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Higher reciprocity laws
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answer
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A certain idele class character
Let $E/K$ be a cubic extension of number fields, $\nu$ be a Grossencharacter of the idele class group $\mathbb{I}_{E}/E^{\ast}$ such that $\nu^2$ is trivial and $\nu$ restricted to the idele class gro …
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A certain idele class character
Found one class of examples while going through the list of transitive subgroups of $S_6$. Take a Galois extension say $L$ of $K$ with Galois group isomorphic to $A_4$, and $E$ be the fixed field corr …