11a
302
(K11a
302
)
1
Arc Sequences
10 6 1 8 2 9 4 11 3 5 7
Solving Sequence
3,6 2,10
1 4 5 11 9 7 8
c
2
c
1
c
3
c
5
c
10
c
9
c
6
c
8
c
4
, c
7
, c
11
Representation Ideals
I =
4
\
i=1
I
u
i
I
u
1
= hu
3
u 1, b + u, u
2
+ ai
I
u
2
= hu
21
7u
19
+ ··· + 5u 1, 86810u
20
51179u
19
+ ··· + 203617b + 498356,
548161u
20
+ 27309u
19
+ ··· + 203617a + 1419959i
I
u
3
= hu
22
6u
20
+ ··· + u + 1, 330474083u
21
170598791u
20
+ ··· + 332950103b + 35950927,
211438488u
21
+ 97373739u
20
+ ··· + 332950103a + 43876857i
I
u
4
= hu
84
u
83
+ ··· 13u + 1, 8.01634 × 10
204
u
83
1.47295 × 10
204
u
82
+ ··· + 2.85391 × 10
204
a 2.38032 × 10
205
,
1.93742 × 10
205
u
83
+ 1.36676 × 10
204
u
82
+ ··· + 2.85391 × 10
204
b 1.87510 × 10
205
i
There are 4 irreducible components with 130 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
3
u 1, b + u, u
2
+ ai
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
10
=
u
2
u
a
1
=
u
2
u + 1
u
2
u 1
a
4
=
2u
2
u
u 1
a
5
=
u
1
a
11
=
u
2
u
a
9
=
u
2
+ u
u
a
7
=
u
2
2
u
2
+ u + 1
a
8
=
2u
1
a
8
=
2u
1
(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 = 0.662359 0.562280I
a = 0.122561 0.744862I
b = 0.662359 + 0.562280I
1.83893 + 3.77083I 5.54852 8.03996I
u = 0.662359 + 0.562280I
a = 0.122561 + 0.744862I
b = 0.662359 0.562280I
1.83893 3.77083I 5.54852 + 8.03996I
u = 1.32472
a = 1.75488
b = 1.32472
9.48162 16.9030
3
II.
I
u
2
= hu
21
7u
19
+ · · · + 5u 1, 8.68 × 10
4
u
20
5.12 × 10
4
u
19
+ · · · + 2.04 ×
10
5
b +4.98 ×10
5
, 5.48× 10
5
u
20
+2.73× 10
4
u
19
+· · ·+ 2.04×10
5
a +1.42 ×10
6
i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
10
=
2.69212u
20
0.134119u
19
+ ··· + 28.2075u 6.97368
0.426340u
20
+ 0.251349u
19
+ ··· + 7.71376u 2.44752
a
1
=
1.85734u
20
0.844581u
19
+ ··· + 20.6981u 4.31433
0.385469u
20
+ 0.103538u
19
+ ··· + 11.0661u 3.11846
a
4
=
0.979437u
20
0.0931160u
19
+ ··· + 4.09981u 0.575374
0.0237357u
20
+ 0.194404u
19
+ ··· 1.65479u + 0.482258
a
5
=
u
u
3
+ u
a
11
=
3.91939u
20
0.521779u
19
+ ··· + 30.2187u 6.71970
1.01138u
20
+ 0.674192u
19
+ ··· + 6.41358u 3.08915
a
9
=
3.11846u
20
0.385469u
19
+ ··· + 20.4938u 4.52616
0.426340u
20
+ 0.251349u
19
+ ··· + 7.71376u 2.44752
a
7
=
0.482258u
20
+ 0.0237357u
19
+ ··· + 5.29877u 0.756499
0.287854u
20
+ 0.284623u
19
+ ··· 5.89970u + 1.78023
a
8
=
0.575374u
20
+ 0.979437u
19
+ ··· 0.173792u + 0.222938
0.482258u
20
0.0237357u
19
+ ··· 5.29877u + 1.75650
a
8
=
0.575374u
20
+ 0.979437u
19
