/* (3,3) isogeny relations using theta constants a1,a2,a3,a4 of half integral characteristics 0000,0011,0010,0001. These are the "f's" of Section 7.4 in David Gruenewald's thesis [Gruenewald 2008]. a1,a2,a3,a4 are theta constants evaluated at tau c1,c2,c3,c4 are theta constants evaluated at 3*tau Below is the (3,3)-isogeny relation ideal: */ isogeny33 := [ a1^6 - 7*a1^4*c1^2 + 24*a1^3*a4*c1*c4 - 3*a1^2*a2^4 - 6*a1^2*a2^2*c2^2 + 24*a1^2*a2*a3*c2*c3 - 3*a1^2*a3^4 - 6*a1^2*a3^2*c3^2 + 3*a1^2*a4^4 + 6*a1^2*a4^2*c4^2 - 21*a1^2*c1^4 + 9*a1^2*c2^4 + 9*a1^2*c3^4 - 9*a1^2*c4^4 + 48*a1*a2*c1^3*c2 + 48*a1*a3*c1^3*c3 - 24*a1*a4*c1^3*c4 - a2^4*c1^2 - 6*a2^2*a3^2*a4^2 + 6*a2^2*a3^2*c4^2 + 6*a2^2*a4^2*c3^2 + 6*a2^2*c1^2*c2^2 + 18*a2^2*c3^2*c4^2 - 24*a2*a3*c1^2*c2*c3 + 48*a2*a4*c1^2*c2*c4 - a3^4*c1^2 + 6*a3^2*a4^2*c2^2 + 6*a3^2*c1^2*c3^2 + 18*a3^2*c2^2*c4^2 + 48*a3*a4*c1^2*c3*c4 + 5*a4^4*c1^2 - 30*a4^2*c1^2*c4^2 + 18*a4^2*c2^2*c3^2 + 27*c1^6 + 27*c1^2*c2^4 + 27*c1^2*c3^4 - 135*c1^2*c4^4 - 162*c2^2*c3^2*c4^2, a1^5*a2 + 2*a1^3*a2*c1^2 + 10*a1^2*a2^2*c1*c2 - 8*a1^2*a2*a3*c1*c3 - 8*a1^2*a2*a4*c1*c4 - 18*a1^2*c1*c2^3 + a1*a2^5 + 2*a1*a2^3*c2^2 - 8*a1*a2^2*a3*c2*c3 - 8*a1*a2^2*a4*c2*c4 + a1*a2*a3^4 + 2*a1*a2*a3^2*c3^2 - 8*a1*a2*a3*a4*c3*c4 + a1*a2*a4^4 + 2*a1*a2*a4^2*c4^2 - 3*a1*a2*c1^4 - 3*a1*a2*c2^4 - 3*a1*a2*c3^4 - 3*a1*a2*c4^4 - 18*a2^2*c1^3*c2 - 6*a3^2*a4^2*c1*c2 - 18*a3^2*c1*c2*c4^2 - 18*a4^2*c1*c2*c3^2 - 54*c1^3*c2^3 + 162*c1*c2*c3^2*c4^2, a1^5*a3 + 2*a1^3*a3*c1^2 - 8*a1^2*a2*a3*c1*c2 + 10*a1^2*a3^2*c1*c3 - 8*a1^2*a3*a4*c1*c4 - 18*a1^2*c1*c3^3 + a1*a2^4*a3 + 2*a1*a2^2*a3*c2^2 - 8*a1*a2*a3^2*c2*c3 - 8*a1*a2*a3*a4*c2*c4 + a1*a3^5 + 2*a1*a3^3*c3^2 - 8*a1*a3^2*a4*c3*c4 + a1*a3*a4^4 + 2*a1*a3*a4^2*c4^2 - 3*a1*a3*c1^4 - 3*a1*a3*c2^4 - 3*a1*a3*c3^4 - 3*a1*a3*c4^4 - 6*a2^2*a4^2*c1*c3 - 18*a2^2*c1*c3*c4^2 - 18*a3^2*c1^3*c3 - 18*a4^2*c1*c2^2*c3 - 54*c1^3*c3^3 + 162*c1*c2^2*c3*c4^2, a1^5*a4 + 2*a1^3*a4*c1^2 - 8*a1^2*a2*a4*c1*c2 - 8*a1^2*a3*a4*c1*c3 + 10*a1^2*a4^2*c1*c4 - 18*a1^2*c1*c4^3 + a1*a2^4*a4 + 2*a1*a2^2*a4*c2^2 - 8*a1*a2*a3*a4*c2*c3 - 8*a1*a2*a4^2*c2*c4 + a1*a3^4*a4 + 2*a1*a3^2*a4*c3^2 - 8*a1*a3*a4^2*c3*c4 + a1*a4^5 + 2*a1*a4^3*c4^2 - 3*a1*a4*c1^4 - 3*a1*a4*c2^4 - 3*a1*a4*c3^4 - 3*a1*a4*c4^4 - 6*a2^2*a3^2*c1*c4 - 18*a2^2*c1*c3^2*c4 - 18*a3^2*c1*c2^2*c4 - 18*a4^2*c1^3*c4 - 54*c1^3*c4^3 + 162*c1*c2^2*c3^2*c4, a1^5*c2 - 6*a1^3*c1^2*c2 + 2*a1^2*a2^3*c1 + 6*a1^2*a2*c1*c2^2 + 24*a1^2*a4*c1*c2*c4 - 3*a1*a2^4*c2 + 8*a1*a2^3*a4*c4 - 6*a1*a2^2*c2^3 + 24*a1*a2*a3*c2^2*c3 - 3*a1*a3^4*c2 - 6*a1*a3^2*c2*c3^2 - 24*a1*a3*a4*c2*c3*c4 + a1*a4^4*c2 - 6*a1*a4^2*c2*c4^2 - 27*a1*c1^4*c2 + 9*a1*c2^5 + 9*a1*c2*c3^4 - 27*a1*c2*c4^4 + 6*a2^3*c1^3 - 6*a2*a3^2*a4^2*c1 - 18*a2*a3^2*c1*c4^2 + 6*a2*a4^2*c1*c3^2 + 18*a2*c1^3*c2^2 - 54*a2*c1*c3^2*c4^2 + 72*a3*c1^3*c2*c3, a1^5*c3 - 6*a1^3*c1^2*c3 + 2*a1^2*a3^3*c1 + 6*a1^2*a3*c1*c3^2 + 24*a1^2*a4*c1*c3*c4 - 3*a1*a2^4*c3 - 6*a1*a2^2*c2^2*c3 + 24*a1*a2*a3*c2*c3^2 - 24*a1*a2*a4*c2*c3*c4 - 3*a1*a3^4*c3 + 8*a1*a3^3*a4*c4 - 6*a1*a3^2*c3^3 + a1*a4^4*c3 - 6*a1*a4^2*c3*c4^2 - 27*a1*c1^4*c3 + 9*a1*c2^4*c3 + 9*a1*c3^5 - 27*a1*c3*c4^4 - 6*a2^2*a3*a4^2*c1 - 18*a2^2*a3*c1*c4^2 + 72*a2*c1^3*c2*c3 + 6*a3^3*c1^3 + 6*a3*a4^2*c1*c2^2 + 18*a3*c1^3*c3^2 - 54*a3*c1*c2^2*c4^2, a1^5*c4 - 6*a1^3*c1^2*c4 + 24*a1^2*a3*c1*c3*c4 + 2*a1^2*a4^3*c1 + 6*a1^2*a4*c1*c4^2 - 3*a1*a2^4*c4 - 6*a1*a2^2*c2^2*c4 - 24*a1*a2*a3*c2*c3*c4 + 24*a1*a2*a4*c2*c4^2 + a1*a3^4*c4 - 6*a1*a3^2*c3^2*c4 + 8*a1*a3*a4^3*c3 - 3*a1*a4^4*c4 - 6*a1*a4^2*c4^3 - 27*a1*c1^4*c4 + 9*a1*c2^4*c4 - 27*a1*c3^4*c4 + 9*a1*c4^5 - 6*a2^2*a3^2*a4*c1 - 18*a2^2*a4*c1*c3^2 + 72*a2*c1^3*c2*c4 + 6*a3^2*a4*c1*c2^2 + 6*a4^3*c1^3 + 18*a4*c1^3*c4^2 - 54*a4*c1*c2^2*c3^2, 2*a1^4*a2^2 + 4*a1^2*a2^2*c1^2 + 6*a1^2*a3^2*a4^2 - 6*a1^2*a3^2*c4^2 - 6*a1^2*a4^2*c3^2 - 18*a1^2*c3^2*c4^2 - 4*a1*a2^3*c1*c2 - 20*a1*a2^2*a4*c1*c4 - 36*a1*a2*c1*c2^3 - 48*a1*a3*c1*c2^2*c3 + 12*a1*a4*c1*c2^2*c4 - a2^6 + 7*a2^4*c2^2 - 