12a
1229
(K12a
1229
)
A knot diagram
1
Linearized knot diagam
5 6 8 1 10 3 11 12 2 7 4 9
Solving Sequence
8,12
9
1,4
5 3 11 7 6 2 10
c
8
c
12
c
4
c
3
c
11
c
7
c
6
c
2
c
10
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−657243u
19
+ 550757u
18
+ ··· + 15052055b − 22884294,
2745998u
19
− 1810107u
18
+ ··· + 885415a + 11576054, u
20
− u
19
+ ··· + 8u − 1i
I
u
2
= h1.61625 × 10
510
u
119
+ 2.95718 × 10
510
u
118
+ ··· + 2.43355 × 10
509
b + 1.95951 × 10
512
,
− 2.49960 × 10
511
u
119
− 4.27348 × 10
511
u
118
+ ··· + 2.45789 × 10
511
a − 1.68445 × 10
513
,
u
120
+ u
119
+ ··· − 1207u − 101i
I
u
3
= h−u
2
+ b, −u
2
+ a + 1, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
I
u
4
= h−890375597269u
23
+ 254192032954u
22
+ ··· + 29055549398b + 3174095591762,
3872069553587u
23
− 1069682860926u
22
+ ··· + 29055549398a − 13742313845163,
u
24
− 10u
22
+ ··· − 11u − 1i
* 4 irreducible components of dim
C
= 0, with total 170 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
= h−6.57 × 10
5
u
19
+ 5.51 × 10
5
u
18
+ · · · + 1.51 × 10
7
b − 2.29 × 10
7
, 2.75 ×
10
6
u
19
− 1.81 × 10
6
u
18
+ · · · + 8.85 × 10
5
a + 1.16 × 10
7
, u
20
− u
19
+ · · · + 8u − 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
−u
3
+ u
a
4
=
−3.10137u
19
+ 2.04436u
18
+ ··· + 46.2868u − 13.0742
0.0436647u
19
− 0.0365902u
18
+ ··· − 2.22938u + 1.52034
a
5
=
−3.38270u
19
+ 1.83814u
18
+ ··· + 48.5281u − 13.6793
0.351266u
19
+ 0.114483u
18
+ ··· − 3.60717u + 1.40274
a
3
=
−3.14503u
19
+ 2.08095u
18
+ ··· + 48.5161u − 14.5945
0.0436647u
19
− 0.0365902u
18
+ ··· − 2.22938u + 1.52034
a
11
=
4.34974u
19
− 3.12294u
18
+ ··· − 60.9551u + 17.5138
−0.605158u
19
+ 0.323827u
18
+ ··· + 7.26222u − 2.59996
a
7
=
5.75707u
19
− 4.24667u
18
+ ··· − 87.5291u + 27.3276
−0.400467u
19
+ 0.658924u
18
+ ··· + 11.8243u − 4.07902
a
6
=
4.69299u
19
− 3.80267u
18
+ ··· − 76.9633u + 24.1825
−0.393392u
19
+ 0.726860u
18
+ ··· + 12.9953u − 4.03535
a
2
=
−4.03535u
19
+ 3.64196u
18
+ ··· + 61.8775u − 19.2875
−0.289803u
19
− 0.784497u
18
+ ··· − 1.34116u + 1.91374
a
10
=
−5.17324u
19
+ 4.24751u
18
+ ··· + 75.3851u − 25.4465
1.22379u
19
− 0.813102u
18
+ ··· − 14.2496u + 4.29959
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
25801680
3010411
u
19
+
13740304
3010411
u
18
+ ··· +
265194524
3010411
u −
69023780
3010411
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
20
+ u
19
+ ··· − 8u − 1
c
2
, c
6
, c
8
c
12
u
20
− u
19
+ ··· + 8u − 1
c
3
, c
9
u
20
+ 3u
19
+ ··· − 4u + 1
c
5
, c
11
u
20
− 3u
19
+ ··· + 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
7
, c
8
c
10
, c
12
y
20
− 21y
19
+ ··· − 22y + 1
c
3
, c
5
, c
9
c
11
y
20
− 9y
19
+ ··· − 58y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.937024 + 0.450242I
a = −0.384605 − 0.337640I
b = −0.751635 − 1.117870I
−3.67791 − 3.10330I −3.51583 + 4.92617I
u = −0.937024 − 0.450242I
a = −0.384605 + 0.337640I
b = −0.751635 + 1.117870I
−3.67791 + 3.10330I −3.51583 − 4.92617I
u = −0.942219
a = −1.69416
b = 1.71447
−6.37866 3.70440
u = −0.090437 + 1.100790I
a = 0.357560 − 1.069910I
b = 0.819196 − 1.038580I
−9.29934 − 6.91821I −7.59605 + 5.76583I
u = −0.090437 − 1.100790I
a = 0.357560 + 1.069910I
