12a
0091
(K12a
0091
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 10 11 4 7 12 1 9 6
Solving Sequence
4,7
8
9,11
12 10 3 6 1 5 2
c
7
c
8
c
11
c
9
c
3
c
6
c
12
c
5
c
2
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.40905 × 10
271
u
117
− 3.19731 × 10
271
u
116
+ ··· + 1.57559 × 10
272
b − 8.05247 × 10
272
,
1.79454 × 10
272
u
117
− 3.91278 × 10
272
u
116
+ ··· + 3.15118 × 10
272
a − 5.43779 × 10
273
,
u
118
− 2u
117
+ ··· − 160u + 32i
I
u
2
= h−2u
2
+ b − u − 3, −5u
2
+ a − 2u − 9, u
3
+ u
2
+ 2u + 1i
I
v
1
= ha, v
4
+ 12v
3
+ 24v
2
+ 29b + 21v + 45, v
5
+ 3v
4
+ 3v
3
+ 8v
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
= h1.41 × 10
271
u
117
− 3.20 × 10
271
u
116
+ · · · + 1.58 × 10
272
b − 8.05 ×
10
272
, 1.79 × 10
272
u
117
− 3.91 × 10
272
u
116
+ · · · + 3.15 × 10
272
a − 5.44 ×
10
273
, u
118
− 2u
117
+ · · · − 160u + 32i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
9
=
u
2
+ 1
u
2
a
11
=
−0.569481u
117
+ 1.24169u
116
+ ··· − 133.388u + 17.2564
−0.0894301u
117
+ 0.202928u
116
+ ··· − 39.7435u + 5.11076
a
12
=
−0.373615u
117
+ 0.817065u
116
+ ··· − 78.1427u + 10.4088
−0.160556u
117
+ 0.336670u
116
+ ··· − 52.1880u + 5.89092
a
10
=
−0.255516u
117
+ 0.458821u
116
+ ··· − 5.26560u − 0.632464
0.187447u
117
− 0.419386u
116
+ ··· + 67.1265u − 6.07320
a
3
=
u
u
3
+ u
a
6
=
−0.321859u
117
+ 0.588545u
116
+ ··· − 26.5015u − 3.74902
−0.120061u
117
+ 0.303595u
116
+ ··· − 65.4915u + 7.49794
a
1
=
−0.381325u
117
+ 0.734164u
116
+ ··· − 16.2430u − 2.30564
−0.0732515u
117
+ 0.0465062u
116
+ ··· + 69.4204u − 15.1813
a
5
=
−0.161618u
117
+ 0.417138u
116
+ ··· − 78.0186u + 13.7872
0.219707u
117
− 0.317027u
116
+ ··· − 61.7756u + 16.0928
a
2
=
−0.305156u
117
+ 0.565775u
116
+ ··· + 3.95305u − 5.31050
−0.0281133u
117
− 0.0595301u
116
+ ··· + 84.6108u − 17.6725
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.287760u
117
− 0.227055u
116
+ ··· − 36.3944u + 24.9413
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
118
+ 65u
117
+ ··· + 172u + 1
c
2
, c
4
u
118
− 7u
117
+ ··· − 2u + 1
c
3
, c
7
u
118
+ 2u
117
+ ··· + 160u + 32
c
5
u
118
+ 67u
116
+ ··· + 196401u + 29189
c
6
u
118
+ 4u
117
+ ··· + 8634757u + 591517
c
8
u
118
− 36u
117
+ ··· − 20992u + 1024
c
9
, c
11
u
118
− 5u
117
+ ··· + 143u − 1
c
10
u
118
+ 20u
117
+ ··· + 156u + 8
c
12
u
118
− 9u
117
+ ··· + 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
118
− 17y
117
+ ··· − 21024y + 1
c
2
, c
4
y
118
− 65y
117
+ ··· − 172y + 1
c
3
, c
7
y
118
+ 36y
117
