12n
0810
(K12n
0810
)
A knot diagram
1
Linearized knot diagam
4 7 11 7 9 3 10 12 5 1 3 8
Solving Sequence
8,12
9
1,3
11 4 10 7 2 6 5
c
8
c
12
c
11
c
3
c
10
c
7
c
2
c
6
c
5
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h46649848211422u
20
− 271752392335713u
19
+ ··· + 2892575498427142b − 407290304844750,
616531903691785u
20
− 4456755156074076u
19
+ ··· + 5785150996854284a − 8643983373087020,
u
21
− 8u
20
+ ··· + 4u − 4i
I
u
2
= h17u
13
a + 3u
13
+ ··· + 90a − 135, 15u
13
a + 26u
13
+ ··· + 180a + 160,
u
14
− 2u
13
+ 8u
12
− 13u
11
+ 26u
10
− 32u
9
+ 44u
8
− 40u
7
+ 42u
6
− 25u
5
+ 25u
4
− 7u
3
+ 10u
2
+ 2i
I
u
3
= h934420413114u
21
a − 2562507066002u
21
+ ··· − 20080961710080a + 99672371759230,
− 58418953866728u
21
a + 52781909440645u
21
+ ··· + 613677712103440a − 532451057055698,
u
22
+ 3u
21
+ ··· − 106u − 16i
I
u
4
= h−11u
9
− 27u
8
− 72u
7
− 123u
6
− 201u
5
− 298u
4
− 405u
3
− 392u
2
+ 4b − 238u − 64,
127u
9
+ 288u
8
+ 805u
7
+ 1315u
6
+ 2210u
5
+ 3201u
4
+ 4367u
3
+ 4163u
2
+ 52a + 2522u + 694,
u
10
+ 3u
9
+ 8u
8
+ 15u
7
+ 25u
6
+ 38u
5
+ 53u
4
+ 58u
3
+ 44u
2
+ 20u + 4i
* 4 irreducible components of dim
C
= 0, with total 103 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
= h4.66 × 10
13
u
20
− 2.72 × 10
14
u
19
+ · · · + 2.89 × 10
15
b − 4.07 × 10
14
, 6.17 ×
10
14
u
20
−4.46×10
15
u
19
+· · ·+5.79×10
15
a−8.64×10
15
, u
21
−8u
20
+· · ·+4u−4i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
u
a
3
=
−0.106571u
20
+ 0.770378u
19
+ ··· − 10.1014u + 1.49417
−0.0161274u
20
+ 0.0939482u
19
+ ··· − 1.66730u + 0.140805
a
11
=
0.138515u
20
− 1.16208u
19
+ ··· − 0.849168u − 2.59979
0.0651459u
20
− 0.521592u
19
+ ··· + 2.89327u − 0.507601
a
4
=
−0.305406u
20
+ 2.43760u
19
+ ··· + 3.23821u − 0.643820
−0.115389u
20
+ 0.953768u
19
+ ··· + 0.0723902u + 0.582350
a
10
=
0.126900u
20
− 1.08035u
19
+ ··· − 1.35677u − 2.38567
0.0535308u
20
− 0.439861u
19
+ ··· + 2.38567u − 0.293478
a
7
=
0.253284u
20
− 2.06665u
19
+ ··· + 5.80307u − 1.73605
0.0247544u
20
− 0.213661u
19
+ ··· + 2.73605u − 0.914119
a
2
=
−0.359528u
20
+ 2.87082u
19
+ ··· + 3.64447u − 1.95837
−0.121837u
20
+ 1.03058u
19
+ ··· + 1.74858u + 0.385598
a
6
=
−0.0469918u
20
+ 0.352826u
19
+ ··· + 9.44776u − 1.95278
−0.0674397u
20
+ 0.517055u
19
+ ··· + 2.01598u − 0.333850
a
5
=
0.0352014u
20
− 0.297738u
19
+ ··· + 7.52731u − 1.52650
−0.0471219u
20
+ 0.366990u
19
+ ··· + 1.71514u − 0.361776
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
41241030794168
131480704473961
u
20
−
392809002780967
131480704473961
u
19
+ ··· −
542346152689020
131480704473961
u +
45491399639710
131480704473961
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
21
− 2u
20
+ ··· − 6u + 1
c
2
, c
6
u
21
+ 13u
20
+ ··· + 312u + 172
c
3
, c
5
, c
9
c
11
u
21
− u
20
+ ··· − 8u + 4
c
7
, c
10
u
21
− u
20
+ ··· − 7u − 1
c
8
, c
12
u
21
− 8u
20
+ ··· + 4u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
21
− 34y
20
