where γ is an odd function and can be evaluated analytically using Eq. B2. The validity of the above identity in Eq. B3 can be easily verified by using the definition of γ in Eq. 22, and the Fourier transform of the hyperbolic cotangent, where γ (Γ) are even (odd) functions. In the present application, the time integrals Eqs. B3,B5 are evaluated numerically using the standard integration package in Scipy.