12a
0972
(K12a
0972
)
A knot diagram
1
Linearized knot diagam
4 6 10 1 12 3 11 5 2 7 8 9
Solving Sequence
1,4
2
5,9
10 3 8 12 6 11 7
c
1
c
4
c
9
c
3
c
8
c
12
c
5
c
11
c
7
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.33659 × 10
517
u
123
− 2.62653 × 10
518
u
122
+ ··· + 7.25046 × 10
517
b − 7.78473 × 10
519
,
7.51746 × 10
517
u
123
+ 5.96534 × 10
518
u
122
+ ··· + 3.62523 × 10
517
a + 2.21034 × 10
520
,
u
124
+ 8u
123
+ ··· + 1020u + 25i
I
u
2
= h−56752991233u
24
+ 158661941328u
23
+ ··· + 5813851019b − 156448380402,
54545560767u
24
− 135581602385u
23
+ ··· + 5813851019a + 178623668066,
u
25
− 3u
24
+ ··· + 12u − 1i
I
u
3
= hb + a − 1, a
2
− au − 1, u
2
+ 1i
I
u
4
= hb
2
− bu − 1, a + u + 1, u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 157 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−3.34 × 10
517
u
123
− 2.63 × 10
518
u
122
+ · · · + 7.25 × 10
517
b − 7.78 ×
10
519
, 7.52 × 10
517
u
123
+ 5.97 × 10
518
u
122
+ · · · + 3.63 × 10
517
a + 2.21 ×
10
520
, u
124
+ 8u
123
+ · · · + 1020u + 25i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
u
a
9
=
−2.07365u
123
− 16.4551u
122
+ ··· − 18728.8u − 609.710
0.460190u
123
+ 3.62257u
122
+ ··· + 3417.67u + 107.369
a
10
=
−2.55174u
123
− 20.2391u
122
+ ··· − 22231.5u − 720.432
0.501200u
123
+ 3.94634u
122
+ ··· + 3388.10u + 106.351
a
3
=
−0.172222u
123
− 1.30964u
122
+ ··· − 2393.35u − 89.8196
−0.0485654u
123
− 0.490524u
122
+ ··· + 30.4635u + 1.72975
a
8
=
−2.10538u
123
− 16.7006u
122
+ ··· − 18765.2u − 611.590
0.491915u
123
+ 3.86811u
122
+ ··· + 3454.04u + 109.249
a
12
=
0.204772u
123
+ 1.65803u
122
+ ··· + 2202.56u + 63.8312
0.111811u
123
+ 0.849694u
122
+ ··· + 584.422u + 21.3400
a
6
=
0.262764u
123
+ 2.05155u
122
+ ··· + 2742.48u + 96.0581
−0.0466158u
123
− 0.277827u
122
+ ··· + 11.3702u + 0.354091
a
11
=
0.0217255u
123
+ 0.115731u
122
+ ··· + 230.179u + 20.1115
0.156984u
123
+ 1.22636u
122
+ ··· − 208.931u − 7.59340
a
7
=
0.0393133u
123
+ 0.404225u
122
+ ··· + 637.111u + 11.6719
−0.179527u
123
− 1.42858u
122
+ ··· + 33.3632u + 2.71980
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.48574u
123
+ 19.4677u
122
+ ··· + 18568.3u + 600.544
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
124
− 8u
123
+ ··· − 1020u + 25
c
2
, c
6
u
124
− 3u
123
+ ··· + 7019u + 802
c
3
u
124
+ u
123
+ ··· − 323613671u + 225151331
c
5
u
124
− 3u
123
+ ··· + 58197u + 6844
c
7
, c
10
, c
11
u
124
− 4u
123
+ ··· + 86u + 31
c
8
u
124
+ 4u
123
+ ··· − 448142u + 166093
c
9
u
124
+ u
123
+ ··· − 308331u + 65281
c
12
u
124
− 4u
123
+ ··· − 307u + 47
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
124
+ 102y
123
+ ··· − 108550y + 625
c
2
, c
6
y
124
− 87y
123
+ ··· − 39793137y + 643204
c
3
y
124
+ 71y
123
+ ··· + 2087042095852583975y + 50693121851071561
c
5
y
124
− 17y
123
+ ··· − 1045038265y + 46840336
c
7
, c
10
, c
11
y
124
− 144y
123
+ ··· − 148446y + 961
c
8
y
124
+ 56y
123
+ ··· + 1616827756682y + 27586884649
c
9
y
124
+ 9y
123
+ ··· + 12388959547y + 4261608961
c
12
y
124
+ 116y
122
+ ··· + 46939y + 2209
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.624909 + 0.789700I
a = −0.853489 + 0.286122I
