11a
103
(K11a
103
)
A knot diagram
1
Linearized knot diagam
6 1 7 10 2 4 3 11 5 9 8
Solving Sequence
2,5
6 1
3,10
4 7 9 11 8
c
5
c
1
c
2
c
4
c
6
c
9
c
10
c
8
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h3278045625361u
33
− 962912057641220u
32
+ ··· + 5173973686763240b − 10139327463448051,
165318083439065u
33
− 292527248838037u
32
+ ··· + 517397368676324a − 3832627237028687,
u
34
− u
33
+ ··· − 8u + 1i
I
u
2
= hu
9
+ 3u
7
+ u
6
+ 3u
5
+ 2u
4
+ 3u
3
+ u
2
+ b + 2u + 1,
u
10
+ u
9
+ 3u
8
+ 3u
7
+ 3u
6
+ 3u
5
+ 3u
4
+ 3u
3
+ 2u
2
+ a + 2u,
u
12
+ 4u
10
+ u
9
+ 6u
8
+ 3u
7
+ 7u
6
+ 3u
5
+ 7u
4
+ 3u
3
+ 3u
2
+ 2u + 1i
I
u
3
= h3a
2
u − 5a
2
− au + 17b − 4a − 14u − 22, a
3
− a
2
u + 5au + 3a − u + 6, u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 52 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
= h3.28 × 10
12
u
33
− 9.63 × 10
14
u
32
+ · · · + 5.17 × 10
15
b − 1.01 × 10
16
, 1.65 ×
10
14
u
33
−2.93×10
14
u
32
+· · ·+5.17×10
14
a−3.83×10
15
, u
34
−u
33
+· · ·−8u+1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
10
=
−0.319519u
33
+ 0.565382u
32
+ ··· − 24.1768u + 7.40751
−0.000633564u
33
+ 0.186107u
32
+ ··· − 10.0234u + 1.95968
a
4
=
−1.45002u
33
+ 1.24609u
32
+ ··· − 56.5835u + 9.19176
−0.466475u
33
+ 0.463665u
32
+ ··· − 14.6958u + 1.41968
a
7
=
−1.41968u
33
+ 0.953207u
32
+ ··· − 24.2367u − 2.33833
0.230732u
33
− 0.201881u
32
+ ··· + 6.37702u − 2.17754
a
9
=
−0.318885u
33
+ 0.379275u
32
+ ··· − 14.1534u + 5.44783
−0.000633564u
33
+ 0.186107u
32
+ ··· − 10.0234u + 1.95968
a
11
=
−2.20913u
33
+ 2.13366u
32
+ ··· − 73.5810u + 10.9803
−0.401588u
33
+ 0.324840u
32
+ ··· − 16.0702u + 1.25226
a
8
=
−1.62080u
33
+ 0.922129u
32
+ ··· − 24.3330u − 2.35478
0.322682u
33
− 0.130017u
32
+ ··· + 4.06483u − 1.68221
a
8
=
−1.62080u
33
+ 0.922129u
32
+ ··· − 24.3330u − 2.35478
0.322682u
33
− 0.130017u
32
+ ··· + 4.06483u − 1.68221
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
2045779387053011
646746710845405
u
33
−
400807807432123
129349342169081
u
32
+ ··· +
62894935432571939
1293493421690810
u +
471857212990363
1293493421690810
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
34
− u
33
+ ··· − 8u + 1
c
2
u
34
+ 11u
33
+ ··· + 24u + 1
c
3
, c
6
, c
7
u
34
− u
33
+ ··· − 10u + 1
c
4
, c
9
u
34
− 2u
33
+ ··· − u + 2
c
8
, c
10
, c
11
u
34
+ 8u
33
+ ··· + 19u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
34
+ 11y
33
+ ··· + 24y + 1
c
2
y
34
+ 31y
33
+ ··· + 916y + 1
c
3
, c
6
, c
7
y
34
+ 39y
33
+ ··· + 56y + 1
c
4
, c
9
y
34
