-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -1, 9, -23, 43, -57, 55, -23, -12, 32, -27, 15, -1, -4, 6, -3, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 731086699811838561, 'disc_rad': 57, 'disc_sign': 1, 'frobs': [[2, [[12, 1], [4, 1]]], [3, [0]], [5, [[6, 2], [2, 2]]], [7, [[6, 2], [2, 2]]], [11, [[3, 4], [1, 4]]], [13, [[12, 1], [4, 1]]], [17, [[4, 4]]], [19, [0]], [23, [[3, 4], [1, 4]]], [29, [[12, 1], [4, 1]]], [31, [[12, 1], [4, 1]]], [37, [[2, 8]]], [41, [[12, 1], [4, 1]]], [43, [[6, 2], [2, 2]]], [47, [[6, 2], [2, 2]]], [53, [[2, 8]]], [59, [[12, 1], [4, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_label': '16T60', 'galt': 60, 'index': 1, 'inessentialp': [], 'is_galois': False, 'iso_number': 1, 'label': '16.0.731086699811838561.1', 'local_algs': ['3.4.0.1', '3.12.16.14', '19.8.4.1', '19.8.4.1'], 'monogenic': 0, 'num_ram': 2, 'r2': 8, 'ramps': [3, 19], 'rd': 13.076696830622021, 'regulator': {'__RealLiteral__': 0, 'data': '188.5109795655095', 'prec': 57}, 'res': {'sib': ['-1,3,-3,-15,36,18,-26,-45,42,-25,-114,-90,77,135,105,29,-30,-54,-16,21,15,-4,-6,0,1']}, 'subfield_mults': [1, 1, 1], 'subfields': ['5.-1.1', '20.1.3.-1.1', '1.1.5.-1.11.1.5.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{7934539}{28097843} a^{15} - \\frac{36032205}{56195686} a^{14} + \\frac{29188960}{28097843} a^{13} - \\frac{1849667}{56195686} a^{12} - \\frac{52396327}{56195686} a^{11} + \\frac{197843763}{56195686} a^{10} - \\frac{276757383}{56195686} a^{9} + \\frac{192830397}{56195686} a^{8} + \\frac{42632706}{28097843} a^{7} - \\frac{438318261}{56195686} a^{6} + \\frac{278020437}{28097843} a^{5} - \\frac{166639012}{28097843} a^{4} + \\frac{191243773}{56195686} a^{3} + \\frac{12604128}{28097843} a^{2} - \\frac{48883008}{28097843} a + \\frac{54187467}{56195686} \\)', '\\( \\frac{1439675}{28097843} a^{15} - \\frac{1042436}{28097843} a^{14} + \\frac{4796478}{28097843} a^{13} + \\frac{5238337}{28097843} a^{12} + \\frac{2871781}{28097843} a^{11} + \\frac{26003980}{28097843} a^{10} + \\frac{7394827}{28097843} a^{9} + \\frac{31041491}{28097843} a^{8} + \\frac{30965325}{28097843} a^{7} - \\frac{4886335}{28097843} a^{6} + \\frac{44439636}{28097843} a^{5} + \\frac{3805798}{28097843} a^{4} + \\frac{25713173}{28097843} a^{3} + \\frac{2791552}{28097843} a^{2} + \\frac{26599057}{28097843} a + \\frac{11171576}{28097843} \\)', '\\( \\frac{4121951}{28097843} a^{15} - \\frac{12822501}{28097843} a^{14} + \\frac{16885383}{28097843} a^{13} + \\frac{4184490}{28097843} a^{12} - \\frac{44445150}{28097843} a^{11} + \\frac{73137660}{28097843} a^{10} - \\frac{90684178}{28097843} a^{9} + \\frac{11130368}{28097843} a^{8} + \\frac{120888211}{28097843} a^{7} - \\frac{265121129}{28097843} a^{6} + \\frac{212163936}{28097843} a^{5} + \\frac{5175839}{28097843} a^{4} - \\frac{192553993}{28097843} a^{3} + \\frac{165988522}{28097843} a^{2} - \\frac{99885883}{28097843} a + \\frac{43348017}{28097843} \\)', '\\( \\frac{8124973}{28097843} a^{15} - \\frac{19902589}{28097843} a^{14} + \\frac{38887720}{28097843} a^{13} - \\frac{13881849}{28097843} a^{12} - \\frac{10397403}{28097843} a^{11} + \\frac{111260698}{28097843} a^{10} - \\frac{156722427}{28097843} a^{9} + \\frac{184442567}{28097843} a^{8} - \\frac{28984792}{28097843} a^{7} - \\frac{171779177}{28097843} a^{6} + \\frac{319111060}{28097843} a^{5} - \\frac{305588939}{28097843} a^{4} + \\frac{234144010}{28097843} a^{3} - \\frac{139320586}{28097843} a^{2} + \\frac{62539061}{28097843} a - \\frac{1599563}{28097843} \\)', '\\( \\frac{10661733}{56195686} a^{15} - \\frac{26264597}{28097843} a^{14} + \\frac{102971233}{56195686} a^{13} - \\frac{117173647}{56195686} a^{12} - \\frac{17575617}{56195686} a^{11} + \\frac{192924721}{56195686} a^{10} - \\frac{556524227}{56195686} a^{9} + \\frac{308198797}{28097843} a^{8} - \\frac{413961979}{56195686} a^{7} - \\frac{172922577}{28097843} a^{6} + \\frac{525756757}{28097843} a^{5} - \\frac{1230722353}{56195686} a^{4} + \\frac{455891920}{28097843} a^{3} - \\frac{257277301}{28097843} a^{2} + \\frac{164996481}{56195686} a - \\frac{12056490}{28097843} \\)', '\\( \\frac{7970339}{56195686} a^{15} + \\frac{1521107}{28097843} a^{14} - \\frac{8969571}{56195686} a^{13} + \\frac{67204139}{56195686} a^{12} - \\frac{244309}{56195686} a^{11} + \\frac{50805557}{56195686} a^{10} + \\frac{132444845}{56195686} a^{9} - \\frac{67541754}{28097843} a^{8} + \\frac{260237729}{56195686} a^{7} + \\frac{888297}{28097843} a^{6} - \\frac{102301823}{28097843} a^{5} + \\frac{380554837}{56195686} a^{4} - \\frac{86356302}{28097843} a^{3} + \\frac{47161030}{28097843} a^{2} - \\frac{48998833}{56195686} a - \\frac{10806226}{28097843} \\)', '\\( \\frac{7934539}{28097843} a^{15} - \\frac{36032205}{56195686} a^{14} + \\frac{29188960}{28097843} a^{13} - \\frac{1849667}{56195686} a^{12} - \\frac{52396327}{56195686} a^{11} + \\frac{197843763}{56195686} a^{10} - \\frac{276757383}{56195686} a^{9} + \\frac{192830397}{56195686} a^{8} + \\frac{42632706}{28097843} a^{7} - \\frac{438318261}{56195686} a^{6} + \\frac{278020437}{28097843} a^{5} - \\frac{166639012}{28097843} a^{4} + \\frac{191243773}{56195686} a^{3} + \\frac{12604128}{28097843} a^{2} - \\frac{48883008}{28097843} a - \\frac{2008219}{56195686} \\)'], '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', '1/2*a^14 - 1/2*a^12 - 1/2*a^11 - 1/2*a^10 - 1/2*a^9 - 1/2*a^8 - 1/2*a^6 - 1/2*a^3 - 1/2', '1/56195686*a^15 - 5048488/28097843*a^14 + 1111075/56195686*a^13 + 19107259/56195686*a^12 + 15673121/56195686*a^11 - 9795169/56195686*a^10 - 12554447/56195686*a^9 - 8559929/28097843*a^8 - 983625/56195686*a^7 + 1446632/28097843*a^6 - 10805966/28097843*a^5 - 4099715/56195686*a^4 + 7014238/28097843*a^3 - 5619997/28097843*a^2 - 25527443/56195686*a + 7866912/28097843']}
Number field data - 16.0.731086699811838561.1