b = −0.642130 − 0.250578I
−0.78763 − 2.51768I 0
u = 0.624909 − 0.789700I
a = −0.853489 − 0.286122I
b = −0.642130 + 0.250578I
−0.78763 + 2.51768I 0
u = 0.349992 + 0.953649I
a = −0.271463 + 1.190640I
b = −0.180959 − 0.264370I
−0.22218 − 1.86679I 0
u = 0.349992 − 0.953649I
a = −0.271463 − 1.190640I
b = −0.180959 + 0.264370I
−0.22218 + 1.86679I 0
u = 0.038725 + 0.970476I
a = −0.88568 − 1.25933I
b = 0.294809 + 0.685819I
1.67473 − 2.05855I 0
u = 0.038725 − 0.970476I
a = −0.88568 + 1.25933I
b = 0.294809 − 0.685819I
1.67473 + 2.05855I 0
u = 0.657665 + 0.795735I
a = 1.047720 − 0.650476I
b = 0.636330 − 0.005582I
4.66580 − 2.56846I 0
u = 0.657665 − 0.795735I
a = 1.047720 + 0.650476I
b = 0.636330 + 0.005582I
4.66580 + 2.56846I 0
u = −0.036730 + 1.033000I
a = 0.160380 + 0.775791I
b = 1.252330 − 0.510097I
1.55085 + 2.30574I 0
u = −0.036730 − 1.033000I
a = 0.160380 − 0.775791I
b = 1.252330 + 0.510097I
1.55085 − 2.30574I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.011380 + 0.252588I
a = −0.0037717 − 0.0751418I
b = −0.897491 + 0.718876I
1.62126 + 8.65715I 0
u = −1.011380 − 0.252588I
a = −0.0037717 + 0.0751418I
b = −0.897491 − 0.718876I
1.62126 − 8.65715I 0
u = −0.246554 + 1.041700I
a = 0.658400 − 0.533464I
b = −1.51137 + 0.43606I
4.55511 − 0.41818I 0
u = −0.246554 − 1.041700I
a = 0.658400 + 0.533464I
b = −1.51137 − 0.43606I
4.55511 + 0.41818I 0
u = 0.270265 + 0.887941I
a = 0.71343 + 2.21385I
b = −0.546317 − 0.768353I
6.82810 − 1.87616I 0
u = 0.270265 − 0.887941I
a = 0.71343 − 2.21385I
b = −0.546317 + 0.768353I
6.82810 + 1.87616I 0
u = −1.071340 + 0.092162I
a = −0.208664 − 0.113413I
b = −0.170158 + 0.674017I
3.77859 − 0.51409I 0
u = −1.071340 − 0.092162I
a = −0.208664 + 0.113413I
b = −0.170158 − 0.674017I
3.77859 + 0.51409I 0
u = 1.063660 + 0.214060I
a = −0.1030460 − 0.0422966I
b = −0.736144 − 0.498925I
−1.84560 − 3.48872I 0
u = 1.063660 − 0.214060I
a = −0.1030460 + 0.0422966I
b = −0.736144 + 0.498925I
−1.84560 + 3.48872I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.200264 + 0.858804I
a = −0.199765 − 1.383860I
b = −0.307680 + 0.078714I
2.90937 + 0.48546I 0
u = 0.200264 − 0.858804I
a = −0.199765 + 1.383860I
b = −0.307680 − 0.078714I
2.90937 − 0.48546I 0
u = 1.013370 + 0.476653I
a = 0.676023 + 0.063001I
b = −0.670930 + 0.897117I
6.99872 + 2.80339I 0
u = 1.013370 − 0.476653I
a = 0.676023 − 0.063001I
b = −0.670930 − 0.897117I
6.99872 − 2.80339I 0
u = −0.799360 + 0.356881I
a = 0.806257 − 0.572661I
b = 0.875329 + 0.298254I
8.64858 − 5.00143I 0
u = −0.799360 − 0.356881I
a = 0.806257 + 0.572661I
b = 0.875329 − 0.298254I
8.64858 + 5.00143I 0
u = 0.266452 + 0.829127I
a = 1.83248 − 0.27359I
b = 0.678402 + 0.277204I
2.39633 − 2.88261I 0
u = 0.266452 − 0.829127I
a = 1.83248 + 0.27359I
b = 0.678402 − 0.277204I
2.39633 + 2.88261I 0
u = −0.220377 + 1.122260I
a = −0.08409 + 1.54094I
b = 1.10225 − 1.21547I
2.13812 + 3.26916I 0
u = −0.220377 − 1.122260I
a = −0.08409 − 1.54094I
b = 1.10225 + 1.21547I
2.13812 − 3.26916I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.033525 + 1.161790I
a = −0.319448 − 0.632001I
b = −1.307690 + 0.414071I
7.68363 + 3.54824I 0
u = −0.033525 − 1.161790I
