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As deepfake content proliferates online, advancing face manipulation forensics has become crucial. To combat this emerging threat, previous methods mainly focus on studying how to distinguish authentic and manipulated face images. Although impressive, image-level classification lacks explainability and is limited to specific application scenarios, spurring recent research on pixel-level prediction for face manipulation forensics. However, existing forgery localization methods suffer from exploring frequency-based forgery traces in the localization network. In this paper, we observe that multi-frequency spectrum information is effective for identifying tampered regions. To this end, a novel Multi-Spectral Class Center Network (MSCCNet) is proposed for face manipulation detection and localization. Specifically, we design a Multi-Spectral Class Center (MSCC) module to learn more generalizable and multi-frequency features. Based on the features of different frequency bands, the MSCC module collects multi-spectral class centers and computes pixel-to-class relations. Applying multi-spectral class-level representations suppresses the semantic information of the visual concepts which is insensitive to manipulated regions of forgery images. Furthermore, we propose a Multi-level Features Aggregation (MFA) module to employ more low-level forgery artifacts and structural textures. Meanwhile, we conduct a comprehensive localization benchmark based on pixel-level FF++ and Dolos datasets. Experimental results quantitatively and qualitatively demonstrate the effectiveness and superiority of the proposed MSCCNet. We expect this work to inspire more studies on pixel-level face manipulation localization. The codes are available (https://github.com/miaoct/MSCCNet).