11n
165
(K11n
165
)
1
Arc Sequences
8 5 1 11 3 10 3 4 7 5 9
Solving Sequence
4,11 5,9
1 3 6 2 8 7 10
c
4
c
11
c
3
c
5
c
2
c
8
c
7
c
10
c
1
, c
6
, c
9
Representation Ideals
I =
6
\
i=1
I
u
i
I
u
1
= hu
2
+ u + 1, a 1, b u 1i
I
u
2
= hu
8
3u
7
+ 2u
6
+ u
5
+ u
3
2u + 1, 20u
7
+ 44u
6
+ 2u
5
32u
4
29u
3
33u
2
+ 17a 6u + 42,
21u
7
53u
6
+ 20u
5
+ 20u
4
+ 16u
3
+ 27u
2
+ 17b + 25u 22i
I
u
3
= hu
8
+ 3u
7
+ 5u
6
+ u
5
3u
4
2u
3
+ 9u
2
+ 4u + 1,
16u
7
44u
6
68u
5
+ 3u
4
+ 50u
3
+ 19u
2
+ 7a 148u 20,
16u
7
+ 47u
6
+ 74u
5
7u
4
69u
3
43u
2
+ 49b + 162u + 60i
I
u
4
= hu
12
u
11
2u
10
+ 2u
9
+ 7u
8
7u
7
6u
6
+ 6u
5
+ 8u
4
6u
3
4u
2
+ 2u + 1, a + 1,
20u
11
+ 32u
10
+ 25u
9
55u
8
114u
7
+ 207u
6
+ 21u
5
134u
4
95u
3
+ 170u
2
+ 7b u 38i
I
u
5
= hu
16
+ u
15
+ ··· 12u + 3, 888520u
15
+ 1796898u
14
+ ··· + 2895435b + 85089,
36253651u
15
70132578u
14
+ ··· + 55013265a 8845230i
I
u
6
= hu
20
2u
19
+ ··· 4u + 1, a 1, 718779630u
19
1228241984u
18
+ ··· + 568693339b 860940183i
There are 6 irreducible components with 66 representations.
1
The knot diagram image is adapter from “C. Livingston and A. H. Moore, KnotInfo: Table of Knot
Invariants, http://www.indiana.edu/ knotinfo”
1
I. I
u
1
= hu
2
+ u + 1, a 1, b u 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
1
u + 1
a
5
=
u
u
a
9
=
0
u
a
1
=
1
0
a
3
=
1
0
a
6
=
0
u
a
2
=
u + 2
u + 1
a
8
=
u
u
a
7
=
0
u
a
10
=
0
u
a
10
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.500000 0.866025I
a = 1.00000
b = 0.500000 0.866025I
2.02988I 3.46410I
u = 0.500000 + 0.866025I
a = 1.00000
b = 0.500000 + 0.866025I
2.02988I 3.46410I
3
II. I
u
2
= hu
8
3u
7
+ 2u
6
+ u
5
+ u
3
2u + 1, 20u
7
+ 44u
6
+ · · · + 17a +
42, 21u
7
53u
6
+ · · · + 17b 22i
(i) Arc colorings
a
4
=
1
0
a
11
=
1.17647u
7
2.58824u
6
+ ··· + 0.352941u 2.47059
1.23529u
7
+ 3.11765u
6
+ ··· 1.47059u + 1.29412
a
5
=
0.294118u
7
+ 0.647059u
6
+ ··· 1.58824u + 1.11765
1.23529u
7
+ 3.11765u
6
+ ··· 1.47059u + 2.29412
a
9
=
0
u
a
1
=
1.17647u
7
2.58824u
6
+ ··· + 0.352941u 2.47059
0.882353u
7
+ 1.94118u
6
+ ··· 0.764706u + 0.352941
a
3
=
0.352941u
7
1.17647u
6
+ ··· 0.294118u 0.941176
2.11765u
7
+ 5.05882u
6
+ ··· 2.23529u + 2.64706
a
6
=
0.294118u
7
+ 0.647059u
6
+ ··· 0.588235u + 1.11765
0.470588u
7
+ 1.23529u
6
+ ··· 0.941176u + 1.58824
a
2
=
0.0588235u
7
+ 0.470588u
6
+ ··· 0.882353u 0.823529
2u
7
+ 5u
6
2u
5
2u
4
u
3
3u
2
2u + 2
a
8
=
u
u
a
7
=
1.35294u
7
3.17647u
6
+ ··· + 1.70588u 1.94118
0.176471u
7
0.588235u
6
+ ··· + 0.352941u 1.47059
a
10
=
0.941176u
7
2.47059u
6
+ ··· 0.117647u 1.17647
1.23529u
7
+ 3.11765u
6
+ ··· 1.47059u + 2.29412
a
10
=
0.941176u
7