a = −0.319448 + 0.632001I
b = −1.307690 − 0.414071I
7.68363 − 3.54824I 0
u = −0.609912 + 0.568440I
a = 1.034620 − 0.462126I
b = −0.563121 − 0.762549I
5.17196 − 3.18037I 0
u = −0.609912 − 0.568440I
a = 1.034620 + 0.462126I
b = −0.563121 + 0.762549I
5.17196 + 3.18037I 0
u = −0.029257 + 1.167110I
a = 0.131424 − 1.388300I
b = −0.87769 + 1.11781I
3.66761 − 0.84831I 0
u = −0.029257 − 1.167110I
a = 0.131424 + 1.388300I
b = −0.87769 − 1.11781I
3.66761 + 0.84831I 0
u = −0.438960 + 1.099790I
a = 0.24387 + 1.89941I
b = 0.482558 − 0.359313I
10.9005 + 9.5975I 0
u = −0.438960 − 1.099790I
a = 0.24387 − 1.89941I
b = 0.482558 + 0.359313I
10.9005 − 9.5975I 0
u = −0.349173 + 1.141460I
a = −0.19828 − 1.61269I
b = −0.99534 + 1.37906I
7.19616 + 6.93974I 0
u = −0.349173 − 1.141460I
a = −0.19828 + 1.61269I
b = −0.99534 − 1.37906I
7.19616 − 6.93974I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.190790 + 0.154668I
a = 0.371080 + 0.177841I
b = 0.341879 − 0.816022I
10.80650 − 1.25200I 0
u = −1.190790 − 0.154668I
a = 0.371080 − 0.177841I
b = 0.341879 + 0.816022I
10.80650 + 1.25200I 0
u = 0.780504 + 0.066163I
a = −0.128713 + 0.108564I
b = 0.844438 + 0.324862I
−1.95401 − 0.57152I 0
u = 0.780504 − 0.066163I
a = −0.128713 − 0.108564I
b = 0.844438 − 0.324862I
−1.95401 + 0.57152I 0
u = −0.290920 + 1.185870I
a = 0.31212 − 1.72148I
b = −0.253177 + 0.413757I
4.68545 + 6.23430I 0
u = −0.290920 − 1.185870I
a = 0.31212 + 1.72148I
b = −0.253177 − 0.413757I
4.68545 − 6.23430I 0
u = 0.690267 + 0.316922I
a = −0.995755 − 0.423093I
b = 0.840804 − 0.709923I
0.16376 + 2.13777I 0
u = 0.690267 − 0.316922I
a = −0.995755 + 0.423093I
b = 0.840804 + 0.709923I
0.16376 − 2.13777I 0
u = 0.395846 + 1.178580I
a = −0.16684 − 1.61000I
b = 1.06584 + 1.46196I
2.91555 − 6.35209I 0
u = 0.395846 − 1.178580I
a = −0.16684 + 1.61000I
b = 1.06584 − 1.46196I
2.91555 + 6.35209I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.596773 + 1.098550I
a = −0.25305 + 1.50933I
b = −0.85387 − 1.45213I
9.03984 − 8.60000I 0
u = 0.596773 − 1.098550I
a = −0.25305 − 1.50933I
b = −0.85387 + 1.45213I
9.03984 + 8.60000I 0
u = −0.060754 + 1.248950I
a = 0.38576 + 1.97999I
b = −0.98013 − 1.70592I
7.48407 + 3.86950I 0
u = −0.060754 − 1.248950I
a = 0.38576 − 1.97999I
b = −0.98013 + 1.70592I
7.48407 − 3.86950I 0
u = −0.002976 + 1.259540I
a = 0.22912 − 2.04140I
b = 0.59661 + 1.30966I
7.65870 − 2.89944I 0
u = −0.002976 − 1.259540I
a = 0.22912 + 2.04140I
b = 0.59661 − 1.30966I
7.65870 + 2.89944I 0
u = 0.141193 + 1.263160I
a = 0.81534 + 1.28478I
b = −1.55246 − 1.20153I
5.07326 − 2.77050I 0
u = 0.141193 − 1.263160I
a = 0.81534 − 1.28478I
b = −1.55246 + 1.20153I
5.07326 + 2.77050I 0
u = −0.148783 + 1.262330I
a = −0.57776 − 1.52603I
b = 1.29356 + 1.51745I
15.0989 + 8.7503I 0
u = −0.148783 − 1.262330I
a = −0.57776 + 1.52603I
b = 1.29356 − 1.51745I
15.0989 − 8.7503I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.582223 + 0.430669I
a = −0.807574 + 0.937034I
b = 0.795687 + 0.282579I
0.186508 − 0.358873I 0
u = −0.582223 − 0.430669I
a = −0.807574 − 0.937034I
b = 0.795687 − 0.282579I
0.186508 + 0.358873I 0
u = 0.081403 + 1.299880I
a = −0.51855 + 1.64065I
