-- eta relations --
g1:=e1^12*e3^12-e1^18*e5^6-6*e1^16*e3^2*e5^4*e15^2-15*e1^14*e3^4*e5^2*e15^4+4*e1^12*e3^6*e15^6-729*e3^18*e15^6+720*e1^11*e3*e5^5*e15^7+8010*e1^9*e3^3*e5^3*e15^9+36090*e1^7*e3^5*e5*e15^11+119250*e1*e3^5*e5^7*e15^11+4130*e1^12*e15^12-7290*e3^12*e15^12-410625*e1^4*e3^2*e5^4*e15^14-972000*e1^2*e3^4*e5^2*e15^16;
g2:=5*e1^6*e5^18-5*e1^14*e3^4*e5^2*e15^4-40*e1^12*e3^6*e15^6-140*e1^11*e3*e5^5*e15^7-360*e1^9*e3^3*e5^3*e15^9-621*e1^7*e3^5*e5*e15^11-27045*e1*e3^5*e5^7*e15^11+211*e1^12*e15^12+29160*e3^12*e15^12+30*e1^6*e5^6*e15^12-625*e5^12*e15^12-44100*e1^4*e3^2*e5^4*e15^14-159165*e1^2*e3^4*e5^2*e15^16+3645*e3^6*e15^18;
g3:=2*e1^13*e5^7-2*e1^12*e3^7*e15+2*e1^11*e3^2*e5^5*e15^2-18*e1^12*e3*e15^7+1458*e3^13*e15^7-1460*e1^6*e3*e5^6*e15^7-3375*e3*e5^12*e15^7-5355*e1^4*e3^3*e5^4*e15^9-6885*e1^2*e3^5*e5^2*e15^11-1575*e1^7*e5*e15^12-3375*e1*e5^7*e15^12+21870*e3^7*e15^13;
g4:=10*e1^7*e5^8-9*e1^6*e3^7*e5*e15-e1^11*e3^2*e15^2+5*e1^5*e3^2*e5^6*e15^2+10*e1^3*e3^4*e5^4*e15^4-45*e1*e3^6*e5^2*e15^6-50*e1^6*e3*e5*e15^7+125*e3*e5^7*e15^7-1125*e1*e5^2*e15^12;
g5:=2*e1^8*e3^5*e5-2*e1^13*e15-10*e1^7*e5^6*e15-175*e3^7*e5^5*e15^2+195*e1^5*e3^2*e5^4*e15^3+865*e1^3*e3^4*e5^2*e15^5+1620*e1*e3^6*e15^7-125*e3*e5^5*e15^8+1125*e1*e15^13;
g6:=e1^7*e3^6*e5-e1^12*e3*e15-5*e1^6*e3*e5^6*e15-125*e3*e5^12*e15+135*e1^4*e3^3*e5^4*e15^3+495*e1^2*e3^5*e5^2*e15^5-125*e1*e5^7*e15^6+810*e3^7*e15^7;
g7:=9*e1*e3^12*e5-10*e1^7*e5^7+e1^6*e3^7*e15-55*e1^5*e3^2*e5^5*e15^2-135*e1^3*e3^4*e5^3*e15^4+45*e1*e3^6*e5*e15^6-125*e3*e5^6*e15^7+1125*e1*e5*e15^12;
g8:=9*e3^13*e5-10*e1^6*e3*e5^7+e1^5*e3^8*e15-55*e1^4*e3^3*e5^5*e15^2-125*e1^2*e3^5*e5^3*e15^4-10*e1^7*e5^2*e15^5-5*e1^5*e3^2*e15^7;
g9:=2*e1^2*e3^5*e5^7-2*e1^7*e5^6*e15+e3^7*e5^5*e15^2-11*e1^5*e3^2*e5^4*e15^3-25*e1^3*e3^4*e5^2*e15^5-25*e3*e5^5*e15^8+225*e1*e15^13;
g10:=25*e3*e5^13-25*e1^4*e3^3*e5^5*e15^2-99*e1^2*e3^5*e5^3*e15^4-e1^7*e5^2*e15^5+25*e1*e5^8*e15^5-162*e3^7*e5*e15^6-18*e1^5*e3^2*e15^7;
g11:=e1^6*e3^5*e5^2-5*e3^5*e5^8-e1^11*e5*e15+35*e1^3*e3^2*e5^5*e15^3+45*e1*e3^4*e5^3*e15^5-90*e1^4*e3*e15^8;
