11n
168
(K11n
168
)
A knot diagram
1
Linearized knot diagam
7 5 1 9 2 9 3 11 7 4 8
Solving Sequence
8,11
9
1,3
4 5 2 6 7 10
c
8
c
11
c
3
c
4
c
2
c
5
c
7
c
10
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h115868u
24
− 821040u
23
+ ··· + 306031b − 602429,
1065901u
24
− 8567064u
23
+ ··· + 1224124a + 13420127, u
25
− 8u
24
+ ··· + 55u − 4i
I
u
2
= h−u
11
a − u
11
+ ··· + b − a, u
10
a + 3u
11
+ ··· + a − 9,
u
12
+ 3u
11
+ 9u
10
+ 16u
9
+ 25u
8
+ 30u
7
+ 28u
6
+ 22u
5
+ 10u
4
+ 3u
3
− u
2
− 2u + 1i
I
u
3
= hu
11
+ 4u
10
+ 11u
9
+ 22u
8
+ 35u
7
+ 47u
6
+ 52u
5
+ 48u
4
+ 37u
3
+ 22u
2
+ b + 10u + 2,
3u
11
+ 15u
10
+ 43u
9
+ 91u
8
+ 151u
7
+ 210u
6
+ 247u
5
+ 242u
4
+ 199u
3
+ 133u
2
+ 5a + 66u + 20,
u
12
+ 5u
11
+ 16u
10
+ 37u
9
+ 67u
8
+ 100u
7
+ 124u
6
+ 129u
5
+ 113u
4
+ 81u
3
+ 47u
2
+ 20u + 5i
* 3 irreducible components of dim
C
= 0, with total 61 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
= h1.16 × 10
5
u
24
− 8.21 × 10
5
u
23
+ · · · + 3.06 × 10
5
b − 6.02 × 10
5
, 1.07 ×
10
6
u
24
−8.57×10
6
u
23
+· · ·+1.22×10
6
a+1.34×10
7
, u
25
−8u
24
+· · ·+55u−4i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
−u
2
a
1
=
u
u
a
3
=
−0.870746u
24
+ 6.99853u
23
+ ··· + 87.0860u − 10.9630
−0.378615u
24
+ 2.68287u
23
+ ··· − 14.1356u + 1.96852
a
4
=
−0.524689u
24
+ 3.93260u
23
+ ··· + 64.2937u − 9.44858
−0.0325588u
24
− 0.383056u
23
+ ··· − 36.9280u + 3.48298
a
5
=
−0.768694u
24
+ 5.93994u
23
+ ··· + 88.7503u − 11.8719
−0.398251u
24
+ 1.85942u
23
+ ··· − 32.9107u + 3.26180
a
2
=
−1.38249u
24
+ 10.8931u
23
+ ··· + 95.0899u − 8.66735
−0.943676u
24
+ 6.44578u
23
+ ··· − 15.9909u + 1.92923
a
6
=
−0.221379u
24
+ 2.09877u
23
+ ··· + 51.1671u − 7.44194
−0.205861u
24
+ 1.51059u
23
+ ··· + 6.56495u − 0.0489787
a
7
=
0.308644u
24
− 2.51950u
23
+ ··· − 38.8206u + 6.17994
0.0434891u
24
− 0.354768u
23
+ ··· + 8.34298u − 1.06062
a
10
=
0.125366u
24
− 0.975163u
23
+ ··· − 16.9600u + 3.39492
−0.190134u
24
+ 1.63610u
23
+ ··· + 19.4081u − 1.61106
a
10
=
0.125366u
24
− 0.975163u
23
+ ··· − 16.9600u + 3.39492
−0.190134u
24
+ 1.63610u
23
+ ··· + 19.4081u − 1.61106
(ii) Obstruction class = −1
(iii) Cusp Shapes =
23011
27821
u
24
−
191892
27821
u
23
+ ··· −
108563
27821
u −
344142
27821
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
25
+ 22u
24
+ ··· + 40960u + 4096
c
2
, c
5
u
25
− 8u
24
+ ··· − 3u + 2
c
3
, c
7
u
25
− 7u
23
+ ··· − 8u + 1
c
4
u
25
− u
24
+ ··· − 80u + 85
c
6
, c
9
u
25
+ 15u
23
+ ··· − u + 1
c
8
, c
11
u
25
+ 8u
24
+ ··· + 55u + 4
c
10
u
25
− 8u
23
+ ··· − 18u + 28
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
25
− 4y
24
+ ··· + 92274688y −16777216
c
2
, c
5
y
25
+ 8y
24
+ ··· − 51y −4
c
3
, c
7
y
25
− 14y
24
+ ··· + 22y −1
c
4
y
25
− 23y
24
+ ··· + 73550y −7225
c
6
, c
9
y
25
+ 30y
24
+ ··· + 3y −1
c
8
, c
11
y
25
+ 16y
24
+ ··· + 753y −16
c
10
y
25
− 16y
24
+ ··· + 4188y −784
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000760 + 0.214781I
