11a
276
(K11a
276
)
1
Arc Sequences
7 5 1 9 2 10 3 11 6 4 8
Solving Sequence
6,10 2,7
1 5 3 8 9 4 11
c
6
c
1
c
5
c
2
c
7
c
9
c
4
c
11
c
3
, c
8
, c
10
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
23
8u
22
+ ··· + 4u 1, 262u
22
1154u
21
+ ··· + 589b 800,
15552u
22
87384u
21
+ ··· + 13547a 117016i
I
u
2
= hu
103
7u
102
+ ··· 488u 403,
1.36185 × 10
358
u
102
+ 1.07641 × 10
359
u
101
+ ··· + 3.79521 × 10
359
b 1.21431 × 10
361
,
8.24119 × 10
360
u
102
+ 6.04595 × 10
361
u
101
+ ··· + 1.52947 × 10
362
a 1.90371 × 10
363
i
There are 2 irreducible components with 126 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
23
8u
22
+ · · · + 4u 1, 262u
22
1154u
21
+ · · · + 589b
800, 15552u
22
87384u
21
+ · · · + 13547a 117016i
(i) Arc colorings
a
6
=
0
u
a
10
=
1.14800u
22
+ 6.45043u
21
+ ··· 30.9054u + 8.63778
0.444822u
22
+ 1.95925u
21
+ ··· 3.07640u + 1.35823
a
2
=
1
0
a
7
=
3.58758u
22
27.7583u
21
+ ··· + 24.2031u 7.21532
0.942349u
22
8.83502u
21
+ ··· 18.5657u + 3.58758
a
1
=
1.58758u
22
11.7583u
21
+ ··· + 30.2031u 8.21532
0.758544u
22
+ 7.03373u
21
+ ··· + 3.43825u 1.02303
a
5
=
u
u
a
3
=
u
2
+ 1
u
2
a
8
=
2.48321u
22
18.3354u
21
+ ··· + 31.3711u 7.93511
2.40976u
22
20.6156u
21
+ ··· 23.6543u + 4.21680
a
9
=
1.14800u
22
+ 6.45043u
21
+ ··· 30.9054u + 8.63778
0.434709u
22
5.66015u
21
+ ··· 12.8628u + 4.09183
a
4
=
0.349007u
22
+ 1.22027u
21
+ ··· 42.5870u + 9.86056
1.26161u
22
9.96376u
21
+ ··· + 3.19296u 0.700893
a
11
=
2.17303u
22
+ 17.0957u
21
+ ··· + 30.1794u 2.01498
1.53303u
22
12.8237u
21
+ ··· 3.16948u + 0.0372038
a
11
=
2.17303u
22
+ 17.0957u
21
+ ··· + 30.1794u 2.01498
1.53303u
22
12.8237u
21
+ ··· 3.16948u + 0.0372038
(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 = 0.367461 0.580992I
a = 0.751679 + 0.585449I
b = 2.79196 0.10326I
3.39178 6.41701I 11.3847 + 13.7261I
u = 0.367461 + 0.580992I
a = 0.751679 0.585449I
b = 2.79196 + 0.10326I
3.39178 + 6.41701I 11.3847 13.7261I
u = 0.070106 0.425749I
a = 0.70649 + 3.28612I
b = 0.596373 0.532808I
7.23583 5.57214I 8.37775 + 4.83062I
u = 0.070106 + 0.425749I
a = 0.70649 3.28612I
b = 0.596373 + 0.532808I
7.23583 + 5.57214I 8.37775 4.83062I
u = 0.065662 0.782989I
a = 0.715183 1.141300I
b = 1.63140 + 0.96747I
1.08785 2.06017I 3.20695 + 2.61947I
u = 0.065662 + 0.782989I
a = 0.715183 + 1.141300I
b = 1.63140 0.96747I
1.08785 + 2.06017I 3.20695 2.61947I
u = 0.081388 1.285201I
a = 0.135450 0.431668I
b = 0.408263 0.601788I
3.40764 + 1.98502I 5.23404 6.40618I
u = 0.081388 + 1.285201I
a = 0.135450 + 0.431668I
b = 0.408263 + 0.601788I
3.40764 1.98502I 5.23404 + 6.40618I
u = 0.128122 0.766434I
a = 1.19589 0.93821I
