12n
0756
(K12n
0756
)
A knot diagram
1
Linearized knot diagam
4 6 8 10 3 10 2 1 12 6 5 9
Solving Sequence
2,6 3,10
7 8 11 5 12 4 1 9
c
2
c
6
c
7
c
10
c
5
c
11
c
4
c
1
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h483881179968216u
33
+ 5103340955384197u
32
+ ··· + 272258240478733b + 3934858860404144,
3.93486 × 10
15
u
33
+ 3.89285 × 10
16
u
32
+ ··· + 2.45032 × 10
15
a + 2.14442 × 10
16
, u
34
+ 11u
33
+ ··· + 21u + 9i
I
u
2
= h−u
15
+ 7u
14
− 24u
13
+ 49u
12
− 62u
11
+ 42u
10
− 29u
8
+ 26u
7
− 10u
6
− 2u
4
+ 4u
3
− au − 4u
2
+ b − 1,
− u
15
a + u
15
+ ··· + a
2
+ 4, u
16
− 7u
15
+ ··· + 4u
2
+ 1i
I
u
3
= h−u
17
+ 9u
16
+ ··· + b + 4, −4u
17
+ 31u
16
+ ··· + a + 2, u
18
− 8u
17
+ ··· − 5u + 1i
I
v
1
= ha, b − 1, v −1i
* 4 irreducible components of dim
C
= 0, with total 85 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
=
h4.84×10
14
u
33
+5.10×10
15
u
32
+· · ·+2.72×10
14
b+3.93×10
15
, 3.93×10
15
u
33
+
3.89 × 10
16
u
32
+ · · · + 2.45 × 10
15
a + 2.14 × 10
16
, u
34
+ 11u
33
+ · · · + 21u + 9i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
10
=
−1.60585u
33
− 15.8871u
32
+ ··· − 20.0006u − 8.75159
−1.77729u
33
− 18.7445u
32
+ ··· − 24.9713u − 14.4527
a
7
=
−4.02250u
33
− 42.8304u
32
+ ··· − 54.3967u − 24.3343
−1.41713u
33
− 19.9565u
32
+ ··· − 59.1382u − 36.2025
a
8
=
−2.60537u
33
− 22.8739u
32
+ ··· + 4.74153u + 11.8682
−1.41713u
33
− 19.9565u
32
+ ··· − 59.1382u − 36.2025
a
11
=
−1.60585u
33
− 15.8871u
32
+ ··· − 20.0006u − 8.75159
−2.58296u
33
− 29.2341u
32
+ ··· − 47.8417u − 30.4483
a
5
=
u
u
3
+ u
a
12
=
0.827038u
33
+ 7.98095u
32
+ ··· + 1.94620u − 0.00708657
1.35433u
33
+ 13.1869u
32
+ ··· + 12.9779u + 4.34003
a
4
=
1.76268u
33
+ 15.3291u
32
+ ··· + 13.1843u − 0.885994
4.06037u
33
+ 40.2803u
32
+ ··· + 38.9023u + 15.8641
a
1
=
1.89598u
33
+ 17.9294u
32
+ ··· + 0.703240u − 0.0246888
0.323409u
33
+ 7.21616u
32
+ ··· + 30.5012u + 20.6792
a
9
=
−0.143799u
33
+ 0.732780u
32
+ ··· + 18.1991u + 8.87919
−0.768908u
33
− 8.48694u
32
+ ··· − 11.1369u − 6.67054
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
146229071976183
272258240478733
u
33
−
3883424336090664
272258240478733
u
32
+ ··· −
16335126702306561
272258240478733
u −
14196656353437762
272258240478733
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
34
− u
33
+ ··· − 14u + 1
c
2
, c
5
u
34
− 11u
33
+ ··· − 21u + 9
c
4
u
34
− 2u
33
+ ··· − 298u + 241
c
6
, c
10
u
34
− 20u
32
+ ··· − 6u
2
+ 1
c
7
u
34
+ 29u
33
+ ··· + 786432u + 65536
c
8
, c
9
, c
12
u
34
+ 8u
33
+ ··· + 96u + 9
c
11
u
34
− u
33
+ ··· − 146u + 538
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
