12a
0559
(K12a
0559
)
A knot diagram
1
Linearized knot diagam
3 7 9 8 11 2 10 12 1 6 5 4
Solving Sequence
2,6
7
3,10
8 11 1 5 12 4 9
c
6
c
2
c
7
c
10
c
1
c
5
c
11
c
4
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.62320 × 10
287
u
131
+ 4.40473 × 10
287
u
130
+ ··· + 3.61885 × 10
287
b + 1.06624 × 10
289
,
− 2.63834 × 10
289
u
131
+ 5.53105 × 10
289
u
130
+ ··· + 3.22078 × 10
289
a + 1.89383 × 10
291
,
u
132
− 2u
131
+ ··· − 568u + 89i
I
u
2
= hu
26
+ u
25
+ ··· + b − 3, u
26
− u
25
+ ··· + a − 4, u
27
− u
26
+ ··· − u + 1i
* 2 irreducible components of dim
C
= 0, with total 159 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−2.62 × 10
287
u
131
+ 4.40 × 10
287
u
130
+ · · · + 3.62 × 10
287
b + 1.07 ×
10
289
, −2.64 × 10
289
u
131
+ 5.53 × 10
289
u
130
+ · · · + 3.22 × 10
289
a + 1.89 ×
10
291
, u
132
− 2u
131
+ · · · − 568u + 89i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
0.819162u
131
− 1.71730u
130
+ ··· − 59.4863u − 58.8003
0.724872u
131
− 1.21716u
130
+ ··· + 89.8247u − 29.4635
a
8
=
−0.161670u
131
+ 0.565376u
130
+ ··· − 192.959u + 20.9352
−1.16897u
131
+ 1.80579u
130
+ ··· + 227.476u − 27.4721
a
11
=
0.0942905u
131
− 0.500140u
130
+ ··· − 149.311u − 29.3368
0.724872u
131
− 1.21716u
130
+ ··· + 89.8247u − 29.4635
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
−0.181553u
131
− 1.14469u
130
+ ··· − 695.765u + 80.9396
−0.710908u
131
+ 2.82353u
130
+ ··· − 208.303u + 36.9135
a
12
=
0.785751u
131
+ 0.104849u
130
+ ··· − 302.478u − 82.3601
−3.50233u
131
+ 7.09633u
130
+ ··· + 998.390u − 103.373
a
4
=
0.203113u
131
− 0.0820425u
130
+ ··· + 102.209u − 54.2446
−0.0191589u
131
+ 0.624928u
130
+ ··· + 112.201u − 26.3748
a
9
=
0.439066u
131
− 1.19115u
130
+ ··· + 406.652u − 120.893
0.884407u
131
− 1.78507u
130
+ ··· − 213.423u + 18.7842
(ii) Obstruction class = −1
(iii) Cusp Shapes = 8.49058u
131
− 24.4730u
130
+ ··· + 488.947u − 51.1479
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
132
+ 50u
131
+ ··· + 410734u + 7921
c
2
, c
6
u
132
− 2u
131
+ ··· − 568u + 89
c
3
u
132
− 2u
131
+ ··· + 29779u + 2021
c
4
u
132
− 6u
131
+ ··· − 1890u + 251
c
5
, c
10
, c
11
u
132
+ u
131
+ ··· + 133u + 11
c
7
u
132
+ u
131
+ ··· + 3639368u − 287749
c
8
u
132
− 22u
130
+ ··· + 185420u + 16129
c
9
u
132
− 5u
131
+ ··· − 4u − 1
c
12
u
132
+ 9u
131
+ ··· + 72u + 11
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
132
+ 74y
131
+ ··· − 5025488686y + 62742241
c
2
, c
6
y
132
− 50y
131
+ ··· − 410734y + 7921
c
3
y
132
+ 28y
131
+ ··· − 150607255y + 4084441
c
4
y
132
− 22y
131
+ ··· − 2514888y + 63001
c
5
, c
10
, c
11
y
132
+ 147y
131
+ ··· − 40855y + 121
c
7
y
132
+ 51y
131
+ ··· − 2120861931094y + 82799487001
c
8
y
132
− 44y
131
+ ··· + 4699377698y + 260144641
c
9
y
132
− 13y
131
+ ··· + 8y + 1
c
12
y
132
+ 27y
131
+ ··· + 6476y + 121
