12a
0634
(K12a
0634
)
A knot diagram
1
Linearized knot diagam
3 7 10 9 11 2 12 1 4 6 5 8
Solving Sequence
3,10 4,7
2 1 6 11 9 5 8 12
c
3
c
2
c
1
c
6
c
10
c
9
c
4
c
8
c
12
c
5
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−2u
24
− 31u
22
+ ··· + 16b − 6, −u
24
+ u
23
+ ··· + 32a − 22, u
25
+ 15u
23
+ ··· − 2u − 2i
I
u
2
= h131149683608665u
33
− 237748805942401u
32
+ ··· + 4229403894019872b − 1000700151544160,
218876053189111u
33
− 464080060606921u
32
+ ··· + 1409801298006624a − 1994609262976856,
u
34
− 2u
33
+ ··· − 36u + 8i
I
u
3
= h−u
2
a + au + u
2
+ b, −2u
2
a + 2a
2
+ 3u
2
− 6a + u + 7, u
3
+ 2u − 1i
I
u
4
= h−u
2
+ b − 1, a − u, u
3
+ 2u − 1i
I
u
5
= ha
3
u + a
3
+ 3a
2
u + 2a
2
+ 3au + b + 5a + u + 3, 2a
4
+ a
3
u + 5a
3
− 2a
2
u + 8a
2
− 3au + 5a − u + 1, u
2
+ 1i
I
u
6
= h−6u
3
a
2
− 9a
2
u
2
+ 11u
3
a + 5a
2
u − 5u
2
a + 30u
3
+ 12a
2
− 2au + 2u
2
+ 43b + 21a + 18u + 26,
2u
3
a
2
+ 2u
3
a + a
3
+ 2a
2
u + u
2
a + 4u
3
+ 2a
2
+ au − u
2
+ 2a + 6u, u
4
+ u
3
+ 2u
2
+ 2u + 1i
I
u
7
= hb − 1, 6a + u − 3, u
2
+ 3i
I
v
1
= ha, b − 1, v −1i
* 8 irreducible components of dim
C
= 0, with total 91 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−2u
24
− 31u
22
+ · · · + 16b − 6, −u
24
+ u
23
+ · · · + 32a − 22, u
25
+
15u
23
+ · · · − 2u − 2i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
7
=
1
32
u
24
−
1
32
u
23
+ ··· +
5
4
u +
11
16
1
8
u
24
+
31
16
u
22
+ ··· −
3
2
u +
3
8
a
2
=
1
32
u
24
−
1
32
u
23
+ ··· +
5
4
u +
11
16
−
3
16
u
24
+
1
8
u
23
+ ··· +
9
8
u −
7
8
a
1
=
−0.156250u
24
+ 0.0937500u
23
+ ··· + 2.37500u − 0.187500
−
3
16
u
24
+
1
8
u
23
+ ··· +
9
8
u −
7
8
a
6
=
1
1
8
u
23
+
7
4
u
21
+ ··· −
1
4
u −
1
4
a
11
=
u
1
8
u
24
+
7
4
u
22
+ ··· −
1
4
u
2
+
3
4
u
a
9
=
−u
u
3
+ u
a
5
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
1
32
u
24
−
3
32
u
23
+ ··· −
11
8
u −
1
16
1
16
u
24
+
1
16
u
23
+ ··· +
1
2
u −
1
8
a
12
=
u
3
+ 2u
1
8
u
24
+
7
4
u
22
+ ··· −
1
4
u
2
+
3
4
u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
7
8
u
24
+
3
8
u
23
+ ··· +
1
2
u +
7
4
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
25
+ 10u
24
+ ··· + 1455u + 169
c
2
, c
6
u
25
− 6u
24
+ ··· + 57u − 13
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
25
+ 15u
23
+ ··· − 2u − 2
c
7
, c
8
, c
12
u
25
+ 6u
24
+ ··· − 3u − 13
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
25
+ 14y
24
+ ··· + 367199y −28561
c
2
, c
6
y
25
− 10y
24
+ ··· + 1455y −169
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y
25
+ 30y
24
+ ··· − 24y −4
c
7
, c
8
, c
12
y
25
− 26y
24
+ ··· + 191y −169
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.755535 + 0.415934I
a = −0.08824 − 1.55070I
b = −1.036580 + 0.642790I
5.29214 + 6.95092I 9.63817 − 7.49283I
u = 0.755535 − 0.415934I
a = −0.08824 + 1.55070I
b = −1.036580 − 0.642790I
