Hilbert modular form data - 3.3.761.1-23.2-e

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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': 3, 'dimension': 8, 'disc': 761, 'field_bad_primes': [761], 'field_label': '3.3.761.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.761.1-23.2-e', 'label_nsuffix': 4, 'label_suffix': 'e', 'level_bad_primes': [23], 'level_ideal': '[23, 23, -w^2 + 2]', 'level_label': '23.2', 'level_norm': 23, 'parallel_weight': 2, 'short_label': '23.2-e', 'weight': '[2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[23, 23, -w^2 + 2]', -1]], 'hecke_eigenvalues': ['e', '-291/5419*e^7 + 1372/5419*e^6 + 2470/5419*e^5 - 15908/5419*e^4 - 3164/5419*e^3 + 48100/5419*e^2 - 555/5419*e - 24438/5419', '144/5419*e^7 - 232/5419*e^6 - 1334/5419*e^5 + 2453/5419*e^4 - 1898/5419*e^3 - 7154/5419*e^2 + 25135/5419*e + 3769/5419', '-13/5419*e^7 + 322/5419*e^6 - 858/5419*e^5 - 2517/5419*e^4 + 7773/5419*e^3 + 119/5419*e^2 - 10360/5419*e + 26115/5419', '-131/5419*e^7 - 90/5419*e^6 + 2192/5419*e^5 + 64/5419*e^4 - 11294/5419*e^3 + 12454/5419*e^2 + 17739/5419*e - 29884/5419', '-216/5419*e^7 + 348/5419*e^6 + 2001/5419*e^5 - 970/5419*e^4 - 2572/5419*e^3 - 10945/5419*e^2 - 7898/5419*e + 24151/5419', '409/5419*e^7 - 960/5419*e^6 - 5520/5419*e^5 + 7908/5419*e^4 + 27650/5419*e^3 - 11664/5419*e^2 - 54639/5419*e + 15409/5419', '658/5419*e^7 - 458/5419*e^6 - 10762/5419*e^5 + 5263/5419*e^4 + 52592/5419*e^3 - 20196/5419*e^2 - 73382/5419*e + 36264/5419', '-522/5419*e^7 + 841/5419*e^6 + 8900/5419*e^5 - 12279/5419*e^4 - 45955/5419*e^3 + 48964/5419*e^2 + 66714/5419*e - 30597/5419', '-391/5419*e^7 + 931/5419*e^6 + 6708/5419*e^5 - 12343/5419*e^4 - 34661/5419*e^3 + 47348/5419*e^2 + 38137/5419*e - 44065/5419', 1, '-316/5419*e^7 - 93/5419*e^6 + 6239/5419*e^5 + 2595/5419*e^4 - 34069/5419*e^3 - 17116/5419*e^2 + 41632/5419*e + 15362/5419', '844/5419*e^7 - 2564/5419*e^6 - 9324/5419*e^5 + 26269/5419*e^4 + 28916/5419*e^3 - 61499/5419*e^2 - 28949/5419*e + 16521/5419', '119/5419*e^7 - 1697/5419*e^6 + 2435/5419*e^5 + 15537/5419*e^4 - 27384/5419*e^3 - 29018/5419*e^2 + 34808/5419*e + 27312/5419', '-1090/5419*e^7 + 1154/5419*e^6 + 14764/5419*e^5 - 7203/5419*e^4 - 57736/5419*e^3 - 7113/5419*e^2 + 57586/5419*e + 28295/5419', '-550/5419*e^7 + 284/5419*e^6 + 7052/5419*e^5 + 641/5419*e^4 - 18792/5419*e^3 - 14974/5419*e^2 - 20211/5419*e - 7697/5419', '870/5419*e^7 - 3208/5419*e^6 - 7608/5419*e^5 + 31303/5419*e^4 + 18789/5419*e^3 - 72575/5419*e^2 - 51581/5419*e + 56414/5419', '-1427/5419*e^7 + 1998/5419*e^6 + 19617/5419*e^5 - 16594/5419*e^4 - 80916/5419*e^3 + 22650/5419*e^2 + 100407/5419*e + 17480/5419', '-64/5419*e^7 - 499/5419*e^6 + 6614/5419*e^5 + 114/5419*e^4 - 67195/5419*e^3 + 21845/5419*e^2 + 162839/5419*e - 28168/5419', '517/5419*e^7 - 1134/5419*e^6 - 9230/5419*e^5 + 13812/5419*e^4 + 50612/5419*e^3 - 30577/5419*e^2 - 61528/5419*e - 42728/5419', '303/5419*e^7 + 415/5419*e^6 - 7097/5419*e^5 - 5112/5419*e^4 + 47261/5419*e^3 + 22654/5419*e^2 - 73668/5419*e - 27180/5419', '769/5419*e^7 - 1540/5419*e^6 - 8855/5419*e^5 + 16750/5419*e^4 + 22905/5419*e^3 - 56644/5419*e^2 + 5489/5419*e + 108826/5419', '1008/5419*e^7 - 1624/5419*e^6 - 14757/5419*e^5 + 17171/5419*e^4 + 62580/5419*e^3 - 55497/5419*e^2 - 62491/5419*e + 48059/5419', '1622/5419*e^7 - 1409/5419*e^6 - 28423/5419*e^5 + 21835/5419*e^4 + 143148/5419*e^3 - 94882/5419*e^2 - 167186/5419*e + 51410/5419', '252/5419*e^7 - 406/5419*e^6 + 375/5419*e^5 + 2938/5419*e^4 - 27707/5419*e^3 - 4391/5419*e^2 + 61598/5419*e - 16435/5419', '-315/5419*e^7 - 2202/5419*e^6 + 11724/5419*e^5 + 20713/5419*e^4 - 91358/5419*e^3 - 22961/5419*e^2 + 174986/5419*e - 56677/5419', '-439/5419*e^7 - 798/5419*e^6 + 8959/5419*e^5 + 12128/5419*e^4 - 59317/5419*e^3 - 40584/5419*e^2 + 123688/5419*e - 5582/5419', '-2050/5419*e^7 + 4507/5419*e^6 + 27270/5419*e^5 - 43426/5419*e^4 - 117336/5419*e^3 + 82126/5419*e^2 + 175420/5419*e - 4057/5419', '1423/5419*e^7 - 4400/5419*e^6 - 14462/5419*e^5 + 47083/5419*e^4 + 28284/5419*e^3 - 118488/5419*e^2 + 27295/5419*e + 43078/5419', '-548/5419*e^7 + 1485/5419*e^6 + 7184/5419*e^5 - 17313/5419*e^4 - 30409/5419*e^3 + 49202/5419*e^2 + 35156/5419*e - 43/5419', '-488/5419*e^7 - 418/5419*e^6 + 16563/5419*e^5 - 8614/5419*e^4 - 118807/5419*e^3 + 72413/5419*e^2 + 184265/5419*e - 25116/5419', '303/5419*e^7 + 415/5419*e^6 - 1678/5419*e^5 - 10531/5419*e^4 - 23186/5419*e^3 + 55168/5419*e^2 + 137673/5419*e - 43437/5419', '227/5419*e^7 - 1871/5419*e^6 - 1275/5419*e^5 + 21441/5419*e^4 - 9841/5419*e^3 - 53350/5419*e^2 + 49595/5419*e + 12527/5419', '1336/5419*e^7 + 256/5419*e^6 - 25623/5419*e^5 - 1025/5419*e^4 + 146165/5419*e^3 - 21817/5419*e^2 - 243374/5419*e + 51526/5419', '-839/5419*e^7 + 2857/5419*e^6 + 4235/5419*e^5 - 27802/5419*e^4 + 26036/5419*e^3 + 59369/5419*e^2 - 90036/5419*e + 2614/5419', '-535/5419*e^7 + 1163/5419*e^6 + 8042/5419*e^5 - 14796/5419*e^4 - 27344/5419*e^3 + 54502/5419*e^2 - 19512/5419*e - 53253/5419', '-1387/5419*e^7 + 4342/5419*e^6 + 22257/5419*e^5 - 55953/5419*e^4 - 112753/5419*e^3 + 184437/5419*e^2 + 156461/5419*e - 73295/5419', '-24/5419*e^7 + 1845/5419*e^6 - 1584/5419*e^5 - 22988/5419*e^4 + 14767/5419*e^3 + 48157/5419*e^2 - 14124/5419*e + 81560/5419', '-1284/5419*e^7 - 1544/5419*e^6 + 29055/5419*e^5 + 5674/5419*e^4 - 166419/5419*e^3 + 43017/5419*e^2 + 219786/5419*e - 31349/5419', '-31/5419*e^7 + 351/5419*e^6 - 2046/5419*e^5 + 1918/5419*e^4 + 20203/5419*e^3 - 46403/5419*e^2 - 42629/5419*e + 119799/5419', '999/5419*e^7 + 1100/5419*e^6 - 20770/5419*e^5 - 15835/5419*e^4 + 122985/5419*e^3 + 67555/5419*e^2 - 189715/5419*e - 35155/5419', '-70/5419*e^7 + 1317/5419*e^6 - 4620/5419*e^5 - 5633/5419*e^4 + 43522/5419*e^3 - 29789/5419*e^2 - 73709/5419*e + 106021/5419', '-755/5419*e^7 + 4528/5419*e^6 + 4360/5419*e^5 - 50305/5419*e^4 + 14994/5419*e^3 + 142803/5419*e^2 - 62278/5419*e - 93181/5419', '868/5419*e^7 + 1010/5419*e^6 - 18578/5419*e^5 + 486/5419*e^4 + 95434/5419*e^3 - 60885/5419*e^2 - 101529/5419*e + 54179/5419', '-540/5419*e^7 + 6289/5419*e^6 - 3126/5419*e^5 - 72872/5419*e^4 + 74855/5419*e^3 + 213783/5419*e^2 - 198572/5419*e - 126578/5419', '762/5419*e^7 + 2385/5419*e^6 - 20155/5419*e^5 - 23372/5419*e^4 + 125883/5419*e^3 + 43880/5419*e^2 - 174748/5419*e + 17009/5419', '1944/5419*e^7 - 3132/5419*e^6 - 34266/5419*e^5 + 35825/5419*e^4 + 191137/5419*e^3 - 101998/5419*e^2 - 319086/5419*e + 80686/5419', '2129/5419*e^7 - 3129/5419*e^6 - 32894/5419*e^5 + 33294/5419*e^4 + 143465/5419*e^3 - 67009/5419*e^2 - 153314/5419*e - 62102/5419', '49/5419*e^7 - 380/5419*e^6 - 2185/5419*e^5 + 4485/5419*e^4 + 26976/5419*e^3 + 802/5419*e^2 - 76834/5419*e - 18399/5419', '-398/5419*e^7 - 563/5419*e^6 + 827/5419*e^5 + 17982/5419*e^4 + 35803/5419*e^3 - 95983/5419*e^2 - 163776/5419*e + 97135/5419', '130/5419*e^7 + 2199/5419*e^6 - 13096/5419*e^5 - 7344/5419*e^4 + 101097/5419*e^3 - 66218/5419*e^2 - 118579/5419*e + 101923/5419', '783/5419*e^7 - 3971/5419*e^6 - 2512/5419*e^5 + 31966/5419*e^4 - 25900/5419*e^3 - 30094/5419*e^2 + 57080/5419*e - 32680/5419', '794/5419*e^7 - 75/5419*e^6 - 12624/5419*e^5 - 1753/5419*e^4 + 64648/5419*e^3 - 2266/5419*e^2 - 112564/5419*e + 63607/5419', '-82/5419*e^7 - 470/5419*e^6 + 7/5419*e^5 + 9968/5419*e^4 + 15682/5419*e^3 - 51772/5419*e^2 - 59095/5419*e + 65516/5419', '1182/5419*e^7 - 98/5419*e^6 - 24949/5419*e^5 + 10426/5419*e^4 + 141120/5419*e^3 - 80850/5419*e^2 - 144338/5419*e + 96191/5419', '-3003/5419*e^7 + 3935/5419*e^6 + 40238/5419*e^5 - 28689/5419*e^4 - 160696/5419*e^3 + 16651/5419*e^2 + 202541/5419*e + 28313/5419', '-691/5419*e^7 - 5811/5419*e^6 + 24841/5419*e^5 + 63380/5419*e^4 - 172504/5419*e^3 - 149992/5419*e^2 + 268012/5419*e - 21661/5419', '-659/5419*e^7 - 2852/5419*e^6 + 16115/5419*e^5 + 41647/5419*e^4 - 103683/5419*e^3 - 169043/5419*e^2 + 173045/5419*e + 95384/5419', '2024/5419*e^7 + 1556/5419*e^6 - 39824/5419*e^5 - 15798/5419*e^4 + 219586/5419*e^3 + 21073/5419*e^2 - 293682/5419*e + 2097/5419', '204/5419*e^7 - 2135/5419*e^6 - 2793/5419*e^5 + 27409/5419*e^4 + 28922/5419*e^3 - 103161/5419*e^2 - 102125/5419*e + 125009/5419', '1015/5419*e^7 - 130/5419*e^6 - 25133/5419*e^5 + 13941/5419*e^4 + 160105/5419*e^3 - 85574/5419*e^2 - 261584/5419*e + 9820/5419', '-1775/5419*e^7 + 4365/5419*e^6 + 18325/5419*e^5 - 35618/5419*e^4 - 42912/5419*e^3 + 35423/5419*e^2 + 31084/5419*e + 51272/5419', '3192/5419*e^7 - 6949/5419*e^6 - 44021/5419*e^5 + 76954/5419*e^4 + 181913/5419*e^3 - 216383/5419*e^2 - 202404/5419*e + 142252/5419', '1536/5419*e^7 + 1138/5419*e^6 - 34099/5419*e^5 - 13574/5419*e^4 + 219997/5419*e^3 + 44715/5419*e^2 - 423719/5419*e + 20333/5419', '296/5419*e^7 + 4340/5419*e^6 - 18397/5419*e^5 - 34396/5419*e^4 + 139401/5419*e^3 + 9379/5419*e^2 - 194296/5419*e + 173629/5419', '-262/5419*e^7 - 5599/5419*e^6 + 20641/5419*e^5 + 54318/5419*e^4 - 174320/5419*e^3 - 94310/5419*e^2 + 322685/5419*e - 32673/5419', '-3082/5419*e^7 + 2557/5419*e^6 + 51281/5419*e^5 - 23976/5419*e^4 - 251853/5419*e^3 + 55724/5419*e^2 + 283396/5419*e + 7768/5419', '39/5419*e^7 - 966/5419*e^6 - 2845/5419*e^5 + 18389/5419*e^4 + 25452/5419*e^3 - 92480/5419*e^2 - 66462/5419*e + 62549/5419', '-2231/5419*e^7 + 6906/5419*e^6 + 31581/5419*e^5 - 87641/5419*e^4 - 147088/5419*e^3 + 289288/5419*e^2 + 201667/5419*e - 116911/5419', '1300/5419*e^7 - 5105/5419*e^6 - 17161/5419*e^5 + 62035/5419*e^4 + 78902/5419*e^3 - 196146/5419*e^2 - 150761/5419*e + 49229/5419', '86/5419*e^7 + 2872/5419*e^6 - 10581/5419*e^5 - 24200/5419*e^4 + 91140/5419*e^3 + 55487/5419*e^2 - 171568/5419*e - 120655/5419', '-961/5419*e^7 + 43/5419*e^6 + 17859/5419*e^5 - 5570/5419*e^4 - 83596/5419*e^3 + 35475/5419*e^2 + 92860/5419*e - 36179/5419', '1011/5419*e^7 - 2532/5419*e^6 - 14559/5419*e^5 + 28173/5419*e^4 + 74959/5419*e^3 - 94708/5419*e^2 - 139301/5419*e + 70378/5419', '-1168/5419*e^7 + 3086/5419*e^6 + 9616/5419*e^5 - 27724/5419*e^4 - 5679/5419*e^3 + 26115/5419*e^2 - 9993/5419*e + 130795/5419', '-988/5419*e^7 - 2623/5419*e^6 + 32334/5419*e^5 + 9211/5419*e^4 - 227521/5419*e^3 + 68653/5419*e^2 + 366887/5419*e - 134089/5419', '-81/5419*e^7 - 7998/5419*e^6 + 21749/5419*e^5 + 82276/5419*e^4 - 177082/5419*e^3 - 187673/5419*e^2 + 242248/5419*e - 1104/5419', '273/5419*e^7 - 1343/5419*e^6 - 3658/5419*e^5 + 20343/5419*e^4 + 15594/5419*e^3 - 100041/5419*e^2 - 15457/5419*e + 101865/5419', '116/5419*e^7 - 789/5419*e^6 - 14020/5419*e^5 + 31630/5419*e^4 + 128226/5419*e^3 - 190310/5419*e^2 - 246036/5419*e + 156725/5419', '-1035/5419*e^7 - 1042/5419*e^6 + 18394/5419*e^5 + 8448/5419*e^4 - 65611/5419*e^3 - 3448/5419*e^2 - 31974/5419*e - 32170/5419', '3834/5419*e^7 - 6177/5419*e^6 - 55839/5419*e^5 + 68698/5419*e^4 + 246156/5419*e^3 - 197249/5419*e^2 - 328554/5419*e + 79351/5419', '-1906/5419*e^7 - 1144/5419*e^6 + 36774/5419*e^5 + 7798/5419*e^4 - 189681/5419*e^3 + 4525/5419*e^2 + 233069/5419*e - 16545/5419', '1213/5419*e^7 - 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2622/5419*e^6 - 6948/5419*e^5 + 22818/5419*e^4 - 23039/5419*e^3 - 11807/5419*e^2 + 181902/5419*e - 29953/5419', '2781/5419*e^7 - 12609/5419*e^6 - 22376/5419*e^5 + 141190/5419*e^4 + 8729/5419*e^3 - 398951/5419*e^2 + 89494/5419*e + 227569/5419', '1591/5419*e^7 - 1058/5419*e^6 - 41307/5419*e^5 + 34591/5419*e^4 + 282569/5419*e^3 - 200894/5419*e^2 - 491603/5419*e + 176628/5419', '4111/5419*e^7 - 10537/5419*e^6 - 48395/5419*e^5 + 107323/5419*e^4 + 140974/5419*e^3 - 223128/5419*e^2 - 49031/5419*e - 74426/5419', '-1471/5419*e^7 - 2748/5419*e^6 + 27551/5419*e^5 + 36997/5419*e^4 - 161320/5419*e^3 - 104919/5419*e^2 + 312949/5419*e + 6243/5419', '-3458/5419*e^7 - 1052/5419*e^6 + 64398/5419*e^5 + 7853/5419*e^4 - 327580/5419*e^3 + 15397/5419*e^2 + 408936/5419*e - 130624/5419', '7541/5419*e^7 - 15461/5419*e^6 - 98384/5419*e^5 + 161161/5419*e^4 + 365661/5419*e^3 - 400005/5419*e^2 - 311875/5419*e + 117031/5419', '-2715/5419*e^7 + 3471/5419*e^6 + 48408/5419*e^5 - 61716/5419*e^4 - 240358/5419*e^3 + 262455/5419*e^2 + 296163/5419*e - 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76525/5419', '-803/5419*e^7 + 8218/5419*e^6 - 4227/5419*e^5 - 80024/5419*e^4 + 60785/5419*e^3 + 179508/5419*e^2 - 14660/5419*e - 163078/5419', '1135/5419*e^7 - 9355/5419*e^6 + 4463/5419*e^5 + 96367/5419*e^4 - 130490/5419*e^3 - 223398/5419*e^2 + 329260/5419*e - 45745/5419', '105/5419*e^7 - 4685/5419*e^6 + 23187/5419*e^5 + 27416/5419*e^4 - 