12a
0007
(K12a
0007
)
A knot diagram
1
Linearized knot diagam
3 5 6 8 2 10 11 4 12 1 9 7
Solving Sequence
9,11
12
4,10
8 5 7 1 6 3 2
c
11
c
9
c
8
c
4
c
7
c
12
c
6
c
3
c
2
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3.08638 × 10
606
u
134
− 6.53711 × 10
606
u
133
+ ··· + 2.81019 × 10
607
b − 1.77254 × 10
608
,
1.92887 × 10
608
u
134
+ 5.80661 × 10
608
u
133
+ ··· + 1.40510 × 10
607
a + 7.83298 × 10
608
,
u
135
+ 3u
134
+ ··· + 23u − 1i
I
u
2
= h−u
4
b − u
3
b + 2u
4
+ u
2
b + 4u
3
+ b
2
− b − u + 2, a, u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 145 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
= h3.09 × 10
606
u
134
− 6.54 × 10
606
u
133
+ · · · + 2.81 × 10
607
b − 1.77 ×
10
608
, 1.93 × 10
608
u
134
+ 5.81 × 10
608
u
133
+ · · · + 1.41 × 10
607
a + 7.83 ×
10
608
, u
135
+ 3u
134
+ · · · + 23u − 1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
4
=
−13.7277u
134
− 41.3254u
133
+ ··· + 1183.14u − 55.7469
−0.109828u
134
+ 0.232621u
133
+ ··· − 105.020u + 6.30755
a
10
=
u
−u
3
+ u
a
8
=
10.5104u
134
+ 28.1213u
133
+ ··· − 1273.21u + 77.3616
5.06292u
134
+ 13.4726u
133
+ ··· + 44.0782u − 4.59033
a
5
=
−13.0648u
134
− 34.5807u
133
+ ··· + 1060.19u − 61.4604
−3.59206u
134
− 9.85582u
133
+ ··· + 61.8222u − 1.81266
a
7
=
5.44751u
134
+ 14.6486u
133
+ ··· − 1317.28u + 81.9520
5.06292u
134
+ 13.4726u
133
+ ··· + 44.0782u − 4.59033
a
1
=
−5.24791u
134
− 8.31601u
133
+ ··· − 654.297u + 37.1633
1.85841u
134
+ 4.39282u
133
+ ··· + 18.2202u − 2.17981
a
6
=
10.4058u
134
+ 26.7954u
133
+ ··· − 1291.76u + 80.7778
4.74187u
134
+ 13.2057u
133
+ ··· + 1.89833u − 3.03646
a
3
=
−5.13933u
134
− 9.01892u
133
+ ··· − 9.48553u − 6.83756
−2.44953u
134
− 7.38833u
133
+ ··· + 199.596u − 10.1484
a
2
=
5.18030u
134
+ 17.5516u
133
+ ··· − 757.386u + 41.6323
−0.304850u
134
− 2.35761u
133
+ ··· + 245.506u − 12.4320
(ii) Obstruction class = −1
(iii) Cusp Shapes = −9.36282u
134
− 20.3123u
133
+ ··· − 666.463u + 49.0376
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
135
+ 64u
134
+ ··· + 158u − 1
c
2
, c
5
u
135
+ 6u
134
+ ··· − 2u − 1
c
3
u
135
− 6u
134
+ ··· + 18532724u − 1174793
c
4
, c
8
u
135
− u
134
+ ··· + 5120u − 1024
c
6
u
135
+ 3u
134
+ ··· + 12401u − 47809
c
7
u
135
− 3u
134
+ ··· + 17948537u − 2522669
c
9
, c
11
u
135
+ 3u
134
+ ··· + 23u − 1
c
10
u
135
− 23u
134
+ ··· + 3u − 1
c
12
u
135
+ 9u
134
+ ··· + 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
135
+ 20y
134
+ ··· + 22410y −1
c
2
, c
5
y
135
+ 64y
134
+ ··· + 158y −1
c
3
y
135
− 24y
134
+ ··· + 270394515667686y −1380138592849
c
4
, c
8
y
135
+ 55y
134
+ ··· − 24117248y −1048576
c
6
y
135
+ 149y
134
+ ··· − 218902272299y −2285700481
c
7
y
135
+ 85y
134
+ ··· + 285856654348325y −6363858883561
c
9
, c
11
y
135
− 95y
134
+ ··· − 23y −1
c
10
y
135
+ 9y
134
+ ··· − 23y −1
c
12
y
135
− 23y
134
+ ··· + 9y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.568524 + 0.805822I
