11a
160
(K11a
160
)
1
Arc Sequences
5 1 10 8 2 9 4 11 3 7 6
Solving Sequence
2,5 6,9
7 1 3 10 11 8 4
c
5
c
6
c
1
c
2
c
9
c
11
c
8
c
4
c
3
, c
7
, c
10
Representation Ideals
I =
3
\
i=1
I
u
i
I
u
1
= ha
56
+ 5a
55
+ ··· 568911a + 115201,
1.97971 × 10
323
u 2.66648 × 10
319
a
55
+ ··· 1.83206 × 10
325
a + 8.71595 × 10
324
,
9.38399 × 10
330
b 9.21036 × 10
326
a
55
+ ··· 6.42411 × 10
332
a + 2.76911 × 10
332
i
I
u
2
= hu
14
+ u
13
3u
12
4u
11
+ 4u
10
+ 7u
9
u
8
7u
7
3u
6
+ 4u
5
+ 4u
4
2u
3
2u
2
+ u + 1,
2u
12
+ 5u
10
+ u
9
7u
8
2u
7
+ 3u
6
+ 5u
5
4u
3
+ b + 2u 1,
2u
13
+ 2u
12
7u
11
7u
10
+ 11u
9
+ 12u
8
7u
7
12u
6
3u
5
+ 9u
4
+ 6u
3
6u
2
+ a 2u + 3i
I
u
3
= hu
30
6u
29
+ ··· 26u + 4, u
29
+ 10u
28
+ ··· + 2b + 6, 7u
29
+ 32u
28
+ ··· + 4a + 28i
There are 3 irreducible components with 100 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
= ha
56
+ 5a
55
+ · · · 568911a + 115201, 1.98 × 10
323
u 2.67 ×
10
319
a
55
+ · · · 1.83 × 10
325
a + 8.72 × 10
324
, 9.38 × 10
330
b 9.21 ×
10
326
a
55
+ · · · 6.42 × 10
332
a + 2.77 × 10
332
i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
0.000134691a
55
+ 0.000721496a
54
+ ··· + 92.5419a 44.0264
a
6
=
0.000134691a
55
0.000721496a
54
+ ··· 92.5419a + 44.0264
0.000134691a
55
+ 0.000721496a
54
+ ··· + 92.5419a 44.0264
a
9
=
a
0.0000981497a
55
+ 0.000527261a
54
+ ··· + 68.4582a 29.5089
a
7
=
0.000108614a
55
0.000580282a
54
+ ··· 73.5690a + 36.9219
0.0000983652a
55
+ 0.000525446a
54
+ ··· + 67.6797a 33.4147
a
1
=
1
0.000224355a
55
+ 0.00120535a
54
+ ··· + 157.764a 69.2477
a
3
=
0.000224355a
55
+ 0.00120535a
54
+ ··· + 157.764a 68.2477
0.000179951a
55
0.000973999a
54
+ ··· 128.550a + 49.1321
a
10
=
5.12014 × 10
6
a
55
+ 0.0000254707a
54
+ ··· + 3.48247a 2.21675
0.000160385a
55
+ 0.000863267a
54
+ ··· + 113.725a 47.6164
a
11
=
0.0000444044a
55
+ 0.000231352a
54
+ ··· + 29.2140a 19.1157
0.000179951a
55
+ 0.000973999a
54
+ ··· + 128.550a 49.1321
a
8
=
0.0000455080a
55
+ 0.000238518a
54
+ ··· + 29.8287a 18.7716
0.000177037a
55
+ 0.000956458a
54
+ ··· + 125.901a 49.0687
a
4
=
0.000180605a
55
+ 0.000970455a
54
+ ··· + 127.621a 55.7602
0.000146770a
55
0.000793816a
54
+ ··· 104.884a + 39.6746
a
4
=
0.000180605a
55
+ 0.000970455a
54
+ ··· + 127.621a 55.7602
0.000146770a
55
0.000793816a
54
+ ··· 104.884a + 39.6746
(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 = 0.403136 0.584808I
a = 2.10410 0.37419I
b = 0.665986 + 0.109048I
6.29745 2.65847I 8.31651 + 4.88661I
u = 0.403136 + 0.584808I
a = 2.10410 + 0.37419I
b = 0.665986 0.109048I
6.29745 + 2.65847I 8.31651 4.88661I
u = 1.068409 + 0.522447I
a = 2.08386 1.11179I
b = 2.52924 + 1.26212I
4.37100 7.10173I 3.67153 + 9.79536I
u = 1.068409 0.522447I
a = 2.08386 + 1.11179I
b = 2.52924 1.26212I
4.37100 + 7.10173I 3.67153 9.79536I
u = 0.989783 + 0.381937I
a = 1.95882 1.05533I
b = 2.97668 + 1.55524I
3.24009 + 3.43472I 0.49073 3.99358I
