12a
0163
(K12a
0163
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 11 1 12 4 7 6 8 10
Solving Sequence
4,8
9
3,12
7 10 1 2 5 6 11
c
8
c
3
c
7
c
9
c
12
c
1
c
4
c
6
c
11
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.70227 × 10
92
u
46
− 1.37672 × 10
93
u
45
+ ··· + 1.44449 × 10
95
b + 1.08193 × 10
96
,
7.39204 × 10
93
u
46
− 4.58246 × 10
94
u
45
+ ··· + 1.15559 × 10
96
a − 1.33533 × 10
96
,
u
47
− 7u
46
+ ··· − 3840u + 1024i
I
u
2
= h5222u
6
a
5
− 8511u
6
a
4
+ ··· + 2180a + 5110, 4u
6
a
5
+ 36u
6
a
4
+ ··· − 226a + 143,
u
7
+ 3u
6
+ 6u
5
+ 7u
4
+ 5u
3
+ u
2
− 2u − 2i
I
u
3
= h−17789137958u
23
+ 33220776343u
22
+ ··· + 123456179965b + 41044745272,
252494650879u
23
+ 77492790641u
22
+ ··· + 123456179965a + 1483502755409,
u
24
+ 6u
22
+ ··· + 3u + 1i
I
u
4
= h−1.70628 × 10
51
a
11
u
4
− 5.47351 × 10
51
a
10
u
4
+ ··· + 1.45842 × 10
53
a − 6.78636 × 10
52
,
− 2a
11
u
4
− 3a
10
u
4
+ ··· − 130a + 65, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
I
v
1
= ha, 8v
3
+ 12v
2
+ b + 10v + 3, 8v
4
+ 12v
3
+ 12v
2
+ 5v + 1i
I
v
2
= ha, b
6
+ b
5
+ 2b
4
+ 2b
3
+ 2b
2
+ 2b + 1, v −1i
* 6 irreducible components of dim
C
= 0, with total 183 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
=
h2.70×10
92
u
46
−1.38×10
93
u
45
+· · ·+1.44×10
95
b+1.08×10
96
, 7.39×10
93
u
46
−
4.58×10
94
u
45
+· · ·+1.16×10
96
a−1.34×10
96
, u
47
−7u
46
+· · ·−3840u+1024i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
3
=
u
u
3
+ u
a
12
=
−0.00639675u
46
+ 0.0396546u
45
+ ··· − 14.8799u + 1.15554
−0.00187074u
46
+ 0.00953085u
45
+ ··· + 22.6210u − 7.49001
a
7
=
−0.0000443720u
46
− 0.00293863u
45
+ ··· + 8.66522u − 3.07371
0.00506215u
46
− 0.0334217u
45
+ ··· + 15.5213u − 0.178246
a
10
=
−0.00734661u
46
+ 0.0494083u
45
+ ··· − 26.6084u + 6.57684
−0.00878269u
46
+ 0.0635338u
45
+ ··· − 64.5424u + 16.8381
a
1
=
−0.00512383u
46
+ 0.0323413u
45
+ ··· − 19.6023u + 5.34126
−0.00609386u
46
+ 0.0454792u
45
+ ··· − 47.5840u + 16.4994
a
2
=
−0.00947552u
46
+ 0.0616360u
45
+ ··· − 36.3597u + 9.72772
−0.00791514u
46
+ 0.0611719u
45
+ ··· − 64.3672u + 22.0811
a
5
=
0.000300958u
46
− 0.00639035u
45
+ ··· + 19.6905u − 7.54804
0.00542479u
46
− 0.0387317u
45
+ ··· + 39.2928u − 12.8893
a
6
=
−0.00471682u
46
+ 0.0299700u
45
+ ··· − 4.49600u − 3.29609
0.000362637u
46
− 0.00530999u
45
+ ··· + 23.7715u − 12.7111
a
11
=
−0.00826750u
46
+ 0.0491855u
45
+ ··· + 7.74105u − 6.33447
−0.00187074u
46
+ 0.00953085u
45
+ ··· + 22.6210u − 7.49001
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00835732u
46
− 0.0282602u
45
+ ··· − 74.8752u + 42.3285
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
47
+ 23u
46
+ ··· − 6912u + 4096
c
2
, c
4
u
47
− 3u
46
+ ··· − 240u + 64
c
3
, c
8
u
47
− 7u
46
+ ··· − 3840u + 1024
c
5
, c
7
, c
10
c
11
u
47
+ 17u
45
+ ··· − 2u + 1
c
6
, c
9
u
47
+ u
46
+ ··· + 5u + 1
c
12
u
47
+ 42u
46
+ ··· + 3997696u + 131072
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
47
+ 5y
46
+ ··· + 1065680896y −16777216
c
2
, c
4
y
47
− 23y
46
+ ··· − 6912y −4096
c
3
, c
8
y
47
+ 21y
46
+ ··· − 11206656y −1048576
c
5
, c
7
, c
10
c
11
y
47
+ 34y
46
+ ··· + 22y −1
c
6
, c
9
y
47
+ 5y
46
+ ··· − 15y −1
c
12
y
47
− 14y
46
+ ··· + 571230650368y −17179869184
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.844803 + 0.585454I
a = 0.382028 − 0.284959I
b = 0.689635 + 0.097512I
−3.73817 + 2.80492I −12.41752 − 2.95382I
u = 0.844803 − 0.585454I
a = 0.382028 + 0.284959I
b = 0.689635 − 0.097512I
−3.73817 − 2.80492I −12.41752 + 2.95382I
u = −0.116889 + 1.045570I
a = 0.478482 − 0.129287I
b = −0.463355 + 0.003045I
2.60054 + 2.28168I −2.56476 − 2.68089I
u = −0.116889 − 1.045570I
a = 0.478482 + 0.129287I
b = −0.463355 − 0.003045I
2.60054 − 2.28168I −2.56476 + 2.68089I
u = 0.591706 + 0.725415I
a = 0.318073 + 1.144250I
b = −0.683715 + 0.183509I
−4.06475 − 0.35498I −12.38504 + 2.03288I
u = 0.591706 − 0.725415I
a = 0.318073 − 1.144250I
b = −0.683715 − 0.183509I
−4.06475 + 0.35498I −12.38504 − 2.03288I
u = 0.522530 + 0.927802I
a = 0.377878 − 0.342484I
b = 0.879419 + 0.351776I
−3.41339 − 4.10815I −9.71270 + 5.53020I
u = 0.522530 − 0.927802I
a = 0.377878 + 0.342484I
b = 0.879419 − 0.351776I
−3.41339 + 4.10815I −9.71270 − 5.53020I
u = −0.528718 + 0.973805I
a = 0.234475 − 0.625940I
b = −0.651818 − 0.000458I
0.27510 + 3.56602I −7.20697 − 3.60380I
u = −0.528718 − 0.973805I
a = 0.234475 + 0.625940I
b = −0.651818 + 0.000458I
0.27510 − 3.56602I −7.20697 + 3.60380I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.378274 + 1.041930I
