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hmf_forms • Show schema
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{'deg': 2, 'dimension': 12, 'disc': 348, 'field_bad_primes': [2, 3, 29], 'field_label': '2.2.348.1', 'is_CM': 'no', 'is_base_change': 'yes', 'label': '2.2.348.1-1.1-g', 'label_nsuffix': 6, 'label_suffix': 'g', 'level_bad_primes': [], 'level_ideal': '[1, 1, 1]', 'level_label': '1.1', 'level_norm': 1, 'parallel_weight': 2, 'short_label': '1.1-g', 'weight': '[2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [], 'hecke_eigenvalues': ['-1/1024*e^11 + 9/128*e^9 - 451/256*e^7 + 273/16*e^5 - 697/16*e^3 + 20*e', '1/1024*e^11 - 9/128*e^9 + 451/256*e^7 - 273/16*e^5 + 697/16*e^3 - 19*e', 1, 1, '-1/1024*e^11 + 37/512*e^9 - 471/256*e^7 + 2251/128*e^5 - 599/16*e^3 + 25/8*e', '-1/1024*e^11 + 37/512*e^9 - 471/256*e^7 + 2251/128*e^5 - 599/16*e^3 + 25/8*e', '-3/1024*e^11 + 107/512*e^9 - 1325/256*e^7 + 6293/128*e^5 - 1879/16*e^3 + 327/8*e', '-3/1024*e^11 + 107/512*e^9 - 1325/256*e^7 + 6293/128*e^5 - 1879/16*e^3 + 327/8*e', '1/512*e^10 - 15/128*e^8 + 303/128*e^6 - 567/32*e^4 + 34*e^2 - 3', '1/512*e^10 - 15/128*e^8 + 303/128*e^6 - 567/32*e^4 + 34*e^2 - 3', '1/64*e^8 - 3/4*e^6 + 159/16*e^4 - 45/2*e^2 + 7', '3/512*e^11 - 109/256*e^9 + 1373/128*e^7 - 6619/64*e^5 + 1993/8*e^3 - 345/4*e', '-3/1024*e^11 + 53/256*e^9 - 1301/256*e^7 + 3069/64*e^5 - 921/8*e^3 + 35*e', '-3/1024*e^11 + 53/256*e^9 - 1301/256*e^7 + 3069/64*e^5 - 921/8*e^3 + 35*e', '5/1024*e^11 - 183/512*e^9 + 2319/256*e^7 - 11209/128*e^5 + 1659/8*e^3 - 481/8*e', '5/1024*e^11 - 183/512*e^9 + 2319/256*e^7 - 11209/128*e^5 + 1659/8*e^3 - 481/8*e', '1/256*e^11 - 141/512*e^9 + 431/64*e^7 - 8063/128*e^5 + 2327/16*e^3 - 303/8*e', '1/256*e^11 - 141/512*e^9 + 431/64*e^7 - 8063/128*e^5 + 2327/16*e^3 - 303/8*e', '1/128*e^8 - 3/8*e^6 + 163/32*e^4 - 57/4*e^2 + 25/2', '-1/512*e^10 + 15/128*e^8 - 307/128*e^6 + 603/32*e^4 - 351/8*e^2 + 27/2', '-1/512*e^10 + 15/128*e^8 - 307/128*e^6 + 603/32*e^4 - 351/8*e^2 + 27/2', '1/32*e^6 - 9/8*e^4 + 79/8*e^2 - 21/2', '1/32*e^6 - 9/8*e^4 + 79/8*e^2 - 21/2', '1/512*e^11 - 71/512*e^9 + 437/128*e^7 - 4109/128*e^5 + 591/8*e^3 - 175/8*e', '1/512*e^11 - 71/512*e^9 + 437/128*e^7 - 4109/128*e^5 + 591/8*e^3 - 175/8*e', '-1/512*e^10 + 15/128*e^8 - 307/128*e^6 + 603/32*e^4 - 343/8*e^2 + 3/2', '-1/512*e^10 + 15/128*e^8 - 307/128*e^6 + 603/32*e^4 - 343/8*e^2 + 3/2', '-5/1024*e^11 + 183/512*e^9 - 2323/256*e^7 + 11297/128*e^5 - 3445/16*e^3 + 567/8*e', '-5/1024*e^11 + 183/512*e^9 - 2323/256*e^7 + 11297/128*e^5 - 3445/16*e^3 + 567/8*e', '1/64*e^7 - 11/16*e^5 + 127/16*e^3 - 43/4*e', '1/64*e^7 - 11/16*e^5 + 127/16*e^3 - 43/4*e', '-1/512*e^10 + 15/128*e^8 - 303/128*e^6 + 567/32*e^4 - 35*e^2 + 15', '-1/512*e^10 + 15/128*e^8 - 303/128*e^6 + 567/32*e^4 - 35*e^2 + 15', '5/256*e^8 - 15/16*e^6 + 823/64*e^4 - 309/8*e^2 + 31/4', '5/256*e^8 - 15/16*e^6 + 823/64*e^4 - 309/8*e^2 + 31/4', '-1/256*e^11 + 9/32*e^9 - 225/32*e^7 + 1081/16*e^5 - 2661/16*e^3 + 277/4*e', '-1/256*e^11 + 9/32*e^9 - 225/32*e^7 + 1081/16*e^5 - 2661/16*e^3 + 277/4*e', '3/256*e^8 - 9/16*e^6 + 481/64*e^4 - 147/8*e^2 + 89/4', '3/1024*e^11 - 109/512*e^9 + 1377/256*e^7 - 6707/128*e^5 + 133*e^3 - 503/8*e', '3/1024*e^11 - 109/512*e^9 + 1377/256*e^7 - 6707/128*e^5 + 133*e^3 - 503/8*e', '1/256*e^9 - 3/16*e^7 + 155/64*e^5 - 29/8*e^3 - 49/4*e', '1/256*e^9 - 3/16*e^7 + 155/64*e^5 - 29/8*e^3 - 49/4*e', '5/1024*e^11 - 89/256*e^9 + 2199/256*e^7 - 5201/64*e^5 + 3061/16*e^3 - 251/4*e', '5/1024*e^11 - 89/256*e^9 + 2199/256*e^7 - 5201/64*e^5 + 3061/16*e^3 - 251/4*e', '1/256*e^10 - 15/64*e^8 + 307/64*e^6 - 603/16*e^4 + 347/4*e^2 - 15', '1/256*e^10 - 15/64*e^8 + 307/64*e^6 - 603/16*e^4 + 347/4*e^2 - 15', '-1/256*e^10 + 15/64*e^8 - 301/64*e^6 + 549/16*e^4 - 465/8*e^2 - 9/2', '-1/256*e^10 + 15/64*e^8 - 301/64*e^6 + 549/16*e^4 - 465/8*e^2 - 9/2', '15/256*e^8 - 45/16*e^6 + 2405/64*e^4 - 735/8*e^2 + 85/4', '15/256*e^8 - 45/16*e^6 + 2405/64*e^4 - 735/8*e^2 + 85/4', '11/1024*e^11 - 99/128*e^9 + 4953/256*e^7 - 2977/16*e^5 + 7317/16*e^3 - 377/2*e', '11/1024*e^11 - 99/128*e^9 + 4953/256*e^7 - 2977/16*e^5 + 7317/16*e^3 - 377/2*e', '1/256*e^10 - 15/64*e^8 + 303/64*e^6 - 567/16*e^4 + 69*e^2 - 18', '1/256*e^10 - 15/64*e^8 + 303/64*e^6 - 567/16*e^4 + 69*e^2 - 18', '-3/512*e^10 + 45/128*e^8 - 909/128*e^6 + 1701/32*e^4 - 102*e^2 + 9', '-3/512*e^10 + 45/128*e^8 - 909/128*e^6 + 1701/32*e^4 - 102*e^2 + 9', '-3/128*e^8 + 9/8*e^6 - 465/32*e^4 + 99/4*e^2 + 9/2', '-3/128*e^8 + 9/8*e^6 - 465/32*e^4 + 99/4*e^2 + 