12a
0350
(K12a
0350
)
A knot diagram
1
Linearized knot diagam
3 6 9 7 11 2 12 4 1 5 10 8
Solving Sequence
3,9 4,6
2 7 5 1 10 8 12 11
c
3
c
2
c
6
c
4
c
1
c
9
c
8
c
12
c
11
c
5
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.64650 × 10
477
u
119
− 2.04219 × 10
477
u
118
+ ··· + 5.37967 × 10
477
b + 4.63499 × 10
477
,
− 3.01914 × 10
477
u
119
− 5.15986 × 10
477
u
118
+ ··· + 1.39872 × 10
478
a − 8.49918 × 10
477
,
u
120
+ u
119
+ ··· + 20u − 4i
I
u
2
= h−3au + b − 6a − 2u − 5, 18a
2
− 3au + 30a − 4u + 15, u
2
− 2i
I
v
1
= ha, b − v, v
2
+ v + 1i
* 3 irreducible components of dim
C
= 0, with total 126 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−1.65 × 10
477
u
119
− 2.04 × 10
477
u
118
+ · · · + 5.38 × 10
477
b + 4.63 ×
10
477
, −3.02 × 10
477
u
119
− 5.16 × 10
477
u
118
+ · · · + 1.40 × 10
478
a − 8.50 ×
10
477
, u
120
+ u
119
+ · · · + 20u − 4i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
6
=
0.215851u
119
+ 0.368900u
118
+ ··· − 7.05008u + 0.607642
0.306060u
119
+ 0.379613u
118
+ ··· + 5.50411u − 0.861574
a
2
=
−0.332303u
119
− 0.00324083u
118
+ ··· + 13.9294u + 1.86986
0.0130671u
119
− 0.181215u
118
+ ··· − 8.87043u + 1.39199
a
7
=
1.04132u
119
+ 1.06701u
118
+ ··· − 15.4491u + 4.99065
−0.237104u
119
− 0.338198u
118
+ ··· + 5.15503u − 0.569560
a
5
=
−0.224721u
119
+ 0.373611u
118
+ ··· + 35.9761u − 7.40116
0.00695986u
119
+ 0.265753u
118
+ ··· + 10.9571u − 2.73290
a
1
=
−0.319236u
119
− 0.184456u
118
+ ··· + 5.05899u + 3.26185
0.0130671u
119
− 0.181215u
118
+ ··· − 8.87043u + 1.39199
a
10
=
−1.29087u
119
− 0.889115u
118
+ ··· + 28.2364u − 6.80811
−0.0403642u
119
+ 0.0496315u
118
+ ··· + 0.215259u + 0.360299
a
8
=
u
u
3
+ u
a
12
=
−0.476243u
119
− 0.238640u
118
+ ··· + 10.5808u + 2.24891
−0.0571666u
119
− 0.190125u
118
+ ··· − 6.03312u + 0.790341
a
11
=
−0.281956u
119
+ 0.848688u
118
+ ··· + 44.4292u − 6.63066
0.0206301u
119
+ 0.0726329u
118
+ ··· − 0.388572u + 0.172894
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.797956u
119
+ 1.82037u
118
+ ··· + 33.6708u − 21.8023
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
120
+ 44u
119
+ ··· − 3756u + 289
c
2
, c
6
u
120
− 2u
119
+ ··· + 64u + 17
c
3
, c
8
u
120
+ u
119
+ ··· + 20u − 4
c
4
28561(28561u
120
+ 43940u
119
+ ··· − 1.49875 × 10
8
u + 1.98894 × 10
7
)
c
5
, c
10
u
120
+ u
119
+ ··· − 36u − 4
c
7
, c
12
u
120
+ 3u
119
+ ··· − 495u − 343
c
9
28561(28561u
120
+ 160381u
119
+ ··· − 9126759u − 5810977)
c
11
u
120
+ 55u
119
+ ··· + 208u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
120
+ 68y
119
+ ··· − 12388564y + 83521
c
2
, c
6
y
120
+ 44y
119
+ ··· − 3756y + 289
c
3
, c
8
y
120
+ 65y
119
+ ··· + 176y + 16
c
4
815730721
· (8.16 × 10
8
y
120
+ 3.97 × 10
10
y
119
+ ··· − 1.14 × 10
16
y + 3.96 × 10
14
)
