12a
1260
(K12a
1260
)
A knot diagram
1
Linearized knot diagam
5 7 9 10 11 12 3 1 4 2 6 8
Solving Sequence
3,9
4 10
1,5
8 7 2 11 12 6
c
3
c
9
c
4
c
8
c
7
c
2
c
10
c
12
c
6
c
1
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.25260 × 10
169
u
87
+ 4.64928 × 10
169
u
86
+ ··· + 1.00310 × 10
170
b − 5.41733 × 10
169
,
− 1.51686 × 10
169
u
87
− 8.93383 × 10
169
u
86
+ ··· + 1.00310 × 10
170
a − 4.70692 × 10
171
,
u
88
− 45u
86
+ ··· + 44u − 1i
I
u
2
= h−29u
15
− 34u
14
+ ··· + 73b − 87, −82u
15
+ 70u
14
+ ··· + 73a + 119,
u
16
− 9u
14
+ 34u
12
− u
11
− 72u
10
+ 7u
9
+ 95u
8
− 19u
7
− 76u
6
+ 24u
5
+ 26u
4
− 12u
3
+ 4u
2
− 1i
I
u
3
= hb, a − 1, u + 1i
I
u
4
= hb − 1, a, u + 1i
I
u
5
= hb + 1, a − 1, u − 1i
I
v
1
= ha, b − 1, v + 1i
* 6 irreducible components of dim
C
= 0, with total 108 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
= h−4.25 × 10
169
u
87
+ 4.65 × 10
169
u
86
+ · · · + 1.00 × 10
170
b − 5.42 ×
10
169
, −1.52 × 10
169
u
87
− 8.93 × 10
169
u
86
+ · · · + 1.00 × 10
170
a − 4.71 ×
10
171
, u
88
− 45u
86
+ · · · + 44u − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
10
=
u
−u
3
+ u
a
1
=
0.151218u
87
+ 0.890626u
86
+ ··· + 92.0941u + 46.9239
0.423948u
87
− 0.463494u
86
+ ··· + 16.2841u + 0.540062
a
5
=
−u
2
+ 1
u
4
− 2u
2
a
8
=
0.289659u
87
+ 1.45974u
86
+ ··· + 185.969u + 46.5951
0.352924u
87
− 0.532037u
86
+ ··· + 16.0338u + 0.601752
a
7
=
−0.0632654u
87
+ 1.99177u
86
+ ··· + 169.935u + 45.9934
0.352924u
87
− 0.532037u
86
+ ··· + 16.0338u + 0.601752
a
2
=
−0.232052u
87
+ 1.30060u
86
+ ··· + 80.2068u + 46.2469
0.257568u
87
− 0.257637u
86
+ ··· + 11.0024u + 0.658405
a
11
=
2.82460u
87
− 2.45778u
86
+ ··· + 259.385u + 42.0583
−0.158379u
87
+ 0.283717u
86
+ ··· − 2.29390u + 0.979181
a
12
=
2.32651u
87
− 2.66880u
86
+ ··· + 154.491u − 6.36215
−0.123834u
87
+ 0.152593u
86
+ ··· + 0.0420976u − 0.0772851
a
6
=
2.90389u
87
− 3.07386u
86
+ ··· + 116.798u + 43.8565
−0.0923931u
87
+ 0.118452u
86
+ ··· − 3.90791u + 0.961875
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.12053u
87
− 1.26633u
86
+ ··· + 131.631u − 8.78215
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
88
+ 8u
87
+ ··· + 24u − 7
c
2
, c
7
u
88
+ 2u
87
+ ··· + 2042u + 301
c
3
, c
4
, c
9
u
88
− 45u
86
+ ··· − 44u − 1
c
5
, c
6
, c
11
u
88
− 45u
86
+ ··· + 44u − 1
c
8
, c
12
u
88
− 2u
87
+ ··· − 2042u + 301
c
10
u
88
− 8u
87
+ ··· − 24u − 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
88
− 8y
87
+ ··· − 8654y + 49
c
2
, c
7
, c
8
c
12
y
88
− 52y
87
+ ··· − 2985028y + 90601
c
3
, c
4
, c
5
c
6
, c
9
, c
11
y
88