+ ··· − 36y −1
c
2
, c
6
y
21
− 29y
20
+ ··· − 27872y −29584
c
3
, c
5
, c
9
c
11
y
21
+ 29y
20
+ ··· − 16y −16
c
7
, c
10
y
21
− 13y
20
+ ··· + 37y −1
c
8
, c
12
y
21
+ 16y
20
+ ··· − 112y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.358666 + 0.930307I
a = 0.433917 − 0.430001I
b = 0.68140 − 1.26020I
−6.17334 + 2.74245I −5.58156 − 4.02860I
u = 0.358666 − 0.930307I
a = 0.433917 + 0.430001I
b = 0.68140 + 1.26020I
−6.17334 − 2.74245I −5.58156 + 4.02860I
u = 0.558265 + 0.983614I
a = 0.066116 + 0.477640I
b = −0.337788 + 0.285816I
−0.28143 + 3.09051I 6.95527 − 0.27871I
u = 0.558265 − 0.983614I
a = 0.066116 − 0.477640I
b = −0.337788 − 0.285816I
−0.28143 − 3.09051I 6.95527 + 0.27871I
u = 0.467681 + 0.621789I
a = 0.629405 − 0.116067I
b = 0.424881 + 0.293762I
0.781678 + 1.149180I 3.85794 − 2.68827I
u = 0.467681 − 0.621789I
a = 0.629405 + 0.116067I
b = 0.424881 − 0.293762I
0.781678 − 1.149180I 3.85794 + 2.68827I
u = −0.650483 + 0.373679I
a = −0.417963 + 0.786598I
b = −0.613311 − 0.464168I
−1.10763 − 1.39427I −5.26731 + 0.64134I
u = −0.650483 − 0.373679I
a = −0.417963 − 0.786598I
b = −0.613311 + 0.464168I
−1.10763 + 1.39427I −5.26731 − 0.64134I
u = 0.438404
a = −1.90341
b = 0.0963240
−3.84208 0.707770
u = −0.08373 + 1.60426I
a = 0.881615 + 0.250414I
b = 2.24248 − 0.27198I
−9.64118 − 4.00759I −5.72656 + 3.33654I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.08373 − 1.60426I
a = 0.881615 − 0.250414I
b = 2.24248 + 0.27198I
−9.64118 + 4.00759I −5.72656 − 3.33654I
u = −0.08952 + 1.60605I
a = −1.216710 − 0.134957I
b = −2.38466 + 0.31900I
−11.06540 + 2.33214I −6.29844 − 1.85979I
u = −0.08952 − 1.60605I
a = −1.216710 + 0.134957I
b = −2.38466 − 0.31900I
−11.06540 − 2.33214I −6.29844 + 1.85979I
u = 1.66299 + 0.39397I
a = −0.337684 − 0.955286I
b = −0.335651 + 0.310065I
−14.7810 + 7.3026I −5.27461 − 4.46000I
u = 1.66299 − 0.39397I
a = −0.337684 + 0.955286I
b = −0.335651 − 0.310065I
−14.7810 − 7.3026I −5.27461 + 4.46000I
u = −0.158569 + 0.231883I
a = 2.58481 − 3.49981I
b = −0.190649 − 1.004700I
−4.17541 + 3.55934I −6.90301 − 4.21100I
u = −0.158569 − 0.231883I
a = 2.58481 + 3.49981I
b = −0.190649 + 1.004700I
−4.17541 − 3.55934I −6.90301 + 4.21100I
u = 0.61630 + 1.71869I
a = 1.082550 − 0.037150I
b = 2.48651 + 0.06539I
18.1211 + 15.3149I −5.71313 − 5.94319I
u = 0.61630 − 1.71869I
a = 1.082550 + 0.037150I
b = 2.48651 − 0.06539I
18.1211 − 15.3149I −5.71313 + 5.94319I
u = 1.09920 + 1.70202I
a = −0.754346 − 0.282941I
b = −2.02137 − 0.12495I
−18.2820 + 2.4257I −8.90248 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.09920 − 1.70202I
a = −0.754346 + 0.282941I
b = −2.02137 + 0.12495I
−18.2820 − 2.4257I −8.90248 + 0.I
7
II. I
u
2
= h17u
13
a + 3u
13
+ · · · + 90a − 135, 15u
13
a + 26u
13
+ · · · + 180a +
160, u
14
− 2u
13
+ · · · + 10u
2
+ 2i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
u
a
3
=
a
−0.894737au
13
− 0.157895u
13
+ ··· − 4.73684a + 7.10526
a
11
=
