12a
0821
(K12a
0821
)
A knot diagram
1
Linearized knot diagam
4 5 7 9 11 10 1 12 2 6 3 8
Solving Sequence
8,12 4,9
5 1 2 10 7 3 6 11
c
8
c
4
c
12
c
1
c
9
c
7
c
3
c
6
c
11
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.72675 × 10
263
u
121
+ 6.46926 × 10
262
u
120
+ ··· + 5.79158 × 10
262
b + 2.48722 × 10
263
,
− 8.49488 × 10
262
u
121
− 4.05282 × 10
262
u
120
+ ··· + 5.79158 × 10
262
a + 1.38533 × 10
264
,
u
122
+ 60u
120
+ ··· − 18u + 1i
I
u
2
= h1390u
25
− 2769u
24
+ ··· + 509b − 880, 259u
25
− 1267u
24
+ ··· + 509a − 4214,
u
26
− u
25
+ ··· − 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 148 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
= h1.73 × 10
263
u
121
+ 6.47 × 10
262
u
120
+ · · · + 5.79 × 10
262
b + 2.49 ×
10
263
, −8.49 × 10
262
u
121
− 4.05 × 10
262
u
120
+ · · · + 5.79 × 10
262
a + 1.39 ×
10
264
, u
122
+ 60u
120
+ · · · − 18u + 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
4
=
1.46676u
121
+ 0.699777u
120
+ ··· + 170.001u − 23.9197
−2.98148u
121
− 1.11701u
120
+ ··· + 45.9338u − 4.29454
a
9
=
1
−u
2
a
5
=
1.77570u
121
− 0.496966u
120
+ ··· + 227.064u − 28.9140
−4.01873u
121
− 3.76337u
120
+ ··· + 67.7841u − 5.49129
a
1
=
u
u
a
2
=
8.98546u
121
+ 5.82372u
120
+ ··· + 129.978u − 18.8375
7.95443u
121
+ 7.03759u
120
+ ··· − 157.645u + 8.82072
a
10
=
−4.62391u
121
+ 3.55481u
120
+ ··· − 46.0186u + 11.4590
−7.69569u
121
+ 7.64762u
120
+ ··· − 100.145u + 6.26253
a
7
=
u
2
+ 1
u
2
a
3
=
3.23207u
121
+ 0.625734u
120
+ ··· + 214.441u − 27.8862
−1.25329u
121
− 2.67980u
120
+ ··· + 72.6941u − 5.78329
a
6
=
3.31846u
121
− 6.79592u
120
+ ··· + 310.776u − 24.6475
−3.19180u
121
− 13.6438u
120
+ ··· + 200.032u − 12.4801
a
11
=
−0.0220914u
121
− 1.65462u
120
+ ··· + 186.723u − 25.3586
−2.95145u
121
− 3.32993u
120
+ ··· + 93.4416u − 6.90577
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4.67507u
121
+ 0.727293u
120
+ ··· + 484.082u − 41.7114
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
122
+ 4u
121
+ ··· − 88956u + 26901
c
2
u
122
− 4u
121
+ ··· + 88956u + 26901
c
3
u
122
− 2u
121
+ ··· + 565031u − 52219
c
4
u
122
+ u
121
+ ··· + 68u
2
− 1
c
5
, c
6
, c
10
u
122
+ 60u
120
+ ··· + 18u + 1
c
7
, c
8
, c
12
u
122
+ 60u
120
+ ··· − 18u + 1
c
9
u
122
− u
121
+ ··· + 68u
2
− 1
c
11
u
122
+ 2u
121
+ ··· − 565031u − 52219
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
y
122
− 30y
121
+ ··· − 23656173156y + 723663801
c
3
, c
11
y
122
− 18y
121
+ ··· − 76906534499y + 2726823961
c
4
, c
9
y
122
+ 21y
121
+ ··· − 136y + 1
c
5
, c
6
, c
7
c
8
, c
10
, c
12
y
122
+ 120y
121
+ ··· − 222y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.838123 + 0.469947I