2.47059u
6
+ ··· 0.117647u 1.17647
1.23529u
7
+ 3.11765u
6
+ ··· 1.47059u + 2.29412
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
4
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.815445 0.385168I
a = 0.547587 + 0.458183I
b = 0.500000 + 0.866025I
3.39192 + 0.56550I 7.53952 + 2.54518I
u = 0.815445 + 0.385168I
a = 0.547587 0.458183I
b = 0.500000 0.866025I
3.39192 0.56550I 7.53952 2.54518I
u = 0.014287 0.946719I
a = 0.69099 + 1.79235I
b = 0.500000 + 0.866025I
3.39192 4.62527I 7.53952 + 4.38302I
u = 0.014287 + 0.946719I
a = 0.69099 1.79235I
b = 0.500000 0.866025I
3.39192 + 4.62527I 7.53952 4.38302I
u = 0.623004 0.162710I
a = 1.074157 0.898780I
b = 0.500000 + 0.866025I
3.39192 + 0.56550I 7.53952 + 2.54518I
u = 0.623004 + 0.162710I
a = 1.074157 + 0.898780I
b = 0.500000 0.866025I
3.39192 0.56550I 7.53952 2.54518I
u = 1.70673 0.62857I
a = 0.187261 + 0.485732I
b = 0.500000 0.866025I
3.39192 + 4.62527I 7.53952 4.38302I
u = 1.70673 + 0.62857I
a = 0.187261 0.485732I
b = 0.500000 + 0.866025I
3.39192 4.62527I 7.53952 + 4.38302I
5
III. I
u
3
=
hu
8
+3u
7
+· · ·+4u+1, 16u
7
44u
6
+· · ·+7a20, 16u
7
+47u
6
+· · ·+49b+60i
(i) Arc colorings
a
4
=
1
0
a
11
=
16
7
u
7
+
44
7
u
6
+ ··· +
148
7
u +
20
7
0.326531u
7
0.959184u
6
+ ··· 3.30612u 1.22449
a
5
=
0.551020u
7
+ 1.02041u
6
+ ··· + 5.20408u 3.32653
0.326531u
7
0.959184u
6
+ ··· 3.30612u 0.224490
a
9
=
0
u
a
1
=
16
7
u
7
+
44
7
u
6
+ ··· +
148
7
u +
20
7
0.326531u
7
0.816327u
6
+ ··· 3.30612u 0.653061
a
3
=
0.673469u
7
2.18367u
6
+ ··· 6.69388u 4.34694
1
7
u
6
+
2
7
u
5
+ ···
8
7
u
2
+
4
7
a
6
=
2.16327u
7
+ 5.26531u
6
+ ··· + 20.6531u 3.24490
0.673469u
7
1.75510u
6
+ ··· 6.69388u 0.632653
a
2
=
2.20408u
7
+ 5.93878u
6
+ ··· + 20.8163u + 2.12245
0.408163u
7
1.16327u
6
+ ··· 3.63265u 1.38776
a
8
=
u
u
a
7
=
0.346939u
7
+ 1.36735u
6
+ ··· + 3.38776u + 4.69388
0.102041u
7
+ 0.0408163u
6
+ ··· + 1.40816u 0.653061
a
10
=
0.877551u
7
+ 1.97959u
6
+ ··· + 8.51020u 3.10204
0.326531u
7
0.959184u
6
+ ··· 3.30612u 0.224490
a
10
=
0.877551u
7
+ 1.97959u
6
+ ··· + 8.51020u 3.10204
0.326531u
7
0.959184u
6
+ ··· 3.30612u 0.224490
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
6
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.27422 1.00737I
a = 0.649100 + 0.068363I
b = 0.500000 + 0.866025I
3.39192 4.62527I 7.53952 + 4.38302I
u = 1.27422 + 1.00737I
a = 0.649100 0.068363I
b = 0.500000 0.866025I
3.39192 + 4.62527I 7.53952 4.38302I
u = 0.90959 1.55027I
a = 0.057185 0.170403I
b = 0.500000 0.866025I
3.39192 0.56550I 7.53952 2.54518I
u = 0.90959 + 1.55027I
a = 0.057185 + 0.170403I
b = 0.500000 + 0.866025I
