-- eta relations --
g1:=e1^6*e3^6-e1^10*e7^2-4*e1^5*e3^5*e7*e21+27*e3^10*e21^2-21*e1^4*e3^4*e7^2*e21^2-98*e1^6*e3^2*e21^4-1029*e1^2*e3^2*e7^4*e21^4+392*e1^5*e3*e7*e21^5+4802*e1*e3*e7^5*e21^5-2646*e3^6*e21^6-686*e1^4*e7^2*e21^6;
g2:=e1^7*e7^5-e1^6*e3^5*e21+e1^5*e3^4*e7*e21^2-27*e3^9*e21^3+27*e1^4*e3^3*e7^2*e21^3+98*e1^3*e3^2*e7^3*e21^4+3*e1^6*e3*e21^5+343*e1^2*e3*e7^4*e21^5-42*e1^5*e7*e21^6;
g3:=e1^2*e7^10-e1^4*e3^4*e7^2*e21^2-2*e1^6*e3^2*e21^4-17*e1^2*e3^2*e7^4*e21^4+8*e1^5*e3*e7*e21^5+94*e1*e3*e7^5*e21^5-54*e3^6*e21^6-14*e1^4*e7^2*e21^6+7*e7^6*e21^6-27*e3^2*e21^10;
g4:=e1^2*e3^6*e7-e1^6*e7^3-4*e1*e3^5*e7^2*e21+7*e3^4*e7^3*e21^2-e1^3*e3^3*e21^3+7*e1^2*e3^2*e7*e21^4-49*e1*e3*e7^2*e21^5;
g5:=e1*e3^6*e7^2-e1^5*e7^4-4*e3^5*e7^3*e21+6*e1^2*e3^3*e7*e21^3+28*e1*e3^2*e7^2*e21^4-7*e1^3*e21^6;
g6:=e1^3*e3^3*e7^3-e1^6*e3^2*e21-7*e1^2*e3^2*e7^4*e21+4*e1^5*e3*e7*e21^2+49*e1*e3*e7^5*e21^2-27*e3^6*e21^3-7*e1^4*e7^2*e21^3;
g7:=e3^6*e7^3-e1^4*e7^5-4*e1^2*e3^4*e7*e21^2-6*e1*e3^3*e7^2*e21^3+4*e1^3*e3*e21^5-7*e1^2*e7*e21^6;
g8:=2*e1^3*e3^2*e7^4-2*e1^6*e3*e7*e21-7*e1^2*e3*e7^5*e21+e1^5*e7^2*e21^2+9*e3^5*e7*e21^3-63*e1*e3^2*e21^6;
g9:=e1^2*e3^3*e7^4-e1^5*e3^2*e7*e21-4*e1*e3^2*e7^5*e21+e1^4*e3*e7^2*e21^2+7*e3*e7^6*e21^2-e1^3*e7^3*e21^3-27*e3^3*e21^6;
g10:=e1^3*e3*e7^5-e1^6*e7^2*e21-3*e1*e3^5*e7*e21^2+6*e3^4*e7^2*e21^3+3*e1^2*e3^2*e21^5-42*e1*e3*e7*e21^6;
g11:=e1^2*e3^2*e7^5-e1^5*e3*e7^2*e21-14*e1*e3*e7^6*e21+9*e3^6*e7*e21^2+2*e1^4*e7^3*e21^2-9*e1*e3^3*e21^5;
g12:=4*e1*e3^3*e7^5-4*e1^4*e3^2*e7^2*e21-7*e3^2*e7^6*e21-6*e1^3*e3*e7^3*e21^2+e1^6*e21^3+27*e3^4*e21^5;
g13:=e1^3*e7^6-e1^2*e3^5*e7*e21+e1*e3^4*e7^2*e21^2-e3^3*e7^3*e21^3+e1^3*e3^2*e21^4-4*e1^2*e3*e7*e21^5+7*e1*e7^2*e21^6;
g14:=7*e1^2*e3*e7^6-6*e1*e3^6*e7*e21-e1^5*e7^3*e21+3*e3^5*e7^2*e21^2+6*e1^2*e3^3*e21^4-21*e1*e3^2*e7*e21^5;
g15:=e1*e3^2*e7^6+8*e3*e7^7*e21-e1^7*e21^2-14*e1^3*e7^4*e21^2-27*e1*e3^4*e21^4-18*e3^3*e7*e21^5-90*e1*e21^8;
g16:=7*e3^3*e7^6-6*e1^3*e3^2*e7^3*e21-e1^6*e3*e21^2-28*e1^2*e3*e7^4*e21^2+4*e1^5*e7*e21^3-27*e3^5*e21^4;
g17:=4*e1*e3*e7^7-3*e3^6*e7^2*e21-e1^4*e7^4*e21+6*e1*e3^3*e7*e21^4-3*e1^2*e21^7;