b = 0.819196 + 1.038580I
−9.29934 + 6.91821I −7.59605 − 5.76583I
u = 1.162070 + 0.230203I
a = 0.805749 + 0.802349I
b = −0.512403 − 0.143211I
3.67791 + 3.10330I 3.51583 − 4.92617I
u = 1.162070 − 0.230203I
a = 0.805749 − 0.802349I
b = −0.512403 + 0.143211I
3.67791 − 3.10330I 3.51583 + 4.92617I
u = 0.692420 + 0.175493I
a = −0.62416 − 1.52463I
b = 0.164619 − 1.165220I
0.945117I 0. − 6.62663I
u = 0.692420 − 0.175493I
a = −0.62416 + 1.52463I
b = 0.164619 + 1.165220I
− 0.945117I 0. + 6.62663I
u = −1.357150 + 0.312893I
a = 0.405622 + 0.858786I
b = −1.145400 + 0.490357I
9.29934 − 6.91821I 7.59605 + 5.76583I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.357150 − 0.312893I
a = 0.405622 − 0.858786I
b = −1.145400 − 0.490357I
9.29934 + 6.91821I 7.59605 − 5.76583I
u = 1.43028 + 0.61765I
a = 0.527948 − 0.948587I
b = −1.34101 − 1.03066I
19.4225I 0. − 9.88055I
u = 1.43028 − 0.61765I
a = 0.527948 + 0.948587I
b = −1.34101 + 1.03066I
− 19.4225I 0. + 9.88055I
u = 1.56596
a = −0.0875994
b = −0.956582
1.07560 8.20320
u = 1.57822
a = −0.828201
b = 1.36600
8.74433 11.3570
u = 0.141085 + 0.364901I
a = 0.816431 + 1.084900I
b = 0.280693 + 0.450979I
0.971689I 0. − 6.75018I
u = 0.141085 − 0.364901I
a = 0.816431 − 1.084900I
b = 0.280693 − 0.450979I
− 0.971689I 0. + 6.75018I
u = −1.69718
a = −0.563631
b = 0.137177
−1.07560 −8.20320
u = 0.207256
a = −6.59087
b = 1.30709
−8.74433 −11.3570
u = −1.79455
a = 0.955379
b = −1.59627
6.37866 −3.70440
6
II. I
u
2
= h1.62 × 10
510
u
119
+ 2.96 × 10
510
u
118
+ · · · + 2.43 × 10
509
b + 1.96 ×
10
512
, −2.50 × 10
511
u
119
− 4.27 × 10
511
u
118
+ · · · + 2.46 × 10
511
a − 1.68 ×
10
513
, u
120
+ u
119
+ · · · − 1207u − 101i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
−u
3
+ u
a
4
=
1.01697u
119
+ 1.73868u
118
+ ··· + 1250.63u + 68.5325
−6.64154u
119
− 12.1517u
118
+ ··· − 10621.1u − 805.207
a
5
=
5.75809u
119
+ 10.3986u
118
+ ··· + 8895.14u + 648.617
−5.12212u
119
− 9.38884u
118
+ ··· − 8185.42u − 620.921
a
3
=
7.65852u
119
+ 13.8904u
118
+ ··· + 11871.7u + 873.739
−6.64154u
119
− 12.1517u
118
+ ··· − 10621.1u − 805.207
a
11
=
−1.11875u
119
− 2.64304u
118
+ ··· − 1268.92u − 121.688
−2.20452u
119
− 4.10235u
118
+ ··· − 3190.02u − 238.655
a
7
=
−3.36432u
119
− 6.52962u
118
+ ··· − 4543.21u − 344.737
3.27162u
119
+ 6.24353u
118
+ ··· + 4661.08u + 355.334
a
6
=
10.5896u
119
+ 19.1853u
118
+ ··· + 16483.5u + 1214.74
−8.57234u
119
− 15.5835u
118
+ ··· − 13957.2u − 1056.32
a
2
=
−11.1962u
119
− 20.8532u
118
+ ··· − 16571.6u − 1239.72
8.28041u
119
+ 15.5128u
118
+ ··· + 12526.9u + 951.367
a
10
=
−2.27197u
119
− 4.78743u
118
+ ··· − 2978.31u − 251.605
1.58455u
119
+ 2.95319u
118
+ ··· + 2593.22u + 203.741
(ii) Obstruction class = −1
(iii) Cusp Shapes = −36.0800u
119
− 67.2942u
118
+ ··· − 54086.0u − 4089.21
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
120
− u
119
+ ··· + 1207u − 101
c
2
, c
6
, c
8
c
12
u
120
+ u
119
+ ··· − 1207u − 101
c
3
, c
9
u
120
− 7u
117
+ ··· − 175u − 575
c
5
, c
11
u
120
+ 7u
117
+ ··· + 175u − 575
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
7
, c
8
c
10
, c
12
y
120
− 73y
119
+ ··· − 569059y + 10201
c
3
, c
5
, c
9
c
11
y
120
