12a
1196
(K12a
1196
)
A knot diagram
1
Linearized knot diagam
4 10 11 1 12 2 3 5 6 7 8 9
Solving Sequence
5,12 6,9
10 1 4 2 8 11 3 7
c
5
c
9
c
12
c
4
c
1
c
8
c
11
c
3
c
7
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.08642 × 10
59
u
46
− 4.09896 × 10
60
u
45
+ ··· + 9.38798 × 10
59
b − 4.54188 × 10
62
,
− 1.10886 × 10
59
u
46
+ 4.10726 × 10
60
u
45
+ ··· + 1.87760 × 10
60
a + 2.91033 × 10
62
,
u
47
− 39u
46
+ ··· − 102400u + 8192i
I
u
2
= h−1.13339 × 10
29
u
70
− 4.82195 × 10
30
u
69
+ ··· + 4.88548 × 10
24
b + 2.41929 × 10
31
,
− 4.83859 × 10
30
au
70
− 8.29715 × 10
30
u
70
+ ··· + 6.34635 × 10
31
a + 6.92021 × 10
31
,
u
71
+ 22u
70
+ ··· − 55u − 5i
I
u
3
= h2.16517 × 10
20
u
30
+ 3.26536 × 10
21
u
29
+ ··· + 1.19902 × 10
21
b + 2.70066 × 10
20
,
2.70066 × 10
20
u
30
+ 3.72737 × 10
21
u
29
+ ··· + 1.19902 × 10
21
a + 4.45709 × 10
21
, u
31
+ 13u
30
+ ··· + u − 1i
I
u
4
= h4u
3
+ 5au − 11u
2
+ 5b + 17u − 11, 11u
3
a − 24u
2
a − 6u
3
+ 25a
2
+ 33au + 29u
2
− 14a − 43u + 44,
u
4
− 4u
3
+ 8u
2
− 9u + 5i
I
u
5
= hb − u + 2, 3a + 2u − 3, u
2
− 3u + 3i
I
u
6
= hau + b − u, a
2
− a − u + 1, u
2
− u + 1i
* 6 irreducible components of dim
C
= 0, with total 234 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
= h1.09 × 10
59
u
46
− 4.10 × 10
60
u
45
+ · · · + 9.39 × 10
59
b − 4.54 ×
10
62
, −1.11 × 10
59
u
46
+ 4.11 × 10
60
u
45
+ · · · + 1.88 × 10
60
a + 2.91 ×
10
62
, u
47
− 39u
46
+ · · · − 102400u + 8192i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
9
=
0.0590573u
46
− 2.18751u
45
+ ··· + 1965.57u − 155.003
−0.115724u
46
+ 4.36618u
45
+ ··· − 5892.46u + 483.797
a
10
=
0.0904063u
46
− 3.49531u
45
+ ··· + 7439.50u − 619.221
0.184438u
46
− 6.83157u
45
+ ··· + 3087.53u − 214.057
a
1
=
0.0254493u
46
− 0.964977u
45
+ ··· + 1631.99u − 133.385
−0.0275439u
46
+ 1.05235u
45
+ ··· − 2471.62u + 208.480
a
4
=
0.0448796u
46
− 1.72346u
45
+ ··· + 3562.00u − 289.190
−0.00498553u
46
+ 0.226727u
45
+ ··· − 1693.46u + 142.014
a
2
=
−0.0169903u
46
+ 0.589287u
45
+ ··· + 1838.44u − 163.476
0.0629036u
46
− 2.42072u
45
+ ··· + 4884.80u − 405.666
a
8
=
−0.0566672u
46
+ 2.17867u
45
+ ··· − 3926.89u + 328.794
−0.115724u
46
+ 4.36618u
45
+ ··· − 5892.46u + 483.797
a
11
=
−0.00777706u
46
+ 0.294739u
45
+ ··· − 701.230u + 57.9358
−0.00568240u
46
+ 0.207365u
45
+ ··· + 140.398u − 17.1594
a
3
=
−0.0481510u
46
+ 1.87081u
45
+ ··· − 3664.83u + 303.197
−0.132055u
46
+ 4.93655u
45
+ ··· − 4297.19u + 336.475
a
7
=
0.0320196u
46
− 1.33035u
45
+ ··· + 7164.01u − 616.138
0.163583u
46
− 6.19951u
45
+ ··· + 8115.42u − 654.306
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0277438u
46
+ 0.925540u
45
+ ··· − 1341.39u + 155.582
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
47
− 23u
46
+ ··· − 13056u + 1024
c
2
, c
7
u
47
+ 3u
46
+ ··· + 2u + 1
c
3
, c
6
u
47
+ 2u
46
+ ··· − 5u + 2
c
5
u
47
− 39u
46
+ ··· − 102400u + 8192
c
8
, c
12
u
47
+ 2u
46
+ ··· + 12u + 1
c
9
, c
11
u
47
− u
46
+ ··· − 1149u + 457
c
10
u
47
+ 27u
46
+ ··· − 608u − 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
47
+ 39y
46
+ ··· − 19595264y −1048576
c
2
, c
7
y
47
− 21y
46
+ ··· + 40y −1
c
3
, c
6
y
47
+ 4y
46
+ ··· − 67y −4
c
5
y
47
+ y
46
+ ··· − 2097152000y −67108864
c
8
, c
12
y
47
+ 16y
46
+ ··· + 60y −1
c
9
, c
11
y
47
− 27y
46
+ ··· + 3980855y −208849
c
10
y
47
+ y
46
+ ··· + 18944y −1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.789858 + 0.572021I
a = 0.795254 + 0.602395I
b = −0.283556 − 0.930709I
3.17145 + 1.69281I 0
u = 0.789858 − 0.572021I
a = 0.795254 − 0.602395I
b = −0.283556 + 0.930709I
3.17145 − 1.69281I 0
u = 0.106416 + 1.060570I
a = −0.169028 − 0.771034I
b = −0.799746 + 0.261315I
−2.73254 − 6.81022I 0
u = 0.106416 − 1.060570I
a = −0.169028 + 0.771034I
b = −0.799746 − 0.261315I
−2.73254 + 6.81022I 0
u = 0.323409 + 1.054660I
a = 0.342192 + 0.658803I
b = 0.584148 − 0.573961I
−0.33944 + 1.43644I 0
u = 0.323409 − 1.054660I
a = 0.342192 − 0.658803I
b = 0.584148 + 0.573961I
−0.33944 − 1.43644I 0
u = 0.674599 + 0.980557I
a = 0.362289 + 1.183380I
b = 0.91597 − 1.15355I
1.96072 + 3.71013I 0
u = 0.674599 − 0.980557I
a = 0.362289 − 1.183380I
b = 0.91597 + 1.15355I
1.96072 − 3.71013I 0
u = 0.624716 + 0.471470I
a = 0.373351 + 1.327370I
b = 0.392576 − 1.005250I
0.432423 + 1.337180I 0
u = 0.624716 − 0.471470I
a = 0.373351 − 1.327370I
b = 0.392576 + 1.005250I
0.432423 − 1.337180I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.020792 + 0.725962I
a = 0.450343 + 1.201190I
b = 0.862651 − 0.351907I
−3.02055 + 2.57813I −8.49493 − 6.08362I
u = 0.020792 − 0.725962I
a = 0.450343 − 1.201190I
b = 0.862651 + 0.351907I
−3.02055 − 2.57813I −8.49493 + 6.08362I
u = −1.30541
a = 0.0836022
b = 0.109135
−2.49946 0
u = 0.298531 + 0.575032I
a = −0.34160 − 1.76890I
b = −0.915194 + 0.724506I
−2.40724 − 2.07518I −6.28983 + 0.97864I
u = 0.298531 − 0.575032I
a = −0.34160 + 1.76890I
b = −0.915194 − 0.724506I
−2.40724 + 2.07518I −6.28983 − 0.97864I
u = 1.210210 + 0.716417I
a = −0.093445 + 1.110070I
b = 0.90836 − 1.27648I
10.14280 + 2.59316I 0
u = 1.210210 − 0.716417I
a = −0.093445 − 1.110070I
b = 0.90836 + 1.27648I