a = −1.186920 + 0.557168I
b = −1.55948 + 0.08612I
−7.52069 − 3.51563I 0
u = −0.568524 − 0.805822I
a = −1.186920 − 0.557168I
b = −1.55948 − 0.08612I
−7.52069 + 3.51563I 0
u = −0.907886 + 0.454916I
a = 0.68514 − 1.26035I
b = 0.880008 + 0.743585I
−6.41600 − 1.19724I 0
u = −0.907886 − 0.454916I
a = 0.68514 + 1.26035I
b = 0.880008 − 0.743585I
−6.41600 + 1.19724I 0
u = −1.007480 + 0.177190I
a = 1.317070 + 0.096501I
b = 0.423505 + 0.082153I
0.05421 − 4.55763I 0
u = −1.007480 − 0.177190I
a = 1.317070 − 0.096501I
b = 0.423505 − 0.082153I
0.05421 + 4.55763I 0
u = 1.026060 + 0.044609I
a = −0.688975 + 0.420532I
b = −2.76943 + 3.04188I
1.53614 + 3.00834I 0
u = 1.026060 − 0.044609I
a = −0.688975 − 0.420532I
b = −2.76943 − 3.04188I
1.53614 − 3.00834I 0
u = 0.116944 + 1.020390I
a = 0.391000 + 0.849314I
b = 0.775161 − 0.064942I
1.03911 + 2.79672I 0
u = 0.116944 − 1.020390I
a = 0.391000 − 0.849314I
b = 0.775161 + 0.064942I
1.03911 − 2.79672I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.419714 + 0.963008I
a = −1.113320 + 0.500212I
b = −1.64463 + 0.09604I
−7.94598 + 4.71009I 0
u = −0.419714 − 0.963008I
a = −1.113320 − 0.500212I
b = −1.64463 − 0.09604I
−7.94598 − 4.71009I 0
u = 1.051520 + 0.006262I
a = 0.564038 + 0.595897I
b = 3.87487 + 1.91741I
2.86400 + 1.41798I 0
u = 1.051520 − 0.006262I
a = 0.564038 − 0.595897I
b = 3.87487 − 1.91741I
2.86400 − 1.41798I 0
u = 1.043770 + 0.152675I
a = −0.464877 − 0.956012I
b = −2.93917 − 0.27243I
−2.46009 + 0.50056I 0
u = 1.043770 − 0.152675I
a = −0.464877 + 0.956012I
b = −2.93917 + 0.27243I
−2.46009 − 0.50056I 0
u = 0.083016 + 1.051850I
a = −0.870439 + 0.409276I
b = −1.83729 − 0.09226I
0.83592 + 5.69951I 0
u = 0.083016 − 1.051850I
a = −0.870439 − 0.409276I
b = −1.83729 + 0.09226I
0.83592 − 5.69951I 0
u = −1.021600 + 0.270915I
a = 0.998429 − 0.892064I
b = 1.221320 + 0.406339I
−2.95130 − 3.55729I 0
u = −1.021600 − 0.270915I
a = 0.998429 + 0.892064I
b = 1.221320 − 0.406339I
−2.95130 + 3.55729I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.055660 + 0.106193I
a = 1.077190 + 0.842689I
b = 0.517475 + 0.017390I
1.92024 − 4.49255I 0
u = −1.055660 − 0.106193I
a = 1.077190 − 0.842689I
b = 0.517475 − 0.017390I
1.92024 + 4.49255I 0
u = 0.080608 + 0.921052I
a = 0.873120 − 0.320604I
b = 1.97968 + 0.02512I
0.007085 + 0.583291I 0
u = 0.080608 − 0.921052I
a = 0.873120 + 0.320604I
b = 1.97968 − 0.02512I
0.007085 − 0.583291I 0
u = −1.085860 + 0.069941I
a = 0.275746 + 1.215720I
b = 0.321621 − 1.157430I
3.24444 − 3.62921I 0
u = −1.085860 − 0.069941I
a = 0.275746 − 1.215720I
b = 0.321621 + 1.157430I
3.24444 + 3.62921I 0
u = 1.089220 + 0.056094I
a = 0.086119 + 0.368937I
b = 0.55341 − 6.16169I
2.17840 + 2.18123I 0
u = 1.089220 − 0.056094I
a = 0.086119 − 0.368937I
b = 0.55341 + 6.16169I
2.17840 − 2.18123I 0
u = 0.009853 + 1.093610I
a = −0.435161 − 0.909331I
b = −0.811741 + 0.004845I
−1.01744 + 7.35867I 0
u = 0.009853 − 1.093610I
a = −0.435161 + 0.909331I