3.39192 + 0.56550I 7.53952 + 2.54518I
u = 0.212157 0.243648I
a = 1.77002 5.27444I
b = 0.500000 + 0.866025I
3.39192 + 0.56550I 7.53952 + 2.54518I
u = 0.212157 + 0.243648I
a = 1.77002 + 5.27444I
b = 0.500000 0.866025I
3.39192 0.56550I 7.53952 2.54518I
u = 0.895964 0.566778I
a = 1.52369 + 0.16047I
b = 0.500000 0.866025I
3.39192 + 4.62527I 7.53952 4.38302I
u = 0.895964 + 0.566778I
a = 1.52369 0.16047I
b = 0.500000 + 0.866025I
3.39192 4.62527I 7.53952 + 4.38302I
7
IV. I
u
4
= hu
12
u
11
+ · · · + 2u + 1, a + 1, 20u
11
+ 32u
10
+ · · · + 7b 38i
(i) Arc colorings
a
4
=
1
0
a
11
=
1
20
7
u
11
32
7
u
10
+ ··· +
1
7
u +
38
7
a
5
=
20
7
u
11
32
7
u
10
+ ··· +
1
7
u +
45
7
31
7
u
11
44
7
u
10
+ ···
17
7
u +
75
7
a
9
=
0
u
a
1
=
1
20
7
u
11
32
7
u
10
+ ··· +
1
7
u +
38
7
a
3
=
20
7
u
11
32
7
u
10
+ ··· +
1
7
u +
45
7
37
7
u
11
62
7
u
10
+ ···
9
7
u +
99
7
a
6
=
5
7
u
11
8
7
u
10
+ ···
5
7
u
1
7
12
7
u
11
8
7
u
10
+ ···
19
7
u
1
7
a
2
=
3
7
u
11
9
7
u
10
+ ··· +
4
7
u +
5
7
23
7
u
11
41
7
u
10
+ ··· +
5
7
u +
50
7
a
8
=
u
u
a
7
=
3.42857u
11
+ 5.28571u
10
+ ··· 1.57143u 7.71429
8.14286u
11
+ 13.4286u
10
+ ··· 2.85714u 21.5714
a
10
=
11
7
u
11
12
7
u
10
+ ···
18
7
u +
30
7
9
7
u
11
+
13
7
u
10
+ ···
33
7
u +
6
7
a
10
=
11
7
u
11
12
7
u
10
+ ···
18
7
u +
30
7
9
7
u
11
+
13
7
u
10
+ ···
33
7
u +
6
7
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
8
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.18358 0.88580I
a = 1.00000
b = 0.15023 + 1.48785I
7.90320 4.59198I 10.36791 + 8.72045I
u = 1.18358 + 0.88580I
a = 1.00000
b = 0.15023 1.48785I
7.90320 + 4.59198I 10.36791 8.72045I
u = 0.737321 0.666987I
a = 1.00000
b = 0.521062 + 0.781668I
2.29385 + 5.81227I 0.92217 3.42975I
u = 0.737321 + 0.666987I
a = 1.00000
b = 0.521062 0.781668I
2.29385 5.81227I 0.92217 + 3.42975I
u = 0.472602 0.062197I
a = 1.00000
b = 0.70225 1.75863I
4.57255 1.04234I 18.3535 + 2.2196I
u = 0.472602 + 0.062197I
a = 1.00000
b = 0.70225 + 1.75863I
4.57255 + 1.04234I 18.3535 2.2196I
u = 0.843277 0.197663I
a = 1.00000
b = 0.598105 + 0.452600I
3.20993 + 2.02643I 9.74479 3.88837I
u = 0.843277 + 0.197663I
a = 1.00000
b = 0.598105 0.452600I
3.20993 2.02643I 9.74479 + 3.88837I
u = 0.934560 0.720234I
a = 1.00000
b = 0.385704 0.856791I
2.75349 + 1.52030I 2.99434 1.95006I
u = 0.934560 + 0.720234I
a = 1.00000
b = 0.385704 + 0.856791I
2.75349 1.52030I 2.99434 + 1.95006I
9
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.115664 0.840164I
a = 1.00000
b = 0.456174 0.803369I
2.52113 + 5.90216I 4.45034 3.90745I
u = 1.115664 + 0.840164I
a = 1.00000
b = 0.456174 + 0.803369I
2.52113 5.90216I 4.45034 + 3.90745I
10
V.
