Question: At the end of which year did tribes from the place where the Celts are said to have migrated from invade the Roman empire?

Knowledge 1: Celts
The history of pre-Celtic Europe and the exact relationship between ethnic, linguistic and cultural factors in the Celtic world remains uncertain and controversial. The exact geographic spread of the ancient Celts is disputed; in particular, the ways in which the Iron Age inhabitants of Great Britain and Ireland should be regarded as Celts have become a subject of controversy. According to one theory, the common root of the Celtic languages, the Proto - Celtic language, arose in the Late Bronze Age Urnfield culture of Central Europe, which flourished from around 1200 BC. According to a theory proposed in the 19th century, the first people to adopt cultural characteristics regarded as Celtic were the people of the Iron Age Hallstatt culture in central Europe (c. 800 -- 450 BC), named for the rich grave finds in Hallstatt, Austria. Thus this area is sometimes called the ``Celtic homeland ''. By or during the later La Tène period (c. 450 BC up to the Roman conquest), this Celtic culture was supposed to have expanded by trans - cultural diffusion or migration to the British Isles (Insular Celts), France and the Low Countries (Gauls), Bohemia, Poland and much of Central Europe, the Iberian Peninsula (Celtiberians, Celtici, Lusitanians and Gallaeci) and northern Italy (Golasecca culture and Cisalpine Gauls) and, following the Celtic settlement of Eastern Europe beginning in 279 BC, as far east as central Anatolia (Galatians) in modern - day Turkey. [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: Celts
The history of pre-Celtic Europe and the exact relationship between ethnic, linguistic and cultural factors in the Celtic world remains uncertain and controversial. The exact geographic spread of the ancient Celts is disputed; in particular, the ways in which the Iron Age inhabitants of Great Britain and Ireland should be regarded as Celts have become a subject of controversy. According to one theory, the common root of the Celtic languages, the Proto - Celtic language, arose in the Late Bronze Age Urnfield culture of Central Europe, which flourished from around 1200 BC. According to a theory proposed in the 19th century, the first people to adopt cultural characteristics regarded as Celtic were the people of the Iron Age Hallstatt culture in central Europe (c. 800 -- 450 BC), named for the rich grave finds in Hallstatt, Austria. Thus this area is sometimes called the ``Celtic homeland ''. By or during the later La Tène period (c. 450 BC up to the Roman conquest), this Celtic culture was supposed to have expanded by trans - cultural diffusion or migration to the British Isles (Insular Celts), France and the Low Countries (Gauls), Bohemia, Poland and much of Central Europe, the Iberian Peninsula (Celtiberians, Celtici, Lusitanians and Gallaeci) and northern Italy (Golasecca culture and Cisalpine Gauls) and, following the Celtic settlement of Eastern Europe beginning in 279 BC, as far east as central Anatolia (Galatians) in modern - day Turkey. [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: Celts
The history of pre-Celtic Europe and the exact relationship between ethnic, linguistic and cultural factors in the Celtic world remains uncertain and controversial. The exact geographic spread of the ancient Celts is disputed; in particular, the ways in which the Iron Age inhabitants of Great Britain and Ireland should be regarded as Celts have become a subject of controversy. According to one theory, the common root of the Celtic languages, the Proto - Celtic language, arose in the Late Bronze Age Urnfield culture of Central Europe, which flourished from around 1200 BC. According to a theory proposed in the 19th century, the first people to adopt cultural characteristics regarded as Celtic were the people of the Iron Age Hallstatt culture in central Europe (c. 800 -- 450 BC), named for the rich grave finds in Hallstatt, Austria. Thus this area is sometimes called the ``Celtic homeland ''. By or during the later La Tène period (c. 450 BC up to the Roman conquest), this Celtic culture was supposed to have expanded by trans - cultural diffusion or migration to the British Isles (Insular Celts), France and the Low Countries (Gauls), Bohemia, Poland and much of Central Europe, the Iberian Peninsula (Celtiberians, Celtici, Lusitanians and Gallaeci) and northern Italy (Golasecca culture and Cisalpine Gauls) and, following the Celtic settlement of Eastern Europe beginning in 279 BC, as far east as central Anatolia (Galatians) in modern - day Turkey. [SEP] Knowledge 2: British Isles
At the time of the Roman Empire, about two thousand years ago, various tribes, which spoke Celtic dialects of the Insular Celtic group, were inhabiting the islands. The Romans expanded their civilisation to control southern Great Britain but were impeded in advancing any further, building Hadrian's Wall to mark the northern frontier of their empire in 122 AD. At that time, Ireland was populated by a people known as Hiberni, the northern third or so of Great Britain by a people known as Picts and the southern two thirds by Britons.

Answer: 406