12a
0299
(K12a
0299
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 1 5 11 12 4 9 7
Solving Sequence
2,6
3 1 7 5
8,10
4 11 12 9
c
2
c
1
c
6
c
5
c
7
c
4
c
10
c
12
c
9
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
88
+ u
87
+ ··· + b + 2u, 2u
87
− u
86
+ ··· + a + 2u, u
89
− 2u
88
+ ··· − 3u + 1i
I
u
2
= hu
8
+ u
7
− 2u
6
− 2u
5
+ u
4
+ u
3
+ u
2
+ b + u, u
8
+ u
7
− 2u
6
− 2u
5
+ u
4
+ u
3
+ u
2
+ a + u,
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1i
* 2 irreducible components of dim
C
= 0, with total 98 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
= hu
88
+u
87
+· · ·+b+2u, 2u
87
−u
86
+· · ·+a+2u, u
89
−2u
88
+· · ·−3u+1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
1
=
−u
2
+ 1
−u
4
a
7
=
u
5
− 2u
3
+ u
u
7
− u
5
+ u
a
5
=
u
u
a
8
=
−u
9
+ 2u
7
− u
5
− 2u
3
+ u
−u
9
+ 3u
7
− 3u
5
+ u
a
10
=
−2u
87
+ u
86
+ ··· + 4u
2
− 2u
−u
88
− u
87
+ ··· + 6u
2
− 2u
a
4
=
−u
20
+ 5u
18
− 11u
16
+ 10u
14
+ 2u
12
− 13u
10
+ 9u
8
− 3u
4
+ u
2
+ 1
−u
20
+ 6u
18
− 16u
16
+ 22u
14
− 13u
12
− 4u
10
+ 10u
8
− 4u
6
− u
4
+ 2u
2
a
11
=
u
86
− u
85
+ ··· − 5u + 1
u
88
− u
87
+ ··· + 3u
2
− u
a
12
=
−u
8
+ 3u
6
− 3u
4
+ 1
−u
10
+ 2u
8
− u
6
− 2u
4
+ u
2
a
9
=
−u
87
+ u
86
+ ··· − 3u + 1
−u
87
+ u
86
+ ··· + 5u
2
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 10u
88
− 13u
87
+ ··· + 23u − 17
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
89
+ 48u
88
+ ··· + 5u + 1
c
2
, c
5
u
89
+ 2u
88
+ ··· − 3u − 1
c
3
u
89
+ 2u
88
+ ··· − 65179u − 27289
c
4
, c
10
u
89
+ u
88
+ ··· − 1024u − 512
c
6
, c
12
u
89
+ 6u
88
+ ··· + 11u + 1
c
7
u
89
− 12u
88
+ ··· − 4727u + 841
c
8
, c
9
, c
11
u
89
− 10u
88
+ ··· + 9u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
89
− 12y
88
+ ··· + 13y −1
c
2
, c
5
y
89
− 48y
88
+ ··· + 5y −1
c
3
y
89
− 48y
88
+ ··· + 8750550417y −744689521
c
4
, c
10
y
89
+ 57y
88
+ ··· − 262144y −262144
c
6
, c
12
y
89
+ 72y
88
+ ··· + 173y −1
c
7
y
89
− 12y
88
+ ··· + 56852441y −707281
c
8
, c
9
, c
11
y
89
− 88y
88
+ ··· + 17y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.882130 + 0.459832I
a = 0.753928 + 0.019303I
b = 1.18116 + 0.90759I
−1.67152 − 2.05041I 0
u = 0.882130 − 0.459832I
a = 0.753928 − 0.019303I
b = 1.18116 − 0.90759I
−1.67152 + 2.05041I 0
u = −0.888667 + 0.501711I
a = −1.68269 + 2.08780I
b = −0.63536 + 2.43657I
−3.19630 + 4.44922I 0
u = −0.888667 − 0.501711I
a = −1.68269 − 2.08780I
b = −0.63536 − 2.43657I
−3.19630 − 4.44922I 0
u = 0.878638 + 0.524715I
a = −2.02016 − 0.27913I
b = −2.24474 − 1.41150I
−0.67711 − 6.71445I 0
