/*
  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, -6, -7, 0, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([23,23,-w^2 + 2*w + 5])

primes_array = [
[4, 2, w^3 - w^2 - 5*w - 2],\
[9, 3, w^3 - w^2 - 5*w - 1],\
[11, 11, -w^3 + w^2 + 6*w + 2],\
[11, 11, w - 1],\
[13, 13, w^3 - 2*w^2 - 4*w + 2],\
[13, 13, -w^2 + w + 4],\
[23, 23, w^2 - 2*w - 2],\
[23, 23, w^3 - w^2 - 6*w - 3],\
[23, 23, -w^2 + 2*w + 5],\
[23, 23, -w + 2],\
[37, 37, 2*w^3 - 2*w^2 - 12*w - 1],\
[37, 37, w^3 - 2*w^2 - 5*w + 2],\
[37, 37, w^3 - 2*w^2 - 5*w + 3],\
[37, 37, -w^3 + w^2 + 6*w - 2],\
[47, 47, w^2 - 2*w - 1],\
[47, 47, w^2 - 2*w - 6],\
[59, 59, 2*w - 1],\
[59, 59, -2*w^3 + 2*w^2 + 12*w + 3],\
[73, 73, -w^3 + w^2 + 7*w + 1],\
[83, 83, -w^3 + w^2 + 4*w + 3],\
[83, 83, 2*w^3 - 2*w^2 - 11*w - 4],\
[107, 107, w^3 - w^2 - 4*w - 5],\
[107, 107, -2*w^3 + 2*w^2 + 11*w + 6],\
[121, 11, 2*w^3 - 2*w^2 - 10*w - 3],\
[131, 131, 2*w^3 - 3*w^2 - 7*w + 2],\
[131, 131, 3*w^3 - 2*w^2 - 18*w - 6],\
[157, 157, -2*w^3 + 2*w^2 + 9*w],\
[157, 157, -2*w^3 + 4*w^2 + 8*w - 3],\
[167, 167, -2*w^3 + w^2 + 11*w + 10],\
[167, 167, -3*w^3 + 4*w^2 + 14*w + 4],\
[169, 13, -2*w^3 + 2*w^2 + 10*w + 7],\
[179, 179, -w^3 + 6*w + 2],\
[179, 179, 2*w^3 - 3*w^2 - 9*w + 4],\
[181, 181, 2*w^2 - w - 8],\
[181, 181, 3*w^3 - 5*w^2 - 14*w + 3],\
[181, 181, -3*w^3 + 3*w^2 + 18*w + 2],\
[181, 181, w^3 - 7*w - 9],\
[191, 191, -2*w^3 + 3*w^2 + 10*w + 1],\
[191, 191, w^2 - 6],\
[193, 193, w^3 - 3*w^2 - 4*w + 3],\
[193, 193, 2*w^3 - 4*w^2 - 9*w + 8],\
[229, 229, -2*w^3 + 2*w^2 + 13*w + 3],\
[229, 229, w^2 - w - 8],\
[239, 239, w^3 - 7*w - 2],\
[239, 239, -w^3 + 2*w^2 + 3*w - 5],\
[241, 241, -3*w^3 + 3*w^2 + 16*w + 2],\
[241, 241, 2*w^3 - 2*w^2 - 9*w - 1],\
[251, 251, -2*w^3 + 3*w^2 + 8*w - 3],\
[251, 251, -2*w^3 + w^2 + 12*w + 4],\
[251, 251, w^3 + w^2 - 7*w - 7],\
[251, 251, 2*w^3 - 3*w^2 - 10*w - 2],\
[263, 263, 3*w^3 - 4*w^2 - 16*w],\
[263, 263, w^2 + w - 4],\
[277, 277, 2*w^2 - w - 7],\
[277, 277, 3*w^3 - 5*w^2 - 14*w + 4],\
[313, 313, 2*w^3 - 4*w^2 - 9*w + 3],\
[313, 313, -w^3 + 3*w^2 + 4*w - 8],\
[337, 337, 2*w^3 - 2*w^2 - 13*w - 1],\
[337, 337, w^3 - w^2 - 8*w - 2],\
[347, 347, 4*w^3 - 4*w^2 - 22*w + 1],\
[347, 347, -2*w^3 + 5*w^2 + 6*w - 10],\
[347, 347, -4*w^3 + 5*w^2 + 20*w + 3],\
[347, 347, -3*w^2 + 4*w + 9],\
[349, 349, -4*w^3 + 5*w^2 + 19*w + 4],\
[349, 349, -w^3 + 4*w^2 + w - 11],\
[349, 349, 2*w^3 - 3*w^2 - 9*w - 4],\
[349, 349, w^3 - 6*w - 10],\
[361, 19, -w^3 + 3*w^2 + 4*w - 4],\
[361, 19, -2*w^3 + 4*w^2 + 9*w - 7],\
[397, 397, 3*w^3 - 3*w^2 - 14*w - 6],\
[397, 397, -2*w^3 + 5*w^2 + 6*w - 6],\
[397, 397, 3*w^2 - 4*w - 13],\
[397, 397, -4*w^3 + 4*w^2 + 21*w + 7],\
