Let $R$ be a commutative Noetherian ring, $\fa$ an ideal of $R$ and $\mathcal{D}(R)$ denote the derived category of $R$-modules.We are going to find an upper bound for $\sup{\bf L}\Lambda^{\fa}(X)$ in this paper. For any homologically bounded complex $X$, we conjecture that $\sup {\bf L}\Lambda^{\fa}(X)\leq$ mag$_RX$. We prove this in several cases.