34
− 21y
33
+ ··· − 30y + 1
c
2
, c
5
y
34
+ 11y
33
+ ··· + 657y + 81
c
4
y
34
+ 26y
33
+ ··· + 316558y + 58081
c
6
, c
10
y
34
− 40y
33
+ ··· − 12y + 1
c
7
y
34
+ y
33
+ ··· − 8589934592y + 4294967296
c
8
, c
9
, c
12
y
34
+ 36y
33
+ ··· + 1764y + 81
c
11
y
34
+ 33y
33
+ ··· + 1472172y + 289444
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.617972 + 0.761093I
a = 0.484846 + 0.412540I
b = 0.014360 − 0.623951I
−5.56320 − 2.89554I −3.61991 + 4.02356I
u = 0.617972 − 0.761093I
a = 0.484846 − 0.412540I
b = 0.014360 + 0.623951I
−5.56320 + 2.89554I −3.61991 − 4.02356I
u = 0.038145 + 1.165360I
a = −0.381274 + 0.286643I
b = 0.348587 + 0.433388I
1.75955 − 1.35815I −1.81191 + 5.60161I
u = 0.038145 − 1.165360I
a = −0.381274 − 0.286643I
b = 0.348587 − 0.433388I
1.75955 + 1.35815I −1.81191 − 5.60161I
u = 0.786577 + 0.094576I
a = 0.448211 − 0.707202I
b = −0.419437 + 0.513879I
−7.08614 + 0.56989I −6.88337 − 1.97676I
u = 0.786577 − 0.094576I
a = 0.448211 + 0.707202I
b = −0.419437 − 0.513879I
−7.08614 − 0.56989I −6.88337 + 1.97676I
u = −0.987179 + 0.772832I
a = −1.38314 − 0.38450I
b = −1.66256 + 0.68936I
−12.90960 + 1.80005I −9.74318 − 1.73892I
u = −0.987179 − 0.772832I
a = −1.38314 + 0.38450I
b = −1.66256 − 0.68936I
−12.90960 − 1.80005I −9.74318 + 1.73892I
u = −0.864073 + 0.947878I
a = 0.781162 + 0.983524I
b = 1.60724 + 0.10939I
−5.54695 + 0.38370I −5.58940 + 0.I
u = −0.864073 − 0.947878I
a = 0.781162 − 0.983524I
b = 1.60724 − 0.10939I
−5.54695 − 0.38370I −5.58940 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.895563 + 0.939492I
a = 1.30517 + 0.59397I
b = 1.72689 − 0.69426I
−5.59448 + 6.17261I −5.46977 − 4.89495I
u = −0.895563 − 0.939492I
a = 1.30517 − 0.59397I
b = 1.72689 + 0.69426I
−5.59448 − 6.17261I −5.46977 + 4.89495I
u = −1.029620 + 0.852087I
a = −0.867778 − 0.816243I
b = −1.58899 − 0.10100I
−6.37716 − 4.69861I 0
u = −1.029620 − 0.852087I
a = −0.867778 + 0.816243I
b = −1.58899 + 0.10100I
−6.37716 + 4.69861I 0
u = 0.057536 + 0.646281I
a = −1.089740 − 0.207466I
b = −0.071382 + 0.716216I
1.02980 − 1.33350I 1.03223 + 2.72223I
u = 0.057536 − 0.646281I
a = −1.089740 + 0.207466I
b = −0.071382 − 0.716216I
1.02980 + 1.33350I 1.03223 − 2.72223I
u = −0.408705 + 0.478881I
a = 1.90923 + 0.05986I
b = 0.808975 − 0.889829I
−0.23675 + 2.91229I 7.01197 − 0.68590I
u = −0.408705 − 0.478881I
a = 1.90923 − 0.05986I
b = 0.808975 + 0.889829I
−0.23675 − 2.91229I 7.01197 + 0.68590I
u = −0.820293 + 1.120390I
a = −0.568921 − 0.975842I
b = −1.56001 − 0.16306I
−11.78150 + 4.90128I 0
u = −0.820293 − 1.120390I
a = −0.568921 + 0.975842I
b = −1.56001 + 0.16306I
