12n
0313
(K12n
0313
)
A knot diagram
1
Linearized knot diagam
3 6 7 11 8 2 10 6 12 5 7 9
Solving Sequence
7,10 2,8
6 3 1 5 11 12 4 9
c
7
c
6
c
2
c
1
c
5
c
10
c
11
c
4
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−41545u
14
+ 62711u
13
+ ··· + 83381b + 22577,
− 56191u
14
+ 116417u
13
+ ··· + 83381a + 99262,
u
15
− 2u
14
+ u
13
+ 2u
12
+ 4u
11
− 12u
10
+ 7u
9
+ 4u
8
+ 10u
7
− 28u
6
+ 13u
5
+ 3u
4
− 5u
3
+ 5u
2
− 3u + 1i
I
u
2
= h−2u
8
− 6u
7
− 7u
6
+ 4u
5
+ 15u
4
+ 8u
3
− 10u
2
+ b − 15u − 5,
− 2u
8
− 6u
7
− 8u
6
+ 3u
5
+ 15u
4
+ 12u
3
− 9u
2
+ a − 16u − 8,
u
9
+ 3u
8
+ 4u
7
− u
6
− 7u
5
− 6u
4
+ 3u
3
+ 8u
2
+ 5u + 1i
I
u
3
= h−u
5
− 3u
4
− 3u
3
− u
2
+ b − u − 1, −u
5
− 3u
4
− 3u
3
− u
2
+ a − u − 1, u
6
+ 3u
5
+ 4u
4
+ 3u
3
+ 3u
2
+ 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 30 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
= h−41545u
14
+ 62711u
13
+ · · · + 83381b + 22577, −5.62 × 10
4
u
14
+
1.16 × 10
5
u
13
+ · · · + 8.34 × 10
4
a + 9.93 × 10
4
, u
15
− 2u
14
+ · · · − 3u + 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
2
=
0.673907u
14
− 1.39621u
13
+ ··· + 1.05994u − 1.19046
0.498255u
14
− 0.752102u
13
+ ··· + 1.28760u − 0.270769
a
8
=
1
−u
2
a
6
=
−0.828462u
14
+ 1.02276u
13
+ ··· − 3.35724u + 0.995263
0.862870u
14
− 1.23046u
13
+ ··· + 2.60733u − 1.50841
a
3
=
0.651875u
14
− 1.12205u
13
+ ··· + 0.0277281u − 0.890826
0.0258572u
14
− 0.477447u
13
+ ··· + 0.528826u − 0.465442
a
1
=
0.0135522u
14
− 0.409794u
13
+ ··· − 1.03081u − 0.189216
−0.240930u
14
+ 0.319773u
13
+ ··· − 1.40889u + 0.529341
a
5
=
−1.22448u
14
+ 1.65231u
13
+ ··· − 4.89055u + 1.86951
1.00210u
14
− 1.42187u
13
+ ··· + 2.69877u − 1.67090
a
11
=
−0.582255u
14
+ 0.870858u
13
+ ··· − 0.677157u + 1.06481
0.560224u
14
− 0.596707u
13
+ ··· + 1.64494u − 0.765174
a
12
=
−0.0220314u
14
+ 0.274151u
13
+ ··· + 0.967786u + 0.299637
0.560224u
14
− 0.596707u
13
+ ··· + 1.64494u − 0.765174
a
4
=
0.626018u
14
− 0.644607u
13
+ ··· − 0.501097u − 0.425385
0.0258572u
14
− 0.477447u
13
+ ··· + 0.528826u − 0.465442
a
9
=
0.539284u
14
− 0.621928u
13
+ ··· + 1.09609u − 0.0144038
−0.201365u
14
+ 0.389765u
13
+ ··· + 0.0153152u + 0.510560
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
473234
83381
u
14
+
693041
83381
u
13
+ ··· −
1183972
83381
u +
479281
83381
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
+ 19u
14
+ ··· − 13464u − 2209
c
2
, c
6
u
15
− u
