Hilbert modular form data - 2.2.133.1-23.2-e

Formats: - HTML - YAML - JSON - 2024-06-07T17:03:46.609527

• hmf_forms •

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

  
  {'deg': 2, 'dimension': 14, 'disc': 133, 'field_bad_primes': [7, 19], 'field_label': '2.2.133.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.133.1-23.2-e', 'label_nsuffix': 4, 'label_suffix': 'e', 'level_bad_primes': [23], 'level_ideal': '[23,23,w - 8]', 'level_label': '23.2', 'level_norm': 23, 'parallel_weight': 2, 'short_label': '23.2-e', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[23,23,w - 8]', -1]], 'hecke_eigenvalues': ['e', '155/594*e^13 - 5111/594*e^11 + 7333/66*e^9 - 208585/297*e^7 + 436243/198*e^5 - 907552/297*e^3 + 48490/33*e', '7/18*e^12 - 122/9*e^10 + 369/2*e^8 - 22021/18*e^6 + 11980/3*e^4 - 51119/9*e^2 + 2778', -1, '-7/6*e^12 + 119/3*e^10 - 1055/2*e^8 + 20551/6*e^6 - 10983*e^4 + 46262/3*e^2 - 7467', '-20/9*e^12 + 665/9*e^10 - 962*e^8 + 55154/9*e^6 - 58057/3*e^4 + 242579/9*e^2 - 13011', '-53/198*e^13 + 862/99*e^11 - 2439/22*e^9 + 136817/198*e^7 - 70604/33*e^5 + 290857/99*e^3 - 15473/11*e', '193/297*e^13 - 6433/297*e^11 + 9326/33*e^9 - 535549/297*e^7 + 564110/99*e^5 - 2354206/297*e^3 + 125974/33*e', '-101/594*e^13 + 3347/594*e^11 - 1607/22*e^9 + 137440/297*e^7 - 287209/198*e^5 + 593191/297*e^3 - 31211/33*e', '47/18*e^12 - 787/9*e^10 + 2293/2*e^8 - 132329/18*e^6 + 70034/3*e^4 - 293626/9*e^2 + 15780', 1, '1/6*e^12 - 14/3*e^10 + 99/2*e^8 - 1483/6*e^6 + 592*e^4 - 1922/3*e^2 + 249', '-181/297*e^13 + 12203/594*e^11 - 8945/33*e^9 + 1038647/594*e^7 - 1105627/198*e^5 + 2330353/297*e^3 - 126025/33*e', '-14/99*e^13 + 1021/198*e^11 - 802/11*e^9 + 98695/198*e^7 - 109667/66*e^5 + 235382/99*e^3 - 12739/11*e', '23/66*e^13 - 394/33*e^11 + 3519/22*e^9 - 69053/66*e^7 + 37188/11*e^5 - 158056/33*e^3 + 25757/11*e', '2/27*e^13 - 71/27*e^11 + 109/3*e^9 - 6590/27*e^7 + 7267/9*e^5 - 31628/27*e^3 + 1778/3*e', '-1/9*e^12 + 22/9*e^10 - 16*e^8 + 82/9*e^6 + 628/3*e^4 - 4202/9*e^2 + 255', '47/18*e^12 - 787/9*e^10 + 2293/2*e^8 - 132311/18*e^6 + 69986/3*e^4 - 292969/9*e^2 + 15705', '-224/297*e^13 + 15049/594*e^11 - 3665/11*e^9 + 1272715/594*e^7 - 1350521/198*e^5 + 2835314/297*e^3 - 152212/33*e', '-28/297*e^13 + 2339/594*e^11 - 2033/33*e^9 + 270353/594*e^7 - 319027/198*e^5 + 717274/297*e^3 - 40273/33*e', '155/198*e^13 - 5111/198*e^11 + 7333/22*e^9 - 208585/99*e^7 + 436243/66*e^5 - 907750/99*e^3 + 48655/11*e', '-497/594*e^13 + 16415/594*e^11 - 23587/66*e^9 + 671941/297*e^7 - 1407955/198*e^5 + 2938798/297*e^3 - 158206/33*e', '-10/297*e^13 + 202/297*e^11 - 38/11*e^9 - 2393/297*e^7 + 9157/99*e^5 - 42443/297*e^3 + 1489/33*e', '-112/297*e^13 + 3688/297*e^11 - 1761/11*e^9 + 300136/297*e^7 - 313796/99*e^5 + 1309846/297*e^3 - 70562/33*e', '514/297*e^13 - 17392/297*e^11 + 8529/11*e^9 - 1489888/297*e^7 + 1588649/99*e^5 - 6690592/297*e^3 + 360722/33*e', '-785/594*e^13 + 26549/594*e^11 - 13015/22*e^9 + 1136620/297*e^7 - 2424673/198*e^5 + 5111875/297*e^3 - 276119/33*e', '59/9*e^12 - 1973/9*e^10 + 2870*e^8 - 165398/9*e^6 + 174892/3*e^4 - 733172/9*e^2 + 39417', 'e^12 - 32*e^10 + 401*e^8 - 2464*e^6 + 7552*e^4 - 10352*e^2 + 4957', '11/9*e^12 - 386/9*e^10 + 587*e^8 - 35174/9*e^6 + 38341/3*e^4 - 163244/9*e^2 + 8829', '-11/3*e^12 + 362/3*e^10 - 1555*e^8 + 29426/3*e^6 - 30702*e^4 + 127421/3*e^2 - 20389', '23/9*e^12 - 749/9*e^10 + 1061*e^8 - 59603/9*e^6 + 61600/3*e^4 - 253868/9*e^2 + 13476', '2*e^12 - 66*e^10 + 853*e^8 - 5397*e^6 + 16947*e^4 - 23520*e^2 + 11310', '-188/297*e^13 + 5936/297*e^11 - 2712/11*e^9 + 441854/297*e^7 - 442480/99*e^5 + 1783952/297*e^3 - 93559/33*e', '-577/594*e^13 + 19417/594*e^11 - 28415/66*e^9 + 823046/297*e^7 - 1746407/198*e^5 + 3657650/297*e^3 - 195425/33*e', '208/297*e^13 - 14165/594*e^11 + 3492/11*e^9 - 1224893/594*e^7 + 1308385/198*e^5 - 2748664/297*e^3 + 147275/33*e', '-437/297*e^13 + 14312/297*e^11 - 20395/33*e^9 + 1152716/297*e^7 - 1198567/99*e^5 + 4969499/297*e^3 - 265880/33*e', '955/297*e^13 - 63827/594*e^11 + 15465/11*e^9 - 5344535/594*e^7 + 5647699/198*e^5 - 11826244/297*e^3 + 635132/33*e', '-13/198*e^13 + 223/198*e^11 - 25/22*e^9 - 7342/99*e^7 + 30229/66*e^5 - 84904/99*e^3 + 5408/11*e', '-7/9*e^12 + 217/9*e^10 - 292*e^8 + 15604/9*e^6 - 15491/3*e^4 + 63034/9*e^2 - 3369', '-37/6*e^12 + 614/3*e^10 - 5319/2*e^8 + 101443/6*e^6 - 53277*e^4 + 222119/3*e^2 - 35669', '11/6*e^12 - 184/3*e^10 + 1607/2*e^8 - 30899/6*e^6 + 16354*e^4 - 68629/3*e^2 + 11086', '-46/9*e^12 + 1507/9*e^10 - 2148*e^8 + 121411/9*e^6 - 126209/3*e^4 + 522811/9*e^2 - 27894', '-632/297*e^13 + 42145/594*e^11 - 30571/33*e^9 + 3515341/594*e^7 - 3709943/198*e^5 + 7766300/297*e^3 - 417602/33*e', '2/99*e^13 - 80/99*e^11 + 135/11*e^9 - 8768/99*e^7 + 10108/33*e^5 - 44120/99*e^3 + 