  Let $\Sigma$ be a compact orientable surface of finite type with at least one
boundary component. Let $f \in \textup{Mod}(\Sigma)$ be a pseudo Anosov mapping
class. We prove a conjecture of McMullen by showing that there exists a finite
cover $\widetilde{\Sigma} \to \Sigma$ and a lift $\widetilde{f}$ of $f$ such
that $\wt{f}_*: H_1(\wt{\Sigma}; \mathbb{Z}) \to H_1(\wt{\Sigma}; \mathbb{Z})$
has an eigenvalue off the unit circle.