b = −0.785286 − 0.992413I
15.6448 − 7.6267I 0
u = 0.081403 − 1.299880I
a = −0.51855 − 1.64065I
b = −0.785286 + 0.992413I
15.6448 + 7.6267I 0
u = −1.281450 + 0.242845I
a = −0.0408311 + 0.0638631I
b = 0.800570 − 0.747453I
9.7223 + 12.0177I 0
u = −1.281450 − 0.242845I
a = −0.0408311 − 0.0638631I
b = 0.800570 + 0.747453I
9.7223 − 12.0177I 0
u = −0.115983 + 1.313350I
a = −0.728401 + 1.047250I
b = −0.012768 − 0.426251I
5.94688 + 1.48446I 0
u = −0.115983 − 1.313350I
a = −0.728401 − 1.047250I
b = −0.012768 + 0.426251I
5.94688 − 1.48446I 0
u = 0.066845 + 1.328250I
a = −0.222917 + 1.234220I
b = 0.93865 − 1.26825I
11.16820 − 3.35347I 0
u = 0.066845 − 1.328250I
a = −0.222917 − 1.234220I
b = 0.93865 + 1.26825I
11.16820 + 3.35347I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.604253 + 0.284274I
a = 0.160861 + 0.209823I
b = 1.024820 − 0.722652I
−0.03123 + 3.63182I 0
u = −0.604253 − 0.284274I
a = 0.160861 − 0.209823I
b = 1.024820 + 0.722652I
−0.03123 − 3.63182I 0
u = 1.361590 + 0.259806I
a = 0.134042 − 0.046505I
b = 0.642655 + 0.623399I
5.07896 − 5.21597I 0
u = 1.361590 − 0.259806I
a = 0.134042 + 0.046505I
b = 0.642655 − 0.623399I
5.07896 + 5.21597I 0
u = 0.115361 + 0.594013I
a = 0.183050 − 1.248340I
b = −0.617168 − 0.084784I
2.92156 + 0.53654I 0
u = 0.115361 − 0.594013I
a = 0.183050 + 1.248340I
b = −0.617168 + 0.084784I
2.92156 − 0.53654I 0
u = 0.035448 + 0.595180I
a = 2.31588 − 0.64381I
b = −1.57212 + 0.38454I
2.11788 + 1.98122I 0
u = 0.035448 − 0.595180I
a = 2.31588 + 0.64381I
b = −1.57212 − 0.38454I
2.11788 − 1.98122I 0
u = 0.38607 + 1.36862I
a = −0.363176 − 1.353110I
b = 1.04682 + 1.11374I
2.61430 − 4.84266I 0
u = 0.38607 − 1.36862I
a = −0.363176 + 1.353110I
b = 1.04682 − 1.11374I
2.61430 + 4.84266I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.292312 + 0.489399I
a = 0.199051 − 0.458548I
b = −1.39633 + 0.54910I
5.76997 − 0.74612I 0
u = 0.292312 − 0.489399I
a = 0.199051 + 0.458548I
b = −1.39633 − 0.54910I
5.76997 + 0.74612I 0
u = −0.48655 + 1.34999I
a = −0.289379 − 1.255350I
b = −0.694847 + 1.007670I
8.26791 + 4.86057I 0
u = −0.48655 − 1.34999I
a = −0.289379 + 1.255350I
b = −0.694847 − 1.007670I
8.26791 − 4.86057I 0
u = −0.535208 + 0.098659I
a = −0.78607 + 1.44928I
b = −0.847060 − 0.155911I
1.50743 − 2.98404I 0
u = −0.535208 − 0.098659I
a = −0.78607 − 1.44928I
b = −0.847060 + 0.155911I
1.50743 + 2.98404I 0
u = −0.27166 + 1.43808I
a = −0.60645 + 1.74606I
b = 1.25703 − 1.39510I
5.51165 + 6.94398I 0
u = −0.27166 − 1.43808I
a = −0.60645 − 1.74606I
b = 1.25703 + 1.39510I
5.51165 − 6.94398I 0
u = 0.43515 + 1.40233I
a = −0.136616 − 0.696627I
b = 0.511825 + 0.563146I
2.33121 − 3.38566I 0
u = 0.43515 − 1.40233I
a = −0.136616 + 0.696627I
b = 0.511825 − 0.563146I
2.33121 + 3.38566I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.53394 + 1.37569I
a = 0.277630 + 1.121480I
b = 0.344681 − 1.123800I
7.91427 + 6.40094I 0
u = −0.53394 − 1.37569I
a = 0.277630 − 1.121480I
b = 0.344681 + 1.123800I
7.91427 − 6.40094I 0
u = −0.68743 + 1.30596I
a = 0.419653 + 0.188089I
b = −0.122827 − 0.473467I
4.33526 − 2.51765I 0
u = −0.68743 − 1.30596I
a = 0.419653 − 0.188089I
b = −0.122827 + 0.473467I
