11a
299
(K11a
299
)
A knot diagram
1
Linearized knot diagam
4 8 1 9 2 11 10 5 3 7 6
Solving Sequence
6,11
7
1,4
2 3 5 10 8 9
c
6
c
11
c
1
c
3
c
5
c
10
c
7
c
9
c
2
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.98094 × 10
27
u
50
+ 3.57674 × 10
27
u
49
+ ··· + 5.12235 × 10
28
b − 4.16694 × 10
28
,
4.56338 × 10
28
u
50
+ 8.09970 × 10
28
u
49
+ ··· + 5.12235 × 10
28
a + 2.57618 × 10
28
, u
51
+ 2u
50
+ ··· + u
2
− 1i
I
u
2
= hu
2
+ 5b + 3u + 4, 4u
2
+ 5a − 8u + 6, u
3
− u
2
+ 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 54 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−3.98×10
27
u
50
+3.58×10
27
u
49
+· · ·+5.12×10
28
b−4.17×10
28
, 4.56×
10
28
u
50
+8.10×10
28
u
49
+· · ·+5.12 ×10
28
a+2.58×10
28
, u
51
+2u
50
+· · ·+u
2
−1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
1
=
−u
u
a
4
=
−0.890878u
50
− 1.58125u
49
+ ··· + 2.76933u − 0.502929
0.0777171u
50
− 0.0698262u
49
+ ··· − 0.830913u + 0.813483
a
2
=
−0.911790u
50
− 1.62215u
49
+ ··· + 3.55461u − 0.444712
0.00216816u
50
− 0.149791u
49
+ ··· − 0.143535u + 0.845107
a
3
=
−0.848184u
50
− 1.53135u
49
+ ··· + 1.95617u − 0.527682
0.0350226u
50
− 0.119723u
49
+ ··· − 0.0177518u + 0.838236
a
5
=
0.219194u
50
+ 0.0575194u
49
+ ··· − 2.71987u + 0.983462
0.568042u
50
+ 1.43143u
49
+ ··· − 0.564791u + 0.0862524
a
10
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
1.21389u
50
+ 2.29120u
49
+ ··· − 2.54183u + 0.639066
−0.214736u
50
− 0.901043u
49
+ ··· + 1.59632u + 0.327975
a
9
=
1.21389u
50
+ 2.29120u
49
+ ··· − 2.54183u + 0.639066
−0.214736u
50
− 0.901043u
49
+ ··· + 1.59632u + 0.327975
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0485520u
50
− 0.908190u
49
+ ··· − 14.7258u − 8.93442
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
51
− 4u
50
+ ··· − 49u + 25
c
2
u
51
+ u
50
+ ··· + 380u + 200
c
4
, c
8
u
51
+ 2u
50
+ ··· + 4u + 1
c
5
5(5u
51
− 28u
50
+ ··· − 30u + 857)
c
6
, c
7
, c
10
c
11
u
51
− 2u
50
+ ··· − u
2
+ 1
c
9
5(5u
51
− 9u
50
+ ··· + 1703u + 239)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
51
− 26y
50
+ ··· + 17851y −625
c
2
y
51
+ 21y
50
+ ··· − 118000y −40000
c
4
, c
8
y
51
+ 28y
50
+ ··· + 2y −1
c
5
25(25y
51
+ 176y
50
+ ··· − 1375442y −734449)
c
6
, c
7
, c
10
c
11
y
51
+ 60y
50
+ ··· + 2y −1
c
9
25(25y
51
+ 739y
50
+ ··· − 637947y −57121)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.552527 + 0.820307I
a = 0.48391 − 1.52868I
b = −1.72817 + 0.85216I
2.62483 + 11.59540I −7.79067 − 8.85645I
u = −0.552527 − 0.820307I
a = 0.48391 + 1.52868I
b = −1.72817 − 0.85216I
