Solvabilizer number of PSL2 for prime powers congruent to one modulo four

Let $q$ be a prime power satisfying

$$q\equiv 1 \mod 4.$$

Set $G=\operatorname{PSL}_{2}(q)$.

PSL2 congruence conjecture.

$$\alpha(G)=q.$$

This is proposed as a further generalization of the theorem for $\operatorname{PSL}_{2}(2^f)$ and is supported in the paper by the computational table.