g18:=e3^2*e7^7-2*e1^3*e3*e7^4*e21+e1^6*e7*e21^2-9*e3^4*e7*e21^4+36*e1*e3*e21^7;
g19:=e3*e7^8-e1^3*e7^5*e21-3*e1*e3^4*e7*e21^3-3*e3^3*e7^2*e21^4+3*e1^2*e3*e21^6-6*e1*e7*e21^7;
g20:=e3^7*e7+7*e3*e7^7-e1^7*e21-14*e1^3*e7^4*e21-28*e1*e3^4*e21^3-14*e3^3*e7*e21^4-91*e1*e21^7;
g21:=e1^4*e3*e7^3+10*e3*e7^7-e1^7*e21-13*e1^3*e7^4*e21-27*e1*e3^4*e21^3-27*e3^3*e7*e21^4-81*e1*e21^7;
g22:=e3^4*e7^4-e1^3*e3^3*e7*e21-3*e1^2*e3^2*e7^2*e21^2-7*e1*e3*e7^3*e21^3+e1^4*e21^4;
-- Somos eta relations --
x21_8_28a:=81*e3^7*e7-91*e1^4*e3*e7^3-343*e3*e7^7+10*e1^7*e21+49*e1^3*e7^4*e21+189*e1*e3^4*e21^3+1323*e3^3*e7*e21^4;
x21_8_28b:=-e3^7*e7+e1^4*e3*e7^3+3*e3*e7^7+e1^3*e7^4*e21+e1*e3^4*e21^3-13*e3^3*e7*e21^4+10*e1*e21^7;
x21_8_28c:=-27*e3^7*e7+14*e1^4*e3*e7^3-49*e3*e7^7+13*e1^7*e21+196*e1^3*e7^4*e21+378*e1*e3^4*e21^3+1323*e1*e21^7;
x21_8_28d:=-e3^7*e7-7*e3*e7^7+e1^7*e21+14*e1^3*e7^4*e21+28*e1*e3^4*e21^3+14*e3^3*e7*e21^4+91*e1*e21^7;
x21_8_40:=e3^4*e7^4-e1^3*e3^3*e7*e21-3*e1^2*e3^2*e7^2*e21^2-7*e1*e3*e7^3*e21^3+e1^4*e21^4;
x21_9_35:=3*e3^7*e7^2-7*e1^4*e3*e7^4+4*e1^7*e7*e21-42*e1*e3^4*e7*e21^3+147*e1^2*e3*e21^6;
x21_9_37:=2*e1^3*e3^2*e7^4-2*e1^6*e3*e7*e21-7*e1^2*e3*e7^5*e21+e1^5*e7^2*e21^2+9*e3^5*e7*e21^3-63*e1*e3^2*e21^6;
x21_9_41:=e1^3*e3*e7^5-e1^6*e7^2*e21-3*e1*e3^5*e7*e21^2+6*e3^4*e7^2*e21^3+3*e1^2*e3^2*e21^5-42*e1*e3*e7*e21^6;
x21_9_43:=e1^2*e3^2*e7^5-e1^5*e3*e7^2*e21-14*e1*e3*e7^6*e21+9*e3^6*e7*e21^2+2*e1^4*e7^3*e21^2-9*e1*e3^3*e21^5;
x21_9_47:=-7*e1^2*e3*e7^6+6*e1*e3^6*e7*e21+e1^5*e7^3*e21-3*e3^5*e7^2*e21^2-6*e1^2*e3^3*e21^4+21*e1*e3^2*e7*e21^5;
x21_9_55:=e3^2*e7^7-2*e1^3*e3*e7^4*e21+e1^6*e7*e21^2-9*e3^4*e7*e21^4+36*e1*e3*e21^7;
x21_12_48:=e1^6*e7^6-e1^5*e3^5*e7*e21+e1^4*e3^4*e7^2*e21^2-7*e1^2*e3^2*e7^4*e21^4+49*e1*e3*e7^5*e21^5-27*e3^6*e21^6;
-- Relation relations --
relationRelations := [_
x21_8_28a-81*g20+91*g21,_
x21_8_28b+g20-1*g21,_
x21_8_28c+27*g20-14*g21,_
x21_8_28d+g20,_
x21_8_40-1*g22,_
x21_9_35-49*g19-3*e7*g20+7*e7*g21,_
x21_9_37-1*g8,_
x21_9_41-1*g10,_
x21_9_43-1*g11,_
x21_9_47+g14,_
x21_9_55-1*g18,_
x21_12_48-e21^3*g6-e1^3*g13];