12a
0131
(K12a
0131
)
A knot diagram
1
Linearized knot diagam
3 5 8 6 2 11 10 4 12 1 9 7
Solving Sequence
9,12 4,10
8 3 7 1 11 6 5 2
c
9
c
8
c
3
c
7
c
12
c
11
c
6
c
4
c
2
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.64768 × 10
518
u
124
− 8.42800 × 10
518
u
123
+ ··· + 4.89215 × 10
516
b + 1.49453 × 10
519
,
3.73739 × 10
519
u
124
− 1.18654 × 10
520
u
123
+ ··· + 9.78430 × 10
516
a + 2.09349 × 10
520
,
u
125
− 3u
124
+ ··· + 17u + 1i
I
u
2
= hb, −u
5
a + 2u
4
a + u
5
− 3u
4
− 2u
2
a + 3u
3
+ a
2
+ au − 2u + 1, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 137 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
= h2.65 × 10
518
u
124
− 8.43 × 10
518
u
123
+ · · · + 4.89 × 10
516
b + 1.49 ×
10
519
, 3.74 × 10
519
u
124
− 1.19 × 10
520
u
123
+ · · · + 9.78 × 10
516
a + 2.09 ×
10
520
, u
125
− 3u
124
+ · · · + 17u + 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
4
=
−381.979u
124
+ 1212.70u
123
+ ··· − 24299.3u − 2139.65
−54.1209u
124
+ 172.276u
123
+ ··· − 3476.17u − 305.495
a
10
=
1
−u
2
a
8
=
182.743u
124
− 578.359u
123
+ ··· + 11566.7u + 1015.20
12.4867u
124
− 41.0452u
123
+ ··· + 888.570u + 77.2473
a
3
=
−525.800u
124
+ 1672.25u
123
+ ··· − 33602.3u − 2955.69
−87.0132u
124
+ 275.060u
123
+ ··· − 5477.59u − 481.773
a
7
=
162.525u
124
− 515.547u
123
+ ··· + 10348.7u + 907.820
14.2770u
124
− 45.0112u
123
+ ··· + 905.020u + 79.4042
a
1
=
−136.294u
124
+ 433.527u
123
+ ··· − 8784.44u − 770.986
−24.6461u
124
+ 77.8439u
123
+ ··· − 1546.01u − 136.294
a
11
=
−u
u
a
6
=
169.080u
124
− 534.889u
123
+ ··· + 10684.5u + 937.972
7.72249u
124
− 25.6696u
123
+ ··· + 569.242u + 49.2525
a
5
=
−591.960u
124
+ 1881.43u
123
+ ··· − 37752.9u − 3321.58
−94.7243u
124
+ 300.362u
123
+ ··· − 6018.61u − 528.924
a
2
=
99.7178u
124
− 314.202u
123
+ ··· + 6266.98u + 544.092
−18.8512u
124
+ 58.0831u
123
+ ··· − 1084.59u − 96.9655
(ii) Obstruction class = −1
(iii) Cusp Shapes = −323.549u
124
+ 1024.38u
123
+ ··· − 20264.6u − 1780.82
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
125
+ 41u
124
+ ··· − 145u − 1
c
2
, c
5
u
125
+ 7u
124
+ ··· − 9u − 1
c
3
, c
8
u
125
− u
124
+ ··· + 20480u − 4096
c
6
u
125
+ 3u
124
+ ··· − 6561489u + 604147
c
7
u
125
+ 9u
124
+ ··· + 391375u + 25489
c
9
, c
11
u
125
+ 3u
124
+ ··· + 17u − 1
c
10
u
125
− 21u
124
+ ··· − 3u + 1
c
12
u
125
− 9u
124
+ ··· − 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
125
+ 93y
124
+ ··· + 5099y −1
c
2
, c
5
y
125
+ 41y
124
+ ··· − 145y −1
c
3
, c
8
y
125
− 65y
124
+ ··· + 301989888y −16777216
c
6
y
125
− 91y
124
+ ··· − 24775319389441y −364993597609
c
7
y
125
− 127y
124
+ ··· + 36942460527y −649689121
c
9
, c
11
y
125
− 83y
124
+ ··· − 17y −1
c
10
y
125
− 3y
124
+ ··· − 17y −1
c
12
y
125
+ 21y
124
