Given the Toeplitz matrix
$$X = \begin{pmatrix} ~~~~\textbf{1} ~~~~\textbf{c} ~~~~\textbf{d} ~~~~0 ~~~~0 ~~~~0 ~~~~\textbf{d}~~~~ \\ ~~~~\textbf{c} ~~~~\textbf{1} ~~~~\textbf{c} ~~~~\textbf{d} ~~~~0 ~~~~0 ~~~~0~~~~ \\ ~~~~\textbf{d} ~~~~\textbf{c} ~~~~\textbf{1} ~~~~\textbf{c} ~~~~\textbf{d} ~~~~0 ~~~~0~~~~ \\ ~~~~0 ~~~~\textbf{d} ~~~~\textbf{c} ~~~~\textbf{1} ~~~~\textbf{c} ~~~~\textbf{d} ~~~~0~~~~ \\ ~~~~0 ~~~~0 ~~~~\textbf{d} ~~~~\textbf{c} ~~~~\textbf{1} ~~~~\textbf{c} ~~~~\textbf{d}~~~~ \\ ~~~~0 ~~~~0 ~~~~0 ~~~~\textbf{d} ~~~~\textbf{c} ~~~~\textbf{1} ~~~\textbf{c}~~~~ \\ ~~~~\textbf{d} ~~~~0 ~~~~0 ~~~~0 ~~~~\textbf{d} ~~~~\textbf{c} ~~~~\textbf{1}~~~~ \\ \end{pmatrix}$$
where $d$ and $c$ are different values between $-1$ and $0$. Furthermore,
$$2c + 2d = -1$$
My questions are to find expressions for
Second largest eigenvalue modulus (SLEM) or eigenvalues
Inverse of $X$
Thanks