r[12][i] + r[-12][i])
+ 46376*(r[13][i] + r[-13][i])
- 5984*(r[14][i] + r[-14][i])
+ 561*(r[15][i] + r[-15][i])
- 34*(r[16][i] + r[-16][i])
+ (r[17][i] + r[-17][i])
- 2333606220*r0[i]
- 526990546285693391412999218213683200000000*r36[i]
- 518664095654379435828673830565907005440000000*r38[i]
- 373138241060740797524227217357125818777600000000*r40[i]
- 219618160307546307818407858079592245845032960000000*r42[i]
) // 295232799039604140847618609643520000000 for i in range(len(r0))]
r32 = [(-565722720*(r[1][i] + r[-1][i])
+ 471435600*(r[2][i] + r[-2][i])
- 347373600*(r[3][i] + r[-3][i])
+ 225792840*(r[4][i] + r[-4][i])
- 129024480*(r[5][i] + r[-5][i])
+ 64512240*(r[6][i] + r[-6][i])
- 28048800*(r[7][i] + r[-7][i])
+ 10518300*(r[8][i] + r[-8][i])
- 3365856*(r[9][i] + r[-9][i])
+ 906192*(r[10][i] + r[-10][i])
- 201376*(r[11][i] + r[-11][i])
+ 35960*(r[12][i] + r[-12][i])
- 4960*(r[13][i] + r[-13][i])
+ 496*(r[14][i] + r[-14][i])
- 32*(r[15][i] + r[-15][i])
+ (r[16][i] + r[-16][i])
+ 601080390*r0[i]
- 393643732052805521130158146191360000000*r34[i]
- 326527475737802179777466182265733120000000*r36[i]
- 198969979872214920293886346099446251520000000*r38[i]
- 99626745669333527035567016277524852244480000000*r40[i]
- 43498703313314018776504938348732045412270080000000*r42[i]
) // 263130836933693530167218012160000000 for i in range(len(r0))]
r30 = [(145422675*(r[1][i] + r[-1][i])
- 119759850*(r[2][i] + r[-2][i])
+ 86493225*(r[3][i] + r[-3][i])
- 54627300*(r[4][i] + r[-4][i])
+ 30045015*(r[5][i] + r[-5][i])
- 14307150*(r[6][i] + r[-6][i])
+ 5852925*(r[7][i] + r[-7][i])
- 2035800*(r[8][i] + r[-8][i])
+ 593775*(r[9][i] + r[-9][i])
- 142506*(r[10][i] + r[-10][i])
+ 27405*(r[11][i] + r[-11][i])
- 4060*(r[12][i] + r[-12][i])
+ 435*(r[13][i] + r[-13][i])
- 30*(r[14][i] + r[-14][i])
+ (r[15][i] + r[-15][i])
- 155117520*r0[i]
- 328913546167116912709022515200000000*r32[i]
- 227575282593028191903372678266880000000*r34[i]
- 116309421454977381321426414757478400000000*r36[i]
- 49083095586740430887431564189583278080000000*r38[i]
- 18139371393109511951007844941215406489600000000*r40[i]
- 6083845843389094496001274537210012898426880000000*r42[i]
) // 265252859812191058636308480000000 for i in range(len(r0))]
r28 = [(-37442160*(r[1][i] + r[-1][i])
+ 30421755*(r[2][i] + r[-2][i])
- 21474180*(r[3][i] + r[-3][i])
+ 13123110*(r[4][i] + r[-4][i])
- 6906900*(r[5][i] + r[-5][i])
+ 3108105*(r[6][i] + r[-6][i])
- 1184040*(r[7][i] + r[-7][i])
+ 376740*(r[8][i] + r[-8][i])
- 98280*(r[9][i] + r[-9][i])
+ 20475*(r[10][i] + r[-10][i])
- 3276*(r[11][i] + r[-11][i])
+ 378*(r[12][i] + r[-12][i])
- 28*(r[13][i] + r[-13][i])
+ (r[14][i] + r[-14][i])
+ 40116600*r0[i]
- 309461669780889568409026560000000*r30[i]
- 176516936443019409820508749824000000*r32[i]
- 74833313645455216256514439249920000000*r34[i]
- 26337328459046574816219104447299584000000*r36[i]
- 8155948144934385059006601147769159680000000*r38[i]
- 2301709517171786559798286695904076365824000000*r40[i]
- 605758813130095139988659617361096909783040000000*r42[i]
) // 304888344611713860501504000000 for i in range(len(r0))]
r26 = [(9657700*(r[1][i] + r[-1][i])
- 7726160*(r[2][i] + r[-2][i])
+ 5311735*(r[3][i] + r[-3][i])
- 3124550*(r[4][i] + r[-4][i])
+ 1562275*(r[5][i] + r[-5][i])
- 657800*(r[6][i] + r[-6][i])
+ 230230*(r[7][i] + r[-7][i])
- 65780*(r[8][i] + r[-8][i])
+ 14950*(r[9][i] + r[-9][i])
- 2600*(r[10][i] + r[-10][i])
+ 325*(r[11][i] + r[-11][i])
- 26*(r[12][i] + r[-12][i])
+ (r[13][i] + r[-13][i])
- 10400600*r0[i]
- 330295706662690015543296000000*r28[i]
- 153257207891488167212089344000000*r30[i]
- 53222214421459539592188788736000000*r32[i]
- 15436506593303376230082373484544000000*r34[i]
- 3960094929842931739454572322881536000000*r36[i]
- 930084233815670751630942950980583424000000*r38[i]
- 204528766884160018873274371645367648256000000*r40[i]
- 42768601883241439058698435075343591276544000000*r42[i]
) // 403291461126605635584000000 for i in range(len(r0))]
r24 = [(-2496144*(r[1][i] + r[-1][i])
+ 1961256*(r[2][i] + r[-2][i])
- 1307504*(r[3][i] + r[-3][i])
+ 735471*(r[4][i] + r[-4][i])
- 346104*(r[5][i] + r[-5][i])
+ 134596*(r[6][i] + r[-6][i])
- 42504*(r[7][i] + r[-7][i])
+ 10626*(r[8][i] + r[-8][i])
- 2024*(r[9][i] + r[-9][i])
+ 276*(r[10][i] + r[-10][i])
- 24*(r[11][i] + r[-11][i])
+ (r[12][i] + r[-12][i])
+ 2704156*r0[i]
- 403291461126605635584000000*r26[i]
- 149903436100759314746572800000*r28[i]
- 42033455827381598974377984000000*r30[i]
- 9910695932425713906157643366400000*r32[i]
- 2078962023961017163954848006144000000*r34[i]
- 401274139495715827174031120636313600000*r36[i]
- 72837740568171787457915404507152384000000*r38[i]
- 12620369661259070567869332718886859571200000*r40[i]
- 2109601340251819353520575234140712075264000000*r42[i]
) // 620448401733239439360000 for i in range(len(r0))]
r22 = [(646646*(r[1][i] + r[-1][i])
- 497420*(r[2][i] + r[-2][i])
+ 319770*(r[3][i] + r[-3][i])
- 170544*(r[4][i] + r[-4][i])
+ 74613*(r[5][i] + r[-5][i])
- 26334*(r[6][i] + r[-6][i])
+ 7315*(r[7][i] + r[-7][i])
- 1540*(r[8][i] + r[-8][i])
+ 231*(r[9][i] + r[-9][i])
- 22*(r[10][i] + r[-10][i])
+ (r[11][i] + r[-11][i])
- 705432*r0[i]
- 568744368255469486080000*r24[i]
- 166357727714724824678400000*r26[i]
- 37042320704478727628390400000*r28[i]
- 6988909951599209517839155200000*r30[i]
- 1180836611760352104108962611200000*r32[i]
- 184607985589364774573429361868800000*r34[i]
- 27272218262298384682708194086092800000*r36[i]
- 3861838803337560097698395778726297600000*r38[i]
- 529471212011799260411940801849645465600000*r40[i]
- 70801221927358337925257947461388534087680000*r42[i]
) // 1124000727777607680000 for i in range(len(r0))]
r20 = [(-167960*(r[1][i] + r[-1][i])
+ 125970*(r[2][i] + r[-2][i])
- 77520*(r[3][i] + r[-3][i])
+ 38760*(r[4][i] + r[-4][i])
- 15504*(r[5][i] + r[-5][i])
+ 4845*(r[6][i] + r[-6][i])
- 1140*(r[7][i] + r[-7][i])
+ 190*(r[8][i] + r[-8][i])
- 20*(r[9][i] + r[-9][i])
+ (r[10][i] + r[-10][i])
+ 184756*r0[i]
- 936667273148006400000*r22[i]
- 211124803367560642560000*r24[i]
- 36608302274885332992000000*r26[i]
- 5425950533240873322086400000*r28[i]
- 725494605231272191451136000000*r30[i]
- 90317652741043657957240012800000*r32[i]
- 10681064948020015063470219264000000*r34[i]
- 1216234618180639720975550420582400000*r36[i]
- 134607612138429628983625351999488000000*r38[i]
- 14578366393789236829898507440652451840000*r40[i]
- 1552719574083291045891061928041363046400000*r42[i]
) // 2432902008176640000 for i in range(len(r0))]
r18 = [(43758*(r[1][i] + r[-1][i])
- 31824*(r[2][i] + r[-2][i])
+ 18564*(r[3][i] + r[-3][i])
- 8568*(r[4][i] + r[-4][i])
+ 3060*(r[5][i] + r[-5][i])
- 816*(r[6][i] + r[-6][i])
+ 153*(r[7][i] + r[-7][i])
- 18*(r[8][i] + r[-8][i])
+ (r[9][i] + r[-9][i])
- 48620*r0[i]
- 1824676506132480000*r20[i]
- 309100200138842112000*r22[i]
- 40778478784550707200000*r24[i]
- 4645053436190368481280000*r26[i]
- 481314610282065419059200000*r28[i]
- 46758400573464312663490560000*r30[i]
- 4340262299778024388805836800000*r32[i]
- 389810850996416354285601300480000*r34[i]
- 34168816632541202331763973529600000*r36[i]
- 2941066263016510346147295370272768000*r38[i]
- 249691933432545691845292589410836480000*r40[i]
- 20977168972570956554158853986478948352000*r42[i]
) // 6402373705728000 for i in range(len(r0))]
r16 = [(-11440*(r[1][i] + r[-1][i])
+ 8008*(r[2][i] + r[-2][i])
- 4368*(r[3][i] + r[-3][i])
+ 1820*(r[4][i] + r[-4][i])
- 560*(r[5][i] + r[-5][i])
+ 120*(r[6][i] + r[-6][i])
- 16*(r[7][i] + r[-7][i])
+ (r[8][i] + r[-8][i])
+ 12870*r0[i]
- 4268249137152000*r18[i]
- 527128768438272000*r20[i]
- 51442361350668288000*r22[i]
- 4385609982489415680000*r24[i]
- 343350594609952849920000*r26[i]
- 25398422028160175554560000*r28[i]
- 1806640043553643996938240000*r30[i]
- 124998708216981630040289280000*r32[i]
- 8477574188991756975915909120000*r34[i]
- 566640901244029272138606256128000*r36[i]
- 37469170353622071265887792218112000*r38[i]
- 2457916223969789263693314523533312000*r40[i]
- 160273272592069873142621634191720448000*r42[i]
) // 20922789888000 for i in range(len(r0))]
r14 = [(3003*(r[1][i] + r[-1][i])
- 2002*(r[2][i] + r[-2][i])
+ 1001*(r[3][i] + r[-3][i])
- 364*(r[4][i] + r[-4][i])
+ 91*(r[5][i] + r[-5][i])
- 14*(r[6][i] + r[-6][i])
+ (r[7][i] + r[-7][i])
- 3432*r0[i]
- 12204960768000*r16[i]
- 1058170098585600*r18[i]
- 73775500710912000*r20[i]
- 4555411900194355200*r22[i]
- 261131482210959360000*r24[i]
- 14266599888013304832000*r26[i]
- 754754307297469839360000*r28[i]
- 39057272623118392651008000*r30[i]
- 1990236929603886055572480000*r32[i]
- 100317304785653440333283635200*r34[i]
- 5017302808350824370904132608000*r36[i]
- 249538838908236261152065923225600*r38[i]
- 12360976075014001109372936189952000*r40[i]
- 610513898001512036824535103712051200*r42[i]
) // 87178291200 for i in range(len(r0))]
r12 = [(-792*(r[1][i] + r[-1][i])
+ 495*(r[2][i] + r[-2][i])
- 220*(r[3][i] + r[-3][i])
+ 66*(r[4][i] + r[-4][i])
- 12*(r[5][i] + r[-5][i])
+ (r[6][i] + r[-6][i])
+ 924*r0[i]
- 43589145600*r14[i]
- 2528170444800*r16[i]
- 120467944396800*r18[i]
- 5167100908569600*r20[i]
- 208331313744153600*r22[i]
- 8083281646573056000*r24[i]
- 305994026290208256000*r26[i]
- 11397316294188849024000*r28[i]
- 419948192698268217984000*r30[i]
- 15360962830016613243033600*r32[i]
- 559092713482449420732057600*r34[i]
- 20280226917834433943755084800*r36[i]
- 733917409397935785284098636800*r38[i]
- 26516869922120782776160606617600*r40[i]
- 957005191789297958689924263321600*r42[i]
) // 479001600 for i in range(len(r0))]
r10 = [(210*(r[1][i] + r[-1][i])
- 120*(r[2][i] + r[-2][i])
+ 45*(r[3][i] + r[-3][i])
- 10*(r[4][i] + r[-4][i])
+ (r[5][i] + r[-5][i])
- 252*r0[i]
- 199584000*r12[i]
- 7264857600*r14[i]
- 223134912000*r16[i]
- 6289809926400*r18[i]
- 169058189664000*r20[i]
- 4419351149875200*r22[i]
- 113605204648320000*r24[i]
- 2890388998040544000*r26[i]
- 73066712935376160000*r28[i]
- 1839605249083010572800*r30[i]
- 46197360620085939264000*r32[i]
- 1158251761107990889401600*r34[i]
- 29009396635576994764512000*r36[i]
- 726084725720412923735270400*r38[i]
- 18165716613255899607139584000*r40[i]
- 454360504471895403926563219200*r42[i]
) // 3628800 for i in range(len(r0))]
r8 = [(-56*(r[1][i] + r[-1][i])
+ 28*(r[2][i] + r[-2][i])
- 8*(r[3][i] + r[-3][i])
+ (r[4][i] + r[-4][i])
+ 70*r0[i]
- 1209600*r10[i]
- 25280640*r12[i]
- 461260800*r14[i]
- 7904856960*r16[i]
- 131254905600*r18[i]
- 2143293425280*r20[i]
- 34682510016000*r22[i]
- 558432020361600*r24[i]
- 8966533159584000*r26[i]
- 143749174428961920*r28[i]
- 2302548811229721600*r30[i]
- 36863840064915642240*r32[i]
- 590028976413583660800*r34[i]
- 9442331455422829138560*r36[i]
- 151094113839739041753600*r38[i]
- 2417657116643486089706880*r40[i]
- 38683875524088319997472000*r42[i]
) // 40320 for i in range(len(r0))]
r6 = [(15*(r[1][i] + r[-1][i])
- 6*(r[2][i] + r[-2][i])
+ (r[3][i] + r[-3][i])
- 20*r0[i]
- 10080*r8[i]
- 105840*r10[i]
- 1013760*r12[i]
- 9369360*r14[i]
- 85307040*r16[i]
- 771695280*r18[i]
- 6960985920*r20[i]
- 62711787600*r22[i]
- 564657746400*r24[i]
- 5082926350320*r26[i]
- 45750363684480*r28[i]
- 411769379287440*r30[i]
- 3705988838096160*r32[i]
- 33354157240902960*r34[i]
- 300188445960277440*r36[i]
- 2701700136811100880*r38[i]
- 24315317723974324320*r40[i]
- 218837925486466585200*r42[i]
) // 720 for i in range(len(r0))]
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
- 504*r8[i]
- 2040*r10[i]
- 8184*r12[i]
- 32760*r14[i]
- 131064*r16[i]
- 524280*r18[i]
- 2097144*r20[i]
- 8388600*r22[i]
- 33554424*r24[i]
- 134217720*r26[i]
- 536870904*r28[i]
- 2147483640*r30[i]
- 8589934584*r32[i]
- 34359738360*r34[i]
- 137438953464*r36[i]
- 549755813880*r38[i]
- 2199023255544*r40[i]
- 8796093022200*r42[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
- 2*r8[i]
- 2*r10[i]
- 2*r12[i]
- 2*r14[i]
- 2*r16[i]
- 2*r18[i]
- 2*r20[i]
- 2*r22[i]
- 2*r24[i]
- 2*r26[i]
- 2*r28[i]
- 2*r30[i]
- 2*r32[i]
- 2*r34[i]
- 2*r36[i]
- 2*r38[i]
- 2*r40[i]
- 2*r42[i]
) // 2 for i in range(len(r0))]
r41 = [(24466267020*r[1][i]
- 42550029600*r[2][i]
+ 50528160150*r[3][i]
- 48507033744*r[4][i]
+ 39645171810*r[5][i]
- 28192122176*r[6][i]
+ 17620076360*r[7][i]
- 9721421440*r[8][i]
+ 4739192952*r[9][i]
- 2038362560*r[10][i]
+ 770755843*r[11][i]
- 254795320*r[12][i]
+ 73066305*r[13][i]
- 17985552*r[14][i]
+ 3746990*r[15][i]
- 648128*r[16][i]
+ 90610*r[17][i]
- 9840*r[18][i]
+ 779*r[19][i]
- 40*r[20][i]
+ r[21][i]
- 6564120420*r0[i]
+ 3534526380*r2[i]
- 7928802420*r4[i]
+ 39562131180*r6[i]
- 355997149620*r8[i]
+ 5162772055980*r10[i]
- 112466379416820*r12[i]
+ 3509804003100780*r14[i]
- 151808102304340020*r16[i]
+ 8890838711788769580*r18[i]
- 693867758978013455220*r20[i]
+ 71436574576557715366380*r22[i]
- 9656103679244476561098420*r24[i]
+ 1714541855816811795973995180*r26[i]
- 402505898503128791422102405620*r28[i]
+ 126699650825847516884027712559980*r30[i]
- 54827934277723571354991704981312820*r32[i]
+ 34051732695777105364083032869387764780*r34[i]
- 32827430653262026254340815579045378556020*r36[i]
+ 58129225653125966892251726413185365757113580*r38[i]
- 338476895760295138790385051321218766549279671220*r40[i]
- 2149763077602671437231704105519918866633843849089620*r42[i]
) // 33452526613163807108170062053440751665152000000000 for i in range(len(r0))]
r39 = [(-6564120420*r[1][i]
+ 11338026180*r[2][i]
- 13309856820*r[3][i]
+ 12570420330*r[4][i]
- 10056336264*r[5][i]
+ 6962078952*r[6][i]
- 4211628008*r[7][i]
+ 2234741392*r[8][i]
- 1040310648*r[9][i]
+ 423830264*r[10][i]
- 150391384*r[11][i]
+ 46142811*r[12][i]
- 12118314*r[13][i]
+ 2686866*r[14][i]
- 493506*r[15][i]
+ 73112*r[16][i]
- 8398*r[17][i]
+ 702*r[18][i]
- 38*r[19][i]
+ r[20][i]
+ 1767263190*r0[i]
- 955277400*r2[i]
+ 2156197560*r4[i]
- 10855425000*r6[i]
+ 98876533560*r8[i]
- 1456859058600*r10[i]
+ 32382608125560*r12[i]
- 1036360772970600*r14[i]
+ 46242812090245560*r16[i]
- 2813858311510281000*r18[i]
+ 230141619686501005560*r20[i]
- 25097337236284407949800*r22[i]
+ 3642002181929040219157560*r24[i]
- 706474912755087069174777000*r26[i]
+ 185490702479102020671448093560*r28[i]
- 67501512373123369695638979402600*r30[i]
+ 35506616897715366055874618759845560*r32[i]
- 29173319982987640073110629923442306600*r34[i]
+ 44272025958057634433180503709478279085560*r36[i]
- 222019441630075420847480526017947263931809000*r38[i]
- 1219813882056330049405575791394671579625372874440*r40[i]
- 58541921573036662439297608593521315414016000000000*r41[i]
- 2435494701008122308521041585840935773426259964069800*r42[i]
) // 20397882081197443358640281739902897356800000000 for i in range(len(r0))]
r37 = [(1767263190*r[1][i]
- 3029594040*r[2][i]
+ 3511574910*r[3][i]
- 3257112960*r[4][i]
+ 2544619500*r[5][i]
- 1709984304*r[6][i]
+ 997490844*r[7][i]
- 506662016*r[8][i]
+ 223926516*r[9][i]
- 85795600*r[10][i]
+ 28312548*r[11][i]
- 7970688*r[12][i]
+ 1888887*r[13][i]
- 369852*r[14][i]
+ 58275*r[15][i]
- 7104*r[16][i]
+ 629*r[17][i]
- 36*r[18][i]
+ r[19][i]
- 477638700*r0[i]
+ 259289580*r2[i]
- 589294500*r4[i]
+ 2996657580*r6[i]
- 27670359300*r8[i]
+ 415064933580*r10[i]
- 9439543875300*r12[i]
+ 310922483993580*r14[i]
- 14379880666402500*r16[i]
+ 914767168887053580*r18[i]
- 79051272004645620900*r20[i]
+ 9231401536061270849580*r22[i]
- 1459700260139475814330500*r24[i]
+ 315843905250429722227637580*r26[i]
- 95612546130070295522414451300*r28[i]
+ 42177612582297377823299737193580*r30[i]
- 29268533564152352561039458453023300*r32[i]
+ 37747202396256876155482291281278813580*r34[i]
- 161759954125032708920885781040309430206500*r36[i]
- 763162014442847423121851269222329739576686420*r38[i]
- 33996470135329072264400469566504828928000000000*r39[i]
- 1314149222797294391875041342296266627244339280900*r40[i]
- 45857838565545385577449793398258363740979200000000*r41[i]
- 1479444354242422663436299123473954120225396734970420*r42[i]
) // 13763753091226345046315979581580902400000000 for i in range(len(r0))]
r35 = [(-477638700*r[1][i]
+ 811985790*r[2][i]
- 927983760*r[3][i]
+ 843621600*r[4][i]
- 641886000*r[5][i]
+ 417225900*r[6][i]
- 233646504*r[7][i]
+ 112971936*r[8][i]
- 47071640*r[9][i]
+ 16811300*r[10][i]
- 5101360*r[11][i]
+ 1298528*r[12][i]
- 272272*r[13][i]
+ 45815*r[14][i]
- 5950*r[15][i]
+ 560*r[16][i]
- 34*r[17][i]
+ r[18][i]
+ 129644790*r0[i]
- 70715340*r2[i]
+ 161960940*r4[i]
- 832930740*r6[i]
+ 7810859340*r8[i]
- 119578066740*r10[i]
+ 2791740107340*r12[i]
- 95062235276340*r14[i]
+ 4584012079172940*r16[i]
- 307268933913567540*r18[i]
+ 28355038085389144140*r20[i]
- 3597774935929125068340*r22[i]
+ 632729503874459828228940*r24[i]
- 157381528472579148083026740*r26[i]
+ 57577884185625191071239755340*r28[i]
- 33404393172944223690128125810740*r30[i]
+ 36271128388074981554067219056171340*r32[i]
- 131671692334895976886647813958596908340*r34[i]
- 529104107360143104505564190890974500955060*r36[i]
- 21792609061108379656666967670836428800000000*r37[i]
- 779765567254824678774814590170424618060927540*r38[i]
- 25214048683702395262763681595157748121600000000*r39[i]
- 754531895504954495472529428607358759602244935860*r40[i]
- 21229190210645503978483385444330514048614400000000*r41[i]
- 567902644449952014090537079509460539320563935596340*r42[i]
) // 10333147966386144929666651337523200000000 for i in range(len(r0))]
r33 = [(129644790*r[1][i]
- 218349120*r[2][i]
+ 245642760*r[3][i]
- 218349120*r[4][i]
+ 161280600*r[5][i]
- 100975680*r[6][i]
+ 53993940*r[7][i]
- 24682944*r[8][i]
+ 9612108*r[9][i]
- 3164480*r[10][i]
+ 870232*r[11][i]
- 196416*r[12][i]
+ 35464*r[13][i]
- 4928*r[14][i]
+ 495*r[15][i]
- 32*r[16][i]
+ r[17][i]
- 35357670*r0[i]
+ 19389690*r2[i]
- 44796870*r4[i]
+ 233344890*r6[i]
- 2227139910*r8[i]
+ 34903389690*r10[i]
- 839988260550*r12[i]
+ 29734601940090*r14[i]
- 1506293149214790*r16[i]
+ 107487540061668090*r18[i]
- 10743535525710258630*r20[i]
+ 1511267716903778445690*r22[i]
- 304525956073869018848070*r24[i]
+ 91234873454404063067344890*r26[i]
- 43747586259736794619504039110*r28[i]
+ 39574917458915050445099774637690*r30[i]
- 120523981455993504966525708346887750*r32[i]
- 408775192473644376465790167368394203910*r34[i]
- 15499721949579217394499977006284800000000*r35[i]
- 511206585269023792365556128001469646849990*r36[i]
- 15254826342775865759666877369585500160000000*r37[i]
- 421754497238984285335705463354740490210507910*r38[i]
- 10974654148845317574241976981091935846400000000*r39[i]
- 271793538072560300468434911462753194293644181830*r40[i]
- 6459357656104303171129642884693889583677440000000*r41[i]
- 148248369194001435848413334991598692517822202402310*r42[i]
) // 8683317618811886495518194401280000000 for i in range(len(r0))]
r31 = [(-35357670*r[1][i]
+ 58929450*r[2][i]
- 65132550*r[3][i]
+ 56448210*r[4][i]
- 40320150*r[5][i]
+ 24192090*r[6][i]
- 12271350*r[7][i]
+ 5259150*r[8][i]
- 1893294*r[9][i]
+ 566370*r[10][i]
- 138446*r[11][i]
+ 26970*r[12][i]
- 4030*r[13][i]
+ 434*r[14][i]
- 30*r[15][i]
+ r[16][i]
+ 9694845*r0[i]
- 5348880*r2[i]
+ 12480720*r4[i]
- 65969520*r6[i]
+ 642563280*r8[i]
- 10347602160*r10[i]
+ 258040917840*r12[i]
- 9564008626800*r14[i]
+ 514021079720400*r16[i]
- 39590373677587440*r18[i]
+ 4371353677873146960*r20[i]
- 701971899866535028080*r22[i]
+ 169737570795219895373520*r24[i]
- 66396273378844288679892720*r26[i]
+ 49448835121192219782326176080*r28[i]
- 124963193751534047864734415925360*r30[i]
- 354113410826574103722030528083469360*r32[i]
- 12301366626650172535317442068480000000*r33[i]
- 372225904019072507165665501545458070000*r34[i]
- 10203983616806318118045818195804160000000*r35[i]
- 259484653500223872483011119661283865786800*r36[i]
- 6217811871006716259183948315607695360000000*r37[i]
- 141956901865997956445469727796622341498870640*r38[i]
- 3113335802166672719861469258672651632640000000*r39[i]
- 66003822624082868383556482555741495612650600240*r40[i]
- 1359334478541063086765779323397876419133440000000*r41[i]
- 27303356587963564025554884815930553997263574871280*r42[i]
) // 8222838654177922817725562880000000 for i in range(len(r0))]
r29 = [(9694845*r[1][i]
- 15967980*r[2][i]
+ 17298645*r[3][i]
- 14567280*r[4][i]
+ 10015005*r[5][i]
- 5722860*r[6][i]
+ 2731365*r[7][i]
- 1085760*r[8][i]
+ 356265*r[9][i]
- 95004*r[10][i]
+ 20097*r[11][i]
- 3248*r[12][i]
+ 377*r[13][i]
- 28*r[14][i]
+ r[15][i]
- 2674440*r0[i]
+ 1485800*r2[i]
- 3506488*r4[i]
+ 18850280*r6[i]
- 188004088*r8[i]
+ 3125835560*r10[i]
- 81314498488*r12[i]
+ 3185384180840*r14[i]
- 184064268909688*r16[i]
+ 15598375633694120*r18[i]
- 1958105850969957688*r20[i]
+ 375744491571024583400*r22[i]
- 118117302690774819242488*r24[i]
+ 71447614092662750198256680*r26[i]
- 147980747895225006590333244088*r28[i]
- 346368637877614395127589803878040*r30[i]
- 10963784872237230423634083840000000*r31[i]
- 302766527792977996357877082103322488*r32[i]
- 7585842753100939730112422608896000000*r33[i]
- 176553572119721839407097582006071612760*r34[i]
- 3876980715165912710714213825249280000000*r35[i]
- 81213796311764134505181592648745883717688*r36[i]
- 1636103186224681029581052139652775936000000*r37[i]
- 31895543813319775842490572300866856117139480*r38[i]
- 604645713103650398366928164707180216320000000*r39[i]
- 11189653759353064214370349765226592602607549688*r40[i]
- 202794861446303149866709151240333763280896000000*r41[i]
- 3608799207440735942926262565268791718882246250200*r42[i]
) // 8841761993739701954543616000000 for i in range(len(r0))]
r27 = [(-2674440*r[1][i]
+ 4345965*r[2][i]
- 4601610*r[3][i]
+ 3749460*r[4][i]
- 2466750*r[5][i]
+ 1332045*r[6][i]
- 592020*r[7][i]
+ 215280*r[8][i]
- 63180*r[9][i]
+ 14625*r[10][i]
- 2574*r[11][i]
+ 324*r[12][i]
- 26*r[13][i]
+ r[14][i]
+ 742900*r0[i]
- 416024*r2[i]
+ 994840*r4[i]
- 5454824*r6[i]
+ 55944280*r8[i]
- 966290024*r10[i]
+ 26454613720*r12[i]
- 1109329691624*r14[i]
+ 70212852387160*r16[i]
- 6733670404619624*r18[i]
+ 1005318113348848600*r20[i]
- 249581050854994274024*r22[i]
+ 120719220687299365182040*r24[i]
- 202039976682357297272094824*r26[i]
- 385557844336439370252173428520*r28[i]
- 11052202492174627443179520000000*r29[i]
- 276888650579451671741587901762024*r30[i]
- 6304176301536407493589598208000000*r31[i]
- 133535841584115505205141919375399080*r32[i]
- 2672618344480543437732658544640000000*r33[i]
- 51095126335993498323380094454901195624*r34[i]
- 940618873537377672007825158832128000000*r35[i]
- 16776403501444391106926987629186000345640*r36[i]
- 291283862319085180678807183848898560000000*r37[i]
- 4942310839108515578583708125038854650555624*r38[i]
- 82203911327563805707081667710859870208000000*r39[i]
- 1343752600475734599375534320311340373516684200*r40[i]
- 21634243326074826428166414905753461063680000000*r41[i]
- 343672532983087585902951862991031321905844242024*r42[i]
) // 10888869450418352160768000000 for i in range(len(r0))]
r25 = [(742900*r[1][i]
- 1188640*r[2][i]
+ 1225785*r[3][i]
- 961400*r[4][i]
+ 600875*r[5][i]
- 303600*r[6][i]
+ 123970*r[7][i]
- 40480*r[8][i]
+ 10350*r[9][i]
- 2000*r[10][i]
+ 275*r[11][i]
- 24*r[12][i]
+ r[13][i]
- 208012*r0[i]
+ 117572*r2[i]
- 285532*r4[i]
+ 1602692*r6[i]
- 16996252*r8[i]
+ 307475012*r10[i]
- 8966430172*r12[i]
+ 409745686532*r14[i]
- 29195711499292*r16[i]
+ 3312133208909252*r18[i]
- 636215671041835612*r20[i]
+ 241648300078174135172*r22[i]
- 321511316149669476991132*r24[i]
- 492817676505266866078123708*r26[i]
- 12703681025488077520896000000*r27[i]
- 286779648275654636997381637852*r28[i]
- 5894507995826467969695744000000*r29[i]
- 112914054231542703053832892635388*r30[i]
- 2047008246979213061238030336000000*r31[i]
- 35501568925223446300815211192767772*r32[i]
- 593711792050129855003168210944000000*r33[i]
- 9632134956680435093368218113996247868*r34[i]
- 152311343455497374594406627803136000000*r35[i]
- 2356318736218539774396037820111678892892*r36[i]
- 35772470531371951985805498114637824000000*r37[i]
- 534273042749950920189640352996759062689148*r38[i]
- 7866491034006154572049014294052601856000000*r39[i]
- 114383224059606274110181105712262975351245212*r40[i]
- 1644946226278516886873016733667061202944000000*r41[i]
- 23426103831558846665144911501028780920365367228*r42[i]
) // 15511210043330985984000000 for i in range(len(r0))]
r23 = [(-208012*r[1][i]
+ 326876*r[2][i]
- 326876*r[3][i]
+ 245157*r[4][i]
- 144210*r[5][i]
+ 67298*r[6][i]
- 24794*r[7][i]
+ 7084*r[8][i]
- 1518*r[9][i]
+ 230*r[10][i]
- 22*r[11][i]
+ r[12][i]
+ 58786*r0[i]
- 33592*r2[i]
+ 83096*r4[i]
- 479752*r6[i]
+ 5299736*r8[i]
- 101549512*r10[i]
+ 3208453976*r12[i]
- 164071220872*r14[i]
+ 13743680753816*r16[i]
- 1993276972245832*r18[i]
+ 581947914140407256*r20[i]
- 603916464771468176392*r22[i]
- 730803773459954540777704*r24[i]
- 16803810880275234816000000*r25[i]
- 339155768243774227716964552*r26[i]
- 6245976504198304781107200000*r27[i]
- 107413822788261782335458993064*r28[i]
- 1751393992807566623932416000000*r29[i]
- 27365156266821215807862420562312*r30[i]
- 412945663851071412756568473600000*r31[i]
- 6053949680529454447550745704030824*r32[i]
- 86623417665042381831452000256000000*r33[i]
- 1214146547565910406028014931410521672*r34[i]
- 16719755812321492798917963359846400000*r35[i]
- 226758627215029497194516602329808882984*r36[i]
- 3034905857007157810746475187798016000000*r37[i]
- 40151799724774280996886476759684489594632*r38[i]
- 525848735885794606994555529953619148800000*r39[i]
- 6825564942475643900873841059427230143341544*r40[i]
- 87900055843825806396690634755863003136000000*r41[i]
- 1124090333957827218160935737032127911249333192*r42[i]
) // 25852016738884976640000 for i in range(len(r0))]
r21 = [(58786*r[1][i]
- 90440*r[2][i]
+ 87210*r[3][i]
- 62016*r[4][i]
+ 33915*r[5][i]
- 14364*r[6][i]
+ 4655*r[7][i]
- 1120*r[8][i]
+ 189*r[9][i]
- 20*r[10][i]
+ r[11][i]
- 16796*r0[i]
+ 9724*r2[i]
- 24596*r4[i]
+ 147004*r6[i]
- 1708916*r8[i]
+ 35240284*r10[i]
- 1237329236*r12[i]
+ 73853629564*r14[i]
- 7850527669556*r16[i]
+ 1717351379730844*r18[i]
- 1359124435588313876*r20[i]
- 1272410676942417239876*r22[i]
- 25852016738884976640000*r23[i]
- 462292539259962003646196*r24[i]
- 7561714896123855667200000*r25[i]
- 115761644587269354830466596*r26[i]
- 1683741850203578528563200000*r27[i]
- 23512975860299444963550050516*r28[i]
- 317677725072691341719961600000*r29[i]
- 4176614976496441445095962733316*r30[i]
- 53674391443652368368589209600000*r31[i]
- 676635955671282540673335079110836*r32[i]
- 8391272072243853389701334630400000*r33[i]
- 102611708232289325546408008313624036*r34[i]
- 1239646284649926576486736094822400000*r35[i]
- 14819283410691765614379616648600811156*r36[i]
- 175538127424434549895381626305740800000*r37[i]
- 2062659648435073986802743885440046722756*r38[i]
- 24066873273263602745997309174983884800000*r39[i]
- 279069134864297423784787795404361206735476*r40[i]
- 3218237360334469905693543066426751549440000*r41[i]
- 36932670876144577834192017462238998576813476*r42[i]
) // 51090942171709440000 for i in range(len(r0))]
r19 = [(-16796*r[1][i]
+ 25194*r[2][i]
- 23256*r[3][i]
+ 15504*r[4][i]
- 7752*r[5][i]
+ 2907*r[6][i]
- 798*r[7][i]
+ 152*r[8][i]
- 18*r[9][i]
+ r[10][i]
+ 4862*r0[i]
- 2860*r2[i]
+ 7436*r4[i]
- 46420*r6[i]
+ 576236*r8[i]
- 13098580*r10[i]
+ 532310636*r12[i]
- 39968611540*r14[i]
+ 6350631494636*r16[i]
- 3730771315561300*r18[i]
- 2637991952943407764*r20[i]
- 46833363657400320000*r21[i]
- 734121065118879803860*r22[i]
- 10556240168378032128000*r23[i]
- 142438684135271315212564*r24[i]
- 1830415113744266649600000*r25[i]
- 22632897298190126259675220*r26[i]
- 271297526662043666104320000*r27[i]
- 3170344993810020486920015764*r28[i]
- 36274730261563609572556800000*r29[i]
- 407775103607650299563627591380*r30[i]
- 4515882637052182897862000640000*r31[i]
- 49377994276343186011748723193364*r32[i]
- 534053247401000753173510963200000*r33[i]
- 5722063606154183864914875339648340*r34[i]
- 60811730909031986048777521029120000*r35[i]
- 641729418431834160625738740379401364*r36[i]
- 6730380606921481449181267599974400000*r37[i]
- 70207898580127312813466155395513222100*r38[i]
- 728918319689461841494925372032622592000*r39[i]
- 7536441803725213229125462424550696575764*r40[i]
- 77635978704164552294553096402068152320000*r41[i]
- 797177898990753876072852178329776532568660*r42[i]
) // 121645100408832000 for i in range(len(r0))]
r17 = [(4862*r[1][i]
- 7072*r[2][i]
+ 6188*r[3][i]
- 3808*r[4][i]
+ 1700*r[5][i]
- 544*r[6][i]
+ 119*r[7][i]
- 16*r[8][i]
+ r[9][i]
- 1430*r0[i]
+ 858*r2[i]
- 2310*r4[i]
+ 15258*r6[i]
- 206790*r8[i]
+ 5386458*r10[i]
- 272513670*r12[i]
+ 30255826458*r14[i]
- 12765597850950*r16[i]
- 6622557957272742*r18[i]
- 101370917007360000*r19[i]
- 1375210145685786630*r20[i]
- 17172233341046784000*r21[i]
- 201832098313986359142*r22[i]
- 2265471043586150400000*r23[i]
- 24529324224160803328710*r24[i]
- 258058524232798248960000*r25[i]
- 2652208374242713043720742*r26[i]
- 26739700571225856614400000*r27[i]
- 265323404171486113659725190*r28[i]
- 2597688920748017370193920000*r29[i]
- 25147613788240222384169485542*r30[i]
- 241125683321001354933657600000*r31[i]
- 2293170112631184981695915264070*r32[i]
- 21656158388689797460311183360000*r33[i]
- 203283794784841444836991831621542*r34[i]
- 1898267590696733462875776307200000*r35[i]
- 17646072330245312137111933794073350*r36[i]
- 163392570167583908119294187237376000*r37[i]
- 1507754227229479379470312529237936742*r38[i]
- 13871774079585871769182921633935360000*r39[i]
- 127291574907112728538906245247680921030*r40[i]
- 1165398276253942030786602999248830464000*r41[i]
- 10648249156718669259487809979675840079142*r42[i]
) // 355687428096000 for i in range(len(r0))]
r15 = [(-1430*r[1][i]
+ 2002*r[2][i]
- 1638*r[3][i]
+ 910*r[4][i]
- 350*r[5][i]
+ 90*r[6][i]
- 14*r[7][i]
+ r[8][i]
+ 429*r0[i]
- 264*r2[i]
+ 744*r4[i]
- 5304*r6[i]
+ 81384*r8[i]
- 2605944*r10[i]
+ 192387624*r12[i]
- 55942352184*r14[i]
- 20546119600536*r16[i]
- 266765571072000*r17[i]
- 3083760849804024*r18[i]
- 32945548027392000*r19[i]
- 332500281299403096*r20[i]
- 3215147584416768000*r21[i]
- 30076927429146721464*r22[i]
- 274100623905588480000*r23[i]
- 2446077617962088140056*r24[i]
- 21459412163122053120000*r25[i]
- 185641639183185136464504*r26[i]
- 1587401376760010972160000*r27[i]
- 13442713420403849918131416*r28[i]
- 112915002722102749808640000*r29[i]
- 941961013910760913890393144*r30[i]
- 7812419263561351877518080000*r31[i]
- 64474322285718607792730497176*r32[i]
- 529848386811984810994744320000*r33[i]
- 4338547620121893769542630267384*r34[i]
- 35415056327751829508662891008000*r35[i]
- 288317531175033442515609896757336*r36[i]
- 2341823147101379454117987013632000*r37[i]
- 18983391549723892653716655806647224*r38[i]
- 153619763998111828980832157720832000*r39[i]
- 1241292607509331793516191597844431896*r40[i]
- 10017079537004367071413852136982528000*r41[i]
- 80746194097372251940077615903073292664*r42[i]
) // 1307674368000 for i in range(len(r0))]
r13 = [(429*r[1][i]
- 572*r[2][i]
+ 429*r[3][i]
- 208*r[4][i]
+ 65*r[5][i]
- 12*r[6][i]
+ r[7][i]
- 132*r0[i]
+ 84*r2[i]
- 252*r4[i]
+ 2004*r6[i]
- 37212*r8[i]
+ 1710324*r10[i]
- 325024572*r12[i]
- 80789566956*r14[i]
- 871782912000*r15[i]
- 8422900930332*r16[i]
- 75583578470400*r17[i]
- 643521842437836*r18[i]
- 5269678622208000*r19[i]
- 41890044885642492*r20[i]
- 325386564299596800*r21[i]
- 2481686964269990316*r22[i]
- 18652248729354240000*r23[i]
- 138536531588626169052*r24[i]
- 1019042849143807488000*r25[i]
- 7436421488952386592396*r26[i]
- 53911021949819274240000*r27[i]
- 388701690499592948238012*r28[i]
- 2789805187365599475072000*r29[i]
- 19946749502047187160692076*r30[i]
- 142159780685991861112320000*r31[i]
- 1010433303980489860989897372*r32[i]
- 7165521770403817166663116800*r33[i]
- 50716588034439244118483617356*r34[i]
- 358378772025058883636009472000*r35[i]
- 2528902640579773012941059115132*r36[i]
- 17824202779159732939433280230400*r37[i]
- 125502611080965065134883934376236*r38[i]
- 882926862501000079240924013568000*r39[i]
- 6206986746547700738292160195379292*r40[i]
- 43608135571536574058895364550860800*r41[i]
- 306213499909407501334225902520456716*r42[i]
) // 6227020800 for i in range(len(r0))]
r11 = [(-132*r[1][i]
+ 165*r[2][i]
- 110*r[3][i]
+ 44*r[4][i]
- 10*r[5][i]
+ r[6][i]
+ 42*r0[i]
- 28*r2[i]
+ 92*r4[i]
- 868*r6[i]
+ 22652*r8[i]
- 2620708*r10[i]
- 415790788*r12[i]
- 3632428800*r13[i]
- 28616744548*r14[i]
- 210680870400*r15[i]
- 1479485236228*r16[i]
- 10038995366400*r17[i]
- 66394067988388*r18[i]
- 430591742380800*r19[i]
- 2750479262009668*r20[i]
- 17360942812012800*r21[i]
- 108550450893568228*r22[i]
- 673606803881088000*r23[i]
- 4154688725062207108*r24[i]
- 25499502190850688000*r25[i]
- 155878445775166700068*r26[i]
- 949776357849070752000*r27[i]
- 5771581202353414724548*r28[i]
- 34995682724855684832000*r29[i]
- 211811399872933910999908*r30[i]
- 1280080235834717770252800*r31[i]
- 7726641919200262371657988*r32[i]
- 46591059456870785061004800*r33[i]
- 280704018540064430354883748*r34[i]
- 1690018909819536161979590400*r35[i]
- 10169113413821714748538703428*r36[i]
- 61159784116494648773674886400*r37[i]
- 367684638335977863351585967588*r38[i]
- 2209739160176731898013383884800*r39[i]
- 13276598260065161268654185556868*r40[i]
- 79750432649108163224160355276800*r41[i]
- 478956917715683026467561165467428*r42[i]
) // 39916800 for i in range(len(r0))]
r9 = [(42*r[1][i]
- 48*r[2][i]
+ 27*r[3][i]
- 8*r[4][i]
+ r[5][i]
- 14*r0[i]
+ 10*r2[i]
- 38*r4[i]
+ 490*r6[i]
- 31238*r8[i]
- 2922230*r10[i]
- 19958400*r11[i]
- 124075238*r12[i]
- 726485760*r13[i]
- 4084385750*r14[i]
- 22313491200*r15[i]
- 119387268038*r16[i]
- 628980992640*r17[i]
- 3275389222070*r18[i]
- 16905818966400*r19[i]
- 86665431465638*r20[i]
- 441935114987520*r21[i]
- 2244295389943190*r22[i]
- 11360520464832000*r23[i]
- 57360469753884038*r24[i]
- 289038899804054400*r25[i]
- 1454155949521941110*r26[i]
- 7306671293537616000*r27[i]
- 36677059892827099238*r28[i]
- 183960524908301057280*r29[i]
- 922104761587650687830*r30[i]
- 4619736062008593926400*r31[i]
- 23135540444136227047238*r32[i]
- 115825176110799088940160*r33[i]
- 579715876176320506935350*r34[i]
- 2900939663557699476451200*r35[i]
- 14514140349055749129024038*r36[i]
- 72608472572041292373527040*r37[i]
- 363193454272347163609915670*r38[i]
- 1816571661325589960713958400*r39[i]
- 9085275939429279963731685638*r40[i]
- 45436050447189540392656321920*r41[i]
- 227218935892633882388998540790*r42[i]
) // 362880 for i in range(len(r0))]
r7 = [(-14*r[1][i]
+ 14*r[2][i]
- 6*r[3][i]
+ r[4][i]
+ 5*r0[i]
- 4*r2[i]
+ 20*r4[i]
- 604*r6[i]
- 29740*r8[i]
- 151200*r9[i]
- 708604*r10[i]
- 3160080*r11[i]
- 13645900*r12[i]
- 57657600*r13[i]
- 239967004*r14[i]
- 988107120*r15[i]
- 4037604460*r16[i]
- 16406863200*r17[i]
- 66398623804*r18[i]
- 267911678160*r19[i]
- 1078605601420*r20[i]
- 4335313752000*r21[i]
- 17403958407004*r22[i]
- 69804002545200*r23[i]
- 279780634372780*r24[i]
- 1120816644948000*r25[i]
- 4488349371924604*r26[i]
- 17968646803620240*r27[i]
- 71920337041294540*r28[i]
- 287818601403715200*r29[i]
- 1151686172846664604*r30[i]
- 4607980008114455280*r31[i]
- 18435626012705982700*r32[i]
- 73753622051697957600*r33[i]
- 295047842329672995004*r34[i]
- 1180291431927853642320*r35[i]
- 4721465916019935893260*r36[i]
- 18886764229967380219200*r37[i]
- 75549758619456576163804*r38[i]
- 302207139580435761213360*r39[i]
- 1208852873637267995922220*r40[i]
- 4835484440511039999684000*r41[i]
- 19342156599960850372299004*r42[i]
) // 5040 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
- 1680*r7[i]
- 5542*r8[i]
- 17640*r9[i]
- 54958*r10[i]
- 168960*r11[i]
- 515062*r12[i]
- 1561560*r13[i]
- 4717438*r14[i]
- 14217840*r15[i]
- 42784582*r16[i]
- 128615880*r17[i]
- 386371918*r18[i]
- 1160164320*r19[i]
- 3482590102*r20[i]
- 10451964600*r21[i]
- 31364282398*r22[i]
- 94109624400*r23[i]
- 282362427622*r24[i]
- 847154391720*r25[i]
- 2541597392878*r26[i]
- 7625060614080*r27[i]
- 22875718713142*r28[i]
- 68628229881240*r29[i]
- 205886837127358*r30[i]
- 617664806349360*r31[i]
- 1853003008982662*r32[i]
- 5559026206817160*r33[i]
- 16677112980189838*r34[i]
- 50031407660046240*r35[i]
- 150094360419092182*r36[i]
- 450283356135183480*r37[i]
- 1350850618161364318*r38[i]
- 4052552953995720720*r39[i]
- 12157661061010417702*r40[i]
- 36472987581077764200*r41[i]
- 109418971539326314798*r42[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
- 126*r7[i]
- 254*r8[i]
- 510*r9[i]
- 1022*r10[i]
- 2046*r11[i]
- 4094*r12[i]
- 8190*r13[i]
- 16382*r14[i]
- 32766*r15[i]
- 65534*r16[i]
- 131070*r17[i]
- 262142*r18[i]
- 524286*r19[i]
- 1048574*r20[i]
- 2097150*r21[i]
- 4194302*r22[i]
- 8388606*r23[i]
- 16777214*r24[i]
- 33554430*r25[i]
- 67108862*r26[i]
- 134217726*r27[i]
- 268435454*r28[i]
- 536870910*r29[i]
- 1073741822*r30[i]
- 2147483646*r31[i]
- 4294967294*r32[i]
- 8589934590*r33[i]
- 17179869182*r34[i]
- 34359738366*r35[i]
- 68719476734*r36[i]
- 137438953470*r37[i]
- 274877906942*r38[i]
- 549755813886*r39[i]
- 1099511627774*r40[i]
- 2199023255550*r41[i]
- 4398046511102*r42[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
- r7[i]
- r8[i]
- r9[i]
- r10[i]
- r11[i]
- r12[i]
- r13[i]
- r14[i]
- r15[i]
- r16[i]
- r17[i]
- r18[i]
- r19[i]
- r20[i]
- r21[i]
- r22[i]
- r23[i]
- r24[i]
- r25[i]
- r26[i]
- r27[i]
- r28[i]
- r29[i]
- r30[i]
- r31[i]
- r32[i]
- r33[i]
- r34[i]
- r35[i]
- r36[i]
- r37[i]
- r38[i]
- r39[i]
- r40[i]
- r41[i]
- r42[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42)
def natural_interpolate_23(r):
r0 = r[0]
r44 = r['infinity']
r42 = [(513791607420*(r[1][i] + r[-1][i])
- 446775310800*(r[2][i] + r[-2][i])
+ 353697121050*(r[3][i] + r[-3][i])
- 254661927156*(r[4][i] + r[-4][i])
+ 166509721602*(r[5][i] + r[-5][i])
- 98672427616*(r[6][i] + r[-6][i])
+ 52860229080*(r[7][i] + r[-7][i])
- 25518731280*(r[8][i] + r[-8][i])
+ 11058116888*(r[9][i] + r[-9][i])
- 4280561376*(r[10][i] + r[-10][i])
+ 1471442973*(r[11][i] + r[-11][i])
- 445891810*(r[12][i] + r[-12][i])
+ 118030185*(r[13][i] + r[-13][i])
- 26978328*(r[14][i] + r[-14][i])
+ 5245786*(r[15][i] + r[-15][i])
- 850668*(r[16][i] + r[-16][i])
+ 111930*(r[17][i] + r[-17][i])
- 11480*(r[18][i] + r[-18][i])
+ 861*(r[19][i] + r[-19][i])
- 42*(r[20][i] + r[-20][i])
+ (r[21][i] + r[-21][i])
- 538257874440*r0[i]
- 4651975255879785344076345169275577808059367424000000000*r44[i]
) // 1405006117752879898543142606244511569936384000000000 for i in range(len(r0))]
r40 = [(-131282408400*(r[1][i] + r[-1][i])
+ 113380261800*(r[2][i] + r[-2][i])
- 88732378800*(r[3][i] + r[-3][i])
+ 62852101650*(r[4][i] + r[-4][i])
- 40225345056*(r[5][i] + r[-5][i])
+ 23206929840*(r[6][i] + r[-6][i])
- 12033222880*(r[7][i] + r[-7][i])
+ 5586853480*(r[8][i] + r[-8][i])
- 2311801440*(r[9][i] + r[-9][i])
+ 847660528*(r[10][i] + r[-10][i])
- 273438880*(r[11][i] + r[-11][i])
+ 76904685*(r[12][i] + r[-12][i])
- 18643560*(r[13][i] + r[-13][i])
+ 3838380*(r[14][i] + r[-14][i])
- 658008*(r[15][i] + r[-15][i])
+ 91390*(r[16][i] + r[-16][i])
- 9880*(r[17][i] + r[-17][i])
+ 780*(r[18][i] + r[-18][i])
- 40*(r[19][i] + r[-19][i])
+ (r[20][i] + r[-20][i])
+ 137846528820*r0[i]
- 2341676862921466497571904343740852616560640000000000*r42[i]
- 3655123415334117056059985490145096849189502976000000000*r44[i]
) // 815915283247897734345611269596115894272000000000 for i in range(len(r0))]
r38 = [(33578000610*(r[1][i] + r[-1][i])
- 28781143380*(r[2][i] + r[-2][i])
+ 22239974430*(r[3][i] + r[-3][i])
- 15471286560*(r[4][i] + r[-4][i])
+ 9669554100*(r[5][i] + r[-5][i])
- 5414950296*(r[6][i] + r[-6][i])
+ 2707475148*(r[7][i] + r[-7][i])
- 1203322288*(r[8][i] + r[-8][i])
+ 472733756*(r[9][i] + r[-9][i])
- 163011640*(r[10][i] + r[-10][i])
+ 48903492*(r[11][i] + r[-11][i])
- 12620256*(r[12][i] + r[-12][i])
+ 2760681*(r[13][i] + r[-13][i])
- 501942*(r[14][i] + r[-14][i])
+ 73815*(r[15][i] + r[-15][i])
- 8436*(r[16][i] + r[-16][i])
+ 703*(r[17][i] + r[-17][i])
- 38*(r[18][i] + r[-18][i])
+ (r[19][i] + r[-19][i])
- 35345263800*r0[i]
- 1291865865142504746047217843527183499264000000000*r40[i]
- 1742597865490724651943092149133817822157209600000000*r42[i]
- 1703614521144184428726371303487541532883419136000000000*r44[i]
) // 523022617466601111760007224100074291200000000 for i in range(len(r0))]
r36 = [(-8597496600*(r[1][i] + r[-1][i])
+ 7307872110*(r[2][i] + r[-2][i])
- 5567902560*(r[3][i] + r[-3][i])
+ 3796297200*(r[4][i] + r[-4][i])
- 2310789600*(r[5][i] + r[-5][i])
+ 1251677700*(r[6][i] + r[-6][i])
- 600805296*(r[7][i] + r[-7][i])
+ 254186856*(r[8][i] + r[-8][i])
- 94143280*(r[9][i] + r[-9][i])
+ 30260340*(r[10][i] + r[-10][i])
- 8347680*(r[11][i] + r[-11][i])
+ 1947792*(r[12][i] + r[-12][i])
- 376992*(r[13][i] + r[-13][i])
+ 58905*(r[14][i] + r[-14][i])
- 7140*(r[15][i] + r[-15][i])
+ 630*(r[16][i] + r[-16][i])
- 36*(r[17][i] + r[-17][i])
+ (r[18][i] + r[-18][i])
+ 9075135300*r0[i]
- 784533926199901667640010836150111436800000000*r38[i]
- 907705752613286229459492537425678932377600000000*r40[i]
- 764250847583238143225401875995898505750118400000000*r42[i]
- 524336156604477506256224109002957345627779891200000000*r44[i]
) // 371993326789901217467999448150835200000000 for i in range(len(r0))]
r34 = [(2203961430*(r[1][i] + r[-1][i])
- 1855967520*(r[2][i] + r[-2][i])
+ 1391975640*(r[3][i] + r[-3][i])
- 927983760*(r[4][i] + r[-4][i])
+ 548354040*(r[5][i] + r[-5][i])
- 286097760*(r[6][i] + r[-6][i])
+ 131128140*(r[7][i] + r[-7][i])
- 52451256*(r[8][i] + r[-8][i])
+ 18156204*(r[9][i] + r[-9][i])
- 5379616*(r[10][i] + r[-10][i])
+ 1344904*(r[11][i] + r[-11][i])
- 278256*(r[12][i] + r[-12][i])
+ 46376*(r[13][i] + r[-13][i])
- 5984*(r[14][i] + r[-14][i])
+ 561*(r[15][i] + r[-15][i])
- 34*(r[16][i] + r[-16][i])
+ (r[17][i] + r[-17][i])
- 2333606220*r0[i]
- 526990546285693391412999218213683200000000*r36[i]
- 518664095654379435828673830565907005440000000*r38[i]
- 373138241060740797524227217357125818777600000000*r40[i]
- 219618160307546307818407858079592245845032960000000*r42[i]
- 112275193446419212026758411812279514001781555200000000*r44[i]
) // 295232799039604140847618609643520000000 for i in range(len(r0))]
r32 = [(-565722720*(r[1][i] + r[-1][i])
+ 471435600*(r[2][i] + r[-2][i])
- 347373600*(r[3][i] + r[-3][i])
+ 225792840*(r[4][i] + r[-4][i])
- 129024480*(r[5][i] + r[-5][i])
+ 64512240*(r[6][i] + r[-6][i])
- 28048800*(r[7][i] + r[-7][i])
+ 10518300*(r[8][i] + r[-8][i])
- 3365856*(r[9][i] + r[-9][i])
+ 906192*(r[10][i] + r[-10][i])
- 201376*(r[11][i] + r[-11][i])
+ 35960*(r[12][i] + r[-12][i])
- 4960*(r[13][i] + r[-13][i])
+ 496*(r[14][i] + r[-14][i])
- 32*(r[15][i] + r[-15][i])
+ (r[16][i] + r[-16][i])
+ 601080390*r0[i]
- 393643732052805521130158146191360000000*r34[i]
- 326527475737802179777466182265733120000000*r36[i]
- 198969979872214920293886346099446251520000000*r38[i]
- 99626745669333527035567016277524852244480000000*r40[i]
- 43498703313314018776504938348732045412270080000000*r42[i]
- 17170843124850370546818528558187736420780605440000000*r44[i]
) // 263130836933693530167218012160000000 for i in range(len(r0))]
r30 = [(145422675*(r[1][i] + r[-1][i])
- 119759850*(r[2][i] + r[-2][i])
+ 86493225*(r[3][i] + r[-3][i])
- 54627300*(r[4][i] + r[-4][i])
+ 30045015*(r[5][i] + r[-5][i])
- 14307150*(r[6][i] + r[-6][i])
+ 5852925*(r[7][i] + r[-7][i])
- 2035800*(r[8][i] + r[-8][i])
+ 593775*(r[9][i] + r[-9][i])
- 142506*(r[10][i] + r[-10][i])
+ 27405*(r[11][i] + r[-11][i])
- 4060*(r[12][i] + r[-12][i])
+ 435*(r[13][i] + r[-13][i])
- 30*(r[14][i] + r[-14][i])
+ (r[15][i] + r[-15][i])
- 155117520*r0[i]
- 328913546167116912709022515200000000*r32[i]
- 227575282593028191903372678266880000000*r34[i]
- 116309421454977381321426414757478400000000*r36[i]
- 49083095586740430887431564189583278080000000*r38[i]
- 18139371393109511951007844941215406489600000000*r40[i]
- 6083845843389094496001274537210012898426880000000*r42[i]
- 1895875482185729033390420637976407213657292800000000*r44[i]
) // 265252859812191058636308480000000 for i in range(len(r0))]
r28 = [(-37442160*(r[1][i] + r[-1][i])
+ 30421755*(r[2][i] + r[-2][i])
- 21474180*(r[3][i] + r[-3][i])
+ 13123110*(r[4][i] + r[-4][i])
- 6906900*(r[5][i] + r[-5][i])
+ 3108105*(r[6][i] + r[-6][i])
- 1184040*(r[7][i] + r[-7][i])
+ 376740*(r[8][i] + r[-8][i])
- 98280*(r[9][i] + r[-9][i])
+ 20475*(r[10][i] + r[-10][i])
- 3276*(r[11][i] + r[-11][i])
+ 378*(r[12][i] + r[-12][i])
- 28*(r[13][i] + r[-13][i])
+ (r[14][i] + r[-14][i])
+ 40116600*r0[i]
- 309461669780889568409026560000000*r30[i]
- 176516936443019409820508749824000000*r32[i]
- 74833313645455216256514439249920000000*r34[i]
- 26337328459046574816219104447299584000000*r36[i]
- 8155948144934385059006601147769159680000000*r38[i]
- 2301709517171786559798286695904076365824000000*r40[i]
- 605758813130095139988659617361096909783040000000*r42[i]
- 151061790397229175366153301919734749322543104000000*r44[i]
) // 304888344611713860501504000000 for i in range(len(r0))]
r26 = [(9657700*(r[1][i] + r[-1][i])
- 7726160*(r[2][i] + r[-2][i])
+ 5311735*(r[3][i] + r[-3][i])
- 3124550*(r[4][i] + r[-4][i])
+ 1562275*(r[5][i] + r[-5][i])
- 657800*(r[6][i] + r[-6][i])
+ 230230*(r[7][i] + r[-7][i])
- 65780*(r[8][i] + r[-8][i])
+ 14950*(r[9][i] + r[-9][i])
- 2600*(r[10][i] + r[-10][i])
+ 325*(r[11][i] + r[-11][i])
- 26*(r[12][i] + r[-12][i])
+ (r[13][i] + r[-13][i])
- 10400600*r0[i]
- 330295706662690015543296000000*r28[i]
- 153257207891488167212089344000000*r30[i]
- 53222214421459539592188788736000000*r32[i]
- 15436506593303376230082373484544000000*r34[i]
- 3960094929842931739454572322881536000000*r36[i]
- 930084233815670751630942950980583424000000*r38[i]
- 204528766884160018873274371645367648256000000*r40[i]
- 42768601883241439058698435075343591276544000000*r42[i]
- 8599134589431485780708409429924529774657536000000*r44[i]
) // 403291461126605635584000000 for i in range(len(r0))]
r24 = [(-2496144*(r[1][i] + r[-1][i])
+ 1961256*(r[2][i] + r[-2][i])
- 1307504*(r[3][i] + r[-3][i])
+ 735471*(r[4][i] + r[-4][i])
- 346104*(r[5][i] + r[-5][i])
+ 134596*(r[6][i] + r[-6][i])
- 42504*(r[7][i] + r[-7][i])
+ 10626*(r[8][i] + r[-8][i])
- 2024*(r[9][i] + r[-9][i])
+ 276*(r[10][i] + r[-10][i])
- 24*(r[11][i] + r[-11][i])
+ (r[12][i] + r[-12][i])
+ 2704156*r0[i]
- 403291461126605635584000000*r26[i]
- 149903436100759314746572800000*r28[i]
- 42033455827381598974377984000000*r30[i]
- 9910695932425713906157643366400000*r32[i]
- 2078962023961017163954848006144000000*r34[i]
- 401274139495715827174031120636313600000*r36[i]
- 72837740568171787457915404507152384000000*r38[i]
- 12620369661259070567869332718886859571200000*r40[i]
- 2109601340251819353520575234140712075264000000*r42[i]
- 342864867500163789441705220714949009654415360000*r44[i]
) // 620448401733239439360000 for i in range(len(r0))]
r22 = [(646646*(r[1][i] + r[-1][i])
- 497420*(r[2][i] + r[-2][i])
+ 319770*(r[3][i] + r[-3][i])
- 170544*(r[4][i] + r[-4][i])
+ 74613*(r[5][i] + r[-5][i])
- 26334*(r[6][i] + r[-6][i])
+ 7315*(r[7][i] + r[-7][i])
- 1540*(r[8][i] + r[-8][i])
+ 231*(r[9][i] + r[-9][i])
- 22*(r[10][i] + r[-10][i])
+ (r[11][i] + r[-11][i])
- 705432*r0[i]
- 568744368255469486080000*r24[i]
- 166357727714724824678400000*r26[i]
- 37042320704478727628390400000*r28[i]
- 6988909951599209517839155200000*r30[i]
- 1180836611760352104108962611200000*r32[i]
- 184607985589364774573429361868800000*r34[i]
- 27272218262298384682708194086092800000*r36[i]
- 3861838803337560097698395778726297600000*r38[i]
- 529471212011799260411940801849645465600000*r40[i]
- 70801221927358337925257947461388534087680000*r42[i]
- 9284304296436839352157882253583122352046080000*r44[i]
) // 1124000727777607680000 for i in range(len(r0))]
r20 = [(-167960*(r[1][i] + r[-1][i])
+ 125970*(r[2][i] + r[-2][i])
- 77520*(r[3][i] + r[-3][i])
+ 38760*(r[4][i] + r[-4][i])
- 15504*(r[5][i] + r[-5][i])
+ 4845*(r[6][i] + r[-6][i])
- 1140*(r[7][i] + r[-7][i])
+ 190*(r[8][i] + r[-8][i])
- 20*(r[9][i] + r[-9][i])
+ (r[10][i] + r[-10][i])
+ 184756*r0[i]
- 936667273148006400000*r22[i]
- 211124803367560642560000*r24[i]
- 36608302274885332992000000*r26[i]
- 5425950533240873322086400000*r28[i]
- 725494605231272191451136000000*r30[i]
- 90317652741043657957240012800000*r32[i]
- 10681064948020015063470219264000000*r34[i]
- 1216234618180639720975550420582400000*r36[i]
- 134607612138429628983625351999488000000*r38[i]
- 14578366393789236829898507440652451840000*r40[i]
- 1552719574083291045891061928041363046400000*r42[i]
- 163243281617906068079686557318998305013760000*r44[i]
) // 2432902008176640000 for i in range(len(r0))]
r18 = [(43758*(r[1][i] + r[-1][i])
- 31824*(r[2][i] + r[-2][i])
+ 18564*(r[3][i] + r[-3][i])
- 8568*(r[4][i] + r[-4][i])
+ 3060*(r[5][i] + r[-5][i])
- 816*(r[6][i] + r[-6][i])
+ 153*(r[7][i] + r[-7][i])
- 18*(r[8][i] + r[-8][i])
+ (r[9][i] + r[-9][i])
- 48620*r0[i]
- 1824676506132480000*r20[i]
- 309100200138842112000*r22[i]
- 40778478784550707200000*r24[i]
- 4645053436190368481280000*r26[i]
- 481314610282065419059200000*r28[i]
- 46758400573464312663490560000*r30[i]
- 4340262299778024388805836800000*r32[i]
- 389810850996416354285601300480000*r34[i]
- 34168816632541202331763973529600000*r36[i]
- 2941066263016510346147295370272768000*r38[i]
- 249691933432545691845292589410836480000*r40[i]
- 20977168972570956554158853986478948352000*r42[i]
- 1748194308191420862068509392967461273600000*r44[i]
) // 6402373705728000 for i in range(len(r0))]
r16 = [(-11440*(r[1][i] + r[-1][i])
+ 8008*(r[2][i] + r[-2][i])
- 4368*(r[3][i] + r[-3][i])
+ 1820*(r[4][i] + r[-4][i])
- 560*(r[5][i] + r[-5][i])
+ 120*(r[6][i] + r[-6][i])
- 16*(r[7][i] + r[-7][i])
+ (r[8][i] + r[-8][i])
+ 12870*r0[i]
- 4268249137152000*r18[i]
- 527128768438272000*r20[i]
- 51442361350668288000*r22[i]
- 4385609982489415680000*r24[i]
- 343350594609952849920000*r26[i]
- 25398422028160175554560000*r28[i]
- 1806640043553643996938240000*r30[i]
- 124998708216981630040289280000*r32[i]
- 8477574188991756975915909120000*r34[i]
- 566640901244029272138606256128000*r36[i]
- 37469170353622071265887792218112000*r38[i]
- 2457916223969789263693314523533312000*r40[i]
- 160273272592069873142621634191720448000*r42[i]
- 10404012781412834769965673013161000960000*r44[i]
) // 20922789888000 for i in range(len(r0))]
r14 = [(3003*(r[1][i] + r[-1][i])
- 2002*(r[2][i] + r[-2][i])
+ 1001*(r[3][i] + r[-3][i])
- 364*(r[4][i] + r[-4][i])
+ 91*(r[5][i] + r[-5][i])
- 14*(r[6][i] + r[-6][i])
+ (r[7][i] + r[-7][i])
- 3432*r0[i]
- 12204960768000*r16[i]
- 1058170098585600*r18[i]
- 73775500710912000*r20[i]
- 4555411900194355200*r22[i]
- 261131482210959360000*r24[i]
- 14266599888013304832000*r26[i]
- 754754307297469839360000*r28[i]
- 39057272623118392651008000*r30[i]
- 1990236929603886055572480000*r32[i]
- 100317304785653440333283635200*r34[i]
- 5017302808350824370904132608000*r36[i]
- 249538838908236261152065923225600*r38[i]
- 12360976075014001109372936189952000*r40[i]
- 610513898001512036824535103712051200*r42[i]
- 30089355946979742032883786297815040000*r44[i]
) // 87178291200 for i in range(len(r0))]
r12 = [(-792*(r[1][i] + r[-1][i])
+ 495*(r[2][i] + r[-2][i])
- 220*(r[3][i] + r[-3][i])
+ 66*(r[4][i] + r[-4][i])
- 12*(r[5][i] + r[-5][i])
+ (r[6][i] + r[-6][i])
+ 924*r0[i]
- 43589145600*r14[i]
- 2528170444800*r16[i]
- 120467944396800*r18[i]
- 5167100908569600*r20[i]
- 208331313744153600*r22[i]
- 8083281646573056000*r24[i]
- 305994026290208256000*r26[i]
- 11397316294188849024000*r28[i]
- 419948192698268217984000*r30[i]
- 15360962830016613243033600*r32[i]
- 559092713482449420732057600*r34[i]
- 20280226917834433943755084800*r36[i]
- 733917409397935785284098636800*r38[i]
- 26516869922120782776160606617600*r40[i]
- 957005191789297958689924263321600*r42[i]
- 34512162491005016706155579824512000*r44[i]
) // 479001600 for i in range(len(r0))]
r10 = [(210*(r[1][i] + r[-1][i])
- 120*(r[2][i] + r[-2][i])
+ 45*(r[3][i] + r[-3][i])
- 10*(r[4][i] + r[-4][i])
+ (r[5][i] + r[-5][i])
- 252*r0[i]
- 199584000*r12[i]
- 7264857600*r14[i]
- 223134912000*r16[i]
- 6289809926400*r18[i]
- 169058189664000*r20[i]
- 4419351149875200*r22[i]
- 113605204648320000*r24[i]
- 2890388998040544000*r26[i]
- 73066712935376160000*r28[i]
- 1839605249083010572800*r30[i]
- 46197360620085939264000*r32[i]
- 1158251761107990889401600*r34[i]
- 29009396635576994764512000*r36[i]
- 726084725720412923735270400*r38[i]
- 18165716613255899607139584000*r40[i]
- 454360504471895403926563219200*r42[i]
- 11362494160594553046963852960000*r44[i]
) // 3628800 for i in range(len(r0))]
r8 = [(-56*(r[1][i] + r[-1][i])
+ 28*(r[2][i] + r[-2][i])
- 8*(r[3][i] + r[-3][i])
+ (r[4][i] + r[-4][i])
+ 70*r0[i]
- 1209600*r10[i]
- 25280640*r12[i]
- 461260800*r14[i]
- 7904856960*r16[i]
- 131254905600*r18[i]
- 2143293425280*r20[i]
- 34682510016000*r22[i]
- 558432020361600*r24[i]
- 8966533159584000*r26[i]
- 143749174428961920*r28[i]
- 2302548811229721600*r30[i]
- 36863840064915642240*r32[i]
- 590028976413583660800*r34[i]
- 9442331455422829138560*r36[i]
- 151094113839739041753600*r38[i]
- 2417657116643486089706880*r40[i]
- 38683875524088319997472000*r42[i]
- 618954263309240362088323200*r44[i]
) // 40320 for i in range(len(r0))]
r6 = [(15*(r[1][i] + r[-1][i])
- 6*(r[2][i] + r[-2][i])
+ (r[3][i] + r[-3][i])
- 20*r0[i]
- 10080*r8[i]
- 105840*r10[i]
- 1013760*r12[i]
- 9369360*r14[i]
- 85307040*r16[i]
- 771695280*r18[i]
- 6960985920*r20[i]
- 62711787600*r22[i]
- 564657746400*r24[i]
- 5082926350320*r26[i]
- 45750363684480*r28[i]
- 411769379287440*r30[i]
- 3705988838096160*r32[i]
- 33354157240902960*r34[i]
- 300188445960277440*r36[i]
- 2701700136811100880*r38[i]
- 24315317723974324320*r40[i]
- 218837925486466585200*r42[i]
- 1969541593260989932800*r44[i]
) // 720 for i in range(len(r0))]
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
- 504*r8[i]
- 2040*r10[i]
- 8184*r12[i]
- 32760*r14[i]
- 131064*r16[i]
- 524280*r18[i]
- 2097144*r20[i]
- 8388600*r22[i]
- 33554424*r24[i]
- 134217720*r26[i]
- 536870904*r28[i]
- 2147483640*r30[i]
- 8589934584*r32[i]
- 34359738360*r34[i]
- 137438953464*r36[i]
- 549755813880*r38[i]
- 2199023255544*r40[i]
- 8796093022200*r42[i]
- 35184372088824*r44[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
- 2*r8[i]
- 2*r10[i]
- 2*r12[i]
- 2*r14[i]
- 2*r16[i]
- 2*r18[i]
- 2*r20[i]
- 2*r22[i]
- 2*r24[i]
- 2*r26[i]
- 2*r28[i]
- 2*r30[i]
- 2*r32[i]
- 2*r34[i]
- 2*r36[i]
- 2*r38[i]
- 2*r40[i]
- 2*r42[i]
- 2*r44[i]
) // 2 for i in range(len(r0))]
r43 = [(-91482563640*r[1][i]
+ 160094486370*r[2][i]
- 192113383644*r[3][i]
+ 187187399448*r[4][i]
- 155989499540*r[5][i]
+ 113649492522*r[6][i]
- 73153696336*r[7][i]
+ 41802112192*r[8][i]
- 21238169904*r[9][i]
+ 9586673915*r[10][i]
- 3834669566*r[11][i]
+ 1353412788*r[12][i]
- 418913482*r[13][i]
+ 112784399*r[14][i]
- 26127660*r[15][i]
+ 5133856*r[16][i]
- 839188*r[17][i]
+ 111069*r[18][i]
- 11438*r[19][i]
+ 860*r[20][i]
- 42*r[21][i]
+ r[22][i]
+ 24466267020*r0[i]
- 13128240840*r2[i]
+ 29286075720*r4[i]
- 144956522040*r6[i]
+ 1290252243720*r8[i]
- 18448766253240*r10[i]
+ 394763466531720*r12[i]
- 12048763425424440*r14[i]
+ 507104531694579720*r16[i]
- 28726839421461491640*r18[i]
+ 2153064433503155907720*r20[i]
- 211041986898764840790840*r22[i]
+ 26870132026261051008915720*r24[i]
- 4433779344005175981028538040*r26[i]
+ 950513389106656928711222883720*r28[i]
- 266877172369028643812085068829240*r30[i]
+ 99651017964870751887504875569971720*r32[i]
- 50788156610571325953562659420384640440*r34[i]
+ 36915961449056930526009630202648137219720*r36[i]
- 41419014418447665040750851917674255257827640*r38[i]
+ 84934578551016826327683205574058431012558547720*r40[i]
- 570180937724400876712836731188276811777920749126840*r42[i]
- 4158439692009034639969470592464099450041235634033244280*r44[i]
) // 60415263063373835637355132068513997507264512000000000 for i in range(len(r0))]
r41 = [(24466267020*r[1][i]
- 42550029600*r[2][i]
+ 50528160150*r[3][i]
- 48507033744*r[4][i]
+ 39645171810*r[5][i]
- 28192122176*r[6][i]
+ 17620076360*r[7][i]
- 9721421440*r[8][i]
+ 4739192952*r[9][i]
- 2038362560*r[10][i]
+ 770755843*r[11][i]
- 254795320*r[12][i]
+ 73066305*r[13][i]
- 17985552*r[14][i]
+ 3746990*r[15][i]
- 648128*r[16][i]
+ 90610*r[17][i]
- 9840*r[18][i]
+ 779*r[19][i]
- 40*r[20][i]
+ r[21][i]
- 6564120420*r0[i]
+ 3534526380*r2[i]
- 7928802420*r4[i]
+ 39562131180*r6[i]
- 355997149620*r8[i]
+ 5162772055980*r10[i]
- 112466379416820*r12[i]
+ 3509804003100780*r14[i]
- 151808102304340020*r16[i]
+ 8890838711788769580*r18[i]
- 693867758978013455220*r20[i]
+ 71436574576557715366380*r22[i]
- 9656103679244476561098420*r24[i]
+ 1714541855816811795973995180*r26[i]
- 402505898503128791422102405620*r28[i]
+ 126699650825847516884027712559980*r30[i]
- 54827934277723571354991704981312820*r32[i]
+ 34051732695777105364083032869387764780*r34[i]
- 32827430653262026254340815579045378556020*r36[i]
+ 58129225653125966892251726413185365757113580*r38[i]
- 338476895760295138790385051321218766549279671220*r40[i]
- 2149763077602671437231704105519918866633843849089620*r42[i]
- 110761315616185365335151075458942328763318272000000000*r43[i]
- 4942256826876098689793689711313418888604591478522994420*r44[i]
) // 33452526613163807108170062053440751665152000000000 for i in range(len(r0))]
r39 = [(-6564120420*r[1][i]
+ 11338026180*r[2][i]
- 13309856820*r[3][i]
+ 12570420330*r[4][i]
- 10056336264*r[5][i]
+ 6962078952*r[6][i]
- 4211628008*r[7][i]
+ 2234741392*r[8][i]
- 1040310648*r[9][i]
+ 423830264*r[10][i]
- 150391384*r[11][i]
+ 46142811*r[12][i]
- 12118314*r[13][i]
+ 2686866*r[14][i]
- 493506*r[15][i]
+ 73112*r[16][i]
- 8398*r[17][i]
+ 702*r[18][i]
- 38*r[19][i]
+ r[20][i]
+ 1767263190*r0[i]
- 955277400*r2[i]
+ 2156197560*r4[i]
- 10855425000*r6[i]
+ 98876533560*r8[i]
- 1456859058600*r10[i]
+ 32382608125560*r12[i]
- 1036360772970600*r14[i]
+ 46242812090245560*r16[i]
- 2813858311510281000*r18[i]
+ 230141619686501005560*r20[i]
- 25097337236284407949800*r22[i]
+ 3642002181929040219157560*r24[i]
- 706474912755087069174777000*r26[i]
+ 185490702479102020671448093560*r28[i]
- 67501512373123369695638979402600*r30[i]
+ 35506616897715366055874618759845560*r32[i]
- 29173319982987640073110629923442306600*r34[i]
+ 44272025958057634433180503709478279085560*r36[i]
- 222019441630075420847480526017947263931809000*r38[i]
- 1219813882056330049405575791394671579625372874440*r40[i]
- 58541921573036662439297608593521315414016000000000*r41[i]
- 2435494701008122308521041585840935773426259964069800*r42[i]
- 91378085383352926401499637253627421229737574400000000*r43[i]
- 3166734413390519310621011935324774315544541946854082440*r44[i]
) // 20397882081197443358640281739902897356800000000 for i in range(len(r0))]
r37 = [(1767263190*r[1][i]
- 3029594040*r[2][i]
+ 3511574910*r[3][i]
- 3257112960*r[4][i]
+ 2544619500*r[5][i]
- 1709984304*r[6][i]
+ 997490844*r[7][i]
- 506662016*r[8][i]
+ 223926516*r[9][i]
- 85795600*r[10][i]
+ 28312548*r[11][i]
- 7970688*r[12][i]
+ 1888887*r[13][i]
- 369852*r[14][i]
+ 58275*r[15][i]
- 7104*r[16][i]
+ 629*r[17][i]
- 36*r[18][i]
+ r[19][i]
- 477638700*r0[i]
+ 259289580*r2[i]
- 589294500*r4[i]
+ 2996657580*r6[i]
- 27670359300*r8[i]
+ 415064933580*r10[i]
- 9439543875300*r12[i]
+ 310922483993580*r14[i]
- 14379880666402500*r16[i]
+ 914767168887053580*r18[i]
- 79051272004645620900*r20[i]
+ 9231401536061270849580*r22[i]
- 1459700260139475814330500*r24[i]
+ 315843905250429722227637580*r26[i]
- 95612546130070295522414451300*r28[i]
+ 42177612582297377823299737193580*r30[i]
- 29268533564152352561039458453023300*r32[i]
+ 37747202396256876155482291281278813580*r34[i]
- 161759954125032708920885781040309430206500*r36[i]
- 763162014442847423121851269222329739576686420*r38[i]
- 33996470135329072264400469566504828928000000000*r39[i]
- 1314149222797294391875041342296266627244339280900*r40[i]
- 45857838565545385577449793398258363740979200000000*r41[i]
- 1479444354242422663436299123473954120225396734970420*r42[i]
- 44831961082741695492799244828619514023247872000000000*r43[i]
- 1290525734288850664269099373480698875776359383538646500*r44[i]
) // 13763753091226345046315979581580902400000000 for i in range(len(r0))]
r35 = [(-477638700*r[1][i]
+ 811985790*r[2][i]
- 927983760*r[3][i]
+ 843621600*r[4][i]
- 641886000*r[5][i]
+ 417225900*r[6][i]
- 233646504*r[7][i]
+ 112971936*r[8][i]
- 47071640*r[9][i]
+ 16811300*r[10][i]
- 5101360*r[11][i]
+ 1298528*r[12][i]
- 272272*r[13][i]
+ 45815*r[14][i]
- 5950*r[15][i]
+ 560*r[16][i]
- 34*r[17][i]
+ r[18][i]
+ 129644790*r0[i]
- 70715340*r2[i]
+ 161960940*r4[i]
- 832930740*r6[i]
+ 7810859340*r8[i]
- 119578066740*r10[i]
+ 2791740107340*r12[i]
- 95062235276340*r14[i]
+ 4584012079172940*r16[i]
- 307268933913567540*r18[i]
+ 28355038085389144140*r20[i]
- 3597774935929125068340*r22[i]
+ 632729503874459828228940*r24[i]
- 157381528472579148083026740*r26[i]
+ 57577884185625191071239755340*r28[i]
- 33404393172944223690128125810740*r30[i]
+ 36271128388074981554067219056171340*r32[i]
- 131671692334895976886647813958596908340*r34[i]
- 529104107360143104505564190890974500955060*r36[i]
- 21792609061108379656666967670836428800000000*r37[i]
- 779765567254824678774814590170424618060927540*r38[i]
- 25214048683702395262763681595157748121600000000*r39[i]
- 754531895504954495472529428607358759602244935860*r40[i]
- 21229190210645503978483385444330514048614400000000*r41[i]
- 567902644449952014090537079509460539320563935596340*r42[i]
- 14564893239013264062672891916748815156327219200000000*r43[i]
- 360416016142646161224945882401067658836071135991963060*r44[i]
) // 10333147966386144929666651337523200000000 for i in range(len(r0))]
r33 = [(129644790*r[1][i]
- 218349120*r[2][i]
+ 245642760*r[3][i]
- 218349120*r[4][i]
+ 161280600*r[5][i]
- 100975680*r[6][i]
+ 53993940*r[7][i]
- 24682944*r[8][i]
+ 9612108*r[9][i]
- 3164480*r[10][i]
+ 870232*r[11][i]
- 196416*r[12][i]
+ 35464*r[13][i]
- 4928*r[14][i]
+ 495*r[15][i]
- 32*r[16][i]
+ r[17][i]
- 35357670*r0[i]
+ 19389690*r2[i]
- 44796870*r4[i]
+ 233344890*r6[i]
- 2227139910*r8[i]
+ 34903389690*r10[i]
- 839988260550*r12[i]
+ 29734601940090*r14[i]
- 1506293149214790*r16[i]
+ 107487540061668090*r18[i]
- 10743535525710258630*r20[i]
+ 1511267716903778445690*r22[i]
- 304525956073869018848070*r24[i]
+ 91234873454404063067344890*r26[i]
- 43747586259736794619504039110*r28[i]
+ 39574917458915050445099774637690*r30[i]
- 120523981455993504966525708346887750*r32[i]
- 408775192473644376465790167368394203910*r34[i]
- 15499721949579217394499977006284800000000*r35[i]
- 511206585269023792365556128001469646849990*r36[i]
- 15254826342775865759666877369585500160000000*r37[i]
- 421754497238984285335705463354740490210507910*r38[i]
- 10974654148845317574241976981091935846400000000*r39[i]
- 271793538072560300468434911462753194293644181830*r40[i]
- 6459357656104303171129642884693889583677440000000*r41[i]
- 148248369194001435848413334991598692517822202402310*r42[i]
- 3302211571953506236081129759184691588287692800000000*r43[i]
- 71676123253955938571177412178194687158760951558339270*r44[i]
) // 8683317618811886495518194401280000000 for i in range(len(r0))]
r31 = [(-35357670*r[1][i]
+ 58929450*r[2][i]
- 65132550*r[3][i]
+ 56448210*r[4][i]
- 40320150*r[5][i]
+ 24192090*r[6][i]
- 12271350*r[7][i]
+ 5259150*r[8][i]
- 1893294*r[9][i]
+ 566370*r[10][i]
- 138446*r[11][i]
+ 26970*r[12][i]
- 4030*r[13][i]
+ 434*r[14][i]
- 30*r[15][i]
+ r[16][i]
+ 9694845*r0[i]
- 5348880*r2[i]
+ 12480720*r4[i]
- 65969520*r6[i]
+ 642563280*r8[i]
- 10347602160*r10[i]
+ 258040917840*r12[i]
- 9564008626800*r14[i]
+ 514021079720400*r16[i]
- 39590373677587440*r18[i]
+ 4371353677873146960*r20[i]
- 701971899866535028080*r22[i]
+ 169737570795219895373520*r24[i]
- 66396273378844288679892720*r26[i]
+ 49448835121192219782326176080*r28[i]
- 124963193751534047864734415925360*r30[i]
- 354113410826574103722030528083469360*r32[i]
- 12301366626650172535317442068480000000*r33[i]
- 372225904019072507165665501545458070000*r34[i]
- 10203983616806318118045818195804160000000*r35[i]
- 259484653500223872483011119661283865786800*r36[i]
- 6217811871006716259183948315607695360000000*r37[i]
- 141956901865997956445469727796622341498870640*r38[i]
- 3113335802166672719861469258672651632640000000*r39[i]
- 66003822624082868383556482555741495612650600240*r40[i]
- 1359334478541063086765779323397876419133440000000*r41[i]
- 27303356587963564025554884815930553997263574871280*r42[i]
- 536588847651574079588079017443366763149393920000000*r43[i]
- 10345842549438556817463474698578198121859964179733680*r44[i]
) // 8222838654177922817725562880000000 for i in range(len(r0))]
r29 = [(9694845*r[1][i]
- 15967980*r[2][i]
+ 17298645*r[3][i]
- 14567280*r[4][i]
+ 10015005*r[5][i]
- 5722860*r[6][i]
+ 2731365*r[7][i]
- 1085760*r[8][i]
+ 356265*r[9][i]
- 95004*r[10][i]
+ 20097*r[11][i]
- 3248*r[12][i]
+ 377*r[13][i]
- 28*r[14][i]
+ r[15][i]
- 2674440*r0[i]
+ 1485800*r2[i]
- 3506488*r4[i]
+ 18850280*r6[i]
- 188004088*r8[i]
+ 3125835560*r10[i]
- 81314498488*r12[i]
+ 3185384180840*r14[i]
- 184064268909688*r16[i]
+ 15598375633694120*r18[i]
- 1958105850969957688*r20[i]
+ 375744491571024583400*r22[i]
- 118117302690774819242488*r24[i]
+ 71447614092662750198256680*r26[i]
- 147980747895225006590333244088*r28[i]
- 346368637877614395127589803878040*r30[i]
- 10963784872237230423634083840000000*r31[i]
- 302766527792977996357877082103322488*r32[i]
- 7585842753100939730112422608896000000*r33[i]
- 176553572119721839407097582006071612760*r34[i]
- 3876980715165912710714213825249280000000*r35[i]
- 81213796311764134505181592648745883717688*r36[i]
- 1636103186224681029581052139652775936000000*r37[i]
- 31895543813319775842490572300866856117139480*r38[i]
- 604645713103650398366928164707180216320000000*r39[i]
- 11189653759353064214370349765226592602607549688*r40[i]
- 202794861446303149866709151240333763280896000000*r41[i]
- 3608799207440735942926262565268791718882246250200*r42[i]
- 63195849406190967779680687932546907121909760000000*r43[i]
- 1091041918456432706911605989934195570136050930818488*r44[i]
) // 8841761993739701954543616000000 for i in range(len(r0))]
r27 = [(-2674440*r[1][i]
+ 4345965*r[2][i]
- 4601610*r[3][i]
+ 3749460*r[4][i]
- 2466750*r[5][i]
+ 1332045*r[6][i]
- 592020*r[7][i]
+ 215280*r[8][i]
- 63180*r[9][i]
+ 14625*r[10][i]
- 2574*r[11][i]
+ 324*r[12][i]
- 26*r[13][i]
+ r[14][i]
+ 742900*r0[i]
- 416024*r2[i]
+ 994840*r4[i]
- 5454824*r6[i]
+ 55944280*r8[i]
- 966290024*r10[i]
+ 26454613720*r12[i]
- 1109329691624*r14[i]
+ 70212852387160*r16[i]
- 6733670404619624*r18[i]
+ 1005318113348848600*r20[i]
- 249581050854994274024*r22[i]
+ 120719220687299365182040*r24[i]
- 202039976682357297272094824*r26[i]
- 385557844336439370252173428520*r28[i]
- 11052202492174627443179520000000*r29[i]
- 276888650579451671741587901762024*r30[i]
- 6304176301536407493589598208000000*r31[i]
- 133535841584115505205141919375399080*r32[i]
- 2672618344480543437732658544640000000*r33[i]
- 51095126335993498323380094454901195624*r34[i]
- 940618873537377672007825158832128000000*r35[i]
- 16776403501444391106926987629186000345640*r36[i]
- 291283862319085180678807183848898560000000*r37[i]
- 4942310839108515578583708125038854650555624*r38[i]
- 82203911327563805707081667710859870208000000*r39[i]
- 1343752600475734599375534320311340373516684200*r40[i]
- 21634243326074826428166414905753461063680000000*r41[i]
- 343672532983087585902951862991031321905844242024*r42[i]
- 5395063942758184834505475068561955332947968000000*r43[i]
- 83804941354439477195910293019964343299641959230760*r44[i]
) // 10888869450418352160768000000 for i in range(len(r0))]
r25 = [(742900*r[1][i]
- 1188640*r[2][i]
+ 1225785*r[3][i]
- 961400*r[4][i]
+ 600875*r[5][i]
- 303600*r[6][i]
+ 123970*r[7][i]
- 40480*r[8][i]
+ 10350*r[9][i]
- 2000*r[10][i]
+ 275*r[11][i]
- 24*r[12][i]
+ r[13][i]
- 208012*r0[i]
+ 117572*r2[i]
- 285532*r4[i]
+ 1602692*r6[i]
- 16996252*r8[i]
+ 307475012*r10[i]
- 8966430172*r12[i]
+ 409745686532*r14[i]
- 29195711499292*r16[i]
+ 3312133208909252*r18[i]
- 636215671041835612*r20[i]
+ 241648300078174135172*r22[i]
- 321511316149669476991132*r24[i]
- 492817676505266866078123708*r26[i]
- 12703681025488077520896000000*r27[i]
- 286779648275654636997381637852*r28[i]
- 5894507995826467969695744000000*r29[i]
- 112914054231542703053832892635388*r30[i]
- 2047008246979213061238030336000000*r31[i]
- 35501568925223446300815211192767772*r32[i]
- 593711792050129855003168210944000000*r33[i]
- 9632134956680435093368218113996247868*r34[i]
- 152311343455497374594406627803136000000*r35[i]
- 2356318736218539774396037820111678892892*r36[i]
- 35772470531371951985805498114637824000000*r37[i]
- 534273042749950920189640352996759062689148*r38[i]
- 7866491034006154572049014294052601856000000*r39[i]
- 114383224059606274110181105712262975351245212*r40[i]
- 1644946226278516886873016733667061202944000000*r41[i]
- 23426103831558846665144911501028780920365367228*r42[i]
- 330735945747364837719554208843251145179136000000*r43[i]
- 4633465747908141417306051485893140722291346976732*r44[i]
) // 15511210043330985984000000 for i in range(len(r0))]
r23 = [(-208012*r[1][i]
+ 326876*r[2][i]
- 326876*r[3][i]
+ 245157*r[4][i]
- 144210*r[5][i]
+ 67298*r[6][i]
- 24794*r[7][i]
+ 7084*r[8][i]
- 1518*r[9][i]
+ 230*r[10][i]
- 22*r[11][i]
+ r[12][i]
+ 58786*r0[i]
- 33592*r2[i]
+ 83096*r4[i]
- 479752*r6[i]
+ 5299736*r8[i]
- 101549512*r10[i]
+ 3208453976*r12[i]
- 164071220872*r14[i]
+ 13743680753816*r16[i]
- 1993276972245832*r18[i]
+ 581947914140407256*r20[i]
- 603916464771468176392*r22[i]
- 730803773459954540777704*r24[i]
- 16803810880275234816000000*r25[i]
- 339155768243774227716964552*r26[i]
- 6245976504198304781107200000*r27[i]
- 107413822788261782335458993064*r28[i]
- 1751393992807566623932416000000*r29[i]
- 27365156266821215807862420562312*r30[i]
- 412945663851071412756568473600000*r31[i]
- 6053949680529454447550745704030824*r32[i]
- 86623417665042381831452000256000000*r33[i]
- 1214146547565910406028014931410521672*r34[i]
- 16719755812321492798917963359846400000*r35[i]
- 226758627215029497194516602329808882984*r36[i]
- 3034905857007157810746475187798016000000*r37[i]
- 40151799724774280996886476759684489594632*r38[i]
- 525848735885794606994555529953619148800000*r39[i]
- 6825564942475643900873841059427230143341544*r40[i]
- 87900055843825806396690634755863003136000000*r41[i]
- 1124090333957827218160935737032127911249333192*r42[i]
- 14286036145840157893404384196456208735600640000*r43[i]
- 180556939553256275799275906968519352499771598504*r44[i]
) // 25852016738884976640000 for i in range(len(r0))]
r21 = [(58786*r[1][i]
- 90440*r[2][i]
+ 87210*r[3][i]
- 62016*r[4][i]
+ 33915*r[5][i]
- 14364*r[6][i]
+ 4655*r[7][i]
- 1120*r[8][i]
+ 189*r[9][i]
- 20*r[10][i]
+ r[11][i]
- 16796*r0[i]
+ 9724*r2[i]
- 24596*r4[i]
+ 147004*r6[i]
- 1708916*r8[i]
+ 35240284*r10[i]
- 1237329236*r12[i]
+ 73853629564*r14[i]
- 7850527669556*r16[i]
+ 1717351379730844*r18[i]
- 1359124435588313876*r20[i]
- 1272410676942417239876*r22[i]
- 25852016738884976640000*r23[i]
- 462292539259962003646196*r24[i]
- 7561714896123855667200000*r25[i]
- 115761644587269354830466596*r26[i]
- 1683741850203578528563200000*r27[i]
- 23512975860299444963550050516*r28[i]
- 317677725072691341719961600000*r29[i]
- 4176614976496441445095962733316*r30[i]
- 53674391443652368368589209600000*r31[i]
- 676635955671282540673335079110836*r32[i]
- 8391272072243853389701334630400000*r33[i]
- 102611708232289325546408008313624036*r34[i]
- 1239646284649926576486736094822400000*r35[i]
- 14819283410691765614379616648600811156*r36[i]
- 175538127424434549895381626305740800000*r37[i]
- 2062659648435073986802743885440046722756*r38[i]
- 24066873273263602745997309174983884800000*r39[i]
- 279069134864297423784787795404361206735476*r40[i]
- 3218237360334469905693543066426751549440000*r41[i]
- 36932670876144577834192017462238998576813476*r42[i]
- 422013831656219970552631011526505561456640000*r43[i]
- 4803667893589610545887832027829424971473267796*r44[i]
) // 51090942171709440000 for i in range(len(r0))]
r19 = [(-16796*r[1][i]
+ 25194*r[2][i]
- 23256*r[3][i]
+ 15504*r[4][i]
- 7752*r[5][i]
+ 2907*r[6][i]
- 798*r[7][i]
+ 152*r[8][i]
- 18*r[9][i]
+ r[10][i]
+ 4862*r0[i]
- 2860*r2[i]
+ 7436*r4[i]
- 46420*r6[i]
+ 576236*r8[i]
- 13098580*r10[i]
+ 532310636*r12[i]
- 39968611540*r14[i]
+ 6350631494636*r16[i]
- 3730771315561300*r18[i]
- 2637991952943407764*r20[i]
- 46833363657400320000*r21[i]
- 734121065118879803860*r22[i]
- 10556240168378032128000*r23[i]
- 142438684135271315212564*r24[i]
- 1830415113744266649600000*r25[i]
- 22632897298190126259675220*r26[i]
- 271297526662043666104320000*r27[i]
- 3170344993810020486920015764*r28[i]
- 36274730261563609572556800000*r29[i]
- 407775103607650299563627591380*r30[i]
- 4515882637052182897862000640000*r31[i]
- 49377994276343186011748723193364*r32[i]
- 534053247401000753173510963200000*r33[i]
- 5722063606154183864914875339648340*r34[i]
- 60811730909031986048777521029120000*r35[i]
- 641729418431834160625738740379401364*r36[i]
- 6730380606921481449181267599974400000*r37[i]
- 70207898580127312813466155395513222100*r38[i]
- 728918319689461841494925372032622592000*r39[i]
- 7536441803725213229125462424550696575764*r40[i]
- 77635978704164552294553096402068152320000*r41[i]
- 797177898990753876072852178329776532568660*r42[i]
- 8162164080895303403984327865949915250688000*r43[i]
- 83359491110673172494030048846026790563932564*r44[i]
) // 121645100408832000 for i in range(len(r0))]
r17 = [(4862*r[1][i]
- 7072*r[2][i]
+ 6188*r[3][i]
- 3808*r[4][i]
+ 1700*r[5][i]
- 544*r[6][i]
+ 119*r[7][i]
- 16*r[8][i]
+ r[9][i]
- 1430*r0[i]
+ 858*r2[i]
- 2310*r4[i]
+ 15258*r6[i]
- 206790*r8[i]
+ 5386458*r10[i]
- 272513670*r12[i]
+ 30255826458*r14[i]
- 12765597850950*r16[i]
- 6622557957272742*r18[i]
- 101370917007360000*r19[i]
- 1375210145685786630*r20[i]
- 17172233341046784000*r21[i]
- 201832098313986359142*r22[i]
- 2265471043586150400000*r23[i]
- 24529324224160803328710*r24[i]
- 258058524232798248960000*r25[i]
- 2652208374242713043720742*r26[i]
- 26739700571225856614400000*r27[i]
- 265323404171486113659725190*r28[i]
- 2597688920748017370193920000*r29[i]
- 25147613788240222384169485542*r30[i]
- 241125683321001354933657600000*r31[i]
- 2293170112631184981695915264070*r32[i]
- 21656158388689797460311183360000*r33[i]
- 203283794784841444836991831621542*r34[i]
- 1898267590696733462875776307200000*r35[i]
- 17646072330245312137111933794073350*r36[i]
- 163392570167583908119294187237376000*r37[i]
- 1507754227229479379470312529237936742*r38[i]
- 13871774079585871769182921633935360000*r39[i]
- 127291574907112728538906245247680921030*r40[i]
- 1165398276253942030786602999248830464000*r41[i]
- 10648249156718669259487809979675840079142*r42[i]
- 97121906010634492337139410720414515200000*r43[i]
- 884471146488697462546213719879378982015110*r44[i]
) // 355687428096000 for i in range(len(r0))]
r15 = [(-1430*r[1][i]
+ 2002*r[2][i]
- 1638*r[3][i]
+ 910*r[4][i]
- 350*r[5][i]
+ 90*r[6][i]
- 14*r[7][i]
+ r[8][i]
+ 429*r0[i]
- 264*r2[i]
+ 744*r4[i]
- 5304*r6[i]
+ 81384*r8[i]
- 2605944*r10[i]
+ 192387624*r12[i]
- 55942352184*r14[i]
- 20546119600536*r16[i]
- 266765571072000*r17[i]
- 3083760849804024*r18[i]
- 32945548027392000*r19[i]
- 332500281299403096*r20[i]
- 3215147584416768000*r21[i]
- 30076927429146721464*r22[i]
- 274100623905588480000*r23[i]
- 2446077617962088140056*r24[i]
- 21459412163122053120000*r25[i]
- 185641639183185136464504*r26[i]
- 1587401376760010972160000*r27[i]
- 13442713420403849918131416*r28[i]
- 112915002722102749808640000*r29[i]
- 941961013910760913890393144*r30[i]
- 7812419263561351877518080000*r31[i]
- 64474322285718607792730497176*r32[i]
- 529848386811984810994744320000*r33[i]
- 4338547620121893769542630267384*r34[i]
- 35415056327751829508662891008000*r35[i]
- 288317531175033442515609896757336*r36[i]
- 2341823147101379454117987013632000*r37[i]
- 18983391549723892653716655806647224*r38[i]
- 153619763998111828980832157720832000*r39[i]
- 1241292607509331793516191597844431896*r40[i]
- 10017079537004367071413852136982528000*r41[i]
- 80746194097372251940077615903073292664*r42[i]
- 650250798838302173122854563322562560000*r43[i]
- 5232061257212799699445154857325986640856*r44[i]
) // 1307674368000 for i in range(len(r0))]
r13 = [(429*r[1][i]
- 572*r[2][i]
+ 429*r[3][i]
- 208*r[4][i]
+ 65*r[5][i]
- 12*r[6][i]
+ r[7][i]
- 132*r0[i]
+ 84*r2[i]
- 252*r4[i]
+ 2004*r6[i]
- 37212*r8[i]
+ 1710324*r10[i]
- 325024572*r12[i]
- 80789566956*r14[i]
- 871782912000*r15[i]
- 8422900930332*r16[i]
- 75583578470400*r17[i]
- 643521842437836*r18[i]
- 5269678622208000*r19[i]
- 41890044885642492*r20[i]
- 325386564299596800*r21[i]
- 2481686964269990316*r22[i]
- 18652248729354240000*r23[i]
- 138536531588626169052*r24[i]
- 1019042849143807488000*r25[i]
- 7436421488952386592396*r26[i]
- 53911021949819274240000*r27[i]
- 388701690499592948238012*r28[i]
- 2789805187365599475072000*r29[i]
- 19946749502047187160692076*r30[i]
- 142159780685991861112320000*r31[i]
- 1010433303980489860989897372*r32[i]
- 7165521770403817166663116800*r33[i]
- 50716588034439244118483617356*r34[i]
- 358378772025058883636009472000*r35[i]
- 2528902640579773012941059115132*r36[i]
- 17824202779159732939433280230400*r37[i]
- 125502611080965065134883934376236*r38[i]
- 882926862501000079240924013568000*r39[i]
- 6206986746547700738292160195379292*r40[i]
- 43608135571536574058895364550860800*r41[i]
- 306213499909407501334225902520456716*r42[i]
- 2149239710498553002348841878415360000*r43[i]
- 15079178774724614117506008765315297852*r44[i]
) // 6227020800 for i in range(len(r0))]
r11 = [(-132*r[1][i]
+ 165*r[2][i]
- 110*r[3][i]
+ 44*r[4][i]
- 10*r[5][i]
+ r[6][i]
+ 42*r0[i]
- 28*r2[i]
+ 92*r4[i]
- 868*r6[i]
+ 22652*r8[i]
- 2620708*r10[i]
- 415790788*r12[i]
- 3632428800*r13[i]
- 28616744548*r14[i]
- 210680870400*r15[i]
- 1479485236228*r16[i]
- 10038995366400*r17[i]
- 66394067988388*r18[i]
- 430591742380800*r19[i]
- 2750479262009668*r20[i]
- 17360942812012800*r21[i]
- 108550450893568228*r22[i]
- 673606803881088000*r23[i]
- 4154688725062207108*r24[i]
- 25499502190850688000*r25[i]
- 155878445775166700068*r26[i]
- 949776357849070752000*r27[i]
- 5771581202353414724548*r28[i]
- 34995682724855684832000*r29[i]
- 211811399872933910999908*r30[i]
- 1280080235834717770252800*r31[i]
- 7726641919200262371657988*r32[i]
- 46591059456870785061004800*r33[i]
- 280704018540064430354883748*r34[i]
- 1690018909819536161979590400*r35[i]
- 10169113413821714748538703428*r36[i]
- 61159784116494648773674886400*r37[i]
- 367684638335977863351585967588*r38[i]
- 2209739160176731898013383884800*r39[i]
- 13276598260065161268654185556868*r40[i]
- 79750432649108163224160355276800*r41[i]
- 478956917715683026467561165467428*r42[i]
- 2876013540917084725512964985376000*r43[i]
- 17267443120712778679894991796314308*r44[i]
) // 39916800 for i in range(len(r0))]
r9 = [(42*r[1][i]
- 48*r[2][i]
+ 27*r[3][i]
- 8*r[4][i]
+ r[5][i]
- 14*r0[i]
+ 10*r2[i]
- 38*r4[i]
+ 490*r6[i]
- 31238*r8[i]
- 2922230*r10[i]
- 19958400*r11[i]
- 124075238*r12[i]
- 726485760*r13[i]
- 4084385750*r14[i]
- 22313491200*r15[i]
- 119387268038*r16[i]
- 628980992640*r17[i]
- 3275389222070*r18[i]
- 16905818966400*r19[i]
- 86665431465638*r20[i]
- 441935114987520*r21[i]
- 2244295389943190*r22[i]
- 11360520464832000*r23[i]
- 57360469753884038*r24[i]
- 289038899804054400*r25[i]
- 1454155949521941110*r26[i]
- 7306671293537616000*r27[i]
- 36677059892827099238*r28[i]
- 183960524908301057280*r29[i]
- 922104761587650687830*r30[i]
- 4619736062008593926400*r31[i]
- 23135540444136227047238*r32[i]
- 115825176110799088940160*r33[i]
- 579715876176320506935350*r34[i]
- 2900939663557699476451200*r35[i]
- 14514140349055749129024038*r36[i]
- 72608472572041292373527040*r37[i]
- 363193454272347163609915670*r38[i]
- 1816571661325589960713958400*r39[i]
- 9085275939429279963731685638*r40[i]
- 45436050447189540392656321920*r41[i]
- 227218935892633882388998540790*r42[i]
- 1136249416059455304696385296000*r43[i]
- 5681866032591044240951769048038*r44[i]
) // 362880 for i in range(len(r0))]
r7 = [(-14*r[1][i]
+ 14*r[2][i]
- 6*r[3][i]
+ r[4][i]
+ 5*r0[i]
- 4*r2[i]
+ 20*r4[i]
- 604*r6[i]
- 29740*r8[i]
- 151200*r9[i]
- 708604*r10[i]
- 3160080*r11[i]
- 13645900*r12[i]
- 57657600*r13[i]
- 239967004*r14[i]
- 988107120*r15[i]
- 4037604460*r16[i]
- 16406863200*r17[i]
- 66398623804*r18[i]
- 267911678160*r19[i]
- 1078605601420*r20[i]
- 4335313752000*r21[i]
- 17403958407004*r22[i]
- 69804002545200*r23[i]
- 279780634372780*r24[i]
- 1120816644948000*r25[i]
- 4488349371924604*r26[i]
- 17968646803620240*r27[i]
- 71920337041294540*r28[i]
- 287818601403715200*r29[i]
- 1151686172846664604*r30[i]
- 4607980008114455280*r31[i]
- 18435626012705982700*r32[i]
- 73753622051697957600*r33[i]
- 295047842329672995004*r34[i]
- 1180291431927853642320*r35[i]
- 4721465916019935893260*r36[i]
- 18886764229967380219200*r37[i]
- 75549758619456576163804*r38[i]
- 302207139580435761213360*r39[i]
- 1208852873637267995922220*r40[i]
- 4835484440511039999684000*r41[i]
- 19342156599960850372299004*r42[i]
- 77369282913655045261040400*r43[i]
- 309479101196178257662005580*r44[i]
) // 5040 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
- 1680*r7[i]
- 5542*r8[i]
- 17640*r9[i]
- 54958*r10[i]
- 168960*r11[i]
- 515062*r12[i]
- 1561560*r13[i]
- 4717438*r14[i]
- 14217840*r15[i]
- 42784582*r16[i]
- 128615880*r17[i]
- 386371918*r18[i]
- 1160164320*r19[i]
- 3482590102*r20[i]
- 10451964600*r21[i]
- 31364282398*r22[i]
- 94109624400*r23[i]
- 282362427622*r24[i]
- 847154391720*r25[i]
- 2541597392878*r26[i]
- 7625060614080*r27[i]
- 22875718713142*r28[i]
- 68628229881240*r29[i]
- 205886837127358*r30[i]
- 617664806349360*r31[i]
- 1853003008982662*r32[i]
- 5559026206817160*r33[i]
- 16677112980189838*r34[i]
- 50031407660046240*r35[i]
- 150094360419092182*r36[i]
- 450283356135183480*r37[i]
- 1350850618161364318*r38[i]
- 4052552953995720720*r39[i]
- 12157661061010417702*r40[i]
- 36472987581077764200*r41[i]
- 109418971539326314798*r42[i]
- 328256932210164988800*r43[i]
- 984770831814867055222*r44[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
- 126*r7[i]
- 254*r8[i]
- 510*r9[i]
- 1022*r10[i]
- 2046*r11[i]
- 4094*r12[i]
- 8190*r13[i]
- 16382*r14[i]
- 32766*r15[i]
- 65534*r16[i]
- 131070*r17[i]
- 262142*r18[i]
- 524286*r19[i]
- 1048574*r20[i]
- 2097150*r21[i]
- 4194302*r22[i]
- 8388606*r23[i]
- 16777214*r24[i]
- 33554430*r25[i]
- 67108862*r26[i]
- 134217726*r27[i]
- 268435454*r28[i]
- 536870910*r29[i]
- 1073741822*r30[i]
- 2147483646*r31[i]
- 4294967294*r32[i]
- 8589934590*r33[i]
- 17179869182*r34[i]
- 34359738366*r35[i]
- 68719476734*r36[i]
- 137438953470*r37[i]
- 274877906942*r38[i]
- 549755813886*r39[i]
- 1099511627774*r40[i]
- 2199023255550*r41[i]
- 4398046511102*r42[i]
- 8796093022206*r43[i]
- 17592186044414*r44[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
- r7[i]
- r8[i]
- r9[i]
- r10[i]
- r11[i]
- r12[i]
- r13[i]
- r14[i]
- r15[i]
- r16[i]
- r17[i]
- r18[i]
- r19[i]
- r20[i]
- r21[i]
- r22[i]
- r23[i]
- r24[i]
- r25[i]
- r26[i]
- r27[i]
- r28[i]
- r29[i]
- r30[i]
- r31[i]
- r32[i]
- r33[i]
- r34[i]
- r35[i]
- r36[i]
- r37[i]
- r38[i]
- r39[i]
- r40[i]
- r41[i]
- r42[i]
- r43[i]
- r44[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44)
def natural_interpolate_24(r):
r0 = r[0]
r46 = r['infinity']
r44 = [(-2012616400080*(r[1][i] + r[-1][i])
+ 1761039350070*(r[2][i] + r[-2][i])
- 1408831480056*(r[3][i] + r[-3][i])
+ 1029530696964*(r[4][i] + r[-4][i])
- 686353797976*(r[5][i] + r[-5][i])
+ 416714805914*(r[6][i] + r[-6][i])
- 229911617056*(r[7][i] + r[-7][i])
+ 114955808528*(r[8][i] + r[-8][i])
- 51915526432*(r[9][i] + r[-9][i])
+ 21090682613*(r[10][i] + r[-10][i])
- 7669339132*(r[11][i] + r[-11][i])
+ 2481256778*(r[12][i] + r[-12][i])
- 708930508*(r[13][i] + r[-13][i])
+ 177232627*(r[14][i] + r[-14][i])
- 38320568*(r[15][i] + r[-15][i])
+ 7059052*(r[16][i] + r[-16][i])
- 1086008*(r[17][i] + r[-17][i])
+ 135751*(r[18][i] + r[-18][i])
- 13244*(r[19][i] + r[-19][i])
+ 946*(r[20][i] + r[-20][i])
- 44*(r[21][i] + r[-21][i])
+ (r[22][i] + r[-22][i])
+ 2104098963720*r0[i]
- 10088140626322163074725559952800467303763028213760000000000*r46[i]
) // 2658271574788448768043625811014615890319638528000000000 for i in range(len(r0))]
r42 = [(513791607420*(r[1][i] + r[-1][i])
- 446775310800*(r[2][i] + r[-2][i])
+ 353697121050*(r[3][i] + r[-3][i])
- 254661927156*(r[4][i] + r[-4][i])
+ 166509721602*(r[5][i] + r[-5][i])
- 98672427616*(r[6][i] + r[-6][i])
+ 52860229080*(r[7][i] + r[-7][i])
- 25518731280*(r[8][i] + r[-8][i])
+ 11058116888*(r[9][i] + r[-9][i])
- 4280561376*(r[10][i] + r[-10][i])
+ 1471442973*(r[11][i] + r[-11][i])
- 445891810*(r[12][i] + r[-12][i])
+ 118030185*(r[13][i] + r[-13][i])
- 26978328*(r[14][i] + r[-14][i])
+ 5245786*(r[15][i] + r[-15][i])
- 850668*(r[16][i] + r[-16][i])
+ 111930*(r[17][i] + r[-17][i])
- 11480*(r[18][i] + r[-18][i])
+ 861*(r[19][i] + r[-19][i])
- 42*(r[20][i] + r[-20][i])
+ (r[21][i] + r[-21][i])
- 538257874440*r0[i]
- 4651975255879785344076345169275577808059367424000000000*r44[i]
- 8345643609048334907272963233680386587658505158656000000000*r46[i]
) // 1405006117752879898543142606244511569936384000000000 for i in range(len(r0))]
r40 = [(-131282408400*(r[1][i] + r[-1][i])
+ 113380261800*(r[2][i] + r[-2][i])
- 88732378800*(r[3][i] + r[-3][i])
+ 62852101650*(r[4][i] + r[-4][i])
- 40225345056*(r[5][i] + r[-5][i])
+ 23206929840*(r[6][i] + r[-6][i])
- 12033222880*(r[7][i] + r[-7][i])
+ 5586853480*(r[8][i] + r[-8][i])
- 2311801440*(r[9][i] + r[-9][i])
+ 847660528*(r[10][i] + r[-10][i])
- 273438880*(r[11][i] + r[-11][i])
+ 76904685*(r[12][i] + r[-12][i])
- 18643560*(r[13][i] + r[-13][i])
+ 3838380*(r[14][i] + r[-14][i])
- 658008*(r[15][i] + r[-15][i])
+ 91390*(r[16][i] + r[-16][i])
- 9880*(r[17][i] + r[-17][i])
+ 780*(r[18][i] + r[-18][i])
- 40*(r[19][i] + r[-19][i])
+ (r[20][i] + r[-20][i])
+ 137846528820*r0[i]
- 2341676862921466497571904343740852616560640000000000*r42[i]
- 3655123415334117056059985490145096849189502976000000000*r44[i]
- 4119688019118574531237133429498603530973935042560000000000*r46[i]
) // 815915283247897734345611269596115894272000000000 for i in range(len(r0))]
r38 = [(33578000610*(r[1][i] + r[-1][i])
- 28781143380*(r[2][i] + r[-2][i])
+ 22239974430*(r[3][i] + r[-3][i])
- 15471286560*(r[4][i] + r[-4][i])
+ 9669554100*(r[5][i] + r[-5][i])
- 5414950296*(r[6][i] + r[-6][i])
+ 2707475148*(r[7][i] + r[-7][i])
- 1203322288*(r[8][i] + r[-8][i])
+ 472733756*(r[9][i] + r[-9][i])
- 163011640*(r[10][i] + r[-10][i])
+ 48903492*(r[11][i] + r[-11][i])
- 12620256*(r[12][i] + r[-12][i])
+ 2760681*(r[13][i] + r[-13][i])
- 501942*(r[14][i] + r[-14][i])
+ 73815*(r[15][i] + r[-15][i])
- 8436*(r[16][i] + r[-16][i])
+ 703*(r[17][i] + r[-17][i])
- 38*(r[18][i] + r[-18][i])
+ (r[19][i] + r[-19][i])
- 35345263800*r0[i]
- 1291865865142504746047217843527183499264000000000*r40[i]
- 1742597865490724651943092149133817822157209600000000*r42[i]
- 1703614521144184428726371303487541532883419136000000000*r44[i]
- 1352221478318945952566471137817160521323572835123200000000*r46[i]
) // 523022617466601111760007224100074291200000000 for i in range(len(r0))]
r36 = [(-8597496600*(r[1][i] + r[-1][i])
+ 7307872110*(r[2][i] + r[-2][i])
- 5567902560*(r[3][i] + r[-3][i])
+ 3796297200*(r[4][i] + r[-4][i])
- 2310789600*(r[5][i] + r[-5][i])
+ 1251677700*(r[6][i] + r[-6][i])
- 600805296*(r[7][i] + r[-7][i])
+ 254186856*(r[8][i] + r[-8][i])
- 94143280*(r[9][i] + r[-9][i])
+ 30260340*(r[10][i] + r[-10][i])
- 8347680*(r[11][i] + r[-11][i])
+ 1947792*(r[12][i] + r[-12][i])
- 376992*(r[13][i] + r[-13][i])
+ 58905*(r[14][i] + r[-14][i])
- 7140*(r[15][i] + r[-15][i])
+ 630*(r[16][i] + r[-16][i])
- 36*(r[17][i] + r[-17][i])
+ (r[18][i] + r[-18][i])
+ 9075135300*r0[i]
- 784533926199901667640010836150111436800000000*r38[i]
- 907705752613286229459492537425678932377600000000*r40[i]
- 764250847583238143225401875995898505750118400000000*r42[i]
- 524336156604477506256224109002957345627779891200000000*r44[i]
- 311351658482338919180732210200430367625645444300800000000*r46[i]
) // 371993326789901217467999448150835200000000 for i in range(len(r0))]
r34 = [(2203961430*(r[1][i] + r[-1][i])
- 1855967520*(r[2][i] + r[-2][i])
+ 1391975640*(r[3][i] + r[-3][i])
- 927983760*(r[4][i] + r[-4][i])
+ 548354040*(r[5][i] + r[-5][i])
- 286097760*(r[6][i] + r[-6][i])
+ 131128140*(r[7][i] + r[-7][i])
- 52451256*(r[8][i] + r[-8][i])
+ 18156204*(r[9][i] + r[-9][i])
- 5379616*(r[10][i] + r[-10][i])
+ 1344904*(r[11][i] + r[-11][i])
- 278256*(r[12][i] + r[-12][i])
+ 46376*(r[13][i] + r[-13][i])
- 5984*(r[14][i] + r[-14][i])
+ 561*(r[15][i] + r[-15][i])
- 34*(r[16][i] + r[-16][i])
+ (r[17][i] + r[-17][i])
- 2333606220*r0[i]
- 526990546285693391412999218213683200000000*r36[i]
- 518664095654379435828673830565907005440000000*r38[i]
