/*
  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![-9, -1, 1];
F<w> := NumberField(g);
ZF := Integers(F);

NN := ideal<ZF | {37, 37, 2*w - 1}>;

primesArray := [
[3, 3, -w + 3],
[3, 3, -w - 2],
[4, 2, 2],
[7, 7, w + 1],
[7, 7, -w + 2],
[11, 11, w + 4],
[11, 11, -w + 5],
[25, 5, 5],
[37, 37, 2*w - 1],
[41, 41, 3*w - 8],
[41, 41, 3*w + 5],
[47, 47, -w - 7],
[47, 47, w - 8],
[53, 53, -3*w - 4],
[53, 53, 3*w - 7],
[67, 67, 4*w - 11],
[67, 67, 4*w + 7],
[71, 71, 3*w - 5],
[71, 71, -3*w - 2],
[73, 73, -3*w - 11],
[73, 73, 3*w - 14],
[83, 83, 3*w - 2],
[83, 83, 3*w - 1],
[101, 101, -w - 10],
[101, 101, w - 11],
[107, 107, 2*w - 13],
[107, 107, -2*w - 11],
[127, 127, 3*w - 16],
[127, 127, -3*w - 13],
[137, 137, 6*w - 17],
[137, 137, 6*w + 11],
[139, 139, -4*w - 1],
[139, 139, 4*w - 5],
[149, 149, 9*w - 29],
[149, 149, 9*w + 20],
[151, 151, 8*w + 17],
[151, 151, 8*w - 25],
[157, 157, -3*w - 14],
[157, 157, 3*w - 17],
[169, 13, -13],
[173, 173, -w - 13],
[173, 173, w - 14],
[181, 181, 7*w - 20],
[181, 181, 7*w + 13],
[197, 197, 9*w + 19],
[197, 197, 9*w - 28],
[211, 211, 5*w - 7],
[211, 211, -5*w - 2],
[223, 223, 3*w - 19],
[223, 223, -3*w - 16],
[229, 229, 5*w - 4],
[229, 229, 5*w - 1],
[233, 233, -6*w - 7],
[233, 233, 6*w - 13],
[263, 263, -w - 16],
[263, 263, w - 17],
[269, 269, 6*w - 11],
[269, 269, -6*w - 5],
[271, 271, 7*w - 17],
[271, 271, -7*w - 10],
[289, 17, -17],
[293, 293, -4*w - 19],
[293, 293, 4*w - 23],
[307, 307, 11*w + 23],
[307, 307, 11*w - 34],
[317, 317, -6*w - 1],
[317, 317, 6*w - 7],
[337, 337, 3*w - 22],
[337, 337, -3*w - 19],
[349, 349, 10*w - 29],
[349, 349, 10*w + 19],
[359, 359, 7*w - 32],
[359, 359, -7*w - 25],
[361, 19, -19],
[367, 367, -8*w - 11],
[367, 367, 8*w - 19],
[373, 373, 13*w - 41],
[373, 373, 13*w + 28],
[379, 379, -3*w - 20],
[379, 379, 3*w - 23],
[397, 397, -7*w - 4],
[397, 397, 7*w - 11],
[419, 419, 5*w - 28],
[419, 419, -5*w - 23],
[433, 433, -7*w - 1],
[433, 433, 7*w - 8],
[443, 443, 9*w - 22],
[443, 443, -9*w - 13],
[491, 491, 12*w - 35],
[491, 491, 12*w + 23],
[509, 509, 9*w - 20],
[509, 509, -9*w - 11],
[521, 521, 15*w - 47],
[521, 521, 15*w + 32],
[529, 23, -23],
[571, 571, 13*w - 38],
[571, 571, 13*w + 25],
[593, 593, 9*w - 17],
[593, 593, -9*w - 8],
[599, 599, 15*w + 31],
[599, 599, 15*w - 46],
[601, 601, 10*w - 23],
[601, 601, -10*w - 13],
[613, 613, 11*w + 17],
[613, 613, 11*w - 28],
[617, 617, -9*w - 7],
[617, 617, 9*w - 16],
[619, 619, 3*w - 28],
[619, 619, -3*w - 25],
[641, 641, -w - 25],
[641, 641, w - 26],
[659, 659, -9*w - 5],
[659, 659, 9*w - 14],
[673, 673, -3*w - 26],
[673, 673, 3*w - 29],
[677, 677, 9*w - 13],
[677, 677, -9*w - 4],
[691, 691, -6*w - 29],
[691, 691, 6*w - 35],
[719, 719, -9*w - 1],
[719, 719, 9*w - 10],
[733, 733, 9*w - 43],
[733, 733, -9*w - 34],
[739, 739, -11*w - 14],
[739, 739, 11*w - 25],
[743, 743, 9*w - 2],
[743, 743, 9*w - 7],
[751, 751, 13*w + 22],
[751, 751, 13*w - 35],
[761, 761, -5*w - 29],
[761, 761, 5*w - 34],
[773, 773, 21*w - 68],
[773, 773, 21*w + 47],
[787, 787, 3*w - 31],
[787, 787, -3*w - 28],
[811, 811, 9*w + 35],
[811, 811, 9*w - 44],
[821, 821, 15*w + 28],
[821, 821, 15*w - 43],
[823, 823, 6*w - 37],
[823, 823, -6*w - 31],
[839, 839, 10*w - 47],
[839, 839, -10*w - 37],
[841, 29, -29],
[863, 863, 2*w - 31],
[863, 863, -2*w - 29],
[877, 877, 22*w + 49],
[877, 877, 22*w - 71],
[881, 881, 18*w + 37],
[881, 881, 18*w - 55],
[887, 887, 21*w - 67],
[887, 887, 21*w + 46],
[929, 929, 8*w - 43],
[929, 929, -8*w - 35],
[937, 937, 11*w - 19],
[937, 937, -11*w - 8],
[941, 941, -4*w - 31],
[941, 941, 4*w - 35],
[953, 953, -7*w - 34],
[953, 953, 7*w - 41],
[961, 31, -31],
[971, 971, -12*w - 13],
[971, 971, 12*w - 25],
[983, 983, -w - 31],
[983, 983, w - 32],
[1009, 1009, 11*w - 16],
[1009, 1009, -11*w - 5],
[1033, 1033, 17*w + 32],
[1033, 1033, 17*w - 49],
[1039, 1039, -3*w - 32],
[1039, 1039, 3*w - 35],
[1061, 1061, 18*w - 53],
[1061, 1061, 18*w + 35],
[1063, 1063, 11*w - 13],
[1063, 1063, -11*w - 2],
[1069, 1069, -12*w - 43],
[1069, 1069, 12*w - 55],
[1103, 1103, 24*w + 53],
[1103, 1103, 24*w - 77],
[1109, 1109, 21*w - 65],
[1109, 1109, 21*w + 44],
[1117, 1117, 11*w - 7],
[1117, 1117, 11*w - 4],
[1151, 1151, -15*w - 23],
[1151, 1151, 15*w - 38],
[1163, 1163, 12*w - 19],
[1163, 1163, -12*w - 7],
[1181, 1181, -w - 34],
[1181, 1181, w - 35],
[1187, 1187, -7*w - 37],
[1187, 1187, 7*w - 44],
[1193, 1193, 27*w + 61],
[1193, 1193, 27*w - 88],
[1217, 1217, 21*w + 43],
[1217, 1217, 21*w - 64],
[1231, 1231, -9*w - 40],
[1231, 1231, 9*w - 49],
[1237, 1237, -14*w - 17],
[1237, 1237, 14*w - 31],
