Boston Marathon Bomber Dzhokhar Tsarnaev's convictions or death sentence should be tossed because it was impossible for him to get a fair trial in the same city where the shrapnel-packed, pressure cooker bombs exploded, his lawyers told a federal appeals court on Thursday.

In a 500-page brief filed in the 1st U.S. District Court of Appeals, Tsarnaev's legal team outlined a host of other problems with his 2015 trial, during which the defense admitted from the outset that he and his older brother carried out the attack. His appellate lawyers are also pointing to issues with jurors, certain testimony from surviving victims and the defense's inability to tell jurors about links between Tsarnaev's brother and an unsolved triple killing in 2011.

His lawyers argue the trial court judge's "first fundamental error" was denying the defense's repeated requests to move the case out of a city that was "traumatized by the bombings, ordered to shelter in place during the manhunt, saturated by prejudicial publicity and united in the Boston Strong movement."

"This case should not have been tried in Boston," the attorneys wrote.

Tsarnaev was sentenced to death just over two years after he and his brother set off bombs near the Boston Marathon's finish line on April 15, 2013, killing three people and wounding more than 260. He was convicted of all 30 charges against him, including conspiracy and use of weapon of mass destruction.

Tsarnaev admitted at his sentencing that he committed the attack— saying "If there's any lingering doubt about that, let there be no more" — and apologized to victims and their loved ones. The defense had sought to portray Tsarnaev as an impressionable teenager who was lured by his brother into participating in the deadly plot.

Tsarnaev, now 25, is behind bars at the supermax prison in Florence, Colorado. His 26-year-old brother, Tamerlan Tsarnaev, died in a gunbattle with police a few days after the bombing.

His lawyers pushed several times to move the trial, arguing the intense media scrutiny and number of people touched by the bombings in Boston would taint the jury pool. But U.S. District Judge George O'Toole refused, saying he believed a fair and impartial jury in the city could be found.

A three judge panel of the 1st Circuit agreed, noting that other high-profile terrorism cases such as the 1993 World Trade Center bombing took place in the cities where the attacks occurred.

Among the dozens of other issues Tsarnaev's lawyers are raising on appeal are two jurors they say should have been dismissed for lying to the court about their online comments and discussions about the case before the trial.

One juror said in Twitter posts that that she was "locked down" with her family and retweeted another post calling Tsarnaev a "piece of garbage," but told the court she had not commented on the case or been asked to shelter in place, the attorneys say. On the day of Tsarnaev's sentencing, the juror changed her Facebook profile picture to an image that said "BOSTON STRONG," the attorneys say.

Tsarnaev's lawyers are also challenging the judge's refusal to allow the defense to tell the jury about evidence tying Tamerlan to the killings of three people in the Boston suburb of Waltham in 2011. The defense sought to use the killings to underscore their argument that Tamerlan was the mastermind and coerced his brother into participating in the attacks.

Prosecutors have said Tamerlan's friend, Ibragim Todashev, implicated him in the killings of three men whose bodies were found sprinkled with marijuana, their throats cut. Todashev was shot to death by an FBI agent after authorities said he charged another investigator with a pole while being questioned about the Tsarnaevs.

"This evidence that Tamerlan was a cold-blooded killer who convinced a friend to join him in his crimes strongly supported the defense's central argument in mitigation: 26-year-old Tamerlan, a former New England Golden Gloves heavyweight boxing champion, was a violent man who planned and led the bombings, and Jahar, his 19-year-old younger brother, who had no history of violence, participated in it only under Tamerlan's influence," his lawyers wrote.

Tamerlan was never charged in the killings, which prosecutors have said remain under investigation.

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This story has been corrected to show that the Boston Marathon bomber's first name is Dzhokhar, not Dzkhokhar.

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