12a
0960
(K12a
0960
)
A knot diagram
1
Linearized knot diagam
4 6 10 9 12 11 3 5 1 7 2 8
Solving Sequence
6,11 3,7
8 2 12 5 10 4 1 9
c
6
c
7
c
2
c
11
c
5
c
10
c
3
c
1
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h6.32511 × 10
1035
u
175
+ 4.24899 × 10
1036
u
174
+ ··· + 4.69972 × 10
1036
b + 3.27998 × 10
1038
,
8.00347 × 10
1038
u
175
+ 5.25942 × 10
1039
u
174
+ ··· + 4.41303 × 10
1039
a + 3.29768 × 10
1041
,
u
176
+ 6u
175
+ ··· − 5650u + 939i
I
u
2
= h−1.39268 × 10
28
u
33
+ 3.61198 × 10
28
u
32
+ ··· + 5.54335 × 10
28
b + 8.01444 × 10
28
,
− 1.75682 × 10
28
u
33
+ 3.90770 × 10
28
u
32
+ ··· + 5.54335 × 10
28
a − 1.15604 × 10
29
,
u
34
+ 16u
32
+ ··· − 15u + 1i
I
u
3
= hb + u, a + u + 1, u
2
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 212 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
= h6.33 × 10
1035
u
175
+ 4.25 × 10
1036
u
174
+ · · · + 4.70 × 10
1036
b + 3.28 ×
10
1038
, 8.00 × 10
1038
u
175
+ 5.26 × 10
1039
u
174
+ · · · + 4.41 × 10
1039
a + 3.30 ×
10
1041
, u
176
+ 6u
175
+ · · · − 5650u + 939i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
−0.181360u
175
− 1.19179u
174
+ ··· + 305.464u − 74.7260
−0.134585u
175
− 0.904096u
174
+ ··· + 323.722u − 69.7909
a
7
=
1
−u
2
a
8
=
−0.00219584u
175
− 0.100916u
174
+ ··· + 398.465u − 64.6077
0.0390647u
175
+ 0.184706u
174
+ ··· + 246.044u − 35.5061
a
2
=
−0.0467749u
175
− 0.287698u
174
+ ··· − 18.2581u − 4.93505
−0.134585u
175
− 0.904096u
174
+ ··· + 323.722u − 69.7909
a
12
=
0.00720057u
175
+ 0.0727156u
174
+ ··· − 80.4218u + 10.4860
−0.171963u
175
− 0.989112u
174
+ ··· − 298.311u + 29.0343
a
5
=
0.111561u
175
+ 0.549967u
174
+ ··· + 607.097u − 85.9822
−0.319703u
175
− 1.89062u
174
+ ··· − 365.057u + 23.6912
a
10
=
−u
u
3
+ u
a
4
=
−0.0710434u
175
− 0.435873u
174
+ ··· − 20.1901u − 7.61312
−0.0970434u
175
− 0.650749u
174
+ ··· + 221.741u − 48.6175
a
1
=
0.0186189u
175
+ 0.0662415u
174
+ ··· + 232.284u − 37.5107
−0.112061u
175
− 0.612880u
174
+ ··· − 344.134u + 45.3503
a
9
=
0.0861891u
175
+ 0.595903u
174
+ ··· − 265.966u + 55.0977
0.0391470u
175
− 0.195411u
174
+ ··· + 1864.59u − 304.617
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.92136u
175
+ 12.8967u
174
+ ··· − 4562.99u + 988.525
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
176
+ 7u
175
+ ··· + 69156u + 17323
c
2
4(4u
176
− 42u
175
+ ··· + 4u + 3)
c
3
4(4u
176
+ 18u
175
+ ··· + 1.69296 × 10
9
u + 1.02369 × 10
8
)
c
4
, c
8
u
176
+ 6u
175
+ ··· − 5650u + 939
c
5
4(4u
176
− 18u
175
+ ··· − 1.69296 × 10
9
u + 1.02369 × 10
8
)
c
6
, c
10
u
176
− 6u
175
+ ··· + 5650u + 939
c
7
u
176
+ u
175
+ ··· − 12001832u + 1637744
c
9
4(4u
176
+ 42u
175
+ ··· − 4u + 3)
c
11
u
176
− 7u
175
+ ··· − 69156u + 17323
c
12
u
176
− u
175
+ ··· + 12001832u + 1637744
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
176
+ 11y
175
+ ··· + 18368043448y + 300086329
c
2
, c
9
16(16y
176
+ 164y
175
+ ··· + 632y + 9)
c
3
, c
5
16(16y
176
+ 1348y
175
+ ··· + 6.24455 × 10
17
y + 1.04794 × 10
16
)
c
4
, c
6
, c
8
c
10
y
176
+ 134y
175
+ ··· + 23450330y + 881721
c
7
, c
12
y
176
+ 51y
175
+ ··· + 119113228533312y + 2682205409536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.268225 + 0.962582I
a = 0.20659 + 2.76799I
b = −0.264729 + 0.026201I
2.66927 − 10.63920I 0
u = −0.268225 − 0.962582I
a = 0.20659 − 2.76799I
b = −0.264729 − 0.026201I
2.66927 + 10.63920I 0
u = −0.639498 + 0.779579I
a = −0.914982 − 0.304342I
b = 0.645237 − 0.266582I
0.73655 − 2.57695I 0
u = −0.639498 − 0.779579I
a = −0.914982 + 0.304342I
b = 0.645237 + 0.266582I
0.73655 + 2.57695I 0
u = −0.403534 + 0.894931I
a = −0.490359 − 1.134190I
b = 0.150323 − 0.171101I
0.36799 − 1.98151I 0
u = −0.403534 − 0.894931I
a = −0.490359 + 1.134190I
