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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -3, 2, 2, -1, -2, -1, 2, 2, 0, 1, -2, -1, 1], 'conductor': 0, 'degree': 13, 'dirichlet_group': [], 'disc_abs': 4082190012125, 'disc_rad': 163287600485, 'disc_sign': 1, 'frobs': [[2, [[7, 1], [6, 1]]], [3, [[10, 1], [3, 1]]], [5, [0]], [7, [[13, 1]]], [11, [[8, 1], [3, 1], [2, 1]]], [13, [[7, 1], [4, 1], [2, 1]]], [17, [[11, 1], [2, 1]]], [19, [[7, 1], [4, 1], [2, 1]]], [23, [[11, 1], [2, 1]]], [29, [[7, 1], [2, 3]]], [31, [[7, 1], [2, 2], [1, 2]]], [37, [[12, 1], [1, 1]]], [41, [[12, 1], [1, 1]]], [43, [[7, 1], [6, 1]]], [47, [[5, 1], [4, 1], [2, 2]]], [53, [[9, 1], [4, 1]]], [59, [[8, 1], [3, 1], [2, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [4670265600, 3113510400, 3113510400], 'galois_label': '13T9', 'galt': 9, 'grd': 604253.4026112618, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '13.1.4082190012125.1', 'local_algs': ['5.3.0.1', '5.4.3.1', '5.6.0.1', '73.1.0.1', '73.2.1.2', '73.10.0.1', 'm447363289.1.1.0', 'm447363289.1.1.0', 'm447363289.1.2.0', 'm447363289.2.1.1', 'm447363289.1.3.0', 'm447363289.1.4.0'], 'monogenic': 0, 'num_ram': 3, 'r2': 6, 'ramps': [5, 73, 447363289], 'rd': 9.33401960871, 'regulator': {'__RealLiteral__': 0, 'data': '6.75913142567', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( \\frac{250}{143} a^{12} - \\frac{152}{143} a^{11} - \\frac{547}{143} a^{10} + \\frac{31}{143} a^{9} + \\frac{3}{143} a^{8} + \\frac{36}{11} a^{7} + \\frac{656}{143} a^{6} - \\frac{2}{143} a^{5} - \\frac{431}{143} a^{4} - \\frac{324}{143} a^{3} + \\frac{381}{143} a^{2} + \\frac{66}{13} a - \\frac{486}{143} \\)', '\\( \\frac{259}{143} a^{12} + \\frac{29}{143} a^{11} - \\frac{589}{143} a^{10} - \\frac{370}{143} a^{9} - \\frac{248}{143} a^{8} + \\frac{27}{11} a^{7} + \\frac{1064}{143} a^{6} + \\frac{785}{143} a^{5} + \\frac{70}{143} a^{4} - \\frac{529}{143} a^{3} - \\frac{179}{143} a^{2} + \\frac{43}{13} a - \\frac{150}{143} \\)', '\\( \\frac{72}{143} a^{12} - \\frac{125}{143} a^{11} - \\frac{193}{143} a^{10} + \\frac{224}{143} a^{9} + \\frac{137}{143} a^{8} + \\frac{16}{11} a^{7} + \\frac{118}{143} a^{6} - \\frac{425}{143} a^{5} - \\frac{425}{143} a^{4} - \\frac{67}{143} a^{3} + \\frac{382}{143} a^{2} + \\frac{24}{13} a - \\frac{315}{143} \\)', '\\( \\frac{265}{143} a^{12} - \\frac{184}{143} a^{11} - \\frac{617}{143} a^{10} + \\frac{30}{143} a^{9} + \\frac{109}{143} a^{8} + \\frac{54}{11} a^{7} + \\frac{764}{143} a^{6} - \\frac{25}{143} a^{5} - \\frac{740}{143} a^{4} - \\frac{761}{143} a^{3} + \\frac{258}{143} a^{2} + \\frac{58}{13} a - \\frac{498}{143} \\)', '\\( \\frac{34}{11} a^{12} - \\frac{8}{11} a^{11} - \\frac{78}{11} a^{10} - \\frac{25}{11} a^{9} - \\frac{12}{11} a^{8} + \\frac{64}{11} a^{7} + \\frac{126}{11} a^{6} + \\frac{52}{11} a^{5} - \\frac{47}{11} a^{4} - \\frac{79}{11} a^{3} + \\frac{5}{11} a^{2} + 7 a - \\frac{36}{11} \\)'], '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', '1/143*a^12 + 36/143*a^11 + 43/143*a^10 + 19/143*a^9 - 12/143*a^8 - 1/11*a^7 - 50/143*a^6 + 8/143*a^5 + 8/143*a^4 + 9/143*a^3 + 49/143*a^2 - 4/13*a - 58/143']}