The contribution of the conductivity to the spectrum of the generalized dielectric constant or susceptibility of molecular ionic liquids is analyzed, both in theoretical terms and computationally by means of molecular dynamics simulation of the concrete system 1-ethyl-3-methyl-imidazolium dicyanoamide at 300 K. As a central quantity the simulated current autocorrelation function is modeled by a carefully designed fit function. This not only gives a satisfactory numerical representation but yields the correct conductivity upon integration. In addition the fit function can be Fourier-Laplace transformed analytically. Both, the real and imaginary parts of the transform show expected behavior, in particular, the right limits for zero frequency. This altogether demonstrates that the components of the fit function are of physical relevance.