11a
266
(K11a
266
)
1
Arc Sequences
10 9 1 11 2 3 4 5 6 8 7
Solving Sequence
4,11 5,7
8 9 1 3 2 6 10
c
4
c
7
c
8
c
11
c
3
c
2
c
6
c
10
c
1
, c
5
, c
9
Representation Ideals
I =
4
\
i=1
I
u
i
I
u
1
= h3b
4
+ 4b
2
+ 3b + 3, 6b
3
+ 9b
2
5b + 11u + 18, 3b
3
+ 12b
2
14b + 33a + 13i
I
u
2
= hu
16
8u
15
+ ··· 3u
2
+ 1, 3013u
15
+ 22471u
14
+ ··· + 1751b + 4844,
4844u
15
+ 35739u
14
+ ··· + 1751a + 8173i
I
u
3
= hu
30
19u
29
+ ··· 288u + 32,
5.18165 × 10
13
u
29
1.39954 × 10
15
u
28
+ ··· + 2.00092 × 10
15
b 3.95097 × 10
16
,
9.87743 × 10
15
u
29
1.88086 × 10
17
u
28
+ ··· + 1.60074 × 10
16
a 3.75598 × 10
17
i
I
u
4
= h3b
94
+ 15b
93
+ ··· 14505b 1083,
8.17190 × 10
549
u + 5.23199 × 10
547
b
93
+ ··· 1.27103 × 10
552
b 9.49459 × 10
550
,
1.92735 × 10
549
b
93
8.86068 × 10
549
b
92
+ ··· + 2.45157 × 10
550
a + 1.32966 × 10
552
i
There are 4 irreducible components with 144 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
= h3b
4
+4b
2
+3b+3, 6b
3
+9b
2
5b+11u+18, 3b
3
+12b
2
14b+33a+13i
(i) Arc colorings
a
4
=
1
0
a
11
=
0.0909091b
3
0.363636b
2
+ 0.424242b 0.393939
b
a
5
=
0.363636b
3
0.545455b
2
+ 0.303030b + 0.909091
b
2
a
7
=
0
0.545455b
3
0.818182b
2
+ 0.454545b 1.63636
a
8
=
0.545455b
3
0.818182b
2
+ 0.454545b 1.63636
0.545455b
3
0.818182b
2
+ 0.454545b 1.63636
a
9
=
1.27273b
3
+ 0.0909091b
2
+ 1.06061b + 0.181818
1.18182b
3
0.272727b
2
+ 1.81818b 0.545455
a
1
=
0.0909091b
3
0.363636b
2
+ 0.424242b 0.393939
1.36364b
3
+ 0.545455b
2
1.63636b 0.909091
a
3
=
0.727273b
3
+ 0.0909091b
2
0.606061b 0.151515
0.818182b
3
+ 1.72727b
2
2.18182b + 1.45455
a
2
=
0.909091b
3
+ 0.636364b
2
+ 1.75758b 0.0606061
0.272727b
3
+ 1.90909b
2
+ 0.272727b 0.181818
a
6
=
0.151515b
3
+ 0.272727b
2
0.707071b 0.121212
1.27273b
3
+ 0.0909091b
2
+ 0.0606061b + 1.18182
a
10
=
b
3
+ b
2
+
4
3
b +
1
3
1.09091b
3
+ 1.36364b
2
+ 1.90909b + 0.727273
a
10
=
b
3
+ b
2
+
4
3
b +
1
3
1.09091b
3
+ 1.36364b
2
+ 1.90909b + 0.727273
(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 = 1.50000 0.86603I
a = 0.583749 0.456809I
b = 0.480016 0.613405I
1.64493 + 6.08965I 2.5000 13.9526I
u = 1.50000 + 0.86603I
a = 0.583749 + 0.456809I
b = 0.480016 + 0.613405I
1.64493 6.08965I 2.5000 + 13.9526I
u = 1.50000 + 0.86603I
a = 0.417083 0.168134I
b = 0.480016 1.190755I
1.64493 6.08965I 2.5000 + 13.9526I
u = 1.50000 0.86603I
a = 0.417083 + 0.168134I
b = 0.480016 + 1.190755I
1.64493 + 6.08965I 2.5000 13.9526I
3
II. I
u
2
= hu
16
8u
15
+ · · · 3u
2
+ 1, 3013u
15
+ 22471u
14
+ · · · + 1751b +
4844, 4844u
15
+ 35739u
14
+ · · · + 1751a + 8173i
(i) Arc colorings
a
4
=
1
0
a
11
=
2.76642u
15
20.4106u
14
+ ··· + 1.10623u 4.66762
1.72073u
15
12.8332u
14
+ ··· 4.66762u 2.76642
a
5
=
1.91034u
15
14.0794u
14
+ ··· 6.20617u 5.80640
1.20331u
15
9.11936u
14
+ ··· 6.80640u 1.91034
a
7
=
0
u
a
8
=
u
u
a
9
=
3.70645u
15
27.2153u
14
+ ··· 8.84694u 2.35979
2.19532u
15
15.6933u
14
+ ··· 2.06682u 4.40263
a
1
=
2.76642u
15
20.4106u
14
+ ··· + 1.10623u 4.66762
0.788121u
15
5.70988u
14
+ ··· 1.90120u 1.04569
a
3
=
0.707025u
15
4.96002u
14
+ ··· + 0.600228u 3.89606
0.937179u
15
7.08110u
14
+ ··· 4.18903u 0.0108509
a
2
=
5.13478u
15
+ 37.7533u
14
+ ··· + 11.4672u + 4.55854
3.67276u
15
+ 26.2770u
14
+ ··· + 5.23015u + 5.72016
a
6
=
1.51114u
15
+ 11.5220u
14
+ ··· + 6.78013u 2.04283
0.0491148u
15
0.0456882u
14
+ ··· 2.54312u + 1.88121
a
10
=
2.17133u
15
15.4152u
14
+ ··· + 2.15191u 3.87950
1.12564u
15
7.83781u
14
+ ··· 3.62193u 1.97830
a
10
=
2.17133u
15
15.4152u
14
+ ··· + 2.15191u 3.87950
1.12564u
15
7.83781u
14
+ ··· 3.62193u 1.97830
