12n
0357
(K12n
0357
)
A knot diagram
1
Linearized knot diagam
3 5 12 10 2 9 3 4 6 4 9 8
Solving Sequence
4,12 3,9
8 1 7 6 11 10 5 2
c
3
c
8
c
12
c
7
c
6
c
11
c
10
c
4
c
2
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h1.81165 × 10
192
u
72
− 4.45965 × 10
192
u
71
+ ··· + 9.74080 × 10
191
b + 1.06210 × 10
193
,
− 9.93968 × 10
192
u
72
+ 2.39622 × 10
193
u
71
+ ··· + 2.92224 × 10
192
a − 7.03543 × 10
193
, u
73
− 3u
72
+ ··· + u − 3i
I
u
2
= h377188189u
23
+ 1378863855u
22
+ ··· + 61167471b + 138784360,
− 64492387u
23
− 295831704u
22
+ ··· + 61167471a − 153446503, u
24
+ 4u
23
+ ··· − u
3
+ 1i
* 2 irreducible components of dim
C
= 0, with total 97 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
= h1.81 × 10
192
u
72
− 4.46 × 10
192
u
71
+ · · · + 9.74 × 10
191
b + 1.06 ×
10
193
, −9.94 × 10
192
u
72
+ 2.40 × 10
193
u
71
+ · · · + 2.92 × 10
192
a − 7.04 ×
10
193
, u
73
− 3u
72
+ · · · + u − 3i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
3
=
1
−u
2
a
9
=
3.40139u
72
− 8.19995u
71
+ ··· + 26.4023u + 24.0755
−1.85986u
72
+ 4.57832u
71
+ ··· − 12.4794u − 10.9036
a
8
=
1.54153u
72
− 3.62163u
71
+ ··· + 13.9229u + 13.1719
−1.85986u
72
+ 4.57832u
71
+ ··· − 12.4794u − 10.9036
a
1
=
0.412176u
72
− 0.538736u
71
+ ··· − 4.02065u + 8.34606
−0.637800u
72
+ 1.60567u
71
+ ··· − 1.74620u − 1.17888
a
7
=
3.10355u
72
− 7.42149u
71
+ ··· + 22.7807u + 21.0665
−2.37832u
72
+ 5.83272u
71
+ ··· − 16.2793u − 13.5621
a
6
=
1.78414u
72
− 3.70642u
71
+ ··· − 2.38936u + 13.1688
−1.67153u
72
+ 4.07471u
71
+ ··· − 6.22334u − 6.79645
a
11
=
1.38239u
72
− 2.91513u
71
+ ··· − 1.21923u + 8.34771
−0.332419u
72
+ 0.770717u
71
+ ··· + 0.944775u + 1.17723
a
10
=
1.04998u
72
− 2.14441u
71
+ ··· − 0.274455u + 9.52494
−0.332419u
72
+ 0.770717u
71
+ ··· + 0.944775u + 1.17723
a
5
=
−2.32714u
72
+ 5.56801u
71
+ ··· − 11.8243u − 12.4425
1.62628u
72
− 4.17318u
71
+ ··· + 13.8386u + 5.94494
a
2
=
0.792639u
72
− 1.56032u
71
+ ··· − 2.81319u + 7.43157
−0.787015u
72
+ 1.97749u
71
+ ··· − 2.76778u − 1.53829
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5.04634u
72
+ 12.1280u
71
+ ··· − 38.4236u − 37.4607
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
73
+ 41u
72
+ ··· − 695u − 36
c
2
, c
5
u
73
− u
72
+ ··· + 19u + 6
c
3
u
73
− 3u
72
+ ··· + u − 3
c
4
, c
10
u
73
+ u
72
+ ··· + 135u + 175
c
6
, c
9
u
73
− u
72
+ ··· − 473u + 111
c
7
u
73
+ u
72
+ ··· − 508170u + 63873
c
8
u
73
− u
72
+ ··· + 73u + 42
c
11
u
73
− 5u
72
+ ··· − 8735u + 369
c
12
u
73
− u
72
+ ··· − 6229u + 3053
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
73
− 3y
72
+ ··· + 212737y −1296
c
2
, c
5
y
73
+ 41y
72
+ ··· − 695y −36
c
3
y
73
+ 9y
72
+ ··· + 217y −9
c
4
, c
10
y
73
+ 27y
72
+ ··· − 448325y −30625
c
6
, c
9
y
73