14
+ ··· + 52u − 47
c
3
u
15
+ 16u
14
+ ··· + 571220u − 516295
c
4
, c
10
u
15
− 4u
14
+ ··· + 124u − 11
c
5
, c
8
u
15
+ 2u
14
+ ··· − 193u − 131
c
7
u
15
+ 2u
14
+ ··· − 3u − 1
c
9
, c
12
u
15
− 4u
13
+ ··· + 95u − 23
c
11
u
15
− 10u
14
+ ··· + 1544u − 1961
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
+ 27y
14
+ ··· + 93308080y −4879681
c
2
, c
6
y
15
+ 19y
14
+ ··· − 13464y −2209
c
3
y
15
− 268y
14
+ ··· − 3653087564750y −266560527025
c
4
, c
10
y
15
+ 28y
14
+ ··· + 22856y −121
c
5
, c
8
y
15
− 26y
14
+ ··· + 40393y −17161
c
7
y
15
− 2y
14
+ ··· − y −1
c
9
, c
12
y
15
− 8y
14
+ ··· + 2493y −529
c
11
y
15
+ 12y
14
+ ··· − 79903546y −3845521
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.898089 + 0.122561I
a = 0.851665 + 0.429887I
b = −0.813523 − 0.857386I
8.21514 + 3.43846I 8.39038 − 0.14759I
u = 0.898089 − 0.122561I
a = 0.851665 − 0.429887I
b = −0.813523 + 0.857386I
8.21514 − 3.43846I 8.39038 + 0.14759I
u = −0.727637
a = 0.282926
b = 0.679431
1.43379 8.32270
u = −0.776726 + 1.064100I
a = 0.198165 + 1.273550I
b = −0.90296 + 1.50976I
1.61435 − 4.09120I 1.62171 + 2.87173I
u = −0.776726 − 1.064100I
a = 0.198165 − 1.273550I
b = −0.90296 − 1.50976I
1.61435 + 4.09120I 1.62171 − 2.87173I
u = −1.20953 + 0.78183I
a = −0.907869 − 0.069228I
b = −0.45282 − 1.51307I
3.12702 − 2.88040I 2.11466 + 1.70139I
u = −1.20953 − 0.78183I
a = −0.907869 + 0.069228I
b = −0.45282 + 1.51307I
3.12702 + 2.88040I 2.11466 − 1.70139I
u = −0.067561 + 0.552036I
a = 1.49637 − 1.52360I
b = −0.032891 − 0.581799I
−1.07742 − 1.06518I −5.69949 + 4.71826I
u = −0.067561 − 0.552036I
a = 1.49637 + 1.52360I
b = −0.032891 + 0.581799I
−1.07742 + 1.06518I −5.69949 − 4.71826I
u = 0.402433 + 0.347088I
a = −1.35119 + 0.98940I
b = 0.547092 + 0.828723I
0.07543 + 2.01877I 0.10830 − 4.30124I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.402433 − 0.347088I
a = −1.35119 − 0.98940I
b = 0.547092 − 0.828723I
0.07543 − 2.01877I 0.10830 + 4.30124I
u = 1.10914 + 1.03230I
a = −0.75781 + 1.35948I
b = 1.04371 + 1.80853I
−11.8911 + 11.0679I 2.10881 − 4.27183I
u = 1.10914 − 1.03230I
a = −0.75781 − 1.35948I
b = 1.04371 − 1.80853I
−11.8911 − 11.0679I 2.10881 + 4.27183I
u = 1.00798 + 1.14054I
a = 0.829204 − 0.703970I
b = 0.77167 − 1.94892I
−12.29490 − 3.15413I 1.69429 + 0.52217I
u = 1.00798 − 1.14054I
a = 0.829204 + 0.703970I
b = 0.77167 + 1.94892I
−12.29490 + 3.15413I 1.69429 − 0.52217I
6
II.
