11n
166
(K11n
166
)
A knot diagram
1
Linearized knot diagam
5 7 1 10 2 9 2 11 4 6 7
Solving Sequence
1,5 2,7
3 6 8 11 9 10 4
c
1
c
2
c
5
c
7
c
11
c
8
c
10
c
4
c
3
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h1.30687 × 10
68
u
41
− 1.54062 × 10
68
u
40
+ ··· + 9.86366 × 10
67
b + 1.76058 × 10
68
,
− 2.28329 × 10
67
u
41
− 9.73388 × 10
67
u
40
+ ··· + 9.86366 × 10
67
a + 5.08435 × 10
68
,
u
42
− 2u
41
+ ··· − 12u − 1i
I
u
2
= h−33u
12
− 73u
11
+ ··· + 23b − 41, −242u
12
− 589u
11
+ ··· + 23a − 362,
u
13
+ 3u
12
+ 2u
11
− 3u
10
− 9u
9
− 9u
8
+ 5u
7
+ 18u
6
+ 7u
5
− 9u
4
− 9u
3
+ 3u + 1i
* 2 irreducible components of dim
C
= 0, with total 55 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
= h1.31 × 10
68
u
41
− 1.54 × 10
68
u
40
+ · · · + 9.86 × 10
67
b + 1.76 ×
10
68
, −2.28 × 10
67
u
41
− 9.73 × 10
67
u
40
+ · · · + 9.86 × 10
67
a + 5.08 ×
10
68
, u
42
− 2u
41
+ · · · − 12u − 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
7
=
0.231485u
41
+ 0.986842u
40
+ ··· + 194.921u − 5.15463
−1.32493u
41
+ 1.56192u
40
+ ··· − 20.7796u − 1.78491
a
3
=
5.28014u
41
− 6.60175u
40
+ ··· + 194.483u + 34.5032
−0.411012u
41
+ 0.388919u
40
+ ··· − 0.134181u − 0.550999
a
6
=
−u
−u
3
+ u
a
8
=
2.74943u
41
− 1.78847u
40
+ ··· + 233.329u − 1.91990
0.549437u
41
− 0.604447u
40
+ ··· + 8.86516u + 0.475658
a
11
=
−3.86650u
41
+ 4.37940u
40
+ ··· − 154.682u − 24.8689
−1.84296u
41
+ 2.51664u
40
+ ··· − 43.9754u − 2.80259
a
9
=
−10.3413u
41
+ 13.9461u
40
+ ··· − 201.572u − 32.5039
7.39043u
41
− 10.4148u
40
+ ··· + 159.817u + 12.0772
a
10
=
−2.07285u
41
+ 1.91194u
40
+ ··· − 116.180u − 21.9484
−2.88801u
41
+ 4.05483u
40
+ ··· − 67.2450u − 4.60324
a
4
=
5.69115u
41
− 6.99067u
40
+ ··· + 194.617u + 35.0542
−0.411012u
41
+ 0.388919u
40
+ ··· − 0.134181u − 0.550999
a
4
=
5.69115u
41
− 6.99067u
40
+ ··· + 194.617u + 35.0542
−0.411012u
41
+ 0.388919u
40
+ ··· − 0.134181u − 0.550999
(ii) Obstruction class = −1
(iii) Cusp Shapes = 29.0951u
41
− 41.2441u
40
+ ··· + 827.490u + 68.4277
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
42
+ 2u
41
+ ··· + 12u − 1
c
2
, c
7
u
42
+ u
41
+ ··· + 29u + 151
c
3
u
42
− 3u
41
+ ··· + 75u + 19
c
4
, c
9
u
42
+ 3u
41
+ ··· + 21u + 13
c
6
u
42
+ 6u
41
+ ··· + 15u + 1
c
8
u
42
− 6u
41
+ ··· − 87352u + 17077
c
10
u
42
− 2u
41
+ ··· − 423u − 43
c
11
u
42
+ u
41
+ ··· + 2205u + 297
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
42
− 30y
41
+ ··· − 44y + 1
c
2
, c
7
y
42