+ ··· + 20992y + 1024
c
5
y
118
+ 134y
117
+ ··· + 56845137931y + 851997721
c
6
y
118
+ 46y
117
+ ··· − 9372454336793y + 349892361289
c
8
y
118
+ 84y
117
+ ··· − 237633536y + 1048576
c
9
, c
11
y
118
− 91y
117
+ ··· − 21455y + 1
c
10
y
118
+ 24y
117
+ ··· − 6288y + 64
c
12
y
118
− 25y
117
+ ··· − 26y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.728017 + 0.694463I
a = 1.47342 + 0.86530I
b = 0.767924 + 0.400602I
−1.43969 − 2.21556I 0
u = −0.728017 − 0.694463I
a = 1.47342 − 0.86530I
b = 0.767924 − 0.400602I
−1.43969 + 2.21556I 0
u = 0.619537 + 0.765048I
a = 1.78016 + 0.17358I
b = 0.818692 + 0.835076I
−1.23232 − 1.59626I 0
u = 0.619537 − 0.765048I
a = 1.78016 − 0.17358I
b = 0.818692 − 0.835076I
−1.23232 + 1.59626I 0
u = −0.298455 + 0.934841I
a = 0.29656 − 1.43402I
b = −0.263877 + 0.281634I
−1.47083 + 5.17351I 0
u = −0.298455 − 0.934841I
a = 0.29656 + 1.43402I
b = −0.263877 − 0.281634I
−1.47083 − 5.17351I 0
u = 0.198124 + 0.953787I
a = −0.264398 + 0.390388I
b = 0.12045 − 2.76563I
0.04031 − 2.55048I 0
u = 0.198124 − 0.953787I
a = −0.264398 − 0.390388I
b = 0.12045 + 2.76563I
0.04031 + 2.55048I 0
u = −0.068591 + 0.971611I
a = −1.225790 + 0.651510I
b = 0.974512 − 0.440905I
−5.08436 + 4.73741I 0
u = −0.068591 − 0.971611I
a = −1.225790 − 0.651510I
b = 0.974512 + 0.440905I
−5.08436 − 4.73741I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.031110 + 0.197972I
a = −0.688682 − 0.721892I
b = −0.985148 − 0.601427I
−3.61891 − 7.05319I 0
u = −1.031110 − 0.197972I
a = −0.688682 + 0.721892I
b = −0.985148 + 0.601427I
−3.61891 + 7.05319I 0
u = 1.050710 + 0.063861I
a = −0.544435 − 0.438588I
b = −0.843272 − 0.325269I
−3.31472 − 2.51883I 0
u = 1.050710 − 0.063861I
a = −0.544435 + 0.438588I
b = −0.843272 + 0.325269I
−3.31472 + 2.51883I 0
u = −0.272135 + 1.025000I
a = 0.308053 + 0.319914I
b = −0.256239 − 0.968837I
3.78308 + 0.01802I 0
u = −0.272135 − 1.025000I
a = 0.308053 − 0.319914I
b = −0.256239 + 0.968837I
3.78308 − 0.01802I 0
u = −0.735517 + 0.778817I
a = −0.61695 − 1.66149I
b = −0.955699 − 0.607070I
−4.73869 − 0.40842I 0
u = −0.735517 − 0.778817I
a = −0.61695 + 1.66149I
b = −0.955699 + 0.607070I
−4.73869 + 0.40842I 0
u = 0.107153 + 1.069730I
a = −0.597452 + 0.680996I
b = −0.573835 − 0.928627I
4.36870 − 2.02817I 0
u = 0.107153 − 1.069730I
a = −0.597452 − 0.680996I
b = −0.573835 + 0.928627I
4.36870 + 2.02817I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.781234 + 0.740647I
a = −0.934177 − 0.255699I
b = −1.238870 − 0.360891I
−10.10770 + 4.91047I 0
