11a
271
(K11a
271
)
1
Arc Sequences
10 9 1 7 2 3 11 5 6 8 4
Solving Sequence
2,9 3,6
7 10 1 5 4 8 11
c
2
c
6
c
9
c
1
c
5
c
4
c
8
c
11
c
3
, c
7
, c
10
Representation Ideals
I =
5
\
i=1
I
u
i
I
u
1
= hu
2
+ u + 1, a + 1, b 1i
I
u
2
= hu
10
+ 2u
9
+ 3u
8
+ 3u
7
+ 5u
6
+ 6u
5
+ 3u
4
+ 3u
3
+ 3u
2
+ u + 1,
u
9
17u
8
41u
7
60u
6
68u
5
96u
4
110u
3
72u
2
+ 31b 29u 33,
30u
9
+ 76u
8
+ 114u
7
+ 126u
6
+ 180u
5
+ 245u
4
+ 138u
3
+ 83u
2
+ 31a + 95u + 29i
I
u
3
= hu
8
2u
7
+ 2u
6
u
5
+ 4u
4
4u
3
+ u
2
u + 1, a + 1, u
7
4u
6
+ 5u
5
u
4
+ u
3
6u
2
+ 5b + 3u + 3i
I
u
4
= hu
23
+ u
22
+ ··· u 1, a 1,
13836209641757u
22
+ 11133241477660u
21
+ ··· + 5669307193153b + 9041969577747i
I
u
5
= hu
82
+ 5u
81
+ ··· 61u + 11,
1.00827 × 10
325
u
81
6.79975 × 10
325
u
80
+ ··· + 6.30829 × 10
325
b 3.99854 × 10
326
,
4.16480 × 10
326
u
81
3.01111 × 10
327
u
80
+ ··· + 6.93912 × 10
326
a 4.26189 × 10
328
i
There are 5 irreducible components with 125 representations.
1
The knot diagram image is adapter from “C. Livingston and A. H. Moore, KnotInfo: Table of Knot
Invariants, http://www.indiana.edu/ knotinfo”
1
I. I
u
1
= hu
2
+ u + 1, a + 1, b 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
1
1
a
3
=
0
1
a
6
=
0
u
a
7
=
0
u
a
10
=
1
u
a
1
=
u + 1
u 1
a
5
=
u
u
a
4
=
u
u + 1
a
8
=
1
1
a
11
=
u
2u 1
a
11
=
u
2u 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.500000 0.866025I
a = 1.00000
b = 1.00000
4.05977I 6.00000 6.92820I
u = 0.500000 + 0.866025I
a = 1.00000
b = 1.00000
4.05977I 6.00000 + 6.92820I
3
II. I
u
2
=
hu
10
+2u
9
+· · ·+u+1, u
9
17u
8
+· · ·+31b33, 30u
9
+76u
8
+· · ·+31a+29i
(i) Arc colorings
a
2
=
1
0
a
9
=
0.967742u
9
2.45161u
8
+ ··· 3.06452u 0.935484
0.0322581u
9
+ 0.548387u
8
+ ··· + 0.935484u + 1.06452
a
3
=
0.516129u
9
0.774194u
8
+ ··· + 0.0322581u + 0.967742
0.322581u
9
+ 0.483871u
8
+ ··· 1.64516u 0.354839
a
6
=
0
u
a
7
=
0.483871u
9
+ 1.22581u
8
+ ··· + 3.03226u + 0.967742
0.612903u
9
+ 0.419355u
8
+ ··· 2.22581u 1.77419
a
10
=
0.967742u
9
2.45161u
8
+ ··· 3.06452u 0.935484
0.225806u
9
+ 0.161290u
8
+ ··· 0.548387u + 0.548387
a
1
=
0.322581u
9
+ 0.483871u
8
+ ··· 0.645161u 0.354839
1.12903u
9
2.19355u
8
+ ··· 1.74194u 0.258065
a
5
=
u
u
a
4
=
0.677419u
9
0.516129u
8
+ ··· + 1.35484u + 1.64516
0.645161u
9
+ 0.967742u
8
+ ··· 1.29032u 0.709677
a
8
=
0.451613u
9
1.67742u
8
+ ··· 2.09677u 0.903226
0.483871u
9
0.225806u
8
+ ··· 0.0322581u + 1.03226
a
11
=
0.838710u
9
2.25806u
8
+ ··· 0.322581u 0.677419
0.0322581u
9
+ 0.548387u
8
+ ··· 2.06452u 0.935484
a
11
=
0.838710u
9
2.25806u
8
+ ··· 0.322581u 0.677419
0.0322581u
9
+ 0.548387u
8
+ ··· 2.06452u 0.935484
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
4
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.018423 0.244155I
a = 0.239792 0.549347I
b = 0.738091 + 0.154992I
0.29233 + 3.70382I 8.25691 5.45417I
u = 1.018423 + 0.244155I
a = 0.239792 + 0.549347I
b = 0.738091 0.154992I