+ ··· − 9y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.003630 + 0.091762I
a = −3.97740 − 2.38530I
b = 0.818217 − 0.461607I
−0.01102 − 2.45400I 0
u = −1.003630 − 0.091762I
a = −3.97740 + 2.38530I
b = 0.818217 + 0.461607I
−0.01102 + 2.45400I 0
u = −0.982156 + 0.100911I
a = −2.15785 + 4.64167I
b = 0.310656 + 0.355934I
1.72895 − 2.62928I 0
u = −0.982156 − 0.100911I
a = −2.15785 − 4.64167I
b = 0.310656 − 0.355934I
1.72895 + 2.62928I 0
u = −0.112173 + 0.977335I
a = −0.393390 + 1.060410I
b = 0.267605 + 0.980914I
0.76237 − 1.42438I 0
u = −0.112173 − 0.977335I
a = −0.393390 − 1.060410I
b = 0.267605 − 0.980914I
0.76237 + 1.42438I 0
u = 0.239455 + 0.994751I
a = 0.314123 − 0.696394I
b = −0.594765 − 0.685477I
−4.30119 − 2.18209I 0
u = 0.239455 − 0.994751I
a = 0.314123 + 0.696394I
b = −0.594765 + 0.685477I
−4.30119 + 2.18209I 0
u = 1.013110 + 0.179661I
a = −2.25528 + 0.34509I
b = 1.304260 + 0.497331I
−0.34954 + 4.52947I 0
u = 1.013110 − 0.179661I
a = −2.25528 − 0.34509I
b = 1.304260 − 0.497331I
−0.34954 − 4.52947I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.039630 + 0.023694I
a = 0.67319 − 3.23584I
b = 0.130567 + 0.838675I
2.45673 − 2.54518I 0
u = −1.039630 − 0.023694I
a = 0.67319 + 3.23584I
b = 0.130567 − 0.838675I
2.45673 + 2.54518I 0
u = −0.109764 + 1.042850I
a = −0.728339 − 0.206603I
b = 1.040380 − 0.309779I
1.20280 − 4.30451I 0
u = −0.109764 − 1.042850I
a = −0.728339 + 0.206603I
b = 1.040380 + 0.309779I
1.20280 + 4.30451I 0
u = −1.05632
a = 5.26697
b = −0.911297
3.09971 0
u = 1.053350 + 0.126987I
a = −1.83858 + 0.07436I
b = 1.248250 − 0.599242I
1.78016 + 4.49817I 0
u = 1.053350 − 0.126987I
a = −1.83858 − 0.07436I
b = 1.248250 + 0.599242I
1.78016 − 4.49817I 0
u = −1.038390 + 0.225291I
a = −0.352291 + 0.467094I
b = −0.188310 + 0.258966I
1.92047 − 0.80353I 0
u = −1.038390 − 0.225291I
a = −0.352291 − 0.467094I
b = −0.188310 − 0.258966I
1.92047 + 0.80353I 0
u = −0.046115 + 1.076500I
a = 0.299835 − 0.965828I
b = −0.395582 − 1.031400I
0.16327 − 6.85626I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.046115 − 1.076500I
a = 0.299835 + 0.965828I
b = −0.395582 + 1.031400I
0.16327 + 6.85626I 0
u = 0.625338 + 0.884155I
a = −0.088385 + 0.576244I
b = 0.879634 + 0.009949I
−0.67458 − 2.99174I 0
u = 0.625338 − 0.884155I
a = −0.088385 − 0.576244I
b = 0.879634 − 0.009949I
−0.67458 + 2.99174I 0
u = 1.080410 + 0.075085I
a = −0.351541 + 0.913041I
b = 0.52839 − 1.46115I
3.28804 + 3.77271I 0
u = 1.080410 − 0.075085I
a = −0.351541 − 0.913041I
b = 0.52839 + 1.46115I
3.28804 − 3.77271I 0
u = 0.850915 + 0.292810I
a = −0.792606 − 0.010998I
b = 0.682547 + 0.867427I
−2.63980 + 3.08960I 0
u = 0.850915 − 0.292810I
a = −0.792606 + 0.010998I
b = 0.682547 − 0.867427I
−2.63980 − 3.08960I 0
u = 1.106890 + 0.037877I
a = 0.553072 + 0.744699I
b = −0.56971 − 1.42281I
