11a
171
(K11a
171
)
1
Arc Sequences
5 1 7 8 2 9 10 11 3 4 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 =
4
\
i=1
I
u
i
\
I
v
1
I
u
1
= ha
2
a 1, u 1, b + a + 1i
I
u
2
= hu
16
+ 2u
15
2u
14
8u
13
u
12
+ 14u
11
+ 10u
10
11u
9
15u
8
+ u
7
+ 11u
6
+ 6u
5
2u
4
4u
3
+ 2u + 1,
u
15
u
14
4u
13
+ 2u
12
+ 10u
11
2u
10
14u
9
2u
8
+ 12u
7
+ 4u
6
3u
5
4u
4
2u
3
+ 2u
2
+ b + u 1,
2u
15
+ 4u
14
+ ··· + a + 3i
I
u
3
= ha
62
5a
60
+ ··· 41640182a + 1319939,
4.63091 × 10
449
u 6.79296 × 10
443
a
61
+ ··· 2.17373 × 10
452
a + 1.17964 × 10
451
,
1.75511 × 10
452
b 7.56804 × 10
445
a
61
+ ··· 2.41348 × 10
454
a + 1.40045 × 10
453
i
I
u
4
= hu
46
5u
45
+ ··· 5u + 1, 409894u
45
1529480u
44
+ ··· + 69383a 210129,
756529u
45
+ 2769060u
44
+ ··· + 69383b + 430369i
I
v
1
= hb 1, v 1, ai
There are 5 irreducible components with 127 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
2
a 1, u 1, b + a + 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
1
a
6
=
1
1
a
9
=
a
a 1
a
7
=
a 1
a
a
1
=
1
1
a
3
=
0
1
a
10
=
a
2a 1
a
11
=
1
1
a
8
=
a 1
a
a
4
=
a 2
2
a
4
=
a 2
2
(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 = 1.00000
a = 0.618034
b = 0.381966
3.28987 17.0000
u = 1.00000
a = 1.61803
b = 2.61803
3.28987 17.0000
3
II.
I
u
2
= hu
16
+2u
15
+· · ·+2u +1, u
15
u
14
+· · ·+b 1, 2u
15
+4u
14
+· · ·+a +3i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
6
=
u
u
a
9
=
2u
15
4u
14
+ ··· 3u 3
u
15
+ u
14
+ ··· u + 1
a
7
=
u
15
3u
14
+ ··· u 4
u
15
+ 3u
13
+ ··· + u
2
+ 1
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
10
=
u
15
2u
14
+ ··· u 1
u
15
+ 4u
13
+ ··· u
2
2u
a
11
=
u
4
u
2
+ 1
u
4
a
8
=
u
15
2u
14
+ ··· u 2
u
14
+ u
13
+ ··· 2u
2
+ 1
a
4
=
3u
15
+ 3u
14
+ ··· + 4u + 2
3u
15
4u
14
+ ··· 3u 3
a
4
=
3u
15
+ 3u
14
+ ··· + 4u + 2
3u
15
4u
14
+ ··· 3u 3
(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 = 1.151853 0.528952I
a = 1.78773 0.12345I
b = 2.79766 + 0.54759I
3.34287 9.35884I 5.15004 + 8.71081I
u = 1.151853 + 0.528952I
a = 1.78773 + 0.12345I
b = 2.79766 0.54759I
3.34287 + 9.35884I 5.15004 8.71081I
u = 1.024365 0.459927I
a = 1.83150 + 0.28698I
b = 2.40940 1.33188I
0.384219 + 0.628959I 3.48364 2.80361I
u = 1.024365 + 0.459927I
a = 1.83150 0.28698I
b = 2.40940 + 1.33188I
0.384219 0.628959I 3.48364 + 2.80361I
u = 0.877768 0.808431I
a = 0.0157840 0.0653165I
b = 0.277512 0.092078I
3.87749 3.01517I 33.6443 + 18.9911I
u = 0.877768 + 0.808431I
a = 0.0157840 + 0.0653165I
b = 0.277512 + 0.092078I
3.87749 + 3.01517I 33.6443 18.9911I
u = 0.590891 0.389110I
a = 0.19688 + 2.25256I
b = 0.899899 0.946271I
1.05595 4.33077I 0.04563 + 8.60569I
u = 0.590891 + 0.389110I
a = 0.19688 2.25256I
b = 0.899899 + 0.946271I
1.05595 + 4.33077I 0.04563 8.60569I
u = 0.197391 0.752145I
a = 0.61989 1.71626I
b = 0.231089 + 0.506366I
0.60305 + 4.58234I 2.40249 6.00817I
u = 0.197391 + 0.752145I
a = 0.61989 + 1.71626I
b = 0.231089 0.506366I
0.60305 4.58234I 2.40249 + 6.00817I
5
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.632624 0.437790I
a = 0.836076 + 0.294587I
