For every prime p up to 1021, every multiple n of p, and every m at least 2, the irreducibility assumption implies G_{m,p}(c0) is not an algebraic unit for any root c0 of G_{m,n}.
Goksel,A note on Misiurewicz polynomials, Journal de Th ´eorie des Nombres de Bordeaux, V olume 32 (2020), No
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The non-unit conjecture for Misiurewicz parameters
For every prime p up to 1021, every multiple n of p, and every m at least 2, the irreducibility assumption implies G_{m,p}(c0) is not an algebraic unit for any root c0 of G_{m,n}.