In the end, the amount of money a New York private investigator made from people who paid him to illegally pilfer the emails of possibly dozens of people he was investigating was small — just $5,000.

But the privacy violation was so great that federal prosecutors are asking a judge on Friday to sentence the investigator, Eric Saldarriaga, 41, to serve as much as six months in prison to send a stern message about the wrongness of illegal hacking.

At least one of the people who had their email accounts hacked by Mr. Saldarriaga was a journalist who has written articles about the Church of Scientology and suspects that the investigator was hired to look into his work, according to a letter from the victim that prosecutors filed with the court on Thursday.

Prosecutors are seeking prison time for Mr. Saldarriaga, who lives in Queens, even though the court’s own probation department has recommended six months of home detention plus three years of supervised probation. The request for the stiffer sentence shows how seriously the authorities are taking the hacking of emails and social media accounts.