-- eta relations --
g1:=6*e1^7*e5^4*e15^3-6*e1^9*e3^3*e9*e45-54*e1^6*e3^3*e9^4*e45-162*e1^3*e3^3*e9^7*e45+42*e1^9*e3*e9*e15^2*e45+294*e1^6*e5^3*e9*e15^3*e45+498*e1^5*e3^2*e5^2*e9^2*e15*e45^2+684*e1^7*e3^2*e5*e15*e45^3+2658*e1^7*e5*e15^3*e45^3-750*e1*e5^7*e15^3*e45^3+10242*e1^6*e3^2*e9*e15*e45^4+20802*e1^6*e9*e15^3*e45^4+38118*e1^2*e3^3*e5^2*e9^2*e45^5-40740*e1^4*e3^3*e5*e45^6+27936*e1*e3^3*e5*e9^3*e45^6-165425*e1*e3^2*e5^4*e15*e45^6-93445*e1^4*e3*e5*e15^2*e45^6+561615*e1*e3*e5*e9^3*e15^2*e45^6-334500*e1*e5^4*e15^3*e45^6-60228*e1^3*e3^3*e9*e45^7+4374*e3^3*e9^4*e45^7-57375*e3^2*e5^3*e9*e15*e45^7+200955*e1^3*e3*e9*e15^2*e45^7-609525*e3*e9^4*e15^2*e45^7+983250*e5^3*e9*e15^3*e45^7-2189775*e1*e3^2*e5*e15*e45^9-2970000*e1*e5*e15^3*e45^9-2261925*e3^2*e9*e15*e45^10;
g2:=e1^9*e9^3+9*e1^6*e9^6+27*e1^3*e9^9-e1^7*e3^3*e5*e15-7*e1^7*e3*e5*e15^3-35*e1^6*e3^3*e9*e15*e45-96*e1^6*e3*e9*e15^3*e45-247*e1^4*e5^4*e9^2*e45^2-195*e1^6*e5^3*e45^3-223*e1^4*e3^2*e5*e15^2*e45^3+800*e1^4*e5*e15^4*e45^3-798*e1^5*e5^2*e9*e45^4-693*e1^3*e3^2*e9*e15^2*e45^4+1125*e1^3*e9*e15^4*e45^4+1620*e9^4*e15^4*e45^4-3429*e1^4*e5*e9^2*e45^5-2025*e1*e5*e9^5*e45^5-273*e1^6*e45^6-1647*e1^3*e9^3*e45^6-729*e9^6*e45^6-855*e1*e3^3*e5*e15*e45^6-2025*e1*e3*e5*e15^3*e45^6-4455*e3^3*e9*e15*e45^7-6075*e3*e9*e15^3*e45^7;
g3:=2*e1^7*e5*e9^2*e15^2-2*e1^9*e3^2*e45-18*e1^6*e3^2*e9^3*e45-54*e1^3*e3^2*e9^6*e45+14*e1^9*e15^2*e45+98*e1^4*e3^3*e5*e15^3*e45-28*e1^5*e3*e5^2*e9*e15*e45^2-70*e1^3*e3^3*e9*e15^3*e45^2+660*e1^4*e3*e5*e9^2*e15*e45^3+386*e1^6*e3*e15*e45^4+1124*e1^3*e5^3*e15^2*e45^4-14370*e1*e5*e15^6*e45^4-18*e1^2*e3^2*e5^2*e9*e45^5+11754*e1^2*e5^2*e9*e15^2*e45^5+3432*e3^2*e9*e15^4*e45^5+12834*e1*e3^2*e5*e9^2*e45^6+19002*e1*e5*e9^2*e15^2*e45^6-7254*e1^3*e3^2*e45^7+1458*e3^2*e9^3*e45^7-26015*e3*e5^3*e15*e45^7+8645*e1^3*e15^2*e45^7+34101*e9^3*e15^2*e45^7-170505*e3*e15*e45^10;
g4:=e15^12-e5^9*e45^3-9*e5^6*e45^6-27*e5^3*e45^9;
g5:=5*e1^4*e5^4*e9^2*e15-5*e1^9*e3*e45-45*e1^6*e3*e9^3*e45-135*e1^3*e3*e9^6*e45+20*e1^6*e5^3*e15*e45+110*e1^4*e3^2*e5*e15^3*e45-100*e1^4*e5*e15^5*e45+255*e1^5*e5^2*e9*e15*e45^2+480*e1^3*e3^2*e9*e15^3*e45^2+345*e1^4*e5*e9^2*e15*e45^3-345*e1^6*e15*e45^4+3132*e9^6*e15*e45^4-465*e1*e3^3*e5*e15^2*e45^4-3750*e1*e3*e5*e15^4*e45^4+1503*e1^2*e3*e5^2*e9*e45^5-234*e3^3*e9*e15^2*e45^5-12465*e3*e9*e15^4*e45^5+4023*e1*e3*e5*e9^2*e45^6+540*e1^3*e3*e45^7+6777*e3*e9^3*e45^7;
g6:=11*e1^5*e3*e5^2*e15^3-11*e1^9*e9*e45-99*e1^6*e9^4*e45-297*e1^3*e9^7*e45+55*e1^4*e3^3*e5*e9*e15*e45+165*e1^4*e3*e5*e9*e15^3*e45+319*e1^3*e3^3*e9^2*e15*e45^2+40*e5^3*e9^2*e15^4*e45^2+462*e1^4*e5^4*e45^3+411*e1^2*e3^2*e5^2*e15^2*e45^3-10175*e15^8*e45^3+690*e1^3*e5^3*e9*e45^4-1666*e1*e3^2*e5*e9*e15^2*e45^4+13400*e1*e5*e9*e15^4*e45^4-1239*e1^2*e5^2*e9^2*e45^5+8892*e3^2*e9^2*e15^2*e45^5+13860*e9^2*e15^4*e45^5+1327*e1^4*e5*e45^6-5562*e1*e5*e9^3*e45^6+1689*e1^3*e9*e45^7+8019*e9^4*e45^7;
g7:=10*e1^3*e15^8-10*e1^5*e5^2*e9^2*e45^2-20*e1^7*e5*e45^3-50*e1*e5^7*e45^3+783*e1*e5*e9^6*e45^3-40*e1^2*e3^3*e5^2*e15*e45^3-520*e1^2*e3*e5^2*e15^3*e45^3+420*e3^3*e15^5*e45^3-63*e1^6*e9*e45^4+405*e5^6*e9*e45^4-720*e1^3*e9^4*e45^4-840*e1*e3^3*e5*e9*e15*e45^4-3270*e1*e3*e5*e9*e15^3*e45^4-2160*e3^3*e9^2*e15*e45^5-450*e1*e5^4*e45^6+2295*e1*e5*e45^9;
g8:=e1^2*e3^3*e5^2*e9^2*e15-e1^9*e45-9*e1^6*e9^3*e45-27*e1^3*e9^6*e45+2*e1^4*e3^3*e5*e15*e45+9*e1^4*e3*e5*e15^3*e45+21*e1^3*e3^3*e9*e15*e45^2+28*e1^3*e3*e9*e15^3*e45^2-125*e5^3*e9*e15^4*e45^2+129*e1*e5^4*e9^2*e45^3+176*e1^3*e5^3*e45^4+480*e1*e3^2*e5*e15^2*e45^4-30*e1*e5*e15^4*e45^4+525*e1^2*e5^2*e9*e45^5+837*e3^2*e9*e15^2*e45^5-405*e9*e15^4*e45^5+2160*e1*e5*e9^2*e45^6+72*e1^3*e45^7+729*e9^3*e45^7;
