12a
0310
(K12a
0310
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 9 2 12 1 11 5 7 4
Solving Sequence
2,6
3
7,12
8 4 1 9 5 11 10
c
2
c
6
c
7
c
3
c
1
c
8
c
5
c
11
c
10
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h2.27433 × 10
354
u
137
+ 1.24436 × 10
355
u
136
+ ··· + 1.06021 × 10
355
b − 9.00762 × 10
355
,
1.69855 × 10
354
u
137
+ 8.78430 × 10
354
u
136
+ ··· + 1.06021 × 10
355
a − 4.05574 × 10
356
,
u
138
+ 7u
137
+ ··· + 1836u + 216i
I
u
2
= h7u
29
− 7u
28
+ ··· + b − 1, 6u
29
− 7u
28
+ ··· + a − 9, u
30
− u
29
+ ··· − u + 1i
I
u
3
= h−5169a
6
u + 14986a
5
u + ··· − 286138a + 106454,
a
7
− 2a
6
u − 11a
5
u + 6a
5
+ 24a
4
u − 38a
4
+ 4a
3
u + 46a
3
− 48a
2
u − 2a
2
+ 28au − 25a − u + 6, u
2
− u + 1i
* 3 irreducible components of dim
C
= 0, with total 182 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
= h2.27 × 10
354
u
137
+ 1.24 × 10
355
u
136
+ · · · + 1.06 × 10
355
b − 9.01 ×
10
355
, 1.70 × 10
354
u
137
+ 8.78 × 10
354
u
136
+ · · · + 1.06 × 10
355
a − 4.06 ×
10
356
, u
138
+ 7u
137
+ · · · + 1836u + 216i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
12
=
−0.160209u
137
− 0.828543u
136
+ ··· + 203.274u + 38.2541
−0.214516u
137
− 1.17370u
136
+ ··· + 19.3693u + 8.49607
a
8
=
0.380098u
137
+ 2.08238u
136
+ ··· − 240.204u − 56.1677
0.0620701u
137
− 0.0770345u
136
+ ··· − 794.079u − 113.783
a
4
=
0.205743u
137
+ 1.62270u
136
+ ··· + 376.900u + 42.9007
0.407264u
137
+ 2.77702u
136
+ ··· + 574.740u + 61.4601
a
1
=
u
2
+ 1
−u
4
a
9
=
−0.0740279u
137
− 0.834982u
136
+ ··· − 801.708u − 118.094
−0.248617u
137
− 2.06032u
136
+ ··· − 1061.70u − 139.977
a
5
=
0.249137u
137
+ 2.01530u
136
+ ··· + 1083.50u + 153.271
0.207662u
137
+ 1.53167u
136
+ ··· + 417.061u + 47.7159
a
11
=
−0.147415u
137
− 0.716549u
136
+ ··· + 255.807u + 45.8145
−0.201723u
137
− 1.06170u
136
+ ··· + 71.9021u + 16.0565
a
10
=
−0.231859u
137
− 2.11061u
136
+ ··· − 1274.80u − 174.147
−0.403432u
137
− 3.02889u
136
+ ··· − 1012.28u − 119.100
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.117732u
137
− 0.757477u
136
+ ··· − 388.494u − 88.6881
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
138
+ 57u
137
+ ··· + 802224u + 46656
c
2
, c
6
u
138
+ 7u
137
+ ··· + 1836u + 216
c
3
u
138
− u
137
+ ··· − 54398u + 10041
c
4
, c
10
u
138
− u
137
+ ··· − 30u + 19
c
5
u
138
− 3u
137
+ ··· − 5664770u + 21046851
c
7
, c
11
u
138
− 3u
137
+ ··· + 378940u + 19571
c
8
u
138
+ u
137
+ ··· − 50u + 1
c
9
u
138
+ 71u
137
+ ··· + 3712u + 361
c
12
u
138
+ 13u
137
+ ··· − 310u + 77
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
138
+ 57y
137
+ ··· + 94721944320y + 2176782336
c
2
, c
6
y
138
+ 57y
137
+ ··· + 802224y + 46656
c
3
y
138
+ 31y
137
+ ··· + 4830062936y + 100821681
c
4
, c
10
y
138
− 71y
137
+ ··· − 3712y + 361
c
5
y
138
+ 45y
137
+ ··· + 9711800845573616y + 442969937016201
c
7
, c
11
y
138
− 101y
137
+ ··· − 89234996574y + 383024041
c
8
y
138
− 3y
137
+ ··· − 576y + 1
c
9
y
138
+ 13y
137
+ ··· + 3788760y + 130321
c
12
y
138
− 11y
137
+ ··· − 433668y + 5929
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.323280 + 0.949945I
a = 0.483460 + 0.228596I
b = 0.108033 − 1.022500I
−0.19526 − 4.44594I 0
u = 0.323280 − 0.949945I
a = 0.483460 − 0.228596I
b = 0.108033 + 1.022500I
−0.19526 + 4.44594I 0
u = 0.760685 + 0.685269I
a = −1.33908 − 1.81762I
b = −2.12515 − 0.84369I
6.65208 + 0.07508I 0
u = 0.760685 − 0.685269I
a = −1.33908 + 1.81762I
b = −2.12515 + 0.84369I
6.65208 − 0.07508I 0
