12a
0809
(K12a
0809
)
A knot diagram
1
Linearized knot diagam
4 5 6 10 9 11 12 3 2 1 7 8
Solving Sequence
7,12 3,8
9 1 11 6 4 5 2 10
c
7
c
8
c
12
c
11
c
6
c
3
c
5
c
2
c
10
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h148539u
48
− 527493u
47
+ ··· + 8051b − 394683, 95347u
48
− 282451u
47
+ ··· + 32204a + 36495,
u
49
− 5u
48
+ ··· + 17u + 4i
I
u
2
= h2517u
34
a + 42256u
34
+ ··· + 6152a + 31050, 6u
34
a − 3u
34
+ ··· + 6a − 17, u
35
+ 2u
34
+ ··· + 4u − 1i
I
u
3
= hu
12
+ u
11
− 6u
10
− 6u
9
+ 12u
8
+ 13u
7
− 9u
6
− 12u
5
+ 2u
4
+ 4u
3
+ u
2
+ b + u + 1,
− u
14
+ u
13
+ 8u
12
− 7u
11
− 23u
10
+ 17u
9
+ 28u
8
− 16u
7
− 13u
6
+ 5u
5
+ u
4
− 3u
3
+ 3u
2
+ a + 2u + 1,
u
15
− 2u
14
− 7u
13
+ 15u
12
+ 17u
11
− 40u
10
− 18u
9
+ 45u
8
+ 14u
7
− 22u
6
− 13u
5
+ 8u
4
+ u
3
+ u
2
+ 1i
I
u
4
= hau + b + u + 1, a
2
+ 3au + 2a + u + 4, u
2
+ u − 1i
* 4 irreducible components of dim
C
= 0, with total 138 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
= h148539u
48
− 527493u
47
+ · · · + 8051b − 394683, 95347u
48
−
282451u
47
+ · · · + 32204a + 36495, u
49
− 5u
48
+ · · · + 17u + 4i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
−2.96072u
48
+ 8.77068u
47
+ ··· − 24.7516u − 1.13324
−18.4498u
48
+ 65.5189u
47
+ ··· + 241.353u + 49.0229
a
8
=
1
u
2
a
9
=
−7.08294u
48
+ 17.6739u
47
+ ··· + 1.25894u + 5.64181
−27.2013u
48
+ 89.0489u
47
+ ··· + 287.738u + 59.6427
a
1
=
−u
−u
3
+ u
a
11
=
u
u
a
6
=
−u
2
+ 1
−u
2
a
4
=
−4.22094u
48
+ 9.52301u
47
+ ··· − 21.4049u + 0.492516
−11.5817u
48
+ 33.6645u
47
+ ··· + 72.2484u + 16.8837
a
5
=
−8.39172u
48
+ 25.3461u
47
+ ··· + 57.0803u + 14.9414
−12.9692u
48
+ 37.3577u
47
+ ··· + 90.6477u + 20.3169
a
2
=
4.12132u
48
− 18.5185u
47
+ ··· − 157.649u − 27.2511
2.08806u
48
− 10.1386u
47
+ ··· − 96.3135u − 16.4853
a
10
=
−u
5
+ 2u
3
+ u
−u
7
+ 3u
5
− 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1218
83
u
48
−
2750
83
u
47
+ ··· +
7009
83
u −
594
83
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
49
+ 8u
48
+ ··· + 17u − 1
c
2
u
49
+ 26u
48
+ ··· + 11u + 2
c
4
, c
8
u
49
+ 5u
47
+ ··· + 3u + 1
c
5
, c
9
u
49
− u
48
+ ··· + 27u
2
+ 1
c
6
, c
7
, c
11
c
12
u
49
− 5u
48
+ ··· + 17u + 4
c
10
u
49
− 9u
48
+ ··· − 1017u + 2272
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
49
− 22y
48
+ ··· + 199y −1
c
2
y
49
+ 20y
47
+ ··· + 89y −4
c
4
, c
8
y
49
+ 10y
48
+ ··· − 9y −1
c
5
, c
9
y
49
+ 25y
48
+ ··· − 54y −1
c
6
, c
7
, c
11
c
12
y
49
− 55y
48
+ ··· + 137y −16
c
10
y
49
+ 9y
48
+ ··· − 108326159y −5161984
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.860395 + 0.482404I
a = 0.024941 + 0.522248I
b = −0.236258 + 0.004668I
−1.333090 − 0.442268I −22.7302 − 2.7893I
u = −0.860395 − 0.482404I
a = 0.024941 − 0.522248I
b = −0.236258 − 0.004668I
−1.333090 + 0.442268I −22.7302 + 2.7893I
u = 1.038190 + 0.218664I
a = 0.962395 + 0.159463I
b = 0.063672 − 0.241113I
−3.12377 − 8.13177I 0. + 9.34743I
