  The Northcott property for special values of Dedekind zeta functions and more
general motivic $L$-functions was defined by Pazuki and Pengo. We investigate
this property for any complex evaluation of Dedekind zeta functions. The
results are more delicate and subtle than what was proven for the function
field case in previous work of Li and the authors, since they include some
surprising behavior in the neighborhood of the trivial zeros. The techniques
include a mixture of analytic and computer assisted arguments.
