1 3 ( 1 1 1 1 1 1 1 1 1 1 1 1 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 1 1 1 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 1 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 1 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 1 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 1 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 1 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 1 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] ) \frac{1}{3}\left(\begin{array}{ccccccccc} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) \\ 1 & 1 & 1 & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) \\ 1 & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] \\ 1 & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] \\ 1 & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] \\ 1 & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] \\ 1 & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] \\ 1 & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] \\\end{array}\right) 3 1 ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎛ 1 1 1 1 1 1 1 1 1 1 1 1 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 1 1 1 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 1 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 1 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 1 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 1 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 1 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 1 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎞
( 0 , 0 , 0 , − 4 9 , − 4 9 , − 1 9 , − 1 9 , 2 9 , 2 9 ) \begin{array}{l}\left(0,0,0,-\frac{4}{9},-\frac{4}{9},-\frac{1}{9},-\frac{1}{9},\frac{2}{9},\frac{2}{9}\right)\end{array} ( 0 , 0 , 0 , − 9 4 , − 9 4 , − 9 1 , − 9 1 , 9 2 , 9 2 )
1 3 ( 1 1 1 1 1 1 1 1 1 1 1 1 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 1 1 1 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 1 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 1 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 1 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 1 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 1 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 1 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] ) \frac{1}{3}\left(\begin{array}{ccccccccc} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) \\ 1 & 1 & 1 & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) \\ 1 & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] \\ 1 & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] \\ 1 & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] \\ 1 & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] \\ 1 & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] \\ 1 & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] \\\end{array}\right) 3 1 ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎛ 1 1 1 1 1 1 1 1 1 1 1 1 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 1 1 1 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 1 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 1 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 1 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 1 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 1 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 1 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎞
( 0 , 0 , 0 , − 1 9 , − 1 9 , 2 9 , 2 9 , − 4 9 , − 4 9 ) \begin{array}{l}\left(0,0,0,-\frac{1}{9},-\frac{1}{9},\frac{2}{9},\frac{2}{9},-\frac{4}{9},-\frac{4}{9}\right)\end{array} ( 0 , 0 , 0 , − 9 1 , − 9 1 , 9 2 , 9 2 , − 9 4 , − 9 4 )
1 3 ( 1 1 1 1 1 1 1 1 1 1 1 1 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 1 1 1 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 1 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 1 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 1 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 1 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 1 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 1 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] ) \frac{1}{3}\left(\begin{array}{ccccccccc} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) \\ 1 & 1 & 1 & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) \\ 1 & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] \\ 1 & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] \\ 1 & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] \\ 1 & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] \\ 1 & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] \\ 1 & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] \\\end{array}\right) 3 1 ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎛ 1 1 1 1 1 1 1 1 1 1 1 1 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 1 1 1 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 1 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 1 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 1 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 1 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 1 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 1 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎞
( 0 , 0 , 0 , 2 9 , 2 9 , − 4 9 , − 4 9 , − 1 9 , − 1 9 ) \begin{array}{l}\left(0,0,0,\frac{2}{9},\frac{2}{9},-\frac{4}{9},-\frac{4}{9},-\frac{1}{9},-\frac{1}{9}\right)\end{array} ( 0 , 0 , 0 , 9 2 , 9 2 , − 9 4 , − 9 4 , − 9 1 , − 9 1 )
1 3 ( 1 1 1 1 1 1 1 1 1 1 1 1 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 1 1 1 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 1 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 1 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 1 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 1 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 1 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 1 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] ) \frac{1}{3}\left(\begin{array}{ccccccccc} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) \\ 1 & 1 & 1 & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) \\ 1 & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] \\ 1 & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] \\ 1 & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] \\ 1 & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] \\ 1 & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] \\ 1 & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] \\\end{array}\right) 3 1 ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎛ 1 1 1 1 1 1 1 1 1 1 1 1 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 1 1 1 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 1 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 1 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 1 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 1 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 1 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 1 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎞
( 0 , 0 , 0 , 4 9 , 4 9 , 1 9 , 1 9 , − 2 9 , − 2 9 ) \begin{array}{l}\left(0,0,0,\frac{4}{9},\frac{4}{9},\frac{1}{9},\frac{1}{9},-\frac{2}{9},-\frac{2}{9}\right)\end{array} ( 0 , 0 , 0 , 9 4 , 9 4 , 9 1 , 9 1 , − 9 2 , − 9 2 )
1 3 ( 1 1 1 1 1 1 1 1 1 1 1 1 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 1 1 1 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 1 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 1 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 1 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 1 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 1 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 1 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] ) \frac{1}{3}\left(\begin{array}{ccccccccc} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) \\ 1 & 1 & 1 & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) \\ 1 & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] \\ 1 & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] \\ 1 & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] \\ 1 & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] \\ 1 & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] \\ 1 & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] \\\end{array}\right) 3 1 ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎛ 1 1 1 1 1 1 1 1 1 1 1 1 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 1 1 1 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 1 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 1 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 1 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 1 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 1 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 1 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎞
( 0 , 0 , 0 , 1 9 , 1 9 , − 2 9 , − 2 9 , 4 9 , 4 9 ) \begin{array}{l}\left(0,0,0,\frac{1}{9},\frac{1}{9},-\frac{2}{9},-\frac{2}{9},\frac{4}{9},\frac{4}{9}\right)\end{array} ( 0 , 0 , 0 , 9 1 , 9 1 , − 9 2 , − 9 2 , 9 4 , 9 4 )
1 3 ( 1 1 1 1 1 1 1 1 1 1 1 1 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 1 1 1 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 1 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 1 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 1 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 1 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 1 1 2 ( − 1 − i 3 ) 1 2 ( − 1 + i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 1 1 2 ( − 1 + i 3 ) 1 2 ( − 1 − i 3 ) 3 Root [ 729 x 6 + 27 x 3 + 1 , 6 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 5 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 2 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 1 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 4 ] 3 Root [ 729 x 6 + 27 x 3 + 1 , 3 ] ) \frac{1}{3}\left(\begin{array}{ccccccccc} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) \\ 1 & 1 & 1 & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) \\ 1 & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] \\ 1 & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] \\ 1 & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] \\ 1 & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] \\ 1 & \frac{1}{2} \left(-1-i \sqrt{3}\right) & \frac{1}{2} \left(-1+i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] \\ 1 & \frac{1}{2} \left(-1+i \sqrt{3}\right) & \frac{1}{2} \left(-1-i \sqrt{3}\right) & 3 \text{Root}\left[729 x^6+27 x^3+1,6\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,5\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,2\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,1\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,4\right] & 3 \text{Root}\left[729 x^6+27 x^3+1,3\right] \\\end{array}\right) 3 1 ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎛ 1 1 1 1 1 1 1 1 1 1 1 1 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 1 1 1 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 1 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 1 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 1 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 1 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 1 2 1 ( − 1 − i 3 ) 2 1 ( − 1 + i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 1 2 1 ( − 1 + i 3 ) 2 1 ( − 1 − i 3 ) 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 6 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 5 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 2 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 1 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 4 ] 3 Root [ 7 2 9 x 6 + 2 7 x 3 + 1 , 3 ] ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎞
( 0 , 0 , 0 , − 2 9 , − 2 9 , 4 9 , 4 9 , 1 9 , 1 9 ) \begin{array}{l}\left(0,0,0,-\frac{2}{9},-\frac{2}{9},\frac{4}{9},\frac{4}{9},\frac{1}{9},\frac{1}{9}\right)\end{array} ( 0 , 0 , 0 , − 9 2 , − 9 2 , 9 4 , 9 4 , 9 1 , 9 1 )