What is the regulatory landing distance for turboprops under FAR 121-135?
Each aircraft manufacturer is going to supply that data as part of its Aircraft Operating Manual. Operators must use these documents to determine required landing length, and this computation must be calculated during the planning phase of the flight by taking into consideration the estimated weight of the aircraft at the arrival time, as well as forecast winds, runway conditions and types of runways.

The regulatory "mandate" for doing these computations is found in the text of Parts 121.195 and 121.197, as well as 135.385 and 135.387. The relevant parts of each are pasted below, but the full text should be consulted for additional requirements and possible exemptions.




  121.195. Detination Airport. no person operating a turbine engine powered airplane may take off that airplane unless its weight on arrival, allowing for
  normal consumption of fuel and oil in flight (in accordance with the
  landing distance set forth in the Airplane Flight Manual for the
  elevation of the destination airport and the wind conditions
  anticipated there at the time of landing), would allow a full stop
  landing at the intended destination airport within 60 percent of the
  effective length of each runway described below from a point 50 feet
  above the intersection of the obstruction clearance plane and the
  runway.





  121.197.   Alternate airports. No person may list an airport as an alternate airport in a dispatch or flight release for a turbine engine
  powered airplane unless (based on the assumptions in §121.195 (b))
  that airplane at the weight anticipated at the time of arrival can be
  brought to a full stop landing within 70 percent of the effective
  length of the runway from a point 50 feet above the intersection of
  the obstruction clearance plane and the runway.





  135.385. Destination Airport. No person operating a turbine engine powered airplane may take off that airplane unless its weight on
  arrival, allowing for normal consumption of fuel and oil in flight (in
  accordance with the landing distance in the Airplane Flight Manual for
  the elevation of the destination airport and the wind conditions
  expected there at the time of landing), would allow a full stop
  landing at the intended destination airport within 60 percent of the
  effective length of each runway described below from a point 50 feet
  above the intersection of the obstruction clearance plane and the
  runway.





  135.387. Alternate Airports. No person may select an airport as an alternate airport for a turbine
  engine powered airplane unless (based on the
  assumptions in §135.385(b)) that airplane, at the weight expected at
  the time of arrival, can be brought to a full stop landing within 70
  percent of the effective length of the runway for
  turbo-propeller-powered airplanes and 60 percent of the effective
  length of the runway for turbojet airplanes, from a point 50 feet
  above the intersection of the obstruction clearance plane and the
  runway.