a = 0.55552 + 1.57805I
b = −0.164802 − 0.759470I
−1.01111 − 1.34745I −8.38291 − 3.53586I
u = −0.378274 − 1.041930I
a = 0.55552 − 1.57805I
b = −0.164802 + 0.759470I
−1.01111 + 1.34745I −8.38291 + 3.53586I
u = 0.806009 + 0.772506I
a = −0.251056 + 0.347370I
b = −0.286940 − 0.929982I
−0.81815 − 8.32208I −3.76133 + 11.43016I
u = 0.806009 − 0.772506I
a = −0.251056 − 0.347370I
b = −0.286940 + 0.929982I
−0.81815 + 8.32208I −3.76133 − 11.43016I
u = 0.364619 + 1.136610I
a = 0.68230 − 2.35146I
b = 0.50792 + 1.37152I
3.40359 − 9.98566I −2.62320 + 6.71929I
u = 0.364619 − 1.136610I
a = 0.68230 + 2.35146I
b = 0.50792 − 1.37152I
3.40359 + 9.98566I −2.62320 − 6.71929I
u = −1.203240 + 0.185614I
a = −0.141165 + 0.382761I
b = −0.43658 − 1.36501I
5.86998 − 7.58123I −1.27065 + 3.88153I
u = −1.203240 − 0.185614I
a = −0.141165 − 0.382761I
b = −0.43658 + 1.36501I
5.86998 + 7.58123I −1.27065 − 3.88153I
u = 0.658190 + 1.049420I
a = 0.023470 + 0.617425I
b = −0.763224 − 0.063672I
−2.27485 − 8.39804I −10.61831 + 8.01791I
u = 0.658190 − 1.049420I
a = 0.023470 − 0.617425I
b = −0.763224 + 0.063672I
−2.27485 + 8.39804I −10.61831 − 8.01791I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.117325 + 0.702557I
a = 0.366852 + 0.421918I
b = 0.708072 − 0.641224I
−1.83722 + 0.84307I −4.20177 + 0.72689I
u = 0.117325 − 0.702557I
a = 0.366852 − 0.421918I
b = 0.708072 + 0.641224I
−1.83722 − 0.84307I −4.20177 − 0.72689I
u = 1.194080 + 0.493935I
a = −0.138037 − 0.364269I
b = −0.54468 + 1.40917I
4.46440 + 12.91220I −3.19580 − 7.97672I
u = 1.194080 − 0.493935I
a = −0.138037 + 0.364269I
b = −0.54468 − 1.40917I
4.46440 − 12.91220I −3.19580 + 7.97672I
u = −0.529603 + 0.452776I
a = 0.463480 + 0.338892I
b = 0.572558 − 0.322699I
−1.134430 + 0.669866I −7.99633 − 3.35670I
u = −0.529603 − 0.452776I
a = 0.463480 − 0.338892I
b = 0.572558 + 0.322699I
−1.134430 − 0.669866I −7.99633 + 3.35670I
u = −0.593581
a = 0.650414
b = 0.304199
−1.03435 −10.4580
u = 0.230767 + 0.543413I
a = −0.171169 − 0.354083I
b = −0.618665 + 1.130340I
1.16202 + 7.20671I 1.21848 + 2.56039I
u = 0.230767 − 0.543413I
a = −0.171169 + 0.354083I
b = −0.618665 − 1.130340I
1.16202 − 7.20671I 1.21848 − 2.56039I
u = 1.41557 + 0.19018I
a = 0.238371 + 0.686766I
b = 0.267051 − 0.946782I
1.14395 + 4.11529I 0. − 15.1609I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41557 − 0.19018I
a = 0.238371 − 0.686766I
b = 0.267051 + 0.946782I
1.14395 − 4.11529I 0. + 15.1609I
u = −1.22540 + 0.75189I
a = −0.246090 − 0.506658I
b = −0.113298 + 1.119510I
3.81471 + 4.15254I 0
u = −1.22540 − 0.75189I
a = −0.246090 + 0.506658I
b = −0.113298 − 1.119510I
3.81471 − 4.15254I 0
u = −0.60695 + 1.32433I
a = 0.83079 + 1.66964I
b = 0.56919 − 1.47090I
9.5566 + 13.8984I 0
u = −0.60695 − 1.32433I
a = 0.83079 − 1.66964I
b = 0.56919 + 1.47090I
9.5566 − 13.8984I 0
u = 0.75973 + 1.26376I
a = 1.05216 − 1.49784I
b = 0.63326 + 1.46597I
6.9588 − 19.8841I 0
u = 0.75973 − 1.26376I
a = 1.05216 + 1.49784I
b = 0.63326 − 1.46597I
6.9588 + 19.8841I 0
u = 0.99117 + 1.12526I
a = −0.548310 + 0.653114I
b = 0.034489 − 1.053340I
0.02289 + 1.75896I 0
u = 0.99117 − 1.12526I
a = −0.548310 − 0.653114I
b = 0.034489 + 1.053340I
0.02289 − 1.75896I 0
u = −0.00707 + 1.54573I
a = −0.12787 + 1.62424I
b = 0.30210 − 1.45757I
12.5387 + 8.5475I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.00707 − 1.54573I
a = −0.12787 − 1.62424I
b = 0.30210 + 1.45757I
12.5387 − 8.5475I 0
u = 0.75783 + 1.35531I
a = −0.77762 + 1.33679I
b = −0.448938 − 1.118610I
4.59247 − 11.54410I 0
u = 0.75783 − 1.35531I
a = −0.77762 − 1.33679I
b = −0.448938 + 1.118610I
4.59247 + 11.54410I 0
u = −0.25517 + 1.56898I
a = −0.38203 − 1.44288I
b = 0.18549 + 1.40391I
12.10480 − 1.94711I 0
u = −0.25517 − 1.56898I
a = −0.38203 + 1.44288I
b = 0.18549 − 1.40391I
12.10480 + 1.94711I 0
u = −0.60622 + 1.51689I
a = −0.54574 − 1.36308I
b = −0.325270 + 1.113800I
7.05094 + 5.09408I 0
u = −0.60622 − 1.51689I
a = −0.54574 + 1.36308I
b = −0.325270 − 1.113800I
7.05094 − 5.09408I 0
9
II. I
u
2
= h5222u
6
a
5
− 8511u
6
a
4
+ · · · + 2180a + 5110, 4u
6
a
5
+ 36u
6
a
4
+ · · · −
226a + 143, u
7
+ 3u
6
+ 6u
5
+ 7u
4
+ 5u
3
+ u
2
− 2u − 2i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
3
=
u
u
3
+ u
a
12
=
a
−1.16329a
5
u
6
+ 1.89597a
4
u
6
+ ··· − 0.485632a − 1.13834
a
7
=
1.14881a
5
u
6
− 2.32880a
4
u
6
+ ··· − 0.264647a − 2.56315
1.40031a
5
u
6
− 1.46536a
4
u
6
+ ··· + 5.84495a − 0.453553
a
10
=