- 373138241060740797524227217357125818777600000000*r40[i]
- 219618160307546307818407858079592245845032960000000*r42[i]
- 112275193446419212026758411812279514001781555200000000*r44[i]
- 51713216892097268029263570056035419810630708756480000000*r46[i]
) // 295232799039604140847618609643520000000 for i in range(len(r0))]
r32 = [(-565722720*(r[1][i] + r[-1][i])
+ 471435600*(r[2][i] + r[-2][i])
- 347373600*(r[3][i] + r[-3][i])
+ 225792840*(r[4][i] + r[-4][i])
- 129024480*(r[5][i] + r[-5][i])
+ 64512240*(r[6][i] + r[-6][i])
- 28048800*(r[7][i] + r[-7][i])
+ 10518300*(r[8][i] + r[-8][i])
- 3365856*(r[9][i] + r[-9][i])
+ 906192*(r[10][i] + r[-10][i])
- 201376*(r[11][i] + r[-11][i])
+ 35960*(r[12][i] + r[-12][i])
- 4960*(r[13][i] + r[-13][i])
+ 496*(r[14][i] + r[-14][i])
- 32*(r[15][i] + r[-15][i])
+ (r[16][i] + r[-16][i])
+ 601080390*r0[i]
- 393643732052805521130158146191360000000*r34[i]
- 326527475737802179777466182265733120000000*r36[i]
- 198969979872214920293886346099446251520000000*r38[i]
- 99626745669333527035567016277524852244480000000*r40[i]
- 43498703313314018776504938348732045412270080000000*r42[i]
- 17170843124850370546818528558187736420780605440000000*r44[i]
- 6276444318289938061108840583768656479667869450240000000*r46[i]
) // 263130836933693530167218012160000000 for i in range(len(r0))]
r30 = [(145422675*(r[1][i] + r[-1][i])
- 119759850*(r[2][i] + r[-2][i])
+ 86493225*(r[3][i] + r[-3][i])
- 54627300*(r[4][i] + r[-4][i])
+ 30045015*(r[5][i] + r[-5][i])
- 14307150*(r[6][i] + r[-6][i])
+ 5852925*(r[7][i] + r[-7][i])
- 2035800*(r[8][i] + r[-8][i])
+ 593775*(r[9][i] + r[-9][i])
- 142506*(r[10][i] + r[-10][i])
+ 27405*(r[11][i] + r[-11][i])
- 4060*(r[12][i] + r[-12][i])
+ 435*(r[13][i] + r[-13][i])
- 30*(r[14][i] + r[-14][i])
+ (r[15][i] + r[-15][i])
- 155117520*r0[i]
- 328913546167116912709022515200000000*r32[i]
- 227575282593028191903372678266880000000*r34[i]
- 116309421454977381321426414757478400000000*r36[i]
- 49083095586740430887431564189583278080000000*r38[i]
- 18139371393109511951007844941215406489600000000*r40[i]
- 6083845843389094496001274537210012898426880000000*r42[i]
- 1895875482185729033390420637976407213657292800000000*r44[i]
- 557995741137378415081398016214860854983503380480000000*r46[i]
) // 265252859812191058636308480000000 for i in range(len(r0))]
r28 = [(-37442160*(r[1][i] + r[-1][i])
+ 30421755*(r[2][i] + r[-2][i])
- 21474180*(r[3][i] + r[-3][i])
+ 13123110*(r[4][i] + r[-4][i])
- 6906900*(r[5][i] + r[-5][i])
+ 3108105*(r[6][i] + r[-6][i])
- 1184040*(r[7][i] + r[-7][i])
+ 376740*(r[8][i] + r[-8][i])
- 98280*(r[9][i] + r[-9][i])
+ 20475*(r[10][i] + r[-10][i])
- 3276*(r[11][i] + r[-11][i])
+ 378*(r[12][i] + r[-12][i])
- 28*(r[13][i] + r[-13][i])
+ (r[14][i] + r[-14][i])
+ 40116600*r0[i]
- 309461669780889568409026560000000*r30[i]
- 176516936443019409820508749824000000*r32[i]
- 74833313645455216256514439249920000000*r34[i]
- 26337328459046574816219104447299584000000*r36[i]
- 8155948144934385059006601147769159680000000*r38[i]
- 2301709517171786559798286695904076365824000000*r40[i]
- 605758813130095139988659617361096909783040000000*r42[i]
- 151061790397229175366153301919734749322543104000000*r44[i]
- 36109056667467121621981604705290955376859545600000000*r46[i]
) // 304888344611713860501504000000 for i in range(len(r0))]
r26 = [(9657700*(r[1][i] + r[-1][i])
- 7726160*(r[2][i] + r[-2][i])
+ 5311735*(r[3][i] + r[-3][i])
- 3124550*(r[4][i] + r[-4][i])
+ 1562275*(r[5][i] + r[-5][i])
- 657800*(r[6][i] + r[-6][i])
+ 230230*(r[7][i] + r[-7][i])
- 65780*(r[8][i] + r[-8][i])
+ 14950*(r[9][i] + r[-9][i])
- 2600*(r[10][i] + r[-10][i])
+ 325*(r[11][i] + r[-11][i])
- 26*(r[12][i] + r[-12][i])
+ (r[13][i] + r[-13][i])
- 10400600*r0[i]
- 330295706662690015543296000000*r28[i]
- 153257207891488167212089344000000*r30[i]
- 53222214421459539592188788736000000*r32[i]
- 15436506593303376230082373484544000000*r34[i]
- 3960094929842931739454572322881536000000*r36[i]
- 930084233815670751630942950980583424000000*r38[i]
- 204528766884160018873274371645367648256000000*r40[i]
- 42768601883241439058698435075343591276544000000*r42[i]
- 8599134589431485780708409429924529774657536000000*r44[i]
- 1676115909489027560076829587121962388192493568000000*r46[i]
) // 403291461126605635584000000 for i in range(len(r0))]
r24 = [(-2496144*(r[1][i] + r[-1][i])
+ 1961256*(r[2][i] + r[-2][i])
- 1307504*(r[3][i] + r[-3][i])
+ 735471*(r[4][i] + r[-4][i])
- 346104*(r[5][i] + r[-5][i])
+ 134596*(r[6][i] + r[-6][i])
- 42504*(r[7][i] + r[-7][i])
+ 10626*(r[8][i] + r[-8][i])
- 2024*(r[9][i] + r[-9][i])
+ 276*(r[10][i] + r[-10][i])
- 24*(r[11][i] + r[-11][i])
+ (r[12][i] + r[-12][i])
+ 2704156*r0[i]
- 403291461126605635584000000*r26[i]
- 149903436100759314746572800000*r28[i]
- 42033455827381598974377984000000*r30[i]
- 9910695932425713906157643366400000*r32[i]
- 2078962023961017163954848006144000000*r34[i]
- 401274139495715827174031120636313600000*r36[i]
- 72837740568171787457915404507152384000000*r38[i]
- 12620369661259070567869332718886859571200000*r40[i]
- 2109601340251819353520575234140712075264000000*r42[i]
- 342864867500163789441705220714949009654415360000*r44[i]
- 54497476891656721001996702786930540928565248000000*r46[i]
) // 620448401733239439360000 for i in range(len(r0))]
r22 = [(646646*(r[1][i] + r[-1][i])
- 497420*(r[2][i] + r[-2][i])
+ 319770*(r[3][i] + r[-3][i])
- 170544*(r[4][i] + r[-4][i])
+ 74613*(r[5][i] + r[-5][i])
- 26334*(r[6][i] + r[-6][i])
+ 7315*(r[7][i] + r[-7][i])
- 1540*(r[8][i] + r[-8][i])
+ 231*(r[9][i] + r[-9][i])
- 22*(r[10][i] + r[-10][i])
+ (r[11][i] + r[-11][i])
- 705432*r0[i]
- 568744368255469486080000*r24[i]
- 166357727714724824678400000*r26[i]
- 37042320704478727628390400000*r28[i]
- 6988909951599209517839155200000*r30[i]
- 1180836611760352104108962611200000*r32[i]
- 184607985589364774573429361868800000*r34[i]
- 27272218262298384682708194086092800000*r36[i]
- 3861838803337560097698395778726297600000*r38[i]
- 529471212011799260411940801849645465600000*r40[i]
- 70801221927358337925257947461388534087680000*r42[i]
- 9284304296436839352157882253583122352046080000*r44[i]
- 1198819215976330165063918942164935021513932800000*r46[i]
) // 1124000727777607680000 for i in range(len(r0))]
r20 = [(-167960*(r[1][i] + r[-1][i])
+ 125970*(r[2][i] + r[-2][i])
- 77520*(r[3][i] + r[-3][i])
+ 38760*(r[4][i] + r[-4][i])
- 15504*(r[5][i] + r[-5][i])
+ 4845*(r[6][i] + r[-6][i])
- 1140*(r[7][i] + r[-7][i])
+ 190*(r[8][i] + r[-8][i])
- 20*(r[9][i] + r[-9][i])
+ (r[10][i] + r[-10][i])
+ 184756*r0[i]
- 936667273148006400000*r22[i]
- 211124803367560642560000*r24[i]
- 36608302274885332992000000*r26[i]
- 5425950533240873322086400000*r28[i]
- 725494605231272191451136000000*r30[i]
- 90317652741043657957240012800000*r32[i]
- 10681064948020015063470219264000000*r34[i]
- 1216234618180639720975550420582400000*r36[i]
- 134607612138429628983625351999488000000*r38[i]
- 14578366393789236829898507440652451840000*r40[i]
- 1552719574083291045891061928041363046400000*r42[i]
- 163243281617906068079686557318998305013760000*r44[i]
- 16988641998903346735554689301227465785344000000*r46[i]
) // 2432902008176640000 for i in range(len(r0))]
r18 = [(43758*(r[1][i] + r[-1][i])
- 31824*(r[2][i] + r[-2][i])
+ 18564*(r[3][i] + r[-3][i])
- 8568*(r[4][i] + r[-4][i])
+ 3060*(r[5][i] + r[-5][i])
- 816*(r[6][i] + r[-6][i])
+ 153*(r[7][i] + r[-7][i])
- 18*(r[8][i] + r[-8][i])
+ (r[9][i] + r[-9][i])
- 48620*r0[i]
- 1824676506132480000*r20[i]
- 309100200138842112000*r22[i]
- 40778478784550707200000*r24[i]
- 4645053436190368481280000*r26[i]
- 481314610282065419059200000*r28[i]
- 46758400573464312663490560000*r30[i]
- 4340262299778024388805836800000*r32[i]
- 389810850996416354285601300480000*r34[i]
- 34168816632541202331763973529600000*r36[i]
- 2941066263016510346147295370272768000*r38[i]
- 249691933432545691845292589410836480000*r40[i]
- 20977168972570956554158853986478948352000*r42[i]
- 1748194308191420862068509392967461273600000*r44[i]
- 144787366874617417267158756772391629455360000*r46[i]
) // 6402373705728000 for i in range(len(r0))]
r16 = [(-11440*(r[1][i] + r[-1][i])
+ 8008*(r[2][i] + r[-2][i])
- 4368*(r[3][i] + r[-3][i])
+ 1820*(r[4][i] + r[-4][i])
- 560*(r[5][i] + r[-5][i])
+ 120*(r[6][i] + r[-6][i])
- 16*(r[7][i] + r[-7][i])
+ (r[8][i] + r[-8][i])
+ 12870*r0[i]
- 4268249137152000*r18[i]
- 527128768438272000*r20[i]
- 51442361350668288000*r22[i]
- 4385609982489415680000*r24[i]
- 343350594609952849920000*r26[i]
- 25398422028160175554560000*r28[i]
- 1806640043553643996938240000*r30[i]
- 124998708216981630040289280000*r32[i]
- 8477574188991756975915909120000*r34[i]
- 566640901244029272138606256128000*r36[i]
- 37469170353622071265887792218112000*r38[i]
- 2457916223969789263693314523533312000*r40[i]
- 160273272592069873142621634191720448000*r42[i]
- 10404012781412834769965673013161000960000*r44[i]
- 673078263437696563365695181553779671040000*r46[i]
) // 20922789888000 for i in range(len(r0))]
r14 = [(3003*(r[1][i] + r[-1][i])
- 2002*(r[2][i] + r[-2][i])
+ 1001*(r[3][i] + r[-3][i])
- 364*(r[4][i] + r[-4][i])
+ 91*(r[5][i] + r[-5][i])
- 14*(r[6][i] + r[-6][i])
+ (r[7][i] + r[-7][i])
- 3432*r0[i]
- 12204960768000*r16[i]
- 1058170098585600*r18[i]
- 73775500710912000*r20[i]
- 4555411900194355200*r22[i]
- 261131482210959360000*r24[i]
- 14266599888013304832000*r26[i]
- 754754307297469839360000*r28[i]
- 39057272623118392651008000*r30[i]
- 1990236929603886055572480000*r32[i]
- 100317304785653440333283635200*r34[i]
- 5017302808350824370904132608000*r36[i]
- 249538838908236261152065923225600*r38[i]
- 12360976075014001109372936189952000*r40[i]
- 610513898001512036824535103712051200*r42[i]
- 30089355946979742032883786297815040000*r44[i]
- 1480659654975370272651825844120998144000*r46[i]
) // 87178291200 for i in range(len(r0))]
r12 = [(-792*(r[1][i] + r[-1][i])
+ 495*(r[2][i] + r[-2][i])
- 220*(r[3][i] + r[-3][i])
+ 66*(r[4][i] + r[-4][i])
- 12*(r[5][i] + r[-5][i])
+ (r[6][i] + r[-6][i])
+ 924*r0[i]
- 43589145600*r14[i]
- 2528170444800*r16[i]
- 120467944396800*r18[i]
- 5167100908569600*r20[i]
- 208331313744153600*r22[i]
- 8083281646573056000*r24[i]
- 305994026290208256000*r26[i]
- 11397316294188849024000*r28[i]
- 419948192698268217984000*r30[i]
- 15360962830016613243033600*r32[i]
- 559092713482449420732057600*r34[i]
- 20280226917834433943755084800*r36[i]
- 733917409397935785284098636800*r38[i]
- 26516869922120782776160606617600*r40[i]
- 957005191789297958689924263321600*r42[i]
- 34512162491005016706155579824512000*r44[i]
- 1243937698905379082423800102273152000*r46[i]
) // 479001600 for i in range(len(r0))]
r10 = [(210*(r[1][i] + r[-1][i])
- 120*(r[2][i] + r[-2][i])
+ 45*(r[3][i] + r[-3][i])
- 10*(r[4][i] + r[-4][i])
+ (r[5][i] + r[-5][i])
- 252*r0[i]
- 199584000*r12[i]
- 7264857600*r14[i]
- 223134912000*r16[i]
- 6289809926400*r18[i]
- 169058189664000*r20[i]
- 4419351149875200*r22[i]
- 113605204648320000*r24[i]
- 2890388998040544000*r26[i]
- 73066712935376160000*r28[i]
- 1839605249083010572800*r30[i]
- 46197360620085939264000*r32[i]
- 1158251761107990889401600*r34[i]
- 29009396635576994764512000*r36[i]
- 726084725720412923735270400*r38[i]
- 18165716613255899607139584000*r40[i]
- 454360504471895403926563219200*r42[i]
- 11362494160594553046963852960000*r44[i]
- 284118059898561657806684273088000*r46[i]
) // 3628800 for i in range(len(r0))]
r8 = [(-56*(r[1][i] + r[-1][i])
+ 28*(r[2][i] + r[-2][i])
- 8*(r[3][i] + r[-3][i])
+ (r[4][i] + r[-4][i])
+ 70*r0[i]
- 1209600*r10[i]
- 25280640*r12[i]
- 461260800*r14[i]
- 7904856960*r16[i]
- 131254905600*r18[i]
- 2143293425280*r20[i]
- 34682510016000*r22[i]
- 558432020361600*r24[i]
- 8966533159584000*r26[i]
- 143749174428961920*r28[i]
- 2302548811229721600*r30[i]
- 36863840064915642240*r32[i]
- 590028976413583660800*r34[i]
- 9442331455422829138560*r36[i]
- 151094113839739041753600*r38[i]
- 2417657116643486089706880*r40[i]
- 38683875524088319997472000*r42[i]
- 618954263309240362088323200*r44[i]
- 9903378507277068408849408000*r46[i]
) // 40320 for i in range(len(r0))]
r6 = [(15*(r[1][i] + r[-1][i])
- 6*(r[2][i] + r[-2][i])
+ (r[3][i] + r[-3][i])
- 20*r0[i]
- 10080*r8[i]
- 105840*r10[i]
- 1013760*r12[i]
- 9369360*r14[i]
- 85307040*r16[i]
- 771695280*r18[i]
- 6960985920*r20[i]
- 62711787600*r22[i]
- 564657746400*r24[i]
- 5082926350320*r26[i]
- 45750363684480*r28[i]
- 411769379287440*r30[i]
- 3705988838096160*r32[i]
- 33354157240902960*r34[i]
- 300188445960277440*r36[i]
- 2701700136811100880*r38[i]
- 24315317723974324320*r40[i]
- 218837925486466585200*r42[i]
- 1969541593260989932800*r44[i]
- 17725875394880072059920*r46[i]
) // 720 for i in range(len(r0))]
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
- 504*r8[i]
- 2040*r10[i]
- 8184*r12[i]
- 32760*r14[i]
- 131064*r16[i]
- 524280*r18[i]
- 2097144*r20[i]
- 8388600*r22[i]
- 33554424*r24[i]
- 134217720*r26[i]
- 536870904*r28[i]
- 2147483640*r30[i]
- 8589934584*r32[i]
- 34359738360*r34[i]
- 137438953464*r36[i]
- 549755813880*r38[i]
- 2199023255544*r40[i]
- 8796093022200*r42[i]
- 35184372088824*r44[i]
- 140737488355320*r46[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
- 2*r8[i]
- 2*r10[i]
- 2*r12[i]
- 2*r14[i]
- 2*r16[i]
- 2*r18[i]
- 2*r20[i]
- 2*r22[i]
- 2*r24[i]
- 2*r26[i]
- 2*r28[i]
- 2*r30[i]
- 2*r32[i]
- 2*r34[i]
- 2*r36[i]
- 2*r38[i]
- 2*r40[i]
- 2*r42[i]
- 2*r44[i]
- 2*r46[i]
) // 2 for i in range(len(r0))]
r45 = [(343059613650*r[1][i]
- 603784920024*r[2][i]
+ 731508653106*r[3][i]
- 722477682080*r[4][i]
+ 612815891050*r[5][i]
- 456442180920*r[6][i]
+ 301758997386*r[7][i]
- 177996090624*r[8][i]
+ 93865125915*r[9][i]
- 44246187300*r[10][i]
+ 18609425835*r[11][i]
- 6960408624*r[12][i]
+ 2304024151*r[13][i]
- 670609940*r[14][i]
+ 170173575*r[15][i]
- 37234560*r[16][i]
+ 6923301*r[17][i]
- 1072764*r[18][i]
+ 134805*r[19][i]
- 13200*r[20][i]
+ 945*r[21][i]
- 44*r[22][i]
+ r[23][i]
- 91482563640*r0[i]
+ 48932534040*r2[i]
- 108606356040*r4[i]
+ 533667580440*r6[i]
- 4703763586440*r8[i]
+ 66408505338840*r10[i]
- 1398457857168840*r12[i]
+ 41847457290489240*r14[i]
- 1719246675671583240*r16[i]
+ 94585481325000311640*r18[i]
- 6843422433568588589640*r20[i]
+ 642897110978465333366040*r22[i]
- 77770562351946223415228040*r24[i]
+ 12062233927817328810997492440*r26[i]
- 2397961353314881501418831818440*r28[i]
+ 613494954527608404597659277810840*r30[i]
- 203877970345571868715766678319960840*r32[i]
+ 89457569257636570186619080797284721240*r34[i]
- 53237495951641479759332571910597970535240*r36[i]
+ 44930968310714379648812137260536985281903640*r38[i]
- 58241166312158469946465066186170960196371701640*r40[i]
+ 137360888551881485527132727024151255460985294318040*r42[i]
- 1056294346650368430047563515157012073181421862576900040*r44[i]
- 8792490299555933486634712872596976297794618720689003795560*r46[i]
) // 119622220865480194561963161495657715064383733760000000000 for i in range(len(r0))]
r43 = [(-91482563640*r[1][i]
+ 160094486370*r[2][i]
- 192113383644*r[3][i]
+ 187187399448*r[4][i]
- 155989499540*r[5][i]
+ 113649492522*r[6][i]
- 73153696336*r[7][i]
+ 41802112192*r[8][i]
- 21238169904*r[9][i]
+ 9586673915*r[10][i]
- 3834669566*r[11][i]
+ 1353412788*r[12][i]
- 418913482*r[13][i]
+ 112784399*r[14][i]
- 26127660*r[15][i]
+ 5133856*r[16][i]
- 839188*r[17][i]
+ 111069*r[18][i]
- 11438*r[19][i]
+ 860*r[20][i]
- 42*r[21][i]
+ r[22][i]
+ 24466267020*r0[i]
- 13128240840*r2[i]
+ 29286075720*r4[i]
- 144956522040*r6[i]
+ 1290252243720*r8[i]
- 18448766253240*r10[i]
+ 394763466531720*r12[i]
- 12048763425424440*r14[i]
+ 507104531694579720*r16[i]
- 28726839421461491640*r18[i]
+ 2153064433503155907720*r20[i]
- 211041986898764840790840*r22[i]
+ 26870132026261051008915720*r24[i]
- 4433779344005175981028538040*r26[i]
+ 950513389106656928711222883720*r28[i]
- 266877172369028643812085068829240*r30[i]
+ 99651017964870751887504875569971720*r32[i]
- 50788156610571325953562659420384640440*r34[i]
+ 36915961449056930526009630202648137219720*r36[i]
- 41419014418447665040750851917674255257827640*r38[i]
+ 84934578551016826327683205574058431012558547720*r40[i]
- 570180937724400876712836731188276811777920749126840*r42[i]
- 4158439692009034639969470592464099450041235634033244280*r44[i]
- 229275923325503706243762726200010620540068823040000000000*r45[i]
- 10938400640270606999512627385384658646639850257084618154040*r46[i]
) // 60415263063373835637355132068513997507264512000000000 for i in range(len(r0))]
r41 = [(24466267020*r[1][i]
- 42550029600*r[2][i]
+ 50528160150*r[3][i]
- 48507033744*r[4][i]
+ 39645171810*r[5][i]
- 28192122176*r[6][i]
+ 17620076360*r[7][i]
- 9721421440*r[8][i]
+ 4739192952*r[9][i]
- 2038362560*r[10][i]
+ 770755843*r[11][i]
- 254795320*r[12][i]
+ 73066305*r[13][i]
- 17985552*r[14][i]
+ 3746990*r[15][i]
- 648128*r[16][i]
+ 90610*r[17][i]
- 9840*r[18][i]
+ 779*r[19][i]
- 40*r[20][i]
+ r[21][i]
- 6564120420*r0[i]
+ 3534526380*r2[i]
- 7928802420*r4[i]
+ 39562131180*r6[i]
- 355997149620*r8[i]
+ 5162772055980*r10[i]
- 112466379416820*r12[i]
+ 3509804003100780*r14[i]
- 151808102304340020*r16[i]
+ 8890838711788769580*r18[i]
- 693867758978013455220*r20[i]
+ 71436574576557715366380*r22[i]
- 9656103679244476561098420*r24[i]
+ 1714541855816811795973995180*r26[i]
- 402505898503128791422102405620*r28[i]
+ 126699650825847516884027712559980*r30[i]
- 54827934277723571354991704981312820*r32[i]
+ 34051732695777105364083032869387764780*r34[i]
- 32827430653262026254340815579045378556020*r36[i]
+ 58129225653125966892251726413185365757113580*r38[i]
- 338476895760295138790385051321218766549279671220*r40[i]
- 2149763077602671437231704105519918866633843849089620*r42[i]
- 110761315616185365335151075458942328763318272000000000*r43[i]
- 4942256826876098689793689711313418888604591478522994420*r44[i]
- 198705800215436545411261029373342537801392979968000000000*r45[i]
- 7372979698612811191617476736621847607367673634869335740820*r46[i]
) // 33452526613163807108170062053440751665152000000000 for i in range(len(r0))]
r39 = [(-6564120420*r[1][i]
+ 11338026180*r[2][i]
- 13309856820*r[3][i]
+ 12570420330*r[4][i]
- 10056336264*r[5][i]
+ 6962078952*r[6][i]
- 4211628008*r[7][i]
+ 2234741392*r[8][i]
- 1040310648*r[9][i]
+ 423830264*r[10][i]
- 150391384*r[11][i]
+ 46142811*r[12][i]
- 12118314*r[13][i]
+ 2686866*r[14][i]
- 493506*r[15][i]
+ 73112*r[16][i]
- 8398*r[17][i]
+ 702*r[18][i]
- 38*r[19][i]
+ r[20][i]
+ 1767263190*r0[i]
- 955277400*r2[i]
+ 2156197560*r4[i]
- 10855425000*r6[i]
+ 98876533560*r8[i]
- 1456859058600*r10[i]
+ 32382608125560*r12[i]
- 1036360772970600*r14[i]
+ 46242812090245560*r16[i]
- 2813858311510281000*r18[i]
+ 230141619686501005560*r20[i]
- 25097337236284407949800*r22[i]
+ 3642002181929040219157560*r24[i]
- 706474912755087069174777000*r26[i]
+ 185490702479102020671448093560*r28[i]
- 67501512373123369695638979402600*r30[i]
+ 35506616897715366055874618759845560*r32[i]
- 29173319982987640073110629923442306600*r34[i]
+ 44272025958057634433180503709478279085560*r36[i]
- 222019441630075420847480526017947263931809000*r38[i]
- 1219813882056330049405575791394671579625372874440*r40[i]
- 58541921573036662439297608593521315414016000000000*r41[i]
- 2435494701008122308521041585840935773426259964069800*r42[i]
- 91378085383352926401499637253627421229737574400000000*r43[i]
- 3166734413390519310621011935324774315544541946854082440*r44[i]
- 102992200477964363280928335737465088274348376064000000000*r45[i]
- 3179252903572284408695210045628305460118381385145907089000*r46[i]
) // 20397882081197443358640281739902897356800000000 for i in range(len(r0))]
r37 = [(1767263190*r[1][i]
- 3029594040*r[2][i]
+ 3511574910*r[3][i]
- 3257112960*r[4][i]
+ 2544619500*r[5][i]
- 1709984304*r[6][i]
+ 997490844*r[7][i]
- 506662016*r[8][i]
+ 223926516*r[9][i]
- 85795600*r[10][i]
+ 28312548*r[11][i]
- 7970688*r[12][i]
+ 1888887*r[13][i]
- 369852*r[14][i]
+ 58275*r[15][i]
- 7104*r[16][i]
+ 629*r[17][i]
- 36*r[18][i]
+ r[19][i]
- 477638700*r0[i]
+ 259289580*r2[i]
- 589294500*r4[i]
+ 2996657580*r6[i]
- 27670359300*r8[i]
+ 415064933580*r10[i]
- 9439543875300*r12[i]
+ 310922483993580*r14[i]
- 14379880666402500*r16[i]
+ 914767168887053580*r18[i]
- 79051272004645620900*r20[i]
+ 9231401536061270849580*r22[i]
- 1459700260139475814330500*r24[i]
+ 315843905250429722227637580*r26[i]
- 95612546130070295522414451300*r28[i]
+ 42177612582297377823299737193580*r30[i]
- 29268533564152352561039458453023300*r32[i]
+ 37747202396256876155482291281278813580*r34[i]
- 161759954125032708920885781040309430206500*r36[i]
- 763162014442847423121851269222329739576686420*r38[i]
- 33996470135329072264400469566504828928000000000*r39[i]
- 1314149222797294391875041342296266627244339280900*r40[i]
- 45857838565545385577449793398258363740979200000000*r41[i]
- 1479444354242422663436299123473954120225396734970420*r42[i]
- 44831961082741695492799244828619514023247872000000000*r43[i]
- 1290525734288850664269099373480698875776359383538646500*r44[i]
- 35584775745235419804380819416241066350620337766400000000*r45[i]
- 945953923580279776552772789184754415724912490598746182420*r46[i]
) // 13763753091226345046315979581580902400000000 for i in range(len(r0))]
r35 = [(-477638700*r[1][i]
+ 811985790*r[2][i]
- 927983760*r[3][i]
+ 843621600*r[4][i]
- 641886000*r[5][i]
+ 417225900*r[6][i]
- 233646504*r[7][i]
+ 112971936*r[8][i]
- 47071640*r[9][i]
+ 16811300*r[10][i]
- 5101360*r[11][i]
+ 1298528*r[12][i]
- 272272*r[13][i]
+ 45815*r[14][i]
- 5950*r[15][i]
+ 560*r[16][i]
- 34*r[17][i]
+ r[18][i]
+ 129644790*r0[i]
- 70715340*r2[i]
+ 161960940*r4[i]
- 832930740*r6[i]
+ 7810859340*r8[i]
- 119578066740*r10[i]
+ 2791740107340*r12[i]
- 95062235276340*r14[i]
+ 4584012079172940*r16[i]
- 307268933913567540*r18[i]
+ 28355038085389144140*r20[i]
- 3597774935929125068340*r22[i]
+ 632729503874459828228940*r24[i]
- 157381528472579148083026740*r26[i]
+ 57577884185625191071239755340*r28[i]
- 33404393172944223690128125810740*r30[i]
+ 36271128388074981554067219056171340*r32[i]
- 131671692334895976886647813958596908340*r34[i]
- 529104107360143104505564190890974500955060*r36[i]
- 21792609061108379656666967670836428800000000*r37[i]
- 779765567254824678774814590170424618060927540*r38[i]
- 25214048683702395262763681595157748121600000000*r39[i]
- 754531895504954495472529428607358759602244935860*r40[i]
- 21229190210645503978483385444330514048614400000000*r41[i]
- 567902644449952014090537079509460539320563935596340*r42[i]
- 14564893239013264062672891916748815156327219200000000*r43[i]
- 360416016142646161224945882401067658836071135991963060*r44[i]
- 8648657180064969977242561394456399100712373452800000000*r45[i]
- 202069375902424923136583586389997599181812580415819762740*r46[i]
) // 10333147966386144929666651337523200000000 for i in range(len(r0))]
r33 = [(129644790*r[1][i]
- 218349120*r[2][i]
+ 245642760*r[3][i]
- 218349120*r[4][i]
+ 161280600*r[5][i]
- 100975680*r[6][i]
+ 53993940*r[7][i]
- 24682944*r[8][i]
+ 9612108*r[9][i]
- 3164480*r[10][i]
+ 870232*r[11][i]
- 196416*r[12][i]
+ 35464*r[13][i]
- 4928*r[14][i]
+ 495*r[15][i]
- 32*r[16][i]
+ r[17][i]
- 35357670*r0[i]
+ 19389690*r2[i]
- 44796870*r4[i]
+ 233344890*r6[i]
- 2227139910*r8[i]
+ 34903389690*r10[i]
- 839988260550*r12[i]
+ 29734601940090*r14[i]
- 1506293149214790*r16[i]
+ 107487540061668090*r18[i]
- 10743535525710258630*r20[i]
+ 1511267716903778445690*r22[i]
- 304525956073869018848070*r24[i]
+ 91234873454404063067344890*r26[i]
- 43747586259736794619504039110*r28[i]
+ 39574917458915050445099774637690*r30[i]
- 120523981455993504966525708346887750*r32[i]
- 408775192473644376465790167368394203910*r34[i]
- 15499721949579217394499977006284800000000*r35[i]
- 511206585269023792365556128001469646849990*r36[i]
- 15254826342775865759666877369585500160000000*r37[i]
- 421754497238984285335705463354740490210507910*r38[i]
- 10974654148845317574241976981091935846400000000*r39[i]
- 271793538072560300468434911462753194293644181830*r40[i]
- 6459357656104303171129642884693889583677440000000*r41[i]
- 148248369194001435848413334991598692517822202402310*r42[i]
- 3302211571953506236081129759184691588287692800000000*r43[i]
- 71676123253955938571177412178194687158760951558339270*r44[i]
- 1520976967414625530272457942824571170900903198720000000*r45[i]
- 31639609352600382246311701401196841805566037174158815110*r46[i]
) // 8683317618811886495518194401280000000 for i in range(len(r0))]
r31 = [(-35357670*r[1][i]
+ 58929450*r[2][i]
- 65132550*r[3][i]
+ 56448210*r[4][i]
- 40320150*r[5][i]
+ 24192090*r[6][i]
- 12271350*r[7][i]
+ 5259150*r[8][i]
- 1893294*r[9][i]
+ 566370*r[10][i]
- 138446*r[11][i]
+ 26970*r[12][i]
- 4030*r[13][i]
+ 434*r[14][i]
- 30*r[15][i]
+ r[16][i]
+ 9694845*r0[i]
- 5348880*r2[i]
+ 12480720*r4[i]
- 65969520*r6[i]
+ 642563280*r8[i]
- 10347602160*r10[i]
+ 258040917840*r12[i]
- 9564008626800*r14[i]
+ 514021079720400*r16[i]
- 39590373677587440*r18[i]
+ 4371353677873146960*r20[i]
- 701971899866535028080*r22[i]
+ 169737570795219895373520*r24[i]
- 66396273378844288679892720*r26[i]
+ 49448835121192219782326176080*r28[i]
- 124963193751534047864734415925360*r30[i]
- 354113410826574103722030528083469360*r32[i]
- 12301366626650172535317442068480000000*r33[i]
- 372225904019072507165665501545458070000*r34[i]
- 10203983616806318118045818195804160000000*r35[i]
- 259484653500223872483011119661283865786800*r36[i]
- 6217811871006716259183948315607695360000000*r37[i]
- 141956901865997956445469727796622341498870640*r38[i]
- 3113335802166672719861469258672651632640000000*r39[i]
- 66003822624082868383556482555741495612650600240*r40[i]
- 1359334478541063086765779323397876419133440000000*r41[i]
- 27303356587963564025554884815930553997263574871280*r42[i]
- 536588847651574079588079017443366763149393920000000*r43[i]
- 10345842549438556817463474698578198121859964179733680*r44[i]
- 196138884946560564409651268242770514989620920320000000*r45[i]
- 3663204676820752962698443093474820599422678195673015920*r46[i]
) // 8222838654177922817725562880000000 for i in range(len(r0))]
r29 = [(9694845*r[1][i]
- 15967980*r[2][i]
+ 17298645*r[3][i]
- 14567280*r[4][i]
+ 10015005*r[5][i]
- 5722860*r[6][i]
+ 2731365*r[7][i]
- 1085760*r[8][i]
+ 356265*r[9][i]
- 95004*r[10][i]
+ 20097*r[11][i]
- 3248*r[12][i]
+ 377*r[13][i]
- 28*r[14][i]
+ r[15][i]
- 2674440*r0[i]
+ 1485800*r2[i]
- 3506488*r4[i]
+ 18850280*r6[i]
- 188004088*r8[i]
+ 3125835560*r10[i]
- 81314498488*r12[i]
+ 3185384180840*r14[i]
- 184064268909688*r16[i]
+ 15598375633694120*r18[i]
- 1958105850969957688*r20[i]
+ 375744491571024583400*r22[i]
- 118117302690774819242488*r24[i]
+ 71447614092662750198256680*r26[i]
- 147980747895225006590333244088*r28[i]
- 346368637877614395127589803878040*r30[i]
- 10963784872237230423634083840000000*r31[i]
- 302766527792977996357877082103322488*r32[i]
- 7585842753100939730112422608896000000*r33[i]
- 176553572119721839407097582006071612760*r34[i]
- 3876980715165912710714213825249280000000*r35[i]
- 81213796311764134505181592648745883717688*r36[i]
- 1636103186224681029581052139652775936000000*r37[i]
- 31895543813319775842490572300866856117139480*r38[i]
- 604645713103650398366928164707180216320000000*r39[i]
- 11189653759353064214370349765226592602607549688*r40[i]
- 202794861446303149866709151240333763280896000000*r41[i]
- 3608799207440735942926262565268791718882246250200*r42[i]
- 63195849406190967779680687932546907121909760000000*r43[i]
- 1091041918456432706911605989934195570136050930818488*r44[i]
- 18599858037912613836046600540495361832783446016000000*r45[i]
- 313534044032502214538190505667405050039920730329536920*r46[i]
) // 8841761993739701954543616000000 for i in range(len(r0))]
r27 = [(-2674440*r[1][i]
+ 4345965*r[2][i]
- 4601610*r[3][i]
+ 3749460*r[4][i]
- 2466750*r[5][i]
+ 1332045*r[6][i]
- 592020*r[7][i]
+ 215280*r[8][i]
- 63180*r[9][i]
+ 14625*r[10][i]
- 2574*r[11][i]
+ 324*r[12][i]
- 26*r[13][i]
+ r[14][i]
+ 742900*r0[i]
- 416024*r2[i]
+ 994840*r4[i]
- 5454824*r6[i]
+ 55944280*r8[i]
- 966290024*r10[i]
+ 26454613720*r12[i]
- 1109329691624*r14[i]
+ 70212852387160*r16[i]
- 6733670404619624*r18[i]
+ 1005318113348848600*r20[i]
- 249581050854994274024*r22[i]
+ 120719220687299365182040*r24[i]
- 202039976682357297272094824*r26[i]
- 385557844336439370252173428520*r28[i]
- 11052202492174627443179520000000*r29[i]
- 276888650579451671741587901762024*r30[i]
- 6304176301536407493589598208000000*r31[i]
- 133535841584115505205141919375399080*r32[i]
- 2672618344480543437732658544640000000*r33[i]
- 51095126335993498323380094454901195624*r34[i]
- 940618873537377672007825158832128000000*r35[i]
- 16776403501444391106926987629186000345640*r36[i]
- 291283862319085180678807183848898560000000*r37[i]
- 4942310839108515578583708125038854650555624*r38[i]
- 82203911327563805707081667710859870208000000*r39[i]
- 1343752600475734599375534320311340373516684200*r40[i]
- 21634243326074826428166414905753461063680000000*r41[i]
- 343672532983087585902951862991031321905844242024*r42[i]
- 5395063942758184834505475068561955332947968000000*r43[i]
- 83804941354439477195910293019964343299641959230760*r44[i]
- 1289609166695254343642200168046105549173555200000000*r45[i]
- 19678461460501652805347265575009996073778349586894824*r46[i]
) // 10888869450418352160768000000 for i in range(len(r0))]
r25 = [(742900*r[1][i]
- 1188640*r[2][i]
+ 1225785*r[3][i]
- 961400*r[4][i]
+ 600875*r[5][i]
- 303600*r[6][i]
+ 123970*r[7][i]
- 40480*r[8][i]
+ 10350*r[9][i]
- 2000*r[10][i]
+ 275*r[11][i]
- 24*r[12][i]
+ r[13][i]
- 208012*r0[i]
+ 117572*r2[i]
- 285532*r4[i]
+ 1602692*r6[i]
- 16996252*r8[i]
+ 307475012*r10[i]
- 8966430172*r12[i]
+ 409745686532*r14[i]
- 29195711499292*r16[i]
+ 3312133208909252*r18[i]
- 636215671041835612*r20[i]
+ 241648300078174135172*r22[i]
- 321511316149669476991132*r24[i]
- 492817676505266866078123708*r26[i]
- 12703681025488077520896000000*r27[i]
- 286779648275654636997381637852*r28[i]
- 5894507995826467969695744000000*r29[i]
- 112914054231542703053832892635388*r30[i]
- 2047008246979213061238030336000000*r31[i]
- 35501568925223446300815211192767772*r32[i]
- 593711792050129855003168210944000000*r33[i]
- 9632134956680435093368218113996247868*r34[i]
- 152311343455497374594406627803136000000*r35[i]
- 2356318736218539774396037820111678892892*r36[i]
- 35772470531371951985805498114637824000000*r37[i]
- 534273042749950920189640352996759062689148*r38[i]
- 7866491034006154572049014294052601856000000*r39[i]
- 114383224059606274110181105712262975351245212*r40[i]
- 1644946226278516886873016733667061202944000000*r41[i]
- 23426103831558846665144911501028780920365367228*r42[i]
- 330735945747364837719554208843251145179136000000*r43[i]
- 4633465747908141417306051485893140722291346976732*r44[i]
- 64465996518808752310647291812383168776634368000000*r45[i]
- 891389875128429665004288245297052393567100598170108*r46[i]
) // 15511210043330985984000000 for i in range(len(r0))]
r23 = [(-208012*r[1][i]
+ 326876*r[2][i]
- 326876*r[3][i]
+ 245157*r[4][i]
- 144210*r[5][i]
+ 67298*r[6][i]
- 24794*r[7][i]
+ 7084*r[8][i]
- 1518*r[9][i]
+ 230*r[10][i]
- 22*r[11][i]
+ r[12][i]
+ 58786*r0[i]
- 33592*r2[i]
+ 83096*r4[i]
- 479752*r6[i]
+ 5299736*r8[i]
- 101549512*r10[i]
+ 3208453976*r12[i]
- 164071220872*r14[i]
+ 13743680753816*r16[i]
- 1993276972245832*r18[i]
+ 581947914140407256*r20[i]
- 603916464771468176392*r22[i]
- 730803773459954540777704*r24[i]
- 16803810880275234816000000*r25[i]
- 339155768243774227716964552*r26[i]
- 6245976504198304781107200000*r27[i]
- 107413822788261782335458993064*r28[i]
- 1751393992807566623932416000000*r29[i]
- 27365156266821215807862420562312*r30[i]
- 412945663851071412756568473600000*r31[i]
- 6053949680529454447550745704030824*r32[i]
- 86623417665042381831452000256000000*r33[i]
- 1214146547565910406028014931410521672*r34[i]
- 16719755812321492798917963359846400000*r35[i]
- 226758627215029497194516602329808882984*r36[i]
- 3034905857007157810746475187798016000000*r37[i]
- 40151799724774280996886476759684489594632*r38[i]
- 525848735885794606994555529953619148800000*r39[i]
- 6825564942475643900873841059427230143341544*r40[i]
- 87900055843825806396690634755863003136000000*r41[i]
- 1124090333957827218160935737032127911249333192*r42[i]
- 14286036145840157893404384196456208735600640000*r43[i]
- 180556939553256275799275906968519352499771598504*r44[i]
- 2270728203819030041749862616122105872023552000000*r45[i]
- 28430855249825246651314973609548475795532583689352*r46[i]
) // 25852016738884976640000 for i in range(len(r0))]
r21 = [(58786*r[1][i]
- 90440*r[2][i]
+ 87210*r[3][i]
- 62016*r[4][i]
+ 33915*r[5][i]
- 14364*r[6][i]
+ 4655*r[7][i]
- 1120*r[8][i]
+ 189*r[9][i]
- 20*r[10][i]
+ r[11][i]
- 16796*r0[i]
+ 9724*r2[i]
- 24596*r4[i]
+ 147004*r6[i]
- 1708916*r8[i]
+ 35240284*r10[i]
- 1237329236*r12[i]
+ 73853629564*r14[i]
- 7850527669556*r16[i]
+ 1717351379730844*r18[i]
- 1359124435588313876*r20[i]
- 1272410676942417239876*r22[i]
- 25852016738884976640000*r23[i]
- 462292539259962003646196*r24[i]
- 7561714896123855667200000*r25[i]
- 115761644587269354830466596*r26[i]
- 1683741850203578528563200000*r27[i]
- 23512975860299444963550050516*r28[i]
- 317677725072691341719961600000*r29[i]
- 4176614976496441445095962733316*r30[i]
- 53674391443652368368589209600000*r31[i]
- 676635955671282540673335079110836*r32[i]
- 8391272072243853389701334630400000*r33[i]
- 102611708232289325546408008313624036*r34[i]
- 1239646284649926576486736094822400000*r35[i]
- 14819283410691765614379616648600811156*r36[i]
- 175538127424434549895381626305740800000*r37[i]
- 2062659648435073986802743885440046722756*r38[i]
- 24066873273263602745997309174983884800000*r39[i]
- 279069134864297423784787795404361206735476*r40[i]
- 3218237360334469905693543066426751549440000*r41[i]
- 36932670876144577834192017462238998576813476*r42[i]
- 422013831656219970552631011526505561456640000*r43[i]
- 4803667893589610545887832027829424971473267796*r44[i]
- 54491782544378643866541770098406137341542400000*r45[i]
- 616254801390825608499920295882691673585117080196*r46[i]
) // 51090942171709440000 for i in range(len(r0))]
r19 = [(-16796*r[1][i]
+ 25194*r[2][i]
- 23256*r[3][i]
+ 15504*r[4][i]
- 7752*r[5][i]
+ 2907*r[6][i]
- 798*r[7][i]
+ 152*r[8][i]
- 18*r[9][i]
+ r[10][i]
+ 4862*r0[i]
- 2860*r2[i]
+ 7436*r4[i]
- 46420*r6[i]
+ 576236*r8[i]
- 13098580*r10[i]
+ 532310636*r12[i]
- 39968611540*r14[i]
+ 6350631494636*r16[i]
- 3730771315561300*r18[i]
- 2637991952943407764*r20[i]
- 46833363657400320000*r21[i]
- 734121065118879803860*r22[i]
- 10556240168378032128000*r23[i]
- 142438684135271315212564*r24[i]
- 1830415113744266649600000*r25[i]
- 22632897298190126259675220*r26[i]
- 271297526662043666104320000*r27[i]
- 3170344993810020486920015764*r28[i]
- 36274730261563609572556800000*r29[i]
- 407775103607650299563627591380*r30[i]
- 4515882637052182897862000640000*r31[i]
- 49377994276343186011748723193364*r32[i]
- 534053247401000753173510963200000*r33[i]
- 5722063606154183864914875339648340*r34[i]
- 60811730909031986048777521029120000*r35[i]
- 641729418431834160625738740379401364*r36[i]
- 6730380606921481449181267599974400000*r37[i]
- 70207898580127312813466155395513222100*r38[i]
- 728918319689461841494925372032622592000*r39[i]
- 7536441803725213229125462424550696575764*r40[i]
- 77635978704164552294553096402068152320000*r41[i]
- 797177898990753876072852178329776532568660*r42[i]
- 8162164080895303403984327865949915250688000*r43[i]
- 83359491110673172494030048846026790563932564*r44[i]
- 849432099945167336777734465061373289267200000*r45[i]
- 8638438243166451781593809976801426668242424020*r46[i]
) // 121645100408832000 for i in range(len(r0))]
r17 = [(4862*r[1][i]
- 7072*r[2][i]
+ 6188*r[3][i]
- 3808*r[4][i]
+ 1700*r[5][i]
- 544*r[6][i]
+ 119*r[7][i]
- 16*r[8][i]
+ r[9][i]
- 1430*r0[i]
+ 858*r2[i]
- 2310*r4[i]
+ 15258*r6[i]
- 206790*r8[i]
+ 5386458*r10[i]
- 272513670*r12[i]
+ 30255826458*r14[i]
- 12765597850950*r16[i]
- 6622557957272742*r18[i]
- 101370917007360000*r19[i]
- 1375210145685786630*r20[i]
- 17172233341046784000*r21[i]
- 201832098313986359142*r22[i]
- 2265471043586150400000*r23[i]
- 24529324224160803328710*r24[i]
- 258058524232798248960000*r25[i]
- 2652208374242713043720742*r26[i]
- 26739700571225856614400000*r27[i]
- 265323404171486113659725190*r28[i]
- 2597688920748017370193920000*r29[i]
- 25147613788240222384169485542*r30[i]
- 241125683321001354933657600000*r31[i]
- 2293170112631184981695915264070*r32[i]
- 21656158388689797460311183360000*r33[i]
- 203283794784841444836991831621542*r34[i]
- 1898267590696733462875776307200000*r35[i]
- 17646072330245312137111933794073350*r36[i]
- 163392570167583908119294187237376000*r37[i]
- 1507754227229479379470312529237936742*r38[i]
- 13871774079585871769182921633935360000*r39[i]
- 127291574907112728538906245247680921030*r40[i]
- 1165398276253942030786602999248830464000*r41[i]
- 10648249156718669259487809979675840079142*r42[i]
- 97121906010634492337139410720414515200000*r43[i]
- 884471146488697462546213719879378982015110*r44[i]
- 8043742604145412070397708709577312747520000*r45[i]
- 73065283527546375984492393431422365909536742*r46[i]
) // 355687428096000 for i in range(len(r0))]
r15 = [(-1430*r[1][i]
+ 2002*r[2][i]
- 1638*r[3][i]
+ 910*r[4][i]
- 350*r[5][i]
+ 90*r[6][i]
- 14*r[7][i]
+ r[8][i]
+ 429*r0[i]
- 264*r2[i]
+ 744*r4[i]
- 5304*r6[i]
+ 81384*r8[i]
- 2605944*r10[i]
+ 192387624*r12[i]
- 55942352184*r14[i]
- 20546119600536*r16[i]
- 266765571072000*r17[i]
- 3083760849804024*r18[i]
- 32945548027392000*r19[i]
- 332500281299403096*r20[i]
- 3215147584416768000*r21[i]
- 30076927429146721464*r22[i]
- 274100623905588480000*r23[i]
- 2446077617962088140056*r24[i]
- 21459412163122053120000*r25[i]
- 185641639183185136464504*r26[i]
- 1587401376760010972160000*r27[i]
- 13442713420403849918131416*r28[i]
- 112915002722102749808640000*r29[i]
- 941961013910760913890393144*r30[i]
- 7812419263561351877518080000*r31[i]
- 64474322285718607792730497176*r32[i]
- 529848386811984810994744320000*r33[i]
- 4338547620121893769542630267384*r34[i]
- 35415056327751829508662891008000*r35[i]
- 288317531175033442515609896757336*r36[i]
- 2341823147101379454117987013632000*r37[i]
- 18983391549723892653716655806647224*r38[i]
- 153619763998111828980832157720832000*r39[i]
- 1241292607509331793516191597844431896*r40[i]
- 10017079537004367071413852136982528000*r41[i]
- 80746194097372251940077615903073292664*r42[i]
- 650250798838302173122854563322562560000*r43[i]
- 5232061257212799699445154857325986640856*r44[i]
- 42067391464856035210355948847111229440000*r45[i]
- 338018548004311349729166172709579357563704*r46[i]
) // 1307674368000 for i in range(len(r0))]
r13 = [(429*r[1][i]
- 572*r[2][i]
+ 429*r[3][i]
- 208*r[4][i]
+ 65*r[5][i]
- 12*r[6][i]
+ r[7][i]
- 132*r0[i]
+ 84*r2[i]
- 252*r4[i]
+ 2004*r6[i]
- 37212*r8[i]
+ 1710324*r10[i]
- 325024572*r12[i]
- 80789566956*r14[i]
- 871782912000*r15[i]
- 8422900930332*r16[i]
- 75583578470400*r17[i]
- 643521842437836*r18[i]
- 5269678622208000*r19[i]
- 41890044885642492*r20[i]
- 325386564299596800*r21[i]
- 2481686964269990316*r22[i]
- 18652248729354240000*r23[i]
- 138536531588626169052*r24[i]
- 1019042849143807488000*r25[i]
- 7436421488952386592396*r26[i]
- 53911021949819274240000*r27[i]
- 388701690499592948238012*r28[i]
- 2789805187365599475072000*r29[i]
- 19946749502047187160692076*r30[i]
- 142159780685991861112320000*r31[i]
- 1010433303980489860989897372*r32[i]
- 7165521770403817166663116800*r33[i]
- 50716588034439244118483617356*r34[i]
- 358378772025058883636009472000*r35[i]
- 2528902640579773012941059115132*r36[i]
- 17824202779159732939433280230400*r37[i]
- 125502611080965065134883934376236*r38[i]
- 882926862501000079240924013568000*r39[i]
- 6206986746547700738292160195379292*r40[i]
- 43608135571536574058895364550860800*r41[i]
- 306213499909407501334225902520456716*r42[i]
- 2149239710498553002348841878415360000*r43[i]
- 15079178774724614117506008765315297852*r44[i]
- 105761403926812162332273274580071296000*r45[i]
- 741573481088337285231858048220674626796*r46[i]
) // 6227020800 for i in range(len(r0))]
r11 = [(-132*r[1][i]
+ 165*r[2][i]
- 110*r[3][i]
+ 44*r[4][i]
- 10*r[5][i]
+ r[6][i]
+ 42*r0[i]
- 28*r2[i]
+ 92*r4[i]
- 868*r6[i]
+ 22652*r8[i]
- 2620708*r10[i]
- 415790788*r12[i]
- 3632428800*r13[i]
- 28616744548*r14[i]
- 210680870400*r15[i]
- 1479485236228*r16[i]
- 10038995366400*r17[i]
- 66394067988388*r18[i]
- 430591742380800*r19[i]
- 2750479262009668*r20[i]
- 17360942812012800*r21[i]
- 108550450893568228*r22[i]
- 673606803881088000*r23[i]
- 4154688725062207108*r24[i]
- 25499502190850688000*r25[i]
- 155878445775166700068*r26[i]
- 949776357849070752000*r27[i]
- 5771581202353414724548*r28[i]
- 34995682724855684832000*r29[i]
- 211811399872933910999908*r30[i]
- 1280080235834717770252800*r31[i]
- 7726641919200262371657988*r32[i]
- 46591059456870785061004800*r33[i]
- 280704018540064430354883748*r34[i]
- 1690018909819536161979590400*r35[i]
- 10169113413821714748538703428*r36[i]
- 61159784116494648773674886400*r37[i]
- 367684638335977863351585967588*r38[i]
- 2209739160176731898013383884800*r39[i]
- 13276598260065161268654185556868*r40[i]
- 79750432649108163224160355276800*r41[i]
- 478956917715683026467561165467428*r42[i]
- 2876013540917084725512964985376000*r43[i]
- 17267443120712778679894991796314308*r44[i]
- 103661474908781590201983341856096000*r45[i]
- 622252957609245047342724399262599268*r46[i]
) // 39916800 for i in range(len(r0))]
r9 = [(42*r[1][i]
- 48*r[2][i]
+ 27*r[3][i]
- 8*r[4][i]
+ r[5][i]
- 14*r0[i]
+ 10*r2[i]
- 38*r4[i]
+ 490*r6[i]
- 31238*r8[i]
- 2922230*r10[i]
- 19958400*r11[i]
- 124075238*r12[i]
- 726485760*r13[i]
- 4084385750*r14[i]
- 22313491200*r15[i]
- 119387268038*r16[i]
- 628980992640*r17[i]
- 3275389222070*r18[i]
- 16905818966400*r19[i]
- 86665431465638*r20[i]
- 441935114987520*r21[i]
- 2244295389943190*r22[i]
- 11360520464832000*r23[i]
- 57360469753884038*r24[i]
- 289038899804054400*r25[i]
- 1454155949521941110*r26[i]
- 7306671293537616000*r27[i]
- 36677059892827099238*r28[i]
- 183960524908301057280*r29[i]
- 922104761587650687830*r30[i]
- 4619736062008593926400*r31[i]
- 23135540444136227047238*r32[i]
- 115825176110799088940160*r33[i]
- 579715876176320506935350*r34[i]
- 2900939663557699476451200*r35[i]
- 14514140349055749129024038*r36[i]
- 72608472572041292373527040*r37[i]
- 363193454272347163609915670*r38[i]
- 1816571661325589960713958400*r39[i]
- 9085275939429279963731685638*r40[i]
- 45436050447189540392656321920*r41[i]
- 227218935892633882388998540790*r42[i]
- 1136249416059455304696385296000*r43[i]
- 5681866032591044240951769048038*r44[i]
- 28411805989856165780668427308800*r45[i]
- 142068933310062230858345890602710*r46[i]
) // 362880 for i in range(len(r0))]
r7 = [(-14*r[1][i]
+ 14*r[2][i]
- 6*r[3][i]
+ r[4][i]
+ 5*r0[i]
- 4*r2[i]
+ 20*r4[i]
- 604*r6[i]
- 29740*r8[i]
- 151200*r9[i]
- 708604*r10[i]
- 3160080*r11[i]
- 13645900*r12[i]
- 57657600*r13[i]
- 239967004*r14[i]
- 988107120*r15[i]
- 4037604460*r16[i]
- 16406863200*r17[i]
- 66398623804*r18[i]
- 267911678160*r19[i]
- 1078605601420*r20[i]
- 4335313752000*r21[i]
- 17403958407004*r22[i]
- 69804002545200*r23[i]
- 279780634372780*r24[i]
- 1120816644948000*r25[i]
- 4488349371924604*r26[i]
- 17968646803620240*r27[i]
- 71920337041294540*r28[i]
- 287818601403715200*r29[i]
- 1151686172846664604*r30[i]
- 4607980008114455280*r31[i]
- 18435626012705982700*r32[i]
- 73753622051697957600*r33[i]
- 295047842329672995004*r34[i]
- 1180291431927853642320*r35[i]
- 4721465916019935893260*r36[i]
- 18886764229967380219200*r37[i]
- 75549758619456576163804*r38[i]
- 302207139580435761213360*r39[i]
- 1208852873637267995922220*r40[i]
- 4835484440511039999684000*r41[i]
- 19342156599960850372299004*r42[i]
- 77369282913655045261040400*r43[i]
- 309479101196178257662005580*r44[i]
- 1237922313409633551106176000*r45[i]
- 4951706979513788347008408604*r46[i]
) // 5040 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
- 1680*r7[i]
- 5542*r8[i]
- 17640*r9[i]
- 54958*r10[i]
- 168960*r11[i]
- 515062*r12[i]
- 1561560*r13[i]
- 4717438*r14[i]
- 14217840*r15[i]
- 42784582*r16[i]
- 128615880*r17[i]
- 386371918*r18[i]
- 1160164320*r19[i]
- 3482590102*r20[i]
- 10451964600*r21[i]
- 31364282398*r22[i]
- 94109624400*r23[i]
- 282362427622*r24[i]
- 847154391720*r25[i]
- 2541597392878*r26[i]
- 7625060614080*r27[i]
- 22875718713142*r28[i]
- 68628229881240*r29[i]
- 205886837127358*r30[i]
- 617664806349360*r31[i]
- 1853003008982662*r32[i]
- 5559026206817160*r33[i]
- 16677112980189838*r34[i]
- 50031407660046240*r35[i]
- 150094360419092182*r36[i]
- 450283356135183480*r37[i]
- 1350850618161364318*r38[i]
- 4052552953995720720*r39[i]
- 12157661061010417702*r40[i]
- 36472987581077764200*r41[i]
- 109418971539326314798*r42[i]
- 328256932210164988800*r43[i]
- 984770831814867055222*r44[i]
- 2954312565813345343320*r45[i]
- 8862937838177524385278*r46[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
- 126*r7[i]
- 254*r8[i]
- 510*r9[i]
- 1022*r10[i]
- 2046*r11[i]
- 4094*r12[i]
- 8190*r13[i]
- 16382*r14[i]
- 32766*r15[i]
- 65534*r16[i]
- 131070*r17[i]
- 262142*r18[i]
- 524286*r19[i]
- 1048574*r20[i]
- 2097150*r21[i]
- 4194302*r22[i]
- 8388606*r23[i]
- 16777214*r24[i]
- 33554430*r25[i]
- 67108862*r26[i]
- 134217726*r27[i]
- 268435454*r28[i]
- 536870910*r29[i]
- 1073741822*r30[i]
- 2147483646*r31[i]
- 4294967294*r32[i]
- 8589934590*r33[i]
- 17179869182*r34[i]
- 34359738366*r35[i]
- 68719476734*r36[i]
- 137438953470*r37[i]
- 274877906942*r38[i]
- 549755813886*r39[i]
- 1099511627774*r40[i]
- 2199023255550*r41[i]
- 4398046511102*r42[i]
- 8796093022206*r43[i]
- 17592186044414*r44[i]
- 35184372088830*r45[i]
- 70368744177662*r46[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
- r7[i]
- r8[i]
- r9[i]
- r10[i]
- r11[i]
- r12[i]
- r13[i]
- r14[i]
- r15[i]
- r16[i]
- r17[i]
- r18[i]
- r19[i]
- r20[i]
- r21[i]
- r22[i]
- r23[i]
- r24[i]
- r25[i]
- r26[i]
- r27[i]
- r28[i]
- r29[i]
- r30[i]
- r31[i]
- r32[i]
- r33[i]
- r34[i]
- r35[i]
- r36[i]
- r37[i]
- r38[i]
- r39[i]
- r40[i]
- r41[i]
- r42[i]
- r43[i]
- r44[i]
- r45[i]
- r46[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46)
def natural_interpolate_25(r):
r0 = r[0]
r48 = r['infinity']
r46 = [(7890371113950*(r[1][i] + r[-1][i])
- 6943526580276*(r[2][i] + r[-2][i])
+ 5608233007146*(r[3][i] + r[-3][i])
- 4154246671960*(r[4][i] + r[-4][i])
+ 2818953098830*(r[5][i] + r[-5][i])
- 1749695026860*(r[6][i] + r[-6][i])
+ 991493848554*(r[7][i] + r[-7][i])
- 511738760544*(r[8][i] + r[-8][i])
+ 239877544005*(r[9][i] + r[-9][i])
- 101766230790*(r[10][i] + r[-10][i])
+ 38910617655*(r[11][i] + r[-11][i])
- 13340783196*(r[12][i] + r[-12][i])
+ 4076350421*(r[13][i] + r[-13][i])
- 1101716330*(r[14][i] + r[-14][i])
+ 260932815*(r[15][i] + r[-15][i])
- 53524680*(r[16][i] + r[-16][i])
+ 9366819*(r[17][i] + r[-17][i])
- 1370754*(r[18][i] + r[-18][i])
+ 163185*(r[19][i] + r[-19][i])
- 15180*(r[20][i] + r[-20][i])
+ 1035*(r[21][i] + r[-21][i])
- 46*(r[22][i] + r[-22][i])
+ (r[23][i] + r[-23][i])
- 8233430727600*r0[i]
- 23793338219027472619152720674132302157166182179799040000000000*r48[i]
) // 5502622159812088949850305428800254892961651752960000000000 for i in range(len(r0))]
r44 = [(-2012616400080*(r[1][i] + r[-1][i])
+ 1761039350070*(r[2][i] + r[-2][i])
- 1408831480056*(r[3][i] + r[-3][i])
+ 1029530696964*(r[4][i] + r[-4][i])
- 686353797976*(r[5][i] + r[-5][i])
+ 416714805914*(r[6][i] + r[-6][i])
- 229911617056*(r[7][i] + r[-7][i])
+ 114955808528*(r[8][i] + r[-8][i])
- 51915526432*(r[9][i] + r[-9][i])
+ 21090682613*(r[10][i] + r[-10][i])
- 7669339132*(r[11][i] + r[-11][i])
+ 2481256778*(r[12][i] + r[-12][i])
- 708930508*(r[13][i] + r[-13][i])
+ 177232627*(r[14][i] + r[-14][i])
- 38320568*(r[15][i] + r[-15][i])
+ 7059052*(r[16][i] + r[-16][i])
- 1086008*(r[17][i] + r[-17][i])
+ 135751*(r[18][i] + r[-18][i])
- 13244*(r[19][i] + r[-19][i])
+ 946*(r[20][i] + r[-20][i])
- 44*(r[21][i] + r[-21][i])
+ (r[22][i] + r[-22][i])
+ 2104098963720*r0[i]
- 10088140626322163074725559952800467303763028213760000000000*r46[i]
- 20672617771459376572727617455278717598871197415636992000000000*r48[i]
) // 2658271574788448768043625811014615890319638528000000000 for i in range(len(r0))]
r42 = [(513791607420*(r[1][i] + r[-1][i])
- 446775310800*(r[2][i] + r[-2][i])
+ 353697121050*(r[3][i] + r[-3][i])
- 254661927156*(r[4][i] + r[-4][i])
+ 166509721602*(r[5][i] + r[-5][i])
- 98672427616*(r[6][i] + r[-6][i])
+ 52860229080*(r[7][i] + r[-7][i])
- 25518731280*(r[8][i] + r[-8][i])
+ 11058116888*(r[9][i] + r[-9][i])
- 4280561376*(r[10][i] + r[-10][i])
+ 1471442973*(r[11][i] + r[-11][i])
- 445891810*(r[12][i] + r[-12][i])
+ 118030185*(r[13][i] + r[-13][i])
- 26978328*(r[14][i] + r[-14][i])
+ 5245786*(r[15][i] + r[-15][i])
- 850668*(r[16][i] + r[-16][i])
+ 111930*(r[17][i] + r[-17][i])
- 11480*(r[18][i] + r[-18][i])
+ 861*(r[19][i] + r[-19][i])
- 42*(r[20][i] + r[-20][i])
+ (r[21][i] + r[-21][i])
- 538257874440*r0[i]
- 4651975255879785344076345169275577808059367424000000000*r44[i]
- 8345643609048334907272963233680386587658505158656000000000*r46[i]
- 10774531600512501036897720551649645765494516918255616000000000*r48[i]
) // 1405006117752879898543142606244511569936384000000000 for i in range(len(r0))]
r40 = [(-131282408400*(r[1][i] + r[-1][i])
+ 113380261800*(r[2][i] + r[-2][i])
- 88732378800*(r[3][i] + r[-3][i])
+ 62852101650*(r[4][i] + r[-4][i])
- 40225345056*(r[5][i] + r[-5][i])
+ 23206929840*(r[6][i] + r[-6][i])
- 12033222880*(r[7][i] + r[-7][i])
+ 5586853480*(r[8][i] + r[-8][i])
- 2311801440*(r[9][i] + r[-9][i])
+ 847660528*(r[10][i] + r[-10][i])
- 273438880*(r[11][i] + r[-11][i])
+ 76904685*(r[12][i] + r[-12][i])
- 18643560*(r[13][i] + r[-13][i])
+ 3838380*(r[14][i] + r[-14][i])
- 658008*(r[15][i] + r[-15][i])
+ 91390*(r[16][i] + r[-16][i])
- 9880*(r[17][i] + r[-17][i])
+ 780*(r[18][i] + r[-18][i])
- 40*(r[19][i] + r[-19][i])
+ (r[20][i] + r[-20][i])
+ 137846528820*r0[i]
- 2341676862921466497571904343740852616560640000000000*r42[i]
- 3655123415334117056059985490145096849189502976000000000*r44[i]
- 4119688019118574531237133429498603530973935042560000000000*r46[i]
- 3757340713824985498498548346794211825654347639816192000000000*r48[i]
) // 815915283247897734345611269596115894272000000000 for i in range(len(r0))]
r38 = [(33578000610*(r[1][i] + r[-1][i])
- 28781143380*(r[2][i] + r[-2][i])
+ 22239974430*(r[3][i] + r[-3][i])
- 15471286560*(r[4][i] + r[-4][i])
+ 9669554100*(r[5][i] + r[-5][i])
- 5414950296*(r[6][i] + r[-6][i])
+ 2707475148*(r[7][i] + r[-7][i])
- 1203322288*(r[8][i] + r[-8][i])
+ 472733756*(r[9][i] + r[-9][i])
- 163011640*(r[10][i] + r[-10][i])
+ 48903492*(r[11][i] + r[-11][i])
- 12620256*(r[12][i] + r[-12][i])
+ 2760681*(r[13][i] + r[-13][i])
- 501942*(r[14][i] + r[-14][i])
+ 73815*(r[15][i] + r[-15][i])
- 8436*(r[16][i] + r[-16][i])
+ 703*(r[17][i] + r[-17][i])
- 38*(r[18][i] + r[-18][i])
+ (r[19][i] + r[-19][i])
- 35345263800*r0[i]
- 1291865865142504746047217843527183499264000000000*r40[i]
- 1742597865490724651943092149133817822157209600000000*r42[i]
- 1703614521144184428726371303487541532883419136000000000*r44[i]
- 1352221478318945952566471137817160521323572835123200000000*r46[i]
- 925912385499308009244605568293800045079467288166400000000000*r48[i]
) // 523022617466601111760007224100074291200000000 for i in range(len(r0))]
r36 = [(-8597496600*(r[1][i] + r[-1][i])
+ 7307872110*(r[2][i] + r[-2][i])
- 5567902560*(r[3][i] + r[-3][i])
+ 3796297200*(r[4][i] + r[-4][i])
- 2310789600*(r[5][i] + r[-5][i])
+ 1251677700*(r[6][i] + r[-6][i])
- 600805296*(r[7][i] + r[-7][i])
+ 254186856*(r[8][i] + r[-8][i])
- 94143280*(r[9][i] + r[-9][i])
+ 30260340*(r[10][i] + r[-10][i])
- 8347680*(r[11][i] + r[-11][i])
+ 1947792*(r[12][i] + r[-12][i])
- 376992*(r[13][i] + r[-13][i])
+ 58905*(r[14][i] + r[-14][i])
- 7140*(r[15][i] + r[-15][i])
+ 630*(r[16][i] + r[-16][i])
- 36*(r[17][i] + r[-17][i])
+ (r[18][i] + r[-18][i])
+ 9075135300*r0[i]
- 784533926199901667640010836150111436800000000*r38[i]
- 907705752613286229459492537425678932377600000000*r40[i]
- 764250847583238143225401875995898505750118400000000*r42[i]
- 524336156604477506256224109002957345627779891200000000*r44[i]
- 311351658482338919180732210200430367625645444300800000000*r46[i]
- 166036590632320367531429334375544068072103816986624000000000*r48[i]
) // 371993326789901217467999448150835200000000 for i in range(len(r0))]
r34 = [(2203961430*(r[1][i] + r[-1][i])
- 1855967520*(r[2][i] + r[-2][i])
+ 1391975640*(r[3][i] + r[-3][i])
- 927983760*(r[4][i] + r[-4][i])
+ 548354040*(r[5][i] + r[-5][i])
- 286097760*(r[6][i] + r[-6][i])
+ 131128140*(r[7][i] + r[-7][i])
- 52451256*(r[8][i] + r[-8][i])
+ 18156204*(r[9][i] + r[-9][i])
- 5379616*(r[10][i] + r[-10][i])
+ 1344904*(r[11][i] + r[-11][i])
- 278256*(r[12][i] + r[-12][i])
+ 46376*(r[13][i] + r[-13][i])
- 5984*(r[14][i] + r[-14][i])
+ 561*(r[15][i] + r[-15][i])
- 34*(r[16][i] + r[-16][i])
+ (r[17][i] + r[-17][i])
- 2333606220*r0[i]
- 526990546285693391412999218213683200000000*r36[i]
- 518664095654379435828673830565907005440000000*r38[i]
- 373138241060740797524227217357125818777600000000*r40[i]
- 219618160307546307818407858079592245845032960000000*r42[i]
- 112275193446419212026758411812279514001781555200000000*r44[i]
- 51713216892097268029263570056035419810630708756480000000*r46[i]
- 21987290206937420965021290881182668895459624353792000000000*r48[i]
) // 295232799039604140847618609643520000000 for i in range(len(r0))]
r32 = [(-565722720*(r[1][i] + r[-1][i])
+ 471435600*(r[2][i] + r[-2][i])
- 347373600*(r[3][i] + r[-3][i])
+ 225792840*(r[4][i] + r[-4][i])
- 129024480*(r[5][i] + r[-5][i])
+ 64512240*(r[6][i] + r[-6][i])
- 28048800*(r[7][i] + r[-7][i])
+ 10518300*(r[8][i] + r[-8][i])
- 3365856*(r[9][i] + r[-9][i])
+ 906192*(r[10][i] + r[-10][i])
- 201376*(r[11][i] + r[-11][i])
+ 35960*(r[12][i] + r[-12][i])
- 4960*(r[13][i] + r[-13][i])
+ 496*(r[14][i] + r[-14][i])
- 32*(r[15][i] + r[-15][i])
+ (r[16][i] + r[-16][i])
+ 601080390*r0[i]
- 393643732052805521130158146191360000000*r34[i]
- 326527475737802179777466182265733120000000*r36[i]
- 198969979872214920293886346099446251520000000*r38[i]
- 99626745669333527035567016277524852244480000000*r40[i]
- 43498703313314018776504938348732045412270080000000*r42[i]
- 17170843124850370546818528558187736420780605440000000*r44[i]
- 6276444318289938061108840583768656479667869450240000000*r46[i]
- 2160301520690503531404610021529918026938609932697600000000*r48[i]
) // 263130836933693530167218012160000000 for i in range(len(r0))]
r30 = [(145422675*(r[1][i] + r[-1][i])
- 119759850*(r[2][i] + r[-2][i])
+ 86493225*(r[3][i] + r[-3][i])
- 54627300*(r[4][i] + r[-4][i])
+ 30045015*(r[5][i] + r[-5][i])
- 14307150*(r[6][i] + r[-6][i])
+ 5852925*(r[7][i] + r[-7][i])
- 2035800*(r[8][i] + r[-8][i])
+ 593775*(r[9][i] + r[-9][i])
- 142506*(r[10][i] + r[-10][i])
+ 27405*(r[11][i] + r[-11][i])
- 4060*(r[12][i] + r[-12][i])
+ 435*(r[13][i] + r[-13][i])
- 30*(r[14][i] + r[-14][i])
+ (r[15][i] + r[-15][i])
- 155117520*r0[i]
- 328913546167116912709022515200000000*r32[i]
- 227575282593028191903372678266880000000*r34[i]
- 116309421454977381321426414757478400000000*r36[i]
- 49083095586740430887431564189583278080000000*r38[i]
- 18139371393109511951007844941215406489600000000*r40[i]
- 6083845843389094496001274537210012898426880000000*r42[i]
- 1895875482185729033390420637976407213657292800000000*r44[i]
- 557995741137378415081398016214860854983503380480000000*r46[i]
- 156963921056606539204438549741946823549156065280000000000*r48[i]
) // 265252859812191058636308480000000 for i in range(len(r0))]
r28 = [(-37442160*(r[1][i] + r[-1][i])
+ 30421755*(r[2][i] + r[-2][i])
- 21474180*(r[3][i] + r[-3][i])
+ 13123110*(r[4][i] + r[-4][i])
- 6906900*(r[5][i] + r[-5][i])
+ 3108105*(r[6][i] + r[-6][i])
- 1184040*(r[7][i] + r[-7][i])
+ 376740*(r[8][i] + r[-8][i])
- 98280*(r[9][i] + r[-9][i])
+ 20475*(r[10][i] + r[-10][i])
- 3276*(r[11][i] + r[-11][i])
+ 378*(r[12][i] + r[-12][i])
- 28*(r[13][i] + r[-13][i])
+ (r[14][i] + r[-14][i])
+ 40116600*r0[i]
- 309461669780889568409026560000000*r30[i]
- 176516936443019409820508749824000000*r32[i]
- 74833313645455216256514439249920000000*r34[i]
- 26337328459046574816219104447299584000000*r36[i]
- 8155948144934385059006601147769159680000000*r38[i]
- 2301709517171786559798286695904076365824000000*r40[i]
- 605758813130095139988659617361096909783040000000*r42[i]
- 151061790397229175366153301919734749322543104000000*r44[i]
- 36109056667467121621981604705290955376859545600000000*r46[i]
- 8344518734397260673326477690101230819337996075008000000*r48[i]
) // 304888344611713860501504000000 for i in range(len(r0))]
r26 = [(9657700*(r[1][i] + r[-1][i])
- 7726160*(r[2][i] + r[-2][i])
+ 5311735*(r[3][i] + r[-3][i])
- 3124550*(r[4][i] + r[-4][i])
+ 1562275*(r[5][i] + r[-5][i])
- 657800*(r[6][i] + r[-6][i])
+ 230230*(r[7][i] + r[-7][i])
- 65780*(r[8][i] + r[-8][i])
+ 14950*(r[9][i] + r[-9][i])
- 2600*(r[10][i] + r[-10][i])
+ 325*(r[11][i] + r[-11][i])
- 26*(r[12][i] + r[-12][i])
+ (r[13][i] + r[-13][i])
- 10400600*r0[i]
- 330295706662690015543296000000*r28[i]
- 153257207891488167212089344000000*r30[i]
- 53222214421459539592188788736000000*r32[i]
- 15436506593303376230082373484544000000*r34[i]
- 3960094929842931739454572322881536000000*r36[i]
- 930084233815670751630942950980583424000000*r38[i]
- 204528766884160018873274371645367648256000000*r40[i]
- 42768601883241439058698435075343591276544000000*r42[i]
- 8599134589431485780708409429924529774657536000000*r44[i]
- 1676115909489027560076829587121962388192493568000000*r46[i]
- 318686948683222526304282057035116495208098824192000000*r48[i]
) // 403291461126605635584000000 for i in range(len(r0))]
r24 = [(-2496144*(r[1][i] + r[-1][i])
+ 1961256*(r[2][i] + r[-2][i])
- 1307504*(r[3][i] + r[-3][i])
+ 735471*(r[4][i] + r[-4][i])
- 346104*(r[5][i] + r[-5][i])
+ 134596*(r[6][i] + r[-6][i])
- 42504*(r[7][i] + r[-7][i])
+ 10626*(r[8][i] + r[-8][i])
- 2024*(r[9][i] + r[-9][i])
+ 276*(r[10][i] + r[-10][i])
- 24*(r[11][i] + r[-11][i])
+ (r[12][i] + r[-12][i])
+ 2704156*r0[i]
- 403291461126605635584000000*r26[i]
- 149903436100759314746572800000*r28[i]
- 42033455827381598974377984000000*r30[i]
- 9910695932425713906157643366400000*r32[i]
- 2078962023961017163954848006144000000*r34[i]
- 401274139495715827174031120636313600000*r36[i]
- 72837740568171787457915404507152384000000*r38[i]
- 12620369661259070567869332718886859571200000*r40[i]
- 2109601340251819353520575234140712075264000000*r42[i]
- 342864867500163789441705220714949009654415360000*r44[i]
- 54497476891656721001996702786930540928565248000000*r46[i]
- 8509384879617502075402808457393042025589086617600000*r48[i]
) // 620448401733239439360000 for i in range(len(r0))]
r22 = [(646646*(r[1][i] + r[-1][i])
- 497420*(r[2][i] + r[-2][i])
+ 319770*(r[3][i] + r[-3][i])
- 170544*(r[4][i] + r[-4][i])
+ 74613*(r[5][i] + r[-5][i])
- 26334*(r[6][i] + r[-6][i])
+ 7315*(r[7][i] + r[-7][i])
- 1540*(r[8][i] + r[-8][i])
+ 231*(r[9][i] + r[-9][i])
- 22*(r[10][i] + r[-10][i])
+ (r[11][i] + r[-11][i])
- 705432*r0[i]
- 568744368255469486080000*r24[i]
- 166357727714724824678400000*r26[i]
- 37042320704478727628390400000*r28[i]
- 6988909951599209517839155200000*r30[i]
- 1180836611760352104108962611200000*r32[i]
- 184607985589364774573429361868800000*r34[i]
- 27272218262298384682708194086092800000*r36[i]
- 3861838803337560097698395778726297600000*r38[i]
- 529471212011799260411940801849645465600000*r40[i]
- 70801221927358337925257947461388534087680000*r42[i]
- 9284304296436839352157882253583122352046080000*r44[i]
- 1198819215976330165063918942164935021513932800000*r46[i]
- 152905877736629296164560458459124226796014796800000*r48[i]
) // 1124000727777607680000 for i in range(len(r0))]
r20 = [(-167960*(r[1][i] + r[-1][i])
+ 125970*(r[2][i] + r[-2][i])
- 77520*(r[3][i] + r[-3][i])
+ 38760*(r[4][i] + r[-4][i])
- 15504*(r[5][i] + r[-5][i])
+ 4845*(r[6][i] + r[-6][i])
- 1140*(r[7][i] + r[-7][i])
+ 190*(r[8][i] + r[-8][i])
- 20*(r[9][i] + r[-9][i])
+ (r[10][i] + r[-10][i])
+ 184756*r0[i]
- 936667273148006400000*r22[i]
- 211124803367560642560000*r24[i]
- 36608302274885332992000000*r26[i]
- 5425950533240873322086400000*r28[i]
- 725494605231272191451136000000*r30[i]
- 90317652741043657957240012800000*r32[i]
- 10681064948020015063470219264000000*r34[i]
- 1216234618180639720975550420582400000*r36[i]
- 134607612138429628983625351999488000000*r38[i]
- 14578366393789236829898507440652451840000*r40[i]
- 1552719574083291045891061928041363046400000*r42[i]
- 163243281617906068079686557318998305013760000*r44[i]
- 16988641998903346735554689301227465785344000000*r46[i]
- 1753883399302689292116989257696255397727436800000*r48[i]
) // 2432902008176640000 for i in range(len(r0))]
r18 = [(43758*(r[1][i] + r[-1][i])
- 31824*(r[2][i] + r[-2][i])
+ 18564*(r[3][i] + r[-3][i])
- 8568*(r[4][i] + r[-4][i])
+ 3060*(r[5][i] + r[-5][i])
- 816*(r[6][i] + r[-6][i])
+ 153*(r[7][i] + r[-7][i])
- 18*(r[8][i] + r[-8][i])
+ (r[9][i] + r[-9][i])
- 48620*r0[i]
- 1824676506132480000*r20[i]
- 309100200138842112000*r22[i]
- 40778478784550707200000*r24[i]
- 4645053436190368481280000*r26[i]
- 481314610282065419059200000*r28[i]
- 46758400573464312663490560000*r30[i]
- 4340262299778024388805836800000*r32[i]
- 389810850996416354285601300480000*r34[i]
- 34168816632541202331763973529600000*r36[i]
- 2941066263016510346147295370272768000*r38[i]
- 249691933432545691845292589410836480000*r40[i]
- 20977168972570956554158853986478948352000*r42[i]
- 1748194308191420862068509392967461273600000*r44[i]
- 144787366874617417267158756772391629455360000*r46[i]
- 11933738665455945947029762024119178565222400000*r48[i]
) // 6402373705728000 for i in range(len(r0))]
r16 = [(-11440*(r[1][i] + r[-1][i])
+ 8008*(r[2][i] + r[-2][i])
- 4368*(r[3][i] + r[-3][i])
+ 1820*(r[4][i] + r[-4][i])
- 560*(r[5][i] + r[-5][i])
+ 120*(r[6][i] + r[-6][i])
- 16*(r[7][i] + r[-7][i])
+ (r[8][i] + r[-8][i])
+ 12870*r0[i]
- 4268249137152000*r18[i]
- 527128768438272000*r20[i]
- 51442361350668288000*r22[i]
- 4385609982489415680000*r24[i]
- 343350594609952849920000*r26[i]
- 25398422028160175554560000*r28[i]
- 1806640043553643996938240000*r30[i]
- 124998708216981630040289280000*r32[i]
- 8477574188991756975915909120000*r34[i]
- 566640901244029272138606256128000*r36[i]
- 37469170353622071265887792218112000*r38[i]
- 2457916223969789263693314523533312000*r40[i]
- 160273272592069873142621634191720448000*r42[i]
- 10404012781412834769965673013161000960000*r44[i]
- 673078263437696563365695181553779671040000*r46[i]
- 43432367177206668920840929822030938501120000*r48[i]
) // 20922789888000 for i in range(len(r0))]
r14 = [(3003*(r[1][i] + r[-1][i])
- 2002*(r[2][i] + r[-2][i])
+ 1001*(r[3][i] + r[-3][i])
- 364*(r[4][i] + r[-4][i])
+ 91*(r[5][i] + r[-5][i])
- 14*(r[6][i] + r[-6][i])
+ (r[7][i] + r[-7][i])
- 3432*r0[i]
- 12204960768000*r16[i]
- 1058170098585600*r18[i]
- 73775500710912000*r20[i]
- 4555411900194355200*r22[i]
- 261131482210959360000*r24[i]
- 14266599888013304832000*r26[i]
- 754754307297469839360000*r28[i]
- 39057272623118392651008000*r30[i]
- 1990236929603886055572480000*r32[i]
- 100317304785653440333283635200*r34[i]
- 5017302808350824370904132608000*r36[i]
- 249538838908236261152065923225600*r38[i]
- 12360976075014001109372936189952000*r40[i]
- 610513898001512036824535103712051200*r42[i]
- 30089355946979742032883786297815040000*r44[i]
- 1480659654975370272651825844120998144000*r46[i]
- 72778719754993922352940597980542622720000*r48[i]
) // 87178291200 for i in range(len(r0))]
r12 = [(-792*(r[1][i] + r[-1][i])
+ 495*(r[2][i] + r[-2][i])
- 220*(r[3][i] + r[-3][i])
+ 66*(r[4][i] + r[-4][i])
- 12*(r[5][i] + r[-5][i])
+ (r[6][i] + r[-6][i])
+ 924*r0[i]
- 43589145600*r14[i]
- 2528170444800*r16[i]
- 120467944396800*r18[i]
- 5167100908569600*r20[i]
- 208331313744153600*r22[i]
- 8083281646573056000*r24[i]
- 305994026290208256000*r26[i]
- 11397316294188849024000*r28[i]
- 419948192698268217984000*r30[i]
- 15360962830016613243033600*r32[i]
- 559092713482449420732057600*r34[i]
- 20280226917834433943755084800*r36[i]
- 733917409397935785284098636800*r38[i]
- 26516869922120782776160606617600*r40[i]
- 957005191789297958689924263321600*r42[i]
- 34512162491005016706155579824512000*r44[i]
- 1243937698905379082423800102273152000*r46[i]
- 44819260744500257106087286005881088000*r48[i]
) // 479001600 for i in range(len(r0))]
r10 = [(210*(r[1][i] + r[-1][i])
- 120*(r[2][i] + r[-2][i])
+ 45*(r[3][i] + r[-3][i])
- 10*(r[4][i] + r[-4][i])
+ (r[5][i] + r[-5][i])
- 252*r0[i]
- 199584000*r12[i]
- 7264857600*r14[i]
- 223134912000*r16[i]
- 6289809926400*r18[i]
- 169058189664000*r20[i]
- 4419351149875200*r22[i]
- 113605204648320000*r24[i]
- 2890388998040544000*r26[i]
- 73066712935376160000*r28[i]
- 1839605249083010572800*r30[i]
- 46197360620085939264000*r32[i]
- 1158251761107990889401600*r34[i]
- 29009396635576994764512000*r36[i]
- 726084725720412923735270400*r38[i]
- 18165716613255899607139584000*r40[i]
- 454360504471895403926563219200*r42[i]
- 11362494160594553046963852960000*r44[i]
- 284118059898561657806684273088000*r46[i]
- 7103842801529696381323903273920000*r48[i]
) // 3628800 for i in range(len(r0))]
r8 = [(-56*(r[1][i] + r[-1][i])
+ 28*(r[2][i] + r[-2][i])
- 8*(r[3][i] + r[-3][i])
+ (r[4][i] + r[-4][i])
+ 70*r0[i]
- 1209600*r10[i]
- 25280640*r12[i]
- 461260800*r14[i]
- 7904856960*r16[i]
- 131254905600*r18[i]
- 2143293425280*r20[i]
- 34682510016000*r22[i]
- 558432020361600*r24[i]
- 8966533159584000*r26[i]
- 143749174428961920*r28[i]
- 2302548811229721600*r30[i]
- 36863840064915642240*r32[i]
- 590028976413583660800*r34[i]
- 9442331455422829138560*r36[i]
- 151094113839739041753600*r38[i]
- 2417657116643486089706880*r40[i]
- 38683875524088319997472000*r42[i]
- 618954263309240362088323200*r44[i]
- 9903378507277068408849408000*r46[i]
- 158455048765455207825625883520*r48[i]
) // 40320 for i in range(len(r0))]
r6 = [(15*(r[1][i] + r[-1][i])
- 6*(r[2][i] + r[-2][i])
+ (r[3][i] + r[-3][i])
- 20*r0[i]
- 10080*r8[i]
- 105840*r10[i]
- 1013760*r12[i]
- 9369360*r14[i]
- 85307040*r16[i]
- 771695280*r18[i]
- 6960985920*r20[i]
- 62711787600*r22[i]
- 564657746400*r24[i]
- 5082926350320*r26[i]
- 45750363684480*r28[i]
- 411769379287440*r30[i]
- 3705988838096160*r32[i]
- 33354157240902960*r34[i]
- 300188445960277440*r36[i]
- 2701700136811100880*r38[i]
- 24315317723974324320*r40[i]
- 218837925486466585200*r42[i]
- 1969541593260989932800*r44[i]
- 17725875394880072059920*r46[i]
- 159532882776045299198880*r48[i]
) // 720 for i in range(len(r0))]
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
- 504*r8[i]
- 2040*r10[i]
- 8184*r12[i]
- 32760*r14[i]
- 131064*r16[i]
- 524280*r18[i]
- 2097144*r20[i]
- 8388600*r22[i]
- 33554424*r24[i]
- 134217720*r26[i]
- 536870904*r28[i]
- 2147483640*r30[i]
- 8589934584*r32[i]
- 34359738360*r34[i]
- 137438953464*r36[i]
- 549755813880*r38[i]
- 2199023255544*r40[i]
- 8796093022200*r42[i]
- 35184372088824*r44[i]
- 140737488355320*r46[i]
- 562949953421304*r48[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
- 2*r8[i]
- 2*r10[i]
- 2*r12[i]
- 2*r14[i]
- 2*r16[i]
- 2*r18[i]
- 2*r20[i]
- 2*r22[i]
- 2*r24[i]
- 2*r26[i]
- 2*r28[i]
- 2*r30[i]
- 2*r32[i]
- 2*r34[i]
- 2*r36[i]
- 2*r38[i]
- 2*r40[i]
- 2*r42[i]
- 2*r44[i]
- 2*r46[i]
- 2*r48[i]
) // 2 for i in range(len(r0))]
r47 = [(-1289904147324*r[1][i]
+ 2282138106804*r[2][i]
- 2789279908316*r[3][i]
+ 2789279908316*r[4][i]
- 2404551645100*r[5][i]
+ 1827459250276*r[6][i]
- 1237956266316*r[7][i]
+ 751616304549*r[8][i]
- 409972529754*r[9][i]
+ 200966926350*r[10][i]
- 88425447594*r[11][i]
+ 34834267234*r[12][i]
- 12239066866*r[13][i]
+ 3815417606*r[14][i]
- 1048191650*r[15][i]
+ 251565996*r[16][i]
- 52153926*r[17][i]
+ 9203634*r[18][i]
- 1355574*r[19][i]
+ 162150*r[20][i]
- 15134*r[21][i]
+ 1034*r[22][i]
- 46*r[23][i]
+ r[24][i]
+ 343059613650*r0[i]
- 182965127280*r2[i]
+ 404225281200*r4[i]
- 1973179787280*r6[i]
+ 17237751438000*r8[i]
- 240592045595280*r10[i]
+ 4994170279690800*r12[i]
- 146823806097131280*r14[i]
+ 5903690350090119600*r16[i]
- 316485671150054075280*r18[i]
+ 22198064042219526404400*r20[i]
- 2009394413056841321867280*r22[i]
+ 232532372014701449341825200*r24[i]
- 34201309524439700202831707280*r26[i]
+ 6378595465863797572545515262000*r28[i]
- 1510321457529226404281297600555280*r30[i]
+ 456430932151854961874111940707194800*r32[i]
- 177879954967657922123999080680411131280*r34[i]
+ 90948410673639301600046982211812755703600*r36[i]
- 62713181699432641518049958716708665011915280*r38[i]
+ 61017960828891287286335064536456771132612468400*r40[i]
- 90771056129445230547328475921502515772170837147280*r42[i]
+ 244690112718607318914399753695429565221879804118769200*r44[i]
- 2142766872532178730068138061640892672650431299718846827280*r46[i]
- 20243597746218463146623496754059816935278614102767681978514000*r48[i]
) // 258623241511168180642964355153611979969197632389120000000000 for i in range(len(r0))]
r45 = [(343059613650*r[1][i]
- 603784920024*r[2][i]
+ 731508653106*r[3][i]
- 722477682080*r[4][i]
+ 612815891050*r[5][i]
- 456442180920*r[6][i]
+ 301758997386*r[7][i]
- 177996090624*r[8][i]
+ 93865125915*r[9][i]
- 44246187300*r[10][i]
+ 18609425835*r[11][i]
- 6960408624*r[12][i]
+ 2304024151*r[13][i]
- 670609940*r[14][i]
+ 170173575*r[15][i]
- 37234560*r[16][i]
+ 6923301*r[17][i]
- 1072764*r[18][i]
+ 134805*r[19][i]
- 13200*r[20][i]
+ 945*r[21][i]
- 44*r[22][i]
+ r[23][i]
- 91482563640*r0[i]
+ 48932534040*r2[i]
- 108606356040*r4[i]
+ 533667580440*r6[i]
- 4703763586440*r8[i]
+ 66408505338840*r10[i]
- 1398457857168840*r12[i]
+ 41847457290489240*r14[i]
- 1719246675671583240*r16[i]
+ 94585481325000311640*r18[i]
- 6843422433568588589640*r20[i]
+ 642897110978465333366040*r22[i]
- 77770562351946223415228040*r24[i]
+ 12062233927817328810997492440*r26[i]
- 2397961353314881501418831818440*r28[i]
+ 613494954527608404597659277810840*r30[i]
- 203877970345571868715766678319960840*r32[i]
+ 89457569257636570186619080797284721240*r34[i]
- 53237495951641479759332571910597970535240*r36[i]
+ 44930968310714379648812137260536985281903640*r38[i]
- 58241166312158469946465066186170960196371701640*r40[i]
+ 137360888551881485527132727024151255460985294318040*r42[i]
- 1056294346650368430047563515157012073181421862576900040*r44[i]
- 8792490299555933486634712872596976297794618720689003795560*r46[i]
- 517246483022336361285928710307223959938395264778240000000000*r47[i]
- 26309260636200890673464765332665424581880256812272026952850440*r48[i]
) // 119622220865480194561963161495657715064383733760000000000 for i in range(len(r0))]
r43 = [(-91482563640*r[1][i]
+ 160094486370*r[2][i]
- 192113383644*r[3][i]
+ 187187399448*r[4][i]
- 155989499540*r[5][i]
+ 113649492522*r[6][i]
- 73153696336*r[7][i]
+ 41802112192*r[8][i]
- 21238169904*r[9][i]
+ 9586673915*r[10][i]
- 3834669566*r[11][i]
+ 1353412788*r[12][i]
- 418913482*r[13][i]
+ 112784399*r[14][i]
- 26127660*r[15][i]
+ 5133856*r[16][i]
- 839188*r[17][i]
+ 111069*r[18][i]
- 11438*r[19][i]
+ 860*r[20][i]
- 42*r[21][i]
+ r[22][i]
+ 24466267020*r0[i]
- 13128240840*r2[i]
+ 29286075720*r4[i]
- 144956522040*r6[i]
+ 1290252243720*r8[i]
- 18448766253240*r10[i]
+ 394763466531720*r12[i]
- 12048763425424440*r14[i]
+ 507104531694579720*r16[i]
- 28726839421461491640*r18[i]
+ 2153064433503155907720*r20[i]
- 211041986898764840790840*r22[i]
+ 26870132026261051008915720*r24[i]
- 4433779344005175981028538040*r26[i]
+ 950513389106656928711222883720*r28[i]
- 266877172369028643812085068829240*r30[i]
+ 99651017964870751887504875569971720*r32[i]
- 50788156610571325953562659420384640440*r34[i]
+ 36915961449056930526009630202648137219720*r36[i]
- 41419014418447665040750851917674255257827640*r38[i]
+ 84934578551016826327683205574058431012558547720*r40[i]
- 570180937724400876712836731188276811777920749126840*r42[i]
- 4158439692009034639969470592464099450041235634033244280*r44[i]
- 229275923325503706243762726200010620540068823040000000000*r45[i]
- 10938400640270606999512627385384658646639850257084618154040*r46[i]
- 469832222078622194834718578529061763610709032173568000000000*r47[i]
- 18609787245585710799825274640865231563879706109002975534476280*r48[i]
) // 60415263063373835637355132068513997507264512000000000 for i in range(len(r0))]
r41 = [(24466267020*r[1][i]
- 42550029600*r[2][i]
+ 50528160150*r[3][i]
- 48507033744*r[4][i]
+ 39645171810*r[5][i]
- 28192122176*r[6][i]
+ 17620076360*r[7][i]
- 9721421440*r[8][i]
+ 4739192952*r[9][i]
- 2038362560*r[10][i]
+ 770755843*r[11][i]
- 254795320*r[12][i]
+ 73066305*r[13][i]
- 17985552*r[14][i]
+ 3746990*r[15][i]
- 648128*r[16][i]
+ 90610*r[17][i]
- 9840*r[18][i]
+ 779*r[19][i]
- 40*r[20][i]
+ r[21][i]
- 6564120420*r0[i]
+ 3534526380*r2[i]
- 7928802420*r4[i]
+ 39562131180*r6[i]
- 355997149620*r8[i]
+ 5162772055980*r10[i]
- 112466379416820*r12[i]
+ 3509804003100780*r14[i]
- 151808102304340020*r16[i]
+ 8890838711788769580*r18[i]
- 693867758978013455220*r20[i]
+ 71436574576557715366380*r22[i]
- 9656103679244476561098420*r24[i]
+ 1714541855816811795973995180*r26[i]
- 402505898503128791422102405620*r28[i]
+ 126699650825847516884027712559980*r30[i]
- 54827934277723571354991704981312820*r32[i]
+ 34051732695777105364083032869387764780*r34[i]
- 32827430653262026254340815579045378556020*r36[i]
+ 58129225653125966892251726413185365757113580*r38[i]
- 338476895760295138790385051321218766549279671220*r40[i]
- 2149763077602671437231704105519918866633843849089620*r42[i]
- 110761315616185365335151075458942328763318272000000000*r43[i]
- 4942256826876098689793689711313418888604591478522994420*r44[i]
- 198705800215436545411261029373342537801392979968000000000*r45[i]
- 7372979698612811191617476736621847607367673634869335740820*r46[i]
- 256536466678869072307088584563086803940345640910848000000000*r47[i]
- 8465458808946796165763451715680655749443289544616664687661620*r48[i]
) // 33452526613163807108170062053440751665152000000000 for i in range(len(r0))]
r39 = [(-6564120420*r[1][i]
+ 11338026180*r[2][i]
- 13309856820*r[3][i]
+ 12570420330*r[4][i]
- 10056336264*r[5][i]
+ 6962078952*r[6][i]
- 4211628008*r[7][i]
+ 2234741392*r[8][i]
- 1040310648*r[9][i]
+ 423830264*r[10][i]
- 150391384*r[11][i]
+ 46142811*r[12][i]
- 12118314*r[13][i]
+ 2686866*r[14][i]
- 493506*r[15][i]
+ 73112*r[16][i]
- 8398*r[17][i]
+ 702*r[18][i]
- 38*r[19][i]
+ r[20][i]
+ 1767263190*r0[i]
- 955277400*r2[i]
+ 2156197560*r4[i]
- 10855425000*r6[i]
+ 98876533560*r8[i]
- 1456859058600*r10[i]
+ 32382608125560*r12[i]
- 1036360772970600*r14[i]
+ 46242812090245560*r16[i]
- 2813858311510281000*r18[i]
+ 230141619686501005560*r20[i]
- 25097337236284407949800*r22[i]
+ 3642002181929040219157560*r24[i]
- 706474912755087069174777000*r26[i]
+ 185490702479102020671448093560*r28[i]
- 67501512373123369695638979402600*r30[i]
+ 35506616897715366055874618759845560*r32[i]
- 29173319982987640073110629923442306600*r34[i]
+ 44272025958057634433180503709478279085560*r36[i]
- 222019441630075420847480526017947263931809000*r38[i]
- 1219813882056330049405575791394671579625372874440*r40[i]
- 58541921573036662439297608593521315414016000000000*r41[i]
- 2435494701008122308521041585840935773426259964069800*r42[i]
- 91378085383352926401499637253627421229737574400000000*r43[i]
- 3166734413390519310621011935324774315544541946854082440*r44[i]
- 102992200477964363280928335737465088274348376064000000000*r45[i]
- 3179252903572284408695210045628305460118381385145907089000*r46[i]
- 93933517845624637462463708669855295641358690995404800000000*r47[i]
- 2673604876174888392329293291823128228151672865125704677946440*r48[i]
) // 20397882081197443358640281739902897356800000000 for i in range(len(r0))]
r37 = [(1767263190*r[1][i]
- 3029594040*r[2][i]
+ 3511574910*r[3][i]
- 3257112960*r[4][i]
+ 2544619500*r[5][i]
- 1709984304*r[6][i]
+ 997490844*r[7][i]
- 506662016*r[8][i]
+ 223926516*r[9][i]
- 85795600*r[10][i]
+ 28312548*r[11][i]
- 7970688*r[12][i]
+ 1888887*r[13][i]
- 369852*r[14][i]
+ 58275*r[15][i]
- 7104*r[16][i]
+ 629*r[17][i]
- 36*r[18][i]
+ r[19][i]
- 477638700*r0[i]
+ 259289580*r2[i]
- 589294500*r4[i]
+ 2996657580*r6[i]
- 27670359300*r8[i]
+ 415064933580*r10[i]
- 9439543875300*r12[i]
+ 310922483993580*r14[i]
- 14379880666402500*r16[i]
+ 914767168887053580*r18[i]
- 79051272004645620900*r20[i]
+ 9231401536061270849580*r22[i]
- 1459700260139475814330500*r24[i]
+ 315843905250429722227637580*r26[i]
- 95612546130070295522414451300*r28[i]
+ 42177612582297377823299737193580*r30[i]
- 29268533564152352561039458453023300*r32[i]
+ 37747202396256876155482291281278813580*r34[i]
- 161759954125032708920885781040309430206500*r36[i]
- 763162014442847423121851269222329739576686420*r38[i]
- 33996470135329072264400469566504828928000000000*r39[i]
- 1314149222797294391875041342296266627244339280900*r40[i]
- 45857838565545385577449793398258363740979200000000*r41[i]
- 1479444354242422663436299123473954120225396734970420*r42[i]
- 44831961082741695492799244828619514023247872000000000*r43[i]
- 1290525734288850664269099373480698875776359383538646500*r44[i]
- 35584775745235419804380819416241066350620337766400000000*r45[i]
- 945953923580279776552772789184754415724912490598746182420*r46[i]
- 24366115407876526559068567586678948554722823372800000000000*r47[i]
- 610645775114510996953480313967173146186867766220019295823300*r48[i]
) // 13763753091226345046315979581580902400000000 for i in range(len(r0))]
r35 = [(-477638700*r[1][i]
+ 811985790*r[2][i]
- 927983760*r[3][i]
+ 843621600*r[4][i]
- 641886000*r[5][i]
+ 417225900*r[6][i]
- 233646504*r[7][i]
+ 112971936*r[8][i]
- 47071640*r[9][i]
+ 16811300*r[10][i]
- 5101360*r[11][i]
+ 1298528*r[12][i]
- 272272*r[13][i]
+ 45815*r[14][i]
- 5950*r[15][i]
+ 560*r[16][i]
- 34*r[17][i]
+ r[18][i]
+ 129644790*r0[i]
- 70715340*r2[i]
+ 161960940*r4[i]
- 832930740*r6[i]
+ 7810859340*r8[i]
- 119578066740*r10[i]
+ 2791740107340*r12[i]
- 95062235276340*r14[i]
+ 4584012079172940*r16[i]
- 307268933913567540*r18[i]
+ 28355038085389144140*r20[i]
- 3597774935929125068340*r22[i]
+ 632729503874459828228940*r24[i]
- 157381528472579148083026740*r26[i]
+ 57577884185625191071239755340*r28[i]
- 33404393172944223690128125810740*r30[i]
+ 36271128388074981554067219056171340*r32[i]
- 131671692334895976886647813958596908340*r34[i]
- 529104107360143104505564190890974500955060*r36[i]
- 21792609061108379656666967670836428800000000*r37[i]
- 779765567254824678774814590170424618060927540*r38[i]
- 25214048683702395262763681595157748121600000000*r39[i]
- 754531895504954495472529428607358759602244935860*r40[i]
- 21229190210645503978483385444330514048614400000000*r41[i]
- 567902644449952014090537079509460539320563935596340*r42[i]
- 14564893239013264062672891916748815156327219200000000*r43[i]
- 360416016142646161224945882401067658836071135991963060*r44[i]
- 8648657180064969977242561394456399100712373452800000000*r45[i]
- 202069375902424923136583586389997599181812580415819762740*r46[i]
- 4612127517564454653650814843765113002002883805184000000000*r47[i]
- 103121612921980129969364006657783463883530860291974593108660*r48[i]
) // 10333147966386144929666651337523200000000 for i in range(len(r0))]
r33 = [(129644790*r[1][i]
- 218349120*r[2][i]
+ 245642760*r[3][i]
- 218349120*r[4][i]
+ 161280600*r[5][i]
- 100975680*r[6][i]
+ 53993940*r[7][i]
- 24682944*r[8][i]
+ 9612108*r[9][i]
- 3164480*r[10][i]
+ 870232*r[11][i]
- 196416*r[12][i]
+ 35464*r[13][i]
- 4928*r[14][i]
+ 495*r[15][i]
- 32*r[16][i]
+ r[17][i]
- 35357670*r0[i]
+ 19389690*r2[i]
- 44796870*r4[i]
+ 233344890*r6[i]
- 2227139910*r8[i]
+ 34903389690*r10[i]
- 839988260550*r12[i]
+ 29734601940090*r14[i]
- 1506293149214790*r16[i]
+ 107487540061668090*r18[i]
- 10743535525710258630*r20[i]
+ 1511267716903778445690*r22[i]
- 304525956073869018848070*r24[i]
+ 91234873454404063067344890*r26[i]
- 43747586259736794619504039110*r28[i]
+ 39574917458915050445099774637690*r30[i]
- 120523981455993504966525708346887750*r32[i]
- 408775192473644376465790167368394203910*r34[i]
- 15499721949579217394499977006284800000000*r35[i]
- 511206585269023792365556128001469646849990*r36[i]
- 15254826342775865759666877369585500160000000*r37[i]
- 421754497238984285335705463354740490210507910*r38[i]
- 10974654148845317574241976981091935846400000000*r39[i]
- 271793538072560300468434911462753194293644181830*r40[i]
- 6459357656104303171129642884693889583677440000000*r41[i]
- 148248369194001435848413334991598692517822202402310*r42[i]
- 3302211571953506236081129759184691588287692800000000*r43[i]
- 71676123253955938571177412178194687158760951558339270*r44[i]
- 1520976967414625530272457942824571170900903198720000000*r45[i]
- 31639609352600382246311701401196841805566037174158815110*r46[i]
- 646685006086394734265332084740666732219400716288000000000*r47[i]
- 13012191241624225597793637611655297834798932917962602378310*r48[i]
) // 8683317618811886495518194401280000000 for i in range(len(r0))]
r31 = [(-35357670*r[1][i]
+ 58929450*r[2][i]
- 65132550*r[3][i]
+ 56448210*r[4][i]
- 40320150*r[5][i]
+ 24192090*r[6][i]
- 12271350*r[7][i]
+ 5259150*r[8][i]
- 1893294*r[9][i]
+ 566370*r[10][i]
- 138446*r[11][i]
+ 26970*r[12][i]
- 4030*r[13][i]
+ 434*r[14][i]
- 30*r[15][i]
+ r[16][i]
+ 9694845*r0[i]
- 5348880*r2[i]
+ 12480720*r4[i]
- 65969520*r6[i]
+ 642563280*r8[i]
- 10347602160*r10[i]
+ 258040917840*r12[i]
- 9564008626800*r14[i]
+ 514021079720400*r16[i]
- 39590373677587440*r18[i]
+ 4371353677873146960*r20[i]
- 701971899866535028080*r22[i]
+ 169737570795219895373520*r24[i]
- 66396273378844288679892720*r26[i]
+ 49448835121192219782326176080*r28[i]
- 124963193751534047864734415925360*r30[i]
- 354113410826574103722030528083469360*r32[i]
- 12301366626650172535317442068480000000*r33[i]
- 372225904019072507165665501545458070000*r34[i]
- 10203983616806318118045818195804160000000*r35[i]
- 259484653500223872483011119661283865786800*r36[i]
- 6217811871006716259183948315607695360000000*r37[i]
- 141956901865997956445469727796622341498870640*r38[i]
- 3113335802166672719861469258672651632640000000*r39[i]
- 66003822624082868383556482555741495612650600240*r40[i]
- 1359334478541063086765779323397876419133440000000*r41[i]
- 27303356587963564025554884815930553997263574871280*r42[i]
- 536588847651574079588079017443366763149393920000000*r43[i]
- 10345842549438556817463474698578198121859964179733680*r44[i]
- 196138884946560564409651268242770514989620920320000000*r45[i]
- 3663204676820752962698443093474820599422678195673015920*r46[i]
- 67509422521578235356394063172809938341831560396800000000*r47[i]
- 1229367058216339817971318602200240769989331897298761411120*r48[i]
) // 8222838654177922817725562880000000 for i in range(len(r0))]
r29 = [(9694845*r[1][i]
- 15967980*r[2][i]
+ 17298645*r[3][i]
- 14567280*r[4][i]
+ 10015005*r[5][i]
- 5722860*r[6][i]
+ 2731365*r[7][i]
- 1085760*r[8][i]
+ 356265*r[9][i]
- 95004*r[10][i]
+ 20097*r[11][i]
- 3248*r[12][i]
+ 377*r[13][i]
- 28*r[14][i]
+ r[15][i]
- 2674440*r0[i]
+ 1485800*r2[i]
- 3506488*r4[i]
+ 18850280*r6[i]
- 188004088*r8[i]
+ 3125835560*r10[i]
- 81314498488*r12[i]
+ 3185384180840*r14[i]
- 184064268909688*r16[i]
+ 15598375633694120*r18[i]
- 1958105850969957688*r20[i]
+ 375744491571024583400*r22[i]
- 118117302690774819242488*r24[i]
+ 71447614092662750198256680*r26[i]
- 147980747895225006590333244088*r28[i]
- 346368637877614395127589803878040*r30[i]
- 10963784872237230423634083840000000*r31[i]
- 302766527792977996357877082103322488*r32[i]
- 7585842753100939730112422608896000000*r33[i]
- 176553572119721839407097582006071612760*r34[i]
- 3876980715165912710714213825249280000000*r35[i]
- 81213796311764134505181592648745883717688*r36[i]
- 1636103186224681029581052139652775936000000*r37[i]
- 31895543813319775842490572300866856117139480*r38[i]
- 604645713103650398366928164707180216320000000*r39[i]
- 11189653759353064214370349765226592602607549688*r40[i]
- 202794861446303149866709151240333763280896000000*r41[i]
- 3608799207440735942926262565268791718882246250200*r42[i]
- 63195849406190967779680687932546907121909760000000*r43[i]
- 1091041918456432706911605989934195570136050930818488*r44[i]
- 18599858037912613836046600540495361832783446016000000*r45[i]
- 313534044032502214538190505667405050039920730329536920*r46[i]
- 5232130701886884640147951658064894118305202176000000000*r47[i]
- 86524070613240340349034843422074253070890184188704404088*r48[i]
) // 8841761993739701954543616000000 for i in range(len(r0))]
r27 = [(-2674440*r[1][i]
+ 4345965*r[2][i]
- 4601610*r[3][i]
+ 3749460*r[4][i]
- 2466750*r[5][i]
+ 1332045*r[6][i]
- 592020*r[7][i]
+ 215280*r[8][i]
- 63180*r[9][i]
+ 14625*r[10][i]
- 2574*r[11][i]
+ 324*r[12][i]
- 26*r[13][i]
+ r[14][i]
+ 742900*r0[i]
- 416024*r2[i]
+ 994840*r4[i]
- 5454824*r6[i]
+ 55944280*r8[i]
- 966290024*r10[i]
+ 26454613720*r12[i]
- 1109329691624*r14[i]
+ 70212852387160*r16[i]
- 6733670404619624*r18[i]
+ 1005318113348848600*r20[i]
- 249581050854994274024*r22[i]
+ 120719220687299365182040*r24[i]
- 202039976682357297272094824*r26[i]
- 385557844336439370252173428520*r28[i]
- 11052202492174627443179520000000*r29[i]
- 276888650579451671741587901762024*r30[i]
- 6304176301536407493589598208000000*r31[i]
- 133535841584115505205141919375399080*r32[i]
- 2672618344480543437732658544640000000*r33[i]
- 51095126335993498323380094454901195624*r34[i]
- 940618873537377672007825158832128000000*r35[i]
- 16776403501444391106926987629186000345640*r36[i]
- 291283862319085180678807183848898560000000*r37[i]
- 4942310839108515578583708125038854650555624*r38[i]
- 82203911327563805707081667710859870208000000*r39[i]
- 1343752600475734599375534320311340373516684200*r40[i]
- 21634243326074826428166414905753461063680000000*r41[i]
- 343672532983087585902951862991031321905844242024*r42[i]
- 5395063942758184834505475068561955332947968000000*r43[i]
- 83804941354439477195910293019964343299641959230760*r44[i]
- 1289609166695254343642200168046105549173555200000000*r45[i]
- 19678461460501652805347265575009996073778349586894824*r46[i]
- 298018526228473595475945631789329672119214145536000000*r47[i]
- 4482734138598481574681074400900490010744661138946801320*r48[i]
) // 10888869450418352160768000000 for i in range(len(r0))]
r25 = [(742900*r[1][i]
- 1188640*r[2][i]
+ 1225785*r[3][i]
- 961400*r[4][i]
+ 600875*r[5][i]
- 303600*r[6][i]
+ 123970*r[7][i]
- 40480*r[8][i]
+ 10350*r[9][i]
- 2000*r[10][i]
+ 275*r[11][i]
- 24*r[12][i]
+ r[13][i]
- 208012*r0[i]
+ 117572*r2[i]
- 285532*r4[i]
+ 1602692*r6[i]
- 16996252*r8[i]
+ 307475012*r10[i]
- 8966430172*r12[i]
+ 409745686532*r14[i]
- 29195711499292*r16[i]
+ 3312133208909252*r18[i]
- 636215671041835612*r20[i]
+ 241648300078174135172*r22[i]
- 321511316149669476991132*r24[i]
- 492817676505266866078123708*r26[i]
- 12703681025488077520896000000*r27[i]
- 286779648275654636997381637852*r28[i]
- 5894507995826467969695744000000*r29[i]
- 112914054231542703053832892635388*r30[i]
- 2047008246979213061238030336000000*r31[i]
- 35501568925223446300815211192767772*r32[i]
- 593711792050129855003168210944000000*r33[i]
- 9632134956680435093368218113996247868*r34[i]
- 152311343455497374594406627803136000000*r35[i]
- 2356318736218539774396037820111678892892*r36[i]
- 35772470531371951985805498114637824000000*r37[i]
- 534273042749950920189640352996759062689148*r38[i]
- 7866491034006154572049014294052601856000000*r39[i]
- 114383224059606274110181105712262975351245212*r40[i]
- 1644946226278516886873016733667061202944000000*r41[i]
- 23426103831558846665144911501028780920365367228*r42[i]
- 330735945747364837719554208843251145179136000000*r43[i]
- 4633465747908141417306051485893140722291346976732*r44[i]
- 64465996518808752310647291812383168776634368000000*r45[i]
- 891389875128429665004288245297052393567100598170108*r46[i]
- 12257190333970097165549309885966019046465339392000000*r47[i]
- 167703402046599761376513697620930939990159551304359452*r48[i]
) // 15511210043330985984000000 for i in range(len(r0))]
r23 = [(-208012*r[1][i]
+ 326876*r[2][i]
- 326876*r[3][i]
+ 245157*r[4][i]
- 144210*r[5][i]
+ 67298*r[6][i]
- 24794*r[7][i]
+ 7084*r[8][i]
- 1518*r[9][i]
+ 230*r[10][i]
- 22*r[11][i]
+ r[12][i]
+ 58786*r0[i]
- 33592*r2[i]
+ 83096*r4[i]
- 479752*r6[i]
+ 5299736*r8[i]
- 101549512*r10[i]
+ 3208453976*r12[i]
- 164071220872*r14[i]
+ 13743680753816*r16[i]
- 1993276972245832*r18[i]
+ 581947914140407256*r20[i]
- 603916464771468176392*r22[i]
- 730803773459954540777704*r24[i]
- 16803810880275234816000000*r25[i]
- 339155768243774227716964552*r26[i]
- 6245976504198304781107200000*r27[i]
- 107413822788261782335458993064*r28[i]
- 1751393992807566623932416000000*r29[i]