+ ··· 0.173792u + 0.222938
0.482258u
20
0.0237357u
19
+ ··· 5.29877u + 1.75650
(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 = 1.36146 0.57065I
a = 0.843025 0.608835I
b = 1.304894 0.034538I
10.21620 + 5.64989I 15.0241 3.8611I
u = 1.36146 + 0.57065I
a = 0.843025 + 0.608835I
b = 1.304894 + 0.034538I
10.21620 5.64989I 15.0241 + 3.8611I
u = 1.188641 0.329356I
a = 1.011511 0.120494I
b = 0.284184 + 0.245258I
5.15265 + 4.73162I 8.09798 4.44428I
u = 1.188641 + 0.329356I
a = 1.011511 + 0.120494I
b = 0.284184 0.245258I
5.15265 4.73162I 8.09798 + 4.44428I
u = 1.111706 0.428960I
a = 1.95911 + 0.31173I
b = 1.78476 0.65605I
4.95885 + 9.25397I 8.29327 10.96531I
u = 1.111706 + 0.428960I
a = 1.95911 0.31173I
b = 1.78476 + 0.65605I
4.95885 9.25397I 8.29327 + 10.96531I
u = 0.928185 0.189936I
a = 0.674396 0.216214I
b = 0.735536 + 1.073719I
3.43423 + 3.77228I 11.55133 4.69984I
u = 0.928185 + 0.189936I
a = 0.674396 + 0.216214I
b = 0.735536 1.073719I
3.43423 3.77228I 11.55133 + 4.69984I
u = 0.067511 1.157489I
a = 0.0502069 0.0817577I
b = 0.997381 + 0.629444I
1.79260 6.58426I 8.00865 + 7.58329I
u = 0.067511 + 1.157489I
a = 0.0502069 + 0.0817577I
b = 0.997381 0.629444I
1.79260 + 6.58426I 8.00865 7.58329I
5
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.305278 0.294373I
a = 0.94021 1.42121I
b = 0.223914 0.503703I
0.730644 1.059893I 8.01231 + 6.34216I
u = 0.305278 + 0.294373I
a = 0.94021 + 1.42121I
b = 0.223914 + 0.503703I
0.730644 + 1.059893I 8.01231 6.34216I
u = 0.372563 0.410285I
a = 0.39105 + 1.43567I
b = 0.909633 + 0.829475I
0.48724 + 1.81194I 3.30153 2.05952I
u = 0.372563 + 0.410285I
a = 0.39105 1.43567I
b = 0.909633 0.829475I
0.48724 1.81194I 3.30153 + 2.05952I
u = 0.789234
a = 1.20750
b = 0.556308
1.38786 6.70343
u = 0.827440 0.723293I
a = 0.126743 0.809716I
b = 0.567919 + 0.288839I
2.18487 3.00976I 10.87376 0.69402I
u = 0.827440 + 0.723293I
a = 0.126743 + 0.809716I
b = 0.567919 0.288839I
2.18487 + 3.00976I 10.87376 + 0.69402I
u = 1.205892 0.106741I
a = 1.92936 + 0.40120I
b = 1.207310 0.326297I
8.49324 2.76851I 15.4777 + 0.9885I
u = 1.205892 + 0.106741I
a = 1.92936 0.40120I
b = 1.207310 + 0.326297I
8.49324 + 2.76851I 15.4777 0.9885I
u = 1.41669 0.52365I
a = 1.55271 + 0.10596I
b = 1.38942 1.03688I
11.2036 18.3943I 11.0076 + 9.0976I
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.41669 + 0.52365I
a = 1.55271 0.10596I
b = 1.38942 + 1.03688I
11.2036 + 18.3943I 11.0076 9.0976I
6
III.
