1\\ charpoly_s2new.gp
2\\ This is a table of characteristic polynomials of the
3\\ Hecke operators T_p acting on the space S_2^{new}(Gamma_0(N))
4\\ of weight 2 cuspidal newforms for Gamma_0(N).
5\\ The cases in which S_k = S_k^{new} are omitted, since
6\\ they appear in other tables.
7\\ William Stein ([email protected]), October, 1998.
8
9{
10T=matrix(500,97,m,n,0);
11T[402,2]=(x + 1)^5*(x -1)^6;
12T[402,3]=(x -1)^5*(x + 1)^6;
13T[402,5]=(x + 3)*(x -1)*(x^2 -12)*(x^2 -x -10)*(x^3 -3*x^2 -4*x + 4)*(x -2)^2;
14T[402,7]=(x + 3)*(x + 1)*(x -2)*(x^2 + x -10)*(x^2 -6*x + 6)*(x^3 -x^2 -4*x + 2)*(x );
15T[402,11]=(x + 4)*(x^3 -28*x + 16)*(x + 2)^2*(x )^2*(x -4)^3;
16T[402,13]=(x + 2)*(x^2 + 2*x -2)*(x^3 + 6*x^2 -22*x -136)*(x )*(x + 4)^2*(x -4)^2;
17T[402,17]=(x -6)*(x + 6)*(x^2 -12)*(x^3 + 2*x^2 -28*x + 8)*(x -2)^2*(x + 2)^2;
18T[402,19]=(x -4)*(x + 4)*(x^2 + 2*x -40)*(x -2)^3*(x + 2)^4;
19T[402,23]=(x + 3)*(x + 9)*(x + 6)*(x -4)*(x^2 -9*x + 10)*(x^2 -14*x + 46)*(x^3 -3*x^2 -36*x + 54);
20T[402,29]=(x -8)*(x + 2)*(x^2 + 2*x -74)*(x^3 -6*x^2 -22*x + 136)*(x + 4)^2*(x )^2;
21T[402,31]=(x + 9)*(x -5)*(x -2)*(x^2 + 7*x + 2)*(x^2 -10*x -2)*(x^3 + 13*x^2 + 52*x + 62)*(x );
22T[402,37]=(x + 3)*(x -6)*(x + 7)*(x^2 -15*x + 46)*(x^3 + 7*x^2 -136*x -1028)*(x + 2)^3;
23T[402,41]=(x + 10)*(x + 2)*(x^2 + 4*x -8)*(x^2 + x -10)*(x^3 -5*x^2 -84*x + 344)*(x -3)^2;
24T[402,43]=(x + 1)*(x + 7)*(x^2 + 11*x + 20)*(x^2 -8*x -32)*(x^3 + x^2 -104*x -352)*(x -4)^2;
25T[402,47]=(x + 8)*(x -12)*(x + 6)*(x^2 + 10*x -16)*(x^2 -2*x -74)*(x^3 + 10*x^2 -46*x -128)*(x );
26T[402,53]=(x + 6)*(x -9)*(x -2)*(x + 3)*(x^2 -8*x + 4)*(x^2 + 3*x -90)*(x^3 -15*x^2 + 68*x -92);
27T[402,59]=(x + 8)*(x -3)*(x + 3)*(x^2 + 7*x -80)*(x^2 + 12*x + 24)*(x^3 -3*x^2 -60*x + 8)*(x );
28T[402,61]=(x -8)*(x -6)*(x^2 + 14*x + 8)*(x^2 + 6*x + 6)*(x^3 -58*x -124)*(x + 10)^2;
29T[402,67]=(x + 1)^5*(x -1)^6;
30T[402,71]=(x + 14)*(x + 4)*(x + 12)*(x -4)*(x^2 -6*x -18)*(x^2 + 14*x + 8)*(x^3 -6*x^2 -46*x + 232);
31T[402,73]=(x^2 -13*x -50)*(x^3 + x^2 -56*x -172)*(x + 6)^2*(x -6)^2*(x -11)^2;
32T[402,79]=(x + 2)*(x -8)*(x^2 + 6*x -32)*(x^2 -6*x -18)*(x^3 + 26*x^2 + 130*x -464)*(x )^2;
33T[402,83]=(x -15)*(x + 16)*(x -9)*(x + 12)*(x^2 -15*x -36)*(x^3 + 3*x^2 -184*x -544)*(x^2 -16*x + 16);
34T[402,89]=(x -16)*(x^2 + 18*x + 40)*(x^3 -16*x^2 + 20*x + 368)*(x )*(x + 10)^2*(x + 6)^2;
35T[402,97]=(x -8)*(x + 6)*(x + 2)*(x^2 + 14*x + 8)*(x^2 -108)*(x^3 -4*x^2 -92*x + 496)*(x );
36
37T[403,2]=(x^2 -3*x + 1)*(x^7 -2*x^6 -9*x^5 + 17*x^4 + 20*x^3 -37*x^2 + x + 4)*(x^8 + x^7 -11*x^6 -10*x^5 + 37*x^4 + 33*x^3 -36*x^2 -33*x -4)*(x^6 + 2*x^5 -7*x^4 -13*x^3 + 6*x^2 + 7*x -3)*(x^8 + 5*x^7 -30*x^5 -24*x^4 + 54*x^3 + 54*x^2 -28*x -29);
38T[403,3]=(x^7 -5*x^6 + 28*x^4 -25*x^3 -21*x^2 + 15*x + 8)*(x^8 -7*x^7 + 8*x^6 + 42*x^5 -107*x^4 + 15*x^3 + 141*x^2 -104*x + 16)*(x^6 + 5*x^5 + 4*x^4 -10*x^3 -11*x^2 + x + 1)*(x^8 + 3*x^7 -12*x^6 -36*x^5 + 31*x^4 + 97*x^3 -29*x^2 -72*x + 12)*(x + 2)^2;
39T[403,5]=(x^2 -5)*(x^7 -11*x^6 + 38*x^5 -27*x^4 -75*x^3 + 80*x^2 + 39*x -4)*(x^8 -11*x^7 + 32*x^6 + 35*x^5 -263*x^4 + 126*x^3 + 537*x^2 -346*x -232)*(x^6 + 9*x^5 + 20*x^4 -19*x^3 -75*x^2 + 14*x + 39)*(x^8 + 15*x^7 + 83*x^6 + 192*x^5 + 99*x^4 -225*x^3 -158*x^2 + 90*x + 3);
40T[403,7]=(x^7 -4*x^6 -7*x^5 + 24*x^4 + 7*x^3 -23*x^2 -7*x + 2)*(x^8 + 2*x^7 -39*x^6 -42*x^5 + 527*x^4 + 185*x^3 -2717*x^2 + 250*x + 3824)*(x^6 -29*x^4 -6*x^3 + 175*x^2 + 121*x -113)*(x^8 + 4*x^7 -20*x^6 -88*x^5 + 46*x^4 + 335*x^3 + 50*x^2 -181*x + 29)*(x -1)^2;
41T[403,11]=(x^2 -20)*(x^7 -8*x^6 -3*x^5 + 99*x^4 + 10*x^3 -307*x^2 -17*x + 283)*(x^8 + 2*x^7 -31*x^6 -51*x^5 + 238*x^4 + 267*x^3 -631*x^2 -319*x + 484)*(x^8 + 5*x^7 -56*x^6 -309*x^5 + 705*x^4 + 4994*x^3 + 769*x^2 -17712*x -14580)*(x^6 + 5*x^5 -18*x^4 -49*x^3 + 147*x^2 -76*x + 9);
42T[403,13]=(x + 1)^15*(x -1)^16;
43T[403,17]=(x^2 -6*x + 4)*(x^7 -7*x^6 -20*x^5 + 227*x^4 -433*x^3 + 421*x -184)*(x^8 -7*x^7 -48*x^6 + 349*x^5 + 589*x^4 -4864*x^3 -1393*x^2 + 20046*x -9064)*(x^6 + 23*x^5 + 194*x^4 + 709*x^3 + 873*x^2 -758*x -1821)*(x^8 + 11*x^7 -10*x^6 -313*x^5 + 51*x^4 + 2638*x^3 -783*x^2 -4546*x -1940);
44T[403,19]=(x^7 -x^6 -37*x^5 -2*x^4 + 369*x^3 + 352*x^2 -185*x -40)*(x^8 + 5*x^7 -73*x^6 -232*x^5 + 1533*x^4 + 1764*x^3 -4951*x^2 -568*x + 1616)*(x^6 -7*x^5 -77*x^4 + 460*x^3 + 1315*x^2 -5042*x + 2779)*(x^8 + 9*x^7 -46*x^6 -489*x^5 + 74*x^4 + 4150*x^3 + 760*x^2 -8448*x + 3557)*(x -1)^2;
45T[403,23]=(x^2 + 6*x + 4)*(x^7 -6*x^6 -76*x^5 + 392*x^4 + 1229*x^3 -3636*x^2 -8263*x -3812)*(x^8 -14*x^7 + 2*x^6 + 678*x^5 -1885*x^4 -9248*x^3 + 34879*x^2 + 37276*x -171104)*(x^6 + 18*x^5 + 92*x^4 + 2*x^3 -899*x^2 -746*x + 2271)*(x^8 -86*x^6 + 84*x^5 + 1331*x^4 -268*x^3 -5687*x^2 -1446*x + 3452);
46T[403,29]=(x^2 -6*x + 4)*(x^7 + 2*x^6 -108*x^5 -7*x^4 + 2544*x^3 -1544*x^2 -8245*x -3670)*(x^8 -12*x^7 -14*x^6 + 533*x^5 -1550*x^4 -232*x^3 + 3257*x^2 + 700*x -428)*(x^6 + 18*x^5 + 82*x^4 -225*x^3 -2444*x^2 -4102*x + 1821)*(x^8 + 12*x^7 -84*x^6 -1333*x^5 -194*x^4 + 34630*x^3 + 74915*x^2 -116214*x -315444);
47T[403,31]=(x -1)^13*(x + 1)^18;
48T[403,37]=(x^2 + 6*x -36)*(x^7 -28*x^6 + 284*x^5 -1043*x^4 -1923*x^3 + 27295*x^2 -79133*x + 77417)*(x^8 -2*x^7 -66*x^6 + 161*x^5 + 1107*x^4 -2659*x^3 -4617*x^2 + 10693*x -2690)*(x^8 + 9*x^7 -131*x^6 -1340*x^5 + 3685*x^4 + 56502*x^3 + 48639*x^2 -506978*x -852812)*(x^6 + 13*x^5 -55*x^4 -1010*x^3 -1875*x^2 + 2966*x + 2371);
49T[403,41]=(x^2 -5)*(x^7 -3*x^6 -133*x^5 + 354*x^4 + 4210*x^3 -9517*x^2 -17215*x -4690)*(x^8 -13*x^7 -71*x^6 + 976*x^5 + 2854*x^4 -20463*x^3 -56379*x^2 + 78708*x + 214652)*(x^6 + 5*x^5 -139*x^4 -886*x^3 + 1920*x^2 + 13021*x -9633)*(x^8 + 25*x^7 + 148*x^6 -803*x^5 -10517*x^4 -24675*x^3 + 25545*x^2 + 80829*x + 18859);
50T[403,43]=(x^2 + 10*x -20)*(x^7 + x^6 -119*x^5 + 188*x^4 + 2040*x^3 -3461*x^2 -6227*x + 2536)*(x^8 + 5*x^7 -127*x^6 -740*x^5 + 2834*x^4 + 19087*x^3 -297*x^2 -60804*x -15488)*(x^6 + 7*x^5 -101*x^4 -706*x^3 + 532*x^2 + 1541*x + 599)*(x^8 -7*x^7 -199*x^6 + 1396*x^5 + 9678*x^4 -72663*x^3 + 4871*x^2 + 206378*x -149092);
51T[403,47]=(x^2 -80)*(x^7 + x^6 -219*x^5 + 346*x^4 + 13154*x^3 -47087*x^2 -47793*x + 39428)*(x^8 -23*x^7 + 85*x^6 + 1118*x^5 -6578*x^4 -4123*x^3 + 26089*x^2 -488*x -7040)*(x^6 + 9*x^5 -95*x^4 -500*x^3 + 2666*x^2 + 233*x -5361)*(x^8 + 17*x^7 -135*x^6 -3612*x^5 -9174*x^4 + 111609*x^3 + 469061*x^2 -47520*x -120144);