− 90y
87
+ ··· − 2260y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.544396 + 0.875051I
a = 0.172978 − 1.352960I
b = −0.73139 − 1.57973I
−6.7713 + 12.4764I 0
u = 0.544396 − 0.875051I
a = 0.172978 + 1.352960I
b = −0.73139 + 1.57973I
−6.7713 − 12.4764I 0
u = −0.956317
a = 0.992268
b = 0.0789854
1.64464 0
u = −0.550886 + 0.922977I
a = 0.155827 + 1.167370I
b = −0.80126 + 1.56648I
− 7.97391I 0
u = −0.550886 − 0.922977I
a = 0.155827 − 1.167370I
b = −0.80126 − 1.56648I
7.97391I 0
u = 1.044190 + 0.280270I
a = 1.230330 − 0.059806I
b = 0.217785 − 0.468266I
−3.22549 − 0.27919I 0
u = 1.044190 − 0.280270I
a = 1.230330 + 0.059806I
b = 0.217785 + 0.468266I
−3.22549 + 0.27919I 0
u = 0.626742 + 0.927794I
a = −0.821523 + 0.627692I
b = −0.11768 + 1.41906I
−6.58637 − 6.59944I 0
u = 0.626742 − 0.927794I
a = −0.821523 − 0.627692I
b = −0.11768 − 1.41906I
−6.58637 + 6.59944I 0
u = −0.526613 + 0.684785I
a = −0.70312 − 1.33388I
b = −0.07245 − 1.51969I
−10.02960 − 5.54243I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.526613 − 0.684785I
a = −0.70312 + 1.33388I
b = −0.07245 + 1.51969I
−10.02960 + 5.54243I 0
u = −0.805240
a = 0.391426
b = 0.460790
1.79603 4.53920
u = −0.490581 + 0.616011I
a = 1.06304 + 1.42760I
b = −0.392573 + 1.100110I
−10.08020 + 1.09732I −7.74441 + 1.20458I
u = −0.490581 − 0.616011I
a = 1.06304 − 1.42760I
b = −0.392573 − 1.100110I
−10.08020 − 1.09732I −7.74441 − 1.20458I
u = 0.380832 + 0.662466I
a = −0.403337 + 1.333500I
b = −0.048598 + 1.374050I
−3.00788 + 3.35782I −5.57246 − 6.97970I
u = 0.380832 − 0.662466I
a = −0.403337 − 1.333500I
b = −0.048598 − 1.374050I
−3.00788 − 3.35782I −5.57246 + 6.97970I
u = 0.626620 + 0.396753I
a = −0.672933 − 0.809314I
b = 0.130586 + 0.547089I
3.00788 + 3.35782I 5.57246 − 6.97970I
u = 0.626620 − 0.396753I
a = −0.672933 + 0.809314I
b = 0.130586 − 0.547089I
3.00788 − 3.35782I 5.57246 + 6.97970I
u = 0.632191 + 0.322594I
a = 1.203060 + 0.462563I
b = 0.381995 − 0.016239I
−3.16087 + 0.64620I −1.05710 − 2.19885I
u = 0.632191 − 0.322594I
a = 1.203060 − 0.462563I
b = 0.381995 + 0.016239I
−3.16087 − 0.64620I −1.05710 + 2.19885I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.290410 + 0.165984I
a = −0.757711 − 1.016430I
b = 0.65828 − 1.36329I
−2.30892 − 6.65783I 0
u = −1.290410 − 0.165984I
a = −0.757711 + 1.016430I
b = 0.65828 + 1.36329I
−2.30892 + 6.65783I 0
u = 0.256030 + 0.614830I
a = 0.80597 + 1.28225I
b = 0.303511 + 0.806251I
−4.48010 + 2.66437I −3.74602 − 3.99855I
u = 0.256030 − 0.614830I
a = 0.80597 − 1.28225I
b = 0.303511 − 0.806251I
−4.48010 − 2.66437I −3.74602 + 3.99855I