I
u
3
= hu
22
6u
20
+ · · · + u + 1, 3.30 × 10
8
u
21
1.71 × 10
8
u
20
+ · · · + 3.33 ×
10
8
b +3.60 ×10
7
, 2.11× 10
8
u
21
+9.74× 10
7
u
20
+· · ·+ 3.33×10
8
a +4.39 ×10
7
i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
10
=
0.635046u
21
0.292457u
20
+ ··· 1.34171u 0.131782
0.992563u
21
+ 0.512385u
20
+ ··· 1.17373u 0.107977
a
1
=
0.889535u
21
+ 0.0966271u
20
+ ··· 0.989738u 0.475909
0.0212194u
21
+ 0.0240420u
20
+ ··· 2.18136u 0.983265
a
4
=
0.386153u
21
0.405453u
20
+ ··· + 1.41651u + 1.50722
0.493967u
21
0.175818u
20
+ ··· + 2.18607u 0.167488
a
5
=
u
u
3
+ u
a
11
=
0.336298u
21
0.780801u
20
+ ··· 2.34934u 0.00706984
0.863842u
21
+ 0.316590u
20
+ ··· 0.649099u + 0.255654
a
9
=
0.357518u
21
0.804843u
20
+ ··· 0.167975u 0.0238052
0.992563u
21
+ 0.512385u
20
+ ··· 1.17373u 0.107977
a
7
=
0.0573463u
21
+ 0.336094u
20
+ ··· 3.47754u 0.657519
0.0219546u
21
+ 0.762143u
20
+ ··· + 1.34055u 0.187482
a
8
=
0.652627u
21
0.172652u
20
+ ··· 2.19868u 1.11453
0.670297u
21
+ 0.330174u
20
+ ··· 0.834144u 0.0125608
a
8
=
0.652627u
21
0.172652u
20
+ ··· 2.19868u 1.11453
0.670297u
21
+ 0.330174u
20
+ ··· 0.834144u 0.0125608
(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 = 1.36566 0.38329I
a = 1.60654 0.00056I
b = 1.19451 0.76861I
8.58189 + 6.24482I 12.19966 3.97801I
u = 1.36566 + 0.38329I
a = 1.60654 + 0.00056I
b = 1.19451 + 0.76861I
8.58189 6.24482I 12.19966 + 3.97801I
u = 1.220703 0.018399I
a = 1.075786 + 0.004794I
b = 1.047590 + 0.787761I
4.05165 + 2.03043I 8.21995 2.84126I
u = 1.220703 + 0.018399I
a = 1.075786 0.004794I
b = 1.047590 0.787761I
4.05165 2.03043I 8.21995 + 2.84126I
u = 0.996853 0.278091I
a = 1.329729 0.474336I
b = 1.116111 + 0.772027I
2.14439 + 3.53044I 4.95647 3.30554I
u = 0.996853 + 0.278091I
a = 1.329729 + 0.474336I
b = 1.116111 0.772027I
2.14439 3.53044I 4.95647 + 3.30554I
u = 0.456280 0.389882I
a = 1.22510 + 1.37492I
b = 0.063660 + 0.989377I
0.122720 1.50261
u = 0.456280 + 0.389882I
a = 1.22510 1.37492I
b = 0.063660 0.989377I
0.122720 1.50261
u = 0.40576 1.50605I
a = 0.181803 + 0.126321I
b = 0.277976 + 0.054179I
0.50092 + 2.11174I 5.15528 + 11.05035I
u = 0.40576 + 1.50605I
a = 0.181803 0.126321I
b = 0.277976 0.054179I
0.50092 2.11174I 5.15528 11.05035I
8
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.041486 0.760088I
a = 0.332109 0.176049I
b = 0.856724 0.482949I
4.05165 2.03043I 8.21995 + 2.84126I
u = 0.041486 + 0.760088I
a = 0.332109 + 0.176049I
b = 0.856724 + 0.482949I
4.05165 + 2.03043I 8.21995 2.84126I
u = 0.024657 0.437672I
a = 1.02449 + 1.22474I
b = 0.770375 + 0.789792I
2.14439 + 3.53044I 4.95647 3.30554I
u = 0.024657 + 0.437672I
a = 1.02449 1.22474I
b = 0.770375 0.789792I
2.14439 3.53044I 4.95647 + 3.30554I
u = 0.831103 0.513463I
a = 1.27286 1.19665I
b = 0.024234 + 1.029537I