−11.78150 − 4.90128I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.604289 + 0.013218I
a = −0.378817 − 0.481577I
b = 0.222550 + 0.296019I
−1.274770 − 0.384208I −8.74964 + 1.21480I
u = 0.604289 − 0.013218I
a = −0.378817 + 0.481577I
b = 0.222550 − 0.296019I
−1.274770 + 0.384208I −8.74964 − 1.21480I
u = 0.179208 + 1.386880I
a = −0.004281 − 0.231777I
b = −0.320681 + 0.047473I
3.60390 − 3.49818I 0
u = 0.179208 − 1.386880I
a = −0.004281 + 0.231777I
b = −0.320681 − 0.047473I
3.60390 + 3.49818I 0
u = −0.921912 + 1.064770I
a = −1.164080 − 0.612631I
b = −1.72549 + 0.67468I
−5.70649 + 11.80860I 0
u = −0.921912 − 1.064770I
a = −1.164080 + 0.612631I
b = −1.72549 − 0.67468I
−5.70649 − 11.80860I 0
u = −1.18586 + 0.88378I
a = 0.828149 + 0.702104I
b = 1.60257 + 0.10069I
−13.6579 − 8.0903I 0
u = −1.18586 − 0.88378I
a = 0.828149 − 0.702104I
b = 1.60257 − 0.10069I
−13.6579 + 8.0903I 0
u = 0.015596 + 0.513842I
a = −0.46506 − 2.17864I
b = −1.112220 + 0.272947I
−6.30723 − 0.15068I −5.27928 − 0.30128I
u = 0.015596 − 0.513842I
a = −0.46506 + 2.17864I
b = −1.112220 − 0.272947I
−6.30723 + 0.15068I −5.27928 + 0.30128I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.98134 + 1.14252I
a = 1.086540 + 0.575543I
b = 1.72383 − 0.67659I
−12.7634 + 15.8697I 0
u = −0.98134 − 1.14252I
a = 1.086540 − 0.575543I
b = 1.72383 + 0.67659I
−12.7634 − 15.8697I 0
u = 0.29522 + 1.50720I
a = 0.126447 + 0.293981I
b = 0.405758 − 0.277368I
−2.05904 − 5.25800I 0
u = 0.29522 − 1.50720I
a = 0.126447 − 0.293981I
b = 0.405758 + 0.277368I
−2.05904 + 5.25800I 0
8
II. I
u
2
=
h−u
15
+7u
14
+· · · +b−1, −u
15
a+u
15
+· · · +a
2
+4, u
16
−7u
15
+· · · +4u
2
+1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
10
=
a
u
15
− 7u
14
+ ··· + au + 1
a
7
=
u
15
a + u
15
+ ··· + a − 1
−1
a
8
=
u
15
a + u
15
+ ··· + a + 4u
−1
a
11
=
a
u
15
− 7u
14
+ ··· + au + 1
a
5
=
u
u
3
+ u
a
12
=
−u
15
+ 7u
14
+ ··· + a − u
2u
12
− 11u
11
+ ··· + au + 1
a
4
=
u
15
− 7u
14
+ ··· + a + 5u
−u
15
a + 7u
14
a + ··· − u + 1
a
1
=
u
15
− 7u
14
+ ··· − a + 3u
−u
13
a + 5u
12
a + ··· − au − 1
a
9
=
u
15
− 7u
14
+ ··· + a + 2u
u
9
a − 3u
8
a + ··· + au − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
15
− 20u
14
+ 44u
13
− 28u
12
− 80u
11
+ 252u
10
− 360u
9
+
348u
8
− 260u
7
+ 192u
6
− 136u
5
+ 116u
4
− 72u
3
+ 48u
2
− 16u + 14
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
32
− u
31
+ ··· − 3u + 22
c
2
, c
5
(u
16
+ 7u
15
+ ··· + 4u
2
+ 1)
2
c
4
u
32
+ u
31
+ ··· − 6241u + 2648
c
6
, c
10
u
32
− u
31
+ ··· − 935u + 566
c
7
(u − 1)
32
c
8
, c
9
, c
12
(u
16
− 3u
15
+ ··· + 4u
2
+ 1)
2
c
11
u
32
− u
31
+ ··· − 7126u + 521
