# Number fields downloaded from the LMFDB on 06 June 2026. # Search link: https://www.lmfdb.org/NumberField/?completions=151.1.4.3a1.1 # Query "{'local_algs': {'$contains': ['151.1.4.3a1.1']}}" returned 818 fields, sorted by degree. # Each entry in the following data list has the form: # [Label, Polynomial, Discriminant, Galois group, Class group] # For more details, see the definitions at the bottom of the file. "4.0.13771804.1" [151, 0, 0, 0, 1] 13771804 "4T3" [21] "4.0.27543608.1" [1034, -387, 57, -1, 1] 27543608 "4T3" [7] "4.0.37872461.1" [128, 66, 57, -1, 1] 37872461 "4T3" [7] "4.0.65416069.1" [4464, 75, -74, -2, 1] 65416069 "4T3" [7] "4.0.68859020.1" [430, 217, 57, -1, 1] 68859020 "4T3" [14] "4.0.68859020.2" [4658, -840, 57, -1, 1] 68859020 "4T3" [14] "4.0.106731481.1" [5715, 519, -94, -1, 1] 106731481 "4T3" [21] "4.0.110174432.1" [7550, 0, 151, 0, 1] 110174432 "4T3" [42] "4.0.123946236.1" [1359, 0, 0, 0, 1] 123946236 "4T3" [14] "4.0.148046893.1" [6470, -991, 57, -1, 1] 148046893 "4T3" [7] "4.0.161818697.1" [11108, -76, 77, -2, 1] 161818697 "4T3" [63] "4.2.165261648.1" [-519, -378, -74, -2, 1] -165261648 "4T5" [] "4.0.203134109.1" [7225, -85, 208, -1, 1] 203134109 "4T3" [7] "4.0.203134109.2" [5715, 66, -94, -1, 1] 203134109 "4T5" [2] "4.0.220348864.1" [604, 0, 0, 0, 1] 220348864 "4T3" [14] "4.2.306422639.1" [-778, 519, -94, -1, 1] -306422639 "4T5" [] "4.0.344295100.1" [3775, 0, 0, 0, 1] 344295100 "4T3" [2, 42] "4.0.354623953.1" [4960, 368, -94, -1, 1] 354623953 "4T3" [7] "4.0.437254777.1" [21872, -387, -245, -1, 1] 437254777 "4T3" [21] "4.0.478570189.1" [32852, -227, 228, -2, 1] 478570189 "4T3" [21] "4.0.495784944.1" [151, 0, 151, 0, 1] 495784944 "4T3" [76] "4.4.495784944.1" [151, 0, -151, 0, 1] 495784944 "4T3" [] "4.0.550872160.1" [24160, 0, 302, 0, 1] 550872160 "4T3" [2, 14] "4.0.574972817.1" [1595, -76, 77, -2, 1] 574972817 "4T3" [259] "4.2.623174131.1" [-9083, -538, 208, -1, 1] -623174131 "4T5" [] "4.0.657603641.1" [45083, -76, 77, -2, 1] 657603641 "4T3" [7] "4.0.674818396.1" [7399, 0, 0, 0, 1] 674818396 "4T3" [28] "4.2.678261347.1" [2869, -1963, 0, 0, 1] -678261347 "4T5" [] "4.0.740234465.1" [2048, -76, 77, -2, 1] 740234465 "4T3" [14] "4.0.767778073.1" [9792, -840, -94, -1, 1] 767778073 "4T3" [7] "4.0.781549877.1" [8584, -1142, 57, -1, 1] 781549877 "4T3" [7] "4.0.798764632.1" [35032, 0, 302, 0, 1] 798764632 "4T3" [28] "4.0.822865289.1" [7376, -236, 208, -1, 1] 822865289 "4T3" [7] "4.0.864180701.1" [2350, 75, -74, -2, 1] 864180701 "4T3" [7] "4.2.953697427.1" [-4553, -1897, -245, -1, 1] -953697427 "4T5" [] "4.0.1015670545.1" [2803, -76, 77, -2, 1] 1015670545 "4T3" [14] "4.0.1046657104.1" [71725, 0, 302, 0, 1] 1046657104 "4T3" [2, 42] "4.0.1056985957.1" [11000, 1274, 57, -1, 1] 1056985957 "4T3" [35] "4.0.1070757761.1" [45881, -2501, 208, -1, 1] 1070757761 "4T3" [7] "4.0.1101744320.1" [48320, 0, 302, 0, 1] 1101744320 "4T3" [2, 14] "4.0.1101744320.2" [48320, 0, -302, 0, 1] 1101744320 "4T3" [2, 140] "4.0.1139616781.1" [11000, -840, 208, -1, 1] 1139616781 "4T3" [7] "4.2.1160274487.1" [-7875, -2350, -245, -1, 1] -1160274487 "4T5" [] "4.0.1194703997.1" [3256, 75, -74, -2, 1] 1194703997 "4T3" [7] "4.2.1270448919.1" [-3539, 226, -225, -2, 1] -1270448919 "4T3" [] "4.0.1318650233.1" [62189, -1293, -396, -1, 1] 1318650233 "4T3" [7] "4.0.1335864988.1" [62189, 1727, -396, -1, 1] 1335864988 "4T3" [84] "4.4.1349636792.1" [883, 217, -94, -1, 1] 1349636792 "4T5" [] "4.0.1401281057.1" [3860, -76, 77, -2, 1] 1401281057 "4T3" [14] "4.2.1449482371.1" [-16072, -2643, -74, -2, 1] -1449482371 "4T5" [] "4.2.1487354832.1" [-4077, 0, 0, 0, 1] -1487354832 "4T3" [2] "4.2.1487354832.2" [-453, 0, 0, 0, 1] -1487354832 "4T3" [2] "4.2.1487354832.3" [-2180, 1132, 228, -2, 1] -1487354832 "4T5" [2, 2] "4.0.1511455489.1" [14624, 972, 208, -1, 1] 1511455489 "4T3" [7] "4.2.1545884999.1" [-4251, 2482, -245, -1, 1] -1545884999 "4T5" [] "4.0.1594086313.1" [20060, 66, -245, -1, 1] 1594086313 "4T3" [21] "4.0.1676717137.1" [114845, 226, -225, -2, 1] 1676717137 "4T3" [7] "4.0.1690488941.1" [77440, -2803, -245, -1, 1] 1690488941 "4T3" [105] "4.0.1704260745.1" [116959, -680, 681, -2, 1] 1704260745 "4T3" [2, 70] "4.2.1766233863.1" [3148, 1274, 57, -1, 1] -1766233863 "4T3" [2] "4.0.1983139776.1" [5436, 0, 0, 0, 1] 1983139776 "4T3" [2, 14] "4.4.1983139776.1" [604, 0, -302, 0, 1] 1983139776 "4T3" [] "4.2.2024455188.1" [4356, -4917, 57, -1, 1] -2024455188 "4T3" [32] "4.4.2093314208.1" [538, -76, -225, -2, 1] 2093314208 "4T5" [] "4.0.2093314208.1" [22952, 0, 302, 0, 1] 2093314208 "4T3" [2, 210] "4.0.2327434876.1" [25519, 0, 0, 0, 1] 2327434876 "4T3" [14] "4.0.2423837504.1" [26576, 0, 302, 0, 1] 2423837504 "4T3" [2, 14] "4.4.3098655900.1" [4960, -2350, -396, -1, 1] 3098655900 "4T3" [2] "4.4.3191615577.1" [8692, 226, -225, -2, 1] 3191615577 "4T3" [] "4.4.3250145744.1" [236, -76, -74, -2, 1] 3250145744 "4T5" [2] "4.0.3525581824.1" [25519, 0, -302, 0, 1] 3525581824 "4T3" [24] "4.0.3525581824.2" [25519, 0, 302, 0, 1] 3525581824 "4T3" [24] "4.0.3811346757.1" [5413, -991, 57, -1, 1] 3811346757 "4T3" [2, 78] "4.0.3980051356.1" [43639, 0, 0, 0, 1] 3980051356 "4T3" [2, 14] "4.0.4293359897.1" [50864, 972, -396, -1, 1] 4293359897 "4T3" [28] "4.4.4462064496.1" [3105, -378, -225, -2, 1] 4462064496 "4T5" [] "4.4.4654869752.1" [9792, 368, -245, -1, 1] 4654869752 "4T5" [] "4.2.4723728772.1" [-1057, 0, 0, 0, 1] -4723728772 "4T3" [2] "4.2.4723728772.2" [-51793, 0, 0, 0, 1] -4723728772 "4T3" [2] "4.0.4734057625.1" [51921, 5049, -94, -1, 1] 4734057625 "4T3" [2, 4, 12] "4.0.4734057625.2" [62901, -378, 379, -2, 1] 4734057625 "4T3" [2, 2, 48] "4.4.4926862881.1" [1444, 226, -225, -2, 1] 4926862881 "4T3" [] "4.0.4957849440.1" [54360, 0, 453, 0, 1] 4957849440 "4T3" [2, 2, 14] "4.0.4971621244.1" [54511, 0, 0, 0, 1] 4971621244 "4T3" [2, 28] "4.0.5508721600.1" [15100, 0, 0, 0, 1] 5508721600 "4T3" [2, 2, 14] "4.0.5508721600.2" [29596, 0, 302, 0, 1] 5508721600 "4T3" [3, 24] "4.2.5949419328.1" [-16308, 0, 0, 0, 1] -5949419328 "4T3" [2] "4.2.5949419328.2" [-1812, 0, 0, 0, 1] -5949419328 "4T3" [2] "4.4.6579479361.1" [17903, 528, -527, -2, 1] 6579479361 "4T3" [] "4.4.6786056421.1" [35311, 368, -396, -1, 1] 6786056421 "4T5" [2] "4.0.6885902000.1" [755, 0, 0, 0, 1] 6885902000 "4T3" [2, 4, 12] "4.0.7051163648.1" [302, 0, 0, 0, 1] 7051163648 "4T3" [2, 12] "4.0.7051163648.2" [1208, 0, 0, 0, 1] 7051163648 "4T3" [4, 60] "4.2.7564163347.1" [-3949, 2331, -245, -1, 1] -7564163347 "4T5" [4] "4.2.7564163347.2" [17644, 368, -245, -1, 1] -7564163347 "4T5" [4] "4.0.8177008625.1" [72716, -378, 379, -2, 1] 8177008625 "4T3" [2, 2, 12] "4.0.8538518480.1" [23405, 0, 302, 0, 1] 8538518480 "4T3" [2, 2, 182] "4.2.8707223079.1" [-23924, 226, -225, -2, 1] -8707223079 "4T3" [] "4.4.10797094336.1" [21744, 0, -302, 0, 1] 10797094336 "4T3" [2] "4.0.12119187520.1" [132880, 0, 302, 0, 1] 12119187520 "4T3" [2, 2, 84] "4.4.12146731128.1" [-3798, 1878, -245, -1, 1] 12146731128 "4T5" [2] "4.4.13000582976.1" [-4983, -2416, -302, 0, 1] 13000582976 "4T5" [2] "4.0.14171186316.1" [169248, 6408, 661, -1, 1] 14171186316 "4T3" [2, 2, 20] "4.0.14846004712.1" [162778, 0, 1057, 0, 1] 14846004712 "4T3" [2, 104] "4.0.14997494556.1" [164439, 0, 0, 0, 1] 14997494556 "4T3" [2, 2, 14] "4.0.15369333264.1" [4681, 0, 151, 0, 1] 15369333264 "4T3" [2, 244] "4.4.16746513664.1" [33220, -2416, -604, 0, 1] 16746513664 "4T5" [] "4.4.18313056369.1" [5521, 226, -225, -2, 1] 18313056369 "4T3" [] "4.0.27543608000.1" [3020, 0, 0, 0, 1] 27543608000 "4T3" [2, 6, 12] "4.4.30986559000.1" [-7724, 8069, -849, -1, 1] 30986559000 "4T3" [4] "4.2.32391283008.1" [-260928, 0, 906, 0, 1] -32391283008 "4T3" [2, 2] "4.0.33286450268.1" [364967, 0, 1208, 0, 1] 33286450268 "4T3" [2730] "4.0.35541583173.1" [33801, -7635, 661, -1, 1] 35541583173 "4T3" [4, 132] "4.4.36161314353.1" [10957, 226, -225, -2, 1] 36161314353 "4T3" [] "4.2.37183870800.1" [-11325, 0, 0, 0, 1] -37183870800 "4T3" [2, 2] "4.0.37238958016.1" [102076, 0, 0, 0, 1] 37238958016 "4T3" [2, 28] "4.0.38970762369.1" [137538, -9447, 661, -1, 1] 38970762369 "4T3" [2, 2, 448] "4.4.38970762369.1" [2048, 528, -527, -2, 1] 38970762369 "4T3" [2] "4.4.40623378849.1" [12316, 226, -225, -2, 1] 40623378849 "4T3" [6] "4.0.46052912576.1" [2019776, 0, 302, 0, 1] 46052912576 "4T3" [2, 2, 42] "4.2.46479838500.1" [-20385, 0, 0, 0, 1] -46479838500 "4T3" [4, 12] "4.2.46479838500.2" [-229694, 23924, -849, -1, 1] -46479838500 "4T3" [2, 4] "4.2.50353158375.1" [-5804, 1132, -1131, -2, 1] -50353158375 "4T3" [4] "4.0.63460472832.1" [10872, 0, 0, 0, 1] 63460472832 "4T3" [2, 24] "4.2.72880386768.1" [-199773, 0, 0, 0, 1] -72880386768 "4T3" [2, 88] "4.2.72880386768.2" [-22197, 0, 0, 0, 1] -72880386768 "4T3" [2, 8] "4.0.73593077625.1" [1062111, -13071, -1604, -1, 1] 73593077625 "4T3" [2, 2, 24] "4.2.75579660352.1" [-4228, 0, 0, 0, 1] -75579660352 "4T3" [2, 2] "4.4.86376754688.1" [41525, -6040, -906, 0, 1] 86376754688 "4T5" [2] "4.0.105102965177.1" [972568, 2180, 1718, -1, 1] 105102965177 "4T3" [2, 916] "4.0.107457943661.1" [294988, -1737, 1738, -2, 1] 107457943661 "4T3" [400] "4.4.113534752176.1" [311211, 0, -3624, 0, 1] 113534752176 "4T3" [2] "4.0.119869782016.1" [1483726, 0, 2416, 0, 1] 119869782016 "4T3" [2, 12, 24] "4.0.119869782016.2" [415854, 0, -1208, 0, 1] 119869782016 "4T3" [2, 2, 24] "4.4.123946236000.1" [96640, 0, -755, 0, 1] 123946236000 "4T3" [2, 20] "4.4.133972109312.1" [27482, -2416, -604, 0, 1] 133972109312 "4T5" [4] "4.0.185392582497.1" [551731, -4615, 1416, -1, 1] 185392582497 "4T3" [2, 1000] "4.4.188921607272.1" [-142912, -27256, -1433, -2, 1] 188921607272 "4T5" [2] "4.2.190381418496.1" [-906, 0, 0, 0, 1] -190381418496 "4T3" [12] "4.4.226738981056.1" [456624, 0, -2114, 0, 1] 226738981056 "4T3" [2, 2] "4.4.245633896144.1" [1113021, 0, -2114, 0, 1] 245633896144 "4T3" [2, 10] "4.0.247892472000.1" [27180, 0, 0, 0, 1] 247892472000 "4T3" [6, 6, 24] "4.0.263385751500.1" [307866, 11844, 661, -1, 1] 263385751500 "4T3" [2, 4, 132] "4.4.285572127744.1" [59343, -4832, -906, 0, 1] 285572127744 "4T5" [2] "4.4.317302364160.1" [255190, 0, -1208, 0, 1] 317302364160 "4T3" [12] "4.0.337409198000.1" [36995, 0, 0, 0, 1] 337409198000 "4T3" [2, 2, 24] "4.0.407425049536.1" [1116796, 0, 0, 0, 1] 407425049536 "4T3" [2, 2, 14] "4.0.558346806621.1" [194767, 2482, 812, -1, 1] 558346806621 "4T3" [4, 252] "4.0.578415768000.1" [570780, 0, 1510, 0, 1] 578415768000 "4T3" [2, 24, 96] "4.0.684816725704.1" [271324, 18488, 359, -1, 1] 684816725704 "4T3" [2, 312] "4.0.707109833429.1" [169271, -8909, 0, 0, 1] 707109833429 "4T5" [2, 2, 12] "4.2.781484460931.1" [-313174, -9211, 0, 0, 1] -781484460931 "4T5" [4] "4.0.833194142000.1" [2283875, 0, 0, 0, 1] 833194142000 "4T3" [2, 2, 2, 6, 84] "4.0.881395456000.1" [1510, 0, 0, 0, 1] 881395456000 "4T3" [2, 4, 16] "4.0.895511555100.1" [118210, 14260, 359, -1, 1] 895511555100 "4T3" [4, 4, 56] "4.0.1081152030069.1" [362679, 1878, 1114, -1, 1] 1081152030069 "4T3" [2, 4, 324] "4.0.1648812019145.1" [885592, 31172, -698, -1, 1] 1648812019145 "4T3" [6, 2448] "4.0.1889216072720.1" [45904, -22952, 2869, 0, 1] 1889216072720 "4T3" [2, 4, 40] "4.0.3030206591169.1" [978004, 368, 1869, -1, 1] 3030206591169 "4T3" [2, 2, 1490] "4.0.3786474878976.1" [1459566, 0, 2416, 0, 1] 3786474878976 "4T3" [4, 1608] "4.4.6045491432704.1" [7003229, -22952, -5738, 0, 1] 6045491432704 "4T5" [2] "4.0.6045491432704.1" [2869, 0, 0, 0, 1] 6045491432704 "4T3" [2, 4, 40] "4.0.7441701022881.1" [912772, 22112, 57, -1, 1] 7441701022881 "4T3" [4, 540] "4.2.10000973890368.1" [-3045972, 0, 0, 0, 1] -10000973890368 "4T3" [2, 2, 12] "4.4.11313757334864.1" [291213, -31182, -4453, -2, 1] 11313757334864 "4T5" [2, 2, 8] "4.2.13323851974243.1" [-2455434, -185211, -2963, -1, 1] -13323851974243 "4T5" [4] "4.0.14420369894625.1" [961696, 5804, 1416, -1, 1] 14420369894625 "4T3" [2, 2, 2, 3036] "4.2.20415807705691.1" [-9481615, 73452, -3416, -1, 1] -20415807705691 "4T5" [4] "4.2.26322644615723.1" [4879089, 50198, -3718, -1, 1] -26322644615723 "4T5" [4] "4.4.45255029339456.1" [-1535132, -155908, -4453, -2, 1] 45255029339456 "4T5" [2, 2, 2] "4.4.48363931461632.1" [2530458, -413136, -11476, 0, 1] 48363931461632 "4T5" [2, 4] "4.2.73176249876283.1" [-418270, -41827, 0, 0, 1] -73176249876283 "4T5" [4] "4.0.73675925354913.1" [891028, 29360, -547, -1, 1] 73675925354913 "4T3" [2, 2, 8890] "4.0.124857554143141.1" [3744475, 115581, 6248, -1, 1] 124857554143141 "4T5" [2, 4] "4.0.124857554143141.2" [3798556, -49981, 0, 0, 1] 124857554143141 "4T5" NULL "4.0.141904668416000.1" [233628710, 0, -30200, 0, 1] 141904668416000 "4T3" [4, 16, 400] "4.0.175516047184625.1" [934516, 14864, 661, -1, 1] 175516047184625 "4T3" [2, 2, 2, 3300] "4.2.256907704918411.1" [-4122927, 361560, -7946, -1, 1] -256907704918411 "4T5" [4] "5.3.716133808.1" [128, -136, 16, 4, -2, 1] -716133808 "5T5" [] "5.1.1101744320.1" [-768, 296, 48, -29, -2, 1] 1101744320 "5T5" [] "5.1.1115516124.1" [624, -168, 96, -2, -2, 1] 1115516124 "5T5" [2] "5.1.1208475801.1" [-21, 57, -18, 11, -1, 1] 1208475801 "5T5" [] "5.1.1349636792.2" [32, 152, -20, -10, -2, 1] 1349636792 "5T5" [] "5.1.1666388284.1" [496, -101, -62, 20, -2, 1] 1666388284 "5T5" [5] "5.1.2478924720.1" [-160, 195, -82, 12, -2, 1] 2478924720 "5T5" [] "5.3.2974709664.1" [-1588, 782, 38, -41, -2, 1] -2974709664 "5T5" [] "5.3.2974709664.2" [-258, -266, -151, -45, -1, 1] -2974709664 "5T5" [] "5.1.3525581824.1" [-2480, -73, -64, -50, 0, 1] 3525581824 "5T5" [] "5.1.3525581824.2" [2180, 444, 44, -12, 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"8T35" [2] "8.6.1848420243341312.2" [-302, 0, 1208, 0, -592, 0, 28, 0, 1] -1848420243341312 "8T35" [] "8.2.1848420243341312.2" [-302, 0, 2416, 0, 744, 0, 52, 0, 1] -1848420243341312 "8T35" [2] "8.8.1848420243341312.1" [14798, 0, -6040, 0, 876, 0, -52, 0, 1] 1848420243341312 "8T30" [] "8.0.1848420243341312.1" [14798, 0, 6040, 0, 876, 0, 52, 0, 1] 1848420243341312 "8T30" [166] "8.4.1848420243341312.1" [14798, 0, -4832, 0, -132, 0, 28, 0, 1] 1848420243341312 "8T30" [] "8.4.1848420243341312.2" [14798, 0, 4832, 0, -132, 0, -28, 0, 1] 1848420243341312 "8T30" [2] "8.4.2180558255816704.3" [3337, -16956, -17972, -4108, 452, 92, -76, -4, 1] 2180558255816704 "8T29" [] "8.0.2180558255816704.6" [8057, -2236, -1192, -2548, 2012, -148, 104, -4, 1] 2180558255816704 "8T29" [2] "8.0.2572377317408768.1" [940, -4728, 8091, -5222, 1337, -212, 67, -2, 1] 2572377317408768 "8T35" [7] "8.0.2572377317408768.2" [2992, 5232, 4172, 2080, 908, 168, 51, -2, 1] 2572377317408768 "8T35" [7] "8.0.2572377317408768.3" [4678, 3448, 198, -80, 359, -12, -37, 0, 1] 2572377317408768 "8T35" [105] "8.0.2572377317408768.4" [12875, 3764, 1554, 712, 4, -108, -2, 0, 1] 2572377317408768 "8T35" [7] "8.0.5144754634817536.1" [151, 0, 0, 0, 484, 0, -44, 0, 1] 5144754634817536 "8T35" [7] "8.0.5144754634817536.2" [151, 0, 0, 0, 484, 0, 44, 0, 1] 5144754634817536 "8T35" [7] "8.2.7393680973365248.7" [-302, 0, 0, 0, -68, 0, 0, 0, 1] -7393680973365248 "8T26" [2] "8.2.7393680973365248.9" [-302, 0, 0, 0, 12, 0, 0, 0, 1] -7393680973365248 "8T26" [2] "8.2.7393680973365248.22" [-1208, 0, 0, 0, -136, 0, 0, 0, 1] -7393680973365248 "8T26" [2] "8.2.7393680973365248.24" [-1208, 0, 0, 0, 24, 0, 0, 0, 1] -7393680973365248 "8T26" [6] "8.0.7393680973365248.1" [1208, 0, 0, 0, 80, 0, 0, 0, 1] 7393680973365248 "8T26" [10] "8.0.7393680973365248.2" [1208, 0, 0, 0, 128, 0, 0, 0, 1] 7393680973365248 "8T26" [10] "8.0.7393680973365248.6" [87278, 0, 8456, 0, -448, 0, -24, 0, 1] 7393680973365248 "8T35" [2] "8.0.7393680973365248.7" [159758, 0, 32616, 0, 2008, 0, 80, 0, 1] 7393680973365248 "8T35" [2] "8.4.7393680973365248.7" [87278, 0, -8456, 0, -448, 0, 24, 0, 1] 7393680973365248 "8T35" [2] "8.4.7393680973365248.8" [159758, 0, -32616, 0, 2008, 0, -80, 0, 1] 7393680973365248 "8T35" [2] "8.0.7393680973365248.14" [302, 0, 0, 0, 40, 0, 0, 0, 1] 7393680973365248 "8T26" [10] "8.0.7393680973365248.15" [302, 0, 0, 0, 64, 0, 0, 0, 1] 7393680973365248 "8T26" [10] "8.0.8722233023266816.4" [22801, 0, 13288, 0, -1812, 0, 88, 0, 1] 8722233023266816 "8T29" [2] "8.0.8722233023266816.5" [22801, 0, 40468, 0, 3020, 0, 92, 0, 1] 8722233023266816 "8T29" [18] "8.4.8722233023266816.6" [22801, 0, -40468, 0, 3020, 0, -92, 0, 1] 8722233023266816 "8T29" [] "8.4.8722233023266816.7" [22801, 0, -13288, 0, -1812, 0, -88, 0, 1] 8722233023266816 "8T29" [] "8.0.10289509269635072.1" [1681, 574, 3225, 254, 644, -34, 49, -2, 1] 10289509269635072 "8T31" [42] "8.0.10289509269635072.2" [19328, 0, -7248, 0, 1289, 0, -18, 0, 1] 10289509269635072 "8T35" [14] "8.0.10289509269635072.3" [77312, 0, -9664, 0, 1326, 0, -64, 0, 1] 10289509269635072 "8T31" [3, 42] "8.0.10289509269635072.4" [590, -2236, 3594, -2072, 715, -108, 16, 0, 1] 10289509269635072 "8T35" [14] "8.0.10663451025065549.1" [65792, -37504, 21836, -5258, 2059, -197, 87, -3, 1] 10663451025065549 "8T28" [4] "8.4.10663451025065549.1" [29632, 31408, -9252, -9614, -629, 423, 26, -2, 1] 10663451025065549 "8T28" [] "8.0.12138405466522624.2" [23606, 5014, 4425, 1820, 444, 70, 30, -2, 1] 12138405466522624 "8T18" [21] "8.2.17444466046533632.3" [-182408, 0, -38656, 0, 1812, 0, 28, 0, 1] -17444466046533632 "8T35" [] "8.2.17444466046533632.4" [-182408, 0, -7248, 0, 604, 0, -52, 0, 1] -17444466046533632 "8T35" [] "8.2.17444466046533632.5" [-182408, 0, 7248, 0, 604, 0, 52, 0, 1] -17444466046533632 "8T35" [] "8.2.17444466046533632.6" [-182408, 0, 38656, 0, 1812, 0, -28, 0, 1] -17444466046533632 "8T35" [] "8.2.17444466046533632.8" [-45602, 0, -11476, 0, 1510, 0, -40, 0, 1] -17444466046533632 "8T35" [] "8.2.17444466046533632.9" [-45602, 0, -7852, 0, -302, 0, -12, 0, 1] -17444466046533632 "8T35" [] "8.2.17444466046533632.10" [-45602, 0, 7852, 0, -302, 0, 12, 0, 1] -17444466046533632 "8T35" [] "8.2.17444466046533632.11" [-45602, 0, 11476, 0, 1510, 0, 40, 0, 1] -17444466046533632 "8T35" [] "8.2.20579018539270144.1" [-172823, -124060, -27980, -652, 1550, 300, 12, -4, 1] -20579018539270144 "8T26" [2] "8.0.20579018539270144.1" [241600, 0, -21744, 0, 1435, 0, -46, 0, 1] 20579018539270144 "8T35" [21] "8.0.20579018539270144.2" [241600, 0, 21744, 0, 1435, 0, 46, 0, 1] 20579018539270144 "8T35" [7] "8.4.36050924760663157.1" [78732, -196992, -132775, -8000, 5286, 375, -101, -3, 1] 36050924760663157 "8T28" [] "8.0.36050924760663157.1" [114989, -50894, 16080, -6013, 958, -173, 40, 0, 1] 36050924760663157 "8T28" [2] "8.0.41158037078540288.1" [7550, 0, -604, 0, 167, 0, -8, 0, 1] 41158037078540288 "8T35" [14] "8.0.41158037078540288.2" [7550, 0, 604, 0, 167, 0, 8, 0, 1] 41158037078540288 "8T35" [14] "8.0.41158037078540288.3" [19328, 0, 0, 0, 361, 0, -38, 0, 1] 41158037078540288 "8T31" [42] "8.0.41158037078540288.4" [77312, 0, 9664, 0, 1326, 0, 64, 0, 1] 41158037078540288 "8T31" [3, 42] "8.0.48553621866090496.2" [2500, 0, -3528, 0, 1357, 0, 14, 0, 1] 48553621866090496 "8T18" [3, 42] "8.0.82316074157080576.1" [9664, 0, -4832, 0, 704, 0, 20, 0, 1] 82316074157080576 "8T35" [7, 7] "8.0.82316074157080576.2" [9664, 0, 4832, 0, 704, 0, -20, 0, 1] 82316074157080576 "8T35" [21] "8.0.82316074157080576.4" [604, 0, -604, 0, 176, 0, 10, 0, 1] 82316074157080576 "8T35" [7] "8.0.82316074157080576.5" [604, 0, 604, 0, 176, 0, -10, 0, 1] 82316074157080576 "8T35" [7] "8.0.97107243732180992.3" [6962, 0, 572, 0, -127, 0, -8, 0, 1] 97107243732180992 "8T35" [105] "8.0.97107243732180992.4" [120050, 0, 13867, 0, 783, 0, 27, 0, 1] 97107243732180992 "8T35" [7] "8.0.97107243732180992.6" [128, 0, 368, 0, 963, 0, -1, 0, 1] 97107243732180992 "8T35" [21] "8.4.139555728372269056.1" [-5134, -314080, -47112, 24160, 3004, -520, -80, 0, 1] 139555728372269056 "8T29" [2] "8.4.139555728372269056.2" [90751, 66440, -40468, -36240, -4522, -280, -84, 0, 1] 139555728372269056 "8T29" [2] "8.4.139555728372269056.3" [1117249, 0, -138316, 0, 7550, 0, -188, 0, 1] 139555728372269056 "8T29" [2] "8.4.139555728372269056.4" [1117249, 0, -116572, 0, -1510, 0, -4, 0, 1] 139555728372269056 "8T29" [2] "8.0.139555728372269056.8" [1117249, 0, 116572, 0, -1510, 0, 4, 0, 1] 139555728372269056 "8T29" [4] "8.0.139555728372269056.9" [1117249, 0, 138316, 0, 7550, 0, 188, 0, 1] 139555728372269056 "8T29" [4] "8.0.139555728372269056.10" [1250431, 78520, 10268, 12080, 3386, -280, 108, 0, 1] 139555728372269056 "8T29" [4] "8.0.139555728372269056.12" [415854, -326160, 125632, -24160, 3712, -520, 104, 0, 1] 139555728372269056 "8T29" [20] "8.0.164632148314161152.1" [19328, 0, -4832, 0, 471, 0, -26, 0, 1] 164632148314161152 "8T31" [84] "8.0.164632148314161152.2" [19328, 0, 4832, 0, 471, 0, 26, 0, 1] 164632148314161152 "8T31" [3, 42] "8.0.164632148314161152.3" [77312, 