u = 0.801138 + 0.553328I
a = 0.463585 + 0.478130I
b = −0.213753 − 0.624818I
−1.68579 − 7.34118I 0
u = 0.801138 − 0.553328I
a = 0.463585 − 0.478130I
b = −0.213753 + 0.624818I
−1.68579 + 7.34118I 0
u = 0.875262 + 0.421574I
a = −0.58037 − 1.80626I
b = −1.49669 − 0.75441I
0.30791 − 5.36080I 0
u = 0.875262 − 0.421574I
a = −0.58037 + 1.80626I
b = −1.49669 + 0.75441I
0.30791 + 5.36080I 0
u = −0.831916 + 0.626363I
a = −1.06965 + 1.74488I
b = −1.90743 + 0.75097I
7.31279 + 5.38938I 0
u = −0.831916 − 0.626363I
a = −1.06965 − 1.74488I
b = −1.90743 − 0.75097I
7.31279 − 5.38938I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.593104 + 0.751298I
a = 1.06027 − 2.02579I
b = 1.52125 − 0.44292I
4.36335 + 0.38616I 0
u = −0.593104 − 0.751298I
a = 1.06027 + 2.02579I
b = 1.52125 + 0.44292I
4.36335 − 0.38616I 0
u = 0.330124 + 0.999756I
a = 0.542401 + 0.642123I
b = 0.35058 + 1.43107I
−0.419083 + 1.060100I 0
u = 0.330124 − 0.999756I
a = 0.542401 − 0.642123I
b = 0.35058 − 1.43107I
−0.419083 − 1.060100I 0
u = −0.480691 + 0.939248I
a = −2.87238 + 2.39939I
b = −3.46961 + 1.69138I
−4.42962 − 6.92429I 0
u = −0.480691 − 0.939248I
a = −2.87238 − 2.39939I
b = −3.46961 − 1.69138I
−4.42962 + 6.92429I 0
u = −0.439143 + 0.816060I
a = −2.69054 + 3.08949I
b = −3.16623 + 2.24819I
−3.95035 + 3.15119I 0
u = −0.439143 − 0.816060I
a = −2.69054 − 3.08949I
b = −3.16623 − 2.24819I
−3.95035 − 3.15119I 0
u = −0.951536 + 0.502856I
a = −0.70754 + 1.62353I
b = −1.61602 + 0.61146I
5.33287 + 8.32927I 0
u = −0.951536 − 0.502856I
a = −0.70754 − 1.62353I
b = −1.61602 − 0.61146I
5.33287 − 8.32927I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.399085 + 1.001540I
a = 0.837137 + 1.011990I
b = 1.013180 + 0.120356I
−4.66972 + 1.37466I 0
u = −0.399085 − 1.001540I
a = 0.837137 − 1.011990I
b = 1.013180 − 0.120356I
−4.66972 − 1.37466I 0
u = −0.090055 + 1.088100I
a = −0.338874 + 0.955777I
b = −1.070320 + 0.722200I
−4.30114 + 1.33462I 0
u = −0.090055 − 1.088100I
a = −0.338874 − 0.955777I
b = −1.070320 − 0.722200I
−4.30114 − 1.33462I 0
u = 1.030790 + 0.361032I
a = 0.523241 + 1.008720I
b = 1.50088 + 0.65091I
5.25592 + 1.03879I 0
u = 1.030790 − 0.361032I
a = 0.523241 − 1.008720I
b = 1.50088 − 0.65091I
5.25592 − 1.03879I 0
u = −0.719777 + 0.821692I
a = 0.94526 − 1.71005I
b = 1.76139 − 0.43491I
5.28806 − 1.39704I 0
u = −0.719777 − 0.821692I
a = 0.94526 + 1.71005I
b = 1.76139 + 0.43491I
5.28806 + 1.39704I 0
u = −0.619725 + 0.658570I
a = 0.442655 − 0.650121I
b = −0.329622 − 0.326393I
−1.96482 + 2.30501I 0
u = −0.619725 − 0.658570I
a = 0.442655 + 0.650121I
b = −0.329622 + 0.326393I
−1.96482 − 2.30501I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.719423 + 0.545668I
a = 0.490330 − 0.445730I
b = −0.125810 + 0.613284I
0.70027 + 2.74370I 0
u = −0.719423 − 0.545668I
a = 0.490330 + 0.445730I
b = −0.125810 − 0.613284I
0.70027 − 2.74370I 0
u = −0.584908 + 0.928785I
a = 0.854248 + 0.679562I
b = 1.013770 − 0.006712I
−2.71118 − 7.05562I 0
u = −0.584908 − 0.928785I
a = 0.854248 − 0.679562I
b = 1.013770 + 0.006712I
−2.71118 + 7.05562I 0
u = −0.597159 + 0.921827I
a = 1.14235 − 1.50319I
b = 2.40530 − 0.83158I
3.82844 − 5.11364I 0
u = −0.597159 − 0.921827I
a = 1.14235 + 1.50319I
b = 2.40530 + 0.83158I
3.82844 + 5.11364I 0
u = −1.078680 + 0.229525I
a = 0.482278 − 0.895697I
b = 1.41770 − 0.58682I
3.27001 + 3.57478I 0
u = −1.078680 − 0.229525I
a = 0.482278 + 0.895697I
b = 1.41770 + 0.58682I
3.27001 − 3.57478I 0
u = 0.996646 + 0.479594I