b = 0.026066 1.061264I
1.10121 2.89037I 1.29781 + 2.83273I
u = 0.632624 + 0.437790I
a = 0.836076 0.294587I
b = 0.026066 + 1.061264I
1.10121 + 2.89037I 1.29781 2.83273I
u = 1.020343 0.486012I
a = 1.029157 0.452903I
b = 0.91414 + 1.41991I
0.21632 + 6.81045I 4.49677 10.12296I
u = 1.020343 + 0.486012I
a = 1.029157 + 0.452903I
b = 0.91414 1.41991I
0.21632 6.81045I 4.49677 + 10.12296I
u = 1.189300 0.317097I
a = 1.088110 + 0.049738I
b = 1.72266 0.70693I
4.77806 1.04547I 8.97927 + 2.31364I
u = 1.189300 + 0.317097I
a = 1.088110 0.049738I
b = 1.72266 + 0.70693I
4.77806 + 1.04547I 8.97927 2.31364I
6
III. I
u
3
= ha
62
5a
60
+ · · · 41640182a + 1319939, 4.63 × 10
449
u 6.79 ×
10
443
a
61
+ · · · 2.17 × 10
452
a + 1.18 × 10
451
, 1.76 × 10
452
b 7.57 ×
10
445
a
61
+ · · · 2.41 × 10
454
a + 1.40 × 10
453
i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
1.46687 × 10
6
a
61
+ 1.06141 × 10
7
a
60
+ ··· + 469.397a 25.4732
a
6
=
1.46687 × 10
6
a
61
1.06141 × 10
7
a
60
+ ··· 469.397a + 25.4732
1.46687 × 10
6
a
61
+ 1.06141 × 10
7
a
60
+ ··· + 469.397a 25.4732
a
9
=
a
4.31199 × 10
7
a
61
+ 3.09000 × 10
8
a
60
+ ··· + 137.511a 7.97928
a
7
=
1.36963 × 10
6
a
61
1.02244 × 10
7
a
60
+ ··· 436.440a + 23.7012
2.87983 × 10
7
a
61
+ 2.05858 × 10
8
a
60
+ ··· + 90.9542a 5.37044
a
1
=
1
2.32647 × 10
6
a
61
+ 1.74920 × 10
7
a
60
+ ··· + 742.175a 39.1627
a
3
=
2.32647 × 10
6
a
61
+ 1.74920 × 10
7
a
60
+ ··· + 742.175a 38.1627
7.17012 × 10
7
a
61
6.81558 × 10
8
a
60
+ ··· 215.868a + 10.0601
a
10
=
2.92181 × 10
6
a
61
2.07876 × 10
7
a
60
+ ··· 939.621a + 49.5755
2.58100 × 10
6
a
61
+ 2.03100 × 10
7
a
60
+ ··· + 812.321a 42.6596
a
11
=
1.60945 × 10
6
a
61
+ 1.06764 × 10
7
a
60
+ ··· + 526.308a 28.1026
7.17012 × 10
7
a
61
+ 6.81558 × 10
8
a
60
+ ··· + 215.868a 10.0601
a
8
=
5.77520 × 10
7
a
61
+ 6.72879 × 10
8
a
60
+ ··· + 162.359a 7.77369
1.31112 × 10
6
a
61
1.04854 × 10
7
a
60
+ ··· 415.982a + 21.3926
a
4
=
3.16453 × 10
8
a
61
1.78068 × 10
8
a
60
+ ··· 1.23768a + 0.576707
8.05075 × 10
7
a
61
+ 5.04584 × 10
8
a
60
+ ··· + 273.972a 15.9451
a
4
=
3.16453 × 10
8
a
61
1.78068 × 10
8
a
60
+ ··· 1.23768a + 0.576707
8.05075 × 10
7
a
61
+ 5.04584 × 10
8
a
60
+ ··· + 273.972a 15.9451
(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 = 1.057022 + 0.392863I
a = 2.43314 0.54577I
b = 2.69526 + 0.95587I
1.41458 1.86246I 6.47152 + 4.51832I
u = 1.057022 0.392863I
a = 2.43314 + 0.54577I
b = 2.69526 0.95587I
1.41458 + 1.86246I 6.47152 4.51832I
u = 1.037233 + 0.490832I
a = 2.05442 0.53637I
b = 3.37617 + 0.87454I
0.442167 0.494118I 0.11941 + 1.82079I
u = 1.037233 0.490832I
a = 2.05442 + 0.53637I
b = 3.37617 0.87454I
0.442167 + 0.494118I 0.11941 1.82079I
u = 1.157762 0.512519I
a = 1.94037 0.36721I
b = 3.39713 + 0.70582I
5.08886 9.19357I 11.4929 + 8.9901I
u = 1.157762 + 0.512519I
a = 1.94037 + 0.36721I
b = 3.39713 0.70582I
5.08886 + 9.19357I 11.4929 8.9901I
u = 1.11799
a = 1.54119
b = 2.40394
2.94773 9.04294
u = 1.229733 + 0.258953I
a = 1.41847 0.04576I
b = 2.14272 0.39708I
3.97519 + 1.59170I 1.35198 10.14097I
