11a
347
(K11a
347
)
A knot diagram
1
Linearized knot diagam
9 6 1 10 8 3 11 2 5 4 7
Solving Sequence
5,9 2,10
1 4 11 3 8 6 7
c
9
c
1
c
4
c
10
c
3
c
8
c
5
c
7
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h256000670808631u
21
+ 674760339816179u
20
+ ··· + 232517605023576b + 5745913318570412,
3.63354 × 10
15
u
21
+ 9.67535 × 10
15
u
20
+ ··· + 1.86014 × 10
15
a + 8.31691 × 10
16
, u
22
+ 3u
21
+ ··· + 56u + 8i
I
u
2
= h2u
17
a + 2u
17
+ ··· + a + 6, −10u
17
a + 23u
17
+ ··· − 19a + 63, u
18
− u
17
+ ··· + 3u − 1i
I
u
3
= hb − 1, 4a − u + 2, u
2
+ 2i
I
v
1
= ha, b + 1, 2v −1i
* 4 irreducible components of dim
C
= 0, with total 61 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
=
h2.56×10
14
u
21
+6.75×10
14
u
20
+· · ·+2.33×10
14
b+5.75×10
15
, 3.63×10
15
u
21
+
9.68 × 10
15
u
20
+ · · · + 1.86 × 10
15
a + 8.32 × 10
16
, u
22
+ 3u
21
+ · · · + 56u + 8i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
2
=
−1.95337u
21
− 5.20141u
20
+ ··· − 184.686u − 44.7112
−1.10099u
21
− 2.90198u
20
+ ··· − 104.609u − 24.7117
a
10
=
1
u
2
a
1
=
−0.852375u
21
− 2.29943u
20
+ ··· − 80.0775u − 19.9995
−1.10099u
21
− 2.90198u
20
+ ··· − 104.609u − 24.7117
a
4
=
u
u
3
+ u
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
3
=
−0.410016u
21
− 1.10389u
20
+ ··· − 37.5475u − 9.64240
−0.733210u
21
− 1.92174u
20
+ ··· − 68.1510u − 16.3230
a
8
=
−0.193796u
21
− 0.498389u
20
+ ··· − 16.9193u − 2.65074
−1.07925u
21
− 2.88821u
20
+ ··· − 100.094u − 23.3142
a
6
=
−0.293649u
21
− 0.752180u
20
+ ··· − 26.8185u − 5.67130
−0.746302u
21
− 1.99347u
20
+ ··· − 69.2277u − 16.3438
a
7
=
1.06840u
21
+ 2.85509u
20
+ ··· + 101.338u + 25.2691
−0.787989u
21
− 2.09142u
20
+ ··· − 72.2901u − 16.6414
a
7
=
1.06840u
21
+ 2.85509u
20
+ ··· + 101.338u + 25.2691
−0.787989u
21
− 2.09142u
20
+ ··· − 72.2901u − 16.6414
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
1537891371251021
310023473364768
u
21
+
3975035432412625
310023473364768
u
20
+ ··· +
461879710488329
1099374019024
u +
7058304318144475
77505868341192
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
8
c
11
u
22
+ u
21
+ ··· − 7u − 3
c
2
, c
6
u
22
− 9u
20
+ ··· + 7u − 24
c
3
, c
5
8(8u
22
− 20u
21
+ ··· − 2u
2
+ 1)
c
4
, c
9
, c
10
u
22
+ 3u
21
+ ··· + 56u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
8
c
11
y
22
+ 9y
21
+ ··· − 55y + 9
c
2
, c
6
y
22
− 18y
21
+ ··· + 335y + 576
c
3
, c
5
64(64y
22
− 240y
21
+ ··· − 4y + 1)
c
4
, c
9
, c
10
y
22
+ 21y
21
+ ··· − 480y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.923083 + 0.449241I
a = 0.46489 − 1.80679I
b = −0.471805 − 1.329800I
−9.5532 + 10.8949I −8.89518 − 7.36414I
