the foundation of equivariant stable homotopy theory is laid by lewis-may-steinberger in the 80's, while people's understanding of the computational aspect of the subject is very limited even until today. the reason is that the equivariant homotopy groups are $ro(g)$-graded, and even the coefficient rings of eilenberg-maclane spectra involve complicated combinatorics of cell structures. in this talk i'll illustrate the advantages of tate squares in doing $ro(g)$-graded computations. several eilenberg-maclane spectra of particular interest will be discussed: the eilenberg-maclane spectra associated with the constant mackey functors $\mathbb{z}$, $\mathbb{f}_2$, and the burnside ring. time permitting, i'll also talk about some structures of the homotopy of $hm$, for $m$ a general $c_{2^n}$-mackey functor.