-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 0, 8, 0, -12, 0, -120, 0, -218, 0, 120, 0, -12, 0, -8, 0, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 484116351470433472610304, 'disc_rad': 6, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[4, 2], [2, 2], [1, 4]]], [7, [[4, 4]]], [11, [[4, 4]]], [13, [[4, 4]]], [17, [[4, 4]]], [19, [[4, 4]]], [23, [[4, 2], [2, 4]]], [29, [[4, 2], [2, 4]]], [31, [[4, 4]]], [37, [[4, 4]]], [41, [[4, 4]]], [43, [[4, 4]]], [47, [[4, 4]]], [53, [[4, 2], [2, 2], [1, 4]]], [59, [[4, 2], [2, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [2240, 256], 'galois_label': '16T867', 'galt': 867, 'grd': 35.93907196672871, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 54, 'label': '16.4.484116351470433472610304.54', 'local_algs': ['2.16.66.994', '3.2.1.2', '3.2.1.2', '3.4.2.1', '3.8.4.1'], 'minimal_sibling': [81, 0, 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'81,0,432,0,-432,0,-2112,0,2912,0,-6400,0,17344,0,-23568,0,28434,0,-32464,0,23312,0,-9920,0,3360,0,-768,0,128,0,-16,0,1']}, 'subfield_mults': [1, 1, 1], 'subfields': ['-6.0.1', '-2.0.4.0.1', '9.0.-12.0.-14.0.-4.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{15} - 8 a^{13} - 12 a^{11} + 120 a^{9} - 218 a^{7} - 120 a^{5} - 12 a^{3} + 8 a \\)', '\\( \\frac{61}{160} a^{14} - \\frac{129}{40} a^{12} - \\frac{499}{160} a^{10} + \\frac{3791}{80} a^{8} - \\frac{16749}{160} a^{6} - \\frac{4}{5} a^{4} + \\frac{467}{160} a^{2} + \\frac{71}{80} \\)', '\\( \\frac{39}{160} a^{14} - \\frac{157}{80} a^{12} - \\frac{451}{160} a^{10} + \\frac{2349}{80} a^{8} - \\frac{8771}{160} a^{6} - \\frac{2071}{80} a^{4} - \\frac{217}{160} a^{2} - \\frac{1}{80} \\)', '\\( -\\frac{71}{64} a^{15} + \\frac{577}{64} a^{13} + \\frac{1}{16} a^{12} + \\frac{779}{64} a^{11} - \\frac{1}{2} a^{10} - \\frac{8621}{64} a^{9} - \\frac{3}{4} a^{8} + \\frac{16579}{64} a^{7} + \\frac{15}{2} a^{6} + \\frac{6443}{64} a^{5} - \\frac{219}{16} a^{4} - \\frac{143}{64} a^{3} - \\frac{15}{2} a^{2} - \\frac{231}{64} a + \\frac{1}{8} \\)', '\\( \\frac{57}{160} a^{15} - \\frac{241}{80} a^{13} - \\frac{463}{160} a^{11} + \\frac{1761}{40} a^{9} - \\frac{15673}{160} a^{7} + \\frac{227}{80} a^{5} - \\frac{801}{160} a^{3} - \\frac{11}{10} a \\)', '\\( -\\frac{47}{320} a^{15} + \\frac{1}{16} a^{14} + \\frac{377}{320} a^{13} - \\frac{1}{2} a^{12} + \\frac{563}{320} a^{11} - \\frac{3}{4} a^{10} - \\frac{5709}{320} a^{9} + \\frac{15}{2} a^{8} + \\frac{10283}{320} a^{7} - \\frac{219}{16} a^{6} + \\frac{6291}{320} a^{5} - \\frac{29}{4} a^{4} - \\frac{919}{320} a^{3} + \\frac{13}{8} a^{2} - \\frac{519}{320} a - \\frac{1}{4} \\)', '\\( \\frac{47}{320} a^{15} + \\frac{1}{16} a^{14} - \\frac{377}{320} a^{13} - \\frac{1}{2} a^{12} - \\frac{563}{320} a^{11} - \\frac{3}{4} a^{10} + \\frac{5709}{320} a^{9} + \\frac{15}{2} a^{8} - \\frac{10283}{320} a^{7} - \\frac{219}{16} a^{6} - \\frac{6291}{320} a^{5} - \\frac{29}{4} a^{4} + \\frac{919}{320} a^{3} + \\frac{13}{8} a^{2} + \\frac{519}{320} a - \\frac{1}{4} \\)', '\\( \\frac{3}{5} a^{15} + \\frac{113}{320} a^{14} - \\frac{771}{160} a^{13} - \\frac{943}{320} a^{12} - \\frac{567}{80} a^{11} - \\frac{1037}{320} a^{10} + \\frac{11607}{160} a^{9} + \\frac{13971}{320} a^{8} - \\frac{5311}{40} a^{7} - \\frac{29397}{320} a^{6} - \\frac{11593}{160} a^{5} - \\frac{4149}{320} a^{4} + \\frac{481}{80} a^{3} + \\frac{1801}{320} a^{2} + \\frac{477}{160} a + \\frac{361}{320} \\)', '\\( -\\frac{83}{320} a^{15} - \\frac{119}{320} a^{14} + \\frac{623}{320} a^{13} + \\frac{1009}{320} a^{12} + \\frac{1307}{320} a^{11} + \\frac{971}{320} a^{10} - \\frac{9331}{320} a^{9} - \\frac{14953}{320} a^{8} + \\frac{13367}{320} a^{7} + \\frac{32771}{320} a^{6} + \\frac{16869}{320} a^{5} + \\frac{1667}{320} a^{4} + \\frac{9769}{320} a^{3} - \\frac{4863}{320} a^{2} + \\frac{1159}{320} a - \\frac{1603}{320} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4 - 1/2', '1/4*a^5 - 1/4*a^4 - 1/2*a^3 - 1/2*a^2 - 1/4*a + 1/4', '1/4*a^6 - 1/4*a^4 + 1/4*a^2 - 1/4', '1/4*a^7 - 1/4*a^4 - 1/4*a^3 - 1/2*a^2 - 1/2*a + 1/4', '1/8*a^8 - 1/4*a^4 - 3/8', '1/16*a^9 - 1/16*a^8 - 1/8*a^5 + 1/8*a^4 + 5/16*a - 5/16', '1/16*a^10 - 1/16*a^8 - 1/8*a^6 + 1/8*a^4 + 5/16*a^2 - 5/16', '1/16*a^11 - 1/16*a^8 - 1/8*a^7 + 1/8*a^4 + 5/16*a^3 - 5/16', '1/32*a^12 - 1/32*a^8 + 3/32*a^4 + 5/32', '1/64*a^13 - 1/64*a^12 - 1/32*a^11 - 1/32*a^10 + 1/64*a^9 - 1/64*a^8 + 1/16*a^7 + 1/16*a^6 - 1/64*a^5 + 1/64*a^4 - 5/32*a^3 - 5/32*a^2 + 15/64*a - 15/64', '1/320*a^14 - 1/320*a^12 - 9/320*a^10 - 3/320*a^8 - 29/320*a^6 - 43/320*a^4 - 83/320*a^2 - 73/320', '1/320*a^15 - 1/320*a^13 - 9/320*a^11 - 3/320*a^9 - 29/320*a^7 + 37/320*a^5 - 1/4*a^4 + 77/320*a^3 - 1/2*a^2 - 153/320*a + 1/4']}
Number field data - 16.4.484116351470433472610304.54