I
u
2
= h−2u
8
−6u
7
+· · ·+b −5, −2u
8
−6u
7
+· · ·+a −8, u
9
+3u
8
+· · ·+5u +1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
2
=
2u
8
+ 6u
7
+ 8u
6
− 3u
5
− 15u
4
− 12u
3
+ 9u
2
+ 16u + 8
2u
8
+ 6u
7
+ 7u
6
− 4u
5
− 15u
4
− 8u
3
+ 10u
2
+ 15u + 5
a
8
=
1
−u
2
a
6
=
4u
8
+ 11u
7
+ 13u
6
− 8u
5
− 27u
4
− 17u
3
+ 18u
2
+ 29u + 12
u
8
+ 2u
7
+ 2u
6
− 3u
5
− 4u
4
− 2u
3
+ 5u
2
+ 3u + 1
a
3
=
7u
8
+ 18u
7
+ 21u
6
− 15u
5
− 42u
4
− 26u
3
+ 31u
2
+ 43u + 18
2u
7
+ 4u
6
+ 3u
5
− 7u
4
− 8u
3
+ 10u + 5
a
1
=
10u
8
+ 25u
7
+ 28u
6
− 23u
5
− 58u
4
− 33u
3
+ 44u
2
+ 58u + 23
−3u
8
− 6u
7
− 5u
6
+ 10u
5
+ 13u
4
+ 2u
3
− 15u
2
− 10u
a
5
=
3u
8
+ 9u
7
+ 11u
6
− 5u
5
− 23u
4
− 15u
3
+ 13u
2
+ 25u + 10
2u
8
+ 4u
7
+ 4u
6
− 6u
5
− 8u
4
− 3u
3
+ 10u
2
+ 7u + 2
a
11
=
9u
8
+ 22u
7
+ 23u
6
− 23u
5
− 51u
4
− 23u
3
+ 42u
2
+ 49u + 15
−4u
8
− 10u
7
− 10u
6
+ 11u
5
+ 24u
4
+ 9u
3
− 20u
2
− 22u − 5
a
12
=
5u
8
+ 12u
7
+ 13u
6
− 12u
5
− 27u
4
− 14u
3
+ 22u
2
+ 27u + 10
−4u
8
− 10u
7
− 10u
6
+ 11u
5
+ 24u
4
+ 9u
3
− 20u
2
− 22u − 5
a
4
=
7u
8
+ 16u
7
+ 17u
6
− 18u
5
− 35u
4
− 18u
3
+ 31u
2
+ 33u + 13
2u
7
+ 4u
6
+ 3u
5
− 7u
4
− 8u
3
+ 10u + 5
a
9
=
−4u
8
− 11u
7
− 13u
6
+ 8u
5
+ 27u
4
+ 17u
3
− 18u
2
− 29u − 12
−4u
8
− 9u
7
− 9u
6
+ 11u
5
+ 20u
4
+ 8u
3
− 19u
2
− 18u − 5
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6u
8
− 13u
7
− 11u
6
+ 19u
5
+ 27u
4
+ 5u
3
− 30u
2
− 16u − 2
7
(iv) u-Polynomials at the component
8
Crossings u-Polynomials at each crossing
c
1
u
9
− 3u
8
+ 6u
7
− 9u
6
+ 12u
5
− 10u
4
+ 3u
3
+ 4u
2
− 4u + 1
c
2
u
9
− u
8
+ 2u
7
− u
6
+ 2u
5
+ u
3
+ 2u
2
+ 1
c
3
u
9
+ u
8
+ 5u
7
+ 10u
6
+ u
5
+ u
4
+ 12u
3
+ 9u
2
+ 2u + 1
c
4
u
9
+ 5u
7
+ u
6
+ 7u
5
+ 5u
4
+ u
3
+ 6u
2
− 2u + 1
c
5
u
9
+ 3u
8
+ u
7
− 5u
6
− 5u
5
+ 4u
4
+ 9u
3
− 4u + 1
c
6
u
9
+ u
8
+ 2u
7
+ u
6
+ 2u
5
+ u
3
− 2u
2
− 1
c
7
u
9
+ 3u
8
+ 4u
7
− u
6
− 7u
5
− 6u
4
+ 3u
3
+ 8u
2
+ 5u + 1
c
8
u
9
− 3u
8
+ u
7
+ 5u
6
− 5u
5
− 4u
4
+ 9u
3
− 4u − 1
c
9
u
9
+ 2u
7
− u
6
− 2u
4
− u
3
− 2u
2
− u − 1
c
10
u
9
+ 5u
7
− u
6
+ 7u
5
− 5u
4
+ u
3
− 6u
2
− 2u − 1
c
11
u
9
+ 6u
8
+ 10u
7
+ 4u
6
+ 11u
5
+ 23u
4
+ 10u
3
+ 6u
2
+ 13u + 5
c
12
u
9
+ 2u
7
+ u
6
+ 2u
4
− u
3
+ 2u
2
− u + 1
9
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
9
+ 3y
8
+ 6y
7
+ 9y
6
+ 16y
5
+ 2y
4
+ 11y
3
− 20y
2
+ 8y −1
c
2
, c
6
y
9
+ 3y
