etaRelations:=[e1^21*e3*e6^6-e1^16*e2^6*e4^5*e12-16*e1^8*e2^6*e4^13*e12+21*e1^15*e2^2*e3^3*e4^2*e6^4*e12^2+96*e1^16*e2^2*e4*e6^4*e12^5+599*e1^13*e2^4*e3*e6^2*e12^8+6561*e1^4*e2*e3^4*e6^11*e12^8+755*e1^7*e2^6*e3^3*e4^2*e12^10-3294*e1^5*e2^6*e3*e4^4*e12^12-5613*e1^8*e2^6*e4*e12^13+4096*e2^6*e4^9*e12^13-22545*e1^8*e4*e6^6*e12^13-127602*e1^5*e2^2*e3*e6^4*e12^16-1141128*e2^3*e6^9*e12^16+1184976*e2^2*e4^5*e6^4*e12^17-511920*e2^4*e4*e6^2*e12^21, e1^6*e6^19-e1^13*e2*e3^3*e12^8+27*e3^10*e6^7*e12^8-7*e1^11*e2*e3*e4^2*e12^10-32*e1^3*e2*e3*e4^10*e12^10-25*e1^6*e2^2*e4^2*e6^5*e12^10+8*e1^6*e2*e4^7*e12^11-27*e1^3*e2^4*e3*e4*e6^3*e12^13+498*e1*e2*e3^7*e12^16-877*e2^6*e3^2*e6*e12^16+963*e3^2*e6^7*e12^16-2568*e2*e3^2*e4*e12^21, e1^16*e4^8+16*e1^8*e4^16-e1^15*e2^3*e3^3*e6^3-15*e1^13*e2^3*e3*e4^2*e6^3*e12^2-84*e1^10*e2^5*e3^2*e4*e6*e12^5-113*e1^12*e3^4*e12^8+11340*e1^2*e2^2*e3^2*e6^10*e12^8-588*e1^10*e3^2*e4^2*e12^10-8800*e1^5*e3*e4^7*e12^11-36288*e2*e4^7*e6^5*e12^11-2960*e1^8*e4^4*e12^12-4096*e4^12*e12^12-432*e1^2*e2^3*e3^2*e4*e6^3*e12^13+122688*e2^3*e4^3*e6^3*e12^15, 3*e2^2*e6^22+e1^4*e3^12*e12^8-4*e1^7*e2^3*e3^3*e6^3*e12^8-24*e1^5*e2^3*e3*e4^2*e6^3*e12^10-72*e1^2*e2^5*e3^2*e4*e6*e12^13-112*e1*e3^5*e4^3*e12^15+120*e1^4*e3^4*e12^16+192*e1^2*e3^2*e4^2*e12^18, e6^24-e3^16*e12^8-16*e3^8*e12^16, e1^16*e2*e6^5-e1^16*e4^5*e12-16*e1^8*e4^13*e12+16*e1^10*e2^3*e3^2*e4^2*e6^3*e12^2+33*e1^7*e2^5*e3^3*e4*e6*e12^5+23*e1^8*e2^5*e6*e12^8-729*e1^4*e2*e3^4*e6^5*e12^8+748*e1^7*e3^3*e4^2*e12^10+2400*e1^5*e3*e4^4*e12^12-3456*e2*e4^4*e6^5*e12^12-224*e1^8*e4*e12^13+4096*e4^9*e12^13-3456*e2^3*e6^3*e12^16, 3*e1^2*e2*e6^17-2*e1^7*e3*e4^6*e12^6-e1^10*e4^3*e12^7-9*e1*e3^11*e12^8-6*e2^5*e3^6*e6*e12^8-3*e1^4*e2^3*e3^2*e6^3*e12^8+48*e1^2*e2^3*e4^2*e6^3*e12^10+24*e3^6*e4*e12^13-96*e1*e3^3*e12^16, 