We consider Hermitian Toeplitz matrices \(T_{n}(A_{n})\) generated by symbols \(A_{n}\) that depend on the matrix size \(n\) . These symbols take the form \( A_{n}(\theta )=a_{0}(\theta )+\sum _{k=1}^{\infty }\beta _{n,k}\,a_{k}(\theta ), \) where \(A_{n}\) and \(a_{0}\) belong to the simple-loop class \({{\,\textrm{SL}\,}}^{\alpha }\) for some \(\alpha \geqslant 2\) . Under suitable assumptions on the decay of the coefficients \(\beta _{n,k}\) and the regularity of the functions \(a_{k}\) , we prove that the eigenvalues of \(T_{n}(A_{n})\) admit a full asymptotic expansion uniformly in the bulk of the spectrum. This work generalizes previous results for fixed and finitely perturbed simple-loop symbols.
