12n
0589
(K12n
0589
)
A knot diagram
1
Linearized knot diagam
3 7 10 11 9 2 11 4 6 1 9 4
Solving Sequence
2,7 3,10
4 1 11 6 9 5 8 12
c
2
c
3
c
1
c
10
c
6
c
9
c
5
c
8
c
12
c
4
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2.15027 × 10
88
u
78
+ 3.02788 × 10
88
u
77
+ ··· + 2.41970 × 10
87
b − 3.63043 × 10
89
,
2.91093 × 10
89
u
78
+ 3.67504 × 10
89
u
77
+ ··· + 1.57280 × 10
88
a − 4.88443 × 10
90
, u
79
+ 2u
78
+ ··· − u − 13i
I
u
2
= h−696u
22
+ 792u
21
+ ··· + 302b − 1145, −655u
22
+ 334u
21
+ ··· + 151a − 725,
u
23
− u
22
+ ··· + 3u − 1i
* 2 irreducible components of dim
C
= 0, with total 102 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
= h2.15 × 10
88
u
78
+ 3.03 × 10
88
u
77
+ · · · + 2.42 × 10
87
b − 3.63 × 10
89
, 2.91 ×
10
89
u
78
+3.68×10
89
u
77
+· · ·+1.57×10
88
a−4.88×10
90
, u
79
+2u
78
+· · ·−u−13i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
10
=
−18.5079u
78
− 23.3662u
77
+ ··· − 380.443u + 310.556
−8.88654u
78
− 12.5135u
77
+ ··· − 158.149u + 150.037
a
4
=
−1.64242u
78
− 5.44213u
77
+ ··· − 146.208u + 80.9180
−3.47633u
78
− 9.10119u
77
+ ··· − 197.562u + 125.360
a
1
=
−u
2
+ 1
−u
4
a
11
=
−12.0911u
78
− 16.6948u
77
+ ··· − 315.397u + 227.813
−5.48169u
78
− 10.3261u
77
+ ··· − 177.652u + 129.008
a
6
=
u
u
a
9
=
−11.3809u
78
− 15.4740u
77
+ ··· − 263.755u + 201.485
−1.75952u
78
− 4.62127u
77
+ ··· − 41.4612u + 40.9657
a
5
=
−10.4501u
78
− 16.1921u
77
+ ··· − 418.113u + 259.056
3.24517u
78
+ 1.05048u
77
+ ··· − 92.9910u + 13.4345
a
8
=
25.1053u
78
+ 33.6322u
77
+ ··· + 612.317u − 456.608
22.1871u
78
+ 27.8524u
77
+ ··· + 413.354u − 348.620
a
12
=
−11.2839u
78
− 11.8219u
77
+ ··· − 210.236u + 164.805
−9.08712u
78
− 6.33482u
77
+ ··· − 59.2341u + 78.4719
(ii) Obstruction class = −1
(iii) Cusp Shapes = 25.2924u
78
+ 32.9982u
77
+ ··· + 728.389u − 509.327
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
79
+ 36u
78
+ ··· + 3641u + 169
c
2
, c
6
u
79
− 2u
78
+ ··· − u + 13
c
3
u
79
+ 2u
78
+ ··· − 49u + 29
c
4
u
79
− 2u
78
+ ··· + 107183u + 13051
c
5
, c
9
u
79
+ 3u
78
+ ··· + 12688u + 2456
c
7
u
79
− 3u
78
+ ··· − 2215654u + 836419
c
8
u
79
− u
78
+ ··· + 77402u + 12427
c
10
u
79
− 9u
78
+ ··· + 106u + 47
c
11
u
79
+ 2u
78
+ ··· + 84233u + 4289
c
12
u
79
+ 12u
78
+ ··· + 280u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
79
+ 24y
78
+ ··· − 134679y −28561
c
2
, c
6
y
79
− 36y
78
+ ··· + 3641y −169
c
3
y
79
+ 2y
78
+ ··· − 1079y −841
c
4
y
79
− 90y
78
+ ··· + 7988152207y −170328601
