12a
0680
(K12a
0680
)
A knot diagram
1
Linearized knot diagam
3 7 11 12 8 2 5 6 4 1 9 10
Solving Sequence
5,8
6
9,12
4 10 1 7 11 3 2
c
5
c
8
c
4
c
9
c
12
c
7
c
11
c
3
c
2
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.30506 × 10
89
u
105
+ 1.23026 × 10
90
u
104
+ ··· + 1.08124 × 10
88
b + 1.22301 × 10
89
,
− 6.32954 × 10
88
u
105
− 3.69628 × 10
89
u
104
+ ··· + 2.70309 × 10
87
a − 6.48561 × 10
88
, u
106
+ 7u
105
+ ··· − u
2
+ 1i
I
u
2
= h−2a
4
− 9a
3
− 10a
2
+ 5b − 11a − 4, a
5
+ 5a
4
+ 6a
3
+ 3a
2
+ a + 1, u − 1i
I
u
3
= hb + u + 2, a − 2u − 3, u
2
+ u − 1i
* 3 irreducible components of dim
C
= 0, with total 113 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
= h2.31 × 10
89
u
105
+ 1.23 × 10
90
u
104
+ · · · + 1.08 × 10
88
b + 1.22 ×
10
89
, −6.33 × 10
88
u
105
− 3.70 × 10
89
u
104
+ · · · + 2.70 × 10
87
a − 6.49 ×
10
88
, u
106
+ 7u
105
+ · · · − u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
6
=
1
u
2
a
9
=
−u
−u
3
+ u
a
12
=
23.4159u
105
+ 136.742u
104
+ ··· − 46.1677u + 23.9933
−21.3187u
105
− 113.783u
104
+ ··· + 3.78375u − 11.3113
a
4
=
−251.012u
105
− 1411.63u
104
+ ··· + 127.509u − 179.204
−241.071u
105
− 1355.21u
104
+ ··· + 127.389u − 176.226
a
10
=
65.9369u
105
+ 378.466u
104
+ ··· − 60.0074u + 53.8430
23.5122u
105
+ 140.434u
104
+ ··· − 18.7637u + 22.2506
a
1
=
−91.6179u
105
− 515.563u
104
+ ··· + 31.6304u − 63.6344
−95.0632u
105
− 536.170u
104
+ ··· + 47.1533u − 69.1269
a
7
=
u
u
a
11
=
−37.2311u
105
− 201.840u
104
+ ··· − 16.8240u − 18.5106
−81.3556u
105
− 452.020u
104
+ ··· + 35.0871u − 54.7541
a
3
=
72.6372u
105
+ 410.221u
104
+ ··· − 24.5715u + 50.5987
127.336u
105
+ 721.871u
104
+ ··· − 67.1446u + 94.7937
a
2
=
166.039u
105
+ 941.534u
104
+ ··· − 79.2707u + 121.844
220.738u
105
+ 1253.18u
104
+ ··· − 121.844u + 166.039
(ii) Obstruction class = −1
(iii) Cusp Shapes = 117.650u
105
+ 684.548u
104
+ ··· − 74.1017u + 98.6648
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
106
+ 36u
105
+ ··· + 15872u + 1024
c
2
, c
6
u
106
− 2u
105
+ ··· − 32u − 32
c
3
u
106
+ u
105
+ ··· + 294900u − 153931
c
4
u
106
+ 5u
105
+ ··· + 117392u + 6541
c
5
, c
7
, c
8
u
106
− 7u
105
+ ··· − u
2
+ 1
c
9
u
106
+ 9u
105
+ ··· − 2u − 1
c
10
, c
12
u
106
+ 4u
105
+ ··· + 63u + 1
c
11
u
106
− 18u
105
+ ··· − 64u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
106
+ 60y
105
+ ··· − 50987008y + 1048576
c
2
, c
6
y
106
− 36y
105
+ ··· − 15872y + 1024
c
3
y
106
+ 47y
105
+ ··· − 1112070735948y + 23694752761
c
4
y
106
+ 119y
105
+ ··· − 11945791032y + 42784681
c
