12a
0969
(K12a
0969
)
A knot diagram
1
Linearized knot diagam
4 6 10 1 9 2 12 11 3 5 8 7
Solving Sequence
7,12
8
1,4
2 5 6 11 9 10 3
c
7
c
12
c
1
c
4
c
6
c
11
c
8
c
10
c
3
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.36400 × 10
116
u
90
− 5.03510 × 10
116
u
89
+ ··· + 7.67306 × 10
116
b + 1.44976 × 10
118
,
− 8.64013 × 10
119
u
90
− 2.09303 × 10
120
u
89
+ ··· + 5.34812 × 10
119
a + 2.44441 × 10
121
,
u
91
+ 3u
90
+ ··· + 129u + 17i
I
u
2
= h−u
20
− 2u
19
+ ··· + b − 1, u
21
− u
20
+ ··· + a − 7, u
22
+ 2u
21
+ ··· + 4u + 1i
* 2 irreducible components of dim
C
= 0, with total 113 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−2.36 × 10
116
u
90
− 5.04 × 10
116
u
89
+ · · · + 7.67 × 10
116
b + 1.45 ×
10
118
, −8.64 × 10
119
u
90
− 2.09 × 10
120
u
89
+ · · · + 5.35 × 10
119
a + 2.44 ×
10
121
, u
91
+ 3u
90
+ · · · + 129u + 17i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
u
a
4
=
1.61554u
90
+ 3.91359u
89
+ ··· − 201.269u − 45.7060
0.308091u
90
+ 0.656205u
89
+ ··· − 77.7660u − 18.8941
a
2
=
−0.882014u
90
− 3.56244u
89
+ ··· − 190.889u − 17.8701
−0.381868u
90
− 1.43162u
89
+ ··· + 13.2970u + 4.16919
a
5
=
1.03636u
90
+ 2.41410u
89
+ ··· − 137.714u − 34.4014
−0.271098u
90
− 0.843285u
89
+ ··· − 14.2107u − 7.58951
a
6
=
1.62034u
90
+ 3.98249u
89
+ ··· − 197.673u − 41.7998
0.189004u
90
+ 0.362786u
89
+ ··· − 70.2633u − 15.9802
a
11
=
−u
u
3
+ u
a
9
=
u
2
+ 1
−u
4
− 2u
2
a
10
=
1.55728u
90
+ 3.97321u
89
+ ··· + 15.5789u − 16.1108
1.11898u
90
+ 2.89964u
89
+ ··· + 76.9656u − 2.20818
a
3
=
−0.354207u
90
− 2.05941u
89
+ ··· − 175.052u − 17.2076
−0.735965u
90
− 2.79677u
89
+ ··· − 263.469u − 28.2611
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.24325u
90
+ 10.4665u
89
+ ··· + 642.496u + 57.8550
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
91
− 5u
90
+ ··· − 53u + 37
c
2
, c
6
u
91
− u
90
+ ··· + 59093u + 8017
c
3
, c
9
u
91
+ u
90
+ ··· + 587u + 251
c
5
u
91
+ 3u
90
+ ··· − 4003055u − 530711
c
7
, c
8
, c
11
c
12
u
91
+ 3u
90
+ ··· + 129u + 17
c
10
u
91
− u
90
+ ··· − 79317u + 19177
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
91
+ 45y
90
+ ··· − 55059y −1369
c
2
, c
6
y
91
+ 77y
90
+ ··· − 1702552331y −64272289
c
3
, c
9
y
91
− 63y
90
+ ··· + 809421y −63001
c
5
y
91
− 49y
90
+ ··· + 8286890991737y −281654165521
c
7
, c
8
, c
11
c
12
y
91
+ 113y
90
+ ··· − 12021y −289
c
10
y
91
− 29y
90
+ ··· + 8475331727y −367757329
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.253030 + 1.006480I
