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hmf_forms • Show schema
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{'deg': 2, 'dimension': 16, 'disc': 280, 'field_bad_primes': [2, 5, 7], 'field_label': '2.2.280.1', 'is_CM': 'no', 'is_base_change': 'yes', 'label': '2.2.280.1-5.1-h', 'label_nsuffix': 7, 'label_suffix': 'h', 'level_bad_primes': [5], 'level_ideal': '[5, 5, -3*w + 25]', 'level_label': '5.1', 'level_norm': 5, 'parallel_weight': 2, 'short_label': '5.1-h', 'weight': '[2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[5, 5, -3*w + 25]', -1]], 'hecke_eigenvalues': ['e', '1/176*e^15 + 25/176*e^13 + 16/11*e^11 + 719/88*e^9 + 613/22*e^7 + 609/11*e^5 + 591/11*e^3 + 173/11*e', '1/176*e^15 + 25/176*e^13 + 16/11*e^11 + 719/88*e^9 + 613/22*e^7 + 609/11*e^5 + 591/11*e^3 + 173/11*e', 1, '-3/88*e^15 - 43/44*e^13 - 977/88*e^11 - 2795/44*e^9 - 4239/22*e^7 - 3291/11*e^5 - 4485/22*e^3 - 389/11*e', '-1/44*e^14 - 25/44*e^12 - 245/44*e^10 - 1207/44*e^8 - 1583/22*e^6 - 1028/11*e^4 - 505/11*e^2 - 54/11', '-1/44*e^14 - 25/44*e^12 - 245/44*e^10 - 1207/44*e^8 - 1583/22*e^6 - 1028/11*e^4 - 505/11*e^2 - 54/11', '-1/44*e^15 - 61/88*e^13 - 183/22*e^11 - 4383/88*e^9 - 1721/11*e^7 - 11009/44*e^5 - 3947/22*e^3 - 450/11*e', '-1/44*e^15 - 61/88*e^13 - 183/22*e^11 - 4383/88*e^9 - 1721/11*e^7 - 11009/44*e^5 - 3947/22*e^3 - 450/11*e', '1/44*e^15 + 61/88*e^13 + 743/88*e^11 + 2307/44*e^9 + 3871/22*e^7 + 6841/22*e^5 + 5531/22*e^3 + 593/11*e', '1/44*e^15 + 61/88*e^13 + 743/88*e^11 + 2307/44*e^9 + 3871/22*e^7 + 6841/22*e^5 + 5531/22*e^3 + 593/11*e', '1/44*e^14 + 25/44*e^12 + 245/44*e^10 + 1207/44*e^8 + 797/11*e^6 + 2155/22*e^4 + 560/11*e^2 - 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3603/2*e^5 - 2779/2*e^3 - 339*e', '-1/8*e^15 - 4*e^13 - 403/8*e^11 - 635/2*e^9 - 1056*e^7 - 3603/2*e^5 - 2779/2*e^3 - 339*e', '5/44*e^15 + 283/88*e^13 + 3231/88*e^11 + 4783/22*e^9 + 7835/11*e^7 + 27759/22*e^5 + 23607/22*e^3 + 3196/11*e', '5/44*e^15 + 283/88*e^13 + 3231/88*e^11 + 4783/22*e^9 + 7835/11*e^7 + 27759/22*e^5 + 23607/22*e^3 + 3196/11*e', '-23/176*e^15 - 575/176*e^13 - 1373/44*e^11 - 12467/88*e^9 - 6707/22*e^7 - 5365/22*e^5 + 311/11*e^3 + 575/11*e', '-23/176*e^15 - 575/176*e^13 - 1373/44*e^11 - 12467/88*e^9 - 6707/22*e^7 - 5365/22*e^5 + 311/11*e^3 + 575/11*e', '-1/22*e^14 - 61/44*e^12 - 355/22*e^10 - 3943/44*e^8 - 2683/11*e^6 - 3354/11*e^4 - 1428/11*e^2 - 86/11', '-1/22*e^14 - 61/44*e^12 - 355/22*e^10 - 3943/44*e^8 - 2683/11*e^6 - 3354/11*e^4 - 1428/11*e^2 - 86/11', '7/88*e^15 + 41/22*e^13 + 1341/88*e^11 + 949/22*e^9 - 1065/22*e^7 - 9997/22*e^5 - 14659/22*e^3 - 2341/11*e', '7/88*e^15 + 41/22*e^13 + 1341/88*e^11 + 949/22*e^9 - 1065/22*e^7 - 9997/22*e^5 - 14659/22*e^3 - 