11n
158
(K11n
158
)
A knot diagram
1
Linearized knot diagam
9 8 1 10 2 3 1 6 4 5 8
Solving Sequence
2,9 1,6
5 8 3 4 7 11 10
c
1
c
5
c
8
c
2
c
3
c
7
c
11
c
10
c
4
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, −159345685747u
18
+ 147982590951u
17
+ ··· + 96727442787a + 357093230263,
u
19
− u
18
+ ··· − u + 1i
I
u
2
= hb + u, 4343u
12
+ 7110u
11
+ ··· + 4787a + 1912,
u
13
+ u
12
− u
11
− 3u
10
− 2u
9
+ u
8
− 2u
6
+ u
5
− 4u
4
− 2u
3
− 2u
2
− 1i
I
u
3
= h1.31062 × 10
16
u
15
− 1.74217 × 10
16
u
14
+ ··· + 9.51505 × 10
17
b + 6.50537 × 10
17
,
1.97533 × 10
15
u
15
− 3.11116 × 10
14
u
14
+ ··· + 5.49461 × 10
17
a + 2.28716 × 10
17
, u
16
− 3u
15
+ ··· + 14u + 41i
* 3 irreducible components of dim
C
= 0, with total 48 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
= hb − u, −1.59 × 10
11
u
18
+ 1.48 × 10
11
u
17
+ · · · + 9.67 × 10
10
a +
3.57 × 10
11
, u
19
− u
18
+ · · · − u + 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
1
=
1
u
2
a
6
=
1.64737u
18
− 1.52989u
17
+ ··· + 32.1590u − 3.69175
u
a
5
=
1.64737u
18
− 1.52989u
17
+ ··· + 31.1590u − 3.69175
u
a
8
=
2.27741u
18
− 2.43525u
17
+ ··· + 37.2324u − 9.52801
0.111340u
18
− 0.0665068u
17
+ ··· + 2.52989u + 0.117475
a
3
=
−0.820898u
18
+ 0.672626u
17
+ ··· − 23.6867u − 3.53398
0.162954u
18
− 0.347555u
17
+ ··· + 0.470733u − 0.393621
a
4
=
−1.01209u
18
+ 0.851055u
17
+ ··· − 23.4848u − 2.99209
0.340664u
18
− 0.462435u
17
+ ··· + 0.649162u − 0.380858
a
7
=
2.55969u
18
− 2.59941u
17
+ ··· + 42.1976u − 9.56837
−0.0125024u
18
− 0.0176043u
17
+ ··· + 2.36573u − 0.000645074
a
11
=
2.20417u
18
− 1.64059u
17
+ ··· + 52.9687u + 7.25501
−0.191192u
18
+ 0.178429u
17
+ ··· + 0.201893u + 0.541893
a
10
=
0.426507u
18
− 0.339257u
17
+ ··· + 12.4593u + 5.79766
−0.340664u
18
+ 0.462435u
17
+ ··· − 0.649162u + 0.380858
a
10
=
0.426507u
18
− 0.339257u
17
+ ··· + 12.4593u + 5.79766
−0.340664u
18
+ 0.462435u
17
+ ··· − 0.649162u + 0.380858
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
162836171512
96727442787
u
18
−
43813217810
32242480929
u
17
+ ··· +
1086609567736
32242480929
u +
428864721314
96727442787
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
19
− u
18
+ ··· − u + 1
c
2
u
19
− 10u
17
+ ··· + 21u + 6
c
3
u
19
− 9u
18
+ ··· + 52u − 16
c
4
, c
9
, c
10
u
19
− 9u
18
+ ··· − 4u
2
+ 16
c
6
, c
7
, c
11
u
19
+ u
18
+ ··· + 2u + 1
c
8
u
19
+ 9u
18
+ ··· + 34u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
19
+ 15y
18
+ ··· − 47y −1
c
2
y
19
− 20y
18
+ ··· + 273y −36
c
3
y
19
− 25y
18
+ ··· + 6064y −256
c
4
, c
9
, c
10
y
19
− 17y
18
+ ··· + 128y −256
c
6
, c
7
, c
11
y
19
− 33y
18
+ ··· + 12y −1
c
8
y
19
− y
18
+ ··· − 116y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.074551 + 1.005150I
a = 0.755499 − 0.268182I
b = −0.074551 + 1.005150I
−6.47985 − 3.00781I −9.19206 + 3.40012I