- 27365156266821215807862420562312*r30[i]
- 412945663851071412756568473600000*r31[i]
- 6053949680529454447550745704030824*r32[i]
- 86623417665042381831452000256000000*r33[i]
- 1214146547565910406028014931410521672*r34[i]
- 16719755812321492798917963359846400000*r35[i]
- 226758627215029497194516602329808882984*r36[i]
- 3034905857007157810746475187798016000000*r37[i]
- 40151799724774280996886476759684489594632*r38[i]
- 525848735885794606994555529953619148800000*r39[i]
- 6825564942475643900873841059427230143341544*r40[i]
- 87900055843825806396690634755863003136000000*r41[i]
- 1124090333957827218160935737032127911249333192*r42[i]
- 14286036145840157893404384196456208735600640000*r43[i]
- 180556939553256275799275906968519352499771598504*r44[i]
- 2270728203819030041749862616122105872023552000000*r45[i]
- 28430855249825246651314973609548475795532583689352*r46[i]
- 354557703317395919808450352391376751066211942400000*r47[i]
- 4405868085478593275690315869491622501390761293845864*r48[i]
) // 25852016738884976640000 for i in range(len(r0))]
r21 = [(58786*r[1][i]
- 90440*r[2][i]
+ 87210*r[3][i]
- 62016*r[4][i]
+ 33915*r[5][i]
- 14364*r[6][i]
+ 4655*r[7][i]
- 1120*r[8][i]
+ 189*r[9][i]
- 20*r[10][i]
+ r[11][i]
- 16796*r0[i]
+ 9724*r2[i]
- 24596*r4[i]
+ 147004*r6[i]
- 1708916*r8[i]
+ 35240284*r10[i]
- 1237329236*r12[i]
+ 73853629564*r14[i]
- 7850527669556*r16[i]
+ 1717351379730844*r18[i]
- 1359124435588313876*r20[i]
- 1272410676942417239876*r22[i]
- 25852016738884976640000*r23[i]
- 462292539259962003646196*r24[i]
- 7561714896123855667200000*r25[i]
- 115761644587269354830466596*r26[i]
- 1683741850203578528563200000*r27[i]
- 23512975860299444963550050516*r28[i]
- 317677725072691341719961600000*r29[i]
- 4176614976496441445095962733316*r30[i]
- 53674391443652368368589209600000*r31[i]
- 676635955671282540673335079110836*r32[i]
- 8391272072243853389701334630400000*r33[i]
- 102611708232289325546408008313624036*r34[i]
- 1239646284649926576486736094822400000*r35[i]
- 14819283410691765614379616648600811156*r36[i]
- 175538127424434549895381626305740800000*r37[i]
- 2062659648435073986802743885440046722756*r38[i]
- 24066873273263602745997309174983884800000*r39[i]
- 279069134864297423784787795404361206735476*r40[i]
- 3218237360334469905693543066426751549440000*r41[i]
- 36932670876144577834192017462238998576813476*r42[i]
- 422013831656219970552631011526505561456640000*r43[i]
- 4803667893589610545887832027829424971473267796*r44[i]
- 54491782544378643866541770098406137341542400000*r45[i]
- 616254801390825608499920295882691673585117080196*r46[i]
- 6950267169846786189298202657232919399818854400000*r47[i]
- 78194975030419808376759755992062291704460984792116*r48[i]
) // 51090942171709440000 for i in range(len(r0))]
r19 = [(-16796*r[1][i]
+ 25194*r[2][i]
- 23256*r[3][i]
+ 15504*r[4][i]
- 7752*r[5][i]
+ 2907*r[6][i]
- 798*r[7][i]
+ 152*r[8][i]
- 18*r[9][i]
+ r[10][i]
+ 4862*r0[i]
- 2860*r2[i]
+ 7436*r4[i]
- 46420*r6[i]
+ 576236*r8[i]
- 13098580*r10[i]
+ 532310636*r12[i]
- 39968611540*r14[i]
+ 6350631494636*r16[i]
- 3730771315561300*r18[i]
- 2637991952943407764*r20[i]
- 46833363657400320000*r21[i]
- 734121065118879803860*r22[i]
- 10556240168378032128000*r23[i]
- 142438684135271315212564*r24[i]
- 1830415113744266649600000*r25[i]
- 22632897298190126259675220*r26[i]
- 271297526662043666104320000*r27[i]
- 3170344993810020486920015764*r28[i]
- 36274730261563609572556800000*r29[i]
- 407775103607650299563627591380*r30[i]
- 4515882637052182897862000640000*r31[i]
- 49377994276343186011748723193364*r32[i]
- 534053247401000753173510963200000*r33[i]
- 5722063606154183864914875339648340*r34[i]
- 60811730909031986048777521029120000*r35[i]
- 641729418431834160625738740379401364*r36[i]
- 6730380606921481449181267599974400000*r37[i]
- 70207898580127312813466155395513222100*r38[i]
- 728918319689461841494925372032622592000*r39[i]
- 7536441803725213229125462424550696575764*r40[i]
- 77635978704164552294553096402068152320000*r41[i]
- 797177898990753876072852178329776532568660*r42[i]
- 8162164080895303403984327865949915250688000*r43[i]
- 83359491110673172494030048846026790563932564*r44[i]
- 849432099945167336777734465061373289267200000*r45[i]
- 8638438243166451781593809976801426668242424020*r46[i]
- 87694169965134464605849462884812769886371840000*r47[i]
- 888832151283066038746077396233689115965303967764*r48[i]
) // 121645100408832000 for i in range(len(r0))]
r17 = [(4862*r[1][i]
- 7072*r[2][i]
+ 6188*r[3][i]
- 3808*r[4][i]
+ 1700*r[5][i]
- 544*r[6][i]
+ 119*r[7][i]
- 16*r[8][i]
+ r[9][i]
- 1430*r0[i]
+ 858*r2[i]
- 2310*r4[i]
+ 15258*r6[i]
- 206790*r8[i]
+ 5386458*r10[i]
- 272513670*r12[i]
+ 30255826458*r14[i]
- 12765597850950*r16[i]
- 6622557957272742*r18[i]
- 101370917007360000*r19[i]
- 1375210145685786630*r20[i]
- 17172233341046784000*r21[i]
- 201832098313986359142*r22[i]
- 2265471043586150400000*r23[i]
- 24529324224160803328710*r24[i]
- 258058524232798248960000*r25[i]
- 2652208374242713043720742*r26[i]
- 26739700571225856614400000*r27[i]
- 265323404171486113659725190*r28[i]
- 2597688920748017370193920000*r29[i]
- 25147613788240222384169485542*r30[i]
- 241125683321001354933657600000*r31[i]
- 2293170112631184981695915264070*r32[i]
- 21656158388689797460311183360000*r33[i]
- 203283794784841444836991831621542*r34[i]
- 1898267590696733462875776307200000*r35[i]
- 17646072330245312137111933794073350*r36[i]
- 163392570167583908119294187237376000*r37[i]
- 1507754227229479379470312529237936742*r38[i]
- 13871774079585871769182921633935360000*r39[i]
- 127291574907112728538906245247680921030*r40[i]
- 1165398276253942030786602999248830464000*r41[i]
- 10648249156718669259487809979675840079142*r42[i]
- 97121906010634492337139410720414515200000*r43[i]
- 884471146488697462546213719879378982015110*r44[i]
- 8043742604145412070397708709577312747520000*r45[i]
- 73065283527546375984492393431422365909536742*r46[i]
- 662985481414219219279431223562176586956800000*r47[i]
- 6010229010788429141870217066922217223929803590*r48[i]
) // 355687428096000 for i in range(len(r0))]
r15 = [(-1430*r[1][i]
+ 2002*r[2][i]
- 1638*r[3][i]
+ 910*r[4][i]
- 350*r[5][i]
+ 90*r[6][i]
- 14*r[7][i]
+ r[8][i]
+ 429*r0[i]
- 264*r2[i]
+ 744*r4[i]
- 5304*r6[i]
+ 81384*r8[i]
- 2605944*r10[i]
+ 192387624*r12[i]
- 55942352184*r14[i]
- 20546119600536*r16[i]
- 266765571072000*r17[i]
- 3083760849804024*r18[i]
- 32945548027392000*r19[i]
- 332500281299403096*r20[i]
- 3215147584416768000*r21[i]
- 30076927429146721464*r22[i]
- 274100623905588480000*r23[i]
- 2446077617962088140056*r24[i]
- 21459412163122053120000*r25[i]
- 185641639183185136464504*r26[i]
- 1587401376760010972160000*r27[i]
- 13442713420403849918131416*r28[i]
- 112915002722102749808640000*r29[i]
- 941961013910760913890393144*r30[i]
- 7812419263561351877518080000*r31[i]
- 64474322285718607792730497176*r32[i]
- 529848386811984810994744320000*r33[i]
- 4338547620121893769542630267384*r34[i]
- 35415056327751829508662891008000*r35[i]
- 288317531175033442515609896757336*r36[i]
- 2341823147101379454117987013632000*r37[i]
- 18983391549723892653716655806647224*r38[i]
- 153619763998111828980832157720832000*r39[i]
- 1241292607509331793516191597844431896*r40[i]
- 10017079537004367071413852136982528000*r41[i]
- 80746194097372251940077615903073292664*r42[i]
- 650250798838302173122854563322562560000*r43[i]
- 5232061257212799699445154857325986640856*r44[i]
- 42067391464856035210355948847111229440000*r45[i]
- 338018548004311349729166172709579357563704*r46[i]
- 2714522948575416807552558113876933656320000*r47[i]
- 21788917503304477212565325243539420555704216*r48[i]
) // 1307674368000 for i in range(len(r0))]
r13 = [(429*r[1][i]
- 572*r[2][i]
+ 429*r[3][i]
- 208*r[4][i]
+ 65*r[5][i]
- 12*r[6][i]
+ r[7][i]
- 132*r0[i]
+ 84*r2[i]
- 252*r4[i]
+ 2004*r6[i]
- 37212*r8[i]
+ 1710324*r10[i]
- 325024572*r12[i]
- 80789566956*r14[i]
- 871782912000*r15[i]
- 8422900930332*r16[i]
- 75583578470400*r17[i]
- 643521842437836*r18[i]
- 5269678622208000*r19[i]
- 41890044885642492*r20[i]
- 325386564299596800*r21[i]
- 2481686964269990316*r22[i]
- 18652248729354240000*r23[i]
- 138536531588626169052*r24[i]
- 1019042849143807488000*r25[i]
- 7436421488952386592396*r26[i]
- 53911021949819274240000*r27[i]
- 388701690499592948238012*r28[i]
- 2789805187365599475072000*r29[i]
- 19946749502047187160692076*r30[i]
- 142159780685991861112320000*r31[i]
- 1010433303980489860989897372*r32[i]
- 7165521770403817166663116800*r33[i]
- 50716588034439244118483617356*r34[i]
- 358378772025058883636009472000*r35[i]
- 2528902640579773012941059115132*r36[i]
- 17824202779159732939433280230400*r37[i]
- 125502611080965065134883934376236*r38[i]
- 882926862501000079240924013568000*r39[i]
- 6206986746547700738292160195379292*r40[i]
- 43608135571536574058895364550860800*r41[i]
- 306213499909407501334225902520456716*r42[i]
- 2149239710498553002348841878415360000*r43[i]
- 15079178774724614117506008765315297852*r44[i]
- 105761403926812162332273274580071296000*r45[i]
- 741573481088337285231858048220674626796*r46[i]
- 5198479982499565882352899855753044480000*r47[i]
- 36434172034715569203746509369098022198812*r48[i]
) // 6227020800 for i in range(len(r0))]
r11 = [(-132*r[1][i]
+ 165*r[2][i]
- 110*r[3][i]
+ 44*r[4][i]
- 10*r[5][i]
+ r[6][i]
+ 42*r0[i]
- 28*r2[i]
+ 92*r4[i]
- 868*r6[i]
+ 22652*r8[i]
- 2620708*r10[i]
- 415790788*r12[i]
- 3632428800*r13[i]
- 28616744548*r14[i]
- 210680870400*r15[i]
- 1479485236228*r16[i]
- 10038995366400*r17[i]
- 66394067988388*r18[i]
- 430591742380800*r19[i]
- 2750479262009668*r20[i]
- 17360942812012800*r21[i]
- 108550450893568228*r22[i]
- 673606803881088000*r23[i]
- 4154688725062207108*r24[i]
- 25499502190850688000*r25[i]
- 155878445775166700068*r26[i]
- 949776357849070752000*r27[i]
- 5771581202353414724548*r28[i]
- 34995682724855684832000*r29[i]
- 211811399872933910999908*r30[i]
- 1280080235834717770252800*r31[i]
- 7726641919200262371657988*r32[i]
- 46591059456870785061004800*r33[i]
- 280704018540064430354883748*r34[i]
- 1690018909819536161979590400*r35[i]
- 10169113413821714748538703428*r36[i]
- 61159784116494648773674886400*r37[i]
- 367684638335977863351585967588*r38[i]
- 2209739160176731898013383884800*r39[i]
- 13276598260065161268654185556868*r40[i]
- 79750432649108163224160355276800*r41[i]
- 478956917715683026467561165467428*r42[i]
- 2876013540917084725512964985376000*r43[i]
- 17267443120712778679894991796314308*r44[i]
- 103661474908781590201983341856096000*r45[i]
- 622252957609245047342724399262599268*r46[i]
- 3734938395375021425507273833823424000*r47[i]
- 22416734056596928549732496421419871748*r48[i]
) // 39916800 for i in range(len(r0))]
r9 = [(42*r[1][i]
- 48*r[2][i]
+ 27*r[3][i]
- 8*r[4][i]
+ r[5][i]
- 14*r0[i]
+ 10*r2[i]
- 38*r4[i]
+ 490*r6[i]
- 31238*r8[i]
- 2922230*r10[i]
- 19958400*r11[i]
- 124075238*r12[i]
- 726485760*r13[i]
- 4084385750*r14[i]
- 22313491200*r15[i]
- 119387268038*r16[i]
- 628980992640*r17[i]
- 3275389222070*r18[i]
- 16905818966400*r19[i]
- 86665431465638*r20[i]
- 441935114987520*r21[i]
- 2244295389943190*r22[i]
- 11360520464832000*r23[i]
- 57360469753884038*r24[i]
- 289038899804054400*r25[i]
- 1454155949521941110*r26[i]
- 7306671293537616000*r27[i]
- 36677059892827099238*r28[i]
- 183960524908301057280*r29[i]
- 922104761587650687830*r30[i]
- 4619736062008593926400*r31[i]
- 23135540444136227047238*r32[i]
- 115825176110799088940160*r33[i]
- 579715876176320506935350*r34[i]
- 2900939663557699476451200*r35[i]
- 14514140349055749129024038*r36[i]
- 72608472572041292373527040*r37[i]
- 363193454272347163609915670*r38[i]
- 1816571661325589960713958400*r39[i]
- 9085275939429279963731685638*r40[i]
- 45436050447189540392656321920*r41[i]
- 227218935892633882388998540790*r42[i]
- 1136249416059455304696385296000*r43[i]
- 5681866032591044240951769048038*r44[i]
- 28411805989856165780668427308800*r45[i]
- 142068933310062230858345890602710*r46[i]
- 710384280152969638132390327392000*r47[i]
- 3552079855654080764219631870487238*r48[i]
) // 362880 for i in range(len(r0))]
r7 = [(-14*r[1][i]
+ 14*r[2][i]
- 6*r[3][i]
+ r[4][i]
+ 5*r0[i]
- 4*r2[i]
+ 20*r4[i]
- 604*r6[i]
- 29740*r8[i]
- 151200*r9[i]
- 708604*r10[i]
- 3160080*r11[i]
- 13645900*r12[i]
- 57657600*r13[i]
- 239967004*r14[i]
- 988107120*r15[i]
- 4037604460*r16[i]
- 16406863200*r17[i]
- 66398623804*r18[i]
- 267911678160*r19[i]
- 1078605601420*r20[i]
- 4335313752000*r21[i]
- 17403958407004*r22[i]
- 69804002545200*r23[i]
- 279780634372780*r24[i]
- 1120816644948000*r25[i]
- 4488349371924604*r26[i]
- 17968646803620240*r27[i]
- 71920337041294540*r28[i]
- 287818601403715200*r29[i]
- 1151686172846664604*r30[i]
- 4607980008114455280*r31[i]
- 18435626012705982700*r32[i]
- 73753622051697957600*r33[i]
- 295047842329672995004*r34[i]
- 1180291431927853642320*r35[i]
- 4721465916019935893260*r36[i]
- 18886764229967380219200*r37[i]
- 75549758619456576163804*r38[i]
- 302207139580435761213360*r39[i]
- 1208852873637267995922220*r40[i]
- 4835484440511039999684000*r41[i]
- 19342156599960850372299004*r42[i]
- 77369282913655045261040400*r43[i]
- 309479101196178257662005580*r44[i]
- 1237922313409633551106176000*r45[i]
- 4951706979513788347008408604*r46[i]
- 19806881095681900978203235440*r47[i]
- 79227683915609817008158719340*r48[i]
) // 5040 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
- 1680*r7[i]
- 5542*r8[i]
- 17640*r9[i]
- 54958*r10[i]
- 168960*r11[i]
- 515062*r12[i]
- 1561560*r13[i]
- 4717438*r14[i]
- 14217840*r15[i]
- 42784582*r16[i]
- 128615880*r17[i]
- 386371918*r18[i]
- 1160164320*r19[i]
- 3482590102*r20[i]
- 10451964600*r21[i]
- 31364282398*r22[i]
- 94109624400*r23[i]
- 282362427622*r24[i]
- 847154391720*r25[i]
- 2541597392878*r26[i]
- 7625060614080*r27[i]
- 22875718713142*r28[i]
- 68628229881240*r29[i]
- 205886837127358*r30[i]
- 617664806349360*r31[i]
- 1853003008982662*r32[i]
- 5559026206817160*r33[i]
- 16677112980189838*r34[i]
- 50031407660046240*r35[i]
- 150094360419092182*r36[i]
- 450283356135183480*r37[i]
- 1350850618161364318*r38[i]
- 4052552953995720720*r39[i]
- 12157661061010417702*r40[i]
- 36472987581077764200*r41[i]
- 109418971539326314798*r42[i]
- 328256932210164988800*r43[i]
- 984770831814867055222*r44[i]
- 2954312565813345343320*r45[i]
- 8862937838177524385278*r46[i]
- 26588813796007549866480*r47[i]
- 79766441950972603020742*r48[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
- 126*r7[i]
- 254*r8[i]
- 510*r9[i]
- 1022*r10[i]
- 2046*r11[i]
- 4094*r12[i]
- 8190*r13[i]
- 16382*r14[i]
- 32766*r15[i]
- 65534*r16[i]
- 131070*r17[i]
- 262142*r18[i]
- 524286*r19[i]
- 1048574*r20[i]
- 2097150*r21[i]
- 4194302*r22[i]
- 8388606*r23[i]
- 16777214*r24[i]
- 33554430*r25[i]
- 67108862*r26[i]
- 134217726*r27[i]
- 268435454*r28[i]
- 536870910*r29[i]
- 1073741822*r30[i]
- 2147483646*r31[i]
- 4294967294*r32[i]
- 8589934590*r33[i]
- 17179869182*r34[i]
- 34359738366*r35[i]
- 68719476734*r36[i]
- 137438953470*r37[i]
- 274877906942*r38[i]
- 549755813886*r39[i]
- 1099511627774*r40[i]
- 2199023255550*r41[i]
- 4398046511102*r42[i]
- 8796093022206*r43[i]
- 17592186044414*r44[i]
- 35184372088830*r45[i]
- 70368744177662*r46[i]
- 140737488355326*r47[i]
- 281474976710654*r48[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
- r7[i]
- r8[i]
- r9[i]
- r10[i]
- r11[i]
- r12[i]
- r13[i]
- r14[i]
- r15[i]
- r16[i]
- r17[i]
- r18[i]
- r19[i]
- r20[i]
- r21[i]
- r22[i]
- r23[i]
- r24[i]
- r25[i]
- r26[i]
- r27[i]
- r28[i]
- r29[i]
- r30[i]
- r31[i]
- r32[i]
- r33[i]
- r34[i]
- r35[i]
- r36[i]
- r37[i]
- r38[i]
- r39[i]
- r40[i]
- r41[i]
- r42[i]
- r43[i]
- r44[i]
- r45[i]
- r46[i]
- r47[i]
- r48[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48)
def natural_interpolate_26(r):
r0 = r[0]
r50 = r['infinity']
r48 = [(-30957699535776*(r[1][i] + r[-1][i])
+ 27385657281648*(r[2][i] + r[-2][i])
- 22314239266528*(r[3][i] + r[-3][i])
+ 16735679449896*(r[4][i] + r[-4][i])
- 11541847896480*(r[5][i] + r[-5][i])
+ 7309837001104*(r[6][i] + r[-6][i])
- 4244421484512*(r[7][i] + r[-7][i])
+ 2254848913647*(r[8][i] + r[-8][i])
- 1093260079344*(r[9][i] + r[-9][i])
+ 482320623240*(r[10][i] + r[-10][i])
- 192928249296*(r[11][i] + r[-11][i])
+ 69668534468*(r[12][i] + r[-12][i])
- 22595200368*(r[13][i] + r[-13][i])
+ 6540715896*(r[14][i] + r[-14][i])
- 1677106640*(r[15][i] + r[-15][i])
+ 377348994*(r[16][i] + r[-16][i])
- 73629072*(r[17][i] + r[-17][i])
+ 12271512*(r[18][i] + r[-18][i])
- 1712304*(r[19][i] + r[-19][i])
+ 194580*(r[20][i] + r[-20][i])
- 17296*(r[21][i] + r[-21][i])
+ 1128*(r[22][i] + r[-22][i])
- 48*(r[23][i] + r[-23][i])
+ (r[24][i] + r[-24][i])
+ 32247603683100*r0[i]
- 60828186403426756087225216332129537688755283137921024000000000000*r50[i]
) // 12413915592536072670862289047373375038521486354677760000000000 for i in range(len(r0))]
r46 = [(7890371113950*(r[1][i] + r[-1][i])
- 6943526580276*(r[2][i] + r[-2][i])
+ 5608233007146*(r[3][i] + r[-3][i])
- 4154246671960*(r[4][i] + r[-4][i])
+ 2818953098830*(r[5][i] + r[-5][i])
- 1749695026860*(r[6][i] + r[-6][i])
+ 991493848554*(r[7][i] + r[-7][i])
- 511738760544*(r[8][i] + r[-8][i])
+ 239877544005*(r[9][i] + r[-9][i])
- 101766230790*(r[10][i] + r[-10][i])
+ 38910617655*(r[11][i] + r[-11][i])
- 13340783196*(r[12][i] + r[-12][i])
+ 4076350421*(r[13][i] + r[-13][i])
- 1101716330*(r[14][i] + r[-14][i])
+ 260932815*(r[15][i] + r[-15][i])
- 53524680*(r[16][i] + r[-16][i])
+ 9366819*(r[17][i] + r[-17][i])
- 1370754*(r[18][i] + r[-18][i])
+ 163185*(r[19][i] + r[-19][i])
- 15180*(r[20][i] + r[-20][i])
+ 1035*(r[21][i] + r[-21][i])
- 46*(r[22][i] + r[-22][i])
+ (r[23][i] + r[-23][i])
- 8233430727600*r0[i]
- 23793338219027472619152720674132302157166182179799040000000000*r48[i]
- 55378994704786442521077957369042933270804289023482265600000000000*r50[i]
) // 5502622159812088949850305428800254892961651752960000000000 for i in range(len(r0))]
r44 = [(-2012616400080*(r[1][i] + r[-1][i])
+ 1761039350070*(r[2][i] + r[-2][i])
- 1408831480056*(r[3][i] + r[-3][i])
+ 1029530696964*(r[4][i] + r[-4][i])
- 686353797976*(r[5][i] + r[-5][i])
+ 416714805914*(r[6][i] + r[-6][i])
- 229911617056*(r[7][i] + r[-7][i])
+ 114955808528*(r[8][i] + r[-8][i])
- 51915526432*(r[9][i] + r[-9][i])
+ 21090682613*(r[10][i] + r[-10][i])
- 7669339132*(r[11][i] + r[-11][i])
+ 2481256778*(r[12][i] + r[-12][i])
- 708930508*(r[13][i] + r[-13][i])
+ 177232627*(r[14][i] + r[-14][i])
- 38320568*(r[15][i] + r[-15][i])
+ 7059052*(r[16][i] + r[-16][i])
- 1086008*(r[17][i] + r[-17][i])
+ 135751*(r[18][i] + r[-18][i])
- 13244*(r[19][i] + r[-19][i])
+ 946*(r[20][i] + r[-20][i])
- 44*(r[21][i] + r[-21][i])
+ (r[22][i] + r[-22][i])
+ 2104098963720*r0[i]
- 10088140626322163074725559952800467303763028213760000000000*r46[i]
- 20672617771459376572727617455278717598871197415636992000000000*r48[i]
- 30390960789555990223010654132076029106169285558507929600000000000*r50[i]
) // 2658271574788448768043625811014615890319638528000000000 for i in range(len(r0))]
r42 = [(513791607420*(r[1][i] + r[-1][i])
- 446775310800*(r[2][i] + r[-2][i])
+ 353697121050*(r[3][i] + r[-3][i])
- 254661927156*(r[4][i] + r[-4][i])
+ 166509721602*(r[5][i] + r[-5][i])
- 98672427616*(r[6][i] + r[-6][i])
+ 52860229080*(r[7][i] + r[-7][i])
- 25518731280*(r[8][i] + r[-8][i])
+ 11058116888*(r[9][i] + r[-9][i])
- 4280561376*(r[10][i] + r[-10][i])
+ 1471442973*(r[11][i] + r[-11][i])
- 445891810*(r[12][i] + r[-12][i])
+ 118030185*(r[13][i] + r[-13][i])
- 26978328*(r[14][i] + r[-14][i])
+ 5245786*(r[15][i] + r[-15][i])
- 850668*(r[16][i] + r[-16][i])
+ 111930*(r[17][i] + r[-17][i])
- 11480*(r[18][i] + r[-18][i])
+ 861*(r[19][i] + r[-19][i])
- 42*(r[20][i] + r[-20][i])
+ (r[21][i] + r[-21][i])
- 538257874440*r0[i]
- 4651975255879785344076345169275577808059367424000000000*r44[i]
- 8345643609048334907272963233680386587658505158656000000000*r46[i]
- 10774531600512501036897720551649645765494516918255616000000000*r48[i]
- 11221709145032637985686395016457126546359868596714209280000000000*r50[i]
) // 1405006117752879898543142606244511569936384000000000 for i in range(len(r0))]
r40 = [(-131282408400*(r[1][i] + r[-1][i])
+ 113380261800*(r[2][i] + r[-2][i])
- 88732378800*(r[3][i] + r[-3][i])
+ 62852101650*(r[4][i] + r[-4][i])
- 40225345056*(r[5][i] + r[-5][i])
+ 23206929840*(r[6][i] + r[-6][i])
- 12033222880*(r[7][i] + r[-7][i])
+ 5586853480*(r[8][i] + r[-8][i])
- 2311801440*(r[9][i] + r[-9][i])
+ 847660528*(r[10][i] + r[-10][i])
- 273438880*(r[11][i] + r[-11][i])
+ 76904685*(r[12][i] + r[-12][i])
- 18643560*(r[13][i] + r[-13][i])
+ 3838380*(r[14][i] + r[-14][i])
- 658008*(r[15][i] + r[-15][i])
+ 91390*(r[16][i] + r[-16][i])
- 9880*(r[17][i] + r[-17][i])
+ 780*(r[18][i] + r[-18][i])
- 40*(r[19][i] + r[-19][i])
+ (r[20][i] + r[-20][i])
+ 137846528820*r0[i]
- 2341676862921466497571904343740852616560640000000000*r42[i]
- 3655123415334117056059985490145096849189502976000000000*r44[i]
- 4119688019118574531237133429498603530973935042560000000000*r46[i]
- 3757340713824985498498548346794211825654347639816192000000000*r48[i]
- 2947359606908914693821004025256012800585708025466060800000000000*r50[i]
) // 815915283247897734345611269596115894272000000000 for i in range(len(r0))]
r38 = [(33578000610*(r[1][i] + r[-1][i])
- 28781143380*(r[2][i] + r[-2][i])
+ 22239974430*(r[3][i] + r[-3][i])
- 15471286560*(r[4][i] + r[-4][i])
+ 9669554100*(r[5][i] + r[-5][i])
- 5414950296*(r[6][i] + r[-6][i])
+ 2707475148*(r[7][i] + r[-7][i])
- 1203322288*(r[8][i] + r[-8][i])
+ 472733756*(r[9][i] + r[-9][i])
- 163011640*(r[10][i] + r[-10][i])
+ 48903492*(r[11][i] + r[-11][i])
- 12620256*(r[12][i] + r[-12][i])
+ 2760681*(r[13][i] + r[-13][i])
- 501942*(r[14][i] + r[-14][i])
+ 73815*(r[15][i] + r[-15][i])
- 8436*(r[16][i] + r[-16][i])
+ 703*(r[17][i] + r[-17][i])
- 38*(r[18][i] + r[-18][i])
+ (r[19][i] + r[-19][i])
- 35345263800*r0[i]
- 1291865865142504746047217843527183499264000000000*r40[i]
- 1742597865490724651943092149133817822157209600000000*r42[i]
- 1703614521144184428726371303487541532883419136000000000*r44[i]
- 1352221478318945952566471137817160521323572835123200000000*r46[i]
- 925912385499308009244605568293800045079467288166400000000000*r48[i]
- 567701817594292628086492254286076775983065657711263744000000000*r50[i]
) // 523022617466601111760007224100074291200000000 for i in range(len(r0))]
r36 = [(-8597496600*(r[1][i] + r[-1][i])
+ 7307872110*(r[2][i] + r[-2][i])
- 5567902560*(r[3][i] + r[-3][i])
+ 3796297200*(r[4][i] + r[-4][i])
- 2310789600*(r[5][i] + r[-5][i])
+ 1251677700*(r[6][i] + r[-6][i])
- 600805296*(r[7][i] + r[-7][i])
+ 254186856*(r[8][i] + r[-8][i])
- 94143280*(r[9][i] + r[-9][i])
+ 30260340*(r[10][i] + r[-10][i])
- 8347680*(r[11][i] + r[-11][i])
+ 1947792*(r[12][i] + r[-12][i])
- 376992*(r[13][i] + r[-13][i])
+ 58905*(r[14][i] + r[-14][i])
- 7140*(r[15][i] + r[-15][i])
+ 630*(r[16][i] + r[-16][i])
- 36*(r[17][i] + r[-17][i])
+ (r[18][i] + r[-18][i])
+ 9075135300*r0[i]
- 784533926199901667640010836150111436800000000*r38[i]
- 907705752613286229459492537425678932377600000000*r40[i]
- 764250847583238143225401875995898505750118400000000*r42[i]
- 524336156604477506256224109002957345627779891200000000*r44[i]
- 311351658482338919180732210200430367625645444300800000000*r46[i]
- 166036590632320367531429334375544068072103816986624000000000*r48[i]
- 81499841025612949496109930847966440863640763389444096000000000*r50[i]
) // 371993326789901217467999448150835200000000 for i in range(len(r0))]
r34 = [(2203961430*(r[1][i] + r[-1][i])
- 1855967520*(r[2][i] + r[-2][i])
+ 1391975640*(r[3][i] + r[-3][i])
- 927983760*(r[4][i] + r[-4][i])
+ 548354040*(r[5][i] + r[-5][i])
- 286097760*(r[6][i] + r[-6][i])
+ 131128140*(r[7][i] + r[-7][i])
- 52451256*(r[8][i] + r[-8][i])
+ 18156204*(r[9][i] + r[-9][i])
- 5379616*(r[10][i] + r[-10][i])
+ 1344904*(r[11][i] + r[-11][i])
- 278256*(r[12][i] + r[-12][i])
+ 46376*(r[13][i] + r[-13][i])
- 5984*(r[14][i] + r[-14][i])
+ 561*(r[15][i] + r[-15][i])
- 34*(r[16][i] + r[-16][i])
+ (r[17][i] + r[-17][i])
- 2333606220*r0[i]
- 526990546285693391412999218213683200000000*r36[i]
- 518664095654379435828673830565907005440000000*r38[i]
- 373138241060740797524227217357125818777600000000*r40[i]
- 219618160307546307818407858079592245845032960000000*r42[i]
- 112275193446419212026758411812279514001781555200000000*r44[i]
- 51713216892097268029263570056035419810630708756480000000*r46[i]
- 21987290206937420965021290881182668895459624353792000000000*r48[i]
- 8778185176019659621127125508818359337012951782732595200000000*r50[i]
) // 295232799039604140847618609643520000000 for i in range(len(r0))]
r32 = [(-565722720*(r[1][i] + r[-1][i])
+ 471435600*(r[2][i] + r[-2][i])
- 347373600*(r[3][i] + r[-3][i])
+ 225792840*(r[4][i] + r[-4][i])
- 129024480*(r[5][i] + r[-5][i])
+ 64512240*(r[6][i] + r[-6][i])
- 28048800*(r[7][i] + r[-7][i])
+ 10518300*(r[8][i] + r[-8][i])
- 3365856*(r[9][i] + r[-9][i])
+ 906192*(r[10][i] + r[-10][i])
- 201376*(r[11][i] + r[-11][i])
+ 35960*(r[12][i] + r[-12][i])
- 4960*(r[13][i] + r[-13][i])
+ 496*(r[14][i] + r[-14][i])
- 32*(r[15][i] + r[-15][i])
+ (r[16][i] + r[-16][i])
+ 601080390*r0[i]
- 393643732052805521130158146191360000000*r34[i]
- 326527475737802179777466182265733120000000*r36[i]
- 198969979872214920293886346099446251520000000*r38[i]
- 99626745669333527035567016277524852244480000000*r40[i]
- 43498703313314018776504938348732045412270080000000*r42[i]
- 17170843124850370546818528558187736420780605440000000*r44[i]
- 6276444318289938061108840583768656479667869450240000000*r46[i]
- 2160301520690503531404610021529918026938609932697600000000*r48[i]
- 708745398984922590930383206855670263857046959528345600000000*r50[i]
) // 263130836933693530167218012160000000 for i in range(len(r0))]
r30 = [(145422675*(r[1][i] + r[-1][i])
- 119759850*(r[2][i] + r[-2][i])
+ 86493225*(r[3][i] + r[-3][i])
- 54627300*(r[4][i] + r[-4][i])
+ 30045015*(r[5][i] + r[-5][i])
- 14307150*(r[6][i] + r[-6][i])
+ 5852925*(r[7][i] + r[-7][i])
- 2035800*(r[8][i] + r[-8][i])
+ 593775*(r[9][i] + r[-9][i])
- 142506*(r[10][i] + r[-10][i])
+ 27405*(r[11][i] + r[-11][i])
- 4060*(r[12][i] + r[-12][i])
+ 435*(r[13][i] + r[-13][i])
- 30*(r[14][i] + r[-14][i])
+ (r[15][i] + r[-15][i])
- 155117520*r0[i]
- 328913546167116912709022515200000000*r32[i]
- 227575282593028191903372678266880000000*r34[i]
- 116309421454977381321426414757478400000000*r36[i]
- 49083095586740430887431564189583278080000000*r38[i]
- 18139371393109511951007844941215406489600000000*r40[i]
- 6083845843389094496001274537210012898426880000000*r42[i]
- 1895875482185729033390420637976407213657292800000000*r44[i]
- 557995741137378415081398016214860854983503380480000000*r46[i]
- 156963921056606539204438549741946823549156065280000000000*r48[i]
- 42576613536662088106792709282326106111384171273256960000000*r50[i]
) // 265252859812191058636308480000000 for i in range(len(r0))]
r28 = [(-37442160*(r[1][i] + r[-1][i])
+ 30421755*(r[2][i] + r[-2][i])
- 21474180*(r[3][i] + r[-3][i])
+ 13123110*(r[4][i] + r[-4][i])
- 6906900*(r[5][i] + r[-5][i])
+ 3108105*(r[6][i] + r[-6][i])
- 1184040*(r[7][i] + r[-7][i])
+ 376740*(r[8][i] + r[-8][i])
- 98280*(r[9][i] + r[-9][i])
+ 20475*(r[10][i] + r[-10][i])
- 3276*(r[11][i] + r[-11][i])
+ 378*(r[12][i] + r[-12][i])
- 28*(r[13][i] + r[-13][i])
+ (r[14][i] + r[-14][i])
+ 40116600*r0[i]
- 309461669780889568409026560000000*r30[i]
- 176516936443019409820508749824000000*r32[i]
- 74833313645455216256514439249920000000*r34[i]
- 26337328459046574816219104447299584000000*r36[i]
- 8155948144934385059006601147769159680000000*r38[i]
- 2301709517171786559798286695904076365824000000*r40[i]
- 605758813130095139988659617361096909783040000000*r42[i]
- 151061790397229175366153301919734749322543104000000*r44[i]
- 36109056667467121621981604705290955376859545600000000*r46[i]
- 8344518734397260673326477690101230819337996075008000000*r48[i]
- 1876453005146379321858026862378389310967569941790720000000*r50[i]
) // 304888344611713860501504000000 for i in range(len(r0))]
r26 = [(9657700*(r[1][i] + r[-1][i])
- 7726160*(r[2][i] + r[-2][i])
+ 5311735*(r[3][i] + r[-3][i])
- 3124550*(r[4][i] + r[-4][i])
+ 1562275*(r[5][i] + r[-5][i])
- 657800*(r[6][i] + r[-6][i])
+ 230230*(r[7][i] + r[-7][i])
- 65780*(r[8][i] + r[-8][i])
+ 14950*(r[9][i] + r[-9][i])
- 2600*(r[10][i] + r[-10][i])
+ 325*(r[11][i] + r[-11][i])
- 26*(r[12][i] + r[-12][i])
+ (r[13][i] + r[-13][i])
- 10400600*r0[i]
- 330295706662690015543296000000*r28[i]
- 153257207891488167212089344000000*r30[i]
- 53222214421459539592188788736000000*r32[i]
- 15436506593303376230082373484544000000*r34[i]
- 3960094929842931739454572322881536000000*r36[i]
- 930084233815670751630942950980583424000000*r38[i]
- 204528766884160018873274371645367648256000000*r40[i]
- 42768601883241439058698435075343591276544000000*r42[i]
- 8599134589431485780708409429924529774657536000000*r44[i]
- 1676115909489027560076829587121962388192493568000000*r46[i]
- 318686948683222526304282057035116495208098824192000000*r48[i]
- 59389194499215983294435493136240165006801607589888000000*r50[i]
) // 403291461126605635584000000 for i in range(len(r0))]
r24 = [(-2496144*(r[1][i] + r[-1][i])
+ 1961256*(r[2][i] + r[-2][i])
- 1307504*(r[3][i] + r[-3][i])
+ 735471*(r[4][i] + r[-4][i])
- 346104*(r[5][i] + r[-5][i])
+ 134596*(r[6][i] + r[-6][i])
- 42504*(r[7][i] + r[-7][i])
+ 10626*(r[8][i] + r[-8][i])
- 2024*(r[9][i] + r[-9][i])
+ 276*(r[10][i] + r[-10][i])
- 24*(r[11][i] + r[-11][i])
+ (r[12][i] + r[-12][i])
+ 2704156*r0[i]
- 403291461126605635584000000*r26[i]
- 149903436100759314746572800000*r28[i]
- 42033455827381598974377984000000*r30[i]
- 9910695932425713906157643366400000*r32[i]
- 2078962023961017163954848006144000000*r34[i]
- 401274139495715827174031120636313600000*r36[i]
- 72837740568171787457915404507152384000000*r38[i]
- 12620369661259070567869332718886859571200000*r40[i]
- 2109601340251819353520575234140712075264000000*r42[i]
- 342864867500163789441705220714949009654415360000*r44[i]
- 54497476891656721001996702786930540928565248000000*r46[i]
- 8509384879617502075402808457393042025589086617600000*r48[i]
- 1309755467175539670340841790934034624876228640768000000*r50[i]
) // 620448401733239439360000 for i in range(len(r0))]
r22 = [(646646*(r[1][i] + r[-1][i])
- 497420*(r[2][i] + r[-2][i])
+ 319770*(r[3][i] + r[-3][i])
- 170544*(r[4][i] + r[-4][i])
+ 74613*(r[5][i] + r[-5][i])
- 26334*(r[6][i] + r[-6][i])
+ 7315*(r[7][i] + r[-7][i])
- 1540*(r[8][i] + r[-8][i])
+ 231*(r[9][i] + r[-9][i])
- 22*(r[10][i] + r[-10][i])
+ (r[11][i] + r[-11][i])
- 705432*r0[i]
- 568744368255469486080000*r24[i]
- 166357727714724824678400000*r26[i]
- 37042320704478727628390400000*r28[i]
- 6988909951599209517839155200000*r30[i]
- 1180836611760352104108962611200000*r32[i]
- 184607985589364774573429361868800000*r34[i]
- 27272218262298384682708194086092800000*r36[i]
- 3861838803337560097698395778726297600000*r38[i]
- 529471212011799260411940801849645465600000*r40[i]
- 70801221927358337925257947461388534087680000*r42[i]
- 9284304296436839352157882253583122352046080000*r44[i]
- 1198819215976330165063918942164935021513932800000*r46[i]
- 152905877736629296164560458459124226796014796800000*r48[i]
- 19311905336609987288869864510609701436067866214400000*r50[i]
) // 1124000727777607680000 for i in range(len(r0))]
r20 = [(-167960*(r[1][i] + r[-1][i])
+ 125970*(r[2][i] + r[-2][i])
- 77520*(r[3][i] + r[-3][i])
+ 38760*(r[4][i] + r[-4][i])
- 15504*(r[5][i] + r[-5][i])
+ 4845*(r[6][i] + r[-6][i])
- 1140*(r[7][i] + r[-7][i])
+ 190*(r[8][i] + r[-8][i])
- 20*(r[9][i] + r[-9][i])
+ (r[10][i] + r[-10][i])
+ 184756*r0[i]
- 936667273148006400000*r22[i]
- 211124803367560642560000*r24[i]
- 36608302274885332992000000*r26[i]
- 5425950533240873322086400000*r28[i]
- 725494605231272191451136000000*r30[i]
- 90317652741043657957240012800000*r32[i]
- 10681064948020015063470219264000000*r34[i]
- 1216234618180639720975550420582400000*r36[i]
- 134607612138429628983625351999488000000*r38[i]
- 14578366393789236829898507440652451840000*r40[i]
- 1552719574083291045891061928041363046400000*r42[i]
- 163243281617906068079686557318998305013760000*r44[i]
- 16988641998903346735554689301227465785344000000*r46[i]
- 1753883399302689292116989257696255397727436800000*r48[i]
- 179923160623142188671570235338790827627528192000000*r50[i]
) // 2432902008176640000 for i in range(len(r0))]
r18 = [(43758*(r[1][i] + r[-1][i])
- 31824*(r[2][i] + r[-2][i])
+ 18564*(r[3][i] + r[-3][i])
- 8568*(r[4][i] + r[-4][i])
+ 3060*(r[5][i] + r[-5][i])
- 816*(r[6][i] + r[-6][i])
+ 153*(r[7][i] + r[-7][i])
- 18*(r[8][i] + r[-8][i])
+ (r[9][i] + r[-9][i])
- 48620*r0[i]
- 1824676506132480000*r20[i]
- 309100200138842112000*r22[i]
- 40778478784550707200000*r24[i]
- 4645053436190368481280000*r26[i]
- 481314610282065419059200000*r28[i]
- 46758400573464312663490560000*r30[i]
- 4340262299778024388805836800000*r32[i]
- 389810850996416354285601300480000*r34[i]
- 34168816632541202331763973529600000*r36[i]
- 2941066263016510346147295370272768000*r38[i]
- 249691933432545691845292589410836480000*r40[i]
- 20977168972570956554158853986478948352000*r42[i]
- 1748194308191420862068509392967461273600000*r44[i]
- 144787366874617417267158756772391629455360000*r46[i]
- 11933738665455945947029762024119178565222400000*r48[i]
- 979923136258156862399188048479194930964357120000*r50[i]
) // 6402373705728000 for i in range(len(r0))]
r16 = [(-11440*(r[1][i] + r[-1][i])
+ 8008*(r[2][i] + r[-2][i])
- 4368*(r[3][i] + r[-3][i])
+ 1820*(r[4][i] + r[-4][i])
- 560*(r[5][i] + r[-5][i])
+ 120*(r[6][i] + r[-6][i])
- 16*(r[7][i] + r[-7][i])
+ (r[8][i] + r[-8][i])
+ 12870*r0[i]
- 4268249137152000*r18[i]
- 527128768438272000*r20[i]
- 51442361350668288000*r22[i]
- 4385609982489415680000*r24[i]
- 343350594609952849920000*r26[i]
- 25398422028160175554560000*r28[i]
- 1806640043553643996938240000*r30[i]
- 124998708216981630040289280000*r32[i]
- 8477574188991756975915909120000*r34[i]
- 566640901244029272138606256128000*r36[i]
- 37469170353622071265887792218112000*r38[i]
- 2457916223969789263693314523533312000*r40[i]
- 160273272592069873142621634191720448000*r42[i]
- 10404012781412834769965673013161000960000*r44[i]
- 673078263437696563365695181553779671040000*r46[i]
- 43432367177206668920840929822030938501120000*r48[i]
- 2797138392082425352298525252125310293524480000*r50[i]
) // 20922789888000 for i in range(len(r0))]
r14 = [(3003*(r[1][i] + r[-1][i])
- 2002*(r[2][i] + r[-2][i])
+ 1001*(r[3][i] + r[-3][i])
- 364*(r[4][i] + r[-4][i])
+ 91*(r[5][i] + r[-5][i])
- 14*(r[6][i] + r[-6][i])
+ (r[7][i] + r[-7][i])
- 3432*r0[i]
- 12204960768000*r16[i]
- 1058170098585600*r18[i]
- 73775500710912000*r20[i]
- 4555411900194355200*r22[i]
- 261131482210959360000*r24[i]
- 14266599888013304832000*r26[i]
- 754754307297469839360000*r28[i]
- 39057272623118392651008000*r30[i]
- 1990236929603886055572480000*r32[i]
- 100317304785653440333283635200*r34[i]
- 5017302808350824370904132608000*r36[i]
- 249538838908236261152065923225600*r38[i]
- 12360976075014001109372936189952000*r40[i]
- 610513898001512036824535103712051200*r42[i]
- 30089355946979742032883786297815040000*r44[i]
- 1480659654975370272651825844120998144000*r46[i]
- 72778719754993922352940597980542622720000*r48[i]
- 3574314373450201242087397187099658871296000*r50[i]
) // 87178291200 for i in range(len(r0))]
r12 = [(-792*(r[1][i] + r[-1][i])
+ 495*(r[2][i] + r[-2][i])
- 220*(r[3][i] + r[-3][i])
+ 66*(r[4][i] + r[-4][i])
- 12*(r[5][i] + r[-5][i])
+ (r[6][i] + r[-6][i])
+ 924*r0[i]
- 43589145600*r14[i]
- 2528170444800*r16[i]
- 120467944396800*r18[i]
- 5167100908569600*r20[i]
- 208331313744153600*r22[i]
- 8083281646573056000*r24[i]
- 305994026290208256000*r26[i]
- 11397316294188849024000*r28[i]
- 419948192698268217984000*r30[i]
- 15360962830016613243033600*r32[i]
- 559092713482449420732057600*r34[i]
- 20280226917834433943755084800*r36[i]
- 733917409397935785284098636800*r38[i]
- 26516869922120782776160606617600*r40[i]
- 957005191789297958689924263321600*r42[i]
- 34512162491005016706155579824512000*r44[i]
- 1243937698905379082423800102273152000*r46[i]
- 44819260744500257106087286005881088000*r48[i]
- 1614431094051811175741477051443876608000*r50[i]
) // 479001600 for i in range(len(r0))]
r10 = [(210*(r[1][i] + r[-1][i])
- 120*(r[2][i] + r[-2][i])
+ 45*(r[3][i] + r[-3][i])
- 10*(r[4][i] + r[-4][i])
+ (r[5][i] + r[-5][i])
- 252*r0[i]
- 199584000*r12[i]
- 7264857600*r14[i]
- 223134912000*r16[i]
- 6289809926400*r18[i]
- 169058189664000*r20[i]
- 4419351149875200*r22[i]
- 113605204648320000*r24[i]
- 2890388998040544000*r26[i]
- 73066712935376160000*r28[i]
- 1839605249083010572800*r30[i]
- 46197360620085939264000*r32[i]
- 1158251761107990889401600*r34[i]
- 29009396635576994764512000*r36[i]
- 726084725720412923735270400*r38[i]
- 18165716613255899607139584000*r40[i]
- 454360504471895403926563219200*r42[i]
- 11362494160594553046963852960000*r44[i]
- 284118059898561657806684273088000*r46[i]
- 7103842801529696381323903273920000*r48[i]
- 177610330992631300501801888177516800*r50[i]
) // 3628800 for i in range(len(r0))]
r8 = [(-56*(r[1][i] + r[-1][i])
+ 28*(r[2][i] + r[-2][i])
- 8*(r[3][i] + r[-3][i])
+ (r[4][i] + r[-4][i])
+ 70*r0[i]
- 1209600*r10[i]
- 25280640*r12[i]
- 461260800*r14[i]
- 7904856960*r16[i]
- 131254905600*r18[i]
- 2143293425280*r20[i]
- 34682510016000*r22[i]
- 558432020361600*r24[i]
- 8966533159584000*r26[i]
- 143749174428961920*r28[i]
- 2302548811229721600*r30[i]
- 36863840064915642240*r32[i]
- 590028976413583660800*r34[i]
- 9442331455422829138560*r36[i]
- 151094113839739041753600*r38[i]
- 2417657116643486089706880*r40[i]
- 38683875524088319997472000*r42[i]
- 618954263309240362088323200*r44[i]
- 9903378507277068408849408000*r46[i]
- 158455048765455207825625883520*r48[i]
- 2535289714088718783746769273600*r50[i]
) // 40320 for i in range(len(r0))]
r6 = [(15*(r[1][i] + r[-1][i])
- 6*(r[2][i] + r[-2][i])
+ (r[3][i] + r[-3][i])
- 20*r0[i]
- 10080*r8[i]
- 105840*r10[i]
- 1013760*r12[i]
- 9369360*r14[i]
- 85307040*r16[i]
- 771695280*r18[i]
- 6960985920*r20[i]
- 62711787600*r22[i]
- 564657746400*r24[i]
- 5082926350320*r26[i]
- 45750363684480*r28[i]
- 411769379287440*r30[i]
- 3705988838096160*r32[i]
- 33354157240902960*r34[i]
- 300188445960277440*r36[i]
- 2701700136811100880*r38[i]
- 24315317723974324320*r40[i]
- 218837925486466585200*r42[i]
- 1969541593260989932800*r44[i]
- 17725875394880072059920*r46[i]
- 159532882776045299198880*r48[i]
- 1435795961872906295429040*r50[i]
) // 720 for i in range(len(r0))]
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
- 504*r8[i]
- 2040*r10[i]
- 8184*r12[i]
- 32760*r14[i]
- 131064*r16[i]
- 524280*r18[i]
- 2097144*r20[i]
- 8388600*r22[i]
- 33554424*r24[i]
- 134217720*r26[i]
- 536870904*r28[i]
- 2147483640*r30[i]
- 8589934584*r32[i]
- 34359738360*r34[i]
- 137438953464*r36[i]
- 549755813880*r38[i]
- 2199023255544*r40[i]
- 8796093022200*r42[i]
- 35184372088824*r44[i]
- 140737488355320*r46[i]
- 562949953421304*r48[i]
- 2251799813685240*r50[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
- 2*r8[i]
- 2*r10[i]
- 2*r12[i]
- 2*r14[i]
- 2*r16[i]
- 2*r18[i]
- 2*r20[i]
- 2*r22[i]
- 2*r24[i]
- 2*r26[i]
- 2*r28[i]
- 2*r30[i]
- 2*r32[i]
- 2*r34[i]
- 2*r36[i]
- 2*r38[i]
- 2*r40[i]
- 2*r42[i]
- 2*r44[i]
- 2*r46[i]
- 2*r48[i]
- 2*r50[i]
) // 2 for i in range(len(r0))]
r49 = [(4861946401452*r[1][i]
- 8643460269248*r[2][i]
+ 10649977831752*r[3][i]
- 10772391370048*r[4][i]
+ 9425842448792*r[5][i]
- 7297426411968*r[6][i]
+ 5054988087457*r[7][i]
- 3151161405168*r[8][i]
+ 1772528290407*r[9][i]
- 900331830048*r[10][i]
+ 412652088772*r[11][i]
- 170333048928*r[12][i]
+ 63127818572*r[13][i]
- 20918093728*r[14][i]
+ 6163366902*r[15][i]
- 1603477568*r[16][i]
+ 365077482*r[17][i]
- 71916768*r[18][i]
+ 12076932*r[19][i]
- 1695008*r[20][i]
+ 193452*r[21][i]
- 17248*r[22][i]
+ 1127*r[23][i]
- 48*r[24][i]
+ r[25][i]
- 1289904147324*r0[i]
+ 686119227300*r2[i]
- 1509462300060*r4[i]
+ 7323923844900*r6[i]
- 63466456620060*r8[i]
+ 876655994638500*r10[i]
- 17962494591036060*r12[i]
+ 519729378435224100*r14[i]
- 20498730418437708060*r16[i]
+ 1073773191888393761700*r18[i]
- 73266053614681083996060*r20[i]
+ 6418563118124648605611300*r22[i]
- 714493710681785410524780060*r24[i]
+ 100357569802461927273985332900*r26[i]
- 17717998874943470330819342460060*r28[i]
+ 3928707238871982933864962858686500*r30[i]
- 1096834043813751169204010169826956060*r32[i]
+ 388004275037568389575404928401474632100*r34[i]
- 175870982185451189351017757509405335708060*r36[i]
+ 103991298038492644018924403718805266597329700*r38[i]
- 82506842083007670338625750577445488484693676060*r40[i]
+ 91947467567672513735818977678842895400970978139300*r42[i]
- 156026356786659861162429714318097107470538947633340060*r44[i]
+ 477994672122502000860149649242839645232774457016507620900*r46[i]
- 4741041014119120622582667190202604787803330381303410474700060*r48[i]
- 50576092532930275709972631359425317424152381858024219560152465500*r50[i]
) // 608281864034267560872252163321295376887552831379210240000000000 for i in range(len(r0))]
r47 = [(-1289904147324*r[1][i]
+ 2282138106804*r[2][i]
- 2789279908316*r[3][i]
+ 2789279908316*r[4][i]
- 2404551645100*r[5][i]
+ 1827459250276*r[6][i]
- 1237956266316*r[7][i]
+ 751616304549*r[8][i]
- 409972529754*r[9][i]
+ 200966926350*r[10][i]
- 88425447594*r[11][i]
+ 34834267234*r[12][i]
- 12239066866*r[13][i]
+ 3815417606*r[14][i]
- 1048191650*r[15][i]
+ 251565996*r[16][i]
- 52153926*r[17][i]
+ 9203634*r[18][i]
- 1355574*r[19][i]
+ 162150*r[20][i]
- 15134*r[21][i]
+ 1034*r[22][i]
- 46*r[23][i]
+ r[24][i]
+ 343059613650*r0[i]
- 182965127280*r2[i]
+ 404225281200*r4[i]
- 1973179787280*r6[i]
+ 17237751438000*r8[i]
- 240592045595280*r10[i]
+ 4994170279690800*r12[i]
- 146823806097131280*r14[i]
+ 5903690350090119600*r16[i]
- 316485671150054075280*r18[i]
+ 22198064042219526404400*r20[i]
- 2009394413056841321867280*r22[i]
+ 232532372014701449341825200*r24[i]
- 34201309524439700202831707280*r26[i]
+ 6378595465863797572545515262000*r28[i]
- 1510321457529226404281297600555280*r30[i]
+ 456430932151854961874111940707194800*r32[i]
- 177879954967657922123999080680411131280*r34[i]
+ 90948410673639301600046982211812755703600*r36[i]
- 62713181699432641518049958716708665011915280*r38[i]
+ 61017960828891287286335064536456771132612468400*r40[i]
- 90771056129445230547328475921502515772170837147280*r42[i]
+ 244690112718607318914399753695429565221879804118769200*r44[i]
- 2142766872532178730068138061640892672650431299718846827280*r46[i]
- 20243597746218463146623496754059816935278614102767681978514000*r48[i]
- 1267253883404724085150525340252698701849068398706688000000000000*r49[i]
- 68540933797288160408485956779561102500745596951326307091686715280*r50[i]
) // 258623241511168180642964355153611979969197632389120000000000 for i in range(len(r0))]
r45 = [(343059613650*r[1][i]
- 603784920024*r[2][i]
+ 731508653106*r[3][i]
- 722477682080*r[4][i]
+ 612815891050*r[5][i]
- 456442180920*r[6][i]
+ 301758997386*r[7][i]
- 177996090624*r[8][i]
+ 93865125915*r[9][i]
- 44246187300*r[10][i]
+ 18609425835*r[11][i]
- 6960408624*r[12][i]
+ 2304024151*r[13][i]
- 670609940*r[14][i]
+ 170173575*r[15][i]
- 37234560*r[16][i]
+ 6923301*r[17][i]
- 1072764*r[18][i]
+ 134805*r[19][i]
- 13200*r[20][i]
+ 945*r[21][i]
- 44*r[22][i]
+ r[23][i]
- 91482563640*r0[i]
+ 48932534040*r2[i]
- 108606356040*r4[i]
+ 533667580440*r6[i]
- 4703763586440*r8[i]
+ 66408505338840*r10[i]
- 1398457857168840*r12[i]
+ 41847457290489240*r14[i]
- 1719246675671583240*r16[i]
+ 94585481325000311640*r18[i]
- 6843422433568588589640*r20[i]
+ 642897110978465333366040*r22[i]
- 77770562351946223415228040*r24[i]
+ 12062233927817328810997492440*r26[i]
- 2397961353314881501418831818440*r28[i]
+ 613494954527608404597659277810840*r30[i]
- 203877970345571868715766678319960840*r32[i]
+ 89457569257636570186619080797284721240*r34[i]
- 53237495951641479759332571910597970535240*r36[i]
+ 44930968310714379648812137260536985281903640*r38[i]
- 58241166312158469946465066186170960196371701640*r40[i]
+ 137360888551881485527132727024151255460985294318040*r42[i]
- 1056294346650368430047563515157012073181421862576900040*r44[i]
- 8792490299555933486634712872596976297794618720689003795560*r46[i]
- 517246483022336361285928710307223959938395264778240000000000*r47[i]
- 26309260636200890673464765332665424581880256812272026952850440*r48[i]
- 1203891189234487880892999073240063766756614978771353600000000000*r49[i]
- 50764977622809978549916904649893168100296473949517793816320917160*r50[i]
) // 119622220865480194561963161495657715064383733760000000000 for i in range(len(r0))]
r43 = [(-91482563640*r[1][i]
+ 160094486370*r[2][i]
- 192113383644*r[3][i]
+ 187187399448*r[4][i]
- 155989499540*r[5][i]
+ 113649492522*r[6][i]
- 73153696336*r[7][i]
+ 41802112192*r[8][i]
- 21238169904*r[9][i]
+ 9586673915*r[10][i]
- 3834669566*r[11][i]
+ 1353412788*r[12][i]
- 418913482*r[13][i]
+ 112784399*r[14][i]
- 26127660*r[15][i]
+ 5133856*r[16][i]
- 839188*r[17][i]
+ 111069*r[18][i]
- 11438*r[19][i]
+ 860*r[20][i]
- 42*r[21][i]
+ r[22][i]
+ 24466267020*r0[i]
- 13128240840*r2[i]
+ 29286075720*r4[i]
- 144956522040*r6[i]
+ 1290252243720*r8[i]
- 18448766253240*r10[i]
+ 394763466531720*r12[i]
- 12048763425424440*r14[i]
+ 507104531694579720*r16[i]
- 28726839421461491640*r18[i]
+ 2153064433503155907720*r20[i]
- 211041986898764840790840*r22[i]
+ 26870132026261051008915720*r24[i]
- 4433779344005175981028538040*r26[i]
+ 950513389106656928711222883720*r28[i]
- 266877172369028643812085068829240*r30[i]
+ 99651017964870751887504875569971720*r32[i]
- 50788156610571325953562659420384640440*r34[i]
+ 36915961449056930526009630202648137219720*r36[i]
- 41419014418447665040750851917674255257827640*r38[i]
+ 84934578551016826327683205574058431012558547720*r40[i]
- 570180937724400876712836731188276811777920749126840*r42[i]
- 4158439692009034639969470592464099450041235634033244280*r44[i]
- 229275923325503706243762726200010620540068823040000000000*r45[i]
- 10938400640270606999512627385384658646639850257084618154040*r46[i]
- 469832222078622194834718578529061763610709032173568000000000*r47[i]
- 18609787245585710799825274640865231563879706109002975534476280*r48[i]
- 690703654308090686886605775729000661503847399056998400000000000*r49[i]
- 24295755635821397902484226724698036360412358674335136584603405240*r50[i]
) // 60415263063373835637355132068513997507264512000000000 for i in range(len(r0))]
r41 = [(24466267020*r[1][i]
- 42550029600*r[2][i]
+ 50528160150*r[3][i]
- 48507033744*r[4][i]
+ 39645171810*r[5][i]
- 28192122176*r[6][i]
+ 17620076360*r[7][i]
- 9721421440*r[8][i]
+ 4739192952*r[9][i]
- 2038362560*r[10][i]
+ 770755843*r[11][i]
- 254795320*r[12][i]
+ 73066305*r[13][i]
- 17985552*r[14][i]
+ 3746990*r[15][i]
- 648128*r[16][i]
+ 90610*r[17][i]
- 9840*r[18][i]
+ 779*r[19][i]
- 40*r[20][i]
+ r[21][i]
- 6564120420*r0[i]
+ 3534526380*r2[i]
- 7928802420*r4[i]
+ 39562131180*r6[i]
- 355997149620*r8[i]
+ 5162772055980*r10[i]
- 112466379416820*r12[i]
+ 3509804003100780*r14[i]
- 151808102304340020*r16[i]
+ 8890838711788769580*r18[i]
- 693867758978013455220*r20[i]
+ 71436574576557715366380*r22[i]
- 9656103679244476561098420*r24[i]
+ 1714541855816811795973995180*r26[i]
- 402505898503128791422102405620*r28[i]
+ 126699650825847516884027712559980*r30[i]
- 54827934277723571354991704981312820*r32[i]
+ 34051732695777105364083032869387764780*r34[i]
- 32827430653262026254340815579045378556020*r36[i]
+ 58129225653125966892251726413185365757113580*r38[i]
- 338476895760295138790385051321218766549279671220*r40[i]
- 2149763077602671437231704105519918866633843849089620*r42[i]
- 110761315616185365335151075458942328763318272000000000*r43[i]
- 4942256826876098689793689711313418888604591478522994420*r44[i]
- 198705800215436545411261029373342537801392979968000000000*r45[i]
- 7372979698612811191617476736621847607367673634869335740820*r46[i]
- 256536466678869072307088584563086803940345640910848000000000*r47[i]
- 8465458808946796165763451715680655749443289544616664687661620*r48[i]
- 267183551072205666325866548010883965389520680874147840000000000*r49[i]
- 8117979331672354072521723205205099479673234187982104799090936020*r50[i]
) // 33452526613163807108170062053440751665152000000000 for i in range(len(r0))]
r39 = [(-6564120420*r[1][i]
+ 11338026180*r[2][i]
- 13309856820*r[3][i]
+ 12570420330*r[4][i]
- 10056336264*r[5][i]
+ 6962078952*r[6][i]
- 4211628008*r[7][i]
+ 2234741392*r[8][i]
- 1040310648*r[9][i]
+ 423830264*r[10][i]
- 150391384*r[11][i]
+ 46142811*r[12][i]
- 12118314*r[13][i]
+ 2686866*r[14][i]
- 493506*r[15][i]
+ 73112*r[16][i]
- 8398*r[17][i]
+ 702*r[18][i]
- 38*r[19][i]
+ r[20][i]
+ 1767263190*r0[i]
- 955277400*r2[i]
+ 2156197560*r4[i]
- 10855425000*r6[i]
+ 98876533560*r8[i]
- 1456859058600*r10[i]
+ 32382608125560*r12[i]
- 1036360772970600*r14[i]
+ 46242812090245560*r16[i]
- 2813858311510281000*r18[i]
+ 230141619686501005560*r20[i]
- 25097337236284407949800*r22[i]
+ 3642002181929040219157560*r24[i]
- 706474912755087069174777000*r26[i]
+ 185490702479102020671448093560*r28[i]
- 67501512373123369695638979402600*r30[i]
+ 35506616897715366055874618759845560*r32[i]
- 29173319982987640073110629923442306600*r34[i]
+ 44272025958057634433180503709478279085560*r36[i]
- 222019441630075420847480526017947263931809000*r38[i]
- 1219813882056330049405575791394671579625372874440*r40[i]
- 58541921573036662439297608593521315414016000000000*r41[i]
- 2435494701008122308521041585840935773426259964069800*r42[i]
- 91378085383352926401499637253627421229737574400000000*r43[i]
- 3166734413390519310621011935324774315544541946854082440*r44[i]
- 102992200477964363280928335737465088274348376064000000000*r45[i]
- 3179252903572284408695210045628305460118381385145907089000*r46[i]
- 93933517845624637462463708669855295641358690995404800000000*r47[i]
- 2673604876174888392329293291823128228151672865125704677946440*r48[i]
- 73683990172722867345525100631400320014642700636651520000000000*r49[i]
- 1974418989189660654416775142028601893909607175588350467588706600*r50[i]
) // 20397882081197443358640281739902897356800000000 for i in range(len(r0))]
r37 = [(1767263190*r[1][i]
- 3029594040*r[2][i]
+ 3511574910*r[3][i]
- 3257112960*r[4][i]
+ 2544619500*r[5][i]
- 1709984304*r[6][i]
+ 997490844*r[7][i]
- 506662016*r[8][i]
+ 223926516*r[9][i]
- 85795600*r[10][i]
+ 28312548*r[11][i]
- 7970688*r[12][i]
+ 1888887*r[13][i]
- 369852*r[14][i]
+ 58275*r[15][i]
- 7104*r[16][i]
+ 629*r[17][i]
- 36*r[18][i]
+ r[19][i]
- 477638700*r0[i]
+ 259289580*r2[i]
- 589294500*r4[i]
+ 2996657580*r6[i]
- 27670359300*r8[i]
+ 415064933580*r10[i]
- 9439543875300*r12[i]
+ 310922483993580*r14[i]
- 14379880666402500*r16[i]
+ 914767168887053580*r18[i]
- 79051272004645620900*r20[i]
+ 9231401536061270849580*r22[i]
- 1459700260139475814330500*r24[i]
+ 315843905250429722227637580*r26[i]
- 95612546130070295522414451300*r28[i]
+ 42177612582297377823299737193580*r30[i]
- 29268533564152352561039458453023300*r32[i]
+ 37747202396256876155482291281278813580*r34[i]
- 161759954125032708920885781040309430206500*r36[i]
- 763162014442847423121851269222329739576686420*r38[i]
- 33996470135329072264400469566504828928000000000*r39[i]
- 1314149222797294391875041342296266627244339280900*r40[i]
- 45857838565545385577449793398258363740979200000000*r41[i]
- 1479444354242422663436299123473954120225396734970420*r42[i]
- 44831961082741695492799244828619514023247872000000000*r43[i]
- 1290525734288850664269099373480698875776359383538646500*r44[i]
- 35584775745235419804380819416241066350620337766400000000*r45[i]
- 945953923580279776552772789184754415724912490598746182420*r46[i]
- 24366115407876526559068567586678948554722823372800000000000*r47[i]
- 610645775114510996953480313967173146186867766220019295823300*r48[i]
- 14939521515639279686486638270686230946922780466085888000000000*r49[i]
- 357801113228416003019399250210317079666322369514337123812946420*r50[i]
) // 13763753091226345046315979581580902400000000 for i in range(len(r0))]
r35 = [(-477638700*r[1][i]
+ 811985790*r[2][i]
- 927983760*r[3][i]
+ 843621600*r[4][i]
- 641886000*r[5][i]
+ 417225900*r[6][i]
- 233646504*r[7][i]
+ 112971936*r[8][i]
- 47071640*r[9][i]
+ 16811300*r[10][i]
- 5101360*r[11][i]
+ 1298528*r[12][i]
- 272272*r[13][i]
+ 45815*r[14][i]
- 5950*r[15][i]
+ 560*r[16][i]
- 34*r[17][i]
+ r[18][i]
+ 129644790*r0[i]
- 70715340*r2[i]
+ 161960940*r4[i]
- 832930740*r6[i]
+ 7810859340*r8[i]
- 119578066740*r10[i]
+ 2791740107340*r12[i]
- 95062235276340*r14[i]
+ 4584012079172940*r16[i]
- 307268933913567540*r18[i]
+ 28355038085389144140*r20[i]
- 3597774935929125068340*r22[i]
+ 632729503874459828228940*r24[i]
- 157381528472579148083026740*r26[i]
+ 57577884185625191071239755340*r28[i]
- 33404393172944223690128125810740*r30[i]
+ 36271128388074981554067219056171340*r32[i]
- 131671692334895976886647813958596908340*r34[i]
- 529104107360143104505564190890974500955060*r36[i]
- 21792609061108379656666967670836428800000000*r37[i]
- 779765567254824678774814590170424618060927540*r38[i]
- 25214048683702395262763681595157748121600000000*r39[i]
- 754531895504954495472529428607358759602244935860*r40[i]
- 21229190210645503978483385444330514048614400000000*r41[i]
- 567902644449952014090537079509460539320563935596340*r42[i]
- 14564893239013264062672891916748815156327219200000000*r43[i]
- 360416016142646161224945882401067658836071135991963060*r44[i]
- 8648657180064969977242561394456399100712373452800000000*r45[i]
- 202069375902424923136583586389997599181812580415819762740*r46[i]
- 4612127517564454653650814843765113002002883805184000000000*r47[i]
- 103121612921980129969364006657783463883530860291974593108660*r48[i]
- 2263884472933693041558609190221290023990021205262336000000000*r49[i]
- 48895910164254390571448366914991646721674728906975264997394740*r50[i]
) // 10333147966386144929666651337523200000000 for i in range(len(r0))]
r33 = [(129644790*r[1][i]
- 218349120*r[2][i]
+ 245642760*r[3][i]
- 218349120*r[4][i]
+ 161280600*r[5][i]
- 100975680*r[6][i]
+ 53993940*r[7][i]
- 24682944*r[8][i]
+ 9612108*r[9][i]
- 3164480*r[10][i]
+ 870232*r[11][i]
- 196416*r[12][i]
+ 35464*r[13][i]
- 4928*r[14][i]
+ 495*r[15][i]
- 32*r[16][i]
+ r[17][i]
- 35357670*r0[i]
+ 19389690*r2[i]
- 44796870*r4[i]
+ 233344890*r6[i]
- 2227139910*r8[i]
+ 34903389690*r10[i]
- 839988260550*r12[i]
+ 29734601940090*r14[i]
- 1506293149214790*r16[i]
+ 107487540061668090*r18[i]
- 10743535525710258630*r20[i]
+ 1511267716903778445690*r22[i]
- 304525956073869018848070*r24[i]
+ 91234873454404063067344890*r26[i]
- 43747586259736794619504039110*r28[i]
+ 39574917458915050445099774637690*r30[i]
- 120523981455993504966525708346887750*r32[i]
- 408775192473644376465790167368394203910*r34[i]
- 15499721949579217394499977006284800000000*r35[i]
- 511206585269023792365556128001469646849990*r36[i]
- 15254826342775865759666877369585500160000000*r37[i]
- 421754497238984285335705463354740490210507910*r38[i]
- 10974654148845317574241976981091935846400000000*r39[i]
- 271793538072560300468434911462753194293644181830*r40[i]
- 6459357656104303171129642884693889583677440000000*r41[i]
- 148248369194001435848413334991598692517822202402310*r42[i]
- 3302211571953506236081129759184691588287692800000000*r43[i]
- 71676123253955938571177412178194687158760951558339270*r44[i]
- 1520976967414625530272457942824571170900903198720000000*r45[i]
- 31639609352600382246311701401196841805566037174158815110*r46[i]
- 646685006086394734265332084740666732219400716288000000000*r47[i]
- 13012191241624225597793637611655297834798932917962602378310*r48[i]
- 258181916941754694739033103200539980500380934786252800000000*r49[i]
- 5058734882305856045540073713691835327365626096838684137474310*r50[i]
) // 8683317618811886495518194401280000000 for i in range(len(r0))]
r31 = [(-35357670*r[1][i]
+ 58929450*r[2][i]
- 65132550*r[3][i]
+ 56448210*r[4][i]
- 40320150*r[5][i]
+ 24192090*r[6][i]
- 12271350*r[7][i]
+ 5259150*r[8][i]
- 1893294*r[9][i]
+ 566370*r[10][i]
- 138446*r[11][i]
+ 26970*r[12][i]
- 4030*r[13][i]
+ 434*r[14][i]
- 30*r[15][i]
+ r[16][i]
+ 9694845*r0[i]
- 5348880*r2[i]
+ 12480720*r4[i]
- 65969520*r6[i]
+ 642563280*r8[i]
- 10347602160*r10[i]
+ 258040917840*r12[i]
- 9564008626800*r14[i]
+ 514021079720400*r16[i]
- 39590373677587440*r18[i]
+ 4371353677873146960*r20[i]
- 701971899866535028080*r22[i]
+ 169737570795219895373520*r24[i]
- 66396273378844288679892720*r26[i]
+ 49448835121192219782326176080*r28[i]
- 124963193751534047864734415925360*r30[i]
- 354113410826574103722030528083469360*r32[i]
- 12301366626650172535317442068480000000*r33[i]
- 372225904019072507165665501545458070000*r34[i]
- 10203983616806318118045818195804160000000*r35[i]
- 259484653500223872483011119661283865786800*r36[i]
- 6217811871006716259183948315607695360000000*r37[i]
- 141956901865997956445469727796622341498870640*r38[i]
- 3113335802166672719861469258672651632640000000*r39[i]
- 66003822624082868383556482555741495612650600240*r40[i]
- 1359334478541063086765779323397876419133440000000*r41[i]
- 27303356587963564025554884815930553997263574871280*r42[i]
- 536588847651574079588079017443366763149393920000000*r43[i]
- 10345842549438556817463474698578198121859964179733680*r44[i]
- 196138884946560564409651268242770514989620920320000000*r45[i]
- 3663204676820752962698443093474820599422678195673015920*r46[i]
- 67509422521578235356394063172809938341831560396800000000*r47[i]
- 1229367058216339817971318602200240769989331897298761411120*r48[i]
- 22148293718278830966574475214239695745532717485260800000000*r49[i]
- 395185352573696509925259966545790692473196837003978017048560*r50[i]
) // 8222838654177922817725562880000000 for i in range(len(r0))]
r29 = [(9694845*r[1][i]
- 15967980*r[2][i]
+ 17298645*r[3][i]
- 14567280*r[4][i]
+ 10015005*r[5][i]
- 5722860*r[6][i]
+ 2731365*r[7][i]
- 1085760*r[8][i]
+ 356265*r[9][i]
- 95004*r[10][i]
+ 20097*r[11][i]
- 3248*r[12][i]
+ 377*r[13][i]
- 28*r[14][i]
+ r[15][i]
- 2674440*r0[i]
+ 1485800*r2[i]
- 3506488*r4[i]
+ 18850280*r6[i]
- 188004088*r8[i]
+ 3125835560*r10[i]
- 81314498488*r12[i]
+ 3185384180840*r14[i]
- 184064268909688*r16[i]
+ 15598375633694120*r18[i]
- 1958105850969957688*r20[i]
+ 375744491571024583400*r22[i]
- 118117302690774819242488*r24[i]
+ 71447614092662750198256680*r26[i]
- 147980747895225006590333244088*r28[i]
- 346368637877614395127589803878040*r30[i]
- 10963784872237230423634083840000000*r31[i]
- 302766527792977996357877082103322488*r32[i]
- 7585842753100939730112422608896000000*r33[i]
- 176553572119721839407097582006071612760*r34[i]
- 3876980715165912710714213825249280000000*r35[i]
- 81213796311764134505181592648745883717688*r36[i]
- 1636103186224681029581052139652775936000000*r37[i]
- 31895543813319775842490572300866856117139480*r38[i]
- 604645713103650398366928164707180216320000000*r39[i]
- 11189653759353064214370349765226592602607549688*r40[i]
- 202794861446303149866709151240333763280896000000*r41[i]
- 3608799207440735942926262565268791718882246250200*r42[i]
- 63195849406190967779680687932546907121909760000000*r43[i]
- 1091041918456432706911605989934195570136050930818488*r44[i]
- 18599858037912613836046600540495361832783446016000000*r45[i]
- 313534044032502214538190505667405050039920730329536920*r46[i]
- 5232130701886884640147951658064894118305202176000000000*r47[i]
- 86524070613240340349034843422074253070890184188704404088*r48[i]
- 1419220451222069603559756976077536870379472375775232000000*r49[i]
- 23107896008521043617173872183497904829674956287283293591640*r50[i]
) // 8841761993739701954543616000000 for i in range(len(r0))]
r27 = [(-2674440*r[1][i]
+ 4345965*r[2][i]
- 4601610*r[3][i]
+ 3749460*r[4][i]
- 2466750*r[5][i]
+ 1332045*r[6][i]
- 592020*r[7][i]
+ 215280*r[8][i]
- 63180*r[9][i]
+ 14625*r[10][i]
- 2574*r[11][i]
+ 324*r[12][i]
- 26*r[13][i]
+ r[14][i]
+ 742900*r0[i]
- 416024*r2[i]
+ 994840*r4[i]
- 5454824*r6[i]
+ 55944280*r8[i]
- 966290024*r10[i]
+ 26454613720*r12[i]
- 1109329691624*r14[i]
+ 70212852387160*r16[i]
- 6733670404619624*r18[i]
+ 1005318113348848600*r20[i]
- 249581050854994274024*r22[i]
+ 120719220687299365182040*r24[i]
- 202039976682357297272094824*r26[i]
- 385557844336439370252173428520*r28[i]
- 11052202492174627443179520000000*r29[i]
- 276888650579451671741587901762024*r30[i]
- 6304176301536407493589598208000000*r31[i]
- 133535841584115505205141919375399080*r32[i]
- 2672618344480543437732658544640000000*r33[i]
- 51095126335993498323380094454901195624*r34[i]
- 940618873537377672007825158832128000000*r35[i]
- 16776403501444391106926987629186000345640*r36[i]
- 291283862319085180678807183848898560000000*r37[i]
- 4942310839108515578583708125038854650555624*r38[i]
- 82203911327563805707081667710859870208000000*r39[i]
- 1343752600475734599375534320311340373516684200*r40[i]
- 21634243326074826428166414905753461063680000000*r41[i]
- 343672532983087585902951862991031321905844242024*r42[i]
- 5395063942758184834505475068561955332947968000000*r43[i]
- 83804941354439477195910293019964343299641959230760*r44[i]
- 1289609166695254343642200168046105549173555200000000*r45[i]
- 19678461460501652805347265575009996073778349586894824*r46[i]
- 298018526228473595475945631789329672119214145536000000*r47[i]
- 4482734138598481574681074400900490010744661138946801320*r48[i]
- 67016178755227832923500959370656761105984640778240000000*r49[i]
- 996343679402015421123803198306389561979045588249233394024*r50[i]
) // 10888869450418352160768000000 for i in range(len(r0))]
r25 = [(742900*r[1][i]
- 1188640*r[2][i]
+ 1225785*r[3][i]
- 961400*r[4][i]
+ 600875*r[5][i]
- 303600*r[6][i]
+ 123970*r[7][i]
- 40480*r[8][i]
+ 10350*r[9][i]
- 2000*r[10][i]
+ 275*r[11][i]
- 24*r[12][i]
+ r[13][i]
- 208012*r0[i]
+ 117572*r2[i]
- 285532*r4[i]
+ 1602692*r6[i]
- 16996252*r8[i]
+ 307475012*r10[i]
- 8966430172*r12[i]
+ 409745686532*r14[i]
- 29195711499292*r16[i]
+ 3312133208909252*r18[i]
- 636215671041835612*r20[i]
+ 241648300078174135172*r22[i]
- 321511316149669476991132*r24[i]
- 492817676505266866078123708*r26[i]
- 12703681025488077520896000000*r27[i]
- 286779648275654636997381637852*r28[i]
- 5894507995826467969695744000000*r29[i]
- 112914054231542703053832892635388*r30[i]
- 2047008246979213061238030336000000*r31[i]
- 35501568925223446300815211192767772*r32[i]
- 593711792050129855003168210944000000*r33[i]
- 9632134956680435093368218113996247868*r34[i]
- 152311343455497374594406627803136000000*r35[i]
- 2356318736218539774396037820111678892892*r36[i]
- 35772470531371951985805498114637824000000*r37[i]
- 534273042749950920189640352996759062689148*r38[i]
- 7866491034006154572049014294052601856000000*r39[i]
- 114383224059606274110181105712262975351245212*r40[i]
- 1644946226278516886873016733667061202944000000*r41[i]
- 23426103831558846665144911501028780920365367228*r42[i]
- 330735945747364837719554208843251145179136000000*r43[i]
- 4633465747908141417306051485893140722291346976732*r44[i]
- 64465996518808752310647291812383168776634368000000*r45[i]
- 891389875128429665004288245297052393567100598170108*r46[i]
- 12257190333970097165549309885966019046465339392000000*r47[i]
- 167703402046599761376513697620930939990159551304359452*r48[i]
- 2284199788431383972862903582163083269492369522688000000*r49[i]
- 30985395797162515638045004419632302359171420946744265788*r50[i]
) // 15511210043330985984000000 for i in range(len(r0))]
r23 = [(-208012*r[1][i]
+ 326876*r[2][i]
- 326876*r[3][i]
+ 245157*r[4][i]
- 144210*r[5][i]
+ 67298*r[6][i]
- 24794*r[7][i]
+ 7084*r[8][i]
- 1518*r[9][i]
+ 230*r[10][i]
- 22*r[11][i]
+ r[12][i]
+ 58786*r0[i]
- 33592*r2[i]
+ 83096*r4[i]
- 479752*r6[i]
+ 5299736*r8[i]
- 101549512*r10[i]
+ 3208453976*r12[i]
- 164071220872*r14[i]
+ 13743680753816*r16[i]
- 1993276972245832*r18[i]
+ 581947914140407256*r20[i]
- 603916464771468176392*r22[i]
- 730803773459954540777704*r24[i]
- 16803810880275234816000000*r25[i]
- 339155768243774227716964552*r26[i]
- 6245976504198304781107200000*r27[i]
- 107413822788261782335458993064*r28[i]
- 1751393992807566623932416000000*r29[i]
- 27365156266821215807862420562312*r30[i]
- 412945663851071412756568473600000*r31[i]
- 6053949680529454447550745704030824*r32[i]
- 86623417665042381831452000256000000*r33[i]
- 1214146547565910406028014931410521672*r34[i]
- 16719755812321492798917963359846400000*r35[i]
- 226758627215029497194516602329808882984*r36[i]
- 3034905857007157810746475187798016000000*r37[i]
- 40151799724774280996886476759684489594632*r38[i]
- 525848735885794606994555529953619148800000*r39[i]
- 6825564942475643900873841059427230143341544*r40[i]
- 87900055843825806396690634755863003136000000*r41[i]
- 1124090333957827218160935737032127911249333192*r42[i]
- 14286036145840157893404384196456208735600640000*r43[i]
- 180556939553256275799275906968519352499771598504*r44[i]
- 2270728203819030041749862616122105872023552000000*r45[i]
- 28430855249825246651314973609548475795532583689352*r46[i]
- 354557703317395919808450352391376751066211942400000*r47[i]
- 4405868085478593275690315869491622501390761293845864*r48[i]
- 54573144465647486264201741288918109369842860032000000*r49[i]
- 674011661674309854738045921738777159802726884618615112*r50[i]
) // 25852016738884976640000 for i in range(len(r0))]
r21 = [(58786*r[1][i]
- 90440*r[2][i]
+ 87210*r[3][i]
- 62016*r[4][i]
+ 33915*r[5][i]
- 14364*r[6][i]
+ 4655*r[7][i]
- 1120*r[8][i]
+ 189*r[9][i]
- 20*r[10][i]
+ r[11][i]
- 16796*r0[i]
+ 9724*r2[i]
- 24596*r4[i]
+ 147004*r6[i]
- 1708916*r8[i]
+ 35240284*r10[i]
- 1237329236*r12[i]
+ 73853629564*r14[i]
- 7850527669556*r16[i]
+ 1717351379730844*r18[i]
- 1359124435588313876*r20[i]
- 1272410676942417239876*r22[i]
- 25852016738884976640000*r23[i]
- 462292539259962003646196*r24[i]
- 7561714896123855667200000*r25[i]
- 115761644587269354830466596*r26[i]
- 1683741850203578528563200000*r27[i]
- 23512975860299444963550050516*r28[i]
- 317677725072691341719961600000*r29[i]
- 4176614976496441445095962733316*r30[i]
- 53674391443652368368589209600000*r31[i]
- 676635955671282540673335079110836*r32[i]
- 8391272072243853389701334630400000*r33[i]
- 102611708232289325546408008313624036*r34[i]
- 1239646284649926576486736094822400000*r35[i]
- 14819283410691765614379616648600811156*r36[i]
- 175538127424434549895381626305740800000*r37[i]
- 2062659648435073986802743885440046722756*r38[i]
- 24066873273263602745997309174983884800000*r39[i]
- 279069134864297423784787795404361206735476*r40[i]
- 3218237360334469905693543066426751549440000*r41[i]
- 36932670876144577834192017462238998576813476*r42[i]
- 422013831656219970552631011526505561456640000*r43[i]
- 4803667893589610545887832027829424971473267796*r44[i]
- 54491782544378643866541770098406137341542400000*r45[i]
- 616254801390825608499920295882691673585117080196*r46[i]
- 6950267169846786189298202657232919399818854400000*r47[i]
- 78194975030419808376759755992062291704460984792116*r48[i]
- 877813878936817604039539295936804610730357555200000*r49[i]
- 9834901482219684549861282981457686724945206826306916*r50[i]
) // 51090942171709440000 for i in range(len(r0))]
r19 = [(-16796*r[1][i]
+ 25194*r[2][i]
- 23256*r[3][i]
+ 15504*r[4][i]
- 7752*r[5][i]
+ 2907*r[6][i]
- 798*r[7][i]
+ 152*r[8][i]
- 18*r[9][i]
+ r[10][i]
+ 4862*r0[i]
- 2860*r2[i]
+ 7436*r4[i]
- 46420*r6[i]
+ 576236*r8[i]
- 13098580*r10[i]
+ 532310636*r12[i]
- 39968611540*r14[i]
+ 6350631494636*r16[i]
- 3730771315561300*r18[i]
- 2637991952943407764*r20[i]
- 46833363657400320000*r21[i]
- 734121065118879803860*r22[i]
- 10556240168378032128000*r23[i]
- 142438684135271315212564*r24[i]
- 1830415113744266649600000*r25[i]
- 22632897298190126259675220*r26[i]
- 271297526662043666104320000*r27[i]
- 3170344993810020486920015764*r28[i]
- 36274730261563609572556800000*r29[i]
- 407775103607650299563627591380*r30[i]
- 4515882637052182897862000640000*r31[i]
- 49377994276343186011748723193364*r32[i]
- 534053247401000753173510963200000*r33[i]
- 5722063606154183864914875339648340*r34[i]
- 60811730909031986048777521029120000*r35[i]
- 641729418431834160625738740379401364*r36[i]
- 6730380606921481449181267599974400000*r37[i]
- 70207898580127312813466155395513222100*r38[i]
- 728918319689461841494925372032622592000*r39[i]
- 7536441803725213229125462424550696575764*r40[i]
- 77635978704164552294553096402068152320000*r41[i]
- 797177898990753876072852178329776532568660*r42[i]
- 8162164080895303403984327865949915250688000*r43[i]
- 83359491110673172494030048846026790563932564*r44[i]
- 849432099945167336777734465061373289267200000*r45[i]
- 8638438243166451781593809976801426668242424020*r46[i]
- 87694169965134464605849462884812769886371840000*r47[i]
- 888832151283066038746077396233689115965303967764*r48[i]
- 8996158031157109433578511766939541381376409600000*r49[i]
- 90938713449996246641127353860256309887114389604180*r50[i]
) // 121645100408832000 for i in range(len(r0))]
r17 = [(4862*r[1][i]
- 7072*r[2][i]
+ 6188*r[3][i]
- 3808*r[4][i]
+ 1700*r[5][i]
- 544*r[6][i]
+ 119*r[7][i]
- 16*r[8][i]
+ r[9][i]
- 1430*r0[i]
+ 858*r2[i]
- 2310*r4[i]
+ 15258*r6[i]
- 206790*r8[i]
+ 5386458*r10[i]
- 272513670*r12[i]
+ 30255826458*r14[i]
- 12765597850950*r16[i]
- 6622557957272742*r18[i]
- 101370917007360000*r19[i]
- 1375210145685786630*r20[i]
- 17172233341046784000*r21[i]
- 201832098313986359142*r22[i]
- 2265471043586150400000*r23[i]
- 24529324224160803328710*r24[i]
- 258058524232798248960000*r25[i]
- 2652208374242713043720742*r26[i]
- 26739700571225856614400000*r27[i]
- 265323404171486113659725190*r28[i]
- 2597688920748017370193920000*r29[i]
- 25147613788240222384169485542*r30[i]
- 241125683321001354933657600000*r31[i]
- 2293170112631184981695915264070*r32[i]
- 21656158388689797460311183360000*r33[i]
- 203283794784841444836991831621542*r34[i]
- 1898267590696733462875776307200000*r35[i]
- 17646072330245312137111933794073350*r36[i]
- 163392570167583908119294187237376000*r37[i]
- 1507754227229479379470312529237936742*r38[i]
- 13871774079585871769182921633935360000*r39[i]
- 127291574907112728538906245247680921030*r40[i]
- 1165398276253942030786602999248830464000*r41[i]
- 10648249156718669259487809979675840079142*r42[i]
- 97121906010634492337139410720414515200000*r43[i]
- 884471146488697462546213719879378982015110*r44[i]
- 8043742604145412070397708709577312747520000*r45[i]
- 73065283527546375984492393431422365909536742*r46[i]
- 662985481414219219279431223562176586956800000*r47[i]
- 6010229010788429141870217066922217223929803590*r48[i]
- 54440174236564270133288224915510829498019840000*r49[i]
- 492755135434761578293305350886942317529465637542*r50[i]
) // 355687428096000 for i in range(len(r0))]
r15 = [(-1430*r[1][i]
+ 2002*r[2][i]
- 1638*r[3][i]
+ 910*r[4][i]
- 350*r[5][i]
+ 90*r[6][i]
- 14*r[7][i]
+ r[8][i]
+ 429*r0[i]
- 264*r2[i]
+ 744*r4[i]
- 5304*r6[i]
+ 81384*r8[i]
- 2605944*r10[i]
+ 192387624*r12[i]
- 55942352184*r14[i]
- 20546119600536*r16[i]
- 266765571072000*r17[i]
- 3083760849804024*r18[i]
- 32945548027392000*r19[i]
- 332500281299403096*r20[i]
- 3215147584416768000*r21[i]
- 30076927429146721464*r22[i]
- 274100623905588480000*r23[i]
- 2446077617962088140056*r24[i]
- 21459412163122053120000*r25[i]
- 185641639183185136464504*r26[i]
- 1587401376760010972160000*r27[i]
- 13442713420403849918131416*r28[i]
- 112915002722102749808640000*r29[i]
- 941961013910760913890393144*r30[i]
- 7812419263561351877518080000*r31[i]
- 64474322285718607792730497176*r32[i]
- 529848386811984810994744320000*r33[i]
- 4338547620121893769542630267384*r34[i]
- 35415056327751829508662891008000*r35[i]
- 288317531175033442515609896757336*r36[i]
- 2341823147101379454117987013632000*r37[i]
- 18983391549723892653716655806647224*r38[i]
- 153619763998111828980832157720832000*r39[i]
- 1241292607509331793516191597844431896*r40[i]
- 10017079537004367071413852136982528000*r41[i]
- 80746194097372251940077615903073292664*r42[i]
- 650250798838302173122854563322562560000*r43[i]
- 5232061257212799699445154857325986640856*r44[i]
- 42067391464856035210355948847111229440000*r45[i]
- 338018548004311349729166172709579357563704*r46[i]
- 2714522948575416807552558113876933656320000*r47[i]
- 21788917503304477212565325243539420555704216*r48[i]
- 174821149505151584518657828257831893345280000*r49[i]
- 1402141896338776811136967582554033500226820344*r50[i]
) // 1307674368000 for i in range(len(r0))]
r13 = [(429*r[1][i]
- 572*r[2][i]
+ 429*r[3][i]
- 208*r[4][i]
+ 65*r[5][i]
- 12*r[6][i]
+ r[7][i]
- 132*r0[i]
+ 84*r2[i]
- 252*r4[i]
+ 2004*r6[i]
- 37212*r8[i]
+ 1710324*r10[i]
- 325024572*r12[i]
- 80789566956*r14[i]
- 871782912000*r15[i]
- 8422900930332*r16[i]
- 75583578470400*r17[i]
- 643521842437836*r18[i]
- 5269678622208000*r19[i]
- 41890044885642492*r20[i]
- 325386564299596800*r21[i]
- 2481686964269990316*r22[i]
- 18652248729354240000*r23[i]
- 138536531588626169052*r24[i]
- 1019042849143807488000*r25[i]
- 7436421488952386592396*r26[i]
- 53911021949819274240000*r27[i]
- 388701690499592948238012*r28[i]
- 2789805187365599475072000*r29[i]
- 19946749502047187160692076*r30[i]
- 142159780685991861112320000*r31[i]
- 1010433303980489860989897372*r32[i]
- 7165521770403817166663116800*r33[i]
- 50716588034439244118483617356*r34[i]
- 358378772025058883636009472000*r35[i]
- 2528902640579773012941059115132*r36[i]
- 17824202779159732939433280230400*r37[i]
- 125502611080965065134883934376236*r38[i]
- 882926862501000079240924013568000*r39[i]
- 6206986746547700738292160195379292*r40[i]
- 43608135571536574058895364550860800*r41[i]
- 306213499909407501334225902520456716*r42[i]
- 2149239710498553002348841878415360000*r43[i]
- 15079178774724614117506008765315297852*r44[i]
- 105761403926812162332273274580071296000*r45[i]
- 741573481088337285231858048220674626796*r46[i]
- 5198479982499565882352899855753044480000*r47[i]
- 36434172034715569203746509369098022198812*r48[i]
- 255308169532157231577671227649975633664000*r49[i]
- 1788771440213892011837337228527544587734476*r50[i]
) // 6227020800 for i in range(len(r0))]
r11 = [(-132*r[1][i]
+ 165*r[2][i]
- 110*r[3][i]
+ 44*r[4][i]
- 10*r[5][i]
+ r[6][i]
+ 42*r0[i]
- 28*r2[i]
+ 92*r4[i]
- 868*r6[i]
+ 22652*r8[i]
- 2620708*r10[i]
- 415790788*r12[i]
- 3632428800*r13[i]
- 28616744548*r14[i]
- 210680870400*r15[i]
- 1479485236228*r16[i]
- 10038995366400*r17[i]
- 66394067988388*r18[i]
- 430591742380800*r19[i]
- 2750479262009668*r20[i]
- 17360942812012800*r21[i]
- 108550450893568228*r22[i]
- 673606803881088000*r23[i]
- 4154688725062207108*r24[i]
- 25499502190850688000*r25[i]
- 155878445775166700068*r26[i]
- 949776357849070752000*r27[i]
- 5771581202353414724548*r28[i]
- 34995682724855684832000*r29[i]
- 211811399872933910999908*r30[i]
- 1280080235834717770252800*r31[i]
- 7726641919200262371657988*r32[i]
- 46591059456870785061004800*r33[i]
- 280704018540064430354883748*r34[i]
- 1690018909819536161979590400*r35[i]
- 10169113413821714748538703428*r36[i]
- 61159784116494648773674886400*r37[i]
- 367684638335977863351585967588*r38[i]
- 2209739160176731898013383884800*r39[i]
- 13276598260065161268654185556868*r40[i]
- 79750432649108163224160355276800*r41[i]
- 478956917715683026467561165467428*r42[i]
- 2876013540917084725512964985376000*r43[i]
- 17267443120712778679894991796314308*r44[i]
- 103661474908781590201983341856096000*r45[i]
- 622252957609245047342724399262599268*r46[i]
- 3734938395375021425507273833823424000*r47[i]
- 22416734056596928549732496421419871748*r48[i]
- 134535924504317597978456420953656384000*r49[i]
- 807393154821611376674434030676868979108*r50[i]
) // 39916800 for i in range(len(r0))]
r9 = [(42*r[1][i]
- 48*r[2][i]
+ 27*r[3][i]
- 8*r[4][i]
+ r[5][i]
- 14*r0[i]
+ 10*r2[i]
- 38*r4[i]
+ 490*r6[i]
- 31238*r8[i]
- 2922230*r10[i]
- 19958400*r11[i]
- 124075238*r12[i]
- 726485760*r13[i]
- 4084385750*r14[i]
- 22313491200*r15[i]
- 119387268038*r16[i]
- 628980992640*r17[i]
- 3275389222070*r18[i]
- 16905818966400*r19[i]
- 86665431465638*r20[i]
- 441935114987520*r21[i]
- 2244295389943190*r22[i]
- 11360520464832000*r23[i]
- 57360469753884038*r24[i]
- 289038899804054400*r25[i]
- 1454155949521941110*r26[i]
- 7306671293537616000*r27[i]
- 36677059892827099238*r28[i]
- 183960524908301057280*r29[i]
- 922104761587650687830*r30[i]
- 4619736062008593926400*r31[i]
- 23135540444136227047238*r32[i]
- 115825176110799088940160*r33[i]
- 579715876176320506935350*r34[i]
- 2900939663557699476451200*r35[i]
- 14514140349055749129024038*r36[i]
- 72608472572041292373527040*r37[i]
- 363193454272347163609915670*r38[i]
- 1816571661325589960713958400*r39[i]
- 9085275939429279963731685638*r40[i]
- 45436050447189540392656321920*r41[i]
- 227218935892633882388998540790*r42[i]
- 1136249416059455304696385296000*r43[i]
- 5681866032591044240951769048038*r44[i]
- 28411805989856165780668427308800*r45[i]
- 142068933310062230858345890602710*r46[i]
- 710384280152969638132390327392000*r47[i]
- 3552079855654080764219631870487238*r48[i]
- 17761033099263130050180188817751680*r49[i]
- 88807700784593943012315384189973430*r50[i]
) // 362880 for i in range(len(r0))]
r7 = [(-14*r[1][i]
+ 14*r[2][i]
- 6*r[3][i]
+ r[4][i]
+ 5*r0[i]
- 4*r2[i]
+ 20*r4[i]
- 604*r6[i]
- 29740*r8[i]
- 151200*r9[i]
- 708604*r10[i]
- 3160080*r11[i]
- 13645900*r12[i]
- 57657600*r13[i]
- 239967004*r14[i]
- 988107120*r15[i]
- 4037604460*r16[i]
- 16406863200*r17[i]
- 66398623804*r18[i]
- 267911678160*r19[i]
- 1078605601420*r20[i]
- 4335313752000*r21[i]
- 17403958407004*r22[i]
- 69804002545200*r23[i]
- 279780634372780*r24[i]
- 1120816644948000*r25[i]
- 4488349371924604*r26[i]
- 17968646803620240*r27[i]
- 71920337041294540*r28[i]
- 287818601403715200*r29[i]
- 1151686172846664604*r30[i]
- 4607980008114455280*r31[i]
- 18435626012705982700*r32[i]
- 73753622051697957600*r33[i]
- 295047842329672995004*r34[i]
- 1180291431927853642320*r35[i]
- 4721465916019935893260*r36[i]
- 18886764229967380219200*r37[i]
- 75549758619456576163804*r38[i]
- 302207139580435761213360*r39[i]
- 1208852873637267995922220*r40[i]
- 4835484440511039999684000*r41[i]
- 19342156599960850372299004*r42[i]
- 77369282913655045261040400*r43[i]
- 309479101196178257662005580*r44[i]
- 1237922313409633551106176000*r45[i]
- 4951706979513788347008408604*r46[i]
- 19806881095681900978203235440*r47[i]
- 79227683915609817008158719340*r48[i]
- 316911214261089847968346159200*r49[i]
- 1267646292840319012979866380604*r50[i]
) // 5040 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
- 1680*r7[i]
- 5542*r8[i]
- 17640*r9[i]
- 54958*r10[i]
- 168960*r11[i]
- 515062*r12[i]
- 1561560*r13[i]
- 4717438*r14[i]
- 14217840*r15[i]
- 42784582*r16[i]
- 128615880*r17[i]
- 386371918*r18[i]
- 1160164320*r19[i]
- 3482590102*r20[i]
- 10451964600*r21[i]
- 31364282398*r22[i]
- 94109624400*r23[i]
- 282362427622*r24[i]
- 847154391720*r25[i]
- 2541597392878*r26[i]
- 7625060614080*r27[i]
- 22875718713142*r28[i]
- 68628229881240*r29[i]
- 205886837127358*r30[i]
- 617664806349360*r31[i]
- 1853003008982662*r32[i]
- 5559026206817160*r33[i]
- 16677112980189838*r34[i]
- 50031407660046240*r35[i]
- 150094360419092182*r36[i]
- 450283356135183480*r37[i]
- 1350850618161364318*r38[i]
- 4052552953995720720*r39[i]
- 12157661061010417702*r40[i]
- 36472987581077764200*r41[i]
- 109418971539326314798*r42[i]
- 328256932210164988800*r43[i]
- 984770831814867055222*r44[i]
- 2954312565813345343320*r45[i]
- 8862937838177524385278*r46[i]
- 26588813796007549866480*r47[i]
- 79766441950972603020742*r48[i]
- 239299326978817715904840*r49[i]
- 717897983188252961399758*r50[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
- 126*r7[i]
- 254*r8[i]
- 510*r9[i]
- 1022*r10[i]
- 2046*r11[i]
- 4094*r12[i]
- 8190*r13[i]
- 16382*r14[i]
- 32766*r15[i]
- 65534*r16[i]
- 131070*r17[i]
- 262142*r18[i]
- 524286*r19[i]
- 1048574*r20[i]
- 2097150*r21[i]
- 4194302*r22[i]
- 8388606*r23[i]
- 16777214*r24[i]
- 33554430*r25[i]
- 67108862*r26[i]
- 134217726*r27[i]
- 268435454*r28[i]
- 536870910*r29[i]
- 1073741822*r30[i]
- 2147483646*r31[i]
- 4294967294*r32[i]
- 8589934590*r33[i]
- 17179869182*r34[i]
- 34359738366*r35[i]
- 68719476734*r36[i]
- 137438953470*r37[i]
- 274877906942*r38[i]
- 549755813886*r39[i]
- 1099511627774*r40[i]
- 2199023255550*r41[i]
- 4398046511102*r42[i]
- 8796093022206*r43[i]
- 17592186044414*r44[i]
- 35184372088830*r45[i]
- 70368744177662*r46[i]
- 140737488355326*r47[i]
- 281474976710654*r48[i]
- 562949953421310*r49[i]
- 1125899906842622*r50[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
- r7[i]
- r8[i]
- r9[i]
- r10[i]
- r11[i]
- r12[i]
- r13[i]
- r14[i]
- r15[i]
- r16[i]
- r17[i]
- r18[i]
- r19[i]
- r20[i]
- r21[i]
- r22[i]
- r23[i]
- r24[i]
- r25[i]
- r26[i]
- r27[i]
- r28[i]
- r29[i]
- r30[i]
- r31[i]
- r32[i]
- r33[i]
- r34[i]
- r35[i]
- r36[i]
- r37[i]
- r38[i]
- r39[i]
- r40[i]
- r41[i]
- r42[i]
- r43[i]
- r44[i]
- r45[i]
- r46[i]
- r47[i]
- r48[i]
- r49[i]
- r50[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50)
def natural_interpolate_27(r):
r0 = r[0]
r52 = r['infinity']
r50 = [(121548660036300*(r[1][i] + r[-1][i])
- 108043253365600*(r[2][i] + r[-2][i])
+ 88749815264600*(r[3][i] + r[-3][i])
- 67327446062800*(r[4][i] + r[-4][i])
+ 47129212243960*(r[5][i] + r[-5][i])
- 30405943383200*(r[6][i] + r[-6][i])
+ 18053528883775*(r[7][i] + r[-7][i])
- 9847379391150*(r[8][i] + r[-8][i])
+ 4923689695575*(r[9][i] + r[-9][i])
- 2250829575120*(r[10][i] + r[-10][i])
+ 937845656300*(r[11][i] + r[-11][i])
- 354860518600*(r[12][i] + r[-12][i])
+ 121399651100*(r[13][i] + r[-13][i])
- 37353738800*(r[14][i] + r[-14][i])
+ 10272278170*(r[15][i] + r[-15][i])
- 2505433700*(r[16][i] + r[-16][i])
+ 536878650*(r[17][i] + r[-17][i])
- 99884400*(r[18][i] + r[-18][i])
+ 15890700*(r[19][i] + r[-19][i])
- 2118760*(r[20][i] + r[-20][i])
+ 230300*(r[21][i] + r[-21][i])
- 19600*(r[22][i] + r[-22][i])
+ 1225*(r[23][i] + r[-23][i])
- 50*(r[24][i] + r[-24][i])
+ (r[25][i] + r[-25][i])
- 126410606437752*r0[i]
- 168037864939466413690959660117507847865186469668506828800000000000000*r52[i]
) // 30414093201713378043612608166064768844377641568960512000000000000 for i in range(len(r0))]
r48 = [(-30957699535776*(r[1][i] + r[-1][i])
+ 27385657281648*(r[2][i] + r[-2][i])
- 22314239266528*(r[3][i] + r[-3][i])
+ 16735679449896*(r[4][i] + r[-4][i])
- 11541847896480*(r[5][i] + r[-5][i])
+ 7309837001104*(r[6][i] + r[-6][i])
- 4244421484512*(r[7][i] + r[-7][i])
+ 2254848913647*(r[8][i] + r[-8][i])
- 1093260079344*(r[9][i] + r[-9][i])
+ 482320623240*(r[10][i] + r[-10][i])
- 192928249296*(r[11][i] + r[-11][i])
+ 69668534468*(r[12][i] + r[-12][i])
- 22595200368*(r[13][i] + r[-13][i])
+ 6540715896*(r[14][i] + r[-14][i])
- 1677106640*(r[15][i] + r[-15][i])
+ 377348994*(r[16][i] + r[-16][i])
- 73629072*(r[17][i] + r[-17][i])
+ 12271512*(r[18][i] + r[-18][i])
- 1712304*(r[19][i] + r[-19][i])
+ 194580*(r[20][i] + r[-20][i])
- 17296*(r[21][i] + r[-21][i])
+ 1128*(r[22][i] + r[-22][i])
- 48*(r[23][i] + r[-23][i])
+ (r[24][i] + r[-24][i])
+ 32247603683100*r0[i]
- 60828186403426756087225216332129537688755283137921024000000000000*r50[i]
- 159972047422372025833793596431867471167657519124418501017600000000000*r52[i]
) // 12413915592536072670862289047373375038521486354677760000000000 for i in range(len(r0))]
r46 = [(7890371113950*(r[1][i] + r[-1][i])
- 6943526580276*(r[2][i] + r[-2][i])
+ 5608233007146*(r[3][i] + r[-3][i])
- 4154246671960*(r[4][i] + r[-4][i])
+ 2818953098830*(r[5][i] + r[-5][i])
- 1749695026860*(r[6][i] + r[-6][i])
+ 991493848554*(r[7][i] + r[-7][i])
- 511738760544*(r[8][i] + r[-8][i])
+ 239877544005*(r[9][i] + r[-9][i])
- 101766230790*(r[10][i] + r[-10][i])
+ 38910617655*(r[11][i] + r[-11][i])
- 13340783196*(r[12][i] + r[-12][i])
+ 4076350421*(r[13][i] + r[-13][i])
- 1101716330*(r[14][i] + r[-14][i])
+ 260932815*(r[15][i] + r[-15][i])
- 53524680*(r[16][i] + r[-16][i])
+ 9366819*(r[17][i] + r[-17][i])
- 1370754*(r[18][i] + r[-18][i])
+ 163185*(r[19][i] + r[-19][i])
- 15180*(r[20][i] + r[-20][i])
+ 1035*(r[21][i] + r[-21][i])
- 46*(r[22][i] + r[-22][i])
+ (r[23][i] + r[-23][i])
- 8233430727600*r0[i]
- 23793338219027472619152720674132302157166182179799040000000000*r48[i]
- 55378994704786442521077957369042933270804289023482265600000000000*r50[i]
- 92204777033212927855282293501621091950025889999533532774400000000000*r52[i]
) // 5502622159812088949850305428800254892961651752960000000000 for i in range(len(r0))]
r44 = [(-2012616400080*(r[1][i] + r[-1][i])
+ 1761039350070*(r[2][i] + r[-2][i])
- 1408831480056*(r[3][i] + r[-3][i])
+ 1029530696964*(r[4][i] + r[-4][i])
- 686353797976*(r[5][i] + r[-5][i])
+ 416714805914*(r[6][i] + r[-6][i])
- 229911617056*(r[7][i] + r[-7][i])
+ 114955808528*(r[8][i] + r[-8][i])
- 51915526432*(r[9][i] + r[-9][i])
+ 21090682613*(r[10][i] + r[-10][i])
- 7669339132*(r[11][i] + r[-11][i])
+ 2481256778*(r[12][i] + r[-12][i])
- 708930508*(r[13][i] + r[-13][i])
+ 177232627*(r[14][i] + r[-14][i])
- 38320568*(r[15][i] + r[-15][i])
+ 7059052*(r[16][i] + r[-16][i])
- 1086008*(r[17][i] + r[-17][i])
+ 135751*(r[18][i] + r[-18][i])
- 13244*(r[19][i] + r[-19][i])
+ 946*(r[20][i] + r[-20][i])
- 44*(r[21][i] + r[-21][i])
+ (r[22][i] + r[-22][i])
+ 2104098963720*r0[i]
- 10088140626322163074725559952800467303763028213760000000000*r46[i]
- 20672617771459376572727617455278717598871197415636992000000000*r48[i]
- 30390960789555990223010654132076029106169285558507929600000000000*r50[i]
- 35940698724546850336855815971061681513098805595301121884160000000000*r52[i]
) // 2658271574788448768043625811014615890319638528000000000 for i in range(len(r0))]
r42 = [(513791607420*(r[1][i] + r[-1][i])
- 446775310800*(r[2][i] + r[-2][i])
+ 353697121050*(r[3][i] + r[-3][i])
- 254661927156*(r[4][i] + r[-4][i])
+ 166509721602*(r[5][i] + r[-5][i])
- 98672427616*(r[6][i] + r[-6][i])
+ 52860229080*(r[7][i] + r[-7][i])
- 25518731280*(r[8][i] + r[-8][i])
+ 11058116888*(r[9][i] + r[-9][i])
- 4280561376*(r[10][i] + r[-10][i])
+ 1471442973*(r[11][i] + r[-11][i])
- 445891810*(r[12][i] + r[-12][i])
+ 118030185*(r[13][i] + r[-13][i])
- 26978328*(r[14][i] + r[-14][i])
+ 5245786*(r[15][i] + r[-15][i])
- 850668*(r[16][i] + r[-16][i])
+ 111930*(r[17][i] + r[-17][i])
- 11480*(r[18][i] + r[-18][i])
+ 861*(r[19][i] + r[-19][i])
- 42*(r[20][i] + r[-20][i])
+ (r[21][i] + r[-21][i])
- 538257874440*r0[i]
- 4651975255879785344076345169275577808059367424000000000*r44[i]
- 8345643609048334907272963233680386587658505158656000000000*r46[i]
- 10774531600512501036897720551649645765494516918255616000000000*r48[i]
- 11221709145032637985686395016457126546359868596714209280000000000*r50[i]
- 10024126976056544454447469133748446849553291271003522990080000000000*r52[i]
) // 1405006117752879898543142606244511569936384000000000 for i in range(len(r0))]
r40 = [(-131282408400*(r[1][i] + r[-1][i])
+ 113380261800*(r[2][i] + r[-2][i])
- 88732378800*(r[3][i] + r[-3][i])
+ 62852101650*(r[4][i] + r[-4][i])
- 40225345056*(r[5][i] + r[-5][i])
+ 23206929840*(r[6][i] + r[-6][i])
- 12033222880*(r[7][i] + r[-7][i])
+ 5586853480*(r[8][i] + r[-8][i])
- 2311801440*(r[9][i] + r[-9][i])
+ 847660528*(r[10][i] + r[-10][i])
- 273438880*(r[11][i] + r[-11][i])
+ 76904685*(r[12][i] + r[-12][i])
- 18643560*(r[13][i] + r[-13][i])
+ 3838380*(r[14][i] + r[-14][i])
- 658008*(r[15][i] + r[-15][i])
+ 91390*(r[16][i] + r[-16][i])
- 9880*(r[17][i] + r[-17][i])
+ 780*(r[18][i] + r[-18][i])
- 40*(r[19][i] + r[-19][i])
+ (r[20][i] + r[-20][i])
+ 137846528820*r0[i]
- 2341676862921466497571904343740852616560640000000000*r42[i]
- 3655123415334117056059985490145096849189502976000000000*r44[i]
- 4119688019118574531237133429498603530973935042560000000000*r46[i]
- 3757340713824985498498548346794211825654347639816192000000000*r48[i]
- 2947359606908914693821004025256012800585708025466060800000000000*r50[i]
- 2064558678210662377343329526788684890767865636215995760640000000000*r52[i]
) // 815915283247897734345611269596115894272000000000 for i in range(len(r0))]
r38 = [(33578000610*(r[1][i] + r[-1][i])
- 28781143380*(r[2][i] + r[-2][i])
+ 22239974430*(r[3][i] + r[-3][i])
- 15471286560*(r[4][i] + r[-4][i])
+ 9669554100*(r[5][i] + r[-5][i])
- 5414950296*(r[6][i] + r[-6][i])
+ 2707475148*(r[7][i] + r[-7][i])
- 1203322288*(r[8][i] + r[-8][i])
+ 472733756*(r[9][i] + r[-9][i])
- 163011640*(r[10][i] + r[-10][i])
+ 48903492*(r[11][i] + r[-11][i])
- 12620256*(r[12][i] + r[-12][i])
+ 2760681*(r[13][i] + r[-13][i])
- 501942*(r[14][i] + r[-14][i])
+ 73815*(r[15][i] + r[-15][i])
- 8436*(r[16][i] + r[-16][i])
+ 703*(r[17][i] + r[-17][i])
- 38*(r[18][i] + r[-18][i])
+ (r[19][i] + r[-19][i])
- 35345263800*r0[i]
- 1291865865142504746047217843527183499264000000000*r40[i]
- 1742597865490724651943092149133817822157209600000000*r42[i]
- 1703614521144184428726371303487541532883419136000000000*r44[i]
