11a
264
(K11a
264
)
A knot diagram
1
Linearized knot diagam
8 5 1 2 11 10 4 3 6 7 9
Solving Sequence
6,9
10 7 11
1,3
4 5 2 8
c
9
c
6
c
10
c
11
c
3
c
5
c
2
c
8
c
1
, c
4
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.58776 × 10
22
u
67
− 1.04955 × 10
22
u
66
+ ··· + 6.72818 × 10
21
b − 1.04955 × 10
22
,
− 1.38153 × 10
22
u
67
− 3.05107 × 10
21
u
66
+ ··· + 1.34564 × 10
22
a − 4.56619 × 10
22
, u
68
+ 2u
67
+ ··· − u + 1i
I
u
2
= hb − 1, a − 1, u + 1i
* 2 irreducible components of dim
C
= 0, with total 69 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−1.59×10
22
u
67
−1.05×10
22
u
66
+· · ·+6.73×10
21
b−1.05×10
22
, −1.38×
10
22
u
67
−3.05×10
21
u
66
+· · ·+1.35×10
22
a−4.57×10
22
, u
68
+2u
67
+· · ·−u+1i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
7
=
−u
−u
3
+ u
a
11
=
−u
2
+ 1
−u
4
+ 2u
2
a
1
=
−u
4
+ u
2
+ 1
−u
4
+ 2u
2
a
3
=
1.02668u
67
+ 0.226739u
66
+ ··· − 5.75514u + 3.39334
2.35987u
67
+ 1.55993u
66
+ ··· − 4.15327u + 1.55993
a
4
=
1.05999u
67
+ 0.260761u
66
+ ··· − 4.14749u + 3.50999
2.55846u
67
+ 1.75923u
66
+ ··· − 4.46922u + 1.75923
a
5
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
2
=
0.993337u
67
+ 0.193196u
66
+ ··· − 4.92153u + 3.37667
2.56028u
67
+ 1.76014u
66
+ ··· − 3.73681u + 1.76014
a
8
=
3.14602u
67
+ 2.35429u
66
+ ··· − 8.42884u + 4.83181
4.94843u
67
+ 4.15426u
66
+ ··· − 7.38265u + 4.14843
a
8
=
3.14602u
67
+ 2.35429u
66
+ ··· − 8.42884u + 4.83181
4.94843u
67
+ 4.15426u
66
+ ··· − 7.38265u + 4.14843
(ii) Obstruction class = −1
(iii) Cusp Shapes =
112903197958402042595072
6728175072045015305047
u
67
+
107383851493598493478554
6728175072045015305047
u
66
+ ··· −
240969492070676803449102
6728175072045015305047
u +
132818595949549446790132
6728175072045015305047
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
68
+ 4u
67
+ ··· − u − 1
c
2
, c
4
u
68
+ 2u
67
+ ··· − 7u − 1
c
3
u
68
− 11u
67
+ ··· + 2u + 2
c
5
u
68
− 3u
67
+ ··· + 533u
2
− 32
c
6
, c
9
, c
10
u
68
+ 2u
67
+ ··· − u + 1
c
7
u
68
− 4u
67
+ ··· + 30u − 4
c
8
u
68
− 2u
67
+ ··· + 19u − 1
c
11
u
68
+ 14u
67
+ ··· + 18491u + 1583
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
68
+ 10y
67
+ ··· + y + 1
c
2
, c
4
y
68
− 42y
67
+ ··· − 51y + 1
c
3
y
68
− 9y
67
+ ··· − 56y + 4
c
5
y
68
− 9y
67
+ ··· − 34112y + 1024
c
6
, c
9
, c
10
y
68
− 62y
67
+ ··· + y + 1
c
7
y
68
− 66y
67
+ ··· − 1036y + 16
c
8
y
68
− 62y
67
+ ··· − 127y + 1
c
11
y
68
+ 30y
67
+ ··· + 27393653y + 2505889
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.117970 + 0.060011I
a = 1.62448 − 0.34631I
b = 0.285160 + 0.839416I
1.61585 − 1.78744I 0
u = 1.117970 − 0.060011I
a = 1.62448 + 0.34631I
b = 0.285160 − 0.839416I
1.61585 + 1.78744I 0
u = −0.789092 + 0.387196I
a = 0.444694 + 0.296358I
b = 0.781342 + 0.135971I