2516/11*e', '299/594*e^13 - 9485/594*e^11 + 4357/22*e^9 - 357022/297*e^7 + 719047/198*e^5 - 1455481/297*e^3 + 76982/33*e', '115/198*e^13 - 3709/198*e^11 + 5205/22*e^9 - 144962/99*e^7 + 297707/66*e^5 - 612080/99*e^3 + 32449/11*e', '-41/18*e^12 + 694/9*e^10 - 2041/2*e^8 + 118661/18*e^6 - 63098/3*e^4 + 264742/9*e^2 - 14211', '5/2*e^12 - 85*e^10 + 2261/2*e^8 - 14689/2*e^6 + 23588*e^4 - 33252*e^2 + 16185', '61/9*e^12 - 2044/9*e^10 + 2979*e^8 - 171952/9*e^6 + 181958/3*e^4 - 761956/9*e^2 + 40881', '-17/2*e^12 + 285*e^10 - 7481/2*e^8 + 48007/2*e^6 - 76254*e^4 + 106553*e^2 - 51513', '47/297*e^13 - 3265/594*e^11 + 821/11*e^9 - 293395/594*e^7 + 318161/198*e^5 - 672896/297*e^3 + 36235/33*e', '-412/297*e^13 + 13609/297*e^11 - 6520/11*e^9 + 1114891/297*e^7 - 1168676/99*e^5 + 4881220/297*e^3 - 262304/33*e', '-194/297*e^13 + 6473/297*e^11 - 3133/11*e^9 + 540923/297*e^7 - 571408/99*e^5 + 2392997/297*e^3 - 127936/33*e', '-463/198*e^13 + 7874/99*e^11 - 23283/22*e^9 + 1361839/198*e^7 - 728791/33*e^5 + 3076895/99*e^3 - 166157/11*e', '19/3*e^12 - 631/3*e^10 + 2735*e^8 - 52201/3*e^6 + 54879*e^4 - 229015/3*e^2 + 36783', '-20/9*e^12 + 683/9*e^10 - 1013*e^8 + 59366/9*e^6 - 63538/3*e^4 + 267275/9*e^2 - 14337', '89/198*e^13 - 3065/198*e^11 + 4583/22*e^9 - 135391/99*e^7 + 292429/66*e^5 - 622399/99*e^3 + 33838/11*e', '-769/297*e^13 + 50927/594*e^11 - 36689/33*e^9 + 4191857/594*e^7 - 4400287/198*e^5 + 9181651/297*e^3 - 492136/33*e', '1/9*e^12 - 40/9*e^10 + 67*e^8 - 4303/9*e^6 + 4904/3*e^4 - 21187/9*e^2 + 1119', '-17/6*e^12 + 292/3*e^10 - 2615/2*e^8 + 51431/6*e^6 - 27723*e^4 + 117520/3*e^2 - 19047', '-13/3*e^12 + 442/3*e^10 - 1960*e^8 + 38209/3*e^6 - 40889*e^4 + 172525/3*e^2 - 27879', '809/297*e^13 - 54127/594*e^11 + 13126/11*e^9 - 4538617/594*e^7 + 4795829/198*e^5 - 10029995/297*e^3 + 537286/33*e', '1201/594*e^13 - 40813/594*e^11 + 60305/66*e^9 - 1763471/297*e^7 + 3778037/198*e^5 - 7995971/297*e^3 + 432953/33*e', '118/99*e^13 - 3928/99*e^11 + 5688/11*e^9 - 326440/99*e^7 + 344120/33*e^5 - 1441711/99*e^3 + 77428/11*e', '16/11*e^13 - 1071/22*e^11 + 7014/11*e^9 - 89809/22*e^7 + 284467/22*e^5 - 197915/11*e^3 + 95055/11*e', '-1/2*e^12 + 18*e^10 - 505/2*e^8 + 3441/2*e^6 - 5744*e^4 + 8292*e^2 - 4125', '31/3*e^12 - 1036/3*e^10 + 4518*e^8 - 86719/3*e^6 + 91580*e^4 - 383017/3*e^2 + 61583', '23/6*e^12 - 382/3*e^10 + 3311/2*e^8 - 63161/6*e^6 + 33169*e^4 - 138238/3*e^2 + 22185', '25/18*e^12 - 410/9*e^10 + 1169/2*e^8 - 66031/18*e^6 + 34288/3*e^4 - 142037/9*e^2 + 7563', '1477/297*e^13 - 98063/594*e^11 + 70817/33*e^9 - 8107949/594*e^7 + 8523193/198*e^5 - 17787367/297*e^3 + 952909/33*e', '-547/198*e^13 + 9257/99*e^11 - 27237/22*e^9 + 1585159/198*e^7 - 843973/33*e^5 + 3543362/99*e^3 - 190019/11*e', '173/18*e^12 - 2884/9*e^10 + 8367/2*e^8 - 480953/18*e^6 + 253688/3*e^4 - 1061335/9*e^2 + 56979', '-41/6*e^12 + 682/3*e^10 - 5923/2*e^8 + 113255/6*e^6 - 59626*e^4 + 249025/3*e^2 - 40007', '-68/297*e^13 + 5341/594*e^11 - 4447/33*e^9 + 573157/594*e^7 - 660647/198*e^5 + 1458104/297*e^3 - 80363/33*e', '-283/594*e^13 + 4868/297*e^11 - 14543/66*e^9 + 857641/594*e^7 - 460876/99*e^5 + 1938143/297*e^3 - 104087/33*e', '-82/27*e^13 + 5489/54*e^11 - 1332*e^9 + 461027/54*e^7 - 487927/18*e^5 + 1023238/27*e^3 - 55001/3*e', '709/297*e^13 - 47711/594*e^11 + 11635/11*e^9 - 4043561/594*e^7 + 4289533/198*e^5 - 8984869/297*e^3 + 481424/33*e', '437/297*e^13 - 14609/297*e^11 + 21253/33*e^9 - 1225481/297*e^7 + 1297171/99*e^5 - 5446778/297*e^3 + 293237/33*e', '373/297*e^13 - 12148/297*e^11 + 17219/33*e^9 - 968566/297*e^7 + 1003283/99*e^5 - 4148590/297*e^3 + 220150/33*e', '71/18*e^12 - 1177/9*e^10 + 3395/2*e^8 - 194039/18*e^6 + 101825/3*e^4 - 424498/9*e^2 + 22725', '-1/6*e^12 + 23/3*e^10 - 253/2*e^8 + 5767/6*e^6 - 3429*e^4 + 15152/3*e^2 - 2489', '-9/2*e^12 + 153*e^10 - 4069/2*e^8 + 26421/2*e^6 - 42374*e^4 + 59557*e^2 - 28869', '-4/9*e^12 + 124/9*e^10 - 167*e^8 + 8932/9*e^6 - 8846/3*e^4 + 35482/9*e^2 - 1857', '43/6*e^12 - 722/3*e^10 + 6327/2*e^8 - 121975/6*e^6 + 64647*e^4 - 271037/3*e^2 + 43649', '49/6*e^12 - 815/3*e^10 + 7077/2*e^8 - 135307/6*e^6 + 71251*e^4 - 297914/3*e^2 + 47959', '43/9*e^12 - 1432/9*e^10 + 2075*e^8 - 119167/9*e^6 + 125648/3*e^4 - 525868/9*e^2 + 28266', '-20/3*e^12 + 659/3*e^10 - 2834*e^8 + 53684/3*e^6 - 56067*e^4 + 232985/3*e^2 - 37352', '-8*e^12 + 266*e^10 - 3464*e^8 + 22077*e^6 - 69766*e^4 + 97257*e^2 - 46973', '5*e^12 - 169*e^10 + 2235*e^8 - 14441*e^6 + 46131*e^4 - 64673*e^2 + 31323', '-430/297*e^13 + 14032/297*e^11 - 6639/11*e^9 + 1121038/297*e^7 - 1160945/99*e^5 + 4796863/297*e^3 - 255248/33*e', '-764/297*e^13 + 25610/297*e^11 - 37336/33*e^9 + 2155634/297*e^7 - 2281777/99*e^5 + 9559718/297*e^3 - 512972/33*e', '17/22*e^13 - 559/22*e^11 + 7187/22*e^9 - 22568/11*e^7 + 