11a
352
(K11a
352
)
1
Arc Sequences
7 6 1 11 10 9 4 3 2 5 8
Solving Sequence
2,6 3,9
7 10 1 4 5 8 11
c
2
c
6
c
9
c
1
c
3
c
5
c
8
c
11
c
4
, c
7
, c
10
Representation Ideals
I =
8
\
i=1
I
u
i
I
u
1
= hu 1, a + 1, b + 1i
I
u
2
= hu
4
u
3
+ u
2
+ 1, a, b ui
I
u
3
= hu
8
u
7
2u
6
+ 4u
5
+ 9u
4
u
3
7u
2
u + 2, u
7
+ u
6
+ 2u
5
4u
4
9u
3
+ u
2
+ 2a + 7u + 1,
3u
7
2u
6
5u
5
+ 8u
4
+ 28u
3
+ 13u
2
+ 2b 5u 8i
I
u
4
= hu
10
+ u
9
u
8
2u
7
+ 5u
6
+ 3u
5
3u
3
u + 1, b u,
53u
9
+ 78u
8
5u
7
93u
6
+ 212u
5
+ 237u
4
+ 167u
3
30u
2
+ 22a 32u 71i
I
u
5
= hu
14
+ u
13
2u
12
2u
11
+ 7u
10
+ 9u
9
3u
8
6u
7
+ 5u
6
+ 5u
5
4u
4
3u
3
+ u
2
+ u + 1, b u,
3u
13
+ 5u
12
3u
11
11u
10
+ 14u
9
+ 40u
8
+ 21u
7
28u
6
17u
5
+ 19u
4
+ 16u
3
31u
2
+ 11a 28u + 11i
I
u
6
= hu
16
+ u
15
2u
14
u
13
+ 6u
12
+ u
11
+ 7u
10
10u
9
+ 20u
8
7u
7
+ 15u
6
29u
5
+ 10u
4
6u
3
+ 12u
2
6u + 1,
70376091u
15
+ 105211369u
14
+ ··· + 33620957a 105666681,
97686376u
15
+ 129907845u
14
+ ··· + 168104785b 283592621i
I
u
7
= hu
16
+ 2u
15
+ ··· + 5u + 1, b + u, 469u
15
+ 583u
14
+ ··· + 23a + 498i
I
u
8
= hu
32
u
31
+ ··· + 400u + 361,
2.05478 × 10
44
u
31
+ 3.96587 × 10
44
u
30
+ ··· + 1.88328 × 10
45
a 8.31772 × 10
46
,
6.83744 × 10
50
u
31
+ 1.12280 × 10
51
u
30
+ ··· + 3.04300 × 10
51
b 4.23786 × 10
53
i
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
There are 8 irreducible components with 101 representations.
2
I. I
u
1
= hu 1, a + 1, b + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
1
a
3
=
1
1
a
9
=
1
1
a
7
=
1
0
a
10
=
0
1
a
1
=
1
0
a
4
=
0
1
a
5
=
0
1
a
8
=
1
1
a
11
=
0
1
a
11
=
0
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 = 1.00000
3.28987 12.0000
4
II. I
u
2
= hu
4
u
3
+ u
2
+ 1, a, b ui
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
0
u
a
7
=
0
u
a
10
=
u
u
a
1
=
1
u
2
a
4
=
1
u
2
a
5
=
u
3
u
3
+ u
a
8
=
u
u
3
+ u
a
11
=
u
2
+ 1
u
3
u
2
1
a
11
=
u
2
+ 1
u
3
u
2
1
(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 = 0.351808 0.720342I
a = 0
b = 0.351808 0.720342I
0.21101 1.41510I 1.82674 + 4.90874I
u = 0.351808 + 0.720342I
a = 0
b = 0.351808 + 0.720342I
0.21101 + 1.41510I 1.82674 4.90874I
u = 0.851808 0.911292I
a = 0
b = 0.851808 0.911292I
6.79074 + 3.16396I 1.82674 2.56480I
u = 0.851808 + 0.911292I
a = 0
b = 0.851808 + 0.911292I
6.79074 3.16396I 1.82674 + 2.56480I
6
III. I
u
3
= hu
8
u
7
2u
6
+ 4u
5
+ 9u
4
u
3
7u
2
u + 2, u
7
+ u
6
+ · · · +
2a + 1, 3u
7
2u
6
+ · · · + 2b 8i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
1
2
u
7
1
2
u
6
+ ···
7
2
u
1
2
3
2
u
7
+ u
6
+ ··· +
5
2
u + 4
a
7
=
1
2
u
7
1
2
u
6
+ ···
7
2
u
1
2
3
2
u
7
+ u
6
+ ··· +
7
2
u + 4
a
10
=
2u
7
3
2
u
6
+ ··· 6u
9
2
3
2
u
7
+ u
6
+ ··· +
5
2
u + 4
a
1
=
2u
7
1
2
u
6
+ ···
15
2
u
9
2
1
2
u
7
+
1
2
u
6
+ ···
5
2
u 4
a
4
=
2u
7
+
1
2
u
6
+ ··· +
15
2
u +
11
2
1
2
u
7
1
2
u
6
+ ··· +
5
2
u + 4
a
5
=
1
2
u
7
+
1
2
u
6
+ ··· +
19
2
u
2
11
2
3
2
u
7
2u
6
+ ··· 5u + 1
a
8
=
2u
7
3
2
u
6
+ ··· 7u
9
2
1
2
u
7
+ u
