-
nf_fields • Show schema
{'cm': True, 'coeffs': [65536, 0, -49152, 0, 16384, 0, -9216, 0, 6912, 0, -5952, 0, 3008, 0, -1116, 0, 581, 0, -279, 0, 188, 0, -93, 0, 27, 0, -9, 0, 4, 0, -3, 0, 1], 'conductor': 420, 'degree': 32, 'dirichlet_group': [1, 391, 139, 13, 407, 281, 29, 419, 293, 167, 41, 43, 307, 181, 323, 197, 71, 209, 211, 349, 223, 97, 251, 337, 239, 113, 83, 169, 377, 379, 253, 127], 'disc_abs': 366225584701948244050176000000000000000000000000, 'disc_rad': 210, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [0]], [11, [[2, 16]]], [13, [[4, 8]]], [17, [[4, 8]]], [19, [[2, 16]]], [23, [[4, 8]]], [29, [[2, 16]]], [31, [[2, 16]]], [37, [[4, 8]]], [41, [[2, 16]]], [43, [[4, 8]]], [47, [[4, 8]]], [53, [[4, 8]]], [59, [[2, 16]]]], 'gal_is_abelian': True, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [32, 16, 24, 16], 'galois_label': '32T34', 'galt': 34, 'grd': 30.645530678223075, 'inessentialp': [2], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '32.0.366225584701948244050176000000000000000000000000.1', 'local_algs': ['2.8.8.1', '2.8.8.1', '2.8.8.1', '2.8.8.1', '3.8.4.1', '3.8.4.1', '3.8.4.1', '3.8.4.1', '5.8.6.1', '5.8.6.1', '5.8.6.1', '5.8.6.1', '7.8.4.1', '7.8.4.1', '7.8.4.1', '7.8.4.1'], 'monogenic': -1, 'num_ram': 4, 'r2': 16, 'ramps': [2, 3, 5, 7], 'rd': 30.6455306782, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'subfields': ['1.0.1', '-35.0.1', '9.-1.1', '-26.-1.1', '105.0.1', '-3.0.1', '1.-1.1', '-1.-1.1', '5.0.1', '-7.0.1', '2.-1.1', '-5.-1.1', '21.0.1', '-15.0.1', '4.-1.1', '81.0.-17.0.1', '676.0.53.0.1', '1.0.-1.0.1', '64.0.-19.0.1', '1225.0.35.0.1', '81.-9.-8.-1.1', '141.-12.13.-2.1', '1.0.3.0.1', '4.0.-3.0.1', '25.0.11.0.1', '16.0.-7.0.1', '29.16.-15.-2.1', '14.-14.15.-2.1', '25.0.-25.0.1', '196.0.-7.0.1', '4.2.5.-1.1', '9.0.-1.0.1', '15.-15.4.-1.1', '81.0.3.0.1', '16.0.-13.0.1', '16.0.13.0.1', '4.0.-11.0.1', '4.0.11.0.1', '505.-40.41.-2.1', '105.0.1.-2.1', '114.6.-5.-2.1', '274.26.-25.-2.1', '1.8.-7.-2.1', '4.0.1.0.1', '1.0.-5.0.1', '22.2.-1.-2.1', '1.1.2.-1.1', '25.0.-5.0.1', '49.0.7.0.1', '4.-2.-1.-1.1', '2205.0.-105.0.1', '151.-26.26.-1.1', '1.4.-4.-1.1', '45.0.15.0.1', '5.0.-5.0.1', '1.-1.1.-1.1', '11.9.-9.-1.1', '245.0.35.0.1', '6561.0.1377.0.208.0.17.0.1', '16.0.-36.0.37.0.-9.0.1', '225.0.105.0.16.0.-7.0.1', '1780.700.-566.-254.93.38.-8.-4.1', '904.288.-218.-134.53.14.0.-4.1', '1.0.-3.0.8.0.-3.0.1', '16.0.12.0.5.0.3.0.1', '1.0.-15.0.32.0.-15.0.1', '16.40.-2.-86.69.-34.16.-4.1', '3844.128.-1388.-208.249.40.-23.-2.1', '196.-196.-14.-154.183.-2.-11.-2.1', '16.8.