12n
0654
(K12n
0654
)
A knot diagram
1
Linearized knot diagam
3 8 12 11 8 10 2 5 3 6 4 9
Solving Sequence
5,11
4
9,12
1 3 8 6 2 7 10
c
4
c
11
c
12
c
3
c
8
c
5
c
2
c
7
c
10
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
18
− 5u
17
+ ··· + b − 7, −5u
18
+ 23u
17
+ ··· + 2a + 19, u
19
− 5u
18
+ ··· − 11u + 2i
I
u
2
= h−u
8
− u
7
− 6u
6
− 5u
5
− 11u
4
− 7u
3
− 6u
2
+ b − 2u,
− u
8
− 2u
7
− 7u
6
− 11u
5
− 16u
4
− 18u
3
− 13u
2
+ a − 8u − 2,
u
11
+ 2u
10
+ 9u
9
+ 14u
8
+ 29u
7
+ 34u
6
+ 40u
5
+ 32u
4
+ 20u
3
+ 7u
2
− 1i
I
u
3
= hu
2
a − au + 3u
2
+ 4b − a + u + 5, −u
2
a + a
2
− au − u
2
− 2a − 2u − 4, u
3
+ 2u − 1i
I
u
4
= h−u
3
a − u
3
− 2au − u
2
+ b − a − 2u − 1, −u
3
a + u
3
+ a
2
+ 2u
2
+ a + 2u, u
4
+ u
3
+ 2u
2
+ 2u + 1i
* 4 irreducible components of dim
C
= 0, with total 44 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
18
−5u
17
+· · ·+b−7, −5u
18
+23u
17
+· · ·+2a+19, u
19
−5u
18
+· · ·−11u+2i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
9
=
5
2
u
18
−
23
2
u
17
+ ··· + 30u −
19
2
−u
18
+ 5u
17
+ ··· − 22u + 7
a
12
=
−u
u
3
+ u
a
1
=
−
1
2
u
18
+
5
2
u
17
+ ··· − 5u +
3
2
−u
18
+ 4u
17
+ ··· − 5u + 1
a
3
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
7
2
u
18
−
33
2
u
17
+ ··· + 52u −
33
2
−u
18
+ 5u
17
+ ··· − 22u + 7
a
6
=
−
5
2
u
18
+
23
2
u
17
+ ··· − 34u +
17
2
u
18
− 5u
17
+ ··· + 20u − 5
a
2
=
−
1
2
u
18
+
3
2
u
17
+ ··· − 2u +
1
2
u
18
− 4u
17
+ ··· + 6u − 1
a
7
=
4u
18
− 19u
17
+ ··· + 63u − 19
−u
18
+ 5u
17
+ ··· − 24u + 8
a
10
=
7
2
u
18
−
33
2
u
17
+ ··· + 54u −
33
2
−u
18
+ 5u
17
+ ··· − 27u + 9
(ii) Obstruction class = −1
(iii) Cusp Shapes = −u
17
+ 5u
16
− 22u
15
+ 64u
14
− 159u
13
+ 316u
12
− 537u
11
+
764u
10
− 924u
9
+ 932u
8
− 775u
7
+ 509u
6
− 237u
5
+ 56u
4
+ 27u
3
− 33u
2
+ 17u − 8
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
+ 29u
18
+ ··· − 5u + 1
c
2
, c
7
, c
12
u
19
+ u
18
+ ··· + u + 1
c
3
, c
4
, c
11
u
19
− 5u
18
+ ··· − 11u + 2
c
5
, c
8
u
19
+ 10u
17
+ ··· − 3u + 1
c
6
, c
10
u
19
+ 15u
18
+ ··· + 1280u + 128
c
9
u
19
− 18u
17
+ ··· + u + 142
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
− 85y
18
+ ··· + 107y −1
c
2
, c
7
, c
12
y
19
− 29y
18
+ ··· − 5y −1
c
3
, c
4
, c
11
y
19
+ 21y
18
+ ··· + 49y −4
c
5
, c
8
y
19
+ 20y
18
+ ··· + 29y −1
c
6
, c
10
y
19
