12a
0687
(K12a
0687
)
A knot diagram
1
Linearized knot diagam
3 7 12 8 11 9 2 5 1 6 4 10
Solving Sequence
5,11 6,8
9 7 4 12 3 2 10 1
c
5
c
8
c
6
c
4
c
11
c
3
c
2
c
10
c
12
c
1
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.88489 × 10
881
u
156
+ 5.04115 × 10
881
u
155
+ ··· + 1.36721 × 10
885
b + 7.83741 × 10
885
,
1.51590 × 10
887
u
156
+ 1.49559 × 10
887
u
155
+ ··· + 3.82955 × 10
888
a + 1.83695 × 10
890
,
u
157
+ u
156
+ ··· − 13732u + 2801i
I
u
2
= h6.98058 × 10
29
u
45
+ 2.34056 × 10
31
u
44
+ ··· + 8.45573 × 10
29
b + 5.19010 × 10
31
,
− 1.05603 × 10
31
u
45
+ 6.43040 × 10
31
u
44
+ ··· + 8.45573 × 10
29
a + 1.26598 × 10
32
,
u
46
+ 16u
44
+ ··· − 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 203 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−7.88 × 10
881
u
156
+ 5.04 × 10
881
u
155
+ · · · + 1.37 × 10
885
b + 7.84 ×
10
885
, 1.52 × 10
887
u
156
+ 1.50 × 10
887
u
155
+ · · · + 3.83 × 10
888
a + 1.84 ×
10
890
, u
157
+ u
156
+ · · · − 13732u + 2801i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
u
2
a
8
=
−0.0395843u
156
− 0.0390538u
155
+ ··· + 6.00367u − 47.9679
0.000576714u
156
− 0.000368718u
155
+ ··· + 16.8195u − 5.73242
a
9
=
−0.0401610u
156
− 0.0386851u
155
+ ··· − 10.8158u − 42.2355
0.000576714u
156
− 0.000368718u
155
+ ··· + 16.8195u − 5.73242
a
7
=
0.0292302u
156
+ 0.0194863u
155
+ ··· + 288.828u − 15.3680
−0.00382346u
156
+ 0.0105651u
155
+ ··· − 249.524u + 42.7915
a
4
=
−0.00864217u
156
− 0.0147723u
155
+ ··· + 8.42837u − 22.7494
0.0132793u
156
− 0.0288943u
155
+ ··· + 805.874u − 143.749
a
12
=
−0.0126184u
156
+ 0.0133006u
155
+ ··· − 460.460u + 95.0835
−0.0388728u
156
− 0.0404769u
155
+ ··· + 87.6322u − 45.1102
a
3
=
0.0360791u
156
+ 0.0376727u
155
+ ··· + 34.8247u + 5.35530
0.0150618u
156
+ 0.00404137u
155
+ ··· + 265.235u − 37.9961
a
2
=
0.0142652u
156
− 0.00878578u
155
+ ··· + 398.926u − 78.0566
−0.0136596u
156
− 0.0457142u
155
+ ··· + 646.176u − 134.161
a
10
=
u
u
3
+ u
a
1
=
0.0143267u
156
+ 0.0367680u
155
+ ··· − 444.852u + 111.218
−0.0316780u
156
− 0.0280375u
155
+ ··· − 19.9885u − 19.2345
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0904845u
156
+ 0.0524635u
155
+ ··· + 426.624u − 32.7175
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
157
+ 75u
156
+ ··· − 314997534u − 13845841
c
2
, c
7
u
157
+ u
156
+ ··· + 6588u + 3721
c
3
, c
11
u
157
− 4u
156
+ ··· + 14174519u − 1906367
c
4
, c
8
u
157
+ 3u
156
+ ··· + 8u + 1
c
5
, c
10
u
157
+ u
156
+ ··· − 13732u + 2801
c
6
u
157
− 3u
156
+ ··· − 346340u + 292121
c
9
, c
12
u
157
+ 4u
156
+ ··· + 13669u + 2263
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
157
+ 39y
156
+ ··· − 7046372593682426y −191707312997281
c
2
, c
7
y
157
+ 75y
156
+ ··· − 314997534y −13845841
c
3
, c
11
y
157
+ 114y
156
+ ··· − 60423847276045y −3634235138689
c
4
, c
8
y
157
− 75y
156
+ ··· + 6y −1
c
5
, c
10
y
157
+ 99y
156
+ ··· − 1215170132y −7845601
c
6
y
157
− 3y
156
+ ··· − 13877806866712y −85334678641
c
9
, c
12
y
157
+ 78y
156
+ ··· − 296376829y −5121169
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.983424 + 0.118249I
a = −1.292700 − 0.555427I
b = −1.021630 − 0.532125I
2.09693 − 1.77887I 0
u = −0.983424 − 0.118249I
a = −1.292700 + 0.555427I
b = −1.021630 + 0.532125I
2.09693 + 1.77887I 0
u = −0.953573 + 0.264717I
a = −1.39252 − 0.44034I
b = −0.477503 − 0.472794I
1.38071 + 2.57286I 0
u = −0.953573 − 0.264717I
a = −1.39252 + 0.44034I
b = −0.477503 + 0.472794I
1.38071 − 2.57286I 0
u = 0.646783 + 0.777333I
