12a
0048
(K12a
0048
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 9 10 4 11 1 12 8 6
Solving Sequence
2,5 3,9
6 1 10 7 4 12 11 8
c
2
c
5
c
1
c
9
c
6
c
4
c
12
c
10
c
8
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h5.88695 × 10
226
u
139
+ 3.54230 × 10
227
u
138
+ ··· + 2.19679 × 10
225
b − 1.39977 × 10
227
,
− 1.53329 × 10
227
u
139
− 1.75240 × 10
228
u
138
+ ··· + 2.19679 × 10
225
a − 5.19955 × 10
227
,
u
140
+ 11u
139
+ ··· + 5u + 1i
I
u
2
= ha
3
+ a
2
+ b, a
4
+ a
2
− a + 1, u − 1i
I
u
3
= h3a
5
+ a
4
+ 5a
3
+ 3a
2
+ b + 2a + 4, a
6
+ a
5
+ 2a
4
+ 2a
3
+ 2a
2
+ 2a + 1, u − 1i
* 3 irreducible components of dim
C
= 0, with total 150 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h5.89 × 10
226
u
139
+ 3.54 × 10
227
u
138
+ · · · + 2.20 × 10
225
b − 1.40 ×
10
227
, −1.53 × 10
227
u
139
− 1.75 × 10
228
u
138
+ · · · + 2.20 × 10
225
a − 5.20 ×
10
227
, u
140
+ 11u
139
+ · · · + 5u + 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
u
2
a
9
=
69.7967u
139
+ 797.709u
138
+ ··· + 88.8689u + 236.689
−26.7979u
139
− 161.249u
138
+ ··· + 136.086u + 63.7186
a
6
=
480.698u
139
+ 4767.03u
138
+ ··· + 1232.37u + 469.393
728.821u
139
+ 7333.60u
138
+ ··· + 2537.70u + 602.691
a
1
=
−u
2
+ 1
−u
4
a
10
=
82.0957u
139
+ 1002.56u
138
+ ··· + 303.107u + 313.689
−74.9368u
139
− 514.534u
138
+ ··· + 292.890u + 117.321
a
7
=
−14.2692u
139
− 127.488u
138
+ ··· + 14.2050u − 0.190764
−29.4738u
139
− 285.330u
138
+ ··· − 71.1553u − 14.2692
a
4
=
u
u
a
12
=
−201.075u
139
− 2109.48u
138
+ ··· − 821.483u − 254.837
−216.675u
139
− 2363.19u
138
+ ··· − 1211.53u − 298.416
a
11
=
148.855u
139
+ 1559.41u
138
+ ··· + 437.161u + 239.438
130.468u
139
+ 1417.38u
138
+ ··· + 697.783u + 181.413
a
8
=
−13.2474u
139
− 129.302u
138
+ ··· − 17.6313u − 9.59894
−28.4520u
139
− 287.145u
138
+ ··· − 102.992u − 23.6774
(ii) Obstruction class = −1
(iii) Cusp Shapes = 25.0878u
139
− 46.6962u
138
+ ··· − 1004.65u − 85.3740
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
140
+ 69u
139
+ ··· + 221u + 1
c
2
, c
4
u
140
− 11u
139
+ ··· − 5u + 1
c
3
, c
7
u
140
− u
139
+ ··· − 8192u + 1024
c
5
u
140
− 2u
139
+ ··· − 24012u + 5887
c
6
u
140
+ 2u
139
+ ··· − 10624u + 1216
c
8
, c
11
u
140
+ 2u
139
+ ··· + 14u + 1
c
9
u
140
+ 14u
139
+ ··· + 2u + 1
c
10
u
140
+ 58u
139
+ ··· + 14u + 1
c
12
u
140
− 10u
139
+ ··· − 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
140
+ 15y
139
+ ··· − 2817y + 1
c
2
, c
4
y
140
− 69y
139
+ ··· − 221y + 1
c
3
, c
7
y
140
− 63y
139
+ ··· − 25690112y + 1048576
c
5
y
140
+ 142y
139
+ ··· + 261556046y + 34656769
c
6
y
140
+ 150y
139
+ ··· + 35716096y + 1478656
c
8
, c
