Direct numerical solution of the coordinate space Balitsky-Kovchegov equation at next-to-leading order

We present the first numerical solution to the next-to-leading-order Balitsky-Kovchegov equation in coordinate space in the large-Nc limit. In addition to the dipole operator, we also solve the evolution of the ``conformal dipole'' for which the conformal invariance breaking double logarithmic term is absent from the evolution equation. The next-to-leading-order corrections are shown to slow down the evolution. We show that the solution depends strongly on the details of the initial condition and that the solution to the equation is not positive definite with all initial conditions relevant for phenomenological applications.