u = −0.781234 − 0.740647I
a = −0.934177 + 0.255699I
b = −1.238870 + 0.360891I
−10.10770 − 4.91047I 0
u = 0.073380 + 0.920134I
a = 1.340470 − 0.353995I
b = 0.22772 + 2.02067I
0.35506 − 1.51453I 0
u = 0.073380 − 0.920134I
a = 1.340470 + 0.353995I
b = 0.22772 − 2.02067I
0.35506 + 1.51453I 0
u = 0.149078 + 1.079460I
a = −0.299400 + 0.181175I
b = −0.577685 − 0.021582I
2.39623 − 2.35738I 0
u = 0.149078 − 1.079460I
a = −0.299400 − 0.181175I
b = −0.577685 + 0.021582I
2.39623 + 2.35738I 0
u = 0.774685 + 0.781985I
a = −1.34750 + 0.88167I
b = −1.62710 + 0.76393I
−10.59630 + 3.65695I 0
u = 0.774685 − 0.781985I
a = −1.34750 − 0.88167I
b = −1.62710 − 0.76393I
−10.59630 − 3.65695I 0
u = 0.671146 + 0.874204I
a = −2.53705 − 1.93340I
b = 0.07171 − 3.51471I
−2.69730 − 2.59523I 0
u = 0.671146 − 0.874204I
a = −2.53705 + 1.93340I
b = 0.07171 + 3.51471I
−2.69730 + 2.59523I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.733283 + 0.829346I
a = 1.083570 − 0.004026I
b = 0.983747 + 0.467908I
−5.24563 + 0.71971I 0
u = −0.733283 − 0.829346I
a = 1.083570 + 0.004026I
b = 0.983747 − 0.467908I
−5.24563 − 0.71971I 0
u = −0.860621 + 0.704440I
a = 1.75129 + 0.01594I
b = 0.994519 − 0.476642I
−4.58238 − 2.28560I 0
u = −0.860621 − 0.704440I
a = 1.75129 − 0.01594I
b = 0.994519 + 0.476642I
−4.58238 + 2.28560I 0
u = −0.813787 + 0.761771I
a = −2.92793 + 2.83260I
b = −0.01957 + 3.55757I
−6.47446 − 1.37228I 0
u = −0.813787 − 0.761771I
a = −2.92793 − 2.83260I
b = −0.01957 − 3.55757I
−6.47446 + 1.37228I 0
u = 0.735658 + 0.847408I
a = −2.02367 + 0.59992I
b = −0.878692 − 0.438850I
−4.87783 − 3.64446I 0
u = 0.735658 − 0.847408I
a = −2.02367 − 0.59992I
b = −0.878692 + 0.438850I
−4.87783 + 3.64446I 0
u = −0.916744 + 0.664952I
a = −1.17136 − 0.96980I
b = −1.45365 − 0.84782I
−6.64707 − 7.57494I 0
u = −0.916744 − 0.664952I
a = −1.17136 + 0.96980I
b = −1.45365 + 0.84782I
−6.64707 + 7.57494I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.303072 + 1.095470I
a = −1.100800 − 0.632360I
b = −0.735767 + 0.867376I
3.47785 + 6.81881I 0
u = −0.303072 − 1.095470I
a = −1.100800 + 0.632360I
b = −0.735767 − 0.867376I
3.47785 − 6.81881I 0
u = 0.810779 + 0.816732I
a = −1.74709 + 1.34427I
b = −0.916937 − 0.534062I
−8.95504 − 0.66716I 0
u = 0.810779 − 0.816732I
a = −1.74709 − 1.34427I
b = −0.916937 + 0.534062I
−8.95504 + 0.66716I 0
u = 0.644423 + 0.956924I
a = −0.709447 + 1.104300I
b = −1.000890 + 0.308103I
−0.60803 − 3.39602I 0
u = 0.644423 − 0.956924I
a = −0.709447 − 1.104300I
b = −1.000890 − 0.308103I
−0.60803 + 3.39602I 0
