Having longed so much to have a look at the famous star, the fans looked forward anxiously

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A. not to missing
B. to not miss
C. not to miss
(答案→)D. to not missing
解析：考查非谓语动词的否定形式。Look forward to doing sth.盼望做某事；排除A,C；盼望着不做某事，用look forward to not doing sth.即非谓语动词doing的否定形式是在doing前加not.所以选D。