a = −0.64453 − 1.55949I
b = −1.56709 − 0.55145I
2.91389 − 13.58860I 0
u = 0.996646 − 0.479594I
a = −0.64453 + 1.55949I
b = −1.56709 + 0.55145I
2.91389 + 13.58860I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.570025 + 0.950620I
a = −0.389622 − 0.531561I
b = 0.572161 − 0.766847I
0.86560 − 6.38011I 0
u = −0.570025 − 0.950620I
a = −0.389622 + 0.531561I
b = 0.572161 + 0.766847I
0.86560 + 6.38011I 0
u = 0.548997 + 0.698275I
a = 1.08824 + 2.19982I
b = 1.42208 + 0.39958I
2.21535 − 5.27635I 0
u = 0.548997 − 0.698275I
a = 1.08824 − 2.19982I
b = 1.42208 − 0.39958I
2.21535 + 5.27635I 0
u = 0.564026 + 0.968718I
a = 1.23961 + 1.45847I
b = 2.53662 + 0.81384I
1.34717 + 9.77817I 0
u = 0.564026 − 0.968718I
a = 1.23961 − 1.45847I
b = 2.53662 − 0.81384I
1.34717 − 9.77817I 0
u = −0.266933 + 1.089480I
a = 0.411875 − 0.354237I
b = 0.322519 − 1.267820I
−3.17108 + 3.91786I 0
u = −0.266933 − 1.089480I
a = 0.411875 + 0.354237I
b = 0.322519 + 1.267820I
−3.17108 − 3.91786I 0
u = −0.164916 + 0.860488I
a = 0.599830 − 0.193590I
b = 0.214859 + 0.999503I
1.38836 + 0.83662I 0
u = −0.164916 − 0.860488I
a = 0.599830 + 0.193590I
b = 0.214859 − 0.999503I
1.38836 − 0.83662I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.520582 + 0.702605I
a = 0.478088 − 0.364264I
b = 0.037388 + 0.812572I
1.66387 + 1.91116I 0
u = −0.520582 − 0.702605I
a = 0.478088 + 0.364264I
b = 0.037388 − 0.812572I
1.66387 − 1.91116I 0
u = 0.042173 + 1.126530I
a = −0.531546 − 1.174140I
b = −1.24634 − 0.96390I
−7.35847 − 5.89473I 0
u = 0.042173 − 1.126530I
a = −0.531546 + 1.174140I
b = −1.24634 + 0.96390I
−7.35847 + 5.89473I 0
u = 0.763284 + 0.408398I
a = 0.550601 + 0.516451I
b = −0.194341 − 0.457642I
−3.05106 + 0.17655I 0
u = 0.763284 − 0.408398I
a = 0.550601 − 0.516451I
b = −0.194341 + 0.457642I
−3.05106 − 0.17655I 0
u = −0.407542 + 1.071160I
a = −0.659775 − 0.129486I
b = −1.298270 − 0.503505I
−5.09715 − 2.91594I 0
u = −0.407542 − 1.071160I
a = −0.659775 + 0.129486I
b = −1.298270 + 0.503505I
−5.09715 + 2.91594I 0
u = 0.781994 + 0.841327I
a = 0.86760 + 1.57118I
b = 1.89224 + 0.39385I
3.94008 + 5.80075I 0
u = 0.781994 − 0.841327I
a = 0.86760 − 1.57118I
b = 1.89224 − 0.39385I
3.94008 − 5.80075I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.511774 + 1.029730I
a = −1.36061 + 0.55979I
b = −1.96792 + 1.14221I
0.75603 + 5.26566I 0
u = 0.511774 − 1.029730I
a = −1.36061 − 0.55979I
b = −1.96792 − 1.14221I
0.75603 − 5.26566I 0
u = 0.142818 + 1.148110I
a = −0.570941 − 0.752056I
b = −1.32602 − 0.52170I
−8.04836 + 2.50326I 0
u = 0.142818 − 1.148110I
a = −0.570941 + 0.752056I
b = −1.32602 + 0.52170I
−8.04836 − 2.50326I 0
u = −0.723297 + 0.906738I
a = 0.98176 − 1.42393I
b = 2.19296 − 0.62674I
5.04090 − 4.11717I 0
u = −0.723297 − 0.906738I
a = 0.98176 + 1.42393I
b = 2.19296 + 0.62674I
5.04090 + 4.11717I 0
u = −0.422900 + 1.101240I
a = 0.103900 − 0.497296I
b = 0.213509 − 1.160610I
−4.99467 − 4.32481I 0
u = −0.422900 − 1.101240I
a = 0.103900 + 0.497296I
b = 0.213509 + 1.160610I
−4.99467 + 4.32481I 0
u = 0.663826 + 0.980340I
a = −1.71885 − 2.03719I
b = −2.54130 − 1.27181I
5.74476 + 5.32645I 0
u = 0.663826 − 0.980340I
a = −1.71885 + 2.03719I
b = −2.54130 + 1.27181I
5.74476 − 5.32645I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.777023 + 0.911427I
a = 0.92311 + 1.40843I
b = 2.12712 + 0.48932I
3.73479 + 0.06546I 0
u = 0.777023 − 0.911427I
a = 0.92311 − 1.40843I
b = 2.12712 − 0.48932I
3.73479 − 0.06546I 0
u = −0.538027 + 1.072180I
a = −1.363050 − 0.168615I