+ 8y
33
+ ··· + 19y + 4
c
8
, c
10
, c
11
y
34
+ 36y
33
+ ··· + 495y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.261633 + 0.992110I
a = 0.38508 + 2.26064I
b = 0.132179 + 0.885169I
−3.37245 − 0.54787I −11.62744 + 0.56640I
u = −0.261633 − 0.992110I
a = 0.38508 − 2.26064I
b = 0.132179 − 0.885169I
−3.37245 + 0.54787I −11.62744 − 0.56640I
u = −0.026982 + 1.057990I
a = −0.20134 − 1.50601I
b = −0.756642 − 0.885148I
1.40352 + 2.86614I −6.42514 − 2.90312I
u = −0.026982 − 1.057990I
a = −0.20134 + 1.50601I
b = −0.756642 + 0.885148I
1.40352 − 2.86614I −6.42514 + 2.90312I
u = 0.744389 + 0.572496I
a = 0.029128 − 1.295630I
b = 0.536369 − 0.967768I
5.18197 − 3.30193I 1.74557 + 3.15747I
u = 0.744389 − 0.572496I
a = 0.029128 + 1.295630I
b = 0.536369 + 0.967768I
5.18197 + 3.30193I 1.74557 − 3.15747I
u = 0.441745 + 0.826611I
a = 0.076268 + 0.399359I
b = 0.507078 − 0.314037I
−0.14247 + 1.88117I −0.09008 − 3.89150I
u = 0.441745 − 0.826611I
a = 0.076268 − 0.399359I
b = 0.507078 + 0.314037I
−0.14247 − 1.88117I −0.09008 + 3.89150I
u = 0.625868 + 0.866379I
a = −0.47867 + 2.30688I
b = −0.064010 + 1.041080I
1.54356 + 2.45179I −3.02847 − 2.63078I
u = 0.625868 − 0.866379I
a = −0.47867 − 2.30688I
b = −0.064010 − 1.041080I
1.54356 − 2.45179I −3.02847 + 2.63078I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.807854 + 0.740004I
a = −0.120969 − 0.562485I
b = 0.748669 − 0.433849I
6.89618 − 1.36512I 4.50793 + 2.51852I
u = −0.807854 − 0.740004I
a = −0.120969 + 0.562485I
b = 0.748669 + 0.433849I
6.89618 + 1.36512I 4.50793 − 2.51852I
u = −0.492701 + 0.994382I
a = −1.29280 − 2.00761I
b = 0.397288 − 0.911636I
−1.90809 − 5.35995I −5.93507 + 8.80123I
u = −0.492701 − 0.994382I
a = −1.29280 + 2.00761I
b = 0.397288 + 0.911636I
−1.90809 + 5.35995I −5.93507 − 8.80123I
u = 1.062640 + 0.522537I
a = 0.515909 + 0.514851I
b = −0.866234 + 0.973628I
14.3477 − 6.6660I 4.12754 + 3.29257I
u = 1.062640 − 0.522537I
a = 0.515909 − 0.514851I
b = −0.866234 − 0.973628I
14.3477 + 6.6660I 4.12754 − 3.29257I
u = 0.708232 + 0.962390I
a = −0.202503 − 0.408506I
b = −0.875730 + 0.863176I
6.14429 + 2.35773I 0.48410 − 2.53993I
u = 0.708232 − 0.962390I
a = −0.202503 + 0.408506I
b = −0.875730 − 0.863176I
6.14429 − 2.35773I 0.48410 + 2.53993I
u = −1.057880 + 0.566930I
a = 0.584986 + 0.484797I
b = −0.913890 + 0.874570I
14.6663 + 0.1016I 4.57906 + 1.48156I
u = −1.057880 − 0.566930I
a = 0.584986 − 0.484797I
b = −0.913890 − 0.874570I
14.6663 − 0.1016I 4.57906 − 1.48156I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.698424 + 1.002800I