a = 0.181546 + 0.179308I
b = 1.019350 − 0.663007I
−4.81720 + 2.41116I −4.79174 − 2.48268I
u = 1.000760 − 0.214781I
a = 0.181546 − 0.179308I
b = 1.019350 + 0.663007I
−4.81720 − 2.41116I −4.79174 + 2.48268I
u = −1.012850 + 0.261202I
a = −0.316874 + 0.202205I
b = −0.149236 + 0.123502I
1.91022 − 0.92265I 6.06720 + 6.51070I
u = −1.012850 − 0.261202I
a = −0.316874 − 0.202205I
b = −0.149236 − 0.123502I
1.91022 + 0.92265I 6.06720 − 6.51070I
u = 0.041993 + 0.934875I
a = 1.48887 + 0.80671I
b = 1.113720 − 0.401444I
−3.12369 + 0.06362I −5.51965 + 0.12740I
u = 0.041993 − 0.934875I
a = 1.48887 − 0.80671I
b = 1.113720 + 0.401444I
−3.12369 − 0.06362I −5.51965 − 0.12740I
u = 0.011472 + 1.113580I
a = 1.64705 + 0.28486I
b = 1.055800 − 0.669349I
−3.62398 + 0.55768I −7.12692 − 1.89809I
u = 0.011472 − 1.113580I
a = 1.64705 − 0.28486I
b = 1.055800 + 0.669349I
−3.62398 − 0.55768I −7.12692 + 1.89809I
u = 0.247489 + 1.108210I
a = −1.82938 − 0.09919I
b = −1.12346 + 1.07222I
1.38725 + 4.87941I −6.34329 + 0.12140I
u = 0.247489 − 1.108210I
a = −1.82938 + 0.09919I
b = −1.12346 − 1.07222I
1.38725 − 4.87941I −6.34329 − 0.12140I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.168910 + 0.049676I
a = −0.170031 + 0.065726I
b = −0.991209 + 0.696352I
−4.29953 + 9.06645I −3.72304 − 7.02542I
u = 1.168910 − 0.049676I
a = −0.170031 − 0.065726I
b = −0.991209 − 0.696352I
−4.29953 − 9.06645I −3.72304 + 7.02542I
u = −0.159099 + 1.201110I
a = −1.015220 − 0.149383I
b = −0.657268 + 0.350420I
−1.98209 − 2.65903I −3.09005 + 4.34714I
u = −0.159099 − 1.201110I
a = −1.015220 + 0.149383I
b = −0.657268 − 0.350420I
−1.98209 + 2.65903I −3.09005 − 4.34714I
u = 0.442257 + 0.365564I
a = 1.133650 − 0.436737I
b = −0.647135 − 0.820882I
3.61375 − 2.05944I −4.90254 + 7.19693I
u = 0.442257 − 0.365564I
a = 1.133650 + 0.436737I
b = −0.647135 + 0.820882I
3.61375 + 2.05944I −4.90254 − 7.19693I
u = 0.42788 + 1.38215I
a = 1.70744 + 0.14723I
b = 1.36183 − 0.94506I
−9.79096 + 7.40216I −7.26136 − 3.90619I
u = 0.42788 − 1.38215I
a = 1.70744 − 0.14723I
b = 1.36183 + 0.94506I
−9.79096 − 7.40216I −7.26136 + 3.90619I
u = 0.53216 + 1.39760I
a = −1.63900 − 0.14616I
b = −1.38003 + 0.93988I
−8.8717 + 15.0132I −5.71790 − 7.82964I
u = 0.53216 − 1.39760I
a = −1.63900 + 0.14616I
b = −1.38003 − 0.93988I
−8.8717 − 15.0132I −5.71790 + 7.82964I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.68747 + 1.33439I
a = 0.628461 + 0.691868I
b = 1.015420 + 0.130266I
−7.96688 + 3.80546I −9.00823 − 2.72232I
u = 0.68747 − 1.33439I
a = 0.628461 − 0.691868I
b = 1.015420 − 0.130266I
−7.96688 − 3.80546I −9.00823 + 2.72232I
u = 0.54107 + 1.49661I
a = −0.679365 − 0.581046I
b = −0.907003 − 0.057306I
−8.86649 − 2.64359I −10.06958 + 2.50086I
u = 0.54107 − 1.49661I
a = −0.679365 + 0.581046I
b = −0.907003 + 0.057306I
−8.86649 + 2.64359I −10.06958 − 2.50086I
u = 0.140989
a = −3.52430
b = 0.578442
−0.898624 −11.0260
7
II.
