12n
0206
(K12n
0206
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 10 12 3 11 7 1 9 6
Solving Sequence
8,11
9
3,12
7 4 10 6 1 5 2
c
8
c
11
c
7
c
3
c
9
c
6
c
12
c
5
c
2
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.77675 × 10
197
u
70
+ 4.00240 × 10
198
u
69
+ ··· + 3.80449 × 10
199
b − 8.85680 × 10
199
,
2.02424 × 10
200
u
70
− 1.02963 × 10
201
u
69
+ ··· + 1.09950 × 10
202
a + 1.24156 × 10
202
,
u
71
− 7u
70
+ ··· + 1199u − 289i
I
u
2
= hb, −u
8
+ 2u
7
+ u
6
− 4u
5
+ u
4
+ 2u
3
− 2u
2
+ a + 2u − 1, u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
I
u
3
= h−171088a
4
+ 309672a
3
+ 100148a
2
+ 704465b + 873471a + 152355,
17a
5
− 38a
4
− 12a
3
− 9a
2
− 10a − 25, u + 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
= h−7.78 × 10
197
u
70
+ 4.00 × 10
198
u
69
+ · · · + 3.80 × 10
199
b − 8.86 ×
10
199
, 2.02 × 10
200
u
70
− 1.03 × 10
201
u
69
+ · · · + 1.10 × 10
202
a + 1.24 ×
10
202
, u
71
− 7u
70
+ · · · + 1199u − 289i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
−u
2
a
3
=
−0.0184106u
70
+ 0.0936457u
69
+ ··· + 9.76637u − 1.12921
0.0204410u
70
− 0.105202u
69
+ ··· − 9.58566u + 2.32798
a
12
=
u
−u
3
+ u
a
7
=
−0.0466645u
70
+ 0.293619u
69
+ ··· + 48.3665u − 15.5876
0.00479198u
70
− 0.0596147u
69
+ ··· − 19.3624u + 7.08009
a
4
=
−0.499170u
70
+ 2.77736u
69
+ ··· + 345.003u − 99.7107
0.764567u
70
− 4.26654u
69
+ ··· − 532.480u + 154.683
a
10
=
−0.00565571u
70
+ 0.0323636u
69
+ ··· − 10.6763u + 2.61138
−0.0117731u
70
+ 0.0884774u
69
+ ··· + 12.9410u − 4.08451
a
6
=
0.0204023u
70
− 0.0946454u
69
+ ··· − 5.82381u + 0.885137
−0.0282610u
70
+ 0.125290u
69
+ ··· + 4.42743u + 0.0851660
a
1
=
0.0315678u
70
− 0.179416u
69
+ ··· − 15.1787u + 6.46648
−0.0909233u
70
+ 0.522261u
69
+ ··· + 72.4293u − 21.7615
a
5
=
−0.0494570u
70
+ 0.305968u
69
+ ··· + 35.8439u − 12.8556
−0.0269343u
70
+ 0.100857u
69
+ ··· − 6.16962u + 3.55182
a
2
=
−0.0104954u
70
+ 0.0542240u
69
+ ··· + 21.5025u − 5.67968
0.00909595u
70
− 0.0238410u
69
+ ··· + 9.22630u − 2.63364
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0764562u
70
− 0.447130u
69
+ ··· − 71.2982u + 17.0357
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
u
71
− 2u
70
+ ··· − 33184u − 9248
c
6
, c
12
u
71
− 3u
70
+ ··· − 3u + 1
c
8
, c
11
u
71
+ 7u
70
+ ··· + 1199u + 289
c
9
17(17u
71
+ 58u
70
+ ··· − 338322u − 76541)
c
10
17(17u
71
− 28u
70
+ ··· − 3303678u − 843836)
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
y
71
− 30y
70
+ ··· + 374507008y −85525504
c
6
, c
12
y
71
+ 49y
70
+ ··· + 41y −1
c
8
, c
11
y
71
− 63y
70
+ ··· + 1811567y −83521
c
9
289(289y
71
− 11218y
70
+ ··· + 5.96694 × 10
10
y −5.85852 × 10
9
)
c
10
289
· (289y
71
− 16424y
70
+ ··· + 1192944884236y −712059194896)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.756660 + 0.652760I
a = −0.194768 + 0.364860I
b = 0.637235 + 0.065847I
−2.82440 + 2.46359I 0
u = 0.756660 − 0.652760I
a = −0.194768 − 0.364860I
b = 0.637235 − 0.065847I
−2.82440 − 2.46359I 0
u = −0.101769 + 0.975404I
a = −0.013185 − 0.296664I
b = 1.37199 − 0.46590I
2.23860 − 6.33244I 0
u = −0.101769 − 0.975404I
