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nf_fields • Show schema
{'class_group': [2, 2], 'class_number': 4, 'cm': False, 'coeffs': [4051, 1081, -2018, -382, 395, 37, -33, -1, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 15890703125, 'disc_rad': 2255, 'disc_sign': 1, 'frobs': [[2, [[8, 1]]], [3, [[8, 1]]], [5, [0]], [7, [[8, 1]]], [11, [0]], [13, [[8, 1]]], [17, [[8, 1]]], [19, [[2, 4]]], [23, [[8, 1]]], [29, [[2, 4]]], [31, [[2, 2], [1, 4]]], [37, [[8, 1]]], [41, [0]], [43, [[8, 1]]], [47, [[8, 1]]], [53, [[8, 1]]], [59, [[4, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [28, 16, 16], 'galois_label': '8T16', 'galt': 16, 'grd': 86.83344366434605, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 3, 'label': '8.0.15890703125.3', 'local_algs': ['5.8.7.2', '11.1.0.1', '11.1.0.1', '11.1.0.1', '11.1.0.1', '11.2.1.2', '11.2.1.2', '41.1.0.1', '41.1.0.1', '41.2.0.1', '41.2.1.2', '41.2.1.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 4, 'ramps': [5, 11, 41], 'rd': 18.8426893967, 'regulator': {'__RealLiteral__': 0, 'data': '78.6445211452', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.-1.1', '1.-1.1.-1.1'], 'torsion_gen': '\\( \\frac{32038}{6677011} a^{7} + \\frac{80741}{6677011} a^{6} - \\frac{1087105}{6677011} a^{5} - \\frac{146512}{607001} a^{4} + \\frac{12044059}{6677011} a^{3} + \\frac{1162494}{607001} a^{2} - \\frac{39142166}{6677011} a - \\frac{50047773}{6677011} \\)', 'torsion_order': 10, 'units': ['\\( \\frac{33688}{6677011} a^{7} + \\frac{119912}{6677011} a^{6} - \\frac{1107246}{6677011} a^{5} - \\frac{222681}{607001} a^{4} + \\frac{12398831}{6677011} a^{3} + \\frac{1611748}{607001} a^{2} - \\frac{40131000}{6677011} a - \\frac{48957717}{6677011} \\)', '\\( \\frac{112664}{6677011} a^{7} - \\frac{578882}{6677011} a^{6} - \\frac{1844666}{6677011} a^{5} + \\frac{1132500}{607001} a^{4} + \\frac{5496258}{6677011} a^{3} - \\frac{7328541}{607001} a^{2} + \\frac{3969747}{6677011} a + \\frac{177644795}{6677011} \\)', '\\( \\frac{645632}{6677011} a^{7} + \\frac{953520}{6677011} a^{6} - \\frac{20053408}{6677011} a^{5} - \\frac{2210432}{607001} a^{4} + \\frac{218886967}{6677011} a^{3} + \\frac{24029000}{607001} a^{2} - \\frac{813005282}{6677011} a - \\frac{1212663736}{6677011} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/6677011*a^7 + 1978847/6677011*a^6 - 2504903/6677011*a^5 - 268966/607001*a^4 - 817213/6677011*a^3 - 148351/607001*a^2 - 2048216/6677011*a - 2208823/6677011']}
Number field data - 8.0.15890703125.3