I
u
2
= h−u
11
a−u
11
+· · ·+b−a, u
10
a+3u
11
+· · ·+a−9, u
12
+3u
11
+· · ·−2u+1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
−u
2
a
1
=
u
u
a
3
=
a
u
11
a + u
11
+ ··· − 2au + a
a
4
=
−u
11
a − 2u
10
a + ··· + 3au + u
u
11
+ 4u
10
+ ··· + au + u
a
5
=
u
10
+ 2u
9
+ ··· + a + 1
−u
11
a + u
11
+ ··· − a + u
a
2
=
u
9
a − u
10
+ ··· + a − 2
−u
11
− 4u
10
+ ··· + a + 2u
a
6
=
u
11
a + 2u
10
a + ··· − u + 3
u
11
+ 4u
10
+ ··· − 2a − u
a
7
=
u
9
a − u
10
+ ··· + a − 2
−u
11
− 4u
10
+ ··· + a + u
a
10
=
−2u
11
a − 6u
10
a + ··· − a + 2
−u
11
a + u
11
+ ··· − a + 5u
a
10
=
−2u
11
a − 6u
10
a + ··· − a + 2
−u
11
a + u
11
+ ··· − a + 5u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
11
+ 4u
10
+ 12u
9
− 4u
7
− 20u
6
− 28u
5
− 12u
4
− 8u
3
+ 12u
2
+ 8u − 6
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
24
c
2
, c
5
(u
12
+ 5u
11
+ ··· + 3u
2
+ 1)
2
c
3
, c
7
u
24
− u
23
+ ··· − 4u + 1
c
4
u
24
+ u
23
+ ··· + 162u + 27
c
6
, c
9
u
24
+ 3u
23
+ ··· + 400u + 109
c
8
, c
11
(u
12
− 3u
11
+ ··· + 2u + 1)
2
c
10
u
24
+ u
23
+ ··· − 774u + 135
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y −1)
24
c
2
, c
5
(y
12
+ y
11
+ ··· + 6y + 1)
2
c
3
, c
7
y
24
+ 3y
23
+ ··· − 8y + 1
c
4
y
24
− 21y
23
+ ··· + 93636y + 729
c
6
, c
9
y
24
+ 15y
23
+ ··· − 39228y + 11881
c
8
, c
11
(y
12
+ 9y
11
+ ··· − 6y + 1)
2
c
10
y
24
− 17y
23
+ ··· − 49896y + 18225
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002830 + 0.154838I
a = −0.348206 + 0.268306I
b = −0.387233 − 0.109050I
1.93604 − 0.91968I 3.53074 + 7.18196I
u = −1.002830 + 0.154838I
a = −0.263185 + 0.207938I
b = 0.097566 + 0.372381I
1.93604 − 0.91968I 3.53074 + 7.18196I
u = −1.002830 − 0.154838I
a = −0.348206 − 0.268306I
b = −0.387233 + 0.109050I
1.93604 + 0.91968I 3.53074 − 7.18196I
u = −1.002830 − 0.154838I
a = −0.263185 − 0.207938I
b = 0.097566 − 0.372381I
1.93604 + 0.91968I 3.53074 − 7.18196I
u = 0.170454 + 1.138930I
a = −0.96275 − 1.64559I
b = −1.07597 − 2.21108I
−6.29691 + 5.40399I −10.52298 − 8.56336I
u = 0.170454 + 1.138930I
a = 2.66189 − 0.86518I
b = 0.624755 − 0.225337I
−6.29691 + 5.40399I −10.52298 − 8.56336I
u = 0.170454 − 1.138930I
a = −0.96275 + 1.64559I
b = −1.07597 + 2.21108I
−6.29691 − 5.40399I −10.52298 + 8.56336I
u = 0.170454 − 1.138930I
a = 2.66189 + 0.86518I
b = 0.624755 + 0.225337I
−6.29691 − 5.40399I −10.52298 + 8.56336I
