12n
0257
(K12n
0257
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 12 10 11 4 7 5 7 10
Solving Sequence
5,10 3,11
2 1 4 12 6 7 8 9
c
10
c
2
c
1
c
4
c
12
c
5
c
6
c
7
c
9
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.90485 × 10
17
u
17
− 2.51658 × 10
17
u
16
+ ··· + 3.03349 × 10
16
b − 4.02818 × 10
17
,
2.08713 × 10
17
u
17
− 2.72839 × 10
17
u
16
+ ··· + 7.58374 × 10
15
a − 3.96132 × 10
17
, u
18
− u
17
+ ··· − 4u + 1i
I
u
2
= h3u
11
− u
10
+ u
9
− 9u
8
− 6u
7
− 3u
6
+ 4u
5
+ 18u
4
+ 12u
3
+ 7u
2
+ b − 3u − 3,
− 4u
11
+ 3u
10
− 2u
9
+ 13u
8
+ 2u
7
+ 2u
6
− 9u
5
− 20u
4
− 8u
3
− u
2
+ a + 8u + 4,
u
12
− 3u
9
− 3u
8
− u
7
+ 2u
6
+ 7u
5
+ 6u
4
+ 2u
3
− 2u
2
− 3u − 1i
I
u
3
= hu
3
+ 3u
2
+ 18b − 17u + 46, −5u
3
+ 3u
2
+ 36a − 41u − 32, u
4
− u
3
+ 7u
2
+ 6u − 4i
I
u
4
= h2b + u − 1, a − u − 1, u
2
+ u − 1i
I
u
5
= hb − u − 1, −2u
3
+ 3u
2
+ 66a + 19u − 1, u
4
+ 4u
3
+ 7u
2
+ 6u + 11i
* 5 irreducible components of dim
C
= 0, with total 40 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
= h1.90 × 10
17
u
17
− 2.52 × 10
17
u
16
+ · · · + 3.03 × 10
16
b − 4.03 × 10
17
, 2.09 ×
10
17
u
17
−2.73×10
17
u
16
+· · ·+7.58×10
15
a−3.96×10
17
, u
18
−u
17
+· · ·−4u+1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
3
=
−27.5212u
17
+ 35.9768u
16
+ ··· − 342.299u + 52.2344
−6.27938u
17
+ 8.29598u
16
+ ··· − 84.9277u + 13.2790
a
11
=
1
−u
2
a
2
=
−27.5212u
17
+ 35.9768u
16
+ ··· − 342.299u + 52.2344
−11.3536u
17
+ 14.8220u
16
+ ··· − 146.271u + 21.7346
a
1
=
−7.55482u
17
+ 8.52485u
16
+ ··· − 73.2580u + 8.96058
−1.14106u
17
+ 1.22922u
16
+ ··· − 9.94123u + 0.881867
a
4
=
−12.4658u
17
+ 7.03725u
16
+ ··· + 23.8108u − 25.5769
−1.03310u
17
+ 1.07235u
16
+ ··· − 13.6155u + 0.722053
a
12
=
−6.41376u
17
+ 7.29563u
16
+ ··· − 63.3168u + 8.07871
−1.14106u
17
+ 1.22922u
16
+ ··· − 9.94123u + 0.881867
a
6
=
6.19684u
17
− 0.924141u
16
+ ··· − 69.5089u + 28.5882
0.881867u
17
+ 0.259189u
16
+ ··· − 17.5763u + 6.41376
a
7
=
7.07871u
17
− 0.664952u
16
+ ··· − 87.0852u + 35.0020
0.881867u
17
+ 0.259189u
16
+ ··· − 17.5763u + 6.41376
a
8
=
7.07871u
17
− 0.664952u
16
+ ··· − 86.0852u + 35.0020
0.881867u
17
+ 0.259189u
16
+ ··· − 17.5763u + 6.41376
a
9
=
22.1744u
17
− 27.4894u
16
+ ··· + 263.201u − 35.7652
5.27270u
17
− 6.06640u
16
+ ··· + 53.3756u − 6.19684
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
2063530662655740221
30334945780497320
u
17
+
4790167344610047657
60669891560994640
u
16
+ ··· −
39519432929474093823
60669891560994640
u +
3918064914900190251
60669891560994640