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
32
+ 3y
31
+ ··· − 8501y + 484
c
2
, c
5
(y
16
+ y
15
+ ··· + 8y + 1)
2
c
4
y
32
+ 27y
31
+ ··· − 50744273y + 7011904
c
6
, c
10
y
32
− 21y
31
+ ··· + 1943323y + 320356
c
7
(y −1)
32
c
8
, c
9
, c
12
(y
16
+ 17y
15
+ ··· + 8y + 1)
2
c
11
y
32
+ 31y
31
+ ··· − 10138750y + 271441
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.169969 + 0.896844I
a = 1.167190 − 0.569541I
b = 1.196600 − 0.338289I
−4.54212 − 5.27528I −2.32627 + 5.08255I
u = 0.169969 + 0.896844I
a = 0.120024 + 1.356990I
b = −0.709175 − 0.949980I
−4.54212 − 5.27528I −2.32627 + 5.08255I
u = 0.169969 − 0.896844I
a = 1.167190 + 0.569541I
b = 1.196600 + 0.338289I
−4.54212 + 5.27528I −2.32627 − 5.08255I
u = 0.169969 − 0.896844I
a = 0.120024 − 1.356990I
b = −0.709175 + 0.949980I
−4.54212 + 5.27528I −2.32627 − 5.08255I
u = 0.994597 + 0.824777I
a = 0.903954 − 0.390401I
b = 1.68673 + 0.18194I
−4.64054 − 2.72058I −11.67920 − 0.63367I
u = 0.994597 + 0.824777I
a = −1.094760 + 0.724905I
b = −1.221060 − 0.357269I
−4.64054 − 2.72058I −11.67920 − 0.63367I
u = 0.994597 − 0.824777I
a = 0.903954 + 0.390401I
b = 1.68673 − 0.18194I
−4.64054 + 2.72058I −11.67920 + 0.63367I
u = 0.994597 − 0.824777I
a = −1.094760 − 0.724905I
b = −1.221060 + 0.357269I
−4.64054 + 2.72058I −11.67920 + 0.63367I
u = −0.533203 + 0.423490I
a = −0.456982 + 0.102875I
b = −0.11581 + 1.97266I
−6.78417 + 7.00115I −9.7078 − 10.6678I
u = −0.533203 + 0.423490I
a = −1.93498 + 2.16281I
b = −0.200098 + 0.248380I
−6.78417 + 7.00115I −9.7078 − 10.6678I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.533203 − 0.423490I
a = −0.456982 − 0.102875I
b = −0.11581 − 1.97266I
−6.78417 − 7.00115I −9.7078 + 10.6678I
u = −0.533203 − 0.423490I
a = −1.93498 − 2.16281I
b = −0.200098 − 0.248380I
−6.78417 − 7.00115I −9.7078 + 10.6678I
u = −0.060033 + 0.625164I
a = −1.305950 + 0.474680I
b = −0.963080 + 0.863595I
1.16901 − 1.70911I 6.35818 + 0.41032I
u = −0.060033 + 0.625164I
a = −1.51535 − 1.39501I
b = 0.218353 + 0.844927I
1.16901 − 1.70911I 6.35818 + 0.41032I
u = −0.060033 − 0.625164I
a = −1.305950 − 0.474680I
b = −0.963080 − 0.863595I
1.16901 + 1.70911I 6.35818 − 0.41032I
u = −0.060033 − 0.625164I
a = −1.51535 + 1.39501I
b = 0.218353 − 0.844927I
1.16901 + 1.70911I 6.35818 − 0.41032I
u = −0.325762 + 0.486223I
a = 0.810374 − 0.142795I
b = 0.35796 − 1.68857I
0.44082 + 3.30359I −0.44501 − 13.24031I
u = −0.325762 + 0.486223I
a = 2.73734 − 1.09777I
b = 0.194559 − 0.440540I
0.44082 + 3.30359I −0.44501 − 13.24031I
u = −0.325762 − 0.486223I
a = 0.810374 + 0.142795I
b = 0.35796 + 1.68857I