5.29214 − 6.95092I 9.63817 + 7.49283I
u = −0.781688 + 0.222090I
a = 0.567778 − 0.932154I
b = −0.523390 + 0.782479I
6.80658 − 1.60733I 12.68937 + 1.64186I
u = −0.781688 − 0.222090I
a = 0.567778 + 0.932154I
b = −0.523390 − 0.782479I
6.80658 + 1.60733I 12.68937 − 1.64186I
u = 0.048749 + 1.304960I
a = 0.055343 − 0.974408I
b = −0.941899 + 1.022970I
1.65681 + 3.64991I 0.77498 − 3.11405I
u = 0.048749 − 1.304960I
a = 0.055343 + 0.974408I
b = −0.941899 − 1.022970I
1.65681 − 3.64991I 0.77498 + 3.11405I
u = 0.071780 + 0.652870I
a = 0.451606 − 0.184043I
b = 0.898942 + 0.773875I
4.71249 − 2.92993I 11.02910 + 1.21081I
u = 0.071780 − 0.652870I
a = 0.451606 + 0.184043I
b = 0.898942 − 0.773875I
4.71249 + 2.92993I 11.02910 − 1.21081I
u = −0.570291 + 0.288945I
a = 0.18281 + 2.07363I
b = −0.957814 − 0.478527I
−0.33137 − 3.73744I 6.36857 + 8.33061I
u = −0.570291 − 0.288945I
a = 0.18281 − 2.07363I
b = −0.957814 + 0.478527I
−0.33137 + 3.73744I 6.36857 − 8.33061I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.09300 + 1.43892I
a = 0.448195 + 0.914529I
b = −0.567898 − 0.881693I
−7.75327 − 0.62404I 1.11905 + 1.82325I
u = 0.09300 − 1.43892I
a = 0.448195 − 0.914529I
b = −0.567898 + 0.881693I
−7.75327 + 0.62404I 1.11905 − 1.82325I
u = 0.34989 + 1.44000I
a = 0.447471 + 0.624414I
b = −0.241733 − 1.058110I
−3.68401 + 9.94366I 4.37752 − 5.16617I
u = 0.34989 − 1.44000I
a = 0.447471 − 0.624414I
b = −0.241733 + 1.058110I
−3.68401 − 9.94366I 4.37752 + 5.16617I
u = 0.32103 + 1.50150I
a = −0.46525 − 1.45818I
b = −1.198590 + 0.622421I
−12.0801 + 10.8715I −1.24061 − 6.62726I
u = 0.32103 − 1.50150I
a = −0.46525 + 1.45818I
b = −1.198590 − 0.622421I
−12.0801 − 10.8715I −1.24061 + 6.62726I
u = −0.40263 + 1.50474I
a = −0.57474 + 1.36291I
b = −1.262700 − 0.622947I
−6.8511 − 15.9422I 2.15332 + 8.18122I
u = −0.40263 − 1.50474I
a = −0.57474 − 1.36291I
b = −1.262700 + 0.622947I
−6.8511 + 15.9422I 2.15332 − 8.18122I
u = −0.116143 + 0.395232I
a = 0.523724 + 0.083480I
b = 0.862091 − 0.296810I
−1.35428 + 1.12969I 0.98953 − 1.48650I
u = −0.116143 − 0.395232I
a = 0.523724 − 0.083480I
b = 0.862091 + 0.296810I
−1.35428 − 1.12969I 0.98953 + 1.48650I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.13068 + 1.60153I
a = 0.436301 − 0.037125I
b = 1.275520 + 0.193623I
−15.0829 + 1.6460I −4.49592 − 1.15064I
u = 0.13068 − 1.60153I
a = 0.436301 + 0.037125I
b = 1.275520 − 0.193623I
−15.0829 − 1.6460I −4.49592 + 1.15064I
u = 0.369219
a = 2.02103
b = −0.505202
0.738512 14.6480
u = −0.08452 + 1.78825I
a = 0.504494 + 0.068165I
b = 0.946646 − 0.263021I
−12.82360 + 1.06304I 4.27303 − 7.22736I
u = −0.08452 − 1.78825I
a = 0.504494 − 0.068165I
b = 0.946646 + 0.263021I
−12.82360 − 1.06304I 4.27303 + 7.22736I
7
II. I
u
2
=
h1.31×10
14
u
33
−2.38×10
14
u
32
+· · ·+4.23×10
15
b−1.00×10