1.68421au
13
+ 0.552632u
13
+ ··· − 0.789474a − 1.36842
2.15789au
13
+ 1.05263u
13
+ ··· + 1.89474a − 3.36842
a
4
=
−1.52632au
13
− 1.60526u
13
+ ··· + 2.68421a + 4.73684
−1.36842au
13
− 2.10526u
13
+ ··· − 4.42105a + 4.73684
a
10
=
0.947368au
13
+ 0.552632u
13
+ ··· − 3.63158a + 0.631579
1.42105au
13
+ 1.05263u
13
+ ··· − 0.947368a − 1.36842
a
7
=
−0.842105au
13
+ 0.131579u
13
+ ··· + 1.89474a + 4.57895
−0.842105au
13
+ 1.15789u
13
+ ··· + 1.89474a + 10.8947
a
2
=
1.05263au
13
− 2.94737au
12
+ ··· − 2.36842a − 3
0.157895au
13
+ 1.36842u
13
+ ··· − 8.10526a + 11.4211
a
6
=
−2.36842au
13
+ 0.131579u
13
+ ··· + 1.57895a + 4.57895
−0.684211au
13
− 0.368421u
13
+ ··· + 1.78947a + 4.57895
a
5
=
−2.36842au
13
+ 1.81579u
13
+ ··· + 1.57895a + 3.78947
−0.684211au
13
+ 0.473684u
13
+ ··· + 1.78947a + 2.68421
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
259
19
u
13
+
710
19
u
12
−
2393
19
u
11
+
4643
19
u
10
−
8461
19
u
9
+
11424
19
u
8
−
750u
7
+
13647
19
u
6
−
12079
19
u
5
+
7345
19
u
4
−
4827
19
u
3
+
1525
19
u
2
−
998
19
u −
68
19
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
28
− 16u
27
+ ··· − 82u + 83
c
2
(u
14
+ 5u
13
+ ··· + 4u
2
+ 2)
2
c
3
, c
9
u
28
+ u
27
+ ··· − 20u + 4
c
5
, c
11
u
28
− u
27
+ ··· + 20u + 4
c
6
(u
14
− 5u
13
+ ··· + 4u
2
+ 2)
2
c
7
, c
10
u
28
− 6u
27
+ ··· − 17u + 1
c
8
(u
14
− 2u
13
+ ··· + 10u
2
+ 2)
2
c
12
(u
14
+ 2u
13
+ ··· + 10u
2
+ 2)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
28
− 34y
27
+ ··· − 56026y + 6889
c
2
, c
6
(y
14
− 5y
13
+ ··· + 16y + 4)
2
c
3
, c
5
, c
9
c
11
y
28
+ 13y
27
+ ··· + 160y + 16
c
7
, c
10
y
28
− 6y
27
+ ··· − 123y + 1
c
8
, c
12
(y
14
+ 12y
13
+ ··· + 40y + 4)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.234413 + 0.959941I
a = 0.798128 + 0.657503I
b = 2.55872 − 0.31570I
−7.07210 + 0.95011I −10.11138 + 0.50859I
u = 0.234413 + 0.959941I
a = 0.576102 − 0.304813I
b = −0.069432 − 1.006050I
−7.07210 + 0.95011I −10.11138 + 0.50859I
u = 0.234413 − 0.959941I
a = 0.798128 − 0.657503I
b = 2.55872 + 0.31570I
−7.07210 − 0.95011I −10.11138 − 0.50859I
u = 0.234413 − 0.959941I
a = 0.576102 + 0.304813I
b = −0.069432 + 1.006050I
−7.07210 − 0.95011I −10.11138 − 0.50859I
u = 1.022560 + 0.623679I
a = −0.178045 − 1.091150I
b = 0.060144 + 0.373874I
−2.39227 − 1.39378I −5.43366 + 1.94339I
u = 1.022560 + 0.623679I
a = 0.502605 + 0.670944I
b = 0.944156 + 0.116934I
−2.39227 − 1.39378I −5.43366 + 1.94339I
u = 1.022560 − 0.623679I
a = −0.178045 + 1.091150I
b = 0.060144 − 0.373874I
−2.39227 + 1.39378I −5.43366 − 1.94339I
u = 1.022560 − 0.623679I
a = 0.502605 − 0.670944I
b = 0.944156 − 0.116934I
−2.39227 + 1.39378I −5.43366 − 1.94339I
u = 0.575362 + 1.105550I
a = −1.079860 − 0.029997I
b = −2.72538 − 0.46723I
−4.15197 + 6.97492I −7.34754 − 10.51051I
u = 0.575362 + 1.105550I
a = 0.522348 + 0.114656I
b = 0.536465 + 0.133213I
−4.15197 + 6.97492I −7.34754 − 10.51051I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.575362 − 1.105550I
