11a
264
(K11a
264
)
1
Arc Sequences
8 5 1 2 11 10 4 3 6 7 9
Solving Sequence
1,8 2,4
5 3 9 7 11 10 6
c
1
c
4
c
3
c
8
c
7
c
11
c
10
c
6
c
2
, c
5
, c
9
Representation Ideals
I = I
u
1
\
I
v
1
I
u
1
= hu
68
+ 11u
67
+ ··· 2u + 2, 7.63507 × 10
171
u
67
+ 7.74863 × 10
172
u
66
+ ··· + 2.04355 × 10
172
b + 3.77436 × 10
172
,
1.82343 × 10
172
u
67
+ 1.99057 × 10
173
u
66
+ ··· + 1.02178 × 10
172
a 4.57446 × 10
171
i
I
v
1
= hb + 1, v 1, ai
There are 2 irreducible components with 69 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
68
+11u
67
+· · ·2u+2, 7.64×10
171
u
67
+7.75×10
172
u
66
+· · ·+2.04×10
172
b+
3.77×10
172
, 1.82×10
172
u
67
+1.99×10
173
u
66
+· · ·+1.02×10
172
a4.57×10
171
i
(i) Arc colorings
a
1
=
1
0
a
8
=
1.78457u
67
19.4815u
66
+ ··· + 18.9175u + 0.447697
0.373618u
67
3.79174u
66
+ ··· + 3.89148u 1.84696
a
2
=
0.0356116u
67
+ 0.708514u
66
+ ··· 0.229638u 3.45424
0.740739u
67
7.63945u
66
+ ··· + 6.29362u 2.37755
a
4
=
0
u
a
5
=
0.776350u
67
8.34796u
66
+ ··· + 6.52326u + 1.07669
0.740739u
67
7.63945u
66
+ ··· + 6.29362u 2.37755
a
3
=
u
u
a
9
=
2.05215u
67
22.4909u
66
+ ··· + 21.4008u + 0.786316
0.641195u
67
6.80112u
66
+ ··· + 6.37477u 1.50834
a
7
=
1.78457u
67
19.4815u
66
+ ··· + 18.9175u + 0.447697
0.811014u
67
8.52797u
66
+ ··· + 7.75810u 2.14444
a
11
=
0.587621u
67
6.75774u
66
+ ··· + 12.5831u + 6.62210
0.387152u
67
4.03737u
66
+ ··· + 3.72765u 0.963345
a
10
=
0.859417u
67
+ 9.17922u
66
+ ··· 6.18980u + 2.33935
0.312830u
67
+ 3.29206u
66
+ ··· 2.72517u + 0.784802
a
6
=
1.55131u
67
16.8754u
66
+ ··· + 13.4223u + 1.46941
0.624662u
67
6.51742u
66
+ ··· + 5.57899u 1.69358
a
6
=
1.55131u
67
16.8754u
66
+ ··· + 13.4223u + 1.46941
0.624662u
67
6.51742u
66
+ ··· + 5.57899u 1.69358
(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 = 1.58546 0.38843I
a = 0.154703 + 0.036597I
b = 0.067003 + 0.787844I
1.04447 3.83678I 0.36447 + 2.84381I
u = 1.58546 + 0.38843I
a = 0.154703 0.036597I
b = 0.067003 0.787844I
1.04447 + 3.83678I 0.36447 2.84381I
u = 1.33749 0.53044I
a = 0.286715 0.005605I
b = 0.104125 0.751546I
4.02663 0.82768I 6.36438 + 2.50645I
u = 1.33749 + 0.53044I
a = 0.286715 + 0.005605I
b = 0.104125 + 0.751546I
4.02663 + 0.82768I 6.36438 2.50645I
u = 1.20670 1.01698I
a = 0.161475 + 1.075942I
b = 0.95747 + 1.15857I
3.5302 16.2353I 5.08024 + 9.23538I
u = 1.20670 + 1.01698I
a = 0.161475 1.075942I
b = 0.95747 1.15857I
3.5302 + 16.2353I 5.08024 9.23538I
u = 1.161811 0.794862I
a = 0.161915 1.128557I
b = 0.91191 1.17529I
5.86514 6.36902I 7.23290 + 4.56192I
u = 1.161811 + 0.794862I
a = 0.161915 + 1.128557I
b = 0.91191 + 1.17529I