u = −0.923083 − 0.449241I
a = 0.46489 + 1.80679I
b = −0.471805 + 1.329800I
−9.5532 − 10.8949I −8.89518 + 7.36414I
u = 1.051430 + 0.225174I
a = 0.06569 + 1.67599I
b = −0.304231 + 1.040140I
−3.20816 − 4.89414I −6.47528 + 9.10540I
u = 1.051430 − 0.225174I
a = 0.06569 − 1.67599I
b = −0.304231 − 1.040140I
−3.20816 + 4.89414I −6.47528 − 9.10540I
u = −0.879824 + 0.816752I
a = 0.559661 − 1.087650I
b = 0.313637 − 1.227100I
−8.56742 − 4.93041I −9.24363 + 4.50732I
u = −0.879824 − 0.816752I
a = 0.559661 + 1.087650I
b = 0.313637 + 1.227100I
−8.56742 + 4.93041I −9.24363 − 4.50732I
u = −0.123835 + 1.345220I
a = 0.527565 − 0.232201I
b = −1.43217 + 0.42237I
4.03174 + 1.74144I −4.49330 − 4.13639I
u = −0.123835 − 1.345220I
a = 0.527565 + 0.232201I
b = −1.43217 − 0.42237I
4.03174 − 1.74144I −4.49330 + 4.13639I
u = −0.613996 + 1.252680I
a = −0.426413 + 1.140360I
b = 0.267923 + 0.935360I
0.17781 + 3.00927I −2.42568 − 8.45199I
u = −0.613996 − 1.252680I
a = −0.426413 − 1.140360I
b = 0.267923 − 0.935360I
0.17781 − 3.00927I −2.42568 + 8.45199I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.051311 + 0.543007I
a = 0.085673 + 0.510275I
b = 0.531392 + 0.374501I
0.81916 + 1.15831I 3.24306 − 4.91464I
u = 0.051311 − 0.543007I
a = 0.085673 − 0.510275I
b = 0.531392 − 0.374501I
0.81916 − 1.15831I 3.24306 + 4.91464I
u = 0.07053 + 1.46071I
a = 0.392040 + 0.012145I
b = −0.893893 − 0.461606I
7.21746 + 0.43098I 4.81736 − 2.08890I
u = 0.07053 − 1.46071I
a = 0.392040 − 0.012145I
b = −0.893893 + 0.461606I
7.21746 − 0.43098I 4.81736 + 2.08890I
u = 0.38554 + 1.45702I
a = −0.858101 − 1.123100I
b = 0.519928 − 1.174350I
2.25077 − 9.90431I −2.68871 + 7.61704I
u = 0.38554 − 1.45702I
a = −0.858101 + 1.123100I
b = 0.519928 + 1.174350I
2.25077 + 9.90431I −2.68871 − 7.61704I
u = −0.34668 + 1.51369I
a = −1.07441 + 0.97292I
b = 0.60863 + 1.34961I
−3.2485 + 15.4927I −5.17708 − 7.97844I
u = −0.34668 − 1.51369I
a = −1.07441 − 0.97292I
b = 0.60863 − 1.34961I
−3.2485 − 15.4927I −5.17708 + 7.97844I
u = −0.364239
a = 0.703521
b = 1.25729
−0.360724 −18.5120
u = −0.342457
a = −1.98069
b = −0.295995
−1.11076 −11.5720
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.18195 + 1.70803I
a = 0.276992 + 0.588080I
b = −0.120052 + 0.802501I
1.76897 − 0.99297I 2.13017 + 4.98419I
u = 0.18195 − 1.70803I
a = 0.276992 − 0.588080I
b = −0.120052 − 0.802501I
1.76897 + 0.99297I 2.13017 − 4.98419I
7
II. I
u
2
= h2u
17
a + 2u
17
+ · · · + a + 6, −10u
17
a + 23u
17
+ · · · − 19a +
63, u
18
− u
17
+ · · · + 3u − 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
2
=
a
−
2
5
u
17
a −
2
5
u
17
+ ··· −
1
5
a −
6
5
a
10
=
1
