are solved for analytic derivatives. Of course, the choice of shift parameters (level-shift and IPEA shift parameters) can affect the convergence rate. In the Supplementary Material, the dependence of the convergence rate on the choice of the imaginary level-shift and IPEA parameters is briefly discussed. In short, as long as the parameters are chosen reasonably (e.g., less than 1.0), the convergence of these linear equations is smooth and the behavior is marginally affected.