12n
0752
(K12n
0752
)
A knot diagram
1
Linearized knot diagam
4 6 8 10 2 12 3 1 12 5 6 9
Solving Sequence
9,12 4,10
5 1 2 6 8 3 7 11
c
9
c
4
c
12
c
1
c
5
c
8
c
3
c
7
c
11
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h744551414u
26
+ 8999949826u
25
+ ··· + 22161981703b − 63305998448,
51229810238u
26
− 249479535086u
25
+ ··· + 199457835327a − 467102435595,
u
27
− 7u
26
+ ··· + 69u − 9i
I
u
2
= h4u
16
a + 26u
16
+ ··· + 14a + 91, 3u
16
a + u
16
+ ··· + 2a
2
+ 8a, u
17
+ 3u
16
+ ··· + 6u + 2i
I
u
3
= h−u
11
− 4u
10
− 12u
9
− 25u
8
− 41u
7
− 54u
6
− 58u
5
− 51u
4
− 36u
3
− 20u
2
+ b − 8u − 2,
2u
12
+ 3u
11
+ 8u
10
− u
9
− 16u
8
− 58u
7
− 96u
6
− 131u
5
− 128u
4
− 105u
3
− 60u
2
+ 5a − 28u − 4,
u
13
+ 4u
12
+ 14u
11
+ 32u
10
+ 62u
9
+ 96u
8
+ 127u
7
+ 142u
6
+ 136u
5
+ 110u
4
+ 75u
3
+ 41u
2
+ 18u + 5i
I
u
4
= hau + 3b − 4a + u − 1, 2a
2
+ au + 2a + 4u + 3, u
2
+ 2i
I
v
1
= ha, b − v + 2, v
2
− 3v + 1i
I
v
2
= ha, b + 1, v −1i
* 6 irreducible components of dim
C
= 0, with total 81 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
=
h7.45×10
8
u
26
+9.00×10
9
u
25
+· · ·+2.22×10
10
b−6.33×10
10
, 5.12×10
10
u
26
−
2.49 × 10
11
u
25
+ · · · + 1.99 × 10
11
a − 4.67 × 10
11
, u
27
− 7u
26
+ · · · + 69u − 9i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
4
=
−0.256845u
26
+ 1.25079u
25
+ ··· − 19.8801u + 2.34186
−0.0335959u
26
− 0.406099u
25
+ ··· − 23.3945u + 2.85651
a
10
=
1
−u
2
a
5
=
−0.427192u
26
+ 2.42462u
25
+ ··· − 7.83439u + 0.274214
−0.209462u
26
+ 0.793385u
25
+ ··· − 23.1446u + 3.02389
a
1
=
u
u
a
2
=
−0.373198u
26
+ 2.43639u
25
+ ··· + 40.6429u − 5.57365
0.0280075u
26
− 0.274253u
25
+ ··· − 15.2417u + 2.73067
a
6
=
0.127411u
26
− 0.794874u
25
+ ··· − 16.3288u + 2.33469
−0.220571u
26
+ 1.67833u
25
+ ··· + 25.7235u − 4.23181
a
8
=
u
2
+ 1
u
2
a
3
=
0.229738u
26
− 1.43782u
25
+ ··· − 31.4394u + 3.80620
0.547129u
26
− 3.69315u
25
+ ··· − 20.0642u + 2.31161
a
7
=
0.127411u
26
− 0.794874u
25
+ ··· − 16.3288u + 2.33469
−0.175997u
26
+ 1.30098u
25
+ ··· + 20.1770u − 3.35878
a
11
=
0.0573242u
26
− 0.330383u
25
+ ··· − 10.9429u + 1.67117
−0.215260u
26
+ 1.35737u
25
+ ··· + 7.85099u − 1.02783
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
23743057753
22161981703
u
26
+
150829290172
22161981703
u
25
+ ··· +
2639501882667
22161981703
u −
630292627959
22161981703