- 1352221478318945952566471137817160521323572835123200000000*r46[i]
- 925912385499308009244605568293800045079467288166400000000000*r48[i]
- 567701817594292628086492254286076775983065657711263744000000000*r50[i]
- 319529132633551445730754266569514531984165615759324610560000000000*r52[i]
) // 523022617466601111760007224100074291200000000 for i in range(len(r0))]
r36 = [(-8597496600*(r[1][i] + r[-1][i])
+ 7307872110*(r[2][i] + r[-2][i])
- 5567902560*(r[3][i] + r[-3][i])
+ 3796297200*(r[4][i] + r[-4][i])
- 2310789600*(r[5][i] + r[-5][i])
+ 1251677700*(r[6][i] + r[-6][i])
- 600805296*(r[7][i] + r[-7][i])
+ 254186856*(r[8][i] + r[-8][i])
- 94143280*(r[9][i] + r[-9][i])
+ 30260340*(r[10][i] + r[-10][i])
- 8347680*(r[11][i] + r[-11][i])
+ 1947792*(r[12][i] + r[-12][i])
- 376992*(r[13][i] + r[-13][i])
+ 58905*(r[14][i] + r[-14][i])
- 7140*(r[15][i] + r[-15][i])
+ 630*(r[16][i] + r[-16][i])
- 36*(r[17][i] + r[-17][i])
+ (r[18][i] + r[-18][i])
+ 9075135300*r0[i]
- 784533926199901667640010836150111436800000000*r38[i]
- 907705752613286229459492537425678932377600000000*r40[i]
- 764250847583238143225401875995898505750118400000000*r42[i]
- 524336156604477506256224109002957345627779891200000000*r44[i]
- 311351658482338919180732210200430367625645444300800000000*r46[i]
- 166036590632320367531429334375544068072103816986624000000000*r48[i]
- 81499841025612949496109930847966440863640763389444096000000000*r50[i]
- 37466461814083366759359795735852259604455926584422957056000000000*r52[i]
) // 371993326789901217467999448150835200000000 for i in range(len(r0))]
r34 = [(2203961430*(r[1][i] + r[-1][i])
- 1855967520*(r[2][i] + r[-2][i])
+ 1391975640*(r[3][i] + r[-3][i])
- 927983760*(r[4][i] + r[-4][i])
+ 548354040*(r[5][i] + r[-5][i])
- 286097760*(r[6][i] + r[-6][i])
+ 131128140*(r[7][i] + r[-7][i])
- 52451256*(r[8][i] + r[-8][i])
+ 18156204*(r[9][i] + r[-9][i])
- 5379616*(r[10][i] + r[-10][i])
+ 1344904*(r[11][i] + r[-11][i])
- 278256*(r[12][i] + r[-12][i])
+ 46376*(r[13][i] + r[-13][i])
- 5984*(r[14][i] + r[-14][i])
+ 561*(r[15][i] + r[-15][i])
- 34*(r[16][i] + r[-16][i])
+ (r[17][i] + r[-17][i])
- 2333606220*r0[i]
- 526990546285693391412999218213683200000000*r36[i]
- 518664095654379435828673830565907005440000000*r38[i]
- 373138241060740797524227217357125818777600000000*r40[i]
- 219618160307546307818407858079592245845032960000000*r42[i]
- 112275193446419212026758411812279514001781555200000000*r44[i]
- 51713216892097268029263570056035419810630708756480000000*r46[i]
- 21987290206937420965021290881182668895459624353792000000000*r48[i]
- 8778185176019659621127125508818359337012951782732595200000000*r50[i]
- 3332107853530764777529629230140567884444349753800523776000000000*r52[i]
) // 295232799039604140847618609643520000000 for i in range(len(r0))]
r32 = [(-565722720*(r[1][i] + r[-1][i])
+ 471435600*(r[2][i] + r[-2][i])
- 347373600*(r[3][i] + r[-3][i])
+ 225792840*(r[4][i] + r[-4][i])
- 129024480*(r[5][i] + r[-5][i])
+ 64512240*(r[6][i] + r[-6][i])
- 28048800*(r[7][i] + r[-7][i])
+ 10518300*(r[8][i] + r[-8][i])
- 3365856*(r[9][i] + r[-9][i])
+ 906192*(r[10][i] + r[-10][i])
- 201376*(r[11][i] + r[-11][i])
+ 35960*(r[12][i] + r[-12][i])
- 4960*(r[13][i] + r[-13][i])
+ 496*(r[14][i] + r[-14][i])
- 32*(r[15][i] + r[-15][i])
+ (r[16][i] + r[-16][i])
+ 601080390*r0[i]
- 393643732052805521130158146191360000000*r34[i]
- 326527475737802179777466182265733120000000*r36[i]
- 198969979872214920293886346099446251520000000*r38[i]
- 99626745669333527035567016277524852244480000000*r40[i]
- 43498703313314018776504938348732045412270080000000*r42[i]
- 17170843124850370546818528558187736420780605440000000*r44[i]
- 6276444318289938061108840583768656479667869450240000000*r46[i]
- 2160301520690503531404610021529918026938609932697600000000*r48[i]
- 708745398984922590930383206855670263857046959528345600000000*r50[i]
- 223674822768508974680116468563119084809897119542327377920000000*r52[i]
) // 263130836933693530167218012160000000 for i in range(len(r0))]
r30 = [(145422675*(r[1][i] + r[-1][i])
- 119759850*(r[2][i] + r[-2][i])
+ 86493225*(r[3][i] + r[-3][i])
- 54627300*(r[4][i] + r[-4][i])
+ 30045015*(r[5][i] + r[-5][i])
- 14307150*(r[6][i] + r[-6][i])
+ 5852925*(r[7][i] + r[-7][i])
- 2035800*(r[8][i] + r[-8][i])
+ 593775*(r[9][i] + r[-9][i])
- 142506*(r[10][i] + r[-10][i])
+ 27405*(r[11][i] + r[-11][i])
- 4060*(r[12][i] + r[-12][i])
+ 435*(r[13][i] + r[-13][i])
- 30*(r[14][i] + r[-14][i])
+ (r[15][i] + r[-15][i])
- 155117520*r0[i]
- 328913546167116912709022515200000000*r32[i]
- 227575282593028191903372678266880000000*r34[i]
- 116309421454977381321426414757478400000000*r36[i]
- 49083095586740430887431564189583278080000000*r38[i]
- 18139371393109511951007844941215406489600000000*r40[i]
- 6083845843389094496001274537210012898426880000000*r42[i]
- 1895875482185729033390420637976407213657292800000000*r44[i]
- 557995741137378415081398016214860854983503380480000000*r46[i]
- 156963921056606539204438549741946823549156065280000000000*r48[i]
- 42576613536662088106792709282326106111384171273256960000000*r50[i]
- 11212252160226319834044842958792572575603224385840742400000000*r52[i]
) // 265252859812191058636308480000000 for i in range(len(r0))]
r28 = [(-37442160*(r[1][i] + r[-1][i])
+ 30421755*(r[2][i] + r[-2][i])
- 21474180*(r[3][i] + r[-3][i])
+ 13123110*(r[4][i] + r[-4][i])
- 6906900*(r[5][i] + r[-5][i])
+ 3108105*(r[6][i] + r[-6][i])
- 1184040*(r[7][i] + r[-7][i])
+ 376740*(r[8][i] + r[-8][i])
- 98280*(r[9][i] + r[-9][i])
+ 20475*(r[10][i] + r[-10][i])
- 3276*(r[11][i] + r[-11][i])
+ 378*(r[12][i] + r[-12][i])
- 28*(r[13][i] + r[-13][i])
+ (r[14][i] + r[-14][i])
+ 40116600*r0[i]
- 309461669780889568409026560000000*r30[i]
- 176516936443019409820508749824000000*r32[i]
- 74833313645455216256514439249920000000*r34[i]
- 26337328459046574816219104447299584000000*r36[i]
- 8155948144934385059006601147769159680000000*r38[i]
- 2301709517171786559798286695904076365824000000*r40[i]
- 605758813130095139988659617361096909783040000000*r42[i]
- 151061790397229175366153301919734749322543104000000*r44[i]
- 36109056667467121621981604705290955376859545600000000*r46[i]
- 8344518734397260673326477690101230819337996075008000000*r48[i]
- 1876453005146379321858026862378389310967569941790720000000*r50[i]
- 412683020050097630454766497837161869694785723928936448000000*r52[i]
) // 304888344611713860501504000000 for i in range(len(r0))]
r26 = [(9657700*(r[1][i] + r[-1][i])
- 7726160*(r[2][i] + r[-2][i])
+ 5311735*(r[3][i] + r[-3][i])
- 3124550*(r[4][i] + r[-4][i])
+ 1562275*(r[5][i] + r[-5][i])
- 657800*(r[6][i] + r[-6][i])
+ 230230*(r[7][i] + r[-7][i])
- 65780*(r[8][i] + r[-8][i])
+ 14950*(r[9][i] + r[-9][i])
- 2600*(r[10][i] + r[-10][i])
+ 325*(r[11][i] + r[-11][i])
- 26*(r[12][i] + r[-12][i])
+ (r[13][i] + r[-13][i])
- 10400600*r0[i]
- 330295706662690015543296000000*r28[i]
- 153257207891488167212089344000000*r30[i]
- 53222214421459539592188788736000000*r32[i]
- 15436506593303376230082373484544000000*r34[i]
- 3960094929842931739454572322881536000000*r36[i]
- 930084233815670751630942950980583424000000*r38[i]
- 204528766884160018873274371645367648256000000*r40[i]
- 42768601883241439058698435075343591276544000000*r42[i]
- 8599134589431485780708409429924529774657536000000*r44[i]
- 1676115909489027560076829587121962388192493568000000*r46[i]
- 318686948683222526304282057035116495208098824192000000*r48[i]
- 59389194499215983294435493136240165006801607589888000000*r50[i]
- 10888114924031601962481145504131710392319020299190272000000*r52[i]
) // 403291461126605635584000000 for i in range(len(r0))]
r24 = [(-2496144*(r[1][i] + r[-1][i])
+ 1961256*(r[2][i] + r[-2][i])
- 1307504*(r[3][i] + r[-3][i])
+ 735471*(r[4][i] + r[-4][i])
- 346104*(r[5][i] + r[-5][i])
+ 134596*(r[6][i] + r[-6][i])
- 42504*(r[7][i] + r[-7][i])
+ 10626*(r[8][i] + r[-8][i])
- 2024*(r[9][i] + r[-9][i])
+ 276*(r[10][i] + r[-10][i])
- 24*(r[11][i] + r[-11][i])
+ (r[12][i] + r[-12][i])
+ 2704156*r0[i]
- 403291461126605635584000000*r26[i]
- 149903436100759314746572800000*r28[i]
- 42033455827381598974377984000000*r30[i]
- 9910695932425713906157643366400000*r32[i]
- 2078962023961017163954848006144000000*r34[i]
- 401274139495715827174031120636313600000*r36[i]
- 72837740568171787457915404507152384000000*r38[i]
- 12620369661259070567869332718886859571200000*r40[i]
- 2109601340251819353520575234140712075264000000*r42[i]
- 342864867500163789441705220714949009654415360000*r44[i]
- 54497476891656721001996702786930540928565248000000*r46[i]
- 8509384879617502075402808457393042025589086617600000*r48[i]
- 1309755467175539670340841790934034624876228640768000000*r50[i]
- 199264959019086425512537383104357541174886386420940800000*r52[i]
) // 620448401733239439360000 for i in range(len(r0))]
r22 = [(646646*(r[1][i] + r[-1][i])
- 497420*(r[2][i] + r[-2][i])
+ 319770*(r[3][i] + r[-3][i])
- 170544*(r[4][i] + r[-4][i])
+ 74613*(r[5][i] + r[-5][i])
- 26334*(r[6][i] + r[-6][i])
+ 7315*(r[7][i] + r[-7][i])
- 1540*(r[8][i] + r[-8][i])
+ 231*(r[9][i] + r[-9][i])
- 22*(r[10][i] + r[-10][i])
+ (r[11][i] + r[-11][i])
- 705432*r0[i]
- 568744368255469486080000*r24[i]
- 166357727714724824678400000*r26[i]
- 37042320704478727628390400000*r28[i]
- 6988909951599209517839155200000*r30[i]
- 1180836611760352104108962611200000*r32[i]
- 184607985589364774573429361868800000*r34[i]
- 27272218262298384682708194086092800000*r36[i]
- 3861838803337560097698395778726297600000*r38[i]
- 529471212011799260411940801849645465600000*r40[i]
- 70801221927358337925257947461388534087680000*r42[i]
- 9284304296436839352157882253583122352046080000*r44[i]
- 1198819215976330165063918942164935021513932800000*r46[i]
- 152905877736629296164560458459124226796014796800000*r48[i]
- 19311905336609987288869864510609701436067866214400000*r50[i]
- 2419865045937700153119519054510295236128129836646400000*r52[i]
) // 1124000727777607680000 for i in range(len(r0))]
r20 = [(-167960*(r[1][i] + r[-1][i])
+ 125970*(r[2][i] + r[-2][i])
- 77520*(r[3][i] + r[-3][i])
+ 38760*(r[4][i] + r[-4][i])
- 15504*(r[5][i] + r[-5][i])
+ 4845*(r[6][i] + r[-6][i])
- 1140*(r[7][i] + r[-7][i])
+ 190*(r[8][i] + r[-8][i])
- 20*(r[9][i] + r[-9][i])
+ (r[10][i] + r[-10][i])
+ 184756*r0[i]
- 936667273148006400000*r22[i]
- 211124803367560642560000*r24[i]
- 36608302274885332992000000*r26[i]
- 5425950533240873322086400000*r28[i]
- 725494605231272191451136000000*r30[i]
- 90317652741043657957240012800000*r32[i]
- 10681064948020015063470219264000000*r34[i]
- 1216234618180639720975550420582400000*r36[i]
- 134607612138429628983625351999488000000*r38[i]
- 14578366393789236829898507440652451840000*r40[i]
- 1552719574083291045891061928041363046400000*r42[i]
- 163243281617906068079686557318998305013760000*r44[i]
- 16988641998903346735554689301227465785344000000*r46[i]
- 1753883399302689292116989257696255397727436800000*r48[i]
- 179923160623142188671570235338790827627528192000000*r50[i]
- 18364686854092318474868714992301176836519274905600000*r52[i]
) // 2432902008176640000 for i in range(len(r0))]
r18 = [(43758*(r[1][i] + r[-1][i])
- 31824*(r[2][i] + r[-2][i])
+ 18564*(r[3][i] + r[-3][i])
- 8568*(r[4][i] + r[-4][i])
+ 3060*(r[5][i] + r[-5][i])
- 816*(r[6][i] + r[-6][i])
+ 153*(r[7][i] + r[-7][i])
- 18*(r[8][i] + r[-8][i])
+ (r[9][i] + r[-9][i])
- 48620*r0[i]
- 1824676506132480000*r20[i]
- 309100200138842112000*r22[i]
- 40778478784550707200000*r24[i]
- 4645053436190368481280000*r26[i]
- 481314610282065419059200000*r28[i]
- 46758400573464312663490560000*r30[i]
- 4340262299778024388805836800000*r32[i]
- 389810850996416354285601300480000*r34[i]
- 34168816632541202331763973529600000*r36[i]
- 2941066263016510346147295370272768000*r38[i]
- 249691933432545691845292589410836480000*r40[i]
- 20977168972570956554158853986478948352000*r42[i]
- 1748194308191420862068509392967461273600000*r44[i]
- 144787366874617417267158756772391629455360000*r46[i]
- 11933738665455945947029762024119178565222400000*r48[i]
- 979923136258156862399188048479194930964357120000*r50[i]
- 80229698384887928012137580653965134357931417600000*r52[i]
) // 6402373705728000 for i in range(len(r0))]
r16 = [(-11440*(r[1][i] + r[-1][i])
+ 8008*(r[2][i] + r[-2][i])
- 4368*(r[3][i] + r[-3][i])
+ 1820*(r[4][i] + r[-4][i])
- 560*(r[5][i] + r[-5][i])
+ 120*(r[6][i] + r[-6][i])
- 16*(r[7][i] + r[-7][i])
+ (r[8][i] + r[-8][i])
+ 12870*r0[i]
- 4268249137152000*r18[i]
- 527128768438272000*r20[i]
- 51442361350668288000*r22[i]
- 4385609982489415680000*r24[i]
- 343350594609952849920000*r26[i]
- 25398422028160175554560000*r28[i]
- 1806640043553643996938240000*r30[i]
- 124998708216981630040289280000*r32[i]
- 8477574188991756975915909120000*r34[i]
- 566640901244029272138606256128000*r36[i]
- 37469170353622071265887792218112000*r38[i]
- 2457916223969789263693314523533312000*r40[i]
- 160273272592069873142621634191720448000*r42[i]
- 10404012781412834769965673013161000960000*r44[i]
- 673078263437696563365695181553779671040000*r46[i]
- 43432367177206668920840929822030938501120000*r48[i]
- 2797138392082425352298525252125310293524480000*r50[i]
- 179874692542903270845206591460923776914677760000*r52[i]
) // 20922789888000 for i in range(len(r0))]
r14 = [(3003*(r[1][i] + r[-1][i])
- 2002*(r[2][i] + r[-2][i])
+ 1001*(r[3][i] + r[-3][i])
- 364*(r[4][i] + r[-4][i])
+ 91*(r[5][i] + r[-5][i])
- 14*(r[6][i] + r[-6][i])
+ (r[7][i] + r[-7][i])
- 3432*r0[i]
- 12204960768000*r16[i]
- 1058170098585600*r18[i]
- 73775500710912000*r20[i]
- 4555411900194355200*r22[i]
- 261131482210959360000*r24[i]
- 14266599888013304832000*r26[i]
- 754754307297469839360000*r28[i]
- 39057272623118392651008000*r30[i]
- 1990236929603886055572480000*r32[i]
- 100317304785653440333283635200*r34[i]
- 5017302808350824370904132608000*r36[i]
- 249538838908236261152065923225600*r38[i]
- 12360976075014001109372936189952000*r40[i]
- 610513898001512036824535103712051200*r42[i]
- 30089355946979742032883786297815040000*r44[i]
- 1480659654975370272651825844120998144000*r46[i]
- 72778719754993922352940597980542622720000*r48[i]
- 3574314373450201242087397187099658871296000*r50[i]
- 175435230758177290496267410991246070236160000*r52[i]
) // 87178291200 for i in range(len(r0))]
r12 = [(-792*(r[1][i] + r[-1][i])
+ 495*(r[2][i] + r[-2][i])
- 220*(r[3][i] + r[-3][i])
+ 66*(r[4][i] + r[-4][i])
- 12*(r[5][i] + r[-5][i])
+ (r[6][i] + r[-6][i])
+ 924*r0[i]
- 43589145600*r14[i]
- 2528170444800*r16[i]
- 120467944396800*r18[i]
- 5167100908569600*r20[i]
- 208331313744153600*r22[i]
- 8083281646573056000*r24[i]
- 305994026290208256000*r26[i]
- 11397316294188849024000*r28[i]
- 419948192698268217984000*r30[i]
- 15360962830016613243033600*r32[i]
- 559092713482449420732057600*r34[i]
- 20280226917834433943755084800*r36[i]
- 733917409397935785284098636800*r38[i]
- 26516869922120782776160606617600*r40[i]
- 957005191789297958689924263321600*r42[i]
- 34512162491005016706155579824512000*r44[i]
- 1243937698905379082423800102273152000*r46[i]
- 44819260744500257106087286005881088000*r48[i]
- 1614431094051811175741477051443876608000*r50[i]
- 58142963949556229658359411701218990105600*r52[i]
) // 479001600 for i in range(len(r0))]
r10 = [(210*(r[1][i] + r[-1][i])
- 120*(r[2][i] + r[-2][i])
+ 45*(r[3][i] + r[-3][i])
- 10*(r[4][i] + r[-4][i])
+ (r[5][i] + r[-5][i])
- 252*r0[i]
- 199584000*r12[i]
- 7264857600*r14[i]
- 223134912000*r16[i]
- 6289809926400*r18[i]
- 169058189664000*r20[i]
- 4419351149875200*r22[i]
- 113605204648320000*r24[i]
- 2890388998040544000*r26[i]
- 73066712935376160000*r28[i]
- 1839605249083010572800*r30[i]
- 46197360620085939264000*r32[i]
- 1158251761107990889401600*r34[i]
- 29009396635576994764512000*r36[i]
- 726084725720412923735270400*r38[i]
- 18165716613255899607139584000*r40[i]
- 454360504471895403926563219200*r42[i]
- 11362494160594553046963852960000*r44[i]
- 284118059898561657806684273088000*r46[i]
- 7103842801529696381323903273920000*r48[i]
- 177610330992631300501801888177516800*r50[i]
- 4440486450890050497235584413672544000*r52[i]
) // 3628800 for i in range(len(r0))]
r8 = [(-56*(r[1][i] + r[-1][i])
+ 28*(r[2][i] + r[-2][i])
- 8*(r[3][i] + r[-3][i])
+ (r[4][i] + r[-4][i])
+ 70*r0[i]
- 1209600*r10[i]
- 25280640*r12[i]
- 461260800*r14[i]
- 7904856960*r16[i]
- 131254905600*r18[i]
- 2143293425280*r20[i]
- 34682510016000*r22[i]
- 558432020361600*r24[i]
- 8966533159584000*r26[i]
- 143749174428961920*r28[i]
- 2302548811229721600*r30[i]
- 36863840064915642240*r32[i]
- 590028976413583660800*r34[i]
- 9442331455422829138560*r36[i]
- 151094113839739041753600*r38[i]
- 2417657116643486089706880*r40[i]
- 38683875524088319997472000*r42[i]
- 618954263309240362088323200*r44[i]
- 9903378507277068408849408000*r46[i]
- 158455048765455207825625883520*r48[i]
- 2535289714088718783746769273600*r50[i]
- 40564715829993365422700852403840*r52[i]
) // 40320 for i in range(len(r0))]
r6 = [(15*(r[1][i] + r[-1][i])
- 6*(r[2][i] + r[-2][i])
+ (r[3][i] + r[-3][i])
- 20*r0[i]
- 10080*r8[i]
- 105840*r10[i]
- 1013760*r12[i]
- 9369360*r14[i]
- 85307040*r16[i]
- 771695280*r18[i]
- 6960985920*r20[i]
- 62711787600*r22[i]
- 564657746400*r24[i]
- 5082926350320*r26[i]
- 45750363684480*r28[i]
- 411769379287440*r30[i]
- 3705988838096160*r32[i]
- 33354157240902960*r34[i]
- 300188445960277440*r36[i]
- 2701700136811100880*r38[i]
- 24315317723974324320*r40[i]
- 218837925486466585200*r42[i]
- 1969541593260989932800*r44[i]
- 17725875394880072059920*r46[i]
- 159532882776045299198880*r48[i]
- 1435795961872906295429040*r50[i]
- 12922163724410151069418560*r52[i]
) // 720 for i in range(len(r0))]
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
- 504*r8[i]
- 2040*r10[i]
- 8184*r12[i]
- 32760*r14[i]
- 131064*r16[i]
- 524280*r18[i]
- 2097144*r20[i]
- 8388600*r22[i]
- 33554424*r24[i]
- 134217720*r26[i]
- 536870904*r28[i]
- 2147483640*r30[i]
- 8589934584*r32[i]
- 34359738360*r34[i]
- 137438953464*r36[i]
- 549755813880*r38[i]
- 2199023255544*r40[i]
- 8796093022200*r42[i]
- 35184372088824*r44[i]
- 140737488355320*r46[i]
- 562949953421304*r48[i]
- 2251799813685240*r50[i]
- 9007199254740984*r52[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
- 2*r8[i]
- 2*r10[i]
- 2*r12[i]
- 2*r14[i]
- 2*r16[i]
- 2*r18[i]
- 2*r20[i]
- 2*r22[i]
- 2*r24[i]
- 2*r26[i]
- 2*r28[i]
- 2*r30[i]
- 2*r32[i]
- 2*r34[i]
- 2*r36[i]
- 2*r38[i]
- 2*r40[i]
- 2*r42[i]
- 2*r44[i]
- 2*r46[i]
- 2*r48[i]
- 2*r50[i]
- 2*r52[i]
) // 2 for i in range(len(r0))]
r51 = [(-18367353072152*r[1][i]
+ 32798844771700*r[2][i]
- 40715807302800*r[3][i]
+ 41620603020640*r[4][i]
- 36921502679600*r[5][i]
+ 29075683360185*r[6][i]
- 20558563992050*r[7][i]
+ 13129839188200*r[8][i]
- 7596549816030*r[9][i]
+ 3985844039275*r[10][i]
- 1895969056520*r[11][i]
+ 816446005200*r[12][i]
- 317506779800*r[13][i]
+ 111127372930*r[14][i]
- 34848305100*r[15][i]
+ 9735399520*r[16][i]
- 2405549300*r[17][i]
+ 520987950*r[18][i]
- 97765640*r[19][i]
+ 15660400*r[20][i]
- 2099160*r[21][i]
+ 229075*r[22][i]
- 19550*r[23][i]
+ 1224*r[24][i]
- 50*r[25][i]
+ r[26][i]
+ 4861946401452*r0[i]
- 2579808294648*r2[i]
+ 5653622432952*r4[i]
- 27280100477448*r6[i]
+ 234657881740152*r8[i]
- 3210736324810248*r10[i]
+ 65015030756447352*r12[i]
- 1854200415783543048*r14[i]
+ 71870433940146354552*r16[i]
- 3687349223477219875848*r18[i]
+ 245473564244803456261752*r20[i]
- 20888307287949627757008648*r22[i]
+ 2246840224563905580570968952*r24[i]
- 303094970433352624372214141448*r26[i]
+ 51019602983331540473045839276152*r28[i]
- 10691645514373727983810335922474248*r30[i]
+ 2790651091406916364299868206057983352*r32[i]
- 910446673933990019203515025763541207048*r34[i]
+ 373948949766422140435706410007606455890552*r36[i]
- 195681514530799165910557748483841641873539848*r38[i]
+ 132897106175336006092720191507876479916677797752*r40[i]
- 120554003537142419244816814513161495212294682672648*r42[i]
+ 152971535906456634616842226470152212508964788768504952*r44[i]
- 294458451533217960963210426417324728393814119257507805448*r46[i]
+ 1019832500675924760582251357311129578949356520774019156812152*r48[i]
- 11400247815546832449432199417474318613528727464280459760480138248*r50[i]
- 136675603482281861796246376772747198814333993503815350676473360480648*r52[i]
) // 1551118753287382280224243016469303211063259720016986112000000000000 for i in range(len(r0))]
r49 = [(4861946401452*r[1][i]
- 8643460269248*r[2][i]
+ 10649977831752*r[3][i]
- 10772391370048*r[4][i]
+ 9425842448792*r[5][i]
- 7297426411968*r[6][i]
+ 5054988087457*r[7][i]
- 3151161405168*r[8][i]
+ 1772528290407*r[9][i]
- 900331830048*r[10][i]
+ 412652088772*r[11][i]
- 170333048928*r[12][i]
+ 63127818572*r[13][i]
- 20918093728*r[14][i]
+ 6163366902*r[15][i]
- 1603477568*r[16][i]
+ 365077482*r[17][i]
- 71916768*r[18][i]
+ 12076932*r[19][i]
- 1695008*r[20][i]
+ 193452*r[21][i]
- 17248*r[22][i]
+ 1127*r[23][i]
- 48*r[24][i]
+ r[25][i]
- 1289904147324*r0[i]
+ 686119227300*r2[i]
- 1509462300060*r4[i]
+ 7323923844900*r6[i]
- 63466456620060*r8[i]
+ 876655994638500*r10[i]
- 17962494591036060*r12[i]
+ 519729378435224100*r14[i]
- 20498730418437708060*r16[i]
+ 1073773191888393761700*r18[i]
- 73266053614681083996060*r20[i]
+ 6418563118124648605611300*r22[i]
- 714493710681785410524780060*r24[i]
+ 100357569802461927273985332900*r26[i]
- 17717998874943470330819342460060*r28[i]
+ 3928707238871982933864962858686500*r30[i]
- 1096834043813751169204010169826956060*r32[i]
+ 388004275037568389575404928401474632100*r34[i]
- 175870982185451189351017757509405335708060*r36[i]
+ 103991298038492644018924403718805266597329700*r38[i]
- 82506842083007670338625750577445488484693676060*r40[i]
+ 91947467567672513735818977678842895400970978139300*r42[i]
- 156026356786659861162429714318097107470538947633340060*r44[i]
+ 477994672122502000860149649242839645232774457016507620900*r46[i]
- 4741041014119120622582667190202604787803330381303410474700060*r48[i]
- 50576092532930275709972631359425317424152381858024219560152465500*r50[i]
- 3360757298789328273819193202350156957303729393370136576000000000000*r51[i]
- 192818334124303175599491864945168536471848882690784611504742445276060*r52[i]
) // 608281864034267560872252163321295376887552831379210240000000000 for i in range(len(r0))]
r47 = [(-1289904147324*r[1][i]
+ 2282138106804*r[2][i]
- 2789279908316*r[3][i]
+ 2789279908316*r[4][i]
- 2404551645100*r[5][i]
+ 1827459250276*r[6][i]
- 1237956266316*r[7][i]
+ 751616304549*r[8][i]
- 409972529754*r[9][i]
+ 200966926350*r[10][i]
- 88425447594*r[11][i]
+ 34834267234*r[12][i]
- 12239066866*r[13][i]
+ 3815417606*r[14][i]
- 1048191650*r[15][i]
+ 251565996*r[16][i]
- 52153926*r[17][i]
+ 9203634*r[18][i]
- 1355574*r[19][i]
+ 162150*r[20][i]
- 15134*r[21][i]
+ 1034*r[22][i]
- 46*r[23][i]
+ r[24][i]
+ 343059613650*r0[i]
- 182965127280*r2[i]
+ 404225281200*r4[i]
- 1973179787280*r6[i]
+ 17237751438000*r8[i]
- 240592045595280*r10[i]
+ 4994170279690800*r12[i]
- 146823806097131280*r14[i]
+ 5903690350090119600*r16[i]
- 316485671150054075280*r18[i]
+ 22198064042219526404400*r20[i]
- 2009394413056841321867280*r22[i]
+ 232532372014701449341825200*r24[i]
- 34201309524439700202831707280*r26[i]
+ 6378595465863797572545515262000*r28[i]
- 1510321457529226404281297600555280*r30[i]
+ 456430932151854961874111940707194800*r32[i]
- 177879954967657922123999080680411131280*r34[i]
+ 90948410673639301600046982211812755703600*r36[i]
- 62713181699432641518049958716708665011915280*r38[i]
+ 61017960828891287286335064536456771132612468400*r40[i]
- 90771056129445230547328475921502515772170837147280*r42[i]
+ 244690112718607318914399753695429565221879804118769200*r44[i]
- 2142766872532178730068138061640892672650431299718846827280*r46[i]
- 20243597746218463146623496754059816935278614102767681978514000*r48[i]
- 1267253883404724085150525340252698701849068398706688000000000000*r49[i]
- 68540933797288160408485956779561102500745596951326307091686715280*r50[i]
- 3332750987966083871537366592330572315992864981758718771200000000000*r51[i]
- 149233459487753154020208258958096224473270440522821423115697370901200*r52[i]
) // 258623241511168180642964355153611979969197632389120000000000 for i in range(len(r0))]
r45 = [(343059613650*r[1][i]
- 603784920024*r[2][i]
+ 731508653106*r[3][i]
- 722477682080*r[4][i]
+ 612815891050*r[5][i]
- 456442180920*r[6][i]
+ 301758997386*r[7][i]
- 177996090624*r[8][i]
+ 93865125915*r[9][i]
- 44246187300*r[10][i]
+ 18609425835*r[11][i]
- 6960408624*r[12][i]
+ 2304024151*r[13][i]
- 670609940*r[14][i]
+ 170173575*r[15][i]
- 37234560*r[16][i]
+ 6923301*r[17][i]
- 1072764*r[18][i]
+ 134805*r[19][i]
- 13200*r[20][i]
+ 945*r[21][i]
- 44*r[22][i]
+ r[23][i]
- 91482563640*r0[i]
+ 48932534040*r2[i]
- 108606356040*r4[i]
+ 533667580440*r6[i]
- 4703763586440*r8[i]
+ 66408505338840*r10[i]
- 1398457857168840*r12[i]
+ 41847457290489240*r14[i]
- 1719246675671583240*r16[i]
+ 94585481325000311640*r18[i]
- 6843422433568588589640*r20[i]
+ 642897110978465333366040*r22[i]
- 77770562351946223415228040*r24[i]
+ 12062233927817328810997492440*r26[i]
- 2397961353314881501418831818440*r28[i]
+ 613494954527608404597659277810840*r30[i]
- 203877970345571868715766678319960840*r32[i]
+ 89457569257636570186619080797284721240*r34[i]
- 53237495951641479759332571910597970535240*r36[i]
+ 44930968310714379648812137260536985281903640*r38[i]
- 58241166312158469946465066186170960196371701640*r40[i]
+ 137360888551881485527132727024151255460985294318040*r42[i]
- 1056294346650368430047563515157012073181421862576900040*r44[i]
- 8792490299555933486634712872596976297794618720689003795560*r46[i]
- 517246483022336361285928710307223959938395264778240000000000*r47[i]
- 26309260636200890673464765332665424581880256812272026952850440*r48[i]
- 1203891189234487880892999073240063766756614978771353600000000000*r49[i]
- 50764977622809978549916904649893168100296473949517793816320917160*r50[i]
- 2004451674635063649027875945687415042391867173902902886400000000000*r51[i]
- 74960269321392846499824811474695597918673304894478483366348507552840*r52[i]
) // 119622220865480194561963161495657715064383733760000000000 for i in range(len(r0))]
r43 = [(-91482563640*r[1][i]
+ 160094486370*r[2][i]
- 192113383644*r[3][i]
+ 187187399448*r[4][i]
- 155989499540*r[5][i]
+ 113649492522*r[6][i]
- 73153696336*r[7][i]
+ 41802112192*r[8][i]
- 21238169904*r[9][i]
+ 9586673915*r[10][i]
- 3834669566*r[11][i]
+ 1353412788*r[12][i]
- 418913482*r[13][i]
+ 112784399*r[14][i]
- 26127660*r[15][i]
+ 5133856*r[16][i]
- 839188*r[17][i]
+ 111069*r[18][i]
- 11438*r[19][i]
+ 860*r[20][i]
- 42*r[21][i]
+ r[22][i]
+ 24466267020*r0[i]
- 13128240840*r2[i]
+ 29286075720*r4[i]
- 144956522040*r6[i]
+ 1290252243720*r8[i]
- 18448766253240*r10[i]
+ 394763466531720*r12[i]
- 12048763425424440*r14[i]
+ 507104531694579720*r16[i]
- 28726839421461491640*r18[i]
+ 2153064433503155907720*r20[i]
- 211041986898764840790840*r22[i]
+ 26870132026261051008915720*r24[i]
- 4433779344005175981028538040*r26[i]
+ 950513389106656928711222883720*r28[i]
- 266877172369028643812085068829240*r30[i]
+ 99651017964870751887504875569971720*r32[i]
- 50788156610571325953562659420384640440*r34[i]
+ 36915961449056930526009630202648137219720*r36[i]
- 41419014418447665040750851917674255257827640*r38[i]
+ 84934578551016826327683205574058431012558547720*r40[i]
- 570180937724400876712836731188276811777920749126840*r42[i]
- 4158439692009034639969470592464099450041235634033244280*r44[i]
- 229275923325503706243762726200010620540068823040000000000*r45[i]
- 10938400640270606999512627385384658646639850257084618154040*r46[i]
- 469832222078622194834718578529061763610709032173568000000000*r47[i]
- 18609787245585710799825274640865231563879706109002975534476280*r48[i]
- 690703654308090686886605775729000661503847399056998400000000000*r49[i]
- 24295755635821397902484226724698036360412358674335136584603405240*r50[i]
- 816834061921519325837632181160492761661336490802298224640000000000*r51[i]
- 26420216400737828039776597843354259258729442541873887374106278588280*r52[i]
) // 60415263063373835637355132068513997507264512000000000 for i in range(len(r0))]
r41 = [(24466267020*r[1][i]
- 42550029600*r[2][i]
+ 50528160150*r[3][i]
- 48507033744*r[4][i]
+ 39645171810*r[5][i]
- 28192122176*r[6][i]
+ 17620076360*r[7][i]
- 9721421440*r[8][i]
+ 4739192952*r[9][i]
- 2038362560*r[10][i]
+ 770755843*r[11][i]
- 254795320*r[12][i]
+ 73066305*r[13][i]
- 17985552*r[14][i]
+ 3746990*r[15][i]
- 648128*r[16][i]
+ 90610*r[17][i]
- 9840*r[18][i]
+ 779*r[19][i]
- 40*r[20][i]
+ r[21][i]
- 6564120420*r0[i]
+ 3534526380*r2[i]
- 7928802420*r4[i]
+ 39562131180*r6[i]
- 355997149620*r8[i]
+ 5162772055980*r10[i]
- 112466379416820*r12[i]
+ 3509804003100780*r14[i]
- 151808102304340020*r16[i]
+ 8890838711788769580*r18[i]
- 693867758978013455220*r20[i]
+ 71436574576557715366380*r22[i]
- 9656103679244476561098420*r24[i]
+ 1714541855816811795973995180*r26[i]
- 402505898503128791422102405620*r28[i]
+ 126699650825847516884027712559980*r30[i]
- 54827934277723571354991704981312820*r32[i]
+ 34051732695777105364083032869387764780*r34[i]
- 32827430653262026254340815579045378556020*r36[i]
+ 58129225653125966892251726413185365757113580*r38[i]
- 338476895760295138790385051321218766549279671220*r40[i]
- 2149763077602671437231704105519918866633843849089620*r42[i]
- 110761315616185365335151075458942328763318272000000000*r43[i]
- 4942256826876098689793689711313418888604591478522994420*r44[i]
- 198705800215436545411261029373342537801392979968000000000*r45[i]
- 7372979698612811191617476736621847607367673634869335740820*r46[i]
- 256536466678869072307088584563086803940345640910848000000000*r47[i]
- 8465458808946796165763451715680655749443289544616664687661620*r48[i]
- 267183551072205666325866548010883965389520680874147840000000000*r49[i]
- 8117979331672354072521723205205099479673234187982104799090936020*r50[i]
- 238669689906108201296368312708296353560792649309607690240000000000*r51[i]
- 6818076027538551619225591166422355976547652044865002983244581608820*r52[i]
) // 33452526613163807108170062053440751665152000000000 for i in range(len(r0))]
r39 = [(-6564120420*r[1][i]
+ 11338026180*r[2][i]
- 13309856820*r[3][i]
+ 12570420330*r[4][i]
- 10056336264*r[5][i]
+ 6962078952*r[6][i]
- 4211628008*r[7][i]
+ 2234741392*r[8][i]
- 1040310648*r[9][i]
+ 423830264*r[10][i]
- 150391384*r[11][i]
+ 46142811*r[12][i]
- 12118314*r[13][i]
+ 2686866*r[14][i]
- 493506*r[15][i]
+ 73112*r[16][i]
- 8398*r[17][i]
+ 702*r[18][i]
- 38*r[19][i]
+ r[20][i]
+ 1767263190*r0[i]
- 955277400*r2[i]
+ 2156197560*r4[i]
- 10855425000*r6[i]
+ 98876533560*r8[i]
- 1456859058600*r10[i]
+ 32382608125560*r12[i]
- 1036360772970600*r14[i]
+ 46242812090245560*r16[i]
- 2813858311510281000*r18[i]
+ 230141619686501005560*r20[i]
- 25097337236284407949800*r22[i]
+ 3642002181929040219157560*r24[i]
- 706474912755087069174777000*r26[i]
+ 185490702479102020671448093560*r28[i]
- 67501512373123369695638979402600*r30[i]
+ 35506616897715366055874618759845560*r32[i]
- 29173319982987640073110629923442306600*r34[i]
+ 44272025958057634433180503709478279085560*r36[i]
- 222019441630075420847480526017947263931809000*r38[i]
- 1219813882056330049405575791394671579625372874440*r40[i]
- 58541921573036662439297608593521315414016000000000*r41[i]
- 2435494701008122308521041585840935773426259964069800*r42[i]
- 91378085383352926401499637253627421229737574400000000*r43[i]
- 3166734413390519310621011935324774315544541946854082440*r44[i]
- 102992200477964363280928335737465088274348376064000000000*r45[i]
- 3179252903572284408695210045628305460118381385145907089000*r46[i]
- 93933517845624637462463708669855295641358690995404800000000*r47[i]
- 2673604876174888392329293291823128228151672865125704677946440*r48[i]
- 73683990172722867345525100631400320014642700636651520000000000*r49[i]
- 1974418989189660654416775142028601893909607175588350467588706600*r50[i]
- 51613966955266559433583238169717122269196640905399894016000000000*r51[i]
- 1320028845480376778241459745623130669629332621855587804526269234440*r52[i]
) // 20397882081197443358640281739902897356800000000 for i in range(len(r0))]
r37 = [(1767263190*r[1][i]
- 3029594040*r[2][i]
+ 3511574910*r[3][i]
- 3257112960*r[4][i]
+ 2544619500*r[5][i]
- 1709984304*r[6][i]
+ 997490844*r[7][i]
- 506662016*r[8][i]
+ 223926516*r[9][i]
- 85795600*r[10][i]
+ 28312548*r[11][i]
- 7970688*r[12][i]
+ 1888887*r[13][i]
- 369852*r[14][i]
+ 58275*r[15][i]
- 7104*r[16][i]
+ 629*r[17][i]
- 36*r[18][i]
+ r[19][i]
- 477638700*r0[i]
+ 259289580*r2[i]
- 589294500*r4[i]
+ 2996657580*r6[i]
- 27670359300*r8[i]
+ 415064933580*r10[i]
- 9439543875300*r12[i]
+ 310922483993580*r14[i]
- 14379880666402500*r16[i]
+ 914767168887053580*r18[i]
- 79051272004645620900*r20[i]
+ 9231401536061270849580*r22[i]
- 1459700260139475814330500*r24[i]
+ 315843905250429722227637580*r26[i]
- 95612546130070295522414451300*r28[i]
+ 42177612582297377823299737193580*r30[i]
- 29268533564152352561039458453023300*r32[i]
+ 37747202396256876155482291281278813580*r34[i]
- 161759954125032708920885781040309430206500*r36[i]
- 763162014442847423121851269222329739576686420*r38[i]
- 33996470135329072264400469566504828928000000000*r39[i]
- 1314149222797294391875041342296266627244339280900*r40[i]
- 45857838565545385577449793398258363740979200000000*r41[i]
- 1479444354242422663436299123473954120225396734970420*r42[i]
- 44831961082741695492799244828619514023247872000000000*r43[i]
- 1290525734288850664269099373480698875776359383538646500*r44[i]
- 35584775745235419804380819416241066350620337766400000000*r45[i]
- 945953923580279776552772789184754415724912490598746182420*r46[i]
- 24366115407876526559068567586678948554722823372800000000000*r47[i]
- 610645775114510996953480313967173146186867766220019295823300*r48[i]
- 14939521515639279686486638270686230946922780466085888000000000*r49[i]
- 357801113228416003019399250210317079666322369514337123812946420*r50[i]
- 8408661385093459098177743857092487683793831993666437120000000000*r51[i]
- 194295554214245025331172354056693339192813114298766754673003451300*r52[i]
) // 13763753091226345046315979581580902400000000 for i in range(len(r0))]
r35 = [(-477638700*r[1][i]
+ 811985790*r[2][i]
- 927983760*r[3][i]
+ 843621600*r[4][i]
- 641886000*r[5][i]
+ 417225900*r[6][i]
- 233646504*r[7][i]
+ 112971936*r[8][i]
- 47071640*r[9][i]
+ 16811300*r[10][i]
- 5101360*r[11][i]
+ 1298528*r[12][i]
- 272272*r[13][i]
+ 45815*r[14][i]
- 5950*r[15][i]
+ 560*r[16][i]
- 34*r[17][i]
+ r[18][i]
+ 129644790*r0[i]
- 70715340*r2[i]
+ 161960940*r4[i]
- 832930740*r6[i]
+ 7810859340*r8[i]
- 119578066740*r10[i]
+ 2791740107340*r12[i]
- 95062235276340*r14[i]
+ 4584012079172940*r16[i]
- 307268933913567540*r18[i]
+ 28355038085389144140*r20[i]
- 3597774935929125068340*r22[i]
+ 632729503874459828228940*r24[i]
- 157381528472579148083026740*r26[i]
+ 57577884185625191071239755340*r28[i]
- 33404393172944223690128125810740*r30[i]
+ 36271128388074981554067219056171340*r32[i]
- 131671692334895976886647813958596908340*r34[i]
- 529104107360143104505564190890974500955060*r36[i]
- 21792609061108379656666967670836428800000000*r37[i]
- 779765567254824678774814590170424618060927540*r38[i]
- 25214048683702395262763681595157748121600000000*r39[i]
- 754531895504954495472529428607358759602244935860*r40[i]
- 21229190210645503978483385444330514048614400000000*r41[i]
- 567902644449952014090537079509460539320563935596340*r42[i]
- 14564893239013264062672891916748815156327219200000000*r43[i]
- 360416016142646161224945882401067658836071135991963060*r44[i]
- 8648657180064969977242561394456399100712373452800000000*r45[i]
- 202069375902424923136583586389997599181812580415819762740*r46[i]
- 4612127517564454653650814843765113002002883805184000000000*r47[i]
- 103121612921980129969364006657783463883530860291974593108660*r48[i]
- 2263884472933693041558609190221290023990021205262336000000000*r49[i]
- 48895910164254390571448366914991646721674728906975264997394740*r50[i]
- 1040735050391204632204438770440340544568220182900637696000000000*r51[i]
- 21862169403162391239341958599750577577387707221098019982750324660*r52[i]
) // 10333147966386144929666651337523200000000 for i in range(len(r0))]
r33 = [(129644790*r[1][i]
- 218349120*r[2][i]
+ 245642760*r[3][i]
- 218349120*r[4][i]
+ 161280600*r[5][i]
- 100975680*r[6][i]
+ 53993940*r[7][i]
- 24682944*r[8][i]
+ 9612108*r[9][i]
- 3164480*r[10][i]
+ 870232*r[11][i]
- 196416*r[12][i]
+ 35464*r[13][i]
- 4928*r[14][i]
+ 495*r[15][i]
- 32*r[16][i]
+ r[17][i]
- 35357670*r0[i]
+ 19389690*r2[i]
- 44796870*r4[i]
+ 233344890*r6[i]
- 2227139910*r8[i]
+ 34903389690*r10[i]
- 839988260550*r12[i]
+ 29734601940090*r14[i]
- 1506293149214790*r16[i]
+ 107487540061668090*r18[i]
- 10743535525710258630*r20[i]
+ 1511267716903778445690*r22[i]
- 304525956073869018848070*r24[i]
+ 91234873454404063067344890*r26[i]
- 43747586259736794619504039110*r28[i]
+ 39574917458915050445099774637690*r30[i]
- 120523981455993504966525708346887750*r32[i]
- 408775192473644376465790167368394203910*r34[i]
- 15499721949579217394499977006284800000000*r35[i]
- 511206585269023792365556128001469646849990*r36[i]
- 15254826342775865759666877369585500160000000*r37[i]
- 421754497238984285335705463354740490210507910*r38[i]
- 10974654148845317574241976981091935846400000000*r39[i]
- 271793538072560300468434911462753194293644181830*r40[i]
- 6459357656104303171129642884693889583677440000000*r41[i]
- 148248369194001435848413334991598692517822202402310*r42[i]
- 3302211571953506236081129759184691588287692800000000*r43[i]
- 71676123253955938571177412178194687158760951558339270*r44[i]
- 1520976967414625530272457942824571170900903198720000000*r45[i]
- 31639609352600382246311701401196841805566037174158815110*r46[i]
- 646685006086394734265332084740666732219400716288000000000*r47[i]
- 13012191241624225597793637611655297834798932917962602378310*r48[i]
- 258181916941754694739033103200539980500380934786252800000000*r49[i]
- 5058734882305856045540073713691835327365626096838684137474310*r50[i]
- 98003172162669552280283212651193173071892639817662464000000000*r51[i]
- 1879290113304215911642155827929295380860361801862580501733354950*r52[i]
) // 8683317618811886495518194401280000000 for i in range(len(r0))]
r31 = [(-35357670*r[1][i]
+ 58929450*r[2][i]
- 65132550*r[3][i]
+ 56448210*r[4][i]
- 40320150*r[5][i]
+ 24192090*r[6][i]
- 12271350*r[7][i]
+ 5259150*r[8][i]
- 1893294*r[9][i]
+ 566370*r[10][i]
- 138446*r[11][i]
+ 26970*r[12][i]
- 4030*r[13][i]
+ 434*r[14][i]
- 30*r[15][i]
+ r[16][i]
+ 9694845*r0[i]
- 5348880*r2[i]
+ 12480720*r4[i]
- 65969520*r6[i]
+ 642563280*r8[i]
- 10347602160*r10[i]
+ 258040917840*r12[i]
- 9564008626800*r14[i]
+ 514021079720400*r16[i]
- 39590373677587440*r18[i]
+ 4371353677873146960*r20[i]
- 701971899866535028080*r22[i]
+ 169737570795219895373520*r24[i]
- 66396273378844288679892720*r26[i]
+ 49448835121192219782326176080*r28[i]
- 124963193751534047864734415925360*r30[i]
- 354113410826574103722030528083469360*r32[i]
- 12301366626650172535317442068480000000*r33[i]
- 372225904019072507165665501545458070000*r34[i]
- 10203983616806318118045818195804160000000*r35[i]
- 259484653500223872483011119661283865786800*r36[i]
- 6217811871006716259183948315607695360000000*r37[i]
- 141956901865997956445469727796622341498870640*r38[i]
- 3113335802166672719861469258672651632640000000*r39[i]
- 66003822624082868383556482555741495612650600240*r40[i]
- 1359334478541063086765779323397876419133440000000*r41[i]
- 27303356587963564025554884815930553997263574871280*r42[i]
- 536588847651574079588079017443366763149393920000000*r43[i]
- 10345842549438556817463474698578198121859964179733680*r44[i]
- 196138884946560564409651268242770514989620920320000000*r45[i]
- 3663204676820752962698443093474820599422678195673015920*r46[i]
- 67509422521578235356394063172809938341831560396800000000*r47[i]
- 1229367058216339817971318602200240769989331897298761411120*r48[i]
- 22148293718278830966574475214239695745532717485260800000000*r49[i]
- 395185352573696509925259966545790692473196837003978017048560*r50[i]
- 6989838211515905458753639642597471400309284985697730560000000*r51[i]
- 122657793546790877104838252566375468764736099620191835404656560*r52[i]
) // 8222838654177922817725562880000000 for i in range(len(r0))]
r29 = [(9694845*r[1][i]
- 15967980*r[2][i]
+ 17298645*r[3][i]
- 14567280*r[4][i]
+ 10015005*r[5][i]
- 5722860*r[6][i]
+ 2731365*r[7][i]
- 1085760*r[8][i]
+ 356265*r[9][i]
- 95004*r[10][i]
+ 20097*r[11][i]
- 3248*r[12][i]
+ 377*r[13][i]
- 28*r[14][i]
+ r[15][i]
- 2674440*r0[i]
+ 1485800*r2[i]
- 3506488*r4[i]
+ 18850280*r6[i]
- 188004088*r8[i]
+ 3125835560*r10[i]
- 81314498488*r12[i]
+ 3185384180840*r14[i]
- 184064268909688*r16[i]
+ 15598375633694120*r18[i]
- 1958105850969957688*r20[i]
+ 375744491571024583400*r22[i]
- 118117302690774819242488*r24[i]
+ 71447614092662750198256680*r26[i]
- 147980747895225006590333244088*r28[i]
- 346368637877614395127589803878040*r30[i]
- 10963784872237230423634083840000000*r31[i]
- 302766527792977996357877082103322488*r32[i]
- 7585842753100939730112422608896000000*r33[i]
- 176553572119721839407097582006071612760*r34[i]
- 3876980715165912710714213825249280000000*r35[i]
- 81213796311764134505181592648745883717688*r36[i]
- 1636103186224681029581052139652775936000000*r37[i]
- 31895543813319775842490572300866856117139480*r38[i]
- 604645713103650398366928164707180216320000000*r39[i]
- 11189653759353064214370349765226592602607549688*r40[i]
- 202794861446303149866709151240333763280896000000*r41[i]
- 3608799207440735942926262565268791718882246250200*r42[i]
- 63195849406190967779680687932546907121909760000000*r43[i]
- 1091041918456432706911605989934195570136050930818488*r44[i]
- 18599858037912613836046600540495361832783446016000000*r45[i]
- 313534044032502214538190505667405050039920730329536920*r46[i]
- 5232130701886884640147951658064894118305202176000000000*r47[i]
- 86524070613240340349034843422074253070890184188704404088*r48[i]
- 1419220451222069603559756976077536870379472375775232000000*r49[i]
- 23107896008521043617173872183497904829674956287283293591640*r50[i]
- 373741738674210661134828098626419085853440812861358080000000*r51[i]
- 6008307669591671335816649438311816911003850182297118574066488*r52[i]
) // 8841761993739701954543616000000 for i in range(len(r0))]
r27 = [(-2674440*r[1][i]
+ 4345965*r[2][i]
- 4601610*r[3][i]
+ 3749460*r[4][i]
- 2466750*r[5][i]
+ 1332045*r[6][i]
- 592020*r[7][i]
+ 215280*r[8][i]
- 63180*r[9][i]
+ 14625*r[10][i]
- 2574*r[11][i]
+ 324*r[12][i]
- 26*r[13][i]
+ r[14][i]
+ 742900*r0[i]
- 416024*r2[i]
+ 994840*r4[i]
- 5454824*r6[i]
+ 55944280*r8[i]
- 966290024*r10[i]
+ 26454613720*r12[i]
- 1109329691624*r14[i]
+ 70212852387160*r16[i]
- 6733670404619624*r18[i]
+ 1005318113348848600*r20[i]
- 249581050854994274024*r22[i]
+ 120719220687299365182040*r24[i]
- 202039976682357297272094824*r26[i]
- 385557844336439370252173428520*r28[i]
- 11052202492174627443179520000000*r29[i]
- 276888650579451671741587901762024*r30[i]
- 6304176301536407493589598208000000*r31[i]
- 133535841584115505205141919375399080*r32[i]
- 2672618344480543437732658544640000000*r33[i]
- 51095126335993498323380094454901195624*r34[i]
- 940618873537377672007825158832128000000*r35[i]
- 16776403501444391106926987629186000345640*r36[i]
- 291283862319085180678807183848898560000000*r37[i]
- 4942310839108515578583708125038854650555624*r38[i]
- 82203911327563805707081667710859870208000000*r39[i]
- 1343752600475734599375534320311340373516684200*r40[i]
- 21634243326074826428166414905753461063680000000*r41[i]
- 343672532983087585902951862991031321905844242024*r42[i]
- 5395063942758184834505475068561955332947968000000*r43[i]
- 83804941354439477195910293019964343299641959230760*r44[i]
- 1289609166695254343642200168046105549173555200000000*r45[i]
- 19678461460501652805347265575009996073778349586894824*r46[i]
- 298018526228473595475945631789329672119214145536000000*r47[i]
- 4482734138598481574681074400900490010744661138946801320*r48[i]
- 67016178755227832923500959370656761105984640778240000000*r49[i]
- 996343679402015421123803198306389561979045588249233394024*r50[i]
- 14738679287503486801955946351327209631956632997462016000000*r51[i]
- 217035109012403108518173019970634230404031272801464219811880*r52[i]
) // 10888869450418352160768000000 for i in range(len(r0))]
r25 = [(742900*r[1][i]
- 1188640*r[2][i]
+ 1225785*r[3][i]
- 961400*r[4][i]
+ 600875*r[5][i]
- 303600*r[6][i]
+ 123970*r[7][i]
- 40480*r[8][i]
+ 10350*r[9][i]
- 2000*r[10][i]
+ 275*r[11][i]
- 24*r[12][i]
+ r[13][i]
- 208012*r0[i]
+ 117572*r2[i]
- 285532*r4[i]
+ 1602692*r6[i]
- 16996252*r8[i]
+ 307475012*r10[i]
- 8966430172*r12[i]
+ 409745686532*r14[i]
- 29195711499292*r16[i]
+ 3312133208909252*r18[i]
- 636215671041835612*r20[i]
+ 241648300078174135172*r22[i]
- 321511316149669476991132*r24[i]
- 492817676505266866078123708*r26[i]
- 12703681025488077520896000000*r27[i]
- 286779648275654636997381637852*r28[i]
- 5894507995826467969695744000000*r29[i]
- 112914054231542703053832892635388*r30[i]
- 2047008246979213061238030336000000*r31[i]
- 35501568925223446300815211192767772*r32[i]
- 593711792050129855003168210944000000*r33[i]
- 9632134956680435093368218113996247868*r34[i]
- 152311343455497374594406627803136000000*r35[i]
- 2356318736218539774396037820111678892892*r36[i]
- 35772470531371951985805498114637824000000*r37[i]
- 534273042749950920189640352996759062689148*r38[i]
- 7866491034006154572049014294052601856000000*r39[i]
- 114383224059606274110181105712262975351245212*r40[i]
- 1644946226278516886873016733667061202944000000*r41[i]
- 23426103831558846665144911501028780920365367228*r42[i]
- 330735945747364837719554208843251145179136000000*r43[i]
- 4633465747908141417306051485893140722291346976732*r44[i]
- 64465996518808752310647291812383168776634368000000*r45[i]
- 891389875128429665004288245297052393567100598170108*r46[i]
- 12257190333970097165549309885966019046465339392000000*r47[i]
- 167703402046599761376513697620930939990159551304359452*r48[i]
- 2284199788431383972862903582163083269492369522688000000*r49[i]
- 30985395797162515638045004419632302359171420946744265788*r50[i]
- 418773650924292383172351750158911938166116165353472000000*r51[i]
- 5640938886725051055672433299961125394581606270770949985372*r52[i]
) // 15511210043330985984000000 for i in range(len(r0))]
r23 = [(-208012*r[1][i]
+ 326876*r[2][i]
- 326876*r[3][i]
+ 245157*r[4][i]
- 144210*r[5][i]
+ 67298*r[6][i]
- 24794*r[7][i]
+ 7084*r[8][i]
- 1518*r[9][i]
+ 230*r[10][i]
- 22*r[11][i]
+ r[12][i]
+ 58786*r0[i]
- 33592*r2[i]
+ 83096*r4[i]
- 479752*r6[i]
+ 5299736*r8[i]
- 101549512*r10[i]
+ 3208453976*r12[i]
- 164071220872*r14[i]
+ 13743680753816*r16[i]
- 1993276972245832*r18[i]
+ 581947914140407256*r20[i]
- 603916464771468176392*r22[i]
- 730803773459954540777704*r24[i]
- 16803810880275234816000000*r25[i]
- 339155768243774227716964552*r26[i]
- 6245976504198304781107200000*r27[i]
- 107413822788261782335458993064*r28[i]
- 1751393992807566623932416000000*r29[i]
- 27365156266821215807862420562312*r30[i]
- 412945663851071412756568473600000*r31[i]
- 6053949680529454447550745704030824*r32[i]
- 86623417665042381831452000256000000*r33[i]
- 1214146547565910406028014931410521672*r34[i]
- 16719755812321492798917963359846400000*r35[i]
- 226758627215029497194516602329808882984*r36[i]
- 3034905857007157810746475187798016000000*r37[i]
- 40151799724774280996886476759684489594632*r38[i]
- 525848735885794606994555529953619148800000*r39[i]
- 6825564942475643900873841059427230143341544*r40[i]
- 87900055843825806396690634755863003136000000*r41[i]
- 1124090333957827218160935737032127911249333192*r42[i]
- 14286036145840157893404384196456208735600640000*r43[i]
- 180556939553256275799275906968519352499771598504*r44[i]
- 2270728203819030041749862616122105872023552000000*r45[i]
- 28430855249825246651314973609548475795532583689352*r46[i]
- 354557703317395919808450352391376751066211942400000*r47[i]
- 4405868085478593275690315869491622501390761293845864*r48[i]
- 54573144465647486264201741288918109369842860032000000*r49[i]
- 674011661674309854738045921738777159802726884618615112*r50[i]
- 8302706625795267729689057629348230882286932767539200000*r51[i]
- 102034139431103779464508421919001500494414946039191875624*r52[i]
) // 25852016738884976640000 for i in range(len(r0))]
r21 = [(58786*r[1][i]
- 90440*r[2][i]
+ 87210*r[3][i]
- 62016*r[4][i]
+ 33915*r[5][i]
- 14364*r[6][i]
+ 4655*r[7][i]
- 1120*r[8][i]
+ 189*r[9][i]
- 20*r[10][i]
+ r[11][i]
- 16796*r0[i]
+ 9724*r2[i]
- 24596*r4[i]
+ 147004*r6[i]
- 1708916*r8[i]
+ 35240284*r10[i]
- 1237329236*r12[i]
+ 73853629564*r14[i]
- 7850527669556*r16[i]
+ 1717351379730844*r18[i]
- 1359124435588313876*r20[i]
- 1272410676942417239876*r22[i]
- 25852016738884976640000*r23[i]
- 462292539259962003646196*r24[i]
- 7561714896123855667200000*r25[i]
- 115761644587269354830466596*r26[i]
- 1683741850203578528563200000*r27[i]
- 23512975860299444963550050516*r28[i]
- 317677725072691341719961600000*r29[i]
- 4176614976496441445095962733316*r30[i]
- 53674391443652368368589209600000*r31[i]
- 676635955671282540673335079110836*r32[i]
- 8391272072243853389701334630400000*r33[i]
- 102611708232289325546408008313624036*r34[i]
- 1239646284649926576486736094822400000*r35[i]
- 14819283410691765614379616648600811156*r36[i]
- 175538127424434549895381626305740800000*r37[i]
- 2062659648435073986802743885440046722756*r38[i]
- 24066873273263602745997309174983884800000*r39[i]
- 279069134864297423784787795404361206735476*r40[i]
- 3218237360334469905693543066426751549440000*r41[i]
- 36932670876144577834192017462238998576813476*r42[i]
- 422013831656219970552631011526505561456640000*r43[i]
- 4803667893589610545887832027829424971473267796*r44[i]
- 54491782544378643866541770098406137341542400000*r45[i]
- 616254801390825608499920295882691673585117080196*r46[i]
- 6950267169846786189298202657232919399818854400000*r47[i]
- 78194975030419808376759755992062291704460984792116*r48[i]
- 877813878936817604039539295936804610730357555200000*r49[i]
- 9834901482219684549861282981457686724945206826306916*r50[i]
- 109993865724440916050887229750467965278551356211200000*r51[i]
- 1228217338997580254122488729377687743870958069616892436*r52[i]
) // 51090942171709440000 for i in range(len(r0))]
r19 = [(-16796*r[1][i]
+ 25194*r[2][i]
- 23256*r[3][i]
+ 15504*r[4][i]
- 7752*r[5][i]
+ 2907*r[6][i]
- 798*r[7][i]
+ 152*r[8][i]
- 18*r[9][i]
+ r[10][i]
+ 4862*r0[i]
- 2860*r2[i]
+ 7436*r4[i]
- 46420*r6[i]
+ 576236*r8[i]
- 13098580*r10[i]
+ 532310636*r12[i]
- 39968611540*r14[i]
+ 6350631494636*r16[i]
- 3730771315561300*r18[i]
- 2637991952943407764*r20[i]
- 46833363657400320000*r21[i]
- 734121065118879803860*r22[i]
- 10556240168378032128000*r23[i]
- 142438684135271315212564*r24[i]
- 1830415113744266649600000*r25[i]
- 22632897298190126259675220*r26[i]
- 271297526662043666104320000*r27[i]
- 3170344993810020486920015764*r28[i]
- 36274730261563609572556800000*r29[i]
- 407775103607650299563627591380*r30[i]
- 4515882637052182897862000640000*r31[i]
- 49377994276343186011748723193364*r32[i]
- 534053247401000753173510963200000*r33[i]
- 5722063606154183864914875339648340*r34[i]
- 60811730909031986048777521029120000*r35[i]
- 641729418431834160625738740379401364*r36[i]
- 6730380606921481449181267599974400000*r37[i]
- 70207898580127312813466155395513222100*r38[i]
- 728918319689461841494925372032622592000*r39[i]
- 7536441803725213229125462424550696575764*r40[i]
- 77635978704164552294553096402068152320000*r41[i]
- 797177898990753876072852178329776532568660*r42[i]
- 8162164080895303403984327865949915250688000*r43[i]
- 83359491110673172494030048846026790563932564*r44[i]
- 849432099945167336777734465061373289267200000*r45[i]
- 8638438243166451781593809976801426668242424020*r46[i]
- 87694169965134464605849462884812769886371840000*r47[i]
- 888832151283066038746077396233689115965303967764*r48[i]
- 8996158031157109433578511766939541381376409600000*r49[i]
- 90938713449996246641127353860256309887114389604180*r50[i]
- 918234342704615923743435749615058841825963745280000*r51[i]
- 9262393601318313123889045816028965261306516208457364*r52[i]
) // 121645100408832000 for i in range(len(r0))]
r17 = [(4862*r[1][i]
- 7072*r[2][i]
+ 6188*r[3][i]
- 3808*r[4][i]
+ 1700*r[5][i]
- 544*r[6][i]
+ 119*r[7][i]
- 16*r[8][i]
+ r[9][i]
- 1430*r0[i]
+ 858*r2[i]
- 2310*r4[i]
+ 15258*r6[i]
- 206790*r8[i]
+ 5386458*r10[i]
- 272513670*r12[i]
+ 30255826458*r14[i]
- 12765597850950*r16[i]
- 6622557957272742*r18[i]
- 101370917007360000*r19[i]
- 1375210145685786630*r20[i]
- 17172233341046784000*r21[i]
- 201832098313986359142*r22[i]
- 2265471043586150400000*r23[i]
- 24529324224160803328710*r24[i]
- 258058524232798248960000*r25[i]
- 2652208374242713043720742*r26[i]
- 26739700571225856614400000*r27[i]
- 265323404171486113659725190*r28[i]
- 2597688920748017370193920000*r29[i]
- 25147613788240222384169485542*r30[i]
- 241125683321001354933657600000*r31[i]
- 2293170112631184981695915264070*r32[i]
- 21656158388689797460311183360000*r33[i]
- 203283794784841444836991831621542*r34[i]
- 1898267590696733462875776307200000*r35[i]
- 17646072330245312137111933794073350*r36[i]
- 163392570167583908119294187237376000*r37[i]
- 1507754227229479379470312529237936742*r38[i]
- 13871774079585871769182921633935360000*r39[i]
- 127291574907112728538906245247680921030*r40[i]
- 1165398276253942030786602999248830464000*r41[i]
- 10648249156718669259487809979675840079142*r42[i]
- 97121906010634492337139410720414515200000*r43[i]
- 884471146488697462546213719879378982015110*r44[i]
- 8043742604145412070397708709577312747520000*r45[i]
- 73065283527546375984492393431422365909536742*r46[i]
- 662985481414219219279431223562176586956800000*r47[i]
- 6010229010788429141870217066922217223929803590*r48[i]
- 54440174236564270133288224915510829498019840000*r49[i]
- 492755135434761578293305350886942317529465637542*r50[i]
- 4457205465827107111785421147442507464329523200000*r51[i]
- 40294548566019835134386988604297024831948411774470*r52[i]
) // 355687428096000 for i in range(len(r0))]
r15 = [(-1430*r[1][i]
+ 2002*r[2][i]
- 1638*r[3][i]
+ 910*r[4][i]
- 350*r[5][i]
+ 90*r[6][i]
- 14*r[7][i]
+ r[8][i]
+ 429*r0[i]
- 264*r2[i]
+ 744*r4[i]
- 5304*r6[i]
+ 81384*r8[i]
- 2605944*r10[i]
+ 192387624*r12[i]
- 55942352184*r14[i]
- 20546119600536*r16[i]
- 266765571072000*r17[i]
- 3083760849804024*r18[i]
- 32945548027392000*r19[i]
- 332500281299403096*r20[i]
- 3215147584416768000*r21[i]
- 30076927429146721464*r22[i]
- 274100623905588480000*r23[i]
- 2446077617962088140056*r24[i]
- 21459412163122053120000*r25[i]
- 185641639183185136464504*r26[i]
- 1587401376760010972160000*r27[i]
- 13442713420403849918131416*r28[i]
- 112915002722102749808640000*r29[i]
- 941961013910760913890393144*r30[i]
- 7812419263561351877518080000*r31[i]
- 64474322285718607792730497176*r32[i]
- 529848386811984810994744320000*r33[i]
- 4338547620121893769542630267384*r34[i]
- 35415056327751829508662891008000*r35[i]
- 288317531175033442515609896757336*r36[i]
- 2341823147101379454117987013632000*r37[i]
- 18983391549723892653716655806647224*r38[i]
- 153619763998111828980832157720832000*r39[i]
- 1241292607509331793516191597844431896*r40[i]
- 10017079537004367071413852136982528000*r41[i]
- 80746194097372251940077615903073292664*r42[i]
- 650250798838302173122854563322562560000*r43[i]
- 5232061257212799699445154857325986640856*r44[i]
- 42067391464856035210355948847111229440000*r45[i]
- 338018548004311349729166172709579357563704*r46[i]
- 2714522948575416807552558113876933656320000*r47[i]
- 21788917503304477212565325243539420555704216*r48[i]
- 174821149505151584518657828257831893345280000*r49[i]
- 1402141896338776811136967582554033500226820344*r50[i]
- 11242168283931454427825411966307736057167360000*r51[i]
- 90112723368126633235251766101448928377940741976*r52[i]
) // 1307674368000 for i in range(len(r0))]
r13 = [(429*r[1][i]
- 572*r[2][i]
+ 429*r[3][i]
- 208*r[4][i]
+ 65*r[5][i]
- 12*r[6][i]
+ r[7][i]
- 132*r0[i]
+ 84*r2[i]
- 252*r4[i]
+ 2004*r6[i]
- 37212*r8[i]
+ 1710324*r10[i]
- 325024572*r12[i]
- 80789566956*r14[i]
- 871782912000*r15[i]
- 8422900930332*r16[i]
- 75583578470400*r17[i]
- 643521842437836*r18[i]
- 5269678622208000*r19[i]
- 41890044885642492*r20[i]
- 325386564299596800*r21[i]
- 2481686964269990316*r22[i]
- 18652248729354240000*r23[i]
- 138536531588626169052*r24[i]
- 1019042849143807488000*r25[i]
- 7436421488952386592396*r26[i]
- 53911021949819274240000*r27[i]
- 388701690499592948238012*r28[i]
- 2789805187365599475072000*r29[i]
- 19946749502047187160692076*r30[i]
- 142159780685991861112320000*r31[i]
- 1010433303980489860989897372*r32[i]
- 7165521770403817166663116800*r33[i]
- 50716588034439244118483617356*r34[i]
- 358378772025058883636009472000*r35[i]
- 2528902640579773012941059115132*r36[i]
- 17824202779159732939433280230400*r37[i]
- 125502611080965065134883934376236*r38[i]
- 882926862501000079240924013568000*r39[i]
- 6206986746547700738292160195379292*r40[i]
- 43608135571536574058895364550860800*r41[i]
- 306213499909407501334225902520456716*r42[i]
- 2149239710498553002348841878415360000*r43[i]
- 15079178774724614117506008765315297852*r44[i]
- 105761403926812162332273274580071296000*r45[i]
- 741573481088337285231858048220674626796*r46[i]
- 5198479982499565882352899855753044480000*r47[i]
- 36434172034715569203746509369098022198812*r48[i]
- 255308169532157231577671227649975633664000*r49[i]
- 1788771440213892011837337228527544587734476*r50[i]
- 12531087911298377892590529356517576445440000*r51[i]
- 87775753902632879954790735906635276359730172*r52[i]
) // 6227020800 for i in range(len(r0))]
r11 = [(-132*r[1][i]
+ 165*r[2][i]
- 110*r[3][i]
+ 44*r[4][i]
- 10*r[5][i]
+ r[6][i]
+ 42*r0[i]
- 28*r2[i]
+ 92*r4[i]
- 868*r6[i]
+ 22652*r8[i]
- 2620708*r10[i]
- 415790788*r12[i]
- 3632428800*r13[i]
- 28616744548*r14[i]
- 210680870400*r15[i]
- 1479485236228*r16[i]
- 10038995366400*r17[i]
- 66394067988388*r18[i]
- 430591742380800*r19[i]
- 2750479262009668*r20[i]
- 17360942812012800*r21[i]
- 108550450893568228*r22[i]
- 673606803881088000*r23[i]
- 4154688725062207108*r24[i]
- 25499502190850688000*r25[i]
- 155878445775166700068*r26[i]
- 949776357849070752000*r27[i]
- 5771581202353414724548*r28[i]
- 34995682724855684832000*r29[i]
- 211811399872933910999908*r30[i]
- 1280080235834717770252800*r31[i]
- 7726641919200262371657988*r32[i]
- 46591059456870785061004800*r33[i]
- 280704018540064430354883748*r34[i]
- 1690018909819536161979590400*r35[i]
- 10169113413821714748538703428*r36[i]
- 61159784116494648773674886400*r37[i]
- 367684638335977863351585967588*r38[i]
- 2209739160176731898013383884800*r39[i]
- 13276598260065161268654185556868*r40[i]
- 79750432649108163224160355276800*r41[i]
- 478956917715683026467561165467428*r42[i]
- 2876013540917084725512964985376000*r43[i]
- 17267443120712778679894991796314308*r44[i]
- 103661474908781590201983341856096000*r45[i]
- 622252957609245047342724399262599268*r46[i]
- 3734938395375021425507273833823424000*r47[i]
- 22416734056596928549732496421419871748*r48[i]
- 134535924504317597978456420953656384000*r49[i]
- 807393154821611376674434030676868979108*r50[i]
- 4845246995796352471529950975101582508800*r51[i]
- 29075922420664314894010979796628180325188*r52[i]
) // 39916800 for i in range(len(r0))]
r9 = [(42*r[1][i]
- 48*r[2][i]
+ 27*r[3][i]
- 8*r[4][i]
+ r[5][i]
- 14*r0[i]
+ 10*r2[i]
- 38*r4[i]
+ 490*r6[i]
- 31238*r8[i]
- 2922230*r10[i]
- 19958400*r11[i]
- 124075238*r12[i]
- 726485760*r13[i]
- 4084385750*r14[i]
- 22313491200*r15[i]
- 119387268038*r16[i]
- 628980992640*r17[i]
- 3275389222070*r18[i]
- 16905818966400*r19[i]
- 86665431465638*r20[i]
- 441935114987520*r21[i]
- 2244295389943190*r22[i]
- 11360520464832000*r23[i]
- 57360469753884038*r24[i]
- 289038899804054400*r25[i]
- 1454155949521941110*r26[i]
- 7306671293537616000*r27[i]
- 36677059892827099238*r28[i]
- 183960524908301057280*r29[i]
- 922104761587650687830*r30[i]
- 4619736062008593926400*r31[i]
- 23135540444136227047238*r32[i]
- 115825176110799088940160*r33[i]
- 579715876176320506935350*r34[i]
- 2900939663557699476451200*r35[i]
- 14514140349055749129024038*r36[i]
- 72608472572041292373527040*r37[i]
- 363193454272347163609915670*r38[i]
- 1816571661325589960713958400*r39[i]
- 9085275939429279963731685638*r40[i]
- 45436050447189540392656321920*r41[i]
- 227218935892633882388998540790*r42[i]
- 1136249416059455304696385296000*r43[i]
- 5681866032591044240951769048038*r44[i]
- 28411805989856165780668427308800*r45[i]
- 142068933310062230858345890602710*r46[i]
- 710384280152969638132390327392000*r47[i]
- 3552079855654080764219631870487238*r48[i]
- 17761033099263130050180188817751680*r49[i]
- 88807700784593943012315384189973430*r50[i]
- 444048645089005049723558441367254400*r51[i]
- 2220283790147933078276819155128739238*r52[i]
) // 362880 for i in range(len(r0))]
r7 = [(-14*r[1][i]
+ 14*r[2][i]
- 6*r[3][i]
+ r[4][i]
+ 5*r0[i]
- 4*r2[i]
+ 20*r4[i]
- 604*r6[i]
- 29740*r8[i]
- 151200*r9[i]
- 708604*r10[i]
- 3160080*r11[i]
- 13645900*r12[i]
- 57657600*r13[i]
- 239967004*r14[i]
- 988107120*r15[i]
- 4037604460*r16[i]
- 16406863200*r17[i]
- 66398623804*r18[i]
- 267911678160*r19[i]
- 1078605601420*r20[i]
- 4335313752000*r21[i]
- 17403958407004*r22[i]
- 69804002545200*r23[i]
- 279780634372780*r24[i]
- 1120816644948000*r25[i]
- 4488349371924604*r26[i]
- 17968646803620240*r27[i]
- 71920337041294540*r28[i]
- 287818601403715200*r29[i]
- 1151686172846664604*r30[i]
- 4607980008114455280*r31[i]
- 18435626012705982700*r32[i]
- 73753622051697957600*r33[i]
- 295047842329672995004*r34[i]
- 1180291431927853642320*r35[i]
- 4721465916019935893260*r36[i]
- 18886764229967380219200*r37[i]
- 75549758619456576163804*r38[i]
- 302207139580435761213360*r39[i]
- 1208852873637267995922220*r40[i]
- 4835484440511039999684000*r41[i]
- 19342156599960850372299004*r42[i]
- 77369282913655045261040400*r43[i]
- 309479101196178257662005580*r44[i]
- 1237922313409633551106176000*r45[i]
- 4951706979513788347008408604*r46[i]
- 19806881095681900978203235440*r47[i]
- 79227683915609817008158719340*r48[i]
- 316911214261089847968346159200*r49[i]
- 1267646292840319012979866380604*r50[i]
- 5070589478749170677837606550480*r51[i]
- 20282370837160398114302240879500*r52[i]
) // 5040 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
- 1680*r7[i]
- 5542*r8[i]
- 17640*r9[i]
- 54958*r10[i]
- 168960*r11[i]
- 515062*r12[i]
- 1561560*r13[i]
- 4717438*r14[i]
- 14217840*r15[i]
- 42784582*r16[i]
- 128615880*r17[i]
- 386371918*r18[i]
- 1160164320*r19[i]
- 3482590102*r20[i]
- 10451964600*r21[i]
- 31364282398*r22[i]
- 94109624400*r23[i]
- 282362427622*r24[i]
- 847154391720*r25[i]
- 2541597392878*r26[i]
- 7625060614080*r27[i]
- 22875718713142*r28[i]
- 68628229881240*r29[i]
- 205886837127358*r30[i]
- 617664806349360*r31[i]
- 1853003008982662*r32[i]
- 5559026206817160*r33[i]
- 16677112980189838*r34[i]
- 50031407660046240*r35[i]
- 150094360419092182*r36[i]
- 450283356135183480*r37[i]
- 1350850618161364318*r38[i]
- 4052552953995720720*r39[i]
- 12157661061010417702*r40[i]
- 36472987581077764200*r41[i]
- 109418971539326314798*r42[i]
- 328256932210164988800*r43[i]
- 984770831814867055222*r44[i]
- 2954312565813345343320*r45[i]
- 8862937838177524385278*r46[i]
- 26588813796007549866480*r47[i]
- 79766441950972603020742*r48[i]
- 239299326978817715904840*r49[i]
- 717897983188252961399758*r50[i]
- 2153693954068358511569760*r51[i]
- 6461081871212274789450262*r52[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
- 126*r7[i]
- 254*r8[i]
- 510*r9[i]
- 1022*r10[i]
- 2046*r11[i]
- 4094*r12[i]
- 8190*r13[i]
- 16382*r14[i]
- 32766*r15[i]
- 65534*r16[i]
- 131070*r17[i]
- 262142*r18[i]
- 524286*r19[i]
- 1048574*r20[i]
- 2097150*r21[i]
- 4194302*r22[i]
- 8388606*r23[i]
- 16777214*r24[i]
- 33554430*r25[i]
- 67108862*r26[i]
- 134217726*r27[i]
- 268435454*r28[i]
- 536870910*r29[i]
- 1073741822*r30[i]
- 2147483646*r31[i]
- 4294967294*r32[i]
- 8589934590*r33[i]
- 17179869182*r34[i]
- 34359738366*r35[i]
- 68719476734*r36[i]
- 137438953470*r37[i]
- 274877906942*r38[i]
- 549755813886*r39[i]
- 1099511627774*r40[i]
- 2199023255550*r41[i]
- 4398046511102*r42[i]
- 8796093022206*r43[i]
- 17592186044414*r44[i]
- 35184372088830*r45[i]
- 70368744177662*r46[i]
- 140737488355326*r47[i]
- 281474976710654*r48[i]
- 562949953421310*r49[i]
- 1125899906842622*r50[i]
- 2251799813685246*r51[i]
- 4503599627370494*r52[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
- r7[i]
- r8[i]
- r9[i]
- r10[i]
- r11[i]
- r12[i]
- r13[i]
- r14[i]
- r15[i]
- r16[i]
- r17[i]
- r18[i]
- r19[i]
- r20[i]
- r21[i]
- r22[i]
- r23[i]
- r24[i]
- r25[i]
- r26[i]
- r27[i]
- r28[i]
- r29[i]
- r30[i]
- r31[i]
- r32[i]
- r33[i]
- r34[i]
- r35[i]
- r36[i]
- r37[i]
- r38[i]
- r39[i]
- r40[i]
- r41[i]
- r42[i]
- r43[i]
- r44[i]
- r45[i]
- r46[i]
- r47[i]
- r48[i]
- r49[i]
- r50[i]
- r51[i]
- r52[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52)
def natural_interpolate_28(r):
r0 = r[0]
r54 = r['infinity']
r52 = [(-477551179875952*(r[1][i] + r[-1][i])
+ 426384982032100*(r[2][i] + r[-2][i])
- 352870329957600*(r[3][i] + r[-3][i])
+ 270533919634160*(r[4][i] + r[-4][i])
- 191991813933920*(r[5][i] + r[-5][i])
+ 125994627894135*(r[6][i] + r[-6][i])
- 76360380541900*(r[7][i] + r[-7][i])
+ 42671977361650*(r[8][i] + r[-8][i])
- 21945588357420*(r[9][i] + r[-9][i])
+ 10363194502115*(r[10][i] + r[-10][i])
- 4481381406320*(r[11][i] + r[-11][i])
+ 1768966344600*(r[12][i] + r[-12][i])
- 635013559600*(r[13][i] + r[-13][i])
+ 206379406870*(r[14][i] + r[-14][i])
- 60403728840*(r[15][i] + r[-15][i])
+ 15820024220*(r[16][i] + r[-16][i])
- 3679075400*(r[17][i] + r[-17][i])
+ 752538150*(r[18][i] + r[-18][i])
- 133784560*(r[19][i] + r[-19][i])
+ 20358520*(r[20][i] + r[-20][i])
- 2598960*(r[21][i] + r[-21][i])
+ 270725*(r[22][i] + r[-22][i])
- 22100*(r[23][i] + r[-23][i])
+ 1326*(r[24][i] + r[-24][i])
- 52*(r[25][i] + r[-25][i])
+ (r[26][i] + r[-26][i])
+ 495918532948104*r0[i]
- 500161344235022991022867609146559759013770223238917205786624000000000000*r54[i]
) // 80658175170943878571660636856403766975289505440883277824000000000000 for i in range(len(r0))]
r50 = [(121548660036300*(r[1][i] + r[-1][i])
- 108043253365600*(r[2][i] + r[-2][i])
+ 88749815264600*(r[3][i] + r[-3][i])
- 67327446062800*(r[4][i] + r[-4][i])
+ 47129212243960*(r[5][i] + r[-5][i])
- 30405943383200*(r[6][i] + r[-6][i])
+ 18053528883775*(r[7][i] + r[-7][i])
- 9847379391150*(r[8][i] + r[-8][i])
+ 4923689695575*(r[9][i] + r[-9][i])
- 2250829575120*(r[10][i] + r[-10][i])
+ 937845656300*(r[11][i] + r[-11][i])
- 354860518600*(r[12][i] + r[-12][i])
+ 121399651100*(r[13][i] + r[-13][i])
- 37353738800*(r[14][i] + r[-14][i])
+ 10272278170*(r[15][i] + r[-15][i])
- 2505433700*(r[16][i] + r[-16][i])
+ 536878650*(r[17][i] + r[-17][i])
- 99884400*(r[18][i] + r[-18][i])
+ 15890700*(r[19][i] + r[-19][i])
- 2118760*(r[20][i] + r[-20][i])
+ 230300*(r[21][i] + r[-21][i])
- 19600*(r[22][i] + r[-22][i])
+ 1225*(r[23][i] + r[-23][i])
- 50*(r[24][i] + r[-24][i])
+ (r[25][i] + r[-25][i])
- 126410606437752*r0[i]
- 168037864939466413690959660117507847865186469668506828800000000000000*r52[i]
- 496955181771977971849644098831517709276502465397642095493120000000000000*r54[i]
) // 30414093201713378043612608166064768844377641568960512000000000000 for i in range(len(r0))]
r48 = [(-30957699535776*(r[1][i] + r[-1][i])
+ 27385657281648*(r[2][i] + r[-2][i])
- 22314239266528*(r[3][i] + r[-3][i])
+ 16735679449896*(r[4][i] + r[-4][i])
- 11541847896480*(r[5][i] + r[-5][i])
+ 7309837001104*(r[6][i] + r[-6][i])
- 4244421484512*(r[7][i] + r[-7][i])
+ 2254848913647*(r[8][i] + r[-8][i])
- 1093260079344*(r[9][i] + r[-9][i])
+ 482320623240*(r[10][i] + r[-10][i])
- 192928249296*(r[11][i] + r[-11][i])
+ 69668534468*(r[12][i] + r[-12][i])
- 22595200368*(r[13][i] + r[-13][i])
+ 6540715896*(r[14][i] + r[-14][i])
- 1677106640*(r[15][i] + r[-15][i])
+ 377348994*(r[16][i] + r[-16][i])
- 73629072*(r[17][i] + r[-17][i])
+ 12271512*(r[18][i] + r[-18][i])
- 1712304*(r[19][i] + r[-19][i])
+ 194580*(r[20][i] + r[-20][i])
- 17296*(r[21][i] + r[-21][i])
+ 1128*(r[22][i] + r[-22][i])
- 48*(r[23][i] + r[-23][i])
+ (r[24][i] + r[-24][i])
+ 32247603683100*r0[i]
- 60828186403426756087225216332129537688755283137921024000000000000*r50[i]
- 159972047422372025833793596431867471167657519124418501017600000000000*r52[i]
- 300157876302214652121781965684412846831829138854612706525184000000000000*r54[i]
) // 12413915592536072670862289047373375038521486354677760000000000 for i in range(len(r0))]
r46 = [(7890371113950*(r[1][i] + r[-1][i])
- 6943526580276*(r[2][i] + r[-2][i])
+ 5608233007146*(r[3][i] + r[-3][i])
- 4154246671960*(r[4][i] + r[-4][i])
+ 2818953098830*(r[5][i] + r[-5][i])
- 1749695026860*(r[6][i] + r[-6][i])
+ 991493848554*(r[7][i] + r[-7][i])
- 511738760544*(r[8][i] + r[-8][i])
+ 239877544005*(r[9][i] + r[-9][i])
- 101766230790*(r[10][i] + r[-10][i])
+ 38910617655*(r[11][i] + r[-11][i])
- 13340783196*(r[12][i] + r[-12][i])
+ 4076350421*(r[13][i] + r[-13][i])
- 1101716330*(r[14][i] + r[-14][i])
+ 260932815*(r[15][i] + r[-15][i])
- 53524680*(r[16][i] + r[-16][i])
+ 9366819*(r[17][i] + r[-17][i])
- 1370754*(r[18][i] + r[-18][i])
+ 163185*(r[19][i] + r[-19][i])
- 15180*(r[20][i] + r[-20][i])
+ 1035*(r[21][i] + r[-21][i])
- 46*(r[22][i] + r[-22][i])
+ (r[23][i] + r[-23][i])
- 8233430727600*r0[i]
- 23793338219027472619152720674132302157166182179799040000000000*r48[i]
- 55378994704786442521077957369042933270804289023482265600000000000*r50[i]
- 92204777033212927855282293501621091950025889999533532774400000000000*r52[i]
- 123173573410381619032735872322455238373678223392026561137868800000000000*r54[i]
) // 5502622159812088949850305428800254892961651752960000000000 for i in range(len(r0))]
r44 = [(-2012616400080*(r[1][i] + r[-1][i])
+ 1761039350070*(r[2][i] + r[-2][i])
- 1408831480056*(r[3][i] + r[-3][i])
+ 1029530696964*(r[4][i] + r[-4][i])
- 686353797976*(r[5][i] + r[-5][i])
+ 416714805914*(r[6][i] + r[-6][i])
- 229911617056*(r[7][i] + r[-7][i])
+ 114955808528*(r[8][i] + r[-8][i])
- 51915526432*(r[9][i] + r[-9][i])
+ 21090682613*(r[10][i] + r[-10][i])
- 7669339132*(r[11][i] + r[-11][i])
+ 2481256778*(r[12][i] + r[-12][i])
- 708930508*(r[13][i] + r[-13][i])
+ 177232627*(r[14][i] + r[-14][i])
- 38320568*(r[15][i] + r[-15][i])
+ 7059052*(r[16][i] + r[-16][i])
- 1086008*(r[17][i] + r[-17][i])
+ 135751*(r[18][i] + r[-18][i])
- 13244*(r[19][i] + r[-19][i])
+ 946*(r[20][i] + r[-20][i])
- 44*(r[21][i] + r[-21][i])
+ (r[22][i] + r[-22][i])
+ 2104098963720*r0[i]
- 10088140626322163074725559952800467303763028213760000000000*r46[i]
- 20672617771459376572727617455278717598871197415636992000000000*r48[i]
- 30390960789555990223010654132076029106169285558507929600000000000*r50[i]
- 35940698724546850336855815971061681513098805595301121884160000000000*r52[i]
- 36360946421379657670852826531045915291694648992864408489164800000000000*r54[i]
) // 2658271574788448768043625811014615890319638528000000000 for i in range(len(r0))]
r42 = [(513791607420*(r[1][i] + r[-1][i])
- 446775310800*(r[2][i] + r[-2][i])
+ 353697121050*(r[3][i] + r[-3][i])
- 254661927156*(r[4][i] + r[-4][i])
+ 166509721602*(r[5][i] + r[-5][i])
- 98672427616*(r[6][i] + r[-6][i])
+ 52860229080*(r[7][i] + r[-7][i])
- 25518731280*(r[8][i] + r[-8][i])
+ 11058116888*(r[9][i] + r[-9][i])
- 4280561376*(r[10][i] + r[-10][i])
+ 1471442973*(r[11][i] + r[-11][i])
- 445891810*(r[12][i] + r[-12][i])
+ 118030185*(r[13][i] + r[-13][i])
- 26978328*(r[14][i] + r[-14][i])
+ 5245786*(r[15][i] + r[-15][i])
- 850668*(r[16][i] + r[-16][i])
+ 111930*(r[17][i] + r[-17][i])
- 11480*(r[18][i] + r[-18][i])
+ 861*(r[19][i] + r[-19][i])
- 42*(r[20][i] + r[-20][i])
+ (r[21][i] + r[-21][i])
- 538257874440*r0[i]
- 4651975255879785344076345169275577808059367424000000000*r44[i]
- 8345643609048334907272963233680386587658505158656000000000*r46[i]
- 10774531600512501036897720551649645765494516918255616000000000*r48[i]
- 11221709145032637985686395016457126546359868596714209280000000000*r50[i]
- 10024126976056544454447469133748446849553291271003522990080000000000*r52[i]
- 7975810040319696718196547333113180442555266076076498338447360000000000*r54[i]
) // 1405006117752879898543142606244511569936384000000000 for i in range(len(r0))]
r40 = [(-131282408400*(r[1][i] + r[-1][i])
+ 113380261800*(r[2][i] + r[-2][i])
- 88732378800*(r[3][i] + r[-3][i])
+ 62852101650*(r[4][i] + r[-4][i])
- 40225345056*(r[5][i] + r[-5][i])
+ 23206929840*(r[6][i] + r[-6][i])
- 12033222880*(r[7][i] + r[-7][i])
+ 5586853480*(r[8][i] + r[-8][i])
- 2311801440*(r[9][i] + r[-9][i])
+ 847660528*(r[10][i] + r[-10][i])
- 273438880*(r[11][i] + r[-11][i])
+ 76904685*(r[12][i] + r[-12][i])
- 18643560*(r[13][i] + r[-13][i])
+ 3838380*(r[14][i] + r[-14][i])
- 658008*(r[15][i] + r[-15][i])
+ 91390*(r[16][i] + r[-16][i])
- 9880*(r[17][i] + r[-17][i])
+ 780*(r[18][i] + r[-18][i])
- 40*(r[19][i] + r[-19][i])
+ (r[20][i] + r[-20][i])
+ 137846528820*r0[i]
- 2341676862921466497571904343740852616560640000000000*r42[i]
- 3655123415334117056059985490145096849189502976000000000*r44[i]
- 4119688019118574531237133429498603530973935042560000000000*r46[i]
- 3757340713824985498498548346794211825654347639816192000000000*r48[i]
- 2947359606908914693821004025256012800585708025466060800000000000*r50[i]
- 2064558678210662377343329526788684890767865636215995760640000000000*r52[i]
- 1324288918192605206277308466563916626202444615070944696729600000000000*r54[i]
) // 815915283247897734345611269596115894272000000000 for i in range(len(r0))]
r38 = [(33578000610*(r[1][i] + r[-1][i])
- 28781143380*(r[2][i] + r[-2][i])
+ 22239974430*(r[3][i] + r[-3][i])
- 15471286560*(r[4][i] + r[-4][i])
+ 9669554100*(r[5][i] + r[-5][i])
- 5414950296*(r[6][i] + r[-6][i])
+ 2707475148*(r[7][i] + r[-7][i])
- 1203322288*(r[8][i] + r[-8][i])
+ 472733756*(r[9][i] + r[-9][i])
- 163011640*(r[10][i] + r[-10][i])
+ 48903492*(r[11][i] + r[-11][i])
- 12620256*(r[12][i] + r[-12][i])
+ 2760681*(r[13][i] + r[-13][i])
- 501942*(r[14][i] + r[-14][i])
+ 73815*(r[15][i] + r[-15][i])
- 8436*(r[16][i] + r[-16][i])
+ 703*(r[17][i] + r[-17][i])
- 38*(r[18][i] + r[-18][i])
+ (r[19][i] + r[-19][i])
- 35345263800*r0[i]
- 1291865865142504746047217843527183499264000000000*r40[i]
- 1742597865490724651943092149133817822157209600000000*r42[i]
- 1703614521144184428726371303487541532883419136000000000*r44[i]
- 1352221478318945952566471137817160521323572835123200000000*r46[i]
- 925912385499308009244605568293800045079467288166400000000000*r48[i]
- 567701817594292628086492254286076775983065657711263744000000000*r50[i]
- 319529132633551445730754266569514531984165615759324610560000000000*r52[i]
- 168027862191313285572462163036203023050148820066814862032896000000000*r54[i]
) // 523022617466601111760007224100074291200000000 for i in range(len(r0))]
r36 = [(-8597496600*(r[1][i] + r[-1][i])
+ 7307872110*(r[2][i] + r[-2][i])
- 5567902560*(r[3][i] + r[-3][i])
+ 3796297200*(r[4][i] + r[-4][i])
- 2310789600*(r[5][i] + r[-5][i])
+ 1251677700*(r[6][i] + r[-6][i])
- 600805296*(r[7][i] + r[-7][i])
+ 254186856*(r[8][i] + r[-8][i])
- 94143280*(r[9][i] + r[-9][i])
+ 30260340*(r[10][i] + r[-10][i])
- 8347680*(r[11][i] + r[-11][i])
+ 1947792*(r[12][i] + r[-12][i])
- 376992*(r[13][i] + r[-13][i])
+ 58905*(r[14][i] + r[-14][i])
- 7140*(r[15][i] + r[-15][i])
+ 630*(r[16][i] + r[-16][i])
- 36*(r[17][i] + r[-17][i])
+ (r[18][i] + r[-18][i])
+ 9075135300*r0[i]
- 784533926199901667640010836150111436800000000*r38[i]
- 907705752613286229459492537425678932377600000000*r40[i]
- 764250847583238143225401875995898505750118400000000*r42[i]
- 524336156604477506256224109002957345627779891200000000*r44[i]
- 311351658482338919180732210200430367625645444300800000000*r46[i]
- 166036590632320367531429334375544068072103816986624000000000*r48[i]
- 81499841025612949496109930847966440863640763389444096000000000*r50[i]
- 37466461814083366759359795735852259604455926584422957056000000000*r52[i]
- 16337589523211774449719906648393247646243600903141698043904000000000*r54[i]
) // 371993326789901217467999448150835200000000 for i in range(len(r0))]
r34 = [(2203961430*(r[1][i] + r[-1][i])
- 1855967520*(r[2][i] + r[-2][i])
+ 1391975640*(r[3][i] + r[-3][i])
- 927983760*(r[4][i] + r[-4][i])
+ 548354040*(r[5][i] + r[-5][i])
- 286097760*(r[6][i] + r[-6][i])
+ 131128140*(r[7][i] + r[-7][i])
- 52451256*(r[8][i] + r[-8][i])
+ 18156204*(r[9][i] + r[-9][i])
- 5379616*(r[10][i] + r[-10][i])
+ 1344904*(r[11][i] + r[-11][i])
- 278256*(r[12][i] + r[-12][i])
+ 46376*(r[13][i] + r[-13][i])
- 5984*(r[14][i] + r[-14][i])
+ 561*(r[15][i] + r[-15][i])
- 34*(r[16][i] + r[-16][i])
+ (r[17][i] + r[-17][i])
- 2333606220*r0[i]
- 526990546285693391412999218213683200000000*r36[i]
- 518664095654379435828673830565907005440000000*r38[i]
- 373138241060740797524227217357125818777600000000*r40[i]
- 219618160307546307818407858079592245845032960000000*r42[i]
- 112275193446419212026758411812279514001781555200000000*r44[i]
- 51713216892097268029263570056035419810630708756480000000*r46[i]
- 21987290206937420965021290881182668895459624353792000000000*r48[i]
- 8778185176019659621127125508818359337012951782732595200000000*r50[i]
- 3332107853530764777529629230140567884444349753800523776000000000*r52[i]
- 1213942320816658090297153525238443731761121646974842689290240000000*r54[i]
) // 295232799039604140847618609643520000000 for i in range(len(r0))]
r32 = [(-565722720*(r[1][i] + r[-1][i])
+ 471435600*(r[2][i] + r[-2][i])
- 347373600*(r[3][i] + r[-3][i])
+ 225792840*(r[4][i] + r[-4][i])
- 129024480*(r[5][i] + r[-5][i])
+ 64512240*(r[6][i] + r[-6][i])
- 28048800*(r[7][i] + r[-7][i])
+ 10518300*(r[8][i] + r[-8][i])
- 3365856*(r[9][i] + r[-9][i])
+ 906192*(r[10][i] + r[-10][i])
- 201376*(r[11][i] + r[-11][i])
+ 35960*(r[12][i] + r[-12][i])
- 4960*(r[13][i] + r[-13][i])
+ 496*(r[14][i] + r[-14][i])
- 32*(r[15][i] + r[-15][i])
+ (r[16][i] + r[-16][i])
+ 601080390*r0[i]
- 393643732052805521130158146191360000000*r34[i]
- 326527475737802179777466182265733120000000*r36[i]
- 198969979872214920293886346099446251520000000*r38[i]
- 99626745669333527035567016277524852244480000000*r40[i]
- 43498703313314018776504938348732045412270080000000*r42[i]
- 17170843124850370546818528558187736420780605440000000*r44[i]
- 6276444318289938061108840583768656479667869450240000000*r46[i]
- 2160301520690503531404610021529918026938609932697600000000*r48[i]
- 708745398984922590930383206855670263857046959528345600000000*r50[i]
- 223674822768508974680116468563119084809897119542327377920000000*r52[i]
- 68383308771682806793482300167280717706332061193589825208320000000*r54[i]
) // 263130836933693530167218012160000000 for i in range(len(r0))]
r30 = [(145422675*(r[1][i] + r[-1][i])
- 119759850*(r[2][i] + r[-2][i])
+ 86493225*(r[3][i] + r[-3][i])
- 54627300*(r[4][i] + r[-4][i])
+ 30045015*(r[5][i] + r[-5][i])
- 14307150*(r[6][i] + r[-6][i])
+ 5852925*(r[7][i] + r[-7][i])
- 2035800*(r[8][i] + r[-8][i])
+ 593775*(r[9][i] + r[-9][i])
- 142506*(r[10][i] + r[-10][i])
+ 27405*(r[11][i] + r[-11][i])
- 4060*(r[12][i] + r[-12][i])
+ 435*(r[13][i] + r[-13][i])
- 30*(r[14][i] + r[-14][i])
+ (r[15][i] + r[-15][i])
- 155117520*r0[i]
- 328913546167116912709022515200000000*r32[i]
- 227575282593028191903372678266880000000*r34[i]
- 116309421454977381321426414757478400000000*r36[i]
- 49083095586740430887431564189583278080000000*r38[i]
- 18139371393109511951007844941215406489600000000*r40[i]
- 6083845843389094496001274537210012898426880000000*r42[i]
- 1895875482185729033390420637976407213657292800000000*r44[i]
- 557995741137378415081398016214860854983503380480000000*r46[i]
- 156963921056606539204438549741946823549156065280000000000*r48[i]
- 42576613536662088106792709282326106111384171273256960000000*r50[i]
- 11212252160226319834044842958792572575603224385840742400000000*r52[i]
- 2881790963494506901155736518846659656145189066632341749760000000*r54[i]
) // 265252859812191058636308480000000 for i in range(len(r0))]
r28 = [(-37442160*(r[1][i] + r[-1][i])
+ 30421755*(r[2][i] + r[-2][i])
- 21474180*(r[3][i] + r[-3][i])
+ 13123110*(r[4][i] + r[-4][i])
- 6906900*(r[5][i] + r[-5][i])
+ 3108105*(r[6][i] + r[-6][i])
- 1184040*(r[7][i] + r[-7][i])
+ 376740*(r[8][i] + r[-8][i])
- 98280*(r[9][i] + r[-9][i])
+ 20475*(r[10][i] + r[-10][i])
- 3276*(r[11][i] + r[-11][i])
+ 378*(r[12][i] + r[-12][i])
- 28*(r[13][i] + r[-13][i])
+ (r[14][i] + r[-14][i])
+ 40116600*r0[i]
- 309461669780889568409026560000000*r30[i]
- 176516936443019409820508749824000000*r32[i]
- 74833313645455216256514439249920000000*r34[i]
- 26337328459046574816219104447299584000000*r36[i]
- 8155948144934385059006601147769159680000000*r38[i]
- 2301709517171786559798286695904076365824000000*r40[i]
- 605758813130095139988659617361096909783040000000*r42[i]
- 151061790397229175366153301919734749322543104000000*r44[i]
- 36109056667467121621981604705290955376859545600000000*r46[i]
- 8344518734397260673326477690101230819337996075008000000*r48[i]
- 1876453005146379321858026862378389310967569941790720000000*r50[i]
- 412683020050097630454766497837161869694785723928936448000000*r52[i]
- 89117286812387026652769979577207299516771181236259389440000000*r54[i]
) // 304888344611713860501504000000 for i in range(len(r0))]
r26 = [(9657700*(r[1][i] + r[-1][i])
- 7726160*(r[2][i] + r[-2][i])
+ 5311735*(r[3][i] + r[-3][i])
- 3124550*(r[4][i] + r[-4][i])
+ 1562275*(r[5][i] + r[-5][i])
- 657800*(r[6][i] + r[-6][i])
+ 230230*(r[7][i] + r[-7][i])
- 65780*(r[8][i] + r[-8][i])
+ 14950*(r[9][i] + r[-9][i])
- 2600*(r[10][i] + r[-10][i])
+ 325*(r[11][i] + r[-11][i])
- 26*(r[12][i] + r[-12][i])
+ (r[13][i] + r[-13][i])
- 10400600*r0[i]
- 330295706662690015543296000000*r28[i]
- 153257207891488167212089344000000*r30[i]
- 53222214421459539592188788736000000*r32[i]
- 15436506593303376230082373484544000000*r34[i]
- 3960094929842931739454572322881536000000*r36[i]
- 930084233815670751630942950980583424000000*r38[i]
- 204528766884160018873274371645367648256000000*r40[i]
- 42768601883241439058698435075343591276544000000*r42[i]
- 8599134589431485780708409429924529774657536000000*r44[i]
- 1676115909489027560076829587121962388192493568000000*r46[i]
- 318686948683222526304282057035116495208098824192000000*r48[i]
- 59389194499215983294435493136240165006801607589888000000*r50[i]
- 10888114924031601962481145504131710392319020299190272000000*r52[i]
- 1969613645523746908242462889216091458065590581736767488000000*r54[i]
) // 403291461126605635584000000 for i in range(len(r0))]
r24 = [(-2496144*(r[1][i] + r[-1][i])
+ 1961256*(r[2][i] + r[-2][i])
- 1307504*(r[3][i] + r[-3][i])
+ 735471*(r[4][i] + r[-4][i])
- 346104*(r[5][i] + r[-5][i])
+ 134596*(r[6][i] + r[-6][i])
- 42504*(r[7][i] + r[-7][i])
+ 10626*(r[8][i] + r[-8][i])
- 2024*(r[9][i] + r[-9][i])
+ 276*(r[10][i] + r[-10][i])
- 24*(r[11][i] + r[-11][i])
+ (r[12][i] + r[-12][i])
+ 2704156*r0[i]
- 403291461126605635584000000*r26[i]
- 149903436100759314746572800000*r28[i]
- 42033455827381598974377984000000*r30[i]
- 9910695932425713906157643366400000*r32[i]
- 2078962023961017163954848006144000000*r34[i]
- 401274139495715827174031120636313600000*r36[i]
- 72837740568171787457915404507152384000000*r38[i]
- 12620369661259070567869332718886859571200000*r40[i]
- 2109601340251819353520575234140712075264000000*r42[i]
- 342864867500163789441705220714949009654415360000*r44[i]
- 54497476891656721001996702786930540928565248000000*r46[i]
- 8509384879617502075402808457393042025589086617600000*r48[i]
- 1309755467175539670340841790934034624876228640768000000*r50[i]
- 199264959019086425512537383104357541174886386420940800000*r52[i]
- 30029919604106055758327357685117168899526367314444288000000*r54[i]
) // 620448401733239439360000 for i in range(len(r0))]
r22 = [(646646*(r[1][i] + r[-1][i])
- 497420*(r[2][i] + r[-2][i])
+ 319770*(r[3][i] + r[-3][i])
- 170544*(r[4][i] + r[-4][i])
+ 74613*(r[5][i] + r[-5][i])
- 26334*(r[6][i] + r[-6][i])
+ 7315*(r[7][i] + r[-7][i])
- 1540*(r[8][i] + r[-8][i])
+ 231*(r[9][i] + r[-9][i])
- 22*(r[10][i] + r[-10][i])
+ (r[11][i] + r[-11][i])
- 705432*r0[i]
- 568744368255469486080000*r24[i]
- 166357727714724824678400000*r26[i]
- 37042320704478727628390400000*r28[i]
- 6988909951599209517839155200000*r30[i]
- 1180836611760352104108962611200000*r32[i]
- 184607985589364774573429361868800000*r34[i]
- 27272218262298384682708194086092800000*r36[i]
- 3861838803337560097698395778726297600000*r38[i]
- 529471212011799260411940801849645465600000*r40[i]
- 70801221927358337925257947461388534087680000*r42[i]
- 9284304296436839352157882253583122352046080000*r44[i]
- 1198819215976330165063918942164935021513932800000*r46[i]
- 152905877736629296164560458459124226796014796800000*r48[i]
- 19311905336609987288869864510609701436067866214400000*r50[i]
- 2419865045937700153119519054510295236128129836646400000*r52[i]
- 301288155885052369662851151922188867269975615240601600000*r54[i]
) // 1124000727777607680000 for i in range(len(r0))]
r20 = [(-167960*(r[1][i] + r[-1][i])
+ 125970*(r[2][i] + r[-2][i])
- 77520*(r[3][i] + r[-3][i])
+ 38760*(r[4][i] + r[-4][i])
- 15504*(r[5][i] + r[-5][i])
+ 4845*(r[6][i] + r[-6][i])
- 1140*(r[7][i] + r[-7][i])
+ 190*(r[8][i] + r[-8][i])
- 20*(r[9][i] + r[-9][i])
+ (r[10][i] + r[-10][i])
+ 184756*r0[i]
- 936667273148006400000*r22[i]
- 211124803367560642560000*r24[i]
- 36608302274885332992000000*r26[i]
- 5425950533240873322086400000*r28[i]
- 725494605231272191451136000000*r30[i]
- 90317652741043657957240012800000*r32[i]
- 10681064948020015063470219264000000*r34[i]
- 1216234618180639720975550420582400000*r36[i]
- 134607612138429628983625351999488000000*r38[i]
- 14578366393789236829898507440652451840000*r40[i]
- 1552719574083291045891061928041363046400000*r42[i]
- 163243281617906068079686557318998305013760000*r44[i]
- 16988641998903346735554689301227465785344000000*r46[i]
- 1753883399302689292116989257696255397727436800000*r48[i]
- 179923160623142188671570235338790827627528192000000*r50[i]
- 18364686854092318474868714992301176836519274905600000*r52[i]
- 1866955970795489260131483779878624434707941429248000000*r54[i]
) // 2432902008176640000 for i in range(len(r0))]
r18 = [(43758*(r[1][i] + r[-1][i])
- 31824*(r[2][i] + r[-2][i])
+ 18564*(r[3][i] + r[-3][i])
- 8568*(r[4][i] + r[-4][i])
+ 3060*(r[5][i] + r[-5][i])
- 816*(r[6][i] + r[-6][i])
+ 153*(r[7][i] + r[-7][i])
- 18*(r[8][i] + r[-8][i])
+ (r[9][i] + r[-9][i])
- 48620*r0[i]
- 1824676506132480000*r20[i]
- 309100200138842112000*r22[i]
- 40778478784550707200000*r24[i]
- 4645053436190368481280000*r26[i]
- 481314610282065419059200000*r28[i]
- 46758400573464312663490560000*r30[i]
- 4340262299778024388805836800000*r32[i]
- 389810850996416354285601300480000*r34[i]
- 34168816632541202331763973529600000*r36[i]
- 2941066263016510346147295370272768000*r38[i]
- 249691933432545691845292589410836480000*r40[i]
- 20977168972570956554158853986478948352000*r42[i]
- 1748194308191420862068509392967461273600000*r44[i]
- 144787366874617417267158756772391629455360000*r46[i]
- 11933738665455945947029762024119178565222400000*r48[i]
- 979923136258156862399188048479194930964357120000*r50[i]
- 80229698384887928012137580653965134357931417600000*r52[i]
- 6553647225094050569861777249958218558728336220160000*r54[i]
) // 6402373705728000 for i in range(len(r0))]
r16 = [(-11440*(r[1][i] + r[-1][i])
+ 8008*(r[2][i] + r[-2][i])
- 4368*(r[3][i] + r[-3][i])
+ 1820*(r[4][i] + r[-4][i])
- 560*(r[5][i] + r[-5][i])
+ 120*(r[6][i] + r[-6][i])
- 16*(r[7][i] + r[-7][i])
+ (r[8][i] + r[-8][i])
+ 12870*r0[i]
- 4268249137152000*r18[i]
- 527128768438272000*r20[i]
- 51442361350668288000*r22[i]
- 4385609982489415680000*r24[i]
- 343350594609952849920000*r26[i]
- 25398422028160175554560000*r28[i]
- 1806640043553643996938240000*r30[i]
- 124998708216981630040289280000*r32[i]
- 8477574188991756975915909120000*r34[i]
- 566640901244029272138606256128000*r36[i]
- 37469170353622071265887792218112000*r38[i]
- 2457916223969789263693314523533312000*r40[i]
- 160273272592069873142621634191720448000*r42[i]
- 10404012781412834769965673013161000960000*r44[i]
- 673078263437696563365695181553779671040000*r46[i]
- 43432367177206668920840929822030938501120000*r48[i]
- 2797138392082425352298525252125310293524480000*r50[i]
- 179874692542903270845206591460923776914677760000*r52[i]
- 11554084778127771883812326032137020779396055040000*r54[i]
) // 20922789888000 for i in range(len(r0))]
r14 = [(3003*(r[1][i] + r[-1][i])
- 2002*(r[2][i] + r[-2][i])
+ 1001*(r[3][i] + r[-3][i])
- 364*(r[4][i] + r[-4][i])
+ 91*(r[5][i] + r[-5][i])
- 14*(r[6][i] + r[-6][i])
