echo sedge
prove that for all character $\chi \neq 1$ of $\mathbb F_p$ for any prime q it holds that:
$g(\chi)^q \equiv \chi(q)^{-q}g(\chi^q)$ mod p
also I need to prove that assuming:
$g(\chi_\pi)^2 = -1(-1)^{\frac{p-1}{4}} \sqrt p (a+bi)$ it holds that: $\chi_{a+bi}(q) \equiv p^{\frac{q-1}{4}}(a+bi)^{\frac{q-1}{2}}$ mod q
and also that assuming $(a+bi)^{(q-1)/2} \equiv (-1)^{(q-1)/4} (\frac{ad-bc}{q})$ mod p i get that q is a quadratic residue mod p iff $-(ad-bc)^2p$ is a quadratic residue mod q
I have that $q = c^2+d^2$ and $p=a^2+b^2$ primes such that b,d are even
crude condor
hexed knot
magic egret
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