140219/22*e^5 - 95715/11*e^3 + 44999/11*e', '706/297*e^13 - 23686/297*e^11 + 34565/33*e^9 - 1997491/297*e^7 + 2115431/99*e^5 - 8857507/297*e^3 + 474856/33*e', '-503/198*e^13 + 17051/198*e^11 - 25125/22*e^9 + 732316/99*e^7 - 1562095/66*e^5 + 3283564/99*e^3 - 176038/11*e', '-19/18*e^13 + 607/18*e^11 - 843/2*e^9 + 23225/9*e^7 - 47231/6*e^5 + 96629/9*e^3 - 5155*e', '4/3*e^12 - 133/3*e^10 + 578*e^8 - 11071/3*e^6 + 11672*e^4 - 48616/3*e^2 + 7751', '23/3*e^12 - 770/3*e^10 + 3364*e^8 - 64691/3*e^6 + 68463*e^4 - 287117/3*e^2 + 46313', '11/9*e^12 - 332/9*e^10 + 432*e^8 - 22151/9*e^6 + 20962/3*e^4 - 81380/9*e^2 + 4149', '14/3*e^12 - 473/3*e^10 + 2085*e^8 - 40436/3*e^6 + 43119*e^4 - 181910/3*e^2 + 29487', '25/33*e^13 - 835/33*e^11 + 3638/11*e^9 - 69736/33*e^7 + 73528/11*e^5 - 307036/33*e^3 + 49250/11*e', '262/297*e^13 - 16901/594*e^11 + 11855/33*e^9 - 1319987/594*e^7 + 1355125/198*e^5 - 2788435/297*e^3 + 147865/33*e', '11/2*e^12 - 183*e^10 + 4769/2*e^8 - 30409/2*e^6 + 48066*e^4 - 67010*e^2 + 32350', '59/6*e^12 - 985/3*e^10 + 8583/2*e^8 - 164597/6*e^6 + 86865*e^4 - 363451/3*e^2 + 58522', '1670/297*e^13 - 111127/594*e^11 + 26806/11*e^9 - 9222409/594*e^7 + 9701969/198*e^5 - 20223842/297*e^3 + 1080412/33*e', '-565/297*e^13 + 37379/594*e^11 - 8967/11*e^9 + 3070247/594*e^7 - 3219289/198*e^5 + 6711703/297*e^3 - 360596/33*e', '-2425/594*e^13 + 40679/297*e^11 - 39575/22*e^9 + 6861775/594*e^7 - 3635353/99*e^5 + 15247514/297*e^3 - 820291/33*e', '-1262/297*e^13 + 42065/297*e^11 - 20332/11*e^9 + 3504593/297*e^7 - 3695446/99*e^5 + 15454127/297*e^3 - 828574/33*e', '11/3*e^12 - 380/3*e^10 + 1709*e^8 - 33713/3*e^6 + 36397*e^4 - 154241/3*e^2 + 24993', '-163/18*e^12 + 2675/9*e^10 - 7639/2*e^8 + 432451/18*e^6 - 225028/3*e^4 + 932342/9*e^2 - 49707', '37/9*e^12 - 1219/9*e^10 + 1748*e^8 - 99424/9*e^6 + 103988/3*e^4 - 432883/9*e^2 + 23163', '-15/2*e^12 + 253*e^10 - 6681/2*e^8 + 43123/2*e^6 - 68867*e^4 + 96675*e^2 - 46925', '70/9*e^12 - 2350/9*e^10 + 3431*e^8 - 198376/9*e^6 + 210287/3*e^4 - 882367/9*e^2 + 47427', '-85/6*e^12 + 1415/3*e^10 - 12299/2*e^8 + 235387/6*e^6 - 124071*e^4 + 519158/3*e^2 - 83649', '74/9*e^12 - 2438/9*e^10 + 3495*e^8 - 198659/9*e^6 + 207541/3*e^4 - 862490/9*e^2 + 46059', '-9/2*e^12 + 154*e^10 - 4123/2*e^8 + 26949/2*e^6 - 43491*e^4 + 61463*e^2 - 29969', '505/198*e^13 - 16735/198*e^11 + 24127/22*e^9 - 689378/99*e^7 + 1447199/66*e^5 - 3017435/99*e^3 + 161544/11*e', '397/297*e^13 - 26513/594*e^11 + 19268/33*e^9 - 2220923/594*e^7 + 2351029/198*e^5 - 4940875/297*e^3 + 266908/33*e', '-563/198*e^13 + 18461/198*e^11 - 26337/22*e^9 + 744937/99*e^7 - 1549591/66*e^5 + 3208309/99*e^3 - 170856/11*e', '124/27*e^13 - 4168/27*e^11 + 2031*e^9 - 352690/27*e^7 + 374120/9*e^5 - 1569193/27*e^3 + 84242/3*e', '-9/2*e^12 + 152*e^10 - 4021/2*e^8 + 26009/2*e^6 - 41632*e^4 + 58577*e^2 - 28514', '-2/3*e^12 + 83/3*e^10 - 430*e^8 + 9452/3*e^6 - 11014*e^4 + 48398/3*e^2 - 7920', '41/3*e^12 - 1370/3*e^10 + 5974*e^8 - 114662/3*e^6 + 121100*e^4 - 506651/3*e^2 + 81510', '-1/3*e^12 + 49/3*e^10 - 280*e^8 + 6556/3*e^6 - 7959*e^4 + 35782/3*e^2 - 5940', '14/3*e^12 - 470/3*e^10 + 2059*e^8 - 39683/3*e^6 + 42022*e^4 - 175652/3*e^2 + 28167', '-56/9*e^12 + 1907/9*e^10 - 2822*e^8 + 165134/9*e^6 - 176668/3*e^4 + 744158/9*e^2 - 40011', '13/2*e^12 - 215*e^10 + 5569/2*e^8 - 35297/2*e^6 + 55487*e^4 - 77048*e^2 + 37079', '10*e^12 - 333*e^10 + 4341*e^8 - 27679*e^6 + 87438*e^4 - 121688*e^2 + 58637', '-2045/297*e^13 + 68039/297*e^11 - 32829/11*e^9 + 5649770/297*e^7 - 5949829/99*e^5 + 24862250/297*e^3 - 1332382/33*e', '-691/297*e^13 + 23977/297*e^11 - 36110/33*e^9 + 2147353/297*e^7 - 2330483/99*e^5 + 9935575/297*e^3 - 540334/33*e', '-58/11*e^13 + 3881/22*e^11 - 25412/11*e^9 + 325383/22*e^7 - 1030889/22*e^5 + 717710/11*e^3 - 345442/11*e', '-2/3*e^13 + 62/3*e^11 - 250*e^9 + 4442/3*e^7 - 4392*e^5 + 17774/3*e^3 - 2825*e', '395/297*e^13 - 13325/297*e^11 + 6517/11*e^9 - 1135799/297*e^7 + 1208785/99*e^5 - 5082776/297*e^3 + 273511/33*e', '-1822/297*e^13 + 121505/594*e^11 - 88148/33*e^9 + 10139147/594*e^7 - 10707613/198*e^5 + 22447075/297*e^3 - 1208686/33*e', '-11/2*e^12 + 186*e^10 - 4923/2*e^8 + 31837/2*e^6 - 50906*e^4 + 71444*e^2 - 34611', '11/2*e^12 - 181*e^10 + 4665/2*e^8 - 29423/2*e^6 + 46027*e^4 - 63584*e^2 + 30465', '-455/297*e^13 + 29371/594*e^11 - 6866/11*e^9 + 2289511/594*e^7 - 2340257/198*e^5 + 4774658/297*e^3 - 250717/33*e', '-643/198*e^13 + 21661/198*e^11 - 31737/22*e^9 + 920693/99*e^7 - 1958135/66*e^5 + 4117835/99*e^3 - 221506/11*e', '6*e^12 - 197*e^10 + 2533*e^8 - 15945*e^6 + 49826*e^4 - 68866*e^2 + 33079', '1/18*e^12 - 11/9*e^10 + 15/2*e^8 + 71/18*e^6 - 434/3*e^4 + 2380/9*e^2 - 99', '-5/3*e^12 + 176/3*e^10 - 806*e^8 + 16175/3*e^6 - 17738*e^4 + 76136/3*e^2 - 12453', '121/18*e^12 - 