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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -3, 3, 2, -9, 10, -3, -5, 7, -5, 2, 0, 1, -2, 3, -2, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 117135062500000000, 'disc_rad': 370, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[12, 1], [4, 1]]], [5, [0]], [7, [[12, 1], [4, 1]]], [11, [[3, 4], [1, 4]]], [13, [[4, 4]]], [17, [[4, 4]]], [19, [[4, 4]]], [23, [[4, 4]]], [29, [[4, 4]]], [31, [[4, 4]]], [37, [0]], [41, [[3, 4], [1, 4]]], [43, [[4, 4]]], [47, [[12, 1], [4, 1]]], [53, [[12, 1], [4, 1]]], [59, [[2, 8]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [64, 72, 48], 'galois_label': '16T181', 'galt': 181, 'grd': 32.28605847922135, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '16.0.117135062500000000.1', 'local_algs': ['2.4.1.0a1.1', '2.4.3.8a1.2', '5.4.4.12a1.4', '37.4.1.0a1.1', '37.4.1.0a1.1', '37.4.2.4a1.2'], 'minimal_sibling': [-19, -78, -60, 93, 133, -18, -105, -20, 47, 9, -11, -1, 1], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 3, 'r2': 8, 'ramps': [2, 5, 37], 'rd': 11.6625342481, 'regulator': {'__RealLiteral__': 0, 'data': '333.853446138', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-1.-1.1', '1.-1.1.-1.1', '4.-3.5.-1.1', '1.1.1.0.0.0.1.-1.1'], 'torsion_gen': '\\( \\frac{54}{41} a^{15} - \\frac{125}{41} a^{14} + \\frac{193}{41} a^{13} - \\frac{168}{41} a^{12} + \\frac{116}{41} a^{11} - \\frac{76}{41} a^{10} + \\frac{179}{41} a^{9} - \\frac{359}{41} a^{8} + \\frac{510}{41} a^{7} - \\frac{426}{41} a^{6} + \\frac{45}{41} a^{5} + \\frac{437}{41} a^{4} - \\frac{433}{41} a^{3} + \\frac{157}{41} a^{2} + \\frac{86}{41} a - \\frac{60}{41} \\)', 'torsion_order': 10, 'units': ['\\( \\frac{60}{41} a^{15} - \\frac{66}{41} a^{14} + \\frac{55}{41} a^{13} + \\frac{73}{41} a^{12} - \\frac{108}{41} a^{11} + \\frac{116}{41} a^{10} + \\frac{44}{41} a^{9} - \\frac{121}{41} a^{8} + \\frac{61}{41} a^{7} + \\frac{210}{41} a^{6} - \\frac{606}{41} a^{5} + \\frac{645}{41} a^{4} - \\frac{103}{41} a^{3} - \\frac{313}{41} a^{2} + \\frac{337}{41} a - \\frac{94}{41} \\)', '\\( \\frac{54}{41} a^{15} - \\frac{125}{41} a^{14} + \\frac{193}{41} a^{13} - \\frac{168}{41} a^{12} + \\frac{116}{41} a^{11} - \\frac{76}{41} a^{10} + \\frac{179}{41} a^{9} - \\frac{359}{41} a^{8} + \\frac{510}{41} a^{7} - \\frac{426}{41} a^{6} + \\frac{45}{41} a^{5} + \\frac{437}{41} a^{4} - \\frac{433}{41} a^{3} + \\frac{157}{41} a^{2} + \\frac{86}{41} a - \\frac{101}{41} \\)', '\\( \\frac{57}{41} a^{15} - \\frac{75}{41} a^{14} + \\frac{83}{41} a^{13} + \\frac{14}{41} a^{12} - \\frac{37}{41} a^{11} + \\frac{61}{41} a^{10} + \\frac{91}{41} a^{9} - \\frac{158}{41} a^{8} + \\frac{183}{41} a^{7} + \\frac{56}{41} a^{6} - \\frac{383}{41} a^{5} + \\frac{541}{41} a^{4} - \\frac{145}{41} a^{3} - \\frac{201}{41} a^{2} + \\frac{232}{41} a - \\frac{77}{41} \\)', '\\( \\frac{66}{41} a^{15} - \\frac{48}{41} a^{14} + \\frac{40}{41} a^{13} + \\frac{109}{41} a^{12} - \\frac{127}{41} a^{11} + \\frac{144}{41} a^{10} + \\frac{32}{41} a^{9} - \\frac{88}{41} a^{8} - \\frac{19}{41} a^{7} + \\frac{272}{41} a^{6} - \\frac{724}{41} a^{5} + \\frac{607}{41} a^{4} - \\frac{60}{41} a^{3} - \\frac{373}{41} a^{2} + \\frac{342}{41} a - \\frac{128}{41} \\)', '\\( \\frac{61}{41} a^{15} - \\frac{145}{41} a^{14} + \\frac{155}{41} a^{13} - \\frac{85}{41} a^{12} - \\frac{36}{41} a^{11} + \\frac{25}{41} a^{10} + \\frac{83}{41} a^{9} - \\frac{341}{41} a^{8} + \\frac{362}{41} a^{7} - \\frac{176}{41} a^{6} - \\frac{407}{41} a^{5} + \\frac{830}{41} a^{4} - \\frac{499}{41} a^{3} - \\frac{159}{41} a^{2} + \\frac{331}{41} a - \\frac{127}{41} \\)', '\\( \\frac{53}{41} a^{15} - \\frac{87}{41} a^{14} + \\frac{134}{41} a^{13} - \\frac{51}{41} a^{12} + \\frac{44}{41} a^{11} + \\frac{15}{41} a^{10} + \\frac{140}{41} a^{9} - \\frac{221}{41} a^{8} + \\frac{332}{41} a^{7} - \\frac{163}{41} a^{6} - \\frac{195}{41} a^{5} + \\frac{416}{41} a^{4} - \\frac{283}{41} a^{3} - \\frac{79}{41} a^{2} + \\frac{174}{41} a - \\frac{109}{41} \\)', '\\( \\frac{3}{41} a^{15} - \\frac{73}{41} a^{14} + \\frac{54}{41} a^{13} - \\frac{105}{41} a^{12} - \\frac{30}{41} a^{11} - \\frac{27}{41} a^{10} - \\frac{47}{41} a^{9} - \\frac{168}{41} a^{8} + \\frac{165}{41} a^{7} - \\frac{174}{41} a^{6} - \\frac{18}{41} a^{5} + \\frac{391}{41} a^{4} - \\frac{327}{41} a^{3} + \\frac{93}{41} a^{2} + \\frac{146}{41} a - \\frac{140}{41} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11', 'a^12', 'a^13', 'a^14', '1/41*a^15 + 3/41*a^14 + 18/41*a^13 + 6/41*a^12 - 10/41*a^11 - 9/41*a^10 - 2/41*a^9 - 15/41*a^8 + 14/41*a^7 - 17/41*a^6 - 6/41*a^5 - 20/41*a^4 + 14/41*a^3 - 10/41*a^2 - 6/41*a + 8/41']}
Number field data - 16.0.117135062500000000.1