11a
124
(K11a
124
)
A knot diagram
1
Linearized knot diagam
5 1 10 7 2 9 3 6 11 4 8
Solving Sequence
3,10 4,7
5 8 11 1 2 9 6
c
3
c
4
c
7
c
10
c
11
c
2
c
9
c
6
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
17
2u
16
+ ··· + 2b 1, 8u
18
u
17
+ ··· + 8a + 1, u
19
u
18
+ ··· + 2u + 1i
I
u
2
= h−3.29428 × 10
43
u
59
7.32537 × 10
43
u
58
+ ··· + 3.61424 × 10
43
b 3.73726 × 10
43
,
1.15786 × 10
44
u
59
2.56717 × 10
44
u
58
+ ··· + 3.61424 × 10
43
a 1.16229 × 10
44
, u
60
+ 3u
59
+ ··· + 2u + 1i
I
u
3
= hb, 2a 2u + 3, u
2
u 1i
* 3 irreducible components of dim
C
= 0, with total 81 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
= hu
17
2u
16
+· · ·+2b1, 8u
18
u
17
+· · ·+8a+1, u
19
u
18
+· · ·+2u+1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
7
=
u
18
+
1
8
u
17
+ ··· +
29
8
u
1
8
1
2
u
17
+ u
16
+ ··· +
5
2
u +
1
2
a
5
=
0.812500u
18
0.312500u
17
+ ··· 2.75000u + 0.687500
u
3
u
a
8
=
u
18
+
5
8
u
17
+ ··· +
9
8
u
5
8
1
2
u
17
+ u
16
+ ··· +
5
2
u +
1
2
a
11
=
u
u
3
+ u
a
1
=
13
16
u
18
5
16
u
17
+ ···
11
4
u
5
16
u
2
a
2
=
5
16
u
18
1
8
u
17
+ ···
29
16
u +
1
2
u
4
a
9
=
u
3
u
5
u
3
+ u
a
6
=
u
18
+
3
8
u
17
+ ··· +
23
8
u
3
8
u
5
u
3
+ u
a
6
=
u
18
+
3
8
u
17
+ ··· +
23
8
u
3
8
u
5
u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
5
8
u
18
+
15
16
u
17
+ ···
147
16
u
275
16
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
10
u
19
u
18
+ ··· + 2u + 1
c
2
, c
9
u
19
+ 11u
18
+ ··· + 10u + 1
c
4
, c
11
4(4u
19
6u
18
+ ··· + u + 1)
c
6
, c
8
u
19
+ u
18
+ ··· + 72u + 16
c
7
u
19
+ 5u
18
+ ··· + 576u + 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
10
y
19
11y
18
+ ··· + 10y 1
c
2
, c
9
y
19
3y
18
+ ··· + 6y 1
c
4
, c
11
16(16y
19
44y
18
+ ··· + 27y 1)
c
6
, c
8
y
19
11y
18
+ ··· + 5152y 256
c
7
y
19
+ 3y
18
+ ··· + 84480y 4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.419051 + 0.893130I
a = 0.135730 0.103762I
b = 0.724967 + 1.151790I
2.04820 + 6.16450I 8.26103 3.38099I
u = 0.419051 0.893130I
a = 0.135730 + 0.103762I
b = 0.724967 1.151790I
2.04820 6.16450I 8.26103 + 3.38099I
u = 0.899345 + 0.246437I
a = 2.14777 1.01558I
b = 1.204930 + 0.354128I
3.77143 0.86442I 19.7475 + 1.3057I
u = 0.899345 0.246437I
a = 2.14777 + 1.01558I
b = 1.204930 0.354128I
3.77143 + 0.86442I 19.7475 1.3057I
u = 1.003450 + 0.392686I
a = 1.58170 + 0.42470I
b = 0.13937 + 1.76374I
5.55704 + 4.23947I 20.3915 6.1738I
u = 1.003450 0.392686I
a = 1.58170 0.42470I
b = 0.13937 1.76374I
5.55704 4.23947I 20.3915 + 6.1738I
u = 0.552607 + 0.734353I
a = 0.356653 + 0.052498I
b = 0.56635 1.31894I
4.59036 + 0.49883I 5.13235 + 1.11737I
u = 0.552607 0.734353I
a = 0.356653 0.052498I
b = 0.56635 + 1.31894I