3*e1^7*e6^12-3*e1^12*e3*e4*e12^5-32*e1^4*e3*e4^9*e12^5+9*e1^7*e2*e4*e6^5*e12^5+8*e1^7*e4^6*e12^6+81*e1*e3^10*e12^8-63*e2^5*e3^5*e6*e12^8+93*e1^4*e2^3*e3*e6^3*e12^8-216*e3^5*e4*e12^13+864*e1*e3^2*e12^16, 3*e1^10*e3^2*e6^6-243*e2^2*e6^16-2*e1^5*e2^6*e3*e4^5*e12-e1^8*e2^6*e4^2*e12^2+12*e1^8*e4^2*e6^6*e12^2+246*e1^5*e2^2*e3*e4*e6^4*e12^5+528*e2^2*e4^6*e6^4*e12^6+684*e1^2*e2^4*e3^2*e6^2*e12^8+144*e2^4*e4^2*e6^2*e12^10, e2^3*e6^15-e1^5*e2^3*e3*e4*e6^3*e12^5+e1^3*e3^7*e12^8-6*e1^2*e2^5*e3^2*e6*e12^8-4*e1*e3^5*e4^2*e12^10-16*e1^2*e3^2*e4*e12^13, 64*e3*e4^16+3*e1^11*e2*e6^5-3*e1^11*e4^5*e12-16*e1^3*e4^13*e12-48*e1^5*e2^3*e3^2*e4^2*e6^3*e12^2-285*e1^2*e2^5*e3^3*e4*e6*e12^5+243*e1^4*e3^5*e12^8-750*e1^3*e2^5*e6*e12^8-1620*e1^2*e3^3*e4^2*e12^10-5184*e1^3*e4*e12^13, 3*e1^7*e3^3*e6^6+27*e1^2*e2*e3^2*e6^11-2*e1^2*e2^6*e3^2*e4^5*e12-e1^5*e2^6*e3*e4^2*e12^2-15*e1^5*e3*e4^2*e6^6*e12^2-24*e4^7*e6^6*e12^3-54*e1^2*e2^2*e3^2*e4*e6^4*e12^5+72*e2^2*e4^3*e6^4*e12^7, 3*e1^9*e6^7-81*e2^3*e3^3*e6^10-3*e1^8*e2*e3^3*e4^2*e12^2+52*e1^6*e2*e3*e4^4*e12^4+32*e1^9*e2*e4*e12^5+576*e2^4*e3^3*e4*e6^3*e12^5-1440*e1*e2^4*e6^3*e12^8, 3*e1^8*e2*e6^7-3*e1^7*e2^2*e3^3*e4^2*e12^2-2*e1^5*e2^2*e3*e4^4*e12^4-72*e2^3*e4^4*e6^5*e12^4+5*e1^8*e2^2*e4*e12^5+81*e3^8*e4*e6^2*e12^5+162*e1*e3^5*e6^2*e12^8-216*e2^5*e6^3*e12^8, 3*e1^5*e3^4*e6^6+27*e2*e3^3*e6^11-2*e2^6*e3^3*e4^5*e12-e1^3*e2^6*e3^2*e4^2*e12^2-15*e1^3*e3^2*e4^2*e6^6*e12^2-78*e2^2*e3^3*e4*e6^4*e12^5+24*e1*e2^2*e6^4*e12^8, 18*e1^5*e3^3*e4*e6^6-16*e2^6*e3^2*e4^6*e12-4*e1^3*e2^6*e3*e4^3*e12^2+2*e1^6*e2^6*e12^3+81*e1^2*e2^2*e3^4*e6^4*e12^3+9*e1^6*e6^6*e12^3, 3*e1^4*e3^4*e4*e6^6-2*e1^2*e2^6*e3^2*e4^3*e12^2-e1^5*e2^6*e3*e12^3+3*e1^5*e3*e6^6*e12^3+54*e2*e6^11*e12^3-60*e4^5*e6^6*e12^4+36*e2^2*e4*e6^4*e12^8, 3*e1^5*e2^3*e6^7-3*e1^4*e2^4*e3^3*e4^2*e12^2+9*e3^7*e4^2*e6^4*e12^2-8*e1^2*e2^4*e3*e4^4*e12^4+2*e1^5*e2^4*e4*e12^5-18*e1*e3^4*e4*e6^4*e12^5-72*e1^2*e3*e6^4*e12^8, 