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
7
u
27
− u
26
+ ··· + 10u − 1
c
2
, c
5
u
27
+ 11u
26
+ ··· − 78u − 9
c
4
, c
10
u
27
− 2u
26
+ ··· + u + 1
c
6
, c
11
u
27
− 2u
26
+ ··· + 4u + 3
c
8
, c
9
, c
12
u
27
+ 7u
26
+ ··· + 69u + 9
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
27
− 25y
26
+ ··· + 26y −1
c
2
, c
5
y
27
− 7y
26
+ ··· − 54y −81
c
4
, c
10
y
27
− 22y
26
+ ··· + 29y −1
c
6
, c
11
y
27
+ 22y
26
+ ··· + 124y −9
c
8
, c
9
, c
12
y
27
+ 25y
26
+ ··· − 1917y −81
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.953904 + 0.354754I
a = −1.047780 + 0.649531I
b = −0.214567 − 0.456094I
4.79569 + 10.60650I −1.90397 − 7.23090I
u = 0.953904 − 0.354754I
a = −1.047780 − 0.649531I
b = −0.214567 + 0.456094I
4.79569 − 10.60650I −1.90397 + 7.23090I
u = 0.933040 + 0.188802I
a = 1.160420 − 0.702560I
b = 0.051443 + 0.277504I
4.62437 + 2.47514I −0.34993 − 2.26822I
u = 0.933040 − 0.188802I
a = 1.160420 + 0.702560I
b = 0.051443 − 0.277504I
4.62437 − 2.47514I −0.34993 + 2.26822I
u = −0.478298 + 1.051980I
a = 0.189785 − 0.449325I
b = −0.036183 − 0.475615I
−0.42491 − 2.93654I 4.22853 + 4.23030I
u = −0.478298 − 1.051980I
a = 0.189785 + 0.449325I
b = −0.036183 + 0.475615I
−0.42491 + 2.93654I 4.22853 − 4.23030I
u = −0.645899 + 0.517518I
a = 0.674135 + 0.117637I
b = 0.442860 − 0.100682I
1.19510 − 1.40624I 0.86573 + 1.18666I
u = −0.645899 − 0.517518I
a = 0.674135 − 0.117637I
b = 0.442860 + 0.100682I
1.19510 + 1.40624I 0.86573 − 1.18666I
u = 0.721039 + 0.972434I
a = −0.052879 − 0.387807I
b = 0.717442 − 0.773808I
2.98852 − 4.83503I −4.24483 + 4.00030I
u = 0.721039 − 0.972434I
a = −0.052879 + 0.387807I
b = 0.717442 + 0.773808I
2.98852 + 4.83503I −4.24483 − 4.00030I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.553346 + 1.170330I
a = −0.353880 + 0.426742I
b = −1.03955 + 0.97978I
1.66563 + 2.80958I −3.84805 − 1.74078I
u = 0.553346 − 1.170330I
a = −0.353880 − 0.426742I
b = −1.03955 − 0.97978I
1.66563 − 2.80958I −3.84805 + 1.74078I
u = 0.654565
a = −1.70509
b = 0.498180
−7.54449 −20.1420
u = 0.025050 + 1.359590I
a = −0.84354 + 1.28631I
b = −0.46291 + 2.19675I
−6.22130 + 0.13227I −6.04494 + 0.29033I
u = 0.025050 − 1.359590I
a = −0.84354 − 1.28631I
b = −0.46291 − 2.19675I
−6.22130 − 0.13227I −6.04494 − 0.29033I
u = 0.255910 + 1.345710I
a = 0.724542 − 1.206850I
b = 0.67761 − 2.38128I