b = 0.150323 + 0.171101I
0.36799 + 1.98151I 0
u = 0.024715 + 0.972378I
a = −1.005110 − 0.313765I
b = 1.063340 − 0.252710I
4.15953 − 4.46103I 0
u = 0.024715 − 0.972378I
a = −1.005110 + 0.313765I
b = 1.063340 + 0.252710I
4.15953 + 4.46103I 0
u = −0.098010 + 1.027020I
a = −1.36993 − 1.20050I
b = −1.62456 − 0.79093I
0.714090 − 0.355524I 0
u = −0.098010 − 1.027020I
a = −1.36993 + 1.20050I
b = −1.62456 + 0.79093I
0.714090 + 0.355524I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.644866 + 0.808232I
a = 0.648376 − 0.508937I
b = −0.917957 − 0.040537I
5.16399 + 2.60014I 0
u = 0.644866 − 0.808232I
a = 0.648376 + 0.508937I
b = −0.917957 + 0.040537I
5.16399 − 2.60014I 0
u = 0.445760 + 0.834063I
a = 0.33232 − 1.43020I
b = −0.592928 − 0.020233I
4.91221 + 2.00569I 0
u = 0.445760 − 0.834063I
a = 0.33232 + 1.43020I
b = −0.592928 + 0.020233I
4.91221 − 2.00569I 0
u = −1.035470 + 0.205784I
a = −0.078531 − 0.548387I
b = 0.803386 + 0.258956I
5.06643 + 0.78586I 0
u = −1.035470 − 0.205784I
a = −0.078531 + 0.548387I
b = 0.803386 − 0.258956I
5.06643 − 0.78586I 0
u = −0.376648 + 0.863700I
a = −1.31412 − 0.99638I
b = −0.776206 − 0.933078I
0.557762 − 0.871550I 0
u = −0.376648 − 0.863700I
a = −1.31412 + 0.99638I
b = −0.776206 + 0.933078I
0.557762 + 0.871550I 0
u = −0.783561 + 0.519734I
a = −0.283303 − 0.093269I
b = 1.072940 − 0.564679I
3.57396 − 6.11171I 0
u = −0.783561 − 0.519734I
a = −0.283303 + 0.093269I
b = 1.072940 + 0.564679I
3.57396 + 6.11171I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.060870 + 0.134806I
a = −0.091627 + 0.411572I
b = −0.939105 + 0.646913I
3.81603 − 2.52639I 0
u = −1.060870 − 0.134806I
a = −0.091627 − 0.411572I
b = −0.939105 − 0.646913I
3.81603 + 2.52639I 0
u = 0.267369 + 1.038610I
a = 0.13106 − 1.76673I
b = −0.93471 − 1.32000I
−1.21991 + 3.70716I 0
u = 0.267369 − 1.038610I
a = 0.13106 + 1.76673I
b = −0.93471 + 1.32000I
−1.21991 − 3.70716I 0
u = 0.064822 + 1.096500I
a = −0.123853 − 0.899928I
b = −1.44021 − 0.54781I
−1.86863 + 2.42778I 0
u = 0.064822 − 1.096500I
a = −0.123853 + 0.899928I
b = −1.44021 + 0.54781I
−1.86863 − 2.42778I 0
u = 0.934012 + 0.592825I
a = 0.733403 + 0.144804I
b = −0.694203 − 0.400242I
3.48356 + 4.14986I 0
u = 0.934012 − 0.592825I
a = 0.733403 − 0.144804I
b = −0.694203 + 0.400242I
3.48356 − 4.14986I 0
u = −0.879145 + 0.157980I
a = −0.391182 + 0.079087I
b = −0.965060 − 0.533810I
2.95882 + 1.25298I 0
u = −0.879145 − 0.157980I
a = −0.391182 − 0.079087I
b = −0.965060 + 0.533810I
2.95882 − 1.25298I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.026972 + 1.111890I
a = 0.25218 − 1.81916I
b = −0.913965 − 0.993863I
−2.35849 + 1.91634I 0
u = −0.026972 − 1.111890I
a = 0.25218 + 1.81916I
b = −0.913965 + 0.993863I
−2.35849 − 1.91634I 0
u = −0.101098 + 1.112320I
a = 0.747997 − 1.118490I
b = 1.92440 − 0.61397I
− 3.38648I 0
u = −0.101098 − 1.112320I
a = 0.747997 + 1.118490I
b = 1.92440 + 0.61397I
3.38648I 0
u = 0.830377 + 0.295226I
a = 0.534674 + 0.299283I
b = 0.997971 − 0.739870I
7.09688 − 7.79945I 0
u = 0.830377 − 0.295226I
a = 0.534674 − 0.299283I
b = 0.997971 + 0.739870I
7.09688 + 7.79945I 0
u = 0.677700 + 0.890752I
a = 0.315340 − 0.670034I
b = −0.069785 + 0.255534I
2.35849 + 1.91634I 0
u = 0.677700 − 0.890752I
a = 0.315340 + 0.670034I
b = −0.069785 − 0.255534I
2.35849 − 1.91634I 0
u = 0.023366 + 0.878538I
a = −0.844146 + 0.914953I
b = −0.042200 + 0.652552I
−1.21414 − 1.52821I 0
u = 0.023366 − 0.878538I
a = −0.844146 − 0.914953I
b = −0.042200 − 0.652552I
−1.21414 + 1.52821I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.470352 + 1.021550I
a = −0.817745 + 0.675912I
b = −0.352475 + 1.104280I
−0.557762 − 0.871550I 0
u = 0.470352 − 1.021550I
a = −0.817745 − 0.675912I
