-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [36, 0, -96, 0, 272, 0, -320, 0, 220, 0, -80, 0, 24, 0, 0, 0, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 382511685112441262309376, 'disc_rad': 6, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[8, 2]]], [7, [[8, 1], [4, 1], [2, 2]]], [11, [[4, 3], [2, 1], [1, 2]]], [13, [[8, 2]]], [17, [[4, 4]]], [19, [[4, 2], [2, 2], [1, 4]]], [23, [[4, 4]]], [29, [[8, 2]]], [31, [[8, 1], [4, 1], [2, 2]]], [37, [[8, 2]]], [41, [[4, 2], [2, 4]]], [43, [[4, 4]]], [47, [[4, 4]]], [53, [[8, 2]]], [59, [[2, 6], [1, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [5076, 512], 'galois_label': '16T1276', 'galt': 1276, 'grd': 53.79918827448669, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 45, 'label': '16.0.382511685112441262309376.45', 'local_algs': ['2.1.16.72d1.85', '3.2.1.0a1.1', '3.1.2.1a1.1', '3.1.2.1a1.1', '3.2.1.0a1.1', '3.2.2.2a1.1', '3.4.1.0a1.1'], 'maximal_cm_subfield': [2, 0, 1], 'minimal_sibling': [3, 0, -8, 0, 8, 0, -16, 0, 38, 0, -48, 0, 32, 0, -8, 0, 1], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 2, 'r2': 8, 'ramps': [2, 3], 'rd': 29.779355491267186, 'regulator': {'__RealLiteral__': 0, 'data': '754380.7895771225', 'prec': 57}, 'res': {'sib': ['1,0,-16,0,112,0,-488,0,1534,0,-3568,0,6312,0,-8792,0,9837,0,-8792,0,6312,0,-3568,0,1534,0,-488,0,112,0,-16,0,1', '1,0,0,0,-24,0,0,0,156,0,0,0,-168,0,0,0,2374,0,0,0,-168,0,0,0,156,0,0,0,-24,0,0,0,1', '1,0,0,0,-744,0,0,0,433116,0,0,0,-31320,0,0,0,7366,0,0,0,-2904,0,0,0,-36,0,0,0,24,0,0,0,1', '1,0,0,0,24,0,0,0,156,0,0,0,168,0,0,0,2374,0,0,0,168,0,0,0,156,0,0,0,24,0,0,0,1', '1,0,0,0,744,0,0,0,433116,0,0,0,31320,0,0,0,7366,0,0,0,2904,0,0,0,-36,0,0,0,-24,0,0,0,1', '1,0,16,0,112,0,488,0,1534,0,3568,0,6312,0,8792,0,9837,0,8792,0,6312,0,3568,0,1534,0,488,0,112,0,16,0,1', '1034289,0,-5062176,0,9662040,0,-8876736,0,4167700,0,-1447392,0,882328,0,-403584,0,72726,0,-30048,0,15848,0,-960,0,564,0,96,0,40,0,0,0,1', '1034289,0,5062176,0,9662040,0,8876736,0,4167700,0,1447392,0,882328,0,403584,0,72726,0,30048,0,15848,0,960,0,564,0,-96,0,40,0,0,0,1', '104976,0,0,0,-70144,0,0,0,27936,0,0,0,-512,0,0,0,-1640,0,0,0,896,0,0,0,200,0,0,0,0,0,0,0,1', '104976,0,0,0,112896,0,0,0,449824,0,0,0,131456,0,0,0,31128,0,0,0,2752,0,0,0,1224,0,0,0,32,0,0,0,1', '104976,0,0,0,70144,0,0,0,27936,0,0,0,512,0,0,0,-1640,0,0,0,-896,0,0,0,200,0,0,0,0,0,0,0,1', '108,0,-288,0,384,0,-352,0,236,0,-96,0,16,0,0,0,1', '108,0,288,0,384,0,352,0,236,0,96,0,16,0,0,0,1', '112209,119904,890128,303680,1540768,-2537760,2035584,4508608,-5950220,-175136,3403504,-2358272,386720,-428512,-64192,-15104,377622,-198112,21104,20672,56096,32,4544,-6592,-940,-608,656,0,32,-32,0,0,1', '1156,0,-19136,0,53984,0,319456,0,512144,0,105920,0,-213936,0,-10816,0,53652,0,-11936,0,-2224,0,752,0,312,0,-32,0,-24,0,0,0,1', '1156,0,19136,0,53984,0,-319456,0,512144,0,-105920,0,-213936,0,10816,0,53652,0,11936,0,-2224,0,-752,0,312,0,32,0,-24,0,0,0,1', '1161,1008,16400,-1760,26096,-134992,-72704,208320,68300,21648,248688,-206944,-233680,169360,199456,-1408,-20762,-27120,-18608,-6176,8624,12368,-4960,-2624,956,112,48,-32,16,-16,0,0,1', '11664,0,-62208,0,238464,0,-622080,0,1005408,0,1342464,0,864832,0,110592,0,-174360,0,-86848,0,-3872,0,7296,0,1672,0,-64,0,-48,0,0,0,1', '11664,0,0,0,0,0,0,0,-4320,0,0,0,-5504,0,0,0,616,0,0,0,896,0,0,0,728,0,0,0,-32,0,0,0,1', '11664,0,62208,0,238464,0,622080,0,1005408,0,-1342464,0,864832,0,-110592,0,-174360,0,86848,0,-3872,0,-7296,0,1672,0,64,0,-48,0,0,0,1', '118,-704,48,8192,-17408,-17152,128496,-260992,344488,-397888,451984,-468576,403336,-284512,190384,-152320,131480,-91648,41088,-8256,2416,-6352,5456,-1792,100,-80,224,-128,24,0,0,0,1', '12,0,-32,0,96,0,-144,0,132,0,-80,0,32,0,-8,0,1', '12,0,32,0,96,0,144,0,132,0,80,0,32,0,8,0,1', '1284,-4416,-4480,77184,-91712,-241216,765088,-75072,-794944,441728,1251552,-241344,1137952,-703264,126208,-398336,48452,-22048,136640,64704,59360,24544,11216,2144,2112,-960,560,-224,80,-16,0,0,1', '12897,50832,110592,222816,595936,1287568,1833056,1626880,1066652,602480,952944,955744,1022768,432656,366128,95488,230638,96240,124320,10592,15552,-19472,-2400,-7168,604,-1136,496,-160,112,-16,16,0,1', '1296,0,-2304,0,832,0,-2304,0,2496,0,5888,0,11168,0,16128,0,13576,0,8128,0,3280,0,576,0,-16,0,-64,0,-24,0,0,0,1', '1296,0,0,0,-10368,0,0,0,28384,0,0,0,-3648,0,0,0,10328,0,0,0,-4704,0,0,0,1016,0,0,0,-48,0,0,0,1', '1296,0,0,0,-2304,0,0,0,20320,0,0,0,-25088,0,0,0,77016,0,0,0,22208,0,0,0,3096,0,0,0,64,0,0,0,1', '1296,0,0,0,-5504,0,0,0,67296,0,0,0,80960,0,0,0,46168,0,0,0,9952,0,0,0,1016,0,0,0,48,0,0,0,1', '1296,0,0,0,-70272,0,0,0,1028320,0,0,0,-502336,0,0,0,639576,0,0,0,-81632,0,0,0,1656,0,0,0,80,0,0,0,1', '1296,0,0,0,2304,0,0,0,20320,0,0,0,25088,0,0,0,77016,0,0,0,-22208,0,0,0,3096,0,0,0,-64,0,0,0,1', '1296,0,0,0,5504,0,0,0,67296,0,0,0,-80960,0,0,0,46168,0,0,0,-9952,0,0,0,1016,0,0,0,-48,0,0,0,1', '1296