222434/5419*e^3 + 25717/5419*e^2 + 405899/5419*e - 10009/5419', '-1074/5419*e^7 - 76/5419*e^6 + 26658/5419*e^5 - 15360/5419*e^4 - 194024/5419*e^3 + 137803/5419*e^2 + 419237/5419*e - 127233/5419', '-2971/5419*e^7 + 1475/5419*e^6 + 53188/5419*e^5 - 17908/5419*e^4 - 286959/5419*e^3 + 68047/5419*e^2 + 448971/5419*e - 152687/5419', '3151/5419*e^7 - 7184/5419*e^6 - 35889/5419*e^5 + 71100/5419*e^4 + 81374/5419*e^3 - 150146/5419*e^2 + 52546/5419*e - 36331/5419', '310/5419*e^7 + 1909/5419*e^6 - 22892/5419*e^5 - 2923/5419*e^4 + 215233/5419*e^3 - 77870/5419*e^2 - 511197/5419*e + 129665/5419', '415/5419*e^7 + 2643/5419*e^6 - 5124/5419*e^5 - 51373/5419*e^4 + 3637/5419*e^3 + 224216/5419*e^2 + 68110/5419*e - 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201722/5419*e + 43017/5419', '2992/5419*e^7 - 7831/5419*e^6 - 40964/5419*e^5 + 84084/5419*e^4 + 189366/5419*e^3 - 217887/5419*e^2 - 341780/5419*e + 48808/5419', '-1668/5419*e^7 + 881/5419*e^6 + 36225/5419*e^5 - 26156/5419*e^4 - 184840/5419*e^3 + 157830/5419*e^2 + 113020/5419*e - 227452/5419', '-2944/5419*e^7 - 1278/5419*e^6 + 49551/5419*e^5 + 32339/5419*e^4 - 256833/5419*e^3 - 154796/5419*e^2 + 397123/5419*e + 91536/5419', '2303/5419*e^7 - 1603/5419*e^6 - 43086/5419*e^5 + 4873/5419*e^4 + 259938/5419*e^3 + 32275/5419*e^2 - 435664/5419*e + 72734/5419', '2556/5419*e^7 - 4118/5419*e^6 - 42645/5419*e^5 + 31348/5419*e^4 + 234551/5419*e^3 + 16620/5419*e^2 - 408701/5419*e - 129539/5419', '-634/5419*e^7 - 1387/5419*e^6 + 17765/5419*e^5 + 12306/5419*e^4 - 89035/5419*e^3 - 71313/5419*e^2 - 4617/5419*e + 201897/5419', '140/5419*e^7 - 2634/5419*e^6 - 1598/5419*e^5 + 49199/5419*e^4 + 5079/5419*e^3 - 254724/5419*e^2 - 15152/5419*e + 145612/5419', '3701/5419*e^7 - 12887/5419*e^6 - 32103/5419*e^5 + 108392/5419*e^4 + 51395/5419*e^3 - 86401/5419*e^2 + 7729/5419*e - 277908/5419', '1770/5419*e^7 - 4658/5419*e^6 - 29493/5419*e^5 + 53408/5419*e^4 + 139692/5419*e^3 - 82064/5419*e^2 - 128859/5419*e - 189625/5419', '-926/5419*e^7 + 7513/5419*e^6 - 1507/5419*e^5 - 81329/5419*e^4 + 73470/5419*e^3 + 237325/5419*e^2 - 127688/5419*e - 281564/5419', '-3003/5419*e^7 + 9354/5419*e^6 + 34819/5419*e^5 - 104555/5419*e^4 - 128182/5419*e^3 + 298439/5419*e^2 + 251312/5419*e - 69229/5419', '2280/5419*e^7 - 1867/5419*e^6 - 22928/5419*e^5 + 10841/5419*e^4 + 11494/5419*e^3 + 4140/5419*e^2 + 192952/5419*e - 42382/5419', '-1416/5419*e^7 - 4944/5419*e^6 + 47438/5419*e^5 + 30972/5419*e^4 - 364279/5419*e^3 + 50478/5419*e^2 + 711099/5419*e - 173440/5419', '-524/5419*e^7 - 360/5419*e^6 + 14187/5419*e^5 + 5675/5419*e^4 - 104785/5419*e^3 - 42307/5419*e^2 + 195593/5419*e + 48453/5419', '977/5419*e^7 - 6692/5419*e^6 - 546/5419*e^5 + 67860/5419*e^4 - 74368/5419*e^3 - 150671/5419*e^2 + 198344/5419*e + 86573/5419'], 'hecke_polynomial': 'x^8 - 2*x^7 - 17*x^6 + 29*x^5 + 91*x^4 - 124*x^3 - 149*x^2 + 136*x + 17', 'label': '3.3.761.1-23.2-e'}
• hmf_fields •

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

  
  {'degree': 3, 'discriminant': 761, 'ideals': ['[1, 1, 1]', '[3, 3, w + 1]', '[7, 7, w - 1]', '[8, 2, 2]', '[9, 3, -w^2 + 2*w + 4]', '[9, 9, w - 2]', '[11, 11, -w^2 + 2*w + 2]', '[13, 13, -w^2 + w + 4]', '[19, 19, w + 3]', '[19, 19, -w^2 + 2*w + 5]', '[19, 19, -w^2 + 3*w + 2]', '[21, 21, w^2 - 2*w - 6]', '[23, 23, w^2 - w - 3]', '[23, 23, -w^2 + 2]', '[23, 23, -w + 4]', '[24, 6, 2*w + 2]', '[27, 3, 3]', '[27, 27, w^2 - w - 2]', '[31, 31, w^2 - 5]', '[33, 33, -2*w + 1]', '[39, 39, -w^2 - w + 3]', '[43, 43, w^2 - 3*w - 3]', '[49, 7, w^2 - 6]', '[49, 49, -w^2 + 8]', '[53, 53, 2*w - 5]', '[56, 14, 2*w - 2]', '[57, 57, w + 4]', '[57, 57, 2*w^2 - 3*w - 8]', '[57, 57, -w^2 + 7]', '[61, 61, 2*w^2 - 2*w - 9]', '[63, 21, 2*w^2 - 4*w - 5]', '[63, 63, w^2 - 3*w + 2]', '[64, 4, 4]', '[69, 69, -w^2 + 3*w + 4]', '[69, 69, w^2 + 2*w - 2]', '[69, 69, w - 5]', '[71, 71, 2*w - 3]', '[72, 6, -2*w^2 + 4*w + 8]', '[72, 18, 2*w - 4]', '[73, 73, 2*w^2 - 5*w - 5]', '[77, 77, 3*w + 4]', '[81, 9, w^2 + w - 4]', '[81, 9, 3*w + 3]', '[81, 81, w^2 - 2*w - 9]', '[83, 83, w^2 - w - 9]', '[88, 22, -2*w^2 + 4*w + 4]', '[91, 91, w^2 - 3*w - 5]', '[93, 