11a
280
(K11a
280
)
1
Arc Sequences
6 9 1 10 2 4 11 3 5 8 7
Solving Sequence
2,9 3,5
6 10 1 4 7 8 11
c
2
c
5
c
9
c
1
c
4
c
6
c
8
c
11
c
3
, c
7
, c
10
Representation Ideals
I =
4
\
i=1
I
u
i
I
u
1
= hu
12
+ u
11
+ 6u
10
+ 4u
9
+ 15u
8
+ 6u
7
+ 18u
6
+ 4u
5
+ 12u
4
+ u
3
+ 6u
2
+ u + 2,
u
9
u
8
4u
7
2u
6
6u
5
2u
4
3u
3
2u
2
+ b 2u 1,
u
11
+ u
10
+ 6u
9
+ 2u
8
+ 13u
7
2u
6
+ 14u
5
8u
4
+ 8u
3
5u
2
+ 2a + 2u 3i
I
u
2
= hu
22
+ 14u
21
+ ··· + 1344u + 128, 41u
21
534u
20
+ ··· + 64b 5184,
81u
21
1052u
20
+ ··· + 128a 3712i
I
u
3
= hb
18
+ 5b
16
+ ··· 50b + 17,
2105832678b
17
+ 17708562289u + ··· + 108427927189b 38848951730,
72700962062b
17
+ 4898934371b
16
+ ··· + 761468178427a 1480794843934i
I
u
4
= ha
24
+ 5a
22
+ ··· + 5a + 43, 3.16350 × 10
24
u 8.10884 × 10
25
a
23
+ ··· + 4.73544 × 10
27
a 4.24757 × 10
27
,
4.96670 × 10
26
b + 1.86365 × 10
28
a
23
+ ··· 1.08774 × 10
30
a + 9.80615 × 10
29
i
There are 4 irreducible components with 76 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
12
+ u
11
+ · · · + u + 2, u
9
u
8
+ · · · + b 1, u
11
+ u
10
+ · · · + 2a 3i
(i) Arc colorings
a
2
=
1
0
a
9
=
1
2
u
11
1
2
u
10
+ ··· u +
3
2
u
9
+ u
8
+ 4u
7
+ 2u
6
+ 6u
5
+ 2u
4
+ 3u
3
+ 2u
2
+ 2u + 1
a
3
=
1
2
u
11
+
1
2
u
10
+ ··· u +
3
2
u
10
u
9
5u
8
3u
7
10u
6
3u
5
8u
4
u
3
4u
2
1
a
5
=
0
u
a
6
=
u
u
a
10
=
1
2
u
11
1
2
u
10
+ ··· u +
3
2
u
10
3u
8
+ 2u
7
4u
6
+ 4u
5
u
4
+ u
3
+ u + 1
a
1
=
u
2
+ 1
u
2
a
4
=
1
2
u
11
+
1
2
u
10
+ ··· u +
1
2
u
11
+ 4u
9
2u
8
+ 7u
7
7u
6
+ 5u
5
7u
4
+ 3u
3
4u
2
+ 2u 1
a
7
=
1
2
u
11
3
2
u
10
+ ···
7
2
u
2
5
2
u
11
u
10
+ ··· 3u + 1
a
8
=
2u
10
+ u
9
+ 9u
8
+ u
7
+ 17u
6
3u
5
+ 13u
4
4u
3
+ 5u
2
2u + 2
2u
11
+ 2u
10
+ 10u
9
+ 5u
8
+ 19u
7
+ 3u
6
+ 15u
5
u
4
+ 7u
3
+ 3u
a
11
=
5
2
u
11
5
2
u
10
+ ··· 5u
1
2
u
10
+ 2u
9
+ 7u
8
+ 7u
7
+ 15u
6
+ 7u
5
+ 14u
4
+ 8u
2
+ 2u + 5
a
11
=
5
2
u
11
5
2
u
10
+ ··· 5u
1
2
u
10
+ 2u
9
+ 7u
8
+ 7u
7
+ 15u
6
+ 7u
5
+ 14u
4
+ 8u
2
+ 2u + 5
(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 = 0.68102 1.43177I
a = 0.325823 + 0.401631I
b = 0.353153 0.740023I
1.75746 2.66133I 12.8054 + 12.9695I
u = 0.68102 + 1.43177I
a = 0.325823 0.401631I
b = 0.353153 + 0.740023I
1.75746 + 2.66133I 12.8054 12.9695I
u = 0.483540 0.658126I
a = 0.659029 0.177955I
b = 0.201550 + 0.519773I
1.60251 + 2.75174I 4.88343 6.08146I
u = 0.483540 + 0.658126I
a = 0.659029 + 0.177955I
b = 0.201550 0.519773I
1.60251 2.75174I 4.88343 + 6.08146I
u = 0.304944 0.791823I
a = 0.710678 0.464685I
b = 0.584665 0.421028I
3.88659 + 5.94873I 0.46248 5.63778I
u = 0.304944 + 0.791823I
