11n
124
(K11n
124
)
A knot diagram
1
Linearized knot diagam
7 1 11 8 9 2 5 3 7 8 9
Solving Sequence
1,7
2 3
6,9
5 8 11 4 10
c
1
c
2
c
6
c
5
c
8
c
11
c
3
c
10
c
4
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h1.78739 × 10
29
u
38
− 5.50902 × 10
28
u
37
+ ··· + 1.67323 × 10
29
b + 1.20675 × 10
29
,
− 1.82393 × 10
30
u
38
+ 7.78408 × 10
29
u
37
+ ··· + 1.17126 × 10
30
a + 1.39048 × 10
30
,
u
39
+ 12u
37
+ ··· + 14u + 7i
I
u
2
= h−u
9
− 2u
7
− 4u
5
− 4u
3
+ u
2
+ b − 3u + 1, −u
9
− u
8
− 2u
7
− u
6
− 3u
5
− 2u
4
− 3u
3
+ a − u − 1,
u
10
+ u
9
+ 3u
8
+ 2u
7
+ 5u
6
+ 3u
5
+ 6u
4
+ 2u
3
+ 4u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 49 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h1.79 × 10
29
u
38
− 5.51 × 10
28
u
37
+ · · · + 1.67 × 10
29
b + 1.21 ×
10
29
, −1.82 × 10
30
u
38
+ 7.78 × 10
29
u
37
+ · · · + 1.17 × 10
30
a + 1.39 ×
10
30
, u
39
+ 12u
37
+ · · · + 14u + 7i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
6
=
−u
u
3
+ u
a
9
=
1.55724u
38
− 0.664589u
37
+ ··· + 7.55322u − 1.18716
−1.06823u
38
+ 0.329244u
37
+ ··· − 6.46213u − 0.721210
a
5
=
0.737177u
38
+ 0.407586u
37
+ ··· + 13.5161u + 4.88745
−2.22063u
38
− 0.382128u
37
+ ··· − 28.9097u − 7.31310
a
8
=
1.34253u
38
− 0.801447u
37
+ ··· + 4.38094u − 2.85956
−2.08428u
38
+ 0.937331u
37
+ ··· − 8.48023u + 2.57739
a
11
=
0.596770u
38
− 0.670897u
37
+ ··· − 3.69102u − 2.60571
−1.27517u
38
+ 2.12949u
37
+ ··· + 15.8112u + 14.1929
a
4
=
−0.639576u
38
+ 0.925361u
37
+ ··· + 6.56459u + 5.74668
2.68940u
38
− 1.07792u
37
+ ··· + 15.6841u − 1.72061
a
10
=
1.55724u
38
− 0.664589u
37
+ ··· + 7.55322u − 1.18716
−2.21877u
38
+ 1.13010u
37
+ ··· − 8.05855u + 3.93091
a
10
=
1.55724u
38
− 0.664589u
37
+ ··· + 7.55322u − 1.18716
−2.21877u
38
+ 1.13010u
37
+ ··· − 8.05855u + 3.93091
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.03813u
38
− 1.76931u
37
+ ··· + 10.1449u − 9.34970
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
39
+ 12u
37
+ ··· + 14u + 7
c
2
u
39
+ 24u
38
+ ··· − 280u − 49
c
3
u
39
+ 3u
38
+ ··· + 9u + 1
c
4
, c
7
u
39
− 3u
38
+ ··· − 9u + 1
c
5
u
39
+ u
38
+ ··· − 1365u + 253
c
8
u
39
+ u
38
+ ··· − 11u + 1
c
9
u
39
− u
38
+ ··· − 265u + 47
c
10
u
39
+ 3u
38
+ ··· − 19u + 1
c
11
u
39
− u
38
+ ··· + 90u + 209
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
39
+ 24y
38
+ ··· − 280y −49
c
2
y
39
− 12y
38
+ ··· − 29400y −2401
c
3
y
39
+ 35y
38
+ ··· − 63y −1
c
4
, c
7
y
39
+ y
38
+ ··· + 37y −1
c
5
y
39
− 43y
38
+ ··· − 1224387y −64009
c
8
y
39
+ 9y
38
+ ··· + 31y −1
c
9
y
39
− 37y
38