b = 0.996612 0.134612I
1.64013 2.16694I 5.84411 2.66864I
u = 0.128122 + 0.766434I
a = 1.19589 + 0.93821I
b = 0.996612 + 0.134612I
1.64013 + 2.16694I 5.84411 + 2.66864I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.14889 1.52244I
a = 0.059518 + 0.368860I
b = 0.636709 0.336940I
1.36627 + 4.91196I 10.94228 4.46028I
u = 0.14889 + 1.52244I
a = 0.059518 0.368860I
b = 0.636709 + 0.336940I
1.36627 4.91196I 10.94228 + 4.46028I
u = 0.180334 1.113193I
a = 1.004996 0.130972I
b = 0.314461 + 0.005335I
3.01480 + 3.49113I 0.56270 8.28702I
u = 0.180334 + 1.113193I
a = 1.004996 + 0.130972I
b = 0.314461 0.005335I
3.01480 3.49113I 0.56270 + 8.28702I
u = 0.54703 1.38797I
a = 0.605644 + 0.626716I
b = 1.56689 0.97704I
1.65661 + 8.03479I 10.73175 6.86683I
u = 0.54703 + 1.38797I
a = 0.605644 0.626716I
b = 1.56689 + 0.97704I
1.65661 8.03479I 10.73175 + 6.86683I
u = 0.727207 0.990773I
a = 0.978718 0.369642I
b = 1.73090 + 0.99799I
2.85361 + 5.57806I 8.34402 8.14975I
u = 0.727207 + 0.990773I
a = 0.978718 + 0.369642I
b = 1.73090 0.99799I
2.85361 5.57806I 8.34402 + 8.14975I
u = 0.778675
a = 1.48034
b = 1.38123
3.56069 10.8568
u = 0.779836 0.625536I
a = 0.723120 1.030708I
b = 1.390896 + 0.219209I
3.85538 + 0.13822I 11.25047 3.93197I
4
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.779836 + 0.625536I
a = 0.723120 + 1.030708I
b = 1.390896 0.219209I
3.85538 0.13822I 11.25047 + 3.93197I
u = 1.52108 0.21817I
a = 0.583416 + 0.256722I
b = 1.85600 0.19430I
6.19249 1.08021I 7.69289 + 6.14791I
u = 1.52108 + 0.21817I
a = 0.583416 0.256722I
b = 1.85600 + 0.19430I
6.19249 + 1.08021I 7.69289 6.14791I
5
II. I
u
2
= hu
103
7u
102
+ · · · 488u 403, 1.36 × 10
358
u
102
+ 1.08 ×
10
359
u
101
+ · · · + 3.80 × 10
359
b 1.21 × 10
361
, 8.24 × 10
360
u
102
+ 6.05 ×
10
361
u
101
+ · · · + 1.53 × 10
362
a 1.90 × 10
363
i
(i) Arc colorings
a
6
=
0
u
a
10
=
0.0538827u
102
0.395297u
101
+ ··· 65.9357u + 12.4469
0.0358834u
102
0.283624u
101
+ ··· 15.8498u + 31.9958
a
2
=
1
0
a
7
=
0.0344385u
102
0.202148u
101
+ ··· 55.0715u 36.7480
0.00122724u
102
+ 0.0144401u
101
+ ··· 0.920512u + 6.01740
a
1
=
0.0281050u
102
0.195211u
101
+ ··· 28.4022u 11.2220
0.0386065u
102
0.278258u
101
+ ··· 33.5525u + 14.6365
a
5
=
u
u
a
3
=
u
2
+ 1
u
2
a
8
=
0.0208439u
102
0.113882u
101
+ ··· 41.9428u 35.0609
0.0137007u
102
0.0829974u
101
+ ··· 19.2248u + 0.393853
a
9
=
0.0538827u
102
0.395297u
101
+ ··· 65.9357u + 12.4469
0.0509241u
102
0.395784u
101
+ ··· 28.7228u + 39.2974
a
4
=
0.00887451u
102
+ 0.0444439u
101
+ ··· + 21.2786u + 27.0800
0.0809653u
102
+ 0.564032u
101
+ ··· + 114.141u + 5.83696
a
11
=
0.0144975u
102
0.119918u
101
