12a
1170
(K12a
1170
)
A knot diagram
1
Linearized knot diagam
4 10 7 9 11 3 1 12 2 5 6 8
Solving Sequence
5,10
11
3,6
7 12 2 9 4 1 8
c
10
c
5
c
6
c
11
c
2
c
9
c
4
c
1
c
8
c
3
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h4.42559 × 10
207
u
102
− 2.50511 × 10
206
u
101
+ ··· + 7.24447 × 10
208
b − 6.34599 × 10
209
,
− 3.30509 × 10
211
u
102
+ 6.96912 × 10
210
u
101
+ ··· + 1.25329 × 10
211
a + 5.02027 × 10
213
,
u
103
+ u
102
+ ··· + 988u − 173i
I
u
2
= h−14120u
26
+ 4722u
25
+ ··· + 7787b − 8083, 18524u
26
+ 2179u
25
+ ··· + 7787a − 2475,
u
27
− 14u
25
+ ··· + 4u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 130 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
= h4.43 × 10
207
u
102
− 2.51 × 10
206
u
101
+ · · · + 7.24 × 10
208
b − 6.35 ×
10
209
, −3.31 × 10
211
u
102
+ 6.97 × 10
210
u
101
+ · · · + 1.25 × 10
211
a + 5.02 ×
10
213
, u
103
+ u
102
+ · · · + 988u − 173i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
3
=
2.63712u
102
− 0.556064u
101
+ ··· + 2614.38u − 400.566
−0.0610892u
102
+ 0.00345796u
101
+ ··· − 49.6740u + 8.75976
a
6
=
u
−u
3
+ u
a
7
=
3.52331u
102
− 0.839955u
101
+ ··· + 3545.53u − 544.506
0.762710u
102
− 0.270469u
101
+ ··· + 839.144u − 128.842
a
12
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
2.57603u
102
− 0.552606u
101
+ ··· + 2564.71u − 391.806
−0.0610892u
102
+ 0.00345796u
101
+ ··· − 49.6740u + 8.75976
a
9
=
2.21085u
102
− 0.181129u
101
+ ··· + 1993.54u − 299.459
−0.120933u
102
+ 0.117634u
101
+ ··· − 172.565u + 26.1483
a
4
=
−1.00730u
102
+ 0.411475u
101
+ ··· − 1126.72u + 174.496
−1.64707u
102
+ 0.609439u
101
+ ··· − 1807.03u + 281.022
a
1
=
0.0593670u
102
− 0.0345648u
101
+ ··· + 33.9575u − 4.09273
1.01418u
102
− 0.128591u
101
+ ··· + 934.610u − 140.366
a
8
=
2.90932u
102
− 0.278749u
101
+ ··· + 2654.63u − 398.843
1.52886u
102
− 0.105690u
101
+ ··· + 1374.19u − 208.465
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.09664u
102
+ 0.747844u
101
+ ··· − 2298.53u + 369.408
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
103
− 4u
102
+ ··· + 63177613u − 8582393
c
2
, c
9
u
103
− u
102
+ ··· + 1650u + 121
c
3
, c
6
u
103
− 43u
101
+ ··· + 295139u + 37247
c
4
u
103
+ 3u
102
+ ··· − 1835136u − 186624
c
5
, c
10
, c
11
u
103
− u
102
+ ··· + 988u + 173
c
7
, c
8
, c
12
u
103
− 2u
102
+ ··· − 30u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
103
− 52y
102
+ ··· + 1577684931052899y −73657469606449
c
2
, c
9
y
103
− 65y
102
+ ··· + 1848880y −14641
c
3