u = 0.878638 − 0.524715I
a = −2.02016 + 0.27913I
b = −2.24474 + 1.41150I
−0.67711 + 6.71445I 0
u = −1.025820 + 0.036404I
a = 0.502695 − 0.628539I
b = 0.32711 − 1.73815I
−4.46205 + 2.45218I 0
u = −1.025820 − 0.036404I
a = 0.502695 + 0.628539I
b = 0.32711 + 1.73815I
−4.46205 − 2.45218I 0
u = 1.03027
a = 1.17910
b = 0.0366382
−6.56879 0
u = −0.813408 + 0.506521I
a = 0.72584 − 1.39872I
b = 0.04222 − 1.45621I
1.77552 + 2.79390I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.813408 − 0.506521I
a = 0.72584 + 1.39872I
b = 0.04222 + 1.45621I
1.77552 − 2.79390I 0
u = −0.766346 + 0.574188I
a = 1.27704 + 1.89699I
b = 1.89555 + 1.02015I
−1.59917 + 2.27839I 0
u = −0.766346 − 0.574188I
a = 1.27704 − 1.89699I
b = 1.89555 − 1.02015I
−1.59917 − 2.27839I 0
u = 0.890309 + 0.555777I
a = 2.77606 − 0.04434I
b = 2.96738 + 1.34186I
−6.80614 − 10.62200I 0
u = 0.890309 − 0.555777I
a = 2.77606 + 0.04434I
b = 2.96738 − 1.34186I
−6.80614 + 10.62200I 0
u = −1.077470 + 0.067927I
a = −0.953464 − 0.030989I
b = −0.55769 + 1.30402I
−11.16480 + 6.01176I 0
u = −1.077470 − 0.067927I
a = −0.953464 + 0.030989I
b = −0.55769 − 1.30402I
−11.16480 − 6.01176I 0
u = 1.005540 + 0.481619I
a = −0.59169 + 1.64061I
b = −1.41901 + 0.72669I
−8.38626 + 0.32211I 0
u = 1.005540 − 0.481619I
a = −0.59169 − 1.64061I
b = −1.41901 − 0.72669I
−8.38626 − 0.32211I 0
u = 0.879956
a = −0.438903
b = 0.0434340
−1.41507 −6.32080
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.719693 + 0.498115I
a = −1.64541 − 0.16716I
b = −1.37251 + 0.55867I
2.04791 + 1.35241I 2.73599 − 3.49653I
u = −0.719693 − 0.498115I
a = −1.64541 + 0.16716I
b = −1.37251 − 0.55867I
2.04791 − 1.35241I 2.73599 + 3.49653I
u = 0.604923 + 0.586080I
a = −1.17479 − 2.59369I
b = 0.40029 − 1.92697I
−6.00205 + 6.09456I −5.95965 − 2.74749I
u = 0.604923 − 0.586080I
a = −1.17479 + 2.59369I
b = 0.40029 + 1.92697I
−6.00205 − 6.09456I −5.95965 + 2.74749I
u = 0.139683 + 0.824970I
a = 1.78560 + 1.23758I
b = 0.01328 + 1.71548I
−10.5541 + 11.1165I −9.09484 − 6.04502I
u = 0.139683 − 0.824970I
a = 1.78560 − 1.23758I
b = 0.01328 − 1.71548I
−10.5541 − 11.1165I −9.09484 + 6.04502I
u = 1.125280 + 0.324670I
a = 0.020945 + 1.149410I
b = −0.391515 + 0.232413I
−7.90994 + 0.10402I 0
u = 1.125280 − 0.324670I
a = 0.020945 − 1.149410I
b = −0.391515 − 0.232413I
−7.90994 − 0.10402I 0
u = 0.070097 + 0.824515I
a = −1.33999 − 0.65701I
b = 0.428690 − 0.050398I
−12.56960 − 1.39660I −11.14850 + 0.59888I
u = 0.070097 − 0.824515I
a = −1.33999 + 0.65701I
b = 0.428690 + 0.050398I