b = −0.811741 − 0.004845I
−1.01744 − 7.35867I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.416447 + 0.803539I
a = 1.191210 − 0.476871I
b = 1.59991 − 0.15322I
−4.35305 + 0.80319I 0
u = −0.416447 − 0.803539I
a = 1.191210 + 0.476871I
b = 1.59991 + 0.15322I
−4.35305 − 0.80319I 0
u = 1.040580 + 0.349191I
a = 0.446852 − 0.394829I
b = 0.190132 + 1.142410I
1.54023 − 0.58667I 0
u = 1.040580 − 0.349191I
a = 0.446852 + 0.394829I
b = 0.190132 − 1.142410I
1.54023 + 0.58667I 0
u = 0.438285 + 1.007090I
a = 0.454121 + 0.675347I
b = 0.821512 − 0.305548I
1.20916 + 1.59276I 0
u = 0.438285 − 1.007090I
a = 0.454121 − 0.675347I
b = 0.821512 + 0.305548I
1.20916 − 1.59276I 0
u = −1.097860 + 0.038828I
a = −0.637062 + 1.120900I
b = −0.771440 − 0.894856I
4.13066 − 2.35961I 0
u = −1.097860 − 0.038828I
a = −0.637062 − 1.120900I
b = −0.771440 + 0.894856I
4.13066 + 2.35961I 0
u = 1.096500 + 0.092685I
a = 0.573386 + 0.848744I
b = 3.09848 + 0.80652I
1.79298 + 3.12616I 0
u = 1.096500 − 0.092685I
a = 0.573386 − 0.848744I
b = 3.09848 − 0.80652I
1.79298 − 3.12616I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.111950 + 0.006804I
a = −1.126920 + 0.487485I
b = −0.423626 − 0.004236I
4.49122 − 0.85357I 0
u = −1.111950 − 0.006804I
a = −1.126920 − 0.487485I
b = −0.423626 + 0.004236I
4.49122 + 0.85357I 0
u = 0.885186 + 0.050073I
a = −0.740848 + 0.127427I
b = −0.10936 − 2.32435I
0.92608 + 2.64149I 0
u = 0.885186 − 0.050073I
a = −0.740848 − 0.127427I
b = −0.10936 + 2.32435I
0.92608 − 2.64149I 0
u = −0.118952 + 0.869942I
a = −0.328619 − 1.037610I
b = −0.719254 − 0.066072I
−2.45542 + 0.43451I 0
u = −0.118952 − 0.869942I
a = −0.328619 + 1.037610I
b = −0.719254 + 0.066072I
−2.45542 − 0.43451I 0
u = 1.125470 + 0.117732I
a = −0.612434 − 0.905025I
b = −2.86154 − 0.78542I
−0.46769 + 8.00362I 0
u = 1.125470 − 0.117732I
a = −0.612434 + 0.905025I
b = −2.86154 + 0.78542I
−0.46769 − 8.00362I 0
u = −1.040870 + 0.448369I
a = −0.587288 + 1.058760I
b = −1.02358 − 1.03227I
−2.40247 − 5.42914I 0
u = −1.040870 − 0.448369I
a = −0.587288 − 1.058760I
b = −1.02358 + 1.03227I
−2.40247 + 5.42914I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.15383
a = 0.248512
b = −0.617227
2.30295 0
u = 0.797291 + 0.240741I
a = 0.152484 + 1.301610I
b = 1.96500 − 0.41263I
−3.03176 + 0.85487I 0
u = 0.797291 − 0.240741I
a = 0.152484 − 1.301610I
b = 1.96500 + 0.41263I
−3.03176 − 0.85487I 0
u = −1.159770 + 0.238949I
a = −0.866476 + 0.823520I
b = −1.34363 − 0.63804I
2.64360 − 6.29046I 0
u = −1.159770 − 0.238949I
a = −0.866476 − 0.823520I
b = −1.34363 + 0.63804I
2.64360 + 6.29046I 0
u = −1.067580 + 0.544991I
a = 0.719832 − 0.975059I
b = 1.25728 + 0.91896I
−5.87319 − 10.08940I 0
u = −1.067580 − 0.544991I
a = 0.719832 + 0.975059I
b = 1.25728 − 0.91896I
−5.87319 + 10.08940I 0
u = −0.087955 + 1.201330I
a = 0.944422 − 0.493344I
b = 1.70851 + 0.01513I
−5.66349 + 5.47096I 0
u = −0.087955 − 1.201330I
a = 0.944422 + 0.493344I
