The man accused of trying to kill President Donald Trump at a White House Correspondents’ dinner has agreed to remain jailed for now as his lawyers cast doubt on the Department of Justice’s account of the shooting. Cole Tomas Allen did not enter a plea during a brief appearance before U.S. Magistrate Moxila Upadhyaya on Thursday. Prosecutors allege Allen planned his attack for weeks, and tracked Trump’s movements online before he ran through a magnetometer at the Washington Hilton Saturday night while holding a long gun and disrupted one of the highest-profile annual events in the nation’s capital. Allen was injured during the attack but was not shot. A Secret Service officer was shot but was wearing a bullet-resistant vest and survived, officials say. Prosecutors have said they believe Allen fired his shotgun at least once and that a Secret Service agent fired five shots. They have not publicly confirmed that it was Allen’s bullet that struck the agent’s vest.…