−12.56960 + 1.39660I −11.14850 − 0.59888I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.127151 + 0.808870I
a = −1.86816 − 1.03664I
b = −0.334206 − 1.268780I
−4.17538 + 6.91543I −6.85978 − 6.00800I
u = 0.127151 − 0.808870I
a = −1.86816 + 1.03664I
b = −0.334206 + 1.268780I
−4.17538 − 6.91543I −6.85978 + 6.00800I
u = −0.114199 + 0.807947I
a = −0.871998 − 0.500386I
b = −0.900709 + 1.046200I
−6.70509 − 4.38760I −8.59798 + 3.04801I
u = −0.114199 − 0.807947I
a = −0.871998 + 0.500386I
b = −0.900709 − 1.046200I
−6.70509 + 4.38760I −8.59798 − 3.04801I
u = 0.723406 + 0.376492I
a = −0.861306 − 0.408790I
b = −0.262843 + 0.271220I
−1.03887 − 1.52700I −7.90188 + 3.36186I
u = 0.723406 − 0.376492I
a = −0.861306 + 0.408790I
b = −0.262843 − 0.271220I
−1.03887 + 1.52700I −7.90188 − 3.36186I
u = 0.100576 + 0.799788I
a = 1.75921 + 0.69555I
b = 0.308103 + 0.514595I
−4.99438 + 1.66944I −8.98744 − 0.29481I
u = 0.100576 − 0.799788I
a = 1.75921 − 0.69555I
b = 0.308103 − 0.514595I
−4.99438 − 1.66944I −8.98744 + 0.29481I
u = 0.607539 + 0.524018I
a = 1.23393 + 1.85731I
b = 0.029011 + 1.174260I
0.07725 + 2.43549I −2.65496 − 3.04260I
u = 0.607539 − 0.524018I
a = 1.23393 − 1.85731I
b = 0.029011 − 1.174260I
0.07725 − 2.43549I −2.65496 + 3.04260I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.135680 + 0.431611I
a = −0.670399 − 0.816876I
b = −0.073487 − 0.404468I
−2.93289 − 1.90377I 0
u = 1.135680 − 0.431611I
a = −0.670399 + 0.816876I
b = −0.073487 + 0.404468I
−2.93289 + 1.90377I 0
u = −0.130036 + 0.763493I
a = 0.493983 + 0.363346I
b = 0.579994 − 0.453479I
−0.97886 − 3.00729I −0.67481 + 3.35384I
u = −0.130036 − 0.763493I
a = 0.493983 − 0.363346I
b = 0.579994 + 0.453479I
−0.97886 + 3.00729I −0.67481 − 3.35384I
u = −0.215646 + 0.736694I
a = 0.352487 − 1.192880I
b = −1.03050 − 0.98350I
−3.94866 − 3.37994I −8.08194 + 3.34507I
u = −0.215646 − 0.736694I
a = 0.352487 + 1.192880I
b = −1.03050 + 0.98350I
−3.94866 + 3.37994I −8.08194 − 3.34507I
u = −1.164480 + 0.443069I
a = −1.67272 + 1.68727I
b = −1.35179 + 2.31894I
−5.89254 + 3.02421I 0
u = −1.164480 − 0.443069I
a = −1.67272 − 1.68727I
b = −1.35179 − 2.31894I
−5.89254 − 3.02421I 0
u = −1.152870 + 0.481167I
a = 1.67874 − 0.72539I
b = 1.44055 − 1.35851I
−2.53850 + 6.10163I 0
u = −1.152870 − 0.481167I
a = 1.67874 + 0.72539I
b = 1.44055 + 1.35851I
−2.53850 − 6.10163I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.187870 + 0.391862I
a = 0.525322 − 0.087694I
b = 0.100629 + 0.162477I
−4.81156 − 0.89382I 0
u = 1.187870 − 0.391862I
a = 0.525322 + 0.087694I
b = 0.100629 − 0.162477I
−4.81156 + 0.89382I 0
u = 1.168200 + 0.464328I
