12n
0713
(K12n
0713
)
A knot diagram
1
Linearized knot diagam
4 11 7 9 11 2 12 1 2 7 5 8
Solving Sequence
2,11 3,7
4 1 6 5 12 10 9 8
c
2
c
3
c
1
c
6
c
5
c
11
c
10
c
9
c
8
c
4
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h2.57826 × 10
217
u
63
− 3.05321 × 10
217
u
62
+ ··· + 2.05878 × 10
220
b − 1.16715 × 10
221
,
1.17201 × 10
218
u
63
+ 2.06381 × 10
219
u
62
+ ··· + 8.44100 × 10
221
a + 2.64039 × 10
222
,
u
64
+ 38u
62
+ ··· − 3396u + 328i
I
u
2
= h−363987470832210u
18
+ 225606528026540u
17
+ ··· + 4316043181765921b − 66280635064865,
7.51222 × 10
15
u
18
− 5.60654 × 10
15
u
17
+ ··· + 3.88444 × 10
16
a + 1.80154 × 10
16
, u
19
− u
18
+ ··· + 5u − 9i
* 2 irreducible components of dim
C
= 0, with total 83 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
= h2.58 × 10
217
u
63
− 3.05 × 10
217
u
62
+ · · · + 2.06 × 10
220
b − 1.17 ×
10
221
, 1.17 × 10
218
u
63
+ 2.06 × 10
219
u
62
+ · · · + 8.44 × 10
221
a + 2.64 ×
10
222
, u
64
+ 38u
62
+ · · · − 3396u + 328i
(i) Arc colorings
a
2
=
1
0
a
11
=
0
u
a
3
=
1
u
2
a
7
=
−0.000138847u
63
− 0.00244499u
62
+ ··· + 21.3318u − 3.12805
−0.00125233u
63
+ 0.00148302u
62
+ ··· − 41.5747u + 5.66913
a
4
=
−0.00791855u
63
+ 0.00212409u
62
+ ··· − 118.662u + 14.1417
−0.00457474u
63
− 0.000971202u
62
+ ··· − 26.4167u + 2.01978
a
1
=
−0.0135367u
63
− 0.00367954u
62
+ ··· − 88.7259u + 10.0079
−0.00159543u
63
− 0.00175310u
62
+ ··· + 22.4981u − 3.38442
a
6
=
−0.00139117u
63
− 0.000961969u
62
+ ··· − 20.2429u + 2.54108
−0.00125233u
63
+ 0.00148302u
62
+ ··· − 41.5747u + 5.66913
a
5
=
−0.00139117u
63
− 0.000961969u
62
+ ··· − 20.2429u + 2.54108
−0.00238057u
63
+ 0.000801163u
62
+ ··· − 44.3852u + 5.98465
a
12
=
0.0251528u
63
+ 0.00622070u
62
+ ··· + 174.801u − 20.8026
0.000927416u
63
+ 0.000804470u
62
+ ··· − 5.52337u + 0.525490
a
10
=
−0.0230195u
63
− 0.00337024u
62
+ ··· − 204.054u + 24.8603
−0.00135242u
63
− 0.00130024u
62
+ ··· + 10.8548u − 1.49184
a
9
=
−0.0243719u
63
− 0.00467049u
62
+ ··· − 193.200u + 23.3684
−0.00135242u
63
− 0.00130024u
62
+ ··· + 10.8548u − 1.49184
a
8
=
−0.0159602u
63
− 0.00446479u
62
+ ··· − 111.349u + 13.1348
−0.000210627u
63
+ 0.000910006u
62
+ ··· − 23.7656u + 3.66319
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0161918u
63
− 0.00558987u
62
+ ··· + 220.422u − 20.8374
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
64
− 7u
63
+ ··· − 2062u + 473
c
2
u
64
+ 38u
62
+ ··· + 3396u + 328
c
3
u
64
− 3u
63
+ ··· − 1741810u − 196291
c
4
u
64
+ 3u
63
+ ··· − 160u − 64
c
5
, c
11
u
64
+ 13u
62
+ ··· − 400u + 44
c
6
u
64
+ u
63
+ ··· + 6587u + 761
c
7
, c
8
, c
12
u
64
+ 2u
63
+ ··· − 14u − 1
c
9
u
64
− u
63
+ ··· − 132u − 4
c
10
u
64
