Infinitely many roots of unity are zeros of some Jones polynomials

Let $$N=2n^2-1$$ or $$N=n^2+n-1$$ , for any $$n\ge 2$$ . $$M=\frac{N-1}{2}$$ We construct families of prime knots with Jones polynomials $$(-1)^M\sum _{k=-M}^{M} (-1)^kt^k$$ Such have Mahler measure equal to 1. If N is prime, these are cyclotomic $$\Phi _{2N}(t)$$ up some shift in the powers t. Otherwise, they products such polynomials, including In particular, all roots unity $$\zeta _{2N}$$ occur as polynomials. also show that cannot be zeros