+ ··· + 4.62504u + 13.8209
0.0973934u
102
0.689027u
101
+ ··· 114.675u 5.70752
a
11
=
0.0144975u
102
0.119918u
101
+ ··· + 4.62504u + 13.8209
0.0973934u
102
0.689027u
101
+ ··· 114.675u 5.70752
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
6
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.250780 0.379567I
a = 0.755866 + 0.628142I
b = 1.70855 0.07648I
6.51949 + 11.45360I 11.46961 7.53777I
u = 1.250780 + 0.379567I
a = 0.755866 0.628142I
b = 1.70855 + 0.07648I
6.51949 11.45360I 11.46961 + 7.53777I
u = 0.997797 0.337687I
a = 0.914565 0.800527I
b = 1.57597 0.01117I
1.60861 + 6.49346I 8.27656 6.49945I
u = 0.997797 + 0.337687I
a = 0.914565 + 0.800527I
b = 1.57597 + 0.01117I
1.60861 6.49346I 8.27656 + 6.49945I
u = 0.787507 0.165567I
a = 0.308249 0.859774I
b = 1.049053 0.255898I
3.43026 + 6.84438I 9.15397 4.49126I
u = 0.787507 + 0.165567I
a = 0.308249 + 0.859774I
b = 1.049053 + 0.255898I
3.43026 6.84438I 9.15397 + 4.49126I
u = 0.71899 1.29384I
a = 0.824046 + 0.535716I
b = 1.96278 1.05730I
3.5615 18.3556I 9.12186 + 9.75434I
u = 0.71899 + 1.29384I
a = 0.824046 0.535716I
b = 1.96278 + 1.05730I
3.5615 + 18.3556I 9.12186 9.75434I
u = 0.707014 0.733446I
a = 0.497092 + 1.306457I
b = 1.42492 0.03804I
4.11139 + 0.22883I 23.0645 9.9560I
u = 0.707014 + 0.733446I
a = 0.497092 1.306457I
b = 1.42492 + 0.03804I
4.11139 0.22883I 23.0645 + 9.9560I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.699895 0.808558I
a = 0.902871 0.044001I
b = 1.50010 1.00434I
1.79270 5.83133I 4.37495 + 11.72999I
u = 0.699895 + 0.808558I
a = 0.902871 + 0.044001I
b = 1.50010 + 1.00434I
1.79270 + 5.83133I 4.37495 11.72999I
u = 0.650819 0.969315I
a = 1.171893 + 0.523718I
b = 1.86022 1.03562I
3.38380 5.47099I 23.4612 + 7.3952I
u = 0.650819 + 0.969315I
a = 1.171893 0.523718I
b = 1.86022 + 1.03562I
3.38380 + 5.47099I 23.4612 7.3952I
u = 0.643097 1.209475I
a = 0.887240 0.599304I
b = 1.92371 + 1.03987I
1.07559 12.41716I 6.11651 + 9.15139I
u = 0.643097 + 1.209475I
a = 0.887240 + 0.599304I
b = 1.92371 1.03987I
1.07559 + 12.41716I 6.11651 9.15139I
u = 0.538432 1.183132I
a = 0.725428 + 0.601462I
b = 0.091830 + 0.211760I
0.49197 11.78543I 6.76696 + 7.54929I
u = 0.538432 + 1.183132I
a = 0.725428 0.601462I
b = 0.091830 0.211760I
0.49197 + 11.78543I 6.76696 7.54929I
u = 0.518705 0.861282I
a = 0.975689 0.827182I
b = 1.48774 0.23556I
7.13489 + 2.71411I 12.34571 0.09973I
u = 0.518705 + 0.861282I
a = 0.975689 + 0.827182I
b = 1.48774 + 0.23556I
7.13489 2.71411I 12.34571 + 0.09973I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.489837 0.034034I
a = 0.31502 + 1.39415I
b = 0.754518 + 0.448116I
1.49461 + 1.97845I 4.28245 4.91364I
u = 0.489837 + 0.034034I
a = 0.31502 1.39415I
b = 0.754518 0.448116I
1.49461 1.97845I 4.28245 + 4.91364I
u = 0.479629 0.882514I
a = 0.581261 + 0.895083I
b = 0.348507 + 0.241036I
1.43885 + 1.18607I 9.77826 4.17842I
u = 0.479629 + 0.882514I
a = 0.581261 0.895083I
b = 0.348507 0.241036I
1.43885 1.18607I 9.77826 + 4.17842I
u = 0.475647 1.073992I
a = 0.694062 0.471509I
b = 1.34093 + 1.19565I
4.06422 1.55716I 1.01910 + 3.43250I
u = 0.475647 + 1.073992I
a = 0.694062 + 0.471509I
b = 1.34093 1.19565I
4.06422 + 1.55716I 1.01910 3.43250I
u = 0.449933 1.100628I
a = 0.836810 0.665364I
b = 0.094251 0.353467I
4.14010 5.70398I 3.69437 + 8.44382I
u = 0.449933 + 1.100628I
a = 0.836810 + 0.665364I
b = 0.094251 + 0.353467I
4.14010 + 5.70398I 3.69437 8.44382I
u = 0.407779 1.086476I
a = 0.646023 0.806960I
b = 1.97079 0.36796I
5.82282 8.40734I 11.7057 + 8.1163I
u = 0.407779 + 1.086476I
a = 0.646023 + 0.806960I
b = 1.97079 + 0.36796I
5.82282 + 8.40734I 11.7057 8.1163I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.398821 0.764709I
a = 0.72324 1.72551I
b = 0.656964 + 0.794802I
7.53811 6.57319I 10.7861 + 9.5758I
u = 0.398821 + 0.764709I
a = 0.72324 + 1.72551I
b = 0.656964 0.794802I
7.53811 + 6.57319I 10.7861 9.5758I
u = 0.384228 0.508730I
a = 1.04863 2.00336I
b = 0.764599 + 1.084790I
7.70780 + 4.93574I 13.95059 + 1.93244I
u = 0.384228 + 0.508730I
a = 1.04863 + 2.00336I
b = 0.764599 1.084790I
7.70780 4.93574I 13.95059 1.93244I
u = 0.379160 0.955588I
a = 0.771313 + 0.956550I
b = 1.80058 0.03585I
2.24342 2.29276I 11.17550 + 2.52944I
u = 0.379160 + 0.955588I
a = 0.771313 0.956550I
b = 1.80058 + 0.03585I
2.24342 + 2.29276I 11.17550 2.52944I
u = 0.349292 0.676278I
a = 0.75826 + 1.77722I
b = 0.967113 0.777631I
3.16691 0.95888I 8.49547 + 8.23721I
u = 0.349292 + 0.676278I
a = 0.75826 1.77722I
b = 0.967113 + 0.777631I
3.16691 + 0.95888I 8.49547 8.23721I
u = 0.297376 1.269471I
a = 0.474754 + 0.565810I
b = 1.10444 1.37275I
0.99501 + 2.77150I 6.59714 0.88540I
u = 0.297376 + 1.269471I
a = 0.474754 0.565810I
b = 1.10444 + 1.37275I
0.99501 2.77150I 6.59714 + 0.88540I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.150410 1.384598I
a = 0.278668 0.527954I
b = 0.117978 + 0.227357I
4.53262 + 2.55951I 0.78378 5.41774I
u = 0.150410 + 1.384598I
a = 0.278668 + 0.527954I
b = 0.117978 0.227357I
4.53262 2.55951I 0.78378 + 5.41774I
u = 0.094558 0.706895I
a = 1.42914 + 0.68508I
b = 0.862791 + 0.534569I
1.62245 + 2.60387I 5.4773 13.5890I
u = 0.094558 + 0.706895I
a = 1.42914 0.68508I
b = 0.862791 0.534569I
1.62245 2.60387I 5.4773 + 13.5890I
u = 0.078376 0.926671I
a = 0.695459 + 1.124835I
b = 1.31443 0.89316I