I
u
5
= hu
16
+ u
15
+ · · · 12u + 3, 8.89 × 10
5
u
15
+ 1.80 × 10
6
u
14
+ · · · + 2.90 ×
10
6
b+8.51×10
4
, 3.63×10
7
u
15
7.01×10
7
u
14
+· · ·+5.50×10
7
a8.85×10
6
i
(i) Arc colorings
a
4
=
1
0
a
11
=
0.658998u
15
+ 1.27483u
14
+ ··· + 6.33197u + 0.160784
0.306869u
15
0.620597u
14
+ ··· 3.79921u 0.0293873
a
5
=
1.58389u
15
2.18158u
14
+ ··· 25.1804u + 10.6178
0.306869u
15
0.620597u
14
+ ··· 3.79921u + 0.970613
a
9
=
0
u
a
1
=
0.658998u
15
+ 1.27483u
14
+ ··· + 6.33197u + 0.160784
0.0388927u
15
0.129935u
14
+ ··· + 1.61378u 1.87688
a
3
=
1.03600u
15
1.85201u
14
+ ··· 13.7021u + 2.16594
0.890285u
15
1.48746u
14
+ ··· 12.9038u + 5.21168
a
6
=
1.56932u
15
1.89217u
14
+ ··· 28.8758u + 11.5409
1.32109u
15
+ 1.92893u
14
+ ··· + 19.0996u 7.74855
a
2
=
0.198694u
15
+ 0.512389u
14
+ ··· 1.22364u + 2.51476
0.421412u
15
0.892377u
14
+ ··· 5.94182u + 0.477096
a
8
=
u
u
a
7
=
0.752497u
15
1.39772u
14
+ ··· 7.34263u + 0.189540
0.673915u
15
0.972203u
14
+ ··· 9.24369u + 4.52387
a
10
=
1.27702u
15
1.56098u
14
+ ··· 21.3812u + 9.64714
0.306869u
15
0.620597u
14
+ ··· 3.79921u + 0.970613
a
10
=
1.27702u
15
1.56098u
14
+ ··· 21.3812u + 9.64714
0.306869u
15
0.620597u
14
+ ··· 3.79921u + 0.970613
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
11
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 1.59236 0.24028I
a = 0.185520 0.619009I
b = 0.500000 + 0.866025I
2.24108 + 2.65615I 1.29059 6.81528I
u = 1.59236 + 0.24028I
a = 0.185520 + 0.619009I
b = 0.500000 0.866025I
2.24108 2.65615I 1.29059 + 6.81528I
u = 0.940007 0.283478I
a = 0.527442 + 0.018221I
b = 0.500000 0.866025I
2.24108 2.65615I 1.29059 + 6.81528I
u = 0.940007 + 0.283478I
a = 0.527442 0.018221I
b = 0.500000 + 0.866025I
2.24108 + 2.65615I 1.29059 6.81528I
u = 0.928296 1.033704I
a = 1.005334 + 0.334153I
b = 0.500000 + 0.866025I
2.24108 6.71592I 1.29059 + 13.74348I
u = 0.928296 + 1.033704I
a = 1.005334 0.334153I
b = 0.500000 0.866025I
2.24108 + 6.71592I 1.29059 13.74348I
u = 0.444152 0.941106I
a = 0.44426 1.48234I
b = 0.500000 0.866025I
2.24108 2.65615I 1.29059 + 6.81528I
u = 0.444152 + 0.941106I
a = 0.44426 + 1.48234I
b = 0.500000 + 0.866025I
2.24108 + 2.65615I 1.29059 6.81528I
u = 0.396935 0.265570I
a = 0.18278 + 4.35177I
b = 0.500000 0.866025I
2.24108 + 6.71592I 1.29059 13.74348I