c
5
, c
10
y
120
− 55y
119
+ ··· − 208y + 16
c
7
, c
12
y
120
− 69y
119
+ ··· − 633301y + 117649
c
9
815730721
· (8.16 × 10
8
y
120
+ 1.20 × 10
10
y
119
+ ··· − 3.67 × 10
14
y + 3.38 × 10
13
)
c
11
y
120
+ 25y
119
+ ··· − 26880y + 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.202989 + 0.990498I
a = 1.83289 − 0.71222I
b = −0.954993 + 0.764552I
−0.32290 − 2.49959I 0
u = 0.202989 − 0.990498I
a = 1.83289 + 0.71222I
b = −0.954993 − 0.764552I
−0.32290 + 2.49959I 0
u = 0.125340 + 0.971618I
a = 2.29726 − 1.15154I
b = −0.720096 + 0.848381I
−0.16867 − 2.70921I 0
u = 0.125340 − 0.971618I
a = 2.29726 + 1.15154I
b = −0.720096 − 0.848381I
−0.16867 + 2.70921I 0
u = −0.215875 + 0.921340I
a = −2.05386 − 0.66138I
b = 0.97482 + 1.02658I
−1.27200 + 6.24574I 0
u = −0.215875 − 0.921340I
a = −2.05386 + 0.66138I
b = 0.97482 − 1.02658I
−1.27200 − 6.24574I 0
u = 1.067700 + 0.000614I
a = 0.699094 + 0.164069I
b = −0.790349 + 0.550536I
−0.94837 + 7.62370I 0
u = 1.067700 − 0.000614I
a = 0.699094 − 0.164069I
b = −0.790349 − 0.550536I
−0.94837 − 7.62370I 0
u = 0.147019 + 1.070360I
a = 1.49597 + 0.11383I
b = 0.387476 + 0.924439I
0.041800 + 0.517074I 0
u = 0.147019 − 1.070360I
a = 1.49597 − 0.11383I
b = 0.387476 − 0.924439I
0.041800 − 0.517074I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.852150 + 0.335345I
a = 0.862162 − 0.729618I
b = 0.007238 − 1.142000I
−6.79846 − 6.21229I 0
u = −0.852150 − 0.335345I
a = 0.862162 + 0.729618I
b = 0.007238 + 1.142000I
−6.79846 + 6.21229I 0
u = 0.914607
a = 0.851655
b = −0.435552
−5.82465 0
u = 0.780664 + 0.465076I
a = −1.096220 − 0.807047I
b = −0.008377 − 0.989825I
−4.16799 + 1.47675I 0
u = 0.780664 − 0.465076I
a = −1.096220 + 0.807047I
b = −0.008377 + 0.989825I
−4.16799 − 1.47675I 0
u = −0.887719 + 0.193758I
a = −0.588745 + 0.560769I
b = 0.650690 + 0.951781I
2.29091 + 2.82384I 0
u = −0.887719 − 0.193758I
a = −0.588745 − 0.560769I
b = 0.650690 − 0.951781I
2.29091 − 2.82384I 0
u = 0.240892 + 1.065480I
a = −0.498725 + 0.703933I
b = −0.317623 − 0.022486I
1.14757 + 2.11836I 0
u = 0.240892 − 1.065480I
a = −0.498725 − 0.703933I
b = −0.317623 + 0.022486I
1.14757 − 2.11836I 0
u = 0.290138 + 0.858508I
a = −0.03373 − 2.51112I
b = 0.281653 − 0.886609I
−0.31268 − 4.67708I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.290138 − 0.858508I
a = −0.03373 + 2.51112I
b = 0.281653 + 0.886609I
−0.31268 + 4.67708I 0
u = 0.258264 + 1.075510I
a = 1.50891 − 0.07679I
b = −1.143560 + 0.311585I
1.67115 − 7.31624I 0
u = 0.258264 − 1.075510I
a = 1.50891 + 0.07679I
b = −1.143560 − 0.311585I
1.67115 + 7.31624I 0
u = 0.764474 + 0.461851I
a = −0.298629 + 0.362400I
b = 0.670058 + 0.722219I
2.98659 + 2.31380I 0
u = 0.764474 − 0.461851I
a = −0.298629 − 0.362400I
b = 0.670058 − 0.722219I
2.98659 − 2.31380I 0
