-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [3969, 0, -44712, 0, 44388, 0, -20088, 0, 6210, 0, -1512, 0, 252, 0, -24, 0, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 9803356117276277820358656, 'disc_rad': 6, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[4, 4]]], [7, [[4, 2], [2, 2], [1, 4]]], [11, [[8, 2]]], [13, [[4, 4]]], [17, [[4, 4]]], [19, [[8, 2]]], [23, [[4, 2], [2, 4]]], [29, [[4, 4]]], [31, [[4, 4]]], [37, [[4, 4]]], [41, [[4, 4]]], [43, [[8, 2]]], [47, [[2, 4], [1, 8]]], [53, [[4, 4]]], [59, [[8, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [548, 96], 'galois_label': '16T243', 'galt': 243, 'grd': 44.32263892833827, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 110, 'label': '16.8.9803356117276277820358656.110', 'local_algs': ['2.1.16.64l1.182', '3.2.4.6a1.1', '3.2.4.6a1.1'], 'monogenic': 0, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 4, 'ramps': [2, 3], 'rd': 36.47211291127644, 'regulator': {'__RealLiteral__': 0, 'data': '11649698.970758608', 'prec': 60}, 'res': {'sib': ['-188,-448,9568,-10176,-12640,170048,-862528,1748064,-2045872,383232,6595264,-15348576,11985712,6628928,-22105120,18172704,-1573476,-9750944,8860816,-2501664,-1458384,1630432,-500640,-130480,165304,-50944,-2784,6704,-1816,32,80,-16,1', '-194,10720,-9584,101536,-165112,142048,-469968,-529360,1265444,1350128,1740112,373744,-1766784,-4099760,-511936,2018016,1559746,112800,-577712,-287056,3024,89808,29768,-7632,-11716,-1568,1392,816,16,-96,-16,0,1', '26244,0,-419904,0,2274480,0,-6088608,0,8123976,0,-2449440,0,-1932336,0,244944,0,611712,0,-370656,0,147528,0,-44064,0,9252,0,-1584,0,240,0,-24,0,1', '26244,0,419904,0,2274480,0,6088608,0,8123976,0,2449440,0,-1932336,0,-244944,0,611712,0,370656,0,147528,0,44064,0,9252,0,1584,0,240,0,24,0,1', '321489,0,262440,0,-1854576,0,1102248,0,4408992,0,-8917128,0,8302824,0,-4764744,0,1732590,0,-353160,0,15984,0,7992,0,-144,0,-792,0,216,0,-24,0,1', '324,0,-1296,0,864,0,0,0,252,0,-216,0,0,0,0,0,1', '324,0,1296,0,864,0,0,0,252,0,216,0,0,0,0,0,1', '367684,-4903744,31635232,-132227328,403279232,-956407168,1833994496,-2918988576,3929271776,-4537896288,4548316384,-3994118784,3097559824,-2136440320,1320343808,-738655968,379392660,-181430624,81065872,-33425664,12558816,-4386752,1512960,-528208,174448,-52336,16272,-6016,2216,-640,128,-16,1', '3969,0,44712,0,44388,0,20088,0,6210,0,1512,0,252,0,24,0,1', '6469,-65184,317704,-972432,2079140,-3349920,4407408,-5188800,6041132,-7283376,8888816,-10192704,10602136,-9806400,8261712,-6176832,4397881,-2802624,1716552,-960672,507508,-242112,120856,-42048,24398,-4368,3936,-192,452,0,32,0,1', '6561,0,-367416,0,34922016,0,-8170632,0,12270528,0,-5522904,0,2803248,0,-1945944,0,1430946,0,-818424,0,330048,0,-95688,0,20160,0,-3096,0,336,0,-24,0,1', '6561,0,-52488,0,174960,0,-314928,0,373248,0,-408240,0,493776,0,-507384,0,360450,0,-169128,0,54864,0,-15120