Hilbert modular form data - 2.2.161.1-8.3-b

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• hmf_forms •

  Column	Type
  deg	smallint
  dimension	integer
  disc	bigint
  field_bad_primes	integer[]
  field_label	text
  is_CM	text
  is_base_change	text
  label	text
  label_nsuffix	smallint
  label_suffix	text
  level_bad_primes	integer[]
  level_ideal	text
  level_label	text
  level_norm	integer
  parallel_weight	smallint
  short_label	text
  weight	text

  
  {'deg': 2, 'dimension': 12, 'disc': 161, 'field_bad_primes': [7, 23], 'field_label': '2.2.161.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.161.1-8.3-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [2], 'level_ideal': '[8, 8, -7*w + 48]', 'level_label': '8.3', 'level_norm': 8, 'parallel_weight': 2, 'short_label': '8.3-b', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[2, 2, w + 6]', 1]], 'hecke_eigenvalues': [0, '-37/6848*e^10 + 765/3424*e^8 - 2711/856*e^6 + 15989/856*e^4 - 18125/428*e^2 + 2565/107', 'e', '205/22256*e^11 - 1043/2782*e^9 + 7208/1391*e^7 - 163945/5564*e^5 + 178337/2782*e^3 - 50264/1391*e', '-193/89024*e^11 + 3921/44512*e^9 - 6725/5564*e^7 + 74443/11128*e^5 - 73971/5564*e^3 + 9062/1391*e', '19/3424*e^10 - 777/3424*e^8 + 5369/1712*e^6 - 3725/214*e^4 + 14465/428*e^2 - 2397/214', '-905/89024*e^11 + 9175/22256*e^9 - 126231/22256*e^7 + 357519/11128*e^5 - 195271/2782*e^3 + 118175/2782*e', '-1121/89024*e^11 + 5717/11128*e^9 - 158225/22256*e^7 + 447147/11128*e^5 - 117687/1391*e^3 + 119129/2782*e', '-129/6848*e^11 + 1309/1712*e^9 - 17987/1712*e^7 + 50407/856*e^5 - 26187/214*e^3 + 11885/214*e', '857/89024*e^11 - 8673/22256*e^9 + 118503/22256*e^7 - 327401/11128*e^5 + 81047/1391*e^3 - 51195/2782*e', '37/3424*e^10 - 765/1712*e^8 + 2711/428*e^6 - 15989/428*e^4 + 18125/214*e^2 - 4916/107', '-23/3424*e^10 + 873/3424*e^8 - 5373/1712*e^6 + 1576/107*e^4 - 9581/428*e^2 + 1077/214', '-19/3424*e^10 + 777/3424*e^8 - 5369/1712*e^6 + 3725/214*e^4 - 14465/428*e^2 + 2397/214', '1077/44512*e^11 - 44359/44512*e^9 + 312019/22256*e^7 - 227041/2782*e^5 + 1014587/5564*e^3 - 293973/2782*e', '-647/44512*e^11 + 25907/44512*e^9 - 173559/22256*e^7 + 231453/5564*e^5 - 431525/5564*e^3 + 67151/2782*e', '1/32*e^10 - 41/32*e^8 + 285/16*e^6 - 201/2*e^4 + 825/4*e^2 - 185/2', '3/1712*e^10 - 251/3424*e^8 + 1825/1712*e^6 - 2775/428*e^4 + 5835/428*e^2 + 375/214', '1617/89024*e^11 - 32779/44512*e^9 + 112781/11128*e^7 - 640595/11128*e^5 + 707113/5564*e^3 - 109113/1391*e', '-627/89024*e^11 + 12767/44512*e^9 - 22107/5564*e^7 + 253447/11128*e^5 - 282703/5564*e^3 + 39811/1391*e', '25/5564*e^11 - 7903/44512*e^9 + 51881/22256*e^7 - 33303/2782*e^5 + 103657/5564*e^3 + 23735/2782*e', '11/2782*e^11 - 6899/44512*e^9 + 44153/22256*e^7 - 26469/2782*e^5 + 73469/5564*e^3 - 3873/2782*e', '-71/22256*e^11 + 1601/11128*e^9 - 6411/2782*e^7 + 89215/5564*e^5 - 129877/2782*e^3 + 63454/1391*e', '285/5564*e^11 - 46299/22256*e^9 + 318395/11128*e^7 - 893679/5564*e^5 + 466585/1391*e^3 - 220111/1391*e', '173/44512*e^11 - 7469/44512*e^9 + 57097/22256*e^7 - 96437/5564*e^5 + 281823/5564*e^3 - 131123/2782*e', '425/22256*e^11 - 34631/44512*e^9 + 238925/22256*e^7 - 167619/2782*e^5 + 687097/5564*e^3 - 131771/2782*e', '7/214*e^10 - 2307/1712*e^8 + 16213/856*e^6 - 23439/214*e^4 + 50715/214*e^2 - 12871/107', '55/1712*e^10 - 4459/3424*e^8 + 30605/1712*e^6 - 42957/428*e^4 + 90711/428*e^2 - 22657/214', '-93/3424*e^10 + 3837/3424*e^8 - 27057/1712*e^6 + 9857/107*e^4 - 86537/428*e^2 + 21633/214', '-35/428*e^10 + 11321/3424*e^8 - 77427/1712*e^6 + 108207/428*e^4 - 226825/428*e^2 + 55795/214', '-151/3424*e^10 + 6085/3424*e^8 - 41453/1712*e^6 + 14450/107*e^4 - 122077/428*e^2 + 31169/214', '-643/44512*e^11 + 26667/44512*e^9 - 188963/22256*e^7 + 137539/2782*e^5 - 591559/5564*e^3 + 132029/2782*e', '-945/44512*e^11 + 38837/44512*e^9 - 272297/22256*e^7 + 394209/5564*e^5 - 868027/5564*e^3 + 223257/2782*e', '-135/3424*e^10 + 5487/3424*e^8 - 37799/1712*e^6 + 26591/214*e^4 - 110583/428*e^2 + 26819/214', '37/1712*e^10 - 2953/3424*e^8 + 19655/1712*e^6 - 25879/428*e^4 + 47141/428*e^2 - 6075/214', '-23/3424*e^10 + 873/3424*e^8 - 5373/1712*e^6 + 1576/107*e^4 - 9153/428*e^2 - 2347/214', '-277/3424*e^10 + 11249/3424*e^8 - 77317/1712*e^6 + 54239/214*e^4 - 228241/428*e^2 + 55929/214', '35/856*e^10 - 5607/3424*e^8 + 37697/1712*e^6 - 51161/428*e^4 + 