−11.88730 + 3.29707I −9.75000 + 3.82687I
u = 0.255910 − 1.345710I
a = 0.724542 + 1.206850I
b = 0.67761 + 2.38128I
−11.88730 − 3.29707I −9.75000 − 3.82687I
u = 0.00342 + 1.44547I
a = −0.51617 + 1.50351I
b = −0.02636 + 2.23591I
−6.76916 + 0.50453I −6.09785 − 2.87578I
u = 0.00342 − 1.44547I
a = −0.51617 − 1.50351I
b = −0.02636 − 2.23591I
−6.76916 − 0.50453I −6.09785 + 2.87578I
u = 0.38425 + 1.40937I
a = −0.04227 + 1.48372I
b = 0.22763 + 2.62497I
−0.46126 + 7.18382I −3.58916 − 3.85062I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.38425 − 1.40937I
a = −0.04227 − 1.48372I
b = 0.22763 − 2.62497I
−0.46126 − 7.18382I −3.58916 + 3.85062I
u = 0.37205 + 1.48920I
a = −0.05733 − 1.69219I
b = −0.38069 − 2.77325I
−1.1155 + 15.3839I −5.17512 − 7.69230I
u = 0.37205 − 1.48920I
a = −0.05733 + 1.69219I
b = −0.38069 + 2.77325I
−1.1155 − 15.3839I −5.17512 + 7.69230I
u = 0.01460 + 1.56688I
a = 0.523915 − 1.145590I
b = 0.30647 − 1.70007I
−6.50814 − 3.09204I −6.77423 + 4.55905I
u = 0.01460 − 1.56688I
a = 0.523915 + 1.145590I
b = 0.30647 + 1.70007I
−6.50814 + 3.09204I −6.77423 − 4.55905I
u = 0.080303 + 0.257685I
a = −0.67306 − 2.09112I
b = −0.512295 + 0.381584I
−1.138560 + 0.334603I −9.24522 − 1.52255I
u = 0.080303 − 0.257685I
a = −0.67306 + 2.09112I
b = −0.512295 − 0.381584I
−1.138560 − 0.334603I −9.24522 + 1.52255I
7
II. I
u
2
= h4u
16
a + 26u
16
+ · · · + 14a + 91, 3u
16
a + u
16
+ · · · + 2a
2
+ 8a, u
17
+
3u
16
+ · · · + 6u + 2i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
4
=
a
−0.108108au
16
− 0.702703u
16
+ ··· − 0.378378a − 2.45946
a
10
=
1
−u
2
a
5
=
−0.108108au
16
− 0.702703u
16
+ ··· + 0.621622a − 2.45946
−0.297297au
16
− 1.43243u
16
+ ··· − 0.540541a − 2.51351
a
1
=
u
u
a
2
=
0.0270270au
16
+ 0.175676u
16
+ ··· − 2.40541a − 1.13514
0.729730au
16
+ 0.243243u
16
+ ··· + 0.0540541a − 1.64865
a
6
=
−0.243243au
16
− 0.581081u
16
+ ··· − 1.35135a − 2.78378
0.0540541au
16
− 0.648649u
16
+ ··· − 0.810811a − 2.27027
a
8
=
u
2
+ 1
u
2
a
3
=
0.189189au
16
− 0.270270u
16
+ ··· + 1.16216a − 2.94595
−u
16
− 3u
15
+ ··· − 5u − 3
a
7
=
−0.243243au
16
− 0.581081u
16
+ ··· − 1.35135a − 2.78378
−0.270270au
16
− 0.756757u
16
+ ··· + 0.0540541a − 2.64865
a
11
=
0.0810811au
16
− 0.472973u
16
+ ··· − 0.216216a − 2.40541
−0.324324au
16
− 0.108108u
16
+ ··· − 1.13514a − 2.37838
