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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [2, 4, -2, 16, 28, -12, 34, -12, 11, -2, 1], 'conductor': 0, 'degree': 10, 'dirichlet_group': [], 'disc_abs': 327680000000, 'disc_rad': 10, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[8, 1], [2, 1]]], [5, [0]], [7, [[8, 1], [2, 1]]], [11, [[10, 1]]], [13, [[5, 1], [4, 1], [1, 1]]], [17, [[4, 1], [2, 2], [1, 2]]], [19, [[4, 2], [2, 1]]], [23, [[8, 1], [2, 1]]], [29, [[5, 2]]], [31, [[4, 2], [2, 1]]], [37, [[5, 1], [4, 1], [1, 1]]], [41, [[4, 2], [1, 2]]], [43, [[8, 1], [2, 1]]], [47, [[8, 1], [2, 1]]], [53, [[4, 1], [2, 2], [1, 2]]], [59, [[4, 2], [2, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [2300, 920], 'galois_label': '10T33', 'galt': 33, 'grd': 46.69568412632977, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '10.0.327680000000.1', 'local_algs': ['2.2.2.1', '2.8.20.103', '5.1.0.1', '5.4.2.2', '5.5.5.4'], 'monogenic': 0, 'num_ram': 2, 'r2': 5, 'ramps': [2, 5], 'rd': 14.1757156617, 'regulator': {'__RealLiteral__': 0, 'data': '303.206408045', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['1.0.1'], 'torsion_gen': '\\( \\frac{7}{8} a^{9} - \\frac{17}{8} a^{8} + \\frac{41}{4} a^{7} - \\frac{59}{4} a^{6} + \\frac{69}{2} a^{5} - 26 a^{4} + \\frac{67}{2} a^{3} - \\frac{7}{2} a^{2} - \\frac{9}{4} a + \\frac{15}{4} \\)', 'torsion_order': 4, 'units': ['\\( \\frac{1}{4} a^{9} - \\frac{3}{4} a^{8} + \\frac{7}{2} a^{7} - \\frac{11}{2} a^{6} + 12 a^{5} - 8 a^{4} + 9 a^{3} + 3 a^{2} - \\frac{5}{2} a - \\frac{1}{2} \\)', '\\( \\frac{1}{4} a^{9} - \\frac{3}{4} a^{8} + \\frac{7}{2} a^{7} - \\frac{13}{2} a^{6} + 14 a^{5} - 15 a^{4} + 15 a^{3} - 6 a^{2} - \\frac{7}{2} a + \\frac{3}{2} \\)', '\\( \\frac{1}{8} a^{9} - \\frac{7}{8} a^{8} + \\frac{11}{4} a^{7} - \\frac{29}{4} a^{6} + \\frac{23}{2} a^{5} - 15 a^{4} + \\frac{23}{2} a^{3} - \\frac{9}{2} a^{2} - \\frac{3}{4} a + \\frac{9}{4} \\)', '\\( \\frac{1}{4} a^{9} - \\frac{3}{4} a^{8} + \\frac{7}{2} a^{7} - \\frac{11}{2} a^{6} + 13 a^{5} - 10 a^{4} + 14 a^{3} - a^{2} - \\frac{1}{2} a + \\frac{3}{2} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', '1/8*a^9 + 1/8*a^8 - 1/4*a^7 - 1/4*a^6 - 1/2*a^5 - 1/2*a^3 - 1/2*a^2 + 1/4*a + 1/4']}
Number field data - 10.0.327680000000.1