12n
0016
(K12n
0016
)
A knot diagram
1
Linearized knot diagam
3 5 6 8 2 10 4 12 6 8 9 11
Solving Sequence
4,7
8
5,10
11 6 3 2 1 9 12
c
7
c
4
c
10
c
6
c
3
c
2
c
1
c
9
c
11
c
5
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= hb + u, 224074u
9
+ 244456u
8
+ ··· + 85463a + 346296,
u
10
+ u
9
− 7u
8
− 14u
7
+ 16u
6
+ 17u
5
− 3u
4
− 10u
3
− 3u
2
+ u − 1i
I
u
2
= h5.86389 × 10
37
u
19
+ 1.09059 × 10
38
u
18
+ ··· + 1.52045 × 10
41
b − 1.97465 × 10
40
,
− 1.68947 × 10
39
u
19
− 3.22641 × 10
39
u
18
+ ··· + 1.21636 × 10
42
a − 1.00257 × 10
42
,
u
20
+ 2u
19
+ ··· − 2048u + 1024i
I
u
3
= hb, u
4
a − 2u
3
a − 3u
4
− u
2
a + 3u
3
+ a
2
+ 3au + 7u
2
− 5u − 4, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
I
v
1
= ha, 8286v
9
− 14092v
8
+ ··· + 8095b + 12581,
v
10
− v
9
− 2v
8
− 19v
7
+ 12v
6
+ 35v
5
+ 50v
4
+ 34v
3
+ 17v
2
+ 5v + 1i
* 4 irreducible components of dim
C
= 0, with total 50 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
= hb+u, 224074u
9
+244456u
8
+· · ·+85463a+346296, u
10
+u
9
+· · ·+u−1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
5
=
−u
−u
3
+ u
a
10
=
−2.62188u
9
− 2.86037u
8
+ ··· + 12.1063u − 4.05200
−u
a
11
=
−2.43179u
9
− 2.58767u
8
+ ··· + 10.7229u − 4.29049
0.0122626u
9
− 0.0607046u
8
+ ··· − 0.892515u + 0.0826088
a
6
=
−0.238489u
9
− 0.0483952u
8
+ ··· − 1.43012u − 1.62188
−u
2
a
3
=
−0.367925u
9
− 0.606110u
8
+ ··· + 3.87427u + 0.559587
−0.0122626u
9
+ 0.0607046u
8
+ ··· + 0.892515u − 0.0826088
a
2
=
−0.404257u
9
− 0.758316u
8
+ ··· + 4.08826u + 0.692697
−0.122310u
9
− 0.00902145u
8
+ ··· + 0.758071u − 0.331594
a
1
=
0.238489u
9
+ 0.0483952u
8
+ ··· + 1.43012u + 1.62188
−0.0826088u
9
− 0.0948715u
8
+ ··· + 0.428583u − 0.190094
a
9
=
−2.81198u
9
− 3.13308u
8
+ ··· + 13.4897u − 3.81351
u
3
− u
a
12
=
−1.14164u
9
− 0.462949u
8
+ ··· − 5.42663u − 7.69845
0.122310u
9
+ 0.00902145u
8
+ ··· − 0.758071u + 0.331594
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
765256
85463
u
9
−
1261184
85463
u
8
+
4740376
85463
u
7
+
14048256
85463
u
6
−
4533392
85463
u
5
−
19248384
85463
u
4
−
7535280
85463
u
3
+
7955648
85463
u
2
+
7424384
85463
u +
490522
85463
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
u
10
+ 5u
9
+ 13u
8
+ 12u
7
− 12u
6
− 51u
5
− 65u
4
− 44u
3
− 13u
2
+ u + 1
c
2
, c
5
, c
8
c
11
u
10
+ 3u
9
+ 7u
8
+ 10u
7
+ 12u
6
+ 13u
5
+ 11u
4
+ 10u
3
+ 5u
2
+ 3u + 1
c
3
, c
10
u
10
− 3u
9
− 9u
8
+ 36u
7
− 12u
6
− 7u
5
− 23u
4
+ 13u
3
+ 16u
2
+ 3u + 2
c
4
, c
6
, c
7
c
9
u
10
+ u
9
− 7u
8
− 14u
7
+ 16u
6
+ 17u
5
− 3u
4
− 10u
3
− 3u
2
+ u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
12
y
10
+ y
9
+ ··· − 27y + 1
c
2
, c
5
, c
8
c
11
y
10
+ 5y
9
+ 13y
8
+ 12y
7
− 12y
6
− 51y
5
− 65y
4
− 44y
3
− 13y
2
+ y + 1
c
3
, c
10
y
10
− 27y
9
+ ··· + 55y + 4
c
4
, c
6
, c
7
c
9
y
10
− 15y
9
+ ··· + 5y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.051110 + 0.169733I
a = 0.075124 + 0.218323I
b = −1.051110 − 0.169733I
−6.66754 − 7.26680I −14.1481 + 8.5135I
u = 1.051110 − 0.169733I
