@Control The Crazy is right, if you have a library card, you can go to www.rvl.info and sign in using your library card. However if you do not have a computer or internet access, you can call any library in the city and they will tell you your fines over the phone. If you have time to stop by a library, they will print off a copy of all the fines that you have on your account.
If you have an online library account, it's listed under your account information. If you don't, you'd have to call them or go by there & ask. Hope this helps!
Call the library
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