Homological eigenvalues of lifts of pseudo-Anosov mapping classes to finite covers

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