  We study the distribution of overlaps of glassy minima, taking proper care of
residual symmetries of the system. Ensembles of locally stable, low lying
glassy states are efficiently generated by rapid cooling from the liquid phase
which has been equilibrated at a temperature $T_{run}$. Varying $T_{run}$, we
observe a transition from a regime where a broad range of states are sampled to
a regime where the system is almost always trapped in a metastable glassy
state. We do not observe any structure in the distribution of overlaps of
glassy minima, but find only very weak correlations, comparable in size to
those of two liquid configurations.