11
y
140
+ 58y
139
+ ··· + 14y + 1
c
9
y
140
+ 10y
139
+ ··· + 14y + 1
c
10
y
140
+ 50y
139
+ ··· − 2010y + 1
c
12
y
140
+ 14y
139
+ ··· + 10y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.342968 + 0.929621I
a = 1.35534 + 0.86261I
b = −0.303012 − 0.058151I
4.92055 − 8.62646I 0
u = −0.342968 − 0.929621I
a = 1.35534 − 0.86261I
b = −0.303012 + 0.058151I
4.92055 + 8.62646I 0
u = −0.940954 + 0.310093I
a = −1.00907 + 1.00614I
b = −0.62230 + 1.81875I
−1.78233 − 1.83282I 0
u = −0.940954 − 0.310093I
a = −1.00907 − 1.00614I
b = −0.62230 − 1.81875I
−1.78233 + 1.83282I 0
u = −0.982775 + 0.239312I
a = 0.92340 − 1.08802I
b = 0.85110 − 1.99683I
−4.37037 − 6.99484I 0
u = −0.982775 − 0.239312I
a = 0.92340 + 1.08802I
b = 0.85110 + 1.99683I
−4.37037 + 6.99484I 0
u = −0.313843 + 0.961586I
a = −1.51506 − 0.83479I
b = 0.480798 + 0.216981I
2.9856 − 14.5493I 0
u = −0.313843 − 0.961586I
a = −1.51506 + 0.83479I
b = 0.480798 − 0.216981I
2.9856 + 14.5493I 0
u = 0.895882 + 0.410358I
a = 0.737122 − 0.522383I
b = −1.16839 − 1.04334I
0.79500 − 3.33230I 0
u = 0.895882 − 0.410358I
a = 0.737122 + 0.522383I
b = −1.16839 + 1.04334I
0.79500 + 3.33230I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.928796 + 0.320294I
a = 0.41566 + 2.57834I
b = 2.39910 + 3.21755I
−1.66193 + 0.85450I 0
u = 0.928796 − 0.320294I
a = 0.41566 − 2.57834I
b = 2.39910 − 3.21755I
−1.66193 − 0.85450I 0
u = 0.938441 + 0.410293I
a = −0.278288 + 0.769078I
b = 0.432906 + 1.251360I
−1.82288 − 1.42035I 0
u = 0.938441 − 0.410293I
a = −0.278288 − 0.769078I
b = 0.432906 − 1.251360I
−1.82288 + 1.42035I 0
u = 1.038840 + 0.126611I
a = 1.02386 + 1.05217I
b = 6.21349 + 1.31481I
−2.14003 − 2.45951I 0
u = 1.038840 − 0.126611I
a = 1.02386 − 1.05217I
b = 6.21349 − 1.31481I
−2.14003 + 2.45951I 0
u = −0.980690 + 0.381123I
a = 0.357441 − 1.087270I
b = −0.26536 − 1.65226I
−2.17880 + 4.32767I 0
u = −0.980690 − 0.381123I
a = 0.357441 + 1.087270I
b = −0.26536 + 1.65226I
−2.17880 − 4.32767I 0
u = −0.426331 + 0.962752I
a = −0.868941 − 0.376457I
b = 0.138975 + 0.269813I
3.40573 − 1.43298I 0
u = −0.426331 − 0.962752I
a = −0.868941 + 0.376457I
b = 0.138975 − 0.269813I
3.40573 + 1.43298I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.998116 + 0.346400I
a = −0.89627 − 3.02269I
b = −3.41213 − 4.72470I
−1.93443 − 3.19824I 0
u = 0.998116 − 0.346400I
a = −0.89627 + 3.02269I
b = −3.41213 + 4.72470I
−1.93443 + 3.19824I 0
u = −0.902938 + 0.241403I
a = −0.130518 + 1.318270I
b = 0.45541 + 1.86743I
−5.78935 + 0.68606I 0
u = −0.902938 − 0.241403I
a = −0.130518 − 1.318270I
b = 0.45541 − 1.86743I
−5.78935 − 0.68606I 0
u = 0.387215 + 0.848725I
a = 0.133458 + 0.695504I