5
+ ···
11
2
u
2
+ 3
a
11
=
u
7
+ u
6
4u
5
+ u
4
+ 16u
3
+ 15u
2
5u 7
u
7
+ 3u
5
3u
4
12u
3
7u
2
+ 5u + 2
a
11
=
u
7
+ u
6
4u
5
+ u
4
+ 16u
3
+ 15u
2
5u 7
u
7
+ 3u
5
3u
4
12u
3
7u
2
+ 5u + 2
(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 = 0.987376 0.750545I
a = 0.641892 0.487928I
b = 0.635568 + 0.030203I
3.07886 1.41510I 10.17326 + 4.90874I
u = 0.987376 + 0.750545I
a = 0.641892 + 0.487928I
b = 0.635568 0.030203I
3.07886 + 1.41510I 10.17326 4.90874I
u = 0.797853 0.337246I
a = 1.063372 0.449479I
b = 1.64966 + 1.24854I
10.08061 3.16396I 13.82674 + 2.56480I
u = 0.797853 + 0.337246I
a = 1.063372 + 0.449479I
b = 1.64966 1.24854I
10.08061 + 3.16396I 13.82674 2.56480I
u = 0.635568 0.030203I
a = 1.56985 0.07460I
b = 0.987376 + 0.750545I
3.07886 + 1.41510I 10.17326 4.90874I
u = 0.635568 + 0.030203I
a = 1.56985 + 0.07460I
b = 0.987376 0.750545I
3.07886 1.41510I 10.17326 + 4.90874I
u = 1.64966 1.24854I
a = 0.385414 0.291699I
b = 0.797853 + 0.337246I
10.08061 + 3.16396I 13.82674 2.56480I
u = 1.64966 + 1.24854I
a = 0.385414 + 0.291699I
b = 0.797853 0.337246I
10.08061 3.16396I 13.82674 + 2.56480I
8
IV. I
u
4
=
hu
10
+u
9
u
8
2u
7
+5u
6
+3u
5
3u
3
u+1, bu, 53u
9
+78u
8
+· · ·+22a71i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
2.40909u
9
3.54545u
8
+ ··· + 1.45455u + 3.22727
u
a
7
=
1.81818u
9
+ 3.09091u
8
+ ··· + 0.0909091u 0.454545
1.04545u
9
+ 1.72727u
8
+ ··· 0.272727u 1.13636
a
10
=
2.40909u
9
3.54545u
8
+ ··· + 0.454545u + 3.22727
u
a
1
=
4.22727u
9
+ 7.63636u
8
+ ··· 4.36364u 6.68182
u
2
1
a
4
=
4.81818u
9
+ 10.0909u
8
+ ··· + 1.09091u 6.45455
1.81818u
9
+ 3.09091u
8
+ ··· 0.909091u 3.45455
a
5
=
0.272727u
9
0.363636u
8
+ ··· + 2.63636u + 1.81818
1.04545u
9
+ 1.72727u
8
+ ··· 0.272727u 1.13636
a
8
=
3.45455u
9
5.27273u
8
+ ··· + 1.72727u + 4.36364
0.227273u
9
0.636364u
8
+ ··· + 1.36364u + 0.681818
a
11
=
6.04545u
9
+ 10.7273u
8
+ ··· 5.27273u 10.1364
0.409091u
9
+ 0.545455u
8
+ ··· 0.454545u 1.22727
a
11
=
6.04545u
9
+ 10.7273u
8
+ ··· 5.27273u 10.1364
0.409091u
9
+ 0.545455u
8
+ ··· 0.454545u 1.22727
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
9
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.37084 0.99078I
a = 0.922638 0.109964I
b = 1.37084 0.99078I
12.0871 17.1582I 6.40595 + 8.48495I
u = 1.37084 + 0.99078I
a = 0.922638 + 0.109964I
b = 1.37084 + 0.99078I
12.0871 + 17.1582I 6.40595 8.48495I
u = 0.751611 0.596797I
a = 1.95307 0.04587I
b = 0.751611 0.596797I
2.14694 6.57736I 5.40678 + 10.73292I
u = 0.751611 + 0.596797I
a = 1.95307 + 0.04587I
b = 0.751611 + 0.596797I
2.14694 + 6.57736I 5.40678 10.73292I
u = 0.112541 0.658708I
a = 0.522337 0.072962I
b = 0.112541 0.658708I
0.232399 1.335331I 1.84390 + 5.86434I
u = 0.112541 + 0.658708I
a = 0.522337 + 0.072962I
b = 0.112541 + 0.658708I
0.232399 + 1.335331I 1.84390 5.86434I
u = 0.650130 0.116508I
a = 0.68097 + 2.87321I
b = 0.650130 0.116508I
9.27048 + 0.95500I 15.6058 6.9472I
u = 0.650130 + 0.116508I
