12n
0868
(K12n
0868
)
A knot diagram
1
Linearized knot diagam
4 6 12 11 8 2 10 12 6 5 2 8
Solving Sequence
2,4 1,8
12 9 3 11 5 6 7 10
c
1
c
12
c
8
c
3
c
11
c
4
c
5
c
6
c
10
c
2
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h63u
7
+ 216u
6
+ 255u
5
− 250u
4
− 354u
3
+ 222u
2
+ 419b + 903u − 430,
− 389u
7
− 1633u
6
− 2213u
5
− 1815u
4
+ 11u
3
− 2947u
2
+ 10475a + 2525u − 8904,
u
8
+ 2u
7
+ 2u
6
− 5u
5
+ u
4
+ 3u
3
+ 15u
2
− 14u + 5i
I
u
2
= h−6u
9
+ 22u
8
− 42u
6
+ 19u
4
− 56u
3
− 36u
2
+ 3b − 26u − 2,
4u
9
− 18u
8
+ 12u
7
+ 30u
6
− 26u
5
− 17u
4
+ 54u
3
− 5u
2
+ 3a − 14u − 15,
u
10
− 3u
9
− 2u
8
+ 6u
7
+ 4u
6
− 2u
5
+ 7u
4
+ 11u
3
+ 10u
2
+ 4u + 1i
I
u
3
= h−9660231u
15
+ 63732863u
14
+ ··· + 108707188b + 103207804,
97383821u
15
− 778749368u
14
+ ··· + 108707188a − 952070632, u
16
− 8u
15
+ ··· − 16u + 4i
I
u
4
= h−3u
3
− 15u
2
+ 2b − 33u − 26, 9u
3
+ 35u
2
+ 28a + 67u + 34, u
4
+ 7u
3
+ 23u
2
+ 38u + 28i
I
u
5
= h−u
3
− u
2
+ 2b − 3u, u
3
− 3u
2
+ 4a + u − 10, u
4
+ u
3
+ 5u
2
+ 2u + 4i
I
u
6
= h−u
7
+ 6u
6
+ u
5
+ 20u
4
− 3u
3
+ 10u
2
+ 56b − 2u − 24,
2u
7
+ 2u
6
+ 5u
5
+ 16u
4
− u
3
+ 36u
2
+ 14a + 11u + 20, u
8
+ 5u
6
+ 2u
5
+ 9u
4
+ 8u
3
+ 12u
2
+ 8u + 4i
I
u
7
= hu
2
+ b − u + 1, a, u
4
− 2u
3
+ 2u
2
− u + 1i
I
u
8
= h4u
3
+ 9u
2
+ 11b + u − 15, −18u
3
− 24u
2
+ 55a − 10u + 40, u
4
− 5u + 5i
I
u
9
= hb − u, a + 1, u
2
+ 1i
* 9 irreducible components of dim
C
= 0, with total 60 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).
1
I. I
u
1
= h63u
7
+ 216u
6
+ · · · + 419b − 430, −389u
7
− 1633u
6
+ · · · + 10475a −
8904, u
8
+ 2u
7
+ · · · − 14u + 5i
(i) Arc colorings
a
2
=
1
0
a
4
=
0
u
a
1
=
1
−u
2
a
8
=
0.0371360u
7
+ 0.155895u
6
+ ··· − 0.241050u + 0.850024
−0.150358u
7
− 0.515513u
6
+ ··· − 2.15513u + 1.02625
a
12
=
−0.101289u
7
− 0.175847u
6
+ ··· − 0.558473u + 1.33451
−u
a
9
=
0.0456325u
7
+ 0.0707399u
6
+ ··· − 2.89260u + 1.80029
−0.183771u
7
− 0.630072u
6
+ ··· − 0.300716u + 0.143198
a
3
=
0.00507876u
7
− 0.102587u
6
+ ··· + 0.934129u + 0.406224
−0.0381862u
7
+ 0.0119332u
6
+ ··· + 0.119332u + 0.133652
a
11
=
−0.101289u
7
− 0.175847u
6
+ ··· − 1.55847u + 1.33451
−u
a
5
=
−0.0712936u
7
− 0.0787208u
6
+ ··· − 0.827208u + 0.673527
−0.0381862u
7
+ 0.0119332u
6
+ ··· + 0.119332u + 0.133652
a
6
=
−0.152916u
7
− 0.215714u
6
+ ··· − 2.19714u + 0.859208
0.176611u
7
+ 0.319809u
6
+ ··· + 1.19809u − 0.618138
a
7
=
0.0236945u
7
+ 0.104095u
6
+ ··· − 0.999045u + 0.241069
0.176611u
7
+ 0.319809u
6
+ ··· + 1.19809u − 0.618138
a
10
=
−0.218219u
7
− 0.375607u
6
+ ··· − 2.30807u + 1.81497
−0.0816229u
7
− 0.136993u
6
+ ··· − 1.36993u + 0.185680
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
61428
52375
u
7
+
145366
52375
u
6
+
182076
52375
u
5
−
39694
10475
u
4
+
38278
52375
u
3
+
248544
52375
u
2
+
32336
2095
u −
602992
52375
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
c
11
u
8
− 2u
7
+ 2u
6
+ 5u
5
+ u
4
− 3u
3
+ 15u
2
+ 14u + 5
c
2
, c
6
, c
8
c
12
u
8
− u
7
− 8u
6
+ 9u
5
+ 23u
4
− 13u
3
+ 16u
2
− 4u + 2
c
3
, c
9
5(5u
8
+ 29u
7
+ ··· + 864u + 160)