g9:=40*e5^8*e9-40*e1^4*e3^2*e9*e15^2-160*e1^5*e5*e9^2*e45-441*e1^2*e5*e9^5*e45-390*e3^3*e5^2*e9^2*e15*e45-150*e3*e5^2*e9^2*e15^3*e45+111*e1^7*e45^2+480*e1^4*e9^3*e45^2+605*e1^2*e3^3*e5*e15*e45^2+2855*e1^2*e3*e5*e15^3*e45^2+225*e5^5*e9*e45^3+1665*e1*e3^3*e9*e15*e45^3+4815*e1*e3*e9*e15^3*e45^3+360*e1*e5^3*e45^5+2025*e1*e45^8;
g10:=9*e1^3*e5*e9^5-10*e1*e3^3*e5^2*e9^2*e15+e1^8*e45+25*e1^3*e3^3*e5*e15*e45+45*e1^3*e3*e5*e15^3*e45-20*e1*e5^5*e9*e45^2+80*e1^2*e3^3*e9*e15*e45^2+190*e1^2*e3*e9*e15^3*e45^2+160*e1^2*e5^3*e45^4+120*e3^2*e5*e15^2*e45^4-300*e5*e15^4*e45^4+60*e1*e5^2*e9*e45^5+540*e5*e9^2*e45^6+720*e1^2*e45^7;
g11:=9*e1^2*e5*e9^6-10*e1^3*e3*e5^2*e15^3+e1^7*e9*e45-5*e1^2*e3^3*e5*e9*e15*e45-15*e1^2*e3*e5*e9*e15^3*e45+85*e5^5*e9^2*e45^2-105*e1*e3^3*e9^2*e15*e45^2-15*e1*e3*e9^2*e15^3*e45^2-40*e1^2*e5^4*e45^3-200*e3^2*e5^2*e15^2*e45^3-50*e5^2*e15^4*e45^3-360*e1*e5^3*e9*e45^4+90*e5^2*e9^2*e45^5+120*e1^2*e5*e45^6-945*e1*e9*e45^7;
g12:=54*e1*e5*e9^7-60*e1^2*e3*e5^2*e9*e15^3+6*e1^6*e9^2*e45-30*e1*e3^3*e5*e9^2*e15*e45-90*e1^3*e3^3*e15*e45^2-325*e3^2*e5^3*e15^2*e45^2+25*e1^3*e3*e15^3*e45^2+675*e3*e9^3*e15^3*e45^2-330*e1*e5^4*e9*e45^3-360*e5^3*e9^2*e45^4+450*e1^2*e5^2*e45^5-2295*e3^2*e15^2*e45^5-270*e1*e5*e9*e45^6;
g13:=9*e5*e9^8+e1^5*e9^3*e45-10*e1^3*e3^3*e5*e15*e45-25*e1^3*e3*e5*e15^3*e45+75*e1*e5^5*e9*e45^2-155*e1^2*e3^3*e9*e15*e45^2-225*e1^2*e3*e9*e15^3*e45^2-325*e5^4*e9^2*e45^3-300*e1^2*e5^3*e45^4+500*e3^2*e5*e15^2*e45^4+875*e5*e15^4*e45^4+300*e1*e5^2*e9*e45^5-1575*e5*e9^2*e45^6-1425*e1^2*e45^7;
g14:=87*e9^8*e15-87*e1^3*e3^3*e15^2*e45-215*e1^3*e3*e15^4*e45-730*e3*e9^3*e15^4*e45-46*e1^4*e3*e5*e9*e45^2-414*e1*e3*e5*e9^4*e45^2+315*e1*e5^4*e9*e15*e45^2+167*e1^3*e3*e9^2*e45^3+87*e3*e9^5*e45^3+2280*e5^3*e9^2*e15*e45^3-545*e1^2*e5^2*e15*e45^4-3580*e3^2*e15^3*e45^4-2650*e15^5*e45^4-435*e1*e5*e9*e15*e45^5+4770*e9^2*e15*e45^6;
g15:=2*e1^3*e3^2*e9^2*e15^2-2*e1^7*e5*e45+63*e1*e5*e9^6*e45-8*e1^2*e3^3*e5^2*e15*e45-46*e1^2*e3*e5^2*e15^3*e45+48*e3^3*e15^5*e45-5*e1^6*e9*e45^2+15*e5^6*e9*e45^2-54*e1^3*e9^4*e45^2-68*e1*e3^3*e5*e9*e15*e45^2-286*e1*e3*e5*e9*e15^3*e45^2-162*e3^3*e9^2*e15*e45^3+36*e3*e9^2*e15^3*e45^3+20*e1*e5^4*e45^4-60*e5^3*e9*e45^5+315*e1*e5*e45^7;
g16:=3*e1^2*e3^3*e9^2*e15^2-3*e1^6*e3*e5*e45-27*e1^3*e3*e5*e9^3*e45+15*e1^3*e5^4*e15*e45-15*e1*e3^2*e5^2*e15^3*e45-75*e1*e5^2*e15^5*e45+9*e1^5*e3*e9*e45^2+135*e1^2*e5^3*e9*e15*e45^2+75*e3^2*e5*e9*e15^3*e45^2-15*e1*e5^2*e9^2*e15*e45^3-50*e3*e5^4*e45^4-40*e1^3*e5*e15*e45^4-135*e5*e9^3*e15*e45^4+270*e1^2*e9*e15*e45^5+675*e3*e5*e45^7;
g17:=e1^4*e9^2*e15^3-e1^3*e3^3*e5^2*e45-9*e3^3*e5^2*e9^3*e45+10*e1^3*e3*e5^2*e15^2*e45+25*e3*e5^2*e9^3*e15^2*e45-50*e1*e3*e15^6*e45+3*e1^2*e3^3*e5*e9*e45^2+50*e1^2*e3*e5*e9*e15^2*e45^2-125*e3^2*e5^2*e15*e45^4;
g18:=11*e1^3*e3*e9^2*e15^3-40*e5^3*e9^2*e15^4-11*e1^4*e5^4*e45+29*e1^2*e3^2*e5^2*e15^2*e45+275*e15^8*e45+80*e1^3*e5^3*e9*e45^2+313*e1*e3^2*e5*e9*e15^2*e45^2-365*e1*e5*e9*e15^4*e45^2+315*e1^2*e5^2*e9^2*e45^3+18*e3^2*e9^2*e15^2*e45^3-495*e9^2*e15^4*e45^3-73*e1^4*e5*e45^4+810*e1*e5*e9^3*e45^4-6*e1^3*e9*e45^5;
g19:=20*e1^5*e15^4-20*e1^6*e5*e9*e45+275*e5^7*e9*e45-180*e1^3*e5*e9^4*e45-729*e5*e9^7*e45-115*e1*e3^3*e5^2*e9*e15*e45+175*e1*e3*e5^2*e9*e15^3*e45-21*e1^5*e9^2*e45^2-45*e3^3*e5*e9^2*e15*e45^2+1125*e3*e5*e9^2*e15^3*e45^2-500*e1*e5^5*e45^3-90*e1^2*e3^3*e15*e45^3+150*e1^2*e3*e15^3*e45^3+1500*e5^4*e9*e45^4-2025*e1*e5^2*e45^6;