20*a2^3*a3*c2*c3 - 2*a2^2*a3^4 - 4*a2^2*a3^2*c3^2 - 4*a2^2*a3*a4*c3*c4 + 3*a2^2*a4^4 + 6*a2^2*a4^2*c4^2 - 6*a2^2*c1^4 + 21*a2^2*c2^4 + 6*a2^2*c3^4 - 9*a2^2*c4^4 + 12*a2*a3*c2^3*c3 - 48*a2*a4*c2^3*c4 - 4*a3^4*c2^2 - 6*a3^2*a4^2*c1^2 - 18*a3^2*c1^2*c4^2 + 24*a3^2*c2^2*c3^2 - 36*a3*a4*c2^2*c3*c4 + a4^4*c2^2 - 18*a4^2*c1^2*c3^2 - 6*a4^2*c2^2*c4^2 + 162*c1^2*c3^2*c4^2 - 27*c2^6 + 108*c2^2*c3^4 - 27*c2^2*c4^4, a1^4*a2*a3 + 2*a1^2*a2*a3*c1^2 - 6*a1^2*a4^2*c2*c3 - 18*a1^2*c2*c3*c4^2 - 8*a1*a2^2*a3*c1*c2 - 8*a1*a2*a3^2*c1*c3 - 8*a1*a2*a3*a4*c1*c4 + a2^5*a3 + 2*a2^3*a3*c2^2 + 10*a2^2*a3^2*c2*c3 - 8*a2^2*a3*a4*c2*c4 - 18*a2^2*c2*c3^3 + a2*a3^5 + 2*a2*a3^3*c3^2 - 8*a2*a3^2*a4*c3*c4 + a2*a3*a4^4 + 2*a2*a3*a4^2*c4^2 - 3*a2*a3*c1^4 - 3*a2*a3*c2^4 - 3*a2*a3*c3^4 - 3*a2*a3*c4^4 - 18*a3^2*c2^3*c3 - 18*a4^2*c1^2*c2*c3 + 162*c1^2*c2*c3*c4^2 - 54*c2^3*c3^3, a1^4*a2*a4 + 2*a1^2*a2*a4*c1^2 - 6*a1^2*a3^2*c2*c4 - 18*a1^2*c2*c3^2*c4 - 8*a1*a2^2*a4*c1*c2 - 8*a1*a2*a3*a4*c1*c3 - 8*a1*a2*a4^2*c1*c4 + a2^5*a4 + 2*a2^3*a4*c2^2 - 8*a2^2*a3*a4*c2*c3 + 10*a2^2*a4^2*c2*c4 - 18*a2^2*c2*c4^3 + a2*a3^4*a4 + 2*a2*a3^2*a4*c3^2 - 8*a2*a3*a4^2*c3*c4 + a2*a4^5 + 2*a2*a4^3*c4^2 - 3*a2*a4*c1^4 - 3*a2*a4*c2^4 - 3*a2*a4*c3^4 - 3*a2*a4*c4^4 - 18*a3^2*c1^2*c2*c4 - 18*a4^2*c2^3*c4 + 162*c1^2*c2*c3^2*c4 - 54*c2^3*c4^3, 3*a1^4*a2*c1 - 2*a1^3*a2^2*c2 - 8*a1^3*a2*a4*c4 - 6*a1^3*c2^3 + 6*a1^2*a2*c1^3 - 6*a1*a2^2*c1^2*c2 - 24*a1*a2*a3*c1^2*c3 + 6*a1*a3^2*a4^2*c2 + 18*a1*a3^2*c2*c4^2 - 6*a1*a4^2*c2*c3^2 - 18*a1*c1^2*c2^3 + 54*a1*c2*c3^2*c4^2 - a2^5*c1 + 6*a2^3*c1*c2^2 - 24*a2^2*a4*c1*c2*c4 + 3*a2*a3^4*c1 + 6*a2*a3^2*c1*c3^2 + 24*a2*a3*a4*c1*c3*c4 - a2*a4^4*c1 + 6*a2*a4^2*c1*c4^2 - 9*a2*c1^5 + 27*a2*c1*c2^4 - 9*a2*c1*c3^4 + 27*a2*c1*c4^4 - 72*a3*c1*c2^3*c3, a1^4*a2*c2 - a1^4*a4*c4 - 6*a1^2*a2*c1^2*c2 + 6*a1^2*a4*c1^2*c4 - a1*a2^4*c1 + 6*a1*a2^2*c1*c2^2 + a1*a4^4*c1 - 6*a1*a4^2*c1*c4^2 - 9*a1*c1*c2^4 + 9*a1*c1*c4^4 + a2^4*a4*c4 - 6*a2^2*a4*c2^2*c4 - a2*a4^4*c2 + 6*a2*a4^2*c2*c4^2 + 9*a2*c1^4*c2 - 9*a2*c2*c4^4 - 9*a4*c1^4*c4 + 9*a4*c2^4*c4, a1^4*a2*c3 + 6*a1^2*a3*c2*c4^2 + 6*a1*a2^2*c1*c2*c3 + 2*a1*a2*a3^3*c1 - 6*a1*a2*a3*c1*c3^2 - 18*a1*c1*c2^3*c3 - 6*a2^2*a4*c2*c3*c4 - 2*a2*a3^3*a4*c4 + 6*a2*a3*a4*c3^2*c4 - a2*a4^4*c3 - 9*a2*c1^4*c3 + 9*a2*c3*c4^4 - 6*a3*a4^2*c1^2*c2 + 18*a4*c2^3*c3*c4, a1^4*a2*c4 + 6*a1^2*a4*c2*c3^2 + 6*a1*a2^2*c1*c2*c4 + 2*a1*a2*a4^3*c1 - 6*a1*a2*a4*c1*c4^2 - 18*a1*c1*c2^3*c4 - 6*a2^2*a3*c2*c3*c4 - a2*a3^4*c4 - 2*a2*a3*a4^3*c3 + 6*a2*a3*a4*c3*c4^2 - 9*a2*c1^4*c4 + 9*a2*c3^4*c4 - 6*a3^2*a4*c1^2*c2 + 18*a3*c2^3*c3*c4, 2*a1^4*a3^2 + 6*a1^2*a2^2*a4^2 - 6*a1^2*a2^2*c4^2 + 4*a1^2*a3^2*c1^2 - 6*a1^2*a4^2*c2^2 - 18*a1^2*c2^2*c4^2 - 48*a1*a2*c1*c2*c3^2 - 4*a1*a3^3*c1*c3 - 20*a1*a3^2*a4*c1*c4 - 36*a1*a3*c1*c3^3 + 12*a1*a4*c1*c3^2*c4 - 2*a2^4*a3^2 - 4*a2^4*c3^2 - 4*a2^2*a3^2*c2^2 - 6*a2^2*a4^2*c1^2 - 18*a2^2*c1^2*c4^2 + 24*a2^2*c2^2*c3^2 - 20*a2*a3^3*c2*c3 - 4*a2*a3^2*a4*c2*c4 + 12*a2*a3*c2*c3^3 - 36*a2*a4*c2*c3^2*c4 - a3^6 + 7*a3^4*c3^2 + 3*a3^2*a4^4 + 6*a3^2*a4^2*c4^2 - 6*a3^2*c1^4 + 6*a3^2*c2^4 + 21*a3^2*c3^4 - 9*a3^2*c4^4 - 48*a3*a4*c3^3*c4 + a4^4*c3^2 - 18*a4^2*c1^2*c2^2 - 6*a4^2*c3^2*c4^2 + 162*c1^2*c2^2*c4^2 + 108*c2^4*c3^2 - 27*c3^6 - 27*c3^2*c4^4, a1^4*a3*a4 - 6*a1^2*a2^2*c3*c4 + 2*a1^2*a3*a4*c1^2 - 18*a1^2*c2^2*c3*c4 - 8*a1*a2*a3*a4*c1*c2 - 8*a1*a3^2*a4*c1*c3 - 8*a1*a3*a4^2*c1*c4 + a2^4*a3*a4 + 2*a2^2*a3*a4*c2^2 - 18*a2^2*c1^2*c3*c4 - 8*a2*a3^2*a4*c2*c3 - 8*a2*a3*a4^2*c2*c4 + a3^5*a4 + 2*a3^3*a4*c3^2 + 10*a3^2*a4^2*c3*c4 - 18*a3^2*c3*c4^3 + a3*a4^5 + 2*a3*a4^3*c4^2 - 3*a3*a4*c1^4 - 3*a3*a4*c2^4 - 3*a3*a4*c3^4 - 3*a3*a4*c4^4 - 18*a4^2*c3^3*c4 + 162*c1^2*c2^2*c3*c4 - 54*c3^3*c4^3, 3*a1^4*a3*c1 - 2*a1^3*a3^2*c3 - 8*a1^3*a3*a4*c4 - 6*a1^3*c3^3 + 6*a1^2*a3*c1^3 + 6*a1*a2^2*a4^2*c3 + 18*a1*a2^2*c3*c4^2 - 24*a1*a2*a3*c1^2*c2 - 6*a1*a3^2*c1^2*c3 - 6*a1*a4^2*c2^2*c3 - 18*a1*c1^2*c3^3 + 54*a1*c2^2*c3*c4^2 + 3*a2^4*a3*c1 + 6*a2^2*a3*c1*c2^2 + 24*a2*a3*a4*c1*c2*c4 - 