b = −0.352475 − 1.104280I
−0.557762 + 0.871550I 0
u = 0.114042 + 0.860315I
a = 1.72126 + 1.60013I
b = 0.335767 + 0.247262I
4.26370 + 5.24171I 0
u = 0.114042 − 0.860315I
a = 1.72126 − 1.60013I
b = 0.335767 − 0.247262I
4.26370 − 5.24171I 0
u = 1.124160 + 0.135421I
a = 0.0183299 + 0.1167330I
b = 0.897822 + 0.718916I
9.56721I 0
u = 1.124160 − 0.135421I
a = 0.0183299 − 0.1167330I
b = 0.897822 − 0.718916I
− 9.56721I 0
u = 1.134820 + 0.012898I
a = 0.145238 − 0.137047I
b = −0.800713 + 0.819560I
4.74657 − 5.78864I 0
u = 1.134820 − 0.012898I
a = 0.145238 + 0.137047I
b = −0.800713 − 0.819560I
4.74657 + 5.78864I 0
u = 0.211037 + 1.122750I
a = 0.78851 + 1.92789I
b = 0.059339 + 0.307011I
−3.57396 + 6.11171I 0
u = 0.211037 − 1.122750I
a = 0.78851 − 1.92789I
b = 0.059339 − 0.307011I
−3.57396 − 6.11171I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.001013 + 1.148490I
a = −0.98183 + 2.37273I
b = −1.50663 + 2.73217I
1.35989I 0
u = −0.001013 − 1.148490I
a = −0.98183 − 2.37273I
b = −1.50663 − 2.73217I
− 1.35989I 0
u = −0.808811 + 0.251963I
a = −0.374053 − 0.160347I
b = 0.972817 + 0.672275I
5.82720 + 2.39611I 0
u = −0.808811 − 0.251963I
a = −0.374053 + 0.160347I
b = 0.972817 − 0.672275I
5.82720 − 2.39611I 0
u = −1.140450 + 0.185524I
a = −0.1273220 + 0.0056730I
b = 0.757413 − 0.581272I
1.72222 − 4.16466I 0
u = −1.140450 − 0.185524I
a = −0.1273220 − 0.0056730I
b = 0.757413 + 0.581272I
1.72222 + 4.16466I 0
u = 0.148981 + 1.152230I
a = −0.03835 − 2.55744I
b = −0.161877 − 1.346620I
−3.48356 + 4.14986I 0
u = 0.148981 − 1.152230I
a = −0.03835 + 2.55744I
b = −0.161877 + 1.346620I
−3.48356 − 4.14986I 0
u = 0.066521 + 1.167430I
a = −1.20052 + 2.06543I
b = 0.574828 + 0.697169I
0.34239 + 9.94779I 0
u = 0.066521 − 1.167430I
a = −1.20052 − 2.06543I
b = 0.574828 − 0.697169I
0.34239 − 9.94779I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.139493 + 1.165120I
a = 1.03445 − 1.79000I
b = 1.37499 − 1.73173I
−4.74657 + 5.78864I 0
u = 0.139493 − 1.165120I
a = 1.03445 + 1.79000I
b = 1.37499 + 1.73173I
−4.74657 − 5.78864I 0
u = −1.168010 + 0.123906I
a = 0.0472676 + 0.0869947I
b = −0.932006 + 0.765765I
4.8150 − 15.2799I 0
u = −1.168010 − 0.123906I
a = 0.0472676 − 0.0869947I
b = −0.932006 − 0.765765I
4.8150 + 15.2799I 0
u = −0.444112 + 1.106260I
a = −0.248358 − 1.101280I
b = 1.100570 − 0.726079I
2.54244 − 6.02885I 0
u = −0.444112 − 1.106260I
a = −0.248358 + 1.101280I
b = 1.100570 + 0.726079I
2.54244 + 6.02885I 0
u = 0.369330 + 1.135860I
a = 0.38784 + 1.87651I
b = 1.15621 + 1.18315I
5.28153 − 0.05412I 0
u = 0.369330 − 1.135860I
a = 0.38784 − 1.87651I
b = 1.15621 − 1.18315I
5.28153 + 0.05412I 0
u = 0.421997 + 1.117810I
a = 0.14744 + 1.88223I
b = 1.19242 + 1.46359I
4.55064 + 12.36270I 0
u = 0.421997 − 1.117810I
a = 0.14744 − 1.88223I
b = 1.19242 − 1.46359I
4.55064 − 12.36270I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.086297 + 1.207990I
a = 0.091655 + 1.206830I
b = 0.786546 + 1.005650I
−4.06814 − 2.11224I 0
u = −0.086297 − 1.207990I
a = 0.091655 − 1.206830I
b = 0.786546 − 1.005650I
−4.06814 + 2.11224I 0
u = −0.015094 + 1.211720I
a = 0.52307 + 2.43209I
b = −0.290438 + 0.909069I
−5.50478 − 3.73249I 0
u = −0.015094 − 1.211720I
a = 0.52307 − 2.43209I
b = −0.290438 − 0.909069I
−5.50478 + 3.73249I 0
u = 0.197595 + 1.201170I
a = 0.612317 + 0.083975I
b = −0.634411 − 0.166502I
−2.54244 + 6.02885I 0
u = 0.197595 − 1.201170I
a = 0.612317 − 0.083975I
b = −0.634411 + 0.166502I
−2.54244 − 6.02885I 0
u = −0.414859 + 1.144780I
a = −0.21956 − 1.83248I
b = 0.964642 − 0.861682I
3.06057 − 6.86382I 0
u = −0.414859 − 1.144780I
a = −0.21956 + 1.83248I
b = 0.964642 + 0.861682I
3.06057 + 6.86382I 0
u = −0.548999 + 0.556766I
a = 1.63812 − 0.27825I
b = −0.893248 − 0.015748I
