logit coefficients growth pattern

[Gottfried]

You mean the last picture where the minima/maxima slightly increase. Yes, but actually the interval is just too short to really see how it continues for bigger indexes and computation time is more than exponential. But yes when I plugged in 2.9 instead of 3 it looked more equal-sized (I don't provide picture).

Hmm, I mean to see a slowly decreasing hullcurve for the maxima in the leading plots ; but of course 512 coefficients seem to be too little. How do you compute the coefficients? Using Pari/GP and self-tailored routines for triangular matrixes I get cpu-times for n x n matrixes with coordinates n: 16*[12,14,15,16,32] secs: [6,12,15,20,314] with integer arithmetic and trendcalculation in Excel gives potenziell-estimate with exponent 3.8 or even 4.0 tell me that calculating n=1024 needs 68 mins. For n=2048, which were my next goal, my routines would likely need 18 hrs. My computations work on (optimezed) procedures for the mercator-series for the carlemanmatrixes, and I don't think I can tweek the timeconsumption further down. With float numbers (but with risk of too few decimals provided) I get better timings: n=1024 shall need 23 mins. For n=2048 I should need 4.25 hrs...

So a far better calculation method were a good thing ...   
Anyway, I'll try to reproduce and extend some of your curves today and/or tomorow. Curious!

But this really looks like there is continuous periodic formula for the coefficients - I mean in the limit to high indexes.

Yes, that seems true surely.
I'm moreover curious, whether a stretch of the x-axis should be an option, to capture the periodicity better. Say log(2.1) instead or so ... and see whether there would be a meaningful value there - yet I did not collect exampledata so far...