12a
0188
(K12a
0188
)
A knot diagram
1
Linearized knot diagam
3 5 9 8 2 4 11 6 12 1 7 10
Solving Sequence
4,8 5,11
7 12 6 9 10 3 2 1
c
4
c
7
c
11
c
6
c
8
c
9
c
3
c
2
c
1
c
5
, c
10
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.42605 × 10
1018
u
118
− 1.10416 × 10
1019
u
117
+ ··· + 2.49080 × 10
1022
b − 2.03299 × 10
1022
,
3.47903 × 10
1021
u
118
+ 6.79805 × 10
1021
u
117
+ ··· + 6.61059 × 10
1024
a − 1.30130 × 10
1025
,
u
119
+ 2u
118
+ ··· + 8762u + 1327i
I
u
2
= hu
8
− 2u
6
+ 2u
4
+ u
3
+ b − u + 1, a, u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 128 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−7.43 × 10
1018
u
118
− 1.10 × 10
1019
u
117
+ · · · + 2.49 × 10
1022
b −
2.03 × 10
1022
, 3.48 × 10
1021
u
118
+ 6.80 × 10
1021
u
117
+ · · · + 6.61 × 10
1024
a −
1.30 × 10
1025
, u
119
+ 2u
118
+ · · · + 8762u + 1327i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
−u
2
a
11
=
−0.000526281u
118
− 0.00102836u
117
+ ··· − 12.9920u + 1.96851
0.000298139u
118
+ 0.000443295u
117
+ ··· + 2.48668u + 0.816199
a
7
=
−0.00204675u
118
− 0.00374735u
117
+ ··· − 44.8125u − 10.1681
0.000217932u
118
+ 0.000446866u
117
+ ··· + 2.65443u + 1.01512
a
12
=
−0.00340766u
118
− 0.00621070u
117
+ ··· − 43.0873u − 17.5112
−0.0000110966u
118
− 0.0000853887u
117
+ ··· + 0.224165u + 0.246586
a
6
=
−0.00226468u
118
− 0.00419422u
117
+ ··· − 47.4669u − 11.1832
0.000217932u
118
+ 0.000446866u
117
+ ··· + 2.65443u + 1.01512
a
9
=
0.000279013u
118
+ 0.000673242u
117
+ ··· − 23.4449u + 9.53210
0.000478417u
118
+ 0.000913280u
117
+ ··· + 4.42620u + 2.18078
a
10
=
0.000991558u
118
+ 0.00190829u
117
+ ··· + 2.65205u + 5.62220
0.000451996u
118
+ 0.000840247u
117
+ ··· + 8.82580u + 1.76896
a
3
=
−0.00208611u
118
− 0.00412377u
117
+ ··· − 34.1619u − 20.6382
−0.000442936u
118
− 0.000823798u
117
+ ··· − 10.8522u − 2.78052
a
2
=
−0.00157316u
118
− 0.00308242u
117
+ ··· − 25.6536u − 17.7935
−0.000473190u
118
− 0.000917918u
117
+ ··· − 10.0361u − 2.76001
a
1
=
−0.00406489u
118
− 0.00755589u
117
+ ··· − 73.4388u − 20.9068
−0.000730125u
118
− 0.00137620u
117
+ ··· − 12.0660u − 1.83313
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00267969u
118
+ 0.00463437u
117
+ ··· + 47.3827u + 19.3117
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
119
+ 48u
118
+ ··· − 10u − 1
c
2
, c
5
u
119
+ 2u
118
+ ··· − 10u − 1
c
3
u
119
− 6u
118
+ ··· − 3844u − 1441
c
4
u
119
− 2u
118
+ ··· + 8762u − 1327
c
6
u
119
+ 12u
118
+ ··· − 2u − 1
c
7
, c
11
u
119
− u
118
+ ··· + 4096u − 512
c
8
u
119
+ 10u
118
+ ··· − 2u − 1
c
9
, c
10
, c
12
u
119
− 10u
118
