11a
126
(K11a
126
)
A knot diagram
1
Linearized knot diagam
5 1 10 8 2 9 3 6 11 4 7
Solving Sequence
4,10 7,11
1 3 8 5 2 9 6
c
10
c
11
c
3
c
7
c
4
c
2
c
9
c
6
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−3u
17
+ 2u
16
+ ··· + 8b 8, 7u
17
2u
16
+ ··· + 8a 20, u
18
+ u
17
+ ··· + 3u + 1i
I
u
2
= h−2.20753 × 10
40
u
55
+ 6.11690 × 10
40
u
54
+ ··· + 4.92510 × 10
40
b 2.71302 × 10
40
,
1.18198 × 10
40
u
55
2.66851 × 10
40
u
54
+ ··· + 4.92510 × 10
40
a 1.69808 × 10
41
, u
56
3u
55
+ ··· 2u + 1i
I
u
3
= h2b u 2, 2a u 2, u
2
+ u 1i
* 3 irreducible components of dim
C
= 0, with total 76 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−3u
17
+2u
16
+· · ·+8b8, 7u
17
2u
16
+· · ·+8a20, u
18
+u
17
+· · ·+3u+1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
7
=
7
8
u
17
+
1
4
u
16
+ ···
15
8
u +
5
2
3
8
u
17
1
4
u
16
+ ···
3
8
u + 1
a
11
=
1
u
2
a
1
=
1
2
u
17
3
16
u
16
+ ··· +
7
8
u
13
16
1
2
u
17
3
16
u
16
+ ···
1
8
u
13
16
a
3
=
u
u
a
8
=
3
8
u
17
+
1
4
u
16
+ ···
11
8
u +
5
2
1
8
u
17
1
4
u
16
+ ··· +
1
8
u + 1
a
5
=
1
2
u
17
3
16
u
16
+ ··· +
7
8
u
29
16
1
2
u
17
3
16
u
16
+ ··· +
7
8
u
13
16
a
2
=
0.187500u
17
0.0625000u
16
+ ··· + 0.562500u 0.312500
0.187500u
17
0.0625000u
16
+ ··· + 0.562500u 0.312500
a
9
=
u
2
+ 1
u
4
a
6
=
5
8
u
17
+
1
4
u
16
+ ···
5
8
u + 2
5
8
u
17
+
1
4
u
16
+ ···
5
8
u + 1
a
6
=
5
8
u
17
+
1
4
u
16
+ ···
5
8
u + 2
5
8
u
17
+
1
4
u
16
+ ···
5
8
u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
37
8
u
17
+
49
16
u
16
19u
15
161
16
u
14
+
175
4
u
13
+
625
16
u
12
1021
16
u
11
79u
10
+
489
8
u
9
+
1847
16
u
8
101
4
u
7
481
4
u
6
63
8
u
5
+
313
4
u
4
+
403
16
u
3
275
8
u
2
77
4
u +
115
16
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
10
u
18
u
17
+ ··· 3u + 1
c
2
, c
9
u
18
+ 9u
17
+ ··· + 19u + 1
c
4
, c
11
4(4u
18
2u
17
+ ··· 10u
2
+ 1)
c
6
, c
8
u
18
u
17
+ ··· + 24u 16
c
7
u
18
+ 5u
17
+ ··· 384u 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
10
y
18
9y
17
+ ··· 19y + 1
c
2
, c
9
y
18
+ 3y
17
+ ··· 159y + 1
c
4
, c
11
16(16y
18
140y
17
+ ··· 20y + 1)
c
6
, c
8
y
18
13y
17
+ ··· + 736y + 256
c
7
y
18
3y
17
+ ··· 104960y + 4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.797207 + 0.665416I
a = 1.148400 0.556457I
b = 1.65807 + 1.34345I
5.71206 2.89420I 7.03507 + 3.97344I
u = 0.797207 0.665416I
a = 1.148400 + 0.556457I
b = 1.65807 1.34345I
5.71206 + 2.89420I 7.03507 3.97344I
u = 0.544045 + 0.930838I
a = 1.159100 + 0.772519I
b = 0.041004 + 1.409830I
8.53344 5.24003I 5.37319 + 1.81946I
u = 0.544045 0.930838I
a = 1.159100 0.772519I
b = 0.041004 1.409830I
8.53344 + 5.24003I 5.37319 1.81946I
u = 0.615364 + 0.642798I
a = 1.64986 0.81674I
b = 0.16727 1.68913I
2.54047 0.51745I 4.03732 + 0.45208I
u = 0.615364 0.642798I