10.14280 − 2.59316I 0
u = 0.016785 + 0.585660I
a = 0.708909 + 0.408464I
b = 0.227322 − 0.422036I
−0.136287 + 1.304410I −1.20224 − 5.79186I
u = 0.016785 − 0.585660I
a = 0.708909 − 0.408464I
b = 0.227322 + 0.422036I
−0.136287 − 1.304410I −1.20224 + 5.79186I
u = 0.025935 + 0.489011I
a = 1.60407 + 2.15189I
b = 1.010700 − 0.840218I
0.30273 + 6.30888I −2.19256 − 11.23940I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.025935 − 0.489011I
a = 1.60407 − 2.15189I
b = 1.010700 + 0.840218I
0.30273 − 6.30888I −2.19256 + 11.23940I
u = 1.18191 + 0.97444I
a = −0.112442 − 1.005100I
b = −0.84651 + 1.29750I
8.05895 + 6.03050I 0
u = 1.18191 − 0.97444I
a = −0.112442 + 1.005100I
b = −0.84651 − 1.29750I
8.05895 − 6.03050I 0
u = 1.35978 + 0.81114I
a = 0.080566 − 0.958947I
b = −0.88739 + 1.23860I
8.74035 + 7.98020I 0
u = 1.35978 − 0.81114I
a = 0.080566 + 0.958947I
b = −0.88739 − 1.23860I
8.74035 − 7.98020I 0
u = 1.24199 + 1.08453I
a = 0.064228 + 0.996984I
b = 1.00149 − 1.30790I
8.2473 + 21.8470I 0
u = 1.24199 − 1.08453I
a = 0.064228 − 0.996984I
b = 1.00149 + 1.30790I
8.2473 − 21.8470I 0
u = 1.21311 + 1.14031I
a = −0.111952 − 0.975187I
b = −0.97621 + 1.31067I
9.1579 + 13.1525I 0
u = 1.21311 − 1.14031I
a = −0.111952 + 0.975187I
b = −0.97621 − 1.31067I
9.1579 − 13.1525I 0
u = −0.140578 + 0.193465I
a = 0.65556 − 4.39100I
b = −0.757348 − 0.744107I
5.01435 + 2.53794I 0.84043 − 2.77896I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140578 − 0.193465I
a = 0.65556 + 4.39100I
b = −0.757348 + 0.744107I
5.01435 − 2.53794I 0.84043 + 2.77896I
u = 1.15618 + 1.33193I
a = −0.360678 − 0.340815I
b = −0.036934 + 0.874442I
7.12799 + 2.40033I 0
u = 1.15618 − 1.33193I
a = −0.360678 + 0.340815I
b = −0.036934 − 0.874442I
7.12799 − 2.40033I 0
u = 1.31536 + 1.18518I
a = −0.033298 − 0.670801I
b = −0.751219 + 0.921810I
4.06199 + 7.90337I 0
u = 1.31536 − 1.18518I
a = −0.033298 + 0.670801I
b = −0.751219 − 0.921810I
4.06199 − 7.90337I 0
u = 1.43565 + 1.13278I
a = −0.070763 + 0.656697I
b = 0.845485 − 0.862632I
2.4290 + 15.1963I 0
u = 1.43565 − 1.13278I
a = −0.070763 − 0.656697I
b = 0.845485 + 0.862632I
2.4290 − 15.1963I 0
u = 1.71474 + 0.65476I
a = −0.178004 + 0.533259I
b = 0.654385 − 0.797849I
3.38591 − 3.98691I 0
u = 1.71474 − 0.65476I
a = −0.178004 − 0.533259I
b = 0.654385 + 0.797849I
3.38591 + 3.98691I 0
u = 1.47478 + 1.21882I
a = −0.363781 − 0.353820I
b = 0.105251 + 0.965191I
9.18769 − 3.84376I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.47478 − 1.21882I
a = −0.363781 + 0.353820I
b = 0.105251 − 0.965191I
9.18769 + 3.84376I 0
u = 1.44593 + 1.42503I
a = 0.343723 + 0.269068I
b = −0.113569 − 0.878869I
7.6878 − 12.4770I 0
u = 1.44593 − 1.42503I
a = 0.343723 − 0.269068I
b = −0.113569 + 0.878869I
7.6878 + 12.4770I 0
u = 1.58102 + 1.61441I
a = −0.142057 − 0.292779I
b = −0.248071 + 0.692228I
6.42396 + 1.69767I 0
u = 1.58102 − 1.61441I
a = −0.142057 + 0.292779I
b = −0.248071 − 0.692228I
6.42396 − 1.69767I 0
u = 1.08159 + 2.43719I
a = 0.154769 + 0.090366I
b = 0.052843 − 0.474939I
6.46891 + 5.45398I 0
u = 1.08159 − 2.43719I
a = 0.154769 − 0.090366I
b = 0.052843 + 0.474939I
6.46891 − 5.45398I 0
9
II. I
u
2
= h−1.13 × 10
29
u
70
− 4.82 × 10
30
u
69
+ · · · + 4.89 × 10
24
b + 2.42 ×
10
31
, −4.84 × 10
30
au
70
− 8.30 × 10
30
u
70
+ · · · + 6.35 × 10
31
a + 6.92 ×
10
31
, u
71
+ 22u
70
+ · · · − 55u − 5i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
9
=
a
23199.1u
70
+ 986996.u
69
+ ··· − 4.14818 × 10
7
u − 4.95200 × 10
6
a
10
=
23199.1u
70
+ 986996.u
69
+ ··· + a − 4.95200 × 10
6
687394.u
70
+ 1.49354 × 10
7
u
69
+ ··· − 6.78117 × 10
7
u − 7.33508 × 10
6
a
1
=
23199.1au
70
+ 867570.u
70
+ ··· − 4.95200 × 10
6
a − 8.49164 × 10
6
−302197.u
70
− 6.69779 × 10
6
u
69
+ ··· + 3.92247 × 10
7
u + 4.33785 × 10
6
a
4
=
−239938.au
70
− 2.17987 × 10
6
u
70
+ ··· − 374469.a + 1.84264 × 10
7
1.15630 × 10
6
u
70
+ 2.48006 × 10
7
u
69
+ ··· − 8.91836 × 10
7
u − 9.38837 × 10
6
a
2
=
−2.31944 × 10
6
au
70
+ 3.07476 × 10
6
u
70
+ ··· + 1.54147 × 10
7
a − 2.27294 × 10
7
−1.34228 × 10
6
u
70
− 2.84842 × 10
7
u
69
+ ··· + 7.98915 × 10
7
u + 8.08133 × 10
6
a
8
=
23199.1u
70
+ 986996.u
69
+ ··· + a − 4.95200 × 10
6
23199.1u
70
+ 986996.u
69
+ ··· − 4.14818 × 10
7
u − 4.95200 × 10
6
a
11
=
687394.au
70
+ 676175.u
70
+ ··· − 7.33508 × 10
6
a − 6.73339 × 10
6
664195.au
70
+ 110802.u
70
+ ··· − 2.38308 × 10
6
a − 2.57961 × 10
6
a
3
=
373244.au
70
− 2.32863 × 10
6
u
70
+ ··· + 1.90152 × 10
6
a + 9.68437 × 10
6
−152067.au
70
− 1.85415 × 10
6
u
70
+ ··· + 2.01714 × 10
6
a + 1.32832 × 10
7
a
7
=
288778.au
70
+ 1.33982 × 10
6
u
70
+ ··· − 528893.a − 6.61449 × 10
6
−909066.au
70
+ 877015.u
70
+ ··· + 5.32274 × 10
6
a − 4.34410 × 10
6
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
6672500342500645145827521018811
1221371038010135829969920
u
70
+
70712871267280814406090494060611
610685519005067914984960
u
69
+ ··· −
382511550256794372990851752886051
1221371038010135829969920
u −
119784397586000680545676883339
3816784493781674468656
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
71
+ 14u
70
+ ··· + 566u + 148)