c
4
, c
10
5(5u
8
+ 29u
7
+ 88u
6
+ 173u
5
+ 235u
4
+ 223u
3
+ 142u
2
+ 52u + 8)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
11
y
8
+ 26y
6
− 3y
5
+ 157y
4
− 99y
3
+ 319y
2
− 46y + 25
c
2
, c
6
, c
8
c
12
y
8
− 17y
7
+ 128y
6
− 443y
5
+ 503y
4
+ 607y
3
+ 244y
2
+ 48y + 4
c
3
, c
9
25(25y
8
+ 789y
7
+ ··· − 150016y + 25600)
c
4
, c
10
25
· (25y
8
+ 39y
7
+ 60y
6
− 83y
5
+ 123y
4
+ 427y
3
+ 732y
2
− 432y + 64)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.025930 + 0.701004I
a = −0.761354 + 0.203728I
b = 0.93351 + 1.44138I
−4.59702 − 4.89276I −8.69831 + 5.22490I
u = 1.025930 − 0.701004I
a = −0.761354 − 0.203728I
b = 0.93351 − 1.44138I
−4.59702 + 4.89276I −8.69831 − 5.22490I
u = 0.422794 + 0.334865I
a = 0.741901 − 0.000101I
b = 0.013606 − 0.711717I
−0.740582 − 1.158680I −4.63203 + 6.37231I
u = 0.422794 − 0.334865I
a = 0.741901 + 0.000101I
b = 0.013606 + 0.711717I
−0.740582 + 1.158680I −4.63203 − 6.37231I
u = −0.96585 + 1.28563I
a = 1.086050 − 0.661498I
b = 0.30067 + 1.70085I
13.8260 + 7.0293I 1.39449 − 3.33100I
u = −0.96585 − 1.28563I
a = 1.086050 + 0.661498I
b = 0.30067 − 1.70085I
13.8260 − 7.0293I 1.39449 + 3.33100I
u = −1.48287 + 1.45144I
a = −0.746600 + 0.618962I
b = −0.24778 − 2.35508I
11.2508 + 13.9556I −0.73615 − 5.79535I
u = −1.48287 − 1.45144I
a = −0.746600 − 0.618962I
b = −0.24778 + 2.35508I
11.2508 − 13.9556I −0.73615 + 5.79535I
5
II.
I
u
2
= h−6u
9
+22u
8
+· · ·+3b−2, 4u
9
−18u
8
+· · ·+3 a −15, u
10
−3u
9
+· · ·+4u+1i
(i) Arc colorings
a
2
=
1
0
a
4
=
0
u
a
1
=
1
−u
2
a
8
=
−
4
3
u
9
+ 6u
8
+ ··· +
14
3
u + 5
2u
9
−
22
3
u
8
+ ··· +
26
3
u +
2
3
a
12
=
u
9
− 3u
8
− 2u
7
+ 6u
6
+ 4u
5
− 2u
4
+ 7u
3
+ 11u
2
+ 10u + 4
−3u
9
+
26
3
u
8
+ ··· −
70
3
u −
25
3
a
9
=
−
8
3
u
9
+
26
3
u
8
+ ··· − 11u −
7
3
−
10
3
u
9
+ 12u
8
+ ··· −
61
3
u
2
−
37
3
u
a
3
=
−u
9
+ 3u
8
+ 2u
7
− 6u
6
− 4u
5
+ 2u
4
− 7u
3
− 11u
2
− 10u − 4
3u
9
−
26
3
u
8
+ ··· +
73
3
u +
25
3
a
11
=
−2u
9
+
17
3
u
8
+ ··· −
40
3
u −
13
3
−3u
9
+
26
3
u
8
+ ··· −
70
3
u −
25
3
a
5
=
20
3
u
9
− 22u
8
+ ··· +
104
3
u + 7
14
3
u
9
−
49
3
u
8
+ ··· +
67
3
u +
8
3
a
6
=
6u
9
−
62
3
u
8
+ ··· +
82
3
u +
7
3
−
4
3
u
9
+
16
3
u
8
+ ··· − 2u +
4
3
a
7
=
14
3
u
9
−
46
3
u
8
+ ··· +
76
3
u +
11
3
−
4
3
u
9
+
16
3
u
8
+ ··· − 2u +
4
3
a
10
=
−8.66667u
9
+ 29.3333u
8
+ ··· − 38.3333u − 4.66667
−2u
9
+
20
3
u
8
+ ··· −
31
3
u −
4
3
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −32u
9
+
304
3
u
8
+ 52u
7
− 220u
6
− 92u
5
+
364
3
u
4
−
728
3
u
3
− 324u
2
−
620
3
u −
146
3
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
c
11
u
10
+ 3u
9
− 2u
8
− 6u
7
+ 4u
6
+ 2u
5
+ 7u
4
− 11u
3
+ 10u
2
− 4u + 1
c
2
, c
6
, c
8
c
12
(u
5
+ u
4
+ 2u
3
+ u
2
− u − 1)
2
c
3
, c
9
(u − 1)
10
c
4
, c
10
(u
5
− 3u
4
+ 6u
3
− 7u
2
+ 5u − 3)
2
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
11
y
10
− 13y
9
+ ··· + 4y + 1
c
2
, c
6
, c
8
c
12
(y
5
+ 3y
4
− 3y
2
+ 3y − 1)
2
c
3
, c
9
(y − 1)
10
c
4
, c
10
(y
5
+ 3y
4
+ 4y
3
− 7y
2
− 17y − 9)
2
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.090900 + 0.471848I