+ ··· + 14u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
119
+ 48y
118
+ ··· − 1922y −1
c
2
, c
5
y
119
+ 48y
118
+ ··· − 10y −1
c
3
y
119
− 108y
118
+ ··· − 880963674y −2076481
c
4
y
119
− 132y
118
+ ··· + 73112778y −1760929
c
6
y
119
+ 100y
117
+ ··· − 10y −1
c
7
, c
11
y
119
+ 57y
118
+ ··· − 1572864y −262144
c
8
y
119
− 12y
118
+ ··· + 10y −1
c
9
, c
10
, c
12
y
119
− 108y
118
+ ··· − 162y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.081525 + 0.998574I
a = −1.41965 + 0.28773I
b = −1.59460 − 0.55588I
−13.32730 + 0.47174I 0
u = −0.081525 − 0.998574I
a = −1.41965 − 0.28773I
b = −1.59460 + 0.55588I
−13.32730 − 0.47174I 0
u = −0.970650 + 0.184323I
a = 0.271720 + 1.164900I
b = 0.118861 + 0.924692I
−1.80179 + 3.47511I 0
u = −0.970650 − 0.184323I
a = 0.271720 − 1.164900I
b = 0.118861 − 0.924692I
−1.80179 − 3.47511I 0
u = −0.910650 + 0.368955I
a = 0.869458 + 0.182486I
b = 0.1018280 − 0.0457066I
3.48096 − 0.06555I 0
u = −0.910650 − 0.368955I
a = 0.869458 − 0.182486I
b = 0.1018280 + 0.0457066I
3.48096 + 0.06555I 0
u = 0.704399 + 0.664447I
a = 0.226012 − 0.547602I
b = −0.360213 − 0.109997I
−1.94863 + 2.48320I 0
u = 0.704399 − 0.664447I
a = 0.226012 + 0.547602I
b = −0.360213 + 0.109997I
−1.94863 − 2.48320I 0
u = −0.433604 + 0.853701I
a = 1.036840 − 0.408640I
b = 1.89884 + 0.99868I
−5.55472 − 1.58319I 0
u = −0.433604 − 0.853701I
a = 1.036840 + 0.408640I
b = 1.89884 − 0.99868I
−5.55472 + 1.58319I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.931340 + 0.171300I
a = −0.818031 − 1.114670I
b = −0.761271 − 0.977888I
−4.83003 + 9.97536I 0
u = 0.931340 − 0.171300I
a = −0.818031 + 1.114670I
b = −0.761271 + 0.977888I
−4.83003 − 9.97536I 0
u = 0.518141 + 0.954046I
a = −0.262584 + 1.029370I
b = 0.359089 + 0.250456I
−6.98001 + 4.13299I 0
u = 0.518141 − 0.954046I
a = −0.262584 − 1.029370I
b = 0.359089 − 0.250456I
−6.98001 − 4.13299I 0
u = 0.291778 + 0.865633I
a = 0.064896 + 0.287778I
b = −0.293621 − 1.142710I
0.59145 − 2.37148I 0
u = 0.291778 − 0.865633I
a = 0.064896 − 0.287778I
b = −0.293621 + 1.142710I
0.59145 + 2.37148I 0
u = 0.523885 + 0.730221I
a = −0.611989 − 0.224963I
b = −2.12194 − 0.87948I
−1.23906 + 2.78377I 0
u = 0.523885 − 0.730221I
a = −0.611989 + 0.224963I
b = −2.12194 + 0.87948I
−1.23906 − 2.78377I 0
u = 0.724182 + 0.506626I
a = −1.127460 + 0.362906I
b = −0.0086126 − 0.1190020I
2.82823 + 5.08911I 0
u = 0.724182 − 0.506626I
a = −1.127460 − 0.362906I
b = −0.0086126 + 0.1190020I
2.82823 − 5.08911I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.502056 + 0.713507I
a = −1.39012 − 0.71219I
b = −0.967306 + 0.461819I
