-
nf_fields • Show schema
{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [1164, -1156, -1712, 1208, 734, -104, -72, -2, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 58769636260854016, 'disc_rad': 1786, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[7, 1], [1, 1]]], [5, [[7, 1], [1, 1]]], [7, [[4, 2]]], [11, [[4, 2]]], [13, [[7, 1], [1, 1]]], [17, [[4, 2]]], [19, [0]], [23, [[4, 2]]], [29, [[7, 1], [1, 1]]], [31, [[4, 2]]], [37, [[3, 2], [1, 2]]], [41, [[4, 2]]], [43, [[3, 2], [1, 2]]], [47, [0]], [53, [[7, 1], [1, 1]]], [59, [[4, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [196, 126, 84], 'galois_label': '8T37', 'galt': 37, 'grd': 140.06053834346, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '8.8.58769636260854016.1', 'local_algs': ['2.8.8.11', '19.8.6.2', '47.4.2.2', '47.4.2.2'], 'minimal_sibling': [4, -8, -14, 31, 0, -12, 0, 1], 'monogenic': 0, 'num_ram': 3, 'r2': 0, 'ramps': [2, 19, 47], 'rd': 124.779754072, 'regulator': {'__RealLiteral__': 0, 'data': '424963.918896', 'prec': 44}, 'res': {'sib': ['11,9,-37,-11,35,-9,-3,1', '4,-8,-14,31,0,-12,0,1', '-2693,-11719,46377,59822,-97619,-61323,57823,26960,-12331,-4599,1175,312,-53,-7,1', '-3660872818,69526295506,-472564688776,1316931000420,147536092506,-10736540428686,26575317098116,-12187464447232,-61265886206230,122700792540202,-41222819544560,-146800218487562,199268096920029,-15427189050739,-168967925942658,127234158776203,34026189737926,-90690738763681,27476068024539,26678698966504,-20775361159281,-1267495276381,6338519913970,-1542504780343,-982362816916,535961970597,48198616891,-89351571438,10111733483,8466036659,-2293511302,-407778463,222041832,185071,-12074447,1160892,359519,-65589,-4286,1595,-34,-15,1', '-82624,-37376,271616,60128,-279744,-33968,117408,9112,-22668,-1260,2012,88,-76,-2,1', '1384,34424,-253360,-1293160,7737220,4832936,-48806392,8150552,124067672,-66931708,-153106580,129472396,89814742,-118693500,-13620870,56762984,-10566303,-13593796,5652854,1243264,-1067547,55552,83774,-15768,-2193,820,-22,-12,1', '1553023,-5125218,-91365533,373178962,1590662842,-8649747256,-5826594808,75392048242,-38352389965,-310831810090,370675078793,634162459888,-1244635963752,-498308059200,2201086040180,-388682726928,-2248472017462,1260891647592,1316644243742,-1303794824596,-357004181932,759527370184,-49968327180,-273494673180,79969194510,60248107816,-31812597434,-6895846888,7086318560,-53286472,-966325468,143082024,78170727,-21713598,-3097345,1599290,-3894,-60680,4700,1042,-129,-6,1', '261178544,-2669137184,-4304090640,117916738464,-174082472480,-1635202527760,4289607295504,8412190182832,-32580843314880,-10123533698624,103348308183376,-23210912301712,-176618881675936,87105494760352,182551585224184,-125107161177288,-119749099254104,105698270336588,49675478929568,-58577036015572,-11764625432892,22269410159888,644352421676,-5913903378056,558654580285,1096980008578,-214784739247,-139188241824,41408767768,11361087184,-4995443212,-485467140,391585458,-3018004,-19536430,1585260,572952,-84232,-7740,1980,-11,-18,1', '272,-4304,-108864,-322596,147224,1103276,89196,-1529748,-222670,1124811,124536,-473684,-30092,117399,3252,-17080,-126,1409,0,-60,0,1', '618736,-300672,-18709056,-12879376,160285712,270731136,-170390736,-506749536,21863296,384061352,34886968,-156579984,-17300072,38212952,3251968,-5790796,-241648,540964,-2364,-29700,1328,862,-66,-10,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{7564}{629789} a^{7} - \\frac{2532}{629789} a^{6} - \\frac{1164591}{1259578} a^{5} - \\frac{1581645}{629789} a^{4} + \\frac{4687269}{629789} a^{3} + \\frac{15389826}{629789} a^{2} - \\frac{1011728}{629789} a - \\frac{11478863}{629789} \\)', '\\( \\frac{34409}{629789} a^{7} - \\frac{430351}{1259578} a^{6} - \\frac{3534721}{1259578} a^{5} + \\frac{4800070}{629789} a^{4} + \\frac{17141143}{629789} a^{3} - \\frac{34613348}{629789} a^{2} - \\frac{20410403}{629789} a + \\frac{29482069}{629789} \\)', '\\( \\frac{22822}{629789} a^{7} - \\frac{183467}{1259578} a^{6} - \\frac{2693997}{1259578} a^{5} - \\frac{197239}{629789} a^{4} + \\frac{11066191}{629789} a^{3} + \\frac{9782323}{629789} a^{2} - \\frac{8557814}{629789} a - \\frac{8241517}{629789} \\)', '\\( \\frac{46959}{629789} a^{7} - \\frac{101978}{629789} a^{6} - \\frac{3202835}{629789} a^{5} - \\frac{5115021}{629789} a^{4} + \\frac{26468969}{629789} a^{3} + \\frac{58556276}{629789} a^{2} - \\frac{16055918}{629789} a - \\frac{48818659}{629789} \\)', '\\( \\frac{26205}{629789} a^{7} - \\frac{16432}{629789} a^{6} - \\frac{1991057}{629789} a^{5} - \\frac{5106748}{629789} a^{4} + \\frac{17124898}{629789} a^{3} + \\frac{53074456}{629789} a^{2} - \\frac{16820559}{629789} a - \\frac{52973465}{629789} \\)', '\\( \\frac{293130}{629789} a^{7} - \\frac{688821}{1259578} a^{6} - \\frac{21390974}{629789} a^{5} - \\frac{48121190}{629789} a^{4} + \\frac{175544940}{629789} a^{3} + \\frac{498717057}{629789} a^{2} - \\frac{91085632}{629789} a - \\frac{412820725}{629789} \\)', '\\( \\frac{129489}{1259578} a^{7} - \\frac{492957}{1259578} a^{6} - \\frac{3992487}{629789} a^{5} - \\frac{479761}{629789} a^{4} + \\frac{35065947}{629789} a^{3} + \\frac{19578632}{629789} a^{2} - \\frac{27810393}{629789} a - \\frac{13959397}{629789} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4', '1/2*a^5', '1/2*a^6', '1/1259578*a^7 + 114734/629789*a^6 - 6613/1259578*a^5 + 153138/629789*a^4 + 240394/629789*a^3 - 6726/629789*a^2 + 196763/629789*a - 257745/629789']}
Number field data - 8.8.58769636260854016.1