12a
0360
(K12a
0360
)
A knot diagram
1
Linearized knot diagam
3 6 9 8 7 2 12 11 1 4 5 10
Solving Sequence
8,11 5,9
12 4 3 7 6 2 10 1
c
8
c
11
c
4
c
3
c
7
c
5
c
2
c
10
c
12
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.30570 × 10
1105
u
145
− 4.41286 × 10
1106
u
144
+ ··· + 1.33638 × 10
1108
b − 8.24729 × 10
1108
,
− 6.53292 × 10
1106
u
145
− 8.61380 × 10
1107
u
144
+ ··· + 5.34553 × 10
1108
a − 1.10086 × 10
1110
,
u
146
+ 13u
145
+ ··· + 3712u + 768i
I
u
2
= h7.17507 × 10
32
u
25
− 3.74911 × 10
33
u
24
+ ··· + 2.20341 × 10
33
b − 2.57469 × 10
35
,
7.48722 × 10
34
u
25
− 3.83632 × 10
35
u
24
+ ··· + 1.43222 × 10
35
a − 2.61037 × 10
37
,
u
26
− 6u
25
+ ··· − 1450u + 325i
I
v
1
= ha, −v
2
+ b + 2v, v
4
− 3v
3
+ 2v
2
+ 1i
I
v
2
= ha, −5v
3
+ 16v
2
+ 8b − 40v + 15, v
4
− 3v
3
+ 8v
2
− 3v + 1i
* 4 irreducible components of dim
C
= 0, with total 180 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−3.31 × 10
1105
u
145
− 4.41 × 10
1106
u
144
+ · · · + 1.34 × 10
1108
b −
8.25 × 10
1108
, −6.53 × 10
1106
u
145
− 8.61 × 10
1107
u
144
+ · · · + 5.35 ×
10
1108
a − 1.10 × 10
1110
, u
146
+ 13u
145
+ · · · + 3712u + 768i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
5
=
0.0122213u
145
+ 0.161140u
144
+ ··· + 123.861u + 20.5939
0.00247362u
145
+ 0.0330209u
144
+ ··· + 31.3706u + 6.17135
a
9
=
1
u
2
a
12
=
−0.00406636u
145
− 0.0533296u
144
+ ··· − 47.0455u − 7.79538
−0.000663045u
145
− 0.00907307u
144
+ ··· − 11.0244u − 2.37289
a
4
=
0.00974766u
145
+ 0.128119u
144
+ ··· + 92.4900u + 14.4226
0.00247362u
145
+ 0.0330209u
144
+ ··· + 31.3706u + 6.17135
a
3
=
0.0143319u
145
+ 0.188459u
144
+ ··· + 136.542u + 21.6688
0.00140153u
145
+ 0.0192365u
144
+ ··· + 25.0843u + 5.59915
a
7
=
0.00508132u
145
+ 0.0632419u
144
+ ··· + 9.88946u − 3.18855
0.000960881u
145
+ 0.0115579u
144
+ ··· + 3.55703u − 0.539101
a
6
=
−0.0202071u
145
− 0.269862u
144
+ ··· − 246.988u − 42.3344
−0.000188244u
145
− 0.00491796u
144
+ ··· − 44.8135u − 10.4290
a
2
=
−0.00444409u
145
− 0.0545649u
144
+ ··· − 3.69753u + 4.61182
−0.000951740u
145
− 0.0118936u
144
+ ··· − 7.64145u − 0.530581
a
10
=
−0.00366625u
145
− 0.0476731u
144
+ ··· − 30.5632u − 4.50047
0.000262933u
145
+ 0.00341664u
144
+ ··· − 3.45791u − 0.922013
a
1
=
−0.00241677u
145
− 0.0308188u
144
+ ··· − 10.6699u − 0.449860
−0.000892350u
145
− 0.0114009u
144
+ ··· − 5.71646u − 0.449654
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.00659825u
145
− 0.0907768u
144
+ ··· − 143.657u − 31.5748
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
146
+ 41u
145
+ ··· + 13874u + 441
c
2
, c
6
u
146
− 3u
145
+ ··· + 56u + 21
c
3
u
146
+ 3u
145
+ ··· − 213878079u + 69993509
c
4
u
146
+ 9u
145
+ ··· + 97u + 16
c
7
u
146
− 5u
145
+ ··· + 163744u + 32887
c
8
u
146
− 13u
145
+ ··· − 3712u + 768
c
9
, c
12
u
146
+ 7u
145
+ ··· + 95533u + 4448
c
10
u
146
− 6u
144
+ ··· − 35u + 1
c
11
u
146
+ 2u
145
+ ··· + 153777u + 21323
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
146
+ 141y
145
+ ··· + 10798130y + 194481
c
2
, c
6
y
146
+ 41y
145
+ ··· + 13874y + 441
c
3
y
146
+ 59y
145
+ ··· + 839682611759848865y + 4899091302133081
c
4
y
146
+ 21y
145
+ ··· + 13375y + 256
c
7
y
146
− 39y
145
+ ··· − 49681388466y + 1081554769
c
8
y
146
+ 11y
145
+ ··· + 6373376y + 589824
c
9
, c
12
y
146
+ 97y
145
+ ··· − 4451394729y + 19784704
c
10
y
146
− 12y
145
+ ··· + 265y + 1
c
11
y
146
− 30y
145
+ ··· − 28764118101y + 454670329
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.802454 + 0.588037I
a = −0.531807 − 1.135870I
b = −1.020260 − 0.872880I
3.29509 + 2.59410I 0
u = −0.802454 − 0.588037I
a = −0.531807 + 1.135870I