a = 1.191870 + 0.076057I
b = 0.573207 − 0.271189I
−5.73526 − 5.29132I 0
u = 1.168200 − 0.464328I
a = 1.191870 − 0.076057I
b = 0.573207 + 0.271189I
−5.73526 + 5.29132I 0
u = −1.152500 + 0.516337I
a = −1.97753 − 0.61750I
b = −2.17920 + 0.19476I
−6.67800 + 8.09306I 0
u = −1.152500 − 0.516337I
a = −1.97753 + 0.61750I
b = −2.17920 − 0.19476I
−6.67800 − 8.09306I 0
u = −0.562722 + 0.472511I
a = 2.45276 − 0.28330I
b = 1.55804 − 1.30677I
−2.32225 − 0.35809I −4.17047 − 0.36662I
u = −0.562722 − 0.472511I
a = 2.45276 + 0.28330I
b = 1.55804 + 1.30677I
−2.32225 + 0.35809I −4.17047 + 0.36662I
u = 0.412453 + 0.601624I
a = −0.48507 + 1.52625I
b = −1.61234 − 0.03779I
−6.69419 − 4.61561I −6.55496 + 3.28166I
u = 0.412453 − 0.601624I
a = −0.48507 − 1.52625I
b = −1.61234 + 0.03779I
−6.69419 + 4.61561I −6.55496 − 3.28166I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.215530 + 0.385915I
a = −1.247140 − 0.594809I
b = −0.68781 − 1.42794I
−8.20441 − 2.85842I 0
u = −1.215530 − 0.385915I
a = −1.247140 + 0.594809I
b = −0.68781 + 1.42794I
−8.20441 + 2.85842I 0
u = −1.213090 + 0.402391I
a = 0.473702 + 1.098800I
b = 0.19789 + 2.00303I
−8.89812 + 2.46893I 0
u = −1.213090 − 0.402391I
a = 0.473702 − 1.098800I
b = 0.19789 − 2.00303I
−8.89812 − 2.46893I 0
u = 1.216380 + 0.393944I
a = −1.033210 − 0.020800I
b = −0.130043 − 0.454382I
−10.68610 + 0.27825I 0
u = 1.216380 − 0.393944I
a = −1.033210 + 0.020800I
b = −0.130043 + 0.454382I
−10.68610 − 0.27825I 0
u = −1.224970 + 0.375819I
a = 1.393900 − 0.060385I
b = 0.596587 + 0.850691I
−14.7005 − 7.0565I 0
u = −1.224970 − 0.375819I
a = 1.393900 + 0.060385I
b = 0.596587 − 0.850691I
−14.7005 + 7.0565I 0
u = −1.181940 + 0.500743I
a = −0.141013 + 1.164390I
b = 0.368653 + 1.242040I
−4.04107 + 7.69031I 0
u = −1.181940 − 0.500743I
a = −0.141013 − 1.164390I
b = 0.368653 − 1.242040I
−4.04107 − 7.69031I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.226870 + 0.418077I
a = 0.400302 − 0.686102I
b = 0.48325 − 1.89392I
−16.4614 + 5.7289I 0
u = −1.226870 − 0.418077I
a = 0.400302 + 0.686102I
b = 0.48325 + 1.89392I
−16.4614 − 5.7289I 0
u = 1.199340 + 0.497123I
a = −1.04238 − 1.40168I
b = −1.37797 − 2.26390I
−8.22467 − 6.41149I 0
u = 1.199340 − 0.497123I
a = −1.04238 + 1.40168I
b = −1.37797 + 2.26390I
−8.22467 + 6.41149I 0
u = −1.200190 + 0.503588I
a = 0.43227 − 2.01242I
b = −0.52934 − 2.23286I
−9.90785 + 9.18672I 0
u = −1.200190 − 0.503588I
a = 0.43227 + 2.01242I
b = −0.52934 + 2.23286I
−9.90785 − 9.18672I 0
u = 1.198080 + 0.508599I
a = 1.91009 + 1.81162I
b = 1.99721 + 2.79861I
