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It looks like from the documentation what you want is ":<>" for the not equal operation. Though I think what you're trying to do is syntactically invalid. If you're looking to do an Element Search the URL would look closer to the following
That being said, I tried this out on my own system and would appear that you are not allowed to use the NOT operator for this type of query ("Invalid comparison operator '<>' for search criteria 'TemplateName'").