b = −1.020260 + 0.872880I
3.29509 − 2.59410I 0
u = 0.871003 + 0.506893I
a = 0.403140 − 0.851076I
b = 1.20409 − 1.11526I
−1.65989 − 5.49131I 0
u = 0.871003 − 0.506893I
a = 0.403140 + 0.851076I
b = 1.20409 + 1.11526I
−1.65989 + 5.49131I 0
u = 0.429141 + 0.917197I
a = −0.201495 + 0.959077I
b = −0.87385 + 1.26504I
1.51786 − 4.56864I 0
u = 0.429141 − 0.917197I
a = −0.201495 − 0.959077I
b = −0.87385 − 1.26504I
1.51786 + 4.56864I 0
u = −0.827144 + 0.492973I
a = 0.616486 + 1.195440I
b = 1.07282 + 0.96391I
2.42208 + 8.12198I 0
u = −0.827144 − 0.492973I
a = 0.616486 − 1.195440I
b = 1.07282 − 0.96391I
2.42208 − 8.12198I 0
u = 0.748394 + 0.604038I
a = −0.598029 − 0.270701I
b = 0.205977 − 0.532694I
−1.38423 − 0.78057I 0
u = 0.748394 − 0.604038I
a = −0.598029 + 0.270701I
b = 0.205977 + 0.532694I
−1.38423 + 0.78057I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.508387 + 0.924849I
a = −0.960150 − 0.195445I
b = 0.387156 + 0.376888I
3.13027 + 3.31987I 0
u = −0.508387 − 0.924849I
a = −0.960150 + 0.195445I
b = 0.387156 − 0.376888I
3.13027 − 3.31987I 0
u = 0.053551 + 0.932125I
a = −0.161722 − 1.071830I
b = −1.021500 − 0.623407I
6.30567 + 0.04181I 0
u = 0.053551 − 0.932125I
a = −0.161722 + 1.071830I
b = −1.021500 + 0.623407I
6.30567 − 0.04181I 0
u = 0.137828 + 0.917504I
a = 0.168695 + 1.034250I
b = 1.060330 + 0.607548I
5.81980 − 6.06300I 0
u = 0.137828 − 0.917504I
a = 0.168695 − 1.034250I
b = 1.060330 − 0.607548I
5.81980 + 6.06300I 0
u = 1.078310 + 0.012960I
a = 0.48197 + 1.49587I
b = 0.065355 + 0.580528I
−3.69081 − 0.08768I 0
u = 1.078310 − 0.012960I
a = 0.48197 − 1.49587I
b = 0.065355 − 0.580528I
−3.69081 + 0.08768I 0
u = −0.961574 + 0.533261I
a = 1.22512 − 1.29575I
b = −0.332786 − 0.684088I
6.09233 + 10.74490I 0
u = −0.961574 − 0.533261I
a = 1.22512 + 1.29575I
b = −0.332786 + 0.684088I
6.09233 − 10.74490I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.082670 + 0.263362I
a = −0.663520 + 0.363145I
b = −0.287318 + 0.715534I
1.32164 − 2.89842I 0
u = −1.082670 − 0.263362I
a = −0.663520 − 0.363145I
b = −0.287318 − 0.715534I
1.32164 + 2.89842I 0
u = −0.224981 + 0.850372I
a = 0.344235 + 0.246836I
b = 0.471852 − 0.683778I
−1.85922 − 1.49457I 0
u = −0.224981 − 0.850372I
a = 0.344235 − 0.246836I
b = 0.471852 + 0.683778I
−1.85922 + 1.49457I 0
u = −0.969668 + 0.612996I
a = −1.10536 + 1.17499I
b = 0.373015 + 0.672914I
6.68296 + 4.72439I 0
u = −0.969668 − 0.612996I
a = −1.10536 − 1.17499I
b = 0.373015 − 0.672914I
6.68296 − 4.72439I 0
u = −0.560635 + 1.006060I
a = −0.335631 + 0.864108I
b = 1.19675 + 1.16993I
−1.13829 + 5.55339I 0
u = −0.560635 − 1.006060I
a = −0.335631 − 0.864108I
b = 1.19675 − 1.16993I
−1.13829 − 5.55339I 0
u = 0.092261 + 0.821801I
a = 0.88761 + 1.79345I
b = −0.980157 + 0.518850I
11.02230 − 3.86586I 0
u = 0.092261 − 0.821801I
a = 0.88761 − 1.79345I
b = −0.980157 − 0.518850I
11.02230 + 3.86586I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.617603 + 0.545779I
a = 1.97468 − 0.58063I
b = −0.263967 − 0.519798I
−0.28583 + 5.92748I 0
u = −0.617603 − 0.545779I
a = 1.97468 + 0.58063I
b = −0.263967 + 0.519798I
−0.28583 − 5.92748I 0
u = 0.140250 + 0.810021I
a = −0.90766 − 1.94652I
b = 0.919417 − 0.512843I
10.1797 − 10.3417I 0
u = 0.140250 − 0.810021I
a = −0.90766 + 1.94652I
b = 0.919417 + 0.512843I
10.1797 + 10.3417I 0
u = −0.691017 + 0.436435I
a = −0.465465 − 1.026020I
b = −0.218819 − 1.095490I
1.75912 + 1.15684I 0
u = −0.691017 − 0.436435I
a = −0.465465 + 1.026020I
b = −0.218819 + 1.095490I
1.75912 − 1.15684I 0
u = −0.274708 + 0.752038I
a = 0.123349 + 1.187240I
b = −1.41094 + 0.88937I
10.65860 + 4.70645I 0
u = −0.274708 − 0.752038I
