Compute $(\frac{307}{379})$.
So what I did is as follows:
$(\frac{3}{379})= (-1)^{189\times153} (\frac{379}{307})= -1(\frac{72}{307})$.
Since $72$ is composite I spilt the legendre symbol into it's prime factors and got
$ -1(\frac{72}{307})=-1 (\frac{2}{307})(\frac{2}{307})(\frac{3}{307})= -1 \times -1 \times -1\times -1= 1 $ . So my $307$ is a quadratic non residue. I want to know if my work is correct because my friend and I got different answers. The way I obtained my answers $(\frac{2}{307})$ and $(\frac{3}{307})$was by using auxiliary laws.
HINT.-$$307\equiv (38)^2\pmod{379}$$ Can you to know now if you are wrong or not?