15
, 2.19×10
14
u
33
−
4.64 × 10
14
u
32
+ · · · + 1.41 × 10
15
a − 1.99 × 10
15
, u
34
− 2u
33
+ · · · − 36u + 8i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
7
=
−0.155253u
33
+ 0.329181u
32
+ ··· − 29.1112u + 1.41482
−0.0310090u
33
+ 0.0562133u
32
+ ··· + 2.78205u + 0.236605
a
2
=
0.0670221u
33
− 0.211355u
32
+ ··· + 28.1192u − 2.65059
−0.0233286u
33
+ 0.0485749u
32
+ ··· − 3.94112u + 0.296004
a
1
=
0.0436936u
33
− 0.162780u
32
+ ··· + 24.1780u − 2.35459
−0.0233286u
33
+ 0.0485749u
32
+ ··· − 3.94112u + 0.296004
a
6
=
−0.164018u
33
+ 0.329267u
32
+ ··· − 9.73795u − 1.66269
−0.0499240u
33
+ 0.0898833u
32
+ ··· − 1.35647u + 1.00985
a
11
=
0.123769u
33
− 0.297461u
32
+ ··· + 33.8173u − 5.81214
0.0111960u
33
+ 0.0150363u
32
+ ··· − 3.77992u + 0.912751
a
9
=
−u
u
3
+ u
a
5
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
0.173662u
33
− 0.284141u
32
+ ··· + 14.3998u − 0.525050
−0.00389825u
33
+ 0.0271836u
32
+ ··· − 1.92616u + 0.497794
a
12
=
0.134965u
33
− 0.282425u
32
+ ··· + 28.0374u − 4.89939
−0.0361733u
33
+ 0.110465u
32
+ ··· − 6.82518u + 1.61157
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
11998428764201
44056290562707
u
33
+
35190412311283
88112581125414
u
32
+ ··· +
1450723211244922
44056290562707
u +
103896439660429
44056290562707
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
17
+ 8u
16
+ ··· + 3u + 1)
2
c
2
, c
6
(u
17
+ 2u
16
+ ··· − u − 1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
34
− 2u
33
+ ··· − 36u + 8
c
7
, c
8
, c
12
(u
17
− 2u
16
+ ··· + 3u − 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
17
+ 4y
16
+ ··· − 13y −1)
2
c
2
, c
6
(y
17
− 8y
16
+ ··· + 3y −1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y
34
+ 28y
33
+ ··· + 2192y + 64
c
7
, c
8
, c
12
(y
17
− 16y
16
+ ··· + 19y −1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.864072 + 0.421442I
a = −0.60307 + 1.70997I
b = 1.130680 − 0.513073I
−5.86965 + 6.57063I 0.73995 − 6.43452I
u = 0.864072 − 0.421442I
a = −0.60307 − 1.70997I
b = 1.130680 + 0.513073I
−5.86965 − 6.57063I 0.73995 + 6.43452I
u = 0.701574 + 0.772236I
a = 0.671036 + 0.299184I
b = −1.128570 − 0.359117I
−6.94910 − 1.22724I −2.14847 + 0.85505I
u = 0.701574 − 0.772236I
a = 0.671036 − 0.299184I
b = −1.128570 + 0.359117I
−6.94910 + 1.22724I −2.14847 − 0.85505I
u = −0.400299 + 0.849296I
a = 0.488205 − 0.936880I
b = 0.796399 + 0.723427I
4.74481 − 2.71165I 9.84242 + 3.13710I
u = −0.400299 − 0.849296I
a = 0.488205 + 0.936880I
b = 0.796399 − 0.723427I
4.74481 + 2.71165I 9.84242 − 3.13710I
u = −1.015190 + 0.363118I
a = −0.42443 − 1.39736I
b = 1.172120 + 0.583556I
−0.88663 − 10.83370I 4.89378 + 7.41261I
u = −1.015190 − 0.363118I
a = −0.42443 + 1.39736I
b = 1.172120 − 0.583556I
−0.88663 + 10.83370I 4.89378 − 7.41261I
u = 0.882304 + 0.259295I
