12n
0227
(K12n
0227
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 12 9 3 11 6 1 7 10
Solving Sequence
3,7 8,11
9 12 6 5 2 1 4 10
c
7
c
8
c
11
c
6
c
5
c
2
c
1
c
4
c
10
c
3
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h5.42478 × 10
238
u
70
− 6.98254 × 10
238
u
69
+ ··· + 1.26682 × 10
239
b − 3.55544 × 10
241
,
1.09913 × 10
240
u
70
− 2.05633 × 10
240
u
69
+ ··· + 2.15359 × 10
240
a − 2.29980 × 10
243
,
u
71
− 2u
70
+ ··· − 3584u + 512i
I
u
2
= hb, 9u
4
− 4u
3
+ 3u
2
+ 17a − 18u + 1, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
I
v
1
= ha, 16726v
8
− 41423v
7
+ ··· + 11959b + 26601,
v
9
− 3v
8
− 2v
7
− 6v
6
+ 25v
5
− 11v
4
− 9v
3
+ 2v
2
+ 3v −1i
* 3 irreducible components of dim
C
= 0, with total 85 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
= h5.42 × 10
238
u
70
− 6.98 × 10
238
u
69
+ · · · + 1.27 × 10
239
b − 3.56 ×
10
241
, 1.10 × 10
240
u
70
− 2.06 × 10
240
u
69
+ · · · + 2.15 × 10
240
a − 2.30 ×
10
243
, u
71
− 2u
70
+ · · · − 3584u + 512i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
11
=
−0.510370u
70
+ 0.954840u
69
+ ··· − 3684.20u + 1067.89
−0.428222u
70
+ 0.551187u
69
+ ··· − 1698.21u + 280.659
a
9
=
−0.479721u
70
+ 0.835639u
69
+ ··· − 3127.86u + 850.474
−0.541913u
70
+ 0.734975u
69
+ ··· − 2349.21u + 422.606
a
12
=
−0.938592u
70
+ 1.50603u
69
+ ··· − 5382.41u + 1348.55
−0.428222u
70
+ 0.551187u
69
+ ··· − 1698.21u + 280.659
a
6
=
0.553572u
70
− 0.765321u
69
+ ··· + 2500.77u − 485.024
0.500931u
70
− 0.690180u
69
+ ··· + 2222.19u − 412.967
a
5
=
−0.0335810u
70
+ 0.118905u
69
+ ··· − 557.136u + 207.295
0.242484u
70
− 0.321369u
69
+ ··· + 1009.04u − 176.830
a
2
=
0.276065u
70
− 0.440274u
69
+ ··· + 1566.18u − 384.125
0.242484u
70
− 0.321369u
69
+ ··· + 1009.04u − 176.830
a
1
=
0.276065u
70
− 0.440274u
69
+ ··· + 1566.18u − 384.125
0.192358u
70
− 0.245562u
69
+ ··· + 749.492u − 119.559
a
4
=
u
u
a
10
=
−0.307087u
70
+ 0.617884u
69
+ ··· − 2458.59u + 752.034
−0.192358u
70
+ 0.245562u
69
+ ··· − 749.492u + 119.559
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.22925u
70
− 3.84779u
69
+ ··· + 14361.8u − 3919.67
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
71
+ 27u
70
+ ··· + 121u + 1
c
2
, c
4
u
71
− 11u
70
+ ··· + 17u − 1
c
3
, c
7
u
71
− 2u
70
+ ··· − 3584u + 512
c
5
17(17u
71
+ 58u
70
+ ··· − 338322u − 76541)
c
6
, c
9
u
71
− 3u
70
+ ··· − 3u + 1
c
8
17(17u
71
− 28u
70
+ ··· − 3303678u − 843836)
c
10
, c
12
u
71
+ 7u
70
+ ··· + 1199u + 289
c
11
u
71
− 2u
70
+ ··· − 33184u − 9248
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
71
+ 45y
70
+ ··· + 15729y −1
c
2
, c
4
y
71
− 27y
70
+ ··· + 121y −1
c
3
, c
7
y
71
− 54y
70
+ ··· + 10485760y −262144
c
5
289(289y
71
− 11218y
70
+ ··· + 5.96694 × 10
10
y −5.85852 × 10
9
)
c
6
, c
9
y
71
+ 49y
70
+ ··· + 41y −1
c
8
289
· (289y
71
− 16424y
70
+ ··· + 1192944884236y −712059194896)
c
10
, c
12
y
71
− 63y
70
+ ··· + 1811567y −83521
c
11
y
71
