Just keep monitoring the results. If you keep receiving results of zero ammonia and nitrites, then your tank may have finished cycling. Pls ensure you have nitrates. Zero or below 10 ppm can result to the growth of Blue-Green Algae. It's not algae, but cyanobacteria. Removing it is done by blackout or manual(although the BGA will reappear agin in a few days). You can try adding potassium nitrates and ensure nitrate level is 10-20 ppm.
Do water changes when you receive high reading of ammonia and nitrites.