Primitive Dirichlet character
= Primitive Dirichlet character
A <Dirichlet character> modulo $N$ is primitive if its character on $(\mathbb Z/N\mathbb Z)^\times$ does not factor through reduction to the unit group for any proper divisor of $N$. Its least inducing modulus is called its conductor. Primitivity is essential in the usual formula expressing its finite Fourier transform as a conjugate character times a <Gauss sum of a Dirichlet character>.