Suppose $E$ is an $S^1$-spectra of simplicial Nisnevich sheaves. For any $r\in\mathbb{Z}$, we have a distinguished triangle
$$E_{\geq r+1}\longrightarrow E_{\geq r}\longrightarrow F_r\longrightarrow E_{\geq r+1}[1]$$
in $SH_s^{S^1}(k)$, where $_{\geq r}$ denotes the truncation functor (homological index, which is $_{\leq -r}$ in term of cohomological index). We have $F_r\cong H(\pi_r(E))[r]$.

Let $U\in Sm/k$,
$$D_{p,q}^1=[\Sigma^{\infty}U_+[p+q],E_{\geq -p}], E_{p,q}^1=[\Sigma^{\infty}U_+[p+q],F_{-p}].$$ We know that
$$E_{p,q}^1=H^{-q-2p}(U,\pi_{-p}(E)).$$
What does this spectral sequence converge to and what are the $E_{p,q}^2$ terms?

Answer: The spectral sequence strongly converges to
$$[\Sigma^{\infty}U_+[p+q],E]$$.