/* 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 := PolynomialRing(Rationals()); g := P![18, 0, -12, 0, 1]; F := NumberField(g); ZF := Integers(F); NN := ideal; primesArray := [ [2, 2, -1/3*w^3 - 1/3*w^2 + 3*w + 4], [7, 7, 1/3*w^3 + 1/3*w^2 - 3*w - 3], [7, 7, -1/3*w^2 + w + 1], [7, 7, 1/3*w^2 + w - 1], [7, 7, 1/3*w^3 - 1/3*w^2 - 3*w + 3], [9, 3, w - 3], [41, 41, 1/3*w^3 - 1/3*w^2 - 3*w + 1], [41, 41, -1/3*w^2 + w + 3], [41, 41, 1/3*w^2 + w - 3], [41, 41, -1/3*w^3 - 1/3*w^2 + 3*w + 1], [47, 47, 1/3*w^3 + 1/3*w^2 - 4*w - 1], [47, 47, -1/3*w^3 + 1/3*w^2 + 2*w - 3], [47, 47, 1/3*w^3 + 1/3*w^2 - 2*w - 3], [47, 47, 1/3*w^3 - 1/3*w^2 - 4*w + 1], [89, 89, -1/3*w^3 + 2/3*w^2 + 3*w - 3], [89, 89, 2/3*w^2 + w - 5], [89, 89, 2/3*w^2 - w - 5], [89, 89, 1/3*w^3 + 2/3*w^2 - 3*w - 3], [97, 97, 2/3*w^3 - 1/3*w^2 - 6*w + 5], [97, 97, -w^3 - 5/3*w^2 + 10*w + 15], [97, 97, -5/3*w^3 - 5/3*w^2 + 16*w + 21], [97, 97, -2/3*w^3 - 1/3*w^2 + 6*w + 5], [103, 103, -4/3*w^3 - 4/3*w^2 + 13*w + 17], [103, 103, 1/3*w^3 + w^2 - 5*w - 7], [103, 103, -w^3 - w^2 + 9*w + 11], [103, 103, -2/3*w^3 - 4/3*w^2 + 7*w + 11], [137, 137, -1/3*w^3 - 1/3*w^2 + 3*w - 1], [137, 137, 1/3*w^2 + w - 5], [137, 137, 1/3*w^2 - w - 5], [137, 137, 1/3*w^3 - 1/3*w^2 - 3*w - 1], [151, 151, w^2 - w - 5], [151, 151, 1/3*w^3 + w^2 - 3*w - 7], [151, 151, -1/3*w^3 + w^2 + 3*w - 7], [151, 151, w^2 + w - 5], [191, 191, 1/3*w^3 + 2/3*w^2 - 4*w - 3], [191, 191, 1/3*w^3 + 2/3*w^2 - 2*w - 5], [191, 191, -1/3*w^3 + 2/3*w^2 + 2*w - 5], [191, 191, -1/3*w^3 + 2/3*w^2 + 4*w - 3], [193, 193, 2/3*w^3 + w^2 - 8*w - 7], [193, 193, -1/3*w^3 - 1/3*w^2 + 4*w + 7], [193, 193, -7/3*w^3 - 13/3*w^2 + 26*w + 37], [193, 193, -2/3*w^3 + w^2 + 8*w - 7], [199, 199, 5/3*w^3 + 2*w^2 - 17*w - 23], [199, 199, -2/3*w^3 - 5/3*w^2 + 9*w + 13], [199, 199, -2/3*w^3 - 1/3*w^2 + 5*w + 5], [199, 199, -w^3 - 2*w^2 + 11*w + 17], [233, 233, 1/3*w^3 - 4/3*w^2 - 3*w + 5], [233, 233, 1/3*w^3 - 4/3*w^2 - 5*w + 7], [233, 233, 4/3*w^2 + w - 11], [233, 233, 1/3*w^3 + 4/3*w^2 - 3*w - 5], [239, 239, 1/3*w^3 + w^2 - 4*w - 5], [239, 239, 4/3*w^3 + 4/3*w^2 - 14*w - 17], [239, 239, 4/3*w^3 + 2/3*w^2 - 12*w - 13], [239, 239, -1/3*w^3 + w^2 + 4*w - 5], [241, 241, -2/3*w^3 + 6*w + 1], [241, 241, 2/3*w^3 - 1/3*w^2 - 6*w + 3], [241, 241, -2/3*w^3 - 1/3*w^2 + 6*w + 3], [241, 241, 2/3*w^3 - 6*w + 1], [281, 281, -w^3 - w^2 + 9*w + 13], [281, 281, -2/3*w^3 - 2/3*w^2 + 5*w + 7], [281, 281, -2/3*w^3 + 2/3*w^2 + 5*w - 7], [281, 281, -7/3*w^3 - 3*w^2 + 23*w + 31], [289, 17, w^2 - 5], [289, 17, w^2 - 7], [337, 337, -w^3 + 4/3*w^2 + 8*w - 7], [337, 337, -2*w + 7], [337, 337, 2/3*w^3 - 2*w^2 - 4*w + 11], [337, 337, 1/3*w^3 + 2/3*w^2 - 6*w + 1], [383, 383, 2/3*w^3 + 5/3*w^2 - 8*w - 11], [383, 383, -w^3 - 2/3*w^2 + 10*w + 11], [383, 383, -5/3*w^3 - 4/3*w^2 + 16*w + 19], [383, 383, -4/3*w^3 - 7/3*w^2 + 14*w + 19], [431, 431, -2/3*w^3 + 1/3*w^2 + 4*w - 5], [431, 431, -2/3*w^3 - 1/3*w^2 + 8*w - 1], [431, 431, 2/3*w^3 - 1/3*w^2 - 8*w - 1], [431, 431, 2/3*w^3 + 1/3*w^2 - 4*w - 5], [433, 433, 2/3*w^3 + 7/3*w^2 - 10*w - 15], [433, 433, -3*w^3 - 10/3*w^2 + 30*w + 39], [433, 433, -1/3*w^3 - 4/3*w^2 + 4*w + 9], [433, 433, -4/3*w^3 - 5/3*w^2 + 12*w + 15], [439, 439, -4/3*w^3 - 1/3*w^2 + 11*w + 13], [439, 439, 1/3*w^3 + 2/3*w^2 - 5*w - 5], [439, 439, -3*w^3 - 10/3*w^2 + 29*w + 37], [439, 439, -4/3*w^3 - 7/3*w^2 + 13*w + 19], [479, 479, 1/3*w^2 - 2*w - 5], [479, 479, 2/3*w^3 + 1/3*w^2 - 6*w + 1], [479, 479, 2/3*w^3 - 1/3*w^2 - 6*w - 1], [479, 479, -1/3*w^2 - 2*w + 5], [487, 487, 1/3*w^3 + 4/3*w^2 - 3*w - 7], [487, 487, 4/3*w^2 - w - 9], [487, 487, -4/3*w^2 - w + 9], [487, 487, 1/3*w^3 - 4/3*w^2 - 3*w + 7], [521, 521, 2/3*w^3 - 2/3*w^2 - 5*w - 3], [521, 521, 5/3*w^3 + 7/3*w^2 - 17*w - 21], [521, 521, -7/3*w^3 - 11/3*w^2 + 25*w + 33], [521, 521, -4/3*w^3 - 2/3*w^2 + 13*w + 15], [529, 23, -1/3*w^2 - 3], [529, 23, 