103087/428*e^2 - 26881/214', '-95/6848*e^11 + 499/856*e^9 - 14439/1712*e^7 + 43563/856*e^5 - 25491/214*e^3 + 15997/214*e', '1121/89024*e^11 - 5717/11128*e^9 + 158225/22256*e^7 - 447147/11128*e^5 + 117687/1391*e^3 - 119129/2782*e', '-161/3424*e^10 + 6539/3424*e^8 - 44887/1712*e^6 + 15633/107*e^4 - 128699/428*e^2 + 31935/214', '347/3424*e^10 - 14213/3424*e^8 + 99001/1712*e^6 - 35347/107*e^4 + 301773/428*e^2 - 74345/214', '-223/3424*e^10 + 9097/3424*e^8 - 62925/1712*e^6 + 22240/107*e^4 - 188673/428*e^2 + 48925/214', '-39/3424*e^10 + 1685/3424*e^8 - 12665/1712*e^6 + 9955/214*e^4 - 46113/428*e^2 + 10349/214', '1013/89024*e^11 - 20609/44512*e^9 + 35557/5564*e^7 - 402333/11128*e^5 + 430645/5564*e^3 - 55153/1391*e', '437/89024*e^11 - 8561/44512*e^9 + 3441/1391*e^7 - 135505/11128*e^5 + 107337/5564*e^3 - 9369/1391*e', '-75/1712*e^10 + 771/428*e^8 - 10791/428*e^6 + 30889/214*e^4 - 32376/107*e^2 + 14198/107', '-9/107*e^10 + 2905/856*e^8 - 4940/107*e^6 + 54509/214*e^4 - 55468/107*e^2 + 25026/107', '1297/89024*e^11 - 27013/44512*e^9 + 48379/5564*e^7 - 580763/11128*e^5 + 690399/5564*e^3 - 122780/1391*e', '-599/89024*e^11 + 12645/44512*e^9 - 46133/11128*e^7 + 279231/11128*e^5 - 298941/5564*e^3 + 10770/1391*e', '-143/6848*e^11 + 2893/3424*e^9 - 9853/856*e^7 + 53993/856*e^5 - 52815/428*e^3 + 4520/107*e', '4529/89024*e^11 - 92761/44512*e^9 + 161775/5564*e^7 - 1862205/11128*e^5 + 2050741/5564*e^3 - 287564/1391*e', '247/3424*e^10 - 10101/3424*e^8 + 70225/1712*e^6 - 50137/214*e^4 + 216293/428*e^2 - 57269/214', '331/3424*e^10 - 13401/3424*e^8 + 91709/1712*e^6 - 63891/214*e^4 + 264385/428*e^2 - 60793/214', '335/3424*e^10 - 13711/3424*e^8 + 95351/1712*e^6 - 67919/214*e^4 + 289247/428*e^2 - 71243/214', '3/1712*e^10 - 251/3424*e^8 + 1825/1712*e^6 - 2775/428*e^4 + 4979/428*e^2 + 2087/214', '235/89024*e^11 - 513/5564*e^9 + 21143/22256*e^7 - 30203/11128*e^5 - 8577/2782*e^3 + 31071/2782*e', '-1149/89024*e^11 + 11495/22256*e^9 - 154387/22256*e^7 + 418581/11128*e^5 - 105977/1391*e^3 + 107661/2782*e', '115/11128*e^11 - 19707/44512*e^9 + 146729/22256*e^7 - 229977/5564*e^5 + 556811/5564*e^3 - 163101/2782*e', '31/3424*e^11 - 1279/3424*e^9 + 9019/1712*e^7 - 13107/428*e^5 + 28061/428*e^3 - 5285/214*e', '137/3424*e^10 - 5535/3424*e^8 + 37587/1712*e^6 - 25609/214*e^4 + 100223/428*e^2 - 21023/214', '239/3424*e^10 - 9695/3424*e^8 + 66579/1712*e^6 - 23341/107*e^4 + 195031/428*e^2 - 45143/214', '621/89024*e^11 - 13337/44512*e^9 + 25343/5564*e^7 - 340445/11128*e^5 + 496621/5564*e^3 - 121519/1391*e', '-795/89024*e^11 + 16281/44512*e^9 - 56347/11128*e^7 + 312957/11128*e^5 - 302119/5564*e^3 + 30445/1391*e', '4171/89024*e^11 - 85041/44512*e^9 + 294731/11128*e^7 - 1684753/11128*e^5 + 1861523/5564*e^3 - 285962/1391*e', '-817/89024*e^11 + 16973/44512*e^9 - 15225/2782*e^7 + 371389/11128*e^5 - 458069/5564*e^3 + 77208/1391*e', '-931/89024*e^11 + 20053/44512*e^9 - 75641/11128*e^7 + 490561/11128*e^5 - 655651/5564*e^3 + 138316/1391*e', '-4415/89024*e^11 + 89681/44512*e^9 - 308809/11128*e^7 + 1743033/11128*e^5 - 1858723/5564*e^3 + 240366/1391*e', '115/3424*e^10 - 2343/1712*e^8 + 4067/214*e^6 - 46821/428*e^4 + 51719/214*e^2 - 12162/107', '-137/3424*e^10 + 2821/1712*e^8 - 9905/428*e^6 + 57103/428*e^4 - 60865/214*e^2 + 14524/107', '93/856*e^10 - 15027/3424*e^8 + 102557/1712*e^6 - 142625/428*e^4 + 295323/428*e^2 - 68021/214', '35/3424*e^10 - 1375/3424*e^8 + 9023/1712*e^6 - 5927/214*e^4 + 20823/428*e^2 + 957/214', '149/3424*e^10 - 192/107*e^8 + 21635/856*e^6 - 63081/428*e^4 + 35597/107*e^2 - 20783/107', '265/3424*e^10 - 665/214*e^8 + 36031/856*e^6 - 99611/428*e^4 + 51976/107*e^2 - 25825/107', '-4239/89024*e^11 + 86927/44512*e^9 - 152189/5564*e^7 + 1770773/11128*e^5 - 1999341/5564*e^3 + 294690/1391*e', '2125/89024*e^11 - 42941/44512*e^9 + 18340/1391*e^7 - 821403/11128*e^5 + 881475/5564*e^3 - 122522/1391*e', '1407/89024*e^11 - 14541/22256*e^9 + 207053/22256*e^7 - 622543/11128*e^5 + 185664/1391*e^3 - 213821/2782*e', '641/89024*e^11 - 3207/11128*e^9 + 86509/22256*e^7 - 237773/11128*e^5 + 121991/2782*e^3 - 66933/2782*e', '3473/44512*e^11 - 70673/22256*e^9 + 122053/2782*e^7 - 346153/1391*e^5 + 742683/1391*e^3 - 388243/1391*e', '519/44512*e^11 - 2627/5564*e^9 + 72431/11128*e^7 - 208633/5564*e^5 + 121300/1391*e^3 - 87491/1391*e', '-6881/89024*e^11 + 70283/22256*e^9 - 977087/22256*e^7 + 2798279/11128*e^5 - 