/*
  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.<x> = PolynomialRing(QQ)
g = P([29, 11, -10, -2, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([11, 11, -w - 1])

primes_array = [
[11, 11, -w - 1],\
[11, 11, w^2 - 5],\
[11, 11, -w^2 + 2*w + 4],\
[11, 11, w - 2],\
[16, 2, 2],\
[19, 19, w^2 - 2*w - 5],\
[19, 19, -w^2 + 6],\
[25, 5, -2*w^2 + 2*w + 11],\
[29, 29, w],\
[29, 29, 2*w^2 - w - 10],\
[29, 29, -2*w^2 + 3*w + 9],\
[29, 29, w - 1],\
[31, 31, w^3 - 6*w - 6],\
[31, 31, -w^3 + 3*w^2 + 3*w - 11],\
[41, 41, w^3 - 4*w^2 - 2*w + 16],\
[41, 41, w^3 - 5*w^2 - 2*w + 24],\
[59, 59, w^3 - w^2 - 5*w - 2],\
[59, 59, 2*w^2 - w - 13],\
[61, 61, w^3 - w^2 - 6*w + 3],\
[61, 61, -w^3 + 2*w^2 + 5*w - 3],\
[71, 71, 2*w^2 - w - 16],\
[71, 71, -w^3 + 3*w^2 + 4*w - 10],\
[71, 71, -w^3 + 7*w + 4],\
[71, 71, w^3 - 5*w^2 - 2*w + 23],\
[79, 79, -w^3 + 4*w^2 + 3*w - 16],\
[79, 79, w^3 + w^2 - 8*w - 10],\
[81, 3, -3],\
[131, 131, 4*w^2 - 5*w - 24],\
[131, 131, 4*w^2 - 3*w - 25],\
[139, 139, w^2 + w - 9],\
[139, 139, -w^3 + w^2 + 6*w - 5],\
[149, 149, w^3 - w^2 - 4*w + 2],\
[149, 149, w^3 - 2*w^2 - 3*w + 2],\
[151, 151, -w^3 + 7*w + 3],\
[151, 151, -w^3 + 3*w^2 + 4*w - 9],\
[179, 179, -w^3 - 2*w^2 + 10*w + 16],\
[179, 179, -w^3 + 3*w^2 + 3*w - 6],\
[179, 179, w^3 - 6*w - 1],\
[179, 179, w^3 - 5*w^2 - 3*w + 23],\
[191, 191, w^3 - 6*w^2 - w + 27],\
[191, 191, w^3 + 3*w^2 - 10*w - 21],\
[199, 199, -w^3 + 2*w^2 + 6*w - 4],\
[199, 199, -4*w^2 + 3*w + 22],\
[199, 199, 4*w^2 - 5*w - 21],\
[199, 199, 3*w^2 - 4*w - 12],\
[239, 239, -w^3 + w^2 + 4*w - 6],\
[239, 239, 2*w^3 - 5*w^2 - 9*w + 17],\
[239, 239, 2*w^3 - w^2 - 13*w - 5],\
[239, 239, w^3 - 8*w^2 + 2*w + 41],\
[241, 241, -w^3 + 5*w^2 + 4*w - 25],\
[241, 241, w^3 - 6*w - 8],\
[241, 241, -w^3 + 3*w^2 + 3*w - 13],\
[241, 241, w^3 - 5*w^2 + w + 19],\
[269, 269, w^2 - 2*w - 10],\
[269, 269, w^2 - 11],\
[271, 271, w^3 + 2*w^2 - 8*w - 18],\
[271, 271, 2*w^3 - 13*w - 10],\
[271, 271, 2*w^3 + w^2 - 15*w - 16],\
[271, 271, w^3 - 5*w^2 - w + 23],\
[289, 17, 2*w^2 - 11],\
[289, 17, -2*w^2 + 4*w + 9],\
[311, 311, w^3 - 4*w^2 - 3*w + 10],\
[311, 311, w^3 - 7*w^2 - w + 34],\
[331, 331, w^3 - w^2 - 7*w + 4],\
[331, 331, w^3 - 2*w^2 - 6*w + 3],\
[349, 349, w^3 + w^2 - 6*w - 12],\
[349, 349, -w^3 + 4*w^2 + w - 16],\
[361, 19, 4*w^2 - 4*w - 21],\
[379, 379, w^3 - 3*w^2 - 3*w + 15],\
[379, 379, 2*w^3 - 2*w^2 - 12*w + 1],\
[379, 379, -2*w^3 + 4*w^2 + 10*w - 11],\
[379, 379, w^3 - 6*w - 10],\
[401, 401, -2*w^3 + 7*w^2 + 8*w - 30],\
[401, 401, -w^3 + 2*w^2 + 6*w - 2],\
[419, 419, 5*w^2 - 4*w - 26],\
[419, 419, 5*w^2 - 6*w - 25],\
[421, 421, 3*w^2 - w - 20],\
[421, 421, -2*w^3 + 2*w^2 + 10*w + 3],\
[431, 431, w^2 - 3*w - 5],\
[431, 431, w^2 + w - 7],\
[449, 449, 2*w^3 - 13*w - 7],\
[449, 449, -2*w^3 + 6*w^2 + 7*w - 18],\
[461, 461, w^3 - w^2 - 8*w + 3],\
[461, 461, -w^3 + 2*w^2 + 7*w - 5],\
[491, 491, w^3 - 3*w^2 - 6*w + 15],\
[491, 491, w^3 - 9*w - 7],\
