/*
  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, -5, 0, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([31, 31, -w^3 + 6*w + 2])

primes_array = [
[2, 2, w + 1],\
[5, 5, w^3 - 4*w],\
[8, 2, w^3 - w^2 - 4*w + 3],\
[11, 11, w^3 - 5*w + 1],\
[17, 17, -w^3 - w^2 + 5*w + 4],\
[23, 23, -w^2 + 2],\
[29, 29, -w^2 - w + 3],\
[31, 31, -w^3 + 6*w + 2],\
[43, 43, w^3 - 6*w],\
[47, 47, 2*w^3 - 9*w],\
[47, 47, -2*w^3 + w^2 + 8*w - 2],\
[53, 53, -4*w^3 + 2*w^2 + 18*w - 5],\
[59, 59, w^2 - w - 5],\
[59, 59, 3*w^3 - 15*w - 5],\
[71, 71, w^3 - 3*w - 3],\
[81, 3, -3],\
[83, 83, -2*w^3 + 8*w + 3],\
[89, 89, -2*w^3 + 11*w - 2],\
[101, 101, 2*w^3 - w^2 - 10*w],\
[101, 101, 2*w^3 - 2*w^2 - 10*w + 3],\
[107, 107, 3*w^3 - 15*w - 1],\
[107, 107, 4*w^3 - 2*w^2 - 18*w + 3],\
[109, 109, 2*w^3 - 10*w + 3],\
[109, 109, 3*w^3 - 2*w^2 - 13*w + 3],\
[113, 113, 3*w^3 - w^2 - 15*w + 2],\
[113, 113, 3*w^3 - 13*w - 5],\
[121, 11, 3*w^3 - 13*w - 1],\
[125, 5, -2*w^3 + w^2 + 7*w + 1],\
[127, 127, 2*w^3 - 8*w - 1],\
[127, 127, -w^3 + 2*w^2 + 3*w - 3],\
[137, 137, 2*w^3 - 10*w + 1],\
[137, 137, 2*w^3 - 11*w],\
[139, 139, 2*w^3 - 9*w - 6],\
[157, 157, -4*w^3 - w^2 + 19*w + 7],\
[163, 163, 5*w^3 - 2*w^2 - 25*w + 7],\
[167, 167, w^2 + w - 5],\
[167, 167, -w^3 + 2*w^2 + 4*w - 6],\
[169, 13, -w^3 + w^2 + 3*w - 4],\
[169, 13, w^2 - 2*w - 4],\
[173, 173, -2*w^3 + w^2 + 11*w - 7],\
[173, 173, w - 4],\
[181, 181, w + 4],\
[181, 181, -2*w - 5],\
[191, 191, -w^3 + 2*w^2 + 6*w - 6],\
[191, 191, 2*w^3 - w^2 - 11*w + 1],\
[193, 193, -3*w^3 + 16*w],\
[227, 227, 6*w^3 - 3*w^2 - 27*w + 5],\
[227, 227, 2*w^3 - 11*w - 2],\
[229, 229, -2*w^3 + w^2 + 10*w - 6],\
[233, 233, 4*w^3 - 3*w^2 - 17*w + 5],\
[233, 233, 2*w^3 + w^2 - 7*w - 5],\
[233, 233, w^3 - 7*w - 1],\
[233, 233, 2*w^3 - 7*w],\
[239, 239, 2*w^2 - 2*w - 7],\
[239, 239, -4*w^3 + w^2 + 18*w],\
[241, 241, w^3 - 5*w - 5],\
[263, 263, -4*w^3 + w^2 + 20*w - 4],\
[269, 269, w^3 + 2*w^2 - 6*w - 6],\
[271, 271, 2*w^3 + w^2 - 12*w - 8],\
[277, 277, w^3 + w^2 - 7*w - 6],\
[283, 283, 6*w^3 - 3*w^2 - 27*w + 7],\
[283, 283, -3*w^3 + 3*w^2 + 13*w - 8],\
[293, 293, -2*w^3 + w^2 + 9*w + 3],\
[293, 293, 4*w^3 - w^2 - 19*w + 3],\
[313, 313, 2*w^2 - w - 4],\
[313, 313, -2*w^3 + 2*w^2 + 8*w - 1],\
[317, 317, 3*w^3 + w^2 - 13*w - 10],\
[331, 331, w^3 + 2*w^2 - 4*w - 6],\
[349, 349, -w^3 + 3*w^2 + w - 4],\
[353, 353, 3*w^3 - 14*w],\
[353, 353, -2*w^3 + w^2 + 7*w + 5],\
[361, 19, -5*w^3 + w^2 + 23*w - 2],\
[361, 19, -2*w^3 + 7*w + 6],\
[373, 373, -w^3 + 4*w - 4],\
