One loop amplitude for Heterotic string on T²

We revisit the results of one loop string amplitude calculations for the Heterotic string theory compactified on a torus with or without Wilson lines. We give the complete elliptic genus and the harmonic part of the CP-even amplitude for the gauge groups $SO(32)$, $E_8 \times E_8$, $SO(16)^2$ and $SO(8)^4$.