12n
0867
(K12n
0867
)
A knot diagram
1
Linearized knot diagam
4 6 10 8 12 3 1 6 7 4 7 5
Solving Sequence
3,10
4
7,11
12 6 2 1 5 9 8
c
3
c
10
c
11
c
6
c
2
c
1
c
5
c
9
c
8
c
4
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, −81072715476u
25
+ 52576364860u
24
+ ··· + 3386368973a + 151407587225,
u
26
− 7u
24
+ ··· − 2u − 1i
I
u
2
= h−6.03995 × 10
146
u
63
− 9.04955 × 10
146
u
62
+ ··· + 5.66297 × 10
148
b − 4.48747 × 10
149
,
− 1.13952 × 10
150
u
63
− 1.92915 × 10
150
u
62
+ ··· + 4.19060 × 10
150
a − 1.96444 × 10
152
,
u
64
+ 2u
63
+ ··· + 171u + 37i
I
u
3
= hb + u, 106u
13
− 38u
12
+ ··· + 29a + 111, u
14
− 4u
12
+ 8u
10
− 10u
8
+ u
7
+ 5u
6
− u
5
+ 2u
4
− u
3
− 2u
2
+ u + 1i
I
u
4
= hu
11
− 4u
9
+ 5u
7
− 3u
5
+ 5u
3
+ b − 4u,
− 3u
11
− 4u
10
+ 11u
9
+ 14u
8
− 11u
7
− 13u
6
+ 4u
5
+ 5u
4
− 12u
3
− 17u
2
+ 2a + 8u + 8,
u
12
− 4u
10
+ 5u
8
− 3u
6
+ 5u
4
− 4u
2
+ 1i
I
u
5
= hb + u − 1, a + u − 1, u
2
− u + 1i
* 5 irreducible components of dim
C
= 0, with total 118 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
= hb − u, −8.11 × 10
10
u
25
+ 5.26 × 10
10
u
24
+ · · · + 3.39 × 10
9
a + 1.51 ×
10
11
, u
26
− 7u
24
+ · · · − 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
7
=
23.9409u
25
− 15.5259u
24
+ ··· − 17.7599u − 44.7109
u
a
11
=
u
−u
3
+ u
a
12
=
14.9186u
25
− 4.47512u
24
+ ··· + 9.17407u − 31.5817
5.21774u
25
− 3.42933u
24
+ ··· − 2.57347u − 10.1364
a
6
=
23.9409u
25
− 15.5259u
24
+ ··· − 18.7599u − 44.7109
u
a
2
=
−15.5259u
25
+ 7.24164u
24
+ ··· + 3.17090u + 24.9409
u
2
a
1
=
−20.9154u
25
+ 9.26554u
24
+ ··· + 2.12830u + 32.1825
1.96019u
25
− 0.497707u
24
+ ··· + 1.34172u − 2.02390
a
5
=
−46.2583u
25
+ 23.0203u
24
+ ··· + 7.38663u + 78.1426
2.51848u
25
− 0.734211u
24
+ ··· + 3.08951u − 4.29711
a
9
=
27.4397u
25
− 10.7838u
24
+ ··· + 6.93525u − 57.8914
7.24164u
25
− 5.38952u
24
+ ··· − 6.11087u − 15.5259
a
8
=
17.7388u
25
− 9.73803u
24
+ ··· − 4.81229u − 36.4461
2.02390u
25
− 1.96019u
24
+ ··· − 2.53740u − 5.38952
(ii) Obstruction class = −1
(iii) Cusp Shapes =
39142336274
3386368973
u
25
−
35272648620
3386368973
u
24
+ ··· −
7281974472
260489921
u −
23728803050
3386368973
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
26
− 21u
25
+ ··· + 7680u − 512
c
2
, c
3
, c
6
c
10
u
26
− 7u
24
+ ··· + 2u − 1
c
4
, c
7
u
26
+ 5u
24
+ ··· − 8u + 1
c
5
, c
12
u
26
− 11u
25
+ ··· + 304u − 24
c
8
, c
11
u
26
− 2u
25
+ ··· − 80u + 19
c
9
u
26
− 21u
25
+ ··· − 16284u + 1096
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
26
− y
25
+ ··· − 3932160y + 262144
c
2
, c
3
, c
6
c
10
y
26
− 14y
25
+ ··· − 24y + 1
c
4
, c
7
y
26
+ 10y
25
+ ··· − 36y + 1
c
5
, c
12
y
26
+ 17y
25
+ ··· − 2656y + 576
c
8
, c
11
y
26
+ 22y
25
+ ··· − 7236y + 361
c
9
y
26
+ 5y
25
+ ··· − 35876688y + 1201216
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.783583 + 0.497565I
a = −0.552401 + 0.963003I
b = −0.783583 + 0.497565I
2.97189 − 1.12917I 11.90635 + 3.31876I
u = −0.783583 − 0.497565I
a = −0.552401 − 0.963003I
b = −0.783583 − 0.497565I
2.97189 + 1.12917I 11.90635 − 3.31876I
u = −1.086820 + 0.182504I
a = 0.465254 − 0.140063I
