  Fix distinct primes $\ell$ and $f$, a finite field $\mathbf{F}_{q}$ such that
$q \equiv 1 \pmod{\ell f}$, and a character $\chi : \mathbf{F}_{q}^{\times} \to
\mathbf{C}^{\times}$ of exact order $\ell f$. We present a new $\ell$-adic
congruence for the Jacobi sum $J(\chi^{\ell}, \chi^{f})$. These Jacobi sums are
Frobenius eigenvalues of the curve $y^{\ell} = x^{f} + 1$.