2.62483 − 11.59540I −7.79067 + 8.85645I
u = 0.589306 + 0.788540I
a = −0.51919 − 1.38595I
b = 1.55822 + 0.77897I
−0.80955 − 5.70999I −10.32903 + 7.24097I
u = 0.589306 − 0.788540I
a = −0.51919 + 1.38595I
b = 1.55822 − 0.77897I
−0.80955 + 5.70999I −10.32903 − 7.24097I
u = −0.433100 + 0.988087I
a = 0.85921 − 1.15463I
b = −0.784864 + 0.164197I
3.75291 − 3.24873I −11.00000 + 0.I
u = −0.433100 − 0.988087I
a = 0.85921 + 1.15463I
b = −0.784864 − 0.164197I
3.75291 + 3.24873I −11.00000 + 0.I
u = −0.376973 + 0.809467I
a = 1.031830 − 0.475824I
b = −0.043546 − 0.349975I
5.59371 + 5.41403I −4.14016 − 6.52359I
u = −0.376973 − 0.809467I
a = 1.031830 + 0.475824I
b = −0.043546 + 0.349975I
5.59371 − 5.41403I −4.14016 + 6.52359I
u = 0.249787 + 0.812726I
a = −0.469781 − 0.492664I
b = −0.095865 + 0.184201I
1.73380 − 1.81855I −6.35906 + 4.36354I
u = 0.249787 − 0.812726I
a = −0.469781 + 0.492664I
b = −0.095865 − 0.184201I
1.73380 + 1.81855I −6.35906 − 4.36354I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.493565 + 0.692270I
a = 0.247144 − 1.224100I
b = −1.21189 + 1.00104I
4.68147 + 1.04951I −4.16172 − 4.32794I
u = −0.493565 − 0.692270I
a = 0.247144 + 1.224100I
b = −1.21189 − 1.00104I
4.68147 − 1.04951I −4.16172 + 4.32794I
u = 0.773905 + 0.191317I
a = −0.320071 − 0.624747I
b = 1.381640 − 0.030498I
−2.64708 + 1.15805I −10.73331 − 5.02870I
u = 0.773905 − 0.191317I
a = −0.320071 + 0.624747I
b = 1.381640 + 0.030498I
−2.64708 − 1.15805I −10.73331 + 5.02870I
u = −0.744224 + 0.089987I
a = 0.047354 − 0.638462I
b = −1.47794 − 0.27354I
0.42114 − 7.27131I −10.81656 + 5.67006I
u = −0.744224 − 0.089987I
a = 0.047354 + 0.638462I
b = −1.47794 + 0.27354I
0.42114 + 7.27131I −10.81656 − 5.67006I
u = 0.128736 + 0.681128I
a = 1.63090 − 0.76962I
b = −1.72989 + 2.00427I
1.377800 + 0.247335I −11.41702 + 6.59841I
u = 0.128736 − 0.681128I
a = 1.63090 + 0.76962I
b = −1.72989 − 2.00427I
1.377800 − 0.247335I −11.41702 − 6.59841I
u = 0.328726 + 0.602476I
a = −0.683354 + 0.933926I
b = −1.027660 − 0.198210I
0.09032 − 4.00238I −9.47119 + 9.47766I
u = 0.328726 − 0.602476I
a = −0.683354 − 0.933926I
b = −1.027660 + 0.198210I
0.09032 + 4.00238I −9.47119 − 9.47766I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.309159 + 1.281950I
a = −0.53813 − 1.48328I
b = 0.630951 + 0.896457I
1.88408 − 2.74356I 0
u = 0.309159 − 1.281950I
a = −0.53813 + 1.48328I
b = 0.630951 − 0.896457I
1.88408 + 2.74356I 0
u = −0.235448 + 0.507844I
a = 0.06586 + 1.89337I
b = 1.226960 − 0.240501I
−1.46138 + 0.98661I −12.15795 − 1.22039I
u = −0.235448 − 0.507844I
a = 0.06586 − 1.89337I