u = −1.332760 + 0.075603I
a = 0.383553 − 0.133032I
b = −0.72980 − 2.09934I
−0.73946 − 5.72891I 0
u = −1.332760 − 0.075603I
a = 0.383553 + 0.133032I
b = −0.72980 + 2.09934I
−0.73946 + 5.72891I 0
u = 0.046403 + 0.655074I
a = 0.97658 + 2.01070I
b = 0.346649 + 1.136090I
−6.33662 + 3.76157I −7.20888 − 3.14007I
u = 0.046403 − 0.655074I
a = 0.97658 − 2.01070I
b = 0.346649 − 1.136090I
−6.33662 − 3.76157I −7.20888 + 3.14007I
u = 1.351740 + 0.050237I
a = 0.442915 + 0.276216I
b = −0.28906 + 1.51830I
4.48010 + 2.66437I 0
u = 1.351740 − 0.050237I
a = 0.442915 − 0.276216I
b = −0.28906 − 1.51830I
4.48010 − 2.66437I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.056050 + 0.642532I
a = −0.290198 + 0.685997I
b = −0.896143 + 1.090400I
−4.40917 + 3.69922I −5.51020 − 1.14634I
u = −0.056050 − 0.642532I
a = −0.290198 − 0.685997I
b = −0.896143 − 1.090400I
−4.40917 − 3.69922I −5.51020 + 1.14634I
u = −0.460085 + 0.450465I
a = −1.32663 + 1.18708I
b = −0.076543 − 0.470061I
−3.10880 − 6.58471I −0.37873 + 8.01558I
u = −0.460085 − 0.450465I
a = −1.32663 − 1.18708I
b = −0.076543 + 0.470061I
−3.10880 + 6.58471I −0.37873 − 8.01558I
u = −1.36627
a = −1.73217
b = 0.905398
−5.98531 0
u = −0.065579 + 1.364860I
a = −0.206231 − 0.675181I
b = −0.46530 − 1.83137I
0.948873I 0
u = −0.065579 − 1.364860I
a = −0.206231 + 0.675181I
b = −0.46530 + 1.83137I
− 0.948873I 0
u = −1.369400 + 0.028835I
a = 0.631175 + 0.431447I
b = −0.235673 + 0.962981I
3.16087 − 0.64620I 0
u = −1.369400 − 0.028835I
a = 0.631175 − 0.431447I
b = −0.235673 − 0.962981I
3.16087 + 0.64620I 0
u = 1.363230 + 0.171215I
a = −0.660268 + 0.782881I
b = 0.82120 + 1.43394I
3.73467 + 5.37166I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.363230 − 0.171215I
a = −0.660268 − 0.782881I
b = 0.82120 − 1.43394I
3.73467 − 5.37166I 0
u = 1.389570 + 0.149869I
a = 0.927337 − 0.538716I
b = −0.314300 − 0.811935I
−4.13711 + 1.41359I 0
u = 1.389570 − 0.149869I
a = 0.927337 + 0.538716I
b = −0.314300 + 0.811935I
−4.13711 − 1.41359I 0
u = 1.372250 + 0.279237I
a = −0.344312 + 0.347855I
b = 0.74007 + 1.38034I
4.40917 + 3.69922I 0
u = 1.372250 − 0.279237I
a = −0.344312 − 0.347855I
b = 0.74007 − 1.38034I
4.40917 − 3.69922I 0
u = 1.407000 + 0.024006I
a = −1.034020 + 0.207877I
b = 1.75773 + 0.53215I
3.22549 + 0.27919I 0
u = 1.407000 − 0.024006I
a = −1.034020 − 0.207877I
b = 1.75773 − 0.53215I
3.22549 − 0.27919I 0
u = −1.388970 + 0.229409I
a = −0.261110 − 0.746581I
b = 0.79581 − 1.49955I
0.73946 − 5.72891I 0
u = −1.388970 − 0.229409I
a = −0.261110 + 0.746581I
b = 0.79581 + 1.49955I
0.73946 + 5.72891I 0