5.86514 + 6.36902I 7.23290 4.56192I
u = 1.16144 0.97870I
a = 0.407935 + 0.218312I
b = 0.195371 + 0.761931I
1.61585 + 1.78744I 2.93246 3.80199I
u = 1.16144 + 0.97870I
a = 0.407935 0.218312I
b = 0.195371 0.761931I
1.61585 1.78744I 2.93246 + 3.80199I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.14759 0.99753I
a = 0.149369 1.081954I
b = 0.95671 1.17047I
2.14422 12.53144I 0.96253 + 9.09999I
u = 1.14759 + 0.99753I
a = 0.149369 + 1.081954I
b = 0.95671 + 1.17047I
2.14422 + 12.53144I 0.96253 9.09999I
u = 1.08648 0.91920I
a = 0.137598 + 1.101827I
b = 0.94429 + 1.18767I
0.98004 8.32019I 3.03705 + 4.05424I
u = 1.08648 + 0.91920I
a = 0.137598 1.101827I
b = 0.94429 1.18767I
0.98004 + 8.32019I 3.03705 4.05424I
u = 0.85595 1.38131I
a = 0.398419 0.425462I
b = 0.287595 0.775121I
3.16652 + 4.38642I 3.50297 8.69988I
u = 0.85595 + 1.38131I
a = 0.398419 + 0.425462I
b = 0.287595 + 0.775121I
3.16652 4.38642I 3.50297 + 8.69988I
u = 0.843156 0.087663I
a = 0.17379 1.42461I
b = 0.540664 1.189196I
7.51905 4.91195I 10.39266 + 6.15614I
u = 0.843156 + 0.087663I
a = 0.17379 + 1.42461I
b = 0.540664 + 1.189196I
7.51905 + 4.91195I 10.39266 6.15614I
u = 0.83027 1.55508I
a = 0.349712 + 0.454278I
b = 0.308090 + 0.797666I
2.19159 + 7.63799I 1.67320 8.44065I
u = 0.83027 + 1.55508I
a = 0.349712 0.454278I
b = 0.308090 0.797666I
2.19159 7.63799I 1.67320 + 8.44065I
4
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.827317 0.939704I
a = 0.070145 + 1.097650I
b = 0.97905 + 1.24389I
2.43714 8.63386I 1.26538 + 7.78902I
u = 0.827317 + 0.939704I
a = 0.070145 1.097650I
b = 0.97905 1.24389I
2.43714 + 8.63386I 1.26538 7.78902I
u = 0.681115 0.853960I
a = 0.022689 1.117110I
b = 0.99097 1.29764I
5.87942 4.77825I 3.42142 + 5.10036I
u = 0.681115 + 0.853960I
a = 0.022689 + 1.117110I
b = 0.99097 + 1.29764I
5.87942 + 4.77825I 3.42142 5.10036I
u = 0.662765 0.274951I
a = 0.35831 1.67065I
b = 0.394353 0.840764I
6.78935 5.03593I 9.17271 + 1.54631I
u = 0.662765 + 0.274951I
a = 0.35831 + 1.67065I
b = 0.394353 + 0.840764I
6.78935 + 5.03593I 9.17271 1.54631I
u = 0.645948 0.073451I
a = 0.05816 + 1.49848I
b = 0.316522 + 1.372648I
1.07152 2.12045I 9.29687 + 6.29711I
u = 0.645948 + 0.073451I
a = 0.05816 1.49848I
b = 0.316522 1.372648I
1.07152 + 2.12045I 9.29687 6.29711I
u = 0.643175 0.975099I
a = 0.661647 + 0.435420I
b = 0.270954 + 0.680189I
1.99649 + 1.29641I 0.17607 2.27315I
u = 0.643175 + 0.975099I
a = 0.661647 0.435420I
b = 0.270954 0.680189I
1.99649 1.29641I 0.17607 + 2.27315I
5
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.534588 0.738631I
a = 0.039722 + 1.146302I
b = 1.01178 + 1.37890I
1.95788 0.88165I 0.08011 + 3.60490I
