12a
0316
(K12a
0316
)
A knot diagram
1
Linearized knot diagam
3 6 8 11 2 9 10 5 1 12 4 7
Solving Sequence
2,6 3,9
7 1 10 5 8 4 12 11
c
2
c
6
c
1
c
9
c
5
c
8
c
3
c
12
c
11
c
4
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h6.27132 × 10
469
u
176
+ 1.45967 × 10
471
u
175
+ ··· + 6.67248 × 10
470
b + 1.46517 × 10
471
,
4.71016 × 10
471
u
176
+ 1.68292 × 10
472
u
175
+ ··· + 6.67248 × 10
470
a + 1.35006 × 10
472
,
u
177
+ 4u
176
+ ··· + 10u + 1i
I
u
2
= h3206229u
36
− 851287u
35
+ ··· + 53147b − 2921496,
3206229u
36
− 851287u
35
+ ··· + 53147a − 3134084, u
37
+ u
36
+ ··· + 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 214 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
= h6.27 × 10
469
u
176
+ 1.46 × 10
471
u
175
+ · · · + 6.67 × 10
470
b + 1.47 ×
10
471
, 4.71 × 10
471
u
176
+ 1.68 × 10
472
u
175
+ · · · + 6.67 × 10
470
a + 1.35 ×
10
472
, u
177
+ 4u
176
+ · · · + 10u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
−7.05907u
176
− 25.2217u
175
+ ··· − 135.362u − 20.2332
−0.0939879u
176
− 2.18760u
175
+ ··· − 25.6168u − 2.19583
a
7
=
−1.26084u
176
− 3.18185u
175
+ ··· + 0.522136u + 4.94160
−1.02841u
176
− 2.49536u
175
+ ··· + 7.10073u + 1.76271
a
1
=
−u
2
+ 1
−u
4
a
10
=
−11.7961u
176
− 40.9296u
175
+ ··· − 191.660u − 25.4602
−4.25227u
176
− 15.3984u
175
+ ··· − 63.4411u − 6.27080
a
5
=
u
u
a
8
=
−10.8853u
176
− 37.9312u
175
+ ··· − 176.659u − 25.0594
−3.92024u
176
− 14.8971u
175
+ ··· − 66.9138u − 7.02204
a
4
=
5.45380u
176
+ 22.5815u
175
+ ··· + 155.803u + 18.4036
−3.53508u
176
− 8.38983u
175
+ ··· − 20.8326u − 2.85652
a
12
=
−2.20492u
176
− 9.94931u
175
+ ··· − 123.233u − 13.6295
3.43657u
176
+ 12.3261u
175
+ ··· + 48.1433u + 6.89118
a
11
=
−14.5338u
176
− 46.8491u
175
+ ··· − 189.484u − 18.3827
−7.41726u
176
− 23.1558u
175
+ ··· − 69.7149u − 6.96208
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18.8317u
176
− 63.9674u
175
+ ··· − 313.568u − 37.3249
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
177
+ 80u
176
+ ··· + 34u + 1
c
2
, c
5
u
177
+ 4u
176
+ ··· + 10u + 1
c
3
u
177
+ u
176
+ ··· + 220952u − 6793
c
4
, c
11
u
177
+ 36u
175
+ ··· − 195u + 59
c
6
u
177
− 17u
176
+ ··· − 962894u + 202189
c
7
u
177
+ 8u
176
+ ··· + 79u − 1
c
8
u
177
+ u
176
+ ··· − 377547059u − 63518701
c
9
u
177
+ 18u
176
+ ··· − 5792u − 523
c
10
u
177
+ 72u
176
+ ··· − 103103u − 3481
c
12
u
177
+ 5u
176
+ ··· + 895865u − 154903
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
177
+ 44y
176
+ ··· − 2218y −1
c
2
, c
5
y
177
− 80y
176
+ ··· + 34y −1
c
3
y
177
− 17y
176
+ ··· + 37538868580y −46144849
c
4
, c
11
y
177
+ 72y
176
+ ··· − 103103y −3481
c
6
y
177
− 27y
176
+ ··· − 44453979886y −40880391721
c
7
y
177
+ 12y
176
+ ··· + 549y −1
c
8
y
177
− 37y
176
+ ··· + 270860312130815791y −4034625376727401
c
9
y
177
+ 8y
176
+ ··· − 28982616y −273529
c
10
y
177
+ 72y
176
+ ··· − 1149837415y −12117361
c
12
y
177
+ 31y
176
+ ··· − 1661817074137y −23994939409
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.864110 + 0.503380I
a = 1.64210 − 0.28849I
b = 0.453580 + 0.130110I
3.02236 + 0.80080I 0
u = 0.864110 − 0.503380I
a = 1.64210 + 0.28849I
b = 0.453580 − 0.130110I
3.02236 − 0.80080I 0
u = 0.854454 + 0.530174I
a = 0.581132 − 1.206900I
b = 1.18512 − 2.00320I
3.02605 − 4.97258I 0
u = 0.854454 − 0.530174I
a = 0.581132 + 1.206900I
b = 1.18512 + 2.00320I
3.02605 + 4.97258I 0
u = 0.628733 + 0.785612I
a = −0.722882 + 0.572565I
b = 0.538006 − 0.109119I
6.22275 + 0.33470I 0
u = 0.628733 − 0.785612I
a = −0.722882 − 0.572565I
b = 0.538006 + 0.109119I
6.22275 − 0.33470I 0
u = −0.995131 + 0.150101I
a = −0.730128 + 0.587590I
b = −1.69476 + 1.26240I
0.137829 + 1.011590I 0
