/* This code can be loaded, or copied and paste using cpaste, into Sage. It will load the data associated to the HMF, including the field, level, and Hecke and Atkin-Lehner eigenvalue data. */ P. = PolynomialRing(QQ) g = P([-33, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([23,23,w - 8]) primes_array = [ [3, 3, -w + 6],\ [3, 3, -w - 5],\ [4, 2, 2],\ [7, 7, 3*w - 19],\ [11, 11, -2*w - 11],\ [11, 11, -2*w + 13],\ [13, 13, w + 4],\ [13, 13, -w + 5],\ [19, 19, 5*w - 31],\ [23, 23, -w - 7],\ [23, 23, w - 8],\ [25, 5, -5],\ [31, 31, -w - 1],\ [31, 31, w - 2],\ [41, 41, 6*w + 31],\ [41, 41, 6*w - 37],\ [43, 43, -3*w - 17],\ [43, 43, -3*w + 20],\ [59, 59, 3*w - 17],\ [59, 59, 3*w + 14],\ [89, 89, 3*w + 13],\ [89, 89, 3*w - 16],\ [97, 97, 2*w - 7],\ [97, 97, -2*w - 5],\ [103, 103, 8*w + 41],\ [103, 103, 8*w - 49],\ [137, 137, 11*w - 70],\ [137, 137, 11*w + 59],\ [149, 149, -w - 13],\ [149, 149, w - 14],\ [163, 163, -3*w - 20],\ [163, 163, 3*w - 23],\ [167, 167, -3*w - 10],\ [167, 167, 3*w - 13],\ [173, 173, 6*w - 35],\ [173, 173, 6*w + 29],\ [181, 181, 5*w + 23],\ [181, 181, 5*w - 28],\ [191, 191, 2*w - 19],\ [191, 191, -2*w - 17],\ [197, 197, 4*w - 29],\ [197, 197, -4*w - 25],\ [223, 223, 7*w - 41],\ [223, 223, 7*w + 34],\ [227, 227, -3*w - 7],\ [227, 227, 3*w - 10],\ [233, 233, 13*w + 70],\ [233, 233, 13*w - 83],\ [239, 239, -w - 16],\ [239, 239, w - 17],\ [241, 241, 11*w + 56],\ [241, 241, 11*w - 67],\ [257, 257, 3*w - 8],\ [257, 257, -3*w - 5],\ [263, 263, -7*w + 47],\ [263, 263, -7*w - 40],\ [269, 269, -3*w - 4],\ [269, 269, 3*w - 7],\ [277, 277, 9*w - 59],\ [277, 277, -9*w - 50],\ [289, 17, -17],\ [293, 293, -3*w - 1],\ [293, 293, 3*w - 4],\ [307, 307, -4*w - 13],\ [307, 307, 4*w - 17],\ [347, 347, -w - 19],\ [347, 347, w - 20],\ [359, 359, 5*w + 32],\ [359, 359, -5*w + 37],\ [383, 383, 21*w - 130],\ [383, 383, 24*w - 149],\ [389, 389, -20*w + 127],\ [389, 389, 25*w - 158],\ [409, 409, 10*w - 59],\ [409, 409, 10*w + 49],\ [433, 433, 14*w + 71],\ [433, 433, 14*w - 85],\ [439, 439, -7*w + 38],\ [439, 439, 7*w + 31],\ [443, 443, 2*w - 25],\ [443, 443, -2*w - 23],\ [457, 457, -3*w - 26],\ [457, 457, 3*w - 29],\ [463, 463, 18*w + 97],\ [463, 463, 18*w - 115],\ [491, 491, 17*w - 109],\ [491, 491, 17*w + 92],\ [499, 499, -9*w + 61],\ [499, 499, -9*w - 52],\ [509, 509, 15*w + 76],\ [509, 509, 15*w - 91],\ [521, 521, 6*w - 29],\ [521, 521, -6*w - 23],\ [523, 523, -4*w - 1],\ [523, 523, 4*w - 5],\ [541, 541, -12*w - 67],\ [541, 541, 12*w - 79],\ [557, 