Selberg's primitive-function and orthogonality conjectures

Let $\mathcal{S}$ be the Selberg class, let $F,F'\in\mathcal{S}$ be primitive functions, and let $a_F(n)$ and $a_{F'}(n)$ denote their Dirichlet coefficients. Selberg's primitive-function and orthogonality conjectures. For any primitive function $F$, $n_F=1$. For two distinct primitive functions $F$ and $F'$,

$$\sum_{p\leqslant T} \frac{a_F(p)\overline{a_{F'}(p)}}{p} = \mathcal{O}(1).$$

These are the further Selberg conjectures stated after the conjecture governing $n_F$; the supplied source gives no resolution status.