a = 0.818660 − 0.409892I
b = 0.283894 + 0.627860I
0.76614 + 4.56382I 0
u = 0.838123 − 0.469947I
a = 0.818660 + 0.409892I
b = 0.283894 − 0.627860I
0.76614 − 4.56382I 0
u = 0.841269 + 0.462133I
a = 0.777756 − 0.677243I
b = 0.178743 + 0.731523I
6.3817 + 14.0924I 0
u = 0.841269 − 0.462133I
a = 0.777756 + 0.677243I
b = 0.178743 − 0.731523I
6.3817 − 14.0924I 0
u = −0.838892 + 0.460556I
a = −0.832115 − 0.584852I
b = −0.209869 + 0.671328I
− 9.93331I 0
u = −0.838892 − 0.460556I
a = −0.832115 + 0.584852I
b = −0.209869 − 0.671328I
9.93331I 0
u = −0.748963 + 0.730792I
a = −0.403585 + 0.258143I
b = 0.458631 + 0.520460I
−0.76614 + 4.56382I 0
u = −0.748963 − 0.730792I
a = −0.403585 − 0.258143I
b = 0.458631 − 0.520460I
−0.76614 − 4.56382I 0
u = 0.765545 + 0.715335I
a = 0.417658 + 0.229663I
b = −0.593332 + 0.425549I
5.65939 − 8.69735I 0
u = 0.765545 − 0.715335I
a = 0.417658 − 0.229663I
b = −0.593332 − 0.425549I
5.65939 + 8.69735I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.753448 + 0.757254I
a = 0.452640 + 0.269754I
b = −0.155081 + 0.532232I
0.859456I 0
u = 0.753448 − 0.757254I
a = 0.452640 − 0.269754I
b = −0.155081 − 0.532232I
− 0.859456I 0
u = −0.791477 + 0.441571I
a = −0.533249 − 0.353695I
b = −0.410805 + 0.653910I
8.75467 − 1.57080I 0
u = −0.791477 − 0.441571I
a = −0.533249 + 0.353695I
b = −0.410805 − 0.653910I
8.75467 + 1.57080I 0
u = −0.503041 + 0.739634I
a = −0.336565 + 1.073680I
b = −0.015210 − 0.301055I
3.72560 − 4.59585I 0
u = −0.503041 − 0.739634I
a = −0.336565 − 1.073680I
b = −0.015210 + 0.301055I
3.72560 + 4.59585I 0
u = 0.774139 + 0.438683I
a = −0.226396 + 0.512883I
b = 0.159616 − 0.241386I
0.68901 + 2.32956I 0
u = 0.774139 − 0.438683I
a = −0.226396 − 0.512883I
b = 0.159616 + 0.241386I
0.68901 − 2.32956I 0
u = −0.823729 + 0.772937I
a = −0.297970 + 0.287398I
b = 0.0772759 − 0.0086507I
7.93258 − 3.68575I 0
u = −0.823729 − 0.772937I
a = −0.297970 − 0.287398I
b = 0.0772759 + 0.0086507I
7.93258 + 3.68575I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.197149 + 1.198090I
a = −0.391660 + 1.133070I
b = −0.066020 + 0.786727I
2.05232 − 3.09473I 0
u = −0.197149 − 1.198090I
a = −0.391660 − 1.133070I
b = −0.066020 − 0.786727I
2.05232 + 3.09473I 0
u = 0.368459 + 0.681988I
a = 0.333044 + 0.118458I
b = 0.411642 + 0.445181I
1.64135I 0
u = 0.368459 − 0.681988I
a = 0.333044 − 0.118458I
b = 0.411642 − 0.445181I
− 1.64135I 0
u = 0.088735 + 1.239840I
a = −1.085920 + 0.666668I
b = −0.097880 + 0.543491I
4.34712 − 3.42917I 0
u = 0.088735 − 1.239840I
a = −1.085920 − 0.666668I
b = −0.097880 − 0.543491I
4.34712 + 3.42917I 0
u = −0.746540 + 0.095924I
a = −0.179409 − 0.123127I