b = −1.086820 + 0.182504I
1.13119 − 2.61384I 9.69860 + 3.81800I
u = −1.086820 − 0.182504I
a = 0.465254 + 0.140063I
b = −1.086820 − 0.182504I
1.13119 + 2.61384I 9.69860 − 3.81800I
u = 1.086220 + 0.199675I
a = 0.091019 + 0.925043I
b = 1.086220 + 0.199675I
2.34848 − 2.40757I 11.72048 + 1.43873I
u = 1.086220 − 0.199675I
a = 0.091019 − 0.925043I
b = 1.086220 − 0.199675I
2.34848 + 2.40757I 11.72048 − 1.43873I
u = 0.793430 + 0.080832I
a = −0.31402 + 1.95659I
b = 0.793430 + 0.080832I
2.86846 − 2.53404I 13.29449 + 3.41848I
u = 0.793430 − 0.080832I
a = −0.31402 − 1.95659I
b = 0.793430 − 0.080832I
2.86846 + 2.53404I 13.29449 − 3.41848I
u = 0.843436 + 0.905238I
a = −0.58396 + 1.35722I
b = 0.843436 + 0.905238I
−8.06090 − 4.16985I 4.50695 + 1.21035I
u = 0.843436 − 0.905238I
a = −0.58396 − 1.35722I
b = 0.843436 − 0.905238I
−8.06090 + 4.16985I 4.50695 − 1.21035I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.27855
a = −1.03578
b = 1.27855
6.69425 −5.31560
u = −0.947242 + 0.861971I
a = 0.449801 + 1.090630I
b = −0.947242 + 0.861971I
−2.70506 − 1.24876I 6.24886 − 0.86995I
u = −0.947242 − 0.861971I
a = 0.449801 − 1.090630I
b = −0.947242 − 0.861971I
−2.70506 + 1.24876I 6.24886 + 0.86995I
u = −1.152600 + 0.696627I
a = 0.876822 + 1.038740I
b = −1.152600 + 0.696627I
−4.95525 − 4.75697I 1.31627 + 5.46968I
u = −1.152600 − 0.696627I
a = 0.876822 − 1.038740I
b = −1.152600 − 0.696627I
−4.95525 + 4.75697I 1.31627 − 5.46968I
u = 0.983614 + 0.927361I
a = −0.149538 + 1.130440I
b = 0.983614 + 0.927361I
−6.37802 + 8.08526I 2.98916 − 6.73051I
u = 0.983614 − 0.927361I
a = −0.149538 − 1.130440I
b = 0.983614 − 0.927361I
−6.37802 − 8.08526I 2.98916 + 6.73051I
u = 1.18953 + 0.78832I
a = −0.510132 + 1.196150I
b = 1.18953 + 0.78832I
−0.89949 + 11.85540I 9.91635 − 8.77683I
u = 1.18953 − 0.78832I
a = −0.510132 − 1.196150I
b = 1.18953 − 0.78832I
−0.89949 − 11.85540I 9.91635 + 8.77683I
u = −0.554736 + 0.043432I
a = −0.54182 + 5.22386I
b = −0.554736 + 0.043432I
−2.22203 + 4.95013I 10.15122 + 4.02452I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.554736 − 0.043432I
a = −0.54182 − 5.22386I
b = −0.554736 − 0.043432I
−2.22203 − 4.95013I 10.15122 − 4.02452I
u = −1.19248 + 0.84134I
a = 0.41575 + 1.36350I
b = −1.19248 + 0.84134I
−5.8498 − 17.7947I 7.31708 + 9.41599I
u = −1.19248 − 0.84134I
a = 0.41575 − 1.36350I
b = −1.19248 − 0.84134I
−5.8498 + 17.7947I 7.31708 − 9.41599I
u = 0.364116 + 0.322517I
a = −0.38283 − 1.70403I
b = 0.364116 + 0.322517I
−3.28701 + 1.79973I 8.03339 − 3.90573I
u = 0.364116 − 0.322517I
a = −0.38283 + 1.70403I
b = 0.364116 − 0.322517I
−3.28701 − 1.79973I 8.03339 + 3.90573I
u = −0.364326
a = 0.507910
b = −0.364326
0.612463 16.1170
7
II. I
u
2
= h−6.04 × 10
146
u
63
− 9.05 × 10
146
u
62
+ · · · + 5.66 × 10
148
b − 4.49 ×
10
149
, −1.14 × 10
150
u
63
− 1.93 × 10
150
u
62
+ · · · + 4.19 × 10
150
a − 1.96 ×
10
152
, u
64
+ 2u
63
+ · · · + 171u + 37i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
7
=
0.271924u
63
+ 0.460353u
62
+ ··· + 44.0665u + 46.8772
0.0106657u
63
+ 0.0159802u
62
+ ··· + 13.7655u + 7.92425
a
11
=
u
−u
3
+ u
a
12