2060/9*e^10 + 6099/2*e^8 - 357241/18*e^6 + 191464/3*e^4 - 809381/9*e^2 + 43689', '3431/594*e^13 - 115757/594*e^11 + 56611/22*e^9 - 4932199/297*e^7 + 10496701/198*e^5 - 22074814/297*e^3 + 1188416/33*e', '116/99*e^13 - 3947/99*e^11 + 5839/11*e^9 - 342026/99*e^7 + 367474/33*e^5 - 1566287/99*e^3 + 85659/11*e', '205/198*e^13 - 6913/198*e^11 + 10147/22*e^9 - 295217/99*e^7 + 630797/66*e^5 - 1336886/99*e^3 + 72570/11*e', '268/297*e^13 - 8839/297*e^11 + 12689/33*e^9 - 722383/297*e^7 + 755753/99*e^5 - 3144733/297*e^3 + 169273/33*e', '41/9*e^12 - 1415/9*e^10 + 2120*e^8 - 125438/9*e^6 + 135454/3*e^4 - 574358/9*e^2 + 31062', '-655/198*e^13 + 21943/198*e^11 - 31975/22*e^9 + 922841/99*e^7 - 1954235/66*e^5 + 4099913/99*e^3 - 220595/11*e', '269/297*e^13 - 8780/297*e^11 + 12454/33*e^9 - 699542/297*e^7 + 721141/99*e^5 - 2951270/297*e^3 + 155252/33*e', '4*e^12 - 140*e^10 + 1912*e^8 - 12711*e^6 + 41546*e^4 - 59029*e^2 + 28757', '14/3*e^12 - 461/3*e^10 + 1981*e^8 - 37502/3*e^6 + 39166*e^4 - 162986/3*e^2 + 26163', '25/9*e^13 - 1667/18*e^11 + 1209*e^9 - 139001/18*e^7 + 146695/6*e^5 - 307132/9*e^3 + 16491*e', '-26/27*e^13 + 842/27*e^11 - 1186/3*e^9 + 66257/27*e^7 - 68155/9*e^5 + 280403/27*e^3 - 14978/3*e', '-32/3*e^12 + 1046/3*e^10 - 4463*e^8 + 83915/3*e^6 - 87070*e^4 + 360083/3*e^2 - 57536', 'e^12 - 33*e^10 + 427*e^8 - 2705*e^6 + 8482*e^4 - 11651*e^2 + 5504', '-70/99*e^13 + 4313/198*e^11 - 2877/11*e^9 + 303791/198*e^7 - 296215/66*e^5 + 585781/99*e^3 - 30365/11*e', '-115/22*e^13 + 1948/11*e^11 - 51641/22*e^9 + 334353/22*e^7 - 534808/11*e^5 + 749734/11*e^3 - 362639/11*e', '23/6*e^12 - 382/3*e^10 + 3313/2*e^8 - 63281/6*e^6 + 33302*e^4 - 139234/3*e^2 + 22432', '-115/9*e^12 + 3871/9*e^10 - 5667*e^8 + 328480/9*e^6 - 348827/3*e^4 + 1463803/9*e^2 - 78576', '77/9*e^12 - 2612/9*e^10 + 3851*e^8 - 224627/9*e^6 + 239824/3*e^4 - 1010660/9*e^2 + 54468', '22/3*e^12 - 754/3*e^10 + 3368*e^8 - 66070/3*e^6 + 71032*e^4 - 300247/3*e^2 + 48552', '650/99*e^13 - 21644/99*e^11 + 31357/11*e^9 - 1800497/99*e^7 + 1898242/33*e^5 - 7945679/99*e^3 + 427244/11*e', '-2129/297*e^13 + 142897/594*e^11 - 104278/33*e^9 + 12052981/594*e^7 - 12767375/198*e^5 + 26752118/297*e^3 - 1436096/33*e', '-419/594*e^13 + 7291/297*e^11 - 7343/22*e^9 + 1314671/594*e^7 - 716867/99*e^5 + 3081724/297*e^3 - 170051/33*e', '48/11*e^13 - 1590/11*e^11 + 20624/11*e^9 - 130902/11*e^7 + 411922/11*e^5 - 571833/11*e^3 + 275320/11*e'], 'hecke_polynomial': 'x^14 - 40*x^12 + 657*x^10 - 5671*x^8 + 27240*x^6 - 70570*x^4 + 87156*x^2 - 39204', 'label': '2.2.133.1-23.2-e'}
• hmf_fields •

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

  
  {'degree': 2, 'discriminant': 133, 'ideals': ['[1, 1, 1]', '[3, 3, -w + 6]', '[3, 3, -w - 5]', '[4, 2, 2]', '[7, 7, 3*w - 19]', '[9, 3, 3]', '[9, 9, -w + 7]', '[9, 9, w + 6]', '[11, 11, -2*w - 11]', '[11, 11, -2*w + 13]', '[12, 6, -2*w + 12]', '[12, 6, -2*w - 10]', '[13, 13, w + 4]', '[13, 13, -w + 5]', '[16, 4, 4]', '[19, 19, 5*w - 31]', '[21, 21, w + 3]', '[21, 21, w - 4]', '[23, 23, -w - 7]', '[23, 23, w - 8]', '[25, 5, -5]', '[27, 9, -3*w + 18]', '[27, 9, -3*w - 15]', '[27, 27, -w - 2]', '[27, 27, -w + 3]', '[28, 14, 6*w - 38]', '[31, 31, -w - 1]', '[31, 31, w - 2]', '[33, 33, w]', '[33, 33, 2*w - 11]', '[33, 33, -2*w - 9]', '[33, 33, -w + 1]', '[36, 6, 6]', '[36, 18, -2*w + 14]', '[36, 18, 2*w + 12]', '[39, 39, w + 8]', '[39, 39, 5*w - 32]', '[39, 39, 5*w + 27]', '[39, 39, w - 9]', '[41, 41, 6*w + 31]', '[41, 41, 6*w - 37]', '[43, 43, -3*w - 17]', '[43, 43, -3*w + 20]', '[44, 22, -4*w - 22]', '[44, 22, -4*w + 26]', '[48, 12, -4*w + 24]', '[48, 12, -4*w - 20]', '[49, 7, 7]', '[52, 26, 2*w + 8]', '[52, 26, -2*w + 10]', '[57, 57, -w - 9]', '[57, 57, w - 10]', '[59, 59, 3*w - 17]', '[59, 59, 3*w + 14]', '[63, 21, 9*w - 57]', '[63, 63, 2*w - 15]', '[63, 63, -2*w - 13]', '[64, 8, 8]', '[69, 69, 13*w - 81]', '[69, 69, 2*w - 9]', '[69, 69, 2*w + 7]', '[69, 69, 13*w + 68]', '[75, 15, 5*w - 30]', '[75, 15, 5*w + 25]', '[76, 38, 10*w - 62]', '[77, 77, -w - 10]', '[77, 77, -w + 11]', '[81, 9, 9]', '[81, 27, -3*w + 21]', '[81, 27, 3*w + 18]', '[81, 81, -8*w + 51]', '[81, 81, 8*w + 43]', '[84, 42, 2*w + 6]', '[84, 42, 2*w - 8]', '[89, 89, 3*w + 13]', '[89, 89, 3*w - 16]', '[91, 91, -4*w + 23]', '[91, 91, 4*w + 19]', '[92, 46, -2*w - 14]', '[92, 46, 2*w - 16]', '[93, 93, -4*w - 23]', '[93, 93, 7*w + 38]', '[93, 93, 7*w - 45]', '[93, 93, -4*w + 27]', '[97, 97, 2*w - 7]', '[97, 97, -2*w - 5]', '[99, 33, -6*w - 33]', '[99, 33, -6*w + 39]', '[99, 99, -w - 11]', '[99, 99, 5*w - 33]', '[99, 99, 5*w + 28]', '[99, 99, -w + 12]', '[100, 10, -10]', '[103, 103, 8*w + 41]', '[103, 103, 8*w - 49]', '[108, 18, -6*w + 36]', '[108, 18, -6*w - 30]', '[108, 54, -2*w - 4]', '[108, 54, -2*w + 6]', '[112, 