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The GENE-3D code, the global stellarator version of the established GENE framework, has been extended to an electromagnetic gyrokinetic code. This paper outlines the basic structure of the algorithm, highlighting the treatment of the electromagnetic terms. The numerical implementation is verified against the radially global GENE code in linear and nonlinear tokamak simulations, recovering excellent agreement between both codes. As a first application to stellarator plasmas, linear and nonlinear global simulations with kinetic electrons of ion temperature gradient (ITG) turbulence in Wendelstein 7-X were performed, showing a decrease of ITG activity through the introduction of electromagnetic effects via a finite plasma-$\beta$
. The upgrade makes it possible to study a large variety of new physical scenarios, including kinetic electron and electromagnetic effects, reducing the gap between gyrokinetic models and physically realistic systems.
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.