52T[403,53]=(x^2 -18*x + 76)*(x^7 -29*x^6 + 220*x^5 + 771*x^4 -15431*x^3 + 42444*x^2 + 74489*x -270268)*(x^8 -25*x^7 + 70*x^6 + 2067*x^5 -10865*x^4 -31170*x^3 + 139247*x^2 + 131586*x -354728)*(x^6 + 31*x^5 + 334*x^4 + 1421*x^3 + 1489*x^2 -2780*x -3633)*(x^8 + 15*x^7 -615*x^5 -1065*x^4 + 6006*x^3 + 12445*x^2 + 3666*x -828);
53T[403,59]=(x^2 + 6*x -11)*(x^7 -3*x^6 -308*x^5 + 655*x^4 + 23179*x^3 -47642*x^2 -320055*x -250090)*(x^8 + 5*x^7 -252*x^6 -533*x^5 + 20139*x^4 + 4450*x^3 -558165*x^2 + 306434*x + 3991768)*(x^6 + x^5 -136*x^4 + 71*x^3 + 3945*x^2 -9040*x -1359)*(x^8 + 15*x^7 -93*x^6 -2164*x^5 -2369*x^4 + 78357*x^3 + 271540*x^2 -245226*x -1314177);
54T[403,61]=(x^2 -14*x + 4)*(x^7 -5*x^6 -112*x^5 + 380*x^4 + 4207*x^3 -5379*x^2 -55645*x -54112)*(x^8 + 9*x^7 -240*x^6 -1784*x^5 + 15963*x^4 + 82241*x^3 -220813*x^2 -255762*x + 360296)*(x^6 + 15*x^5 -94*x^4 -1998*x^3 -8179*x^2 -12413*x -6223)*(x^8 -11*x^7 -194*x^6 + 1174*x^5 + 14097*x^4 -4869*x^3 -181171*x^2 -86010*x + 493348);
55T[403,67]=(x^7 + 32*x^6 + 396*x^5 + 2380*x^4 + 7156*x^3 + 9871*x^2 + 3853*x -1718)*(x^8 -22*x^7 -98*x^6 + 4424*x^5 -7356*x^4 -239515*x^3 + 426459*x^2 + 4314658*x + 2879368)*(x^6 + 28*x^5 + 164*x^4 -1422*x^3 -13236*x^2 + 16051*x + 221807)*(x^8 -18*x^7 + 62*x^6 + 534*x^5 -3756*x^4 + 2345*x^3 + 30349*x^2 -75928*x + 52672)*(x + 8)^2;
56T[403,71]=(x^7 -5*x^6 -265*x^5 + 374*x^4 + 18035*x^3 + 27020*x^2 -263745*x -662786)*(x^8 + 17*x^7 -123*x^6 -2108*x^5 + 8017*x^4 + 54818*x^3 -251619*x^2 + 161766*x + 183184)*(x^6 -x^5 -279*x^4 + 864*x^3 + 11201*x^2 -26476*x + 627)*(x^8 + 7*x^7 -178*x^6 -1019*x^5 + 8926*x^4 + 30514*x^3 -134152*x^2 -82100*x + 79141)*(x -3)^2;
57T[403,73]=(x^7 -x^6 -356*x^5 + 2165*x^4 + 28353*x^3 -337304*x^2 + 1173025*x -1339357)*(x^8 + 27*x^7 + 60*x^6 -4519*x^5 -54015*x^4 -234362*x^3 -377005*x^2 -158445*x -18442)*(x^6 + 20*x^5 + 88*x^4 -293*x^3 -2370*x^2 -2768*x + 1721)*(x^8 -24*x^7 + 70*x^6 + 2109*x^5 -16192*x^4 + 8782*x^3 + 124625*x^2 -11292*x -173100)*(x -14)^2;
58T[403,79]=(x^7 + 15*x^6 -57*x^5 -1080*x^4 + 1013*x^3 + 23774*x^2 -3949*x -158222)*(x^8 + 23*x^7 -x^6 -3496*x^5 -22577*x^4 + 80746*x^3 + 1241889*x^2 + 4078386*x + 4121696)*(x^6 + 15*x^5 -83*x^4 -1398*x^3 + 1747*x^2 + 30026*x + 15161)*(x^8 -33*x^7 + 165*x^6 + 4478*x^5 -46599*x^4 -37302*x^3 + 1341563*x^2 -576904*x -10460864)*(x -4)^2;
59T[403,83]=(x^2 -12*x -44)*(x^7 -17*x^6 -129*x^5 + 3426*x^4 -14042*x^3 -4525*x^2 + 37081*x + 24052)*(x^8 + 25*x^7 -63*x^6 -4056*x^5 + 28*x^4 + 198399*x^3 -187587*x^2 -1440920*x + 1073104)*(x^6 -x^5 -73*x^4 + 52*x^3 + 1284*x^2 -1013*x -4077)*(x^8 + 13*x^7 -191*x^6 -1706*x^5 + 15238*x^4 + 56199*x^3 -430353*x^2 -555000*x + 3798748);
60T[403,89]=(x^2 + 6*x + 4)*(x^7 -26*x^6 + 107*x^5 + 2020*x^4 -19527*x^3 + 51024*x^2 -26458*x + 1429)*(x^8 -2*x^7 -435*x^6 + 1530*x^5 + 56173*x^4 -267802*x^3 -2084566*x^2 + 13417739*x -14681734)*(x^6 + x^5 -252*x^4 -1046*x^3 + 4039*x^2 + 16681*x -3681)*(x^8 + 23*x^7 -94*x^6 -3658*x^5 + 7327*x^4 + 155233*x^3 -756655*x^2 + 1110594*x -462276);
61T[403,97]=(x^2 -4*x -41)*(x^7 -11*x^6 -340*x^5 + 4446*x^4 + 7660*x^3 -190630*x^2 + 316577*x + 357056)*(x^8 + 15*x^7 -350*x^6 -5446*x^5 + 24426*x^4 + 412000*x^3 -344577*x^2 -4009002*x + 5096888)*(x^6 + 5*x^5 -252*x^4 -612*x^3 + 16576*x^2 -2356*x -1351)*(x^8 + 17*x^7 -125*x^6 -2773*x^5 + 4230*x^4 + 142406*x^3 -63055*x^2 -2271810*x + 2246337);
62
63T[404,2]=(x )^9;
64T[404,3]=(x + 2)*(x^7 -2*x^6 -17*x^5 + 36*x^4 + 64*x^3 -148*x^2 + 11*x + 58)*(x );
65T[404,5]=(x -3)*(x + 1)*(x^7 -31*x^5 + 8*x^4 + 262*x^3 -160*x^2 -503*x + 250);
66T[404,7]=(x + 2)*(x -2)*(x^7 -2*x^6 -39*x^5 + 62*x^4 + 438*x^3 -474*x^2 -1365*x + 698);
67T[404,11]=(x + 2)*(x + 6)*(x^7 -4*x^6 -43*x^5 + 122*x^4 + 548*x^3 -1178*x^2 -2085*x + 3482);
68T[404,13]=(x -5)*(x + 3)*(x^7 -4*x^6 -55*x^5 + 244*x^4 + 534*x^3 -2528*x^2 + 25*x + 58);
69T[404,17]=(x + 1)*(x -3)*(x^7 -4*x^6 -59*x^5 + 280*x^4 -18*x^3 -912*x^2 + 441*x + 522);
70T[404,19]=(x -5)*(x -1)*(x^7 + 4*x^6 -96*x^5 -352*x^4 + 2544*x^3 + 7680*x^2 -18624*x -48640);
71T[404,23]=(x^7 -8*x^6 -88*x^5 + 896*x^4 + 592*x^3 -22208*x^2 + 44736*x + 19456)*(x -3)^2;
72T[404,29]=(x + 2)*(x^7 -6*x^6 -124*x^5 + 584*x^4 + 4720*x^3 -14752*x^2 -50240*x + 67456)*(x );
73T[404,31]=(x -5)*(x + 3)*(x^7 -4*x^6 -92*x^5 + 208*x^4 + 1152*x^3 -768*x^2 -5184*x -3840);
74T[404,37]=(x + 10)*(x + 2)*(x^7 -32*x^6 + 373*x^5 -1740*x^4 + 142*x^3 + 27080*x^2 -87079*x + 84646);
75T[404,41]=(x -2)*(x -12)*(x^7 + 14*x^6 -32*x^5 -1152*x^4 -5120*x^3 -8576*x^2 -5632*x -1024);
76T[404,43]=(x -8)*(x -4)*(x^7 + 24*x^6 + 144*x^5 -288*x^4 -3344*x^3 + 1344*x^2 + 13376*x + 5888);
77T[404,47]=(x^7 + 4*x^6 -184*x^5 -112*x^4 + 8752*x^3 -25472*x^2 + 13632*x + 11776)*(x + 3)^2;
78T[404,53]=(x + 6)*(x^7 -6*x^6 -156*x^5 + 840*x^4 + 5248*x^3 -18432*x^2 -52672*x + 70016)*(x );
79T[404,59]=(x -12)*(x + 6)*(x^7 + 30*x^6 + 345*x^5 + 1878*x^4 + 4726*x^3 + 4002*x^2 -1381*x -1774);
80T[404,61]=(x + 10)*(x -8)*(x^7 -10*x^6 -100*x^5 + 808*x^4 + 3312*x^3 -20576*x^2 -36800*x + 161152);
81T[404,67]=(x -2)*(x + 10)*(x^7 + 2*x^6 -173*x^5 -1032*x^4 + 1864*x^3 + 16996*x^2 -4909*x -61150);
82T[404,71]=(x + 1)*(x + 9)*(x^7 -396*x^5 + 288*x^4 + 42880*x^3 -78528*x^2 -1031872*x + 1203968);
83T[404,73]=(x -2)*(x + 4)*(x^7 + 14*x^6 -264*x^5 -4496*x^4 + 7296*x^3 + 314880*x^2 + 780288*x -1811456);
84T[404,79]=(x -5)*(x -1)*(x^7 -24*x^6 -120*x^5 + 5776*x^4 -14256*x^3 -341760*x^2 + 1682112*x + 148224);
85T[404,83]=(x + 12)*(x -4)*(x^7 + 24*x^6 + 61*x^5 -1498*x^4 -5032*x^3 + 20302*x^2 + 58147*x + 9026);
86T[404,89]=(x -6)*(x + 6)*(x^7 + 6*x^6 -192*x^5 -816*x^4 + 7792*x^3 + 27744*x^2 -25408*x + 5248);
87T[404,97]=(x -2)*(x + 2)*(x^7 + 8*x^6 -303*x^5 -2144*x^4 + 4230*x^3 + 26736*x^2 -19671*x -72770);
88
89T[405,2]=(x + 2)*(x + 1)*(x -2)*(x -1)*(x^2 -2*x -2)*(x^2 + 2*x -2)*(x^3 + x^2 -5*x -3)*(x^3 -x^2 -5*x + 3)*(x )^2;
90T[405,3]=(x )^16;
91T[405,5]=(x + 1)^8*(x -1)^8;
92T[405,7]=(x + 3)^2*(x -2)^2*(x^2 + 6*x + 6)^2*(x^3 -5*x^2 + 3*x + 3)^2*(x )^2;
93T[405,11]=(x -2)*(x -5)*(x -3)*(x + 5)*(x + 2)*(x + 3)*(x^2 + 8*x + 13)*(x^2 -8*x + 13)*(x^3 -2*x^2 -8*x + 12)*(x^3 + 2*x^2 -8*x -12);
94T[405,13]=(x + 4)^2*(x -4)^2*(x + 2)^2*(x^2 + 4*x -8)^2*(x^3 -4*x^2 -4*x + 4)^2;
95T[405,17]=(x -6)*(x + 6)*(x^2 + 2*x -2)*(x^2 -2*x -2)*(x^3 + 2*x^2 -8*x -12)*(x^3 -2*x^2 -8*x + 12)*(x + 4)^2*(x -4)^2;
96T[405,19]=(x + 1)^2*(x + 8)^2*(x + 5)^2*(x^2 -2*x -11)^2*(x^3 -4*x^2 -4*x + 4)^2;
97T[405,23]=(x -3)*(x + 3)*(x^3 + 3*x^2 -33*x -117)*(x^3 -3*x^2 -33*x + 117)*(x -6)^2*(x + 6)^2*(x^2 -12)^2;
98T[405,29]=(x + 9)*(x -9)*(x -5)*(x -1)*(x + 5)*(x + 1)*(x^2 -4*x -23)*(x^2 + 4*x -23)*(x^3 + 7*x^2 -29*x -51)*(x^3 -7*x^2 -29*x + 51);
