The following paper gives a classification of the character tables of irreducible representations of $SL(3,GF(q))$ where $q$ is a power of a prime number, and $ GF(q)$ a finite field of $q$ elements.

WILLIAM A. SIMPSON AND J. SUTHERLAND FRAME
Can. J. Math., Vol. XXV, No. 3,1973, pp. 486-494
THE CHARACTER TABLES FOR
SL(3, q ), SU(3, *•), PSL(3, q), PSU(3, q *)

Here I would to ask "do we have a classification of the character tables of irreducible representations of $SL(3,Z_q)$, where $Z_q=Z/qZ$?"