a = 0.68097 2.87321I
b = 0.650130 + 0.116508I
9.27048 0.95500I 15.6058 + 6.9472I
u = 1.084862 0.878124I
a = 1.172394 0.044326I
b = 1.084862 0.878124I
3.86930 + 13.03598I 4.42534 9.74427I
u = 1.084862 + 0.878124I
a = 1.172394 + 0.044326I
b = 1.084862 + 0.878124I
3.86930 13.03598I 4.42534 + 9.74427I
10
V. I
u
5
= hu
14
+ u
13
+ · · · + u + 1, b u, 3u
13
+ 5u
12
+ · · · + 11a + 11i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
0.272727u
13
0.454545u
12
+ ··· + 2.54545u 1
u
a
7
=
0.727273u
13
0.818182u
12
+ ··· 3.72727u 1.45455
0.0909091u
13
0.0909091u
12
+ ··· + 0.545455u 0.181818
a
10
=
0.272727u
13
0.454545u
12
+ ··· + 1.54545u 1
u
a
1
=
0.0909091u
13
+ 1.45455u
12
+ ··· + 0.363636u + 0.454545
0.0909091u
13
0.181818u
12
+ ··· 0.727273u 0.272727
a
4
=
1
11
u
13
+
20
11
u
12
+ ··· +
20
11
u + 1
0.0909091u
13
0.0909091u
12
+ ··· 0.454545u 0.181818
a
5
=
0.909091u
13
0.636364u
12
+ ··· 2.81818u 1.09091
0.0909091u
13
0.0909091u
12
+ ··· + 0.545455u 0.181818
a
8
=
4
11
u
13
4
11
u
12
+ ··· + 2u
9
11
0.0909091u
13
+ 0.272727u
12
+ ··· + 0.909091u 0.181818
a
11
=
0.454545u
13
+ 0.545455u
12
+ ··· + 1.72727u + 1.09091
0.363636u
13
0.272727u
12
+ ··· 0.0909091u + 0.0909091
a
11
=
0.454545u
13
+ 0.545455u
12
+ ··· + 1.72727u + 1.09091
0.363636u
13
0.272727u
12
+ ··· 0.0909091u + 0.0909091
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
11
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.997484 0.221219I
a = 0.93278 + 1.44094I
b = 0.997484 0.221219I
11.8056 8.5528I 9.47503 + 5.91683I
u = 0.997484 + 0.221219I
a = 0.93278 1.44094I
b = 0.997484 + 0.221219I
11.8056 + 8.5528I 9.47503 5.91683I
u = 0.987810 0.814945I
a = 0.639076 0.004390I
b = 0.987810 0.814945I
0.56973 3.46571I 1.80998 + 1.90405I
u = 0.987810 + 0.814945I
a = 0.639076 + 0.004390I
b = 0.987810 + 0.814945I
0.56973 + 3.46571I 1.80998 1.90405I
u = 0.952255 0.761533I
a = 1.248986 + 0.247891I
b = 0.952255 0.761533I
3.76584 3.52764I 10.39771 + 1.47160I
u = 0.952255 + 0.761533I
a = 1.248986 0.247891I
b = 0.952255 + 0.761533I
3.76584 + 3.52764I 10.39771 1.47160I
u = 0.183150 0.498043I
a = 2.30752 0.64462I
b = 0.183150 0.498043I
0.56973 + 3.46571I 1.80998 1.90405I
u = 0.183150 + 0.498043I
a = 2.30752 + 0.64462I
b = 0.183150 + 0.498043I
0.56973 3.46571I 1.80998 + 1.90405I
u = 0.544274 0.740063I
a = 0.969277 0.162176I
b = 0.544274 0.740063I
2.67359 5.12551
u = 0.544274 + 0.740063I
a = 0.969277 + 0.162176I
b = 0.544274 + 0.740063I
2.67359 5.12551
12
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.762614 0.234450I
a = 2.29290 0.72813I
b = 0.762614 0.234450I
3.76584 3.52764I 10.39771 + 1.47160I
u = 0.762614 + 0.234450I
a = 2.29290 + 0.72813I
b = 0.762614 + 0.234450I
3.76584 + 3.52764I 10.39771 1.47160I
u = 1.31381 0.93342I
a = 0.866181 + 0.021406I
b = 1.31381 0.93342I
11.8056 + 8.5528I 9.47503 5.91683I
u = 1.31381 + 0.93342I
a = 0.866181 0.021406I
b = 1.31381 + 0.93342I
11.8056 8.5528I 9.47503 + 5.91683I
13
VI.
