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ModelsLNpatchmethodMSE
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38096down-sampled0.447
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Running time (s) with L = 336
Datasetw. patchw.o. patchGain
Traffic46410040x 22
Electricity3005730x19
Weather156680x4
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ModelsPatchTST/64PatchTST/42DLinearFEDformer AutoformerInformerPyraformerLogTrans MSE
MetricMSE MAEMSEMAE MSEMSE MAEMSE MAEMSE MAEMSE MAEMAE
960.149 0.1980.1520.199 0.176MAE 0.2370.2380.3140.2490.3290.3540.4050.896 0.5560.4580.490
Aaaeer192 336 7200.1940.2410.1970.243 0.2200.2820.2750.3290.3250.3700.4190.4340.6220.624 0.6580.589
0.245 0.282 0.3140.2490.2830.2650.3190.339 0.3770.351 0.3910.5830.5430.7390.7530.7970.652
0.3340.3200.3350.323 0.3620.3890.4090.4150.4260.9160.7051.0040.9340.8690.675
[ee960.360 0.2490.3670.2510.4100.2820.5760.3590.5970.371 0.7330.4102.0850.4680.6840.384
1920.379 0.2560.3850.2590.4230.2870.6100.3800.6070.382 0.7770.4350.8670.467 0.6850.390
3360.392 0.2640.3980.2650.4360.296 0.6080.3750.6230.3870.7760.4340.8690.4690.7340.408
7200.432 0.2860.4340.2870.4660.3150.6210.3750.639 0.3950.8270.4660.8810.4730.7170.396
960.129 0.2220.1300.2220.1400.2370.1860.3020.1960.313 0.3040.3930.3860.449 0.2580.357
1920.147 0.2400.1480.2400.1530.249 0.1970.3110.2110.3240.3270.4170.3860.4430.2660.368
erielaa3360.163 0.2590.1670.2610.1690.2670.2130.3280.214 0.3270.3330.4220.3780.4430.2800.380
7200.197 0.2900.2020.2910.2030.3010.2330.3440.2360.342 0.3510.4270.3760.445 0.2830.376
241.319 0.7541.5220.8142.2151.0812.6241.0952.906 1.1824.6571.4491.4202.0124.4801.444
ç›®361.579 0.8701.4300.8341.9630.9632.5161.0212.5851.038 4.6501.4637.3942.0314.7991.467
481.553 0.8151.6730.8542.1301.0242.5051.0413.0241.1455.004 1.5427.5512.057 4.8001.468
601.470 0.7881.5290.8622.3681.0962.7421.1222.761 1.1145.0711.5437.6622.1005.2781.560
FTLLI960.370 0.4000.3750.3990.3750.3990.3760.4150.435 0.4460.9410.7690.6640.6120.8780.740
1920.413 0.4290.4140.4210.4050.4160.4230.4460.4560.4571.0070.7860.7900.681 1.0370.824
3360.422 0.4400.4310.4360.4390.4430.4440.4620.4860.487 1.0380.7840.8910.738 1.2380.932
TLLE720 960.447 0.4680.4490.4660.4720.4900.4690.4920.515 0.5171.1440.8570.9630.7821.1350.852
0.274 0.3370.2740.3360.2890.3530.3320.3740.3320.3681.5490.9520.6450.597 2.1161.197
192 3360.341 0.3820.3390.3790.3830.4180.4070.4460.426 0.4343.7921.5420.7880.6834.3151.635
LLI7200.329 0.384 0.379 0.4220.331 0.3790.380 0.4220.448 0.6050.465 0.5510.400 0.4120.447 0.4690.477 0.479 0.453 0.4904.215 3.6561.642 1.6190.907 0.9630.747 0.7831.124 3.1881.604 1.540
960.293 0.3460.2900.342
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ModelsPatchTSTDLinearFEDformerAutoformerInformer
Fine-tuningLin. Prob.Sup.