b = −2.04684 − 0.74021I
−1.44300 − 11.00510I 0
u = −0.538027 − 1.072180I
a = −1.363050 + 0.168615I
b = −2.04684 + 0.74021I
−1.44300 + 11.00510I 0
u = −0.087234 + 0.792376I
a = 0.748133 + 0.385415I
b = −0.155133 + 0.214003I
−1.50983 + 1.66829I 0
u = −0.087234 − 0.792376I
a = 0.748133 − 0.385415I
b = −0.155133 − 0.214003I
−1.50983 − 1.66829I 0
u = 0.553269 + 1.075870I
a = 0.042987 + 0.687902I
b = 0.017960 + 0.385961I
0.44272 + 3.44736I 0
u = 0.553269 − 1.075870I
a = 0.042987 − 0.687902I
b = 0.017960 − 0.385961I
0.44272 − 3.44736I 0
u = 0.631032 + 0.468979I
a = 0.573629 − 0.179992I
b = 0.688767 − 0.226916I
2.24325 + 1.22888I 0
u = 0.631032 − 0.468979I
a = 0.573629 + 0.179992I
b = 0.688767 + 0.226916I
2.24325 − 1.22888I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.636133 + 1.047580I
a = −0.282943 − 0.363157I
b = 0.565230 − 0.933050I
−0.77613 − 7.96761I 0
u = −0.636133 − 1.047580I
a = −0.282943 + 0.363157I
b = 0.565230 + 0.933050I
−0.77613 + 7.96761I 0
u = −0.688707 + 1.031180I
a = −1.67633 + 1.76406I
b = −2.54328 + 1.03588I
6.07304 − 11.06380I 0
u = −0.688707 − 1.031180I
a = −1.67633 − 1.76406I
b = −2.54328 − 1.03588I
6.07304 + 11.06380I 0
u = 1.075570 + 0.620271I
a = 0.745044 + 1.085970I
b = 1.68617 + 0.62259I
5.62213 + 2.48282I 0
u = 1.075570 − 0.620271I
a = 0.745044 − 1.085970I
b = 1.68617 − 0.62259I
5.62213 − 2.48282I 0
u = 0.597712 + 1.096410I
a = −0.192094 + 0.367419I
b = 0.493155 + 0.982708I
−5.07060 + 4.96676I 0
u = 0.597712 − 1.096410I
a = −0.192094 − 0.367419I
b = 0.493155 − 0.982708I
−5.07060 − 4.96676I 0
u = 0.664444 + 1.069000I
a = −0.276412 + 0.314716I
b = 0.588337 + 0.971677I
−3.23471 + 12.86910I 0
u = 0.664444 − 1.069000I
a = −0.276412 − 0.314716I
b = 0.588337 − 0.971677I
−3.23471 − 12.86910I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.302296 + 1.246920I
a = 0.094735 + 0.895059I
b = 0.425561 + 0.194124I
−0.16648 + 5.11992I 0
u = 0.302296 − 1.246920I
a = 0.094735 − 0.895059I
b = 0.425561 − 0.194124I
−0.16648 − 5.11992I 0
u = 0.074324 + 1.293770I
a = 0.338939 − 0.984478I
b = 0.696779 − 0.093011I
−5.68762 − 2.51487I 0
u = 0.074324 − 1.293770I
a = 0.338939 + 0.984478I
b = 0.696779 + 0.093011I
−5.68762 + 2.51487I 0
u = 0.645555 + 1.129550I
a = −1.88462 − 1.37420I
b = −2.76464 − 0.75003I
−1.80938 + 10.97010I 0
u = 0.645555 − 1.129550I
a = −1.88462 + 1.37420I
b = −2.76464 + 0.75003I
−1.80938 − 10.97010I 0
u = 0.244494 + 0.643770I
a = 0.76207 − 2.36619I
b = 0.706778 − 0.673471I
2.39370 − 1.40141I 0. + 5.49402I
u = 0.244494 − 0.643770I
a = 0.76207 + 2.36619I
b = 0.706778 + 0.673471I
2.39370 + 1.40141I 0. − 5.49402I
u = −0.580109 + 1.178520I
a = 0.077039 − 0.742938I
b = 0.090919 − 0.226102I
−1.17695 − 7.64881I 0
u = −0.580109 − 1.178520I
a = 0.077039 + 0.742938I
b = 0.090919 + 0.226102I
−1.17695 + 7.64881I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.647351 + 0.209309I
a = 0.120385 + 0.295507I
b = 0.820360 + 0.611365I
1.62706 + 2.70564I 5.17311 − 4.72189I
u = −0.647351 − 0.209309I
a = 0.120385 − 0.295507I
b = 0.820360 − 0.611365I
1.62706 − 2.70564I 5.17311 + 4.72189I
u = 0.054137 + 1.320230I
a = 0.251919 + 0.956170I
b = 0.608280 + 0.099273I
−1.69042 + 5.78135I 0
u = 0.054137 − 1.320230I
a = 0.251919 − 0.956170I
b = 0.608280 − 0.099273I
−1.69042 − 5.78135I 0
u = −0.695481 + 1.134280I
a = −1.70206 + 1.36644I
b = −2.62301 + 0.71926I
3.3860 − 14.3434I 0
u = −0.695481 − 1.134280I
a = −1.70206 − 1.36644I
b = −2.62301 − 0.71926I
3.3860 + 14.3434I 0
