11a
351
(K11a
351
)
1
Arc Sequences
7 6 1 10 11 9 4 3 2 5 8
Solving Sequence
5,11 6,8
1 10 4 3 9 2 7
c
5
c
11
c
10
c
4
c
3
c
8
c
2
c
7
c
1
, c
6
, c
9
Representation Ideals
I =
9
\
i=1
I
u
i
1
The knot diagram image is adapter from “C. Livingston and A. H. Mo ore, KnotInfo: Table of Knot
Invariants, http://www.indiana.edu/ knotinfo”
1
I
u
1
= hu 1, b, a + 1i
I
u
2
= hu
5
+ u
4
+ 8u
3
+ 3u
2
+ 3u + 1, 4u
4
+ 2u
3
35u
2
+ 29a + 26u 51,
4u
4
+ 2u
3
35u
2
+ 29b + 26u 22i
I
u
3
= hu
12
+ 2u
11
+ 17u
10
+ 26u
9
+ 99u
8
+ 100u
7
+ 199u
6
+ 139u
5
+ 140u
4
+ 72u
3
+ 26u
2
+ 5u + 1,
68352179u
11
150643728u
10
+ ··· + 238823623a 690373802,
68352179u
11
150643728u
10
+ ··· + 238823623b 451550179i
I
u
4
= hu
20
u
19
+ ··· + u + 1, 1.71226 × 10
20
u
19
2.58611 × 10
20
u
18
+ ··· + 3.47691 × 10
20
a + 8.46760 × 10
20
,
1.71226 × 10
20
u
19
2.58611 × 10
20
u
18
+ ··· + 3.47691 × 10
20
b + 4.99069 × 10
20
i
I
u
5
= hu
16
u
15
+ ··· 3u + 1, 2566363708u
15
+ 1502488752u
14
+ ··· + 1877848174a 245728543,
2566363708u
15
+ 1502488752u
14
+ ··· + 1877848174b + 1632119631i
I
u
6
= hu
5
2u
4
+ 9u
3
21u
2
+ 23u 11, 20u
4
31u
3
+ 183u
2
+ 113b 332u + 288,
171u
4
+ 56u
3
1220u
2
+ 1243a + 1347u 677i
I
u
7
= hu
5
3u
4
+ 7u
3
14u
2
+ 3u 1, 15u
4
+ 41u
3
73u
2
+ 79b + 180u + 3,
107u
4
+ 303u
3
684u
2
+ 79a + 1363u 26i
I
u
8
= hu
20
+ 5u
19
+ ··· + 12884u + 2659,
9.39787 × 10
40
u
19
+ 4.39559 × 10
41
u
18
+ ··· + 3.29482 × 10
44
b + 5.41381 × 10
44
,
1.14252 × 10
49
u
19
+ 5.15624 × 10
49
u
18
+ ··· + 7.20235 × 10
51
a + 4.69806 × 10
52
i
I
u
9
= hu
40
5u
39
+ ··· + 1394u + 223,
8.03391 × 10
150
u
39
+ 3.81842 × 10
151
u
38
+ ··· + 3.02285 × 10
153
b 5.95039 × 10
153
,
3.27663 × 10
178
u
39
+ 1.75397 × 10
179
u
38
+ ··· + 5.84389 × 10
180
a + 3.24376 × 10
181
i
There are 9 irreducible components with 124 representations.
2
I. I
u
1
= hu 1, b, a + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
1
0
a
6
=
1
0
a
8
=
0
1
a
1
=
1
1
a
10
=
1
0
a
4
=
1
0
a
3
=
0
1
a
9
=
0
1
a
2
=
1
1
a
7
=
1
1
a
7
=
1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
3
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.00000
a = 1.00000
b = 0
3.28987 12.0000
4
II. I
u
2
= hu
5
+ u
4
+ 8u
3
+ 3u
2
+ 3u + 1, 4u
4
+ 2u
3
35u
2
+ 29a + 26u
51, 4u
4
+ 2u
3
35u
2
+ 29b + 26u 22i
(i) Arc colorings
a
5
=
1
0
a
11
=
0.137931u
4
0.0689655u
3
+ ··· 0.896552u + 1.75862
0.137931u
4
0.0689655u
3
+ ··· 0.896552u + 0.758621
a
6
=
0.586207u
4
0.206897u
3
+ ··· + 1.31034u 0.724138
0.448276u
4
0.275862u
3
+ ··· + 0.413793u 0.965517
a
8
=
0
u
a
1
=
0.137931u
4
0.0689655u
3
+ ··· 0.896552u + 1.75862
0.448276u
4
+ 0.275862u
3
+ ··· 0.413793u + 0.965517
a
10
=
1
0.137931u
4
0.0689655u
3
+ ··· 0.896552u + 0.758621
a
4
=
0.137931u
4
0.0689655u
3
+ ··· 0.896552u + 1.75862
0.448276u
4
+ 0.275862u
3
+ ··· 0.413793u + 0.965517
a
3
=
0.137931u
4
0.0689655u
3
+ ··· 0.896552u + 1.75862
0.448276u
4
+ 0.275862u
3
+ ··· 0.413793u + 0.965517
a
9
=
0.586207u
4
0.206897u
3
+ ··· + 1.31034u 0.724138
0.448276u
4
0.275862u
3
+ ··· + 0.413793u 0.965517
a
2
=
0.482759u
4
0.758621u
3
+ ··· 2.86207u + 0.344828
u
a
7
=
0.586207u
4
0.206897u
3
+ ··· + 1.31034u 0.724138
0.448276u
4
0.275862u
3
+ ··· + 0.413793u 0.965517
a
7
=
0.586207u
4
0.206897u
3
+ ··· + 1.31034u 0.724138
0.448276u
4
0.275862u
3
+ ··· + 0.413793u 0.965517
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
5
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.345770
a = 2.21774
b = 1.21774
2.40108 3.48114
u = 0.32314 2.69669I
a = 0.418784 0.219165I
b = 1.41878 0.21917I
5.87256 + 4.40083I 6.74431 3.49859I
u = 0.32314 + 2.69669I
a = 0.418784 + 0.219165I
b = 1.41878 + 0.21917I
5.87256 4.40083I 6.74431 + 3.49859I
u = 0.003977 0.626138I
a = 1.30992 + 0.54991I
b = 0.309916 + 0.549911I
0.32910 + 1.53058I 2.51511 4.43065I
u = 0.003977 + 0.626138I
a = 1.30992 0.54991I
b = 0.309916 0.549911I
0.32910 1.53058I 2.51511 + 4.43065I
6
III.
