In analytic number theory and related branches of mathematics, a complex-valued arithmetic function χ : Z → C {\displaystyle \chi :\mathbb {Z} \rightarrow \mathbb {C} } is a Dirichlet character of modulus m m if for all integers a a and b b : χ = χ χ ; {\displaystyle \chi =\chi \chi ;} that is, χ \chi is completely multiplicative. Wikipedia