11n
176
(K11n
176
)
A knot diagram
1
Linearized knot diagam
6 9 1 7 2 10 11 2 4 5 9
Solving Sequence
1,6 2,9
3 4 5 8 11 7 10
c
1
c
2
c
3
c
5
c
8
c
11
c
7
c
10
c
4
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h9.28358 × 10
73
u
46
+ 4.54756 × 10
74
u
45
+ ··· + 1.24850 × 10
77
b + 1.15944 × 10
77
,
2.16945 × 10
75
u
46
− 2.78753 × 10
76
u
45
+ ··· + 3.74550 × 10
77
a − 4.53039 × 10
78
, u
47
− u
46
+ ··· − 21u + 6i
I
u
2
= h411u
15
+ 80u
14
+ ··· + 327b − 544, 1184u
15
+ 48u
14
+ ··· + 327a + 175,
u
16
+ 4u
14
+ u
13
+ 3u
12
− 10u
10
− 9u
9
− 30u
8
− 19u
7
− 33u
6
− 18u
5
− 21u
4
− 10u
3
− 7u
2
− 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 63 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
= h9.28 × 10
73
u
46
+ 4.55 × 10
74
u
45
+ · · · + 1.25 × 10
77
b + 1.16 × 10
77
, 2.17 ×
10
75
u
46
−2.79×10
76
u
45
+· · ·+3.75×10
77
a−4.53×10
78
, u
47
−u
46
+· · ·−21u+6i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
9
=
−0.00579214u
46
+ 0.0744235u
45
+ ··· + 7.90890u + 12.0956
−0.000743579u
46
− 0.00364242u
45
+ ··· + 0.922897u − 0.928667
a
3
=
−0.0143049u
46
+ 0.0978976u
45
+ ··· + 4.71215u + 13.6102
0.0228505u
46
− 0.0369206u
45
+ ··· + 1.75270u − 0.870753
a
4
=
−0.0371555u
46
+ 0.134818u
45
+ ··· + 2.95945u + 14.4810
0.0228505u
46
− 0.0369206u
45
+ ··· + 1.75270u − 0.870753
a
5
=
−u
u
3
+ u
a
8
=
−0.0170297u
46
+ 0.0889078u
45
+ ··· + 5.50999u + 13.4360
−0.00951166u
46
+ 0.00323251u
45
+ ··· + 0.787290u − 0.909186
a
11
=
−0.0661464u
46
+ 0.0255355u
45
+ ··· − 15.5094u − 5.85559
−0.00201782u
46
+ 0.0234904u
45
+ ··· − 1.29675u + 0.627088
a
7
=
−0.235637u
46
+ 0.255083u
45
+ ··· − 29.2766u + 8.54904
−0.0237208u
46
+ 0.0372482u
45
+ ··· + 0.0651824u − 0.264345
a
10
=
−0.0864183u
46
+ 0.0400257u
45
+ ··· − 15.5328u − 5.69635
0.00595648u
46
+ 0.0186824u
45
+ ··· − 1.27359u + 0.433152
a
10
=
−0.0864183u
46
+ 0.0400257u
45
+ ··· − 15.5328u − 5.69635
0.00595648u
46
+ 0.0186824u
45
+ ··· − 1.27359u + 0.433152
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.581599u
46
+ 0.705867u
45
+ ··· − 67.0569u + 21.0318
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
47
− u
46
+ ··· − 21u + 6
c
2
, c
8
u
47
− u
46
+ ··· − 17271u + 4993
c
3
u
47
− 4u
46
+ ··· + 503u − 103
c
4
u
47
+ 3u
46
+ ··· + 3u + 1
c
6
u
47
+ 5u
46
+ ··· + 25u − 25
c
7
u
47
+ u
46
+ ··· − 9496u + 1136
c
9
u
47
+ 2u
46
+ ··· − 115u − 38
c
10
u
47
− 9u
45
+ ··· + 1771u − 137
c
11
u
47
+ 26u
45
+ ··· − 7818u + 1097
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
47
+ 35y
46
+ ··· − 1923y −36
c
2
, c
8
y
47
+ 67y
46
+ ··· − 225548161y −24930049
c
3
y
47
− 58y
46
+ ··· + 257953y −10609
c
4
y
47
− 7y