0.29233 3.70382I 8.25691 + 5.45417I
u = 0.92429 1.22549I
a = 0.559223 + 0.004571I
b = 1.41821 + 0.85833I
3.01018 + 5.17259I 0.22749 12.15389I
u = 0.92429 + 1.22549I
a = 0.559223 0.004571I
b = 1.41821 0.85833I
3.01018 5.17259I 0.22749 + 12.15389I
u = 0.110083 0.618014I
a = 0.66742 + 1.52901I
b = 0.738091 + 0.154992I
0.29233 + 3.70382I 8.25691 5.45417I
u = 0.110083 + 0.618014I
a = 0.66742 1.52901I
b = 0.738091 0.154992I
0.29233 3.70382I 8.25691 + 5.45417I
u = 0.511282 0.689550I
a = 1.78807 + 0.01461I
b = 1.41821 0.85833I
3.01018 5.17259I 0.22749 + 12.15389I
u = 0.511282 + 0.689550I
a = 1.78807 0.01461I
b = 1.41821 + 0.85833I
3.01018 + 5.17259I 0.22749 12.15389I
u = 0.541512 1.019506I
a = 0.559914 0.828551I
b = 0.639756
2.14584 12.9412
u = 0.541512 + 1.019506I
a = 0.559914 + 0.828551I
b = 0.639756
2.14584 12.9412
5
III. I
u
3
= hu
8
2u
7
+ 2u
6
u
5
+ 4u
4
4u
3
+ u
2
u + 1, a + 1, u
7
4u
6
+
5u
5
u
4
+ u
3
6u
2
+ 5b + 3u + 3i
(i) Arc colorings
a
2
=
1
0
a
9
=
1
1
5
u
7
+
4
5
u
6
+ ···
3
5
u
3
5
a
3
=
1
5
u
7
4
5
u
6
+ ··· +
3
5
u +
8
5
u
2
+ u
a
6
=
0
u
a
7
=
4
5
u
7
6
5
u
6
+ ···
13
5
u +
2
5
3
5
u
7
7
5
u
6
+ ··· +
9
5
u
1
5
a
10
=
1
1
5
u
7
+
4
5
u
6
+ ···
3
5
u
3
5
a
1
=
1
5
u
7
4
5
u
6
+ ··· +
3
5
u +
8
5
2
5
u
7
8
5
u
6
+ ··· +
11
5
u
4
5
a
5
=
u
u
a
4
=
2
5
u
7
8
5
u
6
+ ··· +
21
5
u
4
5
u
7
+ 2u
6
2u
5
3u
3
+ 3u
2
+ u 1
a
8
=
1
5
u
7
4
5
u
6
+ ··· +
3
5
u
7
5
2
5
u
7
+
8
5
u
6
+ ···
6
5
u
1
5
a
11
=
u
7
+ 2u
6
2u
5
+ u
4
4u
3
+ 4u
2
u
1
5
u
7
+
1
5
u
6
+ ···
12
5
u +
3
5
a
11
=
u
7
+ 2u
6
2u
5
+ u
4
4u
3
+ 4u
2
u
1
5
u
7
+
1
5
u
6
+ ···
12
5
u +
3
5
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
6
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.680972 0.950020I
a = 1.00000
b = 1.00369 1.11783I
2.76768 + 3.32852I 2.54114 3.52732I
u = 0.680972 + 0.950020I
a = 1.00000
b = 1.00369 + 1.11783I
2.76768 3.32852I 2.54114 + 3.52732I
u = 0.270542 0.596264I
a = 1.00000
b = 0.682189 + 0.673488I
4.08734 8.79857I 1.87665 + 4.90674I
u = 0.270542 + 0.596264I
a = 1.00000
b = 0.682189 0.673488I
4.08734 + 8.79857I 1.87665 4.90674I
u = 0.774472 0.243504I
a = 1.00000
b = 0.501703 0.133216I
2.72625 0.35304I 9.09708 + 6.47245I
u = 0.774472 + 0.243504I
a = 1.00000
b = 0.501703 + 0.133216I
2.72625 + 0.35304I 9.09708 6.47245I
u = 1.17704 1.09763I
a = 1.00000
b = 1.180207 + 0.629670I
0.83890 7.80261I 8.9851 + 11.5999I
u = 1.17704 + 1.09763I
a = 1.00000
b = 1.180207 0.629670I
0.83890 + 7.80261I 8.9851 11.5999I
7
IV. I
u
4
= hu
23
+ u
22
+ · · · u 1, a 1, 1.38 × 10
13
u
22
+ 1.11 × 10
13
u
21
+
· · · + 5.67 × 10
12
b + 9.04 × 10
12
i
(i) Arc colorings
a
2
=
1
0
a
9
=
1
2.44055u
22
1.96377u
21
+ ··· 1.03149u 1.59490
a
3
=
2.44055u
22
1.96377u
21
+ ··· 1.03149u 0.594899
3.65928u
22
+ 3.48551u
21
+ ··· + 3.07183u + 5.08904
a
6
=
0
u
a
7
=
0.779768u
22
+ 0.112870u
21
+ ··· 1.67743u + 1.22181
0.158891u
22
0.393218u
21
+ ··· 0.610300u 1.40049
a
10
=
1