g20:=e1^4*e3*e15^4-e1^5*e3*e5*e9*e45-9*e1^2*e3*e5*e9^4*e45+8*e1^2*e5^4*e9*e15*e45-2*e3^2*e5^2*e9*e15^3*e45+3*e1^4*e3*e9^2*e45^2+13*e1*e5^3*e9^2*e15*e45^2-9*e1^3*e5^2*e15*e45^3-17*e5^2*e9^3*e15*e45^3-9*e1*e3^2*e15^3*e45^3+70*e1*e15^5*e45^3-34*e1^2*e5*e9*e15*e45^4+81*e1*e9^2*e15*e45^5+85*e3*e5^2*e45^6;
g21:=e1^3*e3^2*e15^4-e1^4*e3^2*e5*e9*e45-9*e1*e3^2*e5*e9^4*e45+8*e1^4*e5*e9*e15^2*e45+22*e1*e5*e9^4*e15^2*e45+3*e1^3*e3^2*e9^2*e45^2+9*e1^3*e9^2*e15^2*e45^2-30*e9^5*e15^2*e45^2-6*e1^2*e3*e5^2*e15*e45^3+28*e3^3*e15^3*e45^3+55*e3*e15^5*e45^3-71*e1*e3*e5*e9*e15*e45^4+51*e3*e9^2*e15*e45^5;
g22:=5*e1^3*e3*e5*e15^4-5*e1^4*e3*e5^2*e9*e45-5*e1^2*e3^3*e9*e15^2*e45+30*e1^2*e3*e9*e15^4*e45-30*e1^3*e3*e5*e9^2*e45^2-36*e3*e5*e9^5*e45^2+5*e5^4*e9^2*e15*e45^2+11*e1^5*e3*e45^3+60*e1^2*e5^3*e15*e45^3+155*e3^2*e5*e15^3*e45^3-175*e5*e15^5*e45^3+120*e1*e5^2*e9*e15*e45^4+315*e5*e9^2*e15*e45^5+240*e1^2*e15*e45^6;
g23:=20*e1^4*e9*e15^4-20*e1^5*e5*e9^2*e45-36*e1^2*e5*e9^5*e45-150*e3*e5^2*e9^2*e15^3*e45+16*e1^7*e45^2+60*e1^4*e9^3*e45^2+190*e1^2*e3^3*e5*e15*e45^2+400*e1^2*e3*e5*e15^3*e45^2+225*e5^5*e9*e45^3+405*e1*e3^3*e9*e15*e45^3+1125*e1*e3*e9*e15^3*e45^3+2025*e1*e45^8;
g24:=2*e1^3*e3*e9*e15^4-2*e1^4*e3*e5*e9^2*e45-4*e1*e5^4*e9^2*e15*e45+2*e1^6*e3*e45^2+6*e1^3*e3*e9^3*e45^2+6*e1^3*e5^3*e15*e45^2+20*e1*e3^2*e5*e15^3*e45^2-30*e1*e5*e15^5*e45^2+24*e1^2*e5^2*e9*e15*e45^3+18*e3^2*e9*e15^3*e45^3+18*e1*e5*e9^2*e15*e45^4-45*e3*e5^3*e45^5+33*e1^3*e15*e45^5+27*e9^3*e15*e45^5-135*e3*e45^8;
g25:=40*e5^4*e9*e15^4-40*e1^2*e3^3*e9^2*e15*e45-83*e1^2*e3*e9^2*e15^3*e45+3*e1^3*e5^4*e45^2-197*e1*e3^2*e5^2*e15^2*e45^2-15*e1*e5^2*e15^4*e45^2-305*e1^2*e5^3*e9*e45^3-474*e3^2*e5*e9*e15^2*e45^3+645*e5*e9*e15^4*e45^3-750*e1*e5^2*e9^2*e45^4+195*e1^3*e5*e45^5-1161*e5*e9^3*e45^5-360*e1^2*e9*e45^6;
g26:=20*e1^3*e9^2*e15^4+9*e1*e5*e9^6*e45-20*e1^2*e3^3*e5^2*e15*e45+10*e1^2*e3*e5^2*e15^3*e45+70*e3^3*e15^5*e45+e1^6*e9*e45^2-50*e5^6*e9*e45^2-5*e1*e3^3*e5*e9*e15*e45^2-115*e1*e3*e5*e9*e15^3*e45^2+90*e3*e9^2*e15^3*e45^3+50*e1*e5^4*e45^4-150*e5^3*e9*e45^5;
g27:=6*e1^2*e3*e9^2*e15^4-6*e1^3*e5^4*e15*e45-6*e1*e3^2*e5^2*e15^3*e45+30*e1*e5^2*e15^5*e45-30*e1^2*e5^3*e9*e15*e45^2-12*e3^2*e5*e9*e15^3*e45^2-30*e1*e5^2*e9^2*e15*e45^3+5*e3*e5^4*e45^4-5*e1^3*e5*e15*e45^4+27*e5*e9^3*e15*e45^4-135*e3*e5*e45^7;
g28:=40*e1^2*e9^3*e15^4-25*e5^7*e9*e45+81*e5*e9^7*e45-15*e1*e3^3*e5^2*e9*e15*e45-25*e1*e3*e5^2*e9*e15^3*e45+9*e1^5*e9^2*e45^2+45*e3^3*e5*e9^2*e15*e45^2-225*e3*e5*e9^2*e15^3*e45^2+30*e1^2*e3^3*e15*e45^3-50*e1^2*e3*e15^3*e45^3-225*e1*e5^2*e45^6;
g29:=40*e1*e9^4*e15^4-9*e1^2*e5*e9^5*e45-30*e3^3*e5^2*e9^2*e15*e45+50*e3*e5^2*e9^2*e15^3*e45-e1^7*e45^2-35*e1^2*e3^3*e5*e15*e45^2-25*e1^2*e3*e5*e15^3*e45^2-75*e5^5*e9*e45^3-75*e1*e3^3*e9*e15*e45^3-125*e1*e3*e9*e15^3*e45^3-675*e1*e45^8;
g30:=12*e9^5*e15^4-9*e1*e5*e9^6*e45-2*e1^2*e3*e5^2*e15^3*e45-14*e3^3*e15^5*e45-e1^6*e9*e45^2-5*e1*e3^3*e5*e9*e15*e45^2-7*e1*e3*e5*e9*e15^3*e45^2-78*e3*e9^2*e15^3*e45^3-10*e1*e5^4*e45^4+30*e5^3*e9*e45^5-90*e1*e5*e45^7;
g31:=5*e1^3*e3*e15^5-5*e1^4*e3*e5*e9*e15*e45-5*e1*e5^4*e9*e15^2*e45+5*e1^3*e3*e9^2*e15*e45^2+66*e3*e9^5*e15*e45^2-60*e5^3*e9^2*e15^2*e45^2+19*e1^2*e3^2*e5^2*e45^3+18*e1^2*e5^2*e15^2*e45^3-54*e3^2*e15^4*e45^3+35*e15^6*e45^3+54*e1*e3^2*e5*e9*e45^4+63*e1*e5*e9*e15^2*e45^4+66*e3^2*e9^2*e45^5-63*e9^2*e15^2*e45^5;
g32:=6*e1^2*e3^2*e15^5-6*e1^3*e3^2*e5*e9*e15*e45-5*e3*e5^4*e9*e15^2*e45-e1^3*e5*e9*e15^3*e45+3*e5*e9^4*e15^3*e45+6*e1^2*e9^2*e15^3*e45^2+12*e1*e3^3*e5^2*e45^3+30*e1*e3*e5^2*e15^2*e45^3+18*e3^3*e5*e9*e45^4-15*e3*e5*e9*e15^2*e45^4;