b = −0.869086 + 0.200995I
5.88305 + 0.42236I 0
u = −0.746540 − 0.095924I
a = −0.179409 + 0.123127I
b = −0.869086 − 0.200995I
5.88305 − 0.42236I 0
u = 0.003647 + 1.266340I
a = −0.29736 + 1.76121I
b = −0.56996 + 2.78197I
−1.52569 + 1.86247I 0
u = 0.003647 − 1.266340I
a = −0.29736 − 1.76121I
b = −0.56996 − 2.78197I
−1.52569 − 1.86247I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002380 + 0.776849I
a = −0.120919 + 0.203444I
b = −0.0511940 − 0.0802179I
7.91219 − 3.65289I 0
u = −1.002380 − 0.776849I
a = −0.120919 − 0.203444I
b = −0.0511940 + 0.0802179I
7.91219 + 3.65289I 0
u = 0.011904 + 1.269570I
a = 0.64871 + 2.17404I
b = 1.19618 + 3.55643I
4.40280 − 4.90152I 0
u = 0.011904 − 1.269570I
a = 0.64871 − 2.17404I
b = 1.19618 − 3.55643I
4.40280 + 4.90152I 0
u = 0.126163 + 1.271520I
a = 0.026835 + 0.828486I
b = −0.674272 + 0.970458I
−2.39484 + 2.47343I 0
u = 0.126163 − 1.271520I
a = 0.026835 − 0.828486I
b = −0.674272 − 0.970458I
−2.39484 − 2.47343I 0
u = 0.387895 + 0.597696I
a = 0.165680 + 1.337830I
b = −0.149993 − 0.321583I
−1.18377 + 3.27789I −7.72431 − 9.92436I
u = 0.387895 − 0.597696I
a = 0.165680 − 1.337830I
b = −0.149993 + 0.321583I
−1.18377 − 3.27789I −7.72431 + 9.92436I
u = 0.034387 + 1.288040I
a = 0.469851 + 0.313970I
b = −0.454940 + 0.131391I
−2.11977 + 2.41437I 0
u = 0.034387 − 1.288040I
a = 0.469851 − 0.313970I
b = −0.454940 − 0.131391I
−2.11977 − 2.41437I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.591507 + 0.393541I
a = −0.692120 + 0.928039I
b = 0.454824 − 0.527439I
1.52569 + 1.86247I 0
u = 0.591507 − 0.393541I
a = −0.692120 − 0.928039I
b = 0.454824 + 0.527439I
1.52569 − 1.86247I 0
u = −0.559765 + 0.386642I
a = 0.475141 + 1.153770I
b = −0.108108 − 0.733708I
−1.67571 − 3.29126I −7.51122 + 8.90970I
u = −0.559765 − 0.386642I
a = 0.475141 − 1.153770I
b = −0.108108 + 0.733708I
−1.67571 + 3.29126I −7.51122 − 8.90970I
u = 0.668209
a = 0.293080
b = 0.741541
1.02756 9.74990
u = −0.223878 + 1.319960I
a = 0.348405 + 1.026390I
b = 1.14248 + 1.74084I
1.94229 + 0.21639I 0
u = −0.223878 − 1.319960I
a = 0.348405 − 1.026390I
b = 1.14248 − 1.74084I
1.94229 − 0.21639I 0
u = 0.094887 + 1.340650I
a = −0.54452 − 2.88908I
b = −0.85968 − 3.19953I
3.76570 + 7.21033I 0
u = 0.094887 − 1.340650I
a = −0.54452 + 2.88908I
b = −0.85968 + 3.19953I
3.76570 − 7.21033I 0
u = 0.572996 + 0.313961I
a = −0.573007 + 1.232680I
b = 0.029546 − 1.023280I
2.97533 + 5.05203I 2.55990 − 8.99574I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.572996 − 0.313961I
a = −0.573007 − 1.232680I
b = 0.029546 + 1.023280I
2.97533 − 5.05203I 2.55990 + 8.99574I
u = 0.211626 + 0.612080I
a = −0.181398 + 0.533514I
b = −0.45860 + 1.36493I
