A circulant matrix has the form where each row is a cyclic shift of the previous row. The $3 \times 3$ circulant with first row $(2, 1, 1)$ is $C = \begin{pmatrix} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \end{pmatrix}$

Eigenvalues of circulant matrices satisfy $\lambda_k = \sum_{j=0}^{n-1} c_j \omega^{jk}$ where $\omega = e^{2\pi i/n}$. Which value is an eigenvalue of $C$?