0.50092 2.11174I 5.15528 11.05035I
u = 0.831103 + 0.513463I
a = 1.27286 + 1.19665I
b = 0.024234 1.029537I
0.50092 + 2.11174I 5.15528 + 11.05035I
u = 0.934195 0.222884I
a = 1.98665 + 1.58078I
b = 0.879814 + 0.359757I
7.04578 7.81545I 13.0279 + 5.9552I
u = 0.934195 + 0.222884I
a = 1.98665 1.58078I
b = 0.879814 0.359757I
7.04578 + 7.81545I 13.0279 5.9552I
u = 1.274882 0.054997I
a = 0.257710 0.116488I
b = 0.216019 + 0.842080I
8.58189 + 6.24482I 12.19966 3.97801I
u = 1.274882 + 0.054997I
a = 0.257710 + 0.116488I
b = 0.216019 0.842080I
8.58189 6.24482I 12.19966 + 3.97801I
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.42191 0.45186I
a = 1.333419 + 0.069874I
b = 1.29904 + 0.80185I
7.04578 7.81545I 13.0279 + 5.9552I
u = 1.42191 + 0.45186I
a = 1.333419 0.069874I
b = 1.29904 0.80185I
7.04578 + 7.81545I 13.0279 5.9552I
9
IV. I
u
4
=
hu
84
u
83
+· · ·13u+1, 8.02×10
204
u
83
1.47×10
204
u
82
+· · ·+2.85×10
204
a
2.38×10
205
, 1.94×10
205
u
83
+1.37×10
204
u
82
+· · ·+2.85×10
204
b1.88×10
205
i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
10
=
2.80890u
83
+ 0.516116u
82
+ ··· 106.773u + 8.34055
6.78864u
83
0.478907u
82
+ ··· 76.5519u + 6.57029
a
1
=
3.38419u
83
0.362972u
82
+ ··· + 77.5673u + 7.17563
2.53005u
83
0.224618u
82
+ ··· 43.3946u + 3.81230
a
4
=
2.24631u
83
+ 0.604610u
82
+ ··· 192.633u + 22.6033
2.43802u
83
+ 0.303260u
82
+ ··· + 7.34022u 1.81171
a
5
=
u
u
3
+ u
a
11
=
4.55591u
83
+ 1.15513u
82
+ ··· 27.0524u + 1.66528
5.34136u
83
0.404432u
82
+ ··· 59.5879u + 5.24176
a
9
=
3.97974u
83
+ 0.995023u
82
+ ··· 30.2214u + 1.77026
6.78864u
83
0.478907u
82
+ ··· 76.5519u + 6.57029
a
7
=
5.43747u
83
+ 0.177775u
82
+ ··· + 43.6461u + 4.25595
1.66531u
83
0.0104175u
82
+ ··· 30.8069u + 1.97472
a
8
=
2.47215u
83
0.763880u
82
+ ··· + 175.607u 18.2174
2.61767u
83
0.377913u
82
+ ··· 16.3564u + 2.21693
a
8
=
2.47215u
83
0.763880u
82
+ ··· + 175.607u 18.2174
2.61767u
83
0.377913u
82
+ ··· 16.3564u + 2.21693
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
10
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.55256 0.46316I
a = 0.960208 0.267593I
b = 0.878289 0.947608I
6.34003 + 8.91423I 8.8427 12.4313I
u = 1.55256 + 0.46316I
a = 0.960208 + 0.267593I
b = 0.878289 + 0.947608I
6.34003 8.91423I 8.8427 + 12.4313I
u = 1.52347 0.60928I
a = 0.567285 0.456782I
b = 0.938984 + 0.052647I
10.74165 5.71330I 15.2364 + 3.4446I
u = 1.52347 + 0.60928I
a = 0.567285 + 0.456782I
b = 0.938984 0.052647I
10.75840 + 5.70483I 15.2364 3.4446I
u = 1.39980 0.47856I
a = 1.021700 + 0.576699I
b = 0.927889 0.295498I
9.93256 + 3.56952I 15.9668 2.5214I
u = 1.39980 + 0.47856I
a = 1.021700 0.576699I
b = 0.927889 + 0.295498I
9.93256 3.56952I 15.9668 + 2.5214I
u = 1.39804 0.51884I
a = 1.50066 0.14841I
b = 1.36732 + 1.06245I
6.42748 + 12.43877I 9.13234 8.26213I
