// Balancing Conditions
5*h0(0)+13/2*h1(0)-h0(5)-1/2*h1(6)+1/2*h1(2)-5/2*h1(1)-3/2*h1(5)-2*h0(1)-h0(3)+1/2*h1(7)+7/2*h1(4)-5/2*h1(3)+2*h0(4)   ,
3*h0(4)-5/2*h1(5)-3/2*h1(6)+9/2*h1(4)+6*h0(0)-7/2*h1(1)-1/2*h1(2)-3/2*h1(3)-3*h0(1)-h0(2)-2*h0(5)+15/2*h1(0)+3/2*h1(7)   ,
4*h0(4)-5*h1(5)-h1(6)+6*h1(4)+8*h0(0)-9*h1(1)+3*h1(2)-2*h1(3)-7*h0(1)+h0(2)-3*h0(5)+10*h1(0)+2*h1(7)   ,
h0(3)-h1(3)+3*h1(7)+9*h0(0)+7*h1(4)+11*h1(0)+5*h0(4)-4*h0(5)-2*h1(6)+2*h1(2)-10*h1(1)-6*h1(5)-8*h0(1)   ,
3*h0(4)+7/2*h1(4)+9/2*h1(0)+3/2*h1(3)+5/2*h1(7)+2*h0(3)+4*h0(0)-3*h0(5)-3/2*h1(6)+3/2*h1(2)-15/2*h1(1)-9/2*h1(5)-6*h0(1)   ,
h0(4)-5/2*h1(5)+1/2*h1(6)+3/2*h1(4)+2*h0(0)-11/2*h1(1)+7/2*h1(2)-1/2*h1(3)-4*h0(1)+2*h0(2)-h0(5)+5/2*h1(0)+1/2*h1(7)   ,
// Self Orthogonality Conditions 
2*h0(0)*h0(4)+2*h0(2)*h0(5)+2*h0(3)*h0(4)+2*h0(1)*h0(5)   ,
2*h1(4)*h1(7)+2*h1(3)*h1(7)+2*h1(4)*h1(0)+2*h1(5)*h1(6)+2*h1(6)*h1(2)+2*h1(5)*h1(1)   ,
2*h2(1)*h2(5)-2*h2(2)*h2(5)-2*h2(3)*h2(4)+2*h2(0)*h2(4)   ,
-2*h3(4)*h3(7)+2*h3(5)*h3(1)+2*h3(6)*h3(2)+2*h3(3)*h3(7)-2*h3(5)*h3(6)+2*h3(4)*h3(0)   ,
2*h0(2)*h0(1)+2*h0(3)*h0(0)   ,
2*h1(3)*h1(4)+2*h1(5)*h1(2)+2*h1(6)*h1(1)+2*h1(0)*h1(7)   ,
-2*h2(2)*h2(1)-2*h2(3)*h2(0)   ,
-2*h3(3)*h3(4)-2*h3(5)*h3(2)-2*h3(6)*h3(1)-2*h3(0)*h3(7)   ,
2*h1(3)*h1(0)+2*h1(1)*h1(2)   ,
-2*h3(1)*h3(2)-2*h3(3)*h3(0)   ,
// Cross Orthogonality Conditions 
h0(1)*h1(2)+h0(2)*h1(1)+h0(3)*h1(0)+h0(0)*h1(3)   ,
-h0(1)*h3(2)-h0(2)*h3(1)-h0(3)*h3(0)-h0(0)*h3(3)   ,
-h1(1)*h3(2)-h1(2)*h3(1)-h1(3)*h3(0)-h1(0)*h3(3)   ,
-h2(1)*h3(2)-h2(2)*h3(1)-h2(3)*h3(0)-h2(0)*h3(3)   ,
h0(3)*h1(4)+h0(4)*h1(3)+h0(5)*h1(2)+h0(5)*h1(1)+h0(0)*h1(7)+h0(4)*h1(0)+h0(1)*h1(6)+h0(2)*h1(5)   ,
-h0(1)*h2(2)-h0(0)*h2(3)-h0(2)*h2(1)-h0(3)*h2(0)   ,