(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 = 0.814551 0.560407I
a = 0.383583 0.381679I
b = 0.098551 + 0.525860I
2.37780 + 3.65031I 5.77914 4.75975I
u = 0.814551 + 0.560407I
a = 0.383583 + 0.381679I
b = 0.098551 0.525860I
2.37780 3.65031I 5.77914 + 4.75975I
u = 0.233083 0.187405I
a = 2.22092 3.15779I
b = 0.074127 + 1.152242I
1.67458 + 2.27154I 1.49720 3.30379I
u = 0.233083 + 0.187405I
a = 2.22092 + 3.15779I
b = 0.074127 1.152242I
1.67458 2.27154I 1.49720 + 3.30379I
u = 0.275790 0.723292I
a = 1.02479 + 1.14628I
b = 1.111723 0.425093I
3.41791 10.94268I 2.27266 + 9.01140I
u = 0.275790 + 0.723292I
a = 1.02479 1.14628I
b = 1.111723 + 0.425093I
3.41791 + 10.94268I 2.27266 9.01140I
u = 0.656851
a = 3.16856
b = 2.08127
2.63767 12.2565
u = 0.772109 1.166095I
a = 0.405436 + 0.424462I
b = 0.181922 + 0.800508I
4.17810 + 2.37838I 5.85782 3.30047I
u = 0.772109 + 1.166095I
a = 0.405436 0.424462I
b = 0.181922 0.800508I
4.17810 2.37838I 5.85782 + 3.30047I
u = 0.806733 1.141630I
a = 0.754142 + 0.044877I
b = 0.557159 + 0.897156I
3.99183 4.14407I 8.04295 + 6.13289I
5
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.806733 + 1.141630I
a = 0.754142 0.044877I
b = 0.557159 0.897156I
3.99183 + 4.14407I 8.04295 6.13289I
u = 0.877139
a = 1.93092
b = 1.69369
3.85452 16.3089
u = 1.20245 1.45102I
a = 0.288986 0.037331I
b = 0.293323 0.464213I
0.40659 + 2.51099I 3.33911 + 9.63855I
u = 1.20245 + 1.45102I
a = 0.288986 + 0.037331I
b = 0.293323 + 0.464213I
0.40659 2.51099I 3.33911 9.63855I
u = 1.22356 0.97127I
a = 0.930879 + 0.286780I
b = 0.86044 + 1.25503I
2.63766 10.07534I 0.70439 + 5.81996I
u = 1.22356 + 0.97127I
a = 0.930879 0.286780I
b = 0.86044 1.25503I
2.63766 + 10.07534I 0.70439 5.81996I
6
III. I
u
3
= hu
30
19u
29
+ · · · 288u + 32, 5.18 × 10
13
u
29
1.40 ×
10
15
u
28
+ · · · + 2.00 × 10
15
b 3.95 × 10
16
, 9.88 × 10
15
u
29
1.88 × 10
17
u
28
+
· · · + 1.60 × 10
16
a 3.76 × 10
17
i
(i) Arc colorings
a
4
=
1
0
a
11
=
0.617056u
29
+ 11.7500u
28
+ ··· 184.336u + 23.4641
0.0258964u
29
+ 0.699449u
28
+ ··· 154.248u + 19.7458
a
5
=
0.162762u
29
+ 2.53113u
28
+ ··· 53.0122u + 10.7183
0.561337u
29
+ 9.31571u
28
+ ··· 37.1570u + 5.20837
a
7
=
0
u
a
8
=
u
u
a
9
=
2.83400u
29
50.6803u
28
+ ··· + 606.094u 74.7838
4.18132u
29
75.2895u
28
+ ··· + 956.700u 115.915
a
1
=
0.617056u
29
+ 11.7500u
28
+ ··· 184.336u + 23.4641
1.16558u
29
+ 20.5922u
28
+ ··· 181.452u + 20.5745
a
3
=
0.398575u
29
6.78457u
28
+ ··· 15.8552u + 5.50993
0.227356u
29
+ 4.27889u
28
+ ··· 94.9937u + 12.4731
a
2
=
1.09621u
29
17.4984u
28
+ ··· 39.4401u + 8.52082
0.878801u
29
13.4911u
28
+ ··· 106.990u + 14.6412
a
6
=
1.34732u
29
24.6092u
28
+ ··· + 350.606u 41.1316
0.611146u
29
10.6592u
28
+ ··· + 158.912u 18.7114
a
10
=
0.936834u
29
16.1865u
28
+ ··· + 130.777u 13.8346
1.57979u
29
27.2371u
28
+ ··· + 160.866u 17.5529
a
10
=
0.936834u
29
16.1865u
28
+ ··· + 130.777u 13.8346
1.57979u
29
27.2371u
28
+ ··· + 160.866u 17.5529
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
7
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.70202 1.35483I
a = 0.168744 + 0.101365I
b = 0.018870 0.299780I
0.40807 2.90881I 2.85373 + 9.86808I
u = 0.70202 + 1.35483I
a = 0.168744 0.101365I
b = 0.018870 + 0.299780I
0.40807 + 2.90881I 2.85373 9.86808I
u = 0.546613 0.065532I
a = 0.485420 0.807513I
b = 0.318255 + 0.409587I
0.89506 + 1.64854I 1.59568 3.27710I
u = 0.546613 + 0.065532I
a = 0.485420 + 0.807513I
b = 0.318255 0.409587I
0.89506 1.64854I 1.59568 + 3.27710I
u = 0.066198 0.347931I
a = 3.33738 0.23755I
b = 0.138276 1.176903I
5.36512 5.09529I 5.99835 + 3.87317I
u = 0.066198 + 0.347931I
