/* This code can be loaded, or copied and paste using cpaste, into Sage. It will load the data associated to the HMF, including the field, level, and Hecke and Atkin-Lehner eigenvalue data. */ P. = PolynomialRing(QQ) g = P([44, 0, -14, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([19, 19, 1/2*w^3 + w^2 - 4*w - 9]) primes_array = [ [4, 2, -1/2*w^3 + w^2 + 4*w - 8],\ [11, 11, 1/2*w^3 - 3/2*w^2 - 4*w + 11],\ [11, 11, -1/2*w^2 - w + 2],\ [11, 11, -1/2*w^2 + w + 2],\ [19, 19, 1/2*w^3 - 1/2*w^2 - 4*w + 5],\ [19, 19, 1/2*w^3 + w^2 - 4*w - 9],\ [19, 19, 1/2*w^3 - w^2 - 4*w + 9],\ [19, 19, 1/2*w^3 + 1/2*w^2 - 4*w - 5],\ [25, 5, 1/2*w^2 - 1],\ [29, 29, 1/2*w^3 - 4*w - 1],\ [29, 29, -1/2*w^3 + 4*w - 1],\ [31, 31, -w - 1],\ [31, 31, w - 1],\ [41, 41, 1/2*w^3 + 1/2*w^2 - 4*w - 2],\ [41, 41, -1/2*w^3 + 1/2*w^2 + 4*w - 2],\ [49, 7, -1/2*w^3 + 1/2*w^2 + 5*w - 7],\ [49, 7, 3/2*w^3 - 7/2*w^2 - 13*w + 29],\ [59, 59, -1/2*w^3 - 3/2*w^2 + 3*w + 10],\ [59, 59, 1/2*w^3 - 3/2*w^2 - 3*w + 10],\ [61, 61, 1/2*w^2 + w - 6],\ [61, 61, 1/2*w^2 - w - 6],\ [71, 71, w^3 - 5/2*w^2 - 8*w + 20],\ [71, 71, -w^3 + 5/2*w^2 + 10*w - 24],\ [81, 3, -3],\ [101, 101, -1/2*w^3 + 1/2*w^2 + 4*w - 1],\ [101, 101, 1/2*w^3 + 1/2*w^2 - 4*w - 1],\ [109, 109, 3/2*w^2 + w - 12],\ [109, 109, 3/2*w^2 - w - 12],\ [149, 149, 1/2*w^3 + 2*w^2 - 4*w - 15],\ [149, 149, -1/2*w^3 + 2*w^2 + 4*w - 15],\ [151, 151, 1/2*w^3 - 1/2*w^2 - 4*w + 8],\ [151, 151, -w^3 + 5/2*w^2 + 8*w - 18],\ [151, 151, -w^3 + 3/2*w^2 + 10*w - 18],\ [151, 151, -1/2*w^3 - 1/2*w^2 + 4*w + 8],\ [179, 179, 1/2*w^3 + w^2 - 4*w - 5],\ [179, 179, -1/2*w^3 + w^2 + 4*w - 5],\ [181, 181, 1/2*w^3 - 5*w - 3],\ [181, 181, w^3 - 1/2*w^2 - 7*w - 1],\ [181, 181, -1/2*w^3 - 5/2*w^2 + 4*w + 15],\ [181, 181, 1/2*w^3 - 5*w + 3],\ [191, 191, w^3 - 2*w^2 - 7*w + 13],\ [191, 191, -w^3 - 2*w^2 + 7*w + 13],\ [199, 199, -5/2*w^2 - 2*w + 18],\ [199, 199, -5/2*w^2 + 2*w + 18],\ [241, 241, -3/2*w^3 + 7/2*w^2 + 14*w - 30],\ [241, 241, -3/2*w^3 + 5/2*w^2 + 16*w - 30],\ [251, 251, 3/2*w^2 - w - 13],\ [251, 251, 3/2*w^2 + w - 13],\ [269, 269, 1/2*w^3 + 1/2*w^2 - 3*w - 10],\ [269, 269, -w^3 + 1/2*w^2 + 7*w - 8],\ [269, 269, w^3 + 1/2*w^2 - 7*w - 8],\ [269, 269, -1/2*w^3 + 1/2*w^2 + 3*w - 10],\ [271, 271, -w^3 + 8*w + 5],\ [271, 271, -2*w^2 + 2*w + 15],\ [271, 271, 2*w^2 + 2*w - 15],\ [271, 271, w^3 - 8*w + 5],\ [281, 281, -2*w + 3],\ [281, 281, w^3 - 2*w^2 - 12*w + 25],\ [311, 311, 1/2*w^3 + 5/2*w^2 - 3*w - 17],\ [311, 311, -1/2*w^3 + 5/2*w^2 + 3*w - 17],\ [331, 