a = −1.035230 + 0.533846I
b = −1.064440 + 0.310838I
−2.42988 + 0.41909I 0
u = 0.646783 − 0.777333I
a = −1.035230 − 0.533846I
b = −1.064440 − 0.310838I
−2.42988 − 0.41909I 0
u = 0.962659 + 0.205398I
a = 1.209760 − 0.643836I
b = 1.146630 − 0.543092I
0.74143 + 7.22667I 0
u = 0.962659 − 0.205398I
a = 1.209760 + 0.643836I
b = 1.146630 + 0.543092I
0.74143 − 7.22667I 0
u = −0.320494 + 0.969075I
a = 0.051229 − 0.785137I
b = −1.034320 + 0.663947I
−4.31173 + 3.30916I 0
u = −0.320494 − 0.969075I
a = 0.051229 + 0.785137I
b = −1.034320 − 0.663947I
−4.31173 − 3.30916I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.517962 + 0.905954I
a = 1.07818 − 0.94510I
b = 0.076738 + 0.558359I
−0.18244 − 7.76232I 0
u = 0.517962 − 0.905954I
a = 1.07818 + 0.94510I
b = 0.076738 − 0.558359I
−0.18244 + 7.76232I 0
u = −0.125294 + 1.040410I
a = 0.0169154 + 0.0736309I
b = −0.28755 − 1.51200I
3.81414 − 0.90830I 0
u = −0.125294 − 1.040410I
a = 0.0169154 − 0.0736309I
b = −0.28755 + 1.51200I
3.81414 + 0.90830I 0
u = −0.050925 + 1.048040I
a = 0.142537 + 0.947115I
b = 0.355411 − 0.817437I
3.47290 + 2.16111I 0
u = −0.050925 − 1.048040I
a = 0.142537 − 0.947115I
b = 0.355411 + 0.817437I
3.47290 − 2.16111I 0
u = 0.506761 + 0.923868I
a = 1.24946 − 1.18931I
b = 1.005110 + 0.582922I
−1.95131 − 4.96181I 0
u = 0.506761 − 0.923868I
a = 1.24946 + 1.18931I
b = 1.005110 − 0.582922I
−1.95131 + 4.96181I 0
u = 0.816371 + 0.666474I
a = −0.549641 + 0.190487I
b = −0.877011 + 0.666561I
−3.67100 − 1.69687I 0
u = 0.816371 − 0.666474I
a = −0.549641 − 0.190487I
b = −0.877011 − 0.666561I
−3.67100 + 1.69687I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.484533 + 0.779590I
a = −0.354392 − 1.105070I
b = −1.237300 + 0.270956I
−4.40866 − 4.50850I 0
u = −0.484533 − 0.779590I
a = −0.354392 + 1.105070I
b = −1.237300 − 0.270956I
−4.40866 + 4.50850I 0
u = 0.134797 + 0.907142I
a = 2.13452 − 1.41578I
b = 1.053360 + 0.458463I
3.79683 − 5.21301I 0
u = 0.134797 − 0.907142I
a = 2.13452 + 1.41578I
b = 1.053360 − 0.458463I
3.79683 + 5.21301I 0
u = 0.151343 + 0.903789I
a = −1.41628 − 0.05456I
b = −1.49638 + 0.09674I
−1.23675 − 2.85908I 0
u = 0.151343 − 0.903789I
a = −1.41628 + 0.05456I
b = −1.49638 − 0.09674I
−1.23675 + 2.85908I 0
u = −0.088980 + 0.911104I
a = −2.22518 − 1.10650I
b = −1.073320 + 0.405134I
3.90559 − 0.80435I 0
u = −0.088980 − 0.911104I
a = −2.22518 + 1.10650I
b = −1.073320 − 0.405134I
3.90559 + 0.80435I 0
u = −0.129431 + 0.895829I
a = 0.248150 + 1.140630I
b = −0.049560 − 1.201590I
3.28928 + 1.91897I 0
u = −0.129431 − 0.895829I
a = 0.248150 − 1.140630I
b = −0.049560 + 1.201590I
3.28928 − 1.91897I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.612763 + 0.660646I
a = −1.56504 − 0.86691I
b = −1.138800 + 0.640935I
−4.18401 + 1.65000I 0
u = −0.612763 − 0.660646I
a = −1.56504 + 0.86691I
b = −1.138800 − 0.640935I
−4.18401 − 1.65000I 0
u = −0.219192 + 0.873736I
a = 1.133280 + 0.104372I
b = 1.72318 − 0.04282I
−4.54438 + 7.47305I 0
u = −0.219192 − 0.873736I
a = 1.133280 − 0.104372I
b = 1.72318 + 0.04282I
−4.54438 − 7.47305I 0
u = −0.382410 + 0.797108I
a = −1.09618 − 0.93984I
b = 0.154925 + 0.411991I
0.87708 + 2.51431I 0
u = −0.382410 − 0.797108I
a = −1.09618 + 0.93984I
b = 0.154925 − 0.411991I
0.87708 − 2.51431I 0
u = 0.526170 + 0.706597I
a = −0.186604 − 0.941652I
b = −0.386499 + 0.260859I
−4.41300 − 2.16123I 0
u = 0.526170 − 0.706597I
a = −0.186604 + 0.941652I
b = −0.386499 − 0.260859I
−4.41300 + 2.16123I 0
u = 0.236131 + 0.830375I
a = −0.214590 − 1.160790I
b = 0.898111 + 0.411853I