a = 3.33738 + 0.23755I
b = 0.138276 + 1.176903I
5.36512 + 5.09529I 5.99835 3.87317I
u = 0.118097 0.913974I
a = 0.980785 + 0.224045I
b = 0.088944 + 0.922871I
4.05984 + 4.16834I 7.21533 9.98736I
u = 0.118097 + 0.913974I
a = 0.980785 0.224045I
b = 0.088944 0.922871I
4.05984 4.16834I 7.21533 + 9.98736I
u = 0.225426 0.690735I
a = 0.870847 0.960710I
b = 0.859908 + 0.384955I
1.89594 2.12626I 1.09090 + 3.98101I
u = 0.225426 + 0.690735I
a = 0.870847 + 0.960710I
b = 0.859908 0.384955I
1.89594 + 2.12626I 1.09090 3.98101I
8
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.48241 1.42439I
a = 0.515210 + 0.188045I
b = 0.019306 + 0.824574I
5.55355 + 1.97987I 14.2442 2.1459I
u = 0.48241 + 1.42439I
a = 0.515210 0.188045I
b = 0.019306 0.824574I
5.55355 1.97987I 14.2442 + 2.1459I
u = 0.758038 0.703052I
a = 1.55468 0.22638I
b = 1.01935 1.26462I
5.97727 + 1.40898I 5.70108 + 0.75330I
u = 0.758038 + 0.703052I
a = 1.55468 + 0.22638I
b = 1.01935 + 1.26462I
5.97727 1.40898I 5.70108 0.75330I
u = 0.82135 1.49793I
a = 0.306254 0.359706I
b = 0.287272 0.754189I
5.60137 + 11.70804I 5.19142 9.20899I
u = 0.82135 + 1.49793I
a = 0.306254 + 0.359706I
b = 0.287272 + 0.754189I
5.60137 11.70804I 5.19142 + 9.20899I
u = 0.915628 0.496872I
a = 0.880016 0.076391I
b = 0.767811 0.507201I
1.54778 0.98121I 6.08132 + 1.87254I
u = 0.915628 + 0.496872I
a = 0.880016 + 0.076391I
b = 0.767811 + 0.507201I
1.54778 + 0.98121I 6.08132 1.87254I
u = 1.040761 0.325585I
a = 0.157218 1.220586I
b = 0.233778 1.321527I
5.17774 5.90499I 5.32978 + 5.57457I
u = 1.040761 + 0.325585I
a = 0.157218 + 1.220586I
b = 0.233778 + 1.321527I
5.17774 + 5.90499I 5.32978 5.57457I
9
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.18063 0.86676I
a = 0.882838 0.145464I
b = 0.916228 0.936945I
3.99955 4.35128I 6.59095 + 3.41349I
u = 1.18063 + 0.86676I
a = 0.882838 + 0.145464I
b = 0.916228 + 0.936945I
3.99955 + 4.35128I 6.59095 3.41349I
u = 1.200334 0.708116I
a = 1.124048 + 0.541957I
b = 0.96546 + 1.44649I
1.09814 9.90729I 4.86863 + 11.92532I
u = 1.200334 + 0.708116I
a = 1.124048 0.541957I
b = 0.96546 1.44649I
1.09814 + 9.90729I 4.86863 11.92532I
u = 1.20710 1.01760I
a = 1.007442 0.230094I
b = 0.98194 1.30292I
4.2629 20.2286I 1.00488 + 10.53851I
u = 1.20710 + 1.01760I
a = 1.007442 + 0.230094I
b = 0.98194 + 1.30292I
4.2629 + 20.2286I 1.00488 10.53851I
u = 1.33161 1.00419I
a = 0.822863 + 0.339582I
b = 0.75472 + 1.27850I
3.10815 10.44340I 10.9618 + 15.8226I
u = 1.33161 + 1.00419I
a = 0.822863 0.339582I
b = 0.75472 1.27850I
3.10815 + 10.44340I 10.9618 15.8226I
u = 1.40106 1.04994I
a = 0.466238 + 0.116100I
b = 0.531326 + 0.652185I
2.49609 5.04306I 4.14627 + 10.34955I
u = 1.40106 + 1.04994I
a = 0.466238 0.116100I
b = 0.531326 0.652185I
2.49609 + 5.04306I 4.14627 10.34955I
10
IV. I
u
4
= h3b
94
+ 15b
93
+ · · · 14505b 1083, 8.17 × 10
549
u + 5.23 ×
10
547
b
93
+ · · · 1.27 × 10
552
b 9.49 × 10
550
, 1.93 × 10
549
b
93
8.86 ×
10
549
b
92
+ · · · + 2.45 × 10
550
a + 1.33 × 10
552
i
(i) Arc colorings
a
4
=
1
0
a
11
=
0.0786170b
93
+ 0.361429b
92
+ ··· 671.368b 54.2370
b
a
5
=
0.0316562b
93
+ 0.146350b
92
+ ··· 325.876b 27.3807
b
2
a
7
=
0
0.00640241b
93
0.0354286b
92
+ ··· + 155.537b + 11.6186
a
8
=
0.00640241b
93
0.0354286b
92
+ ··· + 155.537b + 11.6186
0.00640241b
93
0.0354286b
92
+ ··· + 155.537b + 11.6186
a
9
=
0.0405508b
93
+ 0.191268b
92
+ ··· 424.877b 34.0508
0.00359727b
93
0.0220380b
92
+ ··· + 135.635b + 10.4370
a
1
=
0.0786170b
93
+ 0.361429b
92
+ ··· 671.368b 54.2370
0.0146129b
93
+ 0.0673372b
92
+ ··· 100.467b 8.68691
a
3
=
0.0397851b
93
+ 0.177041b
92
+ ··· 190.472b 12.2057