,0,2304,0,832,0,2304,0,2496,0,-5888,0,11168,0,-16128,0,13576,0,-8128,0,3280,0,-576,0,-16,0,64,0,-24,0,0,0,1', '131769,0,-557568,0,910912,0,-662176,0,154972,0,-12720,0,72352,0,-2832,0,-37062,0,-12960,0,8640,0,9408,0,3988,0,1008,0,160,0,16,0,1', '131769,0,557568,0,910912,0,662176,0,154972,0,12720,0,72352,0,2832,0,-37062,0,12960,0,8640,0,-9408,0,3988,0,-1008,0,160,0,-16,0,1', '139,1376,14832,42576,20648,114064,1174704,3626416,5987488,6667200,5691008,3506112,1272712,84752,-441536,-404032,-94166,-99136,112336,-23376,54096,-13904,9648,-5616,1280,-1344,560,-160,96,-16,0,0,1', '144,0,-1536,0,1664,0,18176,0,20704,0,-3584,0,-9280,0,256,0,13480,0,-4736,0,-1632,0,1856,0,232,0,0,0,48,0,0,0,1', '144,0,-1536,0,5056,0,-11008,0,80832,0,-141056,0,116384,0,-35520,0,-7976,0,5888,0,976,0,-2112,0,1328,0,-512,0,120,0,-16,0,1', '144,0,0,0,-1280,0,0,0,3168,0,0,0,-256,0,0,0,40,0,0,0,64,0,0,0,8,0,0,0,0,0,0,0,1', '144,0,1536,0,1664,0,-18176,0,20704,0,3584,0,-9280,0,-256,0,13480,0,4736,0,-1632,0,-1856,0,232,0,0,0,48,0,0,0,1', '144,0,1536,0,5056,0,11008,0,80832,0,141056,0,116384,0,35520,0,-7976,0,-5888,0,976,0,2112,0,1328,0,512,0,120,0,16,0,1', '14641,0,0,0,-27000,0,0,0,99684,0,0,0,-87384,0,0,0,32374,0,0,0,-5064,0,0,0,132,0,0,0,24,0,0,0,1', '14641,0,0,0,27000,0,0,0,99684,0,0,0,87384,0,0,0,32374,0,0,0,5064,0,0,0,132,0,0,0,-24,0,0,0,1', '147897,-191760,-242256,842336,191960,-1762384,113920,2062816,-125708,-1679344,9952,1142336,-82408,-547792,31728,262208,13978,-98000,-8112,7072,11224,-4944,3232,32,3260,272,576,0,184,-16,16,0,1', '16,0,0,0,-384,0,0,0,58272,0,0,0,-69312,0,0,0,34456,0,0,0,-8352,0,0,0,744,0,0,0,48,0,0,0,1', '16,0,0,0,0,0,0,0,2592,0,0,0,-12288,0,0,0,64024,0,0,0,6144,0,0,0,648,0,0,0,0,0,0,0,1', '16,0,0,0,384,0,0,0,58272,0,0,0,69312,0,0,0,34456,0,0,0,8352,0,0,0,744,0,0,0,-48,0,0,0,1', '162,1728,720,-31968,81792,104736,-603776,377056,1479856,-2474304,-467424,4140096,-2854984,-1616640,3457104,-1706656,-415788,1061312,-764016,331232,-2864,-166992,160656,-65872,-4340,19152,-9376,1392,632,-416,112,-16,1', '17977,153776,549488,1093504,1452592,1556976,1342576,556288,-557316,-1435120,-1671952,-1131712,-107120,636752,731504,380672,8630,-157488,-104848,-16640,20688,19024,6320,-2560,-2548,-528,112,192,80,-16,-16,0,1', '18,96,176,256,496,64,256,-448,552,-176,240,-80,96,-16,8,0,1', '1809,-2880,1200,21696,12256,-128064,289600,69568,-1682700,-713152,5646672,1318400,-6613728,-2140928,3554368,1686016,-978858,-385856,186576,-73152,15712,43072,-5888,-6336,852,-448,48,0,32,0,0,0,1', '18961,20048,-17280,-38944,-83648,-102128,-23488,169856,469164,456048,43952,-343328,-381904,85008,447952,292352,-28418,-201552,-78880,55264,26336,-13968,-1472,6272,780,-1520,-400,224,112,-16,-16,0,1', '1907,-12816,41952,-87488,134552,-161440,150800,-96640,26248,36032,-57440,38720,17952,-60464,80992,-59520,30214,4496,-14256,16864,-6272,1120,3920,-3008,2656,-1024,656,-160,120,-16,16,0,1', '20857,-178944,761920,-1916064,3238120,-3560832,2458496,-1243584,756204,-250944,-139648,-63456,320040,-342528,260096,-140160,37018,384,6848,-11424,13384,-11136,3968,-1344,740,-192,256,-96,-24,0,0,0,1', '222784,0,-253440,0,822528,0,-805888,0,1862400,0,-2193152,0,1970432,0,184448,0,-575568,0,58816,0,57696,0,-10496,0,-2368,0,608,0,32,0,-16,0,1', '222784,0,253440,0,822528,0,805888,0,1862400,0,2193152,0,1970432,0,-184448,0,-575568,0,-58816,0,57696,0,10496,0,-2368,0,-608,0,32,0,16,0,1', '232324,0,-148800,0,450144,0,-151808,0,-146688,0,110720,0,-156896,0,44256,0,40772,0,-25888,0,8880,0,-768,0,-352,0,-64,0,80,0,-16,0,1', '236196,0,-202176,0,-295488,0,-14688,0,60480,0,60672,0,118000,0,123488,0,97612,0,66848,0,36064,0,14064,0,3952,0,832,0,136,0,16,0,1', '236196,0,-2223936,0,12782592,0,-13935072,0,5099392,0,1942976,0,-3067056,0,1622432,0,-342324,0,-121376,0,121536,0,-45776,0,10704,0,-1696,0,216,0,-16,0,1', '236196,0,202176,0,-295488,0,14688,0,60480,0,-60672,0,118000,0,-123488,0,97612,0,-66848,0,36064,0,-14064,0,3952,0,-832,0,136,0,-16,0,1', '236196,0,2223936,0,12782592,0,13935072,0,5099392,0,-1942976,0,-3067056,0,-1622432,0,-342324,0,121376,0,121536,0,45776,0,10704,0,1696,0,216,0,16,0,1', '2401,0,-21168,0,125592,0,-389584,0,935796,0,-1030160,0,705944,0,-243760,0,61062,0,-37520,0,18792,0,-4208,0,692,0,-304,0,104,0,-16,0,1', '2401,0,21168,0,125592,0,389584,0,935796,0,1030160,0,705944,0,243760,0,61062,0,37520,0,18792,0,4208,0,692,0,304,0,104,0,16,0,1', '243,-1296,4320,864,-8136,42480,68496,33072,22600,-5104,52400,-23792,-4288,-5648,-6880,29056,12102,-7888,-3856,23584,9168,-6672,-1664,1328,1296,-816,-144,368,-40,-16,16,0,1', '243,0,0,1296,432,-6912,9648,-7488,16200,-33024,33136,-12224,-18936,7872,71664,-227824,433350,-620032,739152,-756944,687832,-553312,394176,-247712,136752,-65216,26448,-9120,2704,-672,128,-16,1', '2601,0,14304,0,108760,0,304768,0,118236,0,-142144,0,370072,0,-221312,0,156874,0,-48224,0,14456,0,-1536,0,-108,0,128,0,-40,0,0,0,1', '26244,0,-101952,0,265536