0, -9664, 0, 338, 0, -12, 0, 1] 164632148314161152 "8T31" [3, 42] "8.0.164632148314161152.4" [77312, 0, 9664, 0, 338, 0, 12, 0, 1] 164632148314161152 "8T31" [84] "8.0.194214487464361984.3" [1444, 0, 226, 0, 77, 0, -2, 0, 1] 194214487464361984 "8T9" [3, 42] "8.0.194214487464361984.6" [65536, 0, -6720, 0, 1234, 0, -64, 0, 1] 194214487464361984 "8T29" [21] "8.0.194214487464361984.7" [123904, 0, -20440, 0, 3169, 0, 14, 0, 1] 194214487464361984 "8T18" [14] "8.0.194214487464361984.9" [1024462, -715640, 278989, -48850, 5881, -876, 107, -2, 1] 194214487464361984 "8T9" [3, 42] "8.0.289105049729511989.1" [121193, -22188, 30783, -10693, 5353, -814, 140, -3, 1] 289105049729511989 "8T17" [7] "8.2.329264296628322304.4" [-3442951, 0, 0, 0, -2114, 0, 0, 0, 1] -329264296628322304 "8T26" [2] "8.0.388428974928723968.1" [3872, 0, 96, 0, 238, 0, -9, 0, 1] 388428974928723968 "8T35" [7] "8.0.388428974928723968.2" [14792, 0, -5324, 0, 726, 0, -44, 0, 1] 388428974928723968 "8T35" [21] "8.2.533533087245486443.1" [-313627, 108267, 33522, -18422, 2421, -535, 97, 0, 1] -533533087245486443 "8T30" [] "8.2.558222913489076224.2" [-22801, 0, -36844, 0, 2718, 0, -52, 0, 1] -558222913489076224 "8T35" [4] "8.2.558222913489076224.4" [-22801, 0, -16308, 0, -302, 0, -28, 0, 1] -558222913489076224 "8T35" [4] "8.2.558222913489076224.6" [-22801, 0, 16308, 0, -302, 0, 28, 0, 1] -558222913489076224 "8T35" [2] "8.2.558222913489076224.7" [-22801, 0, 36844, 0, 2718, 0, 52, 0, 1] -558222913489076224 "8T35" [2] "8.2.558222913489076224.17" [-91204, 0, -106304, 0, 3020, 0, 24, 0, 1] -558222913489076224 "8T35" [4] "8.2.558222913489076224.19" [-91204, 0, -41072, 0, 1812, 0, -80, 0, 1] -558222913489076224 "8T35" [4] "8.2.558222913489076224.20" [-91204, 0, 41072, 0, 1812, 0, 80, 0, 1] -558222913489076224 "8T35" [2] "8.2.558222913489076224.21" [-91204, 0, 106304, 0, 3020, 0, -24, 0, 1] -558222913489076224 "8T35" [2] "8.0.600436183687275853.1" [3468177, -596664, -126794, 19087, 7510, -315, -116, -2, 1] 600436183687275853 "8T17" [7] "8.0.776857949857447936.1" [1024, 0, -608, 0, 192, 0, -19, 0, 1] 776857949857447936 "8T29" [7] "8.0.776857949857447936.6" [913936, 0, -28896, 0, -455, 0, 14, 0, 1] 776857949857447936 "8T18" [2, 42] "8.2.1317057186513289216.1" [-13771804, 0, 0, 0, -4228, 0, 0, 0, 1] -1317057186513289216 "8T26" [2] "8.6.1317057186513289216.1" [-10782674, 1540200, -503208, -20536, 26200, 0, -304, 0, 1] -1317057186513289216 "8T35" [] "8.2.1317057186513289216.2" [-13771804, 0, 0, 0, 11476, 0, 0, 0, 1] -1317057186513289216 "8T26" [2] "8.2.1317057186513289216.3" [-10292377, -1560736, 477084, -20536, 25898, 0, 300, 0, 1] -1317057186513289216 "8T35" [2] "8.0.1553715899714895872.2" [23606, -9784, -17772, 4538, 3615, -232, 30, -2, 1] 1553715899714895872 "8T26" [14] "8.0.1553715899714895872.4" [111392, 0, 4576, 0, -508, 0, -16, 0, 1] 1553715899714895872 "8T35" [7] "8.2.1610181104784897899.1" [-1683836, 1388926, -387711, 18140, 6765, -301, -75, -2, 1] -1610181104784897899 "8T30" [4] "8.0.2634114373026578432.1" [337409198, 0, 3921772, 0, -4530, 0, 0, 0, 1] 2634114373026578432 "8T35" [2, 4] "8.4.2634114373026578432.1" [337409198, 0, -8481972, 0, 116874, 0, -604, 0, 1] 2634114373026578432 "8T35" [2] "8.4.2634114373026578432.2" [337409198, 0, -3921772, 0, -4530, 0, 0, 0, 1] 2634114373026578432 "8T35" [2] "8.0.2634114373026578432.2" [337409198, 0, 8481972, 0, 116874, 0, 604, 0, 1] 2634114373026578432 "8T35" [2, 2] "8.2.4849447275114741899.1" [-439772, -159116, 152415, 13351, -6547, -157, 57, -4, 1] -4849447275114741899 "8T30" [] "8.6.5268228746053156864.1" [-9359762, -16715776, 2246336, 338408, -39756, -616, -28, 0, 1] -5268228746053156864 "8T35" [] "8.2.5268228746053156864.1" [-57117438, -15937824, -4298608, -405720, -45192, -1824, -28, 0, 1] -5268228746053156864 "8T35" [2] "8.2.5443689638860136707.1" [-8992557, -5954733, -2254048, 95818, -44191, 1523, -83, -2, 1] -5443689638860136707 "8T30" [2] "8.0.6214863598859583488.2" [2918528, 0, 0, 0, 2869, 0, 0, 0, 1] 6214863598859583488 "8T26" [14] "8.0.6214863598859583488.3" [4560200, 0, -364816, 0, 25066, 0, -302, 0, 1] 6214863598859583488 "8T15" [14] "8.0.6214863598859583488.4" [4560200, 0, 364816, 0, 25066, 0, 302, 0, 1] 6214863598859583488 "8T15" [14] "8.0.8384046442155847681.1" [39686, 11435, 55673, -24759, 2070, 602, 47, -1, 1] 8384046442155847681 "8T19" [84] "8.0.12429727197719166976.1" [6400, 0, -2752, 0, 178, 0, 26, 0, 1] 12429727197719166976 "8T29" [3, 84] "8.0.12429727197719166976.3" [22801, 0, 0, 0, 906, 0, 0, 0, 1] 12429727197719166976 "8T11" [84] "8.0.12429727197719166976.4" [25600, 0, -7744, 0, 658, 0, 12, 0, 1] 12429727197719166976 "8T29" [84] "8.0.12429727197719166976.9" [57002500, 0, 2280100, 0, 22499, 0, -302, 0, 1] 12429727197719166976 "8T9" [84] "8.0.12429727197719166976.10" [218980804, 0, -4468996, 0, 52548, 0, -302, 0, 1] 12429727197719166976 "8T29" [2, 14] "8.0.12429727197719166976.11" [218980804, 0, 4468996, 0, 52548, 0, 302, 0, 1] 12429727197719166976 "8T29" [2, 14] "8.4.21072914984212627456.1" [3442951, 0, 0, 0, -8154, 0, 0, 0, 1] 21072914984212627456 "8T26" [] "8.4.21072914984212627456.2" [3442951, 0, 0, 0, -3926, 0, 0, 0, 1] 21072914984212627456 "8T26" [] "8.4.21072914984212627456.3" [13771804, 0, 0, 0, -16308, 0, 0, 0, 1] 21072914984212627456 "8T26" [] "8.4.21072914984212627456.4" [13771804, 0, 0, 0, -7852, 0, 0, 0, 1] 21072914984212627456 "8T26" [] "8.0.22216138796429206561.1" [181194120, 35969496, 368788, -189293, 27442, 2856, -116, -2, 1] 22216138796429206561 "8T19" [42] "8.0.24859454395438333952.1" [4050, 0, -1044, 0, 113, 0, -10, 0, 1] 24859454395438333952 "8T35" [42] "8.0.24859454395438333952.3" [64800, 0, -8352, 0, 452, 0, -20, 0, 1] 24859454395438333952 "8T35" [14] "8.6.42145829968425254912.1" [-6885902, 0, -3100936, 0, 101472, 0, -604, 0, 1] -42145829968425254912 "8T35" [] "8.2.42145829968425254912.1" [-6885902, 0, -8025952, 0, -27784, 0, 604, 0, 1] -42145829968425254912 "8T35" [146] "8.6.42145829968425254912.2" [-6885902, 0, 8025952, 0, -27784, 0, -604, 0, 1] -42145829968425254912 "8T35" [] "8.2.42145829968425254912.2" [-6885902, 0, 3100936, 0, 101472, 0, 604, 0, 1] -42145829968425254912 "8T35" [6] "8.8.42145829968425254912.1" [337409198, 0, -11309296, 0, 128652, 0, -604, 0, 1] 42145829968425254912 "8T30" [] "8.0.42145829968425254912.1" [159758, 0, 12080, 0, 196, 0, 28, 0, 1] 42145829968425254912 "8T35" [2, 6] "8.4.42145829968425254912.1" [159758, 0, -44696, 0, 3092, 0, -52, 0, 1] 42145829968425254912 "8T35" [2] "8.0.42145829968425254912.2" [159758, 0, 44696, 0, 3092, 0, 52, 0, 1] 42145829968425254912 "8T35" [2, 2] "8.4.42145829968425254912.2" [159758, 0, -12080, 0, 196, 0, -28, 0, 1] 42145829968425254912 "8T35" [2] "8.0.42145829968425254912.3" [639032, 0, 65232, 0, 2808, 0, 80, 0, 1] 42145829968425254912 "8T35" [2, 4] "8.4.42145829968425254912.3" [639032, 