u = −0.619380 + 1.183680I
a = 1.58907 − 1.42556I
b = 1.99060 − 0.80542I
−1.19854 − 2.10164I 0
u = −0.619380 − 1.183680I
a = 1.58907 + 1.42556I
b = 1.99060 + 0.80542I
−1.19854 + 2.10164I 0
u = 0.701357 + 1.160260I
a = −1.68050 − 1.28153I
b = −2.61901 − 0.65046I
0.8019 + 19.7424I 0
u = 0.701357 − 1.160260I
a = −1.68050 + 1.28153I
b = −2.61901 + 0.65046I
0.8019 − 19.7424I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.574856 + 0.287518I
a = 1.12078 + 1.79794I
b = −0.173756 + 0.449467I
0.62289 + 6.55260I 0.79569 − 7.07313I
u = −0.574856 − 0.287518I
a = 1.12078 − 1.79794I
b = −0.173756 − 0.449467I
0.62289 − 6.55260I 0.79569 + 7.07313I
u = −0.442515 + 1.283870I
a = 0.092832 − 0.814295I
b = 0.285363 − 0.158752I
−1.52461 − 1.39344I 0
u = −0.442515 − 1.283870I
a = 0.092832 + 0.814295I
b = 0.285363 + 0.158752I
−1.52461 + 1.39344I 0
u = −0.563604 + 0.302408I
a = 0.91457 − 1.10856I
b = −0.386020 − 0.626067I
−2.58798 − 4.97396I −2.18896 + 7.74445I
u = −0.563604 − 0.302408I
a = 0.91457 + 1.10856I
b = −0.386020 + 0.626067I
−2.58798 + 4.97396I −2.18896 − 7.74445I
u = −0.546115 + 0.328530I
a = −0.10339 − 1.55128I
b = 1.30860 − 1.18613I
1.48239 − 2.88351I 2.73068 + 5.61362I
u = −0.546115 − 0.328530I
a = −0.10339 + 1.55128I
b = 1.30860 + 1.18613I
1.48239 + 2.88351I 2.73068 − 5.61362I
u = 0.883684 + 1.041040I
a = 1.18787 + 1.24925I
b = 1.90647 + 0.61101I
4.36936 + 4.46912I 0
u = 0.883684 − 1.041040I
a = 1.18787 − 1.24925I
b = 1.90647 − 0.61101I
4.36936 − 4.46912I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.151560 + 0.735245I
a = 0.849959 − 1.041800I
b = 1.74133 − 0.56464I
3.91734 − 6.85724I 0
u = −1.151560 − 0.735245I
a = 0.849959 + 1.041800I
b = 1.74133 + 0.56464I
3.91734 + 6.85724I 0
u = −0.029802 + 1.394970I
a = 0.276490 − 0.915696I
b = 0.613593 − 0.046230I
−4.27820 − 10.49320I 0
u = −0.029802 − 1.394970I
a = 0.276490 + 0.915696I
b = 0.613593 + 0.046230I
−4.27820 + 10.49320I 0
u = 0.735140 + 1.193730I
a = 1.46803 + 1.28863I
b = 1.99005 + 0.69111I
2.76805 + 5.32381I 0
u = 0.735140 − 1.193730I
a = 1.46803 − 1.28863I
b = 1.99005 − 0.69111I
2.76805 − 5.32381I 0
u = −1.031340 + 0.956100I
a = 1.04746 − 1.12963I
b = 1.85943 − 0.57530I
3.25250 − 0.71774I 0
u = −1.031340 − 0.956100I
a = 1.04746 + 1.12963I
b = 1.85943 + 0.57530I
3.25250 + 0.71774I 0
u = −0.588927 + 0.058338I
a = 1.085960 − 0.704558I
b = −0.148590 + 0.015823I
−2.13555 + 0.53348I −3.53125 − 0.22076I
u = −0.588927 − 0.058338I
a = 1.085960 + 0.704558I
b = −0.148590 − 0.015823I
−2.13555 − 0.53348I −3.53125 + 0.22076I
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.044817 + 0.580301I
a = −0.41087 + 2.39638I
b = 0.676277 + 0.437953I
1.01732 + 6.59615I −2.16258 − 10.02140I
u = 0.044817 − 0.580301I
a = −0.41087 − 2.39638I
b = 0.676277 − 0.437953I
1.01732 − 6.59615I −2.16258 + 10.02140I
u = 0.333160 + 0.470791I
a = 1.127810 + 0.272185I
b = 0.055086 + 0.521780I
0.35597 + 1.41844I 2.31505 − 4.91320I
u = 0.333160 − 0.470791I
a = 1.127810 − 0.272185I
b = 0.055086 − 0.521780I
0.35597 − 1.41844I 2.31505 + 4.91320I
u = −0.72726 + 1.26387I
a = 1.54171 − 1.22111I
b = 2.04652 − 0.68346I
0.19175 − 10.04230I 0
u = −0.72726 − 1.26387I
a = 1.54171 + 1.22111I
b = 2.04652 + 0.68346I
0.19175 + 10.04230I 0
u = 0.374966 + 0.203972I
a = 2.14400 − 2.07476I
b = 0.137055 − 0.292627I
2.52190 − 1.32522I 1.69570 + 2.54164I
u = 0.374966 − 0.203972I
a = 2.14400 + 2.07476I
b = 0.137055 + 0.292627I
2.52190 + 1.32522I 1.69570 − 2.54164I
18
II.