2
c
2
5u
142
+ 30u
141
+ ··· + 167385u − 47185
c
3
5u
142
+ 30u
141
+ ··· + 6145u + 1339
c
4
(u
71
− 14u
70
+ ··· + 566u − 148)
2
c
5
(u
71
+ 22u
70
+ ··· − 55u − 5)
2
c
6
5u
142
− 30u
141
+ ··· − 6145u + 1339
c
7
− 5u
142
+ 30u
141
+ ··· + 167385u + 47185
c
8
, c
12
− 5u
142
+ 20u
141
+ ··· + 4314935u + 821335
c
9
, c
11
− 5u
142
+ 10u
141
+ ··· − 271556615523u + 71833666691
c
10
(u
71
+ 15u
70
+ ··· + 65u + 5)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
71
+ 62y
70
+ ··· + 341964y −21904)
2
c
2
, c
7
25y
142
− 410y
141
+ ··· − 130716079465y + 2226424225
c
3
, c
6
25y
142
− 60y
141
+ ··· − 31957799y + 1792921
c
5
(y
71
− 12y
70
+ ··· + 1515y −25)
2
c
8
, c
12
25y
142
+ 510y
141
+ ··· + 15566082199365y + 674591182225
c
9
, c
11
25y
142
− 2240y
141
+ ··· − 3.06 × 10
23
y + 5.16 × 10
21
c
10
(y
71
− 7y
70
+ ··· + 1665y −25)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.824672 + 0.570478I
a = −0.187954 − 1.090550I
b = 0.984144 + 0.902469I
−1.74041 − 5.49672I 0
u = −0.824672 + 0.570478I
a = 0.295125 + 1.298490I
b = −0.777137 − 0.792124I
−1.74041 − 5.49672I 0
u = −0.824672 − 0.570478I
a = −0.187954 + 1.090550I
b = 0.984144 − 0.902469I
−1.74041 + 5.49672I 0
u = −0.824672 − 0.570478I
a = 0.295125 − 1.298490I
b = −0.777137 + 0.792124I
−1.74041 + 5.49672I 0
u = −0.653521 + 0.738689I
a = 1.138200 + 0.225871I
b = −0.017427 + 0.499635I
0.87960 + 2.11142I 0
u = −0.653521 + 0.738689I
a = −0.391121 + 0.322434I
b = 0.910684 − 0.693164I
0.87960 + 2.11142I 0
u = −0.653521 − 0.738689I
a = 1.138200 − 0.225871I
b = −0.017427 − 0.499635I
0.87960 − 2.11142I 0
u = −0.653521 − 0.738689I
a = −0.391121 − 0.322434I
b = 0.910684 + 0.693164I
0.87960 − 2.11142I 0
u = −0.659920 + 0.791144I
a = 0.243572 + 0.702275I
b = −0.464563 − 0.227238I
−2.77623 + 0.61894I 0
u = −0.659920 + 0.791144I
a = −0.119461 − 0.487558I
b = 0.716339 + 0.270745I
−2.77623 + 0.61894I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.659920 − 0.791144I
a = 0.243572 − 0.702275I
b = −0.464563 + 0.227238I
−2.77623 − 0.61894I 0
u = −0.659920 − 0.791144I
a = −0.119461 + 0.487558I
b = 0.716339 − 0.270745I
−2.77623 − 0.61894I 0
u = 0.965142 + 0.087688I
a = 0.185351 − 0.854460I
b = −1.27250 + 1.58375I
8.87060 − 1.96256I 0
u = 0.965142 + 0.087688I
a = 1.15979 − 1.74633I
b = −0.253816 + 0.808422I
8.87060 − 1.96256I 0
u = 0.965142 − 0.087688I
a = 0.185351 + 0.854460I
b = −1.27250 − 1.58375I
8.87060 + 1.96256I 0
u = 0.965142 − 0.087688I
a = 1.15979 + 1.74633I
b = −0.253816 − 0.808422I
8.87060 + 1.96256I 0
u = −0.306428 + 0.912839I
a = 1.051020 − 0.593590I
b = 0.535534 + 0.082446I
0.005444 + 0.532261I 0
u = −0.306428 + 0.912839I
a = 0.095820 + 0.554503I
b = −0.219791 − 1.141300I
0.005444 + 0.532261I 0
u = −0.306428 − 0.912839I
a = 1.051020 + 0.593590I
b = 0.535534 − 0.082446I
0.005444 − 0.532261I 0
u = −0.306428 − 0.912839I
a = 0.095820 − 0.554503I
b = −0.219791 + 1.141300I
0.005444 − 0.532261I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.856259 + 0.418034I
a = 0.199182 + 1.016330I
b = −0.591258 − 0.801688I
3.10625 + 2.38586I 0
u = 0.856259 + 0.418034I
a = 0.926724 + 0.483832I
b = 0.254309 − 0.953507I
3.10625 + 2.38586I 0
u = 0.856259 − 0.418034I
a = 0.199182 − 1.016330I
b = −0.591258 + 0.801688I
3.10625 − 2.38586I 0
u = 0.856259 − 0.418034I
a = 0.926724 − 0.483832I
b = 0.254309 + 0.953507I
3.10625 − 2.38586I 0
u = −0.668333 + 0.630821I
a = 0.244078 + 1.244820I
b = −0.467567 − 0.406289I
−2.52859 − 2.05067I 0
u = −0.668333 + 0.630821I
a = −0.066534 − 0.670714I
b = 0.948385 + 0.677987I
−2.52859 − 2.05067I 0
u = −0.668333 − 0.630821I
a = 0.244078 − 1.244820I
b = −0.467567 + 0.406289I
−2.52859 + 2.05067I 0
u = −0.668333 − 0.630821I
a = −0.066534 + 0.670714I
b = 0.948385 − 0.677987I
−2.52859 + 2.05067I 0
u = −0.734328 + 0.551761I
a = −0.190018 − 1.142270I
b = 0.95657 + 1.47779I
1.68399 − 6.46953I 0
u = −0.734328 + 0.551761I
a = −0.13388 + 1.91184I
b = −0.769797 − 0.733958I
1.68399 − 6.46953I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.734328 − 0.551761I
a = −0.190018 + 1.142270I
b = 0.95657 − 1.47779I
1.68399 + 6.46953I 0
u = −0.734328 − 0.551761I
a = −0.13388 − 1.91184I
b = −0.769797 + 0.733958I
1.68399 + 6.46953I 0
u = −0.602775 + 0.959248I
a = 0.079718 + 1.096290I
b = −0.46599 − 1.72736I
2.80463 − 0.98712I 0
u = −0.602775 + 0.959248I
a = 1.07214 − 1.15950I
b = 1.099670 + 0.584349I
2.80463 − 0.98712I 0
u = −0.602775 − 0.959248I
a = 0.079718 − 1.096290I
b = −0.46599 + 1.72736I
2.80463 + 0.98712I 0
u = −0.602775 − 0.959248I
a = 1.07214 + 1.15950I
b = 1.099670 − 0.584349I
2.80463 + 0.98712I 0
u = 0.626316 + 0.977766I
a = −0.070814 − 1.063810I
b = −0.87454 + 1.62900I
2.24238 + 12.49280I 0
u = 0.626316 + 0.977766I
a = −0.77508 − 1.39091I
b = −0.995807 + 0.735522I
2.24238 + 12.49280I 0
u = 0.626316 − 0.977766I
a = −0.070814 + 1.063810I
b = −0.87454 − 1.62900I
2.24238 − 12.49280I 0
u = 0.626316 − 0.977766I
a = −0.77508 + 1.39091I
b = −0.995807 − 0.735522I
2.24238 − 12.49280I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.766108 + 0.227199I
a = 0.146877 − 0.712508I
b = −1.83837 + 1.33856I