4.59036 0.49883I 5.13235 1.11737I
u = 1.034010 + 0.500803I
a = 0.92474 + 1.69869I
b = 1.81071 + 0.75880I
3.99870 8.26948I 17.0118 + 10.4497I
u = 1.034010 0.500803I
a = 0.92474 1.69869I
b = 1.81071 0.75880I
3.99870 + 8.26948I 17.0118 10.4497I
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.047050 + 0.609446I
a = 2.13795 + 0.40305I
b = 1.14750 1.52008I
1.58848 + 10.77560I 11.1069 9.6699I
u = 1.047050 0.609446I
a = 2.13795 0.40305I
b = 1.14750 + 1.52008I
1.58848 10.77560I 11.1069 + 9.6699I
u = 1.136920 + 0.651601I
a = 1.99873 0.44428I
b = 1.05260 + 1.28107I
2.2580 + 17.5240I 13.4299 10.5127I
u = 1.136920 0.651601I
a = 1.99873 + 0.44428I
b = 1.05260 1.28107I
2.2580 17.5240I 13.4299 + 10.5127I
u = 1.36120
a = 0.900530
b = 0.770557
10.4347 25.7620
u = 0.459746 + 0.391888I
a = 0.822946 0.928476I
b = 0.928594 + 0.046627I
0.672184 0.228526I 10.04556 + 0.04203I
u = 0.459746 0.391888I
a = 0.822946 + 0.928476I
b = 0.928594 0.046627I
0.672184 + 0.228526I 10.04556 0.04203I
u = 0.460389
a = 0.746543
b = 0.475486
0.745623 13.0540
u = 1.58350
a = 0.283362
b = 0.279027
10.5925 69.4310
6
II.
I
u
2
= h−3.29×10
43
u
59
7.33×10
43
u
58
+· · ·+3.61×10
43
b3.74×10
43
, 1.16 ×
10
44
u
59
2.57×10
44
u
58
+· · ·+3.61×10
43
a1.16×10
44
, u
60
+3u
59
+· · ·+2u+1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
7
=
3.20362u
59
+ 7.10293u
58
+ ··· + 1.55388u + 3.21587
0.911474u
59
+ 2.02681u
58
+ ··· + 3.08549u + 1.03404
a
5
=
2.28143u
59
5.75495u
58
+ ··· 5.19179u 0.442802
0.263750u
59
0.472714u
58
+ ··· 0.742543u + 0.322096
a
8
=
2.29215u
59
+ 5.07612u
58
+ ··· 1.53161u + 2.18183
0.911474u
59
+ 2.02681u
58
+ ··· + 3.08549u + 1.03404
a
11
=
u
u
3
+ u
a
1
=
0.925654u
59
+ 2.23848u
58
+ ··· + 3.65944u 1.78646
1.35234u
59
3.28016u
58
+ ··· 2.39453u 2.24660
a
2
=
1.46589u
59
+ 5.35398u
58
+ ··· + 3.78505u + 2.43307
0.363163u
59
0.635073u
58
+ ··· 1.17134u + 0.200966
a
9
=
u
3
u
5
u
3
+ u
a
6
=
2.89417u
59
+ 6.43628u
58
+ ··· + 1.32225u + 2.63687
u
5
u
3
+ u
a
6
=
2.89417u
59
+ 6.43628u
58
+ ··· + 1.32225u + 2.63687
u
5
u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2.48951u
59
4.72262u
58
+ ··· 4.88635u 16.4633
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
10
u
60
+ 3u
59
+ ··· + 2u + 1
c
2
, c
9
u
60
+ 25u
59
+ ··· 8u
2
+ 1
c
4
, c
11
u
60
9u
59
+ ··· + 2u + 49
c
6
, c
8
(u
30
2u
29
+ ··· 4u
2
+ 1)
2
c
7
(u
30
2u
29
+ ··· + 2u + 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
10
y
60
25y
59
+ ··· 8y
2
+ 1
c
2
, c
9
y
60
+ 19y
59
+ ··· 16y + 1
c
4
, c
11
y
60
+ 15y
59
+ ··· + 225396y + 2401
c
6
, c
8
(y
30
18y
29
+ ··· 8y + 1)
2
c
7
(y
30
+ 6y
29