−0.68901 + 2.32956I −6.85361 − 8.80115I
u = 0.211626 − 0.612080I
a = −0.181398 − 0.533514I
b = −0.45860 − 1.36493I
−0.68901 − 2.32956I −6.85361 + 8.80115I
u = 0.281078 + 1.336330I
a = 0.930616 − 0.634656I
b = 1.29676 − 1.30744I
−1.94229 + 0.21639I 0
u = 0.281078 − 1.336330I
a = 0.930616 + 0.634656I
b = 1.29676 + 1.30744I
−1.94229 − 0.21639I 0
u = −0.102970 + 1.365190I
a = 0.555873 + 0.182955I
b = 2.00596 + 0.29788I
−2.97533 − 5.05203I 0
u = −0.102970 − 1.365190I
a = 0.555873 − 0.182955I
b = 2.00596 − 0.29788I
−2.97533 + 5.05203I 0
u = −0.597169 + 0.203460I
a = −2.29060 − 0.07482I
b = −0.219353 − 0.076676I
6.69507 + 3.24081I 7.82762 − 0.48317I
u = −0.597169 − 0.203460I
a = −2.29060 + 0.07482I
b = −0.219353 + 0.076676I
6.69507 − 3.24081I 7.82762 + 0.48317I
u = −0.405018 + 0.468237I
a = 0.292180 + 0.281700I
b = 0.72718 + 1.42275I
5.62384 − 6.30894I 0.86595 + 10.40267I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.405018 − 0.468237I
a = 0.292180 − 0.281700I
b = 0.72718 − 1.42275I
5.62384 + 6.30894I 0.86595 − 10.40267I
u = 0.016831 + 1.382940I
a = 0.366374 − 0.827698I
b = −0.61848 − 1.46951I
−2.05232 + 3.09473I 0
u = 0.016831 − 1.382940I
a = 0.366374 + 0.827698I
b = −0.61848 + 1.46951I
−2.05232 − 3.09473I 0
u = 0.118092 + 1.386860I
a = −0.907334 + 0.319639I
b = −2.59599 + 0.67827I
2.63743 + 7.92429I 0
u = 0.118092 − 1.386860I
a = −0.907334 − 0.319639I
b = −2.59599 − 0.67827I
2.63743 − 7.92429I 0
u = −0.078291 + 1.391230I
a = 0.92867 − 2.35012I
b = 1.01328 − 2.92847I
−3.72560 − 4.59585I 0
u = −0.078291 − 1.391230I
a = 0.92867 + 2.35012I
b = 1.01328 + 2.92847I
−3.72560 + 4.59585I 0
u = 0.033130 + 1.400890I
a = −1.05242 − 1.46627I
b = −0.63083 − 2.14230I
−5.88305 + 0.42236I 0
u = 0.033130 − 1.400890I
a = −1.05242 + 1.46627I
b = −0.63083 + 2.14230I
−5.88305 − 0.42236I 0
u = 0.21145 + 1.42791I
a = 0.15300 − 2.14751I
b = −0.57741 − 3.21135I
−2.63743 + 7.92429I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.21145 − 1.42791I
a = 0.15300 + 2.14751I
b = −0.57741 + 3.21135I
−2.63743 − 7.92429I 0
u = −0.28430 + 1.41809I
a = −0.611540 − 1.008500I
b = −0.62489 − 1.88264I
−6.69507 − 3.24081I 0
u = −0.28430 − 1.41809I
a = −0.611540 + 1.008500I
b = −0.62489 + 1.88264I
−6.69507 + 3.24081I 0
u = −0.512822 + 0.202337I
a = 1.029400 + 0.201671I
b = −0.507931 − 0.117189I
−1.54857 + 0.09873I −6.52365 + 0.22723I
u = −0.512822 − 0.202337I
a = 1.029400 − 0.201671I
b = −0.507931 + 0.117189I
−1.54857 − 0.09873I −6.52365 − 0.22723I
u = 0.541620 + 0.049842I
a = 1.57917 + 0.46289I
b = 0.395132 − 0.075128I
1.54857 + 0.09873I 6.52365 + 0.22723I
u = 0.541620 − 0.049842I
a = 1.57917 − 0.46289I