u = 0.989783 0.381937I
a = 1.95882 + 1.05533I
b = 2.97668 1.55524I
3.24009 3.43472I 0.49073 + 3.99358I
u = 1.142594 + 0.546762I
a = 1.76722 0.32328I
b = 2.62210 0.07128I
1.12941 + 10.56112I 0.72348 9.64441I
u = 1.142594 0.546762I
a = 1.76722 + 0.32328I
b = 2.62210 + 0.07128I
1.12941 10.56112I 0.72348 + 9.64441I
u = 1.157218 0.286866I
a = 1.33249 0.77757I
b = 2.15332 + 1.77383I
2.89147 2.50043I 3.32829 + 3.28061I
u = 1.157218 + 0.286866I
a = 1.33249 + 0.77757I
b = 2.15332 1.77383I
2.89147 + 2.50043I 3.32829 3.28061I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.142594 0.546762I
a = 1.235239 0.222693I
b = 1.90738 + 0.21382I
1.12941 6.50135I 0.72348 + 2.71621I
u = 1.142594 + 0.546762I
a = 1.235239 + 0.222693I
b = 1.90738 0.21382I
1.12941 + 6.50135I 0.72348 2.71621I
u = 0.989783 0.381937I
a = 1.220140 0.378199I
b = 2.23605 + 1.75240I
3.24009 + 0.62505I 0.49073 2.93462I
u = 0.989783 + 0.381937I
a = 1.220140 + 0.378199I
b = 2.23605 1.75240I
3.24009 0.62505I 0.49073 + 2.93462I
u = 0.403136 + 0.584808I
a = 1.07336 2.10971I
b = 0.58551 + 1.31953I
6.29745 + 2.65847I 8.31651 4.88661I
u = 0.403136 0.584808I
a = 1.07336 + 2.10971I
b = 0.58551 1.31953I
6.29745 2.65847I 8.31651 + 4.88661I
u = 0.728347 0.560551I
a = 0.649074 0.821249I
b = 0.647471 0.059834I
3.49442 4.22117I 3.23919 + 7.32128I
u = 0.728347 + 0.560551I
a = 0.649074 + 0.821249I
b = 0.647471 + 0.059834I
3.49442 + 4.22117I 3.23919 7.32128I
u = 0.268039 0.757899I
a = 0.356664 1.023902I
b = 0.203199 + 0.355441I
1.42232 + 1.59890I 2.33383 + 0.83184I
u = 0.268039 + 0.757899I
a = 0.356664 + 1.023902I
b = 0.203199 0.355441I
1.42232 1.59890I 2.33383 0.83184I
4
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.728347 + 0.560551I
a = 0.331754 0.142899I
b = 0.984685 0.767771I
3.49442 + 0.16140I 3.23919 0.39308I
u = 0.728347 0.560551I
a = 0.331754 + 0.142899I
b = 0.984685 + 0.767771I
3.49442 0.16140I 3.23919 + 0.39308I
u = 0.728347 + 0.560551I
a = 0.234911 1.018142I
b = 1.09501 + 0.89733I
3.49442 + 4.22117I 3.23919 7.32128I
u = 0.728347 0.560551I
a = 0.234911 + 1.018142I
b = 1.09501 0.89733I
3.49442 4.22117I 3.23919 + 7.32128I
u = 0.268039 0.757899I
a = 0.08590 1.77609I
b = 0.579512 + 0.588261I
1.42232 + 5.65867I 2.33383 6.09636I
u = 0.268039 + 0.757899I
a = 0.08590 + 1.77609I
b = 0.579512 0.588261I
1.42232 5.65867I 2.33383 + 6.09636I
u = 0.403136 0.584808I
a = 0.071863 0.496236I
b = 1.412123 0.069745I
6.29745 + 1.40130I 8.31651 2.04159I
u = 0.403136 + 0.584808I
a = 0.071863 + 0.496236I
b = 1.412123 + 0.069745I
6.29745 1.40130I 8.31651 + 2.04159I
u = 1.157218 + 0.286866I
a = 0.068620 0.476976I
b = 0.302025 + 0.328138I
2.89147 1.55933I 3.32829 + 3.64759I
u = 1.157218 0.286866I
a = 0.068620 + 0.476976I
b = 0.302025 0.328138I
2.89147 + 1.55933I 3.32829 3.64759I
5
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.403136 0.584808I