3*e1^3*e2^5*e6^7-3*e1^2*e2^6*e3^3*e4^2*e12^2+9*e1^2*e3^3*e4^2*e6^6*e12^2-8*e2^6*e3*e4^4*e12^4+2*e1^3*e2^6*e4*e12^5+18*e1^3*e4*e6^6*e12^5, e1^3*e2^2*e6^10-e1^2*e2^3*e3^3*e4^2*e6^3*e12^2-3*e3^9*e4*e12^5+4*e1^3*e2^3*e4*e6^3*e12^5-6*e1*e3^6*e12^8+16*e2^5*e3*e6*e12^8, e1^3*e2^11-e1^8*e2^4*e3*e6-32*e2^4*e3*e4^8*e6+27*e1^3*e2^5*e6^6+108*e1^2*e3^3*e4^2*e6^5*e12^2+216*e1^3*e4*e6^5*e12^5, e1^4*e2^6*e3^4-e1^8*e2^4*e6^2-9*e2^2*e3^8*e6^4-3*e1^4*e3^4*e6^6+8*e1^2*e2^6*e3^2*e4^2*e12^2+24*e1^2*e3^2*e4^2*e6^6*e12^2+96*e4^4*e6^6*e12^4-288*e2^2*e6^4*e12^8, e2^11*e4^3-e1^8*e2^4*e6*e12-8*e2^4*e4^8*e6*e12+27*e1^2*e3^2*e4^2*e6^5*e12^3+54*e4^4*e6^5*e12^5-162*e2^2*e6^3*e12^9, 8*e1^2*e2^4*e3^2*e4^6-4*e1^5*e2^4*e3*e4^3*e12-4*e1^8*e2^4*e12^2-27*e2^2*e3^8*e6^2*e12^2-9*e1^4*e3^4*e6^4*e12^2+72*e1^2*e3^2*e4^2*e6^4*e12^4+288*e4^4*e6^4*e12^6-864*e2^2*e6^2*e12^10, 2*e1^5*e3*e4^8-3*e1^8*e2*e6^5+e1^8*e4^5*e12-6*e1^2*e2^3*e3^2*e4^2*e6^3*e12^2+96*e2^3*e4^4*e6^3*e12^4-81*e3^8*e4*e12^5-162*e1*e3^5*e12^8+144*e2^5*e6*e12^8, 8*e2^4*e3^2*e4^8-9*e1^3*e2^5*e3*e6^5+2*e1^3*e2^4*e3*e4^5*e12-e1^6*e2^4*e4^2*e12^2-27*e1^2*e3^4*e4^2*e6^4*e12^2-54*e1^3*e3*e4*e6^4*e12^5, 8*e2^4*e4^8*e6^2-9*e2^2*e3^8*e6^4-3*e1^4*e3^4*e6^6+4*e1^2*e2^6*e3^2*e4^2*e12^2-12*e1^2*e3^2*e4^2*e6^6*e12^2+8*e2^6*e4^4*e12^4+24*e4^4*e6^6*e12^4-72*e2^2*e6^4*e12^8, e1^4*e2^3*e3^4*e6^3-e1^8*e2*e6^5-4*e1^2*e2^3*e3^2*e4^2*e6^3*e12^2+48*e2^3*e4^4*e6^3*e12^4-36*e3^8*e4*e12^5-72*e1*e3^5*e12^8+48*e2^5*e6*e12^8, 3*e1*e2*e3^8*e6^4+9*e2^6*e3^3*e6^5-9*e3^3*e6^11-8*e2^5*e3^3*e4^5*e12-4*e1^3*e2^5*e3^2*e4^2*e12^2+96*e1*e2*e6^4*e12^8, 3*e2*e3^8*e4*e6^4-2*e1^2*e2^5*e3^2*e4^3*e12^2-e1^5*e2^5*e3*e12^3-9*e2^6*e6^5*e12^3-9*e6^11*e12^3+24*e2*e4*e6^4*e12^8, 3*e3^8*e4^2*e6^4-2*e1^2*e2^4*e3^2*e4^4*e12^2-e1^5*e2^4*e3*e4*e12^3+3*e1*e3^5*e4*e6^4*e12^3-12*e2^5*e4*e6^5*e12^3-6*e1^2*e3^2*e6^4*e12^6, 