Go through the Illinois state interview again, and look for the screen where TurboTax shows you the tentative underpayment penalty and asks if you want to let the state Department of Revenue calculate the penalty, if any. If you respond "no", TurboTax will provide a series of questions, the answers to which could result in reducing or eliminating the penalty.
See this Illinois webpage for more information about the state's underpayment penalty.
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