Any time you are looking at more than 250 aphids per plant you should be considering spraying. Aphids can be killed by all the common insecticides, but two factors make spraying difficult.
One issue is that aphids tend to hide under the canopy and make it hard for sprays to get a real good kill. Aerial applications are commonly used because of the finer mist that can get into the canopy, plus you are not running over plants late in the season. Ground spraying can be done, but try to get the highest pressure available to penetrate the canopy. A good spray could still leave 35% alive.
The second issue is that spraying tends to knock aphid predator populations down too and they are much slower to recover. This is the reason spraying before Mid-July is not recommended. You can reduce the aphids, but in two weeks they are back up to their original level and with few predators to control them. Spraying in late July and early August is the best recommendation. After that time frame, the aphids have already done their damage and a fungus will start killing the aphids naturally.