Generalized Ramanujan conjecture for $SO(n,1)$

Let $G=SO(n,1)$, and let $\widehat{G}^{\operatorname{sph}}_{\operatorname{Aut}}$ denote the automorphic dual of the spherical unitary dual of $G$. Generalized Ramanujan conjecture.

$$\widehat{G}^{\operatorname{sph}}_{\operatorname{Aut}}=i\mathbf{R}\cup\{\rho_{n},\rho_{n}-1,\ldots,\rho_{n}-\lfloor\rho_{n}\rfloor\}.$$

This predicts that the spherical representations occurring automorphically for congruence subgroups have only the tempered parameters and the explicitly listed exceptional parameters. The source gives no evidence of a resolution, so the conjecture is recorded as open.