/* 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([-55, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([5, 5, -2*w + 15]) primes_array = [ [2, 2, w + 1],\ [3, 3, w + 1],\ [3, 3, w + 2],\ [5, 5, -2*w + 15],\ [11, 11, 3*w - 22],\ [13, 13, w + 4],\ [13, 13, w + 9],\ [17, 17, w + 2],\ [17, 17, w + 15],\ [19, 19, -w - 6],\ [19, 19, w - 6],\ [23, 23, w + 3],\ [23, 23, w + 20],\ [47, 47, w + 14],\ [47, 47, w + 33],\ [49, 7, -7],\ [67, 67, w + 16],\ [67, 67, w + 51],\ [73, 73, w + 36],\ [73, 73, w + 37],\ [79, 79, 5*w + 36],\ [79, 79, 5*w - 36],\ [89, 89, -w - 12],\ [89, 89, w - 12],\ [103, 103, w + 40],\ [103, 103, w + 63],\ [131, 131, -6*w - 43],\ [131, 131, -6*w + 43],\ [139, 139, 2*w - 9],\ [139, 139, -2*w - 9],\ [151, 151, 4*w - 27],\ [151, 151, 4*w + 27],\ [163, 163, w + 50],\ [163, 163, w + 113],\ [173, 173, w + 48],\ [173, 173, w + 125],\ [181, 181, -3*w - 26],\ [181, 181, 3*w - 26],\ [193, 193, w + 21],\ [193, 193, w + 172],\ [197, 197, w + 45],\ [197, 197, w + 152],\ [211, 211, 2*w - 3],\ [211, 211, -2*w - 3],\ [223, 223, w + 72],\ [223, 223, w + 151],\ [229, 229, 6*w + 47],\ [229, 229, 6*w - 47],\ [233, 233, w + 88],\ [233, 233, w + 145],\ [239, 239, -3*w - 16],\ [239, 239, 3*w - 16],\ [269, 269, -w - 18],\ [269, 269, w - 18],\ [271, 271, -8*w - 57],\ [271, 271, -8*w + 57],\ [277, 277, w + 71],\ [277, 277, w + 206],\ [293, 293, w + 73],\ [293, 293, w + 220],\ [337, 337, w + 27],\ [337, 337, w + 310],\ [359, 359, 9*w + 64],\ [359, 359, 9*w - 64],\ [367, 367, w + 34],\ [367, 367, w + 333],\ [373, 373, w + 146],\ [373, 373, w + 227],\ [383, 383, w + 173],\ [383, 383, w + 210],\ [389, 389, -5*w - 42],\ [389, 389, 5*w - 42],\ [401, 401, 29*w - 216],\ [401, 401, 11*w - 84],\ [421, 421, -6*w + 49],\ [421, 421, -6*w - 49],\ [431, 431, 3*w - 8],\ [431, 431, -3*w - 8],\ [439, 439, -4*w - 21],\ [439, 439, 4*w - 21],\ [443, 443, w + 99],\ [443, 443, w + 344],\ [449, 449, -8*w - 63],\ [449, 449, -8*w + 63],\ [457, 457, w + 91],\ [457, 457, w + 366],\ [463, 463, w + 38],\ [463, 463, w + 425],\ [467, 467, w + 191],\ [467, 467, w + 276],\ [479, 479, -3*w - 4],\ [479, 479, 3*w - 4],\ [487, 487, w + 223],\ [487, 487, w + 264],\ [491, 491, 3*w - 2],\ [491, 491, -3*w - 2],\ [509, 509, 2*w - 27],\ [509, 509, -2*w - 27],\ [521, 521, -w - 24],\ [521, 521, w - 24],\ [557, 557, w + 75],\ [557, 557, w + 482],\ [571, 571, 11*w + 78],\ [571, 571, 11*w - 78],\ [587, 587, w + 246],\ [587, 587, w + 341],\ [593, 593, w + 184],\ [593, 593, w + 409],\ [613, 613, w + 235],\ [613, 613, w + 378],\ [641, 641, -4*w - 39],\ [641, 641, 4*w - 39],\ [643, 643, w + 174],\ [643, 643, w + 469],\ [647, 647, w + 257],\ [647, 647, w + 390],\ [659, 659, -18*w + 131],\ [659, 659, 30*w - 221],\ [661, 661, 3*w - 34],\ [661, 661, -3*w - 34],\ [673, 673, w + 196],\ [673, 673, w + 477],\ [677, 677, w + 240],\ [677, 677, w + 437],\ [683, 683, w + 136],\ [683, 683, w + 547],\ [709, 709, 21*w - 158],\ [709, 709, 27*w - 202],\ [727, 727, w + 339],\ [727, 727, w + 388],\ [733, 733, w + 39],\ [733, 733, w + 694],\ [739, 739, 10*w - 69],\ [739, 739, 10*w + 69],\ [811, 811, 35*w - 258],\ [811, 811, -19*w + 138],\ [823, 823, w + 177],\ [823, 823, w + 646],\ [829, 829, -6*w - 53],\ [829, 829, 6*w - 53],\ [841, 29, -29],\ [853, 853, w + 316],\ [853, 853, w + 537],\ [857, 857, w + 270],\ [857, 857, w + 587],\ [863, 863, w + 405],\ [863, 863, w + 458],\ [877, 877, w + 377],\ [877, 877, w + 500],\ [881, 881, -19*w + 144],\ [881, 881, -37*w + 276],\ [883, 883, w + 52],\ [883, 883, w + 831],\ [907, 907, w + 350],\ [907, 907, w + 557],\ [919, 919, -8*w - 51],\ [919, 919, 8*w - 51],\ [929, 929, 5*w - 48],\ [929, 929, -5*w - 48],\ [937, 937, w + 176],\ [937, 937, w + 761],\ [947, 947, w + 252],\ [947, 947, w + 695],\ [953, 953, w + 334],\ [953, 953, w + 619],\ [961, 31, -31],\ [983, 983, w + 277],\ [983, 983, w + 706],\ [997, 997, w + 371],\ [997, 997, w + 626]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^12 + 50*x^10 + 737*x^8 + 4580*x^6 + 12472*x^4 + 12272*x^2 + 16 K. = NumberField(heckePol) hecke_eigenvalues_array = [-1783/202352*e^11 - 10933/25294*e^9 - 1235763/202352*e^7 - 3599071/101176*e^5 - 1112907/12647*e^3 - 956224/12647*e, 1783/202352*e^11 + 10933/25294*e^9 + 1235763/202352*e^7 + 3599071/101176*e^5 + 1112907/12647*e^3 + 968871/12647*e, 1783/202352*e^11 + 10933/25294*e^9 + 1235763/202352*e^7 + 3599071/101176*e^5 + 1112907/12647*e^3 + 968871/12647*e, 1, 2769/404704*e^10 + 8415/25294*e^8 + 1834449/404704*e^6 + 4649041/202352*e^4 + 3592341/101176*e^2 - 219359/50588, 4863/809408*e^11 + 30585/101176*e^9 + 3639791/809408*e^7 + 11277179/404704*e^5 + 15105259/202352*e^3 + 7481107/101176*e, 4863/809408*e^11 + 30585/101176*e^9 + 3639791/809408*e^7 + 11277179/404704*e^5 + 15105259/202352*e^3 + 7481107/101176*e, 11797/809408*e^11 + 73415/101176*e^9 + 8579701/809408*e^7 + 26343033/404704*e^5 + 35310685/202352*e^3 + 16981893/101176*e, 11797/809408*e^11 + 73415/101176*e^9 + 8579701/809408*e^7 + 26343033/404704*e^5 + 35310685/202352*e^3 + 16981893/101176*e, -1605/404704*e^10 - 18839/101176*e^8 - 948317/404704*e^6 - 2135331/202352*e^4 - 1382717/101176*e^2 + 83109/50588, -1605/404704*e^10 - 18839/101176*e^8 - 948317/404704*e^6 - 2135331/202352*e^4 - 1382717/101176*e^2 + 83109/50588, 961/404704*e^11 + 10161/101176*e^9 + 359657/404704*e^7 - 20581/202352*e^5 - 2279835/101176*e^3 - 2474109/50588*e, 961/404704*e^11 + 10161/101176*e^9 + 359657/404704*e^7 - 20581/202352*e^5 - 2279835/101176*e^3 - 2474109/50588*e, -2883/404704*e^11 - 30483/101176*e^9 - 1078971/404704*e^7 + 61743/202352*e^5 + 6839505/101176*e^3 + 7422327/50588*e, -2883/404704*e^11 - 30483/101176*e^9 - 1078971/404704*e^7 + 61743/202352*e^5 + 6839505/101176*e^3 + 7422327/50588*e, 4807/202352*e^10 + 111483/101176*e^8 + 2746203/202352*e^6 + 3117455/50588*e^4 + 4438231/50588*e^2 - 140732/12647, -13605/404704*e^11 - 170329/101176*e^9 - 10054493/404704*e^7 - 31012655/202352*e^5 - 41182861/101176*e^3 - 19236643/50588*e, -13605/404704*e^11 - 170329/101176*e^9 - 10054493/404704*e^7 - 31012655/202352*e^5 - 41182861/101176*e^3 - 19236643/50588*e, 3929/809408*e^11 + 31951/101176*e^9 + 5681193/809408*e^7 + 26711677/404704*e^5 + 53702077/202352*e^3 + 36576533/101176*e, 3929/809408*e^11 + 31951/101176*e^9 + 5681193/809408*e^7 + 26711677/404704*e^5 + 53702077/202352*e^3 + 36576533/101176*e, 4655/404704*e^10 + 26827/50588*e^8 + 2589983/404704*e^6 + 5539027/202352*e^4 + 3727427/101176*e^2 + 650867/50588, 4655/404704*e^10 + 26827/50588*e^8 + 2589983/404704*e^6 + 5539027/202352*e^4 + 3727427/101176*e^2 + 650867/50588, 5811/202352*e^10 + 135399/101176*e^8 + 3377367/202352*e^6 + 3940827/50588*e^4 + 6125955/50588*e^2 + 165358/12647, 5811/202352*e^10 + 135399/101176*e^8 + 3377367/202352*e^6 + 3940827/50588*e^4 + 6125955/50588*e^2 + 165358/12647, 3947/404704*e^11 + 51419/101176*e^9 + 3336035/404704*e^7 + 12258521/202352*e^5 + 21356015/101176*e^3 + 13912697/50588*e, 3947/404704*e^11 + 51419/101176*e^9 + 3336035/404704*e^7 + 12258521/202352*e^5 + 21356015/101176*e^3 + 13912697/50588*e, 2729/101176*e^10 + 131777/101176*e^8 + 1770707/101176*e^6 + 8864599/101176*e^4 + 1743580/12647*e^2 + 11379/25294, 2729/101176*e^10 + 131777/101176*e^8 + 1770707/101176*e^6 + 8864599/101176*e^4 + 1743580/12647*e^2 + 11379/25294, 3271/202352*e^10 + 39639/50588*e^8 + 2150031/202352*e^6 + 5472413/101176*e^4 + 4486791/50588*e^2 + 162613/25294, 3271/202352*e^10 + 39639/50588*e^8 + 2150031/202352*e^6 + 5472413/101176*e^4 + 4486791/50588*e^2 + 162613/25294, -8147/202352*e^10 - 98117/50588*e^8 - 5248379/202352*e^6 - 13080157/101176*e^4 - 10356299/50588*e^2 - 242117/25294, -8147/202352*e^10 - 98117/50588*e^8 - 5248379/202352*e^6 - 13080157/101176*e^4 - 10356299/50588*e^2 - 242117/25294, -967/101176*e^11 - 24647/50588*e^9 - 749893/101176*e^7 - 587353/12647*e^5 - 6096629/50588*e^3 - 2568041/25294*e, -967/101176*e^11 - 24647/50588*e^9 - 749893/101176*e^7 - 587353/12647*e^5 - 6096629/50588*e^3 - 2568041/25294*e, 28599/809408*e^11 + 172441/101176*e^9 + 18745223/809408*e^7 + 51207027/404704*e^5 + 56725467/202352*e^3 + 19753443/101176*e, 28599/809408*e^11 + 172441/101176*e^9 + 18745223/809408*e^7 + 51207027/404704*e^5 + 56725467/202352*e^3 + 19753443/101176*e, 1435/101176*e^10 + 33175/50588*e^8 + 810207/101176*e^6 + 901923/25294*e^4 + 1198123/25294*e^2 - 35656/12647, 1435/101176*e^10 + 33175/50588*e^8 + 810207/101176*e^6 + 901923/25294*e^4 + 1198123/25294*e^2 - 35656/12647, 25665/809408*e^11 + 159075/101176*e^9 + 18459521/809408*e^7 + 56474741/404704*e^5 + 75721537/202352*e^3 + 35983465/101176*e, 25665/809408*e^11 + 159075/101176*e^9 + 18459521/809408*e^7 + 56474741/404704*e^5 + 75721537/202352*e^3 + 35983465/101176*e, -32599/809408*e^11 - 201905/101176*e^9 - 23399431/809408*e^7 - 71540595/404704*e^5 - 95926963/202352*e^3 - 45484251/101176*e, -32599/809408*e^11 - 201905/101176*e^9 - 23399431/809408*e^7 - 71540595/404704*e^5 - 95926963/202352*e^3 - 45484251/101176*e, 281/25294*e^10 + 56421/101176*e^8 + 411195/50588*e^6 + 4593937/101176*e^4 + 2104443/25294*e^2 + 177597/25294, 281/25294*e^10 + 56421/101176*e^8 + 411195/50588*e^6 + 4593937/101176*e^4 + 2104443/25294*e^2 + 177597/25294, -25343/404704*e^11 - 313811/101176*e^9 - 18165191/404704*e^7 - 55447373/202352*e^5 - 74775551/101176*e^3 - 37165601/50588*e, -25343/404704*e^11 - 313811/101176*e^9 - 18165191/404704*e^7 - 55447373/202352*e^5 - 74775551/101176*e^3 - 37165601/50588*e, 6, 6, 41259/809408*e^11 + 246977/101176*e^9 + 26310507/809408*e^7 + 68493671/404704*e^5 + 67939915/202352*e^3 + 18485635/101176*e, 41259/809408*e^11 + 246977/101176*e^9 + 26310507/809408*e^7 + 68493671/404704*e^5 + 67939915/202352*e^3 + 18485635/101176*e, -9311/404704*e^10 - 56469/50588*e^8 - 6134511/404704*e^6 - 15593867/202352*e^4 - 12565923/101176*e^2 - 105867/50588, -9311/404704*e^10 - 56469/50588*e^8 - 6134511/404704*e^6 - 15593867/202352*e^4 - 12565923/101176*e^2 - 105867/50588, -1435/101176*e^10 - 33175/50588*e^8 - 810207/101176*e^6 - 901923/25294*e^4 - 1198123/25294*e^2 + 86244/12647, -1435/101176*e^10 - 33175/50588*e^8 - 810207/101176*e^6 - 901923/25294*e^4 - 1198123/25294*e^2 + 86244/12647, -7143/202352*e^10 - 86159/50588*e^8 - 4617215/202352*e^6 - 11433413/101176*e^4 - 8567399/50588*e^2 + 521827/25294, -7143/202352*e^10 - 86159/50588*e^8 - 4617215/202352*e^6 - 11433413/101176*e^4 - 8567399/50588*e^2 + 521827/25294, -24315/809408*e^11 - 152925/101176*e^9 - 18198955/809408*e^7 - 56385895/404704*e^5 - 75526295/202352*e^3 - 37405535/101176*e, -24315/809408*e^11 - 152925/101176*e^9 - 18198955/809408*e^7 - 56385895/404704*e^5 - 75526295/202352*e^3 - 37405535/101176*e, -22731/809408*e^11 - 145709/101176*e^9 - 18173819/809408*e^7 - 61742455/404704*e^5 - 94717607/202352*e^3 - 52213487/101176*e, -22731/809408*e^11 - 145709/101176*e^9 - 18173819/809408*e^7 - 61742455/404704*e^5 - 94717607/202352*e^3 - 52213487/101176*e, -15939/809408*e^11 - 97905/101176*e^9 - 11179939/809408*e^7 - 33920383/404704*e^5 - 45511019/202352*e^3 - 21021251/101176*e, -15939/809408*e^11 - 97905/101176*e^9 - 11179939/809408*e^7 - 33920383/404704*e^5 - 45511019/202352*e^3 - 21021251/101176*e, 7227/404704*e^10 + 22785/25294*e^8 + 5375835/404704*e^6 + 15373451/202352*e^4 + 15032103/101176*e^2 + 1693691/50588, 7227/404704*e^10 + 22785/25294*e^8 + 5375835/404704*e^6 + 15373451/202352*e^4 + 15032103/101176*e^2 + 1693691/50588, -14923/404704*e^11 - 179527/101176*e^9 - 9717715/404704*e^7 - 26572481/202352*e^5 - 30043187/101176*e^3 - 11767229/50588*e, -14923/404704*e^11 - 179527/101176*e^9 - 9717715/404704*e^7 - 26572481/202352*e^5 - 30043187/101176*e^3 - 11767229/50588*e, -24457/809408*e^11 - 147951/101176*e^9 - 16144985/809408*e^7 - 43629677/404704*e^5 - 46525133/202352*e^3 - 15714085/101176*e, -24457/809408*e^11 - 147951/101176*e^9 - 16144985/809408*e^7 - 43629677/404704*e^5 - 46525133/202352*e^3 - 15714085/101176*e, 10777/404704*e^11 + 133321/101176*e^9 + 7751041/404704*e^7 + 24455299/202352*e^5 + 35872525/101176*e^3 + 20403067/50588*e, 10777/404704*e^11 + 133321/101176*e^9 + 7751041/404704*e^7 + 24455299/202352*e^5 + 35872525/101176*e^3 + 20403067/50588*e, 843/25294*e^10 + 19577/12647*e^8 + 483999/25294*e^6 + 1107766/12647*e^4 + 1620054/12647*e^2 + 57720/12647, 843/25294*e^10 + 19577/12647*e^8 + 483999/25294*e^6 + 1107766/12647*e^4 + 1620054/12647*e^2 + 57720/12647, 71/202352*e^10 + 2699/101176*e^8 + 136539/202352*e^6 + 333135/50588*e^4 + 1333463/50588*e^2 + 287258/12647, 71/202352*e^10 + 2699/101176*e^8 + 136539/202352*e^6 + 333135/50588*e^4 + 1333463/50588*e^2 + 287258/12647, 1937/101176*e^10 + 45133/50588*e^8 + 1125789/101176*e^6 + 1313609/25294*e^4 + 2041985/25294*e^2 - 33094/12647, 1937/101176*e^10 + 45133/50588*e^8 + 1125789/101176*e^6 + 1313609/25294*e^4 + 2041985/25294*e^2 - 33094/12647, 7865/404704*e^10 + 22833/25294*e^8 + 4486617/404704*e^6 + 9809689/202352*e^4 + 6492861/101176*e^2 + 484649/50588, 7865/404704*e^10 + 22833/25294*e^8 + 4486617/404704*e^6 + 9809689/202352*e^4 + 6492861/101176*e^2 + 484649/50588, -251/50588*e^10 - 5979/25294*e^8 - 157791/50588*e^6 - 205843/12647*e^4 - 447225/12647*e^2 - 381972/12647, -251/50588*e^10 - 5979/25294*e^8 - 157791/50588*e^6 - 205843/12647*e^4 - 447225/12647*e^2 - 381972/12647, 30395/404704*e^11 + 376703/101176*e^9 + 21716003/404704*e^7 + 64163073/202352*e^5 + 78816219/101176*e^3 + 32311557/50588*e, 30395/404704*e^11 + 376703/101176*e^9 + 21716003/404704*e^7 + 64163073/202352*e^5 + 78816219/101176*e^3 + 32311557/50588*e, 1435/50588*e^10 + 33175/25294*e^8 + 810207/50588*e^6 + 901923/12647*e^4 + 1198123/12647*e^2 - 400134/12647, 1435/50588*e^10 + 33175/25294*e^8 + 810207/50588*e^6 + 901923/12647*e^4 + 1198123/12647*e^2 - 400134/12647, 84589/809408*e^11 + 506199/101176*e^9 + 53921133/809408*e^7 + 140776017/404704*e^5 + 140979997/202352*e^3 + 38990949/101176*e, 84589/809408*e^11 + 506199/101176*e^9 + 53921133/809408*e^7 + 140776017/404704*e^5 + 140979997/202352*e^3 + 38990949/101176*e, 16845/404704*e^11 + 199849/101176*e^9 + 10437029/404704*e^7 + 26531319/202352*e^5 + 25483517/101176*e^3 + 6819011/50588*e, 16845/404704*e^11 + 199849/101176*e^9 + 10437029/404704*e^7 + 26531319/202352*e^5 + 25483517/101176*e^3 + 6819011/50588*e, 7803/202352*e^11 + 24097/12647*e^9 + 5555135/202352*e^7 + 16916183/101176*e^5 + 11446487/25294*e^3 + 5766260/12647*e, 7803/202352*e^11 + 24097/12647*e^9 + 5555135/202352*e^7 + 16916183/101176*e^5 + 11446487/25294*e^3 + 5766260/12647*e, 5857/404704*e^10 + 8427/12647*e^8 + 3224289/404704*e^6 + 6516201/202352*e^4 + 2915061/101176*e^2 - 1043239/50588, 5857/404704*e^10 + 8427/12647*e^8 + 3224289/404704*e^6 + 6516201/202352*e^4 + 2915061/101176*e^2 - 1043239/50588, -30553/404704*e^11 - 380953/101176*e^9 - 22388929/404704*e^7 - 69884819/202352*e^5 - 97141733/101176*e^3 - 49864787/50588*e, -30553/404704*e^11 - 380953/101176*e^9 - 22388929/404704*e^7 - 69884819/202352*e^5 - 97141733/101176*e^3 - 49864787/50588*e, -33067/404704*e^10 - 395427/101176*e^8 - 20803875/404704*e^6 - 50405713/202352*e^4 - 37576299/101176*e^2 + 536247/50588, -33067/404704*e^10 - 395427/101176*e^8 - 20803875/404704*e^6 - 50405713/202352*e^4 - 