11a
52
(K11a
52
)
A knot diagram
1
Linearized knot diagam
5 1 11 2 9 4 3 10 6 8 7
Solving Sequence
5,9
6
2,10
1 3 4 7 8 11
c
5
c
9
c
1
c
2
c
4
c
6
c
8
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.36254 × 10
45
u
69
+ 4.82278 × 10
45
u
68
+ ··· + 1.20308 × 10
45
b + 1.54557 × 10
45
,
− 8.19355 × 10
45
u
69
+ 1.66575 × 10
46
u
68
+ ··· + 1.20308 × 10
45
a + 9.02950 × 10
45
, u
70
− 3u
69
+ ··· + 2u + 1i
I
u
2
= h3b − a − 1, a
2
− a + 7, u − 1i
* 2 irreducible components of dim
C
= 0, with total 72 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−2.36×10
45
u
69
+4.82×10
45
u
68
+· · ·+1.20×10
45
b+1.55×10
45
, −8.19×
10
45
u
69
+1.67×10
46
u
68
+· · ·+1.20×10
45
a+9.03×10
45
, u
70
−3u
69
+· · ·+2u+1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
u
2
a
2
=
6.81046u
69
− 13.8457u
68
+ ··· − 19.7949u − 7.50529
1.96374u
69
− 4.00868u
68
+ ··· − 1.36136u − 1.28468
a
10
=
−u
−u
3
+ u
a
1
=
4.84672u
69
− 9.83700u
68
+ ··· − 18.4335u − 6.22062
1.96374u
69
− 4.00868u
68
+ ··· − 1.36136u − 1.28468
a
3
=
−22.4801u
69
+ 51.8492u
68
+ ··· + 114.630u + 32.1980
0.955391u
69
− 1.83843u
68
+ ··· + 1.87417u + 0.890916
a
4
=
24.1027u
69
− 55.6549u
68
+ ··· − 122.558u − 34.6348
−1.26457u
69
+ 2.55163u
68
+ ··· − 0.684959u − 0.355838
a
7
=
15.0245u
69
− 34.6120u
68
+ ··· − 70.5010u − 21.5396
−2.29156u
69
+ 4.76568u
68
+ ··· + 9.69809u + 2.33641
a
8
=
u
3
u
5
− u
3
+ u
a
11
=
−u
5
− u
−u
7
+ u
5
− 2u
3
+ u
a
11
=
−u
5
− u
−u
7
+ u
5
− 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −136.960u
69
+ 306.752u
68
+ ··· + 605.662u + 186.864
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
70
+ 2u
69
+ ··· + 7u + 1
c
2
u
70
+ 26u
69
+ ··· − 61u + 1
c
3
u
70
+ 7u
69
+ ··· − 4u + 4
c
5
, c
9
u
70
+ 3u
69
+ ··· − 2u + 1
c
6
u
70
− 4u
69
+ ··· − 14859u + 4643
c
7
u
70
− 2u
69
+ ··· + 3989u + 641
c
8
, c
10
u
70
+ 21u
69
+ ··· + 8u + 1
c
11
u
70
+ 7u
69
+ ··· − 4u
2
+ 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
70
+ 26y
69
+ ··· − 61y + 1
c
2
y
70
+ 38y
69
+ ··· − 1741y + 1
c
3
y
70
− 15y
69
+ ··· − 328y + 16
c
5
, c
9
y
70
− 21y
69
+ ··· − 8y + 1
c
6
y
70
− 46y
69
+ ··· + 512636971y + 21557449
c
7
y
70
− 90y
69
+ ··· − 12237909y + 410881
c
8
, c
10
y
70
+ 59y
69
+ ··· + 128y + 1
c
11
y
70
− 9y
69
+ ··· − 8y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.995386 + 0.165662I
a = 0.18980 − 2.80256I
b = 0.036237 − 1.176330I
−5.59225 + 3.69663I 0
u = −0.995386 − 0.165662I
a = 0.18980 + 2.80256I
b = 0.036237 + 1.176330I
−5.59225 − 3.69663I 0
u = −0.828278 + 0.688700I
a = −1.33032 + 1.83011I
b = −0.248336 + 0.844356I
1.83973 + 0.97289I 0
u = −0.828278 − 0.688700I
a = −1.33032 − 1.83011I
b = −0.248336 − 0.844356I
1.83973 − 0.97289I 0
u = 0.996317 + 0.448702I
a = −1.53721 − 1.79701I
b = 0.225350 − 0.984742I
−3.99310 − 2.18696I 0
u = 0.996317 − 0.448702I
a = −1.53721 + 1.79701I
b = 0.225350 + 0.984742I
−3.99310 + 2.18696I 0
u = 0.770782 + 0.776651I