a = −0.201550 − 1.387080I
b = 0.288739 + 0.863831I
1.75994 + 5.51158I 8.25126 − 3.84490I
u = 0.882304 − 0.259295I
a = −0.201550 + 1.387080I
b = 0.288739 − 0.863831I
1.75994 − 5.51158I 8.25126 + 3.84490I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.231948 + 1.077680I
a = −0.17884 + 1.65758I
b = −0.867068
−4.54799 −4.68792 + 0.I
u = −0.231948 − 1.077680I
a = −0.17884 − 1.65758I
b = −0.867068
−4.54799 −4.68792 + 0.I
u = −0.001691 + 1.105180I
a = −0.516445 + 0.866608I
b = 0.621791 − 0.419413I
−1.98005 + 1.46955I 7.63583 − 4.66528I
u = −0.001691 − 1.105180I
a = −0.516445 − 0.866608I
b = 0.621791 + 0.419413I
−1.98005 − 1.46955I 7.63583 + 4.66528I
u = 0.553439 + 1.087560I
a = −0.737070 − 0.832523I
b = −0.374678 + 0.520641I
−0.670307 − 0.433874I 6.56834 − 0.87540I
u = 0.553439 − 1.087560I
a = −0.737070 + 0.832523I
b = −0.374678 − 0.520641I
−0.670307 + 0.433874I 6.56834 + 0.87540I
u = −0.815743 + 0.977729I
a = 0.365441 − 0.177204I
b = −1.072950 + 0.498433I
−2.67943 + 4.64771I 3.56085 − 4.11695I
u = −0.815743 − 0.977729I
a = 0.365441 + 0.177204I
b = −1.072950 − 0.498433I
−2.67943 − 4.64771I 3.56085 + 4.11695I
u = 0.510396 + 0.397212I
a = −0.577773 + 0.030688I
b = 0.796399 + 0.723427I
4.74481 − 2.71165I 9.84242 + 3.13710I
u = 0.510396 − 0.397212I
a = −0.577773 − 0.030688I
b = 0.796399 − 0.723427I
4.74481 + 2.71165I 9.84242 − 3.13710I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.281426 + 1.352580I
a = −0.239793 − 0.110964I
b = −0.374678 − 0.520641I
−0.670307 + 0.433874I 6.56834 + 0.87540I
u = 0.281426 − 1.352580I
a = −0.239793 + 0.110964I
b = −0.374678 + 0.520641I
−0.670307 − 0.433874I 6.56834 − 0.87540I
u = −0.303439 + 1.375590I
a = −0.284613 + 0.260893I
b = 0.288739 − 0.863831I
1.75994 − 5.51158I 8.25126 + 3.84490I
u = −0.303439 − 1.375590I
a = −0.284613 − 0.260893I
b = 0.288739 + 0.863831I
1.75994 + 5.51158I 8.25126 − 3.84490I
u = 0.04104 + 1.42314I
a = −1.165140 − 0.532963I
b = −1.128570 + 0.359117I
−6.94910 + 1.22724I −2.14847 − 0.85505I
u = 0.04104 − 1.42314I
a = −1.165140 + 0.532963I
b = −1.128570 − 0.359117I
−6.94910 − 1.22724I −2.14847 + 0.85505I
u = −0.20733 + 1.42614I
a = 0.93419 − 1.28605I
b = 1.130680 + 0.513073I
−5.86965 − 6.57063I 0.73995 + 6.43452I
u = −0.20733 − 1.42614I
a = 0.93419 + 1.28605I
b = 1.130680 − 0.513073I
−5.86965 + 6.57063I 0.73995 − 6.43452I
u = 0.29669 + 1.49249I
a = 0.89771 + 1.10113I
b = 1.172120 − 0.583556I
−0.88663 + 10.83370I 4.89378 − 7.41261I
u = 0.29669 − 1.49249I
a = 0.89771 − 1.10113I
b = 1.172120 + 0.583556I
−0.88663 − 10.83370I 4.89378 + 7.41261I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.16100 + 1.54040I
a = −0.966662 + 0.555173I
b = −1.072950 − 0.498433I
−2.67943 − 4.64771I 3.56085 + 4.11695I
u = −0.16100 − 1.54040I
a = −0.966662 − 0.555173I
b = −1.072950 + 0.498433I