−1.69763 + 1.29769I 0
u = 0.502056 − 0.713507I
a = −1.39012 + 0.71219I
b = −0.967306 − 0.461819I
−1.69763 − 1.29769I 0
u = −0.745569 + 0.426426I
a = 0.694020 + 0.823774I
b = 2.13911 − 0.28284I
−2.17047 − 4.66203I 0
u = −0.745569 − 0.426426I
a = 0.694020 − 0.823774I
b = 2.13911 + 0.28284I
−2.17047 + 4.66203I 0
u = 0.740896 + 0.427649I
a = 1.58637 + 0.79586I
b = 1.146940 − 0.360044I
−5.78573 + 11.06080I 0
u = 0.740896 − 0.427649I
a = 1.58637 − 0.79586I
b = 1.146940 + 0.360044I
−5.78573 − 11.06080I 0
u = −0.829751 + 0.136679I
a = −0.483041 − 0.984009I
b = −0.273688 − 0.903224I
2.95353 + 0.44405I 0
u = −0.829751 − 0.136679I
a = −0.483041 + 0.984009I
b = −0.273688 + 0.903224I
2.95353 − 0.44405I 0
u = 0.787526 + 0.854331I
a = −0.392445 − 0.361964I
b = −1.80353 + 0.05459I
−1.25021 + 2.82984I 0
u = 0.787526 − 0.854331I
a = −0.392445 + 0.361964I
b = −1.80353 − 0.05459I
−1.25021 − 2.82984I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.617088 + 0.990171I
a = −0.997532 + 0.173407I
b = −2.21128 − 0.72234I
−4.33720 − 6.36777I 0
u = −0.617088 − 0.990171I
a = −0.997532 − 0.173407I
b = −2.21128 + 0.72234I
−4.33720 + 6.36777I 0
u = 0.594816 + 1.013270I
a = 1.054630 + 0.553578I
b = 1.59441 − 0.55796I
−8.87900 + 3.08041I 0
u = 0.594816 − 1.013270I
a = 1.054630 − 0.553578I
b = 1.59441 + 0.55796I
−8.87900 − 3.08041I 0
u = 0.757632 + 0.275547I
a = 0.963052 + 0.883677I
b = 0.94899 + 1.06285I
0.50738 + 6.41058I 0
u = 0.757632 − 0.275547I
a = 0.963052 − 0.883677I
b = 0.94899 − 1.06285I
0.50738 − 6.41058I 0
u = −0.236873 + 0.768309I
a = 1.61254 − 0.81420I
b = 0.833484 + 0.489209I
−2.46876 − 5.01134I 0
u = −0.236873 − 0.768309I
a = 1.61254 + 0.81420I
b = 0.833484 − 0.489209I
−2.46876 + 5.01134I 0
u = 0.798401 + 0.033833I
a = −0.685721 − 0.579893I
b = −2.47569 + 0.92651I
0.107706 + 0.619941I 0
u = 0.798401 − 0.033833I
a = −0.685721 + 0.579893I
b = −2.47569 − 0.92651I
0.107706 − 0.619941I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.795147
a = 0.431976
b = 0.315267
1.04484 10.3180
u = −0.129379 + 0.766634I
a = −0.03485 − 1.95282I
b = −0.036462 + 0.168045I
−4.11769 + 1.69954I −15.5018 + 0.I
u = −0.129379 − 0.766634I
a = −0.03485 + 1.95282I
b = −0.036462 − 0.168045I
−4.11769 − 1.69954I −15.5018 + 0.I
u = 0.570836 + 0.500629I
a = −0.800374 − 0.918343I
b = −1.084630 + 0.861172I
−1.31680 + 1.56421I 0
u = 0.570836 − 0.500629I
a = −0.800374 + 0.918343I
b = −1.084630 − 0.861172I
−1.31680 − 1.56421I 0
u = 0.375955 + 0.638900I
a = 0.616240 + 1.141540I
b = 0.822308 − 0.452547I
0.04303 − 1.98692I 0. + 4.49673I
u = 0.375955 − 0.638900I
