No....The tax software can't know how much was from US Govt dividends. The electronic format for the proper transfer of that information has not been worked out between the financial providers and ALL the tax software companies....so you need up having to provide that information to the software separately
Most Financial providers issue separate forms to tell you what sub $$ amount came from US Govt interest as a % of the total interest that fund added to box 1a (a sub-part of the $$ in box 1a on a 1099-DIV form). A few others have the reported the exact $$ amount on the supplemental sheets in their consolidated 1099-B Forms they send you.
You need to find or calculate that exact $$ info for yourself...or talk to the financial provider to see where they give you the information.
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For those who live in states without an income tax, you can ignore that entirely as it does nothing to reduce your state income taxes...which are already a zero.
____________*Answers are correct to the best of my knowledge when posted, but should not be considered to be legal or official tax advice.*