7.41218 − 3.70027I 0
u = −0.766108 + 0.227199I
a = −2.68191 + 0.95186I
b = −0.049357 − 0.579228I
7.41218 − 3.70027I 0
u = −0.766108 − 0.227199I
a = 0.146877 + 0.712508I
b = −1.83837 − 1.33856I
7.41218 + 3.70027I 0
u = −0.766108 − 0.227199I
a = −2.68191 − 0.95186I
b = −0.049357 + 0.579228I
7.41218 + 3.70027I 0
u = −0.727284 + 0.202634I
a = 0.717941 + 1.218260I
b = 0.680119 − 1.113870I
3.12602 − 9.03029I 0
u = −0.727284 + 0.202634I
a = 1.26376 − 1.17944I
b = 0.769008 + 0.740539I
3.12602 − 9.03029I 0
u = −0.727284 − 0.202634I
a = 0.717941 − 1.218260I
b = 0.680119 + 1.113870I
3.12602 + 9.03029I 0
u = −0.727284 − 0.202634I
a = 1.26376 + 1.17944I
b = 0.769008 − 0.740539I
3.12602 + 9.03029I 0
u = 0.652637 + 1.074260I
a = −0.300909 − 1.021020I
b = −0.575617 + 0.453549I
−1.57416 + 8.84284I 0
u = 0.652637 + 1.074260I
a = −0.070610 − 0.578722I
b = −0.900458 + 0.989609I
−1.57416 + 8.84284I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.652637 − 1.074260I
a = −0.300909 + 1.021020I
b = −0.575617 − 0.453549I
−1.57416 − 8.84284I 0
u = 0.652637 − 1.074260I
a = −0.070610 + 0.578722I
b = −0.900458 − 0.989609I
−1.57416 − 8.84284I 0
u = −0.715680 + 0.181290I
a = −0.103054 + 0.864086I
b = 1.85725 − 1.31818I
6.62178 − 12.35120I 0
u = −0.715680 + 0.181290I
a = 2.87704 − 1.11307I
b = 0.082896 + 0.637092I
6.62178 − 12.35120I 0
u = −0.715680 − 0.181290I
a = −0.103054 − 0.864086I
b = 1.85725 + 1.31818I
6.62178 + 12.35120I 0
u = −0.715680 − 0.181290I
a = 2.87704 + 1.11307I
b = 0.082896 − 0.637092I
6.62178 + 12.35120I 0
u = −0.692516 + 0.244640I
a = 0.069672 − 1.247530I
b = 1.49740 + 1.34373I
8.49212 − 6.49188I 0
u = −0.692516 + 0.244640I
a = 1.31296 + 2.40418I
b = −0.256946 − 0.880976I
8.49212 − 6.49188I 0
u = −0.692516 − 0.244640I
a = 0.069672 + 1.247530I
b = 1.49740 − 1.34373I
8.49212 + 6.49188I 0
u = −0.692516 − 0.244640I
a = 1.31296 − 2.40418I
b = −0.256946 + 0.880976I
8.49212 + 6.49188I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.223570 + 0.329001I
a = 0.529081 + 0.503867I
b = 0.174577 − 0.870418I
3.21058 + 2.53684I 0
u = 1.223570 + 0.329001I
a = 0.045323 + 0.699188I
b = −0.481595 − 0.790585I
3.21058 + 2.53684I 0
u = 1.223570 − 0.329001I
a = 0.529081 − 0.503867I
b = 0.174577 + 0.870418I
3.21058 − 2.53684I 0
u = 1.223570 − 0.329001I
a = 0.045323 − 0.699188I
b = −0.481595 + 0.790585I
3.21058 − 2.53684I 0
u = −0.693365 + 0.221244I
a = −0.751332 − 1.019720I
b = −0.772686 + 0.813888I
3.75246 − 2.19021I 0
u = −0.693365 + 0.221244I
a = −1.35136 + 0.74262I
b = −0.746553 − 0.540808I
3.75246 − 2.19021I 0
u = −0.693365 − 0.221244I
a = −0.751332 + 1.019720I
b = −0.772686 − 0.813888I
3.75246 + 2.19021I 0
u = −0.693365 − 0.221244I
a = −1.35136 − 0.74262I
b = −0.746553 + 0.540808I
3.75246 + 2.19021I 0
u = −0.712454 + 0.139207I
a = −0.253723 + 1.055420I
b = −1.67128 − 1.02980I
6.78398 − 0.48459I 0
u = −0.712454 + 0.139207I
a = −1.98751 − 1.83376I
b = −0.033845 + 0.787256I
6.78398 − 0.48459I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.712454 − 0.139207I
a = −0.253723 − 1.055420I
b = −1.67128 + 1.02980I
6.78398 + 0.48459I 0
u = −0.712454 − 0.139207I
a = −1.98751 + 1.83376I
b = −0.033845 − 0.787256I
6.78398 + 0.48459I 0
u = 0.813544 + 0.992183I
a = 0.240114 + 0.946235I
b = 1.09301 − 1.40163I
1.80284 + 3.80266I 0
u = 0.813544 + 0.992183I
a = 0.304604 + 1.351380I
b = 0.743495 − 1.008040I
1.80284 + 3.80266I 0
u = 0.813544 − 0.992183I
a = 0.240114 − 0.946235I
b = 1.09301 + 1.40163I
1.80284 − 3.80266I 0
u = 0.813544 − 0.992183I
a = 0.304604 − 1.351380I
b = 0.743495 + 1.008040I
1.80284 − 3.80266I 0
u = 0.635897 + 0.171453I
a = 0.331692 + 1.154750I
b = −1.43344 − 1.19785I
5.12448 + 4.20015I 0
u = 0.635897 + 0.171453I
a = 2.57491 + 1.18946I
b = −0.012937 − 0.791170I
5.12448 + 4.20015I 0
u = 0.635897 − 0.171453I
a = 0.331692 − 1.154750I
b = −1.43344 + 1.19785I
5.12448 − 4.20015I 0
u = 0.635897 − 0.171453I
a = 2.57491 − 1.18946I
b = −0.012937 + 0.791170I
5.12448 − 4.20015I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.034531 + 1.350330I
a = −0.481786 − 0.168176I
b = 0.487421 − 0.177522I
4.54386 + 4.92588I 0
u = −0.034531 + 1.350330I
a = 0.140605 + 0.357370I
b = −0.243728 + 0.644760I
4.54386 + 4.92588I 0
u = −0.034531 − 1.350330I
a = −0.481786 + 0.168176I
b = 0.487421 + 0.177522I
4.54386 − 4.92588I 0
u = −0.034531 − 1.350330I
a = 0.140605 − 0.357370I
b = −0.243728 − 0.644760I
4.54386 − 4.92588I 0
u = −1.18052 + 0.80437I
a = −0.894808 + 0.690321I
b = 0.004442 − 0.698249I
4.57981 − 5.54284I 0
u = −1.18052 + 0.80437I
a = 0.277802 − 0.402191I
b = −0.50107 + 1.53469I
4.57981 − 5.54284I 0
u = −1.18052 − 0.80437I
a = −0.894808 − 0.690321I
b = 0.004442 + 0.698249I
4.57981 + 5.54284I 0
u = −1.18052 − 0.80437I
a = 0.277802 + 0.402191I
b = −0.50107 − 1.53469I
4.57981 + 5.54284I 0
u = 0.57433 + 1.30998I
a = 0.170075 + 0.735004I
b = 0.392930 − 0.770957I
−0.587285 + 1.165290I 0
u = 0.57433 + 1.30998I
a = 0.383336 + 0.468015I
b = 0.865161 − 0.644929I
−0.587285 + 1.165290I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.57433 − 1.30998I
a = 0.170075 − 0.735004I
b = 0.392930 + 0.770957I
−0.587285 − 1.165290I 0
