Hilbert modular form data - 4.4.12197.1-25.2-e

Formats: - HTML - YAML - JSON - 2024-06-04T09:32:59.395345

• 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': 12197, 'field_bad_primes': [12197], 'field_label': '4.4.12197.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.12197.1-25.2-e', 'label_nsuffix': 4, 'label_suffix': 'e', 'level_bad_primes': [5], 'level_ideal': '[25, 5, -w^2 + w + 2]', 'level_label': '25.2', 'level_norm': 25, 'parallel_weight': 2, 'short_label': '25.2-e', 'weight': '[2, 2, 2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[5, 5, w + 1]', -1], ['[5, 5, -w + 2]', -1]], 'hecke_eigenvalues': [1, 1, 'e', '-6431/862304*e^7 + 8969/215576*e^6 + 237003/862304*e^5 - 604849/431152*e^4 - 467595/215576*e^3 + 1613453/215576*e^2 + 545175/107788*e - 21463/26947', '6645/862304*e^7 - 14237/215576*e^6 - 100513/862304*e^5 + 856391/431152*e^4 - 568017/215576*e^3 - 1243399/215576*e^2 + 530503/107788*e + 161777/26947', '-10563/862304*e^7 + 23045/215576*e^6 + 136127/862304*e^5 - 1353693/431152*e^4 + 1106753/215576*e^3 + 1457393/215576*e^2 - 1280969/107788*e + 20409/26947', '2849/862304*e^7 - 2831/107788*e^6 - 53573/862304*e^5 + 347861/431152*e^4 - 200613/215576*e^3 - 603871/215576*e^2 + 566037/107788*e + 70622/26947', '-715/107788*e^7 + 9599/215576*e^6 + 18439/107788*e^5 - 277935/215576*e^4 + 4019/107788*e^3 + 111351/53894*e^2 + 317283/53894*e + 123623/26947', '901/431152*e^7 - 791/215576*e^6 - 55949/431152*e^5 + 7321/53894*e^4 + 265349/107788*e^3 - 115705/107788*e^2 - 319311/26947*e - 22278/26947', '-10219/862304*e^7 + 20621/215576*e^6 + 210471/862304*e^5 - 1247525/431152*e^4 + 415145/215576*e^3 + 1756081/215576*e^2 + 148971/107788*e - 49701/26947', '1069/431152*e^7 - 1573/53894*e^6 + 17959/431152*e^5 + 149441/215576*e^4 - 338123/107788*e^3 + 282089/107788*e^2 + 292217/53894*e - 74464/26947', '5469/431152*e^7 - 8457/107788*e^6 - 186717/431152*e^5 + 581179/215576*e^4 + 71978/26947*e^3 - 1710515/107788*e^2 - 299553/53894*e + 284651/26947', '1791/431152*e^7 - 3307/215576*e^6 - 91715/431152*e^5 + 64247/107788*e^4 + 83526/26947*e^3 - 504791/107788*e^2 - 250856/26947*e - 49159/26947', '23631/862304*e^7 - 6166/26947*e^6 - 400171/862304*e^5 + 2949079/431152*e^4 - 1722511/215576*e^3 - 3817345/215576*e^2 + 1698035/107788*e + 207702/26947', '-3231/215576*e^7 + 27775/215576*e^6 + 58751/215576*e^5 - 873233/215576*e^4 + 418807/107788*e^3 + 416531/26947*e^2 - 591065/53894*e - 227379/26947', '-4745/215576*e^7 + 42875/215576*e^6 + 58675/215576*e^5 - 1271325/215576*e^4 + 513149/53894*e^3 + 372758/26947*e^2 - 1204621/53894*e - 159358/26947', '-5633/431152*e^7 + 6373/53894*e^6 + 76073/431152*e^5 - 768409/215576*e^4 + 143307/26947*e^3 + 1064271/107788*e^2 - 954943/53894*e - 34813/26947', '-275/431152*e^7 + 10769/215576*e^6 - 142153/431152*e^5 - 30741/26947*e^4 + 560639/53894*e^3 - 582821/107788*e^2 - 788233/26947*e + 46607/26947', '10391/431152*e^7 - 21833/107788*e^6 - 173299/431152*e^5 + 1300609/215576*e^4 - 760949/107788*e^3 - 1606737/107788*e^2 + 512105/53894*e + 244868/26947', '7603/431152*e^7 - 32575/215576*e^6 - 114063/431152*e^5 + 473567/107788*e^4 - 323001/53894*e^3 - 790099/107788*e^2 + 223428/26947*e - 277505/26947', '-10635/431152*e^7 + 22299/107788*e^6 + 150647/431152*e^5 - 1278153/215576*e^4 + 995825/107788*e^3 + 971245/107788*e^2 - 1006225/53894*e + 201768/26947', '-3685/431152*e^7 + 14959/215576*e^6 + 78449/431152*e^5 - 56229/26947*e^4 + 53633/53894*e^3 + 576105/107788*e^2 + 178752/26947*e - 32973/26947', '8325/431152*e^7 - 14795/107788*e^6 - 223737/431152*e^5 + 926187/215576*e^4 + 26225/107788*e^3 - 1684767/107788*e^2 - 239285/53894*e + 17270/26947', '2845/431152*e^7 - 14401/215576*e^6 - 16837/431152*e^5 + 207467/107788*e^4 - 458281/107788*e^3 - 247633/107788*e^2 + 390953/26947*e - 271984/26947', '4721/107788*e^7 - 78757/215576*e^6 - 40391/53894*e^5 + 2346953/215576*e^4 - 334549/26947*e^3 - 1446855/53894*e^2 + 1203659/53894*e + 48270/26947', '-907/53894*e^7 + 11649/107788*e^6 + 15106/26947*e^5 - 388373/107788*e^4 - 91087/26947*e^3 + 491714/26947*e^2 + 346592/26947*e - 361204/26947', '10227/431152*e^7 - 4386/26947*e^6 - 283943/431152*e^5 + 1113379/215576*e^4 + 100191/107788*e^3 - 2252981/107788*e^2 - 688497/53894*e + 386918/26947', '347/431152*e^7 - 9277/215576*e^6 + 127633/431152*e^5 + 42597/53894*e^4 - 505175/53894*e^3 + 1068969/107788*e^2 + 543073/26947*e - 153663/26947', '-783/431152*e^7 - 344/26947*e^6 + 104011/431152*e^5 + 26561/215576*e^4 - 586561/107788*e^3 + 574113/107788*e^2 + 400929/53894*e + 32460/26947', '4575/431152*e^7 - 17475/215576*e^6 - 114215/431152*e^5 + 274521/107788*e^4 - 38511/107788*e^3 - 1072979/107788*e^2 - 110297/26947*e + 275562/26947', '-6653/862304*e^7 + 1395/26947*e^6 + 173985/862304*e^5 - 722245/431152*e^4 + 52681/215576*e^3 + 1740299/215576*e^2 - 98765/107788*e - 170800/26947', '1023/431152*e^7 - 1257/215576*e^6 - 44623/431152*e^5 + 2257/26947*e^4 + 94017/107788*e^3 + 309829/107788*e^2 + 127583/26947*e - 568960/26947', '23081/862304*e^7 - 38559/215576*e^6 - 684477/862304*e^5 + 2457223/431152*e^4 + 520045/215576*e^3 - 4982987/215576*e^2 - 1454897/107788*e + 200415/26947', '-4661/215576*e^7 + 18687/107788*e^6 + 95629/215576*e^5 - 143896/26947*e^4 + 211413/53894*e^3 + 890519/53894*e^2 - 136891/26947*e + 165714/26947', '-2823/107788*e^7 + 44457/215576*e^6 + 14328/26947*e^5 - 1329893/215576*e^4 + 123900/26947*e^3 + 861221/53894*e^2 - 35165/53894*e - 7014/26947', '-18077/862304*e^7 + 4564/26947*e^6 + 322065/862304*e^5 - 2102277/431152*e^4 + 1099429/215576*e^3 + 1637307/215576*e^2 - 16473/107788*e + 310068/26947', '1477/107788*e^7 - 36261/215576*e^6 + 4130/26947*e^5 + 1014337/215576*e^4 - 847253/53894*e^3 - 240725/53894*e^2 + 2315833/53894*e + 149888/26947', '-355/107788*e^7 + 3123/53894*e^6 - 13607/53894*e^5 - 63189/53894*e^4 + 1090805/107788*e^3 - 275652/26947*e^2 - 581247/26947*e + 246051/26947', '16111/431152*e^7 - 7858/26947*e^6 - 320811/431152*e^5 + 1856479/215576*e^4 - 768987/107788*e^3 - 2052141/107788*e^2 + 93115/53894*e - 110166/26947', '-12071/431152*e^7 + 22391/107788*e^6 + 296523/431152*e^5 - 1370405/215576*e^4 + 166707/107788*e^3 + 2048105/107788*e^2 + 149895/53894*e + 276992/26947', '4659/215576*e^7 - 40451/215576*e^6 - 77261/215576*e^5 + 1218241/215576*e^4 - 340247/53894*e^3 - 410094/26947*e^2 + 381863/53894*e + 337256/26947', '7013/215576*e^7 - 56667/215576*e^6 - 138797/215576*e^5 + 1686129/215576*e^4 - 693743/107788*e^3 - 476663/26947*e^2 + 387313/53894*e - 468201/26947', '-5541/215576*e^7 + 7711/53894*e^6 + 201237/215576*e^5 - 505639/107788*e^4 - 199420/26947*e^3 + 1224367/53894*e^2 + 601244/26947*e - 85720/26947', '-1117/53894*e^7 + 12207/107788*e^6 + 45615/53894*e^5 - 423271/107788*e^4 - 479295/53894*e^3 + 602056/26947*e^2 + 704539/26947*e + 160656/26947', '-2127/107788*e^7 + 30289/215576*e^6 + 51687/107788*e^5 - 909345/215576*e^4 + 122985/107788*e^3 + 631021/53894*e^2 + 299847/53894*e + 48237/26947', '-290/26947*e^7 + 14631/215576*e^6 + 18161/53894*e^5 - 476355/215576*e^4 - 133491/107788*e^3 + 608225/53894*e^2 + 43463/53894*e - 846601/26947', '-5421/215576*e^7 + 26835/215576*e^6 + 230931/215576*e^5 - 966661/215576*e^4 - 322556/26947*e^3 + 833169/26947*e^2 + 1696901/53894*e - 568326/26947', '3653/107788*e^7 - 6314/26947*e^6 - 107925/107788*e^5 + 420529/53894*e^4 + 67991/26947*e^3 - 1067629/26947*e^2 - 90539/26947*e + 597672/26947', '6165/862304*e^7 - 2557/53894*e^6 - 219289/862304*e^5 + 767157/431152*e^4 + 417071/215576*e^3 - 3011283/215576*e^2 - 673899/107788*e + 617436/26947', '-2377/862304*e^7 - 178/26947*e^6 + 245821/862304*e^5 - 124481/431152*e^4 - 1299811/215576*e^3 + 2868655/215576*e^2 + 1070103/107788*e - 265834/26947', '-12191/862304*e^7 + 15065/107788*e^6 + 105147/862304*e^5 - 1837339/431152*e^4 + 1706435/215576*e^3 + 2926537/215576*e^2 - 2967167/107788*e - 454948/26947', '18713/431152*e^7 - 68827/215576*e^6 - 450325/431152*e^5 + 270322/26947*e^4 - 207991/53894*e^3 - 4061785/107788*e^2 + 254413/26947*e + 491157/26947', '-2269/431152*e^7 + 26337/215576*e^6 - 207111/431152*e^5 - 347945/107788*e^4 + 504845/26947*e^3 - 174703/107788*e^2 - 1462982/26947*e - 18577/26947', '20981/431152*e^7 - 51335/107788*e^6 - 153189/431152*e^5 + 2989759/215576*e^4 - 752943/26947*e^3 - 2760563/107788*e^2 + 3091289/53894*e + 83063/26947', '25697/431152*e^7 - 28183/53894*e^6 - 349733/431152*e^5 + 3323501/215576*e^4 - 2509685/107788*e^3 - 3739315/107788*e^2 + 2880577/53894*e + 211850/26947', '8425/862304*e^7 - 16753/215576*e^6 - 172045/862304*e^5 + 1054811/431152*e^4 - 430507/215576*e^3 - 2237147/215576*e^2 + 912111/107788*e + 107949/26947', '10613/215576*e^7 - 69149/215576*e^6 - 325857/215576*e^5 + 2270123/215576*e^4 + 590349/107788*e^3 - 1365311/26947*e^2 - 786815/53894*e + 736773/26947', '16639/431152*e^7 - 60905/215576*e^6 - 427291/431152*e^5 + 480575/53894*e^4 - 36036/26947*e^3 - 3750703/107788*e^2 + 94587/26947*e + 245513/26947', '-37525/431152*e^7 + 37269/53894*e^6 + 758933/431152*e^5 - 4585069/215576*e^4 + 932553/53894*e^3 + 7549431/107788*e^2 - 2310593/53894*e - 808165/26947', '7409/431152*e^7 - 33601/215576*e^6 - 110869/431152*e^5 + 516951/107788*e^4 - 346693/53894*e^3 - 1701781/107788*e^2 + 722316/26947*e + 268445/26947', '-2739/53894*e^7 + 93857/215576*e^6 + 20186/26947*e^5 - 2745045/215576*e^4 + 1945687/107788*e^3 + 1413203/53894*e^2 - 1925003/53894*e - 303613/26947', '493/215576*e^7 - 9509/215576*e^6 + 26331/215576*e^5 + 294907/215576*e^4 - 645645/107788*e^3 - 146307/26947*e^2 + 1665857/53894*e + 351353/26947', '-30867/431152*e^7 + 13799/26947*e^6 + 781551/431152*e^5 - 3387515/215576*e^4 + 275167/107788*e^3 + 5458149/107788*e^2 + 906921/53894*e - 327288/26947', '961/215576*e^7 - 4265/53894*e^6 + 39739/215576*e^5 + 262751/107788*e^4 - 504515/53894*e^3 - 447133/53894*e^2 + 812121/26947*e + 387816/26947', '9865/431152*e^7 - 30613/215576*e^6 - 354657/431152*e^5 + 539995/107788*e^4 + 656279/107788*e^3 - 3454669/107788*e^2 - 229939/26947*e + 392220/26947', '-4707/215576*e^7 + 11861/53894*e^6 + 33047/215576*e^5 - 706969/107788*e^4 + 697447/53894*e^3 + 918259/53894*e^2 - 1009299/26947*e - 338232/26947', '11093/431152*e^7 - 29119/215576*e^6 - 422657/431152*e^5 + 117669/26947*e^4 + 497137/53894*e^3 - 2067565/107788*e^2 - 1015957/26947*e + 36429/26947', '8517/431152*e^7 - 5447/26947*e^6 - 46881/431152*e^5 + 1317581/215576*e^4 - 1402575/107788*e^3 - 1861475/107788*e^2 + 2441351/53894*e + 73116/26947', '-901/215576*e^7 + 791/107788*e^6 + 55949/215576*e^5 - 7321/26947*e^4 - 265349/53894*e^3 + 115705/53894*e^2 + 584728/26947*e - 224914/26947', '28011/431152*e^7 - 124663/215576*e^6 - 313379/431152*e^5 + 1804197/107788*e^4 - 3274067/107788*e^3 - 3274243/107788*e^2 + 1874268/26947*e + 244358/26947', '37781/862304*e^7 - 56915/215576*e^6 - 1277641/862304*e^5 + 3579931/431152*e^4 + 2256973/215576*e^3 - 6635303/215576*e^2 - 6277305/107788*e - 21277/26947', '42013/862304*e^7 - 12487/26947*e^6 - 262769/862304*e^5 + 5589173/431152*e^4 - 6403069/215576*e^3 - 2612315/215576*e^2 + 7317353/107788*e + 9218/26947', '1803/107788*e^7 - 15099/107788*e^6 - 40241/107788*e^5 + 528225/107788*e^4 - 78560/26947*e^3 - 845936/26947*e^2 + 476903/26947*e + 827838/26947', '961/53894*e^7 - 41293/215576*e^6 - 1363/107788*e^5 + 1212757/215576*e^4 - 389249/26947*e^3 - 629811/53894*e^2 + 2374077/53894*e + 96126/26947', '28111/431152*e^7 - 12704/26947*e^6 - 692839/431152*e^5 + 3171131/215576*e^4 - 117553/26947*e^3 - 5820701/107788*e^2 + 399783/53894*e + 577721/26947', '-9959/215576*e^7 + 78289/215576*e^6 + 193967/215576*e^5 - 2295083/215576*e^4 + 1047585/107788*e^3 + 550678/26947*e^2 - 683293/53894*e + 569981/26947', '-6095/431152*e^7 + 33883/215576*e^6 - 46333/431152*e^5 - 465211/107788*e^4 + 396512/26947*e^3 + 199387/107788*e^2 - 911913/26947*e - 120351/26947', '2633/215576*e^7 - 3950/26947*e^6 + 43881/215576*e^5 + 412799/107788*e^4 - 1740469/107788*e^3 + 201233/53894*e^2 + 1147746/26947*e - 180003/26947', '4599/431152*e^7 - 3245/26947*e^6 - 11267/431152*e^5 + 820279/215576*e^4 - 863839/107788*e^3 - 1539693/107788*e^2 + 1475309/53894*e + 60230/26947', '-31345/431152*e^7 + 66711/107788*e^6 + 482725/431152*e^5 - 3954911/215576*e^4 + 2628651/107788*e^3 + 4670867/107788*e^2 - 2628543/53894*e - 17766/26947', '-20455/862304*e^7 + 29141/107788*e^6 - 96605/862304*e^5 - 3335027/431152*e^4 + 4855131/215576*e^3 + 2614417/215576*e^2 - 6403879/107788*e - 317310/26947', '6245/215576*e^7 - 52567/215576*e^6 - 91705/215576*e^5 + 1465253/215576*e^4 - 1066129/107788*e^3 - 123247/26947*e^2 + 445931/53894*e - 483817/26947', '10219/431152*e^7 - 20621/107788*e^6 - 210471/431152*e^5 + 1247525/215576*e^4 - 415145/107788*e^3 - 1756081/107788*e^2 - 148971/53894*e + 153296/26947', '59063/862304*e^7 - 110371/215576*e^6 - 1365779/862304*e^5 + 6824269/431152*e^4 - 1656373/215576*e^3 - 11748373/215576*e^2 + 2012917/107788*e + 504585/26947', '-44719/862304*e^7 + 103297/215576*e^6 + 485115/862304*e^5 - 6064609/431152*e^4 + 5359877/215576*e^3 + 6285093/215576*e^2 - 6566725/107788*e - 36447/26947', '-1083/215576*e^7 - 8955/215576*e^6 + 164511/215576*e^5 + 62841/215576*e^4 - 2016681/107788*e^3 + 617107/26947*e^2 + 2381787/53894*e - 560961/26947', '-27121/431152*e^7 + 11900/26947*e^6 + 708765/431152*e^5 - 2943297/215576*e^4 + 82235/107788*e^3 + 4879235/107788*e^2 + 942417/53894*e - 28716/26947', '-2797/107788*e^7 + 21809/107788*e^6 + 61051/107788*e^5 - 634171/107788*e^4 + 74134/26947*e^3 + 257350/26947*e^2 + 477128/26947*e + 604842/26947', '-967/107788*e^7 + 7829/107788*e^6 + 15365/107788*e^5 - 216495/107788*e^4 + 64119/26947*e^3 + 38345/26947*e^2 + 262927/26947*e - 129148/26947', '-19/431152*e^7 - 7879/215576*e^6 + 93655/431152*e^5 + 25509/26947*e^4 - 355965/53894*e^3 + 223519/107788*e^2 + 657529/26947*e - 453801/26947', '-11663/862304*e^7 + 4409/53894*e^6 + 429819/862304*e^5 - 1205631/431152*e^4 - 929309/215576*e^3 + 3114265/215576*e^2 + 1736829/107788*e + 248358/26947', '-16873/862304*e^7 + 54975/215576*e^6 - 280035/862304*e^5 - 3078039/431152*e^4 + 5523339/215576*e^3 + 1604835/215576*e^2 - 7407303/107788*e - 96999/26947', '63/26947*e^7 - 6059/215576*e^6 + 1537/53894*e^5 + 155055/215576*e^4 - 252457/107788*e^3 + 34661/53894*e^2 + 7005/53894*e - 178381/26947', '-2055/431152*e^7 + 15801/215576*e^6 - 70621/431152*e^5 - 111087/53894*e^4 + 245942/26947*e^3 + 195351/107788*e^2 - 817355/26947*e - 438571/26947', '3099/215576*e^7 - 10557/53894*e^6 + 75657/215576*e^5 + 561633/107788*e^4 - 1180761/53894*e^3 + 117045/53894*e^2 + 1342661/26947*e - 287298/26947', '18297/431152*e^7 - 46209/107788*e^6 - 78997/431152*e^5 + 2697835/215576*e^4 - 3095889/107788*e^3 - 2852543/107788*e^2 + 4015461/53894*e + 388122/26947', '4741/107788*e^7 - 11041/53894*e^6 - 52642/26947*e^5 + 392845/53894*e^4 + 2548655/107788*e^3 - 1278529/26947*e^2 - 2028433/26947*e + 417359/26947', '-5551/215576*e^7 + 21203/107788*e^6 + 131395/215576*e^5 - 337397/53894*e^4 + 71329/26947*e^3 + 1387393/53894*e^2 - 273801/26947*e - 427252/26947', '-39287/431152*e^7 + 154481/215576*e^6 + 826835/431152*e^5 - 1160173/53894*e^4 + 384938/26947*e^3 + 6104751/107788*e^2 - 46567/26947*e + 81137/26947', '38747/431152*e^7 - 165671/215576*e^6 - 610147/431152*e^5 + 2495833/107788*e^4 - 3260963/107788*e^3 - 7002267/107788*e^2 + 2262525/26947*e + 587048/26947', '2871/431152*e^7 - 3937/107788*e^6 - 93939/431152*e^5 + 208009/215576*e^4 + 192575/107788*e^3 - 57109/107788*e^2 - 877239/53894*e + 312132/26947', '-51105/862304*e^7 + 46261/107788*e^6 + 1305877/862304*e^5 - 5840893/431152*e^4 + 407569/215576*e^3 + 11745919/215576*e^2 + 705167/107788*e - 1465662/26947', '-57457/862304*e^7 + 101561/215576*e^6 + 1437125/862304*e^5 - 6200771/431152*e^4 + 663503/215576*e^3 + 9732467/215576*e^2 + 900981/107788*e + 20063/26947', '-11763/431152*e^7 + 9797/53894*e^6 + 378127/431152*e^5 - 1334255/215576*e^4 - 472577/107788*e^3 + 3666645/107788*e^2 + 854903/53894*e - 510322/26947', '-22693/431152*e^7 + 106117/215576*e^6 + 246937/431152*e^5 - 1598323/107788*e^4 + 1363761/53894*e^3 + 4381121/107788*e^2 - 1711992/26947*e - 334009/26947', '8569/431152*e^7 - 3575/215576*e^6 - 632237/431152*e^5 + 84461/53894*e^4 + 762984/26947*e^3 - 3151141/107788*e^2 - 2311286/26947*e + 136521/26947', '-6187/431152*e^7 + 8503/107788*e^6 + 259655/431152*e^5 - 627305/215576*e^4 - 702471/107788*e^3 + 2248945/107788*e^2 + 823719/53894*e - 543456/26947', '47957/862304*e^7 - 26045/53894*e^6 - 742889/862304*e^5 + 6215429/431152*e^4 - 4000061/215576*e^3 - 7593363/215576*e^2 + 4348937/107788*e - 104284/26947', '-1285/107788*e^7 + 34211/215576*e^6 - 28293/107788*e^5 - 903899/215576*e^4 + 1826805/107788*e^3 - 166585/53894*e^2 - 1833149/53894*e + 423807/26947', '-20279/431152*e^7 + 45135/107788*e^6 + 227195/431152*e^5 - 2675341/215576*e^4 + 2503447/107788*e^3 + 3215933/107788*e^2 - 4314905/53894*e - 129820/26947', '-1091/53894*e^7 + 2842/26947*e^6 + 24677/26947*e^5 - 117377/26947*e^4 - 570571/53894*e^3 + 1117839/26947*e^2 + 508292/26947*e - 1040862/26947', '-21301/431152*e^7 + 99033/215576*e^6 + 181793/431152*e^5 - 1412345/107788*e^4 + 719513/26947*e^3 + 1995161/107788*e^2 - 1439610/26947*e - 319857/26947', '-455/431152*e^7 - 4977/53894*e^6 + 325299/431152*e^5 + 401021/215576*e^4 - 2308841/107788*e^3 + 1974389/107788*e^2 + 2586557/53894*e - 197746/26947', '5265/431152*e^7 - 19553/107788*e^6 + 177787/431152*e^5 + 956891/215576*e^4 - 2316879/107788*e^3 + 1528985/107788*e^2 + 2167567/53894*e - 337204/26947', '-92507/862304*e^7 + 97503/107788*e^6 + 1427463/862304*e^5 - 11509711/431152*e^4 + 7850791/215576*e^3 + 13095837/215576*e^2 - 8428707/107788*e - 297334/26947', '-3505/862304*e^7 + 11409/107788*e^6 - 389003/862304*e^5 - 1096781/431152*e^4 + 3645173/215576*e^3 - 1981105/215576*e^2 - 5476233/107788*e + 644630/26947', '141/215576*e^7 - 12121/215576*e^6 + 79353/215576*e^5 + 243075/215576*e^4 - 295588/26947*e^3 + 330057/26947*e^2 + 801227/53894*e - 455232/26947', '1388/26947*e^7 - 81735/215576*e^6 - 140579/107788*e^5 + 2632103/215576*e^4 - 78241/26947*e^3 - 2845117/53894*e^2 + 879335/53894*e + 674898/26947', '3647/53894*e^7 - 111001/215576*e^6 - 39884/26947*e^5 + 3387645/215576*e^4 - 1066003/107788*e^3 - 2591187/53894*e^2 + 1123445/53894*e - 395017/26947', '14101/215576*e^7 - 14901/26947*e^6 - 238825/215576*e^5 + 1782597/107788*e^4 - 1009345/53894*e^3 - 2267043/53894*e^2 + 738867/26947*e + 331632/26947', '5401/215576*e^7 - 15329/107788*e^6 - 208933/215576*e^5 + 294823/53894*e^4 + 217326/26947*e^3 - 2552901/53894*e^2 - 78996/26947*e + 1502082/26947', '-4833/215576*e^7 + 21111/107788*e^6 + 58457/215576*e^5 - 157167/26947*e^4 + 557217/53894*e^3 + 848963/53894*e^2 - 797967/26947*e - 771946/26947', '-15727/215576*e^7 + 61839/107788*e^6 + 351159/215576*e^5 - 981471/53894*e^4 + 552193/53894*e^3 + 3962273/53894*e^2 - 767971/26947*e - 1226998/26947', '13969/215576*e^7 - 53357/107788*e^6 - 319993/215576*e^5 + 812335/53894*e^4 - 350409/53894*e^3 - 2367869/53894*e^2 - 167662/26947*e - 371674/26947', '9765/215576*e^7 - 80341/215576*e^6 - 190773/215576*e^5 + 2468619/215576*e^4 - 1034565/107788*e^3 - 1006519/26947*e^2 + 954237/53894*e + 1060859/26947', '-7117/431152*e^7 + 21323/107788*e^6 - 91735/431152*e^5 - 1079771/215576*e^4 + 2068441/107788*e^3 - 1021385/107788*e^2 - 2274431/53894*e + 120764/26947', '-1141/215576*e^7 + 1200/26947*e^6 - 3439/215576*e^5 - 73901/107788*e^4 + 227195/53894*e^3 - 768237/53894*e^2 + 171156/26947*e + 578616/26947', '1715/431152*e^7 - 1969/53894*e^6 - 40459/431152*e^5 + 271107/215576*e^4 - 8623/26947*e^3 - 850277/107788*e^2 + 96689/53894*e + 21927/26947', '-6937/215576*e^7 + 19429/107788*e^6 + 249223/215576*e^5 - 162210/26947*e^4 - 940401/107788*e^3 + 1703017/53894*e^2 + 811289/26947*e - 751851/26947', '-1249/26947*e^7 + 47443/107788*e^6 + 46417/107788*e^5 - 1382389/107788*e^4 + 