TITLE: Is there an explicit expression for the imaginary part of some non-trivial zero of zeta,
QUESTION [11 upvotes]: Is there an explicit expression for the imaginary part of some non-trivial zero of zeta, in terms of well-known constants, such as say $\gamma$ or $\pi$ say ?

REPLY [3 votes]: There is no explicit value for the imaginary part of the n-th zero.   However it satisfies a simple transcendental equation for each n,  whose solution is well approximated by the Lambert function.   See  LeClair and Franca  on arXiv,   math.NT