+ 7y
18
+ ··· + 98304y −16384
c
9
y
19
− 36y
18
+ ··· − 59071y −20164
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.855612 + 0.517253I
a = −0.909632 − 0.056467I
b = −0.55550 + 1.60326I
−13.4415 − 7.8504I −10.93721 + 4.73909I
u = 0.855612 − 0.517253I
a = −0.909632 + 0.056467I
b = −0.55550 − 1.60326I
−13.4415 + 7.8504I −10.93721 − 4.73909I
u = 0.837505 + 0.614615I
a = 0.803451 − 0.480637I
b = −0.25051 − 1.50923I
−13.15870 + 2.26983I −11.04237 + 0.00811I
u = 0.837505 − 0.614615I
a = 0.803451 + 0.480637I
b = −0.25051 + 1.50923I
−13.15870 − 2.26983I −11.04237 − 0.00811I
u = −0.113992 + 0.724011I
a = 0.100196 + 0.799956I
b = 0.365076 + 0.254010I
1.84434 + 1.33494I −1.83885 − 5.69262I
u = −0.113992 − 0.724011I
a = 0.100196 − 0.799956I
b = 0.365076 − 0.254010I
1.84434 − 1.33494I −1.83885 + 5.69262I
u = 0.030735 + 1.321750I
a = −1.098310 + 0.606917I
b = −0.403445 + 0.928311I
2.98081 + 0.93862I −5.64110 − 2.81933I
u = 0.030735 − 1.321750I
a = −1.098310 − 0.606917I
b = −0.403445 − 0.928311I
2.98081 − 0.93862I −5.64110 + 2.81933I
u = 0.115597 + 1.356600I
a = 1.77650 − 0.51209I
b = 0.91251 − 1.25835I
3.95111 − 4.05741I −5.74595 + 1.84063I
u = 0.115597 − 1.356600I
a = 1.77650 + 0.51209I
b = 0.91251 + 1.25835I
3.95111 + 4.05741I −5.74595 − 1.84063I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.31913 + 1.53475I
a = −1.73237 + 0.83605I
b = −0.85879 + 1.57727I
−6.80749 − 12.16250I −7.67551 + 5.42074I
u = 0.31913 − 1.53475I
a = −1.73237 − 0.83605I
b = −0.85879 − 1.57727I
−6.80749 + 12.16250I −7.67551 − 5.42074I
u = 0.398864 + 0.081266I
a = −0.07628 + 1.71759I
b = 0.427663 − 1.071520I
−0.63713 − 2.25906I −4.49996 + 0.38823I
u = 0.398864 − 0.081266I
a = −0.07628 − 1.71759I
b = 0.427663 + 1.071520I
−0.63713 + 2.25906I −4.49996 − 0.38823I
u = 0.30835 + 1.59968I
a = 0.798169 − 1.114480I
b = 0.029454 − 1.281070I
−5.90194 − 2.02936I −8.97202 + 0.94297I
u = 0.30835 − 1.59968I
a = 0.798169 + 1.114480I
b = 0.029454 + 1.281070I
−5.90194 + 2.02936I −8.97202 − 0.94297I
u = −0.363080
a = −0.809970
b = −0.215750
−0.659169 −15.1130
u = −0.07027 + 1.64614I
a = 0.493254 + 0.199283I
b = 0.441412 − 0.066654I
10.11590 + 2.22289I 2.40930 − 2.51224I
u = −0.07027 − 1.64614I
a = 0.493254 − 0.199283I
b = 0.441412 + 0.066654I
10.11590 − 2.22289I 2.40930 + 2.51224I
6
II.
