-- eta relations --
g1:=e1^8*e2^6*e4^10-e1^12*e2^8*e8^4-4*e1^4*e2^8*e4^8*e8^4+32*e2^10*e4^6*e8^8-16*e1^12*e8^12-256*e1^4*e4^8*e8^12;
g2:=e2^10*e4^8-e1^12*e4^2*e8^4-8*e1^4*e4^10*e8^4-4*e1^8*e2^2*e8^8;
g3:=e2^8*e4^10-e1^4*e2^10*e8^4-4*e1^8*e4^2*e8^8-32*e1^4*e2^2*e8^12;
g4:=e2^12-e1^8*e4^4-8*e1^4*e2^2*e4^2*e8^4;
g5:=e4^12-e1^4*e2^2*e4^2*e8^4-4*e2^4*e8^8;
-- Somos eta relations --
q8_12_24:=-e2^12+e1^8*e4^4+8*e4^12-32*e2^4*e8^8;
t8_12_24:=-e2^12+e1^8*e4^4+8*e1^4*e2^2*e4^2*e8^4;
t8_12_48:=-e4^12+e1^4*e2^2*e4^2*e8^4+4*e2^4*e8^8;
q8_18_36:=-e1^4*e2^12*e4^2+e1^12*e4^6+16*e1^4*e4^14-8*e2^14*e8^4;
x8_18_36a:=-e1^4*e2^12*e4^2+e1^12*e4^6+8*e1^4*e4^14-32*e2^2*e4^12*e8^4+128*e2^6*e8^12;
x8_18_36b:=-e1^4*e2^12*e4^2+e1^12*e4^6+8*e2^14*e8^4-64*e2^2*e4^12*e8^4+256*e2^6*e8^12;
q8_18_52:=-e2^10*e4^8+e1^12*e4^2*e8^4+8*e1^4*e4^10*e8^4+4*e1^8*e2^2*e8^8;
q8_18_56:=-e2^8*e4^10+e1^4*e2^10*e8^4+4*e1^8*e4^2*e8^8+32*e1^4*e2^2*e8^12;
q8_18_60:=e1^4*e4^14-e2^14*e8^4+4*e2^2*e4^12*e8^4-16*e2^6*e8^12;
t8_18_60a:=e1^4*e4^14-e2^14*e8^4+4*e1^4*e2^4*e4^2*e8^8;
t8_18_60b:=-2*e1^4*e4^14+e2^14*e8^4+e1^8*e2^2*e4^4*e8^4;
x8_20_40:=-e2^20+e1^8*e2^8*e4^4+8*e2^8*e4^12-32*e1^8*e4^4*e8^8-256*e1^4*e2^2*e4^2*e8^12;
x8_20_56:=-e2^12*e4^8+8*e4^20+e1^12*e2^2*e4^2*e8^4+4*e1^8*e2^4*e8^8-32*e2^4*e4^8*e8^8;
q8_20_60a:=-e2^10*e4^10+e1^4*e2^12*e8^4+4*e1^4*e4^12*e8^4+16*e1^4*e2^4*e8^12;
q8_20_60b:=-e2^10*e4^10+e1^12*e4^4*e8^4+12*e1^4*e4^12*e8^4-16*e1^4*e2^4*e8^12;
q8_20_60c:=-2*e2^10*e4^10+e1^4*e2^12*e8^4+e1^12*e4^4*e8^4+16*e1^4*e4^12*e8^4;
q8_20_60d:=2*e2^10*e4^10-3*e1^4*e2^12*e8^4+e1^12*e4^4*e8^4-64*e1^4*e2^4*e8^12;
q8_20_60e:=-e2^10*e4^10+e1^4*e2^12*e8^4+8*e1^4*e4^12*e8^4-4*e1^8*e2^2*e4^2*e8^8;
q8_20_60f:=-e2^10*e4^10+e1^12*e4^4*e8^4+12*e1^8*e2^2*e4^2*e8^8+32*e1^4*e2^4*e8^12;
q8_22_64a:=-e2^12*e4^10+e1^8*e4^14+8*e1^8*e2^4*e4^2*e8^8+32*e1^4*e2^6*e8^12;
q8_22_64b:=e2^12*e4^10+e1^8*e4^14-2*e1^4*e2^14*e8^4-32*e1^4*e2^6*e8^12;