331, -1/2*w^3 + 3/2*w^2 + 5*w - 10],\ [331, 331, 1/2*w^3 + 3/2*w^2 - 5*w - 10],\ [349, 349, -1/2*w^2 + 3*w - 3],\ [349, 349, -w^3 + 5/2*w^2 + 11*w - 25],\ [379, 379, 5/2*w^2 - w - 21],\ [379, 379, 5/2*w^2 + w - 21],\ [389, 389, 3/2*w^2 - w - 14],\ [389, 389, 1/2*w^3 - 5/2*w^2 - 3*w + 16],\ [389, 389, -1/2*w^3 - 5/2*w^2 + 3*w + 16],\ [389, 389, 3/2*w^2 + w - 14],\ [409, 409, w^3 + w^2 - 8*w - 7],\ [409, 409, -w^3 + w^2 + 8*w - 7],\ [419, 419, 3/2*w^3 - 5/2*w^2 - 15*w + 28],\ [419, 419, 3/2*w^3 - 7/2*w^2 - 13*w + 28],\ [439, 439, 1/2*w^2 + 2*w - 9],\ [439, 439, -3/2*w^2 + 2*w + 6],\ [439, 439, -3/2*w^2 - 2*w + 6],\ [439, 439, 1/2*w^2 - 2*w - 9],\ [449, 449, -w^3 + 1/2*w^2 + 6*w - 1],\ [449, 449, 1/2*w^2 + 2*w - 5],\ [449, 449, 1/2*w^2 - 2*w - 5],\ [449, 449, w^3 + 1/2*w^2 - 6*w - 1],\ [461, 461, w^3 + 3/2*w^2 - 7*w - 9],\ [461, 461, -w^3 + 3/2*w^2 + 7*w - 9],\ [491, 491, -1/2*w^3 - 1/2*w^2 + 6*w + 7],\ [491, 491, -5/2*w^2 + w + 16],\ [491, 491, 5/2*w^2 + w - 16],\ [491, 491, 1/2*w^3 - 1/2*w^2 - 6*w + 7],\ [499, 499, -1/2*w^3 + 5/2*w^2 + 4*w - 19],\ [499, 499, 1/2*w^3 + 5/2*w^2 - 4*w - 19],\ [541, 541, -1/2*w^3 + 3/2*w^2 + 4*w - 7],\ [541, 541, 1/2*w^3 + 3/2*w^2 - 4*w - 7],\ [569, 569, 1/2*w^2 + 2*w - 2],\ [569, 569, 1/2*w^2 - 2*w - 2],\ [571, 571, -2*w^3 + 9/2*w^2 + 17*w - 39],\ [571, 571, 1/2*w^3 - 1/2*w^2 - 5*w - 2],\ [571, 571, -1/2*w^3 - 1/2*w^2 + 5*w - 2],\ [571, 571, w^3 - 5/2*w^2 - 11*w + 27],\ [599, 599, -w^3 + 2*w^2 + 8*w - 13],\ [599, 599, w^3 + 2*w^2 - 8*w - 13],\ [601, 601, 1/2*w^2 + 2*w - 4],\ [601, 601, 1/2*w^2 - 2*w - 4],\ [619, 619, -1/2*w^3 + 2*w^2 + 6*w - 13],\ [619, 619, 1/2*w^3 + 2*w^2 - 6*w - 13],\ [631, 631, -w^3 - 1/2*w^2 + 6*w - 2],\ [631, 631, w^3 - 1/2*w^2 - 6*w - 2],\ [641, 641, w^3 - 8*w - 1],\ [641, 641, -1/2*w^3 - 1/2*w^2 + 5*w - 1],\ [641, 641, 1/2*w^3 - 1/2*w^2 - 5*w - 1],\ [641, 641, w^3 - 8*w + 1],\ [661, 661, -1/2*w^3 + 7/2*w^2 + 2*w - 25],\ [661, 661, 3/2*w^3 - 9/2*w^2 - 11*w + 32],\ [661, 661, -5/2*w^3 + 13/2*w^2 + 23*w - 56],\ [661, 661, 1/2*w^3 + 7/2*w^2 - 2*w - 25],\ [691, 691, 1/2*w^3 + 7/2*w^2 - 3*w - 28],\ [691, 691, -1/2*w^3 + 7/2*w^2 + 3*w - 28],\ [701, 701, -1/2*w^3 + 1/2*w^2 + 5*w - 10],\ [701, 701, 3/2*w^3 - 5/2*w^2 - 17*w + 34],\ [709, 709, 1/2*w^3 - 5/2*w^2 - 6*w + 17],\ [709, 709, w^3 + 5/2*w^2 - 7*w - 14],\ [709, 709, -w^3 + 5/2*w^2 + 7*w - 14],\ [709, 709, -1/2*w^3 - 5/2*w^2 + 6*w + 17],\ [719, 719, -w^3 + 7/2*w^2 + 8*w - 23],\ [719, 719, w^3 + 7/2*w^2 - 8*w - 23],\ [751, 751, 7/2*w^2 + 2*w - 27],\ [751, 751, 7/2*w^2 - 2*w - 27],\ [761, 761, -1/2*w^3 + 3/2*w^2 + 3*w - 13],\ [761, 761, 1/2*w^3 + 3/2*w^2 - 3*w - 13],\ [769, 769, -w^3 + 7/2*w^2 + 8*w - 25],\ [769, 769, w^3 + 7/2*w^2 - 8*w - 25],\ [809, 809, 2*w^3 - 7/2*w^2 - 20*w + 40],\ [809, 809, -1/2*w^2 + 2*w - 4],\ [811, 811, -1/2*w^2 - 3*w + 8],\ [811, 811, 1/2*w^3 + 3/2*w^2 - 3*w - 18],\ [811, 811, -1/2*w^3 + 3/2*w^2 + 3*w - 18],\ [811, 811, 1/2*w^2 - 3*w - 8],\ [821, 821, 3/2*w^3 - 7/2*w^2 - 16*w + 37],\ [821, 821, -3/2*w^3 + 7/2*w^2 + 12*w - 29],\ [839, 839, 3*w^2 - 2*w - 23],\ [839, 839, 3*w^2 + 2*w - 23],\ [841, 29, -5/2*w^2 + 16],\ [859, 859, 5/2*w^2 + 3*w - 16],\ [859, 859, 5/2*w^2 - 3*w - 16],\ [911, 911, 3*w^2 - 2*w - 17],\ [911, 911, 3*w^2 + 2*w - 17],\ [919, 919, 3*w^2 - w - 23],\ [919, 919, -2*w^2 + 3*w + 15],\ [919, 919, -2*w^2 - 3*w + 15],\ [919, 919, 3*w^2 + w - 23],\ [941, 941, 3/2*w^2 - 3*w - 2],\ [941, 941, 2*w^3 - 11/2*w^2 - 17*w + 42],\ [961, 31, -w^2 + 13],\ [971, 971, 1/2*w^3 + 1/2*w^2 - 6*w - 5],\ [971, 971, -1/2*w^3 + 1/2*w^2 + 6*w - 5],\ [991, 991, w^3 + 3/2*w^2 - 8*w - 8],\ [991, 991, -w^3 + 3/2*w^2 + 8*w - 8]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^12 - 20*x^10 + 138*x^8 - 428*x^6 + 604*x^4 - 317*x^2 + 20 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, 81/181*e^10 - 1384/181*e^8 + 7197/181*e^6 - 14490/181*e^4 + 9924/181*e^2 - 872/181, 28/181*e^11 - 503/181*e^9 + 2937/181*e^7 - 7563/181*e^5 + 8646/181*e^3 - 3079/181*e, -47/181*e^11 + 812/181*e^9 - 4290/181*e^7 + 8629/181*e^5 - 5269/181*e^3 - 475/181*e, -81/181*e^11 + 1384/181*e^9 - 7197/181*e^7 + 14490/181*e^5 - 9924/181*e^3 + 691/181*e, 1, -18/181*e^10 + 388/181*e^8 - 2806/181*e^6 + 7926/181*e^4 - 7937/181*e^2 + 1320/181, 4/181*e^11 - 46/181*e^9 - 20/181*e^7 + 1195/181*e^5 - 3264/181*e^3 + 1939/181*e, -8/181*e^10 + 92/181*e^8 - 141/181*e^6 + 144/181*e^4 - 1436/181*e^2 + 466/181, 85/181*e^11 - 1430/181*e^9 + 7177/181*e^7 - 13295/181*e^5 + 6660/181*e^3 + 1791/181*e, -3/181*e^11 + 125/181*e^9 - 1433/181*e^7 + 5665/181*e^5 - 7869/181*e^3 + 2211/181*e, 76/181*e^11 - 1417/181*e^9 + 8670/181*e^7 - 22545/181*e^5 + 24502/181*e^3 - 8228/181*e, -8/181*e^11 + 92/181*e^9 - 141/181*e^7 + 325/181*e^5 - 3608/181*e^3 + 5172/181*e, -67/181*e^11 + 1223/181*e^9 - 7267/181*e^7 + 18582/181*e^5 - 20805/181*e^3 + 8473/181*e, -67/181*e^11 + 1223/181*e^9 - 7267/181*e^7 + 18582/181*e^5 - 20805/181*e^3 + 8473/181*e, 147/181*e^11 - 2505/181*e^9 + 13021/181*e^7 - 26900/181*e^5 + 22314/181*e^3 - 8065/181*e, -32/181*e^11 + 