When an object in an unstable Lagrange point falls away from that point, where does it end up?

Question

I know L1-3 are saddle points in the potential, and thus small perturbations would cause an object at one of these points to accelerate away from the point, but where would that object end up? For the purposes of this problem assume a 3 body system with M1>>M3 and M2>>M3. If it helps to assume M1>>M2 as well, I am fine with that assumption.