In 2004, Lewis and Mandell constructed an universal coefficient spectral sequence for equivariant multiplicative (co)homology theories. However, there is no example of computation in their paper. In this talk, we will show some computability of this spectral sequence by exploring homological algebra of \(\underline{\mathbb{Z}}\)-modules. Specially, we can give an algebraic interpretation of a gap in homology of some virtual representation spheres.