{
  BOUND = [10^3, 1]; \\ look for integers |x| <= 10^3
  S = [10];
  forvec(v = vector(1, i, [1,10^6]),
    my([c] = v, z1, DD, EE, FF, PP);
    for(b = -300, 300, 
    for (l=1, #S,
    k=S[l];
    u = -floor(b*k^(1/3)+c*k^(2/3));
    for (a = u-20, u+100,
    for (m = 0, 1,
    t = (-1)^m*(a^3+k*b^3+k^2*c^3-3*k*a*b*c);
    if (gcd(t,a^2-k*b*c) != 1, next);
    z1 = -(k*b^2-k*a*c) / (a^2-k*b*c) % t;
    DD = ((z1+t*s)*(a^2-k*b*c)+(k*b^2-k*a*c)) / t;
    EE = ((z1+t*s)*(k*c^2-a*b)+(a^2-k*b*c)) / t;
    FF = ((z1+t*s)*(b^2-a*c)+(k*c^2-a*b)) / t;
    PP = DD^3+k*EE^3+k^2*FF^3-3*k*DD*EE*FF;
    for (j = 1, 2,
      L = hyperellratpoints(12*gcd(t,j)*PP - 3*(t/gcd(t,j))^2, BOUND);
      for (k = 1, #L,
        my([i,AA1] = L[k], [Y,r] = divrem((sign(AA1)*AA1) - 3*(t/gcd(t,j)), 6));
        if (r, next);
        X = Y + (t/gcd(t,j)); Z = z1 + i*t;
        print([X,Y,Z,a,b,c]);
      )
    )
  )
 )
 )
 )
 )
}