99T[405,31]=(x + 9)^2*(x + 1)^2*(x^3 -8*x^2 -60*x + 468)^2*(x )^2*(x + 3)^4;
100T[405,37]=(x -8)^2*(x + 10)^2*(x + 4)^2*(x^2 + 2*x -2)^2*(x^3 -6*x^2 -12*x + 4)^2;
101T[405,41]=(x -7)*(x -3)*(x + 7)*(x + 3)*(x + 5)*(x -5)*(x^2 -4*x -23)*(x^2 + 4*x -23)*(x^3 + 13*x^2 + 19*x + 3)*(x^3 -13*x^2 + 19*x -3);
102T[405,43]=(x + 2)^2*(x + 8)^2*(x + 4)^2*(x^2 + 10*x -2)^2*(x^3 -10*x^2 -4*x + 4)^2;
103T[405,47]=(x -7)*(x + 12)*(x + 2)*(x -2)*(x + 7)*(x -12)*(x^2 -14*x + 46)*(x^2 + 14*x + 46)*(x^3 + 13*x^2 -11*x -369)*(x^3 -13*x^2 -11*x + 369);
104T[405,53]=(x -8)*(x -2)*(x + 6)*(x + 2)*(x -6)*(x + 8)*(x^2 -10*x + 22)*(x^2 + 10*x + 22)*(x^3 + 2*x^2 -20*x -24)*(x^3 -2*x^2 -20*x + 24);
105T[405,59]=(x + 1)*(x + 3)*(x + 14)*(x -1)*(x -3)*(x -14)*(x^2 + 20*x + 97)*(x^2 -20*x + 97)*(x^3 -2*x^2 -20*x + 24)*(x^3 + 2*x^2 -20*x -24);
106T[405,61]=(x + 2)^2*(x -7)^2*(x + 10)^2*(x^3 -x^2 -37*x -71)^2*(x -4)^4;
107T[405,67]=(x -14)^2*(x -6)^2*(x + 3)^2*(x^2 -12)^2*(x^3 -11*x^2 -39*x + 507)^2;
108T[405,71]=(x + 3)*(x -1)*(x -2)*(x -3)*(x + 2)*(x + 1)*(x^2 + 4*x + 1)*(x^2 -4*x + 1)*(x^3 + 10*x^2 -92*x -708)*(x^3 -10*x^2 -92*x + 708);
109T[405,73]=(x -4)^2*(x + 8)^2*(x -2)^2*(x^2 -2*x -74)^2*(x^3 + 8*x^2 -64*x -128)^2;
110T[405,79]=(x + 16)^2*(x + 6)^2*(x -12)^2*(x^2 -24*x + 132)^2*(x^3 -2*x^2 -84*x -24)^2;
111T[405,83]=(x -9)*(x + 9)*(x + 6)*(x -6)*(x -12)*(x + 12)*(x^2 -6*x -18)*(x^2 + 6*x -18)*(x^3 -15*x^2 + 27*x + 81)*(x^3 + 15*x^2 + 27*x -81);
112T[405,89]=(x + 9)*(x -9)*(x -15)^2*(x + 15)^2*(x^2 -27)^2*(x -3)^3*(x + 3)^3;
113T[405,97]=(x + 4)^2*(x -14)^2*(x -2)^2*(x^2 + 2*x -74)^2*(x^3 + 18*x^2 -36*x -1304)^2;
114
115T[406,2]=(x + 1)^6*(x -1)^7;
116T[406,3]=(x + 1)*(x -1)*(x^3 -x^2 -8*x + 4)*(x^4 -x^3 -10*x^2 + 4*x + 8)*(x )*(x -2)^3;
117T[406,5]=(x -2)*(x^2 -2*x -2)*(x^4 + x^3 -14*x^2 -24*x + 4)*(x^3 -5*x^2 + 2*x + 10)*(x )*(x + 3)^2;
118T[406,7]=(x -1)^6*(x + 1)^7;
119T[406,11]=(x + 4)*(x + 3)*(x -4)*(x + 1)*(x^2 -12)*(x^3 -x^2 -24*x -20)*(x^4 -7*x^3 + 8*x^2 + 16*x -16);
120T[406,13]=(x + 2)*(x^2 + 2*x -2)*(x^3 -7*x^2 + 10*x -2)*(x^4 + 7*x^3 -26*x^2 -176*x + 28)*(x )*(x + 1)^2;
121T[406,17]=(x^2 + 2*x -26)*(x^4 -20*x^2 -36*x -16)*(x^3 -8*x^2 + 2*x + 64)*(x )*(x + 4)^3;
122T[406,19]=(x -4)*(x -2)*(x^2 -12)*(x^4 -2*x^3 -20*x^2 + 8*x + 32)*(x^3 + 8*x^2 -12*x -80)*(x + 4)^2;
123T[406,23]=(x + 2)*(x + 6)*(x^2 + 4*x -44)*(x^3 -6*x^2 -28*x + 136)*(x^4 -6*x^3 -8*x^2 + 64*x -32)*(x )^2;
124T[406,29]=(x + 1)^4*(x -1)^9;
125T[406,31]=(x + 1)*(x + 6)*(x -5)*(x + 2)*(x^2 -6*x -18)*(x^3 -5*x^2 -22*x + 106)*(x^4 + 7*x^3 -62*x^2 -388*x + 356);
126T[406,37]=(x + 2)*(x -6)*(x^3 -10*x^2 + 8*x + 80)*(x^4 + 12*x^3 + 24*x^2 -64*x -16)*(x -2)^2*(x + 4)^2;
127T[406,41]=(x + 8)*(x -8)*(x^2 + 2*x -74)*(x^3 -16*x^2 + 18*x + 352)*(x^4 -4*x^3 -148*x^2 + 772*x -448)*(x )^2;
128T[406,43]=(x -3)*(x -4)*(x + 8)*(x + 7)*(x^2 -8*x -32)*(x^3 + 15*x^2 + 32*x -32)*(x^4 + 5*x^3 -32*x^2 -64*x + 256);
129T[406,47]=(x -6)*(x + 9)*(x + 3)*(x -2)*(x^2 -2*x -74)*(x^3 -5*x^2 + 2*x + 10)*(x^4 + 11*x^3 -10*x^2 -236*x -188);
130T[406,53]=(x -3)*(x -6)*(x + 9)*(x + 2)*(x^2 + 4*x -44)*(x^3 -11*x^2 + 16*x + 68)*(x^4 -5*x^3 -46*x^2 + 260*x -248);
131T[406,59]=(x -12)*(x + 4)*(x + 10)*(x^2 -18*x + 78)*(x^4 -16*x^3 -16*x^2 + 916*x -2752)*(x^3 -28*x^2 + 242*x -664)*(x );
132T[406,61]=(x + 2)*(x + 10)*(x -6)*(x^4 + 34*x^3 + 368*x^2 + 1136*x -1376)*(x^3 + 10*x^2 + 8*x -80)*(x -4)^3;
133T[406,67]=(x -8)*(x + 4)*(x^2 -48)*(x^3 + 14*x^2 -32*x -128)*(x^4 -2*x^3 -320*x^2 + 256*x + 24832)*(x -2)^2;
134T[406,71]=(x + 12)*(x -8)*(x -16)*(x + 8)*(x^2 -4*x -44)*(x^3 -8*x^2 -100*x -176)*(x^4 -24*x^3 -56*x^2 + 4784*x -28544);
135T[406,73]=(x -8)*(x + 12)*(x^2 -14*x + 46)*(x^3 + 16*x^2 + 66*x + 80)*(x^4 + 24*x^3 + 132*x^2 -92*x -64)*(x )^2;
136T[406,79]=(x + 13)*(x -5)*(x + 4)*(x + 12)*(x^2 + 12*x + 24)*(x^3 + 3*x^2 -72*x -40)*(x^4 + 9*x^3 -188*x^2 -912*x -544);
137T[406,83]=(x + 6)*(x -12)*(x^2 -2*x -242)*(x^3 + 12*x^2 -142*x -568)*(x^4 + 8*x^3 -296*x^2 -1508*x + 17024)*(x )^2;
138T[406,89]=(x -6)*(x + 14)*(x -4)*(x^2 -22*x + 94)*(x^3 + 10*x^2 -158*x -220)*(x^4 -2*x^3 -124*x^2 + 332*x + 824)*(x );
139T[406,97]=(x -4)*(x -16)*(x -12)*(x -8)*(x^2 + 10*x + 22)*(x^3 + 16*x^2 -78*x -976)*(x^4 + 4*x^3 -148*x^2 -772*x -448);
140
141T[407,2]=(x^4 -x^3 -4*x^2 + 2*x + 3)*(x^4 + x^3 -4*x^2 + 1)*(x^12 -x^11 -18*x^10 + 18*x^9 + 111*x^8 -104*x^7 -274*x^6 + 212*x^5 + 255*x^4 -129*x^3 -78*x^2 + 4*x + 1)*(x^11 -2*x^10 -16*x^9 + 32*x^8 + 89*x^7 -179*x^6 -201*x^5 + 407*x^4 + 168*x^3 -333*x^2 -51*x + 75);
142T[407,3]=(x^11 -24*x^9 + 3*x^8 + 209*x^7 -48*x^6 -824*x^5 + 260*x^4 + 1448*x^3 -560*x^2 -880*x + 400)*(x^12 -8*x^11 + 4*x^10 + 115*x^9 -251*x^8 -396*x^7 + 1528*x^6 -220*x^5 -2592*x^4 + 1440*x^3 + 1328*x^2 -752*x -208)*(x^4 -4*x^2 -x + 1)*(x^4 + 4*x^3 -9*x + 1);
143T[407,5]=(x^11 -x^10 -46*x^9 + 48*x^8 + 767*x^7 -786*x^6 -5700*x^5 + 5224*x^4 + 19152*x^3 -13536*x^2 -24000*x + 9600)*(x^12 -5*x^11 -32*x^10 + 182*x^9 + 275*x^8 -2228*x^7 + 120*x^6 + 10912*x^5 -10016*x^4 -15424*x^3 + 29312*x^2 -15872*x + 2816)*(x^4 -x^3 -4*x^2 + 2*x + 3)*(x^4 + 5*x^3 + 4*x^2 -8*x -9);
144T[407,7]=(x^11 -9*x^10 -8*x^9 + 250*x^8 -297*x^7 -2188*x^6 + 3800*x^5 + 6880*x^4 -12736*x^3 -5632*x^2 + 10240*x + 1024)*(x^12 -7*x^11 -44*x^10 + 416*x^9 + 229*x^8 -8052*x^7 + 11288*x^6 + 50304*x^5 -133760*x^4 + 8320*x^3 + 173056*x^2 -45056*x -38912)*(x^4 + x^3 -4*x^2 + 1)*(x^4 + 7*x^3 + 8*x^2 -30*x -53);
145T[407,11]=(x + 1)^15*(x -1)^16;
146T[407,13]=(x^11 -22*x^10 + 156*x^9 -153*x^8 -2747*x^7 + 9382*x^6 + 6848*x^5 -61630*x^4 + 35796*x^3 + 77376*x^2 -42204*x -10228)*(x^12 -14*x^11 + 735*x^9 -1983*x^8 -13336*x^7 + 54856*x^6 + 81234*x^5 -560040*x^4 + 178164*x^3 + 1945404*x^2 -2543220*x + 604836)*(x^4 + 10*x^3 + 24*x^2 + 11*x -3)*(x^4 + 12*x^3 + 48*x^2 + 71*x + 31);
147T[407,17]=(x^11 -19*x^10 + 52*x^9 + 910*x^8 -4727*x^7 -13530*x^6 + 90030*x^5 + 95942*x^4 -560592*x^3 -504588*x^2 + 447960*x + 343956)*(x^12 -9*x^11 -40*x^10 + 580*x^9 -497*x^8 -10324*x^7 + 30038*x^6 + 28726*x^5 -224024*x^4 + 294348*x^3 -62980*x^2 -97056*x + 41004)*(x^4 + 9*x^3 + 12*x^2 -44*x -21)*(x^4 + 13*x^3 + 46*x^2 + 38*x -27);
148T[407,19]=(x^4 + 2*x^3 -45*x^2 -114*x + 133)*(x^4 + 6*x^3 -31*x^2 -76*x + 63)*(x^12 + 2*x^11 -157*x^10 -176*x^9 + 9135*x^8 + 892*x^7 -234950*x^6 + 239426*x^5 + 2214660*x^4 -4980544*x^3 + 1648064*x^2 + 1585792*x + 170068)*(x^11 -14*x^10 -7*x^9 + 770*x^8 -1579*x^7 -14216*x^6 + 37106*x^5 + 106786*x^4 -238976*x^3 -283676*x^2 + 108792*x -4852);