1/3*w^2 - 7], [569, 569, 2/3*w^3 + 2/3*w^2 - 5*w + 1], [569, 569, 1/3*w^3 - 2/3*w^2 - 5*w + 9], [569, 569, -1/3*w^3 - 2/3*w^2 + 5*w + 9], [569, 569, -2/3*w^3 + 2/3*w^2 + 5*w + 1], [577, 577, -w^3 + 1/3*w^2 + 8*w + 3], [577, 577, -1/3*w^3 - 1/3*w^2 + 6*w + 7], [577, 577, 1/3*w^3 - 1/3*w^2 - 6*w + 7], [577, 577, w^3 + 1/3*w^2 - 8*w + 3], [617, 617, -2/3*w^3 - 5/3*w^2 + 5*w + 7], [617, 617, -5/3*w^2 + 3*w + 5], [617, 617, -8/3*w^3 - 13/3*w^2 + 27*w + 37], [617, 617, -w^3 - 5/3*w^2 + 9*w + 15], [625, 5, -5], [631, 631, -1/3*w^3 - 5/3*w^2 + 3*w + 7], [631, 631, -5/3*w^2 - w + 13], [631, 631, 5/3*w^2 - w - 13], [631, 631, 1/3*w^3 - 5/3*w^2 - 3*w + 7], [673, 673, 2/3*w^3 + 1/3*w^2 - 8*w - 1], [673, 673, -2/3*w^3 - 1/3*w^2 + 4*w + 3], [673, 673, -2/3*w^3 + 1/3*w^2 + 4*w - 3], [673, 673, 2/3*w^3 - 1/3*w^2 - 8*w + 1], [719, 719, 1/3*w^3 - 1/3*w^2 - 6*w + 9], [719, 719, w^3 - 1/3*w^2 - 8*w - 5], [719, 719, w^3 + 1/3*w^2 - 8*w + 5], [719, 719, -1/3*w^3 - 1/3*w^2 + 6*w + 9], [727, 727, 2/3*w^3 + 1/3*w^2 - 5*w - 1], [727, 727, -1/3*w^3 - 1/3*w^2 + 5*w + 3], [727, 727, 1/3*w^3 - 1/3*w^2 - 5*w + 3], [727, 727, -2/3*w^3 + 1/3*w^2 + 5*w - 1], [761, 761, -2/3*w^3 + 1/3*w^2 + 3*w + 3], [761, 761, 7/3*w^3 + 10/3*w^2 - 23*w - 33], [761, 761, 3*w^3 + 10/3*w^2 - 29*w - 39], [761, 761, -2*w^3 - 5/3*w^2 + 17*w + 21], [769, 769, -4/3*w^3 - w^2 + 12*w + 13], [769, 769, -w^3 - 2/3*w^2 + 10*w + 13], [769, 769, -w^3 - 8/3*w^2 + 12*w + 19], [769, 769, -2*w^3 - 3*w^2 + 22*w + 29], [809, 809, -2/3*w^3 - 2/3*w^2 + 7*w + 3], [809, 809, w^2 + w - 11], [809, 809, w^2 - w - 11], [809, 809, 2/3*w^3 - 2/3*w^2 - 7*w + 3], [823, 823, 1/3*w^3 - 5*w - 1], [823, 823, 2/3*w^3 - 5*w - 1], [823, 823, 2/3*w^3 - 5*w + 1], [823, 823, -1/3*w^3 + 5*w - 1], [857, 857, -5/3*w^2 + w + 15], [857, 857, -1/3*w^3 - 5/3*w^2 + 3*w + 5], [857, 857, 1/3*w^3 - 5/3*w^2 - 3*w + 5], [857, 857, 5/3*w^2 + w - 15], [863, 863, -2/3*w^3 - 5/3*w^2 + 10*w + 15], [863, 863, -5/3*w^3 - 8/3*w^2 + 18*w + 27], [863, 863, -3*w^3 - 14/3*w^2 + 32*w + 45], [863, 863, -5/3*w^2 + 4*w + 9], [911, 911, 1/3*w^3 - 2/3*w^2 - 4*w - 1], [911, 911, -1/3*w^3 + 2/3*w^2 + 2*w - 9], [911, 911, 1/3*w^3 + 2/3*w^2 - 2*w - 9], [911, 911, -1/3*w^3 - 2/3*w^2 + 4*w - 1], [919, 919, w^3 + 1/3*w^2 - 9*w - 1], [919, 919, -w^3 - 2/3*w^2 + 9*w + 7], [919, 919, w^3 - 2/3*w^2 - 9*w + 7], [919, 919, -w^3 + 1/3*w^2 + 9*w - 1], [953, 953, -w^3 - w^2 + 9*w + 5], [953, 953, -w^2 - 3*w + 7], [953, 953, w^2 - 3*w - 7], [953, 953, w^3 - w^2 - 9*w + 5], [961, 31, 4/3*w^2 - 7], [961, 31, 4/3*w^2 - 9], [967, 967, -w^3 - 1/3*w^2 + 9*w + 5], [967, 967, w^3 + 2/3*w^2 - 9*w - 5], [967, 967, -w^3 + 2/3*w^2 + 9*w - 5], [967, 967, w^3 - 1/3*w^2 - 9*w + 5], [1009, 1009, 1/3*w^3 + 5/3*w^2 - 4*w - 9], [1009, 1009, -8/3*w^3 - 10/3*w^2 + 26*w + 33], [1009, 1009, 4/3*w^3 + 8/3*w^2 - 16*w - 21], [1009, 1009, 7/3*w^3 + 5/3*w^2 - 22*w - 27], [1049, 1049, -2/3*w^3 + 2/3*w^2 + 5*w - 9], [1049, 1049, -1/3*w^3 - 2/3*w^2 + 5*w - 1], [1049, 1049, 1/3*w^3 - 2/3*w^2 - 5*w - 1], [1049, 1049, 2/3*w^3 + 2/3*w^2 - 5*w - 9], [1063, 1063, w^3 + 2/3*w^2 - 9*w - 13], [1063, 1063, 2*w^3 + w^2 - 17*w - 19], [1063, 1063, -2/3*w^3 - w^2 + 9*w + 11], [1063, 1063, -3*w^3 - 14/3*w^2 + 31*w + 43], [1097, 1097, -2/3*w^3 + 1/3*w^2 + 7*w + 1], [1097, 1097, 1/3*w^3 + 1/3*w^2 - w - 5], [1097, 1097, -1/3*w^3 + 1/3*w^2 + w - 5], [1097, 1097, 2/3*w^3 + 1/3*w^2 - 7*w + 1], [1103, 1103, 2/3*w^2 + 2*w - 7], [1103, 1103, 2/3*w^3 + 2/3*w^2 - 6*w - 1], [1103, 1103, -2/3*w^3 + 2/3*w^2 + 6*w - 1], [1103, 1103, 2/3*w^2 - 2*w - 7], [1151, 1151, -2/3*w^3 + 4*w - 7], [1151, 1151, 2/3*w^3 - 8*w - 7], [1151, 1151, -2/3*w^3 + 8*w - 7], [1151, 1151, 2/3*w^3 - 4*w - 7], [1153, 1153, -1/3*w^3 + 6*w - 5], [1153, 1153, -w^3 + 8*w + 5], [1153, 1153, -w^3 + 8*w - 5], [1153, 1153, 1/3*w^3 - 6*w - 5], [1193, 1193, -1/3*w^3 - 2/3*w^2 + 5*w - 3], [1193, 1193, 