+ ··· + 14483y −2209
c
10
y
39
+ 39y
38
+ ··· − 61y −1
c
11
y
39
− 23y
38
+ ··· + 796448y −43681
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.970374 + 0.165160I
a = −1.38216 + 0.38547I
b = 1.298900 + 0.346398I
−5.72155 + 0.54332I −4.48404 − 0.44801I
u = 0.970374 − 0.165160I
a = −1.38216 − 0.38547I
b = 1.298900 − 0.346398I
−5.72155 − 0.54332I −4.48404 + 0.44801I
u = −0.145422 + 0.960485I
a = −0.312403 + 1.125530I
b = −0.75018 − 1.96873I
−2.60397 − 3.58012I −5.99936 + 4.69227I
u = −0.145422 − 0.960485I
a = −0.312403 − 1.125530I
b = −0.75018 + 1.96873I
−2.60397 + 3.58012I −5.99936 − 4.69227I
u = 0.244496 + 0.924229I
a = 0.771798 + 0.143039I
b = 0.389292 − 0.068286I
−0.62997 + 1.59285I −3.23591 − 4.35949I
u = 0.244496 − 0.924229I
a = 0.771798 − 0.143039I
b = 0.389292 + 0.068286I
−0.62997 − 1.59285I −3.23591 + 4.35949I
u = −0.075811 + 0.941393I
a = −0.57379 − 1.58798I
b = −0.680895 + 0.570692I
1.322390 − 0.422831I −4.94003 − 1.41438I
u = −0.075811 − 0.941393I
a = −0.57379 + 1.58798I
b = −0.680895 − 0.570692I
1.322390 + 0.422831I −4.94003 + 1.41438I
u = −1.067820 + 0.145596I
a = −1.383670 + 0.195517I
b = 1.253910 − 0.603680I
−5.61750 + 7.80414I −3.64994 − 4.73695I
u = −1.067820 − 0.145596I
a = −1.383670 − 0.195517I
b = 1.253910 + 0.603680I
−5.61750 − 7.80414I −3.64994 + 4.73695I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.661560 + 0.856108I
a = −0.105096 − 0.363168I
b = 1.104730 − 0.357036I
5.00877 − 2.57683I 6.58497 + 2.64677I
u = −0.661560 − 0.856108I
a = −0.105096 + 0.363168I
b = 1.104730 + 0.357036I
5.00877 + 2.57683I 6.58497 − 2.64677I
u = −0.365080 + 1.061570I
a = −1.16765 + 0.98033I
b = −0.986442 − 0.985917I
−2.63598 − 6.13265I −3.84561 + 9.40841I
u = −0.365080 − 1.061570I
a = −1.16765 − 0.98033I
b = −0.986442 + 0.985917I
−2.63598 + 6.13265I −3.84561 − 9.40841I
u = 0.518178 + 0.693040I
a = 0.925341 − 0.451847I
b = −0.197420 + 0.429722I
0.23938 + 2.14007I −2.40854 − 4.03571I
u = 0.518178 − 0.693040I
a = 0.925341 + 0.451847I
b = −0.197420 − 0.429722I
0.23938 − 2.14007I −2.40854 + 4.03571I
u = −0.358275 + 0.727858I
a = 1.31473 + 0.56113I
b = −0.235788 + 1.229960I
−2.12535 + 1.41634I −6.42200 + 1.56979I
u = −0.358275 − 0.727858I
a = 1.31473 − 0.56113I
b = −0.235788 − 1.229960I
−2.12535 − 1.41634I −6.42200 − 1.56979I
u = 0.142576 + 1.181590I
a = −0.256537 + 0.091644I
b = −1.63516 + 0.43597I
−4.72844 + 2.99253I −9.56242 − 1.88756I
u = 0.142576 − 1.181590I
a = −0.256537 − 0.091644I
b = −1.63516 − 0.43597I
−4.72844 − 2.99253I −9.56242 + 1.88756I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.461639 + 1.163800I
