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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [5, -20, 40, -40, 24, -4, -4, 0, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 655360000, 'disc_rad': 10, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[4, 2]]], [5, [0]], [7, [[4, 2]]], [11, [[4, 2]]], [13, [[4, 1], [2, 1], [1, 2]]], [17, [[4, 1], [2, 1], [1, 2]]], [19, [[2, 4]]], [23, [[4, 2]]], [29, [[2, 4]]], [31, [[4, 2]]], [37, [[4, 1], [2, 1], [1, 2]]], [41, [[2, 4]]], [43, [[4, 2]]], [47, [[4, 2]]], [53, [[4, 1], [2, 1], [1, 2]]], [59, [[2, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [80, 24], 'galois_label': '8T19', 'galt': 19, 'grd': 18.914832180063517, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 4, 'label': '8.0.655360000.4', 'local_algs': ['2.8.20.76', '5.2.1.2', '5.2.0.1', '5.4.3.1'], 'monogenic': 0, 'num_ram': 2, 'r2': 4, 'ramps': [2, 5], 'rd': 12.6491106407, 'regulator': {'__RealLiteral__': 0, 'data': '46.063440043', 'prec': 40}, 'res': {'sib': ['1,-8,36,-108,228,-340,348,-188,-61,228,-204,68,36,-52,28,-8,1', '1,0,-10,0,59,0,-140,0,166,0,-110,0,44,0,-10,0,1', '1,8,0,-40,204,-312,368,-460,691,-712,408,-76,-36,16,4,-4,1', '61,-212,188,176,-354,52,28,368,-503,220,-88,104,-28,-8,-4,0,1']}, 'subfield_mults': [1, 1], 'subfields': ['1.0.1', '5.0.-4.0.1'], 'torsion_gen': '\\( -\\frac{152}{439} a^{7} - \\frac{128}{439} a^{6} + \\frac{454}{439} a^{5} + \\frac{921}{439} a^{4} - \\frac{2780}{439} a^{3} + \\frac{3970}{439} a^{2} - \\frac{3430}{439} a + \\frac{1122}{439} \\)', 'torsion_order': 4, 'units': ['\\( \\frac{33}{439} a^{7} + \\frac{74}{439} a^{6} - \\frac{139}{439} a^{5} - \\frac{457}{439} a^{4} + \\frac{592}{439} a^{3} + \\frac{819}{439} a^{2} - \\frac{1872}{439} a + \\frac{929}{439} \\)', '\\( \\frac{94}{439} a^{7} + \\frac{264}{439} a^{6} - \\frac{223}{439} a^{5} - \\frac{1488}{439} a^{4} + \\frac{356}{439} a^{3} + \\frac{1854}{439} a^{2} - \\frac{2419}{439} a + \\frac{2899}{439} \\)', '\\( \\frac{346}{439} a^{7} - \\frac{9}{439} a^{6} - \\frac{1484}{439} a^{5} - \\frac{1386}{439} a^{4} + \\frac{8708}{439} a^{3} - \\frac{13323}{439} a^{2} + \\frac{12140}{439} a - \\frac{4853}{439} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/439*a^7 - 184/439*a^6 + 49/439*a^5 + 199/439*a^4 - 155/439*a^3 - 55/439*a^2 + 63/439*a - 198/439']}