4.33526 + 2.51765I 0
u = 0.46522 + 1.40387I
a = 0.134818 + 1.328190I
b = −1.09069 − 1.08181I
3.16484 − 8.86238I 0
u = 0.46522 − 1.40387I
a = 0.134818 − 1.328190I
b = −1.09069 + 1.08181I
3.16484 + 8.86238I 0
u = −0.43002 + 1.44348I
a = 0.24949 − 1.55537I
b = −1.16636 + 1.25954I
6.9765 + 13.7973I 0
u = −0.43002 − 1.44348I
a = 0.24949 + 1.55537I
b = −1.16636 − 1.25954I
6.9765 − 13.7973I 0
u = −0.101430 + 0.473608I
a = 2.81834 − 0.97751I
b = −0.288841 − 0.487196I
5.59899 − 3.09249I 8.90713 + 0.I
u = −0.101430 − 0.473608I
a = 2.81834 + 0.97751I
b = −0.288841 + 0.487196I
5.59899 + 3.09249I 8.90713 + 0.I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.49838 + 1.43173I
a = 0.301067 + 1.199040I
b = 0.889618 − 0.943728I
15.8333 + 4.5792I 0
u = −0.49838 − 1.43173I
a = 0.301067 − 1.199040I
b = 0.889618 + 0.943728I
15.8333 − 4.5792I 0
u = −0.14267 + 1.52286I
a = −0.425047 − 0.509529I
b = 1.112710 + 0.556637I
15.0819 − 1.6516I 0
u = −0.14267 − 1.52286I
a = −0.425047 + 0.509529I
b = 1.112710 − 0.556637I
15.0819 + 1.6516I 0
u = 0.51929 + 1.48104I
a = −0.036046 − 1.242720I
b = 1.12719 + 1.06290I
10.5364 − 11.5662I 0
u = 0.51929 − 1.48104I
a = −0.036046 + 1.242720I
b = 1.12719 − 1.06290I
10.5364 + 11.5662I 0
u = −0.61500 + 1.44586I
a = −0.304008 − 0.973397I
b = −0.179648 + 1.242880I
14.9283 + 7.9258I 0
u = −0.61500 − 1.44586I
a = −0.304008 + 0.973397I
b = −0.179648 − 1.242880I
14.9283 − 7.9258I 0
u = −0.52705 + 1.48373I
a = −0.11920 + 1.42093I
b = 1.15290 − 1.23181I
15.1210 + 18.2859I 0
u = −0.52705 − 1.48373I
a = −0.11920 − 1.42093I
b = 1.15290 + 1.23181I
15.1210 − 18.2859I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.03557 + 1.59893I
a = 1.48233 − 0.63793I
b = −1.90550 + 0.62040I
13.09920 − 1.07183I 0
u = −0.03557 − 1.59893I
a = 1.48233 + 0.63793I
b = −1.90550 − 0.62040I
13.09920 + 1.07183I 0
u = 0.07284 + 1.62369I
a = 0.350406 − 0.365184I
b = 0.301197 + 0.400851I
14.8060 − 1.2582I 0
u = 0.07284 − 1.62369I
a = 0.350406 + 0.365184I
b = 0.301197 − 0.400851I
14.8060 + 1.2582I 0
u = 0.43257 + 1.58022I
a = 0.148827 + 0.857592I
b = −0.609393 − 1.016200I
10.49490 − 2.70483I 0
u = 0.43257 − 1.58022I
a = 0.148827 − 0.857592I
b = −0.609393 + 1.016200I
10.49490 + 2.70483I 0
u = −0.144359 + 0.217920I
a = −1.32019 + 2.13894I
b = 0.190926 + 0.455290I
0.095467 − 1.146130I 1.33446 + 5.20853I
u = −0.144359 − 0.217920I
a = −1.32019 − 2.13894I
b = 0.190926 − 0.455290I
0.095467 + 1.146130I 1.33446 − 5.20853I
u = −0.137483 + 0.053618I
a = 1.88691 + 9.62828I
b = 0.174139 − 1.062900I
11.29770 − 7.33389I 7.61770 + 3.62503I
u = −0.137483 − 0.053618I
a = 1.88691 − 9.62828I
b = 0.174139 + 1.062900I
11.29770 + 7.33389I 7.61770 − 3.62503I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.1074230 + 0.0204538I
a = −2.29690 − 7.62971I
b = −0.195075 + 1.214220I
3.75165 − 3.18681I 7.79230 + 9.47115I
u = −0.1074230 − 0.0204538I
a = −2.29690 + 7.62971I
b = −0.195075 − 1.214220I
3.75165 + 3.18681I 7.79230 − 9.47115I
u = −0.97511 + 1.97865I
a = −0.129208 − 0.152014I
b = −0.085980 + 0.379628I
13.44110 − 3.50918I 0
u = −0.97511 − 1.97865I
a = −0.129208 + 0.152014I
b = −0.085980 − 0.379628I
13.44110 + 3.50918I 0
17
II.
