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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-2, 8, -16, 24, -31, 38, -43, 44, -40, 30, -20, 10, -4, 1], 'conductor': 0, 'degree': 13, 'dirichlet_group': [], 'disc_abs': 29747917088000, 'disc_rad': 9296224090, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[8, 1], [5, 1]]], [5, [0]], [7, [[11, 1], [2, 1]]], [11, [[8, 1], [3, 1], [2, 1]]], [13, [[9, 1], [4, 1]]], [17, [[10, 1], [3, 1]]], [19, [[13, 1]]], [23, [[8, 1], [3, 1], [2, 1]]], [29, [[13, 1]]], [31, [[8, 1], [4, 1], [1, 1]]], [37, [[12, 1], [1, 1]]], [41, [[8, 1], [5, 1]]], [43, [[6, 2], [1, 1]]], [47, [[8, 1], [5, 1]]], [53, [[8, 1], [5, 1]]], [59, [[13, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [12454041600, 4670265600, 3113510400, 3113510400], 'galois_label': '13T9', 'galt': 9, 'grd': 407793.9577709422, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '13.1.29747917088000.1', 'local_algs': ['2.4.8.2', '2.4.0.1', '2.5.0.1', '5.4.3.2', '5.9.0.1', '139.1.0.1', '139.1.0.1', '139.2.1.1', '139.4.0.1', '139.5.0.1', 'm6687931.1.1.0', 'm6687931.1.2.0', 'm6687931.2.1.1', 'm6687931.1.8.0'], 'monogenic': 1, 'num_ram': 4, 'r2': 6, 'ramps': [2, 5, 139, 6687931], 'rd': 10.8747613641, 'regulator': {'__RealLiteral__': 0, 'data': '36.4190725607', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 4 a^{12} - 12 a^{11} + 27 a^{10} - 51 a^{9} + 66 a^{8} - 89 a^{7} + 84 a^{6} - 83 a^{5} + 67 a^{4} - 54 a^{3} + 39 a^{2} - 23 a + 9 \\)', '\\( 16 a^{12} - 52 a^{11} + 120 a^{10} - 227 a^{9} + 304 a^{8} - 402 a^{7} + 391 a^{6} - 381 a^{5} + 310 a^{4} - 253 a^{3} + 185 a^{2} - 110 a + 41 \\)', '\\( 6 a^{12} - 20 a^{11} + 48 a^{10} - 92 a^{9} + 126 a^{8} - 169 a^{7} + 167 a^{6} - 165 a^{5} + 135 a^{4} - 110 a^{3} + 82 a^{2} - 50 a + 19 \\)', '\\( 6 a^{12} - 20 a^{11} + 47 a^{10} - 89 a^{9} + 121 a^{8} - 160 a^{7} + 156 a^{6} - 153 a^{5} + 123 a^{4} - 102 a^{3} + 75 a^{2} - 45 a + 17 \\)', '\\( 10 a^{12} - 33 a^{11} + 76 a^{10} - 143 a^{9} + 192 a^{8} - 252 a^{7} + 245 a^{6} - 238 a^{5} + 193 a^{4} - 159 a^{3} + 116 a^{2} - 68 a + 25 \\)', '\\( 5 a^{12} - 17 a^{11} + 40 a^{10} - 76 a^{9} + 104 a^{8} - 137 a^{7} + 136 a^{6} - 132 a^{5} + 108 a^{4} - 89 a^{3} + 65 a^{2} - 40 a + 15 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11', 'a^12']}