.  \[thm:nonvanishingFormsnu0\] Let $X$ be a minimal $\Q$-factorial projective terminal pair of dimension $n$ such that $\nu(X,K_X)=0$. Let $\pi\colon Y\to X$ be a resolution of $X$, fix a tensor representation $\mathcal E$ of $\Omega_Y^0$, and let $q$ be the rank of $\mathcal E$. If $K_X