/*
  This code can be loaded, or copied and pasted, into Magma.
  It will load the data associated to the HMF, including
  the field, level, and Hecke and Atkin-Lehner eigenvalue data.
  At the *bottom* of the file, there is code to recreate the
  Hilbert modular form in Magma, by creating the HMF space
  and cutting out the corresponding Hecke irreducible subspace.
  From there, you can ask for more eigenvalues or modify as desired.
  It is commented out, as this computation may be lengthy.
*/

P<x> := PolynomialRing(Rationals());
g := P![-3, 0, 1];
F<w> := NumberField(g);
ZF := Integers(F);

NN := ideal<ZF | {49, 7, -7}>;

primesArray := [
[2, 2, -w + 1],
[3, 3, w],
[11, 11, -2*w + 1],
[11, 11, 2*w + 1],
[13, 13, w + 4],
[13, 13, -w + 4],
[23, 23, -3*w + 2],
[23, 23, 3*w + 2],
[25, 5, 5],
[37, 37, 2*w - 7],
[37, 37, -2*w - 7],
[47, 47, -4*w - 1],
[47, 47, 4*w - 1],
[49, 7, -7],
[59, 59, 5*w - 4],
[59, 59, -5*w - 4],
[61, 61, -w - 8],
[61, 61, w - 8],
[71, 71, 5*w - 2],
[71, 71, -5*w - 2],
[73, 73, 3*w - 10],
[73, 73, -3*w - 10],
[83, 83, 6*w - 5],
[83, 83, -6*w - 5],
[97, 97, -w - 10],
[97, 97, w - 10],
[107, 107, -6*w - 1],
[107, 107, 6*w - 1],
[109, 109, 2*w - 11],
[109, 109, -2*w - 11],
[131, 131, -7*w - 4],
[131, 131, 7*w - 4],
[157, 157, 2*w - 13],
[157, 157, -2*w - 13],
[167, 167, 8*w - 5],
[167, 167, -8*w - 5],
[179, 179, 9*w - 8],
[179, 179, -9*w - 8],
[181, 181, 5*w - 16],
[181, 181, -5*w - 16],
[191, 191, -8*w - 1],
[191, 191, 8*w - 1],
[193, 193, -w - 14],
[193, 193, w - 14],
[227, 227, 9*w - 4],
[227, 227, -9*w - 4],
[229, 229, 3*w - 16],
[229, 229, -3*w - 16],
[239, 239, 9*w - 2],
[239, 239, -9*w - 2],
[241, 241, 4*w - 17],
[241, 241, -4*w - 17],
[251, 251, -10*w - 7],
[251, 251, 10*w - 7],
[263, 263, 11*w - 10],
[263, 263, -11*w - 10],
[277, 277, 2*w - 17],
[277, 277, -2*w - 17],
[289, 17, -17],
[311, 311, 12*w - 11],
[311, 311, -12*w - 11],
[313, 313, -4*w - 19],
[313, 313, 4*w - 19],
[337, 337, 7*w - 22],
[337, 337, -7*w - 22],
[347, 347, -11*w - 4],
[347, 347, 11*w - 4],
[349, 349, 2*w - 19],
[349, 349, -2*w - 19],
[359, 359, 11*w - 2],
[359, 359, -11*w - 2],
[361, 19, -19],
[373, 373, -3*w - 20],
[373, 373, 3*w - 20],
[383, 383, 12*w - 7],
[383, 383, -12*w - 7],
[397, 397, -w - 20],
[397, 397, w - 20],
[409, 409, -5*w - 22],
[409, 409, 5*w - 22],
[419, 419, 14*w - 13],
[419, 419, -14*w - 13],
[421, 421, -6*w - 23],
[421, 421, 6*w - 23],
[431, 431, -12*w - 1],
[431, 431, 12*w - 1],
[433, 433, -9*w - 26],
[433, 433, 9*w - 26],
[443, 443, -13*w - 8],
[443, 443, 13*w - 8],
[457, 457, 3*w - 22],
[457, 457, -3*w - 22],
[467, 467, 14*w - 11],
[467, 467, -14*w - 11],
[479, 479, 15*w - 14],
[479, 479, -15*w - 14],
[491, 491, 13*w - 4],
[491, 491, -13*w - 4],
[503, 503, 13*w - 2],
[503, 503, -13*w - 2],
[541, 541, 9*w - 28],
[541, 541, -9*w - 28],
[563, 563, -14*w - 5],
[563, 563, 14*w - 5],
[577, 577, 4*w - 25],
[577, 577, -4*w - 25],
[587, 587, -14*w - 1],
[587, 587, 14*w - 1],
[599, 599, -16*w - 13],
[599, 599, 16*w - 13],
[601, 601, 5*w - 26],
[601, 601, -5*w - 26],
[613, 613, 2*w - 25],
[613, 613, -2*w - 25],
[647, 647, -16*w - 11],
[647, 647, 16*w - 11],
[659, 659, -15*w - 4],
[659, 659, 15*w - 4],
[661, 661, -11*w - 32],
[661, 661, 11*w - 32],
[673, 673, -w - 26],
[673, 673, w - 26],
[683, 683, 18*w - 17],
[683, 683, -18*w - 17],
[709, 709, 5*w - 28],
[709, 709, -5*w - 28],
[719, 719, -16*w - 7],
[719, 719, 16*w - 7],
[733, 733, -6*w - 29],
[733, 733, 6*w - 29],
[743, 743, 16*w - 5],
[743, 743, -16*w - 5],
[757, 757, 3*w - 28],
[757, 757, -3*w - 28],
[769, 769, -8*w - 31],
[769, 769, 8*w - 31],
[827, 827, -19*w - 16],
[827, 827, 19*w - 16],
[829, 829, 2*w - 29],
[829, 829, -2*w - 29],
[839, 839, 20*w - 19],
[839, 839, -20*w - 19],
[841, 29, -29],
[853, 853, 6*w - 31],
[853, 853, -6*w - 31],
[863, 863, 17*w - 2],
[863, 863, -17*w - 2],
[877, 877, 7*w - 32],
[877, 877, -7*w - 32],
[887, 887, 19*w - 14],
[887, 887, -19*w - 14],
[911, 911, 20*w - 17],
[911, 911, -20*w - 17],
[937, 937, -13*w - 38],
[937, 937, 13*w - 38],
[947, 947, 18*w - 5],
[947, 947, -18*w - 5],
[961, 31, -31],
[971, 971, -18*w - 1],
[971, 971, 18*w - 1],
[983, 983, -19*w - 10],
[983, 983, 19*w - 10],
[997, 997, -3*w - 32],
[997, 997, 3*w - 32],
[1009, 1009, -7*w - 34],
[1009, 1009, 7*w - 34],
[1019, 1019, 19*w - 8],
[1019, 1019, -19*w - 8],
[1021, 1021, -w - 32],
[1021, 1021, w - 32],
[1031, 1031, 20*w - 13],
[1031, 1031, -20*w - 13],
[1033, 1033, 8*w - 35],
[1033, 1033, -8*w - 35],
[1069, 1069, 10*w - 37],
[1069, 1069, -10*w - 37],
[1091, 1091, -22*w - 19],
[1091, 1091, 22*w - 19],
[1093, 1093, 13*w - 40],
[1093, 1093, -13*w - 40],
[1103, 1103, 23*w - 22],
[1103, 1103, -23*w - 22],
[1117, 1117, -6*w - 35],
[1117, 1117, 6*w - 35],
[1129, 1129, 3*w - 34],
[1129, 1129, -3*w - 34],
[1151, 1151, -20*w - 7],
[1151, 1151, 20*w - 7],
[1153, 1153, -w - 34],
[1153, 1153, w - 34],
[1163, 1163, 22*w - 17],
[1163, 1163, -22*w - 17],
[1187, 1187, 23*w - 20],
[1187, 1187, -23*w - 20],
[1201, 1201, -9*w - 38],
[1201, 1201, 9*w - 38],
[1213, 1213, 2*w - 35],
[1213, 1213, -2*w - 35],
[1223, 1223, 21*w - 10],
[1223, 1223, -21*w - 10],
[1237, 1237, -11*w - 40],
[1237, 1237, 11*w - 40],
[1249, 1249, 12*w - 41],
[1249, 1249, -12*w - 41],
[1259, 1259, -21*w - 8],
[1259, 1259, 21*w - 8],
[1283, 1283, 22*w - 13],
[1283, 1283, -22*w - 13],
[1297, 1297, -7*w - 38],
[1297, 1297, 7*w - 38],
[1307, 1307, 21*w - 4],
[1307, 1307, -21*w - 4],
[1319, 1319, 21*w - 2],
[1319, 1319, -21*w - 2],
[1321, 1321, 4*w - 37],
[1321, 1321, -4*w - 37],
[1367, 1367, 24*w - 19],
[1367, 1367, -24*w - 19],
[1381, 1381, 10*w - 41],
[1381, 1381, -10*w - 41],
[1427, 1427, -22*w - 5],
[1427, 1427, 22*w - 5],
[1429, 1429, -13*w - 44],
[1429, 1429, 13*w - 44],
[1439, 1439, 24*w - 17],
[1439, 1439, -24*w - 17],
[1451, 1451, -22*w - 1],
[1451, 1451, 22*w - 1],
[1453, 1453, 7*w - 40],
[1453, 1453, -7*w - 40],
[1487, 1487, -23*w - 10],
[1487, 1487, 23*w - 10],
[1489, 1489, 8*w - 41],
[1489, 1489, -8*w - 41],
