Root numbers of Artin representations

The root number of an Artin representation $\rho$, also called the sign, is the constant $W(\rho)$ appearing in the functional equation of the associated L-function, i.e. the complex number $W(\rho)$ of absolute value $1$ such that $\Lambda(s,\rho)=W(\rho)\Lambda(1-s,\overline{\rho})$. It can be expressed as a product of local root numbers.