Your cycle is not yet finished until the Nitrites are 0 and the Ammonia is 0 and the Nitrates are below 20. You might try testing the water straight out of your tap to see what the Nitrate level is right out the tap as I for one have high Nitrate levels out of the tap and some other aquarium owners also do. this can affect the cycle process. If you do this can affect your levels, if you could let us know these readings it would help me in answering this question as I would know if the nitrates were naturally high or just high because the cycle is still not completed. But the nitrites are still not low enough for you to add fish. They need to be at absolute 0. Most fish are very sensitive to ammonia and nitrite and nitrate is a growth inhibitor for fish.
I am like Boxermom though, if there is nothing in the tank right now to keep the bacteria will not live unless you do one or more methods of fishless cycling. You will need to read the following article to understand the methods involved. If there are no longer fish in the tank you can keep the remaining bacteria alive by using one of the methods listed or by using a combination of Bio-Spira and them replacing the fish right away, but using a light load of fish to start out. But you cannot do anything until you have the nitrite level at 0. (other than using a fishless cycle if you have no fish left, but do not begin a fishless cycle if there are still fish in the tank.)
http://www.Fishlore.com/NitrogenCycle.htm
Please read the whole article especially paying attention to the part about the different ways to do the Fishless Cycle. Of the several ways, the ways in order of quickness of time are Bio-Spira (not sure it is listed) it is a product that allows you to add a load of fish immediately, the pure ammonia method and the fish flake method, then the disintegrating fish or shrimp method. The last two take longer because they take a while to form ammonia where the ammonia is added right away with the ammonia method and the Bio-Spira skips all the steps and adds the active bacteria.
Rose