/*
  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([1, -1, -6, 0, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([11, 11, -w^3 + 5*w])

primes_array = [
[3, 3, w + 1],\
[5, 5, -w^3 + 5*w + 2],\
[5, 5, w - 1],\
[11, 11, -w^3 + 5*w],\
[13, 13, -w^3 + w^2 + 6*w - 3],\
[16, 2, 2],\
[19, 19, 2*w^3 - w^2 - 11*w + 2],\
[25, 5, -w^2 + w + 3],\
[27, 3, w^3 - w^2 - 5*w + 4],\
[31, 31, -w - 3],\
[37, 37, -w^3 - w^2 + 6*w + 4],\
[41, 41, w^3 + w^2 - 6*w - 5],\
[43, 43, w^3 - 7*w - 2],\
[47, 47, -2*w^3 + 11*w + 2],\
[61, 61, w^2 - 3],\
[67, 67, w^2 + w - 4],\
[79, 79, -4*w^3 + 2*w^2 + 22*w - 9],\
[97, 97, -3*w^3 + 2*w^2 + 19*w - 6],\
[97, 97, -w^3 + 6*w - 3],\
[97, 97, -3*w^3 + 16*w],\
[97, 97, -w^3 + w^2 + 4*w - 3],\
[101, 101, -2*w^3 + w^2 + 11*w - 6],\
[103, 103, w^3 - w^2 - 7*w],\
[109, 109, -w^3 - w^2 + 6*w + 2],\
[121, 11, 2*w^3 - 11*w + 1],\
[127, 127, -2*w^3 + w^2 + 13*w - 1],\
[127, 127, w^3 - w^2 - 6*w - 2],\
[157, 157, -2*w^3 + 2*w^2 + 10*w - 7],\
[157, 157, w - 4],\
[163, 163, 2*w^3 - w^2 - 13*w + 3],\
[173, 173, -2*w^3 + w^2 + 13*w - 6],\
[173, 173, 2*w^3 - 12*w + 1],\
[173, 173, 2*w^3 - 11*w + 2],\
[173, 173, w^2 + w - 5],\
[179, 179, -2*w^3 + 10*w + 3],\
[181, 181, -w^3 - w^2 + 7*w + 8],\
[191, 191, w^3 - 5*w - 5],\
[191, 191, 2*w^3 - w^2 - 9*w - 1],\
[193, 193, -3*w^3 + 3*w^2 + 19*w - 7],\
[197, 197, -w^3 + w^2 + 6*w - 7],\
[223, 223, w^3 + w^2 - 6*w + 1],\
[227, 227, 6*w^3 - 3*w^2 - 34*w + 9],\
[227, 227, w^3 + w^2 - 8*w],\
[233, 233, 2*w^3 - 13*w - 3],\
[233, 233, -w^3 + 2*w^2 + 4*w - 6],\
[239, 239, -2*w^3 + 10*w + 1],\
[239, 239, w^3 - 8*w - 2],\
[251, 251, -3*w^3 + w^2 + 18*w],\
[251, 251, -5*w^3 + 2*w^2 + 30*w - 11],\
[263, 263, -2*w^3 + w^2 + 10*w + 2],\
[269, 269, 3*w^3 - 18*w - 8],\
[271, 271, 2*w^3 + w^2 - 10*w - 2],\
[271, 271, -3*w^3 + 19*w],\
[277, 277, -w^3 + w^2 + 4*w - 8],\
[277, 277, 2*w^3 + w^2 - 14*w - 8],\
[281, 281, w^3 - 8*w],\
[307, 307, 3*w^3 - w^2 - 16*w + 2],\
[307, 307, 2*w^3 - w^2 - 9*w + 1],\
[307, 307, -2*w^3 + 2*w^2 + 13*w - 7],\
[307, 307, -w^3 + w^2 + 7*w - 6],\
[313, 313, -3*w^3 + w^2 + 15*w + 4],\
[317, 317, -4*w^3 + w^2 + 22*w - 3],\
[317, 317, 2*w^3 - w^2 - 10*w - 3],\
[337, 337, w^3 + w^2 - 4*w - 5],\