a = 0.15759 3.12328I
b = 0.323579 + 0.605290I
6.29660 + 1.40177I 8.31651 2.04159I
u = 0.403136 + 0.584808I
a = 0.15759 + 3.12328I
b = 0.323579 0.605290I
6.29660 1.40177I 8.31651 + 2.04159I
u = 1.068409 + 0.522447I
a = 0.311605 0.978475I
b = 0.55140 + 2.84405I
4.37100 7.10173I 3.67153 + 9.79536I
u = 1.068409 0.522447I
a = 0.311605 + 0.978475I
b = 0.55140 2.84405I
4.37100 + 7.10173I 3.67153 9.79536I
u = 0.989783 0.381937I
a = 0.325577 1.025960I
b = 0.696575 0.131685I
3.24009 3.43472I 0.49073 + 3.99358I
u = 0.989783 + 0.381937I
a = 0.325577 + 1.025960I
b = 0.696575 + 0.131685I
3.24009 + 3.43472I 0.49073 3.99358I
u = 0.268039 0.757899I
a = 0.337228 0.041321I
b = 0.264931 + 0.038791I
1.42232 + 1.59890I 2.33383 + 0.83184I
u = 0.268039 + 0.757899I
a = 0.337228 + 0.041321I
b = 0.264931 0.038791I
1.42232 1.59890I 2.33383 0.83184I
u = 1.068409 + 0.522447I
a = 0.352301 0.823777I
b = 0.609759 0.175780I
4.37100 3.04196I 3.67153 + 2.86716I
u = 1.068409 0.522447I
a = 0.352301 + 0.823777I
b = 0.609759 + 0.175780I
4.37100 + 3.04196I 3.67153 2.86716I
6
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.142594 0.546762I
a = 0.385964 0.017792I
b = 0.685844 0.441788I
1.12941 6.50135I 0.72348 + 2.71621I
u = 1.142594 + 0.546762I
a = 0.385964 + 0.017792I
b = 0.685844 + 0.441788I
1.12941 + 6.50135I 0.72348 2.71621I
u = 0.728347 0.560551I
a = 0.603232 1.006899I
b = 0.379526 + 0.098392I
3.49442 0.16140I 3.23919 + 0.39308I
u = 0.728347 + 0.560551I
a = 0.603232 + 1.006899I
b = 0.379526 0.098392I
3.49442 + 0.16140I 3.23919 0.39308I
u = 0.268039 + 0.757899I
a = 1.01813 2.29187I
b = 0.004032 + 0.379964I
1.42232 5.65867I 2.33383 + 6.09636I
u = 0.268039 0.757899I
a = 1.01813 + 2.29187I
b = 0.004032 0.379964I
1.42232 + 5.65867I 2.33383 6.09636I
u = 1.157218 0.286866I
a = 1.050668 0.150581I
b = 1.74391 + 0.12068I
2.89147 + 1.55933I 3.32829 3.64759I
u = 1.157218 + 0.286866I
a = 1.050668 + 0.150581I
b = 1.74391 0.12068I
2.89147 1.55933I 3.32829 + 3.64759I
u = 1.157218 0.286866I
a = 1.055517 0.354960I
b = 1.61204 0.42139I
2.89147 2.50043I 3.32829 + 3.28061I
u = 1.157218 + 0.286866I
a = 1.055517 + 0.354960I
b = 1.61204 + 0.42139I
2.89147 + 2.50043I 3.32829 3.28061I
7
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.142594 + 0.546762I
a = 1.98359 0.53246I
b = 3.43029 + 1.01518I
1.12941 + 10.56112I 0.72348 9.64441I
u = 1.142594 0.546762I
a = 1.98359 + 0.53246I
b = 3.43029 1.01518I
1.12941 10.56112I 0.72348 + 9.64441I
u = 0.989783 0.381937I
a = 2.01132 1.05092I
b = 1.91519 + 1.06569I
3.24009 + 0.62505I 0.49073 2.93462I
u = 0.989783 + 0.381937I
a = 2.01132 + 1.05092I
b = 1.91519 1.06569I
3.24009 0.62505I 0.49073 + 2.93462I
u = 1.068409 0.522447I
a = 2.34405 0.33409I
b = 3.93521 + 0.16444I
4.37100 + 3.04196I 3.67153 2.86716I
u = 1.068409 + 0.522447I
a = 2.34405 + 0.33409I
b = 3.93521 0.16444I
4.37100 3.04196I 3.67153 + 2.86716I
8
II.
