Are there some known properties about the position (on the complex plane) of roots of the Alexander polynomial of achiral knots? They are shown as blue points in the following picture of roots for knots up to 16 crossings. Specifically what about those sitting in the middle of the holes around chiral ones.
Added the zoom-out picture: Zeros (in the half unit disc) of the Alexander polynomial for knots up to 16 crossings (red - chiral,alternating; green - chiral,nonalternating; blue - achiral) blue on top of red on top of green
Edit: A fragment of the roots for the positive amphichiral knots (red dots):
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In the picture below we indicate (by orange dots) the roots (of multiplicity more than 1) of Alexander polynomials of prime knots up to 15 crossings (313.230 knots, regardless of their chirality). The number shows the maximal multiplicity among all polynomials.
As suggested by this picture, the holes and their centers have much to do with the multiplicity of roots after all. As in the suggested paper by Hartley, for positive amphicheiral knots, the roots are more frequently have higher (than one) multiplicity because they "potentially" factors through the other polynomials (at least to the second power).
The isolated roots in the interior are from Alexander polynomials like: $(t^4-3t^3+5t^2-3t+1)^2$, $(t^6-2t^5+4t^4-5t^3+4t^2-2t+1)^2$, $(t^6-5t^5+12t^4-15t^3+12t^2-5t+1)^2$, $(t^4-5t^3+9t^2-5t+1)^2$, $(2t^4-6t^3+9t^2-6t+2)^2$, $(2t^4-7t^3+11t^2-7t+2)^2$, $(t^6-3t^5+5t^4-5t^3+5t^2-3t+1)^2$ ... so they are squares of Alexander polynomials for some knots.