I
u
3
= hu
12
+ 2u
11
+ · · · + 5u + 1, 6.84 × 10
7
u
11
1.51 × 10
8
u
10
+ · · · + 2.39 ×
10
8
a6.90×10
8
, 6.84×10
7
u
11
1.51×10
8
u
10
+· · ·+2.39×10
8
b4.52×10
8
i
(i) Arc colorings
a
5
=
1
0
a
11
=
0.286204u
11
+ 0.630774u
10
+ ··· + 8.27928u + 2.89073
0.286204u
11
+ 0.630774u
10
+ ··· + 8.27928u + 1.89073
a
6
=
0.884257u
11
1.70277u
10
+ ··· 16.0348u 1.66088
0.598053u
11
1.07199u
10
+ ··· 7.75548u 0.770150
a
8
=
0
u
a
1
=
0.286204u
11
+ 0.630774u
10
+ ··· + 8.27928u + 2.89073
0.307619u
11
+ 0.638949u
10
+ ··· + 7.70124u + 1.83236
a
10
=
1
0.286204u
11
+ 0.630774u
10
+ ··· + 8.27928u + 1.89073
a
4
=
0.286204u
11
+ 0.630774u
10
+ ··· + 8.27928u + 2.89073
0.598053u
11
+ 1.07199u
10
+ ··· + 7.75548u + 0.770150
a
3
=
0.359081u
11
1.03338u
10
+ ··· 15.7101u 1.26569
0.0436767u
11
0.125722u
10
+ ··· 4.33700u 0.314565
a
9
=
1.18661u
11
2.13471u
10
+ ··· 11.1635u + 0.0137134
0.484606u
11
0.798352u
10
+ ··· 3.66254u 0.181774
a
2
=
0.0573767u
11
+ 0.159086u
10
+ ··· + 7.50553u + 2.62533
0.238504u
11
+ 0.480376u
10
+ ··· + 6.94675u + 1.18661
a
7
=
0.00738062u
11
+ 0.0149070u
10
+ ··· 0.300698u 1.17046
0.271539u
11
0.602272u
10
+ ··· 3.80728u 0.955484
a
7
=
0.00738062u
11
+ 0.0149070u
10
+ ··· 0.300698u 1.17046
0.271539u
11
0.602272u
10
+ ··· 3.80728u 0.955484
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
7
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.78384 2.32929I
a = 0.509461
b = 1.50946
10.0009 7.28456
u = 0.78384 + 2.32929I
a = 0.509461
b = 1.50946
10.0009 7.28456
u = 0.318941 0.252664I
a = 1.96286
b = 0.962859
2.30081 4.68187
u = 0.318941 + 0.252664I
a = 1.96286
b = 0.962859
2.30081 4.68187
u = 0.153949 1.343488I
a = 0.463293 + 0.400015I
b = 1.46329 + 0.40002I
3.78738 10.11613I 0.74000 + 10.55076I
u = 0.153949 + 1.343488I
a = 0.463293 0.400015I
b = 1.46329 0.40002I
3.78738 + 10.11613I 0.74000 10.55076I
u = 0.034024 0.270004I
a = 1.23659 1.06770I
b = 0.236594 1.067696I
1.71358 4.97819I 0.7768 + 21.8821I
u = 0.034024 + 0.270004I
a = 1.23659 + 1.06770I
b = 0.236594 + 1.067696I
1.71358 + 4.97819I 0.7768 21.8821I
u = 0.069174 0.990048I
a = 1.23659 + 1.06770I
b = 0.236594 + 1.067696I
1.71358 + 4.97819I 0.7768 21.8821I
u = 0.069174 + 0.990048I
a = 1.23659 1.06770I
b = 0.236594 1.067696I
1.71358 4.97819I 0.7768 + 21.8821I
8
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.22158 2.72899I
a = 0.463293 0.400015I
b = 1.46329 0.40002I
3.78738 + 10.11613I 0.74000 10.55076I
u = 0.22158 + 2.72899I
a = 0.463293 + 0.400015I
b = 1.46329 + 0.40002I
3.78738 10.11613I 0.74000 + 10.55076I
9
IV.
