Denef's holomorphy conjecture for twisted topological zeta functions

Let $F:(\mathbb{C}^{n+1},\mathbf{0})\to(\mathbb{C},\mathbf{0})$ define a germ of an isolated hypersurface singularity. For $x\in F^{-1}(0)$, let $\mathcal{F}_{F,x}$ be the Milnor fiber and let $\mathcal{E}_F$ be the set of eigenvalues of the monodromy on $\widetilde{H}_*(\mathcal{F}_{F,x},\mathbb{C})$; set $\mathcal{E}^{\operatorname{ord}}_F=\{\operatorname{ord}\zeta\mid\zeta\in\mathcal{E}_F\}$. For a set of natural numbers $\mathcal{E}$, let $\overline{\mathcal{E}}$ be the union of the sets of divisors of elements of $\mathcal{E}$. Denef's holomorphy conjecture. If $\ell\notin\overline{\mathcal{E}^{\operatorname{ord}}_F}$ and $\ell>1$, then $Z^{(\ell)}_{\operatorname{top}}(F,s)_\mathbf{0}$ is holomorphic on $\mathbb{C}$ and, in fact, vanishes. This is the topological-zeta-function version of the holomorphy conjecture; the source does not indicate a general resolution.