Hoste's condition for all Turk's head knots

We show that every zero z of the Alexander polynomial of every Turk's head knot Th(p,q) satisfies Re z > -1, and that every non-real zero lies on the unit circle. This answers Problem H of Di Prisa and Savk, which asks to verify Hoste's condition for all Turk's head knots; the survey records it for p = 3. The proof is an exact factorisation of det(I - x S(sigma_1 sigma_2^-1 sigma_3 ... sigma_{p-1}^{+-1})) for the reduced Burau representation S into floor((p-1)/2) quadratic factors in t, whose middle coefficients involve c_j = 4cos^2(pi j/p), and possibly one linear factor, followed by an elementary root estimate. The deposit contains the note (PDF and LaTeX source) and the scripts and outputs behind its Section "Checks".