You can use an online tool such as TaxCaster, (https://turbotax.intuit.com/tax-tools/calculators/taxcaster/) to estimate your total tax liability for the year.
If the pension of $1000 is your only income, then you can divide the total liability for the year over the number of paychecks to calculate the amount to be deducted from each paycheck.
If the $1000 is not your only income, you can use the result from TaxCaster (or other online tool), to calculate your tax rate, (tax liability /total income). You can then use the tax rate to calculate the amount to be deducted from your pension amount.
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