Using multicolored flow charts in an attempt to simplify complex transactions, prosecutors tried to show that Mr. Manafort concealed more than $60 million in income in 31 foreign bank accounts opened in the names of shell companies.

The money came from Ukrainian oligarchs who paid Mr. Manafort to boost the political career of Viktor F. Yanukovych, a pro-Russian politician who, with Mr. Manafort’s help was elected president of Ukraine in 2010.