I
u
2
= hu
14
+u
13
+· · ·+u+1, 2u
12
+5u
10
+· · ·+b1, 2u
13
+2u
12
+· · ·+a+3i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
6
=
u
u
a
9
=
2u
13
2u
12
+ ··· + 2u 3
2u
12
5u
10
u
9
+ 7u
8
+ 2u
7
3u
6
5u
5
+ 4u
3
2u + 1
a
7
=
u
13
4u
11
u
10
+ 8u
9
+ 3u
8
7u
7
6u
6
+ 2u
5
+ 6u
4
+ 2u
3
5u
2
+ 1
u
11
+ u
10
3u
9
3u
8
+ 3u
7
+ 4u
6
2u
4
3u
3
+ 2u
2
+ u 1
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
10
=
u
13
u
12
+ ··· + 2u 1
u
13
+ u
12
+ ··· + 2u
2
2u
a
11
=
u
4
u
2
+ 1
u
4
a
8
=
u
13
u
12
+ ··· + 2u 2
u
12
3u
10
+ 5u
8
+ u
7
3u
6
3u
5
+ 3u
3
u + 1
a
4
=
3u
13
+ u
12
+ ··· 2u + 3
3u
13
2u
12
+ ··· + 2u 3
a
4
=
3u
13
+ u
12
+ ··· 2u + 3
3u
13
2u
12
+ ··· + 2u 3
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
9
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.162208 0.578741I
a = 1.024699 0.124687I
b = 1.68891 + 0.32626I
1.07739 7.66495I 1.03033 + 9.99597I
u = 1.162208 + 0.578741I
a = 1.024699 + 0.124687I
b = 1.68891 0.32626I
1.07739 + 7.66495I 1.03033 9.99597I
u = 1.020859 0.434206I
a = 1.93767 0.63480I
b = 2.88389 0.09189I
3.52230 0.63660I 2.40553 + 3.12380I
u = 1.020859 + 0.434206I
a = 1.93767 + 0.63480I
b = 2.88389 + 0.09189I
3.52230 + 0.63660I 2.40553 3.12380I
u = 0.658163 0.329875I
a = 1.33446 + 1.92643I
b = 1.49254 0.44459I
4.85404 2.75383I 6.20128 + 4.14732I
u = 0.658163 + 0.329875I
a = 1.33446 1.92643I
b = 1.49254 + 0.44459I
4.85404 + 2.75383I 6.20128 4.14732I
u = 0.341418 0.896272I
a = 0.139180 0.812408I
b = 0.035008 + 0.162099I
1.48125 + 2.28994I 0.76956 11.07837I
u = 0.341418 + 0.896272I
a = 0.139180 + 0.812408I
b = 0.035008 0.162099I
1.48125 2.28994I 0.76956 + 11.07837I
u = 0.552395 0.530092I
a = 0.666539 + 0.988386I
b = 0.577372 0.961499I
5.63571 1.41240I 4.95246 0.76426I
u = 0.552395 + 0.530092I
a = 0.666539 0.988386I
b = 0.577372 + 0.961499I
5.63571 + 1.41240I 4.95246 + 0.76426I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.041715 0.508997I
a = 1.323679 + 0.095600I
b = 1.71678 + 0.90848I
4.08559 + 5.66390I 2.38420 4.61852I
u = 1.041715 + 0.508997I
a = 1.323679 0.095600I
b = 1.71678 0.90848I
4.08559 5.66390I 2.38420 + 4.61852I
u = 1.088539 0.205382I
a = 0.717801 0.201681I
b = 1.55670 0.11624I
3.69709 + 0.34310I 7.64356 0.71321I