4.17272 + 2.48498I 0
u = 1.106890 − 0.037877I
a = 0.553072 − 0.744699I
b = −0.56971 + 1.42281I
4.17272 − 2.48498I 0
u = 1.113830 + 0.017169I
a = 2.01483 + 0.00282I
b = −1.46526 − 0.55623I
4.64685 + 0.82915I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.113830 − 0.017169I
a = 2.01483 − 0.00282I
b = −1.46526 + 0.55623I
4.64685 − 0.82915I 0
u = 0.551143 + 0.972708I
a = 0.136281 − 0.596937I
b = −0.911041 − 0.235645I
−0.90323 + 2.21060I 0
u = 0.551143 − 0.972708I
a = 0.136281 + 0.596937I
b = −0.911041 + 0.235645I
−0.90323 − 2.21060I 0
u = −1.114330 + 0.144086I
a = −3.26348 − 1.21677I
b = 1.224000 − 0.514814I
5.73499 − 7.52961I 0
u = −1.114330 − 0.144086I
a = −3.26348 + 1.21677I
b = 1.224000 + 0.514814I
5.73499 + 7.52961I 0
u = −1.122540 + 0.112281I
a = 3.44318 + 1.02925I
b = −1.232750 + 0.406885I
6.52143 − 1.68218I 0
u = −1.122540 − 0.112281I
a = 3.44318 − 1.02925I
b = −1.232750 − 0.406885I
6.52143 + 1.68218I 0
u = 0.056373 + 1.126940I
a = 0.668400 + 0.571949I
b = −1.003520 + 0.542763I
−3.00982 − 6.94600I 0
u = 0.056373 − 1.126940I
a = 0.668400 − 0.571949I
b = −1.003520 − 0.542763I
−3.00982 + 6.94600I 0
u = −0.864045 + 0.092430I
a = 1.48819 − 1.26345I
b = 0.687136 + 0.522380I
−0.39162 + 1.59192I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.864045 − 0.092430I
a = 1.48819 + 1.26345I
b = 0.687136 − 0.522380I
−0.39162 − 1.59192I 0
u = 0.944897 + 0.622415I
a = −0.279539 + 0.291335I
b = 0.766133 + 0.309948I
0.35042 + 8.49800I 0
u = 0.944897 − 0.622415I
a = −0.279539 − 0.291335I
b = 0.766133 − 0.309948I
0.35042 − 8.49800I 0
u = 0.012357 + 0.858107I
a = 1.322470 + 0.205051I
b = −0.804293 + 0.281983I
−1.140860 − 0.185574I 0
u = 0.012357 − 0.858107I
a = 1.322470 − 0.205051I
b = −0.804293 − 0.281983I
−1.140860 + 0.185574I 0
u = 0.668706 + 0.474679I
a = 0.167838 + 0.706366I
b = 0.450382 − 0.628106I
−3.11701 + 0.35524I 0
u = 0.668706 − 0.474679I
a = 0.167838 − 0.706366I
b = 0.450382 + 0.628106I
−3.11701 − 0.35524I 0
u = −0.998504 + 0.639377I
a = −0.153096 − 0.381054I
b = −0.576307 − 0.526668I
0.652314 − 1.029720I 0
u = −0.998504 − 0.639377I
a = −0.153096 + 0.381054I
b = −0.576307 + 0.526668I
0.652314 + 1.029720I 0
u = 1.125470 + 0.392351I
a = 0.359799 + 0.247253I
b = −0.160029 − 0.909740I
1.30610 + 5.13081I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.125470 − 0.392351I
a = 0.359799 − 0.247253I
b = −0.160029 + 0.909740I
1.30610 − 5.13081I 0
u = −1.194780 + 0.075780I
a = 1.42591 − 1.82909I
b = −0.440536 − 0.347780I
2.22327 + 1.42836I 0
u = −1.194780 − 0.075780I
a = 1.42591 + 1.82909I
b = −0.440536 + 0.347780I
2.22327 − 1.42836I 0
u = 1.183740 + 0.261203I
a = 1.89132 − 0.39755I
b = −1.39565 − 0.72651I
7.45341 + 5.28303I 0
u = 1.183740 − 0.261203I
a = 1.89132 + 0.39755I
b = −1.39565 + 0.72651I
7.45341 − 5.28303I 0
