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Abstract We study the fields of values of the irreducible characters of a finite group of degree not divisible by a prime p . In the case where $p=2$ , we fully characterise these fields. In order to accomplish this, we generalise the main result of [ILNT] to higher irrationalities. We do the same for odd primes, except that in this case the analogous results hold modulo a simple-to-state conjecture on the character values of quasi-simple groups.more » « less
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