a = 1.64986 + 0.81674I
b = 0.16727 + 1.68913I
2.54047 + 0.51745I 4.03732 0.45208I
u = 0.910004 + 0.658534I
a = 1.06248 + 1.71896I
b = 0.86916 + 1.64057I
5.01031 + 7.38290I 4.96124 9.00655I
u = 0.910004 0.658534I
a = 1.06248 1.71896I
b = 0.86916 1.64057I
5.01031 7.38290I 4.96124 + 9.00655I
u = 1.122640 + 0.135484I
a = 0.185979 0.361024I
b = 0.351910 + 0.563133I
6.23953 + 2.23591I 10.20911 3.70336I
u = 1.122640 0.135484I
a = 0.185979 + 0.361024I
b = 0.351910 0.563133I
6.23953 2.23591I 10.20911 + 3.70336I
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.015940 + 0.632188I
a = 1.96168 0.59613I
b = 1.46082 2.17214I
0.14328 10.60240I 0.95783 + 10.15251I
u = 1.015940 0.632188I
a = 1.96168 + 0.59613I
b = 1.46082 + 2.17214I
0.14328 + 10.60240I 0.95783 10.15251I
u = 0.733103 + 0.109565I
a = 0.931581 + 0.476227I
b = 0.056089 + 0.202732I
1.331030 0.143749I 7.24003 0.28764I
u = 0.733103 0.109565I
a = 0.931581 0.476227I
b = 0.056089 0.202732I
1.331030 + 0.143749I 7.24003 + 0.28764I
u = 1.107060 + 0.702923I
a = 1.64797 + 0.90506I
b = 1.31912 + 2.15841I
5.0646 17.2092I 0.64160 + 10.07684I
u = 1.107060 0.702923I
a = 1.64797 0.90506I
b = 1.31912 2.15841I
5.0646 + 17.2092I 0.64160 10.07684I
u = 1.64128
a = 0.142074
b = 0.00357888
7.18406 75.4440
u = 0.281225
a = 2.62494
b = 0.907601
1.21562 9.77320
6
II.
I
u
2
= h−2.21×10
40
u
55
+6.12×10
40
u
54
+· · ·+4.93×10
40
b2.71×10
40
, 1.18×
10
40
u
55
2.67×10
40
u
54
+· · ·+4.93×10
40
a1.70×10
41
, u
56
3u
55
+· · ·2u+1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
7
=
0.239991u
55
+ 0.541817u
54
+ ··· 0.125309u + 3.44782
0.448220u
55
1.24198u
54
+ ··· + 1.17141u + 0.550856
a
11
=
1
u
2
a
1
=
0.465735u
55
1.13841u
54
+ ··· 2.39038u + 0.0140502
1.87437u
55
+ 2.39826u
54
+ ··· 5.31879u + 2.17450
a
3
=
u
u
a
8
=
0.279271u
55
+ 0.501862u
54
+ ··· 0.251857u + 3.16698
0.408940u
55
1.28194u
54
+ ··· + 1.04486u + 0.270025
a
5
=
1.72196u
55
+ 4.91727u
54
+ ··· + 4.36565u + 2.02742
0.451888u
55
+ 1.12281u
54
+ ··· + 2.00233u 0.382100
a
2
=
1.61789u
55
6.35830u
54
+ ··· + 4.65412u 4.14564
0.947869u
55
+ 0.758996u
54
+ ··· 1.23143u + 1.01243
a
9
=
u
2
+ 1
u
4
a
6
=
0.561838u
55
1.68667u
54
+ ··· + 1.45064u + 1.21164
0.561838u
55
1.68667u
54
+ ··· + 1.45064u + 0.211643
a
6
=
0.561838u
55
1.68667u
54
+ ··· + 1.45064u + 1.21164
0.561838u
55
1.68667u
54
+ ··· + 1.45064u + 0.211643
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5.79720u
55
16.0245u
54
+ ··· + 9.31856u 11.3670
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
10
u
56
+ 3u
55
+ ··· + 2u + 1
c
2
, c
9
u
56
+ 21u
55
+ ··· 26u
2
+ 1
c
4
, c
11
u
56
7u
55
+ ··· 45726u + 21533
c
6
, c
8
(u
28
+ 2u
27
+ ··· 10u + 1)
2
c
7
(u
28
2u
27
