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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 3, 5, 7, 1, 5, 0, -4, -1, 1], 'conductor': 0, 'degree': 9, 'dirichlet_group': [], 'disc_abs': 37653424128, 'disc_rad': 366, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[6, 1], [3, 1]]], [7, [[4, 1], [2, 2], [1, 1]]], [11, [[6, 1], [2, 1], [1, 1]]], [13, [[4, 1], [2, 2], [1, 1]]], [17, [[6, 1], [3, 1]]], [19, [[4, 1], [2, 2], [1, 1]]], [23, [[6, 1], [3, 1]]], [29, [[4, 1], [3, 1], [2, 1]]], [31, [[4, 1], [2, 2], [1, 1]]], [37, [[9, 1]]], [41, [[6, 1], [2, 1], [1, 1]]], [43, [[9, 1]]], [47, [[4, 1], [3, 1], [2, 1]]], [53, [[2, 4], [1, 1]]], [59, [[4, 1], [3, 1], [2, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [2376, 972, 648], 'galois_label': '9T31', 'galt': 31, 'grd': 63.44452992285394, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '9.1.37653424128.1', 'local_algs': ['2.3.2.1', '2.6.9.1', '3.2.1.1', '3.3.0.1', '3.4.3.2', '61.2.1.2', '61.3.0.1', '61.4.2.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 4, 'ramps': [2, 3, 61], 'rd': 14.9654364217, 'regulator': {'__RealLiteral__': 0, 'data': '140.669792451', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['19.-7.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( \\frac{4}{3} a^{8} - \\frac{5}{3} a^{7} - 5 a^{6} + \\frac{5}{3} a^{5} + 7 a^{4} - \\frac{4}{3} a^{3} + \\frac{23}{3} a^{2} + \\frac{13}{3} a + 1 \\)', '\\( \\frac{1}{3} a^{7} - \\frac{2}{3} a^{6} - a^{5} + \\frac{5}{3} a^{4} + a^{3} - \\frac{7}{3} a^{2} + \\frac{8}{3} a + \\frac{4}{3} \\)', '\\( 3 a^{8} - 2 a^{7} - 15 a^{6} - 3 a^{5} + 23 a^{4} + 10 a^{3} + 12 a^{2} + 19 a + 6 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/3*a^7 + 1/3*a^6 - 1/3*a^4 - 1/3*a^2 - 1/3*a + 1/3', '1/3*a^8 - 1/3*a^6 - 1/3*a^5 + 1/3*a^4 - 1/3*a^3 - 1/3*a - 1/3']}