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
+ 9u
17
+ ··· − 656u + 256
c
2
, c
4
u
18
− 3u
17
+ ··· + 52u − 16
c
3
, c
8
u
18
− 5u
17
+ ··· + 80u + 64
c
5
, c
6
, c
9
u
18
+ 5u
16
+ ··· − 5u − 1
c
7
, c
10
, c
11
u
18
+ u
17
+ ··· + 4u + 1
c
12
u
18
+ 12u
17
+ ··· + 6u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
+ 3y
17
+ ··· + 495872y + 65536
c
2
, c
4
y
18
− 9y
17
+ ··· + 656y + 256
c
3
, c
8
y
18
+ 9y
17
+ ··· − 29440y + 4096
c
5
, c
6
, c
9
y
18
+ 10y
17
+ ··· − 45y + 1
c
7
, c
10
, c
11
y
18
+ 31y
17
+ ··· + 6y + 1
c
12
y
18
− 50y
17
+ ··· − 2700y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.584558 + 0.366182I
a = −0.031695 + 0.764128I
b = −0.238877 + 0.648680I
1.158820 − 0.715487I 6.82546 + 3.87567I
u = −0.584558 − 0.366182I
a = −0.031695 − 0.764128I
b = −0.238877 − 0.648680I
1.158820 + 0.715487I 6.82546 − 3.87567I
u = 1.51394 + 0.18364I
a = −0.619867 + 0.808006I
b = −0.40901 + 1.77160I
10.72160 + 4.05902I −5.48776 − 6.30227I
u = 1.51394 − 0.18364I
a = −0.619867 − 0.808006I
b = −0.40901 − 1.77160I
10.72160 − 4.05902I −5.48776 + 6.30227I
u = −0.022331 + 0.452997I
a = 1.61941 + 0.40552I
b = 0.156583 + 0.047051I
0.21869 − 2.12649I 2.57122 + 5.28808I
u = −0.022331 − 0.452997I
a = 1.61941 − 0.40552I
b = 0.156583 − 0.047051I
0.21869 + 2.12649I 2.57122 − 5.28808I
u = 0.025010 + 0.431550I
a = −1.34703 + 2.60646I
b = 0.250192 + 0.749320I
−2.52651 − 6.83690I 1.00389 + 11.16505I
u = 0.025010 − 0.431550I
a = −1.34703 − 2.60646I
b = 0.250192 − 0.749320I
−2.52651 + 6.83690I 1.00389 − 11.16505I
u = 0.007817 + 0.411255I
a = −0.85304 − 2.78085I
b = 0.325456 − 0.844226I
−3.55439 + 1.25550I −1.98701 − 1.61045I
u = 0.007817 − 0.411255I
a = −0.85304 + 2.78085I
b = 0.325456 + 0.844226I
−3.55439 − 1.25550I −1.98701 + 1.61045I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.75357
a = −0.620403
b = 1.40026
7.06782 −18.1410
u = 0.204909
a = 4.38528
b = 0.536453
−1.30691 −9.62130
u = −1.10465 + 2.31020I
a = 0.029942 + 0.642788I
b = 0.31930 + 2.83217I
−13.4615 − 12.9156I 0
u = −1.10465 − 2.31020I
a = 0.029942 − 0.642788I
b = 0.31930 − 2.83217I
−13.4615 + 12.9156I 0
u = −0.50858 + 2.58223I
a = 0.535381 − 0.129487I
b = −0.444741 − 0.317296I
−8.47225 − 5.66445I 0
u = −0.50858 − 2.58223I
a = 0.535381 + 0.129487I
b = −0.444741 + 0.317296I
−8.47225 + 5.66445I 0
u = 0.19411 + 2.91147I
a = −0.215532 − 0.577704I
b = 0.82274 − 2.38447I
−13.28390 + 2.28868I 0
u = 0.19411 − 2.91147I
a = −0.215532 + 0.577704I
b = 0.82274 + 2.38447I
−13.28390 − 2.28868I 0
6
II.
