# Coefficient data for embedded newform 1638.4.a.e.1.1, downloaded from the LMFDB on 17 December 2025. {"label": "1638.4.a.e.1.1", "an_normalized": [[1.0, 0.0], [-0.7071067811865476, 0.0], [0.0, 0.0], [0.5, 0.0], [0.4472135954999579, 0.0], [0.0, 0.0], [-0.37796447300922725, 0.0], [-0.3535533905932738, 0.0], [0.0, 0.0], [-0.31622776601683794, 0.0], [0.9867644004363173, 0.0], [0.0, 0.0], [-0.2773500981126146, 0.0], [0.2672612419124244, 0.0], [0.0, 0.0], [0.25, 0.0], [-0.3709368382908622, 0.0], [0.0, 0.0], [-0.5675020785219159, 0.0], [0.22360679774997896, 0.0], [0.0, 0.0], [-0.6977477989819978, 0.0], [0.8975185648543653, 0.0], [0.0, 0.0], [-0.8, 0.0], [0.19611613513818404, 0.0], [0.0, 0.0], [-0.18898223650461363, 0.0], [0.3906005389241436, 0.0], [0.0, 0.0], [-0.13325554666502654, 0.0], [-0.1767766952966369, 0.0], [0.0, 0.0], [0.26229195374736647, 0.0], [-0.1690308509457033, 0.0], [0.0, 0.0], [-0.22216079365588823, 0.0], [0.4012845680603073, 0.0], [0.0, 0.0], [-0.15811388300841897, 0.0], 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