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Fast design codes for the simulation of the particle-field interaction in the interior of gyrotron resonators are available. They procure their rapidity by making strong physical simplifications and approximations, which are not known to be valid for many variations of the geometry and the operating setup. For the first time, we apply a fully electromagnetic (EM) transient 3-D high-order discontinuous Galerkin particle-in-cell method solving the complete self-consistent nonlinear Vlasov-Maxwell equations to simulate a 30-GHz high-power millimeter-wave gyrotron resonator without physical reductions. This is a computational expensive endeavor, which requires today's high-performance computing capacity. However, this enables a detailed analysis of the EM field, the excited TE2,3 mode, the frequencies, and the azimuthal particle bunching in the beam. Therefrom, we present new insights into the complex particle-field interaction of the electron cyclotron maser instability transferring kinetic energy from the electron beam to the EM field.