a = −0.561408 + 0.901795I
b = −0.239624 + 0.297217I
−4.37050 + 2.04930I 0
u = 0.253030 − 1.006480I
a = −0.561408 − 0.901795I
b = −0.239624 − 0.297217I
−4.37050 − 2.04930I 0
u = −0.382221 + 0.872059I
a = −0.78902 − 1.24391I
b = 0.134758 − 0.340393I
−8.78899 − 6.69200I 0
u = −0.382221 − 0.872059I
a = −0.78902 + 1.24391I
b = 0.134758 + 0.340393I
−8.78899 + 6.69200I 0
u = −0.592298 + 0.866037I
a = 1.56047 + 0.34982I
b = 1.01433 + 1.56620I
−6.4664 − 13.2635I 0
u = −0.592298 − 0.866037I
a = 1.56047 − 0.34982I
b = 1.01433 − 1.56620I
−6.4664 + 13.2635I 0
u = 0.630431 + 0.846412I
a = 1.59404 − 0.38714I
b = 1.09526 − 1.46656I
−2.07560 + 6.94469I 0
u = 0.630431 − 0.846412I
a = 1.59404 + 0.38714I
b = 1.09526 + 1.46656I
−2.07560 − 6.94469I 0
u = −0.586607 + 0.740100I
a = 1.61009 + 0.36921I
b = 1.27345 + 1.42934I
−7.28302 − 0.64493I 0
u = −0.586607 − 0.740100I
a = 1.61009 − 0.36921I
b = 1.27345 − 1.42934I
−7.28302 + 0.64493I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.383140 + 0.844061I
a = −1.168540 − 0.674150I
b = −0.25614 − 1.62231I
−1.16419 − 6.82328I 0
u = −0.383140 − 0.844061I
a = −1.168540 + 0.674150I
b = −0.25614 + 1.62231I
−1.16419 + 6.82328I 0
u = 0.087898 + 1.089220I
a = 0.237486 − 0.259927I
b = −0.568773 + 0.022573I
−6.24220 + 0.44901I 0
u = 0.087898 − 1.089220I
a = 0.237486 + 0.259927I
b = −0.568773 − 0.022573I
−6.24220 − 0.44901I 0
u = 0.476782 + 0.744759I
a = −0.903469 + 0.549106I
b = −0.196827 + 1.373020I
1.29917 + 3.07151I 0
u = 0.476782 − 0.744759I
a = −0.903469 − 0.549106I
b = −0.196827 − 1.373020I
1.29917 − 3.07151I 0
u = 0.849193 + 0.173893I
a = −0.394385 + 0.552089I
b = 0.36794 + 1.42466I
0.00220 − 2.00961I 0
u = 0.849193 − 0.173893I
a = −0.394385 − 0.552089I
b = 0.36794 − 1.42466I
0.00220 + 2.00961I 0
u = −0.541487 + 1.036860I
a = −0.918599 − 0.986195I
b = −0.056278 − 0.887212I
−7.38711 + 3.94508I 0
u = −0.541487 − 1.036860I
a = −0.918599 + 0.986195I
b = −0.056278 + 0.887212I
−7.38711 − 3.94508I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.822520 + 0.067120I
a = −0.393774 − 0.210431I
b = 0.46423 − 1.43268I
−4.04382 + 8.57679I 0
u = −0.822520 − 0.067120I
a = −0.393774 + 0.210431I
b = 0.46423 + 1.43268I
−4.04382 − 8.57679I 0
u = −0.330329 + 0.695994I
a = −0.0350586 + 0.1285490I
b = −0.446342 − 0.727196I
−4.26951 − 2.65656I 0
u = −0.330329 − 0.695994I
a = −0.0350586 − 0.1285490I
b = −0.446342 + 0.727196I
−4.26951 + 2.65656I 0
u = 0.129252 + 0.718831I
a = 1.29791 + 0.61457I
b = 0.010107 − 0.407997I
−0.46804 + 2.58652I 0