9/2', '-9/1024*e^11 + 331/512*e^9 - 4215/256*e^7 + 20477/128*e^5 - 6095/16*e^3 + 839/8*e', '-9/1024*e^11 + 331/512*e^9 - 4215/256*e^7 + 20477/128*e^5 - 6095/16*e^3 + 839/8*e', '-9/1024*e^11 + 159/256*e^9 - 3899/256*e^7 + 9155/64*e^5 - 5351/16*e^3 + 379/4*e', '-9/1024*e^11 + 159/256*e^9 - 3899/256*e^7 + 9155/64*e^5 - 5351/16*e^3 + 379/4*e', '-7/128*e^8 + 21/8*e^6 - 1141/32*e^4 + 399/4*e^2 - 63/2', '-7/128*e^8 + 21/8*e^6 - 1141/32*e^4 + 399/4*e^2 - 63/2', '5/512*e^11 - 183/256*e^9 + 2317/128*e^7 - 11165/64*e^5 + 6509/16*e^3 - 219/2*e', '5/512*e^11 - 183/256*e^9 + 2317/128*e^7 - 11165/64*e^5 + 6509/16*e^3 - 219/2*e', '-3/256*e^11 + 429/512*e^9 - 333/16*e^7 + 25431/128*e^5 - 483*e^3 + 1437/8*e', '-3/256*e^11 + 429/512*e^9 - 333/16*e^7 + 25431/128*e^5 - 483*e^3 + 1437/8*e', '-19/256*e^8 + 57/16*e^6 - 3057/64*e^4 + 963/8*e^2 - 89/4', '-19/256*e^8 + 57/16*e^6 - 3057/64*e^4 + 963/8*e^2 - 89/4', '9/1024*e^11 - 327/512*e^9 + 4119/256*e^7 - 19857/128*e^5 + 5979/16*e^3 - 1035/8*e', '9/1024*e^11 - 327/512*e^9 + 4119/256*e^7 - 19857/128*e^5 + 5979/16*e^3 - 1035/8*e', '-7/1024*e^11 + 127/256*e^9 - 3201/256*e^7 + 7747/64*e^5 - 2389/8*e^3 + 269/2*e', '-7/1024*e^11 + 127/256*e^9 - 3201/256*e^7 + 7747/64*e^5 - 2389/8*e^3 + 269/2*e', '-1/32*e^6 + 9/8*e^4 - 95/8*e^2 + 69/2', '-1/32*e^6 + 9/8*e^4 - 95/8*e^2 + 69/2', '-7/128*e^8 + 21/8*e^6 - 1141/32*e^4 + 399/4*e^2 - 49/2', '-7/128*e^8 + 21/8*e^6 - 1141/32*e^4 + 399/4*e^2 - 49/2', '-3/1024*e^11 + 111/512*e^9 - 1425/256*e^7 + 7017/128*e^5 - 1101/8*e^3 + 597/8*e', '-3/1024*e^11 + 111/512*e^9 - 1425/256*e^7 + 7017/128*e^5 - 1101/8*e^3 + 597/8*e', '11/256*e^8 - 33/16*e^6 + 1769/64*e^4 - 555/8*e^2 + 45/4', '11/256*e^8 - 33/16*e^6 + 1769/64*e^4 - 555/8*e^2 + 45/4', '23/1024*e^11 - 815/512*e^9 + 10025/256*e^7 - 47281/128*e^5 + 13975/16*e^3 - 2147/8*e', '23/1024*e^11 - 815/512*e^9 + 10025/256*e^7 - 47281/128*e^5 + 13975/16*e^3 - 2147/8*e', '1/512*e^10 - 15/128*e^8 + 303/128*e^6 - 567/32*e^4 + 36*e^2 - 27', '1/512*e^10 - 15/128*e^8 + 303/128*e^6 - 567/32*e^4 + 36*e^2 - 27', '3/512*e^11 - 53/128*e^9 + 1303/128*e^7 - 3099/32*e^5 + 3939/16*e^3 - 535/4*e', '3/512*e^11 - 53/128*e^9 + 1303/128*e^7 - 3099/32*e^5 + 3939/16*e^3 - 535/4*e', '-3/256*e^8 + 9/16*e^6 - 529/64*e^4 + 291/8*e^2 - 