  Given an induced representation of Langlands type $(\pi,V)$ of
$\mathrm{GL}_n(F)$ with $F$ nonarchimedean, we show that there exist explicit
choices of matrix coefficient $\beta$ and Schwartz-Bruhat function $\Phi$ for
which the Godement-Jacquet zeta integral $Z(s,\beta,\Phi)$ attains the
$L$-function $L(s,\pi)$.
