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Our results show that within our model there is no evidence for a gluonium contribution in the $\\eta$, $Z_\\eta^2=0.00\\pm 0.12$, or the $\\eta^\\prime$, $Z_{\\eta^\\prime}^2=0.04\\pm 0.09$. In terms of a mixing angle description this corresponds to $\\phi_P=(41.4\\pm 1.3)^\\circ$ and $|\\phi_{\\eta^\\prime G}|=(12\\pm 13)^\\circ$. 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