u = −0.995131 − 0.150101I
a = −0.730128 − 0.587590I
b = −1.69476 − 1.26240I
0.137829 − 1.011590I 0
u = 0.429828 + 0.910229I
a = −1.26729 + 0.89068I
b = −0.0504466 + 0.0116262I
5.31765 + 9.00835I 0
u = 0.429828 − 0.910229I
a = −1.26729 − 0.89068I
b = −0.0504466 − 0.0116262I
5.31765 − 9.00835I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.431978 + 0.909727I
a = 1.099430 + 0.678193I
b = −0.0703223 + 0.1208490I
−1.84822 − 7.07977I 0
u = −0.431978 − 0.909727I
a = 1.099430 − 0.678193I
b = −0.0703223 − 0.1208490I
−1.84822 + 7.07977I 0
u = −0.430940 + 0.912090I
a = 1.35273 + 0.84882I
b = 0.0209828 − 0.0429838I
3.6105 − 15.0225I 0
u = −0.430940 − 0.912090I
a = 1.35273 − 0.84882I
b = 0.0209828 + 0.0429838I
3.6105 + 15.0225I 0
u = −0.689258 + 0.741416I
a = −1.51421 − 0.54650I
b = −0.990121 − 0.092074I
4.35698 + 0.21526I 0
u = −0.689258 − 0.741416I
a = −1.51421 + 0.54650I
b = −0.990121 + 0.092074I
4.35698 − 0.21526I 0
u = −0.983063 + 0.244776I
a = 0.086827 − 0.874000I
b = −0.92991 − 1.40928I
−3.69375 + 1.07233I 0
u = −0.983063 − 0.244776I
a = 0.086827 + 0.874000I
b = −0.92991 + 1.40928I
−3.69375 − 1.07233I 0
u = 0.556234 + 0.847392I
a = 1.232020 − 0.344639I
b = 0.306913 + 0.299878I
2.34667 + 1.51020I 0
u = 0.556234 − 0.847392I
a = 1.232020 + 0.344639I
b = 0.306913 − 0.299878I
2.34667 − 1.51020I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.814374 + 0.549309I
a = −0.779171 − 0.971826I
b = −1.14533 − 1.70016I
3.39876 − 0.49100I 0
u = −0.814374 − 0.549309I
a = −0.779171 + 0.971826I
b = −1.14533 + 1.70016I
3.39876 + 0.49100I 0
u = −0.880785 + 0.526592I
a = −1.42262 − 0.63982I
b = −0.325054 − 0.362166I
3.20866 + 4.81840I 0
u = −0.880785 − 0.526592I
a = −1.42262 + 0.63982I
b = −0.325054 + 0.362166I
3.20866 − 4.81840I 0
u = 0.673023 + 0.777597I
a = 1.54096 − 0.46393I
b = 0.891807 + 0.136620I
4.16997 + 4.65462I 0
u = 0.673023 − 0.777597I
a = 1.54096 + 0.46393I
b = 0.891807 − 0.136620I
4.16997 − 4.65462I 0
u = 1.016800 + 0.178760I
a = 0.839498 + 0.723029I
b = 1.74110 + 1.69079I
−0.10196 + 3.78125I 0
u = 1.016800 − 0.178760I
a = 0.839498 − 0.723029I
b = 1.74110 − 1.69079I
−0.10196 − 3.78125I 0
u = 0.413682 + 0.948840I
a = −0.745949 + 0.906108I
b = −0.053103 + 0.298477I
4.35149 + 3.60655I 0
u = 0.413682 − 0.948840I
a = −0.745949 − 0.906108I
b = −0.053103 − 0.298477I
4.35149 − 3.60655I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.993594 + 0.291384I
a = 0.844216 + 0.946999I
b = 0.93027 + 2.29117I
−1.66504 + 0.52353I 0
u = 0.993594 − 0.291384I
a = 0.844216 − 0.946999I
b = 0.93027 − 2.29117I
−1.66504 − 0.52353I 0
u = 0.895649 + 0.357166I
a = 1.025610 + 0.918358I
b = 0.45506 + 1.74939I
−1.23431 + 0.87708I 0
u = 0.895649 − 0.357166I
a = 1.025610 − 0.918358I
b = 0.45506 − 1.74939I
−1.23431 − 0.87708I 0
u = −0.605031 + 0.748752I
a = 0.843894 + 0.498704I
b = −0.709249 − 0.239796I
4.30109 − 6.39022I 0
u = −0.605031 − 0.748752I
a = 0.843894 − 0.498704I
b = −0.709249 + 0.239796I
4.30109 + 6.39022I 0
u = 0.966875 + 0.380234I
a = −0.52633 + 1.66575I
b = 0.39230 + 2.53238I
−2.02402 + 4.85256I 0
u = 0.966875 − 0.380234I
a = −0.52633 − 1.66575I
b = 0.39230 − 2.53238I
−2.02402 − 4.85256I 0
u = −0.969471 + 0.379442I
a = 0.287010 + 1.361120I
b = −0.58379 + 2.08508I
−0.854958 + 0.471035I 0
u = −0.969471 − 0.379442I
a = 0.287010 − 1.361120I
b = −0.58379 − 2.08508I
−0.854958 − 0.471035I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.334151 + 0.990251I
a = −0.463534 − 0.392409I
b = −0.004647 + 0.230446I
−0.814141 + 0.510005I 0
u = −0.334151 − 0.990251I
a = −0.463534 + 0.392409I
b = −0.004647 − 0.230446I
−0.814141 − 0.510005I 0
u = 0.981019 + 0.368545I
a = −1.02461 + 0.98094I
b = −0.46481 + 1.88356I