I
u
4
= hu
20
u
19
+· · ·+u+1, 1.71×10
20
u
19
2.59×10
20
u
18
+· · ·+3.48×10
20
a+
8.47 × 10
20
, 1.71 × 10
20
u
19
2.59 × 10
20
u
18
+ · · · + 3.48 × 10
20
b + 4.99 × 10
20
i
(i) Arc colorings
a
5
=
1
0
a
11
=
0.492467u
19
+ 0.743796u
18
+ ··· 1.18254u 2.43538
0.492467u
19
+ 0.743796u
18
+ ··· 1.18254u 1.43538
a
6
=
1.13633u
19
+ 1.79172u
18
+ ··· 1.78305u 2.05637
0.643863u
19
+ 1.04793u
18
+ ··· 0.600503u 1.62099
a
8
=
0
u
a
1
=
0.492467u
19
+ 0.743796u
18
+ ··· 1.18254u 2.43538
0.552018u
19
+ 0.797036u
18
+ ··· 0.941407u 1.68671
a
10
=
1
0.492467u
19
+ 0.743796u
18
+ ··· 1.18254u 1.43538
a
4
=
0.492467u
19
0.743796u
18
+ ··· + 1.18254u + 2.43538
0.643863u
19
1.04793u
18
+ ··· + 0.600503u + 1.62099
a
3
=
1.63247u
19
2.36846u
18
+ ··· 1.32768u + 4.01993
1.77032u
19
2.55863u
18
+ ··· 1.26703u + 3.19593
a
9
=
1.52019u
19
+ 3.37139u
18
+ ··· 0.132031u 3.78099
2.01266u
19
+ 4.11519u
18
+ ··· 1.31458u 4.21637
a
2
=
2.52050u
19
2.98118u
18
+ ··· 7.31818u + 2.31535
2.52050u
19
2.98118u
18
+ ··· 7.31818u + 2.31535
a
7
=
0.906723u
19
+ 1.25647u
18
+ ··· + 3.86295u 1.62880
0.925415u
19
+ 1.44539u
18
+ ··· + 3.56739u 1.88997
a
7
=
0.906723u
19
+ 1.25647u
18
+ ··· + 3.86295u 1.62880
0.925415u
19
+ 1.44539u
18
+ ··· + 3.56739u 1.88997
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
10
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.648079 0.130258I
a = 2.51664 0.24779I
b = 1.51664 0.24779I
2.89253 + 0.54689I 18.6210 11.9306I
u = 0.648079 + 0.130258I
a = 2.51664 + 0.24779I
b = 1.51664 + 0.24779I
2.89253 0.54689I 18.6210 + 11.9306I
u = 0.616396 0.173000I
a = 2.24914 0.01700I
b = 1.249136 0.017001I
0.24582 3.85817I 5.50469 + 2.33081I
u = 0.616396 + 0.173000I
a = 2.24914 + 0.01700I
b = 1.249136 + 0.017001I
0.24582 + 3.85817I 5.50469 2.33081I
u = 0.246079 0.371958I
a = 0.753960 + 0.816549I
b = 0.246040 + 0.816549I
1.82255 + 4.54196I 4.29864 3.11401I
u = 0.246079 + 0.371958I
a = 0.753960 0.816549I
b = 0.246040 0.816549I
1.82255 4.54196I 4.29864 + 3.11401I
u = 0.15826 4.25162I
a = 0.249136 0.017001I
b = 1.249136 0.017001I
0.24582 + 3.85817I 5.50469 2.33081I
u = 0.15826 + 4.25162I
a = 0.249136 + 0.017001I
b = 1.249136 + 0.017001I
0.24582 3.85817I 5.50469 + 2.33081I
u = 0.043320 0.817620I
a = 0.516637 + 0.247787I
b = 1.51664 + 0.24779I
2.89253 + 0.54689I 18.6210 11.9306I
u = 0.043320 + 0.817620I
a = 0.516637 0.247787I
b = 1.51664 0.24779I
2.89253 0.54689I 18.6210 + 11.9306I
11
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.248043 0.891881I
a = 1.24604 0.81655I
b = 0.246040 0.816549I
1.82255 + 4.54196I 4.29864 3.11401I
u = 0.248043 + 0.891881I
a = 1.24604 + 0.81655I
b = 0.246040 + 0.816549I
1.82255 4.54196I 4.29864 + 3.11401I
u = 0.26038 1.64076I
a = 0.374996 + 0.132008I
b = 0.625004 + 0.132008I
2.73306 + 4.26272I 8.25212 5.64920I
u = 0.26038 + 1.64076I
a = 0.374996 0.132008I
b = 0.625004 0.132008I
2.73306 4.26272I 8.25212 + 5.64920I
u = 0.454552 0.091918I
a = 2.41041 + 0.23471I
b = 1.41041 + 0.23471I
3.55383 7.96405I 2.92507 + 6.02428I
u = 0.454552 + 0.091918I
a = 2.41041 0.23471I
b = 1.41041 0.23471I
3.55383 + 7.96405I 2.92507 6.02428I
u = 0.596880 0.358841I
a = 1.62500 0.13201I
b = 0.625004 0.132008I
2.73306 + 4.26272I 8.25212 5.64920I
u = 0.596880 + 0.358841I
a = 1.62500 + 0.13201I
b = 0.625004 + 0.132008I
2.73306 4.26272I 8.25212 + 5.64920I
u = 0.65228 2.99170I
a = 0.410411 + 0.234711I
b = 1.41041 + 0.23471I
3.55383 + 7.96405I 2.92507 6.02428I
u = 0.65228 + 2.99170I
a = 0.410411 0.234711I
b = 1.41041 0.23471I
3.55383 7.96405I 2.92507 + 6.02428I
12
V.
