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{'class_group': [], 'class_number': 1, 'cm': True, 'coeffs': [1, -2, 5, -11, 25, 1, 12, 2, 9, -4, 3, -1, 1], 'conductor': 35, 'degree': 12, 'dirichlet_group': [32, 1, 2, 4, 8, 9, 11, 16, 18, 22, 23, 29], 'disc_abs': 11259376953125, 'disc_rad': 35, 'disc_sign': 1, 'frobs': [[2, [[12, 1]]], [3, [[12, 1]]], [5, [0]], [7, [0]], [11, [[3, 4]]], [13, [[4, 3]]], [17, [[12, 1]]], [19, [[6, 2]]], [23, [[12, 1]]], [29, [[2, 6]]], [31, [[3, 4]]], [37, [[12, 1]]], [41, [[1, 12]]], [43, [[4, 3]]], [47, [[12, 1]]], [53, [[12, 1]]], [59, [[6, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [9, 8], 'galois_label': '12T1', 'galt': 1, 'grd': 12.235626082613623, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.0.11259376953125.1', 'local_algs': ['5.12.9.2', '7.12.8.1'], 'monogenic': 0, 'num_ram': 2, 'r2': 6, 'ramps': [5, 7], 'rd': 12.2356260826, 'regulator': {'__RealLiteral__': 0, 'data': '104.882003477', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-1.-1.1', '1.-2.-1.1', '1.-1.1.-1.1', '-1.-2.7.2.-7.-1.1'], 'torsion_gen': '\\( \\frac{14}{181} a^{11} - \\frac{42}{181} a^{10} + \\frac{56}{181} a^{9} - \\frac{126}{181} a^{8} + \\frac{193}{181} a^{7} - \\frac{168}{181} a^{6} - \\frac{14}{181} a^{5} - \\frac{350}{181} a^{4} + \\frac{154}{181} a^{3} - \\frac{980}{181} a^{2} + \\frac{28}{181} a - \\frac{14}{181} \\)', 'torsion_order': 10, 'units': ['\\( \\frac{9}{181} a^{11} + \\frac{155}{181} a^{6} - \\frac{404}{181} a + 1 \\)', '\\( \\frac{28}{181} a^{11} - \\frac{84}{181} a^{10} + \\frac{112}{181} a^{9} - \\frac{252}{181} a^{8} + \\frac{386}{181} a^{7} - \\frac{336}{181} a^{6} - \\frac{28}{181} a^{5} - \\frac{700}{181} a^{4} + \\frac{308}{181} a^{3} - \\frac{1779}{181} a^{2} + \\frac{56}{181} a - \\frac{28}{181} \\)', '\\( \\frac{9}{181} a^{11} - \\frac{27}{181} a^{10} + \\frac{36}{181} a^{9} - \\frac{81}{181} a^{8} + \\frac{137}{181} a^{7} - \\frac{108}{181} a^{6} - \\frac{9}{181} a^{5} - \\frac{225}{181} a^{4} + \\frac{99}{181} a^{3} - \\frac{449}{181} a^{2} + \\frac{18}{181} a - \\frac{9}{181} \\)', '\\( \\frac{88}{181} a^{11} - \\frac{74}{181} a^{10} + \\frac{241}{181} a^{9} - \\frac{316}{181} a^{8} + \\frac{711}{181} a^{7} + \\frac{313}{181} a^{6} + \\frac{1014}{181} a^{5} + \\frac{168}{181} a^{4} + \\frac{1975}{181} a^{3} - \\frac{869}{181} a^{2} - \\frac{9}{181} a - \\frac{302}{181} \\)', '\\( \\frac{88}{181} a^{11} - \\frac{70}{181} a^{10} + \\frac{241}{181} a^{9} - \\frac{316}{181} a^{8} + \\frac{711}{181} a^{7} + \\frac{313}{181} a^{6} + \\frac{1103}{181} a^{5} + \\frac{168}{181} a^{4} + \\frac{1975}{181} a^{3} - \\frac{869}{181} a^{2} - \\frac{9}{181} a - \\frac{381}{181} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', '1/181*a^9 + 43/181*a^8 + 39/181*a^7 + 48/181*a^6 + 73/181*a^5 + 39/181*a^4 + 48/181*a^3 + 73/181*a^2 + 62/181*a - 49/181', '1/181*a^10 - 23/181*a^5 - 65/181', '1/181*a^11 - 23/181*a^6 - 65/181*a']}