93, 2*w^2 + w - 4]', '[97, 97, 2*w^2 - 3*w - 7]', '[99, 33, 2*w^2 - w - 11]', '[99, 99, -w^2 + 3*w + 7]', '[103, 103, w^2 - 3*w - 6]', '[104, 26, -2*w^2 + 2*w + 8]', '[109, 109, w^2 - 4*w - 3]', '[117, 39, w^2 - 2*w + 2]', '[117, 117, 2*w^2 - 4*w - 9]', '[121, 11, 2*w^2 - w - 7]', '[121, 121, -w - 5]', '[125, 5, -5]', '[127, 127, w^2 + w - 5]', '[129, 129, -w^2 - 2]', '[131, 131, w^2 - 11]', '[133, 133, w^2 + 2*w - 3]', '[133, 133, 2*w^2 - 3*w - 6]', '[133, 133, -2*w^2 - w + 3]', '[137, 137, 3*w^2 - 7*w - 8]', '[137, 137, 2*w^2 - 5*w - 6]', '[137, 137, -w^2 + w - 2]', '[139, 139, 3*w^2 - 2*w - 16]', '[139, 139, 3*w - 2]', '[139, 139, -w^2 + 3*w - 3]', '[143, 143, -w + 6]', '[147, 21, 2*w^2 - 5]', '[147, 147, -2*w^2 + 2*w + 7]', '[151, 151, w^2 + w - 11]', '[152, 38, 2*w + 6]', '[152, 38, -2*w^2 + 4*w + 10]', '[152, 38, -2*w^2 + 6*w + 4]', '[157, 157, 2*w^2 - 3*w - 3]', '[159, 159, 2*w^2 - 3*w - 5]', '[161, 161, 3*w^2 - 3*w - 14]', '[161, 161, -2*w^2 + 9]', '[161, 161, -w^2 + 4*w + 4]', '[163, 163, w^2 - w - 10]', '[168, 42, 2*w^2 - 4*w - 12]', '[169, 13, 2*w^2 - 3*w - 4]', '[169, 169, -2*w^2 + 3*w + 15]', '[171, 57, -2*w^2 + 4*w + 11]', '[171, 57, w^2 - 5*w + 2]', '[171, 57, w^2 - 2*w - 10]', '[171, 171, 3*w^2 - 5*w - 11]', '[171, 171, w^2 + w - 6]', '[171, 171, -2*w^2 + w + 6]', '[173, 173, -3*w^2 + 6*w + 8]', '[183, 183, 2*w^2 + w - 7]', '[184, 46, 2*w^2 - 2*w - 6]', '[184, 46, -2*w^2 + 4]', '[184, 46, -2*w + 8]', '[189, 21, 3*w - 3]', '[189, 189, -3*w^2 + 4*w + 13]', '[191, 191, -4*w^2 + 7*w + 15]', '[192, 12, 4*w + 4]', '[193, 193, 2*w^2 - 3]', '[197, 197, w^2 - 3*w - 11]', '[199, 199, 3*w^2 - 5*w - 16]', '[207, 69, w^2 + w - 10]', '[207, 69, -w^2 - w + 7]', '[207, 69, 2*w^2 - w - 5]', '[207, 207, w^2 + w + 3]', '[207, 207, w^2 - 4*w - 5]', '[207, 207, -2*w^2 + 5*w + 7]', '[209, 209, w^2 + 2*w - 4]', '[209, 209, -2*w^2 + 2*w + 5]', '[209, 209, -3*w + 7]', '[211, 211, w^2 - 4*w - 9]', '[213, 213, 2*w^2 - w - 3]', '[216, 6, 6]', '[216, 54, 2*w^2 - 2*w - 4]', '[217, 217, w + 6]', '[219, 219, -w^2 + 2*w - 3]', '[223, 223, 2*w^2 - w - 4]', '[227, 227, 3*w - 4]', '[229, 229, w^2 + w - 8]', '[231, 231, w^2 + w - 9]', '[241, 241, w^2 - 4*w - 6]', '[243, 9, -3*w^2 + 6*w + 12]', '[243, 27, 3*w - 6]', '[243, 243, -2*w^2 + 6*w + 5]', '[247, 247, 3*w^2 - 6*w - 7]', '[247, 247, w^2 + 3]', '[247, 247, -3*w + 5]', '[248, 62, 2*w^2 - 10]', '[249, 249, w^2 - 4*w - 8]', '[251, 251, w - 7]', '[253, 253, -w^2 + 3*w - 4]', '[253, 253, 3*w^2 - 3*w - 13]', '[253, 253, w^2 - w + 3]', '[257, 257, w^2 - 4*w - 7]', '[263, 263, 3*w^2 - 5*w - 10]', '[263, 263, 2*w^2 - 5*w - 15]', '[263, 263, -w^2 + 6*w - 1]', '[264, 66, -4*w + 2]', '[269, 269, -w^2 - w + 14]', '[273, 273, -w^2 - 2*w - 4]', '[277, 277, 2*w^2 - 5*w - 8]', '[277, 277, w^2 + 3*w - 3]', '[277, 277, 3*w^2 - 4*w - 12]', '[279, 93, 4*w^2 - 5*w - 19]', '[279, 279, -w^2 + w + 11]', '[281, 281, -2*w - 7]', '[291, 291, w^2 + 2*w - 5]', '[293, 293, 3*w^2 - 2*w - 12]', '[297, 33, -3*w^2 + 6*w + 6]', '[297, 297, -2*w^2 + 5*w - 2]', '[299, 299, -2*w^2 + 7*w + 4]', '[299, 299, 3*w + 8]', '[299, 299, w^2 - 2*w - 11]', '[301, 301, -3*w^2 + 6*w + 4]', '[307, 307, 2*w^2 + w - 8]', '[309, 309, -w^2 - 3*w - 5]', '[312, 78, -2*w^2 - 2*w + 6]', '[313, 313, w^2 + 4*w - 2]', '[317, 317, 3*w^2 - 6*w - 5]', '[327, 327, -2*w^2 - w - 2]', '[331, 331, 4*w^2 - 4*w - 19]', '[337, 337, -5*w^2 + 8*w + 21]', '[341, 341, 2*w^2 - 5*w - 9]', '[343, 7, 7]', '[343, 343, 2*w - 9]', '[344, 86, 2*w^2 - 6*w - 6]', '[347, 347, 3*w^2 - 6*w - 13]', '[347, 347, 3*w^2 - 5*w - 22]', '[347, 347, 3*w^2 - 5*w - 9]', '[349, 349, w^2 - 5*w - 11]', '[351, 39, -3*w^2 + 3*w + 12]', '[351, 351, -w - 7]', '[353, 353, -w^2 + 6*w - 7]', '[359, 359, -4*w^2 + 8*w + 11]', '[361, 19, w^2 - 4*w + 6]', '[361, 19, -2*w^2 + 5*w + 14]', '[361, 19, -w^2 + 5*w + 5]', '[361, 361, -w^2 + 2*w - 4]', '[361, 361, -4*w + 3]', '[361, 361, -w^2 - w - 4]', '[363, 33, 3*w^2 + 4*w - 5]', '[363, 363, -4*w^2 + 7*w + 14]', '[367, 367, 3*w^2 - 4*w - 11]', '[371, 371, 2*w^2 - 7*w + 5]', '[373, 373, w^2 + 2*w - 6]', '[375, 15, -5*w - 5]', '[379, 379, 