u = −0.130840 + 0.573179I
a = 0.65890 − 1.98220I
b = 0.322237 − 1.086800I
−0.97901 − 2.75841I −5.08126 + 8.14150I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.130840 − 0.573179I
a = 0.65890 + 1.98220I
b = 0.322237 + 1.086800I
−0.97901 + 2.75841I −5.08126 − 8.14150I
u = −1.42591 + 0.06818I
a = −0.840803 − 0.415925I
b = 1.60696 − 1.35434I
6.33662 − 3.76157I 0
u = −1.42591 − 0.06818I
a = −0.840803 + 0.415925I
b = 1.60696 + 1.35434I
6.33662 + 3.76157I 0
u = 1.46647 + 0.10093I
a = −0.704842 + 0.468820I
b = 1.31192 + 1.93849I
2.30892 + 6.65783I 0
u = 1.46647 − 0.10093I
a = −0.704842 − 0.468820I
b = 1.31192 − 1.93849I
2.30892 − 6.65783I 0
u = 1.48446 + 0.17012I
a = −0.374254 − 1.009550I
b = −0.110571 − 0.245328I
3.24810 + 8.93881I 0
u = 1.48446 − 0.17012I
a = −0.374254 + 1.009550I
b = −0.110571 + 0.245328I
3.24810 − 8.93881I 0
u = −1.48499 + 0.22879I
a = −0.609177 − 0.432217I
b = 0.57535 − 1.65583I
3.10880 − 6.58471I 0
u = −1.48499 − 0.22879I
a = −0.609177 + 0.432217I
b = 0.57535 + 1.65583I
3.10880 + 6.58471I 0
u = −1.52326 + 0.15630I
a = −0.269851 + 0.813956I
b = −0.008636 + 0.188776I
10.02960 − 5.54243I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.52326 − 0.15630I
a = −0.269851 − 0.813956I
b = −0.008636 − 0.188776I
10.02960 + 5.54243I 0
u = 0.468416
a = 2.02913
b = −0.161207
−1.79603 −4.53920
u = −0.182968 + 0.414714I
a = 0.673912 − 0.473992I
b = −0.069737 − 0.313513I
− 0.980224I 0. + 6.52429I
u = −0.182968 − 0.414714I
a = 0.673912 + 0.473992I
b = −0.069737 + 0.313513I
0.980224I 0. − 6.52429I
u = −1.55146 + 0.00460I
a = 0.297746 + 0.497410I
b = 0.480380 + 0.525913I
4.13711 + 1.41359I 0
u = −1.55146 − 0.00460I
a = 0.297746 − 0.497410I
b = 0.480380 − 0.525913I
4.13711 − 1.41359I 0
u = 1.53602 + 0.23736I
a = −0.684226 + 0.390252I
b = 0.35439 + 1.70908I
−3.24810 + 8.93881I 0
u = 1.53602 − 0.23736I
a = −0.684226 − 0.390252I
b = 0.35439 − 1.70908I
−3.24810 − 8.93881I 0
u = 1.57317 + 0.11593I
a = −0.111468 − 0.568515I
b = 0.197956 − 0.165965I
10.08020 + 1.09732I 0
u = 1.57317 − 0.11593I
a = −0.111468 + 0.568515I
b = 0.197956 + 0.165965I
10.08020 − 1.09732I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.54660 + 0.31427I
a = 0.747261 + 0.663781I
b = −1.24413 + 1.53270I
− 16.8310I 0
u = −1.54660 − 0.31427I
a = 0.747261 − 0.663781I
b = −1.24413 − 1.53270I
16.8310I 0
u = 1.54727 + 0.32090I
a = 0.722696 − 0.612610I
b = −1.36798 − 1.43406I
6.7713 + 12.4764I 0
u = 1.54727 − 0.32090I
a = 0.722696 + 0.612610I
b = −1.36798 + 1.43406I
6.7713 − 12.4764I 0
u = 1.38964 + 0.76538I
a = 0.549515 − 0.498041I