37576299/101176*e^2 + 536247/50588, -933/101176*e^10 - 21217/50588*e^8 - 494625/101176*e^6 - 490237/25294*e^4 - 354261/25294*e^2 + 88806/12647, -933/101176*e^10 - 21217/50588*e^8 - 494625/101176*e^6 - 490237/25294*e^4 - 354261/25294*e^2 + 88806/12647, 11049/101176*e^10 + 256141/50588*e^8 + 6302613/101176*e^6 + 7136833/25294*e^4 + 10074585/25294*e^2 - 244468/12647, 11049/101176*e^10 + 256141/50588*e^8 + 6302613/101176*e^6 + 7136833/25294*e^4 + 10074585/25294*e^2 - 244468/12647, -56193/809408*e^11 - 348735/101176*e^9 - 40558833/809408*e^7 - 124226661/404704*e^5 - 166548333/202352*e^3 - 79448037/101176*e, -56193/809408*e^11 - 348735/101176*e^9 - 40558833/809408*e^7 - 124226661/404704*e^5 - 166548333/202352*e^3 - 79448037/101176*e, -15571/404704*e^10 - 185431/101176*e^8 - 9672811/404704*e^6 - 23268225/202352*e^4 - 17676067/101176*e^2 - 673625/50588, -15571/404704*e^10 - 185431/101176*e^8 - 9672811/404704*e^6 - 23268225/202352*e^4 - 17676067/101176*e^2 - 673625/50588, 9519/202352*e^11 + 60227/25294*e^9 + 7234907/202352*e^7 + 22394367/101176*e^5 + 7209536/12647*e^3 + 6104953/12647*e, 9519/202352*e^11 + 60227/25294*e^9 + 7234907/202352*e^7 + 22394367/101176*e^5 + 7209536/12647*e^3 + 6104953/12647*e, 15523/809408*e^11 + 90389/101176*e^9 + 8877971/809408*e^7 + 18397039/404704*e^5 + 6718959/202352*e^3 - 6652105/101176*e, 15523/809408*e^11 + 90389/101176*e^9 + 8877971/809408*e^7 + 18397039/404704*e^5 + 6718959/202352*e^3 - 6652105/101176*e, 4721/809408*e^11 + 35559/101176*e^9 + 5693761/809408*e^7 + 24033397/404704*e^5 + 44106421/202352*e^3 + 29172557/101176*e, 4721/809408*e^11 + 35559/101176*e^9 + 5693761/809408*e^7 + 24033397/404704*e^5 + 44106421/202352*e^3 + 29172557/101176*e, -12555/202352*e^10 - 292015/101176*e^8 - 7249359/202352*e^6 - 8371891/50588*e^4 - 12606171/50588*e^2 - 197784/12647, -12555/202352*e^10 - 292015/101176*e^8 - 7249359/202352*e^6 - 8371891/50588*e^4 - 12606171/50588*e^2 - 197784/12647, 4941/50588*e^11 + 243307/50588*e^9 + 1732177/25294*e^7 + 20344767/50588*e^5 + 50612909/50588*e^3 + 21945461/25294*e, 4941/50588*e^11 + 243307/50588*e^9 + 1732177/25294*e^7 + 20344767/50588*e^5 + 50612909/50588*e^3 + 21945461/25294*e, -7839/404704*e^11 - 109363/101176*e^9 - 7896551/404704*e^7 - 31136141/202352*e^5 - 54861871/101176*e^3 - 34081297/50588*e, -7839/404704*e^11 - 109363/101176*e^9 - 7896551/404704*e^7 - 31136141/202352*e^5 - 54861871/101176*e^3 - 34081297/50588*e, 1525/202352*e^10 + 34815/101176*e^8 + 820833/202352*e^6 + 212731/12647*e^4 + 1172355/50588*e^2 + 183494/12647, 1525/202352*e^10 + 34815/101176*e^8 + 820833/202352*e^6 + 212731/12647*e^4 + 1172355/50588*e^2 + 183494/12647, -2619/50588*e^10 - 60371/25294*e^8 - 1462623/50588*e^6 - 1598003/12647*e^4 - 1974315/12647*e^2 + 524596/12647, -2619/50588*e^10 - 60371/25294*e^8 - 1462623/50588*e^6 - 1598003/12647*e^4 - 1974315/12647*e^2 + 524596/12647, 17381/809408*e^11 + 110095/101176*e^9 + 13259045/809408*e^7 + 41320041/404704*e^5 + 55320869/202352*e^3 + 27904749/101176*e, 17381/809408*e^11 + 