−2.67943 + 4.64771I 3.56085 − 4.11695I
u = 0.005683 + 0.262839I
a = −3.96119 − 3.25601I
b = 0.621791 + 0.419413I
−1.98005 − 1.46955I 7.63583 + 4.66528I
u = 0.005683 − 0.262839I
a = −3.96119 + 3.25601I
b = 0.621791 − 0.419413I
−1.98005 + 1.46955I 7.63583 − 4.66528I
14
III. I
u
3
= h−u
2
a + au + u
2
+ b, −2u
2
a + 2a
2
+ 3u
2
− 6a + u + 7, u
3
+ 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
7
=
a
u
2
a − au − u
2
a
2
=
a
−u
2
a + 2au + u
2
− a
a
1
=
−u
2
a + 2au + u
2
−u
2
a + 2au + u
2
− a
a
6
=
1
u − 1
a
11
=
u
u
2
a
9
=
−u
−u + 1
a
5
=
u
2
+ 1
−u
a
8
=
−u
2
a + au + u
2
− a
−u
2
a + au + u
2
a
12
=
1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
2
+ 4u + 10
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
+ 3u
5
+ u
4
− 3u
3
+ 3u
2
+ 2u + 1
c
2
, c
6
, c
7
c
8
, c
12
u
6
+ u
5
− u
4
+ u
3
+ u
2
− 2u + 1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
(u
3
+ 2u − 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
− 7y
5
+ 25y
4
− 13y
3
+ 23y
2
+ 2y + 1
c
2
, c
6
, c
7
c
8
, c
12
y
6
− 3y
5
+ y
4
+ 3y
3
+ 3y
2
− 2y + 1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
(y
3
+ 4y
2
+ 4y −1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.22670 + 1.46771I
a = 0.493675 − 0.712154I
b = −0.342537 + 0.948428I
−9.44074 − 5.13794I 0.68207 + 3.20902I
u = −0.22670 + 1.46771I
a = 0.403540 + 0.046697I
b = 1.44532 − 0.28297I
−9.44074 − 5.13794I 0.68207 + 3.20902I
u = −0.22670 − 1.46771I
a = 0.493675 + 0.712154I
b = −0.342537 − 0.948428I
−9.44074 + 5.13794I 0.68207 − 3.20902I
u = −0.22670 − 1.46771I
a = 0.403540 − 0.046697I
b = 1.44532 + 0.28297I
−9.44074 + 5.13794I 0.68207 − 3.20902I
u = 0.453398
a = 1.60278 + 1.21084I
b = −0.602785 − 0.300080I
0.787199 12.6360
u = 0.453398
a = 1.60278 − 1.21084I
b = −0.602785 + 0.300080I
0.787199 12.6360
18
IV. I
u
4
= h−u
2
+ b − 1, a − u, u
3
+ 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
7
=
u
u
2
+ 1
a
2
=
u
−u − 1
a
1
=
−1
−u − 1
a
6
=
1
u − 1
a
11
=
u
u
2
a
9
=
−u
−u + 1
a
5
=
u
2
+ 1
−u
a
8
=
−u
2
− u − 1
−u
2
− 1
a
12
=
1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
2
+ 4u + 10
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
+ 3u
2
+ 5u + 4
c
2
, c
6
, c
7
c
8
, c
12
u
3
− u
2
− u + 2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
3
+ 2u − 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
3
+ y
2
+ y −16
c
2
, c
6
, c
7
c
8
, c
12
y
3
− 3y
2
+ 5y −4
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y
3
+ 4y
2
+ 4y −1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.22670 + 1.46771I
a = −0.22670 + 1.46771I
b = −1.102790 − 0.665457I
−9.44074 − 5.13794I 0.68207 + 3.20902I
u = −0.22670 − 1.46771I
a = −0.22670 − 1.46771I
b = −1.102790 + 0.665457I
−9.44074 + 5.13794I 0.68207 − 3.20902I
u = 0.453398
a = 0.453398
b = 1.20557