u = 1.229733 0.258953I
a = 1.41847 + 0.04576I
b = 2.14272 + 0.39708I
3.97519 1.59170I 1.35198 + 10.14097I
u = 1.171535 0.571368I
a = 1.201385 0.152379I
b = 2.09128 + 0.56024I
1.82208 10.29011I 1.64284 + 11.44923I
8
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.171535 + 0.571368I
a = 1.201385 + 0.152379I
b = 2.09128 0.56024I
1.82208 + 10.29011I 1.64284 11.44923I
u = 1.178186 + 0.355689I
a = 1.15895 0.96635I
b = 1.74729 + 0.52652I
6.17761 + 0.88062I 14.6380 2.9072I
u = 1.178186 0.355689I
a = 1.15895 + 0.96635I
b = 1.74729 0.52652I
6.17761 0.88062I 14.6380 + 2.9072I
u = 0.168042 0.738886I
a = 0.92839 2.28845I
b = 0.022116 + 0.301969I
2.24573 + 4.52331I 8.41907 6.24640I
u = 0.168042 + 0.738886I
a = 0.92839 + 2.28845I
b = 0.022116 0.301969I
2.24573 4.52331I 8.41907 + 6.24640I
u = 1.037233 0.490832I
a = 0.771065 0.573122I
b = 0.869891 0.499254I
0.442167 + 0.494118I 0.11941 1.82079I
u = 1.037233 + 0.490832I
a = 0.771065 + 0.573122I
b = 0.869891 + 0.499254I
0.442167 0.494118I 0.11941 + 1.82079I
u = 0.467072 + 0.505817I
a = 0.64319 2.77959I
b = 0.178577 + 0.580009I
2.11162 3.64112I 4.51546 + 4.55522I
u = 0.467072 0.505817I
a = 0.64319 + 2.77959I
b = 0.178577 0.580009I
2.11162 + 3.64112I 4.51546 4.55522I
u = 0.483181 + 0.627527I
a = 0.61496 1.32926I
b = 0.212090 + 0.311787I
2.01990 0.90453I 3.65108 + 0.79331I
9
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.483181 0.627527I
a = 0.61496 + 1.32926I
b = 0.212090 0.311787I
2.01990 + 0.90453I 3.65108 0.79331I
u = 0.168042 + 0.738886I
a = 0.59373 1.59457I
b = 0.782781 + 0.650895I
2.24573 4.52331I 8.41907 + 6.24640I
u = 0.168042 0.738886I
a = 0.59373 + 1.59457I
b = 0.782781 0.650895I
2.24573 + 4.52331I 8.41907 6.24640I
u = 0.271790 0.844936I
a = 0.507480 1.209593I
b = 0.194320 + 0.174273I
0.86287 + 5.06730I 2.75638 8.05298I
u = 0.271790 + 0.844936I
a = 0.507480 + 1.209593I
b = 0.194320 0.174273I
0.86287 5.06730I 2.75638 + 8.05298I
u = 1.11799
a = 0.350438
b = 0.317798
2.94773 9.04294
u = 0.467072 + 0.505817I
a = 0.190163 0.921127I
b = 1.37742 + 0.43065I
2.11162 3.64112I 4.51546 + 4.55522I
u = 0.467072 0.505817I
a = 0.190163 + 0.921127I
b = 1.37742 0.43065I
2.11162 + 3.64112I 4.51546 4.55522I
u = 0.790665 0.695036I
a = 0.0796411 0.0038592I
b = 0.760027 0.202385I
3.79486 2.62922I 6.53544 + 4.19495I
u = 0.790665 + 0.695036I
a = 0.0796411 + 0.0038592I
b = 0.760027 + 0.202385I
3.79486 + 2.62922I 6.53544 4.19495I
10
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.271790 + 0.844936I
a = 0.19575 1.81853I
b = 0.087960 + 0.559361I
0.86287 5.06730I 2.75638 + 8.05298I
u = 0.271790 0.844936I
a = 0.19575 + 1.81853I
b = 0.087960 0.559361I
0.86287 + 5.06730I 2.75638 8.05298I
u = 0.790665 + 0.695036I
a = 0.209439 0.420689I
b = 0.224565 0.075780I
3.79486 + 2.62922I 6.53544 4.19495I
u = 0.790665 0.695036I
a = 0.209439 + 0.420689I
b = 0.224565 + 0.075780I
3.79486 2.62922I 6.53544 + 4.19495I
u = 1.026552 + 0.519350I
a = 0.246653 0.578430I
b = 0.136144 0.054712I
0.44756 + 5.41860I 0.32653 5.88711I
