CoCalc -- Collaborative Calculation in the Cloud
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\\ charpoly_s2.gp
\\ This is a table of characteristic polynomials of the
\\ Hecke operators T_p acting on the space S_2(Gamma_0(N)) 
\\ of weight 2 cusp forms for Gamma_0(N).
\\ William Stein ([email protected]), September, 1998.

{
T=matrix(1500,5,m,n,0);
T[1001,2]=(x + 1)*(x^5 -6*x^3 + x^2 + 5*x -2)*(x^5 + 2*x^4 -4*x^3 -7*x^2 + x + 2)*(x^8 -2*x^7 -12*x^6 + 21*x^5 + 44*x^4 -58*x^3 -58*x^2 + 39*x + 9)*(x^7 -19*x^5 -x^4 + 117*x^3 + 17*x^2 -231*x -72)*(x^4 -6*x^2 + x + 7)*(x^5 + 2*x^4 -4*x^3 -7*x^2 + 3*x + 4)*(x^11 + x^10 -18*x^9 -15*x^8 + 117*x^7 + 78*x^6 -326*x^5 -167*x^4 + 348*x^3 + 143*x^2 -74*x -24)*(x^4 + 2*x^3 -6*x^2 -13*x -5)*(x^2 -2)^2*(x^3 -x^2 -4*x + 2)^2*(x^4 -3*x^3 -x^2 + 5*x + 1)^2*(x^6 -10*x^4 + 2*x^3 + 24*x^2 -7*x -12)^2*(x^2 -5)^3*(x + 2)^7*(x -1)^7*(x )^9;
T[1001,3]=(x^2 -3*x + 1)*(x^2 -x -5)*(x^3 + x^2 -9*x -12)*(x^4 + x^3 -6*x^2 -2*x + 1)*(x^4 + x^3 -4*x^2 -2*x + 3)*(x^5 + 4*x^4 -x^3 -18*x^2 -17*x -1)*(x^7 -6*x^6 + 2*x^5 + 45*x^4 -71*x^3 -31*x^2 + 97*x -38)*(x^5 + 3*x^4 -4*x^3 -8*x^2 + 9*x -2)*(x^5 -7*x^3 -2*x^2 + 3*x + 1)*(x^11 -2*x^10 -22*x^9 + 42*x^8 + 165*x^7 -289*x^6 -514*x^5 + 795*x^4 + 547*x^3 -745*x^2 + 86*x + 32)*(x^8 + x^7 -13*x^6 -7*x^5 + 44*x^4 + 19*x^3 -47*x^2 -18*x + 9)*(x + 2)^2*(x -1)^2*(x^2 -2*x -4)^2*(x^2 -2)^2*(x^3 + 2*x^2 -6*x -8)^2*(x^4 -7*x^2 + 4*x + 1)^2*(x^6 -3*x^5 -11*x^4 + 33*x^3 + 25*x^2 -91*x + 28)^2*(x -2)^3*(x + 3)^3*(x )^3*(x + 1)^6;
T[1001,5]=(x^2 -3*x + 1)*(x^2 + x -5)*(x^3 -x^2 -15*x + 18)*(x^4 + 5*x^3 -16*x + 7)*(x^4 -5*x^3 + 4*x^2 + 8*x -9)*(x^5 + 6*x^4 + 9*x^3 -2*x^2 -7*x + 1)*(x^5 + 4*x^4 -5*x^3 -28*x^2 -23*x -1)*(x^5 -13*x^3 -2*x^2 + 15*x + 7)*(x^7 -9*x^6 + 16*x^5 + 61*x^4 -208*x^3 + 58*x^2 + 228*x -41)*(x^11 -7*x^10 -8*x^9 + 138*x^8 -95*x^7 -896*x^6 + 1011*x^5 + 2307*x^4 -2638*x^3 -1846*x^2 + 1567*x -174)*(x^8 + 5*x^7 -13*x^6 -75*x^5 + 20*x^4 + 225*x^3 + 129*x^2 -10*x -1)*(x -3)^2*(x^2 -6*x + 7)^2*(x^3 -2*x^2 -3*x + 2)^2*(x^4 -16*x^2 + 8*x + 16)^2*(x^6 -x^5 -26*x^4 + 32*x^3 + 152*x^2 -256*x + 96)^2*(x -1)^4*(x + 3)^5*(x + 1)^5*(x + 2)^7;

T[1002,2]=(x^2 -x + 2)*(x^10 + 5*x^8 + 14*x^6 + x^5 + 28*x^4 + 40*x^2 + 32)*(x^16 -3*x^15 + 8*x^14 -14*x^13 + 25*x^12 -36*x^11 + 57*x^10 -81*x^9 + 125*x^8 -162*x^7 + 228*x^6 -288*x^5 + 400*x^4 -448*x^3 + 512*x^2 -384*x + 256)*(x^16 + 3*x^15 + 6*x^14 + 8*x^13 + 9*x^12 + 12*x^11 + 27*x^10 + 59*x^9 + 93*x^8 + 118*x^7 + 108*x^6 + 96*x^5 + 144*x^4 + 256*x^3 + 384*x^2 + 384*x + 256)*(x^10 + 4*x^9 + 11*x^8 + 24*x^7 + 44*x^6 + 67*x^5 + 88*x^4 + 96*x^3 + 88*x^2 + 64*x + 32)*(x^4 + x^3 + 3*x^2 + 2*x + 4)^2*(x^24 -2*x^23 + 7*x^22 -11*x^21 + 27*x^20 -35*x^19 + 71*x^18 -87*x^17 + 175*x^16 -223*x^15 + 447*x^14 -558*x^13 + 989*x^12 -1116*x^11 + 1788*x^10 -1784*x^9 + 2800*x^8 -2784*x^7 + 4544*x^6 -4480*x^5 + 6912*x^4 -5632*x^3 + 7168*x^2 -4096*x + 4096)^2*(x -1)^27*(x + 1)^28;
T[1002,3]=(x^2 + 3)*(x^4 + 3*x^3 + 7*x^2 + 9*x + 9)*(x^6 + x^5 + 4*x^4 + 2*x^3 + 12*x^2 + 9*x + 27)*(x^4 -2*x^2 + 9)*(x^6 -x^5 + 2*x^4 + 2*x^3 + 6*x^2 -9*x + 27)*(x^24 -3*x^23 + 14*x^22 -28*x^21 + 79*x^20 -120*x^19 + 267*x^18 -376*x^17 + 859*x^16 -1572*x^15 + 3591*x^14 -6916*x^13 + 12959*x^12 -20748*x^11 + 32319*x^10 -42444*x^9 + 69579*x^8 -91368*x^7 + 194643*x^6 -262440*x^5 + 518319*x^4 -551124*x^3 + 826686*x^2 -531441*x + 531441)^2*(x^4 + x^3 + 5*x^2 + 3*x + 9)^3*(x -1)^41*(x + 1)^42;
T[1002,5]=(x -2)*(x + 3)*(x^2 + 4*x + 2)*(x^3 + 3*x^2 -x -1)*(x^3 -3*x^2 -7*x + 19)*(x^5 + x^4 -19*x^3 -21*x^2 + 60*x + 24)*(x^4 -5*x^3 + 20*x -8)*(x^7 -5*x^6 -11*x^5 + 93*x^4 -110*x^3 -110*x^2 + 208*x -64)*(x )*(x + 4)^2*(x^2 -2*x -1)^2*(x^3 -13*x + 16)^2*(x^5 + x^4 -9*x^3 -2*x^2 + 17*x -1)^2*(x^2 + 4*x -1)^2*(x^5 + 9*x^4 + 25*x^3 + 12*x^2 -39*x -37)^2*(x^8 -x^7 -21*x^6 + 18*x^5 + 91*x^4 -117*x^3 -18*x^2 + 48*x -2)^2*(x^8 -7*x^7 + 7*x^6 + 50*x^5 -125*x^4 + 9*x^3 + 196*x^2 -124*x -18)^2*(x -3)^3*(x^12 -4*x^11 -41*x^10 + 152*x^9 + 648*x^8 -2136*x^7 -4816*x^6 + 13568*x^5 + 15616*x^4 -37632*x^3 -12544*x^2 + 33792*x -9216)^4*(x + 1)^19;

T[1003,2]=(x -1)*(x -2)*(x^4 + 3*x^3 -2*x^2 -7*x + 1)*(x^16 + 6*x^15 -5*x^14 -90*x^13 -82*x^12 + 456*x^11 + 723*x^10 -951*x^9 -2105*x^8 + 695*x^7 + 2641*x^6 + 151*x^5 -1323*x^4 -301*x^3 + 179*x^2 + 50*x -1)*(x^10 + x^9 -17*x^8 -12*x^7 + 108*x^6 + 44*x^5 -308*x^4 -37*x^3 + 357*x^2 -45*x -81)*(x^22 -5*x^21 -22*x^20 + 138*x^19 + 171*x^18 -1607*x^17 -371*x^16 + 10298*x^15 -2353*x^14 -39728*x^13 + 18176*x^12 + 94814*x^11 -53292*x^10 -138076*x^9 + 81634*x^8 + 115125*x^7 -66881*x^6 -46548*x^5 + 27259*x^4 + 5113*x^3 -4430*x^2 + 540*x + 12)*(x^18 -5*x^17 -16*x^16 + 112*x^15 + 52*x^14 -984*x^13 + 431*x^12 + 4304*x^11 -3825*x^10 -9826*x^9 + 11533*x^8 + 11182*x^7 -15697*x^6 -5604*x^5 + 9201*x^4 + 1189*x^3 -1952*x^2 -100*x + 28)*(x )*(x^5 -9*x^3 + 2*x^2 + 16*x -8)^2*(x + 1)^6;
T[1003,3]=(x -1)*(x -2)*(x -3)*(x^3 -2*x^2 -5*x + 2)*(x^10 + 7*x^9 + 8*x^8 -34*x^7 -56*x^6 + 67*x^5 + 94*x^4 -66*x^3 -39*x^2 + 18*x -1)*(x^22 -7*x^21 -24*x^20 + 260*x^19 + 65*x^18 -3924*x^17 + 3122*x^16 + 31442*x^15 -41051*x^14 -147389*x^13 + 232957*x^12 + 425192*x^11 -712621*x^10 -787756*x^9 + 1209743*x^8 + 971082*x^7 -1052280*x^6 -768268*x^5 + 324016*x^4 + 292480*x^3 + 49984*x^2 + 1472*x -128)*(x^4 + 2*x^3 -5*x^2 -6*x + 4)*(x^16 + 7*x^15 -8*x^14 -154*x^13 -157*x^12 + 1228*x^11 + 2482*x^10 -3944*x^9 -13179*x^8 + 1539*x^7 + 30581*x^6 + 17216*x^5 -25563*x^4 -27478*x^3 -1953*x^2 + 4266*x + 540)*(x^18 -x^17 -35*x^16 + 29*x^15 + 504*x^14 -331*x^13 -3862*x^12 + 1901*x^11 + 16995*x^10 -5784*x^9 -43240*x^8 + 8592*x^7 + 60913*x^6 -3090*x^5 -42652*x^4 -5572*x^3 + 11672*x^2 + 3760*x + 128)*(x^5 + 2*x^4 -8*x^3 -11*x^2 + 13*x -1)^2*(x )^3;
T[1003,5]=(x^3 + 4*x^2 -7*x -26)*(x^10 + 12*x^9 + 46*x^8 + 30*x^7 -182*x^6 -321*x^5 + 40*x^4 + 332*x^3 + 89*x^2 -61*x -1)*(x^22 -19*x^21 + 109*x^20 + 106*x^19 -3263*x^18 + 7528*x^17 + 30628*x^16 -140171*x^15 -76639*x^14 + 1098141*x^13 -580430*x^12 -4676299*x^11 + 5066538*x^10 + 11430392*x^9 -16677059*x^8 -15624562*x^7 + 27853007*x^6 + 10603948*x^5 -23054644*x^4 -2403696*x^3 + 7494640*x^2 -280704*x -41280)*(x^4 -x^3 -8*x^2 + 11*x + 1)*(x^16 + 21*x^15 + 169*x^14 + 568*x^13 -23*x^12 -5510*x^11 -11490*x^10 + 10507*x^9 + 58367*x^8 + 25683*x^7 -107844*x^6 -108569*x^5 + 65928*x^4 + 115076*x^3 + 10885*x^2 -31928*x -10177)*(x^18 -21*x^17 + 158*x^16 -327*x^15 -2075*x^14 + 13075*x^13 -13569*x^12 -86714*x^11 + 274292*x^10 -34459*x^9 -1004202*x^8 + 1403442*x^7 + 351838*x^6 -1914826*x^5 + 754279*x^4 + 701636*x^3 -431600*x^2 -65952*x + 53104)*(x -1)^2*(x^5 -2*x^4 -14*x^3 + 23*x^2 + 19*x + 1)^2*(x + 2)^4;