a = 0.123349 − 1.187240I
b = −1.41094 − 0.88937I
10.65860 − 4.70645I 0
u = −0.314244 + 0.725706I
a = −0.056143 − 1.193680I
b = 1.42312 − 0.94084I
9.7361 + 11.1439I 0
u = −0.314244 − 0.725706I
a = −0.056143 + 1.193680I
b = 1.42312 + 0.94084I
9.7361 − 11.1439I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.233620 + 0.017461I
a = 0.03835 − 1.80354I
b = 0.013633 − 0.692946I
1.01870 + 2.91649I 0
u = 1.233620 − 0.017461I
a = 0.03835 + 1.80354I
b = 0.013633 + 0.692946I
1.01870 − 2.91649I 0
u = −0.085565 + 0.757064I
a = 0.669355 + 0.943391I
b = −1.42801 + 0.48897I
5.87623 + 0.37168I 0
u = −0.085565 − 0.757064I
a = 0.669355 − 0.943391I
b = −1.42801 − 0.48897I
5.87623 − 0.37168I 0
u = 0.813116 + 0.937801I
a = −0.175884 − 0.791862I
b = 0.847508 − 1.095940I
−2.90521 − 2.63874I 0
u = 0.813116 − 0.937801I
a = −0.175884 + 0.791862I
b = 0.847508 + 1.095940I
−2.90521 + 2.63874I 0
u = −0.647518 + 0.386086I
a = 0.51472 + 1.33120I
b = 0.813443 + 1.124790I
−2.51715 + 2.66644I 0
u = −0.647518 − 0.386086I
a = 0.51472 − 1.33120I
b = 0.813443 − 1.124790I
−2.51715 − 2.66644I 0
u = −0.081022 + 0.740045I
a = 0.93571 + 1.67349I
b = −0.241110 − 0.293390I
0.651752 − 0.256863I 0
u = −0.081022 − 0.740045I
a = 0.93571 − 1.67349I
b = −0.241110 + 0.293390I
0.651752 + 0.256863I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.676797 + 0.281890I
a = −1.78827 − 0.18462I
b = −0.060429 − 0.293215I
−0.121350 − 0.755731I 0
u = 0.676797 − 0.281890I
a = −1.78827 + 0.18462I
b = −0.060429 + 0.293215I
−0.121350 + 0.755731I 0
u = −0.163534 + 1.260490I
a = 0.088612 − 0.482634I
b = −1.02625 − 1.83080I
7.40675 + 3.00994I 0
u = −0.163534 − 1.260490I
a = 0.088612 + 0.482634I
b = −1.02625 + 1.83080I
7.40675 − 3.00994I 0
u = 0.082332 + 1.299770I
a = 0.044072 + 0.413505I
b = 0.31001 + 1.95661I
6.39267 − 4.58347I 0
u = 0.082332 − 1.299770I
a = 0.044072 − 0.413505I
b = 0.31001 − 1.95661I
6.39267 + 4.58347I 0
u = −0.041330 + 0.684286I
a = −1.51422 − 0.98978I
b = 1.152000 − 0.167085I
1.92894 − 4.21551I 5.10624 + 4.62566I
u = −0.041330 − 0.684286I
a = −1.51422 + 0.98978I
b = 1.152000 + 0.167085I
1.92894 + 4.21551I 5.10624 − 4.62566I
u = 0.627231 + 0.274078I
a = −1.20586 − 0.86517I
b = 0.739501 − 0.968326I
2.98529 + 2.15718I 0
u = 0.627231 − 0.274078I
a = −1.20586 + 0.86517I
b = 0.739501 + 0.968326I
2.98529 − 2.15718I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.112176 + 0.654366I
a = −0.162580 − 0.770557I
b = 1.66141 − 0.74380I
1.79307 + 4.84713I 7.28682 − 6.07966I
u = −0.112176 − 0.654366I
a = −0.162580 + 0.770557I
b = 1.66141 + 0.74380I
1.79307 − 4.84713I 7.28682 + 6.07966I
u = −0.443688 + 1.266100I
a = 0.012240 − 0.871069I
b = 0.438570 − 1.038990I
9.28459 + 1.01032I 0
u = −0.443688 − 1.266100I
a = 0.012240 + 0.871069I
b = 0.438570 + 1.038990I
9.28459 − 1.01032I 0
u = −0.320464 + 1.303020I
a = −0.046142 + 0.889587I
b = −0.500613 + 1.063090I
9.21295 − 5.35564I 0
u = −0.320464 − 1.303020I
a = −0.046142 − 0.889587I
b = −0.500613 − 1.063090I
9.21295 + 5.35564I 0
u = 0.653144 + 0.069002I
a = 2.17959 + 1.52916I
b = 0.155620 + 0.378066I
−0.67695 + 3.93260I −11.25475 − 6.09214I
u = 0.653144 − 0.069002I
a = 2.17959 − 1.52916I
b = 0.155620 − 0.378066I
−0.67695 − 3.93260I −11.25475 + 6.09214I
u = −0.909955 + 0.998183I
a = −0.164467 − 0.904765I
b = −0.881074 − 0.662215I
3.55387 + 1.89506I 0
u = −0.909955 − 0.998183I
a = −0.164467 + 0.904765I
b = −0.881074 + 0.662215I
3.55387 − 1.89506I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.958639 + 0.954754I
a = −0.286185 + 0.722804I
b = −1.00195 + 1.00927I
0.10078 − 4.29110I 0
u = 0.958639 − 0.954754I
