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An integral representation of the 1-loop partition function for chargedscalars and spinors, minimally coupled to a uniform $U(1)$ field on $S^2$, isgiven in terms of $SO(1,2)$ Harish-Chandra group characters and evaluatedexactly in terms of Hurwitz $\zeta$-functions. Analytically continuing the$U(1)$ field, we interpret the path integrals as quasicanonical partitionfunctions in $dS_2$ with an electric field. The character itself is obtained asa trace over states living at the future boundary of de Sitter and has aquasinormal mode expansion. The imaginary part of the partition functioncaptures Schwinger pair creation in the static patch at finite temperature. Thethermal enhancement is most noticeable for scalar masses below Hubble and leadsto non-monotonicity of the current as a function of the field. This parameterrange, when dimensionally reducing from a charged or rotating Nariai spacetime,is excluded by Swampland-inspired bounds. Around the $AdS_2$ black hole, incontrast to $dS_2$, there is a threshold to pair creation.

Characters, quasinormal modes, and Schwinger pairs in $dS_2$ with flux