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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-17, -3, 6, 12, -6, 12, -12, 6, -3, 1], 'conductor': 0, 'degree': 9, 'dirichlet_group': [], 'disc_abs': 58773123072, 'disc_rad': 6, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[4, 1], [2, 2], [1, 1]]], [7, [[6, 1], [3, 1]]], [11, [[4, 1], [3, 1], [2, 1]]], [13, [[9, 1]]], [17, [[4, 1], [2, 2], [1, 1]]], [19, [[6, 1], [3, 1]]], [23, [[4, 1], [3, 1], [2, 1]]], [29, [[6, 1], [1, 3]]], [31, [[3, 1], [2, 1], [1, 4]]], [37, [[9, 1]]], [41, [[3, 1], [2, 3]]], [43, [[3, 2], [2, 1], [1, 1]]], [47, [[4, 1], [3, 1], [2, 1]]], [53, [[6, 1], [3, 1]]], [59, [[4, 1], [3, 1], [2, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [3024, 2328], 'galois_label': '9T31', 'galt': 31, 'grd': 36.26222647513864, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '9.1.58773123072.1', 'local_algs': ['2.3.2.1', '2.6.10.5', '3.9.15.20'], 'monogenic': 0, 'num_ram': 2, 'r2': 4, 'ramps': [2, 3], 'rd': 15.7244483653, 'regulator': {'__RealLiteral__': 0, 'data': '224.186932991', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-2.0.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{167}{1721} a^{8} - \\frac{887}{3442} a^{7} + \\frac{1611}{3442} a^{6} - \\frac{3139}{3442} a^{5} + \\frac{2819}{3442} a^{4} - \\frac{1729}{3442} a^{3} + \\frac{3727}{3442} a^{2} + \\frac{613}{3442} a - \\frac{2919}{3442} \\)', '\\( \\frac{173}{3442} a^{8} - \\frac{681}{3442} a^{7} + \\frac{1427}{3442} a^{6} - \\frac{2507}{3442} a^{5} + \\frac{4155}{3442} a^{4} - \\frac{3745}{3442} a^{3} + \\frac{3265}{3442} a^{2} - \\frac{3243}{3442} a - \\frac{99}{1721} \\)', '\\( \\frac{549}{3442} a^{8} - \\frac{649}{3442} a^{7} + \\frac{1365}{3442} a^{6} - \\frac{2743}{3442} a^{5} - \\frac{483}{3442} a^{4} - \\frac{683}{3442} a^{3} + \\frac{7337}{3442} a^{2} + \\frac{9525}{3442} a + \\frac{8450}{1721} \\)', '\\( \\frac{57}{3442} a^{8} - \\frac{105}{3442} a^{7} + \\frac{311}{3442} a^{6} + \\frac{129}{3442} a^{5} - \\frac{163}{3442} a^{4} - \\frac{259}{3442} a^{3} - \\frac{2605}{3442} a^{2} - \\frac{4033}{3442} a - \\frac{1107}{1721} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/2*a^6 - 1/2*a^4 - 1/2*a^2 - 1/2', '1/2*a^7 - 1/2*a^5 - 1/2*a^3 - 1/2*a', '1/3442*a^8 - 183/3442*a^7 + 247/3442*a^6 - 1447/3442*a^5 + 601/3442*a^4 + 237/3442*a^3 + 377/3442*a^2 - 735/3442*a - 110/1721']}