u = −0.074551 − 1.005150I
a = 0.755499 + 0.268182I
b = −0.074551 − 1.005150I
−6.47985 + 3.00781I −9.19206 − 3.40012I
u = 0.719291 + 0.870215I
a = 0.618624 + 0.041528I
b = 0.719291 + 0.870215I
−0.22723 + 2.57483I −7.79227 − 4.00370I
u = 0.719291 − 0.870215I
a = 0.618624 − 0.041528I
b = 0.719291 − 0.870215I
−0.22723 − 2.57483I −7.79227 + 4.00370I
u = −0.015666 + 1.186340I
a = 1.00740 − 1.04818I
b = −0.015666 + 1.186340I
−8.13053 + 0.97689I −10.22917 − 0.27205I
u = −0.015666 − 1.186340I
a = 1.00740 + 1.04818I
b = −0.015666 − 1.186340I
−8.13053 − 0.97689I −10.22917 + 0.27205I
u = −0.799079
a = −0.714422
b = −0.799079
−1.52055 −7.33430
u = −0.197897 + 0.643434I
a = −0.839512 + 0.061465I
b = −0.197897 + 0.643434I
−0.928589 + 0.684123I −8.21629 − 4.45735I
u = −0.197897 − 0.643434I
a = −0.839512 − 0.061465I
b = −0.197897 − 0.643434I
−0.928589 − 0.684123I −8.21629 + 4.45735I
u = −0.78204 + 1.18371I
a = −0.553988 + 0.003237I
b = −0.78204 + 1.18371I
−5.79784 − 5.72974I −14.4693 + 5.0563I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.78204 − 1.18371I
a = −0.553988 − 0.003237I
b = −0.78204 − 1.18371I
−5.79784 + 5.72974I −14.4693 − 5.0563I
u = −0.58654 + 1.32638I
a = −1.071040 − 0.314706I
b = −0.58654 + 1.32638I
−8.63276 − 7.82560I −8.78089 + 5.39108I
u = −0.58654 − 1.32638I
a = −1.071040 + 0.314706I
b = −0.58654 − 1.32638I
−8.63276 + 7.82560I −8.78089 − 5.39108I
u = 0.70619 + 1.27768I
a = −0.185916 − 1.077090I
b = 0.70619 + 1.27768I
−15.6607 + 4.6824I −10.38940 − 2.40952I
u = 0.70619 − 1.27768I
a = −0.185916 + 1.077090I
b = 0.70619 − 1.27768I
−15.6607 − 4.6824I −10.38940 + 2.40952I
u = 0.050654 + 0.205531I
a = −4.15202 + 6.06789I
b = 0.050654 + 0.205531I
2.26122 + 2.63337I 2.15678 + 7.21953I
u = 0.050654 − 0.205531I
a = −4.15202 − 6.06789I
b = 0.050654 − 0.205531I
2.26122 − 2.63337I 2.15678 − 7.21953I
u = 1.08010 + 1.60653I
a = 0.778162 − 0.084178I
b = 1.08010 + 1.60653I
−16.5060 + 12.7254I −9.92028 − 5.57941I
u = 1.08010 − 1.60653I
a = 0.778162 + 0.084178I
b = 1.08010 − 1.60653I
−16.5060 − 12.7254I −9.92028 + 5.57941I
6
II.
I
u
2
= hb +u, 4343u
12
+ 7110u
11
+ · · · + 4787a + 1912, u
13
+ u
12
+ · · · − 2u
2
− 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
1
=
1
u
2
a
6
=
−0.907249u
12
− 1.48527u
11
+ ··· + 1.45874u − 0.399415
−u
a
5
=
−0.907249u
12
− 1.48527u
11
+ ··· + 2.45874u − 0.399415
−u
a
8
=
−1.64216u
12
− 2.04115u
11
+ ··· + 2.52663u − 1.91936
0.199081u
12
+ 0.339043u
11
+ ··· + 0.0927512u − 0.578024
a
3
=
−0.578024u
12
− 1.37894u
11
+ ··· + 1.60058u + 2.09275
−0.300606u
12
− 0.253812u
11
+ ··· − 0.757050u + 0.0963025
a
4
=
−0.137456u
12
− 0.933988u
11
+ ··· + 1.77961u + 1.19553
−0.604972u
12
− 0.393357u
11
+ ··· − 0.316482u + 0.100689
a
7
=
−1.74493u
12
− 2.58450u
11
+ ··· + 4.26154u − 2.09839
0.194694u
12
+ 0.639022u
11
+ ··· − 0.0100272u − 1.01859
