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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -4, 3, 12, -2, -20, 2, 16, -1, -4, 1], 'conductor': 0, 'degree': 10, 'dirichlet_group': [], 'disc_abs': 512000000000, 'disc_rad': 10, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[8, 1], [2, 1]]], [5, [0]], [7, [[8, 1], [2, 1]]], [11, [[4, 2], [2, 1]]], [13, [[5, 1], [4, 1], [1, 1]]], [17, [[5, 1], [4, 1], [1, 1]]], [19, [[10, 1]]], [23, [[8, 1], [2, 1]]], [29, [[5, 1], [2, 2], [1, 1]]], [31, [[4, 2], [2, 1]]], [37, [[4, 1], [2, 2], [1, 2]]], [41, [[4, 2], [1, 2]]], [43, [[8, 1], [2, 1]]], [47, [[8, 1], [2, 1]]], [53, [[4, 1], [2, 2], [1, 2]]], [59, [[10, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [1600, 1240], 'galois_label': '10T33', 'galt': 33, 'grd': 48.468937332853066, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '10.0.512000000000.1', 'local_algs': ['2.2.2.1', '2.8.16.69', '5.1.0.1', '5.4.2.2', '5.5.7.3'], 'monogenic': 0, 'num_ram': 2, 'r2': 5, 'ramps': [2, 5], 'rd': 14.8226889821, 'regulator': {'__RealLiteral__': 0, 'data': '382.919458552', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['1.0.1'], 'torsion_gen': '\\( -\\frac{249}{530} a^{9} + \\frac{843}{530} a^{8} + \\frac{85}{53} a^{7} - \\frac{1932}{265} a^{6} - \\frac{1318}{265} a^{5} + \\frac{2274}{265} a^{4} + \\frac{1327}{265} a^{3} - \\frac{296}{53} a^{2} - \\frac{1857}{530} a + \\frac{717}{530} \\)', 'torsion_order': 4, 'units': ['\\( \\frac{153}{530} a^{9} - \\frac{601}{530} a^{8} - \\frac{12}{53} a^{7} + \\frac{1069}{265} a^{6} + \\frac{216}{265} a^{5} - \\frac{1078}{265} a^{4} - \\frac{14}{265} a^{3} + \\frac{111}{53} a^{2} + \\frac{279}{530} a - \\frac{249}{530} \\)', '\\( \\frac{1}{2} a^{9} - \\frac{5}{2} a^{8} + 2 a^{7} + 6 a^{6} - 5 a^{5} - 5 a^{4} + 4 a^{3} + 2 a^{2} - \\frac{1}{2} a - \\frac{1}{2} \\)', '\\( \\frac{387}{530} a^{9} - \\frac{1489}{530} a^{8} - \\frac{74}{53} a^{7} + \\frac{3156}{265} a^{6} + \\frac{1279}{265} a^{5} - \\frac{3927}{265} a^{4} - \\frac{2701}{265} a^{3} + \\frac{181}{53} a^{2} + \\frac{1641}{530} a - \\frac{661}{530} \\)', '\\( \\frac{282}{53} a^{9} - \\frac{1009}{53} a^{8} - \\frac{720}{53} a^{7} + \\frac{4242}{53} a^{6} + \\frac{2433}{53} a^{5} - \\frac{4827}{53} a^{4} - \\frac{2818}{53} a^{3} + \\frac{2420}{53} a^{2} + \\frac{2098}{53} a - \\frac{328}{53} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', '1/2*a^8 - 1/2', '1/530*a^9 + 3/530*a^8 + 2/53*a^7 + 78/265*a^6 + 17/265*a^5 + 109/265*a^4 - 33/265*a^3 + 8/53*a^2 + 33/530*a + 227/530']}
Number field data - 10.0.512000000000.1