12n
0692
(K12n
0692
)
A knot diagram
1
Linearized knot diagam
4 5 8 2 9 11 3 6 12 5 8 10
Solving Sequence
6,11 3,7
8 9 12 5 2 4 1 10
c
6
c
7
c
8
c
11
c
5
c
2
c
4
c
1
c
10
c
3
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h95253872184u
16
+ 167486372440u
15
+ ··· + 176471185595b + 60442442928,
− 241873986280u
16
− 181431543352u
15
+ ··· + 176471185595a + 1319914649856,
u
17
+ u
16
+ ··· − u − 1i
I
u
2
= hu
6
− u
4
+ u
2
+ b + u, u
7
− u
6
− u
5
+ 3u
4
+ u
3
− 3u
2
+ a + 3, u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1i
I
u
3
= h4.46740 × 10
15
u
15
+ 6.27459 × 10
15
u
14
+ ··· + 2.01298 × 10
18
b − 8.81526 × 10
16
,
2.12213 × 10
16
u
15
+ 2.28177 × 10
16
u
14
+ ··· + 4.02597 × 10
18
a − 9.94872 × 10
18
,
u
16
+ u
15
+ ··· − 640u + 256i
I
v
1
= ha, 941v
7
+ 2551v
6
+ 1791v
5
− 6184v
4
− 16309v
3
+ 15249v
2
+ 887b + 4192v −1842,
v
8
+ 2v
7
− 8v
5
− 13v
4
+ 28v
3
− 7v
2
− 3v + 1i
* 4 irreducible components of dim
C
= 0, with total 49 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
= h9.53×10
10
u
16
+1.67×10
11
u
15
+· · ·+1.76×10
11
b+6.04×10
10
, −2.42×
10
11
u
16
−1.81×10
11
u
15
+· · ·+1.76×10
11
a+1.32×10
12
, u
17
+u
16
+· · ·−u−1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
1.37061u
16
+ 1.02811u
15
+ ··· + 7.62117u − 7.47949
−0.539770u
16
− 0.949086u
15
+ ··· + 0.0281086u − 0.342506
a
7
=
1
u
2
a
8
=
0.342506u
16
+ 0.882276u
15
+ ··· + 6.10888u − 0.370615
0.409316u
16
+ 0.397625u
15
+ ··· + 0.882276u + 0.539770
a
9
=
−0.0668101u
16
+ 0.484651u
15
+ ··· + 5.22660u − 0.910385
0.409316u
16
+ 0.397625u
15
+ ··· + 0.882276u + 0.539770
a
12
=
1.08601u
16
+ 0.931667u
15
+ ··· − 6.04983u − 0.704908
−0.202045u
16
− 0.0982208u
15
+ ··· + 0.982581u − 0.563663
a
5
=
−0.380139u
16
− 0.473041u
15
+ ··· + 0.662163u + 1.73660
−0.183525u
16
− 0.292667u
15
+ ··· − 1.16333u − 0.190353
a
2
=
2.20774u
16
+ 2.09139u
15
+ ··· + 8.45012u − 9.06872
−0.720687u
16
− 0.896329u
15
+ ··· + 0.887039u − 0.0425575
a
4
=
1.91038u
16
+ 1.97719u
15
+ ··· + 7.59306u − 7.13699
−0.551461u
16
− 0.673429u
15
+ ··· + 0.977195u + 0.0668101
a
1
=
0.301587u
16
+ 0.217988u
15
+ ··· + 3.13092u − 1.78891
−0.287349u
16
− 0.365150u
15
+ ··· − 0.397625u + 0.0116913
a
10
=
1.19077u
16
+ 1.37427u
15
+ ··· − 1.38476u − 1.92738
−0.0505037u
16
+ 0.0449819u
15
+ ··· + 1.51534u − 0.116444
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
2048919230872
176471185595
u
16
+
1391303845096
176471185595
u
15
+ ··· +
3163149744064
176471185595
u −
6932356318654
176471185595
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
9
, c
12
u
17
− 7u
16
+ ··· − 5u − 1
c
3
, c
6
, c
7
u
17
− u
16
+ ··· − u + 1