q8_22_64c:=e2^12*e4^10-3*e1^8*e4^14+2*e1^12*e2^2*e4^4*e8^4-32*e1^4*e2^6*e8^12;
q8_22_68a:=-e2^10*e4^12+e1^12*e4^6*e8^4+4*e2^14*e8^8+8*e1^8*e2^2*e4^4*e8^8;
q8_22_68b:=-e2^10*e4^12+e1^12*e4^6*e8^4+12*e2^14*e8^8-64*e1^4*e2^4*e4^2*e8^12;
q8_22_68c:=-e2^10*e4^12+e1^12*e4^6*e8^4+16*e1^4*e4^14*e8^4-4*e2^14*e8^8;
x8_24_48:=-e2^24+e1^8*e2^12*e4^4+8*e1^8*e4^16+32*e2^16*e8^8-256*e1^4*e2^6*e4^2*e8^12;
q8_24_48a:=-e2^24+e1^8*e2^12*e4^4+16*e1^8*e4^16-8*e1^12*e2^2*e4^6*e8^4;
q8_24_48b:=-e2^24+e1^8*e2^12*e4^4+8*e1^8*e4^16+32*e1^8*e2^4*e4^4*e8^8;
q8_24_48c:=-e2^24+e1^16*e4^8+16*e2^12*e4^12-128*e1^4*e2^2*e4^14*e8^4;
x8_24_72:=-e1^8*e4^16+8*e4^24+e1^12*e2^2*e4^6*e8^4-4*e2^16*e8^8-32*e2^4*e4^12*e8^8;
q8_24_72a:=-e2^12*e4^12+e1^8*e4^16+8*e2^16*e8^8-32*e1^4*e2^6*e4^2*e8^12;
q8_24_72b:=e2^12*e4^12-2*e1^8*e4^16+e1^12*e2^2*e4^6*e8^4-4*e2^16*e8^8;
q8_24_72c:=-e1^8*e4^16+e1^12*e2^2*e4^6*e8^4+8*e1^4*e2^2*e4^14*e8^4-4*e2^16*e8^8;
q8_24_72d:=-e1^8*e4^16+e1^4*e2^14*e4^2*e8^4-4*e2^16*e8^8+32*e1^4*e2^6*e4^2*e8^12;
q8_24_72e:=-e1^8*e4^16+e1^12*e2^2*e4^6*e8^4+4*e2^16*e8^8-32*e1^4*e2^6*e4^2*e8^12;
q8_24_72f:=-e2^12*e4^12+e1^8*e4^16+4*e2^16*e8^8+4*e1^8*e2^4*e4^4*e8^8;
q8_24_72g:=-e1^8*e4^16+e1^4*e2^14*e4^2*e8^4-8*e1^4*e2^2*e4^14*e8^4+4*e2^16*e8^8;
q8_24_72h:=-e2^12*e4^12+4*e4^24+e1^4*e2^14*e4^2*e8^4-64*e2^8*e8^16;
q8_24_96a:=-2*e4^24+e2^16*e8^8+e1^8*e2^4*e4^4*e8^8+8*e2^4*e4^12*e8^8;
q8_24_96b:=-e4^24+e2^16*e8^8+4*e2^4*e4^12*e8^8-4*e1^4*e2^6*e4^2*e8^12;
q8_26_76:=e1^4*e2^8*e4^14-e2^22*e8^4+4*e1^12*e4^6*e8^8+32*e1^8*e2^2*e4^4*e8^12;
q8_26_92:=-2*e1^4*e4^22+e2^14*e4^8*e8^4+e1^12*e2^4*e4^2*e8^8+4*e1^8*e2^6*e8^12;
-- Relation relations --
relationRelations := [_
q8_12_24+g4-8*g5,_
t8_12_24+g4,_
t8_12_48+g5,_
q8_18_36+(e1^4*e4^2+8*e2^2*e8^4)*g4-16*e1^4*e4^2*g5,_
x8_18_36a+e1^4*e4^2*g4+(-8*e1^4*e4^2+32*e2^2*e8^4)*g5,_
x8_18_36b+(e1^4*e4^2-8*e2^2*e8^4)*g4+64*e2^2*e8^4*g5,_
q8_18_52+g2,_
q8_18_56+g3,_
q8_18_60+e2^2*e8^4*g4+(-e1^4*e4^2-4*e2^2*e8^4)*g5,_
