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キーワード Root of unity "11th" Kummer pdf で、
英文資料検索をしてみた

見繕い2件
1）2019 暗号システムに、Q(ζ11)を使う研究
2）次数 11 の円分数の詳細研究 (1975)、引用文献(1935)、このころならばエクセル使った計算で論文書けたかも

1）
https://eprint.iacr.org/2019/
Cryptology ePrint Archive
All papers in 2019 (1498 results)
https://eprint.iacr.org/2019/870.pdf
The Eleventh Power Residue Symbol
Marc Joye1, Oleksandra Lapiha2, Ky Nguyen2, and David Naccache2
Abstract.
This paper presents an efficient algorithm for computing 11th-power residue symbols in the
cyclotomic field Q(ζ11), where ζ11 is a primitive 11th root of unity. It extends an earlier algorithm due
to Caranay and Scheidler (Int. J. Number Theory, 2010) for the 7th-power residue symbol. The new
algorithm finds applications in the implementation of certain cryptographic schemes.
Our contributions.
This paper takes up the challenge put forward in [3] and presents the first implementation of the Caranay?Scheidler algorithm for the 11th-power residue symbol. The contributions of this
paper are three-fold: We provide explicit conditions for primary algebraic integers in Z[ζ11]; we devise an
efficient algorithm for finding a primary associate; and we give explicit complementary laws for a set of four fundamental units and for the special prime 1 - ζ11.

2）
下記で(1935)の文献が参照されている。88年前だね
https://people.math.carleton.ca/~williams/
KENNETH S. WILLIAMS
https://people.math.carleton.ca/~williams/papers/pdf/076.pdf
The cyclotomic numbers of order eleven ACTA ARITHMETICA (1975)
(次数 11 の円分数)
PHILIP A. LEONARD and KENNETH S. WILLIAMS
References
[2] L. E. Dickson, Cyclotomy, higher congruences, and Waring's problem, I, II,Amer. J. Math. 57 (1935), pp. 391-424, 463-474.
(引用終り)
以上