  We present results of extensive numerical calculations on the ground state of
electrons in the first excited (n=1) Landau level with Coulomb interactions,
and including non-zero thickness effects, for filling factors 12/5 and 13/5 in
the torus geometry. In a region that includes these experimentally-relevant
values, we find that the energy spectrum and the overlaps with the trial states
support the previous hypothesis that the system is in the non-Abelian k = 3
liquid phase we introduced in a previous paper.