I
u
6
= hu
16
+ u
15
+ · · · 6u + 1, 7.04 × 10
7
u
15
+ 1.05 × 10
8
u
14
+ · · · + 3.36 ×
10
7
a 1.06 ×10
8
, 9.77 ×10
7
u
15
+1.30× 10
8
u
14
+· · ·+ 1.68 ×10
8
b 2.84 ×10
8
i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
2.09322u
15
3.12934u
14
+ ··· 20.7617u + 3.14288
0.581104u
15
0.772779u
14
+ ··· 8.57884u + 1.68700
a
7
=
3.09322u
15
4.12934u
14
+ ··· 32.7617u + 9.14288
0.457066u
15
0.395813u
14
+ ··· 7.62313u + 2.82764
a
10
=
1.51212u
15
2.35656u
14
+ ··· 12.1828u + 1.45588
0.581104u
15
0.772779u
14
+ ··· 8.57884u + 1.68700
a
1
=
2.72312u
15
3.66655u
14
+ ··· 26.9046u + 5.63637
1.35990u
15
1.80436u
14
+ ··· 12.3539u + 3.03665
a
4
=
1.79152u
15
+ 1.88626u
14
+ ··· + 21.7314u 6.24949
0.842757u
15
+ 1.01739u
14
+ ··· + 8.19337u 3.18796
a
5
=
2.46716u
15
3.59596u
14
+ ··· 20.6014u + 4.96832
0.168996u
15
0.137567u
14
+ ··· 2.53717u + 1.34692
a
8
=
1.87444u
15
2.85099u
14
+ ··· 16.3063u + 2.49200
0.783111u
15
1.21816u
14
+ ··· 8.44023u + 1.62743
a
11
=
1.74657u
15
2.12566u
14
+ ··· 18.1499u + 3.76193
0.924850u
15
1.37607u
14
+ ··· 9.28267u + 2.25354
a
11
=
1.74657u
15
2.12566u
14
+ ··· 18.1499u + 3.76193
0.924850u
15
1.37607u
14
+ ··· 9.28267u + 2.25354
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
14
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 1.85487 0.75978I
a = 0.394599 + 0.305260I
b = 0.639763 + 1.041820I
6.79074 7.22373I 1.82674 + 9.49300I
u = 1.85487 + 0.75978I
a = 0.394599 0.305260I
b = 0.639763 1.041820I
6.79074 + 7.22373I 1.82674 9.49300I
u = 0.750541 0.814864I
a = 0.880755 + 0.197631I
b = 0.302610 + 0.150019I
0.21101 2.64466I 1.82674 + 2.01946I
u = 0.750541 + 0.814864I
a = 0.880755 0.197631I
b = 0.302610 0.150019I
0.21101 + 2.64466I 1.82674 2.01946I
u = 0.517688 0.732455I
a = 1.110227 + 0.102056I
b = 1.31743 + 0.78795I
0.21101 5.47487I 1.82674 + 11.83695I
u = 0.517688 + 0.732455I
a = 1.110227 0.102056I
b = 1.31743 0.78795I
0.21101 + 5.47487I 1.82674 11.83695I
u = 0.341471 1.045606I
a = 0.607314 0.676527I
b = 0.704770 0.147728I
6.79074 + 0.89580I 1.82674 4.36340I
u = 0.341471 + 1.045606I
a = 0.607314 + 0.676527I
b = 0.704770 + 0.147728I
6.79074 0.89580I 1.82674 + 4.36340I
u = 0.302610 0.150019I
a = 2.46519 + 1.63974I
b = 0.750541 + 0.814864I
0.21101 + 2.64466I 1.82674 2.01946I
u = 0.302610 + 0.150019I
a = 2.46519 1.63974I
b = 0.750541 0.814864I
0.21101 2.64466I 1.82674 + 2.01946I
15
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 0.639763 1.041820I
a = 0.817646 + 0.022172I
b = 1.85487 + 0.75978I
6.79074 + 7.22373I 1.82674 9.49300I
u = 0.639763 + 1.041820I
a = 0.817646 0.022172I
b = 1.85487 0.75978I
6.79074 7.22373I 1.82674 + 9.49300I
u = 0.704770 0.147728I
a = 0.926324 + 1.034639I
b = 0.341471 1.045606I
6.79074 + 0.89580I 1.82674 4.36340I
u = 0.704770 + 0.147728I
a = 0.926324 1.034639I
b = 0.341471 + 1.045606I
6.79074 0.89580I 1.82674 + 4.36340I
u = 1.31743 0.78795I
a = 0.569111 + 0.316977I
b = 0.517688 + 0.732455I
0.21101 + 5.47487I 1.82674 11.83695I
u = 1.31743 + 0.78795I
a = 0.569111 0.316977I
b = 0.517688 0.732455I
0.21101 5.47487I 1.82674 + 11.83695I
16
VII.