, c
6
y
103
− 86y
102
+ ··· + 48391156629y −1387339009
c
4
y
103
+ 17y
102
+ ··· − 8707129344y −34828517376
c
5
, c
10
, c
11
y
103
− 95y
102
+ ··· + 361302y −29929
c
7
, c
8
, c
12
y
103
+ 108y
102
+ ··· + 550y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.163469 + 0.988899I
a = −0.591459 − 0.190851I
b = −0.748728 + 0.545340I
−6.44274 + 2.21725I 0
u = −0.163469 − 0.988899I
a = −0.591459 + 0.190851I
b = −0.748728 − 0.545340I
−6.44274 − 2.21725I 0
u = 0.148774 + 1.006360I
a = −0.533227 − 0.467991I
b = −0.937387 − 0.029345I
−4.91008 − 0.21953I 0
u = 0.148774 − 1.006360I
a = −0.533227 + 0.467991I
b = −0.937387 + 0.029345I
−4.91008 + 0.21953I 0
u = 0.308856 + 0.996841I
a = 0.508556 + 0.686687I
b = 1.308710 − 0.505019I
−13.0326 + 11.9617I 0
u = 0.308856 − 0.996841I
a = 0.508556 − 0.686687I
b = 1.308710 + 0.505019I
−13.0326 − 11.9617I 0
u = −0.355663 + 0.883558I
a = −0.412153 + 0.744444I
b = −1.321570 − 0.470564I
−6.21746 − 8.08999I 0
u = −0.355663 − 0.883558I
a = −0.412153 − 0.744444I
b = −1.321570 + 0.470564I
−6.21746 + 8.08999I 0
u = 1.07709
a = 1.26022
b = −1.65241
−4.86975 0
u = −1.077500 + 0.054072I
a = −0.96184 + 2.44614I
b = 0.754223 − 0.685328I
−7.36224 + 3.53097I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.077500 − 0.054072I
a = −0.96184 − 2.44614I
b = 0.754223 + 0.685328I
−7.36224 − 3.53097I 0
u = −0.602949 + 0.675187I
a = −0.514379 + 0.099696I
b = −1.057750 + 0.378820I
−7.29391 + 1.35242I 0
u = −0.602949 − 0.675187I
a = −0.514379 − 0.099696I
b = −1.057750 − 0.378820I
−7.29391 − 1.35242I 0
u = −0.872020 + 0.737402I
a = −0.379150 − 0.431654I
b = 1.189340 − 0.253433I
−4.73880 + 2.62050I 0
u = −0.872020 − 0.737402I
a = −0.379150 + 0.431654I
b = 1.189340 + 0.253433I
−4.73880 − 2.62050I 0
u = −0.628905 + 0.565862I
a = −1.52949 + 0.21220I
b = −0.148704 − 0.361724I
−7.72167 + 2.60859I 0
u = −0.628905 − 0.565862I
a = −1.52949 − 0.21220I
b = −0.148704 + 0.361724I
−7.72167 − 2.60859I 0
u = −1.171930 + 0.003108I
a = −0.37127 − 2.28954I
b = −0.846318 + 0.077461I
−6.66294 − 3.80860I 0
u = −1.171930 − 0.003108I
a = −0.37127 + 2.28954I
b = −0.846318 − 0.077461I
−6.66294 + 3.80860I 0
u = 0.105899 + 0.791296I
a = 0.802570 − 0.217865I
b = 0.816903 + 0.299056I
−1.41896 − 1.54298I 6.41871 + 1.97711I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.105899 − 0.791296I
a = 0.802570 + 0.217865I
b = 0.816903 − 0.299056I
−1.41896 + 1.54298I 6.41871 − 1.97711I
u = 0.490914 + 0.629055I
a = −0.476329 − 0.380374I
b = −0.003180 + 0.620411I
