12a
0674
(K12a
0674
)
A knot diagram
1
Linearized knot diagam
3 7 11 9 12 8 2 1 5 6 4 10
Solving Sequence
2,7 3,11
4 8 12 1 9 6 5 10
c
2
c
3
c
7
c
11
c
1
c
8
c
6
c
5
c
10
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h7.30354 × 10
106
u
132
+ 1.06306 × 10
107
u
131
+ ··· + 2.46021 × 10
107
b + 6.28959 × 10
107
,
− 1.10982 × 10
109
u
132
+ 1.75925 × 10
109
u
131
+ ··· + 1.30391 × 10
109
a + 6.69976 × 10
107
,
u
133
− u
132
+ ··· + 11u − 1i
I
u
2
= h−u
22
− 2u
20
+ ··· + b + 1, u
22
+ 5u
20
+ ··· + a − 3, u
23
+ 4u
21
+ ··· − 4u
2
− 1i
* 2 irreducible components of dim
C
= 0, with total 156 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
= h7.30 × 10
106
u
132
+ 1.06 × 10
107
u
131
+ · · · + 2.46 × 10
107
b + 6.29 ×
10
107
, −1.11 × 10
109
u
132
+ 1.76 × 10
109
u
131
+ · · · + 1.30 × 10
109
a + 6.70 ×
10
107
, u
133
− u
132
+ · · · + 11u − 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
−u
2
a
11
=
0.851148u
132
− 1.34921u
131
+ ··· − 26.4094u − 0.0513820
−0.296866u
132
− 0.432100u
131
+ ··· + 15.0390u − 2.55652
a
4
=
3.22970u
132
− 2.96146u
131
+ ··· − 120.446u + 17.4193
−0.418462u
132
− 0.951295u
131
+ ··· − 20.2704u + 3.94279
a
8
=
u
u
a
12
=
3.63001u
132
− 2.81263u
131
+ ··· − 119.194u + 18.3141
0.283591u
132
+ 0.101456u
131
+ ··· − 4.05479u + 1.29525
a
1
=
u
2
+ 1
−u
4
a
9
=
u
7
+ 2u
5
+ 2u
3
+ 2u
−u
9
− u
7
− u
5
+ u
a
6
=
u
3
u
3
+ u
a
5
=
2.16708u
132
− 2.13527u
131
+ ··· − 100.925u + 14.9635
−1.70344u
132
− 0.445984u
131
+ ··· − 7.88626u + 2.51137
a
10
=
1.14813u
132
− 0.647471u
131
+ ··· − 25.9002u − 0.124938
−0.299784u
132
+ 0.495982u
131
+ ··· + 22.2916u − 3.35175
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4.84648u
132
+ 2.26486u
131
+ ··· + 85.5361u − 9.94143
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
133
+ 45u
132
+ ··· + 21u − 1
c
2
, c
7
u
133
+ u
132
+ ··· + 11u + 1
c
3
, c
11
u
133
− 47u
131
+ ··· + 8432u + 2069
c
4
, c
9
u
133
− 40u
131
+ ··· − 1016u − 121
c
5
u
133
− u
132
+ ··· + 17u + 3
c
8
u
133
− 5u
132
+ ··· + 5531185u + 580413
c
10
u
133
+ 3u
132
+ ··· − 154743u − 114143
c
12
u
133
+ 19u
132
+ ··· + 419u − 11
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
133
+ 89y
132
+ ··· + 225y −1
c
2
, c
7
y
133
+ 45y
132
+ ··· + 21y −1
c
3
, c
11
y
133
− 94y
132
+ ··· + 138510782y −4280761
c
4
, c
9
y
133
− 80y
132
+ ··· + 653284y −14641
c
5
y
133
+ 5y
132
+ ··· + 175y −9
c
8
y
133
+ 49y
132
+ ··· + 385483097599y −336879250569
c
10
y
133
− 25y
132
+ ··· + 297383627417y −13028624449
c
12
y
133
− 19y
132
+ ··· + 229791y −121
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.829466 + 0.557218I
a = −0.187671 − 0.453469I
b = −1.222830 + 0.285357I
0.27659 − 1.61748I 0
