  The Birch and Swinnerton-Dyer conjecture predicts that the parity of the
algebraic rank of an abelian variety over a global field should be controlled
by the expected sign of the functional equation of its $L$-function, known as
the global root number. In this paper, we give explicit formulae for the local
root numbers as a product of Jacobi symbols. This enables one to compute the
global root number, generalising work of Rohrlich who studies the case of
elliptic curves. We provide similar formulae for the root numbers after
twisting the abelian variety by a self-dual Artin representation. As an
application, we find a rational genus two hyperelliptic curve with a simple
Jacobian whose root number is invariant under quadratic twist.
