12n
0157
(K12n
0157
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 9 10 12 3 11 6 1 7
Solving Sequence
6,11
10 7 9
3,5
2 1 4 12 8
c
10
c
6
c
9
c
5
c
2
c
1
c
4
c
12
c
7
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
16
− 3u
15
+ 6u
14
− 8u
13
+ 12u
12
− 12u
11
+ 12u
10
− 3u
9
− 3u
8
+ 5u
7
− 9u
6
+ 9u
5
− 5u
4
− 6u
3
+ 8b − u − 3,
− 3u
16
+ 5u
15
+ ··· + 4a − 7, u
17
+ 5u
15
+ ··· + 2u − 1i
I
u
2
= h−92905u
29
+ 216359u
28
+ ··· + 130935b + 251026,
263141u
29
− 444141u
28
+ ··· + 130935a − 340714, u
30
− 2u
29
+ ··· − 2u + 1i
I
u
3
= h−u
3
− u
2
+ 2b − 1, u
3
+ a + u + 1, u
4
+ u
2
+ u + 1i
I
u
4
= hu
4
− u
3
+ u
2
+ b − u + 1, u
5
− u
4
+ 2u
3
− 2u
2
+ a + 2u − 2, u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
* 4 irreducible components of dim
C
= 0, with total 57 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
16
−3u
15
+· · ·+8b−3, −3u
16
+5u
15
+· · ·+4a−7, u
17
+5u
15
+· · ·+2u−1i
(i) Arc colorings
a
6
=
0
u
a
11
=
1
0
a
10
=
1
−u
2
a
7
=
−u
u
3
+ u
a
9
=
u
2
+ 1
−u
2
a
3
=
3
4
u
16
−
5
4
u
15
+ ··· −
15
4
u +
7
4
−
1
8
u
16
+
3
8
u
15
+ ··· +
1
8
u +
3
8
a
5
=
−u
5
− 2u
3
− u
u
5
+ u
3
+ u
a
2
=
3
4
u
16
−
1
4
u
15
+ ··· −
15
4
u +
7
4
−
3
8
u
16
+
1
8
u
15
+ ··· +
3
8
u +
1
8
a
1
=
u
15
+ 4u
13
+ ··· − 2u
2
+ 2u
u
2
a
4
=
3
4
u
16
−
9
4
u
15
+ ··· −
19
4
u +
7
4
3
8
u
16
+
7
8
u
15
+ ··· −
11
8
u +
7
8
a
12
=
u
15
+ 4u
13
+ ··· − u
2
+ 2u
−u
4
a
8
=
−u
16
− 4u
14
+ ··· − 2u
2
− u
u
5
+ u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
31
16
u
16
−
43
16
u
15
−
73
8
u
14
−
29
2
u
13
−
107
4
u
12
−
145
4
u
11
−
177
4
u
10
−
851
16
u
9
−
835
16
u
8
−
763
16
u
7
−
625
16
u
6
−
487
16
u
5
−
477
16
u
4
−
127
8
u
3
− 7u
2
−
97
16
u −
115
16
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
+ 3u
16
+ ··· + 209u + 16
c
2
, c
4
u
17
− 3u
16
+ ··· − 15u + 4
c
3
, c
8
u
17
+ 3u
16
+ ··· + 144u + 64
c
5
u
17
− 6u
16
+ ··· + 4u + 4
c
6
, c
7
, c
10
c
12
u
17
+ 5u
15
+ ··· + 2u + 1
c
9
, c
11
u
17
− 10u
16
+ ··· + 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
+ 25y
16
+ ··· + 9953y −256
c
2
, c
4
y
17
− 3y
16
+ ··· + 209y −16
c
3
, c
8
y
17
+ 21y
16
+ ··· − 28416y −4096
c
5
y
17
− 20y
16
+ ··· + 8y −16
c
6
, c
7
, c
10
c
12
y
17
+ 10y
16
+ ··· + 2y −1
c
9
, c
11
y
17
− 2y
16
+ ··· + 62y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.322169 + 0.932839I
a = 1.62275 − 0.13510I
b = −0.887795 − 0.139754I
0.45185 − 4.10615I −5.36541 + 8.40411I
u = 0.322169 − 0.932839I
a = 1.62275 + 0.13510I
b = −0.887795 + 0.139754I
0.45185 + 4.10615I −5.36541 − 8.40411I
u = −0.942204 + 0.079923I
a = 0.14770 − 2.09951I
b = 0.10264 + 1.92963I
5.75170 − 3.64530I −7.03668 + 2.07740I
u = −0.942204 − 0.079923I
a = 0.14770 + 2.09951I
b = 0.10264 − 1.92963I
5.75170 + 3.64530I −7.03668 − 2.07740I
u = 0.644046 + 0.585914I
a = 0.110639 − 0.237693I
b = 0.141114 + 0.412958I