[499, 499, 4*w^2 - 6*w - 23],\
[499, 499, -4*w^2 + 2*w + 25],\
[509, 509, 2*w^3 - 3*w^2 - 11*w + 6],\
[521, 521, -w^3 + 3*w^2 + 2*w - 12],\
[521, 521, -w^3 + 4*w^2 + 2*w - 19],\
[529, 23, w^3 - 7*w^2 - w + 35],\
[529, 23, -w^3 + 3*w^2 + 4*w - 5],\
[541, 541, 2*w^3 - w^2 - 12*w - 5],\
[541, 541, w^3 - 2*w^2 - 7*w + 9],\
[569, 569, w^3 - 8*w - 2],\
[569, 569, -w^3 + 3*w^2 + 5*w - 9],\
[599, 599, -w^3 - 4*w^2 + 10*w + 25],\
[599, 599, -w^3 + 7*w^2 - 36],\
[601, 601, 5*w^2 - 6*w - 26],\
[601, 601, -2*w^3 + 8*w^2 + 6*w - 33],\
[601, 601, -2*w^3 - 2*w^2 + 16*w + 21],\
[601, 601, 5*w^2 - 4*w - 27],\
[619, 619, w^3 + 4*w^2 - 11*w - 26],\
[619, 619, w^3 - 3*w^2 - 5*w + 18],\
[641, 641, -w^3 + 3*w^2 + 6*w - 14],\
[641, 641, -w^3 + 9*w + 6],\
[659, 659, -w^3 - 4*w^2 + 10*w + 28],\
[659, 659, -w^3 + 6*w^2 - w - 27],\
[659, 659, -w^3 - 3*w^2 + 8*w + 23],\
[659, 659, -w^3 + 7*w^2 - w - 33],\
[691, 691, w^3 - w^2 - 8*w + 2],\
[691, 691, 2*w^3 - 2*w^2 - 11*w + 1],\
[701, 701, -w^3 - w^2 + 7*w + 15],\
[701, 701, -w^3 + 4*w^2 + 2*w - 20],\
[709, 709, -2*w^3 - w^2 + 15*w + 15],\
[709, 709, 2*w^3 - 7*w^2 - 7*w + 27],\
[719, 719, -w^3 - 4*w^2 + 13*w + 26],\
[719, 719, w^3 - 7*w^2 - 2*w + 34],\
[739, 739, 2*w^3 + 2*w^2 - 15*w - 24],\
[739, 739, -2*w^3 + 8*w^2 + 5*w - 35],\
[751, 751, -w^3 - 3*w^2 + 9*w + 25],\
[751, 751, -w^3 + 6*w^2 - 30],\
[761, 761, 3*w^3 - 2*w^2 - 16*w - 8],\
[761, 761, -3*w^3 + 7*w^2 + 11*w - 23],\
[769, 769, -2*w^3 + 4*w^2 + 11*w - 10],\
[769, 769, w^3 + 2*w^2 - 9*w - 12],\
[809, 809, -3*w^3 + 3*w^2 + 16*w + 4],\
[809, 809, w^3 + 5*w^2 - 12*w - 30],\
[811, 811, -w^3 - 4*w^2 + 10*w + 27],\
[811, 811, -2*w^3 + 5*w^2 + 9*w - 14],\
[811, 811, -2*w^3 + w^2 + 13*w + 2],\
[811, 811, -w^3 + 7*w^2 - w - 32],\
[821, 821, 2*w^3 - 8*w^2 - 7*w + 35],\
[821, 821, -2*w^3 - 2*w^2 + 17*w + 22],\
[829, 829, -3*w^3 + 20*w + 13],\
[829, 829, -w^3 + 7*w^2 - w - 36],\
[829, 829, w^3 + 4*w^2 - 10*w - 31],\
[829, 829, 2*w^3 - 3*w^2 - 11*w + 14],\
[859, 859, -w^3 + 7*w^2 - 3*w - 31],\
[859, 859, 7*w^2 - 9*w - 39],\
[859, 859, 7*w^2 - 5*w - 41],\
[859, 859, 3*w^3 - 4*w^2 - 17*w + 2],\
[929, 929, w^3 + 5*w^2 - 14*w - 31],\
[929, 929, -2*w^3 + 4*w^2 + 10*w - 5],\
[929, 929, w^3 - 9*w^2 + 4*w + 44],\
[929, 929, -w^3 + 8*w^2 + w - 39],\
[941, 941, -w^3 + 7*w^2 - 34],\
[941, 941, w^3 + 4*w^2 - 11*w - 28],\
[961, 31, -5*w^2 + 5*w + 28],\
[971, 971, -3*w^3 + w^2 + 19*w + 14],\
[971, 971, -3*w^3 + 8*w^2 + 12*w - 31],\
[991, 991, -w^3 - 5*w^2 + 11*w + 35],\
[991, 991, w^3 - 8*w^2 + 2*w + 40]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^7 - 12*x^6 + 36*x^5 + 41*x^4 - 332*x^3 + 459*x^2 - 201*x + 27