a = 0.616240 − 1.141540I
b = 0.822308 + 0.452547I
0.04303 + 1.98692I 0. − 4.49673I
u = 1.054010 + 0.697456I
a = 0.322664 + 0.886342I
b = 0.722677 + 0.463877I
−6.92350 + 1.57130I 0
u = 1.054010 − 0.697456I
a = 0.322664 − 0.886342I
b = 0.722677 − 0.463877I
−6.92350 − 1.57130I 0
u = 1.014670 + 0.830117I
a = −0.766257 − 0.441071I
b = −2.02808 + 0.97952I
0.08564 + 3.67293I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.014670 − 0.830117I
a = −0.766257 + 0.441071I
b = −2.02808 − 0.97952I
0.08564 − 3.67293I 0
u = −1.116610 + 0.688150I
a = −0.373991 − 0.625653I
b = −0.1133530 − 0.0550594I
4.34687 − 3.34050I 0
u = −1.116610 − 0.688150I
a = −0.373991 + 0.625653I
b = −0.1133530 + 0.0550594I
4.34687 + 3.34050I 0
u = −0.676280 + 1.140850I
a = 1.067190 − 0.086743I
b = 2.17392 + 0.53136I
−10.1820 − 10.3208I 0
u = −0.676280 − 1.140850I
a = 1.067190 + 0.086743I
b = 2.17392 − 0.53136I
−10.1820 + 10.3208I 0
u = 0.511226 + 0.390425I
a = −1.70638 − 0.87752I
b = −2.16463 + 0.33752I
−2.26487 + 7.17835I 4.62024 − 8.19598I
u = 0.511226 − 0.390425I
a = −1.70638 + 0.87752I
b = −2.16463 − 0.33752I
−2.26487 − 7.17835I 4.62024 + 8.19598I
u = 1.296190 + 0.410510I
a = 0.165584 + 0.450411I
b = −0.0681928 + 0.0242347I
1.45890 + 7.13045I 0
u = 1.296190 − 0.410510I
a = 0.165584 − 0.450411I
b = −0.0681928 − 0.0242347I
1.45890 − 7.13045I 0
u = 0.598724 + 0.193737I
a = 1.20330 + 1.00148I
b = 2.18553 − 0.49392I
2.70873 + 3.86349I 10.51829 − 7.88352I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.598724 − 0.193737I
a = 1.20330 − 1.00148I
b = 2.18553 + 0.49392I
2.70873 − 3.86349I 10.51829 + 7.88352I
u = −1.325130 + 0.391603I
a = −0.069220 + 0.506720I
b = 0.0222037 + 0.0793625I
2.16952 − 1.09292I 0
u = −1.325130 − 0.391603I
a = −0.069220 − 0.506720I
b = 0.0222037 − 0.0793625I
2.16952 + 1.09292I 0
u = 0.557060 + 0.245089I
a = −1.95713 − 1.42702I
b = −0.762500 + 0.329644I
−0.29654 + 5.98543I −0.0311 − 14.6386I
u = 0.557060 − 0.245089I
a = −1.95713 + 1.42702I
b = −0.762500 − 0.329644I
−0.29654 − 5.98543I −0.0311 + 14.6386I
u = 1.103720 + 0.847498I
a = 0.376493 − 0.597122I
b = 0.0712315 + 0.0826993I
2.91318 + 8.94395I 0
u = 1.103720 − 0.847498I
a = 0.376493 + 0.597122I
b = 0.0712315 − 0.0826993I
2.91318 − 8.94395I 0
u = −0.603058 + 0.015289I
a = 1.088510 + 0.710096I
b = 0.601039 + 1.237240I
−0.08315 − 2.49375I 7.75933 + 3.67875I
u = −0.603058 − 0.015289I
a = 1.088510 − 0.710096I
b = 0.601039 − 1.237240I
−0.08315 + 2.49375I 7.75933 − 3.67875I
u = −1.072730 + 0.905260I
a = 0.385966 + 0.803671I
b = 0.145591 + 0.084751I
