Mode

$x^{3.1}+1=0$

$x^{3.14}+1=0$

$x^{\pi }+1=0$

k

$x_k=\exp \left[i\frac{10}{31}\pi \left(1+2k\right)\right]$

$x_k=\exp \left[i\frac{50}{157}\pi \left(1+2k\right)\right]$

$x_k=\exp \left[i\left(1+2k\right)\right]$

0

$+0.52896+0.84864i$

$+0.53988+0.84175i$

$+0.54030+0.84147i$

1

$-0.99487+0.10117i$

$-0.99021+0.13961i$

$-0.98999+0.14112i$

2

$+0.34731-0.93775i$

$+0.28609-0.95820i$

$+0.28366-0.95892i$

3

$+0.68897+0.72479i$

$+0.75156+0.65966i$

$+0.75390+0.65699i$

4

$-0.95414+0.29936i$

$-0.91300+0.40796i$

$-0.91113+0.41212i$

5

$+0.15143-0.98847i$

$+0.01001-0.99995i$

$+0.00443-0.99999i$

6

$+0.82076+0.57127i$

$+0.90466+0.42614i$

$+0.90745+0.42017i$

7

$-0.87435+0.48530i$

$-0.76461+0.64449i$

$-0.75969+0.65029i$

8

$-0.05065-0.99872i$

$-0.26686-0.96373i$

$-0.27516-0.96140i$

9

$+0.91896+0.39436i$

$+0.98721+0.15940i$

$+0.98870+0.14988i$