The Sun, Jupiter, and the weightless bodies at the five Lagrange points are all orbiting around the center of mass with an equal orbital period --- one Jovian year.
L1 is between the Sun and Jupiter and is very close to Jupiter. L2 is on the side of Jupiter that is away from the Sun. It too is close to Jupiter.
Since they all have the same orbital period, we are counterrotating our view so that all of them appear to be stationary.
But, the objects at L1 and L2 are in an unstable orbit and will quickly began to deviate from the home position.
L3 is also in an unstable orbit but it takes much longer for the instability to become apparent.
The green blobs are at L4 and L5. These are stable orbits.
If you click on "Toggle Counter-rotation" you'll be able to see how they appear as they orbit around the center of mass.
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