+ ··· 20y + 1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.436655 + 0.898161I
a = 0.099230 0.147670I
b = 0.90502 + 1.20796I
0.13306 11.82350I 11.00000 + 6.87881I
u = 0.436655 0.898161I
a = 0.099230 + 0.147670I
b = 0.90502 1.20796I
0.13306 + 11.82350I 11.00000 6.87881I
u = 0.938385 + 0.379407I
a = 1.68614 0.74769I
b = 0.441181 + 0.955338I
3.09259 1.44484I 13.23226 + 3.70712I
u = 0.938385 0.379407I
a = 1.68614 + 0.74769I
b = 0.441181 0.955338I
3.09259 + 1.44484I 13.23226 3.70712I
u = 0.398222 + 0.946146I
a = 0.0703469 0.0182926I
b = 0.704169 + 0.741434I
3.92001 3.29506I 14.4988 + 4.3495I
u = 0.398222 0.946146I
a = 0.0703469 + 0.0182926I
b = 0.704169 0.741434I
3.92001 + 3.29506I 14.4988 4.3495I
u = 0.892854 + 0.516085I
a = 8.30139 + 2.16305I
b = 0.231045
1.58362 80.9296 + 0.I
u = 0.892854 0.516085I
a = 8.30139 2.16305I
b = 0.231045
1.58362 80.9296 + 0.I
u = 0.984616 + 0.331650I
a = 2.35527 0.33318I
b = 1.04495 + 1.40324I
5.12713 2.00252I 19.8433 + 2.5113I
u = 0.984616 0.331650I
a = 2.35527 + 0.33318I
b = 1.04495 1.40324I
5.12713 + 2.00252I 19.8433 2.5113I
10
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.650550 + 0.812563I
a = 0.222812 + 0.168392I
b = 0.070411 0.978282I
3.50080 2.14029I 5.17623 + 3.82275I
u = 0.650550 0.812563I
a = 0.222812 0.168392I
b = 0.070411 + 0.978282I
3.50080 + 2.14029I 5.17623 3.82275I
u = 0.936320 + 0.528594I
a = 2.49741 + 1.41081I
b = 0.562357 + 0.083868I
1.14510 + 4.17705I 16.5884 2.8209I
u = 0.936320 0.528594I
a = 2.49741 1.41081I
b = 0.562357 0.083868I
1.14510 4.17705I 16.5884 + 2.8209I
u = 0.919545 + 0.051720I
a = 1.39527 1.59972I
b = 1.129730 0.530819I
1.66693 + 4.72265I 14.9294 5.7699I
u = 0.919545 0.051720I
a = 1.39527 + 1.59972I
b = 1.129730 + 0.530819I
1.66693 4.72265I 14.9294 + 5.7699I
u = 0.636488 + 0.889069I
a = 0.162077 + 0.177638I
b = 0.405721 0.886114I
1.01444 + 7.41192I 11.0000 9.0404I
u = 0.636488 0.889069I
a = 0.162077 0.177638I
b = 0.405721 + 0.886114I
1.01444 7.41192I 11.0000 + 9.0404I
u = 0.750944 + 0.483602I
a = 2.17802 + 2.09569I
b = 0.562357 0.083868I
1.14510 4.17705I 16.5884 + 2.8209I
u = 0.750944 0.483602I
a = 2.17802 2.09569I
b = 0.562357 + 0.083868I
1.14510 + 4.17705I 16.5884 2.8209I
11
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.519876 + 0.720950I
a = 0.440387 0.033998I
b = 0.84652 1.38646I
3.14940 5.67522I 7.89041 + 4.45785I
u = 0.519876 0.720950I
a = 0.440387 + 0.033998I
b = 0.84652 + 1.38646I
3.14940 + 5.67522I 7.89041 4.45785I
u = 1.017570 + 0.457794I
a = 0.084372 + 1.203970I
b = 1.04495 + 1.40324I
5.12713 2.00252I 19.8433 + 0.I
u = 1.017570 0.457794I
a = 0.084372 1.203970I
b = 1.04495 1.40324I
5.12713 + 2.00252I 19.8433 + 0.I
u = 1.002750 + 0.506811I