1.28403a
4
u
6
− 0.761194a
3
u
6
+ ··· + 0.298507a + 3.07062
0.806416a
4
u
6
+ 0.432836a
3
u
6
+ ··· − 4.20896a − 0.630875
a
1
=
−
1
2
u
6
−
3
2
u
5
+ ··· −
1
2
u
2
+
1
2
u
u
6
+ 2u
5
+ 3u
4
+ 2u
3
− u − 1
a
2
=
−
1
2
u
6
−
1
2
u
5
+ ··· −
1
2
u
2
−
1
2
u
−u
6
− 2u
5
− 3u
4
− 3u
3
− u
2
+ 1
a
5
=
−
1
2
u
6
−
3
2
u
5
+ ··· +
1
2
u + 1
−u
4
− u
3
− u
2
+ 1
a
6
=
1.55358a
5
u
6
− 3.01359a
4
u
6
+ ··· + 1.79394a − 1.80307
0.747160a
5
u
6
− 2.29762a
4
u
6
+ ··· + 1.12631a + 0.230786
a
11
=
−1.16329a
5
u
6
+ 1.89597a
4
u
6
+ ··· + 0.514368a − 1.13834
−1.16329a
5
u
6
+ 1.89597a
4
u
6
+ ··· − 0.485632a − 1.13834
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
20628
4489
u
6
a
4
+
280
67
u
6
a
3
+ ··· −
320
67
a −
18564
4489
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
7
+ 3u
6
+ 7u
5
+ 8u
4
+ 9u
3
+ 6u
2
+ 5u + 1)
6
c
2
, c
4
(u
7
− u
6
− u
5
+ 2u
4
+ u
3
− 2u
2
+ u + 1)
6
c
3
, c
8
(u
7
+ 3u
6
+ 6u
5
+ 7u
4
+ 5u
3
+ u
2
− 2u − 2)
6
c
5
, c
7
, c
10
c
11
u
42
+ u
41
+ ··· − 1560u + 347
c
6
, c
9
u
42
+ 3u
41
+ ··· + 130u + 53
c
12
(u
3
− u
2
+ 1)
14
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
7
+ 5y
6
+ 19y
5
+ 36y
4
+ 49y
3
+ 38y
2
+ 13y − 1)
6
c
2
, c
4
(y
7
− 3y
6
+ 7y
5
− 8y
4
+ 9y
3
− 6y
2
+ 5y − 1)
6
c
3
, c
8
(y
7
+ 3y
6
+ 4y
5
+ y
4
− y
3
+ 7y
2
+ 8y − 4)
6
c
5
, c
7
, c
10
c
11
y
42
+ 33y
41
+ ··· + 486752y + 120409
c
6
, c
9
y
42
− 11y
41
+ ··· − 87496y + 2809
c
12
(y
3
− y
2
+ 2y − 1)
14
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.984140 + 0.426152I
a = 0.737720 + 0.711168I
b = 0.418947 − 0.385328I
−0.184741 − 1.102580I −5.76916 + 1.89286I
u = −0.984140 + 0.426152I
a = −0.793584 − 0.796489I
b = −1.239540 − 0.061605I
−0.18474 − 6.75882I −5.76916 + 7.85175I
u = −0.984140 + 0.426152I
a = 0.841475 + 0.111964I
b = 0.130488 + 1.167740I
3.95284 − 3.93070I 0.76010 + 4.87230I
u = −0.984140 + 0.426152I
a = 0.116149 − 0.835603I
b = 0.365594 + 1.240650I
−0.18474 − 6.75882I −5.76916 + 7.85175I
u = −0.984140 + 0.426152I
a = 0.426938 + 0.617821I
b = 0.031150 − 1.011580I
−0.184741 − 1.102580I −5.76916 + 1.89286I
u = −0.984140 + 0.426152I
a = −0.196042 − 0.513489I
b = −0.69197 − 1.45635I
3.95284 − 3.93070I 0.76010 + 4.87230I
u = −0.984140 − 0.426152I
a = 0.737720 − 0.711168I
b = 0.418947 + 0.385328I
−0.184741 + 1.102580I −5.76916 − 1.89286I
u = −0.984140 − 0.426152I
a = −0.793584 + 0.796489I
b = −1.239540 + 0.061605I
−0.18474 + 6.75882I −5.76916 − 7.85175I
u = −0.984140 − 0.426152I
a = 0.841475 − 0.111964I
b = 0.130488 − 1.167740I
3.95284 + 3.93070I 0.76010 − 4.87230I
u = −0.984140 − 0.426152I
a = 0.116149 + 0.835603I
b = 0.365594 − 1.240650I
−0.18474 + 6.75882I −5.76916 − 7.85175I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.984140 − 0.426152I
a = 0.426938 − 0.617821I
b = 0.031150 + 1.011580I
−0.184741 + 1.102580I −5.76916 − 1.89286I
u = −0.984140 − 0.426152I
a = −0.196042 + 0.513489I
b = −0.69197 + 1.45635I
3.95284 + 3.93070I 0.76010 − 4.87230I
u = −0.167785 + 1.218780I
a = −0.788443 − 0.203769I
b = −0.405655 − 0.307642I
5.76303 + 1.87273I 1.179538 − 0.608619I
u = −0.167785 + 1.218780I
a = −0.363766 + 0.081288I
b = 1.218000 + 0.569803I
5.76303 − 3.78352I 1.17954 + 5.35027I
u = −0.167785 + 1.218780I
a = −0.52032 − 1.78091I
b = 0.47547 + 1.85744I
9.90062 − 0.95540I 7.70880 + 2.37083I
u = −0.167785 + 1.218780I
a = −0.38206 − 1.99236I
b = −0.477401 + 1.254840I
5.76303 + 1.87273I 1.179538 − 0.608619I
u = −0.167785 + 1.218780I
a = −0.49358 + 2.12435I
b = −0.13510 − 1.41647I
9.90062 − 0.95540I 7.70880 + 2.37083I
u = −0.167785 + 1.218780I
a = 0.76890 + 2.37410I
b = −0.078011 − 1.184130I
5.76303 − 3.78352I 1.17954 + 5.35027I
u = −0.167785 − 1.218780I
a = −0.788443 + 0.203769I
b = −0.405655 + 0.307642I
5.76303 − 1.87273I 1.179538 + 0.608619I
u = −0.167785 − 1.218780I
a = −0.363766 − 0.081288I
b = 1.218000 − 0.569803I
5.76303 + 3.78352I 1.17954 − 5.35027I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.167785 − 1.218780I
a = −0.52032 + 1.78091I
b = 0.47547 − 1.85744I
9.90062 + 0.95540I 7.70880 − 2.37083I
u = −0.167785 − 1.218780I
a = −0.38206 + 1.99236I
b = −0.477401 − 1.254840I
5.76303 − 1.87273I 1.179538 + 0.608619I
u = −0.167785 − 1.218780I
a = −0.49358 − 2.12435I
b = −0.13510 + 1.41647I
9.90062 + 0.95540I 7.70880 − 2.37083I
u = −0.167785 − 1.218780I
a = 0.76890 − 2.37410I
b = −0.078011 + 1.184130I
5.76303 + 3.78352I 1.17954 − 5.35027I
u = −0.654547 + 1.202470I
a = −0.141241 + 0.714180I
b = 1.46294 − 0.00954I
