-
nf_fields • Show schema
{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [517, -1177, -222, 2595, -1511, -1806, 2021, 362, -1131, 127, 407, -144, -71, 48, 0, -5, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 53194395371827682204001, 'disc_rad': 231, 'disc_sign': 1, 'frobs': [[2, [[12, 1], [4, 1]]], [3, [0]], [5, [[4, 4]]], [7, [0]], [11, [0]], [13, [[12, 1], [4, 1]]], [17, [[12, 1], [4, 1]]], [19, [[12, 1], [4, 1]]], [23, [[4, 4]]], [29, [[12, 1], [4, 1]]], [31, [[6, 2], [2, 2]]], [37, [[6, 2], [2, 2]]], [41, [[12, 1], [4, 1]]], [43, [[12, 1], [4, 1]]], [47, [[3, 4], [1, 4]]], [53, [[6, 2], [2, 2]]], [59, [[6, 2], [2, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [64, 32, 24], 'galois_label': '16T60', 'galt': 60, 'grd': 52.51177625135337, 'inessentialp': [3], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '16.0.53194395371827682204001.1', 'local_algs': ['3.2.0.1', '3.2.0.1', '3.6.8.4', '3.6.8.4', '7.4.0.1', '7.12.8.2', '11.2.1.2', '11.2.1.2', '11.2.1.2', '11.2.1.2', '11.2.1.2', '11.2.1.2', '11.2.1.2', '11.2.1.2'], 'monogenic': -1, 'num_ram': 3, 'r2': 8, 'ramps': [3, 7, 11], 'rd': 26.324893162176366, 'regulator': {'__RealLiteral__': 0, 'data': '49121.45359495154', 'prec': 57}, 'res': {'sib': ['-9801,40986,11502,-74079,159264,-54387,-58222,95250,-43935,-71337,70287,-61455,-300,15147,7335,-10567,4371,-300,56,-564,288,-40,9,-6,1']}, 'subfield_mults': [1, 1, 1], 'subfields': ['3.-1.1', '75.-30.-3.-1.1', '132.-22.-35.72.4.-16.12.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{633504541}{23473114401} a^{15} - \\frac{8816092900}{70419343203} a^{14} - \\frac{1998516004}{70419343203} a^{13} + \\frac{83963629972}{70419343203} a^{12} - \\frac{100064645774}{70419343203} a^{11} - \\frac{260962284866}{70419343203} a^{10} + \\frac{573102943067}{70419343203} a^{9} + \\frac{123154438633}{23473114401} a^{8} - \\frac{173762621301}{7824371467} a^{7} + \\frac{24344579}{7824371467} a^{6} + \\frac{2832679871455}{70419343203} a^{5} - \\frac{1580074918403}{70419343203} a^{4} - \\frac{2040043330942}{70419343203} a^{3} + \\frac{2030415328900}{70419343203} a^{2} + \\frac{2181031708}{581978043} a - \\frac{52522622474}{6401758473} \\)', '\\( \\frac{10305756136}{70419343203} a^{15} - \\frac{40494252761}{70419343203} a^{14} - \\frac{43883087014}{70419343203} a^{13} + \\frac{447835710161}{70419343203} a^{12} - \\frac{242740508044}{70419343203} a^{11} - \\frac{1760636564933}{70419343203} a^{10} + \\frac{68327071915}{2133919491} a^{9} + \\frac{1280863154507}{23473114401} a^{8} - \\frac{825938451947}{7824371467} a^{7} - \\frac{4659523266775}{70419343203} a^{6} + \\frac{15728502254606}{70419343203} a^{5} - \\frac{835484126402}{70419343203} a^{4} - \\frac{16685692299322}{70419343203} a^{3} + \\frac{7612325936990}{70419343203} a^{2} + \\frac{601578646517}{6401758473} a - \\frac{134762973331}{2133919491} \\)', '\\( \\frac{1309439309}{70419343203} a^{15} - \\frac{7213182871}{70419343203} a^{14} - \\frac{158512252}{6401758473} a^{13} + \\frac{80904115441}{70419343203} a^{12} - \\frac{98101370513}{70419343203} a^{11} - \\frac{344217999562}{70419343203} a^{10} + \\frac{224594768362}{23473114401} a^{9} + \\frac{234450471542}{23473114401} a^{8} - \\frac{758263068188}{23473114401} a^{7} - \\frac{679930672253}{70419343203} a^{6} + \\frac{4797892805617}{70419343203} a^{5} - \\frac{80300165384}{6401758473} a^{4} - \\frac{5944906274783}{70419343203} a^{3} + \\frac{276800174978}{6401758473} a^{2} + \\frac{267243499852}{6401758473} a - \\frac{1954532167}{64664227} \\)', '\\( \\frac{642764752}{70419343203} a^{15} - \\frac{370057135}{7824371467} a^{14} - \\frac{10980700}{6401758473} a^{13} + \\frac{10918519318}{23473114401} a^{12} - \\frac{15163720381}{23473114401} a^{11} - \\frac{110192378440}{70419343203} a^{10} + \\frac{266141859965}{70419343203} a^{9} + \\frac{50545019587}{23473114401} a^{8} - \\frac{262327528291}{23473114401} a^{7} + \\frac{41239955294}{70419343203} a^{6} + \\frac{165815073642}{7824371467} a^{5} - \\frac{75896034101}{6401758473} a^{4} - \\frac{1435921577375}{70419343203} a^{3} + \\frac{39823330376}{2133919491} a^{2} + \\frac{37721861632}{6401758473} a - \\frac{5338405528}{581978043} \\)', '\\( \\frac{3960179195}{70419343203} a^{15} - \\frac{5759988221}{23473114401} a^{14} - \\frac{12388787740}{70419343203} a^{13} + \\frac{61751519098}{23473114401} a^{12} - \\frac{16573627412}{7824371467} a^{11} - \\frac{64658204767}{6401758473} a^{10} + \\frac{1096541814925}{70419343203} a^{9} + \\frac{160369469009}{7824371467} a^{8} - \\frac{1156489054375}{23473114401} a^{7} - \\frac{1563504328085}{70419343203} a^{6} + \\frac{2339582124724}{23473114401} a^{5} - \\frac{1108213324787}{70419343203} a^{4} - \\frac{7201029967870}{70419343203} a^{3} + \\frac{412435215358}{7824371467} a^{2} + \\frac{240234000302}{6401758473} a - \\frac{179474952742}{6401758473} \\)', '\\( \\frac{419261531}{7824371467} a^{15} - \\frac{2000606750}{7824371467} a^{14} + \\frac{121455524}{7824371467} a^{13} + \\frac{52094252680}{23473114401} a^{12} - \\frac{77254449647}{23473114401} a^{11} - \\frac{124462875452}{23473114401} a^{10} + \\frac{377466664471}{23473114401} a^{9} + \\frac{52780382902}{23473114401} a^{8} - \\frac{26653404609}{711306497} a^{7} + \\frac{36251198245}{2133919491} a^{6} + \\frac{448546801755}{7824371467} a^{5} - \\frac{1572273123218}{23473114401} a^{4} - \\frac{211813882570}{23473114401} a^{3} + \\frac{1244699308087}{23473114401} a^{2} - \\frac{58054209155}{2133919491} a + \\frac{4947952520}{2133919491} \\)', '\\( \\frac{747789156}{7824371467} a^{15} - \\frac{28252903315}{70419343203} a^{14} - \\frac{19283540356}{70419343203} a^{13} + \\frac{293080188652}{70419343203} a^{12} - \\frac{22622229721}{6401758473} a^{11} - \\frac{1033052594459}{70419343203} a^{10} + \\frac{1775623394861}{70419343203} a^{9} + \\frac{626253869441}{23473114401} a^{8} - \\frac{1780554141482}{23473114401} a^{7} - \\frac{142171921718}{7824371467} a^{6} + \\frac{10643553095866}{70419343203} a^{5} - \\frac{3739130572472}{70419343203} a^{4} - \\frac{9894833601223}{70419343203} a^{3} + \\frac{7480110683425}{70419343203} a^{2} + \\frac{293988381494}{6401758473} a - \\frac{321558055619}{6401758473} \\)'], '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', '1/33*a^12 + 1/33*a^11 - 2/33*a^10 - 8/33*a^9 + 1/33*a^8 + 2/11*a^7 + 14/33*a^6 - 1/11*a^5 + 16/33*a^4 - 7/33*a^3 - 8/33*a^2 + 1/3*a - 1/3', '1/33*a^13 - 1/11*a^11 - 2/11*a^10 + 3/11*a^9 + 5/33*a^8 + 8/33*a^7 + 16/33*a^6 - 14/33*a^5 + 10/33*a^4 - 1/33*a^3 - 14/33*a^2 + 1/3*a + 1/3', '1/1089*a^14 - 2/1089*a^13 + 1/99*a^12 + 47/1089*a^11 + 257/1089*a^10 + 337/1089*a^9 + 38/121*a^8 + 116/363*a^7 + 94/363*a^6 - 499/1089*a^5 - 127/1089*a^4 + 20/99*a^3 + 257/1089*a^2 - 47/99*a + 38/99', '1/70419343203*a^15 + 4234085/23473114401*a^14 + 399597250/70419343203*a^13 + 85545915/7824371467*a^12 - 8912278781/23473114401*a^11 + 13318120565/70419343203*a^10 + 26503237382/70419343203*a^9 + 4841323301/23473114401*a^8 + 4970716601/23473114401*a^7 + 6757943996/70419343203*a^6 + 4846987009/23473114401*a^5 + 13189007867/70419343203*a^4 - 3188104883/70419343203*a^3 - 87767848/7824371467*a^2 + 1284775762/6401758473*a + 2053123855/6401758473']}
Number field data - 16.0.53194395371827682204001.1