−4.41593 + 2.12959I 0. − 3.53620I
u = 0.490914 − 0.629055I
a = −0.476329 + 0.380374I
b = −0.003180 − 0.620411I
−4.41593 − 2.12959I 0. + 3.53620I
u = 1.22309
a = 0.188600
b = 1.50392
−3.65106 0
u = −0.271827 + 0.725757I
a = 0.220702 + 0.499597I
b = −0.015448 − 0.998350I
−8.96397 − 6.66223I −3.44910 + 5.30281I
u = −0.271827 − 0.725757I
a = 0.220702 − 0.499597I
b = −0.015448 + 0.998350I
−8.96397 + 6.66223I −3.44910 − 5.30281I
u = −0.361443 + 0.682704I
a = 1.48533 − 1.04786I
b = 1.181590 + 0.340135I
−7.85310 − 5.70542I −4.85454 + 6.34482I
u = −0.361443 − 0.682704I
a = 1.48533 + 1.04786I
b = 1.181590 − 0.340135I
−7.85310 + 5.70542I −4.85454 − 6.34482I
u = 0.311724 + 0.705848I
a = 0.298127 + 0.920391I
b = 1.37182 − 0.45974I
−6.19903 + 2.87469I −4.74003 − 2.88086I
u = 0.311724 − 0.705848I
a = 0.298127 − 0.920391I
b = 1.37182 + 0.45974I
−6.19903 − 2.87469I −4.74003 + 2.88086I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.226940 + 0.216577I
a = −1.015060 + 0.249853I
b = 1.63652 − 0.36861I
−9.70259 − 4.17421I 0
u = −1.226940 − 0.216577I
a = −1.015060 − 0.249853I
b = 1.63652 + 0.36861I
−9.70259 + 4.17421I 0
u = 1.257550 + 0.031034I
a = −0.002060 + 1.398640I
b = 0.846329 − 0.213131I
1.05682 − 2.10482I 0
u = 1.257550 − 0.031034I
a = −0.002060 − 1.398640I
b = 0.846329 + 0.213131I
1.05682 + 2.10482I 0
u = 0.464001 + 0.557793I
a = 0.38104 − 1.39756I
b = −1.226570 − 0.062274I
−5.41171 + 1.01005I −5.80459 − 5.38237I
u = 0.464001 − 0.557793I
a = 0.38104 + 1.39756I
b = −1.226570 + 0.062274I
−5.41171 − 1.01005I −5.80459 + 5.38237I
u = −1.272480 + 0.139287I
a = −0.212489 + 0.033918I
b = −1.51526 + 0.05400I
−8.65236 + 0.21313I 0
u = −1.272480 − 0.139287I
a = −0.212489 − 0.033918I
b = −1.51526 − 0.05400I
−8.65236 − 0.21313I 0
u = 1.280880 + 0.143923I
a = 0.77359 + 1.92507I
b = −0.643782 − 1.233920I
1.77334 − 0.63372I 0
u = 1.280880 − 0.143923I
a = 0.77359 − 1.92507I
b = −0.643782 + 1.233920I
1.77334 + 0.63372I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.294700 + 0.130665I
a = 0.30319 − 1.75188I
b = −1.170630 + 0.675828I
2.04315 + 3.44056I 0
u = 1.294700 − 0.130665I
a = 0.30319 + 1.75188I
b = −1.170630 − 0.675828I
2.04315 − 3.44056I 0
u = 1.075950 + 0.773996I
a = 0.346356 − 0.195540I
b = −1.180260 − 0.373125I
−10.84940 − 5.89850I 0
u = 1.075950 − 0.773996I
a = 0.346356 + 0.195540I
b = −1.180260 + 0.373125I
−10.84940 + 5.89850I 0
u = 1.335050 + 0.255112I
a = −0.90176 + 1.98132I
b = 1.135570 − 0.705009I
−8.60939 + 2.09321I 0
