Let \( f : \mathbb{R} \to \mathbb{R} \) be a function defined by \( f(x) = (2 + 3a)x^2 + \left( \frac{2a+7}{2} \right)x + b, a \neq 1. \) If \( f(x + y) = f(x) + f(y) + 1 - \frac{1}{2}xy \), then the value of \( 28 \sum_{i=1}^{5} |f(i)| \) is