u = −0.198711 + 0.822369I
a = 1.68065 − 0.08745I
b = 1.216710 + 0.098619I
−2.78527 + 1.67495I −10.83994 − 4.29836I
u = −0.198711 − 0.822369I
a = 1.68065 + 0.08745I
b = 1.216710 − 0.098619I
−2.78527 − 1.67495I −10.83994 + 4.29836I
u = 0.727212 + 0.897879I
a = 1.51064 − 0.77162I
b = 0.879797 − 0.240211I
−4.72140 − 1.92715I 0
u = 0.727212 − 0.897879I
a = 1.51064 + 0.77162I
b = 0.879797 + 0.240211I
−4.72140 + 1.92715I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.724796 + 0.910439I
a = −1.28567 − 1.26945I
b = −0.772714 + 0.572474I
−4.99704 + 4.83893I 0
u = −0.724796 − 0.910439I
a = −1.28567 + 1.26945I
b = −0.772714 − 0.572474I
−4.99704 − 4.83893I 0
u = 0.862419 + 0.782346I
a = 0.856451 − 0.055709I
b = 0.861279 − 0.560956I
−8.89092 + 3.50469I 0
u = 0.862419 − 0.782346I
a = 0.856451 + 0.055709I
b = 0.861279 + 0.560956I
−8.89092 − 3.50469I 0
u = 0.472880 + 1.066790I
a = 0.462968 − 0.015933I
b = −0.078264 + 0.992701I
2.15836 − 4.75591I 0
u = 0.472880 − 1.066790I
a = 0.462968 + 0.015933I
b = −0.078264 − 0.992701I
2.15836 + 4.75591I 0
u = 0.912938 + 0.730651I
a = 1.55514 − 0.90395I
b = 0.923328 − 0.483625I
−4.65732 + 6.45566I 0
u = 0.912938 − 0.730651I
a = 1.55514 + 0.90395I
b = 0.923328 + 0.483625I
−4.65732 − 6.45566I 0
u = 0.985084 + 0.643042I
a = −0.634652 + 0.233698I
b = −0.940660 + 0.350537I
−5.92496 − 1.10467I 0
u = 0.985084 − 0.643042I
a = −0.634652 − 0.233698I
b = −0.940660 − 0.350537I
−5.92496 + 1.10467I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.776224 + 0.271739I
a = 1.092310 + 0.739985I
b = 0.249569 + 0.782908I
−0.309232 + 0.257103I −3.98318 − 1.23273I
u = 0.776224 − 0.271739I
a = 1.092310 − 0.739985I
b = 0.249569 − 0.782908I
−0.309232 − 0.257103I −3.98318 + 1.23273I
u = −0.711606 + 0.943046I
a = 1.90118 − 0.15709I
b = 1.16281 − 0.91465I
−4.23917 + 5.93059I 0
u = −0.711606 − 0.943046I
a = 1.90118 + 0.15709I
b = 1.16281 + 0.91465I
−4.23917 − 5.93059I 0
u = −0.794840 + 0.119506I
a = 1.29874 + 0.92905I
b = 0.493015 + 0.736937I
0.07573 − 2.96723I −4.49491 + 6.86660I
u = −0.794840 − 0.119506I
a = 1.29874 − 0.92905I
b = 0.493015 − 0.736937I
0.07573 + 2.96723I −4.49491 − 6.86660I
u = 0.733804 + 0.958544I
a = 1.90707 − 1.27205I
b = 1.50062 + 0.92394I
−10.05150 − 9.36822I 0
u = 0.733804 − 0.958544I
a = 1.90707 + 1.27205I
b = 1.50062 − 0.92394I
−10.05150 + 9.36822I 0
u = −0.699988 + 0.988293I
a = −1.85535 − 0.53512I
b = −0.956731 + 0.555562I
−0.57207 + 7.69896I 0
u = −0.699988 − 0.988293I
a = −1.85535 + 0.53512I
b = −0.956731 − 0.555562I