−6.14172 − 1.19459I 0
u = 0.981019 − 0.368545I
a = −1.02461 − 0.98094I
b = −0.46481 − 1.88356I
−6.14172 + 1.19459I 0
u = −0.954229 + 0.434373I
a = −0.738335 + 0.615680I
b = 0.40593 + 2.03400I
−4.50486 + 1.86213I 0
u = −0.954229 − 0.434373I
a = −0.738335 − 0.615680I
b = 0.40593 − 2.03400I
−4.50486 − 1.86213I 0
u = 0.482512 + 0.810071I
a = 1.120650 − 0.605325I
b = 0.180308 + 0.169055I
2.43714 + 1.63530I 0
u = 0.482512 − 0.810071I
a = 1.120650 + 0.605325I
b = 0.180308 − 0.169055I
2.43714 − 1.63530I 0
u = 0.968611 + 0.427868I
a = −0.466538 − 0.976942I
b = 0.23731 − 1.57700I
−1.71516 − 3.91586I 0
u = 0.968611 − 0.427868I
a = −0.466538 + 0.976942I
b = 0.23731 + 1.57700I
−1.71516 + 3.91586I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.007150 + 0.358789I
a = −0.779760 + 0.932037I
b = −0.41402 + 2.57889I
−2.82839 − 4.64321I 0
u = −1.007150 − 0.358789I
a = −0.779760 − 0.932037I
b = −0.41402 − 2.57889I
−2.82839 + 4.64321I 0
u = 0.953295 + 0.486416I
a = 0.397010 − 0.541125I
b = −1.47341 − 1.50063I
−4.20211 − 3.46738I 0
u = 0.953295 − 0.486416I
a = 0.397010 + 0.541125I
b = −1.47341 + 1.50063I
−4.20211 + 3.46738I 0
u = −0.533783 + 0.934684I
a = −0.976099 − 0.139686I
b = −0.106331 + 0.396116I
1.03900 − 5.79820I 0
u = −0.533783 − 0.934684I
a = −0.976099 + 0.139686I
b = −0.106331 − 0.396116I
1.03900 + 5.79820I 0
u = −0.981695 + 0.447205I
a = 0.364521 + 0.474478I
b = −0.228931 + 1.035680I
−1.59398 + 1.86715I 0
u = −0.981695 − 0.447205I
a = 0.364521 − 0.474478I
b = −0.228931 − 1.035680I
−1.59398 − 1.86715I 0
u = −0.686189 + 0.838109I
a = 0.422512 + 0.531598I
b = −0.115585 + 0.289545I
−0.33435 + 2.65275I 0
u = −0.686189 − 0.838109I
a = 0.422512 − 0.531598I
b = −0.115585 − 0.289545I
−0.33435 − 2.65275I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.641662 + 0.873189I
a = −0.467333 + 0.778610I
b = 0.0584398 − 0.0639245I
6.61970 − 4.57530I 0
u = 0.641662 − 0.873189I
a = −0.467333 − 0.778610I
b = 0.0584398 + 0.0639245I
6.61970 + 4.57530I 0
u = 0.976335 + 0.497172I
a = −1.08695 − 1.54329I
b = −0.69036 − 2.42165I
−0.15175 − 5.18017I 0
u = 0.976335 − 0.497172I
a = −1.08695 + 1.54329I
b = −0.69036 + 2.42165I
−0.15175 + 5.18017I 0
u = −0.643816 + 0.892856I
a = 0.394328 + 0.823883I
b = 0.0398039 − 0.0652166I
4.88923 + 10.48330I 0
u = −0.643816 − 0.892856I
a = 0.394328 − 0.823883I
b = 0.0398039 + 0.0652166I
4.88923 − 10.48330I 0
u = −0.984038 + 0.507492I
a = 1.39816 − 1.54570I
b = 1.12239 − 2.46986I
−1.20216 + 10.51620I 0
u = −0.984038 − 0.507492I
a = 1.39816 + 1.54570I
b = 1.12239 + 2.46986I
−1.20216 − 10.51620I 0
u = 1.074180 + 0.314145I
a = −1.187290 + 0.107309I
b = −1.30256 + 0.80314I
−1.71410 − 6.86279I 0
u = 1.074180 − 0.314145I
a = −1.187290 − 0.107309I
b = −1.30256 − 0.80314I
−1.71410 + 6.86279I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.986129 + 0.529695I
a = −0.446989 − 0.969513I
b = 0.45388 − 2.03741I
0.06124 + 6.22009I 0
u = −0.986129 − 0.529695I
a = −0.446989 + 0.969513I
b = 0.45388 + 2.03741I
0.06124 − 6.22009I 0
u = 0.766407 + 0.418178I
a = 0.318503 − 0.142059I
b = −0.02476 − 2.36651I
−3.49282 − 0.33241I 0
u = 0.766407 − 0.418178I
a = 0.318503 + 0.142059I
b = −0.02476 + 2.36651I
−3.49282 + 0.33241I 0
u = 1.013210 + 0.498461I
a = 0.181595 − 0.942807I
b = −0.88594 − 2.57967I
−1.94333 − 10.80760I 0
u = 1.013210 − 0.498461I
a = 0.181595 + 0.942807I
b = −0.88594 + 2.57967I
−1.94333 + 10.80760I 0
u = −0.203869 + 0.844369I
a = 0.240509 + 1.358190I
b = 0.129274 + 0.558191I
2.35834 + 3.63220I 0
u = −0.203869 − 0.844369I
a = 0.240509 − 1.358190I
b = 0.129274 − 0.558191I
2.35834 − 3.63220I 0
u = −1.020510 + 0.488503I
a = 1.28197 − 0.78165I
b = 1.10918 − 1.32805I
−5.32571 + 4.91021I 0
