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hmf_forms • Show schema
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{'deg': 2, 'dimension': 8, 'disc': 492, 'field_bad_primes': [2, 3, 41], 'field_label': '2.2.492.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.492.1-3.1-l', 'label_nsuffix': 11, 'label_suffix': 'l', 'level_bad_primes': [3], 'level_ideal': '[3, 3, w]', 'level_label': '3.1', 'level_norm': 3, 'parallel_weight': 2, 'short_label': '3.1-l', 'weight': '[2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[3, 3, w]', 1]], 'hecke_eigenvalues': ['-1/1914*e^7 + 7/1914*e^6 + 25/957*e^5 - 160/957*e^4 - 299/638*e^3 + 4027/1914*e^2 + 923/319*e - 382/87', -1, '-1/1914*e^7 + 7/1914*e^6 + 25/957*e^5 - 160/957*e^4 - 299/638*e^3 + 4027/1914*e^2 + 1242/319*e - 382/87', '1/1914*e^7 - 7/1914*e^6 - 25/957*e^5 + 160/957*e^4 + 299/638*e^3 - 4027/1914*e^2 - 1242/319*e + 556/87', '-7/5104*e^7 + 17/1914*e^6 + 93/1276*e^5 - 763/1914*e^4 - 433/319*e^3 + 3151/638*e^2 + 7325/957*e - 1043/87', '-7/5104*e^7 + 79/7656*e^6 + 41/638*e^5 - 917/1914*e^4 - 312/319*e^3 + 3657/638*e^2 + 5059/957*e - 745/87', '1/1914*e^7 + 2/957*e^6 - 2/33*e^5 + 23/1914*e^4 + 2525/1914*e^3 - 1783/1914*e^2 - 2562/319*e + 138/29', '-1/1914*e^7 + 3/319*e^6 - 8/957*e^5 - 617/1914*e^4 + 731/1914*e^3 + 6271/1914*e^2 - 78/319*e - 524/87', '-1/957*e^7 + 15/2552*e^6 + 233/3828*e^5 - 1291/3828*e^4 - 941/957*e^3 + 9407/1914*e^2 + 4295/957*e - 1004/87', '-1/957*e^7 + 67/7656*e^6 + 167/3828*e^5 - 423/1276*e^4 - 853/957*e^3 + 6701/1914*e^2 + 6781/957*e - 524/87', '1/116*e^6 - 3/58*e^5 - 27/116*e^4 + 37/29*e^3 + 51/29*e^2 - 180/29*e - 100/29', '-13/15312*e^7 + 5/957*e^6 + 179/3828*e^5 - 1205/3828*e^4 - 1063/1914*e^3 + 8297/1914*e^2 + 349/319*e - 201/29', '-13/15312*e^7 + 17/2552*e^6 + 73/1914*e^5 - 875/3828*e^4 - 1613/1914*e^3 + 4073/1914*e^2 + 1933/319*e - 421/87', '1/348*e^6 - 1/58*e^5 - 9/116*e^4 + 37/87*e^3 + 17/29*e^2 - 60/29*e + 103/87', '1/348*e^6 - 1/58*e^5 - 9/116*e^4 + 37/87*e^3 + 17/29*e^2 - 60/29*e + 103/87', '-7/7656*e^7 + 49/7656*e^6 + 175/3828*e^5 - 280/957*e^4 - 142/319*e^3 + 2447/957*e^2 - 538/319*e - 16/87', '-1/638*e^7 + 53/3828*e^6 + 39/638*e^5 - 739/1276*e^4 - 1877/1914*e^3 + 2041/319*e^2 + 2428/319*e - 608/87', '-1/638*e^7 + 31/3828*e^6 + 61/638*e^5 - 541/1276*e^4 - 3505/1914*e^3 + 1986/319*e^2 + 3110/319*e - 1684/87', '-5/7656*e^7 + 1/319*e^6 + 79/1914*e^5 - 41/319*e^4 - 268/319*e^3 + 1399/957*e^2 + 3574/957*e - 186/29', '-5/7656*e^7 + 23/3828*e^6 + 23/957*e^5 - 277/957*e^4 - 26/319*e^3 + 2917/957*e^2 - 958/957*e + 38/87', '1/957*e^7 + 4/957*e^6 - 4/33*e^5 + 23/957*e^4 + 2525/957*e^3 - 1783/957*e^2 - 5124/319*e + 189/29', '-1/957*e^7 + 6/319*e^6 - 16/957*e^5 - 617/957*e^4 + 731/957*e^3 + 6271/957*e^2 - 156/319*e - 1309/87', '35/7656*e^7 - 89/2552*e^6 - 245/1914*e^5 + 717/638*e^4 + 1085/957*e^3 - 9287/957*e^2 - 4624/957*e + 1862/87', '-35/7656*e^7 + 223/7656*e^6 + 311/1914*e^5 - 309/319*e^4 - 633/319*e^3 + 8165/957*e^2 + 296/33*e - 502/87', '-43/7656*e^7 + 235/7656*e^6 + 159/638*e^5 - 2197/1914*e^4 - 3610/957*e^3 + 3690/319*e^2 + 19996/957*e - 2255/87', '43/7656*e^7 - 367/7656*e^6 - 93/638*e^5 + 1544/957*e^4 + 1168/957*e^3 - 4812/319*e^2 - 8116/957*e + 1985/87', '35/7656*e^7 - 89/2552*e^6 - 245/1914*e^5 + 717/638*e^4 + 1085/957*e^3 - 9287/957*e^2 - 4624/957*e + 1340/87', '-35/7656*e^7 + 223/7656*e^6 + 311/1914*e^5 - 309/319*e^4 - 633/319*e^3 + 8165/957*e^2 + 296/33*e - 1024/87', '-5/3828*e^7 + 13/3828*e^6 + 191/1914*e^5 - 1325/3828*e^4 - 459/319*e^3 + 11173/1914*e^2 + 1153/957*e - 1538/87', '-5/3828*e^7 + 19/1276*e^6 + 59/1914*e^5 - 625/1276*e^4 - 129/319*e^3 + 6091/1914*e^2 + 4079/957*e + 166/29', '1/232*e^7 - 7/232*e^6 - 25/116*e^5 + 40/29*e^4 + 94/29*e^3 - 449/29*e^2 - 366/29*e + 688/29', '1/232*e^7 - 7/232*e^6 - 25/116*e^5 + 40/29*e^4 + 94/29*e^3 - 449/29*e^2 - 366/29*e + 688/29', '5/15312*e^7 + 5/3828*e^6 - 5/132*e^5 + 67/957*e^4 + 490/957*e^3 - 4105/1914*e^2 + 233/319*e + 253/29', '5/15312*e^7 - 15/2552*e^6 + 5/957*e^5 + 133/957*e^4 - 49/957*e^3 - 211/1914*e^2 - 669/319*e - 499/87', '-5/2552*e^7 + 149/7656*e^6 + 81/1276*e^5 - 589/957*e^4 - 1147/957*e^3 + 1256/319*e^2 + 8896/957*e + 60/29', '-5/2552*e^7 + 61/7656*e^6 + 169/1276*e^5 - 611/957*e^4 - 1499/957*e^3 + 3060/319*e^2 - 1048/957*e - 20', '-1/348*e^6 + 1/58*e^5 + 9/116*e^4 - 37/87*e^3 - 17/29*e^2 + 60/29*e - 277/87', '-1/957*e^7 + 7/957*e^6 + 50/957*e^5 - 533/1276*e^4 - 578/957*e^3 + 10925/1914*e^2 + 2029/957*e - 706/87', '-1/957*e^7 + 7/957*e^6 + 50/957*e^5 - 961/3828*e^4 - 1216/957*e^3 + 5183/1914*e^2 + 9047/957*e - 274/29', '-37/15312*e^7 + 157/7656*e^6 + 95/957*e^5 - 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90/29', '-1/58*e^6 + 3/29*e^5 + 27/58*e^4 - 74/29*e^3 - 102/29*e^2 + 360/29*e - 90/29', '-1/638*e^7 + 7/7656*e^6 + 177/1276*e^5 - 260/957*e^4 - 2132/957*e^3 + 1678/319*e^2 + 1520/957*e - 710/29', '-1/638*e^7 + 161/7656*e^6 + 23/1276*e^5 - 700/957*e^4 + 398/957*e^3 + 48/11*e^2 - 2132/957*e + 526/29', '-43/7656*e^7 + 433/7656*e^6 + 30/319*e^5 - 7067/3828*e^4 + 53/957*e^3 + 5373/319*e^2 + 2176/957*e - 2633/87', '43/7656*e^7 - 169/7656*e^6 - 96/319*e^5 + 3503/3828*e^4 + 4831/957*e^3 - 3129/319*e^2 - 25936/957*e + 1607/87', '-1/1276*e^7 + 97/7656*e^6 - 5/1276*e^5 - 102/319*e^4 - 373/957*e^3 + 597/319*e^2 + 3722/319*e + 250/87', '-1/1276*e^7 - 13/7656*e^6 + 105/1276*e^5 - 2/11*e^4 - 1451/957*e^3 + 1895/319*e^2 + 1918/319*e - 2266/87', '-53/15312*e^7 + 71/2552*e^6 + 5/33*e^5 - 1867/1914*e^4 - 3280/957*e^3 + 18631/1914*e^2 + 25639/957*e - 1909/87', '-53/15312*e^7 + 79/3828*e^6 + 745/3828*e^5 - 791/638*e^4 - 2543/957*e^3 + 34009/1914*e^2 + 8897/957*e - 2935/87', '-9/2552*e^7 + 13/7656*e^6 + 221/957*e^5 - 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2624/87*e + 942/29', '-41/3828*e^7 + 265/3828*e^6 + 386/957*e^5 - 778/319*e^4 - 3429/638*e^3 + 44741/1914*e^2 + 28346/957*e - 4064/87', '41/3828*e^7 - 103/1276*e^6 - 320/957*e^5 + 877/319*e^4 + 7031/1914*e^3 - 49229/1914*e^2 - 20426/957*e + 3478/87', '-1/638*e^7 + 9/319*e^6 - 8/319*e^5 - 617/638*e^4 + 731/638*e^3 + 6271/638*e^2 - 234/319*e - 234/29', '1/638*e^7 + 2/319*e^6 - 2/11*e^5 + 23/638*e^4 + 2525/638*e^3 - 1783/638*e^2 - 7686/319*e + 704/29', '43/7656*e^7 - 103/7656*e^6 - 225/638*e^5 + 653/957*e^4 + 6052/957*e^3 - 2568/319*e^2 - 31876/957*e + 2699/87', '-43/7656*e^7 + 499/7656*e^6 + 27/638*e^5 - 3979/1914*e^4 + 1274/957*e^3 + 5934/319*e^2 - 3764/957*e - 1541/87', '49/7656*e^7 - 83/1914*e^6 - 629/1914*e^5 + 4085/1914*e^4 + 5578/957*e^3 - 27854/957*e^2 - 11876/319*e + 1838/29', '49/7656*e^7 - 59/1276*e^6 - 298/957*e^5 + 3755/1914*e^4 + 6128/957*e^3 - 23630/957*e^2 - 15044/319*e + 5150/87', '-1/58*e^7 + 19/174*e^6 + 52/87*e^5 - 308/87*e^4 - 7*e^3 + 2603/87*e^2 + 2444/87*e - 3680/87', '1/58*e^7 - 23/174*e^6 - 40/87*e^5 + 362/87*e^4 + 313/87*e^3 - 3011/87*e^2 - 1004/87*e + 1300/29', '-13/1276*e^7 + 317/3828*e^6 + 262/957*e^5 - 5239/1914*e^4 - 751/319*e^3 + 23723/957*e^2 + 12740/957*e - 3673/87', '13/1276*e^7 - 229/3828*e^6 - 394/957*e^5 + 4051/1914*e^4 + 5509/957*e^3 - 19235/957*e^2 - 28580/957*e + 977/29', '23/5104*e^7 - 75/2552*e^6 - 76/319*e^5 + 6653/3828*e^4 + 4559/1914*e^3 - 14527/638*e^2 - 47/957*e + 2473/87', '23/5104*e^7 - 43/1276*e^6 - 271/1276*e^5 + 4387/3828*e^4 + 8761/1914*e^3 - 6475/638*e^2 - 28339/957*e + 2159/87', '3/638*e^7 - 329/7656*e^6 - 223/1276*e^5 + 3001/1914*e^4 + 977/319*e^3 - 4462/319*e^2 - 21500/957*e + 830/87', '3/638*e^7 - 175/7656*e^6 - 13/44*e^5 + 2759/1914*e^4 + 1395/319*e^3 - 6662/319*e^2 - 11116/957*e + 4306/87', '-19/7656*e^7 - 65/7656*e^6 + 125/638*e^5 + 307/957*e^4 - 3361/957*e^3 - 1459/319*e^2 + 9520/957*e + 898/87', '19/7656*e^7 - 331/7656*e^6 + 73/638*e^5 + 71/66*e^4 - 3965/957*e^3 - 1907/319*e^2 + 26120/957*e - 490/87', '27/2552*e^7 - 299/2552*e^6 - 13/638*e^5 + 2105/638*e^4 - 1440/319*e^3 - 7504/319*e^2 + 10748/319*e + 831/29', '-27/2552*e^7 + 79/2552*e^6 + 343/638*e^5 - 310/319*e^4 - 2630/319*e^3 + 1894/319*e^2 + 9052/319*e + 343/29', '37/1914*e^7 - 617/3828*e^6 - 305/638*e^5 + 19973/3828*e^4 + 3202/957*e^3 - 14660/319*e^2 - 16048/957*e + 6740/87', '-37/1914*e^7 + 419/3828*e^6 + 503/638*e^5 - 14627/3828*e^4 - 10528/957*e^3 + 11294/319*e^2 + 51688/957*e - 4592/87', '15/2552*e^7 - 119/3828*e^6 - 113/319*e^5 + 2213/1276*e^4 + 4915/957*e^3 - 14191/638*e^2 - 3363/319*e + 4136/87', '15/2552*e^7 - 49/957*e^6 - 149/638*e^5 + 2587/1276*e^4 + 3023/957*e^3 - 11705/638*e^2 - 4485/319*e + 544/87', '-2/957*e^7 + 12/319*e^6 - 32/957*e^5 - 1234/957*e^4 + 1462/957*e^3 + 12542/957*e^2 - 312/319*e - 2009/87', '2/957*e^7 + 8/957*e^6 - 8/33*e^5 + 46/957*e^4 + 5050/957*e^3 - 3566/957*e^2 - 10248/319*e + 581/29', '7/1914*e^7 - 21/319*e^6 + 56/957*e^5 + 4319/1914*e^4 - 5117/1914*e^3 - 43897/1914*e^2 + 546/319*e + 5408/87', '-7/1914*e^7 - 14/957*e^6 + 14/33*e^5 - 161/1914*e^4 - 17675/1914*e^3 + 12481/1914*e^2 + 17934/319*e - 386/29', '-31/7656*e^7 + 79/1914*e^6 + 239/1914*e^5 - 6137/3828*e^4 - 1445/957*e^3 + 28363/1914*e^2 + 419/33*e + 28/29', '-31/7656*e^7 + 59/3828*e^6 + 268/957*e^5 - 1261/1276*e^4 - 4789/957*e^3 + 29749/1914*e^2 + 17849/957*e - 4700/87', '23/2552*e^7 - 593/7656*e^6 - 73/638*e^5 + 645/319*e^4 - 3191/1914*e^3 - 7241/638*e^2 + 7874/319*e + 1072/87', '-23/2552*e^7 + 373/7656*e^6 + 183/638*e^5 - 795/638*e^4 - 4949/1914*e^3 + 3501/638*e^2 - 1274/319*e + 2422/87', '71/15312*e^7 - 57/1276*e^6 - 607/3828*e^5 + 1809/1276*e^4 + 2391/638*e^3 - 21727/1914*e^2 - 33665/957*e + 351/29', '71/15312*e^7 - 155/7656*e^6 - 292/957*e^5 + 5933/3828*e^4 + 2677/638*e^3 - 47599/1914*e^2 - 9025/957*e + 175/3', '-1/7656*e^7 - 59/7656*e^6 + 223/3828*e^5 + 175/638*e^4 - 2011/957*e^3 - 103/957*e^2 + 13730/957*e - 2420/87', '-1/7656*e^7 + 73/7656*e^6 - 173/3828*e^5 - 685/1914*e^4 + 1069/957*e^3 + 3263/957*e^2 + 574/957*e + 308/29', '3/58*e^6 - 9/29*e^5 - 81/58*e^4 + 222/29*e^3 + 306/29*e^2 - 1080/29*e - 107/29', '-1/319*e^7 + 18/319*e^6 - 16/319*e^5 - 617/319*e^4 + 731/319*e^3 + 6271/319*e^2 - 468/319*e - 1628/29', '1/319*e^7 + 4/319*e^6 - 4/11*e^5 + 23/319*e^4 + 2525/319*e^3 - 1783/319*e^2 - 15372/319*e + 248/29', '97/15312*e^7 - 115/2552*e^6 - 299/957*e^5 + 1819/957*e^4 + 6074/957*e^3 - 1549/66*e^2 - 42689/957*e + 4925/87', '97/15312*e^7 - 167/3828*e^6 - 1229/3828*e^5 + 687/319*e^4 + 5161/957*e^3 - 54887/1914*e^2 - 30919/957*e + 4991/87', '47/7656*e^7 - 373/7656*e^6 - 1043/3828*e^5 + 9071/3828*e^4 + 3140/957*e^3 - 54107/1914*e^2 - 4501/319*e + 862/29', '47/7656*e^7 - 95/2552*e^6 - 1307/3828*e^5 + 5969/3828*e^4 + 6682/957*e^3 - 1249/66*e^2 - 12883/319*e + 5086/87', '-1/319*e^7 + 25/638*e^6 + 17/319*e^5 - 937/638*e^4 - 83/319*e^3 + 5149/319*e^2 + 3492/319*e - 1486/29', '1/319*e^7 - 3/638*e^6 - 83/319*e^5 + 343/638*e^4 + 59/11*e^3 - 2905/319*e^2 - 11412/319*e + 390/29'], 'hecke_polynomial': 'x^8 - 8*x^7 - 32*x^6 + 304*x^5 + 280*x^4 - 3296*x^3 - 224*x^2 + 7936*x - 3872', 'label': '2.2.492.1-3.1-l'}
-
hmf_fields • Show schema
Hide schema
{'degree': 2, 'discriminant': 492, 'ideals': ['[1, 1, 1]', '[2, 2, -w - 11]', '[3, 3, w]', '[4, 2, 2]', '[6, 6, w + 3]', '[7, 7, w + 2]', '[7, 7, w + 5]', '[8, 4, -2*w - 22]', '[9, 3, 3]', '[12, 6, 2*w]', '[14, 14, w + 5]', '[14, 14, w + 9]', '[16, 4, 4]', '[17, 17, w + 2]', '[17, 17, w + 15]', '[18, 6, -3*w - 33]', '[19, 19, w + 3]', '[19, 19, w + 16]', '[21, 21, -w + 12]', '[21, 21, w + 12]', '[23, 23, -w - 10]', '[23, 23, w - 10]', '[24, 12, 2*w + 6]', '[25, 5, -5]', '[27, 9, 3*w]', '[28, 14, 2*w + 4]', '[28, 14, 2*w + 10]', '[29, 29, w + 6]', '[29, 29, w + 23]', '[32, 8, -4*w - 44]', '[34, 34, w + 15]', '[34, 34, w + 19]', '[36, 6, 6]', '[37, 37, 9*w + 100]', '[37, 37, -2*w - 23]', '[38, 38, w + 3]', '[38, 38, w + 35]', '[41, 41, w]', '[42, 42, -w - 9]', '[42, 42, -w + 9]', '[46, 46, -w - 13]', '[46, 46, 21*w + 233]', '[48, 12, 4*w]', '[49, 7, 7]', '[49, 49, -3*w + 34]', '[49, 49, 3*w + 34]', '[50, 10, 5*w + 55]', '[51, 51, 2*w - 21]', '[51, 51, 2*w + 21]', '[53, 53, w + 21]', '[53, 53, w + 32]', '[54, 18, 3*w + 9]', '[56, 28, 2*w + 10]', '[56, 28, 2*w + 18]', '[57, 57, 4*w - 45]', '[57, 57, 4*w + 45]', '[58, 58, w + 23]', '[58, 58, w + 35]', '[59, 59, -w - 8]', '[59, 59, w - 8]', '[61, 61, 6*w + 67]', '[61, 61, -5*w - 56]', '[63, 21, 3*w + 6]', '[63, 21, 3*w + 15]', '[64, 8, 8]', '[67, 67, w + 18]', '[67, 67, w + 49]', '[68, 34, 2*w + 4]', '[68, 34, 2*w + 30]', '[69, 69, w + 33]', '[69, 69, w + 36]', '[72, 12, -6*w - 66]', '[73, 73, -w - 14]', '[73, 73, w - 14]', '[74, 74, -w - 7]', '[74, 74, w - 7]', '[75, 15, 