−1.54328 − 1.26290I −4.69916 + 2.78148I
u = 0.644046 − 0.585914I
a = 0.110639 + 0.237693I
b = 0.141114 − 0.412958I
−1.54328 + 1.26290I −4.69916 − 2.78148I
u = −0.365355 + 1.127480I
a = −0.001951 + 1.108840I
b = −0.461535 + 0.413910I
5.03884 + 6.08356I −0.37752 − 7.44095I
u = −0.365355 − 1.127480I
a = −0.001951 − 1.108840I
b = −0.461535 − 0.413910I
5.03884 − 6.08356I −0.37752 + 7.44095I
u = −0.603603 + 1.090260I
a = −0.576964 + 0.057793I
b = −0.208622 − 0.448687I
1.68715 + 8.69176I −1.96939 − 9.35770I
u = −0.603603 − 1.090260I
a = −0.576964 − 0.057793I
b = −0.208622 + 0.448687I
1.68715 − 8.69176I −1.96939 + 9.35770I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.204874 + 0.705829I
a = −1.11943 − 2.16921I
b = 0.782082 − 0.120438I
−1.27035 + 1.28580I −7.39957 − 4.02248I
u = −0.204874 − 0.705829I
a = −1.11943 + 2.16921I
b = 0.782082 + 0.120438I
−1.27035 − 1.28580I −7.39957 + 4.02248I
u = 0.445712 + 1.288030I
a = −1.82989 − 0.01952I
b = 0.74942 + 2.06882I
14.2142 − 5.9853I −0.22003 + 3.96763I
u = 0.445712 − 1.288030I
a = −1.82989 + 0.01952I
b = 0.74942 − 2.06882I
14.2142 + 5.9853I −0.22003 − 3.96763I
u = 0.524102 + 1.283480I
a = 1.78460 + 0.35804I
b = −0.69769 − 2.47703I
13.1143 − 14.2375I −1.63337 + 7.74538I
u = 0.524102 − 1.283480I
a = 1.78460 − 0.35804I
b = −0.69769 + 2.47703I
13.1143 + 14.2375I −1.63337 − 7.74538I
u = 0.360012
a = 0.725098
b = 0.460755
−0.866858 −11.8480
6
II.
I
u
2
= h−9.29 × 10
4
u
29
+ 2.16 × 10
5
u
28
+ · · · + 1.31 × 10
5
b + 2.51 × 10
5
, 2.63 ×
10
5
u
29
−4.44×10
5
u
28
+· · · +1.31×10
5
a−3.41×10
5
, u
30
−2u
29
+· · · − 2u +1i
(i) Arc colorings
a
6
=
0
u
a
11
=
1
0
a
10
=
1
−u
2
a
7
=
−u
u
3
+ u
a
9
=
u
2
+ 1
−u
2
a
3
=
−2.00971u
29
+ 3.39207u
28
+ ··· − 5.34987u + 2.60216
0.709551u
29
− 1.65242u
28
+ ··· + 4.31412u − 1.91718
a
5
=
−u
5
− 2u
3
− u
u
5
+ u
3
+ u
a
2
=
−0.985413u
29
+ 2.58805u
28
+ ··· − 1.73251u + 0.970054
−0.0934739u
29
− 1.15465u
28
+ ··· + 1.36986u − 0.724375
a
1
=
−1.10899u
29
+ 2.08162u
28
+ ··· + 7.36940u + 0.914484
0.581747u
29
− 0.918028u
28
+ ··· − 0.836285u − 1.13635
a
4
=
−3.03400u
29
+ 4.19610u
28
+ ··· − 9.96723u + 4.23427
1.30708u
29
− 2.17849u
28
+ ··· + 5.03852u − 2.49276
a
12
=
−1.69073u
29
+ 2.99965u
28
+ ··· + 8.20569u + 1.05083
1.96604u
29
− 2.83797u
28
+ ··· − 1.76339u − 1.51817
a
8
=
−1.24547u
29
+ 1.68839u
28
+ ··· − 2.02714u + 2.58175
0.712292u
29
− 1.03145u
28
+ ··· − 0.916722u − 0.275305
(ii) Obstruction class = −1
(iii) Cusp Shapes =
240791
130935
u
29
−
162874
43645
u
28
+ ··· −
489788
43645
u −
735898
130935
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
15
+ 2u
14
+ ··· − 3u + 1)
2
c
2
, c
4
(u
15
− 4u
14
+ ··· − 3u + 1)
2
c
3
, c
8
(u
15
− u
14
+ ··· + 12u − 8)
2
c
5
(u
15
+ 2u
14
+ ··· + 2u − 1)
2
c
6
, c
7
, c
10
c
12
u
30
+ 2u
29
+ ··· + 2u + 1
c
9
, c
11
u
30
− 18u
29
