Is it possible to analytically find the eigenvalues and eigenvectors of the following matrix?

Question

$M$ is a $R \times R$ dimensional square matrix. The elements of $M$ are \begin{align} [M]_{nm} &= R \hspace{3 cm} when \hspace{.2 cm} n=m, \\ &= \frac{1-e^\frac{2\pi i R (n-m)}{f}}{1-e^\frac{2\pi i (n-m)}{f}} \hspace{1 cm} when \hspace{.2 cm} n \neq m , \end{align} where $n$, $m$ are row and column indices respectively and $f$ is a mixed fraction not larger than $R+1$. Is it possible to analytically find the eigenvalues and eigenvectors of $M$?