,0,-296544,0,-17840,0,188768,0,34352,0,-121312,0,8916,0,12256,0,7936,0,-2480,0,312,0,176,0,56,0,-16,0,1', '26244,0,-145152,0,325440,0,-632352,0,987088,0,-527264,0,168912,0,-5344,0,122836,0,-141824,0,52928,0,-5008,0,-1160,0,112,0,72,0,-16,0,1', '26244,0,-158976,0,407808,0,-542592,0,598096,0,-452160,0,251536,0,-131712,0,61524,0,-24576,0,7904,0,-2496,0,696,0,-96,0,40,0,0,0,1', '26244,0,-202176,0,1084896,0,-3547968,0,6604720,0,-3748320,0,675856,0,420704,0,-297708,0,57312,0,18832,0,-15648,0,5320,0,-1136,0,168,0,-16,0,1', '26244,0,-217728,0,658656,0,-901920,0,561712,0,-43744,0,33776,0,-148320,0,42516,0,10688,0,6736,0,-4624,0,-120,0,144,0,56,0,-16,0,1', '26244,0,-51840,0,185760,0,-457344,0,1158000,0,-1510624,0,1446128,0,-382624,0,-9324,0,-81920,0,63920,0,-14784,0,1192,0,-176,0,88,0,-16,0,1', '26244,0,0,0,139968,0,-101088,0,416016,0,-530496,0,559728,0,-431808,0,282580,0,-124736,0,39872,0,-7792,0,792,0,-32,0,24,0,0,0,1', '26244,0,0,0,139968,0,101088,0,416016,0,530496,0,559728,0,431808,0,282580,0,124736,0,39872,0,7792,0,792,0,32,0,24,0,0,0,1', '26244,0,101952,0,265536,0,296544,0,-17840,0,-188768,0,34352,0,121312,0,8916,0,-12256,0,7936,0,2480,0,312,0,-176,0,56,0,16,0,1', '26244,0,145152,0,325440,0,632352,0,987088,0,527264,0,168912,0,5344,0,122836,0,141824,0,52928,0,5008,0,-1160,0,-112,0,72,0,16,0,1', '26244,0,158976,0,407808,0,542592,0,598096,0,452160,0,251536,0,131712,0,61524,0,24576,0,7904,0,2496,0,696,0,96,0,40,0,0,0,1', '26244,0,202176,0,1084896,0,3547968,0,6604720,0,3748320,0,675856,0,-420704,0,-297708,0,-57312,0,18832,0,15648,0,5320,0,1136,0,168,0,16,0,1', '26244,0,217728,0,658656,0,901920,0,561712,0,43744,0,33776,0,148320,0,42516,0,-10688,0,6736,0,4624,0,-120,0,-144,0,56,0,16,0,1', '26244,0,51840,0,185760,0,457344,0,1158000,0,1510624,0,1446128,0,382624,0,-9324,0,81920,0,63920,0,14784,0,1192,0,176,0,88,0,16,0,1', '26569,0,-136960,0,558272,0,-150528,0,-705588,0,843552,0,656416,0,-499456,0,453834,0,-139584,0,38144,0,-8448,0,1732,0,-160,0,-32,0,0,0,1', '26569,0,136960,0,558272,0,150528,0,-705588,0,-843552,0,656416,0,499456,0,453834,0,139584,0,38144,0,8448,0,1732,0,160,0,-32,0,0,0,1', '27,0,0,0,144,0,-136,0,2,0,24,0,-8,0,0,0,1', '27,0,0,0,144,0,136,0,2,0,-24,0,-8,0,0,0,1', '282148,1274496,3752896,7392384,10692640,11123712,7971136,3205632,543600,1204800,3321920,4333824,3221280,887040,-825216,-1037568,-425508,85824,166304,69312,-1040,-9984,-800,0,-280,-1056,-96,0,80,0,0,0,1', '2916,0,-10368,0,151200,0,-454176,0,1144416,0,-1288352,0,852272,0,-482688,0,251628,0,-99584,0,33712,0,-9456,0,1856,0,-304,0,40,0,0,0,1', '2916,0,-17280,0,125280,0,-292032,0,463648,0,-267168,0,260752,0,-66432,0,28524,0,-2880,0,2576,0,-1632,0,480,0,-48,0,-8,0,0,0,1', '2916,0,-31104,0,448416,0,890784,0,1059552,0,721728,0,518896,0,315008,0,113260,0,40960,0,15536,0,2544,0,384,0,160,0,8,0,0,0,1', '2916,0,-36288,0,166752,0,-344160,0,360096,0,-219808,0,4336,0,84832,0,76652,0,57760,0,39760,0,18480,0,6048,0,1296,0,200,0,16,0,1', '2916,0,10368,0,151200,0,454176,0,1144416,0,1288352,0,852272,0,482688,0,251628,0,99584,0,33712,0,9456,0,1856,0,304,0,40,0,0,0,1', '2916,0,17280,0,125280,0,292032,0,463648,0,267168,0,260752,0,66432,0,28524,0,2880,0,2576,0,1632,0,480,0,48,0,-8,0,0,0,1', '2916,0,31104,0,448416,0,-890784,0,1059552,0,-721728,0,518896,0,-315008,0,113260,0,-40960,0,15536,0,-2544,0,384,0,-160,0,8,0,0,0,1', '2916,0,36288,0,166752,0,344160,0,360096,0,219808,0,4336,0,-84832,0,76652,0,-57760,0,39760,0,-18480,0,6048,0,-1296,0,200,0,-16,0,1', '3,0,-8,0,8,0,-16,0,38,0,-48,0,32,0,-8,0,1', '3,0,8,0,8,0,16,0,38,0,48,0,32,0,8,0,1', '31491,10800,377712,-1251648,2798512,-4181280,4521120,-2972672,68272,3023984,-4716320,4504976,-2829280,837152,560064,-959344,686238,-224464,-51568,53792,106184,-238944,259360,-196608,116192,-56624,23568,-8528,2648,-672,128,-16,1', '324,0,-1024,0,9728,0,-21376,0,62448,0,-85664,0,97488,0,-21792,0,-35532,0,31808,0,17312,0,3904,0,1608,0,-272,0,104,0,-16,0,1', '324,0,-1152,0,15840,0,-46496,0,153808,0,-335360,0,590128,0,-803328,0,794484,0,-557056,0,276752,0,-97488,0,24216,0,-4160,0,472,0,-32,0,1', '324,0,-15552,0,245952,0,-1300608,0,2826352,0,-2608352,0,1860016,0,-1322144,0,676788,0,-226976,0,58816,0,-14400,0,3848,0,-880,0,152,0,-16,0,1', '324,0,-2880,0,11040,0,-30080,0,55248,0,-41600,0,28144,0,-10624,0,-2060,0,4064,0,368,0,-704,0,152,0,64,0,-8,0,0,0,1', '324,0,-3456,0,22176,0,76032,0,148208,0,190432,0,223216,0,222112,0,181108,0,110592,0,49584,0,16640,0,4392,0,944,0,152,0,16,0,1', '324,0,-5760,0,71712,0,337760,0,447184,0,249824,0,226576,0,37152,0,53748,0,-27584,0,18032,0,-8400,0,3096,0,-784,0,136,0,-16,0,1', '324,0,-768,0,736,0,-48,0,-28,0,-64,0,16,0,8,0,1', '324,0,-896,0,3104,0,-4576,0,6352,0,-6848,0,-11216,0,10944,0,4596,0,3456,0,4656,0,-752,0,664,0,-32,0,24,0,0,0,1', '324,0,1152,0,15840,0,46496,0,153808,0,335360,0,590128,0,803328,0,794484,0,557056,0,276752,0,97488,0,24216,0,4160,0,472,0,32,0,1', '324,0,15552,