+ ··· 4u + 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
10
y
56
21y
55
+ ··· 26y
2
+ 1
c
2
, c
9
y
56
+ 27y
55
+ ··· 52y + 1
c
4
, c
11
y
56
29y
55
+ ··· 2262183624y + 463670089
c
6
, c
8
(y
28
22y
27
+ ··· 66y + 1)
2
c
7
(y
28
6y
27
+ ··· 30y + 1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.971251 + 0.124804I
a = 0.196918 + 0.527084I
b = 0.420119 0.173872I
1.74771 0.16605I 4.99428 + 0.74621I
u = 0.971251 0.124804I
a = 0.196918 0.527084I
b = 0.420119 + 0.173872I
1.74771 + 0.16605I 4.99428 0.74621I
u = 0.773544 + 0.668324I
a = 1.50476 + 0.30304I
b = 1.58290 1.72976I
5.42444 2.23797I 6.28915 + 2.63972I
u = 0.773544 0.668324I
a = 1.50476 0.30304I
b = 1.58290 + 1.72976I
5.42444 + 2.23797I 6.28915 2.63972I
u = 1.024720 + 0.056181I
a = 0.040496 0.724145I
b = 0.742982 + 0.278795I
3.40803 4.57637I 7.04537 + 4.19623I
u = 1.024720 0.056181I
a = 0.040496 + 0.724145I
b = 0.742982 0.278795I
3.40803 + 4.57637I 7.04537 4.19623I
u = 0.849827 + 0.601454I
a = 0.730485 + 0.090678I
b = 0.075733 + 0.721488I
3.04440 2.37626I 1.15007 + 2.61756I
u = 0.849827 0.601454I
a = 0.730485 0.090678I
b = 0.075733 0.721488I
3.04440 + 2.37626I 1.15007 2.61756I
u = 0.821914 + 0.476486I
a = 6.19769 1.43982I
b = 5.92604 1.59730I
1.56538 38.9891 + 0.I
u = 0.821914 0.476486I
a = 6.19769 + 1.43982I
b = 5.92604 + 1.59730I
1.56538 38.9891 + 0.I
10
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.544902 + 0.917878I
a = 1.21633 0.96886I
b = 0.16628 1.50273I
6.78989 + 11.25030I 2.95425 5.94443I
u = 0.544902 0.917878I
a = 1.21633 + 0.96886I
b = 0.16628 + 1.50273I
6.78989 11.25030I 2.95425 + 5.94443I
u = 0.929945 + 0.539982I
a = 0.102402 1.353460I
b = 0.38820 1.51941I
0.178243 0
u = 0.929945 0.539982I
a = 0.102402 + 1.353460I
b = 0.38820 + 1.51941I
0.178243 0
u = 0.461286 + 0.983317I
a = 0.709636 + 0.194115I
b = 0.612442 0.750374I
6.16221 6.23957I 5.68801 + 6.28604I
u = 0.461286 0.983317I
a = 0.709636 0.194115I
b = 0.612442 + 0.750374I
6.16221 + 6.23957I 5.68801 6.28604I
u = 0.930933 + 0.567086I
a = 1.55560 + 1.76247I
b = 0.95260 + 2.02285I
1.02186 + 4.25611I 0. 3.95647I
u = 0.930933 0.567086I
a = 1.55560 1.76247I
b = 0.95260 2.02285I
1.02186 4.25611I 0. + 3.95647I
u = 0.504805 + 0.985832I
a = 0.824183 + 0.094134I
b = 0.391866 + 0.938403I
8.10737 8.15514 + 0.I
u = 0.504805 0.985832I
a = 0.824183 0.094134I
b = 0.391866 0.938403I
8.10737 8.15514 + 0.I
11
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.891535 + 0.658098I
a = 0.72629 1.58505I
b = 1.08695 1.10116I
5.42444 2.23797I 6.28915 + 0.I
u = 0.891535 0.658098I
a = 0.72629 + 1.58505I
b = 1.08695 + 1.10116I
5.42444 + 2.23797I 6.28915 + 0.I
u = 0.708258 + 0.542009I
a = 1.80341 0.64145I
b = 1.19190 1.35173I
1.79480 + 0.25822I 3.59957 1.08985I
u = 0.708258 0.542009I