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3u
16
+ 9u
15
+ 35u
14
+ 74u
13
+ 150u
12
+ 231u
11
+ 301u
10
+
324u
9
+ 266u
8
+ 150u
7
+ 22u
6
− 76u
5
− 96u
4
− 61u
3
− 15u
2
+ 12u + 14
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
7
u
34
+ 2u
33
+ ··· + 51u − 23
c
2
, c
5
(u
17
− 4u
16
+ ··· − 4u + 1)
2
c
4
, c
10
u
34
− 15u
32
+ ··· − 37u + 61
c
6
, c
11
u
34
+ 3u
33
+ ··· − 682u − 121
c
8
, c
9
, c
12
(u
17
− 3u
16
+ ··· + 6u − 2)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
34
− 6y
33
+ ··· − 7293y + 529
c
2
, c
5
(y
17
− 2y
16
+ ··· − 4y −1)
2
c
4
, c
10
y
34
− 30y
33
+ ··· − 156553y + 3721
c
6
, c
11
y
34
+ 29y
33
+ ··· + 783838y + 14641
c
8
, c
9
, c
12
(y
17
+ 17y
16
+ ··· + 52y −4)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.700839 + 0.661242I
a = −0.142439 − 0.723173I
b = −0.131868 + 0.225388I
0.33195 − 3.39163I −2.33298 + 11.95319I
u = −0.700839 + 0.661242I
a = 0.440456 − 0.231356I
b = 0.065889 − 0.965375I
0.33195 − 3.39163I −2.33298 + 11.95319I
u = −0.700839 − 0.661242I
a = −0.142439 + 0.723173I
b = −0.131868 − 0.225388I
0.33195 + 3.39163I −2.33298 − 11.95319I
u = −0.700839 − 0.661242I
a = 0.440456 + 0.231356I
b = 0.065889 + 0.965375I
0.33195 + 3.39163I −2.33298 − 11.95319I
u = −0.826403 + 0.349944I
a = 1.075520 + 0.373580I
b = 0.414461 − 0.303701I
1.33448 − 1.66721I 5.61922 + 1.37527I
u = −0.826403 + 0.349944I
a = 0.164500 − 0.258544I
b = 0.390587 + 0.201368I
1.33448 − 1.66721I 5.61922 + 1.37527I
u = −0.826403 − 0.349944I
a = 1.075520 − 0.373580I
b = 0.414461 + 0.303701I
1.33448 + 1.66721I 5.61922 − 1.37527I
u = −0.826403 − 0.349944I
a = 0.164500 + 0.258544I
b = 0.390587 − 0.201368I
1.33448 + 1.66721I 5.61922 − 1.37527I
u = 0.177657 + 1.249920I
a = 0.369639 + 0.260996I
b = −0.914870 + 0.498586I
3.03460 − 1.26688I −4.55357 − 0.56113I
u = 0.177657 + 1.249920I
a = −1.00148 − 1.87787I
b = −1.23762 − 2.66817I
3.03460 − 1.26688I −4.55357 − 0.56113I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.177657 − 1.249920I
a = 0.369639 − 0.260996I
b = −0.914870 − 0.498586I
3.03460 + 1.26688I −4.55357 + 0.56113I
u = 0.177657 − 1.249920I
a = −1.00148 + 1.87787I
b = −1.23762 + 2.66817I
3.03460 + 1.26688I −4.55357 + 0.56113I
u = 0.177527 + 1.341090I
a = 0.078205 − 0.428055I
b = 1.44700 − 0.65077I
2.28668 + 6.31784I −5.66125 − 5.46008I
u = 0.177527 + 1.341090I