u = −1.020510 − 0.488503I
a = 1.28197 + 0.78165I
b = 1.10918 + 1.32805I
−5.32571 − 4.91021I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.454584 + 0.720457I
a = 1.76325 − 0.93699I
b = 0.0092184 + 0.1017300I
4.72116 + 0.61300I 0
u = 0.454584 − 0.720457I
a = 1.76325 + 0.93699I
b = 0.0092184 − 0.1017300I
4.72116 − 0.61300I 0
u = −1.107280 + 0.360761I
a = −0.046154 − 0.532157I
b = −1.35787 − 0.75946I
−2.80776 + 5.90177I 0
u = −1.107280 − 0.360761I
a = −0.046154 + 0.532157I
b = −1.35787 + 0.75946I
−2.80776 − 5.90177I 0
u = −0.443082 + 0.704654I
a = −1.89935 − 0.78762I
b = 0.0903060 + 0.0571122I
4.33274 − 5.54339I 0
u = −0.443082 − 0.704654I
a = −1.89935 + 0.78762I
b = 0.0903060 − 0.0571122I
4.33274 + 5.54339I 0
u = −0.972572 + 0.650132I
a = −0.57392 − 1.55176I
b = −0.79279 − 1.91590I
3.48309 + 5.08902I 0
u = −0.972572 − 0.650132I
a = −0.57392 + 1.55176I
b = −0.79279 + 1.91590I
3.48309 − 5.08902I 0
u = 1.071370 + 0.472682I
a = −0.125573 + 0.151807I
b = 0.754288 + 0.695071I
−2.42037 − 5.73814I 0
u = 1.071370 − 0.472682I
a = −0.125573 − 0.151807I
b = 0.754288 − 0.695071I
−2.42037 + 5.73814I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.727816 + 0.388140I
a = 1.46503 + 1.79064I
b = 0.71399 + 1.66257I
0.80530 + 1.36238I 0
u = 0.727816 − 0.388140I
a = 1.46503 − 1.79064I
b = 0.71399 − 1.66257I
0.80530 − 1.36238I 0
u = −1.034940 + 0.566622I
a = −0.385371 − 1.274380I
b = −0.26876 − 2.61647I
0.18035 + 6.67560I 0
u = −1.034940 − 0.566622I
a = −0.385371 + 1.274380I
b = −0.26876 + 2.61647I
0.18035 − 6.67560I 0
u = 1.110490 + 0.400960I
a = 0.047678 − 0.338435I
b = 1.338290 − 0.291718I
−2.57340 − 1.75170I 0
u = 1.110490 − 0.400960I
a = 0.047678 + 0.338435I
b = 1.338290 + 0.291718I
−2.57340 + 1.75170I 0
u = −0.539683 + 0.613755I
a = −1.52577 − 0.32011I
b = −0.093355 − 0.463207I
1.66757 − 1.98030I 0
u = −0.539683 − 0.613755I
a = −1.52577 + 0.32011I
b = −0.093355 + 0.463207I
1.66757 + 1.98030I 0
u = −0.962996 + 0.686956I
a = 0.305789 + 0.479406I
b = 0.09079 + 1.45512I
−1.20390 + 2.99860I 0
u = −0.962996 − 0.686956I
a = 0.305789 − 0.479406I
b = 0.09079 − 1.45512I
−1.20390 − 2.99860I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.991259 + 0.667775I
a = 0.44316 − 1.57914I
b = 0.84090 − 2.04373I
3.18592 − 10.11620I 0
u = 0.991259 − 0.667775I
a = 0.44316 + 1.57914I
b = 0.84090 + 2.04373I
3.18592 + 10.11620I 0
u = 1.197360 + 0.034337I
a = −0.093939 − 0.740294I
b = 0.29093 − 1.49255I
−5.70441 − 3.92320I 0
u = 1.197360 − 0.034337I
a = −0.093939 + 0.740294I
b = 0.29093 + 1.49255I
−5.70441 + 3.92320I 0
u = 0.431035 + 0.673409I
a = 0.89934 − 1.58988I
b = 0.0987438 − 0.0201630I
4.73101 + 1.60483I 0
u = 0.431035 − 0.673409I
a = 0.89934 + 1.58988I
b = 0.0987438 + 0.0201630I
4.73101 − 1.60483I 0
u = −1.016480 + 0.639805I
a = 0.261850 + 0.617497I
b = 0.96848 + 2.09567I
3.05948 + 11.67370I 0
u = −1.016480 − 0.639805I
a = 0.261850 − 0.617497I
b = 0.96848 − 2.09567I
3.05948 − 11.67370I 0
u = 1.009950 + 0.661821I
a = −0.304566 + 0.574109I
b = −0.88678 + 1.82908I
5.06254 − 5.78643I 0
u = 1.009950 − 0.661821I
a = −0.304566 − 0.574109I
b = −0.88678 − 1.82908I
5.06254 + 5.78643I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.207770 + 0.111088I
a = −0.090639 + 0.505906I
b = −0.501734 + 0.876122I
−3.11096 + 0.52478I 0
u = −1.207770 − 0.111088I
a = −0.090639 − 0.505906I
b = −0.501734 − 0.876122I
−3.11096 − 0.52478I 0
u = −0.677011 + 0.401193I
a = −1.33922 + 2.14785I
b = −0.58887 + 1.74981I
−0.12774 − 6.56719I 0
u = −0.677011 − 0.401193I
a = −1.33922 − 2.14785I
b = −0.58887 − 1.74981I
−0.12774 + 6.56719I 0
u = −1.150310 + 0.396663I
a = 1.029900 + 0.068782I
b = 1.172760 + 0.368957I
