  Recently, it is shown that many Green's functions are not unique at special
points in complex momentum space using AdS/CFT. This phenomenon is similar to
the pole-skipping in holographic chaos, and the special points are typically
located at $\omega_n = -(2\pi T)ni$ with appropriate values of complex wave
number $q_n$. We study finite-coupling corrections to special points. As
examples, we consider four-derivative corrections to gravitational
perturbations and four-dimensional Maxwell perturbations. While $\omega_n$ is
uncorrected, $q_n$ is corrected at finite coupling. Some special points
disappear at particular values of higher-derivative couplings. Special point
locations of the Maxwell scalar and vector modes are related to each other by
the electromagnetic duality.