I
u
2
= h−5.68 × 10
10
u
24
+ 1.59 × 10
11
u
23
+ · · · + 5.81× 10
9
b − 1.56 ×10
11
, 5.45 ×
10
10
u
24
−1.36×10
11
u
23
+· · ·+5.81×10
9
a+1.79×10
11
, u
25
−3u
24
+· · ·+12u−1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
u
a
9
=
−9.38200u
24
+ 23.3204u
23
+ ··· + 257.610u − 30.7238
9.76169u
24
− 27.2903u
23
+ ··· − 260.709u + 26.9096
a
10
=
−22.5428u
24
+ 58.9665u
23
+ ··· + 566.844u − 62.4590
10.0858u
24
− 26.6485u
23
+ ··· − 227.833u + 23.0732
a
3
=
15.1635u
24
− 34.1351u
23
+ ··· − 227.440u + 26.2036
0.0247429u
24
− 3.38012u
23
+ ··· − 75.5561u + 6.67925
a
8
=
−13.3618u
24
+ 32.6426u
23
+ ··· + 291.960u − 33.5546
13.7415u
24
− 36.6125u
23
+ ··· − 295.059u + 29.7404
a
12
=
3.58211u
24
− 3.74055u
23
+ ··· + 28.9720u + 1.80463
8.82286u
24
− 20.9033u
23
+ ··· − 79.4184u + 3.70537
a
6
=
24.1743u
24
− 52.5145u
23
+ ··· − 215.662u + 20.1633
4.38131u
24
− 13.2049u
23
+ ··· − 127.203u + 11.3084
a
11
=
6.89964u
24
− 2.83690u
23
+ ··· + 285.884u − 32.9364
3.55480u
24
− 7.84830u
23
+ ··· − 73.5124u + 7.87747
a
7
=
7.45497u
24
− 6.18940u
23
+ ··· + 259.080u − 33.2308
2.81610u
24
− 5.60481u
23
+ ··· − 34.7801u + 3.55480
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
38880606157
5813851019
u
24
−
204299857999
5813851019
u
23
+ ··· −
5343011314076
5813851019
u +
647995598087
5813851019
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
25
− 3u
24
+ ··· + 12u − 1
c
2
u
25
+ 2u
24
+ ··· − u + 1
c
3
u
25
+ 2u
23
+ ··· − u − 1
c
4
u
25
+ 3u
24
+ ··· + 12u + 1
c
5
u
25
+ 4u
24
+ ··· − u + 1
c
6
u
25
− 2u
24
+ ··· − u − 1
c
7
u
25
− 5u
24
+ ··· + 2u + 1
c
8
u
25
− u
24
+ ··· + 5u
2
+ 1
c
9
u
25
− 2u
23
+ ··· + u + 1
c
10
, c
11
u
25
+ 5u
24
+ ··· + 2u − 1
c
12
u
25
− 5u
24
+ ··· + u − 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
25
+ 23y
24
+ ··· + 12y −1
c
2
, c
6
y
25
− 14y
24
+ ··· + 19y −1
c
3
y
25
+ 4y
24
+ ··· − 41y −1
c
5
y
25
+ 30y
23
+ ··· + y −1
c
7
, c
10
, c
11
y
25
− 35y
24
+ ··· − 20y −1
c
8
y
25
+ 11y
24
+ ··· − 10y −1
c
9
y
25
− 4y
24
+ ··· + y −1
c
12
y
25
− 3y
24
+ ··· + 11y −1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.396533 + 0.918439I
a = 0.246592 − 0.656324I
b = 0.801411 + 0.091216I
2.78380 − 1.71389I 1.54455 + 2.94870I
u = 0.396533 − 0.918439I
a = 0.246592 + 0.656324I
b = 0.801411 − 0.091216I
2.78380 + 1.71389I 1.54455 − 2.94870I
u = −0.522963 + 0.749559I
a = −0.254600 + 0.036431I
b = 0.416621 − 0.514156I
3.86969 − 1.94885I 6.67029 + 1.25514I
u = −0.522963 − 0.749559I
a = −0.254600 − 0.036431I
b = 0.416621 + 0.514156I
3.86969 + 1.94885I 6.67029 − 1.25514I
u = 0.599632 + 0.688427I
a = −0.990660 + 0.161060I
b = −0.660665 − 0.309143I
−0.80491 − 2.72003I −1.4684 + 21.3189I
u = 0.599632 − 0.688427I
a = −0.990660 − 0.161060I
b = −0.660665 + 0.309143I
−0.80491 + 2.72003I −1.4684 − 21.3189I
u = −0.454087 + 1.030360I
a = 1.03190 + 1.63681I
b = 0.113347 − 0.973124I
12.0422 + 9.0646I 9.38473 − 6.78978I
u = −0.454087 − 1.030360I
a = 1.03190 − 1.63681I
b = 0.113347 + 0.973124I
12.0422 − 9.0646I 9.38473 + 6.78978I
u = 0.673443 + 0.377672I
a = −1.022940 − 0.727811I
b = 0.797515 − 0.772015I
4.43310 + 3.33564I −0.43428 − 4.34078I
u = 0.673443 − 0.377672I
a = −1.022940 + 0.727811I