b = 1.226960 + 0.240501I
−1.46138 − 0.98661I −12.15795 + 1.22039I
u = −0.535402 + 0.073202I
a = 0.434598 − 1.044040I
b = −0.708461 − 0.403158I
3.00953 + 2.35838I −8.15249 − 2.65728I
u = −0.535402 − 0.073202I
a = 0.434598 + 1.044040I
b = −0.708461 + 0.403158I
3.00953 − 2.35838I −8.15249 + 2.65728I
u = −0.271262 + 0.396700I
a = 0.75415 + 2.38170I
b = 0.944727 − 0.152860I
−1.67074 + 1.07820I −12.01082 − 5.84608I
u = −0.271262 − 0.396700I
a = 0.75415 − 2.38170I
b = 0.944727 + 0.152860I
−1.67074 − 1.07820I −12.01082 + 5.84608I
u = −0.01718 + 1.55667I
a = −0.37477 + 2.03786I
b = 0.552519 − 1.004140I
5.04838 + 1.69001I 0
u = −0.01718 − 1.55667I
a = −0.37477 − 2.03786I
b = 0.552519 + 1.004140I
5.04838 − 1.69001I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.04180 + 1.57969I
a = −1.09580 + 1.51782I
b = 1.49270 − 0.77222I
5.80181 + 1.83329I 0
u = −0.04180 − 1.57969I
a = −1.09580 − 1.51782I
b = 1.49270 + 0.77222I
5.80181 − 1.83329I 0
u = 0.06969 + 1.58540I
a = 0.646529 + 0.973357I
b = −1.354660 − 0.387992I
7.57583 − 5.34940I 0
u = 0.06969 − 1.58540I
a = 0.646529 − 0.973357I
b = −1.354660 + 0.387992I
7.57583 + 5.34940I 0
u = 0.339596 + 0.188204I
a = −1.55128 + 2.09918I
b = −0.402028 + 0.283631I
−1.01423 + 1.50344I −14.02114 − 0.26378I
u = 0.339596 − 0.188204I
a = −1.55128 − 2.09918I
b = −0.402028 − 0.283631I
−1.01423 − 1.50344I −14.02114 + 0.26378I
u = 0.02693 + 1.61334I
a = 3.90639 − 0.28673I
b = −3.98695 + 0.78800I
9.33157 − 0.28182I 0
u = 0.02693 − 1.61334I
a = 3.90639 + 0.28673I
b = −3.98695 − 0.78800I
9.33157 + 0.28182I 0
u = −0.15866 + 1.61313I
a = 0.90457 − 2.22903I
b = −1.33704 + 1.71038I
12.51670 + 3.55318I 0
u = −0.15866 − 1.61313I
a = 0.90457 + 2.22903I
b = −1.33704 − 1.71038I
12.51670 − 3.55318I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10468 + 1.64228I
a = 0.285194 + 0.100077I
b = 0.495111 − 0.386510I
14.0417 + 7.2484I 0
u = −0.10468 − 1.64228I
a = 0.285194 − 0.100077I
b = 0.495111 + 0.386510I
14.0417 − 7.2484I 0
u = 0.08123 + 1.64771I
a = 0.021744 − 0.179863I
b = −0.560164 + 0.015522I
10.29890 − 3.16367I 0
u = 0.08123 − 1.64771I
a = 0.021744 + 0.179863I
b = −0.560164 − 0.015522I
10.29890 + 3.16367I 0
u = 0.17216 + 1.64138I
a = −1.15226 − 2.05629I
b = 1.58595 + 1.37531I
7.44997 − 8.60283I 0
u = 0.17216 − 1.64138I
a = −1.15226 + 2.05629I
b = 1.58595 − 1.37531I
7.44997 + 8.60283I 0
u = −0.16225 + 1.65033I
a = 1.31880 − 2.12033I
b = −1.83667 + 1.38127I
11.0558 + 14.3418I 0
u = −0.16225 − 1.65033I
a = 1.31880 + 2.12033I
b = −1.83667 − 1.38127I
11.0558 − 14.3418I 0
u = −0.08999 + 1.68712I