2.27436 + 12.75880I −3.97003 − 10.31609I
u = −0.654547 + 1.202470I
a = 0.76606 + 1.40096I
b = 0.152871 − 1.268940I
2.27436 + 7.10253I −3.97003 − 4.35720I
u = −0.654547 + 1.202470I
a = 1.00141 + 1.33815I
b = 0.91938 − 1.48492I
6.41195 + 9.93065I 2.55923 − 7.33664I
u = −0.654547 + 1.202470I
a = −1.57657 − 0.89969I
b = −0.270073 + 1.125830I
6.41195 + 9.93065I 2.55923 − 7.33664I
u = −0.654547 + 1.202470I
a = 0.0226124 + 0.0838717I
b = −0.731518 − 0.356031I
2.27436 + 7.10253I −3.97003 − 4.35720I
u = −0.654547 + 1.202470I
a = −1.08160 − 1.86803I
b = −0.39415 + 1.36343I
2.27436 + 12.75880I −3.97003 − 10.31609I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.654547 − 1.202470I
a = −0.141241 − 0.714180I
b = 1.46294 + 0.00954I
2.27436 − 12.75880I −3.97003 + 10.31609I
u = −0.654547 − 1.202470I
a = 0.76606 − 1.40096I
b = 0.152871 + 1.268940I
2.27436 − 7.10253I −3.97003 + 4.35720I
u = −0.654547 − 1.202470I
a = 1.00141 − 1.33815I
b = 0.91938 + 1.48492I
6.41195 − 9.93065I 2.55923 + 7.33664I
u = −0.654547 − 1.202470I
a = −1.57657 + 0.89969I
b = −0.270073 − 1.125830I
6.41195 − 9.93065I 2.55923 + 7.33664I
u = −0.654547 − 1.202470I
a = 0.0226124 − 0.0838717I
b = −0.731518 + 0.356031I
2.27436 − 7.10253I −3.97003 + 4.35720I
u = −0.654547 − 1.202470I
a = −1.08160 + 1.86803I
b = −0.39415 − 1.36343I
2.27436 − 12.75880I −3.97003 + 10.31609I
u = 0.612945
a = 0.92534 + 1.35436I
b = 0.376065 − 0.940931I
0.95928 + 2.82812I −5.44897 − 2.97945I
u = 0.612945
a = 0.92534 − 1.35436I
b = 0.376065 + 0.940931I
0.95928 − 2.82812I −5.44897 + 2.97945I
u = 0.612945
a = 0.94362 + 1.89521I
b = −0.14327 + 1.43225I
5.09686 − 61.080296 + 0.10I
u = 0.612945
a = 0.94362 − 1.89521I
b = −0.14327 − 1.43225I
5.09686 − 61.080296 + 0.10I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.612945
a = −0.21302 + 2.97475I
b = −0.484219 + 0.283629I
0.95928 + 2.82812I −5.44897 − 2.97945I
u = 0.612945
a = −0.21302 − 2.97475I
b = −0.484219 − 0.283629I
0.95928 − 2.82812I −5.44897 + 2.97945I
17
III.
I
u
3
= h−1.78×10
10
u
23
+3.32×10
10
u
22
+· · ·+1.23×10
11
b+4.10×10
10
, 2.52×
10
11
u
23
+7.75×10
10
u
22
+· · ·+1.23×10
11
a+1.48×10
12
, u
24
+6u
22
+· · ·+3u+1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
3
=
u
u
3
+ u
a
12
=
−2.04522u
23
− 0.627695u
22
+ ··· − 0.358592u − 12.0164
0.144093u
23
− 0.269090u
22
+ ··· + 0.758652u − 0.332464
a
7
=
2.81971u
23
− 2.21363u
22
+ ··· + 17.5956u + 1.17885
0.135846u
23
− 0.0946331u
22
+ ··· + 1.96665u + 0.813872
a
10
=
2.91642u
23
− 1.86706u
22
+ ··· + 15.5197u − 1.44082
0.518872u
23
− 0.183670u
22
+ ··· + 1.36538u + 0.385584
a
1
=
−1.15388u
23
+ 0.396430u
22
+ ··· − 3.81616u − 2.21358
−0.123678u
23
− 0.0283571u
22
+ ··· + 0.0809646u − 0.0612439
a
2
=
−1.29882u
23
+ 0.303702u
22
+ ··· − 3.72961u − 2.53129
−0.208641u
23
− 0.0459699u
22
+ ··· + 0.590643u − 0.286228
a
5
=
1.03969u
23
− 0.317712u
22
+ ··· + 3.93254u + 2.54876
−0.114188u
23
+ 0.0787179u
22
+ ··· + 0.116374u + 0.335186
a
6
=
3.99525u
23
− 2.62597u
22
+ ··· + 23.4948u + 3.54148
0.0216583u
23
− 0.0159152u
22
+ ··· + 2.08303u + 1.14906
a
11
=
−1.90112u
23
− 0.896784u
22
+ ··· + 0.400060u − 12.3489
0.144093u
23
− 0.269090u
22
+ ··· + 0.758652u − 0.332464
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
1639350892343
123456179965
u
23
+
374737028393
123456179965
u
22
+ ··· −
7741933690621
123456179965
u −
4197302002443
123456179965
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
− 12u
23
+ ··· − u + 1
c
2
u
24
+ 4u
23
+ ··· + 3u + 1
c
3
u
24
+ 6u
22
+ ··· − 3u + 1
c
4
u
24
− 4u
23
+ ··· − 3u + 1
c
5
, c
11
u
24
+ 12u
22
+ ··· + 3u + 1
c
6
, c
9
u
24
− 3u
23
+ ··· − 5u
3
+ 1
c
7
, c
10
u
24
+ 12u
22
+ ··· − 3u + 1
c
8
u
24
+ 6u
22
+ ··· + 3u + 1
c
12
u
24
− 12u
23
+ ··· − 6u
2
+ 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
+ 4y
23
+ ··· − 21y + 1
c
2
, c
4
y
24
− 12y
23
+ ··· − y + 1
c
3
, c
8
y
24
+ 12y
23
+ ··· − y + 1
c
5
, c
7
, c
10
c
11
y
24
+ 24y
23
+ ··· + 19y + 1
c
6
, c
9
y
24
− 5y
23
+ ··· − 6y
2
+ 1
c
12
y
24
− 12y
23
+ ··· − 12y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.385812 + 0.959765I
a = 0.214252 + 0.609777I
b = 0.595502 + 0.631954I
1.95079 + 0.48887I −4.75553 + 0.58923I
u = −0.385812 − 0.959765I
a = 0.214252 − 0.609777I
b = 0.595502 − 0.631954I
1.95079 − 0.48887I −4.75553 − 0.58923I
u = −1.077360 + 0.108391I
a = 0.760516 − 0.736995I
b = 0.334692 + 0.897697I
1.59930 − 3.87913I 1.55003 + 6.90819I
u = −1.077360 − 0.108391I
a = 0.760516 + 0.736995I
b = 0.334692 − 0.897697I