u = 0.129252 − 0.718831I
a = 1.29791 − 0.61457I
b = 0.010107 + 0.407997I
−0.46804 − 2.58652I 0
u = 0.089930 + 0.719506I
a = −2.82227 + 0.94821I
b = −1.63207 + 1.65908I
−5.96732 + 3.75531I 0
u = 0.089930 − 0.719506I
a = −2.82227 − 0.94821I
b = −1.63207 − 1.65908I
−5.96732 − 3.75531I 0
u = 0.444816 + 0.571666I
a = −0.811182 − 0.626954I
b = −0.549553 + 1.222830I
−2.37455 + 4.94131I 0
u = 0.444816 − 0.571666I
a = −0.811182 + 0.626954I
b = −0.549553 − 1.222830I
−2.37455 − 4.94131I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.328418 + 1.300620I
a = −1.002710 + 0.773050I
b = −0.615435 + 0.689529I
−4.46238 + 2.26263I 0
u = 0.328418 − 1.300620I
a = −1.002710 − 0.773050I
b = −0.615435 − 0.689529I
−4.46238 − 2.26263I 0
u = 0.129039 + 1.345170I
a = 2.30985 − 0.06214I
b = 1.45692 − 0.23290I
−1.53404 + 3.13690I 0
u = 0.129039 − 1.345170I
a = 2.30985 + 0.06214I
b = 1.45692 + 0.23290I
−1.53404 − 3.13690I 0
u = −0.615697 + 0.164717I
a = −0.865139 − 0.742895I
b = 0.373819 − 1.212440I
−5.70084 − 3.45733I −4.35538 + 2.32913I
u = −0.615697 − 0.164717I
a = −0.865139 + 0.742895I
b = 0.373819 + 1.212440I
−5.70084 + 3.45733I −4.35538 − 2.32913I
u = −0.260413 + 0.575343I
a = −1.81516 + 0.48727I
b = −0.650904 − 1.158450I
−0.38808 − 3.24368I −2.30026 + 0.I
u = −0.260413 − 0.575343I
a = −1.81516 − 0.48727I
b = −0.650904 + 1.158450I
−0.38808 + 3.24368I −2.30026 + 0.I
u = 0.605745 + 0.178172I
a = 0.900250 + 0.429644I
b = 0.419929 − 1.077670I
3.01354 + 0.62860I 6.07513 − 1.71881I
u = 0.605745 − 0.178172I
a = 0.900250 − 0.429644I
b = 0.419929 + 1.077670I
3.01354 − 0.62860I 6.07513 + 1.71881I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.354938 + 0.503980I
a = 1.58658 − 0.00995I
b = −0.125767 + 0.884945I
−0.096196 + 1.233880I −2.89346 + 1.13895I
u = −0.354938 − 0.503980I
a = 1.58658 + 0.00995I
b = −0.125767 − 0.884945I
−0.096196 − 1.233880I −2.89346 − 1.13895I
u = 0.516984 + 0.310035I
a = 1.54678 + 0.12545I
b = −0.346073 − 0.764503I
−1.62456 − 1.58941I −2.19411 − 0.24297I
u = 0.516984 − 0.310035I
a = 1.54678 − 0.12545I
b = −0.346073 + 0.764503I
−1.62456 + 1.58941I −2.19411 + 0.24297I
u = −0.039764 + 0.550957I
a = −3.59783 + 0.41411I
b = −0.878611 − 0.342232I
0.43967 − 2.50241I −6.35136 + 5.68313I
u = −0.039764 − 0.550957I
a = −3.59783 − 0.41411I
b = −0.878611 + 0.342232I
0.43967 + 2.50241I −6.35136 − 5.68313I
u = −0.04384 + 1.49074I
a = 1.238740 + 0.265818I
b = 0.343289 + 0.401998I
−6.54801 − 0.21182I 0
u = −0.04384 − 1.49074I
a = 1.238740 − 0.265818I
