Computing L-functions of $\lambda$-adic representations of global function fields

The L-function $L({\rho }_{\lambda },s)$ of an almost everywhere unramified $\lambda$-adic representation ${\rho }_{\lambda }$ of a global function field ${\mathbb{F}}_q(C)$ is known to be a rational function in $q^{-s}$ satisfying a functional equation up to some complex sign $\epsilon ({\rho }_{\lambda })$. This paper presents a systematic framework to compute the coefficients of $L({\rho }_{\lambda },s)$ and its sign $\epsilon ({\rho }_{\lambda })$ with some explicit examples.