u
2
a
1
=
2
5
u
17
a +
2
5
u
17
+ ··· +
6
5
a +
6
5
−
2
5
u
17
a −
2
5
u
17
+ ··· −
1
5
a −
6
5
a
4
=
u
u
3
+ u
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
3
=
1.06667au
17
− 1.26667u
17
+ ··· + 1.86667a − 1.13333
−0.200000au
17
− 1.53333u
17
+ ··· + 0.400000a − 2.93333
a
8
=
2
5
u
17
a −
34
15
u
17
+ ··· +
6
5
a −
82
15
−
2
5
u
17
a −
2
5
u
17
+ ··· −
1
5
a −
6
5
a
6
=
1.53333au
17
− 1.46667u
17
+ ··· + 2.93333a − 5.40000
−0.400000au
17
− 1.06667u
17
+ ··· + 0.800000a − 1.86667
a
7
=
2
5
u
17
a −
34
15
u
17
+ ··· +
6
5
a −
97
15
−1
a
7
=
2
5
u
17
a −
34
15
u
17
+ ··· +
6
5
a −
97
15
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
17
+ 4u
16
− 36u
15
+ 28u
14
− 124u
13
+ 72u
12
− 196u
11
+
72u
10
− 120u
9
+ 8u
7
− 36u
6
+ 8u
5
− 4u
4
− 16u
3
+ 8u − 14
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
8
c
11
u
36
− 3u
35
+ ··· − 8u + 1
c
2
, c
6
(u
18
+ u
17
+ ··· − u − 1)
2
c
3
, c
5
9(9u
36
+ 27u
35
+ ··· − 20172u + 3559)
c
4
, c
9
, c
10
(u
18
− u
17
+ ··· + 3u − 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
8
c
11
y
36
+ 23y
35
+ ··· − 16y + 1
c
2
, c
6
(y
18
− 15y
17
+ ··· − 7y + 1)
2
c
3
, c
5
81(81y
36
− 1377y
35
+ ··· − 7.10112 × 10
7
y + 1.26665 × 10
7
)
c
4
, c
9
, c
10
(y
18
+ 17y
17
+ ··· − 7y + 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215059 + 1.214380I
a = −1.264270 + 0.313519I
b = 0.816163 + 1.122800I
−5.44315 + 3.22673I −7.05526 − 3.62956I
u = −0.215059 + 1.214380I
a = 0.121854 − 0.436704I
b = 0.27308 − 1.57039I
−5.44315 + 3.22673I −7.05526 − 3.62956I
u = −0.215059 − 1.214380I
a = −1.264270 − 0.313519I
b = 0.816163 − 1.122800I
−5.44315 − 3.22673I −7.05526 + 3.62956I
u = −0.215059 − 1.214380I
a = 0.121854 + 0.436704I
b = 0.27308 + 1.57039I
−5.44315 − 3.22673I −7.05526 + 3.62956I
u = 0.678984 + 0.355286I
a = −0.359076 + 0.145322I
b = −1.008890 + 0.077944I
−5.17867 − 5.71427I −7.06596 + 6.05983I
u = 0.678984 + 0.355286I
a = −0.41568 − 1.94193I
b = 0.46000 − 1.36593I
−5.17867 − 5.71427I −7.06596 + 6.05983I
u = 0.678984 − 0.355286I
a = −0.359076 − 0.145322I
b = −1.008890 − 0.077944I
−5.17867 + 5.71427I −7.06596 − 6.05983I
u = 0.678984 − 0.355286I
a = −0.41568 + 1.94193I
b = 0.46000 + 1.36593I
−5.17867 + 5.71427I −7.06596 − 6.05983I
u = −0.590027 + 0.406016I
a = −0.254655 + 0.532993I
b = −0.430436 + 0.146579I
−0.86368 + 1.88569I −1.68331 − 3.99357I
u = −0.590027 + 0.406016I
a = −0.66911 + 1.67095I
b = 0.259835 + 0.987292I
−0.86368 + 1.88569I −1.68331 − 3.99357I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.590027 − 0.406016I
a = −0.254655 − 0.532993I
b = −0.430436 − 0.146579I
−0.86368 − 1.88569I −1.68331 + 3.99357I