-16.18.23.-9.-4.-1.1', '81.0.9.0.-8.0.1.0.1', '441.0.210.0.67.0.-10.0.1', '225.0.210.0.79.0.-14.0.1', '22801.0.-7176.0.926.0.-51.0.1', '1.0.24.0.26.0.9.0.1', '1.0.-1.0.1.0.-1.0.1', '121.0.279.0.121.0.19.0.1', '421.92.-965.-328.339.58.-35.-2.1', '361.0.48.0.14.0.-3.0.1', '1.0.-23.0.34.0.-12.0.1', '2401.0.343.0.49.0.7.0.1', '781.-1322.1736.-866.529.-118.44.-4.1', '151.27.55.2.29.-2.0.-2.1', '281.-2.36.-66.29.2.4.-4.1', '16.-8.-4.6.-1.3.-1.-1.1', '-20.180.50.-430.141.86.-24.-4.1', '625.125.150.55.41.-11.6.-1.1', '-5.-45.-90.-5.61.9.-14.-1.1', '25.0.125.0.140.0.25.0.1', '194481.0.-9261.0.441.0.-21.0.1', '1681.0.761.0.146.0.16.0.1', '2401.0.2744.0.686.0.49.0.1', '81.0.621.0.306.0.36.0.1', '-59.216.-126.-238.184.54.-29.-2.1', '841.0.272.0.74.0.13.0.1', '1.0.-8.0.14.0.-7.0.1', '81.0.27.0.9.0.3.0.1', '60025.0.-8575.0.980.0.-35.0.1', '121.99.180.-59.79.-9.10.-1.1', '1.-1.0.1.-1.1.0.-1.1', '25.0.25.0.20.0.5.0.1', '256.0.576.0.704.0.1044.0.1029.0.261.0.44.0.9.0.1', '22801.0.-15881.0.11675.0.-3294.0.1259.0.-114.0.50.0.4.0.1', '256.0.192.0.80.0.12.0.-11.0.3.0.5.0.3.0.1', '390625.0.-171875.0.60000.0.-19525.0.6191.0.-781.0.96.0.-11.0.1', '25.0.1125.0.7040.0.10055.0.6231.0.1979.0.336.0.29.0.1', '14641.0.-33759.0.63200.0.-29161.0.9219.0.-1741.0.240.0.-19.0.1', '1.0.1.0.0.0.-1.0.-1.0.-1.0.0.0.1.0.1', '25.0.-725.0.2635.0.-3970.0.3051.0.-1262.0.274.0.-28.0.1', '1.0.5.0.24.0.115.0.551.0.115.0.24.0.5.0.1', '5764801.0.-823543.0.0.0.16807.0.-2401.0.343.0.0.0.-7.0.1', '1.0.23.0.495.0.758.0.879.0.362.0.110.0.12.0.1', '316.376.2356.-2796.-3247.-1434.16454.-23198.19818.-12884.6506.-2658.898.-238.54.-8.1', '256.-128.128.-160.80.8.24.10.-21.5.6.1.5.-5.2.-1.1', '2101.-9304.3134.11566.30374.3214.-5457.-7282.4686.2200.-1452.-442.254.50.-25.-2.1', '256.0.1536.0.4320.0.5124.0.3329.0.1104.0.210.0.21.0.1'], 'torsion_gen': '\\( \\frac{1}{48950} a^{31} - \\frac{7193}{48950} a \\)', 'torsion_order': 60, 'used_grh': True, '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', 'a^15', 'a^16', '1/2*a^17 - 1/2*a^15 - 1/2*a^11 - 1/2*a^9 - 1/2*a^7 - 1/2*a^3 - 1/2*a', '1/4*a^18 + 1/4*a^16 - 1/4*a^12 - 1/4*a^10 - 1/4*a^8 + 1/4*a^4 + 1/4*a^2', '1/8*a^19 + 1/8*a^17 - 1/8*a^13 - 1/8*a^11 - 1/8*a^9 + 1/8*a^5 + 1/8*a^3', '1/176*a^20 - 1/16*a^18 + 1/4*a^16 + 5/16*a^14 - 7/16*a^12 + 43/176*a^10 - 1/4*a^8 - 5/16*a^6 + 7/16*a^4 + 1/4*a^2 - 2/11', '1/352*a^21 - 1/32*a^19 + 1/8*a^17 - 11/32*a^15 + 9/32*a^13 - 133/352*a^11 - 1/8*a^9 + 11/32*a^7 - 9/32*a^5 + 1/8*a^3 + 9/22*a', '1/704*a^22 + 1/704*a^20 - 1/8*a^18 + 5/64*a^16 + 5/64*a^14 + 351/704*a^12 - 29/88*a^10 + 