1.59930 + 3.87913I 1.55003 − 6.90819I
u = 0.008495 + 0.868868I
a = −0.529585 − 0.609146I
b = 0.461312 − 0.571784I
2.95906 + 3.49000I 0.13816 − 7.20591I
u = 0.008495 − 0.868868I
a = −0.529585 + 0.609146I
b = 0.461312 + 0.571784I
2.95906 − 3.49000I 0.13816 + 7.20591I
u = 0.743321 + 0.919032I
a = −0.072413 − 0.523633I
b = 0.161396 + 0.548115I
−1.30077 − 7.57890I −7.21370 + 4.06185I
u = 0.743321 − 0.919032I
a = −0.072413 + 0.523633I
b = 0.161396 − 0.548115I
−1.30077 + 7.57890I −7.21370 − 4.06185I
u = −0.122647 + 1.176190I
a = −0.12178 + 1.86194I
b = −0.21101 − 1.58776I
8.95699 − 0.57004I −1.42659 − 1.30232I
u = −0.122647 − 1.176190I
a = −0.12178 − 1.86194I
b = −0.21101 + 1.58776I
8.95699 + 0.57004I −1.42659 + 1.30232I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.569181 + 0.581107I
a = −0.602978 + 1.183210I
b = 0.284741 − 0.656736I
1.91394 + 3.51457I 0.81290 − 6.37218I
u = −0.569181 − 0.581107I
a = −0.602978 − 1.183210I
b = 0.284741 + 0.656736I
1.91394 − 3.51457I 0.81290 + 6.37218I
u = 0.449036 + 1.170250I
a = 0.45643 − 1.62999I
b = −0.16034 + 1.69292I
7.75271 − 4.61755I −5.14908 + 6.28860I
u = 0.449036 − 1.170250I
a = 0.45643 + 1.62999I
b = −0.16034 − 1.69292I
7.75271 + 4.61755I −5.14908 − 6.28860I
u = 0.615552 + 0.171616I
a = 3.30797 + 1.75043I
b = 0.05347 + 1.55815I
4.79284 + 0.47371I −13.5113 − 10.2243I
u = 0.615552 − 0.171616I
a = 3.30797 − 1.75043I
b = 0.05347 − 1.55815I
4.79284 − 0.47371I −13.5113 + 10.2243I
u = 0.464020 + 1.310710I
a = −0.83858 + 1.39561I
b = −0.434102 − 1.121700I
6.91981 − 4.17688I 0.37708 + 1.71503I
u = 0.464020 − 1.310710I
a = −0.83858 − 1.39561I
b = −0.434102 + 1.121700I
6.91981 + 4.17688I 0.37708 − 1.71503I
u = −0.639779 + 1.245700I
a = −1.08711 − 1.18859I
b = −0.580023 + 1.066030I
4.79955 + 9.96183I −2.92626 − 7.27946I
u = −0.639779 − 1.245700I
a = −1.08711 + 1.18859I
b = −0.580023 − 1.066030I
4.79955 − 9.96183I −2.92626 + 7.27946I
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.847108 + 1.119260I
a = 0.505190 − 1.089610I
b = −0.074936 + 0.774321I
−1.14238 + 1.71576I −18.9155 − 13.5239I
u = 0.847108 − 1.119260I
a = 0.505190 + 1.089610I
b = −0.074936 − 0.774321I
−1.14238 − 1.71576I −18.9155 + 13.5239I
u = −0.332750 + 0.244285I
a = −11.99190 + 1.92092I
b = −0.430698 + 0.709042I
0.27656 + 2.64864I −18.9803 − 22.4027I
u = −0.332750 − 0.244285I
a = −11.99190 − 1.92092I
b = −0.430698 − 0.709042I
0.27656 − 2.64864I −18.9803 + 22.4027I
23
IV. I
u
4
= h−1.71 × 10
51
a
11
u
4
− 5.47 × 10
51
a
10
u
4
+ · · · + 1.46 × 10
53
a − 6.79 ×
10
52
, −2a
11
u
4
− 3a
10
u
4
+ · · · − 130a + 65, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
3
=
u
u
3
+ u
a
12
=
a
0.0732427a
11
u
4
+ 0.234953a
10
u
4
+ ··· − 6.26032a + 2.91308
a
7
=
0.00160005a
11
u
4
− 0.0571426a
10
u
4
+ ··· + 2.90814a + 1.14145
−0.0583572a
11
u
4
− 0.220679a
10
u
4
+ ··· + 14.4659a − 0.113031
a
10
=
0.0334129a
11
u
4
+ 0.219589a
10
u
4
+ ··· − 15.3234a − 2.96658
0.0888781a
11
u
4
+ 0.194926a
10
u
4
+ ··· − 7.20124a + 2.18044
a
1
=
−0.0973345a
11
u
4
− 0.360963a
10
u
4
+ ··· + 19.8860a + 0.469840
0.0240891a
11
u
4
+ 0.191688a
10
u
4
+ ··· − 13.8093a − 2.09320
a
2
=
0.0498218a
11
u
4
+ 0.0533522a
10
u
4
+ ··· + 1.09982a + 1.13373
0.0206355a
11
u
4
− 0.0879363a
10
u
4
+ ··· + 10.5617a + 2.04394
a
5
=
−0.0722419a
11
u
4
− 0.137729a
10
u
4
+ ··· + 2.20329a − 2.38563
0.0250926a
11
u
4
+ 0.223234a
10
u
4
+ ··· − 17.6827a − 2.85547
a
6
=
−0.0716813a
11
u
4
− 0.327262a
10
u
4
+ ··· + 16.0376a + 1.19081
0.0283710a
11
u
4
+ 0.0243660a
10
u
4
+ ··· − 1.23422a + 1.16463
a
11
=
0.0732427a
11
u
4
+ 0.234953a
10
u
4
+ ··· − 5.26032a + 2.91308
0.0732427a
11
u
4
+ 0.234953a
10
u
4
+ ··· − 6.26032a + 2.91308
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0406867a
11
u
4
+ 0.0916623a
10
u
4
+ ··· − 16.2544a + 5.52616
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
10
+ 5u
9
+ ··· + 4u + 1)
6
c
2
, c
4
(u
10
− u
9
− 2u
8
+ 4u
7
− 4u
5
+ 3u
4
+ u
3
− 2u
2
+ 1)
6
c
3
, c
8
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
12
c
5
, c
7
, c
10
c
11
u
60
+ u
59
+ ··· − 840u + 61
c
6
, c
9
u
60
+ 3u
59
+ ··· + 184u + 23
c
12
(u
3
− u
2
+ 1)
20
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
10
− y
9
− 6y
7
+ 22y
6
+ 6y
5
+ 45y
4
+ 15y
3
+ 22y
2
+ 4y + 1)
6
c
2
, c
4
(y
10
− 5y
9
+ ··· − 4y + 1)
6
c
3
, c
8
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
12
c
5
, c
7
, c
10
c
11
y
60
+ 45y
59
+ ··· + 132540y + 3721
c
6
, c
9
y
60
− 15y
59