b = 0.343289 − 0.401998I
−6.54801 + 0.21182I 0
u = −0.506629 + 0.013297I
a = 0.635914 + 1.176010I
b = 0.085659 − 1.171430I
1.39516 − 3.73965I 2.89170 + 5.40187I
u = −0.506629 − 0.013297I
a = 0.635914 − 1.176010I
b = 0.085659 + 1.171430I
1.39516 + 3.73965I 2.89170 − 5.40187I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.456972
a = 1.32803
b = −0.280726
−2.27036 −2.15750
u = 0.220977 + 0.398435I
a = 0.697056 + 0.380194I
b = 0.104360 + 0.315206I
0.003690 + 0.929769I 0.15778 − 7.14917I
u = 0.220977 − 0.398435I
a = 0.697056 − 0.380194I
b = 0.104360 − 0.315206I
0.003690 − 0.929769I 0.15778 + 7.14917I
u = −0.199743 + 0.398483I
a = 1.67316 + 0.34201I
b = −0.234533 + 0.862944I
0.072497 + 1.266220I −4.46493 − 2.74628I
u = −0.199743 − 0.398483I
a = 1.67316 − 0.34201I
b = −0.234533 − 0.862944I
0.072497 − 1.266220I −4.46493 + 2.74628I
u = 0.10145 + 1.56912I
a = −1.34483 + 0.73744I
b = −0.81044 + 1.53567I
−9.60673 + 6.81055I 0
u = 0.10145 − 1.56912I
a = −1.34483 − 0.73744I
b = −0.81044 − 1.53567I
−9.60673 − 6.81055I 0
u = −0.09827 + 1.57654I
a = −1.18204 − 1.29658I
b = −1.08401 − 1.66241I
−11.94870 − 4.17333I 0
u = −0.09827 − 1.57654I
a = −1.18204 + 1.29658I
b = −1.08401 + 1.66241I
−11.94870 + 4.17333I 0
u = 0.00011 + 1.58693I
a = 0.948307 + 0.856943I
b = 0.423379 + 1.197460I
−6.99880 + 1.08422I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.00011 − 1.58693I
a = 0.948307 − 0.856943I
b = 0.423379 − 1.197460I
−6.99880 − 1.08422I 0
u = −0.04388 + 1.59590I
a = 0.08672 − 1.66738I
b = −0.17594 − 1.98522I
−11.93620 − 3.98067I 0
u = −0.04388 − 1.59590I
a = 0.08672 + 1.66738I
b = −0.17594 + 1.98522I
−11.93620 + 3.98067I 0
u = −0.06162 + 1.59587I
a = −1.80580 − 0.79874I
b = −1.06224 − 1.38386I
−7.94061 − 4.34595I 0
u = −0.06162 − 1.59587I
a = −1.80580 + 0.79874I
b = −1.06224 + 1.38386I
−7.94061 + 4.34595I 0
u = −0.042082 + 0.397737I
a = 0.24997 − 2.36679I
b = −0.78595 − 1.78034I
−4.81875 − 3.37599I −7.29184 − 1.97538I
u = −0.042082 − 0.397737I
a = 0.24997 + 2.36679I
b = −0.78595 + 1.78034I
−4.81875 + 3.37599I −7.29184 + 1.97538I
u = −0.00951 + 1.60358I
a = −2.57300 − 0.18687I
b = −1.47153 − 0.38335I
−7.18483 − 2.67195I 0
u = −0.00951 − 1.60358I
a = −2.57300 + 0.18687I
b = −1.47153 + 0.38335I
−7.18483 + 2.67195I 0
u = 0.03262 + 1.61996I
a = 0.792831 − 0.242520I
b = 0.200055 − 0.835980I
−8.56287 + 3.20352I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.03262 − 1.61996I
a = 0.792831 + 0.242520I
b = 0.200055 + 0.835980I
−8.56287 − 3.20352I 0