I
u
2
= h3u
11
−u
10
+· · ·+b−3, −4u
11
+3u
10
+· · ·+a+4, u
12
−3u
9
+· · ·−3u−1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
3
=
4u
11
− 3u
10
+ ··· − 8u − 4
−3u
11
+ u
10
+ ··· + 3u + 3
a
11
=
1
−u
2
a
2
=
4u
11
− 3u
10
+ ··· − 8u − 4
−5u
11
+ 2u
10
+ ··· + 8u + 6
a
1
=
−3u
11
+ u
10
+ 9u
8
+ 6u
7
− 7u
5
− 19u
4
− 11u
3
− u
2
+ 8u + 6
−u
2
− 1
a
4
=
−6u
11
+ 4u
10
+ ··· + 14u + 8
7u
11
− 5u
10
+ ··· − 21u − 13
a
12
=
−3u
11
+ u
10
+ 9u
8
+ 6u
7
− 7u
5
− 19u
4
− 11u
3
+ 8u + 7
−u
2
− 1
a
6
=
7u
11
− 3u
10
+ ··· − 14u − 13
−u
11
+ 3u
8
+ 3u
7
+ u
6
− 2u
5
− 7u
4
− 6u
3
− 2u
2
+ 2u + 3
a
7
=
6u
11
− 3u
10
+ u
9
− 18u
8
− 9u
7
+ 12u
5
+ 35u
4
+ 17u
3
+ u
2
− 12u − 10
−u
11
+ 3u
8
+ 3u
7
+ u
6
− 2u
5
− 7u
4
− 6u
3
− 2u
2
+ 2u + 3
a
8
=
6u
11
− 3u
10
+ u
9
− 18u
8
− 9u
7
+ 12u
5
+ 35u
4
+ 17u
3
+ u
2
− 13u − 10
−u
11
+ 3u
8
+ 3u
7
+ u
6
− 2u
5
− 7u
4
− 5u
3
− 2u
2
+ 2u + 3
a
9
=
10u
11
− 6u
10
+ ··· − 21u − 17
−3u
11
+ u
10
+ 9u
8
+ 6u
7
− 7u
5
− 19u
4
− 11u
3
+ 8u + 7
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 12u
11
− 12u
10
+ 3u
9
− 41u
8
+ 15u
6
+ 38u
5
+ 73u
4
− u
3
− 22u
2
− 57u − 30
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
− 4u
11
+ ··· − 13u + 1
c
2
u
12
+ 4u
11
+ ··· − u + 1
c
3
u
12
+ 6u
10
+ 3u
9
+ 13u
8
+ 7u
7
+ 15u
6
+ 6u
5
+ 2u
3
− 2u
2
− 3u + 1
c
4
u
12
− 4u
11
+ ··· + u + 1
c
5
, c
9
u
12
− 3u
11
+ 2u
10
+ 2u
9
− 6u
8
+ 7u
7
− 2u
6
− u
5
+ 3u
4
− 3u
3
− 1
c
6
u
12
+ 3u
11
+ 2u
10
− 2u
9
− 6u
8
− 7u
7
− 2u
6
+ u
5
+ 3u
4
+ 3u
3
− 1
c
7
, c
10
u
12
− 3u
9
− 3u
8
− u
7
+ 2u
6
+ 7u
5
+ 6u
4
+ 2u
3
− 2u
2
− 3u − 1
c
8
u
12
+ 6u
10
− 3u
9
+ 13u
8
− 7u
7
+ 15u
6
− 6u
5
− 2u
3
− 2u
2
+ 3u + 1
c
11
u
12
+ 3u
9
− 3u
8
+ u
7
+ 2u
6
− 7u
5
+ 6u
4
− 2u
3
− 2u
2
+ 3u − 1
c
12
u
12
− 12u
11
+ ··· − 12u + 9
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
+ 12y
11
+ ··· − 81y + 1
c
2
, c
4
y
12
− 4y
11
+ ··· − 13y + 1
c
3
, c
8
y
12
+ 12y
11
+ ··· − 13y + 1
c
5
, c
6
, c
9
y
12
− 5y
11
+ 4y
10
+ 10y
9
− 27y
7
− 8y
6
+ 25y
5
+ 15y
4
− 5y
3
− 6y
2
+ 1
c
7
, c
10
, c
11
y
12
− 6y
10
− 5y
9
