Irreducible unitary representations of a fondamental group.

Question

Let $C$ be a compact Riemann surface with genus $2$. It is well-known that $\pi_1(C) \simeq F/N$, where $F$ is the free group with $4$ elements (say $a_1,b_1,a_2,b_2$) and $N$ is a normal subgroup generated by the relations $a_1b_1a_1^{-1}b_1^{-1}a_2b_2a_2^{-1}b_2^{-1}$. I have to find all the irreducible representations of $\pi_1(C)$ in the unitary group $U(2)$. How can I do it?