I'm not an aficionado but as far as I can deduce this coin is a 2M obverse and 2M reverse with a minute S Breen-5814? Can anyone more familiar with these confirm or correct me with this? Thanks, Will I used this article and it's helpful pictures to make the determination on the 2M die characteristics http://www.numismaticnews.net/article/new-trade-dollar-type And compared the mint mark to known marked minute s coins below http://auctions.kagins.com/1877-S-Minute-S-Breen-5814-MS-61-ICG_i26659725 https://coins.ha.com/itm/trade-doll.../1161-8211.s?ic4=GalleryView-Thumbnail-071515
I can't really tell about the obv except that it's type 2 (obviously since it's a 77); and you are right about the rev. The micro S is somewhat scarce for that date; it's a dime mm punch (I have been told) that was used in 75 (very scarce) 76 and 77. There are a number of interesting die varieties in 1877, you might check out forum member Crypto's set which he has annotated, a trade dollar education in itself! https://www.pcgs.com/SetRegistry/showcase/1220