u = −0.160215 + 0.875406I
a = −0.178043 + 0.956426I
b = 0.237759 + 0.257881I
1.78046 + 2.19670I 0
u = −0.160215 − 0.875406I
a = −0.178043 − 0.956426I
b = 0.237759 − 0.257881I
1.78046 − 2.19670I 0
u = −1.115540 + 0.028792I
a = −0.719250 + 0.216715I
b = 0.717128 + 0.648150I
0.99396 − 1.73965I 0
u = −1.115540 − 0.028792I
a = −0.719250 − 0.216715I
b = 0.717128 − 0.648150I
0.99396 + 1.73965I 0
u = −0.240281 + 1.106510I
a = −1.232710 + 0.037129I
b = 0.996617 + 0.162947I
2.78737 + 2.78465I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.240281 − 1.106510I
a = −1.232710 − 0.037129I
b = 0.996617 − 0.162947I
2.78737 − 2.78465I 0
u = −0.185554 + 1.130230I
a = −0.482242 + 0.322174I
b = 0.564824 + 0.004451I
2.28964 + 2.10386I 0
u = −0.185554 − 1.130230I
a = −0.482242 − 0.322174I
b = 0.564824 − 0.004451I
2.28964 − 2.10386I 0
u = 0.845851 + 0.117669I
a = 0.432782 + 0.605481I
b = −0.643954 + 1.038350I
0.98227 − 8.35275I 0
u = 0.845851 − 0.117669I
a = 0.432782 − 0.605481I
b = −0.643954 − 1.038350I
0.98227 + 8.35275I 0
u = −0.171786 + 0.834696I
a = −1.92251 − 0.56569I
b = 0.729359 + 1.199970I
−2.12298 + 0.96742I 0
u = −0.171786 − 0.834696I
a = −1.92251 + 0.56569I
b = 0.729359 − 1.199970I
−2.12298 − 0.96742I 0
u = −1.034480 + 0.561437I
a = 1.085660 − 0.500482I
b = −0.207120 − 0.980921I
−8.61583 + 2.18923I 0
u = −1.034480 − 0.561437I
a = 1.085660 + 0.500482I
b = −0.207120 + 0.980921I
−8.61583 − 2.18923I 0
u = 0.509258 + 1.080060I
a = −0.693221 − 0.384489I
b = 0.161413 − 1.188380I
−2.20069 − 6.31530I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.509258 − 1.080060I
a = −0.693221 + 0.384489I
b = 0.161413 + 1.188380I
−2.20069 + 6.31530I 0
u = −1.200420 + 0.103729I
a = 0.773407 + 0.381234I
b = −0.665350 + 1.057800I
−2.44940 − 13.11410I 0
u = −1.200420 − 0.103729I
a = 0.773407 − 0.381234I
b = −0.665350 − 1.057800I
−2.44940 + 13.11410I 0
u = −0.616678 + 1.060240I
a = 0.185913 − 0.231296I
b = 0.017347 − 1.145710I
−6.86455 + 3.65797I 0
u = −0.616678 − 1.060240I
a = 0.185913 + 0.231296I
b = 0.017347 + 1.145710I
−6.86455 − 3.65797I 0
u = 0.071139 + 0.767821I
a = −0.766900 + 0.278980I
b = 0.414325 + 1.037240I
−0.71039 + 1.36487I −6.45479 + 0.I
u = 0.071139 − 0.767821I
a = −0.766900 − 0.278980I
b = 0.414325 − 1.037240I
−0.71039 − 1.36487I −6.45479 + 0.I
u = 1.225120 + 0.196206I
a = −0.734550 + 0.348848I
b = 0.663880 + 0.999341I
−0.04980 + 7.04998I 0
u = 1.225120 − 0.196206I
a = −0.734550 − 0.348848I
b = 0.663880 − 0.999341I
−0.04980 − 7.04998I 0
u = −0.527948 + 1.123740I
a = 0.720724 − 0.101032I
b = −0.139915 − 1.287900I
−4.36117 + 11.26390I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.527948 − 1.123740I
a = 0.720724 + 0.101032I
b = −0.139915 + 1.287900I
−4.36117 − 11.26390I 0
u = 0.040199 + 1.251880I