=
0.624613u
63
+ 1.10102u
62
+ ··· + 36.8238u + 101.708
0.00461596u
63
+ 0.0201036u
62
+ ··· − 5.67814u − 1.77195
a
6
=
0.261258u
63
+ 0.444372u
62
+ ··· + 30.3010u + 38.9530
0.0106657u
63
+ 0.0159802u
62
+ ··· + 13.7655u + 7.92425
a
2
=
0.0485882u
63
+ 0.0990616u
62
+ ··· + 25.2490u + 3.73071
0.0203311u
63
+ 0.00581512u
62
+ ··· + 9.57805u + 11.5410
a
1
=
0.0841362u
63
+ 0.140025u
62
+ ··· + 32.7070u + 15.2019
0.0299378u
63
+ 0.0305460u
62
+ ··· + 5.74066u + 10.4261
a
5
=
0.406605u
63
+ 0.742625u
62
+ ··· − 16.3394u + 64.2704
−0.0987727u
63
− 0.181070u
62
+ ··· + 3.66166u − 12.0388
a
9
=
0.614690u
63
+ 1.08226u
62
+ ··· + 40.7236u + 104.602
−0.0329619u
63
− 0.0652260u
62
+ ··· + 3.48648u − 2.55001
a
8
=
0.207145u
63
+ 0.346285u
62
+ ··· + 38.5161u + 33.4383
0.0910540u
63
+ 0.176548u
62
+ ··· − 11.9099u + 7.81179
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.168425u
63
− 0.321826u
62
+ ··· + 44.9179u − 8.92647
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
32
+ 7u
31
+ ··· + 12u + 1)
2
c
2
, c
3
, c
6
c
10
u
64
− 2u
63
+ ··· − 171u + 37
c
4
, c
7
u
64
− u
63
+ ··· − 4808u − 587
c
5
, c
12
(u
32
+ 5u
31
+ ··· − 69u − 8)
2
c
8
, c
11
u
64
+ 17u
62
+ ··· − 264620u + 37823
c
9
(u
32
+ 13u
31
+ ··· − 1313u − 169)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
32
− 9y
31
+ ··· − 46y + 1)
2
c
2
, c
3
, c
6
c
10
y
64
− 18y
63
+ ··· − 85481y + 1369
c
4
, c
7
y
64
+ 9y
63
+ ··· + 6985670y + 344569
c
5
, c
12
(y
32
+ 25y
31
+ ··· − 505y + 64)
2
c
8
, c
11
y
64
+ 34y
63
+ ··· − 493922520582y + 1430579329
c
9
(y
32
− 15y
31
+ ··· − 543335y + 28561)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.747581 + 0.648100I
a = −0.817423 − 1.099650I
b = −0.61201 − 1.28970I
−6.29180 − 0.24514I −1.25097 + 0.92202I
u = −0.747581 − 0.648100I
a = −0.817423 + 1.099650I
b = −0.61201 + 1.28970I
−6.29180 + 0.24514I −1.25097 − 0.92202I
u = 0.884153 + 0.502618I
a = 0.34258 − 1.42349I
b = −0.228782 + 0.015105I
−3.14442 + 2.14473I 8.00000 − 2.29641I
u = 0.884153 − 0.502618I
a = 0.34258 + 1.42349I
b = −0.228782 − 0.015105I
−3.14442 − 2.14473I 8.00000 + 2.29641I
u = −0.598567 + 0.826676I
a = 0.244371 + 0.711038I
b = 0.897842 + 1.021270I
−6.68309 − 1.04909I 0.34328 + 1.82313I
u = −0.598567 − 0.826676I
a = 0.244371 − 0.711038I
b = 0.897842 − 1.021270I
−6.68309 + 1.04909I 0.34328 − 1.82313I
u = −0.803262 + 0.664543I
a = 0.62981 − 1.29173I
b = 0.762751 − 0.155996I
2.72858 − 3.38419I 16.1240 + 2.3766I
u = −0.803262 − 0.664543I
a = 0.62981 + 1.29173I
b = 0.762751 + 0.155996I
2.72858 + 3.38419I 16.1240 − 2.3766I
u = 0.725397 + 0.757869I
a = 1.002150 − 0.379337I
b = 0.987211 − 0.961056I
−4.99655 − 2.48694I 2.71838 + 6.51745I
u = 0.725397 − 0.757869I
a = 1.002150 + 0.379337I
b = 0.987211 + 0.961056I
−4.99655 + 2.48694I 2.71838 − 6.51745I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.036330 + 0.282218I
a = 0.10487 − 1.70181I
b = 0.555751 − 0.728079I
−0.07031 − 6.41881I 9.84201 + 8.36999I
u = −1.036330 − 0.282218I
a = 0.10487 + 1.70181I
b = 0.555751 + 0.728079I
−0.07031 + 6.41881I 9.84201 − 8.36999I
u = 0.555751 + 0.728079I