a
11
=
−0.399415u
12
− 1.30666u
11
+ ··· + 5.21370u + 2.45874
0.440568u
12
+ 0.444955u
11
+ ··· + 0.179027u − 0.897222
a
10
=
0.374556u
12
+ 0.339879u
11
+ ··· + 1.20389u + 1.04470
0.604972u
12
+ 0.393357u
11
+ ··· + 0.316482u − 0.100689
a
10
=
0.374556u
12
+ 0.339879u
11
+ ··· + 1.20389u + 1.04470
0.604972u
12
+ 0.393357u
11
+ ··· + 0.316482u − 0.100689
(ii) Obstruction class = 1
(iii) Cusp Shapes =
14164
4787
u
12
+
37634
4787
u
11
+ ··· −
78472
4787
u −
64919
4787
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
13
+ u
12
− u
11
− 3u
10
− 2u
9
+ u
8
− 2u
6
+ u
5
− 4u
4
− 2u
3
− 2u
2
− 1
c
2
u
13
− 3u
11
− 2u
10
+ 3u
9
+ u
8
− 9u
7
− 11u
6
+ u
5
− 2u
4
− 10u
3
− 3u
2
− 1
c
3
u
13
+ 10u
12
+ ··· + 19u + 5
c
4
u
13
− 7u
11
+ ··· + 2u + 1
c
6
, c
11
u
13
− u
12
+ ··· + u − 1
c
7
u
13
+ u
12
+ ··· + u + 1
c
8
u
13
− 6u
12
+ ··· − 5u
2
+ 1
c
9
, c
10
u
13
− 7u
11
+ ··· + 2u − 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
13
− 3y
12
+ ··· − 4y −1
c
2
y
13
− 6y
12
+ ··· − 6y −1
c
3
y
13
− 18y
12
+ ··· − 59y −25
c
4
, c
9
, c
10
y
13
− 14y
12
+ ··· + 12y −1
c
6
, c
7
, c
11
y
13
− 7y
12
+ ··· − 9y −1
c
8
y
13
− 2y
12
+ ··· + 10y −1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.900740 + 0.533669I
a = −1.166450 − 0.261249I
b = −0.900740 − 0.533669I
1.59640 + 3.38566I 2.41525 − 6.49353I
u = 0.900740 − 0.533669I
a = −1.166450 + 0.261249I
b = −0.900740 + 0.533669I
1.59640 − 3.38566I 2.41525 + 6.49353I
u = 0.134578 + 0.883277I
a = −1.058690 − 0.319537I
b = −0.134578 − 0.883277I
−8.02879 − 2.87155I −15.3113 + 3.5915I
u = 0.134578 − 0.883277I
a = −1.058690 + 0.319537I
b = −0.134578 + 0.883277I
−8.02879 + 2.87155I −15.3113 − 3.5915I
u = −0.529571 + 0.532870I
a = 0.059596 − 1.149930I
b = 0.529571 − 0.532870I
−5.39720 + 0.76633I −5.46823 + 1.57837I
u = −0.529571 − 0.532870I
a = 0.059596 + 1.149930I
b = 0.529571 + 0.532870I
−5.39720 − 0.76633I −5.46823 − 1.57837I
u = −1.310290 + 0.394846I
a = 0.714514 − 0.488710I
b = 1.310290 − 0.394846I
−1.52980 − 2.82140I −9.56946 + 2.96660I
u = −1.310290 − 0.394846I
a = 0.714514 + 0.488710I
b = 1.310290 + 0.394846I
−1.52980 + 2.82140I −9.56946 − 2.96660I
u = −0.736626 + 1.155190I
a = 0.633923 + 0.241978I
b = 0.736626 − 1.155190I
−4.89940 − 5.64504I −5.13604 + 4.51836I
u = −0.736626 − 1.155190I
a = 0.633923 − 0.241978I
b = 0.736626 + 1.155190I
−4.89940 + 5.64504I −5.13604 − 4.51836I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.266732 + 0.548396I
a = −1.77971 + 1.81477I
b = −0.266732 − 0.548396I
2.09623 + 2.92285I −9.7624 − 12.7438I
u = 0.266732 − 0.548396I
a = −1.77971 − 1.81477I
b = −0.266732 + 0.548396I
2.09623 − 2.92285I −9.7624 + 12.7438I
u = 1.54888
a = 0.193632
b = −1.54888
−13.7330 −11.3360
11
III. I
u
3
=
h1.31×10
16
u
15
−1.74×10
16
u
14
+· · ·+9.52×10
17
b+6.51×10
17
, 1.98×10
15
u
15
−