u = 0.57433 − 1.30998I
a = 0.383336 − 0.468015I
b = 0.865161 + 0.644929I
−0.587285 − 1.165290I 0
u = 0.543618 + 0.148501I
a = 1.01318 + 1.18573I
b = 0.665976 − 1.208700I
0.717238 + 0.672079I 0
u = 0.543618 + 0.148501I
a = −0.57481 + 2.38046I
b = −0.374699 − 0.795043I
0.717238 + 0.672079I 0
u = 0.543618 − 0.148501I
a = 1.01318 − 1.18573I
b = 0.665976 + 1.208700I
0.717238 − 0.672079I 0
u = 0.543618 − 0.148501I
a = −0.57481 − 2.38046I
b = −0.374699 + 0.795043I
0.717238 − 0.672079I 0
u = 1.42648 + 0.21629I
a = −0.678572 − 0.884616I
b = 0.220761 + 0.870153I
5.35046 − 6.50468I 0
u = 1.42648 + 0.21629I
a = −0.241696 − 0.573352I
b = 0.77663 + 1.40866I
5.35046 − 6.50468I 0
u = 1.42648 − 0.21629I
a = −0.678572 + 0.884616I
b = 0.220761 − 0.870153I
5.35046 + 6.50468I 0
u = 1.42648 − 0.21629I
a = −0.241696 + 0.573352I
b = 0.77663 − 1.40866I
5.35046 + 6.50468I 0
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.16414 + 0.91773I
a = −0.018946 − 1.050230I
b = 0.99063 + 1.33831I
6.1667 − 12.8286I 0
u = −1.16414 + 0.91773I
a = −0.034120 + 1.122720I
b = −0.98588 − 1.20522I
6.1667 − 12.8286I 0
u = −1.16414 − 0.91773I
a = −0.018946 + 1.050230I
b = 0.99063 − 1.33831I
6.1667 + 12.8286I 0
u = −1.16414 − 0.91773I
a = −0.034120 − 1.122720I
b = −0.98588 + 1.20522I
6.1667 + 12.8286I 0
u = 0.433087 + 0.214106I
a = −0.002764 + 1.161030I
b = 1.83827 − 2.26474I
4.45638 − 2.54610I 0
u = 0.433087 + 0.214106I
a = −1.33345 + 5.88852I
b = 0.249781 − 0.502236I
4.45638 − 2.54610I 0
u = 0.433087 − 0.214106I
a = −0.002764 − 1.161030I
b = 1.83827 + 2.26474I
4.45638 + 2.54610I 0
u = 0.433087 − 0.214106I
a = −1.33345 − 5.88852I
b = 0.249781 + 0.502236I
4.45638 + 2.54610I 0
u = −1.17470 + 0.97295I
a = −0.144083 + 0.994891I
b = −1.08922 − 1.29993I
9.3164 − 11.7603I 0
u = −1.17470 + 0.97295I
a = −0.006337 − 1.111860I
b = 0.79872 + 1.30888I
9.3164 − 11.7603I 0
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.17470 − 0.97295I
a = −0.144083 − 0.994891I
b = −1.08922 + 1.29993I
9.3164 + 11.7603I 0
u = −1.17470 − 0.97295I
a = −0.006337 + 1.111860I
b = 0.79872 − 1.30888I
9.3164 + 11.7603I 0
u = −1.33183 + 0.75303I
a = −0.100650 + 1.189680I
b = −0.638117 − 0.904818I
3.30590 − 7.28382I 0
u = −1.33183 + 0.75303I
a = −0.071987 − 0.720081I
b = 0.76182 + 1.66025I
3.30590 − 7.28382I 0
u = −1.33183 − 0.75303I
a = −0.100650 − 1.189680I
b = −0.638117 + 0.904818I
3.30590 + 7.28382I 0
u = −1.33183 − 0.75303I
a = −0.071987 + 0.720081I
b = 0.76182 − 1.66025I
3.30590 + 7.28382I 0
u = −1.26244 + 0.92732I
a = −0.123085 + 0.840091I
b = −0.776545 − 0.871804I
2.97338 − 7.62690I 0
u = −1.26244 + 0.92732I
a = −0.070056 − 0.742032I
b = 0.623650 + 1.174700I
2.97338 − 7.62690I 0
u = −1.26244 − 0.92732I
a = −0.123085 − 0.840091I
b = −0.776545 + 0.871804I
2.97338 + 7.62690I 0
u = −1.26244 − 0.92732I
a = −0.070056 + 0.742032I
b = 0.623650 − 1.174700I
2.97338 + 7.62690I 0
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.270040 + 0.302532I
a = 0.712840 − 1.005080I
b = −2.05898 − 0.38627I
4.83661 + 2.72129I 0
u = −0.270040 + 0.302532I
a = −2.67044 − 4.42219I
b = −0.111574 − 0.487069I
4.83661 + 2.72129I 0
u = −0.270040 − 0.302532I
a = 0.712840 + 1.005080I
b = −2.05898 + 0.38627I
4.83661 − 2.72129I 0
u = −0.270040 − 0.302532I
a = −2.67044 + 4.42219I
b = −0.111574 + 0.487069I
4.83661 − 2.72129I 0
u = −1.45105 + 0.77820I
a = 0.253984 + 0.683827I
b = −0.833337 − 0.742961I
−0.47055 − 5.73622I 0
u = −1.45105 + 0.77820I
a = −0.232759 − 0.636845I
b = 0.900697 + 0.794616I
−0.47055 − 5.73622I 0
u = −1.45105 − 0.77820I
a = 0.253984 − 0.683827I
b = −0.833337 + 0.742961I
−0.47055 + 5.73622I 0
u = −1.45105 − 0.77820I
a = −0.232759 + 0.636845I
b = 0.900697 − 0.794616I
−0.47055 + 5.73622I 0
u = −0.63513 + 1.54911I
a = −0.401653 + 0.050472I
b = 0.334457 − 0.513948I
4.55977 + 5.02603I 0
u = −0.63513 + 1.54911I
a = 0.359807 + 0.068383I
b = −0.176914 + 0.654261I
4.55977 + 5.02603I 0
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.63513 − 1.54911I
a = −0.401653 − 0.050472I
b = 0.334457 + 0.513948I
4.55977 − 5.02603I 0
u = −0.63513 − 1.54911I
a = 0.359807 − 0.068383I
b = −0.176914 − 0.654261I
4.55977 − 5.02603I 0
u = −1.10401 + 1.33286I
a = 0.527800 − 0.300292I
b = −0.078937 + 0.702075I
8.37637 + 3.43596I 0
u = −1.10401 + 1.33286I
a = −0.341501 + 0.223641I
b = 0.182448 − 1.035010I
8.37637 + 3.43596I 0
u = −1.10401 − 1.33286I
a = 0.527800 + 0.300292I
b = −0.078937 − 0.702075I
8.37637 − 3.43596I 0
u = −1.10401 − 1.33286I
a = −0.341501 − 0.223641I
b = 0.182448 + 1.035010I
8.37637 − 3.43596I 0
u = 0.192549
a = 0.922979
b = 4.41369
0.543729 −407.280
u = 0.192549
a = −22.9224
b = −0.177719
0.543729 −407.280
u = −1.48139 + 1.21474I
a = −0.006383 + 0.538148I
b = −0.347151 − 0.788128I
1.91594 − 1.91493I 0
u = −1.48139 + 1.21474I
a = 0.120732 − 0.433018I
b = 0.644251 + 0.804962I
1.91594 − 1.91493I 0
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48139 − 1.21474I
a = −0.006383 − 0.538148I
b = −0.347151 + 0.788128I
1.91594 + 1.91493I 0
u = −1.48139 − 1.21474I
a = 0.120732 + 0.433018I
b = 0.644251 − 0.804962I
1.91594 + 1.91493I 0
27
III.
