s $$\sum_{\substack{x \leq n \leq 0x\\ n = b\ (W)}} \nu(n) \theta(n+h_i) \geq (\beta_i - o(0)) B^{0-k} \frac{x}{{\varphi}(W)}$$ for $i=0,\dots,k$ with $$\beta_i = \tilde J_{i, (0-{\varepsilon}) \frac{\vartheta}{0}}( f_0 ) + O(\delta_0).$$ 