a = −1.31008 − 1.51039I
b = −1.036330 − 0.282218I
−0.07031 + 6.41881I 9.84201 − 8.36999I
u = 0.555751 − 0.728079I
a = −1.31008 + 1.51039I
b = −1.036330 + 0.282218I
−0.07031 − 6.41881I 9.84201 + 8.36999I
u = −0.956175 + 0.585855I
a = −1.10599 − 1.51798I
b = 0.771652 − 0.999575I
−5.62629 − 4.62037I 0. + 5.91719I
u = −0.956175 − 0.585855I
a = −1.10599 + 1.51798I
b = 0.771652 + 0.999575I
−5.62629 + 4.62037I 0. − 5.91719I
u = −0.763512 + 0.372948I
a = −0.502038 − 0.729370I
b = 1.54016 − 0.18960I
1.90078 − 6.98033I 8.48263 + 9.40811I
u = −0.763512 − 0.372948I
a = −0.502038 + 0.729370I
b = 1.54016 + 0.18960I
1.90078 + 6.98033I 8.48263 − 9.40811I
u = −0.848626 + 0.788875I
a = −0.463802 − 0.431146I
b = −0.848626 − 0.788875I
−1.48320 8.00000 + 0.I
u = −0.848626 − 0.788875I
a = −0.463802 + 0.431146I
b = −0.848626 + 0.788875I
−1.48320 8.00000 + 0.I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.840232
a = −1.60863
b = 1.33920
5.92790 18.3780
u = −0.916724 + 0.760771I
a = −0.42171 − 1.47210I
b = 1.164150 − 0.693868I
−1.26936 − 5.84614I 0
u = −0.916724 − 0.760771I
a = −0.42171 + 1.47210I
b = 1.164150 + 0.693868I
−1.26936 + 5.84614I 0
u = −0.781283 + 0.173339I
a = 1.41438 + 0.92421I
b = −1.381380 − 0.269991I
1.96444 + 4.61759I 12.02099 + 3.00810I
u = −0.781283 − 0.173339I
a = 1.41438 − 0.92421I
b = −1.381380 + 0.269991I
1.96444 − 4.61759I 12.02099 − 3.00810I
u = 0.537679 + 1.075690I
a = −0.427102 + 0.566369I
b = −0.880132 + 0.860062I
−2.89973 − 5.13287I 0
u = 0.537679 − 1.075690I
a = −0.427102 − 0.566369I
b = −0.880132 − 0.860062I
−2.89973 + 5.13287I 0
u = 0.983968 + 0.716147I
a = 0.34588 − 1.65595I
b = −1.26383 − 0.93490I
−4.21523 + 8.10070I 0
u = 0.983968 − 0.716147I
a = 0.34588 + 1.65595I
b = −1.26383 + 0.93490I
−4.21523 − 8.10070I 0
u = 0.762751 + 0.155996I
a = 0.06884 − 1.92313I
b = −0.803262 − 0.664543I
2.72858 + 3.38419I 16.1240 − 2.3766I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.762751 − 0.155996I
a = 0.06884 + 1.92313I
b = −0.803262 + 0.664543I
2.72858 − 3.38419I 16.1240 + 2.3766I
u = −0.880132 + 0.860062I
a = 0.399579 + 0.566471I
b = 0.537679 + 1.075690I
−2.89973 − 5.13287I 0
u = −0.880132 − 0.860062I
a = 0.399579 − 0.566471I
b = 0.537679 − 1.075690I
−2.89973 + 5.13287I 0
u = 0.771652 + 0.999575I
a = 0.43843 − 1.60921I
b = −0.956175 − 0.585855I
−5.62629 + 4.62037I 0
u = 0.771652 − 0.999575I
a = 0.43843 + 1.60921I
b = −0.956175 + 0.585855I
−5.62629 − 4.62037I 0
u = 0.086806 + 1.285450I
a = 0.352088 − 0.327075I
b = 0.446778 − 0.106968I
−4.09830 − 1.29586I 0
u = 0.086806 − 1.285450I
a = 0.352088 + 0.327075I
b = 0.446778 + 0.106968I
−4.09830 + 1.29586I 0
u = 0.982919 + 0.838355I
a = −0.520314 + 0.687373I
b = −0.650640 + 1.170750I
−7.61349 + 10.61140I 0
u = 0.982919 − 0.838355I
a = −0.520314 − 0.687373I
b = −0.650640 − 1.170750I
−7.61349 − 10.61140I 0
u = 1.33920
a = −1.00927
b = 0.840232
5.92790 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.650640 + 1.170750I
a = 0.550727 + 0.622987I
b = 0.982919 + 0.838355I
−7.61349 + 10.61140I 0
u = −0.650640 − 1.170750I
a = 0.550727 − 0.622987I
b = 0.982919 − 0.838355I
