  We study the vibrational modes of three-dimensional jammed packings of soft
ellipsoids of revolution as a function of particle aspect ratio $\epsilon$ and
packing fraction. At the jamming transition for ellipsoids, as distinct from
the idealized case using spheres where $\epsilon = 1$, there are many
unconstrained and non-trivial rotational degrees of freedom. These constitute a
set of zero-frequency modes that are gradually mobilized into a new rotational
band as $|\epsilon - 1|$ increases. Quite surprisingly, as this new band is
separated from zero frequency by a gap, and lies below the onset frequency for
translational vibrations, $\omega^*$, the presence of these new degrees of
freedom leaves unaltered the basic scenario that the translational spectrum is
determined only by the average contact number. Indeed, $\omega^*$ depends
solely on coordination as it does for compressed packings of spheres. We also
discuss the regime of large $|\epsilon - 1|$, where the two bands merge.