−0.858945 − 0.278785I −10.90600 + 4.39760I
u = −0.789092 − 0.387196I
a = 0.444694 − 0.296358I
b = 0.781342 − 0.135971I
−0.858945 + 0.278785I −10.90600 − 4.39760I
u = −1.18619
a = −2.24020
b = −3.55236
−0.480843 0
u = −0.295738 + 0.755969I
a = −0.356340 − 0.856592I
b = −0.881092 + 0.343602I
0.75568 + 4.48414I −3.17555 − 9.83264I
u = −0.295738 − 0.755969I
a = −0.356340 + 0.856592I
b = −0.881092 − 0.343602I
0.75568 − 4.48414I −3.17555 + 9.83264I
u = 0.654936 + 0.478263I
a = −0.262793 + 0.825026I
b = −1.09654 + 1.08775I
0.98004 + 8.32019I −3.03705 − 4.05424I
u = 0.654936 − 0.478263I
a = −0.262793 − 0.825026I
b = −1.09654 − 1.08775I
0.98004 − 8.32019I −3.03705 + 4.05424I
u = 0.331672 + 0.733733I
a = 1.27124 − 1.30760I
b = 1.18104 + 1.20492I
2.14422 − 12.53140I −0.96253 + 9.09999I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.331672 − 0.733733I
a = 1.27124 + 1.30760I
b = 1.18104 − 1.20492I
2.14422 + 12.53140I −0.96253 − 9.09999I
u = 1.160860 + 0.298872I
a = −0.857448 + 0.085533I
b = −0.730590 − 1.106920I
2.43714 − 8.63386I 0
u = 1.160860 − 0.298872I
a = −0.857448 − 0.085533I
b = −0.730590 + 1.106920I
2.43714 + 8.63386I 0
u = −0.510378 + 0.611213I
a = −0.014066 + 0.208428I
b = −0.251269 − 0.053760I
−1.07152 + 2.12045I −9.29687 − 6.29711I
u = −0.510378 − 0.611213I
a = −0.014066 − 0.208428I
b = −0.251269 + 0.053760I
−1.07152 − 2.12045I −9.29687 + 6.29711I
u = 1.202620 + 0.150968I
a = 0.310744 − 1.092110I
b = 0.502287 + 0.606881I
−2.07579 − 4.13960I 0
u = 1.202620 − 0.150968I
a = 0.310744 + 1.092110I
b = 0.502287 − 0.606881I
−2.07579 + 4.13960I 0
u = −1.222910 + 0.074096I
a = 0.0270535 − 0.1318130I
b = 0.640570 + 0.607903I
−2.03114 + 0.55200I 0
u = −1.222910 − 0.074096I
a = 0.0270535 + 0.1318130I
b = 0.640570 − 0.607903I
−2.03114 − 0.55200I 0
u = 0.034918 + 0.757439I
a = −0.637784 + 0.536346I
b = 0.536253 − 0.988592I
5.87942 + 4.77825I 3.42142 − 5.10036I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.034918 − 0.757439I
a = −0.637784 − 0.536346I
b = 0.536253 + 0.988592I
5.87942 − 4.77825I 3.42142 + 5.10036I
u = 0.331495 + 0.671282I
a = −1.13105 + 1.59075I
b = −0.829572 − 0.867696I
−1.71156 − 6.50364I −3.88138 + 8.46347I
u = 0.331495 − 0.671282I
a = −1.13105 − 1.59075I
b = −0.829572 + 0.867696I
−1.71156 + 6.50364I −3.88138 − 8.46347I
u = −1.235590 + 0.320604I
a = 0.635242 − 0.731984I
b = −0.347845 − 0.842338I
1.95788 − 0.88165I 0
u = −1.235590 − 0.320604I
a = 0.635242 + 0.731984I
b = −0.347845 + 0.842338I
1.95788 + 0.88165I 0
u = −0.380033 + 0.611430I
a = 0.621419 + 0.328599I
b = 0.088275 − 0.617332I
−0.94580 + 1.88496I −5.53016 − 2.61970I
u = −0.380033 − 0.611430I
a = 0.621419 − 0.328599I
b = 0.088275 + 0.617332I
−0.94580 − 1.88496I −5.53016 + 2.61970I
u = 0.269682 + 0.640466I
a = −1.79547 + 0.37187I
b = −0.388129 − 0.452372I
