-- eta relations --
g1:=e1^6*e3*e9^11-e1^12*e3^2*e9*e27^3-6*e1^9*e3^2*e9^4*e27^3-9*e1^6*e3^2*e9^7*e27^3+9*e1^3*e3^2*e9^10*e27^3-27*e1^6*e3^3*e9^3*e27^6-81*e1^3*e3^3*e9^6*e27^6+81*e3^3*e9^9*e27^6-27*e1^9*e27^9-324*e1^6*e9^3*e27^9-1458*e1^3*e9^6*e27^9-1458*e9^9*e27^9+1458*e1^3*e3*e9^2*e27^12+6561*e3*e9^5*e27^12-6561*e3^2*e9*e27^15;
g2:=e1^3*e3^2*e9^11-e1^9*e3^3*e9*e27^3-6*e1^6*e3^3*e9^4*e27^3-9*e1^3*e3^3*e9^7*e27^3+9*e3^3*e9^10*e27^3-27*e1^6*e9^4*e27^6-162*e1^3*e9^7*e27^6-162*e9^10*e27^6-27*e1^6*e3*e27^9+162*e1^3*e3*e9^3*e27^9+729*e3*e9^6*e27^9-729*e3^2*e9^2*e27^12;
g3:=e3^3*e9^11-e1^9*e9^2*e27^3-9*e1^6*e9^5*e27^3-27*e1^3*e9^8*e27^3-18*e9^11*e27^3+9*e1^6*e3*e9*e27^6+54*e1^3*e3*e9^4*e27^6+81*e3*e9^7*e27^6-27*e1^3*e3^2*e27^9-81*e3^2*e9^3*e27^9;
g4:=e9^12-e1^6*e3*e9^2*e27^3-6*e1^3*e3*e9^5*e27^3-9*e3*e9^8*e27^3+9*e1^3*e3^2*e9*e27^6+27*e3^2*e9^4*e27^6-27*e3^3*e27^9;
g5:=e3^4-e1^3*e9-3*e9^4+9*e3*e27^3;
-- Somos eta relations --
q27_4_12:=-e3^4+e1^3*e9+3*e9^4-9*e3*e27^3;
q27_12_36:=-e3^12+e1^9*e9^3+9*e1^3*e3^4*e9^5+81*e1^3*e3*e9^5*e27^3;
x27_12_36a:=-e3^12+e1^3*e3^8*e9+3*e3^8*e9^4-9*e9^12+81*e3^6*e27^6+243*e3^3*e27^9;
x27_12_36b:=-e3^12+e1^9*e9^3+9*e1^6*e9^6+27*e3^4*e9^8-81*e9^12+243*e3*e9^8*e27^3;
x27_12_36c:=e3^12+3*e1^3*e3^8*e9-6*e1^6*e3^4*e9^2+2*e1^9*e9^3-18*e1^3*e3^4*e9^5+9*e1^6*e9^6-243*e1^3*e3^2*e9*e27^6;
q27_12_108:=-e9^12+e1^3*e3^5*e9*e27^3+3*e3^5*e9^4*e27^3+27*e3^3*e27^9;
x27_12_108:=-e9^12+e1^6*e3*e9^2*e27^3+6*e3^5*e9^4*e27^3-9*e3*e9^8*e27^3-9*e3^6*e27^6+54*e3^2*e9^4*e27^6-54*e3^3*e27^9;
x27_16_48:=-e3^16+e1^9*e3^4*e9^3+3*e3^12*e9^4+9*e1^6*e3^4*e9^6-3*e1^9*e9^7-243*e1^3*e3*e9^9*e27^3;
x27_16_120:=-e3^4*e9^12+3*e9^16+e1^3*e3^9*e9*e27^3-27*e3^6*e9^4*e27^6+27*e3^7*e27^9-81*e3^3*e9^4*e27^9;
-- Relation relations --
relationRelations := [_
q27_4_12+g5,_
q27_12_36+27*g4+(e3^8+e1^3*e3^4*e9+e1^6*e9^2+3*e3^4*e9^4-3*e1^3*e9^5+9*e9^8-9*e3^5*e27^3-18*e1^3*e3*e9*e27^3-54*e3*e9^4*e27^3+81*e3^2*e27^6)*g5,_
x27_12_36a+9*g4+(e3^8-9*e3^5*e27^3-9*e1^3*e3*e9*e27^3-27*e3*e9^4*e27^3)*g5,_
x27_12_36b+27*g4+(e3^8+e1^3*e3^4*e9+e1^6*e9^2+3*e3^4*e9^4+6*e1^3*e9^5-18*e9^8-9*e3^5*e27^3-18*e1^3*e3*e9*e27^3-54*e3*e9^4*e27^3+81*e3^2*e27^6)*g5,_
x27_12_36c-27*g4+(-e3^8-4*e1^3*e3^4*e9+2*e1^6*e9^2-3*e3^4*e9^4+3*e1^3*e9^5-9*e9^8+9*e3^5*e27^3+45*e1^3*e3*e9*e27^3+54*e3*e9^4*e27^3-81*e3^2*e27^6)*g5,_
q27_12_108+g4+(-e1^3*e3*e9*e27^3-3*e3*e9^4*e27^3)*g5,_
x27_12_108+g4+(-6*e3*e9^4*e27^3+9*e3^2*e27^6)*g5,_
x27_16_48+(27*e1^3*e9-243*e3*e27^3)*g4+(e3^12+e1^3*e3^8*e9+e1^6*e3^4*e9^2+3*e1^3*e3^4*e9^5-3*e1^6*e9^6+9*e1^3*e9^9-9*e3^9*e27^3-18*e1^3*e3^5*e9*e27^3-27*e1^6*e3*e9^2*e27^3-27*e3^5*e9^4*e27^3-108*e1^3*e3*e9^5*e27^3-81*e3*e9^8*e27^3+81*e3^6*e27^6+243*e1^3*e3^2*e9*e27^6+486*e3^2*e9^4*e27^6-729*e3^3*e27^9)*g5,_
x27_16_120+e3*e9*g3+(-3*e9^4-9*e3*e27^3)*g4+(-e1^3*e3^5*e9*e27^3-e1^6*e3*e9^2*e27^3-3*e1^3*e3*e9^5*e27^3+9*e1^3*e3^2*e9*e27^6+27*e3^2*e9^4*e27^6-27*e3^3*e27^9)*g5];