Unemployment taxes withheld from wrong state

I live in Wisconsin and work in Illinois.  We are reciprocal states so I have never have had any trouble with that at tax time.  This year, I collected unemployment from Illinois for the first time. They withheld both federal and state taxes on my 1099G.  The state taxes were withheld from Illinois, not Wisconsin, so when I filed my state taxes I had to pay again for Wisconsin. Does anyone know what forms I need to fill out to get the Illinois withholdings refunded? I don't have a W-2 or anything else from Illinois.  only a 1099G. 

I started filling out a Schedule NR and a 1040 but got confused along the way.  Do I just leave everything blank on the 1040 other than the line about the 1099? Is there a different form I need?

 

Thank you for your help