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You can put the money into a Traditional IRA as long as you also deposit the amount of any taxes that GE withheld when you received the distribution. This would be called a Rollover and you have 60 days to complete the transaction from the date of your distribution from GE.
If you do not complete the rollover within the time allowed or received a waiver or extension of the 60-day period from the IRS, the amount must be treated as ordinary income. You will also have the additional 10% penalty if you were under 59 1/2 at the time of distribution.
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You will pay tax on the amount you do not deposit as well the 10% penalty. The entire amount ($37211.85) will be shown on your 1040 Line 16a but only the $8397.93 will be listed as taxable on 16b.
You will still get credit on the 1040 for the amount that was withheld for taxes. The federal and GA amounts will be shown on 1040 Line 61. You should receive a 1099R from GE with the distribution and withholding amounts.
Whatever amount you do not deposit will be added to your regular income and taxed as ordinary. On top of having the amount added to your income you will also be subject to a 10% penalty and that will be added to your tax liability.
It is a pretty much given that you will have a penalty in the amount of $840 and if your tax rate is 28% as you suggested then yes the $2351 will be ordinary income tax.