5
, c
7
, c
8
y
106
− 89y
105
+ ··· − 2y + 1
c
9
y
106
− 25y
105
+ ··· − 20y + 1
c
10
, c
12
y
106
− 80y
105
+ ··· − 5699y + 1
c
11
y
106
+ 18y
105
+ ··· − 888y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.676515 + 0.691802I
a = −0.336335 − 0.448876I
b = 0.707004 − 0.745975I
0.39517 + 2.43050I 0
u = 0.676515 − 0.691802I
a = −0.336335 + 0.448876I
b = 0.707004 + 0.745975I
0.39517 − 2.43050I 0
u = 0.155047 + 0.936670I
a = −0.503729 + 0.426978I
b = −0.094660 − 0.739124I
6.24033 − 5.37724I 0
u = 0.155047 − 0.936670I
a = −0.503729 − 0.426978I
b = −0.094660 + 0.739124I
6.24033 + 5.37724I 0
u = 0.154727 + 0.905545I
a = 0.479403 − 1.199780I
b = 0.94668 + 1.37587I
7.1033 − 13.7991I 0
u = 0.154727 − 0.905545I
a = 0.479403 + 1.199780I
b = 0.94668 − 1.37587I
7.1033 + 13.7991I 0
u = 0.545270 + 0.721728I
a = 0.614138 − 0.509648I
b = 0.857426 + 0.932428I
0.75431 − 7.41963I 0
u = 0.545270 − 0.721728I
a = 0.614138 + 0.509648I
b = 0.857426 − 0.932428I
0.75431 + 7.41963I 0
u = 0.900430
a = −5.58526
b = 1.50828
0.491361 0
u = 1.086680 + 0.311551I
a = −0.488568 − 0.839468I
b = 0.502420 − 0.844012I
−0.608988 − 0.539453I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.086680 − 0.311551I
a = −0.488568 + 0.839468I
b = 0.502420 + 0.844012I
−0.608988 + 0.539453I 0
u = −1.107130 + 0.281035I
a = −0.169385 + 0.289596I
b = −0.228945 + 1.090470I
4.76987 + 4.98668I 0
u = −1.107130 − 0.281035I
a = −0.169385 − 0.289596I
b = −0.228945 − 1.090470I
4.76987 − 4.98668I 0
u = 1.147060 + 0.071642I
a = −2.55732 − 0.51006I
b = −0.556726 − 1.145320I
−0.503326 − 1.106790I 0
u = 1.147060 − 0.071642I
a = −2.55732 + 0.51006I
b = −0.556726 + 1.145320I
−0.503326 + 1.106790I 0
u = 0.143266 + 0.836626I
a = −0.737577 + 1.002230I
b = −0.799361 − 0.878727I
2.20961 − 7.79473I 0
u = 0.143266 − 0.836626I
a = −0.737577 − 1.002230I
b = −0.799361 + 0.878727I
2.20961 + 7.79473I 0
u = 1.095120 + 0.407068I
a = −0.491541 + 0.367384I
b = −0.703204 + 0.844493I
−0.70354 + 3.31461I 0
u = 1.095120 − 0.407068I
a = −0.491541 − 0.367384I
b = −0.703204 − 0.844493I
−0.70354 − 3.31461I 0
u = 0.088609 + 0.814986I
a = −0.72225 − 1.64625I
b = −0.008950 + 0.823472I
6.58986 − 4.90925I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.088609 − 0.814986I
a = −0.72225 + 1.64625I
b = −0.008950 − 0.823472I
6.58986 + 4.90925I 0
u = −0.162273 + 0.798920I
a = 0.797320 + 0.306408I
b = −0.100735 − 0.852468I
7.55362 − 0.96837I 0
u = −0.162273 − 0.798920I
a = 0.797320 − 0.306408I
b = −0.100735 + 0.852468I
7.55362 + 0.96837I 0
u = −1.149890 + 0.305354I