a = 0.075124 − 0.218323I
b = −1.051110 + 0.169733I
−6.66754 + 7.26680I −14.1481 − 8.5135I
u = −0.766019
a = 0.342395
b = 0.766019
−1.35955 −6.41950
u = −0.505971 + 0.548673I
a = 0.308348 + 0.874136I
b = 0.505971 − 0.548673I
−1.23733 + 1.36545I −9.59143 − 3.61875I
u = −0.505971 − 0.548673I
a = 0.308348 − 0.874136I
b = 0.505971 + 0.548673I
−1.23733 − 1.36545I −9.59143 + 3.61875I
u = 0.171353 + 0.321669I
a = −4.31436 + 8.42917I
b = −0.171353 − 0.321669I
−0.16069 − 3.80568I 19.6494 + 42.7056I
u = 0.171353 − 0.321669I
a = −4.31436 − 8.42917I
b = −0.171353 + 0.321669I
−0.16069 + 3.80568I 19.6494 − 42.7056I
u = −2.11995 + 1.24678I
a = 0.704601 + 0.550226I
b = 2.11995 − 1.24678I
17.3702 + 13.6949I −8.24581 − 5.79353I
u = −2.11995 − 1.24678I
a = 0.704601 − 0.550226I
b = 2.11995 + 1.24678I
17.3702 − 13.6949I −8.24581 + 5.79353I
u = 2.57293
a = −0.889824
b = −2.57293
−13.9598 −4.90870
5
II. I
u
2
= h5.86 × 10
37
u
19
+ 1.09 × 10
38
u
18
+ · · · + 1.52 × 10
41
b − 1.97 ×
10
40
, −1.69 × 10
39
u
19
− 3.23 × 10
39
u
18
+ · · · + 1.22 × 10
42
a − 1.00 ×
10
42
, u
20
+ 2u
19
+ · · · − 2048u + 1024i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
5
=
−u
−u
3
+ u
a
10
=
0.00138896u
19
+ 0.00265251u
18
+ ··· + 3.64638u + 0.824235
−0.000385667u
19
− 0.000717282u
18
+ ··· − 1.18247u + 0.129872
a
11
=
0.00151255u
19
+ 0.00313681u
18
+ ··· + 3.14973u + 0.822778
−0.000451559u
19
− 0.000899794u
18
+ ··· − 0.823414u − 0.112935
a
6
=
0.000295502u
19
+ 0.000835151u
18
+ ··· − 2.41530u + 0.836394
−1.74761 × 10
−6
u
19
− 0.0000459509u
18
+ ··· + 0.619191u + 0.0512561
a
3
=
−0.000175793u
19
− 0.000736748u
18
+ ··· + 3.47292u − 1.24551
0.000101127u
19
+ 0.000225173u
18
+ ··· + 0.697375u + 0.189635
a
2
=
−0.000515937u
19
− 0.00143281u
18
+ ··· + 3.99150u − 1.66721
0.000576429u
19
+ 0.00110414u
18
+ ··· + 0.494790u + 0.627482
a
1
=
−0.000293754u
19
− 0.000789200u
18
+ ··· + 1.79611u − 0.887650
0.000158683u
19
+ 0.000288930u
18
+ ··· + 0.506931u + 0.257788
a
9
=
0.00144125u
19
+ 0.00289745u
18
+ ··· + 2.51554u + 1.04162
−0.000525250u
19
− 0.000988354u
18
+ ··· − 1.00784u + 0.125174
a
12
=
0.000756916u
19
+ 0.00212323u
18
+ ··· − 1.07571u + 3.13147
−0.000291771u
19
− 0.000735805u
18
+ ··· − 0.338968u − 0.810783
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.00176167u
19
− 0.00309564u
18
+ ··· − 12.6991u − 1.09946
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
u
20
+ 19u
19
+ ··· + 175u + 1
c
2
, c
5
, c
8
c
11
u
20
+ 5u
19
+ ··· + 5u + 1
c
3
, c
10
u
20
− 5u
19
+ ··· + 2619u + 641
c
4
, c
6
, c
7
c
9
u
20
+ 2u
19
+ ··· − 2048u + 1024
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
12
y
20
− 29y
19
+ ··· − 13889y + 1
c
2
, c
5
, c
8
c
11
y
20
+ 19y
19
+ ··· + 175y + 1
c
3
, c
10
y
20
− 53y
19
+ ··· + 71819743y + 410881
c
4
, c
6
, c
7
c
9
y
20
− 50y
19
+ ··· + 4194304y + 1048576
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.804594 + 0.696559I
a = −0.002315 − 0.280709I
b = −1.396170 − 0.196408I
−4.73849 + 3.00338I −7.64371 − 3.35763I