149T[407,23]=(x^11 + 14*x^10 -53*x^9 -1398*x^8 -2039*x^7 + 38532*x^6 + 125656*x^5 -184928*x^4 -819648*x^3 + 152064*x^2 + 912384*x + 311040)*(x^12 -8*x^11 -87*x^10 + 712*x^9 + 1453*x^8 -12400*x^7 -14136*x^6 + 79616*x^5 + 75584*x^4 -188288*x^3 -140544*x^2 + 110848*x -5632)*(x^4 + 4*x^3 -7*x^2 + 1)*(x^4 + 6*x^3 -21*x^2 -74*x + 141);
150T[407,29]=(x^11 -13*x^10 -35*x^9 + 753*x^8 + 487*x^7 -14136*x^6 -7924*x^5 + 83566*x^4 + 51552*x^3 -115452*x^2 -47628*x + 4860)*(x^12 + 17*x^11 -51*x^10 -2139*x^9 -4389*x^8 + 92398*x^7 + 384964*x^6 -1395210*x^5 -9437172*x^4 -2154288*x^3 + 68543280*x^2 + 140124924*x + 82908396)*(x^4 -x^3 -19*x^2 -x + 23)*(x^4 -x^3 -81*x^2 + 289*x + 21);
151T[407,31]=(x^11 -12*x^10 -85*x^9 + 1370*x^8 + 1835*x^7 -58808*x^6 + 15536*x^5 + 1185616*x^4 -818720*x^3 -11433536*x^2 + 6005888*x + 43424000)*(x^12 + 10*x^11 -167*x^10 -2088*x^9 + 5511*x^8 + 133292*x^7 + 199760*x^6 -2822544*x^5 -10379872*x^4 + 6063424*x^3 + 71595392*x^2 + 90376960*x + 22641152)*(x^4 -6*x^3 -35*x^2 + 16*x + 47)*(x^4 + 8*x^3 -57*x^2 -450*x -413);
152T[407,37]=(x -1)^15*(x + 1)^16;
153T[407,41]=(x^11 -8*x^10 -196*x^9 + 1325*x^8 + 10659*x^7 -57610*x^6 -136148*x^5 + 784216*x^4 + 213456*x^3 -3024480*x^2 + 1804608*x -248448)*(x^12 -4*x^11 -250*x^10 + 811*x^9 + 23187*x^8 -56936*x^7 -978752*x^6 + 1562624*x^5 + 18469152*x^4 -9657856*x^3 -121299712*x^2 -122478848*x -20101376)*(x^4 + 6*x^3 -43*x -47)*(x^4 -20*x^3 + 122*x^2 -293*x + 243);
154T[407,43]=(x^11 -21*x^10 -83*x^9 + 4865*x^8 -25275*x^7 -268548*x^6 + 3159672*x^5 -4978498*x^4 -76229352*x^3 + 483772016*x^2 -1151565340*x + 1018403500)*(x^12 -9*x^11 -261*x^10 + 2443*x^9 + 23259*x^8 -244008*x^7 -735584*x^6 + 10730682*x^5 -1853676*x^4 -183638832*x^3 + 364218360*x^2 + 408229524*x -1102166116)*(x^4 + 7*x^3 -31*x^2 -257*x -211)*(x^4 + 7*x^3 -157*x^2 -1103*x + 1679);
155T[407,47]=(x^11 + 14*x^10 -104*x^9 -1566*x^8 + 4039*x^7 + 51824*x^6 -46592*x^5 -591472*x^4 -182880*x^3 + 1676160*x^2 + 1244160*x -366336)*(x^12 -10*x^11 -296*x^10 + 3562*x^9 + 20855*x^8 -360016*x^7 + 152832*x^6 + 10479248*x^5 -21524096*x^4 -101633024*x^3 + 269305088*x^2 + 219353600*x -597852928)*(x^4 + 6*x^3 -64*x^2 -134*x + 303)*(x^4 -2*x^3 -16*x^2 + 18*x + 47);
156T[407,53]=(x^4 + 4*x^3 -106*x^2 -804*x -1447)*(x^4 -8*x^3 -94*x^2 + 520*x + 2157)*(x^12 -16*x^11 -254*x^10 + 5336*x^9 + 5001*x^8 -482148*x^7 + 1385092*x^6 + 15373244*x^5 -82007312*x^4 -76613616*x^3 + 1246606064*x^2 -2695800800*x + 1793344976)*(x^11 + 2*x^10 -334*x^9 -264*x^8 + 35317*x^7 -51966*x^6 -1391512*x^5 + 5022404*x^4 + 8224464*x^3 -46058592*x^2 -8493600*x + 116464080);
157T[407,59]=(x^11 + 30*x^10 + 66*x^9 -5079*x^8 -33245*x^7 + 261264*x^6 + 2231896*x^5 -4517648*x^4 -50693664*x^3 + 3081792*x^2 + 321269376*x + 256770816)*(x^12 -10*x^11 -264*x^10 + 2853*x^9 + 17847*x^8 -215936*x^7 -288856*x^6 + 4365584*x^5 + 3880608*x^4 -23080512*x^3 -17312640*x^2 + 9122560*x + 3667456)*(x^4 + 6*x^3 -174*x^2 -515*x -309)*(x^4 -10*x^3 -96*x^2 + 1441*x -4353);
158T[407,61]=(x^11 -20*x^10 -274*x^9 + 6670*x^8 + 22584*x^7 -774460*x^6 -660704*x^5 + 38861516*x^4 + 5574424*x^3 -781582640*x^2 + 110398560*x + 4605256000)*(x^12 + 2*x^11 -270*x^10 -442*x^9 + 21976*x^8 + 22504*x^7 -586764*x^6 -96608*x^5 + 6131468*x^4 -3651256*x^3 -19582320*x^2 + 17880224*x + 5992256)*(x^4 + 22*x^3 + 164*x^2 + 456*x + 304)*(x^4 + 2*x^3 -172*x^2 -232*x + 6192);
159T[407,67]=(x^11 -7*x^10 -471*x^9 + 3569*x^8 + 73997*x^7 -608900*x^6 -4319472*x^5 + 40169008*x^4 + 55782048*x^3 -799204864*x^2 + 489643264*x + 2503722752)*(x^12 -3*x^11 -399*x^10 + 525*x^9 + 58569*x^8 + 2208*x^7 -3846880*x^6 -3372720*x^5 + 112319616*x^4 + 142443008*x^3 -1181472000*x^2 -1522659072*x + 581470976)*(x^4 + 5*x^3 -163*x^2 -283*x + 3821)*(x^4 + 5*x^3 -95*x^2 -115*x + 1757);
160T[407,71]=(x^11 + 15*x^10 -258*x^9 -3720*x^8 + 20827*x^7 + 269876*x^6 -585212*x^5 -7292356*x^4 + 3956712*x^3 + 65060448*x^2 + 38438400*x -8674800)*(x^12 + 3*x^11 -334*x^10 + 280*x^9 + 36895*x^8 -130652*x^7 -1482692*x^6 + 9203988*x^5 + 6315360*x^4 -165091296*x^3 + 463454640*x^2 -514812096*x + 202327056)*(x^4 -21*x^3 + 122*x^2 -76*x -513)*(x^4 -9*x^3 -138*x^2 + 700*x + 6147);
161T[407,73]=(x^11 -47*x^10 + 806*x^9 -5012*x^8 -15641*x^7 + 362870*x^6 -1562204*x^5 + 845992*x^4 + 7398736*x^3 -8230880*x^2 -7416128*x -1136768)*(x^12 -31*x^11 -132*x^10 + 14228*x^9 -120947*x^8 -1449464*x^7 + 28025256*x^6 -84107744*x^5 -1227284224*x^4 + 12047425280*x^3 -40444159872*x^2 + 40836104192*x + 28329590528)*(x^4 + 33*x^3 + 396*x^2 + 2060*x + 3937)*(x^4 + 31*x^3 + 300*x^2 + 912*x + 19);
162T[407,79]=(x^4 + 4*x^3 -286*x^2 -660*x + 18877)*(x^4 -26*x^3 + 180*x^2 -198*x + 27)*(x^12 -336*x^10 + 434*x^9 + 29973*x^8 -60996*x^7 -752022*x^6 + 754482*x^5 + 6875520*x^4 + 4149056*x^3 -3752292*x^2 -3569136*x -703852)*(x^11 -2*x^10 -442*x^9 -560*x^8 + 68839*x^7 + 300484*x^6 -3668078*x^5 -28027642*x^4 -14582664*x^3 + 271965244*x^2 + 462505880*x -167023700);
163T[407,83]=(x^11 -24*x^10 -234*x^9 + 8909*x^8 -20039*x^7 -775708*x^6 + 4154616*x^5 + 17740352*x^4 -140165952*x^3 -1579008*x^2 + 1133511168*x -1510296576)*(x^12 + 14*x^11 -494*x^10 -7251*x^9 + 68043*x^8 + 1117168*x^7 -2420904*x^6 -60893728*x^5 -15437760*x^4 + 1293147264*x^3 + 1604039680*x^2 -8875956224*x -13854242816)*(x^4 -18*x^3 -138*x^2 + 2617*x + 1899)*(x^4 + 4*x^3 -254*x^2 -1967*x -331);
164T[407,89]=(x^4 + 18*x^3 + 50*x^2 -551*x -2451)*(x^4 + 6*x^3 -140*x^2 -191*x + 257)*(x^12 + 22*x^11 -332*x^10 -10263*x^9 -3939*x^8 + 1268912*x^7 + 5543424*x^6 -50637728*x^5 -340639584*x^4 + 256172544*x^3 + 4353909760*x^2 + 4581238016*x -1990625024)*(x^11 -4*x^10 -302*x^9 -83*x^8 + 20171*x^7 + 6326*x^6 -388964*x^5 + 348856*x^4 + 437136*x^3 -280800*x^2 -123072*x + 9600);
165T[407,97]=(x^11 -25*x^10 -310*x^9 + 13340*x^8 -57107*x^7 -1628170*x^6 + 19416852*x^5 -37452536*x^4 -504371792*x^3 + 3294826784*x^2 -7204302400*x + 4933959040)*(x^12 -63*x^11 + 1456*x^10 -11606*x^9 -93855*x^8 + 2592844*x^7 -17881832*x^6 -800256*x^5 + 697257184*x^4 -4142692416*x^3 + 10327272576*x^2 -9764287488*x -46308096)*(x^4 + 29*x^3 + 164*x^2 -660*x + 497)*(x^4 + 33*x^3 + 400*x^2 + 2102*x + 4013);
166
167T[408,2]=(x )^8;
168T[408,3]=(x + 1)^3*(x -1)^5;
169T[408,5]=(x -2)*(x -3)*(x + 3)*(x^2 + x -14)*(x^2 + x -4)*(x );
170T[408,7]=(x -2)*(x^2 + 2*x -16)*(x )*(x + 4)^2*(x -4)^2;
171T[408,11]=(x -4)*(x -1)*(x + 1)*(x^2 + 9*x + 16)*(x^2 + 3*x -12)*(x );
172T[408,13]=(x -6)*(x -3)*(x + 5)*(x -2)*(x^2 -x -14)*(x^2 + 3*x -2);
173T[408,17]=(x -1)^4*(x + 1)^4;
174T[408,19]=(x + 7)*(x -1)*(x^2 + 3*x -12)*(x^2 + 3*x -36)*(x -4)^2;
175T[408,23]=(x -2)*(x -1)*(x -7)*(x + 4)*(x^2 + 3*x -12)*(x^2 + 11*x + 26);
