  Asymptotically, we analytically derive the form of eigenvectors for two
Fisher-Hartwig symbols besides those which were previously investigated in a
$2016$ work due to Movassagh and Kadanoff, in which the authors characterized
the eigenpairs of Toeplitz matrices generated by Fisher-Hartwig symbols with
one singularity. To perform such computations, we extend their methods which
consists of formulating an eigenvalue problem, obtained by a Wiener-Hopf
method, from which a suitable winding number is defined for passing to Fourier
space, and introducing a factorization dependent upon the winding number, for
other Fisher-Hartwig symbols which have previously been defined in the
literature. Following the computations required for the proof after obtaining
the asymptotic approximation of the eigenvectors, we provide a table from which
eigenvalues of one Fisher-Hartwig symbol for different complex valued functions
$b$ can be inferred.
