  In this paper we compute $RO(G)$-graded homotopy Mackey functors of
$H\underline{\mathbb{Z}}$, the Eilenberg-Mac Lane spectrum of the constant
Mackey functor of integers for cyclic p-groups and give a complete computation
for $G = C_{p^2}$ . We also discuss homological algebra of
$\underline{\mathbb{Z}}$-modules for cyclic $p$-groups, and interactions
between these two. The goal of this paper is to understand various slice
spectral sequences as $RO(G)$-graded spectral sequences of Mackey functors.
