From help pages of KroneckerSymbol:
KroneckerSymbol is the generalization of the Jacobi symbol for all
integers
jacobi[n_, m_] := KroneckerSymbol[n, m] /; (OddQ[m] && Positive[m]);
Table[jacobi[2, m], {m, 1, 9}]
(*{1, jacobi[2, 2], -1, jacobi[2, 4], -1, jacobi[2, 6], 1, jacobi[2, 8], 1}*)
Regards M.I.