93/4', '-3/256*e^8 + 9/16*e^6 - 529/64*e^4 + 291/8*e^2 - 93/4', '-1/32*e^6 + 9/8*e^4 - 71/8*e^2 - 3/2', '-1/32*e^6 + 9/8*e^4 - 71/8*e^2 - 3/2', '1/512*e^10 - 15/128*e^8 + 307/128*e^6 - 603/32*e^4 + 359/8*e^2 - 51/2', '1/512*e^10 - 15/128*e^8 + 307/128*e^6 - 603/32*e^4 + 359/8*e^2 - 51/2', '-3/256*e^11 + 217/256*e^9 - 85/4*e^7 + 13039/64*e^5 - 7787/16*e^3 + 174*e', '-3/256*e^11 + 217/256*e^9 - 85/4*e^7 + 13039/64*e^5 - 7787/16*e^3 + 174*e', '-3/4*e^4 + 18*e^2 - 11', '-3/4*e^4 + 18*e^2 - 11', '-3/256*e^11 + 215/256*e^9 - 1337/64*e^7 + 12773/64*e^5 - 3899/8*e^3 + 837/4*e', '-3/256*e^11 + 215/256*e^9 - 1337/64*e^7 + 12773/64*e^5 - 3899/8*e^3 + 837/4*e', '3/256*e^11 - 219/256*e^9 + 693/32*e^7 - 13437/64*e^5 + 8157/16*e^3 - 171*e', '3/256*e^11 - 219/256*e^9 + 693/32*e^7 - 13437/64*e^5 + 8157/16*e^3 - 171*e', '3/512*e^10 - 45/128*e^8 + 913/128*e^6 - 1737/32*e^4 + 887/8*e^2 - 15/2', '3/512*e^10 - 45/128*e^8 + 913/128*e^6 - 1737/32*e^4 + 887/8*e^2 - 15/2', '1/1024*e^11 - 7/128*e^9 + 243/256*e^7 - 33/8*e^5 - 299/16*e^3 + 69*e', '1/1024*e^11 - 7/128*e^9 + 243/256*e^7 - 33/8*e^5 - 299/16*e^3 + 69*e', '-23/256*e^8 + 69/16*e^6 - 3677/64*e^4 + 1095/8*e^2 - 77/4', '-23/256*e^8 + 69/16*e^6 - 3677/64*e^4 + 1095/8*e^2 - 77/4', '-11/512*e^11 + 201/128*e^9 - 5089/128*e^7 + 12301/32*e^5 - 7333/8*e^3 + 561/2*e', '-11/512*e^11 + 201/128*e^9 - 5089/128*e^7 + 12301/32*e^5 - 7333/8*e^3 + 561/2*e', '25/1024*e^11 - 445/256*e^9 + 11007/256*e^7 - 26161/64*e^5 + 7915/8*e^3 - 689/2*e', '25/1024*e^11 - 445/256*e^9 + 11007/256*e^7 - 26161/64*e^5 + 7915/8*e^3 - 689/2*e', '-9/1024*e^11 + 333/512*e^9 - 4263/256*e^7 + 20787/128*e^5 - 6153/16*e^3 + 741/8*e', '-9/1024*e^11 + 333/512*e^9 - 4263/256*e^7 + 20787/128*e^5 - 6153/16*e^3 + 741/8*e', '-1/512*e^10 + 15/128*e^8 - 303/128*e^6 + 567/32*e^4 - 32*e^2 - 21', '-1/512*e^10 + 15/128*e^8 - 303/128*e^6 + 567/32*e^4 - 32*e^2 - 21', '3/1024*e^11 - 101/512*e^9 + 1189/256*e^7 - 5555/128*e^5 + 2015/16*e^3 - 909/8*e', '3/1024*e^11 - 101/512*e^9 + 1189/256*e^7 - 5555/128*e^5 + 2015/16*e^3 - 909/8*e', '1/4*e^4 - 6*e^2 + 21', '1/4*e^4 - 6*e^2 + 21', '3/64*e^8 - 9/4*e^6 + 489/16*e^4 - 171/2*e^2 + 20', '3/64*e^8 - 9/4*e^6 + 489/16*e^4 - 171/2*e^2 + 20', '-1/64*e^7 + 11/16*e^5 - 127/16*e^3 + 43/4*e', '-1/64*e^7 + 11/16*e^5 - 127/16*e^3 + 43/4*e', '-1/256*e^10 + 15/64*e^8 - 303/64*e^6 + 567/16*e^4 - 70*e^2 + 30', '-1/256*e^10 + 15/64*e^8 - 303/64*e^6 + 567/16*e^4 - 70*e^2 + 30', '-7/128*e^8 + 21/8*e^6 - 1125/32*e^4 + 351/4*e^2 - 73/2', '-7/128*e^8 + 21/8*e^6 - 1125/32*e^4 + 351/4*e^2 - 73/2', '-3/256*e^10 + 45/64*e^8 - 909/64*e^6 + 1701/16*e^4 - 207*e^2 + 54', '-3/256*e^10 + 45/64*e^8 - 909/64*e^6 + 1701/16*e^4 - 207*e^2 + 54', '-23/1024*e^11 + 819/512*e^9 - 10129/256*e^7 + 48109/128*e^5 - 14473/16*e^3 + 2499/8*e', '-23/1024*e^11 + 819/512*e^9 - 10129/256*e^7 + 48109/128*e^5 - 14473/16*e^3 + 2499/8*e', '19/1024*e^11 - 21/16*e^9 + 8245/256*e^7 - 9675/32*e^5 + 1403/2*e^3 - 793/4*e', '19/1024*e^11 - 21/16*e^9 + 8245/256*e^7 - 9675/32*e^5 + 1403/2*e^3 - 793/4*e', '11/1024*e^11 - 387/512*e^9 + 4721/256*e^7 - 22005/128*e^5 + 1571/4*e^3 - 757/8*e', '11/1024*e^11 - 387/512*e^9 + 4721/256*e^7 - 22005/128*e^5 + 1571/4*e^3 - 757/8*e', '-5/1024*e^11 + 177/512*e^9 - 2191/256*e^7 + 10631/128*e^5 - 913/4*e^3 + 1119/8*e', '-5/1024*e^11 + 177/512*e^9 - 2191/256*e^7 + 10631/128*e^5 - 913/4*e^3 + 1119/8*e', '7/1024*e^11 - 251/512*e^9 + 3141/256*e^7 - 15309/128*e^5 + 319*e^3 - 1341/8*e', '7/1024*e^11 - 251/512*e^9 + 3141/256*e^7 - 15309/128*e^5 + 319*e^3 - 1341/8*e', '-7/512*e^11 + 127/128*e^9 - 3203/128*e^7 + 7777/32*e^5 - 9747/16*e^3 + 979/4*e', '-7/512*e^11 + 127/128*e^9 - 3203/128*e^7 + 7777/32*e^5 - 9747/16*e^3 + 979/4*e', '23/1024*e^11 - 821/512*e^9 + 10181/256*e^7 - 48523/128*e^5 + 7361/8*e^3 - 2675/8*e', '23/1024*e^11 - 821/512*e^9 + 10181/256*e^7 - 48523/128*e^5 + 7361/8*e^3 - 2675/8*e', '-3/256*e^11 + 429/512*e^9 - 1333/64*e^7 + 25535/128*e^5 - 7903/16*e^3 + 1519/8*e', '-3/256*e^11 + 429/512*e^9 - 1333/64*e^7 + 25535/128*e^5 - 7903/16*e^3 + 1519/8*e', '-1/256*e^10 + 15/64*e^8 - 313/64*e^6 + 657/16*e^4 - 931/8*e^2 + 93/2', '-1/256*e^10 + 15/64*e^8 - 313/64*e^6 + 657/16*e^4 - 931/8*e^2 + 93/2', '-11/128*e^8 + 33/8*e^6 - 1729/32*e^4 + 435/4*e^2 - 5/2', '-11/128*e^8 + 33/8*e^6 - 1729/32*e^4 + 435/4*e^2 - 5/2', '-5/256*e^11 + 45/32*e^9 - 1125/32*e^7 + 5405/16*e^5 - 13305/16*e^3 + 1385/4*e', '-5/256*e^11 + 45/32*e^9 - 1125/32*e^7 + 5405/16*e^5 - 13305/16*e^3 + 1385/4*e', '-5/1024*e^11 + 169/512*e^9 - 1967/256*e^7 + 8591/128*e^5 - 507/4*e^3 - 249/8*e', '-5/1024*e^11 + 169/512*e^9 - 1967/256*e^7 + 8591/128*e^5 - 507/4*e^3 - 249/8*e', '1/128*e^8 - 3/8*e^6 + 147/32*e^4 - 9/4*e^2 + 49/2', '1/128*e^8 - 3/8*e^6 + 147/32*e^4 - 9/4*e^2 + 49/2', '-9/512*e^11 + 639/512*e^9 - 3941/128*e^7 + 37397/128*e^5 - 5669/8*e^3 + 1903/8*e', '-9/512*e^11 + 639/512*e^9 - 3941/128*e^7 + 37397/128*e^5 - 5669/8*e^3 + 1903/8*e'], 'hecke_polynomial': 'x^12 - 72*x^10 + 1800*x^8 - 17280*x^6 + 42128*x^4 - 15744*x^2 + 256', 'label': '2.2.348.1-1.1-g'}
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hmf_fields • Show schema
Hide schema
{'degree': 2, 'discriminant': 348, 'ideals': ['[1, 1, 1]', '[2, 2, w + 1]', '[3, 3, w]', '[4, 2, 2]', '[6, 6, w - 9]', '[8, 4, 2*w + 2]', '[9, 3, 3]', '[12, 6, 2*w]', '[13, 13, -w + 10]', '[13, 13, w + 10]', '[16, 4, 4]', '[17, 17, w + 6]', '[17, 17, w + 11]', '[18, 6, 3*w + 3]', '[19, 19, w + 7]', '[19, 19, w + 12]', '[23, 23, -w - 8]', '[23, 23, w - 8]', '[24, 12, 2*w - 18]', '[25, 5, -5]', '[26, 26, w + 3]', '[26, 26, w + 23]', '[27, 9, 3*w]', '[29, 29, w]', '[31, 31, w + 5]', '[31, 31, w + 26]', '[32, 8, 4*w + 4]', '[34, 34, -w - 11]', '[34, 34, -w + 11]', '[36, 6, 6]', '[38, 38, w + 7]', '[38, 38, -w + 7]', '[39, 39, w + 3]', '[39, 39, w + 36]', '[41, 41, w + 13]', '[41, 41, w + 28]', '[43, 43, w + 1]', '[43, 43, w + 42]', '[46, 46, w + 15]', '[46, 46, w + 31]', '[48, 12, 4*w]', '[49, 7, -7]', '[50, 10, 5*w + 5]', '[51, 51, w + 6]', '[51, 51, -w + 6]', '[52, 26, -2*w + 20]', '[52, 26, 2*w + 20]', '[54, 18, 3*w - 27]', '[57, 57, -w - 12]', '[57, 57, -w + 12]', '[58, 58, 3*w - 29]', '[59, 59, -2*w + 17]', '[59, 59, 2*w + 17]', '[62, 62, -w - 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150]', '[9972, 1662, -12*w - 150]', '[9976, 4988, 2*w + 174]', '[9976, 4988, 2*w + 4814]', '[9978, 9978, w + 1485]', '[9978, 9978, w + 8493]', '[9979, 9979, w + 1570]', '[9979, 9979, w + 2539]', '[9979, 9979, w + 7440]', '[9979, 9979, w + 8409]', '[9984, 624, 16*w + 48]', '[9984, 624, 16*w + 576]', '[9986, 9986, w + 1639]', '[9986, 9986, w + 8347]', '[9996, 714, -14*w - 84]', '[9996, 714, 14*w - 84]', '[9998, 9998, -11*w - 23]', '[9998, 9998, 11*w - 23]', '[10000, 100, -100]'], 'label': '2.2.348.1', 'narrow_class_no': 