a = 0.075129 − 0.502047I
b = −0.272955 + 0.216622I
−2.04480 + 6.94756I 1.39778 − 11.85170I
u = −1.090900 − 0.471848I
a = 0.075129 + 0.502047I
b = −0.272955 − 0.216622I
−2.04480 − 6.94756I 1.39778 + 11.85170I
u = 0.696642 + 0.968690I
a = 2.05550 + 0.04412I
b = 0.27367 − 2.40783I
−2.04480 − 6.94756I 1.39778 + 11.85170I
u = 0.696642 − 0.968690I
a = 2.05550 − 0.04412I
b = 0.27367 + 2.40783I
−2.04480 + 6.94756I 1.39778 − 11.85170I
u = −0.258396 + 0.483619I
a = −0.19552 + 2.23757I
b = 0.126970 + 0.325073I
2.14309 10.96619 + 0.I
u = −0.258396 − 0.483619I
a = −0.19552 − 2.23757I
b = 0.126970 − 0.325073I
2.14309 10.96619 + 0.I
u = −0.336196 + 0.392322I
a = 0.970972 − 0.269736I
b = −0.03146 + 1.71919I
−9.71882 + 0.63219I −5.88087 − 11.75603I
u = −0.336196 − 0.392322I
a = 0.970972 + 0.269736I
b = −0.03146 − 1.71919I
−9.71882 − 0.63219I −5.88087 + 11.75603I
u = 2.48885 + 0.02726I
a = 0.093920 + 0.941860I
b = −0.59622 − 4.37220I
−9.71882 + 0.63219I −5.88087 − 11.75603I
u = 2.48885 − 0.02726I
a = 0.093920 − 0.941860I
b = −0.59622 + 4.37220I
−9.71882 − 0.63219I −5.88087 + 11.75603I
9
III.
I
u
3
= h−9.66 × 10
6
u
15
+ 6.37 × 10
7
u
14
+ · · · + 1.09 × 10
8
b + 1.03 × 10
8
, 9.74 ×
10
7
u
15
−7.79×10
8
u
14
+· · ·+1.09×10
8
a−9.52×10
8
, u
16
−8u
15
+· · ·−16u+4i
(i) Arc colorings
a
2
=
1
0
a
4
=
0
u
a
1
=
1
−u
2
a
8
=
−0.895836u
15
+ 7.16373u
14
+ ··· − 21.1943u + 8.75812
0.0888647u
15
− 0.586280u
14
+ ··· + 0.782914u − 0.949411
a
12
=
−0.241595u
15
+ 2.01426u
14
+ ··· − 6.73203u + 5.14019
0.268938u
15
− 1.87916u
14
+ ··· + 2.75348u − 1.37285
a
9
=
−0.380234u
15
+ 3.62129u
14
+ ··· − 17.0765u + 9.18951
0.105931u
15
− 0.780917u
14
+ ··· + 4.46533u − 2.37128
a
3
=
−0.222657u
15
+ 2.13510u
14
+ ··· − 10.9785u + 7.76734
0.276444u
15
− 1.95859u
14
+ ··· + 3.06772u − 1.24414
a
11
=
0.0273430u
15
+ 0.135102u
14
+ ··· − 3.97855u + 3.76734
0.268938u
15
− 1.87916u
14
+ ··· + 2.75348u − 1.37285
a
5
=
−0.160445u
15
+ 1.90668u
14
+ ··· − 11.6922u + 6.66721
−0.214232u
15
+ 1.73017u
14
+ ··· − 1.78134u + 0.144015
a
6
=
−0.551916u
15
+ 4.80715u
14
+ ··· − 14.5702u + 7.46698
0.486247u
15
− 4.00893u
14
+ ··· + 11.7313u − 5.24454
a
7
=
−0.0656690u
15
+ 0.798218u
14
+ ··· − 2.83890u + 2.22243
0.486247u
15
− 4.00893u
14
+ ··· + 11.7313u − 5.24454
a
10
=
−0.967203u
15
+ 8.34540u
14
+ ··· − 29.2669u + 13.9380
0.00295473u
15
− 0.352401u
14
+ ··· + 5.57526u − 3.58334
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
18550634
27176797
u
15
+
155969047
27176797
u
14
+ ··· −
461152304
27176797
u +
177121936
27176797
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
c
11
u
16
− 8u
15
+ ··· − 16u + 4
c
2
, c
8
(u
8
+ u
6
− 2u
5
− 2u
4
+ 3u
2
+ 2u + 1)
2
c
3
, c
9
(u
8
− 4u
6
+ 2u
5
+ 7u
4
− 6u
3
− 4u
2
+ 6u − 1)
2
c
4
, c
10
(u
8
+ 2u
6
+ 3u
4
− 2u
2
− 3)
2
c
6
, c
12
(u
8
+ u
6
+ 2u
5
− 2u
4
+ 3u
2
− 2u + 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
11
y
16
− 16y
15
+ ··· − 32y + 16
c
2
, c
6
, c
8
c
12
(y
8
+ 2y
7
− 3y
6
− 2y
5
+ 12y
4
− 2y
3
+ 5y
2
+ 2y + 1)
2
c
3
, c
9
(y
8
− 8y
7
+ 30y
6
− 68y
5
