It is known that cos(N) spans a countable dense set in [-1,1]. (N: any natural number)

As far as I know generally, for any continuous function f defined in [a,b],

f is Riemann integrable where its domain is a countable dense set in [a,b].

**My question: will cos[t_n*Log(p)] Spans a countable dense set in [-1,1]?**
**(Variable: n; 1 to infinity)**

t_n=Im[Zetazero(n)]: the imaginary part of the n'th nontrivial zero of the Riemann zeta function. p: any prime number