a = 0.048581 − 0.495678I
b = −0.67876 − 1.36317I
5.12337 − 3.69187I 0
u = −1.149890 − 0.305354I
a = 0.048581 + 0.495678I
b = −0.67876 + 1.36317I
5.12337 + 3.69187I 0
u = 0.149263 + 0.789775I
a = −0.017817 − 0.679262I
b = 0.937147 + 0.817368I
2.21730 − 3.52862I 0
u = 0.149263 − 0.789775I
a = −0.017817 + 0.679262I
b = 0.937147 − 0.817368I
2.21730 + 3.52862I 0
u = −0.116906 + 0.784426I
a = −0.68138 − 1.33921I
b = −0.83302 + 1.34491I
8.23030 + 7.68453I 0
u = −0.116906 − 0.784426I
a = −0.68138 + 1.33921I
b = −0.83302 − 1.34491I
8.23030 − 7.68453I 0
u = 0.043513 + 0.784836I
a = 0.97448 − 1.51173I
b = 0.047337 + 0.690405I
6.79678 − 0.76185I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.043513 − 0.784836I
a = 0.97448 + 1.51173I
b = 0.047337 − 0.690405I
6.79678 + 0.76185I 0
u = 0.090918 + 0.770718I
a = −0.19936 + 2.47849I
b = 0.00449 − 3.27809I
4.25332 − 2.68884I 0
u = 0.090918 − 0.770718I
a = −0.19936 − 2.47849I
b = 0.00449 + 3.27809I
4.25332 + 2.68884I 0
u = 1.188560 + 0.302224I
a = 3.83111 + 1.32734I
b = −0.04331 + 3.31510I
0.93309 − 1.21144I 0
u = 1.188560 − 0.302224I
a = 3.83111 − 1.32734I
b = −0.04331 − 3.31510I
0.93309 + 1.21144I 0
u = 1.175320 + 0.364112I
a = −1.72182 + 0.97398I
b = 0.035690 − 0.706365I
3.26694 + 0.64913I 0
u = 1.175320 − 0.364112I
a = −1.72182 − 0.97398I
b = 0.035690 + 0.706365I
3.26694 − 0.64913I 0
u = 1.126180 + 0.508705I
a = −0.119120 − 0.489606I
b = 0.89677 − 1.30573I
4.14016 + 8.79112I 0
u = 1.126180 − 0.508705I
a = −0.119120 + 0.489606I
b = 0.89677 + 1.30573I
4.14016 − 8.79112I 0
u = 0.561852 + 0.496019I
a = −1.050810 + 0.090517I
b = −0.594871 − 0.545650I
−2.53589 − 3.13368I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.561852 − 0.496019I
a = −1.050810 − 0.090517I
b = −0.594871 + 0.545650I
−2.53589 + 3.13368I 0
u = 1.136020 + 0.558855I
a = 0.1116020 + 0.0736034I
b = 0.072474 + 0.707088I
3.25541 + 0.12582I 0
u = 1.136020 − 0.558855I
a = 0.1116020 − 0.0736034I
b = 0.072474 − 0.707088I
3.25541 − 0.12582I 0
u = −0.011550 + 0.728370I
a = 0.83282 + 1.32236I
b = 0.689599 − 0.927159I
2.92007 + 2.23216I 0
u = −0.011550 − 0.728370I
a = 0.83282 − 1.32236I
b = 0.689599 + 0.927159I
2.92007 − 2.23216I 0
u = 1.230720 + 0.336990I
a = 0.041104 + 0.919788I
b = −0.044115 − 0.784693I
3.14368 − 3.28642I 0
u = 1.230720 − 0.336990I
a = 0.041104 − 0.919788I
b = −0.044115 + 0.784693I
3.14368 + 3.28642I 0
u = 1.247910 + 0.266698I
a = −1.77028 + 0.30960I
b = −0.785011 − 0.715312I
−0.96936 − 1.83401I 0
u = 1.247910 − 0.266698I
a = −1.77028 − 0.30960I
b = −0.785011 + 0.715312I
