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{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [76, 4, -55, -29, 34, 11, -10, -1, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 558140625, 'disc_rad': 105, 'disc_sign': 1, 'frobs': [[2, [[2, 4]]], [3, [0]], [5, [0]], [7, [0]], [11, [[4, 2]]], [13, [[4, 2]]], [17, [[4, 2]]], [19, [[2, 2], [1, 4]]], [23, [[2, 4]]], [29, [[4, 2]]], [31, [[2, 2], [1, 4]]], [37, [[4, 2]]], [41, [[2, 4]]], [43, [[4, 2]]], [47, [[4, 2]]], [53, [[2, 4]]], [59, [[2, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12, 12, 8], 'galois_label': '8T11', 'galt': 11, 'grd': 20.165893269373882, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.0.558140625.1', 'local_algs': ['3.8.6.1', '5.8.6.1', '7.4.2.2', '7.4.0.1'], 'monogenic': -1, 'num_ram': 3, 'r2': 4, 'ramps': [3, 5, 7], 'rd': 12.3977522757, 'regulator': {'__RealLiteral__': 0, 'data': '31.3606243426', 'prec': 44}, 'res': {'gal': ['256,0,720,0,769,0,735,0,606,0,315,0,94,0,15,0,1'], 'sib': ['-20,-80,-25,55,16,-1,-4,-1,1', '16,-60,82,-45,24,-15,13,0,1', '256,0,720,0,769,0,735,0,606,0,315,0,94,0,15,0,1']}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['1.-1.1', '-1.-1.1', '4.-1.1', '1.1.2.-1.1'], 'torsion_gen': '\\( \\frac{1}{4} a^{5} - \\frac{5}{4} a^{3} + \\frac{5}{4} a + \\frac{5}{2} \\)', 'torsion_order': 6, 'units': ['\\( \\frac{1}{8} a^{7} - \\frac{7}{8} a^{5} + \\frac{17}{8} a^{3} + a^{2} - 2 a - 2 \\)', '\\( \\frac{1}{8} a^{7} - \\frac{3}{8} a^{6} - \\frac{1}{8} a^{5} + \\frac{17}{8} a^{4} - \\frac{17}{8} a^{3} - \\frac{19}{8} a^{2} + \\frac{1}{4} a + 7 \\)', '\\( \\frac{1}{4} a^{5} - \\frac{1}{2} a^{4} - \\frac{3}{4} a^{3} + \\frac{5}{2} a^{2} - \\frac{7}{4} a + \\frac{1}{2} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/2*a^3 - 1/2*a^2 - 1/2*a', '1/2*a^4 - 1/2*a', '1/4*a^5 - 1/4*a^3 + 1/4*a - 1/2', '1/8*a^6 + 1/8*a^4 - 3/8*a^2 - 1/2*a - 1/2', '1/8*a^7 - 1/8*a^5 - 1/8*a^3 - 1/2*a^2 + 1/4*a - 1/2']}