a = −1.079860 + 0.029997I
b = −2.72538 + 0.46723I
−4.15197 − 6.97492I −7.34754 + 10.51051I
u = 0.575362 − 1.105550I
a = 0.522348 − 0.114656I
b = 0.536465 − 0.133213I
−4.15197 − 6.97492I −7.34754 + 10.51051I
u = −0.308303 + 1.211280I
a = −0.807183 + 0.151993I
b = −1.40408 + 1.23092I
−0.266128 − 0.267018I −8.31716 − 0.56328I
u = −0.308303 + 1.211280I
a = 0.108704 + 1.319500I
b = 0.330999 + 0.920896I
−0.266128 − 0.267018I −8.31716 − 0.56328I
u = −0.308303 − 1.211280I
a = −0.807183 − 0.151993I
b = −1.40408 − 1.23092I
−0.266128 + 0.267018I −8.31716 + 0.56328I
u = −0.308303 − 1.211280I
a = 0.108704 − 1.319500I
b = 0.330999 − 0.920896I
−0.266128 + 0.267018I −8.31716 + 0.56328I
u = −0.215278 + 0.705882I
a = −1.367820 − 0.277475I
b = −0.326723 + 1.131580I
1.68909 − 1.91963I 5.71225 − 4.11158I
u = −0.215278 + 0.705882I
a = −0.30229 − 1.41470I
b = −0.465422 − 0.889685I
1.68909 − 1.91963I 5.71225 − 4.11158I
u = −0.215278 − 0.705882I
a = −1.367820 + 0.277475I
b = −0.326723 − 1.131580I
1.68909 + 1.91963I 5.71225 + 4.11158I
u = −0.215278 − 0.705882I
a = −0.30229 + 1.41470I
b = −0.465422 + 0.889685I
1.68909 + 1.91963I 5.71225 + 4.11158I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.272478 + 0.552545I
a = −0.788139 − 0.338457I
b = −0.56920 − 3.14491I
−7.86777 − 4.67761I −14.7715 + 8.0785I
u = −0.272478 + 0.552545I
a = 1.91009 − 0.15679I
b = 0.061739 + 0.382886I
−7.86777 − 4.67761I −14.7715 + 8.0785I
u = −0.272478 − 0.552545I
a = −0.788139 + 0.338457I
b = −0.56920 + 3.14491I
−7.86777 + 4.67761I −14.7715 − 8.0785I
u = −0.272478 − 0.552545I
a = 1.91009 + 0.15679I
b = 0.061739 − 0.382886I
−7.86777 + 4.67761I −14.7715 − 8.0785I
u = −0.03627 + 1.68674I
a = 1.075870 − 0.171245I
b = 2.42178 − 0.08826I
−12.83750 + 2.76839I −7.73098 − 3.24512I
u = −0.03627 + 1.68674I
a = −0.470505 + 0.524657I
b = −1.35376 − 0.78155I
−12.83750 + 2.76839I −7.73098 − 3.24512I
u = −0.03627 − 1.68674I
a = 1.075870 + 0.171245I
b = 2.42178 + 0.08826I
−12.83750 − 2.76839I −7.73098 + 3.24512I
u = −0.03627 − 1.68674I
a = −0.470505 − 0.524657I
b = −1.35376 + 0.78155I
−12.83750 − 2.76839I −7.73098 + 3.24512I
13
III. I
u
3
= h9.34 × 10
11
au
21
− 2.56 × 10
12
u
21
+ · · · − 2.01 × 10
13
a + 9.97 ×
10
13
, −5.84 × 10
13
au
21
+ 5.28 × 10
13
u
21
+ · · · + 6.14 × 10
14
a − 5.32 ×
10
14
, u
22
+ 3u
21
+ · · · − 106u − 16i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
u
a
3
=
a
−0.109662au
21
+ 0.300732u
21
+ ··· + 2.35667a − 11.6974
a
11
=
0.206848au
21
− 0.179565u
21
+ ··· − 5.14198a + 4.64581
−0.00824585au
21
+ 0.183407u
21
+ ··· + 1.51405a − 8.88568
a
4
=
0.214923au
21
− 0.225154u
21
+ ··· − 8.20474a + 11.3428
−0.0858092au
21
+ 0.424867u
21
+ ··· + 3.49268a − 16.8777
a
10
=
0.0946281au
21
− 0.171902u
21
+ ··· − 3.21453a + 3.19075
−0.120466au
21
+ 0.191070u
21
+ ··· + 3.44150a − 10.3407
a
7
=
−0.0513765au
21
− 0.00593995u
21
+ ··· + 1.63862a + 5.20752
−0.0513765au