−7.61349 − 10.61140I 0
u = 1.164150 + 0.693868I
a = 0.566257 − 1.221150I
b = −0.916724 − 0.760771I
−1.26936 + 5.84614I 0
u = 1.164150 − 0.693868I
a = 0.566257 + 1.221150I
b = −0.916724 + 0.760771I
−1.26936 − 5.84614I 0
u = 0.897842 + 1.021270I
a = −0.479918 + 0.296866I
b = −0.598567 + 0.826676I
−6.68309 − 1.04909I 0
u = 0.897842 − 1.021270I
a = −0.479918 − 0.296866I
b = −0.598567 − 0.826676I
−6.68309 + 1.04909I 0
u = 0.571558 + 0.247045I
a = 0.902392 − 0.212211I
b = −1.51966 + 0.17892I
4.37128 + 1.08985I 2.66044 − 9.56608I
u = 0.571558 − 0.247045I
a = 0.902392 + 0.212211I
b = −1.51966 − 0.17892I
4.37128 − 1.08985I 2.66044 + 9.56608I
u = 0.987211 + 0.961056I
a = 0.282372 − 0.765497I
b = 0.725397 − 0.757869I
−4.99655 + 2.48694I 0
u = 0.987211 − 0.961056I
a = 0.282372 + 0.765497I
b = 0.725397 + 0.757869I
−4.99655 − 2.48694I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.381380 + 0.269991I
a = 0.947212 − 0.160105I
b = −0.781283 − 0.173339I
1.96444 − 4.61759I 0
u = −1.381380 − 0.269991I
a = 0.947212 + 0.160105I
b = −0.781283 + 0.173339I
1.96444 + 4.61759I 0
u = −0.61201 + 1.28970I
a = −0.582538 − 0.749981I
b = −0.747581 − 0.648100I
−6.29180 + 0.24514I 0
u = −0.61201 − 1.28970I
a = −0.582538 + 0.749981I
b = −0.747581 + 0.648100I
−6.29180 − 0.24514I 0
u = −1.51966 + 0.17892I
a = −0.361017 − 0.109388I
b = 0.571558 + 0.247045I
4.37128 + 1.08985I 0
u = −1.51966 − 0.17892I
a = −0.361017 + 0.109388I
b = 0.571558 − 0.247045I
4.37128 − 1.08985I 0
u = 0.446778 + 0.106968I
a = 0.739730 − 1.126570I
b = 0.086806 − 1.285450I
−4.09830 + 1.29586I 13.7807 − 5.0145I
u = 0.446778 − 0.106968I
a = 0.739730 + 1.126570I
b = 0.086806 + 1.285450I
−4.09830 − 1.29586I 13.7807 + 5.0145I
u = 1.54016 + 0.18960I
a = 0.390037 − 0.288022I
b = −0.763512 − 0.372948I
1.90078 + 6.98033I 0
u = 1.54016 − 0.18960I
a = 0.390037 + 0.288022I
b = −0.763512 + 0.372948I
1.90078 − 6.98033I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.26383 + 0.93490I
a = −0.257820 − 1.283980I
b = 0.983968 − 0.716147I
−4.21523 − 8.10070I 0
u = −1.26383 − 0.93490I
a = −0.257820 + 1.283980I
b = 0.983968 + 0.716147I
−4.21523 + 8.10070I 0
u = −0.228782 + 0.015105I
a = −4.74409 + 4.43535I
b = 0.884153 + 0.502618I
−3.14442 + 2.14473I 8.08474 − 2.29641I
u = −0.228782 − 0.015105I
a = −4.74409 − 4.43535I
b = 0.884153 − 0.502618I
−3.14442 − 2.14473I 8.08474 + 2.29641I
17
III. I
u
3
= hb + u, 106u
13
− 38u
12
+ · · · + 29a + 111, u
14
− 4u
12
+ · · · + u + 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
7
=
−3.65517u
13
+ 1.31034u
12
+ ··· + 0.586207u − 3.82759
−u
a
11
=
u
−u
3
+ u
a
12
=
1.65517u
13
+ 0.689655u
12
+ ··· − 7.58621u + 4.82759
1.13793u
13
− 0.275862u
12
+ ··· + 0.0344828u + 1.06897
a
6
=
−3.65517u
13
+ 1.31034u
12
+ ··· + 1.58621u − 3.82759
−u
a
2
=
−1.31034u
13
+ 1.62069u
12
+ ··· + 0.172414u − 2.65517
u
2
a
1
=
−1.55172u
13
+ 2.10345u
12
+ ··· − 0.137931u − 4.27586
−0.0344828u
13
+ 0.0689655u
12
+ ··· + 0.241379u + 0.482759
a
5
=
3.79310u
13
− 3.58621u
12
+ ··· + 1.44828u + 5.89655
−0.137931u
13
+ 0.275862u
12
+ ··· − 0.0344828u − 1.06897
a
9
=
0.241379u
13
+ 1.51724u
