Police identified the shooters as Jerad Miller, 31, and his wife, Amanda Miller, 22. The couple shot and killed Igor Soldo and Alyn Beck, two Las Vegas police officers, inside a CiCi’s Pizza. They then went into a nearby Wal-Mart, where they fatally shot Joseph Wilcox, who was shopping in the store and tried to stop the attackers. After a firefight with police officers inside the store, the couple took their own lives.

While authorities said they believed this was an isolated, random act, they also said they were investigating the ideology of the two shooters. They believe that the fact that they placed a swastika on the bodies of one of the people they killed Sunday suggested that they equated law enforcement “with the Nazi movement,” McMahill said. Police also said they are investigating reports that one or both of the Millers went to the Nevada ranch of Cliven Bundy during a standoff with federal authorities earlier this year.

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A neighbor told the Los Angeles Times that on Sunday morning, Jerad Miller had pulled out swastikas and an Army insignia and said he was going to put one on every police officer they killed. “I’m thinking, ‘Right. They’re not going to do that,” Kelly Fielder said. “I should have called the cops. I feel I have the deaths of five people on my shoulders. The signs were there.”

Fielder described Jerad Miller as hateful of the government and of President Obama, while she said Amanda Miller was “a good girl who would do anything to make her man happy.”

The pair had numerous handguns, a shotgun and hundreds of rounds of ammunition with them on Sunday. “It appeared as if they were prepared for a lengthy gun battle,” McMahill said.

Authorities released additional details about how the shooting unfolded in the strip mall about 11 miles away from the lights of the Las Vegas Strip. The couple first went into a CiCi’s Pizza at about 11:20 a.m., finding two officers with the Las Vegas Metropolitan Police Department on their lunch break.

Jerad Miller shot and killed Officer Igor Soldo, 31, who was married with a baby, police said. Both Millers then fired multiple shots at Alyn Beck, 41, a married father of six. The pair then took the slain officers out of their booth and laid them on the ground, covering Beck with a yellow Gadsden flag that read “Don’t Tread on Me” and placing a swastika on his body.

They also pinned a note to Salvo that read, “This is the beginning of the revolution,” McMahill said, and they repeated that phrase to people in the restaurant before leaving and heading to a nearby Wal-Mart.

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Inside the Wal-Mart, Jerad Miller fired a single shot and told the shoppers to get out, again talking about “a revolution.” Joseph Wilcox, who was standing near the registers and carrying a concealed weapon, told his friend he was going to confront the shooters.

Wilcox, 31, “immediately and heroically moved towards” Miller, McMahill said. But as went to confront the shooter, he walked right by Amanda Miller, who shot and killed Wilcox.

“Joseph died attempting to protect others,” Clark County Sheriff Douglas C. Gillespie said at the news conference. “His death is completely senseless.”

Police had by this point received multiple 911 calls from the restaurant and the store. Two five-member police teams wielding rifles and other weapons went into the store, one near the front and one in the back, and began exchanging gunfire with the shooters. Both shooters had gunshot wounds at that point, police said, though it’s unclear exactly when they were wounded and by whom.

The Millers moved to the back of the store, positioned so they could engage officers who approached, McMahill said. Police were able to observe this movement from the Wal-Mart’s surveillance area. Jerad Miller then lay down in front of his wife, who fired several rounds at him, killing him. She took her handgun and “ended her own life with one gunshot wound to the head,” McMahill said.

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Jerad Miller had posted a lengthy statement on his Facebook page last week writing that the country was facing oppression that could only be stopped “with bloodshed.”

The couple apparently was committed to an anti-government belief system typified by hatred of law enforcement and the notion that the federal government has no authority over them, said Heidi Beirich, director of the Southern Poverty Law Center’s Intelligence Project.

“This isn’t the first attack from people who show these kinds of beliefs,” she said Monday in a telephone interview from the organization’s headquarters in Montgomery, Ala. “They come to see the government as the enemy. The fact that these two shot cops is right in that line of thinking.”

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In 2010, a similar strain of anti-government rage resulted in two family members killing two police officers in West Memphis, Ark. That episode concluded in a Wal-Mart parking lot, as Jerry Ralph Kane Jr., and his 16-year-old son, Joseph, died in a firefight with law enforcement officials.

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Earlier this year, a man plotted to kidnap and kill police officers in Las Vegas as part of the anti-government “sovereign citizen” movement, which believes that governments operate illegally. The FBI has called the sovereign citizen extremists a “growing domestic threat,” one that has had violent and fatal encounters with law enforcement officials.

There were 43 violent incidents between law enforcement officials and extremists, with 30 police officers shot and 14 killed, between 2009 and 2013, according to the Anti-Defamation League.

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Police said Monday they were investigating reports that one or both of the Millers went to Bundy’s ranch earlier this year. Bundy’s long dispute with the federal government became a national story in April when an armed group of supporters converged on his Nevada ranch as part of a standoff with Bureau of Land Management agents looking to seize his cattle. Jerad Miller had told people that he went to the ranch but was turned away because he was a convicted felon.

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Ammon Bundy, Cliven Bundy’s son, told the Associated Press on Monday that the Millers were at the ranch for a few days before being told to leave because of their conduct.

Meanwhile, a video located by ThinkProgress on Monday showed a man identified as “Jarad Miller” being interviewed at the Bundy ranch. The Post has not confirmed that this is the same Miller named as one of the shooters in Las Vegas.

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Bundy’s wife, Carol, said Sunday that the shooting and the standoff at the ranch were not related.

“I have not seen or heard anything from the militia and others who have came to our ranch that would, in any way, make me think they had an intent to kill or harm anyone,” she told the Las Vegas Review-Journal.

Interior Secretary Sally Jewell on Monday highlighted the reports saying the shooters had gone to Bundy’s ranch, saying that the rancher had “put our people in grave danger by calling in armed citizens from around the country.”

This post has been updated to add the comment from Ammon Bundy and the video.