3.68925 + 7.20981I 0
u = −0.548999 − 0.556766I
a = 1.63812 + 0.27825I
b = −0.893248 + 0.015748I
3.68925 − 7.20981I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.559022 + 1.082950I
a = −0.452200 + 0.415093I
b = −0.902520 + 0.318618I
0.94606 − 3.28550I 0
u = −0.559022 − 1.082950I
a = −0.452200 − 0.415093I
b = −0.902520 − 0.318618I
0.94606 + 3.28550I 0
u = 1.192480 + 0.266165I
a = −0.151171 + 0.149246I
b = 0.182895 + 0.569084I
−2.95882 − 1.25298I 0
u = 1.192480 − 0.266165I
a = −0.151171 − 0.149246I
b = 0.182895 − 0.569084I
−2.95882 + 1.25298I 0
u = −0.165655 + 1.212300I
a = −0.87511 − 1.65535I
b = −1.24141 − 1.76725I
−0.48745 − 11.58140I 0
u = −0.165655 − 1.212300I
a = −0.87511 + 1.65535I
b = −1.24141 + 1.76725I
−0.48745 + 11.58140I 0
u = −0.443321 + 1.140980I
a = −0.23601 + 1.75950I
b = −1.07486 + 1.34830I
−0.02143 − 6.02789I 0
u = −0.443321 − 1.140980I
a = −0.23601 − 1.75950I
b = −1.07486 − 1.34830I
−0.02143 + 6.02789I 0
u = −0.739507 + 0.139480I
a = 0.665418 + 0.752387I
b = −0.539133 + 0.873326I
2.54480 − 3.04371I 0
u = −0.739507 − 0.139480I
a = 0.665418 − 0.752387I
b = −0.539133 − 0.873326I
2.54480 + 3.04371I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.719017 + 0.214989I
a = 0.242930 + 0.222080I
b = 1.195860 − 0.504125I
8.09100 + 4.09197I 0
u = 0.719017 − 0.214989I
a = 0.242930 − 0.222080I
b = 1.195860 + 0.504125I
8.09100 − 4.09197I 0
u = −0.008982 + 1.252700I
a = −0.01572 + 1.70264I
b = 0.52790 + 1.35832I
−4.91221 − 2.00569I 0
u = −0.008982 − 1.252700I
a = −0.01572 − 1.70264I
b = 0.52790 − 1.35832I
−4.91221 + 2.00569I 0
u = −0.050191 + 1.253150I
a = −0.31549 + 2.02079I
b = −0.52038 + 1.58277I
−5.16399 − 2.60014I 0
u = −0.050191 − 1.253150I
a = −0.31549 − 2.02079I
b = −0.52038 − 1.58277I
−5.16399 + 2.60014I 0
u = 0.014996 + 1.259280I
a = 0.901178 − 0.728416I
b = 1.65392 − 0.62982I
−5.82720 − 2.39611I 0
u = 0.014996 − 1.259280I
a = 0.901178 + 0.728416I
b = 1.65392 + 0.62982I
−5.82720 + 2.39611I 0
u = −0.028980 + 1.259110I
a = −1.225120 − 0.576085I
b = 0.134720 − 0.176441I
−5.06643 − 0.78586I 0
u = −0.028980 − 1.259110I
a = −1.225120 + 0.576085I
b = 0.134720 + 0.176441I
−5.06643 + 0.78586I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.644260 + 0.328994I
a = −0.429477 + 0.062215I
b = −0.536507 + 0.346434I
1.21414 − 1.52821I 0
u = −0.644260 − 0.328994I
a = −0.429477 − 0.062215I
b = −0.536507 − 0.346434I
1.21414 + 1.52821I 0
u = 1.208800 + 0.427166I
a = 0.140690 − 0.134710I
b = −0.914320 − 0.303691I
5.50478 + 3.73249I 0
u = 1.208800 − 0.427166I
a = 0.140690 + 0.134710I
b = −0.914320 + 0.303691I
5.50478 − 3.73249I 0
u = −1.316070 + 0.026205I
a = 0.1041590 − 0.0131460I
b = 0.147484 + 0.679159I
0.02143 + 6.02789I 0
u = −1.316070 − 0.026205I
a = 0.1041590 + 0.0131460I
b = 0.147484 − 0.679159I
0.02143 − 6.02789I 0
u = 0.647711 + 0.147955I
a = 0.320722 − 0.012185I
b = −1.007320 − 0.709967I
1.10536 + 3.47391I 0
u = 0.647711 − 0.147955I
a = 0.320722 + 0.012185I
b = −1.007320 + 0.709967I
1.10536 − 3.47391I 0
u = 0.105534 + 1.332540I
a = −0.594468 − 0.813288I
b = −1.52657 − 0.75402I
−3.06057 + 6.86382I 0
u = 0.105534 − 1.332540I
a = −0.594468 + 0.813288I
b = −1.52657 + 0.75402I
−3.06057 − 6.86382I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.427825 + 1.316160I
a = 0.38324 + 1.66999I
b = −0.706144 + 0.915701I
−1.82065 − 7.38526I 0
u = −0.427825 − 1.316160I
a = 0.38324 − 1.66999I
b = −0.706144 − 0.915701I
−1.82065 + 7.38526I 0
u = 0.156943 + 1.389100I
a = −0.102336 + 0.952588I
b = 0.123164 + 1.245690I
−0.714090 − 0.355524I 0
u = 0.156943 − 1.389100I
a = −0.102336 − 0.952588I
b = 0.123164 − 1.245690I
−0.714090 + 0.355524I 0
u = 0.339218 + 1.364040I
a = −0.34615 − 1.73098I
b = −1.19913 − 1.23564I