0, -113552, 0, 3768, 0, 24, 0, 1] 42145829968425254912 "8T35" [2] "8.0.42145829968425254912.4" [639032, 0, 113552, 0, 3768, 0, -24, 0, 1] 42145829968425254912 "8T35" [2, 4] "8.4.42145829968425254912.4" [639032, 0, -65232, 0, 2808, 0, -80, 0, 1] 42145829968425254912 "8T35" [2] "8.0.42145829968425254912.5" [337409198, 0, 11309296, 0, 128652, 0, 604, 0, 1] 42145829968425254912 "8T30" [2, 11872] "8.4.42145829968425254912.5" [337409198, 0, -8208360, 0, 604, 0, 604, 0, 1] 42145829968425254912 "8T30" [2] "8.4.42145829968425254912.6" [337409198, 0, 8208360, 0, 604, 0, -604, 0, 1] 42145829968425254912 "8T30" [2] "8.0.49718908790876667904.4" [8928, -9664, 5200, -2416, 686, 0, -32, 0, 1] 49718908790876667904 "8T29" [3, 24] "8.0.49718908790876667904.7" [91204, 0, 0, 0, 1812, 0, 0, 0, 1] 49718908790876667904 "8T11" [420] "8.0.49718908790876667904.8" [93636, 0, 7216, 0, 628, 0, -8, 0, 1] 49718908790876667904 "8T9" [2, 420] "8.0.49718908790876667904.11" [228010000, 0, -9120400, 0, 136202, 0, -604, 0, 1] 49718908790876667904 "8T11" [84] "8.0.49718908790876667904.12" [228010000, 0, 0, 0, -15402, 0, 0, 0, 1] 49718908790876667904 "8T11" [2, 42] "8.0.61376199547760860517.1" [885008, 383608, 71157, 18439, 4096, -140, -126, -3, 1] 61376199547760860517 "8T17" [7] "8.2.71686185022842306251.1" [155152, -22352, -39072, -2762, 1341, 18, -3, -2, 1] -71686185022842306251 "8T30" [] "8.0.80563496174068452893.1" [96365828, 9742798, 4677057, 258950, 70748, 1257, 393, -3, 1] 80563496174068452893 "8T28" [2] "8.4.80563496174068452893.1" [5823232, 1387360, -993729, 17366, 22896, -551, -223, -1, 1] 80563496174068452893 "8T28" [] "8.0.84291659936850509824.1" [102076, 0, -4832, 0, 1004, 0, 40, 0, 1] 84291659936850509824 "8T35" [24] "8.4.84291659936850509824.1" [1601959, 0, -189052, 0, -5542, 0, 28, 0, 1] 84291659936850509824 "8T27" [] "8.4.84291659936850509824.2" [1601959, 0, -92412, 0, -2218, 0, 108, 0, 1] 84291659936850509824 "8T27" [] "8.0.84291659936850509824.2" [102076, 0, 4832, 0, 1004, 0, -40, 0, 1] 84291659936850509824 "8T35" [48] "8.0.84291659936850509824.3" [110079, 0, -15100, 0, 1230, 0, -36, 0, 1] 84291659936850509824 "8T35" [48] "8.4.84291659936850509824.3" [1601959, 0, 92412, 0, -2218, 0, -108, 0, 1] 84291659936850509824 "8T27" [] "8.4.84291659936850509824.4" [1601959, 0, 189052, 0, -5542, 0, -28, 0, 1] 84291659936850509824 "8T27" [] "8.0.84291659936850509824.4" [110079, 0, 15100, 0, 1230, 0, 36, 0, 1] 84291659936850509824 "8T35" [24] "8.0.84291659936850509824.6" [5223996, 0, -263344, 0, -716, 0, 96, 0, 1] 84291659936850509824 "8T35" [48] "8.4.84291659936850509824.7" [6407836, 0, -562928, 0, -8668, 0, 80, 0, 1] 84291659936850509824 "8T27" [] "8.0.84291659936850509824.7" [5223996, 0, 263344, 0, -716, 0, -96, 0, 1] 84291659936850509824 "8T35" [24] "8.4.84291659936850509824.8" [6407836, 0, -193280, 0, -6852, 0, 136, 0, 1] 84291659936850509824 "8T27" [] "8.4.84291659936850509824.9" [6407836, 0, 193280, 0, -6852, 0, -136, 0, 1] 84291659936850509824 "8T27" [] "8.0.84291659936850509824.10" [14417631, 0, -347300, 0, 7854, 0, -92, 0, 1] 84291659936850509824 "8T35" [24] "8.4.84291659936850509824.10" [6407836, 0, 562928, 0, -8668, 0, -80, 0, 1] 84291659936850509824 "8T27" [] "8.0.84291659936850509824.11" [14417631, 0, 347300, 0, 7854, 0, 92, 0, 1] 84291659936850509824 "8T35" [48] "8.2.168583319873701019648.5" [-27543608, 0, 0, 0, -3624, 0, 0, 0, 1] -168583319873701019648 "8T26" [4] "8.2.168583319873701019648.7" [-27543608, 0, 0, 0, 20536, 0, 0, 0, 1] -168583319873701019648 "8T26" [4] "8.2.168583319873701019648.11" [-6885902, 0, 0, 0, -1812, 0, 0, 0, 1] -168583319873701019648 "8T26" [4] "8.2.168583319873701019648.13" [-6885902, 0, 0, 0, 10268, 0, 0, 0, 1] -168583319873701019648 "8T26" [12] "8.8.168583319873701019648.1" [3203918, 0, -554472, 0, 19232, 0, -240, 0, 1] 168583319873701019648 "8T27" [] "8.0.168583319873701019648.1" [725102, 0, -59192, 0, 17592, 0, -256, 0, 1] 168583319873701019648 "8T35" [2, 24] "8.4.168583319873701019648.1" [2030648, 0, -285088, 0, 11232, 0, -160, 0, 1] 168583319873701019648 "8T35" [2] "8.8.168583319873701019648.2" [12815672, 0, -1058208, 0, 29168, 0, -312, 0, 1] 168583319873701019648 "8T27" [] "8.4.168583319873701019648.2" [2030648, 0, -4832, 0, -1840, 0, -48, 0, 1] 168583319873701019648 "8T35" [2] "8.0.168583319873701019648.2" [725102, 0, 59192, 0, 17592, 0, 256, 0, 1] 168583319873701019648 "8T35" [24] "8.0.168583319873701019648.3" [1981422, 0, -97848, 0, 2232, 0, -64, 0, 1] 168583319873701019648 "8T35" [2, 24] "8.4.168583319873701019648.3" [3203918, 0, -25368, 0, -7160, 0, -72, 0, 1] 168583319873701019648 "8T27" [2] "8.0.168583319873701019648.4" [1981422, 0, 97848, 0, 2232, 0, 64, 0, 1] 168583319873701019648 "8T35" [24] "8.4.168583319873701019648.4" [3203918, 0, 25368, 0, -7160, 0, 72, 0, 1] 168583319873701019648 "8T27" [2] "8.0.168583319873701019648.5" [2030648, 0, 4832, 0, -1840, 0, 48, 0, 1] 168583319873701019648 "8T35" [2, 4] "8.0.168583319873701019648.6" [2030648, 0, 285088, 0, 11232, 0, 160, 0, 1] 168583319873701019648 "8T35" [2, 70] "8.0.168583319873701019648.7" [3203918, 0, 554472, 0, 19232, 0, 240, 0, 1] 168583319873701019648 "8T27" [2, 1028] "8.4.168583319873701019648.7" [1990025678, 0, -2371304, 0, -93016, 0, 0, 0, 1] 168583319873701019648 "8T35" [2] "8.0.168583319873701019648.8" [6885902, 0, 0, 0, 6040, 0, 0, 0, 1] 168583319873701019648 "8T26" [2, 10] "8.4.168583319873701019648.8" [7960102712, 0, -107985536, 0, 543600, 0, -1208, 0, 1] 168583319873701019648 "8T35" [2] "8.4.168583319873701019648.9" [507662, 0, -72480, 0, 784, 0, 56, 0, 1] 168583319873701019648 "8T35" [2] "8.0.168583319873701019648.9" [6885902, 0, 0, 0, 9664, 0, 0, 0, 1] 168583319873701019648 "8T26" [2, 10] "8.4.168583319873701019648.10" [507662, 0, -70064, 0, 3912, 0, -104, 0, 1] 168583319873701019648 "8T35" [2] "8.0.168583319873701019648.10" [1990025678, 0, 2371304, 0, -93016, 0, 0, 0, 1] 168583319873701019648 "8T35" [2, 12] "8.0.168583319873701019648.11" [7960102712, 0, 107985536, 0, 543600, 0, 1208, 0, 1] 168583319873701019648 "8T35" [4, 8] "8.4.168583319873701019648.11" [12815672, 0, -1159680, 0, -5024, 0, 168, 0, 1] 168583319873701019648 "8T27" [2] "8.4.168583319873701019648.12" [12815672, 0, 1159680, 0, -5024, 0, -168, 0, 1] 168583319873701019648 "8T27" [10] "8.0.168583319873701019648.12" [507662, 0, 70064, 0, 3912, 0, 104, 0, 1] 168583319873701019648 "8T35" [2, 2] "8.0.168583319873701019648.13" [507662, 0, 72480, 0, 784, 0, -56, 0, 1] 168583319873701019648 "8T35" [2, 8] "8.0.168583319873701019648.14" [12815672, 0, 1058208, 0, 29168, 0, 312, 0, 1] 168583319873701019648 "8T27" [2, 1118] "8.0.168583319873701019648.15" [25223342, 0, -1047336, 0, 20088, 0, -192, 0, 1] 168583319873701019648 "8T35" [24] "8.0.168583319873701019648.16" [25223342, 0, 1047336, 0, 20088, 0, 192, 0, 1] 168583319873701019648 "8T35" [2, 