Hilbert modular form data - 4.4.9792.1-28.1-d

Formats: - HTML - YAML - JSON - 2026-03-19T06:58:42.302762

• 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': 4, 'dimension': 8, 'disc': 9792, 'field_bad_primes': [2, 3, 17], 'field_label': '4.4.9792.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.9792.1-28.1-d', 'label_nsuffix': 3, 'label_suffix': 'd', 'level_bad_primes': [2, 7], 'level_ideal': '[28, 14, -w^3 + 4*w^2 + 2*w - 7]', 'level_label': '28.1', 'level_norm': 28, 'parallel_weight': 2, 'short_label': '28.1-d', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[4, 2, w^3 - 3*w^2 - 3*w + 4]', -1], ['[7, 7, w]', -1]], 'hecke_eigenvalues': [1, 1, '3/358*e^6 - 73/358*e^4 + 121/179*e^2 + 422/179', 'e', '-49/12172*e^7 + 1431/12172*e^5 - 1913/3043*e^3 - 3327/3043*e', '45/6086*e^7 - 1811/6086*e^5 + 10407/3043*e^3 - 30902/3043*e', '-49/12172*e^7 + 1431/12172*e^5 - 1913/3043*e^3 - 3327/3043*e', '1/6086*e^7 + 95/6086*e^5 - 2406/3043*e^3 + 21561/3043*e', '47/12172*e^7 - 1621/12172*e^5 + 4319/3043*e^3 - 18234/3043*e', '11/358*e^6 - 387/358*e^4 + 1816/179*e^2 - 3226/179', '-7/179*e^6 + 230/179*e^4 - 1937/179*e^2 + 3878/179', '-47/12172*e^7 + 1621/12172*e^5 - 4319/3043*e^3 + 18234/3043*e', '-93/6086*e^7 + 3337/6086*e^5 - 16639/3043*e^3 + 45809/3043*e', '3/358*e^6 - 73/358*e^4 - 58/179*e^2 + 2212/179', '24/3043*e^7 - 763/3043*e^5 + 6232/3043*e^3 - 14907/3043*e', '-141/6086*e^7 + 4863/6086*e^5 - 22871/3043*e^3 + 51587/3043*e', '11/358*e^6 - 387/358*e^4 + 1637/179*e^2 - 1436/179', '11/358*e^6 - 387/358*e^4 + 1637/179*e^2 - 1436/179', '3/179*e^6 - 73/179*e^4 + 242/179*e^2 + 486/179', '3/179*e^6 - 73/179*e^4 + 242/179*e^2 + 486/179', '3/358*e^6 - 73/358*e^4 + 300/179*e^2 - 1368/179', '-3/179*e^6 + 73/179*e^4 - 421/179*e^2 + 2020/179', '427/12172*e^7 - 14209/12172*e^5 + 31016/3043*e^3 - 63167/3043*e', '47/6086*e^7 - 1621/6086*e^5 + 8638/3043*e^3 - 36468/3043*e', '-91/6086*e^7 + 3527/6086*e^5 - 18408/3043*e^3 + 40243/3043*e', '41/12172*e^7 - 2191/12172*e^5 + 8494/3043*e^3 - 43358/3043*e', '95/6086*e^7 - 3147/6086*e^5 + 11827/3043*e^3 - 2687/3043*e', '-237/12172*e^7 + 7915/12172*e^5 - 16146/3043*e^3 + 11792/3043*e', '-46/3043*e^7 + 1716/3043*e^5 - 19045/3043*e^3 + 58241/3043*e', '3/179*e^7 - 73/179*e^5 + 63/179*e^3 + 3529/179*e', '-10/179*e^6 + 303/179*e^4 - 2000/179*e^2 + 886/179', '-3/179*e^6 + 73/179*e^4 + 116/179*e^2 - 3350/179', '-14/179*e^6 + 460/179*e^4 - 3874/179*e^2 + 7398/179', '11/179*e^6 - 387/179*e^4 + 3632/179*e^2 - 6810/179', '5/358*e^6 - 241/358*e^4 + 1395/179*e^2 - 490/179', '25/358*e^6 - 847/358*e^4 + 3753/179*e^2 - 6746/179', '6/179*e^6 - 146/179*e^4 + 484/179*e^2 + 614/179', '-18/179*e^6 + 617/179*e^4 - 5211/179*e^2 + 8540/179', '-21/179*e^6 + 690/179*e^4 - 5811/179*e^2 + 10918/179', '-17/179*e^6 + 533/179*e^4 - 3758/179*e^2 + 2616/179', '13/716*e^7 - 555/716*e^5 + 1724/179*e^3 - 5112/179*e', '23/3043*e^7 - 858/3043*e^5 + 8001/3043*e^3 + 8917/3043*e', '9/358*e^6 - 219/358*e^4 + 542/179*e^2 - 1240/179', '9/358*e^6 - 219/358*e^4 + 542/179*e^2 - 1240/179', '-97/6086*e^7 + 2957/6086*e^5 - 10058/3043*e^3 + 17382/3043*e', '-55/12172*e^7 + 861/12172*e^5 + 2262/3043*e^3 - 10193/3043*e', '49/3043*e^7 - 1431/3043*e^5 + 7652/3043*e^3 + 13308/3043*e', '49/3043*e^7 - 1431/3043*e^5 + 7652/3043*e^3 + 13308/3043*e', '-9/716*e^7 + 219/716*e^5 - 92/179*e^3 - 1528/179*e', '-11/358*e^7 + 387/358*e^5 - 1816/179*e^3 + 3047/179*e', '66/3043*e^7 - 2859/3043*e^5 + 35396/3043*e^3 - 108701/3043*e', '-43/6086*e^7 + 2001/6086*e^5 - 15219/3043*e^3 + 64895/3043*e', '-17/358*e^6 + 533/358*e^4 - 1700/179*e^2 + 234/179', '5/358*e^6 - 241/358*e^4 + 1574/179*e^2 - 5502/179', '37/358*e^6 - 1139/358*e^4 + 4058/179*e^2 - 3626/179', '19/358*e^6 - 701/358*e^4 + 3690/179*e^2 - 9738/179', '37/12172*e^7 - 2571/12172*e^5 + 13306/3043*e^3 - 68222/3043*e', '-138/3043*e^7 + 5148/3043*e^5 - 54092/3043*e^3 + 144293/3043*e', '243/12172*e^7 - 7345/12172*e^5 + 11971/3043*e^3 - 4926/3043*e', '-2/3043*e^7 - 190/3043*e^5 + 6581/3043*e^3 - 28427/3043*e', '-149/6086*e^7 + 4103/6086*e^5 - 9709/3043*e^3 - 23525/3043*e', '137/12172*e^7 - 5243/12172*e^5 + 14726/3043*e^3 - 67394/3043*e', '33/358*e^6 - 1161/358*e^4 + 5627/179*e^2 - 12184/179', '8/179*e^6 - 314/179*e^4 + 3390/179*e^2 - 6938/179', '31/358*e^6 - 993/358*e^4 + 3458/179*e^2 - 1248/179', '-20/179*e^6 + 606/179*e^4 - 4537/179*e^2 + 7858/179', '-327/12172*e^7 + 11537/12172*e^5 - 26553/3043*e^3 + 33565/3043*e', '33/12172*e^7 - 2951/12172*e^5 + 15075/3043*e^3 - 71785/3043*e', '3/716*e^7 - 73/716*e^5 + 150/179*e^3 - 1937/179*e', '189/3043*e^7 - 6389/3043*e^5 + 55163/3043*e^3 - 102558/3043*e', '3/179*e^6 - 73/179*e^4 - 116/179*e^2 + 4066/179', '7/358*e^6 - 409/358*e^4 + 3027/179*e^2 - 7130/179', '4/179*e^6 - 157/179*e^4 + 1874/179*e^2 - 7228/179', '-4/179*e^6 + 157/179*e^4 - 2232/179*e^2 + 9376/179', '-113/3043*e^7 + 4480/3043*e^5 - 49629/3043*e^3 + 123820/3043*e', '-709/12172*e^7 + 23935/12172*e^5 - 53887/3043*e^3 + 123883/3043*e', '-11/179*e^7 + 387/179*e^5 - 3632/179*e^3 + 8242/179*e', '149/12172*e^7 - 4103/12172*e^5 + 6376/3043*e^3 - 26275/3043*e', '185/6086*e^7 - 6769/6086*e^5 + 32641/3043*e^3 - 55362/3043*e', '-46/3043*e^7 + 1716/3043*e^5 - 19045/3043*e^3 + 49112/3043*e', '-233/6086*e^7 + 8295/6086*e^5 - 41916/3043*e^3 + 128086/3043*e', '-5/358*e^7 + 241/358*e^5 - 1753/179*e^3 + 6576/179*e', '9/179*e^6 - 219/179*e^4 + 726/179*e^2 + 742/179', '21/179*e^6 - 690/179*e^4 + 5274/179*e^2 - 4832/179', '2*e^2 - 30', '31/179*e^6 - 993/179*e^4 + 7990/179*e^2 - 11446/179', '-37/358*e^6 + 1139/358*e^4 - 4237/179*e^2 + 7206/179', '-17/179*e^6 + 533/179*e^4 - 4116/179*e^2 + 6196/179', '-415/12172*e^7 + 15349/12172*e^5 - 39366/3043*e^3 + 113415/3043*e', '-45/3043*e^7 + 1811/3043*e^5 - 23857/3043*e^3 + 92234/3043*e', '-4/179*e^6 + 157/179*e^4 - 1516/179*e^2 + 1142/179', '37/358*e^6 - 1139/358*e^4 + 3521/179*e^2 + 670/179', '7/358*e^6 - 51/358*e^4 - 1269/179*e^2 + 8264/179', '-17/358*e^6 + 533/358*e^4 - 1879/179*e^2 + 4172/179', '245/6086*e^7 - 7155/6086*e^5 + 19130/3043*e^3 + 33270/3043*e', '-37/12172*e^7 + 2571/12172*e^5 - 13306/3043*e^3 + 59093/3043*e', '21/358*e^6 - 869/358*e^4 + 5143/179*e^2 - 12440/179', '17/358*e^6 - 533/358*e^4 + 1521/179*e^2 + 124/179', '353/12172*e^7 - 9067/12172*e^5 + 4404/3043*e^3 + 82406/3043*e', '-28/3043*e^7 + 383/3043*e^5 + 6930/3043*e^3 - 78463/3043*e', '233/6086*e^7 - 8295/6086*e^5 + 41916/3043*e^3 - 118957/3043*e', '-515/6086*e^7 + 18021/6086*e^5 - 84615/3043*e^3 + 191701/3043*e', '18/179*e^6 - 617/179*e^4 + 5748/179*e^2 - 9972/179', '103/6086*e^7 - 2387/6086*e^5 + 1708/3043*e^3 + 41995/3043*e', '607/12172*e^7 - 21453/12172*e^5 + 48787/3043*e^3 - 85412/3043*e', '121/3043*e^7 - 3720/3043*e^5 + 26348/3043*e^3 - 13155/3043*e', '91/3043*e^7 - 3527/3043*e^5 + 39859/3043*e^3 - 138303/3043*e', '-3/179*e^6 + 73/179*e^4 - 600/179*e^2 + 3810/179', '-43/358*e^6 + 1285/358*e^4 - 4479/179*e^2 + 2782/179', '-6/179*e^6 + 146/179*e^4 - 126/179*e^2 - 5626/179', '3/179*e^6 - 73/179*e^4 + 242/179*e^2 + 486/179', '227/6086*e^7 - 8865/6086*e^5 + 50266/3043*e^3 - 169205/3043*e', '195/6086*e^7 - 5819/6086*e^5 + 17710/3043*e^3 + 23313/3043*e', '25/358*e^6 - 847/358*e^4 + 3574/179*e^2 - 7104/179', '-7/179*e^6 + 230/179*e^4 - 1400/179*e^2 - 1492/179', '33/358*e^6 - 1161/358*e^4 + 5627/179*e^2 - 14332/179', '-7/179*e^6 + 230/179*e^4 - 1400/179*e^2 - 1492/179', '-16/179*e^6 + 449/179*e^4 - 2842/179*e^2 + 5284/179', '-319/12172*e^7 + 12297/12172*e^5 - 36177/3043*e^3 + 138067/3043*e', '-339/12172*e^7 + 10397/12172*e^5 - 18203/3043*e^3 + 1575/3043*e', '-15/358*e^6 + 365/358*e^4 - 784/179*e^2 + 1828/179', '-8/179*e^6 + 314/179*e^4 - 3927/179*e^2 + 13024/179', '-219/12172*e^7 + 9625/12172*e^5 - 31714/3043*e^3 + 90207/3043*e', '277/6086*e^7 - 10201/6086*e^5 + 54729/3043*e^3 - 189678/3043*e', '-2*e^2 + 4', '7/179*e^6 - 230/179*e^4 + 1758/179*e^2 - 3520/179', '-19/358*e^6 + 701/358*e^4 - 3511/179*e^2 + 5442/179', '-33/358*e^6 + 1161/358*e^4 - 5269/179*e^2 + 9320/179', '283/6086*e^7 - 9631/6086*e^5 + 43336/3043*e^3 - 99871/3043*e', '65/3043*e^7 - 2954/3043*e^5 + 40208/3043*e^3 - 151823/3043*e', '-7/179*e^6 + 230/179*e^4 - 2295/179*e^2 + 3162/179', '-5/358*e^6 + 241/358*e^4 - 1932/179*e^2 + 11946/179', '-49/3043*e^7 + 1431/3043*e^5 - 7652/3043*e^3 - 4179/3043*e', '48/3043*e^7 - 1526/3043*e^5 + 12464/3043*e^3 - 2427/3043*e', '25/3043*e^7 - 668/3043*e^5 + 4463/3043*e^3 - 20473/3043*e', '3/716*e^7 - 73/716*e^5 + 329/179*e^3 - 4264/179*e', '-2/3043*e^7 - 190/3043*e^5 + 6581/3043*e^3 - 28427/3043*e', '145/12172*e^7 - 4483/12172*e^5 + 14231/3043*e^3 - 108956/3043*e', '-8/179*e^6 + 314/179*e^4 - 3748/179*e^2 + 10160/179', '-9/358*e^6 + 219/358*e^4 - 5/179*e^2 - 3414/179', '341/12172*e^7 - 10207/12172*e^5 + 15797/3043*e^3 + 1728/3043*e', '-205/12172*e^7 + 10955/12172*e^5 - 42470/3043*e^3 + 180274/3043*e', '-20/3043*e^7 + 1143/3043*e^5 - 16351/3043*e^3 + 41331/3043*e', '-25/716*e^7 + 847/716*e^5 - 1608/179*e^3 + 330/179*e', '599/12172*e^7 - 22213/12172*e^5 + 58411/3043*e^3 - 162527/3043*e', '1/716*e^7 - 263/716*e^5 + 1661/179*e^3 - 9715/179*e', '333/6086*e^7 - 10967/6086*e^5 + 44756/3043*e^3 - 71656/3043*e', '127/12172*e^7 - 6193/12172*e^5 + 23713/3043*e^3 - 108253/3043*e', '-143/12172*e^7 + 4673/12172*e^5 - 10551/3043*e^3 + 69657/3043*e', '45/6086*e^7 - 1811/6086*e^5 + 10407/3043*e^3 - 49160/3043*e', '361/12172*e^7 - 8307/12172*e^5 + 866/3043*e^3 + 89532/3043*e', '-405/12172*e^7 + 16299/12172*e^5 - 48353/3043*e^3 + 154274/3043*e', '-217/12172*e^7 + 9815/12172*e^5 - 34120/3043*e^3 + 102639/3043*e', '233/3043*e^7 - 8295/3043*e^5 + 83832/3043*e^3 - 237914/3043*e', '17/358*e^6 - 533/358*e^4 + 1879/179*e^2 - 5604/179', '8/179*e^6 - 314/179*e^4 + 3032/179*e^2 - 4432/179', '-4/179*e^6 + 157/179*e^4 - 1158/179*e^2 + 784/179', '8/179*e^6 - 314/179*e^4 + 3748/179*e^2 - 5148/179', '-87/6086*e^7 + 3907/6086*e^5 - 28032/3043*e^3 + 117358/3043*e', '-313/12172*e^7 + 12867/12172*e^5 - 40352/3043*e^3 + 144933/3043*e', '2*e^2 - 30', '15/358*e^6 - 723/358*e^4 + 4185/179*e^2 - 6482/179', '-19/358*e^6 + 701/358*e^4 - 2795/179*e^2 + 430/179', '7/358*e^6 - 51/358*e^4 - 911/179*e^2 + 4684/179', '-34/179*e^6 + 1066/179*e^4 - 7516/179*e^2 + 3800/179', '523/12172*e^7 - 17261/12172*e^5 + 37248/3043*e^3 - 96332/3043*e', '163/12172*e^7 - 2773/12172*e^5 - 7423/3043*e^3 + 112480/3043*e', '-19/358*e^6 + 343/358*e^4 + 606/179*e^2 - 10310/179', '53/358*e^6 - 1767/358*e^4 + 7448/179*e^2 - 8774/179', '-28/179*e^6 + 920/179*e^4 - 7032/179*e^2 + 7278/179', '-33/179*e^6 + 1161/179*e^4 - 10896/179*e^2 + 21862/179', '327/12172*e^7 - 11537/12172*e^5 + 32639/3043*e^3 - 140070/3043*e', '193/6086*e^7 - 6009/6086*e^5 + 22522/3043*e^3 - 19809/3043*e', '-35/358*e^6 + 971/358*e^4 - 2963/179*e^2 + 7368/179', '-9/179*e^6 + 398/179*e^4 - 5022/179*e^2 + 12146/179', '-91/358*e^6 + 2811/358*e^4 - 10353/179*e^2 + 11424/179', '3/179*e^6 - 73/179*e^4 - 116/179*e^2 + 6214/179', '-975/12172*e^7 + 35181/12172*e^5 - 86877/3043*e^3 + 220152/3043*e', '40/3043*e^7 - 2286/3043*e^5 + 38788/3043*e^3 - 170909/3043*e', '-43/179*e^6 + 1464/179*e^4 - 12896/179*e^2 + 25612/179', '-14/179*e^6 + 460/179*e^4 - 4232/179*e^2 + 9904/179', '5/179*e^6 - 62/179*e^4 - 1506/179*e^2 + 9760/179', '26/179*e^6 - 752/179*e^4 + 4842/179*e^2 - 2948/179', '243/12172*e^7 - 7345/12172*e^5 + 11971/3043*e^3 + 4203/3043*e', '-1265/12172*e^7 + 44147/12172*e^5 - 103167/3043*e^3 + 252441/3043*e', '-225/12172*e^7 + 9055/12172*e^5 - 30582/3043*e^3 + 150287/3043*e', '21/3043*e^7 - 1048/3043*e^5 + 17625/3043*e^3 - 104714/3043*e', '-53/358*e^6 + 1767/358*e^4 - 6553/179*e^2 + 3762/179', '-21/179*e^6 + 690/179*e^4 - 5990/179*e^2 + 13782/179', '-145/12172*e^7 + 4483/12172*e^5 - 8145/3043*e^3 + 57225/3043*e', '147/6086*e^7 - 4293/6086*e^5 + 11478/3043*e^3 + 1704/3043*e', '-3/358*e^6 + 73/358*e^4 + 416/179*e^2 - 11520/179', '47/358*e^6 - 1621/358*e^4 + 6848/179*e^2 - 12840/179', '141/3043*e^7 - 4863/3043*e^5 + 48785/3043*e^3 - 160991/3043*e', '151/6086*e^7 - 3913/6086*e^5 + 4897/3043*e^3 + 48389/3043*e', '-75/358*e^6 + 2541/358*e^4 - 11080/179*e^2 + 17732/179', '22/179*e^6 - 774/179*e^4 + 7443/179*e^2 - 15768/179', '1/6086*e^7 + 95/6086*e^5 - 8492/3043*e^3 + 109808/3043*e', '-609/12172*e^7 + 21263/12172*e^5 - 46381/3043*e^3 + 82109/3043*e', '-365/6086*e^7 + 14013/6086*e^5 - 77312/3043*e^3 + 236787/3043*e', '-61/12172*e^7 + 291/12172*e^5 + 12523/3043*e^3 - 123564/3043*e', '471/6086*e^7 - 16115/6086*e^5 + 71802/3043*e^3 - 111851/3043*e', '423/12172*e^7 - 14589/12172*e^5 + 35828/3043*e^3 - 115418/3043*e', '-11/358*e^6 + 387/358*e^4 - 2174/179*e^2 + 5374/179', '22/179*e^6 - 595/179*e^4 + 3147/179*e^2 - 374/179', '-49/716*e^7 + 1431/716*e^5 - 2092/179*e^3 - 2074/179*e', '229/12172*e^7 - 8675/12172*e^5 + 25770/3043*e^3 - 116294/3043*e', '-33/358*e^6 + 803/358*e^4 - 1152/179*e^2 - 10728/179', '-53/358*e^6 + 1767/358*e^4 - 8164/179*e^2 + 17724/179', '35/179*e^6 - 1150/179*e^4 + 9506/179*e^2 - 11156/179', '5/179*e^6 - 241/179*e^4 + 3864/179*e^2 - 17448/179', '237/3043*e^7 - 7915/3043*e^5 + 67627/3043*e^3 - 123243/3043*e', '1087/12172*e^7 - 36713/12172*e^5 + 79947/3043*e^3 - 150818/3043*e', '39/358*e^6 - 1307/358*e^4 + 5511/179*e^2 - 10624/179', '-59/358*e^6 + 1913/358*e^4 - 7153/179*e^2 + 5066/179', '215/6086*e^7 - 10005/6086*e^5 + 70009/3043*e^3 - 263615/3043*e', '-879/12172*e^7 + 32129/12172*e^5 - 83688/3043*e^3 + 263062/3043*e', '-28/179*e^6 + 920/179*e^4 - 8106/179*e^2 + 19092/179', '17/179*e^6 - 533/179*e^4 + 3042/179*e^2 + 5260/179', '13/12172*e^7 - 4851/12172*e^5 + 33049/3043*e^3 - 208277/3043*e', '-303/3043*e^7 + 10774/3043*e^5 - 106066/3043*e^3 + 262374/3043*e', '617/6086*e^7 - 20503/6086*e^5 + 88729/3043*e^3 - 180396/3043*e', '-11/12172*e^7 + 5041/12172*e^5 - 32412/3043*e^3 + 153763/3043*e', '-16/179*e^6 + 449/179*e^4 - 1768/179*e^2 - 7604/179', '-2/179*e^6 - 11/179*e^4 + 1390/179*e^2 - 3188/179', '465/6086*e^7 - 16685/6086*e^5 + 83195/3043*e^3 - 210787/3043*e', '-611/12172*e^7 + 21073/12172*e^5 - 50061/3043*e^3 + 139666/3043*e', '-1063/12172*e^7 + 38993/12172*e^5 - 96647/3043*e^3 + 205669/3043*e', '-1103/12172*e^7 + 35193/12172*e^5 - 63742/3043*e^3 + 36147/3043*e', '27/358*e^6 - 1015/358*e^4 + 4848/179*e^2 - 9090/179', '9/358*e^6 - 577/358*e^4 + 4480/179*e^2 - 15202/179', '-15/179*e^6 + 544/179*e^4 - 6043/179*e^2 + 18334/179', '89/358*e^6 - 2643/358*e^4 + 8900/179*e^2 - 5858/179', '-33/358*e^6 + 803/358*e^4 - 794/179*e^2 - 12160/179', '-13/179*e^6 + 376/179*e^4 - 3137/179*e^2 + 9708/179', '-17/358*e^6 + 533/358*e^4 - 1163/179*e^2 - 2988/179', '3/358*e^6 + 285/358*e^4 - 3817/179*e^2 + 13310/179', '85/358*e^6 - 2665/358*e^4 + 9395/179*e^2 - 7972/179', '18/179*e^6 - 617/179*e^4 + 5032/179*e^2 - 4960/179', '143/6086*e^7 - 4673/6086*e^5 + 24145/3043*e^3 - 96712/3043*e', '615/6086*e^7 - 20693/6086*e^5 + 93541/3043*e^3 - 205260/3043*e', '-259/12172*e^7 + 5825/12172*e^5 - 1852/3043*e^3 - 21498/3043*e', '-49/12172*e^7 + 1431/12172*e^5 - 1913/3043*e^3 + 24060/3043*e', '-21/179*e^6 + 690/179*e^4 - 5453/179*e^2 + 14856/179', '4/179*e^6 - 157/179*e^4 + 1695/179*e^2 - 10808/179', '-175/12172*e^7 + 1633/12172*e^5 + 21859/3043*e^3 - 214459/3043*e', '779/12172*e^7 - 29457/12172*e^5 + 82268/3043*e^3 - 254761/3043*e', '-497/12172*e^7 + 19731/12172*e^5 - 56354/3043*e^3 + 154486/3043*e', '-655/6086*e^7 + 22979/6086*e^5 - 109892/3043*e^3 + 264849/3043*e', '-687/12172*e^7 + 26025/12172*e^5 - 74267/3043*e^3 + 245420/3043*e', '-347/12172*e^7 + 9637/12172*e^5 - 14665/3043*e^3 + 3578/3043*e', '-7/179*e^6 + 230/179*e^4 - 2116/179*e^2 + 8890/179', '-3/179*e^6 + 73/179*e^4 + 116/179*e^2 - 5498/179', '101/358*e^6 - 3293/358*e^4 + 13322/179*e^2 - 20638/179', '13/358*e^6 - 197/358*e^4 - 490/179*e^2 + 3022/179', '25/179*e^6 - 847/179*e^4 + 6790/179*e^2 - 7764/179', '251/3043*e^7 - 9628/3043*e^5 + 100678/3043*e^3 - 228554/3043*e', '-229/6086*e^7 + 8675/6086*e^5 - 48497/3043*e^3 + 165642/3043*e', '1553/12172*e^7 - 53303/12172*e^5 + 124906/3043*e^3 - 309334/3043*e', '229/12172*e^7 - 8675/12172*e^5 + 19684/3043*e^3 - 18918/3043*e', '252/3043*e^7 - 9533/3043*e^5 + 104995/3043*e^3 - 322367/3043*e', '79/716*e^7 - 2877/716*e^5 + 7351/179*e^3 - 20876/179*e', '-31/358*e^6 + 993/358*e^4 - 3279/179*e^2 - 8418/179', '-23/358*e^6 + 679/358*e^4 - 2479/179*e^2 + 14068/179', '77/358*e^6 - 2709/358*e^4 + 12891/179*e^2 - 26520/179', '-7/179*e^6 + 409/179*e^4 - 6412/179*e^2 + 21062/179', '-45/179*e^6 + 1453/179*e^4 - 12222/179*e^2 + 22782/179', '-33/179*e^6 + 1161/179*e^4 - 10538/179*e^2 + 25800/179', '-34/179*e^6 + 1066/179*e^4 - 7516/179*e^2 + 3800/179', '14/179*e^6 - 460/179*e^4 + 4590/179*e^2 - 12768/179', '-37/179*e^6 + 1139/179*e^4 - 7400/179*e^2 - 2056/179', '-59/358*e^6 + 1913/358*e^4 - 7511/179*e^2 + 17238/179', '57/358*e^6 - 1745/358*e^4 + 6237/179*e^2 - 4870/179', '-59/179*e^6 + 1913/179*e^4 - 15022/179*e^2 + 22304/179', '-71/358*e^6 + 2205/358*e^4 - 7995/179*e^2 + 12686/179', '-13/179*e^6 + 555/179*e^4 - 7254/179*e^2 + 22238/179', '-83/358*e^6 + 2855/358*e^4 - 12417/179*e^2 + 26392/179', '33/179*e^6 - 982/179*e^4 + 6600/179*e^2 - 4678/179', '29/358*e^6 - 825/358*e^4 + 2005/179*e^2 + 380/179', '-33/358*e^6 + 1161/358*e^4 - 4911/179*e^2 + 5740/179', '1197/12172*e^7 - 38435/12172*e^5 + 75423/3043*e^3 - 93916/3043*e', '55/12172*e^7 - 861/12172*e^5 - 8348/3043*e^3 + 134956/3043*e', '-17/358*e^6 + 533/358*e^4 - 1163/179*e^2 - 7284/179', '-99/358*e^6 + 3483/358*e^4 - 15449/179*e^2 + 26886/179', '759/6086*e^7 - 25271/6086*e^5 + 112237/3043*e^3 - 259110/3043*e', '-28/3043*e^7 + 383/3043*e^5 + 3887/3043*e^3 - 20646/3043*e', '-377/6086*e^7 + 12873/6086*e^5 - 57569/3043*e^3 + 151506/3043*e', '-951/12172*e^7 + 37461/12172*e^5 - 109663/3043*e^3 + 354121/3043*e', '15/179*e^6 - 544/179*e^4 + 5148/179*e^2 - 15112/179', '31/179*e^6 - 993/179*e^4 + 7632/179*e^2 - 1422/179', '-319/6086*e^7 + 12297/6086*e^5 - 72354/3043*e^3 + 267005/3043*e', '-285/6086*e^7 + 9441/6086*e^5 - 38524/3043*e^3 + 56749/3043*e', '-77/12172*e^7 - 1229/12172*e^5 + 16556/3043*e^3 - 52612/3043*e', '-1459/12172*e^7 + 50061/12172*e^5 - 110182/3043*e^3 + 193748/3043*e', '25/358*e^6 - 847/358*e^4 + 3037/179*e^2 - 3882/179', '101/358*e^6 - 3293/358*e^4 + 13859/179*e^2 - 27082/179', '-89/358*e^6 + 3001/358*e^4 - 13017/179*e^2 + 27696/179', '3/179*e^6 - 73/179*e^4 + 1316/179*e^2 - 12402/179', '-35/179*e^6 + 1150/179*e^4 - 10043/179*e^2 + 18316/179', '-79/358*e^6 + 2519/358*e^4 - 8258/179*e^2 - 4430/179'], 'hecke_polynomial': 'x^8 - 41*x^6 + 526*x^4 - 2336*x^2 + 2312', 'label': '4.4.9792.1-28.1-d'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 9792, 'ideals': ['[1, 1, 1]', '[4, 2, w^3 - 3*w^2 - 3*w + 4]', '[7, 7, w]', '[7, 7, w^3 - 3*w^2 - 4*w + 5]', '[9, 3, w^3 - 4*w^2 - w + 9]', '[16, 2, 2]', '[17, 17, 2*w^3 - 6*w^2 - 7*w + 8]', '[17, 17, -w^3 + 3*w^2 + 4*w - 3]', '[17, 17, -w + 2]', '[23, 23, 2*w^3 - 7*w^2 - 4*w + 12]', '[23, 23, -w^2 + 2*w + 3]', '[28, 14, -w^3 + 4*w^2 + 2*w - 7]', '[28, 14, 2*w^3 - 7*w^2 - 5*w + 13]', '[31, 31, -2*w^3 + 7*w^2 + 5*w - 12]', '[31, 31, -w^3 + 4*w^2 + 2*w - 8]', '[36, 6, w^3 - 2*w^2 - 6*w + 1]', '[41, 41, 3*w^3 - 10*w^2 - 7*w + 16]', '[41, 41, 2*w^3 - 7*w^2 - 5*w + 10]', '[49, 7, 2*w^3 - 6*w^2 - 6*w + 7]', '[49, 7, 2*w^3 - 6*w^2 - 6*w + 9]', '[49, 49, -w^2 + 2*w + 7]', '[49, 49, -2*w^3 + 7*w^2 + 4*w - 8]', '[63, 21, -2*w^3 + 