u = 0.13259 + 1.62867I
a = −1.24348 + 1.20206I
b = −0.72606 + 1.56533I
−6.82850 + 5.34807I 0
u = 0.13259 − 1.62867I
a = −1.24348 − 1.20206I
b = −0.72606 − 1.56533I
−6.82850 − 5.34807I 0
u = 0.02825 + 1.63775I
a = −2.88026 + 1.42748I
b = −2.20110 + 1.72105I
−14.2601 + 4.2220I 0
u = 0.02825 − 1.63775I
a = −2.88026 − 1.42748I
b = −2.20110 − 1.72105I
−14.2601 − 4.2220I 0
u = −0.18525 + 1.64009I
a = 2.56449 + 0.80433I
b = 1.93148 + 1.24752I
−15.3815 − 3.6242I 0
u = −0.18525 − 1.64009I
a = 2.56449 − 0.80433I
b = 1.93148 − 1.24752I
−15.3815 + 3.6242I 0
u = −0.10744 + 1.66260I
a = −0.254529 − 0.572722I
b = 0.135258 + 0.231828I
−17.5577 − 8.5967I 0
u = −0.10744 − 1.66260I
a = −0.254529 + 0.572722I
b = 0.135258 − 0.231828I
−17.5577 + 8.5967I 0
u = −0.10822 + 1.66536I
a = −1.23552 − 1.50937I
b = −0.60319 − 1.90161I
−9.88898 − 8.72775I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10822 − 1.66536I
a = −1.23552 + 1.50937I
b = −0.60319 + 1.90161I
−9.88898 + 8.72775I 0
u = 0.18270 + 1.66545I
a = 2.28916 − 0.86051I
b = 1.58319 − 1.36510I
−10.6371 + 10.0743I 0
u = 0.18270 − 1.66545I
a = 2.28916 + 0.86051I
b = 1.58319 + 1.36510I
−10.6371 − 10.0743I 0
u = −0.17542 + 1.66854I
a = 2.17852 + 1.00647I
b = 1.46947 + 1.57996I
−15.1212 − 16.2518I 0
u = −0.17542 − 1.66854I
a = 2.17852 − 1.00647I
b = 1.46947 − 1.57996I
−15.1212 + 16.2518I 0
u = 0.08358 + 1.68225I
a = −0.225378 + 0.439636I
b = −0.032799 − 0.242739I
−13.66210 + 3.50921I 0
u = 0.08358 − 1.68225I
a = −0.225378 − 0.439636I
b = −0.032799 + 0.242739I
−13.66210 − 3.50921I 0
u = 0.00179 + 1.73496I
a = −0.485440 + 0.047068I
b = −0.809096 + 0.227849I
−16.3333 + 0.6742I 0
u = 0.00179 − 1.73496I
a = −0.485440 − 0.047068I
b = −0.809096 − 0.227849I
−16.3333 − 0.6742I 0
u = −0.10578 + 1.73887I
a = −0.500551 − 0.414501I
b = −0.187235 − 0.058990I
−17.2736 + 1.3914I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10578 − 1.73887I
a = −0.500551 + 0.414501I
b = −0.187235 + 0.058990I
−17.2736 − 1.3914I 0
14
II.
I
u
2
= h−u
20
−2u
19
+· · ·+b−1, u
21
−u
20
+· · ·+a−7, u
22
+2u
21
+· · ·+4u+1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
u
a
4
=
−u
21
+ u
20
+ ··· + 13u + 7
u
20
+ 2u
19
+ ··· + 5u + 1
a
2
=
−3u
21
− 5u
20
+ ··· − 30u − 3
u
21
+ 2u
20
+ ··· + 6u + 1
a
5
=
−u
21
− u
20
+ ··· + 6u + 5
−u
20
− 2u
19
+ ··· − 2u − 1
a
6
=
−u
21
− 13u
19
+ ··· + 10u + 7
u
7
+ u
6
+ 5u
5
+ 4u
4
+ 7u
3
+ 4u
2
+ 2u
a
11
=
−u
u
3
+ u
a
9
=
u
2
+ 1
−u
4
− 2u
2
a
10
=
2u
21
+ 4u
20
+ ··· + 18u + 3
−u
