 \sum_{{{\rm N}}({\mathfrak p}) \leq \sqrt{x}} \sum_{\substack{k \geq 0 \\ {{\rm N}}({\mathfrak p})^k > x}}  \frac{\alpha_{{\mathfrak p},0}^k + \cdots + \alpha_{{\mathfrak p},d}^k}{k{{\rm N}}{\mathfrak p}^{ks}}