+ 86y
118
+ ··· − 5688625y + 330625
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.571383 + 0.817824I
a = −0.337837 − 0.625440I
b = −0.767765 − 0.308435I
3.58665 + 3.20085I 0
u = 0.571383 − 0.817824I
a = −0.337837 + 0.625440I
b = −0.767765 + 0.308435I
3.58665 − 3.20085I 0
u = 1.015410 + 0.099318I
a = 0.775962 − 0.840114I
b = −1.62880 − 1.21221I
0.87063 + 4.37653I 0
u = 1.015410 − 0.099318I
a = 0.775962 + 0.840114I
b = −1.62880 + 1.21221I
0.87063 − 4.37653I 0
u = 1.029960 + 0.108703I
a = 1.44044 + 1.01116I
b = −1.120920 + 0.163726I
3.43093 + 4.34668I 0
u = 1.029960 − 0.108703I
a = 1.44044 − 1.01116I
b = −1.120920 − 0.163726I
3.43093 − 4.34668I 0
u = −0.376706 + 0.970628I
a = 0.709879 + 0.393674I
b = 0.541187 + 0.911081I
−0.31640 + 3.81201I 0
u = −0.376706 − 0.970628I
a = 0.709879 − 0.393674I
b = 0.541187 − 0.911081I
−0.31640 − 3.81201I 0
u = 0.929577 + 0.130081I
a = −0.52107 − 1.59976I
b = 0.495079 − 0.392935I
0.419089I 0
u = 0.929577 − 0.130081I
a = −0.52107 + 1.59976I
b = 0.495079 + 0.392935I
− 0.419089I 0
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.024900 + 0.276881I
a = 0.15555 − 1.79236I
b = −0.206866 − 0.464700I
0.159819 + 0.791393I 0
u = 1.024900 − 0.276881I
a = 0.15555 + 1.79236I
b = −0.206866 + 0.464700I
0.159819 − 0.791393I 0
u = 0.917589 + 0.114336I
a = −1.05262 − 1.82444I
b = 0.499926 − 0.525485I
−0.159819 + 0.791393I 0
u = 0.917589 − 0.114336I
a = −1.05262 + 1.82444I
b = 0.499926 + 0.525485I
−0.159819 − 0.791393I 0
u = −0.220382 + 1.055820I
a = −0.691368 − 0.822797I
b = −0.802424 − 0.803524I
−5.81721 + 4.62194I 0
u = −0.220382 − 1.055820I
a = −0.691368 + 0.822797I
b = −0.802424 + 0.803524I
−5.81721 − 4.62194I 0
u = −0.430102 + 0.999454I
a = −0.703162 − 0.687615I
b = 0.067673 − 1.048070I
−2.63314 + 3.37265I 0
u = −0.430102 − 0.999454I
a = −0.703162 + 0.687615I
b = 0.067673 + 1.048070I
−2.63314 − 3.37265I 0
u = −0.890569 + 0.149096I
a = 1.29257 + 1.47928I
b = −0.971229 + 0.609138I
−2.63314 − 3.37265I 0
u = −0.890569 − 0.149096I
a = 1.29257 − 1.47928I
b = −0.971229 − 0.609138I
−2.63314 + 3.37265I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.085370 + 0.245075I
a = 0.070673 − 0.888919I
b = −0.472794 − 0.687874I
−0.31640 − 3.81201I 0
u = −1.085370 − 0.245075I
a = 0.070673 + 0.888919I
b = −0.472794 + 0.687874I
−0.31640 + 3.81201I 0
u = −1.121070 + 0.002297I
a = −0.676952 + 0.628951I
b = 1.348580 + 0.398307I
5.58448 + 0.82681I 0
u = −1.121070 − 0.002297I
a = −0.676952 − 0.628951I
b = 1.348580 − 0.398307I
5.58448 − 0.82681I 0
u = 0.956984 + 0.655205I
a = −0.348777 + 0.259561I
b = −0.45047 + 1.69807I
−2.49209 + 10.34980I 0
u = 0.956984 − 0.655205I
a = −0.348777 − 0.259561I
b = −0.45047 − 1.69807I
−2.49209 − 10.34980I 0
u = 0.838810 + 0.018028I
a = −0.022628 − 0.308718I
b = −0.73721 + 1.56066I
0.20224 − 3.55721I 0
u = 0.838810 − 0.018028I
a = −0.022628 + 0.308718I
b = −0.73721 − 1.56066I
0.20224 + 3.55721I 0
u = 1.056600 + 0.487993I
a = 0.272721 − 0.127124I
b = 0.81363 − 1.35709I
−5.81721 + 4.62194I 0
u = 1.056600 − 0.487993I
a = 0.272721 + 0.127124I
b = 0.81363 + 1.35709I
−5.81721 − 4.62194I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.150200 + 0.209306I