b = −1.61522 − 1.16668I
−0.735733 + 0.805121I 0
u = 1.38964 − 0.76538I
a = 0.549515 + 0.498041I
b = −1.61522 + 1.16668I
−0.735733 − 0.805121I 0
u = −1.55532 + 0.34766I
a = 0.703144 + 0.533864I
b = −1.50202 + 1.24799I
6.58637 − 6.59944I 0
u = −1.55532 − 0.34766I
a = 0.703144 − 0.533864I
b = −1.50202 − 1.24799I
6.58637 + 6.59944I 0
u = −0.348838 + 0.201607I
a = −1.17988 − 2.19577I
b = 0.56615 − 1.70296I
−3.73467 − 5.37166I 1.55911 + 10.05150I
u = −0.348838 − 0.201607I
a = −1.17988 + 2.19577I
b = 0.56615 + 1.70296I
−3.73467 + 5.37166I 1.55911 − 10.05150I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.63729
a = 0.262527
b = 0.714802
10.1814 0
u = −1.64283
a = 0.472631
b = 0.932162
5.98531 0
u = −1.51949 + 0.77167I
a = −0.441116 − 0.137343I
b = 0.690791 − 1.226660I
0.735733 + 0.805121I 0
u = −1.51949 − 0.77167I
a = −0.441116 + 0.137343I
b = 0.690791 + 1.226660I
0.735733 − 0.805121I 0
u = 0.181951 + 0.204552I
a = −1.19475 + 3.33617I
b = 0.85351 + 1.27926I
0.97901 + 2.75841I 5.08126 − 8.14150I
u = 0.181951 − 0.204552I
a = −1.19475 − 3.33617I
b = 0.85351 − 1.27926I
0.97901 − 2.75841I 5.08126 + 8.14150I
u = −0.194507
a = 9.99722
b = 0.121019
−10.1814 −34.6250
u = 0.0211852
a = 48.6786
b = 0.899609
−1.64464 −6.06420
13
II. I
u
2
= h−29u
15
− 34u
14
+ · · · + 73b − 87, −82u
15
+ 70u
14
+ · · · + 73a +
119, u
16
− 9u
14
+ · · · + 4u
2
− 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
10
=
u
−u
3
+ u
a
1
=
1.12329u
15
− 0.958904u
14
+ ··· + 8.10959u − 1.63014
0.397260u
15
+ 0.465753u
14
+ ··· − 0.424658u + 1.19178
a
5
=
−u
2
+ 1
u
4
− 2u
2
a
8
=
0.767123u
15
− 0.410959u
14
+ ··· + 14.9041u − 3.69863
0.0410959u
15
+ 0.0136986u
14
+ ··· + 0.369863u + 1.12329
a
7
=
0.726027u
15
− 0.424658u
14
+ ··· + 14.5342u − 4.82192
0.0410959u
15
+ 0.0136986u
14
+ ··· + 0.369863u + 1.12329
a
2
=
0.712329u
15
− 1.09589u
14
+ ··· + 7.41096u − 1.86301
0.410959u
15
+ 0.136986u
14
+ ··· + 0.698630u + 1.23288
a
11
=
1.98630u
15
− 0.671233u
14
+ ··· + 12.8767u − 4.04110
−0.123288u
15
− 0.0410959u
14
+ ··· − 0.109589u − 0.369863
a
12
=
−2.32877u
15
+ 1.89041u
14
+ ··· − 20.9589u + 8.01370
0.397260u
15
+ 0.465753u
14
+ ··· − 0.424658u + 0.191781
a
6
=
−1.75342u
15
− 0.917808u
14
+ ··· − 15.7808u + 4.73973
0.232877u
15
− 0.589041u
14
+ ··· + 4.09589u + 0.698630
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
216
73
u
15
+
512
73
u
14
+ ··· −
2163
73
u +
1031
73
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− 4u
14
+ ··· + 11u
2
− 1
c
2
, c
12
u
16
− 8u
14
+ ··· − 8u
2
+ 1
c
3
, c
4
, c
11
u
16
− 9u
14
+ ··· + 4u
2
− 1
c
5
, c
6
, c