−0.96936 + 1.83401I 0
u = 1.287610 + 0.041503I
a = 1.59815 − 1.53696I
b = 0.533123 − 0.429693I
−4.21617 + 1.15380I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.287610 − 0.041503I
a = 1.59815 + 1.53696I
b = 0.533123 + 0.429693I
−4.21617 − 1.15380I 0
u = 0.053183 + 0.707999I
a = −0.083772 − 0.941084I
b = −0.671860 + 1.142280I
2.69570 − 1.67604I 0
u = 0.053183 − 0.707999I
a = −0.083772 + 0.941084I
b = −0.671860 − 1.142280I
2.69570 + 1.67604I 0
u = −1.30027
a = 1.98068
b = 0.0571525
−1.62200 0
u = 0.408373 + 0.567951I
a = −0.169169 + 0.696148I
b = −0.424876 + 0.326429I
−2.10687 − 0.70084I 0
u = 0.408373 − 0.567951I
a = −0.169169 − 0.696148I
b = −0.424876 − 0.326429I
−2.10687 + 0.70084I 0
u = −1.273780 + 0.296345I
a = 0.509622 + 0.207417I
b = 0.638369 + 1.031440I
−0.99913 + 1.45852I 0
u = −1.273780 − 0.296345I
a = 0.509622 − 0.207417I
b = 0.638369 − 1.031440I
−0.99913 − 1.45852I 0
u = 1.283820 + 0.305322I
a = 2.41448 − 0.52333I
b = 0.765872 + 0.842265I
−1.11938 − 5.96884I 0
u = 1.283820 − 0.305322I
a = 2.41448 + 0.52333I
b = 0.765872 − 0.842265I
−1.11938 + 5.96884I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.327730 + 0.070439I
a = 0.628795 + 0.328662I
b = 0.310662 − 1.052500I
−3.44617 + 3.59566I 0
u = −1.327730 − 0.070439I
a = 0.628795 − 0.328662I
b = 0.310662 + 1.052500I
−3.44617 − 3.59566I 0
u = −1.298730 + 0.338989I
a = 1.63046 + 0.70206I
b = 0.138386 − 0.615485I
2.60474 + 4.81260I 0
u = −1.298730 − 0.338989I
a = 1.63046 − 0.70206I
b = 0.138386 + 0.615485I
2.60474 − 4.81260I 0
u = −1.309800 + 0.298572I
a = 0.211514 − 1.226060I
b = −0.76166 − 1.48938I
−1.58451 + 5.32615I 0
u = −1.309800 − 0.298572I
a = 0.211514 + 1.226060I
b = −0.76166 + 1.48938I
−1.58451 − 5.32615I 0
u = −1.355400 + 0.028503I
a = −0.58848 + 2.45860I
b = −0.11085 + 2.50944I
−4.83518 + 0.65583I 0
u = −1.355400 − 0.028503I
a = −0.58848 − 2.45860I
b = −0.11085 − 2.50944I
−4.83518 − 0.65583I 0
u = −1.326120 + 0.332619I
a = −2.45639 + 1.30296I
b = −0.05400 + 3.24926I
−0.19585 + 6.67821I 0
u = −1.326120 − 0.332619I
a = −2.45639 − 1.30296I
b = −0.05400 − 3.24926I
−0.19585 − 6.67821I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.326560 + 0.356381I
a = 0.003298 + 0.646392I
b = −0.026079 − 0.908207I
2.15213 + 9.12723I 0
u = −1.326560 − 0.356381I
a = 0.003298 − 0.646392I
b = −0.026079 + 0.908207I
2.15213 − 9.12723I 0
u = 1.341230 + 0.339352I
a = −2.35563 + 0.27394I
b = −0.93728 − 1.33270I
3.64308 − 11.74720I 0
u = 1.341230 − 0.339352I
a = −2.35563 − 0.27394I
b = −0.93728 + 1.33270I
3.64308 + 11.74720I 0
