Sample from pdf for discrete r.v

I have a random variable that can take 4 different values (4,8,16,32)and I would like to update it via sampling from its pdf, which is proportional to:

\begin{equation}
    \pi(\nu)\prod_{i=1}^N(\Gamma(\nu/2)(\nu/2)^{(\nu/2)})^{-1} \lambda_i^{(\nu/2 -1)} e^{-\nu\lambda_i/2}
\end{equation}