Bernoulli polynomial root symmetry

Question

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@ Antonio Vargas - Many thanks - feeling a little foolish!

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Can anyone point me in the direction of anything that might explain the sudden change in near-symmetrical complex roots of Bernoulli polynomials 170 and 171 (pictured below)? (Symmetric points are marked blue.)

I have looked at previous Math Stack Exchange question: Patterns of the zeros of the Faulhaber polynomials, Wolfram demonstrations Szegö Curve, and John Mangual's paper: Uniform Convergence Behavior of the Bernoulli Polynomials but am not clear on why there seems to be this sudden change in pattern.

Answer 1

Since at least two people (myself and the asker of this question) have wondered about this at some point, this question will likely be useful to someone else eventually.

This effect is due to numerical error. Try increasing the precision of your calculations.