a = −0.580521 − 0.966304I
b = −0.174351 − 1.283410I
0.52470 + 2.76607I 0
u = 0.770782 − 0.776651I
a = −0.580521 + 0.966304I
b = −0.174351 + 1.283410I
0.52470 − 2.76607I 0
u = −1.045200 + 0.337747I
a = 0.817778 − 0.202767I
b = 0.776298 − 0.488443I
0.03545 + 5.59321I 0
u = −1.045200 − 0.337747I
a = 0.817778 + 0.202767I
b = 0.776298 + 0.488443I
0.03545 − 5.59321I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.851573 + 0.160925I
a = −0.655289 − 0.443715I
b = 0.172499 − 0.029720I
−1.46844 − 0.34695I −5.88246 + 0.51749I
u = 0.851573 − 0.160925I
a = −0.655289 + 0.443715I
b = 0.172499 + 0.029720I
−1.46844 + 0.34695I −5.88246 − 0.51749I
u = −0.928519 + 0.676403I
a = −0.04063 − 1.70730I
b = −0.093994 − 0.803000I
1.51661 + 4.29217I 0
u = −0.928519 − 0.676403I
a = −0.04063 + 1.70730I
b = −0.093994 + 0.803000I
1.51661 − 4.29217I 0
u = −0.007678 + 0.846407I
a = −0.637096 − 0.540258I
b = 0.661839 − 0.998275I
2.09416 − 7.06733I 3.10109 + 7.21627I
u = −0.007678 − 0.846407I
a = −0.637096 + 0.540258I
b = 0.661839 + 0.998275I
2.09416 + 7.06733I 3.10109 − 7.21627I
u = 0.842274 + 0.793739I
a = 0.0857954 − 0.1036380I
b = −0.815235 − 1.138530I
4.87181 + 1.93616I 0
u = 0.842274 − 0.793739I
a = 0.0857954 + 0.1036380I
b = −0.815235 + 1.138530I
4.87181 − 1.93616I 0
u = −0.865807 + 0.768796I
a = 1.77759 − 1.14999I
b = −0.583169 + 0.848078I
3.51311 + 0.58844I 0
u = −0.865807 − 0.768796I
a = 1.77759 + 1.14999I
b = −0.583169 − 0.848078I
3.51311 − 0.58844I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.117840 + 0.306611I
a = −0.58017 + 2.41556I
b = 0.642942 + 1.069940I
−1.65551 + 10.94810I 0
u = −1.117840 − 0.306611I
a = −0.58017 − 2.41556I
b = 0.642942 − 1.069940I
−1.65551 − 10.94810I 0
u = −0.812863 + 0.213562I
a = 0.34965 − 3.03059I
b = −0.583671 − 1.124250I
−1.06806 + 4.56339I −2.77563 − 10.69902I
u = −0.812863 − 0.213562I
a = 0.34965 + 3.03059I
b = −0.583671 + 1.124250I
−1.06806 − 4.56339I −2.77563 + 10.69902I
u = −0.710673 + 0.928532I
a = −0.541662 − 0.437409I
b = 0.689342 − 0.894211I
6.57916 − 2.04356I 0
u = −0.710673 − 0.928532I
a = −0.541662 + 0.437409I
b = 0.689342 + 0.894211I
6.57916 + 2.04356I 0
u = 0.743525 + 0.906502I
a = −0.569223 + 0.509822I
b = 0.725223 + 1.096770I
6.51009 + 10.55950I 0
u = 0.743525 − 0.906502I
a = −0.569223 − 0.509822I
b = 0.725223 − 1.096770I
6.51009 − 10.55950I 0
u = −0.897032 + 0.760443I
a = 3.28347 − 0.31284I
b = −0.578878 − 0.878433I
3.41570 + 5.19038I 0
u = −0.897032 − 0.760443I
a = 3.28347 + 0.31284I
b = −0.578878 + 0.878433I
3.41570 − 5.19038I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.773851 + 0.887444I
a = −0.618601 − 0.280980I
b = 0.933958 − 0.585997I
8.09011 + 4.47407I 0
u = 0.773851 − 0.887444I
a = −0.618601 + 0.280980I
b = 0.933958 + 0.585997I
8.09011 − 4.47407I 0
u = −0.885450 + 0.784206I
a = −0.362536 − 0.180613I
b = −0.356108 − 0.054613I
3.87537 + 2.94930I 0
u = −0.885450 − 0.784206I
a = −0.362536 + 0.180613I