[349, 349, -2*w^3 - w^2 + 11*w + 3],\
[349, 349, -4*w^3 + 2*w^2 + 24*w - 11],\
[353, 353, 3*w^3 - w^2 - 17*w + 7],\
[353, 353, -3*w^3 - 2*w^2 + 17*w + 11],\
[367, 367, 2*w^3 - 11*w - 7],\
[373, 373, -w^3 + w^2 + 4*w - 5],\
[383, 383, -4*w^3 + 3*w^2 + 23*w - 9],\
[383, 383, 4*w^3 - w^2 - 22*w],\
[389, 389, w^2 - 2*w - 5],\
[401, 401, -3*w^3 + 2*w^2 + 16*w - 9],\
[401, 401, 2*w^3 - w^2 - 14*w - 1],\
[409, 409, 2*w^3 + 2*w^2 - 13*w - 9],\
[419, 419, -4*w^3 + 24*w + 7],\
[419, 419, 2*w^2 + 2*w - 7],\
[419, 419, -w^3 + 2*w^2 + 8*w - 6],\
[419, 419, 6*w^3 - 3*w^2 - 33*w + 13],\
[431, 431, 2*w^3 - w^2 - 12*w - 5],\
[439, 439, -3*w^3 + 2*w^2 + 18*w - 4],\
[439, 439, w^3 + 2*w^2 - 7*w - 3],\
[443, 443, 6*w^3 - 3*w^2 - 33*w + 7],\
[449, 449, -3*w^3 + w^2 + 14*w - 4],\
[457, 457, 2*w^3 - 9*w],\
[457, 457, 3*w^3 - w^2 - 16*w - 2],\
[479, 479, 3*w^3 - w^2 - 19*w + 4],\
[487, 487, -w^3 + w^2 + 4*w - 6],\
[491, 491, 3*w^3 + w^2 - 17*w - 5],\
[499, 499, 5*w^3 - 3*w^2 - 28*w + 8],\
[499, 499, 2*w^3 - w^2 - 12*w - 1],\
[503, 503, -2*w^3 - w^2 + 12*w + 3],\
[503, 503, w^3 - 3*w - 4],\
[509, 509, -3*w - 5],\
[509, 509, -4*w^3 + 3*w^2 + 25*w - 10],\
[523, 523, -2*w^3 + w^2 + 14*w - 6],\
[529, 23, 4*w^3 - 2*w^2 - 21*w + 5],\
[529, 23, -3*w^3 - w^2 + 15*w + 6],\
[557, 557, -2*w^3 + w^2 + 13*w + 2],\
[557, 557, 3*w^3 - 2*w^2 - 16*w + 3],\
[569, 569, 2*w^2 - w - 8],\
[587, 587, w^3 + 2*w^2 - 5*w - 16],\
[587, 587, -4*w^3 + w^2 + 25*w - 5],\
[599, 599, w^3 + 2*w^2 - 6*w - 5],\
[599, 599, -5*w^3 + 3*w^2 + 30*w - 15],\
[601, 601, w^3 - 6*w - 6],\
[607, 607, -w^3 + w^2 + 3*w - 4],\
[607, 607, -w^3 + 2*w - 3],\
[613, 613, 6*w^3 - 2*w^2 - 31*w + 11],\
[613, 613, w^3 + w^2 - 4*w - 6],\
[617, 617, 5*w^3 - w^2 - 30*w + 2],\
[617, 617, -2*w^3 + 2*w^2 + 9*w + 3],\
[619, 619, -w^3 + 2*w^2 + 6*w - 5],\
[619, 619, 2*w^3 - w^2 - 11*w - 3],\
[631, 631, -w^3 + 2*w^2 + 5*w - 5],\
[631, 631, -3*w^3 - w^2 + 18*w + 5],\
[647, 647, 6*w^3 - w^2 - 36*w + 2],\
[659, 659, 4*w^3 + w^2 - 24*w - 14],\
[661, 661, 2*w^2 - w - 4],\
[673, 673, 2*w^3 + w^2 - 14*w - 12],\
[677, 677, 3*w^3 + 2*w^2 - 16*w - 7],\
[677, 677, -3*w^3 + w^2 + 15*w + 1],\
[683, 683, 2*w^2 - 2*w - 9],\
[683, 683, 2*w^3 - 14*w + 1],\
[691, 691, 5*w^3 - 2*w^2 - 30*w + 6],\
