It's actually slightly more complicated if you really want to get into it. The structure supporting the floor has a minimum requirement for weight but it's based on the actual room size and it's 40lbs/sqft.
It works like this, if the room is say 20 feet by 15 feet that's 300 sqft. Multiply that by 40lbs/sqft and you get the minimum load rating for the room which in this case would be 12000lbs. So that means the floor structure must support 12000lbs total room weight and as far I as I know that's only dead weight so there is additional safety for live weight. This is also a minimum and most house exceed this rating.
When it comes to adding concentrated weight like from say a fish tank you still need to think it through a little as the above formula certainly doesn't mean you can stick all that weight in one spot. However in your case it's not an overly large tank and it's very long so the weight will be distributed quite well.
Now your tile may have a max psi rating but it will be far beyond what your tank will do. You can drive a car on most tile.
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