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.994996 + 0.006480I
a = −1.74092 − 0.54070I
b = −0.471730 − 0.131016I
−4.62550 − 1.48283I 0
u = 0.994996 − 0.006480I
a = −1.74092 + 0.54070I
b = −0.471730 + 0.131016I
−4.62550 + 1.48283I 0
u = 0.634066 + 0.801263I
a = 0.634491 + 0.575872I
b = 0.13578 − 1.45796I
6.19734 + 4.07644I 0
u = 0.634066 − 0.801263I
a = 0.634491 − 0.575872I
b = 0.13578 + 1.45796I
6.19734 − 4.07644I 0
u = 0.515731 + 0.831149I
a = 0.404778 − 0.164401I
b = 0.051469 − 0.567679I
3.79838 + 2.24121I 0
u = 0.515731 − 0.831149I
a = 0.404778 + 0.164401I
b = 0.051469 + 0.567679I
3.79838 − 2.24121I 0
u = −0.752149 + 0.624524I
a = 1.90916 + 0.67170I
b = 0.034547 − 0.281824I
2.55140 − 1.93292I 0
u = −0.752149 − 0.624524I
a = 1.90916 − 0.67170I
b = 0.034547 + 0.281824I
2.55140 + 1.93292I 0
u = −0.668759 + 0.711722I
a = 0.808567 + 0.081701I
b = 0.589563 + 0.305614I
0.48044 − 1.66584I 0
u = −0.668759 − 0.711722I
a = 0.808567 − 0.081701I
b = 0.589563 − 0.305614I
0.48044 + 1.66584I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.570024 + 0.863514I
a = −0.222453 − 0.052071I
b = −0.734101 − 0.708592I
2.59743 − 8.93120I 0
u = −0.570024 − 0.863514I
a = −0.222453 + 0.052071I
b = −0.734101 + 0.708592I
2.59743 + 8.93120I 0
u = −0.360635 + 0.971464I
a = −0.0362939 − 0.0413371I
b = −0.403332 + 0.366839I
1.52321 + 4.62993I 0
u = −0.360635 − 0.971464I
a = −0.0362939 + 0.0413371I
b = −0.403332 − 0.366839I
1.52321 − 4.62993I 0
u = −0.904663 + 0.509921I
a = −0.826665 − 0.848051I
b = −0.535360 − 0.451714I
−1.89833 + 2.87175I 0
u = −0.904663 − 0.509921I
a = −0.826665 + 0.848051I
b = −0.535360 + 0.451714I
−1.89833 − 2.87175I 0
u = 0.784767 + 0.682639I
a = 1.132960 − 0.122173I
b = 0.413696 + 0.801010I
1.94520 − 2.06908I 0
u = 0.784767 − 0.682639I
a = 1.132960 + 0.122173I
b = 0.413696 − 0.801010I
1.94520 + 2.06908I 0
u = 0.819759 + 0.645897I
a = −0.39488 − 1.50469I
b = 0.01450 + 1.53948I
8.87156 − 6.85147I 0
u = 0.819759 − 0.645897I
a = −0.39488 + 1.50469I
b = 0.01450 − 1.53948I
8.87156 + 6.85147I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.822814 + 0.646545I
a = −1.53339 − 0.88035I
b = −0.966960 + 0.552965I
3.07535 + 5.04428I 0
u = −0.822814 − 0.646545I
a = −1.53339 + 0.88035I
b = −0.966960 − 0.552965I
3.07535 − 5.04428I 0
u = 0.565290 + 0.765188I
a = 0.054701 + 0.324447I
b = −0.693226 + 0.744308I
4.10966 + 0.92164I 0
u = 0.565290 − 0.765188I
a = 0.054701 − 0.324447I
b = −0.693226 − 0.744308I
4.10966 − 0.92164I 0
u = −1.04902
a = 1.07199
b = 0.691178
−1.61809 0
u = 0.868569 + 0.386574I
a = −1.76217 + 0.96278I
b = −0.172034 − 0.799347I
−2.84775 − 1.60335I 0
u = 0.868569 − 0.386574I
a = −1.76217 − 0.96278I
b = −0.172034 + 0.799347I
−2.84775 + 1.60335I 0
u = 0.772456 + 0.715664I
a = 0.742267 − 0.744997I
b = −0.067281 + 0.621184I
2.35190 − 2.68342I 0
u = 0.772456 − 0.715664I
a = 0.742267 + 0.744997I
b = −0.067281 − 0.621184I
