  The aim of this paper is to describe efficient algorithms for computing Maass
waveforms on subgroups of the modular group PSL(2,Z) with general multiplier
systems and real weight. A selection of numerical results obtained with these
algorithms is also presented. Certain operators acting on the spaces of
interest are also discussed. The specific phenomena that were investigated
include the Shimura correspondence for Maass waveforms and the behavior of the
weight-k Laplace spectra for the modular surface as the weight approaches 0.
