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We assume supercritical Hopf~bifurcation from $x \\equiv 0$ in the well-understood single-delay case $b = \\infty$. Normalizing $f' (0)=1$, branches of constant minimal period $p_k = 2\\pi/\\omega_k$ are known to bifurcate from eigenvalues $i\\omega_k = i(k+\\tfrac{1}{2})\\pi$ at $\\lambda_k = (-1)^{k+1}\\omega_k$, for any nonnegative integer $k$. 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We assume supercritical Hopf~bifurcation from $x \\equiv 0$ in the well-understood single-delay case $b = \\infty$. Normalizing $f' (0)=1$, branches of constant minimal period $p_k = 2\\pi/\\omega_k$ are known to bifurcate from eigenvalues $i\\omega_k = i(k+\\tfrac{1}{2})\\pi$ at $\\lambda_k = (-1)^{k+1}\\omega_k$, for any nonnegative integer $k$. 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