2.44055u
22
1.96377u
21
+ ··· 1.03149u 1.59490
a
1
=
2.44055u
22
1.96377u
21
+ ··· 1.03149u 0.594899
2.60333u
22
+ 1.94547u
21
+ ··· + 6.99938u + 4.13549
a
5
=
u
u
a
4
=
0.104674u
22
+ 0.707399u
21
+ ··· 6.72193u 0.734124
3.04793u
22
3.43339u
21
+ ··· + 8.89017u + 3.74256
a
8
=
0.527978u
22
+ 0.770017u
21
+ ··· 1.96377u + 1.47677
2.96852u
22
2.73379u
21
+ ··· + 0.932285u 2.07167
a
11
=
1.07637u
22
0.0757854u
21
+ ··· + 3.79768u + 0.507823
0.976851u
22
+ 0.697631u
21
+ ··· 10.1320u 1.67494
a
11
=
1.07637u
22
0.0757854u
21
+ ··· + 3.79768u + 0.507823
0.976851u
22
+ 0.697631u
21
+ ··· 10.1320u 1.67494
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
8
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.09737 1.14913I
a = 1.00000
b = 1.20107 + 1.07696I
3.0635 + 18.7890I 2.94689 9.73353I
u = 1.09737 + 1.14913I
a = 1.00000
b = 1.20107 1.07696I
3.0635 18.7890I 2.94689 + 9.73353I
u = 1.074707 0.486569I
a = 1.00000
b = 0.065864 + 0.250987I
6.46756 + 3.72990I 2.37255 3.19850I
u = 1.074707 + 0.486569I
a = 1.00000
b = 0.065864 0.250987I
6.46756 3.72990I 2.37255 + 3.19850I
u = 0.961692 0.218056I
a = 1.00000
b = 1.64394 + 0.75505I
6.09809 + 8.12392I 3.40597 8.83423I
u = 0.961692 + 0.218056I
a = 1.00000
b = 1.64394 0.75505I
6.09809 8.12392I 3.40597 + 8.83423I
u = 0.780512 1.128624I
a = 1.00000
b = 0.883633 + 0.620256I
1.41194 + 2.54862I 8.72632 1.31178I
u = 0.780512 + 1.128624I
a = 1.00000
b = 0.883633 0.620256I
1.41194 2.54862I 8.72632 + 1.31178I
u = 0.630153 0.156527I
a = 1.00000
b = 0.165313 1.093691I
4.82355 + 1.72572I 1.86379 3.16589I
u = 0.630153 + 0.156527I
a = 1.00000
b = 0.165313 + 1.093691I
4.82355 1.72572I 1.86379 + 3.16589I
9
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.045174 0.688125I
a = 1.00000
b = 0.408856 + 0.444035I
0.744276 + 1.012619I 5.79242 5.25340I
u = 0.045174 + 0.688125I
a = 1.00000
b = 0.408856 0.444035I
0.744276 1.012619I 5.79242 + 5.25340I
u = 0.165194 0.598626I
a = 1.00000
b = 1.45874 1.25470I
4.00620 1.06800I 20.0904 + 5.7474I
u = 0.165194 + 0.598626I
a = 1.00000
b = 1.45874 + 1.25470I
4.00620 + 1.06800I 20.0904 5.7474I
u = 0.275261 0.522880I
a = 1.00000
b = 1.39814 + 1.67424I
3.75645 9.55892I 6.8688 + 15.7902I
u = 0.275261 + 0.522880I
a = 1.00000
b = 1.39814 1.67424I
3.75645 + 9.55892I 6.8688 15.7902I
u = 0.812260
a = 1.00000
b = 0.522786
2.25842 3.07842
u = 0.91053 1.11280I
a = 1.00000
b = 1.18169 0.99617I
4.74103 7.77621I 9.99957 + 4.77400I
u = 0.91053 + 1.11280I
a = 1.00000
b = 1.18169 + 0.99617I
4.74103 + 7.77621I 9.99957 4.77400I
u = 1.043930 0.545298I
a = 1.00000
b = 0.486704 0.933953I
9.61085 + 2.02294I 3.47785 0.15643I
10
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.043930 + 0.545298I
a = 1.00000
b = 0.486704 + 0.933953I
9.61085 2.02294I 3.47785 + 0.15643I
u = 1.19821 1.01778I
a = 1.00000
b = 1.32980 0.65784I
0.41923 7.68149I 2.73500 + 7.62634I
u = 1.19821 + 1.01778I
a = 1.00000
