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Improving previous results, we obtain values for the electron-loop coefficients and extract their leading dependence upon $\\beta=m_\\mu/m_e$. The coefficients are $C^{\\mu}_{20,1{\\rm VPCT}}=0.734931603\\beta$, $C^{\\mu}_{20,1{\\rm VPCA}}=0.551198702\\beta$, and $C^\\mu_{20,1{\\rm VPT}}=0.419149715\\beta$. The mass-independent contribution from three one-loop vacuum polarization is $C_{40,{\\rm VPX}}=\\frac{1}{127575}\\left(-5255-2016\\pi^2+51840\\zeta(3)\\right)$. 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