-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [4, 0, -16, 0, 72, 0, 32, 0, 14, 0, 16, 0, 4, 0, 0, 0, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 30257271966902092038144, 'disc_rad': 6, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[8, 2]]], [7, [[4, 2], [2, 2], [1, 4]]], [11, [[4, 2], [2, 4]]], [13, [[8, 2]]], [17, [[2, 8]]], [19, [[4, 2], [2, 4]]], [23, [[4, 2], [2, 4]]], [29, [[8, 2]]], [31, [[2, 4], [1, 8]]], [37, [[8, 2]]], [41, [[4, 4]]], [43, [[4, 2], [2, 4]]], [47, [[2, 8]]], [53, [[8, 2]]], [59, [[4, 2], [2, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [564, 64], 'galois_label': '16T283', 'galt': 283, 'grd': 36.72603516807517, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 22, 'label': '16.0.30257271966902092038144.22', 'local_algs': ['2.2.8.62a1.10319', '3.2.2.2a1.2', '3.2.2.2a1.2', '3.4.2.4a1.2'], 'maximal_cm_subfield': [4, 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'8836,0,-26752,0,-66112,0,340928,0,-217088,0,-874336,0,1438336,0,90912,0,-1343556,0,816192,0,-184736,0,5408,0,4864,0,-976,0,128,0,-16,0,1', '8836,0,-69760,0,-97280,0,-78752,0,364912,0,269696,0,-492880,0,-187040,0,342476,0,-31104,0,-53920,0,9744,0,1752,0,-320,0,72,0,-16,0,1', '8836,0,69760,0,-97280,0,78752,0,364912,0,-269696,0,-492880,0,187040,0,342476,0,31104,0,-53920,0,-9744,0,1752,0,320,0,72,0,16,0,1', '8959,19456,64328,44304,17592,-148048,-145040,93504,359240,153664,-136472,-297696,-93424,232640,182928,-9152,-75022,-37936,27112,30000,-464,-3136,4560,4192,1928,624,56,64,56,-16,-16,0,1', '961,0,-1232,0,-3492,0,-2512,0,-694,0,80,0,84,0,16,0,1', '961,0,1232,0,-3492,0,2512,0,-694,0,-80,0,84,0,-16,0,1']}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1, 1, 1], 'subfields': ['-2.0.1', '1.-1.1', '6.0.1', '-2.0.0.0.1', '-18.0.0.0.1', '4.0.2.0.1', '162.0.-216.0.-36.0.0.0.1', '2.0.8.0.-4.0.0.0.1', '4.0.0.0.2.0.0.0.1'], 'torsion_gen': '\\( -\\frac{32}{561} a^{14} - \\frac{7}{561} a^{12} - \\frac{112}{561} a^{10} - \\frac{1073}{1122} a^{8} - \\frac{168}{187} a^{6} - \\frac{994}{561} a^{4} - \\frac{2276}{561} a^{2} + \\frac{505}{561} \\)', 'torsion_order': 6, 'units': ['\\( \\frac{617}{5049} a^{14} + \\frac{305}{10098} a^{12} + \\frac{2440}{5049} a^{10} + \\frac{20531}{10098} a^{8} + \\frac{1220}{561} a^{6} + \\frac{21655}{5049} a^{4} + \\frac{49424}{5049} a^{2} + \\frac{1220}{5049} \\)', '\\( \\frac{622}{5049} a^{14} + \\frac{101}{5049} a^{12} + \\frac{4915}{10098} a^{10} + \\frac{20611}{10098} a^{8} + \\frac{3172}{1683} a^{6} + \\frac{21635}{5049} a^{4} + \\frac{44380}{5049} a^{2} - \\frac{9851}{5049} \\)', '\\( \\frac{230}{1683} a^{15} + \\frac{109}{5049} a^{14} - \\frac{7}{374} a^{13} - \\frac{169}{5049} a^{12} + \\frac{599}{1122} a^{11} + \\frac{662}{5049} a^{10} + \\frac{2411}{1122} a^{9} + \\frac{2305}{10098} a^{8} + \\frac{2594}{1683} a^{7} + \\frac{58}{1683} a^{6} + \\frac{7121}{1683} a^{5} + \\frac{3491}{5049} a^{4} + \\frac{14816}{1683} a^{3} + \\frac{3475}{5049} a^{2} - \\frac{5675}{1683} a - \\frac{6962}{5049} \\)', '\\( \\frac{61}{561} a^{15} + \\frac{334}{5049} a^{14} + \\frac{116}{1683} a^{13} + \\frac{38}{5049} a^{12} + \\frac{734}{1683} a^{11} + \\frac{2899}{10098} a^{10} + \\frac{6481}{3366} a^{9} + \\frac{5477}{5049} a^{8} + \\frac{4238}{1683} a^{7} + \\frac{1660}{1683} a^{6} + \\frac{7309}{1683} a^{5} + \\frac{12689}{5049} a^{4} + \\frac{1641}{187} a^{3} + \\frac{28945}{5049} a^{2} + \\frac{2798}{1683} a - \\frac{257}{5049} \\)', '\\( \\frac{235}{1122} a^{15} + \\frac{113}{1122} a^{14} + \\frac{125}{3366} a^{13} - \\frac{107}{3366} a^{12} + \\frac{2561}{3366} a^{11} + \\frac{1093}{3366} a^{10} + \\frac{5812}{1683} a^{9} + \\frac{5143}{3366} a^{8} + \\frac{5809}{1683} a^{7} + \\frac{1571}{1683} a^{6} + \\frac{10184}{1683} a^{5} + \\frac{2875}{1683} a^{4} + \\frac{2813}{187} a^{3} + \\frac{1172}{187} a^{2} - \\frac{248}{1683} a - \\frac{1363}{1683} \\)', '\\( \\frac{589}{3366} a^{15} - \\frac{43}{918} a^{14} - \\frac{32}{1683} a^{13} - \\frac{11}{918} a^{12} + \\frac{1171}{1683} a^{11} - \\frac{88}{459} a^{10} + \\frac{4600}{1683} a^{9} - \\frac{599}{918} a^{8} + \\frac{1289}{561} a^{7} - \\frac{44}{51} a^{6} + \\frac{8359}{1683} a^{5} - \\frac{781}{459} a^{4} + \\frac{21332}{1683} a^{3} - \\frac{863}{459} a^{2} - \\frac{4744}{1683} a - \\frac{44}{459} \\)', '\\( \\frac{205}{1122} a^{15} - \\frac{1625}{10098} a^{14} + \\frac{152}{1683} a^{13} - \\frac{373}{10098} a^{12} + \\frac{1310}{1683} a^{11} - \\frac{2984}{5049} a^{10} + \\frac{5639}{1683} a^{9} - \\frac{25903}{10098} a^{8} + \\frac{7391}{1683} a^{7} - \\frac{1492}{561} a^{6} + \\frac{12982}{1683} a^{5} - \\frac{26483}{5049} a^{4} + \\frac{9172}{561} a^{3} - \\frac{65608}{5049} a^{2} + \\frac{7574}{1683} a - \\frac{1492}{5049} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', '1/2*a^8', '1/2*a^9', '1/2*a^10', '1/2*a^11', '1/18*a^12 + 2/9*a^10 + 2/9*a^8 + 2/9*a^6 + 1/9*a^4 - 1/3*a^2 - 1/9', '1/18*a^13 + 2/9*a^11 + 2/9*a^9 + 2/9*a^7 + 1/9*a^5 - 1/3*a^3 - 1/9*a', '1/10098*a^14 + 79/5049*a^12 - 419/5049*a^10 + 1691/10098*a^8 + 400/1683*a^6 + 1681/5049*a^4 - 2524/5049*a^2 + 1754/5049', '1/10098*a^15 + 79/5049*a^13 - 419/5049*a^11 + 1691/10098*a^9 + 400/1683*a^7 + 1681/5049*a^5 - 2524/5049*a^3 + 1754/5049*a']}
Number field data - 16.0.30257271966902092038144.22