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{'class_group': [3, 24], 'class_number': 72, 'cm': True, 'coeffs': [256, 0, 4608, 0, 13440, 0, 14784, 0, 7920, 0, 2288, 0, 364, 0, 30, 0, 1], 'conductor': 136, 'degree': 16, 'dirichlet_group': [1, 83, 67, 9, 81, 19, 25, 89, 33, 35, 43, 49, 115, 59, 121, 123], 'disc_abs': 2824911165797606216433664, 'disc_rad': 34, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[8, 2]]], [5, [[8, 2]]], [7, [[8, 2]]], [11, [[8, 2]]], [13, [[2, 8]]], [17, [0]], [19, [[4, 4]]], [23, [[8, 2]]], [29, [[8, 2]]], [31, [[8, 2]]], [37, [[8, 2]]], [41, [[8, 2]]], [43, [[4, 4]]], [47, [[2, 8]]], [53, [[4, 4]]], [59, [[4, 4]]]], 'gal_is_abelian': True, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [24, 14], 'galois_label': '16T5', 'galt': 5, 'grd': 33.74331915933294, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '16.0.2824911165797606216433664.1', 'local_algs': ['2.8.12.2', '2.8.12.2', '17.8.7.3', '17.8.7.3'], 'monogenic': 0, 'num_ram': 2, 'r2': 8, 'ramps': [2, 17], 'rd': 33.7433191593, 'regulator': {'__RealLiteral__': 0, 'data': '3640.01221338', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1, 1, 1], 'subfields': ['2.0.1', '-4.-1.1', '34.0.1', '38.4.-3.-2.1', '1.1.-6.-1.1', '272.0.34.0.1', '307.-2.201.2.42.2.-3.-2.1', '1.4.-10.-10.15.6.-7.-1.1', '272.0.680.0.272.0.34.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{8} a^{6} + \\frac{3}{2} a^{4} + \\frac{9}{2} a^{2} + 2 \\)', '\\( \\frac{1}{128} a^{14} + \\frac{13}{64} a^{12} + \\frac{33}{16} a^{10} + \\frac{83}{8} a^{8} + \\frac{217}{8} a^{6} + \\frac{141}{4} a^{4} + \\frac{39}{2} a^{2} + 3 \\)', '\\( \\frac{1}{128} a^{14} + \\frac{13}{64} a^{12} + \\frac{65}{32} a^{10} + \\frac{155}{16} a^{8} + \\frac{175}{8} a^{6} + \\frac{77}{4} a^{4} + 3 a^{2} - 1 \\)', '\\( \\frac{1}{64} a^{12} + \\frac{11}{32} a^{10} + \\frac{45}{16} a^{8} + \\frac{21}{2} a^{6} + \\frac{35}{2} a^{4} + 11 a^{2} + 2 \\)', '\\( \\frac{1}{16} a^{8} + a^{6} + 5 a^{4} + 8 a^{2} + 3 \\)', '\\( \\frac{1}{4} a^{4} + 2 a^{2} + 3 \\)', '\\( \\frac{1}{32} a^{10} + \\frac{9}{16} a^{8} + \\frac{7}{2} a^{6} + \\frac{35}{4} a^{4} + \\frac{15}{2} a^{2} + 1 \\)'], 'used_grh': True, 'zk': ['1', 'a', '1/2*a^2', '1/2*a^3', '1/4*a^4', '1/4*a^5', '1/8*a^6', '1/8*a^7', '1/16*a^8', '1/16*a^9', '1/32*a^10', '1/32*a^11', '1/64*a^12', '1/64*a^13', '1/128*a^14', '1/128*a^15']}