−1.20612 + 0.95128I 0
u = 0.236131 − 0.830375I
a = −0.214590 + 1.160790I
b = 0.898111 − 0.411853I
−1.20612 − 0.95128I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.056910 + 0.426045I
a = 1.378430 − 0.183130I
b = 1.176020 + 0.065926I
−8.95915 + 1.30472I 0
u = −1.056910 − 0.426045I
a = 1.378430 + 0.183130I
b = 1.176020 − 0.065926I
−8.95915 − 1.30472I 0
u = −0.854770 + 0.762921I
a = 0.606990 + 0.356542I
b = 1.107180 + 0.636268I
−4.12077 − 1.72135I 0
u = −0.854770 − 0.762921I
a = 0.606990 − 0.356542I
b = 1.107180 − 0.636268I
−4.12077 + 1.72135I 0
u = 0.407873 + 1.071970I
a = −0.636057 + 0.959108I
b = −1.037400 − 0.218361I
−1.73344 − 0.63595I 0
u = 0.407873 − 1.071970I
a = −0.636057 − 0.959108I
b = −1.037400 + 0.218361I
−1.73344 + 0.63595I 0
u = −0.745385 + 0.876961I
a = −1.23068 − 0.81672I
b = −0.981818 + 0.850390I
−3.74907 + 7.62415I 0
u = −0.745385 − 0.876961I
a = −1.23068 + 0.81672I
b = −0.981818 − 0.850390I
−3.74907 − 7.62415I 0
u = −0.746880 + 0.880965I
a = 0.742828 + 0.555113I
b = 1.218590 + 0.372567I
−3.66009 + 3.61781I 0
u = −0.746880 − 0.880965I
a = 0.742828 − 0.555113I
b = 1.218590 − 0.372567I
−3.66009 − 3.61781I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.131246 + 0.823567I
a = 1.194740 − 0.415293I
b = 1.57754 + 0.38551I
−5.20350 − 1.29361I 0
u = −0.131246 − 0.823567I
a = 1.194740 + 0.415293I
b = 1.57754 − 0.38551I
−5.20350 + 1.29361I 0
u = −0.376515 + 1.110300I
a = 0.0180237 − 0.0417333I
b = −0.66910 − 1.31854I
6.11212 + 5.28335I 0
u = −0.376515 − 1.110300I
a = 0.0180237 + 0.0417333I
b = −0.66910 + 1.31854I
6.11212 − 5.28335I 0
u = 0.708612 + 0.956040I
a = 1.13424 − 0.86547I
b = 0.780133 + 0.804599I
−2.84437 − 3.98936I 0
u = 0.708612 − 0.956040I
a = 1.13424 + 0.86547I
b = 0.780133 − 0.804599I
−2.84437 + 3.98936I 0
u = 0.130319 + 1.185510I
a = −1.67725 + 1.17605I
b = −1.033190 − 0.359624I
3.25928 − 2.97909I 0
u = 0.130319 − 1.185510I
a = −1.67725 − 1.17605I
b = −1.033190 + 0.359624I
3.25928 + 2.97909I 0
u = 0.727293 + 0.347210I
a = −1.64949 − 0.12002I
b = −1.185650 + 0.272617I
−4.01071 + 2.09725I 0
u = 0.727293 − 0.347210I
a = −1.64949 + 0.12002I
b = −1.185650 − 0.272617I
−4.01071 − 2.09725I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.252364 + 1.169570I
a = 0.543026 + 0.868177I
b = 0.993662 − 0.576624I
1.88635 + 2.96312I 0
u = −0.252364 − 1.169570I
a = 0.543026 − 0.868177I
b = 0.993662 + 0.576624I
1.88635 − 2.96312I 0
u = −0.777869 + 0.932844I
a = −1.73517 − 0.15009I
b = −1.011600 + 0.477461I
4.02418 + 1.15616I 0
u = −0.777869 − 0.932844I
a = −1.73517 + 0.15009I
b = −1.011600 − 0.477461I
4.02418 − 1.15616I 0
u = 0.770158 + 0.143087I
a = 1.61615 − 0.26926I
b = 0.182574 − 0.638116I
−0.29177 − 8.18913I 0
u = 0.770158 − 0.143087I
a = 1.61615 + 0.26926I
b = 0.182574 + 0.638116I
−0.29177 + 8.18913I 0
u = −0.745739 + 0.150142I
a = 1.64583 − 0.38540I
b = 1.310780 + 0.301679I
−6.51205 − 7.33858I 0
u = −0.745739 − 0.150142I
a = 1.64583 + 0.38540I
b = 1.310780 − 0.301679I
−6.51205 + 7.33858I 0
u = 0.325677 + 0.687118I
a = 1.50972 − 2.19629I
b = −0.238481 + 0.091283I
−0.19815 − 7.87590I 0
u = 0.325677 − 0.687118I
a = 1.50972 + 2.19629I
b = −0.238481 − 0.091283I
−0.19815 + 7.87590I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.626984 + 0.406452I
a = 1.08105 − 1.25584I
b = 1.183510 − 0.175680I
−2.66699 + 2.02776I 0
u = 0.626984 − 0.406452I
a = 1.08105 + 1.25584I
b = 1.183510 + 0.175680I
−2.66699 − 2.02776I 0
u = −0.133704 + 1.245720I
a = 1.42031 + 1.39062I
b = 0.999596 − 0.472247I