I
u
5
= hu
16
u
15
+ · · · 3u + 1, 2.57 × 10
9
u
15
+ 1.50 × 10
9
u
14
+ · · · + 1.88 ×
10
9
a2.46×10
8
, 2.57×10
9
u
15
+1.50×10
9
u
14
+· · ·+1.88×10
9
b+1.63×10
9
i
(i) Arc colorings
a
5
=
1
0
a
11
=
1.36665u
15
0.800112u
14
+ ··· + 2.15145u + 0.130856
1.36665u
15
0.800112u
14
+ ··· + 2.15145u 0.869144
a
6
=
1.53692u
15
+ 1.07980u
14
+ ··· + 3.31039u + 0.0941071
0.170265u
15
+ 0.279692u
14
+ ··· + 5.46184u 1.77504
a
8
=
0
u
a
1
=
1.36665u
15
0.800112u
14
+ ··· + 2.15145u + 0.130856
1.66883u
15
0.930857u
14
+ ··· + 2.48442u 1.43568
a
10
=
1
1.36665u
15
0.800112u
14
+ ··· + 2.15145u 0.869144
a
4
=
1.36665u
15
0.800112u
14
+ ··· + 2.15145u + 0.130856
0.170265u
15
0.279692u
14
+ ··· 5.46184u + 1.77504
a
3
=
0.778246u
15
+ 1.87237u
14
+ ··· 12.0611u + 2.23330
0.550644u
15
+ 0.969972u
14
+ ··· 5.16501u + 0.466437
a
9
=
0.0236521u
15
0.184422u
14
+ ··· + 0.252546u 0.0964318
1.66883u
15
+ 0.930857u
14
+ ··· 2.48442u + 1.43568
a
2
=
0.337029u
15
+ 0.615551u
14
+ ··· 6.61025u + 1.59660
u
a
7
=
1.02365u
15
0.815578u
14
+ ··· + 9.74745u 2.90357
0.550644u
15
0.969972u
14
+ ··· + 5.16501u 0.466437
a
7
=
1.02365u
15
0.815578u
14
+ ··· + 9.74745u 2.90357
0.550644u
15
0.969972u
14
+ ··· + 5.16501u 0.466437
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
13
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.40910 2.85717I
a = 0.475270 + 0.355022I
b = 1.47527 + 0.35502I
2.8802 18.5253I 0.82769 + 9.63606I
u = 0.40910 + 2.85717I
a = 0.475270 0.355022I
b = 1.47527 0.35502I
2.8802 + 18.5253I 0.82769 9.63606I
u = 0.39820 1.78676I
a = 0.384083 0.305801I
b = 1.38408 0.30580I
5.25768 + 4.77897I 4.31247 4.75614I
u = 0.39820 + 1.78676I
a = 0.384083 + 0.305801I
b = 1.38408 + 0.30580I
5.25768 4.77897I 4.31247 + 4.75614I
u = 0.182982 0.919584I
a = 1.35539 0.91102I
b = 0.355391 0.911015I
2.9800 13.9622I 2.59981 + 9.26713I
u = 0.182982 + 0.919584I
a = 1.35539 + 0.91102I
b = 0.355391 + 0.911015I
2.9800 + 13.9622I 2.59981 9.26713I
u = 0.145602 0.417872I
a = 1.80466 + 0.91761I
b = 0.804658 + 0.917611I
0.76511 + 3.23091I 8.87467 5.88690I
u = 0.145602 + 0.417872I
a = 1.80466 0.91761I
b = 0.804658 0.917611I
0.76511 3.23091I 8.87467 + 5.88690I
u = 0.103948 0.508572I
a = 1.222025 + 0.535377I
b = 0.222025 + 0.535377I
0.27480 + 1.44128I 1.93375 5.30960I
u = 0.103948 + 0.508572I
a = 1.222025 0.535377I
b = 0.222025 0.535377I
0.27480 1.44128I 1.93375 + 5.30960I
14
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.53821 2.04029I
a = 0.616224 0.035120I
b = 1.61622 0.03512I
8.29097 + 6.33547I 5.46130 6.31546I
u = 0.53821 + 2.04029I
a = 0.616224 + 0.035120I
b = 1.61622 + 0.03512I
8.29097 6.33547I 5.46130 + 6.31546I
u = 0.563286 0.312048I
a = 1.91535 0.71600I
b = 0.915347 0.716000I
1.34679 + 8.40080I 0.52134 6.47139I
u = 0.563286 + 0.312048I
a = 1.91535 + 0.71600I
b = 0.915347 + 0.716000I
1.34679 8.40080I 0.52134 + 6.47139I
u = 0.638329 0.103945I
a = 0.178156 0.590437I
b = 0.821844 0.590437I
2.56459 + 2.34570I 6.28872 0.46963I
u = 0.638329 + 0.103945I
a = 0.178156 + 0.590437I
b = 0.821844 + 0.590437I
2.56459 2.34570I 6.28872 + 0.46963I
15
VI. I
u
6
= hu
5
2u
4
+ 9u
3
21u
2
+ 23u 11, 20u
4
31u
3
+ 183u
2
+ 113b
332u + 288, 171u
4
+ 56u
3
+ · · · + 1243a 677i
(i) Arc colorings
a
5
=
1
0
a
11
=
0.137570u
4
0.0450523u
3
+ ··· 1.08367u + 0.544650
0.176991u
4
+ 0.274336u
3
+ ··· + 2.93805u 2.54867
a
6
=
0.0828640u
4
0.0329847u
3
+ ··· 0.775543u + 1.70233
0.283186u
4
+ 0.238938u
3
+ ··· + 3.30088u 2.47788
a
8
=
0
u
a
1
=
0.137570u
4
0.0450523u
3
+ ··· 1.08367u + 0.544650
0.0265487u
4
+ 0.00884956u
3
+ ··· 0.840708u 0.0176991
a
10
=
0.314562u
4
0.319389u
3
+ ··· 4.02172u + 3.09332
0.176991u
4
+ 0.274336u
3
+ ··· + 2.93805u 2.54867
a
4
=
0.366050u
4
+ 0.271923u
3
+ ··· + 4.07643u 2.18021
0.283186u
4
0.238938u
3
+ ··· 3.30088u + 2.47788
