In this talk we study the 1-level density of low-lying zeros of Dirichlet L-functions attached to real primitive characters of conductor at most X. We obtain an asymptotic expansion of this quantity with lower order terms in descending powers of log X. We show that this is valid under GRH when the support of the Fourier transform of the implied even test function φ is contained in (-2, 2). We also uncover a phase transition when the supremum of the support of the Fourier transform of φ reaches 1, where a new lower order term appears.