a = −0.013185 + 0.296664I
b = 1.37199 + 0.46590I
2.23860 + 6.33244I 0
u = −1.039240 + 0.147728I
a = −1.149230 − 0.251566I
b = 0.004372 − 0.661805I
0.982639 − 0.712583I 0
u = −1.039240 − 0.147728I
a = −1.149230 + 0.251566I
b = 0.004372 + 0.661805I
0.982639 + 0.712583I 0
u = 0.927037 + 0.038295I
a = −0.447729 + 0.814840I
b = 0.487435 − 1.128170I
−4.36546 − 4.32846I −23.3262 − 7.3531I
u = 0.927037 − 0.038295I
a = −0.447729 − 0.814840I
b = 0.487435 + 1.128170I
−4.36546 + 4.32846I −23.3262 + 7.3531I
u = −0.927261
a = 5.50313
b = −0.310196
−0.278739 56.4200
u = −0.354625 + 0.849824I
a = −0.151243 + 0.119016I
b = −1.354200 + 0.058471I
3.26913 − 0.37177I 2.00000 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.354625 − 0.849824I
a = −0.151243 − 0.119016I
b = −1.354200 − 0.058471I
3.26913 + 0.37177I 2.00000 + 0.I
u = −0.376517 + 1.025830I
a = 0.315794 − 1.102330I
b = −0.076693 − 0.947370I
1.59411 − 4.42837I 0
u = −0.376517 − 1.025830I
a = 0.315794 + 1.102330I
b = −0.076693 + 0.947370I
1.59411 + 4.42837I 0
u = 0.347640 + 0.813125I
a = 0.005886 − 0.617262I
b = −0.641537 + 0.013263I
−0.01259 − 2.24943I 5.94216 + 1.24752I
u = 0.347640 − 0.813125I
a = 0.005886 + 0.617262I
b = −0.641537 − 0.013263I
−0.01259 + 2.24943I 5.94216 − 1.24752I
u = −0.290942 + 0.737764I
a = 1.65291 − 0.96848I
b = −0.738712 − 0.025801I
0.03593 − 2.58057I 5.84465 + 3.57644I
u = −0.290942 − 0.737764I
a = 1.65291 + 0.96848I
b = −0.738712 + 0.025801I
0.03593 + 2.58057I 5.84465 − 3.57644I
u = −1.100310 + 0.531566I
a = 0.207077 + 0.459025I
b = 0.420831 + 0.275485I
4.35121 − 1.59493I 0
u = −1.100310 − 0.531566I
a = 0.207077 − 0.459025I
b = 0.420831 − 0.275485I
4.35121 + 1.59493I 0
u = −0.755086
a = −0.418947
b = −0.297760
1.11352 9.05470
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.125800 + 0.537275I
a = 0.138588 − 0.169296I
b = −0.557977 − 0.073436I
2.38069 + 7.27157I 0
u = 1.125800 − 0.537275I
a = 0.138588 + 0.169296I
b = −0.557977 + 0.073436I
2.38069 − 7.27157I 0
u = −1.249910 + 0.134392I
a = −1.18206 + 2.72482I
b = 0.426783 + 0.400297I
2.71880 − 0.77171I 0
u = −1.249910 − 0.134392I
a = −1.18206 − 2.72482I
b = 0.426783 − 0.400297I
2.71880 + 0.77171I 0
u = −0.700057 + 0.193777I
a = 1.12505 − 2.53259I
b = 1.323750 + 0.085283I
5.87495 + 2.45786I 9.24495 − 6.42737I
u = −0.700057 − 0.193777I
a = 1.12505 + 2.53259I
b = 1.323750 − 0.085283I
5.87495 − 2.45786I 9.24495 + 6.42737I
u = 1.29944
a = −1.95041
b = 1.51898
0.852763 0
u = −1.255160 + 0.377546I
a = 1.66912 + 1.11095I
b = −1.44190 + 0.27798I
5.97359 − 4.40312I 0
u = −1.255160 − 0.377546I
a = 1.66912 − 1.11095I
b = −1.44190 − 0.27798I
5.97359 + 4.40312I 0
u = −1.300740 + 0.229793I
a = −1.82719 − 0.88893I
b = 1.43718 + 0.15590I
6.20644 + 1.78085I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.300740 − 0.229793I
a = −1.82719 + 0.88893I
b = 1.43718 − 0.15590I
6.20644 − 1.78085I 0
u = 1.337460 + 0.125412I
a = 0.027859 + 0.614143I
b = 0.18896 − 1.55398I
2.79580 + 3.31170I 0
u = 1.337460 − 0.125412I
a = 0.027859 − 0.614143I
b = 0.18896 + 1.55398I
2.79580 − 3.31170I 0
u = −0.427079 + 0.399427I