−3.68925 + 7.20981I 0
u = 0.339218 − 1.364040I
a = −0.34615 + 1.73098I
b = −1.19913 + 1.23564I
−3.68925 − 7.20981I 0
u = 0.262923 + 1.386140I
a = 0.20141 + 1.42447I
b = 0.332413 + 1.243570I
−4.15953 + 4.46103I 0
u = 0.262923 − 1.386140I
a = 0.20141 − 1.42447I
b = 0.332413 − 1.243570I
−4.15953 − 4.46103I 0
u = 0.267050 + 0.498176I
a = −2.04798 − 1.18116I
b = −1.130150 + 0.267801I
− 0.970114I 0
u = 0.267050 − 0.498176I
a = −2.04798 + 1.18116I
b = −1.130150 − 0.267801I
0.970114I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.60222 + 1.31257I
a = −0.370011 − 0.381225I
b = 0.214141 − 0.318884I
−0.94606 − 3.28550I 0
u = −0.60222 − 1.31257I
a = −0.370011 + 0.381225I
b = 0.214141 + 0.318884I
−0.94606 + 3.28550I 0
u = −0.33879 + 1.41609I
a = −0.214566 + 1.351230I
b = −0.688245 + 1.199240I
−4.26370 − 5.24171I 0
u = −0.33879 − 1.41609I
a = −0.214566 − 1.351230I
b = −0.688245 − 1.199240I
−4.26370 + 5.24171I 0
u = 0.52718 + 1.35767I
a = 0.05036 − 1.46286I
b = −1.19936 − 1.17419I
0.48745 + 11.58140I 0
u = 0.52718 − 1.35767I
a = 0.05036 + 1.46286I
b = −1.19936 + 1.17419I
0.48745 − 11.58140I 0
u = 0.45386 + 1.38998I
a = −0.188177 + 1.242670I
b = 0.742091 + 1.006080I
−8.09100 + 4.09197I 0
u = 0.45386 − 1.38998I
a = −0.188177 − 1.242670I
b = 0.742091 − 1.006080I
−8.09100 − 4.09197I 0
u = −0.49574 + 1.38277I
a = −0.09816 + 1.70669I
b = −0.94267 + 1.16304I
−0.88974 − 8.03757I 0
u = −0.49574 − 1.38277I
a = −0.09816 − 1.70669I
b = −0.94267 − 1.16304I
−0.88974 + 8.03757I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.374110 + 0.371732I
a = −0.07462 − 1.91563I
b = 0.226157 + 0.583762I
4.06814 + 2.11224I 5.75687 + 0.I
u = −0.374110 − 0.371732I
a = −0.07462 + 1.91563I
b = 0.226157 − 0.583762I
4.06814 − 2.11224I 5.75687 + 0.I
u = 0.439715 + 0.258267I
a = −1.39236 − 1.43175I
b = 0.792387 − 0.176904I
−1.10536 − 3.47391I 0. + 6.63568I
u = 0.439715 − 0.258267I
a = −1.39236 + 1.43175I
b = 0.792387 + 0.176904I
−1.10536 + 3.47391I 0. − 6.63568I
u = 0.50475 + 1.40586I
a = 0.10336 + 1.56038I
b = 1.11989 + 1.18585I
−4.8150 + 15.2799I 0
u = 0.50475 − 1.40586I
a = 0.10336 − 1.56038I
b = 1.11989 − 1.18585I
−4.8150 − 15.2799I 0
u = −0.49566 + 1.41952I
a = 0.097768 − 1.335680I
b = 1.12721 − 1.05527I
−3.27302 − 9.87260I 0
u = −0.49566 − 1.41952I
a = 0.097768 + 1.335680I
b = 1.12721 + 1.05527I
−3.27302 + 9.87260I 0
u = −0.52336 + 1.41547I
a = −0.07947 + 1.53199I
b = −1.19266 + 1.16794I
− 21.1926I 0
u = −0.52336 − 1.41547I
a = −0.07947 − 1.53199I
b = −1.19266 − 1.16794I
21.1926I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.032323 + 0.488210I
a = 2.09768 − 1.19956I
b = 0.878672 + 0.483440I
1.86863 + 2.42778I −1.84148 − 3.18567I
u = −0.032323 − 0.488210I
a = 2.09768 + 1.19956I
b = 0.878672 − 0.483440I
1.86863 − 2.42778I −1.84148 + 3.18567I
u = −0.55103 + 1.41142I
a = −0.180781 − 1.213010I
b = 0.71543 − 1.26675I
−4.55064 − 12.36270I 0
u = −0.55103 − 1.41142I
a = −0.180781 + 1.213010I
b = 0.71543 + 1.26675I
−4.55064 + 12.36270I 0
u = −0.45405 + 1.44835I
a = 0.153871 + 1.082070I
b = −0.727446 + 1.088470I
−5.28153 − 0.05412I 0
u = −0.45405 − 1.44835I
a = 0.153871 − 1.082070I
b = −0.727446 − 1.088470I
−5.28153 + 0.05412I 0
u = 0.56779 + 1.40884I
a = 0.202193 − 1.078280I
b = −0.489265 − 1.074590I
−7.09688 + 7.79945I 0
u = 0.56779 − 1.40884I
a = 0.202193 + 1.078280I
b = −0.489265 + 1.074590I
−7.09688 − 7.79945I 0
u = −0.39672 + 1.48404I
a = 0.41948 − 1.35360I
b = 1.34627 − 1.05476I
−2.66927 − 10.63920I 0
u = −0.39672 − 1.48404I
a = 0.41948 + 1.35360I
b = 1.34627 + 1.05476I
−2.66927 + 10.63920I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.45381 + 1.48253I
a = 0.041830 − 0.787075I
b = 0.233612 − 0.401016I
0.02938 − 4.49255I 0
