12a
1178
(K12a
1178
)
A knot diagram
1
Linearized knot diagam
4 10 8 9 11 12 3 1 2 7 6 5
Solving Sequence
5,11
6 12 7
1,9
4 2 8 3 10
c
5
c
11
c
6
c
12
c
4
c
1
c
8
c
3
c
10
c
2
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h56u
34
+ 305u
33
+ ··· + 2b − 284, 21u
34
+ 135u
33
+ ··· + 4a − 182, u
35
+ 7u
34
+ ··· + 32u − 8i
I
u
2
= h3.02051 × 10
26
a
5
u
10
+ 6.10493 × 10
26
a
4
u
10
+ ··· + 8.97858 × 10
27
a − 5.15875 × 10
27
,
6u
10
a
5
+ 3u
10
a
4
+ ··· − 21a − 22, u
11
− u
10
− 4u
9
+ 3u
8
+ 6u
7
− 2u
6
− 2u
5
− 3u
4
− 3u
3
+ 3u
2
+ 2u + 1i
I
u
3
= hu
20
− 9u
18
+ 34u
16
− 66u
14
+ 59u
12
+ 4u
10
+ u
9
− 50u
8
− 4u
7
+ 25u
6
+ 6u
5
+ 9u
4
− 3u
3
− 6u
2
+ b,
− u
19
− u
18
+ ··· + a + 1,
u
21
− 10u
19
+ 42u
17
− 92u
15
+ 99u
13
− 14u
11
+ u
10
− 78u
9
− 5u
8
+ 60u
7
+ 9u
6
+ 9u
5
− 6u
4
− 18u
3
+ 1i
* 3 irreducible components of dim
C
= 0, with total 122 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
= h56u
34
+ 305u
33
+ · · · + 2b − 284, 21u
34
+ 135u
33
+ · · · + 4a −
182, u
35
+ 7u
34
+ · · · + 32u − 8i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
−u
2
a
12
=
u
−u
3
+ u
a
7
=
−u
2
+ 1
u
4
− 2u
2
a
1
=
−u
3
+ 2u
−u
3
+ u
a
9
=
−5.25000u
34
− 33.7500u
33
+ ··· − 225.500u + 45.5000
−28u
34
−
305
2
u
33
+ ··· −
1307
2
u + 142
a
4
=
−
75
2
u
34
−
855
4
u
33
+ ··· −
4301
4
u + 227
69
4
u
34
+
401
4
u
33
+ ··· + 560u − 116
a
2
=
145
8
u
34
+
829
8
u
33
+ ··· + 551u −
229
2
−
1
4
u
34
−
11
4
u
33
+ ··· −
49
2
u + 5
a
8
=
5.75000u
34
+ 32.2500u
33
+ ··· + 158.500u − 34.5000
53
2
u
34
+ 152u
33
+ ··· +
1537
2
u − 162
a
3
=
−
47
8
u
34
−
291
8
u
33
+ ··· − 232u +
95
2
67
4
u
34
+
369
4
u
33
+ ··· +
877
2
u − 93
a
10
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −14u
34
−83u
33
−49u
32
+ 552u
31
+ 749u
30
−1851u
29
−2942u
28
+ 4360u
27
+ 5628u
26
−
8667u
25
− 3703u
24
+ 14324u
23
− 8289u
22
− 14914u
21
+ 26100u
20
− 98u
19
− 31837u
18
+
26886u
17
+11105u
16
−37472u
15
+22359u
14
+14556u
13
−32711u
12
+16400u
11
+10929u
10
−
19848u
9
+ 10674u
8
+ 3645u
7
−8028u
6
+ 5365u
5
−279u
4
−1570u
3
+ 1326u
2
−556u + 122
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
35
− 33u
34
+ ··· − 40960u + 2048
c
2
, c
3
, c
7
c
9
u
35
− u
34
+ ··· + u − 1
c
4
, c
8
u
35
+ 6u
33
+ ··· + 2u − 1
c
5
, c
6
, c
11
u
35
+ 7u
34
+ ··· + 32u − 8
c
10
, c
12
u
35
− 21u
34
+ ··· − 40656u + 2664
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
35
− 11y
34
+ ··· + 14680064y −4194304
c
2
, c
3
, c
7
c
9
y
35
− 35y
34
+ ··· − 17y −1
c
4
, c
8
y
35
+ 12y
34
+ ··· + 12y −1
c
5
, c
6
, c
11
y
35
− 29y
34
+ ··· + 32y −64
c
10
, c
12
y
35
+ 23y
34
+ ··· + 27880992y −7096896
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.139537 + 0.931995I
a = −0.469976 + 1.183650I
b = 0.039825 + 0.846776I
−12.11410 + 3.47580I −9.19807 − 3.18333I
u = 0.139537 − 0.931995I
a = −0.469976 − 1.183650I
b = 0.039825 − 0.846776I
−12.11410 − 3.47580I −9.19807 + 3.18333I
u = 0.105864 + 0.897053I
a = 0.44787 + 2.53244I
b = 0.94342 + 1.35103I
−13.7151 + 12.5847I −5.18347 − 6.53919I
u = 0.105864 − 0.897053I
a = 0.44787 − 2.53244I
b = 0.94342 − 1.35103I
−13.7151 − 12.5847I −5.18347 + 6.53919I
u = 0.636350 + 0.611239I
a = 0.942619 − 0.315270I
b = 0.574414 − 0.905738I
−6.32739 − 3.08954I −4.56075 + 2.58207I
u = 0.636350 − 0.611239I
a = 0.942619 + 0.315270I
b = 0.574414 + 0.905738I
−6.32739 + 3.08954I −4.56075 − 2.58207I
u = 0.472041 + 0.666318I
a = 0.12197 − 1.43044I
b = −0.746358 − 1.022450I
−6.79949 + 7.60511I −4.01817 − 7.64944I
u = 0.472041 − 0.666318I
a = 0.12197 + 1.43044I
b = −0.746358 + 1.022450I
−6.79949 − 7.60511I −4.01817 + 7.64944I
u = 1.179240 + 0.305684I
a = 0.513879 − 0.597102I
b = 0.558931 − 1.032860I
0.229089 + 0.656619I 3.86417 − 1.98226I
u = 1.179240 − 0.305684I
a = 0.513879 + 0.597102I
b = 0.558931 + 1.032860I
0.229089 − 0.656619I 3.86417 + 1.98226I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.088955 + 0.772136I
a = −0.26673 − 2.09268I
b = −0.755605 − 0.993491I
−3.07455 + 3.26826I 1.60586 − 2.42356I
u = 0.088955 − 0.772136I
a = −0.26673 + 2.09268I
b = −0.755605 + 0.993491I
−3.07455 − 3.26826I 1.60586 + 2.42356I
u = 1.139170 + 0.518187I
a = −0.127484 + 0.654094I
b = 0.098871 + 0.884816I
−9.05046 + 1.64505I −6.82659 − 2.03985I
u = 1.139170 − 0.518187I
a = −0.127484 − 0.654094I
b = 0.098871 − 0.884816I
−9.05046 − 1.64505I −6.82659 + 2.03985I
u = 1.174450 + 0.465803I
a = −0.882414 + 0.762013I
b = −0.88026 + 1.32953I
−10.43630 − 7.73132I −2.52329 + 3.10208I
u = 1.174450 − 0.465803I
a = −0.882414 − 0.762013I
b = −0.88026 − 1.32953I
−10.43630 + 7.73132I −2.52329 − 3.10208I
u = −1.299980 + 0.228637I
a = −0.285197 − 1.010500I
b = 0.690456 − 0.023660I
4.00950 − 4.24760I 7.23862 + 6.55308I
u = −1.299980 − 0.228637I
a = −0.285197 + 1.010500I
b = 0.690456 + 0.023660I
4.00950 + 4.24760I 7.23862 − 6.55308I
u = 1.32721
a = 0.210158
b = 0.310775
2.90599 1.01730
u = −1.337390 + 0.048424I
a = 1.165230 − 0.179093I
b = −0.857438 + 0.443510I
6.13792 − 1.57371I 10.75089 + 1.90988I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.337390 − 0.048424I
a = 1.165230 + 0.179093I
b = −0.857438 − 0.443510I
6.13792 + 1.57371I 10.75089 − 1.90988I
u = −1.322170 + 0.332092I
a = −1.14041 − 1.41439I
b = 0.885409 − 0.964095I
1.35102 − 7.25772I 7.15814 + 5.17869I
u = −1.322170 − 0.332092I
a = −1.14041 + 1.41439I
b = 0.885409 + 0.964095I
1.35102 + 7.25772I 7.15814 − 5.17869I
u = −1.350510 + 0.404254I
a = 1.18027 + 1.81624I
b = −0.99393 + 1.35081I
−9.1437 − 17.2482I 0. + 8.79521I
u = −1.350510 − 0.404254I
a = 1.18027 − 1.81624I
b = −0.99393 − 1.35081I
−9.1437 + 17.2482I 0. − 8.79521I
u = −1.37576 + 0.42280I
a = 0.814461 + 0.541541I
b = −0.138556 + 0.789658I
−7.35335 − 8.32792I 0
u = −1.37576 − 0.42280I
a = 0.814461 − 0.541541I
b = −0.138556 − 0.789658I
−7.35335 + 8.32792I 0
u = −1.42904 + 0.19328I
a = −1.014210 − 0.478584I
b = 0.934761 − 1.000360I
−0.66389 − 10.53050I 0. + 8.08764I
u = −1.42904 − 0.19328I
a = −1.014210 + 0.478584I
b = 0.934761 + 1.000360I
−0.66389 + 10.53050I 0. − 8.08764I
u = 0.115996 + 0.532001I
a = −0.741619 − 0.675829I
b = −0.507252 + 0.043187I
−0.37214 + 1.40883I 0.98492 − 6.02743I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.115996 − 0.532001I
a = −0.741619 + 0.675829I
b = −0.507252 − 0.043187I
−0.37214 − 1.40883I 0.98492 + 6.02743I
u = −1.50719 + 0.09928I
a = −0.073091 + 0.314181I
b = −0.521031 − 0.600961I
0.874150 + 0.821107I 0
u = −1.50719 − 0.09928I
a = −0.073091 − 0.314181I
b = −0.521031 + 0.600961I
0.874150 − 0.821107I 0
u = 0.406834 + 0.217699I
a = −0.540240 + 0.373595I
b = 0.518952 + 0.467501I
0.843371 + 0.754361I 6.99963 − 3.56017I
u = 0.406834 − 0.217699I
a = −0.540240 − 0.373595I
b = 0.518952 − 0.467501I
0.843371 − 0.754361I 6.99963 + 3.56017I
8
II. I
u
2
= h3.02 × 10
26
a
5
u
10
+ 6.10 × 10
26
a
4
u
10
+ · · · + 8.98 × 10
27
a − 5.16 ×
10
27
, 6u
10
a
5
+ 3u
10
a
4
+ · · · − 21a − 22, u
11
− u
10
+ · · · + 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
−u
2
a
12
=
u
−u
3
+ u
a
7
=
−u
2
+ 1
u
4
− 2u
2
a
1
=
−u
3
+ 2u
−u
3
+ u
a
9
=
a
−0.268598a
5
u
10
− 0.542878a
4
u
10
+ ··· − 7.98417a + 4.58740
a
4
=
0.321036a
5
u
10
− 0.325338a
4
u
10
+ ··· − 7.53353a − 3.76774
−0.0259755a
5
u
10
+ 0.100771a
4
u
10
+ ··· − 12.9385a − 4.93938
a
2
=
−0.189655a
5
u
10
+ 0.295091a
4
u
10
+ ··· + 3.91116a − 1.41976
0.214494a
5
u
10
− 0.0282051a
4
u
10
+ ··· − 1.53483a + 1.62382
a
8
=
−0.0275683a
5
u
10
+ 0.636168a
4
u
10
+ ··· + 7.09030a + 1.91159
−0.441675a
5
u
10
− 0.266441a
4
u
10
+ ··· − 6.09828a + 5.22750
a
3
=
−0.0475459a
5
u
10
+ 0.162203a
4
u
10
+ ··· + 4.46863a − 1.45142
0.172998a
5
u
10
− 0.210633a
4
u
10
+ ··· − 1.90938a + 2.02365
a
10
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
504039224100025701115835624
374849606289697770228372931
u
10
a
5
−
1172155967916274982800424384
374849606289697770228372931
u
10
a
4
+ ··· −
5075735830037470664374767476
374849606289697770228372931
a +
9670853239799093529630437046
374849606289697770228372931
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
− 1)
22
c
2
, c
3
, c
7
c
9
u
66
+ u
65
+ ··· + 16520u − 4657
c
4
, c
8
u
66
+ 3u
65
+ ··· − 4900u − 599
c
5
, c
6
, c
11
(u
11
− u
10
− 4u
9
+ 3u
8
+ 6u
7
− 2u
6
− 2u
5
− 3u
4
− 3u
3
+ 3u
2
+ 2u + 1)
6
c
10
, c
12
(u
11
+ 3u
10
+ ··· − 2u − 1)
6
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
− y
2
+ 2y −1)
22
c
2
, c
3
, c
7
c
9
y
66
− 57y
65
+ ··· + 855089512y + 21687649
c
4
, c
8
y
66
+ 19y
65
+ ··· + 9965280y + 358801
c
5
, c
6
, c
11
(y
11
− 9y
10
+ ··· − 2y −1)
6
c
10
, c
12
(y
11
+ 11y
10
+ ··· + 6y −1)
6
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.14725
a = −0.681685 + 0.142265I
b = −0.203831 − 1.332020I
0.28470 + 2.82812I −0.86650 − 2.97945I
u = −1.14725
a = −0.681685 − 0.142265I
b = −0.203831 + 1.332020I
0.28470 − 2.82812I −0.86650 + 2.97945I
u = −1.14725
a = −0.31870 + 1.52370I
b = 0.407188 + 0.993368I
0.28470 + 2.82812I −0.86650 − 2.97945I
u = −1.14725
a = −0.31870 − 1.52370I
b = 0.407188 − 0.993368I
0.28470 − 2.82812I −0.86650 + 2.97945I
u = −1.14725
a = −2.88593
b = 1.63935
−3.85288 −7.39580
u = −1.14725
a = −4.00191
b = −0.239197
−3.85288 −7.39580
u = −0.044199 + 0.849205I
a = 0.72801 − 1.52143I
b = 0.825388 − 0.962313I
−7.55328 − 0.21340I −4.55146 − 0.15703I
u = −0.044199 + 0.849205I
a = 0.65416 + 1.77567I
b = −0.047317 + 0.807179I
−7.55328 − 0.21340I −4.55146 − 0.15703I
u = −0.044199 + 0.849205I
a = 0.00071 − 2.02802I
b = 0.774141 − 0.907919I
−7.55328 − 5.86965I −4.55146 + 5.80187I
u = −0.044199 + 0.849205I
a = −0.67415 + 2.52234I
b = 0.057490 + 0.752723I
−11.69090 − 3.04152I −11.08072 + 2.82242I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.044199 + 0.849205I
a = 2.42363 + 2.14160I
b = 1.83368 + 1.32855I
−11.69090 − 3.04152I −11.08072 + 2.82242I
u = −0.044199 + 0.849205I
a = −0.87468 + 3.12856I
b = −1.00287 + 1.66762I
−7.55328 − 5.86965I −4.55146 + 5.80187I
u = −0.044199 − 0.849205I
a = 0.72801 + 1.52143I
b = 0.825388 + 0.962313I
−7.55328 + 0.21340I −4.55146 + 0.15703I
u = −0.044199 − 0.849205I
a = 0.65416 − 1.77567I
b = −0.047317 − 0.807179I
−7.55328 + 0.21340I −4.55146 + 0.15703I
u = −0.044199 − 0.849205I
a = 0.00071 + 2.02802I
b = 0.774141 + 0.907919I
−7.55328 + 5.86965I −4.55146 − 5.80187I
u = −0.044199 − 0.849205I
a = −0.67415 − 2.52234I
b = 0.057490 − 0.752723I
−11.69090 + 3.04152I −11.08072 − 2.82242I
u = −0.044199 − 0.849205I
a = 2.42363 − 2.14160I
b = 1.83368 − 1.32855I
−11.69090 + 3.04152I −11.08072 − 2.82242I
u = −0.044199 − 0.849205I
a = −0.87468 − 3.12856I
b = −1.00287 − 1.66762I
−7.55328 + 5.86965I −4.55146 − 5.80187I
u = −1.232090 + 0.392876I
a = −0.001588 + 1.162910I
b = −0.022577 + 0.868095I
−3.88773 − 4.24511I −1.28155 + 3.61318I
u = −1.232090 + 0.392876I
a = −0.787317 − 0.081147I
b = −0.708436 − 1.070380I
−3.88773 − 4.24511I −1.28155 + 3.61318I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.232090 + 0.392876I
a = −0.113083 − 0.696667I
b = −0.730235 − 0.947386I
−3.88773 + 1.41114I −1.28155 − 2.34572I
u = −1.232090 + 0.392876I
a = 1.43869 + 0.88464I
b = 0.89523 + 1.68771I
−3.88773 + 1.41114I −1.28155 − 2.34572I
u = −1.232090 + 0.392876I
a = 1.52441 + 1.86194I
b = −0.055694 + 0.670879I
−8.02531 − 1.41699I −7.81082 + 0.63373I
u = −1.232090 + 0.392876I
a = 0.32325 + 2.50924I
b = −1.89288 + 1.18137I
−8.02531 − 1.41699I −7.81082 + 0.63373I
u = −1.232090 − 0.392876I
a = −0.001588 − 1.162910I
b = −0.022577 − 0.868095I
−3.88773 + 4.24511I −1.28155 − 3.61318I
u = −1.232090 − 0.392876I
a = −0.787317 + 0.081147I
b = −0.708436 + 1.070380I
−3.88773 + 4.24511I −1.28155 − 3.61318I
u = −1.232090 − 0.392876I
a = −0.113083 + 0.696667I
b = −0.730235 + 0.947386I
−3.88773 − 1.41114I −1.28155 + 2.34572I
u = −1.232090 − 0.392876I
a = 1.43869 − 0.88464I
b = 0.89523 − 1.68771I
−3.88773 − 1.41114I −1.28155 + 2.34572I
u = −1.232090 − 0.392876I
a = 1.52441 − 1.86194I
b = −0.055694 − 0.670879I
−8.02531 + 1.41699I −7.81082 − 0.63373I
u = −1.232090 − 0.392876I
a = 0.32325 − 2.50924I
b = −1.89288 − 1.18137I
−8.02531 + 1.41699I −7.81082 − 0.63373I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.317220 + 0.129556I
a = 0.357508 − 0.783708I
b = −0.127941 + 0.198219I
3.27094 + 0.11860I 5.30912 − 1.13842I
u = 1.317220 + 0.129556I
a = 0.091337 + 0.694344I
b = 0.776455 − 0.377674I
3.27094 + 0.11860I 5.30912 − 1.13842I
u = 1.317220 + 0.129556I
a = 1.51101 − 0.25470I
b = −1.07397 − 1.07535I
3.27094 + 5.77484I 5.30912 − 7.09731I
u = 1.317220 + 0.129556I
a = −0.224220 + 0.066922I
b = 0.99581 − 1.28980I
−0.86664 + 2.94672I −1.22015 − 4.11787I
u = 1.317220 + 0.129556I
a = 0.77168 − 1.59391I
b = −0.357770 − 1.008310I
−0.86664 + 2.94672I −1.22015 − 4.11787I
u = 1.317220 + 0.129556I
a = −1.80083 − 0.09949I
b = 0.610792 + 0.587246I
3.27094 + 5.77484I 5.30912 − 7.09731I
u = 1.317220 − 0.129556I
a = 0.357508 + 0.783708I
b = −0.127941 − 0.198219I
3.27094 − 0.11860I 5.30912 + 1.13842I
u = 1.317220 − 0.129556I
a = 0.091337 − 0.694344I
b = 0.776455 + 0.377674I
3.27094 − 0.11860I 5.30912 + 1.13842I
u = 1.317220 − 0.129556I
a = 1.51101 + 0.25470I
b = −1.07397 + 1.07535I
3.27094 − 5.77484I 5.30912 + 7.09731I
u = 1.317220 − 0.129556I
a = −0.224220 − 0.066922I
b = 0.99581 + 1.28980I
−0.86664 − 2.94672I −1.22015 + 4.11787I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.317220 − 0.129556I
a = 0.77168 + 1.59391I
b = −0.357770 + 1.008310I
−0.86664 − 2.94672I −1.22015 + 4.11787I
u = 1.317220 − 0.129556I
a = −1.80083 + 0.09949I
b = 0.610792 − 0.587246I
3.27094 − 5.77484I 5.30912 + 7.09731I
u = 1.304640 + 0.385413I
a = 0.604532 − 1.165350I
b = −0.919978 − 0.859160I
−3.34246 + 4.64712I −0.26116 − 2.57516I
u = 1.304640 + 0.385413I
a = −1.17144 + 0.97350I
b = 0.108018 + 0.747505I
−3.34246 + 4.64712I −0.26116 − 2.57516I
u = 1.304640 + 0.385413I
a = −1.62199 − 0.36591I
b = −1.76774 + 1.44412I
−7.48004 + 7.47524I −6.79043 − 5.55460I
u = 1.304640 + 0.385413I
a = 0.00454 + 1.73852I
b = −0.053146 + 0.819466I
−7.48004 + 7.47524I −6.79043 − 5.55460I
u = 1.304640 + 0.385413I
a = 1.36908 − 1.57746I
b = −0.807452 − 0.868914I
−3.34246 + 10.30340I −0.26116 − 8.53405I
u = 1.304640 + 0.385413I
a = −1.27201 + 2.16803I
b = 1.09048 + 1.63810I
−3.34246 + 10.30340I −0.26116 − 8.53405I
u = 1.304640 − 0.385413I
a = 0.604532 + 1.165350I
b = −0.919978 + 0.859160I
−3.34246 − 4.64712I −0.26116 + 2.57516I
u = 1.304640 − 0.385413I
a = −1.17144 − 0.97350I
b = 0.108018 − 0.747505I
−3.34246 − 4.64712I −0.26116 + 2.57516I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.304640 − 0.385413I
a = −1.62199 + 0.36591I
b = −1.76774 − 1.44412I
−7.48004 − 7.47524I −6.79043 + 5.55460I
u = 1.304640 − 0.385413I
a = 0.00454 − 1.73852I
b = −0.053146 − 0.819466I
−7.48004 − 7.47524I −6.79043 + 5.55460I
u = 1.304640 − 0.385413I
a = 1.36908 + 1.57746I
b = −0.807452 + 0.868914I
−3.34246 − 10.30340I −0.26116 + 8.53405I
u = 1.304640 − 0.385413I
a = −1.27201 − 2.16803I
b = 1.09048 − 1.63810I
−3.34246 − 10.30340I −0.26116 + 8.53405I
u = −0.271947 + 0.385187I
a = 0.517022 − 0.454203I
b = 0.045920 + 0.690303I
−1.60594 + 1.69682I −0.47805 + 3.07840I
u = −0.271947 + 0.385187I
a = −0.63681 − 1.75387I
b = −1.104940 − 0.853877I
−5.74353 − 1.13130I −7.00731 + 6.05785I
u = −0.271947 + 0.385187I
a = −0.43984 − 1.84859I
b = 0.753427 − 1.132850I
−1.60594 − 3.95942I −0.47805 + 9.03730I
u = −0.271947 + 0.385187I
a = −1.96371 − 0.33369I
b = −0.511166 − 0.764927I
−1.60594 + 1.69682I −0.47805 + 3.07840I
u = −0.271947 + 0.385187I
a = 1.81520 + 0.94189I
b = −0.468912 + 0.757250I
−1.60594 − 3.95942I −0.47805 + 9.03730I
u = −0.271947 + 0.385187I
a = 0.39122 − 4.07994I
b = 0.482757 − 0.696049I
−5.74353 − 1.13130I −7.00731 + 6.05785I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.271947 − 0.385187I
a = 0.517022 + 0.454203I
b = 0.045920 − 0.690303I
−1.60594 − 1.69682I −0.47805 − 3.07840I
u = −0.271947 − 0.385187I
a = −0.63681 + 1.75387I
b = −1.104940 + 0.853877I
−5.74353 + 1.13130I −7.00731 − 6.05785I
u = −0.271947 − 0.385187I
a = −0.43984 + 1.84859I
b = 0.753427 + 1.132850I
−1.60594 + 3.95942I −0.47805 − 9.03730I
u = −0.271947 − 0.385187I
a = −1.96371 + 0.33369I
b = −0.511166 + 0.764927I
−1.60594 − 1.69682I −0.47805 − 3.07840I
u = −0.271947 − 0.385187I
a = 1.81520 − 0.94189I
b = −0.468912 − 0.757250I
−1.60594 + 3.95942I −0.47805 − 9.03730I
u = −0.271947 − 0.385187I
a = 0.39122 + 4.07994I
b = 0.482757 + 0.696049I
−5.74353 + 1.13130I −7.00731 − 6.05785I
18
III. I
u
3
=
hu
20
−9u
18
+· · ·−6u
2
+b, −u
19
−u
18
+· · ·+a+1, u
21
−10u
19
+· · ·−18u
3
+1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
−u
2
a
12
=
u
−u
3
+ u
a
7
=
−u
2
+ 1
u
4
− 2u
2
a
1
=
−u
3
+ 2u
−u
3
+ u
a
9
=
u
19
+ u
18
+ ··· + 5u − 1
−u
20
+ 9u
18
+ ··· + 3u
3
+ 6u
2
a
4
=
−u
20
− u
19
+ ··· + 6u + 3
u
19
− 8u
17
+ ··· + 2u − 1
a
2
=
u
20
+ u
19
+ ··· − 17u
2
− 4u
−u
20
+ u
19
+ ··· + 3u − 1
a
8
=
u
19
+ u
18
+ ··· + 13u
2
+ 5u
−u
20
+ u
19
+ ··· + 9u
3
+ 5u
2
a
3
=
u
20
+ u
19
+ ··· − 17u
2
− 3u
−u
20
+ 2u
19
+ ··· + 2u − 2
a
10
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 7u
20
−4u
19
−59u
18
+ 33u
17
+ 199u
16
−107u
15
−312u
14
+ 155u
13
+ 138u
12
−42u
11
+
219u
10
− 138u
9
− 245u
8
+ 102u
7
− 33u
6
+ 61u
5
+ 85u
4
− 52u
3
+ 20u
2
− 13u − 4
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
21
− 6u
20
+ ··· − 2u
2
+ 1
c
2
, c
7
u
21
+ u
20
+ ··· + u + 1
c
3
, c
9
u
21
− u
20
+ ··· + u − 1
c
4
, c
8
u
21
+ 3u
19
+ ··· + 2u
2
− 1
c
5
, c
6
u
21
− 10u
19
+ ··· − 18u
3
+ 1
c
10
, c
12
u
21
+ 6u
19
+ ··· + 3u
2
− 1
c
11
u
21
− 10u
19
+ ··· − 18u
3
− 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
− 10y
20
+ ··· + 4y −1
c
2
, c
3
, c
7
c
9
y
21
− 21y
20
+ ··· + 15y −1
c
4
, c
8
y
21
+ 6y
20
+ ··· + 4y −1
c
5
, c
6
, c
11
y
21
− 20y
20
+ ··· + 12y
2
− 1
c
10
, c
12
y
21
+ 12y
20
+ ··· + 6y −1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.062614 + 0.857160I
a = −0.87964 + 1.46799I
b = −0.753449 + 0.596686I
−10.38470 + 2.69700I −3.62255 − 0.89519I
u = 0.062614 − 0.857160I
a = −0.87964 − 1.46799I
b = −0.753449 − 0.596686I
−10.38470 − 2.69700I −3.62255 + 0.89519I
u = 1.18462
a = 3.69060
b = −1.03309
−3.22448 8.49570
u = −1.235030 + 0.104057I
a = 0.045191 − 0.732622I
b = 0.152862 − 1.129160I
1.16566 − 3.99750I 3.65944 + 7.63178I
u = −1.235030 − 0.104057I
a = 0.045191 + 0.732622I
b = 0.152862 + 1.129160I
1.16566 + 3.99750I 3.65944 − 7.63178I
u = −1.234780 + 0.272929I
a = −0.531801 − 0.777750I
b = −0.574518 − 1.263340I
−0.513798 + 0.234672I −0.88949 − 1.85883I
u = −1.234780 − 0.272929I
a = −0.531801 + 0.777750I
b = −0.574518 + 1.263340I
−0.513798 − 0.234672I −0.88949 + 1.85883I
u = 1.212920 + 0.392860I
a = −0.25622 + 1.81030I
b = 0.857416 + 0.486218I
−6.84641 + 1.79152I −0.05538 − 3.12575I
u = 1.212920 − 0.392860I
a = −0.25622 − 1.81030I
b = 0.857416 − 0.486218I
−6.84641 − 1.79152I −0.05538 + 3.12575I
u = −0.072517 + 0.710236I
a = −0.05689 − 2.37401I
b = 0.689130 − 1.135240I
−4.06754 − 3.77401I −6.57499 + 5.11487I
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.072517 − 0.710236I
a = −0.05689 + 2.37401I
b = 0.689130 + 1.135240I
−4.06754 + 3.77401I −6.57499 − 5.11487I
u = 1.323560 + 0.298366I
a = 1.40817 − 1.17675I
b = −0.816737 − 1.050640I
0.33148 + 7.43161I −1.41601 − 6.66446I
u = 1.323560 − 0.298366I
a = 1.40817 + 1.17675I
b = −0.816737 + 1.050640I
0.33148 − 7.43161I −1.41601 + 6.66446I
u = −1.316400 + 0.393822I
a = 0.572655 + 0.411414I
b = 0.660701 + 0.695110I
−6.07430 − 7.19164I 0.23497 + 3.77817I
u = −1.316400 − 0.393822I
a = 0.572655 − 0.411414I
b = 0.660701 − 0.695110I
−6.07430 + 7.19164I 0.23497 − 3.77817I
u = 1.391350 + 0.102602I
a = 0.030191 + 0.648490I
b = 0.447297 − 0.579322I
3.05033 − 0.86818I 1.73934 + 7.74915I
u = 1.391350 − 0.102602I
a = 0.030191 − 0.648490I
b = 0.447297 + 0.579322I
3.05033 + 0.86818I 1.73934 − 7.74915I
u = −1.47523
a = −0.307400
b = −0.423333
0.601618 −3.40550
u = 0.385686
a = 3.97045
b = 0.760533
−5.70574 −6.72950
u = −0.179252 + 0.337282I
a = −2.00847 + 0.16947I
b = −0.314759 − 0.878350I
−2.10523 + 2.46905I −7.25568 − 4.96271I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.179252 − 0.337282I
a = −2.00847 − 0.16947I
b = −0.314759 + 0.878350I
−2.10523 − 2.46905I −7.25568 + 4.96271I
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
3
+ u
2
− 1)
22
)(u
21
− 6u
20
+ ··· − 2u
2
+ 1)
· (u
35
− 33u
34
+ ··· − 40960u + 2048)
c
2
, c
7
(u
21
+ u
20
+ ··· + u + 1)(u
35
− u
34
+ ··· + u − 1)
· (u
66
+ u
65
+ ··· + 16520u − 4657)
c
3
, c
9
(u
21
− u
20
+ ··· + u − 1)(u
35
− u
34
+ ··· + u − 1)
· (u
66
+ u
65
+ ··· + 16520u − 4657)
c
4
, c
8
(u
21
+ 3u
19
+ ··· + 2u
2
− 1)(u
35
+ 6u
33
+ ··· + 2u − 1)
· (u
66
+ 3u
65
+ ··· − 4900u − 599)
c
5
, c
6
(u
11
− u
10
− 4u
9
+ 3u
8
+ 6u
7
− 2u
6
− 2u
5
− 3u
4
− 3u
3
+ 3u
2
+ 2u + 1)
6
· (u
21
− 10u
19
+ ··· − 18u
3
+ 1)(u
35
+ 7u
34
+ ··· + 32u − 8)
c
10
, c
12
((u
11
+ 3u
10
+ ··· − 2u − 1)
6
)(u
21
+ 6u
19
+ ··· + 3u
2
− 1)
· (u
35
− 21u
34
+ ··· − 40656u + 2664)
c
11
(u
11
− u
10
− 4u
9
+ 3u
8
+ 6u
7
− 2u
6
− 2u
5
− 3u
4
− 3u
3
+ 3u
2
+ 2u + 1)
6
· (u
21
− 10u
19
+ ··· − 18u
3
− 1)(u
35
+ 7u
34
+ ··· + 32u − 8)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
3
− y
2
+ 2y −1)
22
)(y
21
− 10y
20
+ ··· + 4y −1)
· (y
35
− 11y
34
+ ··· + 14680064y −4194304)
c
2
, c
3
, c
7
c
9
(y
21
− 21y
20
+ ··· + 15y −1)(y
35
− 35y
34
+ ··· − 17y −1)
· (y
66
− 57y
65
+ ··· + 855089512y + 21687649)
c
4
, c
8
(y
21
+ 6y
20
+ ··· + 4y −1)(y
35
+ 12y
34
+ ··· + 12y −1)
· (y
66
+ 19y
65
+ ··· + 9965280y + 358801)
c
5
, c
6
, c
11
((y
11
− 9y
10
+ ··· − 2y −1)
6
)(y
21
− 20y
20
+ ··· + 12y
2
− 1)
· (y
35
− 29y
34
+ ··· + 32y −64)
c
10
, c
12
((y
11
+ 11y
10
+ ··· + 6y −1)
6
)(y
21
+ 12y
20
+ ··· + 6y −1)
· (y
35
+ 23y
34
+ ··· + 27880992y −7096896)
26