b = 1.32980 + 0.65784I
0.41923 + 7.68149I 2.73500 7.62634I
11
V. I
u
5
= hu
82
+ 5u
81
+ · · · 61u + 11, 1.01 × 10
325
u
81
6.80 × 10
325
u
80
+
· · · + 6.31 × 10
325
b 4.00 × 10
326
, 4.16 × 10
326
u
81
3.01 × 10
327
u
80
+ · · · +
6.94 × 10
326
a 4.26 × 10
328
i
(i) Arc colorings
a
2
=
1
0
a
9
=
0.600191u
81
+ 4.33933u
80
+ ··· 323.772u + 61.4184
0.159833u
81
+ 1.07791u
80
+ ··· 21.1357u + 6.33855
a
3
=
0.877917u
81
+ 4.65768u
80
+ ··· + 13.6153u + 10.9495
1.33041u
81
+ 7.44995u
80
+ ··· 57.7314u + 26.4833
a
6
=
0
u
a
7
=
0.977666u
81
5.29968u
80
+ ··· + 96.6330u 27.7790
0.499365u
81
+ 1.72600u
80
+ ··· + 208.409u 36.5417
a
10
=
0.600191u
81
+ 4.33933u
80
+ ··· 323.772u + 61.4184
0.284186u
81
+ 2.02283u
80
+ ··· 96.1746u + 21.0607
a
1
=
1.64452u
81
8.73749u
80
+ ··· + 47.3432u 20.3745
0.995234u
81
+ 5.59444u
80
+ ··· 51.1111u + 23.7688
a
5
=
u
u
a
4
=
1.14764u
81
4.69727u
80
+ ··· 378.075u + 76.5682
1.10516u
81
+ 5.51820u
80
+ ··· + 28.2550u + 4.84552
a
8
=
0.524256u
81
+ 3.56153u
80
+ ··· 233.488u + 43.6300
0.235767u
81
+ 1.85571u
80
+ ··· 111.420u + 24.1269
a
11
=
0.866225u
81
3.81621u
80
+ ··· 202.691u + 27.4490
0.243233u
81
+ 0.984413u
80
+ ··· + 57.7163u 13.0042
a
11
=
0.866225u
81
3.81621u
80
+ ··· 202.691u + 27.4490
0.243233u
81
+ 0.984413u
80
+ ··· + 57.7163u 13.0042
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
12
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 1.63810 0.73785I
a = 0.080255 + 0.310974I
b = 0.377591 0.314083I
0.05211 4.45406I 5.2688 + 13.2582I
u = 1.63810 + 0.73785I
a = 0.080255 0.310974I
b = 0.377591 + 0.314083I
0.05211 + 4.45406I 5.2688 13.2582I
u = 1.35736 1.45054I
a = 0.128294 0.337820I
b = 0.640512 + 0.245312I
3.20535 9.84080I 7.3665 + 12.1750I
u = 1.35736 + 1.45054I
a = 0.128294 + 0.337820I
b = 0.640512 0.245312I
3.20535 + 9.84080I 7.3665 12.1750I
u = 1.26029 1.23384I
a = 0.514901 0.159626I
b = 0.586248 0.430941I
0.21627 + 5.92950I 6.37244 9.73133I
u = 1.26029 + 1.23384I
a = 0.514901 + 0.159626I
b = 0.586248 + 0.430941I
0.21627 5.92950I 6.37244 + 9.73133I
u = 1.15748 1.14271I
a = 0.864434 0.043906I
b = 1.072420 0.604646I
0.53309 + 6.66067I 5.50818 4.99627I
u = 1.15748 + 1.14271I
a = 0.864434 + 0.043906I
b = 1.072420 + 0.604646I
0.53309 6.66067I 5.50818 + 4.99627I
u = 1.15130 1.25481I
a = 0.586287 + 0.093470I
b = 1.19700 + 1.05903I
3.54374 + 4.65960I 5.91432 6.59833I
u = 1.15130 + 1.25481I
a = 0.586287 0.093470I
b = 1.19700 1.05903I
3.54374 4.65960I 5.91432 + 6.59833I
13
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 1.067347 0.558400I
a = 0.712028 0.590623I
b = 0.627557 1.077089I
3.71714 + 2.02101I 4.27581 1.59838I
u = 1.067347 + 0.558400I
a = 0.712028 + 0.590623I
b = 0.627557 + 1.077089I
3.71714 2.02101I 4.27581 + 1.59838I
u = 0.962199 0.981391I
a = 0.440609 + 0.163813I
b = 1.391077 + 0.205521I
2.42232 + 4.46231I 6.31526 4.33383I
u = 0.962199 + 0.981391I
a = 0.440609 0.163813I
b = 1.391077 0.205521I