u = 1.39804 + 0.51884I
a = 1.50066 + 0.14841I
b = 1.36732 1.06245I
6.42748 12.43877I 9.13234 + 8.26213I
u = 1.38593 0.43780I
a = 1.47248 0.00386I
b = 1.32846 0.78944I
5.90536 + 7.10956I 7.76610 3.18386I
u = 1.38593 + 0.43780I
a = 1.47248 + 0.00386I
b = 1.32846 + 0.78944I
5.90536 7.10956I 7.76610 + 3.18386I
11
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.331965 0.037459I
a = 1.18314 0.83290I
b = 1.35866 1.43338I
9.93256 3.56952I 15.9668 + 2.5214I
u = 1.331965 + 0.037459I
a = 1.18314 + 0.83290I
b = 1.35866 + 1.43338I
9.93256 + 3.56952I 15.9668 2.5214I
u = 1.248014 0.079685I
a = 1.85795 0.34215I
b = 1.41535 1.16871I
9.16439 + 2.30003I 15.8707 2.5208I
u = 1.248014 + 0.079685I
a = 1.85795 + 0.34215I
b = 1.41535 + 1.16871I
9.16439 2.30003I 15.8707 + 2.5208I
u = 1.209413 0.050801I
a = 1.57865 0.62605I
b = 0.856376 + 0.171706I
5.14325 + 1.81373I 18.0633 2.4655I
u = 1.209413 + 0.050801I
a = 1.57865 + 0.62605I
b = 0.856376 0.171706I
5.14325 1.81373I 18.0633 + 2.4655I
u = 1.208860 0.113613I
a = 1.24948 1.29597I
b = 1.42986 2.01391I
9.41934 + 8.23155I 15.5082 8.1042I
u = 1.208860 + 0.113613I
a = 1.24948 + 1.29597I
b = 1.42986 + 2.01391I
9.41934 8.23155I 15.5082 + 8.1042I
u = 1.095188 0.136546I
a = 0.596121 0.839742I
b = 0.528751 + 0.778109I
3.31027 + 4.01412I 10.91907 8.56399I
u = 1.095188 + 0.136546I
a = 0.596121 + 0.839742I
b = 0.528751 0.778109I
3.31027 4.01412I 10.91907 + 8.56399I
12
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.092544 0.366898I
a = 1.60708 0.10147I
b = 0.711297 + 0.697297I
0.53461 + 4.05993I 2.13658 6.95533I
u = 1.092544 + 0.366898I
a = 1.60708 + 0.10147I
b = 0.711297 0.697297I
0.53461 4.05993I 2.13658 + 6.95533I
u = 0.985326 0.021789I
a = 1.93810 1.17823I
b = 0.947964 0.368637I
4.13302 + 3.67085I 10.13650 4.07600I
u = 0.985326 + 0.021789I
a = 1.93810 + 1.17823I
b = 0.947964 + 0.368637I
4.13302 3.67085I 10.13650 + 4.07600I
u = 0.787842 0.559097I
a = 1.18409 1.21681I
b = 0.073486 + 1.071998I
0.36053 + 2.27504I 19.2642 16.4838I
u = 0.787842 + 0.559097I
a = 1.18409 + 1.21681I
b = 0.073486 1.071998I
0.36053 2.27504I 19.2642 + 16.4838I
u = 0.529370 0.527660I
a = 0.217817 0.094410I
b = 0.713712 + 0.939195I
3.31027 + 4.01412I 10.91907 8.56399I
u = 0.529370 + 0.527660I
a = 0.217817 + 0.094410I
b = 0.713712 0.939195I
3.31027 4.01412I 10.91907 + 8.56399I
u = 0.478559 0.748201I
a = 0.876962 + 0.549123I
b = 0.017116 + 0.689696I
2.41193 + 0.49575I 6.97126 + 0.76893I
u = 0.478559 + 0.748201I
a = 0.876962 0.549123I
b = 0.017116 0.689696I
2.41193 0.49575I 6.97126 0.76893I
13
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.396919 0.818374I
a = 0.150512 0.842112I
b = 1.076566 0.628616I
2.66616 4.59027I 9.89989 + 8.77883I
u = 0.396919 + 0.818374I
a = 0.150512 + 0.842112I
b = 1.076566 + 0.628616I
