-
hmf_forms • Show schema
{'deg': 4, 'dimension': 12, 'disc': 16317, 'field_bad_primes': [3, 7, 37], 'field_label': '4.4.16317.1', 'is_CM': 'no', 'is_base_change': 'yes', 'label': '4.4.16317.1-25.1-i', 'label_nsuffix': 8, 'label_suffix': 'i', 'level_bad_primes': [5], 'level_ideal': '[25, 5, w^2 - w - 3]', 'level_label': '25.1', 'level_norm': 25, 'parallel_weight': 2, 'short_label': '25.1-i', 'weight': '[2, 2, 2, 2]'} -
hmf_hecke • Show schema
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35658122/189463*e^5 + 76047680/189463*e^3 - 37914305/189463*e', '34417/378926*e^11 - 658152/189463*e^9 + 8790278/189463*e^7 - 97181037/378926*e^5 + 104769825/189463*e^3 - 48785771/189463*e', '34417/378926*e^11 - 658152/189463*e^9 + 8790278/189463*e^7 - 97181037/378926*e^5 + 104769825/189463*e^3 - 48785771/189463*e', '13059/189463*e^11 - 495251/189463*e^9 + 6543342/189463*e^7 - 35658122/189463*e^5 + 76047680/189463*e^3 - 37914305/189463*e', '37676/189463*e^10 - 1406965/189463*e^8 + 18098930/189463*e^6 - 94187063/189463*e^4 + 189210251/189463*e^2 - 93833182/189463', '37676/189463*e^10 - 1406965/189463*e^8 + 18098930/189463*e^6 - 94187063/189463*e^4 + 189210251/189463*e^2 - 93833182/189463', '-30053/378926*e^10 + 557629/189463*e^8 - 7092146/189463*e^6 + 72821395/378926*e^4 - 74750655/189463*e^2 + 44418576/189463', '-9833/378926*e^10 + 161507/189463*e^8 - 1614338/189463*e^6 + 8434609/378926*e^4 + 3887709/189463*e^2 - 6059628/189463', '-9833/378926*e^10 + 161507/189463*e^8 - 1614338/189463*e^6 + 8434609/378926*e^4 + 3887709/189463*e^2 - 6059628/189463', '-30053/378926*e^10 + 557629/189463*e^8 - 7092146/189463*e^6 + 72821395/378926*e^4 - 74750655/189463*e^2 + 44418576/189463', '17508/189463*e^10 - 675640/189463*e^8 + 9184519/189463*e^6 - 52400979/189463*e^4 + 117871149/189463*e^2 - 58728158/189463', '29503/189463*e^10 - 1148617/189463*e^8 + 15760119/189463*e^6 - 90599892/189463*e^4 + 204460524/189463*e^2 - 109085232/189463', '29503/189463*e^10 - 1148617/189463*e^8 + 15760119/189463*e^6 - 90599892/189463*e^4 + 204460524/189463*e^2 - 109085232/189463', '17508/189463*e^10 - 675640/189463*e^8 + 9184519/189463*e^6 - 52400979/189463*e^4 + 117871149/189463*e^2 - 58728158/189463', '38510/189463*e^10 - 1429410/189463*e^8 + 18270943/189463*e^6 - 94458019/189463*e^4 + 188926476/189463*e^2 - 95524458/189463', '38510/189463*e^10 - 1429410/189463*e^8 + 18270943/189463*e^6 - 94458019/189463*e^4 + 188926476/189463*e^2 - 95524458/189463', '-24683/189463*e^11 + 938025/189463*e^9 - 12404746/189463*e^7 + 67437425/189463*e^5 - 141875790/189463*e^3 + 66978873/189463*e', '2121/378926*e^11 - 30926/189463*e^9 + 218388/189463*e^7 + 887955/378926*e^5 - 5566646/189463*e^3 + 7649683/189463*e', '2121/378926*e^11 - 30926/189463*e^9 + 218388/189463*e^7 + 887955/378926*e^5 - 5566646/189463*e^3 + 7649683/189463*e', '-24683/189463*e^11 + 938025/189463*e^9 - 12404746/189463*e^7 + 67437425/189463*e^5 - 141875790/189463*e^3 + 66978873/189463*e', '-46041/378926*e^11 + 879539/189463*e^9 - 11720980/189463*e^7 + 129149803/378926*e^5 - 139957436/189463*e^3 + 75064761/189463*e', '89061/378926*e^11 - 1703774/189463*e^9 + 22807718/189463*e^7 - 253797381/378926*e^5 + 279034779/189463*e^3 - 150266791/189463*e', '89061/378926*e^11 - 1703774/189463*e^9 + 22807718/189463*e^7 - 253797381/378926*e^5 + 279034779/189463*e^3 - 150266791/189463*e', '-46041/378926*e^11 + 879539/189463*e^9 - 11720980/189463*e^7 + 129149803/378926*e^5 - 139957436/189463*e^3 + 75064761/189463*e', '-15095/189463*e^11 + 577760/189463*e^9 - 7735205/189463*e^7 + 42955341/189463*e^5 - 93549724/189463*e^3 + 49375391/189463*e', '-15095/189463*e^11 + 577760/189463*e^9 - 7735205/189463*e^7 + 42955341/189463*e^5 - 93549724/189463*e^3 + 49375391/189463*e', '1725/189463*e^10 - 93449/189463*e^8 + 1783570/189463*e^6 - 14246747/189463*e^4 + 41479975/189463*e^2 - 19134974/189463', '23473/189463*e^10 - 897737/189463*e^8 + 11930735/189463*e^6 - 65095614/189463*e^4 + 138195192/189463*e^2 - 68516548/189463', '23473/189463*e^10 - 897737/189463*e^8 + 11930735/189463*e^6 - 65095614/189463*e^4 + 138195192/189463*e^2 - 68516548/189463', '1725/189463*e^10 - 93449/189463*e^8 + 1783570/189463*e^6 - 14246747/189463*e^4 + 41479975/189463*e^2 - 19134974/189463', '76089/378926*e^11 - 1443348/189463*e^9 + 19019225/189463*e^7 - 205562101/378926*e^5 + 216096406/189463*e^3 - 111376793/189463*e', '76089/378926*e^11 - 1443348/189463*e^9 + 19019225/189463*e^7 - 205562101/378926*e^5 + 216096406/189463*e^3 - 111376793/189463*e', '-4241/378926*e^10 + 63088/189463*e^8 - 364318/189463*e^6 - 5832197/378926*e^4 + 22412872/189463*e^2 - 23438202/189463', '-4241/378926*e^10 + 63088/189463*e^8 - 364318/189463*e^6 - 5832197/378926*e^4 + 22412872/189463*e^2 - 23438202/189463', '-21288/189463*e^11 + 804630/189463*e^9 - 10555707/189463*e^7 + 56851287/189463*e^5 - 120641391/189463*e^3 + 67418662/189463*e', '70353/378926*e^11 - 1333450/189463*e^9 + 17566255/189463*e^7 - 189978155/378926*e^5 + 199662115/189463*e^3 - 100276232/189463*e', '70353/378926*e^11 - 1333450/189463*e^9 + 17566255/189463*e^7 - 189978155/378926*e^5 + 199662115/189463*e^3 - 100276232/189463*e', '-21288/189463*e^11 + 804630/189463*e^9 - 10555707/189463*e^7 + 56851287/189463*e^5 - 120641391/189463*e^3 + 67418662/189463*e', '-11244/189463*e^10 + 434819/189463*e^8 - 5927057/189463*e^6 + 34134767/189463*e^4 - 80189396/189463*e^2 + 48083532/189463', '-11244/189463*e^10 + 434819/189463*e^8 - 5927057/189463*e^6 + 34134767/189463*e^4 - 80189396/189463*e^2 + 48083532/189463', '33430/189463*e^10 - 1293149/189463*e^8 + 17593029/189463*e^6 - 100199829/189463*e^4 + 226013234/189463*e^2 - 122601868/189463', '33430/189463*e^10 - 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309550/189463*e^9 + 4216636/189463*e^7 - 24004912/189463*e^5 + 53525390/189463*e^3 - 31512770/189463*e', '7999/189463*e^11 - 309550/189463*e^9 + 4216636/189463*e^7 - 24004912/189463*e^5 + 53525390/189463*e^3 - 31512770/189463*e', '30345/378926*e^11 - 575643/189463*e^9 + 7598415/189463*e^7 - 82586599/378926*e^5 + 88594022/189463*e^3 - 53429040/189463*e', '-30721/189463*e^11 + 1169129/189463*e^9 - 15498828/189463*e^7 + 84657454/189463*e^5 - 180394565/189463*e^3 + 92829738/189463*e', '315/378926*e^11 + 10414/189463*e^9 - 479679/189463*e^7 + 10996921/378926*e^5 - 18309850/189463*e^3 + 8795274/189463*e', '315/378926*e^11 + 10414/189463*e^9 - 479679/189463*e^7 + 10996921/378926*e^5 - 18309850/189463*e^3 + 8795274/189463*e', '-30721/189463*e^11 + 1169129/189463*e^9 - 15498828/189463*e^7 + 84657454/189463*e^5 - 180394565/189463*e^3 + 92829738/189463*e', '70793/378926*e^10 - 1357999/189463*e^8 + 18186380/189463*e^6 - 201749681/378926*e^4 + 221482275/189463*e^2 - 121733228/189463', '70793/378926*e^10 - 1357999/189463*e^8 + 18186380/189463*e^6 - 201749681/378926*e^4 + 221482275/189463*e^2 - 121733228/189463'], 'hecke_polynomial': 'x^12 - 39*x^10 + 540*x^8 - 3217*x^6 + 8303*x^4 - 7948*x^2 + 2476', 'label': '4.4.16317.1-25.1-i'} -
hmf_fields • Show schema
{'degree': 4, 'discriminant': 16317, 'ideals': ['[1, 1, 1]', '[5, 5, w + 1]', '[5, 5, -w + 2]', '[7, 7, -w^2 + 2*w + 1]', '[7, 7, -w^2 + 2]', '[9, 3, w^3 - w^2 - 4*w]', '[16, 2, 2]', '[17, 17, -w^3 + 2*w^2 + 3*w - 2]', '[17, 17, -w^3 + w^2 + 4*w - 2]', '[25, 5, w^2 - w - 3]', '[25, 5, -w^2 + w + 2]', '[25, 25, w^3 - w^2 - 3*w + 2]', '[25, 25, w^3 - 2*w^2 - 2*w + 1]', '[35, 35, -w^2 + 2*w + 3]', '[35, 35, w^3 - w^2 - 5*w + 2]', '[35, 35, w^3 - 2*w^2 - 4*w + 3]', '[35, 35, -w^2 + 4]', '[37, 37, 2*w - 1]', '[43, 43, -w^3 + 2*w^2 + 2*w - 2]', '[43, 43, w^3 - w^2 - 3*w + 1]', '[45, 15, w^3 - w^2 - 4*w + 3]', '[45, 15, w^3 - 2*w^2 - 3*w + 1]', '[49, 7, w^3 - w^2 - 6*w]', '[49, 7, -w^3 + 6*w + 2]', '[49, 7, w^3 - 3*w^2 - 3*w + 7]', '[59, 59, 2*w - 5]', '[59, 59, -2*w - 3]', '[63, 21, -w^3 + w^2 + 4*w + 3]', '[63, 21, w^3 - 2*w^2 - 3*w + 7]', '[79, 79, -w^3 + 2*w^2 + 5*w - 4]', '[79, 79, -w^3 + w^2 + 6*w - 2]', '[80, 10, 2*w + 2]', '[80, 10, -2*w + 4]', '[81, 3, 3]', '[83, 83, -w^3 + 7*w]', '[83, 83, -w^3 + 2*w^2 + 4*w - 2]', '[83, 83, -w^3 + w^2 + 5*w - 3]', '[83, 83, w^2 - 2*w - 6]', '[85, 85, -w - 3]', '[85, 85, -w^3 + 2*w^2 + 5*w - 5]', '[85, 85, -w^3 + w^2 + 6*w - 1]', '[85, 85, w - 4]', '[89, 89, w^2 - 2*w - 4]', '[89, 89, w^2 - 5]', '[101, 101, -2*w^3 + 5*w^2 + 5*w - 11]', '[101, 101, w^2 + w - 4]', '[101, 101, w^2 - 3*w - 