c
5
, c
8
u
17
− u
16
+ ··· + 3u − 1
c
10
u
17
+ u
16
+ ··· − 699u + 199
c
11
u
17
+ 3u
16
+ ··· − 263u − 83
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
9
, c
12
y
17
− 13y
16
+ ··· + 21y −1
c
3
, c
6
, c
7
y
17
+ 15y
16
+ ··· + 13y −1
c
5
, c
8
y
17
+ 11y
16
+ ··· + 25y −1
c
10
y
17
+ 27y
16
+ ··· + 947097y −39601
c
11
y
17
+ 7y
16
+ ··· + 91413y −6889
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.764077 + 0.442209I
a = −0.0395160 − 0.1081060I
b = −0.706366 − 0.510886I
−4.55533 − 6.93072I −21.1582 + 11.9778I
u = 0.764077 − 0.442209I
a = −0.0395160 + 0.1081060I
b = −0.706366 + 0.510886I
−4.55533 + 6.93072I −21.1582 − 11.9778I
u = −0.791671
a = 0.0812804
b = 0.842612
−8.70952 −30.7710
u = 0.753921 + 0.115715I
a = 2.02750 − 2.62203I
b = 0.82885 − 1.21720I
−0.77832 + 2.01331I −15.1488 − 1.3786I
u = 0.753921 − 0.115715I
a = 2.02750 + 2.62203I
b = 0.82885 + 1.21720I
−0.77832 − 2.01331I −15.1488 + 1.3786I
u = −0.502094 + 0.490826I
a = −0.001938 + 0.710947I
b = 0.852485 − 0.481916I
2.49540 + 2.02523I −6.20824 − 3.33819I
u = −0.502094 − 0.490826I
a = −0.001938 − 0.710947I
b = 0.852485 + 0.481916I
2.49540 − 2.02523I −6.20824 + 3.33819I
u = −0.291694 + 0.477697I
a = −2.80059 − 7.96264I
b = −1.52657 + 1.44231I
−2.45442 − 0.76114I −1.7282 − 15.9915I
u = −0.291694 − 0.477697I
a = −2.80059 + 7.96264I
b = −1.52657 − 1.44231I
−2.45442 + 0.76114I −1.7282 + 15.9915I
u = 0.439135
a = 0.660014
b = −0.311858
−0.644803 −15.2830
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.432752
a = −7.32022
b = −0.938137
−2.91990 −47.5300
u = −0.78485 + 1.87131I
a = −0.389251 − 0.738414I
b = −0.26086 + 1.40299I
11.20130 + 3.50827I −11.32341 − 1.79574I
u = −0.78485 − 1.87131I
a = −0.389251 + 0.738414I
b = −0.26086 − 1.40299I
11.20130 − 3.50827I −11.32341 + 1.79574I
u = 0.93651 + 1.91501I
a = 0.311529 − 0.816594I
b = 1.12325 + 1.48088I
6.80306 − 8.74093I −14.7558 + 4.0661I
u = 0.93651 − 1.91501I
a = 0.311529 + 0.816594I
b = 1.12325 − 1.48088I
6.80306 + 8.74093I −14.7558 − 4.0661I
u = −0.98322 + 2.02620I
a = −0.318282 − 0.900844I
b = −1.60710 + 2.06949I
10.6972 + 14.1953I −12.00000 − 6.60789I
u = −0.98322 − 2.02620I
a = −0.318282 + 0.900844I
b = −1.60710 − 2.06949I
10.6972 − 14.1953I −12.00000 + 6.60789I
6
II. I
u
2
= hu
6
− u
4
+ u
2
+ b + u, u
7
− u
6
− u
5
+ 3u
4
+ u
3
− 3u
2
+ a + 3, u
8
−
u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
−u
7
+ u
6
+ u
5
− 3u
4
− u
3
+ 3u
2
− 3
−u
6
+ u
4
− u
2
− u
a
7
=
1
u
2
a
8
=
1
u
2
a
9
=
−u
2
+ 1
u
2
a
12
=
−u
−u
3
+ u
a
5
=
u
4
− u
2
+ 1
−u
4
a
2
=
−u
7
+ u
6
+ u
5
− 4u
4
− u
3
+ 4u
2
− 4
−u
6
+ 2u
4
− u
2
− u
a
4
=
−u
7
+ u
6
+ u
5
− 3u
