  In this note we compute the 1-loop partition function of spin-$s$ fields on
Euclidean de Sitter space $S^{2n+1}$ using the quasinormal mode method. Instead
of computing the quasinormal mode frequencies from scratch, we use the analytic
continuation prescription $L_{\text{AdS}}\to iL_{\text{dS}}$, appearing in the
dS/CFT correspondence, and Wick rotate the normal mode frequencies of fields on
thermal $\text{AdS}_{2n+1}$ into the quasinormal mode frequencies of fields on
de Sitter space. We compare the quasinormal mode and heat kernel methods of
calculating 1-loop determinants, finding exact agreement, and furthermore
explicitly relate these methods via a sum over the conformal dimension. We
discuss how the Wick rotation of normal modes on thermal $\text{AdS}_{2n+1}$
can be generalized to calculating 1-loop partition functions on the thermal
spherical quotients $S^{2n+1}/\mathbb{Z}_{p}$. We further show that the
quasinormal mode frequencies encode the group theoretic structure of the
spherical spacetimes in question, analogous to the recent analysis made for
thermal AdS in (1910.07607) and (1910.11913).
