Connect cable modem/router to different circuit than audio?

I just got some reversed polarity outlets in my listening room fixed and have a much closer plug for my gear.
I cannot (yet) do a dedicated line. Up to today, my cable modem was plugged into this circuit. There is a way I could put that on a circuit  apart from my audio if it had the potential to add significant noise. Is that something to worry about or would it not matter much? FYI, my wife's office lights, computer, monitors are on this circuit and there are some light cans, too. Just wondering if the router/modem is an especially big source of noise into the circuit?

Thanks for any opinions.