0.787199 12.6360
22
V. I
u
5
= ha
3
u + 3a
2
u + · · · + 5a + 3, a
3
u − 2a
2
u + · · · + 5a + 1, u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
1
a
7
=
a
−a
3
u − a
3
− 3a
2
u − 2a
2
− 3au − 5a − u − 3
a
2
=
−a
−3a
3
u − a
3
− 7a
2
u − 8au − 5a − 3u − 3
a
1
=
−3a
3
u − a
3
− 7a
2
u − 8au − 6a − 3u − 3
−3a
3
u − a
3
− 7a
2
u − 8au − 5a − 3u − 3
a
6
=
−1
2a
3
u − 2a
3
+ 2a
2
u − 6a
2
+ 6au − 4a + 3u − 2
a
11
=
u
2a
3
u + 2a
3
+ 6a
2
u + 2a
2
+ 4au + 6a + 3u + 3
a
9
=
−u
0
a
5
=
0
1
a
8
=
3a
3
u + a
3
+ 7a
2
u + 8au + 6a + 3u + 3
2a
3
u + 2a
3
+ 5a
2
u + 3a
2
+ 4au + 9a + 2u + 4
a
12
=
u
2a
3
u + 2a
3
+ 6a
2
u + 2a
2
+ 4au + 6a + 2u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8a
3
u + 8a
3
+ 20a
2
u + 12a
2
+ 12au + 32a + 16
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
− u
3
+ 3u
2
− 2u + 1)
2
c
2
, c
6
u
8
− u
6
+ 3u
4
− 2u
2
+ 1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
(u
2
+ 1)
4
c
7
, c
8
, c
12
u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
c
2
, c
6
(y
4
− y
3
+ 3y
2
− 2y + 1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
(y + 1)
8
c
7
, c
8
, c
12
(y
4
− 5y
3
+ 7y
2
− 2y + 1)
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.120947 + 1.161380I
b = 0.911292 − 0.851808I
3.50087 + 3.16396I 3.82674 − 2.56480I
u = 1.000000I
a = −0.557947 − 0.114099I
b = −0.720342 + 0.351808I
−3.50087 + 1.41510I 0.17326 − 4.90874I
u = 1.000000I
a = −0.436506 + 0.194538I
b = −0.911292 − 0.851808I
3.50087 − 3.16396I 3.82674 + 2.56480I
u = 1.000000I
a = −1.38460 − 1.74182I
b = 0.720342 + 0.351808I
−3.50087 − 1.41510I 0.17326 + 4.90874I
u = − 1.000000I
a = −0.120947 − 1.161380I
b = 0.911292 + 0.851808I
3.50087 − 3.16396I 3.82674 + 2.56480I
u = − 1.000000I
a = −0.557947 + 0.114099I
b = −0.720342 − 0.351808I
−3.50087 − 1.41510I 0.17326 + 4.90874I
u = − 1.000000I
a = −0.436506 − 0.194538I
b = −0.911292 + 0.851808I
3.50087 + 3.16396I 3.82674 − 2.56480I
u = − 1.000000I
a = −1.38460 + 1.74182I
b = 0.720342 − 0.351808I
−3.50087 + 1.41510I 0.17326 − 4.90874I
26
VI. I
u
6
= h−6u
3
a
2
+ 11u
3
a + · · · + 21a + 26, 2u
3
a
2
+ 2u
3
a + · · · + 2a
2
+
2a, u
4
+ u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
7
=
a
0.139535a
2
u
3
− 0.255814au
3
+ ··· − 0.488372a − 0.604651
a
2
=
0.209302a
2
u
3
+ 0.116279au
3
+ ··· + 0.767442a + 2.09302
0.0930233a
2
u
3
− 0.837209au
3
+ ··· − 0.325581a − 1.06977
a
1
=
0.302326a
2
u
3
− 0.720930au
3
+ ··· + 0.441860a + 1.02326
0.0930233a
2
u
3
− 0.837209au
3
+ ··· − 0.325581a − 1.06977
a
6
=
u
3
+ 2u
−u
3
− u
a
11
=
2u
3
+ u
2
+ 3u + 3
−u
3
− u
2
− u − 2
a
9
=
−u
u
3
+ u
a
5
=
u
2
+ 1
u
3
+ 2u + 1
a
8
=
−0.139535a
2
u
3
+ 0.255814au
3
+ ··· − 0.511628a + 0.604651
−0.139535a
2
u
3
+ 0.255814au
3
+ ··· + 0.488372a + 0.604651
a
12
=
1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