1525029/2782*e^3 + 837287/2782*e', '3987/89024*e^11 - 10207/5564*e^9 + 569575/22256*e^7 - 1635605/11128*e^5 + 442826/1391*e^3 - 465859/2782*e', '-45/3424*e^10 + 1829/3424*e^8 - 12457/1712*e^6 + 8293/214*e^4 - 26589/428*e^2 - 1475/214', '-253/1712*e^10 + 20597/3424*e^8 - 142067/1712*e^6 + 199999/428*e^4 - 418897/428*e^2 + 101055/214', '291/1712*e^10 - 11799/1712*e^8 + 80969/856*e^6 - 113455/214*e^4 + 237683/214*e^2 - 58157/107', '-225/1712*e^10 + 9145/1712*e^8 - 62927/856*e^6 + 88173/214*e^4 - 182165/214*e^2 + 41203/107', '-133/3424*e^10 + 1333/856*e^8 - 17989/856*e^6 + 49475/428*e^4 - 26143/107*e^2 + 15291/107', '93/3424*e^10 - 493/428*e^8 + 14545/856*e^6 - 45527/428*e^4 + 27974/107*e^2 - 18039/107', '-2439/44512*e^11 + 49277/22256*e^9 - 41956/1391*e^7 + 923721/5564*e^5 - 917367/2782*e^3 + 175258/1391*e', '-2083/44512*e^11 + 21379/11128*e^9 - 299197/11128*e^7 + 216063/1391*e^5 - 957299/2782*e^3 + 281720/1391*e', '37/856*e^11 - 6013/3424*e^9 + 41343/1712*e^7 - 14491/107*e^5 + 121995/428*e^3 - 32801/214*e', '-27/44512*e^11 + 1825/44512*e^9 - 21213/22256*e^7 + 50847/5564*e^5 - 187667/5564*e^3 + 88567/2782*e', '-5/1712*e^10 + 347/3424*e^8 - 1829/1712*e^6 + 1629/428*e^4 - 95/428*e^2 - 5119/214', '-431/3424*e^10 + 17299/3424*e^8 - 116847/1712*e^6 + 39977/107*e^4 - 322687/428*e^2 + 72519/214', '163/856*e^10 - 26455/3424*e^8 + 181589/1712*e^6 - 253935/428*e^4 + 527819/428*e^2 - 124993/214', '-583/3424*e^10 + 23729/3424*e^8 - 163865/1712*e^6 + 57980/107*e^4 - 492977/428*e^2 + 123581/214', '-29/856*e^10 + 4817/3424*e^8 - 34463/1712*e^6 + 51831/428*e^4 - 121049/428*e^2 + 35871/214', '-101/3424*e^10 + 4029/3424*e^8 - 27065/1712*e^6 + 18675/214*e^4 - 81477/428*e^2 + 25413/214', '-1997/89024*e^11 + 4975/5564*e^9 - 265877/22256*e^7 + 717905/11128*e^5 - 364089/2782*e^3 + 191157/2782*e', '10513/89024*e^11 - 106413/22256*e^9 + 1456123/22256*e^7 - 4051577/11128*e^5 + 1038447/1391*e^3 - 905259/2782*e', '-2757/44512*e^11 + 111857/44512*e^9 - 766737/22256*e^7 + 532937/2782*e^5 - 2162393/5564*e^3 + 439567/2782*e', '-3409/44512*e^11 + 138205/44512*e^9 - 948861/22256*e^7 + 667127/2782*e^5 - 2848037/5564*e^3 + 772675/2782*e', '-31/5564*e^11 + 9911/44512*e^9 - 67337/22256*e^7 + 95333/5564*e^5 - 200199/5564*e^3 + 4509/2782*e', '583/44512*e^11 - 24157/44512*e^9 + 172425/22256*e^7 - 258991/5564*e^5 + 607895/5564*e^3 - 159319/2782*e', '27/1712*e^10 - 2045/3424*e^8 + 12359/1712*e^6 - 13419/428*e^4 + 13781/428*e^2 + 5729/214', '-15/856*e^10 + 2403/3424*e^8 - 16217/1712*e^6 + 22507/428*e^4 - 49683/428*e^2 + 11337/214', '53/1712*e^10 - 4149/3424*e^8 + 26963/1712*e^6 - 34901/428*e^4 + 65421/428*e^2 - 14347/214', '369/3424*e^10 - 15169/3424*e^8 + 106085/1712*e^6 - 37971/107*e^4 + 322205/428*e^2 - 73933/214', '-2181/89024*e^11 + 1393/1391*e^9 - 312193/22256*e^7 + 922845/11128*e^5 - 558731/2782*e^3 + 404329/2782*e', '349/89024*e^11 - 449/2782*e^9 + 50625/22256*e^7 - 149375/11128*e^5 + 45107/1391*e^3 - 88363/2782*e', '39/1712*e^10 - 789/856*e^8 + 5423/428*e^6 - 7708/107*e^4 + 17118/107*e^2 - 10028/107', '13/107*e^10 - 526/107*e^8 + 7195/107*e^6 - 40075/107*e^4 + 82308/107*e^2 - 36220/107', '7/6848*e^11 - 21/856*e^9 - 157/1712*e^7 + 4627/856*e^5 - 3944/107*e^3 + 12711/214*e', '-3127/89024*e^11 + 15801/11128*e^9 - 431115/22256*e^7 + 1190347/11128*e^5 - 594121/2782*e^3 + 236255/2782*e', '1227/44512*e^11 - 49243/44512*e^9 + 332499/22256*e^7 - 456047/5564*e^5 + 954273/5564*e^3 - 302253/2782*e', '-1021/22256*e^11 + 83569/44512*e^9 - 581019/22256*e^7 + 826297/5564*e^5 - 1743169/5564*e^3 + 383407/2782*e', '-1/856*e^10 - 11/3424*e^8 + 2029/1712*e^6 - 7245/428*e^4 + 31099/428*e^2 - 17905/214', '-137/1712*e^10 + 11177/3424*e^8 - 77635/1712*e^6 + 111745/428*e^4 - 250201/428*e^2 + 72327/214', '-41/832*e^11 + 837/416*e^9 - 363/13*e^7 + 16531/104*e^5 - 17471/52*e^3 + 1897/13*e', '693/89024*e^11 - 14843/44512*e^9 + 55091/11128*e^7 - 342501/11128*e^5 + 413931/5564*e^3 - 67429/1391*e', '-55/1712*e^10 + 4245/3424*e^8 - 26539/1712*e^6 + 30759/428*e^4 - 39565/428*e^2 - 3237/214', '-169/1712*e^10 + 13997/3424*e^8 - 99099/1712*e^6 + 144983/428*e^4 - 322285/428*e^2 + 87587/214', '-8201/89024*e^11 + 166785/44512*e^9 - 287317/5564*e^7 + 3235653/11128*e^5 - 3417025/5564*e^3 + 438946/1391*e', '503/6848*e^11 - 10209/3424*e^9 + 34981/856*e^7 - 193957/856*e^5 + 195123/428*e^3 - 20188/107*e', '301/1712*e^10 - 24613/3424*e^8 + 170839/1712*e^6 - 242473/428*e^4 + 512685/428*e^2 - 121591/214', '231/3424*e^10 - 9289/3424*e^8 + 62933/1712*e^6 - 21560/107*e^4 + 171201/428*e^2 - 38153/214', '-1679/44512*e^11 + 69079/44512*e^9 - 483607/22256*e^7 + 173149/1391*e^5 - 1459755/5564*e^3 + 293263/2782*e', '283/22256*e^11 - 21823/44512*e^9 + 136349/22256*e^7 - 158199/5564*e^5 + 198191/5564*e^3 + 58059/2782*e', '-1507/89024*e^11 + 15355/22256*e^9 - 212025/22256*e^7 + 593251/11128*e^5 - 145631/1391*e^3 + 58007/2782*e', '-1995/89024*e^11 + 19995/22256*e^9 - 268337/22256*e^7 + 718157/11128*e^5 - 339929/2782*e^3 + 117657/2782*e', '655/3424*e^10 - 26741/3424*e^8 + 185337/1712*e^6 - 65770/107*e^4 + 562141/428*e^2 - 145189/214', '141/1712*e^10 - 11369/3424*e^8 + 77215/1712*e^6 - 106029/428*e^4 + 211329/428*e^2 - 41439/214', '-65/3424*e^11 + 1315/1712*e^9 - 4537/428*e^7 + 26371/428*e^5 - 31847/214*e^3 + 13243/107*e', '3167/44512*e^11 - 8121/2782*e^9 + 454247/11128*e^7 - 1310497/5564*e^5 + 721225/1391*e^3 - 408452/1391*e', '1379/89024*e^11 - 27569/44512*e^9 + 92231/11128*e^7 - 492535/11128*e^5 + 465393/5564*e^3 - 50745/1391*e', '-5701/89024*e^11 + 114957/44512*e^9 - 97519/2782*e^7 + 2129051/11128*e^5 - 2053847/5564*e^3 + 155457/1391*e', '399/11128*e^11 - 3999/2782*e^9 + 107613/5564*e^7 - 582037/5564*e^5 + 569759/2782*e^3 - 118329/1391*e', '1949/22256*e^11 - 78983/22256*e^9 + 542727/11128*e^7 - 383537/1391*e^5 + 1664443/2782*e^3 - 477869/1391*e', '-4419/89024*e^11 + 89301/44512*e^9 - 303567/11128*e^7 + 1653505/11128*e^5 - 1565883/5564*e^3 + 94088/1391*e', '85/89024*e^11 - 3053/44512*e^9 + 9333/5564*e^7 - 190985/11128*e^5 + 394137/5564*e^3 - 119408/1391*e', '365/3424*e^10 - 7483/1712*e^8 + 26119/428*e^6 - 150141/428*e^4 + 163919/214*e^2 - 43030/107', '-43/3424*e^10 + 837/1712*e^8 - 2659/428*e^6 + 12451/428*e^4 - 6009/214*e^2 - 3778/107', '-91/3424*e^10 + 1841/1712*e^8 - 6309/428*e^6 + 35293/428*e^4 - 34913/214*e^2 + 3496/107', '-447/3424*e^10 + 9109/1712*e^8 - 7859/107*e^6 + 176617/428*e^4 - 182873/214*e^2 + 43838/107', '-159/1712*e^10 + 13089/3424*e^8 - 91803/1712*e^6 + 132309/428*e^4 - 285929/428*e^2 + 71931/214', '381/3424*e^10 - 15671/3424*e^8 + 109735/1712*e^6 - 78717/214*e^4 + 334731/428*e^2 - 77463/214', '1123/22256*e^11 - 92103/44512*e^9 + 643925/22256*e^7 - 232489/1391*e^5 + 2047061/5564*e^3 - 521527/2782*e', '1137/44512*e^11 - 46869/44512*e^9 + 334121/22256*e^7 - 511899/5564*e^5 + 1320963/5564*e^3 - 517063/2782*e', '217/3424*e^10 - 8953/3424*e^8 + 63133/1712*e^6 - 22964/107*e^4 + 199637/428*e^2 - 44485/214', '19/428*e^10 - 6109/3424*e^8 + 41347/1712*e^6 - 56711/428*e^4 + 113045/428*e^2 - 16715/214', '-187/3424*e^10 + 1871/856*e^8 - 25185/856*e^6 + 68993/428*e^4 - 36142/107*e^2 + 20077/107', '75/3424*e^10 - 83/107*e^8 + 7153/856*e^6 - 12699/428*e^4 + 2278/107*e^2 - 1535/107', '-1731/22256*e^11 + 70327/22256*e^9 - 483659/11128*e^7 + 338849/1391*e^5 - 1399045/2782*e^3 + 285840/1391*e', '-2897/22256*e^11 + 58625/11128*e^9 - 100260/1391*e^7 + 558892/1391*e^5 - 1160667/1391*e^3 + 553011/1391*e', '-29/1712*e^10 + 1231/1712*e^8 - 8803/856*e^6 + 6091/107*e^4 - 20231/214*e^2 + 167/107', '5/428*e^10 - 801/1712*e^8 + 5477/856*e^6 - 8073/214*e^4 + 20413/214*e^2 - 4421/107', '-841/44512*e^11 + 17475/22256*e^9 - 15708/1391*e^7 + 96612/1391*e^5 - 245623/1391*e^3 + 182342/1391*e', '4089/44512*e^11 - 41547/11128*e^9 + 572087/11128*e^7 - 401863/1391*e^5 + 1672011/2782*e^3 - 383545/1391*e', '-4821/44512*e^11 + 98405/22256*e^9 - 85373/1391*e^7 + 1950603/5564*e^5 - 2117077/2782*e^3 + 568999/1391*e', '99/44512*e^11 - 1723/22256*e^9 + 1123/1391*e^7 - 7673/2782*e^5 + 3833/1391*e^3 - 4958/1391*e', '-415/3424*e^10 + 16915/3424*e^8 - 116831/1712*e^6 + 82353/214*e^4 - 346075/428*e^2 + 80795/214', '223/1712*e^10 - 18301/3424*e^8 + 127883/1712*e^6 - 184019/428*e^4 + 401849/428*e^2 - 105447/214', '383/3424*e^10 - 15505/3424*e^8 + 105885/1712*e^6 - 36567/107*e^4 + 293341/428*e^2 - 62893/214', '-101/1712*e^10 + 8165/3424*e^8 - 55735/1712*e^6 + 77589/428*e^4 - 163061/428*e^2 + 48151/214', '203/3424*e^10 - 7975/3424*e^8 + 51991/1712*e^6 - 33649/214*e^4 + 124711/428*e^2 - 26635/214', '6027/89024*e^11 - 15193/5564*e^9 + 825683/22256*e^7 - 2266023/11128*e^5 + 1126539/2782*e^3 - 449831/2782*e', '-1763/89024*e^11 + 1156/1391*e^9 - 267151/22256*e^7 + 803029/11128*e^5 - 229930/1391*e^3 + 238113/2782*e', '3451/89024*e^11 - 34295/22256*e^9 + 452677/22256*e^7 - 1163433/11128*e^5 + 471359/2782*e^3 - 8171/2782*e', '6137/89024*e^11 - 31251/11128*e^9 + 865649/22256*e^7 - 2474723/11128*e^5 + 684484/1391*e^3 - 803399/2782*e', '95/1712*e^10 - 3885/1712*e^8 + 27059/856*e^6 - 39069/214*e^4 + 88375/214*e^2 - 25681/107', '-193/1712*e^10 + 7735/1712*e^8 - 52195/856*e^6 + 35777/107*e^4 - 146551/214*e^2 + 38067/107'], 'hecke_polynomial': 'x^12 - 44*x^10 + 696*x^8 - 5024*x^6 + 17152*x^4 - 25344*x^2 + 10816', 'label': '2.2.161.1-8.3-b'}
