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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [15, -90, 60, 21, -33, 6, -7, 6, -3, 1], 'conductor': 0, 'degree': 9, 'dirichlet_group': [], 'disc_abs': 1228034671875, 'disc_rad': 165, 'disc_sign': -1, 'frobs': [[2, [[6, 1], [3, 1]]], [3, [0]], [5, [0]], [7, [[6, 1], [3, 1]]], [11, [0]], [13, [[2, 3], [1, 3]]], [17, [[6, 1], [3, 1]]], [19, [[6, 1], [3, 1]]], [23, [[2, 4], [1, 1]]], [29, [[2, 3], [1, 3]]], [31, [[3, 3]]], [37, [[3, 3]]], [41, [[6, 1], [3, 1]]], [43, [[6, 1], [3, 1]]], [47, [[2, 4], [1, 1]]], [53, [[2, 4], [1, 1]]], [59, [[2, 4], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [42, 24, 18], 'galois_label': '9T8', 'galt': 8, 'grd': 34.93959039247001, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '9.3.1228034671875.1', 'local_algs': ['3.3.3.2', '3.6.7.4', '5.3.2.1', '5.6.4.1', '11.1.0.1', '11.2.0.1', '11.2.1.1', '11.4.2.1'], 'minimal_sibling': [5, 0, 0, -3, 0, 0, 1], 'monogenic': 0, 'num_ram': 3, 'r2': 3, 'ramps': [3, 5, 11], 'rd': 22.0417273207, 'regulator': {'__RealLiteral__': 0, 'data': '882.852795167', 'prec': 44}, 'res': {'sib': ['27,-81,54,81,-18,117,-374,450,-138,-162,402,-567,589,-423,237,-108,39,-9,1', '3,-216,-15333,63723,-112080,108918,-60182,12057,10968,-13382,7257,-1494,-669,579,-186,25,9,-6,1', '3375,0,0,2700,0,0,3605,0,0,-56,0,0,198,0,0,-28,0,0,1', '5,0,0,-3,0,0,1', '9,9,-3,0,19,23,25,5,7,-1,4,-1,1']}, 'subfield_mults': [1, 1], 'subfields': ['-15.-15.0.1', '-5.0.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{4377}{58474} a^{8} - \\frac{6179}{29237} a^{7} + \\frac{11993}{29237} a^{6} - \\frac{27111}{58474} a^{5} + \\frac{21955}{58474} a^{4} - \\frac{75846}{29237} a^{3} + \\frac{65929}{58474} a^{2} + \\frac{277483}{58474} a - \\frac{362987}{58474} \\)', '\\( \\frac{1251}{116948} a^{8} + \\frac{112}{29237} a^{7} + \\frac{1467}{58474} a^{6} - \\frac{587}{116948} a^{5} - \\frac{1383}{116948} a^{4} - \\frac{9729}{29237} a^{3} - \\frac{89269}{116948} a^{2} + \\frac{15257}{116948} a + \\frac{54097}{116948} \\)', '\\( \\frac{1429}{116948} a^{8} - \\frac{3381}{58474} a^{7} + \\frac{2739}{29237} a^{6} - \\frac{6391}{116948} a^{5} + \\frac{6467}{116948} a^{4} - \\frac{20463}{58474} a^{3} + \\frac{31247}{116948} a^{2} + \\frac{187115}{116948} a - \\frac{297359}{116948} \\)', '\\( \\frac{6031}{116948} a^{8} - \\frac{4323}{29237} a^{7} + \\frac{16489}{58474} a^{6} - \\frac{35355}{116948} a^{5} + \\frac{39305}{116948} a^{4} - \\frac{55543}{29237} a^{3} + \\frac{146843}{116948} a^{2} + \\frac{290205}{116948} a - \\frac{412643}{116948} \\)', '\\( \\frac{567}{58474} a^{8} - \\frac{881}{58474} a^{7} + \\frac{3417}{58474} a^{6} + \\frac{409}{29237} a^{5} + \\frac{9793}{58474} a^{4} - \\frac{13933}{58474} a^{3} + \\frac{7300}{29237} a^{2} + \\frac{11769}{58474} a + \\frac{1249}{29237} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/26*a^7 + 7/26*a^6 - 1/26*a^5 - 5/13*a^4 + 9/26*a^3 - 5/26*a^2 + 3/13*a + 11/26', '1/116948*a^8 + 72/29237*a^7 - 16567/58474*a^6 - 52265/116948*a^5 - 5869/116948*a^4 + 11577/29237*a^3 + 26629/116948*a^2 + 30531/116948*a - 3617/116948']}