[1499, 1499, 26*w - 23],
[1499, 1499, -26*w - 23],
[1511, 1511, 27*w - 26],
[1511, 1511, -27*w - 26],
[1523, 1523, -23*w - 8],
[1523, 1523, 23*w - 8],
[1549, 1549, -10*w - 43],
[1549, 1549, 10*w - 43],
[1559, 1559, 24*w - 13],
[1559, 1559, -24*w - 13],
[1571, 1571, -23*w - 4],
[1571, 1571, 23*w - 4],
[1583, 1583, 23*w - 2],
[1583, 1583, -23*w - 2],
[1597, 1597, -w - 40],
[1597, 1597, w - 40],
[1607, 1607, -24*w - 11],
[1607, 1607, 24*w - 11],
[1609, 1609, 13*w - 46],
[1609, 1609, -13*w - 46],
[1619, 1619, -25*w - 16],
[1619, 1619, 25*w - 16],
[1621, 1621, 14*w - 47],
[1621, 1621, -14*w - 47],
[1657, 1657, 8*w - 43],
[1657, 1657, -8*w - 43],
[1667, 1667, -26*w - 19],
[1667, 1667, 26*w - 19],
[1669, 1669, 2*w - 41],
[1669, 1669, -2*w - 41],
[1681, 41, -41],
[1693, 1693, -9*w - 44],
[1693, 1693, 9*w - 44],
[1741, 1741, 6*w - 43],
[1741, 1741, -6*w - 43],
[1753, 1753, -11*w - 46],
[1753, 1753, 11*w - 46],
[1777, 1777, -12*w - 47],
[1777, 1777, 12*w - 47],
[1787, 1787, 27*w - 20],
[1787, 1787, -27*w - 20],
[1789, 1789, -7*w - 44],
[1789, 1789, 7*w - 44],
[1801, 1801, -4*w - 43],
[1801, 1801, 4*w - 43],
[1811, 1811, 25*w - 8],
[1811, 1811, -25*w - 8],
[1823, 1823, -28*w - 23],
[1823, 1823, 28*w - 23],
[1847, 1847, 29*w - 26],
[1847, 1847, -29*w - 26],
[1849, 43, -43],
[1861, 1861, -5*w - 44],
[1861, 1861, 5*w - 44],
[1871, 1871, 25*w - 2],
[1871, 1871, -25*w - 2],
[1873, 1873, 9*w - 46],
[1873, 1873, -9*w - 46],
[1907, 1907, 26*w - 11],
[1907, 1907, -26*w - 11],
[1931, 1931, 27*w - 16],
[1931, 1931, -27*w - 16],
[1933, 1933, -w - 44],
[1933, 1933, w - 44],
[1979, 1979, 26*w - 7],
[1979, 1979, -26*w - 7],
[1993, 1993, 13*w - 50],
[1993, 1993, -13*w - 50],
[2003, 2003, 26*w - 5],
[2003, 2003, -26*w - 5],
[2017, 2017, -8*w - 47],
[2017, 2017, 8*w - 47],
[2027, 2027, -26*w - 1],
[2027, 2027, 26*w - 1],
[2029, 2029, -15*w - 52],
[2029, 2029, 15*w - 52],
[2039, 2039, -29*w - 22],
[2039, 2039, 29*w - 22],
[2053, 2053, 18*w - 55],
[2053, 2053, -18*w - 55],
[2063, 2063, -28*w - 17],
[2063, 2063, 28*w - 17],
[2087, 2087, 27*w - 10],
[2087, 2087, -27*w - 10],
[2089, 2089, 3*w - 46],
[2089, 2089, -3*w - 46],
[2099, 2099, -31*w - 28],
[2099, 2099, 31*w - 28],
[2111, 2111, 32*w - 31],
[2111, 2111, -32*w - 31],
[2113, 2113, -w - 46],
[2113, 2113, w - 46],
[2137, 2137, 11*w - 50],
[2137, 2137, -11*w - 50],
[2161, 2161, -4*w - 47],
[2161, 2161, 4*w - 47],
[2207, 2207, -31*w - 26],
[2207, 2207, 31*w - 26],
[2221, 2221, -14*w - 53],
[2221, 2221, 14*w - 53],
[2243, 2243, 33*w - 32],
[2243, 2243, -33*w - 32],
[2267, 2267, 29*w - 16],
[2267, 2267, -29*w - 16],
[2269, 2269, 17*w - 56],
[2269, 2269, -17*w - 56],
[2281, 2281, -20*w - 59],
[2281, 2281, 20*w - 59],
[2293, 2293, 6*w - 49],
[2293, 2293, -6*w - 49],
[2339, 2339, 30*w - 19],
[2339, 2339, -30*w - 19],
[2341, 2341, -11*w - 52],
[2341, 2341, 11*w - 52],
[2351, 2351, -28*w - 1],
[2351, 2351, 28*w - 1],
[2377, 2377, 12*w - 53],
[2377, 2377, -12*w - 53],
[2389, 2389, 2*w - 49],
[2389, 2389, -2*w - 49],
[2399, 2399, 31*w - 22],
[2399, 2399, -31*w - 22],
[2411, 2411, 30*w - 17],
[2411, 2411, -30*w - 17],
[2423, 2423, -29*w - 10],
[2423, 2423, 29*w - 10],
[2437, 2437, -14*w - 55],
[2437, 2437, 14*w - 55],
[2447, 2447, -32*w - 25],
[2447, 2447, 32*w - 25],
[2459, 2459, -29*w - 8],
[2459, 2459, 29*w - 8],
[2473, 2473, -3*w - 50],
[2473, 2473, 3*w - 50],
[2521, 2521, 20*w - 61],
[2521, 2521, -20*w - 61],
[2531, 2531, -30*w - 13],
[2531, 2531, 30*w - 13],
[2543, 2543, -32*w - 23],
[2543, 2543, 32*w - 23],
[2557, 2557, -7*w - 52],
[2557, 2557, 7*w - 52],
[2579, 2579, -30*w - 11],
[2579, 2579, 30*w - 11],
[2591, 2591, -33*w - 26],
[2591, 2591, 33*w - 26],
[2593, 2593, -12*w - 55],
[2593, 2593, 12*w - 55],
[2617, 2617, -8*w - 53],
[2617, 2617, 8*w - 53],
[2663, 2663, 36*w - 35],
[2663, 2663, -36*w - 35],
[2677, 2677, 3*w - 52],
[2677, 2677, -3*w - 52],
[2687, 2687, 31*w - 14],
[2687, 2687, -31*w - 14],
[2689, 2689, 15*w - 58],
[2689, 2689, -15*w - 58],
[2699, 2699, -30*w - 1],
[2699, 2699, 30*w - 1],
[2711, 2711, 32*w - 19],
[2711, 2711, -32*w - 19],
[2713, 2713, 16*w - 59],
[2713, 2713, -16*w - 59],
[2749, 2749, -18*w - 61],
[2749, 2749, 18*w - 61],
[2797, 2797, 2*w - 53],
[2797, 2797, -2*w - 53],
[2809, 53, -53],
[2819, 2819, -31*w - 8],
[2819, 2819, 31*w - 8],
[2833, 2833, -8*w - 55],
[2833, 2833, 8*w - 55],
[2843, 2843, -34*w - 25],
[2843, 2843, 34*w - 25],
[2857, 2857, -13*w - 58],
[2857, 2857, 13*w - 58],
[2879, 2879, 31*w - 2],
[2879, 2879, -31*w - 2],
[2903, 2903, -32*w - 13],
[2903, 2903, 32*w - 13],
[2917, 2917, 6*w - 55],
[2917, 2917, -6*w - 55],
[2927, 2927, -36*w - 31],
[2927, 2927, 36*w - 31],
[2939, 2939, -34*w - 23],
[2939, 2939, 34*w - 23],
[2953, 2953, 16*w - 61],
[2953, 2953, -16*w - 61],
[2963, 2963, 38*w - 37],
[2963, 2963, -38*w - 37],
[2999, 2999, 35*w - 26],
[2999, 2999, -35*w - 26],
[3001, 3001, 11*w - 58],
[3001, 3001, -11*w - 58],
[3011, 3011, 33*w - 16],
[3011, 3011, -33*w - 16],
[3023, 3023, 32*w - 7],
[3023, 3023, -32*w - 7],
[3037, 3037, 22*w - 67],
[3037, 3037, -22*w - 67],
[3049, 3049, -12*w - 59],
[3049, 3049, 12*w - 59],
[3061, 3061, 5*w - 56],
[3061, 3061, -5*w - 56],
[3083, 3083, 37*w - 32],
[3083, 3083, -37*w - 32],
[3109, 3109, -3*w - 56],
[3109, 3109, 3*w - 56],
[3119, 3119, 39*w - 38],
[3119, 3119, -39*w - 38],
[3121, 3121, -9*w - 58],
[3121, 3121, 9*w - 58],
[3167, 3167, -33*w - 10],
[3167, 3167, 33*w - 10],
[3169, 3169, -15*w - 62],
[3169, 3169, 15*w - 62],
[3181, 3181, -10*w - 59],
[3181, 3181, 10*w - 59],
[3191, 3191, -35*w - 22],
[3191, 3191, 35*w - 22],
[3203, 3203, 33*w - 8],
[3203, 3203, -33*w - 8],
[3217, 3217, -7*w - 58],
[3217, 3217, 7*w - 58],
[3229, 3229, 17*w - 64],
[3229, 3229, -17*w - 64],
[3251, 3251, 33*w - 4],
[3251, 3251, -33*w - 4],
[3253, 3253, 18*w - 65],
[3253, 3253, -18*w - 65],
[3299, 3299, 34*w - 13],
[3299, 3299, -34*w - 13],
[3301, 3301, -21*w - 68],
[3301, 3301, 21*w - 68],
[3313, 3313, 23*w - 70],
[3313, 3313, -23*w - 70],
[3323, 3323, -37*w - 28],
[3323, 3323, 37*w - 28],