I
u
2
= h−u
8
−u
7
+· · ·+b−2u, −u
8
−2u
7
+· · ·+a−2, u
11
+2u
10
+· · ·+7u
2
−1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
9
=
u
8
+ 2u
7
+ 7u
6
+ 11u
5
+ 16u
4
+ 18u
3
+ 13u
2
+ 8u + 2
u
8
+ u
7
+ 6u
6
+ 5u
5
+ 11u
4
+ 7u
3
+ 6u
2
+ 2u
a
12
=
−u
u
3
+ u
a
1
=
−u
10
− 3u
9
+ ··· − 14u − 3
−u
10
− 2u
9
− 8u
8
− 12u
7
− 22u
6
− 24u
5
− 25u
4
− 17u
3
− 10u
2
− 2u
a
3
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
u
7
+ u
6
+ 6u
5
+ 5u
4
+ 11u
3
+ 7u
2
+ 6u + 2
u
8
+ u
7
+ 6u
6
+ 5u
5
+ 11u
4
+ 7u
3
+ 6u
2
+ 2u
a
6
=
−u
6
− u
5
− 5u
4
− 4u
3
− 7u
2
− 4u − 2
−u
7
− u
6
− 5u
5
− 4u
4
− 7u
3
− 4u
2
− 3u
a
2
=
−u
9
− 2u
8
− 8u
7
− 12u
6
− 22u
5
− 24u
4
− 25u
3
− 17u
2
− 10u − 2
−u
10
− 2u
9
− 8u
8
− 12u
7
− 22u
6
− 24u
5
− 26u
4
− 18u
3
− 12u
2
− 3u
a
7
=
−u
10
− 2u
9
+ ··· − 9u − 2
−u
8
− 2u
7
− 6u
6
− 9u
5
− 11u
4
− 11u
3
− 6u
2
− 3u − 1
a
10
=
u
5
+ u
4
+ 4u
3
+ 3u
2
+ 4u + 2
u
8
+ u
7
+ 6u
6
+ 5u
5
+ 11u
4
+ 7u
3
+ 6u
2
+ 3u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 3u
10
+ 6u
9
+ 27u
8
+ 39u
7
+ 85u
6
+ 85u
5
+ 108u
4
+ 66u
3
+ 41u
2
+ 5u − 11
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
11
− 11u
10
+ ··· + 6u − 1
c
2
u
11
+ u
10
− 5u
9
− 4u
8
+ 8u
7
+ 5u
6
− 6u
5
− 7u
4
+ 3u
2
− 1
c
3
, c
4
u
11
+ 2u
10
+ ··· + 7u
2
− 1
c
5
u
11
+ u
9
− 4u
8
+ 2u
7
− 3u
6
+ 7u
5
− 3u
4
+ 3u
3
− 4u
2
− 1
c
6
u
11
+ 4u
9
+ 3u
8
+ 3u
7
+ 7u
6
+ 3u
5
+ 2u
4
+ 4u
3
+ u
2
+ 1
c
7
, c
12
u
11
− u
10
− 5u
9
+ 4u
8
+ 8u
7
− 5u
6
− 6u
5
+ 7u
4
− 3u
2
+ 1
c
8
u
11
+ u
9
+ 4u
8
+ 2u
7
+ 3u
6
+ 7u
5
+ 3u
4
+ 3u
3
+ 4u
2
+ 1
c
9
u
11
− 5u
9
+ 2u
8
+ 10u
7
+ 3u
6
+ 3u
5
+ u
4
− u
3
+ 2u
2
+ 1
c
10
u
11
+ 4u
9
− 3u
8
+ 3u
7
− 7u
6
+ 3u
5
− 2u
4
+ 4u
3
− u
2
− 1
c
11
u
11
− 2u
10
+ ··· − 7u
2
+ 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
11
− 23y
10
+ ··· − 10y −1
c
2
, c
7
, c
12
y
11
− 11y
10
+ ··· + 6y −1
c
3
, c
4
, c
11
y
11
+ 14y
10
+ ··· + 14y −1
c
5
, c
8
y
11
+ 2y
10
+ 5y
9
+ 2y
8
+ y
6
+ 11y
5
+ y
4
− 21y
3
− 22y
2
− 8y −1
c
6
, c
10
y
11
+ 8y
10
+ 22y
9
+ 21y
8
− y
7
− 11y
6
− y
5
− 2y
3
− 5y
2
− 2y −1
c
9
y
11
− 10y
10