28, 12*w - 76]', '[117, 39, 3*w + 12]', '[117, 39, -3*w + 15]', '[117, 117, -11*w + 68]', '[117, 117, 2*w - 5]', '[117, 117, -2*w - 3]', '[117, 117, 11*w + 57]', '[121, 11, 11]', '[121, 121, -3*w + 22]', '[121, 121, 3*w + 19]', '[123, 123, -w - 12]', '[123, 123, 2*w - 17]', '[123, 123, -2*w - 15]', '[123, 123, w - 13]', '[124, 62, -2*w - 2]', '[124, 62, 2*w - 4]', '[129, 129, 5*w - 29]', '[129, 129, 2*w - 3]', '[129, 129, -2*w - 1]', '[129, 129, -5*w - 24]', '[132, 66, 2*w]', '[132, 66, 4*w - 22]', '[132, 66, -4*w - 18]', '[132, 66, -2*w + 2]', '[133, 133, -2*w + 1]', '[137, 137, 11*w - 70]', '[137, 137, 11*w + 59]', '[143, 143, -9*w - 46]', '[143, 143, 3*w - 14]', '[143, 143, 3*w + 11]', '[143, 143, -9*w + 55]', '[144, 12, 12]', '[144, 36, -4*w + 28]', '[144, 36, 4*w + 24]', '[147, 21, -7*w + 42]', '[147, 21, -7*w - 35]', '[149, 149, -w - 13]', '[149, 149, w - 14]', '[156, 78, 2*w + 16]', '[156, 78, 10*w - 64]', '[156, 78, 10*w + 54]', '[156, 78, 2*w - 18]', '[161, 161, -40*w + 251]', '[161, 161, -5*w + 34]', '[163, 163, -3*w - 20]', '[163, 163, 3*w - 23]', '[164, 82, 12*w + 62]', '[164, 82, 12*w - 74]', '[167, 167, -3*w - 10]', '[167, 167, 3*w - 13]', '[169, 13, 13]', '[169, 169, 9*w + 49]', '[169, 169, -9*w + 58]', '[171, 57, 15*w - 93]', '[171, 171, 4*w + 17]', '[171, 171, 4*w - 21]', '[172, 86, -6*w - 34]', '[172, 86, -6*w + 40]', '[173, 173, 6*w - 35]', '[173, 173, 6*w + 29]', '[175, 35, -15*w + 95]', '[176, 44, -8*w - 44]', '[176, 44, -8*w + 52]', '[177, 177, -w - 14]', '[177, 177, 7*w - 46]', '[177, 177, -7*w - 39]', '[177, 177, w - 15]', '[181, 181, 5*w + 23]', '[181, 181, 5*w - 28]', '[189, 63, 3*w + 9]', '[189, 63, 3*w - 12]', '[189, 189, 10*w + 51]', '[189, 189, 10*w - 61]', '[191, 191, 2*w - 19]', '[191, 191, -2*w - 17]', '[192, 24, -8*w + 48]', '[192, 24, -8*w - 40]', '[196, 14, 14]', '[197, 197, 4*w - 29]', '[197, 197, -4*w - 25]', '[207, 69, -3*w - 21]', '[207, 69, 3*w - 24]', '[207, 207, -w - 15]', '[207, 207, 14*w - 89]', '[207, 207, -14*w - 75]', '[207, 207, w - 16]', '[208, 52, 4*w + 16]', '[208, 52, -4*w + 20]', '[209, 209, -3*w + 11]', '[209, 209, 3*w + 8]', '[217, 217, 13*w - 80]', '[217, 217, -22*w + 137]', '[223, 223, 7*w - 41]', '[223, 223, 7*w + 34]', '[225, 15, 15]', '[225, 45, 5*w - 35]', '[225, 45, -5*w - 30]', '[227, 227, -3*w - 7]', '[227, 227, 3*w - 10]', '[228, 114, -2*w - 18]', '[228, 114, 2*w - 20]', '[231, 231, -16*w + 99]', '[231, 231, 5*w - 27]', '[231, 231, -5*w - 22]', '[231, 231, 16*w + 83]', '[233, 233, 13*w + 70]', '[233, 233, 13*w - 83]', '[236, 118, 6*w - 34]', '[236, 118, 6*w + 28]', '[239, 239, -w - 16]', '[239, 239, w - 17]', '[241, 241, 11*w + 56]', '[241, 241, 11*w - 67]', '[243, 27, -9*w + 54]', '[243, 27, -9*w - 45]', '[243, 81, -3*w - 6]', '[243, 81, -3*w + 9]', '[243, 243, -4*w + 19]', '[243, 243, -4*w - 15]', '[247, 247, -6*w - 35]', '[247, 247, -6*w + 41]', '[252, 42, 18*w - 114]', '[252, 126, 4*w - 30]', '[252, 126, -4*w - 26]', '[253, 253, 3*w - 25]', '[253, 253, 27*w + 143]', '[253, 253, 27*w - 170]', '[253, 253, 3*w + 22]', '[256, 16, 16]', '[257, 257, 3*w - 8]', '[257, 257, -3*w - 5]', '[263, 263, -7*w + 47]', '[263, 263, -7*w - 40]', '[267, 267, -11*w - 60]', '[267, 267, 2*w - 21]', '[267, 267, -2*w - 19]', '[267, 267, 11*w - 71]', '[269, 269, -3*w - 4]', '[269, 269, 3*w - 7]', '[273, 273, w + 17]', '[273, 273, 8*w + 45]', '[273, 273, 8*w - 53]', '[273, 273, w - 18]', '[275, 55, 10*w + 55]', '[275, 55, 10*w - 65]', '[276, 138, 26*w - 162]', '[276, 138, 4*w - 18]', '[276, 138, 4*w + 14]', '[276, 138, 26*w + 136]', '[277, 277, 9*w - 59]', '[277, 277, -9*w - 50]', '[279, 93, -3*w - 3]', '[279, 93, 3*w - 6]', '[279, 279, 8*w - 47]', '[279, 279, 5*w + 21]', '[279, 279, -5*w + 26]', '[279, 279, -8*w - 39]', '[287, 287, -3*w + 5]', '[287, 287, -3*w - 2]', '[289, 17, -17]', '[291, 291, 17*w - 108]', '[291, 291, -5*w + 36]', '[291, 291, -5*w - 31]', '[291, 291, 17*w + 91]', '[293, 293, -3*w - 1]', '[293, 293, 3*w - 4]', '[297, 99, 3*w]', '[297, 99, 6*w - 33]', '[297, 99, -6*w - 27]', '[297, 99, -3*w + 3]', '[297, 297, 17*w + 88]', '[297, 297, 7*w + 33]', '[297, 297, -7*w + 40]', '[297, 297, -17*w + 105]', '[299, 299, -12*w - 61]', '[299, 299, 3*w - 2]', '[299, 299, -3*w + 1]', '[299, 299, 12*w - 73]', '[300, 30, 10*w - 60]', '[300, 30, 10*w + 50]', '[301, 301, -3*w - 23]', '[301, 301, -3*w + 26]', '[304, 76, 20*w - 124]', '[307, 307, -4*w - 13]', '[307, 307, 4*w - 17]', '[308, 154, -2*w - 20]', '[308, 154, -2*w + 22]', '[309, 309, -w - 18]', '[309, 309, -4*w - 27]', '[309, 309, 4*w - 31]', '[309, 309, w - 19]', '[324, 18, 18]', '[324, 54, -6*w + 42]', '[324, 54, 6*w + 36]', '[324, 162, -16*w + 102]', '[324, 162, 16*w + 86]', '[325, 65, -5*w - 20]', '[325, 65, 