21
+ 0.273963u
21
+ ··· + 1.63862a − 11.2984
a
2
=
−0.0731608au
21
+ 0.0271244u
21
+ ··· + 1.84536a + 8.76641
−0.182823au
21
+ 0.730749u
21
+ ··· + 3.20203a − 26.5582
a
6
=
−0.147292au
21
− 0.00593995u
21
+ ··· + 0.898090a + 5.20752
0.0812089au
21
− 0.233617u
21
+ ··· − 1.75460a + 5.54098
a
5
=
−0.147292au
21
+ 0.200908u
21
+ ··· + 0.898090a + 0.0655438
0.0812089au
21
− 0.215094u
21
+ ··· − 1.75460a + 6.65603
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
197897285171
1420147857381
u
21
+
190080141899
1420147857381
u
20
+ ··· +
3122761442852
129104350671
u +
10177990956464
1420147857381
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
44
− 3u
43
+ ··· − 10746u + 4757
c
2
, c
6
(u
22
− 5u
21
+ ··· + 322u − 68)
2
c
3
, c
5
, c
9
c
11
u
44
− 2u
43
+ ··· − 774u + 61
c
7
, c
10
u
44
− 3u
43
+ ··· − 133u + 449
c
8
, c
12
(u
22
+ 3u
21
+ ··· − 106u − 16)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
44
− 63y
43
+ ··· − 533588274y + 22629049
c
2
, c
6
(y
22
− 37y
21
+ ··· − 116468y + 4624)
2
c
3
, c
5
, c
9
c
11
y
44
+ 40y
43
+ ··· − 287122y + 3721
c
7
, c
10
y
44
− 9y
43
+ ··· − 2706301y + 201601
c
8
, c
12
(y
22
+ 25y
21
+ ··· − 228y + 256)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.04270
a = 0.30245 + 1.75266I
b = −0.073263 + 0.573968I
−14.1642 −4.58700
u = −1.04270
a = 0.30245 − 1.75266I
b = −0.073263 − 0.573968I
−14.1642 −4.58700
u = 0.457379 + 1.018200I
a = 0.115964 − 1.048530I
b = 0.090260 − 0.405075I
0.743577 + 0.428047I 0.238159 + 0.175042I
u = 0.457379 + 1.018200I
a = 0.845744 + 0.235877I
b = 1.21774 + 1.09691I
0.743577 + 0.428047I 0.238159 + 0.175042I
u = 0.457379 − 1.018200I
a = 0.115964 + 1.048530I
b = 0.090260 + 0.405075I
0.743577 − 0.428047I 0.238159 − 0.175042I
u = 0.457379 − 1.018200I
a = 0.845744 − 0.235877I
b = 1.21774 − 1.09691I
0.743577 − 0.428047I 0.238159 − 0.175042I
u = 0.226624 + 0.805825I
a = 1.134210 − 0.388448I
b = 0.319328 + 0.933679I
1.44999 + 2.22738I −6.70486 − 11.03214I
u = 0.226624 + 0.805825I
a = −0.158356 + 1.235610I
b = −0.263799 + 1.084790I
1.44999 + 2.22738I −6.70486 − 11.03214I
u = 0.226624 − 0.805825I
a = 1.134210 + 0.388448I
b = 0.319328 − 0.933679I
1.44999 − 2.22738I −6.70486 + 11.03214I
u = 0.226624 − 0.805825I
a = −0.158356 − 1.235610I
b = −0.263799 − 1.084790I
1.44999 − 2.22738I −6.70486 + 11.03214I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.20980
a = 0.294291 + 0.944243I
b = 0.642252 − 0.686297I
−3.72523 −8.18500
u = 1.20980
a = 0.294291 − 0.944243I
b = 0.642252 + 0.686297I
−3.72523 −8.18500
u = −0.689362 + 0.229386I
a = 0.01853 − 1.42171I
b = −0.191657 + 0.548748I
−0.67054 + 1.98597I 1.83458 − 3.47221I
u = −0.689362 + 0.229386I
a = −0.102400 − 0.123929I
b = −0.056853 + 0.708751I
−0.67054 + 1.98597I 1.83458 − 3.47221I
u = −0.689362 − 0.229386I
a = 0.01853 + 1.42171I
b = −0.191657 − 0.548748I
−0.67054 − 1.98597I 1.83458 + 3.47221I
u = −0.689362 − 0.229386I
a = −0.102400 + 0.123929I
