12a
1093
(K12a
1093
)
A knot diagram
1
Linearized knot diagam
4 7 10 1 12 2 11 6 5 3 8 9
Solving Sequence
7,11
8
3,12
2 6 9 5 10 4 1
c
7
c
11
c
2
c
6
c
8
c
5
c
10
c
3
c
1
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h2.41694 × 10
695
u
134
+ 4.64040 × 10
695
u
133
+ ··· + 5.96213 × 10
699
b − 1.44042 × 10
700
,
− 1.38922 × 10
698
u
134
− 1.25918 × 10
698
u
133
+ ··· + 3.78595 × 10
701
a + 4.01348 × 10
701
,
u
135
+ u
134
+ ··· − 29624u + 4064i
I
u
2
= h−8.63325 × 10
19
u
27
− 6.49290 × 10
20
u
26
+ ··· + 3.25555 × 10
19
b + 1.08679 × 10
21
,
2.39039 × 10
20
u
27
+ 1.89818 × 10
21
u
26
+ ··· + 6.51111 × 10
19
a − 4.16427 × 10
21
, u
28
+ 8u
27
+ ··· − 8u + 8i
I
u
3
= h−4a
3
+ 4a
2
+ 3b − 3a + 1, 4a
4
+ 5a
2
+ 2a + 2, u − 1i
* 3 irreducible components of dim
C
= 0, with total 167 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
= h2.42 × 10
695
u
134
+ 4.64 × 10
695
u
133
+ · · · + 5.96 × 10
699
b − 1.44 ×
10
700
, −1.39 × 10
698
u
134
− 1.26 × 10
698
u
133
+ · · · + 3.79 × 10
701
a + 4.01 ×
10
701
, u
135
+ u
134
+ · · · − 29624u + 4064i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u
2
a
3
=
0.000366942u
134
+ 0.000332594u
133
+ ··· + 67.1416u − 1.06010
−0.0000405383u
134
− 0.0000778313u
133
+ ··· − 19.1811u + 2.41594
a
12
=
−u
−u
3
+ u
a
2
=
0.000326403u
134
+ 0.000254762u
133
+ ··· + 47.9605u + 1.35585
−0.0000405383u
134
− 0.0000778313u
133
+ ··· − 19.1811u + 2.41594
a
6
=
−0.000256986u
134
− 0.000372603u
133
+ ··· + 73.1449u − 10.7816
0.0000667386u
134
− 5.85205 × 10
−7
u
133
+ ··· + 24.5301u − 1.64608
a
9
=
−0.000634464u
134
− 0.000889132u
133
+ ··· − 14.6902u − 1.26794
−0.0000357046u
134
− 0.0000865215u
133
+ ··· + 13.6147u − 1.72538
a
5
=
−0.000272618u
134
− 0.000395365u
133
+ ··· + 75.5210u − 11.1880
0.0000860364u
134
+ 0.0000347660u
133
+ ··· + 22.0063u − 1.21078
a
10
=
0.0000129880u
134
− 0.000201145u
133
+ ··· − 28.4490u + 8.78419
−0.0000482932u
134
− 0.0000371033u
133
+ ··· − 18.7256u + 1.31562
a
4
=
−0.000237685u
134
− 0.000772866u
133
+ ··· − 36.2106u + 10.8885
−0.0000422265u
134
− 0.0000873001u
133
+ ··· − 19.4457u + 1.18457
a
1
=
−0.000761097u
134
− 0.00188751u
133
+ ··· − 32.2015u + 9.78192
−0.000255375u
134
− 0.000516647u
133
+ ··· − 21.9195u + 3.00457
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.000378821u
134
+ 0.000233338u
133
+ ··· + 121.501u − 5.44603
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
135
− 9u
134
+ ··· + 167083u + 63886
c
2
, c
6
u
135
− u
134
+ ··· + 144633u + 4946
c
3
, c
10
4(4u
135
+ 36u
134
+ ··· + 2779214u + 127574)
c
5
u
135
− 3u
134
+ ··· + 45913u + 3188
c
7
, c
11
u
135
− u
134
+ ··· − 29624u − 4064
c
8
4(4u
135
− 56u
134
+ ··· + 23579u − 1798)
c
9
u
135
− 3u
134
+ ··· + 48u + 16
c
12
4(4u
135
+ 8u
134
+ ··· − 21656u − 7442)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
135
+ 83y
134
+ ··· − 6695683735y −4081420996
c
2
, c
6
y
135
− 93y
134
+ ··· − 1498427007y −24462916
c
3
, c
10
16(16y
135
+ 1560y
134
+ ··· + 6.92965 × 10
11
y −1.62751 × 10
10
)
c
5
y
135
+ 23y
134
+ ··· − 394825095y −10163344
c
7
, c
11
y
135
− 119y
134
+ ··· − 1894424256y −16516096
c
8
16(16y
135
− 568y
134
+ ··· + 1426485y −3232804)
c
9
y
135
− 11y
134
+ ··· − 9664y −256
c
12
16(16y
135
− 248y
134
+ ··· + 3.86816 × 10
9
y −5.53834 × 10
7
)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.042300 + 0.173887I
a = 0.346749 + 0.407337I
b = −0.307688 + 0.981724I
1.69401 + 1.01081I 0
u = 1.042300 − 0.173887I
a = 0.346749 − 0.407337I
b = −0.307688 − 0.981724I
