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This is the equation in question, although I can see it coming that instead some complex exponential form is going to crop up...

Ideally, I would like to reproduce something like this, but a more realistic start could be simply the use of a complex plot along the lines of complex_plot((3 * x + 7) / (-3 * x - 9), (-5,5), (0,5)). Evidently this is not a good example - for instance, I would like to know how to restrict the domain to the positive imaginary components.

Is there a well-known way of handling these transformations? (I'm working on understanding the basics of modular forms).

This is the equation in question, although I can see it coming that instead some complex exponential form is going to crop up...

Ideally, I would like to reproduce something like this, but a more realistic start could be simply the use of a complex plot along the lines of complex_plot((3 * x + 7) / (-3 * x - 9), (-5,5), (0,5)). Evidently this is not a good example - for instance, I would like to know how to restrict the domain to the positive imaginary components.

Is there a well-known way of handling these transformations?

Here is on possible solution.

(I'm working on understanding the basics of modular forms).

This is the equation in question, although I can see it coming that instead some complex exponential form is going to crop up...

Ideally, I would like to reproduce something like this, but a more realistic start could be simply the use of a complex plot along the lines of complex_plot((3 * x + 7) / (-3 * x - 9), (-5,5), (0,5)). Evidently this is not a good example - for instance, I would like to know how to restrict the domain to the positive imaginary components.

Is there a well-known way of handling these transformations?

Here is on possible solution.

(I'm working on understanding the basics of modular forms).