5*w - 25]', '[336, 84, 4*w + 12]', '[336, 84, 4*w - 16]', '[341, 341, -9*w + 53]', '[341, 341, 15*w - 92]', '[341, 341, 15*w + 77]', '[341, 341, -9*w - 44]', '[343, 49, 21*w - 133]', '[347, 347, -w - 19]', '[347, 347, w - 20]', '[351, 117, 3*w + 24]', '[351, 117, 15*w - 96]', '[351, 117, 15*w + 81]', '[351, 117, 3*w - 27]', '[351, 351, -7*w - 41]', '[351, 351, -2*w + 23]', '[351, 351, -2*w - 21]', '[351, 351, -7*w + 48]', '[356, 178, 6*w + 26]', '[356, 178, 6*w - 32]', '[359, 359, 5*w + 32]', '[359, 359, -5*w + 37]', '[361, 19, -19]', '[363, 33, 11*w - 66]', '[363, 33, 11*w + 55]', '[363, 363, -13*w - 66]', '[363, 363, -4*w + 15]', '[363, 363, -4*w - 11]', '[363, 363, -13*w + 79]', '[364, 182, -8*w + 46]', '[364, 182, 8*w + 38]', '[368, 92, -4*w - 28]', '[368, 92, 4*w - 32]', '[369, 123, 18*w + 93]', '[369, 123, 18*w - 111]', '[369, 369, 5*w - 24]', '[369, 369, 7*w + 32]', '[369, 369, 7*w - 39]', '[369, 369, 5*w + 19]', '[372, 186, -8*w - 46]', '[372, 186, 14*w + 76]', '[372, 186, 14*w - 90]', '[372, 186, -8*w + 54]', '[383, 383, 21*w - 130]', '[383, 383, 24*w - 149]', '[387, 129, -9*w - 51]', '[387, 129, -9*w + 60]', '[387, 387, -w - 20]', '[387, 387, 13*w + 71]', '[387, 387, 13*w - 84]', '[387, 387, -w + 21]', '[388, 194, 4*w - 14]', '[388, 194, -4*w - 10]', '[389, 389, -20*w + 127]', '[389, 389, 25*w - 158]', '[396, 66, -12*w - 66]', '[396, 66, -12*w + 78]', '[396, 198, -2*w - 22]', '[396, 198, 10*w - 66]', '[396, 198, 10*w + 56]', '[396, 198, -2*w + 24]', '[399, 399, -11*w + 72]', '[399, 399, -46*w + 289]', '[400, 20, -20]', '[403, 403, 6*w - 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126]', '[9708, 4854, 136*w + 710]', '[9712, 2428, 32*w + 140]', '[9712, 2428, -32*w + 172]', '[9713, 9713, -16*w - 127]', '[9713, 9713, -7*w + 110]', '[9713, 9713, 7*w + 103]', '[9713, 9713, 16*w - 143]', '[9716, 4858, -82*w + 524]', '[9716, 4858, -152*w + 958]', '[9719, 9719, 27*w - 134]', '[9719, 9719, -27*w - 107]', '[9721, 9721, 86*w - 529]', '[9721, 9721, 86*w + 443]', '[9723, 9723, -169*w + 1054]', '[9723, 9723, 43*w + 206]', '[9723, 9723, -43*w + 249]', '[9723, 9723, 76*w - 465]', '[9725, 1945, -100*w + 635]', '[9725, 1945, 125*w - 790]', '[9732, 4866, -46*w - 260]', '[9732, 4866, 64*w - 414]', '[9732, 4866, 64*w + 350]', '[9732, 4866, -46*w + 306]', '[9739, 9739, -9*w - 107]', '[9739, 9739, 9*w - 116]', '[9743, 9743, 24*w - 109]', '[9743, 9743, -24*w - 85]', '[9747, 171, 57*w - 342]', '[9747, 171, 57*w + 285]', '[9747, 513, 19*w + 38]', '[9747, 513, 19*w - 57]', '[9748, 4874, 24*w + 158]', '[9748, 4874, 24*w - 182]', '[9749, 9749, 18*w - 41]', '[9749, 9749, -18*w - 23]', '[9753, 9753, 8*w - 113]', '[9753, 9753, -19*w + 157]', '[9753, 9753, -19*w - 138]', '[9753, 9753, 8*w + 105]', '[9757, 9757, -23*w - 77]', '[9757, 9757, 67*w + 340]', '[9757, 9757, 67*w - 407]', '[9757, 9757, -23*w + 100]', '[9761, 9761, 81*w - 497]', '[9761, 9761, -30*w - 127]', '[9761, 9761, 30*w - 157]', '[9761, 9761, 81*w + 416]', '[9767, 9767, 74*w + 401]', '[9767, 9767, 74*w - 475]', '[9783, 3261, 63*w + 345]', '[9783, 3261, 63*w - 408]', '[9783, 9783, -47*w + 312]', '[9783, 9783, 11*w + 112]', '[9783, 9783, 11*w - 123]', '[9783, 9783, -47*w - 265]', '[9793, 9793, -221*w + 1381]', '[9793, 9793, 59*w - 355]', '[9799, 9799, 65*w - 394]', '[9799, 9799, -133*w + 827]', '[9799, 9799, 97*w - 599]', '[9799, 9799, 65*w + 329]', '[9801, 99, 99]', '[9801, 297, 33*w - 231]', '[9801, 297, -33*w - 198]', '[9801, 891, 88*w - 561]', '[9801, 891, -88*w - 473]', '[9801, 1089, -27*w + 198]', '[9801, 1089, 27*w + 171]', '[9801, 3267, 3*w + 99]', '[9801, 3267, -105*w + 666]', '[9801, 3267, 105*w + 561]', '[9801, 3267, -3*w + 102]', '[9801, 9801, 40*w + 231]', '[9801, 9801, 23*w + 154]', '[9801, 9801, -23*w + 177]', '[9801, 9801, -40*w + 271]', '[9803, 9803, -33*w + 179]', '[9803, 9803, 33*w + 146]', '[9804, 4902, -20*w + 162]', '[9804, 4902, 134*w - 846]', '[9804, 4902, 134*w + 712]', '[9804, 4902, -20*w - 142]', '[9808, 2452, -36*w - 212]', '[9808, 2452, -36*w + 248]', '[9811, 9811, 15*w - 139]', '[9811, 9811, -15*w - 124]', '[9812, 4906, 42*w + 200]', '[9812, 4906, 18*w - 40]', '[9812, 4906, -18*w - 22]', '[9812, 4906, -42*w + 242]', '[9817, 9817, 61*w - 368]', '[9817, 9817, 61*w + 307]', '[9819, 3273, 63*w + 318]', '[9819, 3273, 63*w - 381]', '[9819, 9819, 52*w + 257]', '[9819, 9819, 20*w + 49]', '[9819, 9819, 20*w - 69]', '[9819, 9819, 52*w - 309]', '[9828, 1638, 6*w + 102]', '[9828, 1638, 48*w + 270]', '[9828, 1638, 48*w - 318]', '[9828, 1638, 6*w - 108]', '[9828, 4914, -62*w - 340]', '[9828, 4914, -22*w + 172]', '[9828, 4914, -22*w - 150]', '[9828, 4914, -62*w + 402]', '[9829, 9829, -21*w - 146]', '[9829, 9829, 21*w - 167]', '[9833, 9833, -21*w - 59]', '[9833, 