2.66616 + 4.59027I 9.89989 8.77883I
u = 0.334826 0.714497I
a = 0.113127 0.180207I
b = 0.313370 + 0.821251I
2.88354 3.04446
u = 0.334826 + 0.714497I
a = 0.113127 + 0.180207I
b = 0.313370 0.821251I
2.88354 3.04446
u = 0.210295 0.240685I
a = 3.56655 + 0.84064I
b = 0.665854 0.321804I
0.89781 2.28879I 4.75450 + 2.28484I
u = 0.210295 + 0.240685I
a = 3.56655 0.84064I
b = 0.665854 + 0.321804I
0.89781 + 2.28879I 4.75450 2.28484I
u = 0.096511 1.182555I
a = 0.0394892 0.0002488I
b = 0.993395 0.687665I
6.42748 + 12.43877I 9.13234 8.26213I
u = 0.096511 + 1.182555I
a = 0.0394892 + 0.0002488I
b = 0.993395 + 0.687665I
6.42748 12.43877I 9.13234 + 8.26213I
u = 0.069362 1.055507I
a = 0.006053 + 0.302515I
b = 1.042160 0.610320I
6.25983 + 0.22821I 12.78452 0.32403I
u = 0.069362 + 1.055507I
a = 0.006053 0.302515I
b = 1.042160 + 0.610320I
6.25983 0.22821I 12.78452 + 0.32403I
14
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.0011085 0.1043922I
a = 11.28362 + 8.01560I
b = 0.866225 0.595290I
5.90536 7.10956I 7.76610 + 3.18386I
u = 0.0011085 + 0.1043922I
a = 11.28362 8.01560I
b = 0.866225 + 0.595290I
5.90536 + 7.10956I 7.76610 3.18386I
u = 0.058275 1.155738I
a = 0.235480 + 0.247651I
b = 0.956335 + 0.271666I
5.14021 + 2.16348I 17.8659 3.3107I
u = 0.058275 + 1.155738I
a = 0.235480 0.247651I
b = 0.956335 0.271666I
5.14021 2.16348I 17.8659 + 3.3107I
u = 0.0781250 0.0575559I
a = 6.07183 5.26345I
b = 1.018547 + 0.454621I
5.14325 + 1.81373I 18.0633 2.4655I
u = 0.0781250 + 0.0575559I
a = 6.07183 + 5.26345I
b = 1.018547 0.454621I
5.14325 1.81373I 18.0633 + 2.4655I
u = 0.152546 0.783755I
a = 0.804335 0.372548I
b = 0.249934 0.532891I
1.30396 0.89340I 6.53370 + 0.64889I
u = 0.152546 + 0.783755I
a = 0.804335 + 0.372548I
b = 0.249934 + 0.532891I
1.30396 + 0.89340I 6.53370 0.64889I
u = 0.254789 0.872661I
a = 0.065466 0.179749I
b = 0.655792 0.532899I
0.89781 2.28879I 4.75450 + 2.28484I
u = 0.254789 + 0.872661I
a = 0.065466 + 0.179749I
b = 0.655792 + 0.532899I
0.89781 + 2.28879I 4.75450 2.28484I
15
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.30112 1.60051I
a = 0.0041748 0.0290256I
b = 0.460657 0.107893I
0.36053 2.27504I 19.2642 + 16.4838I
u = 0.30112 + 1.60051I
a = 0.0041748 + 0.0290256I
b = 0.460657 + 0.107893I
0.36053 + 2.27504I 19.2642 16.4838I
u = 0.358302 0.602891I
a = 0.280820 + 1.307901I
b = 0.512934 0.986421I
4.28784 + 5.30125I 7.89549 5.60852I
u = 0.358302 + 0.602891I
a = 0.280820 1.307901I
b = 0.512934 + 0.986421I
4.28784 5.30125I 7.89549 + 5.60852I
u = 0.415622 0.740224I
a = 0.0020036 0.1082309I
b = 0.069817 0.926327I
0.53461 4.05993I 2.13658 + 6.95533I
u = 0.415622 + 0.740224I
a = 0.0020036 + 0.1082309I
b = 0.069817 + 0.926327I
0.53461 + 4.05993I 2.13658 6.95533I
u = 0.906187 0.158270I
a = 1.40959 1.04548I
b = 0.422407 0.578901I
