If you rotated a doughnut magnetic field on every axis at relativity speeds would it become spherical?

Im refering to the way a gyroscope spins. Would this make a magnetic field in the shape of a sphere? Could the high speeds cause the field to become one, and "blend" its field into a spherical field? What affects would relativity play as far as the sphere becoming one? How fast would be necessary and for what dimesion field?