I
u
2
= h7u
29
−7u
28
+· · ·+b −1, 6u
29
−7u
28
+· · ·+a −9, u
30
−u
29
+· · ·−u +1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
12
=
−6u
29
+ 7u
28
+ ··· − 6u + 9
−7u
29
+ 7u
28
+ ··· − 8u + 1
a
8
=
8u
29
− 8u
28
+ ··· + 37u − 9
u
29
+ 6u
27
+ ··· + 2u
2
+ 8u
a
4
=
−5u
28
+ 4u
27
+ ··· − 2u − 7
u
29
− 4u
28
+ ··· − u + 1
a
1
=
u
2
+ 1
−u
4
a
9
=
7u
29
− 7u
28
+ ··· + 28u − 8
u
29
+ u
28
+ ··· + 7u + 1
a
5
=
13u
29
− 14u
28
+ ··· + 15u − 16
10u
29
+ 69u
27
+ ··· + 23u + 4
a
11
=
−6u
29
+ 7u
28
+ ··· − 6u + 8
−7u
29
+ 7u
28
+ ··· + 8u
2
− 8u
a
10
=
−u
29
+ 15u
28
+ ··· + 7u + 15
8u
29
+ 6u
28
+ ··· + 25u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12u
29
+ 4u
28
− 94u
27
+ 48u
26
− 424u
25
+ 244u
24
− 1334u
23
+
804u
22
− 3245u
21
+ 1948u
20
− 6322u
19
+ 3720u
18
− 10102u
17
+ 5737u
16
− 13335u
15
+
7243u
14
− 14591u
13
+ 7495u
12
− 13069u
11
+ 6355u
10
− 9358u
9
+ 4294u
8
− 5129u
7
+
2181u
6
− 2033u
5
+ 759u
4
− 519u
3
+ 166u
2
− 67u + 14
19
(iv) u-Polynomials at the component
20
Crossings u-Polynomials at each crossing
c
1
u
30
− 15u
29
+ ··· − 19u + 1
c
2
u
30
− u
29
+ ··· − u + 1
c
3
u
30
+ 7u
28
+ ··· + 8u
2
+ 1
c
4
u
30
− 8u
28
+ ··· − 6u
2
+ 1
c
5
u
30
+ 8u
28
+ ··· − 10u
2
+ 1
c
6
u
30
+ u
29
+ ··· + u + 1
c
7
u
30
− 2u
29
+ ··· − 2u + 1
c
8
u
30
+ 4u
28
+ ··· − 4u
4
+ 1
c
9
u
30
− 16u
29
+ ··· − 12u + 1
c
10
u
30
− 8u
28
+ ··· − 6u
2
+ 1
c
11
u
30
+ 2u
29
+ ··· + 2u + 1
c
12
u
30
− 2u
28
+ ··· + 4u + 1
21
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
+ 15y
29
+ ··· + 7y + 1
c
2
, c
6
y
30
+ 15y
29
+ ··· + 19y + 1
c
3
y
30
+ 14y
29
+ ··· + 16y + 1
c
4
, c
10
y
30
− 16y
29
+ ··· − 12y + 1
c
5
y
30
+ 16y
29
+ ··· − 20y + 1
c
7
, c
11
y
30
− 26y
29
+ ··· − 26y + 1
c
8
y
30
+ 8y
29
+ ··· − 8y
2
+ 1
c
9
y
30
+ 32y
28
+ ··· + 4y + 1
c
12
y
30
− 4y
29
+ ··· − 4y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.345063 + 0.914149I
a = −1.90094 + 0.72069I
b = −1.68710 + 1.41281I
−0.97174 − 1.42424I −10.12133 + 1.84484I
u = −0.345063 − 0.914149I
a = −1.90094 − 0.72069I
b = −1.68710 − 1.41281I
−0.97174 + 1.42424I −10.12133 − 1.84484I
u = 0.306226 + 0.980203I
a = −2.08739 + 0.07130I
b = −1.86700 − 0.46851I
−5.12999 + 5.93076I −6.39070 − 5.17366I
u = 0.306226 − 0.980203I
a = −2.08739 − 0.07130I
b = −1.86700 + 0.46851I
−5.12999 − 5.93076I −6.39070 + 5.17366I
u = 0.280242 + 0.887089I
a = −2.00150 − 1.07382I
b = −1.94725 − 1.73761I
−4.75004 − 3.51185I −9.23609 + 4.40207I
u = 0.280242 − 0.887089I
a = −2.00150 + 1.07382I
b = −1.94725 + 1.73761I
−4.75004 + 3.51185I −9.23609 − 4.40207I
u = −0.804256 + 0.760321I
a = 0.69802 − 1.56126I
b = 1.74383 − 0.74616I
4.62612 − 2.32795I 3.70373 + 4.50516I
u = −0.804256 − 0.760321I
a = 0.69802 + 1.56126I
b = 1.74383 + 0.74616I
4.62612 + 2.32795I 3.70373 − 4.50516I
u = −0.356741 + 1.111360I
a = −0.158986 − 1.258650I
b = 0.244135 − 0.831443I
−1.08944 − 4.59780I −4.21797 + 5.14485I
u = −0.356741 − 1.111360I
a = −0.158986 + 1.258650I
b = 0.244135 + 0.831443I
−1.08944 + 4.59780I −4.21797 − 5.14485I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.900131 + 0.752158I
a = 0.59983 + 1.28493I
b = 1.72897 + 0.56974I
3.21175 + 6.43302I −1.14120 − 8.06438I
u = 0.900131 − 0.752158I
a = 0.59983 − 1.28493I
b = 1.72897 − 0.56974I
3.21175 − 6.43302I −1.14120 + 8.06438I
u = −0.516050 + 1.071810I
a = 0.953436 − 0.248629I
b = 1.51274 + 0.30380I
1.21080 − 4.66119I 4.12489 + 3.62621I
u = −0.516050 − 1.071810I
a = 0.953436 + 0.248629I
b = 1.51274 − 0.30380I
1.21080 + 4.66119I 4.12489 − 3.62621I
u = −0.830917 + 0.913416I
a = 1.05487 − 1.20814I