u = −0.804594 − 0.696559I
a = −0.002315 + 0.280709I
b = −1.396170 + 0.196408I
−4.73849 − 3.00338I −7.64371 + 3.35763I
u = −0.257283 + 0.651285I
a = −1.12449 − 2.84653I
b = 0.257283 + 0.651285I
−0.537213 −6 − 1.350198 + 0.10I
u = −0.257283 − 0.651285I
a = −1.12449 + 2.84653I
b = 0.257283 − 0.651285I
−0.537213 −6 − 1.350198 + 0.10I
u = 1.396170 + 0.196408I
a = 0.160795 + 0.137994I
b = 0.804594 − 0.696559I
−4.73849 + 3.00338I −7.64371 − 3.35763I
u = 1.396170 − 0.196408I
a = 0.160795 − 0.137994I
b = 0.804594 + 0.696559I
−4.73849 − 3.00338I −7.64371 + 3.35763I
u = −0.204722 + 0.532348I
a = 1.241470 + 0.214157I
b = −0.241836 − 0.217250I
−0.35106 + 1.66079I −2.53678 − 3.96410I
u = −0.204722 − 0.532348I
a = 1.241470 − 0.214157I
b = −0.241836 + 0.217250I
−0.35106 − 1.66079I −2.53678 + 3.96410I
u = 0.241836 + 0.217250I
a = 0.42599 + 2.16885I
b = 0.204722 − 0.532348I
−0.35106 + 1.66079I −2.53678 − 3.96410I
u = 0.241836 − 0.217250I
a = 0.42599 − 2.16885I
b = 0.204722 + 0.532348I
−0.35106 − 1.66079I −2.53678 + 3.96410I
9
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.55408 + 2.01462I
a = −0.191665 − 0.696885I
b = 0.55408 + 2.01462I
−4.58401 −9.53898 + 0.I
u = −0.55408 − 2.01462I
a = −0.191665 + 0.696885I
b = 0.55408 − 2.01462I
−4.58401 −9.53898 + 0.I
u = 2.55394 + 0.67960I
a = 0.797707 − 0.266076I
b = 2.56756 + 0.95364I
−18.4617 − 6.7670I −6.82707 + 2.49268I
u = 2.55394 − 0.67960I
a = 0.797707 + 0.266076I
b = 2.56756 − 0.95364I
−18.4617 + 6.7670I −6.82707 − 2.49268I
u = −2.56756 + 0.95364I
a = −0.741704 − 0.329004I
b = −2.55394 + 0.67960I
−18.4617 + 6.7670I −6.82707 − 2.49268I
u = −2.56756 − 0.95364I
a = −0.741704 + 0.329004I
b = −2.55394 − 0.67960I
−18.4617 − 6.7670I −6.82707 + 2.49268I
u = 2.62678 + 1.73277I
a = −0.171297 + 0.112997I
b = −2.62678 + 1.73277I
−12.4152 −9.95005 + 0.I
u = 2.62678 − 1.73277I
a = −0.171297 − 0.112997I
b = −2.62678 − 1.73277I
−12.4152 −9.95005 + 0.I
u = −3.43049 + 0.37740I
a = 0.605506 + 0.066614I
b = 3.43049 + 0.37740I
15.2909 −9.14565 + 0.I
u = −3.43049 − 0.37740I
a = 0.605506 − 0.066614I
b = 3.43049 − 0.37740I
15.2909 −9.14565 + 0.I
10
III. I
u
3
= hb, u
4
a − 3u
4
+ · · · + a
2
− 4, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
5
=
−u
−u
3
+ u
a
10
=
a
0
a
11
=
u
2
a + a
u
4
a
a
6
=
1
0
a
3
=
u
u
a
2
=
u
4
− u
2
− 1
u
4
− 2u
2
a
1
=
−1
−u
2
a
9
=
a
0
a
12
=
u
4
+ u
2
a − 2u
3
− u
2
+ a + 3u
u
4
a
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
4
a + 3u
3
a + 3u
4
− 5u
2
a + u
3
− 5au − 7u
2
− a − 3u − 6
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
c
2
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
3
, c
4
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
5
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
6
, c
9
u
10
c
7
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
8
, c
10
, c
12
(u
2
+ u + 1)
5
c
11
(u
2
− u + 1)
5
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
2
c
2
, c
5
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
2
c
3
, c
4
, c
7