a = 1.01930 + 2.21437I
b = 1.22445 + 2.88700I
2.28668 + 6.31784I −5.66125 − 5.46008I
u = 0.177527 − 1.341090I
a = 0.078205 + 0.428055I
b = 1.44700 + 0.65077I
2.28668 − 6.31784I −5.66125 + 5.46008I
u = 0.177527 − 1.341090I
a = 1.01930 − 2.21437I
b = 1.22445 − 2.88700I
2.28668 − 6.31784I −5.66125 + 5.46008I
u = −0.132324 + 1.358820I
a = −1.303170 − 0.221965I
b = −0.815188 − 0.630532I
−7.55907 − 1.70238I −7.27343 + 3.59367I
u = −0.132324 + 1.358820I
a = 0.07650 + 1.87317I
b = 0.16530 + 3.22936I
−7.55907 − 1.70238I −7.27343 + 3.59367I
u = −0.132324 − 1.358820I
a = −1.303170 + 0.221965I
b = −0.815188 + 0.630532I
−7.55907 + 1.70238I −7.27343 − 3.59367I
u = −0.132324 − 1.358820I
a = 0.07650 − 1.87317I
b = 0.16530 − 3.22936I
−7.55907 + 1.70238I −7.27343 − 3.59367I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.31944 + 1.42784I
a = 0.286545 + 0.562334I
b = −0.176253 + 1.206940I
−4.28217 − 5.80165I −2.59768 + 6.29733I
u = −0.31944 + 1.42784I
a = 0.13016 − 1.68353I
b = 0.18891 − 2.61278I
−4.28217 − 5.80165I −2.59768 + 6.29733I
u = −0.31944 − 1.42784I
a = 0.286545 − 0.562334I
b = −0.176253 − 1.206940I
−4.28217 + 5.80165I −2.59768 − 6.29733I
u = −0.31944 − 1.42784I
a = 0.13016 + 1.68353I
b = 0.18891 + 2.61278I
−4.28217 + 5.80165I −2.59768 − 6.29733I
u = 0.523959 + 0.054315I
a = 1.90743 − 1.36602I
b = 0.986066 + 0.652053I
6.73749 + 3.81968I 1.95892 − 3.35628I
u = 0.523959 + 0.054315I
a = −2.25261 − 1.67330I
b = −0.855397 + 0.372276I
6.73749 + 3.81968I 1.95892 − 3.35628I
u = 0.523959 − 0.054315I
a = 1.90743 + 1.36602I
b = 0.986066 − 0.652053I
6.73749 − 3.81968I 1.95892 + 3.35628I
u = 0.523959 − 0.054315I
a = −2.25261 + 1.67330I
b = −0.855397 − 0.372276I
6.73749 − 3.81968I 1.95892 + 3.35628I
u = −0.23365 + 1.55973I
a = −0.266571 + 1.360880I
b = −0.73106 + 2.22334I
−6.94898 − 6.84809I −12.0162 + 9.7020I
u = −0.23365 + 1.55973I
a = −0.43195 − 1.69334I
b = −0.20577 − 2.36976I
−6.94898 − 6.84809I −12.0162 + 9.7020I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.23365 − 1.55973I
a = −0.266571 − 1.360880I
b = −0.73106 − 2.22334I
−6.94898 + 6.84809I −12.0162 − 9.7020I
u = −0.23365 − 1.55973I
a = −0.43195 + 1.69334I
b = −0.20577 + 2.36976I
−6.94898 + 6.84809I −12.0162 − 9.7020I
u = −0.332972
a = −0.266953
b = −1.49504
−3.02943 9.71400
u = −0.332972
a = −5.03314
b = −0.134225
−3.02943 9.71400
14
III.