3*e1^2*e2^5*e3^2*e6^5-2*e1^2*e2^4*e3^2*e4^5*e12-e1^5*e2^4*e3*e4^2*e12^2+9*e1*e3^5*e4^2*e6^4*e12^2-12*e2^5*e4^2*e6^5*e12^2+18*e1^2*e3^2*e4*e6^4*e12^5, 3*e1*e2^5*e3^3*e6^5-2*e1*e2^4*e3^3*e4^5*e12-e1^4*e2^4*e3^2*e4^2*e12^2-3*e3^6*e4^2*e6^4*e12^2+6*e1*e3^3*e4*e6^4*e12^5+24*e1^2*e6^4*e12^8, 3*e1^5*e3*e6^7+27*e2*e6^12-3*e1^4*e2*e3^4*e4^2*e12^2-20*e1^2*e2*e3^2*e4^4*e12^4-4*e1^5*e2*e3*e4*e12^5-72*e2^2*e4*e6^5*e12^5, 9*e4*e6^12-3*e1^2*e2*e3^2*e6^5*e12^3-4*e1^2*e3^2*e4^5*e12^4-2*e1^5*e3*e4^2*e12^5-24*e2*e4^2*e6^5*e12^5, e2^12-e1^5*e2^5*e3*e6-5*e1^4*e3^4*e4^2*e12^2+4*e1^2*e3^2*e4^4*e12^4-12*e1^5*e3*e4*e12^5-72*e2*e4*e6^5*e12^5+64*e4^6*e12^6, 3*e2^4*e3^8-2*e1^4*e2^2*e3^4*e6^2-e1^8*e6^4-16*e1^2*e2^2*e3^2*e4^2*e6^2*e12^2, e3^11*e4-e1^3*e2^3*e3^2*e4*e6^3+4*e1*e2^3*e4^3*e6^3*e12^2-e1*e3^8*e12^3-6*e2^5*e3^3*e6*e12^3+8*e3^3*e4*e12^8-32*e1*e12^11, e1^8*e3*e4^3+32*e3*e4^11-54*e1^3*e2*e4^3*e6^5-e1^11*e12-8*e1^3*e4^8*e12+27*e1^2*e2^3*e3^3*e6^3*e12-108*e2^3*e3*e4^2*e6^3*e12^3, 9*e2^3*e3^6*e6^3+3*e1^4*e2*e3^2*e6^5-8*e1^4*e3^2*e4^5*e12-4*e1^7*e3*e4^2*e12^2-48*e1^2*e2*e4^2*e6^5*e12^2, 4*e1^5*e4^3*e6^4-3*e2^4*e3^7*e12-e1^4*e2^2*e3^3*e6^2*e12+16*e1^2*e2^2*e3*e4^2*e6^2*e12^3, e4^8*e6^4-e1^2*e2^2*e3^2*e4^2*e6^2*e12^2-2*e2^2*e4^4*e6^2*e12^4-3*e2^4*e12^8, 3*e1^5*e2*e3*e6^5+27*e2^2*e6^10-2*e1^5*e3*e4^5*e12-30*e2*e4^5*e6^5*e12-e1^8*e4^2*e12^2+18*e2^3*e4*e6^3*e12^5, 3*e1*e2*e3^5*e6^5-9*e6^12-3*e1^4*e3^4*e4^2*e12^2-4*e1^2*e3^2*e4^4*e12^4+4*e1^5*e3*e4*e12^5+24*e2*e4*e6^5*e12^5, e2^6*e6^6-e1^4*e3^4*e4^2*e12^2-4*e1^2*e3^2*e4^4*e12^4, e2^4*e6^8-e3^8*e4^2*e12^2+4*e1^2*e3^2*e12^8, e4^3*e6^9-e1^2*e2*e3^2*e4^2*e6^2*e12^3-2*e2*e4^4*e6^2*e12^5-2*e2^3*e12^9, e1^4*e2^7-e1^9*e3*e6-32*e1*e3*e4^8*e6+27*e2^3*e3^4*e6^4, e1^5*e2^2*e3^4-e1^9*e6^2+36*e2^3*e3^3*e6^5-32*e2^2*e3^3*e4^5*e12-8*e1^3*e2^2*e3^2*e4^2*e12^2, e1*e2*e3^9-e1^4*e2^4*e6^3-3*e3^4*e6^7+32*e1*e2*e3*e12^8, 