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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [3, 9, 15, 15, 13, 6, 0, -2, -3, 0, 1], 'conductor': 0, 'degree': 10, 'dirichlet_group': [], 'disc_abs': 13202588763, 'disc_rad': 273, 'disc_sign': -1, 'frobs': [[2, [[10, 1]]], [3, [0]], [5, [[10, 1]]], [7, [0]], [11, [[10, 1]]], [13, [0]], [17, [[10, 1]]], [19, [[4, 1], [3, 1], [2, 1], [1, 1]]], [23, [[10, 1]]], [29, [[6, 1], [2, 2]]], [31, [[3, 2], [2, 2]]], [37, [[5, 1], [3, 1], [1, 2]]], [41, [[10, 1]]], [43, [[5, 1], [2, 2], [1, 1]]], [47, [[6, 1], [2, 2]]], [53, [[10, 1]]], [59, [[10, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [30000, 7200, 9600], 'galois_label': '10T41', 'galt': 41, 'grd': 144.2714961265473, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '10.0.13202588763.1', 'local_algs': ['3.4.3.1', '3.6.10.8', '7.2.1.2', '7.2.1.2', '7.3.0.1', '7.3.0.1', '13.2.0.1', '13.2.0.1', '13.3.0.1', '13.3.2.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [3, 7, 13], 'rd': 10.2817232425, 'regulator': {'__RealLiteral__': 0, 'data': '36.6660471848', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['1.-1.1'], 'torsion_gen': '\\( -\\frac{4}{7} a^{9} + \\frac{4}{7} a^{8} + \\frac{9}{7} a^{7} - \\frac{2}{7} a^{6} - \\frac{2}{7} a^{5} - \\frac{18}{7} a^{4} - \\frac{30}{7} a^{3} - \\frac{29}{7} a^{2} - \\frac{27}{7} a - 1 \\)', 'torsion_order': 6, 'units': ['\\( \\frac{3}{49} a^{9} + \\frac{16}{49} a^{8} - \\frac{38}{49} a^{7} - \\frac{29}{49} a^{6} + \\frac{25}{49} a^{5} + \\frac{37}{49} a^{4} + \\frac{122}{49} a^{3} + \\frac{75}{49} a^{2} + \\frac{53}{49} a + \\frac{32}{49} \\)', '\\( \\frac{11}{49} a^{9} + \\frac{12}{49} a^{8} - \\frac{60}{49} a^{7} - \\frac{34}{49} a^{6} + \\frac{52}{49} a^{5} + \\frac{47}{49} a^{4} + \\frac{172}{49} a^{3} + \\frac{219}{49} a^{2} + \\frac{150}{49} a + \\frac{80}{49} \\)', '\\( \\frac{32}{49} a^{9} - \\frac{44}{49} a^{8} - \\frac{60}{49} a^{7} + \\frac{43}{49} a^{6} - \\frac{4}{49} a^{5} + \\frac{173}{49} a^{4} + \\frac{172}{49} a^{3} + \\frac{121}{49} a^{2} + \\frac{136}{49} a - \\frac{46}{49} \\)', '\\( \\frac{15}{49} a^{9} - \\frac{4}{49} a^{8} - \\frac{57}{49} a^{7} - \\frac{5}{49} a^{6} + \\frac{34}{49} a^{5} + \\frac{94}{49} a^{4} + \\frac{134}{49} a^{3} + \\frac{137}{49} a^{2} + \\frac{97}{49} a + \\frac{34}{49} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', '1/7*a^8 - 1/7*a^7 + 3/7*a^6 - 3/7*a^5 - 3/7*a^4 + 1/7*a^3 - 3/7*a^2 + 2/7*a - 2/7', '1/49*a^9 + 3/49*a^8 + 6/49*a^7 + 16/49*a^6 - 1/49*a^5 + 3/49*a^4 + 22/49*a^3 - 17/49*a^2 + 13/49*a - 1/49']}
Number field data - 10.0.13202588763.1