4
− u
3
+ 3u
2
− 3
−u
6
+ u
4
− u
2
− u
a
1
=
−u
4
+ u
2
− 1
u
4
a
10
=
−u
6
+ u
4
− 2u
2
+ 1
−u
7
+ u
6
+ 2u
5
− u
4
− 2u
3
+ 2u
2
+ 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
7
− 4u
6
− 2u
5
+ 5u
4
+ 3u
3
− 5u
2
− 5u − 10
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
, c
7
u
8
c
4
(u + 1)
8
c
5
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
c
6
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
8
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
9
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
10
, c
12
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
c
11
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
8
c
3
, c
7
y
8
c
5
, c
8
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
6
, c
11
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
c
9
, c
10
, c
12
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.570868 + 0.730671I
a = −1.21928 + 2.03110I
b = −1.44082 − 1.43962I
−2.68559 + 1.13123I −18.1377 − 5.3065I
u = 0.570868 − 0.730671I
a = −1.21928 − 2.03110I
b = −1.44082 + 1.43962I
−2.68559 − 1.13123I −18.1377 + 5.3065I
u = −0.855237 + 0.665892I
a = 1.230330 + 0.083902I
b = 0.44992 − 1.37717I
0.51448 + 2.57849I −10.11893 − 3.45077I
u = −0.855237 − 0.665892I
a = 1.230330 − 0.083902I
b = 0.44992 + 1.37717I
0.51448 − 2.57849I −10.11893 + 3.45077I
u = −1.09818
a = −0.337834
b = −0.407427
−8.14766 −12.9880
u = 1.031810 + 0.655470I
a = 0.370895 + 0.073482I
b = 0.136119 + 0.548347I
−4.02461 − 6.44354I −10.82984 + 2.68172I
u = 1.031810 − 0.655470I
a = 0.370895 − 0.073482I
b = 0.136119 − 0.548347I
−4.02461 + 6.44354I −10.82984 − 2.68172I
u = 0.603304
a = −2.42604
b = −0.883019
−2.48997 −13.8390
10
III. I
u
3
=
h4.47×10
15
u
15
+6.27×10
15
u
14
+· · ·+2.01×10
18
b−8.82×10
16
, 2.12×10
16
u
15
+
2.28 × 10
16
u
14
+ · · · + 4.03 × 10
18
a − 9.95 × 10
18
, u
16
+ u
15
+ · · · − 640u + 256i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
−0.00527110u
15
− 0.00566765u
14
+ ··· − 9.23744u + 2.47114
−0.00221929u
15
− 0.00311706u
14
+ ··· − 1.87927u + 0.0437920
a
7
=
1
u
2
a
8
=
0.00131807u
15
− 0.000965283u
14
+ ··· + 5.02090u − 2.85900
0.00125266u
15
+ 0.00142411u
14
+ ··· + 2.92217u − 0.895088
a
9
=
0.0000654109u
15
− 0.00238940u
14
+ ··· + 2.09873u − 1.96392
0.00125266u
15
+ 0.00142411u
14
+ ··· + 2.92217u − 0.895088
a
12
=
0.000844467u
15
− 0.00179388u
14
+ ··· + 1.76050u − 2.43832
0.000597578u
15
+ 0.000131722u
14
+ ··· + 3.26843u − 1.14785
a
5
=
0.00355246u
15
+ 0.00420683u
14
+ ··· + 4.56085u + 0.0559940
0.000931308u
15
+ 0.000874523u
14
+ ··· + 1.47705u + 0.342822
a
2
=
−0.00941161u
15
− 0.0110390u
14
+ ··· − 13.9929u + 1.68523
