Payne was hired in July as an academy cadet and graduated in November.
Investigators have not identified a motive for the ambush shooting of the 22-year-old officer as she investigated a vehicle accident.
Then a gunman emerged from the shadows.
This portrait of Natalie Corona by Richard Laus shows the Davis Police officer who was killed in the line of duty on Thursday.
Police say Limbaugh also shot a flurry of bullets toward others, striking a bystander's backpack and a firefighter in the boot, before fleeing into a home.
Police found the handguns in the home. He had left a backpack at the crime scene with information that led the officers to his home, Pytel said.
No one else was injured in the attack besides Corona, who died at the UC Davis Medical Center in Sacramento. She had just completed six months of field training when she was ambushed while checking driver's licenses during a routine call.
"I'd really like to see as many people as possible from the community attend", Pytel said during Saturday's vigil at Davis' Central Park, which was attended by at least 1,000 people. There, the Sacramento Bee reports, several members of the Davis police force shared anecdotes illustrating Corona's commitment to helping others. Then without warning, he opened fire, killing the rookie officer.
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"There have been a lot of rumors as to why this happened, why he did what he did, and we're hoping this sheds some light", Doroshov said.
In an interview with Fox40, Corona's father described a recent incident in which his daughter helped a man she arrested, leaving him in tears. They were holding a meeting in a nearby church when the shots rang out Thursday night.
She replied, "I know Dad, but I don't mind'".
Police spokesman Lt. Paul Doroshov said the paper was found face up on the gunman's bed.
In the letter, Limbaugh said he notified internal affairs, the media and the Federal Bureau of Investigation. I am highly sensitive to its affect in my inner ear.
"I did my best to appease them, but they have continued for years and I can't live this way anymore", the letter read in part. A suspect walked up and fired at Corona, he said.
Corona is survived by her parents, Merced and Lupe, and her sisters, Jackie, Cathy and Cindy.