2.80674 + 7.95594I 0
u = −0.133704 − 1.245720I
a = 1.42031 − 1.39062I
b = 0.999596 + 0.472247I
2.80674 − 7.95594I 0
u = 0.339817 + 1.214920I
a = 0.0407385 − 0.0339113I
b = 0.617308 − 1.167720I
7.66052 − 0.37824I 0
u = 0.339817 − 1.214920I
a = 0.0407385 + 0.0339113I
b = 0.617308 + 1.167720I
7.66052 + 0.37824I 0
u = 0.640165 + 0.365956I
a = −0.054069 + 0.221356I
b = −0.213191 + 0.801677I
−1.75066 + 3.45252I 0
u = 0.640165 − 0.365956I
a = −0.054069 − 0.221356I
b = −0.213191 − 0.801677I
−1.75066 − 3.45252I 0
u = 0.426623 + 1.190150I
a = −1.151290 + 0.678879I
b = −1.32224 − 0.59496I
−0.15983 − 6.07472I 0
u = 0.426623 − 1.190150I
a = −1.151290 − 0.678879I
b = −1.32224 + 0.59496I
−0.15983 + 6.07472I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.021040 + 1.272170I
a = −0.693871 + 0.166719I
b = 0.536816 + 0.380747I
5.49007 + 1.49266I 0
u = 0.021040 − 1.272170I
a = −0.693871 − 0.166719I
b = 0.536816 − 0.380747I
5.49007 − 1.49266I 0
u = 0.452878 + 1.191700I
a = 0.70334 − 1.32291I
b = 1.073640 + 0.500654I
−1.30030 − 6.59027I 0
u = 0.452878 − 1.191700I
a = 0.70334 + 1.32291I
b = 1.073640 − 0.500654I
−1.30030 + 6.59027I 0
u = 0.712829 + 0.112855I
a = 1.76416 − 0.04418I
b = 1.233130 + 0.188271I
−4.45501 − 3.38045I 0
u = 0.712829 − 0.112855I
a = 1.76416 + 0.04418I
b = 1.233130 − 0.188271I
−4.45501 + 3.38045I 0
u = 0.330624 + 1.262430I
a = −0.653500 + 0.923207I
b = −1.196400 − 0.536399I
−0.24784 − 7.12635I 0
u = 0.330624 − 1.262430I
a = −0.653500 − 0.923207I
b = −1.196400 + 0.536399I
−0.24784 + 7.12635I 0
u = 0.367802 + 1.252950I
a = −0.0958780 − 0.0426635I
b = −0.094302 + 1.077110I
0.22235 − 4.50979I 0
u = 0.367802 − 1.252950I
a = −0.0958780 + 0.0426635I
b = −0.094302 − 1.077110I
0.22235 + 4.50979I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.237519 + 0.641854I
a = −1.73385 − 1.69987I
b = 0.310537 + 0.119313I
0.89751 + 2.53711I 0
u = −0.237519 − 0.641854I
a = −1.73385 + 1.69987I
b = 0.310537 − 0.119313I
0.89751 − 2.53711I 0
u = 1.295290 + 0.267673I
a = −1.276210 + 0.365122I
b = −1.032390 + 0.509616I
−0.24810 + 6.75844I 0
u = 1.295290 − 0.267673I
a = −1.276210 − 0.365122I
b = −1.032390 − 0.509616I
−0.24810 − 6.75844I 0
u = −0.245529 + 1.303530I
a = 0.95196 + 1.09592I
b = 1.157910 − 0.593512I
0.96053 + 3.93024I 0
u = −0.245529 − 1.303530I
a = 0.95196 − 1.09592I
b = 1.157910 + 0.593512I
0.96053 − 3.93024I 0
u = −1.321120 + 0.163287I
a = 1.275800 + 0.314006I
b = 1.130950 + 0.531846I
−2.85813 − 12.78990I 0
u = −1.321120 − 0.163287I
a = 1.275800 − 0.314006I
b = 1.130950 − 0.531846I
−2.85813 + 12.78990I 0
u = −0.449007 + 1.272460I
a = −0.540863 − 1.263800I
b = −1.130470 + 0.491770I
−2.97284 + 11.87020I 0
u = −0.449007 − 1.272460I
a = −0.540863 + 1.263800I
b = −1.130470 − 0.491770I
−2.97284 − 11.87020I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.459011 + 1.277780I
a = 0.0366481 + 0.0116698I
b = −0.422203 + 1.233630I
3.77311 − 12.74680I 0
u = 0.459011 − 1.277780I
a = 0.0366481 − 0.0116698I
b = −0.422203 − 1.233630I
3.77311 + 12.74680I 0
u = 0.038501 + 1.364540I
a = −0.172701 + 0.331003I
b = 0.143783 − 0.895306I
3.79424 + 1.41084I 0
u = 0.038501 − 1.364540I
a = −0.172701 − 0.331003I
b = 0.143783 + 0.895306I
3.79424 − 1.41084I 0
u = 0.747351 + 1.143850I
a = 1.59189 − 0.40142I
b = 1.078190 + 0.539924I
4.99973 − 7.83611I 0
u = 0.747351 − 1.143850I
a = 1.59189 + 0.40142I
b = 1.078190 − 0.539924I
4.99973 + 7.83611I 0
u = 0.052669 + 1.366980I
a = 0.530681 + 0.354263I
b = −0.654916 + 0.209060I
5.66080 + 3.73994I 0