2562721/107788*e^3 + 666073/26947*e^2 - 1369952/26947*e - 481623/26947', '-8181/431152*e^7 + 16287/107788*e^6 + 194697/431152*e^5 - 1077267/215576*e^4 + 195631/107788*e^3 + 2441487/107788*e^2 - 202415/53894*e + 415346/26947', '-1623/215576*e^7 - 1097/53894*e^6 + 165623/215576*e^5 - 8337/107788*e^4 - 468788/26947*e^3 + 902585/53894*e^2 + 1513392/26947*e + 371204/26947', '501/53894*e^7 - 15751/215576*e^6 - 13441/107788*e^5 + 348983/215576*e^4 - 73072/26947*e^3 + 641471/53894*e^2 - 967261/53894*e - 444298/26947', '-20761/215576*e^7 + 20819/26947*e^6 + 396257/215576*e^5 - 2501989/107788*e^4 + 588497/26947*e^3 + 3323829/53894*e^2 - 1086379/26947*e + 179676/26947', '12407/431152*e^7 - 6973/26947*e^6 - 148707/431152*e^5 + 1610719/215576*e^4 - 1373651/107788*e^3 - 1036941/107788*e^2 + 1603995/53894*e - 866410/26947', '-336/26947*e^7 + 7175/107788*e^6 + 13866/26947*e^5 - 224851/107788*e^4 - 341785/53894*e^3 + 132129/26947*e^2 + 1086147/26947*e + 699860/26947', '7919/431152*e^7 - 32015/215576*e^6 - 105931/431152*e^5 + 424569/107788*e^4 - 384975/53894*e^3 + 331541/107788*e^2 + 117540/26947*e - 615621/26947', '-71/107788*e^7 + 3007/26947*e^6 - 75505/107788*e^5 - 163541/53894*e^4 + 600217/26947*e^3 + 4153/26947*e^2 - 2051044/26947*e - 290322/26947', '7749/431152*e^7 - 20763/107788*e^6 + 211/431152*e^5 + 1207143/215576*e^4 - 821331/53894*e^3 - 1046855/107788*e^2 + 2874865/53894*e - 231109/26947', '100587/862304*e^7 - 26636/26947*e^6 - 1476039/862304*e^5 + 12481859/431152*e^4 - 9055351/215576*e^3 - 13103909/215576*e^2 + 9130303/107788*e + 518054/26947', '-2033/53894*e^7 + 11555/53894*e^6 + 38821/26947*e^5 - 386937/53894*e^4 - 716933/53894*e^3 + 972233/26947*e^2 + 1161556/26947*e - 93492/26947', '-22765/431152*e^7 + 104625/215576*e^6 + 261457/431152*e^5 - 1560553/107788*e^4 + 1308297/53894*e^3 + 4002761/107788*e^2 - 1844090/26947*e - 496423/26947', '43799/431152*e^7 - 39947/53894*e^6 - 1090027/431152*e^5 + 4999835/215576*e^4 - 597445/107788*e^3 - 9287297/107788*e^2 - 48741/53894*e + 1069562/26947', '-19299/862304*e^7 + 58283/215576*e^6 - 257873/862304*e^5 - 3074761/431152*e^4 + 5755873/215576*e^3 - 1119511/215576*e^2 - 7000549/107788*e + 407153/26947', '970/26947*e^7 - 39801/107788*e^6 - 4993/53894*e^5 + 1137217/107788*e^4 - 696087/26947*e^3 - 440631/26947*e^2 + 1587340/26947*e + 193716/26947', '84183/862304*e^7 - 88229/107788*e^6 - 1401539/862304*e^5 + 10560019/431152*e^4 - 6303567/215576*e^3 - 13507681/215576*e^2 + 5723959/107788*e + 246038/26947', '-25567/431152*e^7 + 29605/53894*e^6 + 287587/431152*e^5 - 3468875/215576*e^4 + 2853689/107788*e^3 + 3560161/107788*e^2 - 2418527/53894*e + 121818/26947', '-2631/215576*e^7 + 3865/107788*e^6 + 153327/215576*e^5 - 40848/26947*e^4 - 631225/53894*e^3 + 725475/53894*e^2 + 859659/26947*e + 835754/26947', '3397/431152*e^7 - 20927/215576*e^6 - 20369/431152*e^5 + 93999/26947*e^4 - 329383/53894*e^3 - 2520697/107788*e^2 + 1259987/26947*e + 730667/26947', '15805/431152*e^7 - 21129/107788*e^6 - 582465/431152*e^5 + 1342167/215576*e^4 + 1238693/107788*e^3 - 2582291/107788*e^2 - 2565697/53894*e + 21458/26947', '-4831/107788*e^7 + 45299/107788*e^6 + 40089/107788*e^5 - 1324409/107788*e^4 + 686051/26947*e^3 + 670844/26947*e^2 - 2027379/26947*e - 70708/26947', '-19865/431152*e^7 + 35951/107788*e^6 + 467069/431152*e^5 - 2166551/215576*e^4 + 446583/107788*e^3 + 3127955/107788*e^2 + 357021/53894*e - 368134/26947', '1695/215576*e^7 + 1843/53894*e^6 - 180143/215576*e^5 - 67203/107788*e^4 + 524252/26947*e^3 - 416437/53894*e^2 - 1707295/26947*e - 423634/26947', '45473/862304*e^7 - 51485/107788*e^6 - 457525/862304*e^5 + 5857389/431152*e^4 - 5563529/215576*e^3 - 3616279/215576*e^2 + 5096777/107788*e - 521116/26947', '9891/862304*e^7 - 12043/215576*e^6 - 431759/862304*e^5 + 873065/431152*e^4 + 1307135/215576*e^3 - 2617417/215576*e^2 - 2765751/107788*e - 724447/26947', '-8283/431152*e^7 + 10739/107788*e^6 + 323055/431152*e^5 - 727729/215576*e^4 - 823821/107788*e^3 + 2121053/107788*e^2 + 1893449/53894*e - 259366/26947', '4315/431152*e^7 - 238/26947*e^6 - 313287/431152*e^5 + 166115/215576*e^4 + 1537029/107788*e^3 - 1630869/107788*e^2 - 2680673/53894*e + 39378/26947', '-7433/431152*e^7 + 21043/107788*e^6 + 7921/431152*e^5 - 1305139/215576*e^4 + 759357/53894*e^3 + 2168495/107788*e^2 - 2924959/53894*e - 268689/26947', '3877/107788*e^7 - 30943/107788*e^6 - 63275/107788*e^5 + 900989/107788*e^4 - 323451/26947*e^3 - 429449/26947*e^2 + 1197048/26947*e - 668710/26947', '1000/26947*e^7 - 60673/215576*e^6 - 22020/26947*e^5 + 1797781/215576*e^4 - 508849/107788*e^3 - 994359/53894*e^2 - 390537/53894*e - 367291/26947', '11787/862304*e^7 - 18655/107788*e^6 + 48185/862304*e^5 + 2279167/431152*e^4 - 2831875/215576*e^3 - 3324949/215576*e^2 + 5179467/107788*e + 443912/26947', '8899/431152*e^7 - 59613/215576*e^6 + 163517/431152*e^5 + 211160/26947*e^4 - 3041659/107788*e^3 - 1093627/107788*e^2 + 2008358/26947*e + 571028/26947', '24701/431152*e^7 - 70495/215576*e^6 - 903389/431152*e^5 + 600335/53894*e^4 + 1776363/107788*e^3 - 6763641/107788*e^2 - 1217933/26947*e + 417300/26947', '-155/107788*e^7 + 8111/215576*e^6 - 4671/107788*e^5 - 328591/215576*e^4 + 239437/107788*e^3 + 823127/53894*e^2 - 385737/53894*e - 1129095/26947', '21801/431152*e^7 - 45833/107788*e^6 - 354485/431152*e^5 + 2686347/215576*e^4 - 1685549/107788*e^3 - 2762983/107788*e^2 + 1710821/53894*e - 438558/26947', '-37221/862304*e^7 + 20919/53894*e^6 + 446121/862304*e^5 - 5047733/431152*e^4 + 4120953/215576*e^3 + 7530131/215576*e^2 - 4811985/107788*e - 505834/26947', '-9669/431152*e^7 + 2463/26947*e^6 + 494777/431152*e^5 - 755669/215576*e^4 - 1827411/107788*e^3 + 2921723/107788*e^2 + 3032433/53894*e - 30934/26947', '18081/431152*e^7 - 69947/215576*e^6 - 358801/431152*e^5 + 508801/53894*e^4 - 841761/107788*e^3 - 1993545/107788*e^2 - 153592/26947*e - 45226/26947'], 'hecke_polynomial': 'x^8 - 10*x^7 - 5*x^6 + 292*x^5 - 664*x^4 - 596*x^3 + 1920*x^2 + 368*x - 384', 'label': '4.4.12197.1-25.2-e'}
• hmf_fields •

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

  
