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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 0, 7, -12, 29, -22, 5, 10, -5, -2, 1], 'conductor': 0, 'degree': 10, 'dirichlet_group': [], 'disc_abs': 80561164032, 'disc_rad': 654, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [[10, 1]]], [7, [[5, 1], [2, 2], [1, 1]]], [11, [[8, 1], [2, 1]]], [13, [[5, 1], [4, 1], [1, 1]]], [17, [[8, 1], [2, 1]]], [19, [[4, 1], [2, 2], [1, 2]]], [23, [[8, 1], [2, 1]]], [29, [[4, 2], [2, 1]]], [31, [[4, 2], [1, 2]]], [37, [[4, 1], [2, 2], [1, 2]]], [41, [[8, 1], [2, 1]]], [43, [[4, 2], [1, 2]]], [47, [[8, 1], [2, 1]]], [53, [[8, 1], [2, 1]]], [59, [[8, 1], [2, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [1200, 400, 600], 'galois_label': '10T33', 'galt': 33, 'grd': 165.26294753304504, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '10.0.80561164032.1', 'local_algs': ['2.2.0.1', '2.8.8.5', '3.2.1.2', '3.8.4.1', '109.1.0.1', '109.1.0.1', '109.4.3.3', '109.4.0.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 3, 109], 'rd': 12.3200529188, 'regulator': {'__RealLiteral__': 0, 'data': '85.4450012777', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['1.-1.1'], 'torsion_gen': '\\( -\\frac{3}{176} a^{9} - \\frac{31}{176} a^{8} + \\frac{51}{88} a^{7} + \\frac{43}{44} a^{6} - \\frac{475}{176} a^{5} - \\frac{219}{176} a^{4} + \\frac{227}{44} a^{3} - \\frac{11}{2} a^{2} + \\frac{243}{176} a + \\frac{5}{176} \\)', 'torsion_order': 6, 'units': ['\\( \\frac{37}{176} a^{9} - \\frac{87}{176} a^{8} - \\frac{101}{88} a^{7} + \\frac{115}{44} a^{6} + \\frac{285}{176} a^{5} - \\frac{995}{176} a^{4} + \\frac{251}{44} a^{3} - \\frac{3}{2} a^{2} + \\frac{171}{176} a - \\frac{3}{176} \\)', '\\( \\frac{17}{176} a^{9} - \\frac{59}{176} a^{8} - \\frac{25}{88} a^{7} + \\frac{79}{44} a^{6} - \\frac{95}{176} a^{5} - \\frac{607}{176} a^{4} + \\frac{261}{44} a^{3} - 4 a^{2} - \\frac{57}{176} a + \\frac{1}{176} \\)', '\\( \\frac{37}{176} a^{9} - \\frac{87}{176} a^{8} - \\frac{101}{88} a^{7} + \\frac{115}{44} a^{6} + \\frac{285}{176} a^{5} - \\frac{995}{176} a^{4} + \\frac{251}{44} a^{3} - \\frac{3}{2} a^{2} + \\frac{171}{176} a - \\frac{179}{176} \\)', '\\( \\frac{171}{176} a^{9} - \\frac{257}{176} a^{8} - \\frac{531}{88} a^{7} + \\frac{321}{44} a^{6} + \\frac{1995}{176} a^{5} - \\frac{3269}{176} a^{4} + \\frac{591}{44} a^{3} + \\frac{5}{2} a^{2} + \\frac{493}{176} a - \\frac{21}{176} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', '1/2*a^5 - 1/2*a^4 - 1/2*a^3 - 1/2*a^2 - 1/2*a - 1/2', '1/2*a^6 - 1/2', '1/2*a^7 - 1/2*a', '1/2*a^8 - 1/2*a^2', '1/176*a^9 - 19/176*a^8 - 17/88*a^7 - 7/44*a^6 + 41/176*a^5 + 73/176*a^4 - 17/44*a^3 - 81/176*a - 31/176']}
Number field data - 10.0.80561164032.1