[3347, 3347, 34*w - 11],
[3347, 3347, -34*w - 11],
[3359, 3359, -36*w - 23],
[3359, 3359, 36*w - 23],
[3361, 3361, -w - 58],
[3361, 3361, w - 58],
[3371, 3371, 38*w - 31],
[3371, 3371, -38*w - 31],
[3373, 3373, -6*w - 59],
[3373, 3373, 6*w - 59],
[3407, 3407, 39*w - 34],
[3407, 3407, -39*w - 34],
[3433, 3433, -4*w - 59],
[3433, 3433, 4*w - 59],
[3457, 3457, 16*w - 65],
[3457, 3457, -16*w - 65],
[3467, 3467, -34*w - 1],
[3467, 3467, 34*w - 1],
[3469, 3469, 2*w - 59],
[3469, 3469, -2*w - 59],
[3491, 3491, 38*w - 29],
[3491, 3491, -38*w - 29],
[3517, 3517, 18*w - 67],
[3517, 3517, -18*w - 67],
[3527, 3527, 36*w - 19],
[3527, 3527, -36*w - 19],
[3529, 3529, -8*w - 61],
[3529, 3529, 8*w - 61],
[3539, 3539, -39*w - 32],
[3539, 3539, 39*w - 32],
[3541, 3541, 19*w - 68],
[3541, 3541, -19*w - 68],
[3613, 3613, 6*w - 61],
[3613, 3613, -6*w - 61],
[3623, 3623, 37*w - 22],
[3623, 3623, -37*w - 22],
[3637, 3637, -14*w - 65],
[3637, 3637, 14*w - 65],
[3659, 3659, -35*w - 4],
[3659, 3659, 35*w - 4],
[3671, 3671, 35*w - 2],
[3671, 3671, -35*w - 2],
[3673, 3673, 4*w - 61],
[3673, 3673, -4*w - 61],
[3697, 3697, -7*w - 62],
[3697, 3697, 7*w - 62],
[3709, 3709, 2*w - 61],
[3709, 3709, -2*w - 61],
[3719, 3719, 36*w - 13],
[3719, 3719, -36*w - 13],
[3733, 3733, 11*w - 64],
[3733, 3733, -11*w - 64],
[3767, 3767, 36*w - 11],
[3767, 3767, -36*w - 11],
[3769, 3769, -5*w - 62],
[3769, 3769, 5*w - 62],
[3779, 3779, -39*w - 28],
[3779, 3779, 39*w - 28],
[3793, 3793, 12*w - 65],
[3793, 3793, -12*w - 65],
[3803, 3803, -38*w - 23],
[3803, 3803, 38*w - 23],
[3851, 3851, -37*w - 16],
[3851, 3851, 37*w - 16],
[3853, 3853, 9*w - 64],
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[8447, 8447, 56*w - 31],
[8447, 8447, -56*w - 31],
[8461, 8461, -w - 92],
[8461, 8461, w - 92],
[8521, 8521, -19*w - 98],
[8521, 8521, 19*w - 98],
[8543, 8543, -63*w - 58],
[8543, 8543, 63*w - 58],
[8581, 8581, -26*w - 103],
[8581, 8581, 26*w - 103],
[8627, 8627, -54*w - 11],
[8627, 8627, 54*w - 11],
[8629, 8629, -27*w - 104],
[8629, 8629, 27*w - 104],
[8641, 8641, 16*w - 97],
[8641, 8641, -16*w - 97],
[8663, 8663, -61*w - 50],
[8663, 8663, 61*w - 50],
[8677, 8677, 21*w - 100],
[8677, 8677, -21*w - 100],
[8689, 8689, -7*w - 94],
[8689, 8689, 7*w - 94],
[8699, 8699, 54*w - 7],
[8699, 8699, -54*w - 7],
[8713, 8713, -29*w - 106],
[8713, 8713, 29*w - 106],
[8737, 8737, 17*w - 98],
[8737, 8737, -17*w - 98],
[8747, 8747, -54*w - 1],
[8747, 8747, 54*w - 1],
[8761, 8761, -5*w - 94],
[8761, 8761, 5*w - 94],
[8783, 8783, -56*w - 25],
[8783, 8783, 56*w - 25],
[8807, 8807, 64*w - 59],
[8807, 8807, -64*w - 59],
[8819, 8819, 55*w - 16],
[8819, 8819, -55*w - 16],
[8821, 8821, -14*w - 97],
[8821, 8821, 14*w - 97],
[8831, 8831, 65*w - 62],
[8831, 8831, -65*w - 62],
[8867, 8867, -58*w - 35],
[8867, 8867, 58*w - 35],
[8893, 8893, 38*w - 115],
[8893, 8893, -38*w - 115],
[8929, 8929, 15*w - 98],
[8929, 8929, -15*w - 98],
[8941, 8941, -25*w - 104],
[8941, 8941, 25*w - 104],
[8951, 8951, -60*w - 43],
[8951, 8951, 60*w - 43],
[8963, 8963, 57*w - 28],
[8963, 8963, -57*w - 28],
[8999, 8999, -59*w - 38],
[8999, 8999, 59*w - 38],
[9001, 9001, 20*w - 101],
[9001, 9001, -20*w - 101],
[9011, 9011, -55*w - 8],
[9011, 9011, 55*w - 8],
[9013, 9013, 2*w - 95],
[9013, 9013, -2*w - 95],
[9049, 9049, 27*w - 106],
[9049, 9049, -27*w - 106],
[9059, 9059, -55*w - 4],
[9059, 9059, 55*w - 4],
[9109, 9109, 10*w - 97],
[9109, 9109, -10*w - 97],
[9133, 9133, 17*w - 100],
[9133, 9133, -17*w - 100],
[9157, 9157, 22*w - 103],
[9157, 9157, -22*w - 103],
[9181, 9181, -30*w - 109],
[9181, 9181, 30*w - 109],
[9203, 9203, 63*w - 52],
[9203, 9203, -63*w - 52],
[9227, 9227, 61*w - 44],
[9227, 9227, -61*w - 44],
[9239, 9239, -56*w - 13],
[9239, 9239, 56*w - 13],
[9241, 9241, -11*w - 98],
[9241, 9241, 11*w - 98],
[9277, 9277, -33*w - 112],
[9277, 9277, 33*w - 112],
[9311, 9311, 65*w - 58],
[9311, 9311, -65*w - 58],
[9323, 9323, 62*w - 47],
[9323, 9323, -62*w - 47],
[9337, 9337, -36*w - 115],
[9337, 9337, 36*w - 115],
[9349, 9349, 37*w - 116],
[9349, 9349, -37*w - 116],
[9371, 9371, -67*w - 64],
[9371, 9371, 67*w - 64],
[9397, 9397, 2*w - 97],
[9397, 9397, -2*w - 97],
[9419, 9419, -59*w - 32],
[9419, 9419, 59*w - 32],
[9421, 9421, 26*w - 107],
[9421, 9421, -26*w - 107],
[9431, 9431, -60*w - 37],
[9431, 9431, 60*w - 37],
[9433, 9433, -16*w - 101],
[9433, 9433, 16*w - 101],
[9467, 9467, -58*w - 25],
[9467, 9467, 58*w - 25],
[9479, 9479, -64*w - 53],
[9479, 9479, 64*w - 53],
[9491, 9491, -57*w - 16],
[9491, 9491, 57*w - 16],
[9539, 9539, 65*w - 56],
[9539, 9539, -65*w - 56],
[9551, 9551, 57*w - 14],
[9551, 9551, -57*w - 14],
[9587, 9587, 66*w - 59],
[9587, 9587, -66*w - 59],
[9601, 9601, -w - 98],
[9601, 9601, w - 98],
[9613, 9613, 14*w - 101],
[9613, 9613, -14*w - 101],
[9623, 9623, 67*w - 62],
[9623, 9623, -67*w - 62],
[9649, 9649, 23*w - 106],
[9649, 9649, -23*w - 106],
[9661, 9661, -31*w - 112],
[9661, 9661, 31*w - 112],
[9697, 9697, -32*w - 113],
[9697, 9697, 32*w - 113],
[9719, 9719, 61*w - 38],
[9719, 9719, -61*w - 38],
[9721, 9721, 24*w - 107],
[9721, 9721, -24*w - 107],
[9733, 9733, -19*w - 104],
[9733, 9733, 19*w - 104],
[9743, 9743, 57*w - 2],
[9743, 9743, -57*w - 2],
[9767, 9767, -59*w - 26],
[9767, 9767, 59*w - 26],
[9769, 9769, 12*w - 101],
[9769, 9769, -12*w - 101],
[9781, 9781, 35*w - 116],
[9781, 9781, -35*w - 116],
[9791, 9791, 63*w - 46],
[9791, 9791, -63*w - 46],
[9803, 9803, 58*w - 17],
[9803, 9803, -58*w - 17],
[9817, 9817, 37*w - 118],
[9817, 9817, -37*w - 118],
[9829, 9829, -38*w - 119],
[9829, 9829, 38*w - 119],
[9839, 9839, 60*w - 31],
[9839, 9839, -60*w - 31],
[9851, 9851, 62*w - 41],
[9851, 9851, -62*w - 41],
[9887, 9887, -64*w - 49],
[9887, 9887, 64*w - 49],
[9901, 9901, 10*w - 101],
[9901, 9901, -10*w - 101],
[9923, 9923, -58*w - 13],
[9923, 9923, 58*w - 13],
[9949, 9949, -17*w - 104],
[9949, 9949, 17*w - 104],
[9973, 9973, 3*w - 100],
[9973, 9973, -3*w - 100]];
primes := [ideal<ZF | {F!x : x in I}> : I in primesArray];