+ ··· − 4y −1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395494 + 0.824290I
a = 0.720569 + 0.626450I
b = −0.190505 + 0.832468I
0.620962 + 0.437817I −9.18978 − 1.12208I
u = −0.395494 − 0.824290I
a = 0.720569 − 0.626450I
b = −0.190505 − 0.832468I
0.620962 − 0.437817I −9.18978 + 1.12208I
u = −0.568934 + 0.281691I
a = −0.550853 + 0.784586I
b = −0.488844 − 1.076040I
−1.08686 + 2.94207I −9.96542 − 7.42015I
u = −0.568934 − 0.281691I
a = −0.550853 − 0.784586I
b = −0.488844 + 1.076040I
−1.08686 − 2.94207I −9.96542 + 7.42015I
u = 0.125362 + 1.374090I
a = 1.48225 − 0.25773I
b = 1.065730 + 0.479865I
−2.02402 − 1.43083I −5.20918 + 0.10056I
u = 0.125362 − 1.374090I
a = 1.48225 + 0.25773I
b = 1.065730 − 0.479865I
−2.02402 + 1.43083I −5.20918 − 0.10056I
u = −0.20089 + 1.44390I
a = −1.56865 − 0.46843I
b = −0.86003 − 1.16265I
4.55914 + 5.69959I −3.05206 − 5.79000I
u = −0.20089 − 1.44390I
a = −1.56865 + 0.46843I
b = −0.86003 + 1.16265I
4.55914 − 5.69959I −3.05206 + 5.79000I
u = −0.08861 + 1.68680I
a = 0.263127 + 0.581865I
b = −0.069116 + 0.558344I
9.51549 + 2.22958I −11.44069 − 2.17239I
u = −0.08861 − 1.68680I
a = 0.263127 − 0.581865I
b = −0.069116 − 0.558344I
9.51549 − 2.22958I −11.44069 + 2.17239I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.257134
a = 5.30713
b = 1.08552
−6.72007 −5.28570
11
III.
I
u
3
= hu
2
a−au+3u
2
+4b−a+ u+5, −u
2
a+a
2
−au−u
2
−2a−2u−4, u
3
+2u−1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
9
=
a
−
1
4
u
2
a −
3
4
u
2
+ ··· +
1
4
a −
5
4
a
12
=
−u
−u + 1
a
1
=
−
1
4
u
2
a −
3
4
u
2
+ ··· −
3
4
a −
13
4
1
4
u
2
a −
1
4
u
2
+ ··· +
3
4
a −
3
4
a
3
=
u
2
+ 1
−u
a
8
=
1
4
u
2
a +
3
4
u
2
+ ··· +
3
4
a +
5
4
−
1
4
u
2
a −
3
4
u
2
+ ··· +
1
4
a −
5
4
a
6
=
u
2
+ 2
1
4
u
2
a −
5
4
u
2
+ ··· +
3
4
a −
7
4
a
2
=
−
3
4
u
2
a +
3
4
u
2
+ ··· −
5
4
a +
1
4
1
2
u
2
a −
1
2
u
2
+ ··· +
1
2
a −
5
2
a
7
=
−2u
2
− 4
−
1
2
u
2
a +
5
2
u
2
+ ··· −
3
2
a +
7
2
a
10
=
u
2
+ 2
1
4
u
2
a −
5
4
u
2
+ ··· +
3
4
a −
7
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
2
− 4u − 18
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
+ 6u
5
+ 11u
4