u = 1.335050 − 0.255112I
a = −0.90176 − 1.98132I
b = 1.135570 + 0.705009I
−8.60939 − 2.09321I 0
u = −0.095046 + 0.631459I
a = −0.496801 + 1.267380I
b = −1.37659 − 0.50675I
−13.14390 + 1.13556I −8.55420 − 0.03226I
u = −0.095046 − 0.631459I
a = −0.496801 − 1.267380I
b = −1.37659 + 0.50675I
−13.14390 − 1.13556I −8.55420 + 0.03226I
u = −1.351620 + 0.205622I
a = −0.024226 + 0.882590I
b = −1.038360 − 0.313115I
3.21905 − 1.39563I 0
u = −1.351620 − 0.205622I
a = −0.024226 − 0.882590I
b = −1.038360 + 0.313115I
3.21905 + 1.39563I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.313730 + 0.394243I
a = 0.056019 + 0.659577I
b = 1.147300 − 0.264206I
−1.03514 + 5.20228I 0
u = 1.313730 − 0.394243I
a = 0.056019 − 0.659577I
b = 1.147300 + 0.264206I
−1.03514 − 5.20228I 0
u = −1.357810 + 0.216982I
a = −0.55330 + 1.73398I
b = 0.308420 − 1.315980I
3.01469 − 5.61170I 0
u = −1.357810 − 0.216982I
a = −0.55330 − 1.73398I
b = 0.308420 + 1.315980I
3.01469 + 5.61170I 0
u = −1.379540 + 0.031326I
a = 0.69699 + 1.39227I
b = −0.486815 − 0.973303I
4.28030 − 2.60522I 0
u = −1.379540 − 0.031326I
a = 0.69699 − 1.39227I
b = −0.486815 + 0.973303I
4.28030 + 2.60522I 0
u = 1.370240 + 0.187367I
a = 1.26961 − 1.92551I
b = −1.041860 + 0.127705I
−7.44439 + 4.78630I 0
u = 1.370240 − 0.187367I
a = 1.26961 + 1.92551I
b = −1.041860 − 0.127705I
−7.44439 − 4.78630I 0
u = 0.239390 + 0.546734I
a = −1.68003 − 0.75967I
b = −1.083750 + 0.335393I
−1.54209 + 3.82264I −0.07568 − 8.96990I
u = 0.239390 − 0.546734I
a = −1.68003 + 0.75967I
b = −1.083750 − 0.335393I
−1.54209 − 3.82264I −0.07568 + 8.96990I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.391810 + 0.222257I
a = −0.10698 − 1.56171I
b = 1.250250 + 0.503870I
3.67266 − 6.68722I 0
u = −1.391810 − 0.222257I
a = −0.10698 + 1.56171I
b = 1.250250 − 0.503870I
3.67266 + 6.68722I 0
u = −1.32198 + 0.51188I
a = 0.300031 − 1.351340I
b = 1.005000 + 0.620415I
−2.76178 − 7.71289I 0
u = −1.32198 − 0.51188I
a = 0.300031 + 1.351340I
b = 1.005000 − 0.620415I
−2.76178 + 7.71289I 0
u = −1.40594 + 0.20070I
a = 0.443778 − 0.848526I
b = −0.589409 + 0.674801I
3.93805 − 1.47027I 0
u = −1.40594 − 0.20070I
a = 0.443778 + 0.848526I
b = −0.589409 − 0.674801I
3.93805 + 1.47027I 0
u = 0.176451 + 0.548688I
a = 0.987463 + 0.166992I
b = 0.932813 + 0.343087I
−1.44409 − 1.40048I 1.16471 − 2.54727I
u = 0.176451 − 0.548688I
a = 0.987463 − 0.166992I
b = 0.932813 − 0.343087I
−1.44409 + 1.40048I 1.16471 + 2.54727I
u = 1.37131 + 0.39232I
a = −0.065719 − 1.386650I
