I'm not sure what you mean by "put the same amount in." There is still no state withholding to enter from the form 1042-S and likely that will result in an increased state tax.
The 00 in box 3a indicates federal withholding was under chapter 3 in the form 1042 instructions for a foreign person. The code 16 in box 4a indicates an exemption from chapter4 federal withholding as a nonfinancial payment as you are not a financial institution.
A code 16 in box 1 would identify the income as "Scholarship/Fellowship Grant."
Here is a link to the form 1042S for more detailed information if needed.
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