+ 30u
3
+ 81u
2
+ 57u + 16
c
2
, c
7
, c
12
u
6
− 3u
4
+ 4u
3
+ u
2
− 7u − 4
c
3
, c
4
, c
11
(u
3
+ 2u − 1)
2
c
5
, c
8
u
6
+ 2u
5
+ 3u
4
+ 8u
3
+ 9u
2
+ 9u + 2
c
6
, c
10
(u − 1)
6
c
9
u
6
+ 3u
5
− 3u
4
− 9u
3
+ 7u
2
+ 10u − 17
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
− 14y
5
− 77y
4
+ 230y
3
+ 3493y
2
− 657y + 256
c
2
, c
7
, c
12
y
6
− 6y
5
+ 11y
4
− 30y
3
+ 81y
2
− 57y + 16
c
3
, c
4
, c
11
(y
3
+ 4y
2
+ 4y −1)
2
c
5
, c
8
y
6
+ 2y
5
− 5y
4
− 42y
3
− 51y
2
− 45y + 4
c
6
, c
10
(y −1)
6
c
9
y
6
− 15y
5
+ 77y
4
− 217y
3
+ 331y
2
− 338y + 289
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.22670 + 1.46771I
a = −1.54629 − 0.37257I
b = −0.529360 − 0.960345I
2.86100 + 5.13794I −8.68207 − 3.20902I
u = −0.22670 + 1.46771I
a = 1.21680 + 1.17483I
b = 0.63214 + 1.62580I
2.86100 + 5.13794I −8.68207 − 3.20902I
u = −0.22670 − 1.46771I
a = −1.54629 + 0.37257I
b = −0.529360 + 0.960345I
2.86100 − 5.13794I −8.68207 + 3.20902I
u = −0.22670 − 1.46771I
a = 1.21680 − 1.17483I
b = 0.63214 − 1.62580I
2.86100 − 5.13794I −8.68207 + 3.20902I
u = 0.453398
a = −1.29347
b = −1.92103
−7.36693 −20.6360
u = 0.453398
a = 3.95244
b = −0.284535
−7.36693 −20.6360
15
IV. I
u
4
= h−u
3
a − u
3
− 2au − u
2
+ b − a − 2u − 1, −u
3
a + u
3
+ a
2
+ 2u
2
+
a + 2u, u
4
+ u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
9
=
a
u
3
a + u
3
+ 2au + u
2
+ a + 2u + 1
a
12
=
−u
u
3
+ u
a
1
=
u
3
a − u
3
+ au − 2u
2
− 3u
2u
3
− a + 3u + 1
a
3
=
u
2
+ 1
u
3
+ 2u + 1
a
8
=
−u
3
a − u
3
− 2au − u
2
− 2u − 1
u
3
a + u
3
+ 2au + u
2
+ a + 2u + 1
a
6
=
−u
3
− u
2
− 2u − 2
u
3
+ au + 2u
2
+ a + u + 2
a
2
=
−u
3
a − u
2
a − 2u
3
− 2au − u
2
− 2a − 4u − 1
u
3
a + u
2
a + 2u
3
+ au + a + 4u + 3
a
7
=
2u
3
+ 2u
2
+ 4u + 4
−2u
3
− 2au − 4u
2
− 2a − 3u − 4
a
10
=
−u
3
− u
2
− 2u − 2
u
3
+ au + 2u
2
+ a + 2u + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
− 4u − 14
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
+ 15u
7
+ ··· + 966u + 361
c
2
, c
7
, c
12
u
8
− u
7
− 7u
6
+ 3u
5
+ 20u
4
+ 3u
3
− 25u
2
− 4u + 19
c
3
, c
4
, c
11
(u
4
+ u
3
+ 2u
2
+ 2u + 1)
2
c
5
, c
8
u
8
+ 5u
7