0.00213599b
93
+ 0.00243486b
92
+ ··· + 91.0863b + 6.54978
a
2
=
0.0314439b
93
+ 0.138318b
92
+ ··· 130.339b 6.46482
0.00747393b
93
+ 0.0342388b
92
+ ··· 66.2769b 6.03243
a
6
=
0.0469659b
93
+ 0.227155b
92
+ ··· 607.535b 54.9257
0.00279924b
93
+ 0.0154689b
92
+ ··· 27.9821b 3.17255
a
10
=
0.0849849b
93
+ 0.390552b
92
+ ··· 747.077b 61.8800
0.00636788b
93
+ 0.0291233b
92
+ ··· 74.7084b 7.64300
a
10
=
0.0849849b
93
+ 0.390552b
92
+ ··· 747.077b 61.8800
0.00636788b
93
+ 0.0291233b
92
+ ··· 74.7084b 7.64300
(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 = 0.757040
a = 2.31824
b = 2.25394
3.08221 9.23067
u = 0.053079 + 0.373306I
a = 0.336548 + 1.167527I
b = 2.13877 0.70149I
1.67841 + 1.93955I 15.1921 13.7852I
u = 0.053079 0.373306I
a = 0.336548 1.167527I
b = 2.13877 + 0.70149I
1.67841 1.93955I 15.1921 + 13.7852I
u = 0.482594 0.355179I
a = 1.65589 0.22590I
b = 1.61606 0.59445I
1.98777 3.16700I 4.3128 + 13.8397I
u = 0.482594 + 0.355179I
a = 1.65589 + 0.22590I
b = 1.61606 + 0.59445I
1.98777 + 3.16700I 4.3128 13.8397I
u = 0.818561 0.837650I
a = 1.234982 0.200385I
b = 1.10362 1.20641I
5.08486 + 6.93394I 6.67195 7.26599I
u = 0.818561 + 0.837650I
a = 1.234982 + 0.200385I
b = 1.10362 + 1.20641I
5.08486 6.93394I 6.67195 + 7.26599I
u = 1.070774 0.671723I
a = 1.070373 0.461159I
b = 0.958668 0.712289I
0.08320 + 5.80714I 5.40752 6.37276I
u = 1.070774 + 0.671723I
a = 1.070373 + 0.461159I
b = 0.958668 + 0.712289I
0.08320 5.80714I 5.40752 + 6.37276I
u = 1.13715 0.99385I
a = 1.089810 0.218204I
b = 0.94020 1.19251I
3.74054 + 11.30755I 5.50352 11.29218I
12
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.13715 + 0.99385I
a = 1.089810 + 0.218204I
b = 0.94020 + 1.19251I
3.74054 11.30755I 5.50352 + 11.29218I
u = 0.652087 0.253975I
a = 2.11561 + 1.71319I
b = 0.936652 0.569551I
2.00176 + 11.29875I 3.86102 10.57011I
u = 0.652087 + 0.253975I
a = 2.11561 1.71319I
b = 0.936652 + 0.569551I
2.00176 11.29875I 3.86102 + 10.57011I
u = 0.618555 + 0.355905I
a = 1.39832 + 0.73211I
b = 0.899081 0.336787I
0.26046 4.20130I 2.88530 + 9.27658I
u = 0.618555 0.355905I
a = 1.39832 0.73211I
b = 0.899081 + 0.336787I
0.26046 + 4.20130I 2.88530 9.27658I
u = 0.514809 0.936848I
a = 0.763231 0.299947I
b = 0.89733 1.22784I
5.74704 + 2.00651I 10.31615 2.77027I
u = 0.514809 + 0.936848I
a = 0.763231 + 0.299947I
b = 0.89733 + 1.22784I
5.74704 2.00651I 10.31615 + 2.77027I
u = 0.482594 + 0.355179I
a = 1.58409 + 2.39763I
b = 0.879356 0.479120I
1.98777 + 3.16700I 4.3128 13.8397I
u = 0.482594 0.355179I
a = 1.58409 2.39763I
b = 0.879356 + 0.479120I
1.98777 3.16700I 4.3128 + 13.8397I
u = 0.805900 0.453398I
a = 0.734775 0.125038I
b = 0.866819 0.843977I
1.44210 5.12633I 2.94088 + 9.83860I
13
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.805900 + 0.453398I
a = 0.734775 + 0.125038I
b = 0.866819 + 0.843977I
1.44210 + 5.12633I 2.94088 9.83860I
u = 0.629670 + 0.016055I
a = 1.68452 + 1.55954I
b = 0.798496 0.222976I
3.87155 2.62212I 10.88486 + 3.68775I
u = 0.629670 0.016055I
a = 1.68452 1.55954I
b = 0.798496 + 0.222976I
3.87155 + 2.62212I 10.88486 3.68775I
u = 1.12892 1.06195I
a = 0.884866 + 0.104404I
b = 0.796556 1.025075I
0.77111 + 11.39919I 2.82858 11.01059I
u = 1.12892 + 1.06195I
a = 0.884866 0.104404I
b = 0.796556 + 1.025075I
0.77111 11.39919I 2.82858 + 11.01059I
u = 0.805900 + 0.453398I
a = 0.369468 + 1.255109I
b = 0.648847 0.232377I
1.44210 + 5.12633I 2.94088 9.83860I
u = 0.805900 0.453398I
a = 0.369468 1.255109I
b = 0.648847 + 0.232377I
1.44210 5.12633I 2.94088 + 9.83860I
u = 0.605265 + 1.174812I
a = 0.405523 0.170320I