b = 0.395132 + 0.075128I
1.54857 − 0.09873I 6.52365 − 0.22723I
u = −0.20934 + 1.45200I
a = −0.15208 − 1.90295I
b = 0.41340 − 3.02350I
−7.61338 − 6.13503I 0
u = −0.20934 − 1.45200I
a = −0.15208 + 1.90295I
b = 0.41340 + 3.02350I
−7.61338 + 6.13503I 0
u = 0.22745 + 1.45151I
a = 0.50169 − 1.70373I
b = 0.15167 − 2.99070I
−4.40280 + 4.90152I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.22745 − 1.45151I
a = 0.50169 + 1.70373I
b = 0.15167 + 2.99070I
−4.40280 − 4.90152I 0
u = −0.14721 + 1.47595I
a = 1.43924 + 1.51730I
b = 1.07349 + 1.98141I
−0.68291 − 8.38710I 0
u = −0.14721 − 1.47595I
a = 1.43924 − 1.51730I
b = 1.07349 − 1.98141I
−0.68291 + 8.38710I 0
u = −0.10313 + 1.48416I
a = 0.51809 − 1.85788I
b = 0.81572 − 3.00333I
−4.34712 − 3.42917I 0
u = −0.10313 − 1.48416I
a = 0.51809 + 1.85788I
b = 0.81572 + 3.00333I
−4.34712 + 3.42917I 0
u = 0.15950 + 1.50706I
a = −0.33921 − 1.69479I
b = −0.84449 − 2.79461I
−8.01760 + 5.44098I 0
u = 0.15950 − 1.50706I
a = −0.33921 + 1.69479I
b = −0.84449 + 2.79461I
−8.01760 − 5.44098I 0
u = −0.003564 + 0.481131I
a = −0.90114 + 2.00705I
b = 0.593963 − 0.134342I
2.11977 − 2.41437I −0.417958 + 1.258564I
u = −0.003564 − 0.481131I
a = −0.90114 − 2.00705I
b = 0.593963 + 0.134342I
2.11977 + 2.41437I −0.417958 − 1.258564I
u = −0.27675 + 1.49874I
a = −0.03087 + 1.71174I
b = −0.37690 + 2.36519I
2.46634 − 5.42668I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.27675 − 1.49874I
a = −0.03087 − 1.71174I
b = −0.37690 − 2.36519I
2.46634 + 5.42668I 0
u = 0.29702 + 1.50535I
a = 0.093957 − 1.028920I
b = −0.26440 − 1.78844I
−5.62384 + 6.30894I 0
u = 0.29702 − 1.50535I
a = 0.093957 + 1.028920I
b = −0.26440 + 1.78844I
−5.62384 − 6.30894I 0
u = −0.30513 + 1.51162I
a = 0.01748 + 1.82265I
b = −0.37240 + 2.83356I
−6.3817 − 14.0924I 0
u = −0.30513 − 1.51162I
a = 0.01748 − 1.82265I
b = −0.37240 − 2.83356I
−6.3817 + 14.0924I 0
u = 0.30803 + 1.51176I
a = −0.00101 + 1.85616I
b = 0.48528 + 2.90856I
18.2741I 0
u = 0.30803 − 1.51176I
a = −0.00101 − 1.85616I
b = 0.48528 − 2.90856I
− 18.2741I 0
u = 0.30070 + 1.51406I
a = −0.01505 + 1.77596I
b = 0.28514 + 2.67352I
−5.65939 + 8.69735I 0
u = 0.30070 − 1.51406I
a = −0.01505 − 1.77596I
b = 0.28514 − 2.67352I
−5.65939 − 8.69735I 0
u = 0.444045 + 0.017440I
a = −1.054550 + 0.880836I
b = −0.80489 − 1.30581I
8.01760 + 5.44098I 11.84308 − 5.29398I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.444045 − 0.017440I
a = −1.054550 − 0.880836I
b = −0.80489 + 1.30581I
8.01760 − 5.44098I 11.84308 + 5.29398I
u = 0.14067 + 1.55284I
a = −0.54774 + 1.69963I
b = −0.41708 + 2.22737I
−7.93258 + 3.68575I 0
u = 0.14067 − 1.55284I
a = −0.54774 − 1.69963I