− 30y
70
+ ··· + 374507008y −85525504
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.076693 + 0.947370I
a = −0.691781 − 0.148799I
b = −1.37182 + 0.60834I
1.59411 − 4.42837I 0
u = 0.076693 − 0.947370I
a = −0.691781 + 0.148799I
b = −1.37182 − 0.60834I
1.59411 + 4.42837I 0
u = −0.220480 + 0.816559I
a = 0.463726 + 0.218399I
b = 0.558026 + 0.462831I
−1.56511 + 1.33089I −4.35474 − 3.35992I
u = −0.220480 − 0.816559I
a = 0.463726 − 0.218399I
b = 0.558026 − 0.462831I
−1.56511 − 1.33089I −4.35474 + 3.35992I
u = 0.145194 + 0.788536I
a = −0.516702 + 1.147430I
b = −0.761187 − 0.160663I
1.32199 + 0.86803I 2.81463 + 0.68879I
u = 0.145194 − 0.788536I
a = −0.516702 − 1.147430I
b = −0.761187 + 0.160663I
1.32199 − 0.86803I 2.81463 − 0.68879I
u = −0.487435 + 1.128170I
a = 0.0239672 − 0.0816915I
b = 0.080432 + 0.375354I
−4.36546 − 4.32846I 0
u = −0.487435 − 1.128170I
a = 0.0239672 + 0.0816915I
b = 0.080432 − 0.375354I
−4.36546 + 4.32846I 0
u = 0.439418 + 0.621478I
a = 0.206543 + 0.342654I
b = −0.047968 − 0.545007I
0.12984 + 1.53500I 0.43134 − 4.26020I
u = 0.439418 − 0.621478I
a = 0.206543 − 0.342654I
b = −0.047968 + 0.545007I
0.12984 − 1.53500I 0.43134 + 4.26020I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.182323 + 0.721295I
a = 0.56676 − 2.11337I
b = 0.74195 − 1.33427I
4.92838 + 1.62527I 9.65649 − 3.98384I
u = 0.182323 − 0.721295I
a = 0.56676 + 2.11337I
b = 0.74195 + 1.33427I
4.92838 − 1.62527I 9.65649 + 3.98384I
u = 0.738712 + 0.025801I
a = −2.84205 + 2.51257I
b = 0.986916 − 0.482298I
0.03593 − 2.58057I 5.84465 + 3.57644I
u = 0.738712 − 0.025801I
a = −2.84205 − 2.51257I
b = 0.986916 + 0.482298I
0.03593 + 2.58057I 5.84465 − 3.57644I
u = −0.642897 + 0.339317I
a = 1.63273 − 0.52748I
b = −0.210241 + 0.516302I
−2.40004 + 0.50009I −3.16242 + 1.54853I
u = −0.642897 − 0.339317I
a = 1.63273 + 0.52748I
b = −0.210241 − 0.516302I
−2.40004 − 0.50009I −3.16242 − 1.54853I
u = −1.323750 + 0.085283I
a = −1.90895 + 0.72230I
b = 0.663197 − 0.063213I
5.87495 − 2.45786I 0
u = −1.323750 − 0.085283I
a = −1.90895 − 0.72230I
b = 0.663197 + 0.063213I
5.87495 + 2.45786I 0
u = −0.004372 + 0.661805I
a = 1.40629 − 2.21793I
b = −0.395556 − 0.414217I
0.982639 − 0.712583I 1.26468 − 3.38200I
u = −0.004372 − 0.661805I
a = 1.40629 + 2.21793I
b = −0.395556 + 0.414217I
0.982639 + 0.712583I 1.26468 + 3.38200I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.354200 + 0.058471I
a = 1.169270 + 0.041829I
b = −1.151030 − 0.496491I
3.26913 + 0.37177I 0
u = 1.354200 − 0.058471I
a = 1.169270 − 0.041829I
b = −1.151030 + 0.496491I
3.26913 − 0.37177I 0
u = 0.641537 + 0.013263I
a = −0.215156 + 0.261484I
b = −0.477396 − 1.105930I
−0.01259 + 2.24943I 5.94216 − 1.24752I
u = 0.641537 − 0.013263I
a = −0.215156 − 0.261484I
b = −0.477396 + 1.105930I
−0.01259 − 2.24943I 5.94216 + 1.24752I
u = −0.637235 + 0.065847I
a = 0.146928 + 0.026378I
b = −0.083520 + 1.139150I
−2.82440 − 2.46359I 4.30273 + 6.24454I