a = 0.710678 + 0.464685I
b = 0.584665 + 0.421028I
3.88659 5.94873I 0.46248 + 5.63778I
u = 0.177296 1.218928I
a = 1.305658 + 0.234374I
b = 0.51717 1.54995I
4.20993 3.36477I 1.14978 + 1.06937I
u = 0.177296 + 1.218928I
a = 1.305658 0.234374I
b = 0.51717 + 1.54995I
4.20993 + 3.36477I 1.14978 1.06937I
u = 0.250152 1.336197I
a = 1.057362 0.118244I
b = 0.42250 + 1.38326I
7.83316 2.65596I 1.52426 + 0.93584I
u = 0.250152 + 1.336197I
a = 1.057362 + 0.118244I
b = 0.42250 1.38326I
7.83316 + 2.65596I 1.52426 0.93584I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.542055 0.545095I
a = 1.12423 1.23668I
b = 0.064712 1.283162I
1.86805 + 1.05670I 2.71042 0.18734I
u = 0.542055 + 0.545095I
a = 1.12423 + 1.23668I
b = 0.064712 + 1.283162I
1.86805 1.05670I 2.71042 + 0.18734I
4
II. I
u
2
= hu
22
+ 14u
21
+ · · · + 1344u + 128, 41u
21
534u
20
+ · · · + 64b
5184, 81u
21
1052u
20
+ · · · + 128a 3712i
(i) Arc colorings
a
2
=
1
0
a
9
=
81
128
u
21
+
263
32
u
20
+ ··· + 393u + 29
41
64
u
21
+
267
32
u
20
+ ··· +
1643
2
u + 81
a
3
=
59
128
u
21
+
95
16
u
20
+ ··· +
2283
4
u + 61
33
64
u
21
+
53
8
u
20
+ ··· +
1119
2
u + 59
a
5
=
0
u
a
6
=
u
u
a
10
=
81
128
u
21
+
263
32
u
20
+ ··· + 393u + 29
1
64
u
21
+
9
32
u
20
+ ··· +
83
2
u 1
a
1
=
u
2
+ 1
u
2
a
4
=
59
128
u
21
95
16
u
20
+ ···
2283
4
u 60
5
64
u
21
+
9
8
u
20
+ ··· +
151
2
u + 7
a
7
=
131
128
u
21
867
64
u
20
+ ··· 1490u 160
5
32
u
21
+
65
32
u
20
+ ··· +
573
2
u + 31
a
8
=
49
64
u
21
+
655
64
u
20
+ ··· +
1267
2
u + 60
71
64
u
21
+
485
32
u
20
+ ··· + 1749u + 180
a
11
=
1.24219u
21
+ 16.2813u
20
+ ··· + 1386.25u + 141.500
63
64
u
21
+
431
32
u
20
+ ··· + 1752u + 189
a
11
=
1.24219u
21
+ 16.2813u
20
+ ··· + 1386.25u + 141.500
63
64
u
21
+
431
32
u
20
+ ··· + 1752u + 189
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
5
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.37277 0.52957I
a = 0.418563 0.702720I
b = 0.202451 1.186335I
3.56765 + 4.49595I 1.80270 7.56758I
u = 1.37277 + 0.52957I
a = 0.418563 + 0.702720I
b = 0.202451 + 1.186335I
3.56765 4.49595I 1.80270 + 7.56758I
u = 1.201050 0.354294I
a = 0.572275 + 0.879915I
b = 0.375582 + 1.259576I
2.08640 + 9.42284I 1.11756 6.83027I
u = 1.201050 + 0.354294I
a = 0.572275 0.879915I
b = 0.375582 1.259576I
2.08640 9.42284I 1.11756 + 6.83027I
u = 1.15684 1.18640I
a = 0.492187 + 0.462754I
b = 0.020372 + 1.119264I
0.15255 1.75803I 3.02278 + 3.33932I
u = 1.15684 + 1.18640I
a = 0.492187 0.462754I
b = 0.020372 1.119264I
0.15255 + 1.75803I 3.02278 3.33932I
u = 0.721664 0.260594I
a = 1.170702 0.296451I
