However, the Smithsonian Institution in Washington, D.C., does have an extensive collection of rare and historically significant coins, including various types of Double Eagles and other numismatic treasures.
Notably, one coin was sold at auction for over $7 million in 2002, making it one of the most valuable coins in the world.
If there were a unique or notable specimen from 1849, it would likely be a part of a museum collection, and the Smithsonian is indeed known for housing such remarkable artifacts.
To obtain the most accurate and up-to-date information, it is recommended to check directly with the Smithsonian Institution or their National Numismatic Collection, as their collections can evolve over time with new acquisitions and exhibits.
Keep in mind that details about specific coins and collections may have changed since my last update in January 2022, so verifying with the latest sources is advisable.