6*w^2 + 7*w - 7]', '[63, 21, w^3 - 3*w^2 - 2*w + 2]', '[64, 4, 2*w^3 - 6*w^2 - 6*w + 8]', '[68, 34, w^3 - 4*w^2 - 2*w + 11]', '[68, 34, w^2 - w - 5]', '[68, 34, 3*w^3 - 10*w^2 - 8*w + 15]', '[71, 71, w^2 - 2*w - 2]', '[71, 71, 2*w^3 - 7*w^2 - 4*w + 13]', '[73, 73, 3*w^3 - 11*w^2 - 5*w + 19]', '[73, 73, -4*w^3 + 13*w^2 + 10*w - 17]', '[79, 79, 3*w^3 - 9*w^2 - 10*w + 13]', '[79, 79, -2*w^3 + 6*w^2 + 5*w - 8]', '[81, 3, 3]', '[92, 46, w^2 - 3*w - 1]', '[92, 46, -w^3 + 4*w^2 - 9]', '[97, 97, 2*w^3 - 6*w^2 - 8*w + 9]', '[97, 97, 2*w - 1]', '[112, 14, 2*w]', '[112, 14, 2*w^3 - 6*w^2 - 8*w + 10]', '[113, 113, 2*w^3 - 6*w^2 - 7*w + 6]', '[113, 113, -w^3 + 3*w^2 + 2*w - 1]', '[119, 119, -4*w^3 + 13*w^2 + 12*w - 21]', '[119, 119, -w^2 + 2*w]', '[119, 119, -2*w^3 + 7*w^2 + 4*w - 14]', '[119, 119, -2*w^3 + 7*w^2 + 4*w - 15]', '[119, 119, w^2 - 4]', '[119, 119, -w^2 + 2*w + 1]', '[124, 62, -w^3 + 3*w^2 + 5*w - 6]', '[124, 62, -w^3 + 3*w^2 + 5*w - 4]', '[137, 137, w^3 - 2*w^2 - 5*w + 2]', '[137, 137, 2*w^3 - 7*w^2 - 3*w + 12]', '[137, 137, -3*w^3 + 10*w^2 + 7*w - 17]', '[137, 137, -w^3 + 2*w^2 + 6*w - 2]', '[144, 6, 2*w^3 - 8*w^2 - 2*w + 18]', '[153, 51, w^3 - 3*w^2 - 5*w + 5]', '[153, 51, -4*w^3 + 13*w^2 + 10*w - 18]', '[153, 51, -2*w^3 + 5*w^2 + 8*w - 3]', '[161, 161, -3*w^3 + 10*w^2 + 8*w - 14]', '[161, 161, -w^3 + 4*w^2 - 10]', '[161, 161, -w^2 + 3*w]', '[161, 161, w^2 - w - 6]', '[164, 82, w^2 - 3*w + 1]', '[164, 82, -w^3 + 3*w^2 + w - 2]', '[167, 167, -2*w^3 + 7*w^2 + 6*w - 10]', '[167, 167, 3*w^3 - 9*w^2 - 10*w + 10]', '[169, 13, -2*w^3 + 7*w^2 + 2*w - 9]', '[169, 13, -2*w^3 + 5*w^2 + 10*w - 4]', '[193, 193, -2*w^3 + 8*w^2 + 3*w - 13]', '[193, 193, -3*w^3 + 11*w^2 + 6*w - 22]', '[196, 14, -w^3 + 3*w^2 + 3*w - 8]', '[196, 14, -w^3 + 3*w^2 + 3*w]', '[196, 98, 3*w^3 - 8*w^2 - 12*w + 7]', '[196, 98, 4*w^3 - 13*w^2 - 9*w + 17]', '[199, 199, 5*w^3 - 16*w^2 - 14*w + 26]', '[199, 199, w^3 - 2*w^2 - 7*w + 3]', '[207, 69, -w^3 + 4*w^2 + w - 3]', '[207, 69, w^3 - 4*w^2 - w + 12]', '[217, 217, -4*w^3 + 12*w^2 + 13*w - 19]', '[217, 217, 3*w^3 - 9*w^2 - 8*w + 14]', '[217, 217, 2*w^3 - 5*w^2 - 6*w + 7]', '[217, 217, -6*w^3 + 19*w^2 + 18*w - 32]', '[223, 223, -3*w^3 + 8*w^2 + 12*w - 8]', '[223, 223, 3*w^3 - 11*w^2 - 6*w + 17]', '[223, 223, 2*w^3 - 8*w^2 - 3*w + 18]', '[223, 223, -4*w^3 + 13*w^2 + 9*w - 18]', '[233, 233, -3*w^3 + 10*w^2 + 6*w - 16]', '[233, 233, -2*w^3 + 5*w^2 + 9*w - 6]', '[241, 241, -3*w^3 + 9*w^2 + 8*w - 10]', '[241, 241, 4*w^3 - 12*w^2 - 13*w + 15]', '[252, 42, w^2 - w - 7]', '[252, 42, -3*w^3 + 10*w^2 + 8*w - 13]', '[256, 4, 4]', '[257, 257, 2*w^3 - 8*w^2 - w + 16]', '[257, 257, 4*w^3 - 13*w^2 - 11*w + 18]', '[257, 257, -w^3 + 5*w^2 - 2*w - 9]', '[257, 257, -w^3 + 2*w^2 + 4*w + 2]', '[263, 263, 4*w^3 - 14*w^2 - 9*w + 27]', '[263, 263, 5*w^3 - 15*w^2 - 17*w + 25]', '[263, 263, -2*w^3 + 7*w^2 + 6*w - 16]', '[263, 263, -2*w^3 + 7*w^2 + 6*w - 9]', '[271, 271, -w - 4]', '[271, 271, -w^3 + 3*w^2 + 4*w - 9]', '[271, 271, 5*w^3 - 16*w^2 - 14*w + 24]', '[271, 271, -4*w^3 + 14*w^2 + 9*w - 24]', '[272, 34, 4*w^3 - 12*w^2 - 14*w + 16]', '[272, 34, -2*w^3 + 6*w^2 + 8*w - 6]', '[272, 34, -2*w + 4]', '[279, 93, -2*w^3 + 7*w^2 + 6*w - 17]', '[279, 93, -w^3 + 5*w^2 - 16]', '[281, 281, -2*w^3 + 6*w^2 + 5*w - 4]', '[281, 281, -3*w^3 + 9*w^2 + 10*w - 9]', '[281, 281, 3*w^3 - 10*w^2 - 8*w + 12]', '[281, 281, w^2 - w - 8]', '[284, 142, 2*w^3 - 7*w^2 - 3*w + 13]', '[284, 142, w^3 - 2*w^2 - 6*w + 3]', '[287, 287, 4*w^3 - 13*w^2 - 10*w + 22]', '[287, 287, 7*w^3 - 23*w^2 - 20*w + 38]', '[287, 287, -3*w^3 + 9*w^2 + 6*w - 14]', '[287, 287, -4*w^3 + 14*w^2 + 10*w - 21]', '[289, 17, -4*w^3 + 14*w^2 + 9*w - 23]', '[289, 17, -3*w^3 + 9*w^2 + 9*w - 13]', '[289, 17, -w^3 + 5*w^2 - 12]', '[289, 17, -3*w^3 + 9*w^2 + 9*w - 11]', '[289, 289, 4*w^3 - 14*w^2 - 10*w + 27]', '[289, 289, 2*w^3 - 8*w^2 - 4*w + 13]', '[292, 146, -w^3 + 5*w^2 - 3*w - 8]', '[292, 146, -3*w^3 + 10*w^2 + 6*w - 9]', '[311, 311, w^2 - 5]', '[311, 311, -4*w^3 + 13*w^2 + 12*w - 20]', '[313, 313, 6*w^3 - 19*w^2 - 18*w + 31]', '[313, 313, -2*w^3 + 5*w^2 + 6*w - 6]', '[316, 158, 2*w^3 - 7*w^2 - 5*w + 17]', '[316, 158, w^3 - 4*w^2 - 2*w + 3]', '[324, 6, 3*w^3 - 9*w^2 - 9*w + 12]', '[337, 337, 3*w^3 - 11*w^2 - 3*w + 15]', '[337, 337, w^3 - w^2 - 9*w - 5]', '[343, 7, 2*w^3 - 8*w^2 - 5*w + 14]', '[343, 7, -5*w^3 + 17*w^2 + 14*w - 31]', '[343, 49, -2*w^3 + 8*w^2 + 3*w - 14]', '[343, 49, 3*w^3 - 11*w^2 - 6*w + 21]', '[343, 343, -w^3 + 2*w^2 + 7*w]', '[343, 343, -w^3 + 4*w^2 - w - 5]', '[353, 353, -w^3 + 2*w^2 + 5*w - 4]', '[353, 353, w^3 - w^2 - 8*w - 3]', '[353, 353, 3*w^3 - 10*w^2 - 7*w + 19]', '[353, 353, -4*w^3 + 14*w^2 + 7*w - 22]', '[361, 19, -3*w^3 + 11*w^2 + 6*w - 18]', '[361, 19, 2*w^3 - 8*w^2 - 3*w + 17]', '[367, 367, -4*w^3 + 12*w^2 + 13*w - 18]', '[367, 367, 3*w^3 - 9*w^2 - 8*w + 13]', '[368, 46, 4*w^3 - 14*w^2 - 8*w + 24]', '[368, 46, -2*w^2 + 4*w + 6]', '[369, 123, w^3 - 3*w^2 - 5*w + 11]', '[369, 123, w^2 - 4*w - 1]', '[383, 383, 5*w^3 - 17*w^2 - 12*w + 30]', '[383, 383, 2*w^2 - 3*w - 5]', '[383, 383, 3*w^3 - 9*w^2 - 11*w + 11]', '[383, 383, -w^3 + 3*w^2 + w - 1]', '[388, 194, 3*w^3 - 11*w^2 - 7*w + 22]', '[388, 194, -3*w^3 + 11*w^2 + 7*w - 18]', '[391, 391, -w^3 + 2*w^2 + 7*w - 1]', '[391, 391, w^3 - 4*w^2 + w + 6]', '[391, 391, -w^3 + 6*w^2 - 3*w - 18]', '[391, 391, -3*w^3 + 9*w^2 + 8*w - 11]', '[391, 391, -5*w^3 + 18*w^2 + 9*w - 27]', '[391, 391, -4*w^3 + 12*w^2 + 13*w - 16]', '[401, 401, 3*w^3 - 11*w^2 - 8*w + 23]', '[401, 401, 4*w^3 - 14*w^2 - 11*w + 22]', '[431, 431, 2*w^3 - 5*w^2 - 10*w + 8]', '[431, 431, 6*w^3 - 20*w^2 - 15*w + 29]', '[433, 433, -4*w^3 + 12*w^2 + 13*w - 17]', '[433, 433, -3*w^3 + 9*w^2 + 8*w - 12]', '[433, 433, 3*w^3 - 11*w^2 - 6*w + 20]', '[433, 433, -2*w^3 + 8*w^2 + 3*w - 15]', '[439, 439, -3*w^3 + 11*w^2 + 6*w - 19]', '[439, 439, -2*w^3 + 8*w^2 + 3*w - 16]', '[441, 21, -3*w^3 + 8*w^2 + 13*w - 11]', '[441, 21, -4*w^3 + 14*w^2 + 9*w - 28]', '[441, 147, 2*w^3 - 7*w^2 - 3*w + 14]', '[441, 147, -w^3 + 2*w^2 + 6*w - 4]', '[448, 28, -2*w^3 + 8*w^2 + 4*w - 14]', '[448, 28, 4*w^3 - 14*w^2 - 10*w + 26]', '[449, 449, w^3 - 4*w^2 + w + 11]', '[449, 449, -w^3 + 2*w^2 + 7*w - 6]', '[452, 226, -w^3 + 2*w^2 + 4*w + 3]', '[452, 226, 4*w^3 - 13*w^2 - 11*w + 17]', '[457, 457, w^2 - 4*w - 3]', '[457, 457, 4*w^3 - 15*w^2 - 6*w + 27]', '[457, 457, w^2 - 4*w - 2]', '[457, 457, -2*w^3 + 6*w^2 + 8*w - 15]', '[476, 