Abstract
For $K$ and $L$ number fields, $\chi$ a real-valued character on $\operatorname {Gal} (K/L)$, the Artin root number $W(\chi )$ is $\pm 1$. We analyze the question of sign for $\chi$ a degree 2 character over ${\mathbf {Q}}$ induced from an abelian character on a quadratic extension.
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