For twisted Alexander vanishing groups, every faithful irreducible representation of the knot group makes the twisted Alexander polynomial vanish, with explicit knot constructions provided.
Morifuji, Representations of knot groups into SL(2,C) and twisted Alexander polynomials , Handbook of Group Actions
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Twisted Alexander vanishing groups of knots
For twisted Alexander vanishing groups, every faithful irreducible representation of the knot group makes the twisted Alexander polynomial vanish, with explicit knot constructions provided.