Partial in-plan 401k to Roth 401k conversion

I made a partial in-plan in Dec 2023.  I understand the conversion amount will be taxable and I need to pay Federal and NJ estimated taxes by Jan 15 2024 to avoid underpayment penalty.  I have not yet received the 1099-R form.  Please advise how to pay Federal and NJ Estimated taxes.  And how should I later enter them in TurboTax?