c
5
, c
9
y
79
− 37y
78
+ ··· + 161614080y −6031936
c
7
y
79
+ 41y
78
+ ··· − 12372523428214y −699596743561
c
8
y
79
+ 105y
78
+ ··· − 6895853666y −154430329
c
10
y
79
+ 23y
78
+ ··· + 385450y −2209
c
11
y
79
+ 84y
78
+ ··· − 314032055y −18395521
c
12
y
79
− 32y
78
+ ··· + 3520y −64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.940912 + 0.374623I
a = 1.04398 + 1.79768I
b = 1.77718 + 1.09794I
−3.10628 + 1.42293I 0
u = −0.940912 − 0.374623I
a = 1.04398 − 1.79768I
b = 1.77718 − 1.09794I
−3.10628 − 1.42293I 0
u = −0.907169 + 0.464698I
a = 1.56697 + 0.93171I
b = 0.718320 − 0.310140I
−2.40821 + 3.46296I 0
u = −0.907169 − 0.464698I
a = 1.56697 − 0.93171I
b = 0.718320 + 0.310140I
−2.40821 − 3.46296I 0
u = 0.611431 + 0.761311I
a = −0.210481 + 1.145050I
b = −1.68554 + 0.65090I
9.90785 + 3.17209I 0
u = 0.611431 − 0.761311I
a = −0.210481 − 1.145050I
b = −1.68554 − 0.65090I
9.90785 − 3.17209I 0
u = −0.362511 + 0.898774I
a = 0.549996 + 0.889051I
b = 0.831285 − 0.017175I
0.89320 − 3.95862I 0
u = −0.362511 − 0.898774I
a = 0.549996 − 0.889051I
b = 0.831285 + 0.017175I
0.89320 + 3.95862I 0
u = −0.857614 + 0.445269I
a = −0.015635 + 1.020300I
b = 1.60077 + 1.38290I
−2.20981 + 0.24877I 0
u = −0.857614 − 0.445269I
a = −0.015635 − 1.020300I
b = 1.60077 − 1.38290I
−2.20981 − 0.24877I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.941507 + 0.443174I
a = 0.17692 − 1.53807I
b = 0.964686 − 0.947975I
−2.31907 − 1.56521I 0
u = 0.941507 − 0.443174I
a = 0.17692 + 1.53807I
b = 0.964686 + 0.947975I
−2.31907 + 1.56521I 0
u = 0.467521 + 0.836388I
a = −1.24982 + 0.92072I
b = −0.870558 − 0.363496I
−0.94854 + 2.58619I 0
u = 0.467521 − 0.836388I
a = −1.24982 − 0.92072I
b = −0.870558 + 0.363496I
−0.94854 − 2.58619I 0
u = −0.882470 + 0.371777I
a = −1.09764 − 1.93772I
b = −1.59024 − 2.39194I
4.16992 − 1.43305I 0
u = −0.882470 − 0.371777I
a = −1.09764 + 1.93772I
b = −1.59024 + 2.39194I
4.16992 + 1.43305I 0
u = 1.020540 + 0.220943I
a = −0.877902 − 0.130605I
b = 0.274153 − 0.994301I
0.64583 + 1.61580I 0
u = 1.020540 − 0.220943I
a = −0.877902 + 0.130605I
b = 0.274153 + 0.994301I
0.64583 − 1.61580I 0
u = −0.471684 + 0.939721I
a = −1.06369 − 1.04214I
b = −1.211420 + 0.417868I
7.30955 − 10.88550I 0
u = −0.471684 − 0.939721I
a = −1.06369 + 1.04214I
b = −1.211420 − 0.417868I
7.30955 + 10.88550I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.627645 + 0.696624I
a = −0.521853 − 0.958627I
b = −1.092110 − 0.473148I
2.90030 + 0.96581I 0