2/3*w^3 + 2/3*w^2 - 5*w - 11], [1193, 1193, -2/3*w^3 + 2/3*w^2 + 5*w - 11], [1193, 1193, 1/3*w^3 - 2/3*w^2 - 5*w - 3], [1201, 1201, -7/3*w^3 - 4/3*w^2 + 20*w + 23], [1201, 1201, -w^3 + 2/3*w^2 + 8*w - 1], [1201, 1201, w^3 + 2/3*w^2 - 8*w - 1], [1201, 1201, 1/3*w^3 + 2/3*w^2 - 6*w - 7], [1249, 1249, -2/3*w^3 + 2*w^2 + 6*w - 11], [1249, 1249, 2*w^2 + 2*w - 13], [1249, 1249, 2*w^2 - 2*w - 13], [1249, 1249, 2/3*w^3 + 2*w^2 - 6*w - 11], [1289, 1289, w^3 - 2/3*w^2 - 11*w + 3], [1289, 1289, 1/3*w^3 + w^2 - 5*w - 11], [1289, 1289, -1/3*w^3 + w^2 + 5*w - 11], [1289, 1289, -w^3 - 2/3*w^2 + 11*w + 3], [1297, 1297, -1/3*w^3 + 4*w - 7], [1297, 1297, -1/3*w^3 + 2*w - 7], [1297, 1297, 1/3*w^3 - 2*w - 7], [1297, 1297, 1/3*w^3 - 4*w - 7], [1303, 1303, 1/3*w^3 - 2/3*w^2 - 5*w + 13], [1303, 1303, -11/3*w^3 - 13/3*w^2 + 37*w + 49], [1303, 1303, -w^3 - 7/3*w^2 + 11*w + 19], [1303, 1303, -1/3*w^3 - 2/3*w^2 + 5*w + 13], [1399, 1399, 4/3*w^3 + 2/3*w^2 - 11*w + 1], [1399, 1399, -1/3*w^3 - 2/3*w^2 + 7*w + 9], [1399, 1399, 1/3*w^3 - 2/3*w^2 - 7*w + 9], [1399, 1399, -4/3*w^3 + 2/3*w^2 + 11*w + 1], [1433, 1433, w^3 - 9*w - 7], [1433, 1433, 4/3*w^3 + 11/3*w^2 - 17*w - 25], [1433, 1433, -4/3*w^3 - 7/3*w^2 + 13*w + 17], [1433, 1433, -w^3 + 9*w - 7], [1439, 1439, -1/3*w^3 - 4/3*w^2 + 6*w + 11], [1439, 1439, -2*w^3 - 3*w^2 + 22*w + 31], [1439, 1439, 4/3*w^3 + 3*w^2 - 16*w - 25], [1439, 1439, -5/3*w^3 - 10/3*w^2 + 20*w + 29], [1447, 1447, 1/3*w^2 + w - 9], [1447, 1447, 1/3*w^3 - 1/3*w^2 - 3*w - 5], [1447, 1447, -1/3*w^3 - 1/3*w^2 + 3*w - 5], [1447, 1447, 1/3*w^2 - w - 9], [1481, 1481, -2/3*w^3 + 5/3*w^2 + 7*w - 9], [1481, 1481, 1/3*w^3 + 5/3*w^2 - w - 11], [1481, 1481, -1/3*w^3 + 5/3*w^2 + w - 11], [1481, 1481, -2/3*w^3 - 5/3*w^2 + 7*w + 9], [1487, 1487, 2/3*w^3 + 8/3*w^2 - 10*w - 15], [1487, 1487, -w^3 - 1/3*w^2 + 10*w + 9], [1487, 1487, -w^3 + 1/3*w^2 + 10*w - 9], [1487, 1487, -2*w^3 - 10/3*w^2 + 20*w + 27], [1489, 1489, -1/3*w^3 + 5/3*w^2 + 2*w - 9], [1489, 1489, -1/3*w^3 + 5/3*w^2 + 4*w - 11], [1489, 1489, 1/3*w^3 + 5/3*w^2 - 4*w - 11], [1489, 1489, 1/3*w^3 + 5/3*w^2 - 2*w - 9], [1543, 1543, -4*w^3 - 13/3*w^2 + 39*w + 49], [1543, 1543, 4*w^3 + 5*w^2 - 41*w - 55], [1543, 1543, 2/3*w^3 - 2/3*w^2 - 9*w + 1], [1543, 1543, 4/3*w^3 + 5/3*w^2 - 15*w - 17], [1583, 1583, -1/3*w^3 + w^2 + 4*w + 1], [1583, 1583, 1/3*w^3 + w^2 - 2*w - 13], [1583, 1583, -1/3*w^3 + w^2 + 2*w - 13], [1583, 1583, -1/3*w^3 - w^2 + 4*w - 1], [1721, 1721, w^3 - 1/3*w^2 - 7*w + 9], [1721, 1721, 2/3*w^3 + 1/3*w^2 - 9*w + 5], [1721, 1721, -2/3*w^3 + 1/3*w^2 + 9*w + 5], [1721, 1721, w^3 + 1/3*w^2 - 7*w - 9], [1777, 1777, -8/3*w^3 - 3*w^2 + 28*w + 37], [1777, 1777, -w^3 - 2/3*w^2 + 8*w + 7], [1777, 1777, -w^3 + 2/3*w^2 + 8*w - 7], [1777, 1777, -2/3*w^3 - 3*w^2 + 10*w + 19], [1783, 1783, -1/3*w^2 - w - 5], [1783, 1783, -1/3*w^3 + 1/3*w^2 + 3*w - 9], [1783, 1783, 1/3*w^3 + 1/3*w^2 - 3*w - 9], [1783, 1783, -1/3*w^2 + w - 5], [1823, 1823, 2/3*w^3 - 4/3*w^2 - 4*w + 9], [1823, 1823, 2/3*w^3 - 4/3*w^2 - 8*w + 7], [1823, 1823, 2/3*w^3 + 4/3*w^2 - 8*w - 7], [1823, 1823, 2/3*w^3 + 4/3*w^2 - 4*w - 9], [1831, 1831, -w - 7], [1831, 1831, -1/3*w^3 + 3*w - 7], [1831, 1831, 1/3*w^3 - 3*w - 7], [1831, 1831, w - 7], [1871, 1871, -4*w^3 - 13/3*w^2 + 38*w + 49], [1871, 1871, -7/3*w^3 - 10/3*w^2 + 22*w + 31], [1871, 1871, -7/3*w^3 - 4/3*w^2 + 20*w + 25], [1871, 1871, 2/3*w^3 + 1/3*w^2 - 4*w - 7], [1873, 1873, -1/3*w^2 + 4*w - 3], [1873, 1873, 4/3*w^3 + 1/3*w^2 - 12*w - 7], [1873, 1873, 4/3*w^3 - 1/3*w^2 - 12*w + 7], [1873, 1873, 1/3*w^2 + 4*w + 3], [1879, 1879, -1/3*w^3 + 7/3*w^2 + 5*w - 11], [1879, 1879, 2/3*w^3 + 7/3*w^2 - 5*w - 17], [1879, 1879, -2/3*w^3 + 7/3*w^2 + 5*w - 17], [1879, 1879, 1/3*w^3 + 7/3*w^2 - 5*w - 11], [1913, 1913, 1/3*w^3 + 1/3*w^2 - w - 7], [1913, 1913, -2/3*w^3 - 1/3*w^2 + 7*w - 3], [1913, 1913, 2/3*w^3 - 1/3*w^2 - 7*w - 3], [1913, 