2.42232 4.46231I 6.31526 + 4.33383I
u = 0.939641 0.738033I
a = 0.498440 0.148669I
b = 0.760971 + 0.224938I
0.05619 + 2.96133I 4.67276 + 2.55942I
u = 0.939641 + 0.738033I
a = 0.498440 + 0.148669I
b = 0.760971 0.224938I
0.05619 2.96133I 4.67276 2.55942I
u = 0.921298 0.494698I
a = 0.457676 0.362439I
b = 0.651660 0.931019I
3.80604 + 1.84265I 2.21456 1.42669I
u = 0.921298 + 0.494698I
a = 0.457676 + 0.362439I
b = 0.651660 + 0.931019I
3.80604 1.84265I 2.21456 + 1.42669I
u = 0.91626 1.16183I
a = 1.065040 + 0.114066I
b = 1.14017 1.05941I
1.61991 + 12.41906I 5.30475 9.05047I
u = 0.91626 + 1.16183I
a = 1.065040 0.114066I
b = 1.14017 + 1.05941I
1.61991 12.41906I 5.30475 + 9.05047I
14
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.81201 1.25485I
a = 0.593118 + 0.174482I
b = 0.668382 + 0.421181I
1.39039 + 1.97007I 9.76462 4.48787I
u = 0.81201 + 1.25485I
a = 0.593118 0.174482I
b = 0.668382 0.421181I
1.39039 1.97007I 9.76462 + 4.48787I
u = 0.756195 0.784225I
a = 0.791388 + 0.100656I
b = 1.32022 0.96586I
1.45241 + 4.98872I 4.83358 8.14945I
u = 0.756195 + 0.784225I
a = 0.791388 0.100656I
b = 1.32022 + 0.96586I
1.45241 4.98872I 4.83358 + 8.14945I
u = 0.557708 0.843290I
a = 1.66337 0.26519I
b = 1.19700 + 1.05903I
3.54374 + 4.65960I 5.91432 6.59833I
u = 0.557708 + 0.843290I
a = 1.66337 + 0.26519I
b = 1.19700 1.05903I
3.54374 4.65960I 5.91432 + 6.59833I
u = 0.44924 1.41654I
a = 0.531835 + 0.105664I
b = 1.17238 0.89577I
2.07268 + 5.10749I 6.99667 9.62979I
u = 0.44924 + 1.41654I
a = 0.531835 0.105664I
b = 1.17238 + 0.89577I
2.07268 5.10749I 6.99667 + 9.62979I
u = 0.315882 0.644641I
a = 0.98248 2.58704I
b = 0.640512 0.245312I
3.20535 + 9.84080I 7.3665 12.1750I
u = 0.315882 + 0.644641I
a = 0.98248 + 2.58704I
b = 0.640512 + 0.245312I
3.20535 9.84080I 7.3665 + 12.1750I
15
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.263189 0.590031I
a = 1.99397 0.74133I
b = 1.391077 + 0.205521I
2.42232 + 4.46231I 6.31526 4.33383I
u = 0.263189 + 0.590031I
a = 1.99397 + 0.74133I
b = 1.391077 0.205521I
2.42232 4.46231I 6.31526 + 4.33383I
u = 0.262673 0.885953I
a = 1.55172 0.45648I
b = 0.668382 + 0.421181I
1.39039 + 1.97007I 9.76462 4.48787I
u = 0.262673 + 0.885953I
a = 1.55172 + 0.45648I
b = 0.668382 0.421181I
1.39039 1.97007I 9.76462 + 4.48787I
u = 0.261213 1.016348I
a = 0.315896 + 1.170970I
b = 0.378284 0.094720I
0.195730 0.062095I 6.22952 0.53803I
u = 0.261213 + 1.016348I
a = 0.315896 1.170970I
b = 0.378284 + 0.094720I
0.195730 + 0.062095I 6.22952 + 0.53803I
u = 0.215879 0.748644I
a = 0.670369 0.088106I
b = 1.36164 + 1.17423I
1.45360 + 3.78207I 15.3405 7.1796I
u = 0.215879 + 0.748644I
a = 0.670369 + 0.088106I
b = 1.36164 1.17423I
1.45360 3.78207I 15.3405 + 7.1796I
u = 0.147826 0.403018I
a = 1.72835 + 1.77188I
b = 0.298326 + 1.021491I
0.116913 + 1.387899I 6.84622 0.01500I
u = 0.147826 + 0.403018I
a = 1.72835 1.77188I
b = 0.298326 1.021491I
