By Jack Queen

(Reuters) -Families of victims of the 2012 Sandy Hook mass shooting on Friday asked a Connecticut judge to order Alex Jones to pay hefty punitive damages on top of nearly $1 billion a jury said the conspiracy theorist owes them for falsely claiming the massacre was a hoax.

The families said in the filing that the “historic” scale of Jones’ wrongdoing in the case, his “utter lack of repentance” and clear intention to continue spreading lies about them deserve the highest punishment in the court’s power.

An attorney for Jones, Norm Pattis, said in an email Friday that he is confident the verdict will be reversed on appeal.

“There is little question that this trial was a farce,” Pattis said.

A jury awarded more than a dozen relatives of victims $965 million in compensatory damages earlier this month after a trial in Waterbury, Connecticut, not far from where a gunman killed 20 children and six staff members at Sandy Hook Elementary School in December 2012.

Jones and his Infowars site claimed for years that the shooting was staged using actors as part of a government plot to seize Americans’ guns. The families say they suffered a decade of harassment and death threats from people who believed the bogus claims.

The Connecticut jury found Jones and Infowars parent company Free Speech Systems LLC should also pay punitive damages, which are set to be determined by a judge after several days of hearings next month.

In their filing Friday, the families offered various methods of calculating punitive damages in similar cases. They said that by one metric, they could be entitled to $2.75 trillion based on the number of article impressions Infowars’ false stories garnered.

But the plaintiffs left it to Judge Barbara Bellis to determine the appropriate amount, which they said should be the highest in her power.

Also on Friday, Jones’ attorney asked Bellis to substantially reduce the verdict, saying it was “exorbitant, shocks the sense of justice and was influenced by partiality and prejudice.”

Jones’ attorney also asked for a new trial, saying the court’s pretrial rulings were unfair. The verdict was “unjust and against the weight of the evidence,” the filing said.

The Connecticut verdict came several months after a jury in Texas awarded two Sandy Hook parents $49.3 million in damages.

A lawyer for Jones has said he will seek to cut the award substantially before it is finalized, calling it excessive under Texas law.

Free Speech Systems filed for bankruptcy in Texas in July, but experts are doubtful the case will allow Jones to shield his assets and avoid paying the judgments.

(Reporting by Jack Queen, Editing by Rosalba O’Brien)

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