T[1004,2]=(x^34 -2*x^33 + 6*x^32 -10*x^31 + 21*x^30 -30*x^29 + 55*x^28 -94*x^27 + 176*x^26 -296*x^25 + 479*x^24 -744*x^23 + 1058*x^22 -1560*x^21 + 2300*x^20 -3648*x^19 + 5416*x^18 -8000*x^17 + 10832*x^16 -14592*x^15 + 18400*x^14 -24960*x^13 + 33856*x^12 -47616*x^11 + 61312*x^10 -75776*x^9 + 90112*x^8 -96256*x^7 + 112640*x^6 -122880*x^5 + 172032*x^4 -163840*x^3 + 196608*x^2 -131072*x + 131072)*(x^4 + x^3 + 3*x^2 + 2*x + 4)^2*(x + 1)^10*(x -1)^10*(x )^62;
T[1004,3]=(x^7 + 3*x^6 -6*x^5 -18*x^4 + 8*x^3 + 17*x^2 -9*x + 1)*(x^14 -3*x^13 -27*x^12 + 79*x^11 + 274*x^10 -747*x^9 -1422*x^8 + 3287*x^7 + 4161*x^6 -6861*x^5 -6676*x^4 + 5599*x^3 + 4627*x^2 -359*x -196)*(x^5 + x^4 -7*x^3 -4*x^2 + 6*x -1)^2*(x^6 -x^5 -16*x^4 + 9*x^3 + 74*x^2 -8*x -88)^2*(x^5 -2*x^4 -9*x^3 + 14*x^2 + 16*x -8)^2*(x^4 + 2*x^3 -2*x^2 -3*x + 1)^3*(x^17 -38*x^15 + 5*x^14 + 582*x^13 -142*x^12 -4602*x^11 + 1445*x^10 + 20039*x^9 -6280*x^8 -48174*x^7 + 10424*x^6 + 63091*x^5 -3260*x^4 -41362*x^3 -5377*x^2 + 10587*x + 3164)^3*(x + 1)^4*(x -1)^4;
T[1004,5]=(x^14 + 2*x^13 -46*x^12 -71*x^11 + 805*x^10 + 868*x^9 -6511*x^8 -4311*x^7 + 23111*x^6 + 8553*x^5 -28413*x^4 -6291*x^3 + 14183*x^2 + 1509*x -2493)*(x^7 + 2*x^6 -11*x^5 -25*x^4 + 26*x^3 + 81*x^2 + 20*x -27)*(x^2 + 3*x + 1)^2*(x^5 + 6*x^4 + 6*x^3 -18*x^2 -25*x + 7)^2*(x^6 + x^5 -14*x^4 -3*x^3 + 44*x^2 -36*x + 8)^2*(x^2 -5*x + 3)^2*(x^5 -7*x^4 + 9*x^3 + 24*x^2 -52*x + 24)^2*(x^4 + 3*x^3 -2*x^2 -2*x + 1)^3*(x^17 -3*x^16 -54*x^15 + 168*x^14 + 1118*x^13 -3641*x^12 -11152*x^11 + 38721*x^10 + 56108*x^9 -215683*x^8 -141507*x^7 + 649211*x^6 + 155977*x^5 -1041793*x^4 -22991*x^3 + 813550*x^2 -51713*x -228857)^3;

T[1005,2]=(x^4 -4*x^2 -x + 1)*(x^4 + 4*x^3 + 2*x^2 -5*x -3)*(x^4 -2*x^3 -6*x^2 + 9*x + 7)*(x^5 -x^4 -6*x^3 + 5*x^2 + 4*x -1)*(x^7 -4*x^6 -3*x^5 + 25*x^4 -11*x^3 -33*x^2 + 25*x -4)*(x^5 + 2*x^4 -6*x^3 -9*x^2 + 9*x + 4)*(x^8 + 3*x^7 -9*x^6 -30*x^5 + 14*x^4 + 68*x^3 -2*x^2 -37*x + 8)*(x^4 + 2*x^3 -4*x^2 -5*x + 5)*(x + 2)^2*(x^2 -x -1)^2*(x^2 -2)^2*(x^3 -3*x^2 -x + 5)^2*(x^5 -8*x^3 + 13*x + 2)^2*(x^11 -18*x^9 + 2*x^8 + 114*x^7 -24*x^6 -306*x^5 + 86*x^4 + 332*x^3 -109*x^2 -114*x + 46)^2*(x^7 -2*x^6 -12*x^5 + 21*x^4 + 42*x^3 -52*x^2 -39*x -6)^2*(x -1)^3*(x )^3*(x + 1)^4*(x -2)^4*(x^2 + 3*x + 1)^4*(x^2 + x -1)^4;
T[1005,3]=(x^2 + 3)*(x^4 + 4*x^2 + 9)*(x^4 + x^2 + 9)*(x^14 -4*x^13 + 13*x^12 -26*x^11 + 42*x^10 -24*x^9 -19*x^8 + 110*x^7 -57*x^6 -216*x^5 + 1134*x^4 -2106*x^3 + 3159*x^2 -2916*x + 2187)*(x^22 + 6*x^20 + 2*x^19 + 29*x^18 + 6*x^17 + 82*x^16 + 38*x^15 + 230*x^14 -24*x^13 + 538*x^12 + 44*x^11 + 1614*x^10 -216*x^9 + 6210*x^8 + 3078*x^7 + 19926*x^6 + 4374*x^5 + 63423*x^4 + 13122*x^3 + 118098*x^2 + 177147)*(x^2 + 2*x + 3)^2*(x^4 + 3*x^3 + 7*x^2 + 9*x + 9)^2*(x^4 -x^3 + 5*x^2 -3*x + 9)^2*(x -1)^33*(x + 1)^34;
T[1005,5]=(x^2 + x + 5)*(x^6 -x^5 + 12*x^4 -9*x^3 + 60*x^2 -25*x + 125)*(x^10 + 3*x^9 + 16*x^8 + 41*x^7 + 125*x^6 + 276*x^5 + 625*x^4 + 1025*x^3 + 2000*x^2 + 1875*x + 3125)*(x^2 + 5)*(x^2 -2*x + 5)^2*(x^4 -4*x^3 + 9*x^2 -20*x + 25)^2*(x^2 + 3*x + 5)^5*(x + 1)^44*(x -1)^47;

T[1006,2]=(x^2 + x + 2)*(x^52 -4*x^51 + 16*x^50 -46*x^49 + 126*x^48 -293*x^47 + 660*x^46 -1334*x^45 + 2625*x^44 -4763*x^43 + 8483*x^42 -14146*x^41 + 23374*x^40 -36611*x^39 + 57452*x^38 -86483*x^37 + 132413*x^36 -196593*x^35 + 300457*x^34 -448034*x^33 + 689045*x^32 -1031139*x^31 + 1579086*x^30 -2335118*x^29 + 3496164*x^28 -5021949*x^27 + 7259233*x^26 -10043898*x^25 + 13984656*x^24 -18680944*x^23 + 25265376*x^22 -32996448*x^21 + 44098880*x^20 -57348352*x^19 + 76916992*x^18 -100655616*x^17 + 135590912*x^16 -177117184*x^15 + 235323392*x^14 -299917312*x^13 + 382959616*x^12 -463536128*x^11 + 555941888*x^10 -624295936*x^9 + 688128000*x^8 -699400192*x^7 + 692060160*x^6 -614465536*x^5 + 528482304*x^4 -385875968*x^3 + 268435456*x^2 -134217728*x + 67108864)*(x^6 + x^4 + 3*x^3 + 2*x^2 + 8)*(x^20 + 4*x^19 + 16*x^18 + 41*x^17 + 103*x^16 + 208*x^15 + 412*x^14 + 707*x^13 + 1190*x^12 + 1794*x^11 + 2665*x^10 + 3588*x^9 + 4760*x^8 + 5656*x^7 + 6592*x^6 + 6656*x^5 + 6592*x^4 + 5248*x^3 + 4096*x^2 + 2048*x + 1024)*(x^2 -x + 2)^2*(x -1)^20*(x + 1)^21;
T[1006,3]=(x + 1)*(x + 3)*(x^5 + 4*x^4 -11*x^2 -4*x + 1)*(x^12 -5*x^11 -13*x^10 + 94*x^9 + 15*x^8 -616*x^7 + 368*x^6 + 1643*x^5 -1463*x^4 -1556*x^3 + 1284*x^2 + 576*x -208)*(x^12 + 3*x^11 -27*x^10 -78*x^9 + 267*x^8 + 746*x^7 -1120*x^6 -3167*x^5 + 1511*x^4 + 5516*x^3 + 676*x^2 -2080*x -336)*(x^2 -5)*(x^5 -6*x^3 -x^2 + 4*x -1)*(x )*(x -3)^2*(x^3 -x^2 -4*x + 3)^2*(x^26 -4*x^25 -52*x^24 + 211*x^23 + 1175*x^22 -4814*x^21 -15259*x^20 + 62449*x^19 + 127340*x^18 -509651*x^17 -726005*x^16 + 2735786*x^15 + 2939963*x^14 -9813106*x^13 -8635730*x^12 + 23403122*x^11 + 18323065*x^10 -36123133*x^9 -27001213*x^8 + 34013592*x^7 + 25434027*x^6 -17328663*x^5 -13187700*x^4 + 3683025*x^3 + 2752584*x^2 -219997*x -113513)^2*(x^10 + 8*x^9 + 18*x^8 -10*x^7 -85*x^6 -75*x^5 + 54*x^4 + 86*x^3 + 5*x^2 -14*x + 1)^2*(x -1)^6;
T[1006,5]=(x^5 + 3*x^4 -11*x^3 -50*x^2 -55*x -15)*(x^12 -5*x^11 -18*x^10 + 121*x^9 + 41*x^8 -982*x^7 + 746*x^6 + 2939*x^5 -4199*x^4 -1577*x^3 + 5038*x^2 -2320*x + 312)*(x^12 -7*x^11 -18*x^10 + 195*x^9 + 31*x^8 -1922*x^7 + 584*x^6 + 8955*x^5 -1789*x^4 -21065*x^3 -2922*x^2 + 20356*x + 10584)*(x^2 + 2*x -4)*(x^5 + x^4 -9*x^3 -4*x^2 + 7*x + 1)*(x^10 + x^9 -11*x^8 -7*x^7 + 41*x^6 + 7*x^5 -59*x^4 + 16*x^3 + 18*x^2 -9*x + 1)^2*(x^26 -9*x^25 -71*x^24 + 873*x^23 + 1333*x^22 -35769*x^21 + 27305*x^20 + 795330*x^19 -1730386*x^18 -10082887*x^17 + 35969747*x^16 + 64971026*x^15 -407126924*x^14 -30144880*x^13 + 2659470320*x^12 -2703014464*x^11 -9170377216*x^10 + 19446722944*x^9 + 9083193856*x^8 -57597089792*x^7 + 35068894208*x^6 + 60235479040*x^5 -94082748416*x^4 + 22315384832*x^3 + 39809548288*x^2 -32069681152*x + 7351042048)^2*(x + 4)^3*(x + 2)^5*(x )^9;

T[1007,2]=(x -2)*(x^12 + 3*x^11 -12*x^10 -38*x^9 + 47*x^8 + 164*x^7 -68*x^6 -286*x^5 + 37*x^4 + 196*x^3 -9*x^2 -37*x + 7)*(x^12 + 5*x^11 -2*x^10 -42*x^9 -31*x^8 + 116*x^7 + 124*x^6 -130*x^5 -151*x^4 + 54*x^3 + 55*x^2 -3*x -1)*(x^28 -3*x^27 -42*x^26 + 128*x^25 + 773*x^24 -2398*x^23 -8210*x^22 + 25984*x^21 + 55795*x^20 -180640*x^19 -254355*x^18 + 845427*x^17 + 792781*x^16 -2721726*x^15 -1686216*x^14 + 6057517*x^13 + 2381593*x^12 -9243830*x^11 -2066032*x^10 + 9460131*x^9 + 842962*x^8 -6228602*x^7 + 139290*x^6 + 2443827*x^5 -281692*x^4 -487131*x^3 + 89497*x^2 + 31575*x -5878)*(x^26 -6*x^25 -24*x^24 + 204*x^23 + 143*x^22 -2957*x^21 + 1313*x^20 + 23773*x^19 -25728*x^18 -115036*x^17 + 181081*x^16 + 336456*x^15 -713409*x^14 -543569*x^13 + 1698815*x^12 + 280790*x^11 -2424843*x^10 + 511527*x^9 + 1923915*x^8 -940458*x^7 -679950*x^6 + 547980*x^5 + 10922*x^4 -95345*x^3 + 27015*x^2 -2450*x + 33)*(x + 1)^2*(x^3 + x^2 -3*x -1)^2*(x )^2;
T[1007,3]=(x^12 + 5*x^11 -5*x^10 -50*x^9 -7*x^8 + 176*x^7 + 52*x^6 -273*x^5 -40*x^4 + 172*x^3 -21*x^2 -14*x -1)*(x^12 -x^11 -19*x^10 + 18*x^9 + 131*x^8 -108*x^7 -408*x^6 + 253*x^5 + 590*x^4 -222*x^3 -327*x^2 + 56*x + 23)*(x^28 + x^27 -64*x^26 -59*x^25 + 1800*x^24 + 1536*x^23 -29290*x^22 -23364*x^21 + 305595*x^20 + 231601*x^19 -2141802*x^18 -1577354*x^17 + 10276754*x^16 + 7560317*x^15 -33781344*x^14 -25596771*x^13 + 74868552*x^12 + 60334520*x^11 -107680972*x^10 -95673634*x^9 + 92584014*x^8 + 96019821*x^7 -38120682*x^6 -54397184*x^5 + 98147*x^4 + 13004480*x^3 + 3647817*x^2 + 124024*x -20912)*(x^26 -9*x^25 -14*x^24 + 347*x^23 -440*x^22 -5332*x^21 + 13764*x^20 + 39928*x^19 -160745*x^18 -124315*x^17 + 1006188*x^16 -183926*x^15 -3601124*x^14 + 2698549*x^13 + 7183906*x^12 -8455531*x^11 -7245596*x^10 + 12026066*x^9 + 3083386*x^8 -8442598*x^7 -72382*x^6 + 2758367*x^5 -243716*x^4 -316554*x^3 + 37217*x^2 + 6026*x -695)*(x )*(x + 2)^2*(x + 3)^2*(x^3 -3*x^2 -x + 1)^2;
T[1007,5]=(x + 3)*(x^12 + 2*x^11 -18*x^10 -22*x^9 + 126*x^8 + 61*x^7 -383*x^6 + 463*x^4 -127*x^3 -125*x^2 + 24*x -1)*(x^26 -4*x^25 -84*x^24 + 340*x^23 + 2968*x^22 -12207*x^21 -57423*x^20 + 241200*x^19 + 665009*x^18 -2868329*x^17 -4761809*x^16 + 21163194*x^15 + 21320289*x^14 -97060076*x^13 -60418868*x^12 + 273010640*x^11 + 109906096*x^10 -458140960*x^9 -127654144*x^8 + 437918848*x^7 + 92758016*x^6 -222255616*x^5 -42527744*x^4 + 54554624*x^3 + 11268096*x^2 -5029888*x -1228800)*(x^28 -5*x^27 -102*x^26 + 544*x^25 + 4458*x^24 -25901*x^23 -108460*x^22 + 709749*x^21 + 1587413*x^20 -12390844*x^19 -13829770*x^18 + 144214513*x^17 + 60607483*x^16 -1139134517*x^15 + 24332358*x^14 + 6107001516*x^13 -1766329544*x^12 -21888331728*x^11 + 9238391616*x^10 + 50754500288*x^9 -22148574080*x^8 -71685105920*x^7 + 24445007360*x^6 + 55031349248*x^5 -9278138368*x^4 -18207666176*x^3 + 1615060992*x^2 + 2074296320*x -177700864)*(x^12 + 4*x^11 -12*x^10 -64*x^9 + 22*x^8 + 347*x^7 + 189*x^6 -678*x^5 -689*x^4 + 205*x^3 + 361*x^2 + 88*x + 5)*(x -3)^2*(x^3 + 2*x^2 -4*x -4)^2*(x )^2;