b = 0.797515 + 0.772015I
4.43310 − 3.33564I −0.43428 + 4.34078I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.445519 + 1.181260I
a = 0.11767 − 1.61358I
b = 0.98415 + 1.46104I
6.96031 − 7.72852I 4.03159 + 8.91256I
u = 0.445519 − 1.181260I
a = 0.11767 + 1.61358I
b = 0.98415 − 1.46104I
6.96031 + 7.72852I 4.03159 − 8.91256I
u = 0.528550 + 0.447594I
a = 1.84401 + 0.70055I
b = 0.634465 + 0.380510I
4.87746 − 3.64656I 1.63258 + 6.77129I
u = 0.528550 − 0.447594I
a = 1.84401 − 0.70055I
b = 0.634465 − 0.380510I
4.87746 + 3.64656I 1.63258 − 6.77129I
u = −0.318652 + 1.283850I
a = −0.13770 − 1.74819I
b = −0.442802 + 1.266680I
6.26588 + 5.52732I 6.98548 − 5.31379I
u = −0.318652 − 1.283850I
a = −0.13770 + 1.74819I
b = −0.442802 − 1.266680I
6.26588 − 5.52732I 6.98548 + 5.31379I
u = 0.350396 + 1.325240I
a = 0.41285 + 1.48160I
b = −1.15583 − 1.30583I
3.29730 − 5.21881I 8.57149 + 5.00846I
u = 0.350396 − 1.325240I
a = 0.41285 − 1.48160I
b = −1.15583 + 1.30583I
3.29730 + 5.21881I 8.57149 − 5.00846I
u = 0.424493 + 0.266239I
a = 1.44747 + 0.85701I
b = −0.981579 + 0.594218I
−0.42081 + 1.85133I −5.86069 − 1.68765I
u = 0.424493 − 0.266239I
a = 1.44747 − 0.85701I
b = −0.981579 − 0.594218I
−0.42081 − 1.85133I −5.86069 + 1.68765I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.01425 + 1.64121I
a = −1.286330 + 0.308438I
b = 1.69344 − 0.22865I
12.91170 − 0.79888I 3.16117 − 8.46251I
u = −0.01425 − 1.64121I
a = −1.286330 − 0.308438I
b = 1.69344 + 0.22865I
12.91170 + 0.79888I 3.16117 + 8.46251I
u = 0.270555
a = −2.92223
b = 1.20005
5.82532 8.15020
u = −0.74389 + 1.89057I
a = 0.0528490 + 0.0450918I
b = −0.300101 + 0.199881I
13.24880 − 3.52025I 0
u = −0.74389 − 1.89057I
a = 0.0528490 − 0.0450918I
b = −0.300101 − 0.199881I
13.24880 + 3.52025I 0
23
III. I
u
3
= hb + a − 1, a
2
− au − 1, u
2
+ 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
−1
a
5
=
−u
u
a
9
=
a
−a + 1
a
10
=
a − 1
−a + 2
a
3
=
−2au − a + 2u
3au + a − 2u
a
8
=
a − 1
−a + 2
a
12
=
au − a + 2
−au + 2a − 2
a
6
=
au + a − 2u − 1
−au − 2a + 3u + 1
a
11
=
au + 1
−au + a
a
7
=
−au + a − 2
au − 2a + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4au + 8
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
8
(u
2
+ 1)
2
c
2
, c
6
u
4
− u
2
+ 1
c
3
u
4
− 2u
3
+ 5u
2
− 4u + 1
c
5
(u
2
− u + 1)
2
c
7
, c
9
(u + 1)
4
c
10
, c
11
(u − 1)
4
c
12
u
4
− 4u
3
+ 5u
2
− 2u + 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
8
(y + 1)
4
c
2
, c
6
(y
2
− y + 1)
2
c
3
y
4
+ 6y
3
+ 11y
2
− 6y + 1
c
5
(y
2
+ y + 1)
2
c
7
, c
9
, c
10
c
11
(y −1)
4
c
12
y
4
− 6y
3
+ 11y
2
+ 6y + 1
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.866025 + 0.500000I
b = 1.86603 − 0.50000I
3.28987 − 2.02988I 6.00000 + 3.46410I
u = 1.000000I
a = 0.866025 + 0.500000I
b = 0.133975 − 0.500000I
3.28987 + 2.02988I 6.00000 − 3.46410I
u = − 1.000000I
a = −0.866025 − 0.500000I
b = 1.86603 + 0.50000I
3.28987 + 2.02988I 6.00000 − 3.46410I
u = − 1.000000I
a = 0.866025 − 0.500000I
b = 0.133975 + 0.500000I
3.28987 − 2.02988I 6.00000 + 3.46410I
27
IV. I
u
4
= hb
2
− bu − 1, a + u + 1, u
2
+ 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
−1
a
5
=
−u
u
a
9
=
−u − 1
b
a
10
=
−b
2b − u − 1
a
3
=
−b + u
bu + b − u
a
8