5*w]', '[76, 38, 2*w + 6]', '[76, 38, 2*w + 32]', '[79, 79, w + 26]', '[79, 79, w + 53]', '[81, 9, 9]', '[82, 82, w + 41]', '[83, 83, 14*w + 155]', '[83, 83, 3*w + 32]', '[84, 42, -2*w + 24]', '[84, 42, 2*w + 24]', '[87, 87, -w - 6]', '[87, 87, w - 6]', '[89, 89, w + 37]', '[89, 89, w + 52]', '[92, 46, -2*w - 20]', '[92, 46, 2*w - 20]', '[96, 24, 4*w + 12]', '[98, 14, -7*w - 77]', '[98, 98, -w - 5]', '[98, 98, -w + 5]', '[100, 10, -10]', '[101, 101, w + 27]', '[101, 101, w + 74]', '[102, 102, -w - 15]', '[102, 102, w - 15]', '[106, 106, w + 21]', '[106, 106, w + 85]', '[107, 107, -w - 4]', '[107, 107, w - 4]', '[108, 18, 6*w]', '[111, 111, w + 30]', '[111, 111, w + 81]', '[112, 28, 4*w + 8]', '[112, 28, 4*w + 20]', '[114, 114, w + 3]', '[114, 114, -w + 3]', '[116, 58, 2*w + 12]', '[116, 58, 2*w + 46]', '[118, 118, -3*w - 35]', '[118, 118, 19*w + 211]', '[119, 119, w + 2]', '[119, 119, 4*w - 43]', '[119, 119, 4*w + 43]', '[119, 119, w - 2]', '[121, 11, -11]', '[122, 122, -w - 1]', '[122, 122, w - 1]', '[123, 123, -w]', '[126, 42, 3*w + 15]', '[126, 42, 3*w + 27]', '[128, 16, -8*w - 88]', '[131, 131, 2*w - 19]', '[131, 131, -2*w - 19]', '[133, 133, w + 16]', '[133, 133, -2*w + 25]', '[133, 133, -2*w - 25]', '[133, 133, w - 16]', '[134, 134, w + 49]', '[134, 134, w + 85]', '[136, 68, 2*w + 30]', '[136, 68, 2*w + 38]', '[137, 137, w + 64]', '[137, 137, w + 73]', '[138, 138, w + 33]', '[138, 138, w + 105]', '[144, 12, 12]', '[146, 146, 3*w + 31]', '[146, 146, 25*w + 277]', '[147, 21, 7*w]', '[147, 147, w + 54]', '[147, 147, w + 93]', '[148, 74, 18*w + 200]', '[148, 74, -4*w - 46]', '[149, 149, w + 47]', '[149, 149, w + 102]', '[150, 30, 5*w + 15]', '[151, 151, w + 24]', '[151, 151, w + 127]', '[152, 76, 2*w + 6]', '[152, 76, 2*w + 70]', '[153, 51, 3*w + 6]', '[153, 51, 3*w + 45]', '[158, 158, w + 53]', '[158, 158, w + 105]', '[159, 159, -16*w - 177]', '[159, 159, -5*w - 54]', '[161, 161, w + 33]', '[161, 161, w + 79]', '[161, 161, w + 82]', '[161, 161, w + 128]', '[162, 18, -9*w - 99]', '[164, 82, 2*w]', '[166, 166, -w - 17]', '[166, 166, w - 17]', '[168, 84, -2*w - 18]', '[168, 84, -2*w + 18]', '[169, 13, -13]', '[171, 57, 3*w + 9]', '[171, 57, 3*w + 48]', '[174, 174, -5*w - 57]', '[174, 174, 17*w + 189]', '[175, 35, 5*w + 10]', '[175, 35, 5*w + 25]', '[177, 177, w + 51]', '[177, 177, w + 126]', '[178, 178, w + 37]', '[178, 178, w + 141]', '[183, 183, w + 60]', '[183, 183, w + 123]', '[184, 92, -2*w - 26]', '[184, 92, 42*w + 466]', '[189, 63, -3*w + 36]', '[189, 63, 3*w + 36]', '[192, 24, 8*w]', '[196, 14, 14]', '[196, 98, -6*w + 68]', '[196, 98, 6*w + 68]', '[199, 199, w + 83]', '[199, 199, w + 116]', '[200, 20, 10*w + 110]', '[201, 201, -w - 18]', '[201, 201, w - 18]', '[202, 202, w + 27]', '[202, 202, w + 175]', '[203, 203, 6*w - 65]', '[203, 203, -2*w + 17]', '[203, 203, 2*w + 17]', '[203, 203, -6*w - 65]', '[204, 102, 4*w - 42]', '[204, 102, 4*w + 42]', '[207, 69, -3*w - 30]', '[207, 69, 3*w - 30]', '[211, 211, w + 40]', '[211, 211, w + 171]', '[212, 106, 2*w + 42]', '[212, 106, 2*w + 64]', '[214, 214, -7*w - 79]', '[214, 214, 15*w + 167]', '[216, 