• hmf_fields •

  Column	Type
  degree	smallint
  discriminant	bigint
  ideals	jsonb
  label	text
  narrow_class_no	smallint
  primes	jsonb

  
  {'degree': 2, 'discriminant': 161, 'ideals': ['[1, 1, 1]', '[2, 2, w + 6]', '[2, 2, -w + 7]', '[4, 2, 2]', '[4, 4, 13*w + 76]', '[4, 4, -13*w + 89]', '[5, 5, -6*w - 35]', '[5, 5, -6*w + 41]', '[7, 7, 32*w - 219]', '[8, 4, 2*w + 12]', '[8, 4, -2*w + 14]', '[8, 8, -7*w + 48]', '[8, 8, 7*w + 41]', '[9, 3, 3]', '[10, 10, -19*w + 130]', '[10, 10, -w + 6]', '[10, 10, -w - 5]', '[10, 10, -19*w - 111]', '[14, 14, 5*w + 29]', '[14, 14, 5*w - 34]', '[16, 4, 4]', '[16, 8, 26*w + 152]', '[16, 8, -26*w + 178]', '[16, 16, w + 7]', '[16, 16, -w + 8]', '[17, 17, 2*w - 13]', '[17, 17, 2*w + 11]', '[18, 6, 3*w + 18]', '[18, 6, -3*w + 21]', '[19, 19, 4*w + 23]', '[19, 19, 4*w - 27]', '[20, 10, -12*w - 70]', '[20, 10, -12*w + 82]', '[20, 20, -3*w + 20]', '[20, 20, -w - 4]', '[20, 20, -w + 5]', '[20, 20, -3*w - 17]', '[23, 23, 58*w - 397]', '[25, 5, 5]', '[25, 25, 8*w + 47]', '[25, 25, -8*w + 55]', '[28, 14, 64*w - 438]', '[28, 28, w + 3]', '[28, 28, w - 4]', '[29, 29, 20*w - 137]', '[29, 29, -20*w - 117]', '[32, 8, 4*w + 24]', '[32, 8, -4*w + 28]', '[32, 16, -14*w + 96]', '[32, 16, 14*w + 82]', '[32, 32, w + 8]', '[32, 32, -w + 9]', '[34, 34, w + 2]', '[34, 34, 25*w + 146]', '[34, 34, 25*w - 171]', '[34, 34, w - 3]', '[35, 35, 2*w - 15]', '[35, 35, -2*w - 13]', '[36, 6, 6]', '[36, 12, 39*w + 228]', '[36, 12, -39*w + 267]', '[38, 38, w + 1]', '[38, 38, 51*w - 349]', '[38, 38, 51*w + 298]', '[38, 38, w - 2]', '[40, 20, -38*w + 260]', '[40, 20, -2*w + 12]', '[40, 20, -2*w - 10]', '[40, 20, -38*w - 222]', '[40, 40, -w]', '[40, 40, -11*w + 75]', '[40, 40, -11*w - 64]', '[40, 40, -w + 1]', '[45, 15, -18*w - 105]', '[45, 15, -18*w + 123]', '[46, 46, -9*w - 53]', '[46, 46, 9*w - 62]', '[49, 7, 7]', '[50, 10, 5*w + 30]', '[50, 10, -5*w + 35]', '[50, 50, w + 9]', '[50, 50, 71*w + 415]', '[50, 50, -71*w + 486]', '[50, 50, -w + 10]', '[56, 28, 10*w + 58]', '[56, 28, 10*w - 68]', '[56, 56, 3*w + 16]', '[56, 56, 3*w - 19]', '[58, 58, 3*w - 22]', '[58, 58, 33*w - 226]', '[58, 58, -33*w - 193]', '[58, 58, -3*w - 19]', '[61, 61, 2*w - 11]', '[61, 61, -2*w - 9]', '[63, 21, 96*w - 657]', '[64, 8, 8]', '[64, 16, 52*w + 304]', '[64, 16, -52*w + 356]', '[64, 32, 2*w + 14]', '[64, 32, -2*w + 16]', '[64, 64, -15*w + 103]', '[64, 64, 15*w + 88]', '[68, 34, 4*w - 26]', '[68, 34, 4*w + 22]', '[68, 68, 31*w + 181]', '[68, 68, 9*w - 61]', '[68, 68, 9*w + 52]', '[68, 68, 31*w - 212]', '[70, 70, -w - 10]', '[70, 70, -27*w - 158]', '[70, 70, 27*w - 185]', '[70, 70, w - 11]', '[71, 71, -10*w - 59]', '[71, 71, 10*w - 69]', '[72, 12, 6*w + 36]', '[72, 12, -6*w + 42]', '[72, 24, -21*w + 144]', '[72, 24, 21*w + 123]', '[76, 38, 8*w + 46]', '[76, 38, 8*w - 54]', '[76, 76, 17*w - 116]', '[76, 76, 5*w + 28]', '[76, 76, 5*w - 33]', '[76, 76, 17*w + 99]', '[80, 20, -24*w - 140]', '[80, 20, -24*w + 164]', '[80, 40, -6*w + 40]', '[80, 40, -2*w - 8]', '[80, 40, -2*w + 10]', '[80, 40, -6*w - 34]', '[80, 80, -83*w + 568]', '[80, 80, -7*w + 47]', '[80, 80, -7*w - 40]', '[80, 80, -83*w - 485]', '[81, 9, 9]', '[83, 83, -44*w + 301]', '[83, 83, 44*w + 257]', '[85, 85, 4*w - 29]', '[85, 85, -84*w - 491]', '[85, 85, 84*w - 575]', '[85, 85, -4*w - 25]', '[89, 89, -70*w - 409]', '[89, 89, 70*w - 479]', '[90, 30, -57*w + 390]', '[90, 30, -3*w + 18]', '[90, 30, -3*w - 15]', '[90, 30, -57*w - 333]', '[92, 46, 116*w - 794]', '[92, 92, -w - 11]', '[92, 92, w - 12]', '[95, 95, 46*w - 315]', '[95, 95, 2*w - 17]', '[95, 95, -2*w - 15]', '[95, 95, -46*w - 269]', '[97, 97, 2*w - 9]', '[97, 97, -2*w - 7]', '[98, 14, 7*w + 42]', '[98, 14, -7*w + 49]', '[100, 10, 10]', '[100, 20, 65*w + 380]', '[100, 20, -65*w + 445]', '[100, 50, 16*w + 