1.69401 − 1.01081I 0
u = 0.375168 + 0.842996I
a = −1.168620 − 0.783699I
b = 1.266540 + 0.437731I
−0.31064 − 4.93968I 0
u = 0.375168 − 0.842996I
a = −1.168620 + 0.783699I
b = 1.266540 − 0.437731I
−0.31064 + 4.93968I 0
u = 1.022720 + 0.353185I
a = −0.572973 − 0.159218I
b = 0.0470834 − 0.0646180I
−1.88121 − 1.43775I 0
u = 1.022720 − 0.353185I
a = −0.572973 + 0.159218I
b = 0.0470834 + 0.0646180I
−1.88121 + 1.43775I 0
u = 0.354628 + 0.844423I
a = 1.000250 + 0.197229I
b = −1.235060 − 0.186530I
−1.62494 − 3.37205I 0
u = 0.354628 − 0.844423I
a = 1.000250 − 0.197229I
b = −1.235060 + 0.186530I
−1.62494 + 3.37205I 0
u = 0.196400 + 0.873449I
a = 0.010733 + 0.241199I
b = −0.929415 − 0.243228I
−1.17539 − 3.86755I 0
u = 0.196400 − 0.873449I
a = 0.010733 − 0.241199I
b = −0.929415 + 0.243228I
−1.17539 + 3.86755I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.801867 + 0.367668I
a = 0.412833 + 0.031474I
b = −0.442433 − 0.840044I
3.52686 + 1.14515I 0
u = −0.801867 − 0.367668I
a = 0.412833 − 0.031474I
b = −0.442433 + 0.840044I
3.52686 − 1.14515I 0
u = 1.111190 + 0.197400I
a = 0.480641 − 0.738811I
b = 0.182267 + 0.083453I
−0.360365 + 0.099354I 0
u = 1.111190 − 0.197400I
a = 0.480641 + 0.738811I
b = 0.182267 − 0.083453I
−0.360365 − 0.099354I 0
u = 0.022742 + 1.129890I
a = −1.182390 + 0.135167I
b = 1.228750 − 0.290479I
−0.54814 + 5.33540I 0
u = 0.022742 − 1.129890I
a = −1.182390 − 0.135167I
b = 1.228750 + 0.290479I
−0.54814 − 5.33540I 0
u = −0.159127 + 0.855147I
a = −0.227634 + 1.081360I
b = 0.498582 − 0.643015I
4.39896 − 3.63479I 0
u = −0.159127 − 0.855147I
a = −0.227634 − 1.081360I
b = 0.498582 + 0.643015I
4.39896 + 3.63479I 0
u = −1.13139
a = 0.635787
b = 1.35448
−3.56663 0
u = −1.048410 + 0.435361I
a = 0.206817 + 0.414636I
b = 0.165033 − 0.667697I
−1.22010 + 4.85217I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.048410 − 0.435361I
a = 0.206817 − 0.414636I
b = 0.165033 + 0.667697I
−1.22010 − 4.85217I 0
u = 0.954327 + 0.634536I
a = −0.514396 − 1.112860I
b = 1.072350 + 0.058424I
−1.88379 − 0.20890I 0
u = 0.954327 − 0.634536I
a = −0.514396 + 1.112860I
b = 1.072350 − 0.058424I
−1.88379 + 0.20890I 0
u = 1.144330 + 0.102749I
a = −3.05782 + 0.27062I
b = −1.126760 + 0.024099I
−3.55565 − 0.36823I 0
u = 1.144330 − 0.102749I
a = −3.05782 − 0.27062I
b = −1.126760 − 0.024099I
−3.55565 + 0.36823I 0
u = −1.143620 + 0.134733I
a = −0.866453 − 0.423763I
b = −1.138170 + 0.364873I
1.13499 + 5.51192I 0
u = −1.143620 − 0.134733I
a = −0.866453 + 0.423763I
b = −1.138170 − 0.364873I
1.13499 − 5.51192I 0
u = 0.070649 + 0.802633I
a = 0.147155 − 1.238800I
b = 0.925272 + 0.559974I
3.20324 − 8.18296I 0
u = 0.070649 − 0.802633I
a = 0.147155 + 1.238800I
b = 0.925272 − 0.559974I
3.20324 + 8.18296I 0
u = 0.589697 + 0.497831I
a = 1.50479 + 2.22725I
b = −1.042400 − 0.259599I
−2.99902 − 1.02719I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.589697 − 0.497831I
a = 1.50479 − 2.22725I
b = −1.042400 + 0.259599I
−2.99902 + 1.02719I 0
u = 1.247530 + 0.044901I
a = −0.062702 + 1.064240I
b = 0.29135 − 1.59005I
−0.43890 − 2.75667I 0
u = 1.247530 − 0.044901I
a = −0.062702 − 1.064240I
b = 0.29135 + 1.59005I
−0.43890 + 2.75667I 0
u = 1.206180 + 0.321812I
a = −0.699746 − 0.904447I
b = 0.279818 + 0.437371I
−2.64241 − 1.39108I 0
u = 1.206180 − 0.321812I
a = −0.699746 + 0.904447I
b = 0.279818 − 0.437371I
−2.64241 + 1.39108I 0
u = −0.065848 + 0.734715I
a = 1.343790 − 0.368790I
b = 0.249533 + 0.416123I
−2.16498 + 3.13445I 0
u = −0.065848 − 0.734715I
a = 1.343790 + 0.368790I