1913, -1/3*w^3 + 1/3*w^2 + w - 7]]; primes := [ideal : I in primesArray]; heckePol := x^6 + 4*x^5 - 14*x^4 - 60*x^3 - 19*x^2 + 72*x + 44; K := NumberField(heckePol); heckeEigenvaluesArray := [1, 1, e, 1/10*e^5 + 7/20*e^4 - 29/20*e^3 - 103/20*e^2 - 19/20*e + 53/10, 1/5*e^5 + 9/20*e^4 - 73/20*e^3 - 121/20*e^2 + 147/20*e + 61/10, 1/5*e^5 + 9/20*e^4 - 73/20*e^3 - 121/20*e^2 + 147/20*e + 81/10, -1/20*e^5 - 1/20*e^4 + 17/20*e^3 - 1/20*e^2 + 21/10*e + 28/5, -3/20*e^5 - 2/5*e^4 + 14/5*e^3 + 61/10*e^2 - 149/20*e - 87/10, -1/10*e^5 - 7/20*e^4 + 39/20*e^3 + 103/20*e^2 - 131/20*e - 53/10, -3/20*e^5 - 2/5*e^4 + 14/5*e^3 + 61/10*e^2 - 149/20*e - 87/10, 1/5*e^5 + 7/10*e^4 - 17/5*e^3 - 103/10*e^2 + 33/5*e + 58/5, -9/20*e^5 - 6/5*e^4 + 79/10*e^3 + 163/10*e^2 - 257/20*e - 151/10, -3/20*e^5 - 3/20*e^4 + 51/20*e^3 - 3/20*e^2 - 27/10*e + 54/5, 13/20*e^5 + 33/20*e^4 - 231/20*e^3 - 447/20*e^2 + 106/5*e + 141/5, -2/5*e^5 - 7/5*e^4 + 34/5*e^3 + 103/5*e^2 - 46/5*e - 76/5, 7/10*e^5 + 39/20*e^4 - 233/20*e^3 - 531/20*e^2 + 217/20*e + 221/10, 3/5*e^5 + 21/10*e^4 - 97/10*e^3 - 309/10*e^2 + 83/10*e + 179/5, 19/20*e^5 + 59/20*e^4 - 313/20*e^3 - 821/20*e^2 + 88/5*e + 183/5, -11/10*e^5 - 67/20*e^4 + 369/20*e^3 + 963/20*e^2 - 461/20*e - 523/10, -9/20*e^5 - 29/20*e^4 + 143/20*e^3 + 411/20*e^2 - 28/5*e - 93/5, -1/20*e^5 - 1/20*e^4 + 17/20*e^3 + 19/20*e^2 + 21/10*e - 12/5, 13/20*e^5 + 43/20*e^4 - 211/20*e^3 - 617/20*e^2 + 61/5*e + 161/5, 3/10*e^5 + 21/20*e^4 - 97/20*e^3 - 309/20*e^2 + 53/20*e + 159/10, -2/5*e^5 - 9/10*e^4 + 39/5*e^3 + 121/10*e^2 - 111/5*e - 76/5, -2/5*e^5 - 9/10*e^4 + 34/5*e^3 + 111/10*e^2 - 31/5*e - 26/5, 11/20*e^5 + 13/10*e^4 - 101/10*e^3 - 91/5*e^2 + 403/20*e + 209/10, -11/10*e^5 - 18/5*e^4 + 91/5*e^3 + 267/5*e^2 - 203/10*e - 289/5, e^5 + 3*e^4 - 16*e^3 - 42*e^2 + 10*e + 46, 3/5*e^5 + 11/10*e^4 - 56/5*e^3 - 139/10*e^2 + 119/5*e + 64/5, -9/20*e^5 - 29/20*e^4 + 143/20*e^3 + 411/20*e^2 - 3/5*e - 93/5, 19/20*e^5 + 27/10*e^4 - 82/5*e^3 - 194/5*e^2 + 457/20*e + 431/10, 9/20*e^5 + 19/20*e^4 - 163/20*e^3 - 241/20*e^2 + 83/5*e + 33/5, 7/5*e^5 + 39/10*e^4 - 119/5*e^3 - 541/10*e^2 + 146/5*e + 286/5, -29/20*e^5 - 89/20*e^4 + 503/20*e^3 + 1291/20*e^2 - 213/5*e - 393/5, -6/5*e^5 - 69/20*e^4 + 413/20*e^3 + 1001/20*e^2 - 527/20*e - 631/10, -1/10*e^5 - 3/5*e^4 + 17/10*e^3 + 52/5*e^2 - 34/5*e - 114/5, -3/10*e^5 - 11/20*e^4 + 127/20*e^3 + 139/20*e^2 - 443/20*e - 109/10, -13/20*e^5 - 7/5*e^4 + 113/10*e^3 + 161/10*e^2 - 309/20*e - 17/10, -6/5*e^5 - 37/10*e^4 + 97/5*e^3 + 513/10*e^2 - 88/5*e - 218/5, 1/4*e^5 + 1/2*e^4 - 11/2*e^3 - 8*e^2 + 81/4*e + 37/2, -11/20*e^5 - 23/10*e^4 + 81/10*e^3 + 176/5*e^2 + 57/20*e - 359/10, 1/20*e^5 + 1/20*e^4 - 17/20*e^3 + 21/20*e^2 + 19/10*e - 58/5, 9/20*e^5 + 17/10*e^4 - 37/5*e^3 - 134/5*e^2 + 207/20*e + 381/10, -11/20*e^5 - 41/20*e^4 + 167/20*e^3 + 619/20*e^2 - 9/10*e - 202/5, 2/5*e^5 + 7/5*e^4 - 63/10*e^3 - 103/5*e^2 + 37/10*e + 101/5, -7/10*e^5 - 39/20*e^4 + 233/20*e^3 + 531/20*e^2 - 217/20*e - 241/10, 3/10*e^5 + 21/20*e^4 - 107/20*e^3 - 349/20*e^2 + 203/20*e + 319/10, -2/5*e^5 - 9/10*e^4 + 39/5*e^3 + 121/10*e^2 - 126/5*e - 36/5, 19/20*e^5 + 59/20*e^4 - 323/20*e^3 - 821/20*e^2 + 221/10*e + 178/5, 1/5*e^5 - 3/10*e^4 - 49/10*e^3 + 67/10*e^2 + 201/10*e - 17/5, -3/20*e^5 - 3/20*e^4 + 61/20*e^3 + 17/20*e^2 - 41/5*e - 1/5, 9/10*e^5 + 63/20*e^4 - 291/20*e^3 - 947/20*e^2 + 299/20*e + 567/10, -4/5*e^5 - 61/20*e^4 + 247/20*e^3 + 889/20*e^2 - 93/20*e - 479/10, 1/4*e^5 + e^4 - 9/2*e^3 - 31/2*e^2 + 45/4*e + 55/2, -7/5*e^5 - 73/20*e^4 + 481/20*e^3 + 997/20*e^2 - 639/20*e - 467/10, 11/20*e^5 + 41/20*e^4 - 177/20*e^3 - 619/20*e^2 + 32/5*e + 187/5, -17/20*e^5 - 57/20*e^4 + 289/20*e^3 + 843/20*e^2 - 203/10*e - 184/5, 8/5*e^5 + 23/5*e^4 - 267/10*e^3 - 327/5*e^2 + 263/10*e + 339/5, 17/20*e^5 + 57/20*e^4 - 279/20*e^3 - 823/20*e^2 + 89/5*e + 209/5, -8/5*e^5 - 23/5*e^4 + 136/5*e^3 + 327/5*e^2 - 189/5*e - 364/5, -17/20*e^5 - 21/10*e^4 + 76/5*e^3 + 147/5*e^2 - 611/20*e - 363/10, 11/20*e^5 + 13/10*e^4 - 53/5*e^3 - 96/5*e^2 + 533/20*e + 289/10, -e^5 - 11/4*e^4 + 71/4*e^3 + 159/4*e^2 - 109/4*e - 103/2, -33/20*e^5 - 93/20*e^4 + 561/20*e^3 + 1287/20*e^2 - 327/10*e - 306/5, -23/20*e^5 - 17/5*e^4 + 99/5*e^3 + 491/10*e^2 - 689/20*e - 607/10, -19/20*e^5 - 49/20*e^4 + 323/20*e^3 + 631/20*e^2 - 231/10*e - 98/5, -1/10*e^5 - 7/20*e^4 + 29/20*e^3 + 103/20*e^2 - 21/20*e - 83/10, -29/20*e^5 - 79/20*e^4 + 503/20*e^3 + 1101/20*e^2 - 188/5*e - 293/5, -49/20*e^5 - 149/20*e^4 + 813/20*e^3 + 2091/20*e^2 - 431/10*e - 518/5, 21/20*e^5 + 14/5*e^4 - 191/10*e^3 - 387/10*e^2 + 773/20*e + 429/10, 41/20*e^5 + 121/20*e^4 - 697/20*e^3 - 1699/20*e^2 + 459/10*e + 392/5, 13/20*e^5 + 19/10*e^4 - 54/5*e^3 - 133/5*e^2 + 299/20*e + 447/10, -11/4*e^5 - 31/4*e^4 + 189/4*e^3 + 437/4*e^2 - 67*e - 121, 5/4*e^5 + 7/2*e^4 - 43/2*e^3 - 48*e^2 + 117/4*e + 89/2, -33/20*e^5 - 27/5*e^4 + 139/5*e^3 + 801/10*e^2 - 699/20*e - 817/10, 3/20*e^5 + 9/10*e^4 - 23/10*e^3 - 78/5*e^2 - 21/20*e + 227/10, 3/5*e^5 + 37/20*e^4 - 209/20*e^3 - 533/20*e^2 + 331/20*e + 263/10, -9/10*e^5 - 7/5*e^4 + 173/10*e^3 + 78/5*e^2 - 236/5*e - 56/5, 23/20*e^5 + 39/10*e^4 - 193/10*e^3 - 288/5*e^2 + 579/20*e + 657/10, -11/20*e^5 - 13/10*e^4 + 91/10*e^3 + 76/5*e^2 - 103/20*e + 61/10, -9/10*e^5 - 29/10*e^4 + 74/5*e^3 + 411/10*e^2 - 207/10*e - 231/5, 19/20*e^5 + 16/5*e^4 - 77/5*e^3 - 443/10*e^2 + 257/20*e + 281/10, -6/5*e^5 - 27/10*e^4 + 209/10*e^3 + 313/10*e^2 - 291/10*e - 23/5, 4/5*e^5 + 51/20*e^4 - 257/20*e^3 - 759/20*e^2 + 143/20*e + 409/10, -1/4*e^4 - 5/4*e^3 + 9/4*e^2 + 67/4*e + 9/2, 9/20*e^5 + 39/20*e^4 - 113/20*e^3 - 581/20*e^2 - 169/10*e + 188/5, -33/20*e^5 - 22/5*e^4 + 293/10*e^3 + 601/10*e^2 - 1009/20*e - 627/10, -1/4*e^5 + 1/4*e^4 + 25/4*e^3 - 27/4*e^2 - 59/2*e + 6, 3/5*e^5 + 11/10*e^4 - 107/10*e^3 - 109/10*e^2 + 223/10*e - 1/5, -41/20*e^5 - 53/10*e^4 + 361/10*e^3 + 371/5*e^2 - 1253/20*e - 889/10, 3/5*e^5 + 11/10*e^4 - 56/5*e^3 - 119/10*e^2 + 84/5*e - 6/5, -3/5*e^5 - 21/10*e^4 + 51/5*e^3 + 329/10*e^2 - 49/5*e - 244/5, -7/4*e^5 - 21/4*e^4 + 117/4*e^3 + 303/4*e^2 - 37*e - 91, -1/5*e^5 - 9/20*e^4 + 83/20*e^3 + 141/20*e^2 - 177/20*e - 31/10, 7/4*e^5 + 21/4*e^4 - 119/4*e^3 - 311/4*e^2 + 83/2*e + 96, -7/10*e^5 - 11/5*e^4 + 119/10*e^3 + 154/5*e^2 - 93/5*e - 8/5, 7/5*e^5 + 83/20*e^4 - 481/20*e^3 - 1227/20*e^2 + 679/20*e + 747/10, 3/20*e^5 + 33/20*e^4 - 11/20*e^3 - 507/20*e^2 - 183/10*e + 86/5, 3/20*e^5 + 23/20*e^4 - 41/20*e^3 - 377/20*e^2 + 6/5*e + 191/5, 21/10*e^5 + 28/5*e^4 - 377/10*e^3 - 402/5*e^2 + 349/5*e + 514/5, -9/5*e^5 - 91/20*e^4 + 617/20*e^3 + 1199/20*e^2 - 783/20*e - 479/10, 13/10*e^5 + 14/5*e^4 - 231/10*e^3 - 181/5*e^2 + 187/5*e + 152/5, 31/20*e^5 + 101/20*e^4 - 497/20*e^3 - 1399/20*e^2 + 107/5*e + 247/5, 43/20*e^5 + 123/20*e^4 - 741/20*e^3 - 1717/20*e^2 + 251/5*e + 431/5, 13/10*e^5 + 81/20*e^4 - 407/20*e^3 - 1109/20*e^2 + 123/20*e + 659/10, 1/4*e^5 + e^4 - 9/2*e^3 - 35/2*e^2 + 57/4*e + 63/2, -3/5*e^5 - 13/5*e^4 + 77/10*e^3 + 197/5*e^2 + 147/10*e - 249/5, -5/4*e^5 - 7/2*e^4 + 20*e^3 + 48*e^2 - 47/4*e - 91/2, 7/4*e^5 + 11/2*e^4 - 59/2*e^3 - 80*e^2 + 163/4*e + 205/2, -13/10*e^5 - 19/5*e^4 + 221/10*e^3 + 276/5*e^2 - 127/5*e - 362/5, 31/10*e^5 + 91/10*e^4 - 517/10*e^3 - 1289/10*e^2 + 254/5*e + 624/5, 4/5*e^5 + 41/20*e^4 - 277/20*e^3 - 549/20*e^2 + 403/20*e + 459/10, -7/10*e^5 - 27/10*e^4 + 109/10*e^3 + 393/10*e^2 - 18/5*e - 198/5, 3/20*e^5 + 13/20*e^4 - 61/20*e^3 - 127/20*e^2 + 86/5*e - 99/5, -e^5 - 3*e^4 + 31/2*e^3 + 40*e^2 - 11/2*e - 23, -57/20*e^5 - 157/20*e^4 + 979/20*e^3 + 2143/20*e^2 - 324/5*e - 499/5, -4/5*e^5 - 14/5*e^4 + 68/5*e^3 + 201/5*e^2 - 112/5*e - 122/5, -7/4*e^5 - 19/4*e^4 + 121/4*e^3 + 273/4*e^2 - 41*e - 89, -23/10*e^5 - 63/10*e^4 + 381/10*e^3 + 857/10*e^2 - 177/5*e - 342/5, -11/20*e^5 - 23/10*e^4 + 91/10*e^3 + 181/5*e^2 - 