u = 0.396935 + 0.265570I
a = 0.18278 4.35177I
b = 0.500000 + 0.866025I
2.24108 6.71592I 1.29059 + 13.74348I
12
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.500964 0.132390I
a = 1.89368 + 0.06542I
b = 0.500000 + 0.866025I
2.24108 + 2.65615I 1.29059 6.81528I
u = 0.500964 + 0.132390I
a = 1.89368 0.06542I
b = 0.500000 0.866025I
2.24108 2.65615I 1.29059 + 6.81528I
u = 1.22825 1.67883I
a = 0.009634 + 0.229387I
b = 0.500000 + 0.866025I
2.24108 6.71592I 1.29059 + 13.74348I
u = 1.22825 + 1.67883I
a = 0.009634 0.229387I
b = 0.500000 0.866025I
2.24108 + 6.71592I 1.29059 13.74348I
u = 1.27866 0.72903I
a = 0.895736 + 0.297725I
b = 0.500000 0.866025I
2.24108 + 6.71592I 1.29059 13.74348I
u = 1.27866 + 0.72903I
a = 0.895736 0.297725I
b = 0.500000 + 0.866025I
2.24108 6.71592I 1.29059 + 13.74348I
13
VI. I
u
6
= hu
20
2u
19
+ · · · 4u + 1, a 1, 7.19 × 10
8
u
19
1.23 × 10
9
u
18
+
· · · + 5.69 × 10
8
b 8.61 × 10
8
i
(i) Arc colorings
a
4
=
1
0
a
11
=
1
1.26391u
19
+ 2.15976u
18
+ ··· 8.24792u + 1.51389
a
5
=
1.26391u
19
2.15976u
18
+ ··· + 8.24792u 0.513892
0.729169u
19
+ 1.68768u
18
+ ··· 7.98312u + 5.20664
a
9
=
0
u
a
1
=
1
1.26391u
19
+ 2.15976u
18
+ ··· 8.24792u + 1.51389
a
3
=
1.26391u
19
2.15976u
18
+ ··· + 8.24792u 0.513892
0.543626u
19
+ 1.36273u
18
+ ··· 7.56641u + 4.47051
a
6
=
0.0493605u
19
+ 0.0195866u
18
+ ··· + 0.0930939u + 1.24815
1.52184u
19
+ 2.27683u
18
+ ··· 8.95348u + 3.21659
a
2
=
0.0927720u
19
+ 0.162474u
18
+ ··· 0.208354u + 1.36807
1.35669u
19
+ 2.32224u
18
+ ··· 8.45627u + 1.88196
a
8
=
u
u
a
7
=
1.25949u
19
1.63193u
18
+ ··· + 7.11208u + 0.710543
0.828796u
19
+ 2.26957u
18
+ ··· 9.22876u + 4.74286
a
10
=
1.99308u
19
3.84744u
18
+ ··· + 16.2310u 5.72054
2.73197u
19
3.88917u
18
+ ··· + 16.1586u 1.25790
a
10
=
1.99308u
19
3.84744u
18
+ ··· + 16.2310u 5.72054
2.73197u
19
3.88917u
18
+ ··· + 16.1586u 1.25790
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
14
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 1.13829 1.08683I
a = 1.00000
b = 0.69428 1.39946I
2.70163 8.25419I 1.74639 + 5.26030I
u = 1.13829 + 1.08683I
a = 1.00000
b = 0.69428 + 1.39946I
2.70163 + 8.25419I 1.74639 5.26030I
u = 0.759582 0.578288I
a = 1.00000
b = 0.95638 1.20014I
0.87661 1.80368I 0.33009 + 3.39562I
u = 0.759582 + 0.578288I
a = 1.00000