3*e2^2*e3^9+e1^4*e3^5*e6^2-4*e1^3*e2^5*e6^3-8*e1^2*e3^3*e4^2*e6^2*e12^2-32*e1^3*e4*e6^2*e12^5, e1^3*e2^7*e4-e1^8*e3*e4*e6-32*e3*e4^9*e6+27*e1^3*e2*e4*e6^6+108*e2^3*e3*e6^4*e12^3, e2*e3^9*e4-e1^3*e2^4*e4*e6^3-3*e2^6*e3*e6*e12^3-3*e3*e6^7*e12^3+8*e2*e3*e4*e12^8, e3^9*e4^2-e1^3*e2^3*e4^2*e6^3+e1*e3^6*e4*e12^3-4*e2^5*e3*e4*e6*e12^3-2*e1^2*e3^3*e12^6, e1*e2^7*e4^3-27*e1*e2*e4^3*e6^6-e1^9*e6*e12-8*e1*e4^8*e6*e12+27*e2^3*e3^3*e6^4*e12, e2^7*e4^4-e1^8*e4*e6*e12-8*e4^9*e6*e12+27*e2^3*e6^4*e12^4, 2*e1^3*e3^2*e4^6-e1^6*e3*e4^3*e12-36*e1*e2*e4^3*e6^5*e12-e1^9*e12^2+27*e2^3*e3^3*e6^3*e12^2, 2*e1^2*e3^2*e4^7-e1^5*e3*e4^4*e12-9*e2*e4^4*e6^5*e12-e1^8*e4*e12^2+27*e2^3*e6^3*e12^5, 32*e1*e3^2*e4^8-27*e2^3*e3^5*e6^3-9*e1^4*e2*e3*e6^5+8*e1^4*e3*e4^5*e12-4*e1^7*e4^2*e12^2, 8*e3^2*e4^9-9*e1^3*e2*e3*e4*e6^5+2*e1^3*e3*e4^6*e12-e1^6*e4^3*e12^2-27*e2^3*e3^2*e6^3*e12^3, e1*e2^5*e3^4*e6-e1^5*e2^3*e6^3-4*e3^7*e4^2*e12^2+8*e1*e3^4*e4*e12^5+32*e1^2*e3*e12^8, e1^6*e4^3*e6^2-e1^5*e2^2*e3^3*e12-9*e2^3*e3^2*e6^5*e12+8*e2^2*e3^2*e4^5*e12^2+2*e1^3*e2^2*e3*e4^2*e12^3, 2*e4^9*e6^2-e1^2*e2^2*e3^2*e4^3*e12^2-e1^5*e2^2*e3*e12^3-9*e2^3*e6^5*e12^3+2*e2^2*e4^5*e12^4, e1^2*e2^3*e4^3*e6^3-e1*e2^5*e3^3*e6*e12+e3^6*e4^2*e12^3-2*e1*e3^3*e4*e12^6-8*e1^2*e12^9, 4*e1*e2^4*e4^3*e6^3-e1*e2*e3^8*e12-3*e2^6*e3^3*e6*e12+3*e3^3*e6^7*e12-32*e1*e2*e12^9, 4*e2^5*e4^3*e6^3-3*e2^2*e3^8*e12-e1^4*e3^4*e6^2*e12-4*e1^2*e3^2*e4^2*e6^2*e12^3+8*e4^4*e6^2*e12^5-24*e2^2*e12^9, e2^4*e4^4*e6^3-e2*e3^8*e4*e12+3*e6^7*e12^4-8*e2*e4*e12^9, e2^3*e4^5*e6^3-e3^8*e4^2*e12-e1*e3^5*e4*e12^4+e2^5*e4*e6*e12^4+2*e1^2*e3^2*e12^7, 9*e2^2*e3^4*e6^5+3*e1^4*e6^7-12*e1^3*e2*e3^3*e4^2*e12^2-32*e1*e2*e3*e4^4*e12^4+8*e1^4*e2*e4*e12^5, 36*e2*e3*e4^3*e6^6+e1^3*e2^7*e12-e1^8*e3*e6*e12-32*e3*e4^8*e6*e12-9*e1^3*e2*e6^6*e12, e3^3*e4*e6^7-e1*e2^6*e6*e12^3-e1*e6^7*e12^3-8*e1*e2*e4*e12^8, 