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intently; single-mindedly; devotedly; solely; earnestly; with all one's heart
「頓」 has other readings with different meanings.
彼女は頓謝り続けるばかりで説明がなかった。
She kept apologizing earnestly over and over without ever explaining herself.
頓走り続けてようやくゴールにたどり着いた。
The dream I earnestly wished for came true.
頓勉強に打ち込んだおかげで試験に合格した。
I was earnestly waiting for her return.