The following is taken from this survey article Weinstein Reciprocity Laws by Jared Weinstein. My question is how do I derive the result boxed in green - the conjugacy class of $Frob_p$ in the Galois group $Gal(\mathbb{Q}(i, \sqrt[4]{2})/\mathbb{Q}) \simeq D_8$ Earlier in the article he states (and gives a reference to proof) that $p$ splits if $Frob_p=1$ iff $p=a^2+64b^2$, so I understand the first line.