b = 0.024953 − 0.212602I
−0.51232 − 5.68304I 0
u = 0.387215 − 0.848725I
a = 0.133458 − 0.695504I
b = 0.024953 + 0.212602I
−0.51232 + 5.68304I 0
u = 0.981412 + 0.431065I
a = −0.223258 + 0.548511I
b = −0.90942 + 2.53548I
−1.36351 − 5.67921I 0
u = 0.981412 − 0.431065I
a = −0.223258 − 0.548511I
b = −0.90942 − 2.53548I
−1.36351 + 5.67921I 0
u = −0.317603 + 1.029880I
a = 0.738089 + 0.182557I
b = −0.394609 − 0.139943I
2.52813 − 5.97540I 0
u = −0.317603 − 1.029880I
a = 0.738089 − 0.182557I
b = −0.394609 + 0.139943I
2.52813 + 5.97540I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.837908 + 0.678241I
a = 0.121692 + 0.727104I
b = 0.136863 + 0.671886I
−1.95759 − 0.96618I 0
u = 0.837908 − 0.678241I
a = 0.121692 − 0.727104I
b = 0.136863 − 0.671886I
−1.95759 + 0.96618I 0
u = −0.512310 + 0.756618I
a = 0.606670 + 0.399679I
b = −0.935028 − 0.211885I
5.51111 + 0.29685I 0
u = −0.512310 − 0.756618I
a = 0.606670 − 0.399679I
b = −0.935028 + 0.211885I
5.51111 − 0.29685I 0
u = 0.828584 + 0.381334I
a = 0.503067 − 0.205341I
b = 0.16421 − 2.09535I
1.043390 − 0.077155I 0
u = 0.828584 − 0.381334I
a = 0.503067 + 0.205341I
b = 0.16421 + 2.09535I
1.043390 + 0.077155I 0
u = 1.058120 + 0.256603I
a = −1.01557 − 2.26102I
b = −5.06775 − 4.40434I
−2.16722 + 1.22909I 0
u = 1.058120 − 0.256603I
a = −1.01557 + 2.26102I
b = −5.06775 + 4.40434I
−2.16722 − 1.22909I 0
u = −0.466250 + 0.776371I
a = 0.560277 + 0.937047I
b = 0.256482 + 0.978452I
5.25058 − 3.26329I 0
u = −0.466250 − 0.776371I
a = 0.560277 − 0.937047I
b = 0.256482 − 0.978452I
5.25058 + 3.26329I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.559973 + 0.701832I
a = −0.122269 − 1.190060I
b = −0.73943 − 1.42658I
3.91294 + 3.33139I 0
u = −0.559973 − 0.701832I
a = −0.122269 + 1.190060I
b = −0.73943 + 1.42658I
3.91294 − 3.33139I 0
u = −0.474478 + 0.750313I
a = −1.32644 − 0.77916I
b = −0.178485 + 0.171226I
2.53463 − 1.34948I 0
u = −0.474478 − 0.750313I
a = −1.32644 + 0.77916I
b = −0.178485 − 0.171226I
2.53463 + 1.34948I 0
u = −1.044460 + 0.385729I
a = 0.825952 − 0.850078I
b = 0.20319 − 2.10517I
−6.83212 + 1.55059I 0
u = −1.044460 − 0.385729I
a = 0.825952 + 0.850078I
b = 0.20319 + 2.10517I
−6.83212 − 1.55059I 0
u = −0.990638 + 0.518559I
a = −0.081721 − 0.174597I
b = 0.46452 − 1.69676I
−0.811795 − 0.033701I 0
u = −0.990638 − 0.518559I
a = −0.081721 + 0.174597I
b = 0.46452 + 1.69676I
−0.811795 + 0.033701I 0
u = −0.398632 + 0.786333I
a = −0.901507 − 0.177655I
b = 1.060920 + 0.745264I
2.99181 − 5.97516I 0
u = −0.398632 − 0.786333I
a = −0.901507 + 0.177655I
b = 1.060920 − 0.745264I
2.99181 + 5.97516I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.290527 + 0.822481I