g33:=2*e1*e3^3*e15^5-2*e1^2*e3^3*e5*e9*e15*e45-2*e1^2*e3*e5*e9*e15^3*e45-e5^5*e9^2*e45^2-3*e1*e3^3*e9^2*e15*e45^2-3*e1*e3*e9^2*e15^3*e45^2+2*e1^2*e5^4*e45^3+8*e3^2*e5^2*e15^2*e45^3-10*e5^2*e15^4*e45^3+6*e1*e5^3*e9*e45^4+18*e5^2*e9^2*e45^5+6*e1^2*e5*e45^6-27*e1*e9*e45^7;
g34:=40*e3^3*e5*e15^5+5*e5^7*e9*e45+81*e5*e9^7*e45-45*e1*e3^3*e5^2*e9*e15*e45-135*e1*e3*e5^2*e9*e15^3*e45+9*e1^5*e9^2*e45^2-135*e3^3*e5*e9^2*e15*e45^2-225*e3*e5*e9^2*e15^3*e45^2+30*e1^2*e3^3*e15*e45^3-30*e1^2*e3*e15^3*e45^3+45*e1*e5^2*e45^6;
g35:=e1*e5^6*e9-e1^2*e3^3*e5*e9*e15-e1^2*e3*e5*e9*e15^3-5*e5^5*e9^2*e45+3*e1*e3^3*e9^2*e15*e45+3*e1*e3*e9^2*e15^3*e45-2*e1^2*e5^4*e45^2+10*e3^2*e5^2*e15^2*e45^2+10*e5^2*e15^4*e45^2+12*e1*e5^3*e9*e45^3-18*e5^2*e9^2*e45^4-15*e1^2*e5*e45^5+27*e1*e9*e45^6;
g36:=4*e1*e5^5*e9^2-4*e1^2*e3^3*e9^2*e15-5*e1^2*e3*e9^2*e15^3+e1^3*e5^4*e45-7*e1*e3^2*e5^2*e15^2*e45-5*e1*e5^2*e15^4*e45-11*e1^2*e5^3*e9*e45^2-6*e3^2*e5*e9*e15^2*e45^2+15*e5*e9*e15^4*e45^2+6*e1*e5^2*e9^2*e45^3+9*e1^3*e5*e45^4-27*e5*e9^3*e45^4-36*e1^2*e9*e45^5;
g37:=6*e5^6*e9^2-6*e1*e3^3*e5*e9^2*e15-6*e1^3*e3^3*e15*e45-23*e3^2*e5^3*e15^2*e45-e1^3*e3*e15^3*e45+9*e3*e9^3*e15^3*e45-30*e1*e5^4*e9*e45^2+36*e5^3*e9^2*e45^3+18*e1^2*e5^2*e45^4-153*e3^2*e15^2*e45^4-108*e1*e5*e9*e45^5;
g38:=2*e1^4*e5*e9^3+9*e1*e5*e9^6-2*e1^2*e3^3*e5^2*e15-4*e1^2*e3*e5^2*e15^3+2*e3^3*e15^5-e1^6*e9*e45+10*e5^6*e9*e45-6*e1^3*e9^4*e45-17*e1*e3^3*e5*e9*e15*e45-39*e1*e3*e5*e9*e15^3*e45-18*e3^3*e9^2*e15*e45^2-36*e3*e9^2*e15^3*e45^2-20*e1*e5^4*e45^3+60*e5^3*e9*e45^4-90*e1*e5*e45^6;
g39:=6*e1*e3^2*e5^2*e9^3-6*e1^4*e5^2*e15^2-12*e1^2*e3^2*e15^4+30*e1^2*e15^6-6*e1^3*e3^2*e5*e9*e45-18*e3^2*e5*e9^4*e45-25*e3*e5^4*e9*e15*e45-11*e1^3*e5*e9*e15^2*e45+75*e5*e9^4*e15^2*e45+6*e1^2*e9^2*e15^2*e45^2-375*e3*e5*e9*e15*e45^4;
g40:=6*e1*e3*e5^2*e9^4-6*e1^2*e3^3*e9*e15^2-6*e1^3*e3*e5*e9^2*e45-9*e3*e5*e9^5*e45-10*e5^4*e9^2*e15*e45+e1^5*e3*e45^2+5*e1^2*e5^3*e15*e45^2+65*e3^2*e5*e15^3*e45^2-25*e5*e15^5*e45^2+60*e1*e5^2*e9*e15*e45^3+45*e5*e9^2*e15*e45^4-30*e1^2*e15*e45^5;
g41:=9*e3^2*e5^2*e9^4-9*e1^3*e5^2*e9*e15^2-18*e1*e3^2*e9*e15^4-9*e1^2*e3^2*e5*e9^2*e45-39*e1^2*e5*e9^2*e15^2*e45+3*e1^4*e3^2*e45^2-25*e1*e3*e5^3*e15*e45^2-5*e1^4*e15^2*e45^2-126*e1*e9^3*e15^2*e45^2-45*e1*e3*e15*e45^5;
g42:=9*e1*e3*e5*e9^5-10*e1*e5^4*e9^2*e15+e1^6*e3*e45+5*e1^3*e5^3*e15*e45+5*e1*e3^2*e5*e15^3*e45-25*e1*e5*e15^5*e45+30*e1^2*e5^2*e9*e15*e45^2+30*e3^2*e9*e15^3*e45^2-15*e1*e5*e9^2*e15*e45^3-50*e3*e5^3*e45^4+20*e1^3*e15*e45^4;
g43:=9*e3^2*e5*e9^5-10*e1^3*e5*e9^2*e15^2+e1^5*e3^2*e45-25*e1^5*e15^2*e45-355*e1^2*e9^3*e15^2*e45+225*e3^3*e5*e15^3*e45-625*e3*e5*e15^5*e45+100*e1*e3*e5^2*e9*e15*e45^2+1125*e3*e5*e9^2*e15*e45^3-325*e1^2*e3*e15*e45^4;
g44:=15*e1*e5^2*e9^5-14*e1^2*e3^2*e9^2*e15^2+10*e1^2*e9^2*e15^4-e1^6*e5*e45-24*e1^3*e5*e9^3*e45-27*e5*e9^6*e45-5*e1*e3^3*e5^2*e15*e45-25*e1*e3*e5^2*e15^3*e45+5*e1^5*e9*e45^2+15*e3^3*e5*e9*e15*e45^2+75*e3*e5*e9*e15^3*e45^2;
g45:=3*e3*e5^2*e9^5-4*e1*e3^3*e9^2*e15^2-10*e1*e3*e9^2*e15^4+e1^5*e3*e5*e45+6*e1^2*e3*e5*e9^3*e45+5*e1^2*e5^4*e15*e45+5*e3^2*e5^2*e15^3*e45-25*e5^2*e15^5*e45-2*e1^4*e3*e9*e45^2+45*e5^2*e9^2*e15*e45^3+30*e1^2*e5*e15*e45^4-90*e1*e9*e15*e45^5;
g46:=54*e3*e5*e9^6-60*e1*e3^2*e5^2*e15^3+6*e1^5*e3*e9*e45-30*e1^2*e5^3*e9*e15*e45-150*e3^2*e5*e9*e15^3*e45-150*e1*e5^2*e9^2*e15*e45^2+25*e3*e5^4*e45^3+65*e1^3*e5*e15*e45^3-45*e5*e9^3*e15*e45^3+180*e1^2*e9*e15*e45^4+225*e3*e5*e45^6;
g47:=378*e5^2*e9^6-325*e1*e3*e5^3*e15^3-65*e1^4*e15^4-165*e1*e9^3*e15^4+12*e1^5*e5*e9*e45-270*e1^2*e5*e9^4*e45-90*e3^3*e5^2*e9*e15*e45-1050*e3*e5^2*e9*e15^3*e45+90*e1^4*e9^2*e45^2+270*e1*e3^3*e15*e45^3-975*e1*e3*e15^3*e45^3;