24] "8.0.168583319873701019648.17" [27543608, 0, 0, 0, 12080, 0, 0, 0, 1] 168583319873701019648 "8T26" [2, 20] "8.0.168583319873701019648.18" [27543608, 0, 0, 0, 19328, 0, 0, 0, 1] 168583319873701019648 "8T26" [2, 20] "8.0.168583319873701019648.19" [31702752, 0, -782784, 0, 8928, 0, -128, 0, 1] 168583319873701019648 "8T35" [2, 24] "8.0.168583319873701019648.20" [31702752, 0, 782784, 0, 8928, 0, 128, 0, 1] 168583319873701019648 "8T35" [24] "8.0.198875635163506671616.11" [439569, 0, -27436, 0, 2166, 0, -76, 0, 1] 198875635163506671616 "8T29" [4, 60] "8.0.230737681144588600709.1" [245614192, -23572372, 3272920, -688993, -11546, 4539, -18, -1, 1] 230737681144588600709 "8T17" [7] "8.0.243137346822519582749.1" [569411504, -32778180, -871084, 128079, -38311, 1098, -1, -2, 1] 243137346822519582749 "8T17" [8, 112] "8.0.243137346822519582749.2" [19769900, 902980, -403401, 49830, 4893, -755, -45, 0, 1] 243137346822519582749 "8T21" [2, 336] "8.4.732266538542326026749.1" [42734945, 7977236, -4176103, -697833, 60796, 3693, -369, -1, 1] 732266538542326026749 "8T28" [] "8.0.732266538542326026749.1" [823641940, -14621632, 14710741, -178571, 90169, -1063, 359, -4, 1] 732266538542326026749 "8T28" [8] "8.0.795502540654026686464.2" [1296, 0, 864, 0, 5048, 0, 24, 0, 1] 795502540654026686464 "8T18" [2, 24] "8.0.795502540654026686464.5" [28561, 0, -14164, 0, 1618, 0, 52, 0, 1] 795502540654026686464 "8T29" [12, 60] "8.0.795502540654026686464.7" [96721, 0, -3516, 0, -550, 0, 12, 0, 1] 795502540654026686464 "8T18" [4, 120] "8.0.795502540654026686464.11" [887364, 0, -69200, 0, 820, 0, 24, 0, 1] 795502540654026686464 "8T29" [4, 12] "8.0.795502540654026686464.13" [1547536, 0, -28128, 0, -2200, 0, 24, 0, 1] 795502540654026686464 "8T18" [2, 24] "8.0.795502540654026686464.17" [81, 0, 108, 0, 1262, 0, 12, 0, 1] 795502540654026686464 "8T18" [4, 120] "8.0.821997135467880642757.1" [1073236023, -5514369, -20492272, 51944, 167287, -151, -651, 0, 1] 821997135467880642757 "8T21" [168] "8.0.821997135467880642757.2" [1797102288, -83141964, -18920088, -1590435, 236300, 4156, 24, -2, 1] 821997135467880642757 "8T17" [2, 14] "8.0.1161353571696820272581.1" [1706908400, -134165640, 3977812, -235210, 78681, -1429, -114, -1, 1] 1161353571696820272581 "8T17" [7] "8.2.3182010162616106745856.1" [-2682514849, 0, -48338120, 0, -136806, 0, 0, 0, 1] -3182010162616106745856 "8T6" [4] "8.2.3182010162616106745856.2" [-22801, 0, 0, 0, -302, 0, 0, 0, 1] -3182010162616106745856 "8T15" [4] "8.2.3182010162616106745856.3" [-22801, 0, 0, 0, 302, 0, 0, 0, 1] -3182010162616106745856 "8T15" [4] "8.2.3182010162616106745856.4" [-519885601, 0, 0, 0, -103586, 0, 0, 0, 1] -3182010162616106745856 "8T8" [4] "8.2.3182010162616106745856.5" [-519885601, 0, 0, 0, -9362, 0, 0, 0, 1] -3182010162616106745856 "8T8" [36] "8.2.3182010162616106745856.6" [-21911761, 0, -19882472, 0, -136806, 0, 0, 0, 1] -3182010162616106745856 "8T6" [4] "8.2.3182010162616106745856.7" [-91204, 0, 0, 0, -604, 0, 0, 0, 1] -3182010162616106745856 "8T15" [4] "8.2.3182010162616106745856.8" [-91204, 0, 0, 0, 604, 0, 0, 0, 1] -3182010162616106745856 "8T15" [4] "8.8.3182010162616106745856.2" [214534609, 0, -9029196, 0, 121102, 0, -604, 0, 1] 3182010162616106745856 "8T20" [] "8.4.3182010162616106745856.5" [214534609, 0, -6475484, 0, -18422, 0, 604, 0, 1] 3182010162616106745856 "8T20" [2] "8.4.3182010162616106745856.6" [214534609, 0, 6475484, 0, -18422, 0, -604, 0, 1] 3182010162616106745856 "8T20" [2] "8.0.3182010162616106745856.9" [214534609, 0, 9029196, 0, 121102, 0, 604, 0, 1] 3182010162616106745856 "8T20" [2, 5460] "8.0.3182010162616106745856.10" [421010127, 22989448, -1997924, 123216, 57434, -1208, 12, 0, 1] 3182010162616106745856 "8T29" [2, 24] "8.0.3182010162616106745856.11" [514054062, -26051728, -12916432, 357568, 132632, -1208, -592, 0, 1] 3182010162616106745856 "8T29" [2, 48] "8.0.6364020325232213491712.2" [5202, 0, 1312, 0, 1392, 0, -36, 0, 1] 6364020325232213491712 "8T35" [48] "8.0.6364020325232213491712.3" [69192, 0, -20912, 0, 1808, 0, -40, 0, 1] 6364020325232213491712 "8T35" [48] "8.0.6364020325232213491712.6" [8602952, 0, 347632, 0, 8288, 0, 96, 0, 1] 6364020325232213491712 "8T35" [48] "8.0.6364020325232213491712.7" [302642, 0, -48576, 0, 13744, 0, 92, 0, 1] 6364020325232213491712 "8T35" [48] "8.0.10618082521762628869441.1" [4504907011, -157853331, -45910896, 583556, 258241, -2553, -587, -2, 1] 10618082521762628869441 "8T19" [14] "8.4.10824613938449188243901.1" [14843459, -80487, 67385, 26333, -13488, 383, -123, -4, 1] 10824613938449188243901 "8T28" [] "8.0.10824613938449188243901.1" [2097186412, 577710394, 54831279, 2111463, 1209, -5235, -254, 0, 1] 10824613938449188243901 "8T28" [2] "8.2.12165087922284336386843.1" [-21424138619, -320380999, -119075893, -1733636, -235220, -9488, 203, -1, 1] -12165087922284336386843 "8T30" [2] "8.2.25456081300928853966848.1" [-1039771202, 0, 0, 0, -84560, 0, 0, 0, 1] -25456081300928853966848 "8T15" [2] "8.2.25456081300928853966848.2" [-1039771202, 0, 0, 0, -47112, 0, 0, 0, 1] -25456081300928853966848 "8T15" [2] "8.2.25456081300928853966848.3" [-1039771202, 0, 0, 0, 47112, 0, 0, 0, 1] -25456081300928853966848 "8T15" [2] "8.2.25456081300928853966848.4" [-1039771202, 0, 0, 0, 84560, 0, 0, 0, 1] -25456081300928853966848 "8T15" [2] "8.2.25456081300928853966848.5" [-182408, 0, 0, 0, -2416, 0, 0, 0, 1] -25456081300928853966848 "8T6" [2] "8.2.25456081300928853966848.6" [-182408, 0, 0, 0, 0, 0, 0, 0, 1] -25456081300928853966848 "8T8" [2] "8.2.25456081300928853966848.7" [-45602, 0, 0, 0, -1208, 0, 0, 0, 1] -25456081300928853966848 "8T6" [2] "8.2.25456081300928853966848.8" [-45602, 0, 0, 0, 0, 0, 0, 0, 1] -25456081300928853966848 "8T8" [6] "8.0.25456081300928853966848.2" [171698, 0, -83112, 0, 19260, 0, 192, 0, 1] 25456081300928853966848 "8T35" [4, 12] "8.4.25456081300928853966848.2" [182408, 0, 0, 0, -1208, 0, 0, 0, 1] 25456081300928853966848 "8T16" [] "8.0.25456081300928853966848.8" [727218, 0, 62136, 0, 2140, 0, -64, 0, 1] 25456081300928853966848 "8T35" [2, 2, 12] "8.0.25456081300928853966848.12" [474443208, 0, -2918528, 0, 35032, 0, 0, 0, 1] 25456081300928853966848 "8T26" [48] "8.4.25456081300928853966848.12" [1039771202, 0, 0, 0, -160060, 0, 0, 0, 1] 25456081300928853966848 "8T16" [] "8.4.25456081300928853966848.13" [1039771202, 0, 0, 0, -65836, 0, 0, 0, 1] 25456081300928853966848 "8T16" [3] "8.0.25456081300928853966848.13" [474443208, 0, 2918528, 0, 35032, 0, 0, 0, 1] 25456081300928853966848 "8T26" [48] "8.4.25456081300928853966848.15" [45602, 0, 0, 0, -604, 0, 0, 0, 1] 25456081300928853966848 "8T16" [] "8.0.25456081300928853966848.21" [1577646792, 0, -25537120, 0, 90600, 0, 0, 0, 1] 25456081300928853966848 "8T15" [3, 48] "8.0.25456081300928853966848.22" [1577646792, 0, 25537120, 0, 90600, 0, 0, 0, 1] 25456081300928853966848 "8T15" [3, 48] "8.0.25456081300928853966848.37" [11635488, 