12
+ ··· − 12.6897u + 4.62069
1.62069u
13
− 0.241379u
12
+ ··· − 1.34483u + 1.31034
a
8
=
−0.275862u
13
+ 0.551724u
12
+ ··· − 5.06897u + 0.862069
0.482759u
13
+ 0.0344828u
12
+ ··· − 0.379310u + 0.241379
(ii) Obstruction class = 1
(iii) Cusp Shapes =
118
29
u
13
−
207
29
u
12
− 18u
11
+ 28u
10
+
1002
29
u
9
−
1511
29
u
8
−
1261
29
u
7
+
1944
29
u
6
+
327
29
u
5
−
830
29
u
4
+
591
29
u
3
−
749
29
u
2
+
44
29
u +
581
29
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
− 4u
13
+ ··· − 2u + 1
c
2
, c
10
u
14
− 4u
12
+ 8u
10
− 10u
8
− u
7
+ 5u
6
+ u
5
+ 2u
4
+ u
3
− 2u
2
− u + 1
c
3
, c
6
u
14
− 4u
12
+ 8u
10
− 10u
8
+ u
7
+ 5u
6
− u
5
+ 2u
4
− u
3
− 2u
2
+ u + 1
c
4
, c
7
u
14
+ u
11
+ 5u
10
− u
9
+ u
7
+ 3u
6
− 6u
5
+ u
4
+ 2u
3
+ 2u
2
− 3u + 1
c
5
u
14
+ 4u
13
+ ··· + 8u + 1
c
8
, c
11
u
14
+ 2u
13
+ ··· + 27u + 7
c
9
u
14
+ 14u
13
+ ··· + 2333u + 319
c
12
u
14
− 4u
13
+ ··· − 8u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
14
+ 3y
11
+ ··· − 2y + 1
c
2
, c
3
, c
6
c
10
y
14
− 8y
13
+ ··· − 5y + 1
c
4
, c
7
y
14
+ 10y
12
+ ··· − 5y + 1
c
5
, c
12
y
14
+ 10y
13
+ ··· + 4y + 1
c
8
, c
11
y
14
+ 12y
13
+ ··· − y + 49
c
9
y
14
+ 10y
13
+ ··· − 227877y + 101761
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.705264 + 0.481548I
a = −0.65418 − 1.69656I
b = −0.705264 − 0.481548I
1.87287 + 3.91500I 7.22173 − 7.63901I
u = 0.705264 − 0.481548I
a = −0.65418 + 1.69656I
b = −0.705264 + 0.481548I
1.87287 − 3.91500I 7.22173 + 7.63901I
u = 1.197260 + 0.164540I
a = 0.544579 − 0.736189I
b = −1.197260 − 0.164540I
3.96804 + 6.37801I 14.6039 − 5.9971I
u = 1.197260 − 0.164540I
a = 0.544579 + 0.736189I
b = −1.197260 + 0.164540I
3.96804 − 6.37801I 14.6039 + 5.9971I
u = 1.020540 + 0.674600I
a = 0.91974 − 1.32074I
b = −1.020540 − 0.674600I
−3.82504 + 4.57037I 9.01908 − 5.07868I
u = 1.020540 − 0.674600I
a = 0.91974 + 1.32074I
b = −1.020540 + 0.674600I
−3.82504 − 4.57037I 9.01908 + 5.07868I
u = −0.032890 + 0.769702I
a = −0.543523 − 0.781156I
b = 0.032890 − 0.769702I
−4.81955 + 1.15266I 0.22976 − 1.43233I
u = −0.032890 − 0.769702I
a = −0.543523 + 0.781156I
b = 0.032890 + 0.769702I
−4.81955 − 1.15266I 0.22976 + 1.43233I
u = −1.249640 + 0.050920I
a = −0.990118 + 0.119715I
b = 1.249640 − 0.050920I
6.96809 + 0.13335I 21.1617 − 9.9291I
u = −1.249640 − 0.050920I
a = −0.990118 − 0.119715I
b = 1.249640 + 0.050920I
6.96809 − 0.13335I 21.1617 + 9.9291I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.062670 + 0.800901I
a = −0.25516 − 1.44180I
b = 1.062670 − 0.800901I
−3.51744 − 7.29600I 8.08201 + 4.40748I
u = −1.062670 − 0.800901I
a = −0.25516 + 1.44180I
b = 1.062670 + 0.800901I
−3.51744 + 7.29600I 8.08201 − 4.40748I
u = −0.577867 + 0.218364I
a = 0.47866 − 4.77205I
b = 0.577867 − 0.218364I
−2.29191 − 5.40173I 7.1818 + 12.6437I
u = −0.577867 − 0.218364I
a = 0.47866 + 4.77205I
b = 0.577867 + 0.218364I
−2.29191 + 5.40173I 7.1818 − 12.6437I
22
IV. I
u
4
= hu
11
− 4u
9
+ 5u
7
− 3u
5
+ 5u
3
+ b − 4u, −3u
11
− 4u
10
+ · · · + 2a +
8, u
12
− 4u
10
+ 5u
8
− 3u
6
+ 5u
4
− 4u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
7
=
3
2
u
11