b = 0.249533 − 0.416123I
−2.16498 − 3.13445I 0
u = −1.166810 + 0.520013I
a = −0.525072 − 0.212443I
b = 0.364620 + 0.638008I
1.37419 + 8.55632I 0
u = −1.166810 − 0.520013I
a = −0.525072 + 0.212443I
b = 0.364620 − 0.638008I
1.37419 − 8.55632I 0
u = 1.310890 + 0.161661I
a = −0.011416 + 1.141330I
b = −1.55424 − 0.69969I
−10.91190 − 0.94916I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.310890 − 0.161661I
a = −0.011416 − 1.141330I
b = −1.55424 + 0.69969I
−10.91190 + 0.94916I 0
u = −0.480429 + 0.464829I
a = −0.352588 − 0.945776I
b = −0.723371 + 0.738770I
4.27948 + 2.23809I 4.54515 − 5.49892I
u = −0.480429 − 0.464829I
a = −0.352588 + 0.945776I
b = −0.723371 − 0.738770I
4.27948 − 2.23809I 4.54515 + 5.49892I
u = −0.191359 + 0.634607I
a = −1.29441 + 1.35250I
b = −0.239430 − 0.753076I
2.25960 + 8.95544I 0.96042 − 5.62815I
u = −0.191359 − 0.634607I
a = −1.29441 − 1.35250I
b = −0.239430 + 0.753076I
2.25960 − 8.95544I 0.96042 + 5.62815I
u = 0.602700 + 0.272402I
a = −0.387320 − 1.134790I
b = 0.381962 + 0.379655I
−0.73020 − 1.27106I −3.86635 + 5.97415I
u = 0.602700 − 0.272402I
a = −0.387320 + 1.134790I
b = 0.381962 − 0.379655I
−0.73020 + 1.27106I −3.86635 − 5.97415I
u = 1.342040 + 0.066163I
a = 0.936528 + 0.270389I
b = 1.294650 + 0.053531I
−5.87244 − 1.86792I 0
u = 1.342040 − 0.066163I
a = 0.936528 − 0.270389I
b = 1.294650 − 0.053531I
−5.87244 + 1.86792I 0
u = −0.909402 + 0.994660I
a = −0.679504 + 0.080206I
b = −0.711336 − 0.042991I
−0.23833 − 4.47513I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.909402 − 0.994660I
a = −0.679504 − 0.080206I
b = −0.711336 + 0.042991I
−0.23833 + 4.47513I 0
u = 0.233125 + 0.599818I
a = −0.94256 − 1.34302I
b = 0.069701 + 0.451974I
−0.07055 − 2.23972I −1.51477 + 4.66806I
u = 0.233125 − 0.599818I
a = −0.94256 + 1.34302I
b = 0.069701 − 0.451974I
−0.07055 + 2.23972I −1.51477 − 4.66806I
u = −1.363400 + 0.023484I
a = −0.076224 − 0.915469I
b = 0.11300 + 1.77332I
−1.054640 + 0.485171I 0
u = −1.363400 − 0.023484I
a = −0.076224 + 0.915469I
b = 0.11300 − 1.77332I
−1.054640 − 0.485171I 0
u = −1.335590 + 0.317660I
a = 0.395922 − 0.138955I
b = 1.284070 + 0.201909I
−4.79277 + 1.63021I 0
u = −1.335590 − 0.317660I
a = 0.395922 + 0.138955I
b = 1.284070 − 0.201909I
−4.79277 − 1.63021I 0
u = 1.370570 + 0.124918I
a = 0.054734 − 0.900852I
b = 1.72236 + 0.45746I
−8.86658 + 4.55321I 0
u = 1.370570 − 0.124918I
a = 0.054734 + 0.900852I
b = 1.72236 − 0.45746I
−8.86658 − 4.55321I 0
u = −1.364160 + 0.204311I
a = 0.303537 + 1.217300I
b = 1.53226 − 0.40111I
−8.83628 + 8.82618I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.364160 − 0.204311I
a = 0.303537 − 1.217300I
b = 1.53226 + 0.40111I
−8.83628 − 8.82618I 0
u = −0.215689 + 0.577714I
a = −0.480099 − 0.643883I
b = −0.157789 + 0.504487I
1.14682 − 1.00992I 4.28803 + 1.80888I
u = −0.215689 − 0.577714I
a = −0.480099 + 0.643883I
b = −0.157789 − 0.504487I
1.14682 + 1.00992I 4.28803 − 1.80888I
u = 1.366910 + 0.232578I
a = 0.113598 + 1.000880I
b = −0.177813 − 1.256780I
−6.81809 − 6.36491I 0
u = 1.366910 − 0.232578I
a = 0.113598 − 1.000880I
b = −0.177813 + 1.256780I
−6.81809 + 6.36491I 0
u = −1.358780 + 0.296370I
a = 1.028200 + 0.546258I
b = 1.200670 − 0.300277I
−1.36283 + 12.03610I 0
u = −1.358780 − 0.296370I
a = 1.028200 − 0.546258I
b = 1.200670 + 0.300277I
−1.36283 − 12.03610I 0
u = −0.552495 + 1.276640I
a = 0.760402 − 0.645705I
b = −1.231820 + 0.364232I
−0.93888 + 13.06600I 0
u = −0.552495 − 1.276640I
a = 0.760402 + 0.645705I
b = −1.231820 − 0.364232I