MetricMSE 0.144MAE 0.193MSE 0.158MAE 0.209MSE 0.152MAE 0.199MSE 0.176MAE 0.237MSE 0.238MAE 0.314MSE 0.249MAE 0.329MSE 0.354MAE 0.405
waaeet96 1920.1900.2360.2030.2490.1970.2430.2200.2820.2750.3290.3250.3700.4190.434
3360.2440.2800.2510.2850.2490.2830.2650.3190.3390.3770.3510.3910.5830.543
7200.3200.3350.3210.3360.3200.3350.3230.3620.3890.4090.4150.4260.9160.705
960.3520.2440.3990.2940.3670.2510.4100.2820.5760.3590.5970.3710.7330.410
TTgera1920.3710.2530.4120.2980.3850.2590.4230.2870.3800.6070.3820.7770.435
0.610
3360.3810.2570.4250.3060.3980.2650.4360.2960.6080.3750.6230.3870.7760.434
7200.4250.2820.4600.3230.4340.2870.4660.3150.6210.3750.6390.3950.8270.466
rerreera960.1260.2210.1380.2370.1300.2220.1400.2370.1860.3020.1960.3130.3040.393
1920.1450.2380.1560.2520.1480.2400.1530.2490.1970.3110.2110.3240.417
0.1640.2560.1700.2650.1670.2610.1690.2670.3280.2140.3270.327
336 7200.1930.2910.2080.2970.2020.2910.2030.3010.213 0.2330.3440.2360.3420.333 0.3510.422 0.427
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ModelsPatchTSTDLinearFEDformerAutoformerInformer
Fine-tuningLin. Prob.Sup.
MetricMSEMAEMSEMAEMSEMAEMSEMAEMSEMAEMSEMAEMSEMAE
waaeet960.1450.1950.1630.2160.1520.1990.1760.2370.2380.3140.2490.3290.3540.405
1920.1930.2430.2050.2520.1970.2430.2200.2820.2750.3290.3250.3700.4190.434
3360.2440.2800.2530.2890.2490.2830.2650.3190.3390.3770.3510.3910.5830.543
7200.3210.3370.3200.3360.3200.3350.3230.3620.3890.4090.4150.4260.9160.705
[Tara960.3880.2730.4000.2880.3670.2510.4100.2820.5760.3590.5970.3710.7330.410
1920.4000.2770.4120.2930.3850.2590.4230.2870.6100.3800.6070.3820.7770.435
3360.4080.2800.4250.3070.3980.2650.4360.2960.6080.3750.6230.3870.7760.434
7200.4470.3100.4570.3170.4340.2870.4660.3150.6210.3750.6390.3950.8270.466
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ModelsIMP.PatchTSTBTSFTS2VecTNCTS-TCC
TransferredSelf-supervised
MetricsMSEMSEMAEMSEMAEMSEMAEMSEMAEMSEMAEMSEMAE
TTLLI2442.3%0.3120.3620.3220.3690.5410.5190.5990.5340.6320.5960.6530.610
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ModelsPatchTSTFEDformer
P+CICIP
MetricMSE MAEMSEMAEMSEMAEOriginal MSEMAE MSEMAE
waaeet96 1920.1520.1990.1640.2130.168 0.2230.1770.2360.2380.314
0.1970.2430.2050.2500.2130.2620.221 0.2700.2750.329
3360.2490.2830.2550.2890.2660.3000.271 0.3060.3390.377
7200.3200.3350.3270.3430.3510.3590.340 0.3530.3890.409
TTfeee960.3670.2510.3970.2710.5950.376- 10.5760.359
1920.3850.2590.4110.2760.6120.3871 10.6100.380
3360.3980.2650.4230.2820.6510.391- -0.6080.375
7200.4340.2870.4570.30911- -0.6210.375
eeeela960.1300.2220.1360.2310.1960.3070.205 0.3180.1860.302
1920.1480.2400.1640.2630.2150.323- -0.1970.311
3360.1670.2610.1680.2620.2280.338- -0.2130.328
7200.2020.2910.2190.3120.2440.345- 10.2330.344
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ModelsPatchTST/64PatchTST/42DLinearFEDformerAutoformerInformerLogTrans
MetricMSE MAEMSE MAEMSE MAEMSE MAEMSE MAEMSE MAEMSE MAE
FLLT960.0590.1890.0550.1790.0560.1800.079 0.2150.071 0.2060.1930.3770.2830.468
1920.0740.2150.0710.2050.0710.2040.1040.2450.114 0.2620.2170.3950.234 0.409
