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{'class_group': [3], 'class_number': 3, 'cm': True, 'coeffs': [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 'conductor': 52, 'degree': 24, 'dirichlet_group': [1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 41, 43, 45, 47, 49, 51], 'disc_abs': 53885714612646242347927893704704, 'disc_rad': 26, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[6, 4]]], [5, [[4, 6]]], [7, [[12, 2]]], [11, [[12, 2]]], [13, [0]], [17, [[6, 4]]], [19, [[12, 2]]], [23, [[6, 4]]], [29, [[3, 8]]], [31, [[4, 6]]], [37, [[12, 2]]], [41, [[12, 2]]], [43, [[6, 4]]], [47, [[4, 6]]], [53, [[1, 24]]], [59, [[12, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [24, 22], 'galois_label': '24T2', 'galt': 2, 'grd': 20.99639504015924, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '24.0.53885714612646242347927893704704.1', 'local_algs': ['m2.2.12.24', '13.12.11.4', '13.12.11.4'], 'monogenic': 1, 'num_ram': 2, 'r2': 12, 'ramps': [2, 13], 'rd': 20.9963950402, 'regulator': {'__RealLiteral__': 0, 'data': '7239917.885587101', 'prec': 57}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'subfields': ['1.0.1', '-3.-1.1', '13.0.1', '-1.-4.-1.1', '9.0.7.0.1', '3.4.2.-1.1', '13.0.-13.0.1', '1.0.14.0.9.0.1', '-1.-3.6.4.-5.-1.1', '13.0.26.0.13.0.1', '9.0.4.0.18.0.-3.0.1', '1.0.21.0.70.0.84.0.45.0.11.0.1', '1.-1.1.-1.1.-1.1.-1.1.-1.1.-1.1', '13.0.-91.0.182.0.-156.0.65.0.-13.0.1'], 'torsion_gen': '\\( a \\)', 'torsion_order': 52, 'units': ['\\( a^{4} + 1 \\)', '\\( a^{8} + 1 \\)', '\\( a^{20} - a^{14} + 1 \\)', '\\( a^{8} + a^{4} + 1 \\)', '\\( a^{23} + a^{19} + a^{15} + a^{11} + a^{7} + a^{3} \\)', '\\( a - 1 \\)', '\\( a^{3} - 1 \\)', '\\( a^{9} - 1 \\)', '\\( a^{5} - 1 \\)', '\\( a^{7} - 1 \\)', '\\( a^{11} - 1 \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11', 'a^12', 'a^13', 'a^14', 'a^15', 'a^16', 'a^17', 'a^18', 'a^19', 'a^20', 'a^21', 'a^22', 'a^23']}