12n
0483
(K12n
0483
)
A knot diagram
1
Linearized knot diagam
3 5 12 7 2 11 10 3 4 5 9 8
Solving Sequence
4,12 3,10
9 8 1 7 5 2 6 11
c
3
c
9
c
8
c
12
c
7
c
4
c
2
c
5
c
11
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
7
+ u
4
+ 2u
3
+ 2u
2
+ b, −u
5
− u
2
+ a − 2u − 1,
u
12
− u
11
+ u
10
+ 2u
9
+ 2u
8
+ 2u
7
+ u
6
+ 5u
5
+ 6u
4
+ 3u
3
+ 2u
2
+ u + 1i
I
u
2
= hu
17
+ 7u
16
+ ··· + b − 1, 6u
17
+ 47u
16
+ ··· + a + 12, u
18
+ 8u
17
+ ··· + 5u + 1i
I
u
3
= h15u
13
− 39u
12
+ ··· + b − 29, −49u
13
+ 118u
12
+ ··· + a + 75,
u
14
− 3u
13
+ 4u
12
− 3u
11
+ 9u
10
− 21u
9
+ 22u
8
− 7u
7
+ 7u
6
− 31u
5
+ 48u
4
− 41u
3
+ 22u
2
− 7u + 1i
I
u
4
= hb, a + 1, u + 1i
* 4 irreducible components of dim
C
= 0, with total 45 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
7
+ u
4
+ 2u
3
+ 2u
2
+ b, −u
5
− u
2
+ a − 2u − 1, u
12
− u
11
+ · · · + u + 1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
3
=
1
−u
2
a
10
=
u
5
+ u
2
+ 2u + 1
−u
7
− u
4
− 2u
3
− 2u
2
a
9
=
u
7
+ u
5
+ u
4
+ 2u
3
+ 3u
2
+ 2u + 1
−u
7
− u
4
− 2u
3
− 2u
2
a
8
=
u
9
+ u
7
+ u
6
+ 3u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ 2u + 1
−u
11
− u
8
− 3u
7
− 2u
6
− 2u
3
− 2u
2
a
1
=
−u
11
− u
9
− 2u
8
− 3u
7
− 4u
6
− 2u
5
− 4u
4
− 3u
3
− 2u
2
−u
10
− u
9
− u
8
− 3u
7
− 4u
6
− 7u
5
− 5u
4
− 4u
3
− 3u
2
− u − 1
a
7
=
u
11
− u
10
+ u
9
+ u
8
+ 3u
7
+ u
6
+ 4u
4
+ 5u
3
+ 3u
2
+ u
u
a
5
=
−u
9
+ u
8
− u
7
− u
6
− u
5
− u
4
− u
2
− u
u
2
a
2
=
−u
9
− u
8
− u
7
− 2u
6
− 3u
5
− 6u
4
− 4u
3
− 2u
2
− u
u
10
+ u
9
+ u
8
+ u
7
+ 4u
6
+ 5u
5
+ 4u
4
+ 2u
3
+ u
a
6
=
u
11
+ u
10
+ u
9
+ 2u
8
+ 3u
7
+ 5u
6
+ 4u
5
+ 2u
4
+ u
3
+ u
2
u
10
+ u
9
+ u
8
+ 3u
7
+ 4u
6
+ 7u
5
+ 5u
4
+ 4u
3
+ 3u
2
+ u + 1
a
11
=
u
10
+ u
7
+ 2u
6
+ 3u
5
− u
4
− u
3
+ u
2
+ 2u + 1
−u
11
− u
8
− 3u
7
− 2u
6
− 2u
3
− 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
11
+ 6u
10
− 6u
9
− 6u
8
− 6u
7
− 2u
6
− 2u
5
− 20u
4
− 14u
3
− 2u
2
− 2u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
+ 36u
11
+ ··· + 10212u + 784
c
2
, c
5
u
12
+ 4u
11
+ ··· + 34u + 28
c
3
, c
4
u
12
− u
11
+ u
10
+ 2u
9
+ 2u
8
+ 2u
7
+ u
6
+ 5u
5
+ 6u
4
+ 3u
3
+ 2u
2
+ u + 1
c
6
, c
12
u
12
− u
11
+ ··· − 112u + 16
c
7
, c
11
u
12
+ u
11
+ ··· + 3u + 1
c
8
, c
10
u
12
− u
11
+ ··· − u + 1
c
9
u
12
+ 8u
11
+ ··· + 32u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
− 104y
11
+ ··· − 27451376y + 614656
c
2
, c
5
y
12
+ 36y
11
+ ··· + 10212y + 784
c
3
, c
4
y
12
+ y
11
+ ··· + 3y + 1
c
6
, c
12
y
12
− 35y
11