+ 103y
4
− 108y
3
+ 74y
2
− 28y + 1)
2
c
4
, c
10
(y
4
+ 2y
3
+ 3y
2
− 2y − 3)
4
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.200065 + 0.849267I
a = −0.759797 + 0.858070I
b = −0.115947 + 0.816941I
1.05416 − 61.330430 + 0.10I
u = −0.200065 − 0.849267I
a = −0.759797 − 0.858070I
b = −0.115947 − 0.816941I
1.05416 − 61.330430 + 0.10I
u = 0.597550 + 0.533296I
a = −2.32458 − 0.98205I
b = −0.18223 + 2.10815I
−2.27209 − 5.91675I −0.74241 + 2.97163I
u = 0.597550 − 0.533296I
a = −2.32458 + 0.98205I
b = −0.18223 − 2.10815I
−2.27209 + 5.91675I −0.74241 − 2.97163I
u = 1.293270 + 0.159272I
a = −0.119407 + 0.360444I
b = −0.835722 − 0.165494I
−2.27209 − 5.91675I −0.74241 + 2.97163I
u = 1.293270 − 0.159272I
a = −0.119407 − 0.360444I
b = −0.835722 + 0.165494I
−2.27209 + 5.91675I −0.74241 − 2.97163I
u = −0.446252 + 0.506902I
a = −0.466779 + 0.410930I
b = − 1.70507I
−9.66946 −3.84561 + 0.I
u = −0.446252 − 0.506902I
a = −0.466779 − 0.410930I
b = 1.70507I
−9.66946 −3.84561 + 0.I
u = 0.599542 + 0.283398I
a = 0.25980 − 1.48541I
b = 0.115947 + 0.816941I
1.05416 − 61.330430 + 0.10I
u = 0.599542 − 0.283398I
a = 0.25980 + 1.48541I
b = 0.115947 − 0.816941I
1.05416 − 61.330430 + 0.10I
13
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.197290 + 0.687330I
a = 0.028176 − 0.357279I
b = 0.835722 − 0.165494I
−2.27209 + 5.91675I −0.74241 − 2.97163I
u = −1.197290 − 0.687330I
a = 0.028176 + 0.357279I
b = 0.835722 + 0.165494I
−2.27209 − 5.91675I −0.74241 + 2.97163I
u = 0.823346 + 1.136370I
a = 1.41581 + 0.26433I
b = 0.18223 − 2.10815I
−2.27209 − 5.91675I −0.74241 + 2.97163I
u = 0.823346 − 1.136370I
a = 1.41581 − 0.26433I
b = 0.18223 + 2.10815I
−2.27209 + 5.91675I −0.74241 − 2.97163I
u = 2.52990 + 0.08941I
a = −0.033221 − 0.939974I
b = 4.50608I
−9.66946 −3.84561 + 0.I
u = 2.52990 − 0.08941I
a = −0.033221 + 0.939974I
b = − 4.50608I
−9.66946 −3.84561 + 0.I
14
IV. I
u
4
= h−3u
3
− 15u
2
+ 2b − 33u − 26, 9u
3
+ 35u
2
+ 28a + 67u + 34, u
4
+
7u
3
+ 23u
2
+ 38u + 28i
(i) Arc colorings
a
2
=
1
0
a
4
=
0
u
a
1
=
1
−u
2
a
8
=
−0.321429u
3
− 1.25000u
2
− 2.39286u − 1.21429
3
2
u
3
+
15
2
u
2
+
33
2
u + 13
a
12
=
9
28
u
3
+
7
4
u
2
+
137
28
u +
33
7
−
1
2
u
3
−
5
2
u
2
−
13
2
u − 6
a
9
=
−1.89286u
3
− 7.75000u
2
− 15.0357u − 8.42857
7
2
u
3
+
33
2
u
2
+
71
2
u + 26
a
3
=
−
1
7
u
3
−
1
2
u
2
−
11
14
u +
57
14
−u
2
− 2u − 9
a
11
=
−
5
28
u
3
−
3
4
u
2
−
45
28
u −
9
7
−
1
2
u
3
−
5
2
u
2
−
13
2
u − 6
a
5
=
−
1
7
u
3
−
1
2
u
2
−
11
14
u +
1
14
u
2
+ 4u + 5
a
6
=
3
14
u
3
+ 2u
2
+
38
7
u +
93
14
−2u
2
− 7u − 11
a
7
=
3
14
u
3
−
11
7
u −
61
14
−2u
2
− 7u − 11
a
10
=
−
1
7
u
3
−
1
2
u
2
−
11
14
u +
1
14
−u
3
− 5u
2
− 11u − 9
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
3
− 10u
2
− 22u − 18
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
4
− 7u
3
+ 23u
2
− 38u + 28
c
2
, c
6
, c
8
c
12
u
4
− u
3
− 12u
2
+ 5u + 43
c
3
, c
9
u
4
− 4u
3
+ 23u
2
− 38u + 91
c
4
, c
10
(u
2
+ u + 1)
2
c
5
, c
11
u
4
− u
3
+ 5u
2
− 2u + 4
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
4
− 3y
3
+ 53y
2
− 156y + 784
c
2
, c