[379, 379, -w^3 - 2*w^2 + 5*w + 7],\
[383, 383, w^2 - 2*w - 6],\
[389, 389, -4*w^3 + 2*w^2 + 16*w - 5],\
[397, 397, 5*w^3 - 2*w^2 - 24*w + 2],\
[397, 397, 3*w^3 + 2*w^2 - 16*w - 14],\
[401, 401, 2*w^2 - 5],\
[419, 419, -w^3 - w^2 + 9*w + 6],\
[439, 439, 3*w^3 - w^2 - 15*w - 2],\
[449, 449, 4*w^3 + w^2 - 17*w - 5],\
[449, 449, 4*w^3 - w^2 - 17*w - 5],\
[467, 467, -3*w^3 + 16*w - 2],\
[467, 467, 2*w^3 + w^2 - 10*w - 2],\
[479, 479, 4*w^3 - 19*w - 8],\
[491, 491, 3*w - 4],\
[491, 491, -w^3 + 2*w^2 + 5*w - 11],\
[509, 509, -7*w^3 + 3*w^2 + 33*w - 10],\
[509, 509, 4*w^3 - w^2 - 21*w - 3],\
[523, 523, -w^3 - 2*w^2 + 6*w + 2],\
[541, 541, -5*w^3 + 2*w^2 + 26*w - 8],\
[541, 541, 2*w^3 + w^2 - 9*w - 1],\
[571, 571, -4*w^3 + 3*w^2 + 20*w - 14],\
[571, 571, -3*w^3 - w^2 + 15*w + 4],\
[593, 593, w^3 - 4*w - 6],\
[613, 613, 4*w^3 - 2*w^2 - 19*w + 2],\
[617, 617, -w^3 + 3*w - 5],\
[617, 617, -w^3 + 2*w^2 + 3*w - 9],\
[617, 617, 8*w^3 - 3*w^2 - 38*w + 8],\
[617, 617, w^3 - 8*w],\
[619, 619, 6*w^3 - 3*w^2 - 26*w + 4],\
[631, 631, 3*w^3 + w^2 - 17*w - 8],\
[631, 631, w^2 - 3*w - 5],\
[641, 641, -3*w^3 + 2*w^2 + 16*w - 10],\
[643, 643, -2*w^3 + 3*w^2 + 7*w - 9],\
[647, 647, w^3 - w^2 - 3*w - 4],\
[653, 653, 2*w^3 + w^2 - 11*w - 1],\
[653, 653, w^3 + 2*w^2 - 7*w - 9],\
[653, 653, -4*w^3 - w^2 + 17*w + 3],\
[653, 653, 3*w^3 - 2*w^2 - 13*w + 1],\
[661, 661, 2*w^3 - 3*w^2 - 8*w + 8],\
[673, 673, 3*w^3 - 12*w - 2],\
[673, 673, 2*w^3 - w^2 - 12*w],\
[683, 683, -w^3 + 2*w^2 + 2*w - 6],\
[691, 691, -5*w^3 + 22*w + 8],\
[691, 691, 2*w^3 - 12*w - 3],\
[719, 719, 6*w^3 + w^2 - 28*w - 8],\
[733, 733, -3*w^2 + 3*w + 7],\
[733, 733, 3*w^3 - 14*w + 2],\
[733, 733, -w^3 + w^2 + 7*w - 8],\
[733, 733, 2*w^3 - 6*w - 5],\
[751, 751, 3*w^3 + 3*w^2 - 13*w - 12],\
[751, 751, 5*w^3 - 2*w^2 - 25*w + 5],\
[751, 751, -4*w^3 + 3*w^2 + 20*w - 12],\
[751, 751, 2*w^3 + w^2 - 9*w + 1],\
[757, 757, -3*w^3 + w^2 + 11*w + 2],\
[773, 773, w^3 - w^2 - 7*w + 6],\
[787, 787, -9*w^3 + 4*w^2 + 43*w - 13],\
[787, 787, w^2 + 2*w - 6],\
[797, 797, -w^3 + 4*w^2 - 2*w - 6],\
[797, 797, 2*w^3 - w^2 - 9*w + 7],\
[821, 821, -6*w^3 + 27*w + 2],\
[823, 823, 8*w^3 - 4*w^2 - 37*w + 8],\
[827, 827, -3*w^3 + 3*w^2 + 15*w - 4],\
[829, 829, w^3 + w^2 - 3*w - 8],\
[839, 839, 2*w^3 - 3*w^2 - 8*w + 6],\
[839, 839, 8*w^3 - 2*w^2 - 38*w + 3],\
[859, 859, 4*w^3 - 2*w^2 - 18*w + 1],\
[859, 859, -4*w^3 + 4*w^2 + 17*w - 10],\
[863, 863, -4*w^3 + w^2 + 19*w + 3],\
[877, 877, -4*w^3 + w^2 + 18*w + 4],\
[883, 883, -6*w^3 + 3*w^2 + 31*w - 13],\