a = −1.144460 − 0.470450I
b = 0.581196 − 0.418688I
−1.88588 − 6.17613I 0
u = −0.290527 − 0.822481I
a = −1.144460 + 0.470450I
b = 0.581196 + 0.418688I
−1.88588 + 6.17613I 0
u = 0.472564 + 0.729432I
a = −1.57022 + 0.41222I
b = −0.055546 + 0.288364I
−0.05649 + 8.46319I 0
u = 0.472564 − 0.729432I
a = −1.57022 − 0.41222I
b = −0.055546 − 0.288364I
−0.05649 − 8.46319I 0
u = −1.088280 + 0.308082I
a = −0.043277 + 0.880827I
b = 0.71897 + 1.35135I
−4.97493 + 8.44093I 0
u = −1.088280 − 0.308082I
a = −0.043277 − 0.880827I
b = 0.71897 − 1.35135I
−4.97493 − 8.44093I 0
u = −0.769403 + 0.835099I
a = 0.431762 + 1.005890I
b = 0.332293 + 0.402278I
7.67778 + 4.50262I 0
u = −0.769403 − 0.835099I
a = 0.431762 − 1.005890I
b = 0.332293 − 0.402278I
7.67778 − 4.50262I 0
u = −0.652157 + 0.565911I
a = −0.031239 − 0.512620I
b = 0.979124 − 0.815610I
0.24476 + 4.35802I 0
u = −0.652157 − 0.565911I
a = −0.031239 + 0.512620I
b = 0.979124 + 0.815610I
0.24476 − 4.35802I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.148040 + 0.030873I
a = −0.584553 − 0.223460I
b = −0.377488 + 1.193400I
−0.21515 + 1.52425I 0
u = 1.148040 − 0.030873I
a = −0.584553 + 0.223460I
b = −0.377488 − 1.193400I
−0.21515 − 1.52425I 0
u = −0.481013 + 0.698806I
a = −2.93028 + 2.18315I
b = 0.63041 + 1.54512I
2.38264 + 1.08657I 0
u = −0.481013 − 0.698806I
a = −2.93028 − 2.18315I
b = 0.63041 − 1.54512I
2.38264 − 1.08657I 0
u = 1.149730 + 0.158483I
a = 0.446799 + 0.141095I
b = 1.58806 + 2.71640I
−2.03338 + 3.54410I 0
u = 1.149730 − 0.158483I
a = 0.446799 − 0.141095I
b = 1.58806 − 2.71640I
−2.03338 − 3.54410I 0
u = 1.146180 + 0.207310I
a = 0.274420 + 0.481064I
b = 0.747757 + 0.781664I
−2.43454 − 0.65211I 0
u = 1.146180 − 0.207310I
a = 0.274420 − 0.481064I
b = 0.747757 − 0.781664I
−2.43454 + 0.65211I 0
u = −0.413101 + 0.717335I
a = 3.55572 − 2.20425I
b = −0.86064 − 1.38623I
2.07851 − 3.32587I 0
u = −0.413101 − 0.717335I
a = 3.55572 + 2.20425I
b = −0.86064 + 1.38623I
2.07851 + 3.32587I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.050790 + 0.525532I
a = −0.48189 + 1.94948I
b = −0.45554 + 4.01684I
−0.66742 + 3.20117I 0
u = −1.050790 − 0.525532I
a = −0.48189 − 1.94948I
b = −0.45554 − 4.01684I
−0.66742 − 3.20117I 0
u = −1.017740 + 0.590697I
a = −1.006030 − 0.052324I
b = −0.046679 + 0.477681I
2.54912 + 1.64137I 0
u = −1.017740 − 0.590697I
a = −1.006030 + 0.052324I
b = −0.046679 − 0.477681I
2.54912 − 1.64137I 0
u = 0.517253 + 0.639308I
a = 1.42468 − 0.33366I
b = 0.130747 − 0.590468I
1.66936 + 3.03245I 0
u = 0.517253 − 0.639308I
a = 1.42468 + 0.33366I
b = 0.130747 + 0.590468I
1.66936 − 3.03245I 0
u = 1.080400 + 0.473386I