u = 0.829466 − 0.557218I
a = −0.187671 + 0.453469I
b = −1.222830 − 0.285357I
0.27659 + 1.61748I 0
u = −0.734358 + 0.685968I
a = −0.716811 − 0.659771I
b = 1.83044 − 0.96506I
3.13923 + 3.76117I 0
u = −0.734358 − 0.685968I
a = −0.716811 + 0.659771I
b = 1.83044 + 0.96506I
3.13923 − 3.76117I 0
u = −0.721478 + 0.676585I
a = −1.15819 + 1.11373I
b = −2.41017 − 0.73023I
−1.030550 + 0.687025I 0
u = −0.721478 − 0.676585I
a = −1.15819 − 1.11373I
b = −2.41017 + 0.73023I
−1.030550 − 0.687025I 0
u = 0.031969 + 1.014520I
a = 2.90854 − 0.41681I
b = 1.91497 − 0.49345I
−2.20674 + 3.68448I 0
u = 0.031969 − 1.014520I
a = 2.90854 + 0.41681I
b = 1.91497 + 0.49345I
−2.20674 − 3.68448I 0
u = 0.016803 + 1.017960I
a = −2.03758 − 0.46975I
b = −0.510962 − 0.798251I
−6.25026 + 0.49451I 0
u = 0.016803 − 1.017960I
a = −2.03758 + 0.46975I
b = −0.510962 + 0.798251I
−6.25026 − 0.49451I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.685834 + 0.699198I
a = −0.767536 + 0.775321I
b = −1.028360 + 0.947545I
−1.47271 + 0.24934I 0
u = 0.685834 − 0.699198I
a = −0.767536 − 0.775321I
b = −1.028360 − 0.947545I
−1.47271 − 0.24934I 0
u = 0.727677 + 0.651708I
a = 0.35106 − 1.47593I
b = −1.36670 − 0.80541I
1.24829 − 2.40392I 0
u = 0.727677 − 0.651708I
a = 0.35106 + 1.47593I
b = −1.36670 + 0.80541I
1.24829 + 2.40392I 0
u = −0.179511 + 0.956362I
a = −0.351454 − 0.626307I
b = −0.635097 − 0.599965I
−0.91600 − 2.47222I 0
u = −0.179511 − 0.956362I
a = −0.351454 + 0.626307I
b = −0.635097 + 0.599965I
−0.91600 + 2.47222I 0
u = 0.660567 + 0.714040I
a = −0.58202 + 1.66891I
b = 2.34706 + 0.70544I
2.31625 + 3.39587I 0
u = 0.660567 − 0.714040I
a = −0.58202 − 1.66891I
b = 2.34706 − 0.70544I
2.31625 − 3.39587I 0
u = 0.620877 + 0.821547I
a = −0.48379 + 2.02623I
b = 1.33843 + 2.03608I
2.29662 + 5.56622I 0
u = 0.620877 − 0.821547I
a = −0.48379 − 2.02623I
b = 1.33843 − 2.03608I
2.29662 − 5.56622I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.748353 + 0.607521I
a = −0.64066 − 1.32225I
b = −2.30820 − 0.01910I
−0.55990 − 4.34234I 0
u = 0.748353 − 0.607521I
a = −0.64066 + 1.32225I
b = −2.30820 + 0.01910I
−0.55990 + 4.34234I 0
u = −0.806815 + 0.650210I
a = 0.78857 − 1.39267I
b = 2.49807 + 0.68797I
−2.09601 + 6.69318I 0
u = −0.806815 − 0.650210I
a = 0.78857 + 1.39267I
b = 2.49807 − 0.68797I
−2.09601 − 6.69318I 0
u = −0.792322 + 0.671448I
a = −0.02810 + 1.77382I
b = −1.74411 + 0.97162I
5.33307 + 6.48914I 0
u = −0.792322 − 0.671448I
a = −0.02810 − 1.77382I
b = −1.74411 − 0.97162I
5.33307 − 6.48914I 0
u = −0.032707 + 1.038950I
a = −0.471645 + 0.065998I
b = −0.405838 + 0.767883I
−4.17499 − 2.01012I 0
u = −0.032707 − 1.038950I
a = −0.471645 − 0.065998I
b = −0.405838 − 0.767883I