5*w^2 - 9*w - 18]', '[381, 381, 3*w^2 + 2*w - 4]', '[387, 129, -w^2 + 5*w - 8]', '[387, 387, -4*w^2 + 9*w + 7]', '[392, 14, 2*w^2 - 12]', '[392, 98, -2*w^2 + 16]', '[393, 393, 2*w^2 - 5*w - 10]', '[399, 399, w^2 + 3*w - 4]', '[399, 399, -3*w^2 + 7*w + 10]', '[399, 399, w - 8]', '[403, 403, 3*w^2 - 6*w - 20]', '[409, 409, -w^2 - 4]', '[411, 411, -w^2 + 3*w - 5]', '[411, 411, -w^2 + w - 4]', '[411, 411, -w^2 - 7*w - 3]', '[417, 417, 4*w^2 - 13]', '[417, 417, 3*w^2 + w - 2]', '[417, 417, w^2 - 6*w - 4]', '[424, 106, 4*w - 10]', '[427, 427, -2*w^2 + 5*w + 11]', '[429, 429, -w^2 + 5*w + 6]', '[437, 437, 3*w^2 - 5*w - 4]', '[437, 437, -4*w^2 + 9*w + 5]', '[437, 437, -2*w^2 + 2*w + 17]', '[437, 437, -2*w^2 - w + 9]', '[437, 437, 3*w^2 - 8]', '[437, 437, -w^2 + 6*w - 3]', '[437, 437, -w^2 + w + 12]', '[437, 437, 2*w^2 - 5*w - 12]', '[437, 437, 2*w^2 - 13]', '[439, 439, 3*w^2 - 6*w - 14]', '[441, 21, 5*w^2 - 7*w - 23]', '[441, 63, -w^2 + 13]', '[441, 147, w^2 - 5*w - 10]', '[441, 441, -2*w^2 - 3*w + 5]', '[443, 443, -w^2 - 2*w + 13]', '[443, 443, 2*w^2 - 15]', '[443, 443, 3*w^2 - 13]', '[448, 28, 4*w - 4]', '[449, 449, w^2 + 2*w - 7]', '[449, 449, 2*w^2 - 6*w - 7]', '[449, 449, 3*w^2 - 3*w - 11]', '[453, 453, 3*w^2 - 4*w - 10]', '[456, 114, 2*w + 8]', '[456, 114, 4*w^2 - 6*w - 16]', '[456, 114, -2*w^2 + 14]', '[461, 461, -w^2 - 2*w - 5]', '[467, 467, 3*w^2 - 5*w - 7]', '[471, 471, w^2 + 6*w - 1]', '[473, 473, -3*w^2 + 11*w - 2]', '[477, 159, 7*w^2 - 14*w - 22]', '[477, 477, 2*w^2 - 9*w + 10]', '[479, 479, -w^2 + 6*w - 4]', '[483, 483, w^2 - 6*w + 5]', '[483, 483, -3*w^2 + w + 16]', '[483, 483, 3*w^2 - 5*w - 5]', '[488, 122, 4*w^2 - 4*w - 18]', '[489, 489, w^2 - 5*w - 9]', '[491, 491, 3*w^2 - 5*w - 6]', '[497, 497, 2*w^2 - 5*w + 3]', '[499, 499, w^2 - 5*w - 8]', '[504, 42, 4*w^2 - 8*w - 10]', '[504, 126, 2*w^2 - 6*w + 4]', '[507, 39, w^2 + 5*w - 2]', '[507, 507, 3*w^2 - 8*w - 8]', '[509, 509, 3*w^2 - 6*w - 19]', '[511, 511, -5*w^2 + 12*w + 7]', '[512, 8, 8]', '[513, 57, 3*w + 9]', '[513, 57, -3*w^2 + 6*w + 15]', '[513, 57, -3*w^2 + 9*w + 6]', '[513, 513, w^2 + 2*w - 8]', '[513, 513, 3*w^2 + w - 5]', '[513, 513, w^2 + w - 15]', '[519, 519, -4*w + 5]', '[521, 521, 3*w^2 - 2*w - 10]', '[523, 523, 4*w - 9]', '[529, 23, -w^2 - 3*w - 6]', '[529, 23, 4*w^2 - 7*w - 13]', '[529, 23, -3*w^2 + 4*w + 9]', '[529, 529, w + 8]', '[529, 529, w^2 + 2*w - 12]', '[529, 529, w^2 + 3*w - 5]', '[539, 77, 3*w^2 - 7*w - 11]', '[539, 539, 3*w^2 + w - 4]', '[541, 541, 3*w^2 - 3*w - 10]', '[547, 547, 2*w^2 + w - 20]', '[547, 547, w^2 - 6*w - 5]', '[547, 547, 6*w^2 - 11*w - 24]', '[549, 183, 5*w^2 - 4*w - 32]', '[549, 549, -4*w^2 + 7*w + 20]', '[552, 138, -2*w^2 + 6*w + 8]', '[552, 138, 2*w^2 + 4*w - 4]', '[552, 138, 2*w - 10]', '[557, 557, -5*w^2 + 11*w + 11]', '[559, 559, w^2 + 2*w - 9]', '[563, 563, 3*w^2 - 6*w - 16]', '[567, 63, 3*w^2 - 6*w - 18]', '[567, 63, w^2 + w + 5]', '[567, 567, -2*w^2 - w + 10]', '[568, 142, 4*w - 6]', '[569, 569, 4*w^2 - 5*w - 17]', '[573, 573, w^2 + 2*w - 11]', '[576, 12, -4*w^2 + 8*w + 16]', '[576, 36, 4*w - 8]', '[579, 579, 4*w^2 + 9*w - 1]', '[581, 581, -w^2 - 2*w + 10]', '[583, 583, 7*w^2 - 18*w - 12]', '[584, 146, 4*w^2 - 10*w - 10]', '[587, 587, 5*w^2 - 8*w - 20]', '[589, 589, 3*w^2 - 4*w - 8]', '[589, 589, 5*w^2 - 5*w - 24]', '[589, 589, 4*w^2 + w - 14]', '[591, 591, -w^2 - 8*w - 10]', '[593, 593, 5*w - 3]', '[593, 593, 3*w^2 - w - 17]', '[593, 593, w - 9]', '[597, 597, w^2 - 3*w - 13]', '[613, 613, 2*w^2 - w - 19]', '[613, 613, 3*w^2 - 4*w - 5]', '[613, 613, 3*w^2 - w - 8]', '[616, 154, 6*w + 8]', '[617, 617, 3*w^2 - 2*w - 9]', '[617, 617, -w^2 + w - 5]', '[617, 617, 4*w^2 - 6*w - 15]', '[619, 619, -w^2 + 3*w - 6]', '[621, 69, 3*w^2 - 3*w - 9]', '[621, 69, -3*w^2 + 6]', '[621, 69, -3*w + 12]', '[621, 621, 4*w^2 - 8*w - 9]', '[621, 621, w^2 + 5]', '[621, 621, 4*w^2 - 2*w - 21]', '[627, 627, -4*w^2 + 9*w + 13]', '[627, 627, -3*w^2 + 4*w + 7]', '[627, 627, -3*w^2 + 5*w + 23]', '[631, 631, 4*w^2 - 7*w - 21]', '[633, 633, -2*w^2 - 7*w - 8]', '[637, 91, 4*w^2 - 7*w - 24]', '[637, 637, -3*w^2 + 4*w + 6]', '[639, 