b = 0.767600 0.519015I
6.82374 0.02012I 7.10708 2.25648I
u = 0.721664 + 0.260594I
a = 1.170702 + 0.296451I
b = 0.767600 + 0.519015I
6.82374 + 0.02012I 7.10708 + 2.25648I
u = 0.49290 1.67050I
a = 0.802981 + 0.007620I
b = 0.408516 1.337621I
8.96137 + 5.23240I 4.36005 4.78438I
u = 0.49290 + 1.67050I
a = 0.802981 0.007620I
b = 0.408516 + 1.337621I
8.96137 5.23240I 4.36005 + 4.78438I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.492780 1.057534I
a = 0.017774 0.652714I
b = 0.699025 0.302848I
4.51267 + 4.47073I 3.53570 1.33986I
u = 0.492780 + 1.057534I
a = 0.017774 + 0.652714I
b = 0.699025 + 0.302848I
4.51267 4.47073I 3.53570 + 1.33986I
u = 0.48500 1.56416I
a = 0.949139 0.027077I
b = 0.50268 + 1.47148I
10.0188 + 10.9083I 4.45406 7.18292I
u = 0.48500 + 1.56416I
a = 0.949139 + 0.027077I
b = 0.50268 1.47148I
10.0188 10.9083I 4.45406 + 7.18292I
u = 0.46789 1.52014I
a = 1.033322 + 0.076733I
b = 0.60013 1.53489I
3.8405 + 15.3110I 0.76212 7.48531I
u = 0.46789 + 1.52014I
a = 1.033322 0.076733I
b = 0.60013 + 1.53489I
3.8405 15.3110I 0.76212 + 7.48531I
u = 0.421704 0.476349I
a = 0.849185 0.106026I
b = 0.408610 + 0.359797I
0.735294 + 0.892872I 5.94617 4.93873I
u = 0.421704 + 0.476349I
a = 0.849185 + 0.106026I
b = 0.408610 0.359797I
0.735294 0.892872I 5.94617 + 4.93873I
u = 0.420259 0.946349I
a = 0.190053 + 0.410286I
b = 0.468145 0.007430I
0.61105 + 2.59129I 5.45931 3.44339I
u = 0.420259 + 0.946349I
a = 0.190053 0.410286I
b = 0.468145 + 0.007430I
0.61105 2.59129I 5.45931 + 3.44339I
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.232862 1.365444I
a = 0.485061 0.405381I
b = 0.440574 + 0.756721I
1.47923 + 2.31516I 0.190328 + 0.743726I
u = 0.232862 + 1.365444I
a = 0.485061 + 0.405381I
b = 0.440574 0.756721I
1.47923 2.31516I 0.190328 0.743726I
7
III.
I
u
3
= hb
18
+5b
16
+· · ·50b+17, 1.77×10
10
u+2.11×10
9
b
17
+· · ·+1.08×10
11
b
3.88 × 10
10
, 7.27 × 10
10
b
17
+ 4.90 × 10
9
b
16
+ · · · + 7.61 × 10
11
a 1.48 × 10
12
i
(i) Arc colorings
a
2
=
1
0
a
9
=
0.0954747b
17
0.00643354b
16
+ ··· 3.92168b + 1.94466
b
a
3
=
0.00643354b
17
0.0555628b
16
+ ··· + 2.82908b 0.623070
b
2
a
5
=
0
0.118916b
17
0.000946298b
16
+ ··· 6.12291b + 2.19379
a
6
=
0.118916b
17
0.000946298b
16
+ ··· 6.12291b + 2.19379
0.118916b
17
0.000946298b
16
+ ··· 6.12291b + 2.19379
a
10
=
0.0954747b
17
0.00643354b
16
+ ··· 3.92168b + 1.94466
0.0513201b
17
+ 0.0379460b
16
+ ··· + 0.584746b + 1.26324
a
1
=
0.113960b
17
0.0734896b
16
+ ··· 2.32962b + 0.408802
0.113960b
17
0.0734896b
16
+ ··· 2.32962b 0.591198
a
4
=
