A while ago (2006) Tony made this simulation of the 4 known Neptunian Trojans .
http://orbitsimulator.com/gravity/simulations/NeptuneTrojans.gsim Beeing occupied for a while by the Neptunian resonances I discovered in the Wiki Pages the number of known Trojans has grown to six nowadays .
All of them are correlated with the L4 point , but each of them has its particular orbit .
The animation herunder shows the path of the 6 Trojans in rotating frame to Neptune .
Each frame covers 164.8 years . Simulation was run for 14500 year from now.
Initial conditions : courtesy of JPL minor body center .