WTB PCGS AU 58 1837 No Stars Dime. Found it.

FWIW, I love that issue. Good luck to you!

I am also looking for one AU53-MS64 in CAC for my complete Type Set. They are hard to find that is for sure. I can find more early gold $5 and High relief $20 in CAC at 5 to 10 times the price. So these should be common based on the pricing structure. Good luck in finding your AU58. I am a little bit more flexible on the Grade

Here's an 1837 in NGC MS63 CAC from Gerry Fortin:

https://seateddimevarieties.com/FS_Seated_10C_AU_PF.php

Is there a reason for the AU58 grade? I've found, just for myself, that it is hard to focus on completing series. I like the type-set idea and can focus on that because there's so many coins out there to choose from to fit into a type set. I'm of the opinion that as a collector I am somewhat at the mercy of what's available when it comes time to spend on the hobby. If I don't see anything that money tends to go elsewhere pretty quickly. I currently have my desires set on a number of coins, but the money is not there yet to get them, so I wait.

I'm obsessed with all the no-stars type and they are all the same to me, apparently!

https://www.ebay.com/itm/194386280262?hash=item2d42533f46:g:zYAAAOSw3rJhTNr0

NGC 58 but CAC, might cross.