0.116913 1.387899I 6.84622 + 0.01500I
16
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.016198 0.633274I
a = 2.36629 + 1.68444I
b = 0.798131 + 0.112066I
1.92162 + 3.53381I 13.5625 6.1581I
u = 0.016198 + 0.633274I
a = 2.36629 1.68444I
b = 0.798131 0.112066I
1.92162 3.53381I 13.5625 + 6.1581I
u = 0.042051 0.442701I
a = 2.08868 + 3.69613I
b = 0.607579 + 0.018215I
3.37975 + 0.08879I 21.5224 1.1280I
u = 0.042051 + 0.442701I
a = 2.08868 3.69613I
b = 0.607579 0.018215I
3.37975 0.08879I 21.5224 + 1.1280I
u = 0.078758 0.520888I
a = 1.46639 0.19273I
b = 1.36164 1.17423I
1.45360 3.78207I 15.3405 + 7.1796I
u = 0.078758 + 0.520888I
a = 1.46639 + 0.19273I
b = 1.36164 + 1.17423I
1.45360 + 3.78207I 15.3405 7.1796I
u = 0.175648 0.247920I
a = 1.06586 + 3.10648I
b = 0.717655 + 1.200363I
5.03352 + 3.32205I 1.56470 2.95701I
u = 0.175648 + 0.247920I
a = 1.06586 3.10648I
b = 0.717655 1.200363I
5.03352 3.32205I 1.56470 + 2.95701I
u = 0.242358 0.560326I
a = 1.34283 1.06340I
b = 0.651660 + 0.931019I
3.80604 1.84265I 2.21456 + 1.42669I
u = 0.242358 + 0.560326I
a = 1.34283 + 1.06340I
b = 0.651660 0.931019I
3.80604 + 1.84265I 2.21456 1.42669I
17
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.358633 0.507561I
a = 1.84236 0.54951I
b = 0.760971 0.224938I
0.05619 2.96133I 4.67276 2.55942I
u = 0.358633 + 0.507561I
a = 1.84236 + 0.54951I
b = 0.760971 + 0.224938I
0.05619 + 2.96133I 4.67276 + 2.55942I
u = 0.360917 0.450190I
a = 0.77807 3.01490I
b = 0.377591 0.314083I
0.05211 4.45406I 5.2688 + 13.2582I
u = 0.360917 + 0.450190I
a = 0.77807 + 3.01490I
b = 0.377591 + 0.314083I
0.05211 + 4.45406I 5.2688 13.2582I
u = 0.388600 0.705895I
a = 1.80888 + 0.35939I
b = 1.17238 + 0.89577I
2.07268 5.10749I 6.99667 + 9.62979I
u = 0.388600 + 0.705895I
a = 1.80888 0.35939I
b = 1.17238 0.89577I
2.07268 + 5.10749I 6.99667 9.62979I
u = 0.430176 1.027996I
a = 0.831984 0.690126I
b = 0.627557 + 1.077089I
3.71714 2.02101I 4.27581 + 1.59838I
u = 0.430176 + 1.027996I
a = 0.831984 + 0.690126I
b = 0.627557 1.077089I
3.71714 + 2.02101I 4.27581 1.59838I
u = 0.451970 0.836483I
a = 1.77183 0.54929I
b = 0.586248 + 0.430941I
0.21627 5.92950I 6.37244 + 9.73133I
u = 0.451970 + 0.836483I
a = 1.77183 + 0.54929I
b = 0.586248 0.430941I
0.21627 + 5.92950I 6.37244 9.73133I
18
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.458604 0.958483I
a = 0.282099 0.289204I
b = 0.298326 + 1.021491I
0.116913 + 1.387899I 6.84622 0.01500I
u = 0.458604 + 0.958483I
a = 0.282099 + 0.289204I
b = 0.298326 1.021491I
0.116913 1.387899I 6.84622 + 0.01500I
u = 0.662408 1.096044I
a = 0.464929 + 0.885348I
b = 0.693222
1.00058 4.42993
u = 0.662408 + 1.096044I
a = 0.464929 0.885348I
b = 0.693222
1.00058 4.42993
u = 0.677380 0.544511I
a = 1.243487 + 0.158158I
b = 1.32022 + 0.96586I
1.45241 4.98872I 4.83358 + 8.14945I
u = 0.677380 + 0.544511I
a = 1.243487 0.158158I
b = 1.32022 0.96586I
1.45241 + 4.98872I 4.83358 8.14945I
u = 0.889090 0.427117I
