J[2001] := rec | levels := [ 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 2001, 667, 667, 667, 667, 87, 87, 69, 69, 29, 23 ], new_dimensions := [ 1, 1, 1, 2, 2, 2, 4, 5, 7, 7, 10, 11, 14, 16, 20, 10, 12, 13, 16, 2, 3, 1, 2, 2, 2 ], dimensions := [ 1, 1, 1, 2, 2, 2, 4, 5, 7, 7, 10, 11, 14, 16, 20, 20, 24, 26, 32, 4, 6, 2, 4, 8, 8 ], intersection_graph := [ 0, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 0, 1, 1, 1, 1, 1, 1, 169, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 23, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 19, 1, 1, 1, 1, 1, 1, 1, 43, 1, 1, 1, 1, 7, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 19, 0, 1, 1, 1, 1, 1, 1, 1, 253, 1, 1, 1, 1, 23, 1, 11, 23, 11, 1, 1, 1, 1, 1, 23, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 8161, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 991, 29, 1, 1, 1, 1, 1, 1, 1, 1, 169, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 11737, 1, 1, 67, 1, 1, 1, 1, 1, 9, 1, 1, 19, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 212983, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1250999, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 9381191, 1, 1, 121, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3954191, 1, 1, 1, 1, 1, 1, 1, 7, 11, 1, 1, 1, 1, 1, 1, 43, 253, 1, 1, 1, 1, 1, 1, 3954191, 0, 1, 1, 1, 1, 23, 1, 11, 529, 9801, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1250999, 9381191, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 5, 1, 1, 8161, 1, 11737, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 12769, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 991, 1, 212983, 1, 1, 1, 1, 1, 1, 0, 5, 1, 1, 1, 1, 531441, 1, 1, 1, 1, 1, 1, 1, 1, 1, 29, 1, 1, 1, 121, 1, 1, 1, 1, 5, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 23, 1, 1, 67, 1, 1, 1, 1, 23, 1, 1, 1, 1, 0, 1, 1, 529, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 11, 1, 1, 1, 11, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 0, 1, 121, 1, 1, 1, 1, 1, 1, 1, 23, 1, 1, 1, 1, 1, 1, 7, 529, 1, 12769, 1, 1, 529, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 11, 9801, 1, 1, 531441, 1, 1, 1, 121, 1, 0 ], ap_traces := [ [ -1, -1, 3, 0, 3, 3, 0, 8, -1, 1, 7, -5 ], [ 0, -1, 4, -4, 4, -5, -5, 5, 1, -1, -2, 5 ], [ 0, 1, 0, 0, -4, 3, 3, -7, 1, -1, 2, 1 ], [ -2, -2, -4, 0, -4, -4, 0, -4, -2, 2, -16, 0 ], [ 2, -2, -3, 0, -3, -3, 0, -2, 2, -2, -9, 9 ], [ 0, 2, 0, -4, 0, 2, 2, -2, -2, 2, -16, 10 ], [ 0, -4, -2, -2, 0, 0, 2, 4, 4, 4, 2, 4 ], [ -2, -5, -3, -5, -8, 5, 2, -9, 5, 5, -6, 10 ], [ -1, 7, -5, -5, -12, -13, -12, -5, -7, 7, -8, -24 ], [ -3, 7, -3, -5, -4, -18, -3, -4, 7, -7, -22, -25 ], [ 3, -10, 6, 3, 9, -16, 0, 1, -10, 10, 17, 1 ], [ 2, -11, 2, 3, 11, -5, 15, -6, 11, -11, 35, -28 ], [ -2, -14, -3, -3, -12, 13, -14, -9, -14, -14, -28, -12 ], [ -1, 16, 3, 13, 8, 19, -4, 19, -16, -16, 24, 26 ], [ 2, 20, -1, 9, 0, 21, -4, 7, 20, 20, 28, 14 ] ], hecke_fields := [ x - 1, x - 1, x - 1, x^2 + 2*x - 79, x^2 + 7*x - 26, x^2 - 6, x^4 - 6*x^3 - 54*x^2 + 216*x + 324, x^5 + 2*x^4 - 7*x^3 - 13*x^2 + 11*x + 19, x^7 + x^6 - 10*x^5 - 10*x^4 + 29*x^3 + 29*x^2 - 24*x - 23, x^7 + 3*x^6 - 5*x^5 - 18*x^4 + 4*x^3 + 26*x^2 + x - 8, x^10 - 3*x^9 - 14*x^8 + 49*x^7 + 45*x^6 - 254*x^5 + 89*x^4 + 388*x^3 - 441*x^2 + 160*x - 16, x^11 - 2*x^10 - 18*x^9 + 30*x^8 + 124*x^7 - 152*x^6 - 408*x^5 + 285*x^4 + 634*x^3 - 93*x^2 - 369*x - 108, x^14 + 2*x^13 - 18*x^12 - 34*x^11 + 124*x^10 + 216*x^9 - 420*x^8 - 647*x^7 + 750*x^6 + 939*x^5 - 717*x^4 - 604*x^3 + 352*x^2 + 128*x - 64, x^16 + x^15 - 28*x^14 - 27*x^13 + 316*x^12 + 295*x^11 - 1835*x^10 - 1665*x^9 + 5778*x^8 + 5124*x^7 - 9405*x^6 - 8288*x^5 + 6405*x^4 + 6032*x^3 - 400*x^2 - 1088*x - 192, x^20 - 2*x^19 - 33*x^18 + 64*x^17 + 453*x^16 - 846*x^15 - 3353*x^14 + 5985*x^13 + 14484*x^12 - 24566*x^11 - 36791*x^10 + 59410*x^9 + 52109*x^8 - 82362*x^7 - 34967*x^6 + 60661*x^5 + 5201*x^4 - 19624*x^3 + 2768*x^2 + 1408*x - 256 ], atkin_lehners := [ [ 1, 1, -1 ], [ 1, -1, 1 ], [ -1, -1, 1 ], [ 1, 1, -1 ], [ 1, -1, 1 ], [ -1, 1, -1 ], [ 1, -1, -1 ], [ 1, -1, -1 ], [ -1, 1, -1 ], [ -1, -1, 1 ], [ 1, 1, -1 ], [ 1, -1, 1 ], [ 1, 1, 1 ], [ -1, 1, 1 ], [ -1, -1, -1 ] ], component_group_orders := [ [ 7, 1, 1 ], [ 1, 1, 5 ], [ 1, 1, 1 ], [ 1, 1, 1 ], [ 1, 1, 1 ], [ 5, 1, 1 ], [ 43, 7, 5 ], [ 253, 23, 11 ], [ 8161, 1, 7 ], [ 991, 29, 1 ], [ 11737, 67, 1 ], [ 212983, 1, 11 ], [ 1250999, 1, 1 ], [ 28143573, 121, 1 ], [ 304472707, 7, 11 ] ], tamagawa_numbers := [ [ 1, 1, 1 ], [ 1, 1, 1 ], [ 1, 1, 1 ], [ 1, 1, 1 ], [ 1, 1, 1 ], [ 5, 1, 1 ], [ 1, 7, 5 ], [ 1, 23, 11 ], [ 8161, 1, 7 ], [ 991, 29, 1 ], [ 1, 1, 1 ], [ 1, 1, 1 ], [ 1, 1, 1 ], [ 28143573, 1, 1 ], [ 304472707, 7, 11 ] ], torsion_upper_bounds := [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 77 ], torsion_lower_bounds := [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1 ], l_ratios := [ 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 9, 0, 9381191/3, 3954191 ], analytic_sha_upper_bounds := [ 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 9, 0, 1, 1 ], analytic_sha_lower_bounds := [ 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 9, 0, 1, 1/5929 ], eigenvalues := [* [ -1, -1, 3, 0, 3, 3, 0, 8, -1, 1, 7, -5 ], [ 0, -1, 4, -4, 4, -5, -5, 5, 1, -1, -2, 5 ], [ 0, 1, 0, 0, -4, 3, 3, -7, 1, -1, 2, 1 ], [ -1, -1, -2, 0, -1/2*a - 5/2, -2, 1/2*a + 1/2, -1/2*a - 5/2, -1, 1, -8, -1/2*a - 1/2 ], [ 1, -1, 1/3*a - 1/3, 0, 1/3*a - 1/3, 1/3*a - 1/3, 0, 2/3*a + 4/3, 1, -1, -1/3*a - 17/3, 1/3*a + 17/3 ], [ 0, 1, -a, a - 2, 0, 1, a + 1, -1, -1, 1, a - 8, -2*a + 5 ], [ 0, -1, -1/3*a, 1/9*a^2 - 1/3*a - 4, -1/27*a^3 + 1/9*a^2 + 2*a - 2, 1/27*a^3 - 2/9*a^2 - 4/3*a + 5, -1/54*a^3 - 1/9*a^2 + 4/3*a + 5, 1/18*a^3 - 2/9*a^2 - 7/3*a + 5, 1, 1, 1/9*a^2 + 1/3*a - 4, -1/54*a^3 + 1/9*a^2 + 5/3*a - 3 ], [ a, -1, a^4 + a^3 - 7*a^2 - 3*a + 10, -a^4 - a^3 + 6*a^2 + 3*a - 8, a^4 - 8*a^2 + a + 12, -a^3 - a^2 + 4*a + 4, -a^2 + 4, -2*a^4 + 16*a^2 - 2*a - 29, 1, 1, -a^4 - a^3 + 6*a^2 + a - 9, 2*a^4 + a^3 - 12*a^2 - 3*a + 15 ], [ a, 1, -2*a^6 + a^5 + 19*a^4 - 8*a^3 - 50*a^2 + 12*a + 35, 4*a^6 - 2*a^5 - 37*a^4 + 15*a^3 + 92*a^2 - 21*a - 60, a^6 - a^5 - 10*a^4 + 8*a^3 + 28*a^2 - 13*a - 23, -11*a^6 + 6*a^5 + 101*a^4 - 46*a^3 - 250*a^2 + 67*a + 162, 6*a^6 - 3*a^5 - 56*a^4 + 23*a^3 + 144*a^2 - 35*a - 103, 5*a^6 - 3*a^5 - 45*a^4 + 24*a^3 + 108*a^2 - 38*a - 70, -1, 1, -10*a^6 + 4*a^5 + 91*a^4 - 31*a^3 - 222*a^2 + 45*a + 141, 12*a^6 - 5*a^5 - 110*a^4 + 38*a^3 + 271*a^2 - 54*a - 178 ], [ a, 1, -a^4 - a^3 + 5*a^2 + 3*a - 4, a^6 + 2*a^5 - 6*a^4 - 10*a^3 + 9*a^2 + 8*a - 4, a^4 - 6*a^2 - a + 4, -a^6 - a^5 + 7*a^4 + 5*a^3 - 13*a^2 - 6*a + 3, -a^5 + 7*a^3 - 9*a - 1, -a^6 - 2*a^5 + 7*a^4 + 11*a^3 - 15*a^2 - 11*a + 9, 1, -1, -a^6 - a^5 + 8*a^4 + 5*a^3 - 18*a^2 - 3*a + 6, -a^6 + 9*a^4 - 19*a^2 + 2*a + 1 ], [ a, -1, -3/4*a^9 + 7/4*a^8 + 23/2*a^7 - 115/4*a^6 - 205/4*a^5 + 305/2*a^4 + 133/4*a^3 - 519/2*a^2 + 585/4*a - 15, -5/4*a^9 + 11/4*a^8 + 39/2*a^7 - 181/4*a^6 - 361/4*a^5 + 481/2*a^4 + 307/4*a^3 - 411*a^2 + 865/4*a - 21, 21/26*a^9 - 29/13*a^8 - 157/13*a^7 + 953/26*a^6 + 646/13*a^5 - 2520/13*a^4 - 85/26*a^3 + 8467/26*a^2 - 2871/13*a + 404/13, 3/2*a^9 - 7/2*a^8 - 23*a^7 + 115/2*a^6 + 203/2*a^5 - 305*a^4 - 109/2*a^3 + 517*a^2 - 651/2*a + 43, -159/52*a^9 + 389/52*a^8 + 1237/26*a^7 - 6443/52*a^6 - 11203/52*a^5 + 17247/26*a^4 + 7125/52*a^3 - 14809/13*a^2 + 34403/52*a - 976/13, -57/26*a^9 + 137/26*a^8 + 441/13*a^7 - 2271/26*a^6 - 3947/26*a^5 + 6086/13*a^4 + 2281/26*a^3 - 10450/13*a^2 + 12601/26*a - 779/13, -1, 1, -9/4*a^9 + 23/4*a^8 + 69/2*a^7 - 377/4*a^6 - 605/4*a^5 + 995/2*a^4 + 279/4*a^3 - 837*a^2 + 2097/4*a - 67, -61/13*a^9 + 293/26*a^8 + 948/13*a^7 - 2416/13*a^6 - 8601/26*a^5 + 12885/13*a^4 + 2876/13*a^3 - 44157/26*a^2 + 25445/26*a - 1429/13 ], [ a, -1, 1/6*a^10 - 5/6*a^9 - 3/2*a^8 + 21/2*a^7 + 13/6*a^6 - 251/6*a^5 + 9/2*a^4 + 60*a^3 + 2/3*a^2 - 55/2*a - 8, 1/9*a^10 + 1/9*a^9 - 8/3*a^8 - 2/3*a^7 + 187/9*a^6 - 23/9*a^5 - 63*a^4 + 50/3*a^3 + 598/9*a^2 - 13*a - 18, -5/18*a^10 + 31/18*a^9 + 13/6*a^8 - 137/6*a^7 + 1/18*a^6 + 1789/18*a^5 - 35/2*a^4 - 500/3*a^3 - 19/9*a^2 + 191/2*a + 30, a^8 - 2*a^7 - 12*a^6 + 22*a^5 + 44*a^4 - 68*a^3 - 57*a^2 + 52*a + 31, -2/9*a^10 + 7/9*a^9 + 4/3*a^8 - 23/3*a^7 + 58/9*a^6 + 136/9*a^5 - 48*a^4 + 62/3*a^3 + 631/9*a^2 - 36*a - 31, 4/9*a^10 - 23/9*a^9 - 14/3*a^8 + 106/3*a^7 + 136/9*a^6 - 1478/9*a^5 - 33*a^4 + 908/3*a^3 + 826/9*a^2 - 189*a - 87, 1, -1, -1/3*a^10 + 2/3*a^9 + 5*a^8 - 9*a^7 - 82/3*a^6 + 122/3*a^5 + 70*a^4 - 73*a^3 - 256/3*a^2 + 47*a + 40, 1/6*a^10 + 1/6*a^9 - 5/2*a^8 - 7/2*a^7 + 73/6*a^6 + 139/6*a^5 - 39/2*a^4 - 56*a^3 - 4/3*a^2 + 81/2*a + 11 ], [ a, -1, -6/23*a^13 - 11/23*a^12 + 106/23*a^11 + 365/46*a^10 - 1407/46*a^9 - 97/2*a^8 + 4419/46*a^7 + 6257/46*a^6 - 6727/46*a^5 - 349/2*a^4 + 2255/23*a^3 + 2010/23*a^2 - 961/46*a - 272/23, -13/46*a^13 - 17/92*a^12 + 245/46*a^11 + 53/23*a^10 - 880/23*a^9 - 15/2*a^8 + 6081/46*a^7 - 125/23*a^6 - 20835/92*a^5 + 117/2*a^4 + 16319/92*a^3 - 6815/92*a^2 - 2101/46*a + 472/23, 11/92*a^13 + 