+ u
63
+ ··· − 1769u + 1279
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
64
+ 25y
63
+ ··· + 9011076y + 223729
c
2
y
64
+ 76y
63
+ ··· + 188592y + 107584
c
3
y
64
+ 51y
63
+ ··· − 510208710782y + 38530156681
c
4
y
64
− 11y
63
+ ··· − 87040y + 4096
c
5
, c
11
y
64
+ 26y
63
+ ··· + 49616y + 1936
c
6
y
64
+ 69y
63
+ ··· + 3038519y + 579121
c
7
, c
8
, c
12
y
64
− 66y
63
+ ··· − 16y + 1
c
9
y
64
+ 17y
63
+ ··· − 3936y + 16
c
10
y
64
− 87y
63
+ ··· − 27241069y + 1635841
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.335462 + 0.960170I
a = 0.595539 + 0.682559I
b = −0.963148 − 0.475228I
0.911770 − 1.032120I 10.14320 + 0.I
u = −0.335462 − 0.960170I
a = 0.595539 − 0.682559I
b = −0.963148 + 0.475228I
0.911770 + 1.032120I 10.14320 + 0.I
u = 0.947399 + 0.407862I
a = 0.338537 + 0.167075I
b = 0.248342 + 0.496214I
−1.74827 − 1.26516I 0
u = 0.947399 − 0.407862I
a = 0.338537 − 0.167075I
b = 0.248342 − 0.496214I
−1.74827 + 1.26516I 0
u = −0.083732 + 0.833478I
a = 1.045740 − 0.072964I
b = 0.415317 − 0.555202I
3.87313 + 2.36028I 5.21332 − 3.90932I
u = −0.083732 − 0.833478I
a = 1.045740 + 0.072964I
b = 0.415317 + 0.555202I
3.87313 − 2.36028I 5.21332 + 3.90932I
u = −0.274944 + 0.772279I
a = 0.790148 + 0.696555I
b = 0.900831 − 0.923664I
3.41888 + 3.02488I 6.95291 − 3.41925I
u = −0.274944 − 0.772279I
a = 0.790148 − 0.696555I
b = 0.900831 + 0.923664I
3.41888 − 3.02488I 6.95291 + 3.41925I
u = 0.075179 + 0.799821I
a = 0.467257 − 0.575187I
b = −1.259260 − 0.113697I
−0.99222 − 4.14641I 3.23080 + 6.97746I
u = 0.075179 − 0.799821I
a = 0.467257 + 0.575187I
b = −1.259260 + 0.113697I
−0.99222 + 4.14641I 3.23080 − 6.97746I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.413467 + 1.150880I
a = 0.144937 − 1.402750I
b = −0.04335 + 1.55505I
8.44712 − 3.02698I 0
u = 0.413467 − 1.150880I
a = 0.144937 + 1.402750I
b = −0.04335 − 1.55505I
8.44712 + 3.02698I 0
u = 0.040362 + 0.770178I
a = 0.243807 + 0.579784I
b = −1.365740 + 0.360315I
4.98892 + 8.36284I 6.61798 − 6.58755I
u = 0.040362 − 0.770178I
a = 0.243807 − 0.579784I
b = −1.365740 − 0.360315I
4.98892 − 8.36284I 6.61798 + 6.58755I
u = 0.642406 + 0.395793I
a = 0.539832 + 0.618893I
b = 0.406004 + 0.585662I
−1.72328 − 1.35345I 2.84079 + 5.01791I
u = 0.642406 − 0.395793I
a = 0.539832 − 0.618893I
b = 0.406004 − 0.585662I
−1.72328 + 1.35345I 2.84079 − 5.01791I
u = −1.24948
a = 0.543935
b = 0.299788
2.44452 0
u = −0.647244 + 0.349890I
a = −1.55678 + 1.74713I
b = 0.254178 − 0.482779I
3.51271 − 6.62719I 6.97914 + 1.82931I
u = −0.647244 − 0.349890I
a = −1.55678 − 1.74713I
b = 0.254178 + 0.482779I
3.51271 + 6.62719I 6.97914 − 1.82931I
u = −1.313910 + 0.215826I
a = −0.220902 + 0.147842I