a = −0.974076 − 0.823210I
b = −0.177940 + 0.691389I
−0.72258 − 3.71661I 0
u = 0.040199 − 1.251880I
a = −0.974076 + 0.823210I
b = −0.177940 − 0.691389I
−0.72258 + 3.71661I 0
u = 0.151062 + 0.722891I
a = 1.43814 − 0.59435I
b = −0.484144 + 1.294440I
−2.51414 − 4.12934I −16.4536 + 7.0812I
u = 0.151062 − 0.722891I
a = 1.43814 + 0.59435I
b = −0.484144 − 1.294440I
−2.51414 + 4.12934I −16.4536 − 7.0812I
u = −0.641582 + 0.334485I
a = 0.157238 + 0.522437I
b = −0.703427 + 0.562473I
2.37369 + 3.13295I −5.19542 − 2.99721I
u = −0.641582 − 0.334485I
a = 0.157238 − 0.522437I
b = −0.703427 − 0.562473I
2.37369 − 3.13295I −5.19542 + 2.99721I
u = −0.092146 + 1.281900I
a = −1.13710 + 1.04294I
b = 0.542386 − 0.612790I
2.11803 + 1.48065I 0
u = −0.092146 − 1.281900I
a = −1.13710 − 1.04294I
b = 0.542386 + 0.612790I
2.11803 − 1.48065I 0
u = −0.301148 + 1.254700I
a = −1.19267 + 0.79638I
b = 1.046590 − 0.593449I
6.96547 + 6.35967I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.301148 − 1.254700I
a = −1.19267 − 0.79638I
b = 1.046590 + 0.593449I
6.96547 − 6.35967I 0
u = −0.066911 + 0.696541I
a = −2.64854 − 2.78771I
b = −0.335906 − 0.774807I
−0.521713 − 0.088016I −14.1626 + 0.5129I
u = −0.066911 − 0.696541I
a = −2.64854 + 2.78771I
b = −0.335906 + 0.774807I
−0.521713 + 0.088016I −14.1626 − 0.5129I
u = 0.294325 + 1.288810I
a = 1.145480 + 0.813247I
b = −0.966050 − 0.664872I
8.11911 − 1.05080I 0
u = 0.294325 − 1.288810I
a = 1.145480 − 0.813247I
b = −0.966050 + 0.664872I
8.11911 + 1.05080I 0
u = 0.341475 + 1.280630I
a = −1.90105 − 0.00872I
b = 0.602369 − 1.033590I
0.76201 − 6.19196I 0
u = 0.341475 − 1.280630I
a = −1.90105 + 0.00872I
b = 0.602369 + 1.033590I
0.76201 + 6.19196I 0
u = −0.796395 + 1.099760I
a = −1.39317 + 0.55781I
b = 0.680943 + 0.865093I
3.81397 + 2.16376I 0
u = −0.796395 − 1.099760I
a = −1.39317 − 0.55781I
b = 0.680943 − 0.865093I
3.81397 − 2.16376I 0
u = 0.423195 + 1.291600I
a = −1.82406 + 0.03051I
b = 0.763275 − 1.134570I
5.24553 − 12.87400I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.423195 − 1.291600I
a = −1.82406 − 0.03051I
b = 0.763275 + 1.134570I
5.24553 + 12.87400I 0
u = −0.414925 + 1.307140I
a = 1.82897 + 0.01688I
b = −0.763150 − 1.074800I
6.81555 + 7.35933I 0
u = −0.414925 − 1.307140I
a = 1.82897 − 0.01688I
b = −0.763150 + 1.074800I
6.81555 − 7.35933I 0
u = 0.193170 + 0.594552I
a = 0.740458 − 0.666529I
b = −0.098240 + 1.240000I
−2.62261 + 1.47478I −15.3851 − 1.4664I
u = 0.193170 − 0.594552I
a = 0.740458 + 0.666529I
b = −0.098240 − 1.240000I
−2.62261 − 1.47478I −15.3851 + 1.4664I
u = 0.655153 + 1.238030I
a = −0.453361 − 0.509072I
b = 0.676490 + 0.837280I
3.89800 + 3.07288I 0
u = 0.655153 − 1.238030I
a = −0.453361 + 0.509072I
b = 0.676490 − 0.837280I
3.89800 − 3.07288I 0
u = −0.287460 + 0.509167I
