  This document contains additional numerical and graphical evidence to support
some of the conjectures mentioned in \cite{GM3}. We give more evidence for
$\kappa=3,4$ in dimension 2. As mentioned in that article we still don't quite
understand the sets $\boldsymbol{\mu}_{\kappa}(\Delta)$ and
$\boldsymbol{\Theta}_{\kappa}(\Delta)$ on $(0,1/2)$ for $\kappa=3$ in dimension
2. Here we give a bunch more threshold energies for $\kappa = 3$ in dimension
2.