336 7200.0760.2200.0810.2250.0980.2440.1190.2700.107 0.2580.202 0.3810.3860.546
0.0870.2360.0870.2320.1890.3590.1420.2990.1260.2830.183 0.3550.4750.629
960.1310.2840.1290.2820.1310.2790.128 0.2710.1530.3060.2130.3730.2170.379
TILLE192 3360.171 0.1710.329 0.3360.168 0.1850.328 0.3510.1760.3290.1850.3300.2040.3510.2270.387 0.2810.429
0.2230.3800.2240.3830.209 0.2760.367 0.4260.2310.3780.2460.3890.2420.401 0.2930.437
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L24(24)48(36)96(48)192(60)336(104)720(144)
MetricMSE MAEMSE MAEMSE MAEMSE MAEMSE MAEMSE MAE
960.2220.2460.2120.2430.178 0.2190.1600.2040.1520.1990.1470.198
1920.2650.2790.2540.2770.2240.2590.2040.2450.197 0.2430.1900.240
waaeer3360.3250.3220.3100.3160.2780.298 0.2570.2850.2490.2830.2420.282
7200.4040.3740.3850.3650.3500.3460.3290.3380.320 0.3350.3040.328
960.7660.4190.6710.3810.477 0.3050.4010.2670.3670.2510.3650.251
[Yfere1920.7250.3980.6160.3560.4710.2990.4060.2680.385 0.2590.3820.258
3360.7520.4100.6350.3640.4850.3050.4210.2770.398 0.2650.3980.267
7200.7860.4270.6730.3830.5180.325 0.4520.2970.4340.2870.4360.289
960.2680.3160.2250.2930.1740.259 0.1380.2300.1300.2220.1300.224
riea1920.2590.3160.2170.2910.1780.265 0.1490.2430.1480.2400.1470.241
3360.2830.3350.2380.3090.1960.2820.1690.2620.167 0.2610.1630.259
7200.3210.3650.2780.3420.2370.316 0.2110.2990.2020.2910.1970.290
243.0621.1181.6100.8031.2810.704 1.3000.700 1.5220.8141.4700.793
I362.7321.0711.2620.7311.2510.7521.3670.776 1.4300.8341.5180.856
483.0591.1171.9910.8451.9010.8791.6900.8121.6730.8541.8340.921
602.6101.7020.8291.6110.8441.5260.862
960.4641.057 0.4450.4100.4170.3930.4080.3820.7951.5290.3991.656 0.3760.885 0.408
FELLT1920.5210.4740.4690.4480.4450.4340.4280.401 0.4250.375 0.4140.4210.431
3360.5700.4360.413
7200.5750.4980.5160.4690.4840.4510.4510.4360.4310.4450.454
0.3330.5220.5090.4870.4800.4710.4520.4590.4490.4660.4580.477
LLE960.3620.3070.3480.2940.3430.2850.3400.2740.3360.2790.341
1920.4220.4090.3970.3990.3770.3930.3560.3860.3390.3790.3490.386
3360.4420.4320.4120.4200.3810.4090.3500.3950.3310.3800.3750.409
7200.4620.4530.4340.4410.4120.4330.3950.4270.3790.4220.3940.434
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720 96 TLLE0.7440.5540.553
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ModelsPatchTSTFEDformer
P+CIPOriginal
Metric 96MSEMAECI MSE MAEMSEMAEMSEMAE MSEMAE
0.1520.1990.1640.2130.168 0.2230.1770.2360.2380.314
Waaeee1920.197 0.2430.2050.2500.2130.262 0.2210.2700.2750.329
3360.2490.283 0.2550.2890.2660.3000.271 0.3060.3390.377
7200.320 0.3350.3270.3430.3510.3590.340 0.3530.3890.409
96 1920.3670.251 0.3970.2710.595 0.6120.3761 10.5760.359
[Tfeee3360.3850.2590.4110.2760.387--0.6100.380
0.3980.2650.4230.2820.6510.391 -10.6080.375
7200.4340.2870.4570.309111 10.6210.375
960.1300.2220.1360.2310.1960.3070.205 0.3180.1860.302
rreea1920.1480.2400.1640.2630.215 0.323-10.1970.311
3360.1670.2610.1680.2620.2280.338- 10.2130.328
7200.2020.2910.2190.3120.2440.3451 -0.2330.344
ç›®24 361.5220.8142.1111.0482.1570.9642.737 1.0812.6241.095
1.4300.8342.0001.0022.5641.0582.126 0.9352.5161.021
