Let $\rho$ be a depiction of $G$ on $V$. Why are its eigenvalues origins of unity?
I think $G$ is limited. Because instance any kind of $g \in G$ has some limited order $n$, therefore $\rho(g)^n = 1$. It adheres to that the particular polynomial of $\rho(g)$ separates $x^n - 1$.