4, 'primes': ['[2, 2, w + 1]', '[3, 3, w]', '[13, 13, -w + 10]', '[13, 13, w + 10]', '[17, 17, w + 6]', '[17, 17, w + 11]', '[19, 19, w + 7]', '[19, 19, w + 12]', '[23, 23, -w - 8]', '[23, 23, w - 8]', '[25, 5, -5]', '[29, 29, w]', '[31, 31, w + 5]', '[31, 31, w + 26]', '[41, 41, w + 13]', '[41, 41, w + 28]', '[43, 43, w + 1]', '[43, 43, w + 42]', '[49, 7, -7]', '[59, 59, -2*w + 17]', '[59, 59, 2*w + 17]', '[71, 71, -w - 4]', '[71, 71, w - 4]', '[79, 79, w + 18]', '[79, 79, w + 61]', '[83, 83, -w - 2]', '[83, 83, w - 2]', '[89, 89, w + 40]', '[89, 89, w + 49]', '[101, 101, w + 17]', '[101, 101, w + 84]', '[107, 107, -3*w + 26]', '[107, 107, 3*w + 26]', '[109, 109, -w - 14]', '[109, 109, w - 14]', '[113, 113, w + 55]', '[113, 113, w + 58]', '[121, 11, -11]', '[127, 127, w + 50]', '[127, 127, w + 77]', '[137, 137, w + 19]', '[137, 137, w + 118]', '[163, 163, w + 24]', '[163, 163, w + 139]', '[167, 167, 4*w - 35]', '[167, 167, -4*w - 35]', '[179, 179, 2*w - 13]', '[179, 179, -2*w - 13]', '[181, 181, 2*w - 23]', '[181, 181, -2*w - 23]', '[211, 211, w + 64]', '[211, 211, w + 147]', '[227, 227, 2*w - 11]', '[227, 227, -2*w - 11]', '[239, 239, -5*w + 44]', '[239, 239, -8*w + 73]', '[241, 241, 12*w - 113]', '[241, 241, -3*w + 32]', '[269, 269, w + 25]', '[269, 269, w + 244]', '[271, 271, w + 30]', '[271, 271, w + 241]', '[277, 277, 2*w - 25]', '[277, 277, -2*w - 25]', '[293, 293, w + 110]', '[293, 293, w + 183]', '[307, 307, w + 98]', '[307, 307, w + 209]', '[313, 313, -w - 20]', '[313, 313, w - 20]', '[317, 317, w + 74]', '[317, 317, w + 243]', '[331, 331, w + 114]', '[331, 331, w + 217]', '[347, 347, 2*w - 1]', '[347, 347, -2*w - 1]', '[349, 349, -9*w + 86]', '[349, 349, 6*w - 59]', '[367, 367, w + 120]', '[367, 367, w + 247]', '[373, 373, 3*w - 34]', '[373, 373, -3*w - 34]', '[379, 379, w + 128]', '[379, 379, w + 251]', '[383, 383, 3*w - 20]', '[383, 383, -3*w - 20]', '[389, 389, w + 101]', '[389, 389, w + 288]', '[397, 397, -w - 22]', '[397, 397, w - 22]', '[419, 419, -7*w + 62]', '[419, 419, -10*w + 91]', '[431, 431, 4*w - 31]', '[431, 431, -4*w - 31]', '[449, 449, w + 136]', '[449, 449, w + 313]', '[457, 457, -4*w - 43]', '[457, 457, 4*w - 43]', '[461, 461, w + 116]', '[461, 461, w + 345]', '[569, 