2.35190 + 2.68342I 0
u = 0.771908 + 0.729236I
a = −0.053680 + 0.255973I
b = 0.26793 − 1.61185I
10.54430 + 4.25109I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.771908 − 0.729236I
a = −0.053680 − 0.255973I
b = 0.26793 + 1.61185I
10.54430 − 4.25109I 0
u = −1.064160 + 0.060889I
a = 1.55659 − 0.12062I
b = 0.771807 − 0.677807I
−3.49156 − 2.47310I 0
u = −1.064160 − 0.060889I
a = 1.55659 + 0.12062I
b = 0.771807 + 0.677807I
−3.49156 + 2.47310I 0
u = −0.857199 + 0.640093I
a = −1.009080 − 0.133591I
b = 0.25723 + 1.85429I
7.67912 + 1.97784I 0
u = −0.857199 − 0.640093I
a = −1.009080 + 0.133591I
b = 0.25723 − 1.85429I
7.67912 − 1.97784I 0
u = −0.856401 + 0.642335I
a = −2.13306 − 0.42776I
b = −0.36336 + 1.80298I
7.68137 + 3.02430I 0
u = −0.856401 − 0.642335I
a = −2.13306 + 0.42776I
b = −0.36336 − 1.80298I
7.68137 − 3.02430I 0
u = −0.880379 + 0.638494I
a = 0.436321 + 0.517027I
b = 0.885433 + 0.705363I
2.89468 − 0.02986I 0
u = −0.880379 − 0.638494I
a = 0.436321 − 0.517027I
b = 0.885433 − 0.705363I
2.89468 + 0.02986I 0
u = −1.069670 + 0.201549I
a = −0.918165 − 1.030270I
b = −0.356229 − 0.381280I
−3.90078 − 0.34266I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.069670 − 0.201549I
a = −0.918165 + 1.030270I
b = −0.356229 + 0.381280I
−3.90078 + 0.34266I 0
u = 0.883959 + 0.638258I
a = 0.454032 − 0.216708I
b = 0.022800 + 0.763237I
2.08747 − 2.56816I 0
u = 0.883959 − 0.638258I
a = 0.454032 + 0.216708I
b = 0.022800 − 0.763237I
2.08747 + 2.56816I 0
u = −1.090650 + 0.093406I
a = −1.14572 + 1.64113I
b = −0.099797 + 1.342850I
−0.01929 + 3.49571I 0
u = −1.090650 − 0.093406I
a = −1.14572 − 1.64113I
b = −0.099797 − 1.342850I
−0.01929 − 3.49571I 0
u = 0.893330 + 0.649841I
a = 2.99081 − 0.53235I
b = 0.00730 + 1.48977I
8.63942 + 1.80321I 0
u = 0.893330 − 0.649841I
a = 2.99081 + 0.53235I
b = 0.00730 − 1.48977I
8.63942 − 1.80321I 0
u = −0.791276 + 0.772968I
a = 0.534673 + 0.705186I
b = −0.00970 − 1.58542I
10.14180 + 2.60358I 0
u = −0.791276 − 0.772968I
a = 0.534673 − 0.705186I
b = −0.00970 + 1.58542I
10.14180 − 2.60358I 0
u = 0.610674 + 0.649425I
a = −0.793420 + 1.044120I
b = −0.990122 − 0.247008I
1.23734 + 3.50615I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.610674 − 0.649425I
a = −0.793420 − 1.044120I
b = −0.990122 + 0.247008I
1.23734 − 3.50615I 0
u = −0.940716 + 0.613817I
a = −0.712349 + 0.771670I
b = −0.042375 − 0.473375I
1.95733 + 6.81025I 0
u = −0.940716 − 0.613817I
a = −0.712349 − 0.771670I
b = −0.042375 + 0.473375I
1.95733 − 6.81025I 0
u = 0.916598 + 0.667748I
a = −0.090668 + 0.660853I
b = −0.399787 + 0.923608I
1.54193 − 3.15243I 0
u = 0.916598 − 0.667748I
a = −0.090668 − 0.660853I
b = −0.399787 − 0.923608I
1.54193 + 3.15243I 0
u = −1.060320 + 0.411733I
a = 0.725968 + 0.184398I
b = 0.561074 − 0.066298I
−1.75667 + 0.49068I 0
u = −1.060320 − 0.411733I
a = 0.725968 − 0.184398I