+ ··· + 1280y + 256
c
7
, c
11
y
12
+ 11y
11
+ ··· + 175y + 1
c
8
, c
10
y
12
− 25y
11
+ ··· + 21y + 1
c
9
y
12
− 6y
11
+ ··· + 160y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.943494 + 0.203851I
a = −0.445140 + 0.755661I
b = −0.761544 − 0.427838I
−1.86414 + 1.86169I −7.41273 − 3.81862I
u = −0.943494 − 0.203851I
a = −0.445140 − 0.755661I
b = −0.761544 + 0.427838I
−1.86414 − 1.86169I −7.41273 + 3.81862I
u = −0.428222 + 0.989663I
a = −1.95175 + 0.47004I
b = −1.156050 − 0.432518I
2.66700 + 5.59294I 4.27657 − 7.89716I
u = −0.428222 − 0.989663I
a = −1.95175 − 0.47004I
b = −1.156050 + 0.432518I
2.66700 − 5.59294I 4.27657 + 7.89716I
u = −0.433065 + 0.576514I
a = 0.004562 + 0.459402I
b = −0.083913 + 0.568146I
−0.34049 + 1.65634I −1.46994 − 4.66889I
u = −0.433065 − 0.576514I
a = 0.004562 − 0.459402I
b = −0.083913 − 0.568146I
−0.34049 − 1.65634I −1.46994 + 4.66889I
u = 0.308633 + 0.557970I
a = 1.46204 + 1.37428I
b = 1.005310 − 0.551014I
1.99940 − 1.87880I 2.68729 + 1.13887I
u = 0.308633 − 0.557970I
a = 1.46204 − 1.37428I
b = 1.005310 + 0.551014I
1.99940 + 1.87880I 2.68729 − 1.13887I
u = 0.96431 + 1.04939I
a = −0.436521 − 0.813671I
b = −1.55023 − 1.27982I
−18.7687 − 2.1933I −2.97846 + 2.17261I
u = 0.96431 − 1.04939I
a = −0.436521 + 0.813671I
b = −1.55023 + 1.27982I
−18.7687 + 2.1933I −2.97846 − 2.17261I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.03184 + 1.04165I
a = −1.63319 − 0.67021I
b = −1.45358 + 1.34749I
−19.0592 − 12.8315I −3.10274 + 5.68817I
u = 1.03184 − 1.04165I
a = −1.63319 + 0.67021I
b = −1.45358 − 1.34749I
−19.0592 + 12.8315I −3.10274 − 5.68817I
6
II.
I
u
2
= hu
17
+7u
16
+· · ·+b−1, 6u
17
+47u
16
+· · ·+a+12, u
18
+8u
17
+· · ·+5u+1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
3
=
1
−u
2
a
10
=
−6u
17
− 47u
16
+ ··· − 50u − 12
−u
17
− 7u
16
+ ··· − u + 1
a
9
=
−5u
17
− 40u
16
+ ··· − 49u − 13
−u
17
− 7u
16
+ ··· − u + 1
a
8
=
−5u
17
− 39u
16
+ ··· − 45u − 12
u
16
+ 7u
15
+ ··· + 4u + 2
a
1
=
13u
17
+ 99u
16
+ ··· + 84u + 19
−2u
17
− 16u
16
+ ··· − 18u − 6
a
7
=
3u
17
+ 19u
16
+ ··· − 11u − 8
−5u
17
− 38u
16
+ ··· − 29u − 6
a
5
=
21u
17
+ 156u
16
+ ··· + 111u + 22
−6u
17
− 48u
16
+ ··· − 45u − 12
a
2
=
14u
17
+ 107u
16
+ ··· + 90u + 20
−u
17
− 9u
16
+ ··· − 17u − 6
a
6
=
33u
17
+ 249u
16
+ ··· + 195u + 43
−5u
17
− 42u
16
+ ··· − 54u − 16
a
11
=
18u
17
+ 137u
16
+ ··· + 109u + 23
−3u
17
− 26u
16
+ ··· − 34u − 10
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −36u
17
− 268u
16
− 1035u
15
− 2527u
14
− 4242u
13
− 4893u
12
− 3632u
11
− 1032u
10
+
1235u
9
+ 2183u
8
+ 1783u
7
+ 724u
6
− 361u
5
− 832u
4
− 748u
3
− 435u
2
− 188u − 40
7
(iv) u-Polynomials at the component
8
Crossings u-Polynomials at each crossing
c
1
(u
9
− 5u
8
+ 11u
7
− 5u
6
− 6u
5
+ 6u
4
+ 3u
3
− 4u
2
+ 1)
2
c
2
(u
9
− u
8
+ 3u
7
− u
6
+ 2u
5
− 2u
4
− u
3
+ 1)
2
c
3
u
18
+ 8u
17
+ ··· + 5u + 1
c
4
u
18
− 8u
17
+ ··· − 5u + 1
c
5
(u
9
+ u
8
+ 3u
7
+ u
6
+ 2u
5
+ 2u
4
− u
3
− 1)
2
c
6
u
18
+ 4u
17
+ ··· − 64u + 16
c
7
u
18
+ 5u
17
+ ··· + 6u + 1
c
8
u
18
+ 2u
17
+ ··· − u + 1
c
9
u
18
− 6u
16
+ 18u
14
− 32u
12
+ 36u
10
− 21u
8
− u
6
+ 13u
4
− 9u
2
+ 2
c
10
u
18
− 2u
17
+ ··· + u + 1
c
11
u
18
− 5u
17
+ ··· − 6u + 1
c
12
u
18
− 4u
17
+ ··· + 64u + 16
9
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
9
− 3y
8
+ 59y
7
− 91y
6
+ 122y
5
− 102y
4
+ 67y
3
− 28y
2
+ 8y −1)
2
c
2
, c
5
(y
9
+ 5y
8
+ 11y
7
+ 5y
6
− 6y
5
− 6y
4
+ 3y
3
+ 4y
2
− 1)
2
c
3
, c
4
y
18
+ 2y
17
+ ··· + 3y + 1
c
6
, c
12
y
18
− 22y
17
+ ··· − 512y + 256
c
7
, c
11
y
18
− 9y
17
+ ··· − 4y + 1
c
8
, c
10
y
18
− 8y
17
+ ··· − y + 1
c
9
(y
9
− 6y
8
+ 18y
7
− 32y
6
+ 36y
5
− 21y
4
− y
3
+ 13y
2
− 9y + 2)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.777312 + 0.486718I
a = −0.117694 − 0.428312I
b = 0.824936I
−2.92265 −6.32125 + 0.I
u = −0.777312 − 0.486718I
a = −0.117694 + 0.428312I
b = − 0.824936I
−2.92265 −6.32125 + 0.I
u = 0.787271 + 0.193545I
a = −1.94391 + 0.62047I
b = 0.738756 − 0.073670I
−2.59122 − 4.23353I −10.52461 + 5.89343I
u = 0.787271 − 0.193545I
a = −1.94391 − 0.62047I
b = 0.738756 + 0.073670I
−2.59122 + 4.23353I −10.52461 − 5.89343I
u = 0.195408 + 0.775085I
a = 0.783024 + 0.052101I
b = 1.018860 − 0.510794I
0.08023 + 1.48591I −1.59236 − 0.75430I
u = 0.195408 − 0.775085I
a = 0.783024 − 0.052101I
b = 1.018860 + 0.510794I
0.08023 − 1.48591I −1.59236 + 0.75430I
u = −0.913089 + 0.817029I
a = −0.586719 + 0.636830I
b = −1.018860 + 0.510794I
0.08023 + 1.48591I −1.59236 − 0.75430I
u = −0.913089 − 0.817029I
a = −0.586719 − 0.636830I
b = −1.018860 − 0.510794I
0.08023 − 1.48591I −1.59236 + 0.75430I
u = 0.017456 + 0.678862I
a = 1.85849 − 0.76267I
b = 1.298400 − 0.418995I
1.04126 − 5.01228I −1.26831 + 4.06630I
u = 0.017456 − 0.678862I
a = 1.85849 + 0.76267I
b = 1.298400 + 0.418995I
1.04126 + 5.01228I −1.26831 − 4.06630I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.831665 + 1.107580I
a = −1.39851 + 0.58903I
b = −1.298400 − 0.418995I
1.04126 + 5.01228I −1.26831 − 4.06630I