b = 0.639115 1.105943I
4.45949 + 2.25311I 9.64335 2.44283I
u = 0.605265 1.174812I
a = 0.405523 + 0.170320I
b = 0.639115 + 1.105943I
4.45949 2.25311I 9.64335 + 2.44283I
u = 1.22570 + 1.22664I
a = 0.448643 0.008380I
b = 0.574714 1.055860I
2.23455 + 6.04607I 9.9274 11.4207I
14
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.22570 1.22664I
a = 0.448643 + 0.008380I
b = 0.574714 + 1.055860I
2.23455 6.04607I 9.9274 + 11.4207I
u = 1.35575 1.02244I
a = 0.596350 0.410664I
b = 0.569928 0.715005I
2.60428 + 5.02841I 3.35135 8.52552I
u = 1.35575 + 1.02244I
a = 0.596350 + 0.410664I
b = 0.569928 + 0.715005I
2.60428 5.02841I 3.35135 + 8.52552I
u = 1.22570 + 1.22664I
a = 0.664979 0.195943I
b = 0.539623 0.560596I
2.23455 + 6.04607I 9.9274 11.4207I
u = 1.22570 1.22664I
a = 0.664979 + 0.195943I
b = 0.539623 + 0.560596I
2.23455 6.04607I 9.9274 + 11.4207I
u = 0.621232 0.200124I
a = 0.115956 0.480776I
b = 0.50509 1.43287I
1.33437 1.73522I 1.73147 1.18204I
u = 0.621232 + 0.200124I
a = 0.115956 + 0.480776I
b = 0.50509 + 1.43287I
1.33437 + 1.73522I 1.73147 + 1.18204I
u = 0.053079 + 0.373306I
a = 2.64036 + 5.35383I
b = 0.453709 0.063664I
1.67841 + 1.93955I 15.1921 13.7852I
u = 0.053079 0.373306I
a = 2.64036 5.35383I
b = 0.453709 + 0.063664I
1.67841 1.93955I 15.1921 + 13.7852I
u = 0.84453 + 1.32043I
a = 0.406152 0.347547I
b = 0.365705 0.694890I
4.71436 + 3.28575I 12.0478 10.0322I
15
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.84453 1.32043I
a = 0.406152 + 0.347547I
b = 0.365705 + 0.694890I
4.71436 3.28575I 12.0478 + 10.0322I
u = 1.048211 + 0.669398I
a = 0.250476 0.625091I
b = 0.352779 1.012222I
4.37399 + 1.07626I 9.22616 + 2.29912I
u = 1.048211 0.669398I
a = 0.250476 + 0.625091I
b = 0.352779 + 1.012222I
4.37399 1.07626I 9.22616 2.29912I
u = 1.30130 1.15710I
a = 0.231845 + 0.137983I
b = 0.350949 0.607158I
0.65352 2.88892I 10.73565 + 8.41815I
u = 1.30130 + 1.15710I
a = 0.231845 0.137983I
b = 0.350949 + 0.607158I
0.65352 + 2.88892I 10.73565 8.41815I
u = 1.51699 + 0.20467I
a = 0.127332 0.221844I
b = 0.228638 1.317032I
1.20562 + 5.42950I 5.73944 6.25923I
u = 1.51699 0.20467I
a = 0.127332 + 0.221844I
b = 0.228638 + 1.317032I
1.20562 5.42950I 5.73944 + 6.25923I
u = 0.621232 + 0.200124I
a = 1.40977 1.85235I
b = 0.168251 0.275468I
1.33437 + 1.73522I 1.73147 + 1.18204I
u = 0.621232 0.200124I
a = 1.40977 + 1.85235I
b = 0.168251 + 0.275468I
1.33437 1.73522I 1.73147 1.18204I
u = 1.51699 + 0.20467I
a = 0.263065 0.832697I
b = 0.147756 0.362596I
1.20562 + 5.42950I 5.73944 6.25923I
16
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.51699 0.20467I
a = 0.263065 + 0.832697I
b = 0.147756 + 0.362596I
1.20562 5.42950I 5.73944 + 6.25923I
u = 0.605265 + 1.174812I
a = 0.965406 + 0.046636I
b = 0.045355 0.579502I
4.45949 + 2.25311I 9.64335 2.44283I
u = 0.605265 1.174812I
a = 0.965406 0.046636I
b = 0.045355 + 0.579502I
4.45949 2.25311I 9.64335 + 2.44283I
u = 0.472704 0.956320I
a = 1.55642 + 0.37675I
b = 0.067556 0.751847I
5.61718 10.70298I 5.64531 + 8.75378I
u = 0.472704 + 0.956320I
a = 1.55642 0.37675I
b = 0.067556 + 0.751847I
5.61718 + 10.70298I 5.64531 8.75378I
u = 0.514809 + 0.936848I
a = 1.41090 + 0.18251I
b = 0.111914 0.869447I
5.74704 2.00651I 10.31615 + 2.77027I
u = 0.514809 0.936848I
a = 1.41090 0.18251I
b = 0.111914 + 0.869447I
5.74704 + 2.00651I 10.31615 2.77027I
u = 0.84453 1.32043I
a = 0.247766 0.435426I
b = 0.115904 0.829812I
4.71436 3.28575I 12.0478 + 10.0322I
u = 0.84453 + 1.32043I
a = 0.247766 + 0.435426I
b = 0.115904 + 0.829812I
4.71436 + 3.28575I 12.0478 10.0322I
u = 1.048211 0.669398I
a = 0.198981 0.838595I