u = −1.358860 + 0.338855I
a = 1.55642 + 0.45502I
b = 1.148940 − 0.768915I
−2.53934 + 7.60969I 0
u = −1.358860 − 0.338855I
a = 1.55642 − 0.45502I
b = 1.148940 + 0.768915I
−2.53934 − 7.60969I 0
u = −0.592031 + 0.074392I
a = −0.649707 + 0.936556I
b = −0.522555 + 1.081850I
4.78736 + 4.50881I 6.94966 − 4.99876I
u = −0.592031 − 0.074392I
a = −0.649707 − 0.936556I
b = −0.522555 − 1.081850I
4.78736 − 4.50881I 6.94966 + 4.99876I
u = 1.404270 + 0.042876I
a = −1.51859 − 1.14123I
b = −0.817555 − 0.820991I
−1.42389 − 4.99446I 0
u = 1.404270 − 0.042876I
a = −1.51859 + 1.14123I
b = −0.817555 + 0.820991I
−1.42389 + 4.99446I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.359400 + 0.362607I
a = −2.01867 − 0.51673I
b = −0.867947 + 0.881577I
−2.52295 + 12.11160I 0
u = −1.359400 − 0.362607I
a = −2.01867 + 0.51673I
b = −0.867947 − 0.881577I
−2.52295 − 12.11160I 0
u = −1.400470 + 0.183938I
a = −0.959650 − 0.786298I
b = −0.571738 − 0.081049I
−7.82829 + 3.32815I 0
u = −1.400470 − 0.183938I
a = −0.959650 + 0.786298I
b = −0.571738 + 0.081049I
−7.82829 − 3.32815I 0
u = 0.583612
a = −0.270838
b = 0.375844
−0.970312 −9.97770
u = 1.37079 + 0.35678I
a = 0.896498 + 0.357764I
b = 0.023413 + 0.687910I
2.71114 − 3.22315I 0
u = 1.37079 − 0.35678I
a = 0.896498 − 0.357764I
b = 0.023413 − 0.687910I
2.71114 + 3.22315I 0
u = −1.41732 + 0.10081I
a = −1.89535 + 0.45530I
b = −0.827832 + 0.526867I
−8.87200 + 4.93818I 0
u = −1.41732 − 0.10081I
a = −1.89535 − 0.45530I
b = −0.827832 − 0.526867I
−8.87200 − 4.93818I 0
u = −1.37888 + 0.39639I
a = 2.09562 + 0.39181I
b = 1.00111 − 1.41069I
2.2683 + 18.4659I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.37888 − 0.39639I
a = 2.09562 − 0.39181I
b = 1.00111 + 1.41069I
2.2683 − 18.4659I 0
u = −1.38164 + 0.41269I
a = −1.017190 + 0.042585I
b = −0.216270 + 0.731064I
1.40270 + 10.20110I 0
u = −1.38164 − 0.41269I
a = −1.017190 − 0.042585I
b = −0.216270 − 0.731064I
1.40270 − 10.20110I 0
u = −1.44978
a = 1.27717
b = 1.00132
−7.46939 0
u = −1.46808 + 0.17386I
a = 1.82916 − 0.44195I
b = 1.08073 − 1.00280I
−5.89344 + 10.41290I 0
u = −1.46808 − 0.17386I
a = 1.82916 + 0.44195I
b = 1.08073 + 1.00280I
−5.89344 − 10.41290I 0
u = 0.472359 + 0.148831I
a = −1.73562 + 3.12337I
b = 1.16952 − 2.15089I
0.670260 − 0.135177I 27.0189 + 4.6847I
u = 0.472359 − 0.148831I
a = −1.73562 − 3.12337I
b = 1.16952 + 2.15089I
0.670260 + 0.135177I 27.0189 − 4.6847I
u = 0.299380 + 0.376191I
a = −0.66009 − 2.85268I
b = 0.424141 + 0.916734I
1.54060 − 2.24837I −0.25150 + 8.36036I
u = 0.299380 − 0.376191I