u = 1.088539 + 0.205382I
a = 0.717801 + 0.201681I
b = 1.55670 + 0.11624I
3.69709 0.34310I 7.64356 + 0.71321I
11
III. I
u
3
= hu
30
6u
29
+ · · · 26u + 4, u
29
+ 10u
28
+ · · · + 2b + 6, 7u
29
+
32u
28
+ · · · + 4a + 28i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
6
=
u
u
a
9
=
7
4
u
29
8u
28
+ ··· +
187
4
u 7
1
2
u
29
5u
28
+ ··· +
39
2
u 3
a
7
=
6.50000u
29
+ 33.5000u
28
+ ··· 146.500u + 24.5000
15
2
u
29
38u
28
+ ··· +
321
2
u 28
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
10
=
9
4
u
29
13u
28
+ ··· +
249
4
u 10
1
2
u
29
+ 3u
28
+ ···
165
2
u + 17
a
11
=
u
4
u
2
+ 1
u
4
a
8
=
25
4
u
29
31u
28
+ ··· +
529
4
u 22
19
2
u
29
+ 45u
28
+ ···
337
2
u + 29
a
4
=
3u
29
25
2
u
28
+ ··· + 8u +
1
2
9
2
u
29
+ 19u
28
+ ···
63
2
u + 4
a
4
=
3u
29
25
2
u
28
+ ··· + 8u +
1
2
9
2
u
29
+ 19u
28
+ ···
63
2
u + 4
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
12
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.212807 0.208647I
a = 1.273143 + 0.452561I
b = 2.06587 1.35843I
1.15159 + 8.63900I 1.81852 4.95805I
u = 1.212807 + 0.208647I
a = 1.273143 0.452561I
b = 2.06587 + 1.35843I
1.15159 8.63900I 1.81852 + 4.95805I
u = 1.199614 0.446464I
a = 0.588869 0.423908I
b = 1.073552 + 0.251795I
1.92835 6.42721I 4.67944 + 7.09422I
u = 1.199614 + 0.446464I
a = 0.588869 + 0.423908I
b = 1.073552 0.251795I
1.92835 + 6.42721I 4.67944 7.09422I
u = 1.14537
a = 0.848748
b = 1.85228
2.84813 1.74443
u = 1.103297 0.364983I
a = 1.224078 + 0.265513I
b = 2.07517 + 0.51856I
5.00799 1.36896I 7.09046 + 4.51225I
u = 1.103297 + 0.364983I
a = 1.224078 0.265513I
b = 2.07517 0.51856I
5.00799 + 1.36896I 7.09046 4.51225I
u = 0.926063
a = 0.432086
b = 1.70894
2.97639 3.61538
u = 0.179468 0.841852I
a = 0.178998 0.550311I
b = 0.260518 + 0.152154I
1.38263 + 1.72204I 2.32664 + 0.60868I
u = 0.179468 + 0.841852I
a = 0.178998 + 0.550311I
b = 0.260518 0.152154I
1.38263 1.72204I 2.32664 0.60868I
13
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.229199 0.619350I
a = 0.03669 + 1.98223I
b = 0.510637 0.359460I
1.54965 1.73951I 3.40461 + 1.10111I
u = 0.229199 + 0.619350I
a = 0.03669 1.98223I
b = 0.510637 + 0.359460I
1.54965 + 1.73951I 3.40461 1.10111I
u = 0.322085 0.845243I
a = 0.60284 2.06031I
b = 0.144364 + 0.436599I