72*a2*c1*c2*c3^3 - a3^5*c1 + 6*a3^3*c1*c3^2 - 24*a3^2*a4*c1*c3*c4 - a3*a4^4*c1 + 6*a3*a4^2*c1*c4^2 - 9*a3*c1^5 - 9*a3*c1*c2^4 + 27*a3*c1*c3^4 + 27*a3*c1*c4^4, a1^4*a3*c2 + 6*a1^2*a2*c3*c4^2 + 2*a1*a2^3*a3*c1 - 6*a1*a2*a3*c1*c2^2 + 6*a1*a3^2*c1*c2*c3 - 18*a1*c1*c2*c3^3 - 2*a2^3*a3*a4*c4 + 6*a2*a3*a4*c2^2*c4 - 6*a2*a4^2*c1^2*c3 - 6*a3^2*a4*c2*c3*c4 - a3*a4^4*c2 - 9*a3*c1^4*c2 + 9*a3*c2*c4^4 + 18*a4*c2*c3^3*c4, a1^4*a3*c3 - a1^4*a4*c4 - 6*a1^2*a3*c1^2*c3 + 6*a1^2*a4*c1^2*c4 - a1*a3^4*c1 + 6*a1*a3^2*c1*c3^2 + a1*a4^4*c1 - 6*a1*a4^2*c1*c4^2 - 9*a1*c1*c3^4 + 9*a1*c1*c4^4 + a3^4*a4*c4 - 6*a3^2*a4*c3^2*c4 - a3*a4^4*c3 + 6*a3*a4^2*c3*c4^2 + 9*a3*c1^4*c3 - 9*a3*c3*c4^4 - 9*a4*c1^4*c4 + 9*a4*c3^4*c4, a1^4*a3*c4 + 6*a1^2*a4*c2^2*c3 + 6*a1*a3^2*c1*c3*c4 + 2*a1*a3*a4^3*c1 - 6*a1*a3*a4*c1*c4^2 - 18*a1*c1*c3^3*c4 - a2^4*a3*c4 - 6*a2^2*a4*c1^2*c3 - 6*a2*a3^2*c2*c3*c4 - 2*a2*a3*a4^3*c2 + 6*a2*a3*a4*c2*c4^2 + 18*a2*c2*c3^3*c4 - 9*a3*c1^4*c4 + 9*a3*c2^4*c4, 2*a1^4*a4^2 + 6*a1^2*a2^2*a3^2 - 6*a1^2*a2^2*c3^2 - 6*a1^2*a3^2*c2^2 + 4*a1^2*a4^2*c1^2 - 18*a1^2*c2^2*c3^2 - 48*a1*a2*c1*c2*c4^2 - 20*a1*a3*a4^2*c1*c3 + 12*a1*a3*c1*c3*c4^2 - 4*a1*a4^3*c1*c4 - 36*a1*a4*c1*c4^3 - 2*a2^4*a4^2 - 4*a2^4*c4^2 - 6*a2^2*a3^2*c1^2 - 4*a2^2*a4^2*c2^2 - 18*a2^2*c1^2*c3^2 + 24*a2^2*c2^2*c4^2 - 4*a2*a3*a4^2*c2*c3 - 36*a2*a3*c2*c3*c4^2 - 20*a2*a4^3*c2*c4 + 12*a2*a4*c2*c4^3 + 3*a3^4*a4^2 + a3^4*c4^2 + 6*a3^2*a4^2*c3^2 - 18*a3^2*c1^2*c2^2 - 6*a3^2*c3^2*c4^2 - 48*a3*a4*c3*c4^3 - a4^6 + 7*a4^4*c4^2 - 6*a4^2*c1^4 + 6*a4^2*c2^4 - 9*a4^2*c3^4 + 21*a4^2*c4^4 + 162*c1^2*c2^2*c3^2 + 108*c2^4*c4^2 - 27*c3^4*c4^2 - 27*c4^6, 3*a1^4*a4*c1 - 8*a1^3*a3*a4*c3 - 2*a1^3*a4^2*c4 - 6*a1^3*c4^3 + 6*a1^2*a4*c1^3 + 6*a1*a2^2*a3^2*c4 + 18*a1*a2^2*c3^2*c4 - 24*a1*a2*a4*c1^2*c2 - 6*a1*a3^2*c2^2*c4 - 6*a1*a4^2*c1^2*c4 - 18*a1*c1^2*c4^3 + 54*a1*c2^2*c3^2*c4 + 3*a2^4*a4*c1 + 6*a2^2*a4*c1*c2^2 + 24*a2*a3*a4*c1*c2*c3 - 72*a2*c1*c2*c4^3 - a3^4*a4*c1 + 6*a3^2*a4*c1*c3^2 - 24*a3*a4^2*c1*c3*c4 - a4^5*c1 + 6*a4^3*c1*c4^2 - 9*a4*c1^5 - 9*a4*c1*c2^4 + 27*a4*c1*c3^4 + 27*a4*c1*c4^4, a1^4*a4*c2 + 6*a1^2*a2*c3^2*c4 + 2*a1*a2^3*a4*c1 - 6*a1*a2*a4*c1*c2^2 + 6*a1*a4^2*c1*c2*c4 - 18*a1*c1*c2*c4^3 - 2*a2^3*a3*a4*c3 - 6*a2*a3^2*c1^2*c4 + 6*a2*a3*a4*c2^2*c3 - a3^4*a4*c2 - 6*a3*a4^2*c2*c3*c4 + 18*a3*c2*c3*c4^3 - 9*a4*c1^4*c2 + 9*a4*c2*c3^4, a1^4*a4*c3 + 6*a1^2*a3*c2^2*c4 + 2*a1*a3^3*a4*c1 - 6*a1*a3*a4*c1*c3^2 + 6*a1*a4^2*c1*c3*c4 - 18*a1*c1*c3*c4^3 - a2^4*a4*c3 - 6*a2^2*a3*c1^2*c4 - 2*a2*a3^3*a4*c2 + 6*a2*a3*a4*c2*c3^2 - 6*a2*a4^2*c2*c3*c4 + 18*a2*c2*c3*c4^3 - 9*a4*c1^4*c3 + 9*a4*c2^4*c3, a1^4*c1*c2 + 2*a1^3*a2^3 + 6*a1^3*a2*c2^2 - 6*a1^2*c1^3*c2 + 6*a1*a2^3*c1^2 - 6*a1*a2*a3^2*a4^2 + 6*a1*a2*a3^2*c4^2 + 6*a1*a2*a4^2*c3^2 - 30*a1*a2*c1^2*c2^2 + 18*a1*a2*c3^2*c4^2 + 24*a1*a3*c1^2*c2*c3 + 24*a1*a4*c1^2*c2*c4 + a2^4*c1*c2 - 6*a2^2*c1*c2^3 + 24*a2*a3*c1*c2^2*c3 + 24*a2*a4*c1*c2^2*c4 + a3^4*c1*c2 - 6*a3^2*c1*c2*c3^2 + 24*a3*a4*c1*c2*c3*c4 + a4^4*c1*c2 - 6*a4^2*c1*c2*c4^2 - 27*c1^5*c2 - 27*c1*c2^5 - 27*c1*c2*c3^4 - 27*c1*c2*c4^4, a1^4*c1*c3 + 2*a1^3*a3^3 + 6*a1^3*a3*c3^2 - 6*a1^2*c1^3*c3 - 6*a1*a2^2*a3*a4^2 + 6*a1*a2^2*a3*c4^2 + 24*a1*a2*c1^2*c2*c3 + 6*a1*a3^3*c1^2 + 6*a1*a3*a4^2*c2^2 - 30*a1*a3*c1^2*c3^2 + 18*a1*a3*c2^2*c4^2 + 24*a1*a4*c1^2*c3*c4 + a2^4*c1*c3 - 6*a2^2*c1*c2^2*c3 + 24*a2*a3*c1*c2*c3^2 + 24*a2*a4*c1*c2*c3*c4 + a3^4*c1*c3 - 6*a3^2*c1*c3^3 + 24*a3*a4*c1*c3^2*c4 + a4^4*c1*c3 - 6*a4^2*c1*c3*c4^2 - 27*c1^5*c3 - 27*c1*c2^4*c3 - 27*c1*c3^5 - 27*c1*c3*c4^4, a1^4*c1*c4 + 2*a1^3*a4^3 + 6*a1^3*a4*c4^2 - 6*a1^2*c1^3*c4 - 6*a1*a2^2*a3^2*a4 + 6*a1*a2^2*a4*c3^2 + 24*a1*a2*c1^2*c2*c4 + 6*a1*a3^2*a4*c2^2 + 24*a1*a3*c1^2*c3*c4 + 6*a1*a4^3*c1^2 - 30*a1*a4*c1^2*c4^2 + 18*a1*a4*c2^2*c3^2 + a2^4*c1*c4 - 6*a2^2*c1*c2^2*c4 + 24*a2*a3*c1*c2*c3*c4 + 24*a2*a4*c1*c2*c4^2 + a3^4*c1*c4 - 6*a3^2*c1*c3^2*c4 + 24*a3*a4*c1*c3*c4^2 + a4^4*c1*c4 - 6*a4^2*c1*c4^3 - 27*c1^5*c4 - 27*c1*c2^4*c4 - 27*c1*c3^4*c4 - 27*c1*c4^5, 2*a1^4*c2^2 - 6*a1^2*a3^2*a4^2 + 6*a1^2*a3^2*c4^2 + 6*a1^2*a4^2*c3^2 - 12*a1^2*c1^2*c2^2 + 18*a1^2*c3^2*c4^2 + 12*a1*a2^3*c1*c2 + 12*a1*a2^2*a4*c1*c4 + 12*a1*a2*c1*c2^3 + 48*a1*a3*c1*c2^2*c3 + 12*a1*a4*c1*c2^2*c4 + a2^6 - 7*a2^4*c2^2 + 12*a2^3*a3*c2*c3 + 12*a2^2*a3*a4*c3*c4 - 3*a2^2*a4^4 - 6*a2^2*a4^2*c4^2 - 21*a2^2*c2^4 + 9*a2^2*c4^4 + 12*a2*a3*c2^3*c3 + 48*a2*a4*c2^3*c4 + 2*a3^4*c2^2 + 6*a3^2*a4^2*c1^2 + 18*a3^2*c1^2*c4^2 - 12*a3^2*c2^2*c3^2 + 12*a3*a4*c2^2*c3*c4 - a4^4*c2^2 + 18*a4^2*c1^2*c3^2 + 6*a4^2*c2^2*c4^2 - 54*c1^4*c2^2 - 162*c1^2*c3^2*c4^2 + 27*c2^6 - 54*c2^2*c3^4 + 27*c2^2*c4^4, a1^4*c2*c3 - 6*a1^2*a2*a3*a4^2 + 6*a1^2*a2*a3*c4^2 - 6*a1^2*c1^2*c2*c3 + 24*a1*a2*c1*c2^2*c3 + 24*a1*a3*c1*c2*c3^2 + 24*a1*a4*c1*c2*c3*c4 + a2^4*c2*c3 + 2*a2^3*a3^3 + 6*a2^3*a3*c3^2 - 6*a2^2*c2^3*c3 + 6*a2*a3^3*c2^2 + 6*a2*a3*a4^2*c1^2 + 18*a2*a3*c1^2*c4^2 - 30*a2*a3*c2^2*c3^2 + 24*a2*a4*c2^2*c3*c4 + a3^4*c2*c3 - 6*a3^2*c2*c3^3 + 24*a3*a4*c2*c3^2*c4 + a4^4*c2*c3 - 6*a4^2*c2*c3*c4^2 - 27*c1^4*c2*c3 - 27*c2^5*c3 - 27*c2*c3^5 - 27*c2*c3*c4^4, a1^4*c2*c4 - 6*a1^2*a2*a3^2*a4 + 6*a1^2*a2*a4*c3^2 - 6*a1^2*c1^2*c2*c4 + 24*a1*a2*c1*c2^2*c4 + 24*a1*a3*c1*c2*c3*c4 + 24*a1*a4*c1*c2*c4^2 + a2^4*c2*c4 + 2*a2^3*a4^3 + 6*a2^3*a4*c4^2 - 6*a2^2*c2^3*c4 + 6*a2*a3^2*a4*c1^2 + 24*a2*a3*c2^2*c3*c4 + 6*a2*a4^3*c2^2 + 18*a2*a4*c1^2*c3^2 - 30*a2*a4*c2^2*c4^2 + a3^4*c2*c4 - 6*a3^2*c2*c3^2*c4 + 24*a3*a4*c2*c3*c4^2 + a4^4*c2*c4 - 6*a4^2*c2*c4^3 - 27*c1^4*c2*c4 - 27*c2^5*c4 - 27*c2*c3^4*c4 - 27*c2*c4^5, 2*a1^4*c3^2 - 6*a1^2*a2^2*a4^2 + 6*a1^2*a2^2*c4^2 + 6*a1^2*a4^2*c2^2 - 12*a1^2*c1^2*c3^2 + 18*a1^2*c2^2*c4^2 + 48*a1*a2*c1*c2*c3^2 + 12*a1*a3^3*c1*c3 + 12*a1*a3^2*a4*c1*c4 + 12*a1*a3*c1*c3^3 + 12*a1*a4*c1*c3^2*c4 + 2*a2^4*c3^2 + 6*a2^2*a4^2*c1^2 + 18*a2^2*c1^2*c4^2 - 12*a2^2*c2^2*c3^2 + 12*a2*a3^3*c2*c3 + 12*a2*a3^2*a4*c2*c4 + 12*a2*a3*c2*c3^3 + 12*a2*a4*c2*c3^2*c4 + a3^6 - 7*a3^4*c3^2 - 3*a3^2*a4^4 - 6*a3^2*a4^2*c4^2 - 21*a3^2*c3^4 + 9*a3^2*c4^4 + 48*a3*a4*c3^3*c4 - a4^4*c3^2 + 18*a4^2*c1^2*c2^2 + 6*a4^2*c3^2*c4^2 - 54*c1^4*c3^2 - 162*c1^2*c2^2*c4^2 - 54*c2^4*c3^2 + 27*c3^6 + 27*c3^2*c4^4, a1^4*c3*c4 - 6*a1^2*a2^2*a3*a4 + 6*a1^2*a3*a4*c2^2 - 6*a1^2*c1^2*c3*c4 + 24*a1*a2*c1*c2*c3*c4 + 24*a1*a3*c1*c3^2*c4 + 24*a1*a4*c1*c3*c4^2 + a2^4*c3*c4 + 6*a2^2*a3*a4*c1^2 - 6*a2^2*c2^2*c3*c4 + 24*a2*a3*c2*c3^2*c4 + 24*a2*a4*c2*c3*c4^2 + a3^4*c3*c4 + 2*a3^3*a4^3 + 6*a3^3*a4*c4^2 - 6*a3^2*c3^3*c4 + 6*a3*a4^3*c3^2 + 18*a3*a4*c1^2*c2^2 - 30*a3*a4*c3^2*c4^2 + a4^4*c3*c4 - 6*a4^2*c3*c4^3 - 27*c1^4*c3*c4 - 27*c2^4*c3*c4 - 27*c3^5*c4 - 27*c3*c4^5, 2*a1^4*c4^2 - 6*a1^2*a2^2*a3^2 + 6*a1^2*a2^2*c3^2 + 6*a1^2*a3^2*c2^2 - 12*a1^2*c1^2*c4^2 + 18*a1^2*c2^2*c3^2 + 48*a1*a2*c1*c2*c4^2 + 12*a1*a3*a4^2*c1*c3 + 12*a1*a3*c1*c3*c4^2 + 12*a1*a4^3*c1*c4 + 12*a1*a4*c1*c4^3 + 2*a2^4*c4^2 + 6*a2^2*a3^2*c1^2 + 18*a2^2*c1^2*c3^2 - 12*a2^2*c2^2*c4^2 + 12*a2*a3*a4^2*c2*c3 + 12*a2*a3*c2*c3*c4^2 + 12*a2*a4^3*c2*c4 + 12*a2*a4*c2*c4^3 - 3*a3^4*a4^2 - a3^4*c4^2 - 6*a3^2*a4^2*c3^2 + 18*a3^2*c1^2*c2^2 + 6*a3^2*c3^2*c4^2 + 48*a3*a4*c3*c4^3 + a4^6 - 7*a4^4*c4^2 + 9*a4^2*c3^4 - 21*a4^2*c4^4 - 54*c1^4*c4^2 - 162*c1^2*c2^2*c3^2 - 54*c2^4*c4^2 + 27*c3^4*c4^2 + 27*c4^6, a1^3*a2^2*a3 - a1^3*a3*c2^2 - a1^2*a4^2*c1*c3 - 3*a1^2*c1*c3*c4^2 - a1*a2^2*a3*c1^2 - 4*a1*a2*a4^2*c2*c3 - 12*a1*a2*c2*c3*c4^2 + a1*a3^3*a4^2 - a1*a3^3*c4^2 - a1*a3*a4^2*c3^2 - 3*a1*a3*c1^2*c2^2 - 3*a1*a3*c3^2*c4^2 - a2^2*a3^2*c1*c3 - 4*a2^2*a3*a4*c1*c4 - 3*a2^2*c1*c3^3 - 3*a3^2*c1*c2^2*c3 - 12*a3*a4*c1*c2^2*c4 - 3*a4^2*c1^3*c3 + 27*c1^3*c3*c4^2 + 27*c1*c2^2*c3^3, a1^3*a2^2*a4 - a1^3*a4*c2^2 - a1^2*a3^2*c1*c4 - 3*a1^2*c1*c3^2*c4 - a1*a2^2*a4*c1^2 - 4*a1*a2*a3^2*c2*c4 - 12*a1*a2*c2*c3^2*c4 + a1*a3^2*a4^3 - a1*a3^2*a4*c4^2 - a1*a4^3*c3^2 - 3*a1*a4*c1^2*c2^2 - 3*a1*a4*c3^2*c4^2 - 4*a2^2*a3*a4*c1*c3 - a2^2*a4^2*c1*c4 - 3*a2^2*c1*c4^3 - 3*a3^2*c1^3*c4 - 12*a3*a4*c1*c2^2*c3 - 3*a4^2*c1*c2^2*c4 + 27*c1^3*c3^2*c4 + 27*c1*c2^2*c4^3, a1^3*a2^2*c3 + 3*a1^3*c2^2*c3 + 3*a1^2*a3*a4^2*c1 - 