[409, 409, 2*w^3 - 4*w^2 - 10*w + 7],\
[409, 409, -2*w^3 + 4*w^2 + 10*w - 3],\
[421, 421, w^3 - w^2 - 6*w - 6],\
[421, 421, w - 5],\
[431, 431, -3*w^3 + 4*w^2 + 18*w - 4],\
[431, 431, 2*w^3 - 3*w^2 - 6*w + 3],\
[433, 433, 2*w^3 - 15*w - 12],\
[433, 433, w^3 - w^2 - 9*w - 5],\
[443, 443, -3*w^3 + 5*w^2 + 14*w - 9],\
[443, 443, 2*w^3 - 12*w - 13],\
[457, 457, -w^3 + 2*w^2 + 5*w - 8],\
[457, 457, -2*w^3 + 4*w^2 + 9*w - 4],\
[457, 457, 2*w^3 - 2*w^2 - 14*w - 5],\
[457, 457, -w^3 + 3*w^2 + 4*w - 7],\
[467, 467, -2*w^3 + 3*w^2 + 8*w - 4],\
[467, 467, -2*w^3 + w^2 + 12*w + 3],\
[479, 479, w^3 + w^2 - 8*w - 7],\
[479, 479, 2*w^3 - 14*w - 9],\
[479, 479, -2*w^3 + 4*w^2 + 6*w - 5],\
[479, 479, -2*w^3 + 4*w^2 + 7*w - 6],\
[491, 491, -2*w^3 + 3*w^2 + 11*w + 2],\
[491, 491, -w^3 + 2*w^2 + 6*w - 6],\
[541, 541, -4*w^2 + 6*w + 15],\
[541, 541, -2*w^3 + 6*w^2 + 4*w - 11],\
[563, 563, -2*w^3 + w^2 + 14*w],\
[563, 563, -w^2 + 4*w + 9],\
[577, 577, w^2 - 4*w - 4],\
[577, 577, -2*w^3 + w^2 + 14*w + 5],\
[587, 587, w^3 - 4*w^2 + 6],\
[587, 587, -w^3 + 3*w^2 + 6*w - 7],\
[587, 587, 4*w^3 - 6*w^2 - 21*w + 2],\
[587, 587, 3*w^3 - 5*w^2 - 14*w],\
[599, 599, 2*w^3 - 2*w^2 - 7*w - 3],\
[599, 599, 5*w^3 - 5*w^2 - 28*w - 6],\
[601, 601, w^3 + w^2 - 10*w - 10],\
[601, 601, 2*w^3 - 3*w^2 - 10*w - 5],\
[613, 613, w^2 - 4*w - 3],\
[613, 613, 2*w^3 - w^2 - 14*w - 6],\
[625, 5, -5],\
[647, 647, -3*w^3 + 4*w^2 + 17*w + 1],\
[647, 647, -w^3 + 2*w^2 + 7*w - 4],\
[659, 659, -5*w^3 + 7*w^2 + 23*w + 3],\
[659, 659, w^3 - 2*w^2 - w - 2],\
[659, 659, -w^3 + 2*w^2 + 2*w - 6],\
[659, 659, -2*w^3 + w^2 + 13*w + 2],\
[683, 683, -2*w^3 + 3*w^2 + 8*w - 5],\
[683, 683, -2*w^3 + w^2 + 12*w + 2],\
[709, 709, w^3 + w^2 - 10*w - 8],\
[709, 709, 2*w^2 - 5*w - 7],\
[719, 719, w^3 - 5*w - 10],\
[719, 719, -3*w^3 + 4*w^2 + 15*w + 5],\
[733, 733, -w^3 + w^2 + 4*w - 5],\
[733, 733, 2*w^2 - 5*w - 6],\
[733, 733, -2*w^3 + 2*w^2 + 11*w - 4],\
[733, 733, w^3 + w^2 - 10*w - 9],\
[743, 743, -w^3 + 3*w^2 + 2*w - 10],\
[743, 743, 2*w^2 - 3*w - 3],\
[757, 757, 2*w^3 - 3*w^2 - 8*w - 5],\
[757, 757, w^3 - 9*w - 5],\
[757, 757, -2*w^3 + w^2 + 12*w + 12],\
[757, 757, w^3 - 9*w - 4],\
[769, 769, -4*w^3 + 4*w^2 + 21*w + 6],\
[769, 769, 3*w^3 - 3*w^2 - 14*w - 5],\
[827, 827, -2*w^3 + w^2 + 12*w + 1],\
[827, 827, -4*w^3 + 4*w^2 + 22*w + 7],\
[827, 827, 2*w^3 - 2*w^2 - 8*w - 5],\
[827, 827, -2*w^3 + 3*w^2 + 8*w - 6],\
[829, 829, -3*w^3 + w^2 + 17*w + 11],\
[829, 829, -4*w^3 + 2*w^2 + 23*w + 16],\
[839, 839, w^2 + 2*w - 4],\
[839, 839, 2*w^3 + w^2 - 14*w - 13],\
[839, 839, -4*w^3 + 7*w^2 + 16*w - 6],\
[839, 839, -4*w^3 + 5*w^2 + 22*w + 1],\
[863, 863, 2*w^3 - 13*w - 8],\