46
+ ··· + 9y −1
c
6
y
47
− y
46
+ ··· + 17375y −625
c
7
y
47
+ 33y
46
+ ··· + 121024y −1290496
c
9
y
47
− 22y
46
+ ··· + 9957y −1444
c
10
y
47
− 18y
46
+ ··· + 2612553y −18769
c
11
y
47
+ 52y
46
+ ··· + 1652754y −1203409
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.773512 + 0.492443I
a = 0.425302 − 0.252935I
b = 0.018902 + 0.913672I
1.18695 + 2.20702I 6.40904 − 2.67371I
u = −0.773512 − 0.492443I
a = 0.425302 + 0.252935I
b = 0.018902 − 0.913672I
1.18695 − 2.20702I 6.40904 + 2.67371I
u = 0.532721 + 0.951033I
a = 0.114543 + 0.789067I
b = 0.205803 + 0.637663I
−0.32563 + 3.32812I 4.47407 − 5.56859I
u = 0.532721 − 0.951033I
a = 0.114543 − 0.789067I
b = 0.205803 − 0.637663I
−0.32563 − 3.32812I 4.47407 + 5.56859I
u = 0.566468 + 0.943415I
a = 0.177396 + 0.352172I
b = 0.162886 + 0.570692I
−0.16355 + 3.21246I 2.46572 − 3.89028I
u = 0.566468 − 0.943415I
a = 0.177396 − 0.352172I
b = 0.162886 − 0.570692I
−0.16355 − 3.21246I 2.46572 + 3.89028I
u = 0.120942 + 1.100590I
a = 0.380545 − 1.251690I
b = 1.012370 − 0.893281I
−0.026486 − 0.766540I 4.20873 + 2.92644I
u = 0.120942 − 1.100590I
a = 0.380545 + 1.251690I
b = 1.012370 + 0.893281I
−0.026486 + 0.766540I 4.20873 − 2.92644I
u = −1.089520 + 0.393683I
a = 0.293954 + 0.011791I
b = −0.37684 − 1.53640I
−6.00687 − 1.21428I 0. + 1.82170I
u = −1.089520 − 0.393683I
a = 0.293954 − 0.011791I
b = −0.37684 + 1.53640I
−6.00687 + 1.21428I 0. − 1.82170I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.559473 + 1.085530I
a = −0.723467 − 0.239741I
b = 0.109730 − 0.820940I
−0.67448 − 7.25675I 0. + 8.76697I
u = −0.559473 − 1.085530I
a = −0.723467 + 0.239741I
b = 0.109730 + 0.820940I
−0.67448 + 7.25675I 0. − 8.76697I
u = −0.222144 + 1.218960I
a = 0.233025 + 0.690594I
b = −0.662108 + 0.421221I
−3.99416 + 0.19865I 0
u = −0.222144 − 1.218960I
a = 0.233025 − 0.690594I
b = −0.662108 − 0.421221I
−3.99416 − 0.19865I 0
u = −0.135940 + 1.249240I
a = −0.24140 − 2.25011I
b = 0.46236 − 1.85158I
−5.37560 − 5.09376I 5.00000 + 5.21914I
u = −0.135940 − 1.249240I
a = −0.24140 + 2.25011I
b = 0.46236 + 1.85158I
−5.37560 + 5.09376I 5.00000 − 5.21914I
u = 0.008414 + 1.269400I
a = −0.17728 + 2.28677I
b = 0.34057 + 1.47157I
−7.89928 + 0.59442I 0
u = 0.008414 − 1.269400I
a = −0.17728 − 2.28677I
b = 0.34057 − 1.47157I
−7.89928 − 0.59442I 0
u = 0.397415 + 0.585722I
a = 0.858641 − 0.085959I
b = 0.442468 − 0.043886I
0.847784 + 0.991810I 7.10163 − 6.37542I
u = 0.397415 − 0.585722I
a = 0.858641 + 0.085959I
b = 0.442468 + 0.043886I
0.847784 − 0.991810I 7.10163 + 6.37542I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.225548 + 0.638119I
a = 1.033440 + 0.803339I
b = 0.046181 − 0.992925I