u = −0.45381 − 1.48253I
a = 0.041830 + 0.787075I
b = 0.233612 + 0.401016I
0.02938 + 4.49255I 0
u = 0.416635 + 0.116298I
a = 1.94950 + 1.60645I
b = 0.375771 − 0.649892I
1.21991 + 3.70716I 3.65613 + 0.03445I
u = 0.416635 − 0.116298I
a = 1.94950 − 1.60645I
b = 0.375771 + 0.649892I
1.21991 − 3.70716I 3.65613 − 0.03445I
u = −0.24177 + 1.55048I
a = 0.262831 − 0.656420I
b = 0.128568 − 0.352787I
−0.02938 − 4.49255I 0
u = −0.24177 − 1.55048I
a = 0.262831 + 0.656420I
b = 0.128568 + 0.352787I
−0.02938 + 4.49255I 0
u = 0.53462 + 1.50289I
a = −0.205849 − 1.097200I
b = −1.176730 − 0.764126I
−0.34239 + 9.94779I 0
u = 0.53462 − 1.50289I
a = −0.205849 + 1.097200I
b = −1.176730 + 0.764126I
−0.34239 − 9.94779I 0
u = −0.47942 + 1.55291I
a = −0.137027 + 0.541822I
b = −0.430878 + 0.587792I
−2.54480 − 3.04371I 0
u = −0.47942 − 1.55291I
a = −0.137027 − 0.541822I
b = −0.430878 − 0.587792I
−2.54480 + 3.04371I 0
20
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.030070 + 0.303397I
a = −2.28833 − 0.18563I
b = −0.214561 + 0.862499I
−0.36799 − 1.98151I −5.16189 + 2.74306I
u = 0.030070 − 0.303397I
a = −2.28833 + 0.18563I
b = −0.214561 − 0.862499I
−0.36799 + 1.98151I −5.16189 − 2.74306I
u = 0.070987 + 0.282425I
a = −2.21859 − 1.96886I
b = −0.282667 + 0.462908I
− 1.54443I 0. + 2.49541I
u = 0.070987 − 0.282425I
a = −2.21859 + 1.96886I
b = −0.282667 − 0.462908I
1.54443I 0. − 2.49541I
u = 0.184186 + 0.200419I
a = 0.521337 + 0.303755I
b = −0.515096 + 1.111330I
−0.73655 − 2.57695I 5.30271 − 12.37335I
u = 0.184186 − 0.200419I
a = 0.521337 − 0.303755I
b = −0.515096 − 1.111330I
−0.73655 + 2.57695I 5.30271 + 12.37335I
u = 0.238366 + 0.093654I
a = −2.08445 + 3.69097I
b = 0.305214 + 1.093080I
−1.72222 − 4.16466I 0.59107 + 8.58259I
u = 0.238366 − 0.093654I
a = −2.08445 − 3.69097I
b = 0.305214 − 1.093080I
−1.72222 + 4.16466I 0.59107 − 8.58259I
u = 0.29429 + 1.72670I
a = 0.494354 + 0.258175I
b = 0.706659 + 0.143277I
1.82065 + 7.38526I 0
u = 0.29429 − 1.72670I
a = 0.494354 − 0.258175I
b = 0.706659 − 0.143277I
1.82065 − 7.38526I 0
21
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.209217 + 0.094546I
a = 5.38500 − 1.28296I
b = −0.232961 − 0.990092I
3.27302 − 9.87260I 3.12672 + 6.25006I
u = −0.209217 − 0.094546I
a = 5.38500 + 1.28296I
b = −0.232961 + 0.990092I
3.27302 + 9.87260I 3.12672 − 6.25006I
u = 0.72701 + 1.73189I
a = 0.172316 − 0.211777I
b = −0.002081 − 0.350660I
−3.81603 − 2.52639I 0
u = 0.72701 − 1.73189I
a = 0.172316 + 0.211777I
b = −0.002081 + 0.350660I
−3.81603 + 2.52639I 0
u = −0.88272 + 1.73528I
a = −0.204733 − 0.123162I
b = −0.150904 − 0.386644I
0.88974 + 8.03757I 0
u = −0.88272 − 1.73528I
a = −0.204733 + 0.123162I
b = −0.150904 + 0.386644I
0.88974 − 8.03757I 0
22
II. I
u
2
= h−1.39 × 10
28
u
33
+ 3.61 × 10
28
u
32
+ · · · + 5.54 × 10
28
b + 8.01 ×
10
28
, −1.76 × 10
28
u
33
+ 3.91 × 10
28
u
32
+ · · · + 5.54 × 10
28
a − 1.16 ×
10
29
, u
34
+ 16u
32
+ · · · − 15u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
0.316924u
33
− 0.704935u
32
+ ··· + 28.6854u + 2.08546
0.251234u
33
− 0.651588u
32
+ ··· + 22.8146u − 1.44577
a
7
=
1
−u
2
a
8
=
−0.174289u
33
+ 0.164040u
32
+ ··· − 87.3641u + 8.28947
0.0449191u
33
− 0.223032u
32
+ ··· − 16.9296u + 2.43340
a
2
=
0.0656905u
33
− 0.0533476u
32
+ ··· + 5.87079u + 3.53123
0.251234u
33
− 0.651588u
32
+ ··· + 22.8146u − 1.44577
a
12
=
0.264624u
33
− 0.262932u
32
+ ··· + 23.8016u − 0.723715
0.440644u
33
− 0.261551u
32
+ ··· + 8.00456u − 0.743691
a
5
=
−0.212521u
33
− 0.427199u
32
+ ··· − 15.9889u + 3.07893
−0.471540u
33
+ 0.721229u
32
+ ··· − 2.02843u + 0.408987
a
10
=
−u
u
3
+ u
a
4
=
0.165795u
33
− 0.184854u
32
+ ··· + 22.9426u + 2.44271
0.0902815u
33
− 0.463733u
32
+ ··· + 20.6050u − 1.28295
a
1
=
1.38205u