47/92*a^12 - 39/23*a^11 - 202/23*a^10 + 343/46*a^9 + 56*a^8 - 166/23*a^7 - 15225/92*a^6 - 1989/92*a^5 + 917/4*a^4 + 886/23*a^3 - 12241/92*a^2 - 200/23*a + 508/23, 49/184*a^13 + 43/92*a^12 - 429/92*a^11 - 681/92*a^10 + 1409/46*a^9 + 42*a^8 - 4363/46*a^7 - 19119/184*a^6 + 12913/92*a^5 + 837/8*a^4 - 16273/184*a^3 - 646/23*a^2 + 393/23*a + 17/23, -15/368*a^13 - 123/184*a^12 - 17/184*a^11 + 2163/184*a^10 + 729/92*a^9 - 77*a^8 - 5187/92*a^7 + 86257/368*a^6 + 28447/184*a^5 - 5339/16*a^4 - 63397/368*a^3 + 18167/92*a^2 + 2635/46*a - 859/23, 111/368*a^13 + 73/184*a^12 - 1015/184*a^11 - 1231/184*a^10 + 3465/92*a^9 + 42*a^8 - 10965/92*a^7 - 45233/368*a^6 + 32087/184*a^5 + 2715/16*a^4 - 37175/368*a^3 - 2245/23*a^2 + 336/23*a + 395/23, -1, -1, -1/23*a^13 + 31/92*a^12 + 33/23*a^11 - 265/46*a^10 - 683/46*a^9 + 37*a^8 + 1501/23*a^7 - 2597/23*a^6 - 11749/92*a^5 + 165*a^4 + 9101/92*a^3 - 9033/92*a^2 - 923/46*a + 292/23, 151/368*a^13 + 171/184*a^12 - 1215/184*a^11 - 2767/184*a^10 + 3453/92*a^9 + 177/2*a^8 - 8127/92*a^7 - 86161/368*a^6 + 11965/184*a^5 + 4347/16*a^4 + 10413/368*a^3 - 10191/92*a^2 - 678/23*a + 263/23 ], [ a, 1, 147/3904*a^15 + 39/1952*a^14 - 2151/1952*a^13 - 2119/3904*a^12 + 51261/3904*a^11 + 11813/1952*a^10 - 318351/3904*a^9 - 69249/1952*a^8 + 272469/976*a^7 + 14121/122*a^6 - 1976055/3904*a^5 - 791727/3904*a^4 + 99701/244*a^3 + 9876/61*a^2 - 149/2*a - 1767/61, -71/976*a^15 - 19/976*a^14 + 1977/976*a^13 + 253/488*a^12 - 22127/976*a^11 - 5583/976*a^10 + 63597/488*a^9 + 8067/244*a^8 - 24813/61*a^7 - 12675/122*a^6 + 648475/976*a^5 + 41127/244*a^4 - 29547/61*a^3 - 14755/122*a^2 + 175/2*a + 1412/61, -551/3904*a^15 - 191/1952*a^14 + 7719/1952*a^13 + 9971/3904*a^12 - 174713/3904*a^11 - 52573/1952*a^10 + 1021947/3904*a^9 + 285669/1952*a^8 - 818133/976*a^7 - 105303/244*a^6 + 5542347/3904*a^5 + 2591083/3904*a^4 - 132415/122*a^3 - 27735/61*a^2 + 205*a + 4731/61, -141/3904*a^15 - 15/1952*a^14 + 1991/1952*a^13 + 693/3904*a^12 - 45683/3904*a^11 - 3361/1952*a^10 + 272925/3904*a^9 + 17991/1952*a^8 - 225191/976*a^7 - 3573/122*a^6 + 1586665/3904*a^5 + 208365/3904*a^4 - 158663/488*a^3 - 11623/244*a^2 + 64*a + 872/61, 71/488*a^15 + 99/976*a^14 - 1019/244*a^13 - 1299/488*a^12 + 47365/976*a^11 + 27453/976*a^10 - 142505/488*a^9 - 149265/976*a^8 + 469903/488*a^7 + 110541/244*a^6 - 819031/488*a^5 - 693369/976*a^4 + 1285091/976*a^3 + 125083/244*a^2 - 509/2*a - 5691/61, 5/32*a^15 + 1/8*a^14 - 69/16*a^13 - 105/32*a^12 + 1533/32*a^11 + 277/8*a^10 - 8761/32*a^9 - 1491/8*a^8 + 1703/2*a^7 + 2139/4*a^6 - 44513/32*a^5 - 24899/32*a^4 + 16345/16*a^3 + 1957/4*a^2 - 190*a - 79, -1, -1, 207/3904*a^15 + 157/1952*a^14 - 2897/1952*a^13 - 7839/3904*a^12 + 65561/3904*a^11 + 38627/1952*a^10 - 382455/3904*a^9 - 190697/1952*a^8 + 302877/976*a^7 + 61753/244*a^6 - 1996211/3904*a^5 - 1282479/3904*a^4 + 89713/244*a^3 + 44729/244*a^2 - 111/2*a - 1567/61, -473/3904*a^15 - 123/1952*a^14 + 6981/1952*a^13 + 6805/3904*a^12 - 167347/3904*a^11 - 38345/1952*a^10 + 1042141/3904*a^9 + 225045/1952*a^8 - 891965/976*a^7 - 90915/244*a^6 + 6466085/3904*a^5 + 2498665/3904*a^4 - 1310691/976*a^3 - 121319/244*a^2 + 252*a + 5540/61 ], [ a, 1, 59655/6808448*a^19 + 83835/6808448*a^18 - 988659/3404224*a^17 - 1246779/3404224*a^16 + 26985321/6808448*a^15 + 29771565/6808448*a^14 - 24436759/851056*a^13 - 181802773/6808448*a^12 + 808522329/6808448*a^11 + 596421017/6808448*a^10 - 957523175/3404224*a^9 - 124194469/851056*a^8 + 2487007763/6808448*a^7 + 636510631/6808448*a^6 - 404727775/1702112*a^5 + 152363091/6808448*a^4 + 111939515/1702112*a^3 - 34288913/851056*a^2 - 1249039/212764*a + 335923/53191, 148537/3404224*a^19 - 338681/3404224*a^18 - 315071/212764*a^17 + 5286021/1702112*a^16 + 71767335/3404224*a^15 - 135044723/3404224*a^14 - 278428579/1702112*a^13 + 910556129/3404224*a^12 + 2556880073/3404224*a^11 - 3490925219/3404224*a^10 - 1759420645/851056*a^9 + 239471955/106382*a^8 + 11171608865/3404224*a^7 - 9303904093/3404224*a^6 - 4620416463/1702112*a^5 + 5836685909/3404224*a^4 + 1606611015/1702112*a^3 - 406590829/851056*a^2 - 16258787/212764*a + 1523763/53191, 113117/6808448*a^19 + 286133/6808448*a^18 - 1718209/3404224*a^17 - 4533933/3404224*a^16 + 41870219/6808448*a^15 + 117469803/6808448*a^14 - 8106861/212764*a^13 - 800884431/6808448*a^12 + 846624863/6808448*a^11 + 3086463419/6808448*a^10 - 654440223/3404224*a^9 - 1686243093/1702112*a^8 + 477260749/6808448*a^7 + 8047603685/6808448*a^6 + 95627223/851056*a^5 - 4881910035/6808448*a^4 - 135886507/1702112*a^3 + 79689365/425528*a^2 + 96963/106382*a - 511278/53191, -595707/6808448*a^19 + 195465/6808448*a^18 + 9841975/3404224*a^17 - 3114545/3404224*a^16 - 270259309/6808448*a^15 + 82762231/6808448*a^14 + 124951323/425528*a^13 - 597242311/6808448*a^12 - 8642079917/6808448*a^11 + 2553180667/6808448*a^10 + 11075095679/3404224*a^9 - 823813611/851056*a^8 - 32604889607/6808448*a^7 + 9966835125/6808448*a^6 + 6297465011/1702112*a^5 - 8106916351/6808448*a^4 - 2056207027/1702112*a^3 + 178303997/425528*a^2 + 4339999/53191*a - 1309493/53191, 202867/3404224*a^19 - 78181/1702112*a^18 - 6774905/3404224*a^17 + 613921/425528*a^16 + 94271295/3404224*a^15 - 31725389/1702112*a^14 - 709058137/3404224*a^13 + 436217767/3404224*a^12 + 195461249/212764*a^11 - 107939725/212764*a^10 - 8203441237/3404224*a^9 + 498932235/425528*a^8 + 12375653553/3404224*a^7 - 81933111/53191*a^6 - 9802374313/3404224*a^5 + 3672857369/3404224*a^4 + 3330475213/3404224*a^3 - 287102203/851056*a^2 - 17040839/212764*a + 1084711/53191, 16095/1702112*a^19 - 101041/3404224*a^18 - 1039401/3404224*a^17 + 1553165/1702112*a^16 + 1743977/425528*a^15 - 38936723/3404224*a^14 - 101021583/3404224*a^13 + 128152433/1702112*a^12 + 427557079/3404224*a^11 - 951947129/3404224*a^10 - 1066095561/3404224*a^9 + 124929067/212764*a^8 + 185485911/425528*a^7 - 2270424875/3404224*a^6 - 990251463/3404224*a^5 + 322663417/851056*a^4 + 195615347/3404224*a^3 - 40763125/425528*a^2 + 439861/53191*a + 340328/53191, 1, 1, -380439/6808448*a^19 + 254997/6808448*a^18 + 6316839/3404224*a^17 - 