3.16652 − 4.38642I 3.50297 + 8.69988I
u = 0.269682 − 0.640466I
a = −1.79547 − 0.37187I
b = −0.388129 + 0.452372I
3.16652 + 4.38642I 3.50297 − 8.69988I
u = 0.519201 + 0.449531I
a = 0.387665 − 0.121279I
b = 0.876594 − 0.714920I
−2.56416 + 2.72527I −6.71131 − 2.05471I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.519201 − 0.449531I
a = 0.387665 + 0.121279I
b = 0.876594 + 0.714920I
−2.56416 − 2.72527I −6.71131 + 2.05471I
u = −0.287760 + 0.585739I
a = 0.62917 + 2.74974I
b = 2.97079 + 0.03418I
1.45737 + 1.91964I −6.3037 + 14.5674I
u = −0.287760 − 0.585739I
a = 0.62917 − 2.74974I
b = 2.97079 − 0.03418I
1.45737 − 1.91964I −6.3037 − 14.5674I
u = 0.200417 + 0.598294I
a = 0.21915 − 1.51923I
b = −0.151466 + 1.094540I
4.02663 − 0.82768I 6.36438 + 2.50645I
u = 0.200417 − 0.598294I
a = 0.21915 + 1.51923I
b = −0.151466 − 1.094540I
4.02663 + 0.82768I 6.36438 − 2.50645I
u = −1.387550 + 0.178659I
a = −1.33273 − 0.90566I
b = −0.1015170 + 0.0476189I
−3.27007 + 0.60874I 0
u = −1.387550 − 0.178659I
a = −1.33273 + 0.90566I
b = −0.1015170 − 0.0476189I
−3.27007 − 0.60874I 0
u = −1.384820 + 0.228430I
a = −0.487527 + 0.225338I
b = 0.152763 + 1.225140I
−1.04447 + 3.83678I 0
u = −1.384820 − 0.228430I
a = −0.487527 − 0.225338I
b = 0.152763 − 1.225140I
−1.04447 − 3.83678I 0
u = 1.40900 + 0.20274I
a = 3.38868 − 1.70160I
b = 2.12325 + 0.54726I
−4.40750 − 3.63166I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.40900 − 0.20274I
a = 3.38868 + 1.70160I
b = 2.12325 − 0.54726I
−4.40750 + 3.63166I 0
u = −1.40659 + 0.24898I
a = 2.07264 − 0.03363I
b = 0.499440 − 0.349829I
−2.19159 + 7.63799I 0
u = −1.40659 − 0.24898I
a = 2.07264 + 0.03363I
b = 0.499440 + 0.349829I
−2.19159 − 7.63799I 0
u = 1.41203 + 0.23084I
a = −3.59037 + 2.77014I
b = −2.98776 + 0.35138I
−3.98668 − 4.93837I 0
u = 1.41203 − 0.23084I
a = −3.59037 − 2.77014I
b = −2.98776 − 0.35138I
−3.98668 + 4.93837I 0
u = −0.299701 + 0.468468I
a = −0.72565 − 3.29039I
b = −1.96427 − 0.08421I
1.04787 + 1.03844I 5.29717 − 10.86697I
u = −0.299701 − 0.468468I
a = −0.72565 + 3.29039I
b = −1.96427 + 0.08421I
1.04787 − 1.03844I 5.29717 + 10.86697I
u = 1.44219 + 0.10422I
a = −1.73770 + 0.19216I
b = −1.083790 − 0.026822I
−7.53116 − 0.97636I 0
u = 1.44219 − 0.10422I
a = −1.73770 − 0.19216I
b = −1.083790 + 0.026822I
−7.53116 + 0.97636I 0
u = −1.44607 + 0.16100I
a = −1.49025 − 0.86702I
b = −1.051370 − 0.720721I
−8.77213 − 0.51707I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.44607 − 0.16100I
a = −1.49025 + 0.86702I
b = −1.051370 + 0.720721I
−8.77213 + 0.51707I 0
u = −1.43222 + 0.25863I
a = 2.09232 + 0.57329I
b = 0.873644 − 0.951829I
−7.36283 + 9.90141I 0
u = −1.43222 − 0.25863I
a = 2.09232 − 0.57329I
b = 0.873644 + 0.951829I
−7.36283 − 9.90141I 0
u = 1.42820 + 0.29532I
a = 1.51267 − 0.69056I
b = 0.995771 + 0.411922I
