  The linearized spectrum and the algebra of global symmetries of conformal
higher-spin gravity decompose into infinitely many representations of the
conformal algebra. Their characters involve divergent sums over spins. We
propose a suitable regularization adapted to their evaluation and observe that
their characters are actually equal. This result holds in the case of type-A
and type-B (and their higher-depth generalizations) theories and confirms
previous observations on a remarkable rearrangement of dynamical degrees of
freedom in conformal higher-spin gravity after regularization.