481.6730.8542.1671.0292.3481.0222.178 0.9712.5051.041
601.5290.8622.0751.0212.4861.0652.354 1.0262.7421.122
FLLT96 1920.3750.3990.3650.3950.4160.4380.455 0.4590.376 0.4230.415
0.4140.4210.4030.4150.4590.4640.5030.4860.446
336 7200.4310.4360.4300.4330.4840.4800.514 0.5030.4440.462
0.4490.4660.4490.4540.5000.4940.531 0.5200.4690.492
LLE960.2740.3360.2770.3370.3340.3880.348 0.3940.3320.374
1920.3390.3790.3430.3840.3810.4180.3950.424 0.4070.446
3360.3310.3800.3330.3830.3610.4140.369 0.4190.4000.447
7200.3790.4220.3790.4200.4230.4480.433 0.4580.4120.469
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1920.3320.3690.3330.3740.3910.4050.3730.3980.365 0.415
3360.3660.3920.3690.3970.4270.4250.415 0.4210.3920.425
7200.4200.4240.4130.4230.4810.4570.480 0.4590.4460.458
LLE960.1650.2550.1660.2590.1950.2740.208 0.2890.1800.271
1920.2200.2920.2230.2950.2590.3140.2650.3280.252 0.318
3360.2780.3290.2790.3300.2970.3450.3230.365 0.3240.364
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0.4440.4100.420
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ModelsPatchTST/64 (+in)PatchTST/64 (-in)PatchTST/42 (+in)PatchTST/42 (-in)FEDformerAutoformerInformer
MAE
MetricMSE 0.149MAE 0.198MSE 0.161MAE 0.219MSE 0.152MAE 0.199MSE 0.156MAE 0.210MSE 0.238MAE 0.314MSE 0.2490.329MSE 0.354MAE 0.405
Aaaaer96 1920.1940.2410.2010.2540.1970.2430.1990.2500.2750.3290.3250.3700.4190.434
3360.2450.2820.2530.2980.2490.2830.2480.2940.3390.3770.3510.3910.5830.543
7200.3140.3340.3230.3570.3200.3350.3130.3420.3890.4090.4150.4260.9160.705
960.3600.2490.4130.2950.3670.2510.4250.2990.5760.3590.5970.371 0.733
Ttre1920.3790.2560.4250.3020.3850.2590.4390.3020.6100.3800.6070.410 0.435
3360.3920.2640.4350.3070.3160.6230.382 0.3870.777 0.776
7200.4320.2860.4730.3210.398 0.4340.265 0.2870.456 0.4880.3330.6080.3750.434
Friiela0.1290.2220.1330.2300.1300.2220.1310.2260.621 0.1860.375 0.3020.6390.3950.8270.466
960.1470.1480.1960.3130.3040.393
1920.2400.2440.1480.2400.1500.2440.1970.3110.2110.3240.3270.417
3360.163 0.1970.2590.164 0.1960.2620.167 0.2020.2610.1680.2670.2130.3280.2140.3270.3330.422
ç›®7201.3190.2900.2910.2910.201 3.4890.298 1.3450.2330.3440.2360.3420.3510.427
241.5790.7543.5631.3171.5220.8142.6241.0952.9061.1824.6571.449
360.8703.4261.2051.4300.8344.6291.5502.5161.0212.5851.0384.6501.463
481.5530.8154.3091.4491.6730.8543.7461.3832.5051.0413.0241.1455.0041.542
FLLT601.4700.7884.0651.4021.5290.8625.1741.6222.7421.1222.7611.1145.0711.543
960.370 0.4130.4000.3850.4100.3750.3990.3880.4120.3760.4150.4350.4460.9410.769
1920.4290.4170.4320.4140.4210.4300.4380.4230.4460.4560.4571.0070.786
3360.4220.4400.4390.4490.4310.4360.4540.4580.4440.4620.4860.4871.0380.784
LLI7200.4470.4680.4780.4940.4490.4660.4940.4970.4690.4920.5150.5171.1440.857
960.2740.3370.2990.3590.2740.3360.3130.3740.3320.3740.3320.3681.5490.952 1.542
192 3360.341 0.3290.382 0.3840.354 0.3740.404 0.4200.339 0.3310.379 0.3800.402 0.4480.432 0.4650.407 0.4000.446 0.4470.4770.426 0.4790.434 3.792
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ModelsPatchTSTDLinearFEDformerAutoformerInformer
Fine-tuningLin. Prob.Sup.
