Not the greatest but far too many of this date have slipped past me in the last year or 2 so for 19 this one will do until I find a better one in that price range
Looks like you got the 1800/1798 Large Cent. This is the only 1800 Large Cent to have the Style 1 Hair obverse.
looking at a comparison of the 2 with mine beside them, i think you're right, but I won't be sure until it's in hand the sellers pic's are not exactly great.
Obv is definitely the type 1 hair. That die is used on S-190, 191, NC-5 and NC-6. On NC-6 the stem of the uppermost right berry meets the stem above the stem of the upper inner leaf cluster. On all the others they meet at the same point. Not NC-6. NC-5 always has a cud trough the top of AME. Not NC-5. I don't have anything that eliminates 190, but on 191 the die is sinking causes mounding that passes though the O and below the N in ONE, and sinking that creates a mound that eliminates the fraction. This DOES match your coin.