−4.17499 + 2.01012I 0
u = −0.715840 + 0.754563I
a = 0.31363 + 2.33969I
b = −1.53396 + 1.06766I
4.04153 − 3.28866I 0
u = −0.715840 − 0.754563I
a = 0.31363 − 2.33969I
b = −1.53396 − 1.06766I
4.04153 + 3.28866I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.098442 + 1.043060I
a = −0.279989 + 0.448295I
b = −0.167892 − 0.716442I
−0.76631 + 6.36624I 0
u = 0.098442 − 1.043060I
a = −0.279989 − 0.448295I
b = −0.167892 + 0.716442I
−0.76631 − 6.36624I 0
u = −0.616430 + 0.717140I
a = −0.031952 − 0.983535I
b = 0.457556 − 0.705776I
0.299724 − 1.340940I 0
u = −0.616430 − 0.717140I
a = −0.031952 + 0.983535I
b = 0.457556 + 0.705776I
0.299724 + 1.340940I 0
u = 0.843693 + 0.642382I
a = 0.80794 + 1.17541I
b = 2.40663 − 0.59239I
1.37915 − 13.20260I 0
u = 0.843693 − 0.642382I
a = 0.80794 − 1.17541I
b = 2.40663 + 0.59239I
1.37915 + 13.20260I 0
u = 0.461323 + 0.958783I
a = −0.66581 − 1.31575I
b = −0.311258 − 0.419657I
−4.97964 + 3.27878I 0
u = 0.461323 − 0.958783I
a = −0.66581 + 1.31575I
b = −0.311258 + 0.419657I
−4.97964 − 3.27878I 0
u = 0.790248 + 0.731784I
a = 1.023070 + 0.972731I
b = 1.48869 − 0.73894I
5.35487 − 1.32108I 0
u = 0.790248 − 0.731784I
a = 1.023070 − 0.972731I
b = 1.48869 + 0.73894I
5.35487 + 1.32108I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.030359 + 1.083870I
a = −1.61526 − 0.02028I
b = −0.560913 + 0.624414I
−6.20287 − 3.52001I 0
u = −0.030359 − 1.083870I
a = −1.61526 + 0.02028I
b = −0.560913 − 0.624414I
−6.20287 + 3.52001I 0
u = 0.099851 + 1.082680I
a = 1.56114 + 1.06415I
b = 0.75408 + 1.30712I
−8.37138 + 6.25937I 0
u = 0.099851 − 1.082680I
a = 1.56114 − 1.06415I
b = 0.75408 − 1.30712I
−8.37138 − 6.25937I 0
u = 0.804518 + 0.740132I
a = 1.048500 − 0.016324I
b = 0.301561 − 1.325510I
5.44222 − 1.54867I 0
u = 0.804518 − 0.740132I
a = 1.048500 + 0.016324I
b = 0.301561 + 1.325510I
5.44222 + 1.54867I 0
u = −0.884121 + 0.649834I
a = −0.642850 + 0.347536I
b = −1.41407 − 0.63286I
0.82351 + 3.74039I 0
u = −0.884121 − 0.649834I
a = −0.642850 − 0.347536I
b = −1.41407 + 0.63286I
0.82351 − 3.74039I 0
u = −0.832739 + 0.318790I
a = −0.537634 − 0.247620I
b = −0.593936 − 0.023566I
−0.83222 + 2.21045I 0
u = −0.832739 − 0.318790I
a = −0.537634 + 0.247620I
b = −0.593936 + 0.023566I
−0.83222 − 2.21045I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.606513 + 0.929505I
a = 1.87960 + 0.63359I
b = 2.01659 − 0.73061I
1.95980 − 0.77443I 0
u = 0.606513 − 0.929505I
a = 1.87960 − 0.63359I
b = 2.01659 + 0.73061I
1.95980 + 0.77443I 0
u = 0.704739 + 0.857429I
a = 0.46803 + 1.67996I
b = 2.11240 + 0.42062I
4.03992 + 2.69835I 0
u = 0.704739 − 0.857429I
a = 0.46803 − 1.67996I
b = 2.11240 − 0.42062I
4.03992 − 2.69835I 0
u = −0.125717 + 1.119890I