[863, 863, 3*w^3 - 5*w^2 - 12*w + 5],\
[887, 887, 2*w^2 + w - 7],\
[887, 887, -5*w^3 + 7*w^2 + 26*w - 2],\
[911, 911, -3*w^3 + 3*w^2 + 17*w + 7],\
[911, 911, 2*w^2 - 9],\
[911, 911, w^3 - w^2 - 3*w - 5],\
[911, 911, 4*w^3 - 6*w^2 - 20*w + 1],\
[937, 937, -4*w^3 + 5*w^2 + 22*w - 7],\
[937, 937, 4*w^3 - 4*w^2 - 21*w - 2],\
[937, 937, -4*w^2 + 8*w + 13],\
[937, 937, 3*w^3 - 3*w^2 - 14*w - 1],\
[947, 947, 3*w^3 - 4*w^2 - 12*w - 6],\
[947, 947, 3*w^3 - 5*w^2 - 10*w + 4],\
[947, 947, -3*w^3 + 4*w^2 + 19*w + 3],\
[947, 947, -3*w^3 + 4*w^2 + 19*w - 4],\
[971, 971, -3*w^3 + 5*w^2 + 13*w - 7],\
[971, 971, w^3 + w^2 - 7*w - 5],\
[983, 983, -5*w^3 + 8*w^2 + 23*w - 2],\
[983, 983, -w^3 + w^2 + 3*w + 7],\
[1009, 1009, w^3 - w^2 - 6*w - 7],\
[1009, 1009, w - 6],\
[1033, 1033, 4*w^3 - 4*w^2 - 21*w - 5],\
[1033, 1033, -3*w^3 + 3*w^2 + 14*w + 4],\
[1069, 1069, -w^2 - 3],\
[1069, 1069, 2*w^3 - 3*w^2 - 10*w + 8],\
[1103, 1103, -w^3 + 2*w^2 + 7*w - 5],\
[1103, 1103, 3*w^3 - 3*w^2 - 19*w - 7],\
[1103, 1103, 2*w^3 - 11*w - 12],\
[1103, 1103, 3*w^3 - 4*w^2 - 17*w - 2],\
[1117, 1117, -3*w^3 + 3*w^2 + 14*w + 2],\
[1117, 1117, 4*w^3 - 4*w^2 - 21*w - 3],\
[1129, 1129, -w^3 + 2*w^2 + 5*w - 9],\
[1129, 1129, -2*w^3 + w^2 + 15*w + 2],\
[1151, 1151, -3*w^2 + 5*w + 8],\
[1151, 1151, 3*w^3 - 3*w^2 - 18*w - 11],\
[1153, 1153, 3*w^3 - 3*w^2 - 14*w - 3],\
[1153, 1153, -4*w^3 + 4*w^2 + 21*w + 4],\
[1163, 1163, -w^3 + 3*w^2 + w - 9],\
[1163, 1163, -w^3 - w^2 + 9*w + 5],\
[1187, 1187, -3*w^3 + 4*w^2 + 18*w - 6],\
[1187, 1187, -2*w^3 + 11*w + 5],\
[1187, 1187, 2*w^3 - 3*w^2 - 13*w - 4],\
[1187, 1187, 5*w^3 - 7*w^2 - 24*w + 6],\
[1201, 1201, -5*w^3 + 5*w^2 + 30*w + 4],\
[1201, 1201, -5*w - 1],\
[1213, 1213, -6*w^3 + 7*w^2 + 31*w - 2],\
[1213, 1213, 2*w^3 - 6*w^2 - 5*w + 14],\
[1249, 1249, 3*w^3 - 3*w^2 - 13*w - 1],\
[1249, 1249, 3*w^3 - 2*w^2 - 15*w - 4],\
[1249, 1249, -5*w^3 + 6*w^2 + 25*w - 1],\
[1249, 1249, -5*w^3 + 5*w^2 + 27*w + 3],\
[1283, 1283, -w^3 - 3*w^2 + 12*w + 15],\
[1283, 1283, -2*w^3 + 6*w^2 + 3*w - 12],\
[1297, 1297, 5*w^3 - 7*w^2 - 22*w - 2],\
[1297, 1297, 6*w^3 - 8*w^2 - 29*w + 2],\
[1307, 1307, -5*w^3 + 6*w^2 + 27*w + 2],\
[1307, 1307, -3*w^3 + 2*w^2 + 19*w + 2],\
[1319, 1319, 3*w - 4],\
[1319, 1319, -3*w^3 + 3*w^2 + 18*w + 7],\
[1321, 1321, -5*w^3 + 5*w^2 + 27*w + 5],\
[1321, 1321, 4*w^3 - 7*w^2 - 18*w + 7],\
[1367, 1367, -3*w^3 + 4*w^2 + 12*w - 4],\
[1367, 1367, 4*w^3 - 3*w^2 - 23*w - 4],\
[1381, 1381, -2*w^3 + 2*w^2 + 12*w - 5],\
[1381, 1381, 2*w^3 - 16*w - 13],\
[1381, 1381, -2*w - 7],\
[1381, 1381, 2*w^2 - 6*w - 3],\
[1427, 1427, 3*w^3 - 5*w^2 - 15*w - 1],\
[1427, 1427, -w^3 + 3*w^2 + 5*w - 11],\