u = 1.038190 − 0.218664I
a = 0.962395 − 0.159463I
b = 0.063672 + 0.241113I
−3.12377 + 8.13177I 0. − 9.34743I
u = −0.656302 + 0.593975I
a = 1.73077 + 1.26119I
b = 0.157164 + 0.032896I
1.0974 + 15.3120I −6.69862 − 10.70010I
u = −0.656302 − 0.593975I
a = 1.73077 − 1.26119I
b = 0.157164 − 0.032896I
1.0974 − 15.3120I −6.69862 + 10.70010I
u = −0.527749 + 0.624204I
a = −0.344437 − 0.796756I
b = −0.374375 + 0.028886I
−0.22239 + 2.13464I −12.97767 − 4.41434I
u = −0.527749 − 0.624204I
a = −0.344437 + 0.796756I
b = −0.374375 − 0.028886I
−0.22239 − 2.13464I −12.97767 + 4.41434I
u = −0.598351 + 0.535692I
a = −1.55845 − 1.25421I
b = 0.013056 + 0.352563I
−0.78788 + 6.56431I −12.9454 − 9.8564I
u = −0.598351 − 0.535692I
a = −1.55845 + 1.25421I
b = 0.013056 − 0.352563I
−0.78788 − 6.56431I −12.9454 + 9.8564I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.747144
a = 0.385007
b = −0.305862
−1.10744 −7.81270
u = −0.162177 + 0.729155I
a = 0.300367 − 0.459004I
b = 0.409646 − 0.408558I
0.80721 + 4.71794I −9.1417 − 13.3340I
u = −0.162177 − 0.729155I
a = 0.300367 + 0.459004I
b = 0.409646 + 0.408558I
0.80721 − 4.71794I −9.1417 + 13.3340I
u = 0.744466 + 0.003975I
a = −1.81736 + 0.85970I
b = −0.328629 + 0.159289I
−4.13096 + 1.69814I −18.2040 − 4.3712I
u = 0.744466 − 0.003975I
a = −1.81736 − 0.85970I
b = −0.328629 − 0.159289I
−4.13096 − 1.69814I −18.2040 + 4.3712I
u = −0.300631 + 0.671867I
a = 0.481511 + 0.645526I
b = 0.987848 + 0.795214I
2.15150 − 11.04750I −4.44153 + 5.63378I
u = −0.300631 − 0.671867I
a = 0.481511 − 0.645526I
b = 0.987848 − 0.795214I
2.15150 + 11.04750I −4.44153 − 5.63378I
u = 0.485135 + 0.542391I
a = 0.943805 − 0.987006I
b = 0.402923 − 0.436742I
2.90214 − 1.87444I −0.73211 + 3.66192I
u = 0.485135 − 0.542391I
a = 0.943805 + 0.987006I
b = 0.402923 + 0.436742I
2.90214 + 1.87444I −0.73211 − 3.66192I
u = 1.289650 + 0.140107I
a = 0.300793 − 0.515547I
b = −0.125058 + 0.334394I
−2.81136 + 8.04498I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.289650 − 0.140107I
a = 0.300793 + 0.515547I
b = −0.125058 − 0.334394I
−2.81136 − 8.04498I 0
u = 0.506307 + 0.409416I
a = −2.22196 + 1.72599I
b = −0.776269 + 0.644378I
−1.37259 − 1.45940I −10.10356 + 4.62979I
u = 0.506307 − 0.409416I
a = −2.22196 − 1.72599I
b = −0.776269 − 0.644378I
−1.37259 + 1.45940I −10.10356 − 4.62979I
u = −0.340049 + 0.552838I
a = 0.176095 − 0.121875I
b = −0.914800 − 0.629603I
−0.03939 − 2.80450I −9.90854 + 3.00975I
u = −0.340049 − 0.552838I
a = 0.176095 + 0.121875I
b = −0.914800 + 0.629603I
−0.03939 + 2.80450I −9.90854 − 3.00975I
u = −0.537786 + 0.350030I
a = −0.059222 − 1.272190I
b = 0.103070 + 0.635374I
−1.62694 + 1.54828I −11.08710 − 6.22827I
u = −0.537786 − 0.350030I
a = −0.059222 + 1.272190I
b = 0.103070 − 0.635374I
−1.62694 − 1.54828I −11.08710 + 6.22827I
u = 1.47621 + 0.08489I
a = −0.950241 + 0.354999I
b = −1.43618 − 0.18131I
−5.81539 + 0.81969I 0