a = 1.57286 − 0.71666I
b = 0.753208 − 1.001390I
−5.31003 − 12.57920I 0
u = −0.125717 − 1.119890I
a = 1.57286 + 0.71666I
b = 0.753208 + 1.001390I
−5.31003 + 12.57920I 0
u = −0.200863 + 0.846409I
a = 0.176375 − 0.809048I
b = −0.477015 − 0.916584I
−0.62658 − 2.37382I 0
u = −0.200863 − 0.846409I
a = 0.176375 + 0.809048I
b = −0.477015 + 0.916584I
−0.62658 + 2.37382I 0
u = 0.186414 + 1.114970I
a = −1.20302 − 0.78455I
b = −0.457905 − 0.542020I
−6.41500 + 3.24788I 0
u = 0.186414 − 1.114970I
a = −1.20302 + 0.78455I
b = −0.457905 + 0.542020I
−6.41500 − 3.24788I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.772148 + 0.825651I
a = 0.391758 − 1.232690I
b = 2.11636 − 0.54743I
7.77314 − 4.39597I 0
u = −0.772148 − 0.825651I
a = 0.391758 + 1.232690I
b = 2.11636 + 0.54743I
7.77314 + 4.39597I 0
u = −0.745875 + 0.851037I
a = 1.22426 + 1.56138I
b = −0.81524 + 2.03542I
1.29744 − 4.87074I 0
u = −0.745875 − 0.851037I
a = 1.22426 − 1.56138I
b = −0.81524 − 2.03542I
1.29744 + 4.87074I 0
u = −0.038042 + 0.862219I
a = 0.214791 − 0.816636I
b = −0.612395 − 1.183300I
−0.55150 − 2.37818I 0
u = −0.038042 − 0.862219I
a = 0.214791 + 0.816636I
b = −0.612395 + 1.183300I
−0.55150 + 2.37818I 0
u = −0.728576 + 0.876619I
a = −1.44472 + 0.04920I
b = −1.31953 − 1.68646I
1.21316 − 0.72689I 0
u = −0.728576 − 0.876619I
a = −1.44472 − 0.04920I
b = −1.31953 + 1.68646I
1.21316 + 0.72689I 0
u = 0.554991 + 0.997859I
a = 0.215405 + 0.642494I
b = −0.469581 − 0.086362I
−5.67603 + 0.11820I 0
u = 0.554991 − 0.997859I
a = 0.215405 − 0.642494I
b = −0.469581 + 0.086362I
−5.67603 − 0.11820I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.654255 + 0.529002I
a = −0.531318 − 0.948647I
b = −0.516446 − 0.824655I
−1.17576 − 2.23945I 0
u = −0.654255 − 0.529002I
a = −0.531318 + 0.948647I
b = −0.516446 + 0.824655I
−1.17576 + 2.23945I 0
u = −0.078490 + 1.156840I
a = −1.108160 + 0.588652I
b = −0.525310 + 0.610228I
−6.11826 − 0.30468I 0
u = −0.078490 − 1.156840I
a = −1.108160 − 0.588652I
b = −0.525310 − 0.610228I
−6.11826 + 0.30468I 0
u = −0.511698 + 1.051450I
a = 0.094918 − 0.908934I
b = −0.277344 − 0.215663I
−2.94597 + 5.56510I 0
u = −0.511698 − 1.051450I
a = 0.094918 + 0.908934I
b = −0.277344 + 0.215663I
−2.94597 − 5.56510I 0
u = −0.645054 + 0.976463I
a = 0.803186 − 0.367632I
b = 1.239910 + 0.095870I
−0.53546 − 3.67311I 0
u = −0.645054 − 0.976463I
a = 0.803186 + 0.367632I
b = 1.239910 − 0.095870I
−0.53546 + 3.67311I 0
u = 0.341302 + 0.754513I
a = 1.89377 − 0.51903I
b = 0.528550 − 0.778640I
1.72664 − 1.39745I 0
u = 0.341302 − 0.754513I
a = 1.89377 + 0.51903I
b = 0.528550 + 0.778640I
1.72664 + 1.39745I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.656822 + 0.971722I