u = 1.026552 0.519350I
a = 0.246653 + 0.578430I
b = 0.136144 + 0.054712I
0.44756 5.41860I 0.32653 + 5.88711I
u = 0.483181 + 0.627527I
a = 0.277011 0.173898I
b = 0.662449 + 0.543286I
2.01990 0.90453I 3.65108 + 0.79331I
u = 0.483181 0.627527I
a = 0.277011 + 0.173898I
b = 0.662449 0.543286I
2.01990 + 0.90453I 3.65108 0.79331I
u = 1.094170 0.506739I
a = 0.429963 0.931241I
b = 0.75145 + 2.66623I
0.54438 + 8.91512I 2.96887 11.01596I
u = 1.094170 + 0.506739I
a = 0.429963 + 0.931241I
b = 0.75145 2.66623I
0.54438 8.91512I 2.96887 + 11.01596I
11
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.753184 0.319413I
a = 0.50427 1.78730I
b = 0.64697 + 2.15657I
0.12340 4.63553I 7.19066 + 8.64807I
u = 0.753184 + 0.319413I
a = 0.50427 + 1.78730I
b = 0.64697 2.15657I
0.12340 + 4.63553I 7.19066 8.64807I
u = 0.753184 + 0.319413I
a = 0.574105 1.283487I
b = 0.686369 0.034168I
0.12340 + 4.63553I 7.19066 8.64807I
u = 0.753184 0.319413I
a = 0.574105 + 1.283487I
b = 0.686369 + 0.034168I
0.12340 4.63553I 7.19066 + 8.64807I
u = 1.229733 + 0.258953I
a = 0.574647 0.220052I
b = 1.120433 + 0.822844I
3.97519 + 1.59170I 1.35198 10.14097I
u = 1.229733 0.258953I
a = 0.574647 + 0.220052I
b = 1.120433 0.822844I
3.97519 1.59170I 1.35198 + 10.14097I
u = 1.057022 + 0.392863I
a = 0.714448 0.757121I
b = 1.29741 + 2.38718I
1.41458 1.86246I 6.47152 + 4.51832I
u = 1.057022 0.392863I
a = 0.714448 + 0.757121I
b = 1.29741 2.38718I
1.41458 + 1.86246I 6.47152 4.51832I
u = 0.314340 0.572965I
a = 0.76574 2.62474I
b = 0.201731 + 1.318463I
1.67219 4.56405I 2.14197 + 7.53125I
u = 0.314340 + 0.572965I
a = 0.76574 + 2.62474I
b = 0.201731 1.318463I
1.67219 + 4.56405I 2.14197 7.53125I
12
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.178186 + 0.355689I
a = 1.32688 0.67944I
b = 2.26915 + 1.59970I
6.17761 + 0.88062I 14.6380 2.9072I
u = 1.178186 0.355689I
a = 1.32688 + 0.67944I
b = 2.26915 1.59970I
6.17761 0.88062I 14.6380 + 2.9072I
u = 1.026552 0.519350I
a = 1.35631 0.43247I
b = 2.19532 + 1.02850I
0.44756 5.41860I 0.32653 + 5.88711I
u = 1.026552 + 0.519350I
a = 1.35631 + 0.43247I
b = 2.19532 1.02850I
0.44756 + 5.41860I 0.32653 5.88711I
u = 1.157762 0.512519I
a = 1.69383 0.86714I
b = 2.30669 + 0.75531I
5.08886 9.19357I 11.4929 + 8.9901I
u = 1.157762 + 0.512519I
a = 1.69383 + 0.86714I
b = 2.30669 0.75531I
5.08886 + 9.19357I 11.4929 8.9901I
u = 1.171535 + 0.571368I
a = 1.76811 0.05465I
b = 2.74116 + 0.10746I
1.82208 + 10.29011I 1.64284 11.44923I
u = 1.171535 0.571368I
a = 1.76811 + 0.05465I
b = 2.74116 0.10746I
1.82208 10.29011I 1.64284 + 11.44923I
u = 0.314340 0.572965I
a = 2.17131 0.57044I
b = 0.571185 + 0.026600I
1.67219 4.56405I 2.14197 + 7.53125I
u = 0.314340 + 0.572965I
a = 2.17131 + 0.57044I
b = 0.571185 0.026600I
1.67219 + 4.56405I 2.14197 7.53125I
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.094170 0.506739I
a = 2.51343 0.71210I
b = 3.27165 + 0.91207I
0.54438 + 8.91512I 2.96887 11.01596I
u = 1.094170 + 0.506739I
a = 2.51343 + 0.71210I
b = 3.27165 0.91207I
0.54438 8.91512I 2.96887 + 11.01596I
13
IV.