557, -4*w - 31],\ [557, 557, 4*w - 35],\ [563, 563, 12*w - 71],\ [563, 563, 12*w + 59],\ [571, 571, 3*w - 31],\ [571, 571, -3*w - 28],\ [601, 601, 11*w + 53],\ [601, 601, 11*w - 64],\ [607, 607, 8*w + 35],\ [607, 607, -8*w + 43],\ [613, 613, -9*w - 53],\ [613, 613, -9*w + 62],\ [617, 617, -w - 25],\ [617, 617, w - 26],\ [631, 631, -3*w - 29],\ [631, 631, 3*w - 32],\ [653, 653, 19*w + 103],\ [653, 653, 19*w - 122],\ [661, 661, 19*w - 116],\ [661, 661, 19*w + 97],\ [677, 677, 33*w - 205],\ [677, 677, 33*w + 172],\ [701, 701, -13*w + 86],\ [701, 701, -13*w - 73],\ [709, 709, 15*w - 98],\ [709, 709, -15*w - 83],\ [739, 739, -6*w - 41],\ [739, 739, 6*w - 47],\ [757, 757, 3*w - 34],\ [757, 757, -3*w - 31],\ [773, 773, 18*w + 91],\ [773, 773, 18*w - 109],\ [787, 787, 28*w - 173],\ [787, 787, -37*w + 230],\ [797, 797, 6*w - 23],\ [797, 797, -6*w - 17],\ [809, 809, 5*w - 43],\ [809, 809, -5*w - 38],\ [811, 811, 5*w - 7],\ [811, 811, -5*w - 2],\ [821, 821, 7*w - 53],\ [821, 821, 7*w + 46],\ [823, 823, -3*w - 32],\ [823, 823, 3*w - 35],\ [829, 829, 5*w - 4],\ [829, 829, 5*w - 1],\ [839, 839, 15*w - 89],\ [839, 839, 15*w + 74],\ [841, 29, -29],\ [857, 857, 21*w - 128],\ [857, 857, 21*w + 107],\ [883, 883, 27*w + 145],\ [883, 883, 27*w - 172],\ [887, 887, 9*w - 47],\ [887, 887, -9*w - 38],\ [919, 919, 6*w - 49],\ [919, 919, -6*w - 43],\ [941, 941, -6*w - 13],\ [941, 941, 6*w - 19],\ [947, 947, -11*w - 65],\ [947, 947, -11*w + 76],\ [967, 967, -9*w - 56],\ [967, 967, 9*w - 65],\ [971, 971, 9*w + 37],\ [971, 971, 9*w - 46],\ [983, 983, 27*w + 139],\ [983, 983, 27*w - 166]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^14 - 40*x^12 + 657*x^10 - 5671*x^8 + 27240*x^6 - 70570*x^4 + 87156*x^2 - 39204 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, 155/594*e^13 - 5111/594*e^11 + 7333/66*e^9 - 208585/297*e^7 + 436243/198*e^5 - 907552/297*e^3 + 48490/33*e, 7/18*e^12 - 122/9*e^10 + 369/2*e^8 - 22021/18*e^6 + 11980/3*e^4 - 51119/9*e^2 + 2778, -1, -7/6*e^12 + 119/3*e^10 - 1055/2*e^8 + 20551/6*e^6 - 10983*e^4 + 46262/3*e^2 - 7467, -20/9*e^12 + 665/9*e^10 - 962*e^8 + 55154/9*e^6 - 58057/3*e^4 + 242579/9*e^2 - 13011, -53/198*e^13 + 862/99*e^11 - 2439/22*e^9 + 136817/198*e^7 - 70604/33*e^5 + 290857/99*e^3 - 15473/11*e, 193/297*e^13 - 6433/297*e^11 + 9326/33*e^9 - 535549/297*e^7 + 564110/99*e^5 - 2354206/297*e^3 + 125974/33*e, -101/594*e^13 + 3347/594*e^11 - 1607/22*e^9 + 137440/297*e^7 - 287209/198*e^5 + 593191/297*e^3 - 31211/33*e, 47/18*e^12 - 787/9*e^10 + 