6.21887 11.79363I 3.80243 + 6.19160I
u = 0.322085 + 0.845243I
a = 0.60284 + 2.06031I
b = 0.144364 0.436599I
6.21887 + 11.79363I 3.80243 6.19160I
u = 0.439336 0.898767I
a = 0.149276 + 1.039670I
b = 0.0247387 0.1054823I
3.15371 2.25650I 2.07479 + 3.80636I
u = 0.439336 + 0.898767I
a = 0.149276 1.039670I
b = 0.0247387 + 0.1054823I
3.15371 + 2.25650I 2.07479 3.80636I
u = 0.594964 0.357254I
a = 0.703721 0.962503I
b = 0.093934 + 0.683196I
0.55728 + 1.33045I 2.87243 5.52992I
u = 0.594964 + 0.357254I
a = 0.703721 + 0.962503I
b = 0.093934 0.683196I
0.55728 1.33045I 2.87243 + 5.52992I
u = 0.722214 0.756555I
a = 0.568209 + 0.182817I
b = 0.649326 + 0.016156I
8.50027 + 8.77817I 5.31474 7.47276I
u = 0.722214 + 0.756555I
a = 0.568209 0.182817I
b = 0.649326 0.016156I
8.50027 8.77817I 5.31474 + 7.47276I
14
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.902723 0.723773I
a = 0.0616062 + 0.0931721I
b = 0.200889 1.015248I
7.98240 3.24098I 5.21335 + 3.14058I
u = 0.902723 + 0.723773I
a = 0.0616062 0.0931721I
b = 0.200889 + 1.015248I
7.98240 + 3.24098I 5.21335 3.14058I
u = 1.107066 0.415384I
a = 0.931857 + 0.075200I
b = 1.295805 + 0.176596I
2.31526 + 1.75344I 3.75152 0.07888I
u = 1.107066 + 0.415384I
a = 0.931857 0.075200I
b = 1.295805 0.176596I
2.31526 1.75344I 3.75152 + 0.07888I
u = 1.114947 0.506217I
a = 1.71110 0.36386I
b = 2.76244 + 0.06360I
4.02021 + 6.15111I 5.67724 4.92712I
u = 1.114947 + 0.506217I
a = 1.71110 + 0.36386I
b = 2.76244 0.06360I
4.02021 6.15111I 5.67724 + 4.92712I
u = 1.141332 0.635650I
a = 1.040429 0.149657I
b = 1.88846 + 0.23803I
0.98575 + 7.90704I 0.97053 7.34135I
u = 1.141332 + 0.635650I
a = 1.040429 + 0.149657I
b = 1.88846 0.23803I
0.98575 7.90704I 0.97053 + 7.34135I
u = 1.157039 0.588836I
a = 1.88348 0.26441I
b = 3.15373 + 0.65140I
3.7202 + 17.0985I 0.80952 9.70777I
u = 1.157039 + 0.588836I
a = 1.88348 + 0.26441I
b = 3.15373 0.65140I
3.7202 17.0985I 0.80952 + 9.70777I
15
IV. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
1
(1 u + 2u
4
2u
5
2u
6
+ 6u
7
u
8
7u
9
+ 4u
10
+ 4u
11
3u
12
u
13
+ u
14
)
4
(u
14
+ u
13
+ ··· + u + 1)(u
30
+ 6u
29
+ ··· + 26u + 4)
c
2
1
(1 + u + 4u
2
+ 8u
3
+ 14u
4
+ 18u
5
+ 26u
6
+ 44u
7
+ 73u
8
+ 93u
9
+ 86u
10
+ 56u
11
+ 25u
12
+ 7u
13
+ u
14