I
u
4
= hu
46
5u
45
+ · · · 5u + 1, 4.10 × 10
5
u
45
1.53 × 10
6
u
44
+ · · · + 6.94 ×
10
4
a2.10×10
5
, 7.57×10
5
u
45
+2.77×10
6
u
44
+· · ·+6.94×10
4
b+4.30×10
5
i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
6
=
u
u
a
9
=
5.90770u
45
+ 22.0440u
44
+ ··· 12.0178u + 3.02854
10.9037u
45
39.9098u
44
+ ··· + 30.1036u 6.20280
a
7
=
5.54479u
45
+ 22.2577u
44
+ ··· 11.8700u + 3.05705
13.3044u
45
52.8398u
44
+ ··· + 43.3909u 8.99833
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
10
=
5.54479u
45
+ 22.2577u
44
+ ··· 13.8700u + 4.05705
9.01675u
45
34.8571u
44
+ ··· + 31.0442u 6.82680
a
11
=
u
4
u
2
+ 1
u
4
a
8
=
1.62373u
45
+ 5.57638u
44
+ ··· + 6.33544u 0.748123
2.91541u
45
13.6934u
44
+ ··· + 16.9255u 4.24914
a
4
=
6.23964u
45
+ 24.4501u
44
+ ··· 9.52363u + 3.36251
7.16070u
45
30.1314u
44
+ ··· + 28.7291u 6.16768
a
4
=
6.23964u
45
+ 24.4501u
44
+ ··· 9.52363u + 3.36251
7.16070u
45
30.1314u
44
+ ··· + 28.7291u 6.16768
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
14
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.225337 0.349011I
a = 0.889993 + 0.576468I
b = 1.67770 0.41554I
6.99619 7.57481I 10.39877 + 7.23305I
u = 1.225337 + 0.349011I
a = 0.889993 0.576468I
b = 1.67770 + 0.41554I
6.99619 + 7.57481I 10.39877 7.23305I
u = 1.215534 0.243371I
a = 1.46792 0.19964I
b = 2.42629 + 1.03642I
5.60396 + 10.10355I 8.00817 5.63549I
u = 1.215534 + 0.243371I
a = 1.46792 + 0.19964I
b = 2.42629 1.03642I
5.60396 10.10355I 8.00817 + 5.63549I
u = 1.135203 0.294115I
a = 1.50669 + 0.02427I
b = 2.52069 1.05527I
6.20814 + 1.80497I 14.2464 4.3963I
u = 1.135203 + 0.294115I
a = 1.50669 0.02427I
b = 2.52069 + 1.05527I
6.20814 1.80497I 14.2464 + 4.3963I
u = 1.112296 0.261314I
a = 0.924409 0.656226I
b = 2.10936 + 0.51254I
5.91551 1.58146I 13.59206 + 3.66934I
u = 1.112296 + 0.261314I
a = 0.924409 + 0.656226I
b = 2.10936 0.51254I
5.91551 + 1.58146I 13.59206 3.66934I
u = 1.099343 0.465407I
a = 1.34416 0.55405I
b = 2.21094 0.22704I
4.10186 3.81474I 9.79702 + 3.58298I
u = 1.099343 + 0.465407I
a = 1.34416 + 0.55405I
b = 2.21094 + 0.22704I
4.10186 + 3.81474I 9.79702 3.58298I
15
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.059213 0.534264I
a = 0.779953 + 0.039391I
b = 0.983029 + 0.522661I
0.17597 5.33365I 1.16724 + 4.83689I
u = 1.059213 + 0.534264I
a = 0.779953 0.039391I
b = 0.983029 0.522661I
0.17597 + 5.33365I 1.16724 4.83689I
u = 0.881986 0.787307I
a = 0.108733 + 0.190174I
b = 0.212790 0.101868I
3.98279 2.95487I 23.7349 13.5735I
u = 0.881986 + 0.787307I
a = 0.108733 0.190174I
b = 0.212790 + 0.101868I
3.98279 + 2.95487I 23.7349 + 13.5735I
