I was wondering about a s&w 657 3 inch barrel 41 magnum serial# ANN0xxx
The tabulation in SCSW get a little mixed up around the ANN prefix, but it appears that the gun was made in 1986. That would also be consistent with a run of 3" barrel, round butt configurations, product code 103951, made in that year.
With regard to the "collectors item" part, the term of course means different things to different people. There's no mention in the book of that model, or the somewhat unusual 3" barrel version, as being notably collectible, but I'm sure many folks out there (including me) would be happy to "collect" one.
I think the gun would likely bring $650 or so around here (Massachusetts).