−0.00326781u
15
− 0.00500207u
14
+ ··· − 3.20051u − 0.587143
a
4
=
−0.00749346u
15
− 0.00988307u
14
+ ··· − 11.5790u + 0.607025
−0.00129900u
15
− 0.00377384u
14
+ ··· − 0.399220u − 1.24590
a
1
=
−0.00155963u
15
+ 0.00229520u
14
+ ··· − 2.60619u + 2.70441
−0.00272297u
15
− 0.00333262u
14
+ ··· − 4.50999u + 1.52352
a
10
=
−0.0000400338u
15
− 0.00236158u
14
+ ··· + 0.837916u − 1.48462
0.000345643u
15
− 0.00112847u
14
+ ··· + 1.97094u − 0.673787
(ii) Obstruction class = −1
(iii) Cusp Shapes =
−
4129940980039711
1006491371550221696
u
15
−
3800282985571637
1006491371550221696
u
14
+···−
45304359399533900
7863213840236107
u−
73541352487366340
7863213840236107
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
9
, c
12
u
16
− 3u
15
+ ··· − 8u + 1
c
3
, c
6
, c
7
u
16
− u
15
+ ··· + 640u + 256
c
5
, c
8
(u
8
− u
7
+ 3u
6
− 2u
5
+ 3u
4
− 2u
3
− 1)
2
c
10
u
16
+ 3u
15
+ ··· + 2169u + 361
c
11
u
16
− 4u
15
+ ··· − 189u + 297
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
9
, c
12
y
16
+ 9y
15
+ ··· + 4y + 1
c
3
, c
6
, c
7
y
16
+ 33y
15
+ ··· + 606208y + 65536
c
5
, c
8
(y
8
+ 5y
7
+ 11y
6
+ 10y
5
− y
4
− 10y
3
− 6y
2
+ 1)
2
c
10
y
16
+ 31y
15
+ ··· − 741503y + 130321
c
11
y
16
+ 32y
15
+ ··· + 78327y + 88209
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.928106 + 0.575657I
a = 0.314063 − 0.194797I
b = −0.553504 + 0.808003I
−0.290648 −13.26997 + 0.I
u = 0.928106 − 0.575657I
a = 0.314063 + 0.194797I
b = −0.553504 − 0.808003I
−0.290648 −13.26997 + 0.I
u = 0.684023 + 0.882805I
a = 0.471554 − 0.908141I
b = 0.796152 + 0.451692I
−1.15366 + 1.27532I −10.53127 − 1.72199I
u = 0.684023 − 0.882805I
a = 0.471554 + 0.908141I
b = 0.796152 − 0.451692I
−1.15366 − 1.27532I −10.53127 + 1.72199I
u = −0.577755 + 0.986475I
a = 0.367269 − 0.263106I
b = 1.083960 + 0.732960I
2.70026 − 3.63283I −9.34305 + 4.59352I
u = −0.577755 − 0.986475I
a = 0.367269 + 0.263106I
b = 1.083960 − 0.732960I
2.70026 + 3.63283I −9.34305 − 4.59352I
u = 0.153757 + 0.400659I
a = 0.49286 − 2.61690I
b = −0.429065 − 0.463862I
−1.15366 + 1.27532I −10.53127 − 1.72199I
u = 0.153757 − 0.400659I
a = 0.49286 + 2.61690I
b = −0.429065 + 0.463862I
−1.15366 − 1.27532I −10.53127 + 1.72199I
u = −1.61868 + 0.98339I
a = −0.162363 + 0.219097I
b = 1.00687 + 1.86555I
2.70026 + 3.63283I −9.34305 − 4.59352I
u = −1.61868 − 0.98339I
a = −0.162363 − 0.219097I
b = 1.00687 − 1.86555I
2.70026 − 3.63283I −9.34305 + 4.59352I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.05666 + 2.24811I
a = −0.079508 + 0.874899I
b = 0.48785 − 1.75982I
12.42750 + 4.93524I −10.31351 − 3.19667I
u = −0.05666 − 2.24811I
a = −0.079508 − 0.874899I
b = 0.48785 + 1.75982I