a = −1.030630 + 0.288101I
b = 0.294151 + 0.891432I
−0.56479 + 1.45174I −5.69061 − 3.81457I
u = −0.287460 − 0.509167I
a = −1.030630 − 0.288101I
b = 0.294151 − 0.891432I
−0.56479 − 1.45174I −5.69061 + 3.81457I
u = −0.150834 + 0.552483I
a = 0.224663 − 0.926766I
b = −0.284188 + 1.222330I
−2.60685 + 1.42151I −15.3519 − 4.1761I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.150834 − 0.552483I
a = 0.224663 + 0.926766I
b = −0.284188 − 1.222330I
−2.60685 − 1.42151I −15.3519 + 4.1761I
u = 0.52628 + 1.33490I
a = −0.952515 − 0.880427I
b = 0.959021 + 0.573110I
3.19983 − 13.23160I 0
u = 0.52628 − 1.33490I
a = −0.952515 + 0.880427I
b = 0.959021 − 0.573110I
3.19983 + 13.23160I 0
u = −0.53445 + 1.33597I
a = 0.888636 − 0.841711I
b = −0.909341 + 0.611982I
5.11042 + 7.48156I 0
u = −0.53445 − 1.33597I
a = 0.888636 + 0.841711I
b = −0.909341 − 0.611982I
5.11042 − 7.48156I 0
u = 0.74543 + 1.23902I
a = 1.57046 + 0.44108I
b = −0.703722 + 0.938834I
4.89450 − 8.45588I 0
u = 0.74543 − 1.23902I
a = 1.57046 − 0.44108I
b = −0.703722 − 0.938834I
4.89450 + 8.45588I 0
u = 0.551421 + 0.017870I
a = 0.19708 − 1.54303I
b = −0.397472 − 1.008780I
−3.11028 + 2.85114I −15.0953 − 5.2463I
u = 0.551421 − 0.017870I
a = 0.19708 + 1.54303I
b = −0.397472 + 1.008780I
−3.11028 − 2.85114I −15.0953 + 5.2463I
u = −0.39398 + 1.39456I
a = 1.74350 + 0.04414I
b = −0.712038 − 0.891443I
5.99648 + 3.81310I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.39398 − 1.39456I
a = 1.74350 − 0.04414I
b = −0.712038 + 0.891443I
5.99648 − 3.81310I 0
u = −0.60580 + 1.31894I
a = 0.637580 − 0.640539I
b = −0.739316 + 0.759070I
5.43801 + 2.96205I 0
u = −0.60580 − 1.31894I
a = 0.637580 + 0.640539I
b = −0.739316 − 0.759070I
5.43801 − 2.96205I 0
u = 0.52914 + 1.37088I
a = −0.941382 − 0.654409I
b = 0.754936 + 0.529073I
−1.28468 − 5.21244I 0
u = 0.52914 − 1.37088I
a = −0.941382 + 0.654409I
b = 0.754936 − 0.529073I
−1.28468 + 5.21244I 0
u = 0.24828 + 1.44950I
a = 1.118450 + 0.722661I
b = −0.731705 − 0.815881I
6.22710 + 1.68218I 0
u = 0.24828 − 1.44950I
a = 1.118450 − 0.722661I
b = −0.731705 + 0.815881I
6.22710 − 1.68218I 0
u = −0.59764 + 1.35597I
a = −1.89626 + 0.18431I
b = 0.727490 + 1.115030I
1.5129 + 19.3967I 0
u = −0.59764 − 1.35597I
a = −1.89626 − 0.18431I
b = 0.727490 − 1.115030I
1.5129 − 19.3967I 0
u = 0.62148 + 1.34536I
a = 1.84103 + 0.23572I
b = −0.725741 + 1.080140I
3.66188 − 13.51110I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.62148 − 1.34536I
a = 1.84103 − 0.23572I
b = −0.725741 − 1.080140I
3.66188 + 13.51110I 0
u = 0.45750 + 1.47072I
a = −1.59958 + 0.00596I
b = 0.683108 − 0.786787I
3.66093 + 1.77132I 0
u = 0.45750 − 1.47072I
a = −1.59958 − 0.00596I
b = 0.683108 + 0.786787I
3.66093 − 1.77132I 0
u = −0.427567 + 0.124510I
a = −1.27938 + 0.74577I