110095/101176*e^9 + 13259045/809408*e^7 + 41320041/404704*e^5 + 55320869/202352*e^3 + 27904749/101176*e, 24315/809408*e^11 + 152925/101176*e^9 + 18198955/809408*e^7 + 56385895/404704*e^5 + 75526295/202352*e^3 + 37405535/101176*e, 24315/809408*e^11 + 152925/101176*e^9 + 18198955/809408*e^7 + 56385895/404704*e^5 + 75526295/202352*e^3 + 37405535/101176*e, 5101/101176*e^11 + 133703/50588*e^9 + 4313731/101176*e^7 + 7413563/25294*e^5 + 44580905/50588*e^3 + 23507717/25294*e, 5101/101176*e^11 + 133703/50588*e^9 + 4313731/101176*e^7 + 7413563/25294*e^5 + 44580905/50588*e^3 + 23507717/25294*e, -4125/50588*e^10 - 96245/25294*e^8 - 2409369/50588*e^6 - 2833061/12647*e^4 - 4505901/12647*e^2 - 502536/12647, -4125/50588*e^10 - 96245/25294*e^8 - 2409369/50588*e^6 - 2833061/12647*e^4 - 4505901/12647*e^2 - 502536/12647, 11127/404704*e^11 + 156183/101176*e^9 + 11400975/404704*e^7 + 45614749/202352*e^5 + 81787723/101176*e^3 + 51728701/50588*e, 11127/404704*e^11 + 156183/101176*e^9 + 11400975/404704*e^7 + 45614749/202352*e^5 + 81787723/101176*e^3 + 51728701/50588*e, -48051/809408*e^11 - 294781/101176*e^9 - 33304387/809408*e^7 - 96315743/404704*e^5 - 117146503/202352*e^3 - 49677871/101176*e, -48051/809408*e^11 - 294781/101176*e^9 - 33304387/809408*e^7 - 96315743/404704*e^5 - 117146503/202352*e^3 - 49677871/101176*e, 7485/202352*e^10 + 89275/50588*e^8 + 4677829/202352*e^6 + 11389819/101176*e^4 + 9041125/50588*e^2 + 760339/25294, 7485/202352*e^10 + 89275/50588*e^8 + 4677829/202352*e^6 + 11389819/101176*e^4 + 9041125/50588*e^2 + 760339/25294, 10109/404704*e^10 + 115993/101176*e^8 + 5500261/404704*e^6 + 10897071/202352*e^4 + 4447405/101176*e^2 - 2003369/50588, 10109/404704*e^10 + 115993/101176*e^8 + 5500261/404704*e^6 + 10897071/202352*e^4 + 4447405/101176*e^2 - 2003369/50588, -19721/404704*e^11 - 254157/101176*e^9 - 15862369/404704*e^7 - 52048619/202352*e^5 - 73419049/101176*e^3 - 35717623/50588*e, -19721/404704*e^11 - 254157/101176*e^9 - 15862369/404704*e^7 - 52048619/202352*e^5 - 73419049/101176*e^3 - 35717623/50588*e, -5309/50588*e^10 - 123441/25294*e^8 - 3061785/50588*e^6 - 3529141/12647*e^4 - 5282093/12647*e^2 - 175722/12647, -5309/50588*e^10 - 123441/25294*e^8 - 3061785/50588*e^6 - 3529141/12647*e^4 - 5282093/12647*e^2 - 175722/12647, -4949/202352*e^10 - 116881/101176*e^8 - 3019281/202352*e^6 - 3783725/50588*e^4 - 7105157/50588*e^2 - 231432/12647, -18447/809408*e^11 - 126193/101176*e^9 - 17627551/809408*e^7 - 66921323/404704*e^5 - 113518435/202352*e^3 - 69865579/101176*e, -18447/809408*e^11 - 126193/101176*e^9 - 17627551/809408*e^7 - 66921323/404704*e^5 - 113518435/202352*e^3 - 69865579/101176*e, -21523/809408*e^11 - 134585/101176*e^9 - 15859283/809408*e^7 - 48897391/404704*e^5 - 65521203/202352*e^3 - 31944107/101176*e, -21523/809408*e^11 - 134585/101176*e^9 - 15859283/809408*e^7 - 48897391/404704*e^5 - 65521203/202352*e^3 - 31944107/101176*e, -22357/404704*e^11 - 272553/101176*e^9 - 15188813/404704*e^7 - 43168271/202352*e^5 - 51139701/101176*e^3 - 20778795/50588*e, -22357/404704*e^11 - 272553/101176*e^9 - 15188813/404704*e^7 - 43168271/202352*e^5 - 51139701/101176*e^3 - 20778795/50588*e, -95381/809408*e^11 - 583467/101176*e^9 - 65569221/809408*e^7 - 188931657/404704*e^5 - 229388081/202352*e^3 - 95913993/101176*e, -95381/809408*e^11 - 583467/101176*e^9 - 65569221/809408*e^7 - 188931657/404704*e^5 - 229388081/202352*e^3 - 95913993/101176*e, -12053/101176*e^10 - 280057/50588*e^8 - 6933777/101176*e^6 - 7960205/25294*e^4 - 11762309/25294*e^2 - 13596/12647, -12053/101176*e^10 - 280057/50588*e^8 - 6933777/101176*e^6 - 7960205/25294*e^4 - 11762309/25294*e^2 - 13596/12647, 485/25294*e^11 + 53619/50588*e^9 + 945011/50588*e^7 + 7068817/50588*e^5 + 22849557/50588*e^3 + 12652341/25294*e, 485/25294*e^11 + 53619/50588*e^9 + 945011/50588*e^7 + 7068817/50588*e^5 + 22849557/50588*e^3 + 12652341/25294*e, -10553/101176*e^11 - 261155/50588*e^9 - 7540791/101176*e^7 - 11432333/25294*e^5 - 60785833/50588*e^3 - 29508565/25294*e, -10553/101176*e^11 - 261155/50588*e^9 - 7540791/101176*e^7 - 11432333/25294*e^5 - 60785833/50588*e^3 - 29508565/25294*e, 1103/101176*e^10 + 6430/12647*e^8 + 632735/101176*e^6 + 1311959/50588*e^4 + 488267/25294*e^2 - 465081/12647, 1103/101176*e^10 + 6430/12647*e^8 + 632735/101176*e^6 + 1311959/50588*e^4 + 488267/25294*e^2 - 465081/12647, 30921/202352*e^10 + 719429/101176*e^8 + 17876085/202352*e^6 + 20684609/50588*e^4 + 31338297/50588*e^2 + 510338/12647, 30921/202352*e^10 + 719429/101176*e^8 + 17876085/202352*e^6 + 20684609/50588*e^4 + 31338297/50588*e^2 + 510338/12647, 52701/809408*e^11 + 332827/101176*e^9 + 40025133/809408*e^7 + 126727249/404704*e^5 + 175753505/202352*e^3 + 89696153/101176*e, 52701/809408*e^11 + 332827/101176*e^9 + 40025133/809408*e^7 + 126727249/404704*e^5 + 175753505/202352*e^3 + 89696153/101176*e, -1063/12647*e^11 - 206955/50588*e^9 - 2870381/50588*e^7 - 16185529/50588*e^5 - 37784817/50588*e^3 - 14965569/25294*e, -1063/12647*e^11 - 206955/50588*e^9 - 2870381/50588*e^7 - 16185529/50588*e^5 - 37784817/50588*e^3 - 14965569/25294*e, 59269/809408*e^11 + 357127/101176*e^9 + 38790565/809408*e^7 + 106202729/404704*e^5 + 118551101/202352*e^3 + 41526565/101176*e, 59269/809408*e^11 + 357127/101176*e^9 + 38790565/809408*e^7 + 106202729/404704*e^5 + 118551101/202352*e^3 + 41526565/101176*e, 2941/202352*e^10 + 69049/101176*e^8 + 1756953/202352*e^6 + 2136981/50588*e^4 + 3729709/50588*e^2 + 782776/12647, 5821/404704*e^11 + 54441/101176*e^9 + 933461/404704*e^7 - 6742585/202352*e^5 - 25828851/101176*e^3 - 21100557/50588*e, 5821/404704*e^11 + 54441/101176*e^9 + 933461/404704*e^7 - 6742585/202352*e^5 - 25828851/101176*e^3 - 21100557/50588*e, -20599/809408*e^11 - 113513/101176*e^9 - 9436807/809408*e^7 - 10539891/404704*e^5 + 21677525/202352*e^3 + 31708173/101176*e, -20599/809408*e^11 - 113513/101176*e^9 - 9436807/809408*e^7 - 10539891/404704*e^5 + 21677525/202352*e^3 + 31708173/101176*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([5, 5, -2*w + 15])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]