Filing state tax return on unemployment payed by one state while living in a different state.

I was living and working in Arizona. I lost my job and moved to Illinois. I filed for and started receiving unemployment from Arizona. I have not worked since moving to Illinois, unemployment is my only income. Do I have to file a state tax return with Illinois since I received the unemployment while living there, even though it's payed through Arizona? And on my Arizona state tax return do I include the unemployment as income also since it was payed by Arizona?