=
−b
2b − u − 1
a
12
=
bu + b + 1
−bu − 1
a
6
=
−b − 1
u + 1
a
11
=
bu + 1
−bu + 2b − u − 2
a
7
=
−bu − b − 1
bu + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4bu + 8
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
2
+ 1)
2
c
2
, c
6
, c
12
u
4
− u
2
+ 1
c
3
(u
2
+ u + 1)
2
c
5
(u
2
− u + 1)
2
c
7
(u + 1)
4
c
8
u
4
− 2u
3
+ 5u
2
− 4u + 1
c
9
u
4
− 4u
3
+ 5u
2
− 2u + 1
c
10
, c
11
(u − 1)
4
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y + 1)
4
c
2
, c
6
, c
12
(y
2
− y + 1)
2
c
3
, c
5
(y
2
+ y + 1)
2
c
7
, c
10
, c
11
(y −1)
4
c
8
y
4
+ 6y
3
+ 11y
2
− 6y + 1
c
9
y
4
− 6y
3
+ 11y
2
+ 6y + 1
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −1.00000 − 1.00000I
b = −0.866025 + 0.500000I
3.28987 − 2.02988I 6.00000 + 3.46410I
u = 1.000000I
a = −1.00000 − 1.00000I
b = 0.866025 + 0.500000I
3.28987 + 2.02988I 6.00000 − 3.46410I
u = − 1.000000I
a = −1.00000 + 1.00000I
b = −0.866025 − 0.500000I
3.28987 + 2.02988I 6.00000 − 3.46410I
u = − 1.000000I
a = −1.00000 + 1.00000I
b = 0.866025 − 0.500000I
3.28987 − 2.02988I 6.00000 + 3.46410I
31
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ 1)
4
)(u
25
− 3u
24
+ ··· + 12u − 1)(u
124
− 8u
123
+ ··· − 1020u + 25)
c
2
((u
4
− u
2
+ 1)
2
)(u
25
+ 2u
24
+ ··· − u + 1)
· (u
124
− 3u
123
+ ··· + 7019u + 802)
c
3
((u
2
+ u + 1)
2
)(u
4
− 2u
3
+ ··· − 4u + 1)(u
25
+ 2u
23
+ ··· − u − 1)
· (u
124
+ u
123
+ ··· − 323613671u + 225151331)
c
4
((u
2
+ 1)
4
)(u
25
+ 3u
24
+ ··· + 12u + 1)(u
124
− 8u
123
+ ··· − 1020u + 25)
c
5
((u
2
− u + 1)
4
)(u
25
+ 4u
24
+ ··· − u + 1)
· (u
124
− 3u
123
+ ··· + 58197u + 6844)
c
6
((u
4
− u
2
+ 1)
2
)(u
25
− 2u
24
+ ··· − u − 1)
· (u
124
− 3u
123
+ ··· + 7019u + 802)
c
7
((u + 1)
8
)(u
25
− 5u
24
+ ··· + 2u + 1)(u
124
− 4u
123
+ ··· + 86u + 31)
c
8
((u
2
+ 1)
2
)(u
4
− 2u
3
+ ··· − 4u + 1)(u
25
− u
24
+ ··· + 5u
2
+ 1)
· (u
124
+ 4u
123
+ ··· − 448142u + 166093)
c
9
((u + 1)
4
)(u
4
− 4u
3
+ ··· − 2u + 1)(u
25
− 2u
23
+ ··· + u + 1)
· (u
124
+ u
123
+ ··· − 308331u + 65281)
c
10
, c
11
((u − 1)
8
)(u
25
+ 5u
24
+ ··· + 2u − 1)(u
124
− 4u
123
+ ··· + 86u + 31)
c
12
(u
4
− u
2
+ 1)(u
4
− 4u
3
+ ··· − 2u + 1)(u
25
− 5u
24
+ ··· + u − 1)
· (u
124
− 4u
123
+ ··· − 307u + 47)
32
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y + 1)
8
)(y
25
+ 23y
24
+ ··· + 12y −1)
· (y
124
+ 102y
123
+ ··· − 108550y + 625)
c
2
, c
6
((y
2
− y + 1)
4
)(y
25
− 14y
24
+ ··· + 19y −1)
· (y
124
− 87y
123
+ ··· − 39793137y + 643204)
c
3
((y
2
+ y + 1)
2
)(y
4
+ 6y
3
+ ··· − 6y + 1)(y
25
+ 4y
24
+ ··· − 41y −1)
· (y
124
+ 71y
123
+ ··· + 2087042095852583975y + 50693121851071561)
c
5
((y
2
+ y + 1)
4
)(y
25
+ 30y
23
+ ··· + y −1)
· (y
124
− 17y
123
+ ··· − 1045038265y + 46840336)
c
7
, c
10
, c
11
((y −1)
8
)(y
25
− 35y
24
+ ··· − 20y −1)
· (y
124
− 144y
123
+ ··· − 148446y + 961)
c
8
((y + 1)
4
)(y
4
+ 6y
3
+ ··· − 6y + 1)(y
25
+ 11y
24
+ ··· − 10y −1)
· (y
124
+ 56y
123
+ ··· + 1616827756682y + 27586884649)
c
9
((y −1)
4
)(y
4
− 6y
3
+ ··· + 6y + 1)(y
25
− 4y
24
+ ··· + y −1)
· (y
124
+ 9y
123
+ ··· + 12388959547y + 4261608961)
c
12
((y
2
− y + 1)
2
)(y
4
− 6y
3
+ ··· + 6y + 1)(y
25
− 3y
24
+ ··· + 11y −1)
· (y
124
+ 116y
122
+ ··· + 46939y + 2209)
33