238, -3*w^3 + 10*w^2 + 10*w - 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19*w^2 - 15*w + 32]', '[1828, 914, 3*w^3 - 12*w^2 - 4*w + 23]', '[1828, 914, -w^3 + 6*w^2 - 6*w - 11]', '[1828, 914, 4*w^3 - 15*w^2 - 7*w + 27]', '[1828, 914, -9*w^3 + 29*w^2 + 25*w - 46]', '[1831, 1831, w^3 - 2*w^2 - 8*w + 2]', '[1831, 1831, w^2 - 5*w - 2]', '[1841, 1841, -6*w^3 + 19*w^2 + 19*w - 28]', '[1841, 1841, 17*w^3 - 56*w^2 - 51*w + 104]', '[1841, 1841, -11*w^3 + 34*w^2 + 37*w - 59]', '[1841, 1841, 3*w^3 - 8*w^2 - 5*w + 14]', '[1841, 1841, w^3 - 3*w^2 - 1]', '[1841, 1841, -5*w^3 + 18*w^2 + 15*w - 35]', '[1841, 1841, 3*w^3 - 8*w^2 - 12*w + 14]', '[1841, 1841, -4*w^3 + 13*w^2 + 9*w - 24]', '[1847, 1847, 6*w^3 - 20*w^2 - 15*w + 25]', '[1847, 1847, w^3 - w^2 - 6*w - 10]', '[1849, 43, -6*w^3 + 21*w^2 + 14*w - 37]', '[1849, 43, -2*w^3 + 9*w^2 + 2*w - 18]', '[1863, 69, 6*w^3 - 21*w^2 - 12*w + 36]', '[1863, 69, -3*w^2 + 6*w + 9]', '[1871, 1871, -4*w^3 + 13*w^2 + 8*w - 22]', '[1871, 1871, 4*w^3 - 13*w^2 - 12*w + 15]', '[1871, 1871, 4*w^3 - 11*w^2 - 16*w + 17]', '[1871, 1871, w^2 - 10]', '[1873, 1873, -w^3 + 5*w^2 - 20]', '[1873, 1873, -4*w^3 + 14*w^2 + 9*w - 15]', '[1897, 1897, w^3 - 3*w^2 - 7*w + 7]', '[1897, 1897, 12*w^3 - 40*w^2 - 33*w + 71]', '[1897, 1897, -11*w^3 + 35*w^2 + 33*w - 57]', '[1897, 1897, -3*w^3 + 9*w^2 + 13*w - 13]', '[1897, 1897, -6*w^3 + 21*w^2 + 14*w - 35]', '[1897, 1897, 6*w^3 - 19*w^2 - 16*w + 28]', '[1897, 1897, -w^2 - 4*w]', '[1897, 1897, -8*w^3 + 25*w^2 + 28*w - 45]', '[1904, 238, -8*w^3 + 26*w^2 + 24*w - 42]', '[1904, 238, -2*w^2 + 4*w]', '[1904, 238, -4*w^3 + 14*w^2 + 8*w - 28]', '[1904, 238, -4*w^3 + 14*w^2 + 8*w - 30]', '[1904, 238, 2*w^2 - 8]', '[1904, 238, -2*w^2 + 4*w + 2]', '[1913, 1913, -2*w^3 + 6*w^2 + 3*w - 4]', '[1913, 1913, 5*w^3 - 15*w^2 - 18*w + 19]', '[1913, 1913, 6*w^3 - 20*w^2 - 11*w + 30]', '[1913, 1913, 9*w^3 - 30*w^2 - 23*w + 45]', '[1916, 958, -6*w^3 + 17*w^2 + 23*w - 25]', '[1916, 958, 5*w^3 - 16*w^2 - 10*w + 25]', '[1921, 1921, w^3 - w^2 - 9*w - 11]', '[1921, 1921, -4*w^3 + 11*w^2 + 14*w - 11]', '[1921, 1921, -3*w^2 + 6*w + 20]', '[1921, 1921, 7*w^3 - 21*w^2 - 23*w + 27]', '[1921, 1921, 6*w^3 - 19*w^2 - 16*w + 26]', '[1921, 1921, -3*w^3 + 11*w^2 + 3*w - 9]', '[1948, 974, 3*w^2 - 9*w - 13]', '[1948, 974, 3*w^3 - 12*w^2 + 17]', '[1953, 651, 3*w^3 - 10*w^2 - 5*w + 19]', '[1953, 651, 3*w^3 - 8*w^2 - 13*w + 14]', '[1953, 651, 3*w^3 - 7*w^2 - 14*w + 7]', '[1953, 651, 6*w^3 - 20*w^2 - 13*w + 32]', '[1967, 1967, -4*w^3 + 13*w^2 + 6*w - 21]', '[1967, 1967, -6*w^3 + 17*w^2 + 24*w - 26]', '[1967, 1967, 2*w^3 - 9*w^2 + 14]', '[1967, 1967, 3*w^3 - 11*w^2 - 3*w + 21]', '[1967, 1967, 4*w^3 - 14*w^2 - 7*w + 25]', '[1967, 1967, w^3 - w^2 - 9*w + 1]', '[1967, 1967, -4*w^3 + 15*w^2 + 6*w - 31]', '[1967, 1967, w^3 - w^2 - 8*w]', '[1984, 124, -2*w^3 + 6*w^2 + 10*w - 12]', '[1984, 124, -2*w^3 + 6*w^2 + 10*w - 8]', '[1988, 994, -3*w^3 + 11*w^2 + 9*w - 14]', '[1988, 994, 5*w^3 - 16*w^2 - 16*w + 23]', '[1988, 994, w^2 + w - 7]', '[1988, 994, 5*w^3 - 17*w^2 - 15*w + 36]', '[1993, 1993, -8*w^3 + 28*w^2 + 17*w - 43]', '[1993, 1993, 4*w^3 - 13*w^2 - 16*w + 19]', '[1993, 1993, -6*w^3 + 21*w^2 + 14*w - 36]', '[1993, 1993, -2*w^3 + 9*w^2 + 2*w - 19]', '[1999, 1999, -7*w^3 + 22*w^2 + 20*w - 30]', '[1999, 1999, 4*w^3 - 11*w^2 - 13*w + 10]', '[2007, 669, -7*w^3 + 15*w^2 + 38*w - 2]', '[2007, 669, -2*w^3 + 6*w^2 + 4*w - 1]', '[2007, 669, 2*w^3 - 12*w^2 + 5*w + 43]', '[2007, 669, 2*w^3 - 9*w^2 + 2*w + 13]', '[2009, 287, -7*w^3 + 22*w^2 + 24*w - 34]', '[2009, 287, -3*w^3 + 12*w^2 + w - 14]', '[2009, 287, -4*w^3 + 13*w^2 + 7*w - 14]', '[2009, 287, 7*w^3 - 24*w^2 - 16*w + 32]', '[2009, 2009, 14*w^3 - 48*w^2 - 27*w + 68]', '[2009, 2009, 5*w^3 - 16*w^2 - 15*w + 21]', '[2009, 2009, 11*w^3 - 39*w^2 - 22*w + 53]', '[2009, 2009, 7*w^3 - 24*w^2 - 16*w + 42]', '[2012, 1006, -7*w^3 + 24*w^2 + 20*w - 39]', '[2012, 1006, -4*w^3 + 15*w^2 + 11*w - 31]', '[2017, 2017, 4*w^3 - 11*w^2 - 14*w + 12]', '[2017, 2017, -6*w^3 + 19*w^2 + 16*w - 27]', '[2023, 119, -7*w^3 + 24*w^2 + 18*w - 42]', '[2023, 119, 6*w^3 - 19*w^2 - 15*w + 28]', '[2023, 119, 3*w^3 - 12*w^2 - 5*w + 21]', '[2023, 119, 2*w^3 - 8*w^2 + w + 14]', '[2023, 119, w^3 - w^2 - 10*w - 1]', '[2023, 119, -5*w^3 + 14*w^2 + 18*w - 18]', '[2023, 119, 2*w^3 - 9*w^2 - 3*w + 18]', '[2023, 119, -5*w^3 + 18*w^2 + 11*w - 34]', '[2023, 2023, -w^3 + 2*w^2 + 5*w + 7]', '[2023, 2023, 6*w^3 - 19*w^2 - 15*w + 24]', '[2023, 2023, -5*w^3 + 14*w^2 + 18*w - 14]', '[2023, 2023, 3*w^3 - 10*w^2 - 7*w + 8]', '[2039, 2039, -w^3 + 5*w^2 + w - 17]', '[2039, 2039, 2*w^3 - 9*w^2 - 2*w + 26]', '[2039, 2039, -5*w^3 + 17*w^2 + 13*w - 23]', '[2039, 2039, -5*w^3 + 17*w^2 + 15*w - 37]', '[2044, 1022, w^3 - w^2 - 11*w + 4]', '[2044, 1022, 2*w^3 - 7*w^2 - 7*w + 23]', '[2044, 1022, 4*w^3 - 15*w^2 - 3*w + 21]', '[2044, 1022, 3*w^3 - 10*w^2 - 6*w + 7]', '[2063, 2063, 4*w^3 - 14*w^2 - 8*w + 29]', '[2063, 2063, 2*w^2 - 4*w - 1]', '[2081, 2081, w^3 - 3*w^2 + 2*w - 1]', '[2081, 2081, 6*w^3 - 18*w^2 - 23*w + 24]', '[2084, 1042, -4*w^3 + 11*w^2 + 11*w - 9]', '[2084, 1042, -3*w^3 + 7*w^2 + 13*w - 8]', '[2087, 2087, -6*w^3 + 19*w^2 + 14*w - 20]', '[2087, 2087, 2*w^2 - 6*w - 1]', '[2087, 2087, -2*w^3 + 8*w^2 - 19]', '[2087, 2087, 6*w^3 - 17*w^2 - 22*w + 15]', '[2097, 699, w^3 - 3*w^2 - 2*w - 4]', '[2097, 699, -8*w^3 + 21*w^2 + 34*w - 19]', '[2108, 1054, 2*w^3 - 7*w^2 - w + 19]', '[2108, 1054, -3*w^3 + 8*w^2 + 12*w - 15]', '[2108, 1054, -9*w^3 + 30*w^2 + 24*w - 55]', '[2108, 1054, 4*w^3 - 13*w^2 - 9*w + 25]', '[2108, 1054, -5*w^3 + 18*w^2 + 10*w - 39]', '[2108, 1054, -3*w^3 + 8*w^2 + 14*w - 19]', '[2111, 2111, -4*w^3 + 15*w^2 + 4*w - 27]', '[2111, 2111, -6*w^3 + 20*w^2 + 15*w - 37]', '[2113, 2113, 6*w^3 - 19*w^2 - 14*w + 27]', '[2113, 2113, -6*w^3 + 18*w^2 + 16*w - 19]', '[2116, 46, -5*w^3 + 15*w^2 + 15*w - 18]', '[2116, 46, 5*w^3 - 15*w^2 - 15*w + 22]', '[2116, 1058, 3*w^3 - 9*w^2 - 13*w + 16]', '[2116, 1058, w^3 - 3*w^2 - 7*w + 4]', '[2129, 2129, -2*w^3 + 5*w^2 + 5*w - 2]', '[2129, 2129, 5*w^3 - 18*w^2 - 10*w + 38]', '[2129, 2129, 7*w^3 - 22*w^2 - 22*w + 32]', '[2129, 2129, -7*w^3 + 24*w^2 + 17*w - 46]', '[2137, 2137, 4*w^3 - 15*w^2 - 8*w + 25]', '[2137, 2137, -4*w^3 + 15*w^2 + 8*w - 30]', '[2153, 2153, -3*w^3 + 8*w^2 + 14*w - 16]', '[2153, 2153, 2*w^3 - 7*w^2 - w + 16]', '[2161, 2161, -2*w^2 + 4*w - 3]', '[2161, 2161, -2*w^3 + 7*w^2 + 4*w - 19]', '[2161, 2161, -w^2 + 