383/20*e - 559/10, 23/10*e^5 + 131/20*e^4 - 797/20*e^3 - 1879/20*e^2 + 1193/20*e + 989/10, -41/20*e^5 - 141/20*e^4 + 657/20*e^3 + 2099/20*e^2 - 269/10*e - 522/5, -13/20*e^5 - 33/20*e^4 + 251/20*e^3 + 487/20*e^2 - 206/5*e - 161/5, e^5 + 7/4*e^4 - 73/4*e^3 - 75/4*e^2 + 111/4*e - 29/2, -11/20*e^5 - 1/20*e^4 + 237/20*e^3 - 81/20*e^2 - 207/5*e + 13/5, 13/20*e^5 + 53/20*e^4 - 171/20*e^3 - 767/20*e^2 - 64/5*e + 111/5, 29/20*e^5 + 37/10*e^4 - 122/5*e^3 - 239/5*e^2 + 407/20*e + 151/10, -29/20*e^5 - 21/5*e^4 + 127/5*e^3 + 583/10*e^2 - 967/20*e - 651/10, -33/20*e^5 - 83/20*e^4 + 571/20*e^3 + 1097/20*e^2 - 176/5*e - 121/5, -1/4*e^5 - e^4 + 7/2*e^3 + 23/2*e^2 - 21/4*e + 31/2, -3/20*e^5 - 3/20*e^4 + 61/20*e^3 + 17/20*e^2 + 4/5*e + 59/5, 3*e^5 + 9*e^4 - 103/2*e^3 - 129*e^2 + 149/2*e + 151, -13/10*e^5 - 81/20*e^4 + 427/20*e^3 + 1189/20*e^2 - 363/20*e - 469/10, -1/5*e^5 - 7/10*e^4 + 12/5*e^3 + 113/10*e^2 + 32/5*e - 88/5, 3/2*e^5 + 21/4*e^4 - 93/4*e^3 - 301/4*e^2 + 13/4*e + 123/2, -41/20*e^5 - 63/10*e^4 + 168/5*e^3 + 441/5*e^2 - 563/20*e - 889/10, 2/5*e^5 - 1/10*e^4 - 73/10*e^3 + 69/10*e^2 + 57/10*e - 189/5, 11/20*e^5 + 31/20*e^4 - 157/20*e^3 - 469/20*e^2 - 53/5*e + 227/5, -1/2*e^5 - 2*e^4 + 8*e^3 + 28*e^2 - 31/2*e - 15, 23/20*e^5 + 39/10*e^4 - 84/5*e^3 - 278/5*e^2 - 291/20*e + 527/10, 7/10*e^5 + 29/20*e^4 - 273/20*e^3 - 381/20*e^2 + 717/20*e + 91/10, -7/20*e^5 - 8/5*e^4 + 47/10*e^3 + 259/10*e^2 + 89/20*e - 503/10, 9/10*e^5 + 29/10*e^4 - 74/5*e^3 - 391/10*e^2 + 207/10*e + 71/5, -9/10*e^5 - 17/5*e^4 + 69/5*e^3 + 258/5*e^2 - 67/10*e - 211/5, 21/10*e^5 + 117/20*e^4 - 729/20*e^3 - 1633/20*e^2 + 1061/20*e + 723/10, -9/20*e^5 - 6/5*e^4 + 32/5*e^3 + 133/10*e^2 + 73/20*e + 169/10, -11/10*e^5 - 57/20*e^4 + 369/20*e^3 + 813/20*e^2 - 281/20*e - 563/10, 1/20*e^5 + 3/10*e^4 - 1/10*e^3 - 41/5*e^2 - 187/20*e + 419/10, -51/20*e^5 - 141/20*e^4 + 847/20*e^3 + 1899/20*e^2 - 429/10*e - 412/5, -14/5*e^5 - 171/20*e^4 + 957/20*e^3 + 2499/20*e^2 - 1423/20*e - 1479/10, 12/5*e^5 + 143/20*e^4 - 831/20*e^3 - 2087/20*e^2 + 1229/20*e + 1327/10, -23/10*e^5 - 29/5*e^4 + 401/10*e^3 + 406/5*e^2 - 297/5*e - 432/5, 13/20*e^5 + 17/5*e^4 - 83/10*e^3 - 511/10*e^2 - 251/20*e + 467/10, 51/20*e^5 + 73/10*e^4 - 451/10*e^3 - 536/5*e^2 + 1763/20*e + 1459/10, -3/20*e^5 - 19/10*e^4 - 7/10*e^3 + 158/5*e^2 + 701/20*e - 367/10, 8/5*e^5 + 87/20*e^4 - 539/20*e^3 - 1223/20*e^2 + 541/20*e + 503/10, -11/20*e^5 - 31/20*e^4 + 177/20*e^3 + 409/20*e^2 + 3/5*e - 77/5, 11/20*e^5 + 51/20*e^4 - 167/20*e^3 - 769/20*e^2 + 9/10*e + 152/5, e^5 + 9/4*e^4 - 79/4*e^3 - 121/4*e^2 + 209/4*e + 43/2, -3/4*e^5 - 3*e^4 + 11*e^3 + 87/2*e^2 - 1/4*e - 103/2, -37/20*e^5 - 97/20*e^4 + 679/20*e^3 + 1363/20*e^2 - 424/5*e - 419/5, 9/10*e^5 + 33/20*e^4 - 351/20*e^3 - 437/20*e^2 + 799/20*e + 487/10, 7/5*e^5 + 73/20*e^4 - 461/20*e^3 - 957/20*e^2 + 239/20*e + 327/10, 27/20*e^5 + 87/20*e^4 - 439/20*e^3 - 1233/20*e^2 + 153/10*e + 234/5, 43/20*e^5 + 123/20*e^4 - 761/20*e^3 - 1777/20*e^2 + 376/5*e + 491/5, 13/10*e^5 + 43/10*e^4 - 108/5*e^3 - 617/10*e^2 + 359/10*e + 257/5, 3/5*e^5 + 11/10*e^4 - 56/5*e^3 - 129/10*e^2 + 149/5*e + 4/5, -1/5*e^5 - 6/5*e^4 + 17/5*e^3 + 119/5*e^2 - 83/5*e - 338/5, 23/10*e^5 + 141/20*e^4 - 777/20*e^3 - 1969/20*e^2 + 933/20*e + 769/10, -39/10*e^5 - 52/5*e^4 + 663/10*e^3 + 703/5*e^2 - 426/5*e - 636/5, -3/5*e^5 - 13/5*e^4 + 56/5*e^3 + 207/5*e^2 - 179/5*e - 394/5, 3/10*e^5 + 13/10*e^4 - 41/10*e^3 - 187/10*e^2 - 48/5*e + 12/5, 11/20*e^5 + 1/20*e^4 - 237/20*e^3 + 21/20*e^2 + 207/5*e + 147/5, -63/20*e^5 - 42/5*e^4 + 553/10*e^3 + 1191/10*e^2 - 1979/20*e - 1507/10, -1/20*e^5 + 6/5*e^4 + 41/10*e^3 - 193/10*e^2 - 673/20*e + 181/10, -8/5*e^5 - 23/5*e^4 + 257/10*e^3 + 332/5*e^2 - 103/10*e - 309/5, -91/20*e^5 - 64/5*e^4 + 781/10*e^3 + 1817/10*e^2 - 2103/20*e - 1949/10, 1/2*e^5 + 3*e^4 - 9/2*e^3 - 45*e^2 - 33*e + 32, 3/4*e^5 + 13/4*e^4 - 43/4*e^3 - 191/4*e^2 - 1/2*e + 