−0.57207 − 7.69896I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.768945 + 0.945881I
a = 1.136450 − 0.171730I
b = 1.071270 − 0.564160I
−8.55225 − 5.26015I 0
u = 0.768945 − 0.945881I
a = 1.136450 + 0.171730I
b = 1.071270 + 0.564160I
−8.55225 + 5.26015I 0
u = 0.012968 + 0.778903I
a = 1.19691 + 1.18340I
b = 0.0861568 + 0.1023830I
−0.57888 − 1.37786I −5.42870 + 3.04988I
u = 0.012968 − 0.778903I
a = 1.19691 − 1.18340I
b = 0.0861568 − 0.1023830I
−0.57888 + 1.37786I −5.42870 − 3.04988I
u = −0.750545 + 0.978963I
a = −2.01195 + 2.33917I
b = 0.13730 + 3.60565I
−5.80691 + 7.24580I 0
u = −0.750545 − 0.978963I
a = −2.01195 − 2.33917I
b = 0.13730 − 3.60565I
−5.80691 − 7.24580I 0
u = 0.263851 + 1.206760I
a = −0.019525 − 0.492723I
b = 0.851831 + 0.809494I
1.35608 − 6.83479I 0
u = 0.263851 − 1.206760I
a = −0.019525 + 0.492723I
b = 0.851831 − 0.809494I
1.35608 + 6.83479I 0
u = −0.731217 + 1.003590I
a = 0.864596 + 0.997578I
b = 0.952600 − 0.489311I
−9.30286 + 0.82367I 0
u = −0.731217 − 1.003590I
a = 0.864596 − 0.997578I
b = 0.952600 + 0.489311I
−9.30286 − 0.82367I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.001560 + 0.754879I
a = −1.22169 + 1.10354I
b = −1.50099 + 0.97923I
−9.7168 + 12.3498I 0
u = 1.001560 − 0.754879I
a = −1.22169 − 1.10354I
b = −1.50099 − 0.97923I
−9.7168 − 12.3498I 0
u = 0.782873 + 0.988188I
a = −1.31012 + 0.94588I
b = −0.784230 − 0.690147I
−8.24534 − 9.62498I 0
u = 0.782873 − 0.988188I
a = −1.31012 − 0.94588I
b = −0.784230 + 0.690147I
−8.24534 + 9.62498I 0
u = −0.748734 + 1.026430I
a = −1.01991 − 1.11785I
b = −1.189720 − 0.298360I
−3.58852 + 8.27941I 0
u = −0.748734 − 1.026430I
a = −1.01991 + 1.11785I
b = −1.189720 + 0.298360I
−3.58852 − 8.27941I 0
u = −0.417041 + 1.205090I
a = 0.471414 + 0.602822I
b = 1.007400 − 0.960901I
−0.01476 + 12.20380I 0
u = −0.417041 − 1.205090I
a = 0.471414 − 0.602822I
b = 1.007400 + 0.960901I
−0.01476 − 12.20380I 0
u = −1.038270 + 0.766425I
a = −0.598289 − 0.452558I
b = −0.917401 − 0.570045I
−8.92357 − 3.87422I 0
u = −1.038270 − 0.766425I
a = −0.598289 + 0.452558I
b = −0.917401 + 0.570045I
−8.92357 + 3.87422I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.781779 + 1.035930I
a = −1.89500 + 0.43707I
b = −1.048240 − 0.529654I
−3.69576 − 12.71000I 0
u = 0.781779 − 1.035930I
a = −1.89500 − 0.43707I
b = −1.048240 + 0.529654I
−3.69576 + 12.71000I 0
u = −0.097281 + 1.296230I
a = −0.447675 + 0.135304I
b = 0.493133 + 0.312801I
2.08823 − 3.26218I 0
u = −0.097281 − 1.296230I
a = −0.447675 − 0.135304I
