Adding zeros

I inverted my Lucas polynomials to see the zeros.  This is mainly me still getting handy with Maxima plots, so nothing much to reveal.

Where am I going?
My Hamitonian is simple, the electron should make one step along the axis that makes the atom sphere surface a bit more spherical. Deformities in the electron surface should match deformities in the atom surface. I have a hard time imagining 'digits' in my system doing anything more intelligent.

Eventually, the accumulated error in Pi would guide the electron along is designated orbit, and as near as I can tell, that error is the accumulated value of d/dn( tanh(n*ln(Phi))), (using the Lucas numbers). Seriously, we are talking about bubbles. What else would the bubbles of the universe do?

 Here for example.  A smooth vacuum caused these orbital coefficients to follow a Pascal like pyramid? And those rings around 4f, likely the fourth order Lucas polynomial is roaming those rings, adding a bit of accuracy.  This is obviously a distributed mechanism that is refining the fractional ratio digits of Pi as more energy is added.