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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -1, 6, -12, 19, -17, 16, -10, 6, -2, 1], 'conductor': 0, 'degree': 10, 'dirichlet_group': [], 'disc_abs': 19911454263, 'disc_rad': 3477, 'disc_sign': -1, 'frobs': [[2, [[8, 1], [2, 1]]], [3, [0]], [5, [[4, 2], [2, 1]]], [7, [[4, 1], [2, 2], [1, 2]]], [11, [[8, 1], [2, 1]]], [13, [[4, 2], [1, 2]]], [17, [[8, 1], [2, 1]]], [19, [0]], [23, [[8, 1], [2, 1]]], [29, [[8, 1], [2, 1]]], [31, [[5, 1], [4, 1], [1, 1]]], [37, [[4, 1], [2, 2], [1, 2]]], [41, [[10, 1]]], [43, [[4, 1], [2, 2], [1, 2]]], [47, [[10, 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': [400, 400, 600], 'galois_label': '10T33', 'galt': 33, 'grd': 164.7914989407143, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '10.0.19911454263.1', 'local_algs': ['3.10.5.2', '19.1.0.1', '19.1.0.1', '19.4.0.1', '19.4.2.2', '61.1.0.1', '61.4.3.2', '61.5.0.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [3, 19, 61], 'rd': 10.7129800968, 'regulator': {'__RealLiteral__': 0, 'data': '32.6108769459', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['1.-1.1'], 'torsion_gen': '\\( \\frac{3}{11} a^{9} - \\frac{5}{11} a^{8} + \\frac{20}{11} a^{7} - \\frac{27}{11} a^{6} + \\frac{50}{11} a^{5} - \\frac{49}{11} a^{4} + \\frac{59}{11} a^{3} - \\frac{31}{11} a^{2} + \\frac{26}{11} a + \\frac{2}{11} \\)', 'torsion_order': 6, 'units': ['\\( a \\)', '\\( \\frac{2}{11} a^{9} - \\frac{7}{11} a^{8} + \\frac{17}{11} a^{7} - \\frac{40}{11} a^{6} + \\frac{59}{11} a^{5} - \\frac{84}{11} a^{4} + \\frac{87}{11} a^{3} - \\frac{83}{11} a^{2} + \\frac{43}{11} a - \\frac{17}{11} \\)', '\\( \\frac{2}{11} a^{9} - \\frac{7}{11} a^{8} + \\frac{17}{11} a^{7} - \\frac{40}{11} a^{6} + \\frac{59}{11} a^{5} - \\frac{84}{11} a^{4} + \\frac{87}{11} a^{3} - \\frac{83}{11} a^{2} + \\frac{32}{11} a - \\frac{17}{11} \\)', '\\( \\frac{2}{11} a^{9} + \\frac{4}{11} a^{8} + \\frac{6}{11} a^{7} + \\frac{15}{11} a^{6} - \\frac{7}{11} a^{5} + \\frac{37}{11} a^{4} - \\frac{12}{11} a^{3} + \\frac{60}{11} a^{2} - \\frac{1}{11} a + \\frac{16}{11} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', '1/11*a^9 + 2/11*a^8 + 3/11*a^7 + 2/11*a^6 + 2/11*a^5 + 2/11*a^4 + 5/11*a^3 - 3/11*a^2 + 5/11*a - 3/11']}
Number field data - 10.0.19911454263.1