a = −0.66009 + 2.85268I
b = 0.424141 − 0.916734I
1.54060 + 2.24837I −0.25150 − 8.36036I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.56011 + 0.03449I
a = 0.627791 + 0.194798I
b = 0.651640 + 0.137218I
−7.36096 − 0.00988I 0
u = −1.56011 − 0.03449I
a = 0.627791 − 0.194798I
b = 0.651640 − 0.137218I
−7.36096 + 0.00988I 0
u = −0.172518 + 0.021543I
a = 1.81779 + 3.90095I
b = 0.349706 + 0.727257I
0.08921 − 1.51284I 0.39009 + 4.24743I
u = −0.172518 − 0.021543I
a = 1.81779 − 3.90095I
b = 0.349706 − 0.727257I
0.08921 + 1.51284I 0.39009 − 4.24743I
u = 0.024614 + 0.157392I
a = 2.92457 − 5.12463I
b = −0.621769 + 0.285762I
2.53457 + 0.11622I 3.70952 + 2.56780I
u = 0.024614 − 0.157392I
a = 2.92457 + 5.12463I
b = −0.621769 − 0.285762I
2.53457 − 0.11622I 3.70952 − 2.56780I
15
II.
I
u
2
= h−2a
4
− 9a
3
− 10a
2
+ 5b − 11a − 4, a
5
+ 5a
4
+ 6a
3
+ 3a
2
+ a + 1, u − 1i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
1
a
6
=
1
1
a
9
=
−1
0
a
12
=
a
2
5
a
4
+
9
5
a
3
+ 2a
2
+
11
5
a +
4
5
a
4
=
1
5
a
4
+
2
5
a
3
− a
2
−
2
5
a +
7
5
−
1
5
a
4
−
7
5
a
3
+ ··· −
8
5
a +
3
5
a
10
=
−
2
5
a
4
−
14
5
a
3
+ ··· −
16
5
a −
4
5
−
2
5
a
4
−
14
5
a
3
+ ··· −
21
5
a −
4
5
a
1
=
−
2
5
a
4
−
14
5
a
3
+ ··· −
21
5
a −
4
5
−
2
5
a
4
−
14
5
a
3
+ ··· −
21
5
a −
4
5
a
7
=
1
1
a
11
=
2
5
a
4
+
9
5
a
3
+ 2a
2
+
16
5
a +
4
5
2
5
a
4
+
9
5
a
3
+ 2a
2
+
11
5
a +
4
5
a
3
=
−
2
5
a
4
−
14
5
a
3
+ ··· −
21
5
a −
4
5
−
2
5
a
4
−
14
5
a
3
+ ··· −
21
5
a −
4
5
a
2
=
−
2
5
a
4
−
14
5
a
3
+ ··· −
21
5
a −
4
5
−
2
5
a
4
−
14
5
a
3
+ ··· −
21
5
a −
4
5
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
7
5
a
4
−
24
5
a
3
+ 2a
2
+
9
5
a −
44
5
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
5
c
3
, c
12
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
4
, c
11
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
5
(u − 1)
5
c
7
, c
8
(u + 1)
5
c
9
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
c
10
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
5
c
3
, c
10
, c
12
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
4
, c
11
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
5
, c
7
, c
8
(y −1)
5
c
9
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.881366 + 0.489365I
b = −0.339110 + 0.822375I
−1.31583 + 1.53058I −8.42731 − 4.45807I
u = 1.00000
a = −0.881366 − 0.489365I
b = −0.339110 − 0.822375I
−1.31583 − 1.53058I −8.42731 + 4.45807I
u = 1.00000
a = 0.142272 + 0.509071I
b = 0.455697 + 1.200150I
4.22763 − 4.40083I −8.55516 + 1.78781I
u = 1.00000
a = 0.142272 − 0.509071I
b = 0.455697 − 1.200150I