u = −0.637235 − 0.065847I
a = 0.146928 − 0.026378I
b = −0.083520 − 1.139150I
−2.82440 + 2.46359I 4.30273 − 6.24454I
u = 1.334450 + 0.351523I
a = −1.13740 + 0.91626I
b = 0.663249 + 0.125810I
5.32732 + 3.31503I 0
u = 1.334450 − 0.351523I
a = −1.13740 − 0.91626I
b = 0.663249 − 0.125810I
5.32732 − 3.31503I 0
u = 1.392010 + 0.087028I
a = 1.235080 − 0.640698I
b = −1.231910 + 0.578737I
5.60335 − 6.26016I 0
u = 1.392010 − 0.087028I
a = 1.235080 + 0.640698I
b = −1.231910 − 0.578737I
5.60335 + 6.26016I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.426783 + 0.400297I
a = 4.22729 + 5.26355I
b = −0.290627 + 0.848259I
2.71880 + 0.77171I −0.03938 + 7.34337I
u = −0.426783 − 0.400297I
a = 4.22729 − 5.26355I
b = −0.290627 − 0.848259I
2.71880 − 0.77171I −0.03938 − 7.34337I
u = 0.557977 + 0.073436I
a = −0.051806 + 0.142442I
b = 0.646310 + 1.044790I
2.38069 + 7.27157I 12.6640 − 9.5899I
u = 0.557977 − 0.073436I
a = −0.051806 − 0.142442I
b = 0.646310 − 1.044790I
2.38069 − 7.27157I 12.6640 + 9.5899I
u = −1.43718 + 0.15590I
a = −0.944374 − 0.509182I
b = 0.480613 − 0.961739I
6.20644 − 1.78085I 0
u = −1.43718 − 0.15590I
a = −0.944374 + 0.509182I
b = 0.480613 + 0.961739I
6.20644 + 1.78085I 0
u = −1.37199 + 0.46590I
a = 1.173090 + 0.216321I
b = −1.073480 + 0.872449I
2.23860 − 6.33244I 0
u = −1.37199 − 0.46590I
a = 1.173090 − 0.216321I
b = −1.073480 − 0.872449I
2.23860 + 6.33244I 0
u = 0.16002 + 1.45030I
a = −0.0471063 − 0.1086940I
b = 1.33837 − 0.76483I
7.57456 − 9.33161I 0
u = 0.16002 − 1.45030I
a = −0.0471063 + 0.1086940I
b = 1.33837 + 0.76483I
7.57456 + 9.33161I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.44190 + 0.27798I
a = −0.928627 − 0.073907I
b = 0.768169 − 0.880679I
5.97359 + 4.40312I 0
u = 1.44190 − 0.27798I
a = −0.928627 + 0.073907I
b = 0.768169 + 0.880679I
5.97359 − 4.40312I 0
u = −1.47168 + 0.09988I
a = −1.48841 + 0.33110I
b = 2.07259 − 0.81942I
7.18645 − 3.56652I 0
u = −1.47168 − 0.09988I
a = −1.48841 − 0.33110I
b = 2.07259 + 0.81942I
7.18645 + 3.56652I 0
u = −0.420831 + 0.275485I
a = −0.74354 − 2.33627I
b = 1.032730 − 0.604659I
4.35121 + 1.59493I 10.43394 − 0.97479I
u = −0.420831 − 0.275485I
a = −0.74354 + 2.33627I
b = 1.032730 + 0.604659I
4.35121 − 1.59493I 10.43394 + 0.97479I
u = 0.30543 + 1.48272I
a = −0.0549019 + 0.1030280I
b = 1.245940 + 0.346093I
7.30098 + 3.05381I 0
u = 0.30543 − 1.48272I
a = −0.0549019 − 0.1030280I
b = 1.245940 − 0.346093I
7.30098 − 3.05381I 0
u = −1.51898
a = −0.897992
b = 0.945902
0.852763 0
u = 1.45011 + 0.48802I
a = −1.53939 + 0.17087I
b = 1.89726 + 1.26956I
6.09358 + 9.90312I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.45011 − 0.48802I
a = −1.53939 − 0.17087I
b = 1.89726 − 1.26956I
6.09358 − 9.90312I 0
u = 1.55039 + 0.12499I
a = 1.120780 + 0.568665I
b = −1.42403 − 2.23704I
11.13970 + 0.68264I 0
u = 1.55039 − 0.12499I
a = 1.120780 − 0.568665I
b = −1.42403 + 2.23704I
11.13970 − 0.68264I 0
u = −0.18896 + 1.55398I