u = 1.47621 − 0.08489I
a = −0.950241 − 0.354999I
b = −1.43618 + 0.18131I
−5.81539 − 0.81969I 0
u = −1.52067 + 0.14417I
a = −0.937215 − 0.026137I
b = −1.98715 − 0.67865I
−3.73933 + 4.27877I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.52067 − 0.14417I
a = −0.937215 + 0.026137I
b = −1.98715 + 0.67865I
−3.73933 − 4.27877I 0
u = −1.55060 + 0.10978I
a = 1.84193 − 0.18622I
b = 4.05332 + 0.45056I
−8.35293 + 3.28009I 0
u = −1.55060 − 0.10978I
a = 1.84193 + 0.18622I
b = 4.05332 − 0.45056I
−8.35293 − 3.28009I 0
u = 1.54635 + 0.18703I
a = 0.757838 − 0.546719I
b = 1.80903 − 1.20397I
−7.12280 − 5.06000I 0
u = 1.54635 − 0.18703I
a = 0.757838 + 0.546719I
b = 1.80903 + 1.20397I
−7.12280 + 5.06000I 0
u = 1.55747 + 0.09309I
a = 0.98887 − 1.45323I
b = 2.04164 − 2.22854I
−8.74919 − 3.11091I 0
u = 1.55747 − 0.09309I
a = 0.98887 + 1.45323I
b = 2.04164 + 2.22854I
−8.74919 + 3.11091I 0
u = 1.56503 + 0.15811I
a = 2.12720 − 0.54206I
b = 4.43010 − 0.79741I
−8.03789 − 9.09579I 0
u = 1.56503 − 0.15811I
a = 2.12720 + 0.54206I
b = 4.43010 + 0.79741I
−8.03789 + 9.09579I 0
u = −1.59257 + 0.00650I
a = 1.97070 + 0.65045I
b = 4.19761 + 1.43756I
−12.06900 − 1.62283I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.59257 − 0.00650I
a = 1.97070 − 0.65045I
b = 4.19761 − 1.43756I
−12.06900 + 1.62283I 0
u = 1.58602 + 0.18202I
a = −2.19854 + 0.10847I
b = −4.50456 + 0.32567I
−6.4148 − 18.1914I 0
u = 1.58602 − 0.18202I
a = −2.19854 − 0.10847I
b = −4.50456 − 0.32567I
−6.4148 + 18.1914I 0
u = −0.240166 + 0.320881I
a = 0.947458 + 0.195457I
b = −0.450401 + 0.404469I
−0.963675 + 0.866301I −7.31478 − 5.07695I
u = −0.240166 − 0.320881I
a = 0.947458 − 0.195457I
b = −0.450401 − 0.404469I
−0.963675 − 0.866301I −7.31478 + 5.07695I
u = 1.61021 + 0.11898I
a = −1.070280 + 0.513665I
b = −1.94637 + 0.86375I
−9.61044 − 1.58418I 0
u = 1.61021 − 0.11898I
a = −1.070280 − 0.513665I
b = −1.94637 − 0.86375I
−9.61044 + 1.58418I 0
u = −1.64403 + 0.02832I
a = −1.71447 + 0.78931I
b = −3.43609 + 1.41784I
−12.1970 + 8.7921I 0
u = −1.64403 − 0.02832I
a = −1.71447 − 0.78931I
b = −3.43609 − 1.41784I
−12.1970 − 8.7921I 0
9
II. I
u
2
= h2517u
34
a + 42256u
34
+ · · · + 6152a + 31050, 6u
34
a − 3u
34
+ · · · +
6a − 17, u
35
+ 2u
34
+ · · · + 4u − 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
a
−0.143068au
34
− 2.40186u
34
+ ··· − 0.349685a − 1.76491
a
8
=
1
u
2
a
9
=
1.40186au
34
− 0.835844u
34
+ ··· + 1.76491a − 8.26067
1.14671au
34
+ 2.94168u
34
+ ··· − 0.548059a − 2.67055
a
1
=
−u
−u
3
+ u
a
11
=
u
u
a
6
=
−u
2
+ 1
−u
2
a
4
=
0.291480au
34
+ 3.12783u
34
+ ··· + 1.31831a − 0.266015
−0.215483au
34
+ 1.75865u
34
+ ··· − 0.291480a − 5.12783
a
5
=
0.255158au
34
+ 3.22247u
34
+ ··· + 1.31297a + 1.40988
0.112090au
34
+ 1.82061u
34
+ ··· − 0.0367191a − 4.35503
a
2
=
−1.03268au
34
− 3.36554u
34
+ ··· + 3.09691a − 2.75956
−3.43455au
34
− 2.52970u
34
+ ··· + 1.33201a + 3.50111
