Vacantly

Tom had a cigarette hanging out of his mouth while he vacantly stared up at the sky.

Source: tatoeba (2249892)

With an air of nonchalance which, under the circumstances, seemed to me to border upon affectation, he lounged up and down the pavement, and gazed vacantly at the ground, the sky, the opposite houses and the line of railings.

Source: tatoeba (6303816)

Mao gave no indication that he had heard or understood Jakob; his clouded eyes were fixed vacantly on one of the long windows of the old Ming dwelling beyond which the waters of Chung Nan Hai — the Central and South lakes — sparkled in the afternoon sunshine.

Source: wiktionary