I
u
3
= h−u
11
−4u
10
+· · ·+b−2, 2u
12
+3u
11
+· · ·+5a−4, u
13
+4u
12
+· · ·+18u+5i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
4
=
−
2
5
u
12
−
3
5
u
11
+ ··· +
28
5
u +
4
5
u
11
+ 4u
10
+ ··· + 8u + 2
a
10
=
1
−u
2
a
5
=
−
2
5
u
12
−
3
5
u
11
+ ··· −
12
5
u −
11
5
u
11
+ 5u
10
+ ··· + 8u + 2
a
1
=
u
u
a
2
=
4
5
u
12
+
11
5
u
11
+ ··· +
14
5
u +
7
5
−u
11
− 4u
10
+ ··· − 12u − 4
a
6
=
−
1
5
u
12
−
4
5
u
11
+ ··· −
36
5
u −
8
5
−u
12
− 4u
11
+ ··· − 14u − 4
a
8
=
u
2
+ 1
u
2
a
3
=
3
5
u
12
+
12
5
u
11
+ ··· +
58
5
u +
14
5
u
12
+ 4u
11
+ ··· + 8u + 2
a
7
=
−
1
5
u
12
−
4
5
u
11
+ ··· −
36
5
u −
8
5
−u
12
− 4u
11
+ ··· − 13u − 4
a
11
=
−
1
5
u
12
−
4
5
u
11
+ ··· −
11
5
u +
2
5
−u
7
− 2u
6
− 4u
5
− 4u
4
− 2u
3
+ 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 4u
12
+12u
11
+41u
10
+76u
9
+135u
8
+174u
7
+202u
6
+192u
5
+158u
4
+106u
3
+63u
2
+27u+8
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
13
− 3u
11
+ ··· − 5u + 1
c
2
u
13
+ 8u
12
+ ··· + 3u + 1
c
4
u
13
− u
12
+ ··· + 2u − 1
c
5
u
13
− 8u
12
+ ··· + 3u − 1
c
6
u
13
− u
12
+ ··· − u + 1
c
7
u
13
− 3u
11
+ ··· − 5u − 1
c
8
, c
9
u
13
+ 4u
12
+ ··· + 18u + 5
c
10
u
13
+ u
12
+ ··· + 2u + 1
c
11
u
13
+ u
12
+ ··· − u − 1
c
12
u
13
− 4u
12
+ ··· + 18u − 5
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
13
− 6y
12
+ ··· + 5y −1
c
2
, c
5
y
13
− 8y
12
+ ··· − 7y −1
c
4
, c
10
y
13
− 7y
12
+ ··· + 8y −1
c
6
, c
11
y
13
+ 13y
12
+ ··· + 3y −1
c
8
, c
9
, c
12
y
13
+ 12y
12
+ ··· − 86y −25
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.870086 + 0.472668I
a = 0.562228 + 0.256963I
b = 0.058997 − 0.395621I
0.72518 − 2.27010I −3.32570 + 6.32204I
u = −0.870086 − 0.472668I
a = 0.562228 − 0.256963I
b = 0.058997 + 0.395621I
0.72518 + 2.27010I −3.32570 − 6.32204I
u = 0.188480 + 1.095940I
a = 0.015018 + 1.370830I
b = −0.89332 + 1.36698I
3.78493 + 4.55783I −2.53815 − 3.04000I
u = 0.188480 − 1.095940I
a = 0.015018 − 1.370830I
b = −0.89332 − 1.36698I
3.78493 − 4.55783I −2.53815 + 3.04000I
u = 0.201492 + 0.859165I
a = −0.371227 − 1.303860I
b = 0.659133 − 1.181080I
4.68144 − 3.00710I −1.90498 + 2.28394I
u = 0.201492 − 0.859165I
a = −0.371227 + 1.303860I
b = 0.659133 + 1.181080I
4.68144 + 3.00710I −1.90498 − 2.28394I
u = −0.544012 + 1.038490I
a = −0.075020 − 0.146685I
b = −0.404699 − 0.503620I
−0.91635 − 2.84840I −12.09656 + 1.44482I
u = −0.544012 − 1.038490I
a = −0.075020 + 0.146685I
b = −0.404699 + 0.503620I
−0.91635 + 2.84840I −12.09656 − 1.44482I
u = −0.758405
