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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -4, 12, -20, 24, -24, 22, -20, 15, 0, -18, 24, -14, 0, 6, -4, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 8084777718513664, 'disc_rad': 14, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[8, 2]]], [5, [[8, 2]]], [7, [0]], [11, [[4, 4]]], [13, [[8, 2]]], [17, [[4, 2], [2, 4]]], [19, [[8, 2]]], [23, [[2, 8]]], [29, [[4, 4]]], [31, [[2, 8]]], [37, [[4, 4]]], [41, [[4, 2], [2, 4]]], [43, [[4, 4]]], [47, [[2, 8]]], [53, [[2, 8]]], [59, [[8, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [144, 48], 'galois_label': '16T141', 'galt': 141, 'grd': 20.471092479852693, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '16.0.8084777718513664.1', 'local_algs': ['2.16.36.1', '7.2.0.1', '7.2.0.1', '7.2.0.1', '7.2.0.1', '7.8.6.2'], 'minimal_sibling': [-1, -4, -8, -8, -1, 0, -2, 0, 1], 'monogenic': 0, 'num_ram': 2, 'r2': 8, 'ramps': [2, 7], 'rd': 9.8680026001, 'regulator': {'__RealLiteral__': 0, 'data': '60.0447869363', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 2, 2, 1], 'subfields': ['1.0.1', '-2.0.1', '2.0.1', '-2.-4.-2.0.1', '1.-2.1.-2.1', '1.0.0.0.1', '1.0.2.-4.0.-4.2.0.1', '-1.-4.-8.-8.-1.0.-2.0.1', '1.-4.8.-8.7.-8.8.-4.1'], 'torsion_gen': '\\( -\\frac{6779}{5549} a^{15} + \\frac{24166}{5549} a^{14} - \\frac{30716}{5549} a^{13} - \\frac{12449}{5549} a^{12} + \\frac{91350}{5549} a^{11} - \\frac{128887}{5549} a^{10} + \\frac{68247}{5549} a^{9} + \\frac{38897}{5549} a^{8} - \\frac{98984}{5549} a^{7} + \\frac{95823}{5549} a^{6} - \\frac{97834}{5549} a^{5} + \\frac{110584}{5549} a^{4} - \\frac{112216}{5549} a^{3} + \\frac{83622}{5549} a^{2} - \\frac{38870}{5549} a + \\frac{6344}{5549} \\)', 'torsion_order': 8, 'units': ['\\( \\frac{2266}{5549} a^{15} - \\frac{6291}{5549} a^{14} + \\frac{6899}{5549} a^{13} + \\frac{6486}{5549} a^{12} - \\frac{24830}{5549} a^{11} + \\frac{31149}{5549} a^{10} - \\frac{9661}{5549} a^{9} - \\frac{15366}{5549} a^{8} + \\frac{26235}{5549} a^{7} - \\frac{21377}{5549} a^{6} + \\frac{25154}{5549} a^{5} - \\frac{26041}{5549} a^{4} + \\frac{22470}{5549} a^{3} - \\frac{10241}{5549} a^{2} + \\frac{7683}{5549} a + \\frac{3137}{5549} \\)', '\\( \\frac{2568}{5549} a^{15} - \\frac{10068}{5549} a^{14} + \\frac{10615}{5549} a^{13} + \\frac{11293}{5549} a^{12} - \\frac{41304}{5549} a^{11} + \\frac{42015}{5549} a^{10} - \\frac{6766}{5549} a^{9} - \\frac{29942}{5549} a^{8} + \\frac{38890}{5549} a^{7} - \\frac{28149}{5549} a^{6} + \\frac{30534}{5549} a^{5} - \\frac{31980}{5549} a^{4} + \\frac{23775}{5549} a^{3} - \\frac{16670}{5549} a^{2} + \\frac{3873}{5549} a + \\frac{6190}{5549} \\)', '\\( \\frac{5171}{5549} a^{15} - \\frac{17395}{5549} a^{14} + \\frac{19713}{5549} a^{13} + \\frac{11549}{5549} a^{12} - \\frac{62064}{5549} a^{11} + \\frac{80953}{5549} a^{10} - \\frac{43422}{5549} a^{9} - \\frac{17659}{5549} a^{8} + \\frac{51814}{5549} a^{7} - \\frac{64506}{5549} a^{6} + \\frac{78559}{5549} a^{5} - \\frac{85062}{5549} a^{4} + \\frac{78037}{5549} a^{3} - \\frac{60893}{5549} a^{2} + \\frac{28251}{5549} a - \\frac{10583}{5549} \\)', '\\( \\frac{1528}{5549} a^{15} - \\frac{5109}{5549} a^{14} + \\frac{1787}{5549} a^{13} + \\frac{13444}{5549} a^{12} - \\frac{25510}{5549} a^{11} + \\frac{8197}{5549} a^{10} + \\frac{26848}{5549} a^{9} - \\frac{40859}{5549} a^{8} + \\frac{14566}{5549} a^{7} + \\frac{12811}{5549} a^{6} - \\frac{8021}{5549} a^{5} - \\frac{1863}{5549} a^{4} - \\frac{3797}{5549} a^{3} + \\frac{13297}{5549} a^{2} - \\frac{21188}{5549} a + \\frac{9163}{5549} \\)', '\\( \\frac{2721}{5549} a^{15} - \\frac{3952}{5549} a^{14} - \\frac{1724}{5549} a^{13} + \\frac{12828}{5549} a^{12} - \\frac{13012}{5549} a^{11} + \\frac{2246}{5549} a^{10} + \\frac{12395}{5549} a^{9} - \\frac{15792}{5549} a^{8} + \\frac{10519}{5549} a^{7} - \\frac{6003}{5549} a^{6} + \\frac{2832}{5549} a^{5} + \\frac{4828}{5549} a^{4} + \\frac{2626}{5549} a^{3} + \\frac{3353}{5549} a^{2} - \\frac{8751}{5549} a - \\frac{1285}{5549} \\)', '\\( \\frac{754}{5549} a^{15} - \\frac{3734}{5549} a^{14} + \\frac{2516}{5549} a^{13} + \\frac{8290}{5549} a^{12} - \\frac{17832}{5549} a^{11} + \\frac{5374}{5549} a^{10} + \\frac{16415}{5549} a^{9} - \\frac{19414}{5549} a^{8} + \\frac{433}{5549} a^{7} + \\frac{9147}{5549} a^{6} + \\frac{6450}{5549} a^{5} - \\frac{16702}{5549} a^{4} + \\frac{1678}{5549} a^{3} + \\frac{6990}{5549} a^{2} - \\frac{6940}{5549} a + \\frac{5197}{5549} \\)', '\\( \\frac{2868}{5549} a^{15} - \\frac{7977}{5549} a^{14} + \\frac{6332}{5549} a^{13} + \\frac{14194}{5549} a^{12} - \\frac{33268}{5549} a^{11} + \\frac{25946}{5549} a^{10} + \\frac{8935}{5549} a^{9} - \\frac{27113}{5549} a^{8} + \\frac{22430}{5549} a^{7} - \\frac{10512}{5549} a^{6} + \\frac{21914}{5549} a^{5} - \\frac{24981}{5549} a^{4} + \\frac{16362}{5549} a^{3} - \\frac{4719}{5549} a^{2} + \\frac{5233}{5549} a + \\frac{4372}{5549} \\)'], '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', 'a^14', '1/5549*a^15 + 2615/5549*a^14 + 1225/5549*a^13 + 953/5549*a^12 - 1157/5549*a^11 - 405/5549*a^10 - 854/5549*a^9 - 379/5549*a^8 + 685/5549*a^7 + 1668/5549*a^6 + 1451/5549*a^5 - 920/5549*a^4 - 1190/5549*a^3 + 1908/5549*a^2 - 2585/5549*a - 339/5549']}
Number field data - 16.0.8084777718513664.1