b = 0.561074 + 0.066298I
−1.75667 − 0.49068I 0
u = −0.862337 + 0.746269I
a = 1.10193 + 1.14638I
b = 0.01425 − 1.58401I
9.98298 + 2.82606I 0
u = −0.862337 − 0.746269I
a = 1.10193 − 1.14638I
b = 0.01425 + 1.58401I
9.98298 − 2.82606I 0
u = 0.618325 + 0.966155I
a = −0.151389 − 0.572052I
b = −0.24136 + 1.59831I
10.2195 + 12.5934I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618325 − 0.966155I
a = −0.151389 + 0.572052I
b = −0.24136 − 1.59831I
10.2195 − 12.5934I 0
u = −0.848464 + 0.077844I
a = −0.21096 + 3.29126I
b = −0.16663 + 1.42045I
5.59934 + 5.71675I 0
u = −0.848464 − 0.077844I
a = −0.21096 − 3.29126I
b = −0.16663 − 1.42045I
5.59934 − 5.71675I 0
u = 1.005330 + 0.564689I
a = −1.77666 + 0.33734I
b = −0.559377 − 0.541615I
−1.62372 − 6.68253I 0
u = 1.005330 − 0.564689I
a = −1.77666 − 0.33734I
b = −0.559377 + 0.541615I
−1.62372 + 6.68253I 0
u = −0.816595 + 0.161996I
a = −2.65788 + 0.25450I
b = −0.145940 + 1.183650I
−1.54149 + 0.68168I 0
u = −0.816595 − 0.161996I
a = −2.65788 − 0.25450I
b = −0.145940 − 1.183650I
−1.54149 − 0.68168I 0
u = 0.935862 + 0.699498I
a = −2.21328 + 0.14497I
b = −0.32179 − 1.57803I
10.04390 − 9.70702I 0
u = 0.935862 − 0.699498I
a = −2.21328 − 0.14497I
b = −0.32179 + 1.57803I
10.04390 + 9.70702I 0
u = −0.634146 + 0.985622I
a = 0.084459 + 0.505395I
b = −0.22551 − 1.58250I
11.70150 − 4.34034I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.634146 − 0.985622I
a = 0.084459 − 0.505395I
b = −0.22551 + 1.58250I
11.70150 + 4.34034I 0
u = −0.920415 + 0.726208I
a = 1.75168 + 0.54157I
b = 0.04906 − 1.54453I
9.75071 + 3.05257I 0
u = −0.920415 − 0.726208I
a = 1.75168 − 0.54157I
b = 0.04906 + 1.54453I
9.75071 − 3.05257I 0
u = −0.550360 + 1.043380I
a = 0.058196 − 0.472313I
b = 0.01923 + 1.53496I
10.84940 − 2.52048I 0
u = −0.550360 − 1.043380I
a = 0.058196 + 0.472313I
b = 0.01923 − 1.53496I
10.84940 + 2.52048I 0
u = 1.186540 + 0.094281I
a = 1.322460 + 0.412756I
b = 0.747039 + 0.446078I
−4.08907 − 7.51792I 0
u = 1.186540 − 0.094281I
a = 1.322460 − 0.412756I
b = 0.747039 − 0.446078I
−4.08907 + 7.51792I 0
u = 1.008060 + 0.637246I
a = 0.699716 − 0.829854I
b = 1.100490 − 0.415405I
0.07070 − 8.57861I 0
u = 1.008060 − 0.637246I
a = 0.699716 + 0.829854I
b = 1.100490 + 0.415405I
0.07070 + 8.57861I 0
u = −0.992211 + 0.669153I
a = −1.41520 − 0.58729I
b = −0.634108 + 0.248789I
−0.48526 + 6.98577I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.992211 − 0.669153I
a = −1.41520 + 0.58729I
b = −0.634108 − 0.248789I
−0.48526 − 6.98577I 0
u = 0.363034 + 0.711070I
a = 0.578080 − 0.413653I
b = −0.04916 + 1.43592I
4.69090 − 1.42629I 0
u = 0.363034 − 0.711070I
a = 0.578080 + 0.413653I
b = −0.04916 − 1.43592I
4.69090 + 1.42629I 0
u = 0.728610 + 0.293527I
a = 0.902833 + 0.437624I
b = 0.417664 − 0.606910I
−0.22605 + 2.50968I 0
u = 0.728610 − 0.293527I
a = 0.902833 − 0.437624I
b = 0.417664 + 0.606910I
