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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -3, 8, -15, 21, -15, 8, -3, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 67815225, 'disc_rad': 915, 'disc_sign': 1, 'frobs': [[2, [[4, 2]]], [3, [0]], [5, [0]], [7, [[4, 1], [2, 1], [1, 2]]], [11, [[4, 2]]], [13, [[4, 2]]], [17, [[4, 2]]], [19, [[2, 4]]], [23, [[4, 2]]], [29, [[4, 2]]], [31, [[2, 4]]], [37, [[4, 1], [2, 1], [1, 2]]], [41, [[2, 4]]], [43, [[4, 1], [2, 1], [1, 2]]], [47, [[4, 2]]], [53, [[4, 2]]], [59, [[4, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [48, 32, 32], 'galois_label': '8T29', 'galt': 29, 'grd': 39.809879288004915, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.0.67815225.1', 'local_algs': ['3.4.3.1', '3.4.3.1', '5.4.0.1', '5.4.2.2', '61.1.0.1', '61.1.0.1', '61.1.0.1', '61.1.0.1', '61.4.2.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 4, 'ramps': [3, 5, 61], 'rd': 9.52611677304, 'regulator': {'__RealLiteral__': 0, 'data': '17.7886602463', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.-1.1', '3.3.-2.-2.1'], 'torsion_gen': '\\( -\\frac{3}{5} a^{7} + \\frac{6}{5} a^{6} - \\frac{16}{5} a^{5} + \\frac{24}{5} a^{4} - 5 a^{3} - \\frac{3}{5} a^{2} + \\frac{2}{5} a + \\frac{1}{5} \\)', 'torsion_order': 6, 'units': ['\\( \\frac{4}{5} a^{7} - 3 a^{6} + \\frac{38}{5} a^{5} - \\frac{76}{5} a^{4} + \\frac{108}{5} a^{3} - 17 a^{2} + \\frac{29}{5} a - 2 \\)', '\\( a^{7} - \\frac{16}{5} a^{6} + 8 a^{5} - \\frac{77}{5} a^{4} + \\frac{104}{5} a^{3} - \\frac{72}{5} a^{2} + 5 a - \\frac{16}{5} \\)', '\\( \\frac{2}{5} a^{7} - \\frac{4}{5} a^{6} + \\frac{9}{5} a^{5} - \\frac{11}{5} a^{4} + a^{3} + \\frac{22}{5} a^{2} - \\frac{23}{5} a + \\frac{11}{5} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/5*a^6 + 2/5*a^4 + 1/5*a^3 + 2/5*a^2 + 1/5', '1/5*a^7 + 2/5*a^5 + 1/5*a^4 + 2/5*a^3 + 1/5*a']}