The $\Gamma$ function is defined by
$$\Gamma(z)=\int_{0}^{+\infty}t^{z-1}e^{-t}dt$$
where $z$ is a complex number.
We know that if $z$ is real then the values of $\Gamma$ are also real. I am interested in the case where $z$ is complex and the values of $\Gamma$ are real. In particular where $0
Is this case possible?