2*w - 4]', '[2161, 2161, -4*w^3 + 14*w^2 + 8*w - 33]', '[2169, 723, w^3 - 8*w^2 + 9*w + 22]', '[2169, 723, 5*w^3 - 10*w^2 - 30*w + 2]', '[2177, 2177, 5*w^3 - 16*w^2 - 12*w + 28]', '[2177, 2177, w^3 - 5*w]', '[2177, 2177, -11*w^3 + 36*w^2 + 31*w - 65]', '[2177, 2177, -4*w^3 + 11*w^2 + 15*w - 18]', '[2191, 2191, w^3 - 8*w^2 - 2*w + 14]', '[2191, 2191, 18*w^3 - 59*w^2 - 53*w + 106]', '[2191, 2191, -7*w^3 + 24*w^2 + 19*w - 42]', '[2191, 2191, -3*w^3 + 12*w^2 + 7*w - 23]', '[2192, 274, 2*w^3 - 4*w^2 - 10*w + 4]', '[2192, 274, 4*w^3 - 14*w^2 - 6*w + 24]', '[2192, 274, -6*w^3 + 20*w^2 + 14*w - 34]', '[2192, 274, -2*w^3 + 4*w^2 + 12*w - 4]', '[2201, 2201, w^3 - 6*w^2 + 6*w + 8]', '[2201, 2201, 2*w^3 - 8*w^2 - 5*w + 20]', '[2201, 2201, -5*w^3 + 17*w^2 + 14*w - 25]', '[2201, 2201, -8*w^3 + 26*w^2 + 21*w - 34]', '[2207, 2207, -2*w^3 + 9*w^2 - 9]', '[2207, 2207, 7*w^3 - 23*w^2 - 18*w + 30]', '[2209, 47, -w^3 + 3*w^2 + 3*w - 11]', '[2209, 47, w^3 - 3*w^2 - 3*w - 3]', '[2212, 1106, -3*w^3 + 9*w^2 + 13*w - 14]', '[2212, 1106, -5*w^3 + 18*w^2 + 12*w - 35]', '[2212, 1106, -4*w^3 + 15*w^2 + 9*w - 25]', '[2212, 1106, -w^3 + 3*w^2 + 7*w - 6]', '[2231, 2231, -8*w^3 + 27*w^2 + 20*w - 40]', '[2231, 2231, 3*w^2 - 4*w - 15]', '[2231, 2231, 8*w^3 - 25*w^2 - 26*w + 38]', '[2231, 2231, -2*w^3 + 5*w^2 + 4*w - 3]', '[2239, 2239, -5*w^3 + 18*w^2 + 11*w - 30]', '[2239, 2239, 3*w^3 - 12*w^2 - 5*w + 25]', '[2263, 2263, -9*w^3 + 28*w^2 + 28*w - 46]', '[2263, 2263, 2*w^2 - 7*w - 4]', '[2263, 2263, -w^3 + 5*w^2 - 4*w - 11]', '[2263, 2263, -3*w^3 + 10*w^2 + 8*w - 8]', '[2268, 42, -3*w^3 + 12*w^2 + 6*w - 21]', '[2268, 42, 6*w^3 - 21*w^2 - 15*w + 39]', '[2273, 2273, -5*w^3 + 16*w^2 + 10*w - 18]', '[2273, 2273, -6*w^3 + 17*w^2 + 23*w - 18]', '[2281, 2281, -w^3 + 3*w^2 + 7*w - 5]', '[2281, 2281, -3*w^3 + 9*w^2 + 13*w - 15]', '[2287, 2287, -5*w^3 + 18*w^2 + 12*w - 30]', '[2287, 2287, 6*w^3 - 18*w^2 - 19*w + 22]', '[2287, 2287, -4*w^3 + 15*w^2 + 9*w - 30]', '[2287, 2287, 5*w^3 - 15*w^2 - 14*w + 17]', '[2304, 12, 4*w^3 - 16*w^2 - 4*w + 36]', '[2313, 771, -4*w^3 + 8*w^2 + 21*w + 11]', '[2313, 771, 2*w^3 - 3*w^2 - 16*w + 1]', '[2313, 771, 8*w^3 - 22*w^2 - 30*w + 17]', '[2313, 771, w^3 - 9*w^2 + 10*w + 32]', '[2329, 2329, 2*w^3 - 6*w^2 - 10*w + 11]', '[2329, 2329, 7*w^3 - 25*w^2 - 14*w + 38]', '[2329, 2329, 2*w^3 - 10*w^2 + w + 27]', '[2329, 2329, -6*w^3 + 18*w^2 + 23*w - 31]', '[2329, 2329, 4*w^3 - 16*w^2 - 6*w + 37]', '[2329, 2329, w^3 - w^2 - 10*w - 2]', '[2329, 2329, 2*w^3 - 6*w^2 - 10*w + 9]', '[2329, 2329, -w^3 + 7*w^2 - 2*w - 20]', '[2329, 2329, -w^2 + 6*w + 6]', '[2329, 2329, -2*w^3 + 5*w^2 + 12*w - 11]', '[2329, 2329, -10*w^3 + 34*w^2 + 25*w - 55]', '[2329, 2329, -6*w^3 + 23*w^2 + 10*w - 51]', '[2351, 2351, 6*w^3 - 21*w^2 - 10*w + 33]', '[2351, 2351, -6*w^3 + 20*w^2 + 15*w - 39]', '[2359, 2359, -5*w^3 + 18*w^2 + 9*w - 21]', '[2359, 2359, w^3 - 2*w^2 - 7*w - 7]', '[2359, 2359, w^3 - 4*w^2 + w - 2]', '[2359, 2359, w^3 - 6*w^2 + 3*w + 24]', '[2367, 789, 2*w^3 - 6*w^2 - 7*w + 16]', '[2367, 789, 14*w^3 - 42*w^2 - 49*w + 64]', '[2367, 789, -8*w^3 + 29*w^2 + 17*w - 60]', '[2367, 789, -w^3 + w^2 + 10*w + 3]', '[2377, 2377, -8*w^3 + 28*w^2 + 17*w - 45]', '[2377, 2377, 8*w^3 - 25*w^2 - 24*w + 36]', '[2383, 2383, -3*w^3 + 12*w^2 + 5*w - 22]', '[2383, 2383, 5*w^3 - 18*w^2 - 11*w + 33]', '[2393, 2393, -6*w^3 + 20*w^2 + 15*w - 38]', '[2393, 2393, 2*w^3 - 9*w^2 + 3*w + 10]', '[2393, 2393, -7*w^3 + 22*w^2 + 21*w - 29]', '[2393, 2393, -5*w^3 + 18*w^2 + 7*w - 30]', '[2396, 1198, -w^3 + 5*w^2 + w - 18]', '[2396, 1198, -5*w^3 + 17*w^2 + 13*w - 22]', '[2396, 1198, w^3 - 4*w^2 - 4*w + 13]', '[2396, 1198, -4*w^3 + 13*w^2 + 13*w - 17]', '[2401, 7, 7]', '[2401, 49, -6*w^3 + 17*w^2 + 22*w - 21]', '[2401, 49, -5*w^3 + 15*w^2 + 15*w - 21]', '[2401, 49, -5*w^3 + 15*w^2 + 15*w - 19]', '[2401, 49, -6*w^3 + 19*w^2 + 14*w - 26]', '[2401, 343, -3*w^3 + 11*w^2 + 6*w - 28]', '[2401, 343, 2*w^3 - 8*w^2 - 3*w + 7]', '[2401, 2401, 2*w^3 - 6*w^2 - 8*w + 17]', '[2401, 2401, 2*w + 7]', '[2404, 1202, 2*w^3 - 5*w^2 - 7*w + 13]', '[2404, 1202, 5*w^3 - 16*w^2 - 14*w + 33]', '[2417, 2417, -3*w^3 + 8*w^2 + 13*w - 15]', '[2417, 2417, 3*w^3 - 10*w^2 - 5*w + 20]', '[2423, 2423, -5*w^3 + 17*w^2 + 11*w - 31]', '[2423, 2423, 3*w^3 - 9*w^2 - 6*w + 8]', '[2423, 2423, -w^3 + w^2 + 7*w - 1]', '[2423, 2423, -6*w^3 + 18*w^2 + 21*w - 23]', '[2428, 1214, -5*w^3 + 14*w^2 + 18*w - 17]', '[2428, 1214, 6*w^3 - 19*w^2 - 15*w + 27]', '[2439, 813, -2*w^3 + 10*w^2 - 3*w - 29]', '[2439, 813, -8*w^3 + 28*w^2 + 18*w - 53]', '[2439, 813, 5*w^3 - 13*w^2 - 24*w + 20]', '[2439, 813, -2*w^3 + 8*w^2 + 5*w - 27]', '[2441, 2441, -3*w^3 + 11*w^2 + 8*w - 27]', '[2441, 2441, -4*w^3 + 14*w^2 + 11*w - 18]', '[2448, 102, 2*w^3 - 6*w^2 - 10*w + 10]', '[2448, 102, -8*w^3 + 26*w^2 + 20*w - 36]', '[2448, 102, -4*w^3 + 10*w^2 + 16*w - 6]', '[2449, 2449, -6*w^3 + 22*w^2 + 11*w - 41]', '[2449, 2449, 3*w^3 - 11*w^2 - w + 19]', '[2449, 2449, -3*w^3 + 7*w^2 + 17*w - 9]', '[2449, 2449, -3*w^3 + 13*w^2 + 2*w - 24]', '[2468, 1234, 3*w^3 - 9*w^2 - 7*w + 6]', '[2468, 1234, 3*w^3 - 11*w^2 - 9*w + 24]', '[2471, 2471, -2*w^2 - 2*w + 7]', '[2471, 2471, 11*w^3 - 35*w^2 - 36*w + 58]', '[2471, 2471, -4*w^3 + 14*w^2 + 13*w - 21]', '[2471, 2471, -7*w^3 + 23*w^2 + 19*w - 33]', '[2471, 2471, -5*w^3 + 17*w^2 + 16*w - 34]', '[2471, 2471, 10*w^3 - 32*w^2 - 32*w + 53]', '[2471, 2471, -4*w^3 + 14*w^2 + 14*w - 21]', '[2471, 2471, 6*w^3 - 21*w^2 - 14*w + 28]', '[2500, 10, -5*w^3 + 15*w^2 + 15*w - 20]', '[2503, 2503, -2*w^3 + 8*w^2 + 3*w - 24]', '[2503, 2503, -3*w^3 + 11*w^2 + 6*w - 11]', '[2503, 2503, 3*w^3 - 12*w^2 - 5*w + 24]', '[2503, 2503, -5*w^3 + 18*w^2 + 11*w - 31]', '[2511, 93, -6*w^3 + 21*w^2 + 15*w - 36]', '[2511, 93, -3*w^3 + 12*w^2 + 6*w - 24]', '[2521, 2521, -2*w^3 + 7*w^2 + 4*w - 4]', '[2521, 2521, w^2 - 2*w - 11]', '[2524, 1262, -w^3 + 4*w^2 - 15]', '[2524, 1262, -w^2 + 3*w - 5]', '[2524, 1262, -4*w^3 + 11*w^2 + 13*w - 11]', '[2524, 1262, -7*w^3 + 22*w^2 + 20*w - 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8]', '[3001, 3001, 4*w^3 - 9*w^2 - 18*w + 2]', '[3001, 3001, -4*w^3 + 13*w^2 + 12*w - 29]', '[3001, 3001, 5*w^3 - 15*w^2 - 18*w + 32]', '[3001, 3001, -w^2 - 4]', '[3004, 1502, -w^3 + 6*w^2 - 6*w - 13]', '[3004, 1502, -2*w^3 + 9*w^2 - 3*w - 17]', '[3007, 3007, -7*w^3 + 20*w^2 + 24*w - 30]', '[3007, 3007, 8*w^3 - 25*w^2 - 21*w + 40]', '[3007, 3007, -2*w^3 + 7*w^2 + 5*w - 4]', '[3007, 