I
u
7
= hu
16
+ 2u
15
+ · · · + 5u + 1, b + u, 469u
15
+ 583u
14
+ · · · + 23a + 498i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
20.3913u
15
25.3478u
14
+ ··· 93.1739u 21.6522
u
a
7
=
13.9565u
15
18.7391u
14
+ ··· 72.8696u 19.2609
9.26087u
15
14.5652u
14
+ ··· 55.7826u 15.4348
a
10
=
20.3913u
15
25.3478u
14
+ ··· 92.1739u 21.6522
u
a
1
=
27.4783u
15
+ 39.8696u
14
+ ··· + 154.435u + 41.1304
5.13043u
15
+ 10.7826u
14
+ ··· + 44.3913u + 13.2174
a
4
=
9.43478u
15
23.6087u
14
+ ··· 99.3043u 31.3913
5.47826u
15
+ 4.86957u
14
+ ··· + 15.4348u + 2.13043
a
5
=
4.56522u
15
+ 10.3913u
14
+ ··· + 40.6957u + 11.6087
9.26087u
15
14.5652u
14
+ ··· 55.7826u 15.4348
a
8
=
29.6522u
15
39.9130u
14
+ ··· 148.957u 37.0870
0.173913u
15
2.04348u
14
+ ··· 11.5217u 3.95652
a
11
=
21.1739u
15
+ 26.0435u
14
+ ··· + 93.5217u + 20.9565
4.30435u
15
+ 10.8261u
14
+ ··· + 44.9130u + 14.1739
a
11
=
21.1739u
15
+ 26.0435u
14
+ ··· + 93.5217u + 20.9565
4.30435u
15
+ 10.8261u
14
+ ··· + 44.9130u + 14.1739
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
17
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
7
1(vol +
1CS) Cusp shape
u = 1.33922 0.93704I
a = 0.854339 + 0.120132I
b = 1.33922 + 0.93704I
9.31190 6.71368I 4.58299 + 3.37058I
u = 1.33922 + 0.93704I
a = 0.854339 0.120132I
b = 1.33922 0.93704I
9.31190 + 6.71368I 4.58299 3.37058I
u = 0.979599 0.497378I
a = 0.344492 0.753485I
b = 0.979599 + 0.497378I
8.98222 7.40514
u = 0.979599 + 0.497378I
a = 0.344492 + 0.753485I
b = 0.979599 0.497378I
8.98222 7.40514
u = 0.680492 0.363016I
a = 0.38600 1.63618I
b = 0.680492 + 0.363016I
8.77819 7.76739
u = 0.680492 + 0.363016I
a = 0.38600 + 1.63618I
b = 0.680492 0.363016I
8.77819 7.76739
u = 0.608149 0.273746I
a = 1.04509 + 1.46853I
b = 0.608149 + 0.273746I
1.34598 4.15746I 5.62925 + 7.50254I
u = 0.608149 + 0.273746I
a = 1.04509 1.46853I
b = 0.608149 0.273746I
1.34598 + 4.15746I 5.62925 7.50254I
u = 0.221742 0.567751I
a = 0.59533 + 1.35516I
b = 0.221742 + 0.567751I
2.66853 + 4.46324I 5.70149 4.65131I
u = 0.221742 + 0.567751I
a = 0.59533 1.35516I
b = 0.221742 0.567751I
2.66853 4.46324I 5.70149 + 4.65131I
18
Solution to I
u
7
1(vol +
1CS) Cusp shape
u = 0.768136 0.892821I
a = 0.292732 + 0.110158I
b = 0.768136 + 0.892821I
9.31190 6.71368I 4.58299 + 3.37058I
u = 0.768136 + 0.892821I
a = 0.292732 0.110158I
b = 0.768136 0.892821I
9.31190 + 6.71368I 4.58299 3.37058I
u = 0.990925 0.632113I
a = 1.309178 + 0.137158I
b = 0.990925 + 0.632113I
2.66853 + 4.46324I 5.70149 4.65131I
u = 0.990925 + 0.632113I
a = 1.309178 0.137158I
b = 0.990925 0.632113I
2.66853 4.46324I 5.70149 + 4.65131I
u = 1.070137 0.707942I
a = 0.746138 + 0.131526I