6
, c
8
c
12
y
4
− 25y
3
+ 240y
2
− 1057y + 1849
c
3
, c
9
y
4
+ 30y
3
+ 407y
2
+ 2742y + 8281
c
4
, c
10
(y
2
+ y + 1)
2
c
5
, c
11
y
4
+ 9y
3
+ 29y
2
+ 36y + 16
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.82417 + 1.02661I
a = 0.405829 − 0.721109I
b = −0.50000 + 2.59808I
11.51450 + 2.02988I 0. − 3.46410I
u = −1.82417 − 1.02661I
a = 0.405829 + 0.721109I
b = −0.50000 − 2.59808I
11.51450 − 2.02988I 0. + 3.46410I
u = −1.67583 + 1.89264I
a = −0.512972 + 0.454211I
b = −0.50000 − 2.59808I
11.51450 − 2.02988I 0. + 3.46410I
u = −1.67583 − 1.89264I
a = −0.512972 − 0.454211I
b = −0.50000 + 2.59808I
11.51450 + 2.02988I 0. − 3.46410I
18
V. I
u
5
= h−u
3
− u
2
+ 2b − 3u, u
3
− 3u
2
+ 4a + u − 10, u
4
+ u
3
+ 5u
2
+ 2u + 4i
(i) Arc colorings
a
2
=
1
0
a
4
=
0
u
a
1
=
1
−u
2
a
8
=
−
1
4
u
3
+
3
4
u
2
−
1
4
u +
5
2
1
2
u
3
+
1
2
u
2
+
3
2
u
a
12
=
1
2
u
3
+ 2u −
5
2
−
1
2
u
3
−
1
2
u
2
−
5
2
u + 1
a
9
=
−3u
3
+
3
2
u
2
−
15
2
u +
17
2
7
2
u
3
+
1
2
u
2
+
19
2
u − 3
a
3
=
5
4
u
3
+
11
4
u
2
+
31
4
u + 11
−u
2
− 2u − 9
a
11
=
−
1
2
u
2
−
1
2
u −
3
2
−
1
2
u
3
−
1
2
u
2
−
5
2
u + 1
a
5
=
1
4
u
3
−
1
4
u
2
+
3
4
u − 1
−u
3
− 2u
2
− 3u − 3
a
6
=
3
4
u
3
+
9
4
u
2
+
13
4
u + 5
−2u
2
− u − 5
a
7
=
3
4
u
3
+
1
4
u
2
+
9
4
u
−2u
2
− u − 5
a
10
=
1
4
u
3
−
1
4
u
2
+
3
4
u − 1
−u
3
− u
2
− 3u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
3
+ 2u
2
+ 6u + 2
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
4
− u
3
+ 5u
2
− 2u + 4
c
2
, c
6
, c
8
c
12
u
4
− u
3
− 12u
2
+ 5u + 43
c
3
, c
9
u
4
− 4u
3
+ 23u
2
− 38u + 91
c
4
, c
10
(u
2
+ u + 1)
2
c
5
, c
11
u
4
− 7u
3
+ 23u
2
− 38u + 28
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
4
+ 9y
3
+ 29y
2
+ 36y + 16
c
2
, c
6
, c
8
c
12
y
4
− 25y
3
+ 240y
2
− 1057y + 1849
c
3
, c
9
y
4
+ 30y
3
+ 407y
2
+ 2742y + 8281
c
4
, c
10
(y
2
+ y + 1)
2
c
5
, c
11
y
4
− 3y
3
+ 53y
2
− 156y + 784
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.175835 + 1.026610I
a = 1.63907 − 0.28074I
b = −0.500000 + 0.866025I
11.51450 − 2.02988I 0. + 3.46410I
u = −0.175835 − 1.026610I
a = 1.63907 + 0.28074I
b = −0.500000 − 0.866025I
11.51450 + 2.02988I 0. − 3.46410I
u = −0.32417 + 1.89264I
a = −0.889071 + 0.152277I
b = −0.500000 − 0.866025I
11.51450 + 2.02988I 0. − 3.46410I
u = −0.32417 − 1.89264I
a = −0.889071 − 0.152277I
b = −0.500000 + 0.866025I
11.51450 − 2.02988I 0. + 3.46410I
22
VI. I
u
6
= h−u
7
+ 6u
6
+ · · · + 56b − 24, 2u
7
+ 2u
6
+ · · · + 14a + 20, u
8
+
5u
6
+ 2u
5
+ 9u
4
+ 8u
3
+ 12u
2
+ 8u + 4i
(i) Arc colorings
a
2
=
1
0
a
4
=
0
u
a
1
=
1
−u
2
a
8
=
−
1
7
u
7
−
1
7
u
6
+ ··· −
11
14
u −
10
7
1
56
u
7
−
3
28
u
6
+ ··· +
1
28
u +
3
7
a
12
=
−
3
56
u
7
−
3
56
u
6
+ ··· −
6
7
u −
29
28
0.0535714u
7
− 0.0714286u
6
+ ··· + 1.60714u + 0.785714
a
9
=
−0.178571u
7
− 0.0535714u
6
+ ··· − 1.60714u − 2.53571
3
56
u
7
−
4
7
u
6
+ ··· +
17
28
u −
3
14
a
3
=
1
7
u
7
+
1
56
u
6
+ ··· +
15
28
u +
5
28
u
2
+ 2u + 1
a
11
=
−
1
8
u
6
+
1
4
u
5
+ ··· +
3
4
u −
1
4
0.0535714u
7
− 0.0714286u
6
+ ··· + 1.60714u + 0.785714
a
5
=
1
4
u
7
+
1
8
u
6
+ ··· +
9
4