u = 0.431319 0.618019I
a = 0.209693 + 0.745628I
b = 0.398515 0.405749I
2.00312 + 0.77598I 3.08048 0.37837I
u = 0.431319 + 0.618019I
a = 0.209693 0.745628I
b = 0.398515 + 0.405749I
2.00312 0.77598I 3.08048 + 0.37837I
u = 0.092447 0.293184I
a = 0.52277 3.36851I
b = 0.998318 + 0.214289I
1.65225 + 0.00944I 6.31613 + 0.26061I
u = 0.092447 + 0.293184I
a = 0.52277 + 3.36851I
b = 0.998318 0.214289I
1.65225 0.00944I 6.31613 0.26061I
u = 0.132938 0.848595I
a = 0.506025 + 1.047423I
b = 0.346355 0.193036I
2.72587 + 3.54069I 7.48667 4.84167I
u = 0.132938 + 0.848595I
a = 0.506025 1.047423I
b = 0.346355 + 0.193036I
2.72587 3.54069I 7.48667 + 4.84167I
16
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.278150 0.732712I
a = 0.25962 2.50961I
b = 0.470814 + 0.494010I
2.03242 4.83583I 8.60020 + 6.83106I
u = 0.278150 + 0.732712I
a = 0.25962 + 2.50961I
b = 0.470814 0.494010I
2.03242 + 4.83583I 8.60020 6.83106I
u = 0.291347 0.840599I
a = 0.29205 + 2.23800I
b = 0.249354 0.477451I
0.71987 13.43224I 2.36696 + 7.45298I
u = 0.291347 + 0.840599I
a = 0.29205 2.23800I
b = 0.249354 + 0.477451I
0.71987 + 13.43224I 2.36696 7.45298I
u = 0.375652 0.726957I
a = 0.89998 1.19100I
b = 0.342880 0.053077I
1.60276 0.98411I 7.53408 + 0.28472I
u = 0.375652 + 0.726957I
a = 0.89998 + 1.19100I
b = 0.342880 + 0.053077I
1.60276 + 0.98411I 7.53408 0.28472I
u = 0.660174 0.548978I
a = 0.803478 + 1.008650I
b = 0.602150 0.749555I
0.36479 + 3.45703I 5.70781 7.10352I
u = 0.660174 + 0.548978I
a = 0.803478 1.008650I
b = 0.602150 + 0.749555I
0.36479 3.45703I 5.70781 + 7.10352I
u = 0.751399 0.721194I
a = 0.478297 0.175669I
b = 0.754387 + 0.217576I
1.87378 + 10.77038I 1.30875 9.40079I
u = 0.751399 + 0.721194I
a = 0.478297 + 0.175669I
b = 0.754387 0.217576I
1.87378 10.77038I 1.30875 + 9.40079I
17
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.761418 0.115983I
a = 0.927965 + 0.592492I
b = 0.583546 0.562150I
1.37145 + 0.34774I 7.35312 1.68014I
u = 0.761418 + 0.115983I
a = 0.927965 0.592492I
b = 0.583546 + 0.562150I
1.37145 0.34774I 7.35312 + 1.68014I
u = 0.856947 0.701617I
a = 0.164084 + 0.010834I
b = 0.016618 + 0.945437I
1.57181 5.40355I 1.95277 + 5.01520I
u = 0.856947 + 0.701617I
a = 0.164084 0.010834I
b = 0.016618 0.945437I
1.57181 + 5.40355I 1.95277 5.01520I
u = 0.933486 0.444661I
a = 1.082134 + 0.208292I
b = 1.12610 0.98739I
1.098383 + 0.644192I 5.70718 0.44366I
u = 0.933486 + 0.444661I
a = 1.082134 0.208292I
b = 1.12610 + 0.98739I
1.098383 0.644192I 5.70718 + 0.44366I
u = 1.099787 0.438913I
a = 1.65875 + 0.88034I
b = 2.61585 0.70206I
4.28647 + 3.53114I 10.17349 4.71484I
