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Plotting fundamental domains of modular subgroups from generators and cusp widths

I have a number of genus zero, index 24 modular subgroups (some congruence, some not). For each of these subgroups, I have the cusp widths, and a set of generators as explicit 2x2 matrices. How can I use these to plot the fundamental domain for each group? I suspect a lot of this material is in the KFarey package, but I'm having trouble putting it all together.