−4.76047 − 8.29572I 0
u = 1.42820 − 0.29532I
a = 1.51267 + 0.69056I
b = 0.995771 − 0.411922I
−4.76047 + 8.29572I 0
u = 1.44343 + 0.23910I
a = −0.992429 − 0.246388I
b = −0.270661 − 0.756968I
−6.78935 − 5.03593I 0
u = 1.44343 − 0.23910I
a = −0.992429 + 0.246388I
b = −0.270661 + 0.756968I
−6.78935 + 5.03593I 0
u = −0.535825
a = 0.674766
b = 0.706758
−1.06237 −10.5390
u = 0.017671 + 0.533485I
a = 1.06883 − 1.55896I
b = −0.503165 + 0.289761I
1.42554 + 1.52244I 2.08213 − 4.25089I
u = 0.017671 − 0.533485I
a = 1.06883 + 1.55896I
b = −0.503165 − 0.289761I
1.42554 − 1.52244I 2.08213 + 4.25089I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.43939 + 0.28439I
a = −2.65866 − 0.24548I
b = −1.26621 + 1.23765I
−3.5302 + 16.2353I 0
u = −1.43939 − 0.28439I
a = −2.65866 + 0.24548I
b = −1.26621 − 1.23765I
−3.5302 − 16.2353I 0
u = −1.47653 + 0.12229I
a = 1.57572 + 1.49415I
b = 1.21044 + 0.90784I
−5.86514 − 6.36902I 0
u = −1.47653 − 0.12229I
a = 1.57572 − 1.49415I
b = 1.21044 − 0.90784I
−5.86514 + 6.36902I 0
u = 1.47507 + 0.18548I
a = 0.701509 − 0.089471I
b = 0.623036 − 0.135856I
−7.51905 − 4.91195I 0
u = 1.47507 − 0.18548I
a = 0.701509 + 0.089471I
b = 0.623036 + 0.135856I
−7.51905 + 4.91195I 0
u = 0.404020 + 0.224336I
a = 1.76978 − 0.83709I
b = −0.012610 − 0.538393I
1.99649 + 1.29641I −0.17607 − 2.27315I
u = 0.404020 − 0.224336I
a = 1.76978 + 0.83709I
b = −0.012610 + 0.538393I
1.99649 − 1.29641I −0.17607 + 2.27315I
11
II. I
u
2
= hb − 1, a − 1, u + 1i
(i) Arc colorings
a
6
=
0
−1
a
9
=
1
0
a
10
=
1
1
a
7
=
1
0
a
11
=
0
1
a
1
=
1
1
a
3
=
1
1
a
4
=
1
1
a
5
=
0
−1
a
2
=
1
2
a
8
=
0
−1
a
8
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
9
c
10
, c
11
u + 1
c
3
, c
5
u
c
4
, c
6
, c
7
c
8
u − 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
7
, c
8
c
9
, c
10
, c
11
y −1
c
3
, c
5
y
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000
b = 1.00000
0 0
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u + 1)(u
68
+ 4u
67
+ ··· − u − 1)
c
2
(u + 1)(u
68
+ 2u
67
+ ··· − 7u − 1)
c
3
u(u
68
− 11u
67
+ ··· + 2u + 2)
c
4
(u − 1)(u
68
+ 2u
67
+ ··· − 7u − 1)
c
5
u(u
68
− 3u
67
+ ··· + 533u
2
− 32)
c
6
(u − 1)(u
68
+ 2u
67
+ ··· − u + 1)
c
7
(u − 1)(u
68
− 4u
67
+ ··· + 30u − 4)
c
8
(u − 1)(u
68
− 2u
67
+ ··· + 19u − 1)
c
9
, c
10
(u + 1)(u
68
+ 2u
67
+ ··· − u + 1)
c
11
(u + 1)(u
68
+ 14u
67
+ ··· + 18491u + 1583)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)(y
68
+ 10y
67
+ ··· + y + 1)
c
2
, c
4
(y −1)(y
68
− 42y
67
+ ··· − 51y + 1)
c
3
y(y
68
− 9y
67
+ ··· − 56y + 4)
c
5
y(y
68
− 9y
67
+ ··· − 34112y + 1024)
c
6
, c
9
, c
10
(y −1)(y
68
− 62y
67
+ ··· + y + 1)
c
7
(y −1)(y
68
− 66y
67
+ ··· − 1036y + 16)
c
8
(y −1)(y
68
− 62y
67
+ ··· − 127y + 1)
c
11
(y −1)(y
68
+ 30y
67
+ ··· + 2.73937 × 10
7
y + 2505889)
17
