Let $G$ be the group of $F$-points of a connected, reductive group over a $p$-adic field $F$. The unramified character of $G$ are $\chi\circ\psi$ where $\chi$ is an unramified character of $F^{\times}$ and $\psi$ is a \emph{rational character} of $F$. I understand that the determinant is a rational character, but:
What is the definition of a rational character>