12n
0497
(K12n
0497
)
A knot diagram
1
Linearized knot diagam
3 6 9 11 2 1 11 12 3 12 4 7
Solving Sequence
3,6
2 1 7
5,11
4 12 10 9 8
c
2
c
1
c
6
c
5
c
4
c
12
c
10
c
9
c
8
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
26
+ u
25
+ ··· + b − 1, −u
27
+ u
26
+ ··· + 2a − 1, u
28
− 3u
27
+ ··· − 5u + 2i
I
u
2
= h15u
16
a + 46u
16
+ ··· + 16a + 57, 2u
16
a + 2u
16
+ ··· + 2a + 2,
u
17
+ u
16
− 4u
15
− 5u
14
+ 7u
13
+ 11u
12
− 4u
11
− 12u
10
− 3u
9
+ 5u
8
+ 6u
7
+ 2u
6
− 2u
5
− 2u
4
+ u + 1i
I
u
3
= h−u
9
+ u
8
+ 2u
7
− 2u
6
− u
5
+ 2u
4
− 2u
3
+ b + u, −u
9
+ 3u
7
− 3u
5
− u
3
− u
2
+ a + 2u + 1,
u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 72 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−u
26
+u
25
+· · ·+b−1, −u
27
+u
26
+· · ·+2a−1, u
28
−3u
27
+· · ·−5u+2i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
7
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
5
=
u
−u
3
+ u
a
11
=
1
2
u
27
−
1
2
u
26
+ ··· +
1
2
u +
1
2
u
26
− u
25
+ ··· − 2u + 1
a
4
=
5
2
u
27
−
11
2
u
26
+ ··· +
19
2
u −
7
2
u
27
− 2u
26
+ ··· + 4u − 1
a
12
=
−u
8
+ 3u
6
− 3u
4
+ 1
−u
8
+ 2u
6
− 2u
4
a
10
=
−
1
2
u
27
−
1
2
u
26
+ ··· −
1
2
u −
1
2
−u
26
+ u
25
+ ··· + u − 1
a
9
=
−
1
2
u
27
+
1
2
u
26
+ ··· −
3
2
u +
1
2
−u
26
+ u
25
+ ··· + u − 1
a
8
=
−
1
2
u
27
+
1
2
u
26
+ ··· −
3
2
u −
1
2
u
27
− 3u
26
+ ··· + 4u − 3
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 12u
27
− 26u
26
− 60u
25
+ 194u
24
+ 66u
23
− 624u
22
+ 300u
21
+ 1000u
20
− 1212u
19
−
496u
18
+ 1882u
17
− 990u
16
− 1108u
15
+ 1922u
14
− 632u
13
− 1070u
12
+ 1352u
11
−
364u
10
− 552u
9
+ 642u
8
− 188u
7
− 148u
6
+ 140u
5
− 26u
4
− 4u
3
− 26u
2
+ 40u − 18
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
28
+ 15u
27
+ ··· + 5u + 4
c
2
, c
5
u
28
+ 3u
27
+ ··· + 5u + 2
c
3
, c
4
, c
9
c
11
u
28
+ 4u
26
+ ··· + 4u
2
+ 1
c
6
, c
12
u
28
+ 9u
27
+ ··· + 131u + 22
c
7
, c
10
u
28
+ 8u
27
+ ··· + 8u + 1
c
8
u
28
− 27u
27
+ ··· − 1310720u + 131072
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
− 3y
27
+ ··· + 127y + 16
c
2
, c
5
y
28
− 15y
27
+ ··· − 5y + 4
c
3
, c
4
, c
9
c
11
y
28
+ 8y
27
+ ··· + 8y + 1
c
6
, c
12
y
28
+ 21y
27
+ ··· + 4619y + 484
c
7
, c
10
y
28
+ 36y
27
+ ··· − 4y + 1
c
8
y
28
− y
27
+ ··· − 68719476736y + 17179869184
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.838339 + 0.609506I
a = 2.02490 + 0.32117I
b = 1.63543 − 0.56429I
4.54882 − 8.90596I 2.89775 + 8.10604I
u = 0.838339 − 0.609506I
a = 2.02490 − 0.32117I
