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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 0, 6, 0, -10, -60, -130, -60, -10, 0, 6, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 40000000000000000, 'disc_rad': 10, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[3, 4]]], [5, [0]], [7, [[10, 1], [2, 1]]], [11, [[3, 4]]], [13, [[6, 2]]], [17, [[5, 2], [1, 2]]], [19, [[2, 6]]], [23, [[10, 1], [2, 1]]], [29, [[6, 2]]], [31, [[6, 2]]], [37, [[10, 1], [2, 1]]], [41, [[2, 6]]], [43, [[5, 2], [1, 2]]], [47, [[6, 2]]], [53, [[6, 2]]], [59, [[3, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [240, 192], 'galois_label': '12T76', 'galt': 76, 'grd': 52.53055608807534, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 4, 'label': '12.4.40000000000000000.4', 'local_algs': ['2.4.8.3', '2.4.4.1', '2.4.6.1', '5.1.0.1', '5.1.0.1', '5.5.8.6', '5.5.8.6'], 'minimal_sibling': [792, -1440, 380, 1000, -600, -224, 210, 0, -20, 0, 1], 'monogenic': -1, 'num_ram': 2, 'r2': 4, 'ramps': [2, 5], 'rd': 24.1827117512, 'regulator': {'__RealLiteral__': 0, 'data': '22656.4836805', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-7.6.-45.20.-5.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( \\frac{61}{128} a^{11} + \\frac{9}{640} a^{10} + \\frac{363}{128} a^{9} + \\frac{19}{128} a^{8} - \\frac{631}{128} a^{7} - \\frac{3627}{128} a^{6} - \\frac{8029}{128} a^{5} - \\frac{3777}{128} a^{4} - \\frac{811}{128} a^{3} - \\frac{691}{128} a^{2} + \\frac{131}{128} a - \\frac{41}{640} \\)', '\\( \\frac{397}{1280} a^{11} - \\frac{343}{1280} a^{10} + \\frac{455}{256} a^{9} - \\frac{357}{256} a^{8} - \\frac{955}{256} a^{7} - \\frac{3739}{256} a^{6} - \\frac{6193}{256} a^{5} + \\frac{4967}{256} a^{4} + \\frac{3105}{256} a^{3} - \\frac{3283}{256} a^{2} + \\frac{4667}{1280} a - \\frac{1153}{1280} \\)', '\\( \\frac{331}{1280} a^{11} - \\frac{329}{1280} a^{10} + \\frac{433}{256} a^{9} - \\frac{427}{256} a^{8} - \\frac{429}{256} a^{7} - \\frac{3525}{256} a^{6} - \\frac{4887}{256} a^{5} + \\frac{2633}{256} a^{4} + \\frac{503}{256} a^{3} + \\frac{1715}{256} a^{2} + \\frac{1661}{1280} a + \\frac{1041}{1280} \\)', '\\( \\frac{3}{32} a^{11} + \\frac{1}{32} a^{10} + \\frac{21}{32} a^{9} + \\frac{7}{32} a^{8} - \\frac{13}{32} a^{7} - \\frac{183}{32} a^{6} - \\frac{487}{32} a^{5} - \\frac{497}{32} a^{4} - \\frac{537}{32} a^{3} - \\frac{291}{32} a^{2} - \\frac{35}{32} a - \\frac{37}{32} \\)', '\\( \\frac{65}{64} a^{11} + \\frac{1}{64} a^{10} + \\frac{391}{64} a^{9} + \\frac{7}{64} a^{8} - \\frac{643}{64} a^{7} - \\frac{3903}{64} a^{6} - \\frac{8513}{64} a^{5} - \\frac{4093}{64} a^{4} - \\frac{903}{64} a^{3} - \\frac{263}{64} a^{2} + \\frac{127}{64} a - \\frac{193}{64} \\)', '\\( \\frac{641}{640} a^{11} - \\frac{383}{640} a^{10} + \\frac{763}{128} a^{9} - \\frac{485}{128} a^{8} - \\frac{1303}{128} a^{7} - \\frac{7091}{128} a^{6} - \\frac{11901}{128} a^{5} + \\frac{2807}{128} a^{4} + \\frac{5557}{128} a^{3} + \\frac{3541}{128} a^{2} + \\frac{5151}{640} a - \\frac{433}{640} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', '1/2*a^5 - 1/2*a^4 - 1/2*a^3 - 1/2*a^2 - 1/2*a - 1/2', '1/2*a^6 - 1/2', '1/4*a^7 - 1/4*a^5 - 1/4*a^4 + 1/4*a^3 + 1/4*a^2 - 1/4', '1/8*a^8 - 1/8*a^7 - 1/8*a^6 - 1/4*a^5 - 1/2*a^4 + 1/4*a^3 + 1/8*a^2 - 3/8*a - 1/8', '1/8*a^9 + 1/8*a^6 - 1/2*a^4 - 3/8*a^3 - 1/2*a + 1/8', '1/160*a^10 - 1/16*a^9 + 1/32*a^8 - 1/8*a^7 + 1/32*a^6 + 3/16*a^5 + 1/32*a^4 - 3/8*a^3 + 9/32*a^2 + 3/16*a - 79/160', '1/1280*a^11 - 3/1280*a^10 + 3/256*a^9 - 9/256*a^8 + 25/256*a^7 + 41/256*a^6 - 21/256*a^5 + 51/256*a^4 + 101/256*a^3 - 47/256*a^2 - 569/1280*a - 213/1280']}