b = 0.95638 + 1.20014I
0.87661 + 1.80368I 0.33009 3.39562I
u = 0.637356 0.729970I
a = 1.00000
b = 0.434233 0.681862I
0.01507 1.86524I 0.60762 + 4.36679I
u = 0.637356 + 0.729970I
a = 1.00000
b = 0.434233 + 0.681862I
0.01507 + 1.86524I 0.60762 4.36679I
u = 0.596309 0.866871I
a = 1.00000
b = 1.55233 + 0.24672I
5.15014 7.97058I 2.89077 + 7.60145I
u = 0.596309 + 0.866871I
a = 1.00000
b = 1.55233 0.24672I
5.15014 + 7.97058I 2.89077 7.60145I
u = 0.193032 0.732624I
a = 1.00000
b = 0.417870 0.276241I
1.06285 1.12930I 5.13966 + 4.07834I
u = 0.193032 + 0.732624I
a = 1.00000
b = 0.417870 + 0.276241I
1.06285 + 1.12930I 5.13966 4.07834I
15
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 0.259032 0.308320I
a = 1.00000
b = 0.31531 + 1.77818I
4.19435 + 1.15765I 2.14031 7.95914I
u = 0.259032 + 0.308320I
a = 1.00000
b = 0.31531 1.77818I
4.19435 1.15765I 2.14031 + 7.95914I
u = 0.573922 0.912168I
a = 1.00000
b = 1.308827 0.201825I
6.49001 + 1.26443I 4.97798 1.96291I
u = 0.573922 + 0.912168I
a = 1.00000
b = 1.308827 + 0.201825I
6.49001 1.26443I 4.97798 + 1.96291I
u = 0.775515 0.331794I
a = 1.00000
b = 0.99845 + 1.43383I
0.50861 + 7.39141I 3.95189 9.17426I
u = 0.775515 + 0.331794I
a = 1.00000
b = 0.99845 1.43383I
0.50861 7.39141I 3.95189 + 9.17426I
u = 1.14751 0.91448I
a = 1.00000
b = 0.16334 + 1.55905I
7.56901 + 4.35325I 6.00959 + 2.36650I
u = 1.14751 + 0.91448I
a = 1.00000
b = 0.16334 1.55905I
7.56901 4.35325I 6.00959 2.36650I
u = 1.18252 1.08380I
a = 1.00000
b = 0.78960 + 1.39248I
1.5683 + 15.8169I 0.23034 8.70601I
u = 1.18252 + 1.08380I
a = 1.00000
b = 0.78960 1.39248I
1.5683 15.8169I 0.23034 + 8.70601I
16
VII. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
2
+ u + 1)(u
8
2u
7
3u
6
+ u
5
+ 9u
4
+ 16u
3
+ 14u
2
+ 6u + 1)
(u
8
+ u
7
+ 3u
6
2u
5
+ 3u
4
5u
3
7u
2
+ 6u + 7)
(u
12
u
10
+ 3u
8
+ 3u
7
3u
6
+ 4u
5
+ 2u
4
6u
3
+ 9u
2
4u + 3)
(u
16
+ 2u
15
+ ··· + 10u + 25)(u
20
u
19
+ ··· 4u + 1)
c
2
(u
2
+ u + 1)(u
8
3u
7
+ ··· 16u + 7)
(u
8
+ 3u
7
+ 6u
6
+ 13u
5
+ 22u
4
+ 27u
3
+ 22u
2
+ 8u + 1)
(u
12
2u
11
+ 3u
10
u
9
u
8
+ u
7
+ 2u
6
5u
5
+ 8u
4
3u
3
3u
2
+ 2u + 1)
(u
16
u
15
+ ··· 12u + 3)(u
20
+ u
19
+ ··· + 2u + 1)
c
3
u
2
(u
4
2u
3
+ 2u
2
u + 1)
4
(u
4
u
3
+ u
2
+ u + 1)
4
(u
12
+ 7u
11
+ ··· + u
2
+ 1)(u
20
+ 14u
19
+ ··· + 140u + 13)
c
4
(u
2