b = −0.520833 − 0.306625I
−0.410665 + 0.350990I −9.14009 − 0.28858I
u = −0.427567 − 0.124510I
a = −1.27938 − 0.74577I
b = −0.520833 + 0.306625I
−0.410665 − 0.350990I −9.14009 + 0.28858I
u = −0.67604 + 1.40424I
a = −1.68215 + 0.15655I
b = 0.650729 + 1.052630I
−2.80574 + 10.55840I 0
u = −0.67604 − 1.40424I
a = −1.68215 − 0.15655I
b = 0.650729 − 1.052630I
−2.80574 − 10.55840I 0
u = −1.54967 + 0.37438I
a = 0.769588 + 0.204123I
b = −0.577365 + 0.931964I
−6.61511 − 3.02974I 0
u = −1.54967 − 0.37438I
a = 0.769588 − 0.204123I
b = −0.577365 − 0.931964I
−6.61511 + 3.02974I 0
u = 1.60506 + 0.18152I
a = 0.884414 + 0.227938I
b = −0.545678 + 0.787014I
−6.11465 − 1.47265I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.60506 − 0.18152I
a = 0.884414 − 0.227938I
b = −0.545678 − 0.787014I
−6.11465 + 1.47265I 0
u = −0.33661 + 1.58852I
a = −1.030070 + 0.585576I
b = 0.672963 − 0.909232I
3.28785 − 7.00671I 0
u = −0.33661 − 1.58852I
a = −1.030070 − 0.585576I
b = 0.672963 + 0.909232I
3.28785 + 7.00671I 0
u = −0.373865
a = −0.539447
b = −0.335233
−0.794733 −12.4810
u = 0.336296 + 0.040421I
a = 1.66344 + 1.98608I
b = 0.711214 − 0.564146I
−1.12664 − 4.84437I −10.81095 + 6.16099I
u = 0.336296 − 0.040421I
a = 1.66344 − 1.98608I
b = 0.711214 + 0.564146I
−1.12664 + 4.84437I −10.81095 − 6.16099I
u = −0.108600 + 0.306225I
a = 1.42426 − 2.32937I
b = −0.564521 + 1.107430I
−2.48368 − 3.99664I −14.3466 + 4.3294I
u = −0.108600 − 0.306225I
a = 1.42426 + 2.32937I
b = −0.564521 − 1.107430I
−2.48368 + 3.99664I −14.3466 − 4.3294I
u = 0.171725 + 0.147653I
a = −0.47354 − 4.27439I
b = 0.677264 + 0.943220I
−2.15402 + 0.44006I −13.51281 + 1.33837I
u = 0.171725 − 0.147653I
a = −0.47354 + 4.27439I
b = 0.677264 − 0.943220I
−2.15402 − 0.44006I −13.51281 − 1.33837I
16
II. I
u
2
= h−3au + b − 6a − 2u − 5, 18a
2
− 3au + 30a − 4u + 15, u
2
− 2i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
2
a
6
=
a
3au + 6a + 2u + 5
a
2
=
−2au − 4a −
7
6
u −
8
3
3au + 6a + 2u + 4
a
7
=
au + 2a +
5
6
u +
4
3
3au + 6a + 2u + 4
a
5
=
−
2
3
au − a −
4
9
u +
1
9
−3au − 4a − 2u − 1
a
1
=
au + 2a +
5
6
u +
4
3
3au + 6a + 2u + 4
a
10
=
−
2
3
a +
1
18
u −
4
9
au + 2u
a
8
=
u
3u
a
12
=
au + 2a −
1
6
u +
4
3
3au + 6a − u + 4
a
11
=
au +
2
3
a −
1
18
u +
4
9
5au + 6a + 3u + 4
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12au − 24a − 8u − 32
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u
2
− u + 1)
2
c
3
, c
5
, c
8
c
10
(u
2
− 2)
2
c
4
81(81u
4
+ 54u
3
− 9u
2
− 6u + 7)
c
6
(u
2
+ u + 1)
2
c
7
(u + 1)
4
c
9
81(81u
4
+ 108u
3
+ 72u
2
+ 24u + 7)
c
11
(u + 2)
4
c
12
(u − 1)
4
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
(y
2
+ y + 1)
2
c
3
, c
5
, c
8
c
10
(y −2)
4
c
4
6561(6561y
4
− 4374y
3
+ 1863y
2
− 162y + 49)
c
7
, c
12
(y −1)
4
c
9
6561(6561y