b = −0.974871 + 0.522895I
2.78263 + 6.10315I 0
u = 1.37131 − 0.39232I
a = −0.065719 + 1.386650I
b = −0.974871 − 0.522895I
2.78263 − 6.10315I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.39372 + 0.34641I
a = −0.439984 − 0.716866I
b = 0.537474 + 0.809666I
−1.36824 + 2.40734I 0
u = 1.39372 − 0.34641I
a = −0.439984 + 0.716866I
b = 0.537474 − 0.809666I
−1.36824 − 2.40734I 0
u = 1.40623 + 0.29514I
a = 0.50972 + 1.49283I
b = −0.170937 − 1.237640I
−3.63110 + 10.38570I 0
u = 1.40623 − 0.29514I
a = 0.50972 − 1.49283I
b = −0.170937 + 1.237640I
−3.63110 − 10.38570I 0
u = 1.44137 + 0.07431I
a = −0.457323 − 1.145870I
b = 0.195596 + 0.830593I
6.96115 + 1.71433I 0
u = 1.44137 − 0.07431I
a = −0.457323 + 1.145870I
b = 0.195596 − 0.830593I
6.96115 − 1.71433I 0
u = −1.42573 + 0.28898I
a = 0.67409 + 1.73211I
b = −1.29458 − 0.73199I
−0.65286 − 6.52840I 0
u = −1.42573 − 0.28898I
a = 0.67409 − 1.73211I
b = −1.29458 + 0.73199I
−0.65286 + 6.52840I 0
u = 0.136945 + 0.525189I
a = −0.234026 + 0.787036I
b = 0.088035 − 1.093760I
−1.76645 + 2.84055I −5.12535 − 7.41118I
u = 0.136945 − 0.525189I
a = −0.234026 − 0.787036I
b = 0.088035 + 1.093760I
−1.76645 − 2.84055I −5.12535 + 7.41118I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43626 + 0.27026I
a = −0.03467 − 1.53295I
b = −1.312900 + 0.404767I
−2.12327 + 9.20386I 0
u = 1.43626 − 0.27026I
a = −0.03467 + 1.53295I
b = −1.312900 − 0.404767I
−2.12327 − 9.20386I 0
u = −1.44967 + 0.27501I
a = −0.470859 − 1.282600I
b = 0.935619 + 0.271046I
0.81975 − 4.30759I 0
u = −1.44967 − 0.27501I
a = −0.470859 + 1.282600I
b = 0.935619 − 0.271046I
0.81975 + 4.30759I 0
u = −0.444690 + 0.238651I
a = 0.494032 − 0.216745I
b = −0.229109 + 0.464427I
0.875316 − 0.539204I 8.56392 + 3.34487I
u = −0.444690 − 0.238651I
a = 0.494032 + 0.216745I
b = −0.229109 − 0.464427I
0.875316 + 0.539204I 8.56392 − 3.34487I
u = 0.231682 + 0.444621I
a = 1.39827 − 0.99782I
b = 0.1247550 − 0.0207505I
−1.54224 − 0.94902I −3.24191 − 2.63088I
u = 0.231682 − 0.444621I
a = 1.39827 + 0.99782I
b = 0.1247550 + 0.0207505I
−1.54224 + 0.94902I −3.24191 + 2.63088I
u = −1.48951 + 0.18747I
a = 0.338760 − 0.988303I
b = 0.054812 + 0.668005I
2.04907 − 5.05169I 0
u = −1.48951 − 0.18747I
a = 0.338760 + 0.988303I
b = 0.054812 − 0.668005I
2.04907 + 5.05169I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.46206 + 0.34712I
a = −0.45408 + 1.64902I
b = 1.34151 − 0.67420I
−0.41844 + 12.52450I 0
u = 1.46206 − 0.34712I
a = −0.45408 − 1.64902I
b = 1.34151 + 0.67420I