b = 0.155883 0.822895I
4.37399 1.07626I 9.22616 2.29912I
17
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.048211 + 0.669398I
a = 0.198981 + 0.838595I
b = 0.155883 + 0.822895I
4.37399 + 1.07626I 9.22616 + 2.29912I
u = 1.35575 + 1.02244I
a = 0.521505 0.134095I
b = 0.388625 1.166489I
2.60428 5.02841I 3.35135 + 8.52552I
u = 1.35575 1.02244I
a = 0.521505 + 0.134095I
b = 0.388625 + 1.166489I
2.60428 + 5.02841I 3.35135 8.52552I
u = 0.539485 1.107736I
a = 0.582391 + 0.876854I
b = 0.401942 0.724037I
0.215372 + 0.545445I 3.71028 0.03483I
u = 0.539485 + 1.107736I
a = 0.582391 0.876854I
b = 0.401942 + 0.724037I
0.215372 0.545445I 3.71028 + 0.03483I
u = 1.30130 + 1.15710I
a = 0.382299 0.126642I
b = 0.461361 0.088710I
0.65352 + 2.88892I 10.73565 8.41815I
u = 1.30130 1.15710I
a = 0.382299 + 0.126642I
b = 0.461361 + 0.088710I
0.65352 2.88892I 10.73565 + 8.41815I
u = 0.618555 + 0.355905I
a = 0.856636 + 1.037367I
b = 0.604374 0.950521I
0.26046 4.20130I 2.88530 + 9.27658I
u = 0.618555 0.355905I
a = 0.856636 1.037367I
b = 0.604374 + 0.950521I
0.26046 + 4.20130I 2.88530 9.27658I
u = 0.506870 + 0.008508I
a = 4.52767 + 1.22416I
b = 0.654491 0.229597I
1.52745 1.61554I 1.60105 0.11717I
18
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.506870 0.008508I
a = 4.52767 1.22416I
b = 0.654491 + 0.229597I
1.52745 + 1.61554I 1.60105 + 0.11717I
u = 1.070774 + 0.671723I
a = 0.941924 0.074317I
b = 0.83636 1.21279I
0.08320 5.80714I 5.40752 + 6.37276I
u = 1.070774 0.671723I
a = 0.941924 + 0.074317I
b = 0.83636 + 1.21279I
0.08320 + 5.80714I 5.40752 6.37276I
u = 0.818561 + 0.837650I
a = 1.395302 0.045980I
b = 0.84306 1.19851I
5.08486 6.93394I 6.67195 + 7.26599I
u = 0.818561 0.837650I
a = 1.395302 + 0.045980I
b = 0.84306 + 1.19851I
5.08486 + 6.93394I 6.67195 7.26599I
u = 0.911487 0.184056I
a = 1.025633 + 0.074613I
b = 0.932887 0.559511I
1.93536 0.83864I 6.21439 + 1.02495I
u = 0.911487 + 0.184056I
a = 1.025633 0.074613I
b = 0.932887 + 0.559511I
1.93536 + 0.83864I 6.21439 1.02495I
u = 0.911487 0.184056I
a = 1.102476 0.391221I
b = 0.948584 0.120765I
1.93536 0.83864I 6.21439 + 1.02495I
u = 0.911487 + 0.184056I
a = 1.102476 + 0.391221I
b = 0.948584 + 0.120765I
1.93536 + 0.83864I 6.21439 1.02495I
u = 1.13715 + 0.99385I
a = 0.988376 0.184864I
b = 1.02241 1.33124I
3.74054 11.30755I 5.50352 + 11.29218I
19
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.13715 0.99385I
a = 0.988376 + 0.184864I
b = 1.02241 + 1.33124I
3.74054 + 11.30755I 5.50352 11.29218I
u = 0.629670 + 0.016055I
a = 1.258271 + 0.386198I
b = 1.03565 1.00904I
3.87155 2.62212I 10.88486 + 3.68775I
u = 0.629670 0.016055I
a = 1.258271 0.386198I
b = 1.03565 + 1.00904I
3.87155 + 2.62212I 10.88486 3.68775I
u = 0.472704 0.956320I
a = 0.659879 0.255533I
b = 1.09602 1.31035I
5.61718 10.70298I 5.64531 + 8.75378I
u = 0.472704 + 0.956320I
a = 0.659879 + 0.255533I
b = 1.09602 + 1.31035I
5.61718 + 10.70298I 5.64531 8.75378I
u = 1.12892 + 1.06195I
a = 0.827502 0.129601I
b = 1.109816 0.821819I
0.77111 11.39919I 2.82858 + 11.01059I
u = 1.12892 1.06195I
a = 0.827502 + 0.129601I
b = 1.109816 + 0.821819I
0.77111 + 11.39919I 2.82858 11.01059I
u = 0.539485 1.107736I
a = 0.671147 + 0.035991I
b = 1.285514 0.172086I
0.215372 + 0.545445I 3.71028 0.03483I
u = 0.539485 + 1.107736I
a = 0.671147 0.035991I
b = 1.285514 + 0.172086I
0.215372 0.545445I 3.71028 + 0.03483I
u = 0.757040
a = 2.97730
b = 1.75500
3.08221 9.23067
20
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.652087 0.253975I
a = 1.54257 + 0.27262I
b = 1.81467 0.57983I
2.00176 + 11.29875I 3.86102 10.57011I