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [-1, e, 1775/6621*e^6 - 6549/2207*e^5 + 15507/2207*e^4 + 107881/6621*e^3 - 481963/6621*e^2 + 143671/2207*e - 21540/2207, -687/2207*e^6 + 8068/2207*e^5 - 22437/2207*e^4 - 35698/2207*e^3 + 219231/2207*e^2 - 242843/2207*e + 56692/2207, -1879/6621*e^6 + 7302/2207*e^5 - 20234/2207*e^4 - 93149/6621*e^3 + 591008/6621*e^2 - 234106/2207*e + 57797/2207, 722/6621*e^6 - 3063/2207*e^5 + 9855/2207*e^4 + 35239/6621*e^3 - 285787/6621*e^2 + 105575/2207*e - 9489/2207, 776/6621*e^6 - 3072/2207*e^5 + 9296/2207*e^4 + 28099/6621*e^3 - 260026/6621*e^2 + 125411/2207*e - 34384/2207, 3079/6621*e^6 - 11916/2207*e^5 + 32334/2207*e^4 + 162539/6621*e^3 - 952838/6621*e^2 + 350477/2207*e - 87715/2207, -2359/6621*e^6 + 9589/2207*e^5 - 29488/2207*e^4 - 101042/6621*e^3 + 841676/6621*e^2 - 361872/2207*e + 97131/2207, 3497/6621*e^6 - 13457/2207*e^5 + 36181/2207*e^4 + 183289/6621*e^3 - 1067068/6621*e^2 + 401029/2207*e - 103779/2207, -739/6621*e^6 + 2698/2207*e^5 - 6532/2207*e^4 - 37160/6621*e^3 + 190991/6621*e^2 - 80186/2207*e + 34451/2207, 1147/6621*e^6 - 4973/2207*e^5 + 17267/2207*e^4 + 36917/6621*e^3 - 471593/6621*e^2 + 227851/2207*e - 66340/2207, 327/2207*e^6 - 3474/2207*e^5 + 7133/2207*e^4 + 21502/2207*e^3 - 75370/2207*e^2 + 60202/2207*e - 20055/2207, 436/6621*e^6 - 1544/2207*e^5 + 2925/2207*e^4 + 36026/6621*e^3 - 110057/6621*e^2 + 4196/2207*e + 25663/2207, 1103/6621*e^6 - 4230/2207*e^5 + 10938/2207*e^4 + 65050/6621*e^3 - 330982/6621*e^2 + 108695/2207*e - 14585/2207, -1014/2207*e^6 + 11542/2207*e^5 - 29570/2207*e^4 - 57200/2207*e^3 + 294601/2207*e^2 - 305252/2207*e + 74540/2207, -6686/6621*e^6 + 26127/2207*e^5 - 72199/2207*e^4 - 351637/6621*e^3 + 2116525/6621*e^2 - 773521/2207*e + 185151/2207, 10544/6621*e^6 - 40012/2207*e^5 + 103376/2207*e^4 + 582340/6621*e^3 - 3098062/6621*e^2 + 1084986/2207*e - 250638/2207, 3644/6621*e^6 - 14585/2207*e^5 + 42629/2207*e^4 + 180037/6621*e^3 - 1239343/6621*e^2 + 477097/2207*e - 97369/2207, 1627/6621*e^6 - 7260/2207*e^5 + 26521/2207*e^4 + 44810/6621*e^3 - 722261/6621*e^2 + 353410/2207*e - 92432/2207, -1454/6621*e^6 + 5392/2207*e^5 - 12822/2207*e^4 - 91471/6621*e^3 + 405202/6621*e^2 - 114037/2207*e + 14188/2207, 1034/6621*e^6 - 3115/2207*e^5 + 1966/2207*e^4 + 96979/6621*e^3 - 116347/6621*e^2 - 53485/2207*e + 42851/2207, -10666/6621*e^6 + 40768/2207*e^5 - 107181/2207*e^4 - 582884/6621*e^3 + 3196313/6621*e^2 - 1126858/2207*e + 256203/2207, 4099/6621*e^6 - 16500/2207*e^5 + 49240/2207*e^4 + 191726/6621*e^3 - 1422608/6621*e^2 + 575081/2207*e - 124401/2207, -436/6621*e^6 + 1544/2207*e^5 - 2925/2207*e^4 - 36026/6621*e^3 + 110057/6621*e^2 - 8610/2207*e - 3593/2207, 1867/6621*e^6 - 7300/2207*e^5 + 20113/2207*e^4 + 98414/6621*e^3 - 582755/6621*e^2 + 216456/2207*e - 70166/2207, -2158/2207*e^6 + 25356/2207*e^5 - 70797/2207*e^4 - 111434/2207*e^3 + 692955/2207*e^2 - 767006/2207*e + 167521/2207, -2728/6621*e^6 + 10754/2207*e^5 - 30450/2207*e^4 - 136118/6621*e^3 + 871997/6621*e^2 - 342928/2207*e + 107975/2207, -3956/2207*e^6 + 46118/2207*e^5 - 126290/2207*e^4 - 208672/2207*e^3 + 1244256/2207*e^2 - 1362406/2207*e + 313854/2207, 3594/2207*e^6 - 41523/2207*e^5 + 112029/2207*e^4 + 187629/2207*e^3 - 