We present an accurate numerical table for the relativistic corrections to the thermal Sunyaev-Zeldovich effect for clusters of galaxies .
The numerical results for the relativistic corrections have been obtained by numerical integration of the collision term of the Boltzmann equation .
The numerical table is provided for the ranges 0.002 \leq \theta _ { e } \leq 0.100 and 0 \leq X \leq 20 , where \theta _ { e } \equiv k _ { B } T _ { e } / m _ { e } c ^ { 2 } , X \equiv \hbar \omega / k _ { B } T _ { 0 } , T _ { e } is the electron temperature , \omega is the angular frequency of the photon , and T _ { 0 } is the temperature of the cosmic microwave background radiation .
We also present an accurate analytic fitting formula that reproduces the numerical results with high precision .