8
+ 6y
7
+ 9y
6
+ 12y
5
+ 10y
4
+ 3y
3
− 4y
2
− 4y −1
c
3
y
9
+ 9y
8
+ 7y
7
− 68y
6
+ 87y
5
− 139y
4
+ 110y
3
− 35y
2
− 14y −1
c
4
, c
10
y
9
+ 10y
8
+ 39y
7
+ 71y
6
+ 45y
5
− 43y
4
− 89y
3
− 50y
2
− 8y −1
c
5
, c
8
y
9
− 7y
8
+ 21y
7
− 41y
6
+ 75y
5
− 120y
4
+ 131y
3
− 80y
2
+ 16y −1
c
7
y
9
− y
8
+ 8y
7
− 15y
6
+ 23y
5
− 28y
4
+ 37y
3
− 22y
2
+ 9y −1
c
9
, c
12
y
9
+ 4y
8
+ 4y
7
− 3y
6
− 10y
5
− 12y
4
− 9y
3
− 6y
2
− 3y −1
c
11
y
9
− 16y
8
+ 74y
7
− 52y
6
+ 91y
5
− 157y
4
+ 70y
3
− 6y
2
+ 109y −25
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.072880 + 0.352289I
a = −1.056530 − 0.568290I
b = −0.054519 + 0.730817I
7.45475 + 1.27338I 5.64490 − 0.43727I
u = 1.072880 − 0.352289I
a = −1.056530 + 0.568290I
b = −0.054519 − 0.730817I
7.45475 − 1.27338I 5.64490 + 0.43727I
u = −0.692006 + 0.938897I
a = −0.73796 − 1.40715I
b = 0.497907 − 0.965644I
−0.18404 − 4.42541I −3.46550 + 5.77063I
u = −0.692006 − 0.938897I
a = −0.73796 + 1.40715I
b = 0.497907 + 0.965644I
−0.18404 + 4.42541I −3.46550 − 5.77063I
u = −0.654771 + 0.355732I
a = 1.208170 + 0.025665I
b = −0.976768 + 0.741048I
7.61597 − 3.90243I 0.00196 + 5.82113I
u = −0.654771 − 0.355732I
a = 1.208170 − 0.025665I
b = −0.976768 − 0.741048I
7.61597 + 3.90243I 0.00196 − 5.82113I
u = −0.396548
a = 3.50035
b = 0.810638
0.137068 −0.229590
u = −1.02783 + 1.24961I
a = 0.336146 + 1.247420I
b = −0.371939 + 1.075240I
3.13906 − 5.52199I 4.93343 + 8.47719I
u = −1.02783 − 1.24961I
a = 0.336146 − 1.247420I
b = −0.371939 − 1.075240I
3.13906 + 5.52199I 4.93343 − 8.47719I
12
III. I
u
3
= h−u
5
− 3u
4
− 3u
3
− u
2
+ b − u − 1, −u
5
− 3u
4
− 3u
3
− u
2
+ a − u −
1, u
6
+ 3u
5
+ 4u
4
+ 3u
3
+ 3u
2
+ 2u + 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
2
=
u
5
+ 3u
4
+ 3u
3
+ u
2
+ u + 1
u
5
+ 3u
4
+ 3u
3
+ u
2
+ u + 1
a
8
=
1
−u
2
a
6
=
u
5
+ 3u
4
+ 4u
3
+ 3u
2
+ 3u + 2
u
5
+ 3u
4
+ 4u
3
+ 3u
2
+ 3u + 1
a
3
=
2u
5
+ 5u
4
+ 4u
3
+ u
2
+ 3u + 2
u
5
+ 2u
4
+ u
3
+ 2u + 1
a
1
=
u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 3u
u
5
+ 3u
4
+ 4u
3
+ 3u
2
+ 2u
a
5
=
u + 1
u
5
+ 3u
4
+ 3u
3
+ 2u
2
+ 2u + 1
a
11
=
−u
3
− 2u
2
− u
u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 3u + 1
a
12
=
u
5
+ 2u
4
+ u
3
+ 2u + 1
u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 3u + 1
a
4
=
u
5
+ 3u
4
+ 3u
3
+ u
2
+ u + 1
u
5
+ 2u
4