b = 0.039760 − 0.791805I
−1.70737 + 4.39848I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.313910 − 0.215826I
a = −0.220902 − 0.147842I
b = 0.039760 + 0.791805I
−1.70737 − 4.39848I 0
u = −1.002620 + 0.901051I
a = 0.650289 − 0.114573I
b = 0.489302 − 0.434084I
2.48875 + 1.68278I 0
u = −1.002620 − 0.901051I
a = 0.650289 + 0.114573I
b = 0.489302 + 0.434084I
2.48875 − 1.68278I 0
u = 0.21372 + 1.41112I
a = −0.482160 + 1.217250I
b = 0.00954 − 1.79768I
6.23466 − 0.00352I 0
u = 0.21372 − 1.41112I
a = −0.482160 − 1.217250I
b = 0.00954 + 1.79768I
6.23466 + 0.00352I 0
u = −0.329023 + 0.401985I
a = 0.975551 + 0.406906I
b = −0.291314 + 0.190827I
1.055720 − 0.384090I 8.69250 + 1.65178I
u = −0.329023 − 0.401985I
a = 0.975551 − 0.406906I
b = −0.291314 − 0.190827I
1.055720 + 0.384090I 8.69250 − 1.65178I
u = −0.513200
a = 0.799271
b = 1.40728
1.44268 14.7350
u = −0.45260 + 1.42133I
a = −0.683739 − 1.056290I
b = 0.08781 + 1.76465I
11.76650 + 4.51689I 0
u = −0.45260 − 1.42133I
a = −0.683739 + 1.056290I
b = 0.08781 − 1.76465I
11.76650 − 4.51689I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.204121 + 0.364148I
a = 1.076330 − 0.192389I
b = 0.905084 + 0.351582I
−1.66720 − 0.88112I −0.76201 − 1.29100I
u = 0.204121 − 0.364148I
a = 1.076330 + 0.192389I
b = 0.905084 − 0.351582I
−1.66720 + 0.88112I −0.76201 + 1.29100I
u = 1.58492 + 0.27627I
a = −0.296423 − 0.332935I
b = −0.051364 + 0.836910I
4.76022 − 7.21958I 0
u = 1.58492 − 0.27627I
a = −0.296423 + 0.332935I
b = −0.051364 − 0.836910I
4.76022 + 7.21958I 0
u = 0.291913 + 0.225982I
a = −3.00732 − 2.80629I
b = 0.436516 + 0.467769I
−2.93293 + 3.01950I 3.23967 − 1.03009I
u = 0.291913 − 0.225982I
a = −3.00732 + 2.80629I
b = 0.436516 − 0.467769I
−2.93293 − 3.01950I 3.23967 + 1.03009I
u = 0.192418 + 0.305935I
a = 1.86300 − 1.16501I
b = −0.457918 − 0.710588I
7.58427 + 2.24555I 8.62267 − 0.85529I
u = 0.192418 − 0.305935I
a = 1.86300 + 1.16501I
b = −0.457918 + 0.710588I
7.58427 − 2.24555I 8.62267 + 0.85529I
u = 0.01286 + 1.66235I
a = −0.251779 − 1.041480I
b = 0.03327 + 1.75492I
7.78730 − 4.22834I 0
u = 0.01286 − 1.66235I
a = −0.251779 + 1.041480I
b = 0.03327 − 1.75492I
7.78730 + 4.22834I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.39994 + 1.64387I
a = 0.177619 − 0.870097I
b = 0.38697 + 1.58361I
2.98425 − 4.18476I 0
u = 0.39994 − 1.64387I
a = 0.177619 + 0.870097I
b = 0.38697 − 1.58361I
2.98425 + 4.18476I 0
u = 0.283207 + 0.080826I
a = −1.44066 − 3.30718I
b = 0.589344 − 0.669131I
−1.97533 + 1.42210I 0.91620 − 6.10321I
u = 0.283207 − 0.080826I
a = −1.44066 + 3.30718I
b = 0.589344 + 0.669131I
−1.97533 − 1.42210I 0.91620 + 6.10321I
u = 0.24314 + 1.68834I
a = 0.056309 + 1.169580I