[1429, 1429, -w^3 + 4*w^2 + 2*w - 10],\
[1429, 1429, 2*w^3 - 5*w^2 - 7*w + 8],\
[1439, 1439, 4*w^3 - 5*w^2 - 22*w - 2],\
[1439, 1439, w^2 + 2*w - 5],\
[1451, 1451, 3*w^3 - 5*w^2 - 12*w + 6],\
[1451, 1451, 3*w^3 - w^2 - 19*w - 9],\
[1451, 1451, 3*w^3 - 5*w^2 - 11*w + 5],\
[1451, 1451, 2*w^3 - 13*w - 7],\
[1453, 1453, 5*w^3 - 6*w^2 - 25*w - 2],\
[1453, 1453, 3*w^3 - 6*w^2 - 13*w + 10],\
[1487, 1487, 4*w^3 - 5*w^2 - 20*w - 6],\
[1487, 1487, 2*w^3 - w^2 - 10*w - 11],\
[1487, 1487, -3*w^3 + 4*w^2 + 16*w + 4],\
[1487, 1487, w^2 + w - 8],\
[1489, 1489, -4*w^3 + 3*w^2 + 22*w + 7],\
[1489, 1489, -4*w^3 + 5*w^2 + 18*w],\
[1499, 1499, 3*w^3 - 4*w^2 - 16*w - 6],\
[1499, 1499, w^2 + w - 10],\
[1511, 1511, -2*w^3 + w^2 + 9*w + 8],\
[1511, 1511, -5*w^3 + 6*w^2 + 26*w + 4],\
[1523, 1523, 2*w^3 - 5*w^2 - 4*w + 9],\
[1523, 1523, 6*w^3 - 6*w^2 - 33*w + 1],\
[1559, 1559, 2*w^3 - 14*w - 7],\
[1559, 1559, -2*w^3 + 4*w^2 + 6*w - 7],\
[1571, 1571, -4*w^3 + 6*w^2 + 23*w - 7],\
[1571, 1571, -4*w^3 + 8*w^2 + 15*w - 11],\
[1571, 1571, 5*w^3 - 7*w^2 - 23*w - 5],\
[1571, 1571, 4*w^3 - w^2 - 28*w - 13],\
[1597, 1597, w^2 - 5*w - 4],\
[1597, 1597, 5*w^3 - 6*w^2 - 25*w - 1],\
[1597, 1597, -3*w^3 + 2*w^2 + 20*w + 6],\
[1597, 1597, 3*w^3 - 2*w^2 - 15*w - 6],\
[1607, 1607, 3*w^3 - 4*w^2 - 13*w + 6],\
[1607, 1607, 4*w^3 - 3*w^2 - 24*w - 4],\
[1607, 1607, -3*w^3 + 2*w^2 + 17*w + 1],\
[1607, 1607, -2*w^3 + 3*w^2 + 6*w - 5],\
[1609, 1609, -2*w^3 + 2*w^2 + 11*w - 5],\
[1609, 1609, -w^3 + w^2 + 4*w - 6],\
[1609, 1609, w^3 - 6*w^2 + 5*w + 13],\
[1609, 1609, -4*w^3 + 3*w^2 + 21*w + 18],\
[1619, 1619, -3*w^3 + 4*w^2 + 17*w + 3],\
[1619, 1619, -w^3 + 2*w^2 + 7*w - 6],\
[1621, 1621, -w^3 + 2*w^2 + 3*w - 10],\
[1621, 1621, -w^3 + 7*w - 3],\
[1657, 1657, -4*w^3 + 3*w^2 + 22*w + 9],\
[1657, 1657, -4*w^3 + 5*w^2 + 18*w + 2],\
[1667, 1667, 2*w^3 + w^2 - 14*w - 12],\
[1667, 1667, 3*w^3 - 5*w^2 - 15*w - 3],\
[1667, 1667, -4*w^3 + 6*w^2 + 17*w - 5],\
[1667, 1667, 3*w^3 - w^2 - 18*w - 8],\
[1669, 1669, 2*w^3 - 3*w^2 - 15*w - 2],\
[1669, 1669, 2*w^3 - 5*w^2 - 8*w + 18],\
[1681, 41, 4*w^3 - 3*w^2 - 22*w - 8],\
[1681, 41, -4*w^3 + 5*w^2 + 18*w + 1],\
[1693, 1693, -4*w^3 + 4*w^2 + 21*w - 5],\
[1693, 1693, -3*w^3 + 3*w^2 + 14*w - 6],\
[1741, 1741, 2*w^3 - 5*w^2 - 11*w + 4],\
[1741, 1741, -5*w^2 + 7*w + 22],\
[1787, 1787, 4*w^3 - 6*w^2 - 19*w - 2],\
[1787, 1787, 4*w^3 - 4*w^2 - 22*w - 9],\
[1787, 1787, 2*w^3 - 2*w^2 - 8*w - 7],\
[1787, 1787, w^3 + w^2 - 6*w - 13],\
[1801, 1801, 4*w^2 - 4*w - 19],\
[1801, 1801, 3*w^3 - 2*w^2 - 19*w - 16],\
[1801, 1801, -w^3 + 4*w^2 - 2*w - 8],\
[1801, 1801, 4*w^3 - 8*w^2 - 16*w + 5],\
[1811, 1811, 2*w^3 + 2*w^2 - 16*w - 17],\
