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It is a widely accepted fact that state-sponsored Twitter accounts operated during the 2016 US presidential election, spreading millions of tweets with misinformation and inflammatory political content. Whether these social media campaigns of the so-called "troll" accounts were able to manipulate public opinion is still in question. Here, we quantify the influence of troll accounts on Twitter by analyzing 152.5 million tweets (by 9.9 million users) from that period. The data contain original tweets from 822 troll accounts identified as such by Twitter itself. We construct and analyse a very large interaction graph of 9.3 million nodes and 169.9 million edges using graph analysis techniques, along with a game-theoretic centrality measure. Then, we quantify the influence of all Twitter accounts on the overall information exchange as is defined by the retweet cascades. We provide a global influence ranking of all Twitter accounts and we find that one troll account appears in the top-100 and four in the top-1000. This combined with other findings presented in this paper constitute evidence that the driving force of virality and influence in the network came from regular users - users who have not been classified as trolls by Twitter. On the other hand, we find that on average, troll accounts were tens of times more influential than regular users were. Moreover, 23% and 22% of regular accounts in the top-100 and top-1000 respectively, have now been suspended by Twitter. This raises questions about their authenticity and practices during the 2016 US presidential election.