a = 1.45163 + 1.39463I
b = −0.837985 + 0.957359I
5.84725 − 8.71325I −0.27553 + 7.33315I
u = −0.698424 − 1.002800I
a = 1.45163 − 1.39463I
b = −0.837985 − 0.957359I
5.84725 + 8.71325I −0.27553 − 7.33315I
u = −0.744862 + 0.976632I
a = −0.359731 + 0.249557I
b = −0.753616 − 0.286412I
6.18222 − 4.46313I 3.61159 + 3.03058I
u = −0.744862 − 0.976632I
a = −0.359731 − 0.249557I
b = −0.753616 + 0.286412I
6.18222 + 4.46313I 3.61159 − 3.03058I
u = 0.675576 + 1.053520I
a = 0.94684 − 2.18547I
b = −0.437047 − 1.024080I
3.77297 + 8.75654I −1.23706 − 8.00625I
u = 0.675576 − 1.053520I
a = 0.94684 + 2.18547I
b = −0.437047 + 1.024080I
3.77297 − 8.75654I −1.23706 + 8.00625I
u = 0.231881 + 0.577044I
a = 0.813045 + 0.154211I
b = −0.304181 − 0.448448I
0.165045 + 1.193180I 1.28022 − 6.36905I
u = 0.231881 − 0.577044I
a = 0.813045 − 0.154211I
b = −0.304181 + 0.448448I
0.165045 − 1.193180I 1.28022 + 6.36905I
u = −0.779313 + 1.162920I
a = 0.530381 − 0.067533I
b = 0.918270 + 0.834445I
12.8109 − 6.7247I 2.85757 + 2.78604I
u = −0.779313 − 1.162920I
a = 0.530381 + 0.067533I
b = 0.918270 − 0.834445I
12.8109 + 6.7247I 2.85757 − 2.78604I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.756680 + 1.182600I
a = −1.05832 + 1.72508I
b = 0.842815 + 0.996957I
12.2913 + 13.2218I 1.97446 − 7.47226I
u = 0.756680 − 1.182600I
a = −1.05832 − 1.72508I
b = 0.842815 − 0.996957I
12.2913 − 13.2218I 1.97446 + 7.47226I
u = 0.122630 + 0.166148I
a = 4.38106 − 1.67605I
b = 0.726668 − 0.862044I
4.64121 − 2.76844I 5.45074 + 3.04285I
u = 0.122630 − 0.166148I
a = 4.38106 + 1.67605I
b = 0.726668 + 0.862044I
4.64121 + 2.76844I 5.45074 − 3.04285I
8
II.
I
u
2
= hu
9
+ 3u
7
+ · · · + b + 1, u
10
+ u
9
+ · · · + a + 2u, u
12
+ 4u
10
+ · · · + 2u + 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
10
=
−u
10
− u
9
− 3u
8
− 3u
7
− 3u
6
− 3u
5
− 3u
4
− 3u
3
− 2u
2
− 2u
−u
9
− 3u
7
− u
6
− 3u
5
− 2u
4
− 3u
3
− u
2
− 2u − 1
a
4
=
−u
u
3
+ u
a
7
=
−u
2
+ 1
u
4
a
9
=
−u
10
− 3u
8
− 2u
6
− u
4
− u
2
+ 1
−u
9
− 3u
7
− u
6
− 3u
5
− 2u
4
− 3u
3
− u
2
− 2u − 1
a
11
=
u
7
+ 2u
5
−u
9
− 3u
7
− 3u
5
− 2u
3
− u
a
8
=
−u
4
− u
2
+ 1
u
6
+ 2u
4
+ u
2
a
8
=
−u
4
− u
2
+ 1
u
6
+ 2u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
9
− 12u
7
− 4u
6
− 12u
5
− 8u
4
− 16u
3
− 4u
2
− 12u − 6
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
7
u
12
+ 4u
10
+ u
9
+ 6u
8
+ 3u
7
+ 7u
6
+ 3u
5
+ 7u
4
+ 3u
3
+ 3u
2
+ 2u + 1
c
2
u
12
+ 8u
11
+ ··· + 2u + 1
c
4
, c
9
(u
4
+ u
3
+ u
2
+ 1)
3
c
8
, c
10
, c
11