3007, -w^3 + 4*w^2 + 2*w - 16]', '[3017, 3017, -7*w^3 + 24*w^2 + 17*w - 34]', '[3017, 3017, 12*w^3 - 40*w^2 - 31*w + 68]', '[3017, 3017, -w^3 + 4*w^2 + 4*w - 14]', '[3017, 3017, -8*w^3 + 27*w^2 + 17*w - 42]', '[3023, 3023, -2*w^3 + 8*w^2 + 6*w - 19]', '[3023, 3023, 6*w^3 - 20*w^2 - 18*w + 31]', '[3031, 3031, -5*w^3 + 18*w^2 + 12*w - 32]', '[3031, 3031, 9*w^3 - 28*w^2 - 28*w + 44]', '[3031, 3031, -6*w^3 + 18*w^2 + 19*w - 26]', '[3031, 3031, 3*w^3 - 13*w^2 - 6*w + 21]', '[3031, 3031, -10*w^3 + 34*w^2 + 27*w - 64]', '[3031, 3031, -5*w^3 + 15*w^2 + 14*w - 21]', '[3031, 3031, 4*w^3 - 11*w^2 - 11*w + 14]', '[3031, 3031, 4*w^3 - 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22]', '[5167, 5167, 9*w^3 - 31*w^2 - 22*w + 53]', '[5167, 5167, 5*w^3 - 20*w^2 - 7*w + 46]', '[5177, 5177, 7*w^3 - 24*w^2 - 13*w + 38]', '[5177, 5177, -2*w^3 + 4*w^2 + 13*w - 8]', '[5177, 5177, -3*w^3 + 11*w^2 + 2*w - 23]', '[5177, 5177, 3*w^3 - 6*w^2 - 17*w + 3]', '[5183, 5183, -2*w^3 + 7*w^2 + 8*w - 20]', '[5183, 5183, -3*w^3 + 11*w^2 + 3*w - 25]', '[5183, 5183, -w^3 + w^2 + 9*w - 5]', '[5183, 5183, -4*w^3 + 13*w^2 + 14*w - 15]', '[5184, 12, 6*w^3 - 18*w^2 - 18*w + 24]', '[5188, 2594, 2*w^3 - 7*w^2 - 5*w + 3]', '[5188, 2594, -w^3 + 4*w^2 + 2*w - 17]', '[5201, 5201, -6*w^3 + 21*w^2 + 15*w - 28]', '[5201, 5201, 8*w^3 - 26*w^2 - 23*w + 38]', '[5201, 5201, w^3 - w^2 - 4*w - 7]', '[5201, 5201, 3*w^3 - 12*w^2 - 6*w + 32]', '[5209, 5209, -4*w^3 + 13*w^2 + 12*w - 30]', '[5209, 5209, -w^2 - 5]', '[5212, 2606, -7*w^3 + 20*w^2 + 24*w - 29]', '[5212, 2606, -8*w^3 + 25*w^2 + 21*w - 39]', '[5231, 5231, 2*w^3 - 5*w^2 - 6*w - 5]', '[5231, 5231, 6*w^3 - 19*w^2 - 18*w + 20]', '[5233, 5233, 7*w^3 - 25*w^2 - 15*w + 45]', '[5233, 5233, -3*w^3 + 13*w^2 + 3*w - 25]', '[5239, 403, 3*w^3 - 9*w^2 - 14*w + 13]', '[5239, 403, w^3 - 9*w - 18]', '[5239, 403, -2*w^3 + 6*w^2 + 11*w - 12]', '[5239, 403, 9*w^3 - 26*w^2 - 32*w + 30]', '[5257, 5257, -6*w^3 + 18*w^2 + 17*w - 21]', '[5257, 5257, 8*w^3 - 24*w^2 - 26*w + 31]', '[5257, 5257, -6*w^3 + 18*w^2 + 16*w - 21]', '[5257, 5257, 7*w^3 - 21*w^2 - 22*w + 26]', '[5273, 5273, 3*w^3 - 8*w^2 - 8*w + 4]', '[5273, 5273, -8*w^3 + 25*w^2 + 25*w - 34]', '[5276, 2638, 6*w^3 - 23*w^2 - 5*w + 31]', '[5276, 2638, w^3 - 8*w^2 + 10*w + 29]', '[5281, 5281, 9*w^3 - 31*w^2 - 23*w + 57]', '[5281, 5281, -12*w^3 + 39*w^2 + 32*w - 61]', '[5284, 2642, -6*w^3 + 17*w^2 + 21*w - 19]', '[5284, 2642, -7*w^3 + 22*w^2 + 18*w - 29]', '[5287, 5287, -w^3 + 2*w^2 + 5*w - 10]', '[5287, 5287, 3*w^3 - 10*w^2 - 7*w + 25]', '[5287, 5287, 4*w^3 - 9*w^2 - 15*w + 8]', '[5287, 5287, -9*w^3 + 30*w^2 + 26*w - 62]', '[5287, 5287, -7*w^3 + 20*w^2 + 25*w - 26]', '[5287, 5287, -13*w^3 + 42*w^2 + 36*w - 68]', '[5297, 5297, 3*w^3 - 12*w^2 + 26]', '[5297, 5297, 3*w^2 - 9*w - 4]', '[5321, 5321, -w^3 - 2*w^2 + 5*w + 11]', '[5321, 5321, -6*w^3 + 21*w^2 + 17*w - 44]', '[5321, 5321, -5*w^3 + 18*w^2 + 14*w - 26]', '[5321, 5321, 19*w^3 - 62*w^2 - 55*w + 104]', '[5321, 5321, -w^3 + 6*w^2 - 20]', '[5321, 5321, 17*w^3 - 56*w^2 - 51*w + 108]', '[5327, 5327, 12*w^3 - 38*w^2 - 41*w + 61]', '[5327, 5327, -4*w^3 + 15*w^2 + 16*w - 21]', '[5327, 5327, 8*w^3 - 26*w^2 - 25*w + 41]', '[5327, 5327, -4*w^3 + 15*w^2 + 12*w - 21]', '[5327, 5327, -16*w^3 + 52*w^2 + 46*w - 97]', '[5327, 5327, 6*w^3 - 18*w^2 - 15*w + 35]', '[5327, 5327, -8*w^3 + 27*w^2 + 24*w - 54]', '[5327, 5327, w^3 - 5*w^2 - 4*w + 14]', '[5329, 73, -7*w^3 + 21*w^2 + 21*w - 33]', '[5329, 73, 7*w^3 - 21*w^2 - 21*w + 23]', '[5329, 5329, -w^3 + 3*w^2 + 8*w - 6]', '[5329, 5329, 4*w^3 - 12*w^2 - 17*w + 19]', '[5359, 5359, 6*w^3 - 18*w^2 - 15*w + 22]', '[5359, 5359, -w^3 + 11*w + 17]', '[5359, 5359, 5*w^3 - 18*w^2 - 7*w + 18]', '[5359, 5359, -9*w^3 + 27*w^2 + 30*w - 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19]', '[5636, 2818, 3*w^2 - 5*w - 5]', '[5636, 2818, w^2 + w - 11]', '[5636, 2818, -7*w^3 + 24*w^2 + 16*w - 45]', '[5639, 5639, -4*w^3 + 12*w^2 + 8*w - 25]', '[5639, 5639, -8*w^3 + 24*w^2 + 28*w - 45]', '[5641, 5641, -5*w^3 + 13*w^2 + 19*w - 13]', '[5641, 5641, -9*w^3 + 29*w^2 + 23*w - 43]', '[5647, 5647, -7*w^3 + 21*w^2 + 22*w - 31]', '[5647, 5647, 6*w^3 - 18*w^2 - 17*w + 26]', '[5648, 706, -2*w^3 + 4*w^2 + 10*w - 8]', '[5648, 706, 6*w^3 - 20*w^2 - 14*w + 40]', '[5648, 706, 6*w^3 - 20*w^2 - 14*w + 38]', '[5648, 706, -8*w^3 + 28*w^2 + 14*w - 44]', '[5663, 5663, 20*w^3 - 65*w^2 - 58*w + 115]', '[5663, 5663, -2*w^3 + 10*w^2 - 4*w - 29]', '[5663, 5663, -9*w^3 + 29*w^2 + 23*w - 49]', '[5663, 5663, 2*w^3 - 8*w^2 + 3*w + 21]', '[5679, 1893, -6*w^3 + 13*w^2 + 32*w - 4]', '[5679, 1893, -3*w^3 + 7*w^2 + 17*w - 13]', '[5679, 1893, -2*w^3 + 12*w^2 - 8*w - 37]', '[5679, 1893, -8*w^3 + 30*w^2 + 13*w - 61]', '[5689, 5689, -2*w^3 + 6*w^2 + 11*w - 9]', '[5689, 5689, -3*w^3 + 9*w^2 + 14*w - 16]', '[5692, 2846, 7*w^3 - 21*w^2 - 27*w + 36]', '[5692, 2846, -w^3 + 2*w^2 + 8*w - 13]', '[5729, 5729, w^3 - 11*w - 3]', '[5729, 5729, 11*w^3 - 40*w^2 - 15*w + 51]', '[5729, 5729, w^3 - 12*w^2 + 17*w + 51]', '[5729, 5729, -9*w^3 + 32*w^2 + 17*w - 55]', '[5729, 5729, w^3 + 4*w^2 - 21*w - 34]', '[5729, 5729, 5*w^3 - 18*w^2 - 7*w + 32]', '[5732, 2866, -7*w^3 + 20*w^2 + 28*w - 33]', '[5732, 2866, -5*w^3 + 12*w^2 + 24*w - 11]', '[5743, 5743, 7*w^3 - 24*w^2 - 18*w + 52]', '[5743, 5743, 11*w^3 - 34*w^2 - 35*w + 54]', '[5751, 213, 3*w^2 - 6*w - 6]', '[5751, 213, 6*w^3 - 21*w^2 - 12*w + 39]', '[5756, 2878, 7*w^3 - 23*w^2 - 19*w + 30]', '[5756, 2878, -w^3 + w^2 + 5*w + 10]', '[5761, 5761, 12*w^3 - 37*w^2 - 42*w + 62]', '[5761, 5761, 2*w^3 - 6*w^2 - 11*w + 11]', '[5761, 5761, -3*w^3 + 9*w^2 + 14*w - 14]', '[5761, 5761, 2*w^3 - 5*w^2 + 7]', '[5767, 5767, -3*w^3 + 13*w^2 + 4*w - 29]', '[5767, 5767, -8*w^3 + 28*w^2 + 19*w - 46]', '[5767, 5767, -w^3 + 4*w^2 - 4*w - 2]', '[5767, 5767, 4*w^3 - 11*w^2 - 19*w + 12]', '[5769, 1923, 14*w^3 - 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2]', '[967, 967, -3*w^3 + 8*w^2 + 15*w - 6]', '[967, 967, w^3 - 2*w^2 - 5*w - 6]', '[967, 967, 7*w^3 - 22*w^2 - 21*w + 36]', '[983, 983, 5*w^3 - 17*w^2 - 13*w + 25]', '[983, 983, w^3 - 5*w^2 - w + 15]', '[991, 991, -6*w^3 + 21*w^2 + 13*w - 34]', '[991, 991, 7*w^3 - 22*w^2 - 21*w + 33]', '[1009, 1009, w^2 - 2*w + 3]', '[1009, 1009, -2*w^3 + 7*w^2 + 4*w - 18]', '[1031, 1031, -4*w^3 + 15*w^2 + 4*w - 26]', '[1031, 1031, 3*w^2 - 8*w - 9]', '[1033, 1033, 2*w^3 - 4*w^2 - 13*w + 3]', '[1033, 1033, -5*w^3 + 15*w^2 + 19*w - 23]', '[1033, 