−0.22605 − 2.50968I 0
u = 0.194079 + 1.201040I
a = −0.121857 + 0.524657I
b = −0.11940 − 1.48554I
7.67886 − 6.48707I 0
u = 0.194079 − 1.201040I
a = −0.121857 − 0.524657I
b = −0.11940 + 1.48554I
7.67886 + 6.48707I 0
u = 1.125170 + 0.465251I
a = 1.112720 + 0.521304I
b = 0.209271 + 1.325500I
2.42090 − 3.32864I 0
u = 1.125170 − 0.465251I
a = 1.112720 − 0.521304I
b = 0.209271 − 1.325500I
2.42090 + 3.32864I 0
u = −1.056440 + 0.608885I
a = −2.47896 + 0.30344I
b = −0.16650 + 1.54399I
5.32474 + 9.30599I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.056440 − 0.608885I
a = −2.47896 − 0.30344I
b = −0.16650 − 1.54399I
5.32474 − 9.30599I 0
u = 1.207290 + 0.185289I
a = −0.02766 + 1.65031I
b = −0.08721 + 1.50203I
2.40715 + 1.84212I 0
u = 1.207290 − 0.185289I
a = −0.02766 − 1.65031I
b = −0.08721 − 1.50203I
2.40715 − 1.84212I 0
u = 1.037550 + 0.662023I
a = 1.35614 − 0.48994I
b = 0.924834 + 0.683729I
2.72984 − 6.32741I 0
u = 1.037550 − 0.662023I
a = 1.35614 + 0.48994I
b = 0.924834 − 0.683729I
2.72984 + 6.32741I 0
u = −0.959303 + 0.789163I
a = −0.397598 − 0.522486I
b = −0.101230 + 0.195264I
−0.18630 + 3.08030I 0
u = −0.959303 − 0.789163I
a = −0.397598 + 0.522486I
b = −0.101230 − 0.195264I
−0.18630 − 3.08030I 0
u = 1.030710 + 0.697830I
a = −2.42414 + 0.08943I
b = −0.17012 − 1.44439I
5.00651 − 9.72305I 0
u = 1.030710 − 0.697830I
a = −2.42414 − 0.08943I
b = −0.17012 + 1.44439I
5.00651 + 9.72305I 0
u = 0.716992 + 0.124023I
a = 0.92913 + 2.53825I
b = −0.23110 + 1.45080I
5.15288 − 0.10023I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.716992 − 0.124023I
a = 0.92913 − 2.53825I
b = −0.23110 − 1.45080I
5.15288 + 0.10023I 0
u = 1.083560 + 0.675466I
a = −1.100260 − 0.103386I
b = −0.230811 − 0.496578I
2.11983 − 7.86879I 0
u = 1.083560 − 0.675466I
a = −1.100260 + 0.103386I
b = −0.230811 + 0.496578I
2.11983 + 7.86879I 0
u = −1.074050 + 0.695541I
a = 1.46630 + 0.54550I
b = 0.834487 − 0.713525I
1.0717 + 14.7171I 0
u = −1.074050 − 0.695541I
a = 1.46630 − 0.54550I
b = 0.834487 + 0.713525I
1.0717 − 14.7171I 0
u = −1.28440
a = −0.185699
b = 0.0492019
−2.37235 0
u = 0.676925 + 0.208900I
a = 1.124060 + 0.811472I
b = 0.04493 + 1.65565I
5.40133 − 1.09492I 0
u = 0.676925 − 0.208900I
a = 1.124060 − 0.811472I
b = 0.04493 − 1.65565I
5.40133 + 1.09492I 0
u = −1.280300 + 0.220518I
a = 0.983356 − 0.977949I
b = 0.23398 − 1.48521I
2.15856 + 11.02100I 0
u = −1.280300 − 0.220518I
a = 0.983356 + 0.977949I
b = 0.23398 + 1.48521I
2.15856 − 11.02100I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.348525 + 0.590263I
a = 0.771766 − 0.351389I
b = 0.12831 + 1.55884I
7.05598 − 4.45947I −6.00000 + 2.49012I
u = −0.348525 − 0.590263I
a = 0.771766 + 0.351389I
b = 0.12831 − 1.55884I
7.05598 + 4.45947I −6.00000 − 2.49012I
u = 1.101350 + 0.749789I
a = 1.95655 − 0.19479I
b = 0.27540 + 1.60963I
8.7049 − 18.8638I 0
u = 1.101350 − 0.749789I