−0.86473 − 6.53924I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.072730 − 0.905260I
a = 0.385966 − 0.803671I
b = 0.145591 − 0.084751I
−0.86473 + 6.53924I 0
u = 0.882941 + 1.103200I
a = −0.400091 − 0.764413I
b = −1.020920 + 0.649386I
−4.94221 − 5.12424I 0
u = 0.882941 − 1.103200I
a = −0.400091 + 0.764413I
b = −1.020920 − 0.649386I
−4.94221 + 5.12424I 0
u = −0.318663 + 0.484259I
a = −2.37762 + 0.02970I
b = −1.085800 − 0.168980I
−4.38510 − 6.20836I 0.22006 + 4.93300I
u = −0.318663 − 0.484259I
a = −2.37762 − 0.02970I
b = −1.085800 + 0.168980I
−4.38510 + 6.20836I 0.22006 − 4.93300I
u = −0.330925 + 0.466879I
a = −1.28779 − 0.89418I
b = −0.512426 − 0.110999I
−2.62882 + 0.46286I −2.15164 + 0.44651I
u = −0.330925 − 0.466879I
a = −1.28779 + 0.89418I
b = −0.512426 + 0.110999I
−2.62882 − 0.46286I −2.15164 − 0.44651I
u = 0.84400 + 1.19676I
a = 0.994191 + 0.229453I
b = 1.54118 − 0.33264I
−8.51063 + 5.18393I 0
u = 0.84400 − 1.19676I
a = 0.994191 − 0.229453I
b = 1.54118 + 0.33264I
−8.51063 − 5.18393I 0
u = 1.15226 + 0.92165I
a = 0.803741 + 0.336916I
b = 2.21004 − 0.75116I
2.23345 + 8.79850I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.15226 − 0.92165I
a = 0.803741 − 0.336916I
b = 2.21004 + 0.75116I
2.23345 − 8.79850I 0
u = −0.59957 + 1.37808I
a = −0.998240 + 0.354091I
b = −1.60534 − 0.54541I
−11.57620 − 7.68806I 0
u = −0.59957 − 1.37808I
a = −0.998240 − 0.354091I
b = −1.60534 + 0.54541I
−11.57620 + 7.68806I 0
u = −1.05545 + 1.08481I
a = 0.757720 − 0.368846I
b = 2.02465 + 0.94664I
−1.77422 − 9.13916I 0
u = −1.05545 − 1.08481I
a = 0.757720 + 0.368846I
b = 2.02465 − 0.94664I
−1.77422 + 9.13916I 0
u = −0.340103 + 0.282381I
a = −1.06544 − 3.17807I
b = −0.211295 − 0.068606I
−3.81372 − 3.40916I −13.1889 + 9.5632I
u = −0.340103 − 0.282381I
a = −1.06544 + 3.17807I
b = −0.211295 + 0.068606I
−3.81372 + 3.40916I −13.1889 − 9.5632I
u = 1.22430 + 1.02374I
a = −0.851388 − 0.295378I
b = −2.20754 + 0.59133I
−3.21741 + 13.29190I 0
u = 1.22430 − 1.02374I
a = −0.851388 + 0.295378I
b = −2.20754 − 0.59133I
−3.21741 − 13.29190I 0
u = −0.325900 + 0.217465I
a = −0.14200 − 2.00590I
b = −1.81687 + 0.09571I
1.44329 − 2.36124I 8.29903 + 4.18833I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.325900 − 0.217465I
a = −0.14200 + 2.00590I
b = −1.81687 − 0.09571I
1.44329 + 2.36124I 8.29903 − 4.18833I
u = 1.15293 + 1.14161I
a = −0.317074 + 0.765092I
b = −0.105663 − 0.104933I
−2.84169 + 12.19540I 0
u = 1.15293 − 1.14161I
a = −0.317074 − 0.765092I
b = −0.105663 + 0.104933I
−2.84169 − 12.19540I 0
u = −0.249672 + 0.209313I
a = 3.07663 − 1.76750I
b = 1.96638 − 0.09187I
−3.27191 − 0.12438I 1.90527 − 2.70040I