2]', '[101, 101, 2*w^3 - w^2 - 9*w - 3]', '[109, 109, w^3 - w^2 - 6*w - 3]', '[109, 109, -w^3 + 2*w^2 + 5*w - 9]', '[112, 14, -2*w^2 + 4*w + 2]', '[112, 14, -2*w^2 + 4]', '[119, 119, -w^3 + 2*w^2 + 4*w - 1]', '[119, 119, -w^3 + 2*w^2 + 2*w - 5]', '[119, 119, w^3 - w^2 - 3*w - 2]', '[119, 119, -w^3 + w^2 + 5*w - 4]', '[121, 11, w^3 - 8*w]', '[121, 11, w^3 - 3*w^2 - 5*w + 7]', '[125, 5, -w^3 + 3*w^2 + w - 6]', '[125, 5, w^3 - 4*w - 3]', '[125, 25, 2*w^3 - 3*w^2 - 8*w + 7]', '[125, 25, 2*w^3 - 3*w^2 - 8*w + 2]', '[125, 125, -w^2 + 6]', '[125, 125, -w^2 + 2*w + 5]', '[131, 131, w^3 - 5*w - 6]', '[131, 131, -w^3 + 3*w^2 + 2*w - 10]', '[144, 6, 2*w^3 - 2*w^2 - 8*w]', '[153, 51, -2*w^2 + 5*w - 1]', '[153, 51, 2*w^2 + w - 2]', '[163, 163, 2*w^2 - 3*w - 6]', '[163, 163, 2*w^2 - w - 7]', '[167, 167, w^3 - w^2 - 3*w - 4]', '[167, 167, -w^3 + 2*w^2 + 2*w - 7]', '[175, 35, w^3 - w^2 - 7*w + 5]', '[175, 35, w^3 - 2*w^2 - 2*w - 2]', '[175, 35, -w^3 + w^2 + 3*w - 5]', '[175, 35, w^3 - 2*w^2 - 6*w + 2]', '[175, 175, 2*w^3 - 2*w^2 - 8*w + 1]', '[175, 175, w^3 - 2*w^2 - 4*w + 8]', '[175, 175, -w^3 + w^2 + 5*w + 3]', '[175, 175, 2*w^3 - 4*w^2 - 6*w + 7]', '[185, 185, -2*w^2 + 5*w - 2]', '[185, 185, 2*w^2 + w - 1]', '[193, 193, 2*w^3 - 3*w^2 - 7*w + 2]', '[193, 193, 2*w^3 - 3*w^2 - 7*w + 6]', '[215, 215, w^3 - 3*w^2 - 2*w + 3]', '[215, 215, 2*w^3 - 7*w]', '[215, 215, -2*w^3 + 6*w^2 + w - 5]', '[215, 215, -w^3 + 5*w - 1]', '[225, 15, -2*w^3 + 2*w^2 + 11*w]', '[225, 15, -w^2 + w + 7]', '[225, 75, 2*w^3 - 4*w^2 - 9*w + 8]', '[225, 75, 2*w^3 - 2*w^2 - 11*w + 3]', '[227, 227, 2*w^3 - 3*w^2 - 8*w + 1]', '[227, 227, -2*w^3 + 3*w^2 + 8*w - 8]', '[245, 35, w^3 - 3*w^2 - 4*w + 5]', '[245, 35, -2*w^2 - w + 6]', '[245, 35, -w^2 - w + 5]', '[245, 35, -2*w^2 + 5*w + 3]', '[245, 35, -w^2 + 3*w + 3]', '[245, 35, w^3 - 7*w + 1]', '[251, 251, 2*w^2 - w - 9]', '[251, 251, 2*w^2 - 3*w - 8]', '[256, 4, 4]', '[257, 257, w^3 + w^2 - 8*w - 7]', '[257, 257, -4*w^3 + 5*w^2 + 17*w - 1]', '[259, 259, -2*w^3 + w^2 + 4*w - 2]', '[259, 259, -2*w^3 + 5*w^2 - 1]', '[269, 269, 2*w^3 - 2*w^2 - 10*w + 3]', '[269, 269, 2*w^3 - 3*w^2 - 9*w + 2]', '[269, 269, 2*w^3 - 3*w^2 - 9*w + 8]', '[269, 269, -2*w^3 + 4*w^2 + 8*w - 7]', '[272, 34, -2*w^3 + 4*w^2 + 6*w - 4]', '[272, 34, -2*w^3 + 2*w^2 + 8*w - 4]', '[277, 277, w^3 - w^2 - 4*w - 4]', '[277, 277, -w^3 + 2*w^2 + 3*w - 8]', '[289, 17, -2*w^2 + 2*w + 7]', '[289, 17, 2*w^2 - 2*w - 3]', '[289, 289, -2*w^2 + 3*w + 3]', '[289, 289, -2*w^2 + w + 4]', '[293, 293, -w^2 - 2*w + 5]', '[293, 293, -w^3 + 3*w^2 + 3*w - 4]', '[293, 293, w^3 - 6*w + 1]', '[293, 293, -2*w^3 + 4*w^2 + 7*w - 6]', '[295, 295, -2*w^3 + 3*w^2 + 7*w - 3]', '[295, 295, -2*w^2 + 3*w + 5]', '[295, 295, 2*w^2 - w - 6]', '[295, 295, 2*w^2 - 9*w + 10]', '[301, 301, w^2 + 3*w - 4]', '[301, 301, -w^3 - 2*w^2 + 3]', '[301, 301, w^3 - 5*w^2 + 7*w]', '[301, 301, w^2 - 5*w]', '[311, 311, -w^3 + 3*w^2 + w - 7]', '[311, 311, w^3 - 4*w - 4]', '[315, 105, -w^3 + 2*w^2 + 2]', '[315, 105, w^3 - 3*w^2 - 2*w + 2]', '[315, 105, w^3 - 5*w + 2]', '[315, 105, w^3 - w^2 - w + 3]', '[331, 331, -2*w^3 + 4*w^2 + 9*w - 10]', '[331, 331, 2*w^3 - 2*w^2 - 11*w + 1]', '[333, 111, w^3 + w^2 - 6*w - 2]', '[337, 337, 2*w^2 - 3*w - 4]', '[337, 337, -w^3 + 2*w^2 + 6*w - 3]', '[337, 337, w^3 - w^2 - 7*w + 4]', '[337, 337, 2*w^2 - w - 5]', '[343, 7, -w^3 - w^2 + 8*w + 5]', '[343, 7, w^3 - 4*w^2 - 3*w + 11]', '[343, 49, 2*w^3 - 2*w^2 - 11*w + 2]', '[343, 49, 2*w^3 - 4*w^2 - 9*w + 9]', '[353, 353, -3*w^3 + 4*w^2 + 13*w - 2]', '[353, 353, 3*w^3 - 5*w^2 - 12*w + 12]', '[373, 373, -2*w^3 + 6*w^2 + 3*w - 11]', '[373, 373, -w^3 - w^2 + 6*w + 7]', '[373, 373, -w^3 + 4*w^2 + w - 11]', '[373, 373, 2*w^3 - 9*w - 4]', '[379, 379, w^3 - w^2 - 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7]', '[1723, 1723, -4*w^3 + 8*w^2 + 17*w - 18]', '[1737, 579, -5*w^3 + 5*w^2 + 23*w + 6]', '[1737, 579, -w^3 + w^2 + 7*w + 6]', '[1744, 218, 2*w^3 - 2*w^2 - 12*w - 6]', '[1744, 218, -2*w^3 + 4*w^2 + 10*w - 18]', '[1747, 1747, 2*w^3 - 6*w^2 - 10*w + 15]', '[1747, 1747, 2*w^3 - 16*w - 1]', '[1757, 1757, -3*w^3 + 5*w^2 + 8*w - 16]', '[1757, 1757, w^3 + w^2 - 9*w - 7]', '[1757, 1757, w^3 - 