[1249, 1249, -3*w - 35],
[1249, 1249, 3*w - 38],
[1259, 1259, 2*w - 37],
[1259, 1259, -2*w - 35],
[1279, 1279, 16*w - 41],
[1279, 1279, 16*w + 25],
[1283, 1283, -12*w - 1],
[1283, 1283, 12*w - 13],
[1291, 1291, -13*w - 10],
[1291, 1291, 13*w - 23],
[1307, 1307, 12*w - 11],
[1307, 1307, 12*w - 1],
[1321, 1321, 9*w - 50],
[1321, 1321, -9*w - 41],
[1373, 1373, 4*w - 41],
[1373, 1373, -4*w - 37],
[1381, 1381, -13*w - 7],
[1381, 1381, 13*w - 20],
[1399, 1399, 3*w - 40],
[1399, 1399, -3*w - 37],
[1409, 1409, 5*w - 43],
[1409, 1409, -5*w - 38],
[1427, 1427, 21*w - 62],
[1427, 1427, 21*w + 41],
[1433, 1433, 8*w - 49],
[1433, 1433, -8*w - 41],
[1439, 1439, 7*w - 47],
[1439, 1439, -7*w - 40],
[1447, 1447, 19*w - 53],
[1447, 1447, 19*w + 34],
[1453, 1453, 13*w - 17],
[1453, 1453, -13*w - 4],
[1459, 1459, 29*w - 94],
[1459, 1459, 15*w - 67],
[1471, 1471, 23*w + 47],
[1471, 1471, 23*w - 70],
[1481, 1481, 15*w - 32],
[1481, 1481, -15*w - 17],
[1483, 1483, 17*w + 26],
[1483, 1483, 17*w - 43],
[1487, 1487, 27*w + 59],
[1487, 1487, 27*w - 86],
[1489, 1489, 14*w - 25],
[1489, 1489, -14*w - 11],
[1543, 1543, 13*w - 2],
[1543, 1543, 13*w - 11],
[1553, 1553, 18*w + 29],
[1553, 1553, 18*w - 47],
[1579, 1579, 31*w + 70],
[1579, 1579, 31*w - 101],
[1601, 1601, 16*w - 71],
[1601, 1601, 30*w - 97],
[1607, 1607, 24*w + 49],
[1607, 1607, 24*w - 73],
[1619, 1619, 15*w - 29],
[1619, 1619, -15*w - 14],
[1621, 1621, 25*w - 77],
[1621, 1621, 25*w + 52],
[1627, 1627, 28*w - 89],
[1627, 1627, 28*w + 61],
[1637, 1637, 11*w - 58],
[1637, 1637, -11*w - 47],
[1669, 1669, -14*w - 5],
[1669, 1669, 14*w - 19],
[1693, 1693, -12*w + 61],
[1693, 1693, 12*w + 49],
[1699, 1699, 19*w + 31],
[1699, 1699, 19*w - 50],
[1709, 1709, 7*w - 50],
[1709, 1709, -7*w - 43],
[1723, 1723, -3*w - 41],
[1723, 1723, 3*w - 44],
[1777, 1777, 14*w - 13],
[1777, 1777, 14*w - 1],
[1783, 1783, 6*w - 49],
[1783, 1783, -6*w - 43],
[1787, 1787, -14*w - 53],
[1787, 1787, 14*w - 67],
[1801, 1801, 9*w - 55],
[1801, 1801, -9*w - 46],
[1823, 1823, 21*w + 37],
[1823, 1823, 21*w - 58],
[1847, 1847, 24*w - 71],
[1847, 1847, 24*w + 47],
[1849, 43, -43],
[1861, 1861, -17*w - 20],
[1861, 1861, 17*w - 37],
[1871, 1871, 15*w - 22],
[1871, 1871, -15*w - 7],
[1877, 1877, -4*w - 43],
[1877, 1877, 4*w - 47],
[1913, 1913, 27*w - 83],
[1913, 1913, 27*w + 56],
[1931, 1931, -5*w - 44],
[1931, 1931, 5*w - 49],
[1933, 1933, 19*w - 47],
[1933, 1933, -19*w - 28],
[1949, 1949, -15*w - 4],
[1949, 1949, 15*w - 19],
[1951, 1951, -15*w - 56],
[1951, 1951, 15*w - 71],
[1973, 1973, 18*w - 41],
[1973, 1973, -18*w - 23],
[1987, 1987, -3*w - 44],
[1987, 1987, 3*w - 47],
[1997, 1997, 7*w - 53],
[1997, 1997, -7*w - 46],
[1999, 1999, 25*w - 74],
[1999, 1999, 25*w + 49],
[2039, 2039, 15*w - 14],
[2039, 2039, 15*w - 1],
[2063, 2063, 33*w - 106],
[2063, 2063, 33*w + 73],
[2069, 2069, 15*w - 11],
[2069, 2069, 15*w - 4],
[2081, 2081, 15*w - 7],
[2081, 2081, 15*w - 8],
[2083, 2083, 31*w - 98],
[2083, 2083, 31*w + 67],
[2099, 2099, 21*w - 55],
[2099, 2099, 21*w + 34],
[2113, 2113, -9*w - 49],
[2113, 2113, 9*w - 58],
[2137, 2137, 23*w + 41],
[2137, 2137, 23*w - 64],
[2143, 2143, -16*w - 7],
[2143, 2143, 16*w - 23],
[2153, 2153, -w - 46],
[2153, 2153, w - 47],
[2179, 2179, -20*w - 29],
[2179, 2179, 20*w - 49],
[2213, 2213, -18*w - 19],
[2213, 2213, 18*w - 37],
[2221, 2221, 9*w - 59],
[2221, 2221, -9*w - 50],
[2267, 2267, 2*w - 49],
[2267, 2267, -2*w - 47],
[2269, 2269, -3*w - 47],
[2269, 2269, 3*w - 50],
[2273, 2273, 21*w + 32],
[2273, 2273, 21*w - 53],
[2287, 2287, -16*w - 1],
[2287, 2287, 16*w - 17],
[2293, 2293, 17*w - 28],
[2293, 2293, -17*w - 11],
[2297, 2297, -17*w - 62],
[2297, 2297, 17*w - 79],
[2341, 2341, 15*w + 59],
[2341, 2341, 15*w - 74],
[2347, 2347, 19*w - 41],
[2347, 2347, -19*w - 22],
[2357, 2357, 21*w - 52],
[2357, 2357, -21*w - 31],
[2371, 2371, 6*w - 55],
[2371, 2371, -6*w - 49],
[2377, 2377, 29*w + 59],
[2377, 2377, 29*w - 88],
[2389, 2389, -12*w - 55],
[2389, 2389, 12*w - 67],
[2393, 2393, 16*w - 77],
[2393, 2393, -16*w - 61],
[2417, 2417, 33*w - 104],
[2417, 2417, 33*w + 71],
[2441, 2441, -w - 49],
[2441, 2441, w - 50],
[2467, 2467, 3*w - 52],
[2467, 2467, -3*w - 49],
[2543, 2543, 14*w - 73],
[2543, 2543, -14*w - 59],
[2549, 2549, 30*w + 61],
[2549, 2549, 30*w - 91],
[2557, 2557, -9*w - 53],
[2557, 2557, 9*w - 62],
[2579, 2579, 36*w - 115],
[2579, 2579, 36*w + 79],
[2591, 2591, 33*w - 103],
[2591, 2591, 33*w + 70],
[2593, 2593, 34*w + 73],
[2593, 2593, 34*w - 107],
[2617, 2617, 17*w - 16],
[2617, 2617, 17*w - 1],
[2657, 2657, -8*w - 53],
[2657, 2657, 8*w - 61],
[2663, 2663, 11*w - 67],
