  The low energy neutral excitations of incompressible fractional quantum Hall
states are called collective modes or magnetic excitons. This work develops
techniques for computing their dispersion at general filling fractions for
reasonably large systems. New structure is revealed; in particular, the
collective mode at 1/3 is found to possess several minima, with the energy of
the principal minimum significantly smaller than the earlier estimate.
\pacs{73.40.Hm, 73.20.Dx, 73.20.Mf}