−1.008840 + 0.956640I 0
u = −1.150310 − 0.396663I
a = 1.029900 − 0.068782I
b = 1.172760 − 0.368957I
−1.008840 − 0.956640I 0
u = −1.109510 + 0.509073I
a = −1.019910 − 0.403265I
b = −1.93314 − 0.84218I
2.34998 + 0.86622I 0
u = −1.109510 − 0.509073I
a = −1.019910 + 0.403265I
b = −1.93314 + 0.84218I
2.34998 − 0.86622I 0
u = −1.073630 + 0.583236I
a = −0.48076 − 1.47320I
b = −1.05647 − 3.04806I
2.48677 + 10.50110I 0
u = −1.073630 − 0.583236I
a = −0.48076 + 1.47320I
b = −1.05647 + 3.04806I
2.48677 − 10.50110I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.073520 + 0.590068I
a = 0.57156 − 1.43360I
b = 1.27331 − 2.83184I
2.89891 − 5.63480I 0
u = 1.073520 − 0.590068I
a = 0.57156 + 1.43360I
b = 1.27331 + 2.83184I
2.89891 + 5.63480I 0
u = 0.024001 + 0.773556I
a = −0.066380 − 0.835843I
b = 0.053002 + 0.763647I
0.75664 − 2.18053I 0
u = 0.024001 − 0.773556I
a = −0.066380 + 0.835843I
b = 0.053002 − 0.763647I
0.75664 + 2.18053I 0
u = 1.101540 + 0.546410I
a = 0.948856 − 0.721075I
b = 1.84526 − 1.34491I
2.72588 − 6.34808I 0
u = 1.101540 − 0.546410I
a = 0.948856 + 0.721075I
b = 1.84526 + 1.34491I
2.72588 + 6.34808I 0
u = 1.005390 + 0.736212I
a = −0.387763 + 0.458302I
b = −0.885025 + 1.008260I
5.51961 − 1.34491I 0
u = 1.005390 − 0.736212I
a = −0.387763 − 0.458302I
b = −0.885025 − 1.008260I
5.51961 + 1.34491I 0
u = −0.424100 + 0.619781I
a = −0.64402 − 1.80029I
b = −0.0115646 − 0.1115990I
4.41349 + 3.59625I 0
u = −0.424100 − 0.619781I
a = −0.64402 + 1.80029I
b = −0.0115646 + 0.1115990I
4.41349 − 3.59625I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.074910 + 0.639175I
a = 0.341936 − 1.209870I
b = 0.83361 − 2.09047I
0.67305 − 7.06965I 0
u = 1.074910 − 0.639175I
a = 0.341936 + 1.209870I
b = 0.83361 + 2.09047I
0.67305 + 7.06965I 0
u = −0.605691 + 0.429434I
a = −1.013900 + 0.183837I
b = 0.268895 − 1.187210I
1.24190 − 2.04817I 0
u = −0.605691 − 0.429434I
a = −1.013900 − 0.183837I
b = 0.268895 + 1.187210I
1.24190 + 2.04817I 0
u = −0.420295 + 0.607847I
a = 0.347418 + 0.023155I
b = −0.288468 + 0.446331I
−0.33857 + 2.05259I 0
u = −0.420295 − 0.607847I
a = 0.347418 − 0.023155I
b = −0.288468 − 0.446331I
−0.33857 − 2.05259I 0
u = −1.011310 + 0.768024I
a = 0.400895 + 0.407280I
b = 0.910707 + 0.754369I
3.78542 − 4.41512I 0
u = −1.011310 − 0.768024I
a = 0.400895 − 0.407280I
b = 0.910707 − 0.754369I
3.78542 + 4.41512I 0
u = 1.096560 + 0.658026I
a = 0.218148 − 1.118640I
b = 0.72364 − 1.97180I
0.66481 − 7.12625I 0
u = 1.096560 − 0.658026I
a = 0.218148 + 1.118640I
b = 0.72364 + 1.97180I
0.66481 + 7.12625I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.284110 + 0.075213I
a = −0.738730 − 0.622086I
b = −1.53908 − 1.23636I
−2.54229 + 12.16080I 0
u = 1.284110 − 0.075213I
a = −0.738730 + 0.622086I
b = −1.53908 + 1.23636I
−2.54229 − 12.16080I 0
u = −1.286570 + 0.081808I
a = 0.728086 − 0.552802I
b = 1.46142 − 1.03823I
−0.81096 − 6.12839I 0
u = −1.286570 − 0.081808I
a = 0.728086 + 0.552802I
b = 1.46142 + 1.03823I
−0.81096 + 6.12839I 0
u = 1.297720 + 0.059431I
a = −0.493257 − 0.564008I
b = −0.81964 − 1.16945I
−8.06045 + 4.22049I 0
u = 1.297720 − 0.059431I
a = −0.493257 + 0.564008I
b = −0.81964 + 1.16945I
−8.06045 − 4.22049I 0
u = 0.151448 + 0.677292I
a = −0.239174 − 0.493385I
b = 0.217102 + 0.555784I
0.11157 + 1.61027I 0
u = 0.151448 − 0.677292I
a = −0.239174 + 0.493385I
b = 0.217102 − 0.555784I
0.11157 − 1.61027I 0
u = 0.634491 + 0.258463I
a = 0.490582 + 0.774572I
b = −0.94373 − 1.29655I
−0.49221 + 7.04072I 0
u = 0.634491 − 0.258463I
a = 0.490582 − 0.774572I
b = −0.94373 + 1.29655I
−0.49221 − 7.04072I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.141400 + 0.654698I
a = 0.447744 + 1.042120I
b = 0.75561 + 2.17552I