0,245952,0,1300608,0,2826352,0,2608352,0,1860016,0,1322144,0,676788,0,226976,0,58816,0,14400,0,3848,0,880,0,152,0,16,0,1', '324,0,2880,0,-320,0,-105984,0,409248,0,-715968,0,863872,0,-420640,0,386404,0,-221792,0,126176,0,-43392,0,11600,0,-1760,0,256,0,-16,0,1', '324,0,2880,0,11040,0,30080,0,55248,0,41600,0,28144,0,10624,0,-2060,0,-4064,0,368,0,704,0,152,0,-64,0,-8,0,0,0,1', '324,0,3456,0,22176,0,-76032,0,148208,0,-190432,0,223216,0,-222112,0,181108,0,-110592,0,49584,0,-16640,0,4392,0,-944,0,152,0,-16,0,1', '324,0,5760,0,71712,0,-337760,0,447184,0,-249824,0,226576,0,-37152,0,53748,0,27584,0,18032,0,8400,0,3096,0,784,0,136,0,16,0,1', '324,0,768,0,736,0,48,0,-28,0,64,0,16,0,-8,0,1', '324,0,896,0,3104,0,4576,0,6352,0,6848,0,-11216,0,-10944,0,4596,0,-3456,0,4656,0,752,0,664,0,32,0,24,0,0,0,1', '3249,0,-9024,0,214744,0,150432,0,1440732,0,-507520,0,845576,0,-1169504,0,1248758,0,-716864,0,297320,0,-90400,0,20668,0,-3584,0,440,0,-32,0,1', '34969,0,-116096,0,287752,0,-226432,0,164052,0,93632,0,60936,0,-27136,0,4474,0,-256,0,-1784,0,-640,0,284,0,64,0,-24,0,0,0,1', '354,2048,11184,30720,58112,83360,97200,99200,60672,41152,126288,232288,294376,292320,204848,96768,-3420,-80352,-73152,-12896,18960,13872,3280,-704,-1404,-944,-96,224,96,-16,-16,0,1', '36,0,-1344,0,12448,0,5504,0,-48096,0,7456,0,78896,0,20928,0,128524,0,94112,0,105712,0,61440,0,19424,0,3760,0,456,0,32,0,1', '36,0,-1536,0,24448,0,6176,0,701120,0,1850592,0,1716048,0,784384,0,278668,0,69056,0,3200,0,-656,0,176,0,-48,0,24,0,0,0,1', '36,0,-384,0,2176,0,-7520,0,19520,0,-33632,0,39088,0,-6048,0,80780,0,81152,0,22400,0,-9936,0,-1424,0,304,0,104,0,16,0,1', '36,0,-384,0,2368,0,-7360,0,8896,0,160,0,-5520,0,11808,0,-6900,0,1472,0,2784,0,-3168,0,1968,0,-656,0,136,0,-16,0,1', '36,0,-448,0,2816,0,-9632,0,25920,0,-48320,0,49968,0,-18336,0,-6644,0,7328,0,-576,0,-1776,0,-16,0,288,0,104,0,16,0,1', '36,0,-64,0,-112,0,112,0,284,0,192,0,56,0,8,0,1', '36,0,0,0,976,0,-1248,0,1052,0,-256,0,88,0,-16,0,1', '36,0,0,0,976,0,1248,0,1052,0,256,0,88,0,16,0,1', '36,0,1344,0,12448,0,-5504,0,-48096,0,-7456,0,78896,0,-20928,0,128524,0,-94112,0,105712,0,-61440,0,19424,0,-3760,0,456,0,-32,0,1', '36,0,1536,0,24448,0,-6176,0,701120,0,-1850592,0,1716048,0,-784384,0,278668,0,-69056,0,3200,0,656,0,176,0,48,0,24,0,0,0,1', '36,0,384,0,2176,0,7520,0,19520,0,33632,0,39088,0,6048,0,80780,0,-81152,0,22400,0,9936,0,-1424,0,-304,0,104,0,-16,0,1', '36,0,384,0,2368,0,7360,0,8896,0,-160,0,-5520,0,-11808,0,-6900,0,-1472,0,2784,0,3168,0,1968,0,656,0,136,0,16,0,1', '36,0,448,0,2816,0,9632,0,25920,0,48320,0,49968,0,18336,0,-6644,0,-7328,0,-576,0,1776,0,-16,0,-288,0,104,0,-16,0,1', '36,0,64,0,-112,0,-112,0,284,0,-192,0,56,0,-8,0,1', '36,0,96,0,272,0,320,0,220,0,80,0,24,0,0,0,1', '37249,0,-207408,0,418536,0,-186128,0,-355908,0,136592,0,299096,0,97840,0,-8058,0,-19600,0,-8232,0,-1840,0,188,0,304,0,104,0,16,0,1', '37249,0,207408,0,418536,0,186128,0,-355908,0,-136592,0,299096,0,-97840,0,-8058,0,19600,0,-8232,0,1840,0,188,0,-304,0,104,0,-16,0,1', '37636,0,16896,0,-119424,0,-538048,0,99312,0,1377568,0,1619536,0,876192,0,206228,0,-22208,0,-26784,0,-7392,0,-760,0,208,0,104,0,16,0,1', '3888,0,-16128,11520,17856,-20736,6016,-15616,14144,23808,-36736,-9216,34720,4480,-11136,-10496,25752,13056,2752,11456,14928,4480,-4352,-4416,-1152,-256,128,320,104,-32,-16,0,1', '393,-4944,29552,-98624,190424,-139920,-103536,259744,362620,372464,285824,-290592,-54696,64880,139680,172864,44842,35440,72016,75520,39032,12848,2928,352,4404,1392,-800,160,152,-16,0,0,1', '4,0,-32,0,128,0,-256,0,324,0,-80,0,0,0,0,0,1', '4,0,1088,0,95008,0,261696,0,593248,0,879616,0,985600,0,666400,0,257860,0,66976,0,17936,0,3616,0,1424,0,512,0,128,0,16,0,1', '4,0,32,0,128,0,256,0,324,0,80,0,0,0,0,0,1', '40401,0,-185472,0,795928,0,-2258528,0,4681540,0,-7265344,0,8619960,0,-7680480,0,5027670,0,-2398976,0,835752,0,-213408,0,39972,0,-5440,0,520,0,-32,0,1', '40401,0,185472,0,795928,0,2258528,0,4681540,0,7265344,0,8619960,0,7680480,0,5027670,0,2398976,0,835752,0,213408,0,39972,0,5440,0,520,0,32,0,1', '41616,0,-332544,0,1170304,0,-2162688,0,1773792,0,-329728,0,519872,0,26112,0,78376,0,-6464,0,-5024,0,-2304,0,104,0,-64,0,48,0,0,0,1', '41616,0,332544,0,1170304,0,2162688,0,1773792,0,329728,0,519872,0,-26112,0,78376,0,6464,0,-5024,0,2304,0,104,0,64,0,48,0,0,0,1', '418,1344,1520,1024,0,-1344,-688,-128,368,176,32,80,24,-16,-8,0,1', '42834,-208032,1110832,-3170624,3665152,1595200,-6313856,-9529088,49642648,-79236192,64660160,-20821920,-10200552,11481536,1114560,-9120992,9184596,-6425472,4234304,-2701632,1349240,-320016,-164208,220272,-120380,36208,-2288,-3584,2064,-640,128,-16,1', '43312,-459520,893952,3346688,9003456,20056064,32487296,40564480,41453568,35655040,24707840,13633280,5790048,1229312,-548160,-734464,-402872,-126272,49984,79808,32688,-960,-5760,-1472,-224,-160,-160,0,24,0,0,0,1', '4489,0,-28160,0,41608,0,34336,0,-44484,0,-56128,0,62280,0,47