+ 13u
6
+ 23u
5
+ 36u
4
+ 31u
3
+ 31u
2
+ 10u + 7
c
6
, c
10
(u − 1)
8
c
9
u
8
− 4u
7
+ 3u
6
+ 20u
5
+ 8u
4
− 2u
3
+ 28u
2
+ 48u + 31
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
− 35y
7
+ ··· + 84142y + 130321
c
2
, c
7
, c
12
y
8
− 15y
7
+ ··· − 966y + 361
c
3
, c
4
, c
11
(y
4
+ 3y
3
+ 2y
2
+ 1)
2
c
5
, c
8
y
8
+ y
7
+ 11y
6
+ 159y
5
+ 590y
4
+ 993y
3
+ 845y
2
+ 334y + 49
c
6
, c
10
(y −1)
8
c
9
y
8
− 10y
7
+ ··· − 568y + 961
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621744 + 0.440597I
a = −1.40199 + 0.41923I
b = −0.306391 − 1.124160I
−3.28987 + 2.02988I −12.00000 − 3.46410I
u = −0.621744 + 0.440597I
a = 0.523731 + 0.006202I
b = −0.00117 + 1.44231I
−3.28987 + 2.02988I −12.00000 − 3.46410I
u = −0.621744 − 0.440597I
a = −1.40199 − 0.41923I
b = −0.306391 + 1.124160I
−3.28987 − 2.02988I −12.00000 + 3.46410I
u = −0.621744 − 0.440597I
a = 0.523731 − 0.006202I
b = −0.00117 − 1.44231I
−3.28987 − 2.02988I −12.00000 + 3.46410I
u = 0.121744 + 1.306620I
a = 0.999194 − 0.897147I
b = −0.054173 + 0.641191I
−3.28987 − 2.02988I −12.00000 + 3.46410I
u = 0.121744 + 1.306620I
a = −2.62094 − 1.27550I
b = −2.13827 − 1.18907I
−3.28987 − 2.02988I −12.00000 + 3.46410I
u = 0.121744 − 1.306620I
a = 0.999194 + 0.897147I
b = −0.054173 − 0.641191I
−3.28987 + 2.02988I −12.00000 − 3.46410I
u = 0.121744 − 1.306620I
a = −2.62094 + 1.27550I
b = −2.13827 + 1.18907I
−3.28987 + 2.02988I −12.00000 − 3.46410I
19
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 6u
5
+ 11u
4
+ 30u
3
+ 81u
2
+ 57u + 16)
· (u
8
+ 15u
7
+ ··· + 966u + 361)(u
11
− 11u
10
+ ··· + 6u − 1)
· (u
19
+ 29u
18
+ ··· − 5u + 1)
c
2
(u
6
− 3u
4
+ 4u
3
+ u
2
− 7u − 4)
· (u
8
− u
7
− 7u
6
+ 3u
5
+ 20u
4
+ 3u
3
− 25u
2
− 4u + 19)
· (u
11
+ u
10
− 5u
9
− 4u
8
+ 8u
7
+ 5u
6
− 6u
5
− 7u
4
+ 3u
2
− 1)
· (u
19
+ u
18
+ ··· + u + 1)
c
3
, c
4
((u
3
+ 2u − 1)
2
)(u
4
+ u
3
+ 2u
2
+ 2u + 1)
2
(u
11
+ 2u
10
+ ··· + 7u
2
− 1)
· (u
19
− 5u
18
+ ··· − 11u + 2)
c
5
(u
6
+ 2u
5
+ 3u
4
+ 8u
3
+ 9u
2
+ 9u + 2)
· (u
8
+ 5u
7
+ 13u
6
+ 23u
5
+ 36u
4
+ 31u
3
+ 31u
2
+ 10u + 7)
· (u
11
+ u
9
− 4u
8
+ 2u
7
− 3u
6
+ 7u
