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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 0, 0, 0, -18, 0, 0, 0, -41, 0, 0, 0, -2, 0, 0, 0, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 16777216000000000000, 'disc_rad': 10, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[8, 2]]], [5, [0]], [7, [[8, 2]]], [11, [[4, 4]]], [13, [[4, 4]]], [17, [[4, 4]]], [19, [[2, 6], [1, 4]]], [23, [[8, 2]]], [29, [[2, 8]]], [31, [[4, 4]]], [37, [[4, 4]]], [41, [[4, 4]]], [43, [[8, 2]]], [47, [[8, 2]]], [53, [[4, 4]]], [59, [[2, 6], [1, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [72, 24], 'galois_label': '16T28', 'galt': 28, 'grd': 15.905414575341013, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 2, 'label': '16.4.16777216000000000000.2', 'local_algs': ['2.2.8.36b1.11', '5.4.4.12a1.4'], 'minimal_sibling': [5, 0, 0, 0, 2, 0, 0, 0, 1], 'monogenic': 0, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 6, 'ramps': [2, 5], 'rd': 15.9054145753, 'regulator': {'__RealLiteral__': 0, 'data': '2006.84410169', 'prec': 44}, 'res': {'gal': ['625,0,0,0,-250,0,0,0,-25,0,0,0,60,0,0,0,-19,0,0,0,12,0,0,0,-1,0,0,0,-2,0,0,0,1'], 'sib': ['125,0,0,0,10,0,0,0,1', '25,0,0,0,30,0,0,0,39,0,0,0,6,0,0,0,1', '5,0,0,0,2,0,0,0,1']}, 'subfield_mults': [1, 1, 1, 1, 1], 'subfields': ['-1.-1.1', '5.0.-5.0.1', '-1.0.-1.0.1', '-5.0.0.0.1', '-4.16.-16.-8.14.4.-4.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{25}{122} a^{14} - \\frac{22}{61} a^{10} - \\frac{519}{61} a^{6} - \\frac{643}{122} a^{2} \\)', '\\( a \\)', '\\( \\frac{5}{61} a^{15} + \\frac{13}{244} a^{13} - \\frac{23}{244} a^{11} - \\frac{9}{122} a^{9} - \\frac{867}{244} a^{7} - \\frac{265}{122} a^{5} - \\frac{1039}{244} a^{3} - \\frac{471}{244} a \\)', '\\( \\frac{20}{61} a^{15} + \\frac{37}{244} a^{13} - \\frac{153}{244} a^{11} - \\frac{35}{122} a^{9} - \\frac{3285}{244} a^{7} - \\frac{773}{122} a^{5} - \\frac{1777}{244} a^{3} - \\frac{815}{244} a \\)', '\\( \\frac{97}{244} a^{14} + \\frac{7}{244} a^{12} - \\frac{50}{61} a^{10} - \\frac{5}{244} a^{8} - \\frac{991}{61} a^{6} - \\frac{337}{244} a^{4} - \\frac{1553}{244} a^{2} - \\frac{81}{61} \\)', '\\( \\frac{25}{244} a^{15} + \\frac{25}{244} a^{14} + \\frac{7}{244} a^{13} - \\frac{5}{244} a^{12} - \\frac{11}{61} a^{11} - \\frac{11}{61} a^{10} - \\frac{5}{244} a^{9} + \\frac{21}{244} a^{8} - \\frac{519}{122} a^{7} - \\frac{519}{122} a^{6} - \\frac{337}{244} a^{5} + \\frac{171}{244} a^{4} - \\frac{765}{244} a^{3} - \\frac{643}{244} a^{2} - \\frac{223}{122} a - \\frac{15}{122} \\)', '\\( \\frac{117}{244} a^{15} + \\frac{55}{244} a^{14} + \\frac{9}{122} a^{13} + \\frac{3}{122} a^{12} - \\frac{223}{244} a^{11} - \\frac{109}{244} a^{10} - \\frac{39}{244} a^{9} - \\frac{13}{244} a^{8} - \\frac{4831}{244} a^{7} - \\frac{2247}{244} a^{6} - \\frac{701}{244} a^{5} - \\frac{193}{244} a^{4} - \\frac{1235}{122} a^{3} - \\frac{253}{61} a^{2} - \\frac{319}{244} a - \\frac{269}{244} \\)', '\\( \\frac{25}{244} a^{15} + \\frac{25}{122} a^{14} - \\frac{5}{244} a^{13} - \\frac{3}{61} a^{12} - \\frac{11}{61} a^{11} - \\frac{22}{61} a^{10} + \\frac{21}{244} a^{9} + \\frac{13}{122} a^{8} - \\frac{519}{122} a^{7} - \\frac{519}{61} a^{6} + \\frac{171}{244} a^{5} + \\frac{127}{61} a^{4} - \\frac{643}{244} a^{3} - \\frac{352}{61} a^{2} - \\frac{137}{122} a + \\frac{43}{61} \\)', '\\( \\frac{55}{244} a^{15} + \\frac{25}{244} a^{14} - \\frac{15}{122} a^{13} - \\frac{5}{244} a^{12} - \\frac{109}{244} a^{11} - \\frac{11}{61} a^{10} + \\frac{65}{244} a^{9} + \\frac{21}{244} a^{8} - \\frac{2247}{244} a^{7} - \\frac{519}{122} a^{6} + \\frac{1209}{244} a^{5} + \\frac{171}{244} a^{4} - \\frac{253}{61} a^{3} - \\frac{643}{244} a^{2} + \\frac{369}{244} a - \\frac{15}{122} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/2*a^6 - 1/2*a^5 - 1/2*a^3 - 1/2*a - 1/2', '1/2*a^7 - 1/2*a^5 - 1/2*a^4 - 1/2*a^3 - 1/2*a^2 - 1/2', '1/2*a^8 - 1/2*a^4 - 1/2', '1/2*a^9 - 1/2*a^5 - 1/2*a', '1/2*a^10 - 1/2*a^5 - 1/2*a^3 - 1/2*a^2 - 1/2*a - 1/2', '1/2*a^11 - 1/2*a^5 - 1/2*a^4 - 1/2*a^2 - 1/2', '1/244*a^12 - 1/4*a^10 + 2/61*a^8 - 1/4*a^6 + 25/61*a^4 - 1/4*a^2 + 67/244', '1/244*a^13 - 1/4*a^11 + 2/61*a^9 - 1/4*a^7 + 25/61*a^5 - 1/4*a^3 + 67/244*a', '1/244*a^14 - 53/244*a^10 - 1/4*a^8 + 39/244*a^6 - 1/4*a^4 + 3/122*a^2 - 1/4', '1/244*a^15 - 53/244*a^11 - 1/4*a^9 + 39/244*a^7 - 1/4*a^5 + 3/122*a^3 - 1/4*a']}
Number field data - 16.4.16777216000000000000.2