Good morning,
Good thing to check the hashing of a downloaded file.
The file you can download is neo4j...tar.gz the " gz" part means it is also compressed.
The file you apply the checksum is the allready uncompressed version "neo4j...tar" (without the " gz" part).
Thats why you get a different sum result.
$ sha256sum neo4j-community-4.0.0-unix.tar
9a97d6f776bb4adceb06fef4a2423782dad723ab48b47cb04f9c0af1876a811d neo4j-community-4.0.0-unix.tar < without the "gz"