+ (r[7][i] + r[-7][i])
- 3432*r0[i]
- 12204960768000*r16[i]
- 1058170098585600*r18[i]
- 73775500710912000*r20[i]
- 4555411900194355200*r22[i]
- 261131482210959360000*r24[i]
- 14266599888013304832000*r26[i]
- 754754307297469839360000*r28[i]
- 39057272623118392651008000*r30[i]
- 1990236929603886055572480000*r32[i]
- 100317304785653440333283635200*r34[i]
- 5017302808350824370904132608000*r36[i]
- 249538838908236261152065923225600*r38[i]
- 12360976075014001109372936189952000*r40[i]
- 610513898001512036824535103712051200*r42[i]
- 30089355946979742032883786297815040000*r44[i]
- 1480659654975370272651825844120998144000*r46[i]
- 72778719754993922352940597980542622720000*r48[i]
- 3574314373450201242087397187099658871296000*r50[i]
- 175435230758177290496267410991246070236160000*r52[i]
- 8606908326589506468114924551500679297771059200*r54[i]
) // 87178291200 for i in range(len(r0))]
r12 = [(-792*(r[1][i] + r[-1][i])
+ 495*(r[2][i] + r[-2][i])
- 220*(r[3][i] + r[-3][i])
+ 66*(r[4][i] + r[-4][i])
- 12*(r[5][i] + r[-5][i])
+ (r[6][i] + r[-6][i])
+ 924*r0[i]
- 43589145600*r14[i]
- 2528170444800*r16[i]
- 120467944396800*r18[i]
- 5167100908569600*r20[i]
- 208331313744153600*r22[i]
- 8083281646573056000*r24[i]
- 305994026290208256000*r26[i]
- 11397316294188849024000*r28[i]
- 419948192698268217984000*r30[i]
- 15360962830016613243033600*r32[i]
- 559092713482449420732057600*r34[i]
- 20280226917834433943755084800*r36[i]
- 733917409397935785284098636800*r38[i]
- 26516869922120782776160606617600*r40[i]
- 957005191789297958689924263321600*r42[i]
- 34512162491005016706155579824512000*r44[i]
- 1243937698905379082423800102273152000*r46[i]
- 44819260744500257106087286005881088000*r48[i]
- 1614431094051811175741477051443876608000*r50[i]
- 58142963949556229658359411701218990105600*r52[i]
- 2093732846395541754366573918386488419609600*r54[i]
) // 479001600 for i in range(len(r0))]
r10 = [(210*(r[1][i] + r[-1][i])
- 120*(r[2][i] + r[-2][i])
+ 45*(r[3][i] + r[-3][i])
- 10*(r[4][i] + r[-4][i])
+ (r[5][i] + r[-5][i])
- 252*r0[i]
- 199584000*r12[i]
- 7264857600*r14[i]
- 223134912000*r16[i]
- 6289809926400*r18[i]
- 169058189664000*r20[i]
- 4419351149875200*r22[i]
- 113605204648320000*r24[i]
- 2890388998040544000*r26[i]
- 73066712935376160000*r28[i]
- 1839605249083010572800*r30[i]
- 46197360620085939264000*r32[i]
- 1158251761107990889401600*r34[i]
- 29009396635576994764512000*r36[i]
- 726084725720412923735270400*r38[i]
- 18165716613255899607139584000*r40[i]
- 454360504471895403926563219200*r42[i]
- 11362494160594553046963852960000*r44[i]
- 284118059898561657806684273088000*r46[i]
- 7103842801529696381323903273920000*r48[i]
- 177610330992631300501801888177516800*r50[i]
- 4440486450890050497235584413672544000*r52[i]
- 111015812096675961833777653418529945600*r54[i]
) // 3628800 for i in range(len(r0))]
r8 = [(-56*(r[1][i] + r[-1][i])
+ 28*(r[2][i] + r[-2][i])
- 8*(r[3][i] + r[-3][i])
+ (r[4][i] + r[-4][i])
+ 70*r0[i]
- 1209600*r10[i]
- 25280640*r12[i]
- 461260800*r14[i]
- 7904856960*r16[i]
- 131254905600*r18[i]
- 2143293425280*r20[i]
- 34682510016000*r22[i]
- 558432020361600*r24[i]
- 8966533159584000*r26[i]
- 143749174428961920*r28[i]
- 2302548811229721600*r30[i]
- 36863840064915642240*r32[i]
- 590028976413583660800*r34[i]
- 9442331455422829138560*r36[i]
- 151094113839739041753600*r38[i]
- 2417657116643486089706880*r40[i]
- 38683875524088319997472000*r42[i]
- 618954263309240362088323200*r44[i]
- 9903378507277068408849408000*r46[i]
- 158455048765455207825625883520*r48[i]
- 2535289714088718783746769273600*r50[i]
- 40564715829993365422700852403840*r52[i]
- 649036176921062413731673525900800*r54[i]
) // 40320 for i in range(len(r0))]
r6 = [(15*(r[1][i] + r[-1][i])
- 6*(r[2][i] + r[-2][i])
+ (r[3][i] + r[-3][i])
- 20*r0[i]
- 10080*r8[i]
- 105840*r10[i]
- 1013760*r12[i]
- 9369360*r14[i]
- 85307040*r16[i]
- 771695280*r18[i]
- 6960985920*r20[i]
- 62711787600*r22[i]
- 564657746400*r24[i]
- 5082926350320*r26[i]
- 45750363684480*r28[i]
- 411769379287440*r30[i]
- 3705988838096160*r32[i]
- 33354157240902960*r34[i]
- 300188445960277440*r36[i]
- 2701700136811100880*r38[i]
- 24315317723974324320*r40[i]
- 218837925486466585200*r42[i]
- 1969541593260989932800*r44[i]
- 17725875394880072059920*r46[i]
- 159532882776045299198880*r48[i]
- 1435795961872906295429040*r50[i]
- 12922163724410151069418560*r52[i]
- 116299473789907337266996560*r54[i]
) // 720 for i in range(len(r0))]
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
- 504*r8[i]
- 2040*r10[i]
- 8184*r12[i]
- 32760*r14[i]
- 131064*r16[i]
- 524280*r18[i]
- 2097144*r20[i]
- 8388600*r22[i]
- 33554424*r24[i]
- 134217720*r26[i]
- 536870904*r28[i]
- 2147483640*r30[i]
- 8589934584*r32[i]
- 34359738360*r34[i]
- 137438953464*r36[i]
- 549755813880*r38[i]
- 2199023255544*r40[i]
- 8796093022200*r42[i]
- 35184372088824*r44[i]
- 140737488355320*r46[i]
- 562949953421304*r48[i]
- 2251799813685240*r50[i]
- 9007199254740984*r52[i]
- 36028797018963960*r54[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
- 2*r8[i]
- 2*r10[i]
- 2*r12[i]
- 2*r14[i]
- 2*r16[i]
- 2*r18[i]
- 2*r20[i]
- 2*r22[i]
- 2*r24[i]
- 2*r26[i]
- 2*r28[i]
- 2*r30[i]
- 2*r32[i]
- 2*r34[i]
- 2*r36[i]
- 2*r38[i]
- 2*r40[i]
- 2*r42[i]
- 2*r44[i]
- 2*r46[i]
- 2*r48[i]
- 2*r50[i]
- 2*r52[i]
- 2*r54[i]
) // 2 for i in range(len(r0))]
r53 = [(69533550916004*r[1][i]
- 124680849918352*r[2][i]
+ 155851062397940*r[3][i]
- 160878516023680*r[4][i]
+ 144539291740025*r[5][i]
- 115631433392020*r[6][i]
+ 83322650532485*r[7][i]
- 54414792184480*r[8][i]
+ 32308782859535*r[9][i]
- 17464206951100*r[10][i]
+ 8594228157515*r[11][i]
- 3846367846720*r[12][i]
+ 1562586937730*r[13][i]
- 574609830760*r[14][i]
+ 190559382650*r[15][i]
- 56724653440*r[16][i]
+ 15067486070*r[17][i]
- 3545290840*r[18][i]
+ 732179630*r[19][i]
- 131185600*r[20][i]
+ 20087795*r[21][i]
- 2576860*r[22][i]
+ 269399*r[23][i]
- 22048*r[24][i]
+ 1325*r[25][i]
- 52*r[26][i]
+ r[27][i]
- 18367353072152*r0[i]
+ 9723892802904*r2[i]
- 21233806732872*r4[i]
+ 101938316952024*r6[i]
- 870923857821192*r8[i]
+ 11813629724209944*r10[i]
- 236653242227994312*r12[i]
+ 6661211180561048664*r14[i]
- 254153395270440164232*r16[i]
+ 12797090786892473420184*r18[i]
- 833255276258604854522952*r20[i]
+ 69082046666155386510156504*r22[i]
- 7207362865961897332411742472*r24[i]
+ 938124129611900624725430169624*r26[i]
- 151437248027244277344983580174792*r28[i]
+ 30212272010200647359221303097651544*r30[i]
- 7441428742177722398508955844151051912*r32[i]
+ 2266232854869901871497407965509685274264*r34[i]
- 857107282161918028603277004147759001685832*r36[i]
+ 405772096860221176189017929957247080205389784*r38[i]
- 243490395435781263807703083882634443533746668552*r40[i]
+ 188759926346541491475721299645267069314262689230104*r42[i]
- 194640847441735760152914313356873387274986644997072072*r44[i]
+ 279696375173169115852542641714578798351241693643134107224*r46[i]
- 607628834924308414958104349396219007455296518007846747648392*r48[i]
+ 2367696951203027805660226670039629463149515409625476517138613144*r50[i]
- 29693031902220062960308836352100332220249176157939974718889212029512*r52[i]
- 398324183453887237008520156086372422120866135515653348034430817054180136*r54[i]
) // 4274883284060025564298013753389399649690343788366813724672000000000000 for i in range(len(r0))]
r51 = [(-18367353072152*r[1][i]
+ 32798844771700*r[2][i]
- 40715807302800*r[3][i]
+ 41620603020640*r[4][i]
- 36921502679600*r[5][i]
+ 29075683360185*r[6][i]
- 20558563992050*r[7][i]
+ 13129839188200*r[8][i]
- 7596549816030*r[9][i]
+ 3985844039275*r[10][i]
- 1895969056520*r[11][i]
+ 816446005200*r[12][i]
- 317506779800*r[13][i]
+ 111127372930*r[14][i]
- 34848305100*r[15][i]
+ 9735399520*r[16][i]
- 2405549300*r[17][i]
+ 520987950*r[18][i]
- 97765640*r[19][i]
+ 15660400*r[20][i]
- 2099160*r[21][i]
+ 229075*r[22][i]
- 19550*r[23][i]
+ 1224*r[24][i]
- 50*r[25][i]
+ r[26][i]
+ 4861946401452*r0[i]
- 2579808294648*r2[i]
+ 5653622432952*r4[i]
- 27280100477448*r6[i]
+ 234657881740152*r8[i]
- 3210736324810248*r10[i]
+ 65015030756447352*r12[i]
- 1854200415783543048*r14[i]
+ 71870433940146354552*r16[i]
- 3687349223477219875848*r18[i]
+ 245473564244803456261752*r20[i]
- 20888307287949627757008648*r22[i]
+ 2246840224563905580570968952*r24[i]
- 303094970433352624372214141448*r26[i]
+ 51019602983331540473045839276152*r28[i]
- 10691645514373727983810335922474248*r30[i]
+ 2790651091406916364299868206057983352*r32[i]
- 910446673933990019203515025763541207048*r34[i]
+ 373948949766422140435706410007606455890552*r36[i]
- 195681514530799165910557748483841641873539848*r38[i]
+ 132897106175336006092720191507876479916677797752*r40[i]
- 120554003537142419244816814513161495212294682672648*r42[i]
+ 152971535906456634616842226470152212508964788768504952*r44[i]
- 294458451533217960963210426417324728393814119257507805448*r46[i]
+ 1019832500675924760582251357311129578949356520774019156812152*r48[i]
- 11400247815546832449432199417474318613528727464280459760480138248*r50[i]
- 136675603482281861796246376772747198814333993503815350676473360480648*r52[i]
- 9618487389135057519670530945126149211803273523825330880512000000000000*r53[i]
- 584079459970995636352966806308556874401704430470079936394389227138871048*r54[i]
) // 1551118753287382280224243016469303211063259720016986112000000000000 for i in range(len(r0))]
r49 = [(4861946401452*r[1][i]
- 8643460269248*r[2][i]
+ 10649977831752*r[3][i]
- 10772391370048*r[4][i]
+ 9425842448792*r[5][i]
- 7297426411968*r[6][i]
+ 5054988087457*r[7][i]
- 3151161405168*r[8][i]
+ 1772528290407*r[9][i]
- 900331830048*r[10][i]
+ 412652088772*r[11][i]
- 170333048928*r[12][i]
+ 63127818572*r[13][i]
- 20918093728*r[14][i]
+ 6163366902*r[15][i]
- 1603477568*r[16][i]
+ 365077482*r[17][i]
- 71916768*r[18][i]
+ 12076932*r[19][i]
- 1695008*r[20][i]
+ 193452*r[21][i]
- 17248*r[22][i]
+ 1127*r[23][i]
- 48*r[24][i]
+ r[25][i]
- 1289904147324*r0[i]
+ 686119227300*r2[i]
- 1509462300060*r4[i]
+ 7323923844900*r6[i]
- 63466456620060*r8[i]
+ 876655994638500*r10[i]
- 17962494591036060*r12[i]
+ 519729378435224100*r14[i]
- 20498730418437708060*r16[i]
+ 1073773191888393761700*r18[i]
- 73266053614681083996060*r20[i]
+ 6418563118124648605611300*r22[i]
- 714493710681785410524780060*r24[i]
+ 100357569802461927273985332900*r26[i]
- 17717998874943470330819342460060*r28[i]
+ 3928707238871982933864962858686500*r30[i]
- 1096834043813751169204010169826956060*r32[i]
+ 388004275037568389575404928401474632100*r34[i]
- 175870982185451189351017757509405335708060*r36[i]
+ 103991298038492644018924403718805266597329700*r38[i]
- 82506842083007670338625750577445488484693676060*r40[i]
+ 91947467567672513735818977678842895400970978139300*r42[i]
- 156026356786659861162429714318097107470538947633340060*r44[i]
+ 477994672122502000860149649242839645232774457016507620900*r46[i]
- 4741041014119120622582667190202604787803330381303410474700060*r48[i]
- 50576092532930275709972631359425317424152381858024219560152465500*r50[i]
- 3360757298789328273819193202350156957303729393370136576000000000000*r51[i]
- 192818334124303175599491864945168536471848882690784611504742445276060*r52[i]
- 9939103635439559436992881976630354185530049307952841909862400000000000*r53[i]
- 471508555542884903005212240660172655256037627791416369358584244657159900*r54[i]
) // 608281864034267560872252163321295376887552831379210240000000000 for i in range(len(r0))]
r47 = [(-1289904147324*r[1][i]
+ 2282138106804*r[2][i]
- 2789279908316*r[3][i]
+ 2789279908316*r[4][i]
- 2404551645100*r[5][i]
+ 1827459250276*r[6][i]
- 1237956266316*r[7][i]
+ 751616304549*r[8][i]
- 409972529754*r[9][i]
+ 200966926350*r[10][i]
- 88425447594*r[11][i]
+ 34834267234*r[12][i]
- 12239066866*r[13][i]
+ 3815417606*r[14][i]
- 1048191650*r[15][i]
+ 251565996*r[16][i]
- 52153926*r[17][i]
+ 9203634*r[18][i]
- 1355574*r[19][i]
+ 162150*r[20][i]
- 15134*r[21][i]
+ 1034*r[22][i]
- 46*r[23][i]
+ r[24][i]
+ 343059613650*r0[i]
- 182965127280*r2[i]
+ 404225281200*r4[i]
- 1973179787280*r6[i]
+ 17237751438000*r8[i]
- 240592045595280*r10[i]
+ 4994170279690800*r12[i]
- 146823806097131280*r14[i]
+ 5903690350090119600*r16[i]
- 316485671150054075280*r18[i]
+ 22198064042219526404400*r20[i]
- 2009394413056841321867280*r22[i]
+ 232532372014701449341825200*r24[i]
- 34201309524439700202831707280*r26[i]
+ 6378595465863797572545515262000*r28[i]
- 1510321457529226404281297600555280*r30[i]
+ 456430932151854961874111940707194800*r32[i]
- 177879954967657922123999080680411131280*r34[i]
+ 90948410673639301600046982211812755703600*r36[i]
- 62713181699432641518049958716708665011915280*r38[i]
+ 61017960828891287286335064536456771132612468400*r40[i]
- 90771056129445230547328475921502515772170837147280*r42[i]
+ 244690112718607318914399753695429565221879804118769200*r44[i]
- 2142766872532178730068138061640892672650431299718846827280*r46[i]
- 20243597746218463146623496754059816935278614102767681978514000*r48[i]
- 1267253883404724085150525340252698701849068398706688000000000000*r49[i]
- 68540933797288160408485956779561102500745596951326307091686715280*r50[i]
- 3332750987966083871537366592330572315992864981758718771200000000000*r51[i]
- 149233459487753154020208258958096224473270440522821423115697370901200*r52[i]
- 6253289089629471919203790951758600975663107059471098052608000000000000*r53[i]
- 248022574937797150848261199568155307996775458923007620752687158968331280*r54[i]
) // 258623241511168180642964355153611979969197632389120000000000 for i in range(len(r0))]
r45 = [(343059613650*r[1][i]
- 603784920024*r[2][i]
+ 731508653106*r[3][i]
- 722477682080*r[4][i]
+ 612815891050*r[5][i]
- 456442180920*r[6][i]
+ 301758997386*r[7][i]
- 177996090624*r[8][i]
+ 93865125915*r[9][i]
- 44246187300*r[10][i]
+ 18609425835*r[11][i]
- 6960408624*r[12][i]
+ 2304024151*r[13][i]
- 670609940*r[14][i]
+ 170173575*r[15][i]
- 37234560*r[16][i]
+ 6923301*r[17][i]
- 1072764*r[18][i]
+ 134805*r[19][i]
- 13200*r[20][i]
+ 945*r[21][i]
- 44*r[22][i]
+ r[23][i]
- 91482563640*r0[i]
+ 48932534040*r2[i]
- 108606356040*r4[i]
+ 533667580440*r6[i]
- 4703763586440*r8[i]
+ 66408505338840*r10[i]
- 1398457857168840*r12[i]
+ 41847457290489240*r14[i]
- 1719246675671583240*r16[i]
+ 94585481325000311640*r18[i]
- 6843422433568588589640*r20[i]
+ 642897110978465333366040*r22[i]
- 77770562351946223415228040*r24[i]
+ 12062233927817328810997492440*r26[i]
- 2397961353314881501418831818440*r28[i]
+ 613494954527608404597659277810840*r30[i]
- 203877970345571868715766678319960840*r32[i]
+ 89457569257636570186619080797284721240*r34[i]
- 53237495951641479759332571910597970535240*r36[i]
+ 44930968310714379648812137260536985281903640*r38[i]
- 58241166312158469946465066186170960196371701640*r40[i]
+ 137360888551881485527132727024151255460985294318040*r42[i]
- 1056294346650368430047563515157012073181421862576900040*r44[i]
- 8792490299555933486634712872596976297794618720689003795560*r46[i]
- 517246483022336361285928710307223959938395264778240000000000*r47[i]
- 26309260636200890673464765332665424581880256812272026952850440*r48[i]
- 1203891189234487880892999073240063766756614978771353600000000000*r49[i]
- 50764977622809978549916904649893168100296473949517793816320917160*r50[i]
- 2004451674635063649027875945687415042391867173902902886400000000000*r51[i]
- 74960269321392846499824811474695597918673304894478483366348507552840*r52[i]
- 2677686378486556935494258093966418225514743986783186111692800000000000*r53[i]
- 91966010944477715317164988999955404631262474522089414701528792100246760*r54[i]
) // 119622220865480194561963161495657715064383733760000000000 for i in range(len(r0))]
r43 = [(-91482563640*r[1][i]
+ 160094486370*r[2][i]
- 192113383644*r[3][i]
+ 187187399448*r[4][i]
- 155989499540*r[5][i]
+ 113649492522*r[6][i]
- 73153696336*r[7][i]
+ 41802112192*r[8][i]
- 21238169904*r[9][i]
+ 9586673915*r[10][i]
- 3834669566*r[11][i]
+ 1353412788*r[12][i]
- 418913482*r[13][i]
+ 112784399*r[14][i]
- 26127660*r[15][i]
+ 5133856*r[16][i]
- 839188*r[17][i]
+ 111069*r[18][i]
- 11438*r[19][i]
+ 860*r[20][i]
- 42*r[21][i]
+ r[22][i]
+ 24466267020*r0[i]
- 13128240840*r2[i]
+ 29286075720*r4[i]
- 144956522040*r6[i]
+ 1290252243720*r8[i]
- 18448766253240*r10[i]
+ 394763466531720*r12[i]
- 12048763425424440*r14[i]
+ 507104531694579720*r16[i]
- 28726839421461491640*r18[i]
+ 2153064433503155907720*r20[i]
- 211041986898764840790840*r22[i]
+ 26870132026261051008915720*r24[i]
- 4433779344005175981028538040*r26[i]
+ 950513389106656928711222883720*r28[i]
- 266877172369028643812085068829240*r30[i]
+ 99651017964870751887504875569971720*r32[i]
- 50788156610571325953562659420384640440*r34[i]
+ 36915961449056930526009630202648137219720*r36[i]
- 41419014418447665040750851917674255257827640*r38[i]
+ 84934578551016826327683205574058431012558547720*r40[i]
- 570180937724400876712836731188276811777920749126840*r42[i]
- 4158439692009034639969470592464099450041235634033244280*r44[i]
- 229275923325503706243762726200010620540068823040000000000*r45[i]
- 10938400640270606999512627385384658646639850257084618154040*r46[i]
- 469832222078622194834718578529061763610709032173568000000000*r47[i]
- 18609787245585710799825274640865231563879706109002975534476280*r48[i]
- 690703654308090686886605775729000661503847399056998400000000000*r49[i]
- 24295755635821397902484226724698036360412358674335136584603405240*r50[i]
- 816834061921519325837632181160492761661336490802298224640000000000*r51[i]
- 26420216400737828039776597843354259258729442541873887374106278588280*r52[i]
- 826385145940446765246655148432861711174878386201463829299200000000000*r53[i]
- 25100830043691732995573291002742236374870109783293156876807153222256440*r54[i]
) // 60415263063373835637355132068513997507264512000000000 for i in range(len(r0))]
r41 = [(24466267020*r[1][i]
- 42550029600*r[2][i]
+ 50528160150*r[3][i]
- 48507033744*r[4][i]
+ 39645171810*r[5][i]
- 28192122176*r[6][i]
+ 17620076360*r[7][i]
- 9721421440*r[8][i]
+ 4739192952*r[9][i]
- 2038362560*r[10][i]
+ 770755843*r[11][i]
- 254795320*r[12][i]
+ 73066305*r[13][i]
- 17985552*r[14][i]
+ 3746990*r[15][i]
- 648128*r[16][i]
+ 90610*r[17][i]
- 9840*r[18][i]
+ 779*r[19][i]
- 40*r[20][i]
+ r[21][i]
- 6564120420*r0[i]
+ 3534526380*r2[i]
- 7928802420*r4[i]
+ 39562131180*r6[i]
- 355997149620*r8[i]
+ 5162772055980*r10[i]
- 112466379416820*r12[i]
+ 3509804003100780*r14[i]
- 151808102304340020*r16[i]
+ 8890838711788769580*r18[i]
- 693867758978013455220*r20[i]
+ 71436574576557715366380*r22[i]
- 9656103679244476561098420*r24[i]
+ 1714541855816811795973995180*r26[i]
- 402505898503128791422102405620*r28[i]
+ 126699650825847516884027712559980*r30[i]
- 54827934277723571354991704981312820*r32[i]
+ 34051732695777105364083032869387764780*r34[i]
- 32827430653262026254340815579045378556020*r36[i]
+ 58129225653125966892251726413185365757113580*r38[i]
- 338476895760295138790385051321218766549279671220*r40[i]
- 2149763077602671437231704105519918866633843849089620*r42[i]
- 110761315616185365335151075458942328763318272000000000*r43[i]
- 4942256826876098689793689711313418888604591478522994420*r44[i]
- 198705800215436545411261029373342537801392979968000000000*r45[i]
- 7372979698612811191617476736621847607367673634869335740820*r46[i]
- 256536466678869072307088584563086803940345640910848000000000*r47[i]
- 8465458808946796165763451715680655749443289544616664687661620*r48[i]
- 267183551072205666325866548010883965389520680874147840000000000*r49[i]
- 8117979331672354072521723205205099479673234187982104799090936020*r50[i]
- 238669689906108201296368312708296353560792649309607690240000000000*r51[i]
- 6818076027538551619225591166422355976547652044865002983244581608820*r52[i]
- 189900239055230874242774936502694772441792049430392817582080000000000*r53[i]
- 5171618834732319180394479687214193283849620051628630315033942033971220*r54[i]
) // 33452526613163807108170062053440751665152000000000 for i in range(len(r0))]
r39 = [(-6564120420*r[1][i]
+ 11338026180*r[2][i]
- 13309856820*r[3][i]
+ 12570420330*r[4][i]
- 10056336264*r[5][i]
+ 6962078952*r[6][i]
- 4211628008*r[7][i]
+ 2234741392*r[8][i]
- 1040310648*r[9][i]
+ 423830264*r[10][i]
- 150391384*r[11][i]
+ 46142811*r[12][i]
- 12118314*r[13][i]
+ 2686866*r[14][i]
- 493506*r[15][i]
+ 73112*r[16][i]
- 8398*r[17][i]
+ 702*r[18][i]
- 38*r[19][i]
+ r[20][i]
+ 1767263190*r0[i]
- 955277400*r2[i]
+ 2156197560*r4[i]
- 10855425000*r6[i]
+ 98876533560*r8[i]
- 1456859058600*r10[i]
+ 32382608125560*r12[i]
- 1036360772970600*r14[i]
+ 46242812090245560*r16[i]
- 2813858311510281000*r18[i]
+ 230141619686501005560*r20[i]
- 25097337236284407949800*r22[i]
+ 3642002181929040219157560*r24[i]
- 706474912755087069174777000*r26[i]
+ 185490702479102020671448093560*r28[i]
- 67501512373123369695638979402600*r30[i]
+ 35506616897715366055874618759845560*r32[i]
- 29173319982987640073110629923442306600*r34[i]
+ 44272025958057634433180503709478279085560*r36[i]
- 222019441630075420847480526017947263931809000*r38[i]
- 1219813882056330049405575791394671579625372874440*r40[i]
- 58541921573036662439297608593521315414016000000000*r41[i]
- 2435494701008122308521041585840935773426259964069800*r42[i]
- 91378085383352926401499637253627421229737574400000000*r43[i]
- 3166734413390519310621011935324774315544541946854082440*r44[i]
- 102992200477964363280928335737465088274348376064000000000*r45[i]
- 3179252903572284408695210045628305460118381385145907089000*r46[i]
- 93933517845624637462463708669855295641358690995404800000000*r47[i]
- 2673604876174888392329293291823128228151672865125704677946440*r48[i]
- 73683990172722867345525100631400320014642700636651520000000000*r49[i]
- 1974418989189660654416775142028601893909607175588350467588706600*r50[i]
- 51613966955266559433583238169717122269196640905399894016000000000*r51[i]
- 1320028845480376778241459745623130669629332621855587804526269234440*r52[i]
- 33107222954815130156932711664097915655061115376773617418240000000000*r53[i]
- 815957549537661838837381326961271796535482084133007452235898808602600*r54[i]
) // 20397882081197443358640281739902897356800000000 for i in range(len(r0))]
r37 = [(1767263190*r[1][i]
- 3029594040*r[2][i]
+ 3511574910*r[3][i]
- 3257112960*r[4][i]
+ 2544619500*r[5][i]
- 1709984304*r[6][i]
+ 997490844*r[7][i]
- 506662016*r[8][i]
+ 223926516*r[9][i]
- 85795600*r[10][i]
+ 28312548*r[11][i]
- 7970688*r[12][i]
+ 1888887*r[13][i]
- 369852*r[14][i]
+ 58275*r[15][i]
- 7104*r[16][i]
+ 629*r[17][i]
- 36*r[18][i]
+ r[19][i]
- 477638700*r0[i]
+ 259289580*r2[i]
- 589294500*r4[i]
+ 2996657580*r6[i]
- 27670359300*r8[i]
+ 415064933580*r10[i]
- 9439543875300*r12[i]
+ 310922483993580*r14[i]
- 14379880666402500*r16[i]
+ 914767168887053580*r18[i]
- 79051272004645620900*r20[i]
+ 9231401536061270849580*r22[i]
- 1459700260139475814330500*r24[i]
+ 315843905250429722227637580*r26[i]
- 95612546130070295522414451300*r28[i]
+ 42177612582297377823299737193580*r30[i]
- 29268533564152352561039458453023300*r32[i]
+ 37747202396256876155482291281278813580*r34[i]
- 161759954125032708920885781040309430206500*r36[i]
- 763162014442847423121851269222329739576686420*r38[i]
- 33996470135329072264400469566504828928000000000*r39[i]
- 1314149222797294391875041342296266627244339280900*r40[i]
- 45857838565545385577449793398258363740979200000000*r41[i]
- 1479444354242422663436299123473954120225396734970420*r42[i]
- 44831961082741695492799244828619514023247872000000000*r43[i]
- 1290525734288850664269099373480698875776359383538646500*r44[i]
- 35584775745235419804380819416241066350620337766400000000*r45[i]
- 945953923580279776552772789184754415724912490598746182420*r46[i]
- 24366115407876526559068567586678948554722823372800000000000*r47[i]
- 610645775114510996953480313967173146186867766220019295823300*r48[i]
- 14939521515639279686486638270686230946922780466085888000000000*r49[i]
- 357801113228416003019399250210317079666322369514337123812946420*r50[i]
- 8408661385093459098177743857092487683793831993666437120000000000*r51[i]
- 194295554214245025331172354056693339192813114298766754673003451300*r52[i]
- 4421785847139823304538477974636921659214442633337233211392000000000*r53[i]
- 99261104716354759275356708669334064781685960280357361053977678366420*r54[i]
) // 13763753091226345046315979581580902400000000 for i in range(len(r0))]
r35 = [(-477638700*r[1][i]
+ 811985790*r[2][i]
- 927983760*r[3][i]
+ 843621600*r[4][i]
- 641886000*r[5][i]
+ 417225900*r[6][i]
- 233646504*r[7][i]
+ 112971936*r[8][i]
- 47071640*r[9][i]
+ 16811300*r[10][i]
- 5101360*r[11][i]
+ 1298528*r[12][i]
- 272272*r[13][i]
+ 45815*r[14][i]
- 5950*r[15][i]
+ 560*r[16][i]
- 34*r[17][i]
+ r[18][i]
+ 129644790*r0[i]
- 70715340*r2[i]
+ 161960940*r4[i]
- 832930740*r6[i]
+ 7810859340*r8[i]
- 119578066740*r10[i]
+ 2791740107340*r12[i]
- 95062235276340*r14[i]
+ 4584012079172940*r16[i]
- 307268933913567540*r18[i]
+ 28355038085389144140*r20[i]
- 3597774935929125068340*r22[i]
+ 632729503874459828228940*r24[i]
- 157381528472579148083026740*r26[i]
+ 57577884185625191071239755340*r28[i]
- 33404393172944223690128125810740*r30[i]
+ 36271128388074981554067219056171340*r32[i]
- 131671692334895976886647813958596908340*r34[i]
- 529104107360143104505564190890974500955060*r36[i]
- 21792609061108379656666967670836428800000000*r37[i]
- 779765567254824678774814590170424618060927540*r38[i]
- 25214048683702395262763681595157748121600000000*r39[i]
- 754531895504954495472529428607358759602244935860*r40[i]
- 21229190210645503978483385444330514048614400000000*r41[i]
- 567902644449952014090537079509460539320563935596340*r42[i]
- 14564893239013264062672891916748815156327219200000000*r43[i]
- 360416016142646161224945882401067658836071135991963060*r44[i]
- 8648657180064969977242561394456399100712373452800000000*r45[i]
- 202069375902424923136583586389997599181812580415819762740*r46[i]
- 4612127517564454653650814843765113002002883805184000000000*r47[i]
- 103121612921980129969364006657783463883530860291974593108660*r48[i]
- 2263884472933693041558609190221290023990021205262336000000000*r49[i]
- 48895910164254390571448366914991646721674728906975264997394740*r50[i]
- 1040735050391204632204438770440340544568220182900637696000000000*r51[i]
- 21862169403162391239341958599750577577387707221098019982750324660*r52[i]
- 453821931200327068047775184677590212395655580642824945664000000000*r53[i]
- 9319698121456631696400960021555048638297447683852229271473797580340*r54[i]
) // 10333147966386144929666651337523200000000 for i in range(len(r0))]
r33 = [(129644790*r[1][i]
- 218349120*r[2][i]
+ 245642760*r[3][i]
- 218349120*r[4][i]
+ 161280600*r[5][i]
- 100975680*r[6][i]
+ 53993940*r[7][i]
- 24682944*r[8][i]
+ 9612108*r[9][i]
- 3164480*r[10][i]
+ 870232*r[11][i]
- 196416*r[12][i]
+ 35464*r[13][i]
- 4928*r[14][i]
+ 495*r[15][i]
- 32*r[16][i]
+ r[17][i]
- 35357670*r0[i]
+ 19389690*r2[i]
- 44796870*r4[i]
+ 233344890*r6[i]
- 2227139910*r8[i]
+ 34903389690*r10[i]
- 839988260550*r12[i]
+ 29734601940090*r14[i]
- 1506293149214790*r16[i]
+ 107487540061668090*r18[i]
- 10743535525710258630*r20[i]
+ 1511267716903778445690*r22[i]
- 304525956073869018848070*r24[i]
+ 91234873454404063067344890*r26[i]
- 43747586259736794619504039110*r28[i]
+ 39574917458915050445099774637690*r30[i]
- 120523981455993504966525708346887750*r32[i]
- 408775192473644376465790167368394203910*r34[i]
- 15499721949579217394499977006284800000000*r35[i]
- 511206585269023792365556128001469646849990*r36[i]
- 15254826342775865759666877369585500160000000*r37[i]
- 421754497238984285335705463354740490210507910*r38[i]
- 10974654148845317574241976981091935846400000000*r39[i]
- 271793538072560300468434911462753194293644181830*r40[i]
- 6459357656104303171129642884693889583677440000000*r41[i]
- 148248369194001435848413334991598692517822202402310*r42[i]
- 3302211571953506236081129759184691588287692800000000*r43[i]
- 71676123253955938571177412178194687158760951558339270*r44[i]
- 1520976967414625530272457942824571170900903198720000000*r45[i]
- 31639609352600382246311701401196841805566037174158815110*r46[i]
- 646685006086394734265332084740666732219400716288000000000*r47[i]
- 13012191241624225597793637611655297834798932917962602378310*r48[i]
- 258181916941754694739033103200539980500380934786252800000000*r49[i]
- 5058734882305856045540073713691835327365626096838684137474310*r50[i]
- 98003172162669552280283212651193173071892639817662464000000000*r51[i]
- 1879290113304215911642155827929295380860361801862580501733354950*r52[i]
- 35704185906372296773445691918777756816503577852201255567360000000*r53[i]
- 672641472730329564687292228981658860084205881937208343188256907910*r54[i]
) // 8683317618811886495518194401280000000 for i in range(len(r0))]
r31 = [(-35357670*r[1][i]
+ 58929450*r[2][i]
- 65132550*r[3][i]
+ 56448210*r[4][i]
- 40320150*r[5][i]
+ 24192090*r[6][i]
- 12271350*r[7][i]
+ 5259150*r[8][i]
- 1893294*r[9][i]
+ 566370*r[10][i]
- 138446*r[11][i]
+ 26970*r[12][i]
- 4030*r[13][i]
+ 434*r[14][i]
- 30*r[15][i]
+ r[16][i]
+ 9694845*r0[i]
- 5348880*r2[i]
+ 12480720*r4[i]
- 65969520*r6[i]
+ 642563280*r8[i]
- 10347602160*r10[i]
+ 258040917840*r12[i]
- 9564008626800*r14[i]
+ 514021079720400*r16[i]
- 39590373677587440*r18[i]
+ 4371353677873146960*r20[i]
- 701971899866535028080*r22[i]
+ 169737570795219895373520*r24[i]
- 66396273378844288679892720*r26[i]
+ 49448835121192219782326176080*r28[i]
- 124963193751534047864734415925360*r30[i]
- 354113410826574103722030528083469360*r32[i]
- 12301366626650172535317442068480000000*r33[i]
- 372225904019072507165665501545458070000*r34[i]
- 10203983616806318118045818195804160000000*r35[i]
- 259484653500223872483011119661283865786800*r36[i]
- 6217811871006716259183948315607695360000000*r37[i]
- 141956901865997956445469727796622341498870640*r38[i]
- 3113335802166672719861469258672651632640000000*r39[i]
- 66003822624082868383556482555741495612650600240*r40[i]
- 1359334478541063086765779323397876419133440000000*r41[i]
- 27303356587963564025554884815930553997263574871280*r42[i]
- 536588847651574079588079017443366763149393920000000*r43[i]
- 10345842549438556817463474698578198121859964179733680*r44[i]
- 196138884946560564409651268242770514989620920320000000*r45[i]
- 3663204676820752962698443093474820599422678195673015920*r46[i]
- 67509422521578235356394063172809938341831560396800000000*r47[i]
- 1229367058216339817971318602200240769989331897298761411120*r48[i]
- 22148293718278830966574475214239695745532717485260800000000*r49[i]
- 395185352573696509925259966545790692473196837003978017048560*r50[i]
- 6989838211515905458753639642597471400309284985697730560000000*r51[i]
- 122657793546790877104838252566375468764736099620191835404656560*r52[i]
- 2136978399115087712296321880227522428322876912299682037760000000*r53[i]
- 36988121280698718881148076634622109731006022172305430137473913200*r54[i]
) // 8222838654177922817725562880000000 for i in range(len(r0))]
r29 = [(9694845*r[1][i]
- 15967980*r[2][i]
+ 17298645*r[3][i]
- 14567280*r[4][i]
+ 10015005*r[5][i]
- 5722860*r[6][i]
+ 2731365*r[7][i]
- 1085760*r[8][i]
+ 356265*r[9][i]
- 95004*r[10][i]
+ 20097*r[11][i]
- 3248*r[12][i]
+ 377*r[13][i]
- 28*r[14][i]
+ r[15][i]
- 2674440*r0[i]
+ 1485800*r2[i]
- 3506488*r4[i]
+ 18850280*r6[i]
- 188004088*r8[i]
+ 3125835560*r10[i]
- 81314498488*r12[i]
+ 3185384180840*r14[i]
- 184064268909688*r16[i]
+ 15598375633694120*r18[i]
- 1958105850969957688*r20[i]
+ 375744491571024583400*r22[i]
- 118117302690774819242488*r24[i]
+ 71447614092662750198256680*r26[i]
- 147980747895225006590333244088*r28[i]
- 346368637877614395127589803878040*r30[i]
- 10963784872237230423634083840000000*r31[i]
- 302766527792977996357877082103322488*r32[i]
- 7585842753100939730112422608896000000*r33[i]
- 176553572119721839407097582006071612760*r34[i]
- 3876980715165912710714213825249280000000*r35[i]
- 81213796311764134505181592648745883717688*r36[i]
- 1636103186224681029581052139652775936000000*r37[i]
- 31895543813319775842490572300866856117139480*r38[i]
- 604645713103650398366928164707180216320000000*r39[i]
- 11189653759353064214370349765226592602607549688*r40[i]
- 202794861446303149866709151240333763280896000000*r41[i]
- 3608799207440735942926262565268791718882246250200*r42[i]
- 63195849406190967779680687932546907121909760000000*r43[i]
- 1091041918456432706911605989934195570136050930818488*r44[i]
- 18599858037912613836046600540495361832783446016000000*r45[i]
- 313534044032502214538190505667405050039920730329536920*r46[i]
- 5232130701886884640147951658064894118305202176000000000*r47[i]
- 86524070613240340349034843422074253070890184188704404088*r48[i]
- 1419220451222069603559756976077536870379472375775232000000*r49[i]
- 23107896008521043617173872183497904829674956287283293591640*r50[i]
- 373741738674210661134828098626419085853440812861358080000000*r51[i]
- 6008307669591671335816649438311816911003850182297118574066488*r52[i]
- 96059698783150230038524550628221988538172968887744724992000000*r53[i]
- 1528101734176197374675502615836313800063939684531640625652206360*r54[i]
) // 8841761993739701954543616000000 for i in range(len(r0))]
r27 = [(-2674440*r[1][i]
+ 4345965*r[2][i]
- 4601610*r[3][i]
+ 3749460*r[4][i]
- 2466750*r[5][i]
+ 1332045*r[6][i]
- 592020*r[7][i]
+ 215280*r[8][i]
- 63180*r[9][i]
+ 14625*r[10][i]
- 2574*r[11][i]
+ 324*r[12][i]
- 26*r[13][i]
+ r[14][i]
+ 742900*r0[i]
- 416024*r2[i]
+ 994840*r4[i]
- 5454824*r6[i]
+ 55944280*r8[i]
- 966290024*r10[i]
+ 26454613720*r12[i]
- 1109329691624*r14[i]
+ 70212852387160*r16[i]
- 6733670404619624*r18[i]
+ 1005318113348848600*r20[i]
- 249581050854994274024*r22[i]
+ 120719220687299365182040*r24[i]
- 202039976682357297272094824*r26[i]
- 385557844336439370252173428520*r28[i]
- 11052202492174627443179520000000*r29[i]
- 276888650579451671741587901762024*r30[i]
- 6304176301536407493589598208000000*r31[i]
- 133535841584115505205141919375399080*r32[i]
- 2672618344480543437732658544640000000*r33[i]
- 51095126335993498323380094454901195624*r34[i]
- 940618873537377672007825158832128000000*r35[i]
- 16776403501444391106926987629186000345640*r36[i]
- 291283862319085180678807183848898560000000*r37[i]
- 4942310839108515578583708125038854650555624*r38[i]
- 82203911327563805707081667710859870208000000*r39[i]
- 1343752600475734599375534320311340373516684200*r40[i]
- 21634243326074826428166414905753461063680000000*r41[i]
- 343672532983087585902951862991031321905844242024*r42[i]
- 5395063942758184834505475068561955332947968000000*r43[i]
- 83804941354439477195910293019964343299641959230760*r44[i]
- 1289609166695254343642200168046105549173555200000000*r45[i]
- 19678461460501652805347265575009996073778349586894824*r46[i]
- 298018526228473595475945631789329672119214145536000000*r47[i]
- 4482734138598481574681074400900490010744661138946801320*r48[i]
- 67016178755227832923500959370656761105984640778240000000*r49[i]
- 996343679402015421123803198306389561979045588249233394024*r50[i]
- 14738679287503486801955946351327209631956632997462016000000*r51[i]
- 217035109012403108518173019970634230404031272801464219811880*r52[i]
- 3182760243299536666170356413471689268456113615580692480000000*r53[i]
- 46498820464911995110643960090817019186186417071168193972859624*r54[i]
) // 10888869450418352160768000000 for i in range(len(r0))]
r25 = [(742900*r[1][i]
- 1188640*r[2][i]
+ 1225785*r[3][i]
- 961400*r[4][i]
+ 600875*r[5][i]
- 303600*r[6][i]
+ 123970*r[7][i]
- 40480*r[8][i]
+ 10350*r[9][i]
- 2000*r[10][i]
+ 275*r[11][i]
- 24*r[12][i]
+ r[13][i]
- 208012*r0[i]
+ 117572*r2[i]
- 285532*r4[i]
+ 1602692*r6[i]
- 16996252*r8[i]
+ 307475012*r10[i]
- 8966430172*r12[i]
+ 409745686532*r14[i]
- 29195711499292*r16[i]
+ 3312133208909252*r18[i]
- 636215671041835612*r20[i]
+ 241648300078174135172*r22[i]
- 321511316149669476991132*r24[i]
- 492817676505266866078123708*r26[i]
- 12703681025488077520896000000*r27[i]
- 286779648275654636997381637852*r28[i]
- 5894507995826467969695744000000*r29[i]
- 112914054231542703053832892635388*r30[i]
- 2047008246979213061238030336000000*r31[i]
- 35501568925223446300815211192767772*r32[i]
- 593711792050129855003168210944000000*r33[i]
- 9632134956680435093368218113996247868*r34[i]
- 152311343455497374594406627803136000000*r35[i]
- 2356318736218539774396037820111678892892*r36[i]
- 35772470531371951985805498114637824000000*r37[i]
- 534273042749950920189640352996759062689148*r38[i]
- 7866491034006154572049014294052601856000000*r39[i]
- 114383224059606274110181105712262975351245212*r40[i]
- 1644946226278516886873016733667061202944000000*r41[i]
- 23426103831558846665144911501028780920365367228*r42[i]
- 330735945747364837719554208843251145179136000000*r43[i]
- 4633465747908141417306051485893140722291346976732*r44[i]
- 64465996518808752310647291812383168776634368000000*r45[i]
- 891389875128429665004288245297052393567100598170108*r46[i]
- 12257190333970097165549309885966019046465339392000000*r47[i]
- 167703402046599761376513697620930939990159551304359452*r48[i]
- 2284199788431383972862903582163083269492369522688000000*r49[i]
- 30985395797162515638045004419632302359171420946744265788*r50[i]
- 418773650924292383172351750158911938166116165353472000000*r51[i]
- 5640938886725051055672433299961125394581606270770949985372*r52[i]
- 75754370981682573393940880354465056079445791605260288000000*r53[i]
- 1014539155515195896087346280844831091980940427383805672902268*r54[i]
) // 15511210043330985984000000 for i in range(len(r0))]
r23 = [(-208012*r[1][i]
+ 326876*r[2][i]
- 326876*r[3][i]
+ 245157*r[4][i]
- 144210*r[5][i]
+ 67298*r[6][i]
- 24794*r[7][i]
+ 7084*r[8][i]
- 1518*r[9][i]
+ 230*r[10][i]
- 22*r[11][i]
+ r[12][i]
+ 58786*r0[i]
- 33592*r2[i]
+ 83096*r4[i]
- 479752*r6[i]
+ 5299736*r8[i]
- 101549512*r10[i]
+ 3208453976*r12[i]
- 164071220872*r14[i]
+ 13743680753816*r16[i]
- 1993276972245832*r18[i]
+ 581947914140407256*r20[i]
- 603916464771468176392*r22[i]
- 730803773459954540777704*r24[i]
- 16803810880275234816000000*r25[i]
- 339155768243774227716964552*r26[i]
- 6245976504198304781107200000*r27[i]
- 107413822788261782335458993064*r28[i]
- 1751393992807566623932416000000*r29[i]
- 27365156266821215807862420562312*r30[i]
- 412945663851071412756568473600000*r31[i]
- 6053949680529454447550745704030824*r32[i]
- 86623417665042381831452000256000000*r33[i]
- 1214146547565910406028014931410521672*r34[i]
- 16719755812321492798917963359846400000*r35[i]
- 226758627215029497194516602329808882984*r36[i]
- 3034905857007157810746475187798016000000*r37[i]
- 40151799724774280996886476759684489594632*r38[i]
- 525848735885794606994555529953619148800000*r39[i]
- 6825564942475643900873841059427230143341544*r40[i]
- 87900055843825806396690634755863003136000000*r41[i]
- 1124090333957827218160935737032127911249333192*r42[i]
- 14286036145840157893404384196456208735600640000*r43[i]
- 180556939553256275799275906968519352499771598504*r44[i]
- 2270728203819030041749862616122105872023552000000*r45[i]
- 28430855249825246651314973609548475795532583689352*r46[i]
- 354557703317395919808450352391376751066211942400000*r47[i]
- 4405868085478593275690315869491622501390761293845864*r48[i]
- 54573144465647486264201741288918109369842860032000000*r49[i]
- 674011661674309854738045921738777159802726884618615112*r50[i]
- 8302706625795267729689057629348230882286932767539200000*r51[i]
- 102034139431103779464508421919001500494414946039191875624*r52[i]
- 1251246650171085656596973236879882037480265304768512000000*r53[i]
- 15314394051611719851475192053401326069594457012869777662472*r54[i]
) // 25852016738884976640000 for i in range(len(r0))]
r21 = [(58786*r[1][i]
- 90440*r[2][i]
+ 87210*r[3][i]
- 62016*r[4][i]
+ 33915*r[5][i]
- 14364*r[6][i]
+ 4655*r[7][i]
- 1120*r[8][i]
+ 189*r[9][i]
- 20*r[10][i]
+ r[11][i]
- 16796*r0[i]
+ 9724*r2[i]
- 24596*r4[i]
+ 147004*r6[i]
- 1708916*r8[i]
+ 35240284*r10[i]
- 1237329236*r12[i]
+ 73853629564*r14[i]
- 7850527669556*r16[i]
+ 1717351379730844*r18[i]
- 1359124435588313876*r20[i]
- 1272410676942417239876*r22[i]
- 25852016738884976640000*r23[i]
- 462292539259962003646196*r24[i]
- 7561714896123855667200000*r25[i]
- 115761644587269354830466596*r26[i]
- 1683741850203578528563200000*r27[i]
- 23512975860299444963550050516*r28[i]
- 317677725072691341719961600000*r29[i]
- 4176614976496441445095962733316*r30[i]
- 53674391443652368368589209600000*r31[i]
- 676635955671282540673335079110836*r32[i]
- 8391272072243853389701334630400000*r33[i]
- 102611708232289325546408008313624036*r34[i]
- 1239646284649926576486736094822400000*r35[i]
- 14819283410691765614379616648600811156*r36[i]
- 175538127424434549895381626305740800000*r37[i]
- 2062659648435073986802743885440046722756*r38[i]
- 24066873273263602745997309174983884800000*r39[i]
- 279069134864297423784787795404361206735476*r40[i]
- 3218237360334469905693543066426751549440000*r41[i]
- 36932670876144577834192017462238998576813476*r42[i]
- 422013831656219970552631011526505561456640000*r43[i]
- 4803667893589610545887832027829424971473267796*r44[i]
- 54491782544378643866541770098406137341542400000*r45[i]
- 616254801390825608499920295882691673585117080196*r46[i]
- 6950267169846786189298202657232919399818854400000*r47[i]
- 78194975030419808376759755992062291704460984792116*r48[i]
- 877813878936817604039539295936804610730357555200000*r49[i]
- 9834901482219684549861282981457686724945206826306916*r50[i]
- 109993865724440916050887229750467965278551356211200000*r51[i]
- 1228217338997580254122488729377687743870958069616892436*r52[i]
- 13694916176593289530129597814644948512271618874572800000*r53[i]
- 152504503331260902260854535497432382418134663231196077636*r54[i]
) // 51090942171709440000 for i in range(len(r0))]
r19 = [(-16796*r[1][i]
+ 25194*r[2][i]
- 23256*r[3][i]
+ 15504*r[4][i]
- 7752*r[5][i]
+ 2907*r[6][i]
- 798*r[7][i]
+ 152*r[8][i]
- 18*r[9][i]
+ r[10][i]
+ 4862*r0[i]
- 2860*r2[i]
+ 7436*r4[i]
- 46420*r6[i]
+ 576236*r8[i]
- 13098580*r10[i]
+ 532310636*r12[i]
- 39968611540*r14[i]
+ 6350631494636*r16[i]
- 3730771315561300*r18[i]
- 2637991952943407764*r20[i]
- 46833363657400320000*r21[i]
- 734121065118879803860*r22[i]
- 10556240168378032128000*r23[i]
- 142438684135271315212564*r24[i]
- 1830415113744266649600000*r25[i]
- 22632897298190126259675220*r26[i]
- 271297526662043666104320000*r27[i]
- 3170344993810020486920015764*r28[i]
- 36274730261563609572556800000*r29[i]
- 407775103607650299563627591380*r30[i]
- 4515882637052182897862000640000*r31[i]
- 49377994276343186011748723193364*r32[i]
- 534053247401000753173510963200000*r33[i]
- 5722063606154183864914875339648340*r34[i]
- 60811730909031986048777521029120000*r35[i]
- 641729418431834160625738740379401364*r36[i]
- 6730380606921481449181267599974400000*r37[i]
- 70207898580127312813466155395513222100*r38[i]
- 728918319689461841494925372032622592000*r39[i]
- 7536441803725213229125462424550696575764*r40[i]
- 77635978704164552294553096402068152320000*r41[i]
- 797177898990753876072852178329776532568660*r42[i]
- 8162164080895303403984327865949915250688000*r43[i]
- 83359491110673172494030048846026790563932564*r44[i]
- 849432099945167336777734465061373289267200000*r45[i]
- 8638438243166451781593809976801426668242424020*r46[i]
- 87694169965134464605849462884812769886371840000*r47[i]
- 888832151283066038746077396233689115965303967764*r48[i]
- 8996158031157109433578511766939541381376409600000*r49[i]
- 90938713449996246641127353860256309887114389604180*r50[i]
- 918234342704615923743435749615058841825963745280000*r51[i]
- 9262393601318313123889045816028965261306516208457364*r52[i]
- 93347798539774463006574188993931221735397071462400000*r53[i]
- 940020095741410096004864931705566108623177977672605140*r54[i]
) // 121645100408832000 for i in range(len(r0))]
r17 = [(4862*r[1][i]
- 7072*r[2][i]
+ 6188*r[3][i]
- 3808*r[4][i]
+ 1700*r[5][i]
- 544*r[6][i]
+ 119*r[7][i]
- 16*r[8][i]
+ r[9][i]
- 1430*r0[i]
+ 858*r2[i]
- 2310*r4[i]
+ 15258*r6[i]
- 206790*r8[i]
+ 5386458*r10[i]
- 272513670*r12[i]
+ 30255826458*r14[i]
- 12765597850950*r16[i]
- 6622557957272742*r18[i]
- 101370917007360000*r19[i]
- 1375210145685786630*r20[i]
- 17172233341046784000*r21[i]
- 201832098313986359142*r22[i]
- 2265471043586150400000*r23[i]
- 24529324224160803328710*r24[i]
- 258058524232798248960000*r25[i]
- 2652208374242713043720742*r26[i]
- 26739700571225856614400000*r27[i]
- 265323404171486113659725190*r28[i]
- 2597688920748017370193920000*r29[i]
- 25147613788240222384169485542*r30[i]
- 241125683321001354933657600000*r31[i]
- 2293170112631184981695915264070*r32[i]
- 21656158388689797460311183360000*r33[i]
- 203283794784841444836991831621542*r34[i]
- 1898267590696733462875776307200000*r35[i]
- 17646072330245312137111933794073350*r36[i]
- 163392570167583908119294187237376000*r37[i]
- 1507754227229479379470312529237936742*r38[i]
- 13871774079585871769182921633935360000*r39[i]
- 127291574907112728538906245247680921030*r40[i]
- 1165398276253942030786602999248830464000*r41[i]
- 10648249156718669259487809979675840079142*r42[i]
- 97121906010634492337139410720414515200000*r43[i]
- 884471146488697462546213719879378982015110*r44[i]
- 8043742604145412070397708709577312747520000*r45[i]
- 73065283527546375984492393431422365909536742*r46[i]
- 662985481414219219279431223562176586956800000*r47[i]
- 6010229010788429141870217066922217223929803590*r48[i]
- 54440174236564270133288224915510829498019840000*r49[i]
- 492755135434761578293305350886942317529465637542*r50[i]
- 4457205465827107111785421147442507464329523200000*r51[i]
- 40294548566019835134386988604297024831948411774470*r52[i]
- 364091512505225031658987624997678808818240901120000*r53[i]
- 3288369094603737090125334557327653119906621235549542*r54[i]
) // 355687428096000 for i in range(len(r0))]
r15 = [(-1430*r[1][i]
+ 2002*r[2][i]
- 1638*r[3][i]
+ 910*r[4][i]
- 350*r[5][i]
+ 90*r[6][i]
- 14*r[7][i]
+ r[8][i]
+ 429*r0[i]
- 264*r2[i]
+ 744*r4[i]
- 5304*r6[i]
+ 81384*r8[i]
- 2605944*r10[i]
+ 192387624*r12[i]
- 55942352184*r14[i]
- 20546119600536*r16[i]
- 266765571072000*r17[i]
- 3083760849804024*r18[i]
- 32945548027392000*r19[i]
- 332500281299403096*r20[i]
- 3215147584416768000*r21[i]
- 30076927429146721464*r22[i]
- 274100623905588480000*r23[i]
- 2446077617962088140056*r24[i]
- 21459412163122053120000*r25[i]
- 185641639183185136464504*r26[i]
- 1587401376760010972160000*r27[i]
- 13442713420403849918131416*r28[i]
- 112915002722102749808640000*r29[i]
- 941961013910760913890393144*r30[i]
- 7812419263561351877518080000*r31[i]
- 64474322285718607792730497176*r32[i]
- 529848386811984810994744320000*r33[i]
- 4338547620121893769542630267384*r34[i]
- 35415056327751829508662891008000*r35[i]
- 288317531175033442515609896757336*r36[i]
- 2341823147101379454117987013632000*r37[i]
- 18983391549723892653716655806647224*r38[i]
- 153619763998111828980832157720832000*r39[i]
- 1241292607509331793516191597844431896*r40[i]
- 10017079537004367071413852136982528000*r41[i]
- 80746194097372251940077615903073292664*r42[i]
- 650250798838302173122854563322562560000*r43[i]
- 5232061257212799699445154857325986640856*r44[i]
- 42067391464856035210355948847111229440000*r45[i]
- 338018548004311349729166172709579357563704*r46[i]
- 2714522948575416807552558113876933656320000*r47[i]
- 21788917503304477212565325243539420555704216*r48[i]
- 174821149505151584518657828257831893345280000*r49[i]
- 1402141896338776811136967582554033500226820344*r50[i]
- 11242168283931454427825411966307736057167360000*r51[i]
- 90112723368126633235251766101448928377940741976*r52[i]
- 722130298632985742738270377008563798712253440000*r53[i]
- 5785647203879657431846619085033124824223750822584*r54[i]
) // 1307674368000 for i in range(len(r0))]
r13 = [(429*r[1][i]
- 572*r[2][i]
+ 429*r[3][i]
- 208*r[4][i]
+ 65*r[5][i]
- 12*r[6][i]
+ r[7][i]
- 132*r0[i]
+ 84*r2[i]
- 252*r4[i]
+ 2004*r6[i]
- 37212*r8[i]
+ 1710324*r10[i]
- 325024572*r12[i]
- 80789566956*r14[i]
- 871782912000*r15[i]
- 8422900930332*r16[i]
- 75583578470400*r17[i]
- 643521842437836*r18[i]
- 5269678622208000*r19[i]
- 41890044885642492*r20[i]
- 325386564299596800*r21[i]
- 2481686964269990316*r22[i]
- 18652248729354240000*r23[i]
- 138536531588626169052*r24[i]
- 1019042849143807488000*r25[i]
- 7436421488952386592396*r26[i]
- 53911021949819274240000*r27[i]
- 388701690499592948238012*r28[i]
- 2789805187365599475072000*r29[i]
- 19946749502047187160692076*r30[i]
- 142159780685991861112320000*r31[i]
- 1010433303980489860989897372*r32[i]
- 7165521770403817166663116800*r33[i]
- 50716588034439244118483617356*r34[i]
- 358378772025058883636009472000*r35[i]
- 2528902640579773012941059115132*r36[i]
- 17824202779159732939433280230400*r37[i]
- 125502611080965065134883934376236*r38[i]
- 882926862501000079240924013568000*r39[i]
- 6206986746547700738292160195379292*r40[i]
- 43608135571536574058895364550860800*r41[i]
- 306213499909407501334225902520456716*r42[i]
- 2149239710498553002348841878415360000*r43[i]
- 15079178774724614117506008765315297852*r44[i]
- 105761403926812162332273274580071296000*r45[i]
- 741573481088337285231858048220674626796*r46[i]
- 5198479982499565882352899855753044480000*r47[i]
- 36434172034715569203746509369098022198812*r48[i]
- 255308169532157231577671227649975633664000*r49[i]
- 1788771440213892011837337228527544587734476*r50[i]
- 12531087911298377892590529356517576445440000*r51[i]
- 87775753902632879954790735906635276359730172*r52[i]
- 614779166184964747722494610821477092697932800*r53[i]
- 4305547785126634750908211772273402537757507756*r54[i]
) // 6227020800 for i in range(len(r0))]
r11 = [(-132*r[1][i]
+ 165*r[2][i]
- 110*r[3][i]
+ 44*r[4][i]
- 10*r[5][i]
+ r[6][i]
+ 42*r0[i]
- 28*r2[i]
+ 92*r4[i]
- 868*r6[i]
+ 22652*r8[i]
- 2620708*r10[i]
- 415790788*r12[i]
- 3632428800*r13[i]
- 28616744548*r14[i]
- 210680870400*r15[i]
- 1479485236228*r16[i]
- 10038995366400*r17[i]
- 66394067988388*r18[i]
- 430591742380800*r19[i]
- 2750479262009668*r20[i]
- 17360942812012800*r21[i]
- 108550450893568228*r22[i]
- 673606803881088000*r23[i]
- 4154688725062207108*r24[i]
- 25499502190850688000*r25[i]
- 155878445775166700068*r26[i]
- 949776357849070752000*r27[i]
- 5771581202353414724548*r28[i]
- 34995682724855684832000*r29[i]
- 211811399872933910999908*r30[i]
- 1280080235834717770252800*r31[i]
- 7726641919200262371657988*r32[i]
- 46591059456870785061004800*r33[i]
- 280704018540064430354883748*r34[i]
- 1690018909819536161979590400*r35[i]
- 10169113413821714748538703428*r36[i]
- 61159784116494648773674886400*r37[i]
- 367684638335977863351585967588*r38[i]
- 2209739160176731898013383884800*r39[i]
- 13276598260065161268654185556868*r40[i]
- 79750432649108163224160355276800*r41[i]
- 478956917715683026467561165467428*r42[i]
- 2876013540917084725512964985376000*r43[i]
- 17267443120712778679894991796314308*r44[i]
- 103661474908781590201983341856096000*r45[i]
- 622252957609245047342724399262599268*r46[i]
- 3734938395375021425507273833823424000*r47[i]
- 22416734056596928549732496421419871748*r48[i]
- 134535924504317597978456420953656384000*r49[i]
- 807393154821611376674434030676868979108*r50[i]
- 4845246995796352471529950975101582508800*r51[i]
- 29075922420664314894010979796628180325188*r52[i]
- 174477737199628479530547826532207368300800*r53[i]
- 1046977438360831608823005722785678653022948*r54[i]
) // 39916800 for i in range(len(r0))]
r9 = [(42*r[1][i]
- 48*r[2][i]
+ 27*r[3][i]
- 8*r[4][i]
+ r[5][i]
- 14*r0[i]
+ 10*r2[i]
- 38*r4[i]
+ 490*r6[i]
- 31238*r8[i]
- 2922230*r10[i]
- 19958400*r11[i]
- 124075238*r12[i]
- 726485760*r13[i]
- 4084385750*r14[i]
- 22313491200*r15[i]
- 119387268038*r16[i]
- 628980992640*r17[i]
- 3275389222070*r18[i]
- 16905818966400*r19[i]
- 86665431465638*r20[i]
- 441935114987520*r21[i]
- 2244295389943190*r22[i]
- 11360520464832000*r23[i]
- 57360469753884038*r24[i]
- 289038899804054400*r25[i]
- 1454155949521941110*r26[i]
- 7306671293537616000*r27[i]
- 36677059892827099238*r28[i]
- 183960524908301057280*r29[i]
- 922104761587650687830*r30[i]
- 4619736062008593926400*r31[i]
- 23135540444136227047238*r32[i]
- 115825176110799088940160*r33[i]
- 579715876176320506935350*r34[i]
- 2900939663557699476451200*r35[i]
- 14514140349055749129024038*r36[i]
- 72608472572041292373527040*r37[i]
- 363193454272347163609915670*r38[i]
- 1816571661325589960713958400*r39[i]
- 9085275939429279963731685638*r40[i]
- 45436050447189540392656321920*r41[i]
- 227218935892633882388998540790*r42[i]
- 1136249416059455304696385296000*r43[i]
- 5681866032591044240951769048038*r44[i]
- 28411805989856165780668427308800*r45[i]
- 142068933310062230858345890602710*r46[i]
- 710384280152969638132390327392000*r47[i]
- 3552079855654080764219631870487238*r48[i]
- 17761033099263130050180188817751680*r49[i]
- 88807700784593943012315384189973430*r50[i]
- 444048645089005049723558441367254400*r51[i]
- 2220283790147933078276819155128739238*r52[i]
- 11101581209667596183377765341852994560*r53[i]
- 55508555084398602505584708639561804950*r54[i]
) // 362880 for i in range(len(r0))]
r7 = [(-14*r[1][i]
+ 14*r[2][i]
- 6*r[3][i]
+ r[4][i]
+ 5*r0[i]
- 4*r2[i]
+ 20*r4[i]
- 604*r6[i]
- 29740*r8[i]
- 151200*r9[i]
- 708604*r10[i]
- 3160080*r11[i]
- 13645900*r12[i]
- 57657600*r13[i]
- 239967004*r14[i]
- 988107120*r15[i]
- 4037604460*r16[i]
- 16406863200*r17[i]
- 66398623804*r18[i]
- 267911678160*r19[i]
- 1078605601420*r20[i]
- 4335313752000*r21[i]
- 17403958407004*r22[i]
- 69804002545200*r23[i]
- 279780634372780*r24[i]
- 1120816644948000*r25[i]
- 4488349371924604*r26[i]
- 17968646803620240*r27[i]
- 71920337041294540*r28[i]
- 287818601403715200*r29[i]
- 1151686172846664604*r30[i]
- 4607980008114455280*r31[i]
- 18435626012705982700*r32[i]
- 73753622051697957600*r33[i]
- 295047842329672995004*r34[i]
- 1180291431927853642320*r35[i]
- 4721465916019935893260*r36[i]
- 18886764229967380219200*r37[i]
- 75549758619456576163804*r38[i]
- 302207139580435761213360*r39[i]
- 1208852873637267995922220*r40[i]
- 4835484440511039999684000*r41[i]
- 19342156599960850372299004*r42[i]
- 77369282913655045261040400*r43[i]
- 309479101196178257662005580*r44[i]
- 1237922313409633551106176000*r45[i]
- 4951706979513788347008408604*r46[i]
- 19806881095681900978203235440*r47[i]
- 79227683915609817008158719340*r48[i]
- 316911214261089847968346159200*r49[i]
- 1267646292840319012979866380604*r50[i]
- 5070589478749170677837606550480*r51[i]
- 20282370837160398114302240879500*r52[i]
- 81129522115132801716459190737600*r53[i]
- 324518204760004960744377010983004*r54[i]
) // 5040 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
- 1680*r7[i]
- 5542*r8[i]
- 17640*r9[i]
- 54958*r10[i]
- 168960*r11[i]
- 515062*r12[i]
- 1561560*r13[i]
- 4717438*r14[i]
- 14217840*r15[i]
- 42784582*r16[i]
- 128615880*r17[i]
- 386371918*r18[i]
- 1160164320*r19[i]
- 3482590102*r20[i]
- 10451964600*r21[i]
- 31364282398*r22[i]
- 94109624400*r23[i]
- 282362427622*r24[i]
- 847154391720*r25[i]
- 2541597392878*r26[i]
- 7625060614080*r27[i]
- 22875718713142*r28[i]
- 68628229881240*r29[i]
- 205886837127358*r30[i]
- 617664806349360*r31[i]
- 1853003008982662*r32[i]
- 5559026206817160*r33[i]
- 16677112980189838*r34[i]
- 50031407660046240*r35[i]
- 150094360419092182*r36[i]
- 450283356135183480*r37[i]
- 1350850618161364318*r38[i]
- 4052552953995720720*r39[i]
- 12157661061010417702*r40[i]
- 36472987581077764200*r41[i]
- 109418971539326314798*r42[i]
- 328256932210164988800*r43[i]
- 984770831814867055222*r44[i]
- 2954312565813345343320*r45[i]
- 8862937838177524385278*r46[i]
- 26588813796007549866480*r47[i]
- 79766441950972603020742*r48[i]
- 239299326978817715904840*r49[i]
- 717897983188252961399758*r50[i]
- 2153693954068358511569760*r51[i]
- 6461081871212274789450262*r52[i]
- 19383245631651222877832760*r53[i]
- 58149736930982465652462238*r54[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
- 126*r7[i]
- 254*r8[i]
- 510*r9[i]
- 1022*r10[i]
- 2046*r11[i]
- 4094*r12[i]
- 8190*r13[i]
- 16382*r14[i]
- 32766*r15[i]
- 65534*r16[i]
- 131070*r17[i]
- 262142*r18[i]
- 524286*r19[i]
- 1048574*r20[i]
- 2097150*r21[i]
- 4194302*r22[i]
- 8388606*r23[i]
- 16777214*r24[i]
- 33554430*r25[i]
- 67108862*r26[i]
- 134217726*r27[i]
- 268435454*r28[i]
- 536870910*r29[i]
- 1073741822*r30[i]
- 2147483646*r31[i]
- 4294967294*r32[i]
- 8589934590*r33[i]
- 17179869182*r34[i]
- 34359738366*r35[i]
- 68719476734*r36[i]
- 137438953470*r37[i]
- 274877906942*r38[i]
- 549755813886*r39[i]
- 1099511627774*r40[i]
- 2199023255550*r41[i]
- 4398046511102*r42[i]
- 8796093022206*r43[i]
- 17592186044414*r44[i]
- 35184372088830*r45[i]
- 70368744177662*r46[i]
- 140737488355326*r47[i]
- 281474976710654*r48[i]
- 562949953421310*r49[i]
- 1125899906842622*r50[i]
- 2251799813685246*r51[i]
- 4503599627370494*r52[i]
- 9007199254740990*r53[i]
- 18014398509481982*r54[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
- r7[i]
- r8[i]
- r9[i]
- r10[i]
- r11[i]
- r12[i]
- r13[i]
- r14[i]
- r15[i]
- r16[i]
- r17[i]
- r18[i]
- r19[i]
- r20[i]
- r21[i]
- r22[i]
- r23[i]
- r24[i]
- r25[i]
- r26[i]
- r27[i]
- r28[i]
- r29[i]
- r30[i]
- r31[i]
- r32[i]
- r33[i]
- r34[i]
- r35[i]
- r36[i]
- r37[i]
- r38[i]
- r39[i]
- r40[i]
- r41[i]
- r42[i]
- r43[i]
- r44[i]
- r45[i]
- r46[i]
- r47[i]
- r48[i]
- r49[i]
- r50[i]
- r51[i]
- r52[i]
- r53[i]
- r54[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54)
def natural_interpolate_29(r):
r0 = r[0]
r56 = r['infinity']
r54 = [(1877405874732108*(r[1][i] + r[-1][i])
- 1683191473897752*(r[2][i] + r[-2][i])
+ 1402659561581460*(r[3][i] + r[-3][i])
- 1085929983159840*(r[4][i] + r[-4][i])
+ 780512175396135*(r[5][i] + r[-5][i])
- 520341450264090*(r[6][i] + r[-6][i])
+ 321387366339585*(r[7][i] + r[-7][i])
- 183649923622620*(r[8][i] + r[-8][i])
+ 96926348578605*(r[9][i] + r[-9][i])
- 47153358767970*(r[10][i] + r[-10][i])
+ 21094923659355*(r[11][i] + r[-11][i])
- 8654327655120*(r[12][i] + r[-12][i])
+ 3245372870670*(r[13][i] + r[-13][i])
- 1108176102180*(r[14][i] + r[-14][i])
+ 343006888770*(r[15][i] + r[-15][i])
- 95722852680*(r[16][i] + r[-16][i])
+ 23930713170*(r[17][i] + r[-17][i])
- 5317936260*(r[18][i] + r[-18][i])
+ 1040465790*(r[19][i] + r[-19][i])
- 177100560*(r[20][i] + r[-20][i])
+ 25827165*(r[21][i] + r[-21][i])
- 3162510*(r[22][i] + r[-22][i])
+ 316251*(r[23][i] + r[-23][i])
- 24804*(r[24][i] + r[-24][i])
+ 1431*(r[25][i] + r[-25][i])
- 54*(r[26][i] + r[-26][i])
+ (r[27][i] + r[-27][i])
- 1946939425648112*r0[i]
- 1599746822560942766671602706793381136907120452482629032046755840000000000000*r56[i]
) // 230843697339241380472092742683027581083278564571807941132288000000000000 for i in range(len(r0))]
r52 = [(-477551179875952*(r[1][i] + r[-1][i])
+ 426384982032100*(r[2][i] + r[-2][i])
- 352870329957600*(r[3][i] + r[-3][i])
+ 270533919634160*(r[4][i] + r[-4][i])
- 191991813933920*(r[5][i] + r[-5][i])
+ 125994627894135*(r[6][i] + r[-6][i])
- 76360380541900*(r[7][i] + r[-7][i])
+ 42671977361650*(r[8][i] + r[-8][i])
- 21945588357420*(r[9][i] + r[-9][i])
+ 10363194502115*(r[10][i] + r[-10][i])
- 4481381406320*(r[11][i] + r[-11][i])
+ 1768966344600*(r[12][i] + r[-12][i])
- 635013559600*(r[13][i] + r[-13][i])
+ 206379406870*(r[14][i] + r[-14][i])
- 60403728840*(r[15][i] + r[-15][i])
+ 15820024220*(r[16][i] + r[-16][i])
- 3679075400*(r[17][i] + r[-17][i])
+ 752538150*(r[18][i] + r[-18][i])
- 133784560*(r[19][i] + r[-19][i])
+ 20358520*(r[20][i] + r[-20][i])
- 2598960*(r[21][i] + r[-21][i])
+ 270725*(r[22][i] + r[-22][i])
- 22100*(r[23][i] + r[-23][i])
+ 1326*(r[24][i] + r[-24][i])
- 52*(r[25][i] + r[-25][i])
+ (r[26][i] + r[-26][i])
+ 495918532948104*r0[i]
- 500161344235022991022867609146559759013770223238917205786624000000000000*r54[i]
- 1656034210762161123276714653884259362094593209144054868359512064000000000000*r56[i]
) // 80658175170943878571660636856403766975289505440883277824000000000000 for i in range(len(r0))]
r50 = [(121548660036300*(r[1][i] + r[-1][i])
- 108043253365600*(r[2][i] + r[-2][i])
+ 88749815264600*(r[3][i] + r[-3][i])
- 67327446062800*(r[4][i] + r[-4][i])
+ 47129212243960*(r[5][i] + r[-5][i])
- 30405943383200*(r[6][i] + r[-6][i])
+ 18053528883775*(r[7][i] + r[-7][i])
- 9847379391150*(r[8][i] + r[-8][i])
+ 4923689695575*(r[9][i] + r[-9][i])
- 2250829575120*(r[10][i] + r[-10][i])
+ 937845656300*(r[11][i] + r[-11][i])
- 354860518600*(r[12][i] + r[-12][i])
+ 121399651100*(r[13][i] + r[-13][i])
- 37353738800*(r[14][i] + r[-14][i])
+ 10272278170*(r[15][i] + r[-15][i])
- 2505433700*(r[16][i] + r[-16][i])
+ 536878650*(r[17][i] + r[-17][i])
- 99884400*(r[18][i] + r[-18][i])
+ 15890700*(r[19][i] + r[-19][i])
- 2118760*(r[20][i] + r[-20][i])
+ 230300*(r[21][i] + r[-21][i])
- 19600*(r[22][i] + r[-22][i])
+ 1225*(r[23][i] + r[-23][i])
- 50*(r[24][i] + r[-24][i])
+ (r[25][i] + r[-25][i])
- 126410606437752*r0[i]
- 168037864939466413690959660117507847865186469668506828800000000000000*r52[i]
- 496955181771977971849644098831517709276502465397642095493120000000000000*r54[i]
- 1045983785547912130104393377696510043035795431067327440669900800000000000000*r56[i]
) // 30414093201713378043612608166064768844377641568960512000000000000 for i in range(len(r0))]
r48 = [(-30957699535776*(r[1][i] + r[-1][i])
+ 27385657281648*(r[2][i] + r[-2][i])
- 22314239266528*(r[3][i] + r[-3][i])
+ 16735679449896*(r[4][i] + r[-4][i])
- 11541847896480*(r[5][i] + r[-5][i])
+ 7309837001104*(r[6][i] + r[-6][i])
- 4244421484512*(r[7][i] + r[-7][i])
+ 2254848913647*(r[8][i] + r[-8][i])
- 1093260079344*(r[9][i] + r[-9][i])
+ 482320623240*(r[10][i] + r[-10][i])
- 192928249296*(r[11][i] + r[-11][i])
+ 69668534468*(r[12][i] + r[-12][i])
- 22595200368*(r[13][i] + r[-13][i])
+ 6540715896*(r[14][i] + r[-14][i])
- 1677106640*(r[15][i] + r[-15][i])
+ 377348994*(r[16][i] + r[-16][i])
- 73629072*(r[17][i] + r[-17][i])
+ 12271512*(r[18][i] + r[-18][i])
- 1712304*(r[19][i] + r[-19][i])
+ 194580*(r[20][i] + r[-20][i])
- 17296*(r[21][i] + r[-21][i])
+ 1128*(r[22][i] + r[-22][i])
- 48*(r[23][i] + r[-23][i])
+ (r[24][i] + r[-24][i])
+ 32247603683100*r0[i]
- 60828186403426756087225216332129537688755283137921024000000000000*r50[i]
- 159972047422372025833793596431867471167657519124418501017600000000000*r52[i]
- 300157876302214652121781965684412846831829138854612706525184000000000000*r54[i]
- 450770518363896572159998540193680817546151655952668840885537996800000000000*r56[i]
) // 12413915592536072670862289047373375038521486354677760000000000 for i in range(len(r0))]
r46 = [(7890371113950*(r[1][i] + r[-1][i])
- 6943526580276*(r[2][i] + r[-2][i])
+ 5608233007146*(r[3][i] + r[-3][i])
- 4154246671960*(r[4][i] + r[-4][i])
+ 2818953098830*(r[5][i] + r[-5][i])
- 1749695026860*(r[6][i] + r[-6][i])
+ 991493848554*(r[7][i] + r[-7][i])
- 511738760544*(r[8][i] + r[-8][i])
+ 239877544005*(r[9][i] + r[-9][i])
- 101766230790*(r[10][i] + r[-10][i])
+ 38910617655*(r[11][i] + r[-11][i])
- 13340783196*(r[12][i] + r[-12][i])
+ 4076350421*(r[13][i] + r[-13][i])
- 1101716330*(r[14][i] + r[-14][i])
+ 260932815*(r[15][i] + r[-15][i])
- 53524680*(r[16][i] + r[-16][i])
+ 9366819*(r[17][i] + r[-17][i])
- 1370754*(r[18][i] + r[-18][i])
+ 163185*(r[19][i] + r[-19][i])
- 15180*(r[20][i] + r[-20][i])
+ 1035*(r[21][i] + r[-21][i])
- 46*(r[22][i] + r[-22][i])
+ (r[23][i] + r[-23][i])
- 8233430727600*r0[i]
- 23793338219027472619152720674132302157166182179799040000000000*r48[i]
- 55378994704786442521077957369042933270804289023482265600000000000*r50[i]
- 92204777033212927855282293501621091950025889999533532774400000000000*r52[i]
- 123173573410381619032735872322455238373678223392026561137868800000000000*r54[i]
- 140425979426347767846982627377843865753483703589611376414503731200000000000*r56[i]
) // 5502622159812088949850305428800254892961651752960000000000 for i in range(len(r0))]
r44 = [(-2012616400080*(r[1][i] + r[-1][i])
+ 1761039350070*(r[2][i] + r[-2][i])
- 1408831480056*(r[3][i] + r[-3][i])
+ 1029530696964*(r[4][i] + r[-4][i])
- 686353797976*(r[5][i] + r[-5][i])
+ 416714805914*(r[6][i] + r[-6][i])
- 229911617056*(r[7][i] + r[-7][i])
+ 114955808528*(r[8][i] + r[-8][i])
- 51915526432*(r[9][i] + r[-9][i])
+ 21090682613*(r[10][i] + r[-10][i])
- 7669339132*(r[11][i] + r[-11][i])
+ 2481256778*(r[12][i] + r[-12][i])
- 708930508*(r[13][i] + r[-13][i])
+ 177232627*(r[14][i] + r[-14][i])
- 38320568*(r[15][i] + r[-15][i])
+ 7059052*(r[16][i] + r[-16][i])
- 1086008*(r[17][i] + r[-17][i])
+ 135751*(r[18][i] + r[-18][i])
- 13244*(r[19][i] + r[-19][i])
+ 946*(r[20][i] + r[-20][i])
- 44*(r[21][i] + r[-21][i])
+ (r[22][i] + r[-22][i])
+ 2104098963720*r0[i]
- 10088140626322163074725559952800467303763028213760000000000*r46[i]
- 20672617771459376572727617455278717598871197415636992000000000*r48[i]
- 30390960789555990223010654132076029106169285558507929600000000000*r50[i]
- 35940698724546850336855815971061681513098805595301121884160000000000*r52[i]
- 36360946421379657670852826531045915291694648992864408489164800000000000*r54[i]
- 32688930664232620503520635595276360398494773528483108565098168320000000000*r56[i]
) // 2658271574788448768043625811014615890319638528000000000 for i in range(len(r0))]
r42 = [(513791607420*(r[1][i] + r[-1][i])
- 446775310800*(r[2][i] + r[-2][i])
+ 353697121050*(r[3][i] + r[-3][i])
- 254661927156*(r[4][i] + r[-4][i])
+ 166509721602*(r[5][i] + r[-5][i])
- 98672427616*(r[6][i] + r[-6][i])
+ 52860229080*(r[7][i] + r[-7][i])
- 25518731280*(r[8][i] + r[-8][i])
+ 11058116888*(r[9][i] + r[-9][i])
- 4280561376*(r[10][i] + r[-10][i])
+ 1471442973*(r[11][i] + r[-11][i])
- 445891810*(r[12][i] + r[-12][i])
+ 118030185*(r[13][i] + r[-13][i])
- 26978328*(r[14][i] + r[-14][i])
+ 5245786*(r[15][i] + r[-15][i])
- 850668*(r[16][i] + r[-16][i])
+ 111930*(r[17][i] + r[-17][i])
- 11480*(r[18][i] + r[-18][i])
+ 861*(r[19][i] + r[-19][i])
- 42*(r[20][i] + r[-20][i])
+ (r[21][i] + r[-21][i])
- 538257874440*r0[i]
- 4651975255879785344076345169275577808059367424000000000*r44[i]
- 8345643609048334907272963233680386587658505158656000000000*r46[i]
- 10774531600512501036897720551649645765494516918255616000000000*r48[i]
- 11221709145032637985686395016457126546359868596714209280000000000*r50[i]
- 10024126976056544454447469133748446849553291271003522990080000000000*r52[i]
- 7975810040319696718196547333113180442555266076076498338447360000000000*r54[i]
- 5797757744908652417934202553325977005487481966701902535023656960000000000*r56[i]
) // 1405006117752879898543142606244511569936384000000000 for i in range(len(r0))]
r40 = [(-131282408400*(r[1][i] + r[-1][i])
+ 113380261800*(r[2][i] + r[-2][i])
- 88732378800*(r[3][i] + r[-3][i])
+ 62852101650*(r[4][i] + r[-4][i])
- 40225345056*(r[5][i] + r[-5][i])
+ 23206929840*(r[6][i] + r[-6][i])
- 12033222880*(r[7][i] + r[-7][i])
+ 5586853480*(r[8][i] + r[-8][i])
- 2311801440*(r[9][i] + r[-9][i])
+ 847660528*(r[10][i] + r[-10][i])
- 273438880*(r[11][i] + r[-11][i])
+ 76904685*(r[12][i] + r[-12][i])
- 18643560*(r[13][i] + r[-13][i])
+ 3838380*(r[14][i] + r[-14][i])
- 658008*(r[15][i] + r[-15][i])
+ 91390*(r[16][i] + r[-16][i])
- 9880*(r[17][i] + r[-17][i])
+ 780*(r[18][i] + r[-18][i])
- 40*(r[19][i] + r[-19][i])
+ (r[20][i] + r[-20][i])
+ 137846528820*r0[i]
- 2341676862921466497571904343740852616560640000000000*r42[i]
- 3655123415334117056059985490145096849189502976000000000*r44[i]
- 4119688019118574531237133429498603530973935042560000000000*r46[i]
- 3757340713824985498498548346794211825654347639816192000000000*r48[i]
- 2947359606908914693821004025256012800585708025466060800000000000*r50[i]
- 2064558678210662377343329526788684890767865636215995760640000000000*r52[i]
- 1324288918192605206277308466563916626202444615070944696729600000000000*r54[i]
- 791839032295490808003964360962043366439210005332609063463157760000000000*r56[i]
) // 815915283247897734345611269596115894272000000000 for i in range(len(r0))]
r38 = [(33578000610*(r[1][i] + r[-1][i])
- 28781143380*(r[2][i] + r[-2][i])
+ 22239974430*(r[3][i] + r[-3][i])
- 15471286560*(r[4][i] + r[-4][i])
+ 9669554100*(r[5][i] + r[-5][i])
- 5414950296*(r[6][i] + r[-6][i])
+ 2707475148*(r[7][i] + r[-7][i])
- 1203322288*(r[8][i] + r[-8][i])
+ 472733756*(r[9][i] + r[-9][i])
- 163011640*(r[10][i] + r[-10][i])
+ 48903492*(r[11][i] + r[-11][i])
- 12620256*(r[12][i] + r[-12][i])
+ 2760681*(r[13][i] + r[-13][i])
- 501942*(r[14][i] + r[-14][i])
+ 73815*(r[15][i] + r[-15][i])
- 8436*(r[16][i] + r[-16][i])
+ 703*(r[17][i] + r[-17][i])
- 38*(r[18][i] + r[-18][i])
+ (r[19][i] + r[-19][i])
- 35345263800*r0[i]
- 1291865865142504746047217843527183499264000000000*r40[i]
- 1742597865490724651943092149133817822157209600000000*r42[i]
- 1703614521144184428726371303487541532883419136000000000*r44[i]
- 1352221478318945952566471137817160521323572835123200000000*r46[i]
- 925912385499308009244605568293800045079467288166400000000000*r48[i]
- 567701817594292628086492254286076775983065657711263744000000000*r50[i]
- 319529132633551445730754266569514531984165615759324610560000000000*r52[i]
- 168027862191313285572462163036203023050148820066814862032896000000000*r54[i]
- 83628709120699850967965029603710197511722226913937392643604480000000000*r56[i]
) // 523022617466601111760007224100074291200000000 for i in range(len(r0))]
r36 = [(-8597496600*(r[1][i] + r[-1][i])
+ 7307872110*(r[2][i] + r[-2][i])
- 5567902560*(r[3][i] + r[-3][i])
+ 3796297200*(r[4][i] + r[-4][i])
- 2310789600*(r[5][i] + r[-5][i])
+ 1251677700*(r[6][i] + r[-6][i])
- 600805296*(r[7][i] + r[-7][i])
+ 254186856*(r[8][i] + r[-8][i])
- 94143280*(r[9][i] + r[-9][i])
+ 30260340*(r[10][i] + r[-10][i])
- 8347680*(r[11][i] + r[-11][i])
+ 1947792*(r[12][i] + r[-12][i])
- 376992*(r[13][i] + r[-13][i])
+ 58905*(r[14][i] + r[-14][i])
- 7140*(r[15][i] + r[-15][i])
+ 630*(r[16][i] + r[-16][i])
- 36*(r[17][i] + r[-17][i])
+ (r[18][i] + r[-18][i])
+ 9075135300*r0[i]
- 784533926199901667640010836150111436800000000*r38[i]
- 907705752613286229459492537425678932377600000000*r40[i]
- 764250847583238143225401875995898505750118400000000*r42[i]
- 524336156604477506256224109002957345627779891200000000*r44[i]
- 311351658482338919180732210200430367625645444300800000000*r46[i]
- 166036590632320367531429334375544068072103816986624000000000*r48[i]
- 81499841025612949496109930847966440863640763389444096000000000*r50[i]
- 37466461814083366759359795735852259604455926584422957056000000000*r52[i]
- 16337589523211774449719906648393247646243600903141698043904000000000*r54[i]
- 6822946329749604115483663195879851339401939967806211954730598400000000*r56[i]
) // 371993326789901217467999448150835200000000 for i in range(len(r0))]
r34 = [(2203961430*(r[1][i] + r[-1][i])
- 1855967520*(r[2][i] + r[-2][i])
+ 1391975640*(r[3][i] + r[-3][i])
- 927983760*(r[4][i] + r[-4][i])
+ 548354040*(r[5][i] + r[-5][i])
- 286097760*(r[6][i] + r[-6][i])
+ 131128140*(r[7][i] + r[-7][i])
- 52451256*(r[8][i] + r[-8][i])
+ 18156204*(r[9][i] + r[-9][i])
- 5379616*(r[10][i] + r[-10][i])
+ 1344904*(r[11][i] + r[-11][i])
- 278256*(r[12][i] + r[-12][i])
+ 46376*(r[13][i] + r[-13][i])
- 5984*(r[14][i] + r[-14][i])
+ 561*(r[15][i] + r[-15][i])
- 34*(r[16][i] + r[-16][i])
+ (r[17][i] + r[-17][i])
- 2333606220*r0[i]
- 526990546285693391412999218213683200000000*r36[i]
- 518664095654379435828673830565907005440000000*r38[i]
- 373138241060740797524227217357125818777600000000*r40[i]
- 219618160307546307818407858079592245845032960000000*r42[i]
- 112275193446419212026758411812279514001781555200000000*r44[i]
- 51713216892097268029263570056035419810630708756480000000*r46[i]
- 21987290206937420965021290881182668895459624353792000000000*r48[i]
- 8778185176019659621127125508818359337012951782732595200000000*r50[i]
- 3332107853530764777529629230140567884444349753800523776000000000*r52[i]
- 1213942320816658090297153525238443731761121646974842689290240000000*r54[i]
- 427555403157842297318164509581599203745468728634937321088614400000000*r56[i]
) // 295232799039604140847618609643520000000 for i in range(len(r0))]
r32 = [(-565722720*(r[1][i] + r[-1][i])
+ 471435600*(r[2][i] + r[-2][i])
- 347373600*(r[3][i] + r[-3][i])
+ 225792840*(r[4][i] + r[-4][i])
- 129024480*(r[5][i] + r[-5][i])
+ 64512240*(r[6][i] + r[-6][i])
- 28048800*(r[7][i] + r[-7][i])
+ 10518300*(r[8][i] + r[-8][i])
- 3365856*(r[9][i] + r[-9][i])
+ 906192*(r[10][i] + r[-10][i])
- 201376*(r[11][i] + r[-11][i])
+ 35960*(r[12][i] + r[-12][i])
- 4960*(r[13][i] + r[-13][i])
+ 496*(r[14][i] + r[-14][i])
- 32*(r[15][i] + r[-15][i])
+ (r[16][i] + r[-16][i])
+ 601080390*r0[i]
- 393643732052805521130158146191360000000*r34[i]
- 326527475737802179777466182265733120000000*r36[i]
- 198969979872214920293886346099446251520000000*r38[i]
- 99626745669333527035567016277524852244480000000*r40[i]
- 43498703313314018776504938348732045412270080000000*r42[i]
- 17170843124850370546818528558187736420780605440000000*r44[i]
- 6276444318289938061108840583768656479667869450240000000*r46[i]
- 2160301520690503531404610021529918026938609932697600000000*r48[i]
- 708745398984922590930383206855670263857046959528345600000000*r50[i]
- 223674822768508974680116468563119084809897119542327377920000000*r52[i]
- 68383308771682806793482300167280717706332061193589825208320000000*r54[i]
- 20364863681337349385077959469519750111717035219658278269091840000000*r56[i]
) // 263130836933693530167218012160000000 for i in range(len(r0))]
r30 = [(145422675*(r[1][i] + r[-1][i])
- 119759850*(r[2][i] + r[-2][i])
+ 86493225*(r[3][i] + r[-3][i])
- 54627300*(r[4][i] + r[-4][i])
+ 30045015*(r[5][i] + r[-5][i])
- 14307150*(r[6][i] + r[-6][i])
+ 5852925*(r[7][i] + r[-7][i])
- 2035800*(r[8][i] + r[-8][i])
+ 593775*(r[9][i] + r[-9][i])
- 142506*(r[10][i] + r[-10][i])
+ 27405*(r[11][i] + r[-11][i])
- 4060*(r[12][i] + r[-12][i])
+ 435*(r[13][i] + r[-13][i])
- 30*(r[14][i] + r[-14][i])
+ (r[15][i] + r[-15][i])
- 155117520*r0[i]
- 328913546167116912709022515200000000*r32[i]
- 227575282593028191903372678266880000000*r34[i]
- 116309421454977381321426414757478400000000*r36[i]
- 49083095586740430887431564189583278080000000*r38[i]
- 18139371393109511951007844941215406489600000000*r40[i]
- 6083845843389094496001274537210012898426880000000*r42[i]
- 1895875482185729033390420637976407213657292800000000*r44[i]
- 557995741137378415081398016214860854983503380480000000*r46[i]
- 156963921056606539204438549741946823549156065280000000000*r48[i]
- 42576613536662088106792709282326106111384171273256960000000*r50[i]
- 11212252160226319834044842958792572575603224385840742400000000*r52[i]
- 2881790963494506901155736518846659656145189066632341749760000000*r54[i]
- 725935006313040765947950598972668773212258467667822562508800000000*r56[i]
) // 265252859812191058636308480000000 for i in range(len(r0))]
r28 = [(-37442160*(r[1][i] + r[-1][i])
+ 30421755*(r[2][i] + r[-2][i])
- 21474180*(r[3][i] + r[-3][i])
+ 13123110*(r[4][i] + r[-4][i])
- 6906900*(r[5][i] + r[-5][i])
+ 3108105*(r[6][i] + r[-6][i])
- 1184040*(r[7][i] + r[-7][i])
+ 376740*(r[8][i] + r[-8][i])
- 98280*(r[9][i] + r[-9][i])
+ 20475*(r[10][i] + r[-10][i])
- 3276*(r[11][i] + r[-11][i])
+ 378*(r[12][i] + r[-12][i])
- 28*(r[13][i] + r[-13][i])
+ (r[14][i] + r[-14][i])
+ 40116600*r0[i]
- 309461669780889568409026560000000*r30[i]
- 176516936443019409820508749824000000*r32[i]
- 74833313645455216256514439249920000000*r34[i]
- 26337328459046574816219104447299584000000*r36[i]
- 8155948144934385059006601147769159680000000*r38[i]
- 2301709517171786559798286695904076365824000000*r40[i]
- 605758813130095139988659617361096909783040000000*r42[i]
- 151061790397229175366153301919734749322543104000000*r44[i]
- 36109056667467121621981604705290955376859545600000000*r46[i]
- 8344518734397260673326477690101230819337996075008000000*r48[i]
- 1876453005146379321858026862378389310967569941790720000000*r50[i]
- 412683020050097630454766497837161869694785723928936448000000*r52[i]
- 89117286812387026652769979577207299516771181236259389440000000*r54[i]
- 18956016131243809886574217941379995847584738002099836551168000000*r56[i]
) // 304888344611713860501504000000 for i in range(len(r0))]
r26 = [(9657700*(r[1][i] + r[-1][i])
- 7726160*(r[2][i] + r[-2][i])
+ 5311735*(r[3][i] + r[-3][i])
- 3124550*(r[4][i] + r[-4][i])
+ 1562275*(r[5][i] + r[-5][i])
- 657800*(r[6][i] + r[-6][i])
+ 230230*(r[7][i] + r[-7][i])
- 65780*(r[8][i] + r[-8][i])
+ 14950*(r[9][i] + r[-9][i])
- 2600*(r[10][i] + r[-10][i])
+ 325*(r[11][i] + r[-11][i])
- 26*(r[12][i] + r[-12][i])
+ (r[13][i] + r[-13][i])
- 10400600*r0[i]
- 330295706662690015543296000000*r28[i]
- 153257207891488167212089344000000*r30[i]
- 53222214421459539592188788736000000*r32[i]
- 15436506593303376230082373484544000000*r34[i]
- 3960094929842931739454572322881536000000*r36[i]
- 930084233815670751630942950980583424000000*r38[i]
- 204528766884160018873274371645367648256000000*r40[i]
- 42768601883241439058698435075343591276544000000*r42[i]
- 8599134589431485780708409429924529774657536000000*r44[i]
- 1676115909489027560076829587121962388192493568000000*r46[i]
- 318686948683222526304282057035116495208098824192000000*r48[i]
- 59389194499215983294435493136240165006801607589888000000*r50[i]
- 10888114924031601962481145504131710392319020299190272000000*r52[i]
- 1969613645523746908242462889216091458065590581736767488000000*r54[i]
- 352384153836182163735889010772845616197776947067902492672000000*r56[i]
) // 403291461126605635584000000 for i in range(len(r0))]
r24 = [(-2496144*(r[1][i] + r[-1][i])
+ 1961256*(r[2][i] + r[-2][i])
- 1307504*(r[3][i] + r[-3][i])
+ 735471*(r[4][i] + r[-4][i])
- 346104*(r[5][i] + r[-5][i])
+ 134596*(r[6][i] + r[-6][i])
- 42504*(r[7][i] + r[-7][i])
+ 10626*(r[8][i] + r[-8][i])
- 2024*(r[9][i] + r[-9][i])
+ 276*(r[10][i] + r[-10][i])
- 24*(r[11][i] + r[-11][i])
+ (r[12][i] + r[-12][i])
+ 2704156*r0[i]
- 403291461126605635584000000*r26[i]
- 149903436100759314746572800000*r28[i]
- 42033455827381598974377984000000*r30[i]
- 9910695932425713906157643366400000*r32[i]
- 2078962023961017163954848006144000000*r34[i]
- 401274139495715827174031120636313600000*r36[i]
- 72837740568171787457915404507152384000000*r38[i]
- 12620369661259070567869332718886859571200000*r40[i]
- 2109601340251819353520575234140712075264000000*r42[i]
- 342864867500163789441705220714949009654415360000*r44[i]
- 54497476891656721001996702786930540928565248000000*r46[i]
- 8509384879617502075402808457393042025589086617600000*r48[i]
- 1309755467175539670340841790934034624876228640768000000*r50[i]
- 199264959019086425512537383104357541174886386420940800000*r52[i]
- 30029919604106055758327357685117168899526367314444288000000*r54[i]
- 4490619485039820937253033342517920576264823432892789555200000*r56[i]
) // 620448401733239439360000 for i in range(len(r0))]
r22 = [(646646*(r[1][i] + r[-1][i])
- 497420*(r[2][i] + r[-2][i])
+ 319770*(r[3][i] + r[-3][i])
- 170544*(r[4][i] + r[-4][i])
+ 74613*(r[5][i] + r[-5][i])
- 26334*(r[6][i] + r[-6][i])
+ 7315*(r[7][i] + r[-7][i])
- 1540*(r[8][i] + r[-8][i])
+ 231*(r[9][i] + r[-9][i])
- 22*(r[10][i] + r[-10][i])
+ (r[11][i] + r[-11][i])
- 705432*r0[i]
- 568744368255469486080000*r24[i]
- 166357727714724824678400000*r26[i]
- 37042320704478727628390400000*r28[i]
- 6988909951599209517839155200000*r30[i]
- 1180836611760352104108962611200000*r32[i]
- 184607985589364774573429361868800000*r34[i]
- 27272218262298384682708194086092800000*r36[i]
- 3861838803337560097698395778726297600000*r38[i]
- 529471212011799260411940801849645465600000*r40[i]
- 70801221927358337925257947461388534087680000*r42[i]
- 9284304296436839352157882253583122352046080000*r44[i]
- 1198819215976330165063918942164935021513932800000*r46[i]
- 152905877736629296164560458459124226796014796800000*r48[i]
- 19311905336609987288869864510609701436067866214400000*r50[i]
- 2419865045937700153119519054510295236128129836646400000*r52[i]
- 301288155885052369662851151922188867269975615240601600000*r54[i]
- 37318400520598852767385734888888777428502118384425369600000*r56[i]
) // 1124000727777607680000 for i in range(len(r0))]
r20 = [(-167960*(r[1][i] + r[-1][i])
+ 125970*(r[2][i] + r[-2][i])
- 77520*(r[3][i] + r[-3][i])
+ 38760*(r[4][i] + r[-4][i])
- 15504*(r[5][i] + r[-5][i])
+ 4845*(r[6][i] + r[-6][i])
- 1140*(r[7][i] + r[-7][i])
+ 190*(r[8][i] + r[-8][i])
- 20*(r[9][i] + r[-9][i])
+ (r[10][i] + r[-10][i])
+ 184756*r0[i]
- 936667273148006400000*r22[i]
- 211124803367560642560000*r24[i]
- 36608302274885332992000000*r26[i]
- 5425950533240873322086400000*r28[i]
- 725494605231272191451136000000*r30[i]
- 90317652741043657957240012800000*r32[i]
- 10681064948020015063470219264000000*r34[i]
- 1216234618180639720975550420582400000*r36[i]
- 134607612138429628983625351999488000000*r38[i]
- 14578366393789236829898507440652451840000*r40[i]
- 1552719574083291045891061928041363046400000*r42[i]
- 163243281617906068079686557318998305013760000*r44[i]
- 16988641998903346735554689301227465785344000000*r46[i]
- 1753883399302689292116989257696255397727436800000*r48[i]
- 179923160623142188671570235338790827627528192000000*r50[i]
- 18364686854092318474868714992301176836519274905600000*r52[i]
- 1866955970795489260131483779878624434707941429248000000*r54[i]
- 189185983025084665229695853342846566523110910688460800000*r56[i]
) // 2432902008176640000 for i in range(len(r0))]
r18 = [(43758*(r[1][i] + r[-1][i])
- 31824*(r[2][i] + r[-2][i])
+ 18564*(r[3][i] + r[-3][i])
- 8568*(r[4][i] + r[-4][i])
+ 3060*(r[5][i] + r[-5][i])
- 816*(r[6][i] + r[-6][i])
+ 153*(r[7][i] + r[-7][i])
- 18*(r[8][i] + r[-8][i])
+ (r[9][i] + r[-9][i])
- 48620*r0[i]
- 1824676506132480000*r20[i]
- 309100200138842112000*r22[i]
- 40778478784550707200000*r24[i]
- 4645053436190368481280000*r26[i]
- 481314610282065419059200000*r28[i]
- 46758400573464312663490560000*r30[i]
- 4340262299778024388805836800000*r32[i]
- 389810850996416354285601300480000*r34[i]
- 34168816632541202331763973529600000*r36[i]
- 2941066263016510346147295370272768000*r38[i]
- 249691933432545691845292589410836480000*r40[i]
- 20977168972570956554158853986478948352000*r42[i]
- 1748194308191420862068509392967461273600000*r44[i]
- 144787366874617417267158756772391629455360000*r46[i]
- 11933738665455945947029762024119178565222400000*r48[i]
- 979923136258156862399188048479194930964357120000*r50[i]
- 80229698384887928012137580653965134357931417600000*r52[i]
- 6553647225094050569861777249958218558728336220160000*r54[i]
- 534380975174725194355250529012449631615490426675200000*r56[i]
) // 6402373705728000 for i in range(len(r0))]
r16 = [(-11440*(r[1][i] + r[-1][i])
+ 8008*(r[2][i] + r[-2][i])
- 4368*(r[3][i] + r[-3][i])
+ 1820*(r[4][i] + r[-4][i])
- 560*(r[5][i] + r[-5][i])
+ 120*(r[6][i] + r[-6][i])
- 16*(r[7][i] + r[-7][i])
+ (r[8][i] + r[-8][i])
+ 12870*r0[i]
- 4268249137152000*r18[i]
- 527128768438272000*r20[i]
- 51442361350668288000*r22[i]
- 4385609982489415680000*r24[i]
- 343350594609952849920000*r26[i]
- 25398422028160175554560000*r28[i]
- 1806640043553643996938240000*r30[i]
- 124998708216981630040289280000*r32[i]
- 8477574188991756975915909120000*r34[i]
- 566640901244029272138606256128000*r36[i]
- 37469170353622071265887792218112000*r38[i]
- 2457916223969789263693314523533312000*r40[i]
- 160273272592069873142621634191720448000*r42[i]
- 10404012781412834769965673013161000960000*r44[i]
- 673078263437696563365695181553779671040000*r46[i]
- 43432367177206668920840929822030938501120000*r48[i]
- 2797138392082425352298525252125310293524480000*r50[i]
- 179874692542903270845206591460923776914677760000*r52[i]
- 11554084778127771883812326032137020779396055040000*r54[i]
- 741527083798558882116336447949129492912812576768000*r56[i]
) // 20922789888000 for i in range(len(r0))]
r14 = [(3003*(r[1][i] + r[-1][i])
- 2002*(r[2][i] + r[-2][i])
+ 1001*(r[3][i] + r[-3][i])
- 364*(r[4][i] + r[-4][i])
+ 91*(r[5][i] + r[-5][i])
- 14*(r[6][i] + r[-6][i])
+ (r[7][i] + r[-7][i])
- 3432*r0[i]
- 12204960768000*r16[i]
- 1058170098585600*r18[i]
- 73775500710912000*r20[i]
- 4555411900194355200*r22[i]
- 261131482210959360000*r24[i]
- 14266599888013304832000*r26[i]
- 754754307297469839360000*r28[i]
- 39057272623118392651008000*r30[i]
- 1990236929603886055572480000*r32[i]
- 100317304785653440333283635200*r34[i]
- 5017302808350824370904132608000*r36[i]
- 249538838908236261152065923225600*r38[i]
- 12360976075014001109372936189952000*r40[i]
- 610513898001512036824535103712051200*r42[i]
- 30089355946979742032883786297815040000*r44[i]
- 1480659654975370272651825844120998144000*r46[i]
- 72778719754993922352940597980542622720000*r48[i]
- 3574314373450201242087397187099658871296000*r50[i]
- 175435230758177290496267410991246070236160000*r52[i]
- 8606908326589506468114924551500679297771059200*r54[i]
- 422119567380929805536926019476679626483150848000*r56[i]
) // 87178291200 for i in range(len(r0))]
r12 = [(-792*(r[1][i] + r[-1][i])
+ 495*(r[2][i] + r[-2][i])
- 220*(r[3][i] + r[-3][i])
+ 66*(r[4][i] + r[-4][i])
- 12*(r[5][i] + r[-5][i])
+ (r[6][i] + r[-6][i])
+ 924*r0[i]
- 43589145600*r14[i]
- 2528170444800*r16[i]
- 120467944396800*r18[i]
- 5167100908569600*r20[i]
- 208331313744153600*r22[i]
- 8083281646573056000*r24[i]
- 305994026290208256000*r26[i]
- 11397316294188849024000*r28[i]
- 419948192698268217984000*r30[i]
- 15360962830016613243033600*r32[i]
- 559092713482449420732057600*r34[i]
- 20280226917834433943755084800*r36[i]
- 733917409397935785284098636800*r38[i]
- 26516869922120782776160606617600*r40[i]
- 957005191789297958689924263321600*r42[i]
- 34512162491005016706155579824512000*r44[i]
- 1243937698905379082423800102273152000*r46[i]
- 44819260744500257106087286005881088000*r48[i]
- 1614431094051811175741477051443876608000*r50[i]
- 58142963949556229658359411701218990105600*r52[i]
- 2093732846395541754366573918386488419609600*r54[i]
- 75389036557436264384158719712164829058764800*r56[i]
) // 479001600 for i in range(len(r0))]
r10 = [(210*(r[1][i] + r[-1][i])
- 120*(r[2][i] + r[-2][i])
+ 45*(r[3][i] + r[-3][i])
- 10*(r[4][i] + r[-4][i])
+ (r[5][i] + r[-5][i])
- 252*r0[i]
- 199584000*r12[i]
- 7264857600*r14[i]
- 223134912000*r16[i]
- 6289809926400*r18[i]
- 169058189664000*r20[i]
- 4419351149875200*r22[i]
- 113605204648320000*r24[i]
- 2890388998040544000*r26[i]
- 73066712935376160000*r28[i]
- 1839605249083010572800*r30[i]
- 46197360620085939264000*r32[i]
- 1158251761107990889401600*r34[i]
- 29009396635576994764512000*r36[i]
- 726084725720412923735270400*r38[i]
- 18165716613255899607139584000*r40[i]
- 454360504471895403926563219200*r42[i]
- 11362494160594553046963852960000*r44[i]
- 284118059898561657806684273088000*r46[i]
- 7103842801529696381323903273920000*r48[i]
- 177610330992631300501801888177516800*r50[i]
- 4440486450890050497235584413672544000*r52[i]
- 111015812096675961833777653418529945600*r54[i]
- 2775453715672821941461677186080579712000*r56[i]
) // 3628800 for i in range(len(r0))]
r8 = [(-56*(r[1][i] + r[-1][i])
+ 28*(r[2][i] + r[-2][i])
- 8*(r[3][i] + r[-3][i])
+ (r[4][i] + r[-4][i])
+ 70*r0[i]
- 1209600*r10[i]
- 25280640*r12[i]
- 461260800*r14[i]
- 7904856960*r16[i]
- 131254905600*r18[i]
- 2143293425280*r20[i]
- 34682510016000*r22[i]
- 558432020361600*r24[i]
- 8966533159584000*r26[i]
- 143749174428961920*r28[i]
- 2302548811229721600*r30[i]
- 36863840064915642240*r32[i]
- 590028976413583660800*r34[i]
- 9442331455422829138560*r36[i]
- 151094113839739041753600*r38[i]
- 2417657116643486089706880*r40[i]
- 38683875524088319997472000*r42[i]
- 618954263309240362088323200*r44[i]
- 9903378507277068408849408000*r46[i]
- 158455048765455207825625883520*r48[i]
- 2535289714088718783746769273600*r50[i]
- 40564715829993365422700852403840*r52[i]
- 649036176921062413731673525900800*r54[i]
- 10384585343507530854517663366220160*r56[i]
) // 40320 for i in range(len(r0))]
r6 = [(15*(r[1][i] + r[-1][i])
- 6*(r[2][i] + r[-2][i])
+ (r[3][i] + r[-3][i])
- 20*r0[i]
- 10080*r8[i]
- 105840*r10[i]
- 1013760*r12[i]
- 9369360*r14[i]
- 85307040*r16[i]
- 771695280*r18[i]
- 6960985920*r20[i]
- 62711787600*r22[i]
- 564657746400*r24[i]
- 5082926350320*r26[i]
- 45750363684480*r28[i]
- 411769379287440*r30[i]
- 3705988838096160*r32[i]
- 33354157240902960*r34[i]
- 300188445960277440*r36[i]
- 2701700136811100880*r38[i]
- 24315317723974324320*r40[i]
- 218837925486466585200*r42[i]
- 1969541593260989932800*r44[i]
- 17725875394880072059920*r46[i]
- 159532882776045299198880*r48[i]
- 1435795961872906295429040*r50[i]
- 12922163724410151069418560*r52[i]
- 116299473789907337266996560*r54[i]
- 1046695265190029945971887840*r56[i]
) // 720 for i in range(len(r0))]
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
- 504*r8[i]
- 2040*r10[i]
- 8184*r12[i]
- 32760*r14[i]
- 131064*r16[i]
- 524280*r18[i]
- 2097144*r20[i]
- 8388600*r22[i]
- 33554424*r24[i]
- 134217720*r26[i]
- 536870904*r28[i]
- 2147483640*r30[i]
- 8589934584*r32[i]
- 34359738360*r34[i]
- 137438953464*r36[i]
- 549755813880*r38[i]
- 2199023255544*r40[i]
