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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [11, -39, 57, -55, 42, -23, 11, -3, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 240945152, 'disc_rad': 14, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[8, 1]]], [5, [[8, 1]]], [7, [0]], [11, [[4, 1], [1, 4]]], [13, [[8, 1]]], [17, [[4, 2]]], [19, [[8, 1]]], [23, [[2, 4]]], [29, [[4, 1], [1, 4]]], [31, [[2, 4]]], [37, [[4, 1], [1, 4]]], [41, [[2, 4]]], [43, [[4, 1], [2, 2]]], [47, [[2, 4]]], [53, [[4, 1], [1, 4]]], [59, [[8, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [88, 24], 'galois_label': '8T17', 'galt': 17, 'grd': 28.950496621601552, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.0.240945152.1', 'local_algs': ['2.4.11.9', '2.4.0.1', '7.8.6.1'], 'monogenic': 0, 'num_ram': 2, 'r2': 4, 'ramps': [2, 7], 'rd': 11.1619423227, 'regulator': {'__RealLiteral__': 0, 'data': '11.22690469', 'prec': 37}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['2.-1.1', '1.1.0.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{7}{11} a^{7} - \\frac{13}{11} a^{6} + \\frac{59}{11} a^{5} - \\frac{92}{11} a^{4} + \\frac{181}{11} a^{3} - \\frac{186}{11} a^{2} + \\frac{199}{11} a - 8 \\)', '\\( \\frac{3}{11} a^{7} - \\frac{4}{11} a^{6} + \\frac{19}{11} a^{5} - \\frac{30}{11} a^{4} + \\frac{54}{11} a^{3} - \\frac{64}{11} a^{2} + \\frac{68}{11} a - 3 \\)', '\\( \\frac{1}{11} a^{7} - \\frac{5}{11} a^{6} + \\frac{10}{11} a^{5} - \\frac{21}{11} a^{4} + \\frac{18}{11} a^{3} - \\frac{3}{11} a^{2} - \\frac{25}{11} a + 2 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/11*a^7 - 5/11*a^6 - 1/11*a^5 + 1/11*a^4 - 4/11*a^3 - 3/11*a^2 - 3/11*a']}
Number field data - 8.0.240945152.1