JPL Horizons On-Line Ephemeris System provides easy access to key Solar System data and flexible production of highly accurate ephemerides for Solar System objects.
Osculating elements at a given epoch are always an approximation to an object's orbit (i.e. an unperturbed conic orbit or a "two-body" orbit). The real orbit (or the best approximation to such) considers perturbations by all planets, a few of the larger asteroids, a few other physical usually small forces, and requires numerical integration.
Jet Propulsion Laboratory (JPL) ephemerides do not use things such as periods, eccentricities, etc. Instead, JPL integrates the equations of motion in Cartesian coordinates (x,y,z), and adjusts the initial conditions in order to fit modern, highly accurate measurements of planetary positions.
As of August 2015, Horizons now uses ephemeris DE431.