94]', '[100, 50, -16*w + 110]', '[100, 100, 11*w + 65]', '[100, 100, 3*w + 20]', '[100, 100, -3*w + 23]', '[100, 100, -11*w + 76]', '[103, 103, -16*w - 93]', '[103, 103, 16*w - 109]', '[112, 28, 128*w - 876]', '[112, 56, 2*w + 6]', '[112, 56, 2*w - 8]', '[112, 112, 37*w + 216]', '[112, 112, 37*w - 253]', '[115, 115, 4*w + 21]', '[115, 115, 4*w - 25]', '[116, 58, 40*w - 274]', '[116, 58, -40*w - 234]', '[116, 116, -w - 12]', '[116, 116, 5*w - 36]', '[116, 116, -5*w - 31]', '[116, 116, w - 13]', '[119, 119, -22*w + 151]', '[119, 119, 22*w + 129]', '[121, 11, -11]', '[122, 122, 23*w - 157]', '[122, 122, -3*w + 17]', '[122, 122, 3*w + 14]', '[122, 122, -23*w - 134]', '[125, 25, -30*w - 175]', '[125, 25, -30*w + 205]', '[125, 125, -2*w + 7]', '[125, 125, -2*w - 5]', '[126, 42, 15*w + 87]', '[126, 42, 15*w - 102]', '[127, 127, 34*w + 199]', '[127, 127, 34*w - 233]', '[128, 16, 8*w + 48]', '[128, 16, -8*w + 56]', '[128, 32, -28*w + 192]', '[128, 32, 28*w + 164]', '[128, 64, 2*w + 16]', '[128, 64, -2*w + 18]', '[128, 128, 97*w + 567]', '[128, 128, -97*w + 664]', '[133, 133, 12*w + 71]', '[133, 133, -12*w + 83]', '[136, 68, 2*w + 4]', '[136, 68, 50*w + 292]', '[136, 68, 50*w - 342]', '[136, 68, 2*w - 6]', '[136, 136, 115*w - 787]', '[136, 136, 5*w - 32]', '[136, 136, 5*w + 27]', '[136, 136, 115*w + 672]', '[140, 70, 4*w - 30]', '[140, 70, -4*w - 26]', '[140, 140, 59*w - 404]', '[140, 140, 17*w - 117]', '[140, 140, -17*w - 100]', '[140, 140, -59*w - 345]', '[142, 142, -w - 13]', '[142, 142, 129*w - 883]', '[142, 142, -129*w - 754]', '[142, 142, w - 14]', '[144, 12, 12]', '[144, 24, 78*w + 456]', '[144, 24, -78*w + 534]', '[144, 48, 3*w + 21]', '[144, 48, -3*w + 24]', '[145, 145, 14*w - 95]', '[145, 145, 2*w - 5]', '[145, 145, 2*w + 3]', '[145, 145, 14*w + 81]', '[151, 151, 6*w - 43]', '[151, 151, -6*w - 37]', '[152, 76, 2*w + 2]', '[152, 76, 102*w - 698]', '[152, 76, 102*w + 596]', '[152, 76, 2*w - 4]', '[152, 152, 63*w - 431]', '[152, 152, 3*w + 13]', '[152, 152, 3*w - 16]', '[152, 152, 63*w + 368]', '[153, 51, 6*w - 39]', '[153, 51, 6*w + 33]', '[157, 157, 2*w - 3]', '[157, 157, -2*w - 1]', '[160, 40, -76*w + 520]', '[160, 40, -4*w + 24]', '[160, 40, -4*w - 20]', '[160, 40, -76*w - 444]', '[160, 80, -2*w]', '[160, 80, -22*w + 150]', '[160, 80, -22*w - 128]', '[160, 80, -2*w + 2]', '[160, 160, -89*w - 520]', '[160, 160, -13*w - 75]', '[160, 160, -13*w + 88]', '[160, 160, -89*w + 609]', '[161, 161, -2*w + 1]', '[162, 18, 9*w + 54]', '[162, 18, -9*w + 63]', '[163, 163, 2*w - 19]', '[163, 163, -2*w - 17]', '[166, 166, -43*w - 251]', '[166, 166, 7*w + 39]', '[166, 166, -7*w + 46]', '[166, 166, 43*w - 294]', '[169, 13, -13]', '[170, 170, -w - 14]', '[170, 170, -13*w - 77]', '[170, 170, -23*w - 135]', '[170, 170, -53*w - 310]', '[170, 170, 53*w - 363]', '[170, 170, 23*w - 158]', '[170, 170, 13*w - 90]', '[170, 170, w - 15]', '[171, 57, 12*w + 69]', '[171, 57, 12*w - 81]', '[175, 35, 160*w - 1095]', '[175, 175, 8*w - 53]', '[175, 175, 8*w + 45]', '[178, 178, -29*w + 198]', '[178, 178, 11*w - 74]', '[178, 178, -11*w - 63]', '[178, 178, 29*w + 169]', '[179, 179, -110*w - 643]', '[179, 179, 110*w - 753]', '[180, 30, -36*w - 210]', '[180, 30, -36*w + 246]', '[180, 60, -9*w + 60]', '[180, 60, -3*w - 12]', '[180, 60, -3*w + 15]', '[180, 60, -9*w - 51]', '[181, 181, 10*w + 57]', '[181, 181, 10*w - 67]', '[184, 92, -18*w - 106]', '[184, 92, 18*w - 124]', '[184, 184, -5*w - 32]', '[184, 184, 5*w - 37]', '[190, 190, 7*w - 50]', '[190, 190, 29*w - 199]', '[190, 190, 3*w - 25]', '[190, 190, 47*w - 322]', '[190, 190, -47*w - 275]', '[190, 190, -3*w - 22]', '[190, 190, -29*w - 170]', '[190, 190, -7*w - 43]', '[193, 193, 72*w - 493]', '[193, 193, -72*w - 421]', '[194, 194, 5*w + 26]', '[194, 194, -21*w - 122]', '[194, 194, 21*w - 143]', '[194, 194, -5*w + 31]', '[196, 14, 14]', '[196, 28, 91*w + 532]', '[196, 28, -91*w + 623]', '[197, 197, 4*w + 27]', '[197, 197, 4*w - 31]', '[199, 199, 56*w - 383]', '[199, 199, -56*w - 327]', '[200, 20, 10*w + 60]', '[200, 20, -10*w + 70]', '[200, 40, -35*w + 240]', '[200, 40, 35*w + 205]', '[200, 100, 2*w + 18]', '[200, 100, 142*w + 830]', '[200, 100, -142*w + 972]', '[200, 100, -2*w + 20]', '[200, 200, w + 15]', '[200, 200, 41*w + 240]', '[200, 200, -41*w + 281]', '[200, 200, -w + 16]', '[203, 203, -4*w + 23]', '[203, 203, -4*w - 19]', '[206, 206, -205*w - 1198]', '[206, 206, 3*w - 14]', '[206, 206, -3*w - 11]', '[206, 206, 205*w - 1403]', '[207, 69, 174*w - 1191]', '[211, 211, -14*w - 83]', '[211, 211, 14*w - 97]', '[224, 56, 20*w + 116]', '[224, 56, 20*w - 136]', '[224, 112, 6*w + 32]', '[224, 112, 6*w - 38]', '[224, 224, 69*w + 403]', '[224, 224, 69*w - 472]', '[225, 15, 15]', '[225, 75, 24*w + 141]', '[225, 75, -24*w + 165]', '[227, 227, -28*w - 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1461]', '[9973, 9973, 214*w + 1247]', '[9974, 9974, -19*w - 58]', '[9974, 9974, 345*w + 2014]', '[9974, 9974, -345*w + 2359]', '[9974, 9974, 19*w - 77]', '[9980, 4990, 192*w - 1310]', '[9980, 4990, 16*w - 26]', '[9980, 4990, -16*w - 10]', '[9980, 4990, -192*w - 1118]', '[9980, 9980, 93*w + 535]', '[9980, 9980, -777*w - 4540]', '[9980, 9980, -29*w + 169]', '[9980, 9980, -543*w + 3715]', '[9980, 9980, 543*w + 3172]', '[9980, 9980, 29*w + 140]', '[9980, 9980, 777*w - 5317]', '[9980, 9980, -93*w + 628]', '[9981, 3327, 30*w - 177]', '[9981, 3327, 30*w + 147]', '[9986, 9986, 139*w - 957]', '[9986, 9986, 35*w - 261]', '[9986, 9986, -35*w - 226]', '[9986, 9986, -139*w - 818]', '[9991, 9991, -74*w - 443]', '[9991, 9991, 330*w - 2261]', '[9991, 9991, 330*w + 1931]', '[9991, 9991, 74*w - 517]', '[9992, 4996, 438*w + 2558]', '[9992, 4996, -42*w - 226]', '[9992, 4996, 42*w - 268]', '[9992, 4996, -438*w + 2996]', '[9992, 9992, -127*w + 863]', '[9992, 9992, -17*w - 32]', '[9992, 9992, 17*w - 49]', '[9992, 9992, 127*w + 736]', '[9998, 9998, -367*w + 2514]', '[9998, 9998, -47*w + 338]', '[9998, 9998, 47*w + 291]', '[9998, 9998, 367*w + 2147]', '[10000, 100, 100]', '[10000, 200, 650*w + 3800]', '[10000, 200, -650*w + 4450]', '[10000, 400, 25*w + 175]', '[10000, 400, -25*w + 200]', '[10000, 500, 160*w + 940]', '[10000, 500, -160*w + 1100]', '[10000, 1000, 110*w + 650]', '[10000, 1000, 30*w + 200]', '[10000, 1000, -30*w + 230]', '[10000, 1000, -110*w + 760]', '[10000, 2000, -555*w + 3800]', '[10000, 2000, 45*w + 280]', '[10000, 2000, -45*w + 325]', '[10000, 2000, 555*w + 3245]', '[10000, 2500, 448*w + 2620]', '[10000, 2500, -448*w + 3068]', '[10000, 5000, -6*w + 110]', '[10000, 5000, 38*w + 242]', '[10000, 5000, -38*w + 280]', '[10000, 5000, 6*w + 104]', '[10000, 10000, -129*w + 889]', '[10000, 10000, 943*w + 5512]', '[10000, 10000, -943*w + 6455]', '[10000, 10000, 129*w + 760]'], 'label': '2.2.161.1', 'narrow_class_no': 2, 'primes': ['[2, 2, w + 6]', '[2, 2, -w + 7]', '[5, 5, -6*w - 35]', '[5, 5, -6*w + 41]', '[7, 7, 32*w - 219]', '[9, 3, 3]', '[17, 17, 2*w - 13]', '[17, 17, 2*w + 11]', '[19, 19, 4*w + 23]', '[19, 19, 4*w - 27]', '[23, 23, 58*w - 397]', '[29, 29, 20*w - 137]', '[29, 29, -20*w - 117]', '[61, 61, 2*w - 11]', '[61, 61, -2*w - 9]', '[71, 71, -10*w - 59]', '[71, 71, 10*w - 69]', '[83, 83, -44*w + 301]', '[83, 83, 44*w + 257]', '[89, 89, -70*w - 409]', '[89, 89, 70*w - 479]', '[97, 97, 2*w - 9]', '[97, 97, -2*w - 7]', '[103, 103, -16*w - 93]', '[103, 103, 16*w - 109]', '[121, 11, -11]', '[127, 127, 34*w + 199]', '[127, 127, 34*w - 233]', '[151, 151, 6*w - 43]', '[151, 151, -6*w - 37]', '[157, 157, 2*w - 3]', '[157, 157, -2*w - 1]', '[163, 163, 2*w - 19]', '[163, 163, -2*w - 17]', '[169, 13, -13]', '[179, 179, -110*w - 643]', '[179, 179, 110*w - 753]', '[181, 181, 10*w + 57]', '[181, 181, 10*w - 67]', '[193, 193, 72*w - 493]', '[193, 193, -72*w - 421]', '[197, 197, 4*w + 27]', '[197, 197, 4*w - 31]', '[199, 199, 56*w - 383]', '[199, 199, -56*w - 327]', '[211, 211, -14*w - 83]', '[211, 211, 14*w - 97]', '[227, 227, -28*w - 163]', '[227, 227, -28*w + 191]', '[229, 229, -134*w - 783]', '[229, 229, 134*w - 917]', '[233, 233, 8*w - 57]', '[233, 233, -8*w - 49]', '[239, 239, 2*w - 21]', '[239, 239, -2*w - 19]', '[241, 241, -82*w + 561]', '[241, 241, 82*w + 479]', '[251, 251, 108*w + 631]', '[251, 251, 108*w - 739]', '[277, 277, -36*w + 247]', '[277, 277, -36*w - 211]', '[283, 283, -4*w - 17]', '[283, 283, 4*w - 21]', '[293, 293, 6*w + 31]', '[293, 293, -6*w + 37]', '[313, 313, -26*w - 151]', '[313, 313, 26*w - 177]', '[317, 317, 4*w - 33]', '[317, 317, -4*w - 29]', '[331, 331, 10*w - 71]', '[331, 331, -10*w - 61]', '[347, 347, -26*w - 153]', '[347, 347, 26*w - 179]', '[367, 367, 8*w + 43]', '[367, 367, -8*w + 51]', '[383, 383, 24*w - 163]', '[383, 383, -24*w - 139]', '[419, 