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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-9, 36, -12, 15, -14, 0, 2, -3, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 4709390625, 'disc_rad': 915, 'disc_sign': 1, 'frobs': [[2, [[4, 2]]], [3, [0]], [5, [0]], [7, [[4, 2]]], [11, [[4, 2]]], [13, [[4, 2]]], [17, [[4, 2]]], [19, [[2, 4]]], [23, [[4, 2]]], [29, [[2, 2], [1, 4]]], [31, [[2, 2], [1, 4]]], [37, [[4, 2]]], [41, [[2, 4]]], [43, [[4, 2]]], [47, [[4, 2]]], [53, [[4, 2]]], [59, [[2, 2], [1, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [16, 24, 16], 'galois_label': '8T20', 'galt': 20, 'grd': 45.23275582376457, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 2, 'label': '8.4.4709390625.2', 'local_algs': ['3.4.2.2', '3.4.2.2', '5.4.3.1', '5.4.3.1', '61.1.0.1', '61.1.0.1', '61.2.1.1', '61.2.1.2', '61.2.0.1'], 'minimal_sibling': [5, 10, 50, 10, -1, 4, -5, -1, 1], 'monogenic': 0, 'num_ram': 3, 'r2': 2, 'ramps': [3, 5, 61], 'rd': 16.185293879, 'regulator': {'__RealLiteral__': 0, 'data': '84.8366562454', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.-1.1', '1.4.-4.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{61}{1416} a^{7} - \\frac{49}{354} a^{6} + \\frac{49}{708} a^{5} + \\frac{65}{708} a^{4} - \\frac{233}{354} a^{3} + \\frac{1427}{1416} a^{2} - \\frac{81}{472} a + \\frac{285}{472} \\)', '\\( \\frac{25}{472} a^{7} - \\frac{19}{177} a^{6} - \\frac{7}{236} a^{5} - \\frac{11}{708} a^{4} - \\frac{51}{118} a^{3} + \\frac{265}{1416} a^{2} - \\frac{235}{472} a + \\frac{451}{472} \\)', '\\( \\frac{89}{1416} a^{7} - \\frac{113}{708} a^{6} + \\frac{43}{354} a^{5} - \\frac{7}{177} a^{4} - \\frac{677}{708} a^{3} + \\frac{401}{1416} a^{2} - \\frac{389}{472} a + \\frac{263}{472} \\)', '\\( \\frac{29}{354} a^{7} - \\frac{79}{708} a^{6} - \\frac{49}{708} a^{5} - \\frac{65}{708} a^{4} - \\frac{773}{708} a^{3} - \\frac{625}{708} a^{2} - \\frac{130}{59} a + \\frac{123}{236} \\)', '\\( \\frac{55}{1416} a^{7} - \\frac{10}{177} a^{6} + \\frac{79}{708} a^{5} - \\frac{71}{708} a^{4} - \\frac{65}{354} a^{3} + \\frac{37}{1416} a^{2} - \\frac{15}{472} a + \\frac{79}{472} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', '1/2*a^5 - 1/2*a^3 - 1/2*a - 1/2', '1/12*a^6 - 1/4*a^5 - 1/12*a^4 - 1/4*a^3 + 1/12*a^2 - 1/4', '1/1416*a^7 + 5/354*a^6 - 5/708*a^5 - 115/708*a^4 - 73/177*a^3 - 673/1416*a^2 - 129/472*a - 123/472']}
Number field data - 8.4.4709390625.2