a = −0.192927 + 0.923828I
b = 0.74352 + 2.70690I
−6.19030 − 5.36695I 0
u = 1.080400 − 0.473386I
a = −0.192927 − 0.923828I
b = 0.74352 − 2.70690I
−6.19030 + 5.36695I 0
u = 1.039580 + 0.567389I
a = 0.443316 − 1.163190I
b = 0.07752 − 2.31663I
0.11630 − 7.78284I 0
u = 1.039580 − 0.567389I
a = 0.443316 + 1.163190I
b = 0.07752 + 2.31663I
0.11630 + 7.78284I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.839393 + 0.852131I
a = −0.375365 − 1.126760I
b = −0.682131 − 0.637643I
6.51257 + 10.16590I 0
u = −0.839393 − 0.852131I
a = −0.375365 + 1.126760I
b = −0.682131 + 0.637643I
6.51257 − 10.16590I 0
u = −0.895793 + 0.800884I
a = 0.736249 + 0.470315I
b = 0.969097 + 0.407488I
7.30949 + 1.49107I 0
u = −0.895793 − 0.800884I
a = 0.736249 − 0.470315I
b = 0.969097 − 0.407488I
7.30949 − 1.49107I 0
u = −1.055370 + 0.584723I
a = 1.50865 − 1.86417I
b = 1.19876 − 4.01989I
0.69005 + 3.86115I 0
u = −1.055370 − 0.584723I
a = 1.50865 + 1.86417I
b = 1.19876 + 4.01989I
0.69005 − 3.86115I 0
u = −0.843190 + 0.867539I
a = −0.878343 − 0.479849I
b = −0.940281 + 0.010823I
6.51509 − 3.93547I 0
u = −0.843190 − 0.867539I
a = −0.878343 + 0.479849I
b = −0.940281 − 0.010823I
6.51509 + 3.93547I 0
u = −1.050840 + 0.613372I
a = 0.145511 + 0.459291I
b = 0.68200 + 2.06810I
3.90851 + 4.89501I 0
u = −1.050840 − 0.613372I
a = 0.145511 − 0.459291I
b = 0.68200 − 2.06810I
3.90851 − 4.89501I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.063410 + 0.603280I
a = −0.44157 − 1.36334I
b = −1.07733 − 2.39099I
0.79510 + 6.48971I 0
u = −1.063410 − 0.603280I
a = −0.44157 + 1.36334I
b = −1.07733 + 2.39099I
0.79510 − 6.48971I 0
u = 0.739784 + 0.235911I
a = −1.228770 − 0.046617I
b = 1.327670 − 0.162696I
−0.28743 + 2.46726I 0
u = 0.739784 − 0.235911I
a = −1.228770 + 0.046617I
b = 1.327670 + 0.162696I
−0.28743 − 2.46726I 0
u = 1.074460 + 0.591244I
a = −0.369587 + 1.282630I
b = −0.32208 + 2.62276I
−1.85183 − 13.51530I 0
u = 1.074460 − 0.591244I
a = −0.369587 − 1.282630I
b = −0.32208 − 2.62276I
−1.85183 + 13.51530I 0
u = −1.092390 + 0.576031I
a = −1.48479 + 2.32830I
b = −1.24202 + 5.21578I
0.07853 + 8.28625I 0
u = −1.092390 − 0.576031I
a = −1.48479 − 2.32830I
b = −1.24202 − 5.21578I
0.07853 − 8.28625I 0
u = −1.079320 + 0.611948I
a = 0.754645 + 0.504304I
b = 0.154231 + 0.870419I
3.42764 + 8.49889I 0
u = −1.079320 − 0.611948I
a = 0.754645 − 0.504304I
b = 0.154231 − 0.870419I
3.42764 − 8.49889I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.079741 + 0.736165I
a = −0.314998 − 0.249428I
b = −0.229924 + 0.332018I
0.47320 − 1.54565I 0
u = 0.079741 − 0.736165I
a = −0.314998 + 0.249428I
b = −0.229924 − 0.332018I
0.47320 + 1.54565I 0
