ChatGPT is notorious for its intransparent behavior. This paper tries to shed light on this, providing an in-depth analysis of the dark personality traits and conspiracy beliefs of GPT-3.5 and GPT-4. Different psychological tests and questionnaires were employed, including the Dark Factor Test, the Mach-IV Scale, the Generic Conspiracy Belief Scale, and the Conspiracy Mentality Scale. The responses were analyzed computing average scores, standard deviations, and significance tests to investigate differences between GPT-3.5 and GPT-4. For traits that have shown to be interdependent in human studies, correlations were considered. Additionally, system roles corresponding to groups that have shown distinct answering behavior in the corresponding questionnaires were applied to examine the models' ability to reflect characteristics associated with these roles in their responses. Dark personality traits and conspiracy beliefs were not particularly pronounced in either model with little differences between GPT-3.5 and GPT-4. However, GPT-4 showed a pronounced tendency to believe in information withholding. This is particularly intriguing given that GPT-4 is trained on a significantly larger dataset than GPT-3.5. Apparently, in this case an increased data exposure correlates with a greater belief in the control of information. An assignment of extreme political affiliations increased the belief in conspiracy theories. Test sequencing affected the models' responses and the observed correlations, indicating a form of contextual memory.