3*a1^2*a3*c1*c4^2 + 3*a1*a2^2*c1^2*c3 - 3*a1*a3^2*a4^2*c3 + 3*a1*a3^2*c3*c4^2 + 3*a1*a4^2*c3^3 - 27*a1*c1^2*c2^2*c3 + 9*a1*c3^3*c4^2 - a2^2*a3^3*c1 - 3*a2^2*a3*c1*c3^2 - 3*a3^3*c1*c2^2 - 3*a3*a4^2*c1^3 - 9*a3*c1^3*c4^2 + 27*a3*c1*c2^2*c3^2, a1^3*a2^2*c4 + 3*a1^3*c2^2*c4 + 3*a1^2*a3^2*a4*c1 - 3*a1^2*a4*c1*c3^2 + 3*a1*a2^2*c1^2*c4 - 3*a1*a3^2*a4^2*c4 + 3*a1*a3^2*c4^3 + 3*a1*a4^2*c3^2*c4 - 27*a1*c1^2*c2^2*c4 + 9*a1*c3^2*c4^3 - a2^2*a4^3*c1 - 3*a2^2*a4*c1*c4^2 - 3*a3^2*a4*c1^3 - 3*a4^3*c1*c2^2 - 9*a4*c1^3*c3^2 + 27*a4*c1*c2^2*c4^2, a1^3*a2*a3^2 - a1^3*a2*c3^2 - a1^2*a4^2*c1*c2 - 3*a1^2*c1*c2*c4^2 + a1*a2^3*a4^2 - a1*a2^3*c4^2 - a1*a2*a3^2*c1^2 - a1*a2*a4^2*c2^2 - 3*a1*a2*c1^2*c3^2 - 3*a1*a2*c2^2*c4^2 - 4*a1*a3*a4^2*c2*c3 - 12*a1*a3*c2*c3*c4^2 - a2^2*a3^2*c1*c2 - 3*a2^2*c1*c2*c3^2 - 4*a2*a3^2*a4*c1*c4 - 12*a2*a4*c1*c3^2*c4 - 3*a3^2*c1*c2^3 - 3*a4^2*c1^3*c2 + 27*c1^3*c2*c4^2 + 27*c1*c2^3*c3^2, a1^3*a2*a3*a4 - 3*a1^2*c1*c2*c3*c4 - a1*a2^3*c3*c4 - a1*a2*a3*a4*c1^2 - 3*a1*a2*c2^2*c3*c4 - a1*a3^3*c2*c4 - 3*a1*a3*c2*c3^2*c4 - a1*a4^3*c2*c3 - 3*a1*a4*c2*c3*c4^2 - a2^2*a3*a4*c1*c2 - a2*a3^2*a4*c1*c3 - a2*a3*a4^2*c1*c4 - 3*a2*a3*c1*c4^3 - 3*a2*a4*c1*c3^3 - 3*a3*a4*c1*c2^3 + 27*c1^3*c2*c3*c4, 2*a1^3*a2*a3*c2 - 2*a1^3*a3*a4*c4 + 6*a1*a2^2*c3*c4^2 - 6*a1*a2*a3*c1^2*c2 + 6*a1*a3*a4*c1^2*c4 - 6*a1*a4^2*c2^2*c3 + a2^4*a3*c1 + 6*a2*a3^2*c1*c2*c3 - 18*a2*c1*c2*c3^3 - 6*a3^2*a4*c1*c3*c4 - a3*a4^4*c1 - 9*a3*c1*c2^4 + 9*a3*c1*c4^4 + 18*a4*c1*c3^3*c4, 2*a1^3*a2*a3*c3 - 2*a1^3*a2*a4*c4 - 6*a1*a2*a3*c1^2*c3 + 6*a1*a2*a4*c1^2*c4 + 6*a1*a3^2*c2*c4^2 - 6*a1*a4^2*c2*c3^2 + 6*a2^2*a3*c1*c2*c3 - 6*a2^2*a4*c1*c2*c4 + a2*a3^4*c1 - a2*a4^4*c1 - 9*a2*c1*c3^4 + 9*a2*c1*c4^4 - 18*a3*c1*c2^3*c3 + 18*a4*c1*c2^3*c4, a1^3*a2*a3*c4 + 3*a1^2*a4*c1*c2*c3 + 3*a1*a2*a3*c1^2*c4 - 3*a1*a4^2*c2*c3*c4 - 9*a1*c2*c3*c4^3 - a2*a3*a4^3*c1 - 3*a2*a3*a4*c1*c4^2 + 9*a4*c1^3*c2*c3, a1^3*a2*a4^2 - a1^3*a2*c4^2 - a1^2*a3^2*c1*c2 - 3*a1^2*c1*c2*c3^2 + a1*a2^3*a3^2 - a1*a2^3*c3^2 - a1*a2*a3^2*c2^2 - a1*a2*a4^2*c1^2 - 3*a1*a2*c1^2*c4^2 - 3*a1*a2*c2^2*c3^2 - 4*a1*a3^2*a4*c2*c4 - 12*a1*a4*c2*c3^2*c4 - a2^2*a4^2*c1*c2 - 3*a2^2*c1*c2*c4^2 - 4*a2*a3*a4^2*c1*c3 - 12*a2*a3*c1*c3*c4^2 - 3*a3^2*c1^3*c2 - 3*a4^2*c1*c2^3 + 27*c1^3*c2*c3^2 + 27*c1*c2^3*c4^2, 2*a1^3*a2*a4*c2 - 2*a1^3*a3*a4*c3 + 6*a1*a2^2*c3^2*c4 - 6*a1*a2*a4*c1^2*c2 - 6*a1*a3^2*c2^2*c4 + 6*a1*a3*a4*c1^2*c3 + a2^4*a4*c1 + 6*a2*a4^2*c1*c2*c4 - 18*a2*c1*c2*c4^3 - a3^4*a4*c1 - 6*a3*a4^2*c1*c3*c4 + 18*a3*c1*c3*c4^3 - 9*a4*c1*c2^4 + 9*a4*c1*c3^4, a1^3*a2*a4*c3 + 3*a1^2*a3*c1*c2*c4 + 3*a1*a2*a4*c1^2*c3 - 3*a1*a3^2*c2*c3*c4 - 9*a1*c2*c3^3*c4 - a2*a3^3*a4*c1 - 3*a2*a3*a4*c1*c3^2 + 9*a3*c1^3*c2*c4, 4*a1^3*a2*c1*c2 - 4*a1^3*a4*c1*c4 + a1^2*a2^4 + 2*a1^2*a2^2*c2^2 - 4*a1^2*a2*a3*c2*c3 + 4*a1^2*a3*a4*c3*c4 - a1^2*a4^4 - 2*a1^2*a4^2*c4^2 - 3*a1^2*c2^4 + 3*a1^2*c4^4 - 12*a1*a2*c1^3*c2 + 12*a1*a4*c1^3*c4 + a2^4*c1^2 - 6*a2^2*c1^2*c2^2 + 12*a2*a3*c1^2*c2*c3 - 12*a3*a4*c1^2*c3*c4 - a4^4*c1^2 + 6*a4^2*c1^2*c4^2 - 27*c1^2*c2^4 + 27*c1^2*c4^4, a1^3*a2*c3*c4 + a1^2*a3*a4*c1*c2 - a1*a2^3*a3*a4 + a1*a2*a3*a4*c2^2 + 3*a1*a2*c1^2*c3*c4 + a1*a3^2*a4*c2*c3 + a1*a3*a4^2*c2*c4 + 3*a1*a3*c2*c4^3 + 3*a1*a4*c2*c3^3 + 3*a2^2*c1*c2*c3*c4 + a2*a3^3*c1*c4 + 3*a2*a3*c1*c3^2*c4 + a2*a4^3*c1*c3 + 3*a2*a4*c1*c3*c4^2 + 3*a3*a4*c1^3*c2 - 27*c1*c2^3*c3*c4, a1^3*a3^2*a4 - a1^3*a4*c3^2 - a1^2*a2^2*c1*c4 - 3*a1^2*c1*c2^2*c4 - 4*a1*a2^2*a3*c3*c4 + a1*a2^2*a4^3 - a1*a2^2*a4*c4^2 - a1*a3^2*a4*c1^2 - 12*a1*a3*c2^2*c3*c4 - a1*a4^3*c2^2 - 3*a1*a4*c1^2*c3^2 - 3*a1*a4*c2^2*c4^2 - 3*a2^2*c1^3*c4 - 4*a2*a3^2*a4*c1*c2 - 12*a2*a4*c1*c2*c3^2 - a3^2*a4^2*c1*c4 - 3*a3^2*c1*c4^3 - 3*a4^2*c1*c3^2*c4 + 27*c1^3*c2^2*c4 + 27*c1*c3^2*c4^3, a1^3*a3^2*c2 + 3*a1^3*c2*c3^2 + 3*a1^2*a2*a4^2*c1 - 3*a1^2*a2*c1*c4^2 - 3*a1*a2^2*a4^2*c2 + 3*a1*a2^2*c2*c4^2 + 3*a1*a3^2*c1^2*c2 + 3*a1*a4^2*c2^3 - 27*a1*c1^2*c2*c3^2 + 9*a1*c2^3*c4^2 - a2^3*a3^2*c1 - 3*a2^3*c1*c3^2 - 3*a2*a3^2*c1*c2^2 - 3*a2*a4^2*c1^3 - 9*a2*c1^3*c4^2 + 27*a2*c1*c2^2*c3^2, a1^3*a3^2*c4 + 3*a1^3*c3^2*c4 + 3*a1^2*a2^2*a4*c1 - 3*a1^2*a4*c1*c2^2 - 3*a1*a2^2*a4^2*c4 + 3*a1*a2^2*c4^3 + 3*a1*a3^2*c1^2*c4 + 3*a1*a4^2*c2^2*c4 - 27*a1*c1^2*c3^2*c4 + 9*a1*c2^2*c4^3 - 3*a2^2*a4*c1^3 - a3^2*a4^3*c1 - 3*a3^2*a4*c1*c4^2 - 3*a4^3*c1*c3^2 - 9*a4*c1^3*c2^2 + 27*a4*c1*c3^2*c4^2, a1^3*a3*a4^2 - a1^3*a3*c4^2 - a1^2*a2^2*c1*c3 - 3*a1^2*c1*c2^2*c3 + a1*a2^2*a3^3 - a1*a2^2*a3*c3^2 - 4*a1*a2^2*a4*c3*c4 - a1*a3^3*c2^2 - a1*a3*a4^2*c1^2 - 3*a1*a3*c1^2*c4^2 - 3*a1*a3*c2^2*c3^2 - 12*a1*a4*c2^2*c3*c4 - 3*a2^2*c1^3*c3 - 4*a2*a3*a4^2*c1*c2 - 12*a2*a3*c1*c2*c4^2 - a3^2*a4^2*c1*c3 - 3*a3^2*c1*c3*c4^2 - 3*a4^2*c1*c3^3 + 27*c1^3*c2^2*c3 + 27*c1*c3^3*c4^2, a1^3*a3*a4*c2 + 3*a1^2*a2*c1*c3*c4 - 3*a1*a2^2*c2*c3*c4 + 3*a1*a3*a4*c1^2*c2 - 9*a1*c2^3*c3*c4 - a2^3*a3*a4*c1 - 3*a2*a3*a4*c1*c2^2 + 9*a2*c1^3*c3*c4, 4*a1^3*a3*c1*c3 - 4*a1^3*a4*c1*c4 - 4*a1^2*a2*a3*c2*c3 + 4*a1^2*a2*a4*c2*c4 + a1^2*a3^4 + 2*a1^2*a3^2*c3^2 - a1^2*a4^4 - 2*a1^2*a4^2*c4^2 - 3*a1^2*c3^4 + 3*a1^2*c4^4 - 12*a1*a3*c1^3*c3 + 12*a1*a4*c1^3*c4 + 12*a2*a3*c1^2*c2*c3 - 12*a2*a4*c1^2*c2*c4 + a3^4*c1^2 - 6*a3^2*c1^2*c3^2 - a4^4*c1^2 + 6*a4^2*c1^2*c4^2 - 27*c1^2*c3^4 + 27*c1^2*c4^4, a1^3*a3*c2*c4 + a1^2*a2*a4*c1*c3 + a1*a2^2*a4*c2*c3 - a1*a2*a3^3*a4 + a1*a2*a3*a4*c3^2 + a1*a2*a4^2*c3*c4 + 3*a1*a2*c3*c4^3 + 3*a1*a3*c1^2*c2*c4 + 3*a1*a4*c2^3*c3 + a2^3*a3*c1*c4 + 3*a2*a3*c1*c2^2*c4 + 3*a2*a4*c1^3*c3 + 3*a3^2*c1*c2*c3*c4 + a3*a4^3*c1*c2 + 3*a3*a4*c1*c2*c4^2 - 27*c1*c2*c3^3*c4, a1^3*a4^2*c2 + 3*a1^3*c2*c4^2 + 3*a1^2*a2*a3^2*c1 - 3*a1^2*a2*c1*c3^2 - 3*a1*a2^2*a3^2*c2 + 3*a1*a2^2*c2*c3^2 + 3*a1*a3^2*c2^3 + 3*a1*a4^2*c1^2*c2 - 27*a1*c1^2*c2*c4^2 + 9*a1*c2^3*c3^2 - a2^3*a4^2*c1 - 3*a2^3*c1*c4^2 - 3*a2*a3^2*c1^3 - 3*a2*a4^2*c1*c2^2 - 9*a2*c1^3*c3^2 + 27*a2*c1*c2^2*c4^2, a1^3*a4^2*c3 + 3*a1^3*c3*c4^2 + 3*a1^2*a2^2*a3*c1 - 3*a1^2*a3*c1*c2^2 - 3*a1*a2^2*a3^2*c3 + 3*a1*a2^2*c3^3 + 3*a1*a3^2*c2^2*c3 + 3*a1*a4^2*c1^2*c3 - 27*a1*c1^2*c3*c4^2 + 9*a1*c2^2*c3^3 - 3*a2^2*a3*c1^3 - a3^3*a4^2*c1 - 3*a3^3*c1*c4^2 - 3*a3*a4^2*c1*c3^2 - 9*a3*c1^3*c2^2 + 27*a3*c1*c3^2*c4^2, a1^3*a4*c2*c3 + a1^2*a2*a3*c1*c4 + a1*a2^2*a3*c2*c4 + a1*a2*a3^2*c3*c4 - a1*a2*a3*a4^3 + a1*a2*a3*a4*c4^2 + 3*a1*a2*c3^3*c4 + 3*a1*a3*c2^3*c4 + 3*a1*a4*c1^2*c2*c3 + a2^3*a4*c1*c3 + 3*a2*a3*c1^3*c4 + 3*a2*a4*c1*c2^2*c3 + a3^3*a4*c1*c2 + 3*a3*a4*c1*c2*c3^2 + 3*a4^2*c1*c2*c3*c4 - 27*c1*c2*c3*c4^3, a1^2*a2^3*a3 - a1^2*a2*a3*c2^2 - a1^2*a3^2*c2*c3 - 4*a1^2*a3*a4*c2*c4 - 3*a1^2*c2*c3^3 - 4*a1*a2*a4^2*c1*c3 - 12*a1*a2*c1*c3*c4^2 - a2^3*a3*c1^2 - a2^2*a4^2*c2*c3 - 3*a2^2*c2*c3*c4^2 + a2*a3^3*a4^2 - a2*a3^3*c4^2 - a2*a3*a4^2*c3^2 - 3*a2*a3*c1^2*c2^2 - 3*a2*a3*c3^2*c4^2 - 3*a3^2*c1^2*c2*c3 - 12*a3*a4*c1^2*c2*c4 - 3*a4^2*c2^3*c3 + 27*c1^2*c2*c3^3 + 27*c2^3*c3*c4^2, a1^2*a2^3*a4 - a1^2*a2*a4*c2^2 - 4*a1^2*a3*a4*c2*c3 - a1^2*a4^2*c2*c4 - 3*a1^2*c2*c4^3 - 4*a1*a2*a3^2*c1*c4 - 12*a1*a2*c1*c3^2*c4 - a2^3*a4*c1^2 - a2^2*a3^2*c2*c4 - 3*a2^2*c2*c3^2*c4 + a2*a3^2*a4^3 - a2*a3^2*a4*c4^2 - a2*a4^3*c3^2 - 3*a2*a4*c1^2*c2^2 - 3*a2*a4*c3^2*c4^2 - 3*a3^2*c2^3*c4 - 12*a3*a4*c1^2*c2*c3 - 3*a4^2*c1^2*c2*c4 + 27*c1^2*c2*c4^3 + 27*c2^3*c3^2*c4, a1^2*a2^3*c3 + 3*a1^2*a2*c2^2*c3 - a1^2*a3^3*c2 - 3*a1^2*a3*c2*c3^2 + 3*a2^3*c1^2*c3 + 3*a2^2*a3*a4^2*c2 - 3*a2^2*a3*c2*c4^2 - 3*a2*a3^2*a4^2*c3 + 3*a2*a3^2*c3*c4^2 + 3*a2*a4^2*c3^3 - 27*a2*c1^2*c2^2*c3 + 9*a2*c3^3*c4^2 - 3*a3^3*c1^2*c2 - 3*a3*a4^2*c2^3 + 27*a3*c1^2*c2*c3^2 - 9*a3*c2^3*c4^2, a1^2*a2^3*c4 + 3*a1^2*a2*c2^2*c4 - a1^2*a4^3*c2 - 3*a1^2*a4*c2*c4^2 + 3*a2^3*c1^2*c4 + 3*a2^2*a3^2*a4*c2 - 3*a2^2*a4*c2*c3^2 - 3*a2*a3^2*a4^2*c4 + 3*a2*a3^2*c4^3 + 3*a2*a4^2*c3^2*c4 - 27*a2*c1^2*c2^2*c4 + 9*a2*c3^2*c4^3 - 3*a3^2*a4*c2^3 - 3*a4^3*c1^2*c2 + 27*a4*c1^2*c2*c4^2 - 9*a4*c2^3*c3^2, 3*a1^2*a2^2*a3*c2 - 3*a1^2*a2*a3^2*c3 + 3*a1^2*a2*c3^3 - 3*a1^2*a3*c2^3 + a2^3*a4^2*c3 + 3*a2^3*c3*c4^2 - 3*a2^2*a3*c1^2*c2 + 3*a2*a3^2*c1^2*c3 + 3*a2*a4^2*c2^2*c3 + 9*a2*c1^2*c3^3 - 27*a2*c2^2*c3*c4^2 - a3^3*a4^2*c2 - 3*a3^3*c2*c4^2 - 3*a3*a4^2*c2*c3^2 - 9*a3*c1^2*c2^3 + 27*a3*c2*c3^2*c4^2, 6*a1^2*a2^2*a3*c4 + 6*a1^2*a4*c1^2*c3 + 24*a1*a2*a4*c1*c2*c3 - 6*a1*a3^3*a4*c1 - 6*a1*a3*a4*c1*c3^2 - 18*a1*a4^2*c1*c3*c4 - 18*a1*c1*c3*c4^3 + 2*a2^4*a4*c3 + 12*a2^2*a3*c1^2*c4 + 6*a2^2*a4*c2^2*c3 - 2*a2*a3^3*a4*c2 - 18*a2*a3*a4*c2*c3^2 - 6*a2*a4^2*c2*c3*c4 - 54*a2*c2*c3*c4^3 + 3*a3^4*a4*c3 - 2*a3^3*a4^2*c4 - 6*a3^3*c4^3 + 6*a3^2*a4*c3^3 - 6*a3*a4^2*c3^2*c4 + 54*a3*c1^2*c2^2*c4 - 18*a3*c3^2*c4^3 - a4^5*c3 + 6*a4^3*c3*c4^2 + 18*a4*c1^4*c3 - 9*a4*c3^5 + 27*a4*c3*c4^4, 3*a1^2*a2^2*a4*c2 - 3*a1^2*a2*a4^2*c4 + 3*a1^2*a2*c4^3 - 3*a1^2*a4*c2^3 + a2^3*a3^2*c4 + 3*a2^3*c3^2*c4 - 3*a2^2*a4*c1^2*c2 + 3*a2*a3^2*c2^2*c4 + 3*a2*a4^2*c1^2*c4 + 9*a2*c1^2*c4^3 - 27*a2*c2^2*c3^2*c4 - a3^2*a4^3*c2 - 3*a3^2*a4*c2*c4^2 - 3*a4^3*c2*c3^2 - 9*a4*c1^2*c2^3 + 27*a4*c2*c3^2*c4^2, 6*a1^2*a2^2*a4*c3 + 6*a1^2*a3*c1^2*c4 + 24*a1*a2*a3*c1*c2*c4 - 18*a1*a3^2*c1*c3*c4 - 6*a1*a3*a4^3*c1 - 6*a1*a3*a4*c1*c4^2 - 18*a1*c1*c3^3*c4 + 2*a2^4*a3*c4 + 6*a2^2*a3*c2^2*c4 + 12*a2^2*a4*c1^2*c3 - 6*a2*a3^2*c2*c3*c4 - 2*a2*a3*a4^3*c2 - 18*a2*a3*a4*c2*c4^2 - 54*a2*c2*c3^3*c4 - a3^5*c4 + 6*a3^3*c3^2*c4 - 2*a3^2*a4^3*c3 - 6*a3^2*a4*c3*c4^2 + 3*a3*a4^4*c4 + 6*a3*a4^2*c4^3 + 18*a3*c1^4*c4 + 27*a3*c3^4*c4 - 9*a3*c4^5 - 6*a4^3*c3^3 + 54*a4*c1^2*c2^2*c3 - 18*a4*c3^3*c4^2, a1^2*a2^2*c2*c3 - a1^2*a2*a3^3 + a1^2*a2*a3*c3^2 + 4*a1^2*a2*a4*c3*c4 + 3*a1^2*c2^3*c3 + 4*a1*a3*a4^2*c1*c2 + 12*a1*a3*c1*c2*c4^2 - a2^3*a3*a4^2 + a2^3*a3*c4^2 + 3*a2^2*c1^2*c2*c3 + a2*a3^3*c1^2 + a2*a3*a4^2*c2^2 + 3*a2*a3*c1^2*c3^2 + 3*a2*a3*c2^2*c4^2 + 12*a2*a4*c1^2*c3*c4 + a3^2*a4^2*c2*c3 + 3*a3^2*c2*c3*c4^2 + 3*a4^2*c2*c3^3 - 27*c1^2*c2^3*c3 - 27*c2*c3^3*c4^2, a1^2*a2^2*c2*c4 + 4*a1^2*a2*a3*c3*c4 - a1^2*a2*a4^3 + a1^2*a2*a4*c4^2 + 3*a1^2*c2^3*c4 + 4*a1*a3^2*a4*c1*c2 + 12*a1*a4*c1*c2*c3^2 - a2^3*a3^2*a4 + a2^3*a4*c3^2 + 3*a2^2*c1^2*c2*c4 + a2*a3^2*a4*c2^2 + 12*a2*a3*c1^2*c3*c4 + a2*a4^3*c1^2 + 3*a2*a4*c1^2*c4^2 + 3*a2*a4*c2^2*c3^2 + a3^2*a4^2*c2*c4 + 3*a3^2*c2*c4^3 + 3*a4^2*c2*c3^2*c4 - 27*c1^2*c2^3*c4 - 27*c2*c3^2*c4^3, 6*a1^2*a2*a3^2*c4 + 6*a1^2*a4*c1^2*c2 - 6*a1*a2^3*a4*c1 - 6*a1*a2*a4*c1*c2^2 + 24*a1*a3*a4*c1*c2*c3 - 18*a1*a4^2*c1*c2*c4 - 18*a1*c1*c2*c4^3 + 3*a2^4*a4*c2 - 2*a2^3*a3*a4*c3 - 2*a2^3*a4^2*c4 - 6*a2^3*c4^3 + 6*a2^2*a4*c2^3 + 12*a2*a3^2*c1^2*c4 - 18*a2*a3*a4*c2^2*c3 - 6*a2*a4^2*c2^2*c4 + 54*a2*c1^2*c3^2*c4 - 18*a2*c2^2*c4^3 + 2*a3^4*a4*c2 + 6*a3^2*a4*c2*c3^2 - 6*a3*a4^2*c2*c3*c4 - 54*a3*c2*c3*c4^3 - a4^5*c2 + 6*a4^3*c2*c4^2 + 18*a4*c1^4*c2 - 9*a4*c2^5 + 27*a4*c2*c4^4, 4*a1^2*a2*a3*c2*c4 + a1^2*a3^2*c3*c4 - a1^2*a3*a4^3 + a1^2*a3*a4*c4^2 + 3*a1^2*c3^3*c4 + 4*a1*a2^2*a4*c1*c3 + 12*a1*a4*c1*c2^2*c3 - a2^2*a3^3*a4 + a2^2*a3*a4*c3^2 + a2^2*a4^2*c3*c4 + 3*a2^2*c3*c4^3 + 12*a2*a3*c1^2*c2*c4 + a3^3*a4*c2^2 + 3*a3^2*c1^2*c3*c4 + a3*a4^3*c1^2 + 3*a3*a4*c1^2*c4^2 + 3*a3*a4*c2^2*c3^2 + 3*a4^2*c2^2*c3*c4 - 27*c1^2*c3^3*c4 - 27*c2^2*c3*c4^3, 6*a1^2*a2*a4^2*c3 + 6*a1^2*a3*c1^2*c2 - 6*a1*a2^3*a3*c1 - 6*a1*a2*a3*c1*c2^2 - 18*a1*a3^2*c1*c2*c3 + 24*a1*a3*a4*c1*c2*c4 - 18*a1*c1*c2*c3^3 + 3*a2^4*a3*c2 - 2*a2^3*a3^2*c3 - 2*a2^3*a3*a4*c4 - 6*a2^3*c3^3 + 6*a2^2*a3*c2^3 - 6*a2*a3^2*c2^2*c3 - 18*a2*a3*a4*c2^2*c4 + 12*a2*a4^2*c1^2*c3 + 54*a2*c1^2*c3*c4^2 - 18*a2*c2^2*c3^3 - a3^5*c2 + 6*a3^3*c2*c3^2 - 6*a3^2*a4*c2*c3*c4 + 2*a3*a4^4*c2 + 6*a3*a4^2*c2*c4^2 + 18*a3*c1^4*c2 - 9*a3*c2^5 + 27*a3*c2*c3^4 - 54*a4*c2*c3^3*c4, 4*a1^2*a2*a4*c2*c3 - a1^2*a3^3*a4 + a1^2*a3*a4*c3^2 + a1^2*a4^2*c3*c4 + 3*a1^2*c3*c4^3 + 4*a1*a2^2*a3*c1*c4 + 12*a1*a3*c1*c2^2*c4 + a2^2*a3^2*c3*c4 - a2^2*a3*a4^3 + a2^2*a3*a4*c4^2 + 3*a2^2*c3^3*c4 + 12*a2*a4*c1^2*c2*c3 + a3^3*a4*c1^2 + 3*a3^2*c2^2*c3*c4 + a3*a4^3*c2^2 + 3*a3*a4*c1^2*c3^2 + 3*a3*a4*c2^2*c4^2 + 3*a4^2*c1^2*c3*c4 - 27*c1^2*c3*c4^3 - 27*c2^2*c3^3*c4, 6*a1^2*a2*c1^2*c3 + 6*a1^2*a3*a4^2*c2 - 18*a1*a2^2*c1*c2*c3 - 6*a1*a2*a3^3*c1 - 6*a1*a2*a3*c1*c3^2 + 24*a1*a2*a4*c1*c3*c4 - 18*a1*c1*c2^3*c3 - a2^5*c3 + 6*a2^3*c2^2*c3 - 2*a2^2*a3^3*c2 - 6*a2^2*a3*c2*c3^2 - 6*a2^2*a4*c2*c3*c4 + 3*a2*a3^4*c3 - 2*a2*a3^3*a4*c4 + 6*a2*a3^2*c3^3 - 18*a2*a3*a4*c3^2*c4 + 2*a2*a4^4*c3 + 6*a2*a4^2*c3*c4^2 + 18*a2*c1^4*c3 + 27*a2*c2^4*c3 - 9*a2*c3^5 - 6*a3^3*c2^3 + 12*a3*a4^2*c1^2*c2 + 54*a3*c1^2*c2*c4^2 - 18*a3*c2^3*c3^2 - 54*a4*c2^3*c3*c4, 6*a1^2*a2*c1^2*c4 + 6*a1^2*a3^2*a4*c2 - 18*a1*a2^2*c1*c2*c4 + 24*a1*a2*a3*c1*c3*c4 - 6*a1*a2*a4^3*c1 - 6*a1*a2*a4*c1*c4^2 - 18*a1*c1*c2^3*c4 - a2^5*c4 + 6*a2^3*c2^2*c4 - 6*a2^2*a3*c2*c3*c4 - 2*a2^2*a4^3*c2 - 6*a2^2*a4*c2*c4^2 + 2*a2*a3^4*c4 + 6*a2*a3^2*c3^2*c4 - 2*a2*a3*a4^3*c3 - 18*a2*a3*a4*c3*c4^2 + 3*a2*a4^4*c4 + 6*a2*a4^2*c4^3 + 18*a2*c1^4*c4 + 27*a2*c2^4*c4 - 9*a2*c4^5 + 12*a3^2*a4*c1^2*c2 - 54*a3*c2^3*c3*c4 - 6*a4^3*c2^3 + 54*a4*c1^2*c2*c3^2 - 18*a4*c2^3*c4^2, 6*a1^2*a2*c1*c2*c3 - 6*a1^2*a4*c1*c3*c4 + a1*a2^4*c3 + 2*a1*a2*a3^3*c2 - 6*a1*a2*a3*c2*c3^2 - 2*a1*a3^3*a4*c4 + 6*a1*a3*a4*c3^2*c4 - a1*a4^4*c3 - 9*a1*c2^4*c3 + 9*a1*c3*c4^4 + 6*a2^2*a3*c1*c4^2 - 18*a2*c1^3*c2*c3 - 6*a3*a4^2*c1*c2^2 + 18*a4*c1^3*c3*c4, 6*a1^2*a2*c1*c2*c4 - 6*a1^2*a3*c1*c3*c4 + a1*a2^4*c4 + 2*a1*a2*a4^3*c2 - 6*a1*a2*a4*c2*c4^2 - a1*a3^4*c4 - 2*a1*a3*a4^3*c3 + 6*a1*a3*a4*c3*c4^2 - 9*a1*c2^4*c4 + 9*a1*c3^4*c4 + 6*a2^2*a4*c1*c3^2 - 18*a2*c1^3*c2*c4 - 6*a3^2*a4*c1*c2^2 + 18*a3*c1^3*c3*c4, a1^2*a3^3*c4 + 3*a1^2*a3*c3^2*c4 - a1^2*a4^3*c3 - 3*a1^2*a4*c3*c4^2 + 3*a2^2*a3^2*a4*c3 - 3*a2^2*a3*a4^2*c4 + 3*a2^2*a3*c4^3 - 3*a2^2*a4*c3^3 + 3*a3^3*c1^2*c4 - 3*a3^2*a4*c2^2*c3 + 3*a3*a4^2*c2^2*c4 - 27*a3*c1^2*c3^2*c4 + 9*a3*c2^2*c4^3 - 3*a4^3*c1^2*c3 + 27*a4*c1^2*c3*c4^2 - 9*a4*c2^2*c3^3, 3*a1^2*a3^2*a4*c3 - 3*a1^2*a3*a4^2*c4 + 3*a1^2*a3*c4^3 - 3*a1^2*a4*c3^3 + a2^2*a3^3*c4 + 3*a2^2*a3*c3^2*c4 - a2^2*a4^3*c3 - 3*a2^2*a4*c3*c4^2 + 3*a3^3*c2^2*c4 - 3*a3^2*a4*c1^2*c3 + 3*a3*a4^2*c1^2*c4 + 9*a3*c1^2*c4^3 - 27*a3*c2^2*c3^2*c4 - 3*a4^3*c2^2*c3 - 9*a4*c1^2*c3^3 + 27*a4*c2^2*c3*c4^2, 6*a1^2*a3*c1*c2*c3 - 6*a1^2*a4*c1*c2*c4 + 2*a1*a2^3*a3*c3 - 2*a1*a2^3*a4*c4 - 6*a1*a2*a3*c2^2*c3 + 6*a1*a2*a4*c2^2*c4 + a1*a3^4*c2 - a1*a4^4*c2 - 9*a1*c2*c3^4 + 9*a1*c2*c4^4 + 6*a2*a3^2*c1*c4^2 - 6*a2*a4^2*c1*c3^2 - 18*a3*c1^3*c2*c3 + 18*a4*c1^3*c2*c4, a1*a2^3*a3*c4 + 3*a1*a2*a3*c2^2*c4 - a1*a3*a4^3*c2 - 3*a1*a3*a4*c2*c4^2 + 3*a2^2*a4*c1*c2*c3 - 3*a2*a4^2*c1*c3*c4 - 9*a2*c1*c3*c4^3 + 9*a4*c1*c2^3*c3, a1*a2^3*a4*c3 + 3*a1*a2*a4*c2^2*c3 - a1*a3^3*a4*c2 - 3*a1*a3*a4*c2*c3^2 + 3*a2^2*a3*c1*c2*c4 - 3*a2*a3^2*c1*c3*c4 - 9*a2*c1*c3^3*c4 + 9*a3*c1*c2^3*c4, 4*a1*a2^2*a3*c1*c3 - 4*a1*a2^2*a4*c1*c4 - 12*a1*a3*c1*c2^2*c3 + 12*a1*a4*c1*c2^2*c4 - 4*a2^3*a3*c2*c3 + 4*a2^3*a4*c2*c4 - a2^2*a3^4 - 2*a2^2*a3^2*c3^2 + a2^2*a4^4 + 2*a2^2*a4^2*c4^2 + 3*a2^2*c3^4 - 3*a2^2*c4^4 + 12*a2*a3*c2^3*c3 - 12*a2*a4*c2^3*c4 - a3^4*c2^2 + 6*a3^2*c2^2*c3^2 + a4^4*c2^2 - 6*a4^2*c2^2*c4^2 + 27*c2^2*c3^4 - 27*c2^2*c4^4, a1*a2*a3^3*c4 + 3*a1*a2*a3*c3^2*c4 - a1*a2*a4^3*c3 - 3*a1*a2*a4*c3*c4^2 + 3*a3^2*a4*c1*c2*c3 - 3*a3*a4^2*c1*c2*c4 - 9*a3*c1*c2*c4^3 + 9*a4*c1*c2*c3^3, 4*a1*a2*a3^2*c1*c2 - 12*a1*a2*c1*c2*c3^2 - 4*a1*a3^2*a4*c1*c4 + 12*a1*a4*c1*c3^2*c4 - a2^4*a3^2 - a2^4*c3^2 - 2*a2^2*a3^2*c2^2 + 6*a2^2*c2^2*c3^2 - 4*a2*a3^3*c2*c3 + 12*a2*a3*c2*c3^3 + 4*a3^3*a4*c3*c4 + a3^2*a4^4 + 2*a3^2*a4^2*c4^2 + 3*a3^2*c2^4 - 3*a3^2*c4^4 - 12*a3*a4*c3^3*c4 + a4^4*c3^2 - 6*a4^2*c3^2*c4^2 + 27*c2^4*c3^2 - 27*c3^2*c4^4, 4*a1*a2*a4^2*c1*c2 - 12*a1*a2*c1*c2*c4^2 - 4*a1*a3*a4^2*c1*c3 + 12*a1*a3*c1*c3*c4^2 - a2^4*a4^2 - a2^4*c4^2 - 2*a2^2*a4^2*c2^2 + 6*a2^2*c2^2*c4^2 - 4*a2*a4^3*c2*c4 + 12*a2*a4*c2*c4^3 + a3^4*a4^2 + a3^4*c4^2 + 2*a3^2*a4^2*c3^2 - 6*a3^2*c3^2*c4^2 + 4*a3*a4^3*c3*c4 - 12*a3*a4*c3*c4^3 + 3*a4^2*c2^4 - 3*a4^2*c3^4 + 27*c2^4*c4^2 - 27*c3^4*c4^2, a2^4*a3*c3 - a2^4*a4*c4 - 6*a2^2*a3*c2^2*c3 + 6*a2^2*a4*c2^2*c4 - a2*a3^4*c2 + 6*a2*a3^2*c2*c3^2 + a2*a4^4*c2 - 6*a2*a4^2*c2*c4^2 - 9*a2*c2*c3^4 + 9*a2*c2*c4^4 + a3^4*a4*c4 - 6*a3^2*a4*c3^2*c4 - a3*a4^4*c3 + 6*a3*a4^2*c3*c4^2 + 9*a3*c2^4*c3 - 9*a3*c3*c4^4 - 9*a4*c2^4*c4 + 9*a4*c3^4*c4 ] ;