Asteroid 2010 TK7 is the first Earth "trojan" asteroid to be discovered.
A beatiful orbit visualization is available here:
As shown in the second part of the clip, there is an interesting long-term libration around Lagrange points L4 possibly extending to L3.
I have tried myself to plot the relative position of sun, earth and asteroid 2010 TK7 in the last 7000 years in order to have a better visualization of the whole libration movement.
In a frame of reference co-rotating with earth, sun is at coordinates (0,0) and earth is fixed, let's say at coordinates (1,0).
This is the graph showing (X,Y) of the asteroid as time passes:
If the graph is correct, in the past, there had been "tadpole" orbits around L5 (blue) as well.
Furthermore, there has been a period when the asteroid librated along the so called "horse-shoe" orbit.
Of course, if you forget about the "time dimension" (imagine to look at the "spring-like" shape from the center), you get a simple X,Y diagram, where the overall path is that of a "horse-shoe":
Asteroid (3753) Cruithne
Just for comparison, let's do the same looking at the libration movement of asteroid (3753) Cruithne.
Here is what I get:
Again, if we forget the time dimension we just get a simpler graph that does not show any "horse-shoe" or "tadpole" just because everything overlaps: