12a
0918
(K12a
0918
)
A knot diagram
1
Linearized knot diagam
4 6 9 10 3 11 12 2 1 8 7 5
Solving Sequence
6,11
7 12
3,8
2 9 5 1 10 4
c
6
c
11
c
7
c
2
c
8
c
5
c
12
c
10
c
4
c
1
, c
3
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.61929 × 10
286
u
158
+ 3.80106 × 10
286
u
157
+ ··· + 1.62955 × 10
287
b − 5.38191 × 10
287
,
2.14088 × 10
287
u
158
− 1.53484 × 10
287
u
157
+ ··· + 5.26470 × 10
287
a + 9.88848 × 10
287
,
u
159
+ u
158
+ ··· − 92u + 21i
I
u
2
= h−20u
31
+ 59u
30
+ ··· + b + 18, 15u
31
− 43u
30
+ ··· + a − 15, u
32
− 4u
31
+ ··· + 16u
2
+ 1i
I
u
3
= h2a
3
+ a
2
+ b + 5a − 3, a
4
+ 2a
2
− 3a + 1, u + 1i
* 3 irreducible components of dim
C
= 0, with total 195 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−1.62 × 10
286
u
158
+ 3.80 × 10
286
u
157
+ · · · + 1.63 × 10
287
b − 5.38 ×
10
287
, 2.14 × 10
287
u
158
− 1.53 × 10
287
u
157
+ · · · + 5.26 × 10
287
a + 9.89 ×
10
287
, u
159
+ u
158
+ · · · − 92u + 21i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
−u
2
a
12
=
u
−u
3
+ u
a
3
=
−0.406648u
158
+ 0.291533u
157
+ ··· − 1.00413u − 1.87826
0.0993705u
158
− 0.233258u
157
+ ··· − 19.1997u + 3.30269
a
8
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
−0.307277u
158
+ 0.0582749u
157
+ ··· − 20.2038u + 1.42443
0.0993705u
158
− 0.233258u
157
+ ··· − 19.1997u + 3.30269
a
9
=
−0.0964387u
158
− 0.173603u
157
+ ··· − 78.5154u + 12.5849
0.305530u
158
+ 0.139750u
157
+ ··· + 7.38377u − 3.14302
a
5
=
−0.0972956u
158
+ 0.311974u
157
+ ··· + 47.8778u − 9.68921
0.193512u
158
− 0.201770u
157
+ ··· − 33.9621u + 9.32314
a
1
=
0.0386557u
158
+ 0.335671u
157
+ ··· + 9.26981u + 6.53523
0.0211241u
158
− 0.185844u
157
+ ··· + 9.70779u − 5.49922
a
10
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
4
=
−0.0475849u
158
+ 0.215036u
157
+ ··· + 49.7268u − 9.69616
0.197192u
158
− 0.150861u
157
+ ··· − 35.7867u + 9.69243
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.883281u
158
+ 0.157448u
157
+ ··· − 191.867u + 45.9615
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
159
− 11u
158
+ ··· − 136u + 48
c
2
, c
5
u
159
+ 9u
158
+ ··· + 9524u + 1463
c
3
u
159
+ 3u
157
+ ··· − 349u − 31
c
4
u
159
− 2u
158
+ ··· + 576u − 64
c
6
, c
7
, c
11
u
159
− u
158
+ ··· − 92u − 21
c
8
u
159
− 3u
158
+ ··· − 104013506u − 14233459
c
9
u
159
− 7u
158
+ ··· + 113u − 7
c
10
u
159
− 9u
158
+ ··· + 3427840u + 1462272
c
12
u
159
− 3u
158
+ ··· + 35431u + 1013
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
159
+ 3y
158
+ ··· − 82112y −2304
c
2
, c
5
y
159
+ 89y
158
+ ··· + 106035890y −2140369
c
3
y
159
+ 6y
158
+ ··· + 80199y −961
c
4
y
159
− 2y
158
+ ··· + 368640y −4096
c
6
, c
7
, c
11
y
159
− 147y
158
+ ··· − 13502y −441
c
8
y
159
+ 21y
158
+ ··· − 11556131041417374y −202591355104681
c
9
y
159
+ y
158
+ ··· + 4943y −49
c
10
y
159
− 3y
158
+ ··· − 53018876444672y −2138239401984
c
12
y
159
− 5y
158
+ ··· + 327496385y −1026169
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.799273 + 0.595295I
a = 0.654341 − 0.752554I
b = −0.275980 + 1.122700I
3.52667 + 1.67894I 0
u = −0.799273 − 0.595295I
a = 0.654341 + 0.752554I
b = −0.275980 − 1.122700I
3.52667 − 1.67894I 0
u = −0.834666 + 0.572919I
a = −0.119569 + 0.709332I
b = 0.401223 − 1.042960I
3.33713 + 2.17980I 0
u = −0.834666 − 0.572919I
a = −0.119569 − 0.709332I
b = 0.401223 + 1.042960I
3.33713 − 2.17980I 0
u = −0.965631 + 0.329670I
a = 0.760712 − 0.409889I
b = −0.535440 + 1.145240I
1.83061 + 2.86317I 0
u = −0.965631 − 0.329670I
a = 0.760712 + 0.409889I
b = −0.535440 − 1.145240I
1.83061 − 2.86317I 0
u = 0.788784 + 0.547825I
a = −0.440608 − 0.644316I
b = 0.578464 + 1.222480I
2.32567 − 11.12500I 0
u = 0.788784 − 0.547825I
a = −0.440608 + 0.644316I
b = 0.578464 − 1.222480I
2.32567 + 11.12500I 0
u = 0.920641 + 0.229633I
a = −0.082467 − 1.001120I
b = 0.673100 + 0.478718I
−0.75472 + 5.52736I 0
u = 0.920641 − 0.229633I
a = −0.082467 + 1.001120I
b = 0.673100 − 0.478718I
−0.75472 − 5.52736I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.040949 + 0.902867I
a = 0.164336 + 0.065527I
b = 0.314215 + 0.827992I
−2.89952 − 4.98326I 0
u = 0.040949 − 0.902867I
a = 0.164336 − 0.065527I
b = 0.314215 − 0.827992I
−2.89952 + 4.98326I 0
u = 1.088200 + 0.137242I
a = −0.131931 − 0.931019I
b = −0.697721 + 0.987501I
0.83807 + 4.08830I 0
u = 1.088200 − 0.137242I
a = −0.131931 + 0.931019I
b = −0.697721 − 0.987501I
0.83807 − 4.08830I 0
u = −0.311564 + 0.832969I
a = 1.258760 − 0.643598I
b = 0.498950 + 1.111460I
1.69592 − 7.05174I 0
u = −0.311564 − 0.832969I
a = 1.258760 + 0.643598I
b = 0.498950 − 1.111460I
1.69592 + 7.05174I 0
u = −1.089110 + 0.232449I
a = 0.69157 + 1.26424I
b = 0.452532 − 0.926610I
0.97576 + 2.58728I 0
u = −1.089110 − 0.232449I
a = 0.69157 − 1.26424I
b = 0.452532 + 0.926610I
0.97576 − 2.58728I 0
u = −0.334703 + 0.816865I
a = −0.851963 + 0.666394I
b = −0.387709 − 1.243550I
2.08281 − 6.54231I 0
u = −0.334703 − 0.816865I
a = −0.851963 − 0.666394I
b = −0.387709 + 1.243550I
2.08281 + 6.54231I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.079580 + 0.301484I
a = 0.826300 − 0.998104I
b = 0.314490 + 0.631256I
1.81628 − 0.95690I 0
u = −1.079580 − 0.301484I
a = 0.826300 + 0.998104I
b = 0.314490 − 0.631256I
1.81628 + 0.95690I 0
u = 0.318803 + 0.807507I
a = 1.30341 + 0.76194I
b = 0.64770 − 1.28553I
0.8176 + 15.8279I 0
u = 0.318803 − 0.807507I
a = 1.30341 − 0.76194I
b = 0.64770 + 1.28553I
0.8176 − 15.8279I 0
u = 1.164590 + 0.114608I
a = −0.165064 − 0.937360I
b = −1.070590 + 0.508490I
−0.88754 + 2.00188I 0
u = 1.164590 − 0.114608I
a = −0.165064 + 0.937360I
b = −1.070590 − 0.508490I
−0.88754 − 2.00188I 0
u = 1.168020 + 0.107285I
a = −0.472949 − 0.340663I
b = −0.135049 − 1.036230I
5.53395 − 3.26719I 0
u = 1.168020 − 0.107285I
a = −0.472949 + 0.340663I
b = −0.135049 + 1.036230I
5.53395 + 3.26719I 0
u = −1.145600 + 0.258752I
a = 0.469515 + 0.634234I
b = −0.410048 + 0.042409I
0.733678 − 0.678388I 0
u = −1.145600 − 0.258752I
a = 0.469515 − 0.634234I
b = −0.410048 − 0.042409I
0.733678 + 0.678388I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.767881 + 0.268194I
a = 0.158187 + 1.260450I
b = 0.891327 − 0.291243I
−0.58360 − 5.65390I 0
u = 0.767881 − 0.268194I
a = 0.158187 − 1.260450I
b = 0.891327 + 0.291243I
−0.58360 + 5.65390I 0
u = −1.157610 + 0.341316I
a = 0.718535 − 0.181945I
b = 0.336545 + 0.647623I
0.097145 − 0.964697I 0
u = −1.157610 − 0.341316I
a = 0.718535 + 0.181945I
b = 0.336545 − 0.647623I
0.097145 + 0.964697I 0
u = −0.090279 + 0.786792I
a = 0.310754 − 0.764533I
b = 0.267372 − 0.570974I
−3.15929 − 3.12621I 0
u = −0.090279 − 0.786792I
a = 0.310754 + 0.764533I
b = 0.267372 + 0.570974I
−3.15929 + 3.12621I 0
u = −0.211790 + 0.755920I
a = −1.189780 + 0.211965I
b = −0.66281 − 1.29058I
−0.46327 − 6.89398I 0
u = −0.211790 − 0.755920I
a = −1.189780 − 0.211965I
b = −0.66281 + 1.29058I
−0.46327 + 6.89398I 0
u = −0.654320 + 0.409082I
a = 0.167312 + 0.867181I
b = −0.242747 − 1.039940I
2.56240 − 2.58490I 10.69425 + 0.I
u = −0.654320 − 0.409082I
a = 0.167312 − 0.867181I
b = −0.242747 + 1.039940I
2.56240 + 2.58490I 10.69425 + 0.I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.250992 + 0.726443I
a = 0.585723 + 0.489535I
b = 1.153520 + 0.281834I
−2.37858 + 9.47061I 0. − 8.12329I
u = 0.250992 − 0.726443I
a = 0.585723 − 0.489535I
b = 1.153520 − 0.281834I
−2.37858 − 9.47061I 0. + 8.12329I
u = 0.198555 + 0.737587I
a = 0.841334 + 0.969239I
b = 0.407659 − 0.757510I
−2.98906 − 1.75226I 0
u = 0.198555 − 0.737587I
a = 0.841334 − 0.969239I
b = 0.407659 + 0.757510I
−2.98906 + 1.75226I 0
u = −1.23638
a = 1.19932
b = −0.119129
2.36933 0
u = 1.152260 + 0.457534I
a = 0.470420 + 0.899795I
b = 0.446456 − 0.951171I
0.52773 + 9.79628I 0
u = 1.152260 − 0.457534I
a = 0.470420 − 0.899795I
b = 0.446456 + 0.951171I
0.52773 − 9.79628I 0
u = −1.222050 + 0.211477I
a = 0.22886 + 1.60032I
b = −1.076230 − 0.531457I
−0.21243 − 2.76227I 0
u = −1.222050 − 0.211477I
a = 0.22886 − 1.60032I
b = −1.076230 + 0.531457I
−0.21243 + 2.76227I 0
u = −0.321842 + 0.685356I
a = 1.44451 − 0.21818I
b = −0.055055 + 0.871285I
1.41713 − 1.34446I 6.49984 + 3.60403I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.321842 − 0.685356I
a = 1.44451 + 0.21818I
b = −0.055055 − 0.871285I
1.41713 + 1.34446I 6.49984 − 3.60403I
u = 0.286131 + 0.695148I
a = −1.56049 − 0.90920I
b = −0.65062 + 1.32692I
−0.20295 + 7.26883I −2.50391 − 12.76607I
u = 0.286131 − 0.695148I
a = −1.56049 + 0.90920I
b = −0.65062 − 1.32692I
−0.20295 − 7.26883I −2.50391 + 12.76607I
u = −0.214279 + 0.711402I
a = 0.727619 − 0.226998I
b = 0.619242 − 0.291900I
−0.67157 − 2.64961I 2.00000 + 6.28164I
u = −0.214279 − 0.711402I
a = 0.727619 + 0.226998I
b = 0.619242 + 0.291900I
−0.67157 + 2.64961I 2.00000 − 6.28164I
u = −0.479596 + 0.566435I
a = −0.036380 + 0.172804I
b = 0.436232 − 1.015990I
2.36325 − 0.02920I 8.14035 + 4.63595I
u = −0.479596 − 0.566435I
a = −0.036380 − 0.172804I
b = 0.436232 + 1.015990I
2.36325 + 0.02920I 8.14035 − 4.63595I
u = −0.435949 + 0.572076I
a = 1.62006 − 0.86038I
b = 0.585893 + 0.955562I
2.27343 − 3.90732I 9.31934 + 6.35993I
u = −0.435949 − 0.572076I
a = 1.62006 + 0.86038I
b = 0.585893 − 0.955562I
2.27343 + 3.90732I 9.31934 − 6.35993I
u = −0.171511 + 0.685651I
a = 1.68144 − 1.40388I
b = 0.336693 + 1.020650I
−1.71183 − 6.01014I −2.05617 + 9.25308I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.171511 − 0.685651I
a = 1.68144 + 1.40388I
b = 0.336693 − 1.020650I
−1.71183 + 6.01014I −2.05617 − 9.25308I
u = −0.130256 + 0.691140I
a = −0.632396 − 0.435664I
b = −0.701285 − 0.315380I
−2.28898 − 2.81780I −3.69298 + 6.05931I
u = −0.130256 − 0.691140I
a = −0.632396 + 0.435664I
b = −0.701285 + 0.315380I
−2.28898 + 2.81780I −3.69298 − 6.05931I
u = 0.364563 + 0.591898I
a = −0.90629 − 1.42302I
b = −0.643568 + 0.671849I
−1.77482 + 3.92949I −3.83817 − 8.21365I
u = 0.364563 − 0.591898I
a = −0.90629 + 1.42302I
b = −0.643568 − 0.671849I
−1.77482 − 3.92949I −3.83817 + 8.21365I
u = −1.232790 + 0.465501I
a = −0.366440 + 0.564724I
b = 0.116619 − 0.771707I
1.041220 + 0.137927I 0
u = −1.232790 − 0.465501I
a = −0.366440 − 0.564724I
b = 0.116619 + 0.771707I
1.041220 − 0.137927I 0
u = 0.585666 + 0.340842I
a = 0.770744 + 0.950438I
b = −0.528110 − 1.199570I
1.10473 − 3.57300I 1.47051 + 6.16602I
u = 0.585666 − 0.340842I
a = 0.770744 − 0.950438I
b = −0.528110 + 1.199570I
1.10473 + 3.57300I 1.47051 − 6.16602I
u = 0.200680 + 0.637491I
a = −2.45642 + 0.15855I
b = −0.313088 + 1.184000I
2.97283 + 5.99388I 6.42755 − 8.84957I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.200680 − 0.637491I
a = −2.45642 − 0.15855I
b = −0.313088 − 1.184000I
2.97283 − 5.99388I 6.42755 + 8.84957I
u = 1.336350 + 0.088089I
a = 0.77234 + 2.29522I
b = −0.25297 − 1.60145I
7.87064 − 3.40592I 0
u = 1.336350 − 0.088089I
a = 0.77234 − 2.29522I
b = −0.25297 + 1.60145I
7.87064 + 3.40592I 0
u = −1.330760 + 0.168909I
a = −0.78433 + 2.83863I
b = −0.425765 − 1.152930I
3.75885 − 4.25333I 0
u = −1.330760 − 0.168909I
a = −0.78433 − 2.83863I
b = −0.425765 + 1.152930I
3.75885 + 4.25333I 0
u = 1.335890 + 0.172092I
a = 0.075362 + 0.650629I
b = −0.779588 − 0.974467I
3.82140 + 0.23328I 0
u = 1.335890 − 0.172092I
a = 0.075362 − 0.650629I
b = −0.779588 + 0.974467I
3.82140 − 0.23328I 0
u = 1.337140 + 0.226045I
a = 0.920513 − 0.672971I
b = −1.49738 − 0.24928I
0.75338 + 3.18644I 0
u = 1.337140 − 0.226045I
a = 0.920513 + 0.672971I
b = −1.49738 + 0.24928I
0.75338 − 3.18644I 0
u = 0.185771 + 0.615827I
a = 0.242210 − 0.402152I
b = −0.674946 − 0.678322I
−1.75602 − 1.14410I −2.70905 + 3.41357I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.185771 − 0.615827I
a = 0.242210 + 0.402152I
b = −0.674946 + 0.678322I
−1.75602 + 1.14410I −2.70905 − 3.41357I
u = 1.320050 + 0.336037I
a = −0.340469 + 0.295275I
b = 0.210092 + 0.543789I
1.25878 + 7.17293I 0
u = 1.320050 − 0.336037I
a = −0.340469 − 0.295275I
b = 0.210092 − 0.543789I
1.25878 − 7.17293I 0
u = 1.356050 + 0.157256I
a = −1.96433 − 2.89991I
b = −0.070463 + 0.895904I
4.84633 − 2.35882I 0
u = 1.356050 − 0.157256I
a = −1.96433 + 2.89991I
b = −0.070463 − 0.895904I
4.84633 + 2.35882I 0
u = −1.369450 + 0.145280I
a = −1.036070 + 0.881185I
b = −0.270195 + 0.271615I
4.76561 − 5.98459I 0
u = −1.369450 − 0.145280I
a = −1.036070 − 0.881185I
b = −0.270195 − 0.271615I
4.76561 + 5.98459I 0
u = 1.351390 + 0.270479I
a = −0.048448 − 0.646700I
b = −0.902681 + 0.438862I
2.40294 + 6.28854I 0
u = 1.351390 − 0.270479I
a = −0.048448 + 0.646700I
b = −0.902681 − 0.438862I
2.40294 − 6.28854I 0
u = 0.287478 + 0.545861I
a = 2.02886 + 0.08096I
b = 0.331670 − 1.272780I
4.08899 − 1.75406I 6.02942 − 0.78009I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.287478 − 0.545861I
a = 2.02886 − 0.08096I
b = 0.331670 + 1.272780I
4.08899 + 1.75406I 6.02942 + 0.78009I
u = −1.368080 + 0.225606I
a = 1.13965 + 0.97018I
b = −1.42897 + 0.21580I
1.13488 − 3.60883I 0
u = −1.368080 − 0.225606I
a = 1.13965 − 0.97018I
b = −1.42897 − 0.21580I
1.13488 + 3.60883I 0
u = 0.156361 + 0.590337I
a = −0.909143 − 1.010760I
b = −1.254360 − 0.266293I
−3.73265 + 0.64583I −14.3996 − 3.2867I
u = 0.156361 − 0.590337I
a = −0.909143 + 1.010760I
b = −1.254360 + 0.266293I
−3.73265 − 0.64583I −14.3996 + 3.2867I
u = −1.382100 + 0.159658I
a = 0.40621 − 2.75500I
b = −0.27264 + 1.41868I
9.38761 + 1.59220I 0
u = −1.382100 − 0.159658I
a = 0.40621 + 2.75500I
b = −0.27264 − 1.41868I
9.38761 − 1.59220I 0
u = −0.072608 + 0.602082I
a = −1.253030 + 0.070063I
b = −1.283910 + 0.307868I
−3.72634 − 0.20894I −8.98173 − 0.59922I
u = −0.072608 − 0.602082I
a = −1.253030 − 0.070063I
b = −1.283910 − 0.307868I
−3.72634 + 0.20894I −8.98173 + 0.59922I
u = 1.369520 + 0.270922I
a = 1.21441 + 2.78141I
b = 0.269286 − 1.108730I
3.18591 + 9.47700I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.369520 − 0.270922I
a = 1.21441 − 2.78141I
b = 0.269286 + 1.108730I
3.18591 − 9.47700I 0
u = −1.365110 + 0.295551I
a = 0.82503 − 1.91460I
b = 0.271144 + 0.950814I
1.94770 − 1.99435I 0
u = −1.365110 − 0.295551I
a = 0.82503 + 1.91460I
b = 0.271144 − 0.950814I
1.94770 + 1.99435I 0
u = 1.396810 + 0.099721I
a = −0.176525 − 0.092513I
b = 0.612241 + 0.391261I
6.97211 + 1.72636I 0
u = 1.396810 − 0.099721I
a = −0.176525 + 0.092513I
b = 0.612241 − 0.391261I
6.97211 − 1.72636I 0
u = −1.379490 + 0.256508I
a = −1.88048 + 1.78681I
b = −0.403089 − 1.223300I
8.00556 − 9.26916I 0
u = −1.379490 − 0.256508I
a = −1.88048 − 1.78681I
b = −0.403089 + 1.223300I