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
2
c
6
, c
9
y
10
c
8
, c
10
, c
11
c
12
(y
2
+ y + 1)
5
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21774
a = −0.337181 + 0.584015I
b = 0
−2.40108 + 2.02988I −6.80799 − 1.95361I
u = −1.21774
a = −0.337181 − 0.584015I
b = 0
−2.40108 − 2.02988I −6.80799 + 1.95361I
u = −0.309916 + 0.549911I
a = 2.50919 + 0.05217I
b = 0
−0.32910 + 3.56046I −7.97351 − 2.70956I
u = −0.309916 + 0.549911I
a = −1.20942 − 2.19910I
b = 0
−0.329100 − 0.499304I 1.93681 − 0.71136I
u = −0.309916 − 0.549911I
a = 2.50919 − 0.05217I
b = 0
−0.32910 − 3.56046I −7.97351 + 2.70956I
u = −0.309916 − 0.549911I
a = −1.20942 + 2.19910I
b = 0
−0.329100 + 0.499304I 1.93681 + 0.71136I
u = 1.41878 + 0.21917I
a = −0.358089 − 0.327409I
b = 0
−5.87256 − 6.43072I −8.34383 + 2.96651I
u = 1.41878 + 0.21917I
a = −0.104500 + 0.473819I
b = 0
−5.87256 − 2.37095I −12.81148 + 1.72217I
u = 1.41878 − 0.21917I
a = −0.358089 + 0.327409I
b = 0
−5.87256 + 6.43072I −8.34383 − 2.96651I
u = 1.41878 − 0.21917I
a = −0.104500 − 0.473819I
b = 0
−5.87256 + 2.37095I −12.81148 − 1.72217I
14
IV. I
v
1
= ha, 8286v
9
− 14092v
8
+ · · · + 8095b + 12581, v
10
− v
9
+ · · · + 5v + 1i
(i) Arc colorings
a
4
=
v
0
a
7
=
1
0
a
8
=
1
0
a
5
=
v
0
a
10
=
0
−1.02359v
9
+ 1.74083v
8
+ ··· − 2.14256v − 1.55417
a
11
=
1.02359v
9
− 1.74083v
8
+ ··· + 2.14256v + 1.55417
−1.02359v
9
+ 1.74083v
8
+ ··· − 2.14256v − 1.55417
a
6
=
1
0.566770v
9
− 0.910562v
8
+ ··· + 1.12069v − 2.46844
a
3
=
0.343792v
9
− 0.433107v
8
+ ··· + 6.30229v + 0.566770
−1.56677v
9
+ 1.91056v
8
+ ··· − 18.1207v − 2.53156
a
2
=
0.433107v
9
− 0.556763v
8
+ ··· + 6.45448v + 0.910562
−1.56677v
9
+ 1.91056v
8
+ ··· − 18.1207v − 2.53156
a
1
=
−1
−0.566770v
9
+ 0.910562v
8
+ ··· − 1.12069v + 2.46844
a
9
=
−1.02359v
9
+ 1.74083v
8
+ ··· − 2.14256v − 1.55417
−0.515256v
9
+ 0.785300v
8
+ ··· − 0.966523v + 2.10241
a
12
=
−1.96479v
9
+ 3.18777v
8
+ ··· − 3.92341v + 1.99444
1.39802v
9
− 2.27721v
8
+ ··· + 2.80272v − 0.526004
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
4097
1619
v
9
+
9450
1619
v
8
+
1665
1619
v
7
+
67341
1619
v
6
−
147227
1619
v
5
−
55323
1619
v
4
−
14483
1619
v
3
+
69031
1619
v
2
+
28097
1619
v−
3358
1619
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
5
c
2
(u
2
+ u + 1)
5
c
4
, c
7
u
10
c
6
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
8
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
9
, c
10
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
11
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
12
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
5
c
4
, c
7
y
10
c
6
, c
9
, c
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
2
c
8
, c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
2
c
12
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.337181 + 0.584015I
a = 0
b = 1.21774
−2.40108 + 2.02988I −6.80799 − 1.95361I
v = −0.337181 − 0.584015I
a = 0
b = 1.21774
−2.40108 − 2.02988I −6.80799 + 1.95361I
v = −0.104500 + 0.473819I
a = 0