040,0,-1878,0,-24832,0,-8600,0,2656,0,2036,0,192,0,8,0,0,0,1', '4489,0,28160,0,41608,0,-34336,0,-44484,0,56128,0,62280,0,-47040,0,-1878,0,24832,0,-8600,0,-2656,0,2036,0,-192,0,8,0,0,0,1', '46656,0,-124416,0,145152,0,41472,0,-301824,0,-139776,0,285568,0,247296,0,-3408,0,-50752,0,-7136,0,4416,0,1216,0,-64,0,-48,0,0,0,1', '46656,0,124416,0,145152,0,-41472,0,-301824,0,139776,0,285568,0,-247296,0,-3408,0,50752,0,-7136,0,-4416,0,1216,0,64,0,-48,0,0,0,1', '4782969,0,-3499200,0,-13198464,0,7147008,0,14273820,0,-3687600,0,2766976,0,325552,0,-402182,0,21792,0,19520,0,-3424,0,-1708,0,-144,0,64,0,16,0,1', '4782969,0,3499200,0,-13198464,0,-7147008,0,14273820,0,3687600,0,2766976,0,-325552,0,-402182,0,-21792,0,19520,0,3424,0,-1708,0,144,0,64,0,-16,0,1', '48,0,256,-256,1216,1792,8576,12544,24896,22784,31360,23040,47776,18816,54016,-5888,24728,256,38592,-15552,15376,-1536,9472,-3776,4896,-1408,1152,-320,200,-32,16,0,1', '484,0,-2560,0,37856,0,-81312,0,475456,0,537088,0,58416,0,-105568,0,108396,0,24896,0,-12336,0,-1136,0,1168,0,-384,0,104,0,-16,0,1', '484,0,2560,0,37856,0,81312,0,475456,0,-537088,0,58416,0,105568,0,108396,0,-24896,0,-12336,0,1136,0,1168,0,384,0,104,0,16,0,1', '499,-3600,18496,-70880,198712,-431488,762200,-1101920,1322952,-1357872,1195568,-930016,713968,-501296,373320,-259136,163454,-96304,55712,-33056,20288,-6048,5912,-2144,1000,-656,176,-128,40,-16,8,0,1', '5184,0,-53760,0,312064,0,-993792,0,1510272,0,-1005056,0,542336,0,-248832,0,102352,0,-38464,0,12640,0,-3264,0,1040,0,-128,0,48,0,0,0,1', '5184,0,53760,0,312064,0,993792,0,1510272,0,1005056,0,542336,0,248832,0,102352,0,38464,0,12640,0,3264,0,1040,0,128,0,48,0,0,0,1', '5283,31536,74016,104160,104824,46016,27272,66144,14200,-14832,46768,84896,47776,-19504,-42088,-20928,-4194,-9712,-8992,-352,7408,4064,520,-416,-440,-336,-80,128,40,-16,-8,0,1', '531441,0,-1609632,0,2234088,0,-1826496,0,971028,0,-343840,0,75048,0,-8064,0,3286,0,-2912,0,1752,0,-192,0,-76,0,32,0,24,0,0,0,1', '531441,0,-1994544,0,4686984,0,-6496848,0,6380964,0,-4082832,0,1972968,0,-536368,0,48054,0,49648,0,-24904,0,6416,0,-444,0,-176,0,88,0,-16,0,1', '531441,0,0,0,-390744,0,0,0,1609956,0,0,0,801288,0,0,0,170038,0,0,0,20120,0,0,0,1412,0,0,0,56,0,0,0,1', '531441,0,1609632,0,2234088,0,1826496,0,971028,0,343840,0,75048,0,8064,0,3286,0,2912,0,1752,0,192,0,-76,0,-32,0,24,0,0,0,1', '531441,0,1994544,0,4686984,0,6496848,0,6380964,0,4082832,0,1972968,0,536368,0,48054,0,-49648,0,-24904,0,-6416,0,-444,0,176,0,88,0,16,0,1', '54,1056,5072,-11584,7264,8384,-17232,18688,-4488,-5312,12176,-36640,23976,40480,-57488,-16384,47688,-1792,-13568,3712,-4192,336,3472,-1344,-396,432,-240,-32,104,0,-16,0,1', '548001,-2102496,2767840,-452224,-680496,324992,-4165504,6674880,753724,-9992928,11575200,-8465408,5683152,-3388160,1470016,-405888,132358,-182432,191712,-105344,32368,640,-5824,1472,316,-160,160,0,-16,0,0,0,1', '576,0,-4608,0,187648,0,-764928,0,1317888,0,-1078272,0,331136,0,32896,0,25136,0,-72640,0,32608,0,-3584,0,-672,0,0,0,80,0,-16,0,1', '576,0,-7680,0,66304,0,-322560,0,1201152,0,-1987584,0,1738112,0,-922496,0,318512,0,-63040,0,-2144,0,5632,0,-1440,0,0,0,80,0,-16,0,1', '576,0,4608,0,187648,0,764928,0,1317888,0,1078272,0,331136,0,-32896,0,25136,0,72640,0,32608,0,3584,0,-672,0,0,0,80,0,16,0,1', '576,0,7680,0,66304,0,322560,0,1201152,0,1987584,0,1738112,0,922496,0,318512,0,63040,0,-2144,0,-5632,0,-1440,0,0,0,80,0,16,0,1', '59,1056,8000,33632,85088,123984,87152,-27520,-110544,-139920,-145024,-125120,-12040,79072,63168,71936,64914,19616,-11728,-21440,-9640,4848,8752,3008,-2200,-1936,-80,416,112,-32,-16,0,1', '619369,0,-2461312,0,3963648,0,-4538848,0,4458092,0,-2420928,0,791488,0,-485952,0,209386,0,2304,0,-6784,0,-3488,0,356,0,-64,0,64,0,0,0,1', '619369,0,2461312,0,3963648,0,4538848,0,4458092,0,2420928,0,791488,0,485952,0,209386,0,-2304,0,-6784,0,3488,0,356,0,64,0,64,0,0,0,1', '6372,-104832,826944,-2730624,4955104,-5764608,5810944,-7294464,11679888,-16084800,17240576,-11669760,3601408,2404608,-3072512,1519872,-201860,-29376,2272,-4032,25040,-9216,384,0,1176,-96,-64,0,32,0,0,0,1', '6561,0,-11664,0,39528,0,-58320,0,-4212,0,-144,0,95768,0,21552,0,-6330,0,-20400,0,-1512,0,1936,0,1740,0,464,0,104,0,16,0,1', '6561,0,-11664,0,9720,0,-1296,0,-10260,0,12240,0,-3960,0,-7408,0,15494,0,-15600,0,10504,0,-5360,0,2092,0,-592,0,120,0,-16,0,1', '6561,0,-19440,0,-4104,0,51696,0,48588,0,-67184,0,61128,0,-18768,0,18374,0,-20176,0,6152,0,1872,0,-1012,0,-208,0,56,0,16,0,1', '6561,0,-28512,0,57568,0,-72576,0,66888,0,-48832,0,28736,0,-14208,0,6706,0,-2528,0,928,0,-384,0,200,0,-64,0,0,0,0,0,1', '6561,0,-34992,0,110808,0,-182736,0,187596,0,-93744,0,32616,0,-12240,0,-11834,0,4080,0,3624,0,3472,0,2316,0,752,0,152,0,16,0,1', '6561,0,-54432,0,253800,0,-786240,0,1542924,0,-1882592,0,1427352,0,-628608,0,124486,0,7328,0,-3048,0,-2880,0,1100,0,-32,0,-24,0,0,0,1', '6561,0,0,0,-85608,0,0,0,340732,0,0,0,-229528,0,0,0,187302