[1811, 1811, -4*w^3 + 8*w^2 + 14*w - 9],\
[1823, 1823, -3*w^3 + 8*w^2 + 7*w - 14],\
[1823, 1823, -4*w^3 + 4*w^2 + 24*w + 7],\
[1823, 1823, 4*w - 3],\
[1823, 1823, -w^3 - 4*w^2 + 13*w + 19],\
[1847, 1847, 3*w^2 - 2*w - 19],\
[1847, 1847, -7*w^3 + 8*w^2 + 39*w + 2],\
[1861, 1861, -w^3 - 3*w^2 + 8*w + 17],\
[1861, 1861, -6*w^3 + 10*w^2 + 27*w - 6],\
[1861, 1861, -w^3 + 4*w^2 + 3*w - 8],\
[1861, 1861, -3*w^3 + 6*w^2 + 13*w - 9],\
[1871, 1871, 2*w^3 + 2*w^2 - 17*w - 17],\
[1871, 1871, w^3 - 5*w^2 + w + 9],\
[1871, 1871, -5*w^3 + 4*w^2 + 30*w + 12],\
[1871, 1871, -w^3 + 5*w^2 - w - 17],\
[1873, 1873, -4*w^3 + 7*w^2 + 22*w - 5],\
[1873, 1873, 4*w^3 - 2*w^2 - 24*w - 21],\
[1873, 1873, 4*w^2 - 5*w - 17],\
[1873, 1873, -4*w^3 + 6*w^2 + 16*w + 7],\
[1907, 1907, -4*w^3 + 6*w^2 + 15*w + 6],\
[1907, 1907, 3*w^3 - 2*w^2 - 14*w - 10],\
[1907, 1907, -6*w^3 + 9*w^2 + 28*w - 1],\
[1907, 1907, 6*w^3 - 7*w^2 - 31*w - 6],\
[1931, 1931, 6*w^3 - 7*w^2 - 34*w - 2],\
[1931, 1931, 3*w^3 - 20*w - 14],\
[1933, 1933, -3*w^3 + 6*w^2 + 13*w - 6],\
[1933, 1933, w^3 - 10*w - 6],\
[1933, 1933, -2*w^3 + w^2 + 15*w + 4],\
[1933, 1933, -w^3 + 4*w^2 + 3*w - 11],\
[1993, 1993, 6*w^3 - 7*w^2 - 31*w],\
[1993, 1993, 5*w^3 - 8*w^2 - 25*w + 9]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^6 - 16*x^4 + 25*x^2 - 8
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, -1/10*e^5 + 6/5*e^3 + 23/10*e, 1/5*e^4 - 17/5*e^2 + 12/5, 2/5*e^5 - 29/5*e^3 + 9/5*e, -9/10*e^5 + 69/5*e^3 - 133/10*e, 9/10*e^5 - 69/5*e^3 + 133/10*e, -2/5*e^5 + 29/5*e^3 - 14/5*e, -2/5*e^4 + 29/5*e^2 - 44/5, 1, -1/5*e^5 + 17/5*e^3 - 47/5*e, 4/5*e^4 - 63/5*e^2 + 28/5, -7/10*e^5 + 52/5*e^3 - 49/10*e, -3/10*e^5 + 23/5*e^3 - 61/10*e, 1/5*e^4 - 12/5*e^2 - 8/5, e^5 - 15*e^3 + 10*e, -e^4 + 15*e^2 - 16, 2/5*e^5 - 29/5*e^3 + 9/5*e, 4/5*e^4 - 58/5*e^2 + 8/5, -1/5*e^4 + 17/5*e^2 - 2/5, -4/5*e^5 + 63/5*e^3 - 68/5*e, -2*e^4 + 29*e^2 - 20, 8/5*e^5 - 121/5*e^3 + 106/5*e, 9/5*e^4 - 128/5*e^2 + 88/5, -11/10*e^5 + 86/5*e^3 - 257/10*e, -7/5*e^4 + 114/5*e^2 - 144/5, -4/5*e^5 + 58/5*e^3 - 8/5*e, 3/2*e^5 - 22*e^3 + 21/2*e, -3/10*e^5 + 23/5*e^3 - 61/10*e, -1/5*e^5 + 12/5*e^3 + 28/5*e, -2/5*e^4 + 29/5*e^2 - 44/5, 14/5*e^4 - 213/5*e^2 + 138/5, -19/5*e^5 + 293/5*e^3 - 313/5*e, 2*e^2 - 12, 1/10*e^5 - 11/5*e^3 + 57/10*e, 5/2*e^5 - 39*e^3 + 83/2*e, 3/5*e^4 - 51/5*e^2 + 36/5, 2/5*e^4 - 29/5*e^2 + 4/5, -4*e^4 + 59*e^2 - 44, 7/5*e^5 - 104/5*e^3 + 79/5*e, 1/2*e^5 - 6*e^3 - 31/2*e, 3/10*e^5 - 23/5*e^3 + 111/10*e, -8/5*e^4 + 116/5*e^2 - 46/5, -6/5*e^4 + 82/5*e^2 - 62/5, -21/5*e^5 + 317/5*e^3 - 242/5*e, -2*e^2 + 4, 47/10*e^5 - 357/5*e^3 + 609/10*e, 23/10*e^5 - 178/5*e^3 + 331/10*e, -3*e^4 + 45*e^2 - 44, -1/5*e^5 + 12/5*e^3 + 23/5*e, -17/5*e^5 + 264/5*e^3 - 289/5*e, 2*e^4 - 31*e^2 + 8, 7/5*e^4 - 99/5*e^2 + 44/5, -e^3 + 19*e, -33/10*e^5 + 248/5*e^3 - 411/10*e, 1/2*e^5 - 8*e^3 + 13/2*e, 29/10*e^5 - 224/5*e^3 + 553/10*e, 13/10*e^5 - 108/5*e^3 + 421/10*e, 11/5*e^4 - 172/5*e^2 + 212/5, 2*e^4 - 30*e^2 + 16, 16/5*e^5 - 247/5*e^3 + 247/5*e, -3/5*e^4 + 66/5*e^2 - 156/5, -12/5*e^4 + 194/5*e^2 - 244/5, 1/5*e^5 - 17/5*e^3 + 72/5*e, -3/2*e^5 + 23*e^3 - 45/2*e, 21/10*e^5 - 166/5*e^3 + 457/10*e, -9/5*e^4 + 128/5*e^2 - 8/5, -e^4 + 14*e^2 - 28, 37/10*e^5 - 287/5*e^3 + 599/10*e, -5/2*e^5 + 39*e^3 - 83/2*e, -9/2*e^5 + 69*e^3 - 125/2*e, -23/10*e^5 + 168/5*e^3 - 51/10*e, -13/10*e^5 + 113/5*e^3 - 551/10*e, -9/10*e^5 + 74/5*e^3 - 333/10*e, -23/10*e^5 + 193/5*e^3 - 731/10*e, -27/10*e^5 + 207/5*e^3 - 489/10*e, e^2 - 18, 1/5*e^4 - 27/5*e^2 + 22/5, 24/5*e^5 - 373/5*e^3 + 453/5*e, -2/5*e^4 + 39/5*e^2 - 164/5, 24/5*e^4 - 373/5*e^2 + 348/5, -16/5*e^4 + 242/5*e^2 - 92/5, 4/5*e^4 - 58/5*e^2 + 28/5, 4/5*e^5 - 63/5*e^3 + 133/5*e, -7/5*e^4 + 114/5*e^2 - 124/5, -7/10*e^5 + 52/5*e^3 - 49/10*e, 26/5*e^4 - 387/5*e^2 + 292/5, 49/10*e^5 - 384/5*e^3 + 893/10*e, -2*e^4 + 31*e^2 - 12, -3*e^5 + 47*e^3 - 58*e, 31/5*e^5 - 472/5*e^3 + 387/5*e, -12/5*e^5 + 174/5*e^3 - 49/5*e, 27/5*e^4 - 409/5*e^2 + 304/5, -3*e^4 + 47*e^2 - 40, -e^4 + 16*e^2 - 20, 4*e^5 - 62*e^3 + 59*e, -15/2*e^5 + 115*e^3 - 225/2*e, 3/2*e^5 - 25*e^3 + 89/2*e, 17/5*e^5 - 259/5*e^3 + 234/5*e, 9/5*e^4 - 153/5*e^2 + 148/5, 7/5*e^4 - 109/5*e^2 + 84/5, 4/5*e^4 - 73/5*e^2 + 88/5, 23/5*e^5 - 341/5*e^3 + 216/5*e, -3/5*e^5 + 31/5*e^3 + 129/5*e, 4/5*e^4 - 68/5*e^2 + 28/5, e^4 - 15*e^2 + 8, 21/5*e^5 - 322/5*e^3 + 307/5*e, 14/5*e^4 - 208/5*e^2 + 68/5, -19/5*e^4 + 303/5*e^2 - 328/5, 14/5*e^4 - 193/5*e^2 + 28/5, -16/5*e^4 + 232/5*e^2 - 72/5, -8/5*e^4 + 116/5*e^2 + 4/5, 26/5*e^4 - 402/5*e^2 + 362/5, 4/5*e^4 - 78/5*e^2 + 228/5, -24/5*e^5 + 368/5*e^3 - 363/5*e, 13/5*e^4 - 201/5*e^2 + 276/5, 11/5*e^5 - 187/5*e^3 + 382/5*e, 16/5*e^4 - 257/5*e^2 + 252/5, -22/5*e^5 + 339/5*e^3 - 289/5*e, -20, -2/5*e^5 + 29/5*e^3 - 59/5*e, 26/5*e^4 - 392/5*e^2 + 222/5, 29/5*e^4 - 443/5*e^2 + 438/5, -7*e^5 + 108*e^3 - 110*e, -3/5*e^4 + 51/5*e^2 - 56/5, 4/5*e^4 - 43/5*e^2 - 2/5, -4*e^4 + 62*e^2 - 52, -4/5*e^4 + 63/5*e^2 - 58/5, 26/5*e^4 - 392/5*e^2 + 332/5, 4*e^4 - 62*e^2 + 44, -12/5*e^5 + 179/5*e^3 - 99/5*e, -17/5*e^4 + 259/5*e^2 - 224/5, 36/5*e^4 - 532/5*e^2 + 362/5, 36/5*e^4 - 557/5*e^2 + 472/5, 21/5*e^4 - 297/5*e^2 + 202/5, -9/10*e^5 + 79/5*e^3 - 373/10*e, -37/10*e^5 + 277/5*e^3 - 489/10*e, 19/5*e^5 - 308/5*e^3 + 513/5*e, -12/5*e^4 + 209/5*e^2 - 344/5, e^5 - 17*e^3 + 32*e, -22/5*e^4 + 324/5*e^2 - 164/5, -11/10*e^5 + 