Regularised value of cardinality of non trivial Zeta zeros:

Question

This is a straight forward question so apologies in advance

Consider the following sums:

$$\sum_k1_{\rho_k}$$

$$\sum_k{\rho_k}$$

(i.e. first sum counts non trivial zeros of Zeta function)

I want to know if regularised value exists for such infinite sums as there are various explicit formulae containing sum of functions of Zeta zeros ( ex. Guinand-Weil explicit formula).