11a
298
(K11a
298
)
A knot diagram
1
Linearized knot diagam
4 8 1 9 2 11 10 5 3 6 7
Solving Sequence
6,11
7
1,3
4 10 8 2 5 9
c
6
c
11
c
3
c
10
c
7
c
2
c
5
c
9
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h9.88613 × 10
36
u
66
− 3.08299 × 10
36
u
65
+ ··· + 2.08415 × 10
37
b + 1.52499 × 10
37
,
− 1.79254 × 10
37
u
66
− 3.42174 × 10
37
u
65
+ ··· + 2.08415 × 10
37
a − 3.54411 × 10
37
, u
67
+ 2u
66
+ ··· + 2u + 1i
I
u
2
= h5b + u + 3, 5a + 2u + 6, u
2
+ 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
= h9.89×10
36
u
66
−3.08×10
36
u
65
+· · ·+2.08×10
37
b+1.52×10
37
, −1.79×
10
37
u
66
−3.42×10
37
u
65
+· · ·+2.08×10
37
a−3.54×10
37
, u
67
+2u
66
+· · ·+2u+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
1
=
−u
−u
3
+ u
a
3
=
0.860082u
66
+ 1.64179u
65
+ ··· + 1.94258u + 1.70050
−0.474347u
66
+ 0.147925u
65
+ ··· − 0.386242u − 0.731707
a
4
=
1.48932u
66
+ 2.14476u
65
+ ··· + 3.32469u + 2.19964
−0.127700u
66
+ 0.342656u
65
+ ··· − 0.886592u − 0.475343
a
10
=
u
u
a
8
=
−u
4
+ u
2
+ 1
−u
4
+ 2u
2
a
2
=
0.788597u
66
+ 1.72240u
65
+ ··· + 3.47709u + 1.64125
−0.360672u
66
+ 0.258719u
65
+ ··· − 0.433561u − 0.659189
a
5
=
1.04231u
66
+ 1.25813u
65
+ ··· + 2.97728u + 1.55836
0.579023u
66
+ 0.216659u
65
+ ··· + 0.557709u + 0.726240
a
9
=
−1.54293u
66
− 2.24497u
65
+ ··· − 2.88258u − 2.33342
−1.53821u
66
− 1.11120u
65
+ ··· + 0.768914u − 0.642905
a
9
=
−1.54293u
66
− 2.24497u
65
+ ··· − 2.88258u − 2.33342
−1.53821u
66
− 1.11120u
65
+ ··· + 0.768914u − 0.642905
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.85040u
66
− 2.35907u
65
+ ··· + 11.1605u − 13.3066
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
67
− 3u
66
+ ··· − 11u + 25
c
2
u
67
+ u
66
+ ··· + 980u + 100
c
4
, c
8
u
67
+ 2u
66
+ ··· + 4u + 1
c
5
5(5u
67
− 44u
66
+ ··· + 396u + 27)
c
6
, c
10
, c
11
u
67
+ 2u
66
+ ··· + 2u + 1
c
7
u
67
− 6u
66
+ ··· − 618u + 117
c
9
5(5u
67
+ 27u
66
+ ··· + 819u + 81)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
67
− 39y
66
+ ··· + 25671y −625
c
2
y
67
+ 15y
66
+ ··· + 203000y −10000
c
4
, c
8
y
67
+ 36y
66
+ ··· + 4y −1
c
5
25(25y
67
+ 624y
66
+ ··· + 130896y −729)
c
6
, c
10
, c
11
y
67
− 60y
66
+ ··· + 4y −1
c
7
y
67
+ 4y
66
+ ··· + 137160y −13689
c
9
25(25y
67
− 79y
66
+ ··· − 46413y −6561)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.971049 + 0.208920I
a = −0.32714 + 1.78126I
b = −0.115970 + 0.555157I
3.33579 + 2.19465I −7.86655 + 0.I
u = 0.971049 − 0.208920I
a = −0.32714 − 1.78126I
b = −0.115970 − 0.555157I
3.33579 − 2.19465I −7.86655 + 0.I
u = 0.828642 + 0.456356I
a = 1.29398 − 1.09741I
b = 0.975419 + 0.388481I
0.61572 + 7.81558I −11.00000 − 4.31786I
u = 0.828642 − 0.456356I
a = 1.29398 + 1.09741I
b = 0.975419 − 0.388481I
0.61572 − 7.81558I −11.00000 + 4.31786I
u = −0.785572 + 0.521754I
a = −0.876770 − 0.752417I
b = −0.765978 + 0.288301I