u = 0.052669 − 1.366980I
a = 0.530681 − 0.354263I
b = −0.654916 − 0.209060I
5.66080 − 3.73994I 0
u = −0.432461 + 1.298810I
a = 0.0011687 + 0.0425140I
b = 0.403576 + 1.111300I
5.93690 + 7.16886I 0
u = −0.432461 − 1.298810I
a = 0.0011687 − 0.0425140I
b = 0.403576 − 1.111300I
5.93690 − 7.16886I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.583237 + 1.254380I
a = −1.157820 + 0.720669I
b = −1.26101 − 0.81969I
3.95794 − 12.84080I 0
u = 0.583237 − 1.254380I
a = −1.157820 − 0.720669I
b = −1.26101 + 0.81969I
3.95794 + 12.84080I 0
u = −0.558556 + 1.279010I
a = 1.186450 + 0.705371I
b = 1.20369 − 0.77248I
5.64130 + 7.32574I 0
u = −0.558556 − 1.279010I
a = 1.186450 − 0.705371I
b = 1.20369 + 0.77248I
5.64130 − 7.32574I 0
u = −0.600972
a = −1.58786
b = −0.987414
−1.63262 −5.64780
u = −0.650780 + 1.242880I
a = −0.721459 − 0.965293I
b = −1.036010 + 0.338172I
−6.24860 + 4.81413I 0
u = −0.650780 − 1.242880I
a = −0.721459 + 0.965293I
b = −1.036010 − 0.338172I
−6.24860 − 4.81413I 0
u = −0.419493 + 0.410791I
a = −0.366936 + 0.207966I
b = 0.071393 + 0.501900I
−0.277721 + 0.985210I −2.94676 − 4.34748I
u = −0.419493 − 0.410791I
a = −0.366936 − 0.207966I
b = 0.071393 − 0.501900I
−0.277721 − 0.985210I −2.94676 + 4.34748I
u = −0.045202 + 0.583511I
a = −0.40908 + 2.75321I
b = 0.036897 + 0.229878I
3.76914 + 2.68398I −1.73025 − 4.97882I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.045202 − 0.583511I
a = −0.40908 − 2.75321I
b = 0.036897 − 0.229878I
3.76914 − 2.68398I −1.73025 + 4.97882I
u = 0.31455 + 1.40476I
a = −0.936790 + 0.535740I
b = −1.275950 − 0.560640I
−0.27940 − 6.57413I 0
u = 0.31455 − 1.40476I
a = −0.936790 − 0.535740I
b = −1.275950 + 0.560640I
−0.27940 + 6.57413I 0
u = −0.37046 + 1.39500I
a = 0.174358 + 0.235685I
b = 0.435596 + 0.596467I
6.91568 + 3.28190I 0
u = −0.37046 − 1.39500I
a = 0.174358 − 0.235685I
b = 0.435596 − 0.596467I
6.91568 − 3.28190I 0
u = −0.55840 + 1.37381I
a = 1.302700 + 0.526491I
b = 1.053230 − 0.564498I
4.94987 + 3.50091I 0
u = −0.55840 − 1.37381I
a = 1.302700 − 0.526491I
b = 1.053230 + 0.564498I
4.94987 − 3.50091I 0
u = −0.189625 + 0.477716I
a = 1.01655 + 2.21109I
b = 0.091875 − 1.127070I
3.84039 − 2.25089I −3.80296 + 1.82490I
u = −0.189625 − 0.477716I
a = 1.01655 − 2.21109I
b = 0.091875 + 1.127070I
3.84039 + 2.25089I −3.80296 − 1.82490I
u = 0.47707 + 1.41602I
a = −0.322083 + 0.462198I
b = −0.610178 + 0.371512I
5.39444 + 2.59006I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.47707 − 1.41602I
a = −0.322083 − 0.462198I
b = −0.610178 − 0.371512I
5.39444 − 2.59006I 0
u = 0.05339 + 1.49970I
a = −0.369410 + 0.314745I
b = 0.646626 − 0.454842I
3.97294 − 4.06874I 0
u = 0.05339 − 1.49970I
a = −0.369410 − 0.314745I
b = 0.646626 + 0.454842I
3.97294 + 4.06874I 0
u = −0.00308 + 1.50593I
a = 0.394477 + 0.317192I
b = −0.759637 − 0.233739I
4.44799 + 0.34836I 0
u = −0.00308 − 1.50593I
a = 0.394477 − 0.317192I
b = −0.759637 + 0.233739I
4.44799 − 0.34836I 0
u = 0.339641 + 0.357394I
a = −1.95697 + 2.08399I
b = −0.331030 + 0.511934I
3.82757 + 2.65997I −0.57540 − 3.70129I
u = 0.339641 − 0.357394I
a = −1.95697 − 2.08399I
b = −0.331030 − 0.511934I
3.82757 − 2.65997I −0.57540 + 3.70129I
u = 0.21715 + 1.49136I
a = 0.227310 + 0.018632I
b = 0.483598 − 0.681073I
6.64814 + 1.30339I 0
u = 0.21715 − 1.49136I
a = 0.227310 − 0.018632I
b = 0.483598 + 0.681073I
6.64814 − 1.30339I 0
u = 0.63759 + 1.36898I
a = −1.42342 + 0.38493I
b = −0.963488 − 0.453805I
2.74883 + 2.39891I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.63759 − 1.36898I