a = −0.63913 + 1.36002I
b = 0.503840 − 0.019875I
2.49209 − 10.34980I 0
u = −1.150200 − 0.209306I
a = −0.63913 − 1.36002I
b = 0.503840 + 0.019875I
2.49209 + 10.34980I 0
u = −1.163030 + 0.207546I
a = −0.338959 − 0.777400I
b = 0.769100 − 0.908473I
3.58665 − 3.20085I 0
u = −1.163030 − 0.207546I
a = −0.338959 + 0.777400I
b = 0.769100 + 0.908473I
3.58665 + 3.20085I 0
u = −1.18600
a = 0.491723
b = 0.878739
−5.62510 0
u = −1.126730 + 0.405886I
a = −0.590597 − 0.753377I
b = 1.37167 − 1.12469I
2.63314 − 3.37265I 0
u = −1.126730 − 0.405886I
a = −0.590597 + 0.753377I
b = 1.37167 + 1.12469I
2.63314 + 3.37265I 0
u = 0.201452 + 0.768382I
a = −0.00995 + 1.55417I
b = 1.130110 + 0.779101I
−8.18473 0
u = 0.201452 − 0.768382I
a = −0.00995 − 1.55417I
b = 1.130110 − 0.779101I
−8.18473 0
u = 0.789728 + 0.065338I
a = 0.023944 + 1.325150I
b = −0.989671 + 0.407033I
2.63314 − 3.37265I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.789728 − 0.065338I
a = 0.023944 − 1.325150I
b = −0.989671 − 0.407033I
2.63314 + 3.37265I 0
u = −0.131435 + 1.206100I
a = −0.321284 − 0.601557I
b = −0.318465 − 0.633657I
−3.58665 + 3.20085I 0
u = −0.131435 − 1.206100I
a = −0.321284 + 0.601557I
b = −0.318465 + 0.633657I
−3.58665 − 3.20085I 0
u = 0.705980 + 1.009290I
a = 0.412700 − 0.821924I
b = −1.37369 − 1.19804I
−3.43093 − 4.34668I 0
u = 0.705980 − 1.009290I
a = 0.412700 + 0.821924I
b = −1.37369 + 1.19804I
−3.43093 + 4.34668I 0
u = 1.216130 + 0.235698I
a = 0.633659 − 1.087890I
b = −1.02702 − 1.17366I
5.66863I 0
u = 1.216130 − 0.235698I
a = 0.633659 + 1.087890I
b = −1.02702 + 1.17366I
− 5.66863I 0
u = −0.624516 + 0.424975I
a = −1.064150 − 0.150384I
b = −0.569569 − 0.536506I
−2.93285 + 0.71247I 0
u = −0.624516 − 0.424975I
a = −1.064150 + 0.150384I
b = −0.569569 + 0.536506I
−2.93285 − 0.71247I 0
u = 1.231680 + 0.238226I
a = 0.364546 − 0.506098I
b = −0.728486 − 0.358319I
2.93285 + 0.71247I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.231680 − 0.238226I
a = 0.364546 + 0.506098I
b = −0.728486 + 0.358319I
2.93285 − 0.71247I 0
u = −1.253480 + 0.188299I
a = −0.392247 − 1.303990I
b = 0.013415 − 0.259364I
−0.20224 − 3.55721I 0
u = −1.253480 − 0.188299I
a = −0.392247 + 1.303990I
b = 0.013415 + 0.259364I
−0.20224 + 3.55721I 0
u = −1.27931
a = −0.980199
b = 1.55109
5.62510 0
u = −1.231390 + 0.385936I
a = 0.693224 + 0.750299I
b = −1.72377 + 0.96596I
3.43093 − 4.34668I 0
u = −1.231390 − 0.385936I
a = 0.693224 − 0.750299I
b = −1.72377 − 0.96596I
3.43093 + 4.34668I 0
u = −0.181900 + 0.648976I
a = −0.02902 + 2.08615I
b = −0.757463 + 0.706650I
−5.58448 − 0.82681I 0
u = −0.181900 − 0.648976I
a = −0.02902 − 2.08615I
b = −0.757463 − 0.706650I
−5.58448 + 0.82681I 0
u = −0.665722
a = 2.32993
b = −1.25398
−5.62510 0
u = −1.339850 + 0.011748I
a = 0.598326 + 1.018120I
b = −0.350192 − 0.001232I
5.81721 + 4.62194I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.339850 − 0.011748I
a = 0.598326 − 1.018120I
b = −0.350192 + 0.001232I
5.81721 − 4.62194I 0
u = −0.070061 + 1.340720I
a = −0.338608 + 0.782490I
b = −0.88064 + 1.14324I
−4.62976 − 12.68520I 0
u = −0.070061 − 1.340720I
a = −0.338608 − 0.782490I
b = −0.88064 − 1.14324I
−4.62976 + 12.68520I 0
