Interviews with people who have been questioned by Federal Bureau of Investigation agents, or who are cooperating with their inquiry, suggest it is turning into an examination of the police and prosecutor’s outsize, unchecked power in their domain, the eastern half of Long Island, where glaring poverty and fantastic riches exist side by side. Federal investigators appear to be pursuing leads that broadly explore questions of influence and corruption in the criminal justice system. One avenue of inquiry has led agents to seek evidence about whether judgeships are for sale in Suffolk County, according to two people with knowledge of the inquiries.

The United States attorney’s office in Brooklyn, which is overseeing the investigation, has also taken a dim view of some of the surveillance practices employed by the Suffolk County district attorney’s office.

One questionable episode involved a Suffolk County wiretap in which the district attorney’s office listened in on phone calls involving at least a half-dozen F.B.I. agents and assistant United States attorneys, according to three people who have been told about the event. In another episode, a contractor for the district attorney’s office installed a GPS device on a deputy police commissioner’s car at Mr. Burke’s request, in order “to dig up blackmail dirt on her,” a federal prosecutor, James Miskiewicz, said last month in a federal court hearing shortly after Mr. Burke was arrested.

Mr. Spota has denied any knowledge of the episode involving the tracking device. Mr. Miskiewicz called the event “something out of the K.G.B.”

Such comparisons are common in Suffolk County, where officers wield not only police power, but also a degree of political power that would feel foreign in the police departments of most big cities. In Suffolk County, policing is not a middle-class job — officers can make $125,000 in base pay, about $50,000 more than their counterparts in New York City. That figure does not include overtime pay, which can be substantial, or the extra money officers receive for each year on the job. Detectives and sergeants have been known to earn more than $200,000 a year. The police unions on Long Island are so wealthy they have formed a “super PAC” to flood local elections with campaign donations.

Central to the political order is the district attorney, Mr. Spota. In the past year, Justice Department officials have met with county employees, politicians and former police officers who have said that Suffolk County investigations and prosecutions — as well as decisions not to prosecute — are often swayed by political considerations, according to interviews with more than five people who have spoken to F.B.I. agents or prosecutors.