a
3
=
0.228479u
4
+ 0.226870u
3
+ ··· + 2.99276u 1.63556
0.309735u
4
0.230088u
3
+ ··· 4.14159u + 2.46018
a
9
=
0.00482703u
4
+ 0.0893001u
3
+ ··· + 0.880129u 0.633146
0.0265487u
4
0.00884956u
3
+ ··· + 0.840708u + 0.0176991
a
2
=
0.460177u
4
0.513274u
3
+ ··· 6.23894u + 5.02655
u
a
7
=
0.0780370u
4
+ 0.0563154u
3
+ ··· + 0.104586u + 1.06919
0.309735u
4
+ 0.230088u
3
+ ··· + 4.14159u 2.46018
a
7
=
0.0780370u
4
+ 0.0563154u
3
+ ··· + 0.104586u + 1.06919
0.309735u
4
+ 0.230088u
3
+ ··· + 4.14159u 2.46018
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
16
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 0.36526 2.80304I
a = 0.603869 0.245803I
b = 1.41878 0.21917I
2.58269 4.40083I 5.25569 + 3.49859I
u = 0.36526 + 2.80304I
a = 0.603869 + 0.245803I
b = 1.41878 + 0.21917I
2.58269 + 4.40083I 5.25569 3.49859I
u = 0.781782 0.753989I
a = 0.413054 0.310894I
b = 0.309916 0.549911I
2.96077 + 1.53058I 9.48489 4.43065I
u = 0.781782 + 0.753989I
a = 0.413054 + 0.310894I
b = 0.309916 + 0.549911I
2.96077 1.53058I 9.48489 + 4.43065I
u = 1.16697
a = 0.800188
b = 1.21774
0.888787 8.51886
17
VII. I
u
7
= hu
5
3u
4
+ 7u
3
14u
2
+ 3u 1, 15u
4
+ 41u
3
73u
2
+ 79b +
180u + 3, 107u
4
+ 303u
3
+ · · · + 79a 26i
(i) Arc colorings
a
5
=
1
0
a
11
=
1.35443u
4
3.83544u
3
+ ··· 17.2532u + 0.329114
0.189873u
4
0.518987u
3
+ ··· 2.27848u 0.0379747
a
6
=
0.632911u
4
2.06329u
3
+ ··· 9.59494u + 3.87342
0.0379747u
4
0.303797u
3
+ ··· 1.45570u + 0.392405
a
8
=
0
u
a
1
=
1.35443u
4
3.83544u
3
+ ··· 17.2532u + 0.329114
0.0506329u
4
0.405063u
3
+ ··· 1.60759u + 0.189873
a
10
=
1.16456u
4
3.31646u
3
+ ··· 14.9747u + 0.367089
0.189873u
4
0.518987u
3
+ ··· 2.27848u 0.0379747
a
4
=
0.594937u
4
+ 1.75949u
3
+ ··· + 8.13924u 1.48101
0.0379747u
4
+ 0.303797u
3
+ ··· + 1.45570u 0.392405
a
3
=
0.759494u
4
2.07595u
3
+ ··· 9.11392u 1.15190
0.0126582u
4
0.101266u
3
+ ··· 0.151899u 0.202532
a
9
=
0.240506u
4
+ 0.924051u
3
+ ··· + 4.88608u 3.15190
0.0506329u
4
+ 0.405063u
3
+ ··· + 1.60759u 0.189873
a
2
=
1.18987u
4
3.51899u
3
+ ··· 15.2785u + 0.962025
u
a
7
=
0.392405u
4
1.13924u
3
+ ··· 4.70886u + 0.721519
0.0126582u
4
+ 0.101266u
3
+ ··· + 0.151899u + 0.202532
a
7
=
0.392405u
4
1.13924u
3
+ ··· 4.70886u + 0.721519
0.0126582u
4
+ 0.101266u
3
+ ··· + 0.151899u + 0.202532
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
18
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
7
1(vol +
1CS) Cusp shape
u = 0.099584 0.264624I
a = 1.83188 + 4.07697I
b = 0.309916 + 0.549911I
2.96077 1.53058I 9.48489 + 4.43065I
u = 0.099584 + 0.264624I
a = 1.83188 4.07697I
b = 0.309916 0.549911I
2.96077 + 1.53058I 9.48489 4.43065I
u = 0.22299 2.29396I
a = 0.192971 + 0.179096I
b = 1.41878 + 0.21917I
2.58269 + 4.40083I 5.25569 3.49859I
u = 0.22299 + 2.29396I
a = 0.192971 0.179096I
b = 1.41878 0.21917I
2.58269 4.40083I 5.25569 + 3.49859I
u = 2.35485
a = 0.722177
b = 1.21774
0.888787 8.51886
19
VIII. I
u
8
= hu
20
+ 5u
19
+ · · · + 12884u + 2659, 9.40 × 10
40
u
19
+ 4.40 ×
10
41
u
18
+ · · · + 3.29 × 10
44
b + 5.41 × 10
44
, 1.14 × 10
49
u
19
+ 5.16 × 10
49
u
18
+
· · · + 7.20 × 10
51
a + 4.70 × 10
52
i
(i) Arc colorings
a
5
=
1
0
a
11
=
0.00158631u
19
0.00715910u
18
+ ··· 23.5869u 6.52296
0.000285232u
19
0.00133409u
18
+ ··· 4.86278u 1.64313
a
6
=
0.000560395u
19
0.00240175u
18
+ ··· 6.04363u + 0.517565
0.000172857u
19
0.000797827u
18
+ ··· 2.96340u 0.609913
a
8
=
0
u
a
1
=
0.00158631u
19
0.00715910u
18
+ ··· 23.5869u 6.52296
0.000458752u
19
0.00220361u
18
+ ··· 10.5972u 3.69710
a
10
=
0.00130108u
19
0.00582501u
18
+ ··· 18.7242u 4.87983
0.000285232u
19
0.00133409u
18
+ ··· 4.86278u 1.64313
a
4
=
0.000387539u
19
+ 0.00160392u
18
+ ··· + 3.08023u + 0.872522
0.000172857u
19
+ 0.000797827u
18
+ ··· + 2.96340u + 0.609913
a
3
=
0.000681269u
19
0.00276920u
18