0.17581 2.44610I 9.57025 + 3.71800I
u = 0.078376 + 0.926671I
a = 0.695459 1.124835I
b = 1.31443 + 0.89316I
0.17581 + 2.44610I 9.57025 3.71800I
u = 0.054648 0.534235I
a = 0.012037 1.063758I
b = 2.54705 + 0.30135I
3.29751 5.91017I 8.26846 1.15510I
u = 0.054648 + 0.534235I
a = 0.012037 + 1.063758I
b = 2.54705 0.30135I
3.29751 + 5.91017I 8.26846 + 1.15510I
u = 0.025723 0.350925I
a = 1.41429 + 1.47335I
b = 0.432169 + 0.341830I
1.05237 + 1.81935I 6.00348 3.96676I
u = 0.025723 + 0.350925I
a = 1.41429 1.47335I
b = 0.432169 0.341830I
1.05237 1.81935I 6.00348 + 3.96676I
11
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.00527 1.67344I
a = 0.185455 + 0.459418I
b = 0.213220 0.524535I
1.44846 + 6.07423I 8.51983 8.95436I
u = 0.00527 + 1.67344I
a = 0.185455 0.459418I
b = 0.213220 + 0.524535I
1.44846 6.07423I 8.51983 + 8.95436I
u = 0.119143 0.731314I
a = 0.61134 1.50390I
b = 1.14405 + 0.96437I
0.98951 1.68305I 7.59814 + 2.48855I
u = 0.119143 + 0.731314I
a = 0.61134 + 1.50390I
b = 1.14405 0.96437I
0.98951 + 1.68305I 7.59814 2.48855I
u = 0.161211 0.961951I
a = 1.17937 + 0.92301I
b = 0.317665 0.206547I
2.46400 1.88919I 0.150503 0.229729I
u = 0.161211 + 0.961951I
a = 1.17937 0.92301I
b = 0.317665 + 0.206547I
2.46400 + 1.88919I 0.150503 + 0.229729I
u = 0.188979 1.318011I
a = 0.028368 + 0.478675I
b = 0.115951 + 0.772093I
3.37647 + 1.41965I 6.14080 + 6.15322I
u = 0.188979 + 1.318011I
a = 0.028368 0.478675I
b = 0.115951 0.772093I
3.37647 1.41965I 6.14080 6.15322I
u = 0.194067 1.146581I
a = 0.889400 0.245877I
b = 0.332440 + 0.224990I
2.96478 + 2.48304I 1.05092 1.44411I
u = 0.194067 + 1.146581I
a = 0.889400 + 0.245877I
b = 0.332440 0.224990I
2.96478 2.48304I 1.05092 + 1.44411I
12
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.24856 1.42126I
a = 0.210301 0.389861I
b = 0.493829 0.334798I
2.05671 + 4.61879I 1.72164 0.99130I
u = 0.24856 + 1.42126I
a = 0.210301 + 0.389861I
b = 0.493829 + 0.334798I
2.05671 4.61879I 1.72164 + 0.99130I
u = 0.262376 1.197951I
a = 0.614189 0.178048I
b = 0.281055 + 0.180872I
2.77716 + 2.41448I 4.53664 0.91348I
u = 0.262376 + 1.197951I
a = 0.614189 + 0.178048I
b = 0.281055 0.180872I
2.77716 2.41448I 4.53664 + 0.91348I
u = 0.317257 0.747944I
a = 0.323372 + 0.839884I
b = 2.29081 + 0.10120I
0.633867 0.803768I 7.63171 0.92685I
u = 0.317257 + 0.747944I
a = 0.323372 0.839884I
b = 2.29081 0.10120I
0.633867 + 0.803768I 7.63171 + 0.92685I
u = 0.324295 1.140057I
a = 0.741636 0.086926I
b = 0.129026 0.349856I
0.89894 + 3.65454I 5.16377 4.39277I
u = 0.324295 + 1.140057I
a = 0.741636 + 0.086926I
b = 0.129026 + 0.349856I
0.89894 3.65454I 5.16377 + 4.39277I
u = 0.350407 0.995650I