12.42750 − 4.93524I −10.31351 + 3.19667I
u = −0.14941 + 2.37106I
a = 0.048233 + 0.765446I
b = 0.42164 − 1.94931I
8.53095 −13.35437 + 0.I
u = −0.14941 − 2.37106I
a = 0.048233 − 0.765446I
b = 0.42164 + 1.94931I
8.53095 −13.35437 + 0.I
u = 0.13661 + 2.63887I
a = 0.047894 + 0.746119I
b = −0.81390 − 2.89913I
12.42750 − 4.93524I −10.31351 + 3.19667I
u = 0.13661 − 2.63887I
a = 0.047894 − 0.746119I
b = −0.81390 + 2.89913I
12.42750 + 4.93524I −10.31351 − 3.19667I
15
IV. I
v
1
=
ha, 941v
7
+2551v
6
+· · ·+887b−1842, v
8
+2v
7
−8v
5
−13v
4
+28v
3
−7v
2
−3v+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
v
0
a
3
=
0
−1.06088v
7
− 2.87599v
6
+ ··· − 4.72604v + 2.07666
a
7
=
1
0
a
8
=
1
1.62683v
7
+ 3.57497v
6
+ ··· + 1.17926v −3.82638
a
9
=
−1.62683v
7
− 3.57497v
6
+ ··· − 1.17926v + 4.82638
1.62683v
7
+ 3.57497v
6
+ ··· + 1.17926v −3.82638
a
12
=
0.321308v
7
+ 0.456595v
6
+ ··· + 2.05411v −1.62683
0.568207v
7
+ 1.17587v
6
+ ··· + 0.443067v −2.38219
a
5
=
0.755355v
7
+ 1.75761v
6
+ ··· − 2.39910v −1.87711
−2.38219v
7
− 5.33258v
6
+ ··· + 1.21984v + 6.70349
a
2
=
0.244645v
7
+ 0.242390v
6
+ ··· − 4.60090v −1.12289
−3.44419v
7
− 7.94701v
6
+ ··· − 1.00113v + 9.59639
a
4
=
1.06088v
7
+ 2.87599v
6
+ ··· + 4.72604v −2.07666
1.57046v
7
+ 3.65276v
6
+ ··· + 0.432920v −5.01466
a
1
=
1.62683v
7
+ 3.57497v
6
+ ··· + 1.17926v −4.82638
−1.62683v
7
− 3.57497v
6
+ ··· − 1.17926v + 3.82638
a
10
=
−1.30552v
7
− 3.11838v
6
+ ··· + 0.874859v + 3.19955
2.19504v
7
+ 4.75085v
6
+ ··· + 1.62232v −6.20857
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
2247
887
v
7
+
4687
887
v
6
−
426
887
v
5
−
21184
887
v
4
−
35807
887
v
3
+
61378
887
v
2
+
5411
887
v −
17810
887
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
3
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
4
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
c
5
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
c
6
u
8
c
7
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1
c
8
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
9
(u − 1)
8
c
10
u
8
− 2u
7
− u
6
+ 5u
5
+ 4u
4
− 17u
3
+ 17u
2
− 7u + 1
c
11
u
8
+ 3u
7
+ 6u
6
+ 7u
5
+ 13u
4
+ 11u
3
+ 4u
2
+ 3u + 1
c
12
(u + 1)
8
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
c
3
, c
7
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
c
5
, c
8
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
6
y
8
c
9
, c
12
(y −1)
8
c
10
y
8
− 6y
7
+ 29y
6
− 67y
5
+ 126y
4
− 85y
3
+ 59y
2
− 15y + 1
c
11
y
8
+ 3y
7
+ 20y
6
+ 49y
5
+ 47y
4
− 47y
3
− 24y
2
− y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.230330 + 0.083902I
a = 0
b = 0.855237 − 0.665892I
