\begin{definition}[Definition:Dirichlet Character/Primitive Character]
Let $q \in \Z_{>1}$.
Let $\paren {\Z / q \Z}$ denote the ring of integers modulo $q$.
Let $G = \paren {\Z / q \Z}^\times$ be the group of units of $\paren {\Z / q \Z}$.
Let $\C^\times$ be the group of units of $\C$.
Let $\chi_0$ be the trivial (Dirichlet) character modulo $q$.
Let $q^*$ be the least divisor of $q$ such that:
:$\chi = \chi_0 \chi^*$
where $\chi^*$ is some character modulo $q^*$.
If $q = q^*$ then $\chi$ is called '''primitive''', otherwise $\chi$ is '''imprimitive'''.
{{NamedforDef|Johann Peter Gustav Lejeune Dirichlet}}
Category:Definitions/Dirichlet Characters
\end{definition}