  In this paper, we derive sufficient conditions for the localization of
two-dimensional split-step quantum walks with a strong shift. For this purpose,
we analyze the zero points of the function $f$ introduced by Fuda et. al.
(Quantum Inf Process 16(8) 203, 2017) and make these zero points explicit.
These zeros provide a concrete representation of the eigenvalues and
eigenvectors of the evolution operator, and in particular, clarify where
localization occurs. In addition, the eigenvalues obtained here asymptotically
approach threshold resonance in special cases. We also describe the display of
threshold resonances and generalized eigenfunctions.