-h0(2)*h3(5)-h0(1)*h3(6)-h0(0)*h3(7)-h0(4)*h3(0)-h0(5)*h3(1)-h0(4)*h3(3)-h0(5)*h3(2)-h0(3)*h3(4)   ,
-h1(1)*h2(2)-h1(0)*h2(3)-h1(2)*h2(1)-h1(3)*h2(0)   ,
-h1(5)*h3(2)-h1(6)*h3(1)-h1(0)*h3(7)-h1(7)*h3(0)-h1(1)*h3(6)-h1(2)*h3(5)-h1(3)*h3(4)-h1(4)*h3(3)   ,
-h2(3)*h3(4)-h2(4)*h3(3)+h2(4)*h3(0)-h2(5)*h3(2)+h2(5)*h3(1)-h2(1)*h3(6)-h2(2)*h3(5)-h2(0)*h3(7)   ,
h0(1)*h1(1)+h0(2)*h1(6)+h0(1)*h1(5)+h0(4)*h1(7)+h0(3)*h1(3)+h0(4)*h1(4)+h0(0)*h1(0)+h0(5)*h1(5)+h0(0)*h1(4)+h0(5)*h1(6)+h0(2)*h1(2)+h0(3)*h1(7)   ,
-h0(4)*h2(3)-h0(5)*h2(1)-h0(4)*h2(0)-h0(5)*h2(2)-h0(3)*h2(4)+h0(0)*h2(4)-h0(2)*h2(5)+h0(1)*h2(5)   ,
h0(1)*h3(5)-h0(4)*h3(7)-h0(2)*h3(2)-h0(5)*h3(6)+h0(3)*h3(7)-h0(1)*h3(1)+h0(2)*h3(6)-h0(3)*h3(3)-h0(4)*h3(4)-h0(0)*h3(0)-h0(5)*h3(5)+h0(0)*h3(4)   ,
-h1(7)*h2(0)-h1(4)*h2(3)-h1(2)*h2(5)-h1(5)*h2(2)-h1(3)*h2(4)-h1(6)*h2(1)+h1(0)*h2(4)+h1(1)*h2(5)   ,
h1(3)*h3(7)-h1(6)*h3(2)-h1(6)*h3(5)-h1(4)*h3(0)-h1(5)*h3(6)+h1(0)*h3(4)-h1(7)*h3(4)-h1(7)*h3(3)+h1(1)*h3(5)+h1(2)*h3(6)-h1(5)*h3(1)-h1(4)*h3(7)   ,
h2(0)*h3(4)+h2(5)*h3(5)+h2(0)*h3(0)+h2(4)*h3(4)+h2(3)*h3(3)+h2(1)*h3(5)+h2(2)*h3(6)+h2(1)*h3(1)+h2(3)*h3(7)+h2(2)*h3(2)-h2(5)*h3(6)-h2(4)*h3(7)   ,
h0(1)*h1(1)+h0(2)*h1(6)+h0(1)*h1(5)+h0(4)*h1(7)+h0(3)*h1(3)+h0(4)*h1(4)+h0(0)*h1(0)+h0(5)*h1(5)+h0(0)*h1(4)+h0(5)*h1(6)+h0(2)*h1(2)+h0(3)*h1(7)   ,
h0(1)*h3(1)-h0(2)*h3(6)+h0(3)*h3(3)-h0(1)*h3(5)-h0(0)*h3(4)+h0(2)*h3(2)+h0(0)*h3(0)+h0(4)*h3(7)+h0(5)*h3(6)-h0(3)*h3(7)+h0(5)*h3(5)+h0(4)*h3(4)   ,
-h1(7)*h2(3)+h1(5)*h2(5)-h1(6)*h2(2)+h1(4)*h2(4)+h1(3)*h2(3)-h1(5)*h2(1)-h1(4)*h2(0)+h1(2)*h2(2)+h1(0)*h2(0)+h1(1)*h2(1)-h1(6)*h2(5)-h1(7)*h2(4)   ,
h2(0)*h3(4)+h2(5)*h3(5)+h2(0)*h3(0)+h2(4)*h3(4)+h2(3)*h3(3)+h2(1)*h3(5)+h2(2)*h3(6)+h2(1)*h3(1)+h2(3)*h3(7)+h2(2)*h3(2)-h2(5)*h3(6)-h2(4)*h3(7)   ,
