11a
252
(K11a
252
)
A knot diagram
1
Linearized knot diagam
4 7 1 2 11 3 10 6 5 8 9
Solving Sequence
8,11
10
3,7
2 6 9 1 5 4
c
10
c
7
c
2
c
6
c
8
c
11
c
5
c
4
c
1
, c
3
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.11167 × 10
157
u
70
+ 9.80349 × 10
157
u
69
+ ··· + 6.48947 × 10
158
b + 1.66763 × 10
158
,
3.33659 × 10
158
u
70
− 7.80024 × 10
158
u
69
+ ··· + 6.48947 × 10
158
a + 4.59343 × 10
159
, u
71
− 2u
70
+ ··· + 10u + 1i
I
u
2
= h−u
3
+ u
2
+ b − 1, −u
5
+ u
4
− u
2
+ a + u − 1, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 77 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
= h−4.11 × 10
157
u
70
+ 9.80 × 10
157
u
69
+ · · · + 6.49 × 10
158
b + 1.67 ×
10
158
, 3.34 × 10
158
u
70
− 7.80 × 10
158
u
69
+ · · · + 6.49 × 10
158
a + 4.59 ×
10
159
, u
71
− 2u
70
+ · · · + 10u + 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
10
=
1
−u
2
a
3
=
−0.514154u
70
+ 1.20198u
69
+ ··· − 14.4737u − 7.07828
0.0633591u
70
− 0.151068u
69
+ ··· + 3.49569u − 0.256975
a
7
=
u
−u
3
+ u
a
2
=
−0.573953u
70
+ 1.19350u
69
+ ··· − 13.1744u − 7.01032
0.0951502u
70
− 0.228949u
69
+ ··· + 3.45444u − 0.317091
a
6
=
0.174897u
70
− 0.472490u
69
+ ··· + 15.3667u + 5.67523
−0.118550u
70
+ 0.321518u
69
+ ··· − 1.35288u + 0.169544
a
9
=
−0.337748u
70
+ 0.603848u
69
+ ··· − 25.8435u + 0.618193
−0.177165u
70
+ 0.217073u
69
+ ··· − 2.82251u − 0.449303
a
1
=
0.0798159u
70
− 0.254371u
69
+ ··· + 8.28970u + 3.25294
u
3
− u
a
5
=
0.293446u
70
− 0.794009u
69
+ ··· + 16.7196u + 5.50568
−0.118550u
70
+ 0.321518u
69
+ ··· − 1.35288u + 0.169544
a
4
=
−0.360696u
70
+ 0.644610u
69
+ ··· − 4.30465u − 3.28034
0.0395576u
70
− 0.0960173u
69
+ ··· + 2.98896u − 0.198923
a
4
=
−0.360696u
70
+ 0.644610u
69
+ ··· − 4.30465u − 3.28034
0.0395576u
70
− 0.0960173u
69
+ ··· + 2.98896u − 0.198923
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.60654u
70
− 6.89818u
69
+ ··· − 6.61880u − 2.95587
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
u
71
− 7u
70
+ ··· − 3u + 1
c
2
, c
6
u
71
− u
70
+ ··· + 320u + 64
c
5
u
71
+ 6u
70
+ ··· + 2u + 1
c
7
, c
10
u
71
− 2u
70
+ ··· + 10u + 1
c
8
u
71
− 6u
70
+ ··· − 3424u + 319
c
9
u
71
− 2u
70
+ ··· + 35022u + 3953
c
11
u
71
+ 12u
70
+ ··· − 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
y
71
− 67y
70
+ ··· − 45y −1
c
2
, c
6
y
71
+ 39y
70
+ ··· − 36864y −4096
c
5
y
71
+ 12y
70
+ ··· − 6y −1
c
7
, c
10
y
71
− 48y
70
+ ··· − 10y −1
c
8
y
71
− 72y
70
+ ··· + 3210942y −101761
c
9
y
71
− 48y
70
+ ··· − 314283574y −15626209
c
11
y
