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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [12, 38, -43, -7, 13, -8, 5, -3, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 109957989152, 'disc_rad': 1606, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[4, 1], [3, 1], [1, 1]]], [5, [[8, 1]]], [7, [[4, 2]]], [11, [0]], [13, [[8, 1]]], [17, [[6, 1], [2, 1]]], [19, [[4, 1], [3, 1], [1, 1]]], [23, [[4, 1], [2, 1], [1, 2]]], [29, [[4, 1], [2, 2]]], [31, [[6, 1], [2, 1]]], [37, [[4, 1], [3, 1], [1, 1]]], [41, [[4, 2]]], [43, [[8, 1]]], [47, [[6, 1], [2, 1]]], [53, [[8, 1]]], [59, [[4, 1], [2, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [2304, 576, 576], 'galois_label': '8T47', 'galt': 47, 'grd': 113.34901852243803, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.4.109957989152.1', 'local_algs': ['2.1.2.2a1.2', '2.1.2.3a1.2', '2.2.1.0a1.1', '2.2.1.0a1.1', '11.4.1.0a1.1', '11.2.2.2a1.2', '73.4.2.4a1.2'], 'monogenic': -1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 3, 'r2': 2, 'ramps': [2, 11, 73], 'rd': 23.9968009238, 'regulator': {'__RealLiteral__': 0, 'data': '1952.88263128', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-18.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{99}{3632} a^{7} - \\frac{21}{454} a^{6} + \\frac{111}{3632} a^{5} + \\frac{13}{3632} a^{4} - \\frac{201}{1816} a^{3} + \\frac{269}{3632} a^{2} - \\frac{1513}{1816} a - \\frac{967}{908} \\)', '\\( \\frac{99}{3632} a^{7} - \\frac{21}{454} a^{6} + \\frac{111}{3632} a^{5} + \\frac{13}{3632} a^{4} - \\frac{201}{1816} a^{3} + \\frac{269}{3632} a^{2} + \\frac{303}{1816} a - \\frac{59}{908} \\)', '\\( \\frac{357}{3632} a^{7} - \\frac{117}{454} a^{6} + \\frac{1721}{3632} a^{5} - \\frac{3365}{3632} a^{4} + \\frac{2577}{1816} a^{3} - \\frac{4533}{3632} a^{2} - \\frac{5511}{1816} a - \\frac{653}{908} \\)', '\\( \\frac{269}{3632} a^{7} - \\frac{87}{227} a^{6} + \\frac{2833}{3632} a^{5} - \\frac{4789}{3632} a^{4} + \\frac{2453}{1816} a^{3} - \\frac{3965}{3632} a^{2} - \\frac{6083}{1816} a + \\frac{4343}{908} \\)', '\\( \\frac{155}{3632} a^{7} - \\frac{13}{227} a^{6} - \\frac{1257}{3632} a^{5} + \\frac{4221}{3632} a^{4} - \\frac{1773}{1816} a^{3} - \\frac{4715}{3632} a^{2} + \\frac{2483}{1816} a + \\frac{889}{908} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', '1/2*a^5 - 1/2*a^4 - 1/2*a^2 - 1/2*a', '1/2*a^6 - 1/2*a^4 - 1/2*a^3 - 1/2*a', '1/3632*a^7 - 69/454*a^6 - 219/3632*a^5 + 367/3632*a^4 + 53/1816*a^3 + 1727/3632*a^2 - 107/1816*a - 129/908']}
Number field data - 8.4.109957989152.1