+ ··· 7.37261u 0.263498
0.000623484u
19
0.00284512u
18
+ ··· 10.5014u 2.69825
a
9
=
0.00164603u
19
+ 0.00765997u
18
+ ··· + 27.2751u + 7.00805
0.000608023u
19
+ 0.00275306u
18
+ ··· + 9.70287u + 2.89407
a
2
=
0.00177960u
19
0.00830584u
18
+ ··· 29.6691u 8.20198
0.000680394u
19
0.00320091u
18
+ ··· 11.8833u 3.45957
a
7
=
0.000323961u
19
0.00126040u
18
+ ··· 2.98497u 0.385374
0.000109168u
19
+ 0.000463625u
18
+ ··· + 2.27667u + 0.384801
a
7
=
0.000323961u
19
0.00126040u
18
+ ··· 2.98497u 0.385374
0.000109168u
19
+ 0.000463625u
18
+ ··· + 2.27667u + 0.384801
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
20
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
8
1(vol +
1CS) Cusp shape
u = 1.36078 1.36864I
a = 0.453791 + 0.467207I
b = 1.21774
2.40108 + 4.05977I 3.48114 6.92820I
u = 1.36078 + 1.36864I
a = 0.453791 0.467207I
b = 1.21774
2.40108 4.05977I 3.48114 + 6.92820I
u = 1.25724 1.79629I
a = 0.656627 + 0.179803I
b = 1.41878 + 0.21917I
5.87256 + 0.34107I 6.74431 + 3.42962I
u = 1.25724 + 1.79629I
a = 0.656627 0.179803I
b = 1.41878 0.21917I
5.87256 0.34107I 6.74431 3.42962I
u = 0.790730 0.518781I
a = 0.846433 0.410024I
b = 0.309916 + 0.549911I
0.32910 5.59035I 2.51511 + 11.35885I
u = 0.790730 + 0.518781I
a = 0.846433 + 0.410024I
b = 0.309916 0.549911I
0.32910 + 5.59035I 2.51511 11.35885I
u = 0.450859 0.263366I
a = 0.30830 + 2.20048I
b = 0.309916 + 0.549911I
0.32910 + 2.52919I 2.51511 2.49755I
u = 0.450859 + 0.263366I
a = 0.30830 2.20048I
b = 0.309916 0.549911I
0.32910 2.52919I 2.51511 + 2.49755I
u = 0.42250 2.93746I
a = 0.350421 0.054696I
b = 1.41878 0.21917I
5.87256 8.46060I 6.74431 + 10.42679I
u = 0.42250 + 2.93746I
a = 0.350421 + 0.054696I
b = 1.41878 + 0.21917I
5.87256 + 8.46060I 6.74431 10.42679I
21
Solution to I
u
8
1(vol +
1CS) Cusp shape
u = 0.40012 1.68134I
a = 0.265061 0.582629I
b = 1.21774
2.40108 + 4.05977I 3.48114 6.92820I
u = 0.40012 + 1.68134I
a = 0.265061 + 0.582629I
b = 1.21774
2.40108 4.05977I 3.48114 + 6.92820I
u = 0.073756 1.037384I
a = 0.75357 1.34369I
b = 0.309916 0.549911I
0.32910 + 5.59035I 2.51511 11.35885I
u = 0.073756 + 1.037384I
a = 0.75357 + 1.34369I
b = 0.309916 + 0.549911I
0.32910 5.59035I 2.51511 + 11.35885I
u = 0.433979 0.744601I
a = 0.309324 0.055939I
b = 0.309916 + 0.549911I
0.32910 + 2.52919I 2.51511 2.49755I
u = 0.433979 + 0.744601I
a = 0.309324 + 0.055939I
b = 0.309916 0.549911I
0.32910 2.52919I 2.51511 + 2.49755I
u = 0.88751 1.41855I
a = 0.110208 0.286748I
b = 1.41878 0.21917I
5.87256 0.34107I 6.74431 3.42962I
u = 0.88751 + 1.41855I
a = 0.110208 + 0.286748I
b = 1.41878 + 0.21917I
5.87256 + 0.34107I 6.74431 + 3.42962I
u = 0.93451 3.06879I
a = 0.504441 + 0.359924I
b = 1.41878 + 0.21917I
5.87256 + 8.46060I 6.74431 10.42679I
u = 0.93451 + 3.06879I
a = 0.504441 0.359924I
b = 1.41878 0.21917I
5.87256 8.46060I 6.74431 + 10.42679I
22
IX. I
u
9
= hu
40
5u
39
+ · · · + 1394u + 223, 8.03 × 10
150
u
39
+ 3.82 ×
10
151
u
38
+ · · · + 3.02 × 10
153
b 5.95 × 10
153
, 3.28 × 10
178
u
39
+ 1.75 ×
10
179
u
38
+ · · · + 5.84 × 10
180
a + 3.24 × 10
181
i
(i) Arc colorings
a
5
=
1
0
a
11
=
0.00560693u
39
0.0300138u
38
+ ··· 20.0832u 5.55069
0.00265773u
39
0.0126318u
38
+ ··· + 17.8942u + 1.96847
a
6
=
0.0105486u
39
+ 0.0516909u
38
+ ··· 94.4282u 11.8555
0.000267890u
39
0.00178755u
38
+ ··· 1.60484u 2.01249
a
8
=
0
u
a
1
=
0.00560693u
39
0.0300138u
38
+ ··· 20.0832u 5.55069
0.00225835u
39
0.0104403u
38
+ ··· + 19.4029u + 2.40983
a
10
=
0.00294920u
39
0.0173819u
38
+ ··· 37.9774u 7.51916
0.00265773u
39
0.0126318u
38
+ ··· + 17.8942u + 1.96847
a
4
=
0.0108165u
39
0.0534784u
38
+ ··· + 92.8234u + 11.8430
0.000267890u
39
+ 0.00178755u
38
+ ··· + 1.60484u + 2.01249
a
3
=
0.00269131u
39
+ 0.0129152u
38
+ ··· 11.2064u + 0.603274
0.00159326u
39
0.00763890u
38
+ ··· + 2.81739u 0.0731423