u = −1.111260 + 0.599006I
a = 0.029722 − 0.613388I
b = −1.08300 − 2.40282I
0.88219 + 11.18370I 0
u = −1.111260 − 0.599006I
a = 0.029722 + 0.613388I
b = −1.08300 + 2.40282I
0.88219 − 11.18370I 0
u = 1.235710 + 0.264493I
a = 0.605549 + 0.644009I
b = 0.36825 + 1.96922I
−6.69476 + 2.77249I 0
u = 1.235710 − 0.264493I
a = 0.605549 − 0.644009I
b = 0.36825 − 1.96922I
−6.69476 − 2.77249I 0
u = 1.058680 + 0.692380I
a = −0.192799 − 0.514818I
b = −0.221356 − 1.004340I
−2.63922 − 4.76673I 0
u = 1.058680 − 0.692380I
a = −0.192799 + 0.514818I
b = −0.221356 + 1.004340I
−2.63922 + 4.76673I 0
u = −1.178700 + 0.524608I
a = 0.300674 + 0.162765I
b = 0.160493 + 0.623031I
−2.64106 + 6.15310I 0
u = −1.178700 − 0.524608I
a = 0.300674 − 0.162765I
b = 0.160493 − 0.623031I
−2.64106 − 6.15310I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.157590 + 0.580104I
a = −0.268942 − 0.899681I
b = −0.11495 − 2.60569I
−4.44426 + 11.38070I 0
u = −1.157590 − 0.580104I
a = −0.268942 + 0.899681I
b = −0.11495 + 2.60569I
−4.44426 − 11.38070I 0
u = −0.437680 + 0.519280I
a = 2.00279 − 1.41685I
b = −0.447731 − 0.431733I
1.10254 + 1.14634I 0
u = −0.437680 − 0.519280I
a = 2.00279 + 1.41685I
b = −0.447731 + 0.431733I
1.10254 − 1.14634I 0
u = −1.157090 + 0.652916I
a = −0.167899 − 0.878258I
b = −0.62249 − 1.88643I
1.14688 + 7.28909I 0
u = −1.157090 − 0.652916I
a = −0.167899 + 0.878258I
b = −0.62249 + 1.88643I
1.14688 − 7.28909I 0
u = 1.317060 + 0.189115I
a = −0.850340 − 0.566815I
b = −1.63473 − 1.55722I
−0.77366 + 5.05718I 0
u = 1.317060 − 0.189115I
a = −0.850340 + 0.566815I
b = −1.63473 + 1.55722I
−0.77366 − 5.05718I 0
u = −1.180870 + 0.628015I
a = 0.465890 + 1.183290I
b = 1.05045 + 2.73329I
2.3775 + 14.3079I 0
u = −1.180870 − 0.628015I
a = 0.465890 − 1.183290I
b = 1.05045 − 2.73329I
2.3775 − 14.3079I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.203170 + 0.626779I
a = −0.382671 − 1.300470I
b = −1.13716 − 3.14050I
0.2730 + 20.3086I 0
u = −1.203170 − 0.626779I
a = −0.382671 + 1.300470I
b = −1.13716 + 3.14050I
0.2730 − 20.3086I 0
u = 1.258840 + 0.506364I
a = −0.1205850 − 0.0723225I
b = −0.598161 − 0.453292I
−3.36270 + 0.14216I 0
u = 1.258840 − 0.506364I
a = −0.1205850 + 0.0723225I
b = −0.598161 + 0.453292I
−3.36270 − 0.14216I 0
u = 1.350980 + 0.219119I
a = 0.903858 + 0.665369I
b = 1.85937 + 2.10264I
−2.70777 + 10.63070I 0
u = 1.350980 − 0.219119I
a = 0.903858 − 0.665369I
b = 1.85937 − 2.10264I
−2.70777 − 10.63070I 0
u = −1.219100 + 0.647810I
a = −0.025791 + 0.736917I
b = 0.21000 + 1.97168I
−0.24586 + 11.98110I 0
u = −1.219100 − 0.647810I
a = −0.025791 − 0.736917I
b = 0.21000 − 1.97168I
−0.24586 − 11.98110I 0
