"Synthetic samples" based on large language models (LLMs) have been argued to serve as efficient alternatives to surveys of humans, assuming that their training data includes information on human attitudes and behavior. However, LLM-synthetic samples might exhibit bias, for example due to training data and fine-tuning processes being unrepresentative of diverse contexts. Such biases risk reinforcing existing biases in research, policymaking, and society. Therefore, researchers need to investigate if and under which conditions LLM-generated synthetic samples can be used for public opinion prediction. In this study, we examine to what extent LLM-based predictions of individual public opinion exhibit context-dependent biases by predicting the results of the 2024 European Parliament elections. Prompting three LLMs with individual-level background information of 26,000 eligible European voters, we ask the LLMs to predict each person's voting behavior. By comparing them to the actual results, we show that LLM-based predictions of future voting behavior largely fail, their accuracy is unequally distributed across national and linguistic contexts, and they require detailed attitudinal information in the prompt. The findings emphasize the limited applicability of LLM-synthetic samples to public opinion prediction. In investigating their contextual biases, this study contributes to the understanding and mitigation of inequalities in the development of LLMs and their applications in computational social science.