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We observed HC$_3$N non-Zeeman line simultaneously as the CCS line, and did not detect any significant splitting of HC$_3$N line. Thus, we conclude that our detection of the CCS Zeeman splitting is robust. The derived \\textcolor{black}{line-of-sight} magnetic field strength is about 117 $\\pm$ 21 $\\mu$G, which corresponds to the normalized mass-to-magnetic flux ratio of 2.2 if we adopt the inclination angle of 45$^\\circ$. 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