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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [3, 18, 31, 12, -18, -14, 3, 0, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 32788343808, 'disc_rad': 66, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[8, 1]]], [7, [[4, 1], [2, 2]]], [11, [0]], [13, [[6, 1], [2, 1]]], [17, [[4, 1], [3, 1], [1, 1]]], [19, [[8, 1]]], [23, [[4, 2]]], [29, [[2, 3], [1, 2]]], [31, [[4, 1], [3, 1], [1, 1]]], [37, [[4, 1], [2, 1], [1, 2]]], [41, [[3, 1], [2, 1], [1, 3]]], [43, [[4, 1], [2, 2]]], [47, [[6, 1], [2, 1]]], [53, [[8, 1]]], [59, [[6, 1], [2, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [2160, 1376, 576], 'galois_label': '8T47', 'galt': 47, 'grd': 45.18792679018611, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 3, 'label': '8.4.32788343808.3', 'local_algs': ['2.4.6.7', '2.4.4.4', '3.2.1.2', '3.6.6.6', '11.2.1.1', '11.6.3.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 2, 'ramps': [2, 3, 11], 'rd': 20.62837107, 'regulator': {'__RealLiteral__': 0, 'data': '660.647993664', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-8.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{12} a^{7} + \\frac{1}{4} a^{6} - \\frac{1}{6} a^{5} - \\frac{1}{3} a^{4} - \\frac{13}{2} a^{3} + \\frac{13}{6} a^{2} + \\frac{43}{4} a + \\frac{15}{4} \\)', '\\( \\frac{5}{6} a^{7} - \\frac{1}{2} a^{6} + 3 a^{5} - \\frac{40}{3} a^{4} - 6 a^{3} + 12 a^{2} + \\frac{31}{2} a + \\frac{7}{2} \\)', '\\( \\frac{5}{6} a^{7} + \\frac{8}{3} a^{5} - \\frac{34}{3} a^{4} - 14 a^{3} + \\frac{28}{3} a^{2} + \\frac{41}{2} a + 8 \\)', '\\( \\frac{1}{3} a^{7} - \\frac{1}{2} a^{6} + \\frac{4}{3} a^{5} - \\frac{19}{3} a^{4} + 2 a^{3} + \\frac{23}{3} a^{2} - \\frac{1}{2} \\)', '\\( \\frac{1}{4} a^{7} + \\frac{1}{12} a^{6} + \\frac{5}{6} a^{5} - 3 a^{4} - \\frac{29}{6} a^{3} + \\frac{13}{6} a^{2} + \\frac{29}{4} a + \\frac{13}{4} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', '1/3*a^5 - 1/3*a^2', '1/6*a^6 + 1/3*a^3 - 1/2', '1/12*a^7 - 1/12*a^6 - 1/6*a^5 - 1/3*a^4 - 1/6*a^3 + 1/6*a^2 - 1/4*a - 1/4']}
Number field data - 8.4.32788343808.3