heckePol := x^6 - 10*x^4 + 21*x^2 - 8;
K<e> := NumberField(heckePol);

heckeEigenvaluesArray := [e, -1/2*e^5 + 9/2*e^3 - 7*e, 1/2*e^5 - 5*e^3 + 17/2*e, 1/2*e^5 - 5*e^3 + 17/2*e, -1/2*e^4 + 7/2*e^2 - 2, -1/2*e^4 + 7/2*e^2 - 2, 1/2*e^5 - 4*e^3 + 7/2*e, 1/2*e^5 - 4*e^3 + 7/2*e, e^4 - 7*e^2 + 8, -e^4 + 9*e^2 - 12, -e^4 + 9*e^2 - 12, e^5 - 8*e^3 + 7*e, e^5 - 8*e^3 + 7*e, -1, -1/2*e^5 + 7/2*e^3 + 4*e, -1/2*e^5 + 7/2*e^3 + 4*e, 1/2*e^4 - 15/2*e^2 + 14, 1/2*e^4 - 15/2*e^2 + 14, -3/2*e^5 + 12*e^3 - 25/2*e, -3/2*e^5 + 12*e^3 - 25/2*e, e^4 - 7*e^2 + 6, e^4 - 7*e^2 + 6, 1/2*e^5 - 9/2*e^3 + 3*e, 1/2*e^5 - 9/2*e^3 + 3*e, -2, -2, -3/2*e^5 + 14*e^3 - 37/2*e, -3/2*e^5 + 14*e^3 - 37/2*e, -3*e^4 + 25*e^2 - 22, -3*e^4 + 25*e^2 - 22, -5/2*e^5 + 45/2*e^3 - 31*e, -5/2*e^5 + 45/2*e^3 - 31*e, -3/2*e^4 + 29/2*e^2 - 26, -3/2*e^4 + 29/2*e^2 - 26, e^3 - 3*e, e^3 - 3*e, 1/2*e^5 - 2*e^3 - 25/2*e, 1/2*e^5 - 2*e^3 - 25/2*e, 7/2*e^4 - 57/2*e^2 + 30, 7/2*e^4 - 57/2*e^2 + 30, 3/2*e^5 - 16*e^3 + 73/2*e, 3/2*e^5 - 16*e^3 + 73/2*e, e^4 - 11*e^2 + 12, e^4 - 11*e^2 + 12, 7/2*e^5 - 61/2*e^3 + 42*e, 7/2*e^5 - 61/2*e^3 + 42*e, 5/2*e^4 - 35/2*e^2 + 10, 5/2*e^4 - 35/2*e^2 + 10, -3/2*e^5 + 16*e^3 - 85/2*e, -3/2*e^5 + 16*e^3 - 85/2*e, -2*e^4 + 10*e^2 + 14, -2*e^4 + 10*e^2 + 14, -5/2*e^5 + 43/2*e^3 - 32*e, -5/2*e^5 + 43/2*e^3 - 32*e, 7/2*e^5 - 32*e^3 + 85/2*e, 7/2*e^5 - 32*e^3 + 85/2*e, 4*e^4 - 30*e^2 + 24, 4*e^4 - 30*e^2 + 24, -2*e^4 + 16*e^2 + 8, -4*e^5 + 37*e^3 - 55*e, -4*e^5 + 37*e^3 - 55*e, 3*e^4 - 21*e^2 + 10, 3*e^4 - 21*e^2 + 10, -3*e^4 + 23*e^2 - 26, -3*e^4 + 23*e^2 - 26, 3/2*e^5 - 17*e^3 + 95/2*e, 3/2*e^5 - 17*e^3 + 95/2*e, -7/2*e^4 + 65/2*e^2 - 34, -7/2*e^4 + 65/2*e^2 - 34, 1/2*e^5 - 2*e^3 - 5/2*e, 1/2*e^5 - 2*e^3 - 5/2*e, -3*e^4 + 23*e^2 - 2, -2*e^4 + 18*e^2 - 26, -2*e^4 + 18*e^2 - 26, 2*e^5 - 16*e^3 + 10*e, 2*e^5 - 16*e^3 + 10*e, 1/2*e^4 + 1/2*e^2 - 22, 1/2*e^4 + 1/2*e^2 - 22, e^4 - 3*e^2 + 6, e^4 - 3*e^2 + 6, -7/2*e^5 + 61/2*e^3 - 26*e, -7/2*e^5 + 61/2*e^3 - 26*e, -2*e^4 + 24*e^2 - 32, -2*e^4 + 24*e^2 - 32, -9/2*e^5 + 42*e^3 - 139/2*e, -9/2*e^5 + 42*e^3 - 139/2*e, 4*e^4 - 36*e^2 + 34, 4*e^4 - 36*e^2 + 34, -1/2*e^5 + 6*e^3 - 31/2*e, -1/2*e^5 + 6*e^3 - 31/2*e, -e^4 + e^2 + 30, -e^4 + e^2 + 30, -9/2*e^5 + 75/2*e^3 - 42*e, -9/2*e^5 + 75/2*e^3 - 42*e, -e^5 + 2*e^3 + 23*e, -e^5 + 2*e^3 + 23*e, 3/2*e^5 - 16*e^3 + 73/2*e, 3/2*e^5 - 16*e^3 + 73/2*e, 3*e^5 - 31*e^3 + 54*e, 3*e^5 - 31*e^3 + 54*e, 4*e^4 - 34*e^2 + 24, 4*e^4 - 34*e^2 + 24, 11/2*e^5 - 101/2*e^3 + 72*e, 11/2*e^5 - 101/2*e^3 + 72*e, 2*e^4 - 10*e^2 + 6, 2*e^4 - 10*e^2 + 6, -5/2*e^5 + 51/2*e^3 - 56*e, -5/2*e^5 + 51/2*e^3 - 56*e, 5/2*e^5 - 20*e^3 + 55/2*e, 5/2*e^5 - 20*e^3 + 55/2*e, e^4 + e^2 - 38, e^4 + e^2 - 38, -e^4 + 3*e^2 + 18, -e^4 + 3*e^2 + 18, -2*e^5 + 19*e^3 - 43*e, -2*e^5 + 19*e^3 - 43*e, 3/2*e^5 - 17*e^3 + 103/2*e, 3/2*e^5 - 17*e^3 + 103/2*e, -3/2*e^4 + 37/2*e^2 - 58, -3/2*e^4 + 37/2*e^2 - 58, 2*e^4 - 8*e^2 - 16, 2*e^4 - 8*e^2 - 16, 11/2*e^5 - 48*e^3 + 129/2*e, 11/2*e^5 - 48*e^3 + 129/2*e, e^4 - 15*e^2 + 14, e^4 - 15*e^2 + 14, 4*e^5 - 38*e^3 + 58*e, 4*e^5 - 38*e^3 + 58*e, -9/2*e^4 + 71/2*e^2 - 46, -9/2*e^4 + 71/2*e^2 - 46, -5/2*e^5 + 18*e^3 - 23/2*e, -5/2*e^5 + 18*e^3 - 23/2*e, -5*e^4 + 35*e^2 - 2, -5*e^4 + 35*e^2 - 2, 6*e^4 - 54*e^2 + 70, 6*e^4 - 54*e^2 + 70, 3/2*e^5 - 12*e^3 + 25/2*e, 3/2*e^5 - 12*e^3 + 25/2*e, -7/2*e^4 + 65/2*e^2 - 54, -7/2*e^4 + 65/2*e^2 - 54, -6*e^5 + 57*e^3 - 97*e, -6*e^5 + 57*e^3 - 97*e, -12*e^2 + 50, 1/2*e^4 - 23/2*e^2 + 42, 1/2*e^4 - 23/2*e^2 + 42, 5/2*e^5 - 22*e^3 + 67/2*e, 5/2*e^5 - 22*e^3 + 67/2*e, e^4 - 7*e^2 + 10, e^4 - 7*e^2 + 10, 6*e^5 - 59*e^3 + 91*e, 6*e^5 - 59*e^3 + 91*e, -3/2*e^5 + 16*e^3 - 37/2*e, -3/2*e^5 + 16*e^3 - 37/2*e, -11*e^4 + 85*e^2 - 86, -11*e^4 + 85*e^2 - 86, -15/2*e^5 + 67*e^3 - 159/2*e, -15/2*e^5 + 67*e^3 - 159/2*e, 4*e^2 + 26, -3/2*e^5 + 27/2*e^3 - e, -3/2*e^5 + 27/2*e^3 - e, -3*e^5 + 35*e^3 - 94*e, -3*e^5 + 35*e^3 - 94*e, 13/2*e^4 - 123/2*e^2 + 50, 13/2*e^4 - 123/2*e^2 + 50, -5*e^4 + 39*e^2 - 36, -5*e^4 + 39*e^2 - 36, 9/2*e^5 - 32*e^3 + 27/2*e, 9/2*e^5 - 32*e^3 + 27/2*e, 7/2*e^4 - 41/2*e^2 - 2, 7/2*e^4 - 41/2*e^2 - 2, 3/2*e^5 - 16*e^3 + 33/2*e, 3/2*e^5 - 16*e^3 + 33/2*e, -4*e^4 + 34*e^2 - 48, -4*e^4 + 34*e^2 - 48, 5/2*e^4 - 51/2*e^2 + 22, 5/2*e^4 - 51/2*e^2 + 22, 3/2*e^5 - 47/2*e^3 + 79*e, 3/2*e^5 - 47/2*e^3 + 79*e, -5*e^4 + 41*e^2 - 20, -5*e^4 + 41*e^2 - 20, -7/2*e^5 + 34*e^3 - 109/2*e, -7/2*e^5 + 34*e^3 - 109/2*e, 6*e^4 - 50*e^2 + 82, 6*e^4 - 50*e^2 + 82, -4*e^4 + 30*e^2 - 16, -4*e^4 + 30*e^2 - 16, 6*e^5 - 50*e^3 + 48*e, 6*e^5 - 50*e^3 + 48*e, 4*e^2 + 18, 4*e^2 + 18, -9/2*e^5 + 40*e^3 - 115/2*e, -9/2*e^5 + 40*e^3 - 115/2*e, -19/2*e^5 + 78*e^3 - 173/2*e, -19/2*e^5 + 78*e^3 - 173/2*e, -3*e^4 + 17*e^2 - 8, -3*e^4 + 17*e^2 - 8, -3*e^4 + 27*e^2 - 36, -3*e^4 + 27*e^2 - 36, 2*e^5 - 9*e^3 - 23*e, 2*e^5 - 9*e^3 - 23*e, -1/2*e^4 + 7/2*e^2 + 22, -1/2*e^4 + 7/2*e^2 + 22, 4*e^4 - 36*e^2 + 50, 4*e^4 - 36*e^2 + 50, 5/2*e^5 - 57/2*e^3 + 49*e, 5/2*e^5 - 57/2*e^3 + 49*e, 3/2*e^5 - 7*e^3 - 61/2*e, 3/2*e^5 - 7*e^3 - 61/2*e, 3*e^4 - 35*e^2 + 70, 3*e^4 - 35*e^2 + 70, 5/2*e^5 - 61/2*e^3 + 83*e, 5/2*e^5 - 61/2*e^3 + 83*e, -7*e^3 + 53*e, -7*e^3 + 53*e, -13*e^4 + 103*e^2 - 102, -13*e^4 + 103*e^2 - 102, -1/2*e^5 + 2*e^3 + 57/2*e, -1/2*e^5 + 2*e^3 + 57/2*e, 3*e^4 - 25*e^2 + 14, 3*e^4 - 25*e^2 + 14, 27/2*e^5 - 231/2*e^3 + 147*e, 27/2*e^5 - 231/2*e^3 + 147*e, 11*e^4 - 91*e^2 + 108, 11*e^4 - 91*e^2 + 108, -3/2*e^5 + 20*e^3 - 157/2*e, -3/2*e^5 + 20*e^3 - 157/2*e, 9/2*e^5 - 35*e^3 + 69/2*e, 9/2*e^5 - 35*e^3 + 69/2*e, -7*e^4 + 57*e^2 - 42, -7*e^4 + 57*e^2 - 42, 6*e^5 - 54*e^3 + 96*e, 6*e^5 - 54*e^3 + 96*e, -6*e^4 + 62*e^2 - 82, -6*e^4 + 62*e^2 - 82, -21/2*e^5 + 94*e^3 - 291/2*e, -21/2*e^5 + 94*e^3 - 291/2*e, -3*e^5 + 31*e^3 - 82*e, -3*e^5 + 31*e^3 - 82*e, -11/2*e^5 + 47*e^3 - 139/2*e, -11/2*e^5 + 47*e^3 - 139/2*e, 4*e^4 - 34*e^2 + 32, 4*e^4 - 34*e^2 + 32, 6*e^5 - 53*e^3 + 61*e, 6*e^5 - 53*e^3 + 61*e, -5/2*e^5 + 59/2*e^3 - 64*e, -5/2*e^5 + 59/2*e^3 - 64*e, 15/2*e^5 - 72*e^3 + 237/2*e, 15/2*e^5 - 72*e^3 + 237/2*e, 4*e^4 - 28*e^2 + 26, 4*e^4 - 28*e^2 + 26, 11/2*e^5 - 54*e^3 + 253/2*e, 11/2*e^5 - 54*e^3 + 253/2*e, 7*e^4 - 61*e^2 + 42, 7*e^4 - 61*e^2 + 42, -1/2*e^5 - 2*e^3 + 97/2*e, -1/2*e^5 - 2*e^3 + 97/2*e, 5*e^4 - 41*e^2 + 36, 5*e^4 - 41*e^2 + 36, -e^4 + 15*e^2 - 46, -e^4 + 15*e^2 - 46, -3/2*e^5 + 9*e^3 - 7/2*e, -3/2*e^5 + 9*e^3 - 7/2*e, 3/2*e^4 - 45/2*e^2 + 26, 3/2*e^4 - 45/2*e^2 + 26, -2*e^4 + 8*e^2 + 72, -9/2*e^4 + 39/2*e^2 + 58, -9/2*e^4 + 39/2*e^2 + 58, 9/2*e^4 - 71/2*e^2 + 22, 9/2*e^4 - 71/2*e^2 + 22, 11*e^4 - 89*e^2 + 114, 11*e^4 - 89*e^2 + 114, -8*e^4 + 80*e^2 - 94, -8*e^4 + 80*e^2 - 94, 15/2*e^5 - 63*e^3 + 111/2*e, 15/2*e^5 - 63*e^3 + 111/2*e, -2*e^4 + 16*e^2 + 8, -2*e^4 + 16*e^2 + 8, -e^4 + 7*e^2 + 20, -e^4 + 7*e^2 + 20, 11/2*e^5 - 101/2*e^3 + 88*e, 11/2*e^5 - 101/2*e^3 + 88*e, -10*e^5 + 92*e^3 - 110*e, -10*e^5 + 92*e^3 - 110*e, -3*e^5 + 35*e^3 - 106*e, -3*e^5 + 35*e^3 - 106*e, -4*e^4 + 48*e^2 - 58, -17/2*e^4 + 151/2*e^2 - 54, -17/2*e^4 + 151/2*e^2 - 54, -23/2*e^5 + 98*e^3 - 253/2*e, -23/2*e^5 + 98*e^3 - 253/2*e, 8*e^4 - 68*e^2 + 38, 8*e^4 - 68*e^2 + 38, 3/2*e^5 - 7/2*e^3 - 29*e, 3/2*e^5 - 7/2*e^3 - 29*e, -11/2*e^5 + 113/2*e^3 - 94*e, -11/2*e^5 + 113/2*e^3 - 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128, -22*e^4 + 156*e^2 - 128, -3*e^4 + 13*e^2 + 44, -3*e^4 + 13*e^2 + 44, -17/2*e^5 + 163/2*e^3 - 186*e, -17/2*e^5 + 163/2*e^3 - 186*e, -7*e^4 + 91*e^2 - 124, -7*e^4 + 91*e^2 - 124, 25/2*e^5 - 116*e^3 + 455/2*e, 