  We consider how the quasinormal spectrum for the conformal wave operator on
the static patch of de Sitter changes in response to the addition of a small
potential. Since the quasinormal modes and co-modes are explicitly known, we
are able to give explicit formulae for the instantaneous rate of change of each
frequency in terms of the perturbing potential. We verify these exact
computations numerically using a novel technique extending the spectral
hyperboloidal approach of Jaramillo et al. (2021). We propose a definition for
a family of pseudospectra that we show capture the instability properties of
the quasinormal frequencies.
