Is there a tool to download Twitter followers and following list?

Phantombuster can do it. Check out this API: Twitter Follower Collector You can also use phantombuster to automate mass follow to build your audience.

What do you want to extract the list? You can dirrectly run ppc campaign targeting the follower of a specific account

You can download someone else’s Twitter followers and following list with https://www.followersanalysis.com/. Downloading or exporting Twitter followers and following list is easy if done the right way. FollowersAnalysis has helped me export mine as well as someone else’s Twitter followers and following list easily and helped me source research-grade data. You get a detailed Twitter followers list that has numerous insightful metrics that you cannot source otherwise. Although Twitter does provide account data to owners, the data is in JSON format which is not considered a highly versatile format for deriving analytics.

ExportData allows downloading an unlimited amount of Twitter followers & followings of any public Twitter account. It also supports extracting historical tweets since the early days of Twitter in 2006. It gathers hourly historical Twitter trends in 63 countries and ~400 cities as well.

Yes, there is a tool called TwFollow that allows you to download Twitter followers and following lists. TwFollow is a Chrome Extension that can be installed from Chrome Web Store. Once installed, you can use TwFollow to export and download the lists of your Twitter followers and the accounts you are following.