,0,0,0,-23384,0,0,0,1596,0,0,0,-40,0,0,0,1', '6561,0,0,0,18072,0,0,0,59020,0,0,0,53288,0,0,0,20550,0,0,0,3688,0,0,0,204,0,0,0,-40,0,0,0,1', '6561,0,0,0,3240,0,0,0,4860,0,0,0,472,0,0,0,1446,0,0,0,1048,0,0,0,1084,0,0,0,-24,0,0,0,1', '6561,0,11664,0,39528,0,58320,0,-4212,0,144,0,95768,0,-21552,0,-6330,0,20400,0,-1512,0,-1936,0,1740,0,-464,0,104,0,-16,0,1', '6561,0,11664,0,9720,0,1296,0,-10260,0,-12240,0,-3960,0,7408,0,15494,0,15600,0,10504,0,5360,0,2092,0,592,0,120,0,16,0,1', '6561,0,19440,0,-4104,0,-51696,0,48588,0,67184,0,61128,0,18768,0,18374,0,20176,0,6152,0,-1872,0,-1012,0,208,0,56,0,-16,0,1', '6561,0,28512,0,57568,0,72576,0,66888,0,48832,0,28736,0,14208,0,6706,0,2528,0,928,0,384,0,200,0,64,0,0,0,0,0,1', '6561,0,34992,0,110808,0,182736,0,187596,0,93744,0,32616,0,12240,0,-11834,0,-4080,0,3624,0,-3472,0,2316,0,-752,0,152,0,-16,0,1', '6561,0,54432,0,253800,0,786240,0,1542924,0,1882592,0,1427352,0,628608,0,124486,0,-7328,0,-3048,0,2880,0,1100,0,32,0,-24,0,0,0,1', '66564,0,-277824,0,441280,0,25152,0,-181392,0,-205216,0,190064,0,69664,0,-2668,0,-16352,0,3008,0,800,0,-56,0,-80,0,56,0,16,0,1', '66564,0,277824,0,441280,0,-25152,0,-181392,0,205216,0,190064,0,-69664,0,-2668,0,16352,0,3008,0,-800,0,-56,0,80,0,56,0,-16,0,1', '6724,0,-72704,0,445568,0,-816416,0,695888,0,-345760,0,211440,0,-124864,0,27060,0,-5120,0,6560,0,-1360,0,120,0,-80,0,24,0,0,0,1', '6724,0,72704,0,445568,0,816416,0,695888,0,345760,0,211440,0,124864,0,27060,0,5120,0,6560,0,1360,0,120,0,80,0,24,0,0,0,1', '68644,0,-163200,0,464096,0,-186240,0,-1611808,0,299936,0,3632656,0,-1937120,0,709644,0,-96576,0,-432,0,2176,0,0,0,-208,0,88,0,-16,0,1', '68644,0,163200,0,464096,0,186240,0,-1611808,0,-299936,0,3632656,0,1937120,0,709644,0,96576,0,-432,0,-2176,0,0,0,208,0,88,0,16,0,1', '69696,0,-182784,0,256768,0,-299520,0,294528,0,139264,0,372992,0,170496,0,115792,0,34496,0,12256,0,2112,0,176,0,64,0,0,0,0,0,1', '69696,0,182784,0,256768,0,299520,0,294528,0,-139264,0,372992,0,-170496,0,115792,0,-34496,0,12256,0,-2112,0,176,0,-64,0,0,0,0,0,1', '729,0,-11664,0,74520,0,-244512,0,454392,0,-507264,0,363520,0,-164400,0,36742,0,8336,0,-10680,0,4128,0,-520,0,-192,0,96,0,-16,0,1', '729,0,-1512,0,1836,0,-456,0,-262,0,120,0,4,0,-8,0,1', '729,0,-15552,0,124416,0,-438048,0,777276,0,-723120,0,315136,0,14992,0,-76454,0,14368,0,13120,0,-3840,0,-1292,0,368,0,64,0,-16,0,1', '729,0,-1728,0,7584,0,-38720,0,104668,0,-196784,0,220864,0,-161232,0,143898,0,-28384,0,2336,0,2016,0,1236,0,112,0,64,0,16,0,1', '729,0,-3888,0,12960,0,-23760,0,27180,0,-15984,0,4864,0,928,0,-1606,0,656,0,160,0,-112,0,4,0,16,0,0,0,0,0,1', '729,0,-4968,0,12892,0,-21536,0,39654,0,-49192,0,51560,0,-42552,0,25447,0,-11144,0,2656,0,792,0,-694,0,80,0,36,0,-8,0,1', '729,0,-6912,0,1840752,0,-1171584,0,5034940,0,343360,0,1198544,0,204288,0,273754,0,-23168,0,24560,0,-4224,0,116,0,-320,0,16,0,0,0,1', '729,0,-864,-6048,4824,-11520,20256,62400,57292,-117504,-87104,128544,-104104,-95232,421952,-348288,215674,-218112,149088,-59808,30968,-23808,12256,-3264,964,-768,384,-96,24,0,0,0,1', '729,0,-8640,0,62304,0,-306304,0,997468,0,-1651120,0,2004832,0,-1587120,0,957210,0,-387296,0,125984,0,-32544,0,6996,0,-1168,0,160,0,-16,0,1', '729,0,0,0,-7776,0,0,0,20844,0,0,0,18352,0,0,0,4282,0,0,0,320,0,0,0,68,0,0,0,16,0,0,0,1', '729,0,0,0,37584,0,-80352,0,465660,0,-16992,0,274960,0,700352,0,338394,0,-15680,0,-39408,0,96,0,4148,0,736,0,16,0,0,0,1', '729,0,0,0,37584,0,80352,0,465660,0,16992,0,274960,0,-700352,0,338394,0,15680,0,-39408,0,-96,0,4148,0,-736,0,16,0,0,0,1', '729,0,11664,0,74520,0,244512,0,454392,0,507264,0,363520,0,164400,0,36742,0,-8336,0,-10680,0,-4128,0,-520,0,192,0,96,0,16,0,1', '729,0,1512,0,1836,0,456,0,-262,0,-120,0,4,0,8,0,1', '729,0,15552,0,124416,0,438048,0,777276,0,723120,0,315136,0,-14992,0,-76454,0,-14368,0,13120,0,3840,0,-1292,0,-368,0,64,0,16,0,1', '729,0,1728,0,7584,0,38720,0,104668,0,196784,0,220864,0,161232,0,143898,0,28384,0,2336,0,-2016,0,1236,0,-112,0,64,0,-16,0,1', '729,0,3888,0,12960,0,23760,0,27180,0,15984,0,4864,0,-928,0,-1606,0,-656,0,160,0,112,0,4,0,-16,0,0,0,0,0,1', '729,0,4968,0,12892,0,21536,0,39654,0,49192,0,51560,0,42552,0,25447,0,11144,0,2656,0,-792,0,-694,0,-80,0,36,0,8,0,1', '729,0,5184,0,9432,0,-4128,0,-30092,0,-41696,0,60728,0,-43456,0,71674,0,-8064,0,536,0,1312,0,508,0,96,0,24,0,0,0,1', '729,0,6912,0,1840752,0,1171584,0,5034940,0,-343360,0,1198544,0,-204288,0,273754,0,23168,0,24560,0,4224,0,116,0,320,0,16,0,0,0,1', '729,0,8640,0,62304,0,306304,0,997468,0,1651120,0,2004832,0,1587120,0,957210,0,387296,0,125984,0,32544,0,6996,0,1168,0,160,0,16,0,1', '7518564,0,-6945792,0,5762272,0,-295104,0,-1629152,0,1887584,0,-781104,0,27424,0,226668,0,-184704,0,88656,0,-30432,0,7520,0,-1328,0,184,0,-16,0,1', '7518564,0,6945792,0,5762272,0,295104,0,-1629152,0,-1887584,0,-781104,0,-27424,0,226668,0,184704,0,88656,0,30432,0,7520,0,1328,0,184,0,16,0,1', '762129,0,1049760,0,4100472,0,-547