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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [324, 0, 864, 0, 2808, 0, -1632, 0, 418, 0, -128, 0, 36, 0, -8, 0, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 30257271966902092038144, 'disc_rad': 6, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[2, 8]]], [7, [[8, 2]]], [11, [[2, 8]]], [13, [[8, 2]]], [17, [[2, 8]]], [19, [[4, 4]]], [23, [[2, 8]]], [29, [[2, 8]]], [31, [[8, 2]]], [37, [[8, 2]]], [41, [[2, 8]]], [43, [[4, 4]]], [47, [[2, 8]]], [53, [[2, 8]]], [59, [[2, 8]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [62, 8], 'galois_label': '16T13', 'galt': 13, 'grd': 25.412761497225222, 'inessentialp': [3], 'is_galois': True, 'is_minimal_sibling': False, 'iso_number': 101, 'label': '16.0.30257271966902092038144.101', 'local_algs': ['2.16.62.8', '3.4.2.1', '3.4.2.1', '3.4.2.1', '3.4.2.1'], 'minimal_sibling': [24, 0, -32, 0, 24, 0, 0, 0, 1], 'monogenic': -1, 'num_ram': 2, 'r2': 8, 'ramps': [2, 3], 'rd': 25.412761497225222, 'regulator': {'__RealLiteral__': 0, 'data': '200959.74917378288', 'prec': 60}, 'res': {'sib': ['-50,0,16,0,12,0,-8,0,1', '24,0,-32,0,24,0,0,0,1']}, 'subfield_mults': [1, 1, 1, 1, 2, 2, 1, 4, 4], 'subfields': ['1.-1.1', '2.0.1', '-6.0.1', '4.0.-2.0.1', '6.0.-4.0.1', '-2.0.4.0.1', '36.0.24.0.10.0.4.0.1', '24.0.-32.0.24.0.0.0.1', '-50.0.16.0.12.0.-8.0.1'], 'torsion_gen': '\\( \\frac{430}{1045143} a^{14} - \\frac{5561}{1045143} a^{12} + \\frac{8632}{348381} a^{10} - \\frac{201889}{2090286} a^{8} + \\frac{309424}{1045143} a^{6} - \\frac{43990}{38709} a^{4} + \\frac{110168}{38709} a^{2} + \\frac{34061}{38709} \\)', 'torsion_order': 6, 'units': ['\\( \\frac{3104}{1045143} a^{14} - \\frac{53099}{2090286} a^{12} + \\frac{40826}{348381} a^{10} - \\frac{438631}{1045143} a^{8} + \\frac{1435664}{1045143} a^{6} - \\frac{620362}{116127} a^{4} + \\frac{128548}{12903} a^{2} + \\frac{48487}{38709} \\)', '\\( -\\frac{355}{6270858} a^{15} + \\frac{2216}{1741905} a^{14} + \\frac{159337}{31354290} a^{13} - \\frac{1057}{696762} a^{12} - \\frac{129442}{5225715} a^{11} + \\frac{8011}{1161270} a^{10} + \\frac{668699}{6270858} a^{9} + \\frac{33157}{3483810} a^{8} - \\frac{5056864}{15677145} a^{7} + \\frac{59216}{1741905} a^{6} + \\frac{135736}{116127} a^{5} - \\frac{16153}{64515} a^{4} - \\frac{2663348}{580635} a^{3} - \\frac{53765}{12903} a^{2} - \\frac{34517}{580635} a - \\frac{103892}{64515} \\)', '\\( \\frac{63713}{15677145} a^{15} - \\frac{1757}{348381} a^{14} - \\frac{115697}{3135429} a^{13} + \\frac{132403}{3483810} a^{12} + \\frac{1870423}{10451430} a^{11} - \\frac{195571}{1161270} a^{10} - \\frac{20979899}{31354290} a^{9} + \\frac{408401}{696762} a^{8} + \\frac{34818998}{15677145} a^{7} - \\frac{3339811}{1741905} a^{6} - \\frac{4866104}{580635} a^{5} + \\frac{870733}{116127} a^{4} + \\frac{2114678}{116127} a^{3} - \\frac{2182111}{193545} a^{2} - \\frac{4292591}{580635} a - \\frac{151456}{21505} \\)', '\\( -\\frac{63713}{15677145} a^{15} - \\frac{1757}{348381} a^{14} + \\frac{115697}{3135429} a^{13} + \\frac{132403}{3483810} a^{12} - \\frac{1870423}{10451430} a^{11} - \\frac{195571}{1161270} a^{10} + \\frac{20979899}{31354290} a^{9} + \\frac{408401}{696762} a^{8} - \\frac{34818998}{15677145} a^{7} - \\frac{3339811}{1741905} a^{6} + \\frac{4866104}{580635} a^{5} + \\frac{870733}{116127} a^{4} - \\frac{2114678}{116127} a^{3} - \\frac{2182111}{193545} a^{2} + \\frac{4292591}{580635} a - \\frac{151456}{21505} \\)', '\\( -\\frac{7162}{15677145} a^{15} + \\frac{779}{1741905} a^{14} + \\frac{103687}{31354290} a^{13} - \\frac{11867}{3483810} a^{12} - \\frac{79318}{5225715} a^{11} + \\frac{18613}{1161270} a^{10} + \\frac{1622341}{31354290} a^{9} - \\frac{233507}{3483810} a^{8} - \\frac{2411491}{15677145} a^{7} + \\frac{417968}{1741905} a^{6} + \\frac{310091}{580635} a^{5} - \\frac{17229}{21505} a^{4} - \\frac{244808}{580635} a^{3} + \\frac{47228}{64515} a^{2} - \\frac{865463}{580635} a + \\frac{96724}{64515} \\)', '\\( \\frac{63713}{15677145} a^{15} + \\frac{7885}{2090286} a^{14} - \\frac{115697}{3135429} a^{13} - \\frac{315871}{10451430} a^{12} + \\frac{1870423}{10451430} a^{11} + \\frac{460457}{3483810} a^{10} - \\frac{20979899}{31354290} a^{9} - \\frac{963209}{2090286} a^{8} + \\frac{34818998}{15677145} a^{7} + \\frac{7756537}{5225715} a^{6} - \\frac{4866104}{580635} a^{5} - \\frac{677707}{116127} a^{4} + \\frac{2114678}{116127} a^{3} + \\frac{622298}{64515} a^{2} - \\frac{4292591}{580635} a + \\frac{1397096}{193545} \\)', '\\( -\\frac{7162}{15677145} a^{15} + \\frac{388}{580635} a^{14} + \\frac{103687}{31354290} a^{13} - \\frac{1435}{232254} a^{12} - \\frac{79318}{5225715} a^{11} + \\frac{28469}{1161270} a^{10} + \\frac{1622341}{31354290} a^{9} - \\frac{93529}{1161270} a^{8} - \\frac{2411491}{15677145} a^{7} + \\frac{136448}{580635} a^{6} + \\frac{310091}{580635} a^{5} - \\frac{615113}{580635} a^{4} - \\frac{244808}{580635} a^{3} + \\frac{100103}{38709} a^{2} - \\frac{865463}{580635} a + \\frac{47752}{64515} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/3*a^6 - 1/3*a^4 + 1/3*a^2', '1/9*a^7 - 1/9*a^5 - 2/9*a^3 - 1/3*a', '1/18*a^8 + 1/9*a^6 + 2/9*a^4', '1/18*a^9 + 1/3*a^5 + 2/9*a^3 + 1/3*a', '1/18*a^10 - 4/9*a^4', '1/18*a^11 - 4/9*a^5', '1/270*a^12 + 2/135*a^10 - 7/135*a^6 + 10/27*a^4 - 1/45*a^2 + 2/15', '1/270*a^13 + 2/135*a^11 - 7/135*a^7 + 10/27*a^5 - 1/45*a^3 + 2/15*a', '1/10451430*a^14 - 2302/5225715*a^12 + 47011/3483810*a^10 - 83009/10451430*a^8 + 306611/5225715*a^6 - 12304/193545*a^4 - 94934/193545*a^2 - 49877/193545', '1/31354290*a^15 - 2302/15677145*a^13 - 73267/5225715*a^11 + 248813/15677145*a^9 - 854659/15677145*a^7 - 205849/580635*a^5 - 159449/580635*a^3 - 49877/580635*a']}
Number field data - 16.0.30257271966902092038144.101