-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -8, 31, -77, 138, -191, 213, -196, 153, -107, 74, -53, 39, -26, 14, -5, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 2779733938787757, 'disc_rad': 32499579, 'disc_sign': 1, 'frobs': [[2, [[16, 1]]], [3, [0]], [5, [[6, 2], [4, 1]]], [7, [0]], [11, [[6, 2], [4, 1]]], [13, [[6, 1], [4, 2], [2, 1]]], [17, [[6, 2], [4, 1]]], [19, [[4, 4]]], [23, [[4, 4]]], [29, [[8, 2]]], [31, [[4, 3], [2, 2]]], [37, [0]], [41, [[8, 2]]], [43, [[4, 2], [3, 2], [2, 1]]], [47, [[4, 4]]], [53, [[16, 1]]], [59, [[12, 1], [4, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [147456, 147456, 147456, 147456, 147456], 'galois_label': '16T1905', 'galt': 1905, 'grd': 5700.840201233499, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '16.0.2779733938787757.1', 'local_algs': ['3.16.8.1', '7.2.0.1', '7.3.0.1', '7.3.0.1', '7.4.0.1', '7.4.2.1', '37.1.0.1', '37.1.0.1', '37.2.0.1', '37.4.0.1', '37.4.0.1', '37.4.2.1', '151.1.0.1', '151.1.0.1', '151.3.0.1', '151.3.0.1', '151.4.0.1', '151.4.2.1', 'm277.1.1.0', 'm277.1.1.0', 'm277.2.1.1', 'm277.1.4.0', 'm277.1.8.0'], 'monogenic': 0, 'num_ram': 5, 'r2': 8, 'ramps': [3, 7, 37, 151, 277], 'rd': 9.23103083876, 'regulator': {'__RealLiteral__': 0, 'data': '20.5837782538', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.-1.1', '1.-3.2.3.-4.0.4.-3.1'], 'torsion_gen': '\\( -19 a^{15} + 73 a^{14} - 172 a^{13} + 259 a^{12} - 358 a^{11} + 470 a^{10} - 694 a^{9} + 1009 a^{8} - 1411 a^{7} + 1614 a^{6} - 1515 a^{5} + 1126 a^{4} - 629 a^{3} + 235 a^{2} - 49 a + 4 \\)', 'torsion_order': 6, 'units': ['\\( \\frac{61}{7} a^{15} - \\frac{190}{7} a^{14} + \\frac{362}{7} a^{13} - \\frac{365}{7} a^{12} + \\frac{403}{7} a^{11} - \\frac{488}{7} a^{10} + \\frac{878}{7} a^{9} - \\frac{1299}{7} a^{8} + \\frac{1667}{7} a^{7} - \\frac{1160}{7} a^{6} + \\frac{96}{7} a^{5} + 135 a^{4} - \\frac{1473}{7} a^{3} + \\frac{1240}{7} a^{2} - \\frac{599}{7} a + \\frac{134}{7} \\)', '\\( \\frac{36}{7} a^{15} - \\frac{115}{7} a^{14} + \\frac{218}{7} a^{13} - \\frac{213}{7} a^{12} + \\frac{215}{7} a^{11} - \\frac{253}{7} a^{10} + \\frac{478}{7} a^{9} - \\frac{712}{7} a^{8} + \\frac{906}{7} a^{7} - \\frac{554}{7} a^{6} - \\frac{160}{7} a^{5} + 122 a^{4} - \\frac{1136}{7} a^{3} + \\frac{948}{7} a^{2} - \\frac{467}{7} a + \\frac{108}{7} \\)', '\\( \\frac{26}{7} a^{15} - \\frac{99}{7} a^{14} + \\frac{201}{7} a^{13} - \\frac{239}{7} a^{12} + \\frac{242}{7} a^{11} - \\frac{306}{7} a^{10} + \\frac{493}{7} a^{9} - \\frac{781}{7} a^{8} + \\frac{1016}{7} a^{7} - \\frac{887}{7} a^{6} + \\frac{271}{7} a^{5} + 53 a^{4} - \\frac{773}{7} a^{3} + \\frac{750}{7} a^{2} - \\frac{410}{7} a + \\frac{106}{7} \\)', '\\( 3 a^{15} + 4 a^{14} - 31 a^{13} + 94 a^{12} - 142 a^{11} + 199 a^{10} - 248 a^{9} + 373 a^{8} - 550 a^{7} + 823 a^{6} - 975 a^{5} + 942 a^{4} - 712 a^{3} + 398 a^{2} - 142 a + 25 \\)', '\\( 15 a^{15} - 72 a^{14} + 189 a^{13} - 327 a^{12} + 461 a^{11} - 616 a^{10} + 868 a^{9} - 1275 a^{8} + 1808 a^{7} - 2241 a^{6} + 2277 a^{5} - 1877 a^{4} + 1203 a^{3} - 556 a^{2} + 160 a - 21 \\)', '\\( \\frac{68}{7} a^{15} - \\frac{225}{7} a^{14} + \\frac{453}{7} a^{13} - \\frac{519}{7} a^{12} + \\frac{613}{7} a^{11} - \\frac{768}{7} a^{10} + \\frac{1277}{7} a^{9} - \\frac{1887}{7} a^{8} + \\frac{2500}{7} a^{7} - \\frac{2182}{7} a^{6} + \\frac{1104}{7} a^{5} + 21 a^{4} - \\frac{976}{7} a^{3} + \\frac{1030}{7} a^{2} - \\frac{550}{7} a + \\frac{120}{7} \\)', '\\( \\frac{124}{7} a^{15} - \\frac{568}{7} a^{14} + \\frac{1482}{7} a^{13} - \\frac{2528}{7} a^{12} + \\frac{3588}{7} a^{11} - \\frac{4758}{7} a^{10} + \\frac{6765}{7} a^{9} - \\frac{9881}{7} a^{8} + \\frac{14043}{7} a^{7} - \\frac{17246}{7} a^{6} + \\frac{17533}{7} a^{5} - 2050 a^{4} + \\frac{9195}{7} a^{3} - \\frac{4241}{7} a^{2} + \\frac{1235}{7} a - \\frac{167}{7} \\)'], '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', '1/7*a^15 - 3/7*a^14 + 1/7*a^13 - 3/7*a^12 - 2/7*a^11 - 1/7*a^10 + 2/7*a^9 + 2/7*a^8 + 3/7*a^7 - 1/7*a^6 + 1/7*a^5 - 2/7*a^3 + 3/7*a^2 + 2/7*a + 3/7']}
Number field data - 16.0.2779733938787757.1