b = −0.58798 − 1.65311I
5.49499 − 5.40830I 0
u = 0.24314 − 1.68834I
a = 0.056309 − 1.169580I
b = −0.58798 + 1.65311I
5.49499 + 5.40830I 0
u = −0.16084 + 1.73860I
a = 0.230933 + 0.972132I
b = 0.307850 − 1.361670I
4.47021 + 1.14177I 0
u = −0.16084 − 1.73860I
a = 0.230933 − 0.972132I
b = 0.307850 + 1.361670I
4.47021 − 1.14177I 0
u = −0.67469 + 1.61833I
a = 0.214372 + 1.071080I
b = 0.09629 − 1.53447I
5.14768 + 3.33362I 0
u = −0.67469 − 1.61833I
a = 0.214372 − 1.071080I
b = 0.09629 + 1.53447I
5.14768 − 3.33362I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.49546 + 1.71265I
a = 0.092150 + 0.806725I
b = 0.36691 − 1.75692I
8.17146 + 6.66450I 0
u = −0.49546 − 1.71265I
a = 0.092150 − 0.806725I
b = 0.36691 + 1.75692I
8.17146 − 6.66450I 0
u = −0.43824 + 1.74966I
a = −0.035433 − 1.125870I
b = −0.53312 + 1.71047I
5.15081 + 11.10080I 0
u = −0.43824 − 1.74966I
a = −0.035433 + 1.125870I
b = −0.53312 − 1.71047I
5.15081 − 11.10080I 0
u = 0.07921 + 1.82792I
a = 0.167616 − 1.054340I
b = −0.53046 + 1.46401I
13.45120 + 1.32917I 0
u = 0.07921 − 1.82792I
a = 0.167616 + 1.054340I
b = −0.53046 − 1.46401I
13.45120 − 1.32917I 0
u = 0.05911 + 1.89435I
a = −0.290232 + 0.899724I
b = 0.02290 − 1.79203I
14.7249 + 6.6669I 0
u = 0.05911 − 1.89435I
a = −0.290232 − 0.899724I
b = 0.02290 + 1.79203I
14.7249 − 6.6669I 0
u = 0.54843 + 1.85229I
a = −0.061480 + 1.071260I
b = −0.49609 − 1.73014I
11.8878 − 15.3498I 0
u = 0.54843 − 1.85229I
a = −0.061480 − 1.071260I
b = −0.49609 + 1.73014I
11.8878 + 15.3498I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.91204 + 1.79319I
a = 0.271605 − 1.004440I
b = 0.10036 + 1.51621I
10.63020 − 4.22345I 0
u = 0.91204 − 1.79319I
a = 0.271605 + 1.004440I
b = 0.10036 − 1.51621I
10.63020 + 4.22345I 0
u = −0.05374 + 2.23789I
a = 0.164957 − 1.018210I
b = 0.129617 + 1.231340I
12.37100 − 0.19756I 0
u = −0.05374 − 2.23789I
a = 0.164957 + 1.018210I
b = 0.129617 − 1.231340I
12.37100 + 0.19756I 0
11
II.
I
u
2
= h−3.64×10
14
u
18
+2.26×10
14
u
17
+· · ·+4.32×10
15
b−6.63×10
13
, 7.51×
10
15
u
18
−5.61×10
15
u
17
+· · ·+3.88×10
16
a+1.80×10
16
, u
19
−u
18
+· · ·+5u−9i
(i) Arc colorings
a
2
=
1
0
a
11
=
0
u
a
3
=
1
u
2
a
7
=
−0.193393u
18
+ 0.144333u
17
+ ··· − 2.35275u − 0.463784
0.0843336u
18
− 0.0522716u
17
+ ··· + 0.789469u + 0.0153568
a
4
=
0.109059u
18
− 0.0920616u
17
+ ··· + 1.56328u + 2.44843
−0.0485297u
18
+ 0.110929u
17
+ ··· − 0.896544u + 0.847023
a
1
=
0.192472u
18
− 0.326504u
17
+ ··· + 2.51451u − 1.68558
−0.0459865u
18
− 0.101011u
17
+ ··· + 0.541386u − 1.38026
a
6
=
−0.109059u
18
+ 0.0920616u
17
+ ··· − 1.56328u − 0.448427
0.0843336u
18
− 0.0522716u
17
+ ··· + 0.789469u + 0.0153568
a
5
=
−0.109059u