b = 1.070137 + 0.707942I
1.34598 + 4.15746I 5.62925 7.50254I
u = 1.070137 + 0.707942I
a = 0.746138 0.131526I
b = 1.070137 0.707942I
1.34598 4.15746I 5.62925 + 7.50254I
19
VIII. I
u
8
= hu
32
u
31
+ · · · + 400u + 361, 2.05 × 10
44
u
31
+ 3.97 ×
10
44
u
30
+ · · · + 1.88 × 10
45
a 8.32 × 10
46
, 6.84 × 10
50
u
31
+ 1.12 ×
10
51
u
30
+ · · · + 3.04 × 10
51
b 4.24 × 10
53
i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
0.109106u
31
0.210583u
30
+ ··· + 8.04019u + 44.1661
0.224694u
31
0.368977u
30
+ ··· 51.6392u + 139.266
a
7
=
0.101826u
31
0.221895u
30
+ ··· + 11.6271u + 42.6415
0.0174674u
31
+ 0.0109299u
30
+ ··· + 20.3716u 18.5825
a
10
=
0.115588u
31
+ 0.158394u
30
+ ··· + 59.6794u 95.0996
0.224694u
31
0.368977u
30
+ ··· 51.6392u + 139.266
a
1
=
0.0789556u
31
+ 0.0990973u
30
+ ··· + 28.2425u 64.8180
0.0427598u
31
0.108930u
30
+ ··· + 39.7109u 9.45828
a
4
=
0.0563672u
31
+ 0.0644412u
30
+ ··· + 44.8205u 53.8013
0.143266u
31
0.246056u
30
+ ··· 40.3348u + 84.0494
a
5
=
0.0494708u
31
+ 0.0524415u
30
+ ··· + 28.2258u 33.8472
0.168764u
31
0.285267u
30
+ ··· 34.9703u + 95.0712
a
8
=
0.0479203u
31
+ 0.0309101u
30
+ ··· + 60.8827u 58.4666
0.189769u
31
0.324302u
30
+ ··· 28.7392u + 108.773
a
11
=
0.125254u
31
0.173164u
30
+ ··· 85.3461u + 116.162
0.252003u
31
+ 0.433586u
30
+ ··· + 45.5238u 145.096
a
11
=
0.125254u
31
0.173164u
30
+ ··· 85.3461u + 116.162
0.252003u
31
+ 0.433586u
30
+ ··· + 45.5238u 145.096
(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 = 1.41842 2.08296I
a = 0.077342 + 0.245929I
b = 0.609972 0.066421I
10.08061 + 7.22373I 13.8267 9.4930I
u = 1.41842 + 2.08296I
a = 0.077342 0.245929I
b = 0.609972 + 0.066421I
10.08061 7.22373I 13.8267 + 9.4930I
u = 1.32546 0.70058I
a = 0.990083 + 0.271698I
b = 1.41214 + 1.21990I
10.08061 7.22373I 13.8267 + 9.4930I
u = 1.32546 + 0.70058I
a = 0.990083 0.271698I
b = 1.41214 1.21990I
10.08061 + 7.22373I 13.8267 9.4930I
u = 1.073749 0.876252I
a = 1.107931 + 0.077233I
b = 1.118271 + 0.540827I
3.07886 5.47487I 10.1733 + 11.8369I
u = 1.073749 + 0.876252I
a = 1.107931 0.077233I
b = 1.118271 0.540827I
3.07886 + 5.47487I 10.1733 11.8369I
u = 1.053437 0.202017I
a = 1.21230 + 0.76782I
b = 0.761526 + 0.373132I
3.07886 2.64466I 10.17326 + 2.01946I
u = 1.053437 + 0.202017I
a = 1.21230 0.76782I
b = 0.761526 0.373132I
3.07886 + 2.64466I 10.17326 2.01946I
u = 0.924966 0.254177I
a = 0.573351 + 0.360514I
b = 0.830529 + 0.979145I
3.07886 + 2.64466I 10.17326 2.01946I
u = 0.924966 + 0.254177I
a = 0.573351 0.360514I
b = 0.830529 0.979145I
3.07886 2.64466I 10.17326 + 2.01946I
21
Solution to I
u
8
1(vol +
1CS) Cusp shape
u = 0.830529 0.979145I
a = 0.424855 + 0.274842I