MetricMSE 0.144MAE 0.193MSE 0.158MAE 0.209MSE 0.152MAE 0.199MSE 0.176MAE 0.237MSE 0.238MAE MSE 0.314 0.249MAE 0.329MSE 0.354MAE 0.405
waaeer96 192 336 7200.190 0.2440.236 0.2800.203 0.2510.2490.197 0.2430.2200.2820.2750.3290.3250.3700.4190.434
0.2850.249 0.2830.2650.3190.3390.3770.3510.3910.5830.543
0.3200.3210.3360.3200.3350.3230.3620.3890.4090.4150.4260.9160.705
[taeea96 1920.3520.335 0.2440.3990.2940.367 0.2510.4100.2820.5760.3590.5970.3710.7330.410
0.3710.2530.4120.2980.3850.435
3360.3810.257 0.4250.3060.3980.259 0.2650.4230.2870.6100.3800.6070.3820.7770.434
7200.4250.2820.4600.3230.2870.436 0.4660.296 0.3150.608 0.6210.375 0.3750.623 0.6390.387 0.3950.776 0.8270.466
960.1260.2210.434
1920.1380.237 0.2520.130 0.1480.222 0.2400.140 0.1530.2370.1860.3020.1960.3130.3040.393
erneea3360.145 0.1640.238 0.2560.156 0.1700.2650.167 0.2610.1690.249 0.2670.197 0.2130.311 0.3280.211 0.2140.324 0.3270.327 0.3330.417 0.422
7200.1930.2910.2080.2970.2020.427
960.3660.4000.3750.291 0.3990.203 0.3750.301 0.3990.233 0.3760.3440.2360.3420.3510.769
LLT1920.4310.397 0.4430.371 0.4110.4280.414 0.4210.4050.4160.4230.415 0.4460.435 0.4560.446 0.4570.941 1.0070.786
3360.4500.4560.4450.4460.431
7200.4720.436 0.4660.439 0.4720.4430.4440.4620.4860.4871.0380.784
960.484 0.3430.4870.4780.4490.4900.4690.4920.5150.5171.1440.857
1920.284 0.3550.3870.285 0.3560.3440.2740.336 0.2890.3530.3320.3740.3320.3681.5490.952
0.387 0.3390.3790.3830.4180.4070.4460.4260.4343.7921.542
LLI3360.3790.4110.3770.4100.331 0.3800.4480.4650.4000.4470.4770.4794.2151.642
7200.4000.4350.3950.4340.3790.422 0.6050.5510.4120.4690.4530.4903.6561.619
960.2890.3440.2920.348 0.2900.3420.2990.3430.3260.3900.5100.4920.6260.560
[LLI1920.3230.3680.3290.3690.332 0.3690.3350.3650.3650.4150.5140.4950.7250.619
3360.3530.3870.3640.3910.3660.3920.741
7200.3980.4160.4150.4240.369 0.4250.386 0.4210.392 0.4460.425 0.4580.510 0.5270.492 0.4931.005 1.1330.845
LLE960.1660.2560.1670.419 0.2570.420 0.165 0.2550.1670.2600.1800.2710.2050.2930.355
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ModelsPatchTSTDLinearFEDformerAutoformerInformer
Fine-tuningLin. Prob.Sup.