u = −0.831665 − 1.107580I
a = −1.39851 − 0.58903I
b = −1.298400 + 0.418995I
1.04126 − 5.01228I −1.26831 + 4.06630I
u = −0.458886 + 0.399467I
a = 0.31142 − 2.76924I
b = 0.948371 + 0.622031I
−0.35881 + 6.46016I 3.04591 − 10.04151I
u = −0.458886 − 0.399467I
a = 0.31142 + 2.76924I
b = 0.948371 − 0.622031I
−0.35881 − 6.46016I 3.04591 + 10.04151I
u = −0.83752 + 1.26265I
a = −1.41028 + 0.27520I
b = −0.948371 − 0.622031I
−0.35881 + 6.46016I 3.04591 − 10.04151I
u = −0.83752 − 1.26265I
a = −1.41028 − 0.27520I
b = −0.948371 + 0.622031I
−0.35881 − 6.46016I 3.04591 + 10.04151I
u = −1.18166 + 1.05458I
a = −0.995814 + 0.295938I
b = −0.738756 − 0.073670I
−2.59122 + 4.23353I −10.52461 − 5.89343I
u = −1.18166 − 1.05458I
a = −0.995814 − 0.295938I
b = −0.738756 + 0.073670I
−2.59122 − 4.23353I −10.52461 + 5.89343I
13
III. I
u
3
= h15u
13
− 39u
12
+ · · · + b − 29, −49u
13
+ 118u
12
+ · · · + a +
75, u
14
− 3u
13
+ · · · − 7u + 1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
3
=
1
−u
2
a
10
=
49u
13
− 118u
12
+ ··· + 423u − 75
−15u
13
+ 39u
12
+ ··· − 154u + 29
a
9
=
64u
13
− 157u
12
+ ··· + 577u − 104
−15u
13
+ 39u
12
+ ··· − 154u + 29
a
8
=
65u
13
− 161u
12
+ ··· + 604u − 110
−14u
13
+ 36u
12
+ ··· − 146u + 28
a
1
=
−126u
13
+ 308u
12
+ ··· − 1138u + 209
36u
13
− 93u
12
+ ··· + 373u − 71
a
7
=
31u
13
− 81u
12
+ ··· + 326u − 60
−u
13
+ 2u
12
+ ··· − 7u + 1
a
5
=
−5u
13
+ 22u
12
+ ··· − 156u + 37
9u
13
− 19u
12
+ ··· + 59u − 10
a
2
=
−127u
13
+ 311u
12
+ ··· − 1147u + 210
35u
13
− 91u
12
+ ··· + 372u − 71
a
6
=
17u
13
− 28u
12
+ ··· − 38u + 25
28u
13
− 60u
12
+ ··· + 186u − 32
a
11
=
−129u
13
+ 315u
12
+ ··· − 1155u + 211
37u
13
− 96u
12
+ ··· + 385u − 73
(ii) Obstruction class = −1
(iii) Cusp Shapes = 53u
13
− 121u
12
+ 127u
11
− 73u
10
+ 429u
9
− 807u
8
+ 601u
7
+
26u
6
+ 409u
5
− 1340u
4
+ 1590u
3
− 1091u
2
+ 442u − 85
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
7
+ 14u
6
+ 45u
5
− 237u
4
+ 432u
3
− 394u
2
+ 180u − 25)
2
c
2
, c
5
(u
7
− 2u
6
+ 9u
5
− u
4
− 16u
3
+ 8u
2
+ 10u − 5)
2
c
3
, c
4
u
14
− 3u
13
+ ··· − 7u + 1
c
6
, c
12
u
14
+ 4u
13
+ ··· − 5685u + 12167
c
7
, c
11
u
14
+ 6u
13
+ ··· + 168u + 361
c
8
, c
10
u
14
− u
13
+ ··· − u + 1
c
9
(u
7
+ 5u
6
+ 11u
5
+ 10u
4
− u
3
− 11u
2
− 10u − 4)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
7
− 106y
6
+ ··· + 12700y −625)
2
c
2
, c
5
(y
7
+ 14y
6
+ 45y
5
− 237y
4
+ 432y
3
− 394y
2
+ 180y −25)
2
c
3
, c
4
y
14
− y
13
+ ··· − 5y + 1
c
6
, c
12
y
14
− 56y
13
+ ··· + 40244763y + 148035889