+ 2u
10
+ ··· − 4u − 4
−u
11
+ 4u
9
− 5u
7
+ 3u
5
− 5u
3
+ 4u
a
11
=
u
−u
3
+ u
a
12
=
−
5
2
u
11
−
7
2
u
10
+ ··· +
13
2
u +
13
2
2u
11
+ u
10
+ ··· −
11
2
u − 2
a
6
=
5
2
u
11
+ 2u
10
+ ··· − 8u − 4
−u
11
+ 4u
9
− 5u
7
+ 3u
5
− 5u
3
+ 4u
a
2
=
4u
11
+
5
2
u
10
+ ··· −
15
2
u − 7
−u
10
+ 4u
8
− 5u
6
+ 3u
4
− 5u
2
+ 4
a
1
=
6u
11
+ 2u
10
+ ··· −
23
2
u −
11
2
−u
11
− u
10
+ ··· + 2u +
7
2
a
5
=
−
1
2
u
10
− u
9
+ ··· − 4u −
3
2
5
2
u
11
+
3
2
u
10
+ ··· − 3u −
3
2
a
9
=
−2u
11
− 3u
10
+ ··· +
7
2
u +
11
2
3
2
u
11
+ 2u
10
+ ··· − 3u − 4
a
8
=
−
7
2
u
11
−
11
2
u
10
+ ··· + 3u +
17
2
3u
11
+ 4u
10
+ ··· − 5u −
15
2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 12u
11
+ 9u
10
− 43u
9
− 31u
8
+ 42u
7
+ 25u
6
− 17u
5
− 7u
4
+ 52u
3
+ 41u
2
− 27u − 5
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ u
5
− 2u
3
+ u + 1)
2
c
2
, c
3
, c
6
c
10
u
12
− 4u
10
+ 5u
8
− 3u
6
+ 5u
4
− 4u
2
+ 1
c
4
, c
7
u
12
− u
11
+ 2u
10
+ 2u
9
+ 4u
8
− u
7
+ 2u
6
− u
5
+ 4u
4
+ 2u
3
+ 2u
2
− u + 1
c
5
(u
6
− 2u
5
+ 4u
4
− 5u
3
+ 5u
2
− 4u + 2)
2
c
8
, c
11
u
12
− 6u
11
+ ··· − 5u + 1
c
9
(u
6
− u
5
+ 2u
3
− u + 1)
2
c
12
(u
6
+ 2u
5
+ 4u
4
+ 5u
3
+ 5u
2
+ 4u + 2)
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
(y
6
− y
5
+ 4y
4
− 4y
3
+ 4y
2
− y + 1)
2
c
2
, c
3
, c
6
c
10
(y
6
− 4y
5
+ 5y
4
− 3y
3
+ 5y
2
− 4y + 1)
2
c
4
, c
7
y
12
+ 3y
11
+ ··· + 3y + 1
c
5
, c
12
(y
6
+ 4y
5
+ 6y
4
+ 3y
3
+ y
2
+ 4y + 4)
2
c
8
, c
11
y
12
− 4y
10
+ ··· − y + 1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.540561 + 0.841305I
a = 0.156629 − 0.987658I
b = 0.540561 − 0.841305I
−4.99541 + 1.18132I 3.40277 − 1.32440I
u = 0.540561 − 0.841305I
a = 0.156629 + 0.987658I
b = 0.540561 + 0.841305I
−4.99541 − 1.18132I 3.40277 + 1.32440I
u = −0.540561 + 0.841305I
a = −0.833234 − 0.552921I
b = −0.540561 − 0.841305I
−4.99541 + 1.18132I 3.40277 − 1.32440I
u = −0.540561 − 0.841305I
a = −0.833234 + 0.552921I
b = −0.540561 + 0.841305I
−4.99541 − 1.18132I 3.40277 + 1.32440I
u = −0.696578 + 0.098981I
a = 0.829073 − 0.673309I
b = −1.40718 − 0.19996I
4.73737 − 0.78507I 17.3864 − 1.2123I
u = −0.696578 − 0.098981I
a = 0.829073 + 0.673309I
b = −1.40718 + 0.19996I
4.73737 + 0.78507I 17.3864 + 1.2123I
u = 0.696578 + 0.098981I
a = −1.07796 + 1.55420I
b = 1.40718 − 0.19996I
1.90298 − 5.20040I 11.2108 + 9.9662I
u = 0.696578 − 0.098981I
a = −1.07796 − 1.55420I
b = 1.40718 + 0.19996I
1.90298 + 5.20040I 11.2108 − 9.9662I
u = 1.40718 + 0.19996I
a = −0.301314 + 0.434433I
b = 0.696578 − 0.098981I
4.73737 − 0.78507I 17.3864 − 1.2123I
u = 1.40718 − 0.19996I
a = −0.301314 − 0.434433I
b = 0.696578 + 0.098981I
4.73737 + 0.78507I 17.3864 + 1.2123I
26
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.40718 + 0.19996I
a = 0.726806 − 0.590256I
b = −0.696578 − 0.098981I
1.90298 − 5.20040I 11.2108 + 9.9662I
u = −1.40718 − 0.19996I
a = 0.726806 + 0.590256I
b = −0.696578 + 0.098981I
1.90298 + 5.20040I 11.2108 − 9.9662I
27
V. I
u
5
= hb + u − 1, a + u − 1, u
2
− u + 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u + 1
a
7
=
−u + 1
−u + 1
a
11
=
u
u + 1
a
12
=
0
1
a
6
=
0
−u + 1