a
10
=
−u
5
+ 2u
3
+ u
−u
7
+ 3u
5
− 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = u
34
+ 2u
33
−17u
32
−29u
31
+ 126u
30
+ 160u
29
−539u
28
−330u
27
+
1491u
26
− 522u
25
− 2809u
24
+ 4690u
23
+ 3456u
22
− 12414u
21
− 1644u
20
+ 18572u
19
−
3263u
18
− 17872u
17
+ 7947u
16
+ 11650u
15
− 8304u
14
− 4754u
13
+ 5714u
12
+ 816u
11
−
3062u
10
+ 144u
9
+ 1032u
8
− 416u
7
− 370u
6
+ 110u
5
+ 8u
4
− 50u
3
− 9u
2
+ 2u − 11
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
70
− 5u
69
+ ··· + 118u − 11
c
2
(u
35
− 17u
34
+ ··· − 2u + 4)
2
c
4
, c
8
u
70
− 2u
69
+ ··· − 3755u − 389
c
5
, c
9
u
70
− 4u
69
+ ··· − u + 1
c
6
, c
7
, c
11
c
12
(u
35
+ 2u
34
+ ··· + 4u − 1)
2
c
10
(u
35
− 8u
34
+ ··· − 34u − 17)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
70
+ 23y
69
+ ··· − 3012y + 121
c
2
(y
35
− 5y
34
+ ··· + 268y −16)
2
c
4
, c
8
y
70
+ 4y
69
+ ··· − 6317691y + 151321
c
5
, c
9
y
70
− 16y
69
+ ··· + 9y + 1
c
6
, c
7
, c
11
c
12
(y
35
− 40y
34
+ ··· + 12y −1)
2
c
10
(y
35
+ 8y
34
+ ··· + 884y −289)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.666512 + 0.582064I
a = −1.239150 + 0.250233I
b = −0.059661 − 0.188761I
2.64852 − 7.06572I −2.24468 + 9.47416I
u = 0.666512 + 0.582064I
a = 1.50375 − 1.16447I
b = 0.070870 − 0.248710I
2.64852 − 7.06572I −2.24468 + 9.47416I
u = 0.666512 − 0.582064I
a = −1.239150 − 0.250233I
b = −0.059661 + 0.188761I
2.64852 + 7.06572I −2.24468 − 9.47416I
u = 0.666512 − 0.582064I
a = 1.50375 + 1.16447I
b = 0.070870 + 0.248710I
2.64852 + 7.06572I −2.24468 − 9.47416I
u = −1.16124
a = 0.043408 + 0.442130I
b = −0.393345 − 0.073439I
−0.859981 −0.877410
u = −1.16124
a = 0.043408 − 0.442130I
b = −0.393345 + 0.073439I
−0.859981 −0.877410
u = −0.782419 + 0.220868I
a = −0.54049 − 1.41055I
b = −0.306204 + 0.132537I
−2.98205 − 1.23863I −15.1065 + 4.7419I
u = −0.782419 + 0.220868I
a = 1.64861 + 0.56272I
b = −0.050193 + 0.786535I
−2.98205 − 1.23863I −15.1065 + 4.7419I
u = −0.782419 − 0.220868I
a = −0.54049 + 1.41055I
b = −0.306204 − 0.132537I
−2.98205 + 1.23863I −15.1065 − 4.7419I
u = −0.782419 − 0.220868I
a = 1.64861 − 0.56272I
b = −0.050193 − 0.786535I
−2.98205 + 1.23863I −15.1065 − 4.7419I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.20404
a = 0.010704 + 0.441967I
b = −0.418731 − 0.084162I
−0.860321 −1.06770
u = −1.20404
a = 0.010704 − 0.441967I
b = −0.418731 + 0.084162I
−0.860321 −1.06770
u = 0.638463 + 0.472891I
a = 0.00841 − 1.58949I
b = −0.732835 + 0.165675I
−1.26211 − 6.69833I −12.2764 + 10.3456I
u = 0.638463 + 0.472891I
a = −2.23392 + 0.77030I
b = −0.191691 − 0.277776I
−1.26211 − 6.69833I −12.2764 + 10.3456I
u = 0.638463 − 0.472891I
a = 0.00841 + 1.58949I
b = −0.732835 − 0.165675I
−1.26211 + 6.69833I −12.2764 − 10.3456I
u = 0.638463 − 0.472891I
a = −2.23392 − 0.77030I
b = −0.191691 + 0.277776I
−1.26211 + 6.69833I −12.2764 − 10.3456I
u = 0.476081 + 0.547627I
a = 0.849827 − 0.724384I
b = 0.297746 − 0.578232I
2.91093 − 1.88971I −0.44498 + 3.89733I
u = 0.476081 + 0.547627I
a = 1.08918 − 1.23722I
b = 0.547443 − 0.288098I
2.91093 − 1.88971I −0.44498 + 3.89733I
u = 0.476081 − 0.547627I
a = 0.849827 + 0.724384I
b = 0.297746 + 0.578232I
2.91093 + 1.88971I −0.44498 − 3.89733I
u = 0.476081 − 0.547627I
a = 1.08918 + 1.23722I
b = 0.547443 + 0.288098I
2.91093 + 1.88971I −0.44498 − 3.89733I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.525223 + 0.491556I
a = −0.62016 + 1.42991I
b = 0.689553 + 1.077310I
2.43912 + 5.99758I −1.93287 − 10.06250I
u = −0.525223 + 0.491556I
a = −2.07561 − 1.78920I
b = 0.191089 − 0.259118I
2.43912 + 5.99758I −1.93287 − 10.06250I
u = −0.525223 − 0.491556I
a = −0.62016 − 1.42991I
b = 0.689553 − 1.077310I
2.43912 − 5.99758I −1.93287 + 10.06250I
u = −0.525223 − 0.491556I
a = −2.07561 + 1.78920I
b = 0.191089 + 0.259118I
2.43912 − 5.99758I −1.93287 + 10.06250I
u = 0.277580 + 0.662679I
a = 0.736054 − 0.530277I
b = 0.797040 − 0.685996I
3.79715 + 2.86775I 1.19785 − 3.30855I
u = 0.277580 + 0.662679I
a = 0.163136 + 0.349177I
b = −0.295111 + 0.682840I
3.79715 + 2.86775I 1.19785 − 3.30855I
u = 0.277580 − 0.662679I
a = 0.736054 + 0.530277I
b = 0.797040 + 0.685996I
3.79715 − 2.86775I 1.19785 + 3.30855I
u = 0.277580 − 0.662679I
a = 0.163136 − 0.349177I
b = −0.295111 − 0.682840I
3.79715 − 2.86775I 1.19785 + 3.30855I
u = −0.441250 + 0.489469I
a = −0.884679 − 0.035500I
b = −0.971326 − 0.931519I
2.68875 − 2.55506I −0.147951 + 0.889172I
u = −0.441250 + 0.489469I
a = 2.35888 + 1.07821I
b = 0.371733 − 0.548181I
2.68875 − 2.55506I −0.147951 + 0.889172I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.441250 − 0.489469I
a = −0.884679 + 0.035500I
b = −0.971326 + 0.931519I
2.68875 + 2.55506I −0.147951 − 0.889172I
u = −0.441250 − 0.489469I
a = 2.35888 − 1.07821I
b = 0.371733 + 0.548181I
2.68875 + 2.55506I −0.147951 − 0.889172I
u = 0.195556 + 0.466781I
a = 0.358284 + 0.485136I
b = −0.729100 + 0.903609I
−0.07204 + 3.38846I −7.99570 − 4.25357I
u = 0.195556 + 0.466781I
a = 0.96362 + 1.74995I
b = 0.805890 + 0.233688I
−0.07204 + 3.38846I −7.99570 − 4.25357I
u = 0.195556 − 0.466781I
a = 0.358284 − 0.485136I
b = −0.729100 − 0.903609I
−0.07204 − 3.38846I −7.99570 + 4.25357I
u = 0.195556 − 0.466781I
a = 0.96362 − 1.74995I
b = 0.805890 − 0.233688I
−0.07204 − 3.38846I −7.99570 + 4.25357I
u = −1.51268 + 0.13583I
a = −0.621893 + 0.392051I
b = −1.172090 − 0.041405I
−3.63443 + 4.26143I 0
u = −1.51268 + 0.13583I
a = −1.215730 − 0.406169I
b = −2.85058 − 1.22060I
−3.63443 + 4.26143I 0
u = −1.51268 − 0.13583I
a = −0.621893 − 0.392051I
b = −1.172090 + 0.041405I
−3.63443 − 4.26143I 0
u = −1.51268 − 0.13583I
a = −1.215730 + 0.406169I
b = −2.85058 + 1.22060I
−3.63443 − 4.26143I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.51779 + 0.11529I
a = −0.190719 + 1.045250I
b = 0.047370 + 0.888797I
−3.82932 + 0.52023I 0
u = 1.51779 + 0.11529I
a = −2.07253 + 0.17597I
b = −4.69665 + 0.02384I
−3.82932 + 0.52023I 0
u = 1.51779 − 0.11529I
a = −0.190719 − 1.045250I
b = 0.047370 − 0.888797I
−3.82932 − 0.52023I 0
u = 1.51779 − 0.11529I
a = −2.07253 − 0.17597I
b = −4.69665 − 0.02384I
−3.82932 − 0.52023I 0
u = −1.53311 + 0.06521I
a = −0.718843 + 0.254928I
b = −1.17807 + 1.78768I
−6.32420 − 2.55827I −11.80080 + 5.60834I
u = −1.53311 + 0.06521I
a = 1.89671 + 1.84534I
b = 3.23347 + 3.48987I
−6.32420 − 2.55827I −11.80080 + 5.60834I
u = −1.53311 − 0.06521I
a = −0.718843 − 0.254928I
b = −1.17807 − 1.78768I
−6.32420 + 2.55827I −11.80080 − 5.60834I
u = −1.53311 − 0.06521I
a = 1.89671 − 1.84534I
b = 3.23347 − 3.48987I
−6.32420 + 2.55827I −11.80080 − 5.60834I
u = 1.54485 + 0.13337I
a = 0.385384 + 0.615349I
b = 0.65878 + 2.45832I
−4.50128 − 8.20533I 0
u = 1.54485 + 0.13337I
a = 2.79157 − 0.12318I
b = 5.31687 − 0.42575I
−4.50128 − 8.20533I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.54485 − 0.13337I
a = 0.385384 − 0.615349I
b = 0.65878 − 2.45832I
−4.50128 + 8.20533I 0
u = 1.54485 − 0.13337I
a = 2.79157 + 0.12318I
b = 5.31687 + 0.42575I
−4.50128 + 8.20533I 0
u = −1.58137 + 0.13915I
a = −1.53160 − 1.51990I
b = −2.59358 − 2.56426I
−8.76037 + 8.95548I 0
u = −1.58137 + 0.13915I
a = 2.26630 − 0.09882I
b = 4.81897 − 0.31491I
−8.76037 + 8.95548I 0
u = −1.58137 − 0.13915I
a = −1.53160 + 1.51990I
b = −2.59358 + 2.56426I
−8.76037 − 8.95548I 0
u = −1.58137 − 0.13915I
a = 2.26630 + 0.09882I
b = 4.81897 + 0.31491I
−8.76037 − 8.95548I 0
u = 0.384702 + 0.130377I
a = 1.34643 + 1.15599I
b = −0.479286 + 1.191100I
0.28705 + 3.45586I −12.59187 − 3.72340I
u = 0.384702 + 0.130377I
a = −0.33211 + 4.09606I
b = 0.594555 + 0.086997I
0.28705 + 3.45586I −12.59187 − 3.72340I
u = 0.384702 − 0.130377I
a = 1.34643 − 1.15599I
b = −0.479286 − 1.191100I
0.28705 − 3.45586I −12.59187 + 3.72340I
u = 0.384702 − 0.130377I
a = −0.33211 − 4.09606I
b = 0.594555 − 0.086997I
0.28705 − 3.45586I −12.59187 + 3.72340I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.58992 + 0.17781I
a = 1.314390 − 0.220603I
b = 2.77301 − 0.55986I
−4.92419 + 9.89136I 0
u = −1.58992 + 0.17781I
a = −2.04710 − 0.00757I
b = −4.02959 − 0.25930I
−4.92419 + 9.89136I 0
u = −1.58992 − 0.17781I
a = 1.314390 + 0.220603I
b = 2.77301 + 0.55986I
−4.92419 − 9.89136I 0
u = −1.58992 − 0.17781I
a = −2.04710 + 0.00757I
b = −4.02959 + 0.25930I
−4.92419 − 9.89136I 0
u = 1.61834 + 0.05147I
a = 0.99213 − 1.13861I
b = 2.24075 − 2.24946I
−11.22110 + 0.25726I 0
u = 1.61834 + 0.05147I
a = −2.18543 − 0.68568I
b = −4.13160 − 0.81782I
−11.22110 + 0.25726I 0
u = 1.61834 − 0.05147I
a = 0.99213 + 1.13861I
b = 2.24075 + 2.24946I
−11.22110 − 0.25726I 0
u = 1.61834 − 0.05147I
a = −2.18543 + 0.68568I
b = −4.13160 + 0.81782I
−11.22110 − 0.25726I 0
u = 1.65747
a = 0.394240
b = 0.976487
−10.1124 0
u = 1.65747
a = −1.82785
b = −3.32748
−10.1124 0
19
III.