a = 1.95655 + 0.19479I
b = 0.27540 − 1.60963I
8.7049 + 18.8638I 0
u = −1.095040 + 0.762225I
a = 1.72771 + 0.19647I
b = 0.28314 − 1.60368I
10.2481 + 10.6947I 0
u = −1.095040 − 0.762225I
a = 1.72771 − 0.19647I
b = 0.28314 + 1.60368I
10.2481 − 10.6947I 0
u = −0.526860 + 0.369790I
a = 1.258800 − 0.534568I
b = 0.12425 + 1.56373I
7.07452 − 4.51449I −8.15922 + 1.95555I
u = −0.526860 − 0.369790I
a = 1.258800 + 0.534568I
b = 0.12425 − 1.56373I
7.07452 + 4.51449I −8.15922 − 1.95555I
u = 1.000410 + 0.919179I
a = −0.958444 + 0.741591I
b = −0.02560 − 1.46902I
5.55658 − 3.49041I 0
u = 1.000410 − 0.919179I
a = −0.958444 − 0.741591I
b = −0.02560 + 1.46902I
5.55658 + 3.49041I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.154000 + 0.753313I
a = −1.55954 + 0.09926I
b = −0.07285 + 1.52892I
8.95938 + 8.99501I 0
u = −1.154000 − 0.753313I
a = −1.55954 − 0.09926I
b = −0.07285 − 1.52892I
8.95938 − 8.99501I 0
u = 1.150290 + 0.779742I
a = 0.933928 − 0.190095I
b = 0.236000 + 1.223090I
2.04431 − 3.59566I 0
u = 1.150290 − 0.779742I
a = 0.933928 + 0.190095I
b = 0.236000 − 1.223090I
2.04431 + 3.59566I 0
u = 0.338566 + 0.442940I
a = 0.892402 − 0.007273I
b = 0.447394 − 0.581047I
−0.14721 + 2.37366I −6.39573 − 4.68155I
u = 0.338566 − 0.442940I
a = 0.892402 + 0.007273I
b = 0.447394 + 0.581047I
−0.14721 − 2.37366I −6.39573 + 4.68155I
u = 1.43728 + 0.21546I
a = −0.377583 − 0.812593I
b = 0.04929 − 1.42523I
2.52245 + 0.50257I 0
u = 1.43728 − 0.21546I
a = −0.377583 + 0.812593I
b = 0.04929 + 1.42523I
2.52245 − 0.50257I 0
u = −0.316533 + 0.351504I
a = 1.022650 − 0.014973I
b = 0.404679 − 0.316331I
−0.902307 + 0.691481I −8.09755 − 4.83373I
u = −0.316533 − 0.351504I
a = 1.022650 + 0.014973I
b = 0.404679 + 0.316331I
−0.902307 − 0.691481I −8.09755 + 4.83373I
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.314071 + 0.042498I
a = −0.89991 + 4.02084I
b = −0.572934 + 0.019706I
0.75055 + 3.16921I −9.99878 − 2.77340I
u = 0.314071 − 0.042498I
a = −0.89991 − 4.02084I
b = −0.572934 − 0.019706I
0.75055 − 3.16921I −9.99878 + 2.77340I
18
II.
I
u
2
= hu
26
+ u
25
+ · · · + b − 3, u
26
− u
25
+ · · · + a − 4, u
27
− u
26
+ · · · − u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
−u
26
+ u
25
+ ··· − 4u + 4
−u
26
− u
25
+ ··· + 3u + 3
a
8
=
3u
26
− 2u
25
+ ··· + 5u − 5
−2u
26
+ 16u
24
+ ··· + 8u − 6
a
11
=
2u
25
− 3u
24
+ ··· − 7u + 1
−u
26
− u
25
+ ··· + 3u + 3
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
−5u
26
+ 6u
25
+ ··· + 11u − 2
5u
26
− 3u
25
+ ··· − 5u + 3
a
12
=
2u
26
+ 5u
25
+ ··· − 2u − 5
u
24
− 6u
23
+ ··· + u − 9
a
4
=
−u
26
− 2u
25
+ ··· + 6u + 4
4u
26
− 3u
25
+ ··· + 4u − 2
a
9
=
−u
26
+ 6u
24
+ ··· − 4u + 4
−u
26
− u
25
+ ··· + 3u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 20u
26
− 23u
25
− 108u
24
+ 147u
23
+ 321u
22
− 491u
21
− 648u
20
+
1098u
19
+ 896u
18
−1787u
17
−859u
16
+ 2244u