h0(3)*h1(4)+h0(4)*h1(3)+h0(5)*h1(2)+h0(5)*h1(1)+h0(0)*h1(7)+h0(4)*h1(0)+h0(1)*h1(6)+h0(2)*h1(5)   ,
h0(4)*h2(0)+h0(5)*h2(1)+h0(3)*h2(4)+h0(5)*h2(2)+h0(4)*h2(3)-h0(1)*h2(5)-h0(0)*h2(4)+h0(2)*h2(5)   ,
h0(5)*h3(1)+h0(5)*h3(2)+h0(1)*h3(6)+h0(0)*h3(7)+h0(4)*h3(0)+h0(4)*h3(3)+h0(3)*h3(4)+h0(2)*h3(5)   ,
h1(6)*h2(2)-h1(3)*h2(3)-h1(4)*h2(4)-h1(0)*h2(0)-h1(2)*h2(2)-h1(5)*h2(5)+h1(7)*h2(3)+h1(7)*h2(4)+h1(4)*h2(0)-h1(1)*h2(1)+h1(6)*h2(5)+h1(5)*h2(1)   ,
-h1(2)*h3(6)-h1(1)*h3(5)+h1(4)*h3(7)+h1(7)*h3(4)+h1(4)*h3(0)+h1(6)*h3(5)-h1(0)*h3(4)+h1(5)*h3(6)+h1(6)*h3(2)-h1(3)*h3(7)+h1(5)*h3(1)+h1(7)*h3(3)   ,
-h2(3)*h3(4)-h2(4)*h3(3)+h2(4)*h3(0)-h2(5)*h3(2)+h2(5)*h3(1)-h2(1)*h3(6)-h2(2)*h3(5)-h2(0)*h3(7)   ,
h0(1)*h1(2)+h0(0)*h1(3)+h0(3)*h1(0)+h0(2)*h1(1)   ,
h0(1)*h2(2)+h0(2)*h2(1)+h0(0)*h2(3)+h0(3)*h2(0)   ,
h0(1)*h3(2)+h0(0)*h3(3)+h0(2)*h3(1)+h0(3)*h3(0)   ,
h1(6)*h2(1)+h1(5)*h2(2)+h1(2)*h2(5)+h1(3)*h2(4)+h1(7)*h2(0)-h1(0)*h2(4)-h1(1)*h2(5)+h1(4)*h2(3)   ,
h1(1)*h3(6)+h1(7)*h3(0)+h1(0)*h3(7)+h1(6)*h3(1)+h1(5)*h3(2)+h1(4)*h3(3)+h1(3)*h3(4)+h1(2)*h3(5)   ,
-h2(0)*h3(3)-h2(2)*h3(1)-h2(3)*h3(0)-h2(1)*h3(2)   ,
h1(3)*h2(0)+h1(1)*h2(2)+h1(2)*h2(1)+h1(0)*h2(3)   ,
h1(1)*h3(2)+h1(3)*h3(0)+h1(2)*h3(1)+h1(0)*h3(3)   ,
// Normalizations
2*h0(5)^2+2*h0(0)^2+2*h0(1)^2+2*h0(2)^2+2*h0(3)^2+2*h0(4)^2-1/2   ,
2*h1(4)^2+2*h1(0)^2+2*h1(1)^2+2*h1(2)^2+2*h1(3)^2+2*h1(5)^2+2*h1(6)^2+2*h1(7)^2-1/2   ,
2*h2(0)^2+2*h2(1)^2+2*h2(2)^2+2*h2(3)^2+2*h2(4)^2+2*h2(5)^2-1/2   ,
2*h3(6)^2+2*h3(0)^2+2*h3(1)^2+2*h3(2)^2+2*h3(3)^2+2*h3(4)^2+2*h3(5)^2+2*h3(7)^2-1/2   ,
2*h0(0)+2*h0(1)+2*h0(2)+2*h0(3)+2*h0(4)+2*h0(5)-1   ,
2*h1(0)+2*h1(1)+2*h1(2)+2*h1(3)+2*h1(4)+2*h1(5)+2*h1(6)+2*h1(7)-1   ;