81/5*e^3 - 77/10*e, 11/2*e^5 - 85*e^3 + 193/2*e, -33/5*e^5 + 501/5*e^3 - 396/5*e, 7/5*e^5 - 94/5*e^3 - 81/5*e, 1/5*e^4 - 42/5*e^2 + 212/5, 5*e^4 - 79*e^2 + 80, -9/5*e^5 + 138/5*e^3 - 123/5*e, -12/5*e^4 + 174/5*e^2 - 44/5, 31/5*e^5 - 482/5*e^3 + 522/5*e, 36/5*e^4 - 532/5*e^2 + 432/5, 3*e^4 - 46*e^2 + 24, -e^5 + 16*e^3 - 26*e, 23/5*e^5 - 366/5*e^3 + 581/5*e, 6*e^4 - 86*e^2 + 48, -2*e^4 + 30*e^2 + 6, 41/10*e^5 - 306/5*e^3 + 517/10*e, -6/5*e^4 + 102/5*e^2 - 2/5, -7/10*e^5 + 57/5*e^3 - 49/10*e, -e^5 + 14*e^3 + 6*e, -26/5*e^4 + 412/5*e^2 - 432/5, -2/5*e^4 + 4/5*e^2 + 196/5, 31/5*e^5 - 477/5*e^3 + 552/5*e, 12/5*e^4 - 164/5*e^2 - 16/5, 3*e^5 - 47*e^3 + 70*e, 16, 24/5*e^5 - 368/5*e^3 + 373/5*e, -4/5*e^4 + 58/5*e^2 + 12/5, -12/5*e^4 + 184/5*e^2 - 84/5, -7/2*e^5 + 55*e^3 - 133/2*e, 21/10*e^5 - 156/5*e^3 + 227/10*e, -23/5*e^4 + 351/5*e^2 - 286/5, 33/5*e^4 - 501/5*e^2 + 386/5, -3*e^5 + 47*e^3 - 53*e, 14/5*e^4 - 193/5*e^2 + 28/5, 41/5*e^5 - 632/5*e^3 + 637/5*e, -8/5*e^4 + 116/5*e^2 + 64/5, -1/10*e^5 + 11/5*e^3 - 87/10*e, 63/10*e^5 - 483/5*e^3 + 1041/10*e, -2/5*e^4 + 49/5*e^2 - 74/5, -42/5*e^4 + 619/5*e^2 - 554/5, 2*e^5 - 30*e^3 + 8*e, 14/5*e^4 - 183/5*e^2 - 32/5, -49/10*e^5 + 374/5*e^3 - 653/10*e, -3/10*e^5 + 13/5*e^3 + 279/10*e, 14/5*e^4 - 223/5*e^2 + 28/5, -1/5*e^5 - 3/5*e^3 + 218/5*e, 26/5*e^5 - 392/5*e^3 + 247/5*e, 22/5*e^5 - 329/5*e^3 + 149/5*e, 38/5*e^4 - 606/5*e^2 + 576/5, 11/5*e^4 - 182/5*e^2 + 112/5, 31/5*e^4 - 447/5*e^2 + 382/5, 4/5*e^4 - 93/5*e^2 + 318/5, -101/10*e^5 + 771/5*e^3 - 1367/10*e, -19/2*e^5 + 145*e^3 - 253/2*e, -57/10*e^5 + 427/5*e^3 - 559/10*e, 37/10*e^5 - 267/5*e^3 + 139/10*e, 33/10*e^5 - 263/5*e^3 + 891/10*e, 5/2*e^5 - 41*e^3 + 135/2*e, 8/5*e^5 - 141/5*e^3 + 451/5*e, 13/5*e^4 - 191/5*e^2 + 76/5, 19/10*e^5 - 154/5*e^3 + 503/10*e, 89/10*e^5 - 669/5*e^3 + 1103/10*e, -53/5*e^4 + 796/5*e^2 - 656/5, -56/5*e^5 + 857/5*e^3 - 727/5*e, 1/5*e^5 - 7/5*e^3 - 138/5*e, -29/5*e^4 + 423/5*e^2 - 428/5, 17/2*e^5 - 131*e^3 + 261/2*e, 63/10*e^5 - 483/5*e^3 + 981/10*e, -43/5*e^4 + 651/5*e^2 - 516/5, 8/5*e^5 - 116/5*e^3 + 96/5*e, -4/5*e^4 + 88/5*e^2 - 348/5, -19/5*e^4 + 298/5*e^2 - 318/5, 4/5*e^4 - 48/5*e^2 - 152/5, 29/5*e^4 - 458/5*e^2 + 338/5, -3/5*e^4 + 46/5*e^2 - 196/5, -4/5*e^5 + 48/5*e^3 + 162/5*e, 15/2*e^5 - 113*e^3 + 137/2*e, -3/10*e^5 + 43/5*e^3 - 541/10*e, -18/5*e^4 + 261/5*e^2 - 16/5, 33/5*e^5 - 516/5*e^3 + 621/5*e, -e^4 + 20*e^2 - 28, -39/5*e^5 + 603/5*e^3 - 608/5*e, -12/5*e^4 + 214/5*e^2 - 284/5, -3*e^5 + 49*e^3 - 86*e, -43/10*e^5 + 338/5*e^3 - 1031/10*e, -13/2*e^5 + 98*e^3 - 129/2*e, -3/5*e^4 + 21/5*e^2 + 4/5, -61/5*e^5 + 942/5*e^3 - 957/5*e, 33/5*e^4 - 486/5*e^2 + 476/5, 41/5*e^5 - 637/5*e^3 + 