36, 6*w + 18]', '[219, 219, w + 87]', '[219, 219, w + 132]', '[222, 222, w + 81]', '[222, 222, w + 141]', '[224, 56, 4*w + 20]', '[224, 56, 4*w + 36]', '[225, 15, -15]', '[228, 114, 8*w - 90]', '[228, 114, 8*w + 90]', '[232, 116, 2*w + 46]', '[232, 116, 2*w + 70]', '[233, 233, w + 39]', '[233, 233, w + 194]', '[236, 118, -2*w - 16]', '[236, 118, 2*w - 16]', '[237, 237, 2*w - 27]', '[237, 237, -2*w - 27]', '[238, 238, -w - 19]', '[238, 238, -9*w - 101]', '[238, 238, 9*w - 101]', '[238, 238, w - 19]', '[241, 241, -4*w - 47]', '[241, 241, 29*w + 322]', '[242, 22, 11*w + 121]', '[243, 27, 9*w]', '[244, 122, 12*w + 134]', '[244, 122, -10*w - 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147]', '[9879, 9879, 16*w + 147]', '[9879, 9879, 65*w + 714]', '[9881, 9881, w + 410]', '[9881, 9881, w + 9471]', '[9882, 1098, -9*w - 9]', '[9882, 1098, 9*w - 9]', '[9886, 9886, 245*w + 2719]', '[9886, 9886, -19*w - 233]', '[9898, 1414, 7*w + 189]', '[9898, 1414, 7*w + 1225]', '[9898, 9898, w + 2249]', '[9898, 9898, w + 4013]', '[9898, 9898, w + 5885]', '[9898, 9898, w + 7649]', '[9899, 9899, 10*w - 49]', '[9899, 9899, 9*w - 8]', '[9899, 9899, -9*w - 8]', '[9899, 9899, -10*w - 49]', '[9901, 9901, -10*w - 149]', '[9901, 9901, 10*w - 149]', '[9903, 9903, w + 2409]', '[9903, 9903, w + 7494]', '[9907, 9907, w + 434]', '[9907, 9907, w + 9473]', '[9908, 4954, 2*w + 614]', '[9908, 4954, 2*w + 4340]', '[9912, 4956, -2*w - 102]', '[9912, 4956, 34*w + 390]', '[9912, 4956, 34*w - 390]', '[9912, 4956, -2*w + 102]', '[9913, 9913, 87*w + 970]', '[9913, 9913, 4*w - 109]', '[9913, 9913, -4*w - 109]', '[9913, 9913, -56*w - 629]', '[9914, 9914, -9*w - 7]', '[9914, 9914, 9*w - 7]', '[9916, 4958, 2*w + 902]', '[9916, 4958, 2*w + 1170]', '[9916, 4958, 2*w + 3788]', '[9916, 4958, 2*w + 4056]', '[9918, 3306, 3*w + 105]', '[9918, 3306, -9*w - 141]', '[9918, 3306, 9*w - 141]', '[9918, 3306, -3*w + 105]', '[9921, 9921, -5*w - 114]', '[9921, 9921, 5*w - 114]', '[9922, 902, 11*w + 451]', '[9923, 9923, -18*w - 173]', '[9923, 9923, 18*w - 173]', '[9927, 3309, 9*w - 6]', '[9927, 3309, -9*w - 6]', '[9928, 4964, 2*w + 174]', '[9928, 4964, 2*w + 1050]', '[9928, 4964, 2*w + 3914]', '[9928, 4964, 2*w + 4790]', '[9929, 9929, w + 373]', '[9929, 9929, w + 9556]', '[9936, 828, 12*w + 396]', '[9936, 828, 12*w + 432]', '[9938, 9938, -9*w - 5]', '[9938, 9938, 9*w - 5]', '[9939, 9939, w + 264]', '[9939, 9939, w + 9675]', '[9941, 9941, w + 2736]', '[9941, 9941, w + 7205]', '[9946, 9946, w + 3043]', '[9946, 9946, w + 6903]', '[9947, 1421, 42*w - 455]', '[9947, 1421, -14*w + 119]', '[9947, 1421, 14*w + 119]', '[9947, 1421, -42*w - 455]', '[9947, 9947, -9*w + 4]', '[9947, 9947, -17*w - 160]', '[9947, 9947, 17*w - 160]', '[9947, 9947, 9*w + 4]', '[9948, 4974, 2*w + 582]', '[9948, 4974, 2*w + 4392]', '[9950, 1990, 5*w + 415]', '[9950, 1990, 5*w + 1575]', '[9954, 3318, 9*w + 3]', '[9954, 3318, 45*w + 489]', '[9954, 3318, 111*w + 1227]', '[9954, 3318, 9*w - 3]', '[9956, 4978, 2*w + 374]', '[9956, 4978, 2*w + 412]', '[9956, 4978, 2*w + 4566]', '[9956, 4978, 2*w + 4604]', '[9959, 9959, 89*w + 982]', '[9959, 9959, 