8.00556 + 9.26916I 0
u = −1.403520 + 0.086431I
a = −0.497455 − 0.628849I
b = 0.981614 − 0.222678I
5.71530 + 4.79848I 0
u = −1.403520 − 0.086431I
a = −0.497455 + 0.628849I
b = 0.981614 + 0.222678I
5.71530 − 4.79848I 0
u = −1.391830 + 0.201064I
a = −0.93217 + 2.23738I
b = 0.22876 − 1.66694I
9.66378 − 7.08739I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.391830 − 0.201064I
a = −0.93217 − 2.23738I
b = 0.22876 + 1.66694I
9.66378 + 7.08739I 0
u = −1.386000 + 0.246655I
a = 0.921726 − 0.266770I
b = −0.785839 + 0.498129I
3.30331 − 2.00372I 0
u = −1.386000 − 0.246655I
a = 0.921726 + 0.266770I
b = −0.785839 − 0.498129I
3.30331 + 2.00372I 0
u = −1.39993 + 0.21353I
a = 1.17608 − 2.01178I
b = 0.50864 + 1.36234I
9.46503 − 1.05151I 0
u = −1.39993 − 0.21353I
a = 1.17608 + 2.01178I
b = 0.50864 − 1.36234I
9.46503 + 1.05151I 0
u = 1.38973 + 0.28573I
a = −0.215171 + 0.305291I
b = 0.803425 + 0.224199I
4.43971 + 6.27448I 0
u = 1.38973 − 0.28573I
a = −0.215171 − 0.305291I
b = 0.803425 − 0.224199I
4.43971 − 6.27448I 0
u = 1.38660 + 0.30322I
a = −0.90903 − 2.01619I
b = −0.71453 + 1.39926I
4.61255 + 10.72160I 0
u = 1.38660 − 0.30322I
a = −0.90903 + 2.01619I
b = −0.71453 − 1.39926I
4.61255 − 10.72160I 0
u = 1.41466 + 0.12761I
a = 0.25482 − 2.27671I
b = −0.071824 + 1.276080I
8.86441 + 4.13680I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41466 − 0.12761I
a = 0.25482 + 2.27671I
b = −0.071824 − 1.276080I
8.86441 − 4.13680I 0
u = −1.40230 + 0.28947I
a = −0.799094 − 0.602129I
b = 1.269700 − 0.233757I
2.88682 − 13.15910I 0
u = −1.40230 − 0.28947I
a = −0.799094 + 0.602129I
b = 1.269700 + 0.233757I
2.88682 + 13.15910I 0
u = −1.42930 + 0.12679I
a = 0.99232 − 2.26659I
b = −0.355357 + 1.353570I
7.30600 + 1.91757I 0
u = −1.42930 − 0.12679I
a = 0.99232 + 2.26659I
b = −0.355357 − 1.353570I
7.30600 − 1.91757I 0
u = −1.41558 + 0.27321I
a = −0.99899 + 2.49915I
b = −0.66005 − 1.41457I
5.23264 − 10.79800I 0
u = −1.41558 − 0.27321I
a = −0.99899 − 2.49915I
b = −0.66005 + 1.41457I
5.23264 + 10.79800I 0
u = 1.42343 + 0.26174I
a = 1.41395 + 1.31316I
b = 0.103083 − 0.897993I
6.99165 + 4.78322I 0
u = 1.42343 − 0.26174I
a = 1.41395 − 1.31316I
b = 0.103083 + 0.897993I
6.99165 − 4.78322I 0
u = 1.43411 + 0.20911I
a = 0.73448 + 1.85336I
b = 0.724979 − 1.032690I
8.20112 + 6.72484I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43411 − 0.20911I
a = 0.73448 − 1.85336I
b = 0.724979 + 1.032690I
8.20112 − 6.72484I 0
u = −0.498633 + 0.231913I
a = 0.676707 − 0.369974I
b = 0.235110 − 0.126078I
1.125340 − 0.507072I 7.32472 + 1.80737I
u = −0.498633 − 0.231913I
a = 0.676707 + 0.369974I
b = 0.235110 + 0.126078I
1.125340 + 0.507072I 7.32472 − 1.80737I
u = 1.44415 + 0.18611I
a = −0.50108 − 1.52574I
b = 0.395517 + 1.192830I
8.50916 + 2.66886I 0
u = 1.44415 − 0.18611I
a = −0.50108 + 1.52574I
b = 0.395517 − 1.192830I
8.50916 − 2.66886I 0
u = 0.265097 + 0.456539I
a = −0.609248 − 0.288943I
b = 0.10567 + 1.51534I
4.39118 + 4.54039I 5.47207 − 10.36562I
u = 0.265097 − 0.456539I
a = −0.609248 + 0.288943I
b = 0.10567 − 1.51534I
4.39118 − 4.54039I 5.47207 + 10.36562I
u = −1.44253 + 0.32040I
a = 0.95994 − 2.16725I
b = 0.66728 + 1.34561I
6.4467 − 19.9152I 0
u = −1.44253 − 0.32040I
a = 0.95994 + 2.16725I
b = 0.66728 − 1.34561I
6.4467 + 19.9152I 0
u = 1.44201 + 0.33238I
a = 1.04232 + 1.86273I
b = 0.538860 − 1.182240I
7.29386 + 11.26600I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.44201 − 0.33238I
a = 1.04232 − 1.86273I
b = 0.538860 + 1.182240I
7.29386 − 11.26600I 0
u = 1.44792 + 0.32031I
a = −0.83095 − 2.00003I
b = −0.403517 + 1.354990I
7.78199 + 10.65610I 0