b = 0.493133 − 0.312801I
2.08823 + 3.26218I 0
u = −0.758282 + 1.060240I
a = 1.79769 + 0.86896I
b = 1.47421 − 1.04423I
−5.4260 + 13.7420I 0
u = −0.758282 − 1.060240I
a = 1.79769 − 0.86896I
b = 1.47421 + 1.04423I
−5.4260 − 13.7420I 0
u = −0.618650 + 0.289740I
a = 0.95959 − 1.70942I
b = 0.633734 − 0.186169I
−3.65232 − 1.86079I −14.7972 + 4.0060I
u = −0.618650 − 0.289740I
a = 0.95959 + 1.70942I
b = 0.633734 + 0.186169I
−3.65232 + 1.86079I −14.7972 − 4.0060I
u = 0.788712 + 1.087860I
a = 0.910152 − 0.577301I
b = 0.839179 + 0.652694I
−4.55475 − 5.33983I 0
u = 0.788712 − 1.087860I
a = 0.910152 + 0.577301I
b = 0.839179 − 0.652694I
−4.55475 + 5.33983I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.826836 + 1.074140I
a = 1.98937 − 0.70799I
b = 1.54362 + 1.09495I
−8.6750 − 19.0243I 0
u = 0.826836 − 1.074140I
a = 1.98937 + 0.70799I
b = 1.54362 − 1.09495I
−8.6750 + 19.0243I 0
u = 0.069434 + 0.626267I
a = 1.23586 − 2.19265I
b = −0.358586 + 0.688989I
−1.32642 + 1.43233I 0.36847 − 1.82515I
u = 0.069434 − 0.626267I
a = 1.23586 + 2.19265I
b = −0.358586 − 0.688989I
−1.32642 − 1.43233I 0.36847 + 1.82515I
u = −0.847758 + 1.083770I
a = 1.135320 + 0.479648I
b = 0.916105 − 0.765861I
−7.87653 + 10.72040I 0
u = −0.847758 − 1.083770I
a = 1.135320 − 0.479648I
b = 0.916105 + 0.765861I
−7.87653 − 10.72040I 0
u = 0.315350 + 1.371310I
a = −0.243774 − 0.304828I
b = 0.467941 − 0.015413I
1.32897 − 2.54365I 0
u = 0.315350 − 1.371310I
a = −0.243774 + 0.304828I
b = 0.467941 + 0.015413I
1.32897 + 2.54365I 0
u = 0.560432
a = 1.21967
b = 0.286322
−1.12206 −9.21340
u = 0.551319 + 0.060131I
a = 2.81769 − 9.33403I
b = 1.77180 − 2.09281I
−2.75296 + 0.06291I −75.7664 − 36.6206I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.551319 − 0.060131I
a = 2.81769 + 9.33403I
b = 1.77180 + 2.09281I
−2.75296 − 0.06291I −75.7664 + 36.6206I
u = 0.092826 + 0.524249I
a = 1.64965 + 0.99766I
b = 0.113197 + 0.496895I
−0.66149 − 1.45734I −4.35229 + 4.44056I
u = 0.092826 − 0.524249I
a = 1.64965 − 0.99766I
b = 0.113197 − 0.496895I
−0.66149 + 1.45734I −4.35229 − 4.44056I
u = −0.283170 + 0.423021I
a = 2.19250 − 8.03202I
b = −1.021710 − 0.189739I
−4.15362 + 0.40167I −9.52783 − 9.14652I
u = −0.283170 − 0.423021I
a = 2.19250 + 8.03202I
b = −1.021710 + 0.189739I
−4.15362 − 0.40167I −9.52783 + 9.14652I
u = −0.022040 + 0.452263I
a = −1.229100 − 0.307457I
b = −1.51825 − 0.19954I
−7.21260 − 4.35579I 4.39844 + 1.29194I
u = −0.022040 − 0.452263I
a = −1.229100 + 0.307457I
b = −1.51825 + 0.19954I