a = −1.42342 − 0.38493I
b = −0.963488 + 0.453805I
2.74883 − 2.39891I 0
u = 0.66747 + 1.35645I
a = 1.27212 − 0.68061I
b = 1.23066 + 0.69717I
3.31662 − 13.61000I 0
u = 0.66747 − 1.35645I
a = 1.27212 + 0.68061I
b = 1.23066 − 0.69717I
3.31662 + 13.61000I 0
u = −0.65877 + 1.38267I
a = −1.205290 − 0.715124I
b = −1.26938 + 0.73389I
1.0314 + 19.6500I 0
u = −0.65877 − 1.38267I
a = −1.205290 + 0.715124I
b = −1.26938 − 0.73389I
1.0314 − 19.6500I 0
u = −0.74616 + 1.36765I
a = −1.247220 − 0.503616I
b = −1.262280 + 0.580258I
−3.33829 + 10.24030I 0
u = −0.74616 − 1.36765I
a = −1.247220 + 0.503616I
b = −1.262280 − 0.580258I
−3.33829 − 10.24030I 0
u = −0.299514 + 0.289300I
a = −0.416865 + 0.451108I
b = −0.106561 + 0.395371I
−0.229203 + 0.954098I −4.84344 − 6.37951I
u = −0.299514 − 0.289300I
a = −0.416865 − 0.451108I
b = −0.106561 − 0.395371I
−0.229203 − 0.954098I −4.84344 + 6.37951I
u = 1.61514 + 0.14346I
a = 1.226030 − 0.326188I
b = 0.862979 − 0.261391I
−6.00712 + 0.18199I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.61514 − 0.14346I
a = 1.226030 + 0.326188I
b = 0.862979 + 0.261391I
−6.00712 − 0.18199I 0
u = −1.55840 + 0.55366I
a = 1.132040 + 0.376470I
b = 0.964827 + 0.338639I
−6.51689 − 2.37044I 0
u = −1.55840 − 0.55366I
a = 1.132040 − 0.376470I
b = 0.964827 − 0.338639I
−6.51689 + 2.37044I 0
u = −0.31030 + 1.75527I
a = −0.380227 − 0.067746I
b = −0.708452 − 0.391000I
3.65122 − 6.01500I 0
u = −0.31030 − 1.75527I
a = −0.380227 + 0.067746I
b = −0.708452 + 0.391000I
3.65122 + 6.01500I 0
u = 0.0415460 + 0.1091190I
a = 0.19195 − 10.07410I
b = −0.764937 + 0.543673I
−3.63585 + 1.86155I −7.84133 − 2.40057I
u = 0.0415460 − 0.1091190I
a = 0.19195 + 10.07410I
b = −0.764937 − 0.543673I
−3.63585 − 1.86155I −7.84133 + 2.40057I
20
II. I
u
2
= h6.98 × 10
29
u
45
+ 2.34 × 10
31
u
44
+ · · · + 8.46 × 10
29
b + 5.19 ×
10
31
, −1.06 × 10
31
u
45
+ 6.43 × 10
31
u
44
+ · · · + 8.46 × 10
29
a + 1.27 ×
10
32
, u
46
+ 16u
44
+ · · · − 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
u
2
a
8
=
12.4890u
45
− 76.0478u
44
+ ··· + 315.048u − 149.719
−0.825545u
45
− 27.6802u
44
+ ··· + 119.922u − 61.3796
a
9
=
13.3145u
45
− 48.3677u
44
+ ··· + 195.126u − 88.3391
−0.825545u
45
− 27.6802u
44
+ ··· + 119.922u − 61.3796
a
7
=
−232.757u
45
− 37.4947u
44
+ ··· − 300.055u − 75.4728
61.5670u
45
− 4.53304u
44
+ ··· + 133.664u − 4.35858
a
4
=
−45.2136u
45
− 0.906138u
44
+ ··· − 91.8951u + 3.72063
−77.8528u
45
+ 15.2484u
44
+ ··· − 198.612u + 20.5131
a
12
=
−4.97679u
45
+ 33.6336u
44
+ ··· − 147.929u + 66.4505
0.0938617u
45
+ 22.6669u
44
+ ··· − 83.7066u + 45.2136
a
3
=
14.6893u
45
+ 7.81269u
44
+ ··· − 18.6536u + 19.0926
−106.531u
45
+ 16.3146u
44
+ ··· − 266.818u + 22.8050
a
2
=
24.6519u
45
+ 83.4159u
44
+ ··· − 279.280u + 161.009
−111.897u
45
+ 23.1366u
44
+ ··· − 330.581u + 48.1834
a
10
=
u
u
3
+ u
a
1
=
−6.02912u
45
+ 32.2944u
44
+ ··· − 141.375u + 61.9359
−0.00125363u
45
+ 21.9733u
44
+ ··· − 78.7784u + 42.0383
(ii) Obstruction class = 1
(iii) Cusp Shapes = 1715.32u
45
− 169.143u
44
+ ··· + 3931.88u − 329.488
21
(iv) u-Polynomials at the component
22
Crossings u-Polynomials at each crossing
c
1
u
46
− 28u
45
+ ··· − 34u + 1
c
2
u
46
+ 14u
44
+ ··· − 2u + 1
c
3
u
46
+ 3u
45
+ ··· − u + 1
c
4
u
46
+ 2u
45
+ ··· + 2u + 1
c
5
u
46
+ 16u
44
+ ··· − 2u + 1
c
6
u
46
− 6u
45
+ ··· − 32u + 1
c
7
u
46
+ 14u
44
+ ··· + 2u + 1
c
8
u
46
− 2u
45
+ ··· − 2u + 1
c
9
u
46
+ 7u
45
+ ··· − u + 1
c
10
u
46
+ 16u
44
+ ··· + 2u + 1
c
11
u
46
− 3u
45
+ ··· + u + 1
c