u = 0.204706 + 0.546889I
a = −1.82421 + 0.16348I
b = 0.476881 + 0.682865I
−3.82479 + 1.32683I −4.12935 − 0.71634I
u = 0.204706 − 0.546889I
a = −1.82421 − 0.16348I
b = 0.476881 − 0.682865I
−3.82479 − 1.32683I −4.12935 + 0.71634I
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.038251 + 0.576915I
a = −0.814470 + 0.069028I
b = −0.233169 + 0.400339I
0.44265 − 1.56279I 1.64251 + 4.87377I
u = −0.038251 − 0.576915I
a = −0.814470 − 0.069028I
b = −0.233169 − 0.400339I
0.44265 + 1.56279I 1.64251 − 4.87377I
u = 1.37875 + 0.36014I
a = 0.120667 − 0.242214I
b = 0.756897 − 0.437187I
−3.69249 − 3.37191I 0
u = 1.37875 − 0.36014I
a = 0.120667 + 0.242214I
b = 0.756897 + 0.437187I
−3.69249 + 3.37191I 0
u = 1.43268 + 0.10472I
a = 0.033190 − 0.483172I
b = 0.26298 − 1.42989I
−3.90155 + 1.70271I 0
u = 1.43268 − 0.10472I
a = 0.033190 + 0.483172I
b = 0.26298 + 1.42989I
−3.90155 − 1.70271I 0
u = −0.154820 + 0.004285I
a = −3.23465 + 5.03526I
b = −0.497459 + 0.500059I
0.82272 − 1.37291I 5.33346 + 4.38312I
u = −0.154820 − 0.004285I
a = −3.23465 − 5.03526I
b = −0.497459 − 0.500059I
0.82272 + 1.37291I 5.33346 − 4.38312I
u = 0.0976486 + 0.0416017I
a = −8.65657 + 1.71514I
b = 0.586173 + 0.410305I
−0.15035 − 2.79872I 1.55621 + 1.54033I
u = 0.0976486 − 0.0416017I
a = −8.65657 − 1.71514I
b = 0.586173 − 0.410305I
−0.15035 + 2.79872I 1.55621 − 1.54033I
18
II. I
u
2
= ha
3
+ a
2
+ b, a
4
+ a
2
− a + 1, u − 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
1
a
3
=
1
1
a
9
=
a
−a
3
− a
2
a
6
=
a
2
−a
3
+ a
2
− a + 2
a
1
=
0
−1
a
10
=
a
−a
3
− a
2
− a
a
7
=
a
2
− a + 1
a
2
− a + 1
a
4
=
1
1
a
12
=
a
2
− a + 1
−2a
a
11
=
a
3
+ 1
a
3
− a
2
− a
a
8
=
a
2
− a + 1
a
2
− a + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = a
3
− 6a
2
+ 2a − 7
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
7
u
4
c
4
(u + 1)
4
c
5
, c
8
, c
9
u
4
+ u
2
+ u + 1
c
6
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
10
u
4
− 2u
3
+ 3u
2
− u + 1
c
11
u
4
+ u
2
− u + 1
c
12
u
4
+ 2u
3
+ 3u
2
+ u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
7
y
4
c
5
, c
8
, c
9
c
11
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
6
y
4
− y
3
+ 2y
2
+ 7y + 4
c
10
, c
12
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.547424 + 0.585652I
b = 0.442547 − 0.966840I
−0.66484 + 1.39709I −6.04449 − 2.35025I
u = 1.00000
a = 0.547424 − 0.585652I
b = 0.442547 + 0.966840I
−0.66484 − 1.39709I −6.04449 + 2.35025I
u = 1.00000
a = −0.547424 + 1.120870I
b = −0.94255 + 1.62772I
−4.26996 − 7.64338I −0.45551 + 9.20433I
u = 1.00000
a = −0.547424 − 1.120870I
b = −0.94255 − 1.62772I
−4.26996 + 7.64338I −0.45551 − 9.20433I
22
III.
