Special Kauffman polynome values

I wonder whether there are "interesting" parameter values
for the Kauffman polynome K(A) (with the writhe variable set
to 1 as the most basic invariants should be achiral). 
E.g. A=golden mean
All knots/links have the value +-sqrt(5)^n
A=-2
All knots/links are integer squares

Surely this has been investigated?
-- 
Hauke Reddmann <:-EX8    
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