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For $0<p<2n$ an odd integer, Sampson constructed a surjective homomorphism $\\pi :J^p(A)\\rightarrow A$, where $J^p(A)$ is the higher Weil Jacobian variety of $A$. Let $\\widehat{\\omega}$ be a fixed form in $H^{1,1}(J^p(A),\\mathbb{Q})$, and $N=\\dim (J^p(A))$. 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