A B737-300 FLYING IN ZLA AIRSPACE ENCOUNTERS WAKE TURB WHEN FLYING BEHIND A B757.

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OUR B737-300 WAS IN CRUISE AT FL280. WE HAD VISUAL CONTACT AND TCASII ON ANOTHER ACFT AT FL290 APPROX 8 MI AHEAD AND SLIGHTLY R (ABOUT 1 O'CLOCK). THE OTHER ACFT WAS SLOWLY XING IN FRONT OF OUR PATH REMAINING 1000 FT ABOVE. AS WE GOT TO ABOUT WHERE HIS PATH WOULD HAVE BEEN OVER OURS; WE EXPERIENCED A PERIODIC BUFFET ON OUR R WING FOR ABOUT 4 SECONDS FOLLOWED BY A LOSS OF LIFT ON THE R WING WITH THE ACFT ROLLING ABOUT 35 DEGS R WING DOWN. THE AUTOPLT WAS ON AND HELD THE ROLL TO 35 DEGS FOR A SECOND OR 2; THEN SEEMED AS IF IT MIGHT NOT BE ABLE TO MAINTAIN; SO I KICKED OFF THE AUTOPLT AND WAS ABLE TO ROLL WINGS LEVEL AFTER ANOTHER SECOND OR TWO. I NEEDED ABOUT 3/4 AILERON INPUT TO RECOVER. I ASKED ZLA WHAT TYPE ACFT THAT WAS AHEAD AT FL290 AND THEY REPLIED B757. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR PARTICIPATED IN THE WAKE TURB STRUCTURED CALLBACK PROGRAM. THERE WAS ALWAYS A 1000 FT VERT SEPARATION THROUGHOUT THIS INCIDENT. THE B737 WAS ROLLED INTO A 30 DEG R BANK; BUT HAD ENOUGH AILERON CTL TO KEEP THE ACFT FROM ROLLING FURTHER INTO A STEEP BANK. THE FLC RECOGNIZED THE BUFFETING ON THE R WING AS A PRELIMINARY WARNING OF WAKE. THE CAPT DISCONNECTED THE AUTOPLT AND APPLIED CTLS AS NEEDED TO GET WINGS BACK TO LEVEL. WHEN FLC MENTIONED TO ARTCC THEY HAD ENCOUNTERED WAKE FROM A B757 SEVERAL MI AHEAD; THE CTLR WAS VERY SURPRISED; AS IF WAKE COULD NOT BE EXPERIENCED FROM A B757 AT FLT ALTS. THIS WAS AN EVENT OF SHORT DURATION (5-6 SECONDS) AND OF LESSER MAGNITUDE (2 ON A SCALE OF 5).