  We study the slice filtration and associated spectral sequence for a family
of $RO(C_{p^{n}})$-graded suspensions of the Eilenberg-MacLane spectrum for the
constant Mackey functor $\underline{\mathbb Z}$. Since $H\underline{\mathbb Z}$
is the zero slice of the sphere spectrum, this begins an analysis of how one
can describe the slices of a suspension in terms of the original slices.