0.44082 − 3.30359I −0.44501 + 13.24031I
u = −0.325762 − 0.486223I
a = 2.73734 + 1.09777I
b = 0.194559 + 0.440540I
0.44082 − 3.30359I −0.44501 + 13.24031I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.94150 + 1.08351I
a = 0.744681 − 0.655376I
b = 1.45275 + 0.57236I
−3.86336 − 4.39205I −4.86684 + 12.44765I
u = 0.94150 + 1.08351I
a = −0.964817 + 0.502417I
b = −1.41122 − 0.18983I
−3.86336 − 4.39205I −4.86684 + 12.44765I
u = 0.94150 − 1.08351I
a = 0.744681 + 0.655376I
b = 1.45275 − 0.57236I
−3.86336 + 4.39205I −4.86684 − 12.44765I
u = 0.94150 − 1.08351I
a = −0.964817 − 0.502417I
b = −1.41122 + 0.18983I
−3.86336 + 4.39205I −4.86684 − 12.44765I
u = 1.28188 + 0.69445I
a = −0.802703 + 0.270845I
b = −1.91630 − 0.23956I
−11.46350 − 2.54285I −14.4747 + 1.8243I
u = 1.28188 + 0.69445I
a = 1.234000 − 0.481628I
b = 1.217060 + 0.210244I
−11.46350 − 2.54285I −14.4747 + 1.8243I
u = 1.28188 − 0.69445I
a = −0.802703 − 0.270845I
b = −1.91630 + 0.23956I
−11.46350 + 2.54285I −14.4747 − 1.8243I
u = 1.28188 − 0.69445I
a = 1.234000 + 0.481628I
b = 1.217060 − 0.210244I
−11.46350 + 2.54285I −14.4747 − 1.8243I
u = 1.03105 + 1.24797I
a = 0.973554 − 0.495334I
b = 1.334690 + 0.189904I
−9.79453 − 5.66478I −10.85832 + 7.61626I
u = 1.03105 + 1.24797I
a = −0.615581 + 0.560905I
b = −1.62195 − 0.70425I
−9.79453 − 5.66478I −10.85832 + 7.61626I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.03105 − 1.24797I
a = 0.973554 + 0.495334I
b = 1.334690 − 0.189904I
−9.79453 + 5.66478I −10.85832 − 7.61626I
u = 1.03105 − 1.24797I
a = −0.615581 − 0.560905I
b = −1.62195 + 0.70425I
−9.79453 + 5.66478I −10.85832 − 7.61626I
15
III. I
u
3
=
h−u
17
+9u
16
+· · ·+b +4, −4u
17
+31u
16
+· · ·+a +2, u
18
−8u
17
+· · ·−5u +1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
10
=
4u
17
− 31u
16
+ ··· + 19u − 2
u
17
− 9u
16
+ ··· + 18u − 4
a
7
=
−u
15
+ 7u
14
+ ··· − 17u + 3
−u
16
+ 7u
15
+ ··· − 17u
2
+ 4u
a
8
=
u
16
− 8u
15
+ ··· − 21u + 3
−u
16
+ 7u
15
+ ··· − 17u
2
+ 4u
a
11
=
4u
17
− 31u
16
+ ··· + 19u − 2
−2u
16
+ 15u
15
+ ··· + 19u − 5
a
5
=
u
u
3
+ u
a
12
=
4u
17
− 30u
16
+ ··· − 49u
2
+ 12u
u
17
− 9u
16
+ ··· + 17u − 4
a
4
=
−u
17
+ 8u
16
+ ··· − 19u + 3
u
2
− u + 1
a
1
=
u
17
− 8u
16
+ ··· + 16u − 1
−u
4
+ 2u
3
− 3u
2
+ 2u − 1
a
9
=
−u
15
+ 7u
14
+ ··· + 15u
2
− 5u
−u
16
+ 7u
15
+ ··· − 9u
2
+ 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 10u
17
−72u
16
+ 309u
15
−928u
14
+ 2167u
13
−4048u
12
+ 6223u
11
−
7893u
10
+ 8322u
9
−7192u
8
+ 5096u
7
−2875u
6
+ 1341u
5
−497u
4
+ 196u
3
−32u
2
−4u + 1
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
18
+ u
16
+ ··· − 4u + 1
c
2
u
18
− 8u
17