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
3
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
7
y
12
+ 8y
11
+ ··· + 2y + 1
c
2
y
12
− 8y
11
+ ··· + 18y + 1
c
4
, c
9
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
3
c
8
, c
10
, c
11
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
3
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.757780 + 0.691817I
a = −0.537761 − 0.236860I
b = 0.851808 + 0.911292I
6.79074 + 3.16396I 1.82674 − 2.56480I
u = −0.757780 − 0.691817I
a = −0.537761 + 0.236860I
b = 0.851808 − 0.911292I
6.79074 − 3.16396I 1.82674 + 2.56480I
u = 0.737742 + 0.749761I
a = −1.39038 + 0.60728I
b = 0.851808 + 0.911292I
6.79074 + 3.16396I 1.82674 − 2.56480I
u = 0.737742 − 0.749761I
a = −1.39038 − 0.60728I
b = 0.851808 − 0.911292I
6.79074 − 3.16396I 1.82674 + 2.56480I
u = 0.337741 + 0.872538I
a = 1.71032 − 1.02179I
b = −0.351808 − 0.720342I
−0.21101 + 1.41510I −1.82674 − 4.90874I
u = 0.337741 − 0.872538I
a = 1.71032 + 1.02179I
b = −0.351808 + 0.720342I
−0.21101 − 1.41510I −1.82674 + 4.90874I
u = 0.117310 + 1.208580I
a = −0.74302 + 1.91397I
b = −0.351808 + 0.720342I
−0.21101 − 1.41510I −1.82674 + 4.90874I
u = 0.117310 − 1.208580I
a = −0.74302 − 1.91397I
b = −0.351808 − 0.720342I
−0.21101 + 1.41510I −1.82674 − 4.90874I
u = −0.455051 + 0.336038I
a = 0.674975 − 0.426864I
b = −0.351808 − 0.720342I
−0.21101 + 1.41510I −1.82674 − 4.90874I
u = −0.455051 − 0.336038I
a = 0.674975 + 0.426864I
b = −0.351808 + 0.720342I
−0.21101 − 1.41510I −1.82674 + 4.90874I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.02004 + 1.44158I
a = 0.28587 − 1.38654I
b = 0.851808 − 0.911292I
6.79074 − 3.16396I 1.82674 + 2.56480I
u = 0.02004 − 1.44158I
a = 0.28587 + 1.38654I
b = 0.851808 + 0.911292I
6.79074 + 3.16396I 1.82674 − 2.56480I
13
III.
I
u
3
= h3a
2
u−5a
2
−au+17b−4a−14u−22, a
3
−a
2
u+5au+3a−u+6, u
2
+1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
1
a
1
=
−u
0
a
3
=
u
u
a
10
=
a
−0.176471a
2
u + 0.0588235au + ··· + 0.235294a + 1.29412
a
4
=
0.352941a
2
u − 0.117647au + ··· − 0.470588a − 0.588235
0.352941a
2
u − 0.117647au + ··· − 0.470588a − 0.588235
a
7
=
0.411765a
2
u − 0.470588au + ··· + 0.117647a − 0.352941
0.411765a
2
u − 0.470588au + ··· + 0.117647a − 1.35294
a
9
=
0.176471a
2
u − 0.0588235au + ··· + 0.764706a − 1.29412
−0.176471a
2
u + 0.0588235au + ··· + 0.235294a + 1.29412
a
11
=
−0.117647a
2
u − 0.294118au + ··· + 0.823529a − 0.470588
0.235294a
2
u − 0.411765au + ··· + 0.352941a − 1.05882
a
8
=
0.411765a
2
u − 0.470588au + ··· + 0.117647a − 1.35294