3.11 × 10
14
u
14
+ · · · + 5.49 × 10
17
a + 2.29 × 10
17
, u
16
− 3u
15
+ · · · + 14u + 41i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
1
=
1
u
2
a
6
=
−0.00359503u
15
+ 0.000566220u
14
+ ··· − 0.579421u − 0.416256
−0.0137742u
15
+ 0.0183096u
14
+ ··· − 1.40476u − 0.683692
a
5
=
0.0101791u
15
− 0.0177434u
14
+ ··· + 0.825342u + 0.267436
−0.0137742u
15
+ 0.0183096u
14
+ ··· − 1.40476u − 0.683692
a
8
=
0.00188225u
15
+ 0.00703654u
14
+ ··· − 0.906661u + 0.946317
0.00958945u
15
− 0.0187823u
14
+ ··· + 0.0486549u + 0.591789
a
3
=
−0.0135877u
15
+ 0.0698365u
14
+ ··· − 0.200013u + 1.71159
0.00578290u
15
− 0.00717672u
14
+ ··· + 1.12471u + 0.593614
a
4
=
−0.0142111u
15
+ 0.0554273u
14
+ ··· − 1.17466u − 0.0740275
0.0136940u
15
− 0.0307409u
14
+ ··· + 1.37818u + 1.26107
a
7
=
0.0120905u
15
− 0.00811315u
14
+ ··· − 0.603268u + 2.05812
0.000452209u
15
− 0.00935974u
14
+ ··· − 0.586534u − 0.0426882
a
11
=
0.0142111u
15
− 0.0554273u
14
+ ··· + 1.17466u + 0.0740275
−0.000623414u
15
− 0.0144091u
14
+ ··· − 0.974645u − 1.78562
a
10
=
0.0101791u
15
− 0.0177434u
14
+ ··· + 0.825342u + 0.267436
−0.000703594u
15
− 0.0268404u
14
+ ··· − 0.00122333u − 1.20825
a
10
=
0.0101791u
15
− 0.0177434u
14
+ ··· + 0.825342u + 0.267436
−0.000703594u
15
− 0.0268404u
14
+ ··· − 0.00122333u − 1.20825
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
1227691828059108
13401481882079569
u
15
−
4398465163137376
13401481882079569
u
14
+ ···+
68931370501080476
13401481882079569
u −
199658948531840914
13401481882079569
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
16
− 3u
15
+ ··· + 14u + 41
c
2
u
16
− u
15
+ ··· − 398u + 359
c
3
(u
4
+ 3u
3
+ u
2
− 2u + 1)
4
c
4
, c
9
, c
10
(u
2
+ u − 1)
8
c
6
, c
7
, c
11
u
16
− u
15
+ ··· − 314u + 59
c
8
(u
4
− u
3
+ u
2
+ 1)
4
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
16
− y
15
+ ··· + 6528y + 1681
c
2
y
16
− 13y
15
+ ··· − 519558y + 128881
c
3
(y
4
− 7y
3
+ 15y
2
− 2y + 1)
4
c
4
, c
9
, c
10
(y
2
− 3y + 1)
8
c
6
, c
7
, c
11
y
16
− 21y
15
+ ··· − 63668y + 3481
c
8
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
4
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.070726 + 1.109990I
a = −0.866375 + 0.712201I
b = −0.71670 − 1.63688I
−7.02670 + 3.16396I −10.17326 − 2.56480I
u = 0.070726 − 1.109990I
a = −0.866375 − 0.712201I
b = −0.71670 + 1.63688I
−7.02670 − 3.16396I −10.17326 + 2.56480I
u = 0.779961 + 0.810134I
a = 0.678421 + 0.218895I
b = 2.29306 − 1.45821I
−14.02850 + 1.41510I −13.8267 − 4.9087I
u = 0.779961 − 0.810134I
a = 0.678421 − 0.218895I
b = 2.29306 + 1.45821I
−14.02850 − 1.41510I −13.8267 + 4.9087I
u = −0.749741 + 0.435456I
a = 1.37743 − 0.41545I
b = 0.996480 − 0.636712I
0.86898 − 3.16396I −10.17326 + 2.56480I
u = −0.749741 − 0.435456I
a = 1.37743 + 0.41545I
b = 0.996480 + 0.636712I
0.86898 + 3.16396I −10.17326 − 2.56480I
