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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 2, -2, -4, 6, 2, -10, 6, 1, 2, -3, -10, 26, -28, 17, -6, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 7771775074107392, 'disc_rad': 34, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[16, 1]]], [5, [[8, 1], [4, 2]]], [7, [[16, 1]]], [11, [[16, 1]]], [13, [[8, 2]]], [17, [0]], [19, [[8, 2]]], [23, [[16, 1]]], [29, [[8, 1], [2, 2], [1, 4]]], [31, [[16, 1]]], [37, [[8, 1], [4, 2]]], [41, [[8, 1], [2, 2], [1, 4]]], [43, [[8, 2]]], [47, [[4, 4]]], [53, [[4, 2], [2, 4]]], [59, [[8, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [128, 112], 'galois_label': '16T260', 'galt': 260, 'grd': 23.86012979730628, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '16.0.7771775074107392.1', 'local_algs': ['m2.2.8.16', '17.4.2.2', '17.4.0.1', '17.8.7.4'], 'monogenic': 0, 'num_ram': 2, 'r2': 8, 'ramps': [2, 17], 'rd': 9.84368060738, 'regulator': {'__RealLiteral__': 0, 'data': '25.2889722607', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['1.0.1', '1.-2.1.0.1', '1.-2.3.0.-4.4.0.-2.1'], 'torsion_gen': '\\( \\frac{44}{67} a^{15} - \\frac{137}{67} a^{14} + \\frac{80}{67} a^{13} + \\frac{546}{67} a^{12} - \\frac{1699}{67} a^{11} + \\frac{2390}{67} a^{10} - \\frac{1971}{67} a^{9} + \\frac{1067}{67} a^{8} - \\frac{779}{67} a^{7} + \\frac{694}{67} a^{6} - \\frac{54}{67} a^{5} - \\frac{546}{67} a^{4} + \\frac{427}{67} a^{3} + \\frac{53}{67} a^{2} - \\frac{168}{67} a - \\frac{68}{67} \\)', 'torsion_order': 4, 'units': ['\\( \\frac{69}{67} a^{15} - \\frac{393}{67} a^{14} + \\frac{1100}{67} a^{13} - \\frac{1839}{67} a^{12} + \\frac{1881}{67} a^{11} - \\frac{1140}{67} a^{10} + \\frac{419}{67} a^{9} - \\frac{253}{67} a^{8} + \\frac{126}{67} a^{7} + \\frac{330}{67} a^{6} - \\frac{508}{67} a^{5} + \\frac{97}{67} a^{4} + \\frac{260}{67} a^{3} - \\frac{226}{67} a^{2} - \\frac{32}{67} a + \\frac{3}{67} \\)', '\\( \\frac{115}{67} a^{15} - \\frac{655}{67} a^{14} + \\frac{1878}{67} a^{13} - \\frac{3266}{67} a^{12} + \\frac{3604}{67} a^{11} - \\frac{2570}{67} a^{10} + \\frac{1346}{67} a^{9} - \\frac{980}{67} a^{8} + \\frac{679}{67} a^{7} + \\frac{215}{67} a^{6} - \\frac{802}{67} a^{5} + \\frac{318}{67} a^{4} + \\frac{277}{67} a^{3} - \\frac{265}{67} a^{2} - \\frac{98}{67} a + \\frac{72}{67} \\)', '\\( \\frac{9}{67} a^{15} + \\frac{7}{67} a^{14} - \\frac{142}{67} a^{13} + \\frac{468}{67} a^{12} - \\frac{748}{67} a^{11} + \\frac{565}{67} a^{10} - \\frac{24}{67} a^{9} - \\frac{301}{67} a^{8} + \\frac{98}{67} a^{7} + \\frac{11}{67} a^{6} + \\frac{193}{67} a^{5} - \\frac{200}{67} a^{4} - \\frac{103}{67} a^{3} + \\frac{256}{67} a^{2} - \\frac{77}{67} a - \\frac{87}{67} \\)', '\\( \\frac{111}{67} a^{15} - \\frac{606}{67} a^{14} + \\frac{1621}{67} a^{13} - \\frac{2536}{67} a^{12} + \\frac{2254}{67} a^{11} - \\frac{893}{67} a^{10} - \\frac{162}{67} a^{9} + \\frac{129}{67} a^{8} - \\frac{42}{67} a^{7} + \\frac{560}{67} a^{6} - \\frac{657}{67} a^{5} + \\frac{57}{67} a^{4} + \\frac{494}{67} a^{3} - \\frac{349}{67} a^{2} - \\frac{101}{67} a + \\frac{66}{67} \\)', '\\( \\frac{84}{67} a^{15} - \\frac{426}{67} a^{14} + \\frac{1042}{67} a^{13} - \\frac{1394}{67} a^{12} + \\frac{813}{67} a^{11} + \\frac{293}{67} a^{10} - \\frac{827}{67} a^{9} + \\frac{563}{67} a^{8} - \\frac{470}{67} a^{7} + \\frac{728}{67} a^{6} - \\frac{499}{67} a^{5} - \\frac{147}{67} a^{4} + \\frac{401}{67} a^{3} - \\frac{179}{67} a^{2} - \\frac{138}{67} a + \\frac{59}{67} \\)', '\\( \\frac{108}{67} a^{15} - \\frac{720}{67} a^{14} + \\frac{2316}{67} a^{13} - \\frac{4568}{67} a^{12} + \\frac{5831}{67} a^{11} - \\frac{4878}{67} a^{10} + \\frac{2727}{67} a^{9} - \\frac{1334}{67} a^{8} + \\frac{774}{67} a^{7} + \\frac{266}{67} a^{6} - \\frac{1302}{67} a^{5} + \\frac{1084}{67} a^{4} - \\frac{30}{67} a^{3} - \\frac{479}{67} a^{2} + \\frac{148}{67} a + \\frac{95}{67} \\)', '\\( \\frac{59}{67} a^{15} - \\frac{438}{67} a^{14} + \\frac{1496}{67} a^{13} - \\frac{3096}{67} a^{12} + \\frac{4067}{67} a^{11} - \\frac{3346}{67} a^{10} + \\frac{1607}{67} a^{9} - \\frac{529}{67} a^{8} + \\frac{367}{67} a^{7} + \\frac{221}{67} a^{6} - \\frac{1050}{67} a^{5} + \\frac{952}{67} a^{4} + \\frac{32}{67} a^{3} - \\frac{436}{67} a^{2} + \\frac{128}{67} a + \\frac{122}{67} \\)'], 'used_grh': False, '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', '1/67*a^15 - 29/67*a^14 + 14/67*a^13 - 15/67*a^12 - 31/67*a^11 + 33/67*a^10 - 25/67*a^9 - 26/67*a^8 - 4/67*a^7 + 31/67*a^6 + 14/67*a^5 + 15/67*a^4 - 4/67*a^3 + 21/67*a^2 - 16/67*a - 32/67']}
Number field data - 16.0.7771775074107392.1