− 57y
41
+ ··· − 202275y + 22801
c
3
y
42
− 61y
41
+ ··· − 7753y + 361
c
4
, c
9
y
42
− 25y
41
+ ··· − 2261y + 169
c
6
y
42
− 2y
41
+ ··· − 9y + 1
c
8
y
42
− 58y
41
+ ··· − 2530360008y + 291623929
c
10
y
42
+ 10y
41
+ ··· + 9411y + 1849
c
11
y
42
− 57y
41
+ ··· − 501471y + 88209
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.971644 + 0.228980I
a = −0.660225 − 0.077093I
b = 0.121229 − 0.121842I
−1.74908 − 0.43337I −4.63201 + 0.76425I
u = 0.971644 − 0.228980I
a = −0.660225 + 0.077093I
b = 0.121229 + 0.121842I
−1.74908 + 0.43337I −4.63201 − 0.76425I
u = −0.935799 + 0.492680I
a = 0.995156 + 0.254691I
b = 0.697241 − 0.562142I
−1.54069 + 4.15417I −3.00000 − 7.39011I
u = −0.935799 − 0.492680I
a = 0.995156 − 0.254691I
b = 0.697241 + 0.562142I
−1.54069 − 4.15417I −3.00000 + 7.39011I
u = −0.393155 + 0.800612I
a = −0.149356 − 0.205071I
b = −0.541363 + 0.329653I
2.76017 − 1.64933I −1.74728 + 0.60366I
u = −0.393155 − 0.800612I
a = −0.149356 + 0.205071I
b = −0.541363 − 0.329653I
2.76017 + 1.64933I −1.74728 − 0.60366I
u = 1.104400 + 0.249694I
a = 0.436118 − 0.996945I
b = 0.530412 + 0.326797I
−2.78567 − 0.99125I −11.10311 − 4.39500I
u = 1.104400 − 0.249694I
a = 0.436118 + 0.996945I
b = 0.530412 − 0.326797I
−2.78567 + 0.99125I −11.10311 + 4.39500I
u = −1.155180 + 0.226642I
a = 0.752466 + 0.511395I
b = 0.896926 + 1.040480I
−1.88826 − 1.20315I 0
u = −1.155180 − 0.226642I
a = 0.752466 − 0.511395I
b = 0.896926 − 1.040480I
−1.88826 + 1.20315I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.17730
a = 2.81430
b = 1.42191
−4.47617 5.20530
u = 1.255780 + 0.019663I
a = −2.27463 − 0.18547I
b = −1.95961 − 0.66957I
−7.36750 − 2.87143I 0
u = 1.255780 − 0.019663I
a = −2.27463 + 0.18547I
b = −1.95961 + 0.66957I
−7.36750 + 2.87143I 0
u = −1.114120 + 0.594857I
a = −0.017502 − 0.611763I
b = −0.609070 − 0.365005I
0.58975 + 6.86368I 0
u = −1.114120 − 0.594857I
a = −0.017502 + 0.611763I
b = −0.609070 + 0.365005I
0.58975 − 6.86368I 0
u = 0.514470 + 1.177460I
a = −0.0735393 − 0.0954487I
b = −1.57588 + 0.26064I
−5.82264 − 2.10553I 0
u = 0.514470 − 1.177460I
a = −0.0735393 + 0.0954487I
b = −1.57588 − 0.26064I
−5.82264 + 2.10553I 0
u = −1.367560 + 0.254517I
a = −0.890031 + 0.144472I
b = −0.850798 − 0.662707I
−0.09515 + 5.56736I 0
u = −1.367560 − 0.254517I
a = −0.890031 − 0.144472I
b = −0.850798 + 0.662707I
−0.09515 − 5.56736I 0
u = 0.574212 + 0.117339I
a = −0.393410 − 0.999550I
b = −1.252340 − 0.394572I
