Question: At the end of which year did the tribes from the location of the Lusatia invade the Roman Empire?

Knowledge 1: Lower Lusatia
Lower Lusatia (; ; ; ; ) is a historical region in Central Europe, stretching from the southeast of the German state of Brandenburg to the southwest of Lubusz Voivodeship in Poland. Like adjacent Upper Lusatia in the south, Lower Lusatia is a settlement area of the West Slavic Sorbs whose endangered Lower Sorbian language is related to Upper Sorbian and Polish. [SEP] Knowledge 2: Galicia (Spain)
In the early 5th century, the deep crisis suffered by the Roman Empire allowed different tribes of Central Europe (Suebi, Vandals and Alani) to cross the Rhine and penetrate into the rule on 31 December 406. Its progress towards the Iberian Peninsula forced the Roman authorities to establish a treaty (foedus) by which the Suebi would settle peacefully and govern Galicia as imperial allies. So, from 409 Galicia was taken by the Suebi, forming the first medieval kingdom to be created in Europe, in 411, even before the fall of the Roman Empire, being also the first Germanic kingdom to mint coinage in Roman lands. During this period a Briton colony and bishopric (see Mailoc) was established in Northern Galicia (Britonia), probably as foederati and allies of the Suebi. In 585, the Visigothic King Leovigild invaded the Suebic kingdom of Galicia and defeated it, bringing it under Visigoth control.
Knowledge 1: Lower Lusatia
Lower Lusatia (; ; ; ; ) is a historical region in Central Europe, stretching from the southeast of the German state of Brandenburg to the southwest of Lubusz Voivodeship in Poland. Like adjacent Upper Lusatia in the south, Lower Lusatia is a settlement area of the West Slavic Sorbs whose endangered Lower Sorbian language is related to Upper Sorbian and Polish. [SEP] Knowledge 2: Middle Ages
In the Eastern Empire the slow infiltration of the Balkans by the Slavs added a further difficulty for Justinian's successors. It began gradually, but by the late 540s Slavic tribes were in Thrace and Illyrium, and had defeated an imperial army near Adrianople in 551. In the 560s the Avars began to expand from their base on the north bank of the Danube; by the end of the 6th century they were the dominant power in Central Europe and routinely able to force the eastern emperors to pay tribute. They remained a strong power until 796. An additional problem to face the empire came as a result of the involvement of Emperor Maurice (r. 582–602) in Persian politics when he intervened in a succession dispute. This led to a period of peace, but when Maurice was overthrown, the Persians invaded and during the reign of Emperor Heraclius (r. 610–641) controlled large chunks of the empire, including Egypt, Syria, and Asia Minor, until Heraclius' successful counterattack. In 628 the empire secured a peace treaty and recovered all of its lost territories.
Knowledge 1: Lower Lusatia
Lower Lusatia (; ; ; ; ) is a historical region in Central Europe, stretching from the southeast of the German state of Brandenburg to the southwest of Lubusz Voivodeship in Poland. Like adjacent Upper Lusatia in the south, Lower Lusatia is a settlement area of the West Slavic Sorbs whose endangered Lower Sorbian language is related to Upper Sorbian and Polish. [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.

Answer: 406