4*w^2 - 4*w + 14]', '[1757, 1757, -3*w^3 + 4*w^2 + 9*w + 6]', '[1759, 1759, 2*w^3 - 3*w^2 - 13*w + 14]', '[1759, 1759, 2*w^2 - 3*w - 13]', '[1765, 1765, w^2 - 2*w + 5]', '[1765, 1765, 3*w^2 - 10*w + 2]', '[1765, 1765, 3*w^2 + 4*w - 5]', '[1765, 1765, -w^2 - 4]', '[1789, 1789, 5*w^3 - 4*w^2 - 21*w + 1]', '[1789, 1789, 5*w^3 - 11*w^2 - 14*w + 19]', '[1792, 28, -4*w^2 + 8*w + 4]', '[1792, 28, -4*w^2 + 8]', '[1799, 1799, -2*w^3 - 5*w^2 + w + 5]', '[1799, 1799, 2*w^2 - 11]', '[1799, 1799, 2*w^3 - 4*w^2 - 9*w]', '[1799, 1799, -3*w^3 + 6*w^2 + 12*w - 10]', '[1801, 1801, -4*w^3 + 3*w^2 + 16*w]', '[1801, 1801, -3*w^3 + 6*w^2 + 7*w - 5]', '[1801, 1801, 3*w^3 - 3*w^2 - 10*w + 5]', '[1801, 1801, 4*w^3 - 9*w^2 - 10*w + 15]', '[1811, 1811, -w^3 + 2*w^2 - 6]', '[1811, 1811, w^3 - w^2 - w - 5]', '[1813, 259, w^3 - 3*w^2 - 4*w - 2]', '[1813, 259, -3*w^3 + 5*w^2 + 7*w - 9]', '[1813, 259, -3*w^3 + 4*w^2 + 8*w]', '[1823, 1823, w^3 + 2*w^2 - 9*w - 14]', '[1823, 1823, -4*w^3 + 7*w^2 + 17*w - 11]', '[1823, 1823, -w^3 + 2*w^2 + 8*w - 13]', '[1823, 1823, -w^3 + 5*w^2 + 2*w - 20]', '[1831, 1831, 4*w^3 - 3*w^2 - 15*w + 3]', '[1831, 1831, -4*w^3 + 9*w^2 + 9*w - 11]', '[1849, 43, -2*w^3 + 2*w^2 + 13*w]', '[1849, 43, 3*w^3 - 3*w^2 - 17*w]', '[1849, 1849, 2*w^3 - w^2 - 14*w + 2]', '[1849, 1849, -2*w^3 + 5*w^2 + 10*w - 11]', '[1853, 1853, -3*w^2 + 5*w + 11]', '[1853, 1853, 5*w^3 - 6*w^2 - 23*w + 1]', '[1853, 1853, 5*w^3 - 9*w^2 - 20*w + 23]', '[1853, 1853, 6*w^3 - 14*w^2 - 15*w + 22]', '[1865, 1865, -3*w^3 + 4*w^2 + 12*w - 11]', '[1865, 1865, -4*w^3 + w^2 + 18*w + 8]', '[1865, 1865, w^3 + w^2 - 5*w - 10]', '[1865, 1865, w^2 + 2*w - 9]', '[1865, 1865, w^2 - 4*w - 6]', '[1865, 1865, w^3 - 4*w^2 + 13]', '[1865, 1865, -4*w^3 + 11*w^2 + 8*w - 23]', '[1865, 1865, -3*w^3 + 5*w^2 + 11*w - 2]', '[1873, 1873, -2*w^3 + 5*w^2 + 6*w - 18]', '[1873, 1873, w^3 - w^2 - 9*w + 7]', '[1883, 1883, 2*w^3 - 5*w^2 - 8*w + 8]', '[1883, 1883, 3*w^3 - 2*w^2 - 11*w + 5]', '[1883, 1883, 3*w^3 - 8*w^2 - 11*w + 17]', '[1883, 1883, -4*w^3 + 5*w^2 + 14*w - 14]', '[1883, 1883, 4*w^3 - 7*w^2 - 12*w + 1]', '[1883, 1883, 3*w^3 - w^2 - 18*w - 1]', '[1883, 1883, 3*w^3 - 7*w^2 - 6*w + 5]', '[1883, 1883, -2*w^3 + w^2 + 12*w - 3]', '[1889, 1889, 2*w^2 + w - 9]', '[1889, 1889, 2*w^2 - 5*w - 6]', '[1895, 1895, w^3 + w^2 - 10*w + 3]', '[1895, 1895, w^3 - 4*w^2 - 5*w + 13]', '[1895, 1895, 2*w^3 - 4*w^2 - 11*w]', '[1895, 1895, 2*w^3 - 2*w^2 - 11*w + 8]', '[1895, 1895, 2*w^3 - 4*w^2 - 9*w + 3]', '[1895, 1895, -2*w^3 + 2*w^2 + 13*w - 13]', '[1895, 1895, -w^3 - w^2 + 10*w + 5]', '[1895, 1895, -w^3 + 4*w^2 + 5*w - 5]', '[1904, 238, -2*w^3 + 4*w^2 + 8*w - 2]', '[1904, 238, -2*w^3 + 4*w^2 + 4*w - 10]', '[1904, 238, 2*w^3 - 2*w^2 - 6*w - 4]', '[1904, 238, -2*w^3 + 2*w^2 + 10*w - 8]', '[1907, 1907, w^2 + 2*w - 11]', '[1907, 1907, w^3 - 5*w^2 - 4*w + 8]', '[1915, 1915, 4*w^3 - 8*w^2 - 17*w + 19]', '[1915, 1915, 5*w^3 - 4*w^2 - 19*w + 5]', '[1915, 1915, 5*w^3 - 11*w^2 - 12*w + 13]', '[1915, 1915, 4*w^3 - 4*w^2 - 21*w + 2]', '[1933, 1933, w^3 + 2*w^2 - 5*w - 7]', '[1933, 1933, 2*w^3 - 3*w^2 - 12*w + 17]', '[1933, 1933, 2*w^3 - 3*w^2 - 12*w - 4]', '[1933, 1933, -w^3 + 5*w^2 - 2*w - 9]', '[1935, 645, -2*w^3 + 2*w^2 + 5*w + 3]', '[1935, 645, 2*w^3 - w^2 - 3*w + 5]', '[1935, 645, 2*w^3 - 5*w^2 + w - 3]', '[1935, 645, -2*w^3 + 4*w^2 + 3*w - 8]', '[1936, 22, 2*w^3 - 16*w]', '[1936, 22, 2*w^3 - 6*w^2 - 10*w + 14]', '[1939, 1939, 3*w^2 - 2*w - 7]', '[1939, 1939, -w^3 + 7*w^2 + 5*w - 16]', '[1939, 1939, w^3 + 4*w^2 - 16*w - 5]', '[1939, 1939, 3*w^2 - 4*w - 6]', '[1973, 1973, -3*w^3 + 8*w^2 + 5*w - 9]', '[1973, 1973, 3*w^3 - w^2 - 13*w - 6]', '[1973, 1973, -3*w^3 + 8*w^2 + 6*w - 17]', '[1973, 1973, -w^3 + 5*w^2 + 3*w - 17]', '[1975, 395, -3*w^3 + 4*w^2 + 10*w - 7]', '[1975, 395, 2*w^3 + w^2 - 9*w - 4]', '[1975, 395, -3*w^3 + 5*w^2 + 9*w - 4]', '[1975, 395, 2*w^3 + w^2 - 14*w - 4]', '[1975, 1975, 3*w^2 - 2*w - 8]', '[1975, 1975, 5*w^2 - 11*w - 6]', '[1975, 1975, 5*w^2 + w - 12]', '[1975, 1975, 3*w^2 - 4*w - 7]', '[1979, 1979, 3*w^3 - 6*w^2 - 8*w + 2]', '[1979, 1979, -3*w^3 + 3*w^2 + 11*w - 9]', '[2000, 10, -2*w^3 + 6*w^2 + 2*w - 12]', '[2000, 10, 2*w^3 - 8*w - 6]', '[2000, 50, 