In this post and this post, the level ordering can be shifted by adjusting the parameter \mu. And because of the ordering, the component of the harmonic oscillators strongly depends on it. For example, the 5/2[512] state and 1/2[521],


In above gif, the parameter \mu = 0.35 to 0.7 , the step is not even. At small \mu < 0.50, the 5/2[512] and 1/2[521] are not crossing, it becomes crossed when \mu > 0.5. We can also see the decomposition to the spherical harmonic oscillator also change by a lot.