a = −1.92353 + 1.90314I
b = −0.145194 + 0.788536I
1.32199 − 0.86803I 2.81463 − 0.68879I
u = −0.427079 − 0.399427I
a = −1.92353 − 1.90314I
b = −0.145194 − 0.788536I
1.32199 + 0.86803I 2.81463 + 0.68879I
u = 1.41886 + 0.15846I
a = 1.53895 − 0.23615I
b = −1.52848 − 0.82309I
11.07870 + 5.15354I 0
u = 1.41886 − 0.15846I
a = 1.53895 + 0.23615I
b = −1.52848 + 0.82309I
11.07870 − 5.15354I 0
u = 1.44104 + 0.16578I
a = 0.297052 + 0.397374I
b = −0.30543 − 1.48272I
7.30098 + 3.05381I 0
u = 1.44104 − 0.16578I
a = 0.297052 − 0.397374I
b = −0.30543 + 1.48272I
7.30098 − 3.05381I 0
u = 1.43488 + 0.27968I
a = 1.78842 − 0.17343I
b = −1.392010 + 0.087028I
5.60335 + 6.26016I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43488 − 0.27968I
a = 1.78842 + 0.17343I
b = −1.392010 − 0.087028I
5.60335 − 6.26016I 0
u = 1.41280 + 0.42540I
a = −1.61762 + 0.54713I
b = 1.53644 + 0.75409I
7.10450 + 11.36750I 0
u = 1.41280 − 0.42540I
a = −1.61762 − 0.54713I
b = 1.53644 − 0.75409I
7.10450 − 11.36750I 0
u = 1.46463 + 0.27475I
a = 1.65909 − 0.33682I
b = −1.71694 − 0.49452I
9.22845 + 4.28954I 0
u = 1.46463 − 0.27475I
a = 1.65909 + 0.33682I
b = −1.71694 + 0.49452I
9.22845 − 4.28954I 0
u = −0.395946 + 0.275565I
a = −1.84509 + 2.03931I
b = −1.334450 + 0.351523I
5.32732 − 3.31503I 6.14838 + 0.98366I
u = −0.395946 − 0.275565I
a = −1.84509 − 2.03931I
b = −1.334450 − 0.351523I
5.32732 + 3.31503I 6.14838 − 0.98366I
u = 1.52370 + 0.00055I
a = −1.52959 + 0.07213I
b = 1.68752 + 0.56968I
13.45460 − 1.92659I 0
u = 1.52370 − 0.00055I
a = −1.52959 − 0.07213I
b = 1.68752 − 0.56968I
13.45460 + 1.92659I 0
u = −1.48783 + 0.35921I
a = 0.217215 + 0.589103I
b = −0.182323 + 0.721295I
4.92838 − 1.62527I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48783 − 0.35921I
a = 0.217215 − 0.589103I
b = −0.182323 − 0.721295I
4.92838 + 1.62527I 0
u = 1.49034 + 0.37047I
a = −0.216937 − 0.362488I
b = −0.16002 + 1.45030I
7.57456 + 9.33161I 0
u = 1.49034 − 0.37047I
a = −0.216937 + 0.362488I
b = −0.16002 − 1.45030I
7.57456 − 9.33161I 0
u = −0.51104 + 1.45521I
a = −0.384185 − 0.141170I
b = 1.47168 − 0.09988I
7.18645 − 3.56652I 0
u = −0.51104 − 1.45521I
a = −0.384185 + 0.141170I
b = 1.47168 + 0.09988I
7.18645 + 3.56652I 0
u = −0.24999 + 1.52906I
a = 0.386137 + 0.398616I
b = −1.45011 + 0.48802I
6.09358 − 9.90312I 0
u = −0.24999 − 1.52906I
a = 0.386137 − 0.398616I
b = −1.45011 − 0.48802I
6.09358 + 9.90312I 0
u = −0.061861 + 0.437709I
a = −1.22584 + 1.97505I
b = 0.220480 + 0.816559I
−1.56511 − 1.33089I −4.35474 + 3.35992I
u = −0.061861 − 0.437709I
a = −1.22584 − 1.97505I
b = 0.220480 − 0.816559I
−1.56511 + 1.33089I −4.35474 − 3.35992I
u = 1.55314 + 0.57823I
a = 1.46222 − 0.67858I
b = −1.50255 − 0.73985I
11.7776 + 17.0387I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.55314 − 0.57823I
a = 1.46222 + 0.67858I
b = −1.50255 + 0.73985I
11.7776 − 17.0387I 0
u = 1.59834 + 0.47097I
a = −1.50458 + 0.49579I
b = 1.66767 + 0.47111I
13.8741 + 10.1106I 0
u = 1.59834 − 0.47097I
a = −1.50458 − 0.49579I
b = 1.66767 − 0.47111I
13.8741 − 10.1106I 0
u = 0.322877 + 0.075455I
a = 1.04784 − 1.90673I