213, 5*w^2 - 10*w - 14]', '[639, 639, 2*w^2 - 7*w + 6]', '[641, 641, -w^2 - 3*w + 20]', '[643, 643, 3*w^2 - 14]', '[643, 643, w^2 - w - 13]', '[643, 643, 2*w^2 - 9*w + 2]', '[647, 647, 2*w^2 - 6*w - 9]', '[648, 18, 2*w^2 + 2*w - 8]', '[648, 18, 6*w + 6]', '[648, 162, 2*w^2 - 4*w - 18]', '[651, 651, -6*w^2 + 5*w + 29]', '[653, 653, 3*w^2 - 5]', '[657, 219, -w^2 - 4*w + 4]', '[657, 657, -7*w - 4]', '[659, 659, 6*w^2 - 11*w - 21]', '[661, 661, w^2 - 6*w - 6]', '[661, 661, w^2 + 3*w - 6]', '[661, 661, 5*w^2 - 7*w - 22]', '[664, 166, 2*w^2 - 2*w - 18]', '[669, 669, 3*w^2 + 7*w - 2]', '[671, 671, w^2 - 14]', '[673, 673, w^2 - 6*w - 12]', '[677, 677, 4*w^2 - 7*w - 22]', '[677, 677, 3*w^2 - 7*w - 12]', '[677, 677, -2*w^2 - 3]', '[679, 679, -3*w^2 + 8*w + 9]', '[681, 681, 3*w^2 - w - 4]', '[683, 683, -2*w - 9]', '[683, 683, 4*w^2 - 7*w - 12]', '[683, 683, 3*w^2 - 3*w - 8]', '[687, 687, 3*w^2 - w - 7]', '[689, 689, 5*w^2 - 9*w - 22]', '[691, 691, 2*w^2 + w - 11]', '[693, 231, -w^2 + 2*w + 13]', '[693, 693, 3*w^2 - 2*w - 8]', '[701, 701, 3*w^2 - 3*w - 5]', '[704, 44, -4*w^2 + 8*w + 8]', '[709, 709, -w^2 - 2*w - 6]', '[713, 713, -2*w^2 + 6*w + 15]', '[713, 713, -7*w - 11]', '[713, 713, 3*w^2 - w - 21]', '[721, 721, -3*w^2 + 3*w + 7]', '[723, 723, -2*w^2 - 4*w - 5]', '[727, 727, 3*w^2 - w - 6]', '[727, 727, 3*w^2 - w - 27]', '[727, 727, 3*w^2 - w - 5]', '[728, 182, 2*w^2 - 6*w - 10]', '[729, 9, 9]', '[729, 27, 4*w^2 - 5*w - 16]', '[729, 81, 3*w^2 - 3*w - 6]', '[729, 729, -3*w^2 + w + 19]', '[733, 733, -2*w^2 + 9*w - 5]', '[739, 739, 3*w^2 - 4*w - 23]', '[741, 741, -3*w^2 + 2*w + 5]', '[741, 741, 5*w - 4]', '[741, 741, -4*w^2 + 2*w + 15]', '[743, 743, 2*w^2 - 7*w - 7]', '[743, 743, 3*w^2 - w - 20]', '[743, 743, 3*w^2 - 2*w - 7]', '[744, 186, 4*w^2 + 2*w - 8]', '[747, 249, 7*w^2 - 11*w - 34]', '[747, 747, -2*w^2 - w + 19]', '[753, 753, w^2 - 6*w - 7]', '[757, 757, -w - 9]', '[757, 757, 4*w^2 - 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w + 27]'], 'label': '3.3.761.1', 'narrow_class_no': 2, 'primes': ['[3, 3, w + 1]', '[7, 7, w - 1]', '[8, 2, 2]', '[9, 3, -w^2 + 2*w + 4]', '[11, 11, -w^2 + 2*w + 2]', '[13, 13, -w^2 + w + 4]', '[19, 19, w + 3]', '[19, 19, -w^2 + 2*w + 5]', '[19, 19, -w^2 + 3*w + 2]', '[23, 23, w^2 - w - 3]', '[23, 23, -w^2 + 2]', '[23, 23, -w + 4]', '[31, 31, w^2 - 5]', '[43, 43, w^2 - 3*w - 3]', '[49, 7, w^2 - 6]', '[53, 53, 2*w - 5]', '[61, 61, 2*w^2 - 2*w - 9]', '[71, 71, 2*w - 3]', '[73, 73, 2*w^2 - 5*w - 5]', '[83, 83, w^2 - w - 9]', '[97, 97, 2*w^2 - 3*w - 7]', '[103, 103, w^2 - 3*w - 6]', '[109, 109, w^2 - 4*w - 3]', '[121, 11, 2*w^2 - w - 7]', '[125, 5, -5]', '[127, 127, w^2 + w - 5]', '[131, 131, w^2 - 11]', '[137, 137, 3*w^2 - 7*w - 8]', '[137, 137, 2*w^2 - 5*w - 6]', '[137, 137, -w^2 + w - 2]', '[139, 139, 3*w^2 - 2*w - 16]', '[139, 139, 3*w - 2]', '[139, 139, -w^2 + 3*w - 3]', '[151, 151, w^2 + w - 11]', '[157, 157, 2*w^2 - 3*w - 3]', '[163, 163, w^2 - w - 10]', '[169, 13, 2*w^2 - 3*w - 4]', '[173, 173, -3*w^2 + 6*w + 8]', '[191, 191, -4*w^2 + 7*w + 15]', '[193, 193, 2*w^2 - 3]', '[197, 197, w^2 - 3*w - 11]', '[199, 199, 3*w^2 - 5*w - 16]', '[211, 211, w^2 - 4*w - 9]', '[223, 223, 2*w^2 - w - 4]', '[227, 227, 3*w - 4]', '[229, 229, w^2 + w - 8]', '[241, 241, w^2 - 4*w - 6]', '[251, 251, w - 7]', '[257, 257, w^2 - 4*w - 7]', '[263, 263, 3*w^2 - 5*w - 10]', '[263, 263, 2*w^2 - 5*w - 15]', '[263, 263, -w^2 + 6*w - 1]', '[269, 269, -w^2 - w + 14]', '[277, 277, 2*w^2 - 5*w - 8]', '[277, 277, w^2 + 3*w - 3]', '[277, 277, 3*w^2 - 4*w - 12]', '[281, 281, -2*w - 7]', '[293, 293, 3*w^2 - 2*w - 12]', '[307, 307, 2*w^2 + w - 8]', '[313, 313, w^2 + 4*w - 2]', '[317, 317, 3*w^2 - 6*w - 5]', '[331, 331, 4*w^2 - 4*w - 19]', '[337, 337, -5*w^2 + 8*w + 21]', '[347, 347, 3*w^2 - 6*w - 13]', '[347, 347, 3*w^2 - 5*w - 22]', '[347, 347, 3*w^2 - 5*w - 9]', '[349, 349, w^2 - 5*w - 11]', '[353, 353, -w^2 + 6*w - 7]', '[359, 359, -4*w^2 + 8*w + 11]', '[367, 367, 3*w^2 - 4*w - 11]', '[373, 373, w^2 + 2*w - 6]', '[379, 379, 5*w^2 - 9*w - 18]', '[409, 409, -w^2 - 4]', '[439, 439, 3*w^2 - 6*w - 14]', '[443, 