The Slice Spectral Sequence for certain $RO(C_{p^n})$-graded Suspensions of $H\underset{‾}{\mathbb{Z}}$

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 $\underset{‾}{\mathbb{Z}}$. Since $H\underset{‾}{\mathbb{Z}}$ 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.