u = 0.534588 + 0.738631I
a = 0.039722 1.146302I
b = 1.01178 1.37890I
1.95788 + 0.88165I 0.08011 3.60490I
u = 0.527944 0.170809I
a = 0.25717 + 1.81124I
b = 0.236663 + 0.801697I
0.94580 1.88496I 5.53016 + 2.61970I
u = 0.527944 + 0.170809I
a = 0.25717 1.81124I
b = 0.236663 0.801697I
0.94580 + 1.88496I 5.53016 2.61970I
u = 0.22614 1.42460I
a = 0.359198 0.666127I
b = 0.402837 0.730460I
3.27007 0.60874I 3.94872 2.74043I
u = 0.22614 + 1.42460I
a = 0.359198 + 0.666127I
b = 0.402837 + 0.730460I
3.27007 + 0.60874I 3.94872 + 2.74043I
u = 0.069078 0.513569I
a = 0.56158 1.84610I
b = 0.436282 0.464589I
2.03114 0.55200I 4.18654 0.49297I
u = 0.069078 + 0.513569I
a = 0.56158 + 1.84610I
b = 0.436282 + 0.464589I
2.03114 + 0.55200I 4.18654 + 0.49297I
u = 0.083060 0.493299I
a = 0.08403 + 4.22765I
b = 0.401935 + 0.327569I
1.04787 + 1.03844I 5.29717 10.86697I
u = 0.083060 + 0.493299I
a = 0.08403 4.22765I
b = 0.401935 0.327569I
1.04787 1.03844I 5.29717 + 10.86697I
6
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.183722 0.613507I
a = 1.28045 3.25521I
b = 0.489252 0.324333I
4.40750 + 3.63166I 5.32777 10.12292I
u = 0.183722 + 0.613507I
a = 1.28045 + 3.25521I
b = 0.489252 + 0.324333I
4.40750 3.63166I 5.32777 + 10.12292I
u = 0.290032 0.894429I
a = 0.077619 + 0.996489I
b = 0.535819 + 0.582513I
1.42554 + 1.52244I 2.08213 4.25089I
u = 0.290032 + 0.894429I
a = 0.077619 0.996489I
b = 0.535819 0.582513I
1.42554 1.52244I 2.08213 + 4.25089I
u = 0.313600 0.343885I
a = 3.91021 4.84969I
b = 0.445210 0.182632I
1.45737 1.91964I 6.3037 14.5674I
u = 0.313600 + 0.343885I
a = 3.91021 + 4.84969I
b = 0.445210 + 0.182632I
1.45737 + 1.91964I 6.3037 + 14.5674I
u = 0.351186
a = 9.70210
b = 0.413217
0.480843 41.6976
u = 0.398678 0.428750I
a = 3.41446 + 3.52328I
b = 0.500127 + 0.194780I
3.98668 4.93837I 11.5004 8.6584I
u = 0.398678 + 0.428750I
a = 3.41446 3.52328I
b = 0.500127 0.194780I
3.98668 + 4.93837I 11.5004 + 8.6584I
u = 0.519575
a = 0.501262
b = 0.859000
1.06237 10.5392
7
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.594295 0.156526I
a = 0.252667 + 0.331406I
b = 1.53847 + 0.44127I
0.858945 + 0.278785I 10.90600 4.39760I
u = 0.594295 + 0.156526I
a = 0.252667 0.331406I
b = 1.53847 0.44127I
0.858945 0.278785I 10.90600 + 4.39760I
u = 0.657627 0.390727I
a = 0.227905 0.554722I
b = 1.44758 0.75690I
0.75568 + 4.48414I 3.17555 9.83264I
u = 0.657627 + 0.390727I
a = 0.227905 + 0.554722I
b = 1.44758 + 0.75690I
0.75568 4.48414I 3.17555 + 9.83264I
u = 0.712633 1.119975I
a = 0.041919 0.761283I
b = 0.630754 0.687473I
2.07579 + 4.13960I 4.21844 7.37716I
u = 0.712633 + 1.119975I