u = 1.296850 + 0.352743I
a = −0.648681 + 0.933581I
b = 1.42725 + 1.04940I
4.62976 + 12.68520I 0
u = 1.296850 − 0.352743I
a = −0.648681 − 0.933581I
b = 1.42725 − 1.04940I
4.62976 − 12.68520I 0
u = −0.608583 + 0.231833I
a = −0.53449 − 2.09677I
b = 0.972957 − 0.918369I
− 9.23882I 0
u = −0.608583 − 0.231833I
a = −0.53449 + 2.09677I
b = 0.972957 + 0.918369I
9.23882I 0
u = 1.344520 + 0.306984I
a = 0.95576 − 1.11982I
b = −0.871355 − 0.775991I
−0.87063 + 4.37653I 0
u = 1.344520 − 0.306984I
a = 0.95576 + 1.11982I
b = −0.871355 + 0.775991I
−0.87063 − 4.37653I 0
u = −1.238950 + 0.607673I
a = 0.339962 + 0.907990I
b = −0.811381 + 1.152140I
− 9.23882I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.238950 − 0.607673I
a = 0.339962 − 0.907990I
b = −0.811381 − 1.152140I
9.23882I 0
u = −1.267210 + 0.562599I
a = 0.537214 + 1.171070I
b = −1.12824 + 0.90180I
−2.49209 − 10.34980I 0
u = −1.267210 − 0.562599I
a = 0.537214 − 1.171070I
b = −1.12824 − 0.90180I
−2.49209 + 10.34980I 0
u = −0.393843 + 0.466604I
a = 0.35434 − 1.98110I
b = 0.936727 − 0.989096I
− 9.27421I 0
u = −0.393843 − 0.466604I
a = 0.35434 + 1.98110I
b = 0.936727 + 0.989096I
9.27421I 0
u = 1.220870 + 0.671493I
a = −0.025206 + 0.760119I
b = 0.649527 + 0.540729I
0.31640 + 3.81201I 0
u = 1.220870 − 0.671493I
a = −0.025206 − 0.760119I
b = 0.649527 − 0.540729I
0.31640 − 3.81201I 0
u = 1.388360 + 0.181604I
a = −0.728130 + 0.656408I
b = 1.196200 + 0.305442I
8.18473 0
u = 1.388360 − 0.181604I
a = −0.728130 − 0.656408I
b = 1.196200 − 0.305442I
8.18473 0
u = −1.276600 + 0.576075I
a = 0.319149 + 0.918808I
b = −0.784834 + 0.945577I
− 9.27421I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.276600 − 0.576075I
a = 0.319149 − 0.918808I
b = −0.784834 − 0.945577I
9.27421I 0
u = 1.16371 + 0.81575I
a = 0.238433 + 0.658620I
b = 0.678477 + 0.367081I
0.20224 + 3.55721I 0
u = 1.16371 − 0.81575I
a = 0.238433 − 0.658620I
b = 0.678477 − 0.367081I
0.20224 − 3.55721I 0
u = −0.234896 + 0.527579I
a = 0.97983 + 1.60290I
b = −0.443106 + 0.422894I
−2.93285 + 0.71247I −3.42268 + 3.66333I
u = −0.234896 − 0.527579I
a = 0.97983 − 1.60290I
b = −0.443106 − 0.422894I
−2.93285 − 0.71247I −3.42268 − 3.66333I
u = 0.476523 + 0.316358I
a = 1.35382 + 0.54474I
b = −0.141146 − 0.982125I
0.31640 + 3.81201I 0. − 6.79551I
u = 0.476523 − 0.316358I
a = 1.35382 − 0.54474I
b = −0.141146 + 0.982125I
0.31640 − 3.81201I 0. + 6.79551I
u = −1.37325 + 0.41309I
a = −0.957051 − 0.991306I
b = 1.143200 − 0.656374I
−3.43093 − 4.34668I 0
u = −1.37325 − 0.41309I
a = −0.957051 + 0.991306I
b = 1.143200 + 0.656374I
−3.43093 + 4.34668I 0
u = −0.181830 + 0.531149I
a = 0.947794 + 0.607629I
b = 0.27628 + 1.55488I
− 0.419089I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.181830 − 0.531149I
a = 0.947794 − 0.607629I
b = 0.27628 − 1.55488I
0.419089I 0
u = 0.403941 + 0.384818I
a = 0.000885 + 1.300050I
b = 0.75727 + 1.79444I
0.159819 − 0.791393I 8.50855 − 4.94473I
u = 0.403941 − 0.384818I
a = 0.000885 − 1.300050I
b = 0.75727 − 1.79444I
0.159819 + 0.791393I 8.50855 + 4.94473I
u = −1.32190 + 0.62879I
a = 0.291425 + 0.159989I
b = 0.322356 + 0.758523I
−5.58448 + 0.82681I 0
u = −1.32190 − 0.62879I
a = 0.291425 − 0.159989I