T[1008,2]=(x^2 -x + 2)*(x^4 + x^2 + 4)*(x^2 + x + 2)^2*(x -1)^3*(x + 1)^4*(x )^152;
T[1008,3]=(x^2 + 3)^3*(x^2 -2*x + 3)^3*(x^2 + 2*x + 3)^5*(x -1)^15*(x + 1)^16*(x )^116;
T[1008,5]=(x^2 -12)^6*(x -4)^11*(x + 4)^13*(x )^40*(x -2)^44*(x + 2)^49;

T[1009,2]=(x^37 + 7*x^36 -26*x^35 -282*x^34 + 120*x^33 + 5034*x^32 + 3768*x^31 -52460*x^30 -75132*x^29 + 353267*x^28 + 698384*x^27 -1600809*x^26 -4086119*x^25 + 4881226*x^24 + 16413116*x^23 -9427513*x^22 -46888698*x^21 + 8468839*x^20 + 96456778*x^19 + 8563090*x^18 -142473811*x^17 -40439712*x^16 + 148465943*x^15 + 64322055*x^14 -105181661*x^13 -58600151*x^12 + 47250531*x^11 + 31970107*x^10 -11703630*x^9 -9786399*x^8 + 1120550*x^7 + 1424211*x^6 + 3169*x^5 -81691*x^4 -3449*x^3 + 924*x^2 + 21*x -3)*(x^46 -4*x^45 -63*x^44 + 264*x^43 + 1820*x^42 -8062*x^41 -31924*x^40 + 151252*x^39 + 379177*x^38 -1952213*x^37 -3215488*x^36 + 18396151*x^35 + 19945162*x^34 -131084557*x^33 -90603614*x^32 + 721863765*x^31 + 291868289*x^30 -3113483006*x^29 -585236988*x^28 + 10596535281*x^27 + 215950489*x^26 -28537937430*x^25 + 3216179111*x^24 + 60736131909*x^23 -13441185439*x^22 -101594043877*x^21 + 31806919291*x^20 + 132214124470*x^19 -52149084124*x^18 -131718195200*x^17 + 62113443590*x^16 + 97977337399*x^15 -54084895948*x^14 -52298783152*x^13 + 33908084678*x^12 + 18691436731*x^11 -14788566414*x^10 -3841247923*x^9 + 4229751924*x^8 + 225831235*x^7 -718878362*x^6 + 66880086*x^5 + 60731850*x^4 -12566665*x^3 -1510907*x^2 + 611962*x -44367);
T[1009,3]=(x^46 -9*x^45 -56*x^44 + 717*x^43 + 951*x^42 -26101*x^41 + 9919*x^40 + 575389*x^39 -756410*x^38 -8577423*x^37 + 16919268*x^36 + 91359954*x^35 -231739508*x^34 -715073815*x^33 + 2227658449*x^32 + 4152661146*x^31 -15874121062*x^30 -17719328682*x^29 + 86168795524*x^28 + 53115467160*x^27 -361296921446*x^26 -94899915823*x^25 + 1176778710338*x^24 + 2322517661*x^23 -2975970500694*x^22 + 583945258216*x^21 + 5808540242651*x^20 -2039613237867*x^19 -8648002294463*x^18 + 4116676872779*x^17 + 9639813150813*x^16 -5602145050186*x^15 -7821354359727*x^14 + 5288236339986*x^13 + 4424542699545*x^12 -3421131543896*x^11 -1627480001419*x^10 + 1457904271559*x^9 + 341711148976*x^8 -380968105880*x^7 -28794449808*x^6 + 54016732336*x^5 -935351360*x^4 -3332734976*x^3 + 150409472*x^2 + 66671360*x -4117504)*(x^37 + 11*x^36 -4*x^35 -459*x^34 -1101*x^33 + 7687*x^32 + 31899*x^31 -61047*x^30 -437834*x^29 + 124185*x^28 + 3639892*x^27 + 2060546*x^26 -19944392*x^25 -22907735*x^24 + 74512493*x^23 + 123640846*x^22 -190498934*x^21 -427528186*x^20 + 322826744*x^19 + 1018557040*x^18 -321298738*x^17 -1714364511*x^16 + 80607222*x^15 + 2047007261*x^14 + 245526786*x^13 -1716903548*x^12 -373233785*x^11 + 988247725*x^10 + 257753749*x^9 -374840573*x^8 -97015503*x^7 + 87400742*x^6 + 19257045*x^5 -10991858*x^4 -1790563*x^3 + 542808*x^2 + 59889*x + 627);
T[1009,5]=(x^46 -22*x^45 + 105*x^44 + 1138*x^43 -12489*x^42 -2250*x^41 + 482772*x^40 -1321020*x^39 -9360622*x^38 + 49787491*x^37 + 82897048*x^36 -968716392*x^35 + 314831874*x^34 + 11837515806*x^33 -18897678150*x^32 -94172411684*x^31 + 268759784675*x^30 + 454633720108*x^29 -2277219194004*x^28 -762479387779*x^27 + 12957474918796*x^26 -6317141249752*x^25 -50597742539337*x^24 + 57980157919531*x^23 + 131463053611888*x^22 -247908398871097*x^21 -199323477821083*x^20 + 661190863841375*x^19 + 64635176635600*x^18 -1148255552395935*x^17 + 400749552225082*x^16 + 1264921947443969*x^15 -894599444286347*x^14 -802957483987952*x^13 + 906623638751964*x^12 + 212725118734071*x^11 -484291888217087*x^10 + 31357321180553*x^9 + 129823128690949*x^8 -25843247210835*x^7 -16506746120436*x^6 + 3771367862649*x^5 + 1013733990089*x^4 -167989078084*x^3 -26948911441*x^2 + 1630357145*x + 173529774)*(x^37 + 24*x^36 + 183*x^35 -112*x^34 -9002*x^33 -37596*x^32 + 98841*x^31 + 1116752*x^30 + 1276019*x^29 -13283029*x^28 -42811482*x^27 + 59970570*x^26 + 474734737*x^25 + 236083745*x^24 -2769255285*x^23 -4611530942*x^22 + 8303092547*x^21 + 27329783644*x^20 -4604390119*x^19 -87464713409*x^18 -56159327128*x^17 + 155008044793*x^16 + 211347236491*x^15 -116155740968*x^14 -353653811901*x^13 -64354818214*x^12 + 294382889339*x^11 + 190682324484*x^10 -91818646299*x^9 -128754250462*x^8 -16230421356*x^7 + 28822691973*x^6 + 12005940315*x^5 -344921848*x^4 -899499947*x^3 -90899140*x^2 + 14601211*x + 1840531);

T[1010,2]=(x^2 -x + 2)*(x^16 + 5*x^15 + 17*x^14 + 44*x^13 + 97*x^12 + 190*x^11 + 338*x^10 + 549*x^9 + 815*x^8 + 1098*x^7 + 1352*x^6 + 1520*x^5 + 1552*x^4 + 1408*x^3 + 1088*x^2 + 640*x + 256)*(x^18 -2*x^17 + 6*x^16 -11*x^15 + 23*x^14 -33*x^13 + 62*x^12 -81*x^11 + 138*x^10 -173*x^9 + 276*x^8 -324*x^7 + 496*x^6 -528*x^5 + 736*x^4 -704*x^3 + 768*x^2 -512*x + 512)*(x^18 -2*x^17 + 8*x^16 -13*x^15 + 35*x^14 -53*x^13 + 114*x^12 -155*x^11 + 282*x^10 -347*x^9 + 564*x^8 -620*x^7 + 912*x^6 -848*x^5 + 1120*x^4 -832*x^3 + 1024*x^2 -512*x + 512)*(x^12 + 3*x^11 + 8*x^10 + 13*x^9 + 23*x^8 + 31*x^7 + 49*x^6 + 62*x^5 + 92*x^4 + 104*x^3 + 128*x^2 + 96*x + 64)*(x^2 + 2)^2*(x^14 + x^12 + 2*x^11 + x^10 -x^8 -2*x^7 -2*x^6 + 8*x^4 + 32*x^3 + 32*x^2 + 128)^2*(x + 1)^25*(x -1)^26;
T[1010,3]=(x^2 -2)*(x^5 -x^4 -10*x^3 + 7*x^2 + 14*x + 4)*(x^6 -3*x^5 -10*x^4 + 31*x^3 + 18*x^2 -62*x -2)*(x^6 -5*x^5 -2*x^4 + 35*x^3 -20*x^2 -50*x + 32)*(x^7 -3*x^6 -10*x^5 + 31*x^4 + 20*x^3 -64*x^2 -14*x + 8)*(x^3 + 4*x^2 + 2*x -2)*(x^4 + 2*x^3 -8*x^2 -10*x + 16)*(x^3 + 3*x^2 -1)^2*(x^4 + x^3 -8*x^2 + x + 8)^2*(x^6 + x^5 -9*x^4 -8*x^3 + 15*x^2 + 7*x -8)^2*(x^8 + 11*x^7 + 43*x^6 + 62*x^5 -11*x^4 -91*x^3 -34*x^2 + 16*x + 4)^2*(x^9 -7*x^8 + 7*x^7 + 44*x^6 -87*x^5 -63*x^4 + 210*x^3 -28*x^2 -116*x + 28)^2*(x^9 -x^8 -17*x^7 + 14*x^6 + 91*x^5 -57*x^4 -180*x^3 + 88*x^2 + 108*x -52)^2*(x^7 -4*x^6 -7*x^5 + 38*x^4 + 4*x^3 -96*x^2 + 13*x + 68)^4*(x + 2)^5*(x )^5;
T[1010,5]=(x^2 -2*x + 5)*(x^6 + 3*x^5 + 9*x^4 + 13*x^3 + 45*x^2 + 75*x + 125)*(x^8 -3*x^7 + 16*x^6 -38*x^5 + 108*x^4 -190*x^3 + 400*x^2 -375*x + 625)*(x^2 + x + 5)^2*(x^14 + 3*x^13 + 22*x^12 + 57*x^11 + 248*x^10 + 559*x^9 + 1802*x^8 + 3423*x^7 + 9010*x^6 + 13975*x^5 + 31000*x^4 + 35625*x^3 + 68750*x^2 + 46875*x + 78125)^2*(x + 1)^50*(x -1)^51;