+ ··· + 20u
2
+ 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
15
+ 26y
14
+ ··· − 3y −1)
2
c
2
, c
4
(y
15
− 2y
14
+ ··· − 3y −1)
2
c
3
, c
8
(y
15
+ 21y
14
+ ··· − 48y −64)
2
c
5
(y
15
− 20y
14
+ ··· + 20y −1)
2
c
6
, c
7
, c
10
c
12
y
30
+ 18y
29
+ ··· + 20y
2
+ 1
c
9
, c
11
y
30
− 14y
29
+ ··· + 40y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.113884 + 1.019270I
a = 0.083302 − 0.745556I
b = −3.08095 + 2.65889I
2.02375 −13.41313 + 0.I
u = 0.113884 − 1.019270I
a = 0.083302 + 0.745556I
b = −3.08095 − 2.65889I
2.02375 −13.41313 + 0.I
u = 0.968195 + 0.069474I
a = 0.13797 − 2.33358I
b = −0.34781 + 2.07950I
9.38409 + 8.90152I −4.37309 − 5.02376I
u = 0.968195 − 0.069474I
a = 0.13797 + 2.33358I
b = −0.34781 − 2.07950I
9.38409 − 8.90152I −4.37309 + 5.02376I
u = 0.919318 + 0.052871I
a = −0.58314 − 2.24993I
b = 0.20945 + 2.09210I
10.07630 − 1.17157I −3.47853 + 0.84051I
u = 0.919318 − 0.052871I
a = −0.58314 + 2.24993I
b = 0.20945 − 2.09210I
10.07630 + 1.17157I −3.47853 − 0.84051I
u = −0.382683 + 1.019330I
a = −0.100174 + 0.245215I
b = −1.043020 + 0.299494I
4.66000 + 0.70150I 1.29100 − 2.23884I
u = −0.382683 − 1.019330I
a = −0.100174 − 0.245215I
b = −1.043020 − 0.299494I
4.66000 − 0.70150I 1.29100 + 2.23884I
u = −0.205921 + 0.850565I
a = −1.04297 − 1.20710I
b = 1.238940 − 0.251605I
−1.01332 + 1.14653I −7.69630 + 0.14216I
u = −0.205921 − 0.850565I
a = −1.04297 + 1.20710I
b = 1.238940 + 0.251605I
−1.01332 − 1.14653I −7.69630 − 0.14216I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.779082 + 0.386456I
a = −0.002343 − 0.498402I
b = −0.087330 + 0.645001I
−0.36549 − 3.51330I −3.79294 + 4.67402I
u = −0.779082 − 0.386456I
a = −0.002343 + 0.498402I
b = −0.087330 − 0.645001I
−0.36549 + 3.51330I −3.79294 − 4.67402I
u = 0.285236 + 1.100680I
a = 0.248621 + 0.458325I
b = −0.050199 + 0.632654I
1.96945 − 2.58137I −3.99557 + 4.00241I
u = 0.285236 − 1.100680I
a = 0.248621 − 0.458325I
b = −0.050199 − 0.632654I
1.96945 + 2.58137I −3.99557 − 4.00241I
u = 0.581753 + 0.981574I
a = 0.378951 + 0.026508I
b = 0.335458 − 0.088672I
−0.36549 − 3.51330I −3.79294 + 4.67402I
u = 0.581753 − 0.981574I
a = 0.378951 − 0.026508I
b = 0.335458 + 0.088672I
−0.36549 + 3.51330I −3.79294 − 4.67402I
u = −0.221864 + 1.217690I
a = 0.186395 + 0.139826I
b = −0.081740 + 1.033740I
4.66000 − 0.70150I 1.29100 + 2.23884I
u = −0.221864 − 1.217690I
a = 0.186395 − 0.139826I
b = −0.081740 − 1.033740I
4.66000 + 0.70150I 1.29100 − 2.23884I
u = 0.505703 + 1.263210I
a = 1.53273 + 0.65637I
b = −0.01619 − 2.51545I
13.7555 − 3.9297I −0.74800 + 2.37642I
u = 0.505703 − 1.263210I
a = 1.53273 − 0.65637I
b = −0.01619 + 2.51545I
13.7555 + 3.9297I −0.74800 − 2.37642I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.522779 + 1.269460I
a = −1.59728 + 0.42484I
b = 0.39291 − 2.31888I
9.38409 + 8.90152I −4.37309 − 5.02376I
u = −0.522779 − 1.269460I
