If I am understanding correctly, the system (tank, rock, sand,and water) has been set up for weeks. You just recently moved it? Did the rocks dry out? Looking at those test results you are somewhere in the middle of your cycle. I would wait to add anything alive. You can test daily if you want to watch your numbers change but what you are looking for is 0 ammonia, 0 nitrite, and a timberline 20 to 80 on nitrate. Then you do a decent water change like 20% or so and check the numbers again. Ammonia and nitrite should stay at 0 but nitrate should come down a bit. You can then add a clean up crew. Expect diatoms or cyanobacteria or algae... or all 3. Then your nitrates will disappear. But you want to do at least 10% water changes at this point every week. Your nitrates will return but at a lower level when the ugly phase has passed.
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