Detailed doping dependence of the electronic specific heat coefficient γ is studied for La_2-xSr_xCuO₄ (LSCO) single crystals in the slightly-doped regime. We find that γ systematically increases with doping, and furthermore, even for the samples in the antiferromagnetic (AF) regime, γ already acquires finite value and grows with x. This suggests that finite electronic density of states (DOS) is created in the AF regime where the transport shows strong localization at low temperatures, and this means the system is not a real insulator with a clear gap even though it still keeps long range AF order.