a = 1.80341 + 0.64145I
b = 1.19190 + 1.35173I
1.79480 0.25822I 3.59957 + 1.08985I
u = 0.580619 + 0.676764I
a = 1.54612 + 1.05830I
b = 0.28201 + 1.69623I
1.40869 + 5.50421I 1.41360 5.52444I
u = 0.580619 0.676764I
a = 1.54612 1.05830I
b = 0.28201 1.69623I
1.40869 5.50421I 1.41360 + 5.52444I
u = 0.951803 + 0.571144I
a = 1.18336 + 1.45080I
b = 0.60332 + 1.88607I
1.02228 + 4.28090I 0. 5.50918I
u = 0.951803 0.571144I
a = 1.18336 1.45080I
b = 0.60332 1.88607I
1.02228 4.28090I 0. + 5.50918I
u = 0.592057 + 0.963561I
a = 0.611605 0.687945I
b = 0.160465 0.986501I
1.38725 + 3.08785I 0
u = 0.592057 0.963561I
a = 0.611605 + 0.687945I
b = 0.160465 + 0.986501I
1.38725 3.08785I 0
12
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.999541 + 0.623144I
a = 1.77554 + 0.83370I
b = 1.08912 + 2.12886I
1.40869 + 5.50421I 0
u = 0.999541 0.623144I
a = 1.77554 0.83370I
b = 1.08912 2.12886I
1.40869 5.50421I 0
u = 0.739937 + 0.344084I
a = 2.37470 1.34280I
b = 1.53542 1.08705I
1.02186 4.25611I 0.62399 + 3.95647I
u = 0.739937 0.344084I
a = 2.37470 + 1.34280I
b = 1.53542 + 1.08705I
1.02186 + 4.25611I 0.62399 3.95647I
u = 1.039180 + 0.588423I
a = 1.293610 0.288235I
b = 1.25047 1.33963I
3.40803 4.57637I 0
u = 1.039180 0.588423I
a = 1.293610 + 0.288235I
b = 1.25047 + 1.33963I
3.40803 + 4.57637I 0
u = 1.264100 + 0.078163I
a = 0.347630 0.142558I
b = 0.253429 + 0.570123I
0.19607 + 9.25422I 0
u = 1.264100 0.078163I
a = 0.347630 + 0.142558I
b = 0.253429 0.570123I
0.19607 9.25422I 0
u = 0.411787 + 0.603762I
a = 0.922770 + 0.631966I
b = 0.328497 + 0.626270I
1.74771 0.16605I 4.99428 + 0.74621I
u = 0.411787 0.603762I
a = 0.922770 0.631966I
b = 0.328497 0.626270I
1.74771 + 0.16605I 4.99428 0.74621I
13
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.573487 + 0.416145I
a = 2.00076 1.22922I
b = 1.154960 0.470757I
1.02228 4.28090I 0.77729 + 5.50918I
u = 0.573487 0.416145I
a = 2.00076 + 1.22922I
b = 1.154960 + 0.470757I
1.02228 + 4.28090I 0.77729 5.50918I
u = 1.304480 + 0.084655I
a = 0.307054 + 0.104503I
b = 0.233400 0.365360I
1.38725 3.08785I 0
u = 1.304480 0.084655I
a = 0.307054 0.104503I
b = 0.233400 + 0.365360I
1.38725 + 3.08785I 0
u = 1.111330 + 0.708054I
a = 1.46803 0.91270I
b = 1.07109 2.04577I
6.78989 + 11.25030I 0
u = 1.111330 0.708054I
a = 1.46803 + 0.91270I
b = 1.07109 + 2.04577I
6.78989 11.25030I 0
u = 1.098310 + 0.729770I
a = 1.297130 + 0.467739I
b = 1.14041 + 1.34935I
0.19607 9.25422I 0
u = 1.098310 0.729770I
a = 1.297130 0.467739I
b = 1.14041 1.34935I
0.19607 + 9.25422I 0
u = 1.142900 + 0.733018I
a = 0.775534 0.735878I
b = 0.307204 1.333830I
6.16221 + 6.23957I 0
u = 1.142900 0.733018I
a = 0.775534 + 0.735878I
b = 0.307204 + 1.333830I
6.16221 6.23957I 0
14
