Character parity ($\chi (-1)=(-1{)}^a,a\in \{0,1\}$)

The parity determines the gamma factor and theta transformation in the completed Dirichlet L-function. It is the sign of the character at minus one.

A Dirichlet character with odd parity satisfies $\chi (-n)=-\chi (n)$, so its extension to integer arguments is an odd function.

A Dirichlet character with even parity satisfies $\chi (-n)=\chi (n)$, so its extension to integer arguments is an even function.