+ 31y
72
+ ··· − 617429y −12321
c
7
y
73
+ 67y
72
+ ··· − 23854012236y −4079760129
c
8
y
73
− 65y
72
+ ··· + 97561y −1764
c
11
y
73
− 65y
72
+ ··· + 5528239y −136161
c
12
y
73
+ 67y
72
+ ··· − 280201423y −9320809
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.711770 + 0.686911I
a = 0.819664 + 0.526229I
b = −0.706906 + 0.869155I
0.79772 + 1.53809I −4.00000 − 2.08274I
u = −0.711770 − 0.686911I
a = 0.819664 − 0.526229I
b = −0.706906 − 0.869155I
0.79772 − 1.53809I −4.00000 + 2.08274I
u = 0.788897 + 0.509390I
a = −1.278790 + 0.137287I
b = 1.15632 + 1.03791I
1.73594 − 4.46923I −6.52811 + 7.62363I
u = 0.788897 − 0.509390I
a = −1.278790 − 0.137287I
b = 1.15632 − 1.03791I
1.73594 + 4.46923I −6.52811 − 7.62363I
u = 0.224019 + 1.064990I
a = 0.658185 + 0.432289I
b = 0.842425 − 0.465563I
4.02793 + 0.63188I 0
u = 0.224019 − 1.064990I
a = 0.658185 − 0.432289I
b = 0.842425 + 0.465563I
4.02793 − 0.63188I 0
u = −0.059789 + 1.091400I
a = −0.912998 − 0.339473I
b = 1.46708 + 0.13645I
2.19497 + 4.50938I 0
u = −0.059789 − 1.091400I
a = −0.912998 + 0.339473I
b = 1.46708 − 0.13645I
2.19497 − 4.50938I 0
u = −0.450627 + 1.002820I
a = 0.785262 − 0.098480I
b = −1.56929 + 0.22536I
2.19555 + 2.25831I 0
u = −0.450627 − 1.002820I
a = 0.785262 + 0.098480I
b = −1.56929 − 0.22536I
2.19555 − 2.25831I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.845801 + 0.149805I
a = 1.232350 − 0.300012I
b = −1.69495 + 0.48097I
−2.08711 + 5.89222I −9.17584 − 6.36903I
u = −0.845801 − 0.149805I
a = 1.232350 + 0.300012I
b = −1.69495 − 0.48097I
−2.08711 − 5.89222I −9.17584 + 6.36903I
u = −0.801731 + 0.263639I
a = −2.20554 − 0.11514I
b = 0.891373 − 0.091156I
−3.64897 + 2.39805I −12.44182 − 6.41492I
u = −0.801731 − 0.263639I
a = −2.20554 + 0.11514I
b = 0.891373 + 0.091156I
−3.64897 − 2.39805I −12.44182 + 6.41492I
u = −0.732593 + 0.410229I
a = −1.158050 − 0.281195I
b = 1.220740 + 0.683681I
−3.24555 + 0.91435I −8.37859 − 3.23477I
u = −0.732593 − 0.410229I
a = −1.158050 + 0.281195I
b = 1.220740 − 0.683681I
−3.24555 − 0.91435I −8.37859 + 3.23477I
u = −0.756346 + 0.324793I
a = 0.10857 + 1.48519I
b = −0.240810 + 0.118196I
0.03493 + 1.91410I −4.83110 − 3.77039I
u = −0.756346 − 0.324793I
a = 0.10857 − 1.48519I
b = −0.240810 − 0.118196I
0.03493 − 1.91410I −4.83110 + 3.77039I
u = −0.231124 + 1.212990I
a = −0.423648 + 0.609081I
b = −0.716380 + 0.056569I
1.91029 − 2.09743I 0
u = −0.231124 − 1.212990I
a = −0.423648 − 0.609081I
b = −0.716380 − 0.056569I
1.91029 + 2.09743I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.730467 + 0.168977I
a = −0.24056 + 2.55593I
b = 0.124509 − 0.145261I
−1.72884 − 6.88383I −10.38312 + 7.19433I
u = 0.730467 − 0.168977I
a = −0.24056 − 2.55593I
b = 0.124509 + 0.145261I
−1.72884 + 6.88383I −10.38312 − 7.19433I