a = 0.334351 − 0.580821I
b = 0.022884 + 0.143685I
13.10850 − 1.33730I 0
u = −0.08999 − 1.68712I
a = 0.334351 + 0.580821I
b = 0.022884 − 0.143685I
13.10850 + 1.33730I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.295696
a = −0.935819
b = 0.188257
−0.590385 −17.0960
10
II. I
u
2
= hu
2
+ 5b + 3u + 4, 4u
2
+ 5a − 8u + 6, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
1
=
−u
u
a
4
=
−
4
5
u
2
+
8
5
u −
6
5
−
1
5
u
2
−
3
5
u −
4
5
a
2
=
−
4
5
u
2
+
3
5
u −
6
5
−
1
5
u
2
+
2
5
u −
4
5
a
3
=
−
4
5
u
2
+
3
5
u −
6
5
−
1
5
u
2
+
2
5
u −
4
5
a
5
=
−
13
25
u
2
+
6
25
u +
8
25
−
7
25
u
2
+
9
25
u −
13
25
a
10
=
u
u
2
− u + 1
a
8
=
u
2
+ 1
u
2
− u + 1
a
9
=
4
25
u
2
+
27
25
u +
11
25
31
25
u
2
−
22
25
u +
29
25
a
9
=
4
25
u
2
+
27
25
u +
11
25
31
25
u
2
−
22
25
u +
29
25
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
12
25
u
2
+
69
25
u −
408
25
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
3
c
2
u
3
c
3
(u + 1)
3
c
4
u
3
+ u
2
− 1
c
5
5(5u
3
+ 7u
2
+ 4u + 1)
c
6
, c
7
u
3
− u
2
+ 2u − 1
c
8
u
3
− u
2
+ 1
c
9
5(5u
3
+ 4u
2
− u − 1)
c
10
, c
11
u
3
+ u
2
+ 2u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y −1)
3
c
2
y
3
c
4
, c
8
y
3
− y
2
+ 2y −1
c
5
25(25y
3
− 9y
2
+ 2y −1)
c
6
, c
7
, c
10
c
11
y
3
+ 3y
2
+ 2y −1
c
9
25(25y
3
− 26y
2
+ 9y −1)
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = 0.47401 + 1.64160I
b = −0.596576 − 0.896741I
1.37919 − 2.82812I −14.9284 + 3.3378I
u = 0.215080 − 1.307140I
a = 0.47401 − 1.64160I
b = −0.596576 + 0.896741I
1.37919 + 2.82812I −14.9284 − 3.3378I
u = 0.569840
a = −0.548030
b = −1.20685
−2.75839 −14.9030
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
3
)(u
51
− 4u
50
+ ··· − 49u + 25)
c
2
u
3
(u
51
+ u
50
+ ··· + 380u + 200)
c
3
((u + 1)
3
)(u
51
− 4u
50
+ ··· − 49u + 25)
c
4
(u
3
+ u
2
− 1)(u
51
+ 2u
50
+ ··· + 4u + 1)
c
5
25(5u
3
+ 7u
2
+ 4u + 1)(5u
51
− 28u
50
+ ··· − 30u + 857)
c
6
, c
7
(u
3
− u
2
+ 2u − 1)(u
51
− 2u
50
+ ··· − u
2
+ 1)
c
8
(u
3
− u
2
+ 1)(u
51
+ 2u
50
+ ··· + 4u + 1)
c
9
25(5u
3
+ 4u
2
− u − 1)(5u
51
− 9u
50
+ ··· + 1703u + 239)
c
10
, c
11
(u
3
+ u
2
+ 2u + 1)(u
51
− 2u
50
+ ··· − u
2
+ 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
((y −1)
3
)(y
51
− 26y
50
+ ··· + 17851y −625)
c
2
y
3
(y
51
+ 21y
50
+ ··· − 118000y −40000)
c
4
, c
8
(y
3
− y
2
+ 2y −1)(y
51
+ 28y
50
+ ··· + 2y −1)
c
5
625(25y
3
− 9y
2
+ 2y −1)
· (25y
51
+ 176y
50
+ ··· − 1375442y −734449)
c
6
, c
7
, c
10
c
11
(y
3
+ 3y
2
+ 2y −1)(y
51
+ 60y
50
+ ··· + 2y −1)
c
9
625(25y
3
− 26y
2
+ 9y −1)(25y
51
+ 739y
50
+ ··· − 637947y −57121)
16
