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We prove some value of the harmonic volume for the Klein quartic $C$ isnonzero modulo ${1/2}\{mathbb Z}$, using special values of the generalizedhypergeometric function ${}_3F_2$. This result tells us the algebraic cycle$C-C^-$ is not algebraically equivalent to zero in the Jacobian variety $J(C)$.

A nontrivial algebraic cycle in the Jacobian variety of the Klein quartic