u = 1.172770 + 0.313622I
a = −1.87155 + 0.48256I
b = 1.34558 + 0.77808I
6.22986 + 11.45440I 0
u = 1.172770 − 0.313622I
a = −1.87155 − 0.48256I
b = 1.34558 − 0.77808I
6.22986 − 11.45440I 0
u = −0.704619 + 0.330068I
a = 1.12653 − 1.06495I
b = 1.179890 + 0.411487I
4.79797 + 5.99082I 0
u = −0.704619 − 0.330068I
a = 1.12653 + 1.06495I
b = 1.179890 − 0.411487I
4.79797 − 5.99082I 0
u = 1.036090 + 0.650073I
a = 0.130173 − 0.283963I
b = −0.718749 − 0.004737I
0.64386 + 3.59414I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.036090 − 0.650073I
a = 0.130173 + 0.283963I
b = −0.718749 + 0.004737I
0.64386 − 3.59414I 0
u = −0.584340 + 1.104670I
a = −0.201920 + 0.122143I
b = 1.261580 + 0.192500I
6.19530 − 3.43221I 0
u = −0.584340 − 1.104670I
a = −0.201920 − 0.122143I
b = 1.261580 − 0.192500I
6.19530 + 3.43221I 0
u = −0.021698 + 1.281390I
a = −0.408314 − 0.458618I
b = 1.248900 − 0.574848I
3.88678 − 7.08241I 0
u = −0.021698 − 1.281390I
a = −0.408314 + 0.458618I
b = 1.248900 + 0.574848I
3.88678 + 7.08241I 0
u = −0.687479 + 1.083920I
a = 0.125109 − 0.159026I
b = −1.235130 − 0.322869I
5.75964 + 2.41343I 0
u = −0.687479 − 1.083920I
a = 0.125109 + 0.159026I
b = −1.235130 + 0.322869I
5.75964 − 2.41343I 0
u = −0.623835 + 0.327479I
a = −1.18028 + 0.99719I
b = −1.186940 − 0.283113I
5.39776 + 0.24395I 0
u = −0.623835 − 0.327479I
a = −1.18028 − 0.99719I
b = −1.186940 + 0.283113I
5.39776 − 0.24395I 0
u = 0.028319 + 1.301680I
a = 0.381596 + 0.524313I
b = −1.235670 + 0.655146I
2.84254 − 12.99610I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.028319 − 1.301680I
a = 0.381596 − 0.524313I
b = −1.235670 − 0.655146I
2.84254 + 12.99610I 0
u = 1.206280 + 0.562767I
a = −0.134327 − 0.307209I
b = −0.435625 + 0.751365I
−1.27865 + 7.70761I 0
u = 1.206280 − 0.562767I
a = −0.134327 + 0.307209I
b = −0.435625 − 0.751365I
−1.27865 − 7.70761I 0
u = 0.210808 + 0.613821I
a = −0.833651 + 0.257889I
b = 0.118571 + 0.552585I
−1.40641 − 1.21884I 0
u = 0.210808 − 0.613821I
a = −0.833651 − 0.257889I
b = 0.118571 − 0.552585I
−1.40641 + 1.21884I 0
u = 1.296410 + 0.456800I
a = 2.01682 − 0.61181I
b = −1.157670 − 0.272520I
2.84396 + 4.99238I 0
u = 1.296410 − 0.456800I
a = 2.01682 + 0.61181I
b = −1.157670 + 0.272520I
2.84396 − 4.99238I 0
u = −1.358600 + 0.282911I
a = 1.89560 − 0.24501I
b = −0.751539 − 0.210200I
2.34856 + 1.43127I 0
u = −1.358600 − 0.282911I
a = 1.89560 + 0.24501I
b = −0.751539 + 0.210200I
2.34856 − 1.43127I 0
u = 1.394310 + 0.224132I
a = 1.75711 − 0.20635I
b = −1.59703 + 0.10582I
12.64840 + 1.23482I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.394310 − 0.224132I
a = 1.75711 + 0.20635I
b = −1.59703 − 0.10582I
12.64840 − 1.23482I 0
u = 1.34392 + 0.46774I
a = 0.212460 + 0.407369I
b = 0.356486 − 1.260450I
5.23935 + 6.54595I 0