u = 1.44792 − 0.32031I
a = −0.83095 + 2.00003I
b = −0.403517 − 1.354990I
7.78199 − 10.65610I 0
u = −1.46623 + 0.22801I
a = −0.35046 + 2.00234I
b = −0.520060 − 0.833912I
4.17918 − 6.96018I 0
u = −1.46623 − 0.22801I
a = −0.35046 − 2.00234I
b = −0.520060 + 0.833912I
4.17918 + 6.96018I 0
u = −1.54158 + 0.06730I
a = −0.48637 + 1.93480I
b = 0.423099 − 1.272070I
10.20780 + 9.30854I 0
u = −1.54158 − 0.06730I
a = −0.48637 − 1.93480I
b = 0.423099 + 1.272070I
10.20780 − 9.30854I 0
u = −0.005487 + 0.448891I
a = −2.54974 − 0.62221I
b = −0.568904 + 0.992243I
−0.54033 + 2.01867I −2.68262 − 3.08744I
u = −0.005487 − 0.448891I
a = −2.54974 + 0.62221I
b = −0.568904 − 0.992243I
−0.54033 − 2.01867I −2.68262 + 3.08744I
u = 1.58971 + 0.03349I
a = 0.19891 + 1.82666I
b = 0.022223 − 1.145830I
11.83510 + 0.31664I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.58971 − 0.03349I
a = 0.19891 − 1.82666I
b = 0.022223 + 1.145830I
11.83510 − 0.31664I 0
u = 0.233535 + 0.310327I
a = 0.01580 + 1.99878I
b = −0.192951 − 1.356770I
4.22259 − 3.55617I 11.75571 − 4.38189I
u = 0.233535 − 0.310327I
a = 0.01580 − 1.99878I
b = −0.192951 + 1.356770I
4.22259 + 3.55617I 11.75571 + 4.38189I
u = 0.281817 + 0.265812I
a = 1.043980 + 0.163916I
b = −0.629326 − 0.360289I
−1.37561 − 0.94145I −2.52295 + 1.00632I
u = 0.281817 − 0.265812I
a = 1.043980 − 0.163916I
b = −0.629326 + 0.360289I
−1.37561 + 0.94145I −2.52295 − 1.00632I
u = 1.61353 + 0.03083I
a = 0.01106 − 1.76492I
b = 0.135699 + 1.074040I
11.79000 − 0.33406I 0
u = 1.61353 − 0.03083I
a = 0.01106 + 1.76492I
b = 0.135699 − 1.074040I
11.79000 + 0.33406I 0
u = −0.044735 + 0.337560I
a = −6.29736 + 0.56249I
b = 0.048607 − 0.637881I
0.20790 + 4.29893I 2.06844 + 3.27592I
u = −0.044735 − 0.337560I
a = −6.29736 − 0.56249I
b = 0.048607 + 0.637881I
0.20790 − 4.29893I 2.06844 − 3.27592I
20
II. I
u
2
= h−20u
31
+ 59u
30
+ · · · + b + 18, 15u
31
− 43u
30
+ · · · + a − 15, u
32
−
4u
31
+ · · · + 16u
2
+ 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
−u
2
a
12
=
u
−u
3
+ u
a
3
=
−15u
31
+ 43u
30
+ ··· + 3u + 15
20u
31
− 59u
30
+ ··· − 9u − 18
a
8
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
5u
31
− 16u
30
+ ··· − 6u − 3
20u
31
− 59u
30
+ ··· − 9u − 18
a
9
=
50u
31
− 135u
30
+ ··· − 11u − 38
−12u
31
+ 27u
30
+ ··· − 3u + 4
a
5
=
20u
31
− 40u
30
+ ··· − 14u − 7
−20u
31
+ 46u
30
+ ··· + 9u + 14
a
1
=
40u
31
− 104u
30
+ ··· − 41u − 32
−32u
31
+ 82u
30
+ ··· + 17u + 25
a
10
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
4
=
2u
31
+ 4u
30
+ ··· − 7u + 5
−u
31
− 2u
30
+ ··· + u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −131u
31
+ 354u
30
+ 1641u
29
−4684u
28
−9391u
27
+ 27382u
26
+ 33163u
25
−91574u
24
−
82869u
23
+ 186844u
22
+ 157052u
21
− 218430u
20
− 224559u
19
+ 81246u
18
+ 216620u
17
+
149426u
16
− 90371u
15
− 233798u
14
− 67401u
13
+ 96549u
12
+ 108708u
11
+ 51286u
10
−
39137u
9
−53047u
8
−10210u
7
+ 1070u
6
+ 6176u
5
+ 6250u
4
+ 450u
3
+ 1554u
2
+ 34u + 90
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
32
− 6u
31
+ ··· − 27u + 13
c
2
u
32
− 10u
31
+ ··· − 4u + 1
c
3
u
32
+ 7u
30
+ ··· + 7u
2
+ 1
c
4
u
32
+ 7u
30
+ ··· + 7u
2
+ 1
c
5
u
32
+ 10u
31
+ ··· + 4u + 1
c
6
, c
7
u
32
− 4u
31
+ ··· + 16u
2
+ 1
c
8
u
32
− 5u
30
+ ··· + 31u + 11
c
9
u
32
− 2u
31
+ ··· + 4u
2
+ 1
c
10
u
32
− 12u
31
+ ··· − 60u + 13
c
11
u
32
+ 4u
31
+ ··· + 16u
2
+ 1
c
12
u
32
− 2u
31
+ ··· + 19u + 11
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
32
− 12y
31
+ ··· − 1145y + 169
c
2
, c
5
y
32
+ 16y
31
+ ··· + 30y + 1
c
3
y
32
+ 14y
31
+ ··· + 14y + 1
c
4
y
32
+ 14y
31
+ ··· + 14y + 1