b = 1.99297 − 0.55523I
4.16562 − 3.82370I 2.08014 − 0.21144I
u = −0.830917 − 0.913416I
a = 1.05487 + 1.20814I
b = 1.99297 + 0.55523I
4.16562 + 3.82370I 2.08014 + 0.21144I
u = 0.420339 + 1.169090I
a = 0.626849 + 1.054400I
b = 1.127280 + 0.641830I
−2.64347 + 2.39344I −5.42924 − 3.84771I
u = 0.420339 − 1.169090I
a = 0.626849 − 1.054400I
b = 1.127280 − 0.641830I
−2.64347 − 2.39344I −5.42924 + 3.84771I
u = −0.379573 + 0.645839I
a = −0.13105 − 1.59939I
b = 0.0019793 − 0.0425655I
2.85714 + 0.84296I 6.58098 + 2.34755I
u = −0.379573 − 0.645839I
a = −0.13105 + 1.59939I
b = 0.0019793 + 0.0425655I
2.85714 − 0.84296I 6.58098 − 2.34755I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215247 + 0.703613I
a = 0.983053 + 0.263577I
b = 0.452124 + 1.296960I
0.60960 + 2.10521I −3.42504 − 2.77058I
u = −0.215247 − 0.703613I
a = 0.983053 − 0.263577I
b = 0.452124 − 1.296960I
0.60960 − 2.10521I −3.42504 + 2.77058I
u = 0.916579 + 0.881827I
a = 0.857564 + 1.123430I
b = 1.88144 + 0.50574I
2.84562 + 0.25418I −3.03858 + 3.40185I
u = 0.916579 − 0.881827I
a = 0.857564 − 1.123430I
b = 1.88144 − 0.50574I
2.84562 − 0.25418I −3.03858 − 3.40185I
u = 0.550027 + 1.148230I
a = 1.054910 + 0.647364I
b = 1.66827 + 0.16664I
−0.98713 + 9.64890I −1.52998 − 8.02093I
u = 0.550027 − 1.148230I
a = 1.054910 − 0.647364I
b = 1.66827 − 0.16664I
−0.98713 − 9.64890I −1.52998 + 8.02093I
u = 0.351699 + 0.565930I
a = 0.45105 + 1.98461I
b = 0.453714 − 0.034964I
1.30086 − 5.71256I 0.37883 + 4.07751I
u = 0.351699 − 0.565930I
a = 0.45105 − 1.98461I
b = 0.453714 + 0.034964I
1.30086 + 5.71256I 0.37883 − 4.07751I
u = 0.222604 + 0.612148I
a = 1.50028 + 0.90502I
b = 0.693885 − 0.608955I
−0.320875 + 0.454733I −1.33845 + 1.30280I
u = 0.222604 − 0.612148I
a = 1.50028 − 0.90502I
b = 0.693885 + 0.608955I
−0.320875 − 0.454733I −1.33845 − 1.30280I
26
III. I
u
3
= h−5169a
6
u + 1.50 × 10
4
a
5
u + · · · − 2.86 × 10
5
a + 1.06 ×
10
5
, −2a
6
u − 11a
5
u + · · · − 25a + 6, u
2
− u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u + 1
a
7
=
u
u
a
12
=
a
0.159257a
6
u − 0.461719a
5
u + ··· + 8.81591a − 3.27985
a
8
=
−0.00277290a
6
u − 0.0362634a
5
u + ··· − 0.970484a − 0.775549
0.363065a
6
u + 0.370305a
5
u + ··· + 5.64649a + 2.38968
a
4
=
−0.190283a
6
u + 0.430046a
5
u + ··· − 7.53751a + 3.10602
−0.424315a
6
u + 1.10275a
5
u + ··· − 14.6464a + 7.38300
a
1
=
u
u
a
9
=
0.397264a
6
u − 0.293558a
5
u + ··· + 12.7269a − 2.26743
0.763102a
6
u + 0.113011a
5
u + ··· + 19.3439a + 0.897803
a
5
=
0.00388206a
6
u − 0.682565a
5
u + ··· + 1.22534a − 5.31423
0.237915a
6
u − 1.35527a
5
u + ··· + 8.33420a − 9.59121
a
11
=
−0.0207351a
6
u − 0.423021a
5
u + ··· − 0.282990a − 3.19198
0.138522a
6
u − 0.884740a
5
u + ··· + 7.53292a − 6.47182
a
10
=
u
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u + 2
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u + 1)
7
c
2
, c
6
(u
2
− u + 1)
7
c
3
, c
5
u
14
+ 6u
12
+ ··· + 3u + 3
c
4
, c
10
, c
12
u
14
− 2u
12
+ u
10
+ 2u
8
+ u
7
− 2u
6
− u
5
+ u
2
+ u + 1
c
7
, c
9
, c
11
u
14
+ 4u
13
+ ··· − u + 1
c
8
u
14
+ 4u
13
+ ··· − u + 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
(y
2
+ y + 1)
7
c
3
, c
5
y
14
+ 12y
13
+ ··· + 81y + 9
c
4
, c
10
, c
12
y
14
− 4y
13
+ ··· + y + 1
c
7
, c
9
, c
11
y
14
− 4y
13
+ ··· + y + 1
c
8
y
14
+ 12y
13
+ ··· + y + 1
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.522412 + 0.711568I
b = 0.622426 + 0.640601I
2.02988I 0. − 3.46410I
u = 0.500000 + 0.866025I
a = 1.053670 − 0.668061I
b = 1.080820 + 0.054574I
2.02988I 0. − 3.46410I
u = 0.500000 + 0.866025I
a = 0.450802 + 0.313764I
b = 0.012202 − 0.936669I