+ ··· − 14076y + 529
c
12
(y
3
− y
2
+ 2y − 1)
20
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 + 0.822375I
a = −0.308460 − 0.829537I
b = −1.079350 + 0.448931I
−1.05009 − 1.29754I −4.99464 − 1.45120I
u = −0.339110 + 0.822375I
a = −0.005750 + 0.811726I
b = −0.733526 − 0.736114I
−1.05009 + 4.35870I −4.99464 − 7.41010I
u = −0.339110 + 0.822375I
a = 0.475699 + 0.651412I
b = 0.672537 − 0.913276I
−1.05009 + 4.35870I −4.99464 − 7.41010I
u = −0.339110 + 0.822375I
a = 0.332091 − 0.707040I
b = 0.608644 + 1.133040I
−1.05009 − 1.29754I −4.99464 − 1.45120I
u = −0.339110 + 0.822375I
a = 0.472163 + 0.240206I
b = −0.111510 + 0.825614I
3.08749 + 1.53058I 1.53463 − 4.43065I
u = −0.339110 + 0.822375I
a = −1.10658 + 1.03616I
b = 1.092060 − 0.041395I
−1.05009 + 4.35870I −4.99464 − 7.41010I
u = −0.339110 + 0.822375I
a = 0.181691 − 0.337491I
b = −0.592837 − 0.914921I
3.08749 + 1.53058I 1.53463 − 4.43065I
u = −0.339110 + 0.822375I
a = 0.31326 + 1.60794I
b = −0.060888 − 0.451565I
−1.05009 − 1.29754I −4.99464 − 1.45120I
u = −0.339110 + 0.822375I
a = 1.38965 + 1.74838I
b = −0.253872 − 0.843581I
−1.05009 − 1.29754I −4.99464 − 1.45120I
u = −0.339110 + 0.822375I
a = 1.58940 + 2.88329I
b = 0.56963 − 1.39967I
3.08749 + 1.53058I 1.53463 − 4.43065I
27
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 + 0.822375I
a = −2.89507 − 1.92608I
b = −0.041883 + 1.175610I
3.08749 + 1.53058I 1.53463 − 4.43065I
u = −0.339110 + 0.822375I
a = −1.58194 − 3.66991I
b = −0.378916 + 1.167410I
−1.05009 + 4.35870I −4.99464 − 7.41010I
u = −0.339110 − 0.822375I
a = −0.308460 + 0.829537I
b = −1.079350 − 0.448931I
−1.05009 + 1.29754I −4.99464 + 1.45120I
u = −0.339110 − 0.822375I
a = −0.005750 − 0.811726I
b = −0.733526 + 0.736114I
−1.05009 − 4.35870I −4.99464 + 7.41010I
u = −0.339110 − 0.822375I
a = 0.475699 − 0.651412I
b = 0.672537 + 0.913276I
−1.05009 − 4.35870I −4.99464 + 7.41010I
u = −0.339110 − 0.822375I
a = 0.332091 + 0.707040I
b = 0.608644 − 1.133040I
−1.05009 + 1.29754I −4.99464 + 1.45120I
u = −0.339110 − 0.822375I
a = 0.472163 − 0.240206I
b = −0.111510 − 0.825614I
3.08749 − 1.53058I 1.53463 + 4.43065I
u = −0.339110 − 0.822375I
a = −1.10658 − 1.03616I
b = 1.092060 + 0.041395I
−1.05009 − 4.35870I −4.99464 + 7.41010I
u = −0.339110 − 0.822375I
a = 0.181691 + 0.337491I
b = −0.592837 + 0.914921I
3.08749 − 1.53058I 1.53463 + 4.43065I
u = −0.339110 − 0.822375I
a = 0.31326 − 1.60794I
b = −0.060888 + 0.451565I
−1.05009 + 1.29754I −4.99464 + 1.45120I
28
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 − 0.822375I
a = 1.38965 − 1.74838I
b = −0.253872 + 0.843581I
−1.05009 + 1.29754I −4.99464 + 1.45120I
u = −0.339110 − 0.822375I
a = 1.58940 − 2.88329I
b = 0.56963 + 1.39967I
3.08749 − 1.53058I 1.53463 + 4.43065I
u = −0.339110 − 0.822375I
a = −2.89507 + 1.92608I
b = −0.041883 − 1.175610I
3.08749 − 1.53058I 1.53463 + 4.43065I
u = −0.339110 − 0.822375I
a = −1.58194 + 3.66991I
b = −0.378916 − 1.167410I
−1.05009 − 4.35870I −4.99464 + 7.41010I
u = 0.766826
a = 0.886969 + 0.605378I
b = 0.411481 − 0.991149I
1.02189 + 2.82812I −4.02861 − 2.97945I
u = 0.766826
a = 0.886969 − 0.605378I
b = 0.411481 + 0.991149I
1.02189 − 2.82812I −4.02861 + 2.97945I
u = 0.766826
a = 0.142592 + 1.271050I
b = 0.283929 − 1.034350I
1.02189 + 2.82812I −4.02861 − 2.97945I
u = 0.766826
a = 0.142592 − 1.271050I
b = 0.283929 + 1.034350I
1.02189 − 2.82812I −4.02861 + 2.97945I
u = 0.766826
a = −0.372349 + 1.229280I
b = −0.32676 + 1.53371I
5.15947 2.50065 + 0.I
u = 0.766826
a = −0.372349 − 1.229280I
b = −0.32676 − 1.53371I
5.15947 2.50065 + 0.I
29
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.766826
a = 1.46990 + 0.50951I
b = −0.020195 + 1.342860I
5.15947 2.50065 + 0.I
u = 0.766826
a = 1.46990 − 0.50951I
b = −0.020195 − 1.342860I
5.15947 2.50065 + 0.I
u = 0.766826
a = 1.17834 + 1.64060I
b = −0.104669 + 0.123242I
1.02189 + 2.82812I −4.02861 − 2.97945I
u = 0.766826
a = 1.17834 − 1.64060I
b = −0.104669 − 0.123242I
1.02189 − 2.82812I −4.02861 + 2.97945I
u = 0.766826
a = −1.37938 + 1.51827I
b = −0.852652 + 0.310507I
1.02189 + 2.82812I −4.02861 − 2.97945I
u = 0.766826
a = −1.37938 − 1.51827I
b = −0.852652 − 0.310507I
1.02189 − 2.82812I −4.02861 + 2.97945I
u = 0.455697 + 1.200150I
a = −0.867579 − 0.090126I
b = −0.386902 + 0.537495I
4.49337 − 7.22895I −0.76544 + 6.47803I
u = 0.455697 + 1.200150I
a = −0.340253 − 0.607754I
b = 1.388470 + 0.128289I
4.49337 − 7.22895I −0.76544 + 6.47803I
u = 0.455697 + 1.200150I
a = −0.91593 + 1.34753I