2293/2*e^8 - 132329/18*e^6 + 70034/3*e^4 - 293626/9*e^2 + 15780, 1, 1/6*e^12 - 14/3*e^10 + 99/2*e^8 - 1483/6*e^6 + 592*e^4 - 1922/3*e^2 + 249, -181/297*e^13 + 12203/594*e^11 - 8945/33*e^9 + 1038647/594*e^7 - 1105627/198*e^5 + 2330353/297*e^3 - 126025/33*e, -14/99*e^13 + 1021/198*e^11 - 802/11*e^9 + 98695/198*e^7 - 109667/66*e^5 + 235382/99*e^3 - 12739/11*e, 23/66*e^13 - 394/33*e^11 + 3519/22*e^9 - 69053/66*e^7 + 37188/11*e^5 - 158056/33*e^3 + 25757/11*e, 2/27*e^13 - 71/27*e^11 + 109/3*e^9 - 6590/27*e^7 + 7267/9*e^5 - 31628/27*e^3 + 1778/3*e, -1/9*e^12 + 22/9*e^10 - 16*e^8 + 82/9*e^6 + 628/3*e^4 - 4202/9*e^2 + 255, 47/18*e^12 - 787/9*e^10 + 2293/2*e^8 - 132311/18*e^6 + 69986/3*e^4 - 292969/9*e^2 + 15705, -224/297*e^13 + 15049/594*e^11 - 3665/11*e^9 + 1272715/594*e^7 - 1350521/198*e^5 + 2835314/297*e^3 - 152212/33*e, -28/297*e^13 + 2339/594*e^11 - 2033/33*e^9 + 270353/594*e^7 - 319027/198*e^5 + 717274/297*e^3 - 40273/33*e, 155/198*e^13 - 5111/198*e^11 + 7333/22*e^9 - 208585/99*e^7 + 436243/66*e^5 - 907750/99*e^3 + 48655/11*e, -497/594*e^13 + 16415/594*e^11 - 23587/66*e^9 + 671941/297*e^7 - 1407955/198*e^5 + 2938798/297*e^3 - 158206/33*e, -10/297*e^13 + 202/297*e^11 - 38/11*e^9 - 2393/297*e^7 + 9157/99*e^5 - 42443/297*e^3 + 1489/33*e, -112/297*e^13 + 3688/297*e^11 - 1761/11*e^9 + 300136/297*e^7 - 313796/99*e^5 + 1309846/297*e^3 - 70562/33*e, 514/297*e^13 - 17392/297*e^11 + 8529/11*e^9 - 1489888/297*e^7 + 1588649/99*e^5 - 6690592/297*e^3 + 360722/33*e, -785/594*e^13 + 26549/594*e^11 - 13015/22*e^9 + 1136620/297*e^7 - 2424673/198*e^5 + 5111875/297*e^3 - 276119/33*e, 59/9*e^12 - 1973/9*e^10 + 2870*e^8 - 165398/9*e^6 + 174892/3*e^4 - 733172/9*e^2 + 39417, e^12 - 32*e^10 + 401*e^8 - 2464*e^6 + 7552*e^4 - 10352*e^2 + 4957, 11/9*e^12 - 386/9*e^10 + 587*e^8 - 35174/9*e^6 + 38341/3*e^4 - 163244/9*e^2 + 8829, -11/3*e^12 + 362/3*e^10 - 1555*e^8 + 29426/3*e^6 - 30702*e^4 + 127421/3*e^2 - 20389, 23/9*e^12 - 749/9*e^10 + 1061*e^8 - 59603/9*e^6 + 61600/3*e^4 - 253868/9*e^2 + 13476, 2*e^12 - 66*e^10 + 853*e^8 - 5397*e^6 + 16947*e^4 - 23520*e^2 + 11310, -188/297*e^13 + 5936/297*e^11 - 2712/11*e^9 + 441854/297*e^7 - 442480/99*e^5 + 1783952/297*e^3 - 93559/33*e, -577/594*e^13 + 19417/594*e^11 - 28415/66*e^9 + 823046/297*e^7 - 1746407/198*e^5 + 3657650/297*e^3 - 195425/33*e, 208/297*e^13 - 14165/594*e^11 + 3492/11*e^9 - 1224893/594*e^7 + 1308385/198*e^5 - 2748664/297*e^3 + 147275/33*e, -437/297*e^13 + 14312/297*e^11 - 20395/33*e^9 + 1152716/297*e^7 - 1198567/99*e^5 + 