176T[408,29]=(x + 6)*(x -6)*(x^2 + 6*x -8)*(x )*(x -2)^3;
177T[408,31]=(x + 6)*(x + 2)*(x + 4)*(x -6)*(x^2 + 2*x -56)*(x^2 -68);
178T[408,37]=(x -10)*(x -8)*(x^2 + 6*x -48)*(x )*(x + 4)^3;
179T[408,41]=(x + 10)*(x -7)*(x -9)*(x + 6)*(x^2 -7*x -26)*(x^2 -9*x + 6);
180T[408,43]=(x^2 + 13*x + 28)*(x^2 -3*x -36)*(x + 1)^2*(x -4)^2;
181T[408,47]=(x + 4)*(x + 6)*(x + 8)*(x -10)*(x^2 + 10*x + 8)*(x^2 + 6*x -48);
182T[408,53]=(x + 10)^2*(x -6)^3*(x + 2)^3;
183T[408,59]=(x + 10)*(x + 6)*(x^2 + 2*x -152)*(x^2 -2*x -56)*(x + 4)^2;
184T[408,61]=(x + 14)*(x + 12)*(x -8)*(x^2 -10*x -32)*(x )*(x + 4)^2;
185T[408,67]=(x + 4)*(x -12)^2*(x + 12)^2*(x -4)^3;
186T[408,71]=(x -12)*(x + 2)*(x^2 + 2*x -152)*(x + 12)^2*(x + 4)^2;
187T[408,73]=(x + 10)*(x^2 -68)*(x + 14)^2*(x -10)^3;
188T[408,79]=(x + 4)*(x -6)*(x -10)*(x^2 + 2*x -56)*(x -2)^3;
189T[408,83]=(x + 12)*(x -4)*(x^2 -6*x -8)*(x^2 + 2*x -56)*(x + 14)^2;
190T[408,89]=(x + 6)*(x -4)*(x + 2)*(x -8)*(x^2 -10*x + 8)*(x^2 -10*x -32);
191T[408,97]=(x + 2)*(x + 6)*(x^2 + 2*x -56)*(x^2 + 6*x -8)*(x -12)^2;
192
193T[410,2]=(x -1)^7*(x + 1)^8;
194T[410,3]=(x^2 -2*x -2)*(x^2 + 2*x -4)*(x^2 -6)*(x^3 -8*x + 4)*(x -2)^2*(x + 2)^2*(x )^2;
195T[410,5]=(x -1)^7*(x + 1)^8;
196T[410,7]=(x -4)*(x^2 -2*x -16)*(x^2 + 2*x -4)*(x + 2)^4*(x -2)^6;
197T[410,11]=(x + 6)*(x -2)*(x^2 -24)*(x^2 -2*x -4)*(x^3 + 4*x^2 -16*x -48)*(x^2 -2*x -16)*(x )^4;
198T[410,13]=(x + 6)*(x^2 -4*x -8)*(x^3 -8*x^2 -8*x + 112)*(x + 2)^2*(x + 4)^3*(x -4)^4;
199T[410,17]=(x + 6)*(x -2)*(x -8)*(x^2 + 6*x -8)*(x^2 -6*x + 6)*(x^2 -4*x -2)*(x^3 + 2*x^2 -40*x -84)*(x^2 -20)*(x );
200T[410,19]=(x + 6)*(x + 2)*(x -8)*(x^2 + 10*x + 20)*(x^2 -2*x -16)*(x^3 -8*x^2 -8*x + 112)*(x^2 -4*x -8)*(x )^3;
201T[410,23]=(x + 4)*(x^2 -4*x -16)*(x^2 -12)*(x^3 -4*x^2 -16*x + 48)*(x + 6)^2*(x )^5;
202T[410,29]=(x + 2)*(x + 8)*(x + 6)*(x -6)*(x^2 -8*x + 10)*(x^2 + 6*x -18)*(x^2 -2*x -16)*(x^2 -12*x + 16)*(x^3 + 12*x^2 + 40*x + 36);
203T[410,31]=(x -8)*(x^2 -24)*(x^2 -4*x -8)*(x^2 + 12*x + 16)*(x^3 -8*x^2 -48*x + 288)*(x )^5;
204T[410,37]=(x -6)*(x -2)*(x -10)*(x^2 -24)*(x^3 + 2*x^2 -76*x -296)*(x + 2)^2*(x -8)^2*(x + 6)^3;
205T[410,41]=(x -1)^7*(x + 1)^8;
206T[410,43]=(x -8)*(x -4)*(x^2 + 8*x -8)*(x^2 -4*x -64)*(x^2 -4*x -104)*(x^3 -32*x + 32)*(x + 4)^4;
207T[410,47]=(x + 12)*(x + 6)*(x -2)*(x -6)*(x^2 -12*x + 12)*(x^2 -12)*(x^2 -2*x -16)*(x^3 + 6*x^2 -20*x -24)*(x^2 + 6*x -36);
208T[410,53]=(x + 10)*(x -2)*(x + 6)*(x^2 + 4*x -64)*(x^2 -48)*(x^2 + 8*x -8)*(x^3 -176*x + 48)*(x )*(x -4)^2;
209T[410,59]=(x -8)*(x + 4)*(x^2 + 12*x + 16)*(x^2 -4*x -20)*(x^3 + 8*x^2 -56*x -432)*(x^2 -4*x -64)*(x + 6)^2*(x -12)^2;
210T[410,61]=(x + 2)*(x -10)*(x + 10)*(x^2 + 4*x -92)*(x^2 + 4*x -76)*(x^3 -2*x^2 -116*x -344)*(x -2)^5;
211T[410,67]=(x -2)*(x -14)*(x^2 -10*x -50)*(x^2 -8*x + 10)*(x^2 -2*x -44)*(x^3 + 8*x^2 -48*x -388)*(x + 6)^2*(x + 8)^2;
212T[410,71]=(x -10)*(x + 12)*(x^2 + 12*x -32)*(x^2 -6*x -138)*(x^2 -4*x -146)*(x^3 + 14*x^2 + 8*x -324)*(x^2 + 6*x -116)*(x + 4)^2;
213T[410,73]=(x + 10)*(x -2)*(x^2 -12*x + 12)*(x^2 + 8*x -92)*(x^2 + 16*x + 44)*(x^3 -26*x^2 + 156*x + 72)*(x + 6)^4;
214T[410,79]=(x -4)*(x + 8)*(x + 4)*(x + 6)*(x^2 -18*x + 36)*(x^2 + 4*x -50)*(x^2 + 14*x + 22)*(x^3 + 2*x^2 -16*x + 4)*(x -8)^2;
215T[410,83]=(x + 12)*(x^2 + 16*x -16)*(x^2 -272)*(x^3 -8*x^2 -64*x + 384)*(x^2 -48)*(x )*(x + 4)^2*(x + 16)^2;
216T[410,89]=(x + 2)*(x -6)*(x^2 + 4*x -20)*(x^2 + 24*x + 132)*(x^2 -68)*(x^3 -6*x^2 -20*x + 24)*(x -10)^4;
217T[410,97]=(x -18)*(x + 4)*(x -12)*(x -2)*(x^2 + 14*x + 46)*(x^2 -6*x -144)*(x^2 + 12*x + 30)*(x^3 + 10*x^2 -8*x -44)*(x^2 + 16*x + 44);
218
219T[411,2]=(x^3 + 3*x^2 -3)*(x^3 -x^2 -2*x + 1)*(x^5 + x^4 -7*x^3 -10*x^2 + 1)*(x^9 -16*x^7 + x^6 + 82*x^5 -9*x^4 -141*x^3 + 18*x^2 + 52*x + 8)*(x -2)^3;
220T[411,3]=(x -1)^11*(x + 1)^12;
221T[411,5]=(x^3 + 6*x^2 + 9*x + 1)*(x^3 -2*x^2 -3*x + 5)*(x^3 + 2*x^2 -x -1)*(x^5 -6*x^4 + 2*x^3 + 29*x^2 -13*x -41)*(x^9 -6*x^8 -15*x^7 + 130*x^6 + x^5 -816*x^4 + 464*x^3 + 1608*x^2 -925*x -482);
222T[411,7]=(x^3 -13*x + 13)*(x^3 + 3*x^2 -4*x + 1)*(x^3 + 3*x^2 -3)*(x^5 + x^4 -9*x^3 -8*x^2 + 18*x + 13)*(x^9 -7*x^8 -18*x^7 + 212*x^6 -196*x^5 -1292*x^4 + 2254*x^3 + 1409*x^2 -3651*x + 584);
223T[411,11]=(x^3 + 9*x^2 + 24*x + 19)*(x^3 + 3*x^2 -4*x -13)*(x^3 -4*x^2 -12*x + 40)*(x^5 -x^4 -22*x^3 + 31*x^2 + 120*x -208)*(x^9 -7*x^8 -50*x^7 + 395*x^6 + 520*x^5 -6292*x^4 + 3112*x^3 + 22496*x^2 -23040*x -2048);
224T[411,13]=(x^3 + 11*x^2 + 38*x + 41)*(x^3 -2*x^2 -16*x -8)*(x^3 + 3*x^2 -6*x -17)*(x^5 + x^4 -54*x^3 + 33*x^2 + 784*x -1516)*(x^9 -7*x^8 -38*x^7 + 275*x^6 + 244*x^5 -2072*x^4 -856*x^3 + 2976*x^2 -160*x -320);
225T[411,17]=(x^3 + 6*x^2 -9*x -17)*(x^3 -52*x -104)*(x^3 -4*x^2 -11*x + 43)*(x^9 -55*x^7 -19*x^6 + 670*x^5 + 612*x^4 -1056*x^3 -752*x^2 + 320*x + 128)*(x^5 -4*x^4 -41*x^3 + 103*x^2 + 340*x + 200);
226T[411,19]=(x^3 + 4*x^2 -25*x -53)*(x^3 + 3*x^2 -46*x -139)*(x^3 + 3*x^2 -18*x + 17)*(x^5 + 5*x^4 -39*x^3 -112*x^2 + 308*x + 73)*(x^9 -11*x^8 -28*x^7 + 654*x^6 -1622*x^5 -6512*x^4 + 40232*x^3 -78157*x^2 + 65203*x -19804);
227T[411,23]=(x^3 + 3*x^2 -18*x -37)*(x^3 + 4*x^2 -51*x -235)*(x^3 -5*x^2 -22*x + 13)*(x^9 + 3*x^8 -56*x^7 -154*x^6 + 886*x^5 + 2024*x^4 -4370*x^3 -9267*x^2 + 4921*x + 10592)*(x^5 -13*x^4 -25*x^3 + 1054*x^2 -5190*x + 7669);
228T[411,29]=(x^3 + 12*x^2 + 45*x + 51)*(x^3 + 22*x^2 + 159*x + 377)*(x^3 -13*x -13)*(x^5 -22*x^4 + 156*x^3 -373*x^2 + 173*x + 217)*(x^9 -22*x^8 + 109*x^7 + 878*x^6 -11459*x^5 + 44348*x^4 -55116*x^3 -51724*x^2 + 139167*x -25378);
229T[411,31]=(x^3 -3*x^2 -6*x + 17)*(x^3 + 8*x^2 -48*x -320)*(x^3 + 3*x^2 -88*x -377)*(x^5 + 3*x^4 -58*x^3 + 35*x^2 + 260*x + 28)*(x^9 -15*x^8 + 20*x^7 + 541*x^6 -2020*x^5 -3052*x^4 + 21216*x^3 -22336*x^2 + 3328*x + 2048);
230T[411,37]=(x^3 + 9*x^2 + 24*x + 19)*(x^3 + 9*x^2 -64*x -449)*(x^3 + 4*x^2 -51*x -235)*(x^5 -x^4 -9*x^3 + 8*x^2 + 18*x -13)*(x^9 -27*x^8 + 254*x^7 -760*x^6 -2184*x^5 + 16078*x^4 -10026*x^3 -69071*x^2 + 53997*x + 110878);
231T[411,41]=(x^3 + 6*x^2 -63*x -267)*(x^3 + 4*x^2 -39*x -169)*(x^3 + 9*x^2 -25*x -25)*(x^5 -24*x^4 + 219*x^3 -937*x^2 + 1840*x -1268)*(x^9 -5*x^8 -218*x^7 + 337*x^6 + 16344*x^5 + 22602*x^4 -383155*x^3 -1295022*x^2 -74580*x + 2488984);
232T[411,43]=(x^3 -9*x^2 -57*x + 361)*(x^3 + 6*x^2 -40*x -200)*(x^3 + 5*x^2 -29*x -41)*(x^5 -3*x^4 -93*x^3 + 423*x^2 + 596*x -2452)*(x^9 -3*x^8 -167*x^7 + 843*x^6 + 5722*x^5 -37748*x^4 -9760*x^3 + 300576*x^2 -314976*x -11392);
