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nf_fields • Show schema
{'class_group': [2, 2], 'class_number': 4, 'cm': False, 'coeffs': [-9, 44, -26, 24, 41, 16, -6, -4, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 51597803520000, 'disc_rad': 30, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[7, 1], [1, 1]]], [11, [[8, 1]]], [13, [[7, 1], [1, 1]]], [17, [[8, 1]]], [19, [[7, 1], [1, 1]]], [23, [[6, 1], [1, 2]]], [29, [[8, 1]]], [31, [[3, 2], [1, 2]]], [37, [[2, 4]]], [41, [[8, 1]]], [43, [[4, 2]]], [47, [[8, 1]]], [53, [[6, 1], [1, 2]]], [59, [[6, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [924, 504, 168], 'galois_label': '8T43', 'galt': 43, 'grd': 78.16266749191567, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 9, 'label': '8.2.51597803520000.9', 'local_algs': ['2.2.4.22a1.72', '3.1.1.0a1.1', '3.1.1.0a1.1', '3.1.6.9a1.1', '5.1.2.1a1.2', '5.1.2.1a1.1', '5.2.2.2a1.2'], 'monogenic': 0, 'narrow_class_group': [2, 4], 'narrow_class_number': 8, 'num_ram': 3, 'r2': 3, 'ramps': [2, 3, 5], 'rd': 51.7700878328, 'regulator': {'__RealLiteral__': 0, 'data': '6077.06743939', 'prec': 44}, 'res': {'sib': ['1369,1073,796,1161,1887,-756,1879,-673,703,-174,141,-21,16,-1,1', '1574640,6298560,8293104,3919104,-1390932,-10439280,-15008004,719928,11715273,1449504,-4342032,-69120,1498698,184392,-225396,-28992,49671,5400,-6240,-168,558,-8,-36,0,1', '19440,15124320,59536944,751146624,-3421161144,10637295696,-27720240216,51719806656,-66412829304,55485676464,-21585725184,-13902843264,33157703614,-35033765988,27533561574,-17088428016,6919886313,405357978,-3559784825,3592719432,-2483479485,1414787902,-652679397,182182128,29449720,-72833508,56406648,-36316616,22205799,-11765250,4882987,-1593504,480696,-158828,45792,-4776,-3347,2010,-579,96,3,-6,1', '2191537,-12493374,40666741,-92310598,158696545,-215754040,238956676,-219493672,166587262,-99595820,39134854,259228,-15622300,14633764,-8093386,2860804,-464038,-166832,187252,-108824,51742,-21580,7882,-2500,703,-166,37,-6,1', '2700,-11583,8046,-26127,-36018,40869,30180,-13698,-12888,-5349,4830,6213,-1322,-2361,288,516,-132,-81,42,3,-6,1', '283368,-7555860,101665476,-900575304,5818953300,-28744611774,110981939806,-338359986132,817518721386,-1562640262483,2342240931555,-2689483556226,2221476638144,-1041249531897,-240324318507,971327222662,-953438013558,487017194670,-17793520770,-204910764462,196860913812,-97911945273,18536462469,11658903102,-11714148570,4749449832,-549606276,-543170142,410905224,-150732027,24424335,7376226,-7119258,2840422,-664098,45462,37904,-21141,6585,-1426,216,-21,1', '81,-396,1702,-712,-11,-4376,1046,1588,798,1092,546,256,59,-8,22,-4,1', '952785,-2409822,2216151,-1117914,-575718,2335122,-1860717,-770118,2401239,-1340168,-597302,1012680,31015,-902486,843867,-370582,77243,-8568,-3386,16888,-18585,9938,-2713,-54,502,-290,87,-14,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{27} a^{7} - \\frac{2}{9} a^{6} + \\frac{1}{9} a^{5} + \\frac{22}{27} a^{4} + \\frac{5}{9} a^{3} - \\frac{19}{9} a^{2} - \\frac{14}{27} a - \\frac{2}{3} \\)', '\\( \\frac{1}{9} a^{7} - \\frac{1}{3} a^{6} - \\frac{10}{9} a^{5} + \\frac{8}{9} a^{4} + \\frac{23}{3} a^{3} + \\frac{55}{9} a^{2} - \\frac{13}{3} a + 7 \\)', '\\( \\frac{2}{27} a^{7} - \\frac{1}{3} a^{6} - \\frac{1}{3} a^{5} + \\frac{47}{27} a^{4} + \\frac{4}{3} a^{3} + \\frac{2}{3} a^{2} + \\frac{32}{27} a - \\frac{1}{3} \\)', '\\( \\frac{52}{27} a^{7} - \\frac{109}{9} a^{6} + \\frac{152}{9} a^{5} - \\frac{284}{27} a^{4} + \\frac{763}{9} a^{3} - \\frac{707}{9} a^{2} + \\frac{1654}{27} a - \\frac{35}{3} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/3*a^4 - 1/3*a', '1/9*a^5 - 1/9*a^4 - 1/3*a^3 - 1/9*a^2 + 4/9*a', '1/9*a^6 - 1/9*a^4 - 4/9*a^3 + 1/3*a^2 + 1/9*a', '1/27*a^7 + 1/27*a^4 - 1/3*a^2 - 2/27*a + 1/3']}
Number field data - 8.2.51597803520000.9