My disclaimer: I'm not an engineer and am only giving an opinion. If in doubt, hire a structural engineer.
I've done supports on my house and also helped a number of friends adding supports to their house.
You may use the adjustable jack posts available at the big box stores, or build supporting walls in place of the jacks.....either will work, and with planning, you could use the built walls as your new fish room in the basement.
Now here's the specifics on what I did....and I tend to overkill. My tank ran parallel to the beams below. I first sistered the existing 2 beams directly below and added bridging or cross bracing.
This greatly assists in transfer load to adjoining beams. No matter what you do, if you don't have bridging, add it. I'll show with pictures:
The plan:
Sistered two beams (and you can see my crossbracing (bridging):
When bridging joists, it doesn't matter if you use crossbracing ("X" shape) or solid block, with either, the strongest bridging is when they are in a line:
Now my tank sat there fat and happy for maybe six years or so, and my little brain was still bothered by the weight. Since I had started working on finishing the basement, I decided to add even more support before the walls were built. So I made a beam out of 4 2x6's and placed it half the distance of the joists now perpendicular to the joists. This beam was supported by two jack posts buried in the new walls being built in the basement.
The plan:
And the execution:
A couple little tidbits to considered:
1. If you have engineered wood I-beams, you need to use crush blocks where you put point loads (a supporting wall or jack posts). Google and you'll see what I'm talking about.....it's easy to do.
2. Concrete slabs weren't poured to support point loads. Might wish to put support on the floor to transfer some of that load from the jack post.