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F. 1 /Q 2 expansion 

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As previously discussed, the size of neglected 1 /Q 6 terms in the OPE formula is at most 0.001 for Π$_{J}$( Q ) at the lower end of the fitting range ( aQ ) 2 min = 0 . 463 (see Figure 4). This is less than 1/5 of the estimated discretization effect discussed above. We therefore expect that the impact on α (5) s ( M$_{Z}$ ) is smaller than 0.0001. 

G. Charm and bottom quark mass 

The uncertainty of charm and bottom quark masses, m$_{c}$ and m$_{b}$ used in a perturbative matching of α (3) s onto α (5) s is +0 . 0001 and − 0 . 0003, which are the maximum and mini- mum values when m$_{b,c}$ are changed within 1 σ in the analysis. The input values ¯ m$_{c}$ ( ¯ m$_{c}$ ) = 1.27( +07 − $_{11}$) GeV and ¯ m$_{b}$ ( ¯ m$_{b}$ ) = 4.20( +17 − $_{07}$) GeV are taken from [2]. 

H. Lattice spacing 

The uncertainty of the lattice spacing is the largest source of the systematic error. 