u = −0.590027 − 0.406016I
a = −0.66911 − 1.67095I
b = 0.259835 − 0.987292I
−0.86368 − 1.88569I −1.68331 + 3.99357I
u = 0.482433 + 0.528989I
a = −0.01159 − 1.42789I
b = 0.535422 + 0.229537I
−4.41864 + 1.78695I −5.23943 + 0.02251I
u = 0.482433 + 0.528989I
a = −1.59986 − 0.89994I
b = −0.182954 − 1.202280I
−4.41864 + 1.78695I −5.23943 + 0.02251I
u = 0.482433 − 0.528989I
a = −0.01159 + 1.42789I
b = 0.535422 − 0.229537I
−4.41864 − 1.78695I −5.23943 − 0.02251I
u = 0.482433 − 0.528989I
a = −1.59986 + 0.89994I
b = −0.182954 + 1.202280I
−4.41864 − 1.78695I −5.23943 − 0.02251I
u = 0.076050 + 1.298790I
a = −0.36644 + 1.56815I
b = 0.181838 + 1.232260I
0.06375 − 1.57187I −1.80878 + 4.22070I
u = 0.076050 + 1.298790I
a = −1.80534 − 0.43101I
b = 0.393324 − 0.963175I
0.06375 − 1.57187I −1.80878 + 4.22070I
u = 0.076050 − 1.298790I
a = −0.36644 − 1.56815I
b = 0.181838 − 1.232260I
0.06375 + 1.57187I −1.80878 − 4.22070I
u = 0.076050 − 1.298790I
a = −1.80534 + 0.43101I
b = 0.393324 + 0.963175I
0.06375 + 1.57187I −1.80878 − 4.22070I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.663049
a = 0.21254 + 1.83196I
b = −0.53627 + 1.36483I
−9.12242 −12.3720
u = −0.663049
a = 0.21254 − 1.83196I
b = −0.53627 − 1.36483I
−9.12242 −12.3720
u = 0.17132 + 1.45278I
a = 0.948480 + 0.683751I
b = −0.119141 + 0.939188I
1.85527 − 0.55896I −1.51114 − 0.25710I
u = 0.17132 + 1.45278I
a = −0.002433 + 0.666631I
b = 0.197872 + 0.137215I
1.85527 − 0.55896I −1.51114 − 0.25710I
u = 0.17132 − 1.45278I
a = 0.948480 − 0.683751I
b = −0.119141 − 0.939188I
1.85527 + 0.55896I −1.51114 + 0.25710I
u = 0.17132 − 1.45278I
a = −0.002433 − 0.666631I
b = 0.197872 − 0.137215I
1.85527 + 0.55896I −1.51114 + 0.25710I
u = 0.25789 + 1.44398I
a = 0.995814 + 0.788845I
b = −0.69402 + 1.37640I
0.60037 − 9.13509I −2.98695 + 5.86478I
u = 0.25789 + 1.44398I
a = −0.379824 − 0.352640I
b = 1.211220 + 0.140810I
0.60037 − 9.13509I −2.98695 + 5.86478I
u = 0.25789 − 1.44398I
a = 0.995814 − 0.788845I
b = −0.69402 − 1.37640I
0.60037 + 9.13509I −2.98695 − 5.86478I
u = 0.25789 − 1.44398I
a = −0.379824 + 0.352640I
b = 1.211220 − 0.140810I
0.60037 + 9.13509I −2.98695 − 5.86478I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.22144 + 1.45044I
a = 0.938644 − 0.851386I
b = −0.554814 − 1.110360I
5.09742 + 4.87394I 1.52680 − 3.60136I
u = −0.22144 + 1.45044I
a = −0.195603 + 0.086886I
b = 0.855022 − 0.244718I
5.09742 + 4.87394I 1.52680 − 3.60136I
u = −0.22144 − 1.45044I
a = 0.938644 + 0.851386I
b = −0.554814 + 1.110360I
5.09742 − 4.87394I 1.52680 + 3.60136I
u = −0.22144 − 1.45044I
a = −0.195603 − 0.086886I
b = 0.855022 + 0.244718I