,0,4608,0,-1296,0,240,0,-24,0,1', '6561,0,0,0,-104976,0,0,0,166212,0,0,0,-221616,0,0,0,181926,0,0,0,-24624,0,0,0,2052,0,0,0,-144,0,0,0,1', '6561,0,0,0,104976,0,0,0,166212,0,0,0,221616,0,0,0,181926,0,0,0,24624,0,0,0,2052,0,0,0,144,0,0,0,1', '6561,0,0,0,174960,0,0,0,638604,0,0,0,812592,0,0,0,381510,0,0,0,72144,0,0,0,5580,0,0,0,144,0,0,0,1', '656100,0,-3359232,0,7453296,0,2099520,0,-1813752,0,-909792,0,835920,0,-765936,0,486648,0,-238464,0,117720,0,-48816,0,14796,0,-2736,0,336,0,-24,0,1', '81,0,-648,0,1512,0,-1296,0,198,0,216,0,-72,0,0,0,1', '81,0,648,0,1512,0,1296,0,198,0,-216,0,-72,0,0,0,1', '862,-2144,-7520,8896,-39160,180160,-85392,178160,-46084,-897568,1204912,-2897696,3643032,-299552,1302656,82368,-2404226,-1627824,-64112,707984,171696,-105024,-72760,6576,10760,160,-744,144,160,-48,-16,0,1']}, 'subfield_mults': [1, 1, 1, 1, 1], 'subfields': ['-2.0.1', '18.0.-12.0.1', '-9.0.-6.0.1', '-2.0.0.0.1', '7.40.72.40.-10.-16.-8.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( -\\frac{1}{9612} a^{12} + \\frac{1}{534} a^{10} - \\frac{11}{1068} a^{8} + \\frac{1}{89} a^{6} + \\frac{55}{1068} a^{4} - \\frac{19}{178} a^{2} + \\frac{863}{356} \\)', '\\( \\frac{7}{19224} a^{12} - \\frac{7}{1068} a^{10} + \\frac{40}{801} a^{8} - \\frac{55}{267} a^{6} + \\frac{1573}{2136} a^{4} - \\frac{757}{356} a^{2} + \\frac{139}{356} \\)', '\\( -\\frac{31}{38448} a^{14} + \\frac{221}{12816} a^{12} - \\frac{2009}{12816} a^{10} + \\frac{10099}{12816} a^{8} - \\frac{45}{16} a^{6} + \\frac{11849}{1424} a^{4} - \\frac{17317}{1424} a^{2} + \\frac{699}{1424} \\)', '\\( \\frac{73}{38448} a^{14} - \\frac{65}{1602} a^{12} + \\frac{4775}{12816} a^{10} - \\frac{6113}{3204} a^{8} + \\frac{9851}{1424} a^{6} - \\frac{3673}{178} a^{4} + \\frac{46379}{1424} a^{2} - \\frac{2595}{356} \\)', '\\( -\\frac{37}{269136} a^{15} + \\frac{11}{9612} a^{14} + \\frac{839}{269136} a^{13} - \\frac{155}{6408} a^{12} - \\frac{133}{4272} a^{11} + \\frac{469}{2136} a^{10} + \\frac{1145}{6408} a^{9} - \\frac{14237}{12816} a^{8} - \\frac{21757}{29904} a^{7} + \\frac{4259}{1068} a^{6} + \\frac{70817}{29904} a^{5} - \\frac{1039}{89} a^{4} - \\frac{48893}{9968} a^{3} + \\frac{12123}{712} a^{2} + \\frac{2300}{623} a - \\frac{3815}{1424} \\)', '\\( \\frac{97}{67284} a^{15} + \\frac{1}{9612} a^{14} - \\frac{4663}{134568} a^{13} - \\frac{7}{9612} a^{12} + \\frac{4663}{12816} a^{11} - \\frac{11}{1068} a^{10} - \\frac{1163}{534} a^{9} + \\frac{703}{4272} a^{8} + \\frac{1495}{168} a^{7} - \\frac{247}{267} a^{6} - \\frac{428255}{14952} a^{5} + \\frac{7295}{2136} a^{4} + \\frac{625559}{9968} a^{3} - \\frac{23}{2} a^{2} - \\frac{37316}{623} a + \\frac{24595}{1424} \\)', '\\( -\\frac{5}{14952} a^{15} + \\frac{1}{9612} a^{14} + \\frac{1045}{134568} a^{13} - \\frac{17}{4806} a^{12} - \\frac{967}{12816} a^{11} + \\frac{43}{1068} a^{10} + \\frac{433}{1068} a^{9} - \\frac{1019}{4272} a^{8} - \\frac{2791}{1869} a^{7} + \\frac{469}{534} a^{6} + \\frac{69521}{14952} a^{5} - \\frac{6289}{2136} a^{4} - \\frac{80067}{9968} a^{3} + \\frac{911}{178} a^{2} + \\frac{7489}{2492} a - \\frac{1639}{1424} \\)', '\\( \\frac{5}{14952} a^{15} + \\frac{1}{9612} a^{14} - \\frac{1045}{134568} a^{13} - \\frac{35}{9612} a^{12} + \\frac{967}{12816} a^{11} + \\frac{15}{356} a^{10} - \\frac{433}{1068} a^{9} - \\frac{1063}{4272} a^{8} + \\frac{2791}{1869} a^{7} + \\frac{475}{534} a^{6} - \\frac{69521}{14952} a^{5} - \\frac{6179}{2136} a^{4} + \\frac{80067}{9968} a^{3} + \\frac{446}{89} a^{2} - \\frac{7489}{2492} a + \\frac{389}{1424} \\)', '\\( \\frac{19}{33642} a^{15} + \\frac{11}{9612} a^{14} - \\frac{19}{1512} a^{13} - \\frac{17}{712} a^{12} + \\frac{775}{6408} a^{11} + \\frac{457}{2136} a^{10} - \\frac{8417}{12816} a^{9} - \\frac{13663}{12816} a^{8} + \\frac{4679}{1869} a^{7} + \\frac{4045}{1068} a^{6} - \\frac{4821}{623} a^{5} - \\frac{986}{89} a^{4} + \\frac{71569}{4984} a^{3} + \\frac{11283}{712} a^{2} - \\frac{92469}{9968} a - \\frac{109}{1424} \\)', '\\( \\frac{5}{14952} a^{15} + \\frac{11}{19224} a^{14} - \\frac{145}{22428} a^{13} - \\frac{467}{38448} a^{12} + \\frac{667}{12816} a^{11} + \\frac{473}{4272} a^{10} - \\frac{1417}{6408} a^{9} - \\frac{7229}{12816} a^{8} + \\frac{855}{1246} a^{7} + \\frac{545}{267} a^{6} - \\frac{4469}{2492} a^{5} - \\frac{8661}{1424} a^{4} + \\frac{3655}{9968} a^{3} + \\frac{13649}{1424} a^{2} + \\frac{20897}{4984} a - \\frac{2629}{1424} \\)', '\\( -\\frac{17}{12816} a^{15} - \\frac{11}{19224} a^{14} + \\frac{121}{4272} a^{13} + \\frac{457}{38448} a^{12} - \\frac{833}{3204} a^{11} - \\frac{151}{1424} a^{10} + \\frac{1899}{1424} a^{9} + \\frac{6721}{12816} a^{8} - \\frac{20785}{4272} a^{7} - \\frac{493}{267} a^{6} + \\frac{701}{48} a^{5} + \\frac{7539}{1424} a^{4} - \\frac{16441}{712} a^{3} - \\frac{10469}{1424} a^{2} + \\frac{8355}{1424} a + \\frac{1469}{1424} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', '1/3*a^4', '1/3*a^5', '1/3*a^6', '1/3*a^7', '1/144*a^8 - 1/6*a^7 + 1/12*a^6 - 1/6*a^5 + 1/24*a^4 - 1/2*a^3 + 1/4*a^2 - 1/2*a - 1/16', '1/144*a^9 + 1/12*a^7 - 1/6*a^6 + 1/24*a^5 - 1/6*a^4 + 1/4*a^3 - 1/2*a^2 - 1/16*a - 1/2', '1/144*a^10 - 1/6*a^7 + 1/24*a^6 - 1/6*a^5 + 1/12*a^4 - 1/2*a^3 - 1/16*a^2 - 1/2*a - 1/4', '1/144*a^11 + 1/24*a^7 - 1/6*a^6 + 1/12*a^5 - 1/6*a^4 - 1/16*a^3 - 1/2*a^2 - 1/4*a - 1/2', '1/38448*a^12 - 1/2136*a^10 + 11/4272*a^8 + 175/1068*a^6 - 137/1424*a^4 + 19/712*a^2 - 151/1424', '1/38448*a^13 - 1/2136*a^11 + 11/4272*a^9 + 175/1068*a^7 - 137/1424*a^5 + 19/712*a^3 - 151/1424*a', '1/38448*a^14 + 7/6408*a^10 + 1/534*a^8 - 1/6*a^7 + 263/4272*a^6 - 1/6*a^5 + 137/1068*a^4 - 1/2*a^3 - 67/356*a^2 - 1/2*a - 101/356', '1/269136*a^15 - 1/89712*a^13 + 5/2136*a^11 + 1/6408*a^9 + 1049/9968*a^7 + 1247/29904*a^5 - 51/2492*a^3 + 131/623*a']}
Number field data - 16.8.9803356117276277820358656.110