u = −0.381226 + 0.641967I
a = 1.50889 + 1.91893I
b = −0.912723 + 0.730489I
0.64051 + 7.83605I −0.10120 − 10.84671I
u = −0.381226 − 0.641967I
a = 1.50889 − 1.91893I
b = −0.912723 − 0.730489I
0.64051 − 7.83605I −0.10120 + 10.84671I
u = 0.701403 + 0.148645I
a = 0.649579 − 0.015762I
b = −0.403650 + 1.334880I
−4.27706 − 1.66707I −11.95055 + 4.70920I
u = 0.701403 − 0.148645I
a = 0.649579 + 0.015762I
b = −0.403650 − 1.334880I
−4.27706 + 1.66707I −11.95055 − 4.70920I
u = 0.611556 + 0.280959I
a = 2.20649 + 1.40364I
b = −0.374732 − 0.043208I
−3.81796 − 0.17112I −13.7765 + 5.6990I
u = 0.611556 − 0.280959I
a = 2.20649 − 1.40364I
b = −0.374732 + 0.043208I
−3.81796 + 0.17112I −13.7765 − 5.6990I
u = 0.482180 + 0.464629I
a = −2.30819 + 0.81803I
b = 0.987197 + 0.668273I
2.76895 − 3.86000I 4.66691 + 5.55754I
u = 0.482180 − 0.464629I
a = −2.30819 − 0.81803I
b = 0.987197 − 0.668273I
2.76895 + 3.86000I 4.66691 − 5.55754I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.154203 + 0.643235I
a = 0.289103 + 0.115197I
b = 0.75716 − 1.36920I
3.75316 + 2.54664I 5.49076 − 1.40011I
u = −0.154203 − 0.643235I
a = 0.289103 − 0.115197I
b = 0.75716 + 1.36920I
3.75316 − 2.54664I 5.49076 + 1.40011I
u = 0.445982 + 0.474227I
a = −0.072968 + 0.236784I
b = −0.30309 − 2.04304I
−0.13177 − 8.00703I −0.8298 + 14.6532I
u = 0.445982 − 0.474227I
a = −0.072968 − 0.236784I
b = −0.30309 + 2.04304I
−0.13177 + 8.00703I −0.8298 − 14.6532I
u = −0.379636 + 0.465015I
a = −0.062143 + 0.470921I
b = −0.183528 + 0.455346I
−0.084212 + 1.082470I −1.38826 − 6.29344I
u = −0.379636 − 0.465015I
a = −0.062143 − 0.470921I
b = −0.183528 − 0.455346I
−0.084212 − 1.082470I −1.38826 + 6.29344I
u = −0.245626 + 0.530416I
a = −0.835354 − 0.257006I
b = −0.919360 − 0.589306I
0.82387 + 2.32300I −3.12118 − 3.65023I
u = −0.245626 − 0.530416I
a = −0.835354 + 0.257006I
b = −0.919360 + 0.589306I
0.82387 − 2.32300I −3.12118 + 3.65023I
u = 1.09746 + 0.93248I
a = 1.165710 − 0.423069I
b = −1.69073 − 0.35921I
−8.64924 − 0.47663I 0
u = 1.09746 − 0.93248I
a = 1.165710 + 0.423069I
b = −1.69073 + 0.35921I
−8.64924 + 0.47663I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.03821 + 1.44557I
a = 0.419014 + 0.311831I
b = −0.121814 − 0.282796I
7.26330 + 0.79424I 0
u = −0.03821 − 1.44557I
a = 0.419014 − 0.311831I
b = −0.121814 + 0.282796I
7.26330 − 0.79424I 0
u = 0.522346 + 0.135295I
a = −1.73569 − 1.33736I
b = 1.151230 + 0.320801I
2.44865 − 2.72547I −0.98848 + 3.99656I
u = 0.522346 − 0.135295I
a = −1.73569 + 1.33736I
b = 1.151230 − 0.320801I
2.44865 + 2.72547I −0.98848 − 3.99656I
u = 0.529186
a = 2.32017
b = −0.976528
−1.76032 −4.48430
u = 1.03407 + 1.05725I
a = −0.895281 + 0.313648I
b = 1.66291 + 0.49054I
−9.47345 − 4.85925I 0
u = 1.03407 − 1.05725I