−7.33563 − 11.74480I 0
u = 1.198080 − 0.508599I
a = 1.91009 − 1.81162I
b = 1.99721 − 2.79861I
−7.33563 + 11.74480I 0
u = 1.201410 + 0.516744I
a = −2.54195 − 1.66813I
b = −2.50275 − 2.84833I
−13.7024 − 16.0279I 0
u = 1.201410 − 0.516744I
a = −2.54195 + 1.66813I
b = −2.50275 + 2.84833I
−13.7024 + 16.0279I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.214120 + 0.487768I
a = 0.960915 + 0.219353I
b = 1.64886 + 1.19641I
−15.9643 − 3.3550I 0
u = 1.214120 − 0.487768I
a = 0.960915 − 0.219353I
b = 1.64886 − 1.19641I
−15.9643 + 3.3550I 0
u = 0.045537 + 0.676922I
a = 1.077040 − 0.256080I
b = 0.256695 − 1.092910I
−2.59868 + 1.01996I −7.42495 + 0.64864I
u = 0.045537 − 0.676922I
a = 1.077040 + 0.256080I
b = 0.256695 + 1.092910I
−2.59868 − 1.01996I −7.42495 − 0.64864I
u = −0.143647 + 0.650890I
a = −0.915631 + 0.433122I
b = 0.091936 + 0.985043I
0.32466 − 1.74343I −0.09678 + 4.11913I
u = −0.143647 − 0.650890I
a = −0.915631 − 0.433122I
b = 0.091936 − 0.985043I
0.32466 + 1.74343I −0.09678 − 4.11913I
u = 0.379396 + 0.460960I
a = −0.230295 − 1.120240I
b = 0.664172 + 0.181918I
−0.53005 − 1.55644I −3.23373 + 4.26726I
u = 0.379396 − 0.460960I
a = −0.230295 + 1.120240I
b = 0.664172 − 0.181918I
−0.53005 + 1.55644I −3.23373 − 4.26726I
u = −0.557461
a = 2.83655
b = 1.80666
−2.28508 −1.20430
13
II. I
u
2
= hu
8
+ u
7
− 2u
6
− 2u
5
+ u
4
+ u
3
+ u
2
+ b + u, u
8
+ u
7
− 2u
6
− 2u
5
+
u
4
+ u
3
+ u
2
+ a + u, u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
1
=
−u
2
+ 1
−u
4
a
7
=
u
5
− 2u
3
+ u
u
7
− u
5
+ u
a
5
=
u
u
a
8
=
u
8
− 3u
6
+ 3u
4
− 1
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u
3
− 1
a
10
=
−u
8
− u
7
+ 2u
6
+ 2u
5
− u
4
− u
3
− u
2
− u
−u
8
− u
7
+ 2u
6
+ 2u
5
− u
4
− u
3
− u
2
− u
a
4
=
u
u
a
11
=
−u
8
− u
7
+ 2u
6
+ 2u
5
− u
4
− u
3
− u
2
− u
−u
8
− u
7
+ 2u
6
+ 2u
5
− u
4
− u
3
− u
2
− u
a
12
=
−u
8
+ 3u
6
− 3u
4
+ 1
−u
8
− u
7
+ 3u
6
+ 2u
5
− 3u
4
− 2u
3
+ 1
a
9
=
−u
7
− u
6
+ 2u
5
+ 2u
4
− u
3
− u
2
− u − 1
−u
6
+ 2u
4
+ u
3
− u
2
− u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
8
− 6u
7
+ u
6
+ 12u
5
+ 5u
4
− 10u
3
− 7u
2
− 7u − 6
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
2
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
3
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
4
, c
10
u
9
c
5
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
6
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
7
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
8
, c
9
(u − 1)
9
c
11
(u + 1)
9
c
12
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
2
, c
5
