To the south of 사기꾼의 굴 (Swindler's Den), two flawless amethysts can be found at a nearby shrine. One is in plain view and the other is in a small chest.

One can be found in the Tower Section of 막다른절벽동굴 (Blind Cliff Cave).

There is one located in a urn inside of the Shrine of Mehrunes Dagon.

There is one near the Shrine of Mehrunes Dagon. Take the side path to the left and follow it up the mountan. Then look for a small alter on the right.

청소부의 돌무덤 (Dustman's Cairn), just past where 파커스 (Farkas) turns into a werewolf, on a small pedestal.

디벨라의 신전 (Temple Of Dibella)'s Inner Sanctum on a bookshelf.

Two may be found in the Snow Veil Catacombs. These can be collected at any time but also during the "침묵의 대화 (Speaking With Silence)" Thieves Guild quest.

North of 리프튼 (Riften) - A settlement of 쇼르의 돌 (Shor's Stone) - one can be found in 실쟈 (Sylgja)'s house or her possession. (Not always).

During the Thieves Guild quest, "The Pursuit", one may be found in a bowl on Mercer's desk in the tunnels underneath Riftweald Manor, along with many other gems. One can also be found on his person in The Raggon Flagon- Cistern.

Can be found while mining ore veins.

Upon completion of "Bow to the Master", 5 random gems are given to the player as a reward. One of which can be a flawless amethyst.

Sometimes a thief may even carry one.

Found on dead Frost Trolls and Dwarven Spheres.

Silus has a chance to drop Flawless Amethysts if killed during "과거의 조각 (Pieces Of The Past)", the Daedric quest for Mehrunes' Razor.

Sometimes a higher level bandit will carry one.

Forsaken Crypt, In the hall after the first large room in an urn. Gems found here are leveled, meaning the gem found is contingent on Character Level and may not be a Flawless Amethyst.

North of 리프튼 (Riften)

Fort Greenwall - located in one of the chests.

참고: TES Wikia (Flawless Amethyst)