a = −0.895281 − 0.313648I
b = 1.66291 − 0.49054I
−9.47345 + 4.85925I 0
u = 1.08539 + 1.01319I
a = −0.649568 + 0.696904I
b = 1.337990 + 0.293620I
−9.65085 − 2.86615I 0
u = 1.08539 − 1.01319I
a = −0.649568 − 0.696904I
b = 1.337990 − 0.293620I
−9.65085 + 2.86615I 0
u = 0.98164 + 1.12301I
a = 0.809172 − 0.868353I
b = −1.52323 − 0.11626I
−8.01190 − 7.13354I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.98164 − 1.12301I
a = 0.809172 + 0.868353I
b = −1.52323 + 0.11626I
−8.01190 + 7.13354I 0
u = 1.16275 + 0.94037I
a = 1.145480 − 0.346183I
b = −1.44811 − 0.68459I
−8.15838 − 9.01433I 0
u = 1.16275 − 0.94037I
a = 1.145480 + 0.346183I
b = −1.44811 + 0.68459I
−8.15838 + 9.01433I 0
u = −1.08700 + 1.03138I
a = −1.088610 − 0.601686I
b = 1.378680 − 0.228755I
−5.09007 + 3.96389I 0
u = −1.08700 − 1.03138I
a = −1.088610 + 0.601686I
b = 1.378680 + 0.228755I
−5.09007 − 3.96389I 0
u = −1.14886 + 0.98319I
a = −1.095960 − 0.405225I
b = 1.39801 − 0.42975I
−5.17491 + 4.47680I 0
u = −1.14886 − 0.98319I
a = −1.095960 + 0.405225I
b = 1.39801 + 0.42975I
−5.17491 − 4.47680I 0
u = −1.19459 + 0.97908I
a = 0.713464 + 0.719383I
b = −1.268230 − 0.006930I
−3.35645 − 1.89703I 0
u = −1.19459 − 0.97908I
a = 0.713464 − 0.719383I
b = −1.268230 + 0.006930I
−3.35645 + 1.89703I 0
u = −1.06511 + 1.12982I
a = 1.080960 + 0.314940I
b = −1.58993 + 0.59363I
−2.83469 + 10.02650I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.06511 − 1.12982I
a = 1.080960 − 0.314940I
b = −1.58993 − 0.59363I
−2.83469 − 10.02650I 0
u = 1.08721 + 1.11899I
a = −1.142380 + 0.386017I
b = 1.61370 + 0.67386I
−5.8665 − 16.5000I 0
u = 1.08721 − 1.11899I
a = −1.142380 − 0.386017I
b = 1.61370 − 0.67386I
−5.8665 + 16.5000I 0
u = −0.18127 + 1.56234I
a = −0.378264 + 0.227158I
b = 0.261801 − 0.024901I
6.32157 + 5.12094I 0
u = −0.18127 − 1.56234I
a = −0.378264 − 0.227158I
b = 0.261801 + 0.024901I
6.32157 − 5.12094I 0
u = 1.20934 + 1.04042I
a = −0.709244 + 0.702670I
b = 1.371640 − 0.142965I
−6.20784 + 8.23625I 0
u = 1.20934 − 1.04042I
a = −0.709244 − 0.702670I
b = 1.371640 + 0.142965I
−6.20784 − 8.23625I 0
u = −1.10888 + 1.15654I
a = −0.810172 − 0.543238I
b = 1.272410 − 0.096770I
−4.67517 + 3.68408I 0
u = −1.10888 − 1.15654I
a = −0.810172 + 0.543238I
b = 1.272410 + 0.096770I
−4.67517 − 3.68408I 0
u = 1.02752 + 1.23429I
a = 0.580816 − 0.597525I
b = −1.310540 + 0.134265I
−7.25042 + 0.97681I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.02752 − 1.23429I
a = 0.580816 + 0.597525I
b = −1.310540 − 0.134265I
−7.25042 − 0.97681I 0
u = −0.382422 + 0.042516I
a = −0.66270 + 2.29057I
b = −0.928905 − 0.097447I
0.76436 + 2.18087I −2.77786 − 2.58179I
u = −0.382422 − 0.042516I
a = −0.66270 − 2.29057I
b = −0.928905 + 0.097447I
0.76436 − 2.18087I −2.77786 + 2.58179I
12
II.