b = 1.70851 − 0.01513I
−5.66349 − 5.47096I 0
u = −1.188910 + 0.286559I
a = 0.889919 − 0.773016I
b = 1.44145 + 0.59362I
0.38712 − 11.78350I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.188910 − 0.286559I
a = 0.889919 + 0.773016I
b = 1.44145 − 0.59362I
0.38712 + 11.78350I 0
u = 0.019858 + 1.238580I
a = −0.897984 + 0.501763I
b = −1.69963 − 0.06811I
−0.80905 + 8.28455I 0
u = 0.019858 − 1.238580I
a = −0.897984 − 0.501763I
b = −1.69963 + 0.06811I
−0.80905 − 8.28455I 0
u = 0.569961 + 1.127270I
a = −0.531317 − 0.663723I
b = −0.973907 + 0.344786I
−0.79606 − 2.83608I 0
u = 0.569961 − 1.127270I
a = −0.531317 + 0.663723I
b = −0.973907 − 0.344786I
−0.79606 + 2.83608I 0
u = 0.820697 + 0.963046I
a = −0.551140 − 0.561218I
b = −1.062630 + 0.634441I
−1.95084 + 4.11866I 0
u = 0.820697 − 0.963046I
a = −0.551140 + 0.561218I
b = −1.062630 − 0.634441I
−1.95084 − 4.11866I 0
u = 0.562883 + 0.443226I
a = 0.580480 + 0.461713I
b = 0.027447 − 0.872637I
0.66023 + 1.44451I 0
u = 0.562883 − 0.443226I
a = 0.580480 − 0.461713I
b = 0.027447 + 0.872637I
0.66023 − 1.44451I 0
u = 0.008679 + 1.294510I
a = 0.901083 − 0.524151I
b = 1.67286 + 0.06156I
−3.15409 + 13.45310I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.008679 − 1.294510I
a = 0.901083 + 0.524151I
b = 1.67286 − 0.06156I
−3.15409 − 13.45310I 0
u = 0.621734 + 0.332061I
a = 0.11218 + 1.65942I
b = 1.52142 − 0.25068I
−1.58896 − 6.54144I 0
u = 0.621734 − 0.332061I
a = 0.11218 − 1.65942I
b = 1.52142 + 0.25068I
−1.58896 + 6.54144I 0
u = −1.259540 + 0.463280I
a = −0.697654 − 0.564354I
b = −0.284305 − 0.259378I
1.11874 − 5.27197I 0
u = −1.259540 − 0.463280I
a = −0.697654 + 0.564354I
b = −0.284305 + 0.259378I
1.11874 + 5.27197I 0
u = −1.359480 + 0.117427I
a = −0.490412 + 0.278971I
b = −0.235539 + 0.060510I
6.64310 − 2.61859I 0
u = −1.359480 − 0.117427I
a = −0.490412 − 0.278971I
b = −0.235539 − 0.060510I
6.64310 + 2.61859I 0
u = 0.582918 + 0.205812I
a = 0.17559 − 1.61087I
b = −1.40341 + 0.48169I
0.69426 − 1.95174I 0. + 5.64029I
u = 0.582918 − 0.205812I
a = 0.17559 + 1.61087I
b = −1.40341 − 0.48169I
0.69426 + 1.95174I 0. − 5.64029I
u = −1.327410 + 0.462550I
a = −0.578823 + 0.588443I
b = −1.97389 − 1.48784I
4.32893 − 5.56092I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.327410 − 0.462550I
a = −0.578823 − 0.588443I
b = −1.97389 + 1.48784I
4.32893 + 5.56092I 0
u = −1.35402 + 0.47664I
a = 0.553167 + 0.610604I
b = 0.226182 + 0.291609I
5.57738 − 8.05927I 0
u = −1.35402 − 0.47664I
a = 0.553167 − 0.610604I
b = 0.226182 − 0.291609I
5.57738 + 8.05927I 0
u = −1.35698 + 0.49400I
a = 0.637050 − 0.555933I
b = 2.08576 + 1.32571I
5.30424 − 11.13160I 0
u = −1.35698 − 0.49400I
a = 0.637050 + 0.555933I
b = 2.08576 − 1.32571I
5.30424 + 11.13160I 0
u = −1.35082 + 0.52344I
a = −0.575172 − 0.675690I
b = −0.242093 − 0.319687I
3.24218 − 13.03280I 0
u = −1.35082 − 0.52344I
a = −0.575172 + 0.675690I
b = −0.242093 + 0.319687I
3.24218 + 13.03280I 0