−5.18251 − 1.11302I 0.53819 + 5.95442I
u = −0.225548 − 0.638119I
a = 1.033440 − 0.803339I
b = 0.046181 + 0.992925I
−5.18251 + 1.11302I 0.53819 − 5.95442I
u = 0.038224 + 0.668626I
a = 1.304070 − 0.196382I
b = 0.813691 + 0.238509I
0.890036 + 1.096420I 7.02928 − 5.72666I
u = 0.038224 − 0.668626I
a = 1.304070 + 0.196382I
b = 0.813691 − 0.238509I
0.890036 − 1.096420I 7.02928 + 5.72666I
u = −1.36636
a = −1.35558
b = 1.02511
6.55372 22.3580
u = −0.142302 + 1.399620I
a = −0.437418 + 0.681680I
b = 0.707328 + 0.658989I
0.04235 − 4.49004I 0
u = −0.142302 − 1.399620I
a = −0.437418 − 0.681680I
b = 0.707328 − 0.658989I
0.04235 + 4.49004I 0
u = −0.43399 + 1.44976I
a = −0.68286 − 1.56290I
b = 0.05165 − 1.95982I
−11.62380 − 6.41934I 0
u = −0.43399 − 1.44976I
a = −0.68286 + 1.56290I
b = 0.05165 + 1.95982I
−11.62380 + 6.41934I 0
u = 0.32663 + 1.48436I
a = −0.179586 − 0.501442I
b = −1.55279 − 0.21910I
−1.89529 + 6.16204I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.32663 − 1.48436I
a = −0.179586 + 0.501442I
b = −1.55279 + 0.21910I
−1.89529 − 6.16204I 0
u = 1.52172 + 0.04362I
a = 0.1136510 + 0.0768899I
b = −0.26031 + 1.86850I
−3.81730 − 7.05587I 0
u = 1.52172 − 0.04362I
a = 0.1136510 − 0.0768899I
b = −0.26031 − 1.86850I
−3.81730 + 7.05587I 0
u = 0.04978 + 1.52738I
a = 0.10416 + 1.74062I
b = 0.01532 + 1.71376I
−8.82034 + 3.57353I 0
u = 0.04978 − 1.52738I
a = 0.10416 − 1.74062I
b = 0.01532 − 1.71376I
−8.82034 − 3.57353I 0
u = 1.54191
a = 1.02710
b = −1.53198
4.27834 0
u = −0.76218 + 1.43981I
a = 0.91525 + 1.17056I
b = −0.76117 + 1.69718I
−9.04480 − 6.06544I 0
u = −0.76218 − 1.43981I
a = 0.91525 − 1.17056I
b = −0.76117 − 1.69718I
−9.04480 + 6.06544I 0
u = −0.190847 + 0.310941I
a = 1.112970 + 0.105678I
b = 0.339070 + 1.341850I
−2.24296 + 3.68122I 1.56886 + 2.39852I
u = −0.190847 − 0.310941I
a = 1.112970 − 0.105678I
b = 0.339070 − 1.341850I
−2.24296 − 3.68122I 1.56886 − 2.39852I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.362669
a = 0.988687
b = 0.580670
1.51314 7.48840
u = 0.65497 + 1.51204I
a = 0.77642 − 1.33598I
b = −0.62901 − 1.84217I
−8.5771 + 14.5345I 0
u = 0.65497 − 1.51204I
a = 0.77642 + 1.33598I
b = −0.62901 + 1.84217I
−8.5771 − 14.5345I 0
u = 0.078087 + 0.175150I
a = 10.95150 + 4.13339I
b = −0.620164 − 0.192865I
4.93463 + 4.05841I 18.1534 − 7.4874I
u = 0.078087 − 0.175150I
a = 10.95150 − 4.13339I
b = −0.620164 + 0.192865I
4.93463 − 4.05841I 18.1534 + 7.4874I
u = 0.47098 + 1.75190I
a = −0.432971 + 1.203300I
b = 0.09716 + 2.03256I
−9.95883 + 0.76536I 0
u = 0.47098 − 1.75190I
a = −0.432971 − 1.203300I
b = 0.09716 − 2.03256I
−9.95883 − 0.76536I 0
9
II. I
u
2
= h411u
15
+ 80u
14
+ · · · + 327b − 544, 1184u