4*w^3 - 6*w^2 - 16*w + 14]', '[2000, 50, 4*w^3 - 6*w^2 - 16*w + 4]', '[2000, 250, -2*w^2 + 12]', '[2000, 250, -2*w^2 + 4*w + 10]', '[2011, 2011, -w^3 + 2*w^2 + 7*w - 15]', '[2011, 2011, 4*w^3 - 8*w^2 - 11*w + 9]', '[2017, 2017, 5*w^3 - 9*w^2 - 18*w + 20]', '[2017, 2017, -5*w^3 + 6*w^2 + 21*w - 2]', '[2023, 119, 2*w^3 - 7*w^2 + 2*w - 1]', '[2023, 119, -2*w^3 + 3*w^2 + 6*w + 5]', '[2023, 119, -2*w^3 - w^2 + 6*w - 4]', '[2023, 119, 2*w^3 - 3*w^2 - 6*w + 12]', '[2023, 2023, 2*w^3 - 3*w^2 - 12*w + 11]', '[2023, 2023, 2*w^3 - 7*w^2 - w + 12]', '[2023, 2023, -2*w^3 - w^2 + 9*w + 6]', '[2023, 2023, 2*w^3 - 3*w^2 - 12*w + 2]', '[2025, 15, 3*w^2 - 3*w - 9]', '[2025, 15, -3*w^2 + 3*w + 6]', '[2025, 75, 3*w^3 - 3*w^2 - 9*w + 6]', '[2025, 75, 3*w^3 - 6*w^2 - 6*w + 3]', '[2043, 681, -7*w^3 + 6*w^2 + 32*w + 7]', '[2043, 681, w^2 - 4*w - 7]', '[2051, 2051, -3*w^3 + 4*w^2 + 12*w - 12]', '[2051, 2051, -3*w^3 + w^2 + 10*w - 7]', '[2051, 2051, -w^3 - 2*w^2 + 13*w - 2]', '[2051, 2051, -4*w^2 + 9*w - 1]', '[2051, 2051, -4*w^2 - w + 4]', '[2051, 2051, 4*w^3 - 3*w^2 - 9*w + 9]', '[2051, 2051, 3*w^3 - 8*w^2 - 3*w + 1]', '[2051, 2051, 2*w^3 - 6*w^2 + 3*w + 4]', '[2053, 2053, -4*w^3 + 6*w^2 + 14*w - 3]', '[2053, 2053, 4*w^3 - 6*w^2 - 14*w + 13]', '[2057, 187, w^3 + 5*w^2 - 19*w - 7]', '[2057, 187, -3*w^3 + 7*w^2 + 8*w - 18]', '[2057, 187, 3*w^3 - 2*w^2 - 13*w - 6]', '[2057, 187, -w^3 + 8*w^2 + 6*w - 20]', '[2065, 2065, 3*w^3 - 3*w^2 - 19*w + 12]', '[2065, 2065, 5*w^3 - 10*w^2 - 16*w + 17]', '[2065, 2065, -w^3 + 3*w^2 + 7*w - 7]', '[2065, 2065, 2*w^3 - 9*w^2 + 4*w + 15]', '[2065, 2065, w^3 - 2*w^2 - 3*w - 4]', '[2065, 2065, 2*w^3 - 5*w^2 - 8*w + 20]', '[2065, 2065, 4*w^2 - 9]', '[2065, 2065, -3*w^3 + 2*w^2 + 8*w - 10]', '[2075, 415, 4*w^3 - 6*w^2 - 15*w + 1]', '[2075, 415, -3*w^3 + 6*w^2 + 8*w - 1]', '[2075, 415, -2*w^3 + w^2 + 10*w - 3]', '[2075, 415, -3*w^3 + 3*w^2 + 14*w - 5]', '[2075, 415, -3*w^3 + 6*w^2 + 11*w - 9]', '[2075, 415, -2*w^3 + 5*w^2 + 6*w - 6]', '[2075, 415, w^3 + 2*w^2 - 5*w - 11]', '[2075, 415, 4*w^3 - 6*w^2 - 15*w + 16]', '[2075, 2075, -2*w^3 + w^2 + 9*w - 4]', '[2075, 2075, -4*w^3 + 4*w^2 + 19*w - 4]', '[2075, 2075, w^3 + 2*w^2 - 2*w - 7]', '[2075, 2075, 2*w^3 - 3*w^2 - 4*w - 4]', '[2075, 2075, -2*w^3 + 3*w^2 + 4*w - 9]', '[2075, 2075, -w^3 + 5*w^2 - 5*w - 6]', '[2075, 2075, w^2 - 5*w - 4]', '[2075, 2075, -5*w^3 + 5*w^2 + 18*w - 11]', '[2083, 2083, -3*w^3 + 9*w^2 + 5*w - 18]', '[2083, 2083, 3*w^3 - 7*w^2 - 14*w + 14]', '[2083, 2083, 3*w^3 - 2*w^2 - 19*w + 4]', '[2083, 2083, 3*w^3 - 14*w - 7]', '[2096, 262, 2*w^3 - 10*w - 12]', '[2096, 262, -2*w^3 + 6*w^2 + 4*w - 20]', '[2105, 2105, -2*w^3 + 3*w^2 + 4*w - 11]', '[2105, 2105, 4*w^3 - 3*w^2 - 23*w - 6]', '[2105, 2105, -4*w^3 + 9*w^2 + 17*w - 28]', '[2105, 2105, 2*w^3 - 3*w^2 - 4*w - 6]', '[2107, 301, w^3 + 2*w^2 - 9*w - 4]', '[2107, 301, -2*w^3 + 4*w^2 + 12*w - 15]', '[2107, 301, -w^3 - w^2 + 12*w]', '[2107, 301, 2*w^3 - 2*w^2 - 14*w - 1]', '[2107, 301, -3*w^3 + 14*w + 4]', '[2107, 301, w^3 - 4*w^2 - 7*w + 10]', '[2125, 85, -w^3 - 2*w^2 + 6*w + 9]', '[2125, 85, 4*w^3 - 5*w^2 - 16*w + 3]', '[2125, 85, w^3 - 5*w^2 + w + 12]', '[2125, 85, 4*w^3 - 7*w^2 - 14*w + 14]', '[2125, 425, w^3 + 2*w^2 - 5*w - 6]', '[2125, 425, -3*w^3 + 5*w^2 + 9*w - 9]', '[2125, 425, -3*w^3 + 4*w^2 + 10*w - 2]', '[2125, 425, -w^3 + 5*w^2 - 2*w - 8]', '[2125, 2125, -w^3 - w^2 + 12*w - 2]', '[2125, 2125, w^3 - 2*w^2 - 7*w - 4]', '[2125, 2125, -w^3 + w^2 + 8*w - 12]', '[2125, 2125, -w^3 + 4*w^2 + 7*w - 8]', '[2141, 2141, w^3 + w^2 - 4*w - 8]', '[2141, 2141, -w^3 + 4*w^2 - w - 10]', '[2177, 2177, 2*w^3 - 5*w^2 + w - 4]', '[2177, 2177, w^3 + w^2 - 11*w - 4]', '[2177, 2177, -w^3 + 4*w^2 + 6*w - 13]', '[2177, 2177, -2*w^3 + w^2 + 3*w - 6]', '[2183, 2183, -4*w^3 + 9*w^2 + 16*w - 19]', '[2183, 2183, -3*w^3 + 6*w^2 + 8*w - 19]', '[2205, 105, 2*w^3 - 4*w^2 - 9*w + 2]', '[2205, 105, -2*w^3 + 7*w + 5]', '[2205, 105, w^3 - 4*w^2 - 7*w + 3]', '[2205, 105, w^3 + w^2 - 12*w + 7]', '[2205, 105, 2*w^3 - 6*w^2 - w + 10]', '[2205, 105, 2*w^3 - 2*w^2 - 11*w + 9]', '[2209, 47, 3*w^2 - 3*w - 8]', '[2209, 47, 3*w^2 - 3*w - 7]', '[2221, 2221, -w^3 + 2*w^2 + 4*w - 11]', '[2221, 2221, -2*w^3 + 7*w^2 + w - 11]', '[2221, 2221, -2*w^3 - w^2 + 9*w + 5]', '[2221, 2221, w^3 - w^2 - 5*w - 6]', '[2225, 445, w^3 - 3*w - 7]', '[2225, 445, 3*w^3 - w^2 - 16*w - 1]', '[2225, 445, -w^3 + 3*w^2 - 9]', '[2225, 445, -3*w^3 + 8*w^2 + 9*w - 15]', '[2225, 2225, -2*w^3 + 15*w - 2]', '[2225, 2225, -3*w^3 + 3*w^2 + 12*w - 7]', '[2225, 2225, -3*w^3 + 6*w^2 + 9*w - 5]', '[2225, 2225, -2*w^3 + 6*w^2 + 9*w - 11]', '[2227, 2227, 6*w^3 - 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11]', '[9769, 9769, 4*w^3 - 19*w - 8]', '[9781, 9781, -3*w^3 + 6*w^2 + 16*w - 10]', '[9781, 9781, -3*w^3 + 3*w^2 + 19*w - 9]', '[9783, 3261, -w^3 + 5*w^2 + 9*w - 13]', '[9783, 3261, -w^3 - 2*w^2 + 16*w]', '[9787, 9787, -7*w^3 + 12*w^2 + 24*w - 13]', '[9787, 9787, w^3 + 2*w^2 - 16*w + 4]', '[9791, 9791, -4*w^3 + 4*w^2 + 19*w - 8]', '[9791, 9791, -4*w^3 + 8*w^2 + 15*w - 11]', '[9801, 33, 3*w^3 - 24*w]', '[9801, 33, 3*w^3 - 9*w^2 - 15*w + 21]', '[9803, 9803, -3*w^3 + 7*w^2 + 10*w - 8]', '[9803, 9803, 3*w^3 - 2*w^2 - 15*w + 6]', '[9808, 1226, 4*w^3 - 6*w^2 - 22*w + 4]', '[9808, 1226, 2*w^3 + 2*w^2 - 12*w - 6]', '[9808, 1226, 6*w^3 - 8*w^2 - 24*w + 8]', '[9808, 1226, 4*w^3 - 6*w^2 - 22*w + 20]', '[9811, 9811, -3*w^3 + 5*w^2 + 20*w]', '[9811, 9811, -3*w^3 + w^2 + 22*w]', '[9819, 3273, 3*w^3 - w^2 - 20*w - 14]', '[9819, 3273, -2*w^3 - w^2 + 17*w - 3]', '[9829, 9829, w^3 - w^2 - 9*w - 10]', '[9829, 9829, w^3 - 2*w^2 - 8*w + 19]', '[9837, 3279, -5*w^3 + 10*w^2 + 9*w - 2]', '[9837, 3279, 10*w^3 - 7*w^2 - 55*w - 6]', '[9853, 9853, -4*w^3 + 6*w^2 + 12*w - 9]', '[9853, 9853, -w^3 + 6*w^2 - w - 12]', '[9853, 9853, w^3 + 3*w^2 - 8*w - 8]', '[9853, 9853, -4*w^3 + 6*w^2 + 12*w - 5]', '[9865, 9865, 8*w^3 - 2*w^2 - 34*w - 9]', '[9865, 9865, -w^3 + 2*w^2 + 4*w - 14]', '[9865, 9865, -2*w^3 + w^2 + 6*w - 10]', '[9865, 9865, -w^3 + w^2 + 11*w - 6]', '[9865, 9865, -5*w^3 + 11*w^2 + 18*w - 35]', '[9865, 9865, 2*w^3 + 4*w^2 - 9*w - 16]', '[9865, 9865, w^3 - w^2 - 5*w - 9]', '[9865, 9865, -8*w^3 + 22*w^2 + 14*w - 37]', '[9871, 9871, -2*w^3 + 3*w^2 + 14*w - 3]', '[9871, 9871, -2*w^3 + 3*w^2 + 14*w - 12]', '[9873, 3291, 3*w^3 - 5*w^2 - 4*w - 4]', '[9873, 3291, -3*w^3 + 4*w^2 + 5*w - 10]', '[9875, 395, -4*w^3 + 10*w^2 + 6*w - 3]', '[9875, 395, -w^3 + 3*w^2 - 4*w - 6]', '[9875, 395, -w^3 + 8*w^2 - 14*w - 6]', '[9875, 395, 7*w^3 - 5*w^2 - 28*w - 6]', '[9875, 1975, w^3 + 3*w^2 - 11*w - 18]', '[9875, 1975, 4*w^3 + w^2 - 28*w - 15]', '[9875, 1975, -4*w^3 + 13*w^2 + 14*w - 38]', '[9875, 1975, -w^3 + 6*w^2 + 2*w - 25]', '[9875, 9875, -7*w^3 + 10*w^2 + 30*w - 9]', '[9875, 9875, -6*w^3 + 7*w^2 + 30*w - 13]', '[9875, 9875, -6*w^3 + 11*w^2 + 26*w - 18]', '[9875, 9875, -7*w^3 + 11*w^2 + 29*w - 24]', '[9877, 9877, 6*w^3 - 8*w^2 - 31*w + 4]', '[9877, 9877, 7*w^3 - 11*w^2 - 26*w + 23]', '[9877, 9877, 5*w^3 - 9*w^2 - 15*w + 18]', '[9877, 9877, 2*w^3 - w^2 - 16*w + 3]', '[9877, 9877, -2*w^3 + 3*w^2 + 10*w + 6]', '[9877, 9877, w^3 - 6*w^2 + 13]', '[9877, 9877, 4*w^3 - 7*w^2 - 10*w + 5]', '[9877, 9877, 4*w^3 - 8*w^2 - 11*w + 28]', '[9877, 9877, -2*w^3 - 3*w^2 + 8*w + 8]', '[9877, 9877, -5*w^3 + w^2 + 26*w + 13]', '[9877, 9877, -w^3 - 3*w^2 + 9*w + 8]', '[9877, 9877, 2*w^3 - 3*w^2 - 10*w + 17]', '[9877, 9877, 2*w^3 - 5*w^2 - 12*w + 12]', '[9877, 9877, 5*w^3 - 6*w^2 - 18*w + 1]', '[9877, 9877, 5*w^3 - 13*w^2 + w + 3]', '[9877, 9877, -2*w^3 + 5*w^2 + w + 6]', '[9887, 9887, -w^3 + 4*w^2 - 4*w - 8]', '[9887, 9887, w^3 + w^2 - w - 9]', '[9895, 9895, 6*w^3 - 16*w^2 - 3*w + 7]', '[9895, 9895, 3*w^3 - 2*w^2 - 21*w - 1]', '[9895, 9895, -3*w^3 + 7*w^2 + 16*w - 21]', '[9895, 9895, -6*w^3 + 2*w^2 + 17*w - 6]', '[9907, 9907, 5*w^2 - 6*w - 17]', '[9907, 9907, 4*w^3 - 9*w^2 - 5*w + 7]', '[9907, 9907, -3*w^3 + 10*w^2 + 9*w - 26]', '[9907, 9907, 5*w^2 - 4*w - 18]', '[9929, 9929, -5*w^3 + 12*w^2 + 18*w - 25]', '[9929, 9929, -5*w^3 + 8*w^2 + 24*w - 27]', '[9953, 9953, w^2 + 5*w - 12]', '[9953, 9953, -2*w^3 + 4*w^2 + 2*w - 11]', '[9953, 9953, 2*w^3 - 2*w^2 - 4*w - 7]', '[9953, 9953, w^2 - 7*w - 6]', '[9961, 9961, 9*w^2 - 25*w - 2]', '[9961, 9961, w^3 - 2*w^2 - 10*w + 7]', '[9961, 9961, -w^3 + w^2 + 11*w - 4]', '[9961, 9961, 9*w^2 + 7*w - 18]', '[9968, 1246, 4*w^2 + 2*w - 