0.0381529b
17
0.0628191b
16
+ ··· + 3.68251b 0.392744
0.0319178b
17
+ 0.00397222b
16
+ ··· + 1.09097b + 0.444642
a
7
=
0.185177b
17
+ 0.0319163b
16
+ ··· 12.3158b + 4.82001
0.0837045b
17
+ 0.0724798b
16
+ ··· 9.54514b + 3.51844
a
8
=
0.0399119b
17
0.0950387b
16
+ ··· 3.62029b + 2.05403
b
3
+ b
a
11
=
0.0605355b
17
+ 0.0420447b
16
+ ··· + 2.41806b 0.00904618
0.0170138b
17
0.0119503b
16
+ ··· + 0.364535b + 0.858135
a
11
=
0.0605355b
17
+ 0.0420447b
16
+ ··· + 2.41806b 0.00904618
0.0170138b
17
0.0119503b
16
+ ··· + 0.364535b + 0.858135
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
8
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.215080 + 1.307141I
a = 0.950698 + 0.063146I
b = 1.57917 0.11015I
1.48181 + 7.96606I 0.19182 6.18847I
u = 0.215080 1.307141I
a = 0.950698 0.063146I
b = 1.57917 + 0.11015I
1.48181 7.96606I 0.19182 + 6.18847I
u = 0.569840
a = 1.42461 + 0.28269I
b = 0.640673 0.946857I
5.61939 + 5.13794I 6.33744 3.20902I
u = 0.569840
a = 1.42461 0.28269I
b = 0.640673 + 0.946857I
5.61939 5.13794I 6.33744 + 3.20902I
u = 0.215080 + 1.307141I
a = 1.310457 + 0.291410I
b = 0.264938 1.312557I
8.74613 + 2.82812I 12.14562 2.97945I
u = 0.215080 1.307141I
a = 1.310457 0.291410I
b = 0.264938 + 1.312557I
8.74613 2.82812I 12.14562 + 2.97945I
u = 0.569840
a = 0.30031 2.22423I
b = 0.171130 1.267456I
4.60855 5.61636
u = 0.569840
a = 0.30031 + 2.22423I
b = 0.171130 + 1.267456I
4.60855 5.61636
u = 0.215080 1.307141I
a = 0.275589 + 1.162766I
b = 0.287016 1.229115I
1.48181 7.96606I 0.19182 + 6.18847I
u = 0.215080 + 1.307141I
a = 0.275589 1.162766I
b = 0.287016 + 1.229115I
1.48181 + 7.96606I 0.19182 6.18847I
9
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.215080 + 1.307141I
a = 0.571834 + 0.467184I
b = 0.406642 0.608737I
1.48181 2.30982I 0.191821 + 0.229571I
u = 0.215080 1.307141I
a = 0.571834 0.467184I
b = 0.406642 + 0.608737I
1.48181 + 2.30982I 0.191821 0.229571I
u = 0.215080 + 1.307141I
a = 0.403586 + 0.377500I
b = 0.487685 0.847949I
1.48181 2.30982I 0.191821 + 0.229571I
u = 0.215080 1.307141I
a = 0.403586 0.377500I
b = 0.487685 + 0.847949I
1.48181 + 2.30982I 0.191821 0.229571I
u = 0.215080 1.307141I
a = 1.010145 + 0.036474I
b = 0.66277 1.65028I
8.74613 2.82812I 12.14562 + 2.97945I
u = 0.215080 + 1.307141I
a = 1.010145 0.036474I
b = 0.66277 + 1.65028I
8.74613 + 2.82812I 12.14562 2.97945I
u = 0.569840
a = 1.12430 + 1.66162I
b = 0.811802 0.161086I
5.61939 + 5.13794I 6.33744 3.20902I
u = 0.569840
a = 1.12430 1.66162I
b = 0.811802 + 0.161086I
5.61939 5.13794I 6.33744 + 3.20902I
10
IV.