u = 0.001213 + 1.239870I
a = 1.67353 + 1.23840I
b = 1.63727 + 1.77021I
−7.81112 − 2.53747I −14.4387 + 1.7127I
u = 0.001213 + 1.239870I
a = −2.08845 + 1.27481I
b = −0.659423 − 0.044313I
−7.81112 − 2.53747I −14.4387 + 1.7127I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.001213 − 1.239870I
a = 1.67353 − 1.23840I
b = 1.63727 − 1.77021I
−7.81112 + 2.53747I −14.4387 − 1.7127I
u = 0.001213 − 1.239870I
a = −2.08845 − 1.27481I
b = −0.659423 + 0.044313I
−7.81112 + 2.53747I −14.4387 − 1.7127I
u = −0.521704 + 1.146910I
a = 0.562645 − 0.435117I
b = 0.625850 + 0.653229I
−1.08693 − 4.46082I −0.35199 + 4.72827I
u = −0.521704 + 1.146910I
a = −1.54745 + 0.17149I
b = −1.281210 − 0.495305I
−1.08693 − 4.46082I −0.35199 + 4.72827I
u = −0.521704 − 1.146910I
a = 0.562645 + 0.435117I
b = 0.625850 − 0.653229I
−1.08693 + 4.46082I −0.35199 − 4.72827I
u = −0.521704 − 1.146910I
a = −1.54745 − 0.17149I
b = −1.281210 + 0.495305I
−1.08693 + 4.46082I −0.35199 − 4.72827I
u = −0.47799 + 1.39365I
a = 1.107670 + 0.201975I
b = 1.007830 + 0.931272I
−2.89796 − 6.22910I −8.04009 + 11.28166I
u = −0.47799 + 1.39365I
a = −1.344630 + 0.364358I
b = −0.968657 − 0.487749I
−2.89796 − 6.22910I −8.04009 + 11.28166I
u = −0.47799 − 1.39365I
a = 1.107670 − 0.201975I
b = 1.007830 − 0.931272I
−2.89796 + 6.22910I −8.04009 − 11.28166I
u = −0.47799 − 1.39365I
a = −1.344630 − 0.364358I
b = −0.968657 + 0.487749I
−2.89796 + 6.22910I −8.04009 − 11.28166I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.330854 + 0.169612I
a = 1.68415 − 2.07618I
b = 0.708011 + 0.906125I
−3.58234 − 3.33657I −2.17703 + 1.92424I
u = 0.330854 + 0.169612I
a = −3.63521 − 0.47890I
b = −0.828793 + 0.821143I
−3.58234 − 3.33657I −2.17703 + 1.92424I
u = 0.330854 − 0.169612I
a = 1.68415 + 2.07618I
b = 0.708011 − 0.906125I
−3.58234 + 3.33657I −2.17703 − 1.92424I
u = 0.330854 − 0.169612I
a = −3.63521 + 0.47890I
b = −0.828793 − 0.821143I
−3.58234 + 3.33657I −2.17703 − 1.92424I
13
III. I
u
3
=
hu
11
+4u
10
+· · · +b+2, 3u
11
+15u
10
+· · · +5a+20, u
12
+5u
11
+· · · +20u+5i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
−u
2
a
1
=
u
u
a
3
=
−
3
5
u
11
− 3u
10
+ ··· −
66
5
u − 4
−u
11
− 4u
10
+ ··· − 10u − 2
a
4
=
2
5
u
11
+ 2u
10
+ ··· +
24
5
u + 1
u
10
+ 4u
9
+ ··· + 8u + 3
a
5
=
2
5
u
11
+ 2u
10
+ ··· −
6
5
u − 2
u
10
+ 4u
9
+ ··· + 8u + 3
a
2
=
−
9
5
u
11
− 9u
10
+ ··· −
173
5
u − 9
−u
11
− 5u
10