11
− 2u
10
+ ··· − 4u − 1
a
3
=
−u
21
− u
20
+ ··· − 10u + 1
u
21
+ 2u
20
+ ··· + 4u
2
+ 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
−3u
21
−u
20
−37u
19
−3u
18
−173u
17
+60u
16
−325u
15
+503u
14
+127u
13
+1730u
12
+1703u
11
+
3228u
10
+3241u
9
+3473u
8
+2947u
7
+2133u
6
+1361u
5
+694u
4
+283u
3
+106u
2
+25u+11
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
22
− 4u
21
+ ··· + 11u
2
+ 1
c
2
u
22
+ 11u
20
+ ··· + 4u + 1
c
3
u
22
− 7u
20
+ ··· − 5u
2
+ 1
c
4
u
22
+ 4u
21
+ ··· + 11u
2
+ 1
c
5
u
22
+ 4u
21
+ ··· + 2u + 1
c
6
u
22
+ 11u
20
+ ··· − 4u + 1
c
7
, c
8
u
22
+ 2u
21
+ ··· + 4u + 1
c
9
u
22
− 7u
20
+ ··· − 5u
2
+ 1
c
10
u
22
+ 4u
19
+ ··· + 10u
2
+ 1
c
11
, c
12
u
22
− 2u
21
+ ··· − 4u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
22
+ 18y
21
+ ··· + 22y + 1
c
2
, c
6
y
22
+ 22y
21
+ ··· + 18y + 1
c
3
, c
9
y
22
− 14y
21
+ ··· − 10y + 1
c
5
y
22
− 8y
21
+ ··· − 18y + 1
c
7
, c
8
, c
11
c
12
y
22
+ 30y
21
+ ··· + 20y + 1
c
10
y
22
− 4y
20
+ ··· + 20y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.221036 + 0.919122I
a = 0.145042 − 1.360440I
b = −0.52812 − 1.31209I
−6.33099 − 2.20918I −7.01368 + 0.97003I
u = 0.221036 − 0.919122I
a = 0.145042 + 1.360440I
b = −0.52812 + 1.31209I
−6.33099 + 2.20918I −7.01368 − 0.97003I
u = −0.331088 + 0.690472I
a = −1.356670 + 0.365839I
b = −0.519230 − 1.084080I
−0.57451 − 4.10173I −3.58788 + 8.99122I
u = −0.331088 − 0.690472I
a = −1.356670 − 0.365839I
b = −0.519230 + 1.084080I
−0.57451 + 4.10173I −3.58788 − 8.99122I
u = −0.135691 + 1.302840I
a = −2.61209 − 0.22373I
b = −1.71780 − 0.44212I
−2.23134 − 3.47589I −7.21416 + 5.11537I
u = −0.135691 − 1.302840I
a = −2.61209 + 0.22373I
b = −1.71780 + 0.44212I
−2.23134 + 3.47589I −7.21416 − 5.11537I
u = −0.579730 + 0.172913I
a = 0.570289 − 0.245593I
b = −0.411451 + 1.102200I
1.13557 + 1.30166I 3.48273 − 0.87575I
u = −0.579730 − 0.172913I
a = 0.570289 + 0.245593I
b = −0.411451 − 1.102200I
1.13557 − 1.30166I 3.48273 + 0.87575I
u = −0.300051 + 1.373820I
a = 0.951749 + 0.663301I
b = 0.375338 + 0.652780I
−3.85049 − 1.96930I 0.582471 − 0.631843I
u = −0.300051 − 1.373820I
a = 0.951749 − 0.663301I
b = 0.375338 − 0.652780I
−3.85049 + 1.96930I 0.582471 + 0.631843I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.248153 + 0.423204I
a = −1.95607 + 0.54023I
b = −1.15067 + 1.92517I
−4.66669 + 3.88902I −2.31027 − 11.16379I
u = 0.248153 − 0.423204I
a = −1.95607 − 0.54023I
b = −1.15067 − 1.92517I
−4.66669 − 3.88902I −2.31027 + 11.16379I