233T[411,47]=(x^3 + 15*x^2 + 36*x -159)*(x^3 -17*x^2 + 52*x + 167)*(x^3 -18*x^2 + 69*x + 83)*(x^5 -x^4 -51*x^3 + 164*x^2 -124*x + 7)*(x^9 + 37*x^8 + 424*x^7 -16*x^6 -33296*x^5 -186464*x^4 + 300900*x^3 + 4982033*x^2 + 10521885*x -1043240);
234T[411,53]=(x^3 -147*x -637)*(x^3 -11*x^2 -185*x + 2075)*(x^3 -21*x + 17)*(x^5 -2*x^4 -201*x^3 + 583*x^2 + 5024*x + 4604)*(x^9 -x^8 -180*x^7 -221*x^6 + 9746*x^5 + 25840*x^4 -134387*x^3 -341930*x^2 + 521836*x + 405736);
235T[411,59]=(x^3 -4*x^2 -64*x -64)*(x^3 -6*x^2 -9*x + 27)*(x^3 + 6*x^2 -51*x -109)*(x^5 + 8*x^4 -125*x^3 -713*x^2 + 3292*x + 3116)*(x^9 + 4*x^8 -275*x^7 -725*x^6 + 23064*x^5 + 32252*x^4 -530448*x^3 -521920*x^2 + 1884160*x + 2210816);
236T[411,61]=(x^3 + 4*x^2 -51*x -235)*(x^3 + 25*x^2 + 171*x + 251)*(x^3 + 9*x^2 -21*x -53)*(x^9 -19*x^8 -67*x^7 + 2416*x^6 -794*x^5 -76849*x^4 -38487*x^3 + 374382*x^2 + 124915*x -502490)*(x^5 -17*x^4 -18*x^3 + 1650*x^2 -9519*x + 15839);
237T[411,67]=(x^3 -3*x^2 -24*x -1)*(x^3 -8*x^2 -204*x + 1880)*(x^3 + 5*x^2 -78*x -419)*(x^5 + 31*x^4 + 324*x^3 + 1297*x^2 + 1008*x -3008)*(x^9 + 7*x^8 -314*x^7 -3033*x^6 + 22312*x^5 + 323028*x^4 + 235960*x^3 -9096672*x^2 -39121280*x -48586240);
238T[411,71]=(x^3 + 27*x^2 + 168*x -71)*(x^3 + 3*x^2 -153*x -675)*(x^3 -15*x^2 -58*x + 631)*(x^5 -5*x^4 -162*x^3 + 835*x^2 + 5904*x -31616)*(x^9 + 2*x^8 -332*x^7 -737*x^6 + 27348*x^5 + 2375*x^4 -736489*x^3 + 1150720*x^2 + 4380608*x -9204736);
239T[411,73]=(x^3 -9*x^2 -144*x + 333)*(x^3 -5*x^2 -8*x + 41)*(x^3 -91*x -65)*(x^9 -25*x^8 + 94*x^7 + 2108*x^6 -21292*x^5 + 37322*x^4 + 361018*x^3 -2130513*x^2 + 4453861*x -3381566)*(x^5 + 5*x^4 -141*x^3 -744*x^2 + 1798*x + 1849);
240T[411,79]=(x^3 -4*x^2 -12*x + 40)*(x^3 + 18*x^2 -39*x -1303)*(x^3 -6*x^2 -45*x -1)*(x^5 + 22*x^4 + 95*x^3 -287*x^2 -728*x + 1444)*(x^9 -2*x^8 -291*x^7 + 547*x^6 + 29248*x^5 -54688*x^4 -1201256*x^3 + 2426544*x^2 + 16796832*x -42353408);
241T[411,83]=(x^3 + 12*x^2 -204*x -2312)*(x^3 -12*x^2 -36*x + 328)*(x^3 -2*x^2 -133*x + 265)*(x^9 + 44*x^8 + 516*x^7 -2197*x^6 -68759*x^5 -133989*x^4 + 2652568*x^3 + 8967780*x^2 -31367784*x -113136224)*(x^5 -14*x^4 -279*x^3 + 3496*x^2 + 11948*x -91288);
242T[411,89]=(x^3 -8*x^2 -135*x + 953)*(x^3 -10*x^2 + 3*x + 1)*(x^3 -12*x^2 -45*x + 19)*(x^5 + 4*x^4 -112*x^3 -855*x^2 -2023*x -1531)*(x^9 + 4*x^8 -591*x^7 -740*x^6 + 115919*x^5 -68126*x^4 -8030232*x^3 + 9286514*x^2 + 130024933*x + 53425654);
243T[411,97]=(x^3 + 8*x^2 -51*x -239)*(x^3 + 4*x^2 -116*x -40)*(x^3 -30*x^2 + 237*x -361)*(x^5 + 14*x^4 -71*x^3 -911*x^2 -248*x + 6404)*(x^9 + 2*x^8 -351*x^7 -519*x^6 + 27946*x^5 + 61624*x^4 -753272*x^3 -2183584*x^2 + 4839680*x + 15398080);
244
245T[412,2]=(x )^8;
246T[412,3]=(x^2 + 2*x -4)*(x^4 -2*x^3 -5*x^2 + 6*x + 4)*(x + 1)^2;
247T[412,5]=(x^2 + 2*x -4)*(x^2 + x -5)*(x^4 -3*x^3 -7*x^2 + 12*x -4);
248T[412,7]=(x^2 + 3*x + 1)*(x^2 -21)*(x^4 -5*x^3 + 4*x^2 + 5*x -1);
249T[412,11]=(x^2 + 3*x -3)*(x^4 -7*x^3 + 3*x^2 + 48*x -64)*(x + 2)^2;
250T[412,13]=(x^2 + 7*x + 7)*(x^2 + x -1)*(x^4 -19*x^2 + 89);
251T[412,17]=(x^2 + 9*x + 19)*(x^2 -7*x + 7)*(x^4 + 2*x^3 -17*x^2 -18*x + 1);
252T[412,19]=(x^2 -3*x -9)*(x^2 + 11*x + 25)*(x^4 -9*x^2 + 10*x -1);
253T[412,23]=(x^2 + 7*x + 11)*(x^4 -17*x^3 + 79*x^2 -48*x -164)*(x + 6)^2;
254T[412,29]=(x^2 + 3*x -9)*(x^2 + 6*x -12)*(x^4 -3*x^3 -87*x^2 -38*x + 956);
255T[412,31]=(x^2 + 8*x -5)*(x^4 + 4*x^3 -75*x^2 -358*x + 124)*(x -2)^2;
256T[412,37]=(x^2 + 10*x + 20)*(x^4 + 8*x^3 + 3*x^2 -12*x -4)*(x -5)^2;
257T[412,41]=(x^2 -17*x + 71)*(x^4 + 3*x^3 -17*x^2 -32*x + 16)*(x + 4)^2;
258T[412,43]=(x^2 + 8*x -5)*(x^2 -20)*(x^4 -10*x^3 -95*x^2 + 1400*x -4100);
259T[412,47]=(x^2 + 7*x + 7)*(x^2 -4*x -76)*(x^4 -9*x^3 -119*x^2 + 736*x + 916);
260T[412,53]=(x^2 + 12*x + 16)*(x^2 -3*x -129)*(x^4 -11*x^3 -25*x^2 + 242*x + 124);
261T[412,59]=(x^2 + 19*x + 89)*(x^2 -9*x -27)*(x^4 + 10*x^3 -29*x^2 -370*x -211);
262T[412,61]=(x^2 -11*x + 25)*(x^2 + 3*x -29)*(x^4 + 4*x^3 -53*x^2 -94*x + 71);
263T[412,67]=(x^2 -2*x -83)*(x^4 + 12*x^3 -65*x^2 -356*x -356)*(x + 2)^2;
264T[412,71]=(x^2 + 16*x + 44)*(x^2 -15*x + 51)*(x^4 -13*x^3 -101*x^2 + 978*x + 1636);
265T[412,73]=(x^2 -18*x + 76)*(x^2 + x -5)*(x^4 + 15*x^3 + 31*x^2 -30*x -76);
266T[412,79]=(x^2 + 3*x -255)*(x^2 -15*x -45)*(x^4 -69*x^2 -250*x -181);
267T[412,83]=(x^2 + 5*x -41)*(x^2 + 23*x + 121)*(x^4 -12*x^3 -137*x^2 + 2378*x -8189);
268T[412,89]=(x^2 -10*x -100)*(x^2 -22*x + 100)*(x^4 + 8*x^3 -12*x^2 -32*x + 16);
269T[412,97]=(x^2 -23*x + 131)*(x^2 + 14*x + 28)*(x^4 + 39*x^3 + 557*x^2 + 3426*x + 7556);
270
271T[413,2]=(x^2 -5)*(x^5 -5*x^3 -x^2 + 5*x + 1)*(x^5 -4*x^4 -3*x^3 + 29*x^2 -35*x + 11)*(x^9 -13*x^7 + x^6 + 54*x^5 -7*x^4 -75*x^3 + 9*x^2 + 17*x -3)*(x^5 + 2*x^4 -3*x^3 -5*x^2 + x + 1)*(x + 1)^3;
272T[413,3]=(x^2 + x -1)*(x^5 + 7*x^4 + 14*x^3 + 3*x^2 -9*x + 1)*(x^5 -7*x^4 + 8*x^3 + 33*x^2 -67*x + 13)*(x^3 -3*x^2 -x + 4)*(x^5 + 5*x^4 + 4*x^3 -7*x^2 -7*x + 1)*(x^9 -7*x^8 + 7*x^7 + 46*x^6 -94*x^5 -69*x^4 + 243*x^3 -32*x^2 -171*x + 73);
273T[413,5]=(x^2 -2*x -4)*(x^3 -16*x + 8)*(x^5 + 5*x^4 -x^3 -27*x^2 -24*x -1)*(x^5 + 3*x^4 -5*x^3 -5*x^2 + 6*x -1)*(x^9 -3*x^8 -25*x^7 + 77*x^6 + 188*x^5 -589*x^4 -460*x^3 + 1340*x^2 + 448*x -432)*(x^5 -x^4 -5*x^3 + 3*x^2 + 2*x -1);
274T[413,7]=(x -1)^14*(x + 1)^15;
275T[413,11]=(x^2 + 5*x + 5)*(x^3 -3*x^2 -x + 4)*(x^5 -x^4 -36*x^3 -15*x^2 + 199*x + 157)*(x^5 -9*x^4 + 129*x^2 -73*x -481)*(x^5 + 7*x^4 + 6*x^3 -31*x^2 -35*x + 25)*(x^9 -3*x^8 -47*x^7 + 164*x^6 + 492*x^5 -2085*x^4 + 417*x^3 + 2270*x^2 -113*x -423);
276T[413,13]=(x^2 -x -11)*(x^5 + x^4 -13*x^3 -15*x^2 + 42*x + 55)*(x^5 + 17*x^4 + 95*x^3 + 165*x^2 -78*x -139)*(x^3 + 3*x^2 -43*x -98)*(x^5 + 3*x^4 -21*x^3 -23*x^2 + 112*x -47)*(x^9 -13*x^8 + 22*x^7 + 416*x^6 -2398*x^5 + 2337*x^4 + 16559*x^3 -59020*x^2 + 75478*x -34703);
277T[413,17]=(x^5 + 3*x^4 -55*x^3 -176*x^2 + 343*x + 887)*(x^5 -11*x^4 -11*x^3 + 406*x^2 -745*x -1289)*(x^5 + x^4 -43*x^3 + 110*x^2 -37*x -69)*(x^9 -x^8 -55*x^7 + 88*x^6 + 635*x^5 -541*x^4 -2280*x^3 -280*x^2 + 688*x + 48)*(x + 6)^2*(x -2)^3;
278T[413,19]=(x^2 + 3*x + 1)*(x^3 -x^2 -15*x + 28)*(x^5 -4*x^4 -38*x^3 + 81*x^2 + 58*x -79)*(x^5 + 20*x^4 + 138*x^3 + 357*x^2 + 140*x -391)*(x^9 -14*x^8 + 17*x^7 + 511*x^6 -1775*x^5 -4800*x^4 + 22446*x^3 + 11800*x^2 -60806*x -46915)*(x^5 -46*x^3 -63*x^2 + 218*x -71);
279T[413,23]=(x^2 -15*x + 55)*(x^3 -x^2 -27*x + 64)*(x^5 + x^4 -73*x^3 + 9*x^2 + 798*x -209)*(x^5 + 5*x^4 -31*x^3 -97*x^2 + 276*x + 277)*(x^9 -7*x^8 -44*x^7 + 320*x^6 + 206*x^5 -2519*x^4 + 1459*x^3 + 714*x^2 -260*x + 9)*(x^5 + 5*x^4 -53*x^3 -411*x^2 -820*x -379);