−7.21260 + 4.35579I 4.39844 − 1.29194I
u = 0.287194
a = 3.48628
b = 1.33135
−2.30286 −1.96350
16
II. I
u
2
= h−2u
2
+ b − u − 3, −5u
2
+ a − 2u − 9, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
9
=
u
2
+ 1
u
2
a
11
=
5u
2
+ 2u + 9
2u
2
+ u + 3
a
12
=
4u
2
+ 2u + 8
u
2
+ u + 3
a
10
=
5u
2
+ 2u + 9
2u
2
+ u + 3
a
3
=
u
−u
2
− u − 1
a
6
=
−16u
2
− 7u − 27
−5u
2
− 2u − 9
a
1
=
−1
−u
2
a
5
=
1
0
a
2
=
−u
2
− 1
−u
2
− u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −53u
2
− 32u − 104
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
4
u
3
− u
2
+ 1
c
5
, c
6
u
3
− 2u
2
− 3u − 1
c
7
u
3
+ u
2
+ 2u + 1
c
8
u
3
− 3u
2
+ 2u + 1
c
9
(u − 1)
3
c
10
u
3
c
11
(u + 1)
3
c
12
u
3
+ 3u
2
+ 2u − 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
3
+ 3y
2
+ 2y −1
c
2
, c
4
y
3
− y
2
+ 2y −1
c
5
, c
6
y
3
− 10y
2
+ 5y −1
c
8
, c
12
y
3
− 5y
2
+ 10y −1
c
9
, c
11
(y −1)
3
c
10
y
3
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 0.258045 − 0.197115I
b = −0.539798 + 0.182582I
1.37919 + 2.82812I −9.0124 − 12.0277I
u = −0.215080 − 1.307140I
a = 0.258045 + 0.197115I
b = −0.539798 − 0.182582I
1.37919 − 2.82812I −9.0124 + 12.0277I
u = −0.569840
a = 9.48391
b = 3.07960
−2.75839 −102.980
20
III. I
v
1
= ha, v
4
+ 12v
3
+ 24v
2
+ 29b + 21v + 45, v
5
+ 3v
4
+ 3v
3
+ 8v
2
+ v + 1i
(i) Arc colorings
a
4
=
v
0
a
7
=
1
0
a
8
=
1
0
a
9
=
1
0
a
11
=
0
−0.0344828v
4
− 0.413793v
3
+ ··· − 0.724138v −1.55172
a
12
=
0.0344828v
4
+ 0.413793v
3
+ ··· + 0.724138v + 1.55172
−0.0344828v
4
− 0.413793v
3
+ ··· − 0.724138v −1.55172
a
10
=
−0.137931v
4
− 0.655172v
3
+ ··· − 1.89655v −1.20690
0.137931v
4
+ 0.655172v
3
+ ··· + 1.89655v + 2.20690
a
3
=
v
0
a
6
=
1
−0.137931v
4
− 0.655172v
3
+ ··· − 1.89655v −2.20690
a
1
=
−0.310345v
4
− 0.724138v
3
+ ··· − 2.51724v + 0.0344828
v
4
+ 3v
3
+ 3v
2
+ 8v + 1
a
5
=
0.310345v
4
+ 0.724138v
3
+ ··· + 2.51724v −0.0344828
−v
4
− 3v
3
− 3v
2
− 8v −1
a
2
=
−0.310345v
4
− 0.724138v
3
+ ··· − 1.51724v + 0.0344828
v
4
+ 3v
3
+ 3v
2
+ 8v + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
65
29
v
4
+
142
29
v
3
+
81
29
v
2
+
437
29
v −
613
29
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
5
c
3
, c
7
, c
8
u
5
c
4
(u + 1)
5
c
5
, c
10
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
6
, c
9
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
11
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
12
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
5
c
3
, c
7
, c
8
y
5
c
5
, c
10
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