u = 0.652087 + 0.253975I
a = 1.54257 0.27262I
b = 1.81467 + 0.57983I
2.00176 11.29875I 3.86102 + 10.57011I
u = 0.506870 0.008508I
a = 1.283276 + 0.474511I
b = 2.28452 0.65901I
1.52745 + 1.61554I 1.60105 + 0.11717I
u = 0.506870 + 0.008508I
a = 1.283276 0.474511I
b = 2.28452 + 0.65901I
1.52745 1.61554I 1.60105 0.11717I
21
V. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u + 1)
4
(u
16
9u
15
+ ··· 33u + 9)
(u
30
26u
29
+ ··· 12288u + 1024)
(27 + 193u + 911u
2
+ 3087u
3
+ 8926u
4
+ 2.24 × 10
4
u
5
+ 5.12 × 10
4
u
6
+ 1.06 × 10
5
u
7
+ 2.06 × 10
5
u
8
+ 3.72 × 10
5
u
9
+ 6.35 × 10
5
u
10
+ 1.02 × 10
6
u
11
+ 1.57 × 10
6
u
12
+ 2.29 × 10
6
u
13
+ 3.21 × 10
6
u
14
+ 4.31 × 10
6
u
15
+ 5.56 × 10
6
u
16
+ 6.88 × 10
6
u
17
+ 8.19 × 10
6
u
18
+ 9.39 × 10
6
u
19
+ 1.04 × 10
7
u
20
+ 1.11 × 10
7
u
21
+ 1.14 × 10
7
u
22
+ 1.13 × 10
7
u
23
+ 1.09 × 10
7
u
24
+ 1.02 × 10
7
u
25
+ 9.16 × 10
6
u
26
+ 7.99 × 10
6
u
27
+ 6.74 × 10
6
u
28
+ 5.50 × 10
6
u
29
+ 4.34 × 10
6
u
30
+ 3.30 × 10
6
u
31
+ 2.41 × 10
6
u
32
+ 1.70 × 10
6
u
33
+ 1.14 × 10
6
u
34
+ 7.32 × 10
5
u
35
+ 4.45 × 10
5
u
36
+ 2.54 × 10
5
u
37
+ 1.36 × 10
5
u
38
+ 6.80 × 10
4
u
39
+ 3.13 × 10
4
u
40
+ 1.31 × 10
4
u
41
+ 4903u
42
+ 1586u
43
+ 426u
44
+ 89u
45
+ 13u
46
+ u
47
)
2
c
2
(u
2
+ 3u + 3)
2
(u
16
6u
15
+ ··· + u + 1)
(u
30
+ 29u
29
+ ··· + 5632u + 512)
(3 + 30u 127u
2
+ 228u
3
+ 210u
4
1872u
5
+ 2748u
6
+ 3857u
7
1.88 × 10
4
u
8
+ 1.89 × 10
4
u
9
+ 2.32 × 10
4
u
10
7.09 × 10
4
u
11
+ 2.62 × 10
4
u
12
+ 1.07 × 10
5
u
13
1.30 × 10
5
u
14
8.45 × 10
4
u
15
+ 2.68 × 10
5
u
16
1.73 × 10
4
u
17
5.51 × 10
5
u
18
+ 7.93 × 10
5
u
19
3.75 × 10
5
u
20
2.76 × 10
5
u
21
+ 5.99 × 10
5
u
22
5.92 × 10
5
u
23
+ 5.71 × 10
5
u
24
5.62 × 10
5
u
25
+ 3.48 × 10
5
u
26
+ 5.92 × 10
4
u
27
3.78 × 10
5
u
28
+ 4.38 × 10
5
u
29
3.38 × 10
5
u
30
+ 2.26 × 10
5
u
31
1.39 × 10
5
u
32
+ 5.46 × 10
4
u
33
+ 1.62 × 10
4
u
34
4.80 × 10
4
u
35
+ 4.34 × 10
4
u
36
2.63 × 10
4
u
37
+ 1.28 × 10
4
u
38
4843u
39
+ 365u
40
+ 1602u
41
1675u
42
+ 970u
43
368u
44
+ 92u
45
14u
46
+ u
47
)
2
c
3
, c
10
(3u
4
+ 3u
3
+ ··· 5u + 1)(u
16
+ 4u
15
+ ··· + 2u 1)
(u
30
u
28
+ ··· 6u + 1)(3u
94
+ 24u
93
+ ··· + 45u 1)
c
4
(3u
4
+ 4u
2
+ 3u + 3)(u
16
u
14
+ ··· + 3u 1)(u
30
+ 8u
28
+ ··· + 3u + 1)
(3u
94
+ 15u
93
+ ··· 14505u 1083)
c
5
(3u
4
+ 4u
2
+ 3u + 3)(u
16
+ u
15
+ ··· + u
2
1)(u
30
u
29
+ ··· 2u + 1)
(3u
94
+ 3u
93
+ ··· 93u 3)
c
6
(3u
4
3u
3
+ ··· + 2u + 7)(u
16
+ u
15
+ ··· + 2u 1)
(u
30
u
29
+ ··· + 46u + 27)
(3u
94
+ 6u
93
+ ··· + 9495938u 2259497)
c
7
(u
2
3u + 3)
2
(u
16
+ 8u
15
+ ··· 3u
2
+ 1)
(u
30
19u
29
+ ··· 288u + 32)
(3 + 18u + 34u
2
+ 5u
3
114u
4
558u
5
1329u
6
+ 147u
7
+ 6235u
8
+ 6490u
9
1.39 × 10
4
u
10
2.99 × 10
4
u
11
+ 1.06 × 10
4
u
12
+ 8.02 × 10
4
u
13
+ 6.74 × 10
4
u
14
3.46 × 10
4
u
15
7.83 × 10
4
u
16
8636u
17
+ 3.72 × 10
4
u
18
6547u
19
1.57 × 10
4
u
20
+ 5.86 × 10
4
u
21
+ 7.84 × 10
4
u
22
1.50 × 10
4
u
23
8.63 × 10
4
u
24
4.86 × 10
4
u
25
+ 1.47 × 10
4
u
26
+ 2.95 × 10
4
u
27
+ 3.28 × 10
4
u
28
+ 5.74 × 10
4
u
29
+ 6.87 × 10
4
u
30
+ 4.39 × 10
4
u
31
+ 1.14 × 10
4
u
32
2466u
33
4078u
34
5608u
35
6604u
36
4210u
37
925u
38
+ 419u
39
+ 273u
40
+ 68u
41
+ 131u
42
+ 179u
43
+ 120u
44
+ 46u
45
+ 10u
46
+ u
47
)
2
c
8
(3u
4
3u
3
+ ··· + 2u + 7)(u
16
+ u
15
+ ··· + 2u 1)
(u
30
u
29
+ ··· + 46u + 27)
(3u
94
+ 6u
93
+ ··· + 9495938u 2259497)
c
9
(3u
4
+ 4u
2
+ 3u + 3)(u
16
+ u
15
+ ··· + u
2
1)(u
30
u
29
+ ··· 2u + 1)
(3u
94
+ 3u
93
+ ··· 93u 3)
c
11
(3u
4
+ 4u
2
+ 3u + 3)(u
16
u
14
+ ··· + 3u 1)(u
30
+ 8u
28
+ ··· + 3u + 1)
(3u
94
+ 15u
93
+ ··· 14505u 1083)
22