a = −0.286185 − 0.722804I
b = −1.00195 − 1.00927I
0.10078 + 4.29110I 0
u = −0.315970 + 0.548885I
a = −0.18304 − 1.41022I
b = −0.729260 − 0.689517I
1.36793 + 0.94017I 3.85710 − 1.23401I
u = −0.315970 − 0.548885I
a = −0.18304 + 1.41022I
b = −0.729260 + 0.689517I
1.36793 − 0.94017I 3.85710 + 1.23401I
u = 0.813226 + 1.113110I
a = −0.030267 + 0.875027I
b = −0.859728 + 1.100540I
0.15079 − 5.32131I 0
u = 0.813226 − 1.113110I
a = −0.030267 − 0.875027I
b = −0.859728 − 1.100540I
0.15079 + 5.32131I 0
u = 1.254660 + 0.578117I
a = 0.441077 − 0.761605I
b = 1.18284 − 0.95675I
4.19024 − 9.29980I 0
u = 1.254660 − 0.578117I
a = 0.441077 + 0.761605I
b = 1.18284 + 0.95675I
4.19024 + 9.29980I 0
u = −0.465403 + 0.391641I
a = 0.317594 + 1.275180I
b = 0.32207 + 1.53524I
0.07254 − 3.31724I −3.20482 − 2.86742I
u = −0.465403 − 0.391641I
a = 0.317594 − 1.275180I
b = 0.32207 − 1.53524I
0.07254 + 3.31724I −3.20482 + 2.86742I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.298915 + 0.526501I
a = 0.324718 − 1.103420I
b = 1.04305 − 1.59122I
0.227473 − 0.396209I 3.67014 + 9.08431I
u = 0.298915 − 0.526501I
a = 0.324718 + 1.103420I
b = 1.04305 + 1.59122I
0.227473 + 0.396209I 3.67014 − 9.08431I
u = −0.717126 + 1.214700I
a = 0.105752 − 0.882481I
b = −1.07858 − 1.22167I
4.01021 + 9.20227I 0
u = −0.717126 − 1.214700I
a = 0.105752 + 0.882481I
b = −1.07858 + 1.22167I
4.01021 − 9.20227I 0
u = 0.879221 + 1.104450I
a = 0.270707 + 0.368200I
b = −0.121478 + 0.779280I
−2.60636 − 3.62739I 0
u = 0.879221 − 1.104450I
a = 0.270707 − 0.368200I
b = −0.121478 − 0.779280I
−2.60636 + 3.62739I 0
u = 1.25670 + 0.66375I
a = −0.429462 + 0.745416I
b = −1.15696 + 0.95062I
4.51748 − 3.32543I 0
u = 1.25670 − 0.66375I
a = −0.429462 − 0.745416I
b = −1.15696 − 0.95062I
4.51748 + 3.32543I 0
u = 0.556667 + 0.157222I
a = 1.58529 + 0.98466I
b = −0.686976 + 0.957219I
3.33704 − 3.66399I 0.44736 + 4.04098I
u = 0.556667 − 0.157222I
a = 1.58529 − 0.98466I
b = −0.686976 − 0.957219I
3.33704 + 3.66399I 0.44736 − 4.04098I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.99418 + 1.04243I
a = −0.188300 + 0.848592I
b = 0.709545 + 0.629884I
4.09131 + 4.58759I 0
u = −0.99418 − 1.04243I
a = −0.188300 − 0.848592I
b = 0.709545 − 0.629884I
4.09131 − 4.58759I 0
u = −0.87443 + 1.15416I
a = −0.066903 + 0.986336I
b = 1.06573 + 1.18272I
0.57798 + 13.78210I 0
u = −0.87443 − 1.15416I
a = −0.066903 − 0.986336I
b = 1.06573 − 1.18272I
0.57798 − 13.78210I 0
u = 0.144479 + 0.531071I
a = −0.232323 + 0.877556I
b = 0.935011 + 0.242956I
−0.73777 − 1.93423I −1.16196 + 5.89787I
u = 0.144479 − 0.531071I
a = −0.232323 − 0.877556I
b = 0.935011 − 0.242956I
−0.73777 + 1.93423I −1.16196 − 5.89787I
u = 0.96653 + 1.12786I
a = −0.035349 − 0.972317I
b = 0.851919 − 1.103510I
−2.56858 − 8.46422I 0
u = 0.96653 − 1.12786I
a = −0.035349 + 0.972317I
b = 0.851919 + 1.103510I
−2.56858 + 8.46422I 0
u = −1.25107 + 0.83285I
a = 0.504342 − 0.191372I
b = 0.332700 − 0.608096I
−0.72741 − 6.37136I 0
u = −1.25107 − 0.83285I
a = 0.504342 + 0.191372I
b = 0.332700 + 0.608096I
−0.72741 + 6.37136I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.95879 + 1.19437I
a = −0.070193 + 0.281575I
b = 0.722768 + 0.354840I
4.08493 + 3.44456I 0
u = −0.95879 − 1.19437I
a = −0.070193 − 0.281575I
b = 0.722768 − 0.354840I
4.08493 − 3.44456I 0
u = −0.95534 + 1.21871I
a = −0.002971 − 1.124170I
b = −0.796490 − 0.772451I
10.14710 − 0.08191I 0
u = −0.95534 − 1.21871I
a = −0.002971 + 1.124170I
b = −0.796490 + 0.772451I
10.14710 + 0.08191I 0
u = −0.124855 + 0.428054I
a = 0.16953 + 3.86744I
b = 0.389763 + 0.947661I
3.22067 + 6.26738I −2.17854 − 6.95136I
u = −0.124855 − 0.428054I
