Question: The Battle of Vienna took place at Kahlenberg Mountain near Vienna in which year, after the imperial city had been besieged by the Ottoman Empire for two months, In the ensuing war that lasted until 1699, the Ottomans lost almost all of Hungary to the Holy Roman Emperor Leopold I, was the Holy Roman Emperor, King of Hungary, Croatia, and Bohemia?

Context paragraphs:
Jovan Monasterlija: Jovan Monasterlija (; fl.  1683–1706) was a Serbian "vice-voivode" (podvojvoda) and Austrian (Holy Roman Empire) imperial officer that led a Serbian Militia against the Ottoman Empire and other enemies of the Austrian Emperor.  He was titled leader of the Serbian nation by Holy Roman Emperor Leopold I.

Karl Anselm, 4th Prince of Thurn and Taxis: Karl Anselm, 4th Prince of Thurn and Taxis, full German name: "Karl Anselm Fürst von Thurn und Taxis" (2 June 1733, Frankfurt am Main, Free Imperial City of Frankfurt, Holy Roman Empire – 13 November 1805, Winzer bei Regensburg, Electorate of Bavaria, Holy Roman Empire) was the fourth Prince of Thurn and Taxis, Postmaster General of the Imperial Reichspost, and Head of the Princely House of Thurn and Taxis from 17 March 1773 until his death on 13 November 1805.  Karl Anselm served as "Prinzipalkommissar" at the Perpetual Imperial Diet in Regensburg for Joseph II, Holy Roman Emperor and Francis II, Holy Roman Emperor from 1773 to 1797.

Otto Heinrich Fugger, Count of Kirchberg: Otto Heinrich Fugger, Count of Kirchberg and Weissenhorn (1592–1644) was promoted to be a Knight of the Order of the Golden Fleece in 1628.  He was the son of Christoph Fugger von Glött, deceased 1615, the grandson of Johann Fugger, deceased 1598, the great grandson of very wealthy Augsburg city International businessman and banker Anton Fugger (1493–1560).  The 16th century Fugger's, descendents of a German businessmen family tracked down to the 14th century, were the Imperial bankers with King Charles I of Imperial Spain, also Holy Roman Emperor as Charles V (1500–1558), and his brother, also Holy Roman Emperor, Ferdinand I of Habsburg (1503–1564), king of Hungary and Bohemia from 1526, emperor from 1556 by abdication of his brother Charles.

Archduke Alexander Leopold of Austria: Archduke Alexander Leopold of Austria (Alexander Leopold Johann Joseph; Hungarian: "Sándor Lipót" ; 14 August 1772 – 12 July 1795) was Palatine of Hungary, appointed during the reign of his father, Holy Roman Emperor Leopold II, and serving into the reign of his elder brother, Holy Roman Emperor Francis II.

Free Imperial City of Aachen: The Free Imperial City of Aachen, known in English by its French name of Aix-la-Chapelle, was a Free Imperial City and spa of the Holy Roman Empire west of Cologne and southeast of the Low Countries, in the Lower Rhenish–Westphalian Circle.  The pilgrimages, the Coronation of the Holy Roman Emperor, flourishing industries and the privileges conferred by various emperors made it one of the most prosperous market towns of the Holy Roman Empire.

Battle of Vienna: The Battle of Vienna (German: "Schlacht am Kahlen Berge" or "Kahlenberg"; Polish: "bitwa pod Wiedniem" or "odsiecz wiedeńska" (The Relief of Vienna); Modern Turkish: "İkinci Viyana Kuşatması", Ottoman Turkish: "Beç Ḳalʿası Muḥāṣarası") took place at Kahlenberg Mountain near Vienna on 1683 after the imperial city had been besieged by the Ottoman Empire for two months.  The battle was fought by the Habsburg Monarchy, the Polish–Lithuanian Commonwealth and the Holy Roman Empire, under the command of King John III Sobieski against the Ottomans and their vassal and tributary states.  The battle marked the first time the Commonwealth and the Holy Roman Empire had cooperated militarily against the Ottomans, and it is often seen as a turning point in history, after which "the Ottoman Turks ceased to be a menace to the Christian world".  In the ensuing war that lasted until 1699, the Ottomans lost almost all of Hungary to the Holy Roman Emperor Leopold I.