- 8796093022200*r42[i]
- 35184372088824*r44[i]
- 140737488355320*r46[i]
- 562949953421304*r48[i]
- 2251799813685240*r50[i]
- 9007199254740984*r52[i]
- 36028797018963960*r54[i]
- 144115188075855864*r56[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
- 2*r8[i]
- 2*r10[i]
- 2*r12[i]
- 2*r14[i]
- 2*r16[i]
- 2*r18[i]
- 2*r20[i]
- 2*r22[i]
- 2*r24[i]
- 2*r26[i]
- 2*r28[i]
- 2*r30[i]
- 2*r32[i]
- 2*r34[i]
- 2*r36[i]
- 2*r38[i]
- 2*r40[i]
- 2*r42[i]
- 2*r44[i]
- 2*r46[i]
- 2*r48[i]
- 2*r50[i]
- 2*r52[i]
- 2*r54[i]
- 2*r56[i]
) // 2 for i in range(len(r0))]
r55 = [(-263747951750360*r[1][i]
+ 474746313150648*r[2][i]
- 597261490737912*r[3][i]
+ 622147386185325*r[4][i]
- 565588532895750*r[5][i]
+ 459124809056550*r[6][i]
- 336691526641470*r[7][i]
+ 224461017760980*r[8][i]
- 136496564854650*r[9][i]
+ 75831424919250*r[10][i]
- 38499031112850*r[11][i]
+ 17849550788685*r[12][i]
- 7546151552940*r[13][i]
+ 2902365981900*r[14][i]
- 1012453249500*r[15][i]
+ 319076175600*r[16][i]
- 90404916420*r[17][i]
+ 22890247380*r[18][i]
- 5140835700*r[19][i]
+ 1014638625*r[20][i]
- 173938050*r[21][i]
+ 25510914*r[22][i]
- 3137706*r[23][i]
+ 314820*r[24][i]
- 24750*r[25][i]
+ 1430*r[26][i]
- 54*r[27][i]
+ r[28][i]
+ 69533550916004*r0[i]
- 36734706144304*r2[i]
+ 79952007490544*r4[i]
- 382032124043344*r6[i]
+ 3243616097529584*r8[i]
- 43648837265746384*r10[i]
+ 865791864558368624*r12[i]
- 24079307603382105424*r14[i]
+ 905620045214743879664*r16[i]
- 44829468504848086112464*r18[i]
+ 2861056329269746545774704*r20[i]
- 231700008340575126045799504*r22[i]
+ 23520872059470599115258005744*r24[i]
- 2965504017281885370900598638544*r26[i]
+ 461273515398346724648458271164784*r28[i]
- 88130190568611671590209948525941584*r30[i]
+ 20636378464504372130162670555686883824*r32[i]
- 5922122648096407773524065141470107260624*r34[i]
+ 2087767422856024863904434586651201172234864*r36[i]
- 908798968501773051650655986384302515974787664*r38[i]
+ 492644736369466820787268958647730655685774129904*r40[i]
- 336933001130608366011659295551603463237580687754704*r42[i]
+ 296461508362831270729751372233986080685096927813720944*r44[i]
- 345657494345495491402030434838468872949594344235346833744*r46[i]
+ 559702758697443808822859784978939434710705864239596380799984*r48[i]
- 1365850676906400046308447846283281935329037260919461277968536784*r50[i]
+ 5961233014378374946505050098531606468256095554026807613974348199024*r52[i]
- 83514698066320941034057284688489207223027274274724707745745070739615824*r54[i]
- 1248498348142040711686005774772301632161825805512874614534923662110773809936*r56[i]
) // 12696403353658275925965100847566516959580321051449436762275840000000000000 for i in range(len(r0))]
r53 = [(69533550916004*r[1][i]
- 124680849918352*r[2][i]
+ 155851062397940*r[3][i]
- 160878516023680*r[4][i]
+ 144539291740025*r[5][i]
- 115631433392020*r[6][i]
+ 83322650532485*r[7][i]
- 54414792184480*r[8][i]
+ 32308782859535*r[9][i]
- 17464206951100*r[10][i]
+ 8594228157515*r[11][i]
- 3846367846720*r[12][i]
+ 1562586937730*r[13][i]
- 574609830760*r[14][i]
+ 190559382650*r[15][i]
- 56724653440*r[16][i]
+ 15067486070*r[17][i]
- 3545290840*r[18][i]
+ 732179630*r[19][i]
- 131185600*r[20][i]
+ 20087795*r[21][i]
- 2576860*r[22][i]
+ 269399*r[23][i]
- 22048*r[24][i]
+ 1325*r[25][i]
- 52*r[26][i]
+ r[27][i]
- 18367353072152*r0[i]
+ 9723892802904*r2[i]
- 21233806732872*r4[i]
+ 101938316952024*r6[i]
- 870923857821192*r8[i]
+ 11813629724209944*r10[i]
- 236653242227994312*r12[i]
+ 6661211180561048664*r14[i]
- 254153395270440164232*r16[i]
+ 12797090786892473420184*r18[i]
- 833255276258604854522952*r20[i]
+ 69082046666155386510156504*r22[i]
- 7207362865961897332411742472*r24[i]
+ 938124129611900624725430169624*r26[i]
- 151437248027244277344983580174792*r28[i]
+ 30212272010200647359221303097651544*r30[i]
- 7441428742177722398508955844151051912*r32[i]
+ 2266232854869901871497407965509685274264*r34[i]
- 857107282161918028603277004147759001685832*r36[i]
+ 405772096860221176189017929957247080205389784*r38[i]
- 243490395435781263807703083882634443533746668552*r40[i]
+ 188759926346541491475721299645267069314262689230104*r42[i]
- 194640847441735760152914313356873387274986644997072072*r44[i]
+ 279696375173169115852542641714578798351241693643134107224*r46[i]
- 607628834924308414958104349396219007455296518007846747648392*r48[i]
+ 2367696951203027805660226670039629463149515409625476517138613144*r50[i]
- 29693031902220062960308836352100332220249176157939974718889212029512*r52[i]
- 398324183453887237008520156086372422120866135515653348034430817054180136*r54[i]
- 29624941158535977160585235310988539572354082453382019111976960000000000000*r55[i]
- 1900101321417947769567987711973348241577208823166451595420036775627225927432*r56[i]
) // 4274883284060025564298013753389399649690343788366813724672000000000000 for i in range(len(r0))]
r51 = [(-18367353072152*r[1][i]
+ 32798844771700*r[2][i]
- 40715807302800*r[3][i]
+ 41620603020640*r[4][i]
- 36921502679600*r[5][i]
+ 29075683360185*r[6][i]
- 20558563992050*r[7][i]
+ 13129839188200*r[8][i]
- 7596549816030*r[9][i]
+ 3985844039275*r[10][i]
- 1895969056520*r[11][i]
+ 816446005200*r[12][i]
- 317506779800*r[13][i]
+ 111127372930*r[14][i]
- 34848305100*r[15][i]
+ 9735399520*r[16][i]
- 2405549300*r[17][i]
+ 520987950*r[18][i]
- 97765640*r[19][i]
+ 15660400*r[20][i]
- 2099160*r[21][i]
+ 229075*r[22][i]
- 19550*r[23][i]
+ 1224*r[24][i]
- 50*r[25][i]
+ r[26][i]
+ 4861946401452*r0[i]
- 2579808294648*r2[i]
+ 5653622432952*r4[i]
- 27280100477448*r6[i]
+ 234657881740152*r8[i]
- 3210736324810248*r10[i]
+ 65015030756447352*r12[i]
- 1854200415783543048*r14[i]
+ 71870433940146354552*r16[i]
- 3687349223477219875848*r18[i]
+ 245473564244803456261752*r20[i]
- 20888307287949627757008648*r22[i]
+ 2246840224563905580570968952*r24[i]
- 303094970433352624372214141448*r26[i]
+ 51019602983331540473045839276152*r28[i]
- 10691645514373727983810335922474248*r30[i]
+ 2790651091406916364299868206057983352*r32[i]
- 910446673933990019203515025763541207048*r34[i]
+ 373948949766422140435706410007606455890552*r36[i]
- 195681514530799165910557748483841641873539848*r38[i]
+ 132897106175336006092720191507876479916677797752*r40[i]
- 120554003537142419244816814513161495212294682672648*r42[i]
+ 152971535906456634616842226470152212508964788768504952*r44[i]
- 294458451533217960963210426417324728393814119257507805448*r46[i]
+ 1019832500675924760582251357311129578949356520774019156812152*r48[i]
- 11400247815546832449432199417474318613528727464280459760480138248*r50[i]
- 136675603482281861796246376772747198814333993503815350676473360480648*r52[i]
- 9618487389135057519670530945126149211803273523825330880512000000000000*r53[i]
- 584079459970995636352966806308556874401704430470079936394389227138871048*r54[i]
- 31846811745426175447629127959312680040280638637385670545375232000000000000*r55[i]
- 1597184531574749552837896774748024717998448145865885778866996941421634573448*r56[i]
) // 1551118753287382280224243016469303211063259720016986112000000000000 for i in range(len(r0))]
r49 = [(4861946401452*r[1][i]
- 8643460269248*r[2][i]
+ 10649977831752*r[3][i]
- 10772391370048*r[4][i]
+ 9425842448792*r[5][i]
- 7297426411968*r[6][i]
+ 5054988087457*r[7][i]
- 3151161405168*r[8][i]
+ 1772528290407*r[9][i]
- 900331830048*r[10][i]
+ 412652088772*r[11][i]
- 170333048928*r[12][i]
+ 63127818572*r[13][i]
- 20918093728*r[14][i]
+ 6163366902*r[15][i]
- 1603477568*r[16][i]
+ 365077482*r[17][i]
- 71916768*r[18][i]
+ 12076932*r[19][i]
- 1695008*r[20][i]
+ 193452*r[21][i]
- 17248*r[22][i]
+ 1127*r[23][i]
- 48*r[24][i]
+ r[25][i]
- 1289904147324*r0[i]
+ 686119227300*r2[i]
- 1509462300060*r4[i]
+ 7323923844900*r6[i]
- 63466456620060*r8[i]
+ 876655994638500*r10[i]
- 17962494591036060*r12[i]
+ 519729378435224100*r14[i]
- 20498730418437708060*r16[i]
+ 1073773191888393761700*r18[i]
- 73266053614681083996060*r20[i]
+ 6418563118124648605611300*r22[i]
- 714493710681785410524780060*r24[i]
+ 100357569802461927273985332900*r26[i]
- 17717998874943470330819342460060*r28[i]
+ 3928707238871982933864962858686500*r30[i]
- 1096834043813751169204010169826956060*r32[i]
+ 388004275037568389575404928401474632100*r34[i]
- 175870982185451189351017757509405335708060*r36[i]
+ 103991298038492644018924403718805266597329700*r38[i]
- 82506842083007670338625750577445488484693676060*r40[i]
+ 91947467567672513735818977678842895400970978139300*r42[i]
- 156026356786659861162429714318097107470538947633340060*r44[i]
+ 477994672122502000860149649242839645232774457016507620900*r46[i]
- 4741041014119120622582667190202604787803330381303410474700060*r48[i]
- 50576092532930275709972631359425317424152381858024219560152465500*r50[i]
- 3360757298789328273819193202350156957303729393370136576000000000000*r51[i]
- 192818334124303175599491864945168536471848882690784611504742445276060*r52[i]
- 9939103635439559436992881976630354185530049307952841909862400000000000*r53[i]
- 471508555542884903005212240660172655256037627791416369358584244657159900*r54[i]
- 20919675710958242602087867553930200860715908621346548813398016000000000000*r55[i]
- 878041943468001963173367991796909193943439396756549154859435350804240108060*r56[i]
) // 608281864034267560872252163321295376887552831379210240000000000 for i in range(len(r0))]
r47 = [(-1289904147324*r[1][i]
+ 2282138106804*r[2][i]
- 2789279908316*r[3][i]
+ 2789279908316*r[4][i]
- 2404551645100*r[5][i]
+ 1827459250276*r[6][i]
- 1237956266316*r[7][i]
+ 751616304549*r[8][i]
- 409972529754*r[9][i]
+ 200966926350*r[10][i]
- 88425447594*r[11][i]
+ 34834267234*r[12][i]
- 12239066866*r[13][i]
+ 3815417606*r[14][i]
- 1048191650*r[15][i]
+ 251565996*r[16][i]
- 52153926*r[17][i]
+ 9203634*r[18][i]
- 1355574*r[19][i]
+ 162150*r[20][i]
- 15134*r[21][i]
+ 1034*r[22][i]
- 46*r[23][i]
+ r[24][i]
+ 343059613650*r0[i]
- 182965127280*r2[i]
+ 404225281200*r4[i]
- 1973179787280*r6[i]
+ 17237751438000*r8[i]
- 240592045595280*r10[i]
+ 4994170279690800*r12[i]
- 146823806097131280*r14[i]
+ 5903690350090119600*r16[i]
- 316485671150054075280*r18[i]
+ 22198064042219526404400*r20[i]
- 2009394413056841321867280*r22[i]
+ 232532372014701449341825200*r24[i]
- 34201309524439700202831707280*r26[i]
+ 6378595465863797572545515262000*r28[i]
- 1510321457529226404281297600555280*r30[i]
+ 456430932151854961874111940707194800*r32[i]
- 177879954967657922123999080680411131280*r34[i]
+ 90948410673639301600046982211812755703600*r36[i]
- 62713181699432641518049958716708665011915280*r38[i]
+ 61017960828891287286335064536456771132612468400*r40[i]
- 90771056129445230547328475921502515772170837147280*r42[i]
+ 244690112718607318914399753695429565221879804118769200*r44[i]
- 2142766872532178730068138061640892672650431299718846827280*r46[i]
- 20243597746218463146623496754059816935278614102767681978514000*r48[i]
- 1267253883404724085150525340252698701849068398706688000000000000*r49[i]
- 68540933797288160408485956779561102500745596951326307091686715280*r50[i]
- 3332750987966083871537366592330572315992864981758718771200000000000*r51[i]
- 149233459487753154020208258958096224473270440522821423115697370901200*r52[i]
- 6253289089629471919203790951758600975663107059471098052608000000000000*r53[i]
- 248022574937797150848261199568155307996775458923007620752687158968331280*r54[i]
- 9391052465914511919999969587368350365544826165680600851782041600000000000*r55[i]
- 341691518826131979404309157169161042218932134256409704138253052086492312400*r56[i]
) // 258623241511168180642964355153611979969197632389120000000000 for i in range(len(r0))]
r45 = [(343059613650*r[1][i]
- 603784920024*r[2][i]
+ 731508653106*r[3][i]
- 722477682080*r[4][i]
+ 612815891050*r[5][i]
- 456442180920*r[6][i]
+ 301758997386*r[7][i]
- 177996090624*r[8][i]
+ 93865125915*r[9][i]
- 44246187300*r[10][i]
+ 18609425835*r[11][i]
- 6960408624*r[12][i]
+ 2304024151*r[13][i]
- 670609940*r[14][i]
+ 170173575*r[15][i]
- 37234560*r[16][i]
+ 6923301*r[17][i]
- 1072764*r[18][i]
+ 134805*r[19][i]
- 13200*r[20][i]
+ 945*r[21][i]
- 44*r[22][i]
+ r[23][i]
- 91482563640*r0[i]
+ 48932534040*r2[i]
- 108606356040*r4[i]
+ 533667580440*r6[i]
- 4703763586440*r8[i]
+ 66408505338840*r10[i]
- 1398457857168840*r12[i]
+ 41847457290489240*r14[i]
- 1719246675671583240*r16[i]
+ 94585481325000311640*r18[i]
- 6843422433568588589640*r20[i]
+ 642897110978465333366040*r22[i]
- 77770562351946223415228040*r24[i]
+ 12062233927817328810997492440*r26[i]
- 2397961353314881501418831818440*r28[i]
+ 613494954527608404597659277810840*r30[i]
- 203877970345571868715766678319960840*r32[i]
+ 89457569257636570186619080797284721240*r34[i]
- 53237495951641479759332571910597970535240*r36[i]
+ 44930968310714379648812137260536985281903640*r38[i]
- 58241166312158469946465066186170960196371701640*r40[i]
+ 137360888551881485527132727024151255460985294318040*r42[i]
- 1056294346650368430047563515157012073181421862576900040*r44[i]
- 8792490299555933486634712872596976297794618720689003795560*r46[i]
- 517246483022336361285928710307223959938395264778240000000000*r47[i]
- 26309260636200890673464765332665424581880256812272026952850440*r48[i]
- 1203891189234487880892999073240063766756614978771353600000000000*r49[i]
- 50764977622809978549916904649893168100296473949517793816320917160*r50[i]
- 2004451674635063649027875945687415042391867173902902886400000000000*r51[i]
- 74960269321392846499824811474695597918673304894478483366348507552840*r52[i]
- 2677686378486556935494258093966418225514743986783186111692800000000000*r53[i]
- 91966010944477715317164988999955404631262474522089414701528792100246760*r54[i]
- 3052738683181473214064839725605301429423558773687203835097907200000000000*r55[i]
- 98349663276138342734015395366406037072180666393105750993186894401098287240*r56[i]
) // 119622220865480194561963161495657715064383733760000000000 for i in range(len(r0))]
r43 = [(-91482563640*r[1][i]
+ 160094486370*r[2][i]
- 192113383644*r[3][i]
+ 187187399448*r[4][i]
- 155989499540*r[5][i]
+ 113649492522*r[6][i]
- 73153696336*r[7][i]
+ 41802112192*r[8][i]
- 21238169904*r[9][i]
+ 9586673915*r[10][i]
- 3834669566*r[11][i]
+ 1353412788*r[12][i]
- 418913482*r[13][i]
+ 112784399*r[14][i]
- 26127660*r[15][i]
+ 5133856*r[16][i]
- 839188*r[17][i]
+ 111069*r[18][i]
- 11438*r[19][i]
+ 860*r[20][i]
- 42*r[21][i]
+ r[22][i]
+ 24466267020*r0[i]
- 13128240840*r2[i]
+ 29286075720*r4[i]
- 144956522040*r6[i]
+ 1290252243720*r8[i]
- 18448766253240*r10[i]
+ 394763466531720*r12[i]
- 12048763425424440*r14[i]
+ 507104531694579720*r16[i]
- 28726839421461491640*r18[i]
+ 2153064433503155907720*r20[i]
- 211041986898764840790840*r22[i]
+ 26870132026261051008915720*r24[i]
- 4433779344005175981028538040*r26[i]
+ 950513389106656928711222883720*r28[i]
- 266877172369028643812085068829240*r30[i]
+ 99651017964870751887504875569971720*r32[i]
- 50788156610571325953562659420384640440*r34[i]
+ 36915961449056930526009630202648137219720*r36[i]
- 41419014418447665040750851917674255257827640*r38[i]
+ 84934578551016826327683205574058431012558547720*r40[i]
- 570180937724400876712836731188276811777920749126840*r42[i]
- 4158439692009034639969470592464099450041235634033244280*r44[i]
- 229275923325503706243762726200010620540068823040000000000*r45[i]
- 10938400640270606999512627385384658646639850257084618154040*r46[i]
- 469832222078622194834718578529061763610709032173568000000000*r47[i]
- 18609787245585710799825274640865231563879706109002975534476280*r48[i]
- 690703654308090686886605775729000661503847399056998400000000000*r49[i]
- 24295755635821397902484226724698036360412358674335136584603405240*r50[i]
- 816834061921519325837632181160492761661336490802298224640000000000*r51[i]
- 26420216400737828039776597843354259258729442541873887374106278588280*r52[i]
- 826385145940446765246655148432861711174878386201463829299200000000000*r53[i]
- 25100830043691732995573291002742236374870109783293156876807153222256440*r54[i]
- 742930242368923193261832627165371827238517580192797921934049280000000000*r55[i]
- 21488745356673367209649903160436075476069546948355194277325961472924140280*r56[i]
) // 60415263063373835637355132068513997507264512000000000 for i in range(len(r0))]
r41 = [(24466267020*r[1][i]
- 42550029600*r[2][i]
+ 50528160150*r[3][i]
- 48507033744*r[4][i]
+ 39645171810*r[5][i]
- 28192122176*r[6][i]
+ 17620076360*r[7][i]
- 9721421440*r[8][i]
+ 4739192952*r[9][i]
- 2038362560*r[10][i]
+ 770755843*r[11][i]
- 254795320*r[12][i]
+ 73066305*r[13][i]
- 17985552*r[14][i]
+ 3746990*r[15][i]
- 648128*r[16][i]
+ 90610*r[17][i]
- 9840*r[18][i]
+ 779*r[19][i]
- 40*r[20][i]
+ r[21][i]
- 6564120420*r0[i]
+ 3534526380*r2[i]
- 7928802420*r4[i]
+ 39562131180*r6[i]
- 355997149620*r8[i]
+ 5162772055980*r10[i]
- 112466379416820*r12[i]
+ 3509804003100780*r14[i]
- 151808102304340020*r16[i]
+ 8890838711788769580*r18[i]
- 693867758978013455220*r20[i]
+ 71436574576557715366380*r22[i]
- 9656103679244476561098420*r24[i]
+ 1714541855816811795973995180*r26[i]
- 402505898503128791422102405620*r28[i]
+ 126699650825847516884027712559980*r30[i]
- 54827934277723571354991704981312820*r32[i]
+ 34051732695777105364083032869387764780*r34[i]
- 32827430653262026254340815579045378556020*r36[i]
+ 58129225653125966892251726413185365757113580*r38[i]
- 338476895760295138790385051321218766549279671220*r40[i]
- 2149763077602671437231704105519918866633843849089620*r42[i]
- 110761315616185365335151075458942328763318272000000000*r43[i]
- 4942256826876098689793689711313418888604591478522994420*r44[i]
- 198705800215436545411261029373342537801392979968000000000*r45[i]
- 7372979698612811191617476736621847607367673634869335740820*r46[i]
- 256536466678869072307088584563086803940345640910848000000000*r47[i]
- 8465458808946796165763451715680655749443289544616664687661620*r48[i]
- 267183551072205666325866548010883965389520680874147840000000000*r49[i]
- 8117979331672354072521723205205099479673234187982104799090936020*r50[i]
- 238669689906108201296368312708296353560792649309607690240000000000*r51[i]
- 6818076027538551619225591166422355976547652044865002983244581608820*r52[i]
- 189900239055230874242774936502694772441792049430392817582080000000000*r53[i]
- 5171618834732319180394479687214193283849620051628630315033942033971220*r54[i]
- 138041851069253628998433394126808976321130523016711965119610880000000000*r55[i]
- 3618854287358718174247270918277944984495873060746358190596842483089572020*r56[i]
) // 33452526613163807108170062053440751665152000000000 for i in range(len(r0))]
r39 = [(-6564120420*r[1][i]
+ 11338026180*r[2][i]
- 13309856820*r[3][i]
+ 12570420330*r[4][i]
- 10056336264*r[5][i]
+ 6962078952*r[6][i]
- 4211628008*r[7][i]
+ 2234741392*r[8][i]
- 1040310648*r[9][i]
+ 423830264*r[10][i]
- 150391384*r[11][i]
+ 46142811*r[12][i]
- 12118314*r[13][i]
+ 2686866*r[14][i]
- 493506*r[15][i]
+ 73112*r[16][i]
- 8398*r[17][i]
+ 702*r[18][i]
- 38*r[19][i]
+ r[20][i]
+ 1767263190*r0[i]
- 955277400*r2[i]
+ 2156197560*r4[i]
- 10855425000*r6[i]
+ 98876533560*r8[i]
- 1456859058600*r10[i]
+ 32382608125560*r12[i]
- 1036360772970600*r14[i]
+ 46242812090245560*r16[i]
- 2813858311510281000*r18[i]
+ 230141619686501005560*r20[i]
- 25097337236284407949800*r22[i]
+ 3642002181929040219157560*r24[i]
- 706474912755087069174777000*r26[i]
+ 185490702479102020671448093560*r28[i]
- 67501512373123369695638979402600*r30[i]
+ 35506616897715366055874618759845560*r32[i]
- 29173319982987640073110629923442306600*r34[i]
+ 44272025958057634433180503709478279085560*r36[i]
- 222019441630075420847480526017947263931809000*r38[i]
- 1219813882056330049405575791394671579625372874440*r40[i]
- 58541921573036662439297608593521315414016000000000*r41[i]
- 2435494701008122308521041585840935773426259964069800*r42[i]
- 91378085383352926401499637253627421229737574400000000*r43[i]
- 3166734413390519310621011935324774315544541946854082440*r44[i]
- 102992200477964363280928335737465088274348376064000000000*r45[i]
- 3179252903572284408695210045628305460118381385145907089000*r46[i]
- 93933517845624637462463708669855295641358690995404800000000*r47[i]
- 2673604876174888392329293291823128228151672865125704677946440*r48[i]
- 73683990172722867345525100631400320014642700636651520000000000*r49[i]
- 1974418989189660654416775142028601893909607175588350467588706600*r50[i]
- 51613966955266559433583238169717122269196640905399894016000000000*r51[i]
- 1320028845480376778241459745623130669629332621855587804526269234440*r52[i]
- 33107222954815130156932711664097915655061115376773617418240000000000*r53[i]
- 815957549537661838837381326961271796535482084133007452235898808602600*r54[i]
- 19795975807387270200099109024051084160980250133315226586578944000000000*r55[i]
- 473487977004702488781031173032461802620651426788692589976354442780074440*r56[i]
) // 20397882081197443358640281739902897356800000000 for i in range(len(r0))]
r37 = [(1767263190*r[1][i]
- 3029594040*r[2][i]
+ 3511574910*r[3][i]
- 3257112960*r[4][i]
+ 2544619500*r[5][i]
- 1709984304*r[6][i]
+ 997490844*r[7][i]
- 506662016*r[8][i]
+ 223926516*r[9][i]
- 85795600*r[10][i]
+ 28312548*r[11][i]
- 7970688*r[12][i]
+ 1888887*r[13][i]
- 369852*r[14][i]
+ 58275*r[15][i]
- 7104*r[16][i]
+ 629*r[17][i]
- 36*r[18][i]
+ r[19][i]
- 477638700*r0[i]
+ 259289580*r2[i]
- 589294500*r4[i]
+ 2996657580*r6[i]
- 27670359300*r8[i]
+ 415064933580*r10[i]
- 9439543875300*r12[i]
+ 310922483993580*r14[i]
- 14379880666402500*r16[i]
+ 914767168887053580*r18[i]
- 79051272004645620900*r20[i]
+ 9231401536061270849580*r22[i]
- 1459700260139475814330500*r24[i]
+ 315843905250429722227637580*r26[i]
- 95612546130070295522414451300*r28[i]
+ 42177612582297377823299737193580*r30[i]
- 29268533564152352561039458453023300*r32[i]
+ 37747202396256876155482291281278813580*r34[i]
- 161759954125032708920885781040309430206500*r36[i]
- 763162014442847423121851269222329739576686420*r38[i]
- 33996470135329072264400469566504828928000000000*r39[i]
- 1314149222797294391875041342296266627244339280900*r40[i]
- 45857838565545385577449793398258363740979200000000*r41[i]
- 1479444354242422663436299123473954120225396734970420*r42[i]
- 44831961082741695492799244828619514023247872000000000*r43[i]
- 1290525734288850664269099373480698875776359383538646500*r44[i]
- 35584775745235419804380819416241066350620337766400000000*r45[i]
- 945953923580279776552772789184754415724912490598746182420*r46[i]
- 24366115407876526559068567586678948554722823372800000000000*r47[i]
- 610645775114510996953480313967173146186867766220019295823300*r48[i]
- 14939521515639279686486638270686230946922780466085888000000000*r49[i]
- 357801113228416003019399250210317079666322369514337123812946420*r50[i]
- 8408661385093459098177743857092487683793831993666437120000000000*r51[i]
- 194295554214245025331172354056693339192813114298766754673003451300*r52[i]
- 4421785847139823304538477974636921659214442633337233211392000000000*r53[i]
- 99261104716354759275356708669334064781685960280357361053977678366420*r54[i]
- 2200755503176311867578027094834478881887427024050984016936960000000000*r55[i]
- 48247096700384301518009850578340922172400831976100176730089040267290500*r56[i]
) // 13763753091226345046315979581580902400000000 for i in range(len(r0))]
r35 = [(-477638700*r[1][i]
+ 811985790*r[2][i]
- 927983760*r[3][i]
+ 843621600*r[4][i]
- 641886000*r[5][i]
+ 417225900*r[6][i]
- 233646504*r[7][i]
+ 112971936*r[8][i]
- 47071640*r[9][i]
+ 16811300*r[10][i]
- 5101360*r[11][i]
+ 1298528*r[12][i]
- 272272*r[13][i]
+ 45815*r[14][i]
- 5950*r[15][i]
+ 560*r[16][i]
- 34*r[17][i]
+ r[18][i]
+ 129644790*r0[i]
- 70715340*r2[i]
+ 161960940*r4[i]
- 832930740*r6[i]
+ 7810859340*r8[i]
- 119578066740*r10[i]
+ 2791740107340*r12[i]
- 95062235276340*r14[i]
+ 4584012079172940*r16[i]
- 307268933913567540*r18[i]
+ 28355038085389144140*r20[i]
- 3597774935929125068340*r22[i]
+ 632729503874459828228940*r24[i]
- 157381528472579148083026740*r26[i]
+ 57577884185625191071239755340*r28[i]
- 33404393172944223690128125810740*r30[i]
+ 36271128388074981554067219056171340*r32[i]
- 131671692334895976886647813958596908340*r34[i]
- 529104107360143104505564190890974500955060*r36[i]
- 21792609061108379656666967670836428800000000*r37[i]
- 779765567254824678774814590170424618060927540*r38[i]
- 25214048683702395262763681595157748121600000000*r39[i]
- 754531895504954495472529428607358759602244935860*r40[i]
- 21229190210645503978483385444330514048614400000000*r41[i]
- 567902644449952014090537079509460539320563935596340*r42[i]
- 14564893239013264062672891916748815156327219200000000*r43[i]
- 360416016142646161224945882401067658836071135991963060*r44[i]
- 8648657180064969977242561394456399100712373452800000000*r45[i]
- 202069375902424923136583586389997599181812580415819762740*r46[i]
- 4612127517564454653650814843765113002002883805184000000000*r47[i]
- 103121612921980129969364006657783463883530860291974593108660*r48[i]
- 2263884472933693041558609190221290023990021205262336000000000*r49[i]
- 48895910164254390571448366914991646721674728906975264997394740*r50[i]
- 1040735050391204632204438770440340544568220182900637696000000000*r51[i]
- 21862169403162391239341958599750577577387707221098019982750324660*r52[i]
- 453821931200327068047775184677590212395655580642824945664000000000*r53[i]
- 9319698121456631696400960021555048638297447683852229271473797580340*r54[i]
- 189526286937489003207879533218884759427831665772394776520294400000000*r55[i]
- 3820025543901040851611788799472009802308578049073400212351536136443060*r56[i]
) // 10333147966386144929666651337523200000000 for i in range(len(r0))]
r33 = [(129644790*r[1][i]
- 218349120*r[2][i]
+ 245642760*r[3][i]
- 218349120*r[4][i]
+ 161280600*r[5][i]
- 100975680*r[6][i]
+ 53993940*r[7][i]
- 24682944*r[8][i]
+ 9612108*r[9][i]
- 3164480*r[10][i]
+ 870232*r[11][i]
- 196416*r[12][i]
+ 35464*r[13][i]
- 4928*r[14][i]
+ 495*r[15][i]
- 32*r[16][i]
+ r[17][i]
- 35357670*r0[i]
+ 19389690*r2[i]
- 44796870*r4[i]
+ 233344890*r6[i]
- 2227139910*r8[i]
+ 34903389690*r10[i]
- 839988260550*r12[i]
+ 29734601940090*r14[i]
- 1506293149214790*r16[i]
+ 107487540061668090*r18[i]
- 10743535525710258630*r20[i]
+ 1511267716903778445690*r22[i]
- 304525956073869018848070*r24[i]
+ 91234873454404063067344890*r26[i]
- 43747586259736794619504039110*r28[i]
+ 39574917458915050445099774637690*r30[i]
- 120523981455993504966525708346887750*r32[i]
- 408775192473644376465790167368394203910*r34[i]
- 15499721949579217394499977006284800000000*r35[i]
- 511206585269023792365556128001469646849990*r36[i]
- 15254826342775865759666877369585500160000000*r37[i]
- 421754497238984285335705463354740490210507910*r38[i]
- 10974654148845317574241976981091935846400000000*r39[i]
- 271793538072560300468434911462753194293644181830*r40[i]
- 6459357656104303171129642884693889583677440000000*r41[i]
- 148248369194001435848413334991598692517822202402310*r42[i]
- 3302211571953506236081129759184691588287692800000000*r43[i]
- 71676123253955938571177412178194687158760951558339270*r44[i]
- 1520976967414625530272457942824571170900903198720000000*r45[i]
- 31639609352600382246311701401196841805566037174158815110*r46[i]
- 646685006086394734265332084740666732219400716288000000000*r47[i]
- 13012191241624225597793637611655297834798932917962602378310*r48[i]
- 258181916941754694739033103200539980500380934786252800000000*r49[i]
- 5058734882305856045540073713691835327365626096838684137474310*r50[i]
- 98003172162669552280283212651193173071892639817662464000000000*r51[i]
- 1879290113304215911642155827929295380860361801862580501733354950*r52[i]
- 35704185906372296773445691918777756816503577852201255567360000000*r53[i]
- 672641472730329564687292228981658860084205881937208343188256907910*r54[i]
- 12575158916407126391710720870047035404278492018674627090841600000000*r55[i]
- 233452841691483091333119823101860358440277859293807745406578698725190*r56[i]
) // 8683317618811886495518194401280000000 for i in range(len(r0))]
r31 = [(-35357670*r[1][i]
+ 58929450*r[2][i]
- 65132550*r[3][i]
+ 56448210*r[4][i]
- 40320150*r[5][i]
+ 24192090*r[6][i]
- 12271350*r[7][i]
+ 5259150*r[8][i]
- 1893294*r[9][i]
+ 566370*r[10][i]
- 138446*r[11][i]
+ 26970*r[12][i]
- 4030*r[13][i]
+ 434*r[14][i]
- 30*r[15][i]
+ r[16][i]
+ 9694845*r0[i]
- 5348880*r2[i]
+ 12480720*r4[i]
- 65969520*r6[i]
+ 642563280*r8[i]
- 10347602160*r10[i]
+ 258040917840*r12[i]
- 9564008626800*r14[i]
+ 514021079720400*r16[i]
- 39590373677587440*r18[i]
+ 4371353677873146960*r20[i]
- 701971899866535028080*r22[i]
+ 169737570795219895373520*r24[i]
- 66396273378844288679892720*r26[i]
+ 49448835121192219782326176080*r28[i]
- 124963193751534047864734415925360*r30[i]
- 354113410826574103722030528083469360*r32[i]
- 12301366626650172535317442068480000000*r33[i]
- 372225904019072507165665501545458070000*r34[i]
- 10203983616806318118045818195804160000000*r35[i]
- 259484653500223872483011119661283865786800*r36[i]
- 6217811871006716259183948315607695360000000*r37[i]
- 141956901865997956445469727796622341498870640*r38[i]
- 3113335802166672719861469258672651632640000000*r39[i]
- 66003822624082868383556482555741495612650600240*r40[i]
- 1359334478541063086765779323397876419133440000000*r41[i]
- 27303356587963564025554884815930553997263574871280*r42[i]
- 536588847651574079588079017443366763149393920000000*r43[i]
- 10345842549438556817463474698578198121859964179733680*r44[i]
- 196138884946560564409651268242770514989620920320000000*r45[i]
- 3663204676820752962698443093474820599422678195673015920*r46[i]
- 67509422521578235356394063172809938341831560396800000000*r47[i]
- 1229367058216339817971318602200240769989331897298761411120*r48[i]
- 22148293718278830966574475214239695745532717485260800000000*r49[i]
- 395185352573696509925259966545790692473196837003978017048560*r50[i]
- 6989838211515905458753639642597471400309284985697730560000000*r51[i]
- 122657793546790877104838252566375468764736099620191835404656560*r52[i]
- 2136978399115087712296321880227522428322876912299682037760000000*r53[i]
- 36988121280698718881148076634622109731006022172305430137473913200*r54[i]
- 636401990041792168283686233422492190991157350614321195909120000000*r55[i]
- 10890093660642735592022125051191031925197005582724615897049873694000*r56[i]
) // 8222838654177922817725562880000000 for i in range(len(r0))]
r29 = [(9694845*r[1][i]
- 15967980*r[2][i]
+ 17298645*r[3][i]
- 14567280*r[4][i]
+ 10015005*r[5][i]
- 5722860*r[6][i]
+ 2731365*r[7][i]
- 1085760*r[8][i]
+ 356265*r[9][i]
- 95004*r[10][i]
+ 20097*r[11][i]
- 3248*r[12][i]
+ 377*r[13][i]
- 28*r[14][i]
+ r[15][i]
- 2674440*r0[i]
+ 1485800*r2[i]
- 3506488*r4[i]
+ 18850280*r6[i]
- 188004088*r8[i]
+ 3125835560*r10[i]
- 81314498488*r12[i]
+ 3185384180840*r14[i]
- 184064268909688*r16[i]
+ 15598375633694120*r18[i]
- 1958105850969957688*r20[i]
+ 375744491571024583400*r22[i]
- 118117302690774819242488*r24[i]
+ 71447614092662750198256680*r26[i]
- 147980747895225006590333244088*r28[i]
- 346368637877614395127589803878040*r30[i]
- 10963784872237230423634083840000000*r31[i]
- 302766527792977996357877082103322488*r32[i]
- 7585842753100939730112422608896000000*r33[i]
- 176553572119721839407097582006071612760*r34[i]
- 3876980715165912710714213825249280000000*r35[i]
- 81213796311764134505181592648745883717688*r36[i]
- 1636103186224681029581052139652775936000000*r37[i]
- 31895543813319775842490572300866856117139480*r38[i]
- 604645713103650398366928164707180216320000000*r39[i]
- 11189653759353064214370349765226592602607549688*r40[i]
- 202794861446303149866709151240333763280896000000*r41[i]
- 3608799207440735942926262565268791718882246250200*r42[i]
- 63195849406190967779680687932546907121909760000000*r43[i]
- 1091041918456432706911605989934195570136050930818488*r44[i]
- 18599858037912613836046600540495361832783446016000000*r45[i]
- 313534044032502214538190505667405050039920730329536920*r46[i]
- 5232130701886884640147951658064894118305202176000000000*r47[i]
- 86524070613240340349034843422074253070890184188704404088*r48[i]
- 1419220451222069603559756976077536870379472375775232000000*r49[i]
- 23107896008521043617173872183497904829674956287283293591640*r50[i]
- 373741738674210661134828098626419085853440812861358080000000*r51[i]
- 6008307669591671335816649438311816911003850182297118574066488*r52[i]
- 96059698783150230038524550628221988538172968887744724992000000*r53[i]
- 1528101734176197374675502615836313800063939684531640625652206360*r54[i]
- 24197833543768025531598353299088959107075282255594085416960000000*r55[i]
- 381579932407152949331830984156914024593569799681407714277708445688*r56[i]
) // 8841761993739701954543616000000 for i in range(len(r0))]
r27 = [(-2674440*r[1][i]
+ 4345965*r[2][i]
- 4601610*r[3][i]
+ 3749460*r[4][i]
- 2466750*r[5][i]
+ 1332045*r[6][i]
- 592020*r[7][i]
+ 215280*r[8][i]
- 63180*r[9][i]
+ 14625*r[10][i]
- 2574*r[11][i]
+ 324*r[12][i]
- 26*r[13][i]
+ r[14][i]
+ 742900*r0[i]
- 416024*r2[i]
+ 994840*r4[i]
- 5454824*r6[i]
+ 55944280*r8[i]
- 966290024*r10[i]
+ 26454613720*r12[i]
- 1109329691624*r14[i]
+ 70212852387160*r16[i]
- 6733670404619624*r18[i]
+ 1005318113348848600*r20[i]
- 249581050854994274024*r22[i]
+ 120719220687299365182040*r24[i]
- 202039976682357297272094824*r26[i]
- 385557844336439370252173428520*r28[i]
- 11052202492174627443179520000000*r29[i]
- 276888650579451671741587901762024*r30[i]
- 6304176301536407493589598208000000*r31[i]
- 133535841584115505205141919375399080*r32[i]
- 2672618344480543437732658544640000000*r33[i]
- 51095126335993498323380094454901195624*r34[i]
- 940618873537377672007825158832128000000*r35[i]
- 16776403501444391106926987629186000345640*r36[i]
- 291283862319085180678807183848898560000000*r37[i]
- 4942310839108515578583708125038854650555624*r38[i]
- 82203911327563805707081667710859870208000000*r39[i]
- 1343752600475734599375534320311340373516684200*r40[i]
- 21634243326074826428166414905753461063680000000*r41[i]
- 343672532983087585902951862991031321905844242024*r42[i]
- 5395063942758184834505475068561955332947968000000*r43[i]
- 83804941354439477195910293019964343299641959230760*r44[i]
- 1289609166695254343642200168046105549173555200000000*r45[i]
- 19678461460501652805347265575009996073778349586894824*r46[i]
- 298018526228473595475945631789329672119214145536000000*r47[i]
- 4482734138598481574681074400900490010744661138946801320*r48[i]
- 67016178755227832923500959370656761105984640778240000000*r49[i]
- 996343679402015421123803198306389561979045588249233394024*r50[i]
- 14738679287503486801955946351327209631956632997462016000000*r51[i]
- 217035109012403108518173019970634230404031272801464219811880*r52[i]
- 3182760243299536666170356413471689268456113615580692480000000*r53[i]
- 46498820464911995110643960090817019186186417071168193972859624*r54[i]
- 677000576115850353091936355049285565985169214360708448256000000*r55[i]
- 9825975298294418560739533266953207187063157925972397601057878440*r56[i]
) // 10888869450418352160768000000 for i in range(len(r0))]
r25 = [(742900*r[1][i]
- 1188640*r[2][i]
+ 1225785*r[3][i]
- 961400*r[4][i]
+ 600875*r[5][i]
- 303600*r[6][i]
+ 123970*r[7][i]
- 40480*r[8][i]
+ 10350*r[9][i]
- 2000*r[10][i]
+ 275*r[11][i]
- 24*r[12][i]
+ r[13][i]
- 208012*r0[i]
+ 117572*r2[i]
- 285532*r4[i]
+ 1602692*r6[i]
- 16996252*r8[i]
+ 307475012*r10[i]
- 8966430172*r12[i]
+ 409745686532*r14[i]
- 29195711499292*r16[i]
+ 3312133208909252*r18[i]
- 636215671041835612*r20[i]
+ 241648300078174135172*r22[i]
- 321511316149669476991132*r24[i]
- 492817676505266866078123708*r26[i]
- 12703681025488077520896000000*r27[i]
- 286779648275654636997381637852*r28[i]
- 5894507995826467969695744000000*r29[i]
- 112914054231542703053832892635388*r30[i]
- 2047008246979213061238030336000000*r31[i]
- 35501568925223446300815211192767772*r32[i]
- 593711792050129855003168210944000000*r33[i]
- 9632134956680435093368218113996247868*r34[i]
- 152311343455497374594406627803136000000*r35[i]
- 2356318736218539774396037820111678892892*r36[i]
- 35772470531371951985805498114637824000000*r37[i]
- 534273042749950920189640352996759062689148*r38[i]
- 7866491034006154572049014294052601856000000*r39[i]
- 114383224059606274110181105712262975351245212*r40[i]
- 1644946226278516886873016733667061202944000000*r41[i]
- 23426103831558846665144911501028780920365367228*r42[i]
- 330735945747364837719554208843251145179136000000*r43[i]
- 4633465747908141417306051485893140722291346976732*r44[i]
- 64465996518808752310647291812383168776634368000000*r45[i]
- 891389875128429665004288245297052393567100598170108*r46[i]
- 12257190333970097165549309885966019046465339392000000*r47[i]
- 167703402046599761376513697620930939990159551304359452*r48[i]
- 2284199788431383972862903582163083269492369522688000000*r49[i]
- 30985395797162515638045004419632302359171420946744265788*r50[i]
- 418773650924292383172351750158911938166116165353472000000*r51[i]
- 5640938886725051055672433299961125394581606270770949985372*r52[i]
- 75754370981682573393940880354465056079445791605260288000000*r53[i]
- 1014539155515195896087346280844831091980940427383805672902268*r54[i]
- 13553236686007006297534192722032523699914497964150095872000000*r55[i]
- 180645753713035138349646636694817250186535606435585025317966492*r56[i]
) // 15511210043330985984000000 for i in range(len(r0))]
r23 = [(-208012*r[1][i]
+ 326876*r[2][i]
- 326876*r[3][i]
+ 245157*r[4][i]
- 144210*r[5][i]
+ 67298*r[6][i]
- 24794*r[7][i]
+ 7084*r[8][i]
- 1518*r[9][i]
+ 230*r[10][i]
- 22*r[11][i]
+ r[12][i]
+ 58786*r0[i]
- 33592*r2[i]
+ 83096*r4[i]
- 479752*r6[i]
+ 5299736*r8[i]
- 101549512*r10[i]
+ 3208453976*r12[i]
- 164071220872*r14[i]
+ 13743680753816*r16[i]
- 1993276972245832*r18[i]
+ 581947914140407256*r20[i]
- 603916464771468176392*r22[i]
- 730803773459954540777704*r24[i]
- 16803810880275234816000000*r25[i]
- 339155768243774227716964552*r26[i]
- 6245976504198304781107200000*r27[i]
- 107413822788261782335458993064*r28[i]
- 1751393992807566623932416000000*r29[i]
- 27365156266821215807862420562312*r30[i]
- 412945663851071412756568473600000*r31[i]
- 6053949680529454447550745704030824*r32[i]
- 86623417665042381831452000256000000*r33[i]
- 1214146547565910406028014931410521672*r34[i]
- 16719755812321492798917963359846400000*r35[i]
- 226758627215029497194516602329808882984*r36[i]
- 3034905857007157810746475187798016000000*r37[i]
- 40151799724774280996886476759684489594632*r38[i]
- 525848735885794606994555529953619148800000*r39[i]
- 6825564942475643900873841059427230143341544*r40[i]
- 87900055843825806396690634755863003136000000*r41[i]
- 1124090333957827218160935737032127911249333192*r42[i]
- 14286036145840157893404384196456208735600640000*r43[i]
- 180556939553256275799275906968519352499771598504*r44[i]
- 2270728203819030041749862616122105872023552000000*r45[i]
- 28430855249825246651314973609548475795532583689352*r46[i]
- 354557703317395919808450352391376751066211942400000*r47[i]
- 4405868085478593275690315869491622501390761293845864*r48[i]
- 54573144465647486264201741288918109369842860032000000*r49[i]
- 674011661674309854738045921738777159802726884618615112*r50[i]
- 8302706625795267729689057629348230882286932767539200000*r51[i]
- 102034139431103779464508421919001500494414946039191875624*r52[i]
- 1251246650171085656596973236879882037480265304768512000000*r53[i]
- 15314394051611719851475192053401326069594457012869777662472*r54[i]
- 187109145209992539052209722604913357344367643037199564800000*r55[i]
- 2282440022117705675156420050651491739525177949448233198679784*r56[i]
) // 25852016738884976640000 for i in range(len(r0))]
r21 = [(58786*r[1][i]
- 90440*r[2][i]
+ 87210*r[3][i]
- 62016*r[4][i]
+ 33915*r[5][i]
- 14364*r[6][i]
+ 4655*r[7][i]
- 1120*r[8][i]
+ 189*r[9][i]
- 20*r[10][i]
+ r[11][i]
- 16796*r0[i]
+ 9724*r2[i]
- 24596*r4[i]
+ 147004*r6[i]
- 1708916*r8[i]
+ 35240284*r10[i]
- 1237329236*r12[i]
+ 73853629564*r14[i]
- 7850527669556*r16[i]
+ 1717351379730844*r18[i]
- 1359124435588313876*r20[i]
- 1272410676942417239876*r22[i]
- 25852016738884976640000*r23[i]
- 462292539259962003646196*r24[i]
- 7561714896123855667200000*r25[i]
- 115761644587269354830466596*r26[i]
- 1683741850203578528563200000*r27[i]
- 23512975860299444963550050516*r28[i]
- 317677725072691341719961600000*r29[i]
- 4176614976496441445095962733316*r30[i]
- 53674391443652368368589209600000*r31[i]
- 676635955671282540673335079110836*r32[i]
- 8391272072243853389701334630400000*r33[i]
- 102611708232289325546408008313624036*r34[i]
- 1239646284649926576486736094822400000*r35[i]
- 14819283410691765614379616648600811156*r36[i]
- 175538127424434549895381626305740800000*r37[i]
- 2062659648435073986802743885440046722756*r38[i]
- 24066873273263602745997309174983884800000*r39[i]
- 279069134864297423784787795404361206735476*r40[i]
- 3218237360334469905693543066426751549440000*r41[i]
- 36932670876144577834192017462238998576813476*r42[i]
- 422013831656219970552631011526505561456640000*r43[i]
- 4803667893589610545887832027829424971473267796*r44[i]
- 54491782544378643866541770098406137341542400000*r45[i]
- 616254801390825608499920295882691673585117080196*r46[i]
- 6950267169846786189298202657232919399818854400000*r47[i]
- 78194975030419808376759755992062291704460984792116*r48[i]
- 877813878936817604039539295936804610730357555200000*r49[i]
- 9834901482219684549861282981457686724945206826306916*r50[i]
- 109993865724440916050887229750467965278551356211200000*r51[i]
- 1228217338997580254122488729377687743870958069616892436*r52[i]
- 13694916176593289530129597814644948512271618874572800000*r53[i]
- 152504503331260902260854535497432382418134663231196077636*r54[i]
- 1696290932754493307608442494949489883113732653837516800000*r55[i]
- 18847853343293961413885442066505656038216029001597219552756*r56[i]
) // 51090942171709440000 for i in range(len(r0))]
r19 = [(-16796*r[1][i]
+ 25194*r[2][i]
- 23256*r[3][i]
+ 15504*r[4][i]
- 7752*r[5][i]
+ 2907*r[6][i]
- 798*r[7][i]
+ 152*r[8][i]
- 18*r[9][i]
+ r[10][i]
+ 4862*r0[i]
- 2860*r2[i]
+ 7436*r4[i]
- 46420*r6[i]
+ 576236*r8[i]
- 13098580*r10[i]
+ 532310636*r12[i]
- 39968611540*r14[i]
+ 6350631494636*r16[i]
- 3730771315561300*r18[i]
- 2637991952943407764*r20[i]
- 46833363657400320000*r21[i]
- 734121065118879803860*r22[i]
- 10556240168378032128000*r23[i]
- 142438684135271315212564*r24[i]
- 1830415113744266649600000*r25[i]
- 22632897298190126259675220*r26[i]
- 271297526662043666104320000*r27[i]
- 3170344993810020486920015764*r28[i]
- 36274730261563609572556800000*r29[i]
- 407775103607650299563627591380*r30[i]
- 4515882637052182897862000640000*r31[i]
- 49377994276343186011748723193364*r32[i]
- 534053247401000753173510963200000*r33[i]
- 5722063606154183864914875339648340*r34[i]
- 60811730909031986048777521029120000*r35[i]
- 641729418431834160625738740379401364*r36[i]
- 6730380606921481449181267599974400000*r37[i]
- 70207898580127312813466155395513222100*r38[i]
- 728918319689461841494925372032622592000*r39[i]
- 7536441803725213229125462424550696575764*r40[i]
- 77635978704164552294553096402068152320000*r41[i]
- 797177898990753876072852178329776532568660*r42[i]
- 8162164080895303403984327865949915250688000*r43[i]
- 83359491110673172494030048846026790563932564*r44[i]
- 849432099945167336777734465061373289267200000*r45[i]
- 8638438243166451781593809976801426668242424020*r46[i]
- 87694169965134464605849462884812769886371840000*r47[i]
- 888832151283066038746077396233689115965303967764*r48[i]
- 8996158031157109433578511766939541381376409600000*r49[i]
- 90938713449996246641127353860256309887114389604180*r50[i]
- 918234342704615923743435749615058841825963745280000*r51[i]
- 9262393601318313123889045816028965261306516208457364*r52[i]
- 93347798539774463006574188993931221735397071462400000*r53[i]
- 940020095741410096004864931705566108623177977672605140*r54[i]
- 9459299151254233261484792667142328326155545534423040000*r55[i]
- 95126631804495487685309357589162668229325862229818457364*r56[i]
) // 121645100408832000 for i in range(len(r0))]
r17 = [(4862*r[1][i]
- 7072*r[2][i]
+ 6188*r[3][i]
- 3808*r[4][i]
+ 1700*r[5][i]
- 544*r[6][i]
+ 119*r[7][i]
- 16*r[8][i]
+ r[9][i]
- 1430*r0[i]
+ 858*r2[i]
- 2310*r4[i]
+ 15258*r6[i]
- 206790*r8[i]
+ 5386458*r10[i]
- 272513670*r12[i]
+ 30255826458*r14[i]
- 12765597850950*r16[i]
- 6622557957272742*r18[i]
- 101370917007360000*r19[i]
- 1375210145685786630*r20[i]
- 17172233341046784000*r21[i]
- 201832098313986359142*r22[i]
- 2265471043586150400000*r23[i]
- 24529324224160803328710*r24[i]
- 258058524232798248960000*r25[i]
- 2652208374242713043720742*r26[i]
- 26739700571225856614400000*r27[i]
- 265323404171486113659725190*r28[i]
- 2597688920748017370193920000*r29[i]
- 25147613788240222384169485542*r30[i]
- 241125683321001354933657600000*r31[i]
- 2293170112631184981695915264070*r32[i]
- 21656158388689797460311183360000*r33[i]
- 203283794784841444836991831621542*r34[i]
- 1898267590696733462875776307200000*r35[i]
- 17646072330245312137111933794073350*r36[i]
- 163392570167583908119294187237376000*r37[i]
- 1507754227229479379470312529237936742*r38[i]
- 13871774079585871769182921633935360000*r39[i]
- 127291574907112728538906245247680921030*r40[i]
- 1165398276253942030786602999248830464000*r41[i]
- 10648249156718669259487809979675840079142*r42[i]
- 97121906010634492337139410720414515200000*r43[i]
- 884471146488697462546213719879378982015110*r44[i]
- 8043742604145412070397708709577312747520000*r45[i]
- 73065283527546375984492393431422365909536742*r46[i]
- 662985481414219219279431223562176586956800000*r47[i]
- 6010229010788429141870217066922217223929803590*r48[i]
- 54440174236564270133288224915510829498019840000*r49[i]
- 492755135434761578293305350886942317529465637542*r50[i]
- 4457205465827107111785421147442507464329523200000*r51[i]
- 40294548566019835134386988604297024831948411774470*r52[i]
- 364091512505225031658987624997678808818240901120000*r53[i]
- 3288369094603737090125334557327653119906621235549542*r54[i]
- 29687831954151399686402807167358312867527245926400000*r55[i]
- 267931592702357971121614379534668912664625180303255750*r56[i]
) // 355687428096000 for i in range(len(r0))]
r15 = [(-1430*r[1][i]
+ 2002*r[2][i]
- 1638*r[3][i]
+ 910*r[4][i]
- 350*r[5][i]
+ 90*r[6][i]
- 14*r[7][i]
+ r[8][i]
+ 429*r0[i]
- 264*r2[i]
+ 744*r4[i]
- 5304*r6[i]
+ 81384*r8[i]
- 2605944*r10[i]
+ 192387624*r12[i]
- 55942352184*r14[i]
- 20546119600536*r16[i]
- 266765571072000*r17[i]
- 3083760849804024*r18[i]
- 32945548027392000*r19[i]
- 332500281299403096*r20[i]
- 3215147584416768000*r21[i]
- 30076927429146721464*r22[i]
- 274100623905588480000*r23[i]
- 2446077617962088140056*r24[i]
- 21459412163122053120000*r25[i]
- 185641639183185136464504*r26[i]
- 1587401376760010972160000*r27[i]
- 13442713420403849918131416*r28[i]
- 112915002722102749808640000*r29[i]
- 941961013910760913890393144*r30[i]
- 7812419263561351877518080000*r31[i]
- 64474322285718607792730497176*r32[i]
- 529848386811984810994744320000*r33[i]
- 4338547620121893769542630267384*r34[i]
- 35415056327751829508662891008000*r35[i]
- 288317531175033442515609896757336*r36[i]
- 2341823147101379454117987013632000*r37[i]
- 18983391549723892653716655806647224*r38[i]
- 153619763998111828980832157720832000*r39[i]
- 1241292607509331793516191597844431896*r40[i]
- 10017079537004367071413852136982528000*r41[i]
- 80746194097372251940077615903073292664*r42[i]
- 650250798838302173122854563322562560000*r43[i]
- 5232061257212799699445154857325986640856*r44[i]
- 42067391464856035210355948847111229440000*r45[i]
- 338018548004311349729166172709579357563704*r46[i]
- 2714522948575416807552558113876933656320000*r47[i]
- 21788917503304477212565325243539420555704216*r48[i]
- 174821149505151584518657828257831893345280000*r49[i]
- 1402141896338776811136967582554033500226820344*r50[i]
- 11242168283931454427825411966307736057167360000*r51[i]
- 90112723368126633235251766101448928377940741976*r52[i]
- 722130298632985742738270377008563798712253440000*r53[i]
- 5785647203879657431846619085033124824223750822584*r54[i]
- 46345442737409930132271027996820593307050786048000*r55[i]
- 371185586083174668935874345914297403283249129274136*r56[i]
) // 1307674368000 for i in range(len(r0))]
r13 = [(429*r[1][i]
- 572*r[2][i]
+ 429*r[3][i]
- 208*r[4][i]
+ 65*r[5][i]
- 12*r[6][i]
+ r[7][i]
- 132*r0[i]
+ 84*r2[i]
- 252*r4[i]
+ 2004*r6[i]
- 37212*r8[i]
+ 1710324*r10[i]
- 325024572*r12[i]
- 80789566956*r14[i]
- 871782912000*r15[i]
- 8422900930332*r16[i]
- 75583578470400*r17[i]
- 643521842437836*r18[i]
- 5269678622208000*r19[i]
- 41890044885642492*r20[i]
- 325386564299596800*r21[i]
- 2481686964269990316*r22[i]
- 18652248729354240000*r23[i]
- 138536531588626169052*r24[i]
- 1019042849143807488000*r25[i]
- 7436421488952386592396*r26[i]
- 53911021949819274240000*r27[i]
- 388701690499592948238012*r28[i]
- 2789805187365599475072000*r29[i]
- 19946749502047187160692076*r30[i]
- 142159780685991861112320000*r31[i]
- 1010433303980489860989897372*r32[i]
- 7165521770403817166663116800*r33[i]
- 50716588034439244118483617356*r34[i]
- 358378772025058883636009472000*r35[i]
- 2528902640579773012941059115132*r36[i]
- 17824202779159732939433280230400*r37[i]
- 125502611080965065134883934376236*r38[i]
- 882926862501000079240924013568000*r39[i]
- 6206986746547700738292160195379292*r40[i]
- 43608135571536574058895364550860800*r41[i]
- 306213499909407501334225902520456716*r42[i]
- 2149239710498553002348841878415360000*r43[i]
- 15079178774724614117506008765315297852*r44[i]
- 105761403926812162332273274580071296000*r45[i]
- 741573481088337285231858048220674626796*r46[i]
- 5198479982499565882352899855753044480000*r47[i]
- 36434172034715569203746509369098022198812*r48[i]
- 255308169532157231577671227649975633664000*r49[i]
- 1788771440213892011837337228527544587734476*r50[i]
- 12531087911298377892590529356517576445440000*r51[i]
- 87775753902632879954790735906635276359730172*r52[i]
- 614779166184964747722494610821477092697932800*r53[i]
- 4305547785126634750908211772273402537757507756*r54[i]
- 30151397670066414681209001391191401891653632000*r55[i]
- 211135169951589392525478765734151290219989459932*r56[i]
) // 6227020800 for i in range(len(r0))]
r11 = [(-132*r[1][i]
+ 165*r[2][i]
- 110*r[3][i]
+ 44*r[4][i]
- 10*r[5][i]
+ r[6][i]
+ 42*r0[i]
- 28*r2[i]
+ 92*r4[i]
- 868*r6[i]
+ 22652*r8[i]
- 2620708*r10[i]
- 415790788*r12[i]
- 3632428800*r13[i]
- 28616744548*r14[i]
- 210680870400*r15[i]
- 1479485236228*r16[i]
- 10038995366400*r17[i]
- 66394067988388*r18[i]
- 430591742380800*r19[i]
- 2750479262009668*r20[i]
- 17360942812012800*r21[i]
- 108550450893568228*r22[i]
- 673606803881088000*r23[i]
- 4154688725062207108*r24[i]
- 25499502190850688000*r25[i]
- 155878445775166700068*r26[i]
- 949776357849070752000*r27[i]
- 5771581202353414724548*r28[i]
- 34995682724855684832000*r29[i]
- 211811399872933910999908*r30[i]
- 1280080235834717770252800*r31[i]
- 7726641919200262371657988*r32[i]
- 46591059456870785061004800*r33[i]
- 280704018540064430354883748*r34[i]
- 1690018909819536161979590400*r35[i]
- 10169113413821714748538703428*r36[i]
- 61159784116494648773674886400*r37[i]
- 367684638335977863351585967588*r38[i]
- 2209739160176731898013383884800*r39[i]
- 13276598260065161268654185556868*r40[i]
- 79750432649108163224160355276800*r41[i]
- 478956917715683026467561165467428*r42[i]
- 2876013540917084725512964985376000*r43[i]
- 17267443120712778679894991796314308*r44[i]
- 103661474908781590201983341856096000*r45[i]
- 622252957609245047342724399262599268*r46[i]
- 3734938395375021425507273833823424000*r47[i]
- 22416734056596928549732496421419871748*r48[i]
- 134535924504317597978456420953656384000*r49[i]
- 807393154821611376674434030676868979108*r50[i]
- 4845246995796352471529950975101582508800*r51[i]
- 29075922420664314894010979796628180325188*r52[i]
- 174477737199628479530547826532207368300800*r53[i]
- 1046977438360831608823005722785678653022948*r54[i]
- 6282419713119688698679893309347069088230400*r55[i]
- 37697293722049221763903820338234783307370628*r56[i]
) // 39916800 for i in range(len(r0))]
r9 = [(42*r[1][i]
- 48*r[2][i]
+ 27*r[3][i]
- 8*r[4][i]
+ r[5][i]
- 14*r0[i]
+ 10*r2[i]
- 38*r4[i]
+ 490*r6[i]
- 31238*r8[i]
- 2922230*r10[i]
- 19958400*r11[i]
- 124075238*r12[i]
- 726485760*r13[i]
- 4084385750*r14[i]
- 22313491200*r15[i]
- 119387268038*r16[i]
- 628980992640*r17[i]
- 3275389222070*r18[i]
- 16905818966400*r19[i]
- 86665431465638*r20[i]
- 441935114987520*r21[i]
- 2244295389943190*r22[i]
- 11360520464832000*r23[i]
- 57360469753884038*r24[i]
- 289038899804054400*r25[i]
- 1454155949521941110*r26[i]
- 7306671293537616000*r27[i]
- 36677059892827099238*r28[i]
- 183960524908301057280*r29[i]
- 922104761587650687830*r30[i]
- 4619736062008593926400*r31[i]
- 23135540444136227047238*r32[i]
- 115825176110799088940160*r33[i]
- 579715876176320506935350*r34[i]
- 2900939663557699476451200*r35[i]
- 14514140349055749129024038*r36[i]
- 72608472572041292373527040*r37[i]
- 363193454272347163609915670*r38[i]
- 1816571661325589960713958400*r39[i]
- 9085275939429279963731685638*r40[i]
- 45436050447189540392656321920*r41[i]
- 227218935892633882388998540790*r42[i]
- 1136249416059455304696385296000*r43[i]
- 5681866032591044240951769048038*r44[i]
- 28411805989856165780668427308800*r45[i]
- 142068933310062230858345890602710*r46[i]
- 710384280152969638132390327392000*r47[i]
- 3552079855654080764219631870487238*r48[i]
- 17761033099263130050180188817751680*r49[i]
- 88807700784593943012315384189973430*r50[i]
- 444048645089005049723558441367254400*r51[i]
- 2220283790147933078276819155128739238*r52[i]
- 11101581209667596183377765341852994560*r53[i]
- 55508555084398602505584708639561804950*r54[i]
- 277545371567282194146167718608057971200*r55[i]
- 1387737242420707782996791311133835900038*r56[i]
) // 362880 for i in range(len(r0))]
r7 = [(-14*r[1][i]
+ 14*r[2][i]
- 6*r[3][i]
+ r[4][i]
+ 5*r0[i]
- 4*r2[i]
+ 20*r4[i]
- 604*r6[i]
- 29740*r8[i]
- 151200*r9[i]
- 708604*r10[i]
- 3160080*r11[i]
- 13645900*r12[i]
- 57657600*r13[i]
- 239967004*r14[i]
- 988107120*r15[i]
- 4037604460*r16[i]
- 16406863200*r17[i]
- 66398623804*r18[i]
- 267911678160*r19[i]
- 1078605601420*r20[i]
- 4335313752000*r21[i]
- 17403958407004*r22[i]
- 69804002545200*r23[i]
- 279780634372780*r24[i]
- 1120816644948000*r25[i]
- 4488349371924604*r26[i]
- 17968646803620240*r27[i]
- 71920337041294540*r28[i]
- 287818601403715200*r29[i]
- 1151686172846664604*r30[i]
- 4607980008114455280*r31[i]
- 18435626012705982700*r32[i]
- 73753622051697957600*r33[i]
- 295047842329672995004*r34[i]
- 1180291431927853642320*r35[i]
- 4721465916019935893260*r36[i]
- 18886764229967380219200*r37[i]
- 75549758619456576163804*r38[i]
- 302207139580435761213360*r39[i]
- 1208852873637267995922220*r40[i]
- 4835484440511039999684000*r41[i]
- 19342156599960850372299004*r42[i]
- 77369282913655045261040400*r43[i]
- 309479101196178257662005580*r44[i]
- 1237922313409633551106176000*r45[i]
- 4951706979513788347008408604*r46[i]
- 19806881095681900978203235440*r47[i]
- 79227683915609817008158719340*r48[i]
- 316911214261089847968346159200*r49[i]
- 1267646292840319012979866380604*r50[i]
- 5070589478749170677837606550480*r51[i]
- 20282370837160398114302240879500*r52[i]
- 81129522115132801716459190737600*r53[i]
- 324518204760004960744377010983004*r54[i]
- 1298073167938441356814707920777520*r55[i]
- 5192293718449030473173589579142060*r56[i]
) // 5040 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
- 1680*r7[i]
- 5542*r8[i]
- 17640*r9[i]
- 54958*r10[i]
- 168960*r11[i]
- 515062*r12[i]
- 1561560*r13[i]
- 4717438*r14[i]
- 14217840*r15[i]
- 42784582*r16[i]
- 128615880*r17[i]
- 386371918*r18[i]
- 1160164320*r19[i]
- 3482590102*r20[i]
- 10451964600*r21[i]
- 31364282398*r22[i]
- 94109624400*r23[i]
- 282362427622*r24[i]
- 847154391720*r25[i]
- 2541597392878*r26[i]
- 7625060614080*r27[i]
- 22875718713142*r28[i]
- 68628229881240*r29[i]
- 205886837127358*r30[i]
- 617664806349360*r31[i]
- 1853003008982662*r32[i]
- 5559026206817160*r33[i]
- 16677112980189838*r34[i]
- 50031407660046240*r35[i]
- 150094360419092182*r36[i]
- 450283356135183480*r37[i]
- 1350850618161364318*r38[i]
- 4052552953995720720*r39[i]
- 12157661061010417702*r40[i]
- 36472987581077764200*r41[i]
- 109418971539326314798*r42[i]
- 328256932210164988800*r43[i]
- 984770831814867055222*r44[i]
- 2954312565813345343320*r45[i]
- 8862937838177524385278*r46[i]
- 26588813796007549866480*r47[i]
- 79766441950972603020742*r48[i]
- 239299326978817715904840*r49[i]
- 717897983188252961399758*r50[i]
- 2153693954068358511569760*r51[i]
- 6461081871212274789450262*r52[i]
- 19383245631651222877832760*r53[i]
- 58149736930982465652462238*r54[i]
- 174449210865004990995314640*r55[i]
- 523347632739130161061799782*r56[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
- 126*r7[i]
- 254*r8[i]
- 510*r9[i]
- 1022*r10[i]
- 2046*r11[i]
- 4094*r12[i]
- 8190*r13[i]
- 16382*r14[i]
- 32766*r15[i]
- 65534*r16[i]
- 131070*r17[i]
- 262142*r18[i]
- 524286*r19[i]
- 1048574*r20[i]
- 2097150*r21[i]
- 4194302*r22[i]
- 8388606*r23[i]
- 16777214*r24[i]
- 33554430*r25[i]
- 67108862*r26[i]
- 134217726*r27[i]
- 268435454*r28[i]
- 536870910*r29[i]
- 1073741822*r30[i]
- 2147483646*r31[i]
- 4294967294*r32[i]
- 8589934590*r33[i]
- 17179869182*r34[i]
- 34359738366*r35[i]
- 68719476734*r36[i]
- 137438953470*r37[i]
- 274877906942*r38[i]
- 549755813886*r39[i]
- 1099511627774*r40[i]
- 2199023255550*r41[i]
- 4398046511102*r42[i]
- 8796093022206*r43[i]
- 17592186044414*r44[i]
- 35184372088830*r45[i]
- 70368744177662*r46[i]
- 140737488355326*r47[i]
- 281474976710654*r48[i]
- 562949953421310*r49[i]
- 1125899906842622*r50[i]
- 2251799813685246*r51[i]
- 4503599627370494*r52[i]
- 9007199254740990*r53[i]
- 18014398509481982*r54[i]
- 36028797018963966*r55[i]
- 72057594037927934*r56[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
- r7[i]
- r8[i]
- r9[i]
- r10[i]
- r11[i]
- r12[i]
- r13[i]
- r14[i]
- r15[i]
- r16[i]
- r17[i]
- r18[i]
- r19[i]
- r20[i]
- r21[i]
- r22[i]
- r23[i]
- r24[i]
- r25[i]
- r26[i]
- r27[i]
- r28[i]
- r29[i]
- r30[i]
- r31[i]
- r32[i]
- r33[i]
- r34[i]
- r35[i]
- r36[i]
- r37[i]
- r38[i]
- r39[i]
- r40[i]
- r41[i]
- r42[i]
- r43[i]
- r44[i]
- r45[i]
- r46[i]
- r47[i]
- r48[i]
- r49[i]
- r50[i]
- r51[i]
- r52[i]
- r53[i]
- r54[i]
- r55[i]
- r56[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56)
def natural_interpolate_30(r):
r0 = r[0]
r58 = r['infinity']
r56 = [(-7384942649010080*(r[1][i] + r[-1][i])
+ 6646448384109072*(r[2][i] + r[-2][i])
- 5574440580220512*(r[3][i] + r[-3][i])
+ 4355031703297275*(r[4][i] + r[-4][i])
- 3167295784216200*(r[5][i] + r[-5][i])
+ 2142582442263900*(r[6][i] + r[-6][i])
- 1346766106565880*(r[7][i] + r[-7][i])
+ 785613562163430*(r[8][i] + r[-8][i])
- 424655979547800*(r[9][i] + r[-9][i])
+ 212327989773900*(r[10][i] + r[-10][i])
- 97997533741800*(r[11][i] + r[-11][i])
+ 41648951840265*(r[12][i] + r[-12][i])
- 16253249498640*(r[13][i] + r[-13][i])
+ 5804731963800*(r[14][i] + r[-14][i])
- 1889912732400*(r[15][i] + r[-15][i])
+ 558383307300*(r[16][i] + r[-16][i])
- 148902215280*(r[17][i] + r[-17][i])
+ 35607051480*(r[18][i] + r[-18][i])
- 7575968400*(r[19][i] + r[-19][i])
+ 1420494075*(r[20][i] + r[-20][i])
- 231917400*(r[21][i] + r[-21][i])
+ 32468436*(r[22][i] + r[-22][i])
- 3819816*(r[23][i] + r[-23][i])
+ 367290*(r[24][i] + r[-24][i])
- 27720*(r[25][i] + r[-25][i])
+ 1540*(r[26][i] + r[-26][i])
- 56*(r[27][i] + r[-27][i])
+ (r[28][i] + r[-28][i])
+ 7648690600760440*r0[i]
- 5484643106326716667602108124535174262267345409089333490314966466560000000000000*r58[i]
) // 710998587804863451854045647463724949736497978881168458687447040000000000000 for i in range(len(r0))]
r54 = [(1877405874732108*(r[1][i] + r[-1][i])
- 1683191473897752*(r[2][i] + r[-2][i])
+ 1402659561581460*(r[3][i] + r[-3][i])
- 1085929983159840*(r[4][i] + r[-4][i])
+ 780512175396135*(r[5][i] + r[-5][i])
- 520341450264090*(r[6][i] + r[-6][i])
+ 321387366339585*(r[7][i] + r[-7][i])
- 183649923622620*(r[8][i] + r[-8][i])
+ 96926348578605*(r[9][i] + r[-9][i])
- 47153358767970*(r[10][i] + r[-10][i])
+ 21094923659355*(r[11][i] + r[-11][i])
- 8654327655120*(r[12][i] + r[-12][i])
+ 3245372870670*(r[13][i] + r[-13][i])
- 1108176102180*(r[14][i] + r[-14][i])
+ 343006888770*(r[15][i] + r[-15][i])
- 95722852680*(r[16][i] + r[-16][i])
+ 23930713170*(r[17][i] + r[-17][i])
- 5317936260*(r[18][i] + r[-18][i])
+ 1040465790*(r[19][i] + r[-19][i])
- 177100560*(r[20][i] + r[-20][i])
+ 25827165*(r[21][i] + r[-21][i])
- 3162510*(r[22][i] + r[-22][i])
+ 316251*(r[23][i] + r[-23][i])
- 24804*(r[24][i] + r[-24][i])
+ 1431*(r[25][i] + r[-25][i])
- 54*(r[26][i] + r[-26][i])
+ (r[27][i] + r[-27][i])
- 1946939425648112*r0[i]
- 1599746822560942766671602706793381136907120452482629032046755840000000000000*r56[i]
- 5905785344848232411721555712669125143120016574430121597607008534528000000000000*r58[i]
) // 230843697339241380472092742683027581083278564571807941132288000000000000 for i in range(len(r0))]
r52 = [(-477551179875952*(r[1][i] + r[-1][i])
+ 426384982032100*(r[2][i] + r[-2][i])
- 352870329957600*(r[3][i] + r[-3][i])
+ 270533919634160*(r[4][i] + r[-4][i])
- 191991813933920*(r[5][i] + r[-5][i])
+ 125994627894135*(r[6][i] + r[-6][i])
- 76360380541900*(r[7][i] + r[-7][i])
+ 42671977361650*(r[8][i] + r[-8][i])
- 21945588357420*(r[9][i] + r[-9][i])
+ 10363194502115*(r[10][i] + r[-10][i])
- 4481381406320*(r[11][i] + r[-11][i])
+ 1768966344600*(r[12][i] + r[-12][i])
- 635013559600*(r[13][i] + r[-13][i])
+ 206379406870*(r[14][i] + r[-14][i])
- 60403728840*(r[15][i] + r[-15][i])
+ 15820024220*(r[16][i] + r[-16][i])
- 3679075400*(r[17][i] + r[-17][i])
+ 752538150*(r[18][i] + r[-18][i])
- 133784560*(r[19][i] + r[-19][i])
+ 20358520*(r[20][i] + r[-20][i])
- 2598960*(r[21][i] + r[-21][i])
+ 270725*(r[22][i] + r[-22][i])
- 22100*(r[23][i] + r[-23][i])
+ 1326*(r[24][i] + r[-24][i])
- 52*(r[25][i] + r[-25][i])
+ (r[26][i] + r[-26][i])
+ 495918532948104*r0[i]
- 500161344235022991022867609146559759013770223238917205786624000000000000*r54[i]
- 1656034210762161123276714653884259362094593209144054868359512064000000000000*r56[i]
- 3893428125748283888371910343676903962906874492571933463667607076864000000000000*r58[i]
) // 80658175170943878571660636856403766975289505440883277824000000000000 for i in range(len(r0))]
r50 = [(121548660036300*(r[1][i] + r[-1][i])
- 108043253365600*(r[2][i] + r[-2][i])
+ 88749815264600*(r[3][i] + r[-3][i])
- 67327446062800*(r[4][i] + r[-4][i])
+ 47129212243960*(r[5][i] + r[-5][i])
- 30405943383200*(r[6][i] + r[-6][i])
+ 18053528883775*(r[7][i] + r[-7][i])
- 9847379391150*(r[8][i] + r[-8][i])
+ 4923689695575*(r[9][i] + r[-9][i])
- 2250829575120*(r[10][i] + r[-10][i])
+ 937845656300*(r[11][i] + r[-11][i])
- 354860518600*(r[12][i] + r[-12][i])
+ 121399651100*(r[13][i] + r[-13][i])
- 37353738800*(r[14][i] + r[-14][i])
+ 10272278170*(r[15][i] + r[-15][i])
- 2505433700*(r[16][i] + r[-16][i])
+ 536878650*(r[17][i] + r[-17][i])
- 99884400*(r[18][i] + r[-18][i])
+ 15890700*(r[19][i] + r[-19][i])
- 2118760*(r[20][i] + r[-20][i])
+ 230300*(r[21][i] + r[-21][i])
- 19600*(r[22][i] + r[-22][i])
+ 1225*(r[23][i] + r[-23][i])
- 50*(r[24][i] + r[-24][i])
+ (r[25][i] + r[-25][i])
- 126410606437752*r0[i]
- 168037864939466413690959660117507847865186469668506828800000000000000*r52[i]
- 496955181771977971849644098831517709276502465397642095493120000000000000*r54[i]
- 1045983785547912130104393377696510043035795431067327440669900800000000000000*r56[i]
- 1758127635958991683107242284534836779885443701501118310588256092160000000000000*r58[i]
) // 30414093201713378043612608166064768844377641568960512000000000000 for i in range(len(r0))]
r48 = [(-30957699535776*(r[1][i] + r[-1][i])
+ 27385657281648*(r[2][i] + r[-2][i])
- 22314239266528*(r[3][i] + r[-3][i])
+ 16735679449896*(r[4][i] + r[-4][i])
- 11541847896480*(r[5][i] + r[-5][i])
+ 7309837001104*(r[6][i] + r[-6][i])
- 4244421484512*(r[7][i] + r[-7][i])
+ 2254848913647*(r[8][i] + r[-8][i])
- 1093260079344*(r[9][i] + r[-9][i])
+ 482320623240*(r[10][i] + r[-10][i])
- 192928249296*(r[11][i] + r[-11][i])
+ 69668534468*(r[12][i] + r[-12][i])
- 22595200368*(r[13][i] + r[-13][i])
+ 6540715896*(r[14][i] + r[-14][i])
- 1677106640*(r[15][i] + r[-15][i])
+ 377348994*(r[16][i] + r[-16][i])
- 73629072*(r[17][i] + r[-17][i])
+ 12271512*(r[18][i] + r[-18][i])
- 1712304*(r[19][i] + r[-19][i])
+ 194580*(r[20][i] + r[-20][i])
- 17296*(r[21][i] + r[-21][i])
+ 1128*(r[22][i] + r[-22][i])
- 48*(r[23][i] + r[-23][i])
+ (r[24][i] + r[-24][i])
+ 32247603683100*r0[i]
- 60828186403426756087225216332129537688755283137921024000000000000*r50[i]
- 159972047422372025833793596431867471167657519124418501017600000000000*r52[i]
- 300157876302214652121781965684412846831829138854612706525184000000000000*r54[i]
- 450770518363896572159998540193680817546151655952668840885537996800000000000*r56[i]
- 576444828163444989826951966515975912046442589126900517541190303744000000000000*r58[i]
) // 12413915592536072670862289047373375038521486354677760000000000 for i in range(len(r0))]
r46 = [(7890371113950*(r[1][i] + r[-1][i])
- 6943526580276*(r[2][i] + r[-2][i])
+ 5608233007146*(r[3][i] + r[-3][i])
- 4154246671960*(r[4][i] + r[-4][i])
+ 2818953098830*(r[5][i] + r[-5][i])
- 1749695026860*(r[6][i] + r[-6][i])
+ 991493848554*(r[7][i] + r[-7][i])
- 511738760544*(r[8][i] + r[-8][i])
+ 239877544005*(r[9][i] + r[-9][i])
- 101766230790*(r[10][i] + r[-10][i])
+ 38910617655*(r[11][i] + r[-11][i])
- 13340783196*(r[12][i] + r[-12][i])
+ 4076350421*(r[13][i] + r[-13][i])
- 1101716330*(r[14][i] + r[-14][i])
+ 260932815*(r[15][i] + r[-15][i])
- 53524680*(r[16][i] + r[-16][i])
+ 9366819*(r[17][i] + r[-17][i])
- 1370754*(r[18][i] + r[-18][i])
+ 163185*(r[19][i] + r[-19][i])
- 15180*(r[20][i] + r[-20][i])
+ 1035*(r[21][i] + r[-21][i])
- 46*(r[22][i] + r[-22][i])
+ (r[23][i] + r[-23][i])
- 8233430727600*r0[i]
- 23793338219027472619152720674132302157166182179799040000000000*r48[i]
- 55378994704786442521077957369042933270804289023482265600000000000*r50[i]
- 92204777033212927855282293501621091950025889999533532774400000000000*r52[i]
- 123173573410381619032735872322455238373678223392026561137868800000000000*r54[i]
- 140425979426347767846982627377843865753483703589611376414503731200000000000*r56[i]
- 141951429591499493633341525565101471008477060402864452853025682227200000000000*r58[i]
) // 5502622159812088949850305428800254892961651752960000000000 for i in range(len(r0))]
r44 = [(-2012616400080*(r[1][i] + r[-1][i])
+ 1761039350070*(r[2][i] + r[-2][i])
- 1408831480056*(r[3][i] + r[-3][i])
+ 1029530696964*(r[4][i] + r[-4][i])
- 686353797976*(r[5][i] + r[-5][i])
+ 416714805914*(r[6][i] + r[-6][i])
- 229911617056*(r[7][i] + r[-7][i])
+ 114955808528*(r[8][i] + r[-8][i])
- 51915526432*(r[9][i] + r[-9][i])
+ 21090682613*(r[10][i] + r[-10][i])
- 7669339132*(r[11][i] + r[-11][i])
+ 2481256778*(r[12][i] + r[-12][i])
- 708930508*(r[13][i] + r[-13][i])
+ 177232627*(r[14][i] + r[-14][i])
- 38320568*(r[15][i] + r[-15][i])
+ 7059052*(r[16][i] + r[-16][i])
- 1086008*(r[17][i] + r[-17][i])
+ 135751*(r[18][i] + r[-18][i])
- 13244*(r[19][i] + r[-19][i])
+ 946*(r[20][i] + r[-20][i])
- 44*(r[21][i] + r[-21][i])
+ (r[22][i] + r[-22][i])
+ 2104098963720*r0[i]
- 10088140626322163074725559952800467303763028213760000000000*r46[i]
- 20672617771459376572727617455278717598871197415636992000000000*r48[i]
- 30390960789555990223010654132076029106169285558507929600000000000*r50[i]
- 35940698724546850336855815971061681513098805595301121884160000000000*r52[i]
- 36360946421379657670852826531045915291694648992864408489164800000000000*r54[i]
- 32688930664232620503520635595276360398494773528483108565098168320000000000*r56[i]
- 26790800094855758698435498859006506927253786268785824141772272435200000000000*r58[i]
) // 2658271574788448768043625811014615890319638528000000000 for i in range(len(r0))]
r42 = [(513791607420*(r[1][i] + r[-1][i])
- 446775310800*(r[2][i] + r[-2][i])
+ 353697121050*(r[3][i] + r[-3][i])
- 254661927156*(r[4][i] + r[-4][i])
+ 166509721602*(r[5][i] + r[-5][i])
- 98672427616*(r[6][i] + r[-6][i])
+ 52860229080*(r[7][i] + r[-7][i])
- 25518731280*(r[8][i] + r[-8][i])
+ 11058116888*(r[9][i] + r[-9][i])
- 4280561376*(r[10][i] + r[-10][i])
+ 1471442973*(r[11][i] + r[-11][i])
- 445891810*(r[12][i] + r[-12][i])
+ 118030185*(r[13][i] + r[-13][i])
- 26978328*(r[14][i] + r[-14][i])
+ 5245786*(r[15][i] + r[-15][i])
- 850668*(r[16][i] + r[-16][i])
+ 111930*(r[17][i] + r[-17][i])
- 11480*(r[18][i] + r[-18][i])
+ 861*(r[19][i] + r[-19][i])
- 42*(r[20][i] + r[-20][i])
+ (r[21][i] + r[-21][i])
- 538257874440*r0[i]
- 4651975255879785344076345169275577808059367424000000000*r44[i]
- 8345643609048334907272963233680386587658505158656000000000*r46[i]
- 10774531600512501036897720551649645765494516918255616000000000*r48[i]
- 11221709145032637985686395016457126546359868596714209280000000000*r50[i]
- 10024126976056544454447469133748446849553291271003522990080000000000*r52[i]
- 7975810040319696718196547333113180442555266076076498338447360000000000*r54[i]
- 5797757744908652417934202553325977005487481966701902535023656960000000000*r56[i]
- 3920357979117550887691809955593394536428299176498291825228990382080000000000*r58[i]
) // 1405006117752879898543142606244511569936384000000000 for i in range(len(r0))]
r40 = [(-131282408400*(r[1][i] + r[-1][i])
+ 113380261800*(r[2][i] + r[-2][i])
- 88732378800*(r[3][i] + r[-3][i])
+ 62852101650*(r[4][i] + r[-4][i])
- 40225345056*(r[5][i] + r[-5][i])
+ 23206929840*(r[6][i] + r[-6][i])
- 12033222880*(r[7][i] + r[-7][i])
+ 5586853480*(r[8][i] + r[-8][i])
- 2311801440*(r[9][i] + r[-9][i])
+ 847660528*(r[10][i] + r[-10][i])
- 273438880*(r[11][i] + r[-11][i])
+ 76904685*(r[12][i] + r[-12][i])
- 18643560*(r[13][i] + r[-13][i])
+ 3838380*(r[14][i] + r[-14][i])
- 658008*(r[15][i] + r[-15][i])
+ 91390*(r[16][i] + r[-16][i])
- 9880*(r[17][i] + r[-17][i])
+ 780*(r[18][i] + r[-18][i])
- 40*(r[19][i] + r[-19][i])
+ (r[20][i] + r[-20][i])
+ 137846528820*r0[i]
- 2341676862921466497571904343740852616560640000000000*r42[i]
- 3655123415334117056059985490145096849189502976000000000*r44[i]
- 4119688019118574531237133429498603530973935042560000000000*r46[i]
- 3757340713824985498498548346794211825654347639816192000000000*r48[i]
- 2947359606908914693821004025256012800585708025466060800000000000*r50[i]
- 2064558678210662377343329526788684890767865636215995760640000000000*r52[i]
- 1324288918192605206277308466563916626202444615070944696729600000000000*r54[i]
- 791839032295490808003964360962043366439210005332609063463157760000000000*r56[i]
- 447196399146488090711611190566605254693970676118785957909286092800000000000*r58[i]
) // 815915283247897734345611269596115894272000000000 for i in range(len(r0))]
r38 = [(33578000610*(r[1][i] + r[-1][i])
- 28781143380*(r[2][i] + r[-2][i])
+ 22239974430*(r[3][i] + r[-3][i])
- 15471286560*(r[4][i] + r[-4][i])
+ 9669554100*(r[5][i] + r[-5][i])
- 5414950296*(r[6][i] + r[-6][i])
+ 2707475148*(r[7][i] + r[-7][i])
- 1203322288*(r[8][i] + r[-8][i])
+ 472733756*(r[9][i] + r[-9][i])
- 163011640*(r[10][i] + r[-10][i])
+ 48903492*(r[11][i] + r[-11][i])
- 12620256*(r[12][i] + r[-12][i])
+ 2760681*(r[13][i] + r[-13][i])
- 501942*(r[14][i] + r[-14][i])
+ 73815*(r[15][i] + r[-15][i])
- 8436*(r[16][i] + r[-16][i])
+ 703*(r[17][i] + r[-17][i])
- 38*(r[18][i] + r[-18][i])
+ (r[19][i] + r[-19][i])
- 35345263800*r0[i]
- 1291865865142504746047217843527183499264000000000*r40[i]
- 1742597865490724651943092149133817822157209600000000*r42[i]
- 1703614521144184428726371303487541532883419136000000000*r44[i]
- 1352221478318945952566471137817160521323572835123200000000*r46[i]
- 925912385499308009244605568293800045079467288166400000000000*r48[i]
- 567701817594292628086492254286076775983065657711263744000000000*r50[i]
- 319529132633551445730754266569514531984165615759324610560000000000*r52[i]
- 168027862191313285572462163036203023050148820066814862032896000000000*r54[i]
- 83628709120699850967965029603710197511722226913937392643604480000000000*r56[i]
- 39783026532200589585805406140346452284930851510666932752692438630400000000*r58[i]
) // 523022617466601111760007224100074291200000000 for i in range(len(r0))]
r36 = [(-8597496600*(r[1][i] + r[-1][i])
+ 7307872110*(r[2][i] + r[-2][i])
- 5567902560*(r[3][i] + r[-3][i])
+ 3796297200*(r[4][i] + r[-4][i])
- 2310789600*(r[5][i] + r[-5][i])
+ 1251677700*(r[6][i] + r[-6][i])
- 600805296*(r[7][i] + r[-7][i])
+ 254186856*(r[8][i] + r[-8][i])
- 94143280*(r[9][i] + r[-9][i])
+ 30260340*(r[10][i] + r[-10][i])
- 8347680*(r[11][i] + r[-11][i])
+ 1947792*(r[12][i] + r[-12][i])
- 376992*(r[13][i] + r[-13][i])
+ 58905*(r[14][i] + r[-14][i])
- 7140*(r[15][i] + r[-15][i])
+ 630*(r[16][i] + r[-16][i])
- 36*(r[17][i] + r[-17][i])
+ (r[18][i] + r[-18][i])
+ 9075135300*r0[i]
- 784533926199901667640010836150111436800000000*r38[i]
- 907705752613286229459492537425678932377600000000*r40[i]
- 764250847583238143225401875995898505750118400000000*r42[i]
- 524336156604477506256224109002957345627779891200000000*r44[i]
- 311351658482338919180732210200430367625645444300800000000*r46[i]
- 166036590632320367531429334375544068072103816986624000000000*r48[i]
- 81499841025612949496109930847966440863640763389444096000000000*r50[i]
- 37466461814083366759359795735852259604455926584422957056000000000*r52[i]
- 16337589523211774449719906648393247646243600903141698043904000000000*r54[i]
- 6822946329749604115483663195879851339401939967806211954730598400000000*r56[i]
- 2749354418817753028037594157537886830685519147649233697904368025600000000*r58[i]
) // 371993326789901217467999448150835200000000 for i in range(len(r0))]
r34 = [(2203961430*(r[1][i] + r[-1][i])
- 1855967520*(r[2][i] + r[-2][i])
+ 1391975640*(r[3][i] + r[-3][i])
- 927983760*(r[4][i] + r[-4][i])
+ 548354040*(r[5][i] + r[-5][i])
- 286097760*(r[6][i] + r[-6][i])
+ 131128140*(r[7][i] + r[-7][i])
- 52451256*(r[8][i] + r[-8][i])
+ 18156204*(r[9][i] + r[-9][i])
- 5379616*(r[10][i] + r[-10][i])
+ 1344904*(r[11][i] + r[-11][i])
- 278256*(r[12][i] + r[-12][i])
+ 46376*(r[13][i] + r[-13][i])
- 5984*(r[14][i] + r[-14][i])
+ 561*(r[15][i] + r[-15][i])
- 34*(r[16][i] + r[-16][i])
+ (r[17][i] + r[-17][i])
- 2333606220*r0[i]
- 526990546285693391412999218213683200000000*r36[i]
- 518664095654379435828673830565907005440000000*r38[i]
- 373138241060740797524227217357125818777600000000*r40[i]
- 219618160307546307818407858079592245845032960000000*r42[i]
- 112275193446419212026758411812279514001781555200000000*r44[i]
- 51713216892097268029263570056035419810630708756480000000*r46[i]
- 21987290206937420965021290881182668895459624353792000000000*r48[i]
- 8778185176019659621127125508818359337012951782732595200000000*r50[i]
- 3332107853530764777529629230140567884444349753800523776000000000*r52[i]
- 1213942320816658090297153525238443731761121646974842689290240000000*r54[i]
- 427555403157842297318164509581599203745468728634937321088614400000000*r56[i]
- 146412888563076929935007013793883329507786976091953474012530606080000000*r58[i]
) // 295232799039604140847618609643520000000 for i in range(len(r0))]
r32 = [(-565722720*(r[1][i] + r[-1][i])
+ 471435600*(r[2][i] + r[-2][i])
- 347373600*(r[3][i] + r[-3][i])
+ 225792840*(r[4][i] + r[-4][i])
- 129024480*(r[5][i] + r[-5][i])
+ 64512240*(r[6][i] + r[-6][i])
- 28048800*(r[7][i] + r[-7][i])
+ 10518300*(r[8][i] + r[-8][i])
- 3365856*(r[9][i] + r[-9][i])
+ 906192*(r[10][i] + r[-10][i])
- 201376*(r[11][i] + r[-11][i])
+ 35960*(r[12][i] + r[-12][i])
- 4960*(r[13][i] + r[-13][i])
+ 496*(r[14][i] + r[-14][i])
- 32*(r[15][i] + r[-15][i])
+ (r[16][i] + r[-16][i])
+ 601080390*r0[i]
- 393643732052805521130158146191360000000*r34[i]
- 326527475737802179777466182265733120000000*r36[i]
- 198969979872214920293886346099446251520000000*r38[i]
- 99626745669333527035567016277524852244480000000*r40[i]
- 43498703313314018776504938348732045412270080000000*r42[i]
- 17170843124850370546818528558187736420780605440000000*r44[i]
- 6276444318289938061108840583768656479667869450240000000*r46[i]
- 2160301520690503531404610021529918026938609932697600000000*r48[i]
- 708745398984922590930383206855670263857046959528345600000000*r50[i]
- 223674822768508974680116468563119084809897119542327377920000000*r52[i]
- 68383308771682806793482300167280717706332061193589825208320000000*r54[i]
- 20364863681337349385077959469519750111717035219658278269091840000000*r56[i]
- 5933532628684897882400324618377943451626121416158999218896240640000000*r58[i]
) // 263130836933693530167218012160000000 for i in range(len(r0))]
r30 = [(145422675*(r[1][i] + r[-1][i])
- 119759850*(r[2][i] + r[-2][i])
+ 86493225*(r[3][i] + r[-3][i])
- 54627300*(r[4][i] + r[-4][i])
+ 30045015*(r[5][i] + r[-5][i])
- 14307150*(r[6][i] + r[-6][i])
+ 5852925*(r[7][i] + r[-7][i])
- 2035800*(r[8][i] + r[-8][i])
+ 593775*(r[9][i] + r[-9][i])
- 142506*(r[10][i] + r[-10][i])
+ 27405*(r[11][i] + r[-11][i])
- 4060*(r[12][i] + r[-12][i])
+ 435*(r[13][i] + r[-13][i])
- 30*(r[14][i] + r[-14][i])
+ (r[15][i] + r[-15][i])
- 155117520*r0[i]
- 328913546167116912709022515200000000*r32[i]
- 227575282593028191903372678266880000000*r34[i]
- 116309421454977381321426414757478400000000*r36[i]
- 49083095586740430887431564189583278080000000*r38[i]
- 18139371393109511951007844941215406489600000000*r40[i]
- 6083845843389094496001274537210012898426880000000*r42[i]
- 1895875482185729033390420637976407213657292800000000*r44[i]
- 557995741137378415081398016214860854983503380480000000*r46[i]
- 156963921056606539204438549741946823549156065280000000000*r48[i]
- 42576613536662088106792709282326106111384171273256960000000*r50[i]
- 11212252160226319834044842958792572575603224385840742400000000*r52[i]
- 2881790963494506901155736518846659656145189066632341749760000000*r54[i]
- 725935006313040765947950598972668773212258467667822562508800000000*r56[i]
- 179827110454616286939608454377851070360156877287086934363996160000000*r58[i]
) // 265252859812191058636308480000000 for i in range(len(r0))]
r28 = [(-37442160*(r[1][i] + r[-1][i])
+ 30421755*(r[2][i] + r[-2][i])
- 21474180*(r[3][i] + r[-3][i])
+ 13123110*(r[4][i] + r[-4][i])
- 6906900*(r[5][i] + r[-5][i])
+ 3108105*(r[6][i] + r[-6][i])
- 1184040*(r[7][i] + r[-7][i])
+ 376740*(r[8][i] + r[-8][i])
- 98280*(r[9][i] + r[-9][i])
+ 20475*(r[10][i] + r[-10][i])
- 3276*(r[11][i] + r[-11][i])
+ 378*(r[12][i] + r[-12][i])
- 28*(r[13][i] + r[-13][i])
+ (r[14][i] + r[-14][i])
+ 40116600*r0[i]
- 309461669780889568409026560000000*r30[i]
- 176516936443019409820508749824000000*r32[i]
- 74833313645455216256514439249920000000*r34[i]
- 26337328459046574816219104447299584000000*r36[i]
- 8155948144934385059006601147769159680000000*r38[i]
- 2301709517171786559798286695904076365824000000*r40[i]
- 605758813130095139988659617361096909783040000000*r42[i]
- 151061790397229175366153301919734749322543104000000*r44[i]
- 36109056667467121621981604705290955376859545600000000*r46[i]
- 8344518734397260673326477690101230819337996075008000000*r48[i]
- 1876453005146379321858026862378389310967569941790720000000*r50[i]
- 412683020050097630454766497837161869694785723928936448000000*r52[i]
- 89117286812387026652769979577207299516771181236259389440000000*r54[i]
- 18956016131243809886574217941379995847584738002099836551168000000*r56[i]
- 3981781582023940453552878808654750471972128020394902248488960000000*r58[i]
) // 304888344611713860501504000000 for i in range(len(r0))]
r26 = [(9657700*(r[1][i] + r[-1][i])
- 7726160*(r[2][i] + r[-2][i])
+ 5311735*(r[3][i] + r[-3][i])
- 3124550*(r[4][i] + r[-4][i])
+ 1562275*(r[5][i] + r[-5][i])
- 657800*(r[6][i] + r[-6][i])
+ 230230*(r[7][i] + r[-7][i])
- 65780*(r[8][i] + r[-8][i])
+ 14950*(r[9][i] + r[-9][i])
- 2600*(r[10][i] + r[-10][i])
+ 325*(r[11][i] + r[-11][i])
- 26*(r[12][i] + r[-12][i])
+ (r[13][i] + r[-13][i])
- 10400600*r0[i]
- 330295706662690015543296000000*r28[i]
- 153257207891488167212089344000000*r30[i]
- 53222214421459539592188788736000000*r32[i]
- 15436506593303376230082373484544000000*r34[i]
- 3960094929842931739454572322881536000000*r36[i]
- 930084233815670751630942950980583424000000*r38[i]
- 204528766884160018873274371645367648256000000*r40[i]
- 42768601883241439058698435075343591276544000000*r42[i]
- 8599134589431485780708409429924529774657536000000*r44[i]
- 1676115909489027560076829587121962388192493568000000*r46[i]
- 318686948683222526304282057035116495208098824192000000*r48[i]
- 59389194499215983294435493136240165006801607589888000000*r50[i]
- 10888114924031601962481145504131710392319020299190272000000*r52[i]
- 1969613645523746908242462889216091458065590581736767488000000*r54[i]
- 352384153836182163735889010772845616197776947067902492672000000*r56[i]
- 62471824663590669280579714493247557511996439285855834472448000000*r58[i]
) // 403291461126605635584000000 for i in range(len(r0))]
r24 = [(-2496144*(r[1][i] + r[-1][i])
+ 1961256*(r[2][i] + r[-2][i])
- 1307504*(r[3][i] + r[-3][i])
+ 735471*(r[4][i] + r[-4][i])
- 346104*(r[5][i] + r[-5][i])
+ 134596*(r[6][i] + r[-6][i])
- 42504*(r[7][i] + r[-7][i])
+ 10626*(r[8][i] + r[-8][i])
- 2024*(r[9][i] + r[-9][i])
+ 276*(r[10][i] + r[-10][i])
- 24*(r[11][i] + r[-11][i])
+ (r[12][i] + r[-12][i])
+ 2704156*r0[i]
- 403291461126605635584000000*r26[i]
- 149903436100759314746572800000*r28[i]
- 42033455827381598974377984000000*r30[i]
- 9910695932425713906157643366400000*r32[i]
- 2078962023961017163954848006144000000*r34[i]
- 401274139495715827174031120636313600000*r36[i]
- 72837740568171787457915404507152384000000*r38[i]
- 12620369661259070567869332718886859571200000*r40[i]
- 2109601340251819353520575234140712075264000000*r42[i]
- 342864867500163789441705220714949009654415360000*r44[i]
- 54497476891656721001996702786930540928565248000000*r46[i]
- 8509384879617502075402808457393042025589086617600000*r48[i]
- 1309755467175539670340841790934034624876228640768000000*r50[i]
- 199264959019086425512537383104357541174886386420940800000*r52[i]
- 30029919604106055758327357685117168899526367314444288000000*r54[i]
- 4490619485039820937253033342517920576264823432892789555200000*r56[i]
- 667248962933104781692033726981247168122667743684764499968000000*r58[i]
) // 620448401733239439360000 for i in range(len(r0))]
r22 = [(646646*(r[1][i] + r[-1][i])
- 497420*(r[2][i] + r[-2][i])
+ 319770*(r[3][i] + r[-3][i])
- 170544*(r[4][i] + r[-4][i])
+ 74613*(r[5][i] + r[-5][i])
- 26334*(r[6][i] + r[-6][i])
+ 7315*(r[7][i] + r[-7][i])
- 1540*(r[8][i] + r[-8][i])
+ 231*(r[9][i] + r[-9][i])
- 22*(r[10][i] + r[-10][i])
+ (r[11][i] + r[-11][i])
- 705432*r0[i]
- 568744368255469486080000*r24[i]
- 166357727714724824678400000*r26[i]
- 37042320704478727628390400000*r28[i]
- 6988909951599209517839155200000*r30[i]
- 1180836611760352104108962611200000*r32[i]
- 184607985589364774573429361868800000*r34[i]
- 27272218262298384682708194086092800000*r36[i]
- 3861838803337560097698395778726297600000*r38[i]
- 529471212011799260411940801849645465600000*r40[i]
- 70801221927358337925257947461388534087680000*r42[i]
- 9284304296436839352157882253583122352046080000*r44[i]
- 1198819215976330165063918942164935021513932800000*r46[i]
- 152905877736629296164560458459124226796014796800000*r48[i]
- 19311905336609987288869864510609701436067866214400000*r50[i]
- 2419865045937700153119519054510295236128129836646400000*r52[i]
- 301288155885052369662851151922188867269975615240601600000*r54[i]
- 37318400520598852767385734888888777428502118384425369600000*r56[i]
- 4602930387150050300189793405799937182582433565253538611200000*r58[i]
) // 1124000727777607680000 for i in range(len(r0))]
r20 = [(-167960*(r[1][i] + r[-1][i])
+ 125970*(r[2][i] + r[-2][i])
- 77520*(r[3][i] + r[-3][i])
+ 38760*(r[4][i] + r[-4][i])
- 15504*(r[5][i] + r[-5][i])
+ 4845*(r[6][i] + r[-6][i])
- 1140*(r[7][i] + r[-7][i])
+ 190*(r[8][i] + r[-8][i])
- 20*(r[9][i] + r[-9][i])
+ (r[10][i] + r[-10][i])
+ 184756*r0[i]
- 936667273148006400000*r22[i]
- 211124803367560642560000*r24[i]
- 36608302274885332992000000*r26[i]
- 5425950533240873322086400000*r28[i]
- 725494605231272191451136000000*r30[i]
- 90317652741043657957240012800000*r32[i]
- 10681064948020015063470219264000000*r34[i]
- 1216234618180639720975550420582400000*r36[i]
- 134607612138429628983625351999488000000*r38[i]
- 14578366393789236829898507440652451840000*r40[i]
- 1552719574083291045891061928041363046400000*r42[i]
- 163243281617906068079686557318998305013760000*r44[i]
- 16988641998903346735554689301227465785344000000*r46[i]
- 1753883399302689292116989257696255397727436800000*r48[i]
- 179923160623142188671570235338790827627528192000000*r50[i]
- 18364686854092318474868714992301176836519274905600000*r52[i]
- 1866955970795489260131483779878624434707941429248000000*r54[i]
- 189185983025084665229695853342846566523110910688460800000*r56[i]
- 19121663073074862096824580535309387512324977430982656000000*r58[i]
) // 2432902008176640000 for i in range(len(r0))]
r18 = [(43758*(r[1][i] + r[-1][i])
- 31824*(r[2][i] + r[-2][i])
+ 18564*(r[3][i] + r[-3][i])
- 8568*(r[4][i] + r[-4][i])
+ 3060*(r[5][i] + r[-5][i])
- 816*(r[6][i] + r[-6][i])
+ 153*(r[7][i] + r[-7][i])
- 18*(r[8][i] + r[-8][i])
+ (r[9][i] + r[-9][i])
- 48620*r0[i]
- 1824676506132480000*r20[i]
- 309100200138842112000*r22[i]
- 40778478784550707200000*r24[i]
- 4645053436190368481280000*r26[i]
- 481314610282065419059200000*r28[i]
- 46758400573464312663490560000*r30[i]
- 4340262299778024388805836800000*r32[i]
- 389810850996416354285601300480000*r34[i]
- 34168816632541202331763973529600000*r36[i]
- 2941066263016510346147295370272768000*r38[i]
- 249691933432545691845292589410836480000*r40[i]
- 20977168972570956554158853986478948352000*r42[i]
- 1748194308191420862068509392967461273600000*r44[i]
- 144787366874617417267158756772391629455360000*r46[i]
- 11933738665455945947029762024119178565222400000*r48[i]
- 979923136258156862399188048479194930964357120000*r50[i]
- 80229698384887928012137580653965134357931417600000*r52[i]
- 6553647225094050569861777249958218558728336220160000*r54[i]
- 534380975174725194355250529012449631615490426675200000*r56[i]
- 43511766276795099760702891803080853785686045209182208000*r58[i]
) // 6402373705728000 for i in range(len(r0))]
r16 = [(-11440*(r[1][i] + r[-1][i])
+ 8008*(r[2][i] + r[-2][i])
- 4368*(r[3][i] + r[-3][i])
+ 1820*(r[4][i] + r[-4][i])
- 560*(r[5][i] + r[-5][i])
+ 120*(r[6][i] + r[-6][i])
- 16*(r[7][i] + r[-7][i])
+ (r[8][i] + r[-8][i])
+ 12870*r0[i]
- 4268249137152000*r18[i]
- 527128768438272000*r20[i]
- 51442361350668288000*r22[i]
- 4385609982489415680000*r24[i]
- 343350594609952849920000*r26[i]
- 25398422028160175554560000*r28[i]
- 1806640043553643996938240000*r30[i]
- 124998708216981630040289280000*r32[i]
- 8477574188991756975915909120000*r34[i]
- 566640901244029272138606256128000*r36[i]
- 37469170353622071265887792218112000*r38[i]
- 2457916223969789263693314523533312000*r40[i]
- 160273272592069873142621634191720448000*r42[i]
- 10404012781412834769965673013161000960000*r44[i]
- 673078263437696563365695181553779671040000*r46[i]
- 43432367177206668920840929822030938501120000*r48[i]
- 2797138392082425352298525252125310293524480000*r50[i]
- 179874692542903270845206591460923776914677760000*r52[i]
- 11554084778127771883812326032137020779396055040000*r54[i]
- 741527083798558882116336447949129492912812576768000*r56[i]
- 47559042059279191608774394913418690656775961116672000*r58[i]
) // 20922789888000 for i in range(len(r0))]
r14 = [(3003*(r[1][i] + r[-1][i])
- 2002*(r[2][i] + r[-2][i])
+ 1001*(r[3][i] + r[-3][i])
- 364*(r[4][i] + r[-4][i])
+ 91*(r[5][i] + r[-5][i])
- 14*(r[6][i] + r[-6][i])
+ (r[7][i] + r[-7][i])
- 3432*r0[i]
- 12204960768000*r16[i]
- 1058170098585600*r18[i]
- 73775500710912000*r20[i]
- 4555411900194355200*r22[i]
- 261131482210959360000*r24[i]
- 14266599888013304832000*r26[i]
- 754754307297469839360000*r28[i]
- 39057272623118392651008000*r30[i]
- 1990236929603886055572480000*r32[i]
- 100317304785653440333283635200*r34[i]
- 5017302808350824370904132608000*r36[i]
- 249538838908236261152065923225600*r38[i]
- 12360976075014001109372936189952000*r40[i]
- 610513898001512036824535103712051200*r42[i]
- 30089355946979742032883786297815040000*r44[i]
- 1480659654975370272651825844120998144000*r46[i]
- 72778719754993922352940597980542622720000*r48[i]
- 3574314373450201242087397187099658871296000*r50[i]
- 175435230758177290496267410991246070236160000*r52[i]
- 8606908326589506468114924551500679297771059200*r54[i]
- 422119567380929805536926019476679626483150848000*r56[i]
- 20697579606319013871427291841344915696563086745600*r58[i]
) // 87178291200 for i in range(len(r0))]
r12 = [(-792*(r[1][i] + r[-1][i])
+ 495*(r[2][i] + r[-2][i])
- 220*(r[3][i] + r[-3][i])
+ 66*(r[4][i] + r[-4][i])
- 12*(r[5][i] + r[-5][i])