0.411765a
2
u − 0.470588au + ··· + 0.117647a − 2.35294
a
8
=
0.411765a
2
u − 0.470588au + ··· + 0.117647a − 1.35294
0.411765a
2
u − 0.470588au + ··· + 0.117647a − 2.35294
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
20
17
a
2
u −
12
17
a
2
−
16
17
au +
4
17
a −
88
17
u −
12
17
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
7
(u
2
+ 1)
3
c
2
(u + 1)
6
c
4
, c
9
u
6
+ u
4
+ 2u
2
+ 1
c
8
(u
3
− u
2
+ 2u − 1)
2
c
10
, c
11
(u
3
+ u
2
+ 2u + 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
7
(y + 1)
6
c
2
(y −1)
6
c
4
, c
9
(y
3
+ y
2
+ 2y + 1)
2
c
8
, c
10
, c
11
(y
3
+ 3y
2
+ 2y −1)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.479777 + 0.977518I
b = 0.744862 + 0.877439I
3.02413 + 2.82812I −0.49024 − 2.97945I
u = 1.000000I
a = −0.84494 + 2.10208I
b = −0.744862 + 0.877439I
3.02413 − 2.82812I −0.49024 + 2.97945I
u = 1.000000I
a = 1.32472 − 2.07960I
b = − 0.754878I
−1.11345 −7.01951 + 0.I
u = − 1.000000I
a = −0.479777 − 0.977518I
b = 0.744862 − 0.877439I
3.02413 − 2.82812I −0.49024 + 2.97945I
u = − 1.000000I
a = −0.84494 − 2.10208I
b = −0.744862 − 0.877439I
3.02413 + 2.82812I −0.49024 − 2.97945I
u = − 1.000000I
a = 1.32472 + 2.07960I
b = 0.754878I
−1.11345 −7.01951 + 0.I
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
2
+ 1)
3
· (u
12
+ 4u
10
+ u
9
+ 6u
8
+ 3u
7
+ 7u
6
+ 3u
5
+ 7u
4
+ 3u
3
+ 3u
2
+ 2u + 1)
· (u
34
− u
33
+ ··· − 8u + 1)
c
2
((u + 1)
6
)(u
12
+ 8u
11
+ ··· + 2u + 1)(u
34
+ 11u
33
+ ··· + 24u + 1)
c
3
, c
6
, c
7
(u
2
+ 1)
3
· (u
12
+ 4u
10
+ u
9
+ 6u
8
+ 3u
7
+ 7u
6
+ 3u
5
+ 7u
4
+ 3u
3
+ 3u
2
+ 2u + 1)
· (u
34
− u
33
+ ··· − 10u + 1)
c
4
, c
9
((u
4
+ u
3
+ u
2
+ 1)
3
)(u
6
+ u
4
+ 2u
2
+ 1)(u
34
− 2u
33
+ ··· − u + 2)
c
8
(u
3
− u
2
+ 2u − 1)
2
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
3
· (u
34
+ 8u
33
+ ··· + 19u + 4)
c
10
, c
11
(u
3
+ u
2
+ 2u + 1)
2
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
3
· (u
34
+ 8u
33
+ ··· + 19u + 4)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y + 1)
6
)(y
12
+ 8y
11
+ ··· + 2y + 1)(y
34
+ 11y
33
+ ··· + 24y + 1)
c
2
((y −1)
6
)(y
12
− 8y
11
+ ··· + 18y + 1)(y
34
+ 31y
33
+ ··· + 916y + 1)
c
3
, c
6
, c
7
((y + 1)
6
)(y
12
+ 8y
11
+ ··· + 2y + 1)(y
34
+ 39y
33
+ ··· + 56y + 1)
c
4
, c
9
(y
3
+ y
2
+ 2y + 1)
2
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
3
· (y
34
+ 8y
33
+ ··· + 19y + 4)
c
8
, c
10
, c
11
(y
3
+ 3y
2
+ 2y −1)
2
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
3
· (y
34
+ 36y
33
+ ··· + 495y + 16)
19
