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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 12, 58, 144, 182, 80, -28, -16, 11, -4, -8, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 677021181018112, 'disc_rad': 14, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[12, 1]]], [5, [[12, 1]]], [7, [0]], [11, [[6, 2]]], [13, [[4, 3]]], [17, [[6, 1], [3, 2]]], [19, [[12, 1]]], [23, [[6, 2]]], [29, [[2, 6]]], [31, [[6, 1], [3, 2]]], [37, [[6, 2]]], [41, [[2, 3], [1, 6]]], [43, [[2, 6]]], [47, [[6, 1], [3, 2]]], [53, [[6, 2]]], [59, [[12, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [48, 20], 'galois_label': '12T14', 'galt': 14, 'grd': 20.244560739185545, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 2, 'label': '12.6.677021181018112.2', 'local_algs': ['2.12.24.318', '7.3.2.2', '7.3.2.2', '7.6.5.5'], 'minimal_sibling': [8, 0, -12, 0, 4, 0, 1, 0, 2, 0, -3, 0, 1], 'monogenic': 0, 'num_ram': 2, 'r2': 3, 'ramps': [2, 7], 'rd': 17.2140682826, 'regulator': {'__RealLiteral__': 0, 'data': '931.906866489', 'prec': 44}, 'res': {'gal': ['1,0,-8,0,35,0,-118,0,293,0,-532,0,351,0,518,0,125,0,-6,0,7,0,6,0,1'], 'sib': ['8,0,-12,0,4,0,1,0,2,0,-3,0,1']}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-2.0.1', '1.-2.-1.1', '-2.-4.-2.0.1', '-8.0.24.0.-10.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{176}{49} a^{11} + \\frac{4}{49} a^{10} - \\frac{1448}{49} a^{9} - \\frac{97}{7} a^{8} + \\frac{2160}{49} a^{7} - \\frac{422}{7} a^{6} - \\frac{740}{7} a^{5} + \\frac{14871}{49} a^{4} + \\frac{32184}{49} a^{3} + \\frac{23082}{49} a^{2} + \\frac{1104}{7} a + \\frac{1027}{49} \\)', '\\( \\frac{176}{49} a^{11} + \\frac{4}{49} a^{10} - \\frac{1448}{49} a^{9} - \\frac{97}{7} a^{8} + \\frac{2160}{49} a^{7} - \\frac{422}{7} a^{6} - \\frac{740}{7} a^{5} + \\frac{14871}{49} a^{4} + \\frac{32184}{49} a^{3} + \\frac{23082}{49} a^{2} + \\frac{1104}{7} a + \\frac{978}{49} \\)', '\\( a \\)', '\\( \\frac{333}{49} a^{11} - \\frac{82}{49} a^{10} - \\frac{2684}{49} a^{9} - \\frac{87}{7} a^{8} + \\frac{4048}{49} a^{7} - \\frac{934}{7} a^{6} - 161 a^{5} + \\frac{29531}{49} a^{4} + \\frac{53066}{49} a^{3} + \\frac{31869}{49} a^{2} + \\frac{1255}{7} a + \\frac{951}{49} \\)', '\\( \\frac{414}{49} a^{11} - \\frac{87}{49} a^{10} - \\frac{3296}{49} a^{9} - \\frac{138}{7} a^{8} + \\frac{4785}{49} a^{7} - \\frac{1089}{7} a^{6} - \\frac{1434}{7} a^{5} + \\frac{35304}{49} a^{4} + \\frac{68010}{49} a^{3} + \\frac{45069}{49} a^{2} + \\frac{2013}{7} a + \\frac{1783}{49} \\)', '\\( a^{11} - a^{10} - 7 a^{9} + 3 a^{8} + 8 a^{7} - 24 a^{6} - 4 a^{5} + 84 a^{4} + 98 a^{3} + 46 a^{2} + 12 a \\)', '\\( \\frac{15}{7} a^{11} - \\frac{9}{7} a^{10} - \\frac{118}{7} a^{9} + 2 a^{8} + \\frac{181}{7} a^{7} - \\frac{358}{7} a^{6} - \\frac{235}{7} a^{5} + \\frac{1422}{7} a^{4} + 271 a^{3} + \\frac{727}{7} a^{2} + \\frac{82}{7} a - \\frac{4}{7} \\)', '\\( \\frac{101}{7} a^{11} - \\frac{34}{7} a^{10} - \\frac{795}{7} a^{9} - 20 a^{8} + \\frac{1152}{7} a^{7} - \\frac{1991}{7} a^{6} - \\frac{2161}{7} a^{5} + \\frac{8774}{7} a^{4} + 2209 a^{3} + \\frac{9426}{7} a^{2} + \\frac{2717}{7} a + \\frac{296}{7} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', '1/7*a^9 - 2/7*a^8 - 3/7*a^7 + 1/7*a^6 - 3/7*a^5 + 2/7*a^4 + 1/7*a^3 + 3/7*a - 1/7', '1/7*a^10 + 2/7*a^7 - 1/7*a^6 + 3/7*a^5 - 2/7*a^4 + 2/7*a^3 + 3/7*a^2 - 2/7*a - 2/7', '1/49*a^11 - 3/49*a^10 + 1/49*a^9 - 1/7*a^8 - 17/49*a^7 - 2/7*a^6 + 2/7*a^5 - 11/49*a^4 + 19/49*a^3 - 11/49*a^2 - 1/7*a - 16/49']}