+ ··· − 5u + 1
c
4
u
18
− u
17
+ ··· + u
2
+ 1
c
5
u
18
+ 8u
17
+ ··· + 5u + 1
c
6
u
18
+ u
17
+ ··· + 6u
2
+ 1
c
7
u
18
+ 3u
17
+ ··· − 8u + 8
c
8
, c
9
u
18
+ 5u
17
+ ··· − 6u
2
+ 1
c
10
u
18
− u
17
+ ··· + 6u
2
+ 1
c
11
u
18
+ 6u
16
+ ··· + 16u + 8
c
12
u
18
− 5u
17
+ ··· − 6u
2
+ 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
18
+ 2y
17
+ ··· − 6y + 1
c
2
, c
5
y
18
+ 10y
17
+ ··· + 17y + 1
c
4
y
18
+ 13y
17
+ ··· + 2y + 1
c
6
, c
10
y
18
− 5y
17
+ ··· + 12y + 1
c
7
y
18
+ y
17
+ ··· − 416y + 64
c
8
, c
9
, c
12
y
18
+ 19y
17
+ ··· − 12y + 1
c
11
y
18
+ 12y
17
+ ··· − 96y + 64
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.261420 + 1.172120I
a = 0.379841 + 0.478807I
b = −0.461922 + 0.570389I
1.70214 − 0.21758I −3.00572 + 0.40055I
u = 0.261420 − 1.172120I
a = 0.379841 − 0.478807I
b = −0.461922 − 0.570389I
1.70214 + 0.21758I −3.00572 − 0.40055I
u = 0.516070 + 0.482572I
a = −1.70648 − 0.28542I
b = −0.742931 − 0.970796I
−0.60489 − 2.99568I −13.9248 + 5.1291I
u = 0.516070 − 0.482572I
a = −1.70648 + 0.28542I
b = −0.742931 + 0.970796I
−0.60489 + 2.99568I −13.9248 − 5.1291I
u = 0.143682 + 1.295940I
a = −0.350539 + 0.023495I
b = −0.080814 − 0.450902I
4.02945 − 3.56902I 8.87570 + 5.68054I
u = 0.143682 − 1.295940I
a = −0.350539 − 0.023495I
b = −0.080814 + 0.450902I
4.02945 + 3.56902I 8.87570 − 5.68054I
u = 0.972474 + 0.968007I
a = −0.940135 + 0.571481I
b = −1.46745 − 0.35431I
−4.05551 − 3.55831I −5.61870 + 2.86845I
u = 0.972474 − 0.968007I
a = −0.940135 − 0.571481I
b = −1.46745 + 0.35431I
−4.05551 + 3.55831I −5.61870 − 2.86845I
u = 1.170870 + 0.744940I
a = 0.972765 − 0.320087I
b = 1.37742 + 0.34987I
−10.09670 − 2.78092I −6.47448 + 2.85890I
u = 1.170870 − 0.744940I
a = 0.972765 + 0.320087I
b = 1.37742 − 0.34987I
−10.09670 + 2.78092I −6.47448 − 2.85890I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.11352 + 1.42465I
a = 0.375608 − 0.236602I
b = 0.379711 + 0.508250I
−1.61059 − 6.04596I −0.58045 + 7.39747I
u = 0.11352 − 1.42465I
a = 0.375608 + 0.236602I
b = 0.379711 − 0.508250I
−1.61059 + 6.04596I −0.58045 − 7.39747I
u = −0.217488 + 0.441352I
a = −1.94133 + 1.20767I
b = −0.110795 − 1.119460I
−6.05328 + 6.37936I −2.68320 − 4.69289I
u = −0.217488 − 0.441352I
a = −1.94133 − 1.20767I
b = −0.110795 + 1.119460I
−6.05328 − 6.37936I −2.68320 + 4.69289I
u = 0.93840 + 1.19736I
a = 0.718907 − 0.611414I
b = 1.40670 + 0.28704I
−8.67996 − 4.80406I −5.16961 + 2.57260I
u = 0.93840 − 1.19736I
a = 0.718907 + 0.611414I
b = 1.40670 − 0.28704I
−8.67996 + 4.80406I −5.16961 − 2.57260I
u = 0.101058 + 0.432072I
a = 2.49136 + 0.11964I
b = 0.200080 + 1.088540I