−0.93888 − 13.06600I 0
u = −1.375590 + 0.219896I
a = 0.075988 + 0.951451I
b = 0.116657 − 1.130850I
−5.14161 + 5.17075I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.375590 − 0.219896I
a = 0.075988 − 0.951451I
b = 0.116657 + 1.130850I
−5.14161 − 5.17075I 0
u = 1.41743 + 0.07077I
a = −0.725147 + 0.008665I
b = −1.269580 − 0.371743I
−1.74448 − 3.57691I 0
u = 1.41743 − 0.07077I
a = −0.725147 − 0.008665I
b = −1.269580 + 0.371743I
−1.74448 + 3.57691I 0
u = 1.40797 + 0.23590I
a = 0.038714 − 0.960594I
b = −0.03228 + 1.45259I
−2.94161 − 12.06880I 0
u = 1.40797 − 0.23590I
a = 0.038714 + 0.960594I
b = −0.03228 − 1.45259I
−2.94161 + 12.06880I 0
u = −1.41081 + 0.23225I
a = −0.117600 − 1.149320I
b = −1.39130 + 0.37598I
−12.38160 + 4.31096I 0
u = −1.41081 − 0.23225I
a = −0.117600 + 1.149320I
b = −1.39130 − 0.37598I
−12.38160 − 4.31096I 0
u = 0.47262 + 1.35028I
a = 0.662873 + 0.516213I
b = −1.202530 − 0.201857I
−3.72221 − 4.65897I 0
u = 0.47262 − 1.35028I
a = 0.662873 − 0.516213I
b = −1.202530 + 0.201857I
−3.72221 + 4.65897I 0
u = 1.36870 + 0.43012I
a = −0.048845 − 1.093760I
b = 1.53952 + 0.65447I
−4.93365 − 10.71610I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.36870 − 0.43012I
a = −0.048845 + 1.093760I
b = 1.53952 − 0.65447I
−4.93365 + 10.71610I 0
u = −1.40699 + 0.28586I
a = −0.538071 − 0.349707I
b = −1.375900 + 0.165577I
−6.37288 + 7.80768I 0
u = −1.40699 − 0.28586I
a = −0.538071 + 0.349707I
b = −1.375900 − 0.165577I
−6.37288 − 7.80768I 0
u = 0.554723 + 0.096353I
a = −2.19070 − 2.89012I
b = 1.047180 + 0.168131I
−2.57316 − 0.08276I −4.96565 − 4.99334I
u = 0.554723 − 0.096353I
a = −2.19070 + 2.89012I
b = 1.047180 − 0.168131I
−2.57316 + 0.08276I −4.96565 + 4.99334I
u = −1.42651 + 0.18499I
a = 0.120355 − 0.948175I
b = 0.074932 + 0.947346I
−7.64328 + 0.39151I 0
u = −1.42651 − 0.18499I
a = 0.120355 + 0.948175I
b = 0.074932 − 0.947346I
−7.64328 − 0.39151I 0
u = 0.166896 + 0.530884I
a = 2.35827 + 0.99102I
b = −1.339650 + 0.107874I
−7.18424 − 1.37750I −11.02196 + 1.26654I
u = 0.166896 − 0.530884I
a = 2.35827 − 0.99102I
b = −1.339650 − 0.107874I
−7.18424 + 1.37750I −11.02196 − 1.26654I
u = 1.23894 + 0.76058I
a = 0.118410 + 0.507302I
b = 0.769646 − 0.497899I
−0.42265 + 3.03966I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.23894 − 0.76058I
a = 0.118410 − 0.507302I
b = 0.769646 + 0.497899I
−0.42265 − 3.03966I 0
u = −1.45338 + 0.11952I
a = 0.042917 + 0.887662I
b = 1.43555 − 0.65299I
−9.04455 + 1.32229I 0
u = −1.45338 − 0.11952I
a = 0.042917 − 0.887662I
b = 1.43555 + 0.65299I
−9.04455 − 1.32229I 0
u = 1.35728 + 0.55924I
a = 0.160665 + 0.886116I
b = −1.53445 − 0.31053I
−7.62426 − 3.59528I 0
u = 1.35728 − 0.55924I
a = 0.160665 − 0.886116I
b = −1.53445 + 0.31053I
−7.62426 + 3.59528I 0
u = −1.50604 + 0.16491I
a = 0.033133 − 1.095000I
b = −1.16900 + 0.86994I
−9.83470 + 3.48502I 0
u = −1.50604 − 0.16491I
a = 0.033133 + 1.095000I
b = −1.16900 − 0.86994I
−9.83470 − 3.48502I 0
u = −1.48334 + 0.30897I
a = 0.114199 + 0.988801I
b = 1.64351 − 0.68221I
−6.32039 + 9.09736I 0
u = −1.48334 − 0.30897I
a = 0.114199 − 0.988801I
b = 1.64351 + 0.68221I
−6.32039 − 9.09736I 0
u = −1.48380 + 0.30742I
a = −0.089633 − 0.768425I
b = −1.66465 + 0.44823I
−7.61781 + 7.52234I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48380 − 0.30742I
a = −0.089633 + 0.768425I
b = −1.66465 − 0.44823I
−7.61781 − 7.52234I 0
u = 1.48766 + 0.32268I
a = −0.348951 + 0.273680I
b = −1.219050 + 0.019417I
−5.64071 − 1.20331I 0
u = 1.48766 − 0.32268I
a = −0.348951 − 0.273680I