a = 0.0798087 + 0.0002794I
b = −1.030510 − 0.264735I
2.79580 + 3.31170I 0
u = −0.18896 − 1.55398I
a = 0.0798087 − 0.0002794I
b = −1.030510 + 0.264735I
2.79580 − 3.31170I 0
u = −1.53761 + 0.31028I
a = 0.757396 + 0.910802I
b = −1.86995 − 1.88969I
10.80380 − 5.89219I 0
u = −1.53761 − 0.31028I
a = 0.757396 − 0.910802I
b = −1.86995 + 1.88969I
10.80380 + 5.89219I 0
u = 1.50255 + 0.73985I
a = 1.331380 − 0.402936I
b = −1.43302 − 1.19081I
11.7776 + 17.0387I 0
u = 1.50255 − 0.73985I
a = 1.331380 + 0.402936I
b = −1.43302 + 1.19081I
11.7776 − 17.0387I 0
u = 0.310196
a = −11.7418
b = 0.360541
−0.278739 56.4200
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.297760
a = 2.27908
b = −0.569710
1.11352 9.05470
u = −1.53644 + 0.75409I
a = −1.045060 − 0.283594I
b = 1.17961 − 0.86678I
7.10450 − 11.36750I 0
u = −1.53644 − 0.75409I
a = −1.045060 + 0.283594I
b = 1.17961 + 0.86678I
7.10450 + 11.36750I 0
u = −1.66767 + 0.47111I
a = 1.258780 + 0.087385I
b = −1.54465 + 0.98213I
13.8741 − 10.1106I 0
u = −1.66767 − 0.47111I
a = 1.258780 − 0.087385I
b = −1.54465 − 0.98213I
13.8741 + 10.1106I 0
u = 1.52848 + 0.82309I
a = 0.679890 − 0.444350I
b = −1.200100 − 0.331040I
11.07870 + 5.15354I 0
u = 1.52848 − 0.82309I
a = 0.679890 + 0.444350I
b = −1.200100 + 0.331040I
11.07870 − 5.15354I 0
u = −1.68752 + 0.56968I
a = 0.767625 + 0.443423I
b = −1.41908 + 0.00115I
13.45460 + 1.92659I 0
u = −1.68752 − 0.56968I
a = 0.767625 − 0.443423I
b = −1.41908 − 0.00115I
13.45460 − 1.92659I 0
u = 1.71694 + 0.49452I
a = −0.955855 + 0.132868I
b = 1.292340 + 0.569757I
9.22845 + 4.28954I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.71694 − 0.49452I
a = −0.955855 − 0.132868I
b = 1.292340 − 0.569757I
9.22845 − 4.28954I 0
12
II. I
u
2
= hb, 9u
4
− 4u
3
+ 3u
2
+ 17a − 18u + 1, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
11
=
−0.529412u
4
+ 0.235294u
3
+ ··· + 1.05882u − 0.0588235
0
a
9
=
−0.131488u
4
+ 0.463668u
3
+ ··· + 0.910035u + 0.854671
−u
2
a
12
=
−0.529412u
4
+ 0.235294u
3
+ ··· + 1.05882u − 0.0588235
0
a
6
=
−0.0622837u
4
− 0.148789u
3
+ ··· − 0.463668u + 0.404844
−u
4
a
5
=
u
2
+ 1
−u
4
a
2
=
−u
4
− u
2
− 1
−u
4
a
1
=
−u
4
− u
2
− 1
−u
4
+ u
3
+ u
2
+ 1
a
4
=
u
u
a
10
=
0.470588u
4
+ 0.235294u
3
+ ··· + 1.05882u + 0.941176
u
4
− u
3
− u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1429
289
u
4
+
1471
289
u
3
−
1184
289
u
2
+
780
289
u +
2127
289
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
5
− 5u
4
+ 8u
3
− 3u
2
− u − 1
c
2
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
3
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
4
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
5
17(17u
5
− 32u
4
+ 18u
3
+ u
2
− 4u + 1)
c
6
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
7
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
8
17(17u
5
+ 42u
4
+ 43u
3
+ 22u
2
+ 6u + 1)
c
9
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
c
10
(u + 1)
5
c
11
u
5
c
12
(u − 1)
5
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
5
− 9y
4
+ 32y
3
− 35y
2
− 5y −1
c
2
, c
4
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
3
, c
7
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
5
289(289y
5
− 412y
4
+ 252y
3
− 81y
2
+ 14y −1)
c
6
, c
9
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
8
289(289y
5
− 302y
4
+ 205y
3
− 52y
2
− 8y −1)
c
10
, c
12
(y −1)
5
c
11
y
5
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339110 + 0.822375I
a = 0.244471 + 1.039700I
b = 0
1.31583 + 1.53058I 7.29086 − 4.54835I
u = 0.339110 − 0.822375I
a = 0.244471 − 1.039700I
b = 0
1.31583 − 1.53058I 7.29086 + 4.54835I
u = −0.766826
a = −1.26368
b = 0
−0.756147 2.29580
u = −0.455697 + 1.200150I
a = −0.053809 − 0.194708I
b = 0
−4.22763 − 4.40083I 22.3190 + 16.0614I
u = −0.455697 − 1.200150I
a = −0.053809 + 0.194708I
b = 0
−4.22763 + 4.40083I 22.3190 − 16.0614I
18
III.
I
v
1
= ha, 16726v
8
− 41423v
7
+ · · · + 11959b + 26601, v
9
− 3v
8
+ · · · + 3v − 1i
(i) Arc colorings
a
3
=
v
0
a
7
=
1
0
a
8
=
1
0
a
11
=
0
−1.39861v
8
+ 3.46375v
7
+ ··· + 3.94598v −2.22435
a
9
=
1
1.45213v
8
− 3.82515v
7
+ ··· − 3.73944v + 4.14098
a
12
=
−1.39861v
8
+ 3.46375v
7
+ ··· + 3.94598v −2.22435
−1.39861v
8
+ 3.46375v
7
+ ··· + 3.94598v −2.22435
a
6
=
−1.45213v
8
+ 3.82515v
7
+ ··· + 3.73944v −3.14098
−1.21114v
8
+ 2.94147v
7
+ ··· + 5.63826v −2.00702
a
5
=
0.759010v
8
− 2.11631v
7
+ ··· + 0.101179v + 1.86604
v
8
− 3v
7
− 2v
6
− 6v
5
+ 25v
4
− 11v
3
− 9v
2
+ 2v + 3
a
2
=
−0.759010v
8
+ 2.11631v
7
+ ··· + 0.898821v −1.86604
−v
8
+ 3v
7
+ 2v
6
+ 6v
5
− 25v
4
+ 11v
3
+ 9v
2
− 2v −3
a
1
=
−0.759010v
8
+ 2.11631v
7
+ ··· − 0.101179v −1.86604
−v
8
+ 3v
7
+ 2v
6
+ 6v
5
− 25v
4
+ 11v
3
+ 9v
2
− 2v −3
a
4
=
v
0
a
10
=
−0.240990v
8
+ 0.883686v
7
+ ··· − 1.89882v −1.13396
−v
8
+ 3v
7
+ 2v
6
+ 6v
5
− 25v
4
+ 11v
3
+ 9v
2
− 2v −3
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
38011
11959
v
8
−
103132
11959
v
7
−
110061
11959
v
6
−
250712
11959
v
5
+
892353
11959
v
4
−
104528
11959
v
3
−
444297
11959
v
2
−
43711
11959
v +
44549
11959
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
7
u
9
c
4
(u + 1)
9
c
5
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
6
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
8
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
9
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
10
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
11
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
12
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
7
y
9
c
5
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
6
, c
9
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
8
, c
11
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
10
, c
12
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.022450 + 0.246780I
a = 0
b = −0.628449 + 0.875112I
−1.02799 − 2.45442I −3.46097 + 2.82066I