−4.00208 + 12.81910I 0
u = −1.141400 − 0.654698I
a = 0.447744 − 1.042120I
b = 0.75561 − 2.17552I
−4.00208 − 12.81910I 0
u = −1.121680 + 0.690184I
a = 0.001403 − 1.019600I
b = −0.44730 − 1.90854I
−0.80122 + 11.75970I 0
u = −1.121680 − 0.690184I
a = 0.001403 + 1.019600I
b = −0.44730 + 1.90854I
−0.80122 − 11.75970I 0
u = 1.144430 + 0.654477I
a = −0.578454 + 1.185600I
b = −1.13850 + 2.31125I
3.1470 − 14.7517I 0
u = 1.144430 − 0.654477I
a = −0.578454 − 1.185600I
b = −1.13850 − 2.31125I
3.1470 + 14.7517I 0
u = −1.144850 + 0.654743I
a = 0.536120 + 1.244750I
b = 1.12267 + 2.46028I
1.4395 + 20.7720I 0
u = −1.144850 − 0.654743I
a = 0.536120 − 1.244750I
b = 1.12267 − 2.46028I
1.4395 − 20.7720I 0
u = −1.079060 + 0.765489I
a = 0.424703 + 0.553267I
b = 0.217950 + 1.188930I
−1.20942 + 3.19236I 0
u = −1.079060 − 0.765489I
a = 0.424703 − 0.553267I
b = 0.217950 − 1.188930I
−1.20942 − 3.19236I 0
20
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.152480 + 0.666884I
a = −0.610038 + 0.838081I
b = −0.88187 + 1.63953I
2.11726 − 9.47807I 0
u = 1.152480 − 0.666884I
a = −0.610038 − 0.838081I
b = −0.88187 − 1.63953I
2.11726 + 9.47807I 0
u = −1.180110 + 0.641705I
a = −0.191105 − 0.663740I
b = −0.61236 − 1.34118I
−3.39163 + 5.32315I 0
u = −1.180110 − 0.641705I
a = −0.191105 + 0.663740I
b = −0.61236 + 1.34118I
−3.39163 − 5.32315I 0
u = −0.648881 + 0.036092I
a = 0.11541 − 1.59230I
b = −0.84150 − 1.29069I
−3.52867 + 1.18563I −6.52505 − 2.33894I
u = −0.648881 − 0.036092I
a = 0.11541 + 1.59230I
b = −0.84150 + 1.29069I
−3.52867 − 1.18563I −6.52505 + 2.33894I
u = −1.47300
a = 0.469279
b = 0.634655
−2.50835 0
u = 1.47889 + 0.22589I
a = 0.0556634 + 0.0919355I
b = 0.287495 + 0.108538I
−7.07013 − 4.74190I 0
u = 1.47889 − 0.22589I
a = 0.0556634 − 0.0919355I
b = 0.287495 − 0.108538I
−7.07013 + 4.74190I 0
u = −0.071219 + 0.453256I
a = 0.721477 − 0.736546I
b = 0.251352 + 0.377983I
0.427761 + 1.172730I 3.97072 − 6.15691I
21
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.071219 − 0.453256I
a = 0.721477 + 0.736546I
b = 0.251352 − 0.377983I
0.427761 − 1.172730I 3.97072 + 6.15691I
u = −0.293825 + 0.308935I
a = −0.95095 + 2.23466I
b = −0.316383 + 1.006490I
−3.60162 − 1.11181I −5.69253 + 2.09546I
u = −0.293825 − 0.308935I
a = −0.95095 − 2.23466I
b = −0.316383 − 1.006490I
−3.60162 + 1.11181I −5.69253 − 2.09546I
u = −0.176507 + 0.105361I
a = 1.79143 − 4.36130I
b = 0.718621 + 0.524057I
0.94655 + 2.13065I 3.53909 − 3.27688I
u = −0.176507 − 0.105361I
a = 1.79143 + 4.36130I
b = 0.718621 − 0.524057I
0.94655 − 2.13065I 3.53909 + 3.27688I
u = 0.109262 + 0.145309I
a = 5.05773 + 3.28326I
b = −0.809661 − 0.678376I
−0.39898 + 7.14577I 0.37929 − 7.71207I
u = 0.109262 − 0.145309I
a = 5.05773 − 3.28326I
b = −0.809661 + 0.678376I
−0.39898 − 7.14577I 0.37929 + 7.71207I
22
II. I
u
2
= h3.21 × 10
6
u
36
− 8.51 × 10
5
u
35
+ · · · + 5.31 × 10
4
b − 2.92 × 10
6
, 3.21 ×
10
6
u
36
− 8.51 × 10
5
u
35
+ · · · + 5.31 × 10
4
a − 3.13 × 10
6
, u
37
+ u
36
+ · · · + 2u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
−60.3276u
36
+ 16.0176u
35
+ ··· − 134.708u + 58.9701
−60.3276u
36
+ 16.0176u
35
+ ··· − 132.708u + 54.9701
a
7
=
1.93802u
36
− 14.9172u
35
+ ··· − 72.7027u + 24.0016
−58.2978u
36
− 45.2613u
35
+ ··· − 325.009u + 101.099
a
1
=
−u
2
+ 1
−u
4
a
10
=
−69.3193u
36
+ 24.9884u
35
+ ··· − 140.298u + 64.7513
−51.4021u
36
+ 29.9371u
35
+ ··· − 68.7206u + 36.8117
a
5
=
u
u
a
8
=
−59.3276u
36
+ 15.0176u
35
+ ··· − 134.708u + 58.9701
−59.3276u
36
+ 15.0176u
35
+ ··· − 132.708u + 54.9701
a
4
=
3.49015u
36
− 11.0164u
35
+ ··· − 47.3466u + 14.6451
−47.7152u
36
− 5.66967u
35
+ ··· − 133.037u + 46.5210
a
12
=
71.1971u
36
+ 13.8239u
35
