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

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