18
+ 0.0920616u
17
+ ··· − 1.56328u − 0.448427
0.0358039u
18
+ 0.0586574u
17
+ ··· − 0.107076u − 0.137620
a
12
=
0.00205396u
18
+ 0.179383u
17
+ ··· − 2.72735u + 1.54621
0.187705u
18
+ 0.0524445u
17
+ ··· + 0.697793u + 2.93670
a
10
=
0.151338u
18
− 0.164905u
17
+ ··· + 2.78710u + 0.861192
−0.0419331u
18
− 0.0288332u
17
+ ··· + 1.52675u − 1.10364
a
9
=
0.109405u
18
− 0.193738u
17
+ ··· + 4.31384u − 0.242445
−0.0419331u
18
− 0.0288332u
17
+ ··· + 1.52675u − 1.10364
a
8
=
−0.112709u
18
+ 0.299193u
17
+ ··· − 0.988091u + 2.55979
0.0604367u
18
+ 0.175102u
17
+ ··· + 0.648882u + 2.74600
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
4159791503582966
4316043181765921
u
18
+
2428875393014454
4316043181765921
u
17
+ ···−
60944556846167549
4316043181765921
u −
39429270153907668
4316043181765921
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
− 6u
18
+ ··· + 3u − 1
c
2
u
19
− u
18
+ ··· + 5u − 9
c
3
u
19
+ 2u
18
+ ··· + 15u − 9
c
4
u
19
+ u
17
+ ··· + u + 1
c
5
u
19
− u
18
+ ··· − 22u
2
− 4
c
6
u
19
+ 4u
18
+ ··· − 2u + 1
c
7
, c
8
u
19
+ u
18
+ ··· + 3u + 1
c
9
u
19
− u
17
+ ··· + 4u + 4
c
10
u
19
+ 2u
18
+ ··· + 4u + 1
c
11
u
19
+ u
18
+ ··· + 22u
2
+ 4
c
12
u
19
− u
18
+ ··· + 3u − 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
+ 6y
18
+ ··· − 7y −1
c
2
y
19
+ 13y
18
+ ··· + 439y −81
c
3
y
19
+ 20y
18
+ ··· − 405y −81
c
4
y
19
+ 2y
18
+ ··· + y −1
c
5
, c
11
y
19
+ 15y
18
+ ··· − 176y −16
c
6
y
19
+ 10y
18
+ ··· + 10y −1
c
7
, c
8
, c
12
y
19
− 21y
18
+ ··· − 11y −1
c
9
y
19
− 2y
18
+ ··· + 96y −16
c
10
y
19
− 14y
18
+ ··· + 30y −1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.389083 + 0.971159I
a = −0.277741 + 0.595285I
b = 0.932245 − 0.473799I
0.46032 + 1.43826I −0.20028 − 4.42405I
u = 0.389083 − 0.971159I
a = −0.277741 − 0.595285I
b = 0.932245 + 0.473799I
0.46032 − 1.43826I −0.20028 + 4.42405I
u = −0.800104 + 0.507328I
a = 0.388644 − 0.220349I
b = 0.710720 − 0.420295I
−2.27973 + 1.36896I −12.95881 − 5.08171I
u = −0.800104 − 0.507328I
a = 0.388644 + 0.220349I
b = 0.710720 + 0.420295I
−2.27973 − 1.36896I −12.95881 + 5.08171I
u = −0.914926 + 0.042064I
a = 0.09423 + 1.49670I
b = −0.539979 − 0.327295I
2.77115 − 7.45545I 1.04337 + 6.84145I
u = −0.914926 − 0.042064I
a = 0.09423 − 1.49670I
b = −0.539979 + 0.327295I
2.77115 + 7.45545I 1.04337 − 6.84145I
u = 0.947057 + 0.591059I
a = 0.473404 + 0.014503I
b = 0.810839 + 0.917232I
2.33987 − 2.91659I −0.25529 + 5.05539I
u = 0.947057 − 0.591059I
a = 0.473404 − 0.014503I
b = 0.810839 − 0.917232I
2.33987 + 2.91659I −0.25529 − 5.05539I
u = 0.818159
a = 0.221354
b = 1.21245
1.07163 −8.02200
u = −0.555367 + 0.570698I
a = 1.55276 − 0.46301I