g48:=5*e1*e5^5*e9*e15-5*e1^2*e3^3*e9*e15^2-5*e1^2*e3*e9*e15^4+9*e3*e5*e9^5*e45-20*e5^4*e9^2*e15*e45+e1^5*e3*e45^2-5*e1^2*e5^3*e15*e45^2+25*e3^2*e5*e15^3*e45^2+25*e5*e15^5*e45^2+30*e1*e5^2*e9*e15*e45^3-45*e5*e9^2*e15*e45^4-15*e1^2*e15*e45^5;
g49:=25*e5^6*e9*e15+18*e9^7*e15-25*e1*e3^3*e5*e9*e15^2-25*e1*e3*e5*e9*e15^4-18*e1^2*e3*e5^2*e9^2*e45-96*e3^3*e9^2*e15^2*e45-60*e3*e9^2*e15^4*e45+10*e1^4*e3*e5*e45^2-18*e1*e3*e5*e9^3*e45^2+30*e1^3*e3*e9*e45^3+18*e3*e9^4*e45^3+225*e1*e5*e15*e45^5;
g50:=5*e5^5*e9^2*e15-3*e1*e3^3*e9^2*e15^2+15*e1*e3*e9^2*e15^4-2*e1^5*e3*e5*e45-18*e1^2*e3*e5*e9^3*e45-10*e1^2*e5^4*e15*e45-40*e3^2*e5^2*e15^3*e45+50*e5^2*e15^5*e45+6*e1^4*e3*e9*e45^2-30*e1*e5^3*e9*e15*e45^2-90*e5^2*e9^2*e15*e45^3-30*e1^2*e5*e15*e45^4+135*e1*e9*e15*e45^5;
g51:=3*e1^2*e3^2*e9^3*e15-3*e1^5*e15^3-44*e1^2*e9^3*e15^3+35*e3^3*e5*e15^4-75*e3*e5*e15^6+5*e1*e3*e5^2*e9*e15^2*e45-9*e3^3*e5*e9^2*e45^2+135*e3*e5*e9^2*e15^2*e45^2+3*e1^2*e3^3*e45^3-50*e1^2*e3*e15^2*e45^3;
g52:=6*e1*e3^2*e5*e9^3*e15-5*e1*e3*e5^4*e15^2-e1^4*e5*e15^3-3*e1^3*e3^2*e9*e15*e45-9*e3^2*e9^4*e15*e45+5*e3*e5^3*e9*e15^2*e45-2*e1^3*e9*e15^3*e45+9*e9^4*e15^3*e45-3*e1*e3^3*e5*e45^3-15*e1*e3*e5*e15^2*e45^3-9*e3^3*e9*e45^4-45*e3*e9*e15^2*e45^4;
g53:=e3^2*e5^2*e9^3*e15-e1^3*e5^2*e15^3-3*e5^2*e9^3*e15^3+e1*e3^2*e15^5+5*e1*e15^7-e1^2*e3^2*e5*e9*e15*e45-6*e1^2*e5*e9*e15^3*e45+e3^3*e5^2*e45^3+15*e3*e5^2*e15^2*e45^3;
g54:=3*e1^2*e3*e9^4*e15-3*e1^2*e5^3*e9*e15^2-9*e3^2*e5*e9^3*e45^2+10*e3*e5^4*e15*e45^2+2*e1^3*e5*e15^2*e45^2-3*e5*e9^3*e15^2*e45^2+3*e1^2*e3^2*e9*e45^3-6*e1^2*e9*e15^2*e45^3+15*e3*e5*e15*e45^5;
g55:=3*e1*e3^2*e9^4*e15-5*e1*e3*e5^3*e9*e15^2+2*e1^4*e9*e15^3+9*e1*e9^4*e15^3-3*e3^3*e5^2*e9^2*e45+3*e1^2*e3^3*e5*e45^2+3*e1*e3^3*e9*e45^3;
g56:=e1*e3*e5*e9^4*e15-e1*e5^4*e9*e15^2-3*e3*e9^5*e15*e45+3*e5^3*e9^2*e15^2*e45+e1^2*e5^2*e15^2*e45^2+3*e3^2*e15^4*e45^2-5*e15^6*e45^2-2*e1*e3^2*e5*e9*e45^3-3*e1*e5*e9*e15^2*e45^3-3*e3^2*e9^2*e45^4+9*e9^2*e15^2*e45^4;
g57:=9*e3^2*e5*e9^4*e15-10*e3*e5^4*e9*e15^2+e1^3*e5*e9*e15^3+3*e5*e9^4*e15^3-3*e1^2*e9^2*e15^3*e45+3*e1*e3^3*e5^2*e45^2-15*e3*e5*e9*e15^2*e45^3;
g58:=11*e1^2*e9^5*e15-10*e3^3*e5*e9^2*e15^2+25*e3*e5*e9^2*e15^4-e1^4*e3*e5^2*e45-5*e1*e3*e5^2*e9^3*e45-2*e1^2*e3^3*e15^2*e45+5*e1^2*e3*e15^4*e45-e1^3*e3*e5*e9*e45^2-45*e3*e5*e9^4*e45^2+11*e1^2*e3*e9^2*e45^3;
g59:=e1*e3*e9^5*e15-e1^3*e3^2*e5^2*e45-10*e3^2*e5^2*e9^3*e45+8*e1^3*e5^2*e15^2*e45+25*e5^2*e9^3*e15^2*e45-4*e1*e3^2*e15^4*e45-40*e1*e15^6*e45+4*e1^2*e3^2*e5*e9*e45^2+48*e1^2*e5*e9*e15^2*e45^2+e1*e3^2*e9^2*e45^3-3*e1*e9^2*e15^2*e45^3-125*e3*e5^2*e15*e45^4;
g60:=9*e3^2*e9^5*e15-10*e1^3*e9^2*e15^3-15*e9^5*e15^3+e1^2*e3^3*e5^2*e45-13*e1^2*e3*e5^2*e15^2*e45-31*e3^3*e15^4*e45+65*e3*e15^6*e45+6*e1*e3^3*e5*e9*e45^2-3*e1*e3*e5*e9*e15^2*e45^2+9*e3^3*e9^2*e45^3-42*e3*e9^2*e15^2*e45^3;
g61:=6*e1*e9^6*e15-6*e1^3*e3*e5^2*e9*e45-30*e3*e5^2*e9^4*e45+25*e5^5*e9*e15*e45-7*e1*e3^3*e9*e15^2*e45+5*e1*e3*e9*e15^4*e45-6*e1^2*e3*e5*e9^2*e45^2+10*e1^4*e3*e45^3+6*e1*e3*e9^3*e45^3+225*e1*e15*e45^6;
g62:=18*e3*e9^6*e15-18*e1^2*e3^2*e5^2*e9*e45-36*e1^2*e5^2*e9*e15^2*e45+18*e3^2*e9*e15^4*e45-108*e1*e3^2*e5*e9^2*e45^2-186*e1*e5*e9^2*e15^2*e45^2+60*e1^3*e3^2*e45^3+18*e3^2*e9^3*e45^3+25*e3*e5^3*e15*e45^3+5*e1^3*e15^2*e45^3-279*e9^3*e15^2*e45^3+1395*e3*e15*e45^6;
g63:=11*e1*e3^2*e5^3*e15^2-11*e1^4*e3*e15^3-33*e1^2*e5^4*e9*e45-33*e3^2*e5^2*e9*e15^2*e45+120*e5^2*e9*e15^4*e45-54*e1*e5^3*e9^2*e45^2-21*e1^3*e5^2*e45^3-216*e5^2*e9^3*e45^3-225*e1*e15^4*e45^3-72*e1^2*e5*e9*e45^4;