a = 0.16953 − 3.86744I
b = 0.389763 − 0.947661I
3.22067 − 6.26738I −2.17854 + 6.95136I
u = −0.99469 + 1.20464I
a = −0.034102 + 1.124490I
b = 0.776064 + 0.771091I
10.17630 + 6.07102I 0
u = −0.99469 − 1.20464I
a = −0.034102 − 1.124490I
b = 0.776064 − 0.771091I
10.17630 − 6.07102I 0
u = −1.15857 + 1.04836I
a = −0.286287 − 0.454025I
b = −0.947606 − 0.404793I
2.78645 + 5.56447I 0
u = −1.15857 − 1.04836I
a = −0.286287 + 0.454025I
b = −0.947606 + 0.404793I
2.78645 − 5.56447I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.66671 + 1.42349I
a = −0.183175 + 0.380040I
b = −0.734663 + 0.828846I
4.55795 − 4.68763I 0
u = 0.66671 − 1.42349I
a = −0.183175 − 0.380040I
b = −0.734663 − 0.828846I
4.55795 + 4.68763I 0
u = 0.55167 + 1.47597I
a = 0.185991 − 0.311739I
b = 0.687152 − 0.783132I
4.29320 + 1.43417I 0
u = 0.55167 − 1.47597I
a = 0.185991 + 0.311739I
b = 0.687152 + 0.783132I
4.29320 − 1.43417I 0
u = −0.057032 + 0.413051I
a = 0.06908 − 4.04906I
b = −0.411782 − 0.956309I
3.50521 + 0.40441I −1.27968 − 1.36402I
u = −0.057032 − 0.413051I
a = 0.06908 + 4.04906I
b = −0.411782 + 0.956309I
3.50521 − 0.40441I −1.27968 + 1.36402I
u = 0.29573 + 1.55558I
a = −0.139405 + 0.616609I
b = −0.294666 − 0.103183I
8.45007 − 4.01645I 0
u = 0.29573 − 1.55558I
a = −0.139405 − 0.616609I
b = −0.294666 + 0.103183I
8.45007 + 4.01645I 0
u = 0.11916 + 1.58631I
a = 0.055671 − 0.581903I
b = 0.327032 + 0.107858I
8.79268 + 2.27687I 0
u = 0.11916 − 1.58631I
a = 0.055671 + 0.581903I
b = 0.327032 − 0.107858I
8.79268 − 2.27687I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.46966 + 0.62366I
a = 0.257768 + 0.597655I
b = −0.008762 + 0.604709I
−3.83356 + 0.38759I 0
u = 1.46966 − 0.62366I
a = 0.257768 − 0.597655I
b = −0.008762 − 0.604709I
−3.83356 − 0.38759I 0
u = −0.305709 + 0.253315I
a = 0.99812 + 3.00858I
b = 0.391781 + 0.843855I
−2.10847 + 2.41665I −7.89279 − 5.63736I
u = −0.305709 − 0.253315I
a = 0.99812 − 3.00858I
b = 0.391781 − 0.843855I
−2.10847 − 2.41665I −7.89279 + 5.63736I
u = −0.355700 + 0.091311I
a = −0.03410 + 2.58541I
b = 0.150760 + 0.786380I
0.19720 − 2.31992I 1.56244 + 1.36705I
u = −0.355700 − 0.091311I
a = −0.03410 − 2.58541I
b = 0.150760 − 0.786380I
0.19720 + 2.31992I 1.56244 − 1.36705I
u = 0.96640 + 1.33986I
a = −0.056754 + 1.017840I
b = −0.855296 + 1.100900I
4.96333 − 6.71922I 0
u = 0.96640 − 1.33986I
a = −0.056754 − 1.017840I
b = −0.855296 − 1.100900I
4.96333 + 6.71922I 0
u = −0.98394 + 1.33712I
a = −0.044895 − 0.952937I
b = −1.03585 − 1.17641I
9.6218 + 13.1451I 0
u = −0.98394 − 1.33712I
a = −0.044895 + 0.952937I
b = −1.03585 + 1.17641I
9.6218 − 13.1451I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.02833 + 1.31599I
a = 0.053691 + 0.974396I
b = 1.03924 + 1.17085I
8.7975 + 19.6210I 0
u = −1.02833 − 1.31599I
a = 0.053691 − 0.974396I
b = 1.03924 − 1.17085I
8.7975 − 19.6210I 0
u = 1.01666 + 1.32694I
a = 0.044688 − 1.033270I
b = 0.856920 − 1.102340I
4.43125 − 12.88750I 0
u = 1.01666 − 1.32694I
a = 0.044688 + 1.033270I
b = 0.856920 + 1.102340I
4.43125 + 12.88750I 0
u = 0.142656 + 0.106541I
a = 4.69771 − 4.79416I
b = −0.518383 − 0.916779I
−0.63899 + 2.02048I −5.40557 − 3.17001I
u = 0.142656 − 0.106541I
a = 4.69771 + 4.79416I
b = −0.518383 + 0.916779I
−0.63899 − 2.02048I −5.40557 + 3.17001I
u = −1.33087 + 1.24696I
a = −0.351156 − 0.189688I
b = −0.958957 − 0.219321I
8.99976 + 8.86703I 0
u = −1.33087 − 1.24696I
a = −0.351156 + 0.189688I
b = −0.958957 + 0.219321I
8.99976 − 8.86703I 0
u = −1.29302 + 1.29790I
a = 0.310140 + 0.159791I
b = 0.924245 + 0.205463I
9.28156 + 2.80052I 0
u = −1.29302 − 1.29790I
a = 0.310140 − 0.159791I
b = 0.924245 − 0.205463I