b = −1.219050 − 0.019417I
−5.64071 + 1.20331I 0
u = 0.402262 + 0.257570I
a = 1.95201 + 1.22303I
b = 0.415463 + 0.682574I
2.37310 + 1.85175I 1.04912 + 4.13975I
u = 0.402262 − 0.257570I
a = 1.95201 − 1.22303I
b = 0.415463 − 0.682574I
2.37310 − 1.85175I 1.04912 − 4.13975I
u = −1.52532 + 0.08162I
a = −0.206381 + 0.757439I
b = −0.654357 − 1.078820I
−1.97987 − 3.60140I 0
u = −1.52532 − 0.08162I
a = −0.206381 − 0.757439I
b = −0.654357 + 1.078820I
−1.97987 + 3.60140I 0
u = 1.54797 + 0.30024I
a = 0.368668 − 0.644436I
b = 0.946432 + 0.256661I
−0.770708 − 0.402618I 0
u = 1.54797 − 0.30024I
a = 0.368668 + 0.644436I
b = 0.946432 − 0.256661I
−0.770708 + 0.402618I 0
u = 0.006561 + 0.421077I
a = −3.10103 − 0.78230I
b = 1.47845 + 0.02527I
−4.28585 − 6.43451I −6.90078 + 7.59467I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.006561 − 0.421077I
a = −3.10103 + 0.78230I
b = 1.47845 − 0.02527I
−4.28585 + 6.43451I −6.90078 − 7.59467I
u = −1.54733 + 0.47993I
a = −0.082141 − 1.068240I
b = −1.41677 + 0.50168I
−9.9791 + 10.9194I 0
u = −1.54733 − 0.47993I
a = −0.082141 + 1.068240I
b = −1.41677 − 0.50168I
−9.9791 − 10.9194I 0
u = −0.160611 + 0.310524I
a = 0.656557 + 0.375953I
b = −0.869358 − 0.803511I
4.08762 − 3.24713I 9.21382 − 3.43619I
u = −0.160611 − 0.310524I
a = 0.656557 − 0.375953I
b = −0.869358 + 0.803511I
4.08762 + 3.24713I 9.21382 + 3.43619I
u = 0.150937 + 0.313289I
a = 0.97833 + 1.39527I
b = −0.742342 − 0.934781I
4.11166 − 3.33292I 12.2705 + 8.4944I
u = 0.150937 − 0.313289I
a = 0.97833 − 1.39527I
b = −0.742342 + 0.934781I
4.11166 + 3.33292I 12.2705 − 8.4944I
u = 1.59745 + 0.46157I
a = −0.052135 + 1.018600I
b = −1.49284 − 0.62222I
−7.6932 − 19.2467I 0
u = 1.59745 − 0.46157I
a = −0.052135 − 1.018600I
b = −1.49284 + 0.62222I
−7.6932 + 19.2467I 0
u = 1.64496 + 0.49440I
a = −0.025299 − 0.885736I
b = 1.47554 + 0.51149I
−12.0871 − 12.5253I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.64496 − 0.49440I
a = −0.025299 + 0.885736I
b = 1.47554 − 0.51149I
−12.0871 + 12.5253I 0
u = −1.69602 + 0.30220I
a = 0.022326 + 0.807898I
b = 1.085640 − 0.201002I
−6.51925 + 0.92808I 0
u = −1.69602 − 0.30220I
a = 0.022326 − 0.807898I
b = 1.085640 + 0.201002I
−6.51925 − 0.92808I 0
u = −0.72177 + 1.61517I
a = −0.616813 + 0.357221I
b = 1.180720 − 0.179480I
−4.87164 + 5.39508I 0
u = −0.72177 − 1.61517I
a = −0.616813 − 0.357221I
b = 1.180720 + 0.179480I
−4.87164 − 5.39508I 0
u = −0.014582 + 0.225788I
a = 1.66916 + 2.22161I
b = 0.877366 − 0.279079I
−1.56711 + 0.85614I −4.99249 + 0.59420I
u = −0.014582 − 0.225788I
a = 1.66916 − 2.22161I
b = 0.877366 + 0.279079I
−1.56711 − 0.85614I −4.99249 − 0.59420I
u = −1.72626 + 0.43559I
a = 0.020457 + 0.862571I
b = 1.319720 − 0.482481I
−11.56470 + 5.56108I 0
u = −1.72626 − 0.43559I
a = 0.020457 − 0.862571I
b = 1.319720 + 0.482481I
−11.56470 − 5.56108I 0
u = −0.86040 + 1.59480I
a = 0.572015 − 0.247042I
b = −1.131260 + 0.017977I
−1.75043 − 4.32646I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.86040 − 1.59480I
a = 0.572015 + 0.247042I
b = −1.131260 − 0.017977I
−1.75043 + 4.32646I 0
u = −0.036179 + 0.166320I
a = 5.26506 + 1.27592I
b = 0.153818 − 0.957523I
3.35131 + 0.04338I 6.27768 − 0.37776I
u = −0.036179 − 0.166320I
a = 5.26506 − 1.27592I
b = 0.153818 + 0.957523I
3.35131 − 0.04338I 6.27768 + 0.37776I
u = 1.67118 + 0.82464I
a = 0.198220 + 0.642612I
b = −1.384220 − 0.237924I
−7.73090 − 4.06573I 0
u = 1.67118 − 0.82464I
a = 0.198220 − 0.642612I
b = −1.384220 + 0.237924I
−7.73090 + 4.06573I 0
18
II.
