How to determine the parity eigenvalues of time-reversal invariant momenta point from first principle calculation when we judge topological insulator?

This is a question of topological insulator.

Liang Fu and C. L. Kane proposed a method to judge whether an inversion symmetric insulator is a topological insulator or not in their article(L. Fu and C.L. Kane, Phys. Rev. B 76, 045302 (2007)).
The method is just to determine the parity of the occupied band eigenstates at the eight or four(in two dimensions) time-reversal invariant momenta $Gamma_i$in the Brillouin zone. The Z2 invariant is determined by quantity $${{delta }_{i}}=prodlimits_{m=1}^{N}{{{xi }_{2m}}left( {{Gamma }_{i}} right)}$$Where ${{xi _{2m}}left( {{Gamma _i}} right)}
$is the parity eigenvalue of 2m band at $Gamma_i$ point.

My question is how to determine the parity of band state at these points from first principle band calculation(like Wien2K band calculation)?