71
+ 72y
69
+ ··· − 10y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.973828 + 0.280461I
a = −0.382377 + 0.191990I
b = 0.806691 − 0.545143I
0.16886 − 3.43064I 0
u = 0.973828 − 0.280461I
a = −0.382377 − 0.191990I
b = 0.806691 + 0.545143I
0.16886 + 3.43064I 0
u = −1.039510 + 0.064875I
a = 1.72385 − 3.92841I
b = 0.153087 − 0.345660I
−2.19246 + 1.77118I 0
u = −1.039510 − 0.064875I
a = 1.72385 + 3.92841I
b = 0.153087 + 0.345660I
−2.19246 − 1.77118I 0
u = −1.04817
a = 2.58690
b = 0.574511
−4.26740 40.4800
u = −0.093891 + 1.051200I
a = 0.826346 − 0.088868I
b = 1.35016 − 0.97545I
−2.29132 + 4.25686I 0
u = −0.093891 − 1.051200I
a = 0.826346 + 0.088868I
b = 1.35016 + 0.97545I
−2.29132 − 4.25686I 0
u = −1.051030 + 0.111007I
a = −4.50600 − 1.44719I
b = 1.07671 − 1.20500I
−3.57140 + 0.57623I 0
u = −1.051030 − 0.111007I
a = −4.50600 + 1.44719I
b = 1.07671 + 1.20500I
−3.57140 − 0.57623I 0
u = 1.080020 + 0.152289I
a = −0.273682 − 1.001120I
b = 0.031630 − 1.096560I
−2.62165 − 3.78828I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.080020 − 0.152289I
a = −0.273682 + 1.001120I
b = 0.031630 + 1.096560I
−2.62165 + 3.78828I 0
u = 0.202728 + 0.884593I
a = −0.558547 − 0.125884I
b = −0.708883 + 0.771941I
2.34440 + 1.95014I 4.45936 − 2.53493I
u = 0.202728 − 0.884593I
a = −0.558547 + 0.125884I
b = −0.708883 − 0.771941I
2.34440 − 1.95014I 4.45936 + 2.53493I
u = −1.043640 + 0.390448I
a = −0.683454 + 0.373591I
b = 0.003299 − 0.591740I
−1.92491 + 1.08364I 0
u = −1.043640 − 0.390448I
a = −0.683454 − 0.373591I
b = 0.003299 + 0.591740I
−1.92491 − 1.08364I 0
u = 0.599075 + 0.942927I
a = 0.393955 − 0.081858I
b = −0.131439 − 1.112940I
−1.031500 + 0.354146I 0
u = 0.599075 − 0.942927I
a = 0.393955 + 0.081858I
b = −0.131439 + 1.112940I
−1.031500 − 0.354146I 0
u = 1.119810 + 0.032767I
a = 0.413302 − 0.046036I
b = −1.43154 − 0.47309I
−5.71064 − 0.88851I 0
u = 1.119810 − 0.032767I
a = 0.413302 + 0.046036I
b = −1.43154 + 0.47309I
−5.71064 + 0.88851I 0
u = 1.117600 + 0.093371I
a = 0.678615 − 0.967658I
b = −0.93853 − 1.07438I
−4.60632 − 2.57396I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.117600 − 0.093371I
a = 0.678615 + 0.967658I
b = −0.93853 + 1.07438I
−4.60632 + 2.57396I 0
u = −1.126210 + 0.132843I
a = −1.08363 + 2.70605I
b = −0.254130 + 0.145869I
−8.04028 + 4.80757I 0
u = −1.126210 − 0.132843I
a = −1.08363 − 2.70605I
b = −0.254130 − 0.145869I
−8.04028 − 4.80757I 0
u = −0.004277 + 1.135740I
a = 1.65575 + 0.09224I
b = 2.85653 + 0.65690I
0.43763 + 6.35749I 0
u = −0.004277 − 1.135740I
