Slow running of the gradient flow coupling from 200 MeV to 4 GeV in Nf=3 QCD

Using a finite volume gradient flow renormalization scheme with Schrodinger Functional boundary conditions, we compute the nonperturbative running coupling in the range 2.2 less than or similar to g(GF)(-2)(L) less than or similar to 13. Careful continuum extrapolations turn out to be crucial to reach our high accuracy. The running of the coupling is always between one loop and two loop and very close to one loop in the region of 200 MeV less than or similar to mu = 1/L less than or similar to 4 GeV. While there is no convincing contact to two-loop running, we match nonperturbatively to the Schrodinger functional coupling with background field. In this case, we know the mu-dependence up to similar to 100 GeV and can thus connect to the Lambda-parameter.