Relative errors in semimajor axis, eccentricity, argument of pericenter and post-Newtonian energy for a relativistic binary composed of a 50 M_⊙ star in orbit around a 10⁶ M_⊙ supermassive black hole in a a = 1 mpc orbit with an initial eccentricity e₀ ∈ {0.5, 0.7, 0.9}. The initial eccentricity was chosen to be e₀ ∈ {0.5, 0.7, 0.9}. The integration was done using a regularized Hermite integrator, using a time step parameter of η ∈ {0.03, 0.01, 0.003, 0.001} to show convergence (blue, green, red, and orange, respectively).