1.30396 0.89340I 6.53370 + 0.64889I
u = 0.906187 + 0.158270I
a = 1.40959 + 1.04548I
b = 0.422407 + 0.578901I
1.30396 + 0.89340I 6.53370 0.64889I
u = 0.962597 0.318394I
a = 1.377298 0.139751I
b = 0.664367 0.492109I
1.17898 5.35443
u = 0.962597 + 0.318394I
a = 1.377298 + 0.139751I
b = 0.664367 + 0.492109I
1.17898 5.35443
16
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.069758 0.315438I
a = 2.47968 + 0.26967I
b = 0.463529 0.567527I
6.34003 8.91423I 8.8427 + 12.4313I
u = 1.069758 + 0.315438I
a = 2.47968 0.26967I
b = 0.463529 + 0.567527I
6.34003 + 8.91423I 8.8427 12.4313I
u = 1.092249 0.002765I
a = 0.733789 + 0.407597I
b = 0.29106 + 1.51046I
2.41193 0.49575I 6.97126 0.76893I
u = 1.092249 + 0.002765I
a = 0.733789 0.407597I
b = 0.29106 1.51046I
2.41193 + 0.49575I 6.97126 + 0.76893I
u = 1.107921 0.242581I
a = 2.35624 + 0.11814I
b = 2.03515 + 1.07118I
2.66616 4.59027I 9.89989 + 8.77883I
u = 1.107921 + 0.242581I
a = 2.35624 0.11814I
b = 2.03515 1.07118I
2.66616 + 4.59027I 9.89989 8.77883I
u = 1.124538 0.428916I
a = 1.038226 + 0.027685I
b = 1.012965 0.956168I
4.13302 3.67085I 10.13650 + 4.07600I
u = 1.124538 + 0.428916I
a = 1.038226 0.027685I
b = 1.012965 + 0.956168I
4.13302 + 3.67085I 10.13650 4.07600I
u = 1.208235 0.063695I
a = 1.52740 + 1.46381I
b = 0.649430 0.363725I
9.40902 7.37920I 17.2969 + 8.3182I
u = 1.208235 + 0.063695I
a = 1.52740 1.46381I
b = 0.649430 + 0.363725I
9.40902 + 7.37920I 17.2969 8.3182I
17
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.230686 0.043766I
a = 1.50014 + 1.11883I
b = 1.73790 + 1.78298I
5.14021 2.16348I 17.8659 + 3.3107I
u = 1.230686 + 0.043766I
a = 1.50014 1.11883I
b = 1.73790 1.78298I
5.14021 + 2.16348I 17.8659 3.3107I
u = 1.357028 0.020794I
a = 1.26007 0.76022I
b = 0.725277 + 0.025979I
9.16439 + 2.30003I 15.8707 2.5208I
u = 1.357028 + 0.020794I
a = 1.26007 + 0.76022I
b = 0.725277 0.025979I
9.16439 2.30003I 15.8707 + 2.5208I
u = 1.36930 0.49505I
a = 1.51004 + 0.26261I
b = 1.25954 1.06934I
10.75840 5.70483I 15.2364 + 3.4446I
u = 1.36930 + 0.49505I
a = 1.51004 0.26261I
b = 1.25954 + 1.06934I
10.75840 + 5.70483I 15.2364 3.4446I
u = 1.38900 0.54948I
a = 1.44142 0.29334I
b = 1.34989 + 0.51349I
9.41934 8.23155I 15.5082 + 8.1042I
u = 1.38900 + 0.54948I
a = 1.44142 + 0.29334I
b = 1.34989 0.51349I
9.41934 + 8.23155I 15.5082 8.1042I
u = 1.44638 0.30530I
a = 1.57740 + 0.38063I
b = 1.35856 + 1.09530I
9.40902 7.37920I 17.2969 + 8.3182I
u = 1.44638 + 0.30530I
a = 1.57740 0.38063I
b = 1.35856 1.09530I
9.40902 + 7.37920I 17.2969 8.3182I
18
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.46634 0.53685I
a = 0.736389 + 0.411433I
b = 1.112130 0.159293I
6.25983 + 0.22821I 12.78452 0.32403I
u = 1.46634 + 0.53685I
a = 0.736389 0.411433I
b = 1.112130 + 0.159293I
6.25983 0.22821I 12.78452 + 0.32403I