33
+ 0.383365u
32
+ ··· + 82.0387u − 9.45750
0.504970u
33
− 0.128524u
32
+ ··· + 11.6023u − 2.31824
a
9
=
−0.599362u
33
+ 0.0651587u
32
+ ··· − 60.5899u + 5.36567
−0.674433u
33
− 0.538611u
32
+ ··· − 6.37148u + 1.47113
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2.11866u
33
+ 1.35178u
32
+ ··· − 230.782u + 15.7346
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
34
− 7u
33
+ ··· + u + 3
c
2
4(4u
34
+ 18u
33
+ ··· − 5u + 1)
c
3
4(4u
34
+ 14u
33
+ ··· − 17u + 9)
c
4
, c
10
u
34
+ 16u
32
+ ··· + 15u + 1
c
5
4(4u
34
− 14u
33
+ ··· + 17u + 9)
c
6
, c
8
u
34
+ 16u
32
+ ··· − 15u + 1
c
7
u
34
+ 2u
33
+ ··· − 352u + 64
c
9
4(4u
34
− 18u
33
+ ··· + 5u + 1)
c
11
u
34
+ 7u
33
+ ··· − u + 3
c
12
u
34
− 2u
33
+ ··· + 352u + 64
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
34
− 7y
33
+ ··· − 103y + 9
c
2
, c
9
16(16y
34
+ 68y
33
+ ··· + y + 1)
c
3
, c
5
16(16y
34
+ 468y
33
+ ··· + 1925y + 81)
c
4
, c
6
, c
8
c
10
y
34
+ 32y
33
+ ··· − 53y + 1
c
7
, c
12
y
34
+ 26y
33
+ ··· + 17408y + 4096
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.007360 + 0.122162I
a = −0.080049 − 0.345633I
b = 0.874443 − 0.622040I
3.54342 − 2.55169I −0.56417 + 6.84796I
u = −1.007360 − 0.122162I
a = −0.080049 + 0.345633I
b = 0.874443 + 0.622040I
3.54342 + 2.55169I −0.56417 − 6.84796I
u = −0.206243 + 0.996810I
a = 0.99115 + 2.79678I
b = −0.136293 + 0.876696I
1.94369 − 10.56810I −2.94445 + 9.61134I
u = −0.206243 − 0.996810I
a = 0.99115 − 2.79678I
b = −0.136293 − 0.876696I
1.94369 + 10.56810I −2.94445 − 9.61134I
u = 0.832411 + 0.698054I
a = 0.857133 − 0.314389I
b = −0.814595 − 0.117293I
4.30044 + 3.15824I 4.28303 − 3.19970I
u = 0.832411 − 0.698054I
a = 0.857133 + 0.314389I
b = −0.814595 + 0.117293I
4.30044 − 3.15824I 4.28303 + 3.19970I
u = 1.042800 + 0.342130I
a = 0.286450 + 0.016933I
b = −0.859567 − 0.626056I
3.90273 + 5.14015I 3.47152 − 6.22803I
u = 1.042800 − 0.342130I
a = 0.286450 − 0.016933I
b = −0.859567 + 0.626056I
3.90273 − 5.14015I 3.47152 + 6.22803I
u = 0.138397 + 1.100230I
a = −0.20443 + 2.26647I
b = −0.504123 + 1.141290I
−3.90273 + 5.14015I −3.47152 − 6.22803I
u = 0.138397 − 1.100230I
a = −0.20443 − 2.26647I
b = −0.504123 − 1.141290I
−3.90273 − 5.14015I −3.47152 + 6.22803I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.565368 + 0.668168I
a = −1.190060 − 0.195474I
b = 0.676619 − 0.319952I
0.82148 − 2.82425I 5.9302 + 16.2452I
u = −0.565368 − 0.668168I
a = −1.190060 + 0.195474I
b = 0.676619 + 0.319952I
0.82148 + 2.82425I 5.9302 − 16.2452I
u = −0.035377 + 1.189750I
a = 0.93500 + 1.62049I
b = 1.35892 + 1.93635I
− 1.21174I 0. − 10.06752I
u = −0.035377 − 1.189750I
a = 0.93500 − 1.62049I
b = 1.35892 − 1.93635I
1.21174I 0. + 10.06752I
u = −0.053628 + 1.214490I
a = 0.04564 − 2.37578I
b = 0.56540 − 1.36944I
−4.30044 − 3.15824I −4.28303 + 3.19970I
u = −0.053628 − 1.214490I
a = 0.04564 + 2.37578I
b = 0.56540 + 1.36944I
−4.30044 + 3.15824I −4.28303 − 3.19970I
u = −0.126448 + 0.677789I
a = 2.65054 − 0.36149I
b = 1.66659 + 0.41329I
1.22010I 0. − 26.1084I
u = −0.126448 − 0.677789I
a = 2.65054 + 0.36149I
b = 1.66659 − 0.41329I
− 1.22010I 0. + 26.1084I
u = 0.275465 + 1.350330I
a = 0.20645 + 1.59949I
b = 0.534402 + 1.273060I
−5.33925 + 4.90638I −9.92127 − 5.06834I
u = 0.275465 − 1.350330I
a = 0.20645 − 1.59949I
b = 0.534402 − 1.273060I
−5.33925 − 4.90638I −9.92127 + 5.06834I
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.165933 + 0.520579I
a = 2.19236 + 1.06552I
b = −0.872873 − 0.146099I
5.33925 + 4.90638I 9.92127 − 5.06834I
u = 0.165933 − 0.520579I
a = 2.19236 − 1.06552I
b = −0.872873 + 0.146099I
5.33925 − 4.90638I 9.92127 + 5.06834I
u = −0.48249 + 1.37897I
a = 0.02302 − 1.60386I
b = 0.94038 − 1.06608I