u +
9
4
3
28
u
7
+
3
28
u
6
+ ··· +
12
7
u +
15
14
a
6
=
0.392857u
7
− 0.232143u
6
+ ··· + 2.53571u + 1.67857
3
14
u
7
+
3
14
u
6
+ ··· +
10
7
u +
8
7
a
7
=
0.607143u
7
− 0.0178571u
6
+ ··· + 3.96429u + 2.82143
3
14
u
7
+
3
14
u
6
+ ··· +
10
7
u +
8
7
a
10
=
−
1
4
u
7
−
1
8
u
6
+ ··· −
9
4
u −
9
4
1
7
u
7
−
5
14
u
6
+ ··· +
2
7
u −
4
7
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1
2
u
7
+ u
6
−
7
2
u
5
+ 4u
4
−
11
2
u
3
+ 3u
2
− u + 2
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
c
11
u
8
+ 5u
6
− 2u
5
+ 9u
4
− 8u
3
+ 12u
2
− 8u + 4
c
2
, c
6
, c
8
c
12
u
8
− 2u
7
+ u
6
− 6u
5
+ 28u
4
− 22u
3
− 3u
2
+ 6u + 13
c
3
, c
9
(u
4
+ 4u
3
+ 5u
2
+ 2u + 1)
2
c
4
, c
10
(u
2
− u + 1)
4
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
11
y
8
+ 10y
7
+ 43y
6
+ 110y
5
+ 177y
4
+ 160y
3
+ 88y
2
+ 32y + 16
c
2
, c
6
, c
8
c
12
y
8
− 2y
7
+ 33y
6
− 74y
5
+ 564y
4
− 554y
3
+ 1001y
2
− 114y + 169
c
3
, c
9
(y
4
− 6y
3
+ 11y
2
+ 6y + 1)
2
c
4
, c
10
(y
2
+ y + 1)
4
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.329313 + 0.970922I
a = 0.923688 − 0.313292I
b = 0.500000 − 0.133975I
1.64493 − 2.02988I 0. + 3.46410I
u = −0.329313 − 0.970922I
a = 0.923688 + 0.313292I
b = 0.500000 + 0.133975I
1.64493 + 2.02988I 0. − 3.46410I
u = −0.536713 + 0.470922I
a = −0.923688 + 1.052730I
b = 0.500000 + 0.133975I
1.64493 + 2.02988I 0. − 3.46410I
u = −0.536713 − 0.470922I
a = −0.923688 − 1.052730I
b = 0.500000 − 0.133975I
1.64493 − 2.02988I 0. + 3.46410I
u = 0.80559 + 1.29267I
a = −0.557193 − 0.347240I
b = 0.50000 + 1.86603I
1.64493 − 2.02988I 0. + 3.46410I
u = 0.80559 − 1.29267I
a = −0.557193 + 0.347240I
b = 0.50000 − 1.86603I
1.64493 + 2.02988I 0. − 3.46410I
u = 0.06044 + 1.79267I
a = 0.557193 + 0.018785I
b = 0.50000 − 1.86603I
1.64493 + 2.02988I 0. − 3.46410I
u = 0.06044 − 1.79267I
a = 0.557193 − 0.018785I
b = 0.50000 + 1.86603I
1.64493 − 2.02988I 0. + 3.46410I
26
VII. I
u
7
= hu
2
+ b − u + 1, a, u
4
− 2u
3
+ 2u
2
− u + 1i
(i) Arc colorings
a
2
=
1
0
a
4
=
0
u
a
1
=
1
−u
2
a
8
=
0
−u
2
+ u − 1
a
12
=
1
−u
a
9
=
−u
2
+ u − 1
u
3
− 2u
2
+ 2u − 1
a
3
=
u
−u
2
+ u
a
11
=
−u + 1
−u
a
5
=
u
3
− 2u
2
+ u
u
3
− u
2
+ u
a
6
=
u
3
− 2u
2
+ u
u
2
− u + 1
a
7
=
u
3
− u
2
+ 1
u
2
− u + 1
a
10
=
u
3
− 2u
2
+ u
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = u
2
− u − 1
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
7
, c
9
, c
11
u
4
+ 2u
3
+ 2u
2
+ u + 1
c
2
, c
4
, c
6
c
8
, c
10
, c
12
(u
2
+ u + 1)
2
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
7
, c
9
, c
11
y
4
+ 2y
2
+ 3y + 1
c
2
, c
4
, c
6
c
8
, c
10
, c
12
(y
2
+ y + 1)
2
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −0.070696 + 0.758745I
a = 0
b = −0.500000 + 0.866025I
−1.64493 + 2.02988I −1.50000 − 0.86603I
u = −0.070696 − 0.758745I
a = 0
b = −0.500000 − 0.866025I
−1.64493 − 2.02988I −1.50000 + 0.86603I
u = 1.070700 + 0.758745I
a = 0
b = −0.500000 − 0.866025I
−1.64493 − 2.02988I −1.50000 + 0.86603I
u = 1.070700 − 0.758745I
a = 0
b = −0.500000 + 0.866025I
−1.64493 + 2.02988I −1.50000 − 0.86603I
30
VIII.