b = 0.322356 − 0.758523I
−5.58448 − 0.82681I 0
u = 1.45709 + 0.25117I
a = −0.127705 + 0.542587I
b = 0.485835 − 0.028245I
5.58448 + 0.82681I 0
u = 1.45709 − 0.25117I
a = −0.127705 − 0.542587I
b = 0.485835 + 0.028245I
5.58448 − 0.82681I 0
u = −1.30990 + 0.68784I
a = −0.391778 − 0.894180I
b = 1.33961 − 1.18175I
2.49209 − 10.34980I 0
u = −1.30990 − 0.68784I
a = −0.391778 + 0.894180I
b = 1.33961 + 1.18175I
2.49209 + 10.34980I 0
u = 1.22946 + 0.83117I
a = −0.417236 − 0.486944I
b = −0.435299 + 0.086669I
0.87063 + 4.37653I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.22946 − 0.83117I
a = −0.417236 + 0.486944I
b = −0.435299 − 0.086669I
0.87063 − 4.37653I 0
u = 1.40423 + 0.52577I
a = −0.646016 + 0.989197I
b = 1.17056 + 0.98190I
−4.62976 + 12.68520I 0
u = 1.40423 − 0.52577I
a = −0.646016 − 0.989197I
b = 1.17056 − 0.98190I
−4.62976 − 12.68520I 0
u = −0.63469 + 1.37236I
a = 0.408707 + 0.305367I
b = 0.259804 + 0.960943I
−0.20224 + 3.55721I 0
u = −0.63469 − 1.37236I
a = 0.408707 − 0.305367I
b = 0.259804 − 0.960943I
−0.20224 − 3.55721I 0
u = −1.41461 + 0.61654I
a = −0.227152 − 0.907168I
b = 1.025380 − 0.508802I
4.62976 − 12.68520I 0
u = −1.41461 − 0.61654I
a = −0.227152 + 0.907168I
b = 1.025380 + 0.508802I
4.62976 + 12.68520I 0
u = 0.13532 + 1.57756I
a = 0.120473 + 0.305686I
b = 0.465933 + 0.231420I
5.66863I 0
u = 0.13532 − 1.57756I
a = 0.120473 − 0.305686I
b = 0.465933 − 0.231420I
− 5.66863I 0
u = 1.48056 + 0.67558I
a = 0.243610 − 0.653874I
b = −1.021090 − 0.548627I
5.81721 + 4.62194I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.48056 − 0.67558I
a = 0.243610 + 0.653874I
b = −1.021090 + 0.548627I
5.81721 − 4.62194I 0
u = −0.055622 + 0.343280I
a = −1.41422 − 0.37347I
b = −0.65570 − 1.79393I
−0.159819 + 0.791393I −8.50855 + 4.94473I
u = −0.055622 − 0.343280I
a = −1.41422 + 0.37347I
b = −0.65570 + 1.79393I
−0.159819 − 0.791393I −8.50855 − 4.94473I
u = −0.021732 + 0.344096I
a = −2.48909 + 2.39233I
b = −0.555564 + 0.833787I
−3.58665 − 3.20085I −6.93836 + 8.90282I
u = −0.021732 − 0.344096I
a = −2.48909 − 2.39233I
b = −0.555564 − 0.833787I
−3.58665 + 3.20085I −6.93836 − 8.90282I
u = 1.69847
a = −0.517371
b = 0.583185
5.62510 0
u = −0.182421 + 0.010400I
a = −2.28942 − 2.44876I
b = 1.075820 + 0.140423I
2.93285 + 0.71247I 3.42268 + 3.66333I
u = −0.182421 − 0.010400I
a = −2.28942 + 2.44876I
b = 1.075820 − 0.140423I
2.93285 − 0.71247I 3.42268 − 3.66333I
u = −1.35852 + 1.23335I
a = −0.143899 − 0.194437I
b = 0.108243 − 0.945472I
−0.87063 + 4.37653I 0
u = −1.35852 − 1.23335I
a = −0.143899 + 0.194437I
b = 0.108243 + 0.945472I
−0.87063 − 4.37653I 0
21
III. I
u
3
= h−u
2
+ b, −u
2
+ a + 1, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
−u
3
+ u
a
4
=
u
2
− 1
u
2
a
5
=
−u
5
+ 2u
3
− u
−u
5
+ u
3
− u
a
3
=
−1
u
2
a
11
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
7
=
−u
u
3
− u
a
6
=
0
−u
a
2
=
−1
0
a
10
=
−u
2
+ 1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u
4
+ 8u
2
− 8u − 4
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
c
12
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
2
, c
4
, c
8
c
10
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
3
, c
9
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