6
, c
9
, c
11
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
12
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.01014 + 1.59703I
a = 0
b = 0.309916 + 0.549911I
−1.97403 − 1.53058I −13.4575 + 4.4032I
v = −0.01014 − 1.59703I
a = 0
b = 0.309916 − 0.549911I
−1.97403 + 1.53058I −13.4575 − 4.4032I
v = −0.043806 + 0.365575I
a = 0
b = −1.41878 − 0.21917I
−7.51750 − 4.40083I −22.0438 + 5.2094I
v = −0.043806 − 0.365575I
a = 0
b = −1.41878 + 0.21917I
−7.51750 + 4.40083I −22.0438 − 5.2094I
v = −2.89210
a = 0
b = 1.21774
−4.04602 −2.99730
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
3
− u
2
+ 2u − 1)(u
118
+ 65u
117
+ ··· + 172u + 1)
c
2
((u − 1)
5
)(u
3
+ u
2
− 1)(u
118
− 7u
117
+ ··· − 2u + 1)
c
3
u
5
(u
3
− u
2
+ 2u − 1)(u
118
+ 2u
117
+ ··· + 160u + 32)
c
4
((u + 1)
5
)(u
3
− u
2
+ 1)(u
118
− 7u
117
+ ··· − 2u + 1)
c
5
(u
3
− 2u
2
− 3u − 1)(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
· (u
118
+ 67u
116
+ ··· + 196401u + 29189)
c
6
(u
3
− 2u
2
− 3u − 1)(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
· (u
118
+ 4u
117
+ ··· + 8634757u + 591517)
c
7
u
5
(u
3
+ u
2
+ 2u + 1)(u
118
+ 2u
117
+ ··· + 160u + 32)
c
8
u
5
(u
3
− 3u
2
+ 2u + 1)(u
118
− 36u
117
+ ··· − 20992u + 1024)
c
9
((u − 1)
3
)(u
5
+ u
4
+ ··· + u − 1)(u
118
− 5u
117
+ ··· + 143u − 1)
c
10
u
3
(u
5
− u
4
+ ··· + u − 1)(u
118
+ 20u
117
+ ··· + 156u + 8)
c
11
((u + 1)
3
)(u
5
− u
4
+ ··· + u + 1)(u
118
− 5u
117
+ ··· + 143u − 1)
c
12
(u
3
+ 3u
2
+ 2u − 1)(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
· (u
118
− 9u
117
+ ··· + 2u − 1)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
5
)(y
3
+ 3y
2
+ 2y −1)(y
118
− 17y
117
+ ··· − 21024y + 1)
c
2
, c
4
((y −1)
5
)(y
3
− y
2
+ 2y −1)(y
118
− 65y
117
+ ··· − 172y + 1)
c
3
, c
7
y
5
(y
3
+ 3y
2
+ 2y −1)(y
118
+ 36y
117
+ ··· + 20992y + 1024)
c
5
(y
3
− 10y
2
+ 5y −1)(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
· (y
118
+ 134y
117
+ ··· + 56845137931y + 851997721)
c
6
(y
3
− 10y
2
+ 5y −1)(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
· (y
118
+ 46y
117
+ ··· − 9372454336793y + 349892361289)
c
8
y
5
(y
3
− 5y
2
+ 10y −1)(y
118
+ 84y
117
+ ··· − 2.37634 × 10
8
y + 1048576)
c
9
, c
11
(y −1)
3
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
· (y
118
− 91y
117
+ ··· − 21455y + 1)
c
10
y
3
(y
5
+ 3y
4
+ ··· − y −1)(y
118
+ 24y
117
+ ··· − 6288y + 64)
c
12
(y
3
− 5y
2
+ 10y −1)(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
· (y
118
− 25y
117
+ ··· − 26y + 1)
26