280T[413,29]=(x^2 -x -61)*(x^3 -11*x^2 + x + 182)*(x^5 + 2*x^4 -41*x^3 + x^2 + 409*x -535)*(x^5 + 6*x^4 -17*x^3 -123*x^2 -119*x + 65)*(x^5 + 6*x^4 -41*x^3 -243*x^2 + 45*x + 773)*(x^9 + 20*x^8 + 78*x^7 -573*x^6 -3247*x^5 + 6190*x^4 + 33358*x^3 -36202*x^2 -62293*x -10635);
281T[413,31]=(x^2 -10*x + 20)*(x^3 + 2*x^2 -76*x -256)*(x^5 + 4*x^4 -56*x^3 -259*x^2 + 190*x + 1361)*(x^5 + 8*x^4 -60*x^3 -243*x^2 + 1660*x -2081)*(x^9 -16*x^8 + 62*x^7 + 191*x^6 -1686*x^5 + 1999*x^4 + 6904*x^3 -15476*x^2 -704*x + 13232)*(x^5 + 12*x^4 + 34*x^3 + 31*x^2 + 4*x -3);
282T[413,37]=(x^5 + 8*x^4 -104*x^3 -845*x^2 -1676*x -841)*(x^5 + 10*x^4 -185*x^2 -128*x + 901)*(x^3 + 2*x^2 -48*x -128)*(x^5 + 18*x^4 + 60*x^3 -371*x^2 -1298*x + 3187)*(x^9 -4*x^8 -168*x^7 + 721*x^6 + 6414*x^5 -23303*x^4 -53520*x^3 + 131040*x^2 + 140032*x + 18688)*(x -8)^2;
283T[413,41]=(x^2 -20)*(x^3 + 6*x^2 -52*x -56)*(x^5 -11*x^4 + 11*x^3 + 69*x^2 -52*x -1)*(x^5 + x^4 -171*x^3 -141*x^2 + 4372*x + 4931)*(x^9 -3*x^8 -137*x^7 + 113*x^6 + 5340*x^5 + 375*x^4 -68320*x^3 -35128*x^2 + 184832*x -49872)*(x^5 -7*x^4 -71*x^3 + 679*x^2 -1156*x -1069);
284T[413,43]=(x^2 -9*x -41)*(x^3 -23*x^2 + 161*x -356)*(x^5 -15*x^4 + 10*x^3 + 762*x^2 -3947*x + 5717)*(x^5 + 15*x^4 -74*x^3 -1334*x^2 + 1001*x + 13991)*(x^9 -19*x^8 + 65*x^7 + 579*x^6 -2936*x^5 -6614*x^4 + 32337*x^3 + 42687*x^2 -72219*x -60665)*(x^5 + 31*x^4 + 330*x^3 + 1382*x^2 + 1717*x -1061);
285T[413,47]=(x^2 -6*x -36)*(x^3 + 10*x^2 + 12*x -64)*(x^5 + 3*x^4 -175*x^3 -295*x^2 + 5002*x + 9211)*(x^5 + x^4 -55*x^3 + 59*x^2 + 398*x -237)*(x^9 -9*x^8 -177*x^7 + 1557*x^6 + 4708*x^5 -51383*x^4 + 57244*x^3 + 235244*x^2 -562096*x + 321360)*(x^5 -7*x^4 -93*x^3 + 795*x^2 + 84*x -7667);
286T[413,53]=(x^2 -13*x + 31)*(x^3 + 9*x^2 -19*x -58)*(x^5 -x^4 -265*x^3 -223*x^2 + 16542*x + 59275)*(x^5 -9*x^4 -73*x^3 + 625*x^2 + 266*x -4949)*(x^5 -9*x^4 -41*x^3 + 381*x^2 + 346*x -3389)*(x^9 + 9*x^8 -136*x^7 -1130*x^6 + 5888*x^5 + 42767*x^4 -102371*x^3 -495462*x^2 + 692104*x -123693);
287T[413,59]=(x + 1)^14*(x -1)^15;
288T[413,61]=(x^5 + 24*x^4 + 90*x^3 -1431*x^2 -10368*x -10449)*(x^5 + 28*x^4 + 120*x^3 -2159*x^2 -13558*x + 23825)*(x^3 + 2*x^2 -84*x -296)*(x^5 -6*x^4 -200*x^3 + 819*x^2 + 5246*x -10617)*(x^9 -22*x^8 + 86*x^7 + 823*x^6 -5604*x^5 -1343*x^4 + 60364*x^3 -73312*x^2 -73968*x + 58288)*(x + 6)^2;
289T[413,67]=(x^2 -17*x + 61)*(x^5 + 24*x^4 + 99*x^3 -1034*x^2 -6572*x -6205)*(x^5 -32*x^4 + 285*x^3 -120*x^2 -5970*x + 6929)*(x^3 + 3*x^2 -x -4)*(x^5 + 28*x^4 + 235*x^3 + 306*x^2 -3106*x -6173)*(x^9 -22*x^8 -74*x^7 + 5134*x^6 -32596*x^5 -169047*x^4 + 2658429*x^3 -10438647*x^2 + 14830836*x -6935357);
290T[413,71]=(x^3 -8*x^2 -80*x + 128)*(x^5 -15*x^4 -5*x^3 + 399*x^2 -182*x -29)*(x^5 + 13*x^4 -37*x^3 -497*x^2 + 1486*x -185)*(x^9 + 21*x^8 -177*x^7 -5637*x^6 -3162*x^5 + 419279*x^4 + 1057416*x^3 -8835648*x^2 -15064576*x + 54300672)*(x^5 + 9*x^4 -97*x^3 -293*x^2 + 1658*x + 379)*(x -4)^2;
291T[413,73]=(x^2 + 27*x + 181)*(x^5 + 8*x^4 -131*x^3 -933*x^2 -17*x + 3617)*(x^5 -24*x^4 + 205*x^3 -779*x^2 + 1353*x -877)*(x^3 -11*x^2 -135*x + 1154)*(x^5 -209*x^3 + 405*x^2 + 7545*x -7639)*(x^9 -10*x^8 -428*x^7 + 3605*x^6 + 63507*x^5 -410668*x^4 -3865058*x^3 + 15240244*x^2 + 80406737*x -57490187);
292T[413,79]=(x^2 -6*x -116)*(x^5 + 9*x^4 -263*x^3 -1995*x^2 + 8734*x -877)*(x^5 + x^4 -159*x^3 -71*x^2 + 5822*x -3313)*(x^3 + 2*x^2 -108*x -512)*(x^5 + 9*x^4 -159*x^3 -459*x^2 + 5166*x -2309)*(x^9 -11*x^8 -351*x^7 + 3969*x^6 + 33158*x^5 -404237*x^4 -379388*x^3 + 8266172*x^2 -10164512*x + 3173200);
293T[413,83]=(x^3 -4*x^2 -20*x + 16)*(x^5 + 24*x^4 + 161*x^3 + 169*x^2 -657*x + 289)*(x^5 + 24*x^4 + 207*x^3 + 745*x^2 + 889*x -97)*(x^5 -2*x^4 -109*x^3 + 331*x^2 + 1625*x -2293)*(x^9 -14*x^8 -343*x^7 + 3515*x^6 + 39355*x^5 -166023*x^4 -1501476*x^3 + 1056288*x^2 + 10374688*x -5316816)*(x + 6)^2;
294T[413,89]=(x^2 + x -31)*(x^5 -4*x^4 -136*x^3 + 871*x^2 -1464*x + 731)*(x^5 + 8*x^4 -190*x^3 -1433*x^2 + 8922*x + 64957)*(x^3 + 23*x^2 + 145*x + 202)*(x^5 -10*x^4 -126*x^3 + 1945*x^2 -7550*x + 7683)*(x^9 + 8*x^8 -327*x^7 -2133*x^6 + 26005*x^5 + 139376*x^4 -107454*x^3 -475080*x^2 -173984*x + 72195);
295T[413,97]=(x^2 + 19*x + 89)*(x^3 + 9*x^2 -187*x -1214)*(x^5 -2*x^4 -141*x^3 -129*x^2 + 4863*x + 13865)*(x^5 -20*x^4 -141*x^3 + 2877*x^2 + 9517*x -50809)*(x^5 + 10*x^4 -161*x^3 -2241*x^2 -8287*x -9203)*(x^9 -26*x^8 -400*x^7 + 15767*x^6 -26709*x^5 -2575182*x^4 + 19593598*x^3 + 52231694*x^2 -746893479*x + 901594349);
296
297T[414,2]=(x -1)^5*(x + 1)^5;
298T[414,3]=(x )^10;
299T[414,5]=(x + 2)*(x -2)*(x + 4)*(x^2 -2*x -4)*(x^2 -2*x -6)*(x^2 + 2*x -6)*(x );
300T[414,7]=(x + 4)*(x + 2)*(x^2 -20)*(x )*(x -2)^5;
301T[414,11]=(x + 2)*(x -6)*(x^2 -6*x + 4)*(x^2 + 2*x -6)*(x^2 -2*x -6)*(x )^2;
302T[414,13]=(x -2)*(x^2 -20)*(x^2 -28)^2*(x + 2)^3;
303T[414,17]=(x -2)*(x + 2)*(x^2 -4*x -24)*(x^2 + 4*x -24)*(x -4)^2*(x )^2;
304T[414,19]=(x + 2)*(x -2)*(x + 8)*(x^2 + 2*x -44)*(x )*(x^2 -6*x + 2)^2;
305T[414,23]=(x -1)^5*(x + 1)^5;
306T[414,29]=(x + 2)*(x + 6)*(x -6)*(x -2)*(x^2 -8*x -12)*(x^2 -20)*(x^2 + 8*x -12);
307T[414,31]=(x -8)*(x + 8)*(x + 4)*(x^2 -4*x -16)*(x )*(x^2 -8*x -12)^2;
308T[414,37]=(x + 4)*(x -2)*(x + 10)*(x^2 -18*x + 76)*(x )*(x^2 + 2*x -62)^2;
309T[414,41]=(x -2)^2*(x + 10)^2*(x + 6)^3*(x -6)^3;
310T[414,43]=(x -8)*(x -10)*(x + 12)*(x -2)*(x^2 + 14*x + 44)*(x^2 -6*x + 2)^2;
311T[414,47]=(x + 8)*(x -8)*(x + 6)^2*(x -6)^2*(x + 4)^2*(x )^2;
312T[414,53]=(x -4)*(x + 12)*(x^2 + 2*x -6)*(x^2 + 6*x + 4)*(x^2 -2*x -6)*(x + 2)^2;
313T[414,59]=(x -12)*(x -4)*(x^2 -80)*(x + 12)^2*(x )^4;
314T[414,61]=(x + 10)*(x -4)*(x + 8)*(x -2)*(x^2 -6*x + 4)*(x^2 -6*x + 2)^2;
315T[414,67]=(x -8)*(x + 10)*(x + 12)*(x -14)*(x^2 -6*x -36)*(x^2 + 14*x -14)^2;
316T[414,71]=(x^2 -80)*(x -6)^2*(x + 6)^2*(x )^4;
317T[414,73]=(x + 6)*(x -2)*(x -6)*(x + 10)*(x^2 -20)*(x^2 + 4*x -24)^2;
318T[414,79]=(x + 6)*(x + 10)*(x -8)*(x + 12)*(x^2 -20)*(x^2 + 4*x -108)^2;
319T[414,83]=(x -16)*(x^2 -22*x + 114)*(x^2 + 22*x + 114)*(x^2 + 22*x + 116)*(x )*(x + 14)^2;
320T[414,89]=(x + 12)*(x + 18)*(x -6)*(x^2 -12*x + 16)*(x )^5;
321T[414,97]=(x -10)*(x + 6)*(x -6)*(x + 10)*(x^2 + 8*x -4)*(x^2 -8*x -12)^2;
322
323T[415,2]=(x -1)*(x^2 + x -1)*(x^6 -2*x^5 -5*x^4 + 9*x^3 + 5*x^2 -6*x -1)*(x^7 + 3*x^6 -6*x^5 -19*x^4 + 9*x^3 + 28*x^2 -4*x -8)*(x^11 -20*x^9 -x^8 + 146*x^7 + 15*x^6 -464*x^5 -76*x^4 + 567*x^3 + 136*x^2 -100*x -8);
324T[415,3]=(x -3)*(x^2 + x -1)*(x^6 -3*x^5 -9*x^4 + 26*x^3 + 16*x^2 -48*x + 16)*(x^7 + 5*x^6 + x^5 -21*x^4 -10*x^3 + 23*x^2 -2*x -1)*(x^11 -27*x^9 + 4*x^8 + 258*x^7 -71*x^6 -1041*x^5 + 362*x^4 + 1712*x^3 -448*x^2 -1008*x + 64);