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.188260 + 0.731413I
a = 0.389233 + 0.645022I
b = 0.086689 + 0.937967I
3.95861 0
u = 1.188260 0.731413I
a = 0.389233 0.645022I
b = 0.086689 0.937967I
3.95861 0
u = 0.400300 + 0.307611I
a = 2.53207 + 0.99917I
b = 1.040020 + 0.281329I
1.79480 0.25822I 3.59957 + 1.08985I
u = 0.400300 0.307611I
a = 2.53207 0.99917I
b = 1.040020 0.281329I
1.79480 + 0.25822I 3.59957 1.08985I
u = 0.042716 + 0.358832I
a = 3.71030 + 0.19733I
b = 1.097180 + 0.015067I
3.04440 + 2.37626I 1.15007 2.61756I
u = 0.042716 0.358832I
a = 3.71030 0.19733I
b = 1.097180 0.015067I
3.04440 2.37626I 1.15007 + 2.61756I
15
III. I
u
3
= h2b u 2, 2a u 2, u
2
+ u 1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
7
=
1
2
u + 1
1
2
u + 1
a
11
=
1
u + 1
a
1
=
1
2
u +
1
4
3
2
u +
1
4
a
3
=
u
u
a
8
=
1
2
u + 1
1
2
u + 1
a
5
=
1
2
u +
3
4
3
2
u +
3
4
a
2
=
1
4
u +
3
4
9
4
u +
7
4
a
9
=
u
3u 2
a
6
=
1
2
u + 1
5
2
u + 3
a
6
=
1
2
u + 1
5
2
u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 30u
101
4
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
2
+ u 1
c
2
u
2
+ 3u + 1
c
3
, c
5
u
2
u 1
c
4
4(4u
2
+ 2u 1)
c
6
(u + 1)
2
c
7
u
2
c
8
(u 1)
2
c
9
u
2
3u + 1
c
11
4(4u
2
2u 1)
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
10
y
2
3y + 1
c
2
, c
9
y
2
7y + 1
c
4
, c
11
16(16y
2
12y + 1)
c
6
, c
8
(y 1)
2
c
7
y
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
1(vol +
1CS) Cusp shape
u = 0.618034
a = 1.30902
b = 1.30902
0.657974 6.70900
u = 1.61803
a = 0.190983
b = 0.190983
7.23771 73.7910
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
2
+ u 1)(u
18
u
17
+ ··· 3u + 1)(u
56
+ 3u
55
+ ··· + 2u + 1)
c
2
(u
2
+ 3u + 1)(u
18
+ 9u
17
+ ··· + 19u + 1)(u
56
+ 21u
55
+ ··· 26u
2
+ 1)
c
3
, c
5
(u
2
u 1)(u
18
u
17
+ ··· 3u + 1)(u
56
+ 3u
55
+ ··· + 2u + 1)
c
4
16(4u
2
+ 2u 1)(4u
18
2u
17
+ ··· 10u
2
+ 1)
· (u
56
7u
55
+ ··· 45726u + 21533)
c
6
((u + 1)
2
)(u
18
u
17
+ ··· + 24u 16)(u
28
+ 2u
27
+ ··· 10u + 1)
2
c
7
u
2
(u
18
+ 5u
17
+ ··· 384u 64)(u
28
2u
27
+ ··· 4u + 1)
2
c
8
((u 1)
2
)(u
18
u
17
+ ··· + 24u 16)(u
28
+ 2u
27
+ ··· 10u + 1)
2
c
9
(u
2
3u + 1)(u
18
+ 9u
17
+ ··· + 19u + 1)(u
56
+ 21u
55
+ ··· 26u
2
+ 1)
c
11
16(4u
2
2u 1)(4u
18
2u
17
+ ··· 10u
2
+ 1)
· (u
56
7u
55
+ ··· 45726u + 21533)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
10
(y
2
3y + 1)(y
18
9y
17
+ ··· 19y + 1)(y
56
21y
55
+ ··· 26y
2
+ 1)
c
2
, c
9
(y
2
7y + 1)(y
18
+ 3y
17
+ ··· 159y + 1)(y
56
+ 27y
55
+ ··· 52y + 1)
c
4
, c
11
256(16y
2
12y + 1)(16y
18
140y
17
+ ··· 20y + 1)
· (y
56
29y
55
+ ··· 2262183624y + 463670089)
c
6
, c
8
((y 1)
2
)(y
18
13y
17
+ ··· + 736y + 256)
· (y
28
22y
27
+ ··· 66y + 1)
2
c
7
y
2
(y
18
3y
17
+ ··· 104960y + 4096)(y
28
6y
27
+ ··· 30y + 1)
2
21