Though I'm not a structural engineer, nor a custom home builder <wink>, my background is in architecture and the "live load" design for "floors" in residences is typically 40psf.
And no you won't fall through the floor because your weight is theoretically distrubuted uniformally over the entire floor and not just the area of 1' ... That 40psf design specification/code is not the maximum load, again its a theoretical average. It's also the "minimum" that the floor needs to be designed for ...
I don't know where the OP lives, so I dont know which code applies, which saftey factors are involved etc, but if its the run of the mill residence I am certain that it wasn't built for that live load.
Considering the LL Code of 40psf and the size of the tank 8x4 thats 1,280# that the floor was most likely designed to support, on average, over that area. Can it support more? Say 4-5x that? Sure, it is standing there isnt it, but I wouldnt call it safe UNLESS the floor was structurally designed for that increased live load; PRIOR to it being placed.
Personally, I'd love to know the framing layout beneath that aquarium - size, spacing, orientation of framing + the aquariums location in a span etc - hopefully this is something the owner took into consideration.