[701, 701, -2*w^3 + w^2 + 12*w + 2],\
[701, 701, -5*w^3 + 2*w^2 + 26*w],\
[719, 719, 3*w^3 - 18*w + 1],\
[719, 719, 3*w^3 - w^2 - 19*w + 1],\
[727, 727, -3*w^2 - 2*w + 11],\
[727, 727, 2*w^3 + w^2 - 13*w - 2],\
[733, 733, 2*w^3 - 3*w^2 - 8*w + 5],\
[739, 739, -3*w^3 + 16*w - 6],\
[743, 743, -4*w^3 - w^2 + 25*w + 8],\
[751, 751, w^2 - 2*w - 7],\
[751, 751, -3*w^3 + 15*w + 5],\
[757, 757, 3*w^3 - 19*w - 2],\
[761, 761, 2*w^2 + w - 5],\
[769, 769, -2*w^3 + w^2 + 14*w - 9],\
[769, 769, 2*w^2 - w - 7],\
[773, 773, w^3 - w^2 - 5*w - 4],\
[773, 773, w^3 - 3*w - 6],\
[787, 787, 3*w^3 - 19*w - 3],\
[797, 797, 8*w^3 - 3*w^2 - 47*w + 10],\
[809, 809, 4*w^3 - 25*w - 1],\
[811, 811, w^3 - 9*w - 1],\
[821, 821, 6*w^3 - 3*w^2 - 35*w + 8],\
[823, 823, 2*w^3 + w^2 - 10*w + 1],\
[823, 823, -2*w^3 + 2*w^2 + 7*w - 4],\
[829, 829, -5*w^3 + w^2 + 27*w - 4],\
[829, 829, 5*w^3 - 2*w^2 - 26*w + 10],\
[839, 839, w^3 + 2*w^2 - 5*w - 7],\
[839, 839, 3*w^3 - w^2 - 15*w + 2],\
[841, 29, 3*w^3 + w^2 - 14*w - 2],\
[841, 29, 4*w^3 - 2*w^2 - 21*w + 10],\
[857, 857, -8*w^3 + 4*w^2 + 44*w - 11],\
[857, 857, -3*w^3 + 3*w^2 + 20*w - 9],\
[859, 859, w^3 + 2*w^2 - 6*w - 6],\
[877, 877, w^3 - 3*w^2 - 4*w + 14],\
[883, 883, 2*w^3 + w^2 - 10*w - 11],\
[887, 887, 3*w^3 + w^2 - 20*w - 2],\
[919, 919, 7*w^3 - 3*w^2 - 39*w + 9],\
[929, 929, 3*w^3 - 17*w + 2],\
[929, 929, -6*w^3 + 2*w^2 + 35*w - 10],\
[937, 937, w^3 + w^2 - 3*w - 5],\
[937, 937, -2*w^3 + 3*w^2 + 12*w - 12],\
[937, 937, -3*w^3 - 2*w^2 + 19*w + 8],\
[937, 937, 3*w^3 - 2*w^2 - 13*w + 3],\
[941, 941, w^3 + 2*w^2 - 6*w - 8],\
[941, 941, 5*w^3 - w^2 - 28*w - 3],\
[947, 947, -4*w^3 + 2*w^2 + 25*w - 6],\
[953, 953, w^3 - 7*w - 7],\
[953, 953, -3*w^3 + 2*w^2 + 18*w - 3],\
[967, 967, w^3 - 2*w^2 - 5*w - 3],\
[971, 971, w^2 + 2*w - 6],\
[977, 977, 2*w^3 - 11*w - 8],\
[997, 997, -3*w^3 + w^2 + 17*w + 2],\
[997, 997, -2*w^3 + 2*w^2 + 14*w - 7]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^6 + x^5 - 10*x^4 - 8*x^3 + 23*x^2 + 14*x + 2