T[1011,2]=(x + 1)*(x -1)*(x^7 + x^6 -6*x^5 -4*x^4 + 10*x^3 + 4*x^2 -4*x -1)*(x^17 -3*x^16 -24*x^15 + 72*x^14 + 231*x^13 -687*x^12 -1148*x^11 + 3335*x^10 + 3140*x^9 -8736*x^8 -4576*x^7 + 12067*x^6 + 2960*x^5 -7928*x^4 -368*x^3 + 1840*x^2 -64*x -64)*(x^10 + 2*x^9 -10*x^8 -18*x^7 + 33*x^6 + 50*x^5 -38*x^4 -43*x^3 + 9*x^2 + 9*x + 1)*(x^21 -3*x^20 -34*x^19 + 108*x^18 + 472*x^17 -1630*x^16 -3392*x^15 + 13371*x^14 + 12909*x^13 -64603*x^12 -21042*x^11 + 186274*x^10 -12870*x^9 -310356*x^8 + 98628*x^7 + 275679*x^6 -131904*x^5 -110568*x^4 + 69232*x^3 + 10800*x^2 -12096*x + 1728)*(x^15 -3*x^14 -18*x^13 + 56*x^12 + 123*x^11 -402*x^10 -400*x^9 + 1395*x^8 + 643*x^7 -2406*x^6 -496*x^5 + 1843*x^4 + 200*x^3 -388*x^2 -69*x + 1)^2*(x^12 + 6*x^11 + x^10 -54*x^9 -76*x^8 + 135*x^7 + 289*x^6 -97*x^5 -392*x^4 -28*x^3 + 201*x^2 + 36*x -27)^2;
T[1011,3]=(x^30 -9*x^29 + 55*x^28 -252*x^27 + 979*x^26 -3308*x^25 + 10068*x^24 -27945*x^23 + 71859*x^22 -172463*x^21 + 389604*x^20 -832347*x^19 + 1690309*x^18 -3271748*x^17 + 6053033*x^16 -10713728*x^15 + 18159099*x^14 -29445732*x^13 + 45638343*x^12 -67420107*x^11 + 94673772*x^10 -125725527*x^9 + 157155633*x^8 -183347145*x^7 + 198168444*x^6 -195334092*x^5 + 173426913*x^4 -133923132*x^3 + 87687765*x^2 -43046721*x + 14348907)*(x^24 + 11*x^23 + 74*x^22 + 369*x^21 + 1498*x^20 + 5178*x^19 + 15701*x^18 + 42561*x^17 + 104626*x^16 + 235575*x^15 + 489609*x^14 + 944021*x^13 + 1694095*x^12 + 2832063*x^11 + 4406481*x^10 + 6360525*x^9 + 8474706*x^8 + 10342323*x^7 + 11446029*x^6 + 11324286*x^5 + 9828378*x^4 + 7263027*x^3 + 4369626*x^2 + 1948617*x + 531441)*(x + 1)^28*(x -1)^29;
T[1011,5]=(x + 3)*(x^7 + 6*x^6 + 5*x^5 -15*x^4 -5*x^3 + 11*x^2 -x -1)*(x^17 -13*x^16 + 26*x^15 + 343*x^14 -1752*x^13 -745*x^12 + 21021*x^11 -32210*x^10 -63444*x^9 + 177955*x^8 + 33050*x^7 -332682*x^6 + 75453*x^5 + 239432*x^4 -60738*x^3 -54350*x^2 + 8647*x + 3750)*(x^10 + 8*x^9 + 5*x^8 -95*x^7 -179*x^6 + 291*x^5 + 805*x^4 -43*x^3 -980*x^2 -512*x -32)*(x^21 -6*x^20 -61*x^19 + 423*x^18 + 1401*x^17 -12443*x^16 -13252*x^15 + 199177*x^14 -7670*x^13 -1891021*x^12 + 1305339*x^11 + 10853254*x^10 -12175309*x^9 -36670629*x^8 + 52636814*x^7 + 67674400*x^6 -114252907*x^5 -59171895*x^4 + 113091844*x^3 + 18294368*x^2 -34986336*x -2919168)*(x )*(x^15 -10*x^14 + 11*x^13 + 170*x^12 -433*x^11 -1061*x^10 + 3724*x^9 + 2939*x^8 -14061*x^7 -3535*x^6 + 24746*x^5 + 2311*x^4 -17969*x^3 -3070*x^2 + 3900*x + 1048)^2*(x^12 + 10*x^11 + 17*x^10 -132*x^9 -527*x^8 + 35*x^7 + 2998*x^6 + 4271*x^5 -2229*x^4 -10525*x^3 -10100*x^2 -4125*x -625)^2;

T[1012,2]=(x^6 + x^5 + 2*x^4 + 5*x^3 + 4*x^2 + 4*x + 8)*(x^10 + 4*x^9 + 10*x^8 + 18*x^7 + 27*x^6 + 39*x^5 + 54*x^4 + 72*x^3 + 80*x^2 + 64*x + 32)*(x^6 -3*x^5 + 6*x^4 -9*x^3 + 12*x^2 -12*x + 8)*(x^12 -3*x^11 + 8*x^10 -14*x^9 + 25*x^8 -34*x^7 + 53*x^6 -68*x^5 + 100*x^4 -112*x^3 + 128*x^2 -96*x + 64)*(x^2 + 2*x + 2)^2*(x^4 + x^3 + 3*x^2 + 2*x + 4)^2*(x -1)^11*(x + 1)^12*(x )^70;
T[1012,3]=(x^3 -x^2 -6*x -3)*(x^3 + 3*x^2 -2*x -7)*(x^4 -2*x^3 -9*x^2 + 15*x + 11)*(x^4 + 3*x^3 -6*x^2 -23*x -16)*(x + 3)^2*(x^3 -3*x^2 -6*x + 17)^2*(x^3 -3*x^2 -2*x + 5)^2*(x^4 + x^3 -6*x^2 -3*x + 8)^2*(x^5 -x^4 -12*x^3 + 13*x^2 + 22*x -8)^2*(x^3 -3*x^2 + 3)^3*(x^3 + 5*x^2 + 4*x -5)^3*(x^5 + 5*x^4 + 3*x^3 -10*x^2 -4*x + 1)^3*(x^6 -7*x^5 + 11*x^4 + 18*x^3 -56*x^2 + 33*x -4)^3*(x + 2)^6*(x + 1)^6*(x^2 -5)^6*(x -1)^7*(x )^11;
T[1012,5]=(x + 4)*(x -2)*(x^3 + x^2 -4*x -3)*(x^3 + 3*x^2 -6*x -9)*(x^4 -x^3 -10*x^2 + 13*x -2)*(x^4 -5*x^3 -2*x^2 + 23*x + 8)*(x -3)^2*(x + 2)^2*(x^3 + 7*x^2 + 8*x -15)^2*(x^4 -2*x^3 -11*x^2 + 23*x -1)^2*(x^5 -4*x^4 -7*x^3 + 31*x^2 + x -18)^2*(x^3 + 5*x^2 + 4*x -5)^3*(x^5 + 3*x^4 -14*x^3 -43*x^2 -12*x + 16)^3*(x^6 -3*x^5 -12*x^4 + 25*x^3 + 38*x^2 -40*x -32)^3*(x )^3*(x + 1)^4*(x -4)^5*(x^3 -3*x^2 + 3)^5*(x + 3)^6*(x^2 + 2*x -4)^6*(x -1)^8;

T[1013,2]=(x^36 + 7*x^35 -24*x^34 -267*x^33 + 82*x^32 + 4503*x^31 + 3647*x^30 -44199*x^29 -64677*x^28 + 279138*x^27 + 554855*x^26 -1179289*x^25 -3004519*x^24 + 3324963*x^23 + 11129471*x^22 -5860088*x^21 -29141603*x^20 + 4605155*x^19 + 54557877*x^18 + 5065846*x^17 -72861729*x^16 -19891707*x^15 + 68395929*x^14 + 28043944*x^13 -43785026*x^12 -22950839*x^11 + 18081778*x^10 + 11535993*x^9 -4307916*x^8 -3451822*x^7 + 428771*x^6 + 556721*x^5 + 18142*x^4 -38459*x^3 -5117*x^2 + 392*x + 67)*(x^48 -7*x^47 -52*x^46 + 463*x^45 + 1059*x^44 -14112*x^43 -7589*x^42 + 262880*x^41 -98400*x^40 -3346400*x^39 + 3225618*x^38 + 30827283*x^37 -43410039*x^36 -212198827*x^35 + 380107035*x^34 + 1110238155*x^33 -2407879467*x^32 -4440805579*x^31 + 11528890286*x^30 + 13499437716*x^29 -42629199922*x^28 -30456316465*x^27 + 122999468706*x^26 + 47754440057*x^25 -277863045873*x^24 -40739379918*x^23 + 490460108015*x^22 -18064190697*x^21 -671764990628*x^20 + 119800683221*x^19 + 705462827077*x^18 -203421795938*x^17 -558048168761*x^16 + 208547201767*x^15 + 324394140957*x^14 -142289430352*x^13 -134033491027*x^12 + 64986034992*x^11 + 37698941528*x^10 -19239506410*x^9 -6854121537*x^8 + 3461345477*x^7 + 766692512*x^6 -337561089*x^5 -51976495*x^4 + 14205835*x^3 + 2026195*x^2 -117460*x -15455);
T[1013,3]=(x^36 + 19*x^35 + 112*x^34 -99*x^33 -3700*x^32 -10662*x^31 + 33873*x^30 + 227202*x^29 + 60027*x^28 -2065234*x^27 -3491492*x^26 + 9689582*x^25 + 31228742*x^24 -18119990*x^23 -151506906*x^22 -49023961*x^21 + 460141719*x^20 + 422855193*x^19 -893376050*x^18 -1343445559*x^17 + 1033007683*x^16 + 2544027685*x^15 -458090586*x^14 -3098126768*x^13 -505406680*x^12 + 2412615425*x^11 + 974214000*x^10 -1124721733*x^9 -693499885*x^8 + 258363422*x^7 + 240038480*x^6 -7293361*x^5 -33878191*x^4 -5098136*x^3 + 523184*x^2 + 125292*x + 4009)*(x^48 -19*x^47 + 81*x^46 + 688*x^45 -6803*x^44 + 566*x^43 + 188141*x^42 -483537*x^41 -2587596*x^40 + 12829486*x^39 + 15203011*x^38 -180559341*x^37 + 79409310*x^36 + 1612433622*x^35 -2457842788*x^34 -9444886616*x^33 + 25016149136*x^32 + 33765898022*x^31 -157470574029*x^30 -41145152565*x^29 + 681672503957*x^28 -279281780621*x^27 -2082770189263*x^26 + 1953808563394*x^25 + 4438207634849*x^24 -6587940071835*x^23 -6211355881553*x^22 + 14337430519008*x^21 + 4563456358114*x^20 -21388193763010*x^19 + 1047414522122*x^18 + 22117984225092*x^17 -6490532447213*x^16 -15730092131524*x^15 + 7442318392949*x^14 + 7536967013838*x^13 -4681394827876*x^12 -2348211532452*x^11 + 1793790575760*x^10 + 447768248353*x^9 -419405410054*x^8 -46763787971*x^7 + 57348801783*x^6 + 2096110575*x^5 -4267360489*x^4 -10076486*x^3 + 158116281*x^2 -1106324*x -2278165);
T[1013,5]=(x^36 + 5*x^35 -78*x^34 -424*x^33 + 2581*x^32 + 15769*x^31 -46856*x^30 -340486*x^29 + 493052*x^28 + 4759783*x^27 -2652885*x^26 -45468412*x^25 -930329*x^24 + 305305684*x^23 + 128950742*x^22 -1460393725*x^21 -1047208591*x^20 + 4994156078*x^19 + 4710057469*x^18 -12170210547*x^17 -13677755665*x^16 + 20969271783*x^15 + 26705273982*x^14 -25272244859*x^13 -35324556367*x^12 + 21019494274*x^11 + 31300050785*x^10 -11858224958*x^9 -17986210862*x^8 + 4431803629*x^7 + 6264518816*x^6 -1054623889*x^5 -1145184555*x^4 + 145158134*x^3 + 75268126*x^2 -8528069*x -132107)*(x^48 -x^47 -150*x^46 + 166*x^45 + 10437*x^44 -12601*x^43 -447582*x^42 + 582686*x^41 + 13257624*x^40 -18428211*x^39 -288103969*x^38 + 423963300*x^37 + 4762491645*x^36 -7363771212*x^35 -61282167776*x^34 + 98877070837*x^33 + 623099309655*x^32 -1042258534444*x^31 -5054121217107*x^30 + 8707501803119*x^29 + 32886356200361*x^28 -57957078769887*x^27 -172081658968094*x^26 + 307819007026657*x^25 + 723995488381783*x^24 -1302256187857866*x^23 -2442977589403809*x^22 + 4365861612352898*x^21 + 6578633082254178*x^20 -11494644234130587*x^19 -14028471733977724*x^18 + 23438272539872483*x^17 + 23415239998241663*x^16 -36253465897069068*x^15 -30055342734374582*x^14 + 41232398588707677*x^13 + 28838489117643615*x^12 -32846518401334716*x^11 -19701786232421912*x^10 + 16894342198170064*x^9 + 8744469909026032*x^8 -4810235056365504*x^7 -2060704487622016*x^6 + 533438259647744*x^5 + 131840383747584*x^4 -17195424988160*x^3 -2122937176064*x^2 + 101175152640*x + 4073648128);

T[1014,2]=(x^4 -2*x^3 + 3*x^2 -4*x + 4)*(x^4 + x^3 + 2*x + 4)*(x^4 -x^3 -2*x + 4)*(x^6 -3*x^5 + 2*x^4 + x^3 + 4*x^2 -12*x + 8)*(x^6 + 3*x^5 + 2*x^4 -x^3 + 4*x^2 + 12*x + 8)*(x^6 -x^5 + 4*x^4 -3*x^3 + 8*x^2 -4*x + 8)*(x^6 + x^5 + 4*x^4 + 3*x^3 + 8*x^2 + 4*x + 8)*(x^2 + 2)^2*(x^2 + x + 2)^2*(x^4 + 2*x^3 + 3*x^2 + 4*x + 4)^2*(x^6 + 2*x^5 + 5*x^4 + 7*x^3 + 10*x^2 + 8*x + 8)^2*(x^6 -2*x^5 + 5*x^4 -7*x^3 + 10*x^2 -8*x + 8)^2*(x^2 -x + 2)^3*(x^4 + x^2 + 4)^3*(x -1)^30*(x + 1)^31;
T[1014,3]=(x^2 + x + 3)^2*(x^2 + 3)^2*(x^6 -3*x^5 + 5*x^4 -5*x^3 + 15*x^2 -27*x + 27)^2*(x^2 -x + 3)^3*(x^2 + 3*x + 3)^3*(x^2 -2*x + 3)^4*(x^6 + 2*x^5 + 8*x^4 + 11*x^3 + 24*x^2 + 18*x + 27)^4*(x + 1)^45*(x -1)^46;
T[1014,5]=(x^2 + 4*x + 1)*(x^2 -4*x + 1)*(x^3 -x^2 -16*x + 29)*(x^3 + x^2 -16*x -29)*(x^3 -3*x^2 -4*x -1)*(x^3 + 3*x^2 -4*x + 1)*(x^2 -12)^2*(x^2 + 3*x -2)^2*(x^2 -3*x -2)^2*(x^3 + 6*x^2 + 5*x -13)^2*(x^3 -6*x^2 + 5*x + 13)^2*(x^3 + 2*x^2 -8*x -8)^2*(x^3 -2*x^2 -8*x + 8)^2*(x + 2)^4*(x )^4*(x -3)^5*(x^2 -3)^6*(x^2 -8)^6*(x^3 -4*x^2 + 3*x + 1)^6*(x^3 + 4*x^2 + 3*x -1)^6*(x + 3)^7*(x -2)^7*(x -1)^7*(x + 1)^9;