−4.70197 − 3.01261I −11.65660 + 2.21081I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.574212 − 0.117339I
a = −0.393410 + 0.999550I
b = −1.252340 + 0.394572I
−4.70197 + 3.01261I −11.65660 − 2.21081I
u = 0.568925 + 0.051008I
a = −1.46927 − 0.44701I
b = 1.069300 − 0.013204I
−2.53352 − 0.05674I −5.88497 − 7.01523I
u = 0.568925 − 0.051008I
a = −1.46927 + 0.44701I
b = 1.069300 + 0.013204I
−2.53352 + 0.05674I −5.88497 + 7.01523I
u = −0.07204 + 1.42728I
a = −0.086850 − 1.160690I
b = −0.345695 + 1.176360I
5.55360 − 0.39636I 0
u = −0.07204 − 1.42728I
a = −0.086850 + 1.160690I
b = −0.345695 − 1.176360I
5.55360 + 0.39636I 0
u = 1.48422 + 0.23506I
a = −0.717440 − 0.244330I
b = −0.52362 − 1.68426I
−1.15694 − 4.97445I 0
u = 1.48422 − 0.23506I
a = −0.717440 + 0.244330I
b = −0.52362 + 1.68426I
−1.15694 + 4.97445I 0
u = 0.11486 + 1.51372I
a = −0.0321052 + 0.0488945I
b = 2.03791 − 0.23200I
−4.38173 + 6.68735I 0
u = 0.11486 − 1.51372I
a = −0.0321052 − 0.0488945I
b = 2.03791 + 0.23200I
−4.38173 − 6.68735I 0
u = −1.47470 + 0.37744I
a = −1.67468 − 0.56566I
b = −1.90596 + 0.26710I
−12.10630 + 7.14794I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.47470 − 0.37744I
a = −1.67468 + 0.56566I
b = −1.90596 − 0.26710I
−12.10630 − 7.14794I 0
u = −1.62716
a = 1.69579
b = 2.74174
−10.4541 0
u = 1.48967 + 0.67284I
a = 1.32309 − 0.83780I
b = 1.98195 + 0.65769I
−8.8694 − 14.1954I 0
u = 1.48967 − 0.67284I
a = 1.32309 + 0.83780I
b = 1.98195 − 0.65769I
−8.8694 + 14.1954I 0
u = 1.45552 + 0.81312I
a = −1.080210 + 0.896892I
b = −1.75516 − 0.59909I
−8.67069 − 5.62021I 0
u = 1.45552 − 0.81312I
a = −1.080210 − 0.896892I
b = −1.75516 + 0.59909I
−8.67069 + 5.62021I 0
u = −0.049563 + 0.302088I
a = −1.34651 + 0.47011I
b = 0.315782 + 0.486715I
−0.096362 − 1.232180I −1.37808 + 5.47691I
u = −0.049563 − 0.302088I
a = −1.34651 − 0.47011I
b = 0.315782 − 0.486715I
−0.096362 + 1.232180I −1.37808 − 5.47691I
u = −1.68157 + 0.33743I
a = 1.39696 + 0.40870I
b = 2.25961 − 0.16660I
−11.08320 + 0.67325I 0
u = −1.68157 − 0.33743I
a = 1.39696 − 0.40870I
b = 2.25961 + 0.16660I
−11.08320 − 0.67325I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.0650964 + 0.0552947I
a = −17.7931 + 18.4218I
b = −0.172689 − 0.653820I
5.14610 − 3.90439I 9.21708 + 9.57987I
u = −0.0650964 − 0.0552947I
a = −17.7931 − 18.4218I
b = −0.172689 + 0.653820I
5.14610 + 3.90439I 9.21708 − 9.57987I
9
II. I
u
2
= h−33u
12
− 73u
11
+ · · · + 23b − 41, −242u
12
− 589u
11
+ · · · + 23a −
362, u