+ (r[6][i] + r[-6][i])
+ 924*r0[i]
- 43589145600*r14[i]
- 2528170444800*r16[i]
- 120467944396800*r18[i]
- 5167100908569600*r20[i]
- 208331313744153600*r22[i]
- 8083281646573056000*r24[i]
- 305994026290208256000*r26[i]
- 11397316294188849024000*r28[i]
- 419948192698268217984000*r30[i]
- 15360962830016613243033600*r32[i]
- 559092713482449420732057600*r34[i]
- 20280226917834433943755084800*r36[i]
- 733917409397935785284098636800*r38[i]
- 26516869922120782776160606617600*r40[i]
- 957005191789297958689924263321600*r42[i]
- 34512162491005016706155579824512000*r44[i]
- 1243937698905379082423800102273152000*r46[i]
- 44819260744500257106087286005881088000*r48[i]
- 1614431094051811175741477051443876608000*r50[i]
- 58142963949556229658359411701218990105600*r52[i]
- 2093732846395541754366573918386488419609600*r54[i]
- 75389036557436264384158719712164829058764800*r56[i]
- 2714371675958174330325986851026496482637516800*r58[i]
) // 479001600 for i in range(len(r0))]
r10 = [(210*(r[1][i] + r[-1][i])
- 120*(r[2][i] + r[-2][i])
+ 45*(r[3][i] + r[-3][i])
- 10*(r[4][i] + r[-4][i])
+ (r[5][i] + r[-5][i])
- 252*r0[i]
- 199584000*r12[i]
- 7264857600*r14[i]
- 223134912000*r16[i]
- 6289809926400*r18[i]
- 169058189664000*r20[i]
- 4419351149875200*r22[i]
- 113605204648320000*r24[i]
- 2890388998040544000*r26[i]
- 73066712935376160000*r28[i]
- 1839605249083010572800*r30[i]
- 46197360620085939264000*r32[i]
- 1158251761107990889401600*r34[i]
- 29009396635576994764512000*r36[i]
- 726084725720412923735270400*r38[i]
- 18165716613255899607139584000*r40[i]
- 454360504471895403926563219200*r42[i]
- 11362494160594553046963852960000*r44[i]
- 284118059898561657806684273088000*r46[i]
- 7103842801529696381323903273920000*r48[i]
- 177610330992631300501801888177516800*r50[i]
- 4440486450890050497235584413672544000*r52[i]
- 111015812096675961833777653418529945600*r54[i]
- 2775453715672821941461677186080579712000*r56[i]
- 69387277504501464214318836241717452614400*r58[i]
) // 3628800 for i in range(len(r0))]
r8 = [(-56*(r[1][i] + r[-1][i])
+ 28*(r[2][i] + r[-2][i])
- 8*(r[3][i] + r[-3][i])
+ (r[4][i] + r[-4][i])
+ 70*r0[i]
- 1209600*r10[i]
- 25280640*r12[i]
- 461260800*r14[i]
- 7904856960*r16[i]
- 131254905600*r18[i]
- 2143293425280*r20[i]
- 34682510016000*r22[i]
- 558432020361600*r24[i]
- 8966533159584000*r26[i]
- 143749174428961920*r28[i]
- 2302548811229721600*r30[i]
- 36863840064915642240*r32[i]
- 590028976413583660800*r34[i]
- 9442331455422829138560*r36[i]
- 151094113839739041753600*r38[i]
- 2417657116643486089706880*r40[i]
- 38683875524088319997472000*r42[i]
- 618954263309240362088323200*r44[i]
- 9903378507277068408849408000*r46[i]
- 158455048765455207825625883520*r48[i]
- 2535289714088718783746769273600*r50[i]
- 40564715829993365422700852403840*r52[i]
- 649036176921062413731673525900800*r54[i]
- 10384585343507530854517663366220160*r56[i]
- 166153424111055344313959588285241600*r58[i]
) // 40320 for i in range(len(r0))]
r6 = [(15*(r[1][i] + r[-1][i])
- 6*(r[2][i] + r[-2][i])
+ (r[3][i] + r[-3][i])
- 20*r0[i]
- 10080*r8[i]
- 105840*r10[i]
- 1013760*r12[i]
- 9369360*r14[i]
- 85307040*r16[i]
- 771695280*r18[i]
- 6960985920*r20[i]
- 62711787600*r22[i]
- 564657746400*r24[i]
- 5082926350320*r26[i]
- 45750363684480*r28[i]
- 411769379287440*r30[i]
- 3705988838096160*r32[i]
- 33354157240902960*r34[i]
- 300188445960277440*r36[i]
- 2701700136811100880*r38[i]
- 24315317723974324320*r40[i]
- 218837925486466585200*r42[i]
- 1969541593260989932800*r44[i]
- 17725875394880072059920*r46[i]
- 159532882776045299198880*r48[i]
- 1435795961872906295429040*r50[i]
- 12922163724410151069418560*r52[i]
- 116299473789907337266996560*r54[i]
- 1046695265190029945971887840*r56[i]
- 9420257391033725156022666480*r58[i]
) // 720 for i in range(len(r0))]
r4 = [(-4*(r[1][i] + r[-1][i])
+ (r[2][i] + r[-2][i])
+ 6*r0[i]
- 120*r6[i]
- 504*r8[i]
- 2040*r10[i]
- 8184*r12[i]
- 32760*r14[i]
- 131064*r16[i]
- 524280*r18[i]
- 2097144*r20[i]
- 8388600*r22[i]
- 33554424*r24[i]
- 134217720*r26[i]
- 536870904*r28[i]
- 2147483640*r30[i]
- 8589934584*r32[i]
- 34359738360*r34[i]
- 137438953464*r36[i]
- 549755813880*r38[i]
- 2199023255544*r40[i]
- 8796093022200*r42[i]
- 35184372088824*r44[i]
- 140737488355320*r46[i]
- 562949953421304*r48[i]
- 2251799813685240*r50[i]
- 9007199254740984*r52[i]
- 36028797018963960*r54[i]
- 144115188075855864*r56[i]
- 576460752303423480*r58[i]
) // 24 for i in range(len(r0))]
r2 = [((r[1][i] + r[-1][i])
- 2*r0[i]
- 2*r4[i]
- 2*r6[i]
- 2*r8[i]
- 2*r10[i]
- 2*r12[i]
- 2*r14[i]
- 2*r16[i]
- 2*r18[i]
- 2*r20[i]
- 2*r22[i]
- 2*r24[i]
- 2*r26[i]
- 2*r28[i]
- 2*r30[i]
- 2*r32[i]
- 2*r34[i]
- 2*r36[i]
- 2*r38[i]
- 2*r40[i]
- 2*r42[i]
- 2*r44[i]
- 2*r46[i]
- 2*r48[i]
- 2*r50[i]
- 2*r52[i]
- 2*r54[i]
- 2*r56[i]
- 2*r58[i]
) // 2 for i in range(len(r0))]
r57 = [(1002242216651368*r[1][i]
- 1810502068789568*r[2][i]
+ 2291416680811797*r[3][i]
- 2407144796004312*r[4][i]
+ 2212449261033375*r[5][i]
- 1820529677650320*r[6][i]
+ 1356968880100470*r[7][i]
- 922110127018080*r[8][i]
+ 573285572389530*r[9][i]
- 326658445806000*r[10][i]
+ 170679037933635*r[11][i]
- 81744284243160*r[12][i]
+ 35844219876465*r[13][i]
- 14363336766240*r[14][i]
+ 5246348656500*r[15][i]
- 1741010517120*r[16][i]
+ 522776255820*r[17][i]
- 141326246880*r[18][i]
+ 34186557405*r[19][i]
- 7344051000*r[20][i]
+ 1388025639*r[21][i]
- 228097584*r[22][i]
+ 32101146*r[23][i]
- 3792096*r[24][i]
+ 365750*r[25][i]
- 27664*r[26][i]
+ 1539*r[27][i]
- 56*r[28][i]
+ r[29][i]
- 263747951750360*r0[i]
+ 139067101832008*r2[i]
- 301749371899640*r4[i]
+ 1435586142219208*r6[i]
- 12118594340000120*r8[i]
+ 161884743374331208*r10[i]
- 3182019374449911800*r12[i]
+ 87529337757936824008*r14[i]
- 3248976815570811522680*r16[i]
+ 158349682430409973313608*r18[i]
- 9923580543500303314240760*r20[i]
+ 786760565945275886836376008*r22[i]
- 77920790663138781508799794040*r24[i]
+ 9547238666130437127002927547208*r26[i]
- 1436661104948080480105248787030520*r28[i]
+ 264153071890187061309364571665323208*r30[i]
- 59158834835361137154774550924268718200*r32[i]
+ 16118739962159239492313847086442541160008*r34[i]
- 5347555184547813200052870531874405260345080*r36[i]
+ 2166859703551720464338491083284259317823473608*r38[i]
- 1078557296770662670360222907496631544701980919160*r40[i]
+ 665455311907210786180015050798889123854625069640008*r42[i]
- 515842222294937633131823813678852501492617871745768440*r44[i]
+ 512481825744114866705502552866968615791537763443205995208*r46[i]
- 672341506500021005655953501043272036574421887743490851340920*r48[i]
+ 1221131998795722972005911539275382892837484311060515841535835208*r50[i]
- 3332823349698025928359593920805638924693962631253026576543932004600*r52[i]
+ 16225351344799733023493701427115345511005834435569774552932672635416008*r54[i]
- 252933395746719868307952649825453543881147152724607086725401888114468847480*r56[i]
- 4197923713092385360948718611576393240264592726638490329531539317361858302046392*r58[i]
) // 40526919504877216755680601905432322134980384796226602145184481280000000000000 for i in range(len(r0))]
r55 = [(-263747951750360*r[1][i]
+ 474746313150648*r[2][i]
- 597261490737912*r[3][i]
+ 622147386185325*r[4][i]
- 565588532895750*r[5][i]
+ 459124809056550*r[6][i]
- 336691526641470*r[7][i]
+ 224461017760980*r[8][i]
- 136496564854650*r[9][i]
+ 75831424919250*r[10][i]
- 38499031112850*r[11][i]
+ 17849550788685*r[12][i]
- 7546151552940*r[13][i]
+ 2902365981900*r[14][i]
- 1012453249500*r[15][i]
+ 319076175600*r[16][i]
- 90404916420*r[17][i]
+ 22890247380*r[18][i]
- 5140835700*r[19][i]
+ 1014638625*r[20][i]
- 173938050*r[21][i]
+ 25510914*r[22][i]
- 3137706*r[23][i]
+ 314820*r[24][i]
- 24750*r[25][i]
+ 1430*r[26][i]
- 54*r[27][i]
+ r[28][i]
+ 69533550916004*r0[i]
- 36734706144304*r2[i]
+ 79952007490544*r4[i]
- 382032124043344*r6[i]
+ 3243616097529584*r8[i]
- 43648837265746384*r10[i]
+ 865791864558368624*r12[i]
- 24079307603382105424*r14[i]
+ 905620045214743879664*r16[i]
- 44829468504848086112464*r18[i]
+ 2861056329269746545774704*r20[i]
- 231700008340575126045799504*r22[i]
+ 23520872059470599115258005744*r24[i]
- 2965504017281885370900598638544*r26[i]
+ 461273515398346724648458271164784*r28[i]
- 88130190568611671590209948525941584*r30[i]
+ 20636378464504372130162670555686883824*r32[i]
- 5922122648096407773524065141470107260624*r34[i]
+ 2087767422856024863904434586651201172234864*r36[i]
- 908798968501773051650655986384302515974787664*r38[i]
+ 492644736369466820787268958647730655685774129904*r40[i]
- 336933001130608366011659295551603463237580687754704*r42[i]
+ 296461508362831270729751372233986080685096927813720944*r44[i]
- 345657494345495491402030434838468872949594344235346833744*r46[i]
+ 559702758697443808822859784978939434710705864239596380799984*r48[i]
- 1365850676906400046308447846283281935329037260919461277968536784*r50[i]
+ 5961233014378374946505050098531606468256095554026807613974348199024*r52[i]
- 83514698066320941034057284688489207223027274274724707745745070739615824*r54[i]
- 1248498348142040711686005774772301632161825805512874614534923662110773809936*r56[i]
- 97940055470119940492894787938128111826202596590880955184195829760000000000000*r57[i]
- 6622123629554664793578752031982328757099181636326454936192889374707707671462864*r58[i]
) // 12696403353658275925965100847566516959580321051449436762275840000000000000 for i in range(len(r0))]
r53 = [(69533550916004*r[1][i]
- 124680849918352*r[2][i]
+ 155851062397940*r[3][i]
- 160878516023680*r[4][i]
+ 144539291740025*r[5][i]
- 115631433392020*r[6][i]
+ 83322650532485*r[7][i]
- 54414792184480*r[8][i]
+ 32308782859535*r[9][i]
- 17464206951100*r[10][i]
+ 8594228157515*r[11][i]
- 3846367846720*r[12][i]
+ 1562586937730*r[13][i]
- 574609830760*r[14][i]
+ 190559382650*r[15][i]
- 56724653440*r[16][i]
+ 15067486070*r[17][i]
- 3545290840*r[18][i]
+ 732179630*r[19][i]
- 131185600*r[20][i]
+ 20087795*r[21][i]
- 2576860*r[22][i]
+ 269399*r[23][i]
- 22048*r[24][i]
+ 1325*r[25][i]
- 52*r[26][i]
+ r[27][i]
- 18367353072152*r0[i]
+ 9723892802904*r2[i]
- 21233806732872*r4[i]
+ 101938316952024*r6[i]
- 870923857821192*r8[i]
+ 11813629724209944*r10[i]
- 236653242227994312*r12[i]
+ 6661211180561048664*r14[i]
- 254153395270440164232*r16[i]
+ 12797090786892473420184*r18[i]
- 833255276258604854522952*r20[i]
+ 69082046666155386510156504*r22[i]
- 7207362865961897332411742472*r24[i]
+ 938124129611900624725430169624*r26[i]
- 151437248027244277344983580174792*r28[i]
+ 30212272010200647359221303097651544*r30[i]
- 7441428742177722398508955844151051912*r32[i]
+ 2266232854869901871497407965509685274264*r34[i]
- 857107282161918028603277004147759001685832*r36[i]
+ 405772096860221176189017929957247080205389784*r38[i]
- 243490395435781263807703083882634443533746668552*r40[i]
+ 188759926346541491475721299645267069314262689230104*r42[i]
- 194640847441735760152914313356873387274986644997072072*r44[i]
+ 279696375173169115852542641714578798351241693643134107224*r46[i]
- 607628834924308414958104349396219007455296518007846747648392*r48[i]
+ 2367696951203027805660226670039629463149515409625476517138613144*r50[i]
- 29693031902220062960308836352100332220249176157939974718889212029512*r52[i]
- 398324183453887237008520156086372422120866135515653348034430817054180136*r54[i]
- 29624941158535977160585235310988539572354082453382019111976960000000000000*r55[i]
- 1900101321417947769567987711973348241577208823166451595420036775627225927432*r56[i]
- 109366395274967266883732513197576391539259566193150399955685343232000000000000*r57[i]
- 5787014432333693691636306553234126990913508322094724419618650379990272585520616*r58[i]
) // 4274883284060025564298013753389399649690343788366813724672000000000000 for i in range(len(r0))]
r51 = [(-18367353072152*r[1][i]
+ 32798844771700*r[2][i]
- 40715807302800*r[3][i]
+ 41620603020640*r[4][i]
- 36921502679600*r[5][i]
+ 29075683360185*r[6][i]
- 20558563992050*r[7][i]
+ 13129839188200*r[8][i]
- 7596549816030*r[9][i]
+ 3985844039275*r[10][i]
- 1895969056520*r[11][i]
+ 816446005200*r[12][i]
- 317506779800*r[13][i]
+ 111127372930*r[14][i]
- 34848305100*r[15][i]
+ 9735399520*r[16][i]
- 2405549300*r[17][i]
+ 520987950*r[18][i]
- 97765640*r[19][i]
+ 15660400*r[20][i]
- 2099160*r[21][i]
+ 229075*r[22][i]
- 19550*r[23][i]
+ 1224*r[24][i]
- 50*r[25][i]
+ r[26][i]
+ 4861946401452*r0[i]
- 2579808294648*r2[i]
+ 5653622432952*r4[i]
- 27280100477448*r6[i]
+ 234657881740152*r8[i]
- 3210736324810248*r10[i]
+ 65015030756447352*r12[i]
- 1854200415783543048*r14[i]
+ 71870433940146354552*r16[i]
- 3687349223477219875848*r18[i]
+ 245473564244803456261752*r20[i]
- 20888307287949627757008648*r22[i]
+ 2246840224563905580570968952*r24[i]
- 303094970433352624372214141448*r26[i]
+ 51019602983331540473045839276152*r28[i]
- 10691645514373727983810335922474248*r30[i]
+ 2790651091406916364299868206057983352*r32[i]
- 910446673933990019203515025763541207048*r34[i]
+ 373948949766422140435706410007606455890552*r36[i]
- 195681514530799165910557748483841641873539848*r38[i]
+ 132897106175336006092720191507876479916677797752*r40[i]
- 120554003537142419244816814513161495212294682672648*r42[i]
+ 152971535906456634616842226470152212508964788768504952*r44[i]
- 294458451533217960963210426417324728393814119257507805448*r46[i]
+ 1019832500675924760582251357311129578949356520774019156812152*r48[i]
- 11400247815546832449432199417474318613528727464280459760480138248*r50[i]
- 136675603482281861796246376772747198814333993503815350676473360480648*r52[i]
- 9618487389135057519670530945126149211803273523825330880512000000000000*r53[i]
- 584079459970995636352966806308556874401704430470079936394389227138871048*r54[i]
- 31846811745426175447629127959312680040280638637385670545375232000000000000*r55[i]
- 1597184531574749552837896774748024717998448145865885778866996941421634573448*r56[i]
- 74873617802851613237921352763017383902055278703306412762838597632000000000000*r57[i]
- 3318703699187935703810506598811783153922721408334539131405650076951837247203848*r58[i]
) // 1551118753287382280224243016469303211063259720016986112000000000000 for i in range(len(r0))]
r49 = [(4861946401452*r[1][i]
- 8643460269248*r[2][i]
+ 10649977831752*r[3][i]
- 10772391370048*r[4][i]
+ 9425842448792*r[5][i]
- 7297426411968*r[6][i]
+ 5054988087457*r[7][i]
- 3151161405168*r[8][i]
+ 1772528290407*r[9][i]
- 900331830048*r[10][i]
+ 412652088772*r[11][i]
- 170333048928*r[12][i]
+ 63127818572*r[13][i]
- 20918093728*r[14][i]
+ 6163366902*r[15][i]
- 1603477568*r[16][i]
+ 365077482*r[17][i]
- 71916768*r[18][i]
+ 12076932*r[19][i]
- 1695008*r[20][i]
+ 193452*r[21][i]
- 17248*r[22][i]
+ 1127*r[23][i]
- 48*r[24][i]
+ r[25][i]
- 1289904147324*r0[i]
+ 686119227300*r2[i]
- 1509462300060*r4[i]
+ 7323923844900*r6[i]
- 63466456620060*r8[i]
+ 876655994638500*r10[i]
- 17962494591036060*r12[i]
+ 519729378435224100*r14[i]
- 20498730418437708060*r16[i]
+ 1073773191888393761700*r18[i]
- 73266053614681083996060*r20[i]
+ 6418563118124648605611300*r22[i]
- 714493710681785410524780060*r24[i]
+ 100357569802461927273985332900*r26[i]
- 17717998874943470330819342460060*r28[i]
+ 3928707238871982933864962858686500*r30[i]
- 1096834043813751169204010169826956060*r32[i]
+ 388004275037568389575404928401474632100*r34[i]
- 175870982185451189351017757509405335708060*r36[i]
+ 103991298038492644018924403718805266597329700*r38[i]
- 82506842083007670338625750577445488484693676060*r40[i]
+ 91947467567672513735818977678842895400970978139300*r42[i]
- 156026356786659861162429714318097107470538947633340060*r44[i]
+ 477994672122502000860149649242839645232774457016507620900*r46[i]
- 4741041014119120622582667190202604787803330381303410474700060*r48[i]
- 50576092532930275709972631359425317424152381858024219560152465500*r50[i]
- 3360757298789328273819193202350156957303729393370136576000000000000*r51[i]
- 192818334124303175599491864945168536471848882690784611504742445276060*r52[i]
- 9939103635439559436992881976630354185530049307952841909862400000000000*r53[i]
- 471508555542884903005212240660172655256037627791416369358584244657159900*r54[i]
- 20919675710958242602087867553930200860715908621346548813398016000000000000*r55[i]
- 878041943468001963173367991796909193943439396756549154859435350804240108060*r56[i]
- 35162552719179833662144845690696735597708874030022366211765121843200000000000*r57[i]
- 1352434666946563642542290132534935017513578002743918845920318272760079986302300*r58[i]
) // 608281864034267560872252163321295376887552831379210240000000000 for i in range(len(r0))]
r47 = [(-1289904147324*r[1][i]
+ 2282138106804*r[2][i]
- 2789279908316*r[3][i]
+ 2789279908316*r[4][i]
- 2404551645100*r[5][i]
+ 1827459250276*r[6][i]
- 1237956266316*r[7][i]
+ 751616304549*r[8][i]
- 409972529754*r[9][i]
+ 200966926350*r[10][i]
- 88425447594*r[11][i]
+ 34834267234*r[12][i]
- 12239066866*r[13][i]
+ 3815417606*r[14][i]
- 1048191650*r[15][i]
+ 251565996*r[16][i]
- 52153926*r[17][i]
+ 9203634*r[18][i]
- 1355574*r[19][i]
+ 162150*r[20][i]
- 15134*r[21][i]
+ 1034*r[22][i]
- 46*r[23][i]
+ r[24][i]
+ 343059613650*r0[i]
- 182965127280*r2[i]
+ 404225281200*r4[i]
- 1973179787280*r6[i]
+ 17237751438000*r8[i]
- 240592045595280*r10[i]
+ 4994170279690800*r12[i]
- 146823806097131280*r14[i]
+ 5903690350090119600*r16[i]
- 316485671150054075280*r18[i]
+ 22198064042219526404400*r20[i]
- 2009394413056841321867280*r22[i]
+ 232532372014701449341825200*r24[i]
- 34201309524439700202831707280*r26[i]
+ 6378595465863797572545515262000*r28[i]
- 1510321457529226404281297600555280*r30[i]
+ 456430932151854961874111940707194800*r32[i]
- 177879954967657922123999080680411131280*r34[i]
+ 90948410673639301600046982211812755703600*r36[i]
- 62713181699432641518049958716708665011915280*r38[i]
+ 61017960828891287286335064536456771132612468400*r40[i]
- 90771056129445230547328475921502515772170837147280*r42[i]
+ 244690112718607318914399753695429565221879804118769200*r44[i]
- 2142766872532178730068138061640892672650431299718846827280*r46[i]
- 20243597746218463146623496754059816935278614102767681978514000*r48[i]
- 1267253883404724085150525340252698701849068398706688000000000000*r49[i]
- 68540933797288160408485956779561102500745596951326307091686715280*r50[i]
- 3332750987966083871537366592330572315992864981758718771200000000000*r51[i]
- 149233459487753154020208258958096224473270440522821423115697370901200*r52[i]
- 6253289089629471919203790951758600975663107059471098052608000000000000*r53[i]
- 248022574937797150848261199568155307996775458923007620752687158968331280*r54[i]
- 9391052465914511919999969587368350365544826165680600851782041600000000000*r55[i]
- 341691518826131979404309157169161042218932134256409704138253052086492312400*r56[i]
- 12009267253405103954728165969082831500967553940143760782108131328000000000000*r57[i]
- 409446286846863117127823359311606612468159510073586623230903823696994068955280*r58[i]
) // 258623241511168180642964355153611979969197632389120000000000 for i in range(len(r0))]
r45 = [(343059613650*r[1][i]
- 603784920024*r[2][i]
+ 731508653106*r[3][i]
- 722477682080*r[4][i]
+ 612815891050*r[5][i]
- 456442180920*r[6][i]
+ 301758997386*r[7][i]
- 177996090624*r[8][i]
+ 93865125915*r[9][i]
- 44246187300*r[10][i]
+ 18609425835*r[11][i]
- 6960408624*r[12][i]
+ 2304024151*r[13][i]
- 670609940*r[14][i]
+ 170173575*r[15][i]
- 37234560*r[16][i]
+ 6923301*r[17][i]
- 1072764*r[18][i]
+ 134805*r[19][i]
- 13200*r[20][i]
+ 945*r[21][i]
- 44*r[22][i]
+ r[23][i]
- 91482563640*r0[i]
+ 48932534040*r2[i]
- 108606356040*r4[i]
+ 533667580440*r6[i]
- 4703763586440*r8[i]
+ 66408505338840*r10[i]
- 1398457857168840*r12[i]
+ 41847457290489240*r14[i]
- 1719246675671583240*r16[i]
+ 94585481325000311640*r18[i]
- 6843422433568588589640*r20[i]
+ 642897110978465333366040*r22[i]
- 77770562351946223415228040*r24[i]
+ 12062233927817328810997492440*r26[i]
- 2397961353314881501418831818440*r28[i]
+ 613494954527608404597659277810840*r30[i]
- 203877970345571868715766678319960840*r32[i]
+ 89457569257636570186619080797284721240*r34[i]
- 53237495951641479759332571910597970535240*r36[i]
+ 44930968310714379648812137260536985281903640*r38[i]
- 58241166312158469946465066186170960196371701640*r40[i]
+ 137360888551881485527132727024151255460985294318040*r42[i]
- 1056294346650368430047563515157012073181421862576900040*r44[i]
- 8792490299555933486634712872596976297794618720689003795560*r46[i]
- 517246483022336361285928710307223959938395264778240000000000*r47[i]
- 26309260636200890673464765332665424581880256812272026952850440*r48[i]
- 1203891189234487880892999073240063766756614978771353600000000000*r49[i]
- 50764977622809978549916904649893168100296473949517793816320917160*r50[i]
- 2004451674635063649027875945687415042391867173902902886400000000000*r51[i]
- 74960269321392846499824811474695597918673304894478483366348507552840*r52[i]
- 2677686378486556935494258093966418225514743986783186111692800000000000*r53[i]
- 91966010944477715317164988999955404631262474522089414701528792100246760*r54[i]
- 3052738683181473214064839725605301429423558773687203835097907200000000000*r55[i]
- 98349663276138342734015395366406037072180666393105750993186894401098287240*r56[i]
- 3085900643293467252898728816632640674097327400062270714196210483200000000000*r57[i]
- 94574687679290450381400952406492223053801275479696226944501270854570791704360*r58[i]
) // 119622220865480194561963161495657715064383733760000000000 for i in range(len(r0))]
r43 = [(-91482563640*r[1][i]
+ 160094486370*r[2][i]
- 192113383644*r[3][i]
+ 187187399448*r[4][i]
- 155989499540*r[5][i]
+ 113649492522*r[6][i]
- 73153696336*r[7][i]
+ 41802112192*r[8][i]
- 21238169904*r[9][i]
+ 9586673915*r[10][i]
- 3834669566*r[11][i]
+ 1353412788*r[12][i]
- 418913482*r[13][i]
+ 112784399*r[14][i]
- 26127660*r[15][i]
+ 5133856*r[16][i]
- 839188*r[17][i]
+ 111069*r[18][i]
- 11438*r[19][i]
+ 860*r[20][i]
- 42*r[21][i]
+ r[22][i]
+ 24466267020*r0[i]
- 13128240840*r2[i]
+ 29286075720*r4[i]
- 144956522040*r6[i]
+ 1290252243720*r8[i]
- 18448766253240*r10[i]
+ 394763466531720*r12[i]
- 12048763425424440*r14[i]
+ 507104531694579720*r16[i]
- 28726839421461491640*r18[i]
+ 2153064433503155907720*r20[i]
- 211041986898764840790840*r22[i]
+ 26870132026261051008915720*r24[i]
- 4433779344005175981028538040*r26[i]
+ 950513389106656928711222883720*r28[i]
- 266877172369028643812085068829240*r30[i]
+ 99651017964870751887504875569971720*r32[i]
- 50788156610571325953562659420384640440*r34[i]
+ 36915961449056930526009630202648137219720*r36[i]
- 41419014418447665040750851917674255257827640*r38[i]
+ 84934578551016826327683205574058431012558547720*r40[i]
- 570180937724400876712836731188276811777920749126840*r42[i]
- 4158439692009034639969470592464099450041235634033244280*r44[i]
- 229275923325503706243762726200010620540068823040000000000*r45[i]
- 10938400640270606999512627385384658646639850257084618154040*r46[i]
- 469832222078622194834718578529061763610709032173568000000000*r47[i]
- 18609787245585710799825274640865231563879706109002975534476280*r48[i]
- 690703654308090686886605775729000661503847399056998400000000000*r49[i]
- 24295755635821397902484226724698036360412358674335136584603405240*r50[i]
- 816834061921519325837632181160492761661336490802298224640000000000*r51[i]
- 26420216400737828039776597843354259258729442541873887374106278588280*r52[i]
- 826385145940446765246655148432861711174878386201463829299200000000000*r53[i]
- 25100830043691732995573291002742236374870109783293156876807153222256440*r54[i]
- 742930242368923193261832627165371827238517580192797921934049280000000000*r55[i]
- 21488745356673367209649903160436075476069546948355194277325961472924140280*r56[i]
- 608881820337630879509897701341056975619404233381496003222097100800000000000*r57[i]
- 16936203595599754752161124408061029172417207470711836922443662877355050963640*r58[i]
) // 60415263063373835637355132068513997507264512000000000 for i in range(len(r0))]
r41 = [(24466267020*r[1][i]
- 42550029600*r[2][i]
+ 50528160150*r[3][i]
- 48507033744*r[4][i]
+ 39645171810*r[5][i]
- 28192122176*r[6][i]
+ 17620076360*r[7][i]
- 9721421440*r[8][i]
+ 4739192952*r[9][i]
- 2038362560*r[10][i]
+ 770755843*r[11][i]
- 254795320*r[12][i]
+ 73066305*r[13][i]
- 17985552*r[14][i]
+ 3746990*r[15][i]
- 648128*r[16][i]
+ 90610*r[17][i]
- 9840*r[18][i]
+ 779*r[19][i]
- 40*r[20][i]
+ r[21][i]
- 6564120420*r0[i]
+ 3534526380*r2[i]
- 7928802420*r4[i]
+ 39562131180*r6[i]
- 355997149620*r8[i]
+ 5162772055980*r10[i]
- 112466379416820*r12[i]
+ 3509804003100780*r14[i]
- 151808102304340020*r16[i]
+ 8890838711788769580*r18[i]
- 693867758978013455220*r20[i]
+ 71436574576557715366380*r22[i]
- 9656103679244476561098420*r24[i]
+ 1714541855816811795973995180*r26[i]
- 402505898503128791422102405620*r28[i]
+ 126699650825847516884027712559980*r30[i]
- 54827934277723571354991704981312820*r32[i]
+ 34051732695777105364083032869387764780*r34[i]
- 32827430653262026254340815579045378556020*r36[i]
+ 58129225653125966892251726413185365757113580*r38[i]
- 338476895760295138790385051321218766549279671220*r40[i]
- 2149763077602671437231704105519918866633843849089620*r42[i]
- 110761315616185365335151075458942328763318272000000000*r43[i]
- 4942256826876098689793689711313418888604591478522994420*r44[i]
- 198705800215436545411261029373342537801392979968000000000*r45[i]
- 7372979698612811191617476736621847607367673634869335740820*r46[i]
- 256536466678869072307088584563086803940345640910848000000000*r47[i]
- 8465458808946796165763451715680655749443289544616664687661620*r48[i]
- 267183551072205666325866548010883965389520680874147840000000000*r49[i]
- 8117979331672354072521723205205099479673234187982104799090936020*r50[i]
- 238669689906108201296368312708296353560792649309607690240000000000*r51[i]
- 6818076027538551619225591166422355976547652044865002983244581608820*r52[i]
- 189900239055230874242774936502694772441792049430392817582080000000000*r53[i]
- 5171618834732319180394479687214193283849620051628630315033942033971220*r54[i]
- 138041851069253628998433394126808976321130523016711965119610880000000000*r55[i]
- 3618854287358718174247270918277944984495873060746358190596842483089572020*r56[i]
- 93341856645655973516471665609366536581626170869006948219737866240000000000*r57[i]
- 2372435023012906796443937598733811094460548359722599809614428821201823342420*r58[i]
) // 33452526613163807108170062053440751665152000000000 for i in range(len(r0))]
r39 = [(-6564120420*r[1][i]
+ 11338026180*r[2][i]
- 13309856820*r[3][i]
+ 12570420330*r[4][i]
- 10056336264*r[5][i]
+ 6962078952*r[6][i]
- 4211628008*r[7][i]
+ 2234741392*r[8][i]
- 1040310648*r[9][i]
+ 423830264*r[10][i]
- 150391384*r[11][i]
+ 46142811*r[12][i]
- 12118314*r[13][i]
+ 2686866*r[14][i]
- 493506*r[15][i]
+ 73112*r[16][i]
- 8398*r[17][i]
+ 702*r[18][i]
- 38*r[19][i]
+ r[20][i]
+ 1767263190*r0[i]
- 955277400*r2[i]
+ 2156197560*r4[i]
- 10855425000*r6[i]
+ 98876533560*r8[i]
- 1456859058600*r10[i]
+ 32382608125560*r12[i]
- 1036360772970600*r14[i]
+ 46242812090245560*r16[i]
- 2813858311510281000*r18[i]
+ 230141619686501005560*r20[i]
- 25097337236284407949800*r22[i]
+ 3642002181929040219157560*r24[i]
- 706474912755087069174777000*r26[i]
+ 185490702479102020671448093560*r28[i]
- 67501512373123369695638979402600*r30[i]
+ 35506616897715366055874618759845560*r32[i]
- 29173319982987640073110629923442306600*r34[i]
+ 44272025958057634433180503709478279085560*r36[i]
- 222019441630075420847480526017947263931809000*r38[i]
- 1219813882056330049405575791394671579625372874440*r40[i]
- 58541921573036662439297608593521315414016000000000*r41[i]
- 2435494701008122308521041585840935773426259964069800*r42[i]
- 91378085383352926401499637253627421229737574400000000*r43[i]
- 3166734413390519310621011935324774315544541946854082440*r44[i]
- 102992200477964363280928335737465088274348376064000000000*r45[i]
- 3179252903572284408695210045628305460118381385145907089000*r46[i]
- 93933517845624637462463708669855295641358690995404800000000*r47[i]
- 2673604876174888392329293291823128228151672865125704677946440*r48[i]
- 73683990172722867345525100631400320014642700636651520000000000*r49[i]
- 1974418989189660654416775142028601893909607175588350467588706600*r50[i]
- 51613966955266559433583238169717122269196640905399894016000000000*r51[i]
- 1320028845480376778241459745623130669629332621855587804526269234440*r52[i]
- 33107222954815130156932711664097915655061115376773617418240000000000*r53[i]
- 815957549537661838837381326961271796535482084133007452235898808602600*r54[i]
- 19795975807387270200099109024051084160980250133315226586578944000000000*r55[i]
- 473487977004702488781031173032461802620651426788692589976354442780074440*r56[i]
- 11179909978662202267790279764165131367349266902969648947732152320000000000*r57[i]
- 260897388111850530362103067770085967707758603704057497904533734788154297000*r58[i]
) // 20397882081197443358640281739902897356800000000 for i in range(len(r0))]
r37 = [(1767263190*r[1][i]
- 3029594040*r[2][i]
+ 3511574910*r[3][i]
- 3257112960*r[4][i]
+ 2544619500*r[5][i]
- 1709984304*r[6][i]
+ 997490844*r[7][i]
- 506662016*r[8][i]
+ 223926516*r[9][i]
- 85795600*r[10][i]
+ 28312548*r[11][i]
- 7970688*r[12][i]
+ 1888887*r[13][i]
- 369852*r[14][i]
+ 58275*r[15][i]
- 7104*r[16][i]
+ 629*r[17][i]
- 36*r[18][i]
+ r[19][i]
- 477638700*r0[i]
+ 259289580*r2[i]
- 589294500*r4[i]
+ 2996657580*r6[i]
- 27670359300*r8[i]
+ 415064933580*r10[i]
- 9439543875300*r12[i]
+ 310922483993580*r14[i]
- 14379880666402500*r16[i]
+ 914767168887053580*r18[i]
- 79051272004645620900*r20[i]
+ 9231401536061270849580*r22[i]
- 1459700260139475814330500*r24[i]
+ 315843905250429722227637580*r26[i]
- 95612546130070295522414451300*r28[i]
+ 42177612582297377823299737193580*r30[i]
- 29268533564152352561039458453023300*r32[i]
+ 37747202396256876155482291281278813580*r34[i]
- 161759954125032708920885781040309430206500*r36[i]
- 763162014442847423121851269222329739576686420*r38[i]
- 33996470135329072264400469566504828928000000000*r39[i]
- 1314149222797294391875041342296266627244339280900*r40[i]
- 45857838565545385577449793398258363740979200000000*r41[i]
- 1479444354242422663436299123473954120225396734970420*r42[i]
- 44831961082741695492799244828619514023247872000000000*r43[i]
- 1290525734288850664269099373480698875776359383538646500*r44[i]
- 35584775745235419804380819416241066350620337766400000000*r45[i]
- 945953923580279776552772789184754415724912490598746182420*r46[i]
- 24366115407876526559068567586678948554722823372800000000000*r47[i]
- 610645775114510996953480313967173146186867766220019295823300*r48[i]
- 14939521515639279686486638270686230946922780466085888000000000*r49[i]
- 357801113228416003019399250210317079666322369514337123812946420*r50[i]
- 8408661385093459098177743857092487683793831993666437120000000000*r51[i]
- 194295554214245025331172354056693339192813114298766754673003451300*r52[i]
- 4421785847139823304538477974636921659214442633337233211392000000000*r53[i]
- 99261104716354759275356708669334064781685960280357361053977678366420*r54[i]
- 2200755503176311867578027094834478881887427024050984016936960000000000*r55[i]
- 48247096700384301518009850578340922172400831976100176730089040267290500*r56[i]
- 1046921750847383936468563319482801375919232934491235072439274700800000000*r57[i]
- 22505475933314919262348458739677789960911726304737932882414389670234026420*r58[i]
) // 13763753091226345046315979581580902400000000 for i in range(len(r0))]
r35 = [(-477638700*r[1][i]
+ 811985790*r[2][i]
- 927983760*r[3][i]
+ 843621600*r[4][i]
- 641886000*r[5][i]
+ 417225900*r[6][i]
- 233646504*r[7][i]
+ 112971936*r[8][i]
- 47071640*r[9][i]
+ 16811300*r[10][i]
- 5101360*r[11][i]
+ 1298528*r[12][i]
- 272272*r[13][i]
+ 45815*r[14][i]
- 5950*r[15][i]
+ 560*r[16][i]
- 34*r[17][i]
+ r[18][i]
+ 129644790*r0[i]
- 70715340*r2[i]
+ 161960940*r4[i]
- 832930740*r6[i]
+ 7810859340*r8[i]
- 119578066740*r10[i]
+ 2791740107340*r12[i]
- 95062235276340*r14[i]
+ 4584012079172940*r16[i]
- 307268933913567540*r18[i]
+ 28355038085389144140*r20[i]
- 3597774935929125068340*r22[i]
+ 632729503874459828228940*r24[i]
- 157381528472579148083026740*r26[i]
+ 57577884185625191071239755340*r28[i]
- 33404393172944223690128125810740*r30[i]
+ 36271128388074981554067219056171340*r32[i]
- 131671692334895976886647813958596908340*r34[i]
- 529104107360143104505564190890974500955060*r36[i]
- 21792609061108379656666967670836428800000000*r37[i]
- 779765567254824678774814590170424618060927540*r38[i]
- 25214048683702395262763681595157748121600000000*r39[i]
- 754531895504954495472529428607358759602244935860*r40[i]
- 21229190210645503978483385444330514048614400000000*r41[i]
- 567902644449952014090537079509460539320563935596340*r42[i]
- 14564893239013264062672891916748815156327219200000000*r43[i]
- 360416016142646161224945882401067658836071135991963060*r44[i]
- 8648657180064969977242561394456399100712373452800000000*r45[i]
- 202069375902424923136583586389997599181812580415819762740*r46[i]
- 4612127517564454653650814843765113002002883805184000000000*r47[i]
- 103121612921980129969364006657783463883530860291974593108660*r48[i]
- 2263884472933693041558609190221290023990021205262336000000000*r49[i]
- 48895910164254390571448366914991646721674728906975264997394740*r50[i]
- 1040735050391204632204438770440340544568220182900637696000000000*r51[i]
- 21862169403162391239341958599750577577387707221098019982750324660*r52[i]
- 453821931200327068047775184677590212395655580642824945664000000000*r53[i]
- 9319698121456631696400960021555048638297447683852229271473797580340*r54[i]
- 189526286937489003207879533218884759427831665772394776520294400000000*r55[i]
- 3820025543901040851611788799472009802308578049073400212351536136443060*r56[i]
- 76370956078270917445488726598274634185708865212478713830676889600000000*r57[i]
- 1515497157836802114608632160520145002491909940459412885835726359690527540*r58[i]
) // 10333147966386144929666651337523200000000 for i in range(len(r0))]
r33 = [(129644790*r[1][i]
- 218349120*r[2][i]
+ 245642760*r[3][i]
- 218349120*r[4][i]
+ 161280600*r[5][i]
- 100975680*r[6][i]
+ 53993940*r[7][i]
- 24682944*r[8][i]
+ 9612108*r[9][i]
- 3164480*r[10][i]
+ 870232*r[11][i]
- 196416*r[12][i]
+ 35464*r[13][i]
- 4928*r[14][i]
+ 495*r[15][i]
- 32*r[16][i]
+ r[17][i]
- 35357670*r0[i]
+ 19389690*r2[i]
- 44796870*r4[i]
+ 233344890*r6[i]
- 2227139910*r8[i]
+ 34903389690*r10[i]
- 839988260550*r12[i]
+ 29734601940090*r14[i]
- 1506293149214790*r16[i]
+ 107487540061668090*r18[i]
- 10743535525710258630*r20[i]
+ 1511267716903778445690*r22[i]
- 304525956073869018848070*r24[i]
+ 91234873454404063067344890*r26[i]
- 43747586259736794619504039110*r28[i]
+ 39574917458915050445099774637690*r30[i]
- 120523981455993504966525708346887750*r32[i]
- 408775192473644376465790167368394203910*r34[i]
- 15499721949579217394499977006284800000000*r35[i]
- 511206585269023792365556128001469646849990*r36[i]
- 15254826342775865759666877369585500160000000*r37[i]
- 421754497238984285335705463354740490210507910*r38[i]
- 10974654148845317574241976981091935846400000000*r39[i]
- 271793538072560300468434911462753194293644181830*r40[i]
- 6459357656104303171129642884693889583677440000000*r41[i]
- 148248369194001435848413334991598692517822202402310*r42[i]
- 3302211571953506236081129759184691588287692800000000*r43[i]
- 71676123253955938571177412178194687158760951558339270*r44[i]
- 1520976967414625530272457942824571170900903198720000000*r45[i]
- 31639609352600382246311701401196841805566037174158815110*r46[i]
- 646685006086394734265332084740666732219400716288000000000*r47[i]
- 13012191241624225597793637611655297834798932917962602378310*r48[i]
- 258181916941754694739033103200539980500380934786252800000000*r49[i]
- 5058734882305856045540073713691835327365626096838684137474310*r50[i]
- 98003172162669552280283212651193173071892639817662464000000000*r51[i]
- 1879290113304215911642155827929295380860361801862580501733354950*r52[i]
- 35704185906372296773445691918777756816503577852201255567360000000*r53[i]
- 672641472730329564687292228981658860084205881937208343188256907910*r54[i]
- 12575158916407126391710720870047035404278492018674627090841600000000*r55[i]
- 233452841691483091333119823101860358440277859293807745406578698725190*r56[i]
- 4306261428325792056911970993937744985523146355645690412133253120000000*r57[i]
- 78967810154477342180446992930495373302248339231267632809785910552443910*r58[i]
) // 8683317618811886495518194401280000000 for i in range(len(r0))]
r31 = [(-35357670*r[1][i]
+ 58929450*r[2][i]
- 65132550*r[3][i]
+ 56448210*r[4][i]
- 40320150*r[5][i]
+ 24192090*r[6][i]
- 12271350*r[7][i]
+ 5259150*r[8][i]
- 1893294*r[9][i]
+ 566370*r[10][i]
- 138446*r[11][i]
+ 26970*r[12][i]
- 4030*r[13][i]
+ 434*r[14][i]
- 30*r[15][i]
+ r[16][i]
+ 9694845*r0[i]
- 5348880*r2[i]
+ 12480720*r4[i]
- 65969520*r6[i]
+ 642563280*r8[i]
- 10347602160*r10[i]
+ 258040917840*r12[i]
- 9564008626800*r14[i]
+ 514021079720400*r16[i]
- 39590373677587440*r18[i]
+ 4371353677873146960*r20[i]
- 701971899866535028080*r22[i]
+ 169737570795219895373520*r24[i]
- 66396273378844288679892720*r26[i]
+ 49448835121192219782326176080*r28[i]
- 124963193751534047864734415925360*r30[i]
- 354113410826574103722030528083469360*r32[i]
- 12301366626650172535317442068480000000*r33[i]
- 372225904019072507165665501545458070000*r34[i]
- 10203983616806318118045818195804160000000*r35[i]
- 259484653500223872483011119661283865786800*r36[i]
- 6217811871006716259183948315607695360000000*r37[i]
- 141956901865997956445469727796622341498870640*r38[i]
- 3113335802166672719861469258672651632640000000*r39[i]
- 66003822624082868383556482555741495612650600240*r40[i]
- 1359334478541063086765779323397876419133440000000*r41[i]
- 27303356587963564025554884815930553997263574871280*r42[i]
- 536588847651574079588079017443366763149393920000000*r43[i]
- 10345842549438556817463474698578198121859964179733680*r44[i]
- 196138884946560564409651268242770514989620920320000000*r45[i]
- 3663204676820752962698443093474820599422678195673015920*r46[i]
- 67509422521578235356394063172809938341831560396800000000*r47[i]
- 1229367058216339817971318602200240769989331897298761411120*r48[i]
- 22148293718278830966574475214239695745532717485260800000000*r49[i]
- 395185352573696509925259966545790692473196837003978017048560*r50[i]
- 6989838211515905458753639642597471400309284985697730560000000*r51[i]
- 122657793546790877104838252566375468764736099620191835404656560*r52[i]
- 2136978399115087712296321880227522428322876912299682037760000000*r53[i]
- 36988121280698718881148076634622109731006022172305430137473913200*r54[i]
- 636401990041792168283686233422492190991157350614321195909120000000*r55[i]
- 10890093660642735592022125051191031925197005582724615897049873694000*r56[i]
- 185422894646403058825010144324310732863316294254968725590507520000000*r57[i]
- 3142733314263192554436266828370834215722453342881210843923036520153840*r58[i]
) // 8222838654177922817725562880000000 for i in range(len(r0))]
r29 = [(9694845*r[1][i]
- 15967980*r[2][i]
+ 17298645*r[3][i]
- 14567280*r[4][i]
+ 10015005*r[5][i]
- 5722860*r[6][i]
+ 2731365*r[7][i]
- 1085760*r[8][i]
+ 356265*r[9][i]
- 95004*r[10][i]
+ 20097*r[11][i]
- 3248*r[12][i]
+ 377*r[13][i]
- 28*r[14][i]
+ r[15][i]
- 2674440*r0[i]
+ 1485800*r2[i]
- 3506488*r4[i]
+ 18850280*r6[i]
- 188004088*r8[i]
+ 3125835560*r10[i]
- 81314498488*r12[i]
+ 3185384180840*r14[i]
- 184064268909688*r16[i]
+ 15598375633694120*r18[i]
- 1958105850969957688*r20[i]
+ 375744491571024583400*r22[i]
- 118117302690774819242488*r24[i]
+ 71447614092662750198256680*r26[i]
- 147980747895225006590333244088*r28[i]
- 346368637877614395127589803878040*r30[i]
- 10963784872237230423634083840000000*r31[i]
- 302766527792977996357877082103322488*r32[i]
- 7585842753100939730112422608896000000*r33[i]
- 176553572119721839407097582006071612760*r34[i]
- 3876980715165912710714213825249280000000*r35[i]
- 81213796311764134505181592648745883717688*r36[i]
- 1636103186224681029581052139652775936000000*r37[i]
- 31895543813319775842490572300866856117139480*r38[i]
- 604645713103650398366928164707180216320000000*r39[i]
- 11189653759353064214370349765226592602607549688*r40[i]
- 202794861446303149866709151240333763280896000000*r41[i]
- 3608799207440735942926262565268791718882246250200*r42[i]
- 63195849406190967779680687932546907121909760000000*r43[i]
- 1091041918456432706911605989934195570136050930818488*r44[i]
- 18599858037912613836046600540495361832783446016000000*r45[i]
- 313534044032502214538190505667405050039920730329536920*r46[i]
- 5232130701886884640147951658064894118305202176000000000*r47[i]
- 86524070613240340349034843422074253070890184188704404088*r48[i]
- 1419220451222069603559756976077536870379472375775232000000*r49[i]
- 23107896008521043617173872183497904829674956287283293591640*r50[i]
- 373741738674210661134828098626419085853440812861358080000000*r51[i]
- 6008307669591671335816649438311816911003850182297118574066488*r52[i]
- 96059698783150230038524550628221988538172968887744724992000000*r53[i]
- 1528101734176197374675502615836313800063939684531640625652206360*r54[i]
- 24197833543768025531598353299088959107075282255594085416960000000*r55[i]
- 381579932407152949331830984156914024593569799681407714277708445688*r56[i]
- 5994237015153876231320281812595035678671895909569564478799872000000*r57[i]
- 93834176733824481470982472448071659769448489164206322564543397573080*r58[i]
) // 8841761993739701954543616000000 for i in range(len(r0))]
r27 = [(-2674440*r[1][i]
+ 4345965*r[2][i]
- 4601610*r[3][i]
+ 3749460*r[4][i]
- 2466750*r[5][i]
+ 1332045*r[6][i]
- 592020*r[7][i]
+ 215280*r[8][i]
- 63180*r[9][i]
+ 14625*r[10][i]
- 2574*r[11][i]
+ 324*r[12][i]
- 26*r[13][i]
+ r[14][i]
+ 742900*r0[i]
- 416024*r2[i]
+ 994840*r4[i]
- 5454824*r6[i]
+ 55944280*r8[i]
- 966290024*r10[i]
+ 26454613720*r12[i]
- 1109329691624*r14[i]
+ 70212852387160*r16[i]
- 6733670404619624*r18[i]
+ 1005318113348848600*r20[i]
- 249581050854994274024*r22[i]
+ 120719220687299365182040*r24[i]
- 202039976682357297272094824*r26[i]
- 385557844336439370252173428520*r28[i]
- 11052202492174627443179520000000*r29[i]
- 276888650579451671741587901762024*r30[i]
- 6304176301536407493589598208000000*r31[i]
- 133535841584115505205141919375399080*r32[i]
- 2672618344480543437732658544640000000*r33[i]
- 51095126335993498323380094454901195624*r34[i]
- 940618873537377672007825158832128000000*r35[i]
- 16776403501444391106926987629186000345640*r36[i]
- 291283862319085180678807183848898560000000*r37[i]
- 4942310839108515578583708125038854650555624*r38[i]
- 82203911327563805707081667710859870208000000*r39[i]
- 1343752600475734599375534320311340373516684200*r40[i]
- 21634243326074826428166414905753461063680000000*r41[i]
- 343672532983087585902951862991031321905844242024*r42[i]
- 5395063942758184834505475068561955332947968000000*r43[i]
- 83804941354439477195910293019964343299641959230760*r44[i]
- 1289609166695254343642200168046105549173555200000000*r45[i]
- 19678461460501652805347265575009996073778349586894824*r46[i]
- 298018526228473595475945631789329672119214145536000000*r47[i]
- 4482734138598481574681074400900490010744661138946801320*r48[i]
- 67016178755227832923500959370656761105984640778240000000*r49[i]
- 996343679402015421123803198306389561979045588249233394024*r50[i]
- 14738679287503486801955946351327209631956632997462016000000*r51[i]
- 217035109012403108518173019970634230404031272801464219811880*r52[i]
- 3182760243299536666170356413471689268456113615580692480000000*r53[i]
- 46498820464911995110643960090817019186186417071168193972859624*r54[i]
- 677000576115850353091936355049285565985169214360708448256000000*r55[i]
- 9825975298294418560739533266953207187063157925972397601057878440*r56[i]
- 142206485072283587626888528880526802570433143585532223160320000000*r57[i]
- 2052704477572256705026400459282590318295326949208370617580556651624*r58[i]
) // 10888869450418352160768000000 for i in range(len(r0))]
r25 = [(742900*r[1][i]
- 1188640*r[2][i]
+ 1225785*r[3][i]
- 961400*r[4][i]
+ 600875*r[5][i]
- 303600*r[6][i]
+ 123970*r[7][i]
- 40480*r[8][i]
+ 10350*r[9][i]
- 2000*r[10][i]
+ 275*r[11][i]
- 24*r[12][i]
+ r[13][i]
- 208012*r0[i]
+ 117572*r2[i]
- 285532*r4[i]
+ 1602692*r6[i]
- 16996252*r8[i]
+ 307475012*r10[i]
- 8966430172*r12[i]
+ 409745686532*r14[i]
- 29195711499292*r16[i]
+ 3312133208909252*r18[i]
- 636215671041835612*r20[i]
+ 241648300078174135172*r22[i]
- 321511316149669476991132*r24[i]
- 492817676505266866078123708*r26[i]
- 12703681025488077520896000000*r27[i]
- 286779648275654636997381637852*r28[i]
- 5894507995826467969695744000000*r29[i]
- 112914054231542703053832892635388*r30[i]
- 2047008246979213061238030336000000*r31[i]
- 35501568925223446300815211192767772*r32[i]
- 593711792050129855003168210944000000*r33[i]
- 9632134956680435093368218113996247868*r34[i]
- 152311343455497374594406627803136000000*r35[i]
- 2356318736218539774396037820111678892892*r36[i]
- 35772470531371951985805498114637824000000*r37[i]
- 534273042749950920189640352996759062689148*r38[i]
- 7866491034006154572049014294052601856000000*r39[i]
- 114383224059606274110181105712262975351245212*r40[i]
- 1644946226278516886873016733667061202944000000*r41[i]
- 23426103831558846665144911501028780920365367228*r42[i]
- 330735945747364837719554208843251145179136000000*r43[i]
- 4633465747908141417306051485893140722291346976732*r44[i]
- 64465996518808752310647291812383168776634368000000*r45[i]
- 891389875128429665004288245297052393567100598170108*r46[i]
- 12257190333970097165549309885966019046465339392000000*r47[i]
- 167703402046599761376513697620930939990159551304359452*r48[i]
- 2284199788431383972862903582163083269492369522688000000*r49[i]
- 30985395797162515638045004419632302359171420946744265788*r50[i]
- 418773650924292383172351750158911938166116165353472000000*r51[i]
- 5640938886725051055672433299961125394581606270770949985372*r52[i]
- 75754370981682573393940880354465056079445791605260288000000*r53[i]
- 1014539155515195896087346280844831091980940427383805672902268*r54[i]
- 13553236686007006297534192722032523699914497964150095872000000*r55[i]
- 180645753713035138349646636694817250186535606435585025317966492*r56[i]
- 2402762487061179587714604403586444519692170741763685941248000000*r57[i]
- 31898596390773561786184133631815010325239624257282809197944207548*r58[i]
) // 15511210043330985984000000 for i in range(len(r0))]
r23 = [(-208012*r[1][i]
+ 326876*r[2][i]
- 326876*r[3][i]
+ 245157*r[4][i]
- 144210*r[5][i]
+ 67298*r[6][i]
- 24794*r[7][i]
+ 7084*r[8][i]
- 1518*r[9][i]
+ 230*r[10][i]
- 22*r[11][i]
+ r[12][i]
+ 58786*r0[i]
- 33592*r2[i]
+ 83096*r4[i]
- 479752*r6[i]
+ 5299736*r8[i]
- 101549512*r10[i]
+ 3208453976*r12[i]
- 164071220872*r14[i]
+ 13743680753816*r16[i]
- 1993276972245832*r18[i]
+ 581947914140407256*r20[i]
- 603916464771468176392*r22[i]
- 730803773459954540777704*r24[i]
- 16803810880275234816000000*r25[i]
- 339155768243774227716964552*r26[i]
- 6245976504198304781107200000*r27[i]
- 107413822788261782335458993064*r28[i]
- 1751393992807566623932416000000*r29[i]
- 27365156266821215807862420562312*r30[i]
- 412945663851071412756568473600000*r31[i]
- 6053949680529454447550745704030824*r32[i]
- 86623417665042381831452000256000000*r33[i]
- 1214146547565910406028014931410521672*r34[i]
- 16719755812321492798917963359846400000*r35[i]
- 226758627215029497194516602329808882984*r36[i]
- 3034905857007157810746475187798016000000*r37[i]
- 40151799724774280996886476759684489594632*r38[i]
- 525848735885794606994555529953619148800000*r39[i]
- 6825564942475643900873841059427230143341544*r40[i]
- 87900055843825806396690634755863003136000000*r41[i]
- 1124090333957827218160935737032127911249333192*r42[i]
- 14286036145840157893404384196456208735600640000*r43[i]
- 180556939553256275799275906968519352499771598504*r44[i]
- 2270728203819030041749862616122105872023552000000*r45[i]
- 28430855249825246651314973609548475795532583689352*r46[i]
- 354557703317395919808450352391376751066211942400000*r47[i]
- 4405868085478593275690315869491622501390761293845864*r48[i]
- 54573144465647486264201741288918109369842860032000000*r49[i]
- 674011661674309854738045921738777159802726884618615112*r50[i]
- 8302706625795267729689057629348230882286932767539200000*r51[i]
- 102034139431103779464508421919001500494414946039191875624*r52[i]
- 1251246650171085656596973236879882037480265304768512000000*r53[i]
- 15314394051611719851475192053401326069594457012869777662472*r54[i]
- 187109145209992539052209722604913357344367643037199564800000*r55[i]
- 2282440022117705675156420050651491739525177949448233198679784*r56[i]
- 27802040122212699237168071957551965338444489320198520832000000*r57[i]
- 338208376976656361697950520979466672446962935395353773703583432*r58[i]
) // 25852016738884976640000 for i in range(len(r0))]
r21 = [(58786*r[1][i]
- 90440*r[2][i]
+ 87210*r[3][i]
- 62016*r[4][i]
+ 33915*r[5][i]
- 14364*r[6][i]
+ 4655*r[7][i]
- 1120*r[8][i]
+ 189*r[9][i]
- 20*r[10][i]
+ r[11][i]
- 16796*r0[i]
+ 9724*r2[i]
- 24596*r4[i]
+ 147004*r6[i]
- 1708916*r8[i]
+ 35240284*r10[i]
- 1237329236*r12[i]
+ 73853629564*r14[i]
- 7850527669556*r16[i]
+ 1717351379730844*r18[i]
- 1359124435588313876*r20[i]
- 1272410676942417239876*r22[i]
- 25852016738884976640000*r23[i]
- 462292539259962003646196*r24[i]
- 7561714896123855667200000*r25[i]
- 115761644587269354830466596*r26[i]
- 1683741850203578528563200000*r27[i]
- 23512975860299444963550050516*r28[i]
- 317677725072691341719961600000*r29[i]
- 4176614976496441445095962733316*r30[i]
- 53674391443652368368589209600000*r31[i]
- 676635955671282540673335079110836*r32[i]
- 8391272072243853389701334630400000*r33[i]
- 102611708232289325546408008313624036*r34[i]
- 1239646284649926576486736094822400000*r35[i]
- 14819283410691765614379616648600811156*r36[i]
- 175538127424434549895381626305740800000*r37[i]
- 2062659648435073986802743885440046722756*r38[i]
- 24066873273263602745997309174983884800000*r39[i]
- 279069134864297423784787795404361206735476*r40[i]
- 3218237360334469905693543066426751549440000*r41[i]
- 36932670876144577834192017462238998576813476*r42[i]
- 422013831656219970552631011526505561456640000*r43[i]
- 4803667893589610545887832027829424971473267796*r44[i]
- 54491782544378643866541770098406137341542400000*r45[i]
- 616254801390825608499920295882691673585117080196*r46[i]
- 6950267169846786189298202657232919399818854400000*r47[i]
- 78194975030419808376759755992062291704460984792116*r48[i]
- 877813878936817604039539295936804610730357555200000*r49[i]
- 9834901482219684549861282981457686724945206826306916*r50[i]
- 109993865724440916050887229750467965278551356211200000*r51[i]
- 1228217338997580254122488729377687743870958069616892436*r52[i]
- 13694916176593289530129597814644948512271618874572800000*r53[i]
- 152504503331260902260854535497432382418134663231196077636*r54[i]
- 1696290932754493307608442494949489883113732653837516800000*r55[i]
- 18847853343293961413885442066505656038216029001597219552756*r56[i]
- 209224108506820468190445154809088053753746980238797209600000*r57[i]
- 2320543439896457435907968420234632701280456371329787317976356*r58[i]
) // 51090942171709440000 for i in range(len(r0))]
r19 = [(-16796*r[1][i]
+ 25194*r[2][i]
- 23256*r[3][i]
+ 15504*r[4][i]
- 7752*r[5][i]
+ 2907*r[6][i]
- 798*r[7][i]
+ 152*r[8][i]
- 18*r[9][i]
+ r[10][i]
+ 4862*r0[i]
- 2860*r2[i]
+ 7436*r4[i]
- 46420*r6[i]
+ 576236*r8[i]
- 13098580*r10[i]
+ 532310636*r12[i]
- 39968611540*r14[i]
+ 6350631494636*r16[i]
- 3730771315561300*r18[i]
- 2637991952943407764*r20[i]
- 46833363657400320000*r21[i]
- 734121065118879803860*r22[i]
- 10556240168378032128000*r23[i]
- 142438684135271315212564*r24[i]
- 1830415113744266649600000*r25[i]
- 22632897298190126259675220*r26[i]
- 271297526662043666104320000*r27[i]
- 3170344993810020486920015764*r28[i]
- 36274730261563609572556800000*r29[i]
- 407775103607650299563627591380*r30[i]
- 4515882637052182897862000640000*r31[i]
- 49377994276343186011748723193364*r32[i]
- 534053247401000753173510963200000*r33[i]
- 5722063606154183864914875339648340*r34[i]
- 60811730909031986048777521029120000*r35[i]
- 641729418431834160625738740379401364*r36[i]
- 6730380606921481449181267599974400000*r37[i]
- 70207898580127312813466155395513222100*r38[i]
- 728918319689461841494925372032622592000*r39[i]
- 7536441803725213229125462424550696575764*r40[i]
- 77635978704164552294553096402068152320000*r41[i]
- 797177898990753876072852178329776532568660*r42[i]
- 8162164080895303403984327865949915250688000*r43[i]
- 83359491110673172494030048846026790563932564*r44[i]
- 849432099945167336777734465061373289267200000*r45[i]
- 8638438243166451781593809976801426668242424020*r46[i]
- 87694169965134464605849462884812769886371840000*r47[i]
- 888832151283066038746077396233689115965303967764*r48[i]
- 8996158031157109433578511766939541381376409600000*r49[i]
- 90938713449996246641127353860256309887114389604180*r50[i]
- 918234342704615923743435749615058841825963745280000*r51[i]
- 9262393601318313123889045816028965261306516208457364*r52[i]
- 93347798539774463006574188993931221735397071462400000*r53[i]
- 940020095741410096004864931705566108623177977672605140*r54[i]
- 9459299151254233261484792667142328326155545534423040000*r55[i]
- 95126631804495487685309357589162668229325862229818457364*r56[i]
- 956083153653743104841229026765469375616248871549132800000*r57[i]
- 9604295785153755194654527876717123591063888034645559202900*r58[i]
) // 121645100408832000 for i in range(len(r0))]
r17 = [(4862*r[1][i]
- 7072*r[2][i]
+ 6188*r[3][i]
- 3808*r[4][i]
+ 1700*r[5][i]
- 544*r[6][i]
+ 119*r[7][i]
- 16*r[8][i]
+ r[9][i]
- 1430*r0[i]
+ 858*r2[i]
- 2310*r4[i]
+ 15258*r6[i]
- 206790*r8[i]
+ 5386458*r10[i]
- 272513670*r12[i]
+ 30255826458*r14[i]
- 12765597850950*r16[i]
- 6622557957272742*r18[i]
- 101370917007360000*r19[i]
- 1375210145685786630*r20[i]
- 17172233341046784000*r21[i]
- 201832098313986359142*r22[i]
- 2265471043586150400000*r23[i]
- 24529324224160803328710*r24[i]
- 258058524232798248960000*r25[i]
- 2652208374242713043720742*r26[i]
- 26739700571225856614400000*r27[i]
- 265323404171486113659725190*r28[i]
- 2597688920748017370193920000*r29[i]
- 25147613788240222384169485542*r30[i]
- 241125683321001354933657600000*r31[i]
- 2293170112631184981695915264070*r32[i]
- 21656158388689797460311183360000*r33[i]
- 203283794784841444836991831621542*r34[i]
- 1898267590696733462875776307200000*r35[i]
- 17646072330245312137111933794073350*r36[i]
- 163392570167583908119294187237376000*r37[i]
- 1507754227229479379470312529237936742*r38[i]
- 13871774079585871769182921633935360000*r39[i]
- 127291574907112728538906245247680921030*r40[i]
- 1165398276253942030786602999248830464000*r41[i]
- 10648249156718669259487809979675840079142*r42[i]
- 97121906010634492337139410720414515200000*r43[i]
- 884471146488697462546213719879378982015110*r44[i]
- 8043742604145412070397708709577312747520000*r45[i]
- 73065283527546375984492393431422365909536742*r46[i]
- 662985481414219219279431223562176586956800000*r47[i]
- 6010229010788429141870217066922217223929803590*r48[i]
- 54440174236564270133288224915510829498019840000*r49[i]
- 492755135434761578293305350886942317529465637542*r50[i]
- 4457205465827107111785421147442507464329523200000*r51[i]
- 40294548566019835134386988604297024831948411774470*r52[i]
- 364091512505225031658987624997678808818240901120000*r53[i]
- 3288369094603737090125334557327653119906621235549542*r54[i]
- 29687831954151399686402807167358312867527245926400000*r55[i]
- 267931592702357971121614379534668912664625180303255750*r56[i]
- 2417320348710838875594605100171158543649224733843456000*r57[i]
- 21803421488305619170801322564396870819527683367726280742*r58[i]
) // 355687428096000 for i in range(len(r0))]
r15 = [(-1430*r[1][i]
+ 2002*r[2][i]
- 1638*r[3][i]
+ 910*r[4][i]
- 350*r[5][i]
+ 90*r[6][i]
- 14*r[7][i]
+ r[8][i]
+ 429*r0[i]
- 264*r2[i]
+ 744*r4[i]
- 5304*r6[i]
+ 81384*r8[i]
- 2605944*r10[i]
+ 192387624*r12[i]
- 55942352184*r14[i]
- 20546119600536*r16[i]
- 266765571072000*r17[i]
- 3083760849804024*r18[i]
- 32945548027392000*r19[i]
- 332500281299403096*r20[i]
- 3215147584416768000*r21[i]
- 30076927429146721464*r22[i]
- 274100623905588480000*r23[i]
- 2446077617962088140056*r24[i]
- 21459412163122053120000*r25[i]
- 185641639183185136464504*r26[i]
- 1587401376760010972160000*r27[i]
- 13442713420403849918131416*r28[i]
- 112915002722102749808640000*r29[i]
- 941961013910760913890393144*r30[i]
- 7812419263561351877518080000*r31[i]
- 64474322285718607792730497176*r32[i]
- 529848386811984810994744320000*r33[i]
- 4338547620121893769542630267384*r34[i]
- 35415056327751829508662891008000*r35[i]
- 288317531175033442515609896757336*r36[i]
- 2341823147101379454117987013632000*r37[i]
- 18983391549723892653716655806647224*r38[i]
- 153619763998111828980832157720832000*r39[i]
- 1241292607509331793516191597844431896*r40[i]
- 10017079537004367071413852136982528000*r41[i]
- 80746194097372251940077615903073292664*r42[i]
- 650250798838302173122854563322562560000*r43[i]
- 5232061257212799699445154857325986640856*r44[i]
- 42067391464856035210355948847111229440000*r45[i]
- 338018548004311349729166172709579357563704*r46[i]
- 2714522948575416807552558113876933656320000*r47[i]
- 21788917503304477212565325243539420555704216*r48[i]
- 174821149505151584518657828257831893345280000*r49[i]
- 1402141896338776811136967582554033500226820344*r50[i]
- 11242168283931454427825411966307736057167360000*r51[i]
- 90112723368126633235251766101448928377940741976*r52[i]
- 722130298632985742738270377008563798712253440000*r53[i]
- 5785647203879657431846619085033124824223750822584*r54[i]
- 46345442737409930132271027996820593307050786048000*r55[i]
- 371185586083174668935874345914297403283249129274136*r56[i]
- 2972440128704949475548399682088668166048497569792000*r57[i]
- 23800215895013012584326308679319205581074142060130424*r58[i]
) // 1307674368000 for i in range(len(r0))]
r13 = [(429*r[1][i]
- 572*r[2][i]
+ 429*r[3][i]
- 208*r[4][i]
+ 65*r[5][i]
- 12*r[6][i]
+ r[7][i]
- 132*r0[i]
+ 84*r2[i]
- 252*r4[i]
+ 2004*r6[i]
- 37212*r8[i]
+ 1710324*r10[i]
- 325024572*r12[i]
- 80789566956*r14[i]
- 871782912000*r15[i]
- 8422900930332*r16[i]
- 75583578470400*r17[i]
- 643521842437836*r18[i]
- 5269678622208000*r19[i]
- 41890044885642492*r20[i]
- 325386564299596800*r21[i]
- 2481686964269990316*r22[i]
- 18652248729354240000*r23[i]
- 138536531588626169052*r24[i]
- 1019042849143807488000*r25[i]
- 7436421488952386592396*r26[i]
- 53911021949819274240000*r27[i]
- 388701690499592948238012*r28[i]
- 2789805187365599475072000*r29[i]
- 19946749502047187160692076*r30[i]
- 142159780685991861112320000*r31[i]
- 1010433303980489860989897372*r32[i]
- 7165521770403817166663116800*r33[i]
- 50716588034439244118483617356*r34[i]
- 358378772025058883636009472000*r35[i]
- 2528902640579773012941059115132*r36[i]
- 17824202779159732939433280230400*r37[i]
- 125502611080965065134883934376236*r38[i]
- 882926862501000079240924013568000*r39[i]
- 6206986746547700738292160195379292*r40[i]
- 43608135571536574058895364550860800*r41[i]
- 306213499909407501334225902520456716*r42[i]
- 2149239710498553002348841878415360000*r43[i]
- 15079178774724614117506008765315297852*r44[i]
- 105761403926812162332273274580071296000*r45[i]
- 741573481088337285231858048220674626796*r46[i]
- 5198479982499565882352899855753044480000*r47[i]
- 36434172034715569203746509369098022198812*r48[i]
- 255308169532157231577671227649975633664000*r49[i]
- 1788771440213892011837337228527544587734476*r50[i]
- 12531087911298377892590529356517576445440000*r51[i]
- 87775753902632879954790735906635276359730172*r52[i]
- 614779166184964747722494610821477092697932800*r53[i]
- 4305547785126634750908211772273402537757507756*r54[i]
- 30151397670066414681209001391191401891653632000*r55[i]
- 211135169951589392525478765734151290219989459932*r56[i]
- 1478398543308500990816235131524636835468791910400*r57[i]
- 10351504105448519912343628516946177846975433354636*r58[i]
) // 6227020800 for i in range(len(r0))]
r11 = [(-132*r[1][i]
+ 165*r[2][i]
- 110*r[3][i]
+ 44*r[4][i]
- 10*r[5][i]
+ r[6][i]
+ 42*r0[i]
- 28*r2[i]
+ 92*r4[i]
- 868*r6[i]
+ 22652*r8[i]
- 2620708*r10[i]
- 415790788*r12[i]
- 3632428800*r13[i]
- 28616744548*r14[i]
- 210680870400*r15[i]
- 1479485236228*r16[i]
- 10038995366400*r17[i]
- 66394067988388*r18[i]
- 430591742380800*r19[i]
- 2750479262009668*r20[i]
- 17360942812012800*r21[i]
- 108550450893568228*r22[i]
- 673606803881088000*r23[i]
- 4154688725062207108*r24[i]
- 25499502190850688000*r25[i]
- 155878445775166700068*r26[i]
- 949776357849070752000*r27[i]
- 5771581202353414724548*r28[i]
- 34995682724855684832000*r29[i]
- 211811399872933910999908*r30[i]
- 1280080235834717770252800*r31[i]
- 7726641919200262371657988*r32[i]
- 46591059456870785061004800*r33[i]
- 280704018540064430354883748*r34[i]
- 1690018909819536161979590400*r35[i]
- 10169113413821714748538703428*r36[i]
- 61159784116494648773674886400*r37[i]
- 367684638335977863351585967588*r38[i]
- 2209739160176731898013383884800*r39[i]
- 13276598260065161268654185556868*r40[i]
- 79750432649108163224160355276800*r41[i]
- 478956917715683026467561165467428*r42[i]
- 2876013540917084725512964985376000*r43[i]
- 17267443120712778679894991796314308*r44[i]
- 103661474908781590201983341856096000*r45[i]
- 622252957609245047342724399262599268*r46[i]
- 3734938395375021425507273833823424000*r47[i]
- 22416734056596928549732496421419871748*r48[i]
- 134535924504317597978456420953656384000*r49[i]
- 807393154821611376674434030676868979108*r50[i]
- 4845246995796352471529950975101582508800*r51[i]
- 29075922420664314894010979796628180325188*r52[i]
- 174477737199628479530547826532207368300800*r53[i]
- 1046977438360831608823005722785678653022948*r54[i]
- 6282419713119688698679893309347069088230400*r55[i]
- 37697293722049221763903820338234783307370628*r56[i]
- 226197639663181194193832237585541373553126400*r57[i]
- 1357255225090438261356667179220676921014346788*r58[i]
) // 39916800 for i in range(len(r0))]
r9 = [(42*r[1][i]
- 48*r[2][i]
+ 27*r[3][i]
- 8*r[4][i]
+ r[5][i]
- 14*r0[i]
+ 10*r2[i]
- 38*r4[i]
+ 490*r6[i]
- 31238*r8[i]
- 2922230*r10[i]
- 19958400*r11[i]
- 124075238*r12[i]
- 726485760*r13[i]
- 4084385750*r14[i]
- 22313491200*r15[i]
- 119387268038*r16[i]
- 628980992640*r17[i]
- 3275389222070*r18[i]
- 16905818966400*r19[i]
- 86665431465638*r20[i]
- 441935114987520*r21[i]
- 2244295389943190*r22[i]
- 11360520464832000*r23[i]
- 57360469753884038*r24[i]
- 289038899804054400*r25[i]
- 1454155949521941110*r26[i]
- 7306671293537616000*r27[i]
- 36677059892827099238*r28[i]
- 183960524908301057280*r29[i]
- 922104761587650687830*r30[i]
- 4619736062008593926400*r31[i]
- 23135540444136227047238*r32[i]
- 115825176110799088940160*r33[i]
- 579715876176320506935350*r34[i]
- 2900939663557699476451200*r35[i]
- 14514140349055749129024038*r36[i]
- 72608472572041292373527040*r37[i]
- 363193454272347163609915670*r38[i]
- 1816571661325589960713958400*r39[i]
- 9085275939429279963731685638*r40[i]
- 45436050447189540392656321920*r41[i]
- 227218935892633882388998540790*r42[i]
- 1136249416059455304696385296000*r43[i]
- 5681866032591044240951769048038*r44[i]
- 28411805989856165780668427308800*r45[i]
- 142068933310062230858345890602710*r46[i]
- 710384280152969638132390327392000*r47[i]
- 3552079855654080764219631870487238*r48[i]
- 17761033099263130050180188817751680*r49[i]
- 88807700784593943012315384189973430*r50[i]
- 444048645089005049723558441367254400*r51[i]
- 2220283790147933078276819155128739238*r52[i]
- 11101581209667596183377765341852994560*r53[i]
- 55508555084398602505584708639561804950*r54[i]
- 277545371567282194146167718608057971200*r55[i]
- 1387737242420707782996791311133835900038*r56[i]
- 6938727750450146421431883624171745261440*r57[i]
- 34693804905665422905113851276795595729270*r58[i]
) // 362880 for i in range(len(r0))]
r7 = [(-14*r[1][i]
+ 14*r[2][i]
- 6*r[3][i]
+ r[4][i]
+ 5*r0[i]
- 4*r2[i]
+ 20*r4[i]
- 604*r6[i]
- 29740*r8[i]
- 151200*r9[i]
- 708604*r10[i]
- 3160080*r11[i]
- 13645900*r12[i]
- 57657600*r13[i]
- 239967004*r14[i]
- 988107120*r15[i]
- 4037604460*r16[i]
- 16406863200*r17[i]
- 66398623804*r18[i]
- 267911678160*r19[i]
- 1078605601420*r20[i]
- 4335313752000*r21[i]
- 17403958407004*r22[i]
- 69804002545200*r23[i]
- 279780634372780*r24[i]
- 1120816644948000*r25[i]
- 4488349371924604*r26[i]
- 17968646803620240*r27[i]
- 71920337041294540*r28[i]
- 287818601403715200*r29[i]
- 1151686172846664604*r30[i]
- 4607980008114455280*r31[i]
- 18435626012705982700*r32[i]
- 73753622051697957600*r33[i]
- 295047842329672995004*r34[i]
- 1180291431927853642320*r35[i]
- 4721465916019935893260*r36[i]
- 18886764229967380219200*r37[i]
- 75549758619456576163804*r38[i]
- 302207139580435761213360*r39[i]
- 1208852873637267995922220*r40[i]
- 4835484440511039999684000*r41[i]
- 19342156599960850372299004*r42[i]
- 77369282913655045261040400*r43[i]
- 309479101196178257662005580*r44[i]
- 1237922313409633551106176000*r45[i]
- 4951706979513788347008408604*r46[i]
- 19806881095681900978203235440*r47[i]
- 79227683915609817008158719340*r48[i]
- 316911214261089847968346159200*r49[i]
- 1267646292840319012979866380604*r50[i]
- 5070589478749170677837606550480*r51[i]
- 20282370837160398114302240879500*r52[i]
- 81129522115132801716459190737600*r53[i]
- 324518204760004960744377010983004*r54[i]
- 1298073167938441356814707920777520*r55[i]
- 5192293718449030473173589579142060*r56[i]
- 20769178013881918039244948535655200*r57[i]
- 83076721475785062614244197861863804*r58[i]
) // 5040 for i in range(len(r0))]
r5 = [(5*r[1][i]
- 4*r[2][i]
+ r[3][i]
- 2*r0[i]
+ 2*r2[i]
- 22*r4[i]
- 478*r6[i]
- 1680*r7[i]
- 5542*r8[i]
- 17640*r9[i]
- 54958*r10[i]
- 168960*r11[i]
- 515062*r12[i]
- 1561560*r13[i]
- 4717438*r14[i]
- 14217840*r15[i]
- 42784582*r16[i]
- 128615880*r17[i]
- 386371918*r18[i]
- 1160164320*r19[i]
- 3482590102*r20[i]
- 10451964600*r21[i]
- 31364282398*r22[i]
- 94109624400*r23[i]
- 282362427622*r24[i]
- 847154391720*r25[i]
- 2541597392878*r26[i]
- 7625060614080*r27[i]
- 22875718713142*r28[i]
- 68628229881240*r29[i]
- 205886837127358*r30[i]
- 617664806349360*r31[i]
- 1853003008982662*r32[i]
- 5559026206817160*r33[i]
- 16677112980189838*r34[i]
- 50031407660046240*r35[i]
- 150094360419092182*r36[i]
- 450283356135183480*r37[i]
- 1350850618161364318*r38[i]
- 4052552953995720720*r39[i]
- 12157661061010417702*r40[i]
- 36472987581077764200*r41[i]
- 109418971539326314798*r42[i]
- 328256932210164988800*r43[i]
- 984770831814867055222*r44[i]
- 2954312565813345343320*r45[i]
- 8862937838177524385278*r46[i]
- 26588813796007549866480*r47[i]
- 79766441950972603020742*r48[i]
- 239299326978817715904840*r49[i]
- 717897983188252961399758*r50[i]
- 2153693954068358511569760*r51[i]
- 6461081871212274789450262*r52[i]
- 19383245631651222877832760*r53[i]
- 58149736930982465652462238*r54[i]
- 174449210865004990995314640*r55[i]
- 523347632739130161061799782*r56[i]
- 1570042898505620859337111080*r57[i]
- 4710128696093323330314756718*r58[i]
) // 120 for i in range(len(r0))]
r3 = [(-2*r[1][i]
+ r[2][i]
+ 1*r0[i]
- 2*r2[i]
- 14*r4[i]
- 30*r5[i]
- 62*r6[i]
- 126*r7[i]
- 254*r8[i]
- 510*r9[i]
- 1022*r10[i]
- 2046*r11[i]
- 4094*r12[i]
- 8190*r13[i]
- 16382*r14[i]
- 32766*r15[i]
- 65534*r16[i]
- 131070*r17[i]
- 262142*r18[i]
- 524286*r19[i]
- 1048574*r20[i]
- 2097150*r21[i]
- 4194302*r22[i]
- 8388606*r23[i]
- 16777214*r24[i]
- 33554430*r25[i]
- 67108862*r26[i]
- 134217726*r27[i]
- 268435454*r28[i]
- 536870910*r29[i]
- 1073741822*r30[i]
- 2147483646*r31[i]
- 4294967294*r32[i]
- 8589934590*r33[i]
- 17179869182*r34[i]
- 34359738366*r35[i]
- 68719476734*r36[i]
- 137438953470*r37[i]
- 274877906942*r38[i]
- 549755813886*r39[i]
- 1099511627774*r40[i]
- 2199023255550*r41[i]
- 4398046511102*r42[i]
- 8796093022206*r43[i]
- 17592186044414*r44[i]
- 35184372088830*r45[i]
- 70368744177662*r46[i]
- 140737488355326*r47[i]
- 281474976710654*r48[i]
- 562949953421310*r49[i]
- 1125899906842622*r50[i]
- 2251799813685246*r51[i]
- 4503599627370494*r52[i]
- 9007199254740990*r53[i]
- 18014398509481982*r54[i]
- 36028797018963966*r55[i]
- 72057594037927934*r56[i]
- 144115188075855870*r57[i]
- 288230376151711742*r58[i]
) // 6 for i in range(len(r0))]
r1 = [r[1][i]
- r0[i]
- r2[i]
- r3[i]
- r4[i]
- r5[i]
- r6[i]
- r7[i]
- r8[i]
- r9[i]
- r10[i]
- r11[i]
- r12[i]
- r13[i]
- r14[i]
- r15[i]
- r16[i]
- r17[i]
- r18[i]
- r19[i]
- r20[i]
- r21[i]
- r22[i]
- r23[i]
- r24[i]
- r25[i]
- r26[i]
- r27[i]
- r28[i]
- r29[i]
- r30[i]
- r31[i]
- r32[i]
- r33[i]
- r34[i]
- r35[i]
- r36[i]
- r37[i]
- r38[i]
- r39[i]
- r40[i]
- r41[i]
- r42[i]
- r43[i]
- r44[i]
- r45[i]
- r46[i]
- r47[i]
- r48[i]
- r49[i]
- r50[i]
- r51[i]
- r52[i]
- r53[i]
- r54[i]
- r55[i]
- r56[i]
- r57[i]
- r58[i]
for i in range(len(r0))]
return (r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58)
|
996,045 | 26238d8310c5deb17528ea600b5bd18b40c8f108 | #! "C:\Program Files (x86)\Python37-32\python.exe"
import openpyxl
from openpyxl import load_workbook
file = "MOCK_DATA.xlsx"
#load the work book
wb_obj = load_workbook(filename = file)
wsheet = wb_obj['MOCK_DATA']
#store data in a dictionary for convenience
dataDict = {}
for key, *values in wsheet.iter_rows(min_row=2):
dataDict[key.value] = [v.value for v in values]
# print ("Contents of your spreadsheet :\n",dataDict)
#prompt user for input(ID)
userInput = input("Please enter an ID of a person to find a his/her details: ")
#print details of a person associated with above ID
if (int(userInput)) in dataDict:
print("Details requested for the ID:",int(userInput))
print(dataDict.get(int(userInput)))
else:
print("The ID",userInput,"is not found. Please enter a valid id")
|
996,046 | c10fdc2b4961f45864d70246a988fee6c4ca0b19 | # smtplib 发送邮件流程
# 连接到smtp服务器
import smtplib
smtp = smtplib.SMTP('smtp.qq.com', 25)
# 发送SMTP的'hello'信息
# smtp.ehlo()
# Out[24]:
# (250,
# b'smtp.qq.com\nPIPELINING\nSIZE 73400320\nSTARTTLS\nAUTH LOGIN PLAIN\nAUTH=LOGIN\nMAILCOMPRESS\n8BITMIME')
# 将当前会话加密
smtp.starttls()
# Out[25]: (220, b'Ready to start TLS')
# 登陆到SMTP服务器（密码为SMTP服务第三方授权码）
smtp.login('4****1@qq.com', 'b****h')
# Out[26]: (235, b'Authentication successful')
# 发送邮件
smtp.sendmail('4xxx2@qq.com', 'xixxx@163.com', 'Subject:this is test\nthis is a')
# Out[27]: {}
# 关闭连接
smtp.quit()
# email 构造邮件
from email.mime.text import MIMEText
def send_mail(fromuser, password, toaddr, title, msg):
msg = MIMEText(msg)
msg['Subject'] = title
msg['From'] = fromuser
msg['To'] = toaddr
smtp = smtplib.SMTP(SEMP_SERVER, SERVER_PORT)
try:
smtp.ehlo()
smtp.starttls()
smtp.login(from_addr, password)
smtp.sendmail(from_addr, to_add, msg.as_string())
except Exception:
raise
finally:
smtp.quit()
send_mail(from_addr, password, to_add, title, msg)
# 发送附件表格（构造一个APP对象）
msg = MIMEMultipart()
msg['Subject'] = title
msg['From'] = from_addr
msg['To'] = to_addr
msg.attach(MIMEText('kabuka'))
with open('D:\\dsb.xlsx', 'rb') as f:
a = MIMEApplication(f.read())
a.add_header('Content-Disposition', 'attachment', filename='xxx.xlsx')
msg.attach(a)
s = smtplib.SMTP('smtp.qq.com', 25)
s.ehlo()
s.starttls()
s.login(from_addr, password)
s.sendmail(from_addr, to_addr, msg.as_string())
s.quit()
import yagmail
yag = yagmail.SMTP(user='4xxx@qq.com', password='bxxxxh', host='smtp.qq.com')
contents = ['This is the body', ' D:\\dsdfb.xlsx']
yag.send('xxx9@163.com', 'subject', contents)
yag.close()
|
996,047 | a10e4a6fa4d3e74083ef00595536b0cb4b473146 | import pandas as pd
import pygal
from pygal.style import DarkStyle
def spirit():
"""start age"""
data = pd.read_csv("never_female.csv")
line_graph = pygal.Pie(fill=True, interpolate='cubic', style=DarkStyle)
line_graph.x_labels = data.AGE
line_graph.y_labels = map(int, range(0, 400001, 20000))
line_graph.add("10-14 years old", data.TENTOFOURTEEN)
line_graph.add("15-19 years old", data.FIFTHTEENTONINETEEN)
line_graph.add("20-24 years old", data.TWENTYTOTWENTYFOUR)
line_graph.add("25-29 years old", data.TWENTYFIVETOTWENTYNINE)
line_graph.add("30-34 years old", data.THIRTYTOTHIRFOUR)
line_graph.add("35-39 years old", data.THIRFIVETOTHIRNINE)
line_graph.add("Above 40 years old", data.ABOVEFORTY)
line_graph.render_to_file("never_fe.svg")
spirit()
|
996,048 | 772486d949a13627a8c8540e1531a99ad901843b | continua = True
while continua:
try:
x = int(input('Primeiro valor:'))
y = int(input('Segundo valor:'))
if y == 0:
raise ZeroDivisionError
except ValueError:
print('O valor informado deve ser númerico')
except ZeroDivisionError:
print('Impossivel dividir por Zero')
else:
continua = False
z = x/y
print(' O resultado da divisão é: ', z)
|
996,049 | ab88cb9d42934ab40b600826fd5229359920f6c5 | i=0
while i<=100:
print("中秋节快乐",end='')
i+=1
print("热烈庆祝中华人民共和国成立70周年!")
|
996,050 | d978e77ffb92321720ef54bc9c3d0aba0a8ce0d9 | from django.conf.urls import url
from . import views
urlpatterns = [
url('^$' ,views.index),
url(r'^mycrude/$', views.mycrude_list),
url(r'^mycrude/(?P<id>[0-9]+)$', views.mycrude_detail),
]
|
996,051 | 7742430c8f376f5850ca3cb44b06c4ad0b58fb37 | from prodtest import ProduceTestCase
class PretendUpToDatePatternTest(ProduceTestCase):
def test_pretend_up_to_date(self):
# a1
# |
# b1
# / \
# c1 d1
normal = lambda: self.produce('a1')
pretending = lambda: self.produce('a1', **{'-u': 'b%{i}'})
self.assertDirectoryContents(('produce.ini',))
self.assertUpdates((), normal, ('a1', 'b1', 'c1', 'd1'), ())
self.assertUpdates(('c1',), normal, ('a1', 'b1'), ('c1', 'd1'))
self.assertUpdates(('c1',), pretending, (), ('a1', 'b1', 'c1', 'd1'))
self.assertUpdates((), normal, ('a1', 'b1'), ('c1', 'd1'))
self.assertUpdates(('b1',), normal, ('a1',), ('b1', 'c1', 'd1'))
self.assertUpdates(('b1',), pretending, ('a1',), ('b1', 'c1', 'd1'))
|
996,052 | 4c61e35b4054669c3219f78abfa548fbbe985258 | import unittest
from contextlib import contextmanager
class MiCustomManager:
def __init__(self, estado):
self.estado = estado
def __enter__(self):
print("Entrando en el contexto")
return self.estado
def __exit__(self, exc_type, exc_val, exc_tb):
print("Saliendo del contexto")
return True; #Al devolver un True siempre salimos del contexto correctamente. Haya o no haya excepcion
@contextmanager
def openfile(filepath):
file = open(filepath, "r")
yield file
file.close()
class ContextManagerTest(unittest.TestCase):
def test_debeLlamarAUnCustomContextManagerComoClase(self):
with MiCustomManager("miestado") as estado:
self.assertEqual("miestado", estado)
def test_debeLanzarUnaExcecionLlamarAUnCustomContextManager(self):
with MiCustomManager("miestado") as estado:
raise Exception("Mi Excepcion")
def test_debeLlamarAUnContextManagerComoGeneratorYDecorator(self):
with openfile("file.txt") as mifichero:
self.assertEqual("Contenido", mifichero.read())
if __name__ == "__main__":
unittest.main() |
996,053 | 9fe7729a70e77b4c2980c5d2079e8d2894db0750 | import cv2
import numpy as np
import RPi.GPIO as GPIO
LimiarBinarizacao = 125 #este valor eh empirico. Ajuste-o conforme sua necessidade
AreaContornoLimiteMin = 5000 #este valor eh empirico. Ajuste-o conforme sua necessidade
#GPIOs utilizados:
GPIOMotor1 = 18 #Broadcom pi2067n 18 (P1 pin 12)
GPIOMotor2 = 17 #Broadcom pin 17 (P1 pin 11)
#Funcao: trata imagem e retorna se o robo seguidor de linha deve ir para a esqueda ou direita
#Parametros: frame capturado da webcam e primeiro frame capturado
#Retorno: < 0: robo deve ir para a direita
# > 0: robo deve ir para a esquerda
# 0: nada deve ser feito
def TrataImagem(img):
#obtencao das dimensoes da imagem
height = np.size(img,0)
width= np.size(img,1)
QtdeContornos = 0
DirecaoASerTomada = 0
#tratamento da imagem
gray = cv2.cvtColor(img,cv2.COLOR_BGR2GRAY)
gray = cv2.GaussianBlur(gray, (21, 21), 0)
FrameBinarizado = cv2.threshold(gray,LimiarBinarizacao,255,cv2.THRESH_BINARY)[1]
FrameBinarizado = cv2.dilate(FrameBinarizado,None,iterations=2)
FrameBinarizado = cv2.bitwise_not(FrameBinarizado)
#descomente as linhas abaixo se quiser ver o frame apos binarizacao, dilatacao e inversao de cores
#cv2.imshow('F.B.',FrameBinarizado)
#cv2.waitKey(10)
_, cnts, _ = cv2.findContours(FrameBinarizado.copy(), cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)
cv2.drawContours(img,cnts,-1,(255,0,255),3)
for c in cnts:
#se a area do contorno capturado for pequena, nada acontece
if cv2.contourArea(c) < AreaContornoLimiteMin:
continue
QtdeContornos = QtdeContornos + 1
#obtem coordenadas do contorno (na verdade, de um retangulo que consegue abrangir todo ocontorno) e
#realca o contorno com um retangulo.
(x, y, w, h) = cv2.boundingRect(c) #x e y: coordenadas do vertice superior esquerdo
#w e h: respectivamente largura e altura do retangulo
cv2.rectangle(img, (x, y), (x + w, y + h), (0, 255, 0), 2)
#determina o ponto central do contorno e desenha um circulo para indicar
CoordenadaXCentroContorno = (x+x+w)/2
CoordenadaYCentroContorno = (y+y+h)/2
PontoCentralContorno = (CoordenadaXCentroContorno,CoordenadaYCentroContorno)
cv2.circle(img, PontoCentralContorno, 1, (0, 0, 0), 5)
DirecaoASerTomada = CoordenadaXCentroContorno - (width/2) #em relacao a linha central
#output da imagem
#linha em azul: linha central / referencia
#linha em verde: linha que mostra distancia entre linha e a referencia
cv2.line(img,(width/2,0),(width/2,height),(255,0,0),2)
if (QtdeContornos > 0):
cv2.line(img,PontoCentralContorno,(width/2,CoordenadaYCentroContorno),(0,255,0),1)
cv2.imshow('Analise de rota',img)
cv2.waitKey(10)
return DirecaoASerTomada, QtdeContornos
#Programa principal
#Setup dos GPIOs:
GPIO.setmode(GPIO.BCM)
GPIO.setup(GPIOMotor1, GPIO.OUT)
GPIO.setup(GPIOMotor2, GPIO.OUT)
GPIO.output(GPIOMotor1, GPIO.LOW)
GPIO.output(GPIOMotor2, GPIO.LOW)
camera = cv2.VideoCapture(0)
camera.set(3,320)
camera.set(4,240)
#faz algumas leituras de frames antes de consierar a analise
#motivo: algumas camera podem demorar mais para se "acosumar a luminosidade" quando ligam, capturando frames consecutivos com muita variacao de luminosidade. Para nao levar este efeito ao processamento de imagem, capturas sucessivas sao feitas fora do processamento da imagem, dando tempo para a camera "se acostumar" a luminosidade do ambiente
for i in range(0,20):
(grabbed, Frame) = camera.read()
while True:
try:
(grabbed, Frame) = camera.read()
if (grabbed):
Direcao,QtdeLinhas = TrataImagem(Frame)
if (QtdeLinhas == 0):
print "Nenhuma linha encontrada. O robo ira parar."
GPIO.output(GPIOMotor1, GPIO.LOW)
GPIO.output(GPIOMotor2, GPIO.LOW)
continue
if (Direcao > 0):
print "Distancia da linha de referencia: "+str(abs(Direcao))+" pixels a direita"
GPIO.output(GPIOMotor1, GPIO.HIGH)
GPIO.output(GPIOMotor2, GPIO.LOW)
if (Direcao < 0):
print "Distancia da linha de referencia: "+str(abs(Direcao))+" pixels a esquerda"
GPIO.output(GPIOMotor1, GPIO.LOW)
GPIO.output(GPIOMotor2, GPIO.HIGH)
if (Direcao == 0):
print "Exatamente na linha de referencia!"
GPIO.output(GPIOMotor1, GPIO.HIGH)
GPIO.output(GPIOMotor2, GPIO.HIGH)
except (KeyboardInterrupt):
GPIO.output(GPIOMotor1, GPIO.LOW)
GPIO.output(GPIOMotor2, GPIO.LOW)
exit(1) |
996,054 | 46fc04f94749f2dd6759fd7457cba23777f51564 | largura = int(input("digite a largura: "))
altura = int(input("digite a altura: "))
if altura == largura:
cont = largura
while altura > 0:
while cont > 0:
cont = cont - 1
print("#", end= "")
cont = largura
print()
altura = altura - 1
else:
cont = largura
cont2 = altura
while cont2 > 0:
while cont > 0:
cont = cont - 1
if cont2 == altura or cont2 == 1 :
print("#", end= "")
elif cont == largura - 1 or cont == 0:
print ("#", end="")
else:
print(" ",end="")
cont = largura
print()
cont2 = cont2 - 1
|
996,055 | 92d7a4b90a1c838f70f50d1e121382ef2442cef7 | import unittest
class TestDatLoad(unittest.TestCase):
"""
Data Load lambda tests
"""
def test_data_load(self):
print ('to be implemented')
if __name__ == '__main__':
unittest.main()
|
996,056 | 9d0216e47cd6636915004c12ac12be3adcc3f9e6 | def fun(a):
if len(a)==1:
return 0
dp = [0]*len(a)
dp[0]=a[0]
dp[1]=dp[0]+abs(a[0]-a[1])
for i in range(2,len(a)):
dp[i]=min(dp[i-1]+abs(a[i]-a[i-1]) ,dp[i-2]+abs(a[i]-a[i-2]))
return dp[-1]-a[0]
n = int(input())
a = list(map(int , input().split()))
print(fun(a)) |
996,057 | 4413b3b897d95c91235537e5c415538622476634 | # from optionModelsDEF.blackScholesModel import *
# from optionModelsDEF.commonFuncs import *
from optionModelsDEF.commonFuncs import fillDerivativesArray as f
|
996,058 | 4fafab702d70738229f307b96f3453d7577b5076 | # -*- coding: utf-8 -*-
import sys
import Xerces, XQilla
def main():
# Get the XQilla DOMImplementation object
xqillaImplementation = Xerces.DOMImplementationRegistry.getDOMImplementation('XPath2 3.0')
# Create a DOMDocument
document = xqillaImplementation.createDocument()
# Parse an XPath 2 expression
expression = document.createExpression('1 to 100', None)
# Execute the query
result = expression.evaluate(None, Xerces.DOMXPathResult.ITERATOR_RESULT_TYPE, None)
# Iterate over the results, printing them
while result.iterateNext():
print result.getIntegerValue()
return sys.exit(0)
if __name__ == '__main__':
main()
|
996,059 | 1ca587eb7d4b26449dca116350ef3416bbffb432 | # The Best Dictionary in The World
# created in Sleepy Hollow NY on October 28, 2015
# by Aneta Zolkiewicz for Edward Eames
print "You are the best in the world!\n"
world_best_dic = {'you are': "jestes", 'the best': "najlepsza", 'in': "na", 'the world': "swiecie"}
print world_best_dic['you are'], world_best_dic['the best'], world_best_dic['in'], world_best_dic['the world'] + "!\n"
print "Words to learn: \n"
for word in world_best_dic:
print word, " - ", world_best_dic[word]
print " "
word_searched = raw_input("Edziu what word are you looking for? ")
for word in world_best_dic:
if word_searched in world_best_dic:
word = word_searched
print word, " - ", world_best_dic[word]
break
else:
print " Edziu the dictionary doesn't contain that word!"
break
|
996,060 | c71156e02198a12a2025d4aae59bd858626e9e65 | import pdfquery
import scraperwiki
from bs4 import BeautifulSoup
import StringIO
#from pdfquery.cache import FileCache
import re
base_url = "http://dpc.sa.gov.au"
html = scraperwiki.scrape("http://www.dpc.sa.gov.au/lobbyist-who-register")
soup = BeautifulSoup(html, "html5lib")
lobbys = []
for tr in soup.tbody:
lobby = {}
lobby['trading_name'] = tr.find_all('td')[0].text.split("|")[0].strip()
lobby['business_name'] = tr.find_all('td')[1].text.strip() or lobby['trading_name']
lobby['last_updated'] = tr.find_all('td')[2].text.strip()
for a in tr.find_all('a'):
if 'PDF' in a.text:
url = a.get('href')
if url.startswith('/sites'):
url = base_url + url
lobby['pdf_url'] = url
lobbys.append(lobby)
# lobbys = [{'trading_name':'xxx','business_name':'yyy', 'last_updated':'1/1/2016', 'pdf_url':'fff'}]
listpart = re.compile('\. (.*)')
clientlistpart = re.compile('(\d\.|\.|)(.*)')
numberre = re.compile('\d')
clientnumberre = re.compile('\d(\.| )')
page_width = 595.32
page_height = 841.92
for lobby in lobbys:
if True:
print lobby["pdf_url"]
binary = StringIO.StringIO(scraperwiki.scrape(lobby["pdf_url"]))
# binary = open('test.pdf')
pdf = pdfquery.PDFQuery(binary)#, parse_tree_cacher=FileCache("/tmp/"))
pdf.load()
#pdf.tree.write("test2.xml", pretty_print=True, encoding="utf-8")
business_entity_name = lobby['business_name']
last_updated = lobby['last_updated']
trading_name = lobby['trading_name']
if pdf.pq('LTTextBoxHorizontal:contains(".B.N")'):
abn_x = float(pdf.pq('LTTextBoxHorizontal:contains(".B.N")').attr('x1'))
abn_y = float(pdf.pq('LTTextBoxHorizontal:contains(".B.N")').attr('y0'))
if pdf.pq('LTTextBoxHorizontal:contains(".C.N")'):
abn_x = float(pdf.pq('LTTextBoxHorizontal:contains(".C.N")').attr('x1'))
abn_y = float(pdf.pq('LTTextBoxHorizontal:contains(".C.N")').attr('y0'))
abn = pdf.pq(
'LTTextBoxHorizontal:in_bbox("%s, %s, %s, %s")' % (abn_x, abn_y, page_width, abn_y + 15))\
.text().replace(' ','').strip()
scraperwiki.sqlite.save(unique_keys=["abn", "business_name"],
data={'business_name': business_entity_name,
'abn': abn,
'last_updated': last_updated,
'trading_name': trading_name,
},
table_name="lobbyist_firms")
try:
owners = pdf.pq(':in_bbox("%s, %s, %s, %s")' % (0, float(
pdf.pq('LTTextBoxHorizontal:contains("etails of all employees undertaking lobbying activities")').attr(
'y0')) + 10, page_width, float(
pdf.pq('LTTextBoxHorizontal:contains("Australian Securities and Investments Commission")').attr('y1')) - 1))
except:
print "cannot find owners in this PDF, skipping :("
continue
for owner in owners:
if owner.text and '.' in owner.text:
name = listpart.findall(owner.text)[0].strip()
if name and name != 'Please note that, where relevant, this information should match the details':
scraperwiki.sqlite.save(unique_keys=["lobbyist_firm_abn", "name"],
data={'name': name, 'lobbyist_firm_name': business_entity_name,
'lobbyist_firm_abn': abn},
table_name="lobbyist_firm_owners")
employees = pdf.pq(':in_bbox("%s, %s, %s, %s")' % (
0, pdf.pq('LTTextBoxHorizontal:contains("lient Details")').attr('y1'), page_width,
pdf.pq('LTTextBoxHorizontal:contains("etails of all employees undertaking lobbying activities")').attr('y0')))
for employee in employees:
if employee.text and '.' in employee.text:
for part in numberre.split(employee.text):
for name in listpart.findall(part):
name = name.strip()
if name:
scraperwiki.sqlite.save(unique_keys=["lobbyist_firm_abn", "name"],
data={'name': name, 'lobbyist_firm_name': business_entity_name,
'lobbyist_firm_abn': abn},
table_name="lobbyists")
clients = pdf.pq(':in_bbox("%s, %s, %s, %s")' % (
0, pdf.pq('LTTextBoxHorizontal:contains("y completing this form")').attr('y1'), page_width, pdf.pq(
'LTTextBoxHorizontal:contains("lease provide the names of the organisations (or individuals) that are your clients")').attr(
'y0'))
)
for client in clients:
if client.text:
name = clientlistpart.findall(client.text)[0][1].strip()
name = clientnumberre.sub('', clientnumberre.sub('',name))
if name:
scraperwiki.sqlite.save(unique_keys=["lobbyist_firm_abn", "name"],
data={'name': name, 'lobbyist_firm_name': business_entity_name,
'lobbyist_firm_abn': abn},
table_name="lobbyist_clients")
if pdf.pq('LTPage[page_index="1"] LTTextBoxHorizontal:contains("y completing this form")').attr('y1'):
clients = pdf.pq('LTPage[page_index="1"] :in_bbox("%s, %s, %s, %s")' % (
0, pdf.pq('LTPage[page_index="1"] LTTextBoxHorizontal:contains("y completing this form")').attr('y1'),
page_width, page_height))
for client in clients:
if client.text and '.' in client.text:
name = clientlistpart.findall(client.text)[0][1].strip()
name = clientnumberre.sub('', clientnumberre.sub('',name))
if name:
scraperwiki.sqlite.save(unique_keys=["lobbyist_firm_abn", "name"],
data={'name': name, 'lobbyist_firm_name': business_entity_name,
'lobbyist_firm_abn': abn},
table_name="lobbyist_clients")
|
996,061 | ea4147923a64b3b613feb41556d619db8f2f3b47 | # Extract names around each word regex
>>> import re
>>> re.findall(r"([a-zA-Z]+) loves ([a-zA-Z]+)", "Mary loves Mike,Jack loves Lily,Ethan loves Lydia")
[('Mary', 'Mike'), ('Jack', 'Lily'), ('Ethan', 'Lydia')]
|
996,062 | 26b6c7cdd3887e471cfe7b72ae6b0a2cd957e6f9 | from room import Room
from items import Item
# Declare all the rooms
room = {
'outside': Room("Outside Cave Entrance",
"""North of you, the cave mount beckons"""),
'foyer': Room("Foyer",
"""Dim light filters in from the south. Dusty passages run north and east."""),
'overlook': Room("Grand Overlook",
"""A steep cliff appears before you, falling into the darkness.
Ahead to the north, a light flickers in the distance, but there is no way across the chasm."""),
'narrow': Room("Narrow Passage",
"""The narrow passage bends here from west to north.
The smell of gold permeates the air."""),
'treasure': Room("Treasure Chamber",
"""You've found the long-lost treasure chamber!
Search the room to find what riches await! The only exit is to the south."""),
'secret': Room("Secret Chamber",
"""You have entered a secret chamber, who knows what you will find in here.""")
}
# Link rooms together
room['outside'].n_to = room['foyer']
room['foyer'].s_to = room['outside']
room['foyer'].n_to = room['overlook']
room['foyer'].e_to = room['narrow']
room['overlook'].s_to = room['foyer']
room['narrow'].w_to = room['foyer']
room['narrow'].n_to = room['treasure']
room['treasure'].s_to = room['narrow']
room['overlook'].n_to = room['secret']
room['secret'].s_to = room['overlook']
|
996,063 | 6ba5cf5974e59ea5a78a107d14bd98f920e040dc | import numpy as np
from scipy.integrate import odeint
import matplotlib.pyplot as plt
POBLACION_TOTAL = 1.