u = 1.34392 − 0.46774I
a = 0.212460 − 0.407369I
b = 0.356486 + 1.260450I
5.23935 − 6.54595I 0
u = 1.41177 + 0.27659I
a = −1.74801 + 0.27510I
b = 1.59117 + 0.00580I
12.7252 + 7.6247I 0
u = 1.41177 − 0.27659I
a = −1.74801 − 0.27510I
b = 1.59117 − 0.00580I
12.7252 − 7.6247I 0
u = −1.28033 + 0.66068I
a = 1.50434 + 1.03430I
b = −0.931017 + 0.395630I
1.67799 − 4.80704I 0
u = −1.28033 − 0.66068I
a = 1.50434 − 1.03430I
b = −0.931017 − 0.395630I
1.67799 + 4.80704I 0
u = 1.35929 + 0.48402I
a = −1.82786 + 0.65853I
b = 1.280880 + 0.413506I
5.74950 + 9.66103I 0
u = 1.35929 − 0.48402I
a = −1.82786 − 0.65853I
b = 1.280880 − 0.413506I
5.74950 − 9.66103I 0
u = 1.35560 + 0.50945I
a = −0.188960 − 0.410287I
b = −0.474298 + 1.244750I
4.53531 + 12.42450I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.35560 − 0.50945I
a = −0.188960 + 0.410287I
b = −0.474298 − 1.244750I
4.53531 − 12.42450I 0
u = 1.34176 + 0.55145I
a = 1.78812 − 0.84581I
b = −1.164220 − 0.571326I
1.03911 + 12.82610I 0
u = 1.34176 − 0.55145I
a = 1.78812 + 0.84581I
b = −1.164220 + 0.571326I
1.03911 − 12.82610I 0
u = −1.38517 + 0.57374I
a = −0.333577 − 0.332157I
b = −0.185085 − 1.020160I
4.41420 − 4.52899I 0
u = −1.38517 − 0.57374I
a = −0.333577 + 0.332157I
b = −0.185085 + 1.020160I
4.41420 + 4.52899I 0
u = 0.057985 + 0.496616I
a = 0.625520 + 0.187481I
b = 1.165890 − 0.616248I
3.00041 − 8.24027I 2.00000 + 4.16679I
u = 0.057985 − 0.496616I
a = 0.625520 − 0.187481I
b = 1.165890 + 0.616248I
3.00041 + 8.24027I 2.00000 − 4.16679I
u = −1.42505 + 0.47694I
a = 0.390319 + 0.371697I
b = 0.009283 + 1.000550I
4.58964 + 0.88814I 0
u = −1.42505 − 0.47694I
a = 0.390319 − 0.371697I
b = 0.009283 − 1.000550I
4.58964 − 0.88814I 0
u = 1.41127 + 0.57553I
a = −1.61400 + 0.78068I
b = 1.32951 + 0.70113I
8.4195 + 13.4799I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41127 − 0.57553I
a = −1.61400 − 0.78068I
b = 1.32951 − 0.70113I
8.4195 − 13.4799I 0
u = 1.40529 + 0.59972I
a = 1.58505 − 0.82652I
b = −1.29307 − 0.76159I
7.2064 + 19.5482I 0
u = 1.40529 − 0.59972I
a = 1.58505 + 0.82652I
b = −1.29307 + 0.76159I
7.2064 − 19.5482I 0
u = −1.43282 + 0.53553I
a = −1.53681 − 0.52917I
b = 1.060380 − 0.089433I
5.22915 − 1.86813I 0
u = −1.43282 − 0.53553I
a = −1.53681 + 0.52917I
b = 1.060380 + 0.089433I
5.22915 + 1.86813I 0
u = −0.014121 + 0.456602I
a = −0.877616 − 0.209246I
b = −1.165790 + 0.522208I
3.99062 − 2.47202I 4.97922 − 0.67353I
u = −0.014121 − 0.456602I
a = −0.877616 + 0.209246I
b = −1.165790 − 0.522208I
3.99062 + 2.47202I 4.97922 + 0.67353I
u = −1.42562 + 0.83441I
a = 1.102050 + 0.853846I
b = −1.280800 + 0.557576I
7.89271 − 10.20530I 0
u = −1.42562 − 0.83441I
a = 1.102050 − 0.853846I
b = −1.280800 − 0.557576I
7.89271 + 10.20530I 0
u = −1.45842 + 0.78770I
a = −1.148630 − 0.788635I