12
u
46
− 7u
45
+ ··· + u + 1
23
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
46
+ 4y
45
+ ··· − 102y + 1
c
2
, c
7
y
46
+ 28y
45
+ ··· + 34y + 1
c
3
, c
11
y
46
+ 43y
45
+ ··· + 33y + 1
c
4
, c
8
y
46
− 22y
45
+ ··· − 30y + 1
c
5
, c
10
y
46
+ 32y
45
+ ··· + 36y + 1
c
6
y
46
− 2y
45
+ ··· − 176y + 1
c
9
, c
12
y
46
+ 23y
45
+ ··· + 29y + 1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.676863 + 0.816582I
a = 0.791546 + 0.111888I
b = 0.927988 + 0.565609I
−3.99808 + 0.78285I 0
u = −0.676863 − 0.816582I
a = 0.791546 − 0.111888I
b = 0.927988 − 0.565609I
−3.99808 − 0.78285I 0
u = −0.468464 + 0.960672I
a = 2.08926 + 0.38920I
b = 1.045440 − 0.366605I
3.38448 + 0.12988I 0
u = −0.468464 − 0.960672I
a = 2.08926 − 0.38920I
b = 1.045440 + 0.366605I
3.38448 − 0.12988I 0
u = −0.570993 + 0.955021I
a = −0.90280 − 1.20361I
b = −0.732434 + 0.731594I
−3.62454 + 4.03537I 0
u = −0.570993 − 0.955021I
a = −0.90280 + 1.20361I
b = −0.732434 − 0.731594I
−3.62454 − 4.03537I 0
u = 0.344288 + 1.080260I
a = −1.88319 + 0.92693I
b = −1.069420 − 0.438125I
3.87486 − 6.14773I 0
u = 0.344288 − 1.080260I
a = −1.88319 − 0.92693I
b = −1.069420 + 0.438125I
3.87486 + 6.14773I 0
u = −0.484006 + 0.700488I
a = −2.55180 − 1.81919I
b = −0.612911 + 0.326726I
−0.44557 + 8.42071I −7.5330 − 14.9264I
u = −0.484006 − 0.700488I
a = −2.55180 + 1.81919I
b = −0.612911 − 0.326726I
−0.44557 − 8.42071I −7.5330 + 14.9264I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.000930 + 1.220050I
a = 0.155121 − 0.192745I
b = −0.101023 − 0.853366I
6.58963 + 2.46710I 0
u = −0.000930 − 1.220050I
a = 0.155121 + 0.192745I
b = −0.101023 + 0.853366I
6.58963 − 2.46710I 0
u = 0.001428 + 1.221570I
a = 0.062926 + 0.213904I
b = −0.158676 − 1.323780I
4.80139 − 1.45777I 0
u = 0.001428 − 1.221570I
a = 0.062926 − 0.213904I
b = −0.158676 + 1.323780I
4.80139 + 1.45777I 0
u = 0.204820 + 1.242200I
a = −0.97074 + 1.06116I
b = −1.179020 − 0.578827I
1.25425 − 4.52810I 0
u = 0.204820 − 1.242200I
a = −0.97074 − 1.06116I
b = −1.179020 + 0.578827I
1.25425 + 4.52810I 0
u = 0.659118 + 1.075260I
a = 0.940587 − 0.708231I
b = 1.015810 + 0.706124I
−4.13669 − 6.04607I 0
u = 0.659118 − 1.075260I
a = 0.940587 + 0.708231I
b = 1.015810 − 0.706124I
−4.13669 + 6.04607I 0
u = 0.426097 + 0.585771I
a = −0.318290 + 0.144767I
b = −1.38869 + 0.44768I
−6.06491 + 1.20785I −12.59517 − 0.27041I
u = 0.426097 − 0.585771I
a = −0.318290 − 0.144767I
b = −1.38869 − 0.44768I
−6.06491 − 1.20785I −12.59517 + 0.27041I
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.002666 + 0.723712I
a = 0.242370 + 1.244350I
b = 0.171804 − 1.355690I
2.76940 + 1.46244I −10.80628 + 1.44488I
u = −0.002666 − 0.723712I
a = 0.242370 − 1.244350I
b = 0.171804 + 1.355690I
2.76940 − 1.46244I −10.80628 − 1.44488I
u = 0.483445 + 0.537141I
a = 3.17660 − 0.95835I
b = 0.708313 + 0.223508I
0.38412 − 2.98964I −7.56697 + 7.19001I
u = 0.483445 − 0.537141I
a = 3.17660 + 0.95835I
b = 0.708313 − 0.223508I
0.38412 + 2.98964I −7.56697 − 7.19001I
u = 0.000938 + 0.721199I
a = 0.39541 + 2.45962I
b = 0.093863 − 0.871229I
4.55512 − 2.46822I 9.60981 + 3.90298I
u = 0.000938 − 0.721199I
a = 0.39541 − 2.45962I
b = 0.093863 + 0.871229I
4.55512 + 2.46822I 9.60981 − 3.90298I
u = −0.142737 + 1.383180I
a = 0.523644 − 0.220957I
b = −0.612740 − 0.242595I
5.74425 + 2.85384I 0
u = −0.142737 − 1.383180I
a = 0.523644 + 0.220957I
b = −0.612740 + 0.242595I
5.74425 − 2.85384I 0
u = 1.372530 + 0.273357I
a = −1.034930 + 0.397431I
b = −0.994210 + 0.257064I
−6.71587 + 0.29656I 0