2.02988I 0. − 3.46410I
u = 0.500000 + 0.866025I
a = 0.184382 + 0.444857I
b = −0.347082 + 0.354812I
2.02988I 0. − 3.46410I
u = 0.500000 + 0.866025I
a = 1.22636 + 1.72455I
b = 2.45507 + 1.10576I
2.02988I 0. − 3.46410I
u = 0.500000 + 0.866025I
a = 1.33467 + 1.92713I
b = 1.47858 + 0.69636I
2.02988I 0. − 3.46410I
u = 0.500000 + 0.866025I
a = −2.72748 − 2.72175I
b = −3.30202 − 1.91544I
2.02988I 0. − 3.46410I
u = 0.500000 − 0.866025I
a = −0.522412 − 0.711568I
b = 0.622426 − 0.640601I
− 2.02988I 0. + 3.46410I
u = 0.500000 − 0.866025I
a = 1.053670 + 0.668061I
b = 1.080820 − 0.054574I
− 2.02988I 0. + 3.46410I
u = 0.500000 − 0.866025I
a = 0.450802 − 0.313764I
b = 0.012202 + 0.936669I
− 2.02988I 0. + 3.46410I
30
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 − 0.866025I
a = 0.184382 − 0.444857I
b = −0.347082 − 0.354812I
− 2.02988I 0. + 3.46410I
u = 0.500000 − 0.866025I
a = 1.22636 − 1.72455I
b = 2.45507 − 1.10576I
− 2.02988I 0. + 3.46410I
u = 0.500000 − 0.866025I
a = 1.33467 − 1.92713I
b = 1.47858 − 0.69636I
− 2.02988I 0. + 3.46410I
u = 0.500000 − 0.866025I
a = −2.72748 + 2.72175I
b = −3.30202 + 1.91544I
− 2.02988I 0. + 3.46410I
31
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u + 1)
7
)(u
30
− 15u
29
+ ··· − 19u + 1)
· (u
138
+ 57u
137
+ ··· + 802224u + 46656)
c
2
((u
2
− u + 1)
7
)(u
30
− u
29
+ ··· − u + 1)(u
138
+ 7u
137
+ ··· + 1836u + 216)
c
3
(u
14
+ 6u
12
+ ··· + 3u + 3)(u
30
+ 7u
28
+ ··· + 8u
2
+ 1)
· (u
138
− u
137
+ ··· − 54398u + 10041)
c
4
(u
14
− 2u
12
+ u
10
+ 2u
8
+ u
7
− 2u
6
− u
5
+ u
2
+ u + 1)
· (u
30
− 8u
28
+ ··· − 6u
2
+ 1)(u
138
− u
137
+ ··· − 30u + 19)
c
5
(u
14
+ 6u
12
+ ··· + 3u + 3)(u
30
+ 8u
28
+ ··· − 10u
2
+ 1)
· (u
138
− 3u
137
+ ··· − 5664770u + 21046851)
c
6
((u
2
− u + 1)
7
)(u
30
+ u
29
+ ··· + u + 1)(u
138
+ 7u
137
+ ··· + 1836u + 216)
c
7
(u
14
+ 4u
13
+ ··· − u + 1)(u
30
− 2u
29
+ ··· − 2u + 1)
· (u
138
− 3u
137
+ ··· + 378940u + 19571)
c
8
(u
14
+ 4u
13
+ ··· − u + 1)(u
30
+ 4u
28
+ ··· − 4u
4
+ 1)
· (u
138
+ u
137
+ ··· − 50u + 1)
c
9
(u
14
+ 4u
13
+ ··· − u + 1)(u
30
− 16u
29
+ ··· − 12u + 1)
· (u
138
+ 71u
137
+ ··· + 3712u + 361)
c
10
(u
14
− 2u
12
+ u
10
+ 2u
8
+ u
7
− 2u
6
− u
5
+ u
2
+ u + 1)
· (u
30
− 8u
28
+ ··· − 6u
2
+ 1)(u
138
− u
137
+ ··· − 30u + 19)
c
11
(u
14
+ 4u
13
+ ··· − u + 1)(u
30
+ 2u
29
+ ··· + 2u + 1)
· (u
138
− 3u
137
+ ··· + 378940u + 19571)
c
12
(u
14
− 2u
12
+ u
10
+ 2u
8
+ u
7
− 2u
6
− u
5
+ u
2
+ u + 1)
· (u
30
− 2u
28
+ ··· + 4u + 1)(u
138
+ 13u
137
+ ··· − 310u + 77)
32
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
7
)(y
30
+ 15y
29
+ ··· + 7y + 1)
· (y
138
+ 57y
137
+ ··· + 94721944320y + 2176782336)
c
2
, c
6
((y
2
+ y + 1)
7
)(y
30
+ 15y
29
+ ··· + 19y + 1)
· (y
138
+ 57y
137
+ ··· + 802224y + 46656)
c
3
(y
14
+ 12y
13
+ ··· + 81y + 9)(y
30
+ 14y
29
+ ··· + 16y + 1)
· (y
138
+ 31y
137
+ ··· + 4830062936y + 100821681)
c
4
, c
10
(y
14
− 4y
13
+ ··· + y + 1)(y
30
− 16y
29
+ ··· − 12y + 1)
· (y
138
− 71y
137
+ ··· − 3712y + 361)
c
5
(y
14
+ 12y
13
+ ··· + 81y + 9)(y
30
+ 16y
29
+ ··· − 20y + 1)
· (y
138
+ 45y
137
+ ··· + 9711800845573616y + 442969937016201)
c
7
, c
11
(y
14
− 4y
13
+ ··· + y + 1)(y
30
− 26y
29
+ ··· − 26y + 1)
· (y
138
− 101y
137
+ ··· − 89234996574y + 383024041)
c
8
(y
14
+ 12y
13
+ ··· + y + 1)(y
30
+ 8y
29
+ ··· − 8y
2
+ 1)
· (y
138
− 3y
137
+ ··· − 576y + 1)
c
9
(y
14
− 4y
13
+ ··· + y + 1)(y
30
+ 32y
28
+ ··· + 4y + 1)
· (y
138
+ 13y
137
+ ··· + 3788760y + 130321)
c
12
(y
14
− 4y
13
+ ··· + y + 1)(y
30
− 4y
29
+ ··· − 4y + 1)
· (y
138
− 11y
137
+ ··· − 433668y + 5929)
33
