Endomorphism structure of projective special linear group of degree three over a finite field

Automorphism structure
For any prime power $$q$$, the automorphism group of the projective special linear group of degree three $$PSL(3,q)$$ over the finite field $$\mathbb{F}_q$$ is the projective outer semilinear group of degree three $$PO\Gamma L(3,q)$$.

Let $$q = p^r$$ where $$p$$ is the underlying prime. The information is presented below:

Other endomorphisms
Projective special linear group is simple, and in particular $$PSL(3,q)$$ is always simple, so the only endomorphisms are the automorphisms and the trivial endomorphism.