+ 15y
8
+ 25y
7
− 8y
6
− 27y
5
+ 10y
3
+ 4y
2
− 5y + 1
c
12
y
12
− 24y
11
+ ··· − 234y + 81
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.366604 + 0.825368I
a = 1.11814 + 0.91713I
b = −0.413716 + 0.377477I
−2.86185 + 6.14960I −3.55511 − 1.94828I
u = −0.366604 − 0.825368I
a = 1.11814 − 0.91713I
b = −0.413716 − 0.377477I
−2.86185 − 6.14960I −3.55511 + 1.94828I
u = −0.851892
a = −0.391239
b = −2.26079
3.56755 13.7860
u = 0.111536 + 1.194340I
a = 0.317924 − 0.704003I
b = −0.993719 + 0.895794I
−5.28057 − 0.69048I −8.92309 + 4.67234I
u = 0.111536 − 1.194340I
a = 0.317924 + 0.704003I
b = −0.993719 − 0.895794I
−5.28057 + 0.69048I −8.92309 − 4.67234I
u = 0.765921
a = 1.24205
b = −9.03089
2.40622 −53.6250
u = −0.496770 + 1.152800I
a = −0.554307 + 0.648652I
b = 0.388509 + 0.841432I
−0.483582 + 0.496104I −0.592681 − 0.118839I
u = −0.496770 − 1.152800I
a = −0.554307 − 0.648652I
b = 0.388509 − 0.841432I
−0.483582 − 0.496104I −0.592681 + 0.118839I
u = −0.629825 + 0.069225I
a = 1.33711 − 0.51168I
b = −0.874744 + 0.682079I
4.44304 + 1.79476I 4.83493 − 4.62713I
u = −0.629825 − 0.069225I
a = 1.33711 + 0.51168I
b = −0.874744 − 0.682079I
4.44304 − 1.79476I 4.83493 + 4.62713I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.42465 + 0.18625I
a = −0.644266 + 0.830701I
b = −0.46049 + 1.87154I
11.06570 + 3.92660I 15.1553 + 1.2084I
u = 1.42465 − 0.18625I
a = −0.644266 − 0.830701I
b = −0.46049 − 1.87154I
11.06570 − 3.92660I 15.1553 − 1.2084I
11
III. I
u
3
=
hu
3
+3u
2
+18b−17u +46, −5u
3
+3u
2
+36a−41u −32, u
4
−u
3
+7u
2
+6u−4i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
3
=
5
36
u
3
−
1
12
u
2
+
41
36
u +
8
9
−
1
18
u
3
−
1
6
u
2
+
17
18
u −
23
9
a
11
=
1
−u
2
a
2
=
5
36
u
3
−
1
12
u
2
+
41
36
u +
8
9
−
5
18
u
3
+
1
6
u
2
+
13
18
u −
25
9
a
1
=
1
9
u
3
−
1
6
u
2
+
11
18
u +
11
18
−
1
18
u
3
−
1
6
u
2
−
1
18
u −
14
9
a
4
=
1
9
u
3
−
1
6
u
2
+
11
18
u +
11
18
7
18
u
3
−
5
6
u
2
+
7
18
u −
10
9
a
12
=
1
6
u
3
+
2
3
u +
13
6
−
1
18
u
3
−
1
6
u
2
−
1
18
u −
14
9
a
6
=
5
12
u
3
−
1
4
u
2
+
29
12
u +
5
3
−
5
18
u
3
+
1
6
u
2
−
23
18
u −
