Discussion about the social network Twitter often concerns its role in political discourse, involving the question of when an expression of opinion becomes offensive, immoral, and/or illegal, and how to deal with it. Given the growing amount of offensive communication on the internet, there is a demand for new technology that can automatically detect hate speech, to assist content moderation by humans. This comes with new challenges, such as defining exactly what is free speech and what is illegal in a specific country, and knowing exactly what the linguistic characteristics of hate speech are. To shed light on the German situation, we analyzed over 50,000 right-wing German hate tweets posted between August 2017 and April 2018, at the time of the 2017 German federal elections, using both quantitative and qualitative methods. In this paper, we discuss the results of the analysis and demonstrate how the insights can be employed for the development of automatic detection systems.