549/181*e^9 - 2917/181*e^7 + 6368/181*e^5 - 5382/181*e^3 + 959/181*e, -30/181*e^10 + 345/181*e^8 - 212/181*e^6 - 3623/181*e^4 + 5656/181*e^2 - 1420/181, -85/181*e^10 + 1430/181*e^8 - 7177/181*e^6 + 13476/181*e^4 - 8289/181*e^2 + 200/181, -174/181*e^10 + 2906/181*e^8 - 14515/181*e^6 + 27929/181*e^4 - 18020/181*e^2 - 272/181, -120/181*e^10 + 1923/181*e^8 - 8631/181*e^6 + 12477/181*e^4 - 2535/181*e^2 - 612/181, -156/181*e^10 + 2699/181*e^8 - 14243/181*e^6 + 28329/181*e^4 - 18228/181*e^2 + 2028/181, 82/181*e^10 - 1305/181*e^8 + 5925/181*e^6 - 10164/181*e^4 + 7117/181*e^2 - 2152/181, 132/181*e^10 - 2242/181*e^8 + 11467/181*e^6 - 22105/181*e^4 + 13920/181*e^2 - 2802/181, 96/181*e^11 - 1466/181*e^9 + 5674/181*e^7 - 3719/181*e^5 - 9737/181*e^3 + 6173/181*e, 30/181*e^11 - 707/181*e^9 + 5823/181*e^7 - 20269/181*e^5 + 29820/181*e^3 - 14327/181*e, 252/181*e^10 - 4346/181*e^8 + 22994/181*e^6 - 47433/181*e^4 + 33831/181*e^2 - 4000/181, -27/181*e^10 + 582/181*e^8 - 4209/181*e^6 + 11708/181*e^4 - 9643/181*e^2 - 1640/181, -78/181*e^10 + 1440/181*e^8 - 8660/181*e^6 + 21857/181*e^4 - 21965/181*e^2 + 5720/181, -44/181*e^10 + 506/181*e^8 - 142/181*e^6 - 7715/181*e^4 + 15994/181*e^2 - 5220/181, 81/181*e^10 - 1384/181*e^8 + 7378/181*e^6 - 16843/181*e^4 + 16078/181*e^2 - 4492/181, 144/181*e^11 - 2561/181*e^9 + 14303/181*e^7 - 31733/181*e^5 + 25667/181*e^3 - 4768/181*e, -50/181*e^11 + 756/181*e^9 - 2827/181*e^7 + 1262/181*e^5 + 6591/181*e^3 - 5504/181*e, 285/181*e^10 - 4816/181*e^8 + 24639/181*e^6 - 49475/181*e^4 + 36406/181*e^2 - 4972/181, 110/181*e^11 - 2170/181*e^9 + 14473/181*e^7 - 41619/181*e^5 + 51058/181*e^3 - 20073/181*e, 31/181*e^11 - 628/181*e^9 + 4370/181*e^7 - 13228/181*e^5 + 16877/181*e^3 - 8005/181*e, -120/181*e^11 + 1923/181*e^9 - 8450/181*e^7 + 9762/181*e^5 + 8144/181*e^3 - 12015/181*e, 18/181*e^11 - 569/181*e^9 + 5702/181*e^7 - 20958/181*e^5 + 27666/181*e^3 - 9827/181*e, -47/181*e^11 + 993/181*e^9 - 7186/181*e^7 + 21661/181*e^5 - 25179/181*e^3 + 7489/181*e, 61/181*e^11 - 973/181*e^9 + 4401/181*e^7 - 7071/181*e^5 + 2714/181*e^3 + 1017/181*e, 2/181*e^11 - 23/181*e^9 - 10/181*e^7 + 688/181*e^5 - 2899/181*e^3 + 5404/181*e, -e^9 + 16*e^7 - 73*e^5 + 123*e^3 - 76*e, -45/181*e^10 + 608/181*e^8 - 1404/181*e^6 - 3715/181*e^4 + 11923/181*e^2 - 3940/181, -125/181*e^10 + 2252/181*e^8 - 12950/181*e^6 + 30486/181*e^4 - 27415/181*e^2 + 4340/181, 66/181*e^11 - 1121/181*e^9 + 5462/181*e^7 - 7161/181*e^5 - 6615/181*e^3 + 12355/181*e, 95/181*e^11 - 1364/181*e^9 + 4231/181*e^7 + 2634/181*e^5 - 20505/181*e^3 + 14331/181*e, -226/181*e^10 + 4047/181*e^8 - 22762/181*e^6 + 50042/181*e^4 - 38033/181*e^2 + 1852/181, -4/181*e^10 + 46/181*e^8 + 20/181*e^6 - 833/181*e^4 - 356/181*e^2 + 3672/181, 245/181*e^10 - 4356/181*e^8 + 24296/181*e^6 - 53461/181*e^4 + 40086/181*e^2 - 2280/181, 206/181*e^10 - 3455/181*e^8 + 17070/181*e^6 - 29591/181*e^4 + 10913/181*e^2 + 4200/181, -237/181*e^10 + 4264/181*e^8 - 24155/181*e^6 + 53498/181*e^4 - 40822/181*e^2 + 2900/181, -3/181*e^10 + 125/181*e^8 - 1614/181*e^6 + 7837/181*e^4 - 11851/181*e^2 + 220/181, -171/181*e^11 + 2962/181*e^9 - 15978/181*e^7 + 35296/181*e^5 - 29518/181*e^3 + 1680/181*e, 117/181*e^10 - 2160/181*e^8 + 12809/181*e^6 - 29980/181*e^4 + 21816/181*e^2 + 832/181, 211/181*e^10 - 3241/181*e^8 + 13425/181*e^6 - 18459/181*e^4 + 8100/181*e^2 - 3648/181, 6/181*e^11 + 293/181*e^9 - 5822/181*e^7 + 28128/181*e^5 - 47974/181*e^3 + 24176/181*e, 57/181*e^11 - 746/181*e^9 + 1344/181*e^7 + 7300/181*e^5 - 21715/181*e^3 + 11205/181*e, -116/181*e^11 + 1877/181*e^9 - 8470/181*e^7 + 10776/181*e^5 + 7052/181*e^3 - 12791/181*e, -261/181*e^10 + 4540/181*e^8 - 24035/181*e^6 + 46509/181*e^4 - 23772/181*e^2 - 4028/181, -474/181*e^10 + 8166/181*e^8 - 43061/181*e^6 + 87629/181*e^4 - 58114/181*e^2 + 732/181, -17/181*e^11 + 105/181*e^9 + 1714/181*e^7 - 13812/181*e^5 + 28533/181*e^3 - 11725/181*e, 1/181*e^11 + 79/181*e^9 - 1453/181*e^7 + 7222/181*e^5 - 15658/181*e^3 + 13743/181*e, 148/181*e^11 - 2607/181*e^9 + 14102/181*e^7 - 27642/181*e^5 + 9914/181*e^3 + 12737/181*e, 466/181*e^11 - 7893/181*e^9 + 40386/181*e^7 - 79702/181*e^5 + 55049/181*e^3 - 8411/181*e, -618/181*e^10 + 10184/181*e^8 - 49400/181*e^6 + 90402/181*e^4 - 56269/181*e^2 + 5500/181, 270/181*e^10 - 4553/181*e^8 + 23447/181*e^6 - 49748/181*e^4 + 43397/181*e^2 - 8940/181, 81/181*e^10 - 1022/181*e^8 + 1586/181*e^6 + 9402/181*e^4 - 24285/181*e^2 + 8540/181, -272/181*e^10 + 4214/181*e^8 - 18007/181*e^6 + 28064/181*e^4 - 19140/181*e^2 + 7880/181, 440/181*e^10 - 7232/181*e^8 + 34724/181*e^6 - 61134/181*e^4 + 34092/181*e^2 - 5720/181, -224/181*e^10 + 3843/181*e^8 - 20238/181*e^6 + 42042/181*e^4 - 29167/181*e^2 + 740/181, -17/181*e^11 + 467/181*e^9 - 4621/181*e^7 + 20035/181*e^5 - 38075/181*e^3 + 25199/181*e, -274/181*e^11 + 4780/181*e^9 - 25780/181*e^7 + 53983/181*e^5 - 36332/181*e^3 - 1325/181*e, -116/181*e^11 + 1877/181*e^9 - 8289/181*e^7 + 8423/181*e^5 + 13387/181*e^3 - 17497/181*e, 174/181*e^11 - 2906/181*e^9 + 14334/181*e^7 - 25214/181*e^5 + 7341/181*e^3 + 12399/181*e, 440/181*e^10 - 7594/181*e^8 + 40335/181*e^6 - 84302/181*e^4 + 61604/181*e^2 - 5720/181, -145/181*e^11 + 1939/181*e^9 - 4343/181*e^7 - 12051/181*e^5 + 40490/181*e^3 - 22188/181*e, 283/181*e^11 - 4793/181*e^9 + 24830/181*e^7 - 52878/181*e^5 + 49441/181*e^3 - 19064/181*e, -16/181*e^10 + 184/181*e^8 - 101/181*e^6 - 2065/181*e^4 + 3825/181*e^2 - 4860/181, -138/181*e^11 + 2492/181*e^9 - 14333/181*e^7 + 33073/181*e^5 - 25495/181*e^3 - 197/181*e, -159/181*e^11 + 2462/181*e^9 - 10246/181*e^7 + 12817/181*e^5 - 757/181*e^3 + 257/181*e, -206/181*e^11 + 3636/181*e^9 - 20147/181*e^7 + 45157/181*e^5 - 39330/181*e^3 + 9013/181*e, 285/181*e^11 - 5178/181*e^9 + 30431/181*e^7 - 75901/181*e^5 + 79846/181*e^3 - 26873/181*e, 351/181*e^11 - 6118/181*e^9 + 33359/181*e^7 - 74917/181*e^5 + 67982/181*e^3 - 17957/181*e, 192/181*e^11 - 3294/181*e^9 + 17140/181*e^7 - 33140/181*e^5 + 15640/181*e^3 + 7459/181*e, 2/181*e^11 + 339/181*e^9 - 5983/181*e^7 + 29648/181*e^5 - 54665/181*e^3 + 31287/181*e, -94/181*e^10 + 1624/181*e^8 - 8580/181*e^6 + 17801/181*e^4 - 16149/181*e^2 + 5928/181, -148/181*e^10 + 2607/181*e^8 - 14283/181*e^6 + 30176/181*e^4 - 18059/181*e^2 - 4592/181, -405/181*e^11 + 6920/181*e^9 - 36347/181*e^7 + 77518/181*e^5 - 66272/181*e^3 + 15763/181*e, 7/181*e^10 + 10/181*e^8 - 1483/181*e^6 + 8019/181*e^4 - 9694/181*e^2 - 1720/181, 117/181*e^10 - 1979/181*e^8 + 9913/181*e^6 - 17129/181*e^4 + 3897/181*e^2 + 5900/181, -312/181*e^11 + 5398/181*e^9 - 29029/181*e^7 + 64260/181*e^5 - 60710/181*e^3 + 21975/181*e, 70/181*e^11 - 1348/181*e^9 + 8519/181*e^7 - 21894/181*e^5 + 22701/181*e^3 - 8693/181*e, 79/181*e^11 - 1361/181*e^9 + 7569/181*e^7 - 20065/181*e^5 + 26760/181*e^3 - 10439/181*e, 191/181*e^11 - 3192/181*e^9 + 15878/181*e^7 - 29683/181*e^5 + 17361/181*e^3 - 1035/181*e, -55/181*e^10 + 904/181*e^8 - 4431/181*e^6 + 8592/181*e^4 - 4714/181*e^2 - 3448/181, -136/181*e^11 + 2107/181*e^9 - 8551/181*e^7 + 7878/181*e^5 + 8892/181*e^3 - 6377/181*e, 354/181*e^11 - 5881/181*e^9 + 28638/181*e^7 - 49450/181*e^5 + 20103/181*e^3 + 4267/181*e, 126/181*e^10 - 1992/181*e^8 + 8782/181*e^6 - 13309/181*e^4 + 7051/181*e^2 - 7068/181, -718/181*e^11 + 12601/181*e^9 - 69172/181*e^7 + 153561/181*e^5 - 132139/181*e^3 + 32140/181*e, 476/181*e^11 - 8370/181*e^9 + 46128/181*e^7 - 103050/181*e^5 + 88700/181*e^3 - 18496/181*e, 292/181*e^11 - 5168/181*e^9 + 28405/181*e^7 - 59918/181*e^5 + 42459/181*e^3 - 5787/181*e, -250/181*e^11 + 4685/181*e^9 - 29158/181*e^7 + 79615/181*e^5 - 96460/181*e^3 + 38545/181*e, -192/181*e^11 + 3475/181*e^9 - 20217/181*e^7 + 49249/181*e^5 - 49306/181*e^3 + 12813/181*e, -85/181*e^11 + 1611/181*e^9 - 10254/181*e^7 + 28680/181*e^5 - 32181/181*e^3 + 5449/181*e, -212/181*e^10 + 3524/181*e^8 - 17221/181*e^6 + 30423/181*e^4 - 15429/181*e^2 + 1308/181, -130/181*e^10 + 1857/181*e^8 - 6409/181*e^6 + 6322/181*e^4 - 4511/181*e^2 + 4948/181, 280/181*e^11 - 4668/181*e^9 + 22854/181*e^7 - 39611/181*e^5 + 17137/181*e^3 - 201/181*e, -172/181*e^11 + 3064/181*e^9 - 17240/181*e^7 + 39296/181*e^5 - 33951/181*e^3 + 4227/181*e, -18/181*e^11 + 750/181*e^9 - 8417/181*e^7 + 31637/181*e^5 - 40879/181*e^3 + 12723/181*e, -12/181*e^11 - 43/181*e^9 + 2775/181*e^7 - 14264/181*e^5 + 23367/181*e^3 - 10161/181*e, -145/181*e^10 + 2844/181*e^8 - 18099/181*e^6 + 43878/181*e^4 - 35530/181*e^2 + 6048/181, 201/181*e^10 - 3126/181*e^8 + 13113/181*e^6 - 16288/181*e^4 - 754/181*e^2 + 5532/181, -271/181*e^10 + 5198/181*e^8 - 32492/181*e^6 + 80174/181*e^4 - 66835/181*e^2 + 5152/181, 152/181*e^10 - 2653/181*e^8 + 14082/181*e^6 - 26628/181*e^4 + 9365/181*e^2 + 5988/181, -616/181*e^10 + 10342/181*e^8 - 51763/181*e^6 + 96701/181*e^4 - 57177/181*e^2 + 8008/181, 285/181*e^10 - 4454/181*e^8 + 19390/181*e^6 - 30832/181*e^4 + 19392/181*e^2 - 4972/181, 141/181*e^10 - 2255/181*e^8 + 9793/181*e^6 - 10864/181*e^4 - 6094/181*e^2 + 2692/181, -671/181*e^10 + 11065/181*e^8 - 53117/181*e^6 + 89908/181*e^4 - 36189/181*e^2 - 4128/181, -413/181*e^11 + 7193/181*e^9 - 38660/181*e^7 + 80558/181*e^5 - 54495/181*e^3 - 1871/181*e, -127/181*e^11 + 2094/181*e^9 - 9501/181*e^7 + 8983/181*e^5 + 22544/181*e^3 - 30929/181*e, -151/181*e^11 + 2913/181*e^9 - 18974/181*e^7 + 54484/181*e^5 - 68825/181*e^3 + 29475/181*e, 102/181*e^11 - 1354/181*e^9 + 3110/181*e^7 + 6309/181*e^5 - 21330/181*e^3 + 12973/181*e, 98/181*e^11 - 1127/181*e^9 - 128/181*e^7 + 23395/181*e^5 - 56257/181*e^3 + 33116/181*e, -335/181*e^11 + 5572/181*e^9 - 26923/181*e^7 + 43135/181*e^5 - 5018/181*e^3 - 17184/181*e, -279/181*e^10 + 4747/181*e^8 - 24126/181*e^6 + 43937/181*e^4 - 21211/181*e^2 + 912/181, -709/181*e^10 + 12226/181*e^8 - 64873/181*e^6 + 135661/181*e^4 - 99301/181*e^2 + 8312/181, -411/181*e^10 + 7170/181*e^8 - 38851/181*e^6 + 83961/181*e^4 - 67711/181*e^2 + 11678/181, 679/181*e^10 - 11881/181*e^8 + 64299/181*e^6 - 134940/181*e^4 + 95545/181*e^2 - 7922/181, -557/181*e^10 + 9573/181*e^8 - 50429/181*e^6 + 104327/181*e^4 - 76904/181*e^2 + 8870/181, 788/181*e^10 - 13044/181*e^8 + 63211/181*e^6 - 109571/181*e^4 + 