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Share-based payments - Prior VSOP - Development of the virtual shares in this program granted to management and key employees (Details)
€ / shares in Units, € in Millions
12 Months Ended
Mar. 26, 2024
shares
Mar. 22, 2024
shares
Aug. 14, 2023
Dec. 14, 2022
€ / shares
shares
Dec. 12, 2022
shares
Aug. 14, 2022
Oct. 19, 2021
EUR (€)
€ / shares
shares
Oct. 18, 2021
shares
Mar. 11, 2021
EUR (€)
€ / shares
shares
Mar. 10, 2021
shares
Aug. 14, 2020
Dec. 31, 2023
Option
shares
Dec. 31, 2022
Option
shares
Dec. 31, 2021
Option
shares
Prior VSOP                            
Share-based payments                            
Right to exercise percentage of vested virtual shares     10.00%     10.00%         10.00% 10.00%    
Number of shares issued for exercise of stock options | shares   786,746     777,260     765,223   759,677        
Number of shares received | shares   786,746     777,260     765,223   759,677   0 777,260  
Transfer from shareholders to company | shares 786,746     777,260     523,897   390,023          
Treasury shares transferred | shares             241,326   369,654          
Provision for employer taxes | €             € 8   € 26          
Average share price | € / shares       € 6.96     € 34.56   € 69.69          
Former Chief Executive Officer Grant                            
Share-based payments                            
Outstanding at the beginning of the period | Option                       5,614,246 6,426,365 7,951,265
Forfeited during the period | Option                       (11,091) (34,859)  
Exercised during the period | Option                         (777,260) (1,524,900)
Outstanding at the end of the period | Option                       5,603,155 5,614,246 6,426,365
Thereof vested | shares                       5,588,513 5,509,886 6,365,422
Thereof exercisable | Option                       0 0 0