b = −0.056853 − 0.708751I
−0.67054 − 1.98597I 1.83458 + 3.47221I
u = −0.218673 + 1.262490I
a = −0.938783 + 0.384242I
b = −2.44127 − 0.13576I
−5.45881 − 0.93633I −3.90557 + 0.08669I
u = −0.218673 + 1.262490I
a = 0.198203 + 0.659477I
b = 0.083542 + 0.357045I
−5.45881 − 0.93633I −3.90557 + 0.08669I
u = −0.218673 − 1.262490I
a = −0.938783 − 0.384242I
b = −2.44127 + 0.13576I
−5.45881 + 0.93633I −3.90557 − 0.08669I
u = −0.218673 − 1.262490I
a = 0.198203 − 0.659477I
b = 0.083542 − 0.357045I
−5.45881 + 0.93633I −3.90557 − 0.08669I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.511878 + 1.220260I
a = 1.059960 − 0.055249I
b = 2.73012 − 0.26498I
−3.63436 − 6.49284I 0.55712 + 2.91982I
u = −0.511878 + 1.220260I
a = 0.004918 − 0.279283I
b = 0.359462 + 0.234811I
−3.63436 − 6.49284I 0.55712 + 2.91982I
u = −0.511878 − 1.220260I
a = 1.059960 + 0.055249I
b = 2.73012 + 0.26498I
−3.63436 + 6.49284I 0.55712 − 2.91982I
u = −0.511878 − 1.220260I
a = 0.004918 + 0.279283I
b = 0.359462 − 0.234811I
−3.63436 + 6.49284I 0.55712 − 2.91982I
u = −0.50930 + 1.47048I
a = 1.079350 − 0.120269I
b = 1.95737 − 0.81045I
−18.8917 − 5.6090I −7.11087 + 3.25228I
u = −0.50930 + 1.47048I
a = −1.41500 − 0.26394I
b = −2.37405 + 0.02009I
−18.8917 − 5.6090I −7.11087 + 3.25228I
u = −0.50930 − 1.47048I
a = 1.079350 + 0.120269I
b = 1.95737 + 0.81045I
−18.8917 + 5.6090I −7.11087 − 3.25228I
u = −0.50930 − 1.47048I
a = −1.41500 + 0.26394I
b = −2.37405 − 0.02009I
−18.8917 + 5.6090I −7.11087 − 3.25228I
u = −0.347793 + 0.231922I
a = 1.35477 + 0.55673I
b = −0.58926 − 2.54064I
−7.48607 − 4.50242I 3.32541 − 0.00984I
u = −0.347793 + 0.231922I
a = 2.48521 − 1.81552I
b = 0.327911 + 0.393218I
−7.48607 − 4.50242I 3.32541 − 0.00984I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.347793 − 0.231922I
a = 1.35477 − 0.55673I
b = −0.58926 + 2.54064I
−7.48607 + 4.50242I 3.32541 + 0.00984I
u = −0.347793 − 0.231922I
a = 2.48521 + 1.81552I
b = 0.327911 − 0.393218I
−7.48607 + 4.50242I 3.32541 + 0.00984I
u = −0.05840 + 1.62782I
a = −1.107470 − 0.080175I
b = −2.62516 − 0.39573I
−14.5481 − 5.7193I −6.68719 + 3.44042I
u = −0.05840 + 1.62782I
a = −0.294917 − 1.267580I
b = −0.297043 − 0.832997I
−14.5481 − 5.7193I −6.68719 + 3.44042I
u = −0.05840 − 1.62782I
a = −1.107470 + 0.080175I
b = −2.62516 + 0.39573I
−14.5481 + 5.7193I −6.68719 − 3.44042I
u = −0.05840 − 1.62782I
a = −0.294917 + 1.267580I
b = −0.297043 + 0.832997I
−14.5481 + 5.7193I −6.68719 − 3.44042I
u = −0.24944 + 1.66440I
a = 1.056420 − 0.309321I
b = 2.24354 − 0.17069I
−12.76390 + 1.46972I −7.15635 + 2.06549I
u = −0.24944 + 1.66440I
a = 0.022168 + 0.398861I
b = −0.254904 − 1.280220I
−12.76390 + 1.46972I −7.15635 + 2.06549I
u = −0.24944 − 1.66440I
a = 1.056420 + 0.309321I
b = 2.24354 + 0.17069I
−12.76390 − 1.46972I −7.15635 − 2.06549I
u = −0.24944 − 1.66440I
a = 0.022168 − 0.398861I
b = −0.254904 + 1.280220I