v = 1.022450 − 0.246780I
a = 0
b = −0.628449 − 0.875112I
−1.02799 + 2.45442I −3.46097 − 2.82066I
v = −0.483566 + 0.305056I
a = 0
b = −0.140343 + 0.966856I
−3.42837 − 2.09337I −5.97316 + 1.69698I
v = −0.483566 − 0.305056I
a = 0
b = −0.140343 − 0.966856I
−3.42837 + 2.09337I −5.97316 − 1.69698I
v = 0.411691 + 0.129409I
a = 0
b = 0.728966 + 0.986295I
1.95319 + 7.08493I −2.97979 − 2.94778I
v = 0.411691 − 0.129409I
a = 0
b = 0.728966 − 0.986295I
1.95319 − 7.08493I −2.97979 + 2.94778I
v = −1.23246 + 1.62704I
a = 0
b = 0.796005 + 0.733148I
2.72642 − 1.33617I 4.47739 + 4.48124I
v = −1.23246 − 1.62704I
a = 0
b = 0.796005 − 0.733148I
2.72642 + 1.33617I 4.47739 − 4.48124I
v = 3.56378
a = 0
b = −0.512358
−0.446489 −8.12690
22
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
5
− 5u
4
+ ··· − u − 1)(u
71
+ 27u
70
+ ··· + 121u + 1)
c
2
((u − 1)
9
)(u
5
+ u
4
+ ··· + u − 1)(u
71
− 11u
70
+ ··· + 17u − 1)
c
3
u
9
(u
5
− u
4
+ ··· + u − 1)(u
71
− 2u
70
+ ··· − 3584u + 512)
c
4
((u + 1)
9
)(u
5
− u
4
+ ··· + u + 1)(u
71
− 11u
70
+ ··· + 17u − 1)
c
5
289(17u
5
− 32u
4
+ 18u
3
+ u
2
− 4u + 1)
· (u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
· (17u
71
+ 58u
70
+ ··· − 338322u − 76541)
c
6
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
· (u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
71
− 3u
70
+ ··· − 3u + 1)
c
7
u
9
(u
5
+ u
4
+ ··· + u + 1)(u
71
− 2u
70
+ ··· − 3584u + 512)
c
8
289(17u
5
+ 42u
4
+ 43u
3
+ 22u
2
+ 6u + 1)
· (u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (17u
71
− 28u
70
+ ··· − 3303678u − 843836)
c
9
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
71
− 3u
70
+ ··· − 3u + 1)
c
10
(u + 1)
5
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
71
+ 7u
70
+ ··· + 1199u + 289)
c
11
u
5
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
71
− 2u
70
+ ··· − 33184u − 9248)
c
12
(u − 1)
5
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
71
+ 7u
70
+ ··· + 1199u + 289)
23
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
9
(y
5
− 9y
4
+ 32y
3
− 35y
2
− 5y −1)
· (y
71
+ 45y
70
+ ··· + 15729y −1)
c
2
, c
4
((y −1)
9
)(y
5
− 5y
4
+ ··· − y −1)(y
71
− 27y
70
+ ··· + 121y −1)
c
3
, c
7
y
9
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
· (y
71
− 54y
70
+ ··· + 10485760y −262144)
c
5
83521(289y
5
− 412y
4
+ 252y
3
− 81y
2
+ 14y −1)
· (y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (289y
71
− 11218y
70
+ ··· + 59669441588y −5858524681)
c
6
, c
9
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
71
+ 49y
70
+ ··· + 41y −1)
c
8
83521(289y
5
− 302y
4
+ 205y
3
− 52y
2
− 8y −1)
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (289y
71
− 16424y
70
+ ··· + 1192944884236y −712059194896)
c
10
, c
12
(y −1)
5
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
71
− 63y
70
+ ··· + 1811567y −83521)
c
11
y
5
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
71
− 30y
70
+ ··· + 374507008y −85525504)
24