9
u
16
− 9u
14
+ ··· + 4u
2
− 1
c
7
, c
8
u
16
− 8u
14
+ ··· − 8u
2
+ 1
c
10
u
16
− 4u
14
+ ··· + 11u
2
− 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
16
− 8y
15
+ ··· − 22y + 1
c
2
, c
7
, c
8
c
12
y
16
− 16y
15
+ ··· − 16y + 1
c
3
, c
4
, c
5
c
6
, c
9
, c
11
y
16
− 18y
15
+ ··· − 8y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.894685 + 0.648291I
a = −0.656433 + 0.813225I
b = 1.24838 + 1.12322I
−0.557316 + 1.056450I 5.51626 − 2.99054I
u = 0.894685 − 0.648291I
a = −0.656433 − 0.813225I
b = 1.24838 − 1.12322I
−0.557316 − 1.056450I 5.51626 + 2.99054I
u = 1.22010
a = 1.20116
b = −0.366933
0.897993 −6.66870
u = −1.067690 + 0.693113I
a = 0.647664 + 0.208291I
b = −0.248375 + 1.123220I
0.557316 + 1.056450I −5.51626 − 2.99054I
u = −1.067690 − 0.693113I
a = 0.647664 − 0.208291I
b = −0.248375 − 1.123220I
0.557316 − 1.056450I −5.51626 + 2.99054I
u = −1.30286
a = 1.70377
b = −0.383986
−6.60449 −9.40630
u = 1.369670 + 0.150834I
a = −0.384982 + 0.615185I
b = 0.50000 + 2.14104I
6.87722I 0. − 8.46108I
u = 1.369670 − 0.150834I
a = −0.384982 − 0.615185I
b = 0.50000 − 2.14104I
− 6.87722I 0. + 8.46108I
u = −1.374980 + 0.206345I
a = −0.574248 − 0.595246I
b = 1.03532 − 1.60052I
4.39499 − 4.91926I 6.70456 + 5.16183I
u = −1.374980 − 0.206345I
a = −0.574248 + 0.595246I
b = 1.03532 + 1.60052I
4.39499 + 4.91926I 6.70456 − 5.16183I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.532809
a = 1.28066
b = 1.36693
−0.897993 6.66870
u = 0.089624 + 0.423008I
a = 1.52824 − 1.30726I
b = −0.03532 − 1.60052I
−4.39499 − 4.91926I −6.70456 + 5.16183I
u = 0.089624 − 0.423008I
a = 1.52824 + 1.30726I
b = −0.03532 + 1.60052I
−4.39499 + 4.91926I −6.70456 − 5.16183I
u = −1.59630
a = 0.282214
b = 1.38399
6.60449 9.40630
u = 1.65321
a = 0.311106
b = 0.565962
10.0542 −28.6190
u = −0.329576
a = −5.89940
b = 0.434038
−10.0542 28.6190
18
III. I
u
3
= hb, a − 1, u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
−1
a
4
=
1
−1
a
10
=
−1
0
a
1
=
1
0
a
5
=
0
−1
a
8
=
−1
−1
a
7
=
0
−1
a
2
=
1
1
a
11
=
0
1
a
12
=
0
−1
a
6
=
0
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
, c
8
c
9
, c
12
u − 1
c
5
, c
6
, c
11
u
c
10
u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
, c
8
c
9
, c
10
, c
12
y −1
c
5
, c
6
, c
11
y
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000
b = 0
1.64493 6.00000
22
IV. I
u
4
= hb − 1, a, u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
−1
a
4
=
1
−1
a
10
=
−1
0
a
1
=
0
1
a
5
=
0
−1
a
8
=
0
−1
a
7
=
1
−1
a
2
=
0
1
a
11
=
−1
1
a
12
=
0
1
a
6
=
1
−2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