3
+ 4u + 6
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 4u
5
+ 6u
4
+ 3u
3
− u
2
− u + 1)
2
c
2
, c
6
, c
7
c
8
, c
12
(u
6
− 2u
4
− u
3
+ u
2
+ u + 1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
(u
4
+ u
3
+ 2u
2
+ 2u + 1)
3
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
− 4y
5
+ 10y
4
− 11y
3
+ 19y
2
− 3y + 1)
2
c
2
, c
6
, c
7
c
8
, c
12
(y
6
− 4y
5
+ 6y
4
− 3y
3
− y
2
+ y + 1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
(y
4
+ 3y
3
+ 2y
2
+ 1)
3
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621744 + 0.440597I
a = 0.924150 − 1.015430I
b = −1.252310 + 0.237364I
−3.28987 − 2.02988I 4.00000 + 3.46410I
u = −0.621744 + 0.440597I
a = −0.63726 + 1.54652I
b = 0.218964 − 0.666188I
−3.28987 − 2.02988I 4.00000 + 3.46410I
u = −0.621744 + 0.440597I
a = −1.28689 − 2.26314I
b = 1.033350 + 0.428825I
−3.28987 − 2.02988I 4.00000 + 3.46410I
u = −0.621744 − 0.440597I
a = 0.924150 + 1.015430I
b = −1.252310 − 0.237364I
−3.28987 + 2.02988I 4.00000 − 3.46410I
u = −0.621744 − 0.440597I
a = −0.63726 − 1.54652I
b = 0.218964 + 0.666188I
−3.28987 + 2.02988I 4.00000 − 3.46410I
u = −0.621744 − 0.440597I
a = −1.28689 + 2.26314I
b = 1.033350 − 0.428825I
−3.28987 + 2.02988I 4.00000 − 3.46410I
u = 0.121744 + 1.306620I
a = −1.381780 + 0.280337I
b = −1.252310 − 0.237364I
−3.28987 + 2.02988I 4.00000 − 3.46410I
u = 0.121744 + 1.306620I
a = −0.377578 − 0.240530I
b = 0.218964 + 0.666188I
−3.28987 + 2.02988I 4.00000 − 3.46410I
u = 0.121744 + 1.306620I
a = 0.75936 + 1.69224I
b = 1.033350 − 0.428825I
−3.28987 + 2.02988I 4.00000 − 3.46410I
u = 0.121744 − 1.306620I
a = −1.381780 − 0.280337I
b = −1.252310 + 0.237364I
−3.28987 − 2.02988I 4.00000 + 3.46410I
30
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.121744 − 1.306620I
a = −0.377578 + 0.240530I
b = 0.218964 − 0.666188I
−3.28987 − 2.02988I 4.00000 + 3.46410I
u = 0.121744 − 1.306620I
a = 0.75936 − 1.69224I
b = 1.033350 + 0.428825I
−3.28987 − 2.02988I 4.00000 + 3.46410I
31
VII. I
u
7
= hb − 1, 6a + u − 3, u
2
+ 3i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
3
a
7
=
−
1
6
u +
1
2
1
a
2
=
1
6
u +
1
2
−1
a
1
=
1
6
u −
1
2
−1
a
6
=
1
0
a
11
=
u
u
a
9
=
−u
−2u
a
5
=
−2
−3
a
8
=
−
7
6
u +
1
2
−2u + 1
a
12
=
−u
−2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
(u − 1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
2
+ 3
c
6
, c
7
, c
8
(u + 1)
2
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
(y − 1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
(y + 3)
2
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 1.73205I
a = 0.500000 − 0.288675I
b = 1.00000
−13.1595 0
u = − 1.73205I
a = 0.500000 + 0.288675I
b = 1.00000
−13.1595 0
35
VIII. I
v
1
= ha, b − 1, v − 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
1
0
a
4
=
1
0