−0.41844 − 12.52450I 0
u = −0.117083 + 0.475098I
a = 1.09475 − 3.21547I
b = 1.281850 + 0.018230I
−12.26510 − 2.33618I −10.53285 + 3.12812I
u = −0.117083 − 0.475098I
a = 1.09475 + 3.21547I
b = 1.281850 − 0.018230I
−12.26510 + 2.33618I −10.53285 − 3.12812I
u = 1.51553 + 0.04926I
a = −0.266853 − 0.907652I
b = 0.841983 + 0.604287I
0.423741 + 1.047520I 0
u = 1.51553 − 0.04926I
a = −0.266853 + 0.907652I
b = 0.841983 − 0.604287I
0.423741 − 1.047520I 0
u = −1.46779 + 0.40036I
a = 0.28041 + 1.65642I
b = −1.35365 − 0.64128I
−7.3788 − 16.9573I 0
u = −1.46779 − 0.40036I
a = 0.28041 − 1.65642I
b = −1.35365 + 0.64128I
−7.3788 + 16.9573I 0
u = −1.60867 + 0.21300I
a = −0.624560 − 0.561577I
b = 0.816195 + 0.103220I
1.26198 − 4.34942I 0
u = −1.60867 − 0.21300I
a = −0.624560 + 0.561577I
b = 0.816195 − 0.103220I
1.26198 + 4.34942I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.66835
a = 0.793424
b = −0.838679
4.88689 0
u = 0.258533 + 0.051841I
a = −1.52355 − 0.14854I
b = 0.659382 − 0.673270I
−0.93662 + 2.23751I 7.62015 − 5.07795I
u = 0.258533 − 0.051841I
a = −1.52355 + 0.14854I
b = 0.659382 + 0.673270I
−0.93662 − 2.23751I 7.62015 + 5.07795I
15
II. I
u
2
= h−14120u
26
+ 4722u
25
+ · · · + 7787b − 8083, 18524u
26
+ 2179u
25
+
· · · + 7787a − 2475, u
27
− 14u
25
+ · · · + 4u
2
+ 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
3
=
−2.37884u
26
− 0.279825u
25
+ ··· − 1.25029u + 0.317837
1.81328u
26
− 0.606395u
25
+ ··· − 0.629125u + 1.03801
a
6
=
u
−u
3
+ u
a
7
=
−2.82561u
26
− 2.83254u
25
+ ··· + 5.07590u + 2.51470
1.37884u
26
− 1.72017u
25
+ ··· + 0.250289u + 0.682163
a
12
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
−0.565558u
26
− 0.886221u
25
+ ··· − 1.87941u + 1.35585
1.81328u
26
− 0.606395u
25
+ ··· − 0.629125u + 1.03801
a
9
=
3.44728u
26
− 1.01233u
25
+ ··· − 3.80313u + 0.446770
−0.740979u
26
− 1.92359u
25
+ ··· − 1.00141u + 0.553872
a
4
=
1.76178u
26
+ 5.03930u
25
+ ··· − 0.315012u − 2.48658
−1.01233u
26
+ 5.56106u
25
+ ··· + 2.44677u − 4.44728
a
1
=
2.29986u
26
+ 1.15539u
25
+ ··· − 2.91884u + 1.72300
3.97059u
26
+ 4.34879u
25
+ ··· − 2.19468u − 3.84821
a
8
=
4.82612u
26
− 0.732503u
25
+ ··· − 2.55284u + 0.128933
1.27135u
26
− 0.484654u
25
+ ··· − 2.44818u − 0.998844
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
55565
7787
u
26
+
9124
7787
u
25
+ ··· +
61630
7787
u −
61674
7787
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
27
− 9u
26
+ ··· + 9u − 1
c
2
u
27
− 9u
25
+ ··· − 9u
2
+ 1
c
3
u
27
+ 5u
26