15
+ 48u
14
+ · · · + 327a +
175, u
16
+ 4u
14
+ · · · − 2u − 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
9
=
−3.62080u
15
− 0.146789u
14
+ ··· + 7.28440u − 0.535168
−1.25688u
15
− 0.244648u
14
+ ··· + 3.14067u + 1.66361
a
3
=
3.38838u
15
+ 0.290520u
14
+ ··· − 6.79205u + 2.69113
−0.244648u
15
+ 0.782875u
14
+ ··· − 0.850153u − 0.256881
a
4
=
3.63303u
15
− 0.492355u
14
+ ··· − 5.94190u + 2.94801
−0.244648u
15
+ 0.782875u
14
+ ··· − 0.850153u − 0.256881
a
5
=
−u
u
3
+ u
a
8
=
−4.36697u
15
+ 0.507645u
14
+ ··· + 8.05810u − 2.05199
−1.22936u
15
− 0.266055u
14
+ ··· + 2.57798u + 1.00917
a
11
=
0.996942u
15
+ 0.743119u
14
+ ··· − 5.75229u − 0.519878
0.155963u
15
+ 0.100917u
14
+ ··· − 1.63303u − 0.486239
a
7
=
−0.345566u
15
+ 0.972477u
14
+ ··· − 6.00917u − 4.74618
0.207951u
15
− 0.865443u
14
+ ··· − 1.17737u + 0.0183486
a
10
=
1.65749u
15
− 0.103976u
14
+ ··· − 4.59021u − 0.559633
−0.0152905u
15
− 0.284404u
14
+ ··· − 1.76147u + 0.400612
a
10
=
1.65749u
15
− 0.103976u
14
+ ··· − 4.59021u − 0.559633
−0.0152905u
15
− 0.284404u
14
+ ··· − 1.76147u + 0.400612
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
285
109
u
15
+
11
327
u
14
+ ··· +
4073
327
u −
271
327
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
+ 4u
14
+ ··· − 2u − 1
c
2
u
16
+ 4u
14
+ ··· − 3u − 1
c
3
u
16
+ 7u
15
+ ··· + 27u + 9
c
4
u
16
+ 4u
15
+ ··· + u + 1
c
5
u
16
+ 4u
14
+ ··· + 2u − 1
c
6
u
16
+ 2u
14
+ ··· + 3u + 1
c
7
u
16
− 2u
15
+ ··· + 18u − 1
c
8
u
16
+ 4u
14
+ ··· + 3u − 1
c
9
u
16
− u
15
+ ··· − 21u
2
+ 5
c
10
u
16
− u
15
+ ··· − u − 1
c
11
u
16
− 3u
15
+ ··· − 2u − 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
16
+ 8y
15
+ ··· + 10y + 1
c
2
, c
8
y
16
+ 8y
15
+ ··· − 15y + 1
c
3
y
16
− 17y
15
+ ··· − 225y + 81
c
4
y
16
− 6y
15
+ ··· − 9y + 1
c
6
y
16
+ 4y
15
+ ··· − 15y + 1
c
7
y
16
+ 6y
15
+ ··· − 364y + 1
c
9
y
16
− 13y
15
+ ··· − 210y + 25
c
10
y
16
− y
15
+ ··· − 13y + 1
c
11
y
16
+ 5y
15
+ ··· − 10y + 1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.351578 + 0.904816I
a = 1.052930 + 0.365066I
b = 0.941434 + 0.633888I
1.037660 − 0.078170I 8.99757 − 0.56181I
u = −0.351578 − 0.904816I
a = 1.052930 − 0.365066I
b = 0.941434 − 0.633888I
1.037660 + 0.078170I 8.99757 + 0.56181I
u = −0.426826 + 0.970389I
a = 0.491146 − 0.758867I
b = 0.744279 − 0.333017I
0.63338 − 3.05324I 12.18746 + 3.83561I
u = −0.426826 − 0.970389I
a = 0.491146 + 0.758867I
b = 0.744279 + 0.333017I
0.63338 + 3.05324I 12.18746 − 3.83561I
u = 0.437533 + 0.756284I
a = −0.346240 + 0.869346I
b = 0.380134 − 0.976408I
−4.94918 + 0.09603I 3.84796 + 1.04513I
u = 0.437533 − 0.756284I
a = −0.346240 − 0.869346I