64, -1/2*e^5 - 3/4*e^4 + 41/4*e^3 + 43/4*e^2 - 117/4*e - 75/2, 17/20*e^5 + 11/10*e^4 - 167/10*e^3 - 52/5*e^2 + 641/20*e - 187/10, -1/4*e^4 + 5/4*e^3 + 37/4*e^2 - 71/4*e - 53/2, 79/20*e^5 + 56/5*e^4 - 337/5*e^3 - 1573/10*e^2 + 1797/20*e + 1631/10, -71/20*e^5 - 201/20*e^4 + 1207/20*e^3 + 2799/20*e^2 - 689/10*e - 572/5, -17/5*e^5 - 99/10*e^4 + 294/5*e^3 + 1431/10*e^2 - 436/5*e - 876/5, 17/20*e^5 + 31/10*e^4 - 117/10*e^3 - 237/5*e^2 - 499/20*e + 503/10, 57/20*e^5 + 157/20*e^4 - 959/20*e^3 - 2163/20*e^2 + 324/5*e + 579/5, -9/5*e^5 - 43/10*e^4 + 163/5*e^3 + 567/10*e^2 - 317/5*e - 232/5, -1/20*e^5 - 1/20*e^4 + 7/20*e^3 + 39/20*e^2 + 68/5*e + 43/5, -8/5*e^5 - 31/10*e^4 + 146/5*e^3 + 379/10*e^2 - 309/5*e - 194/5, 3/20*e^5 + 3/20*e^4 - 51/20*e^3 + 23/20*e^2 + 17/10*e - 174/5, -1/20*e^5 - 11/20*e^4 + 27/20*e^3 + 269/20*e^2 - 2/5*e - 267/5, 31/20*e^5 + 24/5*e^4 - 128/5*e^3 - 677/10*e^2 + 453/20*e + 889/10, -19/20*e^5 - 11/5*e^4 + 87/5*e^3 + 303/10*e^2 - 837/20*e - 171/10, 3/2*e^5 + 19/4*e^4 - 97/4*e^3 - 263/4*e^2 + 61/4*e + 77/2, -71/20*e^5 - 201/20*e^4 + 1237/20*e^3 + 2879/20*e^2 - 507/5*e - 827/5, 9/4*e^5 + 6*e^4 - 79/2*e^3 - 171/2*e^2 + 293/4*e + 241/2, -9/10*e^5 - 7/5*e^4 + 173/10*e^3 + 63/5*e^2 - 211/5*e + 124/5, -59/20*e^5 - 41/5*e^4 + 499/10*e^3 + 1153/10*e^2 - 1227/20*e - 1171/10, 23/10*e^5 + 39/5*e^4 - 381/10*e^3 - 586/5*e^2 + 267/5*e + 732/5, -11/4*e^5 - 31/4*e^4 + 189/4*e^3 + 441/4*e^2 - 70*e - 129, -31/10*e^5 - 101/10*e^4 + 517/10*e^3 + 1459/10*e^2 - 324/5*e - 704/5, -1/2*e^5 - 5/4*e^4 + 31/4*e^3 + 61/4*e^2 + 29/4*e + 3/2, e^5 + 5/2*e^4 - 18*e^3 - 61/2*e^2 + 40*e - 6, 9/4*e^5 + 13/2*e^4 - 39*e^3 - 97*e^2 + 251/4*e + 289/2, 21/10*e^5 + 117/20*e^4 - 709/20*e^3 - 1673/20*e^2 + 941/20*e + 1283/10, -6/5*e^5 - 89/20*e^4 + 393/20*e^3 + 1341/20*e^2 - 387/20*e - 671/10, -39/20*e^5 - 89/20*e^4 + 693/20*e^3 + 1151/20*e^2 - 273/5*e - 283/5, 9/10*e^5 + 73/20*e^4 - 261/20*e^3 - 1037/20*e^2 - 31/20*e + 577/10, -3/2*e^5 - 19/4*e^4 + 97/4*e^3 + 259/4*e^2 - 117/4*e - 93/2, 1/20*e^5 + 13/10*e^4 + 2/5*e^3 - 131/5*e^2 - 237/20*e + 619/10, 14/5*e^5 + 39/5*e^4 - 248/5*e^3 - 561/5*e^2 + 412/5*e + 722/5, 29/20*e^5 + 69/20*e^4 - 503/20*e^3 - 911/20*e^2 + 198/5*e + 223/5, -29/20*e^5 - 47/10*e^4 + 112/5*e^3 + 329/5*e^2 - 67/20*e - 701/10, 1/5*e^5 + 17/10*e^4 - 9/10*e^3 - 293/10*e^2 - 219/10*e + 153/5, 83/20*e^5 + 253/20*e^4 - 1391/20*e^3 - 3607/20*e^2 + 867/10*e + 866/5, -3/2*e^5 - 17/4*e^4 + 105/4*e^3 + 253/4*e^2 - 193/4*e - 177/2, 9/10*e^5 + 63/20*e^4 - 331/20*e^3 - 927/20*e^2 + 839/20*e + 397/10, 1/5*e^5 + 19/20*e^4 - 23/20*e^3 - 251/20*e^2 - 363/20*e - 189/10, 4/5*e^5 + 41/20*e^4 - 247/20*e^3 - 449/20*e^2 + 33/20*e - 31/10, -1/2*e^5 - 3/2*e^4 + 7*e^3 + 43/2*e^2 + 37/2*e - 37, 1/10*e^5 + 37/20*e^4 + 41/20*e^3 - 633/20*e^2 - 1049/20*e + 223/10, -7/20*e^5 - 21/10*e^4 + 47/10*e^3 + 172/5*e^2 + 189/20*e - 543/10, -41/20*e^5 - 131/20*e^4 + 677/20*e^3 + 1909/20*e^2 - 409/10*e - 482/5, -1/5*e^5 - 1/5*e^4 + 49/10*e^3 + 19/5*e^2 - 261/10*e - 23/5, -9/10*e^5 - 12/5*e^4 + 163/10*e^3 + 158/5*e^2 - 196/5*e - 86/5, -3/20*e^5 - 3/20*e^4 + 41/20*e^3 - 23/20*e^2 + 74/5*e + 219/5, -57/20*e^5 - 157/20*e^4 + 999/20*e^3 + 2263/20*e^2 - 374/5*e - 779/5, e^5 + 2*e^4 - 37/2*e^3 - 25*e^2 + 83/2*e + 49, -31/20*e^5 - 61/20*e^4 + 577/20*e^3 + 779/20*e^2 - 282/5*e - 107/5, -63/20*e^5 - 42/5*e^4 + 543/10*e^3 + 1151/10*e^2 - 1539/20*e - 1177/10, 1/4*e^5 + 3/4*e^4 - 13/4*e^3 - 37/4*e^2 - 33/2*e + 10, -47/20*e^5 - 137/20*e^4 + 849/20*e^3 + 2023/20*e^2 - 444/5*e - 709/5, 8/5*e^5 + 18/5*e^4 - 141/5*e^3 - 212/5*e^2 + 179/5*e - 46/5, -41/10*e^5 - 131/10*e^4 + 687/10*e^3 + 1929/10*e^2 - 454/5*e - 1074/5, -11/20*e^5 - 14/5*e^4 + 48/5*e^3 + 497/10*e^2 - 493/20*e - 1079/10, -13/10*e^5 - 71/20*e^4 + 467/20*e^3 + 1039/20*e^2 - 923/20*e - 579/10, -3/20*e^5 + 7/20*e^4 + 81/20*e^3 - 33/20*e^2 - 96/5*e - 241/5, -37/20*e^5 - 127/20*e^4 + 