u = −0.627645 − 0.696624I
a = −0.521853 + 0.958627I
b = −1.092110 + 0.473148I
2.90030 − 0.96581I 0
u = −1.057960 + 0.098937I
a = 0.378289 + 0.870614I
b = −0.607534 + 0.534343I
−4.85614 − 2.30083I 0
u = −1.057960 − 0.098937I
a = 0.378289 − 0.870614I
b = −0.607534 − 0.534343I
−4.85614 + 2.30083I 0
u = 0.273338 + 0.890041I
a = −0.037137 − 1.377140I
b = 0.452185 − 0.240610I
7.98072 − 0.14474I 0
u = 0.273338 − 0.890041I
a = −0.037137 + 1.377140I
b = 0.452185 + 0.240610I
7.98072 + 0.14474I 0
u = 0.759344 + 0.535178I
a = 1.06812 − 2.48880I
b = 0.58587 − 1.28840I
5.86813 + 1.74808I 0
u = 0.759344 − 0.535178I
a = 1.06812 + 2.48880I
b = 0.58587 + 1.28840I
5.86813 − 1.74808I 0
u = 0.933724 + 0.535155I
a = 0.071714 + 1.051390I
b = −1.12899 + 1.53303I
−1.39285 − 4.16896I 0
u = 0.933724 − 0.535155I
a = 0.071714 − 1.051390I
b = −1.12899 − 1.53303I
−1.39285 + 4.16896I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.542872 + 0.745330I
a = 1.34954 − 0.72392I
b = 1.337630 + 0.203188I
0.17356 + 3.61204I 0
u = 0.542872 − 0.745330I
a = 1.34954 + 0.72392I
b = 1.337630 − 0.203188I
0.17356 − 3.61204I 0
u = 0.930941 + 0.549205I
a = 1.69027 − 0.27289I
b = 2.75476 − 0.40173I
5.30360 − 6.13091I 0
u = 0.930941 − 0.549205I
a = 1.69027 + 0.27289I
b = 2.75476 + 0.40173I
5.30360 + 6.13091I 0
u = −0.815186 + 0.737750I
a = −0.94268 + 1.55544I
b = −0.07515 + 1.62017I
6.71179 + 3.15745I 0
u = −0.815186 − 0.737750I
a = −0.94268 − 1.55544I
b = −0.07515 − 1.62017I
6.71179 − 3.15745I 0
u = 1.019360 + 0.512227I
a = 0.764778 − 0.153365I
b = 0.010158 + 0.738965I
−2.03912 − 4.35351I 0
u = 1.019360 − 0.512227I
a = 0.764778 + 0.153365I
b = 0.010158 − 0.738965I
−2.03912 + 4.35351I 0
u = −0.608761 + 0.981615I
a = −0.335444 + 0.466549I
b = 0.565088 + 0.783410I
8.04761 + 5.62058I 0
u = −0.608761 − 0.981615I
a = −0.335444 − 0.466549I
b = 0.565088 − 0.783410I
8.04761 − 5.62058I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.985708 + 0.605627I
a = −0.81681 − 1.24509I
b = −1.28457 − 0.74568I
1.81620 + 4.04906I 0
u = −0.985708 − 0.605627I
a = −0.81681 + 1.24509I
b = −1.28457 + 0.74568I
1.81620 − 4.04906I 0
u = −1.037610 + 0.540324I
a = −0.45101 − 2.02196I
b = −1.99466 − 1.64145I
2.56496 + 8.05404I 0
u = −1.037610 − 0.540324I
a = −0.45101 + 2.02196I
b = −1.99466 + 1.64145I
2.56496 − 8.05404I 0
u = −0.916312 + 0.741875I
a = 1.36975 − 0.80644I
b = 1.09987 − 1.49474I
6.41833 + 2.47068I 0
u = −0.916312 − 0.741875I
a = 1.36975 + 0.80644I
b = 1.09987 + 1.49474I
6.41833 − 2.47068I 0