u = −1.45560 + 0.14753I
a = 0.240455 − 0.374128I
b = 0.147199 − 0.138505I
5.74020 − 6.92480I 0
u = −1.45560 − 0.14753I
a = 0.240455 + 0.374128I
b = 0.147199 + 0.138505I
5.74020 + 6.92480I 0
u = −1.42106 + 0.35399I
a = 0.356363 + 0.458246I
b = 0.130191 + 0.227548I
6.97880 − 6.19911I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42106 − 0.35399I
a = 0.356363 − 0.458246I
b = 0.130191 − 0.227548I
6.97880 + 6.19911I 0
u = −1.34939 + 0.58154I
a = −0.749894 + 0.593839I
b = −1.99176 − 1.03849I
−1.66694 − 11.66010I 0
u = −1.34939 − 0.58154I
a = −0.749894 − 0.593839I
b = −1.99176 + 1.03849I
−1.66694 + 11.66010I 0
u = 1.40899 + 0.42638I
a = 0.526401 + 0.277205I
b = 2.40117 − 1.31157I
3.69009 − 1.55088I 0
u = 1.40899 − 0.42638I
a = 0.526401 − 0.277205I
b = 2.40117 + 1.31157I
3.69009 + 1.55088I 0
u = 1.34945 + 0.59985I
a = 0.353348 − 0.565384I
b = 0.433960 + 0.600493I
3.37680 + 5.10317I 0
u = 1.34945 − 0.59985I
a = 0.353348 + 0.565384I
b = 0.433960 − 0.600493I
3.37680 − 5.10317I 0
u = −1.48017 + 0.29167I
a = −0.162655 − 0.448875I
b = −0.037753 − 0.216915I
5.89517 − 1.74663I 0
u = −1.48017 − 0.29167I
a = −0.162655 + 0.448875I
b = −0.037753 + 0.216915I
5.89517 + 1.74663I 0
u = −1.39873 + 0.56584I
a = 0.746409 − 0.529605I
b = 2.14095 + 1.03697I
3.6652 − 14.5289I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.39873 − 0.56584I
a = 0.746409 + 0.529605I
b = 2.14095 − 1.03697I
3.6652 + 14.5289I 0
u = 1.28440 + 0.79512I
a = 0.605252 + 0.419898I
b = 1.66223 − 0.91218I
−0.61654 + 3.16359I 0
u = 1.28440 − 0.79512I
a = 0.605252 − 0.419898I
b = 1.66223 + 0.91218I
−0.61654 − 3.16359I 0
u = 1.41568 + 0.54696I
a = −0.568503 − 0.316970I
b = −2.13096 + 1.12927I
4.93681 + 3.31408I 0
u = 1.41568 − 0.54696I
a = −0.568503 + 0.316970I
b = −2.13096 − 1.12927I
4.93681 − 3.31408I 0
u = 1.43165 + 0.51650I
a = −0.302053 + 0.564295I
b = −0.336585 − 0.543926I
4.99306 + 0.38975I 0
u = 1.43165 − 0.51650I
a = −0.302053 − 0.564295I
b = −0.336585 + 0.543926I
4.99306 − 0.38975I 0
u = −0.003009 + 0.471213I
a = −2.50005 + 1.33228I
b = −0.702198 + 0.575510I
−3.04734 + 8.79533I 0.41361 − 4.49618I
u = −0.003009 − 0.471213I
a = −2.50005 − 1.33228I
b = −0.702198 − 0.575510I
−3.04734 − 8.79533I 0.41361 + 4.49618I
u = −1.41292 + 0.58655I
a = −0.775492 + 0.520952I
b = −2.15151 − 0.96722I
1.3407 − 19.9336I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.41292 − 0.58655I
a = −0.775492 − 0.520952I
b = −2.15151 + 0.96722I
1.3407 + 19.9336I 0
u = −0.257301 + 0.376376I
a = 0.32758 + 1.82950I
b = 0.684832 + 0.214295I
−1.81324 + 2.17307I −3.13989 − 3.52849I
u = −0.257301 − 0.376376I
a = 0.32758 − 1.82950I
b = 0.684832 − 0.214295I
−1.81324 − 2.17307I −3.13989 + 3.52849I
u = −0.175057 + 0.371624I
a = −2.29363 + 2.13432I
b = −0.545397 + 0.356266I
−5.15906 + 0.74614I −3.05371 + 1.33058I
u = −0.175057 − 0.371624I
a = −2.29363 − 2.13432I
b = −0.545397 − 0.356266I
−5.15906 − 0.74614I −3.05371 − 1.33058I