0.69529 + 2.31097I −2.41878 − 7.12817I
u = 0.101058 − 0.432072I
a = 2.49136 − 0.11964I
b = 0.200080 − 1.088540I
0.69529 − 2.31097I −2.41878 + 7.12817I
20
IV. I
v
1
= ha, b − 1, v − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
1
0
a
3
=
1
0
a
10
=
0
1
a
7
=
1
1
a
8
=
0
1
a
11
=
−1
1
a
5
=
1
0
a
12
=
0
1
a
4
=
1
1
a
1
=
0
−1
a
9
=
0
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
10
c
11
u + 1
c
2
, c
5
, c
8
c
9
, c
12
u
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
10
c
11
y −1
c
2
, c
5
, c
8
c
9
, c
12
y
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
−1.64493 −6.00000
24
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
(u + 1)(u
18
+ u
16
+ ··· − 4u + 1)(u
32
− u
31
+ ··· − 3u + 22)
· (u
34
− u
33
+ ··· − 14u + 1)
c
2
u(u
16
+ 7u
15
+ ··· + 4u
2
+ 1)
2
(u
18
− 8u
17
+ ··· − 5u + 1)
· (u
34
− 11u
33
+ ··· − 21u + 9)
c
4
(u + 1)(u
18
− u
17
+ ··· + u
2
+ 1)(u
32
+ u
31
+ ··· − 6241u + 2648)
· (u
34
− 2u
33
+ ··· − 298u + 241)
c
5
u(u
16
+ 7u
15
+ ··· + 4u
2
+ 1)
2
(u
18
+ 8u
17
+ ··· + 5u + 1)
· (u
34
− 11u
33
+ ··· − 21u + 9)
c
6
(u + 1)(u
18
+ u
17
+ ··· + 6u
2
+ 1)(u
32
− u
31
+ ··· − 935u + 566)
· (u
34
− 20u
32
+ ··· − 6u
2
+ 1)
c
7
((u − 1)
32
)(u + 1)(u
18
+ 3u
17
+ ··· − 8u + 8)
· (u
34
+ 29u
33
+ ··· + 786432u + 65536)
c
8
, c
9
u(u
16
− 3u
15
+ ··· + 4u
2
+ 1)
2
(u
18
+ 5u
17
+ ··· − 6u
2
+ 1)
· (u
34
+ 8u
33
+ ··· + 96u + 9)
c
10
(u + 1)(u
18
− u
17
+ ··· + 6u
2
+ 1)(u
32
− u
31
+ ··· − 935u + 566)
· (u
34
− 20u
32
+ ··· − 6u
2
+ 1)
c
11
(u + 1)(u
18
+ 6u
16
+ ··· + 16u + 8)(u
32
− u
31
+ ··· − 7126u + 521)
· (u
34
− u
33
+ ··· − 146u + 538)
c
12
u(u
16
− 3u
15
+ ··· + 4u
2
+ 1)
2
(u
18
− 5u
17
+ ··· − 6u
2
+ 1)
· (u
34
+ 8u
33
+ ··· + 96u + 9)
25
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y −1)(y
18
+ 2y
17
+ ··· − 6y + 1)(y
32
+ 3y
31
+ ··· − 8501y + 484)
· (y
34
− 21y
33
+ ··· − 30y + 1)
c
2
, c
5
y(y
16
+ y
15
+ ··· + 8y + 1)
2
(y
18
+ 10y
17
+ ··· + 17y + 1)
· (y
34
+ 11y
33
+ ··· + 657y + 81)
c
4
(y −1)(y
18
+ 13y
17
+ ··· + 2y + 1)
· (y
32
+ 27y
31
+ ··· − 50744273y + 7011904)
· (y
34
+ 26y
33
+ ··· + 316558y + 58081)
c
6
, c
10
(y −1)(y
18
− 5y
17
+ ··· + 12y + 1)
· (y
32
− 21y
31
+ ··· + 1943323y + 320356)
· (y
34
− 40y
33
+ ··· − 12y + 1)
c
7
((y −1)
33
)(y
18
+ y
17
+ ··· − 416y + 64)
· (y
34
+ y
33
+ ··· − 8589934592y + 4294967296)
c
8
, c
9
, c
12
y(y
16
+ 17y
15
+ ··· + 8y + 1)
2
(y
18
+ 19y
17
+ ··· − 12y + 1)
· (y
34
+ 36y
33
+ ··· + 1764y + 81)
c
11
(y −1)(y
18
+ 12y
17
+ ··· − 96y + 64)
· (y
32
+ 31y
31
+ ··· − 10138750y + 271441)
· (y
34
+ 33y
33
+ ··· + 1472172y + 289444)
26