b = −0.41708 − 2.22737I
−7.93258 − 3.68575I 0
u = −0.18374 + 1.55311I
a = 0.40161 − 1.45606I
b = 1.04761 − 2.52368I
−3.76570 − 7.21033I 0
u = −0.18374 − 1.55311I
a = 0.40161 + 1.45606I
b = 1.04761 + 2.52368I
−3.76570 + 7.21033I 0
u = 0.10216 + 1.56588I
a = −0.55103 + 2.11116I
b = −0.44359 + 2.57907I
−7.91219 + 3.65289I 0
u = 0.10216 − 1.56588I
a = −0.55103 − 2.11116I
b = −0.44359 − 2.57907I
−7.91219 − 3.65289I 0
u = −0.414540 + 0.099845I
a = −2.31360 + 2.12787I
b = −0.436622 − 0.246341I
1.67571 − 3.29126I 7.51122 + 8.90970I
u = −0.414540 − 0.099845I
a = −2.31360 − 2.12787I
b = −0.436622 + 0.246341I
1.67571 + 3.29126I 7.51122 − 8.90970I
u = −0.13898 + 1.57065I
a = 0.520682 + 1.204410I
b = 0.44191 + 1.80330I
−8.75467 + 1.57080I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.13898 − 1.57065I
a = 0.520682 − 1.204410I
b = 0.44191 − 1.80330I
−8.75467 − 1.57080I 0
u = 0.381622 + 0.153038I
a = 3.74983 + 2.22249I
b = 0.396790 − 0.342833I
7.61338 + 6.13503I 12.1450 − 9.8024I
u = 0.381622 − 0.153038I
a = 3.74983 − 2.22249I
b = 0.396790 + 0.342833I
7.61338 − 6.13503I 12.1450 + 9.8024I
u = −0.33714 + 1.56324I
a = 0.107214 − 0.797190I
b = 0.57846 − 1.34433I
0.68291 − 8.38710I 0
u = −0.33714 − 1.56324I
a = 0.107214 + 0.797190I
b = 0.57846 + 1.34433I
0.68291 + 8.38710I 0
u = 0.13250 + 1.60991I
a = −0.471533 + 0.981639I
b = −0.45579 + 1.59734I
−2.46634 − 5.42668I 0
u = 0.13250 − 1.60991I
a = −0.471533 − 0.981639I
b = −0.45579 − 1.59734I
−2.46634 + 5.42668I 0
u = −0.313695 + 0.118779I
a = 1.43384 + 1.57346I
b = 0.864812 − 0.896168I
1.18377 − 3.27789I 7.72431 + 9.92436I
u = −0.313695 − 0.118779I
a = 1.43384 − 1.57346I
b = 0.864812 + 0.896168I
1.18377 + 3.27789I 7.72431 − 9.92436I
u = 0.317523 + 0.085220I
a = −2.52056 − 1.69319I
b = 0.666836 + 0.066192I
2.39484 − 2.47343I 1.59037 + 1.05433I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.317523 − 0.085220I
a = −2.52056 + 1.69319I
b = 0.666836 − 0.066192I
2.39484 + 2.47343I 1.59037 − 1.05433I
u = 0.0747499
a = −11.4868
b = −1.16381
−1.02756 −9.74990
17
II. I
u
2
= h1390u
25
− 2769u
24
+ · · · + 509b − 880, 259u
25
− 1267u
24
+ · · · +
509a − 4214, u
26
− u
25
+ · · · − 2u + 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
4
=
−0.508841u
25
+ 2.48919u
24
+ ··· − 13.5324u + 8.27898
−2.73084u
25
+ 5.44008u
24
+ ··· − 10.6798u + 1.72888
a
9
=
1
−u
2
a
5
=
−2.83890u
25
+ 5.75246u
24
+ ··· − 19.7426u + 8.02750
−5.69352u
25
+ 10.0413u
24
+ ··· − 14.8762u + 2.66208
a
1
=
u
u
a
2
=
1.79961u
25
− 5.91159u
24
+ ··· − 3.73477u − 5.00982
5.58546u
25
− 9.72888u
24
+ ··· + 12.8134u − 5.36346
a
10
=
0.218075u
25
− 0.0667976u
24
+ ··· − 10.2004u + 7.45187