[2663, 2663, -11*w - 56],
[2671, 2671, 17*w - 10],
[2671, 2671, 17*w - 7],
[2689, 2689, -19*w - 16],
[2689, 2689, 19*w - 35],
[2711, 2711, 27*w - 77],
[2711, 2711, 27*w + 50],
[2713, 2713, -22*w - 31],
[2713, 2713, 22*w - 53],
[2729, 2729, -17*w - 65],
[2729, 2729, 17*w - 82],
[2731, 2731, 23*w + 35],
[2731, 2731, 23*w - 58],
[2741, 2741, 18*w - 25],
[2741, 2741, -18*w - 7],
[2749, 2749, 15*w + 62],
[2749, 2749, -15*w + 77],
[2791, 2791, 9*w - 64],
[2791, 2791, -9*w - 55],
[2801, 2801, 18*w - 23],
[2801, 2801, -18*w - 5],
[2803, 2803, -6*w - 53],
[2803, 2803, 6*w - 59],
[2819, 2819, 21*w - 46],
[2819, 2819, -21*w - 25],
[2833, 2833, -19*w - 13],
[2833, 2833, 19*w - 32],
[2837, 2837, 27*w - 76],
[2837, 2837, 27*w + 49],
[2861, 2861, 42*w - 137],
[2861, 2861, 42*w + 95],
[2879, 2879, 2*w - 55],
[2879, 2879, -2*w - 53],
[2887, 2887, -3*w - 53],
[2887, 2887, 3*w - 56],
[2897, 2897, -18*w - 1],
[2897, 2897, 18*w - 19],
[2927, 2927, 24*w - 61],
[2927, 2927, 24*w + 37],
[2939, 2939, 39*w + 86],
[2939, 2939, 39*w - 125],
[2953, 2953, 38*w + 83],
[2953, 2953, 38*w - 121],
[2957, 2957, 21*w - 44],
[2957, 2957, -21*w - 23],
[2963, 2963, 36*w - 113],
[2963, 2963, 36*w + 77],
[2969, 2969, -7*w - 55],
[2969, 2969, 7*w - 62],
[2971, 2971, 20*w - 37],
[2971, 2971, -20*w - 17],
[3001, 3001, 23*w - 55],
[3001, 3001, -23*w - 32],
[3023, 3023, -21*w - 22],
[3023, 3023, 21*w - 43],
[3037, 3037, 31*w - 92],
[3037, 3037, 31*w + 61],
[3041, 3041, 11*w - 70],
[3041, 3041, -11*w - 59],
[3061, 3061, 43*w + 97],
[3061, 3061, 43*w - 140],
[3067, 3067, 19*w - 26],
[3067, 3067, -19*w - 7],
[3083, 3083, 27*w - 74],
[3083, 3083, 27*w + 47],
[3109, 3109, 3*w - 58],
[3109, 3109, -3*w - 55],
[3119, 3119, -24*w - 35],
[3119, 3119, 24*w - 59],
[3181, 3181, 22*w - 47],
[3181, 3181, -22*w - 25],
[3191, 3191, 5*w - 61],
[3191, 3191, -5*w - 56],
[3203, 3203, 27*w + 46],
[3203, 3203, 27*w - 73],
[3209, 3209, -21*w - 19],
[3209, 3209, 21*w - 40],
[3229, 3229, -19*w - 1],
[3229, 3229, 19*w - 20],
[3253, 3253, -23*w - 29],
[3253, 3253, 23*w - 52],
[3257, 3257, 16*w + 67],
[3257, 3257, -16*w + 83],
[3259, 3259, 20*w - 31],
[3259, 3259, -20*w - 11],
[3319, 3319, 19*w - 14],
[3319, 3319, 19*w - 5],
[3323, 3323, -21*w - 17],
[3323, 3323, 21*w - 38],
[3329, 3329, -7*w - 58],
[3329, 3329, 7*w - 65],
[3331, 3331, 25*w - 62],
[3331, 3331, -25*w - 37],
[3371, 3371, -14*w - 65],
[3371, 3371, 14*w - 79],
[3407, 3407, -13*w - 64],
[3407, 3407, 13*w - 77],
[3413, 3413, -w - 58],
[3413, 3413, w - 59],
[3457, 3457, 3*w - 61],
[3457, 3457, -3*w - 58],
[3467, 3467, 19*w - 92],
[3467, 3467, -19*w - 73],
[3469, 3469, -15*w - 67],
[3469, 3469, 15*w - 82],
[3481, 59, -59],
[3499, 3499, 35*w + 71],
[3499, 3499, 35*w - 106],
[3511, 3511, -6*w - 59],
[3511, 3511, 6*w - 65],
[3527, 3527, 21*w - 34],
[3527, 3527, -21*w - 13],
[3541, 3541, 9*w - 70],
[3541, 3541, -9*w - 61],
[3559, 3559, 41*w + 89],
[3559, 3559, 41*w - 130],
[3593, 3593, 33*w + 64],
[3593, 3593, 33*w - 97],
[3617, 3617, -21*w - 11],
[3617, 3617, 21*w - 32],
[3623, 3623, 48*w - 157],
[3623, 3623, 48*w + 109],
[3637, 3637, 34*w - 101],
[3637, 3637, 34*w + 67],
[3659, 3659, 21*w - 31],
[3659, 3659, -21*w - 10],
[3673, 3673, -9*w - 62],
[3673, 3673, 9*w - 71],
[3691, 3691, 20*w - 13],
[3691, 3691, 20*w - 7],
[3697, 3697, 24*w - 107],
[3697, 3697, 46*w - 149],
[3701, 3701, 30*w - 83],
[3701, 3701, 30*w + 53],
[3709, 3709, 12*w - 77],
[3709, 3709, -12*w - 65],
[3721, 61, -61],
[3727, 3727, -18*w + 91],
[3727, 3727, 18*w + 73],
[3733, 3733, 37*w - 113],
[3733, 3733, 37*w + 76],
[3767, 3767, 39*w + 82],
[3767, 3767, 39*w - 121],
[3821, 3821, 4*w - 65],
[3821, 3821, -4*w - 61],
[3823, 3823, 3*w - 64],
[3823, 3823, -3*w - 61],
[3847, 3847, 32*w - 91],
[3847, 3847, 32*w + 59],
[3851, 3851, -11*w - 65],
[3851, 3851, 11*w - 76],
[3881, 3881, 27*w - 67],
[3881, 3881, 27*w + 40],
[3889, 3889, 25*w - 56],
[3889, 3889, -25*w - 31],
[3911, 3911, 33*w + 62],
[3911, 3911, 33*w - 95],
[3919, 3919, 31*w - 86],
[3919, 3919, 31*w + 55],
[3923, 3923, 21*w - 23],
[3923, 3923, -21*w - 2],
[3929, 3929, -5*w - 62],
[3929, 3929, 5*w - 67],
[3931, 3931, 21*w - 100],
[3931, 3931, -21*w - 79],
[3943, 3943, 9*w - 73],
[3943, 3943, -9*w - 64],
[3947, 3947, -21*w - 1],
[3947, 3947, 21*w - 22],
[3989, 3989, 21*w - 20],
[3989, 3989, 21*w - 1],
[4003, 4003, 28*w - 71],
[4003, 4003, 28*w + 43],
[4007, 4007, 21*w - 2],
[4007, 4007, 21*w - 19],
[4021, 4021, 35*w + 68],
[4021, 4021, 35*w - 103],
[4049, 4049, 21*w - 5],
[4049, 4049, 21*w - 16],
[4073, 4073, 21*w - 13],
[4073, 4073, 21*w - 8],
[4079, 4079, 21*w - 10],