a = −1.58340
b = 0.355204
−7.22673 5.56510
u = −0.32313 + 1.38540I
a = 0.602248 + 1.222900I
b = 0.65830 + 2.32161I
−11.73130 − 3.93288I −6.70847 + 7.41271I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.32313 − 1.38540I
a = 0.602248 − 1.222900I
b = 0.65830 − 2.32161I
−11.73130 + 3.93288I −6.70847 − 7.41271I
u = −0.27355 + 1.56061I
a = −0.041547 − 1.376770I
b = 0.24399 − 2.09573I
−6.09001 − 6.43621I −3.20871 + 5.54804I
u = −0.27355 − 1.56061I
a = −0.041547 + 1.376770I
b = 0.24399 + 2.09573I
−6.09001 + 6.43621I −3.20871 − 5.54804I
19
IV. I
u
4
= hau + 3b − 4a + u − 1, 2a
2
+ au + 2a + 4u + 3, u
2
+ 2i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
4
=
a
−
1
3
au +
4
3
a −
1
3
u +
1
3
a
10
=
1
2
a
5
=
−
1
3
au +
1
3
a −
1
3
u +
1
3
−au − u + 1
a
1
=
u
u
a
2
=
−
1
3
au +
1
3
a −
5
6
u +
1
3
−
2
3
au +
2
3
a −
5
3
u −
1
3
a
6
=
1
2
u
−
1
3
au −
2
3
a +
2
3
u +
4
3
a
8
=
−1
−2
a
3
=
−
1
3
au +
1
3
a −
1
3
u +
1
3
−au − u + 1
a
7
=
1
2
u
−
1
3
au −
2
3
a −
1
3
u +
4
3
a
11
=
−
1
2
u
1
3
au +
2
3
a +
1
3
u −
4
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
10
u
4
− 2u
3
− u
2
+ 2u + 3
c
2
, c
11
(u − 1)
4
c
4
, c
7
u
4
+ 2u
3
− u
2
− 2u + 3
c
5
, c
6
(u + 1)
4
c
8
, c
9
, c
12
(u
2
+ 2)
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
, c
10
y
4
− 6y
3
+ 15y
2
− 10y + 9
c
2
, c
5
, c
6
c
11
(y −1)
4
c
8
, c
9
, c
12
(y + 2)
4
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = −1.35328 + 1.09665I
b = −0.95408 + 1.62874I
−8.22467 −12.0000
u = 1.414210I
a = 0.35328 − 1.80376I
b = −0.04592 − 3.04296I
−8.22467 −12.0000
u = − 1.414210I
a = −1.35328 − 1.09665I
b = −0.95408 − 1.62874I
−8.22467 −12.0000
u = − 1.414210I
a = 0.35328 + 1.80376I
b = −0.04592 + 3.04296I
−8.22467 −12.0000
23
V. I
v
1
= ha, b − v + 2, v
2
− 3v + 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
v
0
a
4
=
0
v − 2
a
10
=
1
0
a
5
=
v − 2
v − 2
a
1
=
v
0
a
2
=
v
1
a
6
=
−2
v − 3
a
8
=
1
0
a
3
=
v − 2
v − 2
a
7
=
v − 2
v − 3
a
11
=
v − 2
v − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −22
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
u
2
− u − 1
c
2
, c
6
(u − 1)
2
c
5
, c
11
(u + 1)
2
c
7
, c
10
u
2
+ u − 1
c
8
, c
9
, c
12
u
2
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
, c
10
y
2
− 3y + 1
c
2
, c
5
, c
6
c
11
(y − 1)
2
c
8
, c
9
, c
12
y
2
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.381966
a = 0
b = −1.61803
−3.28987 −22.0000
v = 2.61803
a = 0
b = 0.618034
−3.28987 −22.0000
27
VI. I
v
2