b = −1.41878 − 0.21917I
−5.87256 − 2.37095I −12.81148 + 1.72217I
v = −0.104500 − 0.473819I
a = 0
b = −1.41878 + 0.21917I
−5.87256 + 2.37095I −12.81148 − 1.72217I
v = −0.358089 + 0.327409I
a = 0
b = −1.41878 + 0.21917I
−5.87256 + 6.43072I −8.34383 − 2.96651I
v = −0.358089 − 0.327409I
a = 0
b = −1.41878 − 0.21917I
−5.87256 − 6.43072I −8.34383 + 2.96651I
v = −1.20942 + 2.19910I
a = 0
b = 0.309916 + 0.549911I
−0.32910 − 3.56046I −7.97351 + 2.70956I
v = −1.20942 − 2.19910I
a = 0
b = 0.309916 − 0.549911I
−0.32910 + 3.56046I −7.97351 − 2.70956I
v = 2.50919 + 0.05217I
a = 0
b = 0.309916 − 0.549911I
−0.329100 − 0.499304I 1.93681 − 0.71136I
v = 2.50919 − 0.05217I
a = 0
b = 0.309916 + 0.549911I
−0.329100 + 0.499304I 1.93681 + 0.71136I
18
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
5
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
· (u
10
+ 5u
9
+ 13u
8
+ 12u
7
− 12u
6
− 51u
5
− 65u
4
− 44u
3
− 13u
2
+ u + 1)
· (u
20
+ 19u
19
+ ··· + 175u + 1)
c
2
, c
8
(u
2
+ u + 1)
5
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
· (u
10
+ 3u
9
+ 7u
8
+ 10u
7
+ 12u
6
+ 13u
5
+ 11u
4
+ 10u
3
+ 5u
2
+ 3u + 1)
· (u
20
+ 5u
19
+ ··· + 5u + 1)
c
3
(u
2
− u + 1)
5
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
· (u
10
− 3u
9
− 9u
8
+ 36u
7
− 12u
6
− 7u
5
− 23u
4
+ 13u
3
+ 16u
2
+ 3u + 2)
· (u
20
− 5u
19
+ ··· + 2619u + 641)
c
4
, c
6
u
10
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
· (u
10
+ u
9
− 7u
8
− 14u
7
+ 16u
6
+ 17u
5
− 3u
4
− 10u
3
− 3u
2
+ u − 1)
· (u
20
+ 2u
19
+ ··· − 2048u + 1024)
c
5
, c
11
(u
2
− u + 1)
5
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
· (u
10
+ 3u
9
+ 7u
8
+ 10u
7
+ 12u
6
+ 13u
5
+ 11u
4
+ 10u
3
+ 5u
2
+ 3u + 1)
· (u
20
+ 5u
19
+ ··· + 5u + 1)
c
7
, c
9
u
10
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
· (u
10
+ u
9
− 7u
8
− 14u
7
+ 16u
6
+ 17u
5
− 3u
4
− 10u
3
− 3u
2
+ u − 1)
· (u
20
+ 2u
19
+ ··· − 2048u + 1024)
c
10
(u
2
+ u + 1)
5
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
· (u
10
− 3u
9
− 9u
8
+ 36u
7
− 12u
6
− 7u
5
− 23u
4
+ 13u
3
+ 16u
2
+ 3u + 2)
· (u
20
− 5u
19
+ ··· + 2619u + 641)
c
12
(u
2
+ u + 1)
5
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
· (u
10
+ 5u
9
+ 13u
8
+ 12u
7
− 12u
6
− 51u
5
− 65u
4
− 44u
3
− 13u
2
+ u + 1)
· (u
20
+ 19u
19
+ ··· + 175u + 1)
19
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
12
(y
2
+ y + 1)
5
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
2
· (y
10
+ y
9
+ ··· − 27y + 1)(y
20
− 29y
19
+ ··· − 13889y + 1)
c
2
, c
5
, c
8
c
11
(y
2
+ y + 1)
5
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
2
· (y
10
+ 5y
9
+ 13y
8
+ 12y
7
− 12y
6
− 51y
5
− 65y
4
− 44y
3
− 13y
2
+ y + 1)
· (y
20
+ 19y
19
+ ··· + 175y + 1)
c
3
, c
10
(y
2
+ y + 1)
5
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
2
· (y
10
− 27y
9
+ ··· + 55y + 4)
· (y
20
− 53y
19
+ ··· + 71819743y + 410881)
c
4
, c
6
, c
7
c
9
y
10
(y
5
− 5y
4
+ ··· − y − 1)
2
(y
10
− 15y
9
+ ··· + 5y + 1)
· (y
20
− 50y
19
+ ··· + 4194304y + 1048576)
20