659/20*e^3 + 1913/20*e^2 - 369/5*e - 749/5, 7/5*e^5 + 43/20*e^4 - 541/20*e^3 - 447/20*e^2 + 1539/20*e + 307/10, -23/10*e^5 - 34/5*e^4 + 371/10*e^3 + 461/5*e^2 - 172/5*e - 222/5, 1/20*e^5 - 7/10*e^4 - 18/5*e^3 + 59/5*e^2 + 843/20*e - 291/10, 3/4*e^5 + 11/4*e^4 - 45/4*e^3 - 149/4*e^2 - 4*e + 31, -13/20*e^5 - 53/20*e^4 + 201/20*e^3 + 767/20*e^2 + 3/10*e - 36/5, 19/20*e^5 + 16/5*e^4 - 139/10*e^3 - 473/10*e^2 - 113/20*e + 641/10, -63/20*e^5 - 42/5*e^4 + 279/5*e^3 + 1201/10*e^2 - 1829/20*e - 1637/10, 11/4*e^5 + 31/4*e^4 - 189/4*e^3 - 437/4*e^2 + 73*e + 97, -81/20*e^5 - 251/20*e^4 + 1337/20*e^3 + 3529/20*e^2 - 739/10*e - 922/5, 3/5*e^5 + 13/5*e^4 - 41/5*e^3 - 187/5*e^2 - 66/5*e + 54/5, 13/10*e^5 + 19/5*e^4 - 113/5*e^3 - 266/5*e^2 + 489/10*e + 287/5, -69/20*e^5 - 97/10*e^4 + 589/10*e^3 + 679/5*e^2 - 1617/20*e - 1581/10, -5/2*e^5 - 15/2*e^4 + 42*e^3 + 215/2*e^2 - 105/2*e - 139, -9/5*e^5 - 34/5*e^4 + 143/5*e^3 + 506/5*e^2 - 132/5*e - 492/5, 37/20*e^5 + 28/5*e^4 - 161/5*e^3 - 789/10*e^2 + 1071/20*e + 663/10, -33/10*e^5 - 103/10*e^4 + 561/10*e^3 + 1497/10*e^2 - 417/5*e - 822/5, -33/10*e^5 - 44/5*e^4 + 561/10*e^3 + 616/5*e^2 - 307/5*e - 582/5, -33/20*e^5 - 49/10*e^4 + 283/10*e^3 + 358/5*e^2 - 1089/20*e - 957/10, 1/4*e^5 - 1/4*e^4 - 27/4*e^3 + 39/4*e^2 + 34*e - 39, 3/20*e^5 - 11/10*e^4 - 24/5*e^3 + 107/5*e^2 + 329/20*e - 453/10, 37/20*e^5 + 87/20*e^4 - 699/20*e^3 - 1173/20*e^2 + 404/5*e + 359/5, 63/20*e^5 + 183/20*e^4 - 1111/20*e^3 - 2637/20*e^2 + 927/10*e + 756/5, 3/2*e^4 + e^3 - 55/2*e^2 + 94, 57/20*e^5 + 38/5*e^4 - 241/5*e^3 - 1029/10*e^2 + 991/20*e + 853/10, -63/20*e^5 - 193/20*e^4 + 1081/20*e^3 + 2767/20*e^2 - 456/5*e - 881/5, 51/10*e^5 + 68/5*e^4 - 897/10*e^3 - 957/5*e^2 + 769/5*e + 1194/5, 2*e^5 + 4*e^4 - 75/2*e^3 - 49*e^2 + 193/2*e + 47, 13/10*e^5 + 101/20*e^4 - 417/20*e^3 - 1609/20*e^2 + 373/20*e + 999/10, -1/2*e^5 + 17/2*e^3 - 8*e^2 - 5*e + 60, -3/10*e^5 - 3/10*e^4 + 51/10*e^3 + 37/10*e^2 - 17/5*e - 112/5, 1/4*e^5 - 7*e^3 + 11/2*e^2 + 179/4*e - 53/2, 61/20*e^5 + 44/5*e^4 - 263/5*e^3 - 1217/10*e^2 + 1683/20*e + 1199/10, 3/20*e^5 + 9/10*e^4 + 7/10*e^3 - 48/5*e^2 - 661/20*e - 303/10, 53/20*e^5 + 42/5*e^4 - 443/10*e^3 - 1181/10*e^2 + 1349/20*e + 947/10, -12/5*e^5 - 32/5*e^4 + 219/5*e^3 + 458/5*e^2 - 501/5*e - 666/5, -19/5*e^5 - 231/20*e^4 + 1267/20*e^3 + 3299/20*e^2 - 1713/20*e - 2009/10, -19/10*e^5 - 39/10*e^4 + 353/10*e^3 + 481/10*e^2 - 326/5*e - 226/5, 7/20*e^5 + 57/20*e^4 - 69/20*e^3 - 963/20*e^2 - 91/5*e + 249/5, -6/5*e^5 - 49/20*e^4 + 413/20*e^3 + 601/20*e^2 - 447/20*e + 99/10, -17/20*e^5 - 27/20*e^4 + 349/20*e^3 + 453/20*e^2 - 503/10*e - 364/5, -3/20*e^5 - 33/20*e^4 + 1/20*e^3 + 447/20*e^2 + 79/5*e + 29/5, -77/20*e^5 - 207/20*e^4 + 1329/20*e^3 + 2893/20*e^2 - 1033/10*e - 804/5, 67/20*e^5 + 217/20*e^4 - 1159/20*e^3 - 3303/20*e^2 + 973/10*e + 1064/5, -7/4*e^5 - 4*e^4 + 67/2*e^3 + 99/2*e^2 - 387/4*e - 89/2, -49/10*e^5 - 149/10*e^4 + 414/5*e^3 + 2151/10*e^2 - 997/10*e - 1091/5, 29/20*e^5 + 47/10*e^4 - 219/10*e^3 - 339/5*e^2 - 163/20*e + 671/10, -27/10*e^5 - 189/20*e^4 + 863/20*e^3 + 2841/20*e^2 - 587/20*e - 1391/10, -23/10*e^5 - 141/20*e^4 + 767/20*e^3 + 2049/20*e^2 - 843/20*e - 1119/10, -31/20*e^5 - 53/10*e^4 + 118/5*e^3 + 381/5*e^2 + 67/20*e - 659/10, -21/20*e^5 - 13/10*e^4 + 221/10*e^3 + 76/5*e^2 - 1633/20*e - 339/10, -19/10*e^5 - 113/20*e^4 + 671/20*e^3 + 1757/20*e^2 - 1219/20*e - 1347/10, 21/10*e^5 + 33/5*e^4 - 347/10*e^3 - 472/5*e^2 + 139/5*e + 564/5, -8/5*e^5 - 38/5*e^4 + 106/5*e^3 + 582/5*e^2 + 116/5*e - 594/5, -11/10*e^5 - 47/20*e^4 + 379/20*e^3 + 583/20*e^2 - 691/20*e - 393/10]; heckeEigenvalues := AssociativeArray(); for i := 1 to #heckeEigenvaluesArray do heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i]; end for; ALEigenvalues := AssociativeArray(); ALEigenvalues[ideal] := -1; ALEigenvalues[ideal] := -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;