c
6
, c
7
, c
11
y
32
− 34y
31
+ ··· + 32y + 1
c
8
y
32
− 10y
31
+ ··· − 1027y + 121
c
9
y
32
− 10y
31
+ ··· + 8y + 1
c
10
y
32
− 10y
31
+ ··· + 4746y + 169
c
12
y
32
− 18y
31
+ ··· + 211y + 121
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.861640 + 0.468739I
a = 0.363509 − 0.746447I
b = −0.358296 + 1.062330I
2.64681 + 1.99924I 3.61618 − 3.48799I
u = −0.861640 − 0.468739I
a = 0.363509 + 0.746447I
b = −0.358296 − 1.062330I
2.64681 − 1.99924I 3.61618 + 3.48799I
u = −0.026632 + 0.805242I
a = −0.619416 + 0.243843I
b = −0.034090 + 0.577005I
−2.72500 − 3.69960I 1.92797 + 6.47534I
u = −0.026632 − 0.805242I
a = −0.619416 − 0.243843I
b = −0.034090 − 0.577005I
−2.72500 + 3.69960I 1.92797 − 6.47534I
u = −0.257026 + 0.757824I
a = −1.299650 + 0.554795I
b = −0.480312 − 1.217370I
0.75948 − 6.31169I 2.15440 + 6.84456I
u = −0.257026 − 0.757824I
a = −1.299650 − 0.554795I
b = −0.480312 + 1.217370I
0.75948 + 6.31169I 2.15440 − 6.84456I
u = −1.228020 + 0.172790I
a = 0.334623 + 1.073300I
b = −1.089250 − 0.283327I
0.02951 − 1.84558I 0. − 1.45891I
u = −1.228020 − 0.172790I
a = 0.334623 − 1.073300I
b = −1.089250 + 0.283327I
0.02951 + 1.84558I 0. + 1.45891I
u = −1.198040 + 0.413084I
a = −0.695527 + 0.683737I
b = −0.158705 − 0.670021I
0.913593 − 0.672379I 3.52422 + 0.I
u = −1.198040 − 0.413084I
a = −0.695527 − 0.683737I
b = −0.158705 + 0.670021I
0.913593 + 0.672379I 3.52422 + 0.I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.287660 + 0.116722I
a = 1.19451 + 1.07056I
b = 0.281845 + 0.555734I
3.87178 − 3.05491I 0. + 4.56445I
u = 1.287660 − 0.116722I
a = 1.19451 − 1.07056I
b = 0.281845 − 0.555734I
3.87178 + 3.05491I 0. − 4.56445I
u = 1.286940 + 0.325599I
a = −0.299249 − 0.093826I
b = 0.043940 − 0.506237I
1.35179 + 7.74092I 0. − 11.65600I
u = 1.286940 − 0.325599I
a = −0.299249 + 0.093826I
b = 0.043940 + 0.506237I
1.35179 − 7.74092I 0. + 11.65600I
u = −1.368980 + 0.106143I
a = 0.08312 + 1.82802I
b = 0.008286 − 1.393460I
8.39128 − 5.19633I 0
u = −1.368980 − 0.106143I
a = 0.08312 − 1.82802I
b = 0.008286 + 1.393460I
8.39128 + 5.19633I 0
u = 1.374480 + 0.132731I
a = 0.85632 + 2.78141I
b = −0.19284 − 1.49164I
8.65686 − 2.22377I 0
u = 1.374480 − 0.132731I
a = 0.85632 − 2.78141I
b = −0.19284 + 1.49164I
8.65686 + 2.22377I 0
u = 1.364470 + 0.221317I
a = 1.047440 − 0.907916I
b = −1.47085 − 0.17329I
1.52291 + 3.59714I 0
u = 1.364470 − 0.221317I
a = 1.047440 + 0.907916I
b = −1.47085 + 0.17329I
1.52291 − 3.59714I 0
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.134904 + 0.559272I
a = −1.213990 + 0.693389I
b = −1.316650 + 0.176268I
−3.28801 − 0.73142I 5.05008 + 9.17474I
u = −0.134904 − 0.559272I
a = −1.213990 − 0.693389I
b = −1.316650 − 0.176268I
−3.28801 + 0.73142I 5.05008 − 9.17474I
u = −1.42112 + 0.16795I
a = 1.22623 − 2.39996I
b = 0.277752 + 0.775180I
5.49898 − 6.77249I 0
u = −1.42112 − 0.16795I
a = 1.22623 + 2.39996I
b = 0.277752 − 0.775180I
5.49898 + 6.77249I 0
u = 1.40572 + 0.29478I
a = −1.11898 − 2.14076I
b = −0.51898 + 1.33280I
6.05365 + 10.10780I 0
u = 1.40572 − 0.29478I
a = −1.11898 + 2.14076I
b = −0.51898 − 1.33280I
6.05365 − 10.10780I 0
u = 0.158693 + 0.367701I
a = 4.90037 + 2.48601I
b = 0.247489 − 0.661068I
0.20241 + 4.71909I 1.9025 − 15.0884I
u = 0.158693 − 0.367701I
a = 4.90037 − 2.48601I
b = 0.247489 + 0.661068I
0.20241 − 4.71909I 1.9025 + 15.0884I
u = 1.65881 + 0.03507I
a = 0.06888 + 1.63362I
b = −0.135107 − 0.986476I
11.57400 − 0.54117I 0
u = 1.65881 − 0.03507I
a = 0.06888 − 1.63362I
b = −0.135107 + 0.986476I
11.57400 + 0.54117I 0
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.040420 + 0.281790I