[883, 883, 4*w^3 - w^2 - 17*w - 1],\
[887, 887, 3*w^3 - 4*w^2 - 11*w + 11],\
[907, 907, 5*w^3 - 4*w^2 - 21*w + 11],\
[907, 907, -2*w^3 + 2*w^2 + 8*w - 11],\
[911, 911, 2*w^3 - 2*w^2 - 11*w],\
[919, 919, 4*w^3 - 17*w - 2],\
[937, 937, 3*w^3 - 2*w^2 - 15*w + 1],\
[937, 937, 3*w^3 - 17*w + 1],\
[941, 941, 4*w^3 - w^2 - 16*w - 4],\
[953, 953, -2*w^3 + 2*w^2 + 13*w - 6],\
[971, 971, -3*w^3 + 11*w + 9],\
[977, 977, 8*w^3 - 4*w^2 - 39*w + 16],\
[983, 983, 4*w^3 - w^2 - 21*w + 3],\
[983, 983, 2*w^3 - 3*w^2 - 9*w + 7],\
[997, 997, w^3 - w^2 - w - 6],\
[997, 997, w^3 - 9*w - 3]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^14 - 5*x^13 - 10*x^12 + 80*x^11 - 477*x^9 + 305*x^8 + 1313*x^7 - 1265*x^6 - 1603*x^5 + 1976*x^4 + 558*x^3 - 1101*x^2 + 143*x + 83
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, -57/391*e^13 + 13/23*e^12 + 825/391*e^11 - 3716/391*e^10 - 3994/391*e^9 + 23658/391*e^8 + 5824/391*e^7 - 71272/391*e^6 + 9250/391*e^5 + 101462/391*e^4 - 31835/391*e^3 - 57021/391*e^2 + 19477/391*e + 6920/391, 361/391*e^13 - 90/23*e^12 - 4834/391*e^11 + 25229/391*e^10 + 20473/391*e^9 - 157263/391*e^8 - 19551/391*e^7 + 463771/391*e^6 - 68228/391*e^5 - 644287/391*e^4 + 165780/391*e^3 + 344711/391*e^2 - 100155/391*e - 32618/391, -6/391*e^13 + 5/23*e^12 - 263/391*e^11 - 741/391*e^10 + 4251/391*e^9 + 62/391*e^8 - 20645/391*e^7 + 12521/391*e^6 + 39765/391*e^5 - 30169/391*e^4 - 26667/391*e^3 + 16079/391*e^2 + 3038/391*e + 1140/391, 135/391*e^13 - 32/23*e^12 - 1707/391*e^11 + 8266/391*e^10 + 6990/391*e^9 - 46360/391*e^8 - 9966/391*e^7 + 120421/391*e^6 + 1264/391*e^5 - 144839/391*e^4 + 5101/391*e^3 + 66172/391*e^2 - 5795/391*e - 4536/391, 753/391*e^13 - 179/23*e^12 - 10590/391*e^11 + 50963/391*e^10 + 49285/391*e^9 - 323318/391*e^8 - 68830/391*e^7 + 971092/391*e^6 - 99684/391*e^5 - 1374404/391*e^4 + 337377/391*e^3 + 750561/391*e^2 - 221741/391*e - 73081/391, 921/391*e^13 - 227/23*e^12 - 12219/391*e^11 + 63109/391*e^10 + 50685/391*e^9 - 389569/391*e^8 - 42862/391*e^7 + 1137797/391*e^6 - 185165/391*e^5 - 1570905/391*e^4 + 421699/391*e^3 + 845012/391*e^2 - 244636/391*e - 85060/391, -1, -453/391*e^13 + 113/23*e^12 + 5754/391*e^11 - 30726/391*e^10 - 21761/391*e^9 + 184541/391*e^8 + 9017/391*e^7 - 522283/391*e^6 + 102797/391*e^5 + 696773/391*e^4 - 193058/391*e^3 - 361570/391*e^2 + 101903/391*e + 35631/391, 1095/391*e^13 - 257/23*e^12 - 15540/391*e^11 + 73259/391*e^10 + 73640/391*e^9 - 465266/391*e^8 - 110030/391*e^7 + 1398724/391*e^6 - 122340/391*e^5 - 1982394/391*e^4 + 466609/391*e^3 + 1086431/391*e^2 - 310842/391*e - 108345/391, 839/391*e^13 - 197/23*e^12 - 12164/391*e^11 + 56892/391*e^10 + 59907/391*e^9 - 366565/391*e^8 - 100837/391*e^7 + 1117588/391*e^6 - 59689/391*e^5 - 1602120/391*e^4 + 327822/391*e^3 + 882422/391*e^2 - 230617/391*e - 87075/391, -658/391*e^13 + 165/23*e^12 + 8824/391*e^11 - 46464/391*e^10 - 37415/391*e^9 + 291317/391*e^8 + 35924/391*e^7 - 865469/391*e^6 + 122455/391*e^5 + 1214815/391*e^4 - 295788/391*e^3 - 661782/391*e^2 + 178201/391*e + 67543/391, 1177/391*e^13 - 287/23*e^12 - 15986/391*e^11 + 80649/391*e^10 + 69501/391*e^9 - 504301/391*e^8 - 73951/391*e^7 + 1494396/391*e^6 - 213017/391*e^5 - 2097022/391*e^4 + 551102/391*e^3 + 1151854/391*e^2 - 336591/391*e - 120406/391, 574/391*e^13 - 141/23*e^12 - 7423/391*e^11 + 38436/391*e^10 + 29286/391*e^9 - 231408/391*e^8 - 18410/391*e^7 + 656410/391*e^6 - 122138/391*e^5 - 879032/391*e^4 + 250108/391*e^3 + 461871/391*e^2 - 136451/391*e - 47282/391, -235/391*e^13 + 54/23*e^12 + 3319/391*e^11 - 15142/391*e^10 - 15904/391*e^9 + 94574/391*e^8 + 26124/391*e^7 - 280190/391*e^6 + 16336/391*e^5 + 391830/391*e^4 - 87485/391*e^3 - 210042/391*e^2 + 61381/391*e + 18844/391, -2413/391*e^13 + 581/23*e^12 + 32970/391*e^11 - 162915/391*e^10 - 145880/391*e^9 + 1015598/391*e^8 + 173693/391*e^7 - 2996328/391*e^6 + 369948/391*e^5 + 4176882/391*e^4 - 1038140/391*e^3 - 2267655/391*e^2 + 646882/391*e + 229735/391, 1352/391*e^13 - 337/23*e^12 - 17634/391*e^11 + 93073/391*e^10 + 70438/391*e^9 - 569712/391*e^8 - 45728/391*e^7 + 1647210/391*e^6 - 299730/391*e^5 - 2248616/391*e^4 + 631150/391*e^3 + 1196983/391*e^2 - 358208/391*e - 120421/391, -689/391*e^13 + 164/23*e^12 + 9355/391*e^11 - 45405/391*e^10 - 41453/391*e^9 + 278995/391*e^8 + 53140/391*e^7 - 811269/391*e^6 + 83337/391*e^5 + 1116093/391*e^4 - 253121/391*e^3 - 599365/391*e^2 + 158968/391*e + 62094/391, 30/17*e^13 - 7*e^12 - 436/17*e^11 + 2022/17*e^10 + 2154/17*e^9 - 13026/17*e^8 - 3654/17*e^7 + 39684/17*e^6 - 2016/17*e^5 - 56810/17*e^4 + 11530/17*e^3 + 31261/17*e^2 - 8084/17*e - 3218/17, 1066/391*e^13 - 252/23*e^12 - 15182/391*e^11 + 72219/391*e^10 + 72095/391*e^9 - 461708/391*e^8 - 105743/391*e^7 + 1398963/391*e^6 - 136395/391*e^5 - 2001201/391*e^4 + 494705/391*e^3 + 1109732/391*e^2 - 326917/391*e - 111046/391, 179/391*e^13 - 38/23*e^12 - 2776/391*e^11 + 10963/391*e^10 + 15698/391*e^9 - 70014/391*e^8 - 39472/391*e^7 + 208330/391*e^6 + 40440/391*e^5 - 283450/391*e^4 - 5007/391*e^3 + 140892/391*e^2 - 10218/391*e - 11723/391, 1671/391*e^13 - 