−2.70603 − 1.76569I −13.31586 + 3.73920I
u = −0.785572 − 0.521754I
a = −0.876770 + 0.752417I
b = −0.765978 − 0.288301I
−2.70603 + 1.76569I −13.31586 − 3.73920I
u = 1.025940 + 0.403064I
a = 0.638976 + 1.070100I
b = 0.056372 + 0.523175I
1.33655 − 6.86297I 0
u = 1.025940 − 0.403064I
a = 0.638976 − 1.070100I
b = 0.056372 − 0.523175I
1.33655 + 6.86297I 0
u = −0.298287 + 0.796077I
a = 0.133666 − 0.260488I
b = −1.30707 − 0.75572I
−1.12210 + 6.34169I −11.92397 − 6.79037I
u = −0.298287 − 0.796077I
a = 0.133666 + 0.260488I
b = −1.30707 + 0.75572I
−1.12210 − 6.34169I −11.92397 + 6.79037I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.272187 + 0.791950I
a = −0.230884 − 0.195053I
b = 1.67052 − 0.99999I
2.41609 − 12.25380I −8.96204 + 8.44386I
u = 0.272187 − 0.791950I
a = −0.230884 + 0.195053I
b = 1.67052 + 0.99999I
2.41609 + 12.25380I −8.96204 − 8.44386I
u = −1.133230 + 0.269613I
a = 0.275844 + 0.909490I
b = 0.184881 + 0.303565I
−1.02190 + 1.39824I 0
u = −1.133230 − 0.269613I
a = 0.275844 − 0.909490I
b = 0.184881 − 0.303565I
−1.02190 − 1.39824I 0
u = 0.140214 + 0.819901I
a = 0.116857 − 0.337825I
b = −0.481890 − 0.479676I
4.07626 + 2.45751I −5.53723 − 4.39874I
u = 0.140214 − 0.819901I
a = 0.116857 + 0.337825I
b = −0.481890 + 0.479676I
4.07626 − 2.45751I −5.53723 + 4.39874I
u = 0.311992 + 0.700971I
a = −0.145782 − 0.519209I
b = 1.343450 + 0.093089I
4.46866 − 1.41400I −4.95439 + 4.71232I
u = 0.311992 − 0.700971I
a = −0.145782 + 0.519209I
b = 1.343450 − 0.093089I
4.46866 + 1.41400I −4.95439 − 4.71232I
u = 0.195241 + 0.725393I
a = 0.102706 − 0.534072I
b = −1.42665 + 0.06702I
5.66368 − 5.86500I −5.37991 + 6.33692I
u = 0.195241 − 0.725393I
a = 0.102706 + 0.534072I
b = −1.42665 − 0.06702I
5.66368 + 5.86500I −5.37991 − 6.33692I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.271530 + 0.161748I
a = 2.41947 + 0.73704I
b = 2.14316 − 0.56893I
−2.00089 + 2.82137I 0
u = −1.271530 − 0.161748I
a = 2.41947 − 0.73704I
b = 2.14316 + 0.56893I
−2.00089 − 2.82137I 0
u = −0.141220 + 0.702053I
a = −0.075965 − 0.431787I
b = 0.902832 + 0.342246I
1.93198 + 2.14020I −7.90136 − 3.81097I
u = −0.141220 − 0.702053I
a = −0.075965 + 0.431787I
b = 0.902832 − 0.342246I
1.93198 − 2.14020I −7.90136 + 3.81097I
u = 0.657943 + 0.240545I
a = −0.13672 − 1.54848I
b = 0.683159 − 0.173182I
3.10200 − 2.24588I −7.87626 + 2.77695I
u = 0.657943 − 0.240545I
a = −0.13672 + 1.54848I
b = 0.683159 + 0.173182I
3.10200 + 2.24588I −7.87626 − 2.77695I
u = 1.314170 + 0.128201I
a = −1.10038 + 1.03976I
b = −1.66093 + 0.85544I
−5.00722 − 0.73302I 0
u = 1.314170 − 0.128201I
a = −1.10038 − 1.03976I
b = −1.66093 − 0.85544I
−5.00722 + 0.73302I 0
u = −1.320040 + 0.057043I
a = 1.36174 + 0.91804I
b = 1.39912 + 1.18725I
−2.47273 − 2.48121I 0
u = −1.320040 − 0.057043I
a = 1.36174 − 0.91804I
b = 1.39912 − 1.18725I
−2.47273 + 2.48121I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.322170 + 0.229367I
