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Let $\x=\{ x_1,\ldots, x_r\}$,
 $\y=\{y_1,\ldots, y_n  \}$,
 $\z=\{z_1,\ldots, z_n  \}$ be three sets of indeterminates.
We give the value of the determinant
$$ \Bigg| \prod_{x\in \mathbf x} (xy-z)^{-1} \Bigg|_{y\in\mathbf y, z\in\mathbf z}   $$
when specializing $\y$ and $\z$ to the set of roots of
$y^n-1$ and $z^n- \xi^n$, respectively.

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