Verification of the polynomials:

/*
Invariants for D=2
J1=G2^2/H4
J3=G2*H6/H4^2
 (J2=J1/J3=G2*H4/H6)

Invariants for D=5
J2=G2^5/H10
J4=H6*G2^2/H10
 (J1=J4/J2=H6/G2^3)
*/

*******************
allocatemem(2^33)
\p 3000
\r Hilbert.gp
*******************

ch="(...)/Gundlach-Q5/Inert/";


***************

l=2;

Tab=[[0,1,2,1,0],[1,2,2,1,0]];
D(x,y)=y-32;

***************

l=3;

Tab=[[1,2,2,2,2,2,2,2,1,0],[2,2,2,2,2,2,2,2,1,0]];
D(x,y)=4*x^4 + 12*x^3*y^2 + 8748*x^3*y + 12882159*x^3 + 30132*x^2*y^3 + 34698942*x^2*y^2 + 10857300264*x^2*y + 2339378717616*x^2 - 820125*x*y^4 + 34031907000*x*y^3 - 29524500000*y^5;

***************

l=7;

Tab=[[2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 2, 2, 1, 0], [3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 2, 2, 1, 0]];


DD=read(Str(ch,"PolQ5Gundlach-",l,"/DenQ5Gund",l));
D(xx,yy)=substvec(DD,[x,y],[xx,yy]);

*********************************************************************************************************


[J2,J4]=[3+4*I,-5+21*I];
Z=taufromgundNiv5(J2,J4);

L1=vector(l^2+1,i,read(Str(ch,"PolQ5Gundlach-",l,"/NumPhi/numphi",i)));
L2=vector(l^2+1,i,read(Str(ch,"PolQ5Gundlach-",l,"/NumPsi/numpsi",i)));

M=read(Str(ch,"PolQ5Gundlach-",l,"/classeGD5G0",l));

Phi=X^(l^2+1)+sum(i=1,l^2+1,substvec(L1[i],[x,y],[J2,J4])/D(J2,J4)^2/J2^Tab[1][i]*X^(i-1));
Phip=Phi';
Psi=sum(i=1,l^2+1,substvec(L2[i],[x,y],[J2,J4])/D(J2,J4)^2/J2^Tab[2][i]*X^(i-1))/Phip;

for(i=1,l^2+1,z=1/l*mtau5(M[i],Z);[J2p,J4p]=JGundlach([z[1],z[2]]);print(i"  "round(10^1000*subst(Phi,X,J2p))"  "round(10^1000*(J4p-subst(Psi,X,J2p)))));