1033, w^3 - w^2 - 8*w - 10]', '[1033, 1033, 4*w^3 - 14*w^2 - 7*w + 15]', '[1049, 1049, -7*w^3 + 24*w^2 + 16*w - 34]', '[1049, 1049, -5*w^3 + 16*w^2 + 18*w - 24]', '[1063, 1063, w^3 - 4*w^2 + 2*w + 8]', '[1063, 1063, w^3 - 2*w^2 - 4*w - 8]', '[1063, 1063, 7*w^3 - 24*w^2 - 17*w + 39]', '[1063, 1063, w^3 - 2*w^2 - 7*w - 6]', '[1103, 1103, w^3 - 5*w^2 + 3*w + 17]', '[1103, 1103, -w^3 + 5*w^2 - 3*w - 3]', '[1103, 1103, -w^3 + 5*w^2 - 2*w - 6]', '[1103, 1103, -2*w^3 + 8*w^2 + w - 19]', '[1129, 1129, -6*w^3 + 18*w^2 + 20*w - 27]', '[1129, 1129, -4*w^3 + 12*w^2 + 10*w - 17]', '[1151, 1151, w^3 - w^2 - 7*w - 1]', '[1151, 1151, 5*w^3 - 17*w^2 - 11*w + 29]', '[1153, 1153, -2*w^3 + 8*w^2 + 3*w - 23]', '[1153, 1153, -6*w^3 + 18*w^2 + 20*w - 25]', '[1193, 1193, -2*w^3 + 5*w^2 + 9*w - 10]', '[1193, 1193, 3*w^3 - 10*w^2 - 6*w + 20]', '[1201, 1201, 6*w^3 - 19*w^2 - 16*w + 24]', '[1201, 1201, 4*w^3 - 11*w^2 - 14*w + 9]', '[1217, 1217, 7*w^3 - 22*w^2 - 21*w + 30]', '[1217, 1217, 7*w^3 - 23*w^2 - 18*w + 39]', '[1223, 1223, -2*w^3 + 9*w^2 - 15]', '[1223, 1223, -3*w^3 + 9*w^2 + 13*w - 9]', '[1223, 1223, -5*w^3 + 17*w^2 + 12*w - 34]', '[1223, 1223, 4*w^3 - 15*w^2 - 6*w + 30]', '[1231, 1231, -3*w^3 + 7*w^2 + 12*w - 3]', '[1231, 1231, -8*w^3 + 26*w^2 + 21*w - 38]', '[1289, 1289, -4*w^3 + 14*w^2 + 7*w - 24]', '[1289, 1289, -w^3 + w^2 + 8*w + 1]', '[1297, 1297, -4*w^3 + 12*w^2 + 11*w - 15]', '[1297, 1297, -5*w^3 + 15*w^2 + 16*w - 20]', '[1303, 1303, -3*w^3 + 10*w^2 + 7*w - 23]', '[1303, 1303, -w^3 + 2*w^2 + 5*w - 8]', '[1319, 1319, -8*w^3 + 28*w^2 + 15*w - 43]', '[1319, 1319, w^3 + w^2 - 12*w - 12]', '[1321, 1321, w^2 - 2*w - 10]', '[1321, 1321, 2*w^3 - 7*w^2 - 4*w + 5]', '[1367, 1367, -5*w^3 + 17*w^2 + 14*w - 26]', '[1367, 1367, 2*w^3 - 8*w^2 - 5*w + 19]', '[1399, 1399, -2*w^3 + 7*w^2 + 3*w - 4]', '[1399, 1399, w^3 - 2*w^2 - 6*w - 6]', '[1409, 1409, w^3 - 2*w^2 - 3*w - 3]', '[1409, 1409, 3*w^3 - 10*w^2 - 5*w + 18]', '[1409, 1409, -5*w^3 + 16*w^2 + 15*w - 22]', '[1409, 1409, -3*w^3 + 8*w^2 + 13*w - 13]', '[1423, 1423, 7*w^3 - 24*w^2 - 18*w + 44]', '[1423, 1423, -8*w^3 + 26*w^2 + 21*w - 40]', '[1433, 1433, -7*w^3 + 24*w^2 + 17*w - 45]', '[1433, 1433, -3*w^3 + 12*w^2 + 3*w - 29]', '[1439, 1439, -2*w^3 + 6*w^2 + 4*w - 3]', '[1439, 1439, -4*w^3 + 12*w^2 + 14*w - 13]', '[1471, 1471, -w - 6]', '[1471, 1471, -w^3 + 3*w^2 + 4*w - 11]', '[1471, 1471, w^3 - 2*w^2 - 8*w + 4]', '[1471, 1471, w^2 - 5*w - 4]', '[1489, 1489, -2*w^3 + 9*w^2 + 2*w - 17]', '[1489, 1489, -6*w^3 + 21*w^2 + 14*w - 38]', '[1543, 1543, -7*w^3 + 24*w^2 + 19*w - 45]', '[1543, 1543, 2*w^3 - 3*w^2 - 15*w - 4]', '[1543, 1543, -5*w^3 + 18*w^2 + 6*w - 26]', '[1543, 1543, -3*w^3 + 12*w^2 + 7*w - 20]', '[1553, 1553, -4*w^3 + 14*w^2 + 11*w - 20]', '[1553, 1553, -3*w^3 + 11*w^2 + 8*w - 25]', '[1559, 1559, 2*w^2 - 4*w - 3]', '[1559, 1559, 4*w^3 - 14*w^2 - 8*w + 27]', '[1567, 1567, -4*w^3 + 15*w^2 + 3*w - 20]', '[1567, 1567, w^3 - 12*w - 10]', '[1601, 1601, -3*w^3 + 10*w^2 + 10*w - 12]', '[1601, 1601, 2*w^3 - 7*w^2 - 7*w + 18]', '[1607, 1607, -7*w^3 + 23*w^2 + 20*w - 36]', '[1607, 1607, -6*w^3 + 19*w^2 + 18*w - 26]', '[1607, 1607, 2*w^2 - w - 9]', '[1607, 1607, -2*w^3 + 5*w^2 + 6*w - 1]', '[1609, 1609, -4*w^3 + 15*w^2 + 8*w - 24]', '[1609, 1609, 4*w^3 - 15*w^2 - 8*w + 31]', '[1663, 1663, -6*w^3 + 19*w^2 + 13*w - 26]', '[1663, 1663, -7*w^3 + 20*w^2 + 26*w - 26]', '[1681, 41, -5*w^3 + 15*w^2 + 15*w - 17]', '[1697, 1697, -w^3 + 9*w + 6]', '[1697, 1697, -7*w^3 + 24*w^2 + 15*w - 39]', '[1721, 1721, -5*w^3 + 18*w^2 + 13*w - 38]', '[1721, 1721, -w^3 + 6*w^2 - 5*w - 20]', '[1721, 1721, -w^3 + w^2 + 6*w + 11]', '[1721, 1721, 6*w^3 - 20*w^2 - 15*w + 24]', '[1753, 1753, -3*w^3 + 9*w^2 + 13*w - 17]', '[1753, 1753, w^3 - 3*w^2 - 7*w + 3]', '[1753, 1753, -6*w^3 + 22*w^2 + 12*w - 45]', '[1753, 1753, -6*w^3 + 21*w^2 + 16*w - 40]', '[1759, 1759, -2*w^3 + 6*w^2 + w - 8]', '[1759, 1759, 7*w^3 - 21*w^2 - 26*w + 33]', '[1759, 1759, -3*w^3 + 10*w^2 + 10*w - 26]', '[1759, 1759, -5*w^3 + 17*w^2 + 12*w - 37]', '[1783, 1783, -5*w^3 + 18*w^2 + 11*w - 29]', '[1783, 1783, 4*w^3 - 15*w^2 - 7*w + 26]', '[1783, 1783, 3*w^3 - 12*w^2 - 5*w + 26]', '[1783, 1783, -3*w^3 + 12*w^2 + 4*w - 24]', '[1801, 1801, 8*w^3 - 24*w^2 - 27*w + 33]', '[1801, 1801, 4*w^3 - 12*w^2 - 16*w + 19]', '[1801, 1801, 4*w - 1]', '[1801, 1801, 7*w^3 - 21*w^2 - 23*w + 33]', '[1831, 1831, w^3 - 2*w^2 - 8*w + 2]', '[1831, 1831, w^2 - 5*w - 2]', '[1847, 1847, 6*w^3 - 20*w^2 - 15*w + 25]', '[1847, 1847, w^3 - w^2 - 6*w - 10]', '[1849, 43, -6*w^3 + 21*w^2 + 14*w - 37]', '[1849, 43, -2*w^3 + 9*w^2 + 2*w - 18]', '[1871, 1871, -4*w^3 + 13*w^2 + 8*w - 22]', '[1871, 1871, 4*w^3 - 13*w^2 - 12*w + 15]', '[1871, 1871, 4*w^3 - 11*w^2 - 16*w + 17]', '[1871, 1871, w^2 - 10]', '[1873, 1873, -w^3 + 5*w^2 - 20]', '[1873, 1873, -4*w^3 + 14*w^2 + 9*w - 15]', '[1913, 1913, -2*w^3 + 6*w^2 + 3*w - 4]', '[1913, 1913, 5*w^3 - 15*w^2 - 18*w + 19]', '[1913, 1913, 6*w^3 - 20*w^2 - 11*w + 30]', '[1913, 1913, 9*w^3 - 30*w^2 - 23*w + 45]', '[1993, 1993, -8*w^3 + 28*w^2 + 17*w - 43]', '[1993, 1993, 4*w^3 - 13*w^2 - 16*w + 19]', '[1993, 1993, -6*w^3 + 21*w^2 + 14*w - 36]', '[1993, 1993, -2*w^3 + 9*w^2 + 2*w - 19]', '[1999, 1999, -7*w^3 + 22*w^2 + 20*w - 30]', '[1999, 1999, 4*w^3 - 11*w^2 - 13*w + 10]']}
• 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[]
  maximal_cm_subfield	numeric[]
  minimal_sibling	numeric[]
  monogenic	smallint
  narrow_class_group	bigint[]
  narrow_class_number	bigint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	numeric
  relative_class_number	numeric
  subfield_mults	integer[]
  subfields	text[]
  torsion_order	smallint
  unit_signature_rank	smallint
  used_grh	boolean

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [7, 2, -7, -2, 1], 'conductor': 0, 'degree': 4, 'disc_abs': 9792, 'disc_rad': 102, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12, 4, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 20.199009876724155, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.9792.1', 'local_algs': ['2.2.2.6a1.5', '3.2.2.2a1.1', '17.1.1.0a1.1', '17.1.1.0a1.1', '17.1.2.1a1.1'], 'monogenic': 1, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 3, 'r2': 0, 'ramps': [2, 3, 17], 'rd': 9.94758940723, 'regulator': {'__RealLiteral__': 0, 'data': '4.9482532611', 'prec': 40}, 'subfield_mults': [1], 'subfields': ['-2.0.1'], 'torsion_order': 2, 'unit_signature_rank': 3, 'used_grh': False}