  {'degree': 4, 'discriminant': 12197, 'ideals': ['[1, 1, 1]', '[5, 5, w + 1]', '[5, 5, -w + 2]', '[11, 11, w^3 - w^2 - 4*w + 2]', '[13, 13, w^3 - w^2 - 4*w]', '[16, 2, 2]', '[17, 17, -w^2 + w + 3]', '[19, 19, w^3 - 5*w]', '[19, 19, -w + 3]', '[23, 23, 2*w^3 - 2*w^2 - 9*w + 4]', '[23, 23, w^2 - 2]', '[25, 5, w^2 - 3]', '[25, 5, -w^2 + w + 2]', '[25, 25, -w^3 + w^2 + 5*w - 1]', '[25, 25, -w^3 + 4*w - 2]', '[37, 37, -w^3 + 2*w^2 + 4*w - 6]', '[37, 37, -w^3 + w^2 + 6*w - 4]', '[41, 41, w^2 - w - 5]', '[47, 47, w^3 - 6*w + 1]', '[55, 55, -w - 3]', '[55, 55, w^3 - 5*w + 1]', '[61, 61, -w^3 + w^2 + 6*w - 2]', '[65, 65, w^3 - w^2 - 6*w + 3]', '[65, 65, 2*w - 3]', '[67, 67, 2*w^3 - w^2 - 9*w + 2]', '[67, 67, w^3 - 7*w + 3]', '[73, 73, 2*w^3 - w^2 - 9*w]', '[80, 10, 2*w + 2]', '[80, 10, -2*w + 4]', '[81, 3, -3]', '[85, 85, -w^3 + 4*w + 3]', '[85, 85, w^3 - 5*w + 2]', '[89, 89, w^2 + w - 4]', '[95, 95, -w^2 + 2*w + 3]', '[95, 95, w^3 - 7*w + 1]', '[95, 95, -w^3 + w^2 + 3*w - 4]', '[95, 95, -2*w^3 + w^2 + 9*w - 1]', '[101, 101, 2*w + 3]', '[103, 103, -2*w^2 - 3*w + 1]', '[103, 103, -w^3 + 6*w - 2]', '[113, 113, w^3 - 7*w]', '[115, 115, -w^3 + 2*w^2 + 2*w - 4]', '[115, 115, 4*w^3 - 5*w^2 - 16*w + 10]', '[115, 115, w^3 + w^2 - 2*w - 2]', '[115, 115, 2*w^3 - w^2 - 11*w + 2]', '[121, 121, -2*w^3 + 11*w + 1]', '[125, 5, -w^3 + 2*w^2 + 3*w - 6]', '[125, 5, w^3 + w^2 - 3*w - 3]', '[125, 25, 2*w^3 - w^2 - 10*w + 3]', '[125, 25, w^3 - 2*w^2 - 6*w + 7]', '[125, 125, -2*w^3 + 2*w^2 + 8*w - 3]', '[125, 125, w - 4]', '[127, 127, w^3 - 2*w + 3]', '[127, 127, -2*w^3 + 2*w^2 + 9*w - 3]', '[131, 131, -w^3 + w^2 + 4*w - 6]', '[131, 131, 2*w^3 - w^2 - 11*w + 1]', '[137, 137, -2*w^3 + 9*w]', '[143, 143, w^3 - w^2 - 3*w + 5]', '[157, 157, 2*w^2 - w - 2]', '[163, 163, -2*w^3 + 3*w^2 + 8*w - 6]', '[167, 167, w^3 + w^2 - 5*w - 4]', '[169, 169, -w^3 - w^2 + 5*w + 3]', '[173, 173, w^3 - 2*w^2 - 6*w + 3]', '[173, 173, -2*w^3 + w^2 + 7*w + 1]', '[176, 22, 2*w^3 - 2*w^2 - 8*w + 4]', '[179, 179, w^3 + w^2 - 7*w - 5]', '[181, 181, 3*w^3 - 3*w^2 - 13*w + 6]', '[185, 185, w^2 + w - 5]', '[185, 185, 2*w^3 - 2*w^2 - 11*w + 4]', '[185, 185, -w^3 + 2*w^2 + 5*w - 3]', '[185, 185, -2*w^3 + w^2 + 13*w - 9]', '[187, 187, -2*w^2 - w + 4]', '[197, 197, 2*w^3 - 9*w - 4]', '[197, 197, 2*w^3 - w^2 - 9*w + 5]', '[199, 199, -w^3 + 2*w^2 + 4*w - 2]', '[205, 205, w^3 - 6*w - 5]', '[205, 205, -w^3 + 3*w^2 + 3*w - 10]', '[208, 26, 2*w^3 - 2*w^2 - 8*w]', '[209, 209, -w^2 + 2*w + 4]', '[209, 209, w^3 + w^2 - 4*w - 5]', '[211, 211, 2*w^3 - w^2 - 8*w + 3]', '[221, 221, 2*w^3 - 2*w^2 - 10*w + 3]', '[227, 227, 3*w^3 - w^2 - 14*w + 2]', '[229, 229, -w - 4]', '[233, 233, -2*w^3 + 2*w^2 + 11*w - 2]', '[235, 235, -2*w^3 + w^2 + 8*w]', '[235, 235, -w^3 - w^2 + 10*w - 3]', '[239, 239, w^3 - 4*w - 6]', '[241, 241, -w^3 + w^2 + 7*w - 1]', '[247, 247, -2*w^3 + 3*w^2 + 7*w - 4]', '[247, 247, 2*w^3 - w^2 - 10*w + 4]', '[251, 251, w^3 - 5*w - 5]', '[253, 253, -w^3 + w^2 + 7*w - 4]', '[253, 253, 2*w^3 - 3*w^2 - 11*w + 15]', '[256, 4, 4]', '[263, 263, -w^3 + 2*w^2 + 3*w - 7]', '[269, 269, -2*w^3 + 2*w^2 + 9*w - 2]', '[271, 271, 3*w^3 - 4*w^2 - 12*w + 8]', '[272, 34, -2*w^2 + 2*w + 6]', '[275, 55, -2*w^3 + 2*w^2 + 11*w - 6]', '[275, 55, w^3 - 8*w + 3]', '[275, 275, w^2 + w - 6]', '[275, 275, -2*w^2 + 7]', '[277, 277, -2*w^3 + 2*w^2 + 11*w - 5]', '[281, 281, w^3 - 3*w - 3]', '[283, 283, -w^3 + 2*w^2 + 6*w - 8]', '[289, 289, 2*w^3 - w^2 - 8*w + 2]', '[299, 299, -w^3 - w^2 + 7*w]', '[299, 299, -2*w^3 + w^2 + 7*w + 7]', '[304, 38, 2*w^3 - 10*w]', '[304, 38, -2*w + 6]', '[305, 305, -2*w^3 + w^2 + 11*w - 5]', '[305, 305, -w^3 + 2*w^2 + 7*w - 1]', '[313, 313, -w^3 + 2*w^2 + 2*w - 5]', '[313, 313, -w^3 + 2*w^2 + 5*w - 2]', '[317, 317, -w^3 + w^2 + 7*w - 2]', '[317, 317, 2*w^2 - 2*w - 3]', '[323, 323, 3*w^3 - 2*w^2 - 14*w]', '[323, 323, w^3 - w^2 - 7*w + 3]', '[325, 65, w^3 - 2*w^2 - 6*w + 2]', '[325, 65, -2*w^3 + 11*w]', '[325, 325, 2*w^2 - w - 3]', '[325, 325, 2*w^3 - w^2 - 9*w - 4]', '[335, 335, 3*w^3 - 13*w]', '[335, 335, 3*w^3 - 3*w^2 - 14*w + 6]', '[335, 335, 2*w^3 - 2*w^2 - 7*w + 2]', '[335, 335, w^2 - 2*w - 5]', '[337, 337, -3*w^3 + 3*w^2 + 16*w - 11]', '[337, 337, 2*w^3 - 9*w + 1]', '[361, 19, 2*w^3 - 8*w + 3]', '[361, 19, 2*w^3 - 12*w + 1]', '[361, 361, -2*w^3 + w^2 + 10*w - 5]', '[361, 361, 2*w^3 - 2*w^2 - 7*w + 4]', '[365, 365, 3*w^3 - 3*w^2 - 12*w + 2]', '[365, 365, 3*w^3 - 15*w - 2]', '[367, 367, -w^3 + w^2 + 2*w - 4]', '[367, 367, 4*w^3 - 3*w^2 - 19*w + 9]', '[368, 46, 4*w^3 - 4*w^2 - 18*w + 8]', '[368, 46, 2*w^2 - 4]', '[383, 383, -w^3 + 2*w^2 + 7*w]', '[383, 383, 2*w^3 - 4*w^2 - 10*w + 9]', '[383, 383, w^3 + w^2 - 7*w - 6]', '[383, 383, -w^3 + 3*w^2 + 6*w - 10]', '[389, 389, -3*w + 5]', '[389, 389, 2*w^2 - 2*w - 5]', '[391, 391, 5*w^3 - 3*w^2 - 27*w + 10]', '[391, 391, w - 5]', '[397, 397, -w^3 + 2*w^2 + 6*w - 11]', '[397, 397, 3*w^3 - 4*w^2 - 11*w + 8]', '[397, 397, 2*w^3 - 2*w^2 - 7*w + 3]', '[397, 397, -2*w^3 + w^2 + 7*w]', '[400, 10, 2*w^2 - 6]', '[400, 10, -2*w^2 + 2*w + 4]', '[400, 50, -2*w^3 + 2*w^2 + 10*w - 2]', '[400, 50, -2*w^3 + 8*w - 4]', '[401, 401, w^3 - w^2 - 4*w - 3]', '[401, 401, -2*w^3 + w^2 + 10*w - 6]', '[405, 15, -3*w - 3]', '[405, 15, 3*w - 6]', '[407, 407, -3*w^3 + 5*w^2 + 12*w - 13]', '[407, 407, -2*w^3 + 9*w + 6]', '[409, 409, -3*w^3 + 2*w^2 + 16*w]', '[409, 409, -4*w^3 + 2*w^2 + 19*w - 1]', '[419, 419, w^2 - 2*w - 6]', '[419, 419, w^3 - 8*w + 2]', '[421, 421, -w^3 + w^2 + 4*w - 7]', '[425, 85, w^3 - 3*w^2 - 5*w + 9]', '[425, 85, w^2 - 8]', '[425, 425, -2*w^3 + 3*w^2 + 9*w - 6]', '[425, 425, -3*w^3 + w^2 + 16*w - 2]', '[431, 431, 2*w^2 - 5]', '[431, 431, w^2 + 2*w - 5]', '[433, 433, w^3 + 2*w^2 - 8*w - 3]', '[433, 433, -3*w^3 + w^2 + 13*w - 2]', '[437, 437, 6*w^3 - 7*w^2 - 25*w + 14]', '[437, 437, -w^3 - 2*w^2 + 7*w + 9]', '[437, 437, -w^3 + 3*w^2 + 2*w - 6]', '[437, 437, -w^3 + 2*w^2 + 6*w - 1]', '[443, 443, 2*w^3 - w^2 - 12*w + 4]', '[445, 445, -w^3 + w^2 + 6*w - 8]', '[445, 445, w^3 + 2*w^2 - 3*w - 4]', '[449, 449, 3*w + 5]', '[449, 449, 2*w^3 - w^2 - 10*w - 4]', '[451, 451, -4*w^3 + 3*w^2 + 20*w - 9]', '[461, 461, w^3 + w^2 - 4*w - 6]', '[461, 461, 2*w^3 - 4*w^2 - 7*w + 10]', '[463, 463, 2*w^2 - w - 4]', '[467, 467, 2*w^3 + w^2 - 11*w - 6]', '[475, 95, -2*w^3 + 2*w^2 + 11*w - 1]', '[475, 95, 2*w^3 - 2*w^2 - 9*w]', '[475, 95, -w^3 + 3*w^2 + 3*w - 9]', '[475, 95, 2*w^3 - 2*w^2 - 9*w + 10]', '[475, 475, -3*w^3 + 3*w^2 + 13*w - 4]', '[475, 475, 3*w^3 - 4*w^2 - 14*w + 10]', '[475, 475, -w^3 + w^2 + 5*w + 3]', '[475, 475, -3*w^3 + 3*w^2 + 12*w - 4]', '[479, 479, -w^3 + 3*w^2 + 5*w - 8]', '[479, 479, w^3 - 8*w + 1]', '[481, 481, -3*w^3 + 4*w^2 + 15*w - 10]', '[481, 481, -w^3 + 3*w^2 - 5]', '[487, 487, -2*w^3 + 3*w^2 + 11*w - 12]', '[487, 487, -w^3 + 2*w^2 + 7*w - 8]', '[505, 505, -2*w^2 + w + 6]', '[505, 505, -2*w^3 + 3*w^2 + 7*w - 3]', '[509, 509, w^3 + 2*w^2 - 4*w - 7]', '[509, 509, -w^3 + 2*w^2 + 6*w - 10]', '[515, 515, 2*w^3 - w^2 - 7*w + 2]', '[515, 515, -w^3 - w^2 + 11*w - 5]', '[515, 515, -w^3 + 2*w^2 - 3]', '[515, 515, -2*w^3 + w^2 + 7*w - 1]', '[517, 517, -w^3 + 3*w^2 + w - 