a = 1.06264 + 1.11423I
b = 1.239150 + 0.487592I
2.12597 + 4.23565I 11.00000 + 0.I
u = 1.002750 0.506811I
a = 1.06264 1.11423I
b = 1.239150 0.487592I
2.12597 4.23565I 11.00000 + 0.I
u = 0.329797 + 0.800824I
a = 0.234010 + 0.120107I
b = 0.070411 + 0.978282I
3.50080 + 2.14029I 5.17623 3.82275I
u = 0.329797 0.800824I
a = 0.234010 0.120107I
b = 0.070411 0.978282I
3.50080 2.14029I 5.17623 + 3.82275I
u = 1.004570 + 0.573546I
a = 1.55156 + 0.95069I
b = 1.129730 0.530819I
1.66693 + 4.72265I 0
u = 1.004570 0.573546I
a = 1.55156 0.95069I
b = 1.129730 + 0.530819I
1.66693 4.72265I 0
12
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.690400 + 0.444793I
a = 1.012660 + 0.803393I
b = 0.603977
0.361516 10.81395 + 0.I
u = 0.690400 0.444793I
a = 1.012660 0.803393I
b = 0.603977
0.361516 10.81395 + 0.I
u = 0.618191 + 0.540303I
a = 0.281188 0.010801I
b = 0.667178 0.364020I
0.462439 0.119450I 11.28349 + 0.62863I
u = 0.618191 0.540303I
a = 0.281188 + 0.010801I
b = 0.667178 + 0.364020I
0.462439 + 0.119450I 11.28349 0.62863I
u = 0.985228 + 0.669318I
a = 1.058260 + 0.114866I
b = 0.228079 0.908946I
2.48757 3.39736I 0
u = 0.985228 0.669318I
a = 1.058260 0.114866I
b = 0.228079 + 0.908946I
2.48757 + 3.39736I 0
u = 0.789155 + 0.080621I
a = 0.94378 + 1.09560I
b = 0.667178 + 0.364020I
0.462439 + 0.119450I 11.28349 0.62863I
u = 0.789155 0.080621I
a = 0.94378 1.09560I
b = 0.667178 0.364020I
0.462439 0.119450I 11.28349 + 0.62863I
u = 1.035610 + 0.621202I
a = 1.87368 + 0.26667I
b = 0.84652 1.38646I
3.14940 5.67522I 0
u = 1.035610 0.621202I
a = 1.87368 0.26667I
b = 0.84652 + 1.38646I
3.14940 + 5.67522I 0
13
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.343048 + 0.696449I
a = 0.281786 + 0.291123I
b = 0.228079 + 0.908946I
2.48757 + 3.39736I 6.14839 2.65836I
u = 0.343048 0.696449I
a = 0.281786 0.291123I
b = 0.228079 0.908946I
2.48757 3.39736I 6.14839 + 2.65836I
u = 1.265290 + 0.064635I
a = 1.17958 + 1.04775I
b = 0.944732 + 0.854118I
6.23866 + 9.10516I 0
u = 1.265290 0.064635I
a = 1.17958 1.04775I
b = 0.944732 0.854118I
6.23866 9.10516I 0
u = 0.998856 + 0.783376I
a = 0.501826 0.219673I
b = 0.167947 0.687514I
0.072177 1.332500I 0
u = 0.998856 0.783376I
a = 0.501826 + 0.219673I
b = 0.167947 + 0.687514I
0.072177 + 1.332500I 0
u = 1.277600 + 0.094427I
a = 0.865094 + 0.946801I
b = 0.704169 + 0.741434I
3.92001 3.29506I 0
u = 1.277600 0.094427I
a = 0.865094 0.946801I
b = 0.704169 0.741434I
3.92001 + 3.29506I 0
u = 1.191580 + 0.532179I
a = 0.825176 + 0.590327I
b = 0.167947 + 0.687514I
0.072177 + 1.332500I 0
u = 1.191580 0.532179I
a = 0.825176 0.590327I
b = 0.167947 0.687514I
0.072177 1.332500I 0
14
