Question: What is the name of the primary symbol, which is now outlawed outside of the context of art or science, and was widely used even on the state flag?

Documents:
source: Nazi symbolism
text: Nazi symbolism The 20th century German Nazi Party made extensive use of graphic symbolism, especially the "Hakenkreuz" (swastika), which was used as its principal symbol and, in the form of the swastika flag, became the state flag of Nazi Germany.

source: Strafgesetzbuch section 86a
text: Strafgesetzbuch section 86a The German "Strafgesetzbuch" (Criminal Code) in § 86a outlaws "use of symbols of unconstitutional organizations" outside of the contexts of "art or science, research or teaching". This concerns Nazi symbolism in particular and is part of the denazification efforts following the fall of the Third Reich.

source: Flags of counties of the United States
text: Flags of counties of the United States The flags of the counties of the United States of America exhibit a wide variety of regional influences and local histories, as well as widely different styles and design principles. For example, some Floridian and Alabamian municipality flags feature a saltire, due to saltires being used on their state flags. Some Maryland county flags feature the coat of arms of the Calvert family, as it is featured on the Maryland state flag, and due to the Calvert family's prominence in Maryland history. Many counties went decades without a flag, until a certain event, such as a local sesquicentennial or the American bicentennial, spurred the creation of a flag. Frederick County, Maryland is one example, in 1976, it hosted a contest, asking the public to submit their designs to a commission. A panel then reviewed the five winning entries, choosing one to become the official county flag. Frederick County's example is typical of the flag adoption processes that many counties undertook with their flags. The 250th anniversary of Augusta County, Virginia's founding also spurred the creation of a flag, in 1988. Some flags, such as the flags of Montgomery County, Maryland, and Loudoun County, Virginia, were created by foreign entities, such as the College of Arms in the United Kingdom.

source: Flag of Hawaii
text: Flag of Hawaii The flag of the state of Hawaii (Hawaiian: " ") is the official flag symbolizing Hawaii as a U.S. state. The same flag had also previously been used by the kingdom, protectorate, republic, and territory of Hawaii. It is the only U.S. state flag to feature the flag of a foreign country, the Union flag of the United Kingdom, a remnant of the British Empire's influence on Hawaiian history.

source: Flag of Moldova
text: Flag of Moldova The state flag of Moldova is a vertical tricolour of blue, yellow, and red, charged with the coat of arms of Moldova (an eagle holding a shield charged with an aurochs) on the center bar. The obverse is mirrored. The flag ratio is 1:2. Until further provisions, the State Flag of Moldova is used as the national flag and ensign as well, that is, civil, state and war flag and ensign.

source: White Rod
text: White Rod The White Rod, White Wand, Rod of Inauguration, or Wand of Sovereignty, in the Irish language variously called the slat na ríghe (rod of kingship) and slat tighearnais (rod of lordship), was the primary symbol of a Gaelic king or lord's legitimate authority and the principal prop used in his inauguration ceremony. First documented in the 12th century "Life of Máedóc of Ferns", but assumed to have been used long before then, it is last documented in Ireland in the early 17th century. In Scotland the rod was used into the 13th century for the inauguration of its last Gaelic kings, and for the Norse-Gaelic Lords of the Isles into the 15th.

source: Flag of Massachusetts
text: Flag of Massachusetts The flag of the Commonwealth of Massachusetts is the subnational flag of Massachusetts. It has been represented by official but limited-purpose flags since 1776, though until 1908 it had no state flag "per se" to represent its government. A variant of the white flag with blue seal was carried by each of the Massachusetts volunteer regiments during the Civil War alongside the National Colors. An exception were the two "Irish regiments" (the 9th and 28th Volunteers), each of which was permitted to carry an alternative green flag with a harp symbol. The state currently has three official flags: a state flag, a "naval and maritime flag" (despite it no longer having its own navy), and a governor's flag.

source: Goldwork (embroidery)
text: Goldwork (embroidery) Goldwork is the art of embroidery using metal threads. It is particularly prized for the way light plays on it. The term "goldwork" is used even when the threads are imitation gold, silver, or copper. The metal wires used to make the threads have never been entirely gold; they have always been gold-coated silver ("silver-gilt") or cheaper metals, and even then the "gold" often contains a very low percent of real gold. Most metal threads are available in silver and sometimes copper as well as gold; some are available in colors as well.

source: Flag of Mongolia
text: Flag of Mongolia The flag of Mongolia (Mongolian: Монгол улсын төрийн далбаа , state flag of Mongolia) consists of three equal bands, of alternating red, blue and red, with the Soyombo national symbol centering the first red band in yellow. The central blue band is described as the eternal blue sky, while the side red bands represent the ability of Mongolia to thrive in its harsh environment. The Soyombo is a columnar arrangement of abstract and geometric representations of fire, sun, moon, earth, water, and the "taijitu" or yin-yang symbol. The current flag was adopted on February 12, 1992, after the transition of Mongolia to a liberal democracy. It is similar to the flag of 1940, except for the removal of the socialist star on top of the Soyombo.

source: Flag of Saxony
text: Flag of Saxony Both the civil and state flag of the German state of Saxony feature a bicolour of white over green, similar to the Austrian province of Styria. The state flag is similar to the civil flag, except it is defaced in the centre with the coat of arms of Saxony. The colours of both flags were officially decided as state colours in 1815. The aristocracy used mostly and in first time the quadrangular and later the rectangular form.

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Answer: swastika