7]', '[523, 523, -3*w^3 + 12*w + 1]', '[529, 23, 3*w^3 - 2*w^2 - 16*w + 8]', '[529, 23, -2*w^3 + w^2 + 9*w - 8]', '[529, 529, 2*w^3 + w^2 - 8*w - 5]', '[529, 529, 2*w^2 - w - 5]', '[533, 533, -4*w^3 + w^2 + 22*w + 1]', '[547, 547, -w^3 + 3*w^2 + 3*w - 2]', '[547, 547, 3*w^3 - 2*w^2 - 15*w + 7]', '[565, 565, 2*w^3 - 2*w^2 - 10*w - 1]', '[565, 565, w^3 + 2*w^2 - 11*w + 1]', '[569, 569, 2*w^3 - 2*w^2 - 10*w + 1]', '[569, 569, w^3 - 3*w - 6]', '[571, 571, 2*w^3 - 10*w + 1]', '[575, 115, 3*w^3 - w^2 - 18*w + 6]', '[575, 115, w^3 - 3*w - 5]', '[575, 115, -w^3 + 3*w - 5]', '[575, 115, -w^2 + w - 3]', '[575, 575, 2*w^2 - 13]', '[575, 575, -4*w^2 - 4*w + 5]', '[575, 575, 2*w^3 - 9*w + 2]', '[575, 575, -3*w^3 + 5*w^2 + 13*w - 15]', '[577, 577, w^3 - w^2 - 3*w - 4]', '[577, 577, -w^3 + w^2 + 8*w - 5]', '[587, 587, 3*w^3 - 2*w^2 - 14*w + 8]', '[592, 74, -2*w^3 + 4*w^2 + 8*w - 12]', '[592, 74, -2*w^3 + 2*w^2 + 12*w - 8]', '[593, 593, -3*w^3 + 3*w^2 + 16*w - 7]', '[605, 605, w^3 - 2*w^2 - 2*w + 6]', '[605, 605, -3*w^3 + 2*w^2 + 13*w - 5]', '[611, 611, w^3 + 3*w^2 - 11*w - 5]', '[619, 619, -2*w^3 + w^2 + 12*w - 3]', '[625, 5, 5]', '[625, 25, -w^3 + w^2 + 3*w - 8]', '[625, 25, -w^3 + 2*w^2 + w + 3]', '[625, 25, w^3 - 4*w^2 - 8*w + 7]', '[625, 25, 3*w^3 - w^2 - 14*w + 3]', '[625, 125, -2*w^3 + 11*w - 1]', '[625, 125, 3*w^3 - w^2 - 13*w + 1]', '[625, 625, w^2 - 3*w - 4]', '[625, 625, -w^3 + 6*w + 6]', '[629, 629, -4*w^3 + 5*w^2 + 16*w - 11]', '[629, 629, -3*w^3 + 2*w^2 + 12*w - 7]', '[635, 635, -2*w^3 + w^2 + 12*w - 1]', '[635, 635, -2*w^3 + 4*w^2 + 6*w - 5]', '[635, 635, -4*w^3 + 5*w^2 + 15*w - 8]', '[635, 635, w^3 - 3*w^2 - 4*w + 7]', '[641, 641, -w^3 + 3*w^2 + 3*w - 8]', '[643, 643, 2*w^3 - 2*w^2 - 11*w]', '[655, 655, -2*w^3 + 3*w^2 + 11*w - 13]', '[655, 655, 3*w^3 - 2*w^2 - 16*w - 1]', '[655, 655, -w^3 + w - 5]', '[655, 655, 3*w^3 - w^2 - 17*w + 4]', '[656, 82, 2*w^2 - 2*w - 10]', '[659, 659, 2*w^3 + 2*w^2 - 10*w - 11]', '[659, 659, w^3 - 5*w - 6]', '[661, 661, 3*w^3 - w^2 - 13*w]', '[671, 671, -w^3 + 3*w^2 + 4*w - 9]', '[673, 673, -w^3 + 3*w^2 + 3*w - 7]', '[685, 685, -w^3 + w^2 + w + 4]', '[685, 685, -2*w^3 + w^2 + 12*w - 2]', '[691, 691, -3*w^3 + 3*w^2 + 12*w - 8]', '[691, 691, 2*w^3 - w^2 - 8*w + 8]', '[697, 697, w^3 + 2*w^2 - 5*w - 14]', '[701, 701, w^3 - w^2 - 7*w - 4]', '[701, 701, 4*w^3 - 2*w^2 - 17*w + 7]', '[703, 703, w^2 + 2*w - 6]', '[703, 703, -2*w^3 + 3*w^2 + 12*w - 9]', '[703, 703, -3*w^3 + 2*w^2 + 19*w - 13]', '[703, 703, -3*w^3 + 3*w^2 + 14*w - 5]', '[709, 709, 3*w^3 - 3*w^2 - 10*w]', '[715, 715, -3*w^3 + 2*w^2 + 15*w + 1]', '[715, 715, -w^3 - 2*w^2 + 8*w + 4]', '[719, 719, -w^3 + w^2 + 2*w - 6]', '[719, 719, -w^3 + 3*w^2 + 4*w - 8]', '[733, 733, w^3 + w^2 - 4*w - 7]', '[733, 733, -3*w^3 + 2*w^2 + 13*w - 4]', '[733, 733, -w^2 - 3]', '[733, 733, -2*w^3 + 3*w^2 + 8*w - 4]', '[737, 737, w^3 - 2*w^2 - 4*w + 11]', '[737, 737, -4*w^3 + 3*w^2 + 16*w + 1]', '[739, 739, -3*w - 7]', '[743, 743, 3*w^3 - 2*w^2 - 13*w + 3]', '[743, 743, -4*w^3 + 5*w^2 + 16*w - 9]', '[743, 743, w^3 + w^2 - 3*w - 5]', '[743, 743, 3*w^3 - 3*w^2 - 11*w + 2]', '[751, 751, -3*w^3 + 3*w^2 + 16*w - 8]', '[752, 94, 2*w^3 - 12*w + 2]', '[757, 757, 3*w^3 - 3*w^2 - 12*w + 5]', '[757, 757, 2*w^3 - 4*w^2 - 7*w + 13]', '[761, 761, -3*w^3 + 4*w^2 + 16*w - 17]', '[769, 769, -3*w^3 + 4*w^2 + 17*w - 7]', '[769, 769, 3*w^3 + w^2 - 17*w - 6]', '[779, 779, -w^3 + 4*w^2 + 2*w - 15]', '[779, 779, -5*w^3 + 2*w^2 + 24*w]', '[785, 785, 2*w^3 + w^2 - 3*w - 2]', '[785, 785, -2*w^3 + 5*w^2 - 4]', '[793, 793, w^3 + w^2 - 8*w - 5]', '[797, 797, -3*w^3 + 4*w^2 + 11*w - 5]', '[797, 797, -3*w^3 + 5*w^2 + 11*w - 14]', '[799, 799, -4*w^3 + 4*w^2 + 16*w - 3]', '[803, 803, -w^3 + 4*w + 7]', '[811, 811, -3*w^3 + 2*w^2 + 12*w]', '[811, 811, -w^3 + 3*w^2 + 7*w - 4]', '[815, 815, -5*w^3 + 8*w^2 + 16*w - 14]', '[815, 815, -w^3 + w^2 + 8*w - 4]', '[821, 821, w^3 + 2*w^2 - 4*w - 6]', '[823, 823, -2*w^3 + 3*w^2 + 11*w - 5]', '[823, 823, 3*w^3 - 2*w^2 - 15*w + 8]', '[829, 829, -w^3 - w^2 + 4*w + 10]', '[835, 835, 3*w^3 + w^2 - 12*w - 5]', '[835, 835, 2*w^2 - 3*w - 7]', '[839, 839, 3*w^3 - 19*w + 1]', '[845, 845, -w^3 + 2*w^2 + 8*w - 5]', '[845, 845, -2*w^2 + 4*w + 5]', '[851, 851, 5*w^3 - 3*w^2 - 23*w + 1]', '[851, 851, 2*w^3 - 2*w^2 - 10*w + 11]', '[851, 851, 4*w^3 - w^2 - 18*w]', '[851, 851, -3*w^3 + 3*w^2 + 15*w - 5]', '[853, 853, -5*w^3 + 3*w^2 + 23*w - 9]', '[863, 863, w^3 - 4*w^2 - w + 11]', '[865, 865, 3*w^3 - 3*w^2 - 12*w + 7]', '[865, 865, -3*w^2 - 6*w + 2]', '[865, 865, -3*w^3 + 5*w^2 + 7*w]', '[865, 865, -3*w^3 - 2*w^2 + 14*w + 3]', '[871, 871, w^3 - w^2 - 5*w + 8]', '[871, 871, -3*w^3 + 14*w + 7]', '[877, 877, -3*w^3 + 2*w^2 + 17*w - 1]', '[880, 110, -2*w - 6]', '[880, 110, 2*w^3 - 10*w + 2]', '[883, 883, -3*w^3 + 13*w - 1]', '[891, 33, -3*w^3 + 3*w^2 + 12*w - 6]', '[893, 893, 2*w^3 - w^2 - 9*w - 5]', '[893, 893, -2*w^3 - w^2 + 16*w - 4]', '[895, 895, 3*w^3 - w^2 - 15*w - 6]', '[895, 895, 4*w^2 - 6*w - 9]', '[905, 905, 3*w^3 - w^2 - 16*w + 3]', '[905, 905, 6*w^3 - 8*w^2 - 23*w + 15]', '[907, 907, -w^3 + 3*w^2 + 2*w - 10]', '[907, 907, -3*w^3 + w^2 + 11*w - 5]', '[919, 919, -2*w^3 + 3*w^2 + 14*w]', '[919, 919, 2*w^3 - w^2 - 13*w + 6]', '[919, 919, -w^3 + 2*w^2 + w - 5]', '[919, 919, w - 6]', '[925, 185, -w^3 + w^2 + 7*w - 10]', '[925, 185, -w^3 + w^2 + 8*w - 3]', '[925, 185, -3*w^3 + 4*w^2 + 10*w - 7]', '[925, 185, -4*w^3 + 4*w^2 + 17*w - 12]', '[925, 925, 2*w^3 - 4*w^2 - 13*w + 13]', '[925, 925, 4*w^3 - 3*w^2 - 20*w + 10]', '[925, 925, 2*w^3 - 3*w^2 - 7*w + 10]', '[925, 925, w^3 + 2*w^2 - 4*w - 5]', '[935, 935, 3*w^3 - 3*w^2 - 13*w + 3]', '[935, 935, w^3 + 2*w^2 - 6*w - 9]', '[937, 937, 3*w^3 - 2*w^2 - 11*w + 7]', '[943, 943, -w^3 + 4*w^2 + 5*w - 14]', '[943, 943, 2*w^2 + w - 9]', '[949, 949, -5*w^3 + 2*w^2 + 22*w + 7]', '[953, 953, w^3 + w^2 - 4*w - 8]', '[953, 953, w^3 + 2*w^2 - 5*w - 8]', '[961, 31, -w^3 + 2*w^2 + 2*w - 7]', '[961, 31, w^2 - 3*w - 5]', '[967, 967, 3*w^3 - w^2 - 12*w + 3]', '[967, 967, w^2 + 2*w - 7]', '[971, 971, -w^3 + 3*w^2 + 9*w - 1]', '[971, 971, w^3 - w^2 - 4*w - 4]', '[976, 122, -2*w^3 + 2*w^2 + 12*w - 4]', '[977, 977, w^3 + 2*w^2 - 5*w - 13]', '[979, 979, -3*w^3 + 4*w^2 + 14*w - 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3*w^2 - 13*w + 1]', '[1793, 1793, -3*w^3 + 3*w^2 + 19*w - 18]', '[1801, 1801, w^3 + w^2 - 3*w - 7]', '[1801, 1801, -3*w^3 + 2*w^2 + 17*w - 5]', '[1805, 95, -w^2 + 7*w - 7]', '[1805, 95, 4*w^3 - 2*w^2 - 17*w - 1]', '[1805, 95, 2*w^3 - 2*w^2 - 13*w + 8]', '[1805, 95, -3*w^2 + w + 5]', '[1805, 1805, 2*w^3 + w^2 - 9*w + 2]', '[1805, 