  We study the zeros of Poincar\'e series $P_{k,m}$ for the full modular group.
We consider the case where $m \sim \alpha k$ for some constant $\alpha > 0$. We
show that in this case a positive proportion of the zeros lie on the line
$\frac{1}{2} + it$. We further show that if $\alpha > \frac{\log(2)}{2\pi}$
then the imaginary axis also contains a positive proportion of zeros. We also
give a description for the location of the non-real zeros when $\alpha$ is
small.