c
5
, c
11
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
7
, c
8
c
10
, c
12
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
3
, c
5
, c
9
c
11
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 + 0.295542I
a = −0.082955 − 0.592379I
b = 0.917045 − 0.592379I
3.78121 − 1.84861I 7.43343 + 1.58845I
u = −1.002190 − 0.295542I
a = −0.082955 + 0.592379I
b = 0.917045 + 0.592379I
3.78121 + 1.84861I 7.43343 − 1.58845I
u = 0.428243 + 0.664531I
a = −1.258210 + 0.569162I
b = −0.258209 + 0.569162I
−3.78121 − 1.84861I −7.43343 + 1.58845I
u = 0.428243 − 0.664531I
a = −1.258210 − 0.569162I
b = −0.258209 − 0.569162I
−3.78121 + 1.84861I −7.43343 − 1.58845I
u = 1.073950 + 0.558752I
a = −0.158836 + 1.200140I
b = 0.84116 + 1.20014I
11.3860I 0. − 11.02114I
u = 1.073950 − 0.558752I
a = −0.158836 − 1.200140I
b = 0.84116 − 1.20014I
− 11.3860I 0. + 11.02114I
25
IV. I
u
4
= h−8.90 × 10
11
u
23
+ 2.54 × 10
11
u
22
+ · · · + 2.91 × 10
10
b + 3.17 ×
10
12
, 3.87 × 10
12
u
23
− 1.07 × 10
12
u
22
+ · · · + 2.91 × 10
10
a − 1.37 ×
10
13
, u
24
− 10u
22
+ · · · − 11u − 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
−u
3
+ u
a
4
=
−133.264u
23
+ 36.8151u
22
+ ··· + 3521.75u + 472.967
30.6439u
23
− 8.74848u
22
+ ··· − 800.758u − 109.242
a
5
=
−145.583u
23
+ 40.3523u
22
+ ··· + 3844.19u + 516.239
19.1548u
23
− 5.62364u
22
+ ··· − 504.916u − 69.5071
a
3
=
−163.908u
23
+ 45.5636u
22
+ ··· + 4322.51u + 582.209
30.6439u
23
− 8.74848u
22
+ ··· − 800.758u − 109.242
a
11
=
38.6955u
23
− 8.18117u
22
+ ··· − 1133.06u − 165.665
6.28672u
23
− 2.05454u
22
+ ··· − 160.681u − 19.7625
a
7
=
−12.4005u
23
+ 0.904865u
22
+ ··· + 499.269u + 85.9649
−18.7080u
23
+ 5.68416u
22
+ ··· + 471.569u + 60.4196
a
6
=
175.762u
23
− 51.5394u
22
+ ··· − 4505.30u − 589.351
−58.1299u
23
+ 16.5665u
22
+ ··· + 1501.04u + 196.542
a
2
=
−30.9399u
23
+ 5.25752u
22
+ ··· + 918.470u + 138.972
−13.1835u
23
+ 4.63925u
22
+ ··· + 341.190u + 42.1534
a
10
=
87.8916u
23
− 27.4612u
22
+ ··· − 2241.22u − 286.075
−34.9729u
23
+ 10.6527u
22
+ ··· + 901.141u + 117.632
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
3414113766563
14527774699
u
23
−
966004724095
14527774699
u
22
+ ··· −
91077924221825
14527774699
u −
11884483669996
14527774699
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
c
12
u
24
− 10u
22
+ ··· + 11u − 1
c
2
, c
4
, c
8
c
10
u
24
− 10u
22
+ ··· − 11u − 1
c
3
, c
9
u
24
− 3u
23
+ ··· + u − 1
c
5
, c
11
u
24
+ 3u
23
+ ··· − u − 1
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
7
, c
8
c
10
, c
12
y
24
− 20y
23
+ ··· − 43y + 1
c
3
, c
5
, c
9
c
11
y
24
+ y
23
+ ··· − 9y + 1
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.942012 + 0.158290I
a = 0.48886 − 2.41805I
b = −0.156662 − 0.513941I
− 0.622919I 0. − 44.2801I
u = −0.942012 − 0.158290I
a = 0.48886 + 2.41805I
b = −0.156662 + 0.513941I
0.622919I 0. + 44.2801I
u = 0.855341 + 0.650781I
a = −0.310844 + 0.000102I
b = −0.481680 + 1.309900I
− 2.28124I − 60.10 + 0.468753I
u = 0.855341 − 0.650781I
a = −0.310844 − 0.000102I
b = −0.481680 − 1.309900I
2.28124I − 60.10 − 0.468753I
u = 1.070590 + 0.231946I
a = 0.604840 − 0.875971I
b = −1.48893 − 1.35156I