I
u
3
= h2.17 × 10
20
u
30
+ 3.27 × 10
21
u
29
+ · · · + 1.20 × 10
21
b + 2.70 × 10
20
, 2.70 ×
10
20
u
30
+3.73×10
21
u
29
+· · ·+1.20×10
21
a+4.46×10
21
, u
31
+13u
30
+· · ·+u−1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
9
=
−0.225238u
30
− 3.10867u
29
+ ··· + 0.538512u − 3.71726
−0.180578u
30
− 2.72335u
29
+ ··· − 3.49203u − 0.225238
a
10
=
−0.781653u
30
− 10.1366u
29
+ ··· − 2.99817u − 4.12308
0.0315950u
30
− 0.127605u
29
+ ··· − 2.73014u − 0.430711
a
1
=
−2.47668u
30
− 31.7407u
29
+ ··· − 3.64079u − 0.442984
0.456172u
30
+ 5.98489u
29
+ ··· + 3.03370u − 2.47668
a
4
=
−2.62471u
30
− 32.6768u
29
+ ··· + 2.72113u + 1.46548
1.38973u
30
+ 18.1347u
29
+ ··· + 6.02304u − 3.08088
a
2
=
−3.58151u
30
− 44.0380u
29
+ ··· − 6.08463u + 2.51316
2.50817u
30
+ 33.1108u
29
+ ··· + 8.63243u − 4.51507
a
8
=
−0.405816u
30
− 5.83202u
29
+ ··· − 2.95351u − 3.94250
−0.180578u
30
− 2.72335u
29
+ ··· − 3.49203u − 0.225238
a
11
=
−1.50969u
30
− 20.0486u
29
+ ··· − 2.50625u − 4.94017
0.510821u
30
+ 5.70716u
29
+ ··· + 0.100844u − 2.02051
a
3
=
−2.84271u
30
− 35.9753u
29
+ ··· − 7.85276u + 0.379035
1.61788u
30
+ 21.6931u
29
+ ··· + 7.04440u − 3.82265
a
7
=
4.69639u
30
+ 58.7635u
29
+ ··· + 9.91752u + 1.88902
−4.19037u
30
− 51.3479u
29
+ ··· − 9.59810u + 6.61015
(ii) Obstruction class = 1
(iii) Cusp Shapes =
6057336151202140089817
1199024621665907001733
u
30
+
85977313209331721101484
1199024621665907001733
u
29
+ ··· +
42603403175206352257301
1199024621665907001733
u −
18740164022808552357340
1199024621665907001733
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
31
− 10u
30
+ ··· + 164u − 13
c
2
, c
7
u
31
− u
30
+ ··· − 2u + 1
c
3
, c
6
u
31
− u
30
+ ··· − 5u + 1
c
4
u
31
+ 10u
30
+ ··· + 164u + 13
c
5
u
31
+ 13u
30
+ ··· + u − 1
c
8
, c
12
u
31
− u
30
+ ··· − 3u − 1
c
9
, c
11
u
31
− u
30
+ ··· + 5u − 1
c
10
u
31
− 17u
30
+ ··· − 3u + 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
31
+ 26y
30
+ ··· − 7632y −169
c
2
, c
7
y
31
− y
30
+ ··· + 24y −1
c
3
, c
6
y
31
+ 3y
30
+ ··· − 25y −1
c
5
y
31
− y
30
+ ··· + 15y −1
c
8
, c
12
y
31
+ 3y
30
+ ··· + 5y −1
c
9
, c
11
y
31
− 15y
30
+ ··· − 17y −1
c
10
y
31
+ 3y
30
+ ··· + 33y −1
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.802181 + 0.655317I
a = −0.349659 + 0.581209I
b = −0.661366 + 0.237097I
5.34150 + 1.09383I 4.03751 − 1.72481I
u = 0.802181 − 0.655317I
a = −0.349659 − 0.581209I
b = −0.661366 − 0.237097I
5.34150 − 1.09383I 4.03751 + 1.72481I
u = −1.019730 + 0.427277I
a = −0.289931 − 0.356558I
b = 0.448001 + 0.239712I
−2.68713 − 0.07444I −14.9045 + 13.7988I
u = −1.019730 − 0.427277I
a = −0.289931 + 0.356558I
b = 0.448001 − 0.239712I
−2.68713 + 0.07444I −14.9045 − 13.7988I
u = −1.084920 + 0.461034I
a = −0.354893 − 0.897821I
b = 0.798957 + 0.810444I
−1.56708 − 4.47599I −5.79900 + 1.58426I
u = −1.084920 − 0.461034I
a = −0.354893 + 0.897821I
b = 0.798957 − 0.810444I
−1.56708 + 4.47599I −5.79900 − 1.58426I
u = −1.000620 + 0.629369I
a = −0.715706 + 0.518410I
b = 0.389879 − 0.969174I
6.97246 + 4.94250I 5.80804 − 6.30898I
u = −1.000620 − 0.629369I
a = −0.715706 − 0.518410I
b = 0.389879 + 0.969174I
6.97246 − 4.94250I 5.80804 + 6.30898I
u = −0.635261 + 1.019810I
a = −0.412974 + 0.860006I
b = −0.614699 − 0.967484I
−0.06619 − 9.23511I 0. + 9.63622I
u = −0.635261 − 1.019810I
a = −0.412974 − 0.860006I
b = −0.614699 + 0.967484I
−0.06619 + 9.23511I 0. − 9.63622I
31
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.696791 + 1.097990I
a = 0.379316 − 1.101360I
b = 0.94497 + 1.18390I
1.96931 − 3.31975I 3.33536 − 10.13133I
u = −0.696791 − 1.097990I
a = 0.379316 + 1.101360I
b = 0.94497 − 1.18390I
1.96931 + 3.31975I 3.33536 + 10.13133I
u = 0.572633 + 0.293060I
a = 0.62907 − 1.39615I
b = 0.769384 − 0.615126I
5.71965 − 11.63410I 0.60190 + 5.79448I
u = 0.572633 − 0.293060I
a = 0.62907 + 1.39615I
b = 0.769384 + 0.615126I
5.71965 + 11.63410I 0.60190 − 5.79448I
u = −0.462841 + 1.278390I
a = 0.297399 − 0.598990I
b = 0.628094 + 0.657429I
−0.173121 − 0.947660I 6.59549 − 5.94866I
u = −0.462841 − 1.278390I
a = 0.297399 + 0.598990I
b = 0.628094 − 0.657429I
−0.173121 + 0.947660I 6.59549 + 5.94866I
u = −1.356760 + 0.247339I
a = 0.345259 − 0.759369I
b = −0.280613 + 1.115680I
4.81875 − 3.09633I 6.94503 + 0.I
u = −1.356760 − 0.247339I
a = 0.345259 + 0.759369I
b = −0.280613 − 1.115680I
4.81875 + 3.09633I 6.94503 + 0.I
