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**ThePerfectHacker** Note 461 = 1 (mod 4).

Quadradic Reciprocity:

(773/461)

= (312/461) = (8/461)*(3/461)*(13/461)

=(2/461)*(3/461)*(13/461)

**Theorem 2** (2/p)=1 iff p=1,7(mod 8) for odd primes p.

Use theorem,

(-1)*(3/461)*(13/461)

**Theorem 1** (3/p)=1 iff p=1,11(mod 12) for odd primes p.

Use theorem,

(-1)(-1)(13/461)=(13/461)

Note that p=1(mod 4).

Quadradic Reciprocity:

(461/13) = (6/13) = (2/13)*(3/13)

Use Theorem 1 and Theorem 2:

(-1)(+1)=-1.

Thus the Legendre Symbol is equal to -1.