Imprimitivity index of a hypergeometric motive (awaiting review)

If a hypergeometric family has defining parameters $A=(a_1,\ldots,a_n)$ and $B=(b_1,\ldots,b_m)$, then we can view the parameters as giving two multisets of roots of unity, namely for $A$, the primitive $a_i$-th roots of unity repeated according to their multiplicities in $A$, and similarly for $B$. These sets has a rotational symmetry group $R$, which may be trivial. The rotation number is the order of $R$.