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
3
, c
7
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
4
, c
10
y
9
c
6
, c
12
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
8
, c
9
, c
11
(y −1)
9
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.772920 + 0.510351I
a = 0.630598 + 0.707882I
b = 0.630598 + 0.707882I
0.13850 + 2.09337I −1.56547 − 4.18932I
u = −0.772920 − 0.510351I
a = 0.630598 − 0.707882I
b = 0.630598 − 0.707882I
0.13850 − 2.09337I −1.56547 + 4.18932I
u = 0.825933
a = −1.61202
b = −1.61202
−2.84338 −16.7240
u = 1.173910 + 0.391555I
a = 0.552775 + 1.001020I
b = 0.552775 + 1.001020I
−6.01628 − 1.33617I −11.45029 + 1.01794I
u = 1.173910 − 0.391555I
a = 0.552775 − 1.001020I
b = 0.552775 − 1.001020I
−6.01628 + 1.33617I −11.45029 − 1.01794I
u = −0.141484 + 0.739668I
a = −0.481040 − 0.507127I
b = −0.481040 − 0.507127I
−2.26187 − 2.45442I −5.68179 + 2.62939I
u = −0.141484 − 0.739668I
a = −0.481040 + 0.507127I
b = −0.481040 + 0.507127I
−2.26187 + 2.45442I −5.68179 − 2.62939I
u = −1.172470 + 0.500383I
a = −0.896321 − 0.526299I
b = −0.896321 − 0.526299I
−5.24306 + 7.08493I −8.94033 − 5.11095I
u = −1.172470 − 0.500383I
a = −0.896321 + 0.526299I
b = −0.896321 + 0.526299I
−5.24306 − 7.08493I −8.94033 + 5.11095I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
89
+ 48u
88
+ ··· + 5u + 1)
c
2
(u
9
+ u
8
+ ··· − u − 1)(u
89
+ 2u
88
+ ··· − 3u − 1)
c
3
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
89
+ 2u
88
+ ··· − 65179u − 27289)
c
4
, c
10
u
9
(u
89
+ u
88
+ ··· − 1024u − 512)
c
5
(u
9
− u
8
+ ··· − u + 1)(u
89
+ 2u
88
+ ··· − 3u − 1)
c
6
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
89
+ 6u
88
+ ··· + 11u + 1)
c
7
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
89
− 12u
88
+ ··· − 4727u + 841)
c
8
, c
9
((u − 1)
9
)(u
89
− 10u
88
+ ··· + 9u − 1)
c
11
((u + 1)
9
)(u
89
− 10u
88
+ ··· + 9u − 1)
c
12
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
89
+ 6u
88
+ ··· + 11u + 1)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
89
− 12y
88
+ ··· + 13y −1)
c
2
, c
5
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
89
− 48y
88
+ ··· + 5y −1)
c
3
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
89
− 48y
88
+ ··· + 8750550417y −744689521)
c
4
, c
10
y
9
(y
89
+ 57y
88
+ ··· − 262144y −262144)
c
6
, c
12
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
89
+ 72y
88
+ ··· + 173y −1)
c
7
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
89
− 12y
88
+ ··· + 56852441y −707281)
c
8
, c
9
, c
11
((y −1)
9
)(y
89
− 88y
88
+ ··· + 17y −1)
19