443, -w^2 - 2*w + 13]', '[443, 443, 2*w^2 - 15]', '[443, 443, 3*w^2 - 13]', '[449, 449, w^2 + 2*w - 7]', '[449, 449, 2*w^2 - 6*w - 7]', '[449, 449, 3*w^2 - 3*w - 11]', '[461, 461, -w^2 - 2*w - 5]', '[467, 467, 3*w^2 - 5*w - 7]', '[479, 479, -w^2 + 6*w - 4]', '[491, 491, 3*w^2 - 5*w - 6]', '[499, 499, w^2 - 5*w - 8]', '[509, 509, 3*w^2 - 6*w - 19]', '[521, 521, 3*w^2 - 2*w - 10]', '[523, 523, 4*w - 9]', '[541, 541, 3*w^2 - 3*w - 10]', '[547, 547, 2*w^2 + w - 20]', '[547, 547, w^2 - 6*w - 5]', '[547, 547, 6*w^2 - 11*w - 24]', '[557, 557, -5*w^2 + 11*w + 11]', '[563, 563, 3*w^2 - 6*w - 16]', '[569, 569, 4*w^2 - 5*w - 17]', '[587, 587, 5*w^2 - 8*w - 20]', '[593, 593, 5*w - 3]', '[593, 593, 3*w^2 - w - 17]', '[593, 593, w - 9]', '[613, 613, 2*w^2 - w - 19]', '[613, 613, 3*w^2 - 4*w - 5]', '[613, 613, 3*w^2 - w - 8]', '[617, 617, 3*w^2 - 2*w - 9]', '[617, 617, -w^2 + w - 5]', '[617, 617, 4*w^2 - 6*w - 15]', '[619, 619, -w^2 + 3*w - 6]', '[631, 631, 4*w^2 - 7*w - 21]', '[641, 641, -w^2 - 3*w + 20]', '[643, 643, 3*w^2 - 14]', '[643, 643, w^2 - w - 13]', '[643, 643, 2*w^2 - 9*w + 2]', '[647, 647, 2*w^2 - 6*w - 9]', '[653, 653, 3*w^2 - 5]', '[659, 659, 6*w^2 - 11*w - 21]', '[661, 661, w^2 - 6*w - 6]', '[661, 661, w^2 + 3*w - 6]', '[661, 661, 5*w^2 - 7*w - 22]', '[673, 673, w^2 - 6*w - 12]', '[677, 677, 4*w^2 - 7*w - 22]', '[677, 677, 3*w^2 - 7*w - 12]', '[677, 677, -2*w^2 - 3]', '[683, 683, -2*w - 9]', '[683, 683, 4*w^2 - 7*w - 12]', '[683, 683, 3*w^2 - 3*w - 8]', '[691, 691, 2*w^2 + w - 11]', '[701, 701, 3*w^2 - 3*w - 5]', '[709, 709, -w^2 - 2*w - 6]', '[727, 727, 3*w^2 - w - 6]', '[727, 727, 3*w^2 - w - 27]', '[727, 727, 3*w^2 - w - 5]', '[733, 733, -2*w^2 + 9*w - 5]', '[739, 739, 3*w^2 - 4*w - 23]', '[743, 743, 2*w^2 - 7*w - 7]', '[743, 743, 3*w^2 - w - 20]', '[743, 743, 3*w^2 - 2*w - 7]', '[757, 757, -w - 9]', '[757, 757, 4*w^2 - 2*w - 29]', '[757, 757, 2*w^2 - 3*w - 18]', '[761, 761, 3*w^2 - 2*w - 6]', '[761, 761, 3*w^2 - 2*w - 25]', '[773, 773, -5*w - 12]', '[787, 787, -3*w - 10]', '[809, 809, 4*w^2 - w - 19]', '[821, 821, 5*w^2 - 10*w - 19]', '[823, 823, -4*w - 11]', '[827, 827, -7*w - 5]', '[827, 827, 2*w^2 - 6*w - 13]', '[827, 827, -w^2 - 2*w + 18]', '[839, 839, 6*w^2 - 9*w - 26]', '[839, 839, 5*w^2 - 12*w - 13]', '[839, 839, w - 10]', '[857, 857, -w^2 + 4*w - 8]', '[859, 859, 3*w^2 - 8*w - 10]', '[859, 859, 4*w^2 - 9*w - 14]', '[859, 859, 3*w^2 - 26]', '[863, 863, 2*w^2 + 3*w - 7]', '[877, 877, -5*w^2 + 11*w + 9]', '[877, 877, -5*w^2 + 10*w + 13]', '[877, 877, -w^2 + w - 6]', '[881, 881, w^2 - 3*w - 14]', '[883, 883, -w^2 + 3*w - 7]', '[887, 887, -3*w^2 + 6*w - 2]', '[907, 907, w^2 + 3*w - 8]', '[911, 911, 4*w^2 - 6*w - 29]', '[937, 937, -6*w^2 + 11*w + 25]', '[953, 953, 6*w^2 - 6*w - 29]', '[961, 31, -w^2 + 7*w - 5]', '[967, 967, 2*w^2 + w - 14]', '[971, 971, 5*w^2 - 3*w - 27]', '[971, 971, 4*w - 15]', '[971, 971, w^2 - 2*w - 14]', '[977, 977, 3*w^2 - 5*w - 24]', '[983, 983, w^2 - 4*w - 15]', '[991, 991, 6*w^2 - 10*w - 23]', '[991, 991, 5*w^2 - 6*w - 22]', '[991, 991, 3*w^2 + w - 13]']}
• 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': [-1, -6, -1, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 761, 'disc_rad': 761, 'disc_sign': 1, 'frobs': [[2, [[3, 1]]], [3, [[2, 1], [1, 1]]], [5, [[3, 1]]], [7, [[2, 1], [1, 1]]], [11, [[2, 1], [1, 1]]], [13, [[2, 1], [1, 1]]], [17, [[3, 1]]], [19, [[1, 3]]], [23, [[1, 3]]], [29, [[3, 1]]], [31, [[2, 1], [1, 1]]], [37, [[3, 1]]], [41, [[3, 1]]], [43, [[2, 1], [1, 1]]], [47, [[3, 1]]], [53, [[2, 1], [1, 1]]], [59, [[3, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [3], 'galois_label': '3T2', 'galt': 2, 'grd': 27.586228448267445, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.761.1', 'local_algs': ['m761.1.1.0', 'm761.2.1.1'], 'monogenic': 1, 'num_ram': 1, 'r2': 0, 'ramps': [761], 'rd': 9.12980606272, 'regulator': {'__RealLiteral__': 0, 'data': '3.52628052045', 'prec': 44}, 'res': {'gal': ['23,-51,-36,85,-28,-2,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a + 2 \\)'], 'unitsGmodule': [[3, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}