u = −0.249672 − 0.209313I
a = 3.07663 + 1.76750I
b = 1.96638 + 0.09187I
−3.27191 + 0.12438I 1.90527 + 2.70040I
u = −1.24988 + 1.12817I
a = −0.752006 + 0.280830I
b = −2.23877 − 0.75859I
0.2822 − 14.6365I 0
u = −1.24988 − 1.12817I
a = −0.752006 − 0.280830I
b = −2.23877 + 0.75859I
0.2822 + 14.6365I 0
u = 0.124444 + 0.224899I
a = 5.10009 − 0.80710I
b = 0.417693 + 0.392036I
−3.34529 + 0.06544I −11.29700 + 4.85801I
u = 0.124444 − 0.224899I
a = 5.10009 + 0.80710I
b = 0.417693 − 0.392036I
−3.34529 − 0.06544I −11.29700 − 4.85801I
u = −0.188157 + 0.086457I
a = 5.51967 − 2.85856I
b = 0.630832 + 0.163392I
0.52690 − 1.71924I 3.78431 + 7.93043I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.188157 − 0.086457I
a = 5.51967 + 2.85856I
b = 0.630832 − 0.163392I
0.52690 + 1.71924I 3.78431 − 7.93043I
u = −1.37274 + 1.21265I
a = 0.777638 − 0.240188I
b = 2.25489 + 0.59451I
−5.3195 − 19.3518I 0
u = −1.37274 − 1.21265I
a = 0.777638 + 0.240188I
b = 2.25489 − 0.59451I
−5.3195 + 19.3518I 0
u = −1.95924 + 0.85973I
a = −0.310014 − 0.040033I
b = −3.74304 + 0.55704I
−2.33120 − 1.65341I 0
u = −1.95924 − 0.85973I
a = −0.310014 + 0.040033I
b = −3.74304 − 0.55704I
−2.33120 + 1.65341I 0
u = −2.35812 + 0.35439I
a = 0.137818 − 0.327216I
b = 1.11173 + 2.05083I
−0.797814 + 0.550209I 0
u = −2.35812 − 0.35439I
a = 0.137818 + 0.327216I
b = 1.11173 − 2.05083I
−0.797814 − 0.550209I 0
u = −2.57879 + 0.46049I
a = −0.057094 − 0.485866I
b = −0.12860 + 1.44691I
−6.68223 + 1.86961I 0
u = −2.57879 − 0.46049I
a = −0.057094 + 0.485866I
b = −0.12860 − 1.44691I
−6.68223 − 1.86961I 0
u = 2.64863 + 0.49723I
a = 0.242317 + 0.383051I
b = 1.59480 − 1.47606I
−5.11734 + 2.47956I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 2.64863 − 0.49723I
a = 0.242317 − 0.383051I
b = 1.59480 + 1.47606I
−5.11734 − 2.47956I 0
u = 2.70878 + 0.21669I
a = −0.130551 + 0.295921I
b = −1.55050 − 2.44303I
0.027445 + 0.372128I 0
u = 2.70878 − 0.21669I
a = −0.130551 − 0.295921I
b = −1.55050 + 2.44303I
0.027445 − 0.372128I 0
u = 3.15822 + 0.45727I
a = 0.259108 − 0.002744I
b = 4.26093 + 0.09967I
−2.55503 − 2.22852I 0
u = 3.15822 − 0.45727I
a = 0.259108 + 0.002744I
b = 4.26093 − 0.09967I
−2.55503 + 2.22852I 0
u = −3.38066 + 0.13306I
a = 0.106654 + 0.261156I
b = 1.51121 − 2.90197I
−0.25612 + 3.85842I 0
u = −3.38066 − 0.13306I
a = 0.106654 − 0.261156I
b = 1.51121 + 2.90197I
−0.25612 − 3.85842I 0
u = −3.39963 + 0.04174I
a = −0.145484 − 0.352374I
b = −1.21167 + 1.96806I
−5.71911 + 7.03575I 0
u = −3.39963 − 0.04174I
a = −0.145484 + 0.352374I
b = −1.21167 − 1.96806I
−5.71911 − 7.03575I 0
16
II.