200,0,2432188,0,-1970848,0,-638168,0,-339200,0,310294,0,-17568,0,38984,0,-3968,0,348,0,-352,0,24,0,0,0,1', '7641,-16272,68928,-145632,309016,-549104,946208,-1276928,1686660,-1850000,1755024,-1280480,790248,-327248,64976,768,4946,-8336,28736,-24928,20824,-16176,9504,-4608,2588,-1168,336,-224,72,-16,16,0,1', '77254,-564832,2044336,-4557184,7140704,-9475648,11814368,-11428416,5856496,-679616,1794560,-4466400,3260056,-514656,-313248,-274720,499296,-225568,60816,-50880,40552,-15792,3456,592,-2052,464,176,128,-24,-32,0,0,1', '80226,-67968,-1041552,-309792,4176448,5010752,-411792,-2243808,104856,1083680,1309760,1187936,689768,39552,-428928,-261152,-86964,-48512,36848,37856,6360,1520,-928,-2016,-468,192,16,-16,0,0,0,0,1', '804,-384,-64,4224,27680,-46016,122528,-101312,322416,-226432,519168,-164352,770368,-58336,765856,131456,807260,322496,598560,202176,263216,51616,71984,2400,14568,-1600,2368,-384,256,-16,16,0,1', '81,0,-1440,0,6904,0,-2112,0,-21900,0,21344,0,66872,0,4992,0,-17546,0,34720,0,58696,0,28608,0,4436,0,-352,0,-120,0,0,0,1', '81,0,-216,0,288,0,-624,0,1078,0,-416,0,-632,0,560,0,309,0,-392,0,-264,0,168,0,118,0,-16,0,-16,0,0,0,1', '81,0,-24,0,532,0,264,0,278,0,-104,0,52,0,-8,0,1', '81,0,-240,0,244,0,32,0,-98,0,-16,0,20,0,0,0,1', '81,0,-288,0,1144,0,576,0,17268,0,44320,0,86264,0,89472,0,89206,0,80288,0,42568,0,13632,0,2900,0,352,0,72,0,0,0,1', '81,0,-288,0,208,0,-800,0,2636,0,4800,0,7824,0,8384,0,6262,0,4192,0,2672,0,608,0,620,0,0,0,48,0,0,0,1', '81,0,-288,0,856,0,2880,0,600,0,-15296,0,12920,0,768,0,4162,0,-2848,0,-1352,0,192,0,152,0,64,0,24,0,0,0,1', '81,0,-432,0,1368,0,-48,0,14980,0,38896,0,63992,0,103984,0,137814,0,130160,0,82792,0,34928,0,9828,0,1744,0,200,0,16,0,1', '81,0,-432,0,1368,0,1968,0,-13196,0,24624,0,33240,0,-124848,0,228982,0,-140432,0,44136,0,-13168,0,3668,0,-624,0,104,0,-16,0,1', '81,0,-432,0,504,0,6144,0,-9260,0,-32848,0,22776,0,78208,0,34870,0,-21264,0,-8888,0,384,0,1716,0,-112,0,-56,0,0,0,1', '81,0,-432,0,936,0,-1968,0,628,0,20016,0,16680,0,96176,0,180854,0,57200,0,7832,0,4976,0,3156,0,912,0,152,0,16,0,1', '81,0,-648,0,4384,0,-16488,0,36800,0,-54488,0,55120,0,-37448,0,17746,0,-6600,0,2912,0,-1192,0,448,0,-24,0,16,0,-8,0,1', '81,0,-72,0,-44,0,-528,0,606,0,-264,0,1232,0,-760,0,971,0,-824,0,880,0,-616,0,366,0,-144,0,44,0,-8,0,1', '81,0,-72,0,12,0,8,0,22,0,-56,0,44,0,-8,0,1', '81,0,-720,0,1176,0,17056,0,26020,0,-99344,0,76344,0,-23488,0,5526,0,-560,0,-344,0,160,0,-124,0,16,0,8,0,0,0,1', '81,0,0,0,-152,0,0,0,-12,0,0,0,1064,0,0,0,1654,0,0,0,856,0,0,0,212,0,0,0,24,0,0,0,1', '81,0,0,0,-4392,0,0,0,78724,0,0,0,-59848,0,0,0,31062,0,0,0,-4760,0,0,0,612,0,0,0,8,0,0,0,1', '81,0,0,0,-5240,0,0,0,150660,0,0,0,-129880,0,0,0,42838,0,0,0,-6344,0,0,0,356,0,0,0,24,0,0,0,1', '81,0,0,0,-8712,0,0,0,484996,0,0,0,192536,0,0,0,11862,0,0,0,-9272,0,0,0,2148,0,0,0,-88,0,0,0,1', '81,0,0,0,4392,0,0,0,78724,0,0,0,59848,0,0,0,31062,0,0,0,4760,0,0,0,612,0,0,0,-8,0,0,0,1', '81,0,0,0,8712,0,0,0,484996,0,0,0,-192536,0,0,0,11862,0,0,0,9272,0,0,0,2148,0,0,0,88,0,0,0,1', '81,0,1440,0,6904,0,2112,0,-21900,0,-21344,0,66872,0,-4992,0,-17546,0,-34720,0,58696,0,-28608,0,4436,0,352,0,-120,0,0,0,1', '81,0,216,0,288,0,624,0,1078,0,416,0,-632,0,-560,0,309,0,392,0,-264,0,-168,0,118,0,16,0,-16,0,0,0,1', '81,0,24,0,532,0,-264,0,278,0,104,0,52,0,8,0,1', '81,0,240,0,244,0,-32,0,-98,0,16,0,20,0,0,0,1', '81,0,288,0,1144,0,-576,0,17268,0,-44320,0,86264,0,-89472,0,89206,0,-80288,0,42568,0,-13632,0,2900,0,-352,0,72,0,0,0,1', '81,0,288,0,208,0,800,0,2636,0,-4800,0,7824,0,-8384,0,6262,0,-4192,0,2672,0,-608,0,620,0,0,0,48,0,0,0,1', '81,0,288,0,856,0,-2880,0,600,0,15296,0,12920,0,-768,0,4162,0,2848,0,-1352,0,-192,0,152,0,-64,0,24,0,0,0,1', '81,0,432,0,1368,0,-1968,0,-13196,0,-24624,0,33240,0,124848,0,228982,0,140432,0,44136,0,13168,0,3668,0,624,0,104,0,16,0,1', '81,0,432,0,1368,0,48,0,14980,0,-38896,0,63992,0,-103984,0,137814,0,-130160,0,82792,0,-34928,0,9828,0,-1744,0,200,0,-16,0,1', '81,0,432,0,504,0,-6144,0,-9260,0,32848,0,22776,0,-78208,0,34870,0,21264,0,-8888,0,-384,0,1716,0,112,0,-56,0,0,0,1', '81,0,432,0,936,0,1968,0,628,0,-20016,0,16680,0,-96176,0,180854,0,-57200,0,7832,0,-4976,0,3156,0,-912,0,152,0,-16,0,1', '81,0,72,0,-44,0,528,0,606,0,264,0,1232,0,760,0,971,0,824,0,880,0,616,0,366,0,144,0,44,0,8,0,1', '81,0,72,0,12,0,-8,0,22,0,56,0,44,0,8,0,1', '81,0,720,0,1176,0,-17056,0,26020,0,99344,0,76344,0,23488,0,5526,0,560,0,-344,0,-160,0,-124,0,-16,0,8,0,0,0,1', '843,13376,94976,264128,640432,1087952,1575808,1732608,1429824,650224,-246624,-891168,-934120,-516320,15536,267008,238226,76576,-17072,-35936,-12248,-2448,608,-1088,264,304,400,0,-16,-32,0,0,1', '8544,-69120,322816,-952832,1995264,-2900224,2840064,-1362432,-760256,2085888,-1840000,608256,409344,-592000,305216,-15360,-33824,25792,-7744,17984,-6528,256,3232,-1344,-8,128,-80,-32,8,0,0,0,1', '873,5136,45712,95424,132448,212048,265824,214528,105524,-56752,-130800,-202