Diagonalization & Matrix Powers · Superchallenge problem

Let $C = \begin{pmatrix}0&1&0&0\\0&0&1&0\\0&0&0&1\\1&0&0&0\end{pmatrix}$ be the $4\times 4$ cyclic shift matrix. Diagonalize $C$ to find the entry in row 1, column 1 of $(I + C)^{10}$.