a = 0.041919 + 0.761283I
b = 0.630754 + 0.687473I
2.07579 4.13960I 4.21844 + 7.37716I
u = 0.754976 0.484995I
a = 0.174505 + 0.599555I
b = 1.35626 + 0.81310I
4.76047 + 8.29572I 6.39044 8.85186I
u = 0.754976 + 0.484995I
a = 0.174505 0.599555I
b = 1.35626 0.81310I
4.76047 8.29572I 6.39044 + 8.85186I
u = 0.975481 0.054322I
a = 0.005109 0.520940I
b = 1.111178 0.610030I
7.53116 0.97636I 11.30478 0.77103I
u = 0.975481 + 0.054322I
a = 0.005109 + 0.520940I
b = 1.111178 + 0.610030I
7.53116 + 0.97636I 11.30478 + 0.77103I
8
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.17083 0.85699I
a = 0.016545 0.676934I
b = 0.761988 0.717699I
2.56416 + 2.72527I 6.71131 2.05471I
u = 1.17083 + 0.85699I
a = 0.016545 + 0.676934I
b = 0.761988 + 0.717699I
2.56416 2.72527I 6.71131 + 2.05471I
u = 1.25475 1.03944I
a = 0.006660 + 0.672346I
b = 0.738467 + 0.757641I
1.71156 + 6.50364I 3.88138 8.46347I
u = 1.25475 + 1.03944I
a = 0.006660 0.672346I
b = 0.738467 0.757641I
1.71156 6.50364I 3.88138 + 8.46347I
u = 1.34645 0.72555I
a = 0.018116 + 0.652493I
b = 0.810549 + 0.741235I
8.77213 + 0.51707I 10.23177 1.60690I
u = 1.34645 + 0.72555I
a = 0.018116 0.652493I
b = 0.810549 0.741235I
8.77213 0.51707I 10.23177 + 1.60690I
u = 1.36291 1.07756I
a = 0.010648 0.662272I
b = 0.744866 0.780157I
7.36283 + 9.90141I 7.86000 8.10840I
u = 1.36291 + 1.07756I
a = 0.010648 + 0.662272I
b = 0.744866 + 0.780157I
7.36283 9.90141I 7.86000 + 8.10840I
9
II. I
v
1
= hb + 1, v 1, ai
(i) Arc colorings
a
1
=
1
0
a
8
=
0
1
a
2
=
1
1
a
4
=
1
0
a
5
=
0
1
a
3
=
1
0
a
9
=
1
1
a
7
=
1
1
a
11
=
0
1
a
10
=
1
0
a
6
=
0
1
a
6
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
10
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
1
1(vol +
1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
0 0
11
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u + 1)(u
68
+ 4u
67
+ ··· u 1)
c
2
(u + 1)(u
68
+ 2u
67
+ ··· 7u 1)
c
3
(u)(u
68
+ 11u
67
+ ··· 2u + 2)
c
4
(u 1)(u
68
+ 2u
67
+ ··· 7u 1)
c
5
(u)(u
68
+ 3u
67
+ ··· + 533u
2
32)
c
6
(u 1)(u
68
+ 2u
67
+ ··· u + 1)
c
7
(u 1)(u
68
+ 4u
67
+ ··· 30u 4)
c
8
(u 1)(u
68
+ 2u
67
+ ··· 19u 1)
c
9
, c
10
(u + 1)(u
68
+ 2u
67
+ ··· u + 1)
c
11
(u + 1)(u
68
+ 14u
67
+ ··· + 18491u + 1583)
12
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y 1)(y
68
+ 10y
67
+ ··· + y + 1)
c
2
, c
4
(y 1)(y
68
42y
67
+ ··· 51y + 1)
c
3
(y)(y
68
9y
67
+ ··· 56y + 4)
c
5
(y)(y
68
9y
67
+ ··· 34112y + 1024)
c
6
, c
9
, c
10
(y 1)(y
68
62y
67
+ ··· + y + 1)
c
7
(y 1)(y
68
66y
67
+ ··· 1036y + 16)
c
8
(y 1)(y
68
62y
67
+ ··· 127y + 1)
c
11
(y 1)(y
68
+ 30y
67
+ ··· + 2.73937 × 10
7
y + 2505889)
13