a = −1.59728 − 0.42484I
b = 0.39291 + 2.31888I
9.38409 − 8.90152I −4.37309 + 5.02376I
u = −0.431128 + 1.304160I
a = 1.54639 − 0.19135I
b = −0.48250 + 1.97368I
10.07630 + 1.17157I −3.47853 − 0.84051I
u = −0.431128 − 1.304160I
a = 1.54639 + 0.19135I
b = −0.48250 − 1.97368I
10.07630 − 1.17157I −3.47853 + 0.84051I
u = 0.441120 + 1.321990I
a = −1.55605 − 0.47835I
b = 0.28997 + 2.13261I
13.7555 + 3.9297I −0.74800 − 2.37642I
u = 0.441120 − 1.321990I
a = −1.55605 + 0.47835I
b = 0.28997 − 2.13261I
13.7555 − 3.9297I −0.74800 + 2.37642I
u = −0.556485 + 0.018600I
a = 0.802481 − 0.699849I
b = −0.908162 − 0.199648I
1.96945 − 2.58137I −3.99557 + 4.00241I
u = −0.556485 − 0.018600I
a = 0.802481 + 0.699849I
b = −0.908162 + 0.199648I
1.96945 + 2.58137I −3.99557 − 4.00241I
u = 0.284735 + 0.297386I
a = 0.96512 − 3.25062I
b = 0.131164 + 0.467054I
−1.01332 + 1.14653I −7.69630 + 0.14216I
u = 0.284735 − 0.297386I
a = 0.96512 + 3.25062I
b = 0.131164 − 0.467054I
−1.01332 − 1.14653I −7.69630 − 0.14216I
12
III. I
u
3
= h−u
3
− u
2
+ 2b − 1, u
3
+ a + u + 1, u
4
+ u
2
+ u + 1i
(i) Arc colorings
a
6
=
0
u
a
11
=
1
0
a
10
=
1
−u
2
a
7
=
−u
u
3
+ u
a
9
=
u
2
+ 1
−u
2
a
3
=
−u
3
− u − 1
1
2
u
3
+
1
2
u
2
+
1
2
a
5
=
−u
3
+ u
2
−u
2
a
2
=
−u
2
− u − 1
1
2
u
3
+
3
2
u
2
+
1
2
a
1
=
u
3
− u
2
u
2
a
4
=
−u
3
− u − 1
1
2
u
3
+
1
2
u
2
+
1
2
a
12
=
u
3
u
2
+ u + 1
a
8
=
u
2
+ 1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
21
4
u
3
+
11
4
u
2
−
1
2
u −
47
4
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
8
u
4
c
4
(u + 1)
4
c
5
u
4
− 3u
3
+ 4u
2
− 3u + 2
c
6
, c
7
u
4
+ u
2
− u + 1
c
9
, c
11
u
4
+ 2u
3
+ 3u
2
+ u + 1
c
10
, c
12
u
4
+ u
2
+ u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
8
y
4
c
5
y
4
− y
3
+ 2y
2
+ 7y + 4
c
6
, c
7
, c
10
c
12
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
9
, c
11
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.547424 + 0.585652I
a = −0.851808 − 0.911292I
b = 0.677958 − 0.157780I
−2.62503 + 1.39709I −13.6914 − 3.7657I
u = −0.547424 − 0.585652I
a = −0.851808 + 0.911292I
b = 0.677958 + 0.157780I
−2.62503 − 1.39709I −13.6914 + 3.7657I
u = 0.547424 + 1.120870I
a = 0.351808 − 0.720342I
b = −0.927958 + 0.413327I
0.98010 − 7.64338I −4.68363 + 4.91712I
u = 0.547424 − 1.120870I
a = 0.351808 + 0.720342I
b = −0.927958 − 0.413327I
0.98010 + 7.64338I −4.68363 − 4.91712I
16
IV. I
u
4
= hu
4
− u
3
+ u
2
+ b − u + 1, u
5
− u
4
+ 2u
3
− 2u
2
+ a + 2u − 2, u
6
−
u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
6
=
0
u
a
11
=
1
0
a
10
=
1
−u
2
a
7
=
−u
u
3
+ u
a
9
=
u
2
+ 1
−u
2
a
3
=
−u
5
+ u
4
− 2u
3
+ 2u
2
− 2u + 2
−u
4
+ u
3
− u
2
+ u − 1
a
5
=
−u
5
− 2u
3
− u
u
5
+ u
3
+ u
a
2
=
u
4
+ 2u
2
− u + 2
−u
5
− u
4
− u
2
− 1
a
1
=
u
5
+ 2u
3
+ u
−u
5
− u
3
− u
a
4
=
−u
5
+ u
4
− 2u
3
+ 2u
2
− 2u + 2
−u
4
+ u
3
− u
2
+ u − 1
a
12
=
2u
5
+ 3u
3