−0.0903733u
25
+ 0.333988u
24
+ ··· − 11.9980u + 1.74067
a
7
=
u
2
+ 1
u
2
a
3
=
−1.50884u
25
+ 3.48919u
24
+ ··· − 20.5324u + 9.27898
−3.73084u
25
+ 6.44008u
24
+ ··· − 10.6798u + 1.72888
a
6
=
2.05108u
25
− 1.49312u
24
+ ··· + 39.5206u − 0.722986
−3.22200u
25
+ 4.95088u
24
+ ··· − 3.14735u + 4.44990
a
11
=
−3.78193u
25
+ 2.93320u
24
+ ··· + 3.79961u − 11.5481
−2.34578u
25
+ 2.79961u
24
+ ··· + 5.39882u − 1.64440
(ii) Obstruction class = 1
(iii) Cusp Shapes =
806
509
u
25
+
10034
509
u
24
+ ··· −
35559
509
u +
13533
509
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
26
− 13u
25
+ ··· − 16u + 1
c
2
u
26
+ 13u
25
+ ··· + 16u + 1
c
3
u
26
+ 3u
25
+ ··· + 3u + 1
c
4
u
26
+ 10u
24
+ ··· + 10u
2
+ 1
c
5
, c
6
, c
12
u
26
+ u
25
+ ··· + 2u + 1
c
7
, c
8
, c
10
u
26
− u
25
+ ··· − 2u + 1
c
9
u
26
+ 10u
24
+ ··· + 10u
2
+ 1
c
11
u
26
− 3u
25
+ ··· − 3u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
y
26
+ y
25
+ ··· − 8y + 1
c
3
, c
11
y
26
+ 9y
25
+ ··· + 9y + 1
c
4
, c
9
y
26
+ 20y
25
+ ··· + 20y + 1
c
5
, c
6
, c
7
c
8
, c
10
, c
12
y
26
+ 27y
25
+ ··· + 26y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.656652 + 0.601454I
a = 0.154603 − 0.351243I
b = −0.323060 − 0.661061I
− 1.46164I 0. + 5.47579I
u = −0.656652 − 0.601454I
a = 0.154603 + 0.351243I
b = −0.323060 + 0.661061I
1.46164I 0. − 5.47579I
u = 0.023427 + 1.136750I
a = 0.356316 + 0.181219I
b = 1.361400 − 0.237917I
− 1.84045I 0. + 2.56325I
u = 0.023427 − 1.136750I
a = 0.356316 − 0.181219I
b = 1.361400 + 0.237917I
1.84045I 0. − 2.56325I
u = −0.548550 + 0.571374I
a = 0.292699 + 0.771107I
b = 0.171048 − 0.472022I
−0.39608 − 2.87985I 0.41340 + 6.09142I
u = −0.548550 − 0.571374I
a = 0.292699 − 0.771107I
b = 0.171048 + 0.472022I
−0.39608 + 2.87985I 0.41340 − 6.09142I
u = 0.043566 + 1.270810I
a = −0.019588 + 1.284810I
b = −0.89002 + 1.41278I
−2.34929 + 3.35419I −1.98639 − 8.95457I
u = 0.043566 − 1.270810I
a = −0.019588 − 1.284810I
b = −0.89002 − 1.41278I
−2.34929 − 3.35419I −1.98639 + 8.95457I
u = −0.012623 + 1.302060I
a = 0.35115 + 2.17846I
b = 1.24742 + 2.78823I
3.61843 − 5.68648I 0.53148 + 5.38067I
u = −0.012623 − 1.302060I
a = 0.35115 − 2.17846I
b = 1.24742 − 2.78823I
3.61843 + 5.68648I 0.53148 − 5.38067I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.051570 + 0.829687I
a = −0.0525139 + 0.0059226I
b = 0.028788 − 0.254691I
7.80244 + 3.71421I −27.4171 − 22.5074I
u = 1.051570 − 0.829687I
a = −0.0525139 − 0.0059226I
b = 0.028788 + 0.254691I
7.80244 − 3.71421I −27.4171 + 22.5074I
u = 0.082019 + 0.546474I
a = −0.672869 − 0.674063I
b = 0.482992 − 0.908611I
0.39608 − 2.87985I −0.41340 + 6.09142I
u = 0.082019 − 0.546474I