u = 0.686522 + 0.449971I
a = −0.994721 + 0.690689I
b = −0.228585 − 0.178106I
−0.628640 − 0.060262I −8.00000 − 0.61912I
u = 0.686522 − 0.449971I
a = −0.994721 − 0.690689I
b = −0.228585 + 0.178106I
−0.628640 + 0.060262I −8.00000 + 0.61912I
u = −1.138860 + 0.375005I
a = −1.064920 − 0.554165I
b = −1.31033 − 0.94425I
3.56906 + 3.76087I 0
u = −1.138860 − 0.375005I
a = −1.064920 + 0.554165I
b = −1.31033 + 0.94425I
3.56906 − 3.76087I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.017080 + 0.650523I
a = −1.27012 + 1.34740I
b = −1.74770 + 0.03462I
8.68316 − 8.52671I 0
u = 1.017080 − 0.650523I
a = −1.27012 − 1.34740I
b = −1.74770 − 0.03462I
8.68316 + 8.52671I 0
u = 1.055610 + 0.635989I
a = 0.51016 − 1.81699I
b = 1.35422 − 1.71757I
−1.35466 − 8.89232I 0
u = 1.055610 − 0.635989I
a = 0.51016 + 1.81699I
b = 1.35422 + 1.71757I
−1.35466 + 8.89232I 0
u = 0.494380 + 0.579415I
a = −0.834985 + 0.184019I
b = 0.276708 − 0.757910I
−0.472071 + 0.051721I −5.92155 + 0.65415I
u = 0.494380 − 0.579415I
a = −0.834985 − 0.184019I
b = 0.276708 + 0.757910I
−0.472071 − 0.051721I −5.92155 − 0.65415I
u = 1.106110 + 0.651817I
a = −0.42547 + 1.55137I
b = −1.46435 + 1.84739I
−2.85013 − 8.13954I 0
u = 1.106110 − 0.651817I
a = −0.42547 − 1.55137I
b = −1.46435 − 1.84739I
−2.85013 + 8.13954I 0
u = −1.283900 + 0.091471I
a = 0.262627 − 0.128542I
b = 1.262290 + 0.004627I
−6.78094 − 0.09960I 0
u = −1.283900 − 0.091471I
a = 0.262627 + 0.128542I
b = 1.262290 − 0.004627I
−6.78094 + 0.09960I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.313830 + 0.011159I
a = −0.048796 + 0.275193I
b = 0.872827 − 0.172654I
0.65850 + 8.14248I 0
u = 1.313830 − 0.011159I
a = −0.048796 − 0.275193I
b = 0.872827 + 0.172654I
0.65850 − 8.14248I 0
u = −1.156760 + 0.633167I
a = 0.708871 + 1.213790I
b = 1.55018 + 1.10678I
−1.48361 + 9.57252I 0
u = −1.156760 − 0.633167I
a = 0.708871 − 1.213790I
b = 1.55018 − 1.10678I
−1.48361 − 9.57252I 0
u = −1.141240 + 0.679924I
a = −0.65831 − 1.65912I
b = −1.89648 − 1.66806I
5.2565 + 16.8078I 0
u = −1.141240 − 0.679924I
a = −0.65831 + 1.65912I
b = −1.89648 + 1.66806I
5.2565 − 16.8078I 0
u = −0.652165 + 0.009763I
a = −2.17420 + 1.86731I
b = −1.233600 + 0.301725I
4.63896 + 3.70393I −9.04475 − 4.60639I
u = −0.652165 − 0.009763I
a = −2.17420 − 1.86731I
b = −1.233600 − 0.301725I
4.63896 − 3.70393I −9.04475 + 4.60639I
u = −1.091590 + 0.818788I
a = 0.478452 + 0.097869I
b = 0.341198 − 0.516786I
6.60861 + 0.87644I 0
u = −1.091590 − 0.818788I
