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Advancements in science rely on data sharing. In medicine, where personal data are often involved, synthetic tabular data generated by generative adversarial networks (GANs) offer a promising avenue. However, existing GANs struggle to capture the complexities of real-world tabular data, which often contain a mix of continuous and categorical variables with potential imbalances and dependencies. We propose a novel correlation- and mean-aware loss function designed to address these challenges as a regularizer for GANs. To ensure a rigorous evaluation, we establish a comprehensive benchmarking framework using ten real-world datasets and eight established tabular GAN baselines. The proposed loss function demonstrates statistically significant improvements over existing methods in capturing the true data distribution, significantly enhancing the quality of synthetic data generated with GANs. The benchmarking framework shows that the enhanced synthetic data quality leads to improved performance in downstream machine learning (ML) tasks, ultimately paving the way for easier data sharing.