b = 1.63543 + 0.56429I
4.54882 + 8.90596I 2.89775 − 8.10604I
u = 0.921727 + 0.275365I
a = 0.108050 − 0.114256I
b = −0.344737 − 0.488716I
−1.55959 − 1.05431I −1.79804 + 0.46594I
u = 0.921727 − 0.275365I
a = 0.108050 + 0.114256I
b = −0.344737 + 0.488716I
−1.55959 + 1.05431I −1.79804 − 0.46594I
u = 0.703652 + 0.629749I
a = −1.30690 − 1.80011I
b = −1.40201 − 0.27411I
4.93581 + 4.08901I 4.07475 − 1.93995I
u = 0.703652 − 0.629749I
a = −1.30690 + 1.80011I
b = −1.40201 + 0.27411I
4.93581 − 4.08901I 4.07475 + 1.93995I
u = −1.111100 + 0.197384I
a = −0.663263 + 0.454903I
b = 0.402976 + 0.493201I
−1.23154 + 4.92206I −2.90000 − 5.98103I
u = −1.111100 − 0.197384I
a = −0.663263 − 0.454903I
b = 0.402976 − 0.493201I
−1.23154 − 4.92206I −2.90000 + 5.98103I
u = −1.034790 + 0.451847I
a = −1.004190 + 0.787576I
b = −0.429091 − 0.267812I
−0.61833 + 4.24425I 2.47597 − 7.12989I
u = −1.034790 − 0.451847I
a = −1.004190 − 0.787576I
b = −0.429091 + 0.267812I
−0.61833 − 4.24425I 2.47597 + 7.12989I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.192590 + 0.822500I
a = 1.84621 + 0.80888I
b = 1.77610 + 1.30259I
1.19759 + 10.21300I 1.05547 − 6.41912I
u = 0.192590 − 0.822500I
a = 1.84621 − 0.80888I
b = 1.77610 − 1.30259I
1.19759 − 10.21300I 1.05547 + 6.41912I
u = 0.013220 + 0.818433I
a = −1.241790 − 0.286928I
b = −1.169750 − 0.031128I
−4.44025 − 1.37296I 0.48249 + 5.14234I
u = 0.013220 − 0.818433I
a = −1.241790 + 0.286928I
b = −1.169750 + 0.031128I
−4.44025 + 1.37296I 0.48249 − 5.14234I
u = 0.302848 + 0.727841I
a = −0.358063 + 0.787194I
b = −0.755447 − 0.122906I
3.14248 − 2.30749I 3.95704 + 2.80848I
u = 0.302848 − 0.727841I
a = −0.358063 − 0.787194I
b = −0.755447 + 0.122906I
3.14248 + 2.30749I 3.95704 − 2.80848I
u = 1.121240 + 0.535567I
a = 0.156564 + 1.250950I
b = 0.581791 − 0.415759I
0.75026 − 2.48047I 1.02092 + 1.26757I
u = 1.121240 − 0.535567I
a = 0.156564 − 1.250950I
b = 0.581791 + 0.415759I
0.75026 + 2.48047I 1.02092 − 1.26757I
u = −1.217360 + 0.336899I
a = 1.098970 + 0.381945I
b = −1.49642 + 1.46220I
−3.14603 − 6.41259I −3.85247 + 3.94753I
u = −1.217360 − 0.336899I
a = 1.098970 − 0.381945I
b = −1.49642 − 1.46220I
−3.14603 + 6.41259I −3.85247 − 3.94753I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.222980 + 0.448998I
a = 0.044120 − 1.217890I
b = 1.286970 − 0.254811I
−8.11487 + 5.88224I −3.16516 − 8.68270I
u = −1.222980 − 0.448998I
a = 0.044120 + 1.217890I
b = 1.286970 + 0.254811I
−8.11487 − 5.88224I −3.16516 + 8.68270I