I
u
3
= hu
12
+ u
11
+ · · · +b + 1, −u
14
+ u
13
+ · · · +a + 1, u
15
− 2u
14
+ · · · +u
2
+ 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
u
14
− u
13
+ ··· − 2u − 1
−u
12
− u
11
+ ··· − u − 1
a
8
=
1
u
2
a
9
=
3u
14
− u
13
+ ··· − u − 1
5u
14
− 3u
13
+ ··· − u − 3
a
1
=
−u
−u
3
+ u
a
11
=
u
u
a
6
=
−u
2
+ 1
−u
2
a
4
=
5u
14
− 4u
13
+ ··· − 2u − 3
6u
14
− 3u
13
+ ··· − 3u − 5
a
5
=
2u
14
− 2u
13
+ ··· − u − 1
2u
14
− u
13
+ ··· − 2u − 2
a
2
=
3u
14
− u
13
+ ··· − u − 3
5u
14
− 2u
13
+ ··· − 2u − 3
a
10
=
−u
5
+ 2u
3
+ u
−u
7
+ 3u
5
− 2u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −10u
14
+ 3u
13
+ 78u
12
− 14u
11
− 227u
10
− u
9
+ 307u
8
+ 85u
7
−
202u
6
− 117u
5
+ 54u
4
+ 24u
3
+ 18u
2
+ 11u + 7
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
15
− 4u
14
+ ··· + 5u − 1
c
2
u
15
+ 11u
14
+ ··· + 69u + 5
c
4
, c
8
u
15
− 2u
13
+ ··· − u + 1
c
5
, c
9
u
15
− u
14
+ ··· − 2u
2
+ 1
c
6
, c
7
u
15
− 2u
14
+ ··· + u
2
+ 1
c
10
u
15
+ 2u
14
+ ··· + 4u + 1
c
11
, c
12
u
15
+ 2u
14
+ ··· − u
2
− 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
15
+ 12y
14
+ ··· − 7y −1
c
2
y
15
+ 5y
14
+ ··· + 1201y −25
c
4
, c
8
y
15
− 4y
14
+ ··· + 5y −1
c
5
, c
9
y
15
− 5y
14
+ ··· + 4y −1
c
6
, c
7
, c
11
c
12
y
15
− 18y
14
+ ··· − 2y −1
c
10
y
15
− 2y
14
+ ··· − 10y −1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.968088 + 0.372476I
a = −0.059767 + 0.569906I
b = 0.162535 + 0.150354I
−1.117930 + 0.672381I −5.5717 − 15.5217I
u = 0.968088 − 0.372476I
a = −0.059767 − 0.569906I
b = 0.162535 − 0.150354I
−1.117930 − 0.672381I −5.5717 + 15.5217I
u = −0.617443 + 0.491186I
a = −1.52967 − 0.80405I
b = 0.275235 + 0.217089I
0.46809 + 6.63284I −5.87049 − 10.29818I
u = −0.617443 − 0.491186I
a = −1.52967 + 0.80405I
b = 0.275235 − 0.217089I
0.46809 − 6.63284I −5.87049 + 10.29818I
u = −0.334963 + 0.434830I
a = 0.218876 + 0.780240I
b = −0.646634 − 0.822557I
1.34167 − 3.29522I −2.79998 + 3.51950I
u = −0.334963 − 0.434830I
a = 0.218876 − 0.780240I
b = −0.646634 + 0.822557I
1.34167 + 3.29522I −2.79998 − 3.51950I
u = −1.48976 + 0.10689I
a = −0.711932 − 0.669447I
b = −1.26873 − 2.07242I
−4.60411 + 5.60570I −9.56653 − 7.15919I
u = −1.48976 − 0.10689I
a = −0.711932 + 0.669447I
b = −1.26873 + 2.07242I
−4.60411 − 5.60570I −9.56653 + 7.15919I
u = 1.51063 + 0.09194I
a = −1.41929 + 0.71032I
b = −2.56043 + 0.38952I
−4.92279 + 1.66323I −7.24786 − 5.12167I
u = 1.51063 − 0.09194I
a = −1.41929 − 0.71032I
b = −2.56043 − 0.38952I
−4.92279 − 1.66323I −7.24786 + 5.12167I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.209564 + 0.438491I
a = −1.14877 − 1.22839I
b = −0.198242 − 0.661573I
1.25166 − 3.87018I −2.48614 + 6.40598I
u = 0.209564 − 0.438491I
a = −1.14877 + 1.22839I
b = −0.198242 + 0.661573I
1.25166 + 3.87018I −2.48614 − 6.40598I
u = 1.57469 + 0.14763I
a = 2.00341 − 0.20449I
b = 3.95483 − 0.13857I
−6.92174 − 8.98940I −8.76043 + 7.91883I
u = 1.57469 − 0.14763I
a = 2.00341 + 0.20449I