a = 0.093896 + 1.347320I
b = −1.63447 − 0.73754I
−4.83553 − 4.15063I −11.12509 + 1.85834I
u = −0.461639 − 1.163800I
a = 0.093896 − 1.347320I
b = −1.63447 + 0.73754I
−4.83553 + 4.15063I −11.12509 − 1.85834I
u = 0.861374 + 0.909425I
a = 0.420286 − 0.450008I
b = −0.526827 − 0.046250I
0.74799 + 3.17123I −8.85439 − 3.48619I
u = 0.861374 − 0.909425I
a = 0.420286 + 0.450008I
b = −0.526827 + 0.046250I
0.74799 − 3.17123I −8.85439 + 3.48619I
u = 0.715910 + 0.207951I
a = 0.864160 − 0.809698I
b = −0.363007 + 0.664118I
1.08867 + 1.79567I 3.61269 − 3.73862I
u = 0.715910 − 0.207951I
a = 0.864160 + 0.809698I
b = −0.363007 − 0.664118I
1.08867 − 1.79567I 3.61269 + 3.73862I
u = −0.660029
a = 1.75790
b = −0.957650
−1.67672 −6.74230
u = 0.399747 + 1.326200I
a = −0.135365 + 1.304920I
b = 1.029460 − 0.406010I
−10.43670 + 5.23929I −7.47031 − 3.45363I
u = 0.399747 − 1.326200I
a = −0.135365 − 1.304920I
b = 1.029460 + 0.406010I
−10.43670 − 5.23929I −7.47031 + 3.45363I
u = 0.577975 + 1.276160I
a = −0.280369 + 0.960950I
b = 1.89166 − 0.46055I
−9.10381 + 5.07821I 0. − 3.17849I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.577975 − 1.276160I
a = −0.280369 − 0.960950I
b = 1.89166 + 0.46055I
−9.10381 − 5.07821I 0. + 3.17849I
u = 0.421432 + 1.340550I
a = −0.081054 − 0.871471I
b = −1.15598 + 1.11228I
−3.60682 + 6.09591I 0. − 11.09242I
u = 0.421432 − 1.340550I
a = −0.081054 + 0.871471I
b = −1.15598 − 1.11228I
−3.60682 − 6.09591I 0. + 11.09242I
u = −0.58423 + 1.30883I
a = −0.088865 − 1.209820I
b = 1.76564 + 0.87989I
−9.2430 − 13.6991I 0. + 7.27460I
u = −0.58423 − 1.30883I
a = −0.088865 + 1.209820I
b = 1.76564 − 0.87989I
−9.2430 + 13.6991I 0. − 7.27460I
u = −0.39136 + 1.40665I
a = −0.309024 − 0.965300I
b = 1.080110 + 0.188976I
−10.72520 + 2.62440I 0
u = −0.39136 − 1.40665I
a = −0.309024 + 0.965300I
b = 1.080110 − 0.188976I
−10.72520 − 2.62440I 0
u = −0.410850 + 0.313768I
a = 1.30683 − 1.45682I
b = −0.668694 + 1.027300I
−0.53003 + 2.77733I 1.12295 − 3.77344I
u = −0.410850 − 0.313768I
a = 1.30683 + 1.45682I
b = −0.668694 − 1.027300I
−0.53003 − 2.77733I 1.12295 + 3.77344I
8
II. I
u
2
=
h−u
9
−2u
7
−4u
5
−4u
3
+u
2
+b−3u+1, −u
9
−u
8
+· · ·+a−1, u
10
+u
9
+· · ·+u+1i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
6
=
−u
u
3
+ u
a
9
=
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ 2u
4
+ 3u
3
+ u + 1
u
9
+ 2u
7
+ 4u
5
+ 4u
3
− u
2
+ 3u − 1
a
5
=
−2u
9
− 2u
8
− 5u
7
− 3u
6
− 7u
5
− 4u
4
− 8u
3
− 2u
2
− 4u − 1
u
8
+ 2u
6
+ 3u
4
+ u
3
+ 4u
2
+ 2
a
8
=
2u
9
+ 2u
8
+ 5u
