-- eta relations --
g1:=e5^5*e25^5-e1^5*e5^4*e125-5*e1^4*e5^4*e25*e125-15*e1^3*e5^4*e25^2*e125-25*e1^2*e5^4*e25^3*e125-25*e1*e5^4*e25^4*e125-5*e1^5*e5^3*e125^2-25*e1^4*e5^3*e25*e125^2-75*e1^3*e5^3*e25^2*e125^2-125*e1^2*e5^3*e25^3*e125^2-125*e1*e5^3*e25^4*e125^2-15*e1^5*e5^2*e125^3-75*e1^4*e5^2*e25*e125^3-225*e1^3*e5^2*e25^2*e125^3-375*e1^2*e5^2*e25^3*e125^3-375*e1*e5^2*e25^4*e125^3-25*e1^5*e5*e125^4-125*e1^4*e5*e25*e125^4-375*e1^3*e5*e25^2*e125^4-625*e1^2*e5*e25^3*e125^4-625*e1*e5*e25^4*e125^4-25*e1^5*e125^5-125*e1^4*e25*e125^5-375*e1^3*e25^2*e125^5-625*e1^2*e25^3*e125^5-625*e1*e25^4*e125^5;
g2:=e5^6-e1^5*e25-5*e1^4*e25^2-15*e1^3*e25^3-25*e1^2*e25^4-25*e1*e25^5;
g3:=e25^6-e5^5*e125-5*e5^4*e125^2-15*e5^3*e125^3-25*e5^2*e125^4-25*e5*e125^5;
-- Somos eta relations --
x125_7_55:=-e5^6*e25+e1^5*e25^2+5*e1^4*e25^3+15*e1^3*e25^4+25*e1^2*e25^5+25*e1*e5^5*e125+125*e1*e5^4*e125^2+375*e1*e5^3*e125^3+625*e1*e5^2*e125^4+625*e1*e5*e125^5;
x125_7_155:=-e5*e25^6+e1^5*e25*e125+5*e1^4*e25^2*e125+15*e1^3*e25^3*e125+25*e1^2*e25^4*e125+25*e1*e25^5*e125+5*e5^5*e125^2+15*e5^4*e125^3+25*e5^3*e125^4+25*e5^2*e125^5;
x125_8_60:=-e5^7*e25+e1^5*e5*e25^2+5*e1^4*e5*e25^3+15*e1^3*e5*e25^4+25*e1^2*e5*e25^5+25*e1^6*e25*e125+125*e1^5*e25^2*e125+375*e1^4*e25^3*e125+625*e1^3*e25^4*e125+625*e1^2*e25^5*e125+125*e1*e5^5*e125^2+375*e1*e5^4*e125^3+625*e1*e5^3*e125^4+625*e1*e5^2*e125^5;
x125_8_80:=-e5^6*e25^2+e1^5*e25^3+5*e1^4*e25^4+15*e1^3*e25^5+25*e1^2*e5^5*e125+25*e1*e5^5*e25*e125+125*e1^2*e5^4*e125^2+125*e1*e5^4*e25*e125^2+375*e1^2*e5^3*e125^3+375*e1*e5^3*e25*e125^3+625*e1^2*e5^2*e125^4+625*e1*e5^2*e25*e125^4+625*e1^2*e5*e125^5+625*e1*e5*e25*e125^5;
x125_8_160:=-e5^2*e25^6+e1^5*e5*e25*e125+5*e1^4*e5*e25^2*e125+15*e1^3*e5*e25^3*e125+25*e1^2*e5*e25^4*e125+25*e1*e5*e25^5*e125+5*e1^5*e25*e125^2+25*e1^4*e25^2*e125^2+75*e1^3*e25^3*e125^2+125*e1^2*e25^4*e125^2+125*e1*e25^5*e125^2+15*e5^5*e125^3+25*e5^4*e125^4+25*e5^3*e125^5;
x125_8_180:=-e5*e25^7+e1^5*e25^2*e125+5*e1^4*e25^3*e125+15*e1^3*e25^4*e125+25*e1^2*e25^5*e125+25*e1*e5^5*e125^2+5*e5^5*e25*e125^2+125*e1*e5^4*e125^3+15*e5^4*e25*e125^3+375*e1*e5^3*e125^4+25*e5^3*e25*e125^4+625*e1*e5^2*e125^5+25*e5^2*e25*e125^5+625*e1*e5*e125^6;
-- Relation relations --
relationRelations := [_
x125_7_55+e25*g2+25*e1*g3,_
x125_7_155+e125*g2+e5*g3,_
x125_8_60+(e5*e25+25*e1*e125)*g2+25*e1*e5*g3,_
x125_8_80+e25^2*g2+(25*e1^2+25*e1*e25)*g3,_
x125_8_160+(e5*e125+5*e125^2)*g2+e5^2*g3,_
x125_8_180+e25*e125*g2+(e5*e25+25*e1*e125)*g3];