I
u
2
= h3.77 × 10
8
u
23
+ 1.38 × 10
9
u
22
+ · · · + 6.12 × 10
7
b + 1.39 × 10
8
, −6.45 ×
10
7
u
23
−2.96×10
8
u
22
+· · · +6.12×10
7
a−1.53×10
8
, u
24
+4u
23
+· · · −u
3
+1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
3
=
1
−u
2
a
9
=
1.05436u
23
+ 4.83642u
22
+ ··· + 0.636746u + 2.50863
−6.16648u
23
− 22.5424u
22
+ ··· − 2.86681u − 2.26892
a
8
=
−5.11213u
23
− 17.7060u
22
+ ··· − 2.23006u + 0.239705
−6.16648u
23
− 22.5424u
22
+ ··· − 2.86681u − 2.26892
a
1
=
−0.507319u
23
− 2.59043u
22
+ ··· − 5.26978u − 1.75691
2.50293u
23
+ 12.8587u
22
+ ··· − 1.24532u + 5.01141
a
7
=
−3.60920u
23
− 8.84729u
22
+ ··· − 4.47538u + 5.25112
−3.62222u
23
− 11.4716u
22
+ ··· − 1.36388u + 0.578101
a
6
=
−3.13956u
23
− 10.0674u
22
+ ··· + 0.934275u + 2.98255
−9.85454u
23
− 37.4415u
22
+ ··· − 7.12656u − 3.56118
a
11
=
2.22207u
23
+ 6.52071u
22
+ ··· + 3.73821u − 2.62904
−5.23232u
23
− 21.9699u
22
+ ··· − 5.76267u − 4.13928
a
10
=
−3.01024u
23
− 15.4492u
22
+ ··· − 2.02447u − 6.76832
−5.23232u
23
− 21.9699u
22
+ ··· − 5.76267u − 4.13928
a
5
=
−7.56886u
23
− 23.4335u
22
+ ··· − 7.91950u + 3.21038
−3.52029u
23
− 8.69117u
22
+ ··· − 3.89922u + 3.70832
a
2
=
−4.43896u
23
− 21.7559u
22
+ ··· − 4.53179u − 7.32947
−2.34593u
23
− 7.11088u
22
+ ··· − 5.17696u + 1.57248
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
333484440
20389157
u
23
−
1521347308
20389157
u
22
+ ··· −
280854901
20389157
u −
357663045
20389157
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
24
− 14u
23
+ ··· − 18u + 1
c
2
u
24
+ 2u
23
+ ··· + 2u + 1
c
3
u
24
+ 4u
23
+ ··· − u
3
+ 1
c
4
u
24
+ 10u
22
+ ··· + 4u + 3
c
5
u
24
− 2u
23
+ ··· − 2u + 1
c
6
u
24
− 8u
23
+ ··· + 2u + 1
c
7
u
24
+ 4u
22
+ ··· + u + 1
c
8
u
24
− 10u
22
+ ··· + 4u + 5
c
9
u
24
+ 8u
23
+ ··· − 2u + 1
c
10
u
24
+ 10u
22
+ ··· − 4u + 3
c
11
u
24
+ 4u
23
+ ··· − 2u + 1
c
12
u
24
+ 10u
22
+ ··· + 8u + 3
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
+ 6y
23
+ ··· − 6y + 1
c
2
, c
5
y
24
+ 14y
23
+ ··· + 18y + 1
c
3
y
24
+ 14y
23
+ ··· + 14y
2
+ 1
c
4
, c
10
y
24
+ 20y
23
+ ··· + 122y + 9
c
6
, c
9
y
24
+ 12y
23
+ ··· − 2y + 1
c
7
y
24
+ 8y
23
+ ··· − 7y + 1
c
8
y
24
− 20y
23
+ ··· − 286y + 25
c
11
y
24
− 12y
23
+ ··· + 6y + 1
c
12
y
24
+ 20y
23
+ ··· + 80y + 9