a = 2.17180 − 0.91958I
b = −0.104235 + 1.404030I
3.88795 + 3.82857I −3.00373 − 6.33267I
u = −0.040420 − 0.281790I
a = 2.17180 + 0.91958I
b = −0.104235 − 1.404030I
3.88795 − 3.82857I −3.00373 + 6.33267I
27
III. I
u
3
= h2a
3
+ a
2
+ b + 5a − 3, a
4
+ 2a
2
− 3a + 1, u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
−1
a
7
=
1
−1
a
12
=
−1
0
a
3
=
a
−2a
3
− a
2
− 5a + 3
a
8
=
0
−1
a
2
=
−2a
3
− a
2
− 4a + 3
−2a
3
− a
2
− 5a + 3
a
9
=
−a
a
3
+ 2a − 3
a
5
=
a
3
+ a
2
+ 3a − 1
−2a
3
− a
2
− 5a + 4
a
1
=
−2a
3
− a
2
− 4a + 3
−2a
3
− a
2
− 5a + 3
a
10
=
0
−1
a
4
=
a
3
+ a
2
+ 3a − 1
−a
3
− 2a + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5a
3
+ a
2
+ 11a − 6
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
4
c
2
(u
2
− u + 1)
2
c
3
, c
4
u
4
+ u
3
− u
2
− u + 1
c
5
, c
12
(u
2
+ u + 1)
2
c
6
, c
7
(u + 1)
4
c
8
, c
9
u
4
+ 2u
3
+ 2u
2
+ u + 1
c
11
(u − 1)
4
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
4
c
2
, c
5
, c
12
(y
2
+ y + 1)
2
c
3
, c
4
y
4
− 3y
3
+ 5y
2
− 3y + 1
c
6
, c
7
, c
11
(y −1)
4
c
8
, c
9
y
4
+ 2y
2
+ 3y + 1
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.570696 + 0.107280I
b = −0.500000 − 0.866025I
1.64493 − 2.02988I 1.42268 + 1.82047I
u = −1.00000
a = 0.570696 − 0.107280I
b = −0.500000 + 0.866025I
1.64493 + 2.02988I 1.42268 − 1.82047I
u = −1.00000
a = −0.57070 + 1.62477I
b = −0.500000 − 0.866025I
1.64493 − 2.02988I 7.07732 + 2.50966I
u = −1.00000
a = −0.57070 − 1.62477I
b = −0.500000 + 0.866025I
1.64493 + 2.02988I 7.07732 − 2.50966I
31
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
4
(u
32
− 6u
31
+ ··· − 27u + 13)(u
159
− 11u
158
+ ··· − 136u + 48)
c
2
((u
2
− u + 1)
2
)(u
32
− 10u
31
+ ··· − 4u + 1)
· (u
159
+ 9u
158
+ ··· + 9524u + 1463)
c
3
(u
4
+ u
3
− u
2
− u + 1)(u
32
+ 7u
30
+ ··· + 7u
2
+ 1)
· (u
159
+ 3u
157
+ ··· − 349u − 31)
c
4
(u
4
+ u
3
− u
2
− u + 1)(u
32
+ 7u
30
+ ··· + 7u
2
+ 1)
· (u
159
− 2u
158
+ ··· + 576u − 64)
c
5
((u
2
+ u + 1)
2
)(u
32
+ 10u
31
+ ··· + 4u + 1)
· (u
159
+ 9u
158
+ ··· + 9524u + 1463)
c
6
, c
7
((u + 1)
4
)(u
32
− 4u
31
+ ··· + 16u
2
+ 1)(u
159
− u
158
+ ··· − 92u − 21)
c
8
(u
4
+ 2u
3
+ 2u
2
+ u + 1)(u
32
− 5u
30
+ ··· + 31u + 11)
· (u
159
− 3u
158
+ ··· − 104013506u − 14233459)
c
9
(u
4
+ 2u
3
+ 2u
2
+ u + 1)(u
32
− 2u
31
+ ··· + 4u
2
+ 1)
· (u
159
− 7u
158
+ ··· + 113u − 7)
c
10
u
4
(u
32
− 12u
31
+ ··· − 60u + 13)
· (u
159
− 9u
158
+ ··· + 3427840u + 1462272)
c
11
((u − 1)
4
)(u
32
+ 4u
31
+ ··· + 16u
2
+ 1)(u
159
− u
158
+ ··· − 92u − 21)
c
12
((u
2
+ u + 1)
2
)(u
32
− 2u
31
+ ··· + 19u + 11)
· (u
159
− 3u
158
+ ··· + 35431u + 1013)
32
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
4
(y
32
− 12y
31
+ ··· − 1145y + 169)
· (y
159
+ 3y
158
+ ··· − 82112y −2304)
c
2
, c
5
((y
2
+ y + 1)
2
)(y
32
+ 16y
31
+ ··· + 30y + 1)
· (y
159
+ 89y
158
+ ··· + 106035890y −2140369)
c
3
(y
4
− 3y
3
+ 5y
2
− 3y + 1)(y
32
+ 14y
31
+ ··· + 14y + 1)
· (y
159
+ 6y
158
+ ··· + 80199y −961)
c
4
(y
4
− 3y
3
+ 5y
2
− 3y + 1)(y
32
+ 14y
31
+ ··· + 14y + 1)
· (y
159
− 2y
158
+ ··· + 368640y −4096)
c
6
, c
7
, c
11
((y −1)
4
)(y
32
− 34y
31
+ ··· + 32y + 1)
· (y
159
− 147y
158
+ ··· − 13502y −441)
c
8
(y
4
+ 2y
2
+ 3y + 1)(y
32
− 10y
31
+ ··· − 1027y + 121)
· (y
159
+ 21y
158
+ ··· − 11556131041417374y −202591355104681)
c
9
(y
4
+ 2y
2
+ 3y + 1)(y
32
− 10y
31
+ ··· + 8y + 1)
· (y
159
+ y
158
+ ··· + 4943y −49)
c
10
y
4
(y
32
− 10y
31
+ ··· + 4746y + 169)
· (y
159
− 3y
158
+ ··· − 53018876444672y −2138239401984)
c
12
((y
2
+ y + 1)
2
)(y
32
− 18y
31
+ ··· + 211y + 121)
· (y
159
− 5y
158
+ ··· + 327496385y −1026169)
33
