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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [36, 0, 0, 0, -504, 0, 0, 0, 336, 0, 0, 0, -36, 0, 0, 0, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 1378596953991976568487936, 'disc_rad': 6, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[4, 4]]], [7, [[8, 2]]], [11, [[2, 8]]], [13, [[4, 4]]], [17, [[8, 2]]], [19, [[4, 4]]], [23, [[4, 4]]], [29, [[4, 4]]], [31, [[8, 2]]], [37, [[4, 4]]], [41, [[8, 2]]], [43, [[4, 4]]], [47, [[4, 4]]], [53, [[4, 4]]], [59, [[2, 8]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [116, 28], 'galois_label': '16T50', 'galt': 50, 'grd': 32.263749133641326, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 3, 'label': '16.8.1378596953991976568487936.3', 'local_algs': ['2.16.58.68', '3.16.14.1'], 'minimal_sibling': [36, 0, 0, 0, 504, 0, 0, 0, 336, 0, 0, 0, 36, 0, 0, 0, 1], 'monogenic': 0, 'num_ram': 2, 'r2': 4, 'ramps': [2, 3], 'rd': 32.2637491336, 'regulator': {'__RealLiteral__': 0, 'data': '1533253.77477', 'prec': 44}, 'res': {'gal': ['81,0,-1944,0,23328,0,-186624,0,888786,0,-1798200,0,2177280,0,-1845720,0,1163835,0,-558360,0,207360,0,-60120,0,13506,0,-2304,0,288,0,-24,0,1'], 'sib': ['36,0,0,0,504,0,0,0,336,0,0,0,36,0,0,0,1']}, 'subfield_mults': [1, 1, 1, 2, 2, 1, 1], 'subfields': ['-6.0.1', '-3.0.1', '-2.0.1', '3.0.-6.0.1', '6.0.-6.0.1', '1.0.-4.0.1', '1.4.-4.-20.4.20.-4.-4.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{13}{900} a^{14} - \\frac{313}{600} a^{10} + \\frac{1463}{300} a^{6} - \\frac{741}{100} a^{2} \\)', '\\( \\frac{11}{3600} a^{14} + \\frac{1}{300} a^{12} - \\frac{59}{600} a^{10} - \\frac{13}{100} a^{8} + \\frac{443}{600} a^{6} + \\frac{63}{50} a^{4} - \\frac{19}{50} a^{2} - \\frac{23}{50} \\)', '\\( \\frac{11}{3600} a^{14} - \\frac{1}{300} a^{12} - \\frac{59}{600} a^{10} + \\frac{13}{100} a^{8} + \\frac{443}{600} a^{6} - \\frac{63}{50} a^{4} - \\frac{19}{50} a^{2} + \\frac{23}{50} \\)', '\\( \\frac{1}{72} a^{14} - \\frac{1}{2} a^{10} + \\frac{55}{12} a^{6} - \\frac{11}{2} a^{2} - 1 \\)', '\\( \\frac{1}{400} a^{14} - \\frac{1}{300} a^{12} - \\frac{23}{300} a^{10} + \\frac{13}{100} a^{8} + \\frac{89}{200} a^{6} - \\frac{63}{50} a^{4} + \\frac{153}{100} a^{2} + \\frac{73}{50} \\)', '\\( \\frac{23}{720} a^{14} - \\frac{1}{300} a^{12} - \\frac{137}{120} a^{10} + \\frac{13}{100} a^{8} + \\frac{1259}{120} a^{6} - \\frac{63}{50} a^{4} - \\frac{71}{5} a^{2} + \\frac{123}{50} \\)', '\\( \\frac{1}{720} a^{14} - \\frac{1}{120} a^{12} - \\frac{1}{30} a^{10} + \\frac{17}{60} a^{8} - \\frac{17}{120} a^{6} - \\frac{43}{20} a^{4} + \\frac{87}{20} a^{2} - \\frac{8}{5} \\)', '\\( \\frac{3}{200} a^{15} + \\frac{1}{400} a^{14} - \\frac{1}{400} a^{13} + \\frac{1}{80} a^{12} - \\frac{163}{300} a^{11} - \\frac{23}{300} a^{10} + \\frac{23}{300} a^{9} - \\frac{17}{40} a^{8} + \\frac{517}{100} a^{7} + \\frac{89}{200} a^{6} - \\frac{89}{200} a^{5} + \\frac{139}{40} a^{4} - \\frac{441}{50} a^{3} + \\frac{103}{100} a^{2} - \\frac{153}{100} a - \\frac{13}{5} \\)', '\\( \\frac{3}{400} a^{15} - \\frac{1}{1800} a^{14} + \\frac{3}{400} a^{13} - \\frac{1}{240} a^{12} - \\frac{163}{600} a^{11} + \\frac{13}{600} a^{10} - \\frac{163}{600} a^{9} + \\frac{17}{120} a^{8} + \\frac{517}{200} a^{7} - \\frac{22}{75} a^{6} + \\frac{517}{200} a^{5} - \\frac{53}{40} a^{4} - \\frac{104}{25} a^{3} + \\frac{141}{100} a^{2} - \\frac{183}{50} a + \\frac{11}{5} \\)', '\\( \\frac{43}{1800} a^{15} + \\frac{17}{1800} a^{14} + \\frac{1}{75} a^{13} + \\frac{1}{150} a^{12} - \\frac{509}{600} a^{11} - \\frac{49}{150} a^{10} - \\frac{287}{600} a^{9} - \\frac{131}{600} a^{8} + \\frac{571}{75} a^{7} + \\frac{821}{300} a^{6} + \\frac{429}{100} a^{5} + \\frac{177}{100} a^{4} - \\frac{863}{100} a^{3} - \\frac{61}{50} a^{2} - \\frac{459}{100} a - \\frac{67}{100} \\)', '\\( \\frac{19}{1800} a^{15} + \\frac{19}{1800} a^{14} + \\frac{1}{150} a^{13} + \\frac{1}{200} a^{12} - \\frac{37}{100} a^{11} - \\frac{37}{100} a^{10} - \\frac{131}{600} a^{9} - \\frac{67}{600} a^{8} + \\frac{997}{300} a^{7} + \\frac{997}{300} a^{6} + \\frac{177}{100} a^{5} + \\frac{7}{50} a^{4} - \\frac{126}{25} a^{3} - \\frac{126}{25} a^{2} - \\frac{267}{100} a - \\frac{69}{100} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', '1/24*a^8 - 1/2*a^6 + 1/4*a^4 + 1/4', '1/24*a^9 - 1/2*a^7 + 1/4*a^5 + 1/4*a', '1/24*a^10 + 1/4*a^6 + 1/4*a^2', '1/24*a^11 + 1/4*a^7 + 1/4*a^3', '1/1200*a^12 - 7/600*a^8 - 1/2*a^7 - 87/200*a^4 - 1/2*a^2 + 13/50', '1/1200*a^13 - 7/600*a^9 - 87/200*a^5 - 1/2*a^3 + 13/50*a', '1/3600*a^14 + 1/100*a^10 + 163/600*a^6 - 1/2*a^4 + 17/100*a^2', '1/3600*a^15 + 1/100*a^11 + 163/600*a^7 - 1/2*a^5 + 17/100*a^3']}