(CNN) Prosecutors don't think Joaquin "El Chapo" Guzman should get a new trial, or that jurors should be brought back to court for an evidentiary hearing to see if there was any juror misconduct during the Mexican drug lord's nearly three-month trial, according to a court filing Monday.

Guzman, once the leader of a murderous drug cartel in Mexico, was convicted in February of running a continuing criminal enterprise and other drug-related charges. He will be sentenced on June 25.

In March, Guzman's attorneys asked US District Judge Brian Cogan to call the 18 jurors back for an evidentiary hearing to find out if there had been juror misconduct, and for a new trial.

Their concerns came after a February Vice News article that published excerpts of an interview with an anonymous juror, who claimed that "at least five fellow jurors violated the judge's orders by following the case in the media during the trial" and lied to Cogan when asked if they'd been exposed to news coverage that detailed parts of the case that were meant to be excluded from the trial.

In Monday's filing, prosecutors said the court's repeated instruction to jurors, their diligence during the trial, and overwhelming evidence against Guzman show that "the alleged media exposure did not prejudice the defendant."

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