a = 0.478452 − 0.097869I
b = 0.341198 + 0.516786I
6.60861 − 0.87644I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.354853 + 0.520671I
a = −0.83695 − 1.88653I
b = −1.269650 + 0.448387I
4.33372 − 3.68615I −6.79933 + 3.65640I
u = −0.354853 − 0.520671I
a = −0.83695 + 1.88653I
b = −1.269650 − 0.448387I
4.33372 + 3.68615I −6.79933 − 3.65640I
u = 1.231940 + 0.615361I
a = 0.811090 − 0.511199I
b = 1.71104 − 0.49726I
5.09949 − 5.43093I 0
u = 1.231940 − 0.615361I
a = 0.811090 + 0.511199I
b = 1.71104 + 0.49726I
5.09949 + 5.43093I 0
u = 1.379720 + 0.181096I
a = −0.098843 − 0.186105I
b = −0.616745 + 0.001577I
−4.88567 + 0.41876I 0
u = 1.379720 − 0.181096I
a = −0.098843 + 0.186105I
b = −0.616745 − 0.001577I
−4.88567 − 0.41876I 0
u = 0.286502 + 0.487686I
a = 0.661056 − 0.092637I
b = 0.397208 + 0.778164I
−0.67083 − 1.82213I −2.69672 + 4.61690I
u = 0.286502 − 0.487686I
a = 0.661056 + 0.092637I
b = 0.397208 − 0.778164I
−0.67083 + 1.82213I −2.69672 − 4.61690I
u = 0.437288
a = −1.25497
b = 0.141138
−0.841651 −11.1020
12
II. I
u
2
= h−696u
22
+ 792u
21
+ · · · + 302b − 1145, −655u
22
+ 334u
21
+ · · · +
151a − 725, u
23
− u
22
+ · · · + 3u − 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
10
=
4.33775u
22
− 2.21192u
21
+ ··· − 12.4636u + 4.80132
2.30464u
22
− 2.62252u
21
+ ··· − 6.48675u + 3.79139
a
4
=
−1.14901u
22
+ 2.65232u
21
+ ··· + 7.64570u − 3.79470
−0.0860927u
22
+ 1.63245u
21
+ ··· + 0.539735u − 2.12583
a
1
=
−u
2
+ 1
−u
4
a
11
=
1.88411u
22
− 0.937086u
21
+ ··· − 4.83113u + 1.71523
0.298013u
22
− 2.30464u
21
+ ··· − 1.29139u + 1.58940
a
6
=
u
u
a
9
=
2.69205u
22
− 1.21854u
21
+ ··· − 7.16556u + 2.35762
0.658940u
22
− 1.62914u
21
+ ··· − 1.18874u + 1.34768
a
5
=
2.21854u
22
− 0.490066u
21
+ ··· − 4.44702u + 2.66556
0.218543u
22
+ 0.509934u
21
+ ··· − 0.447020u − 0.334437
a
8
=
−5.84106u
22
+ 2.37086u
21
+ ··· + 15.3113u − 7.15232
−4.19868u
22
+ 0.536424u
21
+ ··· + 10.3609u − 4.55960
a
12
=
1.57947u
22
− 2.31457u
21
+ ··· − 5.84437u + 4.42384
1.21192u
22
− 2.17219u
21
+ ··· − 5.75166u + 3.96358
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
452
151
u
22
−
350
151
u
21
+ ··· −
860
151
u −
1253
151
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
23
− 13u
22
+ ··· + 5u − 1
c
2
u
23
− u
22
+ ··· + 3u − 1
c
3
u
23
− u
22
+ ··· − u + 1
c
4
u
23
+ u
22
+ ··· + 13u + 7
c
5
u
23
+ 2u
22
+ ··· + 8u + 8
c
6
u
23
+ u
22
+ ··· + 3u + 1
c
7
u
23
+ 4u
22
+ ··· + 88u − 17
c
8
u
23
+ 8u
21
+ ··· − 2u + 1
c
9
u
23
− 2u
22
