QCD phase diagram for small densities from simulations at imaginary mu

We present results on the QCD phase diagram for small densities without reweighting. Our simulations are performed with an imaginary chemical potential mu_I for which the fermion determinant is positive. On an 8^3x4 lattice with 2 flavors of staggered quarks, we map out the pseudo-critical temperature T_c(mu_I). For mu_I/T < pi/3, this is an analytic function whose Taylor expansion converges rapidly, with truncation errors smaller than statistical ones. The result is analytically continued to give the location of the pseudo-critical line for real mu_B<500 MeV.