We study the distribution of overlaps of glassy minima: taking proper care
of residual symmetries of the system. Ensembles of locally stable, low-lyin
g 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 sampl
ed to a regime where the system is almost always trapped in a metastable gl
assy 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.