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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -3, 13, -1, -15, 14, -2, -3, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 2790703125, 'disc_rad': 105, 'disc_sign': 1, 'frobs': [[2, [[8, 1]]], [3, [0]], [5, [0]], [7, [0]], [11, [[4, 1], [2, 1], [1, 2]]], [13, [[8, 1]]], [17, [[4, 1], [2, 2]]], [19, [[3, 1], [2, 2], [1, 1]]], [23, [[4, 1], [2, 2]]], [29, [[3, 2], [1, 2]]], [31, [[4, 2]]], [37, [[8, 1]]], [41, [[3, 2], [1, 2]]], [43, [[4, 1], [2, 2]]], [47, [[4, 1], [2, 2]]], [53, [[8, 1]]], [59, [[4, 1], [2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [800, 504, 288], 'galois_label': '8T46', 'galt': 46, 'grd': 49.75264603559782, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.4.2790703125.1', 'local_algs': ['3.2.0.1', '3.6.6.1', '5.8.7.2', '7.4.0.1', '7.4.2.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 2, 'ramps': [3, 5, 7], 'rd': 15.1605237405, 'regulator': {'__RealLiteral__': 0, 'data': '55.6162254124', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{9} a^{7} - \\frac{1}{9} a^{6} - \\frac{7}{9} a^{5} + a^{4} + a^{3} - \\frac{22}{9} a^{2} + \\frac{5}{9} a + \\frac{4}{9} \\)', '\\( a \\)', '\\( \\frac{1}{9} a^{7} - \\frac{4}{9} a^{6} + \\frac{2}{9} a^{5} + \\frac{5}{3} a^{4} - \\frac{10}{3} a^{3} + \\frac{14}{9} a^{2} + \\frac{2}{9} a + \\frac{4}{9} \\)', '\\( \\frac{2}{3} a^{7} - 2 a^{6} - a^{5} + \\frac{26}{3} a^{4} - \\frac{32}{3} a^{3} + 2 a^{2} + 5 a - \\frac{2}{3} \\)', '\\( \\frac{1}{9} a^{7} - \\frac{1}{9} a^{6} - \\frac{7}{9} a^{5} + a^{4} + a^{3} - \\frac{31}{9} a^{2} + \\frac{23}{9} a + \\frac{4}{9} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', '1/3*a^5 + 1/3*a^3 + 1/3*a^2 + 1/3', '1/3*a^6 + 1/3*a^4 + 1/3*a^3 + 1/3*a', '1/9*a^7 - 1/9*a^6 - 1/9*a^5 - 1/3*a^3 + 2/9*a^2 - 4/9*a + 1/9']}