[4079, 4079, 21*w - 11],
[4091, 4091, -27*w - 38],
[4091, 4091, 27*w - 65],
[4111, 4111, 21*w - 101],
[4111, 4111, -21*w - 80],
[4133, 4133, 17*w - 91],
[4133, 4133, -17*w - 74],
[4153, 4153, 22*w - 29],
[4153, 4153, -22*w - 7],
[4177, 4177, 47*w - 151],
[4177, 4177, 47*w + 104],
[4211, 4211, 45*w + 98],
[4211, 4211, 45*w - 143],
[4217, 4217, 42*w + 89],
[4217, 4217, 42*w - 131],
[4219, 4219, 44*w + 95],
[4219, 4219, 44*w - 139],
[4229, 4229, 30*w - 79],
[4229, 4229, 30*w + 49],
[4243, 4243, -23*w - 14],
[4243, 4243, 23*w - 37],
[4259, 4259, 10*w - 77],
[4259, 4259, -10*w - 67],
[4271, 4271, 14*w - 85],
[4271, 4271, -14*w - 71],
[4283, 4283, -11*w - 68],
[4283, 4283, 11*w - 79],
[4289, 4289, -13*w - 70],
[4289, 4289, 13*w - 83],
[4339, 4339, -3*w - 65],
[4339, 4339, 3*w - 68],
[4357, 4357, 29*w + 44],
[4357, 4357, 29*w - 73],
[4363, 4363, -9*w - 67],
[4363, 4363, 9*w - 76],
[4373, 4373, 33*w + 59],
[4373, 4373, 33*w - 92],
[4391, 4391, 27*w - 62],
[4391, 4391, -27*w - 35],
[4441, 4441, 22*w - 17],
[4441, 4441, 22*w - 5],
[4447, 4447, 43*w - 134],
[4447, 4447, 43*w + 91],
[4451, 4451, 45*w + 97],
[4451, 4451, 45*w - 142],
[4481, 4481, 30*w - 77],
[4481, 4481, 30*w + 47],
[4493, 4493, 19*w + 79],
[4493, 4493, -19*w + 98],
[4507, 4507, 9*w - 77],
[4507, 4507, -9*w - 68],
[4513, 4513, -23*w - 8],
[4513, 4513, 23*w - 31],
[4517, 4517, 7*w - 74],
[4517, 4517, -7*w - 67],
[4523, 4523, 33*w + 58],
[4523, 4523, 33*w - 91],
[4547, 4547, -w - 67],
[4547, 4547, w - 68],
[4561, 4561, -15*w - 74],
[4561, 4561, 15*w - 89],
[4567, 4567, 6*w - 73],
[4567, 4567, -6*w - 67],
[4591, 4591, -25*w - 22],
[4591, 4591, 25*w - 47],
[4597, 4597, -12*w - 71],
[4597, 4597, 12*w - 83],
[4621, 4621, 23*w - 28],
[4621, 4621, -23*w - 5],
[4637, 4637, 17*w - 94],
[4637, 4637, -17*w - 77],
[4651, 4651, 28*w - 65],
[4651, 4651, -28*w - 37],
[4663, 4663, 21*w + 83],
[4663, 4663, -21*w + 104],
[4673, 4673, -27*w - 32],
[4673, 4673, 27*w - 59],
[4703, 4703, 24*w - 37],
[4703, 4703, -24*w - 13],
[4729, 4729, 31*w - 80],
[4729, 4729, 31*w + 49],
[4733, 4733, -11*w - 71],
[4733, 4733, 11*w - 82],
[4783, 4783, 23*w - 22],
[4783, 4783, 23*w - 1],
[4789, 4789, -25*w - 19],
[4789, 4789, 25*w - 44],
[4799, 4799, -24*w - 11],
[4799, 4799, 24*w - 35],
[4801, 4801, 9*w - 79],
[4801, 4801, -9*w - 70],
[4813, 4813, 53*w - 172],
[4813, 4813, 27*w - 121],
[4817, 4817, 33*w - 89],
[4817, 4817, 33*w + 56],
[4831, 4831, 37*w + 70],
[4831, 4831, 37*w - 107],
[4877, 4877, 51*w + 113],
[4877, 4877, 51*w - 164],
[4909, 4909, 12*w - 85],
[4909, 4909, -12*w - 73],
[4931, 4931, 57*w + 130],
[4931, 4931, 57*w - 187],
[4933, 4933, 47*w - 148],
[4933, 4933, 47*w + 101],
[4937, 4937, 27*w - 56],
[4937, 4937, -27*w - 29],
[4951, 4951, -9*w - 71],
[4951, 4951, 9*w - 80],
[4957, 4957, 26*w - 49],
[4957, 4957, -26*w - 23],
[4967, 4967, -24*w - 7],
[4967, 4967, 24*w - 31],
[4969, 4969, -25*w - 16],
[4969, 4969, 25*w - 41],
[4999, 4999, 40*w - 119],
[4999, 4999, 40*w + 79],
[5011, 5011, 35*w + 62],
[5011, 5011, 35*w - 97],
[5021, 5021, -27*w - 28],
[5021, 5021, 27*w - 55],
[5023, 5023, -29*w - 38],
[5023, 5023, 29*w - 67],
[5039, 5039, -24*w - 5],
[5039, 5039, 24*w - 29],
[5059, 5059, -15*w - 77],
[5059, 5059, 15*w - 92],
[5081, 5081, 42*w + 85],
[5081, 5081, 42*w - 127],
[5099, 5099, 36*w + 65],
[5099, 5099, 36*w - 101],
[5107, 5107, 31*w - 77],
[5107, 5107, 31*w + 46],
[5113, 5113, 43*w - 131],
[5113, 5113, 43*w + 88],
[5147, 5147, 2*w - 73],
[5147, 5147, -2*w - 71],
[5153, 5153, 51*w - 163],
[5153, 5153, 51*w + 112],
[5171, 5171, 5*w - 76],
[5171, 5171, -5*w - 71],
[5179, 5179, 49*w - 155],
[5179, 5179, 49*w + 106],
[5189, 5189, -30*w - 41],
[5189, 5189, 30*w - 71],
[5227, 5227, 28*w - 59],
[5227, 5227, -28*w - 31],
[5233, 5233, 21*w + 86],
[5233, 5233, -21*w + 107],
[5261, 5261, -27*w - 25],
[5261, 5261, 27*w - 52],
[5279, 5279, 24*w - 19],
[5279, 5279, 24*w - 5],
[5281, 5281, -24*w - 91],
[5281, 5281, 24*w - 115],
[5303, 5303, 24*w - 17],
[5303, 5303, 24*w - 7],
[5381, 5381, 33*w + 52],
[5381, 5381, 33*w - 85],
[5393, 5393, -w - 73],
[5393, 5393, w - 74],
[5399, 5399, -7*w - 73],
[5399, 5399, 7*w - 80],
[5413, 5413, -9*w - 74],
[5413, 5413, 9*w - 83],
[5443, 5443, 6*w - 79],
[5443, 5443, -6*w - 73],
[5449, 5449, 41*w + 80],
[5449, 5449, 41*w - 121],
[5477, 5477, 4*w - 77],
[5477, 5477, -4*w - 73],
[5479, 5479, 35*w - 94],
[5479, 5479, 35*w + 59],
[5483, 5483, 27*w - 49],
[5483, 5483, -27*w - 22],
[5501, 5501, 42*w - 125],
[5501, 5501, 42*w + 83],
[5503, 5503, 32*w + 47],
[5503, 5503, 32*w - 79],
[5557, 5557, 12*w - 89],
[5557, 5557, -12*w - 77],