0, 497088, 0, 8560, 0, -128, 0, 1] 25456081300928853966848 "8T35" [2, 24] "8.0.25456081300928853966848.38" [16279218, 0, -1066696, 0, 25180, 0, -256, 0, 1] 25456081300928853966848 "8T35" [2, 24] "8.0.62068436227894333590721.1" [12944869550, 976285535, 151358539, 5180313, 496478, 5150, 972, -2, 1] 62068436227894333590721 "8T19" [28] "8.2.110572247319891230039099.1" [-1667607163, -749948999, -78440090, 1944262, -228387, 10821, -443, -2, 1] -110572247319891230039099 "8T30" [4] "8.0.535383996552234145659841.1" [5055424000, 206054272, -5567200, 1659840, 305936, 5064, 188, -1, 1] 535383996552234145659841 "8T19" [42] "8.2.1634516704705827424829051.1" [880772800, -620503040, 149072729, -16763076, 699275, 19953, -1699, -2, 1] -1634516704705827424829051 "8T30" [10] "8.0.1836928276264934794413293.1" [4591714318444, -16322422312, 1061998845, -20086322, 6851527, -45753, 53, 0, 1] 1836928276264934794413293 "8T17" [2, 14] "8.0.1836928276264934794413293.2" [35607317225, -217533705, 217711489, -354361, 174164, 3617, -1201, -4, 1] 1836928276264934794413293 "8T21" [280] "8.0.16696409345303575735903949.1" [1079641645588, -87792222518, 7889955469, -507413670, 31155871, 50831, -37, -2, 1] 16696409345303575735903949 "8T17" [4, 28] "8.0.16696409345303575735903949.2" [45177490204, 478708118, -477769143, -1879763, 944415, -5443, 1819, -4, 1] 16696409345303575735903949 "8T21" [2, 280] "8.0.246812022410579941149186701.1" [21398867908000, -66159054980, 4563471352, 112626903, 8983575, 17256, 99, -2, 1] 246812022410579941149186701 "8T17" [2, 14] "8.0.246812022410579941149186701.2" [467600275, 58837905, -9823532, -630576, 190941, -1359, -455, 0, 1] 246812022410579941149186701 "8T21" [3, 840] "10.2.19886484976.2" [-4, 16, -22, 18, -7, -9, 6, 10, -7, -1, 1] 19886484976 "10T39" [] "10.0.21129390287.2" [4, -18, 33, -35, 34, -28, 18, -10, 6, -1, 1] -21129390287 "10T39" [] "10.2.23615200909.1" [-1, 1, -4, 0, 4, -11, 0, 3, 0, -1, 1] 23615200909 "10T38" [] "10.0.60902360239.2" [41, 26, -41, -13, 41, -4, -17, 6, 5, -4, 1] -60902360239 "10T39" [] "10.0.65873981483.2" [16, 4, 21, -5, 15, -2, 13, -1, 6, 0, 1] -65873981483 "10T39" [] "10.0.79545939904.3" [19, 19, 55, 9, 14, -2, 8, -1, 3, -1, 1] -79545939904 "10T39" [] "10.0.79545939904.4" [41, -100, 95, -77, 73, -39, 18, -14, 4, -1, 1] -79545939904 "10T39" [] "10.2.79545939904.2" [-4, 10, -7, 23, -25, 18, 9, -1, 8, -1, 1] 79545939904 "10T39" [] "10.2.112818618368.1" [-4, -16, -24, -24, -23, -12, -4, -2, 2, 0, 1] 112818618368 "10T39" [] "10.0.120561815167.2" [43, -108, 85, -50, 71, -64, 33, -13, 7, -4, 1] -120561815167 "10T39" [] "10.0.125533436411.1" [17, -24, 14, 10, -3, -13, 10, -1, -3, 0, 1] -125533436411 "10T39" [] "10.2.132990868277.1" [-19, -38, -43, -8, 27, 16, -1, -2, -1, 0, 1] 132990868277 "10T39" [] "10.2.155125600256.1" [-1, -3, 4, 3, -17, 26, -18, 2, 7, -5, 1] 155125600256 "10T39" [] "10.2.162820595741.2" [-4, 32, -91, 98, -101, 38, -9, -11, 10, -4, 1] 162820595741 "10T39" [] "10.2.187678701961.1" [-47, 71, 2, 0, -63, 25, 16, 1, -6, -1, 1] 187678701961 "10T37" [] "10.0.195136133827.1" [29, -26, 36, -19, 10, -10, 22, -22, 13, -5, 1] -195136133827 "10T39" [] "10.0.225637236736.1" [2, -3, 9, 14, -4, -5, -1, 4, 2, -3, 1] -225637236736 "10T39" [] "10.2.237394914401.2" [-4, -26, 3, -16, 9, 7, -11, -13, -3, 0, 1] 237394914401 "10T39" [] "10.0.239880725023.1" [43, -92, 113, -122, 81, -58, 35, -9, 9, 0, 1] -239880725023 "10T39" [] "10.2.277167884353.2" [-124, 26, 175, -64, -37, 1, -7, 17, -1, -4, 1] 277167884353 "10T39" [] "10.2.282139505597.1" [-1, -116, -29, 102, 25, -11, -7, -8, 1, 0, 1] 282139505597 "10T39" [] "10.2.326884096793.1" [-32, -80, -64, 24, 8, -7, 22, 8, -10, -1, 1] 326884096793 "10T39" [] "10.0.338070244592.1" [43, 124, 108, -18, -57, 5, 23, 3, -4, -1, 1] -338070244592 "10T39" [] "10.0.364171256123.1" [64, -96, 23, -4, 17, 0, -4, 5, -4, -1, 1] -364171256123 "10T39" [] "10.2.381571930477.2" [17, -106, -34, 36, -19, -29, 4, -1, -5, 0, 1] 381571930477 "10T39" [] "10.2.386543551721.2" [43, -141, 159, -99, 17, -47, 8, -10, 2, 0, 1] 386543551721 "10T39" [] "10.4.402980199795.1" [3, -5, -28, 7, 13, 6, -2, -3, 1, -2, 1] -402980199795 "10T39" [] "10.2.426316521673.2" [-31, -70, 37, 65, -30, -4, 6, -10, 10, -5, 1] 426316521673 "10T39" [] "10.2.431288142917.2" [-61, 52, 23, -59, -40, -17, -21, -12, -2, 0, 1] 431288142917 "10T39" [] "10.2.446203006649.1" [-43, -32, -49, 72, 25, 2, -13, -7, 1, 0, 1] 446203006649 "10T39" [] "10.0.457389154448.1" [71, 106, -38, -35, 75, 0, -29, 13, 4, -4, 1] -457389154448 "10T39" [] "10.0.483490165979.1" [67, 2, -37, -51, 15, 17, 16, -6, -4, -1, 1] -483490165979 "10T39" [] "10.2.485975976601.2" [-17, -1, -62, -12, -27, -5, 20, -7, 10, -1, 1] 485975976601 "10T39" [] "10.0.521786109952.2" [11, -45, 94, -101, 87, -68, 41, -23, 10, -3, 1] -521786109952 "10T39" [] "10.0.523263135931.1" [64, -80, 168, -97, 96, -23, 27, 0, 7, 0, 1] -523263135931 "10T39" [] "10.0.538177999663.2" [151, -200, 82, -47, 20, 36, -36, 9, 4, -4, 1] -538177999663 "10T39" [] "10.2.576708064304.2" [-43, -31, -53, -9, 2, -36, -2, -19, 3, -1, 1] 576708064304 "10T39" [] "10.0.578195419136.2" [38, -77, 109, -89, 57, -21, 7, -5, 5, -3, 1] -578195419136 "10T39" [] "10.2.580436780237.1" [-41, 1, 124, -13, -131, 15, 62, -7, -15, 0, 1] 580436780237 "10T39" [] "10.2.610266507701.2" [-76, 190, -39, -64, 62, -24, -4, 4, -2, -1, 1] 610266507701 "10T39" [] "10.0.612752318323.1" [97, -20, -16, 42, 23, 47, 7, -4, 5, -1, 1] -612752318323 "10T39" [] "10.0.616481034256.1" [212, -444, 334, -56, -19, -45, 45, -7, -3, -1, 1] -616481034256 "10T39" [] "10.0.636367519232.1" [43, 92, 136, 90, 76, 0, 28, -12, 13, -4, 1] -636367519232 "10T39" [] "10.2.636367519232.1" [-41, -109, 25, 179, -17, -90, 0, 31, -4, -4, 1] 636367519232 "10T39" [] "10.2.655011098897.2" [-19, -114, 160, -86, 84, -36, -2, -6, 1, 0, 1] 655011098897 "10T39" [] "10.0.672411773251.1" [53, 18, 2, 52, -50, -47, 37, 7, -1, -4, 1] -672411773251 "10T39" [] "10.0.692298258227.1" [136, -264, 478, -511, 478, -310, 178, -70, 25, -5, 1] -692298258227 "10T39" [] "10.4.725364359631.1" [-25, 9, 27, 1, -19, 18, 1, -5, -3, 0, 1] -725364359631 "10T39" [] "10.0.741253578496.1" [2, -2, 6, -1, -3, 2, -6, 4, 2, -3, 1] -741253578496 "10T39" [] "10.0.747423346688.2" [47, -33, 63, -22, 10, 6, -7, 7, 0, -1, 1] -747423346688 "10T39" [] "10.0.761900955643.1" [68, 134, 161, 104, 88, 18, 28, -2, 8, -1, 1] -761900955643 "10T39" [] "10.0.815345884016.2" [157, -259, 328, -357, 271, -173, 91, -39, 16, -4, 1] -815345884016 "10T39" [] "10.2.815345884016.2" [-64, -80, 0, 67, 15, -54, -20, 4, -4, -1, 1] 815345884016 "10T39" [] "10.0.821560410571.1" [163, 32, 92, 34, 11, -29, 15, 6, -1, -1, 1] -821560410571 "10T39" [] "10.0.855118853968.2" [68, -40, 40, 102, -87, 9, 24, -26, 14, -4, 1] -855118853968 "10T39" [] "10.2.855118853968.2" [32, 208, 240, 124, 