VI. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y 1)
4
(y
16
13y
15
+ ··· 27y + 81)
(y
30
2y
29
+ ··· + 12976128y + 1048576)
(729 1.19 × 10
4
y 1.20 × 10
5
y
2
8.69 × 10
5
y
3
4.95 × 10
6
y
4
2.31 × 10
7
y
5
9.13 × 10
7
y
6
3.09 × 10
8
y
7
9.14 × 10
8
y
8
2.37 × 10
9
y
9
5.47 × 10
9
y
10
1.13 × 10
10
y
11
2.09 × 10
10
y
12
3.48 × 10
10
y
13
5.26 × 10
10
y
14
7.22 × 10
10
y
15
9.04 × 10
10
y
16
1.03 × 10
11
y
17
1.08 × 10
11
y
18
1.04 × 10
11
y
19
9.19 × 10
10
y
20
7.49 × 10
10
y
21
5.65 × 10
10
y
22
3.95 × 10
10
y
23
2.57 × 10
10
y
24
1.56 × 10
10
y
25
8.98 × 10
9
y
26
4.89 × 10
9
y
27
2.55 × 10
9
y
28
1.29 × 10
9
y
29
6.33 × 10
8
y
30
3.13 × 10
8
y
31
1.63 × 10
8
y
32
9.31 × 10
7
y
33
5.72 × 10
7
y
34
3.54 × 10
7
y
35
2.06 × 10
7
y
36
1.07 × 10
7
y
37
4.85 × 10
6
y
38
1.88 × 10
6
y
39
6.10 × 10
5
y
40
1.61 × 10
5
y
41
3.35 × 10
4
y
42
4978y
43
410y
44
+ 17y
45
+ 9y
46
+ y
47
)
2
c
2
(y
2
3y + 9)
2
(y
16
10y
15
+ ··· 15y + 1)
(y
30
11y
29
+ ··· + 11665408y + 262144)
(9 + 138y 1189y
2
+ 9492y
3
8.10 × 10
4
y
4
+ 6.13 × 10
5
y
5
3.69 × 10
6
y
6
+ 1.75 × 10
7
y
7
6.74 × 10
7
y
8
+ 2.16 × 10
8
y
9
5.91 × 10
8
y
10
+ 1.40 × 10
9
y
11
2.91 × 10
9
y
12
+ 5.37 × 10
9
y
13
8.90 × 10
9
y
14
+ 1.34 × 10
10
y
15
1.84 × 10
10
y
16
+ 2.33 × 10
10
y
17
2.73 × 10
10
y
18
+ 2.98 × 10
10
y
19
3.04 × 10
10
y
20
+ 2.92 × 10
10
y
21
2.63 × 10
10
y
22
+ 2.24 × 10
10
y
23
1.80 × 10
10
y
24
+ 1.37 × 10
10
y
25
9.92 × 10
9
y
26
+ 6.79 × 10
9
y
27
4.40 × 10
9
y
28
+ 2.70 × 10
9
y
29
1.57 × 10
9
y
30
+ 8.64 × 10
8
y
31
4.50 × 10
8
y
32
+ 2.20 × 10
8
y
33
1.02 × 10
8
y
34
+ 4.41 × 10
7
y
35
1.79 × 10
7
y
36
+ 6.79 × 10
6
y
37
2.39 × 10
6
y
38
+ 7.80 × 10
5
y
39
2.34 × 10
5
y
40
+ 6.38 × 10
4
y
41
1.57 × 10
4
y
42
+ 3402y
43
640y
44
+ 100y
45
12y
46
+ y
47
)
2
c
3
, c
10
(9y
4
+ 33y
3
+ ··· 11y + 1)(y
16
+ 2y
14
+ ··· 26y + 1)
(y
30
2y
29
+ ··· 10y + 1)(9y
94
156y
93
+ ··· 451y + 1)
c
4
(9y
4
+ 24y
3
+ ··· + 15y + 9)(y
16
2y
15
+ ··· + 13y + 1)
(y
30
+ 16y
29
+ ··· + 33y + 1)
(9y
94
165y
93
+ ··· + 14483427y + 1172889)
c
5
(9y
4
+ 24y
3
+ ··· + 15y + 9)(y
16
3y
15
+ ··· 2y + 1)
(y
30
+ 3y
29
+ ··· + 6y + 1)(9y
94
+ 195y
93
+ ··· 885y + 9)
c
6
(9y
4
21y
3
+ ··· 32y + 49)(y
16
7y
15
+ ··· + 8y
2
+ 1)
(y
30
13y
29
+ ··· 5896y + 729)
(9y
94
318y
93
+ ··· 181297638508792y + 5105326693009)
c
7
(y
2
3y + 9)
2
(y
16
+ 2y
15
+ ··· 6y + 1)
(y
30
+ y
29
+ ··· + 11776y + 1024)
(9 + 120y 292y
2
4337y
3
+ 3.97 × 10
4
y
4
9.74 × 10
4
y
5
6.43 × 10
5
y
6
+ 7.65 × 10
6
y
7
4.25 × 10
7
y
8
+ 1.65 × 10
8
y
9
4.93 × 10
8
y
10
+ 1.19 × 10
9
y
11
2.43 × 10
9
y
12
+ 4.24 × 10
9
y
13
6.54 × 10
9
y
14
+ 9.13 × 10
9
y
15
1.17 × 10
10
y
16
+ 1.39 × 10
10
y
17
1.55 × 10
10
y
18
+ 1.61 × 10
10
y
19
1.58 × 10
10
y
20
+ 1.46 × 10
10
y
21
1.28 × 10
10
y
22
+ 1.07 × 10
10
y
23
8.46 × 10
9
y
24
+ 6.36 × 10
9
y
25
4.54 × 10
9
y
26
+ 3.09 × 10
9
y
27
2.00 × 10
9
y
28
+ 1.23 × 10
9
y
29
7.21 × 10
8
y
30
+ 4.02 × 10
8
y
31
2.11 × 10
8
y
32
+ 1.06 × 10
8
y
33
4.98 × 10
7
y
34
+ 2.22 × 10
7
y
35
9.26 × 10
6
y
36
+ 3.62 × 10
6
y
37
1.32 × 10
6
y
38
+ 4.42 × 10
5
y
39
1.37 × 10
5
y
40
+ 3.86 × 10
4
y
41
9709y
42
+ 2235y
43
416y
44
+ 74y
45
8y
46
+ y
47
)
2
c
8
(9y
4
21y
3
+ ··· 32y + 49)(y
16
7y
15
+ ··· + 8y
2
+ 1)
(y
30
13y
29
+ ··· 5896y + 729)
(9y
94
318y
93
+ ··· 181297638508792y + 5105326693009)
c
9
(9y
4
+ 24y
3
+ ··· + 15y + 9)(y
16
3y
15
+ ··· 2y + 1)
(y
30
+ 3y
29
+ ··· + 6y + 1)(9y
94
+ 195y
93
+ ··· 885y + 9)
c
11
(9y
4
+ 24y
3
+ ··· + 15y + 9)(y
16
2y
15
+ ··· + 13y + 1)
(y
30
+ 16y
29
+ ··· + 33y + 1)
(18y
94
330y
93
+ ··· + 28966854y + 2345778)
23