Question: At the end of what year did the tribes from the place where the Rossen culture is located invade the Roman Empire?

Knowledge 1: Rössen culture
The Rössen culture is important as it marks the transition from a broad and widely distributed tradition going back to Central Europe's earliest Neolithic LBK towards the more diversified Middle and Late Neolithic situation characterised by the appearance of complexes like Michelsberg and Funnel Beaker Culture. [SEP] Knowledge 2: Middle Ages
In 376, the Ostrogoths, fleeing from the Huns, received permission from Emperor Valens (r. 364–378) to settle in the Roman province of Thracia in the Balkans. The settlement did not go smoothly, and when Roman officials mishandled the situation, the Ostrogoths began to raid and plunder.[D] Valens, attempting to put down the disorder, was killed fighting the Ostrogoths at the Battle of Adrianople on 9 August 378. As well as the threat from such tribal confederacies from the north, internal divisions within the empire, especially within the Christian Church, caused problems. In 400, the Visigoths invaded the Western Roman Empire and, although briefly forced back from Italy, in 410 sacked the city of Rome. In 406 the Alans, Vandals, and Suevi crossed into Gaul; over the next three years they spread across Gaul and in 409 crossed the Pyrenees Mountains into modern-day Spain. The Migration Period began, where various people, initially largely Germanic peoples, moved across Europe. The Franks, Alemanni, and the Burgundians all ended up in northern Gaul while the Angles, Saxons, and Jutes settled in Britain. In the 430s the Huns began invading the empire; their king Attila (r. 434–453) led invasions into the Balkans in 442 and 447, Gaul in 451, and Italy in 452. The Hunnic threat remained until Attila's death in 453, when the Hunnic confederation he led fell apart. These invasions by the tribes completely changed the political and demographic nature of what had been the Western Roman Empire.
Knowledge 1: Rössen culture
The Rössen culture is important as it marks the transition from a broad and widely distributed tradition going back to Central Europe's earliest Neolithic LBK towards the more diversified Middle and Late Neolithic situation characterised by the appearance of complexes like Michelsberg and Funnel Beaker Culture. [SEP] Knowledge 2: Roman Republic
By 390 BC, several Gallic tribes were invading Italy from the north as their culture expanded throughout Europe. The Romans were alerted to this when a particularly warlike tribe invaded two Etruscan towns close to Rome's sphere of influence. These towns, overwhelmed by the enemy's numbers and ferocity, called on Rome for help. The Romans met the Gauls in pitched battle at the Battle of Allia River around 390–387 BC. The Gauls, led by chieftain Brennus, defeated the Roman army of approximately 15,000 troops, pursued the fleeing Romans back to Rome, and sacked the city before being either driven off or bought off. Romans and Gauls continued to war intermittently in Italy for more than two centuries.[relevant? – discuss]
Knowledge 1: Rössen culture
The Rössen culture is important as it marks the transition from a broad and widely distributed tradition going back to Central Europe's earliest Neolithic LBK towards the more diversified Middle and Late Neolithic situation characterised by the appearance of complexes like Michelsberg and Funnel Beaker Culture. [SEP] Knowledge 2: Middle Ages
By the end of the 5th century the western section of the empire was divided into smaller political units, ruled by the tribes that had invaded in the early part of the century. The deposition of the last emperor of the west, Romulus Augustus, in 476 has traditionally marked the end of the Western Roman Empire.[E] The Eastern Roman Empire, often referred to as the Byzantine Empire after the fall of its western counterpart, had little ability to assert control over the lost western territories. The Byzantine emperors maintained a claim over the territory, but none of the new kings in the west dared to elevate himself to the position of emperor of the west, Byzantine control of most of the Western Empire could not be sustained; the reconquest of the Italian peninsula and Mediterranean periphery by Justinian (r. 527–565) was the sole, and temporary, exception.

Answer: 406