Definition of "enigmatically"

He hurried out, glad to escape, leaving Cora frowning enigmatically under her hair.

1938, Norman Lindsay, Age of Consent, 1st Australian edition, Sydney, N.S.W.: Ure Smith, published 1962, page 234

"Leila!" she said enigmatically. "Have you seen her?" / "I went to her flat last week with Dad—he likes her." / "Delilah is her real name, you know. All men like her. And Captain Fort is her lover."

1919 October, John Galsworthy, chapter I, in Saint’s Progress, London: William Heinemann, published December 1919, part III, 1 §, page 220