Does Nagilum have unlimited powers?

Is Nagilum omnipotent and omnipresent? He's not omniscient as he is doing an experiment to learn more about humans.

He seems omnipotent as he can conjure up any reality (though it is not clear if this requires the expense of limited resources). He seems omnipresent, or at least have the ability to transport anywhere. Even when the enterprise was out of the void Nagilum communicated to Picard on a computer.