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nf_fields • Show schema
{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [1, -5, 8, -10, 28, -25, 36, -50, 35, -50, 36, -25, 28, -10, 8, -5, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 1308342779541015625, 'disc_rad': 55, 'disc_sign': 1, 'frobs': [[2, [[8, 2]]], [3, [[8, 2]]], [5, [0]], [7, [[8, 2]]], [11, [0]], [13, [[8, 2]]], [17, [[8, 2]]], [19, [[2, 8]]], [23, [[8, 2]]], [29, [[2, 8]]], [31, [[2, 4], [1, 8]]], [37, [[8, 2]]], [41, [[2, 8]]], [43, [[8, 2]]], [47, [[8, 2]]], [53, [[8, 2]]], [59, [[4, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [28, 16], 'galois_label': '16T36', 'galt': 36, 'grd': 13.561105554803268, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '16.0.1308342779541015625.1', 'local_algs': ['5.8.7.2', '5.8.7.2', '11.2.1.2', '11.2.1.2', '11.2.1.2', '11.2.1.2', '11.4.2.1', '11.4.2.1'], 'minimal_sibling': [1, -2, 8, -9, 15, -9, 8, -2, 1], 'monogenic': 0, 'num_ram': 2, 'r2': 8, 'ramps': [5, 11], 'rd': 13.5611055548, 'regulator': {'__RealLiteral__': 0, 'data': '826.91591824', 'prec': 40}, 'res': {'gal': ['1,0,7,0,10,0,-110,0,275,0,-404,0,367,0,-355,0,360,0,-70,0,127,0,-6,0,25,0,10,0,10,0,3,0,1'], 'sib': ['1,-2,8,-9,15,-9,8,-2,1', '1,-4,-18,-12,15,7,-8,-1,1', '1,-7,26,-63,111,-146,144,-99,37,11,-26,19,-9,2,1,-2,1', '1,0,-4,0,-18,0,-12,0,15,0,7,0,-8,0,-1,0,1']}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 2, 2, 1], 'subfields': ['-1.-1.1', '14.-1.1', '3.-1.1', '1.-1.1.-1.1', '31.14.-14.-1.1', '16.0.3.0.1', '1.-2.8.-9.15.-9.8.-2.1', '1.-4.-18.-12.15.7.-8.-1.1', '81.-27.-18.15.1.5.-2.-1.1'], 'torsion_gen': '\\( \\frac{791}{4541} a^{15} - \\frac{2409}{4541} a^{14} + \\frac{776}{4541} a^{13} - \\frac{8724}{4541} a^{12} + \\frac{34767}{4541} a^{11} - \\frac{10519}{4541} a^{10} + \\frac{55677}{4541} a^{9} - \\frac{73149}{4541} a^{8} + \\frac{43055}{4541} a^{7} - \\frac{109395}{4541} a^{6} + \\frac{54822}{4541} a^{5} - \\frac{61050}{4541} a^{4} + \\frac{73831}{4541} a^{3} - \\frac{11327}{4541} a^{2} + \\frac{30594}{4541} a - \\frac{12148}{4541} \\)', 'torsion_order': 10, 'units': ['\\( \\frac{103}{239} a^{15} - \\frac{596}{239} a^{14} + \\frac{1213}{239} a^{13} - \\frac{1429}{239} a^{12} + \\frac{2644}{239} a^{11} - \\frac{3050}{239} a^{10} + \\frac{3670}{239} a^{9} - \\frac{3851}{239} a^{8} + \\frac{2935}{239} a^{7} - \\frac{2839}{239} a^{6} + \\frac{1553}{239} a^{5} - \\frac{957}{239} a^{4} + \\frac{193}{239} a^{3} - \\frac{88}{239} a^{2} + \\frac{84}{239} a + \\frac{127}{239} \\)', '\\( \\frac{3880}{4541} a^{15} - \\frac{20031}{4541} a^{14} + \\frac{35339}{4541} a^{13} - \\frac{49971}{4541} a^{12} + \\frac{124202}{4541} a^{11} - \\frac{119457}{4541} a^{10} + \\frac{174245}{4541} a^{9} - \\frac{234428}{4541} a^{8} + \\frac{166225}{4541} a^{7} - \\frac{238739}{4541} a^{6} + \\frac{656}{19} a^{5} - \\frac{115103}{4541} a^{4} + \\frac{120136}{4541} a^{3} - \\frac{28254}{4541} a^{2} + \\frac{39895}{4541} a - \\frac{11795}{4541} \\)', '\\( \\frac{3089}{4541} a^{15} - \\frac{13214}{4541} a^{14} + \\frac{15525}{4541} a^{13} - \\frac{23748}{4541} a^{12} + \\frac{83944}{4541} a^{11} - \\frac{38657}{4541} a^{10} + \\frac{110930}{4541} a^{9} - \\frac{135306}{4541} a^{8} + \\frac{69533}{4541} a^{7} - \\frac{166945}{4541} a^{6} + \\frac{71619}{4541} a^{5} - \\frac{74592}{4541} a^{4} + \\frac{90765}{4541} a^{3} - \\frac{3969}{4541} a^{2} + \\frac{31132}{4541} a - \\frac{13403}{4541} \\)', '\\( \\frac{1061}{4541} a^{15} - \\frac{5910}{4541} a^{14} + \\frac{8641}{4541} a^{13} + \\frac{15}{4541} a^{12} + \\frac{7995}{4541} a^{11} - \\frac{11891}{4541} a^{10} - \\frac{20821}{4541} a^{9} + \\frac{3415}{4541} a^{8} - \\frac{26491}{4541} a^{7} + \\frac{40473}{4541} a^{6} - \\frac{22341}{4541} a^{5} + \\frac{49510}{4541} a^{4} - \\frac{23469}{4541} a^{3} + \\frac{14056}{4541} a^{2} - \\frac{19742}{4541} a + \\frac{4633}{4541} \\)', '\\( \\frac{1918}{4541} a^{15} - \\frac{8392}{4541} a^{14} + \\frac{8973}{4541} a^{13} - \\frac{8108}{4541} a^{12} + \\frac{40209}{4541} a^{11} - \\frac{11304}{4541} a^{10} + \\frac{29166}{4541} a^{9} - \\frac{52752}{4541} a^{8} - \\frac{3998}{4541} a^{7} - \\frac{49057}{4541} a^{6} + \\frac{13510}{4541} a^{5} + \\frac{5534}{4541} a^{4} + \\frac{34908}{4541} a^{3} + \\frac{8004}{4541} a^{2} + \\frac{5364}{4541} a - \\frac{7373}{4541} \\)', '\\( \\frac{2650}{4541} a^{15} - \\frac{8756}{4541} a^{14} - \\frac{1869}{4541} a^{13} + \\frac{9455}{4541} a^{12} + \\frac{42382}{4541} a^{11} + \\frac{27712}{4541} a^{10} + \\frac{12056}{4541} a^{9} - \\frac{43609}{4541} a^{8} - \\frac{35287}{4541} a^{7} - \\frac{73577}{4541} a^{6} + \\frac{2670}{4541} a^{5} - \\frac{10628}{4541} a^{4} + \\frac{62427}{4541} a^{3} + \\frac{11355}{4541} a^{2} + \\frac{19079}{4541} a - \\frac{8655}{4541} \\)', '\\( \\frac{889}{4541} a^{15} - \\frac{7253}{4541} a^{14} + \\frac{22801}{4541} a^{13} - \\frac{35225}{4541} a^{12} + \\frac{42010}{4541} a^{11} - \\frac{72538}{4541} a^{10} + \\frac{99469}{4541} a^{9} - \\frac{79224}{4541} a^{8} + \\frac{108192}{4541} a^{7} - \\frac{79815}{4541} a^{6} + \\frac{62381}{4541} a^{5} - \\frac{68247}{4541} a^{4} + \\frac{12655}{4541} a^{3} - \\frac{25934}{4541} a^{2} + \\frac{12792}{4541} a + \\frac{528}{4541} \\)'], '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', '1/239*a^14 + 109/239*a^13 + 5/239*a^12 - 27/239*a^11 + 52/239*a^10 - 45/239*a^9 + 112/239*a^8 + 96/239*a^7 + 112/239*a^6 - 45/239*a^5 + 52/239*a^4 - 27/239*a^3 + 5/239*a^2 + 109/239*a + 1/239', '1/4541*a^15 - 6/4541*a^14 - 1297/4541*a^13 - 841/4541*a^12 - 1145/4541*a^11 + 189/4541*a^10 - 210/4541*a^9 + 122/4541*a^8 - 1607/4541*a^7 - 1692/4541*a^6 + 208/4541*a^5 - 271/4541*a^4 + 242/4541*a^3 - 1183/4541*a^2 - 823/4541*a - 1310/4541']}
Number field data - 16.0.1308342779541015625.1