4.22763 + 4.40083I −8.55516 − 1.78781I
u = 1.00000
a = −3.52181
b = 0.766826
0.756147 3.96490
19
III. I
u
3
= hb + u + 2, a − 2u − 3, u
2
+ u − 1i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
6
=
1
−u + 1
a
9
=
−u
−u + 1
a
12
=
2u + 3
−u − 2
a
4
=
5u + 9
−3u − 5
a
10
=
4
−2u − 1
a
1
=
2u − 1
u − 1
a
7
=
u
u
a
11
=
2u + 3
−u − 2
a
3
=
1
0
a
2
=
u
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 41
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
2
− 3u + 1
c
2
, c
5
u
2
+ u − 1
c
3
, c
4
, c
9
u
2
+ 3u + 1
c
6
, c
7
, c
8
u
2
− u − 1
c
10
(u + 1)
2
c
11
u
2
c
12
(u − 1)
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
9
y
2
− 7y + 1
c
2
, c
5
, c
6
c
7
, c
8
y
2
− 3y + 1
c
10
, c
12
(y −1)
2
c
11
y
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 4.23607
b = −2.61803
0.657974 41.0000
u = −1.61803
a = −0.236068
b = −0.381966
−7.23771 41.0000
23
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
5
(u
2
− 3u + 1)(u
106
+ 36u
105
+ ··· + 15872u + 1024)
c
2
u
5
(u
2
+ u − 1)(u
106
− 2u
105
+ ··· − 32u − 32)
c
3
(u
2
+ 3u + 1)(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
· (u
106
+ u
105
+ ··· + 294900u − 153931)
c
4
(u
2
+ 3u + 1)(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
· (u
106
+ 5u
105
+ ··· + 117392u + 6541)
c
5
((u − 1)
5
)(u
2
+ u − 1)(u
106
− 7u
105
+ ··· − u
2
+ 1)
c
6
u
5
(u
2
− u − 1)(u
106
− 2u
105
+ ··· − 32u − 32)
c
7
, c
8
((u + 1)
5
)(u
2
− u − 1)(u
106
− 7u
105
+ ··· − u
2
+ 1)
c
9
(u
2
+ 3u + 1)(u
5
+ 3u
4
+ ··· − u − 1)(u
106
+ 9u
105
+ ··· − 2u − 1)
c
10
((u + 1)
2
)(u
5
− u
4
+ ··· + u + 1)(u
106
+ 4u
105
+ ··· + 63u + 1)
c
11
u
2
(u
5
− u
4
+ ··· + u − 1)(u
106
− 18u
105
+ ··· − 64u + 4)
c
12
((u − 1)
2
)(u
5
+ u
4
+ ··· + u − 1)(u
106
+ 4u
105
+ ··· + 63u + 1)
24
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
5
(y
2
− 7y + 1)(y
106
+ 60y
105
+ ··· − 5.09870 × 10
7
y + 1048576)
c
2
, c
6
y
5
(y
2
− 3y + 1)(y
106
− 36y
105
+ ··· − 15872y + 1024)
c
3
(y
2
− 7y + 1)(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
· (y
106
+ 47y
105
+ ··· − 1112070735948y + 23694752761)
c
4
(y
2
− 7y + 1)(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
· (y
106
+ 119y
105
+ ··· − 11945791032y + 42784681)
c
5
, c
7
, c
8
((y −1)
5
)(y
2
− 3y + 1)(y
106
− 89y
105
+ ··· − 2y + 1)
c
9
(y
2
− 7y + 1)(y
5
− y
4
+ ··· + 3y −1)(y
106
− 25y
105
+ ··· − 20y + 1)
c
10
, c
12
((y −1)
2
)(y
5
− 5y
4
+ ··· − y −1)(y
106
− 80y
105
+ ··· − 5699y + 1)
c
11
y
2
(y
5
+ 3y
4
+ ··· − y −1)(y
106
+ 18y
105
+ ··· − 888y + 16)
25