u = 1.187410 + 0.536042I
a = −1.78923 − 1.80447I
b = −1.92014 + 1.45210I
−1.7522 − 15.2166I −2.10611 + 9.57397I
u = 1.187410 − 0.536042I
a = −1.78923 + 1.80447I
b = −1.92014 − 1.45210I
−1.7522 + 15.2166I −2.10611 − 9.57397I
u = 1.218890 + 0.463215I
a = 0.092034 + 0.847732I
b = 1.348210 + 0.129672I
−8.01221 − 3.21387I −2.49318 − 1.97492I
u = 1.218890 − 0.463215I
a = 0.092034 − 0.847732I
b = 1.348210 − 0.129672I
−8.01221 + 3.21387I −2.49318 + 1.97492I
u = −0.413687 + 0.465218I
a = 1.242590 − 0.032918I
b = 0.486106 − 0.112850I
1.140620 − 0.349325I 8.35057 + 1.44622I
u = −0.413687 − 0.465218I
a = 1.242590 + 0.032918I
b = 0.486106 + 0.112850I
1.140620 + 0.349325I 8.35057 − 1.44622I
7
II. I
u
2
=
h15u
16
a+46u
16
+· · ·+16a +57, 2u
16
a+2u
16
+· · ·+2a +2, u
17
+u
16
+· · ·+u +1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
7
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
5
=
u
−u
3
+ u
a
11
=
a
−1.07143au
16
− 3.28571u
16
+ ··· − 1.14286a − 4.07143
a
4
=
−2.64286au
16
− 5.57143u
16
+ ··· − 3.28571a − 6.64286
−0.785714au
16
− 0.142857u
16
+ ··· − 0.571429a + 0.214286
a
12
=
−u
8
+ 3u
6
− 3u
4
+ 1
−u
8
+ 2u
6
− 2u
4
a
10
=
5
14
u
16
a −
4
7
u
16
+ ··· +
5
7
a −
9
14
−0.785714au
16
− 2.64286u
16
+ ··· − 1.07143a − 3.28571
a
9
=
1.14286au
16
+ 2.07143u
16
+ ··· + 1.78571a + 2.64286
−0.785714au
16
− 2.64286u
16
+ ··· − 1.07143a − 3.28571
a
8
=
1.14286au
16
+ 2.07143u
16
+ ··· + 1.78571a + 3.64286
−0.785714au
16
− 2.64286u
16
+ ··· − 1.07143a − 3.28571
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
16
+20u
14
+4u
13
−44u
12
−16u
11
+44u
10
+28u
9
−8u
8
−20u
7
−24u
6
+16u
4
+8u
3
−6
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
17
+ 9u
16
+ ··· + u + 1)
2
c
2
, c
5
(u
17
− u
16
+ ··· + u − 1)
2
c
3
, c
4
, c
9
c
11
u
34
− u
33
+ ··· − 4u + 17
c
6
, c
12
(u
17
− 3u
16
+ ··· + 9u − 3)
2
c
7
, c
10
u
34
+ 15u
33
+ ··· + 3996u + 289
c
8
(u + 1)
34
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
17
− y
16
+ ··· + 9y −1)
2
c
2
, c
5
(y
17
− 9y
16
+ ··· + y −1)
2
c
3
, c
4
, c
9
c
11
y
34
+ 15y
33
+ ··· + 3996y + 289
c
6
, c
12
(y
17
+ 11y
16
+ ··· + 57y −9)
2
c
7
, c
10
y
34
+ 7y
33
+ ··· + 13684y + 83521
c
8
(y −1)
34
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.774885 + 0.615952I
a = 1.95560 − 0.12550I
b = 1.43682 + 0.54249I
5.48114 + 2.39923I 4.86600 − 3.27109I
u = −0.774885 + 0.615952I
a = −1.12508 + 1.73447I
b = −1.313090 + 0.274756I
5.48114 + 2.39923I 4.86600 − 3.27109I
