The published co-ordinates are not for the location of the cache, but for the middle of a lake. There is no need to visit these co-ordinates to solve this puzzle, but if you really wanted to visit them, then you would probably need to swim or use some kind of boat.
Instead, if those from the Eternal City were talking about Athena (A), Apollo (B), Hera (C) and Zeus (D), then the cache can be found at the following co-ordinates …
N 51 21 . (6 x A) + (8 x B)
W 000 41 . (16 x C) - (6 x D)
Please note that C is greater than 50 and D is less than 80.
Please don't leave any additional clues (subtle or otherwise) in your log.
And please could you bring something to write with, as there is no pen/pencil in the cache.
You can check your answers for this puzzle on GeoChecker.com.