g12:=9*e1*e3^10*e5^2-8*e1^6*e3^5*e5*e15-50*e3^5*e5^7*e15-e1^11*e15^2+125*e1^3*e3^2*e5^4*e15^4+450*e1*e3^4*e5^2*e15^6;
g13:=9*e3^11*e5^2-8*e1^5*e3^6*e5*e15-e1^10*e3*e15^2-50*e1^4*e3*e5^6*e15^2-125*e1^2*e3^3*e5^4*e15^4-50*e1^5*e5*e15^7;
g14:=e1*e3^9*e5^3-e1^6*e3^4*e5^2*e15-5*e3^4*e5^8*e15+10*e1^3*e3*e5^5*e15^4+45*e1*e3^3*e5^3*e15^6+10*e1^4*e15^9;
g15:=e3^10*e5^3-2*e1^5*e3^5*e5^2*e15+e1^10*e5*e15^2-25*e1^2*e3^2*e5^5*e15^4+100*e1^3*e3*e15^9;
g16:=9*e1*e3^8*e5^4-9*e1^6*e3^3*e5^3*e15-25*e3^3*e5^9*e15-18*e1^4*e3^5*e5*e15^3-2*e1^9*e15^4+225*e1*e3^2*e5^4*e15^6;
g17:=2*e3^9*e5^4-2*e1^5*e3^4*e5^3*e15-9*e1^3*e3^6*e5*e15^3-e1^8*e3*e15^4-25*e1^2*e3*e5^6*e15^4-25*e1^3*e5*e15^9;
g18:=2*e1*e3^7*e5^5-2*e1^6*e3^2*e5^4*e15-5*e3^2*e5^10*e15-5*e1^4*e3^4*e5^2*e15^3+40*e1*e3*e5^5*e15^6+45*e1^2*e15^11;
g19:=e3^8*e5^5-e1^5*e3^3*e5^4*e15-7*e1^3*e3^5*e5^2*e15^3+2*e1^8*e5*e15^4-25*e3^2*e5^5*e15^6+225*e1*e3*e15^11;
g20:=10*e1*e3^4*e5^8-9*e3^11*e5*e15-e1^5*e3^6*e15^2+5*e1^4*e3*e5^5*e15^3+35*e1^2*e3^3*e5^3*e15^5+5*e1^5*e15^8;
g21:=100*e1*e3^3*e5^9-81*e3^10*e5^2*e15-18*e1^5*e3^5*e5*e15^2-e1^10*e15^3+225*e1^2*e3^2*e5^4*e15^5;
g22:=10*e3^4*e5^9-9*e1^4*e3^6*e5*e15^2-e1^9*e3*e15^3-45*e1^3*e3*e5^6*e15^3-90*e1*e3^3*e5^4*e15^5-45*e1^4*e5*e15^8;
g23:=5*e1*e3^2*e5^10-4*e3^9*e5^3*e15-e1^5*e3^4*e5^2*e15^2+10*e1^2*e3*e5^5*e15^5+5*e1^3*e15^10;
g24:=5*e3^3*e5^10-9*e1^4*e3^5*e5^2*e15^2+4*e1^9*e5*e15^3-90*e1*e3^2*e5^5*e15^5+405*e1^2*e3*e15^10;
g25:=25*e1*e3*e5^11-18*e3^8*e5^4*e15-7*e1^5*e3^3*e5^3*e15^2-9*e1^3*e3^5*e5*e15^4-e1^8*e15^5+25*e1^2*e5^6*e15^5;
g26:=5*e3^2*e5^11-5*e1^4*e3^4*e5^3*e15^2-18*e1^2*e3^6*e5*e15^4-2*e1^7*e3*e15^5-40*e1*e3*e5^6*e15^5-45*e1^2*e5*e15^10;
g27:=e3^6*e5^6-e1^5*e3*e5^5*e15-5*e1^3*e3^3*e5^3*e15^3-9*e1*e3^5*e5*e15^5-e1^6*e15^6;
g28:=e1^3*e3^6*e5^2-e1^8*e3*e5*e15-5*e1^2*e3*e5^7*e15+10*e3^3*e5^5*e15^3-5*e1^3*e5^2*e15^6-90*e1*e3^2*e15^8;
g29:=2*e1^3*e3^5*e5^3-2*e1^8*e5^2*e15-9*e1*e3^7*e5*e15^2-e1^6*e3^2*e15^3+25*e3^2*e5^6*e15^3-225*e1*e3*e5*e15^8;
g30:=e1^2*e3^6*e5^3-e1^7*e3*e5^2*e15-25*e1*e3*e5^8*e15+18*e3^8*e5*e15^2+2*e1^5*e3^3*e15^3-25*e1^2*e5^3*e15^6;
g31:=10*e1^2*e3*e5^8-9*e1*e3^8*e5*e15-e1^6*e3^3*e15^2+5*e3^3*e5^6*e15^2+10*e1^3*e5^3*e15^5-45*e1*e3^2*e5*e15^7;