+ ··· − u − 1
c
4
u
27
+ 9u
24
+ ··· + 6u + 1
c
5
u
27
− 14u
25
+ ··· − 4u
2
− 1
c
6
u
27
− 5u
26
+ ··· − u + 1
c
7
, c
8
u
27
− u
26
+ ··· + 2u
2
+ 1
c
9
u
27
− 9u
25
+ ··· + 9u
2
− 1
c
10
, c
11
u
27
− 14u
25
+ ··· + 4u
2
+ 1
c
12
u
27
+ u
26
+ ··· − 2u
2
− 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
27
− 5y
26
+ ··· + 9y −1
c
2
, c
9
y
27
− 18y
26
+ ··· + 18y −1
c
3
, c
6
y
27
− 27y
26
+ ··· + 23y −1
c
4
y
27
+ 4y
25
+ ··· − 28y −1
c
5
, c
10
, c
11
y
27
− 28y
26
+ ··· − 8y −1
c
7
, c
8
, c
12
y
27
+ 31y
26
+ ··· − 4y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.178461 + 1.059330I
a = −0.501654 + 0.038992I
b = −0.914813 + 0.304102I
−4.49201 + 1.28363I 0.00863 − 4.75604I
u = −0.178461 − 1.059330I
a = −0.501654 − 0.038992I
b = −0.914813 − 0.304102I
−4.49201 − 1.28363I 0.00863 + 4.75604I
u = 1.225950 + 0.044396I
a = −0.053533 − 1.197970I
b = 1.43699 + 0.21234I
−8.81556 + 2.23652I −2.93770 − 1.86369I
u = 1.225950 − 0.044396I
a = −0.053533 + 1.197970I
b = 1.43699 − 0.21234I
−8.81556 − 2.23652I −2.93770 + 1.86369I
u = −1.23985
a = 0.132233
b = −1.57234
−3.33235 12.7060
u = −1.278010 + 0.160463I
a = −0.90757 − 2.42130I
b = 0.747351 + 0.401554I
−5.96314 − 5.05182I 1.73722 + 6.44260I
u = −1.278010 − 0.160463I
a = −0.90757 + 2.42130I
b = 0.747351 − 0.401554I
−5.96314 + 5.05182I 1.73722 − 6.44260I
u = −0.566521 + 0.372171I
a = −2.24929 + 1.20168I
b = −0.750776 + 0.202122I
−8.70764 + 3.10431I −8.61462 − 1.93050I
u = −0.566521 − 0.372171I
a = −2.24929 − 1.20168I
b = −0.750776 − 0.202122I
−8.70764 − 3.10431I −8.61462 + 1.93050I
u = 0.263208 + 0.612353I
a = 1.153050 − 0.124169I
b = 0.792168 + 0.355618I
−1.87135 − 1.81844I −7.99122 + 8.03791I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.263208 − 0.612353I
a = 1.153050 + 0.124169I
b = 0.792168 − 0.355618I
−1.87135 + 1.81844I −7.99122 − 8.03791I
u = 0.637005 + 0.108893I
a = 1.73464 + 0.81603I
b = −1.320340 + 0.115354I
−11.08090 − 1.68505I −3.83078 + 0.31507I
u = 0.637005 − 0.108893I
a = 1.73464 − 0.81603I
b = −1.320340 − 0.115354I
−11.08090 + 1.68505I −3.83078 − 0.31507I
u = −1.351200 + 0.130165I
a = 0.69406 − 1.41117I
b = −0.795438 + 0.980456I
3.04368 + 0.34981I 3.57563 − 0.23318I
u = −1.351200 − 0.130165I
a = 0.69406 + 1.41117I
b = −0.795438 − 0.980456I
3.04368 − 0.34981I 3.57563 + 0.23318I
u = 1.357980 + 0.272155I
a = 0.23312 − 1.66014I
b = −1.020190 + 0.550891I
2.07234 + 5.20061I 0.94399 − 4.84173I
u = 1.357980 − 0.272155I
a = 0.23312 + 1.66014I