I
u
3
= h3a
5
+a
4
+5a
3
+3a
2
+b+2a+4, a
6
+a
5
+2a
4
+2a
3
+2a
2
+2a+1, u−1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
1
a
3
=
1
1
a
9
=
a
−3a
5
− a
4
− 5a
3
− 3a
2
− 2a − 4
a
6
=
a
2
2a
5
+ a
4
+ 3a
3
+ 4a
2
+ 2a + 4
a
1
=
0
−1
a
10
=
a
−3a
5
− a
4
− 5a
3
− 3a
2
− 3a − 4
a
7
=
−a
4
−a
4
a
4
=
1
1
a
12
=
−a
4
−2a
4
− 2a
2
− 2
a
11
=
a
5
+ a
3
+ a
2
+ a
a
5
− a
4
+ a
3
− a
2
+ a − 2
a
8
=
−a
4
−a
4
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3a
5
+ a
4
+ 4a
2
− 3a + 1
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
7
u
6
c
4
(u + 1)
6
c
5
, c
8
, c
9
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
6
(u
3
− u
2
+ 1)
2
c
10
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
11
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
12
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
7
y
6
c
5
, c
8
, c
9
c
11
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
6
(y
3
− y
2
+ 2y −1)
2
c
10
, c
12
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.498832 + 1.001300I
b = 0.69405 + 1.33333I
−1.91067 + 2.82812I −0.06063 − 4.05868I
u = 1.00000
a = 0.498832 − 1.001300I
b = 0.69405 − 1.33333I
−1.91067 − 2.82812I −0.06063 + 4.05868I
u = 1.00000
a = −0.284920 + 1.115140I
b = −0.33764 + 1.86817I
−6.04826 −7.59911 − 2.50363I
u = 1.00000
a = −0.284920 − 1.115140I
b = −0.33764 − 1.86817I
−6.04826 −7.59911 + 2.50363I
u = 1.00000
a = −0.713912 + 0.305839I
b = −3.35641 − 1.89561I
−1.91067 + 2.82812I 5.15973 − 2.26538I
u = 1.00000
a = −0.713912 − 0.305839I
b = −3.35641 + 1.89561I
−1.91067 − 2.82812I 5.15973 + 2.26538I
26
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
10
)(u
140
+ 69u
139
+ ··· + 221u + 1)
c
2
((u − 1)
10
)(u
140
− 11u
139
+ ··· − 5u + 1)
c
3
, c
7
u
10
(u
140
− u
139
+ ··· − 8192u + 1024)
c
4
((u + 1)
10
)(u
140
− 11u
139
+ ··· − 5u + 1)
c
5
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
140
− 2u
139
+ ··· − 24012u + 5887)
c
6
(u
3
− u
2
+ 1)
2
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
· (u
140
+ 2u
139
+ ··· − 10624u + 1216)
c
8
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
140
+ 2u
139
+ ··· + 14u + 1)
c
9
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
140
+ 14u
139
+ ··· + 2u + 1)
c
10
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
140
+ 58u
139
+ ··· + 14u + 1)
c
11
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
140
+ 2u
139
+ ··· + 14u + 1)
c
12
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
140
− 10u
139
+ ··· − 2u + 1)
27
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
10
)(y
140
+ 15y
139
+ ··· − 2817y + 1)
c
2
, c
4
((y −1)
10
)(y
140
− 69y
139
+ ··· − 221y + 1)
c
3
, c
7
y
10
(y
140
− 63y
139
+ ··· − 2.56901 × 10
7
y + 1048576)
c
5
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
140
+ 142y
139
+ ··· + 261556046y + 34656769)
c
6
(y
3
− y
2
+ 2y −1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
140
+ 150y
139
+ ··· + 35716096y + 1478656)
c
8
, c
11
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
140
+ 58y
139
+ ··· + 14y + 1)
c
9
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
140
+ 10y
139
+ ··· + 14y + 1)
c
10
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
140
+ 50y
139
+ ··· − 2010y + 1)
c
12
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
140
+ 14y
139
+ ··· + 10y + 1)
28
