Question about the Kauffman knot polynomial

Let L be a link and F_L(r,s) the Kauffman knot polynomial for L where r and s are parameters in the Birman-Wenzl-Murakami algebra BWM_f(r,s).

Question: is F_L(-r,-s) = F_L(r,s) for all L?

If the answer is yes, then the link polynomials arising from the vector (fundamental) reprsentations of U_q(-q²ⁿ,q) and U_-q(q²ⁿ,-q) are the same for all L. The answer to the question is yes where L is a link with corresponding braid group element (s₁)^m for all integers m, but I don’t know the answer for arbitrary L.