−1.12576 − 7.88778I −6.71072 + 5.79695I
u = −0.48249 − 1.37897I
a = 0.02302 + 1.60386I
b = 0.94038 + 1.06608I
−1.12576 + 7.88778I −6.71072 − 5.79695I
u = 0.37311 + 1.48298I
a = −0.121460 + 0.239187I
b = −0.301139 − 0.019952I
−3.54342 − 2.55169I 0
u = 0.37311 − 1.48298I
a = −0.121460 − 0.239187I
b = −0.301139 + 0.019952I
−3.54342 + 2.55169I 0
u = 0.46619 + 1.49286I
a = −0.273131 − 1.199730I
b = −1.24025 − 0.98229I
−1.94369 + 10.56810I 0
u = 0.46619 − 1.49286I
a = −0.273131 + 1.199730I
b = −1.24025 + 0.98229I
−1.94369 − 10.56810I 0
u = −0.46978 + 1.57404I
a = −0.029144 + 0.179167I
b = 0.105266 − 0.219423I
1.12576 + 7.88778I 0
u = −0.46978 − 1.57404I
a = −0.029144 − 0.179167I
b = 0.105266 + 0.219423I
1.12576 − 7.88778I 0
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.44287 + 1.67050I
a = −0.060407 + 0.596856I
b = −0.219789 + 0.403786I
− 4.69367I 0
u = −0.44287 − 1.67050I
a = −0.060407 − 0.596856I
b = −0.219789 − 0.403786I
4.69367I 0
u = 0.0952517 + 0.0594354I
a = 4.52094 + 1.38019I
b = 0.476613 + 1.047310I
−0.82148 + 2.82425I −5.9302 − 16.2452I
u = 0.0952517 − 0.0594354I
a = 4.52094 − 1.38019I
b = 0.476613 − 1.047310I
−0.82148 − 2.82425I −5.9302 + 16.2452I
29
III. I
u
3
= hb + u, a + u + 1, u
2
+ u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
−u − 1
−u
a
7
=
1
u + 1
a
8
=
1
u + 1
a
2
=
−1
−u
a
12
=
u
−1
a
5
=
u + 1
−1
a
10
=
−u
u + 1
a
4
=
−1
−2u − 1
a
1
=
u
−1
a
9
=
−u + 1
2u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u + 4
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
9
c
10
u
2
− u + 1
c
2
, c
6
, c
8
c
11
u
2
+ u + 1
c
3
(u − 1)
2
c
5
(u + 1)
2
c
7
, c
12
u
2
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
8
, c
9
c
10
, c
11
y
2
+ y + 1
c
3
, c
5
(y −1)
2
c
7
, c
12
y
2
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −0.500000 − 0.866025I
b = 0.500000 − 0.866025I
− 4.05977I 0. + 6.92820I
u = −0.500000 − 0.866025I
a = −0.500000 + 0.866025I
b = 0.500000 + 0.866025I
4.05977I 0. − 6.92820I
33
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)(u
34
− 7u
33
+ ··· + u + 3)
· (u
176
+ 7u
175
+ ··· + 69156u + 17323)
c
2
16(u
2
+ u + 1)(4u
34
+ 18u
33
+ ··· − 5u + 1)
· (4u
176
− 42u
175
+ ··· + 4u + 3)
c
3
16(u − 1)
2
(4u
34
+ 14u
33
+ ··· − 17u + 9)
· (4u
176
+ 18u
175
+ ··· + 1692960025u + 102369073)
c
4
(u
2
− u + 1)(u
34
+ 16u
32
+ ··· + 15u + 1)
· (u
176
+ 6u
175
+ ··· − 5650u + 939)
c
5
16(u + 1)
2
(4u
34
− 14u
33
+ ··· + 17u + 9)
· (4u
176
− 18u
175
+ ··· − 1692960025u + 102369073)
c
6
(u
2
+ u + 1)(u
34
+ 16u
32
+ ··· − 15u + 1)
· (u
176
− 6u
175
+ ··· + 5650u + 939)
c
7
u
2
(u
34
+ 2u
33
+ ··· − 352u + 64)
· (u
176
+ u
175
+ ··· − 12001832u + 1637744)
c
8
(u
2
+ u + 1)(u
34
+ 16u
32
+ ··· − 15u + 1)
· (u
176
+ 6u
175
+ ··· − 5650u + 939)
c
9
16(u
2
− u + 1)(4u
34
− 18u
33
+ ··· + 5u + 1)
· (4u
176
+ 42u
175
+ ··· − 4u + 3)
c
10
(u
2
− u + 1)(u
34
+ 16u
32
+ ··· + 15u + 1)
· (u
176
− 6u
175
+ ··· + 5650u + 939)
c
11
(u
2
+ u + 1)(u
34
+ 7u
33
+ ··· − u + 3)
· (u
176
− 7u
175
+ ··· − 69156u + 17323)
c
12
u
2
(u
34
− 2u
33
+ ··· + 352u + 64)
· (u
176
− u
175
+ ··· + 12001832u + 1637744)
34
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
(y
2
+ y + 1)(y
34
− 7y
33
+ ··· − 103y + 9)
· (y
176
+ 11y
175
+ ··· + 18368043448y + 300086329)
c
2
, c
9
256(y
2
+ y + 1)(16y
34
+ 68y
33
+ ··· + y + 1)
· (16y
176
+ 164y
175
+ ··· + 632y + 9)
c
3
, c
5
256(y −1)
2
(16y
34
+ 468y
33
+ ··· + 1925y + 81)
· (16y
176
+ 1348y
175
+ ··· + 6.24 × 10
17
y + 1.05 × 10
16
)
c
4
, c
6
, c
8
c
10
(y
2
+ y + 1)(y
34
+ 32y
33
+ ··· − 53y + 1)
· (y
176
+ 134y
175
+ ··· + 23450330y + 881721)
c
7
, c
12
y
2
(y
34
+ 26y
33
+ ··· + 17408y + 4096)
· (y
176
+ 51y
175
+ ··· + 119113228533312y + 2682205409536)
35