1805, -3*w^3 + w^2 + 11*w - 3]', '[1805, 1805, -w^3 - w^2 + w - 5]', '[1805, 1805, -3*w^3 + w^2 + 12*w + 6]', '[1808, 226, 2*w^3 - 14*w]', '[1811, 1811, 5*w^3 - 4*w^2 - 26*w + 15]', '[1823, 1823, -6*w^3 + 7*w^2 + 26*w - 19]', '[1825, 365, 3*w^3 - 19*w - 1]', '[1825, 365, 2*w^3 - 11*w + 5]', '[1825, 1825, -w^3 + w^2 + w - 6]', '[1825, 1825, 4*w^3 - 19*w - 9]', '[1831, 1831, 3*w^2 - 3*w - 8]', '[1835, 1835, -w^3 - 2*w^2 + w - 3]', '[1835, 1835, -2*w^3 + 5*w^2 + 5*w - 9]', '[1835, 1835, 5*w^3 - 2*w^2 - 22*w + 5]', '[1835, 1835, 7*w^3 - 7*w^2 - 35*w + 22]', '[1837, 1837, -3*w^3 + 2*w^2 + 17*w - 4]', '[1840, 230, -2*w^3 + 4*w^2 + 4*w - 8]', '[1840, 230, 8*w^3 - 10*w^2 - 32*w + 20]', '[1840, 230, 2*w^3 + 2*w^2 - 4*w - 4]', '[1840, 230, 4*w^3 - 2*w^2 - 22*w + 4]', '[1847, 1847, w^3 + 2*w^2 - 6*w - 15]', '[1859, 1859, 2*w^3 - w^2 - 13*w + 2]', '[1861, 1861, -2*w^3 + w^2 + 13*w - 3]', '[1863, 69, 6*w^3 - 6*w^2 - 27*w + 12]', '[1863, 69, 3*w^2 - 6]', '[1867, 1867, -3*w^3 + 4*w^2 + 15*w - 8]', '[1867, 1867, w^3 - 2*w - 7]', '[1901, 1901, 5*w^3 - 3*w^2 - 23*w + 6]', '[1901, 1901, 3*w^3 + w^2 - 12*w - 6]', '[1903, 1903, w^3 - 3*w^2 - 7*w + 11]', '[1903, 1903, 2*w^3 - 3*w^2 - 6*w - 3]', '[1907, 1907, 4*w^3 - 3*w^2 - 17*w + 3]', '[1913, 1913, -w^3 - 3*w^2 + 10*w + 6]', '[1913, 1913, w^3 - 7*w - 8]', '[1915, 1915, -3*w^3 + 2*w^2 + 11*w - 1]', '[1915, 1915, 4*w^3 - 5*w^2 - 11*w]', '[1915, 1915, w^3 - 4*w^2 + 4*w + 4]', '[1915, 1915, 6*w^3 - 8*w^2 - 23*w + 20]', '[1915, 1915, 2*w^3 - w^2 - 16*w - 3]', '[1915, 1915, -4*w^2 - 7*w + 7]', '[1915, 1915, -4*w^3 + 5*w^2 + 19*w - 21]', '[1915, 1915, w^3 + 4*w^2 - w - 9]', '[1919, 1919, -2*w^2 + 3*w + 9]', '[1919, 1919, w^3 - w^2 - 7]', '[1921, 1921, 5*w^3 - 4*w^2 - 20*w]', '[1927, 1927, 6*w^3 - 4*w^2 - 28*w + 5]', '[1931, 1931, 4*w^3 - 3*w^2 - 18*w - 2]', '[1933, 1933, -3*w^3 + w^2 + 12*w + 7]', '[1936, 242, -4*w^3 + 22*w + 2]', '[1945, 1945, -2*w^3 + 3*w^2 + 11*w - 3]', '[1945, 1945, -2*w^3 + 6*w^2 + w - 10]', '[1945, 1945, -3*w^2 + 2*w + 5]', '[1945, 1945, 2*w^3 - 7*w - 5]', '[1949, 1949, -w^3 + w - 8]', '[1949, 1949, -2*w^3 + 3*w^2 + 9*w - 2]', '[1951, 1951, -2*w^3 + 4*w^2 + 10*w - 7]', '[1951, 1951, 5*w^3 - 4*w^2 - 21*w + 14]', '[1951, 1951, -3*w^3 + 2*w^2 + 11*w - 5]', '[1951, 1951, -w^3 + w^2 + 9*w - 2]', '[1955, 1955, w^2 - 4*w - 5]', '[1955, 1955, 7*w^3 - 5*w^2 - 32*w + 5]', '[1955, 1955, -w^3 + 4*w^2 + 6*w - 5]', '[1955, 1955, 3*w^3 - 6*w^2 - 11*w + 17]', '[1957, 1957, -w^3 - 2*w^2 + 10*w - 2]', '[1957, 1957, w^3 - w^2 - 4*w - 5]', '[1957, 1957, 2*w^3 - 3*w^2 - 10*w + 3]', '[1957, 1957, -2*w^3 - w^2 + 17*w - 7]', '[1969, 1969, -4*w^3 + w^2 + 23*w - 4]', '[1979, 1979, 3*w^3 - w^2 - 15*w - 7]', '[1979, 1979, -4*w^3 - w^2 + 14*w - 3]', '[1985, 1985, 4*w^3 - 7*w^2 - 11*w + 8]', '[1985, 1985, -3*w^3 - 2*w^2 + 13*w + 2]', '[1985, 1985, 2*w^3 - 12*w + 5]', '[1985, 1985, -3*w^3 + 5*w^2 + 8*w - 2]', '[1985, 1985, 7*w^3 - 12*w^2 - 21*w + 19]', '[1985, 1985, 3*w^2 - 2*w - 10]', '[1985, 1985, 5*w^3 - 4*w^2 - 25*w + 6]', '[1985, 1985, 2*w^3 + w^2 - 10*w + 1]', '[1987, 1987, 2*w^3 - 13*w + 6]', '[1991, 1991, 3*w^3 - 4*w^2 - 17*w + 22]', '[1997, 1997, w^3 - 3*w^2 + 7]', '[1999, 1999, 2*w^2 - 5*w - 5]', '[2000, 10, -2*w^3 + 4*w^2 + 6*w - 12]', '[2000, 10, 2*w^3 + 2*w^2 - 6*w - 6]', '[2000, 50, 4*w^3 - 2*w^2 - 20*w + 6]', '[2000, 50, 2*w^3 - 4*w^2 - 12*w + 14]', '[2000, 250, -4*w^3 + 4*w^2 + 16*w - 6]', '[2000, 250, 2*w - 8]', '[2005, 2005, 2*w^3 - 3*w^2 - 2*w - 5]', '[2005, 2005, -3*w^3 + 2*w^2 + 20*w - 14]', '[2005, 2005, w^3 - 10*w - 4]', '[2005, 2005, -3*w^3 + w^2 + 10*w - 4]', '[2011, 2011, -w^3 + 3*w^2 + w - 9]', '[2011, 2011, -w^3 + w^2 + w + 8]', '[2017, 2017, 3*w^3 - 3*w^2 - 17*w + 10]', '[2025, 15, 3*w^2 - 9]', '[2025, 15, 3*w^2 - 3*w - 6]', '[2025, 75, 3*w^3 - 3*w^2 - 15*w + 3]', '[2025, 75, 3*w^3 - 12*w + 6]', '[2027, 2027, -2*w^3 + 4*w^2 + 7*w - 18]', '[2032, 254, 2*w^3 - 4*w + 6]', '[2032, 254, -4*w^3 + 4*w^2 + 18*w - 6]', '[2035, 2035, -w^3 + 2*w^2 + 8*w - 10]', '[2035, 2035, -4*w^3 + 5*w^2 + 18*w - 11]', '[2035, 2035, 3*w^3 - 4*w^2 - 17*w + 11]', '[2035, 2035, 2*w^3 - 5*w^2 - 9*w + 17]', '[2039, 2039, 3*w^3 - w^2 - 11*w + 1]', '[2039, 2039, -w^3 + 3*w^2 + 10*w - 3]', '[2041, 2041, -5*w^2 + 9*w + 1]', '[2045, 2045, 5*w^3 - 21*w - 6]', '[2045, 2045, -5*w^3 + 3*w^2 + 23*w - 3]', '[2045, 2045, w^3 + 3*w^2 - 12*w - 6]', '[2045, 2045, -4*w^3 + 3*w^2 + 25*w + 3]', '[2047, 2047, 3*w^3 + 2*w^2 - 14*w - 10]', '[2047, 2047, 3*w^2 - 3*w - 7]', '[2053, 2053, -w^3 + 4*w^2 + 4*w - 3]', '[2057, 2057, 2*w^3 - 3*w^2 - 13*w + 9]', '[2081, 2081, -5*w^3 + w^2 + 24*w]', '[2083, 2083, -3*w^3 + w^2 + 14*w - 6]', '[2087, 2087, -w^3 + 5*w^2 + w - 17]', '[2095, 2095, -w^3 + 4*w^2 + 2*w - 12]', '[2095, 2095, 2*w^3 - 3*w^2 - 9*w + 1]', '[2095, 2095, w^3 - w^2 - 8*w - 6]', '[2095, 2095, 2*w^3 + 2*w^2 - 9*w - 6]', '[2096, 262, -2*w^3 + 2*w^2 + 8*w - 12]', '[2096, 262, 4*w^3 - 2*w^2 - 22*w + 2]', '[2099, 2099, 4*w^3 - w^2 - 16*w - 5]', '[2105, 2105, -2*w^3 + 3*w^2 + 12*w - 15]', '[2105, 2105, -w^3 - 6]', '[2111, 2111, w^2 - 10]', '[2113, 2113, -2*w^3 + 13*w - 7]', '[2113, 2113, w^3 + w^2 - 8*w - 10]', '[2119, 2119, w^3 - 3*w^2 + 3*w - 6]', '[2125, 85, -2*w^3 + 4*w^2 + 11*w - 7]', '[2125, 85, w^3 + w^2 - 8*w - 8]', '[2125, 425, -w^3 - 2*w^2 + 10*w + 6]', '[2125, 425, 2*w^3 - 4*w^2 - 7*w + 4]', '[2125, 2125, -w^3 + 2*w^2 + 9*w - 4]', '[2125, 2125, 3*w^2 - 7]', '[2137, 2137, 3*w^3 - 2*w^2 - 12*w - 6]', '[2143, 2143, -w^2 - 6*w - 7]', '[2147, 2147, 2*w^3 + 2*w^2 - 18*w + 1]', '[2147, 2147, -4*w^3 + w^2 + 17*w + 6]', '[2153, 2153, 2*w^3 + w^2 - 9*w - 10]', '[2155, 2155, 2*w^3 + 2*w^2 - 5*w - 5]', '[2155, 2155, w^3 + 3*w^2 - 3*w - 5]', '[2155, 2155, -2*w^3 + 4*w^2 + 5*w - 10]', '[2155, 2155, -w^3 + 9*w - 10]', '[2159, 2159, -5*w^3 + 2*w^2 + 28*w - 7]', '[2159, 2159, -2*w^2 - 2*w + 9]', '[2161, 2161, w^3 - w^2 - 6*w - 5]', '[2161, 2161, 5*w^3 - 5*w^2 - 21*w + 6]', '[2165, 2165, -w^3 + 7*w^2 - 10*w - 5]', '[2165, 2165, 4*w^3 - w^2 - 14*w - 4]', '[2165, 2165, -4*w^3 + 4*w^2 + 19*w - 7]', '[2165, 2165, -5*w^3 - w^2 + 20*w + 1]', '[2167, 2167, 4*w^3 - 5*w^2 - 16*w + 17]', '[2167, 2167, -4*w^3 + 3*w^2 + 19*w - 1]', '[2171, 2171, -5*w^3 + 27*w + 4]', '[2185, 2185, -6*w^3 + 6*w^2 + 31*w - 21]', '[2185, 2185, -3*w^2 - 5*w + 8]', '[2185, 2185, w^3 - 6*w^2 + 2*w + 17]', '[2185, 2185, -3*w^3 + 3*w^2 + 10*w - 3]', '[2185, 2185, 5*w^3 - 2*w^2 - 29*w + 8]', '[2185, 2185, w^3 - w - 5]', '[2185, 2185, w^3 + 3*w^2 - 5*w - 20]', '[2185, 2185, 2*w^3 - 2*w^2 - 13*w + 3]', '[2189, 2189, 5*w - 7]', '[2192, 274, -4*w^3 + 18*w]', '[2197, 13, -2*w^3 - w^2 + 15*w - 3]', '[2197, 2197, -w^2 + 4*w - 7]', '[2203, 2203, 6*w^3 - 4*w^2 - 31*w + 7]', '[2203, 2203, 3*w^3 - 4*w^2 - 11*w + 3]', '[2203, 2203, -4*w^3 + 3*w^2 + 19*w + 3]', '[2203, 2203, -5*w^3 + 3*w^2 + 22*w - 12]', '[2209, 2209, 4*w^3 - 4*w^2 - 14*w + 13]', '[2213, 2213, -2*w^3 + 3*w^2 + 11*w - 17]', '[2213, 2213, -3*w^3 + w^2 + 16*w - 5]', '[2215, 2215, 2*w^3 + 2*w^2 - 10*w - 9]', '[2215, 2215, 3*w^3 - 3*w^2 - 14*w + 2]', '[2221, 2221, -3*w^3 + w^2 + 18*w]', '[2221, 2221, -w^3 + w^2 + 6*w - 10]', '[2225, 445, -w^3 + 2*w^2 + w - 7]', '[2225, 445, 2*w^3 - w^2 - 6*w - 7]', '[2225, 2225, w^3 - 5*w^2 - 11*w + 10]', '[2225, 2225, 4*w^3 - 2*w^2 - 17*w + 5]', '[2227, 2227, -2*w^3 + 5*w^2 + 8*w - 17]', '[2227, 2227, 7*w^3 - 4*w^2 - 33*w + 2]', '[2243, 2243, w^3 + w^2 - 2*w - 6]', '[2245, 2245, 3*w^2 + 8*w + 5]', '[2245, 2245, 3*w^3 - 2*w^2 - 10*w - 6]', '[2245, 2245, -3*w^2 + w + 10]', '[2245, 2245, 3*w^3 - w^2 - 20*w - 6]', '[2249, 2249, 6*w^3 - 5*w^2 - 20*w - 5]', '[2249, 2249, -w^3 + w^2 + 5*w + 5]', '[2251, 2251, -3*w^3 + 3*w^2 + 12*w + 4]', '[2251, 2251, 4*w^2 + 2*w - 11]', '[2255, 2255, -5*w^3 + 3*w^2 + 23*w - 5]', '[2255, 2255, -w^3 - 2*w^2 + 8*w + 15]', '[2257, 2257, 3*w^2 - w - 6]', '[2257, 2257, 3*w^3 - 3*w^2 - 14*w + 15]', '[2267, 2267, -2*w^3 + 3*w^2 + 14*w - 3]', '[2267, 2267, -4*w^3 + 4*w^2 + 22*w - 15]', '[2273, 2273, -w^3 + 4*w^2 - 11]', '[2273, 2273, -3*w^3 + w^2 + 18*w - 2]', '[2281, 2281, -2*w^3 + 2*w^2 + 13*w - 7]', '[2287, 2287, -2*w^3 + 3*w^2 + 5*w - 8]', '[2288, 286, 2*w^3 - 2*w^2 - 6*w + 10]', '[2297, 2297, -2*w^3 + w^2 + 5*w - 9]', '[2297, 2297, -3*w^3 + 13*w - 3]', '[2297, 2297, 5*w^3 - 3*w^2 - 23*w + 4]', '[2297, 2297, w^3 + w^2 - 8*w - 9]', '[2299, 2299, 3*w^3 - w^2 - 17*w + 6]', '[2299, 2299, -4*w^3 + 4*w^2 + 20*w - 7]', '[2305, 2305, -w^2 - 3*w + 8]', '[2305, 2305, 3*w^3 + 2*w^2 - 13*w - 7]', '[2305, 2305, 6*w^3 - 11*w^2 - 18*w + 22]', '[2305, 2305, w^2 + w - 11]', '[2309, 2309, -3*w^3 + 4*w^2 + 18*w - 7]', '[2309, 2309, 3*w^3 + 2*w^2 - 11*w - 7]', '[2311, 2311, 2*w^3 - 5*w^2 - 6*w + 13]', '[2315, 2315, -2*w^3 + 5*w^2 + 2*w - 8]', '[2315, 2315, 2*w^3 + w^2 - 5*w - 4]', '[2321, 2321, 2*w^3 - 2*w^2 - 9*w + 12]', '[2323, 2323, 4*w^3 - 3*w^2 - 21*w + 14]', '[2323, 2323, w^3 + 2*w^2 - 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8]', '[509, 509, w^3 + 2*w^2 - 4*w - 7]', '[509, 509, -w^3 + 2*w^2 + 6*w - 10]', '[523, 523, -3*w^3 + 12*w + 1]', '[529, 23, -2*w^3 + w^2 + 9*w - 8]', '[547, 547, -w^3 + 3*w^2 + 3*w - 2]', '[547, 547, 3*w^3 - 2*w^2 - 15*w + 7]', '[569, 569, 2*w^3 - 2*w^2 - 10*w + 1]', '[569, 569, w^3 - 3*w - 6]', '[571, 571, 2*w^3 - 10*w + 1]', '[577, 577, w^3 - w^2 - 3*w - 4]', '[577, 577, -w^3 + w^2 + 8*w - 5]', '[587, 587, 3*w^3 - 2*w^2 - 14*w + 8]', '[593, 593, -3*w^3 + 3*w^2 + 16*w - 7]', '[619, 619, -2*w^3 + w^2 + 12*w - 3]', '[641, 641, -w^3 + 3*w^2 + 3*w - 8]', '[643, 643, 2*w^3 - 2*w^2 - 11*w]', '[659, 659, 2*w^3 + 2*w^2 - 10*w - 11]', '[659, 659, w^3 - 5*w - 6]', '[661, 661, 3*w^3 - w^2 - 13*w]', '[673, 673, -w^3 + 3*w^2 + 3*w - 7]', '[691, 691, -3*w^3 + 3*w^2 + 12*w - 8]', '[691, 691, 2*w^3 - w^2 - 8*w + 8]', '[701, 701, w^3 - w^2 - 7*w - 4]', '[701, 701, 4*w^3 - 2*w^2 - 17*w + 7]', '[709, 709, 3*w^3 - 3*w^2 - 10*w]', '[719, 719, -w^3 + w^2 + 2*w - 6]', '[719, 719, -w^3 + 3*w^2 + 4*w - 8]', '[733, 733, w^3 + w^2 - 4*w - 7]', '[733, 733, -3*w^3 + 2*w^2 + 13*w - 4]', '[733, 733, -w^2 - 3]', '[733, 733, -2*w^3 + 3*w^2 + 8*w - 4]', '[739, 739, -3*w - 7]', '[743, 743, 3*w^3 - 2*w^2 - 13*w + 3]', '[743, 743, -4*w^3 + 5*w^2 + 16*w - 9]', '[743, 743, w^3 + w^2 - 3*w - 5]', '[743, 743, 3*w^3 - 3*w^2 - 11*w + 2]', '[751, 751, -3*w^3 + 3*w^2 + 16*w - 8]', '[757, 757, 3*w^3 - 3*w^2 - 12*w + 5]', '[757, 757, 2*w^3 - 4*w^2 - 7*w + 13]', '[761, 761, -3*w^3 + 4*w^2 + 16*w - 17]', '[769, 769, -3*w^3 + 4*w^2 + 17*w - 7]', '[769, 769, 3*w^3 + w^2 - 17*w - 6]', '[797, 797, -3*w^3 + 4*w^2 + 11*w - 5]', '[797, 797, -3*w^3 + 5*w^2 + 11*w - 14]', '[811, 811, -3*w^3 + 2*w^2 + 12*w]', '[811, 811, -w^3 + 3*w^2 + 7*w - 4]', '[821, 821, w^3 + 2*w^2 - 4*w - 6]', '[823, 823, -2*w^3 + 3*w^2 + 11*w - 5]', '[823, 823, 3*w^3 - 2*w^2 - 15*w + 8]', '[829, 829, -w^3 - w^2 + 4*w + 10]', '[839, 839, 3*w^3 - 19*w + 1]', '[853, 853, -5*w^3 + 3*w^2 + 23*w - 9]', '[863, 863, w^3 - 4*w^2 - w + 11]', '[877, 877, -3*w^3 + 2*w^2 + 17*w - 1]', '[883, 883, -3*w^3 + 13*w - 1]', '[907, 907, -w^3 + 3*w^2 + 2*w - 10]', '[907, 907, -3*w^3 + w^2 + 11*w - 5]', '[919, 919, -2*w^3 + 3*w^2 + 14*w]', '[919, 919, 2*w^3 - w^2 - 13*w + 6]', '[919, 919, -w^3 + 2*w^2 + w - 5]', '[919, 919, w - 6]', '[937, 937, 3*w^3 - 2*w^2 - 11*w + 7]', '[953, 953, w^3 + w^2 - 4*w - 8]', '[953, 953, w^3 + 2*w^2 - 5*w - 8]', '[961, 31, -w^3 + 2*w^2 + 2*w - 7]', '[961, 31, w^2 - 3*w - 5]', '[967, 967, 3*w^3 - w^2 - 12*w + 3]', '[967, 967, w^2 + 2*w - 7]', '[971, 971, -w^3 + 3*w^2 + 9*w - 1]', '[971, 971, w^3 - w^2 - 4*w - 4]', '[977, 977, w^3 + 2*w^2 - 5*w - 13]', '[991, 991, -2*w^3 + 11*w - 2]', '[997, 997, -w^3 + 2*w^2 + 9*w - 1]', '[997, 997, 3*w^3 - 2*w^2 - 12*w + 6]']}
• 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, 3, -5, -1, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 12197, 'disc_rad': 12197, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [[4, 1]]], [5, [[2, 1], [1, 2]]], [7, [[4, 1]]], [11, [[3, 1], [1, 1]]], [13, [[3, 1], [1, 1]]], [17, [[3, 1], [1, 1]]], [19, [[2, 1], [1, 2]]], [23, [[2, 1], [1, 2]]], [29, [[4, 1]]], [31, [[2, 2]]], [37, [[2, 1], [1, 2]]], [41, [[3, 1], [1, 1]]], [43, [[4, 1]]], [47, [[3, 1], [1, 1]]], [53, [[2, 2]]], [59, [[4, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12], 'galois_label': '4T5', 'galt': 5, 'grd': 110.44002897500525, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.12197.1', 'local_algs': ['m12197.1.1.0', 'm12197.1.1.0', 'm12197.2.1.1'], 'monogenic': 1, 'num_ram': 1, 'r2': 0, 'ramps': [12197], 'rd': 10.5090451029, 'regulator': {'__RealLiteral__': 0, 'data': '5.30264841631', 'prec': 44}, 'res': {'gal': ['-46771,2775030,-12918908,-20153824,61708084,57022002,-114340813,-80885446,109543004,65036934,-60267980,-31659496,20039039,9592284,-4139236,-1816210,539074,211828,-44421,-14584,2290,536,-70,-8,1'], 'sib': ['-1567,-123,23490,-37531,-3081,23023,-2526,-4070,596,270,-43,-6,1', '365317,-192718,-136153,8586,8126,-106,-162,0,1', '4458,7691,2715,-151,-123,-3,1', '5,-18,8,19,-7,-3,1', '67,654,-1239,-1277,2336,907,-1486,-349,366,61,-33,-3,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a - 1 \\)', '\\( a^{2} + a - 2 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}