a = 1.65575 − 0.09224I
b = 2.85653 − 0.65690I
0.43763 − 6.35749I 0
u = −0.116710 + 0.856297I
a = −1.89294 + 0.32292I
b = −2.33201 − 0.18461I
−1.12559 + 1.87856I −4.53889 − 4.17402I
u = −0.116710 − 0.856297I
a = −1.89294 − 0.32292I
b = −2.33201 + 0.18461I
−1.12559 − 1.87856I −4.53889 + 4.17402I
u = 0.987158 + 0.647225I
a = −0.078094 − 0.228604I
b = −0.086973 + 0.620891I
−2.28261 − 6.08346I 0
u = 0.987158 − 0.647225I
a = −0.078094 + 0.228604I
b = −0.086973 − 0.620891I
−2.28261 + 6.08346I 0
u = −0.794072 + 0.043433I
a = −0.28211 + 1.87433I
b = −0.540687 − 0.121257I
−1.42339 + 1.14206I −7.64564 − 4.36852I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.794072 − 0.043433I
a = −0.28211 − 1.87433I
b = −0.540687 + 0.121257I
−1.42339 − 1.14206I −7.64564 + 4.36852I
u = 1.192200 + 0.296593I
a = 0.317333 + 1.101890I
b = 0.334681 + 0.650646I
−8.79734 − 8.72585I 0
u = 1.192200 − 0.296593I
a = 0.317333 − 1.101890I
b = 0.334681 − 0.650646I
−8.79734 + 8.72585I 0
u = −0.670063 + 0.347596I
a = −0.08138 + 1.61220I
b = 0.355159 − 0.164091I
−6.99999 − 3.26565I −6.82531 + 6.65441I
u = −0.670063 − 0.347596I
a = −0.08138 − 1.61220I
b = 0.355159 + 0.164091I
−6.99999 + 3.26565I −6.82531 − 6.65441I
u = −0.645193 + 1.117580I
a = 1.213880 − 0.359050I
b = 1.77925 + 1.40756I
−7.91168 + 0.39314I 0
u = −0.645193 − 1.117580I
a = 1.213880 + 0.359050I
b = 1.77925 − 1.40756I
−7.91168 − 0.39314I 0
u = 1.200010 + 0.496938I
a = 0.218730 + 0.009510I
b = −0.699809 − 0.172100I
−0.76386 − 6.94431I 0
u = 1.200010 − 0.496938I
a = 0.218730 − 0.009510I
b = −0.699809 + 0.172100I
−0.76386 + 6.94431I 0
u = 0.003290 + 1.307520I
a = −1.45978 − 0.16433I
b = −2.98943 − 0.91001I
−5.26918 + 10.31530I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.003290 − 1.307520I
a = −1.45978 + 0.16433I
b = −2.98943 + 0.91001I
−5.26918 − 10.31530I 0
u = 0.452314 + 0.404120I
a = −0.369574 + 0.466412I
b = 0.728049 + 0.140839I
1.57443 + 0.30385I 7.03884 + 0.55864I
u = 0.452314 − 0.404120I
a = −0.369574 − 0.466412I
b = 0.728049 − 0.140839I
1.57443 − 0.30385I 7.03884 − 0.55864I
u = 1.328370 + 0.443679I
a = 0.18921 − 1.90014I
b = −2.43997 − 0.05463I
−5.52892 − 6.64078I 0
u = 1.328370 − 0.443679I
a = 0.18921 + 1.90014I
b = −2.43997 + 0.05463I
−5.52892 + 6.64078I 0
u = 1.41902 + 0.24540I
a = −0.31463 + 1.40902I
b = 1.50742 − 0.01617I
−14.7704 − 4.4090I 0
u = 1.41902 − 0.24540I
a = −0.31463 − 1.40902I
b = 1.50742 + 0.01617I
−14.7704 + 4.4090I 0
u = 1.36179 + 0.48894I
a = −0.271842 − 0.047925I
b = 1.037440 + 0.370809I
