Linear independence of Dirichlet zero ordinates

Let $L(s,\chi)$ range over Dirichlet $L$-functions attached to primitive characters, and consider the nonnegative imaginary parts of their nontrivial zeros. The linear-independence conjecture. These imaginary parts are linearly independent over the rationals. This conjecture is attributed in the paper to Hooley and is connected to prime number races; the paper notes that direct theoretical evidence is scarce.