)
4
(u
14
+ 7u
13
+ ··· + 5u + 1)(u
30
+ 14u
29
+ ··· + 28u + 16)
c
3
(u
14
+ u
13
+ ··· + 3u + 1)(u
30
+ u
29
+ ··· u + 1)
(u
56
u
55
+ ··· 362u + 259)
c
4
(u
14
u
13
+ ··· 3u + 1)(u
30
+ u
29
+ ··· u + 1)
(u
56
u
55
+ ··· 362u + 259)
c
5
1
(1 u + 2u
4
2u
5
2u
6
+ 6u
7
u
8
7u
9
+ 4u
10
+ 4u
11
3u
12
u
13
+ u
14
)
4
(u
14
u
13
+ ··· u + 1)(u
30
+ 6u
29
+ ··· + 26u + 4)
c
6
(u
14
+ u
13
+ u
12
3u
11
u
10
u
9
+ 5u
8
2u
7
4u
5
+ 4u
4
+ u
2
2u + 1)
(u
30
u
29
+ ··· + 4u + 1)(u
56
+ 15u
55
+ ··· + 26u + 1)
c
7
(u
14
+ u
13
+ ··· + 3u + 1)(u
30
+ u
29
+ ··· u + 1)
(u
56
u
55
+ ··· 362u + 259)
c
8
(u
14
+ u
13
+ u
12
3u
11
u
10
u
9
+ 5u
8
2u
7
4u
5
+ 4u
4
+ u
2
2u + 1)
(u
30
u
29
+ ··· + 4u + 1)(u
56
+ 15u
55
+ ··· + 26u + 1)
c
9
(u + 1)(u
14
u
13
+ ··· 3u + 1)(u
30
+ u
29
+ ··· u + 1)
(u
55
2u
54
+ ··· 621u + 259)
c
10
(u
2
+ u + 1)
28
(u
14
+ 2u
13
+ u
12
+ 4u
10
+ 4u
9
+ 2u
7
+ 5u
6
+ u
5
u
4
+ 3u
3
+ u
2
u + 1)
(u
30
27u
29
+ ··· 237568u + 16384)
c
11
(u 1)(u
14
+ 3u
13
+ ··· + 3u + 1)(u
30
+ 18u
29
+ ··· 314u 52)
(u
55
11u
54
+ ··· + 675u 81)
16
V. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
(y
14
7y
13
+ ··· 5y + 1)
(1 y + 4y
2
8y
3
+ 14y
4
18y
5
+ 26y
6
44y
7
+ 73y
8
93y
9
+ 86y
10
56y
11
+ 25y
12
7y
13
+ y
14
)
4
(y
30
14y
29
+ ··· 28y + 16)
c
2
(y
14
+ y
13
+ ··· + 7y + 1)
(1 + 7y + 28y
2
+ 64y
3
+ 174y
4
+ 270y
5
+ 274y
6
+ 212y
7
+ 197y
8
+ 55y
9
+ 66y
10
+ 8y
11
+ 13y
12
+ y
13
+ y
14
)
4
(y
30
+ 2y
29
+ ··· + 272y + 256)
c
3
(y
14
15y
13
+ ··· 9y + 1)(y
30
21y
29
+ ··· y + 1)
(y
56
45y
55
+ ··· 2168856y + 67081)
c
4
(y
14
15y
13
+ ··· 9y + 1)(y
30
21y
29
+ ··· y + 1)
(y
56
45y
55
+ ··· 2168856y + 67081)
c
6
(y
14
+ y
13
+ ··· 2y + 1)(y
30
9y
29
+ ··· 22y + 1)
(y
56
+ 11y
55
+ ··· 92y + 1)
c
7
(y
14
15y
13
+ ··· 9y + 1)(y
30
21y
29
+ ··· y + 1)
(y
56
45y
55
+ ··· 2168856y + 67081)
c
8
(y
14
+ y
13
+ ··· 2y + 1)(y
30
9y
29
+ ··· 22y + 1)
(y
56
+ 11y
55
+ ··· 92y + 1)
c
9
(y
14
15y
13
+ ··· 9y + 1)(y
30
21y
29
+ ··· y + 1)
(y
56
45y
55
+ ··· 2168856y + 67081)
c
10
(y
14
2y
13
+ ··· + y + 1)
(y
30
y
29
+ ··· 335544320y + 268435456)
(y
56
+ 28y
55
+ ··· + 28y + 1)
c
11
(y
14
+ 5y
13
+ ··· + y + 1)(y
30
+ 10y
29
+ ··· 170460y + 2704)
(y
56
+ 20y
55
+ ··· + 67068y + 6561)
17