9.28156 − 2.80052I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.98823 + 0.57740I
a = −0.389707 + 0.287305I
b = −0.222276 + 0.546955I
7.17013 − 3.92014I 0
u = −1.98823 − 0.57740I
a = −0.389707 − 0.287305I
b = −0.222276 − 0.546955I
7.17013 + 3.92014I 0
u = −2.00423 + 0.74302I
a = 0.387343 − 0.263312I
b = 0.240941 − 0.531243I
6.75576 − 10.20230I 0
u = −2.00423 − 0.74302I
a = 0.387343 + 0.263312I
b = 0.240941 + 0.531243I
6.75576 + 10.20230I 0
u = 2.30318 + 0.10618I
a = 0.018491 + 0.532841I
b = 0.005633 + 0.556168I
1.63020 + 3.00541I 0
u = 2.30318 − 0.10618I
a = 0.018491 − 0.532841I
b = 0.005633 − 0.556168I
1.63020 − 3.00541I 0
19
II. I
u
2
=
h7.18×10
32
u
25
−3.75×10
33
u
24
+· · ·+2.20×10
33
b−2.57×10
35
, 7.49×10
34
u
25
−
3.84×10
35
u
24
+· · ·+1.43 ×10
35
a−2.61 × 10
37
, u
26
−6u
25
+· · ·−1450u +325i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
5
=
−0.522772u
25
+ 2.67859u
24
+ ··· − 624.387u + 182.261
−0.325635u
25
+ 1.70150u
24
+ ··· − 403.988u + 116.850
a
9
=
1
u
2
a
12
=
0.0869459u
25
− 0.470164u
24
+ ··· + 123.486u − 39.0141
0.0838690u
25
− 0.451703u
24
+ ··· + 116.929u − 34.5525
a
4
=
−0.197137u
25
+ 0.977087u
24
+ ··· − 220.399u + 65.4101
−0.325635u
25
+ 1.70150u
24
+ ··· − 403.988u + 116.850
a
3
=
−0.302807u
25
+ 1.58855u
24
+ ··· − 390.141u + 115.397
−0.248017u
25
+ 1.39983u
24
+ ··· − 402.353u + 124.182
a
7
=
−0.0647902u
25
+ 0.393000u
24
+ ··· − 137.579u + 47.7686
0.0930366u
25
− 0.455846u
24
+ ··· + 80.5038u − 17.7169
a
6
=
0.131551u
25
− 0.730484u
24
+ ··· + 173.588u − 45.7657
−0.175827u
25
+ 0.660728u
24
+ ··· − 42.9804u + 9.38129
a
2
=
−0.0132789u
25
+ 0.0981775u
24
+ ··· − 50.5217u + 18.5112
0.0708953u
25
− 0.319637u
24
+ ··· + 24.5932u + 3.52667
a
10
=
−0.00917141u
25
+ 0.0369071u
24
+ ··· + 1.98027u − 3.05587
0.0122483u
25
− 0.0553687u
24
+ ··· + 6.57666u − 1.40567
a
1
=
0.0881941u
25
− 0.465405u
24
+ ··· + 114.671u − 35.2473
0.0647242u
25
− 0.353226u
24
+ ··· + 92.6603u − 27.0170
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0.244033u
25
− 1.41410u
24
+ ··· + 528.354u − 202.320
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
26
− 8u
25
+ ··· − 22u + 1
c
2
u
26
− 2u
25
+ ··· − 2u + 1
c
3
u
26
− 4u
24
+ ··· − 8u + 1
c
4
u
26
+ 3u
24
+ ··· + 5u
2
+ 1
c
6
u
26
+ 2u
25
+ ··· + 2u + 1
c
7
u
26
− 4u
25
+ ··· + 2u + 1
c
8
u
26
− 6u
25
+ ··· − 1450u + 325
c
9
u
26
− 8u
25
+ ··· − 2u + 1
c
10
u
26
− 2u
24
+ ··· + 5u
2
+ 1
c
11
u
26
+ 5u
24
+ ··· − 2u
2
+ 1
c
12
u
26
+ 8u
25
+ ··· + 2u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
26
+ 28y
25
+ ··· − 50y + 1
c
2
, c
6
y
26
+ 8y
25
+ ··· + 22y + 1
c
3
y
26
− 8y
25
+ ··· + 26y + 1
c
4
y
26
+ 6y
25
+ ··· + 10y + 1
c
7
y
26
− 24y
25
+ ··· − 10y + 1
c
8
y
26
− 14y
25
+ ··· − 506100y + 105625
c
9
, c
12
y
26
+ 12y
25
+ ··· + 22y + 1
c
10
y
26
− 4y
25
+ ··· + 10y + 1
c
11
y
26
+ 10y
25
+ ··· − 4y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.642907 + 0.719704I
a = −0.049670 + 0.987522I
b = −1.12126 + 1.16360I
−1.94746 − 3.72158I −3.38899 + 5.95359I
u = 0.642907 − 0.719704I
a = −0.049670 − 0.987522I
b = −1.12126 − 1.16360I
−1.94746 + 3.72158I −3.38899 − 5.95359I
u = 0.886895 + 0.060397I
a = −0.11730 − 1.58959I
b = −0.067849 − 0.797201I
−0.64567 − 2.56810I −8.79473 + 2.84141I
u = 0.886895 − 0.060397I
a = −0.11730 + 1.58959I
b = −0.067849 + 0.797201I
−0.64567 + 2.56810I −8.79473 − 2.84141I
u = 0.932635 + 0.619144I
a = −0.471311 + 1.025330I
b = −1.17809 + 1.04809I
2.09499 − 8.69478I −3.51881 + 11.95658I
u = 0.932635 − 0.619144I
a = −0.471311 − 1.025330I
b = −1.17809 − 1.04809I
2.09499 + 8.69478I −3.51881 − 11.95658I