I
u
2
= h−8.63×10
19
u
27
−6.49×10
20
u
26
+· · ·+3.26×10
19
b+1.09×10
21
, 2.39×
10
20
u
27
+1.90×10
21
u
26
+· · ·+6.51×10
19
a−4.16×10
21
, u
28
+8u
27
+· · ·−8u+8i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u
2
a
3
=
−3.67124u
27
− 29.1529u
26
+ ··· + 193.957u + 63.9564
2.65185u
27
+ 19.9441u
26
+ ··· − 97.5835u − 33.3826
a
12
=
−u
−u
3
+ u
a
2
=
−1.01939u
27
− 9.20884u
26
+ ··· + 96.3739u + 30.5738
2.65185u
27
+ 19.9441u
26
+ ··· − 97.5835u − 33.3826
a
6
=
−0.708822u
27
− 5.95009u
26
+ ··· + 42.4867u + 17.7117
−2.05568u
27
− 17.8008u
26
+ ··· + 156.338u + 71.5457
a
9
=
2.85416u
27
+ 21.8393u
26
+ ··· − 129.209u − 38.1544
0.306762u
27
+ 1.22461u
26
+ ··· + 17.6117u + 16.9938
a
5
=
−1.25931u
27
− 9.17692u
26
+ ··· + 31.8707u + 5.50419
−2.86301u
27
− 23.7455u
26
+ ··· + 180.775u + 74.3363
a
10
=
0.427332u
27
+ 3.78947u
26
+ ··· − 34.9555u − 13.3036
1.07587u
27
+ 8.28077u
26
+ ··· − 43.0591u − 10.7749
a
4
=
−1.79782u
27
− 15.2972u
26
+ ··· + 136.501u + 56.1966
1.95089u
27
+ 14.9813u
26
+ ··· − 82.1888u − 29.0749
a
1
=
−0.401388u
27
− 4.92700u
26
+ ··· + 64.3024u + 31.7889
0.397796u
27
+ 2.02739u
26
+ ··· + 23.5681u + 16.8218
(ii) Obstruction class = 1
(iii) Cusp Shapes =
394793400711041839109
32555539438267640596
u
27
+
1598655739224354867781
16277769719133820298
u
26
+ ··· −
5870200545912186563669
8138884859566910149
u −
2817020498598265056590
8138884859566910149
19
(iv) u-Polynomials at the component
20
Crossings u-Polynomials at each crossing
c
1
u
28
− 4u
27
+ ··· + 7u + 11
c
2
u
28
− 8u
26
+ ··· − 3u + 1
c
3
u
28
+ 20u
26
+ ··· − 3u + 1
c
4
u
28
+ 4u
27
+ ··· − 7u + 11
c
5
u
28
+ 4u
27
+ ··· + 2u + 1
c
6
u
28
− 8u
26
+ ··· + 3u + 1
c
7
u
28
+ 8u
27
+ ··· − 8u + 8
c
8
u
28
+ 2u
27
+ ··· − 2u + 1
c
9
u
28
− 2u
26
+ ··· − 5u + 1
c
10
u
28
+ 20u
26
+ ··· + 3u + 1
c
11
u
28
− 8u
27
+ ··· + 8u + 8
c
12
u
28
+ 8u
27
+ ··· + 4u + 1
21
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
28
+ 16y
27
+ ··· − 1303y + 121
c
2
, c
6
y
28
− 16y
27
+ ··· − 17y + 1
c
3
, c
10
y
28
+ 40y
27
+ ··· + 25y + 1
c
5
y
28
+ 28y
26
+ ··· + 26y + 1
c
7
, c
11
y
28
− 22y
27
+ ··· − 2400y + 64
c
8
y
28
+ 10y
27
+ ··· + 30y + 1
c
9
y
28
− 4y
27
+ ··· + 7y + 1
c
12
y
28
− 24y
27
+ ··· − 8y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.910839 + 0.434438I
a = 0.312452 + 0.876534I
b = −0.294158 + 0.309787I
0.58923 + 9.74117I −4.79861 − 7.87315I
u = −0.910839 − 0.434438I
a = 0.312452 − 0.876534I
b = −0.294158 − 0.309787I
0.58923 − 9.74117I −4.79861 + 7.87315I
u = −0.680005 + 0.790938I
a = 0.589930 − 0.555705I
b = 0.526735 − 0.131533I
−2.84642 + 4.03958I −8.94088 − 7.34599I
u = −0.680005 − 0.790938I
a = 0.589930 + 0.555705I
b = 0.526735 + 0.131533I
−2.84642 − 4.03958I −8.94088 + 7.34599I
u = 0.868104 + 0.339318I
a = 0.585065 + 0.055680I
b = −0.653088 − 0.182615I
−2.45602 − 1.86090I −11.69528 + 5.63652I
u = 0.868104 − 0.339318I
a = 0.585065 − 0.055680I
b = −0.653088 + 0.182615I
−2.45602 + 1.86090I −11.69528 − 5.63652I