9833, 21*w - 80]', '[9839, 9839, -115*w - 613]', '[9839, 9839, -115*w + 728]', '[9841, 9841, 19*w - 56]', '[9841, 9841, -46*w - 223]', '[9841, 9841, 46*w - 269]', '[9841, 9841, -19*w - 37]', '[9851, 9851, -17*w - 131]', '[9851, 9851, 17*w - 148]', '[9852, 4926, 22*w + 68]', '[9852, 4926, -74*w + 452]', '[9852, 4926, 74*w + 378]', '[9852, 4926, -22*w + 90]', '[9853, 9853, -12*w - 115]', '[9853, 9853, 81*w - 518]', '[9853, 9853, 81*w + 437]', '[9853, 9853, 12*w - 127]', '[9861, 9861, 25*w + 92]', '[9861, 9861, 146*w + 763]', '[9861, 9861, 146*w - 909]', '[9861, 9861, 25*w - 117]', '[9867, 9867, w + 99]', '[9867, 9867, 61*w + 335]', '[9867, 9867, 29*w - 209]', '[9867, 9867, -14*w - 121]', '[9867, 9867, 31*w + 189]', '[9867, 9867, 254*w + 1341]', '[9867, 9867, 73*w - 469]', '[9867, 9867, 2*w - 101]', '[9867, 9867, -2*w - 99]', '[9867, 9867, -73*w - 396]', '[9867, 9867, -254*w + 1595]', '[9867, 9867, -31*w + 220]', '[9867, 9867, 14*w - 135]', '[9867, 9867, -29*w - 180]', '[9867, 9867, -61*w + 396]', '[9867, 9867, -w + 100]', '[9872, 2468, -4*w - 100]', '[9872, 2468, 4*w - 104]', '[9873, 3291, -18*w - 21]', '[9873, 3291, 18*w - 39]', '[9873, 9873, 49*w - 289]', '[9873, 9873, -29*w + 149]', '[9873, 9873, 29*w + 120]', '[9873, 9873, -49*w - 240]', '[9876, 4938, 34*w - 186]', '[9876, 4938, 100*w - 618]', '[9876, 4938, 100*w + 518]', '[9876, 4938, 34*w + 152]', '[9881, 9881, 13*w - 131]', '[9881, 9881, 5*w - 106]', '[9881, 9881, -5*w - 101]', '[9881, 9881, -13*w - 118]', '[9883, 9883, 41*w - 235]', '[9883, 9883, 41*w + 194]', '[9899, 9899, -41*w + 277]', '[9899, 9899, -41*w - 236]', '[9900, 330, 60*w + 330]', '[9900, 330, 60*w - 390]', '[9900, 990, 10*w + 110]', '[9900, 990, -50*w + 330]', '[9900, 990, -50*w - 280]', '[9900, 990, 10*w - 120]', '[9901, 9901, -31*w - 133]', '[9901, 9901, 31*w - 164]', '[9923, 9923, 26*w + 167]', '[9923, 9923, -26*w + 193]', '[9927, 3309, -51*w - 285]', '[9927, 3309, 51*w - 336]', '[9927, 9927, 59*w - 384]', '[9927, 9927, -7*w - 104]', '[9927, 9927, 7*w - 111]', '[9927, 9927, -59*w - 325]', '[9931, 9931, 35*w + 158]', '[9931, 9931, 35*w - 193]', '[9932, 4966, 54*w - 322]', '[9932, 4966, -18*w - 20]', '[9932, 4966, 18*w - 38]', '[9932, 4966, -54*w - 268]', '[9933, 9933, 79*w + 405]', '[9933, 9933, -26*w - 99]', '[9933, 9933, 23*w + 76]', '[9933, 9933, -19*w - 36]', '[9933, 9933, -19*w + 55]', '[9933, 9933, 23*w - 99]', '[9933, 9933, -26*w + 125]', '[9933, 9933, 79*w - 484]', '[9936, 828, 156*w - 972]', '[9936, 828, 24*w - 108]', '[9936, 828, 24*w + 84]', '[9936, 828, 156*w + 816]', '[9936, 2484, 40*w + 188]', '[9936, 2484, 20*w - 68]', '[9936, 2484, 20*w + 48]', '[9936, 2484, 40*w - 228]', '[9937, 9937, -99*w + 629]', '[9937, 9937, -129*w + 815]', '[9939, 9939, 28*w + 113]', '[9939, 9939, 127*w - 789]', '[9939, 9939, 127*w + 662]', '[9939, 9939, 28*w - 141]', '[9941, 9941, -37*w - 217]', '[9941, 9941, -37*w + 254]', '[9948, 4974, 58*w - 378]', '[9948, 4974, 52*w - 342]', '[9948, 4974, -52*w - 290]', '[9948, 4974, -58*w - 320]', '[9959, 9959, 72*w + 367]', '[9959, 9959, -27*w - 106]', '[9959, 9959, 27*w - 133]', '[9959, 9959, 72*w - 439]', '[9961, 9961, -72*w + 463]', '[9961, 9961, -177*w + 1114]', '[9963, 1107, -9*w - 108]', '[9963, 1107, 18*w - 153]', '[9963, 1107, -18*w - 135]', '[9963, 1107, 9*w - 117]', '[9963, 3321, 57*w - 372]', '[9963, 3321, -147*w - 780]', '[9963, 3321, 147*w - 927]', '[9963, 3321, -57*w - 315]', '[9963, 9963, -34*w - 203]', '[9963, 9963, 53*w - 348]', '[9963, 9963, -53*w - 295]', '[9963, 9963, 34*w - 237]', '[9968, 2492, -36*w - 164]', '[9968, 2492, -36*w + 200]', '[9971, 767, -39*w + 221]', '[9971, 767, -39*w - 182]', '[9971, 9971, 21*w + 58]', '[9971, 9971, 45*w - 262]', '[9971, 9971, 45*w + 217]', '[9971, 9971, 21*w - 79]', '[9972, 1662, 54*w - 354]', '[9972, 1662, -54*w - 300]', '[9972, 4986, 8*w - 114]', '[9972, 4986, -56*w - 310]', '[9972, 4986, 56*w - 366]', '[9972, 4986, -8*w - 106]', '[9975, 1995, -55*w + 360]', '[9975, 1995, -230*w + 1445]', '[9984, 624, 16*w + 128]', '[9984, 624, 80*w - 512]', '[9984, 624, 80*w + 432]', '[9984, 624, 16*w - 144]', '[9987, 9987, 37*w - 207]', '[9987, 9987, 92*w + 475]', '[9987, 9987, 92*w - 567]', '[9987, 9987, 37*w + 170]', '[9988, 4994, 106*w + 550]', '[9988, 4994, -38*w - 176]', '[9988, 4994, -38*w + 214]', '[9988, 4994, 106*w - 656]', '[9989, 9989, -18*w - 19]', '[9989, 9989, -18*w + 37]', '[9991, 9991, -138*w + 871]', '[9991, 9991, -42*w + 283]', '[9991, 9991, -42*w - 241]', '[9991, 9991, -93*w + 592]', '[10000, 100, -100]'], 'label': '2.2.133.1', 'narrow_class_no': 2, 'primes': ['[3, 3, -w + 6]', '[3, 3, -w - 5]', '[4, 2, 2]', '[7, 7, 3*w - 19]', '[11, 11, -2*w - 11]', '[11, 11, -2*w + 13]', '[13, 13, w + 4]', '[13, 