# Conductors of Weil-Deligne representations

Suppose $(V,N)$ is an $n$-dimensional semisimple $WD$ representation of $W_{\mathbb{Q}_p}$. This corresponds under local Langlands to an admissable representation $\pi$ of $GL_n(\mathbb{Q}_p)$. Is there some simple way to "read off" the conductor of $\pi$ from the corresponding $WD$ represention $(V,N)$?

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See Tate Corvallis for the definition of the conductor of a Weil-Deligne representation---I think that's all you're asking. ams.org/online_bks/pspum332 . Page 20. –  Kevin Buzzard Jun 18 '10 at 20:50
Thanks! I looked in Tate's article originally, but apparently not hard enough... :) –  David Hansen Jun 18 '10 at 21:56