27/64*a^8 + 27/64*a^6 - 1/8*a^4 + 5/11*a^2 + 5/11', '1/1408*a^23 + 1/1408*a^21 - 1/16*a^19 + 5/128*a^17 - 59/128*a^15 + 351/1408*a^13 - 29/176*a^11 + 27/128*a^9 - 37/128*a^7 + 7/16*a^5 - 3/11*a^3 + 5/22*a', '1/14080*a^24 + 1/2816*a^22 - 1/704*a^20 - 27/1280*a^18 - 123/256*a^16 - 1153/2816*a^14 - 59/3520*a^12 + 565/2816*a^10 + 27/256*a^8 - 7/320*a^6 - 31/88*a^4 - 3/22*a^2 - 14/55', '1/28160*a^25 + 1/5632*a^23 - 1/1408*a^21 - 27/2560*a^19 - 123/512*a^17 - 1153/5632*a^15 - 59/7040*a^13 + 565/5632*a^11 + 27/512*a^9 - 7/640*a^7 + 57/176*a^5 - 3/44*a^3 - 7/55*a', '1/25062400*a^26 + 193/25062400*a^24 - 237/626560*a^22 + 27463/25062400*a^20 + 48389/2278400*a^18 + 1266179/5012480*a^16 + 767593/3132800*a^14 - 1794663/25062400*a^12 - 1911467/5012480*a^10 + 141669/284800*a^8 + 411321/1566400*a^6 - 20597/78320*a^4 - 8869/97900*a^2 + 11667/24475', '1/50124800*a^27 + 193/50124800*a^25 - 237/1253120*a^23 + 27463/50124800*a^21 + 48389/4556800*a^19 + 1266179/10024960*a^17 + 767593/6265600*a^15 - 1794663/50124800*a^13 - 1911467/10024960*a^11 + 141669/569600*a^9 + 411321/3132800*a^7 - 20597/156640*a^5 - 8869/195800*a^3 + 11667/48950*a', '1/100249600*a^28 + 1/100249600*a^26 + 413/12531200*a^24 - 39177/100249600*a^22 + 100983/100249600*a^20 - 10419553/100249600*a^18 - 13933/140800*a^16 + 5837289/100249600*a^14 + 12111721/100249600*a^12 + 2466949/12531200*a^10 - 628117/1566400*a^8 + 741977/1566400*a^6 - 143039/391600*a^4 + 19079/97900*a^2 - 651/24475', '1/200499200*a^29 + 1/200499200*a^27 + 413/25062400*a^25 - 39177/200499200*a^23 + 100983/200499200*a^21 - 10419553/200499200*a^19 - 13933/281600*a^17 - 94412311/200499200*a^15 - 88137879/200499200*a^13 + 2466949/25062400*a^11 - 628117/3132800*a^9 - 824423/3132800*a^7 + 248561/783200*a^5 - 78821/195800*a^3 - 651/48950*a', '1/400998400*a^30 + 1/400998400*a^28 - 1/50124800*a^26 + 5127/400998400*a^24 + 170743/400998400*a^22 + 581391/400998400*a^20 + 3644777/50124800*a^18 - 128966951/400998400*a^16 - 162762007/400998400*a^14 + 9092791/50124800*a^12 + 9525477/25062400*a^10 - 1900949/6265600*a^8 + 655029/1566400*a^6 + 55237/195800*a^4 - 6217/24475*a^2 + 11961/24475', '1/801996800*a^31 + 1/801996800*a^29 - 1/100249600*a^27 + 5127/801996800*a^25 + 170743/801996800*a^23 + 581391/801996800*a^21 + 3644777/100249600*a^19 - 128966951/801996800*a^17 - 162762007/801996800*a^15 - 41032009/100249600*a^13 + 9525477/50124800*a^11 - 1900949/12531200*a^9 - 911371/3132800*a^7 - 140563/391600*a^5 + 9129/24475*a^3 + 11961/48950*a']}
Number field data - 32.0.366225584701948244050176000000000000000000000000.1