b = 0.924966 + 0.254177I
3.07886 2.64466I 10.17326 + 2.01946I
u = 0.830529 + 0.979145I
a = 0.424855 0.274842I
b = 0.924966 0.254177I
3.07886 + 2.64466I 10.17326 2.01946I
u = 0.811814 0.187323I
a = 1.02781 1.53519I
b = 1.324115 + 0.308813I
10.08061 + 0.89580I 13.8267 4.3634I
u = 0.811814 + 0.187323I
a = 1.02781 + 1.53519I
b = 1.324115 0.308813I
10.08061 0.89580I 13.8267 + 4.3634I
u = 0.609972 0.066421I
a = 0.974591 + 0.413894I
b = 1.41842 2.08296I
10.08061 + 7.22373I 13.8267 9.4930I
u = 0.609972 + 0.066421I
a = 0.974591 0.413894I
b = 1.41842 + 2.08296I
10.08061 7.22373I 13.8267 + 9.4930I
u = 0.540037 0.328993I
a = 0.994422 + 0.258182I
b = 1.11104 + 1.26776I
3.07886 + 5.47487I 10.1733 11.8369I
u = 0.540037 + 0.328993I
a = 0.994422 0.258182I
b = 1.11104 1.26776I
3.07886 5.47487I 10.1733 + 11.8369I
u = 0.761526 0.373132I
a = 1.73482 + 0.53372I
b = 1.053437 + 0.202017I
3.07886 + 2.64466I 10.17326 2.01946I
u = 0.761526 + 0.373132I
a = 1.73482 0.53372I
b = 1.053437 0.202017I
3.07886 2.64466I 10.17326 + 2.01946I
22
Solution to I
u
8
1(vol +
1CS) Cusp shape
u = 0.825212 0.300777I
a = 0.738510 + 0.041682I
b = 1.45600 1.57813I
10.08061 + 0.89580I 13.8267 4.3634I
u = 0.825212 + 0.300777I
a = 0.738510 0.041682I
b = 1.45600 + 1.57813I
10.08061 0.89580I 13.8267 + 4.3634I
u = 1.11104 1.26776I
a = 0.159426 + 0.350883I
b = 0.540037 + 0.328993I
3.07886 5.47487I 10.1733 + 11.8369I
u = 1.11104 + 1.26776I
a = 0.159426 0.350883I
b = 0.540037 0.328993I
3.07886 + 5.47487I 10.1733 11.8369I
u = 1.118271 0.540827I
a = 1.182458 + 0.370439I
b = 1.073749 + 0.876252I
3.07886 + 5.47487I 10.1733 11.8369I
u = 1.118271 + 0.540827I
a = 1.182458 0.370439I
b = 1.073749 0.876252I
3.07886 5.47487I 10.1733 + 11.8369I
u = 1.324115 0.308813I
a = 0.627592 0.942187I
b = 0.811814 + 0.187323I
10.08061 0.89580I 13.8267 + 4.3634I
u = 1.324115 + 0.308813I
a = 0.627592 + 0.942187I
b = 0.811814 0.187323I
10.08061 + 0.89580I 13.8267 4.3634I
u = 1.41214 1.21990I
a = 0.824124 + 0.034276I
b = 1.32546 + 0.70058I
10.08061 + 7.22373I 13.8267 9.4930I
u = 1.41214 + 1.21990I
a = 0.824124 0.034276I
b = 1.32546 0.70058I
10.08061 7.22373I 13.8267 + 9.4930I
Solution to I
u
8
1(vol +
1CS) Cusp shape
u = 1.45600 1.57813I
a = 0.260679 + 0.153610I
b = 0.825212 0.300777I
10.08061 + 0.89580I 13.8267 4.3634I
u = 1.45600 + 1.57813I
a = 0.260679 0.153610I
b = 0.825212 + 0.300777I
10.08061 0.89580I 13.8267 + 4.3634I
23
IX. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
8
u(u
4
+ u
3
+ u
2
+ 1)
3
(u
7
+ u
5
u
4
u + 1)
2
(u
10
u
9
+ 7u
8
4u
7
+ 23u
6
9u
5
+ 40u
4
9u
3
+ 33u
2
2u + 10)
(u
16
+ 5u
14
+ 16u
12
+ 29u
10
+ 32u
8
+ 25u
6
+ 21u
4
+ 17u
2
+ 5)
(u
16
3u
15
+ ··· 48u + 13)
