Question: At the end of which year did the tribes from where the Michelsberg culture is from invade the Roman Empire?

Context paragraphs:
paragraph_text: 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.
title: Middle Ages
paragraph_text: The Tamástslikt Cultural Institute is a museum and research institute located on the Umatilla Indian Reservation near Pendleton in eastern Oregon. It is the only Native American museum along the Oregon Trail. The institute is dedicated to the culture of the Cayuse, Umatilla, and Walla Walla tribes of Native Americans. The main permanent exhibition of the museum provides a history of the culture of three tribes, and of the reservation itself. The museum also has a second hall for temporary exhibitions of specific types of Native American art, craftwork, history, and folklore related to the tribes.
title: Tamástslikt Cultural Institute
paragraph_text: 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]
title: Middle Ages
paragraph_text: In the course of his Gallic Wars, Julius Caesar invaded Britain twice: in 55 and 54 BC. The first invasion, in late summer, was unsuccessful, gaining the Romans little else besides a beachhead on the coast of Kent. The second invasion achieved more: the Romans installed a king, Mandubracius, who was friendly to Rome, and they forced the submission of Mandubracius's rival, Cassivellaunus. No territory was conquered and held for Rome; instead, all Roman - occupied territory was restored to the allied Trinovantes, along with the promised tribute of the other tribes in what is now eastern England.
title: Julius Caesar's invasions of Britain
paragraph_text: The Germanic peoples during the Migrations Period came into contact with other peoples; in the case of the populations settling in the territory of modern Germany, they encountered Celts to the south, and Balts and Slavs towards the east. The Limes Germanicus was breached in AD 260. Migrating Germanic tribes commingled with the local Gallo-Roman populations in what is now Swabia and Bavaria. The arrival of the Huns in Europe resulted in Hun conquest of large parts of Eastern Europe, the Huns initially were allies of the Roman Empire who fought against Germanic tribes, but later the Huns cooperated with the Germanic tribe of the Ostrogoths, and large numbers of Germans lived within the lands of the Hunnic Empire of Attila. Attila had both Hunnic and Germanic families and prominent Germanic chiefs amongst his close entourage in Europe. The Huns living in Germanic territories in Eastern Europe adopted an East Germanic language as their lingua franca. A major part of Attila's army were Germans, during the Huns' campaign against the Roman Empire. After Attila's unexpected death the Hunnic Empire collapsed with the Huns disappearing as a people in Europe – who either escaped into Asia, or otherwise blended in amongst Europeans.
title: Germans
paragraph_text: The Slavs under name of the Antes and the Sclaveni make their first appearance in Byzantine records in the early 6th century. Byzantine historiographers under Justinian I (527–565), such as Procopius of Caesarea, Jordanes and Theophylact Simocatta describe tribes of these names emerging from the area of the Carpathian Mountains, the lower Danube and the Black Sea, invading the Danubian provinces of the Eastern Empire.
title: Slavs
paragraph_text: 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.
title: Middle Ages
paragraph_text: 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.
title: Rössen culture
paragraph_text: As the Roman Empire was falling apart, Palermo fell under the control of several Germanic tribes. The first were the Vandals in 440 AD under the rule of their king Geiseric. The Vandals had occupied all the Roman provinces in North Africa by 455 establishing themselves as a significant force. They acquired Corsica, Sardinia and Sicily shortly afterwards. However, they soon lost these newly acquired possessions to the Ostrogoths. The Ostrogothic conquest under Theodoric the Great began in 488; Theodoric supported Roman culture and government unlike the Germanic Goths. The Gothic War took place between the Ostrogoths and the Eastern Roman Empire, also known as the Byzantine Empire. Sicily was the first part of Italy to be taken under control of General Belisarius who was commissioned by Eastern Emperor. Justinian I solidified his rule in the following years.
title: Palermo
paragraph_text: 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.
title: Galicia (Spain)
paragraph_text: Contrarily, having so firmly entrenched themselves into Greek affairs, the Romans now completely ignored the rapidly disintegrating Seleucid empire (perhaps because it posed no threat); and left the Ptolemaic kingdom to decline quietly, while acting as a protector of sorts, in as much as to stop other powers taking Egypt over (including the famous line-in-the-sand incident when the Seleucid Antiochus IV Epiphanes tried to invade Egypt). Eventually, instability in the near east resulting from the power vacuum left by the collapse of the Seleucid empire caused the Roman proconsul Pompey the Great to abolish the Seleucid rump state, absorbing much of Syria into the Roman republic. Famously, the end of Ptolemaic Egypt came as the final act in the republican civil war between the Roman triumvirs Mark Anthony and Augustus Caesar. After the defeat of Anthony and his lover, the last Ptolemaic monarch, Cleopatra VII at the Battle of Actium, Augustus invaded Egypt and took it as his own personal fiefdom. He thereby completed both the destruction of the Hellenistic kingdoms and the Roman republic, and ended (in hindsight) the Hellenistic era.