I
u
8
= h4u
3
+ 9u
2
+ 11b + u − 15, −18u
3
− 24u
2
+ 55a − 10u + 40, u
4
− 5u + 5i
(i) Arc colorings
a
2
=
1
0
a
4
=
0
u
a
1
=
1
−u
2
a
8
=
0.327273u
3
+ 0.436364u
2
+ 0.181818u − 0.727273
−0.363636u
3
− 0.818182u
2
− 0.0909091u + 1.36364
a
12
=
−0.218182u
3
− 0.290909u
2
+ 0.545455u + 0.818182
−u
a
9
=
0.472727u
3
+ 0.963636u
2
− 1.18182u − 0.272727
−0.454545u
3
− 1.27273u
2
+ 1.63636u + 0.454545
a
3
=
0.218182u
3
− 0.509091u
2
− 0.745455u + 2.18182
−0.545455u
3
+ 0.272727u
2
+ 1.36364u − 1.45455
a
11
=
−0.218182u
3
− 0.290909u
2
− 0.454545u + 0.818182
−u
a
5
=
0.127273u
3
+ 0.0363636u
2
− 0.0181818u − 0.727273
0.454545u
3
+ 0.272727u
2
+ 1.36364u − 1.45455
a
6
=
0.236364u
3
+ 0.581818u
2
+ 0.709091u − 1.63636
0.181818u
3
− 0.0909091u
2
− 0.454545u + 0.818182
a
7
=
0.418182u
3
+ 0.490909u
2
+ 0.254545u − 0.818182
0.181818u
3
− 0.0909091u
2
− 0.454545u + 0.818182
a
10
=
−0.0545455u
3
− 0.0727273u
2
− 0.163636u + 0.254545
−0.436364u
3
− 0.181818u
2
− 0.909091u + 1.63636
(ii) Obstruction class = 1
(iii) Cusp Shapes =
2
11
u
3
−
1
11
u
2
−
5
11
u −
35
11
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
c
11
u
4
− 5u + 5
c
2
, c
8
(u
2
− 3u + 1)
2
c
3
, c
9
5(5u
4
+ 30u
2
+ 95u + 61)
c
4
, c
10
5(5u
4
+ 5u
2
+ 1)
c
6
, c
12
(u
2
+ 3u + 1)
2
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
11
y
4
+ 10y
2
− 25y + 25
c
2
, c
6
, c
8
c
12
(y
2
− 7y + 1)
2
c
3
, c
9
25(25y
4
+ 300y
3
+ 1510y
2
− 5365y + 3721)
c
4
, c
10
25(5y
2
+ 5y + 1)
2
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 1.118030 + 0.363271I
a = 0.276393 + 0.850651I
b = − 1.175570I
−4.60582 −3.61803 + 0.I
u = 1.118030 − 0.363271I
a = 0.276393 − 0.850651I
b = 1.175570I
−4.60582 −3.61803 + 0.I
u = −1.11803 + 1.53884I
a = 0.723607 − 0.525731I
b = 1.90211I
11.1856 −6 − 1.381966 + 0.10I
u = −1.11803 − 1.53884I
a = 0.723607 + 0.525731I
b = − 1.90211I
11.1856 −6 − 1.381966 + 0.10I
34
IX. I
u
9
= hb − u, a + 1, u
2
+ 1i
(i) Arc colorings
a
2
=
1
0
a
4
=
0
u
a
1
=
1
1
a
8
=
−1
u
a
12
=
−u
u
a
9
=
−u
2u − 1
a
3
=
−u
2u
a
11
=
0
u
a
5
=
0
u
a
6
=
−u
u − 1
a
7
=
−1
u − 1
a
10
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
c
11
u
2
+ 1
c
2
, c
8
u
2
+ 2u + 2
c
3
, c
9
(u + 1)
2
c
4
, c
10
u
2
c
6
, c
12
u
2
− 2u + 2
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
11
(y + 1)
2
c
2
, c
6
, c
8
c
12
y
2
+ 4
c
3
, c
9
(y − 1)
2
c
4
, c
10
y
2
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −1.00000
b = 1.000000I
1.64493 0
u = − 1.000000I
a = −1.00000
b = − 1.000000I
1.64493 0
38
X. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
