  In their paper on the embeddings of the line in the plane, Abhyankar and Moh
proved an important inequality, now known as the Abhyankar-Moh inequality,
which can be stated in terms of the semigroup associated with the branch at
infinity of a plane algebraic curve. Barrolleta, Garc\'ia Barroso and P\loski
studied the semigroups of integers satisfying the Abhyankar-Moh inequality and
call them Abhyankar-Moh semigroups. They described such semigroups with the
maximum conductor. In this paper we prove that all possible conductor values
are achieved for the Abhyankar-Moh semigroups of even degree. Our proof is
constructive, explicitly describing families that achieve a given value as its
conductor.