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.199272 + 0.958048I
a = −0.889600 + 0.760341I
b = −0.694132 − 0.404316I
4.28901 − 1.44360I 1.41377 + 5.79829I
u = −0.199272 − 0.958048I
a = −0.889600 − 0.760341I
b = −0.694132 + 0.404316I
4.28901 + 1.44360I 1.41377 − 5.79829I
u = −0.837058 + 0.470777I
a = −1.130140 − 0.152035I
b = 0.725967 + 0.268883I
−2.48671 + 2.11960I −2.65124 − 5.25578I
u = −0.837058 − 0.470777I
a = −1.130140 + 0.152035I
b = 0.725967 − 0.268883I
−2.48671 − 2.11960I −2.65124 + 5.25578I
u = −0.283438 + 0.916379I
a = −0.913375 − 0.068108I
b = 1.82850 + 0.22031I
2.10464 + 3.05536I 0.83554 − 7.05948I
u = −0.283438 − 0.916379I
a = −0.913375 + 0.068108I
b = 1.82850 − 0.22031I
2.10464 − 3.05536I 0.83554 + 7.05948I
u = −0.138505 + 1.039690I
a = 0.799603 − 0.465724I
b = 0.703884 − 0.449109I
2.52748 − 1.32868I 1.87192 − 0.43201I
u = −0.138505 − 1.039690I
a = 0.799603 + 0.465724I
b = 0.703884 + 0.449109I
2.52748 + 1.32868I 1.87192 + 0.43201I
u = −0.299383 + 0.788402I
a = 1.086920 + 0.158296I
b = −1.57428 + 0.71805I
3.62116 + 3.70221I 5.08118 − 6.89552I
u = −0.299383 − 0.788402I
a = 1.086920 − 0.158296I
b = −1.57428 − 0.71805I
3.62116 − 3.70221I 5.08118 + 6.89552I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.713401 + 0.354517I
a = 1.78472 + 0.24582I
b = −1.015590 + 0.801786I
2.11896 + 3.55103I −4.92325 − 0.41025I
u = −0.713401 − 0.354517I
a = 1.78472 − 0.24582I
b = −1.015590 − 0.801786I
2.11896 − 3.55103I −4.92325 + 0.41025I
u = 0.421205 + 0.385110I
a = 2.17804 − 0.11797I
b = −0.407933 + 0.616082I
−3.43668 + 0.35997I −5.57821 − 4.47507I
u = 0.421205 − 0.385110I
a = 2.17804 + 0.11797I
b = −0.407933 − 0.616082I
−3.43668 − 0.35997I −5.57821 + 4.47507I
u = 1.04468 + 1.04140I
a = 0.778881 − 0.502263I
b = −1.49157 − 0.38772I
−9.20200 − 3.82998I −4.00000 + 2.33150I
u = 1.04468 − 1.04140I
a = 0.778881 + 0.502263I
b = −1.49157 + 0.38772I
−9.20200 + 3.82998I −4.00000 − 2.33150I
u = 0.421357 + 0.209500I
a = −1.51495 + 1.81192I
b = 0.643573 + 1.174640I
−0.51254 − 7.32074I −6.31406 + 5.93822I
u = 0.421357 − 0.209500I
a = −1.51495 − 1.81192I
b = 0.643573 − 1.174640I
−0.51254 + 7.32074I −6.31406 − 5.93822I
u = −1.14750 + 1.05301I
a = −1.085120 − 0.546883I
b = 1.332100 − 0.203079I