a = 1.08359 + 2.42485I
b = 2.71943 − 0.08747I
1.52248 + 1.75392I 0
u = 0.656822 − 0.971722I
a = 1.08359 − 2.42485I
b = 2.71943 + 0.08747I
1.52248 − 1.75392I 0
u = −0.686713 + 0.950846I
a = −1.057780 + 0.666024I
b = −2.27751 − 0.44997I
3.44069 − 2.09453I 0
u = −0.686713 − 0.950846I
a = −1.057780 − 0.666024I
b = −2.27751 + 0.44997I
3.44069 + 2.09453I 0
u = −0.752125 + 0.911272I
a = 0.86436 − 1.70163I
b = 1.98830 − 0.13165I
7.51253 − 1.35208I 0
u = −0.752125 − 0.911272I
a = 0.86436 + 1.70163I
b = 1.98830 + 0.13165I
7.51253 + 1.35208I 0
u = 0.665252 + 0.980054I
a = 0.39895 − 1.66830I
b = −0.191789 − 1.109800I
−2.32604 + 4.99485I 0
u = 0.665252 − 0.980054I
a = 0.39895 + 1.66830I
b = −0.191789 + 1.109800I
−2.32604 − 4.99485I 0
u = 0.805497
a = −0.774031
b = −0.731813
−2.39408 −14.6460
u = −0.630426 + 1.016410I
a = 0.591166 + 1.183950I
b = 0.224770 + 0.917796I
−2.51213 − 2.78956I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.630426 − 1.016410I
a = 0.591166 − 1.183950I
b = 0.224770 − 0.917796I
−2.51213 + 2.78956I 0
u = 0.832129 + 0.866569I
a = −1.142190 − 0.113565I
b = −1.21470 + 1.17018I
6.18926 − 3.55633I 0
u = 0.832129 − 0.866569I
a = −1.142190 + 0.113565I
b = −1.21470 − 1.17018I
6.18926 + 3.55633I 0
u = −0.676674 + 0.992753I
a = −0.25761 + 2.76596I
b = −2.38314 + 1.63671I
−1.97758 − 6.05966I 0
u = −0.676674 − 0.992753I
a = −0.25761 − 2.76596I
b = −2.38314 − 1.63671I
−1.97758 + 6.05966I 0
u = −0.684739 + 0.992430I
a = 1.41215 − 1.79447I
b = 2.01295 + 0.74891I
2.21734 − 9.19561I 0
u = −0.684739 − 0.992430I
a = 1.41215 + 1.79447I
b = 2.01295 − 0.74891I
2.21734 + 9.19561I 0
u = 0.675705 + 1.002640I
a = −1.16510 − 1.04057I
b = −2.13223 + 0.29372I
0.20916 + 7.78845I 0
u = 0.675705 − 1.002640I
a = −1.16510 + 1.04057I
b = −2.13223 − 0.29372I
0.20916 − 7.78845I 0
u = −0.538646 + 1.083050I
a = −0.489623 + 0.807803I
b = −0.220710 + 0.283354I
−3.21572 − 7.12732I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.538646 − 1.083050I
a = −0.489623 − 0.807803I
b = −0.220710 − 0.283354I
−3.21572 + 7.12732I 0
u = −0.738555 + 0.271606I
a = 0.665243 + 1.138950I
b = 0.542861 + 0.262205I
−0.64572 − 10.08060I 0. + 7.27179I
u = −0.738555 − 0.271606I
a = 0.665243 − 1.138950I
b = 0.542861 − 0.262205I
−0.64572 + 10.08060I 0. − 7.27179I
u = 0.812978 + 0.902870I
a = 0.56029 − 1.43308I
b = −0.98178 − 1.56664I
6.07142 + 9.66919I 0
u = 0.812978 − 0.902870I
a = 0.56029 + 1.43308I
b = −0.98178 + 1.56664I
6.07142 − 9.66919I 0
u = 0.722098 + 0.983360I
a = −0.05574 + 1.53189I
b = 1.65631 + 1.36571I
4.58449 + 7.02851I 0
u = 0.722098 − 0.983360I
a = −0.05574 − 1.53189I
b = 1.65631 − 1.36571I
4.58449 − 7.02851I 0
u = 0.671560 + 1.024450I
a = −1.03693 − 2.42511I
