Induced Dirichlet character (reviewed)

A Dirichlet character $\chi_1$ of modulus $q_1$ is said to be induced by a Dirichlet character $\chi_2$ of modulus $q_2$ dividing $q_1$ if $\chi_1(m)=\chi_2(m)$ for all $m$ coprime to $q_1$.

A Dirichlet character is primitive if it is not induced by any character other than itself; every Dirichlet character is induced by a uniquely determined primitive Dirichlet character.