a = 1.54899 0.85472I
b = 0.461525 0.930289I
6.68388 9.32368I 1.65029 + 9.33817I
u = 0.889090 + 0.427117I
a = 1.54899 + 0.85472I
b = 0.461525 + 0.930289I
6.68388 + 9.32368I 1.65029 9.33817I
u = 0.950394 1.038615I
a = 1.153850 0.058607I
b = 1.072420 + 0.604646I
0.53309 6.66067I 5.50818 + 4.99627I
u = 0.950394 + 1.038615I
a = 1.153850 + 0.058607I
b = 1.072420 0.604646I
0.53309 + 6.66067I 5.50818 4.99627I
19
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.957374 0.281399I
a = 0.098816 + 0.288003I
b = 0.717655 1.200363I
5.03352 3.32205I 1.56470 + 2.95701I
u = 0.957374 + 0.281399I
a = 0.098816 0.288003I
b = 0.717655 + 1.200363I
5.03352 + 3.32205I 1.56470 2.95701I
u = 1.01213 1.42153I
a = 0.494897 + 0.273080I
b = 0.461525 0.930289I
6.68388 9.32368I 1.65029 + 9.33817I
u = 1.01213 + 1.42153I
a = 0.494897 0.273080I
b = 0.461525 + 0.930289I
6.68388 + 9.32368I 1.65029 9.33817I
u = 1.02838 1.52579I
a = 0.280477 0.199658I
b = 0.798131 + 0.112066I
1.92162 + 3.53381I 13.5625 6.1581I
u = 1.02838 + 1.52579I
a = 0.280477 + 0.199658I
b = 0.798131 0.112066I
1.92162 3.53381I 13.5625 + 6.1581I
u = 1.107597 0.626934I
a = 0.214755 0.796057I
b = 0.378284 0.094720I
0.195730 0.062095I 6.22952 0.53803I
u = 1.107597 + 0.626934I
a = 0.214755 + 0.796057I
b = 0.378284 + 0.094720I
0.195730 + 0.062095I 6.22952 + 0.53803I
u = 1.10838 1.13288I
a = 0.928284 + 0.099420I
b = 1.14017 + 1.05941I
1.61991 12.41906I 5.30475 + 9.05047I
u = 1.10838 + 1.13288I
a = 0.928284 0.099420I
b = 1.14017 1.05941I
1.61991 + 12.41906I 5.30475 9.05047I
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 1.54845 1.08008I
a = 0.115883 + 0.205068I
b = 0.607579 0.018215I
3.37975 0.08879I 21.5224 + 1.1280I
u = 1.54845 + 1.08008I
a = 0.115883 0.205068I
b = 0.607579 + 0.018215I
3.37975 + 0.08879I 21.5224 1.1280I
20
VI. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
2
u + 1)(u
5
u
3
+ u
2
+ u 1)
2
(u
8
2u
7
+ 4u
6
+ 2u
5
+ 6u
4
10u
3
+ 6u
2
3u + 1)
(u
23
+ 22u
22
+ ··· + 7424u + 512)(u
82
14u
81
+ ··· 26u + 1)
c
2
(u 1)
2
(1 3u
2
+ 2u
4
+ u
5
)
2
(u
8
2u
7
+ ··· + 3u + 1)
(u
23
+ 19u
22
+ ··· 96u 16)(u
82
16u
81
+ ··· 4u + 1)
c
3
(u
2
+ u + 1)(u
8
+ u
7
+ 4u
6
+ 3u
5
+ 6u
4
+ 4u
3
+ 3u
2
+ 2u + 1)
(u
10
+ 3u
9
+ ··· + 5u + 1)(u
23
+ 10u
21
+ ··· + 6u + 1)
(u
82
+ 4u
81
+ ··· + 1581u + 583)
c
4
(u
2
u + 1)(u
5
u
4
u
3
+ u
2
1)
2
(u
8
u
7
u
6
+ 18u
4
43u
3
+ 40u
2
18u + 5)
(u
23
19u
22
+ ··· 960u + 256)(u
82
+ 22u
81
+ ··· + 2024u + 121)
c
5
(u
2
u + 1)(u
8
+ 2u
7
+ 2u
6
+ u
5
+ 4u
4
+ 4u
3
+ u
2
+ u + 1)
(u
10
2u
9
+ 3u
8
3u
7
+ 5u
6
6u
5
+ 3u
4
3u
3
+ 3u
2
u + 1)
(u
23
+ u
22
+ ··· u 1)(u
82
+ 5u
81
+ ··· 61u + 11)
c
6
u
2
(u
8
+ u
7
2u
6
u
5
+ 5u
4
+ 2u
3
5u
2
+ 4)
(u
10
2u
9
3u
8
+ 4u
7
+ 7u
6
u
5
7u
4
4u
3
+ 2u
2
+ 3u + 1)
(u
23
u
22
+ ··· + 4u + 4)(u
82
+ u
81
+ ··· 5311u + 961)
c
7
(u
2
u + 1)(u
8
u
7
+ 4u
6
3u
5
+ 6u
4
4u
3
+ 3u
2
2u + 1)
(u
10
3u
9
+ ··· 5u + 1)(u
23
+ 10u
21