0.75922 + 5.04540I 3.01002 − 10.31379I
u = 1.070590 − 0.231946I
a = 0.604840 + 0.875971I
b = −1.48893 + 1.35156I
0.75922 − 5.04540I 3.01002 + 10.31379I
u = 0.866934
a = −1.92529
b = 1.48863
−7.67190 −2.90280
u = −1.22624
a = −0.799131
b = 1.52764
6.01573 15.7530
u = 1.273950 + 0.269607I
a = 0.90375 − 1.25218I
b = −0.850713 − 0.797515I
−0.75922 + 5.04540I −3.01002 − 10.31379I
u = 1.273950 − 0.269607I
a = 0.90375 + 1.25218I
b = −0.850713 + 0.797515I
−0.75922 − 5.04540I −3.01002 + 10.31379I
29
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.878983 + 0.966271I
a = −0.533797 + 0.263579I
b = −0.563921 + 0.259610I
0.75922 − 5.04540I 3.01002 + 10.31379I
u = −0.878983 − 0.966271I
a = −0.533797 − 0.263579I
b = −0.563921 − 0.259610I
0.75922 + 5.04540I 3.01002 − 10.31379I
u = −1.248310 + 0.399818I
a = −0.045143 − 1.063800I
b = 0.265944 − 0.202204I
− 2.28124I − 60.10 + 0.468753I
u = −1.248310 − 0.399818I
a = −0.045143 + 1.063800I
b = 0.265944 + 0.202204I
2.28124I − 60.10 − 0.468753I
u = 1.37969
a = 0.477055
b = 0.457732
−6.01573 −15.7530
u = 1.61773
a = −0.920194
b = 1.66910
7.67190 2.90280
u = 0.80590 + 1.44348I
a = 0.303394 − 0.221283I
b = −0.214510 − 0.747474I
−0.75922 − 5.04540I 0. + 10.31379I
u = 0.80590 − 1.44348I
a = 0.303394 + 0.221283I
b = −0.214510 + 0.747474I
−0.75922 + 5.04540I 0. − 10.31379I
u = −0.280614 + 0.170720I
a = 0.40577 − 1.58463I
b = 0.07776 − 2.35522I
0.622919I 0. + 44.2801I
u = −0.280614 − 0.170720I
a = 0.40577 + 1.58463I
b = 0.07776 + 2.35522I
− 0.622919I 0. − 44.2801I
30
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.68097
a = 0.272302
b = −0.658191
6.01573 15.7530
u = −1.70519
a = 0.928246
b = −1.26238
7.67190 0
u = −0.292949
a = −4.30921
b = 1.58284
−7.67190 −2.90280
u = −0.270736
a = 5.64255
b = −0.979929
−6.01573 −15.7530
31
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
20
+ u
19
+ ··· − 8u − 1)
· (u
24
− 10u
22
+ ··· + 11u − 1)(u
120
− u
119
+ ··· + 1207u − 101)
c
2
, c
8
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
20
− u
19
+ ··· + 8u − 1)
· (u
24
− 10u
22
+ ··· − 11u − 1)(u
120
+ u
119
+ ··· − 1207u − 101)
c
3
, c
9
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)(u
20
+ 3u
19
+ ··· − 4u + 1)
· (u
24
− 3u
23
+ ··· + u − 1)(u
120
− 7u
117
+ ··· − 175u − 575)
c
4
, c
10
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
20
+ u
19
+ ··· − 8u − 1)
· (u
24
− 10u
22
+ ··· − 11u − 1)(u
120
− u
119
+ ··· + 1207u − 101)
c
5
, c
11
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)(u
20
− 3u
19
+ ··· + 4u + 1)
· (u
24
+ 3u
23
+ ··· − u − 1)(u
120
+ 7u
117
+ ··· + 175u − 575)
c
6
, c
12
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
20
− u
19
+ ··· + 8u − 1)
· (u
24
− 10u
22
+ ··· + 11u − 1)(u
120
+ u
119
+ ··· − 1207u − 101)
32
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
7
, c
8
c
10
, c
12
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
20
− 21y
19
+ ··· − 22y + 1)
· (y
24
− 20y
23
+ ··· − 43y + 1)(y
120
− 73y
119
+ ··· − 569059y + 10201)
c
3
, c
5
, c
9
c
11
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)(y
20
− 9y
19
+ ··· − 58y + 1)
· (y
24
+ y
23
+ ··· − 9y + 1)(y
120
+ 86y
118
+ ··· − 5688625y + 330625)
33