u = 0.836999 + 0.209158I
a = −0.45024 − 3.76533I
b = 1.016550 + 0.081884I
−3.00802 − 0.33993I −15.1405 − 8.7169I
u = 0.836999 − 0.209158I
a = −0.45024 + 3.76533I
b = 1.016550 − 0.081884I
−3.00802 + 0.33993I −15.1405 + 8.7169I
u = 0.010000 + 1.325500I
a = 0.852023 + 0.160238I
b = −1.252560 − 0.145977I
−2.84947 − 4.84439I −4.79416 + 8.05358I
u = 0.010000 − 1.325500I
a = 0.852023 − 0.160238I
b = −1.252560 + 0.145977I
−2.84947 + 4.84439I −4.79416 − 8.05358I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.344360 + 0.040974I
a = 0.137321 − 0.945020I
b = −0.01652 + 1.63265I
−1.14864 − 1.70263I −4.13504 + 2.39464I
u = −1.344360 − 0.040974I
a = 0.137321 + 0.945020I
b = −0.01652 − 1.63265I
−1.14864 + 1.70263I −4.13504 − 2.39464I
u = 1.334600 + 0.167808I
a = −0.717151 − 0.115563I
b = −1.222900 + 0.091680I
−4.69435 − 0.72547I −5.65126 − 0.44890I
u = 1.334600 − 0.167808I
a = −0.717151 + 0.115563I
b = −1.222900 − 0.091680I
−4.69435 + 0.72547I −5.65126 + 0.44890I
u = −1.40149 + 0.31952I
a = −0.156423 − 1.029110I
b = −1.67721 + 0.49060I
−7.35549 + 9.70199I −6.04463 − 9.23208I
u = −1.40149 − 0.31952I
a = −0.156423 + 1.029110I
b = −1.67721 − 0.49060I
−7.35549 − 9.70199I −6.04463 + 9.23208I
u = −0.492292 + 0.151949I
a = −0.08723 − 1.83695I
b = −0.195745 − 0.773770I
2.33333 + 2.46306I −0.12775 − 9.01325I
u = −0.492292 − 0.151949I
a = −0.08723 + 1.83695I
b = −0.195745 + 0.773770I
2.33333 − 2.46306I −0.12775 + 9.01325I
u = −1.48570 + 0.20641I
a = −0.011308 + 1.052660I
b = 1.226100 − 0.687863I
−10.88640 + 2.96877I −10.70058 + 0.I
u = −1.48570 − 0.20641I
a = −0.011308 − 1.052660I
b = 1.226100 + 0.687863I
−10.88640 − 2.96877I −10.70058 + 0.I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.48158 + 0.34652I
a = 0.099930 + 0.238205I
b = 0.876400 − 0.516074I
−0.26016 + 2.05832I 0
u = 1.48158 − 0.34652I
a = 0.099930 − 0.238205I
b = 0.876400 + 0.516074I
−0.26016 − 2.05832I 0
u = −1.02120 + 1.27692I
a = −0.514136 + 0.101363I
b = −0.656941 − 0.135069I
0.06264 − 4.62577I 0
u = −1.02120 − 1.27692I
a = −0.514136 − 0.101363I
b = −0.656941 + 0.135069I
0.06264 + 4.62577I 0
u = −1.49360 + 0.79240I
a = −0.231274 + 0.715617I
b = 1.45455 − 0.21466I
−7.48967 + 4.17396I 0
u = −1.49360 − 0.79240I
a = −0.231274 − 0.715617I
b = 1.45455 + 0.21466I
−7.48967 − 4.17396I 0
u = 0.298202 + 0.002383I
a = 0.34104 − 1.67044I
b = 0.868783 + 0.906398I
3.82086 − 3.34428I −18.0773 + 7.2866I
u = 0.298202 − 0.002383I
a = 0.34104 + 1.67044I
b = 0.868783 − 0.906398I
3.82086 + 3.34428I −18.0773 − 7.2866I
26
III. I
u
3
= h−4a
3
+ 4a
2
+ 3b − 3a + 1, 4a
4
+ 5a
2
+ 2a + 2, u − 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
1
a
8
=
1
1
a
3
=
a
4
3
a
3
−
4
3
a
2
+ a −
1
3
a
12
=
−1
0
a
2
=
4
3
a
3
−
4
3
a
2
+ 2a −
1
3
4
3
a
3
−
4
3
a
2
+ a −
1
3
a
6
=
4
3
a
3
+
2
3
a
2
+ a +
8
3
1
a
9
=
−4a
3
− a
2
− 3a − 3
−
4
3
a
3
−
2
3
a
2
− a −
2
3
a
5
=
4
3
a
3
+
2
3
a
2
+ a +
5
3
1
a
10
=
−a
2
4
3
a
3
+
2
3
a
2
+ a +
5
3
a
4
=
a
3
+ a
2
3
a
3
−
2
3
a
2
+
1
3
a