15
+ 445u
14
−2209u
13
+ 114u
12
+ 1728u
11
−
459u
10
− 1053u
9
+ 524u
8
+ 485u
7
− 354u
6
− 145u
5
+ 176u
4
+ 22u
3
− 62u
2
+ 15u + 9
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
27
− 13u
26
+ ··· + 9u − 1
c
2
u
27
+ u
26
+ ··· − u − 1
c
3
u
27
+ u
26
+ ··· − 13u
2
− 1
c
4
u
27
+ u
26
+ ··· + 3u − 1
c
5
u
27
+ 18u
25
+ ··· + 2u + 1
c
6
u
27
− u
26
+ ··· − u + 1
c
7
u
27
− 8u
26
+ ··· + 33u − 5
c
8
u
27
− u
26
+ ··· − 11u + 1
c
9
u
27
+ 8u
26
+ ··· − u − 1
c
10
, c
11
u
27
+ 18u
25
+ ··· + 2u − 1
c
12
u
27
+ 8u
25
+ ··· + 3u − 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
27
+ 11y
26
+ ··· − 15y −1
c
2
, c
6
y
27
− 13y
26
+ ··· + 9y −1
c
3
y
27
+ y
26
+ ··· − 26y −1
c
4
y
27
− 5y
26
+ ··· − 9y −1
c
5
, c
10
, c
11
y
27
+ 36y
26
+ ··· + 6y −1
c
7
y
27
+ 16y
26
+ ··· + 129y −25
c
8
y
27
− 11y
26
+ ··· + 29y −1
c
9
y
27
− 12y
26
+ ··· − y −1
c
12
y
27
+ 16y
26
+ ··· − 13y −1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.853162 + 0.647554I
a = 1.60649 + 0.40550I
b = 0.06284 − 1.87341I
7.92917 + 2.52291I 5.44822 − 2.75445I
u = −0.853162 − 0.647554I
a = 1.60649 − 0.40550I
b = 0.06284 + 1.87341I
7.92917 − 2.52291I 5.44822 + 2.75445I
u = 0.690991 + 0.599345I
a = 1.26985 − 0.79580I
b = 0.577860 − 0.201671I
1.76425 + 2.24141I −4.36534 − 3.63893I
u = 0.690991 − 0.599345I
a = 1.26985 + 0.79580I
b = 0.577860 + 0.201671I
1.76425 − 2.24141I −4.36534 + 3.63893I
u = −0.907772 + 0.081189I
a = −1.61468 − 0.76782I
b = −0.185070 − 0.462746I
−3.60291 + 0.41304I −11.57818 − 1.36351I
u = −0.907772 − 0.081189I
a = −1.61468 + 0.76782I
b = −0.185070 + 0.462746I
−3.60291 − 0.41304I −11.57818 + 1.36351I
u = 0.860452 + 0.284653I
a = −2.21496 + 0.10691I
b = −0.067024 − 1.149030I
−1.31757 − 1.24036I −4.75718 + 7.10504I
u = 0.860452 − 0.284653I
a = −2.21496 − 0.10691I
b = −0.067024 + 1.149030I
−1.31757 + 1.24036I −4.75718 − 7.10504I
u = −0.881088 + 0.664586I
a = 0.324729 − 0.741806I
b = −0.084591 − 0.903810I
0.92350 + 2.58995I −9.68822 − 1.59614I
u = −0.881088 − 0.664586I
a = 0.324729 + 0.741806I
b = −0.084591 + 0.903810I
0.92350 − 2.58995I −9.68822 + 1.59614I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.581553 + 0.606085I
a = 0.936509 + 0.087615I
b = 0.13865 + 1.52061I
7.88049 − 4.56272I 2.69007 + 4.12541I
u = −0.581553 − 0.606085I
a = 0.936509 − 0.087615I
b = 0.13865 − 1.52061I
7.88049 + 4.56272I 2.69007 − 4.12541I
u = 0.998416 + 0.622921I
a = −1.170550 + 0.123135I
b = −0.602644 − 0.092277I
0.77074 − 7.11436I −5.64722 + 8.51652I
u = 0.998416 − 0.622921I
a = −1.170550 − 0.123135I
b = −0.602644 + 0.092277I
0.77074 + 7.11436I −5.64722 − 8.51652I
u = −0.544832 + 0.591498I
a = −0.211003 + 1.089280I
b = 0.380251 − 0.301214I
1.44545 + 3.80748I −3.49928 − 7.07651I
u = −0.544832 − 0.591498I
a = −0.211003 − 1.089280I
b = 0.380251 + 0.301214I
1.44545 − 3.80748I −3.49928 + 7.07651I