4969499/297*e^3 - 265880/33*e, 955/297*e^13 - 63827/594*e^11 + 15465/11*e^9 - 5344535/594*e^7 + 5647699/198*e^5 - 11826244/297*e^3 + 635132/33*e, -13/198*e^13 + 223/198*e^11 - 25/22*e^9 - 7342/99*e^7 + 30229/66*e^5 - 84904/99*e^3 + 5408/11*e, -7/9*e^12 + 217/9*e^10 - 292*e^8 + 15604/9*e^6 - 15491/3*e^4 + 63034/9*e^2 - 3369, -37/6*e^12 + 614/3*e^10 - 5319/2*e^8 + 101443/6*e^6 - 53277*e^4 + 222119/3*e^2 - 35669, 11/6*e^12 - 184/3*e^10 + 1607/2*e^8 - 30899/6*e^6 + 16354*e^4 - 68629/3*e^2 + 11086, -46/9*e^12 + 1507/9*e^10 - 2148*e^8 + 121411/9*e^6 - 126209/3*e^4 + 522811/9*e^2 - 27894, -632/297*e^13 + 42145/594*e^11 - 30571/33*e^9 + 3515341/594*e^7 - 3709943/198*e^5 + 7766300/297*e^3 - 417602/33*e, 2/99*e^13 - 80/99*e^11 + 135/11*e^9 - 8768/99*e^7 + 10108/33*e^5 - 44120/99*e^3 + 2516/11*e, 299/594*e^13 - 9485/594*e^11 + 4357/22*e^9 - 357022/297*e^7 + 719047/198*e^5 - 1455481/297*e^3 + 76982/33*e, 115/198*e^13 - 3709/198*e^11 + 5205/22*e^9 - 144962/99*e^7 + 297707/66*e^5 - 612080/99*e^3 + 32449/11*e, -41/18*e^12 + 694/9*e^10 - 2041/2*e^8 + 118661/18*e^6 - 63098/3*e^4 + 264742/9*e^2 - 14211, 5/2*e^12 - 85*e^10 + 2261/2*e^8 - 14689/2*e^6 + 23588*e^4 - 33252*e^2 + 16185, 61/9*e^12 - 2044/9*e^10 + 2979*e^8 - 171952/9*e^6 + 181958/3*e^4 - 761956/9*e^2 + 40881, -17/2*e^12 + 285*e^10 - 7481/2*e^8 + 48007/2*e^6 - 76254*e^4 + 106553*e^2 - 51513, 47/297*e^13 - 3265/594*e^11 + 821/11*e^9 - 293395/594*e^7 + 318161/198*e^5 - 672896/297*e^3 + 36235/33*e, -412/297*e^13 + 13609/297*e^11 - 6520/11*e^9 + 1114891/297*e^7 - 1168676/99*e^5 + 4881220/297*e^3 - 262304/33*e, -194/297*e^13 + 6473/297*e^11 - 3133/11*e^9 + 540923/297*e^7 - 571408/99*e^5 + 2392997/297*e^3 - 127936/33*e, -463/198*e^13 + 7874/99*e^11 - 23283/22*e^9 + 1361839/198*e^7 - 728791/33*e^5 + 3076895/99*e^3 - 166157/11*e, 19/3*e^12 - 631/3*e^10 + 2735*e^8 - 52201/3*e^6 + 54879*e^4 - 229015/3*e^2 + 36783, -20/9*e^12 + 683/9*e^10 - 1013*e^8 + 59366/9*e^6 - 63538/3*e^4 + 267275/9*e^2 - 14337, 89/198*e^13 - 3065/198*e^11 + 4583/22*e^9 - 135391/99*e^7 + 292429/66*e^5 - 622399/99*e^3 + 33838/11*e, -769/297*e^13 + 50927/594*e^11 - 36689/33*e^9 + 4191857/594*e^7 - 4400287/198*e^5 + 9181651/297*e^3 - 492136/33*e, 1/9*e^12 - 40/9*e^10 + 67*e^8 - 4303/9*e^6 + 4904/3*e^4 - 21187/9*e^2 + 1119, -17/6*e^12 + 292/3*e^10 - 2615/2*e^8 + 51431/6*e^6 - 27723*e^4 + 117520/3*e^2 - 19047, -13/3*e^12 + 442/3*e^10 - 1960*e^8 + 38209/3*e^6 - 40889*e^4 + 172525/3*e^2 - 27879, 809/297*e^13 - 54127/594*e^11 + 13126/11*e^9 - 4538617/594*e^7 + 4795829/198*e^5 - 10029995/297*e^3 + 537286/33*e, 1201/594*e^13 - 40813/594*e^11 + 60305/66*e^9 - 1763471/297*e^7 + 3778037/198*e^5 - 7995971/297*e^3 + 432953/33*e, 118/99*e^13 - 3928/99*e^11 + 5688/11*e^9 - 326440/99*e^7 + 344120/33*e^5 - 1441711/99*e^3 + 77428/11*e, 16/11*e^13 - 1071/22*e^11 + 7014/11*e^9 - 89809/22*e^7 + 284467/22*e^5 - 197915/11*e^3 + 95055/11*e, -1/2*e^12 + 18*e^10 - 505/2*e^8 + 3441/2*e^6 - 5744*e^4 + 8292*e^2 - 4125, 31/3*e^12 - 1036/3*e^10 + 4518*e^8 - 86719/3*e^6 + 91580*e^4 - 383017/3*e^2 + 61583, 23/6*e^12 - 382/3*e^10 + 3311/2*e^8 - 63161/6*e^6 + 33169*e^4 - 138238/3*e^2 + 22185, 25/18*e^12 - 410/9*e^10 + 1169/2*e^8 - 66031/18*e^6 + 34288/3*e^4 - 142037/9*e^2 + 7563, 1477/297*e^13 - 98063/594*e^11 + 70817/33*e^9 - 8107949/594*e^7 + 8523193/198*e^5 - 17787367/297*e^3 + 952909/33*e, -547/198*e^13 + 9257/99*e^11 - 27237/22*e^9 + 1585159/198*e^7 - 843973/33*e^5 + 3543362/99*e^3 - 190019/11*e, 173/18*e^12 - 2884/9*e^10 + 8367/2*e^8 - 480953/18*e^6 + 253688/3*e^4 - 1061335/9*e^2 + 56979, -41/6*e^12 + 682/3*e^10 - 5923/2*e^8 + 113255/6*e^6 - 59626*e^4 + 249025/3*e^2 - 40007, -68/297*e^13 + 5341/594*e^11 - 4447/33*e^9 + 573157/594*e^7 - 660647/198*e^5 + 1458104/297*e^3 - 80363/33*e, -283/594*e^13 + 4868/297*e^11 - 14543/66*e^9 + 857641/594*e^7 - 460876/99*e^5 + 1938143/297*e^3 - 104087/33*e, -82/27*e^13 + 5489/54*e^11 - 1332*e^9 + 461027/54*e^7 - 487927/18*e^5 + 1023238/27*e^3 - 55001/3*e, 709/297*e^13 - 47711/594*e^11 + 11635/11*e^9 - 4043561/594*e^7 + 4289533/198*e^5 - 8984869/297*e^3 + 481424/33*e, 437/297*e^13 - 14609/297*e^11 + 21253/33*e^9 - 1225481/297*e^7 + 1297171/99*e^5 - 5446778/297*e^3 + 293237/33*e, 373/297*e^13 - 12148/297*e^11 + 17219/33*e^9 - 968566/297*e^7 + 1003283/99*e^5 - 4148590/297*e^3 + 220150/33*e, 71/18*e^12 - 1177/9*e^10 + 3395/2*e^8 - 194039/18*e^6 + 101825/3*e^4 - 424498/9*e^2 + 22725, -1/6*e^12 + 23/3*e^10 - 253/2*e^8 + 5767/6*e^6 - 3429*e^4 + 15152/3*e^2 - 2489, -9/2*e^12 + 153*e^10 - 4069/2*e^8 + 26421/2*e^6 - 42374*e^4 + 59557*e^2 - 28869, -4/9*e^12 + 124/9*e^10 - 167*e^8 + 8932/9*e^6 - 8846/3*e^4 + 35482/9*e^2 - 1857, 43/6*e^12 - 722/3*e^10 + 6327/2*e^8 - 121975/6*e^6 + 64647*e^4 - 271037/3*e^2 + 43649, 49/6*e^12 - 815/3*e^10 + 7077/2*e^8 - 135307/6*e^6 + 71251*e^4 - 297914/3*e^2 + 47959, 43/9*e^12 - 1432/9*e^10 + 2075*e^8 - 119167/9*e^6 + 125648/3*e^4 - 525868/9*e^2 + 28266, -20/3*e^12 + 659/3*e^10 - 2834*e^8 + 53684/3*e^6 - 56067*e^4 + 232985/3*e^2 - 37352, -8*e^12 + 266*e^10 - 3464*e^8 + 22077*e^6 - 69766*e^4 + 97257*e^2 - 46973, 5*e^12 - 169*e^10 + 2235*e^8 - 14441*e^6 + 46131*e^4 - 64673*e^2 + 31323, -430/297*e^13 + 14032/297*e^11 - 6639/11*e^9 + 1121038/297*e^7 - 1160945/99*e^5 + 4796863/297*e^3 - 255248/33*e, -764/297*e^13 + 25610/297*e^11 - 37336/33*e^9 + 2155634/297*e^7 - 2281777/99*e^5 + 9559718/297*e^3 - 512972/33*e, 17/22*e^13 - 559/22*e^11 + 7187/22*e^9 - 22568/11*e^7 + 140219/22*e^5 - 95715/11*e^3 + 44999/11*e, 706/297*e^13 - 23686/297*e^11 + 34565/33*e^9 - 1997491/297*e^7 + 2115431/99*e^5 - 8857507/297*e^3 + 474856/33*e, -503/198*e^13 + 17051/198*e^11 - 25125/22*e^9 + 732316/99*e^7 - 1562095/66*e^5 + 3283564/99*e^3 - 176038/11*e, -19/18*e^13 + 607/18*e^11 - 843/2*e^9 + 23225/9*e^7 - 47231/6*e^5 + 96629/9*e^3 - 5155*e, 4/3*e^12 - 133/3*e^10 + 578*e^8 - 11071/3*e^6 + 11672*e^4 - 48616/3*e^2 + 7751, 23/3*e^12 - 770/3*e^10 + 3364*e^8 - 64691/3*e^6 + 68463*e^4 - 287117/3*e^2 + 46313, 11/9*e^12 - 332/9*e^10 + 432*e^8 - 22151/9*e^6 + 20962/3*e^4 - 81380/9*e^2 + 4149, 14/3*e^12 - 473/3*e^10 + 2085*e^8 - 40436/3*e^6 + 43119*e^4 - 181910/3*e^2 + 29487, 25/33*e^13 - 835/33*e^11 + 3638/11*e^9 - 69736/33*e^7 + 73528/11*e^5 - 307036/33*e^3 + 49250/11*e, 262/297*e^13 - 16901/594*e^11 + 11855/33*e^9 - 1319987/594*e^7 + 1355125/198*e^5 - 2788435/297*e^3 + 147865/33*e, 11/2*e^12 - 183*e^10 + 4769/2*e^8 - 30409/2*e^6 + 48066*e^4 - 67010*e^2 + 32350, 59/6*e^12 - 985/3*e^10 + 8583/2*e^8 - 164597/6*e^6 + 86865*e^4 - 363451/3*e^2 + 58522, 1670/297*e^13 - 111127/594*e^11 + 26806/11*e^9 - 9222409/594*e^7 + 9701969/198*e^5 - 20223842/297*e^3 + 1080412/33*e, -565/297*e^13 + 37379/594*e^11 - 8967/11*e^9 + 3070247/594*e^7 - 3219289/198*e^5 + 6711703/297*e^3 - 360596/33*e, -2425/594*e^13 + 40679/297*e^11 - 39575/22*e^9 + 6861775/594*e^7 - 3635353/99*e^5 + 15247514/297*e^3 - 820291/33*e, -1262/297*e^13 + 42065/297*e^11 - 20332/11*e^9 + 3504593/297*e^7 - 3695446/99*e^5 + 15454127/297*e^3 - 828574/33*e, 11/3*e^12 - 380/3*e^10 + 1709*e^8 - 33713/3*e^6 + 36397*e^4 - 154241/3*e^2 + 24993, -163/18*e^12 + 2675/9*e^10 - 7639/2*e^8 + 432451/18*e^6 - 225028/3*e^4 + 932342/9*e^2 - 49707, 37/9*e^12 - 1219/9*e^10 + 1748*e^8 - 99424/9*e^6 + 103988/3*e^4 - 432883/9*e^2 + 23163, -15/2*e^12 + 253*e^10 - 6681/2*e^8 + 43123/2*e^6 - 68867*e^4 + 96675*e^2 - 46925, 70/9*e^12 - 2350/9*e^10 + 3431*e^8 - 198376/9*e^6 + 210287/3*e^4 - 882367/9*e^2 + 47427, -85/6*e^12 + 1415/3*e^10 - 12299/2*e^8 + 235387/6*e^6 - 124071*e^4 + 519158/3*e^2 - 83649, 74/9*e^12 - 2438/9*e^10 + 