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Personnel expenses and employee information - Bonus Expenses (Details) - EUR (€)
€ in Millions
 12 Months Ended
Dec. 31, 2022
Dec. 31, 2021
Dec. 31, 2020
Bonus Expenses [Line Items]      
Bonus expense € 633.4 € 428.1 € 407.9
Board of Management      
Bonus Expenses [Line Items]      
Bonus expense 3.8 4.4 5.4
Former Board of Management      
Bonus Expenses [Line Items]      
Bonus expense 0.0 0.2 0.0
Other Employees      
Bonus Expenses [Line Items]      
Bonus expense € 629.6 € 423.5 € 402.5
Minimum      
Bonus Expenses [Line Items]      
Short-term incentive (in percentage) 0.00%    
Maximum      
Bonus Expenses [Line Items]      
Short-term incentive (in percentage) 126.00%