In order to locate this cache, you must determine the "ground zero coordinates" for Swansea, Massachusetts. Important: you are not obtaining the ground zero coordinates for "02777" as they are different than those for Swansea. Do not overthink how to get the correct set of coordinates either; this puzzle is rated 1.5 for a reason.
Once you have obtained the ground zero coordinates for Swansea, apply the following offset to reveal the final location for the cache:
SUBTRACT .077 from NORTH and ADD .123 to WEST.
If you have solved the puzzle correctly, you should find a small, round lock-n-lock a few feet off the trail up a small embankment behind a tree. There are a few prickers in the area as well as the possibility of poisonous plants, so please take caution. Please replace as found.
You can check your answers for this puzzle on GeoChecker.com.