LAS VEGAS — Investigators are looking into whether gunman Stephen Paddock scoped out bigger music festivals in Las Vegas and Chicago — and perhaps Boston’s Fenway Park — before setting up his perch in a casino hotel and raining deadly fire on country music fans.

Paddock booked rooms overlooking the Lollapalooza festival in Chicago in August and the Life Is Beautiful show near the Vegas Strip in late September, according to authorities reconstructing his movements before he undertook the deadliest mass shooting in modern U.S. history.

It was not clear if he contemplated massacres at those sites.

Investigators looking into Paddock also came across mention of Fenway Park, Boston police Lt. Detective Mike McCarthy said, though he provided no further details.

The details came to light as investigators struggled to figure out why the high-stakes gambler opened fire on a crowd of 22,000 Sunday night from the 32nd floor of the Mandalay Bay hotel casino in Las Vegas. He killed 58 people and injured nearly 500 before taking his own life.