3*e4^4*e6^7-2*e1^2*e2*e3^2*e4^3*e12^3-e1^5*e2*e3*e12^4-9*e2^2*e6^5*e12^4, e1^5*e3^5-e1^4*e2^5*e6+9*e2*e3^4*e6^5-8*e1^3*e3^3*e4^2*e12^2-32*e1*e3*e4^4*e12^4, e1*e3^8*e4-e2^5*e3^3*e4*e6-e1^2*e3^5*e12^3+2*e1*e2^5*e6*e12^3-4*e3^3*e4^2*e12^5+16*e1*e4*e12^8, e1^5*e3^2*e4^3+18*e2*e3*e4^3*e6^5-e1^8*e3*e12-16*e3*e4^8*e12-9*e1^3*e2*e6^5*e12+4*e1^3*e4^5*e12^2, e1*e2^5*e4^3*e6-e1^5*e3^4*e12-9*e2*e3^3*e6^5*e12+6*e3^3*e4^5*e12^2-e1^3*e3^2*e4^2*e12^3+8*e1*e4^4*e12^5, e2^5*e3*e4^3*e6-e1^3*e2^5*e6*e12-3*e1^2*e3^3*e4^2*e12^3-6*e1^3*e4*e12^6, e2^5*e4^4*e6-e1^4*e3^4*e4*e12-4*e1^2*e3^2*e4^3*e12^3-9*e2*e6^5*e12^4+8*e4^5*e12^5, 3*e3*e4^2*e6^7-3*e1^2*e2*e3^3*e4*e12^3-8*e2*e3*e4^3*e12^5+2*e1^3*e2*e12^6, e1*e3^6*e4^2-e2^5*e3*e4^2*e6+e1^2*e3^3*e4*e12^3-2*e1^3*e12^6, e3^6*e4^3-e1^2*e2^5*e6*e12-2*e1*e3^3*e4^2*e12^3-8*e1^2*e4*e12^6, 2*e3^3*e4^6-e1^3*e3^2*e4^3*e12-e1^6*e3*e12^2-9*e1*e2*e6^5*e12^2, 9*e2*e3^2*e4*e6^5-8*e3^2*e4^6*e12-2*e1^3*e3*e4^3*e12^2+e1^6*e12^3, 3*e1*e4*e6^7-2*e2*e3^3*e4^3*e12^2-e1^3*e2*e3^2*e12^3, 3*e2*e4*e6^7-2*e4^6*e6^2*e12-e1^2*e2^2*e3^2*e12^3-2*e2^2*e4^2*e12^5, e2^7*e3-e1^5*e3^2*e6-9*e2*e3*e6^6+8*e3*e4^5*e6*e12-4*e1^3*e4^2*e6*e12^2, e1^2*e2*e3^5-e1*e2^6*e6-3*e1*e6^7+4*e2*e3^3*e4^2*e12^2-8*e1*e2*e4*e12^5, e1*e2^2*e3^5-e1^5*e3*e6^2-12*e2*e6^7+8*e4^5*e6^2*e12+8*e2^2*e4*e12^5, e1^2*e3^5*e4-e1*e2^5*e4*e6+2*e3^3*e4^3*e12^2-e1^3*e3^2*e12^3-8*e1*e4^2*e12^5, e1*e2*e3^5*e4-e2^6*e4*e6+3*e4*e6^7-2*e1^2*e2*e3^2*e12^3-8*e2*e4^2*e12^5, e1^2*e3^3*e4^3-e1^5*e3^2*e12-9*e2*e3*e6^5*e12+8*e3*e4^5*e12^2-2*e1^3*e4^2*e12^3, e3^4*e4^4-e1^3*e3^3*e4*e12-4*e1*e3*e4^3*e12^3+e1^4*e12^4, e2^7*e6-e1^5*e3*e6^2-9*e2*e6^7+4*e4^5*e6^2*e12+12*e2^2*e4*e12^5, 2*e1^2*e3^2*e4^3*e6-e2^7*e12-e1^5*e3*e6*e12-9*e2*e6^6*e12+8*e4^5*e6*e12^2, e2^2*e3^4*e4-e1^4*e4*e6^2-4*e1*e2^2*e3*e12^3, 4*e1*e3*e4^3*e6^2-3*e2^2*e3^4*e12-e1^4*e6^2*e12, e1*e4^4*e6^2-e2^2*e3^3*e4*e12+e1*e2^2*e12^4, e3*e4^4*e6^2-e1^3*e4*e6^2*e12-3*e2^2*e3*e12^4];