# Exact eigendecomposition of a specific Toeplitz matrix

I am interested in diagonalizing a general $$n \times n$$ matrix with entries of the form $$$$\frac{1}{|f_i-f_j|^p} \hspace{40px} 1 \le i,j \le n$$$$ where $$f_i,p \in \mathbb{R}$$ for $$1 \le i \le n$$. Notably, the matrix is a symmetric Toeplitz matrix. Is it possible to find the exact eigenvalues and/or the eigenvectors of such a matrix? I would like to diagonalize the general form, but also solutions for special values of $$\{f_i\}$$ and/or $$p$$ would be interesting.