569, w + 35]', '[569, 569, w + 534]', '[587, 587, 3*w - 14]', '[587, 587, -3*w - 14]', '[607, 607, w + 249]', '[607, 607, w + 358]', '[613, 613, 2*w - 31]', '[613, 613, -2*w - 31]', '[617, 617, w + 127]', '[617, 617, w + 490]', '[619, 619, w + 169]', '[619, 619, w + 450]', '[641, 641, w + 37]', '[641, 641, w + 604]', '[647, 647, -9*w + 80]', '[647, 647, -12*w + 109]', '[653, 653, w + 273]', '[653, 653, w + 380]', '[661, 661, -3*w - 38]', '[661, 661, 3*w - 38]', '[673, 673, -13*w + 124]', '[673, 673, 8*w - 79]', '[677, 677, w + 133]', '[677, 677, w + 544]', '[683, 683, -3*w - 10]', '[683, 683, 3*w - 10]', '[709, 709, 10*w - 97]', '[709, 709, -11*w + 106]', '[719, 719, 3*w - 8]', '[719, 719, -3*w - 8]', '[727, 727, w + 304]', '[727, 727, w + 423]', '[739, 739, w + 48]', '[739, 739, w + 691]', '[751, 751, w + 350]', '[751, 751, w + 401]', '[773, 773, w + 297]', '[773, 773, w + 476]', '[797, 797, w + 41]', '[797, 797, w + 756]', '[809, 809, w + 286]', '[809, 809, w + 523]', '[823, 823, w + 160]', '[823, 823, w + 663]', '[859, 859, w + 199]', '[859, 859, w + 660]', '[863, 863, 4*w - 23]', '[863, 863, -4*w - 23]', '[877, 877, 2*w - 35]', '[877, 877, -2*w - 35]', '[881, 881, w + 43]', '[881, 881, w + 838]', '[907, 907, w + 359]', '[907, 907, w + 548]', '[937, 937, -w - 32]', '[937, 937, w - 32]', '[967, 967, w + 455]', '[967, 967, w + 512]']}
-
nf_fields • Show schema
Hide schema
{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [-87, 0, 1], 'conductor': 348, 'degree': 2, 'dirichlet_group': [1, 347], 'disc_abs': 348, 'disc_rad': 174, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[2, 1]]], [7, [[2, 1]]], [11, [[2, 1]]], [13, [[1, 2]]], [17, [[1, 2]]], [19, [[1, 2]]], [23, [[1, 2]]], [29, [0]], [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': [2, 1, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 18.65475810617763, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.348.1', 'local_algs': ['2.2.2.1', '3.2.1.2', '29.2.1.2'], 'monogenic': 1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 3, 29], 'rd': 18.6547581062, 'regulator': {'__RealLiteral__': 0, 'data': '4.02503266055', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 3 a + 28 \\)'], 'used_grh': False, 'zk': ['1', 'a']}