+ ··· + 169.419u − 52.9595
91.3081u
36
+ 23.7980u
35
+ ··· + 259.848u − 85.4942
a
11
=
46.6411u
36
+ 13.3569u
35
+ ··· + 102.760u − 34.4590
32.0798u
36
− 10.1208u
35
+ ··· − 24.5471u + 1.82674
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
27277420
53147
u
36
−
3181402
53147
u
35
+ ··· −
71706772
53147
u +
24913109
53147
23
(iv) u-Polynomials at the component
24
Crossings u-Polynomials at each crossing
c
1
u
37
− 21u
36
+ ··· + 12u − 1
c
2
u
37
+ u
36
+ ··· + 2u − 1
c
3
u
37
− 5u
35
+ ··· + 2u − 1
c
4
u
37
+ u
36
+ ··· + 3u + 1
c
5
u
37
− u
36
+ ··· + 2u + 1
c
6
u
37
+ 18u
36
+ ··· + 18u + 1
c
7
u
37
− 19u
36
+ ··· + 13u − 1
c
8
u
37
+ 2u
36
+ ··· + 5u + 1
c
9
u
37
− 5u
36
+ ··· − 4u + 1
c
10
u
37
− 19u
36
+ ··· − 17u + 1
c
11
u
37
− u
36
+ ··· + 3u − 1
c
12
u
37
− 4u
36
+ ··· − 5u + 1
25
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
37
− y
36
+ ··· − 116y −1
c
2
, c
5
y
37
− 21y
36
+ ··· + 12y −1
c
3
y
37
− 10y
36
+ ··· + 14y −1
c
4
, c
11
y
37
+ 19y
36
+ ··· − 17y −1
c
6
y
37
+ 12y
36
+ ··· − 120y
2
− 1
c
7
y
37
+ 11y
36
+ ··· + 7y −1
c
8
y
37
+ 6y
36
+ ··· + 17y −1
c
9
y
37
− y
36
+ ··· − 2y −1
c
10
y
37
+ 3y
36
+ ··· − 73y −1
c
12
y
37
+ 2y
36
+ ··· + y −1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.636360 + 0.780355I
a = 1.121450 + 0.089933I
b = 0.050971 + 0.294614I
1.94301 + 5.57497I 3.17751 − 6.09733I
u = 0.636360 − 0.780355I
a = 1.121450 − 0.089933I
b = 0.050971 − 0.294614I
1.94301 − 5.57497I 3.17751 + 6.09733I
u = 0.929573 + 0.324747I
a = 0.76409 + 1.46375I
b = 1.40220 + 2.48146I
−0.356489 + 0.688026I −0.683493 − 1.081977I
u = 0.929573 − 0.324747I
a = 0.76409 − 1.46375I
b = 1.40220 − 2.48146I
−0.356489 − 0.688026I −0.683493 + 1.081977I
u = −0.909768 + 0.344427I
a = −0.41618 + 1.59821I
b = −1.13504 + 2.89523I
−1.35075 − 5.66407I −2.15599 + 6.15671I
u = −0.909768 − 0.344427I
a = −0.41618 − 1.59821I
b = −1.13504 − 2.89523I
−1.35075 + 5.66407I −2.15599 − 6.15671I
u = −0.914509 + 0.308324I
a = 0.821358 − 1.031710I
b = 0.372931 + 0.023664I
−1.30915 + 8.39971I −2.21916 − 10.51765I
u = −0.914509 − 0.308324I
a = 0.821358 + 1.031710I
b = 0.372931 − 0.023664I
−1.30915 − 8.39971I −2.21916 + 10.51765I
u = 0.928357 + 0.259036I
a = −0.400360 − 1.136020I
b = −0.155434 − 0.362444I
−0.23011 − 3.12941I −0.31946 + 4.76010I
u = 0.928357 − 0.259036I
a = −0.400360 + 1.136020I
b = −0.155434 + 0.362444I
−0.23011 + 3.12941I −0.31946 − 4.76010I
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.968327 + 0.400339I
a = 0.481131 − 0.276979I
b = −0.995697 + 0.297587I
−4.64121 + 2.66285I −8.78178 − 2.44410I
u = −0.968327 − 0.400339I
a = 0.481131 + 0.276979I
b = −0.995697 − 0.297587I
−4.64121 − 2.66285I −8.78178 + 2.44410I
u = −0.605875 + 0.729762I
a = −1.53601 − 0.15500I
b = −0.351090 + 0.201233I
3.08832 − 1.09963I 5.89565 − 0.28185I
u = −0.605875 − 0.729762I
a = −1.53601 + 0.15500I
b = −0.351090 − 0.201233I
3.08832 + 1.09963I 5.89565 + 0.28185I
u = 0.918262 + 0.172526I
a = 0.763004 + 0.939190I
b = 0.71890 + 1.44586I
−1.46734 + 1.62332I −2.33782 − 6.01993I
u = 0.918262 − 0.172526I
a = 0.763004 − 0.939190I
b = 0.71890 − 1.44586I
−1.46734 − 1.62332I −2.33782 + 6.01993I
u = 0.236700 + 0.883679I
a = 0.226767 − 0.321382I
b = −0.162140 + 0.421168I
−0.924259 − 0.943713I −7.33975 + 6.12981I
u = 0.236700 − 0.883679I
a = 0.226767 + 0.321382I
b = −0.162140 − 0.421168I
−0.924259 + 0.943713I −7.33975 − 6.12981I
u = −0.827293 + 0.346568I
a = −0.307640 + 0.779415I
b = −0.15648 + 2.63330I
−4.06120 + 0.44955I −10.20168 − 0.39324I
u = −0.827293 − 0.346568I
a = −0.307640 − 0.779415I
b = −0.15648 − 2.63330I
−4.06120 − 0.44955I −10.20168 + 0.39324I
29
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.447006 + 0.695397I
