-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [64, 0, -128, 0, 448, 0, 64, 0, 328, 0, 208, 0, 88, 0, 16, 0, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 1378596953991976568487936, 'disc_rad': 6, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[8, 2]]], [7, [[8, 1], [2, 1], [1, 6]]], [11, [[4, 2], [2, 4]]], [13, [[4, 1], [2, 5], [1, 2]]], [17, [[8, 2]]], [19, [[4, 2], [2, 2], [1, 4]]], [23, [[8, 2]]], [29, [[8, 2]]], [31, [[8, 1], [4, 1], [2, 2]]], [37, [[4, 2], [2, 4]]], [41, [[8, 2]]], [43, [[4, 1], [2, 5], [1, 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': [9388, 1792], 'galois_label': '16T1455', 'galt': 1455, 'grd': 62.71882224263865, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 79, 'label': '16.0.1378596953991976568487936.79', 'local_algs': ['2.2.8.58a2.1847', '3.1.8.7a1.1', 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\\frac{243}{6776} a^{8} + \\frac{23}{5082} a^{6} - \\frac{361}{2541} a^{4} + \\frac{139}{2541} a^{2} - \\frac{403}{2541} \\)', '\\( \\frac{61}{3872} a^{15} + \\frac{1145}{81312} a^{14} + \\frac{371}{1452} a^{13} + \\frac{8737}{40656} a^{12} + \\frac{2065}{1452} a^{11} + \\frac{7123}{6776} a^{10} + \\frac{9499}{2904} a^{9} + \\frac{11555}{6776} a^{8} + \\frac{3049}{726} a^{7} + \\frac{11351}{10164} a^{6} - \\frac{1169}{726} a^{5} - \\frac{3590}{847} a^{4} + \\frac{850}{363} a^{3} + \\frac{8945}{2541} a^{2} + \\frac{437}{363} a - \\frac{195}{847} \\)', '\\( \\frac{115}{81312} a^{15} + \\frac{353}{81312} a^{14} + \\frac{401}{13552} a^{13} + \\frac{435}{6776} a^{12} + \\frac{199}{847} a^{11} + \\frac{5903}{20328} a^{10} + \\frac{18269}{20328} a^{9} + \\frac{7055}{20328} a^{8} + \\frac{18805}{10164} a^{7} + \\frac{41}{2541} a^{6} + \\frac{1707}{847} a^{5} - \\frac{8945}{5082} a^{4} + \\frac{117}{847} a^{3} + \\frac{5062}{2541} a^{2} + \\frac{3455}{2541} a - \\frac{332}{2541} \\)', '\\( -\\frac{65}{968} a^{15} + \\frac{433}{13552} a^{14} - \\frac{749}{726} a^{13} + \\frac{22633}{40656} a^{12} - \\frac{629}{121} a^{11} + \\frac{35999}{10164} a^{10} - \\frac{2361}{242} a^{9} + \\frac{217093}{20328} a^{8} - \\frac{3820}{363} a^{7} + \\frac{16971}{847} a^{6} + \\frac{3985}{242} a^{5} + \\frac{85895}{5082} a^{4} - \\frac{1972}{121} a^{3} + \\frac{43069}{2541} a^{2} + \\frac{11372}{363} a + \\frac{38870}{2541} \\)', '\\( -\\frac{239}{3872} a^{15} - \\frac{2131}{81312} a^{14} - \\frac{2929}{2904} a^{13} - \\frac{17107}{40656} a^{12} - \\frac{16723}{2904} a^{11} - \\frac{1942}{847} a^{10} - \\frac{14035}{968} a^{9} - \\frac{101947}{20328} a^{8} - \\frac{5639}{242} a^{7} - \\frac{62989}{10164} a^{6} - \\frac{5441}{726} a^{5} + \\frac{2781}{1694} a^{4} - \\frac{3261}{121} a^{3} - \\frac{21323}{2541} a^{2} + \\frac{1049}{363} a + \\frac{17363}{2541} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', '1/2*a^3', '1/2*a^4', '1/2*a^5', '1/4*a^6', '1/4*a^7', '1/24*a^8 + 1/12*a^6 + 1/3*a^2 - 1/3', '1/24*a^9 + 1/12*a^7 - 1/6*a^3 - 1/3*a', '1/24*a^10 + 1/12*a^6 - 1/6*a^4 - 1/3', '1/48*a^11 - 1/12*a^7 + 1/6*a^5 + 1/3*a', '1/48*a^12 + 1/12*a^6 + 1/3', '1/48*a^13 + 1/12*a^7 + 1/3*a', '1/81312*a^14 - 19/40656*a^12 - 13/847*a^10 - 5/2541*a^8 - 191/3388*a^6 - 103/847*a^4 - 80/847*a^2 - 596/2541', '1/81312*a^15 - 19/40656*a^13 + 223/40656*a^11 - 5/2541*a^9 + 1121/10164*a^7 + 229/5082*a^5 - 80/847*a^3 + 251/2541*a']}
Number field data - 16.0.1378596953991976568487936.79