[5591, 5591, -19*w - 85],
[5591, 5591, 19*w - 104],
[5623, 5623, -21*w - 88],
[5623, 5623, 21*w - 109],
[5651, 5651, 33*w + 50],
[5651, 5651, 33*w - 83],
[5657, 5657, 54*w + 119],
[5657, 5657, 54*w - 173],
[5689, 5689, 61*w + 139],
[5689, 5689, 61*w - 200],
[5701, 5701, 50*w - 157],
[5701, 5701, 50*w + 107],
[5779, 5779, 25*w - 11],
[5779, 5779, 25*w - 14],
[5783, 5783, 33*w - 82],
[5783, 5783, 33*w + 49],
[5813, 5813, -27*w - 17],
[5813, 5813, 27*w - 44],
[5821, 5821, -21*w - 89],
[5821, 5821, 21*w - 110],
[5839, 5839, 18*w - 103],
[5839, 5839, -18*w - 85],
[5843, 5843, -w - 76],
[5843, 5843, w - 77],
[5849, 5849, 45*w + 91],
[5849, 5849, 45*w - 136],
[5857, 5857, 37*w + 64],
[5857, 5857, 37*w - 101],
[5867, 5867, -7*w - 76],
[5867, 5867, 7*w - 83],
[5879, 5879, 39*w + 71],
[5879, 5879, 39*w - 110],
[5923, 5923, 3*w - 79],
[5923, 5923, -3*w - 76],
[5927, 5927, 22*w + 91],
[5927, 5927, -22*w + 113],
[5953, 5953, 49*w + 103],
[5953, 5953, 49*w - 152],
[5987, 5987, -27*w - 14],
[5987, 5987, 27*w - 41],
[6043, 6043, 41*w + 77],
[6043, 6043, 41*w - 118],
[6047, 6047, 2*w - 79],
[6047, 6047, -2*w - 77],
[6067, 6067, -6*w - 77],
[6067, 6067, 6*w - 83],
[6079, 6079, -3*w - 77],
[6079, 6079, 3*w - 80],
[6089, 6089, -5*w - 77],
[6089, 6089, 5*w - 82],
[6101, 6101, 20*w - 109],
[6101, 6101, -20*w - 89],
[6121, 6121, 24*w + 95],
[6121, 6121, -24*w + 119],
[6131, 6131, -10*w - 79],
[6131, 6131, 10*w - 89],
[6133, 6133, 31*w - 68],
[6133, 6133, -31*w - 37],
[6143, 6143, -27*w - 11],
[6143, 6143, 27*w - 38],
[6151, 6151, 40*w + 73],
[6151, 6151, 40*w - 113],
[6163, 6163, -28*w - 19],
[6163, 6163, 28*w - 47],
[6217, 6217, 26*w - 7],
[6217, 6217, 26*w - 19],
[6241, 79, -79],
[6257, 6257, 17*w - 103],
[6257, 6257, -17*w - 86],
[6263, 6263, 63*w + 143],
[6263, 6263, 63*w - 206],
[6269, 6269, -13*w - 82],
[6269, 6269, 13*w - 95],
[6287, 6287, -14*w - 83],
[6287, 6287, 14*w - 97],
[6299, 6299, 45*w - 134],
[6299, 6299, 45*w + 89],
[6301, 6301, 38*w - 103],
[6301, 6301, 38*w + 65],
[6311, 6311, -w - 79],
[6311, 6311, w - 80],
[6317, 6317, 42*w - 121],
[6317, 6317, 42*w + 79],
[6323, 6323, -27*w - 7],
[6323, 6323, 27*w - 34],
[6337, 6337, 34*w - 83],
[6337, 6337, -34*w - 49],
[6343, 6343, 37*w + 61],
[6343, 6343, 37*w - 98],
[6353, 6353, -7*w - 79],
[6353, 6353, 7*w - 86],
[6361, 6361, 35*w + 53],
[6361, 6361, 35*w - 88],
[6367, 6367, -27*w - 101],
[6367, 6367, 27*w - 128],
[6373, 6373, 29*w - 52],
[6373, 6373, -29*w - 23],
[6389, 6389, 30*w - 59],
[6389, 6389, -30*w - 29],
[6397, 6397, 3*w - 82],
[6397, 6397, -3*w - 79],
[6427, 6427, 21*w - 113],
[6427, 6427, -21*w - 92],
[6449, 6449, -23*w + 118],
[6449, 6449, 23*w + 95],
[6491, 6491, 57*w + 125],
[6491, 6491, 57*w - 182],
[6521, 6521, 45*w + 88],
[6521, 6521, 45*w - 133],
[6553, 6553, -24*w + 121],
[6553, 6553, 24*w + 97],
[6577, 6577, 46*w - 137],
[6577, 6577, 46*w + 91],
[6607, 6607, -18*w - 89],
[6607, 6607, 18*w - 107],
[6619, 6619, 41*w + 74],
[6619, 6619, 41*w - 115],
[6653, 6653, 27*w - 23],
[6653, 6653, 27*w - 4],
[6659, 6659, 36*w - 91],
[6659, 6659, 36*w + 55],
[6661, 6661, -15*w - 86],
[6661, 6661, 15*w - 101],
[6701, 6701, 27*w - 20],
[6701, 6701, 27*w - 7],
[6709, 6709, 49*w - 149],
[6709, 6709, 49*w + 100],
[6733, 6733, 9*w - 91],
[6733, 6733, -9*w - 82],
[6737, 6737, 27*w - 16],
[6737, 6737, 27*w - 11],
[6761, 6761, -19*w - 91],
[6761, 6761, 19*w - 110],
[6781, 6781, 58*w - 185],
[6781, 6781, 58*w + 127],
[6829, 6829, -27*w - 103],
[6829, 6829, 27*w - 130],
[6833, 6833, -17*w - 89],
[6833, 6833, 17*w - 106],
[6841, 6841, -21*w - 94],
[6841, 6841, 21*w - 115],
[6857, 6857, 7*w - 89],
[6857, 6857, -7*w - 82],
[6871, 6871, -32*w - 35],
[6871, 6871, 32*w - 67],
[6883, 6883, 44*w - 127],
[6883, 6883, 44*w + 83],
[6907, 6907, -9*w - 83],
[6907, 6907, 9*w - 92],
[6947, 6947, 36*w + 53],
[6947, 6947, 36*w - 89],
[6949, 6949, 12*w - 97],
[6949, 6949, -12*w - 85],
[6959, 6959, 45*w + 86],
[6959, 6959, 45*w - 131],
[6967, 6967, 29*w - 43],
[6967, 6967, -29*w - 14],
[6977, 6977, 8*w - 91],
[6977, 6977, -8*w - 83],
[6983, 6983, -29*w - 107],
[6983, 6983, 29*w - 136],
[6997, 6997, -31*w - 28],
[6997, 6997, 31*w - 59],
[7019, 7019, 2*w - 85],
[7019, 7019, -2*w - 83],
[7027, 7027, -28*w - 1],
[7027, 7027, 28*w - 29],
[7039, 7039, 15*w - 103],
[7039, 7039, -15*w - 88],
[7057, 7057, -3*w - 83],
[7057, 7057, 3*w - 86],
[7079, 7079, 5*w - 88],
[7079, 7079, -5*w - 83],
[7103, 7103, 33*w - 71],
[7103, 7103, -33*w - 38],
[7129, 7129, -29*w - 11],
[7129, 7129, 29*w - 40],
[7151, 7151, 48*w - 143],
[7151, 7151, 48*w + 95],
[7177, 7177, 41*w - 112],