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 6*e^5 + 4*e^4 - 61*e^3 - 29*e^2 + 145*e + 42, -10*e^5 - 7*e^4 + 102*e^3 + 50*e^2 - 244*e - 70, 1, -7*e^5 - 5*e^4 + 72*e^3 + 36*e^2 - 175*e - 52, -3*e^5 - 2*e^4 + 30*e^3 + 14*e^2 - 70*e - 19, -2*e^5 - e^4 + 20*e^3 + 8*e^2 - 46*e - 16, 2*e^5 + e^4 - 20*e^3 - 6*e^2 + 46*e + 8, 8*e^5 + 5*e^4 - 82*e^3 - 36*e^2 + 196*e + 52, 5*e^5 + 4*e^4 - 51*e^3 - 27*e^2 + 122*e + 32, 21*e^5 + 15*e^4 - 215*e^3 - 109*e^2 + 516*e + 154, 16*e^5 + 12*e^4 - 165*e^3 - 86*e^2 + 399*e + 116, 27*e^5 + 20*e^4 - 276*e^3 - 143*e^2 + 664*e + 196, -e^5 + 11*e^3 - 27*e - 4, -16*e^5 - 12*e^4 + 162*e^3 + 84*e^2 - 385*e - 116, 10*e^5 + 6*e^4 - 103*e^3 - 44*e^2 + 248*e + 66, 12*e^5 + 8*e^4 - 122*e^3 - 58*e^2 + 291*e + 84, -26*e^5 - 19*e^4 + 263*e^3 + 135*e^2 - 622*e - 190, 9*e^5 + 6*e^4 - 93*e^3 - 47*e^2 + 228*e + 76, 31*e^5 + 23*e^4 - 316*e^3 - 163*e^2 + 756*e + 222, 9*e^5 + 6*e^4 - 95*e^3 - 45*e^2 + 239*e + 62, -6*e^5 - 4*e^4 + 61*e^3 + 29*e^2 - 140*e - 48, -19*e^5 - 12*e^4 + 193*e^3 + 84*e^2 - 462*e - 120, -12*e^5 - 9*e^4 + 121*e^3 + 61*e^2 - 286*e - 74, -38*e^5 - 27*e^4 + 387*e^3 + 192*e^2 - 930*e - 266, -27*e^5 - 21*e^4 + 275*e^3 + 150*e^2 - 658*e - 200, -10*e^5 - 8*e^4 + 106*e^3 + 59*e^2 - 267*e - 82, -13*e^5 - 9*e^4 + 136*e^3 + 66*e^2 - 336*e - 104, 37*e^5 + 26*e^4 - 372*e^3 - 181*e^2 + 874*e + 244, 7*e^5 + 4*e^4 - 67*e^3 - 28*e^2 + 148*e + 46, 42*e^5 + 30*e^4 - 432*e^3 - 214*e^2 + 1044*e + 302, 16*e^5 + 12*e^4 - 160*e^3 - 85*e^2 + 374*e + 120, 5*e^5 + 4*e^4 - 47*e^3 - 24*e^2 + 102*e + 18, 43*e^5 + 33*e^4 - 436*e^3 - 229*e^2 + 1038*e + 296, 7*e^5 + 4*e^4 - 75*e^3 - 31*e^2 + 193*e + 50, 8*e^5 + 5*e^4 - 78*e^3 - 32*e^2 + 173*e + 36, -64*e^5 - 48*e^4 + 653*e^3 + 340*e^2 - 1570*e - 460, -49*e^5 - 38*e^4 + 498*e^3 + 268*e^2 - 1190*e - 356, 10*e^5 + 8*e^4 - 98*e^3 - 52*e^2 + 224*e + 52, 13*e^5 + 7*e^4 - 134*e^3 - 53*e^2 + 322*e + 80, -20*e^5 - 14*e^4 + 207*e^3 + 102*e^2 - 508*e - 146, -58*e^5 - 43*e^4 + 589*e^3 + 304*e^2 - 1405*e - 416, -31*e^5 - 22*e^4 + 320*e^3 + 160*e^2 - 778*e - 222, 15*e^5 + 11*e^4 - 146*e^3 - 77*e^2 + 326*e + 108, 34*e^5 + 26*e^4 - 343*e^3 - 183*e^2 + 811*e + 242, 2*e^5 + 2*e^4 - 19*e^3 - 12*e^2 + 44*e - 4, 72*e^5 + 51*e^4 - 733*e^3 - 364*e^2 + 1750*e + 504, 62*e^5 + 44*e^4 - 633*e^3 - 315*e^2 + 1517*e + 434, 44*e^5 + 31*e^4 - 450*e^3 - 222*e^2 + 1084*e + 320, -26*e^5 - 18*e^4 + 267*e^3 + 126*e^2 - 645*e - 168, 27*e^5 + 20*e^4 - 