Time-Life also wanted to expand, as its existing space in 1 Rockefeller Plaza had become insufficient by 1953. In August of that year, Rockefeller Center Inc. bought a tract of land on the west side of Sixth Avenue between 50th and 51st streets. Rockefeller Center's managers originally wanted to build an extra NBC studio or a Ford vehicle showroom on the site. However, they changed their minds once they saw Time Inc.'s expansion needs: the company wanted to have its headquarters in a single building. As they would outgrow their existing space in 1 Rockefeller Plaza by 1954, the company would have to move elsewhere. Not wanting to lose Time Inc.'s tenancy, the complex's managers hired Harrison & Abramovitz, composed of Wallace Harrison and Max Abramovitz, to create plans for a building on the newly acquired plot that could house both NBC and Time. NBC later dropped out of the deal because its CEO, David Sarnoff, dissented.In 1956, two years after the demolition of the Center Theatre, officials announced the construction of a new tower, the Time-Life Building, on the western side of Sixth Avenue between 50th and 51st Streets. The 500-foot (150 m), $7 million building ($97.2 in 2018 dollars) would include connections to the existing passageway system and to the Roxy Theater directly to its west. The tower would rise as a 48-story slab, with a plaza to the east and an eight-story annex along its western and northern sides. One of Rockefeller Center's subsidiaries, Westprop Inc., bought the air rights to the original Roxy Theater located next door so that the new tower could conform to the Zoning Resolution of 1916. Time Inc. and Rockefeller Center formed a joint venture, Rock-Time Inc., which would share the tower's rent income between them. Construction on the Time-Life Building's steelwork started in April 1958, and the structure topped out in November of that year. The cornerstone of the building was laid in June 1959, after the building's structure had been completed, and the first tenants began moving into the tower in December 1959.During this time, plans called for Rockefeller Center to expand northward. Rockefeller Center, Uris Buildings Corporation, and Webb and Knapp formed another joint venture, Rock-Uris Corp., to construct a hotel to the west of 75 Rockefeller Center. However, Webb and Knapp faced monetary shortages, and the joint venture found that a hotel was not the most profitable use of the land. The joint venture instead decided to construct a glass-and-concrete 43-story office building on the site, with connections to the complex's underground concourse. In 1961, the building was named after Sperry Corporation, which leased eight floors in the future building. The planned hotel was moved to another site two blocks north, on the west side of Sixth Avenue between 53rd Streets. This became the New York Hilton at Rockefeller Center, which opened in 1963. The hotel's name was misleading because it was located outside the complex and not connected to the underground mall. The mall could not be extended anyway because the 53rd Street subway was in the way. Further expansion of Rockefeller Center on the west side of Sixth Avenue, between the Hilton and the new Time-Life Building, was not possible because the Equitable Life Assurance Society had built a tower in between the two properties.

Question: What building had the Roxy Theater directly to its west?
Answer: the Time-Life Building