+ ··· + 8u − 8
c
10
u
23
− 8u
22
+ ··· + 4u − 1
c
11
u
23
+ 5u
22
+ ··· + u + 1
c
12
u
23
− 5u
22
+ ··· − 28u
2
− 8
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
+ 3y
22
+ ··· − 35y −1
c
2
, c
6
y
23
− 13y
22
+ ··· + 5y −1
c
3
y
23
− 3y
22
+ ··· + 25y −1
c
4
y
23
− 15y
22
+ ··· − 377y −49
c
5
, c
9
y
23
− 18y
22
+ ··· + 768y −64
c
7
y
23
+ 12y
22
+ ··· + 3902y −289
c
8
y
23
+ 16y
22
+ ··· − 10y −1
c
10
y
23
+ 6y
22
+ ··· + 2y −1
c
11
y
23
+ 11y
22
+ ··· + 21y −1
c
12
y
23
− 9y
22
+ ··· − 448y −64
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.965287 + 0.385719I
a = −0.68324 + 1.83490I
b = −1.56709 + 1.13629I
−3.50819 − 1.32177I −22.3687 + 1.0798I
u = 0.965287 − 0.385719I
a = −0.68324 − 1.83490I
b = −1.56709 − 1.13629I
−3.50819 + 1.32177I −22.3687 − 1.0798I
u = −0.754686 + 0.722533I
a = −1.39345 + 0.64128I
b = −0.670981 + 0.711403I
6.60939 + 4.34186I −4.57444 − 6.63960I
u = −0.754686 − 0.722533I
a = −1.39345 − 0.64128I
b = −0.670981 − 0.711403I
6.60939 − 4.34186I −4.57444 + 6.63960I
u = 0.437863 + 0.826816I
a = −1.27002 + 0.83666I
b = −0.911985 − 0.315070I
−1.59333 + 3.37311I −10.90858 − 4.53716I
u = 0.437863 − 0.826816I
a = −1.27002 − 0.83666I
b = −0.911985 + 0.315070I
−1.59333 − 3.37311I −10.90858 + 4.53716I
u = −0.983336 + 0.489926I
a = −1.297940 − 0.449684I
b = −0.449112 + 0.805818I
−2.88701 + 4.40761I −17.3868 − 7.7618I
u = −0.983336 − 0.489926I
a = −1.297940 + 0.449684I
b = −0.449112 − 0.805818I
−2.88701 − 4.40761I −17.3868 + 7.7618I
u = 1.084130 + 0.467715I
a = 1.29340 − 0.63485I
b = 2.26155 − 0.48718I
3.54516 − 5.85101I −9.82180 + 6.28067I
u = 1.084130 − 0.467715I
a = 1.29340 + 0.63485I
b = 2.26155 + 0.48718I
3.54516 + 5.85101I −9.82180 − 6.28067I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.704630 + 0.385059I
a = 0.897277 − 0.755242I
b = −0.96705 − 1.21608I
−1.85596 − 0.62485I −10.44943 + 4.04776I
u = −0.704630 − 0.385059I
a = 0.897277 + 0.755242I
b = −0.96705 + 1.21608I
−1.85596 + 0.62485I −10.44943 − 4.04776I
u = 0.688425 + 0.382723I
a = 1.56817 − 2.80264I
b = 1.18209 − 1.51989I
5.02161 + 2.27444I −6.96616 − 2.99379I
u = 0.688425 − 0.382723I
a = 1.56817 + 2.80264I
b = 1.18209 + 1.51989I
5.02161 − 2.27444I −6.96616 + 2.99379I
u = −1.009220 + 0.751191I
a = 0.390476 − 0.766392I
b = 0.134329 − 1.282050I
5.82923 + 1.29072I −9.50178 − 0.22534I
u = −1.009220 − 0.751191I
a = 0.390476 + 0.766392I
b = 0.134329 + 1.282050I
5.82923 − 1.29072I −9.50178 + 0.22534I
u = 1.120850 + 0.644008I
a = −0.41762 + 1.53390I
