  We report results of the first 3-by-3 "multi-angle" simulation of the
evolution of neutrino flavor in the core collapse supernova environment. In
particular, we follow neutrino flavor transformation in the neutronization
neutrino burst of an O-Ne-Mg core collapse event. Though in a qualitative sense
our results are consistent with those obtained in 3-by-3 single-angle
simulations, at least in terms of neutrino mass hierarchy dependence,
performing multi-angle calculations is found to reduce the adiabaticity of
flavor evolution in the normal neutrino mass hierarchy, resulting in lower swap
energies. Differences between single-angle and multi-angle results are largest
for the normal neutrino mass hierarchy. Our simulations also show that current
uncertainties in the measured mass-squared and mixing angle parameters
translate into uncertainties in neutrino swap energies. Our results show that
at low theta-13 it may be difficult to resolve the neutrino mass hierarchy
using the O-Ne-Mg neutronization neutrino burst.