1
=
2a
3
−
3
2
a
2
+ 2a
−a
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
6
(u
2
+ 1)
2
c
3
4(4u
4
+ 5u
2
+ 2u + 2)
c
5
, c
7
(u − 1)
4
c
8
4(4u
4
+ 12u
3
+ 9u
2
+ 1)
c
9
u
4
+ 2u
3
− 3u
2
− 4u + 8
c
10
4(4u
4
+ 5u
2
− 2u + 2)
c
11
(u + 1)
4
c
12
4(4u
4
+ 4u
3
− 3u
2
− 2u + 2)
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
(y + 1)
4
c
3
, c
10
16(16y
4
+ 40y
3
+ 41y
2
+ 16y + 4)
c
5
, c
7
, c
11
(y −1)
4
c
8
16(16y
4
− 72y
3
+ 89y
2
+ 18y + 1)
c
9
y
4
− 10y
3
+ 41y
2
− 64y + 64
c
12
16(16y
4
− 40y
3
+ 41y
2
− 16y + 4)
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.308302 + 1.060890I
b = − 1.000000I
1.64493 0
u = 1.00000
a = 0.308302 − 1.060890I
b = 1.000000I
1.64493 0
u = 1.00000
a = −0.308302 + 0.560894I
b = 1.000000I
1.64493 0
u = 1.00000
a = −0.308302 − 0.560894I
b = − 1.000000I
1.64493 0
30
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ 1)
2
)(u
28
− 4u
27
+ ··· + 7u + 11)
· (u
135
− 9u
134
+ ··· + 167083u + 63886)
c
2
((u
2
+ 1)
2
)(u
28
− 8u
26
+ ··· − 3u + 1)
· (u
135
− u
134
+ ··· + 144633u + 4946)
c
3
16(4u
4
+ 5u
2
+ 2u + 2)(u
28
+ 20u
26
+ ··· − 3u + 1)
· (4u
135
+ 36u
134
+ ··· + 2779214u + 127574)
c
4
((u
2
+ 1)
2
)(u
28
+ 4u
27
+ ··· − 7u + 11)
· (u
135
− 9u
134
+ ··· + 167083u + 63886)
c
5
((u − 1)
4
)(u
28
+ 4u
27
+ ··· + 2u + 1)
· (u
135
− 3u
134
+ ··· + 45913u + 3188)
c
6
((u
2
+ 1)
2
)(u
28
− 8u
26
+ ··· + 3u + 1)
· (u
135
− u
134
+ ··· + 144633u + 4946)
c
7
((u − 1)
4
)(u
28
+ 8u
27
+ ··· − 8u + 8)(u
135
− u
134
+ ··· − 29624u − 4064)
c
8
16(4u
4
+ 12u
3
+ 9u
2
+ 1)(u
28
+ 2u
27
+ ··· − 2u + 1)
· (4u
135
− 56u
134
+ ··· + 23579u − 1798)
c
9
(u
4
+ 2u
3
− 3u
2
− 4u + 8)(u
28
− 2u
26
+ ··· − 5u + 1)
· (u
135
− 3u
134
+ ··· + 48u + 16)
c
10
16(4u
4
+ 5u
2
− 2u + 2)(u
28
+ 20u
26
+ ··· + 3u + 1)
· (4u
135
+ 36u
134
+ ··· + 2779214u + 127574)
c
11
((u + 1)
4
)(u
28
− 8u
27
+ ··· + 8u + 8)(u
135
− u
134
+ ··· − 29624u − 4064)
c
12
16(4u
4
+ 4u
3
+ ··· − 2u + 2)(u
28
+ 8u
27
+ ··· + 4u + 1)
· (4u
135
+ 8u
134
+ ··· − 21656u − 7442)
31
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y + 1)
4
)(y
28
+ 16y
27
+ ··· − 1303y + 121)
· (y
135
+ 83y
134
+ ··· − 6695683735y −4081420996)
c
2
, c
6
((y + 1)
4
)(y
28
− 16y
27
+ ··· − 17y + 1)
· (y
135
− 93y
134
+ ··· − 1498427007y −24462916)
c
3
, c
10
256(16y
4
+ 40y
3
+ ··· + 16y + 4)(y
28
+ 40y
27
+ ··· + 25y + 1)
· (16y
135
+ 1560y
134
+ ··· + 692965499916y −16275125476)
c
5
((y −1)
4
)(y
28
+ 28y
26
+ ··· + 26y + 1)
· (y
135
+ 23y
134
+ ··· − 394825095y −10163344)
c
7
, c
11
((y −1)
4
)(y
28
− 22y
27
+ ··· − 2400y + 64)
· (y
135
− 119y
134
+ ··· − 1894424256y −16516096)
c
8
256(16y
4
− 72y
3
+ ··· + 18y + 1)(y
28
+ 10y
27
+ ··· + 30y + 1)
· (16y
135
− 568y
134
+ ··· + 1426485y −3232804)
c
9
(y
4
− 10y
3
+ 41y
2
− 64y + 64)(y
28
− 4y
27
+ ··· + 7y + 1)
· (y
135
− 11y
134
+ ··· − 9664y −256)
c
12
256(16y
4
− 40y
3
+ ··· − 16y + 4)(y
28
− 24y
27
+ ··· − 8y + 1)
· (16y
135
− 248y
134
+ ··· + 3868160488y −55383364)
32