b = −2.67378 − 0.90934I
−1.78667 + 9.75979I 0
u = 0.671560 − 1.024450I
a = −1.03693 + 2.42511I
b = −2.67378 + 0.90934I
−1.78667 − 9.75979I 0
u = 0.736094 + 0.984835I
a = −0.955780 + 0.626928I
b = 0.06368 + 1.60344I
4.69335 + 7.34436I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.736094 − 0.984835I
a = −0.955780 − 0.626928I
b = 0.06368 − 1.60344I
4.69335 − 7.34436I 0
u = −0.705800 + 1.013630I
a = −1.58734 + 1.08076I
b = −2.49368 − 0.33295I
4.29914 − 12.14510I 0
u = −0.705800 − 1.013630I
a = −1.58734 − 1.08076I
b = −2.49368 + 0.33295I
4.29914 + 12.14510I 0
u = −0.705551 + 1.027400I
a = 0.35318 − 2.63546I
b = 2.77902 − 1.43894I
−3.23395 − 12.38490I 0
u = −0.705551 − 1.027400I
a = 0.35318 + 2.63546I
b = 2.77902 + 1.43894I
−3.23395 + 12.38490I 0
u = 0.681674 + 1.059760I
a = −0.39846 − 1.54531I
b = −1.58965 − 0.59813I
−1.21666 + 7.24848I 0
u = 0.681674 − 1.059760I
a = −0.39846 + 1.54531I
b = −1.58965 + 0.59813I
−1.21666 − 7.24848I 0
u = 0.716863 + 1.043940I
a = 0.53679 + 2.50587I
b = 2.65728 + 1.28174I
0.1571 + 19.0309I 0
u = 0.716863 − 1.043940I
a = 0.53679 − 2.50587I
b = 2.65728 − 1.28174I
0.1571 − 19.0309I 0
u = −0.732191 + 1.053200I
a = −0.13910 + 1.76630I
b = −1.50536 + 1.04917I
−0.42182 − 9.72536I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.732191 − 1.053200I
a = −0.13910 − 1.76630I
b = −1.50536 − 1.04917I
−0.42182 + 9.72536I 0
u = 0.631573 + 0.306077I
a = 0.64158 − 1.48302I
b = 0.465548 − 0.120069I
−3.91445 + 4.24438I −1.92123 − 5.36402I
u = 0.631573 − 0.306077I
a = 0.64158 + 1.48302I
b = 0.465548 + 0.120069I
−3.91445 − 4.24438I −1.92123 + 5.36402I
u = 0.551738 + 0.219874I
a = −0.21097 + 1.48670I
b = 0.501140 + 0.709999I
3.21681 + 4.50444I 5.50360 − 6.34513I
u = 0.551738 − 0.219874I
a = −0.21097 − 1.48670I
b = 0.501140 − 0.709999I
3.21681 − 4.50444I 5.50360 + 6.34513I
u = −0.560566 + 0.007908I
a = 1.368560 − 0.333118I
b = 0.124178 − 0.100284I
2.06758 − 0.05000I 6.46888 − 1.08460I
u = −0.560566 − 0.007908I
a = 1.368560 + 0.333118I
b = 0.124178 + 0.100284I
2.06758 + 0.05000I 6.46888 + 1.08460I
u = −0.349627 + 0.391770I
a = 0.471373 − 1.143480I
b = 0.197013 − 0.383361I
0.097287 − 1.096420I 1.55163 + 5.86432I
u = −0.349627 − 0.391770I
a = 0.471373 + 1.143480I
b = 0.197013 + 0.383361I
0.097287 + 1.096420I 1.55163 − 5.86432I
u = 0.456044
a = −1.54081
b = −0.959396
−2.76051 −3.94310
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.209120 + 0.155908I
a = −4.65078 − 2.09516I
b = 0.798507 − 0.007645I
1.44067 + 3.00795I 5.79511 − 9.20913I
u = 0.209120 − 0.155908I
a = −4.65078 + 2.09516I
b = 0.798507 + 0.007645I
1.44067 − 3.00795I 5.79511 + 9.20913I
u = 0.202117
a = −3.78734
b = −1.28097
−2.69685 −8.15030
18
II.