b = 1.299280 − 0.458696I
8.74385 − 4.24214I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.45842 − 0.78770I
a = −1.148630 + 0.788635I
b = 1.299280 + 0.458696I
8.74385 + 4.24214I 0
u = 0.028788 + 0.275966I
a = −2.84672 + 3.05328I
b = 0.683163 + 0.017853I
−0.66370 − 2.83474I 3.37234 + 5.05490I
u = 0.028788 − 0.275966I
a = −2.84672 − 3.05328I
b = 0.683163 − 0.017853I
−0.66370 + 2.83474I 3.37234 − 5.05490I
u = −1.68644 + 0.39726I
a = −1.168950 − 0.169636I
b = 1.311260 + 0.345336I
9.42374 − 0.00303I 0
u = −1.68644 − 0.39726I
a = −1.168950 + 0.169636I
b = 1.311260 − 0.345336I
9.42374 + 0.00303I 0
u = 0.159611 + 0.211315I
a = −0.12907 + 1.61974I
b = 0.867715 − 0.605551I
−2.31917 − 2.48205I −2.69773 + 2.44933I
u = 0.159611 − 0.211315I
a = −0.12907 − 1.61974I
b = 0.867715 + 0.605551I
−2.31917 + 2.48205I −2.69773 − 2.44933I
u = −1.71298 + 0.33924I
a = 1.125470 + 0.100393I
b = −1.290840 − 0.457455I
8.75351 + 5.95447I 0
u = −1.71298 − 0.33924I
a = 1.125470 − 0.100393I
b = −1.290840 + 0.457455I
8.75351 − 5.95447I 0
u = −0.164114 + 0.107295I
a = −3.33164 + 0.86262I
b = −0.863198 + 0.199616I
1.45688 − 0.48467I 7.00982 + 0.32488I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.164114 − 0.107295I
a = −3.33164 − 0.86262I
b = −0.863198 − 0.199616I
1.45688 + 0.48467I 7.00982 − 0.32488I
u = −0.177721 + 0.000193I
a = −2.45913 − 5.53903I
b = −0.125986 − 0.790649I
1.04154 + 2.17510I 2.60677 − 4.61609I
u = −0.177721 − 0.000193I
a = −2.45913 + 5.53903I
b = −0.125986 + 0.790649I
1.04154 − 2.17510I 2.60677 + 4.61609I
u = −0.0486880 + 0.1279180I
a = −2.68538 + 5.94050I
b = 0.338372 + 0.815233I
0.62427 − 2.85549I 1.37496 + 1.53556I
u = −0.0486880 − 0.1279180I
a = −2.68538 − 5.94050I
b = 0.338372 − 0.815233I
0.62427 + 2.85549I 1.37496 − 1.53556I
17
II. I
u
2
= hb, −u
5
a + u
5
+ · · · + a
2
+ 1, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
4
=
a
0
a
10
=
1
−u
2
a
8
=
1
0
a
3
=
a
0
a
7
=
−u
2
+ 1
u
4
a
1
=
−u
5
+ 2u
3
− u
u
5
− u
4
− 2u
3
+ u
2
+ u − 1
a
11
=
−u
u
a
6
=
u
5
− 2u
3
+ u
−u
5
+ u
4
+ 2u
3
− u
2
− u + 1
a
5
=
−2u
5
a + 2u
3
a − 2u
2
a − 2au + 2a
2u
5
a − 2u
3
a + 2u
2
a + au − 2a
a
2
=
−2u
5
+ 2u
4
+ 2u
3
− 2u
2
+ a
u
5
− u
4
− 2u
3
+ u
2
+ u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −u
5
a + 5u
4
a + u
5
+ u
3
a − 7u
4
− 5u
2
a + 3u
3
− au + 4u
2
+ a − 6u − 1
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
(u
2
− u + 1)
6
c
2
(u
2
+ u + 1)
6
c
3
, c
8
u
12
c
6
, c
10
, c
11
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
7
, c
12
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
c
9
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
6
c
3
, c
8
y
12
c
6
, c
9
, c
10
c
11
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
c
7
, c
12
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 + 0.295542I