[7177, 7177, 41*w + 71],
[7187, 7187, 22*w - 119],
[7187, 7187, -22*w - 97],
[7211, 7211, 33*w - 70],
[7211, 7211, -33*w - 37],
[7219, 7219, 65*w - 211],
[7219, 7219, 33*w - 148],
[7243, 7243, 28*w - 11],
[7243, 7243, 28*w - 17],
[7253, 7253, 11*w - 97],
[7253, 7253, -11*w - 86],
[7333, 7333, 62*w - 199],
[7333, 7333, 62*w + 137],
[7351, 7351, 53*w - 163],
[7351, 7351, 53*w + 110],
[7393, 7393, 59*w + 128],
[7393, 7393, 59*w - 187],
[7411, 7411, 6*w - 91],
[7411, 7411, -6*w - 85],
[7433, 7433, 16*w - 107],
[7433, 7433, -16*w - 91],
[7477, 7477, -21*w - 97],
[7477, 7477, 21*w - 118],
[7481, 7481, 42*w + 73],
[7481, 7481, 42*w - 115],
[7499, 7499, 36*w - 85],
[7499, 7499, -36*w - 49],
[7507, 7507, 29*w - 31],
[7507, 7507, -29*w - 2],
[7523, 7523, -33*w - 34],
[7523, 7523, 33*w - 67],
[7537, 7537, 27*w - 133],
[7537, 7537, 27*w + 106],
[7541, 7541, -30*w - 13],
[7541, 7541, 30*w - 43],
[7547, 7547, 51*w + 103],
[7547, 7547, 51*w - 154],
[7549, 7549, -35*w - 44],
[7549, 7549, 35*w - 79],
[7559, 7559, 25*w + 103],
[7559, 7559, -25*w + 128],
[7573, 7573, -3*w - 86],
[7573, 7573, 3*w - 89],
[7589, 7589, 39*w + 61],
[7589, 7589, 39*w - 100],
[7621, 7621, 15*w - 106],
[7621, 7621, -15*w - 91],
[7643, 7643, 63*w - 202],
[7643, 7643, 63*w + 139],
[7649, 7649, -30*w - 11],
[7649, 7649, 30*w - 41],
[7669, 7669, 29*w - 4],
[7669, 7669, 29*w - 25],
[7687, 7687, 61*w - 194],
[7687, 7687, 61*w + 133],
[7699, 7699, 31*w - 50],
[7699, 7699, -31*w - 19],
[7703, 7703, 57*w - 178],
[7703, 7703, 57*w + 121],
[7717, 7717, 41*w - 109],
[7717, 7717, 41*w + 68],
[7723, 7723, 29*w - 7],
[7723, 7723, 29*w - 22],
[7759, 7759, 29*w - 19],
[7759, 7759, 29*w - 10],
[7817, 7817, -33*w - 31],
[7817, 7817, 33*w - 64],
[7823, 7823, -w - 88],
[7823, 7823, w - 89],
[7841, 7841, -30*w - 7],
[7841, 7841, 30*w - 37],
[7853, 7853, 42*w - 113],
[7853, 7853, 42*w + 71],
[7877, 7877, 28*w - 137],
[7877, 7877, 28*w + 109],
[7907, 7907, 39*w + 59],
[7907, 7907, 39*w - 98],
[7919, 7919, 7*w - 95],
[7919, 7919, -7*w - 88],
[7921, 89, -89],
[7927, 7927, 3*w - 91],
[7927, 7927, -3*w - 88],
[7951, 7951, -32*w - 23],
[7951, 7951, 32*w - 55],
[7993, 7993, -9*w - 89],
[7993, 7993, 9*w - 98],
[8017, 8017, 71*w + 161],
[8017, 8017, 71*w - 232],
[8039, 8039, -17*w - 95],
[8039, 8039, 17*w - 112],
[8059, 8059, -30*w - 113],
[8059, 8059, 30*w - 143],
[8069, 8069, -30*w - 1],
[8069, 8069, 30*w - 31],
[8087, 8087, 48*w + 91],
[8087, 8087, 48*w - 139],
[8093, 8093, -33*w - 28],
[8093, 8093, 33*w - 61],
[8147, 8147, -26*w + 133],
[8147, 8147, 26*w + 107],
[8161, 8161, 53*w + 107],
[8161, 8161, 53*w - 160],
[8167, 8167, 49*w + 94],
[8167, 8167, 49*w - 143],
[8221, 8221, 15*w - 109],
[8221, 8221, -15*w - 94],
[8263, 8263, -27*w + 136],
[8263, 8263, 27*w + 109],
[8287, 8287, 73*w + 166],
[8287, 8287, 73*w - 239],
[8291, 8291, 10*w - 101],
[8291, 8291, -10*w - 91],
[8297, 8297, 57*w + 119],
[8297, 8297, 57*w - 176],
[8329, 8329, 59*w + 125],
[8329, 8329, 59*w - 184],
[8353, 8353, 21*w - 122],
[8353, 8353, -21*w - 101],
[8363, 8363, -w - 91],
[8363, 8363, w - 92],
[8369, 8369, 39*w - 95],
[8369, 8369, -39*w - 56],
[8387, 8387, 11*w - 103],
[8387, 8387, -11*w - 92],
[8389, 8389, -34*w - 31],
[8389, 8389, 34*w - 65],
[8429, 8429, 45*w + 79],
[8429, 8429, 45*w - 124],
[8443, 8443, 47*w - 133],
[8443, 8443, 47*w + 86],
[8447, 8447, 23*w - 127],
[8447, 8447, -23*w - 104],
[8461, 8461, 36*w - 161],
[8461, 8461, 70*w - 227],
[8501, 8501, -4*w - 91],
[8501, 8501, 4*w - 95],
[8513, 8513, 33*w - 56],
[8513, 8513, -33*w - 23],
[8521, 8521, 55*w - 167],
[8521, 8521, 55*w + 112],
[8537, 8537, -13*w - 94],
[8537, 8537, 13*w - 107],
[8543, 8543, 48*w - 137],
[8543, 8543, 48*w + 89],
[8563, 8563, -9*w - 92],
[8563, 8563, 9*w - 101],
[8573, 8573, 42*w - 109],
[8573, 8573, 42*w + 67],
[8581, 8581, 67*w + 148],
[8581, 8581, 67*w - 215],
[8609, 8609, 66*w - 211],
[8609, 8609, 66*w + 145],
[8647, 8647, 64*w - 203],
[8647, 8647, 64*w + 139],
[8669, 8669, 17*w - 115],
[8669, 8669, -17*w - 98],
[8699, 8699, -5*w - 92],
[8699, 8699, 5*w - 97],
[8707, 8707, 31*w - 2],
[8707, 8707, 31*w - 29],
[8731, 8731, 43*w + 70],
[8731, 8731, 43*w - 113],
[8741, 8741, -33*w - 20],
[8741, 8741, 33*w - 53],
[8753, 8753, 32*w - 151],
[8753, 8753, -32*w - 119],
[8779, 8779, 31*w - 5],
[8779, 8779, 31*w - 26],
[8803, 8803, 21*w - 124],
[8803, 8803, -21*w - 103],
[8807, 8807, 51*w - 149],
[8807, 8807, 51*w + 98],
[8831, 8831, 45*w - 122],
[8831, 8831, 45*w + 77],
[8839, 8839, -15*w - 97],
[8839, 8839, 15*w - 112],
[8887, 8887, 31*w - 14],
[8887, 8887, 31*w - 17],
[8929, 8929, -34*w - 25],
