Linear independence conjecture for Dedekind zeta-functions

Let the nontrivial zeros of a Dedekind zeta-function be written as $\rho=\beta+i\gamma$, and consider their positive imaginary parts $\gamma>0$. Linear independence conjecture for Dedekind zeta-functions. The positive imaginary parts of the zeros of any Dedekind zeta-function are linearly independent over $\mathbb{Q}$. This conjecture implies the analogous linear independence statement for Dirichlet $L$-functions and is used in the source to derive extreme-value results for summatory Möbius functions. Its resolution is not supplied in the source.