I
u
2
= h−u
22
−2u
20
+· · ·+b+1, u
22
+5u
20
+· · ·+a−3, u
23
+4u
21
+· · ·−4u
2
−1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
−u
2
a
11
=
−u
22
− 5u
20
+ ··· + 3u
2
+ 3
u
22
+ 2u
20
+ ··· + 2u − 1
a
4
=
u
21
+ 3u
19
+ ··· + 2u − 1
u
21
+ 4u
19
+ ··· − u
2
− 2u
a
8
=
u
u
a
12
=
−2u
22
+ 2u
21
+ ··· + 2u + 1
u
21
+ 6u
19
+ ··· − 11u
2
− 3
a
1
=
u
2
+ 1
−u
4
a
9
=
u
7
+ 2u
5
+ 2u
3
+ 2u
−u
9
− u
7
− u
5
+ u
a
6
=
u
3
u
3
+ u
a
5
=
2u
21
+ 7u
19
+ ··· + 4u − 3
u
21
+ 4u
19
+ ··· − u − 1
a
10
=
−u
22
− 5u
20
+ ··· + 4u
2
+ 3
u
22
+ 2u
20
+ ··· − 2u
2
+ 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −5u
21
+ 2u
20
− 19u
19
+ 7u
18
− 56u
17
+ 20u
16
− 102u
15
+ 36u
14
− 148u
13
+ 58u
12
−
163u
11
+ 74u
10
− 140u
9
+ 85u
8
− 103u
7
+ 77u
6
− 49u
5
+ 54u
4
− 22u
3
+ 22u
2
− 4u + 4
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
23
− 8u
22
+ ··· − 8u + 1
c
2
u
23
+ 4u
21
+ ··· − 4u
2
− 1
c
3
u
23
− u
22
+ ··· − u + 1
c
4
u
23
− u
22
+ ··· − u + 1
c
5
u
23
+ 2u
20
+ ··· + 3u
2
+ 1
c
7
u
23
+ 4u
21
+ ··· + 4u
2
+ 1
c
8
u
23
+ 4u
21
+ ··· + 7u
2
+ 1
c
9
u
23
+ u
22
+ ··· − u − 1
c
10
u
23
+ 3u
21
+ ··· + 2u
3
+ 1
c
11
u
23
+ u
22
+ ··· − u − 1
c
12
u
23
− 4u
21
+ ··· − 6u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
23
+ 16y
22
+ ··· − 56y
2
− 1
c
2
, c
7
y
23
+ 8y
22
+ ··· − 8y −1
c
3
, c
11
y
23
− 23y
22
+ ··· + 17y −1
c
4
, c
9
y
23
− 17y
22
+ ··· + 23y −1
c
5
y
23
− 2y
21
+ ··· − 6y −1
c
8
y
23
+ 8y
22
+ ··· − 14y −1
c
10
y
23
+ 6y
22
+ ··· + 2y
2
− 1
c
12
y
23
− 8y
22
+ ··· + 6y −1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.814070 + 0.582429I
a = −0.372018 + 0.525342I
b = −1.50347 − 0.15021I
0.21086 + 3.10823I −0.15383 − 2.88731I
u = −0.814070 − 0.582429I
a = −0.372018 − 0.525342I
b = −1.50347 + 0.15021I
0.21086 − 3.10823I −0.15383 + 2.88731I
u = −0.675659 + 0.801513I
a = −0.73256 − 2.61620I
b = 2.05121 − 1.79003I
3.21677 − 4.42137I 5.15637 + 7.65571I
u = −0.675659 − 0.801513I
a = −0.73256 + 2.61620I
b = 2.05121 + 1.79003I
3.21677 + 4.42137I 5.15637 − 7.65571I
u = 0.586855 + 0.709510I
a = −0.869331 + 0.406673I
b = −1.39499 + 0.90288I
−2.10023 + 0.99265I −4.85391 − 4.50359I
u = 0.586855 − 0.709510I
a = −0.869331 − 0.406673I
b = −1.39499 − 0.90288I
−2.10023 − 0.99265I −4.85391 + 4.50359I
u = −0.084974 + 0.905200I
a = 0.998136 + 0.073773I
b = 1.40800 + 0.57777I
−0.49803 − 3.52111I −0.85255 + 7.82342I
u = −0.084974 − 0.905200I
a = 0.998136 − 0.073773I
b = 1.40800 − 0.57777I
−0.49803 + 3.52111I −0.85255 − 7.82342I
u = 0.085110 + 1.090360I
a = −1.55525 − 0.35317I
b = −0.542269 − 0.433067I
−6.06125 + 2.26227I −5.59951 − 1.37868I
u = 0.085110 − 1.090360I
a = −1.55525 + 0.35317I
b = −0.542269 + 0.433067I
−6.06125 − 2.26227I −5.59951 + 1.37868I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.792977 + 0.771338I
a = −1.271050 + 0.212145I
b = −0.315322 + 1.322290I
5.19516 − 2.16291I 2.01913 + 5.25864I