I
u
4
= ha
24
+ 5a
22
+ · · · + 5a + 43, 3.16 × 10
24
u 8.11 × 10
25
a
23
+ · · · + 4.74 ×
10
27
a4.25×10
27
, 4.97×10
26
b+1.86×10
28
a
23
+· · ·1.09×10
30
a+9.81×10
29
i
(i) Arc colorings
a
2
=
1
0
a
9
=
a
37.5229a
23
+ 30.6202a
22
+ ··· + 2190.06a 1974.38
a
3
=
30.6202a
23
+ 24.9915a
22
+ ··· + 1786.76a 1612.48
29.6058a
23
+ 24.1788a
22
+ ··· + 1723.45a 1557.56
a
5
=
0
25.6325a
23
20.7625a
22
+ ··· 1496.90a + 1342.68
a
6
=
25.6325a
23
20.7625a
22
+ ··· 1496.90a + 1342.68
25.6325a
23
20.7625a
22
+ ··· 1496.90a + 1342.68
a
10
=
a
28.6127a
23
+ 23.2540a
22
+ ··· + 1670.26a 1499.33
a
1
=
11.0475a
23
8.91015a
22
+ ··· 644.397a + 576.032
11.0475a
23
8.91015a
22
+ ··· 644.397a + 575.032
a
4
=
17.0819a
23
+ 13.7744a
22
+ ··· + 998.384a 892.786
16.1051a
23
+ 12.8787a
22
+ ··· + 940.053a 836.890
a
7
=
14.9296a
23
12.2110a
22
+ ··· 870.804a + 785.326
81.7409a
23
66.9105a
22
+ ··· 4763.56a + 4302.81
a
8
=
13.3441a
23
10.8715a
22
+ ··· 779.520a + 701.329
83.0792a
23
67.8258a
22
+ ··· 4845.01a + 4371.47
a
11
=
64.4728a
23
52.6389a
22
+ ··· 3756.83a + 3390.20
81.6449a
23
66.8402a
22
+ ··· 4742.18a + 4288.72
a
11
=
64.4728a
23
52.6389a
22
+ ··· 3756.83a + 3390.20
81.6449a
23
66.8402a
22
+ ··· 4742.18a + 4288.72
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
11
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.215080 + 1.307141I
a = 1.099456 0.027472I
b = 1.07429 1.51957I
4.66906 + 4.85801I 3.50976 6.44355I
u = 0.215080 1.307141I
a = 1.099456 + 0.027472I
b = 1.07429 + 1.51957I
4.66906 4.85801I 3.50976 + 6.44355I
u = 0.215080 + 1.307141I
a = 0.929016 0.214301I
b = 0.786120 0.023283I
4.66906 + 0.79824I 3.50976 + 0.48465I
u = 0.215080 1.307141I
a = 0.929016 + 0.214301I
b = 0.786120 + 0.023283I
4.66906 0.79824I 3.50976 0.48465I
u = 0.215080 1.307141I
a = 0.816868 0.000713I
b = 0.39398 + 1.91732I
4.66906 0.79824I 3.50976 0.48465I
u = 0.215080 + 1.307141I
a = 0.816868 + 0.000713I
b = 0.39398 1.91732I
4.66906 + 0.79824I 3.50976 + 0.48465I
u = 0.569840
a = 0.73481 1.94800I
b = 0.05062 1.44264I
0.53148 + 2.02988I 3.01951 3.46410I
u = 0.569840
a = 0.73481 + 1.94800I
b = 0.05062 + 1.44264I
0.53148 2.02988I 3.01951 + 3.46410I
u = 0.569840
a = 0.59313 1.48895I
b = 0.429892 + 0.137875I
0.53148 + 2.02988I 3.01951 3.46410I
u = 0.569840
a = 0.59313 + 1.48895I
b = 0.429892 0.137875I
0.53148 2.02988I 3.01951 + 3.46410I
12
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.215080 1.307141I
a = 0.320479 0.895547I
b = 0.159459 + 1.282096I
4.66906 4.85801I 3.50976 + 6.44355I
u = 0.215080 + 1.307141I
a = 0.320479 + 0.895547I
b = 0.159459 1.282096I
4.66906 + 4.85801I 3.50976 6.44355I
u = 0.569840
a = 0.08883 2.53167I
b = 0.418722 1.110048I
0.53148 2.02988I 3.01951 + 3.46410I
u = 0.569840