419, -4*w - 13]', '[419, 419, 4*w - 17]', '[433, 433, 94*w + 549]', '[433, 433, -94*w + 643]', '[443, 443, 38*w - 261]', '[443, 443, 38*w + 223]', '[449, 449, 8*w - 59]', '[449, 449, -8*w - 51]', '[463, 463, -162*w - 947]', '[463, 463, -162*w + 1109]', '[467, 467, -12*w + 79]', '[467, 467, 12*w + 67]', '[479, 479, -120*w + 821]', '[479, 479, 120*w + 701]', '[487, 487, 6*w + 41]', '[487, 487, 6*w - 47]', '[491, 491, 74*w + 433]', '[491, 491, 74*w - 507]', '[499, 499, -50*w + 343]', '[499, 499, -50*w - 293]', '[503, 503, 16*w + 91]', '[503, 503, 16*w - 107]', '[521, 521, 38*w - 259]', '[521, 521, -38*w - 221]', '[523, 523, -4*w - 9]', '[523, 523, 4*w - 13]', '[541, 541, -20*w - 119]', '[541, 541, 20*w - 139]', '[547, 547, 226*w - 1547]', '[547, 547, -354*w + 2423]', '[563, 563, 4*w - 11]', '[563, 563, -4*w - 7]', '[599, 599, -10*w - 63]', '[599, 599, 10*w - 73]', '[619, 619, 4*w - 7]', '[619, 619, -4*w - 3]', '[643, 643, 4*w - 3]', '[643, 643, 4*w - 1]', '[653, 653, -188*w - 1099]', '[653, 653, -188*w + 1287]', '[661, 661, -10*w + 63]', '[661, 661, 10*w + 53]', '[673, 673, -8*w - 53]', '[673, 673, 8*w - 61]', '[677, 677, -378*w + 2587]', '[677, 677, -262*w + 1793]', '[683, 683, -22*w - 131]', '[683, 683, 22*w - 153]', '[727, 727, 8*w - 47]', '[727, 727, 8*w + 39]', '[733, 733, 34*w - 231]', '[733, 733, -34*w - 197]', '[739, 739, 2*w - 31]', '[739, 739, -2*w - 29]', '[769, 769, -50*w - 291]', '[769, 769, 50*w - 341]', '[773, 773, 6*w - 29]', '[773, 773, -6*w - 23]', '[787, 787, -92*w + 629]', '[787, 787, 92*w + 537]', '[797, 797, -158*w + 1081]', '[797, 797, 158*w + 923]', '[809, 809, -32*w - 189]', '[809, 809, 32*w - 221]', '[821, 821, -316*w - 1847]', '[821, 821, 316*w - 2163]', '[823, 823, -42*w - 247]', '[823, 823, 42*w - 289]', '[839, 839, 64*w + 373]', '[839, 839, 64*w - 437]', '[863, 863, 2*w - 33]', '[863, 863, -2*w - 31]', '[877, 877, 4*w - 41]', '[877, 877, -4*w - 37]', '[881, 881, 30*w - 203]', '[881, 881, -30*w - 173]', '[883, 883, 18*w - 127]', '[883, 883, -18*w - 109]', '[937, 937, -118*w - 689]', '[937, 937, 118*w - 807]', '[941, 941, 18*w + 101]', '[941, 941, -18*w + 119]', '[947, 947, 14*w - 101]', '[947, 947, -14*w - 87]', '[961, 31, -31]', '[967, 967, 54*w - 371]', '[967, 967, 54*w + 317]', '[971, 971, -20*w + 133]', '[971, 971, 20*w + 113]', '[983, 983, 24*w - 161]', '[983, 983, 24*w + 137]', '[991, 991, -126*w + 863]', '[991, 991, -126*w - 737]']}
• nf_fields •

  Column	Type
  class_group	jsonb
  class_number	numeric
  cm	boolean
  coeffs	numeric[]
  conductor	numeric
  degree	smallint
  disc_abs	numeric
  disc_rad	numeric
  disc_sign	smallint
  embeddings_gen_imag	double precision[]
  embeddings_gen_real	double precision[]
  gal_is_abelian	boolean
  gal_is_cyclic	boolean
  gal_is_solvable	boolean
  galois_disc_exponents	numeric[]
  galois_label	text
  galt	integer
  grd	double precision
  index	integer
  inessentialp	integer[]
  is_galois	boolean
  is_minimal_sibling	boolean
  iso_number	smallint
  label	text
  local_algs	text[]
  minimal_sibling	numeric[]
  monogenic	smallint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	numeric
  subfield_mults	integer[]
  subfields	text[]
  torsion_order	smallint
  used_grh	boolean
  dirichlet_group	bigint[]
  frobs	jsonb
  res	jsonb
  source	text
  subfield_inclusions	smallint[]
  torsion_gen	text
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  zk	jsonb

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-40, -1, 1], 'conductor': 161, 'degree': 2, 'dirichlet_group': [1, 160], 'disc_abs': 161, 'disc_rad': 161, 'disc_sign': 1, 'frobs': [[2, [[1, 2]]], [3, [[2, 1]]], [5, [[1, 2]]], [7, [0]], [11, [[2, 1]]], [13, [[2, 1]]], [17, [[1, 2]]], [19, [[1, 2]]], [23, [0]], [29, [[1, 2]]], [31, [[2, 1]]], [37, [[2, 1]]], [41, [[2, 1]]], [43, [[2, 1]]], [47, [[2, 1]]], [53, [[2, 1]]], [59, [[2, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [1, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 12.68857754044952, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.161.1', 'local_algs': ['7.2.1.1', '23.2.1.2'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [7, 23], 'rd': 12.6885775404, 'regulator': {'__RealLiteral__': 0, 'data': '10.0668810976', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 1856 a + 10847 \\)'], 'used_grh': False, 'zk': ['1', 'a']}