= ha, b + 1, v − 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
1
0
a
4
=
0
−1
a
10
=
1
0
a
5
=
−1
−1
a
1
=
1
0
a
2
=
1
1
a
6
=
−1
−1
a
8
=
1
0
a
3
=
−1
−1
a
7
=
0
−1
a
11
=
0
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
28
(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
29
(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
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −1.00000
−1.64493 −6.00000
31
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
(u + 1)(u
2
− u − 1)(u
4
− 2u
3
+ ··· + 2u + 3)(u
13
− 3u
11
+ ··· − 5u + 1)
· (u
27
− u
26
+ ··· + 10u − 1)(u
34
+ 2u
33
+ ··· + 51u − 23)
c
2
u(u − 1)
6
(u
13
+ 8u
12
+ ··· + 3u + 1)(u
17
− 4u
16
+ ··· − 4u + 1)
2
· (u
27
+ 11u
26
+ ··· − 78u − 9)
c
4
(u + 1)(u
2
− u − 1)(u
4
+ 2u
3
+ ··· − 2u + 3)(u
13
− u
12
+ ··· + 2u − 1)
· (u
27
− 2u
26
+ ··· + u + 1)(u
34
− 15u
32
+ ··· − 37u + 61)
c
5
u(u + 1)
6
(u
13
− 8u
12
+ ··· + 3u − 1)(u
17
− 4u
16
+ ··· − 4u + 1)
2
· (u
27
+ 11u
26
+ ··· − 78u − 9)
c
6
((u − 1)
2
)(u + 1)
5
(u
13
− u
12
+ ··· − u + 1)(u
27
− 2u
26
+ ··· + 4u + 3)
· (u
34
+ 3u
33
+ ··· − 682u − 121)
c
7
(u + 1)(u
2
+ u − 1)(u
4
+ 2u
3
+ ··· − 2u + 3)(u
13
− 3u
11
+ ··· − 5u − 1)
· (u
27
− u
26
+ ··· + 10u − 1)(u
34
+ 2u
33
+ ··· + 51u − 23)
c
8
, c
9
u
3
(u
2
+ 2)
2
(u
13
+ 4u
12
+ ··· + 18u + 5)(u
17
− 3u
16
+ ··· + 6u − 2)
2
· (u
27
+ 7u
26
+ ··· + 69u + 9)
c
10
(u + 1)(u
2
+ u − 1)(u
4
− 2u
3
+ ··· + 2u + 3)(u
13
+ u
12
+ ··· + 2u + 1)
· (u
27
− 2u
26
+ ··· + u + 1)(u
34
− 15u
32
+ ··· − 37u + 61)
c
11
((u − 1)
4
)(u + 1)
3
(u
13
+ u
12
+ ··· − u − 1)(u
27
− 2u
26
+ ··· + 4u + 3)
· (u
34
+ 3u
33
+ ··· − 682u − 121)
c
12
u
3
(u
2
+ 2)
2
(u
13
− 4u
12
+ ··· + 18u − 5)(u
17
− 3u
16
+ ··· + 6u − 2)
2
· (u
27
+ 7u
26
+ ··· + 69u + 9)
32
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
(y − 1)(y
2
− 3y + 1)(y
4
− 6y
3
+ ··· − 10y + 9)(y
13
− 6y
12
+ ··· + 5y − 1)
· (y
27
− 25y
26
+ ··· + 26y − 1)(y
34
− 6y
33
+ ··· − 7293y + 529)
c
2
, c
5
y(y − 1)
6
(y
13
− 8y
12
+ ··· − 7y − 1)(y
17
− 2y
16
+ ··· − 4y − 1)
2
· (y
27
− 7y
26
+ ··· − 54y − 81)
c
4
, c
10
(y − 1)(y
2
− 3y + 1)(y
4
− 6y
3
+ ··· − 10y + 9)(y
13
− 7y
12
+ ··· + 8y − 1)
· (y
27
− 22y
26
+ ··· + 29y − 1)(y
34
− 30y
33
+ ··· − 156553y + 3721)
c
6
, c
11
((y − 1)
7
)(y
13
+ 13y
12
+ ··· + 3y − 1)(y
27
+ 22y
26
+ ··· + 124y − 9)
· (y
34
+ 29y
33
+ ··· + 783838y + 14641)
c
8
, c
9
, c
12
y
3
(y + 2)
4
(y
13
+ 12y
12
+ ··· − 86y − 25)
· ((y
17
+ 17y
16
+ ··· + 52y − 4)
2
)(y
27
+ 25y
26
+ ··· − 1917y − 81)
33