g64:=2*e3^2*e5^4*e15^2-2*e1^3*e3*e5*e15^3+9*e1*e5^5*e9*e45-15*e1^2*e3^3*e9*e15*e45-21*e1^2*e3*e9*e15^3*e45-36*e5^4*e9^2*e45^2-30*e1^2*e5^3*e45^3+72*e3^2*e5*e15^2*e45^3+90*e5*e15^4*e45^3+36*e1*e5^2*e9*e45^4-162*e5*e9^2*e45^5-135*e1^2*e45^6;
g65:=11*e3^2*e5^3*e9*e15^2-11*e1^3*e3*e9*e15^3-15*e5^3*e9*e15^4-18*e1*e5^4*e9^2*e45-18*e1^3*e5^3*e45^2-6*e1*e3^2*e5*e15^2*e45^2+90*e1*e5*e15^4*e45^2-63*e1^2*e5^2*e9*e45^3+81*e3^2*e9*e15^2*e45^3-216*e1*e5*e9^2*e45^4-27*e1^3*e45^5;
g66:=6*e5^5*e9*e15^2-6*e1*e3^3*e9*e15^3-6*e1^2*e3*e5*e9^2*e15*e45-17*e1*e3^2*e5^3*e45^2-e1^4*e3*e15*e45^2-45*e1*e3*e9^3*e15*e45^2-36*e3^2*e5^2*e9*e45^3-45*e1*e3^2*e45^5+54*e1*e15^2*e45^5;
g67:=3*e1*e3^2*e5*e9^2*e15^2-3*e1^5*e5^2*e45-12*e1^3*e3^2*e15^2*e45+9*e3^2*e9^3*e15^2*e45-25*e3*e5^3*e15^3*e45+10*e1^3*e15^4*e45+45*e9^3*e15^4*e45-12*e1^4*e5*e9*e45^2-27*e1*e5*e9^4*e45^2-18*e1^3*e9^2*e45^3-45*e3^3*e15*e45^4-225*e3*e15^3*e45^4;
g68:=6*e1^2*e5^2*e9^2*e15^2-6*e1^4*e3^2*e5*e45-54*e1*e3^2*e5*e9^3*e45+35*e1*e3*e5^4*e15*e45+7*e1^4*e5*e15^2*e45+9*e1*e5*e9^3*e15^2*e45+18*e1^3*e3^2*e9*e45^2+45*e3*e5^3*e9*e15*e45^2+9*e1^3*e9*e15^2*e45^2-81*e9^4*e15^2*e45^2-45*e1*e3*e5*e15*e45^4+405*e3*e9*e15*e45^5;
g69:=e3^2*e5^2*e9^2*e15^2-5*e5^2*e9^2*e15^4-e1^4*e5^3*e45+e1^2*e3^2*e5*e15^2*e45+5*e1^2*e5*e15^4*e45-e1^3*e5^2*e9*e45^2+9*e5^2*e9^4*e45^2+9*e1*e3^2*e9*e15^2*e45^2+15*e1*e9*e15^4*e45^2-6*e1^2*e5*e9^2*e45^3-3*e1^4*e45^4;
g70:=e1*e5^3*e9^2*e15^2-e1^3*e3^2*e5^2*e45-9*e3^2*e5^2*e9^3*e45+7*e1^3*e5^2*e15^2*e45+22*e5^2*e9^3*e15^2*e45-3*e1*e3^2*e15^4*e45-35*e1*e15^6*e45+3*e1^2*e3^2*e5*e9*e45^2+41*e1^2*e5*e9*e15^2*e45^2-110*e3*e5^2*e15*e45^4;
g71:=e5^4*e9^2*e15^2-e1^5*e3*e15*e45-15*e1^2*e3*e9^3*e15*e45+10*e1^2*e5^3*e15^2*e45-8*e3^2*e5*e15^4*e45-50*e5*e15^6*e45+3*e1*e3^2*e5^2*e9*e45^2+57*e1*e5^2*e9*e15^2*e45^2+45*e3^2*e5*e9^2*e45^3+90*e5*e9^2*e15^2*e45^3-15*e1^2*e3^2*e45^4+3*e1^2*e15^2*e45^4;
g72:=28*e1*e3^2*e9^3*e15^2-25*e1*e3*e5^3*e15^3-5*e1^4*e15^4-45*e1*e9^3*e15^4+2*e1^5*e5*e9*e45+18*e1^2*e5*e9^4*e45+20*e3^3*e5^2*e9*e15*e45-6*e1^4*e9^2*e45^2+10*e1*e3^3*e15*e45^3-75*e1*e3*e15^3*e45^3;
g73:=2*e3^2*e5*e9^3*e15^2-2*e1^4*e5^2*e9*e45-8*e1^2*e3^2*e9*e15^2*e45-12*e1^3*e5*e9^2*e45^2-27*e5*e9^5*e45^2+3*e1^5*e45^3+5*e3^3*e5*e15*e45^3+75*e3*e5*e15^3*e45^3;
g74:=2*e1^2*e9^4*e15^2-2*e3^3*e5*e9*e15^3+4*e1*e3*e5^2*e9^2*e15*e45+5*e3^2*e5^4*e45^2+e1^3*e3*e5*e15*e45^2-3*e3*e5*e9^3*e15*e45^2+2*e1^2*e3*e9*e15*e45^3+15*e3^2*e5*e45^5;
g75:=18*e3^2*e9^4*e15^2-10*e1^3*e9*e15^4-60*e9^4*e15^4-8*e1^4*e5*e9^2*e45-9*e1*e5*e9^5*e45+7*e1^6*e45^2+24*e1^3*e9^3*e45^2+25*e1*e3^3*e5*e15*e45^2+175*e1*e3*e5*e15^3*e45^2+90*e3^3*e9*e15*e45^3+300*e3*e9*e15^3*e45^3;
g76:=3*e1*e9^5*e15^2-3*e1^3*e3*e5^2*e15*e45-5*e3*e5^2*e9^3*e15*e45-e1*e3^3*e15^3*e45+15*e1*e3*e15^5*e45-13*e1^2*e3*e5*e9*e15*e45^2+3*e1*e3*e9^2*e15*e45^3+25*e3^2*e5^2*e45^4;
g77:=e9^6*e15^2-e1^2*e3*e5^2*e9*e15*e45-2*e3^3*e9*e15^3*e45-e1*e3*e5*e9^2*e15*e45^2-4*e3*e9^3*e15*e45^3-5*e3^2*e45^6;
g78:=29*e3^2*e5^3*e15^3-23*e1^3*e3*e15^4-99*e3*e9^3*e15^4-6*e1^4*e3*e5*e9*e45-54*e1*e3*e5*e9^4*e45+60*e1*e5^4*e9*e15*e45+18*e1^3*e3*e9^2*e45^2+252*e5^3*e9^2*e15*e45^2-90*e1^2*e5^2*e15*e45^3-153*e3^2*e15^3*e45^3-270*e15^5*e45^3+486*e9^2*e15*e45^5;
g79:=50*e3*e5^4*e15^3+10*e1^3*e5*e15^4-60*e1^4*e5^2*e9*e45+36*e1*e5^2*e9^4*e45-246*e1^2*e3^2*e9*e15^2*e45+60*e1^2*e9*e15^4*e45-396*e1^3*e5*e9^2*e45^2-891*e5*e9^5*e45^2+93*e1^5*e45^3+225*e3^3*e5*e15*e45^3+2475*e3*e5*e15^3*e45^3;