25/2*e^5 - 116*e^3 + 455/2*e, -6*e^4 + 34*e^2 - 30, -6*e^4 + 34*e^2 - 30, -17/2*e^5 + 77*e^3 - 209/2*e, -17/2*e^5 + 77*e^3 - 209/2*e, 9/2*e^5 - 75/2*e^3 + 6*e, 9/2*e^5 - 75/2*e^3 + 6*e, 18*e^4 - 166*e^2 + 174, 18*e^4 - 166*e^2 + 174, 11/2*e^5 - 43*e^3 + 115/2*e, 11/2*e^5 - 43*e^3 + 115/2*e, 7/2*e^4 - 89/2*e^2 + 142, 7/2*e^4 - 89/2*e^2 + 142, e^5 + 9*e^3 - 92*e, e^5 + 9*e^3 - 92*e, 22*e^4 - 198*e^2 + 262, 22*e^4 - 198*e^2 + 262, 11/2*e^4 - 101/2*e^2 - 42, 11/2*e^4 - 101/2*e^2 - 42, -5/2*e^5 + 28*e^3 - 43/2*e, -5/2*e^5 + 28*e^3 - 43/2*e, -10*e^5 + 75*e^3 - 79*e, -10*e^5 + 75*e^3 - 79*e, 11/2*e^4 - 117/2*e^2 + 78, 11/2*e^4 - 117/2*e^2 + 78, 33/2*e^5 - 293/2*e^3 + 205*e, 33/2*e^5 - 293/2*e^3 + 205*e, -3*e^4 + 43*e^2 - 124, -3*e^4 + 43*e^2 - 124, -5*e^4 + 63*e^2 - 180, -5*e^4 + 63*e^2 - 180, -3/2*e^5 + 29/2*e^3 - 20*e, -3/2*e^5 + 29/2*e^3 - 20*e, 3*e^5 - 21*e^3 - 36*e, 3*e^5 - 21*e^3 - 36*e, -31/2*e^4 + 305/2*e^2 - 174, -31/2*e^4 + 305/2*e^2 - 174, -26*e^5 + 236*e^3 - 342*e, -26*e^5 + 236*e^3 - 342*e, -3/2*e^4 - 11/2*e^2 + 138, -3/2*e^4 - 11/2*e^2 + 138, -7*e^4 + 57*e^2 + 8, -7*e^4 + 57*e^2 + 8, 21/2*e^4 - 115/2*e^2 - 18, 21/2*e^4 - 115/2*e^2 - 18, 29/2*e^5 - 118*e^3 + 291/2*e, 29/2*e^5 - 118*e^3 + 291/2*e, -14*e^4 + 70*e^2 + 78, -14*e^4 + 70*e^2 + 78, -1/2*e^5 + 4*e^3 - 35/2*e, -1/2*e^5 + 4*e^3 - 35/2*e, 15/2*e^5 - 73*e^3 + 171/2*e, 15/2*e^5 - 73*e^3 + 171/2*e, -27/2*e^5 + 122*e^3 - 329/2*e, -27/2*e^5 + 122*e^3 - 329/2*e, -18*e^4 + 152*e^2 - 88, 13*e^4 - 113*e^2 + 148, 13*e^4 - 113*e^2 + 148, 9*e^4 - 47*e^2 - 62, 9*e^4 - 47*e^2 - 62, -10*e^4 + 72*e^2 - 20, -10*e^4 + 72*e^2 - 20, 11*e^5 - 105*e^3 + 184*e, 11*e^5 - 105*e^3 + 184*e, 1/2*e^4 - 15/2*e^2 + 6, 1/2*e^4 - 15/2*e^2 + 6, 21/2*e^5 - 94*e^3 + 283/2*e, 21/2*e^5 - 94*e^3 + 283/2*e, 12*e^4 - 74*e^2 - 16, 12*e^4 - 74*e^2 - 16, 5*e^4 - 9*e^2 - 172, 5*e^4 - 9*e^2 - 172, -3*e^5 + 30*e^3 - 23*e, -3*e^5 + 30*e^3 - 23*e, -3/2*e^5 + 23/2*e^3 + e, -3/2*e^5 + 23/2*e^3 + e, -19/2*e^5 + 197/2*e^3 - 176*e, -19/2*e^5 + 197/2*e^3 - 176*e, 16*e^2 - 82, 16*e^2 - 82, 9/2*e^5 - 57*e^3 + 345/2*e, 9/2*e^5 - 57*e^3 + 345/2*e, -24*e^4 + 192*e^2 - 174, -24*e^4 + 192*e^2 - 174, -45/2*e^5 + 209*e^3 - 637/2*e, -45/2*e^5 + 209*e^3 - 637/2*e, -51/2*e^4 + 437/2*e^2 - 254, -51/2*e^4 + 437/2*e^2 - 254, 18*e^5 - 145*e^3 + 141*e, 18*e^5 - 145*e^3 + 141*e, -24*e^4 + 180*e^2 - 142, -24*e^4 + 180*e^2 - 142, 13/2*e^5 - 75*e^3 + 393/2*e, 13/2*e^5 - 75*e^3 + 393/2*e, -11*e^4 + 87*e^2 + 28, -11*e^4 + 87*e^2 + 28, -5/2*e^5 + 57/2*e^3 - 65*e, -5/2*e^5 + 57/2*e^3 - 65*e, 21/2*e^4 - 155/2*e^2 + 66, 21/2*e^4 - 155/2*e^2 + 66, 10*e^4 - 96*e^2 + 72, 10*e^4 - 96*e^2 + 72, 13*e^4 - 123*e^2 + 234, 13*e^4 - 123*e^2 + 234, 8*e^4 - 92*e^2 + 134, 8*e^4 - 92*e^2 + 134, -11/2*e^5 + 101/2*e^3 - 96*e, -11/2*e^5 + 101/2*e^3 - 96*e, e^4 - 23*e^2 + 54, e^4 - 23*e^2 + 54, -49/2*e^5 + 214*e^3 - 591/2*e, -49/2*e^5 + 214*e^3 - 591/2*e, -7/2*e^4 + 65/2*e^2 + 6, -7/2*e^4 + 65/2*e^2 + 6, -3/2*e^5 + 18*e^3 - 165/2*e, -3/2*e^5 + 18*e^3 - 165/2*e, -8*e^5 + 74*e^3 - 102*e, -8*e^5 + 74*e^3 - 102*e, -17/2*e^4 + 119/2*e^2 - 10, -17/2*e^4 + 119/2*e^2 - 10, 17*e^4 - 117*e^2 + 98, 17*e^4 - 117*e^2 + 98, -11*e^5 + 94*e^3 - 107*e, -11*e^5 + 94*e^3 - 107*e, 29/2*e^4 - 227/2*e^2 + 54, 29/2*e^4 - 227/2*e^2 + 54, 21/2*e^5 - 245/2*e^3 + 303*e, 21/2*e^5 - 245/2*e^3 + 303*e, 13/2*e^4 - 139/2*e^2 + 154, 13/2*e^4 - 139/2*e^2 + 154, 10*e^4 - 86*e^2 + 106, 10*e^4 - 86*e^2 + 106, -23/2*e^5 + 82*e^3 - 37/2*e, -23/2*e^5 + 82*e^3 - 37/2*e, -15*e^4 + 97*e^2 - 30, -15*e^4 + 97*e^2 - 30, -36*e^2 + 114, -36*e^2 + 114, -13/2*e^5 + 135/2*e^3 - 106*e, -13/2*e^5 + 135/2*e^3 - 106*e, -9*e^4 + 47*e^2 + 70, -9*e^4 + 47*e^2 + 70, -9*e^4 + 91*e^2 - 52, -9*e^4 + 91*e^2 - 52, -29/2*e^5 + 130*e^3 - 