a = 0.14439 − 7.47115I
b = 3.94009 − 5.01080I
−2.87450 − 2.88828I 0
u = 1.322170 − 0.229367I
a = 0.14439 + 7.47115I
b = 3.94009 + 5.01080I
−2.87450 + 2.88828I 0
u = −1.319590 + 0.346942I
a = −0.476943 + 0.014476I
b = −0.666723 + 0.083983I
−0.49228 + 1.74583I 0
u = −1.319590 − 0.346942I
a = −0.476943 − 0.014476I
b = −0.666723 − 0.083983I
−0.49228 − 1.74583I 0
u = −0.219881 + 0.595702I
a = 0.441318 + 0.005243I
b = 1.21996 + 0.96570I
0.06257 + 4.19245I −10.29586 − 9.03236I
u = −0.219881 − 0.595702I
a = 0.441318 − 0.005243I
b = 1.21996 − 0.96570I
0.06257 − 4.19245I −10.29586 + 9.03236I
u = 1.363670 + 0.157603I
a = −0.646817 − 0.030339I
b = −1.52794 + 0.21614I
−6.14223 − 0.20744I 0
u = 1.363670 − 0.157603I
a = −0.646817 + 0.030339I
b = −1.52794 − 0.21614I
−6.14223 + 0.20744I 0
u = −1.367670 + 0.191097I
a = −0.180450 − 1.153580I
b = 0.375829 − 0.704752I
−6.71014 + 3.51832I 0
u = −1.367670 − 0.191097I
a = −0.180450 + 1.153580I
b = 0.375829 + 0.704752I
−6.71014 − 3.51832I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.353030 + 0.281550I
a = 0.61601 − 1.37793I
b = 1.36173 − 1.14425I
−2.79764 − 5.70186I 0
u = 1.353030 − 0.281550I
a = 0.61601 + 1.37793I
b = 1.36173 + 1.14425I
−2.79764 + 5.70186I 0
u = −1.366210 + 0.216084I
a = −0.61315 − 2.12558I
b = −0.72885 − 1.51198I
−6.38128 + 3.82220I 0
u = −1.366210 − 0.216084I
a = −0.61315 + 2.12558I
b = −0.72885 + 1.51198I
−6.38128 − 3.82220I 0
u = −0.078148 + 0.604951I
a = −1.51809 − 0.93623I
b = 2.07351 + 2.80457I
1.52367 − 0.14015I −14.2937 − 4.2199I
u = −0.078148 − 0.604951I
a = −1.51809 + 0.93623I
b = 2.07351 − 2.80457I
1.52367 + 0.14015I −14.2937 + 4.2199I
u = 1.376960 + 0.239051I
a = 0.56095 − 2.53625I
b = 1.18970 − 2.28032I
−5.00444 − 7.26595I 0
u = 1.376960 − 0.239051I
a = 0.56095 + 2.53625I
b = 1.18970 + 2.28032I
−5.00444 + 7.26595I 0
u = −1.374450 + 0.292982I
a = −1.41785 − 1.33123I
b = −2.16228 − 0.85840I
0.68934 + 9.55585I 0
u = −1.374450 − 0.292982I
a = −1.41785 + 1.33123I
b = −2.16228 + 0.85840I
0.68934 − 9.55585I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.41838 + 0.31994I
a = 0.78576 + 2.39619I
b = 1.88722 + 1.70135I
−2.9681 + 16.2798I 0
u = −1.41838 − 0.31994I
a = 0.78576 − 2.39619I
b = 1.88722 − 1.70135I
−2.9681 − 16.2798I 0
u = 0.178834 + 0.510609I
a = −0.270334 + 1.049170I
b = −1.098170 + 0.533111I
−1.45952 − 1.07936I −12.77452 + 1.30331I
u = 0.178834 − 0.510609I
a = −0.270334 − 1.049170I
b = −1.098170 − 0.533111I
−1.45952 + 1.07936I −12.77452 − 1.30331I
u = 1.42924 + 0.31936I
a = −0.63124 + 1.94989I
b = −1.46734 + 1.38386I
−6.62942 − 10.38300I 0
u = 1.42924 − 0.31936I
a = −0.63124 − 1.94989I
b = −1.46734 − 1.38386I
−6.62942 + 10.38300I 0
u = −1.44421 + 0.28194I
a = 1.11075 + 1.15807I
b = 1.42474 + 0.38588I
−1.18945 + 5.01515I 0
u = −1.44421 − 0.28194I
a = 1.11075 − 1.15807I
b = 1.42474 − 0.38588I