c
7
, c
11
y
14
+ 14y
13
+ ··· + 169604y + 130321
c
8
, c
10
y
14
− 33y
13
+ ··· − 19y + 1
c
9
(y
7
− 3y
6
+ 19y
5
− 32y
4
+ 41y
3
− 21y
2
+ 12y −16)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.032790 + 0.667853I
a = −0.440984 + 0.090406I
b = −0.471661 + 0.715058I
−2.57696 + 1.21057I −5.12278 − 3.79229I
u = −1.032790 − 0.667853I
a = −0.440984 − 0.090406I
b = −0.471661 − 0.715058I
−2.57696 − 1.21057I −5.12278 + 3.79229I
u = 0.637347 + 0.231640I
a = −0.05338 − 2.45178I
b = −1.057670 + 0.584877I
−0.84974 − 6.19083I −9.29875 + 3.50078I
u = 0.637347 − 0.231640I
a = −0.05338 + 2.45178I
b = −1.057670 − 0.584877I
−0.84974 + 6.19083I −9.29875 − 3.50078I
u = 0.198510 + 0.598009I
a = 0.99736 + 1.49028I
b = 0.989402
2.30231 4.53226 + 0.I
u = 0.198510 − 0.598009I
a = 0.99736 − 1.49028I
b = 0.989402
2.30231 4.53226 + 0.I
u = 1.04789 + 0.96312I
a = −1.56610 − 0.77379I
b = −1.46537 + 1.27456I
−19.1086 − 5.1850I −3.34460 + 2.00744I
u = 1.04789 − 0.96312I
a = −1.56610 + 0.77379I
b = −1.46537 − 1.27456I
−19.1086 + 5.1850I −3.34460 − 2.00744I
u = 0.555992 + 0.145874I
a = 1.30613 + 1.18459I
b = −0.471661 − 0.715058I
−2.57696 − 1.21057I −5.12278 + 3.79229I
u = 0.555992 − 0.145874I
a = 1.30613 − 1.18459I
b = −0.471661 + 0.715058I
−2.57696 + 1.21057I −5.12278 − 3.79229I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.05150 + 1.03574I
a = −0.404815 − 0.663769I
b = −1.46537 − 1.27456I
−19.1086 + 5.1850I −3.34460 − 2.00744I
u = 1.05150 − 1.03574I
a = −0.404815 + 0.663769I
b = −1.46537 + 1.27456I
−19.1086 − 5.1850I −3.34460 + 2.00744I
u = −0.95844 + 1.25093I
a = −1.338220 + 0.349939I
b = −1.057670 − 0.584877I
−0.84974 + 6.19083I −9.29875 − 3.50078I
u = −0.95844 − 1.25093I
a = −1.338220 − 0.349939I
b = −1.057670 + 0.584877I
−0.84974 − 6.19083I −9.29875 + 3.50078I
18
IV. I
u
4
= hb, a + 1, u + 1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
−1
a
3
=
1
−1
a
10
=
−1
0
a
9
=
−1
0
a
8
=
−2
1
a
1
=
4
−3
a
7
=
−3
1
a
5
=
−2
1
a
2
=
3
−2
a
6
=
−5
3
a
11
=
1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
10
, c
11
u + 1
c
4
, c
5
, c
7
c
8
u − 1
c
6
u − 2
c
9
u
c
12
u + 2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
7
c
8
, c
10
, c
11
y − 1
c
6
, c
12
y − 4
c
9
y
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = 0
−3.28987 −12.0000
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u + 1)(u
7
+ 14u
6
+ 45u
5
− 237u
4
+ 432u
3
− 394u
2
+ 180u − 25)
2
· (u
9
− 5u
8
+ 11u
7
− 5u
6
− 6u
5
+ 6u
4
+ 3u
3
− 4u
2
+ 1)
2