459/2*e, -29/2*e^5 + 130*e^3 - 459/2*e, 4*e^4 - 48*e^2 + 170, 4*e^4 - 48*e^2 + 170, 10*e^5 - 86*e^3 + 92*e, 10*e^5 - 86*e^3 + 92*e, 9/2*e^5 - 54*e^3 + 315/2*e, 9/2*e^5 - 54*e^3 + 315/2*e, 11/2*e^5 - 101/2*e^3 + 24*e, 11/2*e^5 - 101/2*e^3 + 24*e, -13*e^4 + 121*e^2 - 164, -13*e^4 + 121*e^2 - 164, -13/2*e^5 + 40*e^3 + 21/2*e, -13/2*e^5 + 40*e^3 + 21/2*e, -1/2*e^5 + 19/2*e^3 - 14*e, -1/2*e^5 + 19/2*e^3 - 14*e, 49/2*e^4 - 359/2*e^2 + 150, 49/2*e^4 - 359/2*e^2 + 150, -11*e^4 + 75*e^2 - 54, -11*e^4 + 75*e^2 - 54, -e^4 + 37*e^2 - 60, -e^4 + 37*e^2 - 60, -6*e^5 + 67*e^3 - 183*e, -6*e^5 + 67*e^3 - 183*e, -23/2*e^5 + 219/2*e^3 - 191*e, -23/2*e^5 + 219/2*e^3 - 191*e, 19/2*e^5 - 86*e^3 + 209/2*e, 19/2*e^5 - 86*e^3 + 209/2*e, 9*e^4 - 75*e^2 - 2, 9*e^4 - 75*e^2 - 2, -21/2*e^5 + 114*e^3 - 443/2*e, -21/2*e^5 + 114*e^3 - 443/2*e, -9*e^4 + 75*e^2 - 82, -9*e^4 + 75*e^2 - 82, -11*e^4 + 113*e^2 - 226, -11*e^4 + 113*e^2 - 226, 25/2*e^5 - 113*e^3 + 249/2*e, 25/2*e^5 - 113*e^3 + 249/2*e, e^4 + 21*e^2 - 110, e^4 + 21*e^2 - 110, 39/2*e^4 - 361/2*e^2 + 154, 39/2*e^4 - 361/2*e^2 + 154, 11*e^4 - 125*e^2 + 242, 11*e^4 - 125*e^2 + 242, -16*e^4 + 134*e^2 - 128, -16*e^4 + 134*e^2 - 128, -33/2*e^5 + 293/2*e^3 - 189*e, -33/2*e^5 + 293/2*e^3 - 189*e, 27/2*e^5 - 137*e^3 + 431/2*e, 27/2*e^5 - 137*e^3 + 431/2*e, 7*e^5 - 69*e^3 + 84*e, 7*e^5 - 69*e^3 + 84*e, -2*e^4 + 38*e^2 - 138, -2*e^4 + 38*e^2 - 138, -28*e^4 + 238*e^2 - 296, -28*e^4 + 238*e^2 - 296, 47/2*e^5 - 214*e^3 + 553/2*e, 47/2*e^5 - 214*e^3 + 553/2*e, 19/2*e^5 - 175/2*e^3 + 151*e, 19/2*e^5 - 175/2*e^3 + 151*e, 23*e^4 - 181*e^2 + 254, 23*e^4 - 181*e^2 + 254, 7*e^4 - 59*e^2 + 164, 7*e^4 - 59*e^2 + 164, 49/2*e^5 - 419/2*e^3 + 250*e, 49/2*e^5 - 419/2*e^3 + 250*e, 43/2*e^4 - 397/2*e^2 + 218, 43/2*e^4 - 397/2*e^2 + 218, -37/2*e^5 + 176*e^3 - 591/2*e, -37/2*e^5 + 176*e^3 - 591/2*e, 23/2*e^4 - 233/2*e^2 + 114, 23/2*e^4 - 233/2*e^2 + 114, 11/2*e^5 - 58*e^3 + 241/2*e, 11/2*e^5 - 58*e^3 + 241/2*e, -6*e^4 + 76*e^2 - 164, -6*e^4 + 76*e^2 - 164, 35/2*e^5 - 323/2*e^3 + 317*e, 35/2*e^5 - 323/2*e^3 + 317*e, -5/2*e^5 + 16*e^3 + 37/2*e, -5/2*e^5 + 16*e^3 + 37/2*e, -1/2*e^5 + 47/2*e^3 - 132*e, -1/2*e^5 + 47/2*e^3 - 132*e, -7/2*e^5 + 59/2*e^3 - 27*e, -7/2*e^5 + 59/2*e^3 - 27*e, 17*e^5 - 146*e^3 + 221*e, 17*e^5 - 146*e^3 + 221*e, -11/2*e^5 + 58*e^3 - 261/2*e, -11/2*e^5 + 58*e^3 - 261/2*e, 23*e^4 - 199*e^2 + 230, 23*e^4 - 199*e^2 + 230, -22*e^4 + 150*e^2 - 54, -22*e^4 + 150*e^2 - 54, -33*e^5 + 305*e^3 - 414*e, -33*e^5 + 305*e^3 - 414*e, 4*e^4 - 4*e^2 - 38, 4*e^4 - 4*e^2 - 38, -18*e^4 + 168*e^2 - 192, -18*e^4 + 168*e^2 - 192, 25*e^4 - 187*e^2 + 156, 25*e^4 - 187*e^2 + 156, 17*e^5 - 167*e^3 + 316*e, 17*e^5 - 167*e^3 + 316*e, 3*e^4 - 29*e^2 - 10, 3*e^4 - 29*e^2 - 10, -39/2*e^4 + 369/2*e^2 - 222, -39/2*e^4 + 369/2*e^2 - 222, -30*e^5 + 260*e^3 - 362*e, -30*e^5 + 260*e^3 - 362*e, -33/2*e^5 + 138*e^3 - 199/2*e, -33/2*e^5 + 138*e^3 - 199/2*e, 5*e^4 - 53*e^2 + 142, 5*e^4 - 53*e^2 + 142, 11*e^4 - 121*e^2 + 130, 11*e^4 - 121*e^2 + 130, 3*e^5 - 30*e^3 - 9*e, 3*e^5 - 30*e^3 - 9*e, -31/2*e^5 + 283/2*e^3 - 175*e, -31/2*e^5 + 283/2*e^3 - 175*e, 3*e^4 - 21*e^2 + 114, 3*e^4 - 21*e^2 + 114, 14*e^4 - 146*e^2 + 210, 14*e^4 - 146*e^2 + 210, 21/2*e^5 - 114*e^3 + 511/2*e, 21/2*e^5 - 114*e^3 + 511/2*e, 21/2*e^5 - 113*e^3 + 501/2*e, 21/2*e^5 - 113*e^3 + 501/2*e, -12*e^5 + 126*e^3 - 266*e, -12*e^5 + 126*e^3 - 266*e, -59/2*e^4 + 485/2*e^2 - 266, -59/2*e^4 + 485/2*e^2 - 266, 21/2*e^5 - 107*e^3 + 441/2*e, 21/2*e^5 - 107*e^3 + 441/2*e, -9*e^4 + 61*e^2 - 20, -9*e^4 + 61*e^2 - 20, -5/2*e^4 + 27/2*e^2 - 70, -5/2*e^4 + 27/2*e^2 - 70];
heckeEigenvalues := AssociativeArray();
for i := 1 to #heckeEigenvaluesArray do
  heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i];
end for;