u = −0.774885 − 0.615952I
a = 1.95560 + 0.12550I
b = 1.43682 − 0.54249I
5.48114 − 2.39923I 4.86600 + 3.27109I
u = −0.774885 − 0.615952I
a = −1.12508 − 1.73447I
b = −1.313090 − 0.274756I
5.48114 − 2.39923I 4.86600 + 3.27109I
u = 0.758174 + 0.422247I
a = −0.385946 + 0.814951I
b = −0.345721 − 0.443070I
−2.16659 − 1.83062I 3.59303 + 5.22267I
u = 0.758174 + 0.422247I
a = 1.57848 − 1.49239I
b = 0.098207 − 1.328870I
−2.16659 − 1.83062I 3.59303 + 5.22267I
u = 0.758174 − 0.422247I
a = −0.385946 − 0.814951I
b = −0.345721 + 0.443070I
−2.16659 + 1.83062I 3.59303 − 5.22267I
u = 0.758174 − 0.422247I
a = 1.57848 + 1.49239I
b = 0.098207 + 1.328870I
−2.16659 + 1.83062I 3.59303 − 5.22267I
u = −0.231761 + 0.782357I
a = −0.473057 − 0.691325I
b = −0.848798 + 0.084430I
2.86113 − 3.91820I 3.59784 + 2.39256I
u = −0.231761 + 0.782357I
a = 1.63626 − 0.70519I
b = 1.40711 − 1.14265I
2.86113 − 3.91820I 3.59784 + 2.39256I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.231761 − 0.782357I
a = −0.473057 + 0.691325I
b = −0.848798 − 0.084430I
2.86113 + 3.91820I 3.59784 − 2.39256I
u = −0.231761 − 0.782357I
a = 1.63626 + 0.70519I
b = 1.40711 + 1.14265I
2.86113 + 3.91820I 3.59784 − 2.39256I
u = 1.172060 + 0.309872I
a = 0.890855 − 0.052712I
b = −1.06012 − 1.21986I
−1.42208 + 0.50801I −1.57451 + 0.23246I
u = 1.172060 + 0.309872I
a = −0.592391 − 0.231519I
b = 0.574760 − 0.116741I
−1.42208 + 0.50801I −1.57451 + 0.23246I
u = 1.172060 − 0.309872I
a = 0.890855 + 0.052712I
b = −1.06012 + 1.21986I
−1.42208 − 0.50801I −1.57451 − 0.23246I
u = 1.172060 − 0.309872I
a = −0.592391 + 0.231519I
b = 0.574760 + 0.116741I
−1.42208 − 0.50801I −1.57451 − 0.23246I
u = −1.151920 + 0.412149I
a = 0.37723 − 1.47258I
b = 1.58984 − 0.43724I
−7.43223 + 2.05778I −5.01930 − 0.37816I
u = −1.151920 + 0.412149I
a = 1.36789 − 1.01197I
b = 0.14263 + 2.01039I
−7.43223 + 2.05778I −5.01930 − 0.37816I
u = −1.151920 − 0.412149I
a = 0.37723 + 1.47258I
b = 1.58984 + 0.43724I
−7.43223 − 2.05778I −5.01930 + 0.37816I
u = −1.151920 − 0.412149I
a = 1.36789 + 1.01197I
b = 0.14263 − 2.01039I
−7.43223 − 2.05778I −5.01930 + 0.37816I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.756727
a = −2.02895 + 0.42231I
b = −0.610864 − 1.213540I
−4.29463 −6.86910
u = −0.756727
a = −2.02895 − 0.42231I
b = −0.610864 + 1.213540I
−4.29463 −6.86910
u = 1.156820 + 0.481476I
a = 0.604787 + 1.109620I
b = 1.61273 + 0.16388I
−6.93551 − 6.09306I −3.29297 + 6.87425I
u = 1.156820 + 0.481476I
a = −2.32403 − 0.58332I