b = −0.439418 + 0.621478I
0.12984 − 1.53500I 0.43134 + 4.26020I
u = 0.322877 − 0.075455I
a = 1.04784 + 1.90673I
b = −0.439418 − 0.621478I
0.12984 + 1.53500I 0.43134 − 4.26020I
u = 0.198166 + 0.231942I
a = −2.13178 + 1.10932I
b = 0.642897 − 0.339317I
−2.40004 + 0.50009I −3.16242 + 1.54853I
u = 0.198166 − 0.231942I
a = −2.13178 − 1.10932I
b = 0.642897 + 0.339317I
−2.40004 − 0.50009I −3.16242 − 1.54853I
u = −1.81641 + 0.86766I
a = −1.012930 − 0.492741I
b = 1.53761 − 0.31028I
10.80380 − 5.89219I 0
u = −1.81641 − 0.86766I
a = −1.012930 + 0.492741I
b = 1.53761 + 0.31028I
10.80380 + 5.89219I 0
u = −1.94249 + 0.64316I
a = 1.023020 + 0.236973I
b = −1.55039 − 0.12499I
11.13970 + 0.68264I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.94249 − 0.64316I
a = 1.023020 − 0.236973I
b = −1.55039 + 0.12499I
11.13970 − 0.68264I 0
12
II.
I
u
2
= hb, −u
8
+ 2u
7
+ · · · + a − 1, u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
−u
2
a
3
=
u
8
− 2u
7
− u
6
+ 4u
5
− u
4
− 2u
3
+ 2u
2
− 2u + 1
0
a
12
=
u
−u
3
+ u
a
7
=
1
0
a
4
=
u
8
− 2u
7
− u
6
+ 4u
5
− u
4
− 2u
3
+ 2u
2
− 2u + 1
0
a
10
=
−u
2
+ 1
−u
2
a
6
=
u
4
− u
2
+ 1
−u
6
+ 2u
4
− u
2
a
1
=
u
7
− 2u
5
+ 2u
3
−u
8
+ u
7
+ 3u
6
− 2u
5
− 3u
4
+ 2u
3
+ 1
a
5
=
−u
7
+ 2u
5
− 2u
3
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u
3
− 1
a
2
=
u
8
− u
7
− u
6
+ 2u
5
− u
4
+ 2u
2
− 2u + 1
−u
8
+ u
7
+ 3u
6
− 2u
5
− 3u
4
+ 2u
3
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
8
+ u
7
− 2u
6
+ u
5
+ 3u
4
− 5u
3
− 2u
2
+ 3u − 7
13
(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
, c
10
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ 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
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
9
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
11
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
12
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
14
(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
, c
10
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
6
, c
12
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
8
, c
11
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
9
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772920 + 0.510351I
a = −0.483566 − 0.305056I
b = 0
−3.42837 + 2.09337I −5.97316 − 1.69698I
u = 0.772920 − 0.510351I
a = −0.483566 + 0.305056I
b = 0
−3.42837 − 2.09337I −5.97316 + 1.69698I
u = −0.825933
a = 3.56378
b = 0
−0.446489 −8.12690
u = −1.173910 + 0.391555I
a = −1.23246 + 1.62704I
b = 0
2.72642 − 1.33617I 4.47739 + 4.48124I
u = −1.173910 − 0.391555I
a = −1.23246 − 1.62704I
b = 0
2.72642 + 1.33617I 4.47739 − 4.48124I
u = 0.141484 + 0.739668I
a = 1.022450 + 0.246780I
b = 0
−1.02799 − 2.45442I −3.46097 + 2.82066I
u = 0.141484 − 0.739668I
a = 1.022450 − 0.246780I
b = 0
−1.02799 + 2.45442I −3.46097 − 2.82066I
u = 1.172470 + 0.500383I
a = 0.411691 + 0.129409I
b = 0
1.95319 + 7.08493I −2.97979 − 2.94778I
u = 1.172470 − 0.500383I
a = 0.411691 − 0.129409I
b = 0
1.95319 − 7.08493I −2.97979 + 2.94778I
16
III. I
u
3
= h7.04 × 10
5
b − 1.71 × 10
5
a
4
+ · · · + 8.73 × 10