MetricMSEMAEMSEMAE MSEMAEMSEMAEMSEMAEMSEMAEMSEMAE
waaeer96 192 3360.1450.195 0.2430.1630.216 0.2520.152 0.1970.199 0.2430.1760.2370.2380.3140.2490.3290.3540.405
0.1930.2050.2200.2820.2750.3290.3250.3700.4190.434
0.2440.2800.2530.2890.2490.2830.2650.3190.3390.3770.3510.3910.5830.543
YTgera720 960.321 0.3880.3370.3200.3360.3200.3350.3230.3620.3890.4090.4150.4260.9160.705
1920.4000.2730.4000.2880.3670.2510.4100.2820.5760.3590.5970.3710.7330.410
3360.4080.2770.4120.2930.3850.2590.4230.2870.6100.3800.6070.3820.7770.435
7200.4470.280 0.3100.425 0.4570.307 0.3170.398 0.4340.265 0.2870.436 0.4660.2960.6080.3750.6230.3870.7760.434
960.3680.3980.3720.4020.3750.3150.6210.3750.6390.3950.8270.466
1920.4250.4390.4110.4280.4140.399 0.4210.375 0.4050.3990.3760.4150.4350.4460.9410.769
FTLLT3360.4700.4710.4420.4540.4310.4360.4390.416 0.4430.423 0.4440.446 0.4620.456 0.4860.457 0.4871.007 1.0380.786 0.784
7200.4720.4840.4970.5010.4490.4660.4720.4900.4690.4920.5150.5171.1440.857
960.2850.3450.2800.3410.2740.3340.2890.3530.3320.3740.3320.3681.5490.952
LLE1920.3500.3880.3500.3870.3390.3790.3830.4180.4070.4460.4260.4343.7921.542
3360.3780.4100.3730.4100.3310.3800.4480.4650.4000.4470.4770.4794.2151.642
7200.4010.4380.3980.4360.3790.4220.6050.5510.4120.4691.619
[LLI960.2880.3450.2910.3460.2900.3420.2990.3430.453 0.5100.490 0.4923.656 0.6260.560
0.3300.3720.3350.3730.3320.3690.3260.390
192 3360.3590.3920.3650.3910.3660.3920.3350.3650.3650.4150.5140.4950.7250.619
0.4230.4240.4200.4240.3690.3860.3920.4250.5100.492 0.4931.0050.741
7200.4060.4210.4250.4210.4460.4580.5271.1330.845
960.1640.2560.166 0.2210.257 0.2950.165 0.2200.2550.1670.2600.1800.2710.2050.2930.3550.462
TTLLE192 3360.2230.2960.2770.3320.2780.292 0.3290.2240.3030.2520.318 0.3640.278 0.3430.336 0.3790.595 1.2700.586
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MetricMSE MAEMSE MAEMSE MAEMSE MAEMSE MAEMSE MAEMSE MAE
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7200.3200.3351.0590.7410.3270.3560.4190.4280.3840.3890.4030.4280.374
960.3670.2510.7190.3910.7050.4020.6130.369
PTteee1920.3850.2590.6960.3790.7200.4070.6160.388 0.382--0.587 0.6040.366·-
3360.3980.2650.4210.6220.337--0.373--
7200.4340.2870.777 0.8640.420 0.4720.750 --0.6600.408--0.6210.383-=
erera960.1300.2220.2740.3680.2030.2990.2010.3171 1- -0.626 0.1930.382 0.308- -= =
1920.1480.2400.2960.3860.2210.3160.2220.334-0.2010.315
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ç›®7200.2020.2910.3730.4390.3140.3910.2540.361--0.2460.355--
241.5220.8145.7641.6775.5141.6293.4831.2874.2101.5003.2281.2603.2801.264
361.4300.8344.7551.4675.5151.6283.1031.1482.8091.1622.6791.0802.8621.126
481.6730.8544.7631.4695.2631.5742.6691.0853.2181.2672.6221.0782.8341.150
601.5290.8625.2641.5645.3301.6022.7701.1253.6271.3962.8571.1573.1151.240
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TTLLE960.2740.3363.7551.5250.3900.4100.3580.3970.3370.3730.3460.3880.2970.348
1920.3390.3795.6021.9310.4560.463
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