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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -5, 18, -31, 21, -9, 14, 6, -33, 19, 5, -6, 5, -10, 9, -4, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 169561224228515625, 'disc_rad': 165, 'disc_sign': 1, 'frobs': [[2, [[8, 2]]], [3, [0]], [5, [0]], [7, [[8, 2]]], [11, [0]], [13, [[8, 2]]], [17, [[8, 2]]], [19, [[4, 4]]], [23, [[4, 2], [2, 4]]], [29, [[2, 8]]], [31, [[4, 4]]], [37, [[4, 2], [2, 4]]], [41, [[4, 4]]], [43, [[8, 2]]], [47, [[4, 2], [2, 4]]], [53, [[4, 2], [2, 4]]], [59, [[2, 8]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [16, 24, 16], 'galois_label': '16T42', 'galt': 42, 'grd': 19.208102881010017, 'inessentialp': [3], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 2, 'label': '16.0.169561224228515625.2', 'local_algs': ['3.2.1.0a1.1', '3.2.1.0a1.1', '3.2.1.0a1.1', '3.2.1.0a1.1', '3.2.2.2a1.1', '3.2.2.2a1.1', '5.4.2.4a1.2', '5.2.4.6a1.3', '11.4.2.4a1.2', '11.4.2.4a1.2'], 'maximal_cm_subfield': [16, 0, 3, 0, 1], 'minimal_sibling': [1, 1, 1, -2, -3, 2, 1, -1, 1], 'monogenic': -1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 3, 'r2': 8, 'ramps': [3, 5, 11], 'rd': 11.9352881627, 'regulator': {'__RealLiteral__': 0, 'data': '93.9208233904', 'prec': 44}, 'res': {'gal': ['256,0,-256,0,96,0,2396,0,481,0,-3207,0,2213,0,1783,0,-2403,0,556,0,1337,0,-1461,0,886,0,-328,0,84,0,-13,0,1'], 'sib': ['1,-3,3,-9,7,-15,27,-3,-15,-3,27,-15,7,-9,3,-3,1', '1,1,1,-2,-3,2,1,-1,1', '9,-13,10,10,-14,6,3,-3,1']}, 'subfield_mults': [1, 1, 1, 2, 2, 1, 1, 1, 1], 'subfields': ['-1.-1.1', '3.-1.1', '14.-1.1', '-1.2.0.-1.1', '1.1.1.-1.1', '16.0.3.0.1', '1.1.1.-2.-3.2.1.-1.1', '9.-13.10.10.-14.6.3.-3.1', '1.-4.11.-11.18.-13.9.-3.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{906400}{5235327} a^{15} - \\frac{3566264}{5235327} a^{14} + \\frac{6872639}{5235327} a^{13} - \\frac{1966244}{1745109} a^{12} - \\frac{802744}{5235327} a^{11} - \\frac{3639995}{5235327} a^{10} + \\frac{4827181}{5235327} a^{9} + \\frac{7670798}{1745109} a^{8} - \\frac{8258743}{1745109} a^{7} - \\frac{8301}{2731} a^{6} + \\frac{15985562}{5235327} a^{5} + \\frac{4081810}{5235327} a^{4} + \\frac{20980025}{5235327} a^{3} - \\frac{7427242}{1745109} a^{2} - \\frac{1435055}{1745109} a - \\frac{3143501}{5235327} \\)', '\\( \\frac{3748139}{5235327} a^{15} - \\frac{12521116}{5235327} a^{14} + \\frac{25123603}{5235327} a^{13} - \\frac{6750149}{1745109} a^{12} + \\frac{4246021}{5235327} a^{11} - \\frac{20177836}{5235327} a^{10} + \\frac{6004976}{5235327} a^{9} + \\frac{25414871}{1745109} a^{8} - \\frac{2602297}{193901} a^{7} - \\frac{140800}{24579} a^{6} + \\frac{31602502}{5235327} a^{5} - \\frac{7369375}{5235327} a^{4} + \\frac{72774580}{5235327} a^{3} - \\frac{21346267}{1745109} a^{2} + \\frac{6153595}{1745109} a - \\frac{7582219}{5235327} \\)', '\\( \\frac{860995}{5235327} a^{15} - \\frac{1328321}{5235327} a^{14} + \\frac{1538042}{5235327} a^{13} + \\frac{344953}{581703} a^{12} - \\frac{2373664}{5235327} a^{11} - \\frac{5523152}{5235327} a^{10} - \\frac{6331487}{5235327} a^{9} + \\frac{1597664}{581703} a^{8} + \\frac{5149798}{1745109} a^{7} - \\frac{82231}{24579} a^{6} - \\frac{14800471}{5235327} a^{5} - \\frac{252761}{5235327} a^{4} + \\frac{13584152}{5235327} a^{3} + \\frac{639058}{193901} a^{2} - \\frac{394018}{581703} a - \\frac{3913223}{5235327} \\)', '\\( \\frac{1231802}{5235327} a^{15} - \\frac{4451125}{5235327} a^{14} + \\frac{9379723}{5235327} a^{13} - \\frac{3111688}{1745109} a^{12} + \\frac{4146766}{5235327} a^{11} - \\frac{8466427}{5235327} a^{10} + \\frac{3276689}{5235327} a^{9} + \\frac{8665339}{1745109} a^{8} - \\frac{9539684}{1745109} a^{7} - \\frac{479}{2731} a^{6} + \\frac{4297171}{5235327} a^{5} - \\frac{5431315}{5235327} a^{4} + \\frac{30126817}{5235327} a^{3} - \\frac{9725519}{1745109} a^{2} + \\frac{4001408}{1745109} a - \\frac{7542037}{5235327} \\)', '\\( \\frac{3132173}{5235327} a^{15} - \\frac{10441699}{5235327} a^{14} + \\frac{21477763}{5235327} a^{13} - \\frac{5921819}{1745109} a^{12} + \\frac{5532685}{5235327} a^{11} - \\frac{16848058}{5235327} a^{10} + \\frac{6144866}{5235327} a^{9} + \\frac{20404382}{1745109} a^{8} - \\frac{2316612}{193901} a^{7} - \\frac{86392}{24579} a^{6} + \\frac{27820042}{5235327} a^{5} - \\frac{8633548}{5235327} a^{4} + \\frac{54765325}{5235327} a^{3} - \\frac{19899973}{1745109} a^{2} + \\frac{8771176}{1745109} a - \\frac{4757818}{5235327} \\)', '\\( \\frac{1286407}{1745109} a^{15} - \\frac{4722763}{1745109} a^{14} + \\frac{10267793}{1745109} a^{13} - \\frac{10195018}{1745109} a^{12} + \\frac{488202}{193901} a^{11} - \\frac{6970453}{1745109} a^{10} + \\frac{4198273}{1745109} a^{9} + \\frac{24102961}{1745109} a^{8} - \\frac{33789829}{1745109} a^{7} + \\frac{18305}{24579} a^{6} + \\frac{15461224}{1745109} a^{5} - \\frac{10327649}{1745109} a^{4} + \\frac{8267857}{581703} a^{3} - \\frac{30284597}{1745109} a^{2} + \\frac{17361089}{1745109} a - \\frac{4403563}{1745109} \\)', '\\( \\frac{1039367}{5235327} a^{15} - \\frac{4713811}{5235327} a^{14} + \\frac{11469718}{5235327} a^{13} - \\frac{4763090}{1745109} a^{12} + \\frac{8287792}{5235327} a^{11} - \\frac{5162719}{5235327} a^{10} + \\frac{7714196}{5235327} a^{9} + \\frac{5928932}{1745109} a^{8} - \\frac{5445824}{581703} a^{7} + \\frac{97613}{24579} a^{6} + \\frac{26181151}{5235327} a^{5} - \\frac{17850691}{5235327} a^{4} + \\frac{18562105}{5235327} a^{3} - \\frac{14700154}{1745109} a^{2} + \\frac{10991338}{1745109} a - \\frac{4821583}{5235327} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', '1/3*a^10 - 1/3*a^7 - 1/3*a^6 - 1/3*a^5 - 1/3*a^4 - 1/3*a^3 + 1/3*a^2 - 1/3*a - 1/3', '1/3*a^11 - 1/3*a^8 - 1/3*a^7 - 1/3*a^6 - 1/3*a^5 - 1/3*a^4 + 1/3*a^3 - 1/3*a^2 - 1/3*a', '1/3*a^12 - 1/3*a^9 - 1/3*a^8 - 1/3*a^7 - 1/3*a^6 - 1/3*a^5 + 1/3*a^4 - 1/3*a^3 - 1/3*a^2', '1/3*a^13 - 1/3*a^9 - 1/3*a^8 + 1/3*a^7 + 1/3*a^6 + 1/3*a^4 + 1/3*a^3 + 1/3*a^2 - 1/3*a - 1/3', '1/9*a^14 - 1/9*a^12 + 1/9*a^11 + 1/9*a^10 - 1/3*a^9 + 1/9*a^8 + 2/9*a^7 + 4/9*a^6 - 1/9*a^5 + 1/3*a^4 + 4/9*a^3 + 4/9*a^2 - 4/9*a + 4/9', '1/5235327*a^15 - 252806/5235327*a^14 + 480623/5235327*a^13 + 252823/1745109*a^12 - 373867/5235327*a^11 - 778112/5235327*a^10 - 2161760/5235327*a^9 - 360967/1745109*a^8 - 315196/1745109*a^7 - 373/8193*a^6 + 1219865/5235327*a^5 - 865022/5235327*a^4 - 317125/5235327*a^3 + 423956/1745109*a^2 - 473768/1745109*a - 723752/5235327']}
Number field data - 16.0.169561224228515625.2