Notes. There are two separate branches of solution for each model, the “−” sign applies to black holes and naked singularities with 1 <a ≲ a_p:q, while the “+” sign applies to naked singularities with a ≳ a_p:q. The last column indicates the value of a_p:q for each model as well as the related spin value , where the a(x_p:q) function has a local maximum, which implies the “S-like” behaviour of resonant radii x_p:q(a) and the existence of three resonant radii for (see Fig. 3b).