b = −0.470414 − 0.688016I
−1.79164 − 0.64199I 4.02276 − 3.01754I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.555367 − 0.570698I
a = 1.55276 + 0.46301I
b = −0.470414 + 0.688016I
−1.79164 + 0.64199I 4.02276 + 3.01754I
u = 0.699603 + 0.245787I
a = 0.80766 + 1.51414I
b = −0.486775 + 0.028785I
−3.49065 − 3.76561I −3.11008 + 7.06177I
u = 0.699603 − 0.245787I
a = 0.80766 − 1.51414I
b = −0.486775 − 0.028785I
−3.49065 + 3.76561I −3.11008 − 7.06177I
u = 0.70448 + 1.41196I
a = 0.305323 − 0.963046I
b = 0.00641 + 1.66974I
9.00068 − 4.71241I 5.89823 + 4.68766I
u = 0.70448 − 1.41196I
a = 0.305323 + 0.963046I
b = 0.00641 − 1.66974I
9.00068 + 4.71241I 5.89823 − 4.68766I
u = −0.47470 + 1.61232I
a = 0.160463 + 1.124330I
b = 0.17424 − 1.56147I
5.05062 + 2.83722I 3.41245 + 2.37831I
u = −0.47470 − 1.61232I
a = 0.160463 − 1.124330I
b = 0.17424 + 1.56147I
5.05062 − 2.83722I 3.41245 − 2.37831I
u = 0.09579 + 2.08758I
a = −0.004309 − 1.065310I
b = 0.256494 + 1.250070I
12.07760 − 1.14448I 4.65867 + 5.51636I
u = 0.09579 − 2.08758I
a = −0.004309 + 1.065310I
b = 0.256494 − 1.250070I
12.07760 + 1.14448I 4.65867 − 5.51636I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
19
− 6u
18
+ ··· + 3u − 1)(u
64
− 7u
63
+ ··· − 2062u + 473)
c
2
(u
19
− u
18
+ ··· + 5u − 9)(u
64
+ 38u
62
+ ··· + 3396u + 328)
c
3
(u
19
+ 2u
18
+ ··· + 15u − 9)(u
64
− 3u
63
+ ··· − 1741810u − 196291)
c
4
(u
19
+ u
17
+ ··· + u + 1)(u
64
+ 3u
63
+ ··· − 160u − 64)
c
5
(u
19
− u
18
+ ··· − 22u
2
− 4)(u
64
+ 13u
62
+ ··· − 400u + 44)
c
6
(u
19
+ 4u
18
+ ··· − 2u + 1)(u
64
+ u
63
+ ··· + 6587u + 761)
c
7
, c
8
(u
19
+ u
18
+ ··· + 3u + 1)(u
64
+ 2u
63
+ ··· − 14u − 1)
c
9
(u
19
− u
17
+ ··· + 4u + 4)(u
64
− u
63
+ ··· − 132u − 4)
c
10
(u
19
+ 2u
18
+ ··· + 4u + 1)(u
64
+ u
63
+ ··· − 1769u + 1279)
c
11
(u
19
+ u
18
+ ··· + 22u
2
+ 4)(u
64
+ 13u
62
+ ··· − 400u + 44)
c
12
(u
19
− u
18
+ ··· + 3u − 1)(u
64
+ 2u
63
+ ··· − 14u − 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
19
+ 6y
18
+ ··· − 7y −1)(y
64
+ 25y
63
+ ··· + 9011076y + 223729)
c
2
(y
19
+ 13y
18
+ ··· + 439y −81)
· (y
64
+ 76y
63
+ ··· + 188592y + 107584)
c
3
(y
19
+ 20y
18
+ ··· − 405y −81)
· (y
64
+ 51y
63
+ ··· − 510208710782y + 38530156681)
c
4
(y
19
+ 2y
18
+ ··· + y −1)(y
64
− 11y
63
+ ··· − 87040y + 4096)
c
5
, c
11
(y
19
+ 15y
18
+ ··· − 176y −16)(y
64
+ 26y
63
+ ··· + 49616y + 1936)
c
6
(y
19
+ 10y
18
+ ··· + 10y −1)
· (y
64
+ 69y
63
+ ··· + 3038519y + 579121)
c
7
, c
8
, c
12
(y
19
− 21y
18
+ ··· − 11y −1)(y
64
− 66y
63
+ ··· − 16y + 1)
c
9
(y
19
− 2y
18
+ ··· + 96y −16)(y
64
+ 17y
63
+ ··· − 3936y + 16)
c
10
(y
19
− 14y
18
+ ··· + 30y −1)
· (y
64
− 87y
63
+ ··· − 27241069y + 1635841)
18