325T[415,5]=(x + 1)^13*(x -1)^14;
326T[415,7]=(x -1)*(x^2 -5)*(x^6 -15*x^4 -2*x^3 + 52*x^2 + 8*x -16)*(x^7 + 6*x^6 + x^5 -41*x^4 -51*x^3 + 10*x^2 + 9*x + 1)*(x^11 + 3*x^10 -50*x^9 -97*x^8 + 968*x^7 + 664*x^6 -8499*x^5 + 3974*x^4 + 25460*x^3 -34872*x^2 + 10640*x + 1024);
327T[415,11]=(x -3)*(x^6 -4*x^5 -27*x^4 + 108*x^3 + 9*x^2 -256*x + 92)*(x^7 + 2*x^6 -48*x^5 -83*x^4 + 617*x^3 + 907*x^2 -1276*x -508)*(x^11 + x^10 -76*x^9 -49*x^8 + 1991*x^7 + 67*x^6 -21282*x^5 + 19366*x^4 + 75983*x^3 -162888*x^2 + 113756*x -26896)*(x + 2)^2;
328T[415,13]=(x + 6)*(x^2 + 3*x + 1)*(x^6 -7*x^5 -4*x^4 + 29*x^3 -4*x^2 -7*x -1)*(x^7 + 5*x^6 -39*x^5 -156*x^4 + 308*x^3 + 656*x^2 -832*x -256)*(x^11 -x^10 -88*x^9 + 43*x^8 + 2724*x^7 + 615*x^6 -36217*x^5 -34976*x^4 + 170244*x^3 + 283536*x^2 + 56960*x -23296);
329T[415,17]=(x + 7)*(x^2 + 7*x + 11)*(x^6 -21*x^5 + 165*x^4 -608*x^3 + 1096*x^2 -904*x + 272)*(x^7 + 25*x^6 + 245*x^5 + 1177*x^4 + 2702*x^3 + 1693*x^2 -3530*x -4729)*(x^11 -28*x^10 + 277*x^9 -916*x^8 -2084*x^7 + 17999*x^6 -13283*x^5 -66250*x^4 + 44624*x^3 + 11768*x^2 -3968*x + 224);
330T[415,19]=(x -2)*(x^2 + 4*x -1)*(x^6 -2*x^5 -51*x^4 + 296*x^2 + 56*x -368)*(x^7 -6*x^6 -61*x^5 + 370*x^4 + 1196*x^3 -7360*x^2 -7616*x + 47648)*(x^11 + 2*x^10 -95*x^9 + 3036*x^7 -5136*x^6 -28544*x^5 + 96032*x^4 -82176*x^3 -27392*x^2 + 69888*x -25600);
331T[415,23]=(x -4)*(x^2 + 6*x -11)*(x^6 -8*x^5 + 3*x^4 + 116*x^3 -300*x^2 + 144*x + 112)*(x^7 + 9*x^6 -10*x^5 -114*x^4 + 153*x^3 + 169*x^2 -224*x -16)*(x^11 -x^10 -162*x^9 + 90*x^8 + 9109*x^7 -173*x^6 -214052*x^5 -138684*x^4 + 1920752*x^3 + 2544368*x^2 -2366528*x -2873344);
332T[415,29]=(x + 7)*(x^2 + 8*x + 11)*(x^6 -10*x^5 -26*x^4 + 348*x^3 + 146*x^2 -2570*x + 1819)*(x^7 + 2*x^6 -175*x^5 -189*x^4 + 8645*x^3 -2354*x^2 -120863*x + 205301)*(x^11 -21*x^10 + 35*x^9 + 1764*x^8 -9155*x^7 -40772*x^6 + 336913*x^5 + 42993*x^4 -3895185*x^3 + 5060034*x^2 + 9700139*x -16787050);
333T[415,31]=(x -5)*(x^2 + 5*x -5)*(x^6 + 13*x^5 -20*x^4 -583*x^3 -768*x^2 + 5449*x + 11491)*(x^7 -x^6 -183*x^5 -175*x^4 + 11000*x^3 + 26035*x^2 -212624*x -706421)*(x^11 -4*x^10 -242*x^9 + 258*x^8 + 22992*x^7 + 40927*x^6 -928960*x^5 -4147265*x^4 + 8084095*x^3 + 91859073*x^2 + 220945137*x + 178968640);
334T[415,37]=(x + 7)*(x^2 + 5*x -5)*(x^6 -x^5 -93*x^4 -134*x^3 + 2260*x^2 + 8440*x + 8176)*(x^11 + 10*x^10 -63*x^9 -712*x^8 -582*x^7 + 10467*x^6 + 39467*x^5 + 53160*x^4 + 17416*x^3 -18272*x^2 -11072*x + 224)*(x^7 + 13*x^6 -11*x^5 -429*x^4 -494*x^3 + 2803*x^2 + 3846*x -433);
335T[415,41]=(x -6)*(x^6 -10*x^5 -61*x^4 + 666*x^3 -103*x^2 -2108*x + 1424)*(x^7 + 15*x^6 -17*x^5 -1623*x^4 -12852*x^3 -45548*x^2 -77808*x -51904)*(x^11 -39*x^10 + 432*x^9 + 1258*x^8 -51490*x^7 + 206096*x^6 + 1180897*x^5 -7765523*x^4 -8064948*x^3 + 88079132*x^2 + 11575136*x -306688256)*(x + 12)^2;
336T[415,43]=(x -4)*(x^2 -13*x + 31)*(x^6 + 3*x^5 -90*x^4 -181*x^3 + 1606*x^2 + 4203*x + 2581)*(x^7 + 5*x^6 -121*x^5 -532*x^4 + 3516*x^3 + 15032*x^2 + 2016*x -16768)*(x^11 + 13*x^10 -190*x^9 -2507*x^8 + 12798*x^7 + 152341*x^6 -521755*x^5 -3604720*x^4 + 13091484*x^3 + 21621128*x^2 -120891232*x + 114398720);
337T[415,47]=(x + 4)*(x^2 -10*x -20)*(x^6 -14*x^5 -77*x^4 + 1644*x^3 -5853*x^2 + 7182*x -2876)*(x^7 + 12*x^6 -72*x^5 -1040*x^4 + 912*x^3 + 19552*x^2 -6784*x + 512)*(x^11 -8*x^10 -213*x^9 + 1066*x^8 + 17227*x^7 -33564*x^6 -568536*x^5 -162160*x^4 + 5293904*x^3 + 6602784*x^2 + 2454272*x + 262144);
338T[415,53]=(x + 10)*(x^2 -x -101)*(x^6 -9*x^5 -202*x^4 + 1939*x^3 + 6610*x^2 -80981*x + 130229)*(x^7 + 31*x^6 + 337*x^5 + 1386*x^4 -260*x^3 -18480*x^2 -50336*x -42592)*(x^11 -21*x^10 -20*x^9 + 2453*x^8 -8132*x^7 -44675*x^6 + 81791*x^5 + 251446*x^4 + 30068*x^3 -102656*x^2 -27808*x + 2720);
339T[415,59]=(x + 3)*(x^2 + 8*x -29)*(x^6 -20*x^5 + 104*x^4 + 192*x^3 -2440*x^2 + 1664*x + 10487)*(x^7 + 14*x^6 -121*x^5 -2679*x^4 -8859*x^3 + 42778*x^2 + 283227*x + 401671)*(x^11 -5*x^10 -237*x^9 + 1318*x^8 + 16783*x^7 -97176*x^6 -391145*x^5 + 2470761*x^4 + 638297*x^3 -15360362*x^2 + 18991105*x -6278092);
340T[415,61]=(x -5)*(x^2 + 3*x + 1)*(x^6 + 13*x^5 -86*x^4 -1131*x^3 + 1974*x^2 + 17073*x + 5869)*(x^7 -7*x^6 -343*x^5 + 1425*x^4 + 38852*x^3 -44403*x^2 -1385148*x -1496441)*(x^11 -14*x^10 -210*x^9 + 3530*x^8 + 866*x^7 -134727*x^6 + 154908*x^5 + 779017*x^4 -143829*x^3 -1271243*x^2 -760009*x -101918);
341T[415,67]=(x -2)*(x^2 -2*x -19)*(x^6 -16*x^5 -42*x^4 + 1336*x^3 -1844*x^2 -22958*x + 58471)*(x^7 -10*x^6 -247*x^5 + 2704*x^4 + 15816*x^3 -206872*x^2 -74480*x + 3275872)*(x^11 + 42*x^10 + 570*x^9 + 1000*x^8 -40524*x^7 -295738*x^6 + 179735*x^5 + 8176838*x^4 + 22420348*x^3 -21939328*x^2 -152952528*x -143897920);
342T[415,71]=(x -14)*(x^2 -5*x -55)*(x^6 -5*x^5 -247*x^4 + 1422*x^3 + 13348*x^2 -97768*x + 142288)*(x^7 -9*x^6 -321*x^5 + 1362*x^4 + 31896*x^3 + 18784*x^2 -335248*x + 337312)*(x^11 -3*x^10 -211*x^9 + 370*x^8 + 14036*x^7 -15688*x^6 -326912*x^5 + 531232*x^4 + 2392256*x^3 -6632320*x^2 + 4480768*x -501760);
343T[415,73]=(x + 4)*(x^2 -23*x + 131)*(x^6 -3*x^5 -258*x^4 + 933*x^3 + 16894*x^2 -37595*x -369203)*(x^7 + 15*x^6 -241*x^5 -2756*x^4 + 26996*x^3 + 108312*x^2 -1357216*x + 2865536)*(x^11 -3*x^10 -364*x^9 + 839*x^8 + 40392*x^7 -60921*x^6 -1410761*x^5 + 623042*x^4 + 6195844*x^3 + 401264*x^2 -6145040*x -1549568);
344T[415,79]=(x + 14)*(x^6 -2*x^5 -141*x^4 + 530*x^3 + 4000*x^2 -21184*x + 25072)*(x^7 -6*x^6 -243*x^5 + 1632*x^4 + 9052*x^3 -81376*x^2 + 134080*x -49408)*(x^11 + 20*x^10 -137*x^9 -3996*x^8 -2332*x^7 + 220048*x^6 + 576528*x^5 -3163168*x^4 -9064576*x^3 + 8117248*x^2 + 30394368*x + 16744448)*(x -1)^2;
345T[415,83]=(x -1)^8*(x + 1)^19;
346T[415,89]=(x -12)*(x^2 -x -151)*(x^6 -45*x^5 + 513*x^4 + 3438*x^3 -94992*x^2 + 440752*x -27568)*(x^7 + 37*x^6 + 253*x^5 -6404*x^4 -125148*x^3 -849688*x^2 -2462816*x -2454656)*(x^11 -37*x^10 + 407*x^9 + 200*x^8 -32312*x^7 + 211592*x^6 -437984*x^5 -333120*x^4 + 2138944*x^3 -1148672*x^2 -2184960*x + 1570816);
347T[415,97]=(x -8)*(x^11 + 2*x^10 -688*x^9 -3004*x^8 + 172046*x^7 + 1098484*x^6 -17836089*x^5 -151311508*x^4 + 521162956*x^3 + 7028557528*x^2 + 14344573456*x + 5595205504)*(x^6 -22*x^5 + 60*x^4 + 1392*x^3 -8714*x^2 + 7652*x + 10939)*(x^7 + 20*x^6 -63*x^5 -2006*x^4 + 2392*x^3 + 56312*x^2 -69376*x -303104)*(x -3)^2;
348
349T[416,2]=(x )^12;
350T[416,3]=(x -1)*(x + 1)*(x^2 -x -4)*(x^2 -5)*(x^2 + x -4)*(x^4 -13*x^2 + 32);
351T[416,5]=(x -3)^2*(x -1)^2*(x^2 + x -10)^2*(x^2 + 3*x -2)^2;
352T[416,7]=(x + 3)*(x -3)*(x^2 -3*x -2)*(x^2 + 3*x -2)*(x^2 -5)*(x^4 -29*x^2 +