a = −1.35348 − 1.14865I
b = −0.371285 − 0.375676I
3.54644 − 2.96378I 3.90196 + 4.10249I
u = −0.447006 − 0.695397I
a = −1.35348 + 1.14865I
b = −0.371285 + 0.375676I
3.54644 + 2.96378I 3.90196 − 4.10249I
u = 1.087260 + 0.481427I
a = −0.233225 − 0.304898I
b = 0.568726 − 0.764158I
−3.59836 − 3.69556I −6.70217 + 3.70626I
u = 1.087260 − 0.481427I
a = −0.233225 + 0.304898I
b = 0.568726 + 0.764158I
−3.59836 + 3.69556I −6.70217 − 3.70626I
u = 1.016060 + 0.618653I
a = −0.121085 − 1.299260I
b = 0.07576 − 2.51417I
0.74356 − 10.83980I 0. + 10.88143I
u = 1.016060 − 0.618653I
a = −0.121085 + 1.299260I
b = 0.07576 + 2.51417I
0.74356 + 10.83980I 0. − 10.88143I
u = −1.027080 + 0.605357I
a = −0.18778 − 1.52071I
b = −0.50297 − 2.68204I
1.77824 + 6.20689I 0. − 5.59321I
u = −1.027080 − 0.605357I
a = −0.18778 + 1.52071I
b = −0.50297 + 2.68204I
1.77824 − 6.20689I 0. + 5.59321I
u = −1.075070 + 0.601295I
a = −0.718335 − 1.154960I
b = −1.07329 − 2.02633I
1.72174 + 8.01761I 0. − 8.88964I
u = −1.075070 − 0.601295I
a = −0.718335 + 1.154960I
b = −1.07329 + 2.02633I
1.72174 − 8.01761I 0. + 8.88964I
30
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.020840 + 0.791819I
a = 0.394801 − 0.544825I
b = 0.080384 − 1.180470I
−1.13245 − 3.27552I 0. + 41.1711I
u = 1.020840 − 0.791819I
a = 0.394801 + 0.544825I
b = 0.080384 + 1.180470I
−1.13245 + 3.27552I 0. − 41.1711I
u = 1.46097
a = 0.465667
b = 0.692620
−2.45249 0
u = −1.48301 + 0.20333I
a = −0.120677 − 0.151126I
b = −0.349374 − 0.203202I
−7.04467 + 4.84529I 0
u = −1.48301 − 0.20333I
a = −0.120677 + 0.151126I
b = −0.349374 + 0.203202I
−7.04467 − 4.84529I 0
u = 0.254049 + 0.261294I
a = 2.08933 − 2.99081I
b = 0.136624 − 0.995665I
3.00637 − 2.83494I 3.37830 + 2.42808I
u = 0.254049 − 0.261294I
a = 2.08933 + 2.99081I
b = 0.136624 + 0.995665I
3.00637 + 2.83494I 3.37830 − 2.42808I
31
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
37
− 21u
36
+ ··· + 12u − 1)(u
177
+ 80u
176
+ ··· + 34u + 1)
c
2
(u
37
+ u
36
+ ··· + 2u − 1)(u
177
+ 4u
176
+ ··· + 10u + 1)
c
3
(u
37
− 5u
35
+ ··· + 2u − 1)(u
177
+ u
176
+ ··· + 220952u − 6793)
c
4
(u
37
+ u
36
+ ··· + 3u + 1)(u
177
+ 36u
175
+ ··· − 195u + 59)
c
5
(u
37
− u
36
+ ··· + 2u + 1)(u
177
+ 4u
176
+ ··· + 10u + 1)
c
6
(u
37
+ 18u
36
+ ··· + 18u + 1)
· (u
177
− 17u
176
+ ··· − 962894u + 202189)
c
7
(u
37
− 19u
36
+ ··· + 13u − 1)(u
177
+ 8u
176
+ ··· + 79u − 1)
c
8
(u
37
+ 2u
36
+ ··· + 5u + 1)
· (u
177
+ u
176
+ ··· − 377547059u − 63518701)
c
9
(u
37
− 5u
36
+ ··· − 4u + 1)(u
177
+ 18u
176
+ ··· − 5792u − 523)
c
10
(u
37
− 19u
36
+ ··· − 17u + 1)(u
177
+ 72u
176
+ ··· − 103103u − 3481)
c
11
(u
37
− u
36
+ ··· + 3u − 1)(u
177
+ 36u
175
+ ··· − 195u + 59)
c
12
(u
37
− 4u
36
+ ··· − 5u + 1)(u
177
+ 5u
176
+ ··· + 895865u − 154903)
32
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
37
− y
36
+ ··· − 116y −1)(y
177
+ 44y
176
+ ··· − 2218y −1)
c
2
, c
5
(y
37
− 21y
36
+ ··· + 12y −1)(y
177
− 80y
176
+ ··· + 34y −1)
c
3
(y
37
− 10y
36
+ ··· + 14y −1)
· (y
177
− 17y
176
+ ··· + 37538868580y −46144849)
c
4
, c
11
(y
37
+ 19y
36
+ ··· − 17y −1)(y
177
+ 72y
176
+ ··· − 103103y −3481)
c
6
(y
37
+ 12y
36
+ ··· − 120y
2
− 1)
· (y
177
− 27y
176
+ ··· − 44453979886y −40880391721)
c
7
(y
37
+ 11y
36
+ ··· + 7y −1)(y
177
+ 12y
176
+ ··· + 549y −1)
c
8
(y
37
+ 6y
36
+ ··· + 17y −1)
· (y
177
− 37y
176
+ ··· + 270860312130815791y −4034625376727401)
c
9
(y
37
− y
36
+ ··· − 2y −1)(y
177
+ 8y
176
+ ··· − 2.89826 × 10
7
y −273529)
c
10
(y
37
+ 3y
36
+ ··· − 73y −1)
· (y
177
+ 72y
176
+ ··· − 1149837415y −12117361)
c
12
(y
37
+ 2y
36
+ ··· + y −1)
· (y
177
+ 31y
176
+ ··· − 1661817074137y −23994939409)
33
