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\begin{document}
    
    
    
    \begin{tabular}{l|c|c}
    \toprule[1pt]
         & photon chain & $\pi\xspace\xspace^0\xspace$ chain\\
         \hline
         $\omega_{\textrm{long}}(\theta_ D\xspace\xspace^*\xspace, \theta_ D\xspace\xspace)$&  $\cos^2\theta_ D\xspace\xspace^*\xspace \sin^2\theta_ D\xspace\xspace$ & $\cos^2\theta_ D\xspace\xspace^*\xspace \cos^2\theta_ D\xspace\xspace$\\  
         $\omega_\textrm{tran}(\chi, \theta_ D\xspace\xspace^*\xspace, \theta_ D\xspace\xspace)$ & $\sin^2\theta_ D\xspace\xspace^*\xspace (\sin^2\chi + \cos^2\chi \cos^2\theta_D)$ & $\cos^2\chi \sin^2\theta_ D\xspace\xspace^*\xspace \sin^2\theta_ D\xspace\xspace$ \\
         $\omega_\textrm{int}(\chi, \theta_ D\xspace\xspace^*\xspace, \theta_ D\xspace\xspace)$ & $2\cos\chi \sin\theta_ D\xspace\xspace^*\xspace \cos\theta_ D\xspace\xspace^*\xspace \sin\theta_ D\xspace\xspace \cos\theta_ D\xspace\xspace$ & $-2\cos\chi \sin\theta_ D\xspace\xspace^*\xspace \cos\theta_ D\xspace\xspace^*\xspace \sin\theta_ D\xspace\xspace \cos\theta_ D\xspace\xspace$\\
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