T[1015,2]=(x^2 -x -4)*(x^2 -3)*(x^7 + 3*x^6 -7*x^5 -22*x^4 + 12*x^3 + 39*x^2 -8*x -16)*(x^11 -3*x^10 -15*x^9 + 46*x^8 + 75*x^7 -238*x^6 -139*x^5 + 472*x^4 + 58*x^3 -269*x^2 + 16*x + 32)*(x^8 -x^7 -10*x^6 + 11*x^5 + 25*x^4 -25*x^3 -16*x^2 + 9*x + 4)*(x^7 -3*x^6 -6*x^5 + 21*x^4 + 3*x^3 -31*x^2 + 14*x -1)*(x^6 -2*x^5 -8*x^4 + 17*x^3 + 10*x^2 -31*x + 11)*(x^3 + 3*x^2 -4*x -13)*(x + 2)^2*(x -1)^2*(x^2 + x -4)^2*(x^3 -x^2 -3*x + 1)^2*(x^3 -3*x^2 -x + 5)^2*(x^3 + x^2 -3*x -1)^2*(x^3 + x^2 -2*x -1)^2*(x^5 -2*x^4 -8*x^3 + 14*x^2 + 9*x -6)^2*(x -2)^4*(x )^4*(x^2 + 2*x -1)^6*(x + 1)^9;
T[1015,3]=(x + 3)*(x^3 + 3*x^2 -4*x -13)*(x^3 + x^2 -2*x -1)*(x^3 -x^2 -2*x + 1)*(x^6 -x^5 -14*x^4 + 7*x^3 + 54*x^2 + 4*x -40)*(x^7 -x^6 -16*x^5 + 13*x^4 + 68*x^3 -32*x^2 -64*x -16)*(x^8 -4*x^7 -11*x^6 + 57*x^5 -5*x^4 -140*x^3 + 32*x^2 + 80*x + 16)*(x^11 -x^10 -29*x^9 + 28*x^8 + 288*x^7 -269*x^6 -1108*x^5 + 980*x^4 + 1328*x^3 -848*x^2 -384*x + 64)*(x^7 -x^6 -11*x^5 + 8*x^4 + 30*x^3 -17*x^2 -20*x + 12)*(x^3 + 2*x^2 -4*x -4)^2*(x^3 + 3*x^2 -x -5)^2*(x^3 -2*x^2 -4*x + 4)^2*(x^5 + 2*x^4 -10*x^3 -18*x^2 + 11*x + 2)^2*(x -1)^3*(x -2)^3*(x + 1)^4*(x + 2)^4*(x )^4*(x^2 + x -4)^5*(x^2 -2*x -1)^6;
T[1015,5]=(x^2 -2*x + 5)*(x^2 + 4*x + 5)*(x^6 + 5*x^5 + 18*x^4 + 45*x^3 + 90*x^2 + 125*x + 125)*(x^2 -x + 5)*(x^4 + 2*x^2 + 25)*(x^4 -3*x^3 + 8*x^2 -15*x + 25)*(x^10 -5*x^9 + 22*x^8 -71*x^7 + 211*x^6 -484*x^5 + 1055*x^4 -1775*x^3 + 2750*x^2 -3125*x + 3125)*(x^2 + x + 5)^4*(x + 1)^38*(x -1)^41;

T[1016,2]=(x^14 -2*x^13 + 6*x^12 -9*x^11 + 21*x^10 -28*x^9 + 51*x^8 -57*x^7 + 102*x^6 -112*x^5 + 168*x^4 -144*x^3 + 192*x^2 -128*x + 128)*(x^6 + 3*x^5 + 6*x^4 + 9*x^3 + 12*x^2 + 12*x + 8)*(x -1)^5*(x + 1)^6*(x )^94;
T[1016,3]=(x^3 + 3*x^2 -4*x -13)*(x^6 -x^5 -10*x^4 + 9*x^3 + 16*x^2 -8*x -8)*(x^9 + 3*x^8 -16*x^7 -49*x^6 + 68*x^5 + 236*x^4 -48*x^3 -348*x^2 -96*x + 64)*(x^10 -5*x^9 -8*x^8 + 63*x^7 + 2*x^6 -256*x^5 + 68*x^4 + 398*x^3 -108*x^2 -168*x + 64)*(x^2 + 2*x -4)^2*(x^3 + 3*x^2 -1)^2*(x^3 -x^2 -6*x -3)^2*(x^5 + 2*x^4 -10*x^3 -16*x^2 + 10*x + 16)^3*(x^3 + 3*x^2 -3)^4*(x^7 -3*x^6 -12*x^5 + 39*x^4 + 26*x^3 -128*x^2 + 64*x + 16)^4*(x + 2)^6*(x )^9*(x -2)^11;
T[1016,5]=(x^3 -x^2 -10*x -4)*(x^6 + 9*x^5 + 23*x^4 + 2*x^3 -59*x^2 -64*x -16)*(x^9 -12*x^8 + 35*x^7 + 99*x^6 -678*x^5 + 724*x^4 + 1844*x^3 -4860*x^2 + 3720*x -848)*(x^10 + 7*x^9 -9*x^8 -130*x^7 -15*x^6 + 860*x^5 + 180*x^4 -2232*x^3 + 214*x^2 + 1152*x + 128)*(x^3 -2*x^2 -x + 1)*(x^2 -2*x -4)^2*(x^3 -9*x + 9)^2*(x^3 -4*x^2 + x + 3)^2*(x -2)^3*(x + 3)^3*(x^2 + x -4)^3*(x^5 + x^4 -20*x^3 -18*x^2 + 54*x + 54)^3*(x )^3*(x + 1)^4*(x + 2)^4*(x^3 + 6*x^2 + 9*x + 1)^4*(x^7 -8*x^6 + 11*x^5 + 53*x^4 -146*x^3 + 32*x^2 + 128*x -48)^4;

T[1017,2]=(x^2 -2*x -1)*(x^3 -2*x^2 -5*x + 9)*(x^3 -2*x^2 -x + 1)*(x^5 -2*x^4 -8*x^3 + 12*x^2 + 16*x -10)*(x^5 + 2*x^4 -8*x^3 -12*x^2 + 16*x + 10)*(x^5 -7*x^3 + 4*x^2 + 6*x -2)*(x^5 + x^4 -10*x^3 -6*x^2 + 22*x -4)*(x^2 + 2*x -1)^2*(x^5 -7*x^3 -4*x^2 + 6*x + 2)^2*(x^5 -x^4 -10*x^3 + 6*x^2 + 22*x + 4)^2*(x^2 -2)^3*(x^3 + 2*x^2 -5*x -9)^3*(x^3 + 2*x^2 -x -1)^3*(x )^5*(x + 2)^6*(x + 1)^7*(x -2)^8*(x -1)^9;
T[1017,3]=(x^2 -2*x + 3)*(x^4 -2*x^3 + 4*x^2 -6*x + 9)*(x^6 + x^5 + 5*x^4 + 5*x^3 + 15*x^2 + 9*x + 27)*(x^6 + 5*x^5 + 15*x^4 + 31*x^3 + 45*x^2 + 45*x + 27)*(x -1)^9*(x + 1)^10*(x )^74;
T[1017,5]=(x^2 + 3*x -2)*(x^2 -2*x -1)*(x^2 + 2*x -7)*(x^3 -x^2 -9*x + 1)*(x^5 + 3*x^4 -10*x^3 -28*x^2 -17*x -3)*(x^5 -3*x^4 -10*x^3 + 28*x^2 -17*x + 3)*(x^5 -2*x^4 -20*x^3 + 42*x^2 + 93*x -202)*(x^5 + 3*x^4 -6*x^3 -16*x^2 + x + 1)*(x -3)^2*(x^2 -2*x -7)^2*(x^2 -3*x -2)^2*(x^2 + 2*x -1)^2*(x^5 -3*x^4 -6*x^3 + 16*x^2 + x -1)^2*(x^5 + 2*x^4 -20*x^3 -42*x^2 + 93*x + 202)^2*(x + 2)^3*(x + 3)^3*(x^3 + x^2 -9*x -1)^3*(x^2 -12)^4*(x -1)^6*(x -2)^6*(x + 1)^13;

T[1018,2]=(x^28 + 3*x^27 + 17*x^26 + 42*x^25 + 143*x^24 + 305*x^23 + 798*x^22 + 1505*x^21 + 3305*x^20 + 5602*x^19 + 10772*x^18 + 16577*x^17 + 28552*x^16 + 40082*x^15 + 62611*x^14 + 80164*x^13 + 114208*x^12 + 132616*x^11 + 172352*x^10 + 179264*x^9 + 211520*x^8 + 192640*x^7 + 204288*x^6 + 156160*x^5 + 146432*x^4 + 86016*x^3 + 69632*x^2 + 24576*x + 16384)*(x^56 -3*x^55 + 12*x^54 -27*x^53 + 71*x^52 -136*x^51 + 295*x^50 -505*x^49 + 966*x^48 -1559*x^47 + 2830*x^46 -4506*x^45 + 7950*x^44 -12558*x^43 + 21553*x^42 -33714*x^41 + 55968*x^40 -85383*x^39 + 136615*x^38 -203855*x^37 + 318566*x^36 -467482*x^35 + 715176*x^34 -1032717*x^33 + 1557053*x^32 -2218679*x^31 + 3289715*x^30 -4597836*x^29 + 6687825*x^28 -9195672*x^27 + 13158860*x^26 -17749432*x^25 + 24912848*x^24 -33046944*x^23 + 45771264*x^22 -59837696*x^21 + 81552896*x^20 -104373760*x^19 + 139893760*x^18 -174864384*x^17 + 229244928*x^16 -276185088*x^15 + 353124352*x^14 -411500544*x^13 + 521011200*x^12 -590610432*x^11 + 741867520*x^10 -817364992*x^9 + 1012924416*x^8 -1059061760*x^7 + 1237319680*x^6 -1140850688*x^5 + 1191182336*x^4 -905969664*x^3 + 805306368*x^2 -402653184*x + 268435456)*(x -1)^21*(x + 1)^21;
T[1018,3]=(x -1)*(x -2)*(x + 2)*(x^5 + 3*x^4 -x^3 -7*x^2 -2*x + 1)*(x^8 -3*x^7 -11*x^6 + 27*x^5 + 44*x^4 -57*x^3 -72*x^2 + 20*x + 24)*(x^11 + 7*x^10 + 3*x^9 -74*x^8 -130*x^7 + 198*x^6 + 552*x^5 + 11*x^4 -553*x^3 -204*x^2 + 53*x + 17)*(x^15 -6*x^14 -18*x^13 + 167*x^12 -2*x^11 -1672*x^10 + 1718*x^9 + 7315*x^8 -11840*x^7 -12947*x^6 + 29501*x^5 + 4670*x^4 -25053*x^3 + 1656*x^2 + 5724*x + 648)*(x^28 -5*x^27 -48*x^26 + 272*x^25 + 931*x^24 -6405*x^23 -8850*x^22 + 85759*x^21 + 31965*x^20 -721317*x^19 + 164032*x^18 + 3972999*x^17 -2503752*x^16 -14475994*x^15 + 13508475*x^14 + 34330526*x^13 -41204799*x^12 -50312318*x^11 + 75928604*x^10 + 39824769*x^9 -82931046*x^8 -9371818*x^7 + 49394521*x^6 -6602510*x^5 -13320545*x^4 + 3321297*x^3 + 1196222*x^2 -267183*x -31583)^2*(x^14 + 5*x^13 -11*x^12 -81*x^11 + 8*x^10 + 438*x^9 + 183*x^8 -1032*x^7 -579*x^6 + 1074*x^5 + 579*x^4 -417*x^3 -172*x^2 + 29*x + 11)^2;
T[1018,5]=(x -4)*(x + 2)*(x^15 -4*x^14 -39*x^13 + 180*x^12 + 489*x^11 -3057*x^10 -1142*x^9 + 23826*x^8 -20714*x^7 -76270*x^6 + 149214*x^5 + 11003*x^4 -256704*x^3 + 265612*x^2 -105736*x + 13456)*(x^5 + 5*x^4 + 4*x^3 -11*x^2 -17*x -5)*(x^11 + 2*x^10 -35*x^9 -52*x^8 + 429*x^7 + 373*x^6 -2198*x^5 -594*x^4 + 4162*x^3 -440*x^2 -1438*x -197)*(x^8 -3*x^7 -24*x^6 + 67*x^5 + 169*x^4 -407*x^3 -394*x^2 + 656*x + 168)*(x )*(x^28 -x^27 -86*x^26 + 100*x^25 + 3226*x^24 -4251*x^23 -69315*x^22 + 101474*x^21 + 941574*x^20 -1508877*x^19 -8418071*x^18 + 14621274*x^17 + 49979838*x^16 -93690681*x^15 -194106206*x^14 + 394225378*x^13 + 473294393*x^12 -1060961763*x^11 -669570897*x^10 + 1744938012*x^9 + 465995781*x^8 -1643052709*x^7 -73313109*x^6 + 799280568*x^5 -66191620*x^4 -163204400*x^3 + 24714384*x^2 + 6775680*x -395200)^2*(x^14 + 5*x^13 -17*x^12 -121*x^11 -3*x^10 + 866*x^9 + 897*x^8 -2207*x^7 -3776*x^6 + 1189*x^5 + 4603*x^4 + 984*x^3 -1708*x^2 -736*x -16)^2;