u = 1.43520 + 0.74129I
a = −0.628332 − 0.367621I
b = −1.89441 + 0.86459I
3.94029 + 5.57514I 0
u = 1.43520 − 0.74129I
a = −0.628332 + 0.367621I
b = −1.89441 − 0.86459I
3.94029 − 5.57514I 0
u = −0.001674 + 0.384516I
a = 2.85237 − 1.44910I
b = 0.585903 − 0.596946I
−0.60252 + 3.76215I 3.40046 − 1.16553I
u = −0.001674 − 0.384516I
a = 2.85237 + 1.44910I
b = 0.585903 + 0.596946I
−0.60252 − 3.76215I 3.40046 + 1.16553I
u = 1.64516 + 0.19357I
a = 0.106126 − 0.578132I
b = 0.099952 + 0.384211I
0.509155 + 0.687850I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.64516 − 0.19357I
a = 0.106126 + 0.578132I
b = 0.099952 − 0.384211I
0.509155 − 0.687850I 0
u = 1.46077 + 0.80389I
a = 0.650409 + 0.377792I
b = 1.86542 − 0.77769I
1.76178 + 10.59480I 0
u = 1.46077 − 0.80389I
a = 0.650409 − 0.377792I
b = 1.86542 + 0.77769I
1.76178 − 10.59480I 0
u = 1.61720 + 0.40942I
a = −0.211461 + 0.605812I
b = −0.236214 − 0.406084I
4.52600 − 1.48756I 0
u = 1.61720 − 0.40942I
a = −0.211461 − 0.605812I
b = −0.236214 + 0.406084I
4.52600 + 1.48756I 0
u = 1.70202 + 0.39932I
a = 0.190374 − 0.638275I
b = 0.225506 + 0.350588I
2.46679 − 6.31017I 0
u = 1.70202 − 0.39932I
a = 0.190374 + 0.638275I
b = 0.225506 − 0.350588I
2.46679 + 6.31017I 0
u = 0.178980 + 0.082547I
a = 1.96557 − 3.69372I
b = −0.808183 + 0.272252I
1.28270 − 0.95263I 6.92461 + 3.27400I
u = 0.178980 − 0.082547I
a = 1.96557 + 3.69372I
b = −0.808183 − 0.272252I
1.28270 + 0.95263I 6.92461 − 3.27400I
u = 0.140096 + 0.121247I
a = 0.18043 + 3.54028I
b = 0.388156 − 1.202380I
0.35725 + 2.80293I 2.42705 + 0.32410I
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.140096 − 0.121247I
a = 0.18043 − 3.54028I
b = 0.388156 + 1.202380I
0.35725 − 2.80293I 2.42705 − 0.32410I
u = 0.124506 + 0.102205I
a = 4.96081 + 1.61254I
b = 0.151616 − 0.904151I
1.17674 + 1.83944I 5.03946 − 3.87625I
u = 0.124506 − 0.102205I
a = 4.96081 − 1.61254I
b = 0.151616 + 0.904151I
1.17674 − 1.83944I 5.03946 + 3.87625I
u = −0.021895 + 0.151278I
a = 2.88815 + 5.48507I
b = 0.753080 − 0.067463I
−0.44956 + 3.21138I 2.31979 − 2.55499I
u = −0.021895 − 0.151278I
a = 2.88815 − 5.48507I
b = 0.753080 + 0.067463I
−0.44956 − 3.21138I 2.31979 + 2.55499I
18
II. I
u
2
= h−u
4
b + 2u
4
+ · · · − b + 2, a, u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
4
=
0
b
a
10
=
u
−u
3
+ u
a
8
=
0
u
a
5
=
0
b
a
7
=
−u
u
a
1
=
−u
4
+ u
2
+ 1
u
4
− 2u
2
a
6
=
u
4
− u
2
− 1
−u
4
+ 2u
2
a
3
=
u
4
b − u
3
b − 2u
2
b + 3bu − b
−bu + 2b
a
2
=
u
4
b − u
3
b − 2u
2
b + 3bu − b
−u
4
− u
3
− bu + u
2
+ 2b − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
3
b + u
4
− u
2
b + 7u
3
+ 6bu + 2u
2
+ 2b − 9u + 5
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
5
c
2
(u
2
+ u + 1)
5
c
4
, c
8
u
10
c
6
, c
10
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
7
, c
9
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
11
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
12
