  Shephard groups are unitary reflection groups arising as the symmetries of
regular complex polytopes. For a Shephard group, we identify the representation
carried by the principal ideal in the coinvariant algebra generated by the
image of the product of all linear forms defining reflecting hyperplanes. This
representation turns out to have many equivalent guises making it analogous to
the sign representation of a finite Coxeter group. One of these guises is (up
to a twist) the cohomology of the Milnor fiber for the isolated singularity at
0 in the hypersurface defined by any homogeneous invariant of minimal degree.