(79 + 24u + 286u
2
+ 118u
3
+ 508u
4
+ 231u
5
+ 559u
6
+ 249u
7
+ 412u
8
+ 164u
9
+ 199u
10
+ 67u
11
+ 62u
12
+ 13u
13
+ 10u
14
+ u
15
+ u
16
)
2
c
2
(u + 1)(u
4
+ u
3
+ u
2
+ 1)(u
8
+ u
7
+ ··· + u + 2)
(u
10
u
9
+ ··· + u + 1)(u
14
u
13
+ ··· u + 1)
(u
16
u
15
+ ··· + 6u + 1)(u
16
+ 2u
15
+ ··· + 5u + 1)
(u
32
+ u
31
+ ··· 400u + 361)
c
3
u
4
(u + 1)
9
(u
2
+ u + 1)
8
(u
4
+ u
3
2u + 1)
8
(u
10
9u
9
+ ··· 15u + 11)(u
14
13u
13
+ ··· 329u + 47)
(u
16
+ 6u
15
+ ··· u + 1)
c
4
, c
5
, c
10
u(u
4
u
3
+ 3u
2
2u + 1)
14
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
(u
7
+ 4u
6
+ 11u
5
+ 20u
4
+ 26u
3
+ 23u
2
+ 14u + 4)
2
(u
10
+ 6u
9
+ ··· + 40u + 8)
(u
16
+ 11u
14
+ 47u
12
+ 96u
10
+ 90u
8
+ 26u
6
u
4
+ 8u
2
+ 5)
c
6
u
4
(u + 1)
9
(u
2
+ u + 1)
8
(u
4
+ u
3
2u + 1)
8
(u
10
9u
9
+ ··· 15u + 11)(u
14
13u
13
+ ··· 329u + 47)
(u
16
6u
15
+ ··· + u + 1)
c
7
(u + 1)(u
4
+ u
3
+ u
2
+ 1)(u
8
+ u
7
+ ··· + u + 2)
(u
10
u
9
+ ··· + u + 1)(u
14
u
13
+ ··· u + 1)
(u
16
2u
15
+ ··· 5u + 1)(u
16
u
15
+ ··· + 6u + 1)
(u
32
+ u
31
+ ··· 400u + 361)
c
9
(u + 1)(u
4
u
3
+ u
2
+ 1)(u
8
u
7
+ ··· u + 2)
(u
10
+ u
9
+ ··· u + 1)(u
14
+ u
13
+ ··· + u + 1)
(u
16
+ u
15
+ ··· 6u + 1)(u
16
+ 2u
15
+ ··· + 5u + 1)
(u
32
u
31
+ ··· + 400u + 361)
c
11
(u + 1)(u
4
u
3
+ u
2
+ 1)(u
8
u
7
+ ··· u + 2)
(u
10
+ u
9
+ ··· u + 1)(u
14
+ u
13
+ ··· + u + 1)
(u
16
2u
15
+ ··· 5u + 1)(u
16
+ u
15
+ ··· 6u + 1)
(u
32
u
31
+ ··· + 400u + 361)
24
X. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
8
y(y
4
+ y
3
+ 3y
2
+ 2y + 1)
3
(y
7
+ 2y
6
+ y
5
3y
4
2y
3
+ 2y
2
+ y 1)
2
(y
8
+ 5y
7
+ 16y
6
+ 29y
5
+ 32y
4
+ 25y
3
+ 21y
2
+ 17y + 5)
2
(y
10
+ 13y
9
+ ··· + 656y + 100)(y
16
9y
15
+ ··· + 244y + 169)
(6241 + 4.46 × 10
4
y + 1.56 × 10
5
y
2
+ 3.54 × 10
5
y
3
+ 5.76 × 10
5
y
4
+ 7.15 × 10
5
y
5
+ 6.98 × 10
5
y
6
+ 5.46 × 10
5
y
7
+ 3.45 × 10
5
y
8
+ 1.78 × 10
5
y
9
+ 7.40 × 10
4
y
10
+ 2.48 × 10
4
y
11
+ 6578y
12
+ 1335y
13
+ 198y
14
+ 19y
15
+ y
16
)
2
c
2
, c
7
, c
9
c
11
(y 1)(y
4
+ y
3
+ 3y
2
+ 2y + 1)
(y
8
5y
7
+ 30y
6
68y
5
+ 119y
4
127y
3
+ 83y
2
29y + 4)
(y
10
3y
9
+ 15y
8
20y
7
+ 43y
6
17y
5
+ 12y
4
+ 7y
3
6y
2
y + 1)
(y
14
5y
13
+ ··· + y + 1)(y
16
6y
15
+ ··· 3y + 1)
(y
16
5y
15
+ ··· 12y + 1)(y
32
11y
31
+ ··· 2524550y + 130321)
c
3
, c
6
y
4
(y 1)
9
(y
2
+ y + 1)
8
(y
4
y
3
+ 6y
2
4y + 1)
8
(y
10
+ 3y
9
+ ··· + 1601y + 121)(y
14
3y
13
+ ··· + 2397y + 2209)
(y
16
+ 2y
15
+ ··· 9y + 1)
c
4
, c
5
, c
10
y(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
15
(y
7
+ 6y
6
+ 13y
5
+ 16y
4
+ 32y
3
+ 39y
2
+ 12y 16)
2
(y
8
+ 11y
7
+ 47y
6
+ 96y
5
+ 90y
4
+ 26y
3
y
2
+ 8y + 5)
2
(y
10
+ 10y
9
+ ··· + 160y + 64)
25