+ ··· + 6u + 1)
(u
82
+ 4u
81
+ ··· + 1581u + 583)
c
8
u
2
(u
8
+ u
7
2u
6
u
5
+ 5u
4
+ 2u
3
5u
2
+ 4)
(u
10
2u
9
3u
8
+ 4u
7
+ 7u
6
u
5
7u
4
4u
3
+ 2u
2
+ 3u + 1)
(u
23
u
22
+ ··· + 4u + 4)(u
82
+ u
81
+ ··· 5311u + 961)
c
9
(u
2
u + 1)(u
8
+ 2u
7
+ 2u
6
+ u
5
+ 4u
4
+ 4u
3
+ u
2
+ u + 1)
(u
10
2u
9
+ 3u
8
3u
7
+ 5u
6
6u
5
+ 3u
4
3u
3
+ 3u
2
u + 1)
(u
23
+ u
22
+ ··· u 1)(u
82
+ 5u
81
+ ··· 61u + 11)
c
10
(u
2
+ u + 1)(u
8
+ u
7
+ 4u
6
+ 3u
5
+ 6u
4
+ 4u
3
+ 3u
2
+ 2u + 1)
(u
10
+ 3u
9
+ ··· + 5u + 1)(u
23
+ 10u
21
+ ··· + 6u + 1)
(u
82
+ 4u
81
+ ··· + 1581u + 583)
c
11
(u
2
u + 1)(u
8
u
7
+ 4u
6
3u
5
+ 6u
4
4u
3
+ 3u
2
2u + 1)
(u
10
3u
9
+ ··· 5u + 1)(u
23
+ 10u
21
+ ··· + 6u + 1)
(u
82
+ 4u
81
+ ··· + 1581u + 583)
21
VII. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
2
+ y + 1)(y
5
2y
4
+ 3y
3
3y
2
+ 3y 1)
2
(y
8
+ 4y
7
+ 36y
6
+ 16y
5
+ 114y
4
8y
3
12y
2
+ 3y + 1)
(y
23
2y
22
+ ··· + 11599872y 262144)
(y
82
+ 22y
81
+ ··· 18y + 1)
c
2
(y 1)
2
(y
5
4y
4
+ 12y
3
13y
2
+ 6y 1)
2
(y
8
2y
7
+ 9y
6
14y
5
+ 28y
4
19y
3
+ 19y
2
7y + 1)
(y
23
5y
22
+ ··· 6016y 256)(y
82
16y
81
+ ··· 60y + 1)
c
3
(y
2
+ y + 1)(y
8
+ 7y
7
+ 22y
6
+ 37y
5
+ 34y
4
+ 16y
3
+ 5y
2
+ 2y + 1)
(y
10
+ 11y
9
+ 46y
8
+ 91y
7
+ 84y
6
+ 8y
5
46y
4
24y
3
+ 4y
2
+ 3y + 1)
(y
23
+ 20y
22
+ ··· + 20y 1)
(y
82
+ 58y
81
+ ··· + 8444515y + 339889)
c
4
(y
2
+ y + 1)(y
5
3y
4
+ 3y
3
3y
2
+ 2y 1)
2
(y
8
3y
7
+ 37y
6
42y
5
+ 218y
4
419y
3
+ 232y
2
+ 76y + 25)
(y
23
7y
22
+ ··· + 1011712y 65536)
(y
82
+ 26y
81
+ ··· + 459316y + 14641)
c
5
(y
2
+ y + 1)(y
8
+ 8y
6
+ y
5
+ 10y
4
6y
3
+ y
2
+ y + 1)
(y
10
+ 2y
9
+ 7y
8
+ 3y
7
+ y
6
8y
5
+ 3y
4
+ 7y
3
+ 9y
2
+ 5y + 1)
(y
23
3y
22
+ ··· 3y 1)(y
82
+ 13y
81
+ ··· + 6949y + 121)
c
6
y
2
(y
8
5y
7
+ 16y
6
35y
5
+ 57y
4
70y
3
+ 65y
2
40y + 16)
(y
10
10y
9
+ ··· 5y + 1)(y
23
9y
22
+ ··· + 80y 16)
(y
82
31y
81
+ ··· 8782989y + 923521)
c
7
(y
2
+ y + 1)(y
8
+ 7y
7
+ 22y
6
+ 37y
5
+ 34y
4
+ 16y
3
+ 5y
2
+ 2y + 1)
(y
10
+ 11y
9
+ 46y
8
+ 91y
7
+ 84y
6
+ 8y
5
46y
4
24y
3
+ 4y
2
+ 3y + 1)
(y
23
+ 20y
22
+ ··· + 20y 1)
(y
82
+ 58y
81
+ ··· + 8444515y + 339889)
c
8
y
2
(y
8
5y
7
+ 16y
6
35y
5
+ 57y
4
70y
3
+ 65y
2
40y + 16)
(y
10
10y
9
+ ··· 5y + 1)(y
23
9y
22
+ ··· + 80y 16)
(y
82
31y
81
+ ··· 8782989y + 923521)
c
9
(y
2
+ y + 1)(y
8
+ 8y
6
+ y
5
+ 10y
4
6y
3
+ y
2
+ y + 1)
(y
10
+ 2y
9
+ 7y
8
+ 3y
7
+ y
6
8y
5
+ 3y
4
+ 7y
3
+ 9y
2
+ 5y + 1)
(y
23
3y
22
+ ··· 3y 1)(y
82
+ 13y
81
+ ··· + 6949y + 121)
c
10
(y
2
+ y + 1)(y
8
+ 7y
7
+ 22y
6
+ 37y
5
+ 34y
4
+ 16y
3
+ 5y
2
+ 2y + 1)
(y
10
+ 11y
9
+ 46y
8
+ 91y
7
+ 84y
6
+ 8y
5
46y
4
24y
3
+ 4y
2
+ 3y + 1)
(y
23
+ 20y
22
+ ··· + 20y 1)
(y
82
+ 58y
81
+ ··· + 8444515y + 339889)
c
11
(y
2
+ y + 1)(y
8
+ 7y
7
+ 22y
6
+ 37y
5
+ 34y
4
+ 16y
3
+ 5y
2
+ 2y + 1)
(y
10
+ 11y
9
+ 46y
8
+ 91y
7
+ 84y
6
+ 8y
5
46y
4
24y
3
+ 4y
2
+ 3y + 1)
(y
23
+ 20y
22
+ ··· + 20y 1)
(y
82
+ 58y
81
+ ··· + 8444515y + 339889)
22