u = 0.567426 + 0.103550I
a = −1.33204 + 1.29486I
b = −0.889919 + 0.596803I
6.52346 − 3.01769I 6.37648 + 3.90400I
u = 0.567426 − 0.103550I
a = −1.33204 − 1.29486I
b = −0.889919 − 0.596803I
6.52346 + 3.01769I 6.37648 − 3.90400I
32
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.378456 + 0.376128I
a = −0.04346 − 2.36021I
b = 0.904188 + 0.876888I
0.54217 − 5.24068I −2.27502 + 4.94275I
u = −0.378456 − 0.376128I
a = −0.04346 + 2.36021I
b = 0.904188 − 0.876888I
0.54217 + 5.24068I −2.27502 − 4.94275I
u = −1.12172 + 0.95779I
a = −0.065642 + 1.090890I
b = −0.97121 − 1.28655I
7.3437 − 12.1227I 0
u = −1.12172 − 0.95779I
a = −0.065642 − 1.090890I
b = −0.97121 + 1.28655I
7.3437 + 12.1227I 0
u = 0.379341
a = −2.67394
b = −1.01433
0.669105 −2.58600
u = 0.231174 + 0.276345I
a = −0.34972 + 2.92117I
b = −0.888099 + 0.578655I
4.66589 + 3.12670I 3.38653 − 2.87642I
u = 0.231174 − 0.276345I
a = −0.34972 − 2.92117I
b = −0.888099 − 0.578655I
4.66589 − 3.12670I 3.38653 + 2.87642I
u = −1.47519 + 0.75450I
a = 0.253134 + 0.667574I
b = −0.877108 − 0.793809I
0.17612 − 5.82869I 0
u = −1.47519 − 0.75450I
a = 0.253134 − 0.667574I
b = −0.877108 + 0.793809I
0.17612 + 5.82869I 0
u = 0.36921 + 1.95761I
a = −0.153181 − 0.185566I
b = 0.306708 − 0.368382I
6.14411 + 5.62850I 0
33
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.36921 − 1.95761I
a = −0.153181 + 0.185566I
b = 0.306708 + 0.368382I
6.14411 − 5.62850I 0
34
IV. I
u
4
= h4u
3
+ 5au − 11u
2
+ 5b + 17u − 11, 11u
3
a − 6u
3
+ · · · − 14a +
44, u
4
− 4u
3
+ 8u
2
− 9u + 5i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
9
=
a
−
4
5
u
3
+
11
5
u
2
+ ··· −
17
5
u +
11
5
a
10
=
u
2
a −
4
5
u
3
+ ··· + a +
11
5
−3u
3
a +
1
5
u
3
+ ··· + 5a −
14
5
a
1
=
4
5
u
3
a +
1
5
u
3
+ ··· −
11
5
a +
6
5
−u
3
+ 2u
2
− 2u + 1
a
4
=
1
5
u
3
a +
4
5
u
3
+ ··· −
4
5
a −
11
5
u
3
− 3u
2
+ 4u − 1
a
2
=
−
2
5
u
3
a +
2
5
u
3
+ ··· +
8
5
a +
2
5
u
2
− 3u + 2
a
8
=
−
4
5
u
3
+
11
5
u
2
+ ··· + a +
11
5
−
4
5
u
3
+
11
5
u
2
+ ··· −
17
5
u +
11
5
a
11
=
−
1
5
u
3
a +
2
5
u
3
+ ··· +
14
5
a −
3
5
−u
3
a +
6
5
u
3
+ ··· + 5a −
14
5
a
3
=
−0.400000au
3
+ 0.720000u
3
+ ··· − 0.400000a − 2.28000
2u
3
a +
43
25
u
3
+ ··· − 7a −
57
25
a
7
=
−0.160000au
3
− 0.640000u
3
+ ··· + 0.840000a + 2.36000
−2u
3
a + 7u
2
a − u
3
− 10au + 3u
2
+ 5a − 6u + 4
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1972
125
u
3
+
4998
125
u
2
−
7766
125
u +
5953
125
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
+ u
3
+ 4u
2
+ 2u + 3)
2
c
2
, c
7
5(5u
8
− 2u
7
− 4u
6
+ 3u
5
+ 8u
4
+ 6u
3
+ 2u
2
− 7u + 5)
c
3
, c
6
5(5u
8
+ 3u
7
− 11u
6
+ 6u
5
+ 49u
4
− 42u
3
+ 24u
2
− 6u + 1)
c
4
(u
4
− u
3
+ 4u
2
− 2u + 3)
2
c
5
(u
4
− 4u
3
+ 8u
2
− 9u + 5)
2
c
8
, c
12
5(5u
8
− 4u
7
+ 20u
6
− 30u
5
+ 51u
4
− 40u
3
+ 31u
2
− 11u + 5)
c
9
, c
11
5(5u
8
+ u
7
− 9u
6
− 10u
5
+ 31u
4
− 20u
3
− 18u
2
+ 18u + 27)
c
10
(u
4
+ 5u
3
+ 11u
2
+ 11u + 5)
2
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
4
+ 7y
3
+ 18y
2
+ 20y + 9)
2
c
2
, c
7
25(25y
8
− 44y
7
+ 108y
6
− 29y
5
+ 34y
4
− 2y
3
+ 168y
2
− 29y + 25)
c
3
, c
6
25(25y
8
− 119y
7
+ ··· + 12y + 1)
c
5
(y
4
+ 2y
2
− y + 25)
2
c
8
, c
12
25(25y
8
+ 184y
7
+ ··· + 189y + 25)
c
9
, c
11
25(25y
8
− 91y
7
+ ··· − 1296y + 729)
c
10
(y
4
− 3y
3
+ 21y
2
− 11y + 25)
2
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.34381 + 0.62536I
a = −0.088708 − 1.278200I
b = −0.616713 + 0.829872I
3.49532 + 7.54387I 7.2919 − 21.2390I
u = 1.34381 + 0.62536I
a = −0.141007 + 0.683169I
b = 0.68013 − 1.77314I
3.49532 + 7.54387I 7.2919 − 21.2390I
u = 1.34381 − 0.62536I
a = −0.088708 + 1.278200I
b = −0.616713 − 0.829872I
3.49532 − 7.54387I 7.2919 + 21.2390I
u = 1.34381 − 0.62536I
a = −0.141007 − 0.683169I
b = 0.68013 + 1.77314I
3.49532 − 7.54387I 7.2919 + 21.2390I
u = 0.65619 + 1.35843I
a = −0.547159 + 0.053493I
b = −0.031711 + 0.613225I
4.72935 + 4.22398I 3.14010 − 1.25039I
u = 0.65619 + 1.35843I
a = 0.356874 + 0.195730I
b = −0.431704 − 0.708178I
4.72935 + 4.22398I 3.14010 − 1.25039I
u = 0.65619 − 1.35843I
a = −0.547159 − 0.053493I
b = −0.031711 − 0.613225I
4.72935 − 4.22398I 3.14010 + 1.25039I
u = 0.65619 − 1.35843I
a = 0.356874 − 0.195730I
b = −0.431704 + 0.708178I
4.72935 − 4.22398I 3.14010 + 1.25039I
38
V. I
u
5
= hb − u + 2, 3a + 2u − 3, u
2
− 3u + 3i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−3u + 3
a
9
=
−
2