692/5*e, 47/10*e^5 - 347/5*e^3 + 269/10*e, -5/2*e^5 + 36*e^3 + 27/2*e, 16/5*e^4 - 252/5*e^2 + 32/5, -9/5*e^5 + 143/5*e^3 - 253/5*e, 17/5*e^5 - 264/5*e^3 + 254/5*e, -13/5*e^4 + 161/5*e^2 - 16/5, -48/5*e^4 + 736/5*e^2 - 596/5, 12*e^5 - 183*e^3 + 163*e, -27/5*e^5 + 419/5*e^3 - 449/5*e, 48/5*e^4 - 731/5*e^2 + 456/5, -3*e^5 + 50*e^3 - 83*e, 33/5*e^4 - 521/5*e^2 + 536/5, -3/5*e^4 + 71/5*e^2 - 116/5, -63/5*e^5 + 956/5*e^3 - 856/5*e, e^4 - 11*e^2 + 22, -15/2*e^5 + 115*e^3 - 217/2*e, e^4 - 19*e^2 + 86, 43/10*e^5 - 313/5*e^3 + 91/10*e, -22/5*e^4 + 344/5*e^2 - 404/5, -7/5*e^5 + 119/5*e^3 - 349/5*e, -11*e^5 + 165*e^3 - 122*e, 22/5*e^4 - 344/5*e^2 + 284/5, e^4 - 23*e^2 + 80, -7*e^4 + 105*e^2 - 72, 17/5*e^4 - 269/5*e^2 + 124/5, 33/5*e^4 - 476/5*e^2 + 376/5, -18/5*e^4 + 286/5*e^2 - 336/5, -47/5*e^5 + 714/5*e^3 - 659/5*e, -8*e^4 + 115*e^2 - 62, -42/5*e^4 + 644/5*e^2 - 654/5, 67/10*e^5 - 502/5*e^3 + 719/10*e, 83/10*e^5 - 628/5*e^3 + 1121/10*e, 32/5*e^5 - 479/5*e^3 + 409/5*e, -32/5*e^4 + 484/5*e^2 - 504/5, -9/5*e^4 + 148/5*e^2 - 188/5, -26/5*e^5 + 422/5*e^3 - 662/5*e, -23/5*e^4 + 381/5*e^2 - 436/5, -7*e^4 + 102*e^2 - 108, -19/10*e^5 + 164/5*e^3 - 783/10*e, 57/10*e^5 - 432/5*e^3 + 809/10*e, 1/5*e^4 - 22/5*e^2 + 52/5, 4*e^4 - 54*e^2 + 24, -21/10*e^5 + 156/5*e^3 - 117/10*e, 3/10*e^5 - 13/5*e^3 - 449/10*e, -2*e^4 + 33*e^2 + 16, 11/5*e^4 - 192/5*e^2 + 432/5, 52/5*e^5 - 794/5*e^3 + 769/5*e, -31/5*e^5 + 487/5*e^3 - 597/5*e, -63/10*e^5 + 483/5*e^3 - 961/10*e, -52/5*e^4 + 754/5*e^2 - 484/5, 4*e^4 - 61*e^2 + 52, -51/10*e^5 + 381/5*e^3 - 447/10*e, -24/5*e^5 + 388/5*e^3 - 683/5*e, -2/5*e^4 + 34/5*e^2 - 244/5, 34/5*e^4 - 518/5*e^2 + 468/5, -8/5*e^4 + 106/5*e^2 + 24/5, 51/5*e^5 - 787/5*e^3 + 777/5*e, 1/5*e^5 - 7/5*e^3 - 158/5*e, 5*e^5 - 78*e^3 + 91*e, -6/5*e^4 + 82/5*e^2 - 252/5, 29/10*e^5 - 214/5*e^3 + 193/10*e, -109/10*e^5 + 824/5*e^3 - 1313/10*e, -73/10*e^5 + 543/5*e^3 - 651/10*e, 31/10*e^5 - 261/5*e^3 + 1057/10*e, -26/5*e^5 + 407/5*e^3 - 402/5*e, 6/5*e^5 - 102/5*e^3 + 242/5*e, -22/5*e^4 + 334/5*e^2 - 284/5, -48/5*e^4 + 721/5*e^2 - 456/5, -81/10*e^5 + 601/5*e^3 - 757/10*e, -33/5*e^4 + 501/5*e^2 - 486/5, -9/2*e^5 + 71*e^3 - 207/2*e, -13*e^4 + 197*e^2 - 150, 64/5*e^5 - 973/5*e^3 + 878/5*e, 5*e^5 - 75*e^3 + 72*e, 43/5*e^4 - 651/5*e^2 + 576/5, -46/5*e^4 + 692/5*e^2 - 452/5, 2/5*e^4 - 29/5*e^2 - 196/5, -16/5*e^5 + 267/5*e^3 - 562/5*e, 11/10*e^5 - 81/5*e^3 + 237/10*e, 2*e^4 - 27*e^2 + 18, -7*e^4 + 102*e^2 - 62, 5/2*e^5 - 33*e^3 - 53/2*e, -81/10*e^5 + 621/5*e^3 - 1227/10*e, 119/10*e^5 - 909/5*e^3 + 1793/10*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^2 + 2*w + 5])] = -1

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