b = 0.32976 − 1.97974I
8.63095 − 4.40083I 5.76382 + 3.49859I
u = 0.455697 + 1.200150I
a = −0.068281 − 0.306353I
b = −0.607002 + 0.238854I
4.49337 − 1.57271I −0.765442 + 0.519139I
30
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.455697 + 1.200150I
a = 0.64148 − 1.61014I
b = −0.016904 + 1.231170I
4.49337 − 1.57271I −0.765442 + 0.519139I
u = 0.455697 + 1.200150I
a = −0.126723 − 0.218957I
b = 1.163220 − 0.775553I
4.49337 − 1.57271I −0.765442 + 0.519139I
u = 0.455697 + 1.200150I
a = 0.80691 − 1.66440I
b = 0.80322 + 1.56795I
8.63095 − 4.40083I 5.76382 + 3.49859I
u = 0.455697 + 1.200150I
a = −0.90892 + 1.71085I
b = −0.656448 − 1.246570I
4.49337 − 7.22895I −0.76544 + 6.47803I
u = 0.455697 + 1.200150I
a = 0.10394 − 1.98838I
b = −0.10166 + 1.48737I
8.63095 − 4.40083I 5.76382 + 3.49859I
u = 0.455697 + 1.200150I
a = −1.58034 + 1.28725I
b = −0.222841 − 1.200460I
8.63095 − 4.40083I 5.76382 + 3.49859I
u = 0.455697 + 1.200150I
a = 1.29027 − 1.88553I
b = 0.052319 + 1.112940I
4.49337 − 1.57271I −0.765442 + 0.519139I
u = 0.455697 + 1.200150I
a = −0.81679 + 2.23955I
b = −0.326450 − 1.320900I
4.49337 − 7.22895I −0.76544 + 6.47803I
u = 0.455697 − 1.200150I
a = −0.867579 + 0.090126I
b = −0.386902 − 0.537495I
4.49337 + 7.22895I −0.76544 − 6.47803I
u = 0.455697 − 1.200150I
a = −0.340253 + 0.607754I
b = 1.388470 − 0.128289I
4.49337 + 7.22895I −0.76544 − 6.47803I
31
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.455697 − 1.200150I
a = −0.91593 − 1.34753I
b = 0.32976 + 1.97974I
8.63095 + 4.40083I 5.76382 − 3.49859I
u = 0.455697 − 1.200150I
a = −0.068281 + 0.306353I
b = −0.607002 − 0.238854I
4.49337 + 1.57271I −0.765442 − 0.519139I
u = 0.455697 − 1.200150I
a = 0.64148 + 1.61014I
b = −0.016904 − 1.231170I
4.49337 + 1.57271I −0.765442 − 0.519139I
u = 0.455697 − 1.200150I
a = −0.126723 + 0.218957I
b = 1.163220 + 0.775553I
4.49337 + 1.57271I −0.765442 − 0.519139I
u = 0.455697 − 1.200150I
a = 0.80691 + 1.66440I
b = 0.80322 − 1.56795I
8.63095 + 4.40083I 5.76382 − 3.49859I
u = 0.455697 − 1.200150I
a = −0.90892 − 1.71085I
b = −0.656448 + 1.246570I
4.49337 + 7.22895I −0.76544 − 6.47803I
u = 0.455697 − 1.200150I
a = 0.10394 + 1.98838I
b = −0.10166 − 1.48737I
8.63095 + 4.40083I 5.76382 − 3.49859I
u = 0.455697 − 1.200150I
a = −1.58034 − 1.28725I
b = −0.222841 + 1.200460I
8.63095 + 4.40083I 5.76382 − 3.49859I
u = 0.455697 − 1.200150I
a = 1.29027 + 1.88553I
b = 0.052319 − 1.112940I
4.49337 + 1.57271I −0.765442 − 0.519139I
u = 0.455697 − 1.200150I
a = −0.81679 − 2.23955I
b = −0.326450 + 1.320900I
4.49337 + 7.22895I −0.76544 − 6.47803I
32
V. I
v
1
= ha, 8v
3
+ 12v
2
+ b + 10v + 3, 8v
4
+ 12v
3
+ 12v
2
+ 5v + 1i
(i) Arc colorings
a
4
=
v
0
a
8
=
1
0
a
9
=
1
0
a
3
=
v
0
a
12
=
0
−8v
3
− 12v
2
− 10v − 3
a
7
=
1
−8v
3
− 8v
2
− 8v − 1
a
10
=
8v
3
+ 8v
2
+ 8v + 2
16v
3
+ 20v
2
+ 18v + 5
a
1
=
8v
3
+ 12v
2
+ 12v + 4
8v
3
+ 12v
2
+ 12v + 5
a
2
=
8v
3
+ 12v
2
+ 13v + 4
8v
3
+ 12v
2
+ 12v + 5
a
5
=
−8v
3
− 12v
2
− 12v − 4
−8v
3
− 12v
2
− 12v − 5
a
6
=
−4v
2
− 4v − 3
−4v
2
− 4v − 4
a
11
=
−8v
3
− 12v
2
− 10v − 3
−8v
3
− 12v
2
− 10v − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 72v
3
+ 101v
2
+ 96v + 19
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
8
u
4
c
4
(u + 1)
4
c
5
, c
7
u
4
+ u
2
− u + 1
c
6
u
4
+ 2u
3
+ 3u
2
+ u + 1
c
9
u
4
− 2u
3
+ 3u
2
− u + 1
c
10
, c
11
u
4
+ u
2
+ u + 1
c
12
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
4
c
3
, c
8
y
4
c
5
, c
7
, c
10
c
11
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
6
, c
9
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
12
y
4
− y
3
+ 2y
2
+ 7y + 4
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.447562 + 0.776246I
a = 0
b = 0.547424 + 0.585652I
−2.62503 − 1.39709I −12.79646 + 4.25046I
v = −0.447562 − 0.776246I
a = 0
b = 0.547424 − 0.585652I
−2.62503 + 1.39709I −12.79646 − 4.25046I
v = −0.302438 + 0.253422I
a = 0
b = −0.547424 − 1.120870I
0.98010 − 7.64338I −5.07854 + 12.68142I
v = −0.302438 − 0.253422I
a = 0
b = −0.547424 + 1.120870I
0.98010 + 7.64338I −5.07854 − 12.68142I
36
VI. I
v
2
= ha, b
6
+ b
5
+ 2b
4
+ 2b
3
+ 2b
2
+ 2b + 1, v − 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
1
0
a
9
=
1
0
a
3
=
1
0
a
12
=
0
b
a
7
=
1
−b
2
a
10
=
b
2
+ 1
−b
4
a
1
=
b
5
+ 2b
3
+ b
−1
a
2
=
b
5
+ 2b
3
+ b + 1
−1
a
5
=
−b
5
− 2b
3
− b
1
a
6
=
−2b
5
− 3b
3
− b
2
− 2b − 1
−b
5
− b
3
− b
2
− b
a
11
=
b
b
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4b
3
+ 4b − 4
37
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