· (u
12
+ 36u
11
+ ··· + 10212u + 784)
c
2
(u + 1)(u
7
− 2u
6
+ 9u
5
− u
4
− 16u
3
+ 8u
2
+ 10u − 5)
2
· ((u
9
− u
8
+ ··· − u
3
+ 1)
2
)(u
12
+ 4u
11
+ ··· + 34u + 28)
c
3
(u + 1)
· (u
12
− u
11
+ u
10
+ 2u
9
+ 2u
8
+ 2u
7
+ u
6
+ 5u
5
+ 6u
4
+ 3u
3
+ 2u
2
+ u + 1)
· (u
14
− 3u
13
+ ··· − 7u + 1)(u
18
+ 8u
17
+ ··· + 5u + 1)
c
4
(u − 1)
· (u
12
− u
11
+ u
10
+ 2u
9
+ 2u
8
+ 2u
7
+ u
6
+ 5u
5
+ 6u
4
+ 3u
3
+ 2u
2
+ u + 1)
· (u
14
− 3u
13
+ ··· − 7u + 1)(u
18
− 8u
17
+ ··· − 5u + 1)
c
5
(u − 1)(u
7
− 2u
6
+ 9u
5
− u
4
− 16u
3
+ 8u
2
+ 10u − 5)
2
· ((u
9
+ u
8
+ ··· − u
3
− 1)
2
)(u
12
+ 4u
11
+ ··· + 34u + 28)
c
6
(u − 2)(u
12
− u
11
+ ··· − 112u + 16)(u
14
+ 4u
13
+ ··· − 5685u + 12167)
· (u
18
+ 4u
17
+ ··· − 64u + 16)
c
7
(u − 1)(u
12
+ u
11
+ ··· + 3u + 1)(u
14
+ 6u
13
+ ··· + 168u + 361)
· (u
18
+ 5u
17
+ ··· + 6u + 1)
c
8
(u − 1)(u
12
− u
11
+ ··· − u + 1)(u
14
− u
13
+ ··· − u + 1)
· (u
18
+ 2u
17
+ ··· − u + 1)
c
9
u(u
7
+ 5u
6
+ 11u
5
+ 10u
4
− u
3
− 11u
2
− 10u − 4)
2
· (u
12
+ 8u
11
+ ··· + 32u + 8)
· (u
18
− 6u
16
+ 18u
14
− 32u
12
+ 36u
10
− 21u
8
− u
6
+ 13u
4
− 9u
2
+ 2)
c
10
(u + 1)(u
12
− u
11
+ ··· − u + 1)(u
14
− u
13
+ ··· − u + 1)
· (u
18
− 2u
17
+ ··· + u + 1)
c
11
(u + 1)(u
12
+ u
11
+ ··· + 3u + 1)(u
14
+ 6u
13
+ ··· + 168u + 361)
· (u
18
− 5u
17
+ ··· − 6u + 1)
c
12
(u + 2)(u
12
− u
11
+ ··· − 112u + 16)(u
14
+ 4u
13
+ ··· − 5685u + 12167)
· (u
18
− 4u
17
+ ··· + 64u + 16)
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)(y
7
− 106y
6
+ ··· + 12700y − 625)
2
· (y
9
− 3y
8
+ 59y
7
− 91y
6
+ 122y
5
− 102y
4
+ 67y
3
− 28y
2
+ 8y − 1)
2
· (y
12
− 104y
11
+ ··· − 27451376y + 614656)
c
2
, c
5
(y − 1)(y
7
+ 14y
6
+ 45y
5
− 237y
4
+ 432y
3
− 394y
2
+ 180y − 25)
2
· (y
9
+ 5y
8
+ 11y
7
+ 5y
6
− 6y
5
− 6y
4
+ 3y
3
+ 4y
2
− 1)
2
· (y
12
+ 36y
11
+ ··· + 10212y + 784)
c
3
, c
4
(y − 1)(y
12
+ y
11
+ ··· + 3y + 1)(y
14
− y
13
+ ··· − 5y + 1)
· (y
18
+ 2y
17
+ ··· + 3y + 1)
c
6
, c
12
(y − 4)(y
12
− 35y
11
+ ··· + 1280y + 256)
· (y
14
− 56y
13
+ ··· + 40244763y + 148035889)
· (y
18
− 22y
17
+ ··· − 512y + 256)
c
7
, c
11
(y − 1)(y
12
+ 11y
11
+ ··· + 175y + 1)
· (y
14
+ 14y
13
+ ··· + 169604y + 130321)(y
18
− 9y
17
+ ··· − 4y + 1)
c
8
, c
10
(y − 1)(y
12
− 25y
11
+ ··· + 21y + 1)(y
14
− 33y
13
+ ··· − 19y + 1)
· (y
18
− 8y
17
+ ··· − y + 1)
c
9
y(y
7
− 3y
6
+ 19y
5
− 32y
4
+ 41y
3
− 21y
2
+ 12y − 16)
2
· (y
9
− 6y
8
+ 18y
7
− 32y
6
+ 36y
5
− 21y
4
− y
3
+ 13y
2
− 9y + 2)
2
· (y
12
− 6y
11
+ ··· + 160y + 64)
24