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
5
c
4
, c
8
y
10
c
6
, c
10
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
7
, c
9
, c
11
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
12
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.21774
a = 0
b = 1.76091 + 3.04998I
2.40108 − 2.02988I 9.72304 − 3.67600I
u = 1.21774
a = 0
b = 1.76091 − 3.04998I
2.40108 + 2.02988I 9.72304 + 3.67600I
u = 0.309916 + 0.549911I
a = 0
b = 0.864485 + 0.518603I
0.329100 − 0.499304I 3.01153 + 0.88894I
u = 0.309916 + 0.549911I
a = 0
b = 0.016881 − 1.007970I
0.32910 + 3.56046I 3.07628 − 9.77765I
u = 0.309916 − 0.549911I
a = 0
b = 0.864485 − 0.518603I
0.329100 + 0.499304I 3.01153 − 0.88894I
u = 0.309916 − 0.549911I
a = 0
b = 0.016881 + 1.007970I
0.32910 − 3.56046I 3.07628 + 9.77765I
u = −1.41878 + 0.21917I
a = 0
b = 0.369732 − 0.377747I
5.87256 − 6.43072I 6.63163 + 0.01393I
u = −1.41878 + 0.21917I
a = 0
b = −0.512005 − 0.131324I
5.87256 − 2.37095I 3.55752 + 5.27247I
u = −1.41878 − 0.21917I
a = 0
b = 0.369732 + 0.377747I
5.87256 + 6.43072I 6.63163 − 0.01393I
u = −1.41878 − 0.21917I
a = 0
b = −0.512005 + 0.131324I
5.87256 + 2.37095I 3.55752 − 5.27247I
22
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
5
)(u
135
+ 64u
134
+ ··· + 158u − 1)
c
2
((u
2
+ u + 1)
5
)(u
135
+ 6u
134
+ ··· − 2u − 1)
c
3
((u
2
− u + 1)
5
)(u
135
− 6u
134
+ ··· + 1.85327 × 10
7
u − 1174793)
c
4
, c
8
u
10
(u
135
− u
134
+ ··· + 5120u − 1024)
c
5
((u
2
− u + 1)
5
)(u
135
+ 6u
134
+ ··· − 2u − 1)
c
6
((u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
)(u
135
+ 3u
134
+ ··· + 12401u − 47809)
c
7
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
· (u
135
− 3u
134
+ ··· + 17948537u − 2522669)
c
9
((u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
)(u
135
+ 3u
134
+ ··· + 23u − 1)
c
10
((u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
)(u
135
− 23u
134
+ ··· + 3u − 1)
c
11
((u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
)(u
135
+ 3u
134
+ ··· + 23u − 1)
c
12
((u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
)(u
135
+ 9u
134
+ ··· + 3u + 1)
23
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
5
)(y
135
+ 20y
134
+ ··· + 22410y −1)
c
2
, c
5
((y
2
+ y + 1)
5
)(y
135
+ 64y
134
+ ··· + 158y −1)
c
3
(y
2
+ y + 1)
5
· (y
135
− 24y
134
+ ··· + 270394515667686y −1380138592849)
c
4
, c
8
y
10
(y
135
+ 55y
134
+ ··· − 2.41172 × 10
7
y −1048576)
c
6
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
· (y
135
+ 149y
134
+ ··· − 218902272299y −2285700481)
c
7
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
· (y
135
+ 85y
134
+ ··· + 285856654348325y −6363858883561)
c
9
, c
11
((y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
)(y
135
− 95y
134
+ ··· − 23y −1)
c
10
((y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
)(y
135
+ 9y
134
+ ··· − 23y −1)
c
12
((y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
)(y
135
− 23y
134
+ ··· + 9y −1)
24