5
− 3u
4
+ 3u
3
− 4u
2
− 1)
· (u
19
+ 10u
17
+ ··· − 3u + 1)
c
6
(u − 1)
14
(u
11
+ 4u
9
+ 3u
8
+ 3u
7
+ 7u
6
+ 3u
5
+ 2u
4
+ 4u
3
+ u
2
+ 1)
· (u
19
+ 15u
18
+ ··· + 1280u + 128)
c
7
, c
12
(u
6
− 3u
4
+ 4u
3
+ u
2
− 7u − 4)
· (u
8
− u
7
− 7u
6
+ 3u
5
+ 20u
4
+ 3u
3
− 25u
2
− 4u + 19)
· (u
11
− u
10
− 5u
9
+ 4u
8
+ 8u
7
− 5u
6
− 6u
5
+ 7u
4
− 3u
2
+ 1)
· (u
19
+ u
18
+ ··· + u + 1)
c
8
(u
6
+ 2u
5
+ 3u
4
+ 8u
3
+ 9u
2
+ 9u + 2)
· (u
8
+ 5u
7
+ 13u
6
+ 23u
5
+ 36u
4
+ 31u
3
+ 31u
2
+ 10u + 7)
· (u
11
+ u
9
+ 4u
8
+ 2u
7
+ 3u
6
+ 7u
5
+ 3u
4
+ 3u
3
+ 4u
2
+ 1)
· (u
19
+ 10u
17
+ ··· − 3u + 1)
c
9
(u
6
+ 3u
5
− 3u
4
− 9u
3
+ 7u
2
+ 10u − 17)
· (u
8
− 4u
7
+ 3u
6
+ 20u
5
+ 8u
4
− 2u
3
+ 28u
2
+ 48u + 31)
· (u
11
− 5u
9
+ 2u
8
+ 10u
7
+ 3u
6
+ 3u
5
+ u
4
− u
3
+ 2u
2
+ 1)
· (u
19
− 18u
17
+ ··· + u + 142)
c
10
(u − 1)
14
(u
11
+ 4u
9
− 3u
8
+ 3u
7
− 7u
6
+ 3u
5
− 2u
4
+ 4u
3
− u
2
− 1)
· (u
19
+ 15u
18
+ ··· + 1280u + 128)
c
11
((u
3
+ 2u − 1)
2
)(u
4
+ u
3
+ 2u
2
+ 2u + 1)
2
(u
11
− 2u
10
+ ··· − 7u
2
+ 1)
· (u
19
− 5u
18
+ ··· − 11u + 2)
20
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
6
− 14y
5
− 77y
4
+ 230y
3
+ 3493y
2
− 657y + 256)
· (y
8
− 35y
7
+ ··· + 84142y + 130321)(y
11
− 23y
10
+ ··· − 10y −1)
· (y
19
− 85y
18
+ ··· + 107y −1)
c
2
, c
7
, c
12
(y
6
− 6y
5
+ 11y
4
− 30y
3
+ 81y
2
− 57y + 16)
· (y
8
− 15y
7
+ ··· − 966y + 361)(y
11
− 11y
10
+ ··· + 6y −1)
· (y
19
− 29y
18
+ ··· − 5y −1)
c
3
, c
4
, c
11
(y
3
+ 4y
2
+ 4y −1)
2
(y
4
+ 3y
3
+ 2y
2
+ 1)
2
· (y
11
+ 14y
10
+ ··· + 14y −1)(y
19
+ 21y
18
+ ··· + 49y −4)
c
5
, c
8
(y
6
+ 2y
5
− 5y
4
− 42y
3
− 51y
2
− 45y + 4)
· (y
8
+ y
7
+ 11y
6
+ 159y
5
+ 590y
4
+ 993y
3
+ 845y
2
+ 334y + 49)
· (y
11
+ 2y
10
+ 5y
9
+ 2y
8
+ y
6
+ 11y
5
+ y
4
− 21y
3
− 22y
2
− 8y −1)
· (y
19
+ 20y
18
+ ··· + 29y −1)
c
6
, c
10
(y −1)
14
· (y
11
+ 8y
10
+ 22y
9
+ 21y
8
− y
7
− 11y
6
− y
5
− 2y
3
− 5y
2
− 2y −1)
· (y
19
+ 7y
18
+ ··· + 98304y −16384)
c
9
(y
6
− 15y
5
+ 77y
4
− 217y
3
+ 331y
2
− 338y + 289)
· (y
8
− 10y
7
+ ··· − 568y + 961)(y
11
− 10y
10
+ ··· − 4y −1)
· (y
19
− 36y
18
+ ··· − 59071y −20164)
21
