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{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [13, 50, 58, 20, 16, 2, -8, -1, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 29182547241, 'disc_rad': 2109, 'disc_sign': 1, 'frobs': [[2, [[6, 1], [2, 1]]], [3, [0]], [5, [[6, 1], [2, 1]]], [7, [[3, 2], [1, 2]]], [11, [[6, 1], [2, 1]]], [13, [[3, 2], [1, 2]]], [17, [[4, 2]]], [19, [0]], [23, [[6, 1], [2, 1]]], [29, [[6, 1], [2, 1]]], [31, [[3, 2], [1, 2]]], [37, [0]], [41, [[6, 1], [2, 1]]], [43, [[3, 2], [1, 2]]], [47, [[6, 1], [2, 1]]], [53, [[4, 2]]], [59, [[6, 1], [2, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [144, 48, 48], 'galois_label': '8T33', 'galt': 33, 'grd': 137.77155003846042, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.0.29182547241.1', 'local_algs': ['3.2.1.2', '3.6.9.10', '19.2.0.1', '19.2.0.1', '19.4.2.1', '37.2.0.1', '37.2.1.2', '37.2.1.2', '37.2.0.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 4, 'ramps': [3, 19, 37], 'rd': 20.330141419, 'regulator': {'__RealLiteral__': 0, 'data': '277.34579999', 'prec': 40}, 'res': {}, 'subfield_mults': [1], 'subfields': ['1.-1.1'], 'torsion_gen': '\\( -\\frac{361}{2517} a^{7} + \\frac{515}{2517} a^{6} + \\frac{915}{839} a^{5} - \\frac{2144}{2517} a^{4} - \\frac{5210}{2517} a^{3} - \\frac{1452}{839} a^{2} - \\frac{18013}{2517} a - \\frac{7291}{2517} \\)', 'torsion_order': 6, 'units': ['\\( \\frac{196}{2517} a^{7} - \\frac{182}{2517} a^{6} - \\frac{527}{839} a^{5} + \\frac{1178}{2517} a^{4} + \\frac{2501}{2517} a^{3} + \\frac{707}{839} a^{2} + \\frac{10261}{2517} a + \\frac{4600}{2517} \\)', '\\( \\frac{205}{2517} a^{7} + \\frac{349}{2517} a^{6} - \\frac{838}{839} a^{5} - \\frac{4444}{2517} a^{4} + \\frac{7637}{2517} a^{3} + \\frac{7002}{839} a^{2} + \\frac{13750}{2517} a + \\frac{2962}{2517} \\)', '\\( \\frac{1704}{839} a^{7} - \\frac{2661}{839} a^{6} - \\frac{12204}{839} a^{5} + \\frac{10327}{839} a^{4} + \\frac{21829}{839} a^{3} + \\frac{21556}{839} a^{2} + \\frac{86708}{839} a + \\frac{37218}{839} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/3*a^6 - 1/3*a^3 + 1/3', '1/2517*a^7 + 59/2517*a^6 - 221/839*a^5 + 494/2517*a^4 - 548/2517*a^3 - 326/839*a^2 - 731/2517*a - 1021/2517']}