u + 1)(u
2
+ u + 1)
16
(u
12
+ 2u
11
+ ··· + 5u + 3)
(u
20
14u
19
+ ··· 2560u + 256)
c
5
(u
2
+ u + 1)(u
8
3u
7
+ ··· 16u + 7)
(u
8
+ 3u
7
+ 6u
6
+ 13u
5
+ 22u
4
+ 27u
3
+ 22u
2
+ 8u + 1)
(u
12
+ 2u
11
+ 3u
10
+ u
9
u
8
u
7
+ 2u
6
+ 5u
5
+ 8u
4
+ 3u
3
3u
2
2u + 1)
(u
16
u
15
+ ··· 12u + 3)(u
20
+ u
19
+ ··· + 2u + 1)
c
6
u
2
(u
4
+ u
3
+ u
2
u + 1)
4
(u
4
+ 2u
3
+ 2u
2
+ u + 1)
4
(u
12
+ 4u
11
+ ··· + 5u
2
+ 1)(u
20
9u
19
+ ··· 28u + 13)
c
7
(u
2
+ u + 1)(u
8
u
7
+ 5u
6
4u
5
3u
4
3u
3
+ 9u
2
+ 2u + 1)
(u
8
+ 2u
7
u
6
7u
5
9u
4
+ 12u
2
+ 14u + 7)
(u
12
2u
10
+ ··· + 11u + 13)(u
16
2u
15
+ ··· + 264u + 111)
(u
20
+ u
19
+ ··· + 17u + 21)
c
8
, c
11
(u
2
u + 1)(u
8
3u
7
+ 5u
6
u
5
3u
4
+ 2u
3
+ 9u
2
4u + 1)
(u
8
+ 3u
7
+ ··· + 2u + 1)(u
12
+ u
11
+ ··· 2u + 1)
(u
16
u
15
+ ··· + 12u + 3)(u
20
+ 2u
19
+ ··· + 4u + 1)
c
9
u
2
(u
4
+ u
3
+ u
2
u + 1)
4
(u
4
+ 2u
3
+ 2u
2
+ u + 1)
4
(u
12
4u
11
+ ··· + 5u
2
+ 1)(u
20
9u
19
+ ··· 28u + 13)
c
10
(u
2
u + 1)(u
2
+ u + 1)
16
(u
12
2u
11
+ ··· 5u + 3)
(u
20
14u
19
+ ··· 2560u + 256)
17
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
2
+ y + 1)(y
8
10y
7
+ ··· 8y + 1)
(y
8
+ 5y
7
+ 19y
6
+ 10y
5
51y
4
y
3
+ 151y
2
134y + 49)
(y
12
2y
11
+ ··· + 38y + 9)(y
16
+ 34y
14
+ ··· 4150y + 625)
(y
20
5y
19
+ ··· 14y + 1)
c
2
, c
5
(y
2
+ y + 1)(y
8
+ 3y
7
+ 2y
6
23y
5
+ 43y
3
+ 96y
2
20y + 1)
(y
8
+ 9y
7
+ 29y
6
+ 31y
5
27y
4
68y
3
+ 15y
2
+ 94y + 49)
(y
12
+ 2y
11
+ ··· 10y + 1)(y
16
+ 3y
15
+ ··· + 402y + 9)
(y
20
+ 23y
19
+ ··· + 10y + 1)
c
3
y
2
(y
4
+ 2y
2
+ 3y + 1)
4
(y
4
+ y
3
+ 5y
2
+ y + 1)
4
(y
12
+ 3y
11
+ ··· + 2y + 1)(y
20
+ 4y
19
+ ··· + 498y + 169)
c
4
, c
10
(y
2
+ y + 1)
17
(y
12
+ 12y
11
+ ··· + 35y + 9)
(y
20
+ 12y
19
+ ··· 65536y + 65536)
c
6
, c
9
y
2
(y
4
+ 2y
2
+ 3y + 1)
4
(y
4
+ y
3
+ 5y
2
+ y + 1)
4
(y
12
+ 8y
11
+ ··· + 10y + 1)(y
20
+ 9y
19
+ ··· + 698y + 169)
c
7
(y
2
+ y + 1)(y
8
6y
7
+ ··· 28y + 49)
(y
8
+ 9y
7
+ 11y
6
34y
5
+ 81y
4
37y
3
+ 87y
2
+ 14y + 1)
(y
12
4y
11
+ ··· + 139y + 169)(y
16
16y
15
+ ··· 83682y + 12321)
(y
20
19y
19
+ ··· 2641y + 441)
c
8
, c
11
(y
2
+ y + 1)(y
8
5y
7
+ 10y
6
+ 5y
5
12y
4
+ 7y
3
+ 4y
2
4y + 1)
(y
8
+ y
7
+ 13y
6
y
5
+ 81y
4
56y
3
+ 91y
2
+ 2y + 1)
(y
12
5y
11
+ ··· 12y + 1)(y
16
5y
15
+ ··· 102y + 9)
(y
20
+ 20y
18
+ ··· + 4y + 1)
18