a = −0.672869 + 0.674063I
b = 0.482992 + 0.908611I
0.39608 + 2.87985I −0.41340 − 6.09142I
u = 0.18818 + 1.46320I
a = −0.11956 − 1.85596I
b = −0.74287 − 3.16990I
−3.61843 + 5.68648I −0.53148 − 5.38067I
u = 0.18818 − 1.46320I
a = −0.11956 + 1.85596I
b = −0.74287 + 3.16990I
−3.61843 − 5.68648I −0.53148 + 5.38067I
u = 0.402446 + 0.325171I
a = −0.45113 + 2.62360I
b = 0.016848 − 0.489250I
2.34929 + 3.35419I 1.98639 − 8.95457I
u = 0.402446 − 0.325171I
a = −0.45113 − 2.62360I
b = 0.016848 + 0.489250I
2.34929 − 3.35419I 1.98639 + 8.95457I
u = −0.20440 + 1.48760I
a = −0.00472 − 1.65053I
b = 0.45989 − 2.61404I
−6.97584 − 5.65667I −2.83781 + 4.45015I
u = −0.20440 − 1.48760I
a = −0.00472 + 1.65053I
b = 0.45989 + 2.61404I
−6.97584 + 5.65667I −2.83781 − 4.45015I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.18903 + 1.49678I
a = 0.198013 − 1.051980I
b = −0.40594 − 1.46231I
7.24615I 0. − 4.52705I
u = 0.18903 − 1.49678I
a = 0.198013 + 1.051980I
b = −0.40594 + 1.46231I
− 7.24615I 0. + 4.52705I
u = −0.09435 + 1.58711I
a = −0.33912 − 2.15392I
b = −0.23547 − 2.60005I
−7.80244 − 3.71421I 27.4171 + 22.5074I
u = −0.09435 − 1.58711I
a = −0.33912 + 2.15392I
b = −0.23547 + 2.60005I
−7.80244 + 3.71421I 27.4171 − 22.5074I
u = 0.036336 + 0.368318I
a = 2.30672 − 1.76322I
b = −0.171019 − 1.088990I
6.97584 + 5.65667I 2.83781 − 4.45015I
u = 0.036336 − 0.368318I
a = 2.30672 + 1.76322I
b = −0.171019 + 1.088990I
6.97584 − 5.65667I 2.83781 + 4.45015I
23
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
26
− 13u
25
+ ··· − 16u + 1)(u
122
+ 4u
121
+ ··· − 88956u + 26901)
c
2
(u
26
+ 13u
25
+ ··· + 16u + 1)(u
122
− 4u
121
+ ··· + 88956u + 26901)
c
3
(u
26
+ 3u
25
+ ··· + 3u + 1)(u
122
− 2u
121
+ ··· + 565031u − 52219)
c
4
(u
26
+ 10u
24
+ ··· + 10u
2
+ 1)(u
122
+ u
121
+ ··· + 68u
2
− 1)
c
5
, c
6
(u
26
+ u
25
+ ··· + 2u + 1)(u
122
+ 60u
120
+ ··· + 18u + 1)
c
7
, c
8
(u
26
− u
25
+ ··· − 2u + 1)(u
122
+ 60u
120
+ ··· − 18u + 1)
c
9
(u
26
+ 10u
24
+ ··· + 10u
2
+ 1)(u
122
− u
121
+ ··· + 68u
2
− 1)
c
10
(u
26
− u
25
+ ··· − 2u + 1)(u
122
+ 60u
120
+ ··· + 18u + 1)
c
11
(u
26
− 3u
25
+ ··· − 3u + 1)(u
122
+ 2u
121
+ ··· − 565031u − 52219)
c
12
(u
26
+ u
25
+ ··· + 2u + 1)(u
122
+ 60u
120
+ ··· − 18u + 1)
24
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
(y
26
+ y
25
+ ··· − 8y + 1)
· (y
122
− 30y
121
+ ··· − 23656173156y + 723663801)
c
3
, c
11
(y
26
+ 9y
25
+ ··· + 9y + 1)
· (y
122
− 18y
121
+ ··· − 76906534499y + 2726823961)
c
4
, c
9
(y
26
+ 20y
25
+ ··· + 20y + 1)(y
122
+ 21y
121
+ ··· − 136y + 1)
c
5
, c
6
, c
7
c
8
, c
10
, c
12
(y
26
+ 27y
25
+ ··· + 26y + 1)(y
122
+ 120y
121
+ ··· − 222y + 1)
25