13, -w + 5]', '[19, 19, 5*w - 31]', '[23, 23, -w - 7]', '[23, 23, w - 8]', '[25, 5, -5]', '[31, 31, -w - 1]', '[31, 31, w - 2]', '[41, 41, 6*w + 31]', '[41, 41, 6*w - 37]', '[43, 43, -3*w - 17]', '[43, 43, -3*w + 20]', '[59, 59, 3*w - 17]', '[59, 59, 3*w + 14]', '[89, 89, 3*w + 13]', '[89, 89, 3*w - 16]', '[97, 97, 2*w - 7]', '[97, 97, -2*w - 5]', '[103, 103, 8*w + 41]', '[103, 103, 8*w - 49]', '[137, 137, 11*w - 70]', '[137, 137, 11*w + 59]', '[149, 149, -w - 13]', '[149, 149, w - 14]', '[163, 163, -3*w - 20]', '[163, 163, 3*w - 23]', '[167, 167, -3*w - 10]', '[167, 167, 3*w - 13]', '[173, 173, 6*w - 35]', '[173, 173, 6*w + 29]', '[181, 181, 5*w + 23]', '[181, 181, 5*w - 28]', '[191, 191, 2*w - 19]', '[191, 191, -2*w - 17]', '[197, 197, 4*w - 29]', '[197, 197, -4*w - 25]', '[223, 223, 7*w - 41]', '[223, 223, 7*w + 34]', '[227, 227, -3*w - 7]', '[227, 227, 3*w - 10]', '[233, 233, 13*w + 70]', '[233, 233, 13*w - 83]', '[239, 239, -w - 16]', '[239, 239, w - 17]', '[241, 241, 11*w + 56]', '[241, 241, 11*w - 67]', '[257, 257, 3*w - 8]', '[257, 257, -3*w - 5]', '[263, 263, -7*w + 47]', '[263, 263, -7*w - 40]', '[269, 269, -3*w - 4]', '[269, 269, 3*w - 7]', '[277, 277, 9*w - 59]', '[277, 277, -9*w - 50]', '[289, 17, -17]', '[293, 293, -3*w - 1]', '[293, 293, 3*w - 4]', '[307, 307, -4*w - 13]', '[307, 307, 4*w - 17]', '[347, 347, -w - 19]', '[347, 347, w - 20]', '[359, 359, 5*w + 32]', '[359, 359, -5*w + 37]', '[383, 383, 21*w - 130]', '[383, 383, 24*w - 149]', '[389, 389, -20*w + 127]', '[389, 389, 25*w - 158]', '[409, 409, 10*w - 59]', '[409, 409, 10*w + 49]', '[433, 433, 14*w + 71]', '[433, 433, 14*w - 85]', '[439, 439, -7*w + 38]', '[439, 439, 7*w + 31]', '[443, 443, 2*w - 25]', '[443, 443, -2*w - 23]', '[457, 457, -3*w - 26]', '[457, 457, 3*w - 29]', '[463, 463, 18*w + 97]', '[463, 463, 18*w - 115]', '[491, 491, 17*w - 109]', '[491, 491, 17*w + 92]', '[499, 499, -9*w + 61]', '[499, 499, -9*w - 52]', '[509, 509, 15*w + 76]', '[509, 509, 15*w - 91]', '[521, 521, 6*w - 29]', '[521, 521, -6*w - 23]', '[523, 523, -4*w - 1]', '[523, 523, 4*w - 5]', '[541, 541, -12*w - 67]', '[541, 541, 12*w - 79]', '[557, 557, -4*w - 31]', '[557, 557, 4*w - 35]', '[563, 563, 12*w - 71]', '[563, 563, 12*w + 59]', '[571, 571, 3*w - 31]', '[571, 571, -3*w - 28]', '[601, 601, 11*w + 53]', '[601, 601, 11*w - 64]', '[607, 607, 8*w + 35]', '[607, 607, -8*w + 43]', '[613, 613, -9*w - 53]', '[613, 613, -9*w + 62]', '[617, 617, -w - 25]', '[617, 617, w - 26]', '[631, 631, -3*w - 29]', '[631, 631, 3*w - 32]', '[653, 653, 19*w + 103]', '[653, 653, 19*w - 122]', '[661, 661, 19*w - 116]', '[661, 661, 19*w + 97]', '[677, 677, 33*w - 205]', '[677, 677, 33*w + 172]', '[701, 701, -13*w + 86]', '[701, 701, -13*w - 73]', '[709, 709, 15*w - 98]', '[709, 709, -15*w - 83]', '[739, 739, -6*w - 41]', '[739, 739, 6*w - 47]', '[757, 757, 3*w - 34]', '[757, 757, -3*w - 31]', '[773, 773, 18*w + 91]', '[773, 773, 18*w - 109]', '[787, 787, 28*w - 173]', '[787, 787, -37*w + 230]', '[797, 797, 6*w - 23]', '[797, 797, -6*w - 17]', '[809, 809, 5*w - 43]', '[809, 809, -5*w - 38]', '[811, 811, 5*w - 7]', '[811, 811, -5*w - 2]', '[821, 821, 7*w - 53]', '[821, 821, 7*w + 46]', '[823, 823, -3*w - 32]', '[823, 823, 3*w - 35]', '[829, 829, 5*w - 4]', '[829, 829, 5*w - 1]', '[839, 839, 15*w - 89]', '[839, 839, 15*w + 74]', '[841, 29, -29]', '[857, 857, 21*w - 128]', '[857, 857, 21*w + 107]', '[883, 883, 27*w + 145]', '[883, 883, 27*w - 172]', '[887, 887, 9*w - 47]', '[887, 887, -9*w - 38]', '[919, 919, 6*w - 49]', '[919, 919, -6*w - 43]', '[941, 941, -6*w - 13]', '[941, 941, 6*w - 19]', '[947, 947, -11*w - 65]', '[947, 947, -11*w + 76]', '[967, 967, -9*w - 56]', '[967, 967, 9*w - 65]', '[971, 971, 9*w + 37]', '[971, 971, 9*w - 46]', '[983, 983, 27*w + 139]', '[983, 983, 27*w - 166]']}
• 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': [-33, -1, 1], 'conductor': 133, 'degree': 2, 'dirichlet_group': [1, 132], 'disc_abs': 133, 'disc_rad': 133, 'disc_sign': 1, 'frobs': [[2, [[2, 1]]], [3, [[1, 2]]], [5, [[2, 1]]], [7, [0]], [11, [[1, 2]]], [13, [[1, 2]]], [17, [[2, 1]]], [19, [0]], [23, [[1, 2]]], [29, [[2, 1]]], [31, [[1, 2]]], [37, [[2, 1]]], [41, [[1, 2]]], [43, [[1, 2]]], [47, [[2, 1]]], [53, [[2, 1]]], [59, [[1, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [1, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 11.532562594670797, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.133.1', 'local_algs': ['7.2.1.2', '19.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [7, 19], 'rd': 11.5325625947, 'regulator': {'__RealLiteral__': 0, 'data': '5.15325818041', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 15 a + 79 \\)'], 'used_grh': False, 'zk': ['1', 'a']}