13
+ 3u
12
+ · · · + 3u + 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
7
=
10.5217u
12
+ 25.6087u
11
+ ··· + 23.0870u + 15.7391
1.43478u
12
+ 3.17391u
11
+ ··· + 1.73913u + 1.78261
a
3
=
−2.26087u
12
− 5.30435u
11
+ ··· − 3.04348u + 2.13043
−0.695652u
12
− 1.47826u
11
+ ··· − 3.78261u − 1.65217
a
6
=
−u
−u
3
+ u
a
8
=
13.1739u
12
+ 32.8696u
11
+ ··· + 28.6957u + 19.9130
2.04348u
12
+ 5.21739u
11
+ ··· + 1.17391u + 2.47826
a
11
=
0.521739u
12
+ 2.60870u
11
+ ··· + 0.0869565u + 3.73913
−0.217391u
12
− 0.0869565u
11
+ ··· + 0.130435u + 0.608696
a
9
=
2.04348u
12
+ 2.21739u
11
+ ··· + 18.1739u + 5.47826
1.73913u
12
+ 5.69565u
11
+ ··· − 2.04348u + 1.13043
a
10
=
1.65217u
12
+ 5.26087u
11
+ ··· + 2.60870u + 4.17391
−0.826087u
12
− 1.13043u
11
+ ··· − 1.30435u + 0.913043
a
4
=
−1.56522u
12
− 3.82609u
11
+ ··· + 0.739130u + 3.78261
−0.695652u
12
− 1.47826u
11
+ ··· − 3.78261u − 1.65217
a
4
=
−1.56522u
12
− 3.82609u
11
+ ··· + 0.739130u + 3.78261
−0.695652u
12
− 1.47826u
11
+ ··· − 3.78261u − 1.65217
(ii) Obstruction class = 1
(iii) Cusp Shapes =
15
23
u
12
−
17
23
u
11
−
142
23
u
10
−
214
23
u
9
−
218
23
u
8
+
27
23
u
7
+
451
23
u
6
+
459
23
u
5
+
195
23
u
4
+
117
23
u
3
−
246
23
u
2
−
492
23
u −
387
23
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
+ 3u
12
+ ··· + 3u + 1
c
2
u
13
+ 2u
12
+ ··· − 2u + 1
c
3
u
13
+ 8u
12
+ ··· − 46u − 11
c
4
u
13
+ 2u
12
+ ··· − 2u − 1
c
5
u
13
− 3u
12
+ ··· + 3u − 1
c
6
u
13
+ 7u
12
+ ··· − 2u − 1
c
7
u
13
− 2u
12
+ ··· − 2u − 1
c
8
u
13
+ u
12
+ ··· − u − 1
c
9
u
13
− 2u
12
+ ··· − 2u + 1
c
10
u
13
+ u
12
+ ··· + 2u − 1
c
11
u
13
− 2u
12
+ ··· − 2u − 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
13
− 5y
12
+ ··· + 9y −1
c
2
, c
7
y
13
− 4y
12
+ ··· − 8y −1
c
3
y
13
− 16y
12
+ ··· + 774y −121
c
4
, c
9
y
13
− 12y
12
+ ··· + 2y −1
c
6
y
13
− 5y
12
+ ··· − 10y −1
c
8
y
13
+ 11y
12
+ ··· − 7y −1
c
10
y
13
− 5y
12
+ ··· + 2y −1
c
11
y
13
− 8y
12
+ ··· − 8y −1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.059650 + 0.184275I
a = −0.698885 − 0.288098I
b = −0.410177 − 0.918523I
−1.83033 − 2.41287I −3.84698 + 4.49416I
u = 1.059650 − 0.184275I
a = −0.698885 + 0.288098I
b = −0.410177 + 0.918523I
−1.83033 + 2.41287I −3.84698 − 4.49416I
u = 0.798226 + 0.206546I
a = 1.21744 + 0.73252I
b = −0.927123 + 0.095251I
−2.67139 − 0.27850I −30.8698 + 7.4464I
u = 0.798226 − 0.206546I
a = 1.21744 − 0.73252I
b = −0.927123 − 0.095251I
−2.67139 + 0.27850I −30.8698 − 7.4464I
