I don't have an 1837 large cent. I've kicked around the idea of putting together a large cent date set, but the my interest has just not been been strong enough to do it.
Here is an 1838 large cent that PCGS graded AU-58. The obverse picture is a bit grainy, but perhaps it is good enough to give you an idea of how a true AU should look. For the record this coin cost me $325 in 2016.

On the higher end of the scale here is an 1841 large cent in PCGS MS-63, Brown. This came from an EAC dealer, and they cherry pick the best slabbed coins and charge strong prices for them. The point of that statement, don't expect most of the MS-63 graded large cents to look like this.
"If the alligators don't get you the mosquitoes will." OR "There is no Santa Claus in numismatics."