c
11
(u
2
+ 1)(u
4
− 5u + 5)(u
4
− 7u
3
+ ··· − 38u + 28)(u
4
− u
3
+ ··· − 2u + 4)
· (u
4
+ 2u
3
+ 2u
2
+ u + 1)(u
8
+ 5u
6
+ ··· − 8u + 4)
· (u
8
− 2u
7
+ 2u
6
+ 5u
5
+ u
4
− 3u
3
+ 15u
2
+ 14u + 5)
· (u
10
+ 3u
9
− 2u
8
− 6u
7
+ 4u
6
+ 2u
5
+ 7u
4
− 11u
3
+ 10u
2
− 4u + 1)
· (u
16
− 8u
15
+ ··· − 16u + 4)
c
2
, c
8
((u
2
− 3u + 1)
2
)(u
2
+ u + 1)
2
(u
2
+ 2u + 2)(u
4
− u
3
+ ··· + 5u + 43)
2
· (u
5
+ u
4
+ 2u
3
+ u
2
− u − 1)
2
(u
8
+ u
6
− 2u
5
− 2u
4
+ 3u
2
+ 2u + 1)
2
· (u
8
− 2u
7
+ u
6
− 6u
5
+ 28u
4
− 22u
3
− 3u
2
+ 6u + 13)
· (u
8
− u
7
− 8u
6
+ 9u
5
+ 23u
4
− 13u
3
+ 16u
2
− 4u + 2)
c
3
, c
9
25(u − 1)
10
(u + 1)
2
(u
4
− 4u
3
+ 23u
2
− 38u + 91)
2
· (u
4
+ 2u
3
+ 2u
2
+ u + 1)(u
4
+ 4u
3
+ 5u
2
+ 2u + 1)
2
· (5u
4
+ 30u
2
+ 95u + 61)(u
8
− 4u
6
+ ··· + 6u − 1)
2
· (5u
8
+ 29u
7
+ ··· + 864u + 160)
c
4
, c
10
25u
2
(u
2
− u + 1)
4
(u
2
+ u + 1)
6
(5u
4
+ 5u
2
+ 1)
· (u
5
− 3u
4
+ 6u
3
− 7u
2
+ 5u − 3)
2
(u
8
+ 2u
6
+ 3u
4
− 2u
2
− 3)
2
· (5u
8
+ 29u
7
+ 88u
6
+ 173u
5
+ 235u
4
+ 223u
3
+ 142u
2
+ 52u + 8)
c
6
, c
12
(u
2
− 2u + 2)(u
2
+ u + 1)
2
(u
2
+ 3u + 1)
2
(u
4
− u
3
+ ··· + 5u + 43)
2
· (u
5
+ u
4
+ 2u
3
+ u
2
− u − 1)
2
(u
8
+ u
6
+ 2u
5
− 2u
4
+ 3u
2
− 2u + 1)
2
· (u
8
− 2u
7
+ u
6
− 6u
5
+ 28u
4
− 22u
3
− 3u
2
+ 6u + 13)
· (u
8
− u
7
− 8u
6
+ 9u
5
+ 23u
4
− 13u
3
+ 16u
2
− 4u + 2)
39
XI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
11
(y + 1)
2
(y
4
+ 2y
2
+ 3y + 1)(y
4
+ 10y
2
− 25y + 25)
· (y
4
− 3y
3
+ 53y
2
− 156y + 784)(y
4
+ 9y
3
+ 29y
2
+ 36y + 16)
· (y
8
+ 26y
6
− 3y
5
+ 157y
4
− 99y
3
+ 319y
2
− 46y + 25)
· (y
8
+ 10y
7
+ 43y
6
+ 110y
5
+ 177y
4
+ 160y
3
+ 88y
2
+ 32y + 16)
· (y
10
− 13y
9
+ ··· + 4y + 1)(y
16
− 16y
15
+ ··· − 32y + 16)
c
2
, c
6
, c
8
c
12
(y
2
+ 4)(y
2
− 7y + 1)
2
(y
2
+ y + 1)
2
· (y
4
− 25y
3
+ 240y
2
− 1057y + 1849)
2
(y
5
+ 3y
4
− 3y
2
+ 3y − 1)
2
· (y
8
− 17y
7
+ 128y
6
− 443y
5
+ 503y
4
+ 607y
3
+ 244y
2
+ 48y + 4)
· (y
8
− 2y
7
+ 33y
6
− 74y
5
+ 564y
4
− 554y
3
+ 1001y
2
− 114y + 169)
· (y
8
+ 2y
7
− 3y
6
− 2y
5
+ 12y
4
− 2y
3
+ 5y
2
+ 2y + 1)
2
c
3
, c
9
625(y − 1)
12
(y
4
+ 2y
2
+ 3y + 1)(y
4
− 6y
3
+ 11y
2
+ 6y + 1)
2
· (y
4
+ 30y
3
+ 407y
2
+ 2742y + 8281)
2
· (25y
4
+ 300y
3
+ 1510y
2
− 5365y + 3721)
· (y
8
− 8y
7
+ 30y
6
− 68y
5
+ 103y
4
− 108y
3
+ 74y
2
− 28y + 1)
2
· (25y
8
+ 789y
7
+ ··· − 150016y + 25600)
c
4
, c
10
625y
2
(y
2
+ y + 1)
10
(5y
2
+ 5y + 1)
2
(y
4
+ 2y
3
+ 3y
2
− 2y − 3)
4
· (y
5
+ 3y
4
+ 4y
3
− 7y
2
− 17y − 9)
2
· (25y
8
+ 39y
7
+ 60y
6
− 83y
5
+ 123y
4
+ 427y
3
+ 732y
2
− 432y + 64)
40
