-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 8, 16, -12, -54, -8, 78, 12, -62, 20, 28, -36, -5, 20, -2, -4, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 9349208943630483456, 'disc_rad': 6, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[12, 1], [4, 1]]], [7, [[6, 2], [2, 2]]], [11, [[12, 1], [4, 1]]], [13, [[4, 4]]], [17, [[4, 4]]], [19, [[4, 4]]], [23, [[2, 8]]], [29, [[4, 4]]], [31, [[3, 4], [1, 4]]], [37, [[4, 4]]], [41, [[2, 8]]], [43, [[4, 4]]], [47, [[4, 4]]], [53, [[12, 1], [4, 1]]], [59, [[4, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [264, 112], 'galois_label': '16T181', 'galt': 181, 'grd': 24.23672593327708, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '16.8.9349208943630483456.1', 'local_algs': ['2.4.4.44a1.1155', '3.4.1.0a1.1', '3.4.3.12a1.1'], 'minimal_sibling': [8, 0, -24, 0, 33, 0, -26, 0, 15, 0, -6, 0, 1], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 2, 'r2': 4, 'ramps': [2, 3], 'rd': 15.3346345019, 'regulator': {'__RealLiteral__': 0, 'data': '2452.93509651', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-2.0.1', '2.0.-4.0.1', '6.-8.0.0.1', '-1.4.2.-16.19.-16.10.-4.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{315967}{54809} a^{15} - \\frac{1300018}{54809} a^{14} - \\frac{491673}{54809} a^{13} + \\frac{6453458}{54809} a^{12} - \\frac{2498359}{54809} a^{11} - \\frac{11204238}{54809} a^{10} + \\frac{10833171}{54809} a^{9} + \\frac{4835746}{54809} a^{8} - \\frac{21026041}{54809} a^{7} + \\frac{7229132}{54809} a^{6} + \\frac{23924992}{54809} a^{5} - \\frac{6894323}{54809} a^{4} - \\frac{15835894}{54809} a^{3} - \\frac{552472}{54809} a^{2} + \\frac{5150952}{54809} a + \\frac{1266276}{54809} \\)', '\\( \\frac{419196}{54809} a^{15} - \\frac{1807143}{54809} a^{14} - \\frac{252718}{54809} a^{13} + \\frac{8362423}{54809} a^{12} - \\frac{4674982}{54809} a^{11} - \\frac{13352067}{54809} a^{10} + \\frac{15684084}{54809} a^{9} + \\frac{3328043}{54809} a^{8} - \\frac{26605386}{54809} a^{7} + \\frac{13076690}{54809} a^{6} + \\frac{28123408}{54809} a^{5} - \\frac{11897336}{54809} a^{4} - \\frac{18547145}{54809} a^{3} + \\frac{859523}{54809} a^{2} + \\frac{6202426}{54809} a + \\frac{1371687}{54809} \\)', '\\( \\frac{56424}{54809} a^{15} - \\frac{206952}{54809} a^{14} - \\frac{168099}{54809} a^{13} + \\frac{1031630}{54809} a^{12} + \\frac{7526}{54809} a^{11} - \\frac{1877602}{54809} a^{10} + \\frac{1081512}{54809} a^{9} + \\frac{1343193}{54809} a^{8} - \\frac{3170371}{54809} a^{7} - \\frac{278308}{54809} a^{6} + \\frac{4179464}{54809} a^{5} + \\frac{369419}{54809} a^{4} - \\frac{2695381}{54809} a^{3} - \\frac{623160}{54809} a^{2} + \\frac{728922}{54809} a + \\frac{272552}{54809} \\)', '\\( \\frac{93660}{54809} a^{15} - \\frac{438084}{54809} a^{14} + \\frac{104362}{54809} a^{13} + \\frac{1794754}{54809} a^{12} - \\frac{1570091}{54809} a^{11} - \\frac{2379113}{54809} a^{10} + \\frac{3927402}{54809} a^{9} - \\frac{521227}{54809} a^{8} - \\frac{5322503}{54809} a^{7} + \\frac{4210967}{54809} a^{6} + \\frac{4865771}{54809} a^{5} - \\frac{3392754}{54809} a^{4} - \\frac{3143428}{54809} a^{3} + \\frac{649126}{54809} a^{2} + \\frac{1046583}{54809} a + \\frac{127900}{54809} \\)', '\\( \\frac{258149}{54809} a^{15} - \\frac{1131362}{54809} a^{14} - \\frac{87322}{54809} a^{13} + \\frac{5174653}{54809} a^{12} - \\frac{3116434}{54809} a^{11} - \\frac{8153672}{54809} a^{10} + \\frac{9862976}{54809} a^{9} + \\frac{1715266}{54809} a^{8} - \\frac{16263205}{54809} a^{7} + \\frac{8567491}{54809} a^{6} + \\frac{17203593}{54809} a^{5} - \\frac{7517992}{54809} a^{4} - \\frac{11568607}{54809} a^{3} + \\frac{421069}{54809} a^{2} + \\frac{3986706}{54809} a + \\frac{891741}{54809} \\)', '\\( \\frac{225148}{54809} a^{15} - \\frac{946583}{54809} a^{14} - \\frac{251140}{54809} a^{13} + \\frac{4561951}{54809} a^{12} - \\frac{2187989}{54809} a^{11} - \\frac{7581034}{54809} a^{10} + \\frac{8281142}{54809} a^{9} + \\frac{2449103}{54809} a^{8} - \\frac{14835783}{54809} a^{7} + \\frac{6521055}{54809} a^{6} + \\frac{15844483}{54809} a^{5} - \\frac{6128747}{54809} a^{4} - \\frac{10150376}{54809} a^{3} + \\frac{256823}{54809} a^{2} + \\frac{3325516}{54809} a + \\frac{742652}{54809} \\)', '\\( \\frac{92691}{54809} a^{15} - \\frac{357760}{54809} a^{14} - \\frac{266136}{54809} a^{13} + \\frac{1997911}{54809} a^{12} - \\frac{401694}{54809} a^{11} - \\frac{3872422}{54809} a^{10} + \\frac{3103106}{54809} a^{9} + \\frac{2410831}{54809} a^{8} - \\frac{7004789}{54809} a^{7} + \\frac{1462113}{54809} a^{6} + \\frac{8365159}{54809} a^{5} - \\frac{2046868}{54809} a^{4} - \\frac{5549180}{54809} a^{3} - \\frac{127967}{54809} a^{2} + \\frac{1858875}{54809} a + \\frac{446688}{54809} \\)', '\\( \\frac{225393}{54809} a^{15} - \\frac{929787}{54809} a^{14} - \\frac{352661}{54809} a^{13} + \\frac{4681630}{54809} a^{12} - \\frac{1943346}{54809} a^{11} - \\frac{8100549}{54809} a^{10} + \\frac{8233780}{54809} a^{9} + \\frac{3197226}{54809} a^{8} - \\frac{15472001}{54809} a^{7} + \\frac{6063101}{54809} a^{6} + \\frac{16936166}{54809} a^{5} - \\frac{5893685}{54809} a^{4} - \\frac{10884224}{54809} a^{3} - \\frac{42355}{54809} a^{2} + \\frac{3599165}{54809} a + \\frac{804022}{54809} \\)', '\\( \\frac{253803}{54809} a^{15} - \\frac{1118569}{54809} a^{14} - \\frac{82633}{54809} a^{13} + \\frac{5193943}{54809} a^{12} - \\frac{3195093}{54809} a^{11} - \\frac{8320518}{54809} a^{10} + \\frac{10093957}{54809} a^{9} + \\frac{1906689}{54809} a^{8} - \\frac{16550453}{54809} a^{7} + \\frac{8864309}{54809} a^{6} + \\frac{17619377}{54809} a^{5} - \\frac{8159123}{54809} a^{4} - \\frac{12210116}{54809} a^{3} + \\frac{565560}{54809} a^{2} + \\frac{4360839}{54809} a + \\frac{1012266}{54809} \\)', '\\( \\frac{34150}{54809} a^{15} - \\frac{163279}{54809} a^{14} + \\frac{29087}{54809} a^{13} + \\frac{740198}{54809} a^{12} - \\frac{562539}{54809} a^{11} - \\frac{1226087}{54809} a^{10} + \\frac{1517879}{54809} a^{9} + \\frac{295327}{54809} a^{8} - \\frac{2383669}{54809} a^{7} + \\frac{1444339}{54809} a^{6} + \\frac{2809362}{54809} a^{5} - \\frac{1370057}{54809} a^{4} - \\frac{2256289}{54809} a^{3} + \\frac{58234}{54809} a^{2} + \\frac{877674}{54809} a + \\frac{244511}{54809} \\)', '\\( \\frac{410595}{54809} a^{15} - \\frac{1747131}{54809} a^{14} - \\frac{379704}{54809} a^{13} + \\frac{8346799}{54809} a^{12} - \\frac{4281037}{54809} a^{11} - \\frac{13698635}{54809} a^{10} + \\frac{15328243}{54809} a^{9} + \\frac{4057666}{54809} a^{8} - \\frac{26843046}{54809} a^{7} + \\frac{12338278}{54809} a^{6} + \\frac{28716844}{54809} a^{5} - \\frac{11297686}{54809} a^{4} - \\frac{18848392}{54809} a^{3} + \\frac{475198}{54809} a^{2} + \\frac{6397757}{54809} a + \\frac{1337997}{54809} \\)'], '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', '1/54809*a^15 - 16486/54809*a^14 - 20772/54809*a^13 + 27110/54809*a^12 - 24057/54809*a^11 + 19132/54809*a^10 - 17419/54809*a^9 + 10436/54809*a^8 - 15572/54809*a^7 - 12831/54809*a^6 - 27311/54809*a^5 - 6423/54809*a^4 - 27156/54809*a^3 + 14886/54809*a^2 - 25952/54809*a + 11436/54809']}
Number field data - 16.8.9349208943630483456.1