9*w - 2]', '[9959, 9959, -9*w - 2]', '[9959, 9959, 56*w + 613]', '[9961, 9961, -15*w - 194]', '[9961, 9961, 31*w - 358]', '[9961, 9961, -31*w - 358]', '[9961, 9961, 15*w - 194]', '[9962, 9962, 9*w + 1]', '[9962, 9962, -31*w + 329]', '[9962, 9962, 31*w + 329]', '[9962, 9962, -9*w + 1]', '[9963, 1107, -9*w]', '[9968, 2492, 52*w - 568]', '[9968, 2492, 12*w + 88]', '[9968, 2492, -12*w + 88]', '[9968, 2492, -52*w - 568]', '[9969, 9969, w + 942]', '[9969, 9969, w + 9027]', '[9971, 767, -13*w - 104]', '[9971, 767, 13*w - 104]', '[9972, 1662, -6*w - 120]', '[9972, 1662, 6*w - 120]', '[9973, 9973, 86*w + 959]', '[9973, 9973, -57*w - 640]', '[9974, 9974, w + 1169]', '[9974, 9974, w + 8805]', '[9975, 1995, 5*w + 270]', '[9975, 1995, 5*w + 585]', '[9975, 1995, 5*w + 1410]', '[9975, 1995, 5*w + 1725]', '[9983, 9983, 37*w + 398]', '[9983, 9983, -11*w - 70]', '[9983, 9983, 11*w - 70]', '[9983, 9983, 136*w + 1505]', '[9986, 9986, 15*w + 133]', '[9986, 9986, 367*w + 4069]', '[9989, 9989, w + 1157]', '[9989, 9989, w + 3124]', '[9989, 9989, w + 6865]', '[9989, 9989, w + 8832]', '[9996, 714, 28*w - 294]', '[9996, 714, 28*w + 294]', '[9996, 4998, 20*w - 198]', '[9996, 4998, 10*w - 48]', '[9996, 4998, 10*w + 48]', '[9996, 4998, 20*w + 198]', '[9998, 9998, w + 1603]', '[9998, 9998, w + 8395]', '[10000, 100, -100]'], 'label': '2.2.492.1', 'narrow_class_no': 4, 'primes': ['[2, 2, -w - 11]', '[3, 3, w]', '[7, 7, w + 2]', '[7, 7, w + 5]', '[17, 17, w + 2]', '[17, 17, w + 15]', '[19, 19, w + 3]', '[19, 19, w + 16]', '[23, 23, -w - 10]', '[23, 23, w - 10]', '[25, 5, -5]', '[29, 29, w + 6]', '[29, 29, w + 23]', '[37, 37, 9*w + 100]', '[37, 37, -2*w - 23]', '[41, 41, w]', '[53, 53, w + 21]', '[53, 53, w + 32]', '[59, 59, -w - 8]', '[59, 59, w - 8]', '[61, 61, 6*w + 67]', '[61, 61, -5*w - 56]', '[67, 67, w + 18]', '[67, 67, w + 49]', '[73, 73, -w - 14]', '[73, 73, w - 14]', '[79, 79, w + 26]', '[79, 79, w + 53]', '[83, 83, 14*w + 155]', '[83, 83, 3*w + 32]', '[89, 89, w + 37]', '[89, 89, w + 52]', '[101, 101, w + 27]', '[101, 101, w + 74]', '[107, 107, -w - 4]', '[107, 107, w - 4]', '[121, 11, -11]', '[131, 131, 2*w - 19]', '[131, 131, -2*w - 19]', '[137, 137, w + 64]', '[137, 137, w + 73]', '[149, 149, w + 47]', '[149, 149, w + 102]', '[151, 151, w + 24]', '[151, 151, w + 127]', '[169, 13, -13]', '[199, 199, w + 83]', '[199, 199, w + 116]', '[211, 211, w + 40]', '[211, 211, w + 171]', '[233, 233, w + 39]', '[233, 233, w + 194]', '[241, 241, -4*w - 47]', '[241, 241, 29*w + 322]', '[251, 251, 18*w + 199]', '[251, 251, 7*w + 76]', '[257, 257, w + 61]', '[257, 257, w + 196]', '[277, 277, -w - 20]', '[277, 277, w - 20]', '[281, 281, w + 70]', '[281, 281, w + 211]', '[293, 293, w + 65]', '[293, 293, w + 228]', '[317, 317, w + 45]', '[317, 317, w + 272]', '[331, 331, w + 139]', '[331, 331, w + 192]', '[337, 337, -3*w - 38]', '[337, 337, 3*w - 38]', '[349, 349, 2*w - 29]', '[349, 349, -2*w - 29]', '[359, 359, 20*w + 221]', '[359, 359, 9*w + 98]', '[373, 373, -7*w - 80]', '[373, 373, 26*w + 289]', '[409, 409, 25*w + 278]', '[409, 409, -8*w - 91]', '[419, 419, 21*w + 232]', '[419, 