The L-function $L(s,A)= \sum a_n n^{-s}$ of an abelian surface of conductor $N$ has an Euler product of the form $L(s,E)=\prod_p\prod_{j=1}^4\left(1-\alpha_{j,p} p^{-s}\right)^{-1}$ and satisfies the functional equation $\Lambda(s,A)= N^{s/2}\Gamma_{\mathbb C}(s+1/2)^2\cdot L(s,A)= \varepsilon\Lambda(1-s,A),$ where the sign $$\varepsilon$$ is equal to either $$+1$$ or $$-1$$.