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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [4, 0, 32, 0, 20, 0, 8, 0, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 1474560000, 'disc_rad': 30, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[6, 1], [2, 1]]], [11, [[4, 2]]], [13, [[3, 2], [1, 2]]], [17, [[4, 2]]], [19, [[6, 1], [2, 1]]], [23, [[4, 2]]], [29, [[4, 2]]], [31, [[6, 1], [2, 1]]], [37, [[2, 4]]], [41, [[4, 2]]], [43, [[6, 1], [2, 1]]], [47, [[2, 4]]], [53, [[4, 2]]], [59, [[2, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [112, 24, 32], 'galois_label': '8T24', 'galt': 24, 'grd': 25.523718929317052, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 7, 'label': '8.0.1474560000.7', 'local_algs': ['2.1.8.18c1.2', '3.2.1.0a1.1', '3.2.1.0a1.1', '3.2.2.2a1.2', '5.1.1.0a1.1', '5.1.1.0a1.1', '5.1.3.2a1.1', '5.1.3.2a1.1'], 'maximal_cm_subfield': [1, 0, 1], 'minimal_sibling': [4, 0, 8, 0, 2, 0, 1], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 3, 'r2': 4, 'ramps': [2, 3, 5], 'rd': 13.9985420463, 'regulator': {'__RealLiteral__': 0, 'data': '110.474043132', 'prec': 44}, 'res': {'sib': ['4,0,8,0,2,0,1', '-27,0,7,0,1,0,1', '1,0,-2,0,-9,0,-28,0,-9,0,-2,0,1', '1,0,2,0,-9,0,28,0,-9,0,2,0,1', '1,8,56,192,324,88,-528,-876,-5,928,1080,-1088,-620,-144,1624,-1208,459,-752,1272,-1184,692,-272,72,-12,1', '16,0,0,0,48,0,0,0,96,0,0,0,152,0,0,0,156,0,0,0,-12,0,0,0,1', '36,0,0,0,28,0,0,0,8,0,0,0,1', '4,0,0,0,-12,0,0,0,12,0,0,0,1', '5,-60,300,-944,2596,-5548,8288,-9504,10205,-10476,8836,-5652,2530,-456,-152,-36,99,-40,64,-68,30,-12,8,-4,1', '60,-160,160,-144,104,-48,20,-32,2,-12,4,0,1', '81,0,0,0,342,0,0,0,2791,0,0,0,-1092,0,0,0,151,0,0,0,-18,0,0,0,1', '9,-72,288,-744,1372,-1860,1828,-1172,273,336,-428,228,-38,-28,24,-8,1', '9,0,-36,0,10,0,4,0,1', '9,0,-39,0,76,0,-69,0,34,0,-9,0,1']}, 'subfield_mults': [1, 1], 'subfields': ['1.0.1', '2.-4.-4.0.1'], 'torsion_gen': '\\( -\\frac{1}{8} a^{7} - a^{5} - \\frac{9}{4} a^{3} - 3 a \\)', 'torsion_order': 4, 'units': ['\\( \\frac{1}{8} a^{5} + \\frac{1}{2} a^{3} + \\frac{1}{2} a^{2} + \\frac{1}{4} a \\)', '\\( \\frac{1}{4} a^{7} + \\frac{1}{8} a^{6} + \\frac{15}{8} a^{5} + \\frac{3}{4} a^{4} + \\frac{9}{2} a^{3} + \\frac{7}{4} a^{2} + \\frac{27}{4} a + \\frac{5}{2} \\)', '\\( \\frac{1}{8} a^{7} - \\frac{1}{8} a^{6} + \\frac{3}{4} a^{5} - \\frac{3}{8} a^{4} + \\frac{1}{4} a^{3} + \\frac{5}{4} a^{2} - a - \\frac{3}{4} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/8*a^4 - 1/2*a^3 - 1/2*a^2 - 1/2*a + 1/4', '1/8*a^5 - 1/2*a^3 - 1/2*a^2 + 1/4*a', '1/8*a^6 - 1/2*a^3 + 1/4*a^2', '1/8*a^7 + 1/4*a^3']}
Number field data - 8.0.1474560000.7