419, 10*w + 109]', '[431, 431, 3*w - 26]', '[431, 431, -3*w - 26]', '[433, 433, -51*w - 566]', '[433, 433, 4*w + 49]', '[439, 439, w + 92]', '[439, 439, w + 347]', '[443, 443, 2*w - 7]', '[443, 443, -2*w - 7]', '[463, 463, w + 58]', '[463, 463, w + 405]', '[467, 467, 2*w - 5]', '[467, 467, -2*w - 5]', '[491, 491, 2*w - 1]', '[491, 491, -2*w - 1]', '[499, 499, w + 98]', '[499, 499, w + 401]', '[509, 509, w + 122]', '[509, 509, w + 387]', '[521, 521, w + 57]', '[521, 521, w + 464]', '[541, 541, 19*w + 212]', '[541, 541, -14*w - 157]', '[547, 547, w + 42]', '[547, 547, w + 505]', '[557, 557, w + 89]', '[557, 557, w + 468]', '[571, 571, w + 252]', '[571, 571, w + 319]', '[593, 593, w + 230]', '[593, 593, w + 363]', '[599, 599, -4*w - 37]', '[599, 599, 4*w - 37]', '[613, 613, -6*w - 71]', '[613, 613, 49*w + 544]', '[641, 641, w + 63]', '[641, 641, w + 578]', '[643, 643, w + 68]', '[643, 643, w + 575]', '[647, 647, 41*w + 454]', '[647, 647, 8*w + 85]', '[653, 653, w + 164]', '[653, 653, w + 489]', '[661, 661, -w - 28]', '[661, 661, w - 28]', '[691, 691, w + 309]', '[691, 691, w + 382]', '[727, 727, w + 48]', '[727, 727, w + 679]', '[733, 733, 2*w - 35]', '[733, 733, -2*w - 35]', '[743, 743, 4*w - 35]', '[743, 743, -4*w - 35]', '[751, 751, w + 209]', '[751, 751, w + 542]', '[769, 769, -5*w - 62]', '[769, 769, 72*w + 799]', '[773, 773, w + 69]', '[773, 773, w + 704]', '[809, 809, w + 107]', '[809, 809, w + 702]', '[823, 823, w + 348]', '[823, 823, w + 475]', '[829, 829, -3*w - 44]', '[829, 829, 3*w - 44]', '[853, 853, 46*w + 511]', '[853, 853, -9*w - 104]', '[863, 863, 27*w + 298]', '[863, 863, 16*w + 175]', '[877, 877, 2*w - 37]', '[877, 877, -2*w - 37]', '[883, 883, w + 130]', '[883, 883, w + 753]', '[911, 911, 3*w - 14]', '[911, 911, -3*w - 14]', '[919, 919, w + 431]', '[919, 919, w + 488]', '[929, 929, w + 353]', '[929, 929, w + 576]', '[947, 947, 83*w + 920]', '[947, 947, 6*w + 59]', '[961, 31, -31]', '[967, 967, w + 136]', '[967, 967, w + 831]', '[977, 977, w + 193]', '[977, 977, w + 784]', '[983, 983, -8*w - 83]', '[983, 983, 8*w - 83]', '[991, 991, w + 426]', '[991, 991, w + 565]']}
-
nf_fields • Show schema
Hide schema
{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [-123, 0, 1], 'conductor': 492, 'degree': 2, 'dirichlet_group': [1, 491], 'disc_abs': 492, 'disc_rad': 246, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[2, 1]]], [7, [[1, 2]]], [11, [[2, 1]]], [13, [[2, 1]]], [17, [[1, 2]]], [19, [[1, 2]]], [23, [[1, 2]]], [29, [[1, 2]]], [31, [[2, 1]]], [37, [[1, 2]]], [41, [0]], [43, [[2, 1]]], [47, [[2, 1]]], [53, [[1, 2]]], [59, [[1, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [2, 1, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 22.181073012818835, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.492.1', 'local_algs': ['2.2.2.2', '3.2.1.2', '41.2.1.2'], 'monogenic': 1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 3, 41], 'rd': 22.1810730128, 'regulator': {'__RealLiteral__': 0, 'data': '5.49715142831', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 11 a + 122 \\)'], 'used_grh': False, 'zk': ['1', 'a']}