5.09742 − 4.87394I 1.52680 + 3.60136I
u = 0.382766
a = 2.60655 + 3.77847I
b = −0.157243 + 1.036420I
−3.91179 −11.9800
u = 0.382766
a = 2.60655 − 3.77847I
b = −0.157243 − 1.036420I
−3.91179 −11.9800
14
III. I
u
3
= hb − 1, 4a − u + 2, u
2
+ 2i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
2
=
1
4
u −
1
2
1
a
10
=
1
−2
a
1
=
1
4
u −
3
2
1
a
4
=
u
−u
a
11
=
−1
0
a
3
=
3
8
u − 1
−
1
2
u +
1
2
a
8
=
1
4
u +
1
2
1
a
6
=
−
1
8
u +
1
2
1
2
u +
1
2
a
7
=
1
4
u −
1
2
1
a
7
=
1
4
u −
1
2
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
11
(u + 1)
2
c
3
4(4u
2
+ 4u + 3)
c
4
, c
9
, c
10
u
2
+ 2
c
5
4(4u
2
− 4u + 3)
c
6
, c
7
, c
8
(u − 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
11
(y −1)
2
c
3
, c
5
16(16y
2
+ 8y + 9)
c
4
, c
9
, c
10
(y + 2)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = −0.500000 + 0.353553I
b = 1.00000
4.93480 0
u = − 1.414210I
a = −0.500000 − 0.353553I
b = 1.00000
4.93480 0
18
IV. I
v
1
= ha, b + 1, 2v − 1i
(i) Arc colorings
a
5
=
0.5
0
a
9
=
1
0
a
2
=
0
−1
a
10
=
1
0
a
1
=
1
−1
a
4
=
0.5
0
a
11
=
1
0
a
3
=
1
−0.5
a
8
=
1
1
a
6
=
1
0.5
a
7
=
0
1
a
7
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4.5
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
11
u − 1
c
3
2(2u + 1)
c
4
, c
9
, c
10
u
c
5
2(2u − 1)
c
6
, c
7
, c
8
u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
11
y −1
c
3
, c
5
4(4y −1)
c
4
, c
9
, c
10
y
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000
a = 0
b = −1.00000
0 4.50000
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
(u − 1)(u + 1)
2
(u
22
+ u
21
+ ··· − 7u − 3)(u
36
− 3u
35
+ ··· − 8u + 1)
c
2
(u − 1)(u + 1)
2
(u
18
+ u
17
+ ··· − u − 1)
2
(u
22
− 9u
20
+ ··· + 7u − 24)
c
3
576(2u + 1)(4u
2
+ 4u + 3)(8u
22
− 20u
21
+ ··· − 2u
2
+ 1)
· (9u
36
+ 27u
35
+ ··· − 20172u + 3559)
c
4
, c
9
, c
10
u(u
2
+ 2)(u
18
− u
17
+ ··· + 3u − 1)
2
(u
22
+ 3u
21
+ ··· + 56u + 8)
c
5
576(2u − 1)(4u
2
− 4u + 3)(8u
22
− 20u
21
+ ··· − 2u
2
+ 1)
· (9u
36
+ 27u
35
+ ··· − 20172u + 3559)
c
6
((u − 1)
2
)(u + 1)(u
18
+ u
17
+ ··· − u − 1)
2
(u
22
− 9u
20
+ ··· + 7u − 24)
c
7
, c
8
((u − 1)
2
)(u + 1)(u
22
+ u
21
+ ··· − 7u − 3)(u
36
− 3u
35
+ ··· − 8u + 1)
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
8
c
11
((y −1)
3
)(y
22
+ 9y
21
+ ··· − 55y + 9)(y
36
+ 23y
35
+ ··· − 16y + 1)
c
2
, c
6
((y −1)
3
)(y
18
− 15y
17
+ ··· − 7y + 1)
2
· (y
22
− 18y
21
+ ··· + 335y + 576)
c
3
, c
5
331776(4y −1)(16y
2
+ 8y + 9)(64y
22
− 240y
21
+ ··· − 4y + 1)
· (81y
36
− 1377y
35
+ ··· − 71011164y + 12666481)
c
4
, c
9
, c
10
y(y + 2)
2
(y
18
+ 17y
17
+ ··· − 7y + 1)
2
· (y
22
+ 21y
21
+ ··· − 480y + 64)
24
