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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [16, 0, -96, 0, 264, 0, -352, 0, 344, 0, -184, 0, 56, 0, -8, 0, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 4294967296000000000000, 'disc_rad': 10, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[4, 4]]], [5, [0]], [7, [[4, 4]]], [11, [[4, 4]]], [13, [[4, 4]]], [17, [[4, 4]]], [19, [[4, 4]]], [23, [[4, 4]]], [29, [[4, 4]]], [31, [[2, 4], [1, 8]]], [37, [[4, 4]]], [41, [[1, 16]]], [43, [[4, 4]]], [47, [[4, 4]]], [53, [[4, 4]]], [59, [[4, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [96, 24], 'galois_label': '16T17', 'galt': 17, 'grd': 26.74961219905688, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 3, 'label': '16.0.4294967296000000000000.3', 'local_algs': ['m2.4.4.44', '5.16.12.1'], 'monogenic': 0, 'num_ram': 2, 'r2': 8, 'ramps': [2, 5], 'rd': 22.4936530076, 'regulator': {'__RealLiteral__': 0, 'data': '73929.9567996', 'prec': 44}, 'res': {'gal': ['1,0,0,0,0,0,0,0,-11,0,0,0,0,0,0,0,46,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,1'], 'sib': ['1,0,-16,0,-216,0,-312,0,19,0,96,0,-4,0,-8,0,1']}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1, 1, 1], 'subfields': ['-1.-1.1', '-2.0.1', '-10.0.1', '1.-1.1.-1.1', '20.0.10.0.1', '4.0.-6.0.1', '4.0.8.0.-10.0.-4.0.1', '16.0.8.0.4.0.2.0.1', '100.0.0.0.-60.0.0.0.1'], 'torsion_gen': '\\( -\\frac{1826}{31201} a^{14} + \\frac{109929}{249608} a^{12} - \\frac{191063}{62402} a^{10} + \\frac{1156481}{124804} a^{8} - \\frac{481211}{31201} a^{6} + \\frac{385931}{31201} a^{4} - \\frac{277106}{31201} a^{2} + \\frac{52282}{31201} \\)', 'torsion_order': 10, 'units': ['\\( \\frac{1129}{31201} a^{14} - \\frac{71471}{249608} a^{12} + \\frac{62834}{31201} a^{10} - \\frac{409013}{62402} a^{8} + \\frac{386501}{31201} a^{6} - \\frac{791091}{62402} a^{4} + \\frac{298836}{31201} a^{2} - \\frac{109149}{31201} \\)', '\\( \\frac{2445}{124804} a^{14} - \\frac{38315}{249608} a^{12} + \\frac{66269}{62402} a^{10} - \\frac{211957}{62402} a^{8} + \\frac{368005}{62402} a^{6} - \\frac{370855}{62402} a^{4} + \\frac{132360}{31201} a^{2} - \\frac{33828}{31201} \\)', '\\( \\frac{4069}{124804} a^{14} - \\frac{7819}{31201} a^{12} + \\frac{54307}{31201} a^{10} - \\frac{334391}{62402} a^{8} + \\frac{559097}{62402} a^{6} - \\frac{374337}{62402} a^{4} + \\frac{86666}{31201} a^{2} - \\frac{17669}{31201} \\)', '\\( \\frac{23117}{249608} a^{15} + \\frac{1036}{31201} a^{14} - \\frac{88667}{124804} a^{13} - \\frac{73681}{249608} a^{12} + \\frac{610507}{124804} a^{11} + \\frac{126343}{62402} a^{10} - \\frac{936165}{62402} a^{9} - \\frac{901341}{124804} a^{8} + \\frac{747331}{31201} a^{7} + \\frac{410571}{31201} a^{6} - \\frac{1034569}{62402} a^{5} - \\frac{332591}{31201} a^{4} + \\frac{235228}{31201} a^{3} + \\frac{75987}{31201} a^{2} - \\frac{47327}{31201} a - \\frac{17941}{31201} \\)', '\\( \\frac{17}{761} a^{15} - \\frac{6093}{249608} a^{14} - \\frac{469}{3044} a^{13} + \\frac{47071}{249608} a^{12} + \\frac{1595}{1522} a^{11} - \\frac{162311}{124804} a^{10} - \\frac{8255}{3044} a^{9} + \\frac{126241}{31201} a^{8} + \\frac{2310}{761} a^{7} - \\frac{206730}{31201} a^{6} + \\frac{469}{1522} a^{5} + \\frac{167638}{31201} a^{4} - \\frac{530}{761} a^{3} - \\frac{96012}{31201} a^{2} + \\frac{626}{761} a + \\frac{22281}{31201} \\)', '\\( \\frac{148665}{249608} a^{15} + \\frac{90511}{249608} a^{14} - \\frac{1142355}{249608} a^{13} - \\frac{87496}{31201} a^{12} + \\frac{3978865}{124804} a^{11} + \\frac{1219141}{62402} a^{10} - \\frac{12397355}{124804} a^{9} - \\frac{7661207}{124804} a^{8} + \\frac{5372210}{31201} a^{7} + \\frac{6702287}{62402} a^{6} - \\frac{4729972}{31201} a^{5} - \\frac{6046221}{62402} a^{4} + \\frac{3203765}{31201} a^{3} + \\frac{2067645}{31201} a^{2} - \\frac{606550}{31201} a - \\frac{457000}{31201} \\)', '\\( \\frac{6690}{31201} a^{15} - \\frac{2727}{62402} a^{14} - \\frac{219437}{124804} a^{13} + \\frac{47711}{124804} a^{12} + \\frac{765689}{62402} a^{11} - \\frac{169761}{62402} a^{10} - \\frac{5155517}{124804} a^{9} + \\frac{308453}{31201} a^{8} + \\frac{4855615}{62402} a^{7} - \\frac{660632}{31201} a^{6} - \\frac{2495565}{31201} a^{5} + \\frac{1574741}{62402} a^{4} + \\frac{1749751}{31201} a^{3} - \\frac{561322}{31201} a^{2} - \\frac{608746}{31201} a + \\frac{274380}{31201} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4', '1/2*a^5', '1/2*a^6', '1/2*a^7', '1/4*a^8', '1/4*a^9', '1/4*a^10', '1/4*a^11', '1/8*a^12', '1/8*a^13', '1/249608*a^14 + 2979/124804*a^12 - 2957/31201*a^10 + 5361/62402*a^8 + 2787/62402*a^6 - 2979/62402*a^4 + 5961/31201*a^2 - 5826/31201', '1/249608*a^15 + 2979/124804*a^13 - 2957/31201*a^11 + 5361/62402*a^9 + 2787/62402*a^7 - 2979/62402*a^5 + 5961/31201*a^3 - 5826/31201*a']}
Number field data - 16.0.4294967296000000000000.3