[8929, 8929, 34*w - 59],
[8933, 8933, 31*w - 149],
[8933, 8933, -31*w - 118],
[8951, 8951, -33*w - 17],
[8951, 8951, 33*w - 50],
[8963, 8963, -36*w - 37],
[8963, 8963, 36*w - 73],
[9001, 9001, -38*w - 47],
[9001, 9001, 38*w - 85],
[9007, 9007, -27*w + 139],
[9007, 9007, 27*w + 112],
[9029, 9029, 45*w + 76],
[9029, 9029, 45*w - 121],
[9049, 9049, 15*w - 113],
[9049, 9049, -15*w - 98],
[9091, 9091, 47*w + 83],
[9091, 9091, 47*w - 130],
[9103, 9103, 18*w - 119],
[9103, 9103, -18*w - 101],
[9109, 9109, -33*w - 122],
[9109, 9109, 33*w - 155],
[9127, 9127, 56*w + 113],
[9127, 9127, 56*w - 169],
[9151, 9151, 9*w - 104],
[9151, 9151, -9*w - 95],
[9173, 9173, 57*w - 173],
[9173, 9173, 57*w + 116],
[9187, 9187, 71*w - 229],
[9187, 9187, 71*w + 158],
[9203, 9203, 33*w - 46],
[9203, 9203, -33*w - 13],
[9209, 9209, -8*w - 95],
[9209, 9209, 8*w - 103],
[9239, 9239, 39*w - 89],
[9239, 9239, -39*w - 50],
[9241, 9241, 37*w - 77],
[9241, 9241, -37*w - 40],
[9257, 9257, 69*w + 152],
[9257, 9257, 69*w - 221],
[9277, 9277, 12*w - 109],
[9277, 9277, -12*w - 97],
[9283, 9283, 68*w + 149],
[9283, 9283, 68*w - 217],
[9323, 9323, 63*w + 134],
[9323, 9323, 63*w - 197],
[9349, 9349, 55*w - 164],
[9349, 9349, 55*w + 109],
[9371, 9371, -33*w - 10],
[9371, 9371, 33*w - 43],
[9377, 9377, -39*w - 49],
[9377, 9377, 39*w - 88],
[9391, 9391, 32*w - 7],
[9391, 9391, 32*w - 25],
[9397, 9397, -34*w - 19],
[9397, 9397, 34*w - 53],
[9409, 97, -97],
[9419, 9419, 45*w + 74],
[9419, 9419, 45*w - 119],
[9431, 9431, 48*w + 85],
[9431, 9431, 48*w - 133],
[9439, 9439, 35*w - 61],
[9439, 9439, -35*w - 26],
[9461, 9461, 57*w + 115],
[9461, 9461, 57*w - 172],
[9463, 9463, 32*w - 19],
[9463, 9463, 32*w - 13],
[9473, 9473, 33*w - 41],
[9473, 9473, -33*w - 8],
[9479, 9479, 10*w - 107],
[9479, 9479, -10*w - 97],
[9497, 9497, -w - 97],
[9497, 9497, w - 98],
[9521, 9521, 33*w - 40],
[9521, 9521, -33*w - 7],
[9539, 9539, 51*w - 146],
[9539, 9539, 51*w + 95],
[9547, 9547, 18*w - 121],
[9547, 9547, -18*w - 103],
[9587, 9587, -36*w - 31],
[9587, 9587, 36*w - 67],
[9613, 9613, 61*w - 188],
[9613, 9613, 61*w + 127],
[9619, 9619, 3*w - 100],
[9619, 9619, -3*w - 97],
[9623, 9623, 26*w - 139],
[9623, 9623, -26*w - 113],
[9629, 9629, 69*w + 151],
[9629, 9629, 69*w - 220],
[9631, 9631, 30*w + 119],
[9631, 9631, -30*w + 149],
[9661, 9661, 67*w - 212],
[9661, 9661, 67*w + 145],
[9697, 9697, -41*w - 56],
[9697, 9697, 41*w - 97],
[9719, 9719, -25*w - 112],
[9719, 9719, 25*w - 137],
[9721, 9721, 47*w + 80],
[9721, 9721, 47*w - 127],
[9743, 9743, 31*w - 152],
[9743, 9743, 31*w + 121],
[9767, 9767, -33*w - 1],
[9767, 9767, 33*w - 34],
[9769, 9769, 27*w - 142],
[9769, 9769, -27*w - 115],
[9817, 9817, -3*w - 98],
[9817, 9817, 3*w - 101],
[9833, 9833, 33*w - 32],
[9833, 9833, 33*w - 1],
[9839, 9839, -35*w - 128],
[9839, 9839, 35*w - 163],
[9851, 9851, 14*w - 115],
[9851, 9851, -14*w - 101],
[9883, 9883, 52*w - 149],
[9883, 9883, 52*w + 97],
[9907, 9907, -37*w - 34],
[9907, 9907, 37*w - 71],
[9923, 9923, -22*w - 109],
[9923, 9923, 22*w - 131],
[9941, 9941, 33*w - 5],
[9941, 9941, 33*w - 28],
[9949, 9949, 33*w - 158],
[9949, 9949, -33*w - 125]];
primes := [ideal<ZF | {F!x : x in I}> : I in primesArray];

heckePol := x;
K := Rationals(); e := 1;

heckeEigenvaluesArray := [1, 1, -4, -1, -1, 3, 3, -10, 1, -9, -9, 3, 3, -3, -3, -4, -4, -15, -15, 11, 11, 9, 9, 3, 3, 12, 12, -7, -7, -6, -6, -4, -4, 15, 15, 8, 8, -13, -13, -10, 9, 9, -7, -7, 15, 15, -13, -13, -1, -1, 23, 23, -18, -18, 15, 15, -18, -18, 29, 29, 2, -18, -18, -25, -25, -18, -18, 23, 23, -10, -10, -27, -27, -34, 8, 8, 5, 5, 11, 11, 11, 11, 3, 3, 29, 29, -15, -15, -12, -12, 21, 21, 3, 3, -10, 23, 23, 27, 27, -27, -27, -10, -10, -25, -25, -15, -15, -37, -37, -9, -9, -3, -3, -1, -1, 21, 21, -28, -28, 15, 15, -13, -13, 11, 11, -27, -27, 41, 41, -15, -15, 3, 3, 23, 23, 11, 11, -3, -3, 32, 32, 0, 0, -22, -48, -48, -22, -22, -6, -6, -3, -3, 6, 6, -7, -7, 30, 30, -3, -3, -46, -12, -12, -27, -27, 29, 29, 35, 35, 5, 5, 42, 42, 11, 11, -10, -10, -36, -36, -51, -51, -7, -7, 3, 3, -36, -36, -3, -3, -33, -33, 57, 57, -57, -57, -19, -19, 50, 50, -37, -37, -36, -36, -16, -16, -24, -24, -49, -49, 36, 36, -37, -37, 54, 54, 59, 59, -49, -49, -9, -9, 57, 57, 66, 66, -33, -33, -37, -37, -13, -13, -25, -25, 59, 59, -3, -3, 53, 53, -39, -39, -22, -22, 23, 23, 42, 42, -13, -13, 18, 18, 48, 48, 15, 15, 29, 29, 8, 8, 33, 33, 14, 14, -34, -34, 17, 17, -15, -15, -13, -13, 14, 14, -16, -16, 24, 24, -25, -25, 51, 51, -12, -12, -22, -55, -55, -21, -21, -30, -30, 69, 69, 9, 9, 53, 53, -33, -33, -55, -55, -54, -54, 35, 35, 81, 