Order of a Dirichlet character (reviewed)

The order of a Dirichlet character $\chi$ is the least positive integer $n$ such that $\chi^n$ is the trivial character of the same modulus as $\chi$. Equivalently, it is the order $n$ of the image of $\chi$ in $\mathbb{C}^\times$, the group of $n$th roots of unity.