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{'class_group': [13], 'class_number': 13, 'cm': True, 'coeffs': [2401, -2058, 2107, -1757, 1513, -351, 266, -62, 41, -6, 7, -1, 1], 'conductor': 95, 'degree': 12, 'dirichlet_group': [64, 1, 68, 39, 11, 77, 49, 83, 87, 7, 26, 58], 'disc_abs': 33171021564453125, 'disc_rad': 95, 'disc_sign': 1, 'frobs': [[2, [[12, 1]]], [3, [[12, 1]]], [5, [0]], [7, [[4, 3]]], [11, [[1, 12]]], [13, [[12, 1]]], [17, [[12, 1]]], [19, [0]], [23, [[12, 1]]], [29, [[6, 2]]], [31, [[1, 12]]], [37, [[4, 3]]], [41, [[3, 4]]], [43, [[12, 1]]], [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': 23.8083831956814, 'inessentialp': [11], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.0.33171021564453125.1', 'local_algs': ['5.12.9.2', '19.6.4.3', '19.6.4.3'], 'monogenic': -1, 'num_ram': 2, 'r2': 6, 'ramps': [5, 19], 'rd': 23.8083831957, 'regulator': {'__RealLiteral__': 0, 'data': '1234.55163261', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-1.-1.1', '7.-6.-1.1', '1.-1.1.-1.1', '-11.10.47.1.-16.-1.1'], 'torsion_gen': '\\( -\\frac{41}{360437} a^{11} - \\frac{33}{32767} a^{6} + \\frac{294302}{360437} a \\)', 'torsion_order': 10, 'units': ['\\( \\frac{83}{2523059} a^{11} + \\frac{204}{360437} a^{10} - \\frac{1224}{2523059} a^{9} + \\frac{8364}{2523059} a^{8} - \\frac{809}{360437} a^{7} + \\frac{8115}{360437} a^{6} - \\frac{71604}{2523059} a^{5} + \\frac{308652}{2523059} a^{4} - \\frac{51204}{360437} a^{3} + \\frac{2140312}{2523059} a^{2} - \\frac{354278}{360437} a + \\frac{9996}{51491} \\)', '\\( \\frac{82}{360437} a^{11} + \\frac{66}{32767} a^{6} - \\frac{228167}{360437} a \\)', '\\( \\frac{2092}{17661413} a^{11} - \\frac{2092}{17661413} a^{10} + \\frac{83}{2523059} a^{9} - \\frac{12552}{17661413} a^{8} + \\frac{85772}{17661413} a^{7} - \\frac{4184}{569723} a^{6} + \\frac{79496}{2523059} a^{5} - \\frac{858801}{17661413} a^{4} + \\frac{3165196}{17661413} a^{3} - \\frac{525092}{2523059} a^{2} + \\frac{89956}{360437} a - \\frac{12552}{51491} \\)', '\\( \\frac{5553}{2523059} a^{11} + \\frac{3029}{2523059} a^{10} + \\frac{5100}{360437} a^{9} + \\frac{13505}{2523059} a^{8} + \\frac{208080}{2523059} a^{7} - \\frac{30182}{2523059} a^{6} + \\frac{171861}{360437} a^{5} - \\frac{248880}{2523059} a^{4} + \\frac{6386361}{2523059} a^{3} + \\frac{1020}{51491} a^{2} + \\frac{79778}{32767} a - \\frac{89849}{51491} \\)', '\\( \\frac{249}{2523059} a^{11} - \\frac{326}{360437} a^{10} + \\frac{3174}{2523059} a^{9} - \\frac{21689}{2523059} a^{8} + \\frac{331}{360437} a^{7} - \\frac{11665}{360437} a^{6} + \\frac{75184}{2523059} a^{5} - \\frac{800377}{2523059} a^{4} + \\frac{132779}{360437} a^{3} - \\frac{3373366}{2523059} a^{2} - \\frac{32072}{360437} a - \\frac{98451}{51491} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', '1/360437*a^9 + 60066/360437*a^8 + 211/51491*a^7 - 1511/360437*a^6 + 70398/360437*a^5 - 60325/360437*a^4 - 8540/51491*a^3 - 20595/360437*a^2 - 39486/360437*a - 20301/51491', '1/2523059*a^10 - 1/2523059*a^9 - 52716/360437*a^8 + 307469/2523059*a^7 + 1511/2523059*a^6 - 10107/2523059*a^5 - 50229/360437*a^4 + 111271/2523059*a^3 + 1101906/2523059*a^2 - 53206/360437*a + 8828/51491', '1/17661413*a^11 - 1/17661413*a^10 + 1/2523059*a^9 - 6839769/17661413*a^8 + 2584889/17661413*a^7 - 1777/17661413*a^6 + 422222/2523059*a^5 - 2533406/17661413*a^4 + 2773982/17661413*a^3 + 236860/2523059*a^2 - 51204/360437*a - 10052/51491']}