415/23*e^12 - 21963/391*e^11 + 115070/391*e^10 + 88997/391*e^9 - 707773/391*e^8 - 62387/391*e^7 + 2057086/391*e^6 - 371905/391*e^5 - 2821002/391*e^4 + 802242/391*e^3 + 1504494/391*e^2 - 457038/391*e - 151315/391, 92/17*e^13 - 22*e^12 - 1260/17*e^11 + 6160/17*e^10 + 5606/17*e^9 - 38328/17*e^8 - 6840/17*e^7 + 112810/17*e^6 - 13710/17*e^5 - 156798/17*e^4 + 39314/17*e^3 + 84808/17*e^2 - 24392/17*e - 8470/17, -1101/391*e^13 + 262/23*e^12 + 15277/391*e^11 - 74000/391*e^10 - 69389/391*e^9 + 464937/391*e^8 + 90167/391*e^7 - 1381511/391*e^6 + 153503/391*e^5 + 1935021/391*e^4 - 465906/391*e^3 - 1051193/391*e^2 + 289638/391*e + 108703/391, -1266/391*e^13 + 296/23*e^12 + 18015/391*e^11 - 84016/391*e^10 - 86795/391*e^9 + 531157/391*e^8 + 142751/391*e^7 - 1589471/391*e^6 + 84011/391*e^5 + 2240251/391*e^4 - 452243/391*e^3 - 1214875/391*e^2 + 316488/391*e + 115029/391, 364/391*e^13 - 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1481157/391*e^3 - 2919003/391*e^2 + 871696/391*e + 279401/391, 406/391*e^13 - 70/23*e^12 - 7749/391*e^11 + 23162/391*e^10 + 54865/391*e^9 - 169067/391*e^8 - 175363/391*e^7 + 569469/391*e^6 + 238607/391*e^5 - 867083/391*e^4 - 74679/391*e^3 + 460869/391*e^2 - 50996/391*e - 23573/391, -1487/391*e^13 + 369/23*e^12 + 19341/391*e^11 - 102121/391*e^10 - 75082/391*e^9 + 626238/391*e^8 + 25587/391*e^7 - 1814160/391*e^6 + 425150/391*e^5 + 2490032/391*e^4 - 832142/391*e^3 - 1355431/391*e^2 + 436729/391*e + 156237/391, -534/391*e^13 + 146/23*e^12 + 6309/391*e^11 - 40925/391*e^10 - 15789/391*e^9 + 256149/391*e^8 - 65393/391*e^7 - 765559/391*e^6 + 385279/391*e^5 + 1099839/391*e^4 - 620119/391*e^3 - 641269/391*e^2 + 293060/391*e + 82692/391, 3459/391*e^13 - 870/23*e^12 - 44076/391*e^11 + 238529/391*e^10 + 165284/391*e^9 - 1448426/391*e^8 - 39102/391*e^7 + 4158375/391*e^6 - 952082/391*e^5 - 5657999/391*e^4 + 1810713/391*e^3 + 3033858/391*e^2 - 984656/391*e - 315867/391, 3053/391*e^13 - 754/23*e^12 - 39846/391*e^11 + 207938/391*e^10 + 158903/391*e^9 - 1271930/391*e^8 - 95211/391*e^7 + 3682355/391*e^6 - 732437/391*e^5 - 5054841/391*e^4 + 1548350/391*e^3 + 2732126/391*e^2 - 875401/391*e - 284083/391, -1215/391*e^13 + 288/23*e^12 + 16145/391*e^11 - 77913/391*e^10 - 70339/391*e^9 + 464551/391*e^8 + 98687/391*e^7 - 1300403/391*e^6 + 64869/391*e^5 + 1701589/391*e^4 - 254312/391*e^3 - 845397/391*e^2 + 167500/391*e + 72104/391, 2885/391*e^13 - 706/23*e^12 - 39781/391*e^11 + 201266/391*e^10 + 176662/391*e^9 - 1280360/391*e^8 - 195860/391*e^7 + 3865595/391*e^6 - 550770/391*e^5 - 5524995/391*e^4 + 1473803/391*e^3 + 3086934/391*e^2 - 914675/391*e - 332318/391, 8294/391*e^13 - 2028/23*e^12 - 111772/391*e^11 + 567621/391*e^10 + 478624/391*e^9 - 3531718/391*e^8 - 476926/391*e^7 + 10401453/391*e^6 - 1548892/391*e^5 - 14474223/391*e^4 + 3832958/391*e^3 + 7831848/391*e^2 - 2297444/391*e - 791905/391, 910/391*e^13 - 214/23*e^12 - 14200/391*e^11 + 65856/391*e^10 + 75487/391*e^9 - 453449/391*e^8 - 131867/391*e^7 + 1473096/391*e^6 - 125361/391*e^5 - 2236240/391*e^4 + 590401/391*e^3 + 1293577/391*e^2 - 409803/391*e - 127153/391, -3443/391*e^13 + 872/23*e^12 + 44647/391*e^11 - 241245/391*e^10 - 176620/391*e^9 + 1480844/391*e^8 + 110056/391*e^7 - 4298768/391*e^6 + 752202/391*e^5 + 5894198/391*e^4 - 1568343/391*e^3 - 3141902/391*e^2 + 905523/391*e + 307353/391, 5637/391*e^13 - 1328/23*e^12 - 79592/391*e^11 + 376918/391*e^10 + 375806/391*e^9 - 2381962/391*e^8 - 571024/391*e^7 + 7122798/391*e^6 - 536206/391*e^5 - 10036198/391*e^4 + 2164311/391*e^3 + 5459402/391*e^2 - 1439954/391*e - 539270/391, 128/23*e^13 - 556/23*e^12 - 1642/23*e^11 + 9046/23*e^10 + 6257/23*e^9 - 55503/23*e^8 - 2009/23*e^7 + 160923/23*e^6 - 34695/23*e^5 - 219807/23*e^4 + 67979/23*e^3 + 116069/23*e^2 - 37433/23*e - 11555/23, 2272/391*e^13 - 544/23*e^12 - 32308/391*e^11 + 156254/391*e^10 + 153698/391*e^9 - 1002020/391*e^8 - 232856/391*e^7 + 3047565/391*e^6 - 243472/391*e^5 - 4378531/391*e^4 + 957888/391*e^3 + 2443560/391*e^2 - 639222/391*e - 254166/391, -2140/391*e^13 + 457/23*e^12 + 33793/391*e^11 - 135260/391*e^10 - 191698/391*e^9 + 892740/391*e^8 + 449318/391*e^7 - 2776018/391*e^6 - 254434/391*e^5 + 4026822/391*e^4 - 480694/391*e^3 - 2211189/391*e^2 + 479719/391*e + 209536/391, -3736/391*e^13 + 890/23*e^12 + 51419/391*e^11 - 249083/391*e^10 - 232368/391*e^9 + 1548908/391*e^8 + 310538/391*e^7 - 4555411/391*e^6 + 454216/391*e^5 + 6323877/391*e^4 - 1461222/391*e^3 - 3409348/391*e^2 + 935145/391*e + 331743/391, -269/23*e^13 + 1070/23*e^12 + 3845/23*e^11 - 18007/23*e^10 - 18449/23*e^9 + 114828/23*e^8 + 28613/23*e^7 - 346563/23*e^6 + 27127/23*e^5 + 492487/23*e^4 - 112006/23*e^3 - 269294/23*e^2 + 75154/23*e + 26132/23, 3260/391*e^13 - 800/23*e^12 - 43871/391*e^11 + 223532/391*e^10 + 188780/391*e^9 - 1387850/391*e^8 - 203472/391*e^7 + 4074804/391*e^6 - 528404/391*e^5 - 5634510/391*e^4 + 1368674/391*e^3 + 2994786/391*e^2 - 845317/391*e - 279230/391]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([31, 31, -w^3 + 6*w + 2])] = 1

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