u = 0.984240 + 0.685609I
a = 0.476981 − 0.915527I
b = 1.14488 − 1.00038I
2.65402 − 3.22600I −3.00214 + 4.67394I
u = 0.984240 − 0.685609I
a = 0.476981 + 0.915527I
b = 1.14488 + 1.00038I
2.65402 + 3.22600I −3.00214 − 4.67394I
u = −0.549428 + 0.512959I
a = 0.430462 − 0.924955I
b = −1.088500 − 0.086833I
0.87918 + 5.03600I −1.98431 − 8.01124I
u = −0.549428 − 0.512959I
a = 0.430462 + 0.924955I
b = −1.088500 + 0.086833I
0.87918 − 5.03600I −1.98431 + 8.01124I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.901526 + 0.978087I
a = 0.287411 − 0.711914I
b = 0.945344 − 1.042100I
0.04503 − 4.74402I −3.06160 + 13.78611I
u = 0.901526 − 0.978087I
a = 0.287411 + 0.711914I
b = 0.945344 + 1.042100I
0.04503 + 4.74402I −3.06160 − 13.78611I
u = 1.311010 + 0.228540I
a = −0.169705 − 1.061080I
b = −0.072227 − 0.544722I
−3.39487 + 0.57363I −0.02651 − 12.54083I
u = 1.311010 − 0.228540I
a = −0.169705 + 1.061080I
b = −0.072227 + 0.544722I
−3.39487 − 0.57363I −0.02651 + 12.54083I
u = 0.157239 + 1.349560I
a = 0.085502 − 0.409777I
b = 0.11950 − 1.70339I
6.36975 − 4.25224I 4.76761 − 4.59235I
u = 0.157239 − 1.349560I
a = 0.085502 + 0.409777I
b = 0.11950 + 1.70339I
6.36975 + 4.25224I 4.76761 + 4.59235I
u = −0.214575 + 1.360360I
a = −0.148264 + 0.386526I
b = 0.65174 + 1.37751I
6.99718 + 2.92961I −1.03265 − 2.70666I
u = −0.214575 − 1.360360I
a = −0.148264 − 0.386526I
b = 0.65174 − 1.37751I
6.99718 − 2.92961I −1.03265 + 2.70666I
u = −1.400040 + 0.172477I
a = −0.243878 − 0.684805I
b = −0.626936 − 0.109312I
7.61432 + 9.84785I 3.78900 − 7.90385I
u = −1.400040 − 0.172477I
a = −0.243878 + 0.684805I
b = −0.626936 + 0.109312I
7.61432 − 9.84785I 3.78900 + 7.90385I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.46101 + 0.37246I
a = 0.170747 + 0.645580I
b = 0.623516 + 0.167102I
8.10817 + 3.70298I 4.79874 − 3.48112I
u = −1.46101 − 0.37246I
a = 0.170747 − 0.645580I
b = 0.623516 − 0.167102I
8.10817 − 3.70298I 4.79874 + 3.48112I
u = −1.08012 + 1.13039I
a = −0.068718 + 0.538805I
b = 0.681943 + 0.477579I
3.79621 + 3.81566I −3.37216 − 6.96346I
u = −1.08012 − 1.13039I
a = −0.068718 − 0.538805I
b = 0.681943 − 0.477579I
3.79621 − 3.81566I −3.37216 + 6.96346I
u = 1.88873 + 0.07760I
a = −0.028411 − 0.785092I
b = −0.012048 − 0.429242I
1.97277 + 2.99985I 9.82655 − 2.88515I
u = 1.88873 − 0.07760I
a = −0.028411 + 0.785092I
b = −0.012048 + 0.429242I
1.97277 − 2.99985I 9.82655 + 2.88515I
25
III. I
v
1
= ha, −v
2
+ b + 2v, v
4
− 3v
3
+ 2v
2
+ 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
v
0
a
5
=
0
v
2
− 2v
a
9
=
1
0
a
12
=
v
v
3
− 2v
2
+ v −1
a
4
=
−v
2
+ 2v
v
2
− 2v
a
3
=
0
v
2
− 2v
a
7
=
v
3
− v
2
− v
−v
3
+ 2v
2
− v
a
6
=
v
3
− 2v
2
−v
3
+ 3v
2
− 3v + 1
a
2
=
−v
3
+ v
2
+ v
v
3
− 2v
2
+ 1
a
10
=
−v
3
+ 2v
2
+ 1
v
3
− 2v
2
+ v −1
a
1
=
−v
3
+ v
2
+ v
v
3
− 2v
2
+ v
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8v
3
− 16v
2
+ 11v −8
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
9
(u
2
− u + 1)
2
c
2
, c
7
, c
12
(u
2
+ u + 1)
2
c
3
, c
4
u
4
− u
3
+ 2u
2
− 2u + 1
c
8
u
4
c
10
, c
11
u
4
+ u
3
− u
2
− u + 1
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
9
c
12
(y
2
+ y + 1)
2
c
3
, c
4
y
4
+ 3y
3
+ 2y
2
+ 1
c
8
y
4
c
10
, c
11
y
4
− 3y
3
+ 5y
2
− 3y + 1
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.192440 + 0.547877I
a = 0
b = 0.121744 − 1.306620I
− 4.05977I −4.57732 + 8.57184I
v = −0.192440 − 0.547877I
a = 0
b = 0.121744 + 1.306620I
4.05977I −4.57732 − 8.57184I
v = 1.69244 + 0.31815I
a = 0
b = −0.621744 + 0.440597I
− 4.05977I 1.07732 + 7.88265I
v = 1.69244 − 0.31815I
a = 0
b = −0.621744 − 0.440597I
4.05977I 1.07732 − 7.88265I
29
IV. I
v
2
= ha, −5v