u = −0.02321 + 1.54279I
a = 1.65026 + 0.19765I
b = 0.577897 − 0.040634I
−5.73080 + 1.71841I −1.49841 − 3.09787I
u = −0.02321 − 1.54279I
a = 1.65026 − 0.19765I
b = 0.577897 + 0.040634I
−5.73080 − 1.71841I −1.49841 + 3.09787I
u = 0.08611 + 1.56350I
a = −2.12464 + 1.84046I
b = −1.67151 + 2.21312I
−11.62650 + 5.14343I −6.60505 − 7.08912I
u = 0.08611 − 1.56350I
a = −2.12464 − 1.84046I
b = −1.67151 − 2.21312I
−11.62650 − 5.14343I −6.60505 + 7.08912I
u = −0.09577 + 1.61285I
a = −1.36329 − 0.72660I
b = −0.78319 − 1.36885I
−8.51194 − 5.69479I −5.58610 + 4.79033I
u = −0.09577 − 1.61285I
a = −1.36329 + 0.72660I
b = −0.78319 + 1.36885I
−8.51194 + 5.69479I −5.58610 − 4.79033I
u = −0.124088 + 0.350212I
a = 3.84928 − 0.02755I
b = −0.138855 + 0.251058I
0.93991 + 2.16737I 5.57514 + 0.86615I
u = −0.124088 − 0.350212I
a = 3.84928 + 0.02755I
b = −0.138855 − 0.251058I
0.93991 − 2.16737I 5.57514 − 0.86615I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.03433 + 1.74192I
a = −0.253862 − 0.661352I
b = −0.532411 − 0.633806I
−16.1249 − 1.2255I −3.32478 + 7.09444I
u = 0.03433 − 1.74192I
a = −0.253862 + 0.661352I
b = −0.532411 + 0.633806I
−16.1249 + 1.2255I −3.32478 − 7.09444I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
22
− 4u
21
+ ··· + 11u
2
+ 1)(u
91
− 5u
90
+ ··· − 53u + 37)
c
2
(u
22
+ 11u
20
+ ··· + 4u + 1)(u
91
− u
90
+ ··· + 59093u + 8017)
c
3
(u
22
− 7u
20
+ ··· − 5u
2
+ 1)(u
91
+ u
90
+ ··· + 587u + 251)
c
4
(u
22
+ 4u
21
+ ··· + 11u
2
+ 1)(u
91
− 5u
90
+ ··· − 53u + 37)
c
5
(u
22
+ 4u
21
+ ··· + 2u + 1)(u
91
+ 3u
90
+ ··· − 4003055u − 530711)
c
6
(u
22
+ 11u
20
+ ··· − 4u + 1)(u
91
− u
90
+ ··· + 59093u + 8017)
c
7
, c
8
(u
22
+ 2u
21
+ ··· + 4u + 1)(u
91
+ 3u
90
+ ··· + 129u + 17)
c
9
(u
22
− 7u
20
+ ··· − 5u
2
+ 1)(u
91
+ u
90
+ ··· + 587u + 251)
c
10
(u
22
+ 4u
19
+ ··· + 10u
2
+ 1)(u
91
− u
90
+ ··· − 79317u + 19177)
c
11
, c
12
(u
22
− 2u
21
+ ··· − 4u + 1)(u
91
+ 3u
90
+ ··· + 129u + 17)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
22
+ 18y
21
+ ··· + 22y + 1)(y
91
+ 45y
90
+ ··· − 55059y −1369)
c
2
, c
6
(y
22
+ 22y
21
+ ··· + 18y + 1)
· (y
91
+ 77y
90
+ ··· − 1702552331y −64272289)
c
3
, c
9
(y
22
− 14y
21
+ ··· − 10y + 1)(y
91
− 63y
90
+ ··· + 809421y −63001)
c
5
(y
22
− 8y
21
+ ··· − 18y + 1)
· (y
91
− 49y
90
+ ··· + 8286890991737y −281654165521)
c
7
, c
8
, c
11
c
12
(y
22
+ 30y
21
+ ··· + 20y + 1)(y
91
+ 113y
90
+ ··· − 12021y −289)
c
10
(y
22
− 4y
20
+ ··· + 20y + 1)
· (y
91
− 29y
90
+ ··· + 8475331727y −367757329)
22