7
9
a
7
=
5
36
u
3
−
1
12
u
2
+
41
36
u +
8
9
−
5
18
u
3
+
1
6
u
2
−
23
18
u −
7
9
a
8
=
1
12
u
3
−
1
4
u
2
+
1
12
u +
1
3
11
18
u
3
−
7
6
u
2
−
43
18
u +
1
9
a
9
=
−
1
9
u
3
+
1
6
u
2
−
11
18
u −
11
18
−
1
6
u
3
+
1
2
u
2
+
5
6
u +
4
3
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
+ 3u + 1)
2
c
2
, c
4
, c
12
(u
2
− u − 1)
2
c
3
, c
8
(u
2
+ u − 1)
2
c
5
, c
6
, c
9
u
4
+ 4u
3
+ 5u
2
− 8u − 11
c
7
, c
10
, c
11
u
4
+ u
3
+ 7u
2
− 6u − 4
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
− 7y + 1)
2
c
2
, c
3
, c
4
c
8
, c
12
(y
2
− 3y + 1)
2
c
5
, c
6
, c
9
y
4
− 6y
3
+ 67y
2
− 174y + 121
c
7
, c
10
, c
11
y
4
+ 13y
3
+ 53y
2
− 92y + 16
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.06243
a = −0.581719
b = −3.68046
2.96088 −2.00000
u = 0.444394
a = 1.39074
b = −2.17364
2.96088 −2.00000
u = 0.80902 + 2.79600I
a = −0.154508 + 0.533989I
b = 0.42705 + 2.79600I
−12.8305 −2.00000
u = 0.80902 − 2.79600I
a = −0.154508 − 0.533989I
b = 0.42705 − 2.79600I
−12.8305 −2.00000
15
IV. I
u
4
= h2b + u − 1, a − u − 1, u
2
+ u − 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
3
=
u + 1
−
1
2
u +
1
2
a
11
=
1
u − 1
a
2
=
u + 1
−
3
2
u +
1
2
a
1
=
0
−u
a
4
=
u + 1
−
1
2
u +
1
2
a
12
=
u
−u
a
6
=
2u − 1
−u + 1
a
7
=
u
−u + 1
a
8
=
2u
−3u + 2
a
9
=
2u
−3u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
45
4
u +
45
4
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
8
u
2
c
4
(u + 1)
2
c
5
, c
6
u
2
+ 3u + 1
c
7
u
2
− u − 1
c
9
u
2
− 3u + 1
c
10
, c
11
, c
12
u
2
+ u − 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
2
c
3
, c
8
y
2
c
5
, c
6
, c
9
y
2
− 7y + 1
c
7
, c
10
, c
11
c
12
y
2
− 3y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 1.61803
b = 0.190983
−0.657974 4.29710
u = −1.61803
a = −0.618034
b = 1.30902
7.23771 29.4530
19
V. I
u
5
= hb − u − 1, −2u
3
+ 3u
2
+ 66a + 19u − 1, u
4
+ 4u
3
+ 7u
2
+ 6u + 11i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
3
=
0.0303030u
3
− 0.0454545u
2
− 0.287879u + 0.0151515
u + 1
a
11
=
1
−u
2
a
2
=
0.0303030u
3
− 0.0454545u
2
− 0.287879u + 0.0151515
−
1