a
7
=
0
1
a
2
=
1
−1
a
1
=
0
−1
a
6
=
1
0
a
11
=
1
0
a
9
=
1
0
a
5
=
1
0
a
8
=
1
1
a
12
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
36
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
u − 1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
c
6
, c
7
, c
8
u + 1
37
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
y − 1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y
38
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
0 0
39
IX. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
3
(u
3
+ 3u
2
+ 5u + 4)(u
4
− u
3
+ 3u
2
− 2u + 1)
2
· (u
6
+ 3u
5
+ u
4
− 3u
3
+ 3u
2
+ 2u + 1)
· ((u
6
+ 4u
5
+ 6u
4
+ 3u
3
− u
2
− u + 1)
2
)(u
17
+ 8u
16
+ ··· + 3u + 1)
2
· (u
25
+ 10u
24
+ ··· + 1455u + 169)
c
2
(u − 1)
3
(u
3
− u
2
− u + 2)(u
6
− 2u
4
− u
3
+ u
2
+ u + 1)
2
· (u
6
+ u
5
− u
4
+ u
3
+ u
2
− 2u + 1)(u
8
− u
6
+ 3u
4
− 2u
2
+ 1)
· ((u
17
+ 2u
16
+ ··· − u − 1)
2
)(u
25
− 6u
24
+ ··· + 57u − 13)
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u(u
2
+ 1)
4
(u
2
+ 3)(u
3
+ 2u − 1)
3
(u
4
+ u
3
+ 2u
2
+ 2u + 1)
3
· (u
25
+ 15u
23
+ ··· − 2u − 2)(u
34
− 2u
33
+ ··· − 36u + 8)
c
6
(u + 1)
3
(u
3
− u
2
− u + 2)(u
6
− 2u
4
− u
3
+ u
2
+ u + 1)
2
· (u
6
+ u
5
− u
4
+ u
3
+ u
2
− 2u + 1)(u
8
− u
6
+ 3u
4
− 2u
2
+ 1)
· ((u
17
+ 2u
16
+ ··· − u − 1)
2
)(u
25
− 6u
24
+ ··· + 57u − 13)
c
7
, c
8
(u + 1)
3
(u
3
− u
2
− u + 2)(u
6
− 2u
4
− u
3
+ u
2
+ u + 1)
2
· (u
6
+ u
5
− u
4
+ u
3
+ u
2
− 2u + 1)(u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1)
· ((u
17
− 2u
16
+ ··· + 3u − 1)
2
)(u
25
+ 6u
24
+ ··· − 3u − 13)
c
12
(u − 1)
3
(u
3
− u
2
− u + 2)(u
6
− 2u
4
− u
3
+ u
2
+ u + 1)
2
· (u
6
+ u
5
− u
4
+ u
3
+ u
2
− 2u + 1)(u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1)
· ((u
17
− 2u
16
+ ··· + 3u − 1)
2
)(u
25
+ 6u
24
+ ··· − 3u − 13)
40
X. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
3
(y
3
+ y
2
+ y − 16)(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
· (y
6
− 7y
5
+ 25y
4
− 13y
3
+ 23y
2
+ 2y + 1)
· (y
6
− 4y
5
+ 10y
4
− 11y
3
+ 19y
2
− 3y + 1)
2
· ((y
17
+ 4y
16
+ ··· − 13y − 1)
2
)(y
25
+ 14y
24
+ ··· + 367199y − 28561)
c
2
, c
6
(y − 1)
3
(y
3
− 3y
2
+ 5y − 4)(y
4
− y
3
+ 3y
2
− 2y + 1)
2
· (y
6
− 4y
5
+ 6y
4
− 3y
3
− y
2
+ y + 1)
2
· (y
6
− 3y
5
+ y
4
+ 3y
3
+ 3y
2
− 2y + 1)(y
17
− 8y
16
+ ··· + 3y − 1)
2
· (y
25
− 10y
24
+ ··· + 1455y − 169)
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y(y + 1)
8
(y + 3)
2
(y
3
+ 4y
2
+ 4y − 1)
3
(y
4
+ 3y
3
+ 2y
2
+ 1)
3
· (y
25
+ 30y
24
+ ··· − 24y − 4)(y
34
+ 28y
33
+ ··· + 2192y + 64)
c
7
, c
8
, c
12
(y − 1)
3
(y
3
− 3y
2
+ 5y − 4)(y
4
− 5y
3
+ 7y
2
− 2y + 1)
2
· (y
6
− 4y
5
+ 6y
4
− 3y
3
− y
2
+ y + 1)
2
· (y
6
− 3y
5
+ y
4
+ 3y
3
+ 3y
2
− 2y + 1)(y
17
− 16y
16
+ ··· + 19y − 1)
2
· (y
25
− 26y
24
+ ··· + 191y − 169)
41