+ u
3
+ 2u + 1
a
9
=
−u
5
− 2u
4
− u
3
+ u
2
+ 1
u
4
+ 3u
3
+ 3u
2
+ 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
5
+ 2u
4
− 2u
2
− u + 1
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
− 4u
5
+ 8u
4
− 9u
3
+ 8u
2
− 4u + 1
c
2
, c
12
u
6
+ 2u
4
+ u
3
+ 2u
2
+ 1
c
3
u
6
+ 3u
5
+ 4u
4
+ 6u
3
+ 6u
2
+ 2u + 1
c
4
(u
3
+ u
2
+ 2u + 1)
2
c
5
u
6
− u
5
− 3u
4
+ 4u
2
+ 3u + 1
c
6
, c
9
u
6
+ 2u
4
− u
3
+ 2u
2
+ 1
c
7
u
6
+ 3u
5
+ 4u
4
+ 3u
3
+ 3u
2
+ 2u + 1
c
8
u
6
+ u
5
− 3u
4
+ 4u
2
− 3u + 1
c
10
(u
3
− u
2
+ 2u − 1)
2
c
11
u
6
+ 2u
5
+ 4u
4
+ 6u
3
+ 4u
2
+ 5u + 5
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
+ 8y
4
+ 17y
3
+ 8y
2
+ 1
c
2
, c
6
, c
9
c
12
y
6
+ 4y
5
+ 8y
4
+ 9y
3
+ 8y
2
+ 4y + 1
c
3
y
6
− y
5
− 8y
4
+ 2y
3
+ 20y
2
+ 8y + 1
c
4
, c
10
(y
3
+ 3y
2
+ 2y −1)
2
c
5
, c
8
y
6
− 7y
5
+ 17y
4
− 16y
3
+ 10y
2
− y + 1
c
7
y
6
− y
5
+ 4y
4
+ 5y
3
+ 5y
2
+ 2y + 1
c
11
y
6
+ 4y
5
− 14y
3
− 4y
2
+ 15y + 25
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.319307 + 0.797712I
a = −0.425318 − 1.270190I
b = −0.425318 − 1.270190I
4.66906 + 2.82812I 2.68686 − 3.21164I
u = 0.319307 − 0.797712I
a = −0.425318 + 1.270190I
b = −0.425318 + 1.270190I
4.66906 − 2.82812I 2.68686 + 3.21164I
u = −0.500000 + 0.565544I
a = 0.662359 + 0.749187I
b = 0.662359 + 0.749187I
0.531480 1.235367 + 0.288289I
u = −0.500000 − 0.565544I
a = 0.662359 − 0.749187I
b = 0.662359 − 0.749187I
0.531480 1.235367 − 0.288289I
u = −1.31931 + 0.79771I
a = −0.237041 − 0.707911I
b = −0.237041 − 0.707911I
4.66906 − 2.82812I 9.57778 + 1.25753I
u = −1.31931 − 0.79771I
a = −0.237041 + 0.707911I
b = −0.237041 + 0.707911I
4.66906 + 2.82812I 9.57778 − 1.25753I
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
6
− 4u
5
+ 8u
4
− 9u
3
+ 8u
2
− 4u + 1)
· (u
9
− 3u
8
+ 6u
7
− 9u
6
+ 12u
5
− 10u
4
+ 3u
3
+ 4u
2
− 4u + 1)
· (u
15
+ 19u
14
+ ··· − 13464u − 2209)
c
2
(u
6
+ 2u
4
+ u
3
+ 2u
2
+ 1)(u
9
− u
8
+ 2u
7
− u
6
+ 2u
5
+ u
3
+ 2u
2
+ 1)
· (u
15
− u
14
+ ··· + 52u − 47)
c
3
(u
6
+ 3u
5
+ 4u
4
+ 6u
3
+ 6u
2
+ 2u + 1)
· (u
9
+ u
8
+ 5u
7
+ 10u
6
+ u
5
+ u
4
+ 12u
3
+ 9u
2
+ 2u + 1)
· (u
15
+ 16u
14
+ ··· + 571220u − 516295)
c
4
(u
3
+ u
2
+ 2u + 1)
2
(u
9
+ 5u
7
+ u
6
+ 7u
5
+ 5u
4
+ u
3
+ 6u
2
− 2u + 1)
· (u
15
− 4u
14
+ ··· + 124u − 11)
c
5
(u
6
− u
5
− 3u
4
+ 4u
2
+ 3u + 1)
· (u
9
+ 3u
8
+ u
7