ALEigenvalues := AssociativeArray();
ALEigenvalues[ideal<ZF | {49, 7, -7}>] := 1;

// EXAMPLE:
// pp := Factorization(2*ZF)[1][1];
// heckeEigenvalues[pp];

print "To reconstruct the Hilbert newform f, type
  f, iso := Explode(make_newform());";

function make_newform();
 M := HilbertCuspForms(F, NN);
 S := NewSubspace(M);
 // SetVerbose("ModFrmHil", 1);
 NFD := NewformDecomposition(S);
 newforms := [* Eigenform(U) : U in NFD *];

 if #newforms eq 0 then;
  print "No Hilbert newforms at this level";
  return 0;
 end if;

 print "Testing ", #newforms, " possible newforms";
 newforms := [* f: f in newforms | IsIsomorphic(BaseField(f), K) *];
 print #newforms, " newforms have the correct Hecke field";

 if #newforms eq 0 then;
  print "No Hilbert newform found with the correct Hecke field";
  return 0;
 end if;

 autos := Automorphisms(K);
 xnewforms := [* *];
 for f in newforms do;
  if K eq RationalField() then;
   Append(~xnewforms, [* f, autos[1] *]);
  else;
   flag, iso := IsIsomorphic(K,BaseField(f));
   for a in autos do;
    Append(~xnewforms, [* f, a*iso *]);
   end for;
  end if;
 end for;
 newforms := xnewforms;

 for P in primes do;
  xnewforms := [* *];
  for f_iso in newforms do;
   f, iso := Explode(f_iso);
   if HeckeEigenvalue(f,P) eq iso(heckeEigenvalues[P]) then;
    Append(~xnewforms, f_iso);
   end if;
  end for;
  newforms := xnewforms;
  if #newforms eq 0 then;
   print "No Hilbert newform found which matches the Hecke eigenvalues";
   return 0;
  else if #newforms eq 1 then;
   print "success: unique match";
   return newforms[1];
  end if;
  end if;
 end for;
 print #newforms, "Hilbert newforms found which match the Hecke eigenvalues";
 return newforms[1];

end function;