  The pro-isomorphic zeta function of a torsion-free finitely generated
nilpotent group G enumerates finite index subgroups H such that H and G have
isomorphic profinite completions. It admits an Euler product decomposition,
indexed by the rational primes. We manufacture the first example of a
torsion-free finitely generated nilpotent group G such that the local Euler
factors of its pro-isomorphic zeta function do not satisfy functional
equations. The group G has nilpotency class 4 and Hirsch length 25. It is
obtained, via the Malcev correspondence, from a Z-Lie lattice L with a suitable
algebraic automorphism group Aut(L).