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.165050 + 0.599287I
a = 1.281030 + 0.306017I
b = 0.405721 + 0.886114I
1.01444 7.41192I 0
u = 1.165050 0.599287I
a = 1.281030 0.306017I
b = 0.405721 0.886114I
1.01444 + 7.41192I 0
u = 1.140590 + 0.644966I
a = 1.87323 0.27645I
b = 0.90502 + 1.20796I
0.13306 11.82350I 0
u = 1.140590 0.644966I
a = 1.87323 + 0.27645I
b = 0.90502 1.20796I
0.13306 + 11.82350I 0
u = 1.159760 + 0.652820I
a = 1.44051 0.42878I
b = 0.944732 + 0.854118I
6.23866 + 9.10516I 0
u = 1.159760 0.652820I
a = 1.44051 + 0.42878I
b = 0.944732 0.854118I
6.23866 9.10516I 0
u = 0.296291 + 0.465226I
a = 0.28682 1.74341I
b = 1.239150 + 0.487592I
2.12597 + 4.23565I 12.76145 5.43945I
u = 0.296291 0.465226I
a = 0.28682 + 1.74341I
b = 1.239150 0.487592I
2.12597 4.23565I 12.76145 + 5.43945I
u = 0.100373 + 0.382494I
a = 0.41107 2.93021I
b = 0.441181 + 0.955338I
3.09259 1.44484I 13.23226 + 3.70712I
u = 0.100373 0.382494I
a = 0.41107 + 2.93021I
b = 0.441181 0.955338I
3.09259 + 1.44484I 13.23226 3.70712I
15
III. I
u
3
= hb, 2a 2u + 3, u
2
u 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u + 1
a
7
=
u
3
2
0
a
5
=
3
4
u
1
4
u + 1
a
8
=
u
3
2
0
a
11
=
u
u 1
a
1
=
7
4
u +
5
4
u 1
a
2
=
9
4
u +
1
2
3u 2
a
9
=
2u + 1
4u + 2
a
6
=
u
5
2
4u 2
a
6
=
u
5
2
4u 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 30u +
21
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 = 2.11803
b = 0
2.63189 13.2910
u = 1.61803
a = 0.118034
b = 0
10.5276 53.7910
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
2
+ u 1)(u
19
u
18
+ ··· + 2u + 1)(u
60
+ 3u
59
+ ··· + 2u + 1)
c
2
(u
2
+ 3u + 1)(u
19
+ 11u
18
+ ··· + 10u + 1)(u
60
+ 25u
59
+ ··· 8u
2
+ 1)
c
3
, c
5
(u
2
u 1)(u
19
u
18
+ ··· + 2u + 1)(u
60
+ 3u
59
+ ··· + 2u + 1)
c
4
16(4u
2
2u 1)(4u
19
6u
18
+ ··· + u + 1)(u
60
9u
59
+ ··· + 2u + 49)
c
6
((u 1)
2
)(u
19
+ u
18
+ ··· + 72u + 16)(u
30
2u
29
+ ··· 4u
2
+ 1)
2
c
7
u
2
(u
19
+ 5u
18
+ ··· + 576u + 64)(u
30
2u
29
+ ··· + 2u + 1)
2
c
8
((u + 1)
2
)(u
19
+ u
18
+ ··· + 72u + 16)(u
30
2u
29
+ ··· 4u
2
+ 1)
2
c
9
(u
2
3u + 1)(u
19
+ 11u
18
+ ··· + 10u + 1)(u
60
+ 25u
59
+ ··· 8u
2
+ 1)
c
11
16(4u
2
+ 2u 1)(4u
19
6u
18
+ ··· + u + 1)(u
60
9u
59
+ ··· + 2u + 49)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
10
(y
2
3y + 1)(y
19
11y
18
+ ··· + 10y 1)(y
60
25y
59
+ ··· 8y
2
+ 1)
c
2
, c
9
(y
2
7y + 1)(y
19
3y
18
+ ··· + 6y 1)(y
60
+ 19y
59
+ ··· 16y + 1)
c
4
, c
11
256(16y
2
12y + 1)(16y
19
44y
18
+ ··· + 27y 1)
· (y
60
+ 15y
59
+ ··· + 225396y + 2401)
c
6
, c
8
((y 1)
2
)(y
19
11y
18
+ ··· + 5152y 256)
· (y
30
18y
29
+ ··· 8y + 1)
2
c
7
y
2
(y
19
+ 3y
18
+ ··· + 84480y 4096)(y
30
+ 6y
29
+ ··· 20y + 1)
2
21