Question: At the end of which year did tribes from the area where Linear Pottery culture was found invade the Roman Empire?

Knowledge 1: 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. [SEP] Knowledge 2: Middle Ages
The political structure of Western Europe changed with the end of the united Roman Empire. Although the movements of peoples during this period are usually described as "invasions", they were not just military expeditions but migrations of entire peoples into the empire. Such movements were aided by the refusal of the western Roman elites to support the army or pay the taxes that would have allowed the military to suppress the migration. The emperors of the 5th century were often controlled by military strongmen such as Stilicho (d. 408), Aspar (d. 471), Ricimer (d. 472), or Gundobad (d. 516), who were partly or fully of non-Roman background. When the line of western emperors ceased, many of the kings who replaced them were from the same background. Intermarriage between the new kings and the Roman elites was common. This led to a fusion of Roman culture with the customs of the invading tribes, including the popular assemblies that allowed free male tribal members more say in political matters than was common in the Roman state. Material artefacts left by the Romans and the invaders are often similar, and tribal items were often modelled on Roman objects. Much of the scholarly and written culture of the new kingdoms was also based on Roman intellectual traditions. An important difference was the gradual loss of tax revenue by the new polities. Many of the new political entities no longer supported their armies through taxes, instead relying on granting them land or rents. This meant there was less need for large tax revenues and so the taxation systems decayed. Warfare was common between and within the kingdoms. Slavery declined as the supply weakened, and society became more rural.[F]
Knowledge 1: 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. [SEP] Knowledge 2: 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.
Knowledge 1: 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. [SEP] Knowledge 2: History of Germany
The concept of Germany as a distinct region in central Europe can be traced to Roman commander Julius Caesar, who referred to the unconquered area east of the Rhine as Germania, thus distinguishing it from Gaul (France), which he had conquered. The victory of the Germanic tribes in the Battle of the Teutoburg Forest (AD 9) prevented annexation by the Roman Empire, although the Roman provinces of Germania Superior and Germania Inferior were established along the Rhine. Following the Fall of the Western Roman Empire, the Franks conquered the other West Germanic tribes. When the Frankish Empire was divided among Charlemagne's heirs in 843, the eastern part became East Francia. In 962, Otto I became the first emperor of the Holy Roman Empire, the medieval German state.

Answer: 406