-- Somos eta relations --
x15_11_31:=e1^3*e3^6*e5^2-e1^8*e3*e5*e15-5*e1^2*e3*e5^7*e15+10*e3^3*e5^5*e15^3-5*e1^3*e5^2*e15^6-90*e1*e3^2*e15^8;
x15_11_33:=-2*e1^3*e3^5*e5^3+2*e1^8*e5^2*e15+9*e1*e3^7*e5*e15^2+e1^6*e3^2*e15^3-25*e3^2*e5^6*e15^3+225*e1*e3*e5*e15^8;
x15_11_35:=e1^2*e3^6*e5^3-e1^7*e3*e5^2*e15-25*e1*e3*e5^8*e15+18*e3^8*e5*e15^2+2*e1^5*e3^3*e15^3-25*e1^2*e5^3*e15^6;
x15_11_45:=-10*e1^2*e3*e5^8+9*e1*e3^8*e5*e15+e1^6*e3^3*e15^2-5*e3^3*e5^6*e15^2-10*e1^3*e5^3*e15^5+45*e1*e3^2*e5*e15^7;
x15_12_48:=-e3^6*e5^6+e1^5*e3*e5^5*e15+5*e1^3*e3^3*e5^3*e15^3+9*e1*e3^5*e5*e15^5+e1^6*e15^6;
x15_13_45:=e3^10*e5^3-2*e1^5*e3^5*e5^2*e15+e1^10*e5*e15^2-25*e1^2*e3^2*e5^5*e15^4+100*e1^3*e3*e15^9;
x15_13_55:=-100*e1*e3^3*e5^9+81*e3^10*e5^2*e15+18*e1^5*e3^5*e5*e15^2+e1^10*e15^3-225*e1^2*e3^2*e5^4*e15^5;
x15_13_57:=-5*e1*e3^2*e5^10+4*e3^9*e5^3*e15+e1^5*e3^4*e5^2*e15^2-10*e1^2*e3*e5^5*e15^5-5*e1^3*e15^10;
x15_13_59:=5*e3^3*e5^10-9*e1^4*e3^5*e5^2*e15^2+4*e1^9*e5*e15^3-90*e1*e3^2*e5^5*e15^5+405*e1^2*e3*e15^10;
x15_14_50:=-e3^10*e5^4+e1^10*e5^2*e15^2+9*e1^3*e3^7*e5*e15^3+e1^8*e3^2*e15^4+125*e1^3*e3*e5*e15^9;
x15_14_62:=-e3^4*e5^10+e1^9*e3*e5*e15^3+9*e1^3*e3*e5^7*e15^3+9*e1^4*e5^2*e15^8+81*e1^2*e3^2*e15^10;
x15_16_48:=e1^8*e5^8-e1^7*e3^7*e5*e15+e1^6*e3^2*e5^6*e15^2-9*e1^2*e3^6*e5^2*e15^6+125*e1*e3*e5^7*e15^7-81*e3^8*e15^8;
x15_24_96:=-e3^12*e5^12+e1^9*e3^9*e5^3*e15^3+9*e1^3*e3^9*e5^9*e15^3+9*e1^9*e3^3*e5^3*e15^9+125*e1^3*e3^3*e5^9*e15^9+e1^12*e15^12;
-- Relation relations --
relationRelations := [_
x15_11_31-1*g28,_
x15_11_33+g29,_
x15_11_35-1*g30,_
x15_11_45+g31,_
x15_12_48+g27,_
x15_13_45-1*g15,_
x15_13_55+g21,_
x15_13_57+g23,_
x15_13_59-1*g24,_
x15_14_50+e5*g15+e1^2*e15*g29,_
10*x15_14_62+e5*g22+9*e1*e15^2*g28,_
10*x15_16_48-e1*g4+e3*e15*g6+25*e5*e15^2*g26,_
3240*x15_24_96+324*e1^3*e3^2*e5^2*e15^2*g4-162*e1*e3^4*e5^2*e15^3*g5+(1440*e1^3*e3^2*e5^4*e15-15300*e1*e3^4*e5^2*e15^3)*g9+(720*e1^4*e3*e5^3*e15^2+1800*e1^2*e3^3*e5*e15^4)*g10+730*e3*e5^4*e15^6*g11+(-1450*e3*e5^5*e15^5+8055*e1*e15^10)*g12+360*e3*e5^10*g13+565*e1^3*e15^8*g16-5945*e1^2*e15^9*g21-6885*e3^2*e5^3*e15^6*g22];