Selberg's orthogonality conjecture for self-dual cuspidal automorphic representations

Let $\pi$ and $\pi'$ be self-dual unitary cuspidal automorphic representations of $\operatorname{GL}_m(\mathbb A)$ and $\operatorname{GL}_{m'}(\mathbb A)$, respectively, and let $S$ be a finite set of primes. Selberg's orthogonality conjecture. For every $x>0$,

$$\sum_{\substack{p\leq x\\p\notin S}}\frac{\lambda_\pi(p)\lambda_{\pi'}(p)}{p}=\begin{cases}\log\log x+O_{\pi,\pi',S}(1)&\text{if }\pi=\pi',\\O_{\pi,\pi',S}(1)&\text{otherwise}.\end{cases}$$

Here $\lambda_\pi(p)$ and $\lambda_{\pi'}(p)$ are the prime Hecke eigenvalues. This conjecture is presented as an implication of the strong multiplicity one conjecture above; the paper uses it to deduce that conjecture, but no resolution is supplied here.