2341/11*e', '-7/88*e^14 - 131/88*e^12 - 173/22*e^10 + 203/44*e^8 + 1616/11*e^6 + 4267/11*e^4 + 3452/11*e^2 + 218/11', '-7/88*e^14 - 131/88*e^12 - 173/22*e^10 + 203/44*e^8 + 1616/11*e^6 + 4267/11*e^4 + 3452/11*e^2 + 218/11', '-3/88*e^14 - 97/88*e^12 - 615/44*e^10 - 3873/44*e^8 - 6373/22*e^6 - 5337/11*e^4 - 3832/11*e^2 - 400/11', '-3/88*e^14 - 97/88*e^12 - 615/44*e^10 - 3873/44*e^8 - 6373/22*e^6 - 5337/11*e^4 - 3832/11*e^2 - 400/11', '3/44*e^14 + 43/22*e^12 + 461/22*e^10 + 4457/44*e^8 + 2193/11*e^6 + 488/11*e^4 - 2324/11*e^2 - 322/11', '7/176*e^15 + 263/176*e^13 + 1809/88*e^11 + 1472/11*e^9 + 19351/44*e^7 + 32419/44*e^5 + 13455/22*e^3 + 2256/11*e', '7/176*e^15 + 263/176*e^13 + 1809/88*e^11 + 1472/11*e^9 + 19351/44*e^7 + 32419/44*e^5 + 13455/22*e^3 + 2256/11*e', '-17/88*e^15 - 60/11*e^13 - 5375/88*e^11 - 7613/22*e^9 - 23185/22*e^7 - 37441/22*e^5 - 28759/22*e^3 - 3385/11*e', '-17/88*e^15 - 60/11*e^13 - 5375/88*e^11 - 7613/22*e^9 - 23185/22*e^7 - 37441/22*e^5 - 28759/22*e^3 - 3385/11*e', '17/88*e^15 + 60/11*e^13 + 5309/88*e^11 + 14533/44*e^9 + 10289/11*e^7 + 29081/22*e^5 + 18463/22*e^3 + 2296/11*e', '17/88*e^15 + 60/11*e^13 + 5309/88*e^11 + 14533/44*e^9 + 10289/11*e^7 + 29081/22*e^5 + 18463/22*e^3 + 2296/11*e', '9/88*e^15 + 107/44*e^13 + 499/22*e^11 + 9587/88*e^9 + 3295/11*e^7 + 20539/44*e^5 + 7845/22*e^3 + 1178/11*e', '9/88*e^15 + 107/44*e^13 + 499/22*e^11 + 9587/88*e^9 + 3295/11*e^7 + 20539/44*e^5 + 7845/22*e^3 + 1178/11*e', '5/22*e^14 + 57/11*e^12 + 1955/44*e^10 + 7967/44*e^8 + 8163/22*e^6 + 7899/22*e^4 + 1365/11*e^2 + 166/11', '5/22*e^14 + 57/11*e^12 + 1955/44*e^10 + 7967/44*e^8 + 8163/22*e^6 + 7899/22*e^4 + 1365/11*e^2 + 166/11', '-9/88*e^15 - 129/44*e^13 - 2953/88*e^11 - 4319/22*e^9 - 6892/11*e^7 - 23673/22*e^5 - 19065/22*e^3 - 1871/11*e', '-9/88*e^15 - 129/44*e^13 - 2953/88*e^11 - 4319/22*e^9 - 6892/11*e^7 - 23673/22*e^5 - 19065/22*e^3 - 1871/11*e'], 'hecke_polynomial': 'x^16 + 31*x^14 + 384*x^12 + 2424*x^10 + 8252*x^8 + 14748*x^6 + 12128*x^4 + 3008*x^2 + 64', 'label': '2.2.280.1-5.1-h'}
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hmf_fields • Show schema
Hide schema
{'degree': 2, 'discriminant': 280, 'ideals': ['[1, 1, 1]', '[2, 2, w]', '[3, 3, w + 1]', '[3, 3, w + 2]', '[4, 2, 2]', '[5, 5, -3*w + 25]', '[6, 6, -w - 8]', '[6, 6, -w + 8]', '[7, 7, w]', '[8, 4, 2*w]', '[9, 3, 3]', '[9, 9, 2*w + 17]', '[9, 9, -2*w + 17]', '[10, 10, w]', '[11, 11, w - 9]', '[11, 11, -w - 9]', '[12, 6, 2*w + 2]', '[12, 6, 2*w + 4]', '[14, 14, -5*w + 42]', '[15, 15, w + 5]', '[15, 15, w + 10]', '[16, 4, 4]', '[17, 17, w + 6]', '[17, 17, w + 11]', '[18, 6, 3*w]', '[18, 18, w + 4]', '[18, 18, w + 14]', '[20, 10, -6*w + 50]', '[21, 21, -w - 7]', '[21, 21, -w + 7]', '[22, 22, w + 2]', '[22, 22, w + 20]', '[23, 23, w + 1]', '[23, 23, w + 22]', '[24, 12, -2*w - 16]', '[24, 12, -2*w + 16]', '[25, 5, 5]', '[27, 9, 3*w + 3]', '[27, 9, 3*w + 6]', '[27, 27, w + 4]', '[27, 27, w + 23]', '[28, 14, 2*w]', '[30, 30, w + 10]', '[30, 30, -w + 10]', '[31, 31, 4*w - 33]', '[31, 31, 4*w + 33]', '[32, 8, 4*w]', '[33, 33, w + 2]', '[33, 33, w + 13]', '[33, 33, w + 20]', '[33, 33, w + 31]', '[34, 34, w + 6]', '[34, 34, -w + 6]', '[35, 35, w]', '[36, 6, 6]', '[36, 18, 4*w + 34]', '[36, 18, -4*w + 34]', '[37, 37, w + 12]', '[37, 37, w + 25]', '[40, 20, 2*w]', '[42, 42, w + 14]', '[42, 42, w + 28]', '[44, 22, 2*w - 18]', '[44, 22, -2*w - 18]', '[45, 15, -9*w + 75]', '[45, 45, -w - 5]', '[45, 45, -w + 5]', '[46, 46, 3*w - 26]', '[46, 46, 3*w + 26]', '[48, 12, 4*w + 4]', '[48, 12, 4*w + 8]', '[49, 7, 7]', '[50, 10, 5*w]', '[51, 51, w + 11]', '[51, 51, -7*w - 59]', '[51, 51, -7*w + 59]', '[51, 51, w - 11]', '[53, 53, w + 21]', '[53, 53, w + 32]', '[54, 18, -3*w - 24]', '[54, 18, -3*w + 24]', '[54, 54, -w - 4]', '[54, 54, -w + 4]', '[55, 55, 2*w - 15]', '[55, 55, 2*w + 15]', '[56, 28, -10*w + 84]', '[60, 30, 2*w + 10]', '[60, 30, 2*w + 20]', '[61, 61, -w - 3]', '[61, 61, w - 3]', '[62, 62, w + 16]', '[62, 62, w + 46]', '[63, 21, 3*w]', '[63, 63, w + 14]', '[63, 63, w + 49]', '[64, 8, 8]', '[66, 66, w + 2]', '[66, 66, 7*w - 58]', '[66, 66, 7*w + 58]', '[66, 66, w - 2]', '[68, 34, 2*w + 12]', '[68, 34, 2*w + 22]', '[69, 69, -w - 1]', '[69, 69, 5*w + 41]', '[69, 69, -5*w + 41]', '[69, 69, w - 1]', '[70, 70, -w]', '[72, 12, 6*w]', '[72, 36, 2*w + 8]', '[72, 36, 2*w + 28]', '[73, 73, w + 17]', '[73, 73, w + 56]', '[74, 74, -w - 12]', '[74, 74, w - 12]', '[75, 15, 5*w + 5]', '[75, 15, 5*w + 10]', '[77, 77, w + 35]', '[77, 77, w + 42]', '[80, 20, -12*w + 100]', '[81, 9, 9]', '[81, 27, 6*w + 51]', '[81, 27, -6*w + 51]', '[81, 81, -2*w + 19]', '[81, 81, 2*w + 19]', '[83, 83, w + 30]', '[83, 83, w + 53]', '[84, 42, -2*w - 14]', '[84, 42, -2*w + 14]', '[85, 85, w + 40]', '[85, 85, w + 45]', '[88, 44, 2*w + 4]', '[88, 44, 2*w + 40]', '[90, 30, 3*w]', '[90, 90, w + 40]', '[90, 90, w + 50]', '[92, 46, 2*w + 2]', '[92, 46, 2*w + 44]', '[93, 93, w + 16]', '[93, 93, w + 46]', '[93, 93, w + 47]', '[93, 93, w + 77]', '[96, 24, -4*w - 32]', '[96, 24, -4*w + 32]', '[97, 97, w + 19]', '[97, 97, w + 78]', '[98, 14, 7*w]', '[99, 33, 3*w - 27]', '[99, 33, -3*w - 27]', '[99, 99, -w - 13]', '[99, 99, 5*w - 43]', '[99, 99, -5*w - 43]', '[99, 99, w - 13]', '[100, 10, 10]', '[101, 101, 3*w - 23]', '[101, 101, 3*w + 23]', '[102, 102, w + 28]', '[102, 102, w + 40]', '[102, 102, w + 62]', '[102, 102, w + 74]', '[105, 105, 4*w + 35]', '[105, 105, -4*w + 35]', '[106, 106, -21*w + 176]', '[106, 