b = 0.380134 + 0.976408I
−4.94918 − 0.09603I 3.84796 − 1.04513I
u = −1.33401
a = −1.14234
b = 1.45019
4.66021 14.5890
u = 0.045118 + 0.600191I
a = −4.18562 − 0.13881I
b = −0.457773 + 0.219345I
4.54626 − 3.92164I −0.825014 + 0.819860I
u = 0.045118 − 0.600191I
a = −4.18562 + 0.13881I
b = −0.457773 − 0.219345I
4.54626 + 3.92164I −0.825014 − 0.819860I
u = −0.426918 + 0.416046I
a = −0.794820 − 0.479672I
b = 0.231103 − 1.368400I
−2.10953 − 4.31438I 3.92733 + 9.24718I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.426918 − 0.416046I
a = −0.794820 + 0.479672I
b = 0.231103 + 1.368400I
−2.10953 + 4.31438I 3.92733 − 9.24718I
u = 0.473070 + 1.323390I
a = 0.394143 + 0.116229I
b = −0.686442 + 0.076962I
0.84655 + 6.12118I 6.68270 − 6.03281I
u = 0.473070 − 1.323390I
a = 0.394143 − 0.116229I
b = −0.686442 − 0.076962I
0.84655 − 6.12118I 6.68270 + 6.03281I
u = 1.52605
a = 1.18323
b = −1.02090
6.23435 −3.38260
u = 0.15358 + 1.53821I
a = −0.13199 + 1.70834I
b = 0.13262 + 1.73681I
−8.74229 + 3.03673I 2.57896 + 2.26924I
u = 0.15358 − 1.53821I
a = −0.13199 − 1.70834I
b = 0.13262 − 1.73681I
−8.74229 − 3.03673I 2.57896 − 2.26924I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
16
+ 4u
14
+ ··· − 2u − 1)(u
47
− u
46
+ ··· − 21u + 6)
c
2
(u
16
+ 4u
14
+ ··· − 3u − 1)(u
47
− u
46
+ ··· − 17271u + 4993)
c
3
(u
16
+ 7u
15
+ ··· + 27u + 9)(u
47
− 4u
46
+ ··· + 503u − 103)
c
4
(u
16
+ 4u
15
+ ··· + u + 1)(u
47
+ 3u
46
+ ··· + 3u + 1)
c
5
(u
16
+ 4u
14
+ ··· + 2u − 1)(u
47
− u
46
+ ··· − 21u + 6)
c
6
(u
16
+ 2u
14
+ ··· + 3u + 1)(u
47
+ 5u
46
+ ··· + 25u − 25)
c
7
(u
16
− 2u
15
+ ··· + 18u − 1)(u
47
+ u
46
+ ··· − 9496u + 1136)
c
8
(u
16
+ 4u
14
+ ··· + 3u − 1)(u
47
− u
46
+ ··· − 17271u + 4993)
c
9
(u
16
− u
15
+ ··· − 21u
2
+ 5)(u
47
+ 2u
46
+ ··· − 115u − 38)
c
10
(u
16
− u
15
+ ··· − u − 1)(u
47
− 9u
45
+ ··· + 1771u − 137)
c
11
(u
16
− 3u
15
+ ··· − 2u − 1)(u
47
+ 26u
45
+ ··· − 7818u + 1097)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
16
+ 8y
15
+ ··· + 10y + 1)(y
47
+ 35y
46
+ ··· − 1923y − 36)
c
2
, c
8
(y
16
+ 8y
15
+ ··· − 15y + 1)
· (y
47
+ 67y
46
+ ··· − 225548161y − 24930049)
c
3
(y
16
− 17y
15
+ ··· − 225y + 81)
· (y
47
− 58y
46
+ ··· + 257953y − 10609)
c
4
(y
16
− 6y
15
+ ··· − 9y + 1)(y
47
− 7y
46
+ ··· + 9y − 1)
c
6
(y
16
+ 4y
15
+ ··· − 15y + 1)(y
47
− y
46
+ ··· + 17375y − 625)
c
7
(y
16
+ 6y
15
+ ··· − 364y + 1)
· (y
47
+ 33y
46
+ ··· + 121024y − 1290496)
c
9
(y
16
− 13y
15
+ ··· − 210y + 25)(y
47
− 22y
46
+ ··· + 9957y − 1444)
c
10
(y
16
− y
15
+ ··· − 13y + 1)(y
47
− 18y
46
+ ··· + 2612553y − 18769)
c
11
(y
16
+ 5y
15
+ ··· − 10y + 1)
· (y
47
+ 52y
46
+ ··· + 1652754y − 1203409)
16