−5.35357 + 4.13899I −19.8997 − 11.3641I
u = −1.14750 − 1.05301I
a = −1.085120 + 0.546883I
b = 1.332100 + 0.203079I
−5.35357 − 4.13899I −19.8997 + 11.3641I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.21749 + 1.54667I
a = 0.159735 + 0.255362I
b = −0.672542 − 0.322370I
6.81021 + 0.26234I −4.00000 + 2.41284I
u = −0.21749 − 1.54667I
a = 0.159735 − 0.255362I
b = −0.672542 + 0.322370I
6.81021 − 0.26234I −4.00000 − 2.41284I
u = −0.05120 + 1.63287I
a = −0.254705 + 0.022425I
b = 0.622030 − 0.278029I
6.09978 + 5.59765I −4.00000 − 10.59929I
u = −0.05120 − 1.63287I
a = −0.254705 − 0.022425I
b = 0.622030 + 0.278029I
6.09978 − 5.59765I −4.00000 + 10.59929I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
24
− 14u
23
+ ··· − 18u + 1)(u
73
+ 41u
72
+ ··· − 695u − 36)
c
2
(u
24
+ 2u
23
+ ··· + 2u + 1)(u
73
− u
72
+ ··· + 19u + 6)
c
3
(u
24
+ 4u
23
+ ··· − u
3
+ 1)(u
73
− 3u
72
+ ··· + u − 3)
c
4
(u
24
+ 10u
22
+ ··· + 4u + 3)(u
73
+ u
72
+ ··· + 135u + 175)
c
5
(u
24
− 2u
23
+ ··· − 2u + 1)(u
73
− u
72
+ ··· + 19u + 6)
c
6
(u
24
− 8u
23
+ ··· + 2u + 1)(u
73
− u
72
+ ··· − 473u + 111)
c
7
(u
24
+ 4u
22
+ ··· + u + 1)(u
73
+ u
72
+ ··· − 508170u + 63873)
c
8
(u
24
− 10u
22
+ ··· + 4u + 5)(u
73
− u
72
+ ··· + 73u + 42)
c
9
(u
24
+ 8u
23
+ ··· − 2u + 1)(u
73
− u
72
+ ··· − 473u + 111)
c
10
(u
24
+ 10u
22
+ ··· − 4u + 3)(u
73
+ u
72
+ ··· + 135u + 175)
c
11
(u
24
+ 4u
23
+ ··· − 2u + 1)(u
73
− 5u
72
+ ··· − 8735u + 369)
c
12
(u
24
+ 10u
22
+ ··· + 8u + 3)(u
73
− u
72
+ ··· − 6229u + 3053)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
24
+ 6y
23
+ ··· − 6y + 1)(y
73
− 3y
72
+ ··· + 212737y −1296)
c
2
, c
5
(y
24
+ 14y
23
+ ··· + 18y + 1)(y
73
+ 41y
72
+ ··· − 695y −36)
c
3
(y
24
+ 14y
23
+ ··· + 14y
2
+ 1)(y
73
+ 9y
72
+ ··· + 217y −9)
c
4
, c
10
(y
24
+ 20y
23
+ ··· + 122y + 9)(y
73
+ 27y
72
+ ··· − 448325y −30625)
c
6
, c
9
(y
24
+ 12y
23
+ ··· − 2y + 1)(y
73
+ 31y
72
+ ··· − 617429y −12321)
c
7
(y
24
+ 8y
23
+ ··· − 7y + 1)
· (y
73
+ 67y
72
+ ··· − 23854012236y −4079760129)
c
8
(y
24
− 20y
23
+ ··· − 286y + 25)(y
73
− 65y
72
+ ··· + 97561y −1764)
c
11
(y
24
− 12y
23
+ ··· + 6y + 1)(y
73
− 65y
72
+ ··· + 5528239y −136161)
c
12
(y
24
+ 20y
23
+ ··· + 80y + 9)
· (y
73
+ 67y
72
+ ··· − 280201423y −9320809)
22