u = 1.372530 − 0.273357I
a = −1.034930 − 0.397431I
b = −0.994210 − 0.257064I
−6.71587 − 0.29656I 0
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.23600 + 1.39593I
a = 0.976871 + 0.599797I
b = 1.324500 − 0.469051I
−0.68123 + 7.11158I 0
u = −0.23600 − 1.39593I
a = 0.976871 − 0.599797I
b = 1.324500 + 0.469051I
−0.68123 − 7.11158I 0
u = 0.158810 + 0.541604I
a = −0.124709 − 0.269532I
b = −1.54394 − 0.11037I
−5.02859 − 6.89860I −8.91093 + 2.64344I
u = 0.158810 − 0.541604I
a = −0.124709 + 0.269532I
b = −1.54394 + 0.11037I
−5.02859 + 6.89860I −8.91093 − 2.64344I
u = 0.35416 + 1.39298I
a = −0.071380 − 0.562893I
b = 0.722538 − 0.231352I
4.76474 + 2.60239I 0
u = 0.35416 − 1.39298I
a = −0.071380 + 0.562893I
b = 0.722538 + 0.231352I
4.76474 − 2.60239I 0
u = 0.05859 + 1.44264I
a = 0.438150 + 0.612443I
b = −0.515258 − 0.107566I
4.75078 + 0.88801I 0
u = 0.05859 − 1.44264I
a = 0.438150 − 0.612443I
b = −0.515258 + 0.107566I
4.75078 − 0.88801I 0
u = −1.43485 + 0.25258I
a = −1.35650 − 0.48488I
b = −0.926462 − 0.210533I
−6.39713 − 1.58234I 0
u = −1.43485 − 0.25258I
a = −1.35650 + 0.48488I
b = −0.926462 + 0.210533I
−6.39713 + 1.58234I 0
29
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.300761 + 0.351722I
a = 1.09136 − 2.10593I
b = 1.007260 − 0.210584I
−1.78149 + 2.47753I −2.51173 − 4.66389I
u = 0.300761 − 0.351722I
a = 1.09136 + 2.10593I
b = 1.007260 + 0.210584I
−1.78149 − 2.47753I −2.51173 + 4.66389I
u = −0.17711 + 1.58522I
a = 0.181510 + 0.621055I
b = 0.583306 − 0.013344I
3.18920 − 4.97064I 0
u = −0.17711 − 1.58522I
a = 0.181510 − 0.621055I
b = 0.583306 + 0.013344I
3.18920 + 4.97064I 0
u = −0.170363 + 0.323945I
a = −0.851006 − 0.105705I
b = 1.233960 + 0.010776I
−2.25331 + 2.28208I −5.92670 − 2.02422I
u = −0.170363 − 0.323945I
a = −0.851006 + 0.105705I
b = 1.233960 − 0.010776I
−2.25331 − 2.28208I −5.92670 + 2.02422I
30
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
46
− 28u
45
+ ··· − 34u + 1)
· (u
157
+ 75u
156
+ ··· − 314997534u − 13845841)
c
2
(u
46
+ 14u
44
+ ··· − 2u + 1)(u
157
+ u
156
+ ··· + 6588u + 3721)
c
3
(u
46
+ 3u
45
+ ··· − u + 1)(u
157
− 4u
156
+ ··· + 1.41745 × 10
7
u − 1906367)
c
4
(u
46
+ 2u
45
+ ··· + 2u + 1)(u
157
+ 3u
156
+ ··· + 8u + 1)
c
5
(u
46
+ 16u
44
+ ··· − 2u + 1)(u
157
+ u
156
+ ··· − 13732u + 2801)
c
6
(u
46
− 6u
45
+ ··· − 32u + 1)(u
157
− 3u
156
+ ··· − 346340u + 292121)
c
7
(u
46
+ 14u
44
+ ··· + 2u + 1)(u
157
+ u
156
+ ··· + 6588u + 3721)
c
8
(u
46
− 2u
45
+ ··· − 2u + 1)(u
157
+ 3u
156
+ ··· + 8u + 1)
c
9
(u
46
+ 7u
45
+ ··· − u + 1)(u
157
+ 4u
156
+ ··· + 13669u + 2263)
c
10
(u
46
+ 16u
44
+ ··· + 2u + 1)(u
157
+ u
156
+ ··· − 13732u + 2801)
c
11
(u
46
− 3u
45
+ ··· + u + 1)(u
157
− 4u
156
+ ··· + 1.41745 × 10
7
u − 1906367)
c
12
(u
46
− 7u
45
+ ··· + u + 1)(u
157
+ 4u
156
+ ··· + 13669u + 2263)
31
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
46
+ 4y
45
+ ··· − 102y + 1)
· (y
157
+ 39y
156
+ ··· − 7046372593682426y −191707312997281)
c
2
, c
7
(y
46
+ 28y
45
+ ··· + 34y + 1)
· (y
157
+ 75y
156
+ ··· − 314997534y −13845841)
c
3
, c
11
(y
46
+ 43y
45
+ ··· + 33y + 1)
· (y
157
+ 114y
156
+ ··· − 60423847276045y −3634235138689)
c
4
, c
8
(y
46
− 22y
45
+ ··· − 30y + 1)(y
157
− 75y
156
+ ··· + 6y −1)
c
5
, c
10
(y
46
+ 32y
45
+ ··· + 36y + 1)
· (y
157
+ 99y
156
+ ··· − 1215170132y −7845601)
c
6
(y
46
− 2y
45
+ ··· − 176y + 1)
· (y
157
− 3y
156
+ ··· − 13877806866712y −85334678641)
c
9
, c
12
(y
46
+ 23y
45
+ ··· + 29y + 1)
· (y
157
+ 78y
156
+ ··· − 296376829y −5121169)
32
