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line 15 on form 1040 come from form CR line 55.  as stated for the ratio on line 43 to change then either Illinois changed something in column A or B or both.   then the computation of the credit is further dependent on whether you are a full-year Illinois resident or a part-year resident.

we can't see form CR so don't know what exactly IL changed.   you can always call the IL Department of Revenue 

by the way, the tax credit is based on your actual out-of-state taxes not what was withheld.