I
u
2
= hu
8
−2u
6
+2u
4
+u
3
+b−u+1, a, u
9
−u
8
−2u
7
+3u
6
+u
5
−3u
4
+2u
3
−u+1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
−u
2
a
11
=
0
−u
8
+ 2u
6
− 2u
4
− u
3
+ u − 1
a
7
=
0
u
a
12
=
0
−u
8
+ 2u
6
− 2u
4
− u
3
+ u − 1
a
6
=
−u
u
a
9
=
u
3
−u
3
+ u
a
10
=
u
3
−u
8
+ 2u
6
− 2u
4
− 2u
3
+ 2u − 1
a
3
=
u
6
− u
4
+ 1
−u
6
+ 2u
4
− u
2
a
2
=
−u
8
+ 3u
6
− 3u
4
+ 1
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u
3
− 1
a
1
=
−u
3
u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
8
+ u
7
+ 7u
6
− 6u
5
− 6u
4
+ 7u
3
− 5u
2
− 7u + 1
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
2
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
4
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
5
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
6
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
7
, c
11
u
9
c
8
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
9
, c
10
(u − 1)
9
c
12
(u + 1)
9
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
2
, c
5
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
4
, c
6
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
7
, c
11
y
9
c
8
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
9
, c
10
, c
12
(y −1)
9
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772920 + 0.510351I
a = 0
b = −0.225230 − 1.238240I
−3.42837 + 2.09337I −4.41045 − 5.46639I
u = 0.772920 − 0.510351I
a = 0
b = −0.225230 + 1.238240I
−3.42837 − 2.09337I −4.41045 + 5.46639I
u = −0.825933
a = 0
b = −1.77487
−0.446489 −0.182090
u = −1.173910 + 0.391555I
a = 0
b = −0.300113 − 0.434032I
2.72642 − 1.33617I 8.07941 + 3.55369I
u = −1.173910 − 0.391555I
a = 0
b = −0.300113 + 0.434032I
2.72642 + 1.33617I 8.07941 − 3.55369I
u = 0.141484 + 0.739668I
a = 0
b = −1.25758 + 1.97504I
−1.02799 − 2.45442I −2.24638 − 6.63381I
u = 0.141484 − 0.739668I
a = 0
b = −1.25758 − 1.97504I
−1.02799 + 2.45442I −2.24638 + 6.63381I
u = 1.172470 + 0.500383I
a = 0
b = 0.170352 − 0.451655I
1.95319 + 7.08493I 8.66846 − 5.33071I
u = 1.172470 − 0.500383I
a = 0
b = 0.170352 + 0.451655I
1.95319 − 7.08493I 8.66846 + 5.33071I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
119
+ 48u
118
+ ··· − 10u − 1)
c
2
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
119
+ 2u
118
+ ··· − 10u − 1)
c
3
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
119
− 6u
118
+ ··· − 3844u − 1441)
c
4
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
119
− 2u
118
+ ··· + 8762u − 1327)
c
5
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
119
+ 2u
118
+ ··· − 10u − 1)
c
6
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
119
+ 12u
118
+ ··· − 2u − 1)
c
7
, c
11
u
9
(u
119
− u
118
+ ··· + 4096u − 512)
c
8
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
119
+ 10u
118
+ ··· − 2u − 1)
c
9
, c
10
((u − 1)
9
)(u
119
− 10u
118
+ ··· + 14u − 1)
c
12
((u + 1)
9
)(u
119
− 10u
118
+ ··· + 14u − 1)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
119
+ 48y
118
+ ··· − 1922y −1)
c
2
, c
5
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
119
+ 48y
118
+ ··· − 10y −1)
c
3
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
119
− 108y
118
+ ··· − 880963674y −2076481)
c
4
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
119
− 132y
118
+ ··· + 73112778y −1760929)
c
6
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
119
+ 100y
117
+ ··· − 10y −1)
c
7
, c
11
y
9
(y
119
+ 57y
118
+ ··· − 1572864y −262144)
c
8
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
119
− 12y
118
+ ··· + 10y −1)
c
9
, c
10
, c
12
((y −1)
9
)(y
119
− 108y
118
+ ··· − 162y −1)
22