u = −1.058170 + 0.636584I
a = −2.31607 + 0.47367I
b = −0.15867 + 1.48807I
6.39102 + 9.58868I −0.19098 − 9.12583I
u = −1.058170 − 0.636584I
a = −2.31607 − 0.47367I
b = −0.15867 − 1.48807I
6.39102 − 9.58868I −0.19098 + 9.12583I
u = 0.358678 + 0.668768I
a = −0.466956 − 1.003350I
b = 0.09089 + 1.52043I
7.80779 − 5.30819I −0.97544 + 5.25547I
u = 0.358678 − 0.668768I
a = −0.466956 + 1.003350I
b = 0.09089 − 1.52043I
7.80779 + 5.30819I −0.97544 − 5.25547I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.272990 + 0.067492I
a = −0.202479 + 1.295350I
b = −0.09327 + 1.47851I
2.87532 + 1.48837I −1.94624 − 0.78086I
u = 1.272990 − 0.067492I
a = −0.202479 − 1.295350I
b = −0.09327 − 1.47851I
2.87532 − 1.48837I −1.94624 + 0.78086I
u = 0.643418 + 0.315625I
a = −0.90111 − 1.47679I
b = 0.25720 − 1.63028I
5.82969 − 0.19887I 5.14442 + 0.15970I
u = 0.643418 − 0.315625I
a = −0.90111 + 1.47679I
b = 0.25720 + 1.63028I
5.82969 + 0.19887I 5.14442 − 0.15970I
u = −1.29873
a = −0.455393
b = −0.308005
−2.53411 −32.0090
u = 1.15100 + 0.87136I
a = −0.812079 + 0.232272I
b = −0.162421 − 1.187370I
2.04853 − 3.82771I −6.6304 + 23.0923I
u = 1.15100 − 0.87136I
a = −0.812079 − 0.232272I
b = −0.162421 + 1.187370I
2.04853 + 3.82771I −6.6304 − 23.0923I
24
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
27
− 13u
26
+ ··· + 9u − 1)(u
132
+ 50u
131
+ ··· + 410734u + 7921)
c
2
(u
27
+ u
26
+ ··· − u − 1)(u
132
− 2u
131
+ ··· − 568u + 89)
c
3
(u
27
+ u
26
+ ··· − 13u
2
− 1)(u
132
− 2u
131
+ ··· + 29779u + 2021)
c
4
(u
27
+ u
26
+ ··· + 3u − 1)(u
132
− 6u
131
+ ··· − 1890u + 251)
c
5
(u
27
+ 18u
25
+ ··· + 2u + 1)(u
132
+ u
131
+ ··· + 133u + 11)
c
6
(u
27
− u
26
+ ··· − u + 1)(u
132
− 2u
131
+ ··· − 568u + 89)
c
7
(u
27
− 8u
26
+ ··· + 33u − 5)(u
132
+ u
131
+ ··· + 3639368u − 287749)
c
8
(u
27
− u
26
+ ··· − 11u + 1)(u
132
− 22u
130
+ ··· + 185420u + 16129)
c
9
(u
27
+ 8u
26
+ ··· − u − 1)(u
132
− 5u
131
+ ··· − 4u − 1)
c
10
, c
11
(u
27
+ 18u
25
+ ··· + 2u − 1)(u
132
+ u
131
+ ··· + 133u + 11)
c
12
(u
27
+ 8u
25
+ ··· + 3u − 1)(u
132
+ 9u
131
+ ··· + 72u + 11)
25
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
27
+ 11y
26
+ ··· − 15y −1)
· (y
132
+ 74y
131
+ ··· − 5025488686y + 62742241)
c
2
, c
6
(y
27
− 13y
26
+ ··· + 9y −1)(y
132
− 50y
131
+ ··· − 410734y + 7921)
c
3
(y
27
+ y
26
+ ··· − 26y −1)
· (y
132
+ 28y
131
+ ··· − 150607255y + 4084441)
c
4
(y
27
− 5y
26
+ ··· − 9y −1)(y
132
− 22y
131
+ ··· − 2514888y + 63001)
c
5
, c
10
, c
11
(y
27
+ 36y
26
+ ··· + 6y −1)(y
132
+ 147y
131
+ ··· − 40855y + 121)
c
7
(y
27
+ 16y
26
+ ··· + 129y −25)
· (y
132
+ 51y
131
+ ··· − 2120861931094y + 82799487001)
c
8
(y
27
− 11y
26
+ ··· + 29y −1)
· (y
132
− 44y
131
+ ··· + 4699377698y + 260144641)
c
9
(y
27
− 12y
26
+ ··· − y −1)(y
132
− 13y
131
+ ··· + 8y + 1)
c
12
(y
27
+ 16y
26
+ ··· − 13y −1)(y
132
+ 27y
131
+ ··· + 6476y + 121)
26