3
u + 1
u − 2
a
10
=
−
2
3
u + 2
−2u + 1
a
1
=
1
3
u
1
a
4
=
−
1
3
u + 1
−1
a
2
=
2
3
u − 1
2
a
8
=
1
3
u − 1
u − 2
a
11
=
1
3
u − 1
2u − 2
a
3
=
1
−2u + 3
a
7
=
1
3
u
−u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u + 12
39
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
7
(u − 1)
2
c
3
, c
6
, c
8
c
12
u
2
− u + 1
c
5
u
2
− 3u + 3
c
9
, c
11
(u + 1)
2
c
10
u
2
+ u + 1
40
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
7
, c
9
, c
11
(y −1)
2
c
3
, c
6
, c
8
c
10
, c
12
y
2
+ y + 1
c
5
y
2
− 3y + 9
41
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.50000 + 0.86603I
a = − 0.577350I
b = −0.500000 + 0.866025I
4.93480 + 2.02988I 6.00000 − 3.46410I
u = 1.50000 − 0.86603I
a = 0.577350I
b = −0.500000 − 0.866025I
4.93480 − 2.02988I 6.00000 + 3.46410I
42
VI. I
u
6
= hau + b − u, a
2
− a − u + 1, u
2
− u + 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u + 1
a
9
=
a
−au + u
a
10
=
u
−a + u + 1
a
1
=
−au + 1
0
a
4
=
1
0
a
2
=
−au + 1
0
a
8
=
−au + a + u
−au + u
a
11
=
−au − a − u + 1
−a + u
a
3
=
−a − u + 2
2au − a − 2u + 2
a
7
=
−au + 2a + u + 1
−u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u − 1
43
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
4
c
2
, c
7
u
4
− u
3
+ 2u
2
− 2u + 1
c
3
, c
6
u
4
+ 2u
2
+ 3u + 1
c
5
(u
2
− u + 1)
2
c
8
, c
12
u
4
+ u
3
+ 2u
2
+ 2u + 1
c
9
, c
11
u
4
+ 2u
2
− 3u + 1
c
10
(u
2
+ u + 1)
2
44
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
4
c
2
, c
7
, c
8
c
12
y
4
+ 3y
3
+ 2y
2
+ 1
c
3
, c
6
, c
9
c
11
y
4
+ 4y
3
+ 6y
2
− 5y + 1
c
5
, c
10
(y
2
+ y + 1)
2
45
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.070696 − 0.758745I
b = −0.121744 + 1.306620I
0 −2.50000 − 2.59808I
u = 0.500000 + 0.866025I
a = 1.070700 + 0.758745I
b = 0.621744 − 0.440597I
0 −2.50000 − 2.59808I
u = 0.500000 − 0.866025I
a = −0.070696 + 0.758745I
b = −0.121744 − 1.306620I
0 −2.50000 + 2.59808I
u = 0.500000 − 0.866025I
a = 1.070700 − 0.758745I
b = 0.621744 + 0.440597I
0 −2.50000 + 2.59808I
46
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
4
(u − 1)
2
(u
4
+ u
3
+ ··· + 2u + 3)
2
(u
31
− 10u
30
+ ··· + 164u − 13)
· (u
47
− 23u
46
+ ··· − 13056u + 1024)
c
2
, c
7
5(u − 1)
2
(u
4
− u
3
+ 2u
2
− 2u + 1)
· (5u
8
− 2u
7
− 4u
6
+ 3u
5
+ 8u
4
+ 6u
3
+ 2u
2
− 7u + 5)
· (u
31
− u
30
+ ··· − 2u + 1)(u
47
+ 3u
46
+ ··· + 2u + 1)
c
3
, c
6
5(u
2
− u + 1)(u
4
+ 2u
2
+ 3u + 1)
· (5u
8
+ 3u
7
− 11u
6
+ 6u
5
+ 49u
4
− 42u
3
+ 24u
2
− 6u + 1)
· (u
31
− u
30
+ ··· − 5u + 1)(u
47
+ 2u
46
+ ··· − 5u + 2)
c
4
u
4
(u − 1)
2
(u
4
− u
3
+ ··· − 2u + 3)
2
(u
31
+ 10u
30
+ ··· + 164u + 13)
· (u
47
− 23u
46
+ ··· − 13056u + 1024)
c
5
(u
2
− 3u + 3)(u
2
− u + 1)
2
(u
4
− 4u
3
+ 8u
2
− 9u + 5)
2
· (u
31
+ 13u
30
+ ··· + u − 1)(u
47
− 39u
46
+ ··· − 102400u + 8192)
c
8
, c
12
5(u
2
− u + 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)
· (5u
8
− 4u
7
+ 20u
6
− 30u
5
+ 51u
4
− 40u
3
+ 31u
2
− 11u + 5)
· (u
31
− u
30
+ ··· − 3u − 1)(u
47
+ 2u
46
+ ··· + 12u + 1)
c
9
, c
11
5(u + 1)
2
(u
4
+ 2u
2
− 3u + 1)
· (5u
8
+ u
7
− 9u
6
− 10u
5
+ 31u
4
− 20u
3
− 18u
2
+ 18u + 27)
· (u
31
− u
30
+ ··· + 5u − 1)(u
47
− u
46
+ ··· − 1149u + 457)
c
10
(u
2
+ u + 1)
3
(u
4
+ 5u
3
+ 11u
2
+ 11u + 5)
2
· (u
31
− 17u
30
+ ··· − 3u + 1)(u
47
+ 27u
46
+ ··· − 608u − 32)
47
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
4
(y −1)
2
(y
4
+ 7y
3
+ 18y
2
+ 20y + 9)
2
· (y
31
+ 26y
30
+ ··· − 7632y −169)
· (y
47
+ 39y
46
+ ··· − 19595264y −1048576)
c
2
, c
7
25(y −1)
2
(y
4
+ 3y
3
+ 2y
2
+ 1)
· (25y
8
− 44y
7
+ 108y
6
− 29y
5
+ 34y
4
− 2y
3
+ 168y
2
− 29y + 25)
· (y
31
− y
30
+ ··· + 24y −1)(y
47
− 21y
46
+ ··· + 40y −1)
c
3
, c
6
25(y
2
+ y + 1)(y
4
+ 4y
3
+ ··· − 5y + 1)(25y
8
− 119y
7
+ ··· + 12y + 1)
· (y
31
+ 3y
30
+ ··· − 25y −1)(y
47
+ 4y
46
+ ··· − 67y −4)
c
5
(y
2
− 3y + 9)(y
2
+ y + 1)
2
(y
4
+ 2y
2
− y + 25)
2
· (y
31
− y
30
+ ··· + 15y −1)
· (y
47
+ y
46
+ ··· − 2097152000y −67108864)
c
8
, c
12
25(y
2
+ y + 1)(y
4
+ 3y
3
+ 2y
2
+ 1)(25y
8
+ 184y
7
+ ··· + 189y + 25)
· (y
31
+ 3y
30
+ ··· + 5y −1)(y
47
+ 16y
46
+ ··· + 60y −1)
c
9
, c
11
25(y −1)
2
(y
4
+ 4y
3
+ 6y
2
− 5y + 1)
· (25y
8
− 91y
7
+ ··· − 1296y + 729)(y
31
− 15y
30
+ ··· − 17y −1)
· (y
47
− 27y
46
+ ··· + 3980855y −208849)
c
10
(y
2
+ y + 1)
3
(y
4
− 3y
3
+ 21y
2
− 11y + 25)
2
· (y
31
+ 3y
30
+ ··· + 33y −1)(y
47
+ y
46
+ ··· + 18944y −1024)
48
