  We derive the partition function for the Vafa-Witten twist of the
$\mathcal{N}=4$ supersymmetric gauge theory with gauge group SU(N) (for prime
$N$) and arbitrary values of the 't Hooft fluxes $v\in H^{2}(X,\mathbb{Z}_{N})$
on K\"ahler four-manifolds with $b^{+}_2>1$.