b = −0.24092 + 1.93715I
−6.93551 − 6.09306I −3.29297 + 6.87425I
u = 1.156820 − 0.481476I
a = 0.604787 − 1.109620I
b = 1.61273 − 0.16388I
−6.93551 + 6.09306I −3.29297 − 6.87425I
u = 1.156820 − 0.481476I
a = −2.32403 + 0.58332I
b = −0.24092 − 1.93715I
−6.93551 + 6.09306I −3.29297 − 6.87425I
u = −1.162590 + 0.537552I
a = 0.095082 − 1.330870I
b = 0.768573 + 0.266965I
0.12247 + 8.83664I 0.37368 − 5.87120I
u = −1.162590 + 0.537552I
a = −1.77126 + 1.49317I
b = −1.49812 − 1.33018I
0.12247 + 8.83664I 0.37368 − 5.87120I
u = −1.162590 − 0.537552I
a = 0.095082 + 1.330870I
b = 0.768573 − 0.266965I
0.12247 − 8.83664I 0.37368 + 5.87120I
u = −1.162590 − 0.537552I
a = −1.77126 − 1.49317I
b = −1.49812 + 1.33018I
0.12247 − 8.83664I 0.37368 + 5.87120I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.112463 + 0.679715I
a = 0.762089 + 1.010660I
b = 0.06904 + 1.77832I
−3.98789 + 1.70542I −0.10923 − 4.02096I
u = 0.112463 + 0.679715I
a = −2.06756 − 0.51340I
b = −1.282070 − 0.039466I
−3.98789 + 1.70542I −0.10923 − 4.02096I
u = 0.112463 − 0.679715I
a = 0.762089 − 1.010660I
b = 0.06904 − 1.77832I
−3.98789 − 1.70542I −0.10923 + 4.02096I
u = 0.112463 − 0.679715I
a = −2.06756 + 0.51340I
b = −1.282070 + 0.039466I
−3.98789 − 1.70542I −0.10923 + 4.02096I
14
III. I
u
3
= h−u
9
+ u
8
+ · · · + b + u, −u
9
+ 3u
7
− 3u
5
− u
3
− u
2
+ a + 2u +
1, u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
7
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
5
=
u
−u
3
+ u
a
11
=
u
9
− 3u
7
+ 3u
5
+ u
3
+ u
2
− 2u − 1
u
9
− u
8
− 2u
7
+ 2u
6
+ u
5
− 2u
4
+ 2u
3
− u
a
4
=
u
8
+ u
7
− 2u
6
− 2u
5
+ 2u
4
+ 2u
3
+ u
2
+ u
1
a
12
=
−u
8
+ 3u
6
− 3u
4
+ 1
−u
8
+ 2u
6
− 2u
4
a
10
=
u
9
+ u
8
− 3u
7
− 3u
6
+ 3u
5
+ 3u
4
+ u
3
+ u
2
− 2u − 2
u
9
− 2u
7
+ u
5
+ 2u
3
− u
a
9
=
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− u
3
+ u
2
− u − 2
u
9
− 2u
7
+ u
5
+ 2u
3
− u
a
8
=
u
9
− 3u
7
+ 4u
5
− u
3
+ u
2
− u − 1
u
9
− u
8
− 2u
7
+ 2u
6
+ 2u
5
− 2u
4
+ u
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
8
− 8u
6
+ 8u
4
+ 4u
2
− 8
15
(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
, c
5
u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1
c
3
, c
4
, c
9
c
11
(u
2
+ 1)
5
c
6
, c
12
u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1
c
7
, c
10
(u − 1)
10
c
8
u
10
− 10u
9
+ ··· − 108u + 17
16
(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
9
c
11
(y + 1)
10
c
6
, c
12
(y
5
+ 5y
4
+ 8y
3
+ 3y
2
− y + 1)
2
c
7
, c
10
(y −1)
10
c
8
y
10
+ 16y