3495*e^8 - 198659/9*e^6 + 207541/3*e^4 - 862490/9*e^2 + 46059, -9/2*e^12 + 154*e^10 - 4123/2*e^8 + 26949/2*e^6 - 43491*e^4 + 61463*e^2 - 29969, 505/198*e^13 - 16735/198*e^11 + 24127/22*e^9 - 689378/99*e^7 + 1447199/66*e^5 - 3017435/99*e^3 + 161544/11*e, 397/297*e^13 - 26513/594*e^11 + 19268/33*e^9 - 2220923/594*e^7 + 2351029/198*e^5 - 4940875/297*e^3 + 266908/33*e, -563/198*e^13 + 18461/198*e^11 - 26337/22*e^9 + 744937/99*e^7 - 1549591/66*e^5 + 3208309/99*e^3 - 170856/11*e, 124/27*e^13 - 4168/27*e^11 + 2031*e^9 - 352690/27*e^7 + 374120/9*e^5 - 1569193/27*e^3 + 84242/3*e, -9/2*e^12 + 152*e^10 - 4021/2*e^8 + 26009/2*e^6 - 41632*e^4 + 58577*e^2 - 28514, -2/3*e^12 + 83/3*e^10 - 430*e^8 + 9452/3*e^6 - 11014*e^4 + 48398/3*e^2 - 7920, 41/3*e^12 - 1370/3*e^10 + 5974*e^8 - 114662/3*e^6 + 121100*e^4 - 506651/3*e^2 + 81510, -1/3*e^12 + 49/3*e^10 - 280*e^8 + 6556/3*e^6 - 7959*e^4 + 35782/3*e^2 - 5940, 14/3*e^12 - 470/3*e^10 + 2059*e^8 - 39683/3*e^6 + 42022*e^4 - 175652/3*e^2 + 28167, -56/9*e^12 + 1907/9*e^10 - 2822*e^8 + 165134/9*e^6 - 176668/3*e^4 + 744158/9*e^2 - 40011, 13/2*e^12 - 215*e^10 + 5569/2*e^8 - 35297/2*e^6 + 55487*e^4 - 77048*e^2 + 37079, 10*e^12 - 333*e^10 + 4341*e^8 - 27679*e^6 + 87438*e^4 - 121688*e^2 + 58637, -2045/297*e^13 + 68039/297*e^11 - 32829/11*e^9 + 5649770/297*e^7 - 5949829/99*e^5 + 24862250/297*e^3 - 1332382/33*e, -691/297*e^13 + 23977/297*e^11 - 36110/33*e^9 + 2147353/297*e^7 - 2330483/99*e^5 + 9935575/297*e^3 - 540334/33*e, -58/11*e^13 + 3881/22*e^11 - 25412/11*e^9 + 325383/22*e^7 - 1030889/22*e^5 + 717710/11*e^3 - 345442/11*e, -2/3*e^13 + 62/3*e^11 - 250*e^9 + 4442/3*e^7 - 4392*e^5 + 17774/3*e^3 - 2825*e, 395/297*e^13 - 13325/297*e^11 + 6517/11*e^9 - 1135799/297*e^7 + 1208785/99*e^5 - 5082776/297*e^3 + 273511/33*e, -1822/297*e^13 + 121505/594*e^11 - 88148/33*e^9 + 10139147/594*e^7 - 10707613/198*e^5 + 22447075/297*e^3 - 1208686/33*e, -11/2*e^12 + 186*e^10 - 4923/2*e^8 + 31837/2*e^6 - 50906*e^4 + 71444*e^2 - 34611, 11/2*e^12 - 181*e^10 + 4665/2*e^8 - 29423/2*e^6 + 46027*e^4 - 63584*e^2 + 30465, -455/297*e^13 + 29371/594*e^11 - 6866/11*e^9 + 2289511/594*e^7 - 2340257/198*e^5 + 4774658/297*e^3 - 250717/33*e, -643/198*e^13 + 21661/198*e^11 - 31737/22*e^9 + 920693/99*e^7 - 1958135/66*e^5 + 4117835/99*e^3 - 221506/11*e, 6*e^12 - 197*e^10 + 2533*e^8 - 15945*e^6 + 49826*e^4 - 68866*e^2 + 33079, 1/18*e^12 - 11/9*e^10 + 15/2*e^8 + 71/18*e^6 - 434/3*e^4 + 2380/9*e^2 - 99, -5/3*e^12 + 176/3*e^10 - 806*e^8 + 16175/3*e^6 - 17738*e^4 + 76136/3*e^2 - 12453, 121/18*e^12 - 2060/9*e^10 + 6099/2*e^8 - 357241/18*e^6 + 191464/3*e^4 - 809381/9*e^2 + 43689, 3431/594*e^13 - 115757/594*e^11 + 56611/22*e^9 - 4932199/297*e^7 + 10496701/198*e^5 - 22074814/297*e^3 + 1188416/33*e, 116/99*e^13 - 3947/99*e^11 + 5839/11*e^9 - 342026/99*e^7 + 367474/33*e^5 - 1566287/99*e^3 + 85659/11*e, 205/198*e^13 - 6913/198*e^11 + 10147/22*e^9 - 295217/99*e^7 + 630797/66*e^5 - 1336886/99*e^3 + 72570/11*e, 268/297*e^13 - 8839/297*e^11 + 12689/33*e^9 - 722383/297*e^7 + 755753/99*e^5 - 3144733/297*e^3 + 169273/33*e, 41/9*e^12 - 1415/9*e^10 + 2120*e^8 - 125438/9*e^6 + 135454/3*e^4 - 574358/9*e^2 + 31062, -655/198*e^13 + 21943/198*e^11 - 31975/22*e^9 + 922841/99*e^7 - 1954235/66*e^5 + 4099913/99*e^3 - 220595/11*e, 269/297*e^13 - 8780/297*e^11 + 12454/33*e^9 - 699542/297*e^7 + 721141/99*e^5 - 2951270/297*e^3 + 155252/33*e, 4*e^12 - 140*e^10 + 1912*e^8 - 12711*e^6 + 41546*e^4 - 59029*e^2 + 28757, 14/3*e^12 - 461/3*e^10 + 1981*e^8 - 37502/3*e^6 + 39166*e^4 - 162986/3*e^2 + 26163, 25/9*e^13 - 1667/18*e^11 + 1209*e^9 - 139001/18*e^7 + 146695/6*e^5 - 307132/9*e^3 + 16491*e, -26/27*e^13 + 842/27*e^11 - 1186/3*e^9 + 66257/27*e^7 - 68155/9*e^5 + 280403/27*e^3 - 14978/3*e, -32/3*e^12 + 1046/3*e^10 - 4463*e^8 + 83915/3*e^6 - 87070*e^4 + 360083/3*e^2 - 57536, e^12 - 33*e^10 + 427*e^8 - 2705*e^6 + 8482*e^4 - 11651*e^2 + 5504, -70/99*e^13 + 4313/198*e^11 - 2877/11*e^9 + 303791/198*e^7 - 296215/66*e^5 + 585781/99*e^3 - 30365/11*e, -115/22*e^13 + 1948/11*e^11 - 51641/22*e^9 + 334353/22*e^7 - 534808/11*e^5 + 749734/11*e^3 - 362639/11*e, 23/6*e^12 - 382/3*e^10 + 3313/2*e^8 - 63281/6*e^6 + 33302*e^4 - 139234/3*e^2 + 22432, -115/9*e^12 + 3871/9*e^10 - 5667*e^8 + 328480/9*e^6 - 348827/3*e^4 + 1463803/9*e^2 - 78576, 77/9*e^12 - 2612/9*e^10 + 3851*e^8 - 224627/9*e^6 + 239824/3*e^4 - 1010660/9*e^2 + 54468, 22/3*e^12 - 754/3*e^10 + 3368*e^8 - 66070/3*e^6 + 71032*e^4 - 300247/3*e^2 + 48552, 650/99*e^13 - 21644/99*e^11 + 31357/11*e^9 - 1800497/99*e^7 + 1898242/33*e^5 - 7945679/99*e^3 + 427244/11*e, -2129/297*e^13 + 142897/594*e^11 - 104278/33*e^9 + 12052981/594*e^7 - 12767375/198*e^5 + 26752118/297*e^3 - 1436096/33*e, -419/594*e^13 + 7291/297*e^11 - 7343/22*e^9 + 1314671/594*e^7 - 716867/99*e^5 + 3081724/297*e^3 - 170051/33*e, 48/11*e^13 - 1590/11*e^11 + 20624/11*e^9 - 130902/11*e^7 + 411922/11*e^5 - 571833/11*e^3 + 275320/11*e] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([23,23,w - 8])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]