−6.81481 − 9.66907I 0
u = 1.36179 − 0.48894I
a = −0.271842 + 0.047925I
b = 1.037440 − 0.370809I
−6.81481 + 9.66907I 0
u = 1.36248 + 0.53740I
a = 0.15951 + 1.89725I
b = 2.64476 − 0.38758I
−3.85560 − 12.20440I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.36248 − 0.53740I
a = 0.15951 − 1.89725I
b = 2.64476 + 0.38758I
−3.85560 + 12.20440I 0
u = 0.019457 + 0.498656I
a = 2.06316 − 1.12594I
b = 0.125101 − 0.377825I
−5.36921 + 5.60292I −4.23205 − 1.95004I
u = 0.019457 − 0.498656I
a = 2.06316 + 1.12594I
b = 0.125101 + 0.377825I
−5.36921 − 5.60292I −4.23205 + 1.95004I
u = −1.35931 + 0.64552I
a = −0.08241 + 1.81423I
b = −3.25610 − 0.21443I
−4.09299 + 4.00272I 0
u = −1.35931 − 0.64552I
a = −0.08241 − 1.81423I
b = −3.25610 + 0.21443I
−4.09299 − 4.00272I 0
u = −1.45782 + 0.39176I
a = −0.64419 − 1.79501I
b = 2.93443 + 0.40813I
−4.54539 − 0.34097I 0
u = −1.45782 − 0.39176I
a = −0.64419 + 1.79501I
b = 2.93443 − 0.40813I
−4.54539 + 0.34097I 0
u = −1.42285 + 0.53580I
a = 0.953468 − 0.520457I
b = −0.57598 + 1.65551I
−6.35450 + 1.85292I 0
u = −1.42285 − 0.53580I
a = 0.953468 + 0.520457I
b = −0.57598 − 1.65551I
−6.35450 − 1.85292I 0
u = 1.41471 + 0.59221I
a = −0.31168 − 1.72898I
b = −2.57738 + 0.66185I
−9.7419 − 16.8559I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41471 − 0.59221I
a = −0.31168 + 1.72898I
b = −2.57738 − 0.66185I
−9.7419 + 16.8559I 0
u = −0.230568 + 0.263555I
a = −2.27801 + 1.97060I
b = −0.913442 + 0.373094I
−1.31227 + 1.35935I −5.28068 − 4.63416I
u = −0.230568 − 0.263555I
a = −2.27801 − 1.97060I
b = −0.913442 − 0.373094I
−1.31227 − 1.35935I −5.28068 + 4.63416I
u = −1.45197 + 0.82397I
a = 0.15600 − 1.43654I
b = 3.48750 + 0.15031I
−10.25460 + 7.45224I 0
u = −1.45197 − 0.82397I
a = 0.15600 + 1.43654I
b = 3.48750 − 0.15031I
−10.25460 − 7.45224I 0
u = −1.71685 + 0.37143I
a = 0.56832 + 1.29788I
b = −3.07440 − 0.93374I
−11.03720 − 3.15602I 0
u = −1.71685 − 0.37143I
a = 0.56832 − 1.29788I
b = −3.07440 + 0.93374I
−11.03720 + 3.15602I 0
u = 0.039727 + 0.221588I
a = −3.96929 + 1.74892I
b = 0.178650 + 0.492128I
−0.04861 + 2.05474I −0.05845 − 2.58157I
u = 0.039727 − 0.221588I
a = −3.96929 − 1.74892I
b = 0.178650 − 0.492128I
−0.04861 − 2.05474I −0.05845 + 2.58157I
u = −0.125529 + 0.098090I
a = −5.80125 − 1.46490I
b = −0.727087 + 0.471790I
−2.61258 + 0.40782I −2.91513 + 1.25335I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.125529 − 0.098090I
a = −5.80125 + 1.46490I
b = −0.727087 − 0.471790I
−2.61258 − 0.40782I −2.91513 − 1.25335I
12
II.
