  E. Bayer-Fluckiger gave a necessary and sufficient condition for a polynomial
to be realized as the characteristic polynomial of a semisimple isometry of an
even unimodular lattice, by describing the local-global obstruction, and the
author extended the result. This article presents a systematic way to compute
the obstruction. As an application, we give a necessary and sufficient
condition for a Salem number of degree $10$ or $18$ to be realized as the
dynamical degree of an automorphism of nonprojective K3 surface, in terms of
its minimal polynomial.