g80:=25*e3*e5^3*e9*e15^3-15*e1^3*e9*e15^4-75*e9^4*e15^4-10*e1^4*e5*e9^2*e45-18*e1*e5*e9^5*e45+8*e1^6*e45^2+30*e1^3*e9^3*e45^2+20*e1*e3^3*e5*e15*e45^2+200*e1*e3*e5*e15^3*e45^2+90*e3^3*e9*e15*e45^3+375*e3*e9*e15^3*e45^3;
g81:=11*e1*e3*e9^3*e15^3-11*e1^2*e5^4*e9*e45-11*e3^2*e5^2*e9*e15^2*e45+30*e5^2*e9*e15^4*e45-30*e1*e5^3*e9^2*e45^2+3*e1^3*e5^2*e45^3-54*e5^2*e9^3*e45^3+11*e1*e3^2*e15^2*e45^3-15*e1*e15^4*e45^3-18*e1^2*e5*e9*e45^4;
g82:=2*e3*e5*e9^3*e15^3+e1*e5^5*e9*e45-3*e1^2*e3^3*e9*e15*e45-5*e1^2*e3*e9*e15^3*e45-12*e5^4*e9^2*e45^2-6*e1^2*e5^3*e45^3+14*e3^2*e5*e15^2*e45^3+30*e5*e15^4*e45^3-54*e5*e9^2*e45^5-27*e1^2*e45^6;
g83:=33*e3*e9^4*e15^3-25*e5^3*e9*e15^4-8*e1*e5^4*e9^2*e45-8*e1^3*e5^3*e45^2-32*e1*e3^2*e5*e15^2*e45^2+40*e1*e5*e15^4*e45^2-39*e1^2*e5^2*e9*e45^3-30*e3^2*e9*e15^2*e45^3-162*e1*e5*e9^2*e45^4+21*e1^3*e45^5;
g84:=6*e1*e3^2*e5*e15^4-6*e1^2*e3^2*e5^2*e9*e45-6*e1^2*e5^2*e9*e15^2*e45+24*e3^2*e9*e15^4*e45-36*e1*e3^2*e5*e9^2*e45^2-48*e1*e5*e9^2*e15^2*e45^2+18*e1^3*e3^2*e45^3+5*e3*e5^3*e15*e45^3-5*e1^3*e15^2*e45^3-81*e9^3*e15^2*e45^3+405*e3*e15*e45^6;
g85:=5*e1^2*e5^2*e15^4-25*e15^8-5*e1^3*e5^3*e9*e45-5*e1*e3^2*e5*e9*e15^2*e45+40*e1*e5*e9*e15^4*e45-15*e1^2*e5^2*e9^2*e45^2+18*e3^2*e9^2*e15^2*e45^2+45*e9^2*e15^4*e45^2+2*e1^4*e5*e45^3-27*e1*e5*e9^3*e45^3-6*e1^3*e9*e45^4;
g86:=6*e3^2*e5^2*e15^4-5*e1*e3^2*e5^3*e9*e45-e1^4*e3*e9*e15*e45-15*e1*e3*e9^4*e15*e45+6*e1*e5^3*e9*e15^2*e45-12*e3^2*e5^2*e9^2*e45^2-6*e1^2*e5*e15^2*e45^3-15*e1*e3^2*e9*e45^4+18*e1*e9*e15^2*e45^4;
g87:=25*e3*e5^3*e15^4+5*e1^3*e15^5-30*e1^4*e5*e9*e15*e45-105*e1*e5*e9^4*e15*e45-45*e1^3*e9^2*e15*e45^2-9*e9^5*e15*e45^2+9*e1^2*e3*e5^2*e45^3-132*e3^3*e15^2*e45^3+30*e3*e15^4*e45^3+129*e1*e3*e5*e9*e45^4-9*e3*e9^2*e45^5;
g88:=5*e1^2*e5*e9*e15^4-5*e1^3*e5^2*e9^2*e45-36*e5^2*e9^5*e45+27*e1*e3^2*e9^2*e15^2*e45-15*e1*e9^2*e15^4*e45+4*e1^5*e5*e45^2+42*e1^2*e5*e9^3*e45^2+25*e3^3*e5^2*e15*e45^2+100*e3*e5^2*e15^3*e45^2-9*e1^4*e9*e45^3;
g89:=2*e3^2*e5*e9*e15^4-2*e1*e3^2*e5^2*e9^2*e45-4*e1*e5^2*e9^2*e15^2*e45+2*e1^3*e3^2*e5*e45^2+6*e3^2*e5*e9^3*e45^2-5*e3*e5^4*e15*e45^2-e1^3*e5*e15^2*e45^2-7*e5*e9^3*e15^2*e45^2-2*e1^2*e9*e15^2*e45^3+35*e3*e5*e15*e45^5;
g90:=5*e1*e5^2*e9*e15^4-5*e1^2*e5^3*e9^2*e45-6*e3^2*e5*e9^2*e15^2*e45+15*e5*e9^2*e15^4*e45+e1^4*e5^2*e45^2-12*e1*e5^2*e9^3*e45^2+e1^2*e3^2*e15^2*e45^2-5*e1^2*e15^4*e45^2+3*e1^3*e5*e9*e45^3-27*e5*e9^4*e45^3;
g91:=25*e3*e5^2*e9*e15^4-25*e1^4*e9^2*e15*e45-78*e1*e9^5*e15*e45-22*e1^3*e3*e5^2*e45^2-45*e3*e5^2*e9^3*e45^2-49*e1*e3^3*e15^2*e45^2+110*e1*e3*e15^4*e45^2-12*e1^2*e3*e5*e9*e45^3-78*e1*e3*e9^2*e45^4;
g92:=10*e5*e9^3*e15^4-24*e1*e5^2*e9^4*e45+14*e1^2*e3^2*e9*e15^2*e45-20*e1^2*e9*e15^4*e45+24*e1^3*e5*e9^2*e45^2+27*e5*e9^5*e45^2-5*e1^5*e45^3-45*e3^3*e5*e15*e45^3-125*e3*e5*e15^3*e45^3;
g93:=5*e3^2*e15^6-5*e1*e3^2*e5*e9*e15^2*e45-5*e1*e5*e9*e15^4*e45-9*e3^2*e9^2*e15^2*e45^2-e1^4*e5*e45^3-9*e1*e5*e9^3*e45^3+3*e1^3*e9*e45^4;
g94:=2*e3*e15^7-e5^6*e9*e45+e1*e3^3*e5*e9*e15*e45-e1*e3*e5*e9*e15^3*e45+2*e1*e5^4*e45^3-6*e5^3*e9*e45^4+9*e1*e5*e45^6;
g95:=e1*e3^3*e5^3-e1^4*e3^2*e15+3*e1*e3^2*e9^3*e15-5*e1*e3*e5^3*e15^2-e1^4*e15^3-9*e1*e9^3*e15^3+6*e3^3*e5^2*e9*e45+3*e1*e3^3*e45^3-45*e1*e3*e15^2*e45^3;
g96:=e3^3*e5^4-e1^3*e3^2*e5*e15-9*e3^2*e5*e9^3*e15+5*e3*e5^4*e15^2+e1^3*e5*e15^3+3*e5*e9^3*e15^3+6*e1^2*e9*e15^3*e45+9*e3^3*e5*e45^3-15*e3*e5*e15^2*e45^3;
g97:=e1^2*e5^5-e1^3*e3^3*e15-2*e3^2*e5^3*e15^2+e1^3*e3*e15^3+9*e3*e9^3*e15^3-5*e5^3*e15^4+9*e1^2*e5^2*e45^3-18*e3^2*e15^2*e45^3;
g98:=e3^3*e5^3*e9-e1^3*e3^2*e9*e15+9*e3^2*e9^4*e15-15*e3*e5^3*e9*e15^2+3*e1^3*e9*e15^3+9*e9^4*e15^3+6*e1*e3^3*e5*e45^2+9*e3^3*e9*e45^3-45*e3*e9*e15^2*e45^3;