−1.18945 − 5.01515I 0
u = −1.49701 + 0.03536I
a = 0.488640 − 0.267244I
b = −0.258686 − 0.678873I
−7.03449 − 6.70275I 0
u = −1.49701 − 0.03536I
a = 0.488640 + 0.267244I
b = −0.258686 + 0.678873I
−7.03449 + 6.70275I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.224112 + 0.424001I
a = −1.08363 + 1.63534I
b = −0.534595 + 0.408640I
−1.70121 − 1.12219I −12.55043 + 5.69637I
u = 0.224112 − 0.424001I
a = −1.08363 − 1.63534I
b = −0.534595 − 0.408640I
−1.70121 + 1.12219I −12.55043 − 5.69637I
u = 1.57577 + 0.03846I
a = −0.513955 − 0.003599I
b = −0.067086 − 0.129529I
−10.71130 + 0.03287I 0
u = 1.57577 − 0.03846I
a = −0.513955 + 0.003599I
b = −0.067086 + 0.129529I
−10.71130 − 0.03287I 0
u = −0.347952 + 0.238520I
a = 2.05729 + 1.92360I
b = −0.043214 + 0.259142I
−1.03011 − 1.52508I −14.1900 + 0.3808I
u = −0.347952 − 0.238520I
a = 2.05729 − 1.92360I
b = −0.043214 − 0.259142I
−1.03011 + 1.52508I −14.1900 − 0.3808I
u = −0.315598
a = 0.995497
b = −0.236639
−0.581693 −17.2430
11
II. I
u
2
= h5b + u + 3, 5a + 2u + 6, u
2
+ u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
−u + 1
a
1
=
−u
−u + 1
a
3
=
−
2
5
u −
6
5
−
1
5
u −
3
5
a
4
=
3
5
u −
6
5
4
5
u −
8
5
a
10
=
u
u
a
8
=
2u
u
a
2
=
−
2
5
u −
6
5
−
1
5
u −
3
5
a
5
=
−
2
5
u +
1
5
−
1
5
u −
2
5
a
9
=
7
5
u +
2
5
6
5
u +
1
5
a
9
=
7
5
u +
2
5
6
5
u +
1
5
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
72
5
u − 7
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
c
2
u
2
c
3
(u + 1)
2
c
4
, c
6
u
2
+ u − 1
c
5
5(5u
2
+ 5u + 1)
c
7
u
2
− 3u + 1
c
8
, c
10
, c
11
u
2
− u − 1
c
9
5(5u
2
− 1)
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y −1)
2
c
2
y
2
c
4
, c
6
, c
8
c
10
, c
11
y
2
− 3y + 1
c
5
25(25y
2
− 15y + 1)
c
7
y
2
− 7y + 1
c
9
25(5y −1)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −1.44721
b = −0.723607
−2.63189 −15.9000
u = −1.61803
a = −0.552786
b = −0.276393
−10.5276 16.3000
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u
67
− 3u
66
+ ··· − 11u + 25)
c
2
u
2
(u
67
+ u
66
+ ··· + 980u + 100)
c
3
((u + 1)
2
)(u
67
− 3u
66
+ ··· − 11u + 25)
c
4
(u
2
+ u − 1)(u
67
+ 2u
66
+ ··· + 4u + 1)
c
5
25(5u
2
+ 5u + 1)(5u
67
− 44u
66
+ ··· + 396u + 27)
c
6
(u
2
+ u − 1)(u
67
+ 2u
66
+ ··· + 2u + 1)
c
7
(u
2
− 3u + 1)(u
67
− 6u
66
+ ··· − 618u + 117)
c
8
(u
2
− u − 1)(u
67
+ 2u
66
+ ··· + 4u + 1)
c
9
25(5u
2
− 1)(5u
67
+ 27u
66
+ ··· + 819u + 81)
c
10
, c
11
(u
2
− u − 1)(u
67
+ 2u
66
+ ··· + 2u + 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
((y −1)
2
)(y
67
− 39y
66
+ ··· + 25671y −625)
c
2
y
2
(y
67
+ 15y
66
+ ··· + 203000y −10000)
c
4
, c
8
(y
2
− 3y + 1)(y
67
+ 36y
66
+ ··· + 4y −1)
c
5
625(25y
2
− 15y + 1)(25y
67
+ 624y
66
+ ··· + 130896y −729)
c
6
, c
10
, c
11
(y
2
− 3y + 1)(y
67
− 60y
66
+ ··· + 4y −1)
c
7
(y
2
− 7y + 1)(y
67
+ 4y
66
+ ··· + 137160y −13689)
c
9
625(5y −1)
2
(25y
67
− 79y
66
+ ··· − 46413y −6561)
17
