  Structure formation simulations of ultralight bosonic dark matter, ruled by
the Gross-Pitaevskii-Poisson (GPP) system of equations, show that dark matter
clumps to form structures with density profiles consisting of a core surrounded
by a power-law distribution. The core has a density profile similar to that of
spherically symmetric equilibrium configurations of the GPP system. These
configurations have been shown to be stable under a variety of perturbations
and to have attractor properties. It is interesting to know the dominant
frequencies of oscillation of these configurations. One reason is that in
galaxies the effects of perturbations can trigger observable effects for
specific frequency modes. Another reason is that during the process of
structure formation, the oscillation modes can help to characterize a core.
Based on these motivations, in this manuscript we present a systematic
numerical analysis of the reaction of equilibrium configurations to various
axi-symmetric perturbations with modes $l=0,1,2,3,4$. We then calculate the
first few oscillation frequencies of equilibrium configurations for each mode.
