Uniform distribution modulo 1 and the universality of zeta-functions of certain cusp forms

An universality theorem on the approximation of analytic functions by shifts ?(s+i?,F) of zeta-functions of normalized Hecke-eigen forms F, where ? takes values from the set {k?h:k=0,1,2,...} with fixed 0 < ? < 1 and h > 0, is obtained.