I
u
2
= h−u
3
+ u
2
+ b − 1, −u
5
+ u
4
− u
2
+ a + u − 1, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
10
=
1
−u
2
a
3
=
u
5
− u
4
+ u
2
− u + 1
u
3
− u
2
+ 1
a
7
=
u
−u
3
+ u
a
2
=
u
5
− u
4
+ u
2
− u + 1
u
3
− u
2
+ 1
a
6
=
u
−u
3
+ u
a
9
=
−u
3
u
5
− u
3
+ u
a
1
=
−u
3
u
3
− u
a
5
=
u
3
−u
3
+ u
a
4
=
u
5
− u
4
+ u
3
+ u
2
− u + 1
−u
2
+ u + 1
a
4
=
u
5
− u
4
+ u
3
+ u
2
− u + 1
−u
2
+ u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
5
+ 7u
4
− u
3
− 6u
2
+ 5u − 1
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
6
c
2
, c
6
u
6
c
3
, c
4
(u + 1)
6
c
5
, c
8
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
c
7
, c
9
, c
11
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
10
u
6
− u
5
− u
4
+ 2u
3
− u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
(y −1)
6
c
2
, c
6
y
6
c
5
, c
8
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
7
, c
9
, c
10
c
11
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 + 0.295542I
a = 2.25915 + 1.43225I
b = −0.66103 + 1.45708I
−3.53554 + 0.92430I −6.82874 − 7.13914I
u = −1.002190 − 0.295542I
a = 2.25915 − 1.43225I
b = −0.66103 − 1.45708I
−3.53554 − 0.92430I −6.82874 + 7.13914I
u = 0.428243 + 0.664531I
a = 0.655968 − 0.098281I
b = 0.769407 − 0.497010I
0.245672 + 0.924305I 1.12292 − 1.33143I
u = 0.428243 − 0.664531I
a = 0.655968 + 0.098281I
b = 0.769407 + 0.497010I
0.245672 − 0.924305I 1.12292 + 1.33143I
u = 1.073950 + 0.558752I
a = −0.415113 + 0.381252I
b = 0.391622 + 0.558752I
−1.64493 − 5.69302I −0.29418 + 2.69056I
u = 1.073950 − 0.558752I
a = −0.415113 − 0.381252I
b = 0.391622 − 0.558752I
−1.64493 + 5.69302I −0.29418 − 2.69056I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
71
− 7u
70
+ ··· − 3u + 1)
c
2
, c
6
u
6
(u
71
− u
70
+ ··· + 320u + 64)
c
3
, c
4
((u + 1)
6
)(u
71
− 7u
70
+ ··· − 3u + 1)
c
5
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)(u
71
+ 6u
70
+ ··· + 2u + 1)
c
7
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
71
− 2u
70
+ ··· + 10u + 1)
c
8
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)(u
71
− 6u
70
+ ··· − 3424u + 319)
c
9
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
71
− 2u
70
+ ··· + 35022u + 3953)
c
10
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
71
− 2u
70
+ ··· + 10u + 1)
c
11
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
71
+ 12u
70
+ ··· − 2u − 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
((y −1)
6
)(y
71
− 67y
70
+ ··· − 45y −1)
c
2
, c
6
y
6
(y
71
+ 39y
70
+ ··· − 36864y −4096)
c
5
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)(y
71
+ 12y
70
+ ··· − 6y −1)
c
7
, c
10
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
71
− 48y
70
+ ··· − 10y −1)
c
8
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
71
− 72y
70
+ ··· + 3210942y −101761)
c
9
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
71
− 48y
70
+ ··· − 314283574y −15626209)
c
11
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
71
+ 72y
69
+ ··· − 10y −1)
18