a
9
=
0.000994671u
39
+ 0.00793523u
38
+ ··· + 48.4860u + 7.23826
0.00313040u
39
+ 0.0153617u
38
+ ··· 15.9057u 1.58684
a
2
=
0.0228857u
39
+ 0.115656u
38
+ ··· 69.6722u + 4.74821
0.000531265u
39
0.00318644u
38
+ ··· 22.7813u 4.33032
a
7
=
0.0219234u
39
+ 0.107532u
38
+ ··· 173.215u 21.0183
0.00217310u
39
0.0121842u
38
+ ··· 3.79458u 4.28684
a
7
=
0.0219234u
39
+ 0.107532u
38
+ ··· 173.215u 21.0183
0.00217310u
39
0.0121842u
38
+ ··· 3.79458u 4.28684
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
23
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
9
1(vol +
1CS) Cusp shape
u = 1.173966 0.740136I
a = 0.460372 + 0.422524I
b = 1.41878 + 0.21917I
2.58269 + 8.46060I 5.25569 10.42679I
u = 1.173966 + 0.740136I
a = 0.460372 0.422524I
b = 1.41878 0.21917I
2.58269 8.46060I 5.25569 + 10.42679I
u = 1.108966 0.003329I
a = 1.52256 0.45771I
b = 1.41878 0.21917I
2.58269 0.34107I 5.25569 3.42962I
u = 1.108966 + 0.003329I
a = 1.52256 + 0.45771I
b = 1.41878 + 0.21917I
2.58269 + 0.34107I 5.25569 + 3.42962I
u = 0.93579 1.49471I
a = 0.035486 0.394244I
b = 0.309916 0.549911I
2.96077 + 5.59035I 9.4849 11.3589I
u = 0.93579 + 1.49471I
a = 0.035486 + 0.394244I
b = 0.309916 + 0.549911I
2.96077 5.59035I 9.4849 + 11.3589I
u = 0.76269 3.08407I
a = 0.478424 0.182090I
b = 1.41878 0.21917I
2.58269 8.46060I 5.25569 + 10.42679I
u = 0.76269 + 3.08407I
a = 0.478424 + 0.182090I
b = 1.41878 + 0.21917I
2.58269 + 8.46060I 5.25569 10.42679I
u = 0.391422 0.051831I
a = 2.36367 + 0.77570I
b = 0.309916 + 0.549911I
2.96077 + 2.52919I 9.48489 2.49755I
u = 0.391422 + 0.051831I
a = 2.36367 0.77570I
b = 0.309916 0.549911I
2.96077 2.52919I 9.48489 + 2.49755I
24
Solution to I
u
9
1(vol +
1CS) Cusp shape
u = 0.377566 0.590768I
a = 1.91430 + 0.49475I
b = 0.309916 + 0.549911I
2.96077 5.59035I 9.4849 + 11.3589I
u = 0.377566 + 0.590768I
a = 1.91430 0.49475I
b = 0.309916 0.549911I
2.96077 + 5.59035I 9.4849 11.3589I
u = 0.115874 0.264192I
a = 2.95224 3.30584I
b = 1.41878 + 0.21917I
2.58269 + 0.34107I 5.25569 + 3.42962I
u = 0.115874 + 0.264192I
a = 2.95224 + 3.30584I
b = 1.41878 0.21917I
2.58269 0.34107I 5.25569 3.42962I
u = 0.110311 0.718236I
a = 0.255799 0.041030I
b = 1.41878 + 0.21917I
2.58269 + 0.34107I 5.25569 + 3.42962I
u = 0.110311 + 0.718236I
a = 0.255799 + 0.041030I
b = 1.41878 0.21917I
2.58269 0.34107I 5.25569 3.42962I
u = 0.090546 0.661947I
a = 2.09649 1.63443I
b = 0.309916 0.549911I
2.96077 + 5.59035I 9.4849 11.3589I
u = 0.090546 + 0.661947I
a = 2.09649 + 1.63443I
b = 0.309916 + 0.549911I
2.96077 5.59035I 9.4849 + 11.3589I
u = 0.058591 0.864000I
a = 0.599916 0.402371I
b = 1.41878 0.21917I
2.58269 0.34107I 5.25569 3.42962I
u = 0.058591 + 0.864000I
a = 0.599916 + 0.402371I
b = 1.41878 + 0.21917I
2.58269 + 0.34107I 5.25569 + 3.42962I
25
Solution to I
u
9
1(vol +
1CS) Cusp shape
u = 0.001687 0.233740I
a = 1.33884 + 5.27192I
b = 1.21774
0.88879 + 4.05977I 8.51886 6.92820I
u = 0.001687 + 0.233740I
a = 1.33884 5.27192I
b = 1.21774
0.88879 4.05977I 8.51886 + 6.92820I
u = 0.24070 4.58063I
a = 0.398778 + 0.018517I
b = 1.21774
0.88879 + 4.05977I 8.51886 6.92820I
u = 0.24070 + 4.58063I
a = 0.398778 0.018517I
b = 1.21774
0.88879 4.05977I 8.51886 + 6.92820I
u = 0.28194 3.74689I
a = 0.0027037 0.0275947I
b = 1.21774
0.88879 + 4.05977I 8.51886 6.92820I
u = 0.28194 + 3.74689I
a = 0.0027037 + 0.0275947I
b = 1.21774
0.88879 4.05977I 8.51886 + 6.92820I
u = 0.532295 0.629176I
a = 1.56271 + 0.16662I
b = 0.309916 + 0.549911I
2.96077 + 2.52919I 9.48489 2.49755I
u = 0.532295 + 0.629176I
a = 1.56271 0.16662I
b = 0.309916 0.549911I
2.96077 2.52919I 9.48489 + 2.49755I
u = 0.573173 0.968646I
a = 0.932471 0.571315I
b = 0.309916 0.549911I
2.96077 + 5.59035I 9.4849 11.3589I
u = 0.573173 + 0.968646I
a = 0.932471 + 0.571315I
b = 0.309916 + 0.549911I