40, -28, -16, 9, -2, -1, 1] 855118853968 "10T39" [] "10.0.866305001767.1" [92, 114, 99, 64, 4, 22, -15, -11, 11, -5, 1] -866305001767 "10T39" [] "10.2.893648918609.2" [-113, -46, 64, 7, 22, 8, 2, -11, -2, 0, 1] 893648918609 "10T39" [] "10.2.902548946944.1" [8, 24, -20, -16, 60, 24, -20, 0, 0, -2, 1] 902548946944 "10T38" [] "10.2.908563782341.1" [-164, -264, -189, -11, 82, 67, 14, -14, -9, 0, 1] 908563782341 "10T39" [] "10.0.911049592963.2" [289, 517, 161, -333, -241, 77, 91, -6, -15, 0, 1] -911049592963 "10T39" [] "10.0.934664793872.1" [67, -296, 549, -442, 316, -196, 104, -46, 18, -4, 1] -934664793872 "10T39" [2] "10.2.934664793872.1" [-212, 264, -132, 172, -61, 12, -15, -8, 2, 0, 1] 934664793872 "10T39" [] "10.0.945850941671.2" [172, 56, 89, 32, 5, 11, -7, -1, 1, 0, 1] -945850941671 "10T39" [] "10.2.954551278848.1" [1, -13, 43, -40, -19, 1, 23, 2, -7, -1, 1] 954551278848 "10T39" [] "10.2.993081343489.2" [-113, -28, 197, 17, -139, -2, 51, -2, -11, 0, 1] 993081343489 "10T39" [] "10.2.48328397545910877.1" [32, -104, 84, 20, -51, 11, 35, -26, 11, -2, 1] 48328397545910877 "10T13" [] "10.2.776857949857447936.1" [-5865536, -3822820, 2938244, -468028, 80396, -9750, 3862, -312, 44, -3, 1] 776857949857447936 "10T37" [2] "10.2.557677713972434426281.1" [-65589536711, -93529075, 91474871, -6483671, -1033378, -100953, 8966, 0, -1, 0, 1] 557677713972434426281 "10T37" [2, 2] "12.0.347893082190349508633.1" [64, -32, 64, -24, 20, -8, 3, -4, 5, -3, 4, -1, 1] 347893082190349508633 "12T293" [34] "15.3.236236656513512990640321.1" [-1013, -2331, -5130, -7323, -12567, -8514, 4065, 4659, -819, -1243, 84, 198, -8, -18, 0, 1] 236236656513512990640321 "15T89" [] "15.3.236236656513512990640321.2" [12377, -67569, -53802, -1765, 2940, 3636, -2828, -3204, -18, 110, 225, 18, -12, 3, 0, 1] 236236656513512990640321 "15T89" [] "16.10.5776313260441600000000.2" [41, 336, -68, -2032, -1795, 1600, 2246, 36, -740, -268, 18, 76, 38, -8, -10, 0, 1] -5776313260441600000000 "16T1586" [] "16.2.5776313260441600000000.2" [71, 8, -192, -132, 486, 104, -126, -4, -154, -48, 72, -44, 11, -4, -8, 0, 1] -5776313260441600000000 "16T1586" [] "18.6.148204394789719081222144.3" [-1, 6, 4, -2, 55, -120, 211, -88, -13, -176, 58, -8, -54, 32, -33, 2, 3, -2, 1] 148204394789719081222144 "18T837" [] "18.0.22378863613247581264543744.3" [9067, -12118, 17445, -6604, 6605, 1976, -3522, 3334, -614, -1346, 1225, -414, -43, 116, -29, -14, 14, -6, 1] -22378863613247581264543744 "18T836" [2] "18.0.52800131337506012046032896.1" [5443, -7638, 18435, -11300, 14710, -5674, 6010, -2360, 2716, -418, 24, 568, -322, 166, -14, -12, 13, -4, 1] -52800131337506012046032896 "18T785" [] "18.0.3379208405600384770946105344.1" [12409, 53154, 79340, 46568, 55185, 26956, 4927, -13230, 21181, -22832, 16154, -8954, 4598, -1854, 615, -178, 43, -8, 1] -3379208405600384770946105344 "18T785" [] "18.0.2674485052638692028167704281088.1" [126279667, 122712508, -730577, -29285068, -1001763, 4938804, -745364, -1174782, 177876, 239010, -3743, -31954, -3881, 2396, 607, -76, -38, 0, 1] -2674485052638692028167704281088 "18T770" [2] "18.0.171167043368876289802733073989632.1" [3731261704, -3003191776, 1568640152, -254638032, -107079264, 9872608, 47493924, -41373024, 17388268, -4350588, 789992, -155296, 40992, -7004, 1020, -128, 40, -6, 1] -171167043368876289802733073989632 "18T770" [2] "20.0.37499840448565757970611960432375107682304.1" [6547392, 14691456, 12889152, -2624256, -11185968, 674656, 14572416, -10762464, 5301968, -2025168, 779400, -263488, 83613, -18408, 4090, -1104, 135, -48, 6, 0, 1] 37499840448565757970611960432375107682304 "20T1091" [] "20.0.746786737046406398163071373885189541330944.1" [141776649, -208324872, 55737882, 4596912, 35713503, -38533072, 35564634, -24763104, 9029145, -4066224, 1538334, -239424, 151926, -19080, 11330, -1344, 720, -64, 36, 0, 1] 746786737046406398163071373885189541330944 "20T1091" [2] "20.4.1625637067079308361211920707296101971129924583424.1" [-62001172351949, -200869279397300, -280394028516902, -217385440999088, -99575183019051, -25627960177914, -2642178532814, 211891799690, 12911273777, -25749765976, -3691179526, 576374174, 130907688, -7659362, -2628932, 77486, 37362, -180, -298, -2, 1] 1625637067079308361211920707296101971129924583424 "20T1091" [2] # Label -- # Each (global) number field has a unique label of the form d.r.D.i where # # The discriminant portion of the label can take the form \(a_1\) e \(\epsilon_1\) _ \(a_2\) e \(\epsilon_2\) _ \(\cdots\) _ \(a_k\) e \(\epsilon_k\) to mean the absolute value of the # discriminant equals \(a_1^{\epsilon_1}a_2^{\epsilon_2}\cdots a_k^{\epsilon_k}\). The separators are the letter e and the underscore symbol. #Polynomial (coeffs) -- # A **defining polynomial** of a number field $K$ is an irreducible polynomial $f\in\Q[x]$ such that $K\cong \mathbb{Q}(a)$, where $a$ is a root of $f(x)$. Equivalently, it is a polynomial $f\in \Q[x]$ such that $K \cong \Q[x]/(f)$. # A root \(a \in K\) of the defining polynomial is a generator of \(K\). #Discriminant (disc) -- # The **discriminant** of a number field $K$ is the square of the determinant of the matrix # \[ # \left( \begin{array}{ccc} # \sigma_1(\beta_1) & \cdots & \sigma_1(\beta_n) \\ # \vdots & & \vdots \\ # \sigma_n(\beta_1) & \cdots & \sigma_n(\beta_n) \\ # \end{array} \right) # \] # where $\sigma_1,..., \sigma_n$ are the embeddings of $K$ into the complex numbers $\mathbb{C}$, and $\{\beta_1, \ldots, \beta_n\}$ is an integral basis for the ring of integers of $K$. # The discriminant of $K$ is a non-zero integer divisible exactly by the primes which ramify in $K$. #Galois group (galois_label) -- # Let $K$ be a finite degree $n$ separable extension of a field $F$, and $K^{gal}$ be its # Galois (or normal) closure. # The **Galois group** for $K/F$ is the automorphism group $\Aut(K^{gal}/F)$. # This automorphism group acts on the $n$ embeddings $K\hookrightarrow K^{gal}$ via composition. As a result, we get an injection $\Aut(K^{gal}/F)\hookrightarrow S_n$, which is well-defined up to the labelling of the $n$ embeddings, which corresponds to being well-defined up to conjugation in $S_n$. # We use the notation $\Gal(K/F)$ for $\Aut(K/F)$ when $K=K^{gal}$. # There is a naming convention for Galois groups up to degree $47$. #Class group (class_group) -- # The **ideal class group** of a number field $K$ with ring of integers $O_K$ is the group of equivalence classes of ideals, given by the quotient of the multiplicative group of all fractional ideals of $O_K$ by the subgroup of principal fractional ideals. # Since $K$ is a number field, the ideal class group of $K$ is a finite abelian group, and so has the structure of a product of cyclic groups encoded by a finite list $[a_1,\dots,a_n]$, where the $a_i$ are positive integers with $a_i\mid a_{i+1}$ for $1\leq i < n$.