The spectral code BETAS computes plasma equilibrium in a toroidal magnetic field B = [unk]s x [unk]Psi with remarkable accuracy because the finite difference scheme employed in the radial direction allows for discontinuities of the flux function Psi across the nested surfaces s = const. Instability of higher modes in stellarators like the Heliotron E can be detected in roughly an hour on the best supercomputers by calculating bifurcated equilibria that are defined over just one field period. The method has been validated by comparing results about nonlinear saturation of ballooning modes in tokamaks with numerical data from the PEST code.