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A dense neutrino gas, such as the one anticipated in the supernovaenvironment, can experience fast neutrino flavor conversions on scales muchshorter than those expected in vacuum probably provided that the angulardistributions of $\nu_e$ and $\bar\nu_e$ cross each other. We perform adetailed investigation of the neutrino angular distributions obtained bysolving the Boltzmann equations for fixed matter profiles of somerepresentative snapshots during the post-bounce phase of core-collapsesupernovae in multidimensional calculations of an $11.2\mathrm{M}_{\odot}$ anda $27\mathrm{M}_{\odot}$ progenitor models. Although the$11.2\mathrm{M}_{\odot}$ model features $\nu_e - \bar\nu_e$ angular crossingsand the associated fast modes at different time snapshots, the$27\mathrm{M}_{\odot}$ model does not show any crossings within the decouplingregion.  We show that this can be understood by studying the multipole components ofthe neutrino distributions.  In fact, there is a higher chance for the occurrence of $\nu_e - \bar\nu_e$angular crossings for the zones where the multipole components of the neutrinodistributions are strong enough. We also show that there can exist more thanone crossings between the angular distributions of $\nu_e$ and $\bar{\nu}_e$.In addition, apart from the crossings within the neutrino decoupling region,there is a class of $\nu_e-\bar\nu_e$ angular crossings which appears very deepinside the proto-neutron star.

Fast Neutrino Flavor Conversion Modes in Multidimensional Core-collapse Supernova Models: the Role of the Asymmetric Neutrino Distributions