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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 2, 1, 1, -2, 0, 1, -2, -1, -1, 1], 'conductor': 0, 'degree': 10, 'dirichlet_group': [], 'disc_abs': 3196989667, 'disc_rad': 43794379, 'disc_sign': -1, 'frobs': [[2, [[10, 1]]], [3, [[10, 1]]], [5, [[10, 1]]], [7, [[5, 1], [3, 1], [2, 1]]], [11, [[10, 1]]], [13, [[7, 1], [3, 1]]], [17, [[10, 1]]], [19, [[10, 1]]], [23, [[5, 2]]], [29, [0]], [31, [[3, 2], [2, 2]]], [37, [[5, 1], [4, 1], [1, 1]]], [41, [[4, 2], [2, 1]]], [43, [[4, 1], [3, 1], [2, 1], [1, 1]]], [47, [[3, 1], [2, 2], [1, 3]]], [53, [[7, 1], [1, 3]]], [59, [[6, 1], [4, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [1814400, 2419200, 1814400, 1814400], 'galois_label': '10T45', 'galt': 45, 'grd': 13528.915874373493, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '10.4.3196989667.1', 'local_algs': ['29.2.1.2', '29.4.0.1', '29.4.0.1', '73.1.0.1', '73.2.0.1', '73.3.2.1', '73.4.0.1', '137.2.0.1', '137.2.1.1', '137.2.0.1', '137.4.0.1', '151.2.0.1', '151.2.1.2', '151.6.0.1'], 'monogenic': 0, 'num_ram': 4, 'r2': 3, 'ramps': [29, 73, 137, 151], 'rd': 8.92224456239, 'regulator': {'__RealLiteral__': 0, 'data': '4.898963260479714', 'prec': 57}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{25}{71} a^{9} - \\frac{22}{71} a^{8} - \\frac{39}{71} a^{7} - \\frac{49}{71} a^{6} + \\frac{39}{71} a^{5} - \\frac{1}{71} a^{4} + \\frac{1}{71} a^{3} + \\frac{45}{71} a^{2} + \\frac{73}{71} a + \\frac{19}{71} \\)', '\\( a^{9} - a^{8} - a^{7} - 2 a^{6} + a^{5} - 2 a^{3} + a^{2} + a + 2 \\)', '\\( \\frac{9}{71} a^{9} - \\frac{42}{71} a^{8} + \\frac{3}{71} a^{7} + \\frac{42}{71} a^{6} + \\frac{68}{71} a^{5} + \\frac{11}{71} a^{4} - \\frac{11}{71} a^{3} + \\frac{73}{71} a^{2} + \\frac{49}{71} a + \\frac{4}{71} \\)', '\\( \\frac{67}{71} a^{9} - \\frac{76}{71} a^{8} - \\frac{25}{71} a^{7} - \\frac{137}{71} a^{6} + \\frac{25}{71} a^{5} - \\frac{68}{71} a^{4} - \\frac{145}{71} a^{3} + \\frac{78}{71} a^{2} - \\frac{6}{71} a + \\frac{85}{71} \\)', '\\( \\frac{36}{71} a^{9} - \\frac{26}{71} a^{8} - \\frac{59}{71} a^{7} - \\frac{45}{71} a^{6} - \\frac{12}{71} a^{5} + \\frac{44}{71} a^{4} - \\frac{115}{71} a^{3} + \\frac{8}{71} a^{2} + \\frac{54}{71} a + \\frac{16}{71} \\)', '\\( \\frac{86}{71} a^{9} - \\frac{70}{71} a^{8} - \\frac{66}{71} a^{7} - \\frac{214}{71} a^{6} - \\frac{5}{71} a^{5} - \\frac{29}{71} a^{4} - \\frac{184}{71} a^{3} + \\frac{27}{71} a^{2} + \\frac{58}{71} a + \\frac{196}{71} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', '1/71*a^9 + 19/71*a^8 + 24/71*a^7 - 19/71*a^6 - 24/71*a^5 + 17/71*a^4 - 17/71*a^3 + 16/71*a^2 - 34/71*a + 32/71']}
Number field data - 10.4.3196989667.1