enigmatically

Acting in a manner that suggests an enigma.

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

Behaving mysteriously or strangely.

"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."

Functioning in a way that is unexplainable.