a = 0.616901 + 0.885886I
b = 1.76400 1.88575I
1.50077 + 3.70830I 5.47746 5.75308I
u = 0.350407 + 0.995650I
a = 0.616901 0.885886I
b = 1.76400 + 1.88575I
1.50077 3.70830I 5.47746 + 5.75308I
13
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.405031 1.260160I
a = 0.544376 0.668915I
b = 2.06265 + 1.37687I
0.28023 + 8.17446I 5.52866 9.62837I
u = 0.405031 + 1.260160I
a = 0.544376 + 0.668915I
b = 2.06265 1.37687I
0.28023 8.17446I 5.52866 + 9.62837I
u = 0.408980
a = 0.669217
b = 0.232625
0.749139 13.7714
u = 0.455095 1.115798I
a = 0.964778 + 0.647231I
b = 1.275598 0.492896I
0.75621 + 5.36777I 3.56870 5.42923I
u = 0.455095 + 1.115798I
a = 0.964778 0.647231I
b = 1.275598 + 0.492896I
0.75621 5.36777I 3.56870 + 5.42923I
u = 0.48648 1.34918I
a = 0.739119 0.717919I
b = 1.23671 + 0.91612I
0.82407 + 8.70596I 4.43184 12.22096I
u = 0.48648 + 1.34918I
a = 0.739119 + 0.717919I
b = 1.23671 0.91612I
0.82407 8.70596I 4.43184 + 12.22096I
u = 0.523580 1.172208I
a = 0.354575 + 0.501569I
b = 0.475845 0.207780I
1.22583 + 3.66754I 9.11449 4.85815I
u = 0.523580 + 1.172208I
a = 0.354575 0.501569I
b = 0.475845 + 0.207780I
1.22583 3.66754I 9.11449 + 4.85815I
u = 0.62831 1.28395I
a = 0.678564 0.577855I
b = 1.73103 + 1.02904I
0.30412 + 7.10088I 6.38062 5.29755I
14
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.62831 + 1.28395I
a = 0.678564 + 0.577855I
b = 1.73103 1.02904I
0.30412 7.10088I 6.38062 + 5.29755I
u = 0.634530 0.287426I
a = 1.26639 + 1.11112I
b = 0.596884 + 0.107203I
1.62676 1.19848I 7.81911 + 1.19904I
u = 0.634530 + 0.287426I
a = 1.26639 1.11112I
b = 0.596884 0.107203I
1.62676 + 1.19848I 7.81911 1.19904I
u = 0.75385 1.36856I
a = 0.645657 + 0.441160I
b = 2.02654 0.76007I
3.25503 + 8.43750I 13.8757 10.0624I
u = 0.75385 + 1.36856I
a = 0.645657 0.441160I
b = 2.02654 + 0.76007I
3.25503 8.43750I 13.8757 + 10.0624I
u = 0.784658 0.322298I
a = 0.056618 0.551784I
b = 0.204767 + 0.337875I
3.77648 + 1.13028I 11.93912 1.05833I
u = 0.784658 + 0.322298I
a = 0.056618 + 0.551784I
b = 0.204767 0.337875I
3.77648 1.13028I 11.93912 + 1.05833I
u = 0.79524 1.29418I
a = 0.679643 + 0.578450I
b = 1.52433 1.23871I
3.84070 + 7.79723I 14.0097 9.2749I
u = 0.79524 + 1.29418I
a = 0.679643 0.578450I
b = 1.52433 + 1.23871I
3.84070 7.79723I 14.0097 + 9.2749I
u = 0.800452 1.088761I
a = 0.366890 0.504611I
b = 1.70051 + 0.11006I
3.90048 + 2.86379I 12.70957 3.37032I
15
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.800452 + 1.088761I
a = 0.366890 + 0.504611I
b = 1.70051 0.11006I
3.90048 2.86379I 12.70957 + 3.37032I
u = 0.871604 0.692295I
a = 0.970864 0.132154I
b = 1.82464 0.00904I
5.15763 + 4.84349I 15.7399 6.4432I