0.51448 + 2.57849I −10.11893 − 3.45077I
v = 1.230330 − 0.083902I
a = 0
b = 0.855237 + 0.665892I
0.51448 − 2.57849I −10.11893 + 3.45077I
v = 0.370895 + 0.073482I
a = 0
b = −1.031810 − 0.655470I
−4.02461 − 6.44354I −10.82984 + 2.68172I
v = 0.370895 − 0.073482I
a = 0
b = −1.031810 + 0.655470I
−4.02461 + 6.44354I −10.82984 − 2.68172I
v = −0.337834
a = 0
b = 1.09818
−8.14766 −12.9880
v = −1.21928 + 2.03110I
a = 0
b = −0.570868 − 0.730671I
−2.68559 + 1.13123I −18.1377 − 5.3065I
v = −1.21928 − 2.03110I
a = 0
b = −0.570868 + 0.730671I
−2.68559 − 1.13123I −18.1377 + 5.3065I
v = −2.42604
a = 0
b = −0.603304
−2.48997 −13.8390
19
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
9
((u − 1)
8
)(u
8
+ u
7
+ ··· + 2u − 1)(u
16
− 3u
15
+ ··· − 8u + 1)
· (u
17
− 7u
16
+ ··· − 5u − 1)
c
3
, c
6
u
8
(u
8
− u
7
+ ··· + 2u − 1)(u
16
− u
15
+ ··· + 640u + 256)
· (u
17
− u
16
+ ··· − u + 1)
c
4
, c
12
((u + 1)
8
)(u
8
− u
7
+ ··· − 2u − 1)(u
16
− 3u
15
+ ··· − 8u + 1)
· (u
17
− 7u
16
+ ··· − 5u − 1)
c
5
(u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
2
· ((u
8
− u
7
+ ··· − 2u
3
− 1)
2
)(u
17
− u
16
+ ··· + 3u − 1)
c
7
u
8
(u
8
+ u
7
+ ··· − 2u − 1)(u
16
− u
15
+ ··· + 640u + 256)
· (u
17
− u
16
+ ··· − u + 1)
c
8
(u
8
− u
7
+ 3u
6
− 2u
5
+ 3u
4
− 2u
3
− 1)
2
· (u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
2
· (u
17
− u
16
+ ··· + 3u − 1)
c
10
(u
8
− 2u
7
− u
6
+ 5u
5
+ 4u
4
− 17u
3
+ 17u
2
− 7u + 1)
· (u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)(u
16
+ 3u
15
+ ··· + 2169u + 361)
· (u
17
+ u
16
+ ··· − 699u + 199)
c
11
(u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1)
· (u
8
+ 3u
7
+ 6u
6
+ 7u
5
+ 13u
4
+ 11u
3
+ 4u
2
+ 3u + 1)
· (u
16
− 4u
15
+ ··· − 189u + 297)(u
17
+ 3u
16
+ ··· − 263u − 83)
20
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
9
, c
12
(y −1)
8
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
16
+ 9y
15
+ ··· + 4y + 1)(y
17
− 13y
16
+ ··· + 21y −1)
c
3
, c
6
, c
7
y
8
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
16
+ 33y
15
+ ··· + 606208y + 65536)(y
17
+ 15y
16
+ ··· + 13y −1)
c
5
, c
8
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
2
· (y
8
+ 5y
7
+ 11y
6
+ 10y
5
− y
4
− 10y
3
− 6y
2
+ 1)
2
· (y
17
+ 11y
16
+ ··· + 25y −1)
c
10
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
8
− 6y
7
+ 29y
6
− 67y
5
+ 126y
4
− 85y
3
+ 59y
2
− 15y + 1)
· (y
16
+ 31y
15
+ ··· − 741503y + 130321)
· (y
17
+ 27y
16
+ ··· + 947097y −39601)
c
11
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
8
+ 3y
7
+ 20y
6
+ 49y
5
+ 47y
4
− 47y
3
− 24y
2
− y + 1)
· (y
16
+ 32y
15
+ ··· + 78327y + 88209)
· (y
17
+ 7y
16
+ ··· + 91413y −6889)
21