7
+ 3u
6
+ 7u
5
+ 4u
4
+ 7u
3
+ u
2
+ 3u + 1
−u
8
− u
6
+ 2u
5
− u
4
+ 2u
3
− u
2
+ 3u − 1
a
11
=
2u
8
+ u
7
+ 4u
6
+ u
5
+ 6u
4
+ u
3
+ 6u
2
− u + 4
3u
9
+ 2u
8
+ 7u
7
+ 4u
6
+ 12u
5
+ 6u
4
+ 13u
3
+ 3u
2
+ 7u + 2
a
4
=
−3u
9
− 3u
8
− 8u
7
− 6u
6
− 13u
5
− 9u
4
− 14u
3
− 5u
2
− 7u − 3
−u
9
+ u
8
− 2u
7
+ 3u
6
− 3u
5
+ 4u
4
− 4u
3
+ 5u
2
− 4u + 3
a
10
=
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ 2u
4
+ 3u
3
+ u + 1
−u
8
− u
6
+ u
5
− 2u
4
+ u
3
− u
2
+ 2u − 1
a
10
=
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ 2u
4
+ 3u
3
+ u + 1
−u
8
− u
6
+ u
5
− 2u
4
+ u
3
− u
2
+ 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
9
−3u
8
−12u
7
−8u
6
−16u
5
−10u
4
−18u
3
−10u
2
−11u − 6
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
+ u
9
+ 3u
8
+ 2u
7
+ 5u
6
+ 3u
5
+ 6u
4
+ 2u
3
+ 4u
2
+ u + 1
c
2
u
10
+ 5u
9
+ ··· + 7u + 1
c
3
u
10
+ 4u
8
+ 2u
7
+ 6u
6
+ 3u
5
+ 8u
4
+ u
3
+ 5u
2
+ 1
c
4
u
10
− 2u
9
+ 5u
8
− 6u
7
+ 4u
6
− u
5
− 3u
4
+ 3u
3
− u
2
+ 1
c
5
u
10
− u
8
+ 3u
7
− 3u
6
− u
5
+ 4u
4
− 6u
3
+ 5u
2
− 2u + 1
c
6
u
10
− u
9
+ 3u
8
− 2u
7
+ 5u
6
− 3u
5
+ 6u
4
− 2u
3
+ 4u
2
− u + 1
c
7
u
10
+ 2u
9
+ 5u
8
+ 6u
7
+ 4u
6
+ u
5
− 3u
4
− 3u
3
− u
2
+ 1
c
8
u
10
+ 5u
8
+ u
7
+ 8u
6
+ 3u
5
+ 6u
4
+ 2u
3
+ 4u
2
+ 1
c
9
u
10
− 4u
8
− 3u
7
+ 7u
6
+ 8u
5
− 2u
4
− 7u
3
− 2u
2
+ 2u + 1
c
10
u
10
− 2u
9
+ 4u
8
− 6u
7
+ 6u
6
− 6u
5
+ 6u
4
− u
3
− 2u
2
+ 1
c
11
u
10
+ 8u
9
+ ··· + 5u + 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
10
+ 5y
9
+ ··· + 7y + 1
c
2
y
10
+ 5y
9
+ 11y
8
+ 28y
7
+ 69y
6
+ 87y
5
+ 50y
4
+ 32y
3
+ 36y
2
− y + 1
c
3
y
10
+ 8y
9
+ ··· + 10y + 1
c
4
, c
7
y
10
+ 6y
9
+ 9y
8
− 6y
7
− 16y
6
+ 3y
5
+ 17y
4
+ 5y
3
− 5y
2
− 2y + 1
c
5
y
10
− 2y
9
− 5y
8
+ 5y
7
+ 17y
6
+ 3y
5
− 16y
4
− 6y
3
+ 9y
2
+ 6y + 1
c
8
y
10
+ 10y
9
+ ··· + 8y + 1
c
9
y
10
− 8y
9
+ ··· − 8y + 1
c
10
y
10
+ 4y
9
+ 4y
8
+ 4y
6
+ 10y
5
+ 8y
4
− 13y
3
+ 16y
2
− 4y + 1
c
11
y
10
− 2y
9
+ ··· + 15y + 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.283646 + 0.889181I
a = 0.85633 − 1.49046I
b = −0.041082 + 0.470245I
1.77560 + 1.23703I 1.12210 − 5.29149I
u = 0.283646 − 0.889181I
a = 0.85633 + 1.49046I
b = −0.041082 − 0.470245I
1.77560 − 1.23703I 1.12210 + 5.29149I
u = 0.688964 + 0.877700I
a = 0.359578 − 0.617446I
b = −1.45267 − 0.28253I
4.33849 + 2.65528I −5.99132 − 3.67032I
u = 0.688964 − 0.877700I
a = 0.359578 + 0.617446I
b = −1.45267 + 0.28253I
4.33849 − 2.65528I −5.99132 + 3.67032I
u = −0.879557 + 0.842212I
a = 0.319829 + 0.445214I
b = −0.183599 − 0.396507I
1.28605 − 3.24415I 6.98007 + 6.78944I