6
u
3
− u
2
+
1
3
u −
5
6
a
1
=
−0.121212u
3
− 0.318182u
2
− 0.348485u − 0.560606
−
1
6
u
3
−
1
2
u
2
−
1
6
u −
1
3
a
4
=
−0.121212u
3
− 0.318182u
2
− 0.348485u − 0.560606
1
6
u
3
+
3
2
u
2
+
7
6
u +
10
3
a
12
=
0.0454545u
3
+ 0.181818u
2
− 0.181818u − 0.227273
−
1
6
u
3
−
1
2
u
2
−
1
6
u −
1
3
a
6
=
0.227273u
3
+ 0.409091u
2
+ 0.590909u + 0.363636
−
1
6
u
3
+
1
3
u +
1
6
a
7
=
0.0606061u
3
+ 0.409091u
2
+ 0.924242u + 0.530303
−
1
6
u
3
+
1
3
u +
1
6
a
8
=
−0.272727u
3
− 0.590909u
2
− 0.409091u − 1.13636
1
6
u
3
+ 2u
2
−
4
3
u +
23
6
a
9
=
0.121212u
3
+ 0.318182u
2
+ 0.348485u + 0.560606
−
1
2
u
2
+
1
2
u −
3
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
+ 3u + 1)
2
c
2
, c
4
, c
12
(u
2
− u − 1)
2
c
3
, c
8
(u
2
+ u − 1)
2
c
5
, c
6
, c
9
u
4
− u
3
+ 5u
2
+ 2u + 4
c
7
, c
10
, c
11
u
4
− 4u
3
+ 7u
2
− 6u + 11
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
− 7y + 1)
2
c
2
, c
3
, c
4
c
8
, c
12
(y
2
− 3y + 1)
2
c
5
, c
6
, c
9
y
4
+ 9y
3
+ 37y
2
+ 36y + 16
c
7
, c
10
, c
11
y
4
− 2y
3
+ 23y
2
+ 118y + 121
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.118034 + 1.322880I
a = 0.041356 − 0.463500I
b = 1.11803 + 1.32288I
−4.93480 −2.00000
u = 0.118034 − 1.322880I
a = 0.041356 + 0.463500I
b = 1.11803 − 1.32288I
−4.93480 −2.00000
u = −2.11803 + 1.32288I
a = 0.549553 + 0.343238I
b = −1.11803 + 1.32288I
−4.93480 −2.00000
u = −2.11803 − 1.32288I
a = 0.549553 − 0.343238I
b = −1.11803 − 1.32288I
−4.93480 −2.00000
23
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u
2
+ 3u + 1)
4
(u
12
− 4u
11
+ ··· − 13u + 1)
· (u
18
+ 9u
17
+ ··· − 656u + 256)
c
2
((u − 1)
2
)(u
2
− u − 1)
4
(u
12
+ 4u
11
+ ··· − u + 1)
· (u
18
− 3u
17
+ ··· + 52u − 16)
c
3
u
2
(u
2
+ u − 1)
4
· (u
12
+ 6u
10
+ 3u
9
+ 13u
8
+ 7u
7
+ 15u
6
+ 6u
5
+ 2u
3
− 2u
2
− 3u + 1)
· (u
18
− 5u
17
+ ··· + 80u + 64)
c
4
((u + 1)
2
)(u
2
− u − 1)
4
(u
12
− 4u
11
+ ··· + u + 1)
· (u
18
− 3u
17
+ ··· + 52u − 16)
c
5
(u
2
+ 3u + 1)(u
4
− u
3
+ 5u
2
+ 2u + 4)(u
4
+ 4u
3
+ 5u
2
− 8u − 11)
· (u
12
− 3u
11
+ 2u
10
+ 2u
9
− 6u
8
+ 7u
7
− 2u
6
− u
5
+ 3u
4
− 3u
3