a = −0.82520 + 2.42341I
b = 0
1.89061 − 2.95419I 11.02954 + 8.16480I
u = −1.002190 + 0.295542I
a = 2.51133 − 0.49706I
b = 0
1.89061 + 1.10558I −0.484082 − 0.231437I
u = −1.002190 − 0.295542I
a = −0.82520 − 2.42341I
b = 0
1.89061 + 2.95419I 11.02954 − 8.16480I
u = −1.002190 − 0.295542I
a = 2.51133 + 0.49706I
b = 0
1.89061 − 1.10558I −0.484082 + 0.231437I
u = 0.428243 + 0.664531I
a = 0.489858 + 0.681154I
b = 0
−1.89061 + 1.10558I −1.04064 − 1.99047I
u = 0.428243 + 0.664531I
a = −0.834826 + 0.083652I
b = 0
−1.89061 − 2.95419I −3.79900 + 4.11613I
u = 0.428243 − 0.664531I
a = 0.489858 − 0.681154I
b = 0
−1.89061 − 1.10558I −1.04064 + 1.99047I
u = 0.428243 − 0.664531I
a = −0.834826 − 0.083652I
b = 0
−1.89061 + 2.95419I −3.79900 − 4.11613I
u = 1.073950 + 0.558752I
a = 0.458424 − 0.081263I
b = 0
7.72290I 2.83009 − 4.64337I
u = 1.073950 + 0.558752I
a = −0.299588 − 0.356375I
b = 0
3.66314I −2.53591 − 3.55776I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.073950 − 0.558752I
a = 0.458424 + 0.081263I
b = 0
− 7.72290I 2.83009 + 4.64337I
u = 1.073950 − 0.558752I
a = −0.299588 + 0.356375I
b = 0
− 3.66314I −2.53591 + 3.55776I
22
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
((u
2
− u + 1)
6
)(u
125
+ 41u
124
+ ··· − 145u − 1)
c
2
((u
2
+ u + 1)
6
)(u
125
+ 7u
124
+ ··· − 9u − 1)
c
3
, c
8
u
12
(u
125
− u
124
+ ··· + 20480u − 4096)
c
5
((u
2
− u + 1)
6
)(u
125
+ 7u
124
+ ··· − 9u − 1)
c
6
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
· (u
125
+ 3u
124
+ ··· − 6561489u + 604147)
c
7
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
· (u
125
+ 9u
124
+ ··· + 391375u + 25489)
c
9
((u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
)(u
125
+ 3u
124
+ ··· + 17u − 1)
c
10
((u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
)(u
125
− 21u
124
+ ··· − 3u + 1)
c
11
((u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
)(u
125
+ 3u
124
+ ··· + 17u − 1)
c
12
((u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
)(u
125
− 9u
124
+ ··· − 3u + 1)
23
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
6
)(y
125
+ 93y
124
+ ··· + 5099y −1)
c
2
, c
5
((y
2
+ y + 1)
6
)(y
125
+ 41y
124
+ ··· − 145y −1)
c
3
, c
8
y
12
(y
125
− 65y
124
+ ··· + 3.01990 × 10
8
y −1.67772 × 10
7
)
c
6
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
125
− 91y
124
+ ··· − 24775319389441y −364993597609)
c
7
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
125
− 127y
124
+ ··· + 36942460527y −649689121)
c
9
, c
11
((y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
)(y
125
− 83y
124
+ ··· − 17y −1)
c
10
((y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
)(y
125
− 3y
124
+ ··· − 17y −1)
c
12
((y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
)(y
125
+ 21y
124
+ ··· − 9y −1)
24