b = 3.95483 + 0.13857I
−6.92174 + 8.98940I −8.76043 − 7.91883I
u = −1.64161
a = 1.29429
b = 2.56286
−10.4681 −17.3940
24
IV. I
u
4
= hau + b + u + 1, a
2
+ 3au + 2a + u + 4, u
2
+ u − 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
a
−au − u − 1
a
8
=
1
−u + 1
a
9
=
2au + a + u + 5
2au − a − 3u + 2
a
1
=
−u
−u + 1
a
11
=
u
u
a
6
=
u
u − 1
a
4
=
a + u
−au − 2
a
5
=
2a + 3u + 1
−2au + a + 3u − 3
a
2
=
a
−au − u − 1
a
10
=
1
−u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u − 14
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u − 1)
4
c
2
u
4
c
4
, c
5
, c
8
c
9
u
4
+ u
3
+ u
2
+ u + 1
c
6
, c
7
, c
10
(u
2
+ u − 1)
2
c
11
, c
12
(u
2
− u − 1)
2
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y −1)
4
c
2
y
4
c
4
, c
5
, c
8
c
9
y
4
+ y
3
+ y
2
+ y + 1
c
6
, c
7
, c
10
c
11
, c
12
(y
2
− 3y + 1)
2
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −1.92705 + 0.95106I
b = −0.427051 − 0.587785I
−2.63189 −14.6180
u = 0.618034
a = −1.92705 − 0.95106I
b = −0.427051 + 0.587785I
−2.63189 −14.6180
u = −1.61803
a = 1.42705 + 0.58779I
b = 2.92705 + 0.95106I
−10.5276 −12.3820
u = −1.61803
a = 1.42705 − 0.58779I
b = 2.92705 − 0.95106I
−10.5276 −12.3820
28
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
((u − 1)
4
)(u
15
− 4u
14
+ ··· + 5u − 1)(u
49
+ 8u
48
+ ··· + 17u − 1)
· (u
70
− 5u
69
+ ··· + 118u − 11)
c
2
u
4
(u
15
+ 11u
14
+ ··· + 69u + 5)(u
35
− 17u
34
+ ··· − 2u + 4)
2
· (u
49
+ 26u
48
+ ··· + 11u + 2)
c
4
, c
8
(u
4
+ u
3
+ u
2
+ u + 1)(u
15
− 2u
13
+ ··· − u + 1)(u
49
+ 5u
47
+ ··· + 3u + 1)
· (u
70
− 2u
69
+ ··· − 3755u − 389)
c
5
, c
9
(u
4
+ u
3
+ u
2
+ u + 1)(u
15
− u
14
+ ··· − 2u
2
+ 1)
· (u
49
− u
48
+ ··· + 27u
2
+ 1)(u
70
− 4u
69
+ ··· − u + 1)
c
6
, c
7
((u
2
+ u − 1)
2
)(u
15
− 2u
14
+ ··· + u
2
+ 1)(u
35
+ 2u
34
+ ··· + 4u − 1)
2
· (u
49
− 5u
48
+ ··· + 17u + 4)
c
10
((u
2
+ u − 1)
2
)(u
15
+ 2u
14
+ ··· + 4u + 1)
· ((u
35
− 8u
34
+ ··· − 34u − 17)
2
)(u
49
− 9u
48
+ ··· − 1017u + 2272)
c
11
, c
12
((u
2
− u − 1)
2
)(u
15
+ 2u
14
+ ··· − u
2
− 1)(u
35
+ 2u
34
+ ··· + 4u − 1)
2
· (u
49
− 5u
48
+ ··· + 17u + 4)
29
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
((y −1)
4
)(y
15
+ 12y
14
+ ··· − 7y −1)(y
49
− 22y
48
+ ··· + 199y −1)
· (y
70
+ 23y
69
+ ··· − 3012y + 121)
c
2
y
4
(y
15
+ 5y
14
+ ··· + 1201y −25)(y
35
− 5y
34
+ ··· + 268y −16)
2
· (y
49
+ 20y
47
+ ··· + 89y −4)
c
4
, c
8
(y
4
+ y
3
+ y
2
+ y + 1)(y
15
− 4y
14
+ ··· + 5y −1)
· (y
49
+ 10y
48
+ ··· − 9y −1)(y
70
+ 4y
69
+ ··· − 6317691y + 151321)
c
5
, c
9
(y
4
+ y
3
+ y
2
+ y + 1)(y
15
− 5y
14
+ ··· + 4y −1)
· (y
49
+ 25y
48
+ ··· − 54y −1)(y
70
− 16y
69
+ ··· + 9y + 1)
c
6
, c
7
, c
11
c
12
((y
2
− 3y + 1)
2
)(y
15
− 18y
14
+ ··· − 2y −1)
· ((y
35
− 40y
34
+ ··· + 12y −1)
2
)(y
49
− 55y
48
+ ··· + 137y −16)
c
10
((y
2
− 3y + 1)
2
)(y
15
− 2y
14
+ ··· − 10y −1)
· (y
35
+ 8y
34
+ ··· + 884y −289)
2
· (y
49
+ 9y
48
+ ··· − 108326159y −5161984)
30