−12.76390 − 1.46972I −7.15635 − 2.06549I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.31729 + 1.70586I
a = 1.080730 + 0.233949I
b = 2.28353 + 0.03027I
−10.39710 + 5.75297I −8.00445 − 3.25214I
u = 0.31729 + 1.70586I
a = −0.848505 + 0.111896I
b = −2.58780 + 0.06595I
−10.39710 + 5.75297I −8.00445 − 3.25214I
u = 0.31729 − 1.70586I
a = 1.080730 − 0.233949I
b = 2.28353 − 0.03027I
−10.39710 − 5.75297I −8.00445 + 3.25214I
u = 0.31729 − 1.70586I
a = −0.848505 − 0.111896I
b = −2.58780 − 0.06595I
−10.39710 − 5.75297I −8.00445 + 3.25214I
21
IV. I
u
4
= h−11u
9
− 27u
8
+ · · · + 4b − 64, 127u
9
+ 288u
8
+ · · · + 52a +
694, u
10
+ 3u
9
+ · · · + 20u + 4i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
u
a
3
=
−2.44231u
9
− 5.53846u
8
+ ··· − 48.5000u − 13.3462
11
4
u
9
+
27
4
u
8
+ ··· +
119
2
u + 16
a
11
=
3
13
u
9
+
5
52
u
8
+ ··· −
5
2
u −
49
26
7
52
u
9
+
17
52
u
8
+ ··· +
9
2
u +
22
13
a
4
=
−0.884615u
9
− 1.82692u
8
+ ··· − 13.5000u − 3.19231
2.09615u
9
+ 5.01923u
8
+ ··· + 44.5000u + 11.9231
a
10
=
−0.423077u
9
− 1.13462u
8
+ ··· − 12.5000u − 3.96154
−0.519231u
9
− 0.903846u
8
+ ··· − 5.50000u − 0.384615
a
7
=
−
3
26
u
9
−
9
52
u
8
+ ··· + 2u +
57
26
0.403846u
9
+ 0.980769u
8
+ ··· + 9.50000u + 2.07692
a
2
=
−0.653846u
9
− 1.48077u
8
+ ··· − 11u − 3.57692
0.788462u
9
+ 2.05769u
8
+ ··· + 20.5000u + 5.76923
a
6
=
−2.21154u
9
− 5.19231u
8
+ ··· − 42.5000u − 10.7308
2.32692u
9
+ 5.86538u
8
+ ··· + 55.5000u + 15.5385
a
5
=
−4u
9
−
37
4
u
8
+ ··· − 78u −
41
2
3.28846u
9
+ 8.05769u
8
+ ··· + 74.5000u + 20.7692
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
200
13
u
9
−
495
13
u
8
−
1306
13
u
7
−
2250
13
u
6
− 280u
5
−
5416
13
u
4
−
7325
13
u
3
−
7132
13
u
2
− 326u −
1192
13
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
10
− 3u
8
+ 7u
7
− 3u
6
− 9u
5
+ 19u
4
− 21u
3
+ 15u
2
− 6u + 1
c
2
u
10
− 8u
9
+ ··· − 24u + 4
c
3
, c
9
u
10
+ u
9
+ 7u
8
+ 3u
7
+ 15u
6
+ u
5
+ 13u
4
+ 5u
2
+ 1
c
5
, c
11
u
10
− u
9
+ 7u
8
− 3u
7
+ 15u
6
− u
5
+ 13u
4
+ 5u
2
+ 1
c
6
u
10
+ 8u
9
+ ··· + 24u + 4
c
7
, c
10
u
10
− u
9
+ u
8
− u
7
+ 2u
6
− 2u
5
+ 2u
4
− 3u
3
+ 2u
2
− u + 1
c
8
u
10
+ 3u
9
+ ··· + 20u + 4
c
12
u
10
− 3u
9
+ ··· − 20u + 4
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
10
− 6y
9
+ 3y
8
+ 7y
7
+ 51y
6
+ 11y
5
− 29y
4
+ 15y
3
+ 11y
2
− 6y + 1
c
2
, c
6
y
10
− 8y
9
+ ··· − 32y + 16
c
3
, c
5
, c
9
c
11
y
10
+ 13y
9
+ ··· + 10y + 1
c
7
, c
10
y
10
+ y
9
+ 3y
8
+ 3y
7
+ 2y
6
+ 2y
5
− y
3
+ 2y
2
+ 3y + 1
c
8
, c
12
y
10
+ 7y
9
+ ··· − 48y + 16
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.760697 + 0.640528I
a = −0.611876 + 0.249644I
b = −0.814636 + 0.047301I
0.04719 − 1.98946I −0.34774 + 5.27723I
u = −0.760697 − 0.640528I
a = −0.611876 − 0.249644I
b = −0.814636 − 0.047301I
0.04719 + 1.98946I −0.34774 − 5.27723I
u = −0.673976 + 0.906830I
a = −0.267161 + 0.478992I
b = 0.225289 − 0.082571I
−0.78223 − 3.32806I −6.56898 + 6.19086I
u = −0.673976 − 0.906830I
a = −0.267161 − 0.478992I
