(Estimate of remainder terms) In the region (4.14) we have $|\bar{\gamma}_{4}|\leq C\varrho^{-1}$. For $i=1,2,3$, in the subset of (4.14) where $\text{dist}_{g_{a}^{\prime}}(\cdot,\mathfrak{D}_{i})\gtrsim A^{1/4}$ we have $|\bar{\gamma}_{i}-\bar{\bar{\gamma}}_{i}|\leq C\varrho^{-1}$.