b = −1.33726 + 1.77241I
−3.61686 − 8.88790I −13.3243 + 8.1123I
u = 1.120850 − 0.644008I
a = −0.41762 − 1.53390I
b = −1.33726 − 1.77241I
−3.61686 + 8.88790I −13.3243 − 8.1123I
u = −1.299510 + 0.176549I
a = 0.253627 − 0.264770I
b = 1.191850 − 0.068265I
−7.09111 − 0.49453I −17.0782 + 7.2270I
u = −1.299510 − 0.176549I
a = 0.253627 + 0.264770I
b = 1.191850 + 0.068265I
−7.09111 + 0.49453I −17.0782 − 7.2270I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.36565
a = −0.302971
b = −0.808918
−4.53589 −1.44890
u = 0.272004 + 0.397025I
a = −1.18920 + 0.98777I
b = −0.461878 − 0.889928I
−1.47485 − 1.57628I −12.39539 + 2.11690I
u = 0.272004 − 0.397025I
a = −1.18920 − 0.98777I
b = −0.461878 + 0.889928I
−1.47485 + 1.57628I −12.39539 − 2.11690I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
23
− 13u
22
+ ··· + 5u − 1)(u
79
+ 36u
78
+ ··· + 3641u + 169)
c
2
(u
23
− u
22
+ ··· + 3u − 1)(u
79
− 2u
78
+ ··· − u + 13)
c
3
(u
23
− u
22
+ ··· − u + 1)(u
79
+ 2u
78
+ ··· − 49u + 29)
c
4
(u
23
+ u
22
+ ··· + 13u + 7)(u
79
− 2u
78
+ ··· + 107183u + 13051)
c
5
(u
23
+ 2u
22
+ ··· + 8u + 8)(u
79
+ 3u
78
+ ··· + 12688u + 2456)
c
6
(u
23
+ u
22
+ ··· + 3u + 1)(u
79
− 2u
78
+ ··· − u + 13)
c
7
(u
23
+ 4u
22
+ ··· + 88u − 17)(u
79
− 3u
78
+ ··· − 2215654u + 836419)
c
8
(u
23
+ 8u
21
+ ··· − 2u + 1)(u
79
− u
78
+ ··· + 77402u + 12427)
c
9
(u
23
− 2u
22
+ ··· + 8u − 8)(u
79
+ 3u
78
+ ··· + 12688u + 2456)
c
10
(u
23
− 8u
22
+ ··· + 4u − 1)(u
79
− 9u
78
+ ··· + 106u + 47)
c
11
(u
23
+ 5u
22
+ ··· + u + 1)(u
79
+ 2u
78
+ ··· + 84233u + 4289)
c
12
(u
23
− 5u
22
+ ··· − 28u
2
− 8)(u
79
+ 12u
78
+ ··· + 280u + 8)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
23
+ 3y
22
+ ··· − 35y −1)(y
79
+ 24y
78
+ ··· − 134679y −28561)
c
2
, c
6
(y
23
− 13y
22
+ ··· + 5y −1)(y
79
− 36y
78
+ ··· + 3641y −169)
c
3
(y
23
− 3y
22
+ ··· + 25y −1)(y
79
+ 2y
78
+ ··· − 1079y −841)
c
4
(y
23
− 15y
22
+ ··· − 377y −49)
· (y
79
− 90y
78
+ ··· + 7988152207y −170328601)
c
5
, c
9
(y
23
− 18y
22
+ ··· + 768y −64)
· (y
79
− 37y
78
+ ··· + 161614080y −6031936)
c
7
(y
23
+ 12y
22
+ ··· + 3902y −289)
· (y
79
+ 41y
78
+ ··· − 12372523428214y −699596743561)
c
8
(y
23
+ 16y
22
+ ··· − 10y −1)
· (y
79
+ 105y
78
+ ··· − 6895853666y −154430329)
c
10
(y
23
+ 6y
22
+ ··· + 2y −1)(y
79
+ 23y
78
+ ··· + 385450y −2209)
c
11
(y
23
+ 11y
22
+ ··· + 21y −1)
· (y
79
+ 84y
78
+ ··· − 314032055y −18395521)
c
12
(y
23
− 9y
22
+ ··· − 448y −64)(y
79
− 32y
78
+ ··· + 3520y −64)
22