, c
12
u
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
11
u − 1
c
10
u + 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
12
y
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
10
, c
11
y −1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0
b = 1.00000
1.64493 6.00000
26
V. I
u
5
= hb + 1, a − 1, u − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
1
a
4
=
1
−1
a
10
=
1
0
a
1
=
1
−1
a
5
=
0
−1
a
8
=
1
0
a
7
=
1
0
a
2
=
1
0
a
11
=
1
0
a
12
=
0
−1
a
6
=
1
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u − 1
c
2
, c
7
, c
10
u
c
3
, c
4
, c
5
c
6
, c
8
, c
9
c
11
, c
12
u + 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
8
c
9
, c
11
, c
12
y −1
c
2
, c
7
, c
10
y
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000
b = −1.00000
−1.64493 −6.00000
30
VI. I
v
1
= ha, b − 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
−1
0
a
4
=
1
0
a
10
=
−1
0
a
1
=
0
1
a
5
=
1
0
a
8
=
−1
1
a
7
=
−2
1
a
2
=
−1
1
a
11
=
−2
1
a
12
=
1
0
a
6
=
−1
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u − 1
c
2
, c
5
, c
6
c
7
, c
8
, c
10
c
11
, c
12
u + 1
c
3
, c
4
, c
9
u
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y −1
c
3
, c
4
, c
9
y
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
−1.64493 −6.00000
34
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u − 1)
3
(u
16
− 4u
14
+ ··· + 11u
2
− 1)(u
88
+ 8u
87
+ ··· + 24u − 7)
c
2
u(u − 1)
2
(u + 1)(u
16
− 8u
14
+ ··· − 8u
2
+ 1)
· (u
88
+ 2u
87
+ ··· + 2042u + 301)
c
3
, c
4
u(u − 1)
2
(u + 1)(u
16
− 9u
14
+ ··· + 4u
2
− 1)
· (u
88
− 45u
86
+ ··· − 44u − 1)
c
5
, c
6
u(u − 1)(u + 1)
2
(u
16
− 9u
14
+ ··· + 4u
2
− 1)
· (u
88
− 45u
86
+ ··· + 44u − 1)
c
7
u(u − 1)
2
(u + 1)(u
16
− 8u
14
+ ··· − 8u
2
+ 1)
· (u
88
+ 2u
87
+ ··· + 2042u + 301)
c
8
u(u − 1)(u + 1)
2
(u
16
− 8u
14
+ ··· − 8u
2
+ 1)
· (u
88
− 2u
87
+ ··· − 2042u + 301)
c
9
u(u − 1)
2
(u + 1)(u
16
− 9u
14
+ ··· + 4u
2
− 1)
· (u
88
− 45u
86
+ ··· − 44u − 1)
c
10
u(u + 1)
3
(u
16
− 4u
14
+ ··· + 11u
2
− 1)(u
88
− 8u
87
+ ··· − 24u − 7)
c
11
u(u − 1)(u + 1)
2
(u
16
− 9u
14
+ ··· + 4u
2
− 1)
· (u
88
− 45u
86
+ ··· + 44u − 1)
c
12
u(u − 1)(u + 1)
2
(u
16
− 8u
14
+ ··· − 8u
2
+ 1)
· (u
88
− 2u
87
+ ··· − 2042u + 301)
35
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
y(y −1)
3
(y
16
− 8y
15
+ ··· − 22y + 1)(y
88
− 8y
87
+ ··· − 8654y + 49)
c
2
, c
7
, c
8
c
12
y(y −1)
3
(y
16
− 16y
15
+ ··· − 16y + 1)
· (y
88
− 52y
87
+ ··· − 2985028y + 90601)
c
3
, c
4
, c
5
c
6
, c
9
, c
11
y(y −1)
3
(y
16
− 18y
15
+ ··· − 8y + 1)(y
88
− 90y
87
+ ··· − 2260y + 1)
36