Magnate conspiracy: The Magnate conspiracy, also known as the Zriny Frangipani Conspiracy (Croatian: "Zrinsko-frankopanska urota" ) in Croatia, and Wesselényi conspiracy (Hungarian: "Wesselényi-összeesküvés" ) in Hungary, was a 17th-century attempt to throw off Habsburg and other foreign influences over Hungary and Croatia.  The attempted coup was caused by the unpopular Peace of Vasvár, struck in 1664 between Holy Roman Emperor Leopold I and the Ottoman Empire.  The poorly organized attempt at revolt gave the Habsburgs reason to clamp down on their opponents.  It was named after Hungarian Count Ferenc Wesselényi, and by Croatian counts Nikola Zrinski, Petar Zrinski and Fran Krsto Frankopan.

Leopold I, Holy Roman Emperor: Leopold I (name in full: "Leopold Ignaz Joseph Balthasar Felician"; Hungarian: "I. Lipót" ; 9 June 1640 – 5 May 1705) was Holy Roman Emperor, King of Hungary, Croatia, and Bohemia.  The second son of Ferdinand III, Holy Roman Emperor, by his first wife, Maria Anna of Spain, Leopold became heir apparent in 1654 by the death of his elder brother Ferdinand IV.  Elected in 1658, Leopold ruled the Holy Roman Empire until his death in 1705.

Free imperial city: In the Holy Roman Empire, the collective term free and imperial cities (German: "Freie und Reichsstädte" ), briefly worded free imperial city ("Freie Reichsstadt ", Latin: "urbs imperialis libera" ), was used from the fifteenth century to denote a self-ruling city that enjoyed a certain amount of autonomy and was represented in the Imperial Diet.  An imperial city held the status of Imperial immediacy, and as such, was subordinate only to the Holy Roman Emperor, as opposed to a territorial city or town ("Landstadt ") which was subordinate to a territorial prince – be it an ecclesiastical lord (prince-bishop, prince-abbot) or a secular prince (duke ("Herzog "), margrave, count ("Graf "), etc.).

List of monarchs of Prussia: The monarchs of Prussia were members of the House of Hohenzollern who were the hereditary rulers of the former German state of Prussia from its founding in 1525 as the Duchy of Prussia.  The Duchy had evolved out of the Teutonic Order, a Roman Catholic crusader state and theocracy located along the eastern coast of the Baltic Sea.  The Teutonic Knights were under the leadership of a Grand Master, the last of whom, Albert, converted to Protestantism and secularized the lands, which then became the Duchy of Prussia.  The Duchy was initially a vassal of the Kingdom of Poland, as a result of the terms of the Prussian Homage whereby Albert was granted the Duchy as part of the terms of peace following the Prussian War.  When the main line of Prussian Hohenzollerns died out in 1618, the Duchy passed to a different branch of the family, who also reigned as Electors of Brandenburg in the Holy Roman Empire.  While still nominally two different territories, Prussia under the suzerainty of Poland and Brandenburg under the suzerainty of the Holy Roman Empire, the two states are known together historiographically as Brandenburg-Prussia.  Following the Second Northern War, a series of treaties freed the Duchy of Prussia from any vassalage to any other state, making it a fully sovereign Duchy in its own right.  This complex situation (where the Hohenzollern ruler of the independent Duchy of Prussia was also a subject of the Holy Roman Emperor as Elector of Brandenburg) laid the eventual groundwork for the establishment of the Kingdom of Prussia in 1701.  For diplomatic reasons, the rulers of the state were known as the King in Prussia from 1701 to 1772; largely because they still owed fealty to the Emperor as Electors of Brandenburg, the "King in Prussia" title (as opposed to "King of Prussia") avoided offending the Emperor.  As the Prussian state grew through several wars and diplomatic moves throughout the 18th century, it became apparent that Prussia had become a Great Power that did not need to submit meekly to the Holy Roman Empire.  By 1772, the pretense was dropped, and the style "King of Prussia" was adopted.  Thus it remained until 1871, when in the aftermath of the Franco-Prussian War, the King of Prussia Wilhelm I was crowned German Emperor.  From that point forward, though the Kingdom of Prussia retained its status as a constituent state of the German Empire, all remaining Kings of Prussia also served as German Emperor, and that title took precedence.

Supporting paragraphs: Battle of Vienna Leopold I, Holy Roman Emperor
Answer: 1683