u = 1.099787 + 0.438913I
a = 1.65875 0.88034I
b = 2.61585 + 0.70206I
4.28647 3.53114I 10.17349 + 4.71484I
u = 1.115386 0.573899I
a = 1.045263 + 0.757916I
b = 1.97867 1.06928I
3.77845 + 5.97580I 9.62613 4.25022I
u = 1.115386 + 0.573899I
a = 1.045263 0.757916I
b = 1.97867 + 1.06928I
3.77845 5.97580I 9.62613 + 4.25022I
18
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.133412 0.543345I
a = 2.20160 + 0.17621I
b = 3.62113 + 0.20485I
4.51494 + 9.66961I 12.1786 10.5958I
u = 1.133412 + 0.543345I
a = 2.20160 0.17621I
b = 3.62113 0.20485I
4.51494 9.66961I 12.1786 + 10.5958I
u = 1.165266 0.576600I
a = 2.02141 0.01612I
b = 3.34456 0.20372I
3.3293 + 18.6712I 5.27812 10.80266I
u = 1.165266 + 0.576600I
a = 2.02141 + 0.01612I
b = 3.34456 + 0.20372I
3.3293 18.6712I 5.27812 + 10.80266I
u = 1.197318 0.502148I
a = 1.071045 0.441986I
b = 1.66684 + 0.51223I
5.94279 + 1.33870I 10.51571 + 0.17082I
u = 1.197318 + 0.502148I
a = 1.071045 + 0.441986I
b = 1.66684 0.51223I
5.94279 1.33870I 10.51571 0.17082I
19
V. I
v
1
= hb 1, v 1, ai
(i) Arc colorings
a
2
=
1
0
a
5
=
1
0
a
6
=
1
0
a
9
=
0
1
a
7
=
1
1
a
1
=
1
0
a
3
=
1
0
a
10
=
1
1
a
11
=
1
0
a
8
=
1
1
a
4
=
2
1
a
4
=
2
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
20
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
1
1(vol +
1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
1.64493 6.00000
21
VI. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u)(u 1)
2
(u
16
+ 2u
15
+ ··· + 2u + 1)
(1 2u + u
2
+ 4u
4
8u
5
+ 16u
7
10u
8
20u
9
+ 18u
10
+ 48u
11
70u
12
60u
13
+ 184u
14
42u
15
239u
16
+ 230u
17
+ 125u
18
328u
19
+ 70u
20
+ 252u
21
172u
22
104u
23
+ 141u
24
+ 10u
25
65u
26
+ 12u
27
+ 17u
28
6u
29
2u
30
+ u
31
)
2
(u
46
+ 5u
45
+ ··· + 5u + 1)
c
2
(u)(u + 1)
2
(u
16
+ 8u
15
+ ··· + 4u + 1)
(1 + 2u + 9u
2
+ 24u
3
+ 60u
4
+ 128u
5
+ 264u
6
+ 444u
7
+ 670u
8
+ 1092u
9
+ 2058u
10
+ 4076u
11
+ 7858u
12
+ 1.39 × 10
4
u
13
+ 2.15 × 10
4
u
14
+ 2.91 × 10
4
u
15
+ 3.59 × 10
4
u
16
+ 4.39 × 10
4
u
17
+ 5.57 × 10
4
u
18
+ 7.11 × 10
4
u
19
+ 8.42 × 10
4
u
20
+ 8.74 × 10
4
u
21
+ 7.73 × 10
4
u
22
+ 5.75 × 10
4
u
23
+ 3.58 × 10
4
u
24
+ 1.84 × 10
4
u
25
+ 7715u
26
+ 2590u
27
+ 673u
28
+ 128u
29
+ 16u
30
+ u
31
)
2
(u
46
+ 23u
45
+ ··· 11u + 1)
c
3
, c
10
(u + 1)(u
2
u 1)(u
16
+ 4u
14
+ ··· + u + 1)(u
46
u
45
+ ··· + 2u + 1)
(u
62
+ 2u
61
+ ··· + u 1)
c
4
, c
9
(u + 1)(u
2
u 1)(u
16
u
15
+ ··· + 4u
2
+ 1)(u
46
2u
45
+ ··· + u + 1)
(u
62
+ 2u
61
+ ··· 211u + 31)
c
5
(u)(u + 1)
2
(u
16
2u
15
+ ··· 2u + 1)
(1 2u + u
2
+ 4u
4
8u
5
+ 16u
7
10u
8
20u
9
+ 18u
10
+ 48u
11
70u
12
60u