− 1)
· (u
18
+ 5u
16
+ ··· − 5u − 1)
c
6
(u
2
+ 3u + 1)(u
4
− u
3
+ 5u
2
+ 2u + 4)(u
4
+ 4u
3
+ 5u
2
− 8u − 11)
· (u
12
+ 3u
11
+ 2u
10
− 2u
9
− 6u
8
− 7u
7
− 2u
6
+ u
5
+ 3u
4
+ 3u
3
− 1)
· (u
18
+ 5u
16
+ ··· − 5u − 1)
c
7
(u
2
− u − 1)(u
4
− 4u
3
+ 7u
2
− 6u + 11)(u
4
+ u
3
+ 7u
2
− 6u − 4)
· (u
12
− 3u
9
− 3u
8
− u
7
+ 2u
6
+ 7u
5
+ 6u
4
+ 2u
3
− 2u
2
− 3u − 1)
· (u
18
+ u
17
+ ··· + 4u + 1)
c
8
u
2
(u
2
+ u − 1)
4
· (u
12
+ 6u
10
− 3u
9
+ 13u
8
− 7u
7
+ 15u
6
− 6u
5
− 2u
3
− 2u
2
+ 3u + 1)
· (u
18
− 5u
17
+ ··· + 80u + 64)
c
9
(u
2
− 3u + 1)(u
4
− u
3
+ 5u
2
+ 2u + 4)(u
4
+ 4u
3
+ 5u
2
− 8u − 11)
· (u
12
− 3u
11
+ 2u
10
+ 2u
9
− 6u
8
+ 7u
7
− 2u
6
− u
5
+ 3u
4
− 3u
3
− 1)
· (u
18
+ 5u
16
+ ··· − 5u − 1)
c
10
(u
2
+ u − 1)(u
4
− 4u
3
+ 7u
2
− 6u + 11)(u
4
+ u
3
+ 7u
2
− 6u − 4)
· (u
12
− 3u
9
− 3u
8
− u
7
+ 2u
6
+ 7u
5
+ 6u
4
+ 2u
3
− 2u
2
− 3u − 1)
· (u
18
+ u
17
+ ··· + 4u + 1)
c
11
(u
2
+ u − 1)(u
4
− 4u
3
+ 7u
2
− 6u + 11)(u
4
+ u
3
+ 7u
2
− 6u − 4)
· (u
12
+ 3u
9
− 3u
8
+ u
7
+ 2u
6
− 7u
5
+ 6u
4
− 2u
3
− 2u
2
+ 3u − 1)
· (u
18
+ u
17
+ ··· + 4u + 1)
c
12
((u
2
− u − 1)
4
)(u
2
+ u − 1)(u
12
− 12u
11
+ ··· − 12u + 9)
· (u
18
+ 12u
17
+ ··· + 6u − 4)
24
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
2
)(y
2
− 7y + 1)
4
(y
12
+ 12y
11
+ ··· − 81y + 1)
· (y
18
+ 3y
17
+ ··· + 495872y + 65536)
c
2
, c
4
((y −1)
2
)(y
2
− 3y + 1)
4
(y
12
− 4y
11
+ ··· − 13y + 1)
· (y
18
− 9y
17
+ ··· + 656y + 256)
c
3
, c
8
y
2
(y
2
− 3y + 1)
4
(y
12
+ 12y
11
+ ··· − 13y + 1)
· (y
18
+ 9y
17
+ ··· − 29440y + 4096)
c
5
, c
6
, c
9
(y
2
− 7y + 1)(y
4
− 6y
3
+ 67y
2
− 174y + 121)
· (y
4
+ 9y
3
+ 37y
2
+ 36y + 16)
· (y
12
− 5y
11
+ 4y
10
+ 10y
9
− 27y
7
− 8y
6
+ 25y
5
+ 15y
4
− 5y
3
− 6y
2
+ 1)
· (y
18
+ 10y
17
+ ··· − 45y + 1)
c
7
, c
10
, c
11
(y
2
− 3y + 1)(y
4
− 2y
3
+ 23y
2
+ 118y + 121)
· (y
4
+ 13y
3
+ 53y
2
− 92y + 16)
· (y
12
− 6y
10
− 5y
9
+ 15y
8
+ 25y
7
− 8y
6
− 27y
5
+ 10y
3
+ 4y
2
− 5y + 1)
· (y
18
+ 31y
17
+ ··· + 6y + 1)
c
12
((y
2
− 3y + 1)
5
)(y
12
− 24y
11
+ ··· − 234y + 81)
· (y
18
− 50y
17
+ ··· − 2700y + 16)
25
