You will have to call TC to find out.
It's a 54 caliber round ball
100-400 USD
2000
2000
The Thompson Center hawken that I have,has a barrel that is 28 inches long.
On 90% of the guns it is stamped on the right side of the barrel as "Thompson/Center Rochester New Hampshire" and "HAWKEN 45 Cal" along with a serial number on the left side. If not the easiest way would be to go to gunbroker.com or Google and search for Thompson center hawken, compare the pictures and description to what you have.
Most black powder bores have a twist that is relatively slow. Say 1:36 or 1:50. They were 1:48 twist in 45 and 50 caliber
100-400 USD or so
You must call TC
Yes. I've heard of it.
Being a 5 digit serial number puts it early in production , most likely early 80's. However the Hawken was not produced by Thompson Center in .36 caliber, they did make a drop in replacement barrel in .36, but they are very rare. I suspect you may have the Seneca model, this you can determine by measuring across the barrel, flat side to flat side. The Seneca will measure 13/16" across the flats. A Hawken will measure 15/16". The Seneca also has a patch box that is rounded towards the but vs. the Hawken being pointed towards the but. If it is a Seneca .36 in 95% + condition it could be worth in the $500 to 700 range, the Hawken with the .36 drop in barrel would be in the neighborhood of 450 +/-
In a TCA, if it has letter preceding the serial number, it was made after 1971.