T[1019,2]=(x + 2)*(x^28 + 2*x^27 -33*x^26 -64*x^25 + 479*x^24 + 898*x^23 -4031*x^22 -7285*x^21 + 21822*x^20 + 37946*x^19 -79691*x^18 -133302*x^17 + 200127*x^16 + 322906*x^15 -345552*x^14 -542082*x^13 + 402788*x^12 + 625029*x^11 -303971*x^10 -483406*x^9 + 136398*x^8 + 240148*x^7 -29303*x^6 -70935*x^5 + 212*x^4 + 10718*x^3 + 773*x^2 -571*x -48)*(x^55 -2*x^54 -89*x^53 + 176*x^52 + 3726*x^51 -7276*x^50 -97576*x^49 + 187887*x^48 + 1793058*x^47 -3399142*x^46 -24584907*x^45 + 45806073*x^44 + 261103167*x^43 -477252336*x^42 -2201054879*x^41 + 3939126201*x^40 + 14971966018*x^39 -26181407125*x^38 -83097997679*x^37 + 141689818005*x^36 + 379063832185*x^35 -628903261833*x^34 -1427140592109*x^33 + 2299245644303*x^32 + 4441804604371*x^31 -6936322068371*x^30 -11420416486609*x^29 + 17260390204620*x^28 + 24184412258886*x^27 -35341251872869*x^26 -41955045882587*x^25 + 59271079855072*x^24 + 59146559864610*x^23 -80867687437538*x^22 -67001121565796*x^21 + 88923774097008*x^20 + 60058078350116*x^19 -77841548814294*x^18 -41712076475101*x^17 + 53382343169177*x^16 + 21789445202206*x^15 -28090367997086*x^14 -8183875502604*x^13 + 11036779765398*x^12 + 2042322524120*x^11 -3120001535120*x^10 -279777176128*x^9 + 601462338752*x^8 + 3823613824*x^7 -72563252864*x^6 + 4548165888*x^5 + 4663816704*x^4 -525256704*x^3 -107100160*x^2 + 13176832*x + 237568)*(x );
T[1019,3]=(x^28 + 7*x^27 -24*x^26 -270*x^25 + 23*x^24 + 4285*x^23 + 4845*x^22 -36255*x^21 -69427*x^20 + 175084*x^19 + 479763*x^18 -458657*x^17 -1958651*x^16 + 395931*x^15 + 4998357*x^14 + 1187000*x^13 -8040025*x^12 -4272072*x^11 + 7954152*x^10 + 6071538*x^9 -4499166*x^8 -4539216*x^7 + 1179902*x^6 + 1748028*x^5 -14530*x^4 -280826*x^3 -36358*x^2 + 4556*x + 277)*(x^55 -5*x^54 -107*x^53 + 563*x^52 + 5302*x^51 -29634*x^50 -161307*x^49 + 969219*x^48 + 3366414*x^47 -22086519*x^46 -50951113*x^45 + 372735716*x^44 + 575542921*x^43 -4834160281*x^42 -4901410003*x^41 + 49356017606*x^40 + 31148568852*x^39 -403164578284*x^38 -140570255334*x^37 + 2663690582864*x^36 + 369588074045*x^35 -14336096090690*x^34 + 230189525762*x^33 + 63114743611823*x^32 -8020157297969*x^31 -227676914528866*x^30 + 45974925243524*x^29 + 672598579638545*x^28 -165472856277704*x^27 -1622687676393695*x^26 + 427492516575247*x^25 + 3180583810489604*x^24 -819763981328661*x^23 -5024796728576540*x^22 + 1167831401524781*x^21 + 6326391747751981*x^20 -1210969839893414*x^19 -6250095254748790*x^18 + 871462010508683*x^17 + 4745741568853995*x^16 -389117293058937*x^15 -2695389149585446*x^14 + 68230463582973*x^13 + 1106158146307459*x^12 + 26770959539316*x^11 -314326925708396*x^10 -19128728751558*x^9 + 58746160554611*x^8 + 4745517978249*x^7 -6749472535056*x^6 -545645548321*x^5 + 430472286449*x^4 + 24777517877*x^3 -12688441924*x^2 -185750839*x + 92645699)*(x -1)^2;
T[1019,5]=(x^28 + 17*x^27 + 73*x^26 -325*x^25 -3445*x^24 -3626*x^23 + 48243*x^22 + 147571*x^21 -246321*x^20 -1614270*x^19 -352466*x^18 + 8796896*x^17 + 10046659*x^16 -25852431*x^15 -51016687*x^14 + 36328338*x^13 + 131335252*x^12 -1417515*x^11 -190431831*x^10 -68105987*x^9 + 153564681*x^8 + 91574055*x^7 -62548637*x^6 -51134990*x^5 + 9332739*x^4 + 12375202*x^3 + 520423*x^2 -1018164*x -162681)*(x^55 -23*x^54 + 80*x^53 + 2104*x^52 -18615*x^51 -56550*x^50 + 1198776*x^49 -1227839*x^48 -41383447*x^47 + 137083819*x^46 + 859441463*x^45 -4954150183*x^44 -9936356497*x^43 + 109737925326*x^42 + 11659191882*x^41 -1683318757663*x^40 + 1889663035843*x^39 + 18595321699360*x^38 -40543903902982*x^37 -147562767318869*x^36 + 504929751585581*x^35 + 790375508929373*x^34 -4431075991591676*x^33 -2073299853274366*x^32 + 28983087350991023*x^31 -7475327912589636*x^30 -143970322165180544*x^29 + 118775336117459940*x^28 + 543003898929600935*x^27 -733289123504463844*x^26 -1527507097735565103*x^25 + 2981067612119292280*x^24 + 3053223642929059179*x^23 -8755144117408390283*x^22 -3749762882277839932*x^21 + 19058612575495279608*x^20 + 833604366114459708*x^19 -30808732065818777235*x^18 + 6912131395731429731*x^17 + 36560699784741183958*x^16 -15319003532838956896*x^15 -31154697643102155215*x^14 + 17445692960021220106*x^13 + 18468267569405056847*x^12 -12022719916211405396*x^11 -7330408238856063711*x^10 + 4955349513287411269*x^9 + 1885260855150562774*x^8 -1116501263771804633*x^7 -307692186606721828*x^6 + 115597298686230707*x^5 + 27092378548604308*x^4 -4196868236305342*x^3 -935260376097795*x^2 + 45027538291423*x + 10019899822183)*(x + 1)^2;

T[1020,2]=(x^4 -x^3 + x^2 -2*x + 4)*(x^8 -x^7 + x^5 + x^4 + 2*x^3 -8*x + 16)*(x^4 -3*x^3 + 5*x^2 -6*x + 4)*(x^6 + 2*x^4 + x^3 + 4*x^2 + 8)*(x^2 + 2)^2*(x^4 + 2*x^3 + 3*x^2 + 4*x + 4)^2*(x^4 + x^3 + 2*x + 4)^2*(x^2 -x + 2)^2*(x^4 + x^2 + 4)^2*(x^2 + x + 2)^6*(x -1)^17*(x + 1)^18*(x )^104;
T[1020,3]=(x^6 + x^4 + 4*x^3 + 3*x^2 + 27)*(x^2 -3*x + 3)^2*(x^4 + x^3 + 2*x^2 + 3*x + 9)^2*(x^2 -2*x + 3)^3*(x^4 + 4*x^3 + 8*x^2 + 12*x + 9)^3*(x^2 -x + 3)^4*(x^4 -2*x^3 + 4*x^2 -6*x + 9)^5*(x^2 + 3)^7*(x^2 + 2*x + 3)^10*(x -1)^53*(x + 1)^54;
T[1020,5]=(x^2 + x + 5)*(x^2 -x + 5)*(x^2 + 4*x + 5)^2*(x^4 -2*x^2 + 25)^2*(x^2 -3*x + 5)^3*(x^4 -3*x^3 + 8*x^2 -15*x + 25)^3*(x^2 + 5)^6*(x^2 + 2*x + 5)^8*(x -1)^71*(x + 1)^72;

T[1021,2]=(x^47 -11*x^46 -13*x^45 + 562*x^44 -1053*x^43 -12457*x^42 + 43556*x^41 + 151080*x^40 -821208*x^39 -956971*x^38 + 9672573*x^37 + 367401*x^36 -78606727*x^35 + 53803632*x^34 + 460203145*x^33 -576915631*x^32 -1971883605*x^31 + 3562032318*x^30 + 6139700103*x^29 -15287731798*x^28 -13287943150*x^27 + 48316551902*x^26 + 16890014192*x^25 -115022263130*x^24 + 380999457*x^23 + 207750140598*x^22 -54629218819*x^21 -284021120346*x^20 + 133043045472*x^19 + 290798375624*x^18 -187622721764*x^17 -218484322447*x^16 + 178209121212*x^15 + 116260648099*x^14 -117446193726*x^13 -41002699077*x^12 + 53173570146*x^11 + 8168926723*x^10 -15912690565*x^9 -351060349*x^8 + 2912418393*x^7 -199415005*x^6 -277379900*x^5 + 37374190*x^4 + 8585206*x^3 -1874852*x^2 + 88994*x + 169)*(x^37 + 11*x^36 + 10*x^35 -309*x^34 -1017*x^33 + 3214*x^32 + 18915*x^31 -9378*x^30 -181898*x^29 -111172*x^28 + 1071998*x^27 + 1440543*x^26 -4061832*x^25 -8363518*x^24 + 9627999*x^23 + 30295209*x^22 -11539843*x^21 -73965753*x^20 -5452262*x^19 + 123976928*x^18 + 48065134*x^17 -140717873*x^16 -90312381*x^15 + 102881854*x^14 + 93031702*x^13 -42480644*x^12 -56716206*x^11 + 5375657*x^10 + 19565488*x^9 + 2573404*x^8 -3301635*x^7 -1006878*x^6 + 177042*x^5 + 112295*x^4 + 9180*x^3 -2701*x^2 -568*x -31);
T[1021,3]=(x^47 -5*x^46 -89*x^45 + 476*x^44 + 3592*x^43 -20899*x^42 -86668*x^41 + 561770*x^40 + 1383414*x^39 -10350393*x^38 -15166805*x^37 + 138681859*x^36 + 112736624*x^35 -1399200425*x^34 -502264224*x^33 + 10860832041*x^32 + 333304596*x^31 -65712075081*x^30 + 13923436059*x^29 + 312139546464*x^28 -122411928873*x^27 -1167164966739*x^26 + 612047552187*x^25 + 3431666742461*x^24 -2118183522185*x^23 -7897285342798*x^22 + 5338270159577*x^21 + 14112185935706*x^20 -9928904109618*x^19 -19357973424685*x^18 + 13589589137595*x^17 + 20069770016443*x^16 -13514627196498*x^15 -15409022880022*x^14 + 9573127644316*x^13 + 8527492766813*x^12 -4705338329891*x^11 -3278807299139*x^10 + 1551213852652*x^9 + 830973461424*x^8 -327086473088*x^7 -128162742304*x^6 + 40819133184*x^5 + 10578862016*x^4 -2554685440*x^3 -370946048*x^2 + 49034240*x + 4164608)*(x^37 + 7*x^36 -41*x^35 -380*x^34 + 576*x^33 + 9145*x^32 -660*x^31 -129478*x^30 -84314*x^29 + 1206735*x^28 + 1314259*x^27 -7845693*x^26 -10863884*x^25 + 36782171*x^24 + 58700744*x^23 -126777303*x^22 -221329212*x^21 + 324819271*x^20 + 596834679*x^19 -622350200*x^18 -1156098017*x^17 + 894294137*x^16 + 1591311679*x^15 -963353611*x^14 -1514551249*x^13 + 770355146*x^12 + 946946561*x^11 -441134830*x^10 -353165606*x^9 + 164815079*x^8 + 63471191*x^7 -32575937*x^6 -2422538*x^5 + 1952794*x^4 -82048*x^3 -16223*x^2 + 981*x -7);
T[1021,5]=(x^47 -13*x^46 -58*x^45 + 1440*x^44 -847*x^43 -70833*x^42 + 187017*x^41 + 2019286*x^40 -8477331*x^39 -36055612*x^38 + 219799802*x^37 + 389585129*x^36 -3836293553*x^35 -1663644546*x^34 + 48048268661*x^33 -21352127142*x^32 -445109380667*x^31 + 496983811227*x^30 + 3087418260545*x^29 -5309973291768*x^28 -15995219716117*x^27 + 37971513450660*x^26 + 60527843725489*x^25 -198029179893940*x^24 -156281636634975*x^23 + 777565751511581*x^22 + 209355404427317*x^21 -2327937557442282*x^20 + 221617312441251*x^19 + 5330650358021642*x^18 -1951185102039783*x^17 -9308912120141606*x^16 + 5368551907951111*x^15 + 12305522429044450*x^14 -9183283163156723*x^13 -12178077485431369*x^12 + 10765380991596566*x^11 + 8901758528181089*x^10 -8798916137272484*x^9 -4742288234179426*x^8 + 4935202222622063*x^7 + 1824371157905232*x^6 -1813155709892039*x^5 -503013419305198*x^4 + 394089723914471*x^3 + 94676484302921*x^2 -38597484851581*x -9420249451793)*(x^37 + 17*x^36 + 39*x^35 -901*x^34 -5514*x^33 + 13942*x^32 + 189970*x^31 + 114663*x^30 -3270605*x^29 -7294665*x^28 + 31173219*x^27 + 121471356*x^26 -142466527*x^25 -1122991160*x^24 -164394747*x^23 + 6421805464*x^22 + 6387545024*x^21 -22591473915*x^20 -40853230458*x^19 + 42426808028*x^18 + 139724398134*x^17 -6899523200*x^16 -277040977009*x^15 -154950728655*x^14 + 289492568991*x^13 + 335999254477*x^12 -86249557108*x^11 -289861832934*x^10 -88857258596*x^9 + 85385665827*x^8 + 58701723257*x^7 -1991770701*x^6 -10421396706*x^5 -2048102955*x^4 + 424456762*x^3 + 159132074*x^2 + 11261761*x + 213767);