INFECTADOS_INICIAL, RECUPERADOS_INICIAL = 0.03, 0
SUSCEPTIBLES_INICIAL = POBLACION_TOTAL - INFECTADOS_INICIAL - RECUPERADOS_INICIAL
ALFA, BETA = 0.27, 0.043
TIEMPO_DIAS = np.linspace(0, 150, 150)
def modelo_sir(y, t, N, alfa, beta):
S, I, R = y
dSdt = -alfa * S * I / N
dIdt = alfa * S * I / N - beta * I
dRdt = beta * I
return dSdt, dIdt, dRdt
ESTADO_INICIAL = SUSCEPTIBLES_INICIAL, INFECTADOS_INICIAL, RECUPERADOS_INICIAL
ret = odeint(modelo_sir, ESTADO_INICIAL, TIEMPO_DIAS, args=(POBLACION_TOTAL, ALFA, BETA))
S, I, R = ret.T
fig = plt.figure()
ax = fig.add_subplot(111, axisbelow=True)
ax.plot(TIEMPO_DIAS, S, 'b')
ax.plot(TIEMPO_DIAS, I, 'r')
ax.plot(TIEMPO_DIAS, R, 'g')
ax.set_xlabel('Dias')
ax.set_ylabel('% Poblacion')
ax.set_title('Evolucion Epidemia')
ax.set_ylim(0, 1.25)
ax.set_xlim(0, 180)
plt.savefig('evolucion_pandemia.png')
plt.show()
# ITEM C
POBLACION_TOTAL = 1000
INFECTADOS_INICIAL, RECUPERADOS_INICIAL = POBLACION_TOTAL * 0.03, 0
SUSCEPTIBLES_INICIAL = POBLACION_TOTAL - INFECTADOS_INICIAL - RECUPERADOS_INICIAL
CAPACIDAD_SISTEMA_SANITARIO = POBLACION_TOTAL * 0.3
PASO_ALFA = 0.01
TIEMPO_DIAS = np.linspace(0, 250, 250)
ESTADO_INICIAL = SUSCEPTIBLES_INICIAL, INFECTADOS_INICIAL, RECUPERADOS_INICIAL
while True:
se_saturo = False
ret = odeint(modelo_sir, ESTADO_INICIAL, TIEMPO_DIAS, args=(POBLACION_TOTAL, ALFA, BETA))
S, I, R = ret.T
for i in range(len(I)):
if (I[i] > CAPACIDAD_SISTEMA_SANITARIO):
print("Saturado con Alfa: {}".format(ALFA))
ALFA = ALFA - PASO_ALFA;
se_saturo=True
break;
if not se_saturo:
print("NO SATURADO CON ALFA: {}".format(ALFA))
for i in range(len(I)):
if (I[i] < 1):
print("Dia con menos de 1 infectado: {}".format(i))
break
break
fig = plt.figure()
ax = fig.add_subplot(111, axisbelow=True)
ax.plot(TIEMPO_DIAS, S, 'b')
ax.plot(TIEMPO_DIAS, I, 'r')
ax.plot(TIEMPO_DIAS, R, 'g')
ax.plot([0,250], [CAPACIDAD_SISTEMA_SANITARIO,CAPACIDAD_SISTEMA_SANITARIO],'k')
ax.set_xlabel('Dias')
ax.set_ylabel('Cantidad Personas')
ax.set_title('Evolucion Epidemia sin Saturar')
ax.set_ylim(0,POBLACION_TOTAL * 1.10)
ax.set_xlim(0, 250)
ax.plot()
plt.savefig('evolucion_pandemia_sin_saturar.png')
plt.show()
|
996,064 | 81104078d33d89699254099d30d53e4b6910f0ae | import csv
import json
import colorama
from termcolor import cprint
import sys
sys.path.append('../../Code/Algorithms')
sys.path.append('../../Data')
sys.path.append('../../Results')
from read_data import read_data
from smart_grid import SmartGrid, SmartHouse, SmartBattery
def main():
""" fixed, you can now use this as both a function and as script"""
house_path = '../../Data/wijk1_huizen.csv'
battery_path = '../../Data/wijk1_batterijen.txt'
houses, batteries = read_data(house_path, battery_path)
smart_wijk = SmartGrid(51,51)
smart_wijk.add_house_dictionaries(houses)
smart_wijk.add_battery_dictionaries(batteries)
for element in houses:
smart_wijk.create_house(element['position'], element['output'])
for element in batteries:
smart_wijk.create_battery(element['position'], element['capacity'])
solution_reader(smart_wijk, '../../Results/best_brabo_solution.csv')
def solution_reader(smart_wijk, results_path = 'Results/best_brabo_solution.csv'):
"""
Reads the solution from a file
reads a solution from a csv
DEPRECATED DO NOT USE
"""
with open(results_path, 'r') as f:
best_reader = csv.reader(f)
for i, row in enumerate(best_reader):
# for some reason the csv contains empty lists?
if len(row) == 0:
continue
if i == 1:
# print(row[1])
row[1] = row[1].replace("'", '"')
parsed_data = json.loads(row[1])
# print(len(row))
best_houses = parsed_data['DATA']
for connectionz in best_houses:
smart_wijk.connect(connectionz['connected_to'], connectionz['position'])
smart_wijk.prettify()
print(smart_wijk.calc_cost())
smart_wijk.cap_left()
if __name__ == "__main__":
main()
|
996,065 | c3f379a20bd340d9d9827fc87a61f59638543f37 | # 당신은 최근에 코딩 스터지 모임을 새로 만들었습니다.
|
996,066 | 1121eb433f425a5bfde1d68e433a3af98554119c | num = int(input("Number Nakh"))
if (num % 2) == 0:
print("Beki Chhe")
else:
print("Eki Chhe")
if (num % 4) == 0:
print("4 na pada ma aave chhe")
else:
print("4 na pada ma nathi aavto")
num1 = int(input("pelo Number Nakh"))
num2 = int(input("bijo Number Nakh"))
devide = num1 / 2
if devide == num2:
print("Evenly Devide")
else:
print("Not Evenly Devide")
|
996,067 | 9ec1d0c0da5cc232ff4c44caa7f23dac4ed7c7fd |
import re
pattern =re.compile(r'\d+') #用于匹配至少一个数字
m=pattern.match('one12twothree34four') #查找头部，没有匹配
print(m,'\n')
m=pattern.match('one12twothree34four',2,10) #从脚标为2的‘e’开始匹配，并没有匹配
print(m)
m=pattern.match('one12twothree34four',3,10) #从脚标为3的‘1’开始匹配，正好匹配
print(m) # <re.Match object; span=(3, 5), match='12'>
print(m.group(0))
print(m.start(0))
print(m.end(0))
print(m.span(0))
print(m.groups())
|
996,068 | 3b2f1798f70c319c3474b87726e9f46a9f0230fa | import ast
import pytest
import re
import shutil
import tarfile
from poetry.io import NullIO
from poetry.masonry.builders.sdist import SdistBuilder
from poetry.packages import Package
from poetry.poetry import Poetry
from poetry.utils._compat import Path
from poetry.utils._compat import to_str
from poetry.utils.venv import NullVenv
from tests.helpers import get_dependency
fixtures_dir = Path(__file__).parent / "fixtures"
@pytest.fixture(autouse=True)
def setup():
clear_samples_dist()
yield
clear_samples_dist()
def clear_samples_dist():
for dist in fixtures_dir.glob("**/dist"):
if dist.is_dir():
shutil.rmtree(str(dist))
def project(name):
return Path(__file__).parent / "fixtures" / name
def test_convert_dependencies():
package = Package("foo", "1.2.3")
result = SdistBuilder.convert_dependencies(
package,
[
get_dependency("A", "^1.0"),
get_dependency("B", "~1.0"),
get_dependency("C", "1.2.3"),
],
)
main = ["A>=1.0,<2.0", "B>=1.0,<1.1", "C==1.2.3"]
extras = {}
assert result == (main, extras)
package = Package("foo", "1.2.3")
package.extras = {"bar": [get_dependency("A")]}
result = SdistBuilder.convert_dependencies(
package,
[
get_dependency("A", ">=1.2", optional=True),
get_dependency("B", "~1.0"),
get_dependency("C", "1.2.3"),
],
)
main = ["B>=1.0,<1.1", "C==1.2.3"]
extras = {"bar": ["A>=1.2"]}
assert result == (main, extras)
c = get_dependency("C", "1.2.3")
c.python_versions = "~2.7 || ^3.6"
d = get_dependency("D", "3.4.5", optional=True)
d.python_versions = "~2.7 || ^3.4"
package.extras = {"baz": [get_dependency("D")]}
result = SdistBuilder.convert_dependencies(
package,
[
get_dependency("A", ">=1.2", optional=True),
get_dependency("B", "~1.0"),
c,
d,
],
)
main = ["B>=1.0,<1.1"]
extra_python = (
':(python_version >= "2.7" and python_version < "2.8") '
'or (python_version >= "3.6" and python_version < "4.0")'
)
extra_d_dependency = (
'baz:(python_version >= "2.7" and python_version < "2.8") '
'or (python_version >= "3.4" and python_version < "4.0")'
)
extras = {extra_python: ["C==1.2.3"], extra_d_dependency: ["D==3.4.5"]}
assert result == (main, extras)
def test_make_setup():
poetry = Poetry.create(project("complete"))
builder = SdistBuilder(poetry, NullVenv(), NullIO())
setup = builder.build_setup()
setup_ast = ast.parse(setup)
setup_ast.body = [n for n in setup_ast.body if isinstance(n, ast.Assign)]
ns = {}
exec(compile(setup_ast, filename="setup.py", mode="exec"), ns)
assert ns["packages"] == [
"my_package",
"my_package.sub_pkg1",
"my_package.sub_pkg2",
]
assert ns["install_requires"] == ["cachy[msgpack]>=0.2.0,<0.3.0", "cleo>=0.6,<0.7"]
assert ns["entry_points"] == {
"console_scripts": [
"my-2nd-script = my_package:main2",
"my-script = my_package:main",
]
}
assert ns["extras_require"] == {"time": ["pendulum>=1.4,<2.0"]}
def test_find_files_to_add():
poetry = Poetry.create(project("complete"))
builder = SdistBuilder(poetry, NullVenv(), NullIO())
result = builder.find_files_to_add()
assert result == [
Path("LICENSE"),
Path("README.rst"),
Path("my_package/__init__.py"),
Path("my_package/data1/test.json"),
Path("my_package/sub_pkg1/__init__.py"),
Path("my_package/sub_pkg2/__init__.py"),
Path("my_package/sub_pkg2/data2/data.json"),
Path("pyproject.toml"),
]
def test_package():
poetry = Poetry.create(project("complete"))
builder = SdistBuilder(poetry, NullVenv(), NullIO())
builder.build()
sdist = fixtures_dir / "complete" / "dist" / "my-package-1.2.3.tar.gz"
assert sdist.exists()
tar = tarfile.open(str(sdist), "r")
assert "my-package-1.2.3/LICENSE" in tar.getnames()
def test_module():
poetry = Poetry.create(project("module1"))
builder = SdistBuilder(poetry, NullVenv(), NullIO())
builder.build()
sdist = fixtures_dir / "module1" / "dist" / "module1-0.1.tar.gz"
assert sdist.exists()
tar = tarfile.open(str(sdist), "r")
assert "module1-0.1/module1.py" in tar.getnames()
def test_prelease():
poetry = Poetry.create(project("prerelease"))
builder = SdistBuilder(poetry, NullVenv(), NullIO())
builder.build()
sdist = fixtures_dir / "prerelease" / "dist" / "prerelease-0.1b1.tar.gz"
assert sdist.exists()
def test_with_c_extensions():
poetry = Poetry.create(project("extended"))
builder = SdistBuilder(poetry, NullVenv(), NullIO())
builder.build()
sdist = fixtures_dir / "extended" / "dist" / "extended-0.1.tar.gz"
assert sdist.exists()
tar = tarfile.open(str(sdist), "r")
assert "extended-0.1/build.py" in tar.getnames()
assert "extended-0.1/extended/extended.c" in tar.getnames()
def test_with_src_module_file():
poetry = Poetry.create(project("source_file"))
builder = SdistBuilder(poetry, NullVenv(), NullIO())
# Check setup.py
setup = builder.build_setup()
setup_ast = ast.parse(setup)
setup_ast.body = [n for n in setup_ast.body if isinstance(n, ast.Assign)]
ns = {}
exec(compile(setup_ast, filename="setup.py", mode="exec"), ns)
assert ns["package_dir"] == {"": "src"}
assert re.search("'py_modules': 'module_src'", to_str(setup)) is not None
builder.build()
sdist = fixtures_dir / "source_file" / "dist" / "module-src-0.1.tar.gz"
assert sdist.exists()
tar = tarfile.open(str(sdist), "r")
assert "module-src-0.1/src/module_src.py" in tar.getnames()
def test_with_src_module_dir():
poetry = Poetry.create(project("source_package"))
builder = SdistBuilder(poetry, NullVenv(), NullIO())
# Check setup.py
setup = builder.build_setup()
setup_ast = ast.parse(setup)
setup_ast.body = [n for n in setup_ast.body if isinstance(n, ast.Assign)]
ns = {}
exec(compile(setup_ast, filename="setup.py", mode="exec"), ns)
assert ns["package_dir"] == {"": "src"}
assert ns["packages"] == ["package_src"]
builder.build()
sdist = fixtures_dir / "source_package" / "dist" / "package-src-0.1.tar.gz"
assert sdist.exists()
tar = tarfile.open(str(sdist), "r")
assert "package-src-0.1/src/package_src/__init__.py" in tar.getnames()
assert "package-src-0.1/src/package_src/module.py" in tar.getnames()
|
996,069 | 64d6c2c9b9bc3bb659579fa496a8d44eb13a2169 | import random
def generate(count):
"""This module will generate values for requests and write them into a file
Alternatively we can read from db or from file here.
If we care about the memory, we can replace this with generator.
:param count: how many values to generate
:return: lst - list of values to send
"""
lst = []
with open('data.txt', 'w+') as f:
for i in range(0, count):
st = str(random.random())
f.write(st+"\n")
lst.append(st)
return lst
|
996,070 | 4506d703398d64a8bc7347b3905c682f564bcecb | #!/usr/bin/env python
#-*- coding:utf-8 -*-
"""
@author:BanShaoHuan
@file: Python自动生成表情包.py
@time: 2018/05/11
@contact: banshaohuan@163.com
@site:
@software: PyCharm
# code is far away from bugs with the god animal protecting
I love animals. They taste delicious.
┏┓ ┏┓
┏┛┻━━━┛┻┓
┃ ☃ ┃
┃ ┳┛ ┗┳ ┃
┃ ┻ ┃
┗━┓ ┏━┛
┃ ┗━━━┓
┃ 神兽保佑 ┣┓
┃ 永无BUG！ ┏┛
┗┓┓┏━┳┓┏┛
┃┫┫ ┃┫┫
┗┻┛ ┗┻┛
"""
from PIL import Image,ImageDraw,ImageFont
img = Image.open('hah.png')
draw = ImageDraw.Draw(img)
ttfont = ImageFont.truetype('simhei.ttf', 24)
draw.text((32,190), '我的内心毫无波动', fill=(0, 0, 0), font=ttfont)
draw.text((64,220), '甚至还想笑', fill=(0, 0, 0), font=ttfont)
# img.show()
img.save('nice.png') |
996,071 | 98129813f36a577c04068a1b3002ce27668454ec | from sklearn.decomposition import PCA
from keras.utils import normalize as norm_keras
from sklearn.preprocessing import normalize as norm_skl
from numpy import asarray, concatenate, transpose, column_stack, array, isnan, amin, amax, vstack, ndarray
from random import sample
from numpy.random import shuffle
from itertools import chain
from matplotlib import pyplot as plt
# from src.const.cfg import COUNT_SPEAKERS, COUNT_RECORDS_TRAINING, COUNT_RECORDS_TEST
def dimensionality_reduction(dim, features):
pca = PCA(n_components=dim)
# pca = PCA(n_components=cfg.DIMENSIONALITY, svd_solver='full')
reduced = pca.fit_transform(features)
return reduced
def concatenated_data(x, y):
'''
Объедененные данные для обучения ИЛИ тестирования, где в последнем столбце матрицы признаков находятся метки
присутствия диктора.
:param x: матрица признаков 20*800|200*6373.
:param y: матрица меток 20*800|200*1.
:return: общая матрица данных.
'''
data = []
concatenate(x, transpose([y]), axis=1)
return asarray(data)
def concatenated_features(features_20, features_30, proportion_20=(30, 10, 10), proportion_30=(40, 10, 0)):
'''
Объединяет признаки разных наборов данных с разными дикторами (пример для 20 и 30 дикторов,
результат - количество наблюдений для всех 50 дикторов):
train: 20*30+30*40=600+1200=1800;
val: 20*10+30*10=200+300=500;
extract: 20*(30+10+10)=1000;
test: 20*10=200.
:param features: список признаков для 20 и 30 дикторов.
:param proportion: пропорции для обучения, валидации, тестирования.
:return: общий список признаков для 50 дикторов.
'''
count_speakers = int(len(features_20) / sum(proportion_20))
x_train_20, x_test_20 = split_data_wav(features_20,
nb_train=proportion_20[0] + proportion_20[1],
nb_test=proportion_20[2],
count_speakers=count_speakers)
x_train_20, x_val_20 = split_data_wav(x_train_20,
nb_train=proportion_20[0],
nb_test=proportion_20[1],
count_speakers=count_speakers)
count_speakers = int(len(features_30) / sum(proportion_30))
x_train_30, x_val_30 = split_data_wav(features_30,
nb_train=proportion_30[0],
nb_test=proportion_30[1],
count_speakers=count_speakers)
x_train, x_val, x_test = x_train_20 + x_train_30, x_val_20 + x_val_30, change_order_obs(20, x_train_20, x_val_20,
x_test_20)
del x_train_20, x_train_30, x_val_20, x_val_30, x_test_20
# return x_train, x_val, x_test_20
return x_train, x_val, x_test
def change_order_obs(count_speakers=20, *data):
separation, grouped = [], []
for sample in data:
mass = []
size = len(sample)
records = int(size / count_speakers)
# l = [i for i in range(size)]
for i in range(0, size, records):
mass.append(sample[i:i + records])
separation.append(mass)
del mass, sample, data
if type(separation[0][0]) is list:
for i in range(count_speakers):
grouped.append(separation[0][i] + separation[1][i] + separation[2][i])
elif type(separation[0][0]) is ndarray:
for i in range(count_speakers):
grouped.append(vstack((separation[0][i], separation[1][i], separation[2][i])))
else:
raise Exception('Неизвестный тип для группирования входных данных!')
del separation
merged = list(chain.from_iterable(grouped))
del grouped
return merged
def balance_data(x, y, max_true=None, max_false=None):
'''
Балансировка данных, чтобы не было большого разброса 0 и 1.
:param x: массив признаков.
:param y: массив меток 20 дикторов.
:param max_true: макс количество наблюдений, где присутствует диктор.
:param max_false: макс количество наблюдений, где диктор отсутствует.
:var index_true: индексы элементов меток, где диктор присутствует.
:var index_false: индексы элементов меток, где диктор отсутствует.
:var short_index_true: из index_true берутся max_true значений (индексов).
:var short_index_false: из index_false берутся max_false значений (индексов).
:var final_x: берутся строки из матрицы признаков с индексами short_index_true и short_index_false.
:var final_y: генерируются массивы 1 и 0 и объединяются, размеров max_true и max_false соответственно.
:return: ndarray final_x, ndarray final_y
'''
index_true = [i for i, e in enumerate(y) if e == 1]
index_false = [i for i, e in enumerate(y) if e == 0]
MAX_TRUE = len(index_true) if max_true is None or max_true > len(index_true) else max_true
MAX_FALSE = len(index_false) if max_false is None or max_false > len(index_false) else max_false
short_index_true = sample(index_true, MAX_TRUE)
short_index_false = sample(index_false, MAX_FALSE)
final_x = ([x[_i] for _i in short_index_true] + [x[_i] for _i in short_index_false])
final_y = ([1] * MAX_TRUE + [0] * MAX_FALSE)
final_x, final_y = shuffle_data(array(final_x), array(final_y))
return final_x, final_y
def mixing_data(x, y):
'''
Перемешивание строк (наблюдений) в пределах одного диктора.
:param y: метки наличия диктора.
:param x: массив с признаками для 20 дикторов.
:return: перемешенные признаки (final_x) и соответствующие метки (final_y).
'''
combined = column_stack((x, transpose(y)))
shuffle(combined)
final_x = (combined[:, :-1])
final_y = (transpose(combined[:, -1:].astype(int))[0])
return asarray(final_x), asarray(final_y)
def shuffle_data(x, y):
type_features = type(x)
numbered_x = list(enumerate(x))
shuffle(numbered_x)
ind, shuffle_x = zip(*numbered_x)
shuffle_y = []
for obs in ind:
shuffle_y.append(y[obs])
shuffle_y = array(shuffle_y)
if type_features == list:
shuffle_x = list(shuffle_x)
elif type_features == ndarray:
shuffle_x = array(shuffle_x)
else:
raise Exception('Нет алгоритма перемешивания для заданных входных данных.')
return shuffle_x, shuffle_y
def normalize(features):
type_mass = type(features)
axis = features[0].shape
if type_mass == ndarray and len(axis) == 2:
features = norm_keras(features, axis=1)
elif type_mass == ndarray and len(axis) == 1:
features = norm_skl(features, axis=0)
elif type_mass == list and len(axis) == 2:
features = normalize_3D_features(features)
else:
raise Exception('Поданы данные для которых нет алгоритма обработки!')
return features
def normalize_3D_features(features):
'''
Нормализация низкоуровневых признаков (частоты по времени). Итерирование по столбцам наблюдений.
:param features: список признаков.
:return: нормализованные признаки.
'''
x_max, x_min = max_coef(features), min_coef(features)
sub_max_min = x_max - x_min
for rec in features:
for column in range(rec.shape[1]):
rec[:, column] = ((rec[:, column] - x_min) / sub_max_min) - 0.5
return features
def max_coef(features):
'''
Изначально находится максимум по строкам (например: 1500 наблюдений, 129 частот и разная длина фразы;
нормализация по частотам). На выходе: матрица наблюдений*количество частот (например: 1500*129).
После ищется максимум по строкам для всех наблюдений (например, после матрицы 1500*129 на выходе
получится вектор 129).
:param features: список признаков.
:return: вектор нормализации (максимумы).
'''
maximum = []
for rec in features:
maximum.append(amax(rec, axis=1))
return array(maximum).max(axis=0)
def min_coef(features):
minimum = []
for rec in features:
minimum.append(amin(rec, axis=1))
return array(minimum).min(axis=0)
def split_data_wav(data, nb_train=40, nb_test=10, count_speakers=20):
train, test = [], []
all_records = nb_train + nb_test
temp = [data[i:i + all_records] for i in range(0, len(data), all_records)]
for speaker in range(count_speakers):
train.append(temp[speaker][:nb_train])
test.append(temp[speaker][-nb_test:])
train = list(chain(*train))
test = list(chain(*test))
return train, test
def split_data(data, nb_train=40, nb_test=10, count_speakers=20):
train, test = [], []
count_axis = len(data.shape)
all_records = nb_train + nb_test
# для меток
if count_axis <= 1:
temp_data = data.reshape(count_speakers, all_records)
for speaker in range(count_speakers):
train.append(temp_data[speaker][:nb_train])
test.append(temp_data[speaker][-nb_test:])
train, test = array(train), array(test)
train = train.reshape(count_speakers * nb_train)
test = test.reshape(count_speakers * nb_test)
# для матрицы
elif count_axis == 2:
temp_data = data.reshape(count_speakers, all_records, data.shape[1])
for speaker in range(count_speakers):
train.append(temp_data[speaker][:nb_train])
test.append(temp_data[speaker][-nb_test:])
train, test = array(train), array(test)
train = train.reshape(count_speakers * nb_train, data.shape[1])
test = test.reshape(count_speakers * nb_test, data.shape[1])
# для картинок
elif count_axis == 3:
temp_data = data.reshape(count_speakers, all_records, data.shape[1], data.shape[2])
for speaker in range(count_speakers):
train.append(temp_data[speaker][:nb_train])
test.append(temp_data[speaker][-nb_test:])
train, test = array(train), array(test)
train = train.reshape(count_speakers * nb_train, data.shape[1], data.shape[2])
test = test.reshape(count_speakers * nb_test, data.shape[1], data.shape[2])
else:
raise Exception('Количество осей больше 3!')
return train, test
def expansion(lst):
shape = len(lst[0].shape)
size_x = [item.shape[1] for item in lst]
max_x = max(size_x)
index_no_max = [index for index, item in enumerate(lst) if item.shape[1] != max_x]
result = []
for index, item in enumerate(lst):
if index in index_no_max:
difference = array([[0] * (max_x - item.shape[1])] * item.shape[0])
join_array = concatenate((item, difference), axis=1)
result.append(join_array)
else:
result.append(item)
return array(result)
def expansion_1D(lst):
shape = len(lst[0].shape)
size_x = [item.shape[0] for item in lst]
max_x = max(size_x)
index_no_max = [index for index, item in enumerate(lst) if item.shape[0] != max_x]
result = []
for index, item in enumerate(lst):
if index in index_no_max:
difference = array([0] * (max_x - item.shape[0]))
join_array = concatenate((item, difference), axis=0)
result.append(join_array)
else:
result.append(item)
return result
def expansion_3D(lst):
size_x = [item.shape[2] for item in lst]
max_x = max(size_x)
index_no_max = [index for index, item in enumerate(lst) if item.shape[2] != max_x]
result = []
for index, item in enumerate(lst):
if index in index_no_max:
difference = array([[[0] * (max_x - item.shape[2])] * item.shape[1]] * item.shape[0])
join_array = concatenate((item, difference), axis=2)
result.append(join_array)
else:
result.append(item)
# if len(set(item.shape[1] for item in lst)) > 1:
# result = temp(result)
return result
def contraction(lst):
size_x = [item.shape[1] for item in lst]
min_x = min(size_x)
index_no_min = [index for index, item in enumerate(lst) if item.shape[1] != min_x]
result = []
for index, item in enumerate(lst):
if index in index_no_min:
array = item[:, :min_x]
result.append(array)
else:
result.append(item)
return result
def contraction_1D(lst):
size_x = [item.shape[0] for item in lst]
min_x = min(size_x)
index_no_min = [index for index, item in enumerate(lst) if item.shape[0] != min_x]
result = []
for index, item in enumerate(lst):
if index in index_no_min:
array = item[:min_x]
result.append(array)
else:
result.append(item)
return result
def contraction_3D(lst):
size_x = [item.shape[2] for item in lst]
min_x = min(size_x)
index_no_min = [index for index, item in enumerate(lst) if item.shape[2] != min_x]
result = []
for index, item in enumerate(lst):
if index in index_no_min:
array = item[:, :, :min_x]
result.append(array)
else:
result.append(item)
return result
|
996,072 | cbcfffe4ba4deb756f691ede1405be9d451af490 | from src.environment import Environment
from src.action import Action
from src.q_learning.q_agent import QAgent
from src.q_learning.q_episode import QEpisode
from src.performace import Performance
from src.state import State
from src.q_learning.q_function import QFunction
import pickle
class QLearning:
def __init__(self, environment: Environment, epsilon, epsilon_decay_rate, solver='table', q=None):
self.state = State(environment.observation_space)
self.action = Action(environment.action_space, epsilon, epsilon_decay_rate)
if solver == 'table':
self.q = QFunction(learning_rate, discount_rate)
elif solver == 'NN_agent':
self.q = QAgent(learning_rate, discount_rate)
self.q.initialize(self.state, self.action, q)
self.episode = QEpisode(environment, self.state, self.action, self.q)
self.environment = environment
self.performance = Performance()
def train(self, learning, discount, no_of_episodes):
for ep_no in range(no_of_episodes):
self.episode.initialize(learning, discount)
show = True if (ep_no + 1) % 50 == 0 else False # if no_of_episodes - ep_no <= 2 else False
reward = self.episode.play(show=show)
self.performance.append(reward)
if (ep_no + 1) % 10 == 0:
self.performance.print(ep_no + 1, reset=True, custom=f'eps = {self.action.epsilon}')
self.action.go_confident()
self.environment.close()
return self.performance
if __name__ == '__main__':
# environment_name = 'MountainCar-v0'
# environment_name = 'FrozenLake8x8-v0'
environment_name = 'CartPole-v1'
# environment_name = 'DuplicatedInput-v0'
learning_rate = 0.001
discount_rate = 0.95
eps = .99
alpha = 0.0005
solver = 'NN_agent'
episodes = 1000
try:
pickling_on = open(f"models/{environment_name}.pickle", "rb")
q = pickle.load(pickling_on)
pickling_on.close()
print('loading completed')
except FileNotFoundError:
q = None
env = Environment(environment_name)
q_learn = QLearning(environment=env, epsilon=eps, epsilon_decay_rate=alpha, solver=solver)
performance = q_learn.train(learning_rate, discount_rate, episodes)
performance.plot()
pickling_on = open(f"models/{environment_name}.pickle", "wb")
pickle.dump(q_learn.q.current, pickling_on)
pickling_on.close()
|
996,073 | 40d2e354701cb65b18c78beab16be13bd7ab2cbd | # Bomb Rewards Policies
BOMB_NO_REWARD = 0
BOMB_REWARD_PER_STONE_DESTROYED = 1
BOMB_REWARD_PER_STONE_DESTROYED_PROPORTIONAL_TO_EXIT = 2
# Navigation Rewards Policies
NAVIGATION_NO_REWARD = 0
NAVIGATION_REWARD_PROPORTIONAL_TO_EXIT = 1
# Agents
QLEARNING = 0
RMAX = 1
FACTOREDRMAX = 2
SARSA = 4
SARSALAMBDA = 5
DYNA = 6
FACTOREDAGENTS = [FACTOREDRMAX]
REQUIRESNEXTACTION = [SARSA,SARSALAMBDA]
# Task
DETERMINISTIC = 0
STOCHASTIC_NAVIGATION = 1
STOCHASTIC_EXPLOSION = 2 |
996,074 | 3373f324d629d4eecd01c706388d13f938a12175 | import os
import glob
import shutil
import json
from pprint import pprint
import numpy as np
def evaluate_check_point_json(checkpoint_json_file):
with open(checkpoint_json_file) as data_file:
data = json.load(data_file)
loss_history = data['val_loss_history']
checkpoint_pointer = data['val_loss_history_it']
best_i = np.argmin(loss_history)
return loss_history[best_i], checkpoint_pointer[best_i]
def get_latest_checkpoint(path):
newest = max(glob.iglob(path + '/*.json'), key=os.path.getctime)
return newest
def delete_folder_content(folder):
for the_file in os.listdir(folder):
file_path = os.path.join(folder, the_file)
try:
if os.path.isfile(file_path):
os.unlink(file_path)
elif os.path.isdir(file_path): shutil.rmtree(file_path)
except Exception as e:
print(e)
def run_command(command, run):
print command
if run:
os.system(command)
run = False
num_layers = 2
batch_size = 50
data_name = 'BlackOakUppercase'
num_columns = 12
for column_id in range(num_columns):
command = 'python scripts/preprocess.py \\\n' + \
'--input_txt /root/torch-rnn/storage/' + data_name + '/column_' + str(column_id) + '/orig_input/column_' + str(column_id) + '.txt \\\n' + \
'--output_h5 /root/torch-rnn/storage/' + data_name + '/column_' + str(column_id) + '/input/my_data.h5 \\\n' + \
'--output_json /root/torch-rnn/storage/' + data_name + '/column_' + str(column_id) + '/input/my_data.json\n\n'
run_command(command, run)
command = 'th train.lua -input_h5 /root/torch-rnn/storage/' + data_name + '/column_' + str(
column_id) + '/input/my_data.h5 -input_json /root/torch-rnn/storage/' + data_name + '/column_' + str(
column_id) + '/input/my_data.json -checkpoint_name /root/torch-rnn/storage/' + data_name + '/column_' + str(
column_id) + '/cv/checkpoint -rnn_size 128 ' + '-checkpoint_every 100 ' + \
'-num_layers ' + str(num_layers) + ' -batch_size ' + str(batch_size) + '\n\n'
run_command(command, run)
checkpoint_path = '/root/torch-rnn/storage/' + data_name + '/column_' + str(column_id) + '/cv'
latest_checkpoint_file = get_latest_checkpoint(checkpoint_path)
_, checkpoint_index = evaluate_check_point_json(latest_checkpoint_file)
best_checkpoint = checkpoint_path + '/checkpoint_' + str(checkpoint_index) + '.t7'
command = 'th show_activation.lua -length 100 -gpu 0 -gpu_backend cuda -file /root/torch-rnn/storage/' + data_name + '/column_' + str(column_id) + '/orig_input/column_' + str(column_id) + '.txt -output /root/torch-rnn/storage/' + data_name + '/column_' + str(column_id) + '/features/ -checkpoint ' + str(best_checkpoint) + '\n\n'
run_command(command, run)
command = 'python DeepFeatures.py -d /root/torch-rnn/storage/' + data_name + ' -a 2 -c ' + str(column_id) + ' -o /root/torch-rnn/storage/' + data_name + '_avg_state/out' + str(column_id) + '.npz\n\n'
run_command(command, run)
command = 'python DeepFeatures.py -d /root/torch-rnn/storage/' + data_name + ' -a 1 -c ' + str(column_id) + ' -o /root/torch-rnn/storage/' + data_name + '_last_state/out' + str(column_id) + '.npz\n\n'
run_command(command, run)
if run:
delete_folder_content('/root/torch-rnn/storage/' + data_name + '/column_' + str(column_id) + '/features')
|
996,075 | e7390d6311f6e4d56de52698ba6b389df681675c | import torch
import torch.nn as nn
import torch.nn.functional as F
import torchvision.models as models
from torch.autograd import Variable
class EncoderCNN(nn.Module):
def __init__(self, embed_size):
super(EncoderCNN, self).__init__()
resnet = models.resnet50(pretrained=True)
for param in resnet.parameters():
param.requires_grad_(False)
modules = list(resnet.children())[:-1]
self.resnet = nn.Sequential(*modules)
self.embed = nn.Linear(resnet.fc.in_features, embed_size)
self.bn = nn.BatchNorm1d(embed_size)
def forward(self, images):
features = self.resnet(images)
features = features.view(features.size(0), -1)
features = self.bn(self.embed(features))
return features
class DecoderRNN(nn.Module):
def __init__(self, embed_size, hidden_size, vocab_size, num_layers=2):
super(DecoderRNN, self).__init__()
self.num_layers = num_layers
self.hidden_size = hidden_size
self.embedding = nn.Embedding(vocab_size, embed_size)
self.lstm = nn.LSTM(embed_size, hidden_size, num_layers, batch_first=True, dropout=0.5)
self.linear = nn.Linear(hidden_size, vocab_size)
self.dropout = nn.Dropout(0.4)
self.init_weights()
def init_weights(self):
initrange = 0.1
self.embedding.weight.data.uniform_(-initrange, initrange)
self.linear.bias.data.fill_(0)
self.linear.weight.data.uniform_(-initrange, initrange)
def forward(self, features, captions):
# embed tokens in vector space
embeddings = self.embedding(captions)
# append image as first input
inputs = torch.cat((features.unsqueeze(1), embeddings), 1)
rnn_out, rnn_states = self.lstm(inputs)
output = self.linear(self.dropout(rnn_out))
return output[:, 1:]
def sample(self, features, states=None, max_len=20):
" accepts pre-processed image tensor (inputs) and returns predicted sentence (list of tensor ids of length max_len) "
"""Samples captions for given image features (Greedy search)."""
output_ids = []
inputs = features
for i in range(max_len):
# pass data through recurrent network
hiddens, states = self.lstm(inputs, states)
outputs = self.linear(hiddens.squeeze(1))
#logprobs = F.log_softmax(outputs.squeeze(0))
# find maximal predictions
predicted = outputs.data.max(1)[1]
# append results from given step to global results
output_ids.append(predicted.item())
# prepare chosen words for next decoding step
embeddings = self.embedding(predicted)
inputs = embeddings.unsqueeze(1)
return output_ids
def new_sample(self, fc_feats):
sample_max = True
temperature = 0.0
batch_size = fc_feats.size(0)
state = self.init_hidden(batch_size)
seq = []
seqLogprobs = []
for t in range(20 + 2):
if t == 0:
#xt = self.img_embed(fc_feats)
xt = fc_feats
else:
if t == 1: # input <bos>
it = fc_feats.data.new(batch_size).long().zero_()
elif sample_max:
sampleLogprobs, it = torch.max(logprobs.data, 1)
it = it.view(-1).long()
else:
if temperature == 1.0:
prob_prev = torch.exp(logprobs.data).cpu() # fetch prev distribution: shape Nx(M+1)
else:
# scale logprobs by temperature
prob_prev = torch.exp(torch.div(logprobs.data, temperature)).cpu()
it = torch.multinomial(prob_prev, 1).cuda()
sampleLogprobs = logprobs.gather(1, Variable(it, requires_grad=False)) # gather the logprobs at sampled positions
it = it.view(-1).long() # and flatten indices for downstream processing
xt = self.embedding(Variable(it, requires_grad=False))
xt = xt.unsqueeze(0)
if t >= 2:
# stop when all finished
if t == 2:
unfinished = it > 0
else:
unfinished = unfinished * (it > 0)
if unfinished.sum() == 0:
break
it = it * unfinished.type_as(it)
seq.append(it) #seq[t] the input of t+2 time step
seqLogprobs.append(sampleLogprobs.view(-1))
#output, state = self.rnn(xt.unsqueeze(0), state)
output, state = self.lstm(xt, state)
logprobs = F.log_softmax(self.linear(self.dropout(output.squeeze(0))))
return torch.cat([_.unsqueeze(1) for _ in seq], 1), torch.cat([_.unsqueeze(1) for _ in seqLogprobs], 1)
def sample_beam(self, fc_feats, att_feats, opt={}):
beam_size = opt.get('beam_size', 10)
batch_size = fc_feats.size(0)
assert beam_size <= self.vocab_size + 1, 'lets assume this for now, otherwise this corner case causes a few headaches down the road. can be dealt with in future if needed'
seq = torch.LongTensor(self.seq_length, batch_size).zero_()
seqLogprobs = torch.FloatTensor(self.seq_length, batch_size)
# lets process every image independently for now, for simplicity
self.done_beams = [[] for _ in range(batch_size)]
for k in range(batch_size):
state = self.init_hidden(beam_size)
for t in range(2):
if t == 0:
xt = self.img_embed(fc_feats[k:k+1]).expand(beam_size, self.input_encoding_size)
elif t == 1: # input <bos>
it = fc_feats.data.new(beam_size).long().zero_()
xt = self.embed(Variable(it, requires_grad=False))
output, state = self.core(xt.unsqueeze(0), state)
logprobs = F.log_softmax(self.logit(self.dropout(output.squeeze(0))))
self.done_beams[k] = self.beam_search(state, logprobs, opt=opt)
seq[:, k] = self.done_beams[k][0]['seq'] # the first beam has highest cumulative score
seqLogprobs[:, k] = self.done_beams[k][0]['logps']
# return the samples and their log likelihoods
return seq.transpose(0, 1), seqLogprobs.transpose(0, 1)
def init_hidden(self, bsz):
weight = next(self.parameters()).data
return (Variable(weight.new(self.num_layers, bsz, self.hidden_size).zero_()),
Variable(weight.new(self.num_layers, bsz, self.hidden_size).zero_()))
|
996,076 | 7087817c88b5df17cb3f50abd57174561c3dfbb4 | import random
from wordlist import *
POINTS = {"A": 1, "C": 3, "B": 3, "E": 1, "D": 2, "G": 2,
"F": 4, "I": 1, "H": 4, "K": 5, "J": 8, "M": 3,
"L": 1, "O": 1, "N": 1, "Q": 10, "P": 3, "S": 1,
"R": 1, "U": 1, "T": 1, "W": 4, "V": 4, "Y": 4,
"X": 8, "Z": 10}
FREQ_DICT = {'A': 9, 'B': 2, 'C': 2, 'D': 4, 'E': 12, 'F': 2, 'G': 3,
'H': 2,'I': 9, 'J': 1, 'K': 1, 'L': 4, 'M': 2, 'N': 6,
'O': 8,'P': 2, 'Q': 1, 'R': 6, 'S': 4, 'T': 6, 'U': 4,
'V': 2, 'W': 2, 'X': 1, 'Y': 2, 'Z': 1, '_': 2}
def bag_of_letters(letters_DT):
letter = []
for i in letters_DT:
value = letters_DT.get(i)
freq = i * value
if len(freq) <= 1:
letter.append(freq)
else:
letter = letter + [character for character in freq]
return letter
def get_word_value(word, letters_DT):
"""Return: total – score of a word.
The total for a word is the sum of the point for letters in the word, multiply by the value.
word: string – uppercase letters
letters_Dt: integer
"""
total = 0
word = word.upper()
for character in word:
if character not in letters_DT:
return 0
else:
value = letters_DT.get(character)
total = total + value
return total
def raffle_letters(letters_DT):
""" Return: random_letter and new_letter
random_letter: lengths of seven letters that randomly pick by the random function.
new_letter: the letters from random function from random_letter
letters_DT: dictionary
"""
if len(letters_DT) <= 7:
return letters_DT
else:
random_letter = random.sample(letters_DT, 7)
for each in random_letter:
if each in letters_DT:
letters_DT.remove(each)
new_letter = letters_DT
return random_letter, new_letter
def build_word(lst_letters, word):
""" Return: get_word_value(word, POINTS)
w_bank: dictionary
Para: Prompt user to enter the word from the letter tile. Return False if the word isn't the dictionary.
return False if the player no longer have any letter tile in hand
if the player enter a word that is in the dictionary, they earn the point from the combination letter value.
"""
play_letter = lst_letters
empty_tile = play_letter.count('_')
empty_character = 0
w_bank = get_wordlist()
if word not in w_bank:
print('This word is not in our dictionary. You rewared with 0 points. \n')
return False
for character in word:
if character not in play_letter:
empty_character += 1
elif character in play_letter:
play_letter.remove(character)
if empty_character <= empty_tile:
if empty_character >= 1:
for element in range(enpty_character):
play_letter.remove('_')
elif empty_character >= empty_tile:
return('You used a letter not in your hand.'), False
if word in w_bank:
print('Nice! Point: ', str(get_word_value(word, POINTS)), 'for this word. \n')
return get_word_value(word, POINTS)
def game_menu():
"""Return: user_input
Ask user_input to input their choices: D – Draw letters, W – Play word, P – Print user_inout words history
Q – Quit.
upper(): Allow user_input to lowercase then convert the words and letters to uppercase, so it can match the dictionary
Parameter: None
"""
user_input = input('D: Draw letters\n'+'W: Play word\n'+
'P: Print all your words so far\n'+ 'Q: Quit\n\n'+
'Enter your choice below: \n')
user_input = user_input.upper()
return user_input
|
996,077 | 954d65e0c0df8353fcdee7b3437622fe32283553 | import discord
from discord.ext import commands
import hashlib
from hashlib import sha256
import json
import os
## Define your TOKEN environment variable for the bot to work!
token = os.environ.get("TOKEN")
## Define your OWNER environment variable for the bot to work and to recognize the bot owner!
owner = os.environ.get("OWNER")
def get_prefix(bot, message):
hash = bytes(str(message.guild.id), 'ascii')
hash_object = hashlib.sha256(hash)
hex_dig = hash_object.hexdigest()
with open('prefix.json', 'r') as f:
prefixes = json.load(f)
try:
return prefixes[str(hex_dig)]
prefix = prefixes[str(hex_dig)]
## Prefix not found
except KeyError:
prefixes[str(hex_dig)] = 'c!'
return prefixes[str(hex_dig)]
prefix = prefixes[str(hex_dig)]
bot = commands.Bot(command_prefix=get_prefix)
## Removes the help command in order for custom help command to work
bot.remove_command('help')
for i in os.listdir('./cogs'):
if i.endswith('.py'):
bot.load_extension(f'cogs.{i[:-3]}')
print('Extensions loaded!')
@bot.event
async def on_ready():
print('We have logged in as {0.user}. Bot is ready.'.format(bot))
await bot.change_presence(activity=discord.Activity(type=discord.ActivityType.watching, name="mentions for prefix"))
print('Bot status changed!')
@bot.command()
async def extload(ctx, cog):
hash = bytes(str(ctx.message.author.id), 'ascii')
hash_object = hashlib.sha256(hash)
hex_dig = hash_object.hexdigest()
hash = bytes(str(owner), 'ascii')
hash_object = hashlib.sha256(hash)
hex_dig2 = hash_object.hexdigest()
if hex_dig == hex_dig2:
bot.load_extension(f'cogs.{cog}')
await ctx.send(f'Loaded extension `{cog}`!')
else:
await ctx.send("Sorry, but you don't have permission to do that.")
@bot.command()
async def extunload(ctx, cog):
hash = bytes(str(ctx.message.author.id), 'ascii')
hash_object = hashlib.sha256(hash)
hex_dig = hash_object.hexdigest()
hash = bytes(str(owner), 'ascii')
hash_object = hashlib.sha256(hash)
hex_dig2 = hash_object.hexdigest()
if hex_dig == hex_dig2:
bot.unload_extension(f'cogs.{cog}')
await ctx.send(f'Unloaded extension `{cog}`!')
else:
await ctx.send("Sorry, but you don't have permission to do that.")
@bot.command()
async def extreload(ctx, cog):
hash = bytes(str(ctx.message.author.id), 'ascii')
hash_object = hashlib.sha256(hash)
hex_dig = hash_object.hexdigest()
hash = bytes(str(owner), 'ascii')
hash_object = hashlib.sha256(hash)
hex_dig2 = hash_object.hexdigest()
if hex_dig == hex_dig2:
bot.unload_extension(f'cogs.{cog}')
bot.load_extension(f'cogs.{cog}')
await ctx.send(f'Reloaded extension `{cog}`!')
else:
await ctx.send("Sorry, but you don't have permission to do that.")
@bot.command()
async def extlist(ctx):
hash = bytes(str(ctx.message.author.id), 'ascii')
hash_object = hashlib.sha256(hash)
hex_dig = hash_object.hexdigest()
hash = bytes(str(owner), 'ascii')
hash_object = hashlib.sha256(hash)
hex_dig2 = hash_object.hexdigest()
if hex_dig == hex_dig2:
exts = []
for i in os.listdir('./cogs'):
if i.endswith('.py'):
exts.append(i[:-3])
message = ''
for j in exts:
message += f'''`{j}`\n'''
await ctx.send(message)
else:
await ctx.send("Sorry, but you don't have permission to do that.")
bot.run(token)
|
996,078 | 46b0fc4cec8922211a82f58e0ca7072af94f14d3 | from touchworks.api.http import TouchWorks, TouchWorksException
import json
import unittest
import uuid
from touchworks.logger import Logger
import pprint
from nose.tools import raises
import random
logger = Logger.get_logger(__name__)
class TestAPIs(unittest.TestCase):
@classmethod
def setUpClass(cls):
cls.config = json.loads(open('tests/config.json').read())
cls.url = cls.config['server']
cls.svc_username = cls.config['serviceusername']
cls.svc_password = cls.config['servicepassword']
cls.app_name = cls.config['appname']
def setUp(self):
pass
def test_get_dictionary(self):
self.api = TouchWorks(base_url=self.url,
username=self.svc_username,
password=self.svc_password,
app_username=self.config['ehr_username'],
app_name=self.app_name,
cache_token=True)
self.api.get_dictionary('Document_Type_DE')
rtf_doc_types = self.api.find_document_type_by_name('Consult', match_case=False)
for a_type in rtf_doc_types:
logger.debug(pprint.pformat(a_type))
def test_save_note(self):
self.api = TouchWorks(base_url=self.url,
username=self.svc_username,
password=self.svc_password,
app_name=self.app_name,
app_username=self.config['ehr_username'],
cache_token=True)
patients = self.api.search_patients('J*', 'N')
self.api.save_note('hello there', document_type='Consult',
patient_id=patients[0]['ID'],
document_status='Final',
wrapped_in_rtf='Y')
def test_get_encounters(self):
self.api = TouchWorks(base_url=self.url,
username=self.svc_username,
password=self.svc_password,
app_username=self.config['ehr_username'],
app_name=self.app_name,
cache_token=True)
patients = self.api.search_patients('J*', 'N')
if patients and len(patients) >= 5:
for patient in patients[0:5]:
encounters = self.api.get_encounter_list_for_patient(patient_id=patient['ID'])
for encounter in encounters:
logger.debug(pprint.pformat(encounter))
self.api.save_unstructured_document(
ehr_username=self.config['ehr_username'],
patient_id=patient['ID'],
encounter_id=encounter['Encounterid'],
document_content='random note : %s' % str(uuid.uuid4())[0:5])
# if 'ReferringProviderID' in encounter:
logger.debug(pprint.pformat(patient))
def test_search_patients(self):
self.api = TouchWorks(base_url=self.url,
username=self.svc_username,
password=self.svc_password,
app_username=self.config['ehr_username'],
app_name=self.app_name,
cache_token=True)
patients = self.api.search_patients('J*', 'N')
if patients and len(patients) >= 5:
for patient in patients[0:5]:
self.api.get_patient(ehr_username=self.config['ehr_username'],
patient_id=patient['ID'])
logger.debug(pprint.pformat(patient))
def test_get_document_types(self):
self.api = TouchWorks(base_url=self.url,
username=self.svc_username,
password=self.svc_password,
app_username=self.config['ehr_username'],
app_name=self.app_name,
cache_token=True)
types = ['Chart', 'Consult', 'SpecReport', 'ChartCopy']
for type in types:
result = self.api.get_document_type(ehr_username=self.config['ehr_username'],
doc_type='')
logger.debug('\n%s' % pprint.pformat(result))
def test_get_schedule(self):
self.api = TouchWorks(base_url=self.url,
username=self.svc_username,
password=self.svc_password,
app_name=self.app_name,
cache_token=True)
schedules = self.api.get_schedule(ehr_username=self.config['ehr_username'],
start_date='9/1/2015',
end_date='10/4/2015',
changed_since='',
include_pix='',
other_user='',
appointment_types='',
status_filter='')
with open('/tmp/schedules.json', 'w+') as f:
f.write(json.dumps(schedules))
logger.debug('retrieved %s schedules ' % len(schedules))
if schedules and len(schedules) >= 5:
for schedule in schedules[0:5]:
logger.debug(pprint.pformat(schedule))
logger.debug(schedule['patientID'])
self.api.get_patient(ehr_username=self.config['ehr_username'],
patient_id=schedule['patientID'])
@raises(TouchWorksException)
def test_invalid_password(self):
self.api = TouchWorks(base_url=self.url,
username=self.svc_username,
password='wrong password',
app_name=self.app_name,
cache_token=True)
def test_patients(self):
self.api = TouchWorks(base_url=self.url,
username=self.svc_username,
password=self.svc_password,
app_name=self.app_name,
app_username=self.config['ehr_username'],
cache_token=True)
patients = self.api.search_patients('F*')
for patient in random.sample(patients, 3):
encounters = self.api.get_encounter_list_for_patient(patient['ID'])
# get patient clinical summary
for encounter in encounters:
logger.info('encounter : %s' % pprint.pformat(encounter))
clinical_summary = self.api.get_clinical_summary(
patient_id=patient['ID'],
encounter_id_identifer=encounter['Encounterid'],
section='')
logger.info('clinical summary : \n%s' % pprint.pformat(clinical_summary))
# patient activity
activities = self.api.get_patient_activity(patient['ID'])
for activity in activities:
logger.info('\n%s' % pprint.pformat(activity))
|
996,079 | 6416530f9c66ac5526ef0e9060fbe8fa6978de53 | from django import template
from django.urls import reverse
register = template.Library()
navbar_options = [
("Home", reverse("Home")),
("Testing Strips", reverse("Testing Strips")),
("Scheduled Tests", reverse("Scheduled Tests")),
("Test Results", reverse("Graph Results")),
]
option_format = '<li class="nav-item{}"> <a class="nav-link" href="{}">{} </a> </li>'
@register.simple_tag
def get_navbar(page):
navbar = ""
for option in navbar_options:
if page == option[0]:
active = ' active'
else:
active = ''
navbar += option_format.format(active, option[1], option[0])
return navbar
|
996,080 | 9e49d3537cae7b0d727fdda29b854a50a19bf864 | import sys, os
here = os.path.dirname(os.path.realpath(__file__))
vendored_dir = os.path.join(here, 'vendored')
sys.path.append(vendored_dir)
import boto3
import json
import datetime
# Create CloudWatch client
cloudwatch = boto3.client('cloudwatch')
ddb = boto3.client('dynamodb')
aas = boto3.client('application-autoscaling')
# Constants
DEFAULT_DYNAMODB_TABLE_LIMIT = 256
FIVE_MINS_SECS = 300
# We can't use AWS/DynamoDB since its reserved
# We'll let people override it by changing CLOUDWATCH_CUSTOM_NAMESPACE env
DEFAULT_CLOUDWATCH_CUSTOM_NAMESPACE = "Custom_DynamoDB"
CLOUDWATCH_CUSTOM_NAMESPACE = DEFAULT_CLOUDWATCH_CUSTOM_NAMESPACE
if 'CLOUDWATCH_CUSTOM_NAMESPACE' in os.environ:
CLOUDWATCH_CUSTOM_NAMESPACE = os.environ['CLOUDWATCH_CUSTOM_NAMESPACE']
AAS_MAX_RESOURCE_ID_LENGTH = 1600
# Globals
ddb_account_limits = None
ddb_tables = {}
ddb_total_provisioned_rcu = 0
ddb_total_provisioned_wcu = 0
ddb_total_consumed_rcu = 0
ddb_total_consumed_wcu = 0
def success_response(event, context):
body = {
"message": "Executed successfully",
"input": event
}
response = {
"statusCode": 200,
"body": json.dumps(body)
}
return response
def load_dynamodb_limits(event, context):
global ddb_account_limits
ddb_account_limits = ddb.describe_limits()
ddb_account_limits.pop('ResponseMetadata', None)
# Since there's no way to query the max table limit we will allow them to override
# this with an environment variable for the lambda function
if 'DYNAMODB_ACCOUNT_TABLE_LIMIT' in os.environ:
ddb_account_limits['AccountMaxTables'] = os.environ['DYNAMODB_ACCOUNT_TABLE_LIMIT']
else:
ddb_account_limits['AccountMaxTables'] = DEFAULT_DYNAMODB_TABLE_LIMIT
#print(ddb_account_limits)
def load_dynamodb_tables(event, context):
global ddb_tables
global ddb_total_provisioned_rcu
global ddb_total_provisioned_wcu
paginator = ddb.get_paginator('list_tables')
for response in paginator.paginate():
for table_name in response['TableNames']:
#if table_name == 'dynamodb-speed-test-blog':
#if table_name == 'bank':
ddb_tables[table_name] = {}
# print(ddb_tables)
for table in ddb_tables.keys():
response = ddb.describe_table(TableName=table)
#print(response)
if response['Table']['TableStatus'] != 'ACTIVE':
return
# Older tables that existed before the on demand feature shipped might not have this field
if 'BillingModeSummary' in response['Table'] and 'BillingMode' in response['Table']['BillingModeSummary']:
ddb_tables[table]['BillingMode'] = response['Table']['BillingModeSummary']['BillingMode']
else:
ddb_tables[table]['BillingMode'] = "PROVISIONED"
ddb_tables[table]['ProvisionedThroughput'] = response['Table']['ProvisionedThroughput']
# We don't need this field and it messes up our object->json dump
if 'LastIncreaseDateTime' in ddb_tables[table]['ProvisionedThroughput']:
ddb_tables[table]['ProvisionedThroughput'].pop('LastIncreaseDateTime')
if 'LastDecreaseDateTime' in ddb_tables[table]['ProvisionedThroughput']:
ddb_tables[table]['ProvisionedThroughput'].pop('LastDecreaseDateTime')
ddb_total_provisioned_rcu += ddb_tables[table]['ProvisionedThroughput']['ReadCapacityUnits']
ddb_total_provisioned_wcu += ddb_tables[table]['ProvisionedThroughput']['WriteCapacityUnits']
ddb_tables[table]['autoscaling'] = {'ReadCapacityUnits' : None, 'WriteCapacityUnits' : None}
ddb_tables[table]['gsis'] = {}
if 'GlobalSecondaryIndexes' in response['Table']:
for gsi in response['Table']['GlobalSecondaryIndexes']:
ddb_tables[table]['gsis'][gsi['IndexName']] = {}
ddb_tables[table]['gsis'][gsi['IndexName']]['ProvisionedThroughput'] = gsi['ProvisionedThroughput']
# We don't need this field and it messes up our object->json dump
if 'LastIncreaseDateTime' in ddb_tables[table]['gsis'][gsi['IndexName']]['ProvisionedThroughput']:
ddb_tables[table]['gsis'][gsi['IndexName']]['ProvisionedThroughput'].pop('LastIncreaseDateTime')
if 'LastDecreaseDateTime' in ddb_tables[table]['gsis'][gsi['IndexName']]['ProvisionedThroughput']:
ddb_tables[table]['gsis'][gsi['IndexName']]['ProvisionedThroughput'].pop('LastDecreaseDateTime')
ddb_total_provisioned_rcu += ddb_tables[table]['gsis'][gsi['IndexName']]['ProvisionedThroughput']['ReadCapacityUnits']
ddb_total_provisioned_wcu += ddb_tables[table]['gsis'][gsi['IndexName']]['ProvisionedThroughput']['WriteCapacityUnits']
ddb_tables[table]['gsis'][gsi['IndexName']]['autoscaling'] = {'ReadCapacityUnits' : None, 'WriteCapacityUnits' : None}
def gather_dynamodb_consumption(event, context):
global ddb_tables
#gather_table_config(event, context)
# We need a resource ID array with one entry for every table (table/<tableName>) and one entry for every GSI (table/<tableName>/index/<indexName>)
# We can put up to 1600 ResourceIds in the array both for describe_scalable_targets
# https://docs.aws.amazon.com/autoscaling/application/APIReference/API_DescribeScalableTargets.html
# To avoid throttling from the AAS service we will build arrays that have up to 1600 ResourceIds and store an array of those
# arrays which we can loop through afterwards to minimize the number of calls we make to AAS service
# Its possible a customer has had their number of tables account limit increased so there could be thousands of tables and thousands of GSIs
# As we go through the results from the DescribeScalableTargets we will build a map of resource_ids to use in calling DescribeScalingPolicies
dst_resource_id_arrays = []
tmp_dst_resource_ids = []
dsp_resource_ids = {}
for table in ddb_tables.keys():
tmp_dst_resource_ids.append('table/' + table)
if AAS_MAX_RESOURCE_ID_LENGTH == len(tmp_dst_resource_ids):
dst_resource_id_arrays.append(tmp_dst_resource_ids)
tmp_dst_resource_ids = []
for gsi in ddb_tables[table]['gsis'].keys():
tmp_dst_resource_ids.append('table/' + table + '/index/' + gsi)
if AAS_MAX_RESOURCE_ID_LENGTH == len(tmp_dst_resource_ids):
dst_resource_id_arrays.append(tmp_dst_resource_ids)
tmp_dst_resource_ids = []
if len(tmp_dst_resource_ids) > 0:
dst_resource_id_arrays.append(tmp_dst_resource_ids)
for dst_resource_id_array in dst_resource_id_arrays:
aas_paginator = aas.get_paginator('describe_scalable_targets')
for aas_response in aas_paginator.paginate(ServiceNamespace='dynamodb', ResourceIds=dst_resource_id_array):
#print(aas_response)
for target in aas_response['ScalableTargets']:
# The responses will be a mix of tables and indexes so we need to figure out which this is
if target['ScalableDimension'].startswith('dynamodb:table:'):
# ResourceId = "table/<table>
aas_table_name = target['ResourceId'].split('/')[1]
# Slice off the leading "dynamodb:table:" from the Scalable Dimension
aas_scalable_dimension = target['ScalableDimension'][len("dynamodb:table:"):]
ddb_tables[aas_table_name]['autoscaling'][aas_scalable_dimension] = {}
ddb_tables[aas_table_name]['autoscaling'][aas_scalable_dimension]['min'] = target['MinCapacity']
ddb_tables[aas_table_name]['autoscaling'][aas_scalable_dimension]['max'] = target['MaxCapacity']
#tmp_dsp_resources.append({'ResourceId': target['ResourceId'], 'ScalableDimension': target['ScalableDimension'], 'type': 'table'})
dsp_resource_ids[target['ResourceId']] = {'type' : 'table', 'table_name' : aas_table_name}
elif target['ScalableDimension'].startswith('dynamodb:index:'):
# Slice off the leading "table/<table>/index/" from the ResourceId
# ResourceId = "table/<table>/index/<index>"
aas_table_name = target['ResourceId'].split('/')[1]
aas_index_name = target['ResourceId'].split('/')[3]
#aas_index_name = target['ResourceId'][len("table/" + table + "/index/"):]
# Slice off the leading "dynamodb:index:" from the Scalable Dimension
aas_scalable_dimension = target['ScalableDimension'][len("dynamodb:index:"):]
ddb_tables[aas_table_name]['gsis'][aas_index_name]['autoscaling'][aas_scalable_dimension] = {}
ddb_tables[aas_table_name]['gsis'][aas_index_name]['autoscaling'][aas_scalable_dimension]['min'] = target['MinCapacity']
ddb_tables[aas_table_name]['gsis'][aas_index_name]['autoscaling'][aas_scalable_dimension]['max'] = target['MaxCapacity']
#tmp_dsp_resources.append({'ResourceId': target['ResourceId'], 'ScalableDimension': target['ScalableDimension'], 'type': 'index'})
dsp_resource_ids[target['ResourceId']] = {'type' : 'index', 'table_name' : aas_table_name, 'index_name' : aas_index_name}
else:
raise Exception(f"unknown ScalableDimension {target['ScalableDimension']}")
for dsp_resource_id in dsp_resource_ids.keys():
aas_dsp_paginator = aas.get_paginator('describe_scaling_policies')
for aas_policy_response in aas_dsp_paginator.paginate(ServiceNamespace='dynamodb', ResourceId=dsp_resource_id):
for policy in aas_policy_response['ScalingPolicies']:
if 'table' == dsp_resource_ids[dsp_resource_id]['type']:
# Slice off the leading "dynamodb:table:" from the Scalable Dimension
aas_scalable_dimension = policy['ScalableDimension'][len("dynamodb:table:"):]
ddb_tables[dsp_resource_ids[dsp_resource_id]['table_name']]['autoscaling'][aas_scalable_dimension]['target'] = policy['TargetTrackingScalingPolicyConfiguration']['TargetValue']
elif 'index' == dsp_resource_ids[dsp_resource_id]['type']:
# Slice off the leading "dynamodb:index:" from the Scalable Dimension
aas_scalable_dimension = policy['ScalableDimension'][len("dynamodb:index:"):]
ddb_tables[dsp_resource_ids[dsp_resource_id]['table_name']]['gsis'][dsp_resource_ids[dsp_resource_id]['index_name']]['autoscaling'][aas_scalable_dimension]['target'] = aas_policy_response['ScalingPolicies'][0]['TargetTrackingScalingPolicyConfiguration']['TargetValue']
else:
raise Exception(f"unknown resource type {dsp_resource_id['type']}")
def gather_dynamodb_metrics(event, context):
global ddb_tables
global ddb_total_consumed_rcu
global ddb_total_consumed_wcu
for table in ddb_tables.keys():
ddb_tables[table]['metrics'] = {}
# paginator = cloudwatch.get_paginator('list_metrics')
# for response in paginator.paginate(Dimensions=[{'Name': 'TableName','Value': table}],
# Namespace='AWS/DynamoDB'):
# print(response['Metrics'])
response = cloudwatch.get_metric_data(
MetricDataQueries=[
{
'Id' : 'consumed_rcu',
'MetricStat': {
'Metric': {
'Namespace': 'AWS/DynamoDB',
'MetricName': 'ConsumedReadCapacityUnits',
'Dimensions': [{'Name': 'TableName', 'Value': table}]
},
'Period': FIVE_MINS_SECS,
'Stat': 'Average',
'Unit': 'Count'
},
},
{
'Id' : 'consumed_wcu',
'MetricStat': {
'Metric': {
'Namespace': 'AWS/DynamoDB',
'MetricName': 'ConsumedWriteCapacityUnits',
'Dimensions': [{'Name': 'TableName', 'Value': table}]
},
'Period': FIVE_MINS_SECS,
'Stat': 'Average',
'Unit': 'Count'
}
}
],
StartTime=datetime.datetime.now() - datetime.timedelta(minutes=15),
EndTime=datetime.datetime.now(),
MaxDatapoints=5
)
for result in response['MetricDataResults']:
ddb_tables[table]['metrics'][result['Id']] = 0.0
if len(result['Values']) > 0:
ddb_tables[table]['metrics'][result['Id']] = result['Values'][0]
#print(response)
def publish_dynamodb_account_metrics(event, context):
global ddb_tables
global ddb_account_limits
cloudwatch.put_metric_data(
MetricData=[
{
'MetricName': 'AccountTableLimitPct',
'Unit': 'Percent',
'Value': len(ddb_tables.keys()) / ddb_account_limits['AccountMaxTables']
}
],
Namespace=CLOUDWATCH_CUSTOM_NAMESPACE
)
def publish_dynamodb_provisioned_table_metrics(table, event, context):
global ddb_tables
global ddb_account_limits
if ddb_tables[table]['autoscaling']['ReadCapacityUnits'] is not None:
cloudwatch.put_metric_data(
MetricData=[
{
'MetricName': 'ProvisionedReadCapacityAutoScalingPct',
'Dimensions': [{'Name': 'TableName', 'Value': table}],
'Unit': 'Percent',
'Value': ddb_tables[table]['ProvisionedThroughput']['ReadCapacityUnits'] / ddb_tables[table]['autoscaling']['ReadCapacityUnits']['max']
}
],
Namespace=CLOUDWATCH_CUSTOM_NAMESPACE
)
if ddb_tables[table]['autoscaling']['WriteCapacityUnits'] is not None:
cloudwatch.put_metric_data(
MetricData=[
{
'MetricName': 'ProvisionedWriteCapacityAutoScalingPct',
'Dimensions': [{'Name': 'TableName', 'Value': table}],
'Unit': 'Percent',
'Value': ddb_tables[table]['ProvisionedThroughput']['WriteCapacityUnits'] / ddb_tables[table]['autoscaling']['WriteCapacityUnits']['max']
}
],
Namespace=CLOUDWATCH_CUSTOM_NAMESPACE
)
for gsi in ddb_tables[table]['gsis'].keys():
if ddb_tables[table]['gsis'][gsi]['autoscaling']['ReadCapacityUnits'] is not None:
cloudwatch.put_metric_data(
MetricData=[
{
'MetricName': 'ProvisionedReadCapacityAutoScalingPct',
'Dimensions': [{'Name': 'GlobalSecondaryIndexName', 'Value': gsi}, {'Name': 'TableName', 'Value': table}],
'Unit': 'Percent',
'Value': ddb_tables[table]['gsis'][gsi]['ProvisionedThroughput']['ReadCapacityUnits'] / ddb_tables[table]['autoscaling']['ReadCapacityUnits']['max']
}
],
Namespace=CLOUDWATCH_CUSTOM_NAMESPACE
)
if ddb_tables[table]['gsis'][gsi]['autoscaling']['WriteCapacityUnits'] is not None:
cloudwatch.put_metric_data(
MetricData=[
{
'MetricName': 'ProvisionedWriteCapacityAutoScalingPct',
'Dimensions': [{'Name': 'GlobalSecondaryIndexName', 'Value': gsi}, {'Name': 'TableName', 'Value': table}],
'Unit': 'Percent',
'Value': ddb_tables[table]['gsis'][gsi]['ProvisionedThroughput']['WriteCapacityUnits'] / ddb_tables[table]['autoscaling']['WriteCapacityUnits']['max']
}
],
Namespace=CLOUDWATCH_CUSTOM_NAMESPACE
)
def publish_dynamodb_ondemand_table_metrics(table, event, context):
global ddb_tables
global ddb_account_limits
cloudwatch.put_metric_data(
MetricData=[
{
'MetricName': 'ConsumedReadCapacityTableLimitPct',
'Dimensions': [{'Name': 'TableName', 'Value': table}],
'Unit': 'Percent',
'Value': ddb_tables[table]['ProvisionedThroughput']['ReadCapacityUnits'] / ddb_account_limits['TableMaxReadCapacityUnits']
}
],
Namespace=CLOUDWATCH_CUSTOM_NAMESPACE
)
cloudwatch.put_metric_data(
MetricData=[
{
'MetricName': 'ConsumedWriteCapacityTableLimitPct',
'Dimensions': [{'Name': 'TableName', 'Value': table}],
'Unit': 'Percent',
'Value': ddb_tables[table]['ProvisionedThroughput']['WriteCapacityUnits'] / ddb_account_limits['TableMaxWriteCapacityUnits']
}
],
Namespace=CLOUDWATCH_CUSTOM_NAMESPACE
)
def publish_dynamodb_table_metrics(event, context):
global ddb_tables
global ddb_account_limits
for table in ddb_tables.keys():
if ddb_tables[table]['BillingMode'] == 'PROVISIONED':
publish_dynamodb_provisioned_table_metrics(table, event, context)
elif ddb_tables[table]['BillingMode'] == 'PAY_PER_REQUEST':
publish_dynamodb_ondemand_table_metrics(table, event, context)
else:
raise Exception(f"Unknown billing mode {ddb_tables[table]['BillingMode']} for table {table}")
def publish_dynamodb_metrics(event, context):
global ddb_tables
global ddb_account_limits
global ddb_total_provisioned_rcu
global ddb_total_provisioned_wcu
load_dynamodb_limits(event, context)
load_dynamodb_tables(event, context)
gather_dynamodb_consumption(event, context)
gather_dynamodb_metrics(event, context)
# can't use this because sometimes timestamps show up under ProvisionedThroughput.LastIncreaseDateTime
#print(json.dumps(ddb_tables, sort_keys=True, indent=4, separators=(',', ': ')))
#print(ddb_tables)
print(f"Using {len(ddb_tables.keys())} of max {ddb_account_limits['AccountMaxTables']} tables")
print(f"DynamoDB AccountMaxReadCapacityUnits: {ddb_account_limits['AccountMaxReadCapacityUnits']}")
print(f"DynamoDB AccountMaxWriteCapacityUnits: {ddb_account_limits['AccountMaxWriteCapacityUnits']}")
print(f"DynamoDB TableMaxReadCapacityUnits: {ddb_account_limits['TableMaxReadCapacityUnits']}")
print(f"DynamoDB TableMaxWriteCapacityUnits: {ddb_account_limits['TableMaxWriteCapacityUnits']}")
print(f"DynamoDB Total Provisioned RCU: {ddb_total_provisioned_rcu}")
print(f"DynamoDB Total Provisioned WCU: {ddb_total_provisioned_wcu}")
publish_dynamodb_account_metrics(event, context)
publish_dynamodb_table_metrics(event, context)
return success_response(event, context)
if __name__ == "__main__":
response = publish_dynamodb_metrics({}, {})
print(f'{response}')
|
996,081 | e60f92ce944ffa521f0feeba98e12e8f8a7dba71 | # -*- coding: utf-8 -*-
"""
Created on Sat Jun 6 12:13:12 2020
@author: thecr
"""
import pandas
import numpy
import csv
from wordcloud import WordCloud, STOPWORDS, ImageColorGenerator
import matplotlib.pyplot as plt
from sklearn import linear_model
import statsmodels.api as sm
#Read our data from csv
electionInfoData = pandas.read_csv('election_info.csv', header='infer', nrows=436)
gunViolenceData = pandas.read_csv('gun_violence_data.csv', header='infer', nrows=239678)
stateFirearmLawData = pandas.read_csv('state_firearms.csv', header='infer', nrows=1351)
#Trim our data to only include the columns we want
electionInfoData = electionInfoData[['District', 'rep_party_2012', 'winning_party_2012', 'rep_party_2014',
'winning_party_2014', 'rep_party_2016', 'winning_party_2016', 'rep_party_2018',
'winning_party_2018','white','black','latino','asian and pacific island',
'native','other','bach degree or higher among 25up','whiteBA','median_income',
'noncollege_white', 'CITYLAB_CDI']]
gunViolenceData = gunViolenceData[['date','state','n_killed','n_injured','congressional_district',
'gun_type','incident_characteristics','participant_age_group','participant_gender',
'participant_status','participant_type']]
#Drop data that doesn't include the congressional district
gunViolenceData = gunViolenceData[gunViolenceData['congressional_district'] != 0]
gunViolenceData = gunViolenceData.dropna(subset=['congressional_district'])
#split gunViolenceData into 4 data frames based on the year
gunViolenceData2014 = gunViolenceData[gunViolenceData['date'].str.contains('2014')]
gunViolenceData2015 = gunViolenceData[gunViolenceData['date'].str.contains('2015')]
gunViolenceData2016 = gunViolenceData[gunViolenceData['date'].str.contains('2016')]
gunViolenceData2017 = gunViolenceData[gunViolenceData['date'].str.contains('2017')]
#Trim state firearm law data to only include the columns we want
stateFirearmLawData = stateFirearmLawData[['state', 'year','lawtotal']]
#Remove years from state firearm law data that we aren't looking at for this project
indexNames = stateFirearmLawData[stateFirearmLawData['year']==1991].index
stateFirearmLawData.drop(indexNames, inplace=True)
indexNames = stateFirearmLawData[stateFirearmLawData['year']==1992].index
stateFirearmLawData.drop(indexNames, inplace=True)
indexNames = stateFirearmLawData[stateFirearmLawData['year']==1993].index
stateFirearmLawData.drop(indexNames, inplace=True)
indexNames = stateFirearmLawData[stateFirearmLawData['year']==1994].index
stateFirearmLawData.drop(indexNames, inplace=True)
indexNames = stateFirearmLawData[stateFirearmLawData['year']==1995].index
stateFirearmLawData.drop(indexNames, inplace=True)
indexNames = stateFirearmLawData[stateFirearmLawData['year']==1996].index
stateFirearmLawData.drop(indexNames, inplace=True)
indexNames = stateFirearmLawData[stateFirearmLawData['year']==1997].index
stateFirearmLawData.drop(indexNames, inplace=True)
indexNames = stateFirearmLawData[stateFirearmLawData['year']==1998].index
stateFirearmLawData.drop(indexNames, inplace=True)
indexNames = stateFirearmLawData[stateFirearmLawData['year']==1999].index
stateFirearmLawData.drop(indexNames, inplace=True)
indexNames = stateFirearmLawData[stateFirearmLawData['year']==2000].index
stateFirearmLawData.drop(indexNames, inplace=True)
indexNames = stateFirearmLawData[stateFirearmLawData['year']==2001].index
stateFirearmLawData.drop(indexNames, inplace=True)
indexNames = stateFirearmLawData[stateFirearmLawData['year']==2002].index
stateFirearmLawData.drop(indexNames, inplace=True)
indexNames = stateFirearmLawData[stateFirearmLawData['year']==2003].index
stateFirearmLawData.drop(indexNames, inplace=True)
indexNames = stateFirearmLawData[stateFirearmLawData['year']==2004].index
stateFirearmLawData.drop(indexNames, inplace=True)
indexNames = stateFirearmLawData[stateFirearmLawData['year']==2005].index
stateFirearmLawData.drop(indexNames, inplace=True)
indexNames = stateFirearmLawData[stateFirearmLawData['year']==2006].index
stateFirearmLawData.drop(indexNames, inplace=True)
indexNames = stateFirearmLawData[stateFirearmLawData['year']==2007].index
stateFirearmLawData.drop(indexNames, inplace=True)
indexNames = stateFirearmLawData[stateFirearmLawData['year']==2008].index
stateFirearmLawData.drop(indexNames, inplace=True)
indexNames = stateFirearmLawData[stateFirearmLawData['year']==2009].index
stateFirearmLawData.drop(indexNames, inplace=True)
indexNames = stateFirearmLawData[stateFirearmLawData['year']==2010].index
stateFirearmLawData.drop(indexNames, inplace=True)
indexNames = stateFirearmLawData[stateFirearmLawData['year']==2011].index
stateFirearmLawData.drop(indexNames, inplace=True)
indexNames = stateFirearmLawData[stateFirearmLawData['year']==2012].index
stateFirearmLawData.drop(indexNames, inplace=True)
#Define column names for aggregated gun violence data
columnNames = ['state','district','numIncidents','numKilled','numInjured']
#Create aggregated gun violence dataframes for each year that we are looking at
aggregated2014gunViolenceData = pandas.DataFrame(columns = columnNames)
aggregated2015gunViolenceData = pandas.DataFrame(columns = columnNames)
aggregated2016gunViolenceData = pandas.DataFrame(columns = columnNames)
aggregated2017gunViolenceData = pandas.DataFrame(columns = columnNames)
#Group our gun violence data by state and congressional district
grouped2014gunViolenceData = gunViolenceData2014.groupby(['state', 'congressional_district'])
grouped2015gunViolenceData = gunViolenceData2015.groupby(['state', 'congressional_district'])
grouped2016gunViolenceData = gunViolenceData2016.groupby(['state', 'congressional_district'])
grouped2017gunViolenceData = gunViolenceData2017.groupby(['state', 'congressional_district'])
#TODO Wordcloud -- see below
#for name, group in grouped2014gunViolenceData:
# for i in group['incident_characteristcs']:
# wordcloud = WordCloud().generate(i)
# plt.imshaw(wordcloud,interpolation='bilinear')
#Loop through our grouped gun violence data for 2014
incidentCharString2014 = ""
for name, group in grouped2014gunViolenceData:
state = name[0]
district = name[1]
numIncidents = group['n_killed'].count()
numKilled = group['n_killed'].sum()
numInjured = group['n_injured'].sum()
massShooting = 0
officerInvolvedIncident = 0
domesticViolence = 0
murderSuicide = 0
spreeShooting = 0
schoolIncident = 0
#Look for key words in our incident characteristics column
for i in group['incident_characteristics']:
try:
incidentCharString2014 = incidentCharString2014 + i
if(i.find('Mass Shooting') > -1):
massShooting +=1
if(i.find('Officer Involved Incident') > -1):
officerInvolvedIncident +=1
if(i.find('Domestic Violence') > -1):
domesticViolence +=1
if(i.find('Murder/Suicide') > -1):
murderSuicide +=1
if(i.find('Spree Shooting') > -1):
spreeShooting +=1
if(i.find('School Incident') > -1):
schoolIncident +=1
except AttributeError:
print('error')
except TypeError:
print('error')
#Do this outside, concatenate and then create the wordcloud
#wordcloud = WordCloud().generate(i)
#plt.imshow(wordcloud,interpolation='bilinear')
#create an array of our data
data = [[state, district, numIncidents, numKilled, numInjured, massShooting, officerInvolvedIncident, domesticViolence, murderSuicide, spreeShooting, schoolIncident]]
#Create a temp dataframe
tempDf = pandas.DataFrame(data, columns = ['state','district','numIncidents','numKilled','numInjured', 'mass', 'officer', 'domestic','ms','spree','school'])
#Append it to our existing dataframe
aggregated2014gunViolenceData = aggregated2014gunViolenceData.append(tempDf, True)
#print(incidentCharString2014)
#wordcloud = WordCloud().generate(incidentCharString2014)
#plt.imshow(wordcloud, interpolation='bilinear')
#plt.axis('off')
#plt.show()
#Loop through our grouped gun violence data for 2015
for name, group in grouped2015gunViolenceData:
state = name[0]
district = name[1]
numIncidents = group['n_killed'].count()
numKilled = group['n_killed'].sum()
numInjured = group['n_injured'].sum()
massShooting = 0
officerInvolvedIncident = 0
domesticViolence = 0
murderSuicide = 0
spreeShooting = 0
schoolIncident = 0
#Look for key words in our incident characteristics column
for i in group['incident_characteristics']:
try:
if(i.find('Mass Shooting') > -1):
massShooting +=1
if(i.find('Officer Involved Incident') > -1):
officerInvolvedIncident +=1
if(i.find('Domestic Violence') > -1):
domesticViolence +=1
if(i.find('Murder/Suicide') > -1):
murderSuicide +=1
if(i.find('Spree Shooting') > -1):
spreeShooting +=1
if(i.find('School Incident') > -1):
schoolIncident +=1
except AttributeError:
print('error')
#create an array of our data
data = [[state, district, numIncidents, numKilled, numInjured, massShooting, officerInvolvedIncident, domesticViolence, murderSuicide, spreeShooting, schoolIncident]]
#Create a temp dataframe
tempDf = pandas.DataFrame(data, columns = ['state','district','numIncidents','numKilled','numInjured', 'mass', 'officer', 'domestic','ms','spree','school'])
#Append it to our existing dataframe
aggregated2015gunViolenceData = aggregated2015gunViolenceData.append(tempDf, True)
#Loop through our grouped gun violence data for 2016
for name, group in grouped2016gunViolenceData:
state = name[0]
district = name[1]
numIncidents = group['n_killed'].count()
numKilled = group['n_killed'].sum()
numInjured = group['n_injured'].sum()
massShooting = 0
officerInvolvedIncident = 0
domesticViolence = 0
murderSuicide = 0
spreeShooting = 0
schoolIncident = 0
#Look for key words in our incident characteristics column
for i in group['incident_characteristics']:
try:
if(i.find('Mass Shooting') > -1):
massShooting +=1
if(i.find('Officer Involved Incident') > -1):
officerInvolvedIncident +=1
if(i.find('Domestic Violence') > -1):
domesticViolence +=1
if(i.find('Murder/Suicide') > -1):
murderSuicide +=1
if(i.find('Spree Shooting') > -1):
spreeShooting +=1
if(i.find('School Incident') > -1):
schoolIncident +=1
except AttributeError:
print('error')
#create an array of our data
data = [[state, district, numIncidents, numKilled, numInjured, massShooting, officerInvolvedIncident, domesticViolence, murderSuicide, spreeShooting, schoolIncident]]
#Create a temp dataframe
tempDf = pandas.DataFrame(data, columns = ['state','district','numIncidents','numKilled','numInjured', 'mass', 'officer', 'domestic','ms','spree','school'])
#Append it to our existing dataframe
aggregated2016gunViolenceData = aggregated2016gunViolenceData.append(tempDf, True)
#Loop through our grouped gun violence data for 2017
for name, group in grouped2017gunViolenceData:
state = name[0]
district = name[1]
numIncidents = group['n_killed'].count()
numKilled = group['n_killed'].sum()
numInjured = group['n_injured'].sum()
massShooting = 0
officerInvolvedIncident = 0
domesticViolence = 0
murderSuicide = 0
spreeShooting = 0
schoolIncident = 0
#Look for key words in our incident characteristics column
for i in group['incident_characteristics']:
try:
if(i.find('Mass Shooting') > -1):
massShooting +=1
if(i.find('Officer Involved Incident') > -1):
officerInvolvedIncident +=1
if(i.find('Domestic Violence') > -1):
domesticViolence +=1
if(i.find('Murder/Suicide') > -1):
murderSuicide +=1
if(i.find('Spree Shooting') > -1):
spreeShooting +=1
if(i.find('School Incident') > -1):
schoolIncident +=1
except AttributeError:
print('error')
#create an array of our data
data = [[state, district, numIncidents, numKilled, numInjured, massShooting, officerInvolvedIncident, domesticViolence, murderSuicide, spreeShooting, schoolIncident]]
#Create a temp dataframe
tempDf = pandas.DataFrame(data, columns = ['state','district','numIncidents','numKilled','numInjured', 'mass', 'officer', 'domestic','ms','spree','school'])
#Append it to our existing dataframe
aggregated2017gunViolenceData = aggregated2017gunViolenceData.append(tempDf, True)
#Print our reports of aggregated gun violence data for each year from 2014-2017
aggregated2014gunViolenceData.to_csv("2014AggregatedGunViolenceData.csv")
aggregated2015gunViolenceData.to_csv("2015AggregatedGunViolenceData.csv")
aggregated2016gunViolenceData.to_csv("2016AggregatedGunViolenceData.csv")
aggregated2017gunViolenceData.to_csv("2017AggregatedGunViolenceData.csv")
#Convert column numIncidents to be an integer
aggregated2014gunViolenceData['mass'] = aggregated2014gunViolenceData['mass'].astype(int)
#Yearly Breakdown Plots
aggregated2014gunViolenceData.plot.box(figsize=(15,12))
plt.title("2014 Gun Violence Overview")
aggregated2015gunViolenceData.plot.box(figsize=(15,12))
plt.title("2015 Gun Violence Overview")
aggregated2016gunViolenceData.plot.box(figsize=(15,12))
plt.title("2016 Gun Violence Overview")
aggregated2017gunViolenceData.plot.box(figsize=(15,12))
plt.title("2017 Gun Violence Overview")
#Histogram Plots
#aggregated2014gunViolenceData.hist(column='mass')
#plt.title("2014 Mass Shooting Breakdown")
#aggregated2015gunViolenceData.hist(column='mass')
#plt.title("2015 Mass Shooting Breakdown")
#aggregated2016gunViolenceData.hist(column='mass')
#plt.title("2016 Mass Shooting Breakdown")
#aggregated2017gunViolenceData.hist(column='mass')
#plt.title("2017 Mass Shooting Breakdown")
#aggregated2014gunViolenceData.hist(column='officer')
#plt.title("2014 Officer Involved Shooting Breakdown")
#aggregated2015gunViolenceData.hist(column='officer')
#plt.title("2015 Officer Involved Shooting Breakdown")
#aggregated2016gunViolenceData.hist(column='officer')
#plt.title("2016 Officer Involved Shooting Breakdown")
#aggregated2017gunViolenceData.hist(column='officer')
#plt.title("2017 Officer Involved Shooting Breakdown")
#aggregated2014gunViolenceData.hist(column='domestic')
#plt.title("2014 Domestic Violence Shooting Breakdown")
#aggregated2015gunViolenceData.hist(column='domestic')
#plt.title("2015 Domestic Violence Shooting Breakdown")
#aggregated2016gunViolenceData.hist(column='domestic')
#plt.title("2016 Domestic Violence Shooting Breakdown")
#aggregated2017gunViolenceData.hist(column='domestic')
#plt.title("2017 Domestic Violence Shooting Breakdown")
#aggregated2014gunViolenceData.hist(column='school')
#plt.title("2014 School Shooting Breakdown")
#aggregated2015gunViolenceData.hist(column='school')
#plt.title("2015 School Shooting Breakdown")
#aggregated2016gunViolenceData.hist(column='school')
#plt.title("2016 School Shooting Breakdown")
#aggregated2017gunViolenceData.hist(column='school')
#plt.title("2017 School Shooting Breakdown")
#Function to map state codes to state name so that we can merge our data sets
def extractStateFromCode(code):
switcher = {
"AL":"Alabama",
"AK":"Alaska",
"AZ":"Arizona",
"AR":"Arkansas",
"CA":"California",
"CO":"Colorado",
"CT":"Connecticut",
"DE":"Deleware",
"FL":"Florida",
"GA":"Georgia",
"HI":"Hawaii",
"ID":"Idaho",
"IL":"Illinois",
"IN":"Indiana",
"IA":"Iowa",
"KS":"Kansas",
"KY":"Kentucky",
"LA":"Loisiana",
"ME":"Maine",
"MD":"Maryland",
"MA":"Massachusetts",
"MI":"Michigan",
"MN":"Minnesota",
"MS":"Mississippi",
"MO":"Missouri",
"MT":"Montana",
"NE":"Nebraska",
"NV":"Nevada",
"NH":"New Hampshire",
"NJ":"New Jersey",
"NM":"New Mexico",
"NY":"New York",
"NC":"North Carolina",
"ND":"North Dakota",
"OH":"Ohio",
"OK":"Oklahoma",
"OR":"Oregon",
"PA":"Pennsylvania",
"RI":"Rhode Island",
"SC":"South Carolina",
"SD":"South Dakota",
"TN":"Tennessee",
"TX":"Texas",
"UT":"Utah",
"VT":"Vermont",
"VA":"Virginia",
"WA":"Washington",
"WV":"West Virginia",
"WI":"Wisconsin",
"WY":"Wyoming"
}
return switcher.get(code, "Unk")
#Function to extract the district fomr our code
def extractDistrictFromCode(code):
if(code == 'AL'):
return "1"
else:
return code
#electionInfoData.info()
#Function to determine if a congressional seat changed political parties
def determineIfSeatChangedParties(partyA, partyB):
if(partyA == 'Open Post-Redistrict'):
return "false"
elif(partyB == 'NA'):
return "false"
elif(partyA == 'Open-Used to be Dem' and partyB == 'D'):
return "false"
elif(partyA == 'Open-Used to be GOP' and partyB == 'R'):
return "false"
elif(partyA == 'GOP' and partyB == 'R'):
return "false"
elif(partyA == 'DEM' and partyB == 'D'):
return "false"
elif(partyA == partyB):
return "false"
else:
return "true"
#Funciton to determine the party if it's not a "swing" party
def calculatePartyIfNotSwing(repParty2014, winParty2014):
if(repParty2014 == "Open-Used to be Dem" or repParty2014 == 'Open-Used to be GOP'):
return winParty2014
else:
return repParty2014
#Define column names for our data frame to map the districts to their political parties
columnNames = ['state','district','party']
#Create our new dataframe
congressionalDistrictPartyData = pandas.DataFrame(columns = columnNames)
#Loop through our election info data
for index, row in electionInfoData.iterrows():
#Extract our state and district
state = extractStateFromCode(row['District'][0:2])
district = extractDistrictFromCode(row['District'][2:])
#Determine if it's a "Swing" district
swing = determineIfSeatChangedParties(row['rep_party_2014'], row['winning_party_2014'])
if(swing == 'false'):
swing = determineIfSeatChangedParties(row['rep_party_2016'], row['winning_party_2016'])
if(swing == 'false'):
swing = determineIfSeatChangedParties(row['rep_party_2018'], row['winning_party_2018'])
#Calculate the political party affiliated with this district
party = ""
if(swing == "true"):
party = "Swing"
else:
party = calculatePartyIfNotSwing(row['rep_party_2014'], row['winning_party_2014'])
#Create an array of our data
electionData = [[state, district, party]]
#Create a temporary dataframe
tempElectionDf = pandas.DataFrame(electionData, columns=['state','district','party'])
#Append it to our dataframe
congressionalDistrictPartyData = congressionalDistrictPartyData.append(tempElectionDf, True)
#Write our our congressional district party data report
congressionalDistrictPartyData.to_csv("congressionalDistrictPartyData.csv")
#Convet numIncidents to numeric
aggregated2014gunViolenceData['numIncidents'] = pandas.to_numeric(aggregated2014gunViolenceData['numIncidents'])
#Calculate the total number of incidents by state for 2014
total2014IncidentsByState = aggregated2014gunViolenceData.groupby('state').sum()
total2014IncidentsByState = total2014IncidentsByState.reset_index()
total2014IncidentsByState = total2014IncidentsByState[['state','numIncidents']]
total2014IncidentsByState.columns = ['state','2014 Incidents']
#Calculate the total number of incidents by state for 2015
aggregated2015gunViolenceData['numIncidents'] = pandas.to_numeric(aggregated2015gunViolenceData['numIncidents'])
total2015IncidentsByState = aggregated2015gunViolenceData.groupby('state').sum()
total2015IncidentsByState = total2015IncidentsByState.reset_index()
total2015IncidentsByState = total2015IncidentsByState[['state','numIncidents']]
total2015IncidentsByState.columns = ['state','2015 Incidents']
#Calculate the total number of incidents by state for 2016
aggregated2016gunViolenceData['numIncidents'] = pandas.to_numeric(aggregated2016gunViolenceData['numIncidents'])
total2016IncidentsByState = aggregated2016gunViolenceData.groupby('state').sum()
total2016IncidentsByState = total2016IncidentsByState.reset_index()
total2016IncidentsByState = total2016IncidentsByState[['state','numIncidents']]
total2016IncidentsByState.columns = ['state','2016 Incidents']
#Calculate the total number of incidents by state for 2017
aggregated2017gunViolenceData['numIncidents'] = pandas.to_numeric(aggregated2017gunViolenceData['numIncidents'])
total2017IncidentsByState = aggregated2017gunViolenceData.groupby('state').sum()
total2017IncidentsByState = total2017IncidentsByState.reset_index()
total2017IncidentsByState = total2017IncidentsByState[['state','numIncidents']]
total2017IncidentsByState.columns = ['state','2017 Incidents']
#Create four dataframes to hold the state firearms law data for each year from 2014-2017
stateLawData2014 = stateFirearmLawData[stateFirearmLawData['year'] == 2014]
stateLawData2015 = stateFirearmLawData[stateFirearmLawData['year'] == 2015]
stateLawData2016 = stateFirearmLawData[stateFirearmLawData['year'] == 2016]
stateLawData2017 = stateFirearmLawData[stateFirearmLawData['year'] == 2017]
#Rename column names to be more descriptive
stateLawData2014 = stateLawData2014[['state','lawtotal']]
stateLawData2014.columns = ['state','lawtotal2014']
stateLawData2015 = stateLawData2015[['state','lawtotal']]
stateLawData2015.columns = ['state','lawtotal2015']
stateLawData2016 = stateLawData2016[['state','lawtotal']]
stateLawData2016.columns = ['state','lawtotal2016']
stateLawData2017 = stateLawData2017[['state','lawtotal']]
stateLawData2017.columns = ['state','lawtotal2017']
#Merge our incident dataframes and statelaw dataframes
mergedIncidentDataByState = pandas.merge(total2014IncidentsByState, stateLawData2014, on='state',how='inner')
mergedIncidentDataByState = pandas.merge(mergedIncidentDataByState, total2015IncidentsByState, on='state',how='inner')
mergedIncidentDataByState = pandas.merge(mergedIncidentDataByState, stateLawData2015, on='state',how='inner')
mergedIncidentDataByState = pandas.merge(mergedIncidentDataByState, total2016IncidentsByState, on='state',how='inner')
mergedIncidentDataByState = pandas.merge(mergedIncidentDataByState, stateLawData2016, on='state',how='inner')
mergedIncidentDataByState = pandas.merge(mergedIncidentDataByState, total2017IncidentsByState, on='state',how='inner')
mergedIncidentDataByState = pandas.merge(mergedIncidentDataByState, stateLawData2017, on='state',how='inner')
mergedIncidentWithoutLawInformation = mergedIncidentDataByState[['state','2014 Incidents','2015 Incidents','2016 Incidents', '2017 Incidents']]
#Write out our mergedincidents by state report
mergedIncidentDataByState.to_csv("violenceCountsByStateAndYear.csv")
mergedIncidentWithoutLawInformation.to_csv("violenceCountsByStateAndYearWithoutLawInfo.csv")
#Convert district column to float type
congressionalDistrictPartyData['district'] = congressionalDistrictPartyData['district'].astype(float)
#Merge our gun violence data and congressional party data for 2014-2017
mergedIncidentsByCongressionalDistricts2014 = pandas.merge(aggregated2014gunViolenceData, congressionalDistrictPartyData, on=['state','district'], how='inner')
mergedIncidentsByCongressionalDistricts2015 = pandas.merge(aggregated2015gunViolenceData, congressionalDistrictPartyData, on=['state','district'], how='inner')
mergedIncidentsByCongressionalDistricts2016 = pandas.merge(aggregated2016gunViolenceData, congressionalDistrictPartyData, on=['state','district'], how='inner')
mergedIncidentsByCongressionalDistricts2017 = pandas.merge(aggregated2017gunViolenceData, congressionalDistrictPartyData, on=['state','district'], how='inner')
#Write out our reports of merged incidents by congressional districts
mergedIncidentsByCongressionalDistricts2014.to_csv("violenceIncidentsByCongressionalDistrictType2014.csv")
mergedIncidentsByCongressionalDistricts2015.to_csv("violenceIncidentsByCongressionalDistrictType2015.csv")
mergedIncidentsByCongressionalDistricts2016.to_csv("violenceIncidentsByCongressionalDistrictType2016.csv")
mergedIncidentsByCongressionalDistricts2017.to_csv("violenceIncidentsByCongressionalDistrictType2017.csv")
groupedAndMergedIncidentsByCongressionalDistricts2014 = mergedIncidentsByCongressionalDistricts2014.groupby('party')
#Calculate the average number of firearm laws between 2014-2017 per state
averageStateFirearmLawData = stateFirearmLawData.groupby('state').mean()
averageStateFirearmLawData = averageStateFirearmLawData.reset_index()
averageStateFirearmLawData = averageStateFirearmLawData[['state','lawtotal']]
#Count the number of rep, dem and swing seats per state
republicanRepsInState=mergedIncidentsByCongressionalDistricts2014.groupby('state')['party'].apply(lambda x: (x=='R').sum()).reset_index(name='count')
democraticRepsInState=mergedIncidentsByCongressionalDistricts2014.groupby('state')['party'].apply(lambda x: (x=='D').sum()).reset_index(name='count')
swingRepsInState=mergedIncidentsByCongressionalDistricts2014.groupby('state')['party'].apply(lambda x: (x=='Swing').sum()).reset_index(name='count')
#Merge our counts of dems, reps and swings with the average amount of firearm laws between 2014-2017
mergedFirearmLawsWithCongressionInformation = pandas.merge(averageStateFirearmLawData, republicanRepsInState, on=['state'], how='outer')
mergedFirearmLawsWithCongressionInformation = pandas.merge(mergedFirearmLawsWithCongressionInformation, democraticRepsInState, on=['state'], how='outer')
mergedFirearmLawsWithCongressionInformation = pandas.merge(mergedFirearmLawsWithCongressionInformation, swingRepsInState, on=['state'], how='outer')
mergedFirearmLawsWithCongressionInformation.columns = ['state','lawtotal','rep count','dem count','swing count']
#Print our report of firearm law relationship with number of congressional districts by party
mergedFirearmLawsWithCongressionInformation.to_csv("firearmsWithCongressionalInformation.csv")
#Correlation of officer involved shootings
aggregated2014Correlation = aggregated2014gunViolenceData.corr(method='pearson')
aggregated2014Correlation.to_csv('aggregated2014CorrelationInfo.csv')
aggregated2015Correlation = aggregated2015gunViolenceData.corr(method='pearson')
aggregated2015Correlation.to_csv('aggregated2015CorrelationInfo.csv')
aggregated2016Correlation = aggregated2016gunViolenceData.corr(method='pearson')
aggregated2016Correlation.to_csv('aggregated2016CorrelationInfo.csv')
aggregated2017Correlation = aggregated2017gunViolenceData.corr(method='pearson')
aggregated2017Correlation.to_csv('aggregated2017CorrelationInfo.csv')
OIX2014 = aggregated2017gunViolenceData['officer']
OIY2014 = aggregated2017gunViolenceData['numIncidents']
OI2014Reg = linear_model.LinearRegression()
OI2014Model = sm.OLS(OIX2014,OIY2014).fit()
#print(OI2014Model.summary())
mergedIncidentDataByStateCorrelation = mergedIncidentDataByState.corr(method='pearson')
mergedIncidentDataByStateCorrelation.to_csv('mergedIncidentDataByStateCorrelation.csv')
#TODO - LINEAR REGRESSION
#print(mergedIncidentDataByState)
X = mergedIncidentDataByState['lawtotal2017']
Y = mergedIncidentDataByState['2017 Incidents']
regr = linear_model.LinearRegression()
model = sm.OLS(X,Y).fit()
print(model.summary())
|
996,082 | c7a54bbbd5fbaef91c3e479d17b6aad8647d7418 | from app import models
class Queries():
def get_n_comans(self, post):
if type(post) is models.Post:
#returns number of comments on post.
n_answers = models.Post_Comments.query.filter_by(post_id = post.id).count()
return n_answers
elif type(post) is models.Answers:
#returns number of comments on answer
n_answers = models.Answer_Comments.query.filter_by(answer_id = post.id).count()
return n_answers
else:
#returns number of answers on post.
n_answers = models.Answers.query.filter_by(post_id = post.id).count()
return n_answers |
996,083 | 12f17e57ce1a7c35ac8f6f949baacd133afcfaa4 | from django.db import models
from web3 import Web3
class ETHAddressField(models.CharField):
def __init__(self, *args, **kwargs):
kwargs['max_length'] = 42
super().__init__(*args, **kwargs)
def pre_save(self, model_instance, add):
value = getattr(model_instance, self.attname, None)
if value:
return Web3.toChecksumAddress(value)
else:
return super().pre_save(model_instance, add)
|
996,084 | dcffd6c15695a265fbb6e40c772ee3171192aa7a | # -*- coding: utf-8 -*-
# -*- author: Jiangtao -*-
"""setup file"""
from setuptools import setup, find_packages
from os import path as os_path
from codecs import open
this_directory = os_path.abspath(os_path.dirname(__file__))
# 读取文件内容
def read_file(filename):
with open(os_path.join(this_directory, filename), encoding='utf-8') as f:
long_description = f.read()
return long_description
# 获取依赖
def read_requirements(filename):
return [line.strip() for line in read_file(filename).splitlines()
if not line.startswith('#')]
__author__ = 'jiangtao'
__date__ = '2018/09/18'
setup(
name='do-utils', # 名称
version='0.0.3', # 版本号
author='jiangtao', # 作者
author_email='jiangtao.work@gmail.com', # 邮箱
description='Utils for tornado api cache, function timer.', # 简单描述, 显示在PyPI上
long_description=read_file('README.md'), # 详细描述, 读取的Readme文档内容
long_description_content_type="text/markdown", # 指定包文档格式为markdown
url='https://github.com/hustjiangtao/do_utils', # 包含包的项目地址
packages=find_packages(), # 包列表
classifiers=[
'Programming Language :: Python :: 2.7',
'License :: OSI Approved :: Apache Software License',
'Operating System :: OS Independent',
'Intended Audience :: Developers',
],
license='http://www.apache.org/licenses/LICENSE-2.0', # 授权方式
keywords=[
'utils',
'do_utils',
'cache',
'time',
'do_cache',
'do_time',
], # 关键字
install_requires=[
'ujson==1.35',
'xlwt>=1.3.0,<=2.0.0',
'openpyxl>=2.6.2,<=3.0.0',
], # 指定需要安装的依赖
include_package_data=True,
zip_safe=True,
python_requires='>=2.7.14', # python环境
)
|
996,085 | 8eb98ef6cd83ee9dc6cb66168b1c9ebdf6252c86 | import yaml
import pandas as pd
import re
from argparse import ArgumentParser
def parsed_args():
"""
Parse and returns command-line args
Returns:
argparse.Namespace: the parsed arguments
"""
parser = ArgumentParser()
parser.add_argument(
"--input_csv",
default="bios.csv",
type=str,
help="CSV containing the info from the form",
)
parser.add_argument(
"--output_yml",
default="bios.yml",
type=str,
help="Output YAML file",
)
parser.add_argument(
"--output_photos",
default="./assets/img/team/team-photos",
type=str,
help="List of photos URL",
)
return parser.parse_args()
if __name__ == "__main__":
# -----------------------------
# ----- Parse arguments -----
# -----------------------------
args = parsed_args()
print("Args:\n" + "\n".join([f" {k:20}: {v}" for k, v in vars(args).items()]))
# Read CSV
df = pd.read_csv(args.input_csv, index_col=False)
# Rename columns
df.rename(columns={
"Name": "fullname",
"Short bio": "bio",
"Email": "email",
"Website": "website",
"Affiliation": "affiliation",
"Twitter": "twitter",
"Pronouns": "pronouns",
"Photo": "photo",
}, inplace=True)
# Replace Nan with "none"
df.fillna("none", inplace=True)
# Edit Photo item and download photo
f_photos = open(args.output_photos, "w")
for idx in range(len(df)):
photo_orig = df.iloc[idx].photo
if photo_orig != "none":
name_orig = df.iloc[idx].fullname
photo_file = name_orig.lower().replace(" ", "_")
photo_url = re.search('\(([^)]+)', photo_orig).group(1)
photo_ext = photo_url.split(".")[-1].lower()
photo_file_orig = "{}_orig.{}".format(photo_file, photo_ext)
f_photos.write(photo_file_orig + " " + photo_url + "\n")
df.loc[idx, 'photo'] = photo_file + ".jpg"
else:
df.loc[idx, 'photo'] = "none"
f_photos.close()
# Write YAML
df_dict = df.to_dict(orient='records')
with open(args.output_yml, "w") as f:
yaml.dump(df_dict, f)
|
996,086 | a10562113001e8244e2775ee6a9c8945ebea8f9a | """
给定一个整数类型的数组 nums，请编写一个能够返回数组 “中心索引” 的方法。
我们是这样定义数组 中心索引 的：数组中心索引的左侧所有元素相加的和等于右侧所有元素相加的和。
如果数组不存在中心索引，那么我们应该返回 -1。如果数组有多个中心索引，那么我们应该返回最靠近左边的那一个。
示例 1：
输入：
nums = [1, 7, 3, 6, 5, 6]
输出：3
解释：
索引 3 (nums[3] = 6) 的左侧数之和 (1 + 7 + 3 = 11)，与右侧数之和 (5 + 6 = 11) 相等。
同时, 3 也是第一个符合要求的中心索引。
示例 2：
输入：
nums = [1, 2, 3]
输出：-1
解释：
数组中不存在满足此条件的中心索引。
说明：
nums 的长度范围为 [0, 10000]。
任何一个 nums[i] 将会是一个范围在 [-1000, 1000]的整数。
"""
from typing import List
class Solution:
def pivotIndex(self, nums: List[int]) -> int:
len_ = len(nums)
if len_ < 2:
return -1
left_sum, right_sum = 0, sum(nums[1:])
mid = 0
while mid < len_ - 1:
if left_sum == right_sum:
return mid
left_sum += nums[mid]
mid += 1
right_sum -= nums[mid]
return -1 if left_sum != right_sum else mid
if __name__ == '__main__':
nums = [1, -1, 3]
sol = Solution()
print(sol.pivotIndex(nums))
|
996,087 | 3a0294086761647d9b3ed32e1920646ee3d8e9f1 | #题目：有四个数字：1、2、3、4，能组成多少个互不相同且无重复数字的三位数？各是多少？
number = 0
for i in range(1,5,1):
for j in range(1,5,1):
for k in range(1,5,1):
if (i != j) & (j != k) & (i != k):
number = number + 1
print(i,j,k)
print('一共有%d个互不相同且无重复数字的三位数'%number) |
996,088 | f86a5462d028936695cc18b7add4b21a5382d8d2 | star = int(input('ENter the nu of start do you want to print? \n'))
for i in range(star):
print(f"{'*'*(i+1)}")
|
996,089 | 130ffb6051383d778f9adc5b470bffaa7093a6e9 | #!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Thu Oct 4 12:33:10 2018
@author: danamulligan
"""
def ratio(dna):
counter = 0
total = len(dna)
for k in dna:
if k == 'g' or k == 'c':
counter += 1
return counter/total |
996,090 | a619db60c2d8e906fbfeafa9297b503822ad2b7b | import flask
from flask import request, render_template, redirect, url_for
from network_graph.models.graph import Graph
blueprint = flask.Blueprint('main', __name__)
@blueprint.route('/')
def index():
from networkx.readwrite import json_graph
g = Graph()
return render_template(
'main/index.html',
graph=g,
nodes=g.nodes
)
@blueprint.route('delete/<node>')
def delete_node(node):
_delete_node(Graph(), node)
return redirect(url_for('main.index'))
def _delete_node(g, node):
if g.graph.has_node(node):
g.graph.remove_node(node)
g.save()
def _edit_node(g, node):
_delete_node(g, node)
_add_node(g)
def _add_node(g):
new_node = request.form.get('current_node')
nodes = request.form.getlist('node')
weights = request.form.getlist('weight')
return g.add_node_with_edges(new_node, nodes, weights)
@blueprint.route('edit/<node>', methods=('GET', 'POST'))
def edit_node(node):
g = Graph()
if request.method == 'POST':
_edit_node(g, node)
return render_template(
'main/edit.html',
graph=g,
nodes=g.nodes,
node=node,
paths=g.get_paths_from(node)
)
@blueprint.route('add/', methods=('GET', 'POST'))
def add_node():
g = Graph()
node = ''
error = ''
if request.method == 'POST':
new_node = request.form.get('current_node')
nodes = request.form.getlist('node')
weights = request.form.getlist('weight')
if _add_node(g):
return redirect(url_for('main.index'))
error = "Can't create node {}. It already exists.".format(new_node)
return render_template(
'main/edit.html',
graph=g,
nodes=g.nodes,
node=node,
paths=g.get_paths_from(node),
error=error
)
|
996,091 | 0f6c3c01da9804090ad24f44013b9f5589d89438 | '''
Exercise 1
Start the Python interpreter and use it as a calculator.
1. How many seconds are there in 21 minutes and 15 seconds?
2. How many miles are there in 5 kilometers?
3. If you run a 5 kilometer race in 21 minutes and 15 seconds, what is your average pace (time per mile in minutes and seconds)?
4. What is your average speed in miles per hour?
5. Suppose the cover price of a book is $19.95, but bookstores get a 25% discount.
Shipping costs $2.50 for the first copy and $1 for each additional copy. What is the total wholesale cost for 75 copies?
'''
# 1. How many seconds are there in 21 minutes and 15 seconds?
seconds = (21 * 60) + 15
# 2. How many miles are there in 5 kilometers?
miles = 5 / 1.609
# 3. If you run a 5 kilometer race in 21 minutes and 15 seconds, what is your average pace (time per mile in minutes and seconds)?
' seconds per mile = ((21 minutes * 60 seconds in a minute) + 15 seconds) / number of miles in 5 kilometers'
pace = ( (21 * 60) + 15 ) / miles
# 4. What is your average speed in miles per hour?
'miles per hour = 1 mile / ( seconds per mile / 60 seconds in a minute / 60 minutes in an hour )'
mph = 1 / ( pace / 60 / 60 )
# 5. Suppose the cover price of a book is $19.95, but bookstores get a 25% discount.
# Shipping costs $2.50 for the first copy and $1 for each additional copy. What is the total wholesale cost for 75 copies?
coverPrice = 19.95
discount = 0.25
shippingCost1 = 2.5
shippingCost2 = 1
numberOfCopies = 75
totalCoverPrice = numberOfCopies * ( coverPrice * (1 - discount) )
totalShippingCost = shippingCost1 + ( ( numberOfCopies - 1 ) * shippingCost2 )
wholesaleCost = totalCoverPrice + totalShippingCost
# Print in Terminal
print("There are " + str(seconds) + " seconds in 21 minutes and 15 seconds.")
print("There are " + str(miles) + " miles in 5 kilometers.")
print("Your average pace is " + str(round(pace // 60)) + " minutes and " + str(round(pace % 60)) + " seconds per mile. ")
print("Your average speed is " + format(mph, '.2f') + " miles per hour.")
print("The wholesale cost of 75 copies is: $" + format(wholesaleCost, '.2f') + ".") |
996,092 | 4f6dc851465c27678d88b677e2324e1700b76c24 | # Generated by Django 2.1.1 on 2018-09-27 10:06
from django.db import migrations, models
import django.db.models.deletion
import django.utils.timezone
class Migration(migrations.Migration):
initial = True
dependencies = [
]
operations = [
migrations.CreateModel(
name='Database',
fields=[
('id', models.AutoField(auto_created=True, primary_key=True, serialize=False, verbose_name='ID')),
('url', models.CharField(max_length=300)),
('db_name', models.CharField(max_length=100)),
('auth_name', models.CharField(max_length=100)),
('auth_password', models.CharField(max_length=100)),
('complete_url', models.CharField(max_length=500)),
('active', models.BooleanField(default=False)),
('next', models.BooleanField(default=False)),
('updating', models.BooleanField(default=False)),
],
),
migrations.CreateModel(
name='Node',
fields=[
('id', models.AutoField(auto_created=True, primary_key=True, serialize=False, verbose_name='ID')),
('node_id', models.CharField(max_length=200)),
('name', models.CharField(max_length=100)),
('important', models.BooleanField(default=False)),
('first', models.BooleanField(default=False)),
('date', models.DateTimeField(default=django.utils.timezone.now)),
('show_graph', models.BooleanField(default=False)),
('lowest_optimal', models.FloatField(blank=True, null=True)),
('lowest_optimal_required', models.BooleanField(default=True)),
('highest_optimal', models.FloatField(blank=True, null=True)),
('highest_optimal_required', models.BooleanField(default=True)),
('str_optimal', models.CharField(blank=True, max_length=100, null=True)),
('str_optimal_required', models.BooleanField(default=True)),
('database', models.ForeignKey(on_delete=django.db.models.deletion.CASCADE, to='ParameterManager.Database')),
('parent', models.ForeignKey(blank=True, null=True, on_delete=django.db.models.deletion.CASCADE, to='ParameterManager.Node')),
],
),
migrations.CreateModel(
name='Value',
fields=[
('id', models.AutoField(auto_created=True, primary_key=True, serialize=False, verbose_name='ID')),
('date', models.DateTimeField(default=django.utils.timezone.now)),
('float_data', models.FloatField(blank=True, null=True)),
('float_data_required', models.BooleanField(default=True)),
('str_data', models.CharField(blank=True, max_length=100, null=True)),
('str_data_required', models.BooleanField(default=True)),
('detail', models.CharField(blank=True, max_length=100, null=True)),
('detail_required', models.BooleanField(default=True)),
('warning', models.CharField(blank=True, max_length=300, null=True)),
('node', models.ForeignKey(on_delete=django.db.models.deletion.CASCADE, to='ParameterManager.Node')),
],
),
]
|
996,093 | ba24a8d68bf8b7e0b9800efa9c2f4dbed157507e | topics = ["Alaska is the best State because", "The world will end with a Bang and a ", "Cryptocurrencies are a sham", "The Singularity is nigh", "John's Hackathon submission was awarded ", "This years Super Bowl winner will be: ", "Deep Learning has lead to countless jobs being replaced", "The best job in the computer industry is", "The Best Hash Algorithm is", "You should invest in ", "South Park and China ", "Tensor Flow is better than PyTorch because"]
|
996,094 | 3159b09f9d33e30b01209e878d553f8f045e4744 | p=[]
expresão=input('Digite a expressão:\n')
correto=False
for i in expresão:
if i=='(':
p.append(i)
elif i==')':
p.append(i)
print(p)
while p!=[]:
if(p[0]=='(' and p[len(p)-1]==')'):
correto=True
del(p[0])
del(p[len(p)-1])
else:
correto = False
break
if correto ==True:
print('Os parenteses estão corretos')
else:
print('Os parenteses estão incorretos')
|
996,095 | a7969b2e8a000f523879f3821c3d04ac030960bf | #import numpy as np
#from numpy import *
from numpy import array
x=array([1,2,5,6,3,74],int)
print(x) |
996,096 | 239cc8ce7ca3da8c9523d42d268e1a536fbeffd3 | from django.db import models
"""
MVT 中的 M
"""
# Create your models here.
class BookInfo(models.Model):
title=models.CharField(max_length=20)
pub_date=models.DateTimeField()
class HeroInfo(models.Model):
name=models.CharField(max_length=20)
gender=models.BooleanField(default=True)
content=models.CharField(max_length=100)
#book作为外键关联到bookinfo表
book=models.ForeignKey(BookInfo,on_delete=models.CASCADE)
|
996,097 | 80d9462ccae142e3882ec68ddbf3b796dbaab825 | from math import sqrt
from numpy import concatenate
from pandas import DataFrame
from pandas import concat
from sklearn.preprocessing import MinMaxScaler
from sklearn.metrics import mean_squared_error
# Import sklearn.preprocessing.StandardScaler
from sklearn.preprocessing import MinMaxScaler
def series_to_supervised(data, n_in=1, n_out=1, dropnan=True):
n_vars = 1 if type(data) is list else data.shape[1]
df =DataFrame(data)
cols, names = list(), list()
# input sequence (t-n, ... t-1)
for i in range(n_in, 0, -1):
cols.append(df.shift(i))
names += [('var%d(t-%d)' % (j+1, i)) for j in range(n_vars)]
# forecast sequence (t, t+1, ... t+n)
for i in range(0, n_out):
cols.append(df.shift(-i))
if i == 0:
names += [('var%d(t)' % (j+1)) for j in range(n_vars)]
else:
names += [('var%d(t+%d)' % (j+1, i)) for j in range(n_vars)]
# put it all together
agg = concat(cols, axis=1)
agg.columns = names
# drop rows with NaN values
if dropnan:
agg.dropna(inplace=True)
return agg
def split_data(reframed_df,validation_start,testing_start):
reframed=reframed_df.copy()
values= reframed.values
train = values[:validation_start, :]
validation = values[validation_start:testing_start, :]
test = values[testing_start:, :]
# split into input and outputs
train_X, train_y = train[:, :-1], train[:, -1]
validation_X, validation_y = validation[:, :-1], validation[:, -1]
test_X, test_y = test[:, :-1], test[:, -1]
# reshape input to be 3D [samples, timesteps, features]
train_X = train_X.reshape((train_X.shape[0], 1, train_X.shape[1]))
validation_X = validation_X.reshape((validation_X.shape[0], 1, validation_X.shape[1]))
test_X = test_X.reshape((test_X.shape[0], 1, test_X.shape[1]))
#print(train_X.shape, train_y.shape, validation_X.shape, validation_y.shape,test_X.shape, test_y.shape)
return train_X, train_y, validation_X, validation_y,test_X, test_y |
996,098 | 7d54c78dff467eb24613338ec7a0af128040cbfd | """
pyexcel_xlsbr
~~~~~~~~~~~~~~~~~~~
The lower level xlsb file format handler
:copyright: (c) 2019-2020 by Onni Software Ltd & its contributors
:license: New BSD License
"""
# flake8: noqa
from pyexcel_io.io import get_data as read_data
from pyexcel_io.io import isstream
from pyexcel_io.plugins import IOPluginInfoChainV2
from ._version import __author__, __version__
__FILE_TYPE__ = "xlsb"
IOPluginInfoChainV2(__name__).add_a_reader(
locations=["file"],
relative_plugin_class_path="xlsbr.XLSBBook",
file_types=[__FILE_TYPE__],
stream_type="binary",
)
def get_data(afile, file_type=None, **keywords):
"""standalone module function for reading module supported file type"""
if isstream(afile) and file_type is None:
file_type = __FILE_TYPE__
return read_data(afile, file_type=file_type, **keywords)
|
996,099 | 20c3f0794ca0131eb04bb44be3fa17822c16785b | import pandas as pd
import numpy as np
from scipy.stats import norm
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
# input parameters
Sigma = np.array([[1, -0.8], [-0.8, 2]]) # Covariance matrix of the Bivariate Normal distribution
c = np.sqrt(Sigma[1, 1] - Sigma[1, 0] * 1/(Sigma[0, 0]) * Sigma[0, 1]) # SD of conditional f(X2|X1)
# Create grid for x1,x2 and compute conditional pdf
x1 = np.ravel([np.arange(0, 4.51, 0.75)]*301) # grid values for x1\t\t
x2 = np.repeat(np.arange(-10, 5.01, 0.05), len(np.unique(x1))) # grid values for x2
# conditional pdf f(X2|X1)
f = norm.pdf(x2, loc = (Sigma[1, 0]*(1/Sigma[0, 0])*x1),
scale = Sigma[1, 1]-(Sigma[1, 0]**2 / Sigma[0, 0]))
# Conditional means
xm = np.unique(x1) # realized x1
m = pd.DataFrame(data = {"xm": xm, "1": Sigma[1, 0] * xm, "2": [0]*len(xm)}, columns = ["xm", "1", "2"]) # conditional mean
xmf = [-2] + list(xm) + [6]
# plot: shifts in the conditional density
fig = plt.figure(figsize=(10, 10))
ax = fig.add_subplot(111, projection='3d')
ax.scatter(x2, x1, f, c = "black", edgecolors = "black")
ax.scatter(m.iloc[:, 1], m.iloc[:, 0], m.iloc[:, 2], marker = "x", c = "r")
ax.plot(Sigma[1, 0] * np.array(xmf), np.array(xmf), [0]*9, c = "black")
ax.view_init(20, 135)
ax.set_xlim(-10, 5)
ax.set_ylim(-1, 5)
ax.set_zlim(0, 0.4)
ax.xaxis.pane.fill = False
ax.yaxis.pane.fill = False
ax.zaxis.pane.fill = False
plt.title("Conditional Normal Densities f(X2|X1)")
plt.show() |
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