5
a + 1.52 ×
10
5
, 17a
5
− 38a
4
− 12a
3
− 9a
2
− 10a − 25, u + 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
−1
a
9
=
1
−1
a
3
=
a
0.242862a
4
− 0.439585a
3
+ ··· − 1.23991a − 0.216271
a
12
=
−1
0
a
7
=
0.103284a
4
+ 0.0292704a
3
+ ··· − 0.0734103a + 1.35715
−0.224715a
4
+ 0.190522a
3
+ ··· + 0.193364a − 0.749015
a
4
=
−0.0689204a
4
+ 0.584206a
3
+ ··· − 1.12111a − 0.546734
0.493929a
4
− 1.35348a
3
+ ··· + 0.201270a + 0.418261
a
10
=
0.0439681a
4
− 0.241745a
3
+ ··· − 0.314896a + 0.124002
0.0819998a
4
− 0.0403129a
3
+ ··· + 0.183306a − 0.473459
a
6
=
−0.121431a
4
+ 0.219792a
3
+ ··· + 0.119953a + 0.608135
−0.224715a
4
+ 0.190522a
3
+ ··· + 0.193364a − 0.749015
a
1
=
0.0819998a
4
− 0.0403129a
3
+ ··· + 0.183306a − 0.473459
−0.495401a
4
+ 0.288576a
3
+ ··· + 1.15889a + 0.146743
a
5
=
−0.121431a
4
+ 0.219792a
3
+ ··· + 0.119953a + 0.608135
−0.224715a
4
+ 0.190522a
3
+ ··· + 0.193364a − 0.749015
a
2
=
0.236323a
4
− 0.711531a
3
+ ··· + 1.22899a + 0.293826
−0.521753a
4
+ 1.01195a
3
+ ··· − 0.475653a − 0.738773
(ii) Obstruction class = 1
(iii) Cusp Shapes =
3736209
704465
a
4
−
5667821
704465
a
3
−
11426549
704465
a
2
−
1784683
704465
a +
1739879
140893
17
(iv) u-Polynomials at the component
18
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
u
5
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
(u + 1)
5
c
9
17(17u
5
− 32u
4
+ 18u
3
+ u
2
− 4u + 1)
c
10
17(17u
5
+ 42u
4
+ 43u
3
+ 22u
2
+ 6u + 1)
c
11
(u − 1)
5
c
12
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
19
20
(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
y
5
c
6
, c
12
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
8
, c
11
(y −1)
5
c
9
289(289y
5
− 412y
4
+ 252y
3
− 81y
2
+ 14y −1)
c
10
289(289y
5
− 302y
4
+ 205y
3
− 52y
2
− 8y −1)
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.440339 + 0.784105I
b = −0.455697 − 1.200150I
−4.22763 + 4.40083I 22.3190 − 16.0614I
u = −1.00000
a = 0.440339 − 0.784105I
b = −0.455697 + 1.200150I
−4.22763 − 4.40083I 22.3190 + 16.0614I
u = −1.00000
a = −0.643046 + 0.524501I
b = 0.339110 − 0.822375I
1.31583 − 1.53058I 7.29086 + 4.54835I
u = −1.00000
a = −0.643046 − 0.524501I
b = 0.339110 + 0.822375I
1.31583 + 1.53058I 7.29086 − 4.54835I
u = −1.00000
a = 2.64071
b = −0.766826
−0.756147 2.29580
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
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
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
(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
9
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
10
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
11
(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
12
(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)
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
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)
c
6
, c
12
(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
, c
11
(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
9
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
10
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)
24