T[1022,2]=(x^6 + x^4 + x^3 + 2*x^2 + 8)*(x^12 + 3*x^11 + 9*x^10 + 18*x^9 + 36*x^8 + 55*x^7 + 87*x^6 + 110*x^5 + 144*x^4 + 144*x^3 + 144*x^2 + 96*x + 64)*(x^6 -x^5 + 2*x^4 -5*x^3 + 4*x^2 -4*x + 8)*(x^12 + 3*x^11 + 9*x^10 + 18*x^9 + 36*x^8 + 59*x^7 + 91*x^6 + 118*x^5 + 144*x^4 + 144*x^3 + 144*x^2 + 96*x + 64)*(x^18 -2*x^17 + 8*x^16 -14*x^15 + 37*x^14 -58*x^13 + 122*x^12 -171*x^11 + 313*x^10 -391*x^9 + 626*x^8 -684*x^7 + 976*x^6 -928*x^5 + 1184*x^4 -896*x^3 + 1024*x^2 -512*x + 512)*(x^20 -4*x^19 + 11*x^18 -22*x^17 + 40*x^16 -70*x^15 + 123*x^14 -204*x^13 + 321*x^12 -469*x^11 + 679*x^10 -938*x^9 + 1284*x^8 -1632*x^7 + 1968*x^6 -2240*x^5 + 2560*x^4 -2816*x^3 + 2816*x^2 -2048*x + 1024)*(x^2 -x + 2)^2*(x^4 -x^3 + x^2 -2*x + 4)^2*(x^4 + 3*x^3 + 5*x^2 + 6*x + 4)^2*(x -1)^25*(x + 1)^26;
T[1022,3]=(x^2 -2)*(x^3 + 4*x^2 + 2*x -2)*(x^3 -4*x + 2)*(x^6 -2*x^5 -12*x^4 + 18*x^3 + 46*x^2 -38*x -50)*(x^6 -2*x^5 -14*x^4 + 24*x^3 + 48*x^2 -46*x -50)*(x^6 -4*x^5 -2*x^4 + 20*x^3 -14*x^2 -6*x + 2)*(x^6 -2*x^5 -12*x^4 + 22*x^3 + 24*x^2 -22*x -14)*(x^4 -8*x^2 + 4*x + 4)^2*(x^6 -x^5 -6*x^4 + 4*x^3 + 8*x^2 -1)^2*(x^10 + x^9 -34*x^8 -28*x^7 + 440*x^6 + 278*x^5 -2679*x^4 -1138*x^3 + 7540*x^2 + 1576*x -7520)^2*(x^3 -8*x + 4)^2*(x^6 + 5*x^5 + 4*x^4 -10*x^3 -10*x^2 + 4*x + 3)^2*(x^9 + x^8 -22*x^7 -30*x^6 + 138*x^5 + 250*x^4 -167*x^3 -480*x^2 -144*x + 64)^2*(x + 2)^3*(x^2 -x -3)^4*(x^2 + 3*x + 1)^4*(x -2)^6*(x )^12;
T[1022,5]=(x -4)*(x^6 -24*x^4 -8*x^3 + 128*x^2 + 144*x + 16)*(x^6 -20*x^4 + 8*x^3 + 64*x^2 + 16*x -16)*(x^2 -8)*(x^6 -4*x^5 -12*x^4 + 56*x^3 -16*x^2 -80*x + 48)*(x^6 -24*x^4 + 8*x^3 + 160*x^2 -48*x -304)*(x^3 -3*x^2 -2*x + 3)^2*(x^4 -2*x^3 -14*x^2 + 26*x + 2)^2*(x^6 + 2*x^5 -15*x^4 -29*x^3 + 46*x^2 + 59*x -59)^2*(x^10 -x^9 -39*x^8 + 45*x^7 + 509*x^6 -680*x^5 -2299*x^4 + 3603*x^3 + 925*x^2 -2281*x + 554)^2*(x^3 + 2*x^2 -4*x -6)^2*(x^6 + 6*x^5 + 5*x^4 -15*x^3 -4*x^2 + 11*x -3)^2*(x^9 -7*x^8 -7*x^7 + 139*x^6 -203*x^5 -448*x^4 + 1101*x^3 -283*x^2 -401*x + 59)^2*(x^3 + x^2 -4*x + 1)^2*(x + 2)^4*(x^2 + x -3)^4*(x^2 + 3*x + 1)^4*(x -2)^5*(x )^5;

T[1023,2]=(x^3 + 2*x^2 -x -1)*(x^6 + 4*x^5 -x^4 -16*x^3 -6*x^2 + 15*x + 7)*(x^6 -3*x^5 -4*x^4 + 15*x^3 -12*x + 1)*(x^6 + x^5 -10*x^4 -11*x^3 + 22*x^2 + 30*x + 5)*(x^10 -2*x^9 -15*x^8 + 28*x^7 + 75*x^6 -129*x^5 -136*x^4 + 216*x^3 + 56*x^2 -115*x + 25)*(x^10 -2*x^9 -13*x^8 + 24*x^7 + 55*x^6 -91*x^5 -82*x^4 + 124*x^3 + 20*x^2 -53*x + 13)*(x^4 -x^3 -5*x^2 + 4*x + 3)*(x^3 -5*x -1)*(x^2 + 3*x + 1)^2*(x^8 -x^7 -14*x^6 + 11*x^5 + 60*x^4 -31*x^3 -74*x^2 + 5*x + 3)^2*(x^11 -x^10 -20*x^9 + 20*x^8 + 141*x^7 -135*x^6 -421*x^5 + 347*x^4 + 530*x^3 -288*x^2 -239*x + 17)^2*(x^3 -4*x + 1)^2*(x -1)^3*(x + 2)^4*(x^2 + x -1)^5*(x^2 -x -1)^6;
T[1023,3]=(x^8 + 2*x^7 + 7*x^6 + 12*x^5 + 28*x^4 + 36*x^3 + 63*x^2 + 54*x + 81)*(x^16 -4*x^15 + 18*x^14 -50*x^13 + 143*x^12 -320*x^11 + 709*x^10 -1344*x^9 + 2491*x^8 -4032*x^7 + 6381*x^6 -8640*x^5 + 11583*x^4 -12150*x^3 + 13122*x^2 -8748*x + 6561)*(x^22 -4*x^21 + 13*x^20 -32*x^19 + 84*x^18 -192*x^17 + 451*x^16 -950*x^15 + 1987*x^14 -3702*x^13 + 6928*x^12 -11936*x^11 + 20784*x^10 -33318*x^9 + 53649*x^8 -76950*x^7 + 109593*x^6 -139968*x^5 + 183708*x^4 -209952*x^3 + 255879*x^2 -236196*x + 177147)*(x^4 + 2*x^3 + 2*x^2 + 6*x + 9)^2*(x^2 + x + 3)^4*(x -1)^31*(x + 1)^32;
T[1023,5]=(x^2 -5)*(x^3 + 3*x^2 -2*x -3)*(x^3 + 5*x^2 + 6*x + 1)*(x^6 + 3*x^5 -11*x^4 -26*x^3 + 36*x^2 + 43*x -2)*(x^10 -5*x^9 -23*x^8 + 146*x^7 + 32*x^6 -1065*x^5 + 1238*x^4 + 440*x^3 -560*x^2 -272*x -32)*(x^4 -3*x^3 -2*x^2 + 5*x + 2)*(x^6 -7*x^5 + 2*x^4 + 69*x^3 -114*x^2 -20*x + 40)*(x^6 -5*x^5 -4*x^4 + 37*x^3 -2*x^2 -52*x + 8)*(x^10 -3*x^9 -37*x^8 + 116*x^7 + 458*x^6 -1529*x^5 -2074*x^4 + 7896*x^3 + 1712*x^2 -12048*x + 2272)*(x^2 + 4*x -1)^2*(x^2 + 3*x + 1)^2*(x^4 + x^3 -8*x^2 -11*x + 1)^2*(x^8 + 5*x^7 -12*x^6 -77*x^5 -11*x^4 + 176*x^3 + 35*x^2 -77*x + 9)^2*(x^11 -3*x^10 -35*x^9 + 106*x^8 + 423*x^7 -1261*x^6 -2318*x^5 + 6533*x^4 + 5956*x^3 -14599*x^2 -6045*x + 10618)^2*(x^3 + 2*x^2 -5*x -2)^2*(x + 2)^3*(x -1)^12;

T[1024,2]=(x )^105;
T[1024,3]=(x^2 + 4*x + 2)^2*(x^2 + 2*x -2)^2*(x^2 -2*x -2)^2*(x^2 -4*x + 2)^2*(x^4 -8*x^2 + 8)^2*(x^2 -6)^4*(x^2 -8)^5*(x^2 -2)^10*(x -2)^11*(x + 2)^11*(x )^21;
T[1024,5]=(x^2 -18)*(x^2 -4*x + 2)^2*(x^2 + 4*x + 2)^2*(x + 4)^3*(x -4)^3*(x^2 -8)^4*(x^2 -12)^4*(x^2 -6)^4*(x^2 -2)^5*(x -2)^17*(x + 2)^18*(x )^20;

T[1025,2]=(x^3 + 2*x^2 -4*x -7)*(x^3 -4*x + 1)*(x^3 -x^2 -5*x + 1)*(x^5 -7*x^3 + 4*x -1)*(x^5 -7*x^3 + 4*x + 1)*(x^7 + 3*x^6 -6*x^5 -21*x^4 + 5*x^3 + 35*x^2 + 5*x -9)*(x^7 -3*x^6 -6*x^5 + 21*x^4 + 5*x^3 -35*x^2 + 5*x + 9)*(x^2 -x -1)*(x^6 -6*x^4 + 8*x^2 -1)*(x^14 -26*x^12 + 262*x^10 -1281*x^8 + 3109*x^6 -3428*x^4 + 1300*x^2 -1)*(x^2 + x -1)^2*(x^3 -4*x -1)^2*(x^3 -2*x^2 -4*x + 7)^2*(x^2 -x -3)^2*(x^2 + x -3)^3*(x^3 + x^2 -5*x -1)^3*(x -1)^4*(x + 1)^5;
T[1025,3]=(x^2 -x -3)*(x^2 + x -3)*(x^3 -4*x -2)*(x^5 + 4*x^4 -2*x^3 -19*x^2 -12*x + 3)*(x^5 -4*x^4 -2*x^3 + 19*x^2 -12*x -3)*(x^7 -3*x^6 -9*x^5 + 29*x^4 + 7*x^3 -42*x^2 + 13*x + 1)*(x^7 + 3*x^6 -9*x^5 -29*x^4 + 7*x^3 + 42*x^2 + 13*x -1)*(x^6 -8*x^4 + 15*x^2 -4)*(x^14 -32*x^12 + 399*x^10 -2448*x^8 + 7612*x^6 -10700*x^4 + 4268*x^2 -256)*(x -1)^2*(x -3)^2*(x + 2)^2*(x^3 + 2*x^2 -5*x -2)^2*(x^3 -4*x + 2)^3*(x )^3*(x + 3)^4*(x + 1)^4*(x -2)^4*(x^3 -2*x^2 -5*x + 2)^4;
T[1025,5]=(x^6 + 2*x^5 + 11*x^4 + 16*x^3 + 55*x^2 + 50*x + 125)*(x + 1)^6*(x -1)^7*(x )^80;

T[1026,2]=(x^6 -3*x^5 + 6*x^4 -9*x^3 + 12*x^2 -12*x + 8)*(x^6 + 3*x^5 + 6*x^4 + 9*x^3 + 12*x^2 + 12*x + 8)*(x^4 + x^2 + 4)*(x^8 + 5*x^4 + 16)*(x^8 + 2*x^6 + 3*x^4 + 8*x^2 + 16)*(x^6 -x^5 + 2*x^4 -3*x^3 + 4*x^2 -4*x + 8)*(x^6 + x^5 + 2*x^4 + 3*x^3 + 4*x^2 + 4*x + 8)*(x^8 -x^6 -4*x^2 + 16)^2*(x^2 + x + 2)^3*(x^2 -2*x + 2)^4*(x^2 -x + 2)^4*(x^2 + 2*x + 2)^6*(x^2 + 2)^8*(x + 1)^29*(x -1)^30;
T[1026,3]=(x^2 -x + 3)*(x^2 + x + 3)*(x^2 + 2*x + 3)^2*(x + 1)^4*(x -1)^5*(x )^152;
T[1026,5]=(x^2 -x -8)*(x^2 -4*x + 1)*(x^2 + 4*x + 1)*(x^2 + x -8)*(x -4)^2*(x^2 -12)^2*(x^3 -5*x^2 + 4*x + 3)^2*(x^3 -3*x^2 + 3)^2*(x^3 + 5*x^2 + 4*x -3)^2*(x^3 + 3*x^2 -3)^2*(x^4 -20*x^2 + 52)^2*(x^4 -12*x^2 + 12)^2*(x + 4)^4*(x^4 -15*x^2 + 48)^4*(x + 1)^6*(x -1)^8*(x -2)^9*(x + 2)^10*(x + 3)^17*(x -3)^19*(x )^26;

