At the very least, Coinpayments -- or any third party service -- will require a police report. That's hurdle #1 for the OP, and time is of the essence.
For getting back their coins most likely. But if coinpayments is indeed the exchange that received the coins there's no harm done in contacting their support and triggering an investigation. Best case the account containing the stolen coins gets frozen until matters have been clarified.
But IMO you should find out exactly how your computer was compromised and how to secure your computer rather than track a hacker where you can't sue him or get your Bitcoin back.
OP should also wipe their computer and reinstall or factory reset their operating system. Otherwise it's quite likely that the attacker has yet another surprise in store. It would also be smart if OP changed passwords afterwards.