8
+ ··· − 716y + 289
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.822375 + 0.339110I
a = 0.668968 + 0.313470I
b = −0.30992 + 1.54991I
−3.61897 + 1.53058I −4.51511 − 4.43065I
u = −0.822375 − 0.339110I
a = 0.668968 − 0.313470I
b = −0.30992 − 1.54991I
−3.61897 − 1.53058I −4.51511 + 4.43065I
u = 0.822375 + 0.339110I
a = −1.54636 + 1.42897I
b = −0.309916 + 0.450089I
−3.61897 − 1.53058I −4.51511 + 4.43065I
u = 0.822375 − 0.339110I
a = −1.54636 − 1.42897I
b = −0.309916 − 0.450089I
−3.61897 + 1.53058I −4.51511 − 4.43065I
u = 0.766826I
a = −1.58802 − 0.62971I
b = −1.21774 − 1.00000I
−5.69095 −5.48110
u = − 0.766826I
a = −1.58802 + 0.62971I
b = −1.21774 + 1.00000I
−5.69095 −5.48110
u = −1.200150 + 0.455697I
a = −0.641941 − 0.907733I
b = 1.41878 − 1.21917I
−9.16243 + 4.40083I −8.74431 − 3.49859I
u = −1.200150 − 0.455697I
a = −0.641941 + 0.907733I
b = 1.41878 + 1.21917I
−9.16243 − 4.40083I −8.74431 + 3.49859I
u = 1.200150 + 0.455697I
a = 1.10735 + 1.27989I
b = 1.41878 − 0.78083I
−9.16243 − 4.40083I −8.74431 + 3.49859I
u = 1.200150 − 0.455697I
a = 1.10735 − 1.27989I
b = 1.41878 + 0.78083I
−9.16243 + 4.40083I −8.74431 − 3.49859I
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
)(u
17
+ 9u
16
+ ··· + u + 1)
2
· (u
28
+ 15u
27
+ ··· + 5u + 4)
c
2
, c
5
(u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1)(u
17
− u
16
+ ··· + u − 1)
2
· (u
28
+ 3u
27
+ ··· + 5u + 2)
c
3
, c
4
, c
9
c
11
((u
2
+ 1)
5
)(u
28
+ 4u
26
+ ··· + 4u
2
+ 1)(u
34
− u
33
+ ··· − 4u + 17)
c
6
, c
12
(u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1)(u
17
− 3u
16
+ ··· + 9u − 3)
2
· (u
28
+ 9u
27
+ ··· + 131u + 22)
c
7
, c
10
((u − 1)
10
)(u
28
+ 8u
27
+ ··· + 8u + 1)(u
34
+ 15u
33
+ ··· + 3996u + 289)
c
8
((u + 1)
34
)(u
10
− 10u
9
+ ··· − 108u + 17)
· (u
28
− 27u
27
+ ··· − 1310720u + 131072)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
)(y
17
− y
16
+ ··· + 9y −1)
2
· (y
28
− 3y
27
+ ··· + 127y + 16)
c
2
, c
5
((y
5
− 3y
4
+ 4y
3
− y
2
− y + 1)
2
)(y
17
− 9y
16
+ ··· + y −1)
2
· (y
28
− 15y
27
+ ··· − 5y + 4)
c
3
, c
4
, c
9
c
11
((y + 1)
10
)(y
28
+ 8y
27
+ ··· + 8y + 1)(y
34
+ 15y
33
+ ··· + 3996y + 289)
c
6
, c
12
((y
5
+ 5y
4
+ 8y
3
+ 3y
2
− y + 1)
2
)(y
17
+ 11y
16
+ ··· + 57y −9)
2
· (y
28
+ 21y
27
+ ··· + 4619y + 484)
c
7
, c
10
((y −1)
10
)(y
28
+ 36y
27
+ ··· − 4y + 1)
· (y
34
+ 7y
33
+ ··· + 13684y + 83521)
c
8
((y −1)
34
)(y
10
+ 16y
8
+ ··· − 716y + 289)
· (y
28
− y
27
+ ··· − 68719476736y + 17179869184)
20