u = 0.996480 + 0.636712I
a = −1.021930 − 0.261538I
b = −0.749741 − 0.435456I
0.86898 + 3.16396I −10.17326 − 2.56480I
u = 0.996480 − 0.636712I
a = −1.021930 + 0.261538I
b = −0.749741 + 0.435456I
0.86898 − 3.16396I −10.17326 + 2.56480I
u = −0.062069 + 0.700905I
a = −1.063840 − 0.407726I
b = −1.11172 − 0.94845I
−6.13277 − 1.41510I −13.8267 + 4.9087I
u = −0.062069 − 0.700905I
a = −1.063840 + 0.407726I
b = −1.11172 + 0.94845I
−6.13277 + 1.41510I −13.8267 − 4.9087I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.11172 + 0.94845I
a = 0.136782 − 0.531259I
b = −0.062069 − 0.700905I
−6.13277 + 1.41510I −13.8267 − 4.9087I
u = −1.11172 − 0.94845I
a = 0.136782 + 0.531259I
b = −0.062069 + 0.700905I
−6.13277 − 1.41510I −13.8267 + 4.9087I
u = −0.71670 + 1.63688I
a = 0.658359 + 0.232127I
b = 0.070726 − 1.109990I
−7.02670 − 3.16396I −10.17326 + 2.56480I
u = −0.71670 − 1.63688I
a = 0.658359 − 0.232127I
b = 0.070726 + 1.109990I
−7.02670 + 3.16396I −10.17326 − 2.56480I
u = 2.29306 + 1.45821I
a = −0.033000 − 0.293154I
b = 0.779961 − 0.810134I
−14.02850 − 1.41510I −13.8267 + 4.9087I
u = 2.29306 − 1.45821I
a = −0.033000 + 0.293154I
b = 0.779961 + 0.810134I
−14.02850 + 1.41510I −13.8267 − 4.9087I
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
13
+ u
12
− u
11
− 3u
10
− 2u
9
+ u
8
− 2u
6
+ u
5
− 4u
4
− 2u
3
− 2u
2
− 1)
· (u
16
− 3u
15
+ ··· + 14u + 41)(u
19
− u
18
+ ··· − u + 1)
c
2
(u
13
− 3u
11
− 2u
10
+ 3u
9
+ u
8
− 9u
7
− 11u
6
+ u
5
− 2u
4
− 10u
3
− 3u
2
− 1)
· (u
16
− u
15
+ ··· − 398u + 359)(u
19
− 10u
17
+ ··· + 21u + 6)
c
3
((u
4
+ 3u
3
+ u
2
− 2u + 1)
4
)(u
13
+ 10u
12
+ ··· + 19u + 5)
· (u
19
− 9u
18
+ ··· + 52u − 16)
c
4
((u
2
+ u − 1)
8
)(u
13
− 7u
11
+ ··· + 2u + 1)(u
19
− 9u
18
+ ··· − 4u
2
+ 16)
c
6
, c
11
(u
13
− u
12
+ ··· + u − 1)(u
16
− u
15
+ ··· − 314u + 59)
· (u
19
+ u
18
+ ··· + 2u + 1)
c
7
(u
13
+ u
12
+ ··· + u + 1)(u
16
− u
15
+ ··· − 314u + 59)
· (u
19
+ u
18
+ ··· + 2u + 1)
c
8
((u
4
− u
3
+ u
2
+ 1)
4
)(u
13
− 6u
12
+ ··· − 5u
2
+ 1)
· (u
19
+ 9u
18
+ ··· + 34u + 4)
c
9
, c
10
((u
2
+ u − 1)
8
)(u
13
− 7u
11
+ ··· + 2u − 1)(u
19
− 9u
18
+ ··· − 4u
2
+ 16)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
13
− 3y
12
+ ··· − 4y −1)(y
16
− y
15
+ ··· + 6528y + 1681)
· (y
19
+ 15y
18
+ ··· − 47y −1)
c
2
(y
13
− 6y
12
+ ··· − 6y −1)(y
16
− 13y
15
+ ··· − 519558y + 128881)
· (y
19
− 20y
18
+ ··· + 273y −36)
c
3
((y
4
− 7y
3
+ 15y
2
− 2y + 1)
4
)(y
13
− 18y
12
+ ··· − 59y −25)
· (y
19
− 25y
18
+ ··· + 6064y −256)
c
4
, c
9
, c
10
((y
2
− 3y + 1)
8
)(y
13
− 14y
12
+ ··· + 12y −1)
· (y
19
− 17y
18
+ ··· + 128y −256)
c
6
, c
7
, c
11
(y
13
− 7y
12
+ ··· − 9y −1)(y
16
− 21y
15
+ ··· − 63668y + 3481)
· (y
19
− 33y
18
+ ··· + 12y −1)
c
8
((y
4
+ y
3
+ 3y
2
+ 2y + 1)
4
)(y
13
− 2y
12
+ ··· + 10y −1)
· (y
19
− y
18
+ ··· − 116y −16)
18