277*e^3 - 141*e^2 + 672*e + 182, 37*e^5 + 27*e^4 - 376*e^3 - 192*e^2 + 906*e + 266, -75*e^5 - 55*e^4 + 761*e^3 + 389*e^2 - 1812*e - 526, -22*e^5 - 16*e^4 + 223*e^3 + 109*e^2 - 530*e - 142, -40*e^5 - 29*e^4 + 407*e^3 + 206*e^2 - 974*e - 288, 61*e^5 + 45*e^4 - 626*e^3 - 324*e^2 + 1508*e + 450, 60*e^5 + 44*e^4 - 606*e^3 - 308*e^2 + 1435*e + 416, 33*e^5 + 25*e^4 - 341*e^3 - 177*e^2 + 835*e + 242, -8*e^5 - 9*e^4 + 81*e^3 + 59*e^2 - 196*e - 58, -22*e^5 - 13*e^4 + 229*e^3 + 94*e^2 - 558*e - 136, 19*e^5 + 14*e^4 - 195*e^3 - 98*e^2 + 467*e + 112, -34*e^5 - 25*e^4 + 344*e^3 + 177*e^2 - 816*e - 258, 92*e^5 + 68*e^4 - 938*e^3 - 483*e^2 + 2247*e + 650, 42*e^5 + 30*e^4 - 427*e^3 - 217*e^2 + 1016*e + 300, -58*e^5 - 39*e^4 + 595*e^3 + 282*e^2 - 1430*e - 422, -25*e^5 - 16*e^4 + 256*e^3 + 115*e^2 - 610*e - 172, 16*e^5 + 12*e^4 - 161*e^3 - 79*e^2 + 380*e + 96, 5*e^5 + 6*e^4 - 47*e^3 - 39*e^2 + 99*e + 42, 20*e^5 + 10*e^4 - 204*e^3 - 73*e^2 + 486*e + 122, -22*e^5 - 14*e^4 + 227*e^3 + 99*e^2 - 546*e - 150, -54*e^5 - 40*e^4 + 548*e^3 + 281*e^2 - 1306*e - 378, -7*e^5 - 3*e^4 + 73*e^3 + 23*e^2 - 173*e - 42, -9*e^5 - 7*e^4 + 90*e^3 + 48*e^2 - 214*e - 56, -6*e^5 - e^4 + 62*e^3 + 8*e^2 - 141*e - 20, 30*e^5 + 24*e^4 - 303*e^3 - 169*e^2 + 716*e + 224, 9*e^5 + 7*e^4 - 89*e^3 - 48*e^2 + 208*e + 64, 52*e^5 + 36*e^4 - 535*e^3 - 258*e^2 + 1299*e + 368, -30*e^5 - 22*e^4 + 307*e^3 + 153*e^2 - 732*e - 202, 2*e^5 + 2*e^4 - 22*e^3 - 16*e^2 + 56*e + 20, 77*e^5 + 57*e^4 - 784*e^3 - 405*e^2 + 1881*e + 550, -28*e^5 - 20*e^4 + 291*e^3 + 141*e^2 - 716*e - 206, -92*e^5 - 68*e^4 + 941*e^3 + 484*e^2 - 2267*e - 660, -34*e^5 - 24*e^4 + 347*e^3 + 175*e^2 - 818*e - 260, 10*e^5 + 7*e^4 - 97*e^3 - 40*e^2 + 217*e + 28, -31*e^5 - 23*e^4 + 316*e^3 + 156*e^2 - 759*e - 196, -2*e^5 - 2*e^4 + 17*e^3 + 19*e^2 - 31*e - 50, -21*e^5 - 14*e^4 + 219*e^3 + 104*e^2 - 529*e - 160, -9*e^5 - 7*e^4 + 93*e^3 + 51*e^2 - 220*e - 58, -38*e^5 - 25*e^4 + 389*e^3 + 177*e^2 - 932*e - 246, -31*e^5 - 22*e^4 + 310*e^3 + 151*e^2 - 730*e - 194, -31*e^5 - 22*e^4 + 311*e^3 + 153*e^2 - 722*e - 214, 4*e^5 + 4*e^4 - 49*e^3 - 33*e^2 + 138*e + 46, 20*e^5 + 15*e^4 - 210*e^3 - 115*e^2 + 526*e + 166, 2*e^5 + 3*e^4 - 15*e^3 - 14*e^2 + 14*e, 13*e^5 + 8*e^4 - 128*e^3 - 54*e^2 + 293*e + 80, -53*e^5 - 41*e^4 + 542*e^3 + 297*e^2 - 1300*e - 398, 25*e^5 + 15*e^4 - 252*e^3 - 109*e^2 + 584*e + 156, 13*e^5 + 7*e^4 - 138*e^3 - 55*e^2 + 342*e + 86, -79*e^5 - 57*e^4 + 803*e^3 + 404*e^2 - 1911*e - 560, 11*e^5 + 9*e^4 - 108*e^3 - 61*e^2 + 257*e + 74, 5*e^5 + 2*e^4 - 58*e^3 - 17*e^2 + 162*e + 34, -68*e^5 - 47*e^4 + 696*e^3 + 338*e^2 - 1680*e - 476, -e^4 - 7*e^3 + 12*e^2 + 42*e - 28, 12*e^5 + 11*e^4 - 122*e^3 - 71*e^2 + 302*e + 70, 25*e^5 + 18*e^4 - 253*e^3 - 127*e^2 + 592*e + 162, -11*e^5 - 5*e^4 + 117*e^3 + 39*e^2 - 286*e - 76, -32*e^5 - 23*e^4 + 328*e^3 + 163*e^2 - 782*e - 232, 21*e^5 + 14*e^4 - 208*e^3 - 100*e^2 + 479*e + 152, 68*e^5 + 52*e^4 - 691*e^3 - 377*e^2 + 1651*e + 502, -45*e^5 - 35*e^4 + 457*e^3 + 248*e^2 - 1093*e - 328, -48*e^5 - 34*e^4 + 485*e^3 + 239*e^2 - 1156*e - 316, -57*e^5 - 44*e^4 + 584*e^3 + 313*e^2 - 1406*e - 428, 31*e^5 + 26*e^4 - 314*e^3 - 175*e^2 + 749*e + 194, 41*e^5 + 29*e^4 - 416*e^3 - 202*e^2 + 995*e + 276, 56*e^5 + 41*e^4 - 571*e^3 - 286*e^2 + 1372*e + 384, -70*e^5 - 48*e^4 + 711*e^3 + 337*e^2 - 1691*e - 462, -25*e^5 - 16*e^4 + 254*e^3 + 117*e^2 - 600*e - 172, 48*e^5 + 34*e^4 - 497*e^3 - 243*e^2 + 1218*e + 320, -2*e^3 + 2*e^2 + 16*e - 12, -9*e^5 - 6*e^4 + 90*e^3 + 44*e^2 - 196*e - 76, 40*e^5 + 24*e^4 - 412*e^3 - 169*e^2 + 984*e + 246, -5*e^5 - 6*e^4 + 50*e^3 + 42*e^2 - 126*e - 36, -9*e^5 - 7*e^4 + 98*e^3 + 53*e^2 - 250*e - 54, -34*e^5 - 25*e^4 + 348*e^3 + 180*e^2 - 833*e - 224, -22*e^5 - 15*e^4 + 217*e^3 + 107*e^2 - 496*e - 146, -33*e^5 - 24*e^4 + 335*e^3 + 173*e^2 - 802*e - 240, -104*e^5 - 74*e^4 + 1053*e^3 + 523*e^2 - 2492*e - 722, -70*e^5 - 52*e^4 + 713*e^3 + 367*e^2 - 1706*e - 490, -51*e^5 - 33*e^4 + 517*e^3 + 234*e^2 - 1222*e - 324, 9*e^5 + 3*e^4 - 88*e^3 - 22*e^2 + 192*e + 48, -81*e^5 - 54*e^4 + 826*e^3 + 386*e^2 - 1975*e - 564, 19*e^5 + 15*e^4 - 195*e^3 - 104*e^2 + 482*e + 136, -10*e^5 - 9*e^4 + 106*e^3 + 71*e^2 - 264*e - 110, 65*e^5 + 43*e^4 - 667*e^3 - 312*e^2 + 1610*e + 460, 34*e^5 + 24*e^4 - 344*e^3 - 169*e^2 + 814*e + 238, -145*e^5 - 101*e^4 + 1479*e^3 + 725*e^2 - 3539*e - 1022, -83*e^5 - 60*e^4 + 847*e^3 + 424*e^2 - 2049*e - 572, -74*e^5 - 50*e^4 + 762*e^3 + 358*e^2 - 1838*e - 512, -82*e^5 - 61*e^4 + 828*e^3 + 434*e^2 - 1967*e - 592, 4*e^5 - e^4 - 45*e^3 + 112*e + 44, -51*e^5 - 37*e^4 + 515*e^3 + 267*e^2 - 1220*e - 378, 46*e^5 + 33*e^4 - 464*e^3 - 228*e^2 + 1108*e + 294, -16*e^5 - 9*e^4 + 163*e^3 + 54*e^2 - 390*e - 86, -54*e^5 - 36*e^4 + 559*e^3 + 257*e^2 - 1360*e - 370, 142*e^5 + 99*e^4 - 1461*e^3 - 714*e^2 + 3532*e + 1016, 46*e^5 + 35*e^4 - 471*e^3 - 247*e^2 + 1140*e + 328, -97*e^5 - 71*e^4 + 995*e^3 + 508*e^2 - 2412*e - 698, -107*e^5 - 75*e^4 + 1091*e^3 + 535*e^2 - 2624*e - 750, 89*e^5 + 68*e^4 - 909*e^3 - 486*e^2 + 2178*e + 656, -62*e^5 - 45*e^4 + 629*e^3 + 319*e^2 - 1505*e - 434, -3*e^5 + e^4 + 28*e^3 - 5*e^2 - 58*e - 18, 118*e^5 + 84*e^4 - 1206*e^3 - 608*e^2 + 2899*e + 852, -104*e^5 - 73*e^4 + 1061*e^3 + 525*e^2 - 2536*e - 726, 55*e^5 + 39*e^4 - 562*e^3 - 272*e^2 + 1348*e + 360, 71*e^5 + 54*e^4 - 730*e^3 - 389*e^2 + 1760*e + 526, -52*e^5 - 37*e^4 + 531*e^3 + 267*e^2 - 1268*e - 362, 5*e^5 + 3*e^4 - 52*e^3 - 24*e^2 + 128*e + 48, 25*e^5 + 18*e^4 - 264*e^3 - 124*e^2 + 668*e + 166, 37*e^5 + 27*e^4 - 377*e^3 - 184*e^2 + 894*e + 224, -5*e^5 - e^4 + 58*e^3 + 6*e^2 - 149*e - 12, 13*e^5 + 11*e^4 - 132*e^3 - 78*e^2 + 316*e + 120, 5*e^5 + 2*e^4 - 46*e^3 - 9*e^2 + 94*e + 10, 146*e^5 + 105*e^4 - 1491*e^3 - 746*e^2 + 3577*e + 1024, 15*e^5 + 12*e^4 - 150*e^3 - 83*e^2 + 346*e + 92, 77*e^5 + 58*e^4 - 775*e^3 - 407*e^2 + 1832*e + 544, 85*e^5 + 58*e^4 - 878*e^3 - 425*e^2 + 2124*e + 634, -4*e^5 - 7*e^4 + 37*e^3 + 42*e^2 - 84*e - 32, -42*e^5 - 31*e^4 + 433*e^3 + 225*e^2 - 1048*e - 284, 45*e^5 + 28*e^4 - 461*e^3 - 210*e^2 + 1105*e + 324, -38*e^5 - 30*e^4 + 384*e^3 + 208*e^2 - 912*e - 264, -114*e^5 - 81*e^4 + 1166*e^3 + 575*e^2 - 2807*e - 818, 89*e^5 + 63*e^4 - 905*e^3 - 451*e^2 + 2156*e + 634, 11*e^5 + 13*e^4 - 117*e^3 - 91*e^2 + 302*e + 122, -140*e^5 - 95*e^4 + 1426*e^3 + 682*e^2 - 3397*e - 968, -84*e^5 - 61*e^4 + 860*e^3 + 441*e^2 - 2068*e - 616, -22*e^5 - 15*e^4 + 234*e^3 + 108*e^2 - 594*e - 158, -13*e^5 - 11*e^4 + 126*e^3 + 82*e^2 - 284*e - 126, -4*e^5 - 4*e^4 + 44*e^3 + 38*e^2 - 115*e - 44, 146*e^5 + 106*e^4 - 1492*e^3 - 752*e^2 + 3574*e + 1036]
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^3 + 5*w])] = -1

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