Recovered DFs for the densities depicted in Fig. 3 for various values of the specific angular momentum L = l × ℏm⁻¹. Note that (i) we only show L = 0 for β = 0 as the DF is uniform in L for isotropic conditions, cf. Eq. (16), (ii) energies are bound from below by E_c(L), the energy of a circular orbit defined as the minimum of the effective potential V(R)+L²/2a²R² and (iii) both DFs recover a Boltzmann-like, exponential behavior in E. We emphasize that this functional behavior is not imposed by our inversion of Eq. (17).