Rational conjugacy classes and rational characters for some finite simple groups

If $G$ is a finite group, an irreducible complex-valued character $\chi$ is called rational if $\chi (g)$ is rational for all $g\in G$. Also, a conjugacy class $x^G$ is called rational, if for all irreducible complex-valued character $\chi$, the value $\chi (x^G)$ is rational. We prove that for $q$, a power of prime, the group ${\mathrm{P}\mathrm{S}\mathrm{L}}_2(q)$ has same number of rational characters and rational conjugacy classes. Furthermore, we verify that this equality holds for all finite simple groups whose character tables appear in the $\mathit{\text{ATLAS}}\mathit{\text{of}}\mathit{\text{Finite}}\mathit{\text{Groups}}$, except for the Tits group.