a = 0.08883 + 2.53167I
b = 0.418722 + 1.110048I
0.53148 + 2.02988I 3.01951 3.46410I
u = 0.215080 + 1.307141I
a = 0.113690 0.582697I
b = 0.080309 + 1.260447I
4.66906 + 0.79824I 3.50976 + 0.48465I
u = 0.215080 1.307141I
a = 0.113690 + 0.582697I
b = 0.080309 1.260447I
4.66906 0.79824I 3.50976 0.48465I
u = 0.569840
a = 0.754407 0.241953I
b = 0.337989 + 0.848465I
0.53148 + 2.02988I 3.01951 3.46410I
u = 0.569840
a = 0.754407 + 0.241953I
b = 0.337989 0.848465I
0.53148 2.02988I 3.01951 + 3.46410I
u = 0.215080 1.307141I
a = 0.974528 0.038360I
b = 1.239536 0.226298I
4.66906 4.85801I 3.50976 + 6.44355I
u = 0.215080 + 1.307141I
a = 0.974528 + 0.038360I
b = 1.239536 + 0.226298I
4.66906 + 4.85801I 3.50976 6.44355I
13
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.215080 + 1.307141I
a = 1.263535 0.613955I
b = 0.20056 + 1.44305I
4.66906 + 4.85801I 3.50976 6.44355I
u = 0.215080 1.307141I
a = 1.263535 + 0.613955I
b = 0.20056 1.44305I
4.66906 4.85801I 3.50976 + 6.44355I
u = 0.215080 + 1.307141I
a = 1.47642 0.05847I
b = 0.176624 + 1.067609I
4.66906 + 0.79824I 3.50976 + 0.48465I
u = 0.215080 1.307141I
a = 1.47642 + 0.05847I
b = 0.176624 1.067609I
4.66906 0.79824I 3.50976 0.48465I
14
V. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
3
u
2
+ 2u 1)
14
(u
12
+ u
11
+ ··· + u + 2)
(u
22
+ 14u
21
+ ··· + 1344u + 128)
c
2
, c
9
(u
12
+ 6u
10
+ u
9
+ 15u
8
+ 4u
7
+ 17u
6
+ 6u
5
+ 9u
4
+ 4u
3
+ 4u
2
+ 1)
(u
18
+ 5u
16
+ ··· 50u + 17)(u
22
+ 9u
20
+ ··· 3u
2
+ 1)
(u
24
+ u
23
+ ··· + 188u + 43)
c
3
, c
6
(u
12
+ u
11
+ 7u
8
+ 8u
7
+ 2u
6
+ 7u
4
+ 7u
3
+ 3u
2
+ u + 1)
(u
18
+ 2u
17
+ ··· 4u + 1)(u
22
+ u
21
+ ··· 3u + 1)
(u
24
+ 5u
23
+ ··· + 16u + 1)
c
4
, c
8
(u
12
+ 6u
10
u
9
+ 15u
8
4u
7
+ 17u
6
6u
5
+ 9u
4
4u
3
+ 4u
2
+ 1)
(u
18
+ 5u
16
+ ··· 50u + 17)(u
22
+ 9u
20
+ ··· 3u
2
+ 1)
(u
24
+ u
23
+ ··· + 188u + 43)
c
5
(u
3
u
2
+ 2u 1)
14
(u
12
u
11
+ ··· u + 2)
(u
22
+ 14u
21
+ ··· + 1344u + 128)
c
7
(u
3
+ 2u + 1)
6
(1 2u + 2u
2
u
3
+ u
4
)
6
(u
12
2u
11
+ ··· + 5u
2
+ 1)
(u
22
+ 9u
21
+ ··· + 88u + 8)
c
10
, c
11
(u
3
+ 2u + 1)
6
(1 2u + 2u
2
u
3
+ u
4
)
6
(u
12
+ 2u
11
+ ··· + 5u
2
+ 1)
(u
22
+ 9u
21
+ ··· + 88u + 8)
15
VI. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
(y
3
+ 3y
2
+ 2y 1)
14
(y
12
+ 11y
11
+ ··· + 23y + 4)
(y
22
+ 14y
21
+ ··· + 20480y + 16384)
c
2
, c
4
, c
8
c
9
(y
12
+ 12y
11
+ ··· + 8y + 1)(y
18
+ 10y
17
+ ··· + 968y + 289)
(y
22
+ 18y
21
+ ··· 6y + 1)(y
24
+ 25y
23
+ ··· 5588y + 1849)
c
3
, c
6
(y
12
y
11
+ ··· + 5y + 1)(y
18
+ 2y
17
+ ··· + 8y + 1)
(y
22
+ 5y
21
+ ··· + 11y + 1)(y
24
7y
23
+ ··· 64y + 1)
c
7
, c
10
, c
11
(y
3
+ 4y
2
+ 4y 1)
6
(y
4
+ 3y
3
+ 2y
2
+ 1)
6
(y
12
+ 14y
11
+ ··· + 10y + 1)(y
22
+ 21y
21
+ ··· + 224y + 64)
16