4
+ 1134y
2
+ 432y + 49)
c
11
(y −4)
4
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = −0.715482 + 0.084551I
b = 0.500000 + 0.866025I
−6.57974 + 2.02988I −14.0000 − 3.4641I
u = 1.41421
a = −0.715482 − 0.084551I
b = 0.500000 − 0.866025I
−6.57974 − 2.02988I −14.0000 + 3.4641I
u = −1.41421
a = −0.951184 + 0.492799I
b = 0.500000 + 0.866025I
−6.57974 + 2.02988I −14.0000 − 3.4641I
u = −1.41421
a = −0.951184 − 0.492799I
b = 0.500000 − 0.866025I
−6.57974 − 2.02988I −14.0000 + 3.4641I
20
III. I
v
1
= ha, b − v, v
2
+ v + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
v
0
a
4
=
1
0
a
6
=
0
v
a
2
=
1
−v − 1
a
7
=
v
v + 1
a
5
=
0
v
a
1
=
−v
−v − 1
a
10
=
0
−v − 1
a
8
=
v
0
a
12
=
0
−v − 1
a
11
=
0
−v − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v − 10
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
u
2
− u + 1
c
2
u
2
+ u + 1
c
3
, c
5
, c
8
c
10
, c
11
u
2
c
7
, c
9
(u − 1)
2
c
12
(u + 1)
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
y
2
+ y + 1
c
3
, c
5
, c
8
c
10
, c
11
y
2
c
7
, c
9
, c
12
(y − 1)
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = −0.500000 + 0.866025I
−1.64493 − 2.02988I −12.00000 + 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = −0.500000 − 0.866025I
−1.64493 + 2.02988I −12.00000 − 3.46410I
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
3
)(u
120
+ 44u
119
+ ··· − 3756u + 289)
c
2
((u
2
− u + 1)
2
)(u
2
+ u + 1)(u
120
− 2u
119
+ ··· + 64u + 17)
c
3
, c
8
u
2
(u
2
− 2)
2
(u
120
+ u
119
+ ··· + 20u − 4)
c
4
2313441(u
2
− u + 1)(81u
4
+ 54u
3
− 9u
2
− 6u + 7)
· (28561u
120
+ 43940u
119
+ ··· − 149875040u + 19889425)
c
5
, c
10
u
2
(u
2
− 2)
2
(u
120
+ u
119
+ ··· − 36u − 4)
c
6
(u
2
− u + 1)(u
2
+ u + 1)
2
(u
120
− 2u
119
+ ··· + 64u + 17)
c
7
((u − 1)
2
)(u + 1)
4
(u
120
+ 3u
119
+ ··· − 495u − 343)
c
9
2313441(u − 1)
2
(81u
4
+ 108u
3
+ 72u
2
+ 24u + 7)
· (28561u
120
+ 160381u
119
+ ··· − 9126759u − 5810977)
c
11
u
2
(u + 2)
4
(u
120
+ 55u
119
+ ··· + 208u + 16)
c
12
((u − 1)
4
)(u + 1)
2
(u
120
+ 3u
119
+ ··· − 495u − 343)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
3
)(y
120
+ 68y
119
+ ··· − 1.23886 × 10
7
y + 83521)
c
2
, c
6
((y
2
+ y + 1)
3
)(y
120
+ 44y
119
+ ··· − 3756y + 289)
c
3
, c
8
y
2
(y − 2)
4
(y
120
+ 65y
119
+ ··· + 176y + 16)
c
4
5352009260481(y
2
+ y + 1)
· (6561y
4
− 4374y
3
+ 1863y
2
− 162y + 49)
· (8.16 × 10
8
y
120
+ 3.97 × 10
10
y
119
+ ··· − 1.14 × 10
16
y + 3.96 × 10
14
)
c
5
, c
10
y
2
(y − 2)
4
(y
120
− 55y
119
+ ··· − 208y + 16)
c
7
, c
12
((y − 1)
6
)(y
120
− 69y
119
+ ··· − 633301y + 117649)
c
9
5352009260481(y − 1)
2
(6561y
4
+ 1134y
2
+ 432y + 49)
· (8.16 × 10
8
y
120
+ 1.20 × 10
10
y
119
+ ··· − 3.67 × 10
14
y + 3.38 × 10
13
)
c
11
y
2
(y − 4)
4
(y
120
+ 25y
119
+ ··· − 26880y + 256)
26