b = −0.356108 + 0.054613I
3.87537 − 2.94930I 0
u = 0.876344 + 0.799248I
a = −0.044434 + 0.720824I
b = −1.085200 − 0.452446I
6.80863 − 1.13129I 0
u = 0.876344 − 0.799248I
a = −0.044434 − 0.720824I
b = −1.085200 + 0.452446I
6.80863 + 1.13129I 0
u = 1.183560 + 0.155574I
a = −0.19004 − 1.75074I
b = 0.546606 − 0.763209I
−1.30105 − 1.37775I 0
u = 1.183560 − 0.155574I
a = −0.19004 + 1.75074I
b = 0.546606 + 0.763209I
−1.30105 + 1.37775I 0
u = 0.899558 + 0.792619I
a = 0.612904 + 0.759345I
b = −1.082270 + 0.519895I
6.73681 − 4.83956I 0
u = 0.899558 − 0.792619I
a = 0.612904 − 0.759345I
b = −1.082270 − 0.519895I
6.73681 + 4.83956I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.924273 + 0.773355I
a = 1.55359 + 1.40982I
b = −0.78729 + 1.17932I
4.61940 − 7.83060I 0
u = 0.924273 − 0.773355I
a = 1.55359 − 1.40982I
b = −0.78729 − 1.17932I
4.61940 + 7.83060I 0
u = −0.108732 + 0.784297I
a = −0.658484 + 0.376100I
b = 0.720698 + 0.648573I
3.13610 − 1.75909I 5.49516 + 1.80706I
u = −0.108732 − 0.784297I
a = −0.658484 − 0.376100I
b = 0.720698 − 0.648573I
3.13610 + 1.75909I 5.49516 − 1.80706I
u = 0.788707 + 0.062767I
a = 2.20666 + 6.58986I
b = −0.481951 + 0.889150I
−1.27782 − 2.20300I 28.2888 − 15.0727I
u = 0.788707 − 0.062767I
a = 2.20666 − 6.58986I
b = −0.481951 − 0.889150I
−1.27782 + 2.20300I 28.2888 + 15.0727I
u = −0.779588 + 0.927411I
a = −0.779208 + 0.452650I
b = 0.697500 + 0.803718I
6.85272 + 3.28181I 0
u = −0.779588 − 0.927411I
a = −0.779208 − 0.452650I
b = 0.697500 − 0.803718I
6.85272 − 3.28181I 0
u = 1.181350 + 0.278165I
a = 0.60168 + 1.40057I
b = 0.581386 + 0.947779I
−1.93471 + 3.15779I 0
u = 1.181350 − 0.278165I
a = 0.60168 − 1.40057I
b = 0.581386 − 0.947779I
−1.93471 − 3.15779I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.965304 + 0.740829I
a = 1.15589 + 1.48686I
b = −0.116249 + 1.319010I
−0.06465 − 8.51032I 0
u = 0.965304 − 0.740829I
a = 1.15589 − 1.48686I
b = −0.116249 − 1.319010I
−0.06465 + 8.51032I 0
u = 1.005940 + 0.794706I
a = 0.301599 − 0.708101I
b = 0.954425 + 0.553357I
7.36308 − 10.70740I 0
u = 1.005940 − 0.794706I
a = 0.301599 + 0.708101I
b = 0.954425 − 0.553357I
7.36308 + 10.70740I 0
u = 1.029420 + 0.788695I
a = −1.61908 − 1.68690I
b = 0.719263 − 1.118330I
5.6142 − 16.8243I 0
u = 1.029420 − 0.788695I
a = −1.61908 + 1.68690I
b = 0.719263 + 1.118330I
5.6142 + 16.8243I 0
u = −1.016160 + 0.823146I
a = 0.181100 + 0.185446I
b = 0.685303 − 0.740870I
6.10986 + 3.15378I 0
u = −1.016160 − 0.823146I
a = 0.181100 − 0.185446I
b = 0.685303 + 0.740870I
6.10986 − 3.15378I 0
u = −1.055400 + 0.789410I
a = −1.34149 + 1.48669I
b = 0.664262 + 0.939808I
5.50755 + 8.37088I 0
u = −1.055400 − 0.789410I
a = −1.34149 − 1.48669I
b = 0.664262 − 0.939808I
5.50755 − 8.37088I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.654651 + 0.128429I
a = −2.57121 + 1.64254I
b = −0.425524 − 0.842724I
−1.06799 + 1.58770I 1.27174 − 9.61226I
u = 0.654651 − 0.128429I
a = −2.57121 − 1.64254I