g99:=5*e1*e3*e5^4*e9-5*e1^4*e5*e9*e15-15*e1*e5*e9^4*e15+18*e9^5*e15*e45+12*e1^2*e3*e5^2*e45^2-6*e3^3*e15^2*e45^2-60*e3*e15^4*e45^2+57*e1*e3*e5*e9*e45^3+18*e3*e9^2*e45^4;
g100:=6*e1^2*e5^2*e9^3-6*e1^3*e3^2*e15^2-30*e3^2*e9^3*e15^2+25*e3*e5^3*e15^3+5*e1^3*e15^4+15*e9^3*e15^4-6*e1^4*e5*e9*e45-18*e1*e5*e9^4*e45-30*e3^3*e15*e45^3-75*e3*e15^3*e45^3;
g101:=10*e3^3*e5^3*e15-10*e1^3*e3^2*e15^2-54*e3^2*e9^3*e15^2+25*e3*e5^3*e15^3+5*e1^3*e15^4+45*e9^3*e15^4-6*e1^4*e5*e9*e45-54*e1*e5*e9^4*e45+18*e1^3*e9^2*e45^2-225*e3*e15^3*e45^3;
g102:=5*e1^3*e9^3*e15+9*e9^6*e15-5*e1*e3^3*e5*e15^2+e1^2*e3*e5^2*e9*e45-3*e3^3*e9*e15^2*e45-30*e3*e9*e15^4*e45-9*e1*e3*e5*e9^2*e45^2+5*e1^3*e3*e45^3+9*e3*e9^3*e45^3;
g103:=3*e3^3*e9^3*e15-2*e3^2*e5^3*e15^2-e1^3*e3*e15^3-3*e3*e9^3*e15^3+9*e5^3*e9^2*e45^2-6*e3^2*e15^2*e45^3-15*e15^4*e45^3+27*e9^2*e45^5;
g104:=2*e1^2*e5*e9^3*e15-2*e3^3*e5^2*e15^2+3*e1*e3*e5^3*e9*e45+e1^4*e9*e15*e45+9*e1*e9^4*e15*e45+2*e1^2*e3*e5*e45^3+9*e1*e3*e9*e45^4;
g105:=2*e1*e5^2*e9^3*e15-2*e1^2*e3^2*e15^3-5*e3*e5^4*e9*e45+3*e1^3*e5*e9*e15*e45+9*e5*e9^4*e15*e45-10*e1*e3*e5^2*e45^3-45*e3*e5*e9*e45^4;
g106:=2*e5^2*e9^4*e15-2*e1*e3^2*e9*e15^3-2*e1^2*e5*e9^2*e15*e45-5*e1*e3*e5^3*e45^2-e1^4*e15*e45^2-15*e1*e9^3*e15*e45^2-10*e3*e5^2*e9*e45^3-15*e1*e3*e45^5;
g107:=3*e5*e9^5*e15-3*e1^5*e15*e45-40*e1^2*e9^3*e15*e45+25*e3^3*e5*e15^2*e45-75*e3*e5*e15^4*e45+10*e1*e3*e5^2*e9*e45^2+120*e3*e5*e9^2*e45^3-40*e1^2*e3*e45^4;
g108:=6*e3^2*e9^2*e15^3-5*e1*e3*e5^4*e45-e1^4*e5*e15*e45-9*e1*e5*e9^3*e15*e45-10*e3*e5^3*e9*e45^2-2*e1^3*e9*e15*e45^2-15*e1*e3*e5*e45^4;
g109:=6*e1*e5*e9^2*e15^3-3*e3^3*e5^3*e45-3*e1^3*e3^2*e15*e45-9*e3^2*e9^3*e15*e45+5*e3*e5^3*e15^2*e45+e1^3*e15^3*e45+9*e9^3*e15^3*e45-9*e3^3*e45^4-45*e3*e15^2*e45^4;
g110:=e1^2*e3*e5^3-e1^5*e15-15*e1^2*e9^3*e15+12*e3^3*e5*e15^2-30*e3*e5*e15^4+6*e1*e3*e5^2*e9*e45+54*e3*e5*e9^2*e45^2-15*e1^2*e3*e45^3;
g111:=e3*e5^5-e1^3*e5^2*e15-3*e5^2*e9^3*e15+6*e1*e15^5-6*e1^2*e5*e9*e15*e45+15*e3*e5^2*e45^3;
g112:=5*e3*e5^3*e9^2-5*e1^3*e9^2*e15-9*e9^5*e15-6*e1^2*e3*e5^2*e45-12*e3^3*e15^2*e45+30*e3*e15^4*e45-6*e1*e3*e5*e9*e45^2-9*e3*e9^2*e45^3;
g113:=e5^3*e9^3-e1*e3^2*e5*e15^2-e1^2*e5^2*e9*e45-3*e3^2*e9*e15^2*e45-3*e1*e5*e9^2*e45^2+e1^3*e45^3;
g114:=6*e9*e15^5-6*e1*e5*e9^2*e15*e45-5*e3*e5^3*e45^2-e1^3*e15*e45^2-9*e9^3*e15*e45^2-9*e3*e45^5;
g115:=e3^4-e1^2*e5^2-2*e3^2*e15^2+5*e15^4-6*e1*e5*e9*e45-9*e9^2*e45^2;
-- Somos eta relations --
x45_4_12:=-e3^4+e1^2*e5^2+2*e3^2*e15^2-5*e15^4+6*e1*e5*e9*e45+9*e9^2*e45^2;
x45_6_20:=-6*e3^5*e5+5*e1^2*e3*e5^3+e1^5*e15+15*e1^2*e9^3*e15+30*e1*e3*e5^2*e9*e45+15*e1^2*e3*e45^3;
x45_6_28:=-e3*e5^5+e1^3*e5^2*e15+3*e5^2*e9^3*e15-6*e1*e15^5+6*e1^2*e5*e9*e15*e45-15*e3*e5^2*e45^3;
x45_6_36:=5*e3*e5^3*e9^2-5*e1^3*e9^2*e15-9*e9^5*e15-6*e3^5*e45+30*e1*e3*e5*e9*e45^2+45*e3*e9^2*e45^3;
x45_6_84:=-6*e9*e15^5+6*e1*e5*e9^2*e15*e45+5*e3*e5^3*e45^2+e1^3*e15*e45^2+9*e9^3*e15*e45^2+9*e3*e45^5;
x45_8_48:=-e1*e5^4*e9^3+e1^2*e3^2*e5^2*e15^2+e3^4*e15^4-e1^4*e5*e45^3-9*e1*e5*e9^3*e45^3;
x45_8_72a:=-e3^4*e15^4+e1^3*e5^3*e9*e45+3*e1*e3^2*e5*e9*e15^2*e45+3*e1^2*e5^2*e9^2*e45^2+9*e1*e5*e9^3*e45^3;
x45_8_72b:=-e3^4*e15^4+e1^3*e5^3*e9*e45+3*e5^3*e9^4*e45-9*e3^2*e9^2*e15^2*e45^2+3*e1^3*e9*e45^4;
-- Relation relations --
relationRelations := [_
x45_4_12+g115,_
x45_6_20+g110+6*e3*e5*g115,_
x45_6_28+g111,_
x45_6_36-1*g112+6*e3*e45*g115,_
x45_6_84+g114,_
5*x45_8_48-1*g85-2*g93+5*e1*e5*g113-5*e15^4*g115,_
5*x45_8_72a+g85+2*g93+5*e15^4*g115,_
5*x45_8_72b+g85+2*g93-15*e9*e45*g113+5*e15^4*g115];