− u
2
+ 2u − 1
−2u
5
+ u
4
− 3u
3
+ 2u
2
− 3u + 2
a
8
=
u
2
+ 1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
5
− 3u
3
− u
2
− 3u − 6
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
8
u
6
c
4
(u + 1)
6
c
5
(u
3
+ u
2
− 1)
2
c
6
, c
7
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
9
, c
11
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
10
, c
12
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
8
y
6
c
5
(y
3
− y
2
+ 2y −1)
2
c
6
, c
7
, c
10
c
12
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
9
, c
11
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.498832 + 1.001300I
a = −0.398606 − 0.800120I
b = 1.060970 + 0.237841I
−1.37919 + 2.82812I −9.17211 − 2.41717I
u = −0.498832 − 1.001300I
a = −0.398606 + 0.800120I
b = 1.060970 − 0.237841I
−1.37919 − 2.82812I −9.17211 + 2.41717I
u = 0.284920 + 1.115140I
a = 0.215080 − 0.841795I
b = −1.53980 + 0.84179I
2.75839 −6 − 0.655771 + 0.10I
u = 0.284920 − 1.115140I
a = 0.215080 + 0.841795I
b = −1.53980 − 0.84179I
2.75839 −6 − 0.655771 + 0.10I
u = 0.713912 + 0.305839I
a = 1.183530 − 0.507021I
b = −0.521167 − 0.055259I
−1.37919 + 2.82812I −9.17211 − 2.41717I
u = 0.713912 − 0.305839I
a = 1.183530 + 0.507021I
b = −0.521167 + 0.055259I
−1.37919 − 2.82812I −9.17211 + 2.41717I
20
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
10
)(u
15
+ 2u
14
+ ··· − 3u + 1)
2
(u
17
+ 3u
16
+ ··· + 209u + 16)
c
2
((u − 1)
10
)(u
15
− 4u
14
+ ··· − 3u + 1)
2
(u
17
− 3u
16
+ ··· − 15u + 4)
c
3
, c
8
u
10
(u
15
− u
14
+ ··· + 12u − 8)
2
(u
17
+ 3u
16
+ ··· + 144u + 64)
c
4
((u + 1)
10
)(u
15
− 4u
14
+ ··· − 3u + 1)
2
(u
17
− 3u
16
+ ··· − 15u + 4)
c
5
((u
3
+ u
2
− 1)
2
)(u
4
− 3u
3
+ ··· − 3u + 2)(u
15
+ 2u
14
+ ··· + 2u − 1)
2
· (u
17
− 6u
16
+ ··· + 4u + 4)
c
6
, c
7
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
17
+ 5u
15
+ ··· + 2u + 1)(u
30
+ 2u
29
+ ··· + 2u + 1)
c
9
, c
11
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
17
− 10u
16
+ ··· + 2u + 1)(u
30
− 18u
29
+ ··· + 20u
2
+ 1)
c
10
, c
12
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
17
+ 5u
15
+ ··· + 2u + 1)(u
30
+ 2u
29
+ ··· + 2u + 1)
21
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
10
)(y
15
+ 26y
14
+ ··· − 3y −1)
2
· (y
17
+ 25y
16
+ ··· + 9953y −256)
c
2
, c
4
((y −1)
10
)(y
15
− 2y
14
+ ··· − 3y −1)
2
(y
17
− 3y
16
+ ··· + 209y −16)
c
3
, c
8
y
10
(y
15
+ 21y
14
+ ··· − 48y −64)
2
· (y
17
+ 21y
16
+ ··· − 28416y −4096)
c
5
(y
3
− y
2
+ 2y −1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· ((y
15
− 20y
14
+ ··· + 20y −1)
2
)(y
17
− 20y
16
+ ··· + 8y −16)
c
6
, c
7
, c
10
c
12
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
17
+ 10y
16
+ ··· + 2y −1)(y
30
+ 18y
29
+ ··· + 20y
2
+ 1)
c
9
, c
11
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
17
− 2y
16
+ ··· + 62y −1)(y
30
− 14y
29
+ ··· + 40y + 1)
22
