Several different varieties of Large Cents were minted in 1843. Numismedia lists the following approximate retail values for the most common types, as of 07/2010:
Very worn condition - $20
Moderately worn - $28
Slightly worn - $41
Almost no wear - $226
Uncirculated - $450 to $2,220 depending on quality
However some of the varieties can be worth much more in higher grades, so you should have your coin inspected in person by an expert.
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Please look at the coin again, 1857 was the last year the US made a large cent.
Check the date again. US large cents were last made in 1857.
Check the date again. US large cents were last made in 1857.
Check the date again. US large cents were last made in 1857.
You don't have a large cent because the last large cent was made in 1857. Any US cent dated 1863 should be an Indian Head cent. What you might have is a privately made token or something of that sort because it is not a US mint product if it is a large cent or not an Indian Head Cent.