81, -25, -25, -9, -9, -63, -63, -15, -15, 9, 9, -49, -49, -51, -51, -55, -55, 59, 59, -88, -88, 33, 33, 20, 20, -78, -78, 53, 53, -72, -72, 29, 29, -69, -69, 56, 56, -55, -55, 87, 87, -7, -7, -19, -19, 27, 27, -76, -76, -25, -25, -22, -22, -30, -30, 3, 3, -15, -15, 11, 11, 96, 96, 6, 6, -7, -7, 60, 60, 27, 27, 2, 2, 17, 17, -30, -30, 45, 45, 71, 71, -1, -1, 21, 21, 86, 86, -99, -99, -13, -13, 54, 54, -31, -31, -97, -97, -42, -42, 68, 68, 51, 51, -37, -37, -81, -81, 6, 6, 48, 48, 17, 17, -54, -54, 60, 60, -51, -51, -34, -34, 27, 27, -84, -84, -39, -39, -88, -88, 95, 95, -9, -9, -85, -85, 21, 21, -25, -25, 89, 89, 21, 21, -31, -31, -48, -48, 14, 14, -51, -51, 15, 15, -75, -75, -19, -19, -31, -31, 18, 18, 20, 20, -55, -55, 69, 69, 9, 9, -25, -25, 0, 0, 99, 99, -63, -63, 83, 83, 57, 57, 59, 59, 26, -1, -1, -16, -16, -57, -57, 23, 23, -49, -49, -3, -3, 69, 69, -36, -36, -70, -70, 99, 99, -7, -7, 20, 20, 98, 98, -78, -78, 74, 74, -58, -88, -88, -1, -1, -45, -45, -30, -30, -55, -55, 32, 32, -69, -69, 69, 69, -43, -43, 15, 15, -67, -67, -45, -45, -99, -99, 107, 107, -25, -25, 21, 21, -75, -75, -28, -28, -51, -51, -73, -73, -57, -57, 9, 9, 63, 63, -33, -33, -73, -73, 21, 21, -94, -94, 101, 101, 57, 57, 6, 6, 8, 8, 90, 90, 23, 23, -12, -12, 12, 12, -75, -75, 9, 9, -115, -115, -43, -43, 71, 71, -105, -105, 51, 51, -94, -94, -7, -7, -39, -39, -42, -42, 81, 81, 107, 107, 23, 23, 3, 3, -69, -69, -21, -21, -1, -1, 32, 32, 65, 65, -118, -118, -67, -67, 99, 99, 80, 80, 119, 119, 75, 75, -72, -72, -121, -121, 57, 57, 113, 113, 47, 47, -96, -96, 95, 95, 53, 53, -57, -57, -19, -19, -33, -33, 14, 14, -81, -81, 29, 29, 57, 57, -43, -43, -46, -46, -12, -12, -7, -7, 68, 68, -55, -55, 45, 45, -43, -43, 48, 48, 119, 119, 102, 102, 72, 72, -139, -139, 65, 65, 84, 84, -75, -75, -15, -15, -67, -67, 138, 138, -100, -100, 41, 41, 45, 45, 84, 84, 62, 62, 36, 36, -129, -129, 81, 81, -87, -87, -49, -49, 8, 8, 131, 131, -30, -30, -1, -1, -39, -39, 126, 126, 104, 104, -22, -22, 51, 51, 35, 35, -63, -63, 18, 18, -7, -7, -58, -58, 83, 83, 105, 105, -33, -33, -109, -109, 8, 8, 69, 69, 93, 93, 53, 53, -75, -75, -39, -39, 65, 65, 144, 144, -85, -85, 87, 87, 131, 131, 132, 132, 92, 92, 23, 23, -87, -87, 66, 66, -142, -142, 48, 48, 131, 131, 69, 69, -112, -112, 44, 44, 26, 26, -58, -93, -93, -99, -99, 93, 93, -72, -72, -57, -57, 110, 110, -99, -99, -18, -18, 9, 9, 38, 38, 71, 71, -135, -135, -127, -127, 59, 59, -133, -133, -138, -138, 17, 17, -7, -7, 15, 15, 27, 27, 147, 147, 2, 2, -154, -154, 56, 56, 95, 95, 51, 51, -36, -36, -61, -61, -45, -45, 59, 59, 83, 83, -81, -81, 75, 75, 158, 158, 71, 71, -27, -27, 65, 65, 87, 87, 140, 140, 44, 44, 41, 41, 132, 132, -70, -70, 105, 105, -7, -7, 54, 54, -135, -135, 95, 95, -36, -36, 80, 80, -61, -61, -25, -25, -141, -141, -159, -159, -79, -79, -48, -48, -31, -31, -132, -132, 51, 51, 65, 65, -28, -28, -9, -9, -46, -46, -163, -163, 59, 59, -76, -76, 102, 102, 125, 125, 150, 150, 72, 72, 11, 11, 159, 159, 23, 23, -42, -42, 123, 123, 89, 89, 45, 45, -103, -103, 51, 51, -1, -1, -9, -9, 126, 126, -25, -25, -7, -7, -121, -121, -69, -69, -31, -31, 101, 101, -25, -25, -57, -57, 9, 9, -174, -174, -114, -114, 42, 42, -147, -147, -153, -153, -142, 107, 107, 32, 32, -25, -25, 143, 143, -105, -105, -112, -112, -18, -18, 48, 48, -51, -51, 168, 168, -91, -91, -67, -67, -85, -85, 137, 137, 17, 17, -48, -48, 51, 51, 131, 131, -151, -151, -141, -141, -51, -51, -3, -3, 146, 146, -135, -135, 101, 101, -147, -147, 146, 146, 102, 102, -51, -51, 35, 35, 123, 123, 168, 168, -103, -103, 6, 6, 5, 5, 66, 66, 8, 8, -33, -33, 63, 63, -103, -103, -97, -97, 135, 135, -42, -42, -139, -139, -25, -25, 33, 33, 81, 81, -151, -151, -31, -31, -106, -106, -105, -105, 27, 27, 96, 96, -106, -106, -73, -73, -69, -69, -139, -139, 65, 65, 32, 32, 65, 65, -52, -52, -37, -37, 51, 51, 143, 143, 33, 33, 186, 186, -3, -3, -55, -55, -117, -117, 98, 98, -148, -148, 63, 63, -145, -145, 147, 147, 141, 141, -184, -184, 2, 2, -130, -51, -51, 48, 48, 35, 35, -105, -105, 140, 140, 51, 51, -120, -120, -171, -171, -165, -165, -69, -69, 152, 152, -84, -84, 137, 137, -1, -1, 96, 96, -21, -21, -16, -16, -13, -13, -31, -31, 87, 87, -61, -61, -15, -15, 129, 129, -31, -31, -73, -73, 57, 57, 123, 123, -60, -60, -124, -124, 89, 89, -180, -180, 21, 21, 23, 23];
heckeEigenvalues := AssociativeArray();
for i := 1 to #heckeEigenvaluesArray do
  heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i];
end for;

ALEigenvalues := AssociativeArray();
ALEigenvalues[ideal<ZF | {37, 37, 2*w - 1}>] := -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;