u = −0.489582 + 0.589438I
a = 0.667920 + 0.260518I
b = 1.380850 − 0.254889I
−3.97791 + 3.45840I −2.92129 − 5.70901I
u = −0.489582 − 0.589438I
a = 0.667920 − 0.260518I
b = 1.380850 + 0.254889I
−3.97791 − 3.45840I −2.92129 + 5.70901I
u = −1.198530 + 0.532231I
a = −0.230268 − 0.024904I
b = −0.245939 − 0.621339I
1.61052 + 6.86027I 0.95342 − 5.99617I
u = −1.198530 − 0.532231I
a = −0.230268 + 0.024904I
b = −0.245939 + 0.621339I
1.61052 − 6.86027I 0.95342 + 5.99617I
u = −0.576690 + 0.127809I
a = −0.52909 + 4.02030I
b = 0.118700 + 0.564195I
4.79973 − 3.69557I −8.48018 − 0.72494I
u = −0.576690 − 0.127809I
a = −0.52909 − 4.02030I
b = 0.118700 − 0.564195I
4.79973 + 3.69557I −8.48018 + 0.72494I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.24005 + 1.43458I
a = −0.211506 − 1.083560I
b = −0.301086 + 1.145810I
5.52247 − 0.94388I −1.35646 + 9.06354I
u = −0.24005 − 1.43458I
a = −0.211506 + 1.083560I
b = −0.301086 − 1.145810I
5.52247 + 0.94388I −1.35646 − 9.06354I
u = −1.70605
a = 1.56877
b = 2.76956
−10.1961 10.0430
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
13
+ 3u
12
+ ··· + 3u + 1)(u
42
+ 2u
41
+ ··· + 12u − 1)
c
2
(u
13
+ 2u
12
+ ··· − 2u + 1)(u
42
+ u
41
+ ··· + 29u + 151)
c
3
(u
13
+ 8u
12
+ ··· − 46u − 11)(u
42
− 3u
41
+ ··· + 75u + 19)
c
4
(u
13
+ 2u
12
+ ··· − 2u − 1)(u
42
+ 3u
41
+ ··· + 21u + 13)
c
5
(u
13
− 3u
12
+ ··· + 3u − 1)(u
42
+ 2u
41
+ ··· + 12u − 1)
c
6
(u
13
+ 7u
12
+ ··· − 2u − 1)(u
42
+ 6u
41
+ ··· + 15u + 1)
c
7
(u
13
− 2u
12
+ ··· − 2u − 1)(u
42
+ u
41
+ ··· + 29u + 151)
c
8
(u
13
+ u
12
+ ··· − u − 1)(u
42
− 6u
41
+ ··· − 87352u + 17077)
c
9
(u
13
− 2u
12
+ ··· − 2u + 1)(u
42
+ 3u
41
+ ··· + 21u + 13)
c
10
(u
13
+ u
12
+ ··· + 2u − 1)(u
42
− 2u
41
+ ··· − 423u − 43)
c
11
(u
13
− 2u
12
+ ··· − 2u − 1)(u
42
+ u
41
+ ··· + 2205u + 297)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
13
− 5y
12
+ ··· + 9y −1)(y
42
− 30y
41
+ ··· − 44y + 1)
c
2
, c
7
(y
13
− 4y
12
+ ··· − 8y −1)(y
42
− 57y
41
+ ··· − 202275y + 22801)
c
3
(y
13
− 16y
12
+ ··· + 774y −121)(y
42
− 61y
41
+ ··· − 7753y + 361)
c
4
, c
9
(y
13
− 12y
12
+ ··· + 2y −1)(y
42
− 25y
41
+ ··· − 2261y + 169)
c
6
(y
13
− 5y
12
+ ··· − 10y −1)(y
42
− 2y
41
+ ··· − 9y + 1)
c
8
(y
13
+ 11y
12
+ ··· − 7y −1)
· (y
42
− 58y
41
+ ··· − 2530360008y + 291623929)
c
10
(y
13
− 5y
12
+ ··· + 2y −1)(y
42
+ 10y
41
+ ··· + 9411y + 1849)
c
11
(y
13
− 8y
12
+ ··· − 8y −1)(y
42
− 57y
41
+ ··· − 501471y + 88209)
16