t8_18_60a+e2^2*e8^4*g4-e1^4*e4^2*g5,_
t8_18_60b-e2^2*e8^4*g4+2*e1^4*e4^2*g5,_
x8_20_40-8*e4^2*g3+e2^8*g4,_
x8_20_56+e2^2*g2-8*e4^8*g5,_
q8_20_60a+e4^2*g2-e1^4*e8^4*g4+4*e1^4*e8^4*g5,_
q8_20_60b+e4^2*g2-4*e1^4*e8^4*g5,_
q8_20_60c+2*e4^2*g2-e1^4*e8^4*g4,_
q8_20_60d-2*e4^2*g2+3*e1^4*e8^4*g4-16*e1^4*e8^4*g5,_
q8_20_60e+e4^2*g2-e1^4*e8^4*g4,_
q8_20_60f+e4^2*g2+8*e1^4*e8^4*g5,_
q8_22_64a+e2^2*e4^2*g2+(-e1^8*e4^2+8*e1^4*e2^2*e8^4)*g5,_
q8_22_64b-e2^2*e4^2*g2+2*e1^4*e2^2*e8^4*g4+(-e1^8*e4^2-8*e1^4*e2^2*e8^4)*g5,_
q8_22_64c-e2^2*e4^2*g2+(3*e1^8*e4^2-8*e1^4*e2^2*e8^4)*g5,_
q8_22_68a+e4^4*g2-4*e2^2*e8^8*g4+8*e1^4*e4^2*e8^4*g5,_
q8_22_68b+e4^4*g2-12*e2^2*e8^8*g4+8*e1^4*e4^2*e8^4*g5,_
q8_22_68c+e4^4*g2+4*e2^2*e8^8*g4-8*e1^4*e4^2*e8^4*g5,_
x8_24_48+(e2^12+8*e1^4*e2^2*e4^2*e8^4-32*e2^4*e8^8)*g4-8*e1^8*e4^4*g5,_
q8_24_48a+(e2^12+8*e1^4*e2^2*e4^2*e8^4)*g4-16*e1^8*e4^4*g5,_
q8_24_48b+(e2^12+8*e1^4*e2^2*e4^2*e8^4)*g4-8*e1^8*e4^4*g5,_
q8_24_48c-16*e2^2*e4^4*g2+(e2^12+e1^8*e4^4+8*e1^4*e2^2*e4^2*e8^4)*g4,_
x8_24_72+4*e2^4*e8^8*g4+(e1^8*e4^4-8*e4^12-8*e1^4*e2^2*e4^2*e8^4)*g5,_
q8_24_72a+e2^2*e4^4*g2-8*e2^4*e8^8*g4+(-e1^8*e4^4+8*e1^4*e2^2*e4^2*e8^4)*g5,_
q8_24_72b-e2^2*e4^4*g2+4*e2^4*e8^8*g4+(2*e1^8*e4^4-8*e1^4*e2^2*e4^2*e8^4)*g5,_
q8_24_72c+4*e2^4*e8^8*g4+(e1^8*e4^4-8*e1^4*e2^2*e4^2*e8^4)*g5,_
q8_24_72d+(-e1^4*e2^2*e4^2*e8^4+4*e2^4*e8^8)*g4+e1^8*e4^4*g5,_
q8_24_72e-4*e2^4*e8^8*g4+e1^8*e4^4*g5,_
q8_24_72f+e2^2*e4^4*g2-4*e2^4*e8^8*g4+(-e1^8*e4^4+8*e1^4*e2^2*e4^2*e8^4)*g5,_
q8_24_72g+(-e1^4*e2^2*e4^2*e8^4-4*e2^4*e8^8)*g4+(e1^8*e4^4+8*e1^4*e2^2*e4^2*e8^4)*g5,_
q8_24_72h+e2^2*e4^4*g2-e1^4*e2^2*e4^2*e8^4*g4+(-4*e4^12+4*e1^4*e2^2*e4^2*e8^4-16*e2^4*e8^8)*g5,_
q8_24_96a-e2^4*e8^8*g4+(2*e4^12+2*e1^4*e2^2*e4^2*e8^4)*g5,_
q8_24_96b-e2^4*e8^8*g4+(e4^12+e1^4*e2^2*e4^2*e8^4)*g5,_
q8_26_76-e1^4*e4^4*g3+(e2^10*e8^4+8*e1^4*e4^2*e8^8)*g4,_
q8_26_92-e2^4*e8^4*g2+(2*e1^4*e4^10+2*e1^8*e2^2*e8^4)*g5];