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nf_fields • Show schema
{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [-1009, -5524, -7702, -20, 1311, 90, -63, -3, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 74220378765625, 'disc_rad': 205, 'disc_sign': 1, 'frobs': [[2, [[4, 2]]], [3, [[4, 2]]], [5, [0]], [7, [[4, 2]]], [11, [[4, 2]]], [13, [[4, 2]]], [17, [[4, 2]]], [19, [[4, 2]]], [23, [[4, 2]]], [29, [[4, 2]]], [31, [[2, 4]]], [37, [[4, 2]]], [41, [0]], [43, [[4, 2]]], [47, [[4, 2]]], [53, [[4, 2]]], [59, [[2, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [6, 6], 'galois_label': '8T5', 'galt': 5, 'grd': 54.17705527224281, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.8.74220378765625.1', 'local_algs': ['5.4.3.1', '5.4.3.1', '41.4.3.2', '41.4.3.2'], 'monogenic': 0, 'num_ram': 2, 'r2': 0, 'ramps': [5, 41], 'rd': 54.1770552722, 'regulator': {'__RealLiteral__': 0, 'data': '7481.34415348', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-51.-1.1', '-1.-1.1', '-10.-1.1', '81.0.-23.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{49}{788059} a^{7} - \\frac{185}{788059} a^{6} - \\frac{307}{788059} a^{5} - \\frac{6689}{788059} a^{4} - \\frac{19952}{788059} a^{3} + \\frac{253099}{788059} a^{2} + \\frac{197770}{788059} a - \\frac{449623}{788059} \\)', '\\( \\frac{72680}{2364177} a^{7} - \\frac{87689}{788059} a^{6} - \\frac{4365601}{2364177} a^{5} + \\frac{8843945}{2364177} a^{4} + \\frac{88458658}{2364177} a^{3} - \\frac{43827040}{2364177} a^{2} - \\frac{520908343}{2364177} a - \\frac{172113815}{2364177} \\)', '\\( \\frac{12644}{2364177} a^{7} - \\frac{39037}{2364177} a^{6} - \\frac{825884}{2364177} a^{5} + \\frac{455890}{788059} a^{4} + \\frac{17310592}{2364177} a^{3} - \\frac{1863815}{788059} a^{2} - \\frac{102013915}{2364177} a - \\frac{11289458}{788059} \\)', '\\( \\frac{11792}{2364177} a^{7} - \\frac{15807}{788059} a^{6} - \\frac{613051}{2364177} a^{5} + \\frac{1562018}{2364177} a^{4} + \\frac{10303174}{2364177} a^{3} - \\frac{9761572}{2364177} a^{2} - \\frac{51121705}{2364177} a - \\frac{18429284}{2364177} \\)', '\\( \\frac{2743}{788059} a^{7} - \\frac{37660}{2364177} a^{6} - \\frac{417244}{2364177} a^{5} + \\frac{1070251}{2364177} a^{4} + \\frac{2755895}{788059} a^{3} - \\frac{5130908}{2364177} a^{2} - \\frac{16358326}{788059} a - \\frac{263125}{38757} \\)', '\\( \\frac{14798}{788059} a^{7} - \\frac{55870}{788059} a^{6} - \\frac{880773}{788059} a^{5} + \\frac{1920217}{788059} a^{4} + \\frac{17616266}{788059} a^{3} - \\frac{10250592}{788059} a^{2} - \\frac{101825555}{788059} a - \\frac{33338476}{788059} \\)', '\\( \\frac{75272}{788059} a^{7} - \\frac{774002}{2364177} a^{6} - \\frac{13888760}{2364177} a^{5} + \\frac{26245208}{2364177} a^{4} + \\frac{1556074}{12919} a^{3} - \\frac{125246689}{2364177} a^{2} - \\frac{563994914}{788059} a - \\frac{561622793}{2364177} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/183*a^6 - 47/183*a^5 - 40/183*a^4 + 20/61*a^3 - 49/183*a^2 + 11/61*a - 83/183', '1/2364177*a^7 - 2113/2364177*a^6 + 370782/788059*a^5 - 559081/2364177*a^4 - 979351/2364177*a^3 + 333677/2364177*a^2 - 1078787/2364177*a + 230221/2364177']}
Number field data - 8.8.74220378765625.1