48774/181*e^2 + 3150/181, 287/181*e^10 - 5020/181*e^8 + 27163/181*e^6 - 57294/181*e^4 + 42376/181*e^2 - 7170/181, 202/181*e^10 - 3047/181*e^8 + 12203/181*e^6 - 17211/181*e^4 + 14539/181*e^2 - 10590/181, -210/181*e^11 + 3863/181*e^9 - 23023/181*e^7 + 56632/181*e^5 - 51632/181*e^3 + 9065/181*e, 429/181*e^10 - 7015/181*e^8 + 33693/181*e^6 - 62384/181*e^4 + 41439/181*e^2 - 1052/181, 216/181*e^10 - 3932/181*e^8 + 22450/181*e^6 - 47690/181*e^4 + 28274/181*e^2 + 88/181, 366/181*e^11 - 6743/181*e^9 + 40886/181*e^7 - 108491/181*e^5 + 125789/181*e^3 - 42587/181*e, -4/181*e^10 + 227/181*e^8 - 2333/181*e^6 + 4959/181*e^4 + 730/181*e^2 - 3568/181, -748/181*e^10 + 12584/181*e^8 - 63954/181*e^6 + 128580/181*e^4 - 97704/181*e^2 + 14792/181, 1228/181*e^10 - 21000/181*e^8 + 109519/181*e^6 - 222471/181*e^4 + 156895/181*e^2 - 15240/181, 866/181*e^10 - 14303/181*e^8 + 69337/181*e^6 - 123283/181*e^4 + 64042/181*e^2 + 2860/181, 421/181*e^10 - 7647/181*e^8 + 43869/181*e^6 - 97535/181*e^4 + 72764/181*e^2 - 7102/181, 184/181*e^11 - 3564/181*e^9 + 23515/181*e^7 - 69558/181*e^5 + 90586/181*e^3 - 35877/181*e, 104/181*e^11 - 1377/181*e^9 + 2919/181*e^7 + 9712/181*e^5 - 34727/181*e^3 + 29599/181*e, -155/181*e^11 + 2597/181*e^9 - 13162/181*e^7 + 27587/181*e^5 - 30085/181*e^3 + 21020/181*e, 86/181*e^11 - 1170/181*e^9 + 2828/181*e^7 + 7140/181*e^5 - 30537/181*e^3 + 25308/181*e, -588/181*e^10 + 10382/181*e^8 - 57333/181*e^6 + 125700/181*e^4 - 98306/181*e^2 + 10540/181, 43/181*e^11 - 223/181*e^9 - 4378/181*e^7 + 29815/181*e^5 - 57351/181*e^3 + 34012/181*e, -203/181*e^11 + 3692/181*e^9 - 21972/181*e^7 + 57773/181*e^5 - 70014/181*e^3 + 32504/181*e, 248/181*e^10 - 3938/181*e^8 + 17584/181*e^6 - 27451/181*e^4 + 12117/181*e^2 + 1120/181, -25/181*e^11 + 740/181*e^9 - 6934/181*e^7 + 22894/181*e^5 - 23583/181*e^3 - 2209/181*e, -299/181*e^11 + 5339/181*e^9 - 30904/181*e^7 + 79230/181*e^5 - 91409/181*e^3 + 31399/181*e, -122/181*e^10 + 1765/181*e^8 - 6087/181*e^6 + 4187/181*e^4 + 726/181*e^2 + 862/181, -106/181*e^11 + 1581/181*e^9 - 5443/181*e^7 - 2255/181*e^5 + 32015/181*e^3 - 33917/181*e, -505/181*e^11 + 8432/181*e^9 - 41096/181*e^7 + 67191/181*e^5 - 9650/181*e^3 - 29273/181*e, -345/181*e^11 + 5868/181*e^9 - 30312/181*e^7 + 61596/181*e^5 - 50615/181*e^3 + 20232/181*e, -402/181*e^11 + 6795/181*e^9 - 34371/181*e^7 + 64613/181*e^5 - 38493/181*e^3 + 7760/181*e] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([19, 19, 1/2*w^3 + w^2 - 4*w - 9])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]