b = −1.020190 − 0.550891I
2.07234 − 5.20061I 0.94399 + 4.84173I
u = 1.383990 + 0.120392I
a = 0.37532 − 1.45684I
b = −0.145971 + 0.867562I
3.18073 + 3.53763I 1.86571 − 4.35233I
u = 1.383990 − 0.120392I
a = 0.37532 + 1.45684I
b = −0.145971 − 0.867562I
3.18073 − 3.53763I 1.86571 + 4.35233I
u = −0.589097
a = −1.85264
b = 1.38999
−5.80436 −9.10980
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.37965 + 0.42301I
a = 0.072793 − 1.134180I
b = 1.142380 + 0.418935I
−0.41807 − 6.63882I 0. + 6.47149I
u = −1.37965 − 0.42301I
a = 0.072793 + 1.134180I
b = 1.142380 − 0.418935I
−0.41807 + 6.63882I 0. − 6.47149I
u = −1.58090
a = 0.00497375
b = −0.429374
5.63913 9.77320
u = 1.57624 + 0.26978I
a = −0.321916 − 0.141330I
b = 0.621577 + 0.225495I
1.72667 + 3.65087I 3.09245 + 1.60166I
u = 1.57624 − 0.26978I
a = −0.321916 + 0.141330I
b = 0.621577 − 0.225495I
1.72667 − 3.65087I 3.09245 − 1.60166I
u = 0.014394 + 0.311217I
a = 0.62869 − 1.94450I
b = 0.512933 + 0.784386I
−1.46957 − 2.03695I −5.03324 − 0.05675I
u = 0.014394 − 0.311217I
a = 0.62869 + 1.94450I
b = 0.512933 − 0.784386I
−1.46957 + 2.03695I −5.03324 + 0.05675I
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
27
− 9u
26
+ ··· + 9u − 1)
· (u
103
− 4u
102
+ ··· + 63177613u − 8582393)
c
2
(u
27
− 9u
25
+ ··· − 9u
2
+ 1)(u
103
− u
102
+ ··· + 1650u + 121)
c
3
(u
27
+ 5u
26
+ ··· − u − 1)(u
103
− 43u
101
+ ··· + 295139u + 37247)
c
4
(u
27
+ 9u
24
+ ··· + 6u + 1)(u
103
+ 3u
102
+ ··· − 1835136u − 186624)
c
5
(u
27
− 14u
25
+ ··· − 4u
2
− 1)(u
103
− u
102
+ ··· + 988u + 173)
c
6
(u
27
− 5u
26
+ ··· − u + 1)(u
103
− 43u
101
+ ··· + 295139u + 37247)
c
7
, c
8
(u
27
− u
26
+ ··· + 2u
2
+ 1)(u
103
− 2u
102
+ ··· − 30u − 1)
c
9
(u
27
− 9u
25
+ ··· + 9u
2
− 1)(u
103
− u
102
+ ··· + 1650u + 121)
c
10
, c
11
(u
27
− 14u
25
+ ··· + 4u
2
+ 1)(u
103
− u
102
+ ··· + 988u + 173)
c
12
(u
27
+ u
26
+ ··· − 2u
2
− 1)(u
103
− 2u
102
+ ··· − 30u − 1)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
27
− 5y
26
+ ··· + 9y −1)
· (y
103
− 52y
102
+ ··· + 1577684931052899y −73657469606449)
c
2
, c
9
(y
27
− 18y
26
+ ··· + 18y −1)
· (y
103
− 65y
102
+ ··· + 1848880y −14641)
c
3
, c
6
(y
27
− 27y
26
+ ··· + 23y −1)
· (y
103
− 86y
102
+ ··· + 48391156629y −1387339009)
c
4
(y
27
+ 4y
25
+ ··· − 28y −1)
· (y
103
+ 17y
102
+ ··· − 8707129344y −34828517376)
c
5
, c
10
, c
11
(y
27
− 28y
26
+ ··· − 8y −1)(y
103
− 95y
102
+ ··· + 361302y −29929)
c
7
, c
8
, c
12
(y
27
+ 31y
26
+ ··· − 4y −1)(y
103
+ 108y
102
+ ··· + 550y −1)
23
