| The values are listed horizontally in increasing order for each (j, k) under the column headed "cos(2*pi/k) mod j".
The column headed "nov" is the number of values. The values read downwards form A164822.
I call "cos(x) mod j" the "Discrete Cosine of x modulo j".
cos(2*pi/k) mod j can be calculated by expressing cos(2pi) as a polynomial P in cos(2pi/k), for which the coefficients are those of Chebyshev's T(n,x) polynomials (A053120), and then solving P - 1 = 0 mod j by trial and error.
...j.......k.....nov....cos(2*pi/k).mod.j
...2.......1.......1.......1
...3.......1.......1.......1
...........2.......2.......1.......2
...4.......1.......1.......1
...........2.......2.......1.......3
...........3.......1.......1
...5.......1.......1.......1
...........2.......2.......1.......4
...........3.......2.......1.......2
...........4.......2.......1.......4
...6.......1.......1.......1
...........2.......4.......1.......2.......4.......5
...........3.......1.......1
...........4.......5.......1.......2.......3.......4.......5
...........5.......1.......1
...7.......1.......1.......1
...........2.......2.......1.......6
...........3.......2.......1.......3
...........4.......2.......1.......6
...........5.......1.......1
...........6.......4.......1.......3.......4.......6
...8.......1.......1.......1
...........2.......4.......1.......3.......5.......7
...........3.......1.......1
...........4.......7.......1.......2.......3.......4.......5.......6.......7
...........5.......1.......1
...........6.......4.......1.......3.......5.......7
...........7.......1.......1
...9.......1.......1.......1
...........2.......2.......1.......8
...........3.......3.......1.......4.......7
...........4.......4.......1.......3.......6.......8
...........5.......1.......1
...........6.......6.......1.......2.......4.......5.......7.......8
...........7.......1.......1
...........8.......4.......1.......3.......6.......8
..10.......1.......1.......1
...........2.......4.......1.......4.......6.......9
...........3.......2.......1.......7
...........4.......5.......1.......4.......5.......6.......9
...........5.......1.......1
...........6.......8.......1.......2.......3.......4.......6.......7.......8.......9
...........7.......1.......1
...........8.......5.......1.......4.......5.......6.......9
...........9.......2.......1.......7
..11.......1.......1.......1
...........2.......2.......1......10
...........3.......2.......1.......5
...........4.......2.......1......10
...........5.......3.......1.......7.......9
...........6.......4.......1.......5.......6......10
...........7.......1.......1
...........8.......2.......1......10
...........9.......2.......1.......5
..........10.......6.......1.......2.......4.......7.......9......10
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