u = 1.48689 0.57208I
a = 0.816525 0.119314I
b = 0.809610 + 0.627801I
4.28784 5.30125I 7.89549 + 5.60852I
u = 1.48689 + 0.57208I
a = 0.816525 + 0.119314I
b = 0.809610 0.627801I
4.28784 + 5.30125I 7.89549 5.60852I
19
V. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
3
2u
2
+ u 1)(u
21
+ 2u
20
+ ··· + u 1)(u
22
9u
21
+ ··· 11u + 1)
(u
84
+ 2u
83
+ ··· 184899u + 14113)
c
2
(u
3
u 1)(u
21
7u
19
+ ··· + 5u + 1)(u
22
6u
20
+ ··· + u + 1)
(u
84
+ u
83
+ ··· + 13u + 1)
c
3
(u
3
+ u
2
+ 2u + 1)(u
21
+ u
20
+ ··· + 8u + 4)(u
22
+ u
21
+ ··· 8u + 4)
(u
84
+ 8u
83
+ ··· + 1444332u + 360028)
c
4
(u
3
u 1)(u
21
7u
19
+ ··· + 5u + 1)(u
22
6u
20
+ ··· + u + 1)
(u
84
+ u
83
+ ··· + 13u + 1)
c
5
(u
3
u + 1)(u
21
7u
19
+ ··· + 5u + 1)(u
22
6u
20
+ ··· u + 1)
(u
84
+ u
83
+ ··· + 13u + 1)
c
6
(u
3
u
2
+ 2u 1)(u
21
+ u
20
+ ··· + 8u + 4)(u
22
u
21
+ ··· + 8u + 4)
(u
84
+ 8u
83
+ ··· + 1444332u + 360028)
c
7
(u
3
u + 1)(u
21
7u
19
+ ··· + 5u + 1)(u
22
6u
20
+ ··· u + 1)
(u
84
+ u
83
+ ··· + 13u + 1)
c
8
(u
3
+ 2u
2
+ u + 1)(u
21
+ 2u
20
+ ··· + u 1)(u
22
+ 9u
21
+ ··· + 11u + 1)
(u
84
+ 2u
83
+ ··· 184899u + 14113)
c
9
(u
3
u 1)(u
21
7u
19
+ ··· 3u 1)(u
22
u
21
+ ··· 5u + 1)
(u
84
9u
82
+ ··· 7203u + 9091)
c
10
u
3
(u
21
+ 7u
20
+ ··· + 256u + 64)(u
22
+ 7u
20
+ ··· + 84u
2
+ 23)
(u
84
6u
83
+ ··· + 1389190u + 748225)
c
11
(u
3
u + 1)(u
21
7u
19
+ ··· 3u 1)(u
22
+ u
21
+ ··· + 5u + 1)
(u
84
9u
82
+ ··· 7203u + 9091)
20
VI. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
3
2y
2
3y 1)(y
21
+ 32y
19
+ ··· + 25y 1)
(y
22
9y
21
+ ··· 17y + 1)
(y
84
42y
83
+ ··· 25475290137y + 199176769)
c
2
, c
5
(y
3
2y
2
+ y 1)(y
21
14y
20
+ ··· + 7y 1)
(y
22
12y
21
+ ··· + 5y + 1)(y
84
59y
83
+ ··· + 111y + 1)
c
3
(y
3
+ 3y
2
+ 2y 1)(y
21
+ 17y
20
+ ··· 192y 16)
(y
22
+ 3y
21
+ ··· + 256y + 16)
(y
84
+ 30y
83
+ ··· + 3877148205504y + 129620160784)
c
4
(y
3
2y
2
+ y 1)(y
21
14y
20
+ ··· + 7y 1)
(y
22
12y
21
+ ··· + 5y + 1)(y
84
59y
83
+ ··· + 111y + 1)
c
6
(y
3
+ 3y
2
+ 2y 1)(y
21
+ 17y
20
+ ··· 192y 16)
(y
22
+ 3y
21
+ ··· + 256y + 16)
(y
84
+ 30y
83
+ ··· + 3877148205504y + 129620160784)
c
7
(y
3
2y
2
+ y 1)(y
21
14y
20
+ ··· + 7y 1)
(y
22
12y
21
+ ··· + 5y + 1)(y
84
59y
83
+ ··· + 111y + 1)
c
8
(y
3
2y
2
3y 1)(y
21
+ 32y
19
+ ··· + 25y 1)
(y
22
9y
21
+ ··· 17y + 1)
(y
84
42y
83
+ ··· 25475290137y + 199176769)
c
9
(y
3
2y
2
+ y 1)(y
21
14y
20
+ ··· + 7y 1)
(y
22
3y
21
+ ··· 21y + 1)
(y
84
18y
83
+ ··· 1277331827y + 82646281)
c
10
y
3
(23 + 84y + 104y
2
+ 24y
3
26y
4
+ 3y
5
+ 68y
6
+ 88y
7
+ 61y
8
+ 26y
9
+ 7y
10
+ y
11
)
2
(y
21
+ 9y
20
+ ··· 32768y 4096)
(y
84
+ 54y
83
+ ··· + 11697182495450y + 559840650625)
c
11
(y
3
2y
2
+ y 1)(y
21
14y
20
+ ··· + 7y 1)
(y
22
3y
21
+ ··· 21y + 1)
(y
84
18y
83
+ ··· 1277331827y + 82646281)
21