13
+ 184u
14
42u
15
239u
16
+ 230u
17
+ 125u
18
328u
19
+ 70u
20
+ 252u
21
172u
22
104u
23
+ 141u
24
+ 10u
25
65u
26
+ 12u
27
+ 17u
28
6u
29
2u
30
+ u
31
)
2
(u
46
+ 5u
45
+ ··· + 5u + 1)
c
6
, c
8
(u 1)
2
(u + 1)(u
16
5u
15
+ ··· 8u + 1)(u
46
+ 6u
45
+ ··· 9u + 1)
(u
62
3u
61
+ ··· + 378u 49)
c
7
u
3
(u
16
+ 11u
15
+ ··· + 38u + 5)
(2 + 3u 15u
2
32u
3
+ 32u
4
+ 168u
5
+ 100u
6
400u
7
792u
8
+ 14u
9
+ 1862u
10
+ 2316u
11
764u
12
5178u
13
5186u
14
+ 1602u
15
+ 9450u
16
+ 9527u
17
+ 45u
18
1.09 × 10
4
u
19
1.35 × 10
4
u
20
5846u
21
+ 5302u
22
+ 1.23 × 10
4
u
23
+ 1.26 × 10
4
u
24
+ 8835u
25
+ 4593u
26
+ 1806u
27
+ 530u
28
+ 111u
29
+ 15u
30
+ u
31
)
2
(u
46
26u
45
+ ··· u + 1)
c
11
u
3
(u
16
+ 6u
15
+ ··· + 14u + 5)(u
46
15u
45
+ ··· 1885u + 149)
(u
62
+ 18u
61
+ ··· + 1168u + 64)
22
VII. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
(y)(y 1)
2
(y
16
8y
15
+ ··· 4y + 1)
(1 + 2y 9y
2
+ 24y
3
60y
4
+ 128y
5
264y
6
+ 444y
7
670y
8
+ 1092y
9
2058y
10
+ 4076y
11
7858y
12
+ 1.39 × 10
4
y
13
2.15 × 10
4
y
14
+ 2.91 × 10
4
y
15
3.59 × 10
4
y
16
+ 4.39 × 10
4
y
17
5.57 × 10
4
y
18
+ 7.11 × 10
4
y
19
8.42 × 10
4
y
20
+ 8.74 × 10
4
y
21
7.73 × 10
4
y
22
+ 5.75 × 10
4
y
23
3.58 × 10
4
y
24
+ 1.84 × 10
4
y
25
7715y
26
+ 2590y
27
673y
28
+ 128y
29
16y
30
+ y
31
)
2
(y
46
23y
45
+ ··· + 11y + 1)
c
2
(y)(y 1)
2
(y
16
+ 4y
15
+ ··· + 8y + 1)
(1 14y 105y
2
520y
3
1772y
4
5792y
5
2.05 × 10
4
y
6
5.73 × 10
4
y
7
1.42 × 10
5
y
8
3.08 × 10
5
y
9
5.37 × 10
5
y
10
7.30 × 10
5
y
11
1.12 × 10
6
y
12
9.36 × 10
5
y
13
8.35 × 10
5
y
14
5.14 × 10
5
y
15
2.00 × 10
5
y
16
7.18 × 10
4
y
17
+ 4.70 × 10
4
y
18
+ 5.82 × 10
4
y
19
+ 3.65 × 10
4
y
20
+ 3.94 × 10
4
y
21
+ 7828y
22
+ 1.29 × 10
4
y
23
+ 599y
24
+ 2670y
25
27y
26
+ 354y
27
5y
28
+ 28y
29
+ y
31
)
2
(y
46
+ 5y
45
+ ··· 73y + 1)
c
3
(y 1)(y
2
3y + 1)(y
16
+ 8y
15
+ ··· + 5y + 1)
(y
46
19y
45
+ ··· 52y + 1)(y
62
+ 12y
61
+ ··· + 29y + 1)
c
4
(y 1)(y
2
3y + 1)(y
16
+ 5y
15
+ ··· + 8y + 1)(y
46
2y
45
+ ··· + 27y + 1)
(y
62
+ 58y
60
+ ··· 104599y + 961)
c
6
, c
8
(y 1)
3
(y
16
+ 9y
15
+ ··· 8y + 1)(y
46
30y
45
+ ··· 121y + 1)
(y
62
+ 13y
61
+ ··· + 17738y + 2401)
c
7
y
3
(y
16
+ 3y
15
+ ··· + 126y + 25)(y
46
+ 38y
44
+ ··· + 49y + 1)
(y
62
6y
61
+ ··· 552y + 16)
c
9
(y 1)(y
2
3y + 1)(y
16
+ 5y
15
+ ··· + 8y + 1)(y
46
2y
45
+ ··· + 27y + 1)
(y
62
+ 58y
60
+ ··· 104599y + 961)
c
10
(y 1)(y
2
3y + 1)(y
16
+ 8y
15
+ ··· + 5y + 1)
(y
46
19y
45
+ ··· 52y + 1)(y
62
+ 12y
61
+ ··· + 29y + 1)
c
11
y
3
(y
16
6y
14
+ ··· 106y + 25)
(y
46
+ 13y
45
+ ··· + 238229y + 22201)
(y
62
+ 26y
61
+ ··· 106624y + 4096)
23