1104537/2207*e^2 + 1237150/2207*e - 293333/2207, -4510/6621*e^6 + 17672/2207*e^5 - 49522/2207*e^4 - 231548/6621*e^3 + 1465262/6621*e^2 - 547288/2207*e + 121748/2207, -751/2207*e^6 + 8100/2207*e^5 - 17752/2207*e^4 - 47344/2207*e^3 + 188209/2207*e^2 - 161088/2207*e + 19899/2207, -2606/6621*e^6 + 9998/2207*e^5 - 26645/2207*e^4 - 135574/6621*e^3 + 780367/6621*e^2 - 309884/2207*e + 82547/2207, -422/6621*e^6 + 3013/2207*e^5 - 17865/2207*e^4 + 31766/6621*e^3 + 456859/6621*e^2 - 280078/2207*e + 60495/2207, 6092/6621*e^6 - 23821/2207*e^5 + 67313/2207*e^4 + 291136/6621*e^3 - 1956289/6621*e^2 + 791474/2207*e - 191595/2207, -2487/2207*e^6 + 28831/2207*e^5 - 76887/2207*e^4 - 139783/2207*e^3 + 766390/2207*e^2 - 778651/2207*e + 160425/2207, -6641/6621*e^6 + 25016/2207*e^5 - 63469/2207*e^4 - 373036/6621*e^3 + 1925017/6621*e^2 - 657676/2207*e + 122840/2207, 6802/6621*e^6 - 26882/2207*e^5 + 77047/2207*e^4 + 331640/6621*e^3 - 2233823/6621*e^2 + 890434/2207*e - 222281/2207, 9752/6621*e^6 - 37673/2207*e^5 + 102011/2207*e^4 + 512707/6621*e^3 - 3010213/6621*e^2 + 1107452/2207*e - 274679/2207, 67/6621*e^6 - 379/2207*e^5 + 1963/2207*e^4 - 5671/6621*e^3 - 33389/6621*e^2 + 34175/2207*e - 23082/2207, 6653/6621*e^6 - 25018/2207*e^5 + 63590/2207*e^4 + 361150/6621*e^3 - 1886923/6621*e^2 + 688568/2207*e - 198751/2207, -2654/2207*e^6 + 32225/2207*e^5 - 96836/2207*e^4 - 125549/2207*e^3 + 932557/2207*e^2 - 1112761/2207*e + 247082/2207, -362/2207*e^6 + 4595/2207*e^5 - 14261/2207*e^4 - 21043/2207*e^3 + 139719/2207*e^2 - 136291/2207*e + 47005/2207, -2128/6621*e^6 + 8447/2207*e^5 - 24400/2207*e^4 - 101423/6621*e^3 + 697703/6621*e^2 - 283639/2207*e + 70946/2207, -15119/6621*e^6 + 57327/2207*e^5 - 147852/2207*e^4 - 834475/6621*e^3 + 4435330/6621*e^2 - 1567135/2207*e + 367735/2207, -2667/2207*e^6 + 31128/2207*e^5 - 86746/2207*e^4 - 131432/2207*e^3 + 848252/2207*e^2 - 1005702/2207*e + 232815/2207, -1639/2207*e^6 + 17372/2207*e^5 - 35786/2207*e^4 - 107962/2207*e^3 + 390636/2207*e^2 - 292176/2207*e + 10661/2207, -5213/6621*e^6 + 20364/2207*e^5 - 57898/2207*e^4 - 238156/6621*e^3 + 1671220/6621*e^2 - 720186/2207*e + 217583/2207, -6956/6621*e^6 + 26172/2207*e^5 - 64990/2207*e^4 - 415252/6621*e^3 + 1987720/6621*e^2 - 627724/2207*e + 124238/2207, -7553/6621*e^6 + 27375/2207*e^5 - 61630/2207*e^4 - 469471/6621*e^3 + 1936492/6621*e^2 - 557905/2207*e + 107529/2207, 53/6621*e^6 + 359/2207*e^5 - 5167/2207*e^4 + 32473/6621*e^3 + 116384/6621*e^2 - 118101/2207*e + 16559/2207, -4369/2207*e^6 + 51842/2207*e^5 - 148163/2207*e^4 - 217822/2207*e^3 + 1435051/2207*e^2 - 1658628/2207*e + 397922/2207, -9472/6621*e^6 + 36155/2207*e^5 - 94038/2207*e^4 - 534035/6621*e^3 + 2828678/6621*e^2 - 968551/2207*e + 207962/2207, 6097/6621*e^6 - 23454/2207*e^5 + 61662/2207*e^4 + 351290/6621*e^3 - 1853240/6621*e^2 + 591738/2207*e - 120783/2207, 9425/6621*e^6 - 36515/2207*e^5 + 100369/2207*e^4 + 475756/6621*e^3 - 2939257/6621*e^2 + 1119754/2207*e - 272408/2207, 10444/6621*e^6 - 40731/2207*e^5 + 112667/2207*e^4 + 537935/6621*e^3 - 3298541/6621*e^2 + 1250561/2207*e - 313987/2207, -1052/6621*e^6 + 5325/2207*e^5 - 23114/2207*e^4 - 6319/6621*e^3 + 602128/6621*e^2 - 332731/2207*e + 140536/2207, 4516/6621*e^6 - 17673/2207*e^5 + 48479/2207*e^4 + 252089/6621*e^3 - 1446215/6621*e^2 + 476661/2207*e - 85769/2207, -43/2207*e^6 + 1125/2207*e^5 - 7370/2207*e^4 + 3969/2207*e^3 + 67644/2207*e^2 - 89319/2207*e - 17651/2207, 2909/2207*e^6 - 33456/2207*e^5 + 88549/2207*e^4 + 158778/2207*e^3 - 883371/2207*e^2 + 932508/2207*e - 191834/2207, 5177/6621*e^6 - 20358/2207*e^5 + 57535/2207*e^4 + 260572/6621*e^3 - 1686187/6621*e^2 + 649580/2207*e - 148754/2207, 1154/6621*e^6 - 5342/2207*e^5 + 20832/2207*e^4 + 24466/6621*e^3 - 569653/6621*e^2 + 266470/2207*e - 62987/2207, 2396/2207*e^6 - 27682/2207*e^5 + 74686/2207*e^4 + 125086/2207*e^3 - 736358/2207*e^2 + 817410/2207*e - 145530/2207, -9712/6621*e^6 + 38402/2207*e^5 - 109700/2207*e^4 - 488324/6621*e^3 + 3205610/6621*e^2 - 1208994/2207*e + 273976/2207, 7565/6621*e^6 - 31791/2207*e^5 + 103684/2207*e^4 + 298681/6621*e^3 - 2898169/6621*e^2 + 1281795/2207*e - 351172/2207, 19987/6621*e^6 - 76530/2207*e^5 + 202823/2207*e^4 + 1066751/6621*e^3 - 6000041/6621*e^2 + 2191489/2207*e - 527666/2207, 1520/6621*e^6 - 5403/2207*e^5 + 10177/2207*e^4 + 125413/6621*e^3 - 354589/6621*e^2 + 23517/2207*e + 6391/2207, -4840/6621*e^6 + 17727/2207*e^5 - 40711/2207*e^4 - 301943/6621*e^3 + 1251923/6621*e^2 - 357321/2207*e + 85063/2207, -7835/6621*e^6 + 29629/2207*e^5 - 76612/2207*e^4 - 421885/6621*e^3 + 2312515/6621*e^2 - 846881/2207*e + 160046/2207, 4464/2207*e^6 - 50786/2207*e^5 + 130622/2207*e^4 + 248420/2207*e^3 - 1304516/2207*e^2 + 1363851/2207*e - 281270/2207, 4211/2207*e^6 - 47349/2207*e^5 + 118003/2207*e^4 + 241901/2207*e^3 - 1192863/2207*e^2 + 1190981/2207*e - 289504/2207, 2234/2207*e^6 - 25394/2207*e^5 + 66475/2207*e^4 + 115608/2207*e^3 - 656944/2207*e^2 + 766892/2207*e - 226041/2207, 2132/2207*e^6 - 25343/2207*e^5 + 73321/2207*e^4 + 101875/2207*e^3 - 707075/2207*e^2 + 842083/2207*e - 191641/2207, 4920/2207*e^6 - 57635/2207*e^5 + 159865/2207*e^4 + 253601/2207*e^3 - 1562955/2207*e^2 + 1764841/2207*e - 418311/2207, 464/6621*e^6 - 813/2207*e^5 - 4885/2207*e^4 + 72295/6621*e^3 + 53867/6621*e^2 - 121617/2207*e + 87629/2207, 12470/6621*e^6 - 46954/2207*e^5 + 117279/2207*e^4 + 733768/6621*e^3 - 3571870/6621*e^2 + 1152440/2207*e - 217505/2207, 3544/6621*e^6 - 13097/2207*e^5 + 32057/2207*e^4 + 195221/6621*e^3 - 976352/6621*e^2 + 357969/2207*e - 98922/2207, 4077/2207*e^6 - 47282/2207*e^5 + 128295/2207*e^4 + 213517/2207*e^3 - 1262919/2207*e^2 + 1414089/2207*e - 301088/2207, -8299/6621*e^6 + 32649/2207*e^5 - 91590/2207*e^4 - 434591/6621*e^3 + 2689013/6621*e^2 - 974655/2207*e + 229114/2207, 3721/6621*e^6 - 16437/2207*e^5 + 59774/2207*e^4 + 89423/6621*e^3 - 1596314/6621*e^2 + 829075/2207*e - 265737/2207, -588/2207*e^6 + 6915/2207*e^5 - 19994/2207*e^4 - 24511/2207*e^3 + 181490/2207*e^2 - 244095/2207*e + 130538/2207, -228/2207*e^6 + 4528/2207*e^5 - 26760/2207*e^4 + 22790/2207*e^3 + 211982/2207*e^2 - 458714/2207*e + 184388/2207, -15812/6621*e^6 + 60753/2207*e^5 - 163116/2207*e^4 - 826711/6621*e^3 + 4834144/6621*e^2 - 1810662/2207*e + 402150/2207, -71/6621*e^6 - 2563/2207*e^5 + 25952/2207*e^4 - 100717/6621*e^3 - 617132/6621*e^2 + 427090/2207*e - 86977/2207, -1564/2207*e^6 + 20645/2207*e^5 - 73795/2207*e^4 - 46519/2207*e^3 + 671760/2207*e^2 - 966527/2207*e + 248649/2207, -5729/6621*e^6 + 22657/2207*e^5 - 65308/2207*e^4 - 276601/6621*e^3 + 1913542/6621*e^2 - 757447/2207*e + 173463/2207, -9704/6621*e^6 + 37665/2207*e^5 - 103734/2207*e^4 - 494041/6621*e^3 + 3036790/6621*e^2 - 1142788/2207*e + 313120/2207, -2005/2207*e^6 + 21969/2207*e^5 - 50168/2207*e^4 - 125043/2207*e^3 + 519864/2207*e^2 - 441703/2207*e + 71781/2207, -17759/6621*e^6 + 66595/2207*e^5 - 165644/2207*e^4 - 1026859/6621*e^3 + 5019484/6621*e^2 - 1654095/2207*e + 352337/2207, -647/2207*e^6 + 8048/2207*e^5 - 25641/2207*e^4 - 26764/2207*e^3 + 240275/2207*e^2 - 320148/2207*e + 136242/2207, -8857/6621*e^6 + 34949/2207*e^5 - 100527/2207*e^4 - 418193/6621*e^3 + 2890700/6621*e^2 - 1179627/2207*e + 341436/2207, 11218/6621*e^6 - 43067/2207*e^5 + 114954/2207*e^4 + 598913/6621*e^3 - 3423668/6621*e^2 + 1241346/2207*e - 227944/2207, -4279/2207*e^6 + 49590/2207*e^5 - 135509/2207*e^4 - 216480/2207*e^3 + 1330117/2207*e^2 - 1546206/2207*e + 350692/2207, -6716/2207*e^6 + 76189/2207*e^5 - 194331/2207*e^4 - 379304/2207*e^3 + 1952873/2207*e^2 - 1989468/2207*e + 441719/2207, -16390/6621*e^6 + 63792/2207*e^5 - 175933/2207*e^4 - 845678/6621*e^3 + 5166557/6621*e^2 - 1927344/2207*e + 436475/2207, 1290/2207*e^6 - 13887/2207*e^5 + 31298/2207*e^4 + 75146/2207*e^3 - 329930/2207*e^2 + 331322/2207*e - 70774/2207, -1880/2207*e^6 + 20803/2207*e^5 - 50249/2207*e^4 - 104297/2207*e^3 + 498450/2207*e^2 - 551137/2207*e + 178575/2207, -20839/6621*e^6 + 81086/2207*e^5 - 224656/2207*e^4 - 1050470/6621*e^3 + 6592625/6621*e^2 - 2559632/2207*e + 605098/2207, 1039/6621*e^6 - 4955/2207*e^5 + 18385/2207*e^4 + 51197/6621*e^3 - 509873/6621*e^2 + 161695/2207*e - 12136/2207, 175/6621*e^6 - 397/2207*e^5 - 1362/2207*e^4 + 33017/6621*e^3 + 4891/6621*e^2 - 71815/2207*e + 33064/2207, 2765/6621*e^6 - 8921/2207*e^5 + 13351/2207*e^4 + 180025/6621*e^3 - 457699/6621*e^2 + 127727/2207*e - 81424/2207, -8865/2207*e^6 + 102644/2207*e^5 - 277546/2207*e^4 - 465444/2207*e^3 + 2728470/2207*e^2 - 3015810/2207*e + 723695/2207, 3955/6621*e^6 - 16476/2207*e^5 + 54409/2207*e^4 + 122486/6621*e^3 - 1462613/6621*e^2 + 745092/2207*e - 270622/2207, 1989/2207*e^6 - 21961/2207*e^5 + 51891/2207*e^4 + 118821/2207*e^3 - 535344/2207*e^2 + 503523/2207*e - 79324/2207, -3242/6621*e^6 + 12311/2207*e^5 - 30851/2207*e^4 - 200821/6621*e^3 + 933073/6621*e^2 - 254391/2207*e + 47157/2207, 2098/2207*e^6 - 