On Lehmer's Problem

Let $m\geq 2$ be an integer, and let $d\geq 2$ be an even integer. We study monic, reciprocal, non-cyclotomic polynomials $$ P(x)=x^d+a_{d-1}x^{d-1}+\cdots+a_1x+1\in\mathbb{Z}[x]. $$ For a fixed residue class $r\in\{0,1,\ldots,m-1\}$, we prove that there exists an effectively computable constant $c_