T[1027,2]=(x^18 + 6*x^17 -8*x^16 -106*x^15 -57*x^14 + 715*x^13 + 859*x^12 -2323*x^11 -3741*x^10 + 3768*x^9 + 7603*x^8 -2785*x^7 -7585*x^6 + 510*x^5 + 3292*x^4 + 241*x^3 -361*x^2 -32*x + 8)*(x^17 + 10*x^16 + 22*x^15 -90*x^14 -431*x^13 -29*x^12 + 2401*x^11 + 2695*x^10 -5361*x^9 -10562*x^8 + 3217*x^7 + 16039*x^6 + 4113*x^5 -9336*x^4 -4872*x^3 + 1239*x^2 + 959*x + 64)*(x^22 -8*x^21 -3*x^20 + 176*x^19 -281*x^18 -1465*x^17 + 3952*x^16 + 5282*x^15 -23404*x^14 -3893*x^13 + 72142*x^12 -27611*x^11 -118500*x^10 + 81451*x^9 + 98907*x^8 -85881*x^7 -39195*x^6 + 38199*x^5 + 6767*x^4 -6456*x^3 -880*x^2 + 384*x + 64)*(x^21 -9*x^20 + 8*x^19 + 152*x^18 -425*x^17 -792*x^16 + 4160*x^15 + 64*x^14 -18654*x^13 + 13873*x^12 + 43575*x^11 -55324*x^10 -51008*x^9 + 99433*x^8 + 19464*x^7 -91617*x^6 + 14906*x^5 + 40363*x^4 -15992*x^3 -5632*x^2 + 4032*x -576)*(x )*(x + 1)^2*(x^5 -6*x^3 + 8*x -1)^2;
T[1027,3]=(x + 2)*(x^22 -4*x^21 -40*x^20 + 169*x^19 + 665*x^18 -3004*x^17 -6034*x^16 + 29467*x^15 + 33178*x^14 -175861*x^13 -116665*x^12 + 662075*x^11 + 269946*x^10 -1568027*x^9 -407977*x^8 + 2239099*x^7 + 357831*x^6 -1740008*x^5 -91704*x^4 + 584044*x^3 -75684*x^2 -46880*x + 9152)*(x^21 -4*x^20 -32*x^19 + 141*x^18 + 389*x^17 -2024*x^16 -2062*x^15 + 15135*x^14 + 2338*x^13 -62449*x^12 + 22457*x^11 + 138253*x^10 -97076*x^9 -147717*x^8 + 143699*x^7 + 63909*x^6 -88729*x^5 -3716*x^4 + 20796*x^3 -2292*x^2 -1044*x + 16)*(x^17 + 2*x^16 -28*x^15 -51*x^14 + 307*x^13 + 498*x^12 -1686*x^11 -2349*x^10 + 4984*x^9 + 5551*x^8 -8035*x^7 -6251*x^6 + 6680*x^5 + 2817*x^4 -2319*x^3 -279*x^2 + 145*x -10)*(x^18 + 8*x^17 -143*x^15 -219*x^14 + 1000*x^13 + 2226*x^12 -3469*x^11 -9830*x^10 + 6195*x^9 + 22561*x^8 -5139*x^7 -27072*x^6 + 1047*x^5 + 15459*x^4 + 689*x^3 -3513*x^2 -248*x + 208)*(x + 1)^2*(x^5 -x^4 -12*x^3 + 8*x^2 + 24*x -16)^2;
T[1027,5]=(x^22 -5*x^21 -57*x^20 + 312*x^19 + 1233*x^18 -7899*x^17 -11753*x^16 + 104411*x^15 + 26666*x^14 -770047*x^13 + 395489*x^12 + 3098396*x^11 -3477440*x^10 -5764789*x^9 + 11041019*x^8 + 982915*x^7 -13061853*x^6 + 8456392*x^5 + 907812*x^4 -2757892*x^3 + 867628*x^2 -6880*x -23312)*(x^21 -17*x^20 + 81*x^19 + 188*x^18 -2759*x^17 + 4749*x^16 + 27139*x^15 -104127*x^14 -62532*x^13 + 791195*x^12 -581837*x^11 -2838918*x^10 + 4412046*x^9 + 4486547*x^8 -12082177*x^7 -980809*x^6 + 15020685*x^5 -4393106*x^4 -7869740*x^3 + 3451348*x^2 + 1140372*x -449704)*(x^17 + 21*x^16 + 167*x^15 + 530*x^14 -291*x^13 -6221*x^12 -10815*x^11 + 17695*x^10 + 65706*x^9 + 2447*x^8 -150239*x^7 -76540*x^6 + 155002*x^5 + 106799*x^4 -68339*x^3 -51595*x^2 + 10411*x + 7936)*(x^18 + 7*x^17 -25*x^16 -260*x^15 + 69*x^14 + 3665*x^13 + 2963*x^12 -24557*x^11 -31970*x^10 + 82517*x^9 + 125001*x^8 -147872*x^7 -220784*x^6 + 146683*x^5 + 167339*x^4 -78629*x^3 -36365*x^2 + 17928*x -1780)*(x )*(x + 3)^2*(x^5 -7*x^4 + 9*x^3 + 27*x^2 -65*x + 31)^2;

T[1028,2]=(x^14 + 3*x^13 + 11*x^12 + 25*x^11 + 57*x^10 + 102*x^9 + 177*x^8 + 255*x^7 + 354*x^6 + 408*x^5 + 456*x^4 + 400*x^3 + 352*x^2 + 192*x + 128)*(x^28 -2*x^27 + 7*x^26 -10*x^25 + 23*x^24 -27*x^23 + 60*x^22 -69*x^21 + 138*x^20 -141*x^19 + 250*x^18 -225*x^17 + 450*x^16 -458*x^15 + 919*x^14 -916*x^13 + 1800*x^12 -1800*x^11 + 4000*x^10 -4512*x^9 + 8832*x^8 -8832*x^7 + 15360*x^6 -13824*x^5 + 23552*x^4 -20480*x^3 + 28672*x^2 -16384*x + 16384)*(x + 1)^10*(x -1)^11*(x )^64;
T[1028,3]=(x^5 + 3*x^4 -5*x^3 -16*x^2 + 5*x + 15)*(x^14 -5*x^13 -19*x^12 + 122*x^11 + 87*x^10 -1073*x^9 + 216*x^8 + 4228*x^7 -2318*x^6 -7280*x^5 + 4304*x^4 + 4144*x^3 -914*x^2 -378*x + 76)*(x^2 -6)^2*(x^3 -2*x^2 -4*x + 4)^2*(x^5 -8*x^3 + 6*x -2)^2*(x^9 -2*x^8 -20*x^7 + 40*x^6 + 116*x^5 -226*x^4 -204*x^3 + 376*x^2 + 96*x -176)^2*(x + 2)^3*(x^7 + 5*x^6 + x^5 -22*x^4 -17*x^3 + 15*x^2 + 8*x -4)^3*(x^14 -3*x^13 -23*x^12 + 74*x^11 + 173*x^10 -627*x^9 -500*x^8 + 2254*x^7 + 726*x^6 -3988*x^5 -858*x^4 + 3536*x^3 + 960*x^2 -1280*x -512)^3*(x )^4;
T[1028,5]=(x + 4)*(x^14 -7*x^13 -27*x^12 + 279*x^11 + 28*x^10 -3919*x^9 + 4902*x^8 + 21680*x^7 -48128*x^6 -26176*x^5 + 139840*x^4 -88832*x^3 -51712*x^2 + 71936*x -19968)*(x^5 + x^4 -9*x^3 -9*x^2 + 4*x + 3)*(x )*(x^2 -6)^2*(x^3 -4*x^2 + 2*x + 2)^2*(x^9 -4*x^8 -22*x^7 + 86*x^6 + 174*x^5 -612*x^4 -576*x^3 + 1440*x^2 + 640*x -16)^2*(x^5 + 4*x^4 -8*x^3 -48*x^2 -48*x -8)^2*(x^7 + x^6 -15*x^5 -5*x^4 + 52*x^3 -35*x^2 -2*x + 4)^3*(x^14 + x^13 -45*x^12 -21*x^11 + 740*x^10 -41*x^9 -5360*x^8 + 2796*x^7 + 16632*x^6 -14736*x^5 -18208*x^4 + 23232*x^3 -384*x^2 -5120*x + 512)^3*(x + 2)^5;

T[1029,2]=(x^3 + 4*x^2 + 3*x -1)^2*(x^3 -3*x^2 -4*x + 13)^2*(x^9 + 2*x^8 -12*x^7 -21*x^6 + 47*x^5 + 67*x^4 -63*x^3 -64*x^2 + 17*x -1)^2*(x^9 -5*x^8 -5*x^7 + 56*x^6 -37*x^5 -164*x^4 + 189*x^3 + 104*x^2 -172*x + 41)^2*(x -1)^4*(x -2)^4*(x^2 + 2*x -1)^4*(x^3 + x^2 -2*x -1)^4*(x^3 -2*x^2 -x + 1)^4*(x^6 + 2*x^5 -6*x^4 -10*x^3 + 10*x^2 + 11*x -1)^4*(x + 1)^5;
T[1029,3]=(x^12 + 5*x^11 + 17*x^10 + 41*x^9 + 95*x^8 + 193*x^7 + 367*x^6 + 579*x^5 + 855*x^4 + 1107*x^3 + 1377*x^2 + 1215*x + 729)*(x^12 -5*x^11 + 17*x^10 -41*x^9 + 95*x^8 -193*x^7 + 367*x^6 -579*x^5 + 855*x^4 -1107*x^3 + 1377*x^2 -1215*x + 729)*(x^12 -2*x^10 + 19*x^8 -28*x^6 + 171*x^4 -162*x^2 + 729)*(x^2 + 3)^8*(x + 1)^32*(x -1)^33;
T[1029,5]=(x^3 -x^2 -2*x + 1)*(x^3 + x^2 -2*x -1)*(x^9 + x^8 -27*x^7 -8*x^6 + 240*x^5 -109*x^4 -713*x^3 + 847*x^2 -92*x -139)*(x^9 + 6*x^8 -20*x^7 -160*x^6 + 44*x^5 + 1320*x^4 + 904*x^3 -3360*x^2 -4096*x -512)*(x^9 -x^8 -27*x^7 + 8*x^6 + 240*x^5 + 109*x^4 -713*x^3 -847*x^2 -92*x + 139)*(x^9 -6*x^8 -20*x^7 + 160*x^6 + 44*x^5 -1320*x^4 + 904*x^3 + 3360*x^2 -4096*x + 512)*(x^2 -4*x + 2)^2*(x^2 + 4*x + 2)^2*(x^6 -11*x^5 + 38*x^4 -20*x^3 -126*x^2 + 196*x -49)^2*(x^6 -24*x^4 + 164*x^2 -232)^2*(x^6 + 11*x^5 + 38*x^4 + 20*x^3 -126*x^2 -196*x -49)^2*(x -2)^7*(x + 2)^8*(x )^16;

T[1030,2]=(x^8 + x^7 + 5*x^6 + 5*x^5 + 13*x^4 + 10*x^3 + 20*x^2 + 8*x + 16)*(x^28 + x^27 + 6*x^26 + 8*x^25 + 24*x^24 + 36*x^23 + 86*x^22 + 134*x^21 + 262*x^20 + 404*x^19 + 711*x^18 + 1005*x^17 + 1724*x^16 + 2274*x^15 + 3664*x^14 + 4548*x^13 + 6896*x^12 + 8040*x^11 + 11376*x^10 + 12928*x^9 + 16768*x^8 + 17152*x^7 + 22016*x^6 + 18432*x^5 + 24576*x^4 + 16384*x^3 + 24576*x^2 + 8192*x + 16384)*(x^18 -x^17 + 4*x^16 -4*x^15 + 12*x^14 -13*x^13 + 29*x^12 -24*x^11 + 66*x^10 -48*x^9 + 132*x^8 -96*x^7 + 232*x^6 -208*x^5 + 384*x^4 -256*x^3 + 512*x^2 -256*x + 512)*(x^12 -4*x^11 + 11*x^10 -23*x^9 + 43*x^8 -74*x^7 + 111*x^6 -148*x^5 + 172*x^4 -184*x^3 + 176*x^2 -128*x + 64)^2*(x^4 + 3*x^3 + 5*x^2 + 6*x + 4)^2*(x^8 + x^7 + 3*x^6 + 3*x^5 + 7*x^4 + 6*x^3 + 12*x^2 + 8*x + 16)^2*(x -1)^25*(x + 1)^26;
T[1030,3]=(x -1)*(x^2 -x -4)*(x^3 -3*x^2 -6*x + 17)*(x^3 + 5*x^2 + 6*x + 1)*(x^3 -x^2 -6*x + 3)*(x^3 + x^2 -4*x -3)*(x^3 + 3*x^2 -1)*(x^4 -3*x^3 -4*x^2 + 9*x + 8)*(x^5 -4*x^4 -x^3 + 15*x^2 -9*x -4)*(x^4 + 4*x^3 + x^2 -7*x -1)*(x -2)^2*(x^2 + 3*x -1)^2*(x^2 -x -7)^2*(x^4 -2*x^3 -5*x^2 + 12*x -5)^2*(x^4 + x^3 -3*x^2 -x + 1)^2*(x^8 + 3*x^7 -13*x^6 -37*x^5 + 43*x^4 + 98*x^3 -68*x^2 -72*x + 48)^2*(x^9 -3*x^8 -11*x^7 + 34*x^6 + 37*x^5 -113*x^4 -57*x^3 + 121*x^2 + 44*x -5)^2*(x^14 -x