25326/2207*e^5 + 75603/2207*e^4 + 95826/2207*e^3 - 720107/2207*e^2 + 921586/2207*e - 262569/2207, 7839/2207*e^6 - 91096/2207*e^5 + 249820/2207*e^4 + 398060/2207*e^3 - 2443272/2207*e^2 + 2807684/2207*e - 679641/2207, 8515/6621*e^6 - 34892/2207*e^5 + 109217/2207*e^4 + 346442/6621*e^3 - 3062681/6621*e^2 + 1360772/2207*e - 381662/2207, -12401/6621*e^6 + 48046/2207*e^5 - 130377/2207*e^4 - 666382/6621*e^3 + 3873673/6621*e^2 - 1374278/2207*e + 259384/2207, -12731/6621*e^6 + 48101/2207*e^5 - 121566/2207*e^4 - 743398/6621*e^3 + 3700060/6621*e^2 - 1168862/2207*e + 200629/2207, 3065/6621*e^6 - 8971/2207*e^5 + 5341/2207*e^4 + 253651/6621*e^3 - 313111/6621*e^2 - 71053/2207*e + 4894/2207, -5023/6621*e^6 + 18861/2207*e^5 - 47522/2207*e^4 - 289517/6621*e^3 + 1475441/6621*e^2 - 473097/2207*e + 45960/2207, -491/2207*e^6 + 5763/2207*e^5 - 14301/2207*e^4 - 37827/2207*e^3 + 146228/2207*e^2 - 53335/2207*e + 16122/2207, 23134/6621*e^6 - 89193/2207*e^5 + 241728/2207*e^4 + 1190627/6621*e^3 - 7109996/6621*e^2 + 2698629/2207*e - 624742/2207, -1512/2207*e^6 + 16205/2207*e^5 - 34703/2207*e^4 - 95818/2207*e^3 + 366743/2207*e^2 - 333196/2207*e + 71775/2207, -729/2207*e^6 + 5882/2207*e^5 + 1673/2207*e^4 - 71342/2207*e^3 + 39555/2207*e^2 + 172136/2207*e - 109598/2207, -4666/2207*e^6 + 53094/2207*e^5 - 135629/2207*e^4 - 266832/2207*e^3 + 1360679/2207*e^2 - 1365755/2207*e + 319839/2207, -3023/6621*e^6 + 13378/2207*e^5 - 50161/2207*e^4 - 43654/6621*e^3 + 1327033/6621*e^2 - 763214/2207*e + 249166/2207, -17389/6621*e^6 + 67269/2207*e^5 - 182144/2207*e^4 - 918839/6621*e^3 + 5362010/6621*e^2 - 1983123/2207*e + 476599/2207, 13552/6621*e^6 - 52284/2207*e^5 + 141799/2207*e^4 + 697130/6621*e^3 - 4171457/6621*e^2 + 1604334/2207*e - 392225/2207, 9223/6621*e^6 - 37217/2207*e^5 + 111942/2207*e^4 + 419825/6621*e^3 - 3205316/6621*e^2 + 1331727/2207*e - 353717/2207, -6352/2207*e^6 + 73800/2207*e^5 - 200976/2207*e^4 - 333758/2207*e^3 + 1976200/2207*e^2 - 2162160/2207*e + 481454/2207, -4747/6621*e^6 + 16608/2207*e^5 - 33704/2207*e^4 - 304676/6621*e^3 + 1093613/6621*e^2 - 276812/2207*e + 28088/2207, 11552/6621*e^6 - 44594/2207*e^5 + 120161/2207*e^4 + 616792/6621*e^3 - 3572821/6621*e^2 + 1314010/2207*e - 295279/2207, -23066/6621*e^6 + 92860/2207*e^5 - 277090/2207*e^4 - 1070386/6621*e^3 + 7952650/6621*e^2 - 3234964/2207*e + 776492/2207, -8317/6621*e^6 + 32652/2207*e^5 - 92875/2207*e^4 - 403520/6621*e^3 + 2717945/6621*e^2 - 1071754/2207*e + 198422/2207, 1447/6621*e^6 - 7230/2207*e^5 + 31327/2207*e^4 - 2014/6621*e^3 - 777233/6621*e^2 + 455022/2207*e - 200722/2207, 848/2207*e^6 - 11459/2207*e^5 + 41101/2207*e^4 + 31821/2207*e^3 - 377961/2207*e^2 + 477647/2207*e - 99003/2207, 8237/2207*e^6 - 93502/2207*e^5 + 238686/2207*e^4 + 465104/2207*e^3 - 2395878/2207*e^2 + 2460588/2207*e - 562357/2207, 3912/2207*e^6 - 46096/2207*e^5 + 131580/2207*e^4 + 186044/2207*e^3 - 1273584/2207*e^2 + 1543446/2207*e - 385910/2207, -8368/6621*e^6 + 29350/2207*e^5 - 60836/2207*e^4 - 508598/6621*e^3 + 1897256/6621*e^2 - 582878/2207*e + 229168/2207, 6190/2207*e^6 - 73719/2207*e^5 + 212628/2207*e^4 + 304417/2207*e^3 - 2053483/2207*e^2 + 2414001/2207*e - 628175/2207, 2486/2207*e^6 - 29934/2207*e^5 + 89547/2207*e^4 + 108772/2207*e^3 - 841292/2207*e^2 + 1084322/2207*e - 294282/2207, 1322/2207*e^6 - 18317/2207*e^5 + 69785/2207*e^4 + 32415/2207*e^3 - 623399/2207*e^2 + 942613/2207*e - 265353/2207, -7953/2207*e^6 + 91153/2207*e^5 - 238923/2207*e^4 - 439633/2207*e^3 + 2388152/2207*e^2 - 2480877/2207*e + 540100/2207, -236/2207*e^6 + 2325/2207*e^5 - 2725/2207*e^4 - 24461/2207*e^3 + 51959/2207*e^2 + 29045/2207*e - 63257/2207, 2485/6621*e^6 - 11817/2207*e^5 + 47311/2207*e^4 + 42449/6621*e^3 - 1236209/6621*e^2 + 635477/2207*e - 228786/2207, -4813/6621*e^6 + 16619/2207*e^5 - 31059/2207*e^4 - 331997/6621*e^3 + 1023137/6621*e^2 - 210569/2207*e + 36200/2207, -5032/6621*e^6 + 19966/2207*e^5 - 58096/2207*e^4 - 237566/6621*e^3 + 1668674/6621*e^2 - 641928/2207*e + 189518/2207, 1077/2207*e^6 - 12677/2207*e^5 + 35338/2207*e^4 + 55491/2207*e^3 - 334067/2207*e^2 + 381299/2207*e - 204709/2207, -3211/6621*e^6 + 9731/2207*e^5 - 7181/2207*e^4 - 283391/6621*e^3 + 381521/6621*e^2 + 73333/2207*e - 39516/2207, 5868/2207*e^6 - 69144/2207*e^5 + 195163/2207*e^4 + 292308/2207*e^3 - 1894927/2207*e^2 + 2209233/2207*e - 547967/2207, 4204/6621*e^6 - 15414/2207*e^5 + 34298/2207*e^4 + 289664/6621*e^3 - 1092596/6621*e^2 + 236254/2207*e - 47622/2207, 3862/2207*e^6 - 48278/2207*e^5 + 155448/2207*e^4 + 153910/2207*e^3 - 1452172/2207*e^2 + 1929746/2207*e - 515142/2207, 133/6621*e^6 - 2597/2207*e^5 + 21388/2207*e^4 - 77665/6621*e^3 - 499214/6621*e^2 + 389469/2207*e - 121681/2207, -10711/6621*e^6 + 39672/2207*e^5 - 96048/2207*e^4 - 614453/6621*e^3 + 2904488/6621*e^2 - 995519/2207*e + 272167/2207, 856/6621*e^6 - 1614/2207*e^5 - 8289/2207*e^4 + 136454/6621*e^3 + 110905/6621*e^2 - 256440/2207*e + 76767/2207, 4030/6621*e^6 - 15385/2207*e^5 + 40268/2207*e^4 + 223655/6621*e^3 - 1207973/6621*e^2 + 404073/2207*e - 117726/2207, -2013/2207*e^6 + 26387/2207*e^5 - 92343/2207*e^4 - 68565/2207*e^3 + 852002/2207*e^2 - 1170001/2207*e + 318504/2207, 2675/6621*e^6 - 8906/2207*e^5 + 15754/2207*e^4 + 156613/6621*e^3 - 478564/6621*e^2 + 169705/2207*e - 135569/2207, 15217/6621*e^6 - 58079/2207*e^5 + 151415/2207*e^4 + 845549/6621*e^3 - 4517075/6621*e^2 + 1569293/2207*e - 358312/2207, 3979/6621*e^6 - 14273/2207*e^5 + 28167/2207*e^4 + 317207/6621*e^3 - 989165/6621*e^2 + 116085/2207*e + 98408/2207, 2480/2207*e^6 - 32138/2207*e^5 + 112539/2207*e^4 + 72782/2207*e^3 - 1028071/2207*e^2 + 1492626/2207*e - 397805/2207, -16120/6621*e^6 + 61540/2207*e^5 - 163279/2207*e^4 - 841652/6621*e^3 + 4838513/6621*e^2 - 1806094/2207*e + 437799/2207]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([11, 11, -w - 1])] = 1

# EXAMPLE:
# pp = ZF.ideal(2).factor()[0][0]
# hecke_eigenvalues[pp]