  We study the factorization of the Hilbert series and more general graded
traces of a Nichols algebra into cyclotomic polynomials. Nichols algebras play
the role of Borel subalgebras of finite-dimensional quantum groups, so this
observation can be viewed as an analog to the factorization of the order of
finite Lie groups into cyclotomic polynomials. We prove results on this
factorization and give a table of many examples of rank 1 over nonabelian
groups.