106, 9*w - 76]', '[108, 18, 6*w + 6]', '[108, 18, 6*w + 12]', '[108, 54, 2*w + 8]', '[108, 54, 2*w + 46]', '[110, 110, w + 20]', '[110, 110, w + 90]', '[111, 111, 10*w - 83]', '[111, 111, 2*w - 13]', '[111, 111, 2*w + 13]', '[111, 111, 10*w + 83]', '[112, 28, 4*w]', '[115, 115, w + 45]', '[115, 115, w + 70]', '[119, 119, -6*w - 49]', '[119, 119, 6*w - 49]', '[120, 60, 2*w + 20]', '[120, 60, -2*w + 20]', '[121, 11, 11]', '[121, 121, -12*w + 101]', '[121, 121, 12*w + 101]', '[122, 122, w + 58]', '[122, 122, w + 64]', '[124, 62, 8*w - 66]', '[124, 62, 8*w + 66]', '[125, 25, -15*w + 125]', '[126, 42, -15*w + 126]', '[126, 126, w + 14]', '[126, 126, -w + 14]', '[127, 127, w + 18]', '[127, 127, w + 109]', '[128, 16, 8*w]', '[132, 66, 2*w + 4]', '[132, 66, 2*w + 26]', '[132, 66, 2*w + 40]', '[132, 66, 2*w + 62]', '[135, 45, 3*w + 15]', '[135, 45, 3*w + 30]', '[135, 135, w + 50]', '[135, 135, w + 85]', '[136, 68, 2*w + 12]', '[136, 68, -2*w + 12]', '[138, 138, w + 22]', '[138, 138, w + 68]', '[138, 138, w + 70]', '[138, 138, w + 116]', '[140, 70, 2*w]', '[144, 12, 12]', '[144, 36, 8*w + 68]', '[144, 36, -8*w + 68]', '[146, 146, 3*w + 22]', '[146, 146, 3*w - 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389]', '[9959, 9959, 48*w + 389]', '[9959, 9959, -12*w - 11]', '[9960, 4980, 2*w + 1600]', '[9960, 4980, 2*w + 1720]', '[9960, 4980, 2*w + 3260]', '[9960, 4980, 2*w + 3380]', '[9961, 9961, 114*w - 959]', '[9961, 9961, 156*w - 1309]', '[9965, 9965, w + 1125]', '[9965, 9965, w + 8840]', '[9969, 9969, 88*w + 743]', '[9969, 9969, -16*w + 167]', '[9969, 9969, -16*w - 167]', '[9969, 9969, 88*w - 743]', '[9972, 1662, 6*w + 390]', '[9972, 1662, 6*w + 1272]', '[9972, 4986, 2*w + 424]', '[9972, 4986, 2*w + 1792]', '[9972, 4986, 2*w + 3194]', '[9972, 4986, 2*w + 4562]', '[9974, 9974, -15*w - 76]', '[9974, 9974, 15*w - 76]', '[9978, 9978, w + 1366]', '[9978, 9978, w + 1960]', '[9978, 9978, w + 8018]', '[9978, 9978, w + 8612]', '[9979, 9979, 27*w - 247]', '[9979, 9979, -3*w + 103]', '[9979, 9979, 3*w + 103]', '[9979, 9979, -27*w - 247]', '[9980, 4990, 12*w - 10]', '[9980, 4990, -12*w - 10]', '[9981, 3327, -45*w - 363]', '[9981, 3327, -45*w + 363]', '[9981, 9981, -13*w + 43]', '[9981, 9981, -37*w - 293]', '[9981, 9981, -37*w + 293]', '[9981, 9981, -13*w - 43]', '[9982, 9982, w + 574]', '[9982, 9982, w + 3612]', '[9982, 9982, w + 6370]', '[9982, 9982, w + 9408]', '[9985, 9985, w + 2640]', '[9985, 9985, w + 7345]', '[9987, 9987, w + 1174]', '[9987, 9987, w + 2155]', '[9987, 9987, w + 7832]', '[9987, 9987, w + 8813]', '[9988, 4994, 2*w + 1104]', '[9988, 4994, 2*w + 1558]', '[9988, 4994, 2*w + 3436]', '[9988, 4994, 2*w + 3890]', '[9989, 9989, 207*w - 1729]', '[9989, 9989, -87*w + 721]', '[9990, 3330, 3*w + 480]', '[9990, 3330, 3*w + 1590]', '[9990, 3330, 3*w + 1740]', '[9990, 3330, 3*w + 2850]', '[9990, 9990, w + 2380]', '[9990, 9990, w + 2750]', '[9990, 9990, w + 7240]', '[9990, 9990, w + 7610]', '[9996, 714, 14*w + 154]', '[9996, 714, -98*w - 826]', '[9996, 714, -98*w + 826]', '[9996, 714, 14*w - 154]', '[9999, 3333, -120*w + 999]', '[9999, 3333, -12*w + 9]', '[9999, 3333, -12*w - 9]', '[9999, 3333, -120*w - 999]', '[9999, 9999, -14*w - 61]', '[9999, 9999, -62*w + 509]', '[9999, 9999, -16*w + 89]', '[9999, 9999, -74*w + 611]', '[9999, 9999, -74*w - 611]', '[9999, 9999, -16*w - 89]', '[9999, 9999, -62*w - 509]', '[9999, 9999, -14*w + 61]', '[10000, 100, 100]'], 'label': '2.2.280.1', 'narrow_class_no': 4, 'primes': ['[2, 2, w]', '[3, 3, w + 1]', '[3, 3, w + 2]', '[5, 5, -3*w + 25]', '[7, 7, w]', '[11, 11, w - 9]', '[11, 11, -w - 9]', '[17, 17, w + 6]', '[17, 17, w + 11]', '[23, 23, w + 1]', '[23, 23, w + 22]', '[31, 31, 4*w - 33]', '[31, 31, 4*w + 33]', '[37, 37, w + 12]', '[37, 37, w + 25]', '[53, 53, w + 21]', '[53, 53, w + 32]', '[61, 61, -w - 3]', '[61, 61, w - 3]', '[73, 73, w + 17]', '[73, 73, w + 56]', '[83, 83, w + 30]', '[83, 83, w + 53]', '[97, 97, w + 19]', '[97, 97, w + 78]', '[101, 101, 3*w - 23]', '[101, 101, 3*w + 23]', '[127, 127, w + 18]', '[127, 127, w + 109]', '[169, 13, -13]', '[179, 179, 29*w - 243]', '[179, 179, -11*w + 93]', '[181, 181, 7*w + 57]', '[181, 181, 7*w - 57]', '[197, 197, w + 55]', '[197, 197, w + 142]', '[199, 199, 2*w - 9]', '[199, 199, -2*w - 9]', '[211, 211, -3*w - 29]', '[211, 211, 3*w - 29]', '[227, 227, w + 98]', '[227, 227, w + 129]', '[229, 229, 5*w - 39]', '[229, 229, 5*w + 39]', '[257, 257, w + 29]', '[257, 257, w + 228]', '[263, 263, w + 99]', '[263, 263, w + 164]', '[269, 269, -3*w - 19]', '[269, 269, 3*w - 19]', '[271, 271, 2*w - 3]', '[271, 271, -2*w - 3]', '[277, 277, w + 65]', '[277, 277, w + 212]', '[281, 281, 8*w + 69]', '[281, 281, 8*w - 69]', '[283, 283, w + 97]', '[283, 283, w + 186]', '[307, 307, w + 101]', '[307, 307, w + 206]', '[311, 311, 6*w - 47]', '[311, 311, 6*w + 47]', '[313, 313, w + 105]', '[313, 313, w + 208]', '[317, 317, w + 76]', '[317, 317, w + 241]', '[331, 331, 3*w - 31]', '[331, 331, -3*w - 31]', '[349, 349, 37*w - 309]', '[349, 349, 17*w - 141]', '[353, 353, w + 60]', '[353, 353, w + 293]', '[361, 19, -19]', '[373, 373, w + 93]', '[373, 373, w + 280]', '[379, 379, -15*w - 127]', '[379, 379, 15*w - 127]', '[401, 401, -4*w - 39]', '[401, 401, 4*w - 39]', '[433, 433, w + 37]', '[433, 433, w + 396]', '[439, 439, 10*w + 81]', '[439, 439, 10*w - 81]', '[449, 449, 2*w - 27]', '[449, 449, -2*w - 27]', '[461, 461, -3*w - 13]', '[461, 461, 3*w - 13]', '[463, 463, w + 189]', '[463, 463, w + 274]', '[467, 467, w + 213]', '[467, 467, w + 254]', '[479, 479, 18*w - 149]', '[479, 479, 18*w + 149]', '[487, 487, w + 94]', '[487, 487, w + 393]', '[491, 491, 13*w - 111]', '[491, 491, -13*w - 111]', '[499, 499, -27*w + 227]', '[499, 499, 33*w - 277]', '[509, 509, 3*w - 11]', '[509, 509, -3*w - 11]', '[523, 523, w + 240]', '[523, 523, w + 283]', '[557, 557, w + 63]', '[557, 557, w + 494]', '[563, 563, w + 154]', '[563, 563, w + 409]', '[569, 569, 10*w - 87]', '[569, 569, 10*w + 87]', '[571, 571, -9*w + 79]', '[571, 571, -9*w - 79]', '[577, 577, w + 219]', '[577, 577, w + 358]', '[587, 587, w + 230]', '[587, 587, w + 357]', '[593, 593, w + 43]', '[593, 593, w + 550]', '[613, 613, w + 36]', '[613, 613, w + 577]', '[641, 641, 44*w - 369]', '[641, 641, -26*w + 219]', '[643, 643, w + 298]', '[643, 643, w + 345]', '[653, 653, w + 203]', '[653, 653, w + 450]', '[659, 659, -w - 27]', '[659, 659, w - 27]', '[661, 661, -5*w - 33]', '[661, 661, 5*w - 33]', '[719, 719, 54*w - 451]', '[719, 719, 24*w - 199]', '[739, 739, 3*w - 37]', '[739, 739, -3*w - 37]', '[743, 743, w + 263]', '[743, 743, w + 480]', '[757, 757, w + 278]', '[757, 757, w + 479]', '[787, 787, w + 182]', '[787, 787, w + 605]', '[809, 809, 2*w - 33]', '[809, 809, -2*w - 33]', '[823, 823, w + 122]', '[823, 823, w + 701]', '[829, 829, 7*w - 51]', '[829, 829, -7*w - 51]', '[839, 839, 6*w - 41]', '[839, 839, -6*w - 41]', '[841, 29, -29]', '[857, 857, w + 344]', '[857, 857, w + 513]', '[863, 863, w + 374]', '[863, 863, w + 489]', '[877, 877, w + 115]', '[877, 877, w + 762]', '[937, 937, w + 279]', '[937, 937, w + 658]', '[941, 941, 21*w - 173]', '[941, 941, 21*w + 173]', '[967, 967, w + 273]', '[967, 967, w + 694]']}
-
nf_fields • Show schema
Hide schema
{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [-70, 0, 1], 'conductor': 280, 'degree': 2, 'dirichlet_group': [1, 139], 'disc_abs': 280, 'disc_rad': 70, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[1, 2]]], [5, [0]], [7, [0]], [11, [[1, 2]]], [13, [[2, 1]]], [17, [[1, 2]]], [19, [[2, 1]]], [23, [[1, 2]]], [29, [[2, 1]]], [31, [[1, 2]]], [37, [[1, 2]]], [41, [[2, 1]]], [43, [[2, 1]]], [47, [[2, 1]]], [53, [[1, 2]]], [59, [[2, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [3, 1, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 16.73320053068151, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.280.1', 'local_algs': ['2.2.3.4', '5.2.1.1', '7.2.1.2'], 'monogenic': 1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 5, 7], 'rd': 16.7332005307, 'regulator': {'__RealLiteral__': 0, 'data': '6.21859615148', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 30 a - 251 \\)'], 'used_grh': False, 'zk': ['1', 'a']}