14]', '[9968, 1246, 4*w^3 - 6*w^2 - 10*w - 6]', '[9968, 1246, -4*w^3 + 6*w^2 + 10*w - 18]', '[9968, 1246, 4*w^2 - 10*w - 8]', '[9979, 9979, -3*w^3 + 9*w^2 + 19*w - 11]', '[9979, 9979, -6*w^3 + 10*w^2 + 22*w - 17]', '[9979, 9979, -6*w^3 + 8*w^2 + 24*w - 9]', '[9979, 9979, -3*w^3 + 28*w - 14]', '[9989, 9989, -5*w^3 + 13*w^2 + 5*w - 5]', '[9989, 9989, 4*w^3 - 9*w^2 - 9*w + 1]', '[9989, 9989, -6*w^2 + 15*w - 2]', '[9989, 9989, -3*w^3 + 19*w]', '[9989, 9989, -3*w^3 + 9*w^2 + 10*w - 16]', '[9989, 9989, -6*w^2 - 3*w + 7]', '[9989, 9989, -4*w^3 + 3*w^2 + 15*w - 13]', '[9989, 9989, -5*w^3 + 2*w^2 + 16*w - 8]', '[10000, 10, 10]', '[10000, 50, 2*w^2 - 2*w + 6]', '[10000, 50, 2*w^3 - 2*w^2 - 16*w]', '[10000, 50, -2*w^3 + 18*w - 4]', '[10000, 50, -2*w^3 + 6*w^2 + 12*w - 12]', '[10000, 250, -4*w^2 - 6*w + 8]', '[10000, 250, 4*w^2 - 14*w + 2]', '[10000, 1250, -2*w^3 - 2*w^2 + 12*w + 12]', '[10000, 1250, 2*w^3 - 8*w^2 - 2*w + 20]'], 'label': '4.4.16317.1', 'narrow_class_no': 2, 'primes': ['[5, 5, w + 1]', '[5, 5, -w + 2]', '[7, 7, -w^2 + 2*w + 1]', '[7, 7, -w^2 + 2]', '[9, 3, w^3 - w^2 - 4*w]', '[16, 2, 2]', '[17, 17, -w^3 + 2*w^2 + 3*w - 2]', '[17, 17, -w^3 + w^2 + 4*w - 2]', '[25, 5, w^2 - w - 3]', '[37, 37, 2*w - 1]', '[43, 43, -w^3 + 2*w^2 + 2*w - 2]', '[43, 43, w^3 - w^2 - 3*w + 1]', '[59, 59, 2*w - 5]', '[59, 59, -2*w - 3]', '[79, 79, -w^3 + 2*w^2 + 5*w - 4]', '[79, 79, -w^3 + w^2 + 6*w - 2]', '[83, 83, -w^3 + 7*w]', '[83, 83, -w^3 + 2*w^2 + 4*w - 2]', '[83, 83, -w^3 + w^2 + 5*w - 3]', '[83, 83, w^2 - 2*w - 6]', '[89, 89, w^2 - 2*w - 4]', '[89, 89, w^2 - 5]', '[101, 101, -2*w^3 + 5*w^2 + 5*w - 11]', '[101, 101, w^2 + w - 4]', '[101, 101, w^2 - 3*w - 2]', '[101, 101, 2*w^3 - w^2 - 9*w - 3]', '[109, 109, w^3 - w^2 - 6*w - 3]', '[109, 109, -w^3 + 2*w^2 + 5*w - 9]', '[121, 11, w^3 - 8*w]', '[121, 11, w^3 - 3*w^2 - 5*w + 7]', '[131, 131, w^3 - 5*w - 6]', '[131, 131, -w^3 + 3*w^2 + 2*w - 10]', '[163, 163, 2*w^2 - 3*w - 6]', '[163, 163, 2*w^2 - w - 7]', '[167, 167, w^3 - w^2 - 3*w - 4]', '[167, 167, -w^3 + 2*w^2 + 2*w - 7]', '[193, 193, 2*w^3 - 3*w^2 - 7*w + 2]', '[193, 193, 2*w^3 - 3*w^2 - 7*w + 6]', '[227, 227, 2*w^3 - 3*w^2 - 8*w + 1]', '[227, 227, -2*w^3 + 3*w^2 + 8*w - 8]', '[251, 251, 2*w^2 - w - 9]', '[251, 251, 2*w^2 - 3*w - 8]', '[257, 257, w^3 + w^2 - 8*w - 7]', '[257, 257, -4*w^3 + 5*w^2 + 17*w - 1]', '[269, 269, 2*w^3 - 2*w^2 - 10*w + 3]', '[269, 269, 2*w^3 - 3*w^2 - 9*w + 2]', '[269, 269, 2*w^3 - 3*w^2 - 9*w + 8]', '[269, 269, -2*w^3 + 4*w^2 + 8*w - 7]', '[277, 277, w^3 - w^2 - 4*w - 4]', '[277, 277, -w^3 + 2*w^2 + 3*w - 8]', '[289, 17, 2*w^2 - 2*w - 3]', '[293, 293, -w^2 - 2*w + 5]', '[293, 293, -w^3 + 3*w^2 + 3*w - 4]', '[293, 293, w^3 - 6*w + 1]', '[293, 293, -2*w^3 + 4*w^2 + 7*w - 6]', '[311, 311, -w^3 + 3*w^2 + w - 7]', '[311, 311, w^3 - 4*w - 4]', '[331, 331, -2*w^3 + 4*w^2 + 9*w - 10]', '[331, 331, 2*w^3 - 2*w^2 - 11*w + 1]', '[337, 337, 2*w^2 - 3*w - 4]', '[337, 337, -w^3 + 2*w^2 + 6*w - 3]', '[337, 337, w^3 - w^2 - 7*w + 4]', '[337, 337, 2*w^2 - w - 5]', '[353, 353, -3*w^3 + 4*w^2 + 13*w - 2]', '[353, 353, 3*w^3 - 5*w^2 - 12*w + 12]', '[373, 373, -2*w^3 + 6*w^2 + 3*w - 11]', '[373, 373, -w^3 - w^2 + 6*w + 7]', '[373, 373, -w^3 + 4*w^2 + w - 11]', '[373, 373, 2*w^3 - 9*w - 4]', '[379, 379, w^3 - w^2 - 7*w + 1]', '[379, 379, 3*w^3 - 7*w^2 - 7*w + 11]', '[379, 379, 3*w^3 - 2*w^2 - 12*w]', '[379, 379, -w^3 + 2*w^2 + 6*w - 6]', '[383, 383, -3*w^3 + 4*w^2 + 12*w - 8]', '[383, 383, 3*w^3 - 5*w^2 - 11*w + 5]', '[421, 421, 2*w^3 - 2*w^2 - 9*w - 4]', '[421, 421, -2*w^3 + 4*w^2 + 7*w - 13]', '[457, 457, -w^3 + 2*w^2 + 6*w - 5]', '[457, 457, w^3 - w^2 - 7*w + 2]', '[461, 461, -w^3 + 3*w^2 + 4*w - 4]', '[461, 461, -w^3 + 7*w - 2]', '[463, 463, -w^3 + 4*w^2 + 3*w - 10]', '[463, 463, w^3 + w^2 - 8*w - 4]', '[467, 467, -w^3 + 6*w - 2]', '[467, 467, -w^3 + 3*w^2 + 3*w - 3]', '[479, 479, -w^3 + w^2 + w - 4]', '[479, 479, w^3 - 2*w^2 - 3]', '[487, 487, -3*w^3 + 4*w^2 + 12*w - 3]', '[487, 487, -3*w^3 + 5*w^2 + 11*w - 10]', '[499, 499, 3*w^3 - 4*w^2 - 11*w + 8]', '[499, 499, 3*w^3 - 5*w^2 - 10*w + 4]', '[503, 503, -w^3 + 2*w^2 + w - 5]', '[503, 503, w^3 - w^2 - 2*w - 3]', '[521, 521, 2*w^3 - 