2.96077 5.59035I 9.4849 + 11.3589I
26
Solution to I
u
9
1(vol +
1CS) Cusp shape
u = 0.75563 1.38224I
a = 0.202621 + 0.654817I
b = 0.309916 + 0.549911I
2.96077 + 2.52919I 9.48489 2.49755I
u = 0.75563 + 1.38224I
a = 0.202621 0.654817I
b = 0.309916 0.549911I
2.96077 2.52919I 9.48489 + 2.49755I
u = 0.815585 0.018071I
a = 0.791015 0.497019I
b = 0.309916 0.549911I
2.96077 2.52919I 9.48489 + 2.49755I
u = 0.815585 + 0.018071I
a = 0.791015 + 0.497019I
b = 0.309916 + 0.549911I
2.96077 + 2.52919I 9.48489 2.49755I
u = 0.83154 2.87186I
a = 0.357011 + 0.261028I
b = 1.41878 + 0.21917I
2.58269 + 8.46060I 5.25569 10.42679I
u = 0.83154 + 2.87186I
a = 0.357011 0.261028I
b = 1.41878 0.21917I
2.58269 8.46060I 5.25569 + 10.42679I
u = 1.236573 0.588685I
a = 1.143264 0.153569I
b = 1.21774
0.88879 + 4.05977I 8.51886 6.92820I
u = 1.236573 + 0.588685I
a = 1.143264 + 0.153569I
b = 1.21774
0.88879 4.05977I 8.51886 + 6.92820I
u = 2.35658 1.15209I
a = 0.892790 0.162243I
b = 1.41878 0.21917I
2.58269 8.46060I 5.25569 + 10.42679I
u = 2.35658 + 1.15209I
a = 0.892790 + 0.162243I
b = 1.41878 + 0.21917I
2.58269 + 8.46060I 5.25569 10.42679I
27
X. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
8
u(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
3
(u
6
u
4
u
3
+ u
2
1)
2
(u
16
u
15
+ ··· 2u + 2)(u
20
+ 5u
18
+ ··· 14u
2
+ 5)
(u
20
3u
19
+ ··· + 12u + 61)
(7 + 40u + 124u
2
+ 219u
3
+ 401u
4
+ 593u
5
+ 771u
6
+ 890u
7
+ 941u
8
+ 928u
9
+ 768u
10
+ 633u
11
+ 443u
12
+ 294u
13
+ 177u
14
+ 75u
15
+ 44u
16
+ 11u
17
+ 8u
18
+ u
19
+ u
20
)
2
c
2
, c
9
(u 1)(u
5
u
4
u
3
+ 4u
2
3u + 1)(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
(u
5
+ 2u
4
+ 3u
3
u
2
3u 1)
(u
12
+ u
10
+ u
9
+ 8u
8
u
7
+ 8u
6
+ 8u
5
+ 4u
4
u
3
+ 4u
2
+ 3u + 1)
(u
16
u
15
+ ··· u + 1)(u
20
u
19
+ ··· + 6u + 1)
(u
20
+ 3u
19
+ ··· + 5u + 1)(u
40
+ u
39
+ ··· + 24u + 1)
c
3
u
5
(u + 1)
11
(u
2
+ u + 1)
10
(u
4
+ u
3
2u + 1)
10
(u
12
10u
11
+ ··· 102u + 17)(u
16
11u
15
+ ··· 85u + 19)
(u
20
+ 9u
19
+ ··· 3u
2
+ 1)
c
4
, c
5
, c
10
u(u
5
u
4
2u
3
+ u
2
+ u + 1)(u
5
+ u
4
2u
3
u
2
+ u 1)
14
(4 + 2u + u
2
+ 2u
4
3u
5
+ u
6
)
2
(u
16
6u
15
+ ··· 8u + 8)
(u
20
11u
18
+ ··· 26u
2
+ 5)
c
6
u
5
(u 1)(u + 1)
10
(u
2
+ u + 1)
10
(u
4
+ u
3
2u + 1)
10
(u
12
10u
11
+ ··· 102u + 17)(u
16
11u
15
+ ··· 85u + 19)
(u
20
9u
19
+ ··· 3u
2
+ 1)
c
7
, c
11
(u + 1)(u
5
u
4
u
3
+ 4u
2
3u + 1)(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
(u
5
+ 2u
4
+ 3u
3
u
2
3u 1)
(u
12
+ u
10
+ u
9
+ 8u
8
u
7
+ 8u
6
+ 8u
5
+ 4u
4
u
3
+ 4u
2
+ 3u + 1)
(u
16
u
15
+ ··· u + 1)(u
20
3u
19
+ ··· 5u + 1)
(u
20
u
19
+ ··· + 6u + 1)(u
40
+ u
39
+ ··· + 24u + 1)
28
XI. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
8
y(y
5
+ 3y
4
+ 4y
3
+ y
2
y 1)
3
(y
6
2y
5
+ 3y
4
5y
3
+ 3y
2
2y + 1)
2
(5 14y y
2
3y
3
+ 16y
4
+ 39y
5
+ 39y
6
+ 22y
7
+ 12y
8
+ 5y
9
+ y
10
)
2
(y
16
+ 9y
15
+ ··· + 48y + 4)(y
20
13y
19
+ ··· + 17912y + 3721)
(49 + 136y + 3470y
2
+ 1.48 × 10
4
y
3
+ 3.42 × 10
4
y
4
+ 4.68 × 10
4
y
5
+ 3.31 × 10
4
y
6
1.42 × 10
4
y
7
6.78 × 10
4
y
8
8.89 × 10
4
y
9
5.82 × 10
4
y
10
5263y
11
+ 3.19 × 10
4
y
12
+ 3.74 × 10
4
y
13
+ 2.46 × 10
4
y
14
+ 1.08 × 10
4
y
15
+ 3416y
16
+ 787y
17
+ 130y
18
+ 15y
19
+ y
20
)
2
c
2
, c
7
, c
9
c
11
(y 1)(y
5
3y
4
+ ··· + y 1)(y
5
+ 2y
4
+ ··· + 7y 1)
(y
5
+ 3y
4
+ ··· y 1)(y
12
+ 2y
11
+ ··· y + 1)
(y
16
+ 7y
15
+ ··· + 21y + 1)(y
20
9y
19
+ ··· + y + 1)
(y
20
y
19
+ ··· + 8y + 1)(y
40
19y
39
+ ··· 140y + 1)
c
3
, c
6
y
5
(y 1)
11
(y
2
+ y + 1)
10
(y
4
y
3
+ 6y
2
4y + 1)
10
(y
12
+ 6y
11
+ ··· + 918y + 289)(y
16
11y
15
+ ··· + 3795y + 361)
(y
20
3y
19
+ ··· 6y + 1)
c
4
, c
5
, c
10
y(y
5
5y
4
+ 8y
3
3y
2
y 1)
15
(y
6
5y
5
+ 6y
4
+ 8y
3
15y
2
12y + 16)
2
(5 26y + 40y
2
+ 8y
3
35y
4
52y
5
+ 138y
6
117y
7
+ 50y
8
11y
9
+ y
10
)
2
(y
16
12y
15
+ ··· + 160y + 64)
29