+ ··· − 10u − 1
a
6
=
4
5
u
11
+ 4u
10
+ ··· +
43
5
u + 2
u
11
+ 4u
10
+ ··· + 5u + 1
a
7
=
4
5
u
11
+ 4u
10
+ ··· +
48
5
u + 3
u
11
+ 4u
10
+ ··· + 5u + 1
a
10
=
1
5
u
11
+ u
10
+ ··· +
37
5
u + 2
−u
2
− u − 1
a
10
=
1
5
u
11
+ u
10
+ ··· +
37
5
u + 2
−u
2
− u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −4u
11
− 14u
10
− 36u
9
− 61u
8
− 79u
7
− 77u
6
− 49u
5
− 8u
4
+ 24u
3
+ 38u
2
+ 30u + 14
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
− 3u
11
+ ··· + 2u + 5
c
2
u
12
− 5u
11
+ ··· − 3u + 1
c
3
, c
7
u
12
+ u
10
+ 2u
9
+ 4u
8
+ 3u
7
+ 5u
6
+ 5u
5
+ 6u
4
+ 3u
3
+ 3u
2
+ 3u + 1
c
4
u
12
− u
11
+ ··· + 11u + 5
c
5
u
12
+ 5u
11
+ ··· + 3u + 1
c
6
u
12
+ u
10
− 3u
8
− u
7
− 2u
6
− 3u
5
+ 9u
4
+ 2u
3
− 4u
2
+ 1
c
8
u
12
+ 5u
11
+ ··· + 20u + 5
c
9
u
12
+ u
10
− 3u
8
+ u
7
− 2u
6
+ 3u
5
+ 9u
4
− 2u
3
− 4u
2
+ 1
c
10
u
12
− 4u
10
+ u
9
+ 9u
8
− u
7
− 10u
6
+ u
5
+ 7u
4
− 4u
3
+ 2u
2
− 2u + 1
c
11
u
12
− 5u
11
+ ··· − 20u + 5
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
− 3y
11
+ ··· − 104y + 25
c
2
, c
5
y
12
+ 7y
11
+ ··· + 11y + 1
c
3
, c
7
y
12
+ 2y
11
+ ··· − 3y + 1
c
4
y
12
− 7y
11
+ ··· − 11y + 25
c
6
, c
9
y
12
+ 2y
11
+ ··· − 8y + 1
c
8
, c
11
y
12
+ 7y
11
+ ··· + 70y + 25
c
10
y
12
− 8y
11
+ ··· + 2y
2
+ 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.223604 + 0.992901I
a = 1.36241 + 0.84935I
b = 0.351412 + 0.975594I
−5.37548 + 4.45869I −5.23379 − 2.73299I
u = 0.223604 − 0.992901I
a = 1.36241 − 0.84935I
b = 0.351412 − 0.975594I
−5.37548 − 4.45869I −5.23379 + 2.73299I
u = −0.693815 + 0.478519I
a = −0.508326 − 0.424398I
b = 0.603205 − 0.775464I
4.01613 + 1.54035I 3.24789 + 1.08803I
u = −0.693815 − 0.478519I
a = −0.508326 + 0.424398I
b = 0.603205 + 0.775464I
4.01613 − 1.54035I 3.24789 − 1.08803I
u = −0.361271 + 1.125220I
a = 1.62540 − 0.03123I
b = 1.02625 + 1.07318I
1.85485 − 5.48541I 0.93921 + 8.00832I
u = −0.361271 − 1.125220I
a = 1.62540 + 0.03123I
b = 1.02625 − 1.07318I
1.85485 + 5.48541I 0.93921 − 8.00832I
u = 0.075522 + 1.207100I
a = −1.29960 − 0.56401I
b = −0.504389 − 0.932104I
−6.48342 − 2.87353I −6.21901 + 3.05514I
u = 0.075522 − 1.207100I
a = −1.29960 + 0.56401I
b = −0.504389 + 0.932104I
−6.48342 + 2.87353I −6.21901 − 3.05514I
u = −1.199800 + 0.312222I
a = −0.079749 + 0.143999I
b = −0.522926 + 0.172175I
1.62052 − 0.67051I −10.59498 − 6.84644I
u = −1.199800 − 0.312222I