u = 0.792977 − 0.771338I
a = −1.271050 − 0.212145I
b = −0.315322 − 1.322290I
5.19516 + 2.16291I 2.01913 − 5.25864I
u = −0.669570 + 0.917361I
a = 1.67756 − 1.13767I
b = 2.65981 + 1.12563I
2.85498 − 0.78537I 4.77130 − 1.23542I
u = −0.669570 − 0.917361I
a = 1.67756 + 1.13767I
b = 2.65981 − 1.12563I
2.85498 + 0.78537I 4.77130 + 1.23542I
u = 0.616988 + 0.981935I
a = 0.22665 − 1.78791I
b = −0.460344 − 1.107710I
−2.98881 + 3.82032I −4.40423 − 3.41712I
u = 0.616988 − 0.981935I
a = 0.22665 + 1.78791I
b = −0.460344 + 1.107710I
−2.98881 − 3.82032I −4.40423 + 3.41712I
u = 0.735897 + 0.965972I
a = 0.848544 − 0.642851I
b = 0.00491 − 1.70327I
4.59134 + 7.92747I 1.75433 − 12.19435I
u = 0.735897 − 0.965972I
a = 0.848544 + 0.642851I
b = 0.00491 + 1.70327I
4.59134 − 7.92747I 1.75433 + 12.19435I
u = −0.683453 + 1.043280I
a = −0.67535 + 1.86304I
b = −1.89207 + 0.65020I
−1.15495 − 8.70555I −0.88484 + 6.87448I
u = −0.683453 − 1.043280I
a = −0.67535 − 1.86304I
b = −1.89207 − 0.65020I
−1.15495 + 8.70555I −0.88484 − 6.87448I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.655917
a = −0.874755
b = −0.939296
−1.99490 8.35720
u = −0.218060 + 0.540058I
a = 2.16205 − 0.85092I
b = −0.045811 + 0.685467I
1.02147 + 2.40878I −1.13085 − 1.54968I
u = −0.218060 − 0.540058I
a = 2.16205 + 0.85092I
b = −0.045811 − 0.685467I
1.02147 − 2.40878I −1.13085 + 1.54968I
24
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
23
− 8u
22
+ ··· − 8u + 1)(u
133
+ 45u
132
+ ··· + 21u − 1)
c
2
(u
23
+ 4u
21
+ ··· − 4u
2
− 1)(u
133
+ u
132
+ ··· + 11u + 1)
c
3
(u
23
− u
22
+ ··· − u + 1)(u
133
− 47u
131
+ ··· + 8432u + 2069)
c
4
(u
23
− u
22
+ ··· − u + 1)(u
133
− 40u
131
+ ··· − 1016u − 121)
c
5
(u
23
+ 2u
20
+ ··· + 3u
2
+ 1)(u
133
− u
132
+ ··· + 17u + 3)
c
7
(u
23
+ 4u
21
+ ··· + 4u
2
+ 1)(u
133
+ u
132
+ ··· + 11u + 1)
c
8
(u
23
+ 4u
21
+ ··· + 7u
2
+ 1)(u
133
− 5u
132
+ ··· + 5531185u + 580413)
c
9
(u
23
+ u
22
+ ··· − u − 1)(u
133
− 40u
131
+ ··· − 1016u − 121)
c
10
(u
23
+ 3u
21
+ ··· + 2u
3
+ 1)(u
133
+ 3u
132
+ ··· − 154743u − 114143)
c
11
(u
23
+ u
22
+ ··· − u − 1)(u
133
− 47u
131
+ ··· + 8432u + 2069)
c
12
(u
23
− 4u
21
+ ··· − 6u + 1)(u
133
+ 19u
132
+ ··· + 419u − 11)
25
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
23
+ 16y
22
+ ··· − 56y
2
− 1)(y
133
+ 89y
132
+ ··· + 225y −1)
c
2
, c
7
(y
23
+ 8y
22
+ ··· − 8y −1)(y
133
+ 45y
132
+ ··· + 21y −1)
c
3
, c
11
(y
23
− 23y
22
+ ··· + 17y −1)
· (y
133
− 94y
132
+ ··· + 138510782y −4280761)
c
4
, c
9
(y
23
− 17y
22
+ ··· + 23y −1)(y
133
− 80y
132
+ ··· + 653284y −14641)
c
5
(y
23
− 2y
21
+ ··· − 6y −1)(y
133
+ 5y
132
+ ··· + 175y −9)
c
8
(y
23
+ 8y
22
+ ··· − 14y −1)
· (y
133
+ 49y
132
+ ··· + 385483097599y −336879250569)
c
10
(y
23
+ 6y
22
+ ··· + 2y
2
− 1)
· (y
133
− 25y
132
+ ··· + 297383627417y −13028624449)
c
12
(y
23
− 8y
22
+ ··· + 6y −1)(y
133
− 19y
132
+ ··· + 229791y −121)
26