title: Hellenistic period
paragraph_text: In 334 BC, Alexander the Great invaded the Achaemenid Empire, defeating the last Achaemenid emperor, Darius III, at the Battle of Issus. Following the premature death of Alexander, Iran came under the control of the Hellenistic Seleucid Empire. In the middle of the 2nd century BC, the Parthian Empire rose to become the main power in Iran, and the century-long geopolitical arch-rivalry between Romans and Parthians began, culminating in the Roman–Parthian Wars. The Parthian Empire continued as a feudal monarchy for nearly five centuries, until 224 CE, when it was succeeded by the Sassanid Empire. Together with their neighboring arch-rival, the Roman-Byzantines, they made up the world's two most dominant powers at the time, for over four centuries.
title: Iran
paragraph_text: On 12 February 1912, after rounds of negotiations, Longyu issued an imperial edict bringing about the abdication of the child emperor Puyi. This brought an end to over 2,000 years of Imperial China and began an extended period of instability of warlord factionalism. The unorganized political and economic systems combined with a widespread criticism of Chinese culture led to questioning and doubt about the future. In the 1930s, the Empire of Japan invaded Northeast China and founded Manchukuo in 1932, with Puyi, as the emperor. After the invasion by the Soviet Union, Manchukuo collapsed in 1945.
title: Qing dynasty
paragraph_text: Carpetania was an ancient region of what is today Spain, located between the Sierra de Guadarrama, the mountains of Toledo, the river Guadiana and the mountain range of Alcaraz, including approximately, the present independent communities of Madrid and Castile-La Mancha. It was inhabited by the Carpetani, a pre-Roman tribe. To the south dwelt the Oretani, on the northeast were Celtiberians whose tribes are not further specified. On the northwest to the Vaccei and Vettones. This area was easily conquered by the Romans and quickly integrated culturally and politically. Thus it is practically unmentioned in the literature of the conquest. Its main urban nuclei (Toletum, corresponding to present Toledo; Complutum, the present Alcalá de Henares, Consabura, the present Consuegra, Segóbriga (Saelices, River basin) and Laminio) acquired municipal legal statutes soon after the Roman conquest.
title: Carpetania
paragraph_text: 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]
title: Roman Republic
paragraph_text: The Peace of Westphalia (German: Westfälischer Friede) was a series of peace treaties signed between May and October 1648 in the Westphalian cities of Osnabrück and Münster, effectively ending the European wars of religion. These treaties ended the Thirty Years' War (1618 -- 1648) in the Holy Roman Empire between the Habsburgs and their Catholic allies on one side and the Protestant powers (Sweden, Denmark, Dutch, and Holy Roman principalities) and their Catholic (France) Anti-Habsburg allies on the other. The treaties also ended the Eighty Years' War (1568 -- 1648) between Spain and the Dutch Republic, with Spain formally recognising the independence of the Dutch Republic.
title: Peace of Westphalia
paragraph_text: The Germanic tribes are thought to date from the Nordic Bronze Age or the Pre-Roman Iron Age. From southern Scandinavia and north Germany, they expanded south, east and west from the 1st century BC, coming into contact with the Celtic tribes of Gaul as well as Iranian, Baltic, and Slavic tribes in Central and Eastern Europe. Under Augustus, Rome began to invade Germania (an area extending roughly from the Rhine to the Ural Mountains). In 9 AD, three Roman legions led by Varus were defeated by the Cheruscan leader Arminius. By 100 AD, when Tacitus wrote Germania, Germanic tribes had settled along the Rhine and the Danube (the Limes Germanicus), occupying most of the area of modern Germany. However, Austria, Baden Württemberg, southern Bavaria, southern Hessen and the western Rhineland had been conquered and incorporated into Roman provinces: Noricum, Raetia, Germania Superior, and Germania Inferior.
title: Germany
paragraph_text: The Revolt of the Batavi took place in the Roman province of Germania Inferior between AD 69 and 70. It was an uprising against the Roman Empire started by the Batavi, a small but militarily powerful Germanic tribe that inhabited Batavia, on the delta of the river Rhine. They were soon joined by the Celtic tribes from Gallia Belgica and some Germanic tribes.
title: Revolt of the Batavi
paragraph_text: The Treaty of Bärwalde (; ; ) of 23 January 1631 was a treaty concluding an alliance between the Swedish Empire and the Kingdom of France  during the Thirty Years' War, shortly after Sweden had invaded Northern Germany then occupied by Ferdinand II, Holy Roman Emperor's forces. The treaty obliged Sweden to maintain an army of 36,000 troops, and France to fund the Swedish army with an annually 400,000 Reichsthalers.
title: Treaty of Bärwalde
paragraph_text: 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.
title: History of Germany

Reasoning steps:
Michelsberg culture >> located on terrain feature >>>> Central Europe
At the end of which year did Central Europe tribes invade the Roman Empire? >>>> 406

Answer: spans: 406