304,76016,120400,245152,236288,283430,152368,88272,9920,11872,2800,7872,1024,868,-400,272,64,48,-16,0,0,1', '9,0,-120,0,556,0,-960,0,238,0,27336,0,36304,0,-37064,0,-30641,0,-312,0,9512,0,6248,0,1906,0,368,0,60,0,8,0,1', '9,0,-168,0,1228,0,512,0,4110,0,4120,0,11072,0,10680,0,13903,0,10616,0,8728,0,4488,0,1970,0,496,0,108,0,8,0,1', '9,0,-24,0,112,0,-384,0,408,0,40,0,-352,0,384,0,46,0,-136,0,112,0,0,0,8,0,-8,0,0,0,0,0,1', '9,0,-40,0,380,0,40,0,170,0,24,0,20,0,8,0,1', '9,0,-8,0,12,0,24,0,-30,0,-8,0,20,0,-8,0,1', '9,0,0,0,16,0,0,0,36,0,0,0,224,0,0,0,298,0,0,0,112,0,0,0,332,0,0,0,0,0,0,0,1', '9,0,120,0,556,0,960,0,238,0,-27336,0,36304,0,37064,0,-30641,0,312,0,9512,0,-6248,0,1906,0,-368,0,60,0,-8,0,1', '9,0,168,0,1228,0,-512,0,4110,0,-4120,0,11072,0,-10680,0,13903,0,-10616,0,8728,0,-4488,0,1970,0,-496,0,108,0,-8,0,1', '9,0,24,0,112,0,384,0,408,0,-40,0,-352,0,-384,0,46,0,136,0,112,0,0,0,8,0,8,0,0,0,0,0,1', '9,0,40,0,380,0,-40,0,170,0,-24,0,20,0,-8,0,1', '9,0,8,0,12,0,-24,0,-30,0,8,0,20,0,8,0,1', '9,144,-512,-8096,41512,-26640,50224,-84352,106492,-190128,235472,-163232,86664,4016,-106432,71168,17474,-47472,75648,-60832,34824,-15824,9776,1408,1444,848,-112,-32,-56,-16,0,0,1', '953,3728,12336,11680,15120,-34928,-27504,-98880,14052,-9200,24528,55712,95008,3984,52464,-31360,41622,-40784,39344,-17952,16976,-6672,4240,-3392,-12,-208,16,96,96,-16,-16,0,1']}, 'subfield_mults': [1, 1, 1], 'subfields': ['2.0.1', '2.0.0.0.1', '3.0.4.0.10.0.4.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( -\\frac{283}{127536} a^{14} - \\frac{13}{5314} a^{12} - \\frac{241}{5314} a^{10} + \\frac{3587}{31884} a^{8} - \\frac{8321}{63768} a^{6} - \\frac{5542}{7971} a^{4} + \\frac{26801}{15942} a^{2} - \\frac{17307}{5314} \\)', '\\( -\\frac{283}{127536} a^{14} - \\frac{13}{5314} a^{12} - \\frac{241}{5314} a^{10} + \\frac{3587}{31884} a^{8} - \\frac{8321}{63768} a^{6} - \\frac{5542}{7971} a^{4} + \\frac{26801}{15942} a^{2} - \\frac{6679}{5314} \\)', '\\( \\frac{1609}{127536} a^{15} + \\frac{2047}{127536} a^{14} + \\frac{1333}{42512} a^{13} - \\frac{365}{42512} a^{12} + \\frac{13675}{42512} a^{11} + \\frac{15307}{42512} a^{10} - \\frac{2303}{7971} a^{9} - \\frac{95971}{63768} a^{8} + \\frac{38465}{63768} a^{7} + \\frac{231719}{63768} a^{6} + \\frac{30941}{63768} a^{5} - \\frac{348337}{63768} a^{4} - \\frac{171161}{63768} a^{3} + \\frac{174415}{63768} a^{2} + \\frac{5207}{5314} a - \\frac{19545}{10628} \\)', '\\( \\frac{1609}{127536} a^{15} - \\frac{2047}{127536} a^{14} + \\frac{1333}{42512} a^{13} + \\frac{365}{42512} a^{12} + \\frac{13675}{42512} a^{11} - \\frac{15307}{42512} a^{10} - \\frac{2303}{7971} a^{9} + \\frac{95971}{63768} a^{8} + \\frac{38465}{63768} a^{7} - \\frac{231719}{63768} a^{6} + \\frac{30941}{63768} a^{5} + \\frac{348337}{63768} a^{4} - \\frac{171161}{63768} a^{3} - \\frac{174415}{63768} a^{2} + \\frac{5207}{5314} a + \\frac{19545}{10628} \\)', '\\( -\\frac{14}{7971} a^{15} - \\frac{1943}{63768} a^{14} - \\frac{2007}{42512} a^{13} - \\frac{2151}{42512} a^{12} - \\frac{973}{10628} a^{11} - \\frac{16157}{21256} a^{10} - \\frac{64765}{63768} a^{9} + \\frac{78427}{63768} a^{8} + \\frac{17710}{7971} a^{7} - \\frac{106195}{31884} a^{6} - \\frac{400435}{63768} a^{5} + \\frac{76117}{63768} a^{4} + \\frac{101515}{15942} a^{3} + \\frac{64075}{31884} a^{2} - \\frac{18807}{10628} a - \\frac{11959}{10628} \\)', '\\( -\\frac{2061}{21256} a^{15} - \\frac{3079}{127536} a^{14} - \\frac{277}{5314} a^{13} + \\frac{159}{5314} a^{12} - \\frac{12493}{5314} a^{11} - \\frac{11305}{21256} a^{10} + \\frac{137681}{21256} a^{9} + \\frac{170803}{63768} a^{8} - \\frac{188323}{10628} a^{7} - \\frac{423905}{63768} a^{6} + \\frac{111421}{5314} a^{5} + \\frac{173377}{15942} a^{4} - \\frac{31779}{2657} a^{3} - \\frac{324695}{31884} a^{2} - \\frac{2373}{10628} a + \\frac{14791}{10628} \\)', '\\( -\\frac{2759}{127536} a^{15} - \\frac{671}{127536} a^{14} + \\frac{723}{42512} a^{13} + \\frac{927}{42512} a^{12} - \\frac{5591}{10628} a^{11} - \\frac{1171}{10628} a^{10} + \\frac{133511}{63768} a^{9} + \\frac{59963}{63768} a^{8} - \\frac{403117}{63768} a^{7} - \\frac{161461}{63768} a^{6} + \\frac{651791}{63768} a^{5} + \\frac{329171}{63768} a^{4} - \\frac{78814}{7971} a^{3} - \\frac{39952}{7971} a^{2} + \\frac{35585}{10628} a + \\frac{22341}{10628} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', '1/8*a^8 - 1/2*a^4 - 1/4', '1/16*a^9 - 1/2*a^7 - 1/2*a^6 + 1/4*a^5 + 3/8*a', '1/16*a^10 - 1/2*a^7 + 1/4*a^6 + 3/8*a^2', '1/16*a^11 + 1/4*a^7 + 3/8*a^3', '1/16*a^12 + 3/8*a^4 - 1/2', '1/16*a^13 + 3/8*a^5 - 1/2*a', '1/127536*a^14 - 1023/42512*a^12 - 979/42512*a^10 - 407/31884*a^8 - 1/2*a^7 + 3353/63768*a^6 - 7927/63768*a^4 - 15335/63768*a^2 - 237/2657', '1/127536*a^15 - 1023/42512*a^13 - 979/42512*a^11 - 407/31884*a^9 + 3353/63768*a^7 - 7927/63768*a^5 - 15335/63768*a^3 - 237/2657*a']}
Number field data - 16.0.382511685112441262309376.45