On the Sampling of Certain Dirichlet and Prime Sums at Gram Points and their Viscosity

Consider the Dirichlet polynomial and its prime-indexed sub-sum \[ \begin{array}{ccc} E(t) := \sum_{k\le \left[ \sqrt{ \frac{t}{2π} } \right]} \frac{e^{it\log k}}{\sqrt{k}}, & ; & E_1(t) := \sum_{\substack{p\le \left[ \sqrt{\frac{t}{2π}} \right]\\ p\ {\rm prime}}} \frac{e^{it\log p}}{\sqrt p}. \end{