Question: Lincoln Center, Kansas is the county seat of Lincoln County and holds a population of what?

Context paragraphs:
Lincoln County, Nebraska: Lincoln County is a county located in the U.S. state of Nebraska.  As of the 2010 census, the population was 36,288.  Its county seat is North Platte.  Despite the county's name, the state capital city of Lincoln is not located in or near Lincoln County.

Kemmerer, Wyoming: Kemmerer is the largest city in and the county seat of Lincoln County, Wyoming, United States.  The population was 2,656 at the 2010 census.  As the county seat of Lincoln County, Kemmerer is the location of the Lincoln County Courthouse.

Carrizozo, New Mexico: Carrizozo is a town in Lincoln County, New Mexico and is the county seat with a population of 996 at the 2010 census.  Founded in 1899, the town provided the main railroad access for Lincoln County, and the town experienced significant population growth in the early decades of the 1900s.  However, with declining relevance of the railroad, the population of the town has gradually declined.  The town is located at the intersection of U.S. Route 54 and U.S. Route 380.

Lincoln County, Arkansas: Lincoln County is located between the Arkansas Timberlands and Arkansas Delta in the U.S. state of Arkansas.  It is also within the Pine Bluff metro area, and on the outer edge of the Central Arkansas region.  The county is named for Abraham Lincoln, the 16th President of the United States.  Created as Arkansas's 65th county on March 28, 1871, Lincoln County has three incorporated cities, including Star City, the county seat and most populous city.  The county contains 46 unincorporated communities and ghost towns, Cane Creek State Park at the confluence of Cane Creek and Bayou Bartholomew, and nine listings on the National Register of Historic Places to preserve the history and culture of the county.

Pioche, Nevada: Pioche is an unincorporated town in Lincoln County, Nevada, United States, about 180 mi northeast of Las Vegas.  U.S. Route 93 is the main route to Pioche and bypasses the town center just to the east, with Nevada State Route 321 and Nevada State Route 322 providing direct access.  Its elevation is 6060 ft above sea level.  Pioche is the county seat of Lincoln County.  It is named after François Louis Alfred Pioche, a San Francisco financier and land speculator originally from France.  The town's population was 1,002 at the 2010 census.

Lincoln County, Kansas: Lincoln County (standard abbreviation: LC) is a county located in the U.S. state of Kansas.  As of the 2010 census, the county population was 3,241.  The largest city and county seat is Lincoln Center.

Lincoln Municipal Airport (Kansas): Lincoln Municipal Airport (FAA LID: K71) is a public use airport in Lincoln County, Kansas, United States.  It is owned by the City of Lincoln, also known as Lincoln Center, and located two nautical miles (4 km) northwest of the central business district.

Lincoln Center, Kansas: Lincoln Center, more commonly known as Lincoln, is a city in and the county seat of Lincoln County, Kansas, United States.  As of the 2010 census, the city population was 1,297.

Ivanhoe, Minnesota: Ivanhoe is a city in Lincoln County, Minnesota, United States.  The population was 559 at the 2010 census.  Since 1904 it has been the county seat of Lincoln County and is now the least populous county seat in Minnesota.

Hamlin, West Virginia: Hamlin, originally named "Hamline," is a town in Lincoln County, West Virginia, United States, along the Mud River.  The population was recorded as 1,142 at the 2010 census.  It is the county seat of Lincoln County.  Hamlin is a part of the Huntington-Ashland, WV-KY-OH, Metropolitan Statistical Area (MSA).  As of the 2010 census, the MSA had a population of 287,702.  New definitions from February 28, 2013 placed the population at 363,000.

Supporting paragraphs: Lincoln County, Kansas Lincoln Center, Kansas
Answer: 1,297