u = 0.871604 + 0.692295I
a = 0.970864 + 0.132154I
b = 1.82464 + 0.00904I
5.15763 4.84349I 15.7399 + 6.4432I
u = 0.925625 0.809755I
a = 0.438943 0.744290I
b = 0.782106 + 0.809054I
4.90999 + 1.62359I 14.9883 4.1098I
u = 0.925625 + 0.809755I
a = 0.438943 + 0.744290I
b = 0.782106 0.809054I
4.90999 1.62359I 14.9883 + 4.1098I
u = 1.022611 0.353862I
a = 1.113420 0.145105I
b = 1.32062 + 0.80299I
5.91342 + 3.60860I 15.0689 5.5323I
u = 1.022611 + 0.353862I
a = 1.113420 + 0.145105I
b = 1.32062 0.80299I
5.91342 3.60860I 15.0689 + 5.5323I
u = 1.189481 0.353354I
a = 0.715932 0.402068I
b = 1.66313 + 0.20869I
3.45329 0.72831I 5.01760 + 9.69482I
u = 1.189481 + 0.353354I
a = 0.715932 + 0.402068I
b = 1.66313 0.20869I
3.45329 + 0.72831I 5.01760 9.69482I
u = 1.42106 0.29926I
a = 0.624621 + 0.344099I
b = 1.80000 0.58637I
6.78852 0.94980I 22.0527 + 2.0035I
16
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.42106 + 0.29926I
a = 0.624621 0.344099I
b = 1.80000 + 0.58637I
6.78852 + 0.94980I 22.0527 2.0035I
u = 1.45480 0.37098I
a = 0.662253 + 0.250565I
b = 1.86312 + 0.08798I
6.86537 0.18608I 17.4391 0.0590I
u = 1.45480 + 0.37098I
a = 0.662253 0.250565I
b = 1.86312 0.08798I
6.86537 + 0.18608I 17.4391 + 0.0590I
17
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
23
+ 2u
21
+ ··· + 15u + 7)(u
103
+ u
102
+ ··· 35693u + 3817)
c
2
(u
23
8u
22
+ ··· + 4u 1)(u
103
+ 7u
102
+ ··· 488u + 403)
c
3
(u
23
+ 3u
22
+ ··· + 4u + 1)(u
103
+ 8u
102
+ ··· 52u 8)
c
4
(u
23
+ 6u
20
+ ··· + 3u 7)(u
103
+ u
102
+ ··· + 257024u 34816)
c
5
(u
23
+ 8u
22
+ ··· + 4u + 1)(u
103
+ 7u
102
+ ··· 488u + 403)
c
6
(u
23
u
22
+ ··· u 1)(u
103
+ 4u
102
+ ··· + 469u + 109)
c
7
(u
23
u
21
+ ··· + 4u 1)(u
103
+ u
102
+ ··· 6340u 2537)
c
8
(u
23
+ 2u
22
+ ··· 6u 1)(u
103
+ 5u
102
+ ··· + 44u + 1)
c
9
(u
23
+ u
22
+ ··· u + 1)(u
103
+ 4u
102
+ ··· + 469u + 109)
c
10
(u
23
+ u
22
+ ··· + u
2
1)(u
103
+ 2u
102
+ ··· + 366u + 343)
c
11
(u
23
2u
22
+ ··· 6u + 1)(u
103
+ 5u
102
+ ··· + 44u + 1)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
23
+ 4y
22
+ ··· 55y 49)
(y
103
+ 17y
102
+ ··· 648571579y 14569489)
c
2
, c
5
(y
23
+ 12y
22
+ ··· 20y 1)
(y
103
+ 53y
102
+ ··· 6001908y 162409)
c
3
(y
23
9y
22
+ ··· 6y 1)(y
103
16y
102
+ ··· + 1424y 64)
c
4
(y
23
+ 6y
21
+ ··· + 191y 49)
(y
103
23y
102
+ ··· 61678288895y 1212153856)
c
6
, c
9
(y
23
13y
22
+ ··· + 19y 1)(y
103
56y
102
+ ··· + 439051y 11881)
c
7
(y
23
2y
22
+ ··· + 20y 1)
(y
103
17y
102
+ ··· + 318453760y 6436369)
c
8
, c
11
(y
23
+ 18y
22
+ ··· + 2y 1)(y
103
+ 75y
102
+ ··· + 218y 1)
c
10
(y
23
11y
22
+ ··· + 2y 1)(y
103
22y
102
+ ··· 423762y 117649)
19