4*w^2 - 6*w + 3]', '[521, 521, -w^3 + 10*w - 8]', '[521, 521, w^3 - 3*w^2 - 7*w + 1]', '[521, 521, -2*w^3 + 2*w^2 + 8*w - 5]', '[541, 541, 2*w - 7]', '[541, 541, 2*w + 5]', '[547, 547, w^3 - 4*w^2 + 7]', '[547, 547, w^3 + w^2 - 5*w - 4]', '[563, 563, -2*w^3 + 4*w^2 + 7*w - 5]', '[563, 563, -2*w^3 + 2*w^2 + 9*w - 4]', '[587, 587, -w^3 - w^2 + 4*w + 6]', '[587, 587, w^3 - 4*w^2 + w + 8]', '[593, 593, w^2 + w - 7]', '[593, 593, 2*w^3 - 5*w^2 - 4*w + 5]', '[593, 593, -2*w^3 + w^2 + 8*w - 2]', '[593, 593, w^2 - 3*w - 5]', '[613, 613, 2*w^3 - 3*w^2 - 11*w + 2]', '[613, 613, w^3 + w^2 - 6*w - 3]', '[613, 613, 3*w^3 - 4*w^2 - 12*w + 4]', '[613, 613, 2*w^3 - 3*w^2 - 11*w + 10]', '[631, 631, -w^3 - w^2 + 7*w + 6]', '[631, 631, -w^3 + 4*w^2 + 2*w - 11]', '[647, 647, w^2 - 4*w - 3]', '[647, 647, w^2 + 2*w - 6]', '[677, 677, w^2 + w - 8]', '[677, 677, -w^3 + 7*w - 3]', '[677, 677, -w^3 + 3*w^2 + 4*w - 3]', '[677, 677, w^2 - 3*w - 6]', '[709, 709, w^3 - 7*w - 8]', '[709, 709, w^3 - 3*w^2 - 4*w + 14]', '[739, 739, w^3 - w^2 - 4*w - 5]', '[739, 739, -3*w^3 + 3*w^2 + 16*w - 3]', '[739, 739, -3*w^3 + 6*w^2 + 13*w - 13]', '[739, 739, -w^3 + 2*w^2 + 3*w - 9]', '[751, 751, -w - 5]', '[751, 751, w^3 + w^2 - 7*w - 4]', '[751, 751, -w^3 + 4*w^2 + 2*w - 9]', '[751, 751, w - 6]', '[757, 757, -w^3 + 4*w^2 + 2*w - 10]', '[757, 757, w^3 + w^2 - 7*w - 5]', '[761, 761, -3*w^3 + 2*w^2 + 17*w - 1]', '[761, 761, -3*w^3 + 6*w^2 + 9*w - 17]', '[761, 761, 2*w^3 - 5*w^2 - 9*w + 9]', '[761, 761, 2*w^3 - 2*w^2 - 7*w - 6]', '[773, 773, -3*w^3 + 8*w^2 + 6*w - 12]', '[773, 773, w^3 - 4*w - 6]', '[773, 773, -w^3 + 3*w^2 + w - 9]', '[773, 773, -3*w^3 + w^2 + 13*w + 1]', '[797, 797, 3*w^3 - 2*w^2 - 13*w + 1]', '[797, 797, 3*w^3 - 7*w^2 - 8*w + 11]', '[823, 823, 2*w^3 - 3*w^2 - 6*w - 4]', '[823, 823, -2*w^3 + 3*w^2 + 7*w + 3]', '[823, 823, w^3 - 2*w^2 - 7*w - 3]', '[823, 823, -3*w^3 + 5*w^2 + 9*w - 2]', '[857, 857, 2*w^3 - w^2 - 10*w + 1]', '[857, 857, -2*w^3 + 5*w^2 + 6*w - 8]', '[883, 883, 3*w^3 - 3*w^2 - 12*w + 1]', '[883, 883, 3*w^3 - 6*w^2 - 9*w + 11]', '[887, 887, -2*w^3 + 5*w^2 + 7*w - 9]', '[887, 887, -4*w^3 + 6*w^2 + 17*w - 7]', '[887, 887, -2*w^3 + 5*w^2 + 9*w - 16]', '[887, 887, 2*w^3 - w^2 - 11*w + 1]', '[907, 907, -3*w^3 + 3*w^2 + 16*w - 2]', '[907, 907, -3*w^3 + 6*w^2 + 13*w - 14]', '[919, 919, 2*w^3 - 2*w^2 - 7*w + 9]', '[919, 919, -2*w^3 + 2*w^2 + 12*w - 5]', '[929, 929, -2*w^3 + 4*w^2 + 8*w - 5]', '[929, 929, 3*w^3 - 4*w^2 - 11*w + 12]', '[929, 929, 3*w^3 - 5*w^2 - 10*w]', '[929, 929, -2*w^3 + 2*w^2 + 10*w - 5]', '[967, 967, 3*w^3 - 5*w^2 - 9*w + 11]', '[967, 967, -3*w^3 + 7*w^2 + 6*w - 10]', '[971, 971, 2*w^3 - 2*w^2 - 7*w - 5]', '[971, 971, -2*w^3 + w^2 + 8*w - 3]', '[971, 971, 2*w^3 - 5*w^2 - 4*w + 4]', '[971, 971, -2*w^3 + 4*w^2 + 5*w - 12]', '[983, 983, 4*w - 7]', '[983, 983, 2*w^2 - 4*w - 7]', '[983, 983, 2*w^2 - 9]', '[983, 983, 4*w + 3]', '[991, 991, 2*w^3 - 6*w^2 - 5*w + 14]', '[991, 991, -2*w^3 + 11*w + 5]']} -
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 5, -4, -2, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 16317, 'disc_rad': 777, 'disc_sign': 1, 'frobs': [[2, [[4, 1]]], [3, [0]], [5, [[2, 1], [1, 2]]], [7, [0]], [11, [[2, 2]]], [13, [[4, 1]]], [17, [[2, 1], [1, 2]]], [19, [[4, 1]]], [23, [[4, 1]]], [29, [[4, 1]]], [31, [[4, 1]]], [37, [0]], [41, [[2, 2]]], [43, [[2, 1], [1, 2]]], [47, [[2, 2]]], [53, [[2, 2]]], [59, [[2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [4, 4, 4], 'galois_label': '4T3', 'galt': 3, 'grd': 27.874719729532707, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.16317.1', 'local_algs': ['3.4.2.1', '7.2.1.2', '7.2.1.2', '37.2.1.2', '37.2.0.1'], 'monogenic': 1, 'num_ram': 3, 'r2': 0, 'ramps': [3, 7, 37], 'rd': 11.3021242754, 'regulator': {'__RealLiteral__': 0, 'data': '7.02556753637', 'prec': 44}, 'res': {'gal': ['7,-119,15,217,56,-79,-35,0,1'], 'sib': ['1,-1,-7,-1,1', '7,-119,15,217,56,-79,-35,0,1']}, 'subfield_mults': [1], 'subfields': ['-5.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a - 1 \\)', '\\( a \\)', '\\( a^{3} - a^{2} - 3 a + 3 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}
Hilbert modular form data - 4.4.16317.1-25.1-i