b = 0.225289 + 0.082571I
−0.78223 + 3.32806I −6.56898 − 6.19086I
u = −0.658761 + 0.130449I
a = 0.048977 − 1.266850I
b = −0.075967 + 1.183730I
−1.82403 + 2.46122I −7.28347 − 4.94712I
u = −0.658761 − 0.130449I
a = 0.048977 + 1.266850I
b = −0.075967 − 1.183730I
−1.82403 − 2.46122I −7.28347 + 4.94712I
u = 0.85535 + 1.31066I
a = −1.103500 − 0.375117I
b = −1.74453 − 0.36767I
−16.9543 + 3.5243I −4.81696 − 1.77054I
u = 0.85535 − 1.31066I
a = −1.103500 + 0.375117I
b = −1.74453 + 0.36767I
−16.9543 − 3.5243I −4.81696 + 1.77054I
u = −0.26192 + 1.67321I
a = 0.933564 − 0.007475I
b = 2.40984 + 0.15933I
−8.45052 − 6.48343I −3.48284 + 5.23163I
u = −0.26192 − 1.67321I
a = 0.933564 + 0.007475I
b = 2.40984 − 0.15933I
−8.45052 + 6.48343I −3.48284 − 5.23163I
25
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
10
− 3u
8
+ 7u
7
− 3u
6
− 9u
5
+ 19u
4
− 21u
3
+ 15u
2
− 6u + 1)
· (u
21
− 2u
20
+ ··· − 6u + 1)(u
28
− 16u
27
+ ··· − 82u + 83)
· (u
44
− 3u
43
+ ··· − 10746u + 4757)
c
2
(u
10
− 8u
9
+ ··· − 24u + 4)(u
14
+ 5u
13
+ ··· + 4u
2
+ 2)
2
· (u
21
+ 13u
20
+ ··· + 312u + 172)(u
22
− 5u
21
+ ··· + 322u − 68)
2
c
3
, c
9
(u
10
+ u
9
+ 7u
8
+ 3u
7
+ 15u
6
+ u
5
+ 13u
4
+ 5u
2
+ 1)
· (u
21
− u
20
+ ··· − 8u + 4)(u
28
+ u
27
+ ··· − 20u + 4)
· (u
44
− 2u
43
+ ··· − 774u + 61)
c
5
, c
11
(u
10
− u
9
+ 7u
8
− 3u
7
+ 15u
6
− u
5
+ 13u
4
+ 5u
2
+ 1)
· (u
21
− u
20
+ ··· − 8u + 4)(u
28
− u
27
+ ··· + 20u + 4)
· (u
44
− 2u
43
+ ··· − 774u + 61)
c
6
(u
10
+ 8u
9
+ ··· + 24u + 4)(u
14
− 5u
13
+ ··· + 4u
2
+ 2)
2
· (u
21
+ 13u
20
+ ··· + 312u + 172)(u
22
− 5u
21
+ ··· + 322u − 68)
2
c
7
, c
10
(u
10
− u
9
+ u
8
− u
7
+ 2u
6
− 2u
5
+ 2u
4
− 3u
3
+ 2u
2
− u + 1)
· (u
21
− u
20
+ ··· − 7u − 1)(u
28
− 6u
27
+ ··· − 17u + 1)
· (u
44
− 3u
43
+ ··· − 133u + 449)
c
8
(u
10
+ 3u
9
+ ··· + 20u + 4)(u
14
− 2u
13
+ ··· + 10u
2
+ 2)
2
· (u
21
− 8u
20
+ ··· + 4u − 4)(u
22
+ 3u
21
+ ··· − 106u − 16)
2
c
12
(u
10
− 3u
9
+ ··· − 20u + 4)(u
14
+ 2u
13
+ ··· + 10u
2
+ 2)
2
· (u
21
− 8u
20
+ ··· + 4u − 4)(u
22
+ 3u
21
+ ··· − 106u − 16)
2
26
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
10
− 6y
9
+ 3y
8
+ 7y
7
+ 51y
6
+ 11y
5
− 29y
4
+ 15y
3
+ 11y
2
− 6y + 1)
· (y
21
− 34y
20
+ ··· − 36y −1)(y
28
− 34y
27
+ ··· − 56026y + 6889)
· (y
44
− 63y
43
+ ··· − 533588274y + 22629049)
c
2
, c
6
(y
10
− 8y
9
+ ··· − 32y + 16)(y
14
− 5y
13
+ ··· + 16y + 4)
2
· (y
21
− 29y
20
+ ··· − 27872y −29584)
· (y
22
− 37y
21
+ ··· − 116468y + 4624)
2
c
3
, c
5
, c
9
c
11
(y
10
+ 13y
9
+ ··· + 10y + 1)(y
21
+ 29y
20
+ ··· − 16y −16)
· (y
28
+ 13y
27
+ ··· + 160y + 16)(y
44
+ 40y
43
+ ··· − 287122y + 3721)
c
7
, c
10
(y
10
+ y
9
+ 3y
8
+ 3y
7
+ 2y
6
+ 2y
5
− y
3
+ 2y
2
+ 3y + 1)
· (y
21
− 13y
20
+ ··· + 37y −1)(y
28
− 6y
27
+ ··· − 123y + 1)
· (y
44
− 9y
43
+ ··· − 2706301y + 201601)
c
8
, c
12
(y
10
+ 7y
9
+ ··· − 48y + 16)(y
14
+ 12y
13
+ ··· + 40y + 4)
2
· (y
21
+ 16y
20
+ ··· − 112y −16)(y
22
+ 25y
21
+ ··· − 228y + 256)
2
27
