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This paper is devoted to the asymptotic behavior of all eigenvalues ofSymmetric (in general non Hermitian) Toeplitz matrices with moderately smoothsymbols which trace out a simple loop on the complex plane line as thedimension of the matrices increases to infinity. The main result describes theasymptotic structure of all eigenvalues. The constructed expansion is uniformwith respect to the number of eigenvalues.  Keywords: Toeplitz matrices, eigenvalues, asymptotic expansions

Asymptotics of eigenvalues of large symmetric Toeplitz matrices with smooth simple-loop symbols