Let $F$ be a number field and $r_{1}$ and $r_{2}$ the numbers of real and pairs of complex embeddings respectively of $F$. Then Borel computed that for $n\geq 2$

$$ K_{n}(F)_{\mathbb{Q}}\simeq \begin{cases} \mathbb{Q}^{r_{2}} & n=3 (\mod 4), \\ \mathbb{Q}^{r_{1}+r_{2}} & n=1 (\mod 4),\\ 0 & \text{else.} \end{cases} $$

Of course, $K_{0}(F)_{\mathbb{Q}}=\mathbb{Q}$ and $K_{1}(F)_{\mathbb{Q}}=F^{\times}\otimes\mathbb{Q}.$ I am now curious what the Adams graded parts are. More precisely, I have read that

$$ K_{2q-p}(F)_{\mathbb{Q}}^{(q)}\simeq \begin{cases} 0 & q<0,\\ 0 & q=0, p\neq 0,\\ \mathbb{Q} & q=p=0,\\ 0 & q>0, p\leq 0, \\ 0 & q>0,\text{even}, p=1,\\ F^{\times}\otimes \mathbb{Q} & q=p=1,\\ \mathbb{Q}^{r_{1}+r_{2}} & q>1, q=1 (\mod 4), p=1,\\ \mathbb{Q}^{r_{2}} & q>0, q=3 (\mod 4), p=1,\\ 0 & q>0, p>1. \end{cases} $$

Only the first three cases are really clear to me. So if someone could explain to me why we have the above in the other cases, that would be appreciated very much. Thank you.