4039569/3404224*a^16 - 174716497/6808448*a^15 + 105738795/6808448*a^14 + 163257931/851056*a^13 - 741027003/6808448*a^12 - 5732647449/6808448*a^11 + 3015967983/6808448*a^10 + 7514040635/3404224*a^9 - 904794911/851056*a^8 - 22897375291/6808448*a^7 + 9964491865/6808448*a^6 + 4688821643/1702112*a^5 - 7338969931/6808448*a^4 - 1735939675/1702112*a^3 + 305462179/851056*a^2 + 22502347/212764*a - 1344533/53191, 200179/6808448*a^19 + 27333/6808448*a^18 - 1643655/1702112*a^17 - 257865/3404224*a^16 + 89266177/6808448*a^15 + 526491/6808448*a^14 - 324076289/3404224*a^13 + 55131527/6808448*a^12 + 2722049763/6808448*a^11 - 541103477/6808448*a^10 - 1673420461/1702112*a^9 + 141479923/425528*a^8 + 9341243195/6808448*a^7 - 4666244123/6808448*a^6 - 3394409107/3404224*a^5 + 4514798747/6808448*a^4 + 996742067/3404224*a^3 - 101244609/425528*a^2 - 118491/53191*a + 617272/53191 ] *], q_expansions := [* q - q^2 - q^3 - q^4 + 3*q^5 + q^6 + 3*q^8 + q^9 - 3*q^10 + 3*q^11 + q^12 + 3*q^13 - 3*q^15 - q^16 - q^18 + 8*q^19 - 3*q^20 - 3*q^22 - q^23 - 3*q^24 + 4*q^25 - 3*q^26 - q^27 + q^29 + 3*q^30 + 7*q^31 - 5*q^32 - 3*q^33 - q^36 - 5*q^37 + O(q^38), q - q^3 - 2*q^4 + 4*q^5 - 4*q^7 + q^9 + 4*q^11 + 2*q^12 - 5*q^13 - 4*q^15 + 4*q^16 - 5*q^17 + 5*q^19 - 8*q^20 + 4*q^21 + q^23 + 11*q^25 - q^27 + 8*q^28 - q^29 - 2*q^31 - 4*q^33 - 16*q^35 - 2*q^36 + 5*q^37 + O(q^38), q + q^3 - 2*q^4 + q^9 - 4*q^11 - 2*q^12 + 3*q^13 + 4*q^16 + 3*q^17 - 7*q^19 + q^23 - 5*q^25 + q^27 - q^29 + 2*q^31 - 4*q^33 - 2*q^36 + q^37 + O(q^38), q - q^2 - q^3 - q^4 - 2*q^5 + q^6 + 3*q^8 + q^9 + 2*q^10 + (-1/2*a - 5/2)*q^11 + q^12 - 2*q^13 + 2*q^15 - q^16 + (1/2*a + 1/2)*q^17 - q^18 + (-1/2*a - 5/2)*q^19 + 2*q^20 + (1/2*a + 5/2)*q^22 - q^23 - 3*q^24 - q^25 + 2*q^26 - q^27 + q^29 - 2*q^30 - 8*q^31 - 5*q^32 + (1/2*a + 5/2)*q^33 + (-1/2*a - 1/2)*q^34 - q^36 + (-1/2*a - 1/2)*q^37 + O(q^38), q + q^2 - q^3 - q^4 + (1/3*a - 1/3)*q^5 - q^6 - 3*q^8 + q^9 + (1/3*a - 1/3)*q^10 + (1/3*a - 1/3)*q^11 + q^12 + (1/3*a - 1/3)*q^13 + (-1/3*a + 1/3)*q^15 - q^16 + q^18 + (2/3*a + 4/3)*q^19 + (-1/3*a + 1/3)*q^20 + (1/3*a - 1/3)*q^22 + q^23 + 3*q^24 + (-a - 2)*q^25 + (1/3*a - 1/3)*q^26 - q^27 - q^29 + (-1/3*a + 1/3)*q^30 + (-1/3*a - 17/3)*q^31 + 5*q^32 + (-1/3*a + 1/3)*q^33 - q^36 + (1/3*a + 17/3)*q^37 + O(q^38), q + q^3 - 2*q^4 - a*q^5 + (a - 2)*q^7 + q^9 - 2*q^12 + q^13 - a*q^15 + 4*q^16 + (a + 1)*q^17 - q^19 + 2*a*q^20 + (a - 2)*q^21 - q^23 + q^25 + q^27 + (-2*a + 4)*q^28 + q^29 + (a - 8)*q^31 + (2*a - 6)*q^35 - 2*q^36 + (-2*a + 5)*q^37 + O(q^38), q - q^3 - 2*q^4 - 1/3*a*q^5 + (1/9*a^2 - 1/3*a - 4)*q^7 + q^9 + (-1/27*a^3 + 1/9*a^2 + 2*a - 2)*q^11 + 2*q^12 + (1/27*a^3 - 2/9*a^2 - 4/3*a + 5)*q^13 + 1/3*a*q^15 + 4*q^16 + (-1/54*a^3 - 1/9*a^2 + 4/3*a + 5)*q^17 + (1/18*a^3 - 2/9*a^2 - 7/3*a + 5)*q^19 + 2/3*a*q^20 + (-1/9*a^2 + 1/3*a + 4)*q^21 + q^23 + (1/9*a^2 - 5)*q^25 - q^27 + (-2/9*a^2 + 2/3*a + 8)*q^28 + q^29 + (1/9*a^2 + 1/3*a - 4)*q^31 + (1/27*a^3 - 1/9*a^2 - 2*a + 2)*q^33 + (-1/27*a^3 + 1/9*a^2 + 4/3*a)*q^35 - 2*q^36 + (-1/54*a^3 + 1/9*a^2 + 5/3*a - 3)*q^37 + O(q^38), q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (a^4 + a^3 - 7*a^2 - 3*a + 10)*q^5 - a*q^6 + (-a^4 - a^3 + 6*a^2 + 3*a - 8)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^4 + 10*a^2 - a - 19)*q^10 + (a^4 - 8*a^2 + a + 12)*q^11 + (-a^2 + 2)*q^12 + (-a^3 - a^2 + 4*a + 4)*q^13 + (a^4 - a^3 - 10*a^2 + 3*a + 19)*q^14 + (-a^4 - a^3 + 7*a^2 + 3*a - 10)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^2 + 4)*q^17 + a*q^18 + (-2*a^4 + 16*a^2 - 2*a - 29)*q^19 + (a^3 - 2*a - 1)*q^20 + (a^4 + a^3 - 6*a^2 - 3*a + 8)*q^21 + (-2*a^4 - a^3 + 14*a^2 + a - 19)*q^22 + q^23 + (-a^3 + 4*a)*q^24 - a*q^25 + (-a^4 - a^3 + 4*a^2 + 4*a)*q^26 - q^27 + (-a^4 - a^3 + 4*a^2 + 2*a - 3)*q^28 + q^29 + (a^4 - 10*a^2 + a + 19)*q^30 + (-a^4 - a^3 + 6*a^2 + a - 9)*q^31 + (-2*a^4 - a^3 + 13*a^2 + a - 19)*q^32 + (-a^4 + 8*a^2 - a - 12)*q^33 + (-a^3 + 4*a)*q^34 + (-a^3 + 3*a - 4)*q^35 + (a^2 - 2)*q^36 + (2*a^4 + a^3 - 12*a^2 - 3*a + 15)*q^37 + O(q^38), q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-2*a^6 + a^5 + 19*a^4 - 8*a^3 - 50*a^2 + 12*a + 35)*q^5 + a*q^6 + (4*a^6 - 2*a^5 - 37*a^4 + 15*a^3 + 92*a^2 - 21*a - 60)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (3*a^6 - a^5 - 28*a^4 + 8*a^3 + 70*a^2 - 13*a - 46)*q^10 + (a^6 - a^5 - 10*a^4 + 8*a^3 + 28*a^2 - 13*a - 23)*q^11 + (a^2 - 2)*q^12 + (-11*a^6 + 6*a^5 + 101*a^4 - 46*a^3 - 250*a^2 + 67*a + 162)*q^13 + (-6*a^6 + 3*a^5 + 55*a^4 - 24*a^3 - 137*a^2 + 36*a + 92)*q^14 + (-2*a^6 + a^5 + 19*a^4 - 8*a^3 - 50*a^2 + 12*a + 35)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (6*a^6 - 3*a^5 - 56*a^4 + 23*a^3 + 144*a^2 - 35*a - 103)*q^17 + a*q^18 + (5*a^6 - 3*a^5 - 45*a^4 + 24*a^3 + 108*a^2 - 38*a - 70)*q^19 + (-a^3 + 2*a - 1)*q^20 + (4*a^6 - 2*a^5 - 37*a^4 + 15*a^3 + 92*a^2 - 21*a - 60)*q^21 + (-2*a^6 + 18*a^4 - a^3 - 42*a^2 + a + 23)*q^22 - q^23 + (a^3 - 4*a)*q^24 + (7*a^6 - 4*a^5 - 65*a^4 + 31*a^3 + 165*a^2 - 46*a - 114)*q^25 + (17*a^6 - 9*a^5 - 156*a^4 + 69*a^3 + 386*a^2 - 102*a - 253)*q^26 + q^27 + (a^6 - a^5 - 10*a^4 + 7*a^3 + 26*a^2 - 10*a - 18)*q^28 + q^29 + (3*a^6 - a^5 - 28*a^4 + 8*a^3 + 70*a^2 - 13*a - 46)*q^30 + (-10*a^6 + 4*a^5 + 91*a^4 - 31*a^3 - 222*a^2 + 45*a + 141)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^6 - a^5 - 10*a^4 + 8*a^3 + 28*a^2 - 13*a - 23)*q^33 + (-9*a^6 + 4*a^5 + 83*a^4 - 30*a^3 - 209*a^2 + 41*a + 138)*q^34 + (-7*a^6 + 4*a^5 + 65*a^4 - 30*a^3 - 163*a^2 + 44*a + 108)*q^35 + (a^2 - 2)*q^36 + (12*a^6 - 5*a^5 - 110*a^4 + 38*a^3 + 271*a^2 - 54*a - 178)*q^37 + O(q^38), q + a*q^2 + q^3 + (a^2 - 2)*q^4 + (-a^4 - a^3 + 5*a^2 + 3*a - 4)*q^5 + a*q^6 + (a^6 + 2*a^5 - 6*a^4 - 10*a^3 + 9*a^2 + 8*a - 4)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-a^5 - a^4 + 5*a^3 + 3*a^2 - 4*a)*q^10 + (a^4 - 6*a^2 - a + 4)*q^11 + (a^2 - 2)*q^12 + (-a^6 - a^5 + 7*a^4 + 5*a^3 - 13*a^2 - 6*a + 3)*q^13 + (-a^6 - a^5 + 8*a^4 + 5*a^3 - 18*a^2 - 5*a + 8)*q^14 + (-a^4 - a^3 + 5*a^2 + 3*a - 4)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-a^5 + 7*a^3 - 9*a - 1)*q^17 + a*q^18 + (-a^6 - 2*a^5 + 7*a^4 + 11*a^3 - 15*a^2 - 11*a + 9)*q^19 + (-a^6 - a^5 + 7*a^4 + 5*a^3 - 14*a^2 - 6*a + 8)*q^20 + (a^6 + 2*a^5 - 6*a^4 - 10*a^3 + 9*a^2 + 8*a - 4)*q^21 + (a^5 - 6*a^3 - a^2 + 4*a)*q^22 + q^23 + (a^3 - 4*a)*q^24 + (-a^6 - 3*a^5 + 5*a^4 + 16*a^3 - 6*a^2 - 15*a + 3)*q^25 + (2*a^6 + 2*a^5 - 13*a^4 - 9*a^3 + 20*a^2 + 4*a - 8)*q^26 + q^27 + (-a^5 - a^4 + 6*a^3 + 3*a^2 - 7*a)*q^28 - q^29 + (-a^5 - a^4 + 5*a^3 + 3*a^2 - 4*a)*q^30 + (-a^6 - a^5 + 8*a^4 + 5*a^3 - 18*a^2 - 3*a + 6)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (a^4 - 6*a^2 - a + 4)*q^33 + (-a^6 + 7*a^4 - 9*a^2 - a)*q^34 + (2*a^4 + 3*a^3 - 10*a^2 - 11*a + 8)*q^35 + (a^2 - 2)*q^36 + (-a^6 + 9*a^4 - 19*a^2 + 2*a + 1)*q^37 + O(q^38), q + a*q^2 - q^3 + (a^2 - 2)*q^4 + (-3/4*a^9 + 7/4*a^8 + 23/2*a^7 - 115/4*a^6 - 205/4*a^5 + 305/2*a^4 + 133/4*a^3 - 519/2*a^2 + 585/4*a - 15)*q^5 - a*q^6 + (-5/4*a^9 + 11/4*a^8 + 39/2*a^7 - 181/4*a^6 - 361/4*a^5 + 481/2*a^4 + 307/4*a^3 - 411*a^2 + 865/4*a - 21)*q^7 + (a^3 - 4*a)*q^8 + q^9 + (-1/2*a^9 + a^8 + 8*a^7 - 35/2*a^6 - 38*a^5 + 100*a^4 + 63/2*a^3 - 369/2*a^2 + 105*a - 12)*q^10 + (21/26*a^9 - 29/13*a^8 - 157/13*a^7 + 953/26*a^6 + 646/13*a^5 - 2520/13*a^4 - 85/26*a^3 + 8467/26*a^2 - 2871/13*a + 404/13)*q^11 + (-a^2 + 2)*q^12 + (3/2*a^9 - 7/2*a^8 - 23*a^7 + 115/2*a^6 + 203/2*a^5 - 305*a^4 - 109/2*a^3 + 517*a^2 - 651/2*a + 43)*q^13 + (-a^9 + 2*a^8 + 16*a^7 - 34*a^6 - 77*a^5 + 188*a^4 + 74*a^3 - 335*a^2 + 179*a - 20)*q^14 + (3/4*a^9 - 7/4*a^8 - 23/2*a^7 + 115/4*a^6 + 205/4*a^5 - 305/2*a^4 - 133/4*a^3 + 519/2*a^2 - 585/4*a + 15)*q^15 + (a^4 - 6*a^2 + 4)*q^16 + (-159/52*a^9 + 389/52*a^8 + 1237/26*a^7 - 6443/52*a^6 - 11203/52*a^5 + 17247/26*a^4 + 7125/52*a^3 - 14809/13*a^2 + 34403/52*a - 976/13)*q^17 + a*q^18 + (-57/26*a^9 + 137/26*a^8 + 441/13*a^7 - 2271/26*a^6 - 3947/26*a^5 + 6086/13*a^4 + 2281/26*a^3 - 10450/13*a^2 + 12601/26*a - 779/13)*q^19 + (a^9 - 5/2*a^8 - 16*a^7 + 42*a^6 + 151/2*a^5 - 229*a^4 - 57*a^3 + 807/2*a^2 - 449/2*a + 22)*q^20 + (5/4*a^9 - 11/4*a^8 - 39/2*a^7 + 181/4*a^6 + 361/4*a^5 - 481/2*a^4 - 307/4*a^3 + 411*a^2 - 865/4*a + 21)*q^21 + (5/26*a^9 - 10/13*a^8 - 38/13*a^7 + 347/26*a^6 + 147/13*a^5 - 977/13*a^4 + 319/26*a^3 + 3519/26*a^2 - 1276/13*a + 168/13)*q^22 - q^23 + (-a^3 + 4*a)*q^24 + (1/2*a^9 - 3/2*a^8 - 8*a^7 + 51/2*a^6 + 73/2*a^5 - 141*a^4 - 25/2*a^3 + 251*a^2 - 323/2*a + 19)*q^25 + (a^9 - 2*a^8 - 16*a^7 + 34*a^6 + 76*a^5 - 188*a^4 - 65*a^3 + 336*a^2 - 197*a + 24)*q^26 - q^27 + (3/2*a^9 - 7/2*a^8 - 24*a^7 + 117/2*a^6 + 229/2*a^5 - 318*a^4 - 201/2*a^3 + 560*a^2 - 585/2*a + 26)*q^28 + q^29 + (1/2*a^9 - a^8 - 8*a^7 + 35/2*a^6 + 38*a^5 - 100*a^4 - 63/2*a^3 + 369/2*a^2 - 105*a + 12)*q^30 + (-9/4*a^9 + 23/4*a^8 + 69/2*a^7 - 377/4*a^6 - 605/4*a^5 + 995/2*a^4 + 279/4*a^3 - 837*a^2 + 2097/4*a - 67)*q^31 + (a^5 - 8*a^3 + 12*a)*q^32 + (-21/26*a^9 + 29/13*a^8 + 157/13*a^7 - 953/26*a^6 - 646/13*a^5 + 2520/13*a^4 + 85/26*a^3 - 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