8
u
6
c
4
(u + 1)
6
c
5
, c
7
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
6
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
9
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
10
, c
11
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
12
(u
3
− u
2
+ 1)
2
38
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
6
c
3
, c
8
y
6
c
5
, c
7
, c
10
c
11
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
6
, c
9
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
12
(y
3
− y
2
+ 2y − 1)
2
39
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 0.498832 + 1.001300I
−1.37919 − 2.82812I −7.50976 + 2.97945I
v = 1.00000
a = 0
b = 0.498832 − 1.001300I
−1.37919 + 2.82812I −7.50976 − 2.97945I
v = 1.00000
a = 0
b = −0.284920 + 1.115140I
2.75839 −6 − 0.980489 + 0.10I
v = 1.00000
a = 0
b = −0.284920 − 1.115140I
2.75839 −6 − 0.980489 + 0.10I
v = 1.00000
a = 0
b = −0.713912 + 0.305839I
−1.37919 − 2.82812I −7.50976 + 2.97945I
v = 1.00000
a = 0
b = −0.713912 − 0.305839I
−1.37919 + 2.82812I −7.50976 − 2.97945I
40
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
10
(u
7
+ 3u
6
+ 7u
5
+ 8u
4
+ 9u
3
+ 6u
2
+ 5u + 1)
6
· ((u
10
+ 5u
9
+ ··· + 4u + 1)
6
)(u
24
− 12u
23
+ ··· − u + 1)
· (u
47
+ 23u
46
+ ··· − 6912u + 4096)
c
2
(u − 1)
10
(u
7
− u
6
− u
5
+ 2u
4
+ u
3
− 2u
2
+ u + 1)
6
· (u
10
− u
9
− 2u
8
+ 4u
7
− 4u
5
+ 3u
4
+ u
3
− 2u
2
+ 1)
6
· (u
24
+ 4u
23
+ ··· + 3u + 1)(u
47
− 3u
46
+ ··· − 240u + 64)
c
3
u
10
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
12
· ((u
7
+ 3u
6
+ ··· − 2u − 2)
6
)(u
24
+ 6u
22
+ ··· − 3u + 1)
· (u
47
− 7u
46
+ ··· − 3840u + 1024)
c
4
(u + 1)
10
(u
7
− u
6
− u
5
+ 2u
4
+ u
3
− 2u
2
+ u + 1)
6
· (u
10
− u
9
− 2u
8
+ 4u
7
− 4u
5
+ 3u
4
+ u
3
− 2u
2
+ 1)
6
· (u
24
− 4u
23
+ ··· − 3u + 1)(u
47
− 3u
46
+ ··· − 240u + 64)
c
5
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
24
+ 12u
22
+ ··· + 3u + 1)(u
42
+ u
41
+ ··· − 1560u + 347)
· (u
47
+ 17u
45
+ ··· − 2u + 1)(u
60
+ u
59
+ ··· − 840u + 61)
c
6
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
24
− 3u
23
+ ··· − 5u
3
+ 1)(u
42
+ 3u
41
+ ··· + 130u + 53)
· (u
47
+ u
46
+ ··· + 5u + 1)(u
60
+ 3u
59
+ ··· + 184u + 23)
c
7
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
24
+ 12u
22
+ ··· − 3u + 1)(u
42
+ u
41
+ ··· − 1560u + 347)
· (u
47
+ 17u
45
+ ··· − 2u + 1)(u
60
+ u
59
+ ··· − 840u + 61)
c
8
u
10
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
12
· ((u
7
+ 3u
6
+ ··· − 2u − 2)
6
)(u
24
+ 6u
22
+ ··· + 3u + 1)
· (u
47
− 7u
46
+ ··· − 3840u + 1024)
c
9
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
24
− 3u
23
+ ··· − 5u
3
+ 1)(u
42
+ 3u
41
+ ··· + 130u + 53)
· (u
47
+ u
46
+ ··· + 5u + 1)(u
60
+ 3u
59
+ ··· + 184u + 23)
c
10
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
24
+ 12u
22
+ ··· − 3u + 1)(u
42
+ u
41
+ ··· − 1560u + 347)
· (u
47
+ 17u
45
+ ··· − 2u + 1)(u
60
+ u
59
+ ··· − 840u + 61)
c
11
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
24
+ 12u
22
+ ··· + 3u + 1)(u
42
+ u
41
+ ··· − 1560u + 347)
· (u
47
+ 17u
45
+ ··· − 2u + 1)(u
60
+ u
59
+ ··· − 840u + 61)
c
12
((u
3
− u
2
+ 1)
36
)(u
4
+ 3u
3
+ ··· + 3u + 2)(u
24
− 12u
23
+ ··· − 6u
2
+ 1)
· (u
47
+ 42u
46
+ ··· + 3997696u + 131072)
41
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
10
(y
7
+ 5y
6
+ 19y
5
+ 36y
4
+ 49y
3
+ 38y
2
+ 13y − 1)
6
· (y
10
− y
9
− 6y
7
+ 22y
6
+ 6y
5
+ 45y
4
+ 15y
3
+ 22y
2
+ 4y + 1)
6
· (y
24
+ 4y
23
+ ··· − 21y + 1)
· (y
47
+ 5y
46
+ ··· + 1065680896y − 16777216)
c
2
, c
4
(y − 1)
10
(y
7
− 3y
6
+ 7y
5
− 8y
4
+ 9y
3
− 6y
2
+ 5y − 1)
6
· ((y
10
− 5y
9
+ ··· − 4y + 1)
6
)(y
24
− 12y
23
+ ··· − y + 1)
· (y
47
− 23y
46
+ ··· − 6912y − 4096)
c
3
, c
8
y
10
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
12
· ((y
7
+ 3y
6
+ ··· + 8y − 4)
6
)(y
24
+ 12y
23
+ ··· − y + 1)
· (y
47
+ 21y
46
+ ··· − 11206656y − 1048576)
c
5
, c
7
, c
10
c
11
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
24
+ 24y
23
+ ··· + 19y + 1)(y
42
+ 33y
41
+ ··· + 486752y + 120409)
· (y
47
+ 34y
46
+ ··· + 22y − 1)(y
60
+ 45y
59
+ ··· + 132540y + 3721)
c
6
, c
9
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
24
− 5y
23
+ ··· − 6y
2
+ 1)(y
42
− 11y
41
+ ··· − 87496y + 2809)
· (y
47
+ 5y
46
+ ··· − 15y − 1)(y
60
− 15y
59
+ ··· − 14076y + 529)
c
12
(y
3
− y
2
+ 2y − 1)
36
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
24
− 12y
23
+ ··· − 12y + 1)
· (y
47
− 14y
46
+ ··· + 571230650368y − 17179869184)
42