− 5u
6
− 5u
5
+ 4u
4
+ 9u
3
− 4u + 1)
· (u
15
+ 2u
14
+ ··· − 193u − 131)
c
6
(u
6
+ 2u
4
− u
3
+ 2u
2
+ 1)(u
9
+ u
8
+ 2u
7
+ u
6
+ 2u
5
+ u
3
− 2u
2
− 1)
· (u
15
− u
14
+ ··· + 52u − 47)
c
7
(u
6
+ 3u
5
+ 4u
4
+ 3u
3
+ 3u
2
+ 2u + 1)
· (u
9
+ 3u
8
+ 4u
7
− u
6
− 7u
5
− 6u
4
+ 3u
3
+ 8u
2
+ 5u + 1)
· (u
15
+ 2u
14
+ ··· − 3u − 1)
c
8
(u
6
+ u
5
− 3u
4
+ 4u
2
− 3u + 1)
· (u
9
− 3u
8
+ u
7
+ 5u
6
− 5u
5
− 4u
4
+ 9u
3
− 4u − 1)
· (u
15
+ 2u
14
+ ··· − 193u − 131)
c
9
(u
6
+ 2u
4
− u
3
+ 2u
2
+ 1)(u
9
+ 2u
7
− u
6
− 2u
4
− u
3
− 2u
2
− u − 1)
· (u
15
− 4u
13
+ ··· + 95u − 23)
c
10
(u
3
− u
2
+ 2u − 1)
2
(u
9
+ 5u
7
− u
6
+ 7u
5
− 5u
4
+ u
3
− 6u
2
− 2u − 1)
· (u
15
− 4u
14
+ ··· + 124u − 11)
c
11
(u
6
+ 2u
5
+ 4u
4
+ 6u
3
+ 4u
2
+ 5u + 5)
· (u
9
+ 6u
8
+ 10u
7
+ 4u
6
+ 11u
5
+ 23u
4
+ 10u
3
+ 6u
2
+ 13u + 5)
· (u
15
− 10u
14
+ ··· + 1544u − 1961)
c
12
(u
6
+ 2u
4
+ u
3
+ 2u
2
+ 1)(u
9
+ 2u
7
+ u
6
+ 2u
4
− u
3
+ 2u
2
− u + 1)
· (u
15
− 4u
13
+ ··· + 95u − 23)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
6
+ 8y
4
+ 17y
3
+ 8y
2
+ 1)
· (y
9
+ 3y
8
+ 6y
7
+ 9y
6
+ 16y
5
+ 2y
4
+ 11y
3
− 20y
2
+ 8y −1)
· (y
15
+ 27y
14
+ ··· + 93308080y −4879681)
c
2
, c
6
(y
6
+ 4y
5
+ 8y
4
+ 9y
3
+ 8y
2
+ 4y + 1)
· (y
9
+ 3y
8
+ 6y
7
+ 9y
6
+ 12y
5
+ 10y
4
+ 3y
3
− 4y
2
− 4y −1)
· (y
15
+ 19y
14
+ ··· − 13464y −2209)
c
3
(y
6
− y
5
− 8y
4
+ 2y
3
+ 20y
2
+ 8y + 1)
· (y
9
+ 9y
8
+ 7y
7
− 68y
6
+ 87y
5
− 139y
4
+ 110y
3
− 35y
2
− 14y −1)
· (y
15
− 268y
14
+ ··· − 3653087564750y −266560527025)
c
4
, c
10
(y
3
+ 3y
2
+ 2y −1)
2
· (y
9
+ 10y
8
+ 39y
7
+ 71y
6
+ 45y
5
− 43y
4
− 89y
3
− 50y
2
− 8y −1)
· (y
15
+ 28y
14
+ ··· + 22856y −121)
c
5
, c
8
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 10y
2
− y + 1)
· (y
9
− 7y
8
+ 21y
7
− 41y
6
+ 75y
5
− 120y
4
+ 131y
3
− 80y
2
+ 16y −1)
· (y
15
− 26y
14
+ ··· + 40393y −17161)
c
7
(y
6
− y
5
+ 4y
4
+ 5y
3
+ 5y
2
+ 2y + 1)
· (y
9
− y
8
+ 8y
7
− 15y
6
+ 23y
5
− 28y
4
+ 37y
3
− 22y
2
+ 9y −1)
· (y
15
− 2y
14
+ ··· − y −1)
c
9
, c
12
(y
6
+ 4y
5
+ 8y
4
+ 9y
3
+ 8y
2
+ 4y + 1)
· (y
9
+ 4y
8
+ 4y
7
− 3y
6
− 10y
5
− 12y
4
− 9y
3
− 6y
2
− 3y −1)
· (y
15
− 8y
14
+ ··· + 2493y −529)
c
11
(y
6
+ 4y
5
− 14y
3
− 4y
2
+ 15y + 25)
· (y
9
− 16y
8
+ 74y
7
− 52y
6
+ 91y
5
− 157y
4
+ 70y
3
− 6y
2
+ 109y −25)
· (y
15
+ 12y
14
+ ··· − 79903546y −3845521)
18
