  Context. The dynamical evolution of near-parabolic comets strongly depends on
the starting values of the orbital elements derived from the positional
observations. In addition, when drawing conclusions about the origin of these
objects, it is crucial to control the uncertainties of orbital elements at each
stage of the dynamical evolution.
  Aims. I apply a completely homogeneous approach to determine the cometary
orbits and their uncertainties. The resulting catalogue is suitable for the
investigation of the origin and future of near-parabolic comets.
  Methods. First, osculating orbits were determined on the basis of positional
data. Second, the dynamical calculations were performed backwards and forwards
up to 250 au from the Sun to derive original and future barycentric orbits for
each comet. In the present investigation of dynamical evolution, the numerical
calculations for a given object start from the swarm of virtual comets
constructed using the previously determined osculating (nominal) orbit. In this
way, the uncertainties of orbital elements were derived at the end of numerical
calculations.
  Results. Homogeneous sets of orbital elements for osculating, original and
future orbits are given. The catalogue of 119 cometary orbits constitutes about
70 per cent of all the first class so-called Oort spike comets discovered
during the period of 1801-2010 and about 90 per cent of those discovered in
1951-2010, for which observations were completed at the end of 2013.
Non-gravitational (NG) orbits are derived for 45 comets, including asymmetric
NG~solution for six of them. Additionally, the new method for cometary
orbit-quality assessment is applied for all these objects.
