Unit group of $\mathbb{Z}C_m$

Question

By Higman's theorem we know that if $G$ is abelian and finite then $\mathbb{Z}G$ has only trivial units iff G is has exponent $1,2,3,4, \text{or}\ 6$ But what if $G=C_{m}$ where $m \ge 7$. In this case has someone calculated what the $\mathcal{U}({\mathbb{Z}C_m})$ looks like?