u = −0.879557 − 0.842212I
a = 0.319829 − 0.445214I
b = −0.183599 + 0.396507I
1.28605 + 3.24415I 6.98007 − 6.78944I
u = −0.372175 + 1.177670I
a = −0.299227 + 1.055980I
b = −1.51608 − 1.15104I
−4.06424 − 5.03997I −7.43062 + 5.98899I
u = −0.372175 − 1.177670I
a = −0.299227 − 1.055980I
b = −1.51608 + 1.15104I
−4.06424 + 5.03997I −7.43062 − 5.98899I
u = −0.220878 + 0.599013I
a = 1.263490 + 0.484575I
b = −0.80657 + 1.52040I
−1.69097 + 2.38428I −3.68022 − 2.86338I
u = −0.220878 − 0.599013I
a = 1.263490 − 0.484575I
b = −0.80657 − 1.52040I
−1.69097 − 2.38428I −3.68022 + 2.86338I
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
10
+ u
9
+ 3u
8
+ 2u
7
+ 5u
6
+ 3u
5
+ 6u
4
+ 2u
3
+ 4u
2
+ u + 1)
· (u
39
+ 12u
37
+ ··· + 14u + 7)
c
2
(u
10
+ 5u
9
+ ··· + 7u + 1)(u
39
+ 24u
38
+ ··· − 280u − 49)
c
3
(u
10
+ 4u
8
+ 2u
7
+ 6u
6
+ 3u
5
+ 8u
4
+ u
3
+ 5u
2
+ 1)
· (u
39
+ 3u
38
+ ··· + 9u + 1)
c
4
(u
10
− 2u
9
+ 5u
8
− 6u
7
+ 4u
6
− u
5
− 3u
4
+ 3u
3
− u
2
+ 1)
· (u
39
− 3u
38
+ ··· − 9u + 1)
c
5
(u
10
− u
8
+ 3u
7
− 3u
6
− u
5
+ 4u
4
− 6u
3
+ 5u
2
− 2u + 1)
· (u
39
+ u
38
+ ··· − 1365u + 253)
c
6
(u
10
− u
9
+ 3u
8
− 2u
7
+ 5u
6
− 3u
5
+ 6u
4
− 2u
3
+ 4u
2
− u + 1)
· (u
39
+ 12u
37
+ ··· + 14u + 7)
c
7
(u
10
+ 2u
9
+ 5u
8
+ 6u
7
+ 4u
6
+ u
5
− 3u
4
− 3u
3
− u
2
+ 1)
· (u
39
− 3u
38
+ ··· − 9u + 1)
c
8
(u
10
+ 5u
8
+ u
7
+ 8u
6
+ 3u
5
+ 6u
4
+ 2u
3
+ 4u
2
+ 1)
· (u
39
+ u
38
+ ··· − 11u + 1)
c
9
(u
10
− 4u
8
− 3u
7
+ 7u
6
+ 8u
5
− 2u
4
− 7u
3
− 2u
2
+ 2u + 1)
· (u
39
− u
38
+ ··· − 265u + 47)
c
10
(u
10
− 2u
9
+ 4u
8
− 6u
7
+ 6u
6
− 6u
5
+ 6u
4
− u
3
− 2u
2
+ 1)
· (u
39
+ 3u
38
+ ··· − 19u + 1)
c
11
(u
10
+ 8u
9
+ ··· + 5u + 1)(u
39
− u
38
+ ··· + 90u + 209)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
10
+ 5y
9
+ ··· + 7y + 1)(y
39
+ 24y
38
+ ··· − 280y −49)
c
2
(y
10
+ 5y
9
+ 11y
8
+ 28y
7
+ 69y
6
+ 87y
5
+ 50y
4
+ 32y
3
+ 36y
2
− y + 1)
· (y
39
− 12y
38
+ ··· − 29400y −2401)
c
3
(y
10
+ 8y
9
+ ··· + 10y + 1)(y
39
+ 35y
38
+ ··· − 63y −1)
c
4
, c
7
(y
10
+ 6y
9
+ 9y
8
− 6y
7
− 16y
6
+ 3y
5
+ 17y
4
+ 5y
3
− 5y
2
− 2y + 1)
· (y
39
+ y
38
+ ··· + 37y −1)
c
5
(y
10
− 2y
9
− 5y
8
+ 5y
7
+ 17y
6
+ 3y
5
− 16y
4
− 6y
3
+ 9y
2
+ 6y + 1)
· (y
39
− 43y
38
+ ··· − 1224387y −64009)
c
8
(y
10
+ 10y
9
+ ··· + 8y + 1)(y
39
+ 9y
38
+ ··· + 31y −1)
c
9
(y
10
− 8y
9
+ ··· − 8y + 1)(y
39
− 37y
38
+ ··· + 14483y −2209)
c
10
(y
10
+ 4y
9
+ 4y
8
+ 4y
6
+ 10y
5
+ 8y
4
− 13y
3
+ 16y
2
− 4y + 1)
· (y
39
+ 39y
38
+ ··· − 61y −1)
c
11
(y
10
− 2y
9
+ ··· + 15y + 1)(y
39
− 23y
38
+ ··· + 796448y −43681)
14