a
2
=
1
−u
a
1
=
0
−1
a
5
=
0
−u + 1
a
9
=
−u + 1
1
a
8
=
−u + 1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
(u + 1)
2
c
2
, c
3
, c
4
c
6
, c
7
, c
8
c
10
, c
11
u
2
+ u + 1
c
5
, c
12
u
2
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
(y − 1)
2
c
2
, c
3
, c
4
c
6
, c
7
, c
8
c
10
, c
11
y
2
+ y + 1
c
5
, c
12
y
2
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.500000 − 0.866025I
b = 0.500000 − 0.866025I
−3.28987 6.00000
u = 0.500000 − 0.866025I
a = 0.500000 + 0.866025I
b = 0.500000 + 0.866025I
−3.28987 6.00000
31
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u + 1)
2
)(u
6
+ u
5
− 2u
3
+ u + 1)
2
(u
14
− 4u
13
+ ··· − 2u + 1)
· (u
26
− 21u
25
+ ··· + 7680u − 512)(u
32
+ 7u
31
+ ··· + 12u + 1)
2
c
2
, c
10
(u
2
+ u + 1)(u
12
− 4u
10
+ 5u
8
− 3u
6
+ 5u
4
− 4u
2
+ 1)
· (u
14
− 4u
12
+ 8u
10
− 10u
8
− u
7
+ 5u
6
+ u
5
+ 2u
4
+ u
3
− 2u
2
− u + 1)
· (u
26
− 7u
24
+ ··· + 2u − 1)(u
64
− 2u
63
+ ··· − 171u + 37)
c
3
, c
6
(u
2
+ u + 1)(u
12
− 4u
10
+ 5u
8
− 3u
6
+ 5u
4
− 4u
2
+ 1)
· (u
14
− 4u
12
+ 8u
10
− 10u
8
+ u
7
+ 5u
6
− u
5
+ 2u
4
− u
3
− 2u
2
+ u + 1)
· (u
26
− 7u
24
+ ··· + 2u − 1)(u
64
− 2u
63
+ ··· − 171u + 37)
c
4
, c
7
(u
2
+ u + 1)
· (u
12
− u
11
+ 2u
10
+ 2u
9
+ 4u
8
− u
7
+ 2u
6
− u
5
+ 4u
4
+ 2u
3
+ 2u
2
− u + 1)
· (u
14
+ u
11
+ 5u
10
− u
9
+ u
7
+ 3u
6
− 6u
5
+ u
4
+ 2u
3
+ 2u
2
− 3u + 1)
· (u
26
+ 5u
24
+ ··· − 8u + 1)(u
64
− u
63
+ ··· − 4808u − 587)
c
5
u
2
(u
6
− 2u
5
+ ··· − 4u + 2)
2
(u
14
+ 4u
13
+ ··· + 8u + 1)
· (u
26
− 11u
25
+ ··· + 304u − 24)(u
32
+ 5u
31
+ ··· − 69u − 8)
2
c
8
, c
11
(u
2
+ u + 1)(u
12
− 6u
11
+ ··· − 5u + 1)(u
14
+ 2u
13
+ ··· + 27u + 7)
· (u
26
− 2u
25
+ ··· − 80u + 19)(u
64
+ 17u
62
+ ··· − 264620u + 37823)
c
9
((u + 1)
2
)(u
6
− u
5
+ 2u
3
− u + 1)
2
(u
14
+ 14u
13
+ ··· + 2333u + 319)
· (u
26
− 21u
25
+ ··· − 16284u + 1096)
· (u
32
+ 13u
31
+ ··· − 1313u − 169)
2
c
12
u
2
(u
6
+ 2u
5
+ ··· + 4u + 2)
2
(u
14
− 4u
13
+ ··· − 8u + 1)
· (u
26
− 11u
25
+ ··· + 304u − 24)(u
32
+ 5u
31
+ ··· − 69u − 8)
2
32
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
2
(y
6
− y
5
+ 4y
4
− 4y
3
+ 4y
2
− y + 1)
2
· (y
14
+ 3y
11
+ ··· − 2y + 1)(y
26
− y
25
+ ··· − 3932160y + 262144)
· (y
32
− 9y
31
+ ··· − 46y + 1)
2
c
2
, c
3
, c
6
c
10
(y
2
+ y + 1)(y
6
− 4y
5
+ 5y
4
− 3y
3
+ 5y
2
− 4y + 1)
2
· (y
14
− 8y
13
+ ··· − 5y + 1)(y
26
− 14y
25
+ ··· − 24y + 1)
· (y
64
− 18y
63
+ ··· − 85481y + 1369)
c
4
, c
7
(y
2
+ y + 1)(y
12
+ 3y
11
+ ··· + 3y + 1)(y
14
+ 10y
12
+ ··· − 5y + 1)
· (y
26
+ 10y
25
+ ··· − 36y + 1)(y
64
+ 9y
63
+ ··· + 6985670y + 344569)
c
5
, c
12
y
2
(y
6
+ 4y
5
+ ··· + 4y + 4)
2
(y
14
+ 10y
13
+ ··· + 4y + 1)
· (y
26
+ 17y
25
+ ··· − 2656y + 576)(y
32
+ 25y
31
+ ··· − 505y + 64)
2
c
8
, c
11
(y
2
+ y + 1)(y
12
− 4y
10
+ ··· − y + 1)(y
14
+ 12y
13
+ ··· − y + 49)
· (y
26
+ 22y
25
+ ··· − 7236y + 361)
· (y
64
+ 34y
63
+ ··· − 493922520582y + 1430579329)
c
9
(y − 1)
2
(y
6
− y
5
+ 4y
4
− 4y
3
+ 4y
2
− y + 1)
2
· (y
14
+ 10y
13
+ ··· − 227877y + 101761)
· (y
26
+ 5y
25
+ ··· − 35876688y + 1201216)
· (y
32
− 15y
31
+ ··· − 543335y + 28561)
2
33