3
+ 16v
2
+ 8b − 40v + 15, v
4
− 3v
3
+ 8v
2
− 3v + 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
v
0
a
5
=
0
5
8
v
3
− 2v
2
+ 5v −
15
8
a
9
=
1
0
a
12
=
v
3
8
v
3
− v
2
+ 3v −
9
8
a
4
=
−
5
8
v
3
+ 2v
2
− 5v +
15
8
5
8
v
3
− 2v
2
+ 5v −
15
8
a
3
=
0
5
8
v
3
− 2v
2
+ 5v −
15
8
a
7
=
1
8
v
3
+
5
8
−
3
8
v
3
+ v
2
− 3v +
1
8
a
6
=
−
1
4
v
3
+ v
2
− 2v +
3
4
5
8
v
3
− 2v
2
+ 5v −
23
8
a
2
=
−
1
8
v
3
−
5
8
9
8
v
3
− 3v
2
+ 8v −
3
8
a
10
=
−
3
8
v
3
+ v
2
− 2v +
9
8
3
8
v
3
− v
2
+ 3v −
9
8
a
1
=
−
1
8
v
3
−
5
8
3
8
v
3
− v
2
+ 3v −
1
8
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3v
3
+ 9v
2
− 21v − 1
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
9
(u
2
− u + 1)
2
c
2
, c
7
, c
12
(u
2
+ u + 1)
2
c
3
, c
4
u
4
− u
3
+ 2u
2
+ u + 1
c
8
u
4
c
10
, c
11
(u
2
− u − 1)
2
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
9
c
12
(y
2
+ y + 1)
2
c
3
, c
4
y
4
+ 3y
3
+ 8y
2
+ 3y + 1
c
8
y
4
c
10
, c
11
(y
2
− 3y + 1)
2
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 0.190983 + 0.330792I
a = 0
b = −0.80902 + 1.40126I
0 −5.50000 − 5.80948I
v = 0.190983 − 0.330792I
a = 0
b = −0.80902 − 1.40126I
0 −5.50000 + 5.80948I
v = 1.30902 + 2.26728I
a = 0
b = 0.309017 − 0.535233I
0 −5.50000 + 5.80948I
v = 1.30902 − 2.26728I
a = 0
b = 0.309017 + 0.535233I
0 −5.50000 − 5.80948I
33
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
((u
2
− u + 1)
4
)(u
26
− 8u
25
+ ··· − 22u + 1)
· (u
146
+ 41u
145
+ ··· + 13874u + 441)
c
2
((u
2
+ u + 1)
4
)(u
26
− 2u
25
+ ··· − 2u + 1)(u
146
− 3u
145
+ ··· + 56u + 21)
c
3
(u
4
− u
3
+ 2u
2
− 2u + 1)(u
4
− u
3
+ 2u
2
+ u + 1)(u
26
− 4u
24
+ ··· − 8u + 1)
· (u
146
+ 3u
145
+ ··· − 213878079u + 69993509)
c
4
(u
4
− u
3
+ 2u
2
− 2u + 1)(u
4
− u
3
+ 2u
2
+ u + 1)(u
26
+ 3u
24
+ ··· + 5u
2
+ 1)
· (u
146
+ 9u
145
+ ··· + 97u + 16)
c
6
((u
2
− u + 1)
4
)(u
26
+ 2u
25
+ ··· + 2u + 1)(u
146
− 3u
145
+ ··· + 56u + 21)
c
7
((u
2
+ u + 1)
4
)(u
26
− 4u
25
+ ··· + 2u + 1)
· (u
146
− 5u
145
+ ··· + 163744u + 32887)
c
8
u
8
(u
26
− 6u
25
+ ··· − 1450u + 325)(u
146
− 13u
145
+ ··· − 3712u + 768)
c
9
((u
2
− u + 1)
4
)(u
26
− 8u
25
+ ··· − 2u + 1)
· (u
146
+ 7u
145
+ ··· + 95533u + 4448)
c
10
((u
2
− u − 1)
2
)(u
4
+ u
3
− u
2
− u + 1)(u
26
− 2u
24
+ ··· + 5u
2
+ 1)
· (u
146
− 6u
144
+ ··· − 35u + 1)
c
11
((u
2
− u − 1)
2
)(u
4
+ u
3
− u
2
− u + 1)(u
26
+ 5u
24
+ ··· − 2u
2
+ 1)
· (u
146
+ 2u
145
+ ··· + 153777u + 21323)
c
12
((u
2
+ u + 1)
4
)(u
26
+ 8u
25
+ ··· + 2u + 1)
· (u
146
+ 7u
145
+ ··· + 95533u + 4448)
34
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y
2
+ y + 1)
4
)(y
26
+ 28y
25
+ ··· − 50y + 1)
· (y
146
+ 141y
145
+ ··· + 10798130y + 194481)
c
2
, c
6
((y
2
+ y + 1)
4
)(y
26
+ 8y
25
+ ··· + 22y + 1)
· (y
146
+ 41y
145
+ ··· + 13874y + 441)
c
3
(y
4
+ 3y
3
+ 2y
2
+ 1)(y
4
+ 3y
3
+ ··· + 3y + 1)(y
26
− 8y
25
+ ··· + 26y + 1)
· (y
146
+ 59y
145
+ ··· + 839682611759848865y + 4899091302133081)
c
4
(y
4
+ 3y
3
+ 2y
2
+ 1)(y
4
+ 3y
3
+ ··· + 3y + 1)(y
26
+ 6y
25
+ ··· + 10y + 1)
· (y
146
+ 21y
145
+ ··· + 13375y + 256)
c
7
((y
2
+ y + 1)
4
)(y
26
− 24y
25
+ ··· − 10y + 1)
· (y
146
− 39y
145
+ ··· − 49681388466y + 1081554769)
c
8
y
8
(y
26
− 14y
25
+ ··· − 506100y + 105625)
· (y
146
+ 11y
145
+ ··· + 6373376y + 589824)
c
9
, c
12
((y
2
+ y + 1)
4
)(y
26
+ 12y
25
+ ··· + 22y + 1)
· (y
146
+ 97y
145
+ ··· − 4451394729y + 19784704)
c
10
((y
2
− 3y + 1)
2
)(y
4
− 3y
3
+ ··· − 3y + 1)(y
26
− 4y
25
+ ··· + 10y + 1)
· (y
146
− 12y
145
+ ··· + 265y + 1)
c
11
((y
2
− 3y + 1)
2
)(y
4
− 3y
3
+ ··· − 3y + 1)(y
26
+ 10y
25
+ ··· − 4y + 1)
· (y
146
− 30y
145
+ ··· − 28764118101y + 454670329)
35