a = −0.079749 − 0.143999I
b = −0.522926 − 0.172175I
1.62052 + 0.67051I −10.59498 + 6.84644I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.54424 + 1.36667I
a = −1.100140 + 0.144255I
b = −0.953548 − 0.611838I
−2.21233 − 5.51031I −2.13932 + 5.32316I
u = −0.54424 − 1.36667I
a = −1.100140 − 0.144255I
b = −0.953548 + 0.611838I
−2.21233 + 5.51031I −2.13932 − 5.32316I
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
24
)(u
12
− 3u
11
+ ··· + 2u + 5)
· (u
25
+ 22u
24
+ ··· + 40960u + 4096)
c
2
(u
12
− 5u
11
+ ··· − 3u + 1)(u
12
+ 5u
11
+ ··· + 3u
2
+ 1)
2
· (u
25
− 8u
24
+ ··· − 3u + 2)
c
3
, c
7
(u
12
+ u
10
+ 2u
9
+ 4u
8
+ 3u
7
+ 5u
6
+ 5u
5
+ 6u
4
+ 3u
3
+ 3u
2
+ 3u + 1)
· (u
24
− u
23
+ ··· − 4u + 1)(u
25
− 7u
23
+ ··· − 8u + 1)
c
4
(u
12
− u
11
+ ··· + 11u + 5)(u
24
+ u
23
+ ··· + 162u + 27)
· (u
25
− u
24
+ ··· − 80u + 85)
c
5
((u
12
+ 5u
11
+ ··· + 3u
2
+ 1)
2
)(u
12
+ 5u
11
+ ··· + 3u + 1)
· (u
25
− 8u
24
+ ··· − 3u + 2)
c
6
(u
12
+ u
10
− 3u
8
− u
7
− 2u
6
− 3u
5
+ 9u
4
+ 2u
3
− 4u
2
+ 1)
· (u
24
+ 3u
23
+ ··· + 400u + 109)(u
25
+ 15u
23
+ ··· − u + 1)
c
8
((u
12
− 3u
11
+ ··· + 2u + 1)
2
)(u
12
+ 5u
11
+ ··· + 20u + 5)
· (u
25
+ 8u
24
+ ··· + 55u + 4)
c
9
(u
12
+ u
10
− 3u
8
+ u
7
− 2u
6
+ 3u
5
+ 9u
4
− 2u
3
− 4u
2
+ 1)
· (u
24
+ 3u
23
+ ··· + 400u + 109)(u
25
+ 15u
23
+ ··· − u + 1)
c
10
(u
12
− 4u
10
+ u
9
+ 9u
8
− u
7
− 10u
6
+ u
5
+ 7u
4
− 4u
3
+ 2u
2
− 2u + 1)
· (u
24
+ u
23
+ ··· − 774u + 135)(u
25
− 8u
23
+ ··· − 18u + 28)
c
11
(u
12
− 5u
11
+ ··· − 20u + 5)(u
12
− 3u
11
+ ··· + 2u + 1)
2
· (u
25
+ 8u
24
+ ··· + 55u + 4)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
24
)(y
12
− 3y
11
+ ··· − 104y + 25)
· (y
25
− 4y
24
+ ··· + 92274688y −16777216)
c
2
, c
5
((y
12
+ y
11
+ ··· + 6y + 1)
2
)(y
12
+ 7y
11
+ ··· + 11y + 1)
· (y
25
+ 8y
24
+ ··· − 51y −4)
c
3
, c
7
(y
12
+ 2y
11
+ ··· − 3y + 1)(y
24
+ 3y
23
+ ··· − 8y + 1)
· (y
25
− 14y
24
+ ··· + 22y −1)
c
4
(y
12
− 7y
11
+ ··· − 11y + 25)(y
24
− 21y
23
+ ··· + 93636y + 729)
· (y
25
− 23y
24
+ ··· + 73550y −7225)
c
6
, c
9
(y
12
+ 2y
11
+ ··· − 8y + 1)(y
24
+ 15y
23
+ ··· − 39228y + 11881)
· (y
25
+ 30y
24
+ ··· + 3y −1)
c
8
, c
11
(y
12
+ 7y
11
+ ··· + 70y + 25)(y
12
+ 9y
11
+ ··· − 6y + 1)
2
· (y
25
+ 16y
24
+ ··· + 753y −16)
c
10
(y
12
− 8y
11
+ ··· + 2y
2
+ 1)(y
24
− 17y
23
+ ··· − 49896y + 18225)
· (y
25
− 16y
24
+ ··· + 4188y −784)
20