b = −0.425524 + 0.842724I
−1.06799 − 1.58770I 1.27174 + 9.61226I
u = −0.608095 + 0.260027I
a = −0.243882 − 1.135630I
b = −0.760996 − 0.715752I
1.05262 + 2.72622I 4.23016 − 8.33460I
u = −0.608095 − 0.260027I
a = −0.243882 + 1.135630I
b = −0.760996 + 0.715752I
1.05262 − 2.72622I 4.23016 + 8.33460I
u = 0.255521 + 0.549099I
a = −0.808489 + 0.387160I
b = −0.006007 + 0.938840I
−1.97330 − 1.67417I −2.89034 + 3.89687I
u = 0.255521 − 0.549099I
a = −0.808489 − 0.387160I
b = −0.006007 − 0.938840I
−1.97330 + 1.67417I −2.89034 − 3.89687I
u = −0.427977 + 0.312404I
a = −1.221700 − 0.326639I
b = −0.627763 + 0.219249I
1.45022 − 0.18071I 7.16773 − 1.07123I
u = −0.427977 − 0.312404I
a = −1.221700 + 0.326639I
b = −0.627763 − 0.219249I
1.45022 + 0.18071I 7.16773 + 1.07123I
u = −0.152266 + 0.264102I
a = −1.186220 + 0.013858I
b = −0.626147 + 0.914671I
0.59157 − 2.55234I 2.38321 + 1.51119I
u = −0.152266 − 0.264102I
a = −1.186220 − 0.013858I
b = −0.626147 − 0.914671I
0.59157 + 2.55234I 2.38321 − 1.51119I
11
II. I
u
2
= h3b − a − 1, a
2
− a + 7, u − 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
1
a
6
=
1
1
a
2
=
a
1
3
a +
1
3
a
10
=
−1
0
a
1
=
2
3
a −
1
3
1
3
a +
1
3
a
3
=
2
3
a −
4
3
1
3
a −
2
3
a
4
=
2
3
a −
4
3
1
3
a −
2
3
a
7
=
2
3
a +
5
3
1
3
a +
4
3
a
8
=
1
1
a
11
=
−2
−1
a
11
=
−2
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
4
3
a −
7
3
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
2
+ u + 1
c
3
u
2
c
4
, c
6
, c
7
u
2
− u + 1
c
5
, c
8
(u − 1)
2
c
9
, c
10
, c
11
(u + 1)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
7
y
2
+ y + 1
c
3
y
2
c
5
, c
8
, c
9
c
10
, c
11
(y −1)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.50000 + 2.59808I
b = 0.500000 + 0.866025I
−1.64493 + 2.02988I −3.00000 − 3.46410I
u = 1.00000
a = 0.50000 − 2.59808I
b = 0.500000 − 0.866025I
−1.64493 − 2.02988I −3.00000 + 3.46410I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u + 1)(u
70
+ 2u
69
+ ··· + 7u + 1)
c
2
(u
2
+ u + 1)(u
70
+ 26u
69
+ ··· − 61u + 1)
c
3
u
2
(u
70
+ 7u
69
+ ··· − 4u + 4)
c
4
(u
2
− u + 1)(u
70
+ 2u
69
+ ··· + 7u + 1)
c
5
((u − 1)
2
)(u
70
+ 3u
69
+ ··· − 2u + 1)
c
6
(u
2
− u + 1)(u
70
− 4u
69
+ ··· − 14859u + 4643)
c
7
(u
2
− u + 1)(u
70
− 2u
69
+ ··· + 3989u + 641)
c
8
((u − 1)
2
)(u
70
+ 21u
69
+ ··· + 8u + 1)
c
9
((u + 1)
2
)(u
70
+ 3u
69
+ ··· − 2u + 1)
c
10
((u + 1)
2
)(u
70
+ 21u
69
+ ··· + 8u + 1)
c
11
((u + 1)
2
)(u
70
+ 7u
69
+ ··· − 4u
2
+ 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
2
+ y + 1)(y
70
+ 26y
69
+ ··· − 61y + 1)
c
2
(y
2
+ y + 1)(y
70
+ 38y
69
+ ··· − 1741y + 1)
c
3
y
2
(y
70
− 15y
69
+ ··· − 328y + 16)
c
5
, c
9
((y −1)
2
)(y
70
− 21y
69
+ ··· − 8y + 1)
c
6
(y
2
+ y + 1)(y
70
− 46y
69
+ ··· + 5.12637 × 10
8
y + 2.15574 × 10
7
)
c
7
(y
2
+ y + 1)(y
70
− 90y
69
+ ··· − 1.22379 × 10
7
y + 410881)
c
8
, c
10
((y −1)
2
)(y
70
+ 59y
69
+ ··· + 128y + 1)
c
11
((y −1)
2
)(y
70
− 9y
69
+ ··· − 8y + 1)
17
