The nine women and three men got the case Monday after more than three-and-a-half hours of jury instructions from the judge at the Dirksen Federal building.
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They then deliberated for about three hours.
On Tuesday morning, jurors asked their first question, after about 30 minutes of deliberating.
They wanted clarification on one of the charges against one of Burke's co-defendants.
Count 13 is defined as using interstate commerce to facilitate an unlawful activity. It's a charge that only involves Burke's co-defendant, Charles Cui.
Experts say it may indicate that the jury is taking up the counts against the two co-defendants, Cui and Burke's assistant, Pete Andrews, before concentrating on Burke.
The jury was urged by Cui and Andrews' attorneys to do so.
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The question may also indicate the complexity of the charges. Jurors were given 350 pages of jury instructions.
They asked a second question Tuesday afternoon.
Jurors confirmed that Amtrak employees are not considered public.
An attorney for Andrews also said he is in the hospital, and asked if he could remotely join any future hearings.
The jury finished deliberating for the day about 4:45 p.m. They will return at 9 a.m. Wednesday.
Burke faces racketeering, extortion and bribery charges: 14 counts involving four different schemes.
Three involve using his public position to steer tax appeal business to his private law firm from a Burger King in Burke's ward, the Old Post Office and a Binny's Beverage Depot on the Northwest Side.
Prosecutors said he was trying to strong-arm businesses for personal gain.
Will verdict come quickly in Burke trial?
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The big charge against Burke is Count One of the indictment, racketeering, known as RICO. The law was originally used for organized crime.
"There's no other way to say it is just a legally complicated statute, which is an incredibly powerful one for the government when you are at this stage of the case," former federal prosecutor Chris Hotaling said.
For the jury to convict Burke of racketeering, they must agree beyond a reasonable doubt, he committed two "acts" as part of a larger pattern. Prosecutors presented several acts for jurors to choose from.
Burke's attorney said he never demanded anything in exchange for an official act and never received a penny in any of the alleged schemes.
RELATED: Defense attorney of Ed Burke completes closing arguments in federal corruption trial
If Burke is convicted, he could face up to 20 years in prison.
Given the complicated and extensive nature of the case, it's not clear how long it will take the jury to sort through all the evidence and testimony from 38 witnesses before reaching a verdict.
Judge Virginia Kendall said if the jury is still deliberating on Friday, they will be sent home until after New Year's.