  We prove that given a Hecke-Maass form $f$ for $\text{SL}(2, \mathbb{Z})$ and
a sufficiently large prime $q$, there exists a primitive Dirichlet character
$\chi$ of conductor $q$ such that the $L$-values $L(\tfrac{1}{2}, f \otimes
\chi)$ and $L(\tfrac{1}{2}, \chi)$ do not vanish. We expect the same method to
work for any large integer $q$.
