The Copenhagen Manifesto addresses the transformative impact of Generative Artificial Intelligence (AI) on software engineering, originating from the Copenhagen Symposium on Human-Centered Software Engineering AI. Held at Aalborg University Copenhagen from November 26-29, 2023, this symposium was the birthplace of the manifesto. It highlights the dual role of software engineering researchers and practitioners in integrating Generative AI while addressing the ethical, social, legal, and technical challenges it poses. The manifesto emphasizes the importance of ethical and sustainable development, human-centric design, transparency, inclusivity, and environmental sustainability. It calls for a shift towards integrating human values and ethical considerations into technological advancements, ensuring that Generative AI enhances human capabilities and adheres to principles of fairness, transparency, and societal well-being.