12n
0841
(K12n
0841
)
A knot diagram
1
Linearized knot diagam
4 10 9 10 11 4 3 11 7 1 8 5
Solving Sequence
8,11 3,9
4 12 7 10 2 1 6 5
c
8
c
3
c
11
c
7
c
9
c
2
c
1
c
6
c
5
c
4
, c
10
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.90108 × 10
282
u
72
− 2.46888 × 10
282
u
71
+ ··· + 1.59427 × 10
284
b − 3.09209 × 10
284
,
− 4.97935 × 10
284
u
72
+ 5.96759 × 10
284
u
71
+ ··· + 6.85537 × 10
285
a + 1.28477 × 10
286
,
u
73
− u
72
+ ··· − 309u − 43i
I
u
2
= h1.37214 × 10
26
u
32
+ 1.11140 × 10
24
u
31
+ ··· + 5.91097 × 10
25
b − 2.90680 × 10
26
,
6.79162 × 10
26
u
32
+ 1.40659 × 10
27
u
31
+ ··· + 5.91097 × 10
25
a + 1.02213 × 10
27
, u
33
+ 2u
32
+ ··· + u + 1i
* 2 irreducible components of dim
C
= 0, with total 106 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
= h1.90 × 10
282
u
72
− 2.47 × 10
282
u
71
+ · · · + 1.59 × 10
284
b − 3.09 ×
10
284
, −4.98 × 10
284
u
72
+ 5.97 × 10
284
u
71
+ · · · + 6.86 × 10
285
a + 1.28 ×
10
286
, u
73
− u
72
+ · · · − 309u − 43i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
3
=
0.0726344u
72
− 0.0870499u
71
+ ··· − 12.0464u − 1.87411
−0.0119244u
72
+ 0.0154860u
71
+ ··· + 4.04662u + 1.93950
a
9
=
1
−u
2
a
4
=
0.0634815u
72
− 0.0752458u
71
+ ··· − 9.33095u − 0.554483
−0.0114519u
72
+ 0.0149796u
71
+ ··· + 3.62096u + 1.82549
a
12
=
u
u
a
7
=
−0.0358045u
72
+ 0.0472121u
71
+ ··· − 5.21020u + 16.8882
−0.00222320u
72
+ 0.00250582u
71
+ ··· − 2.28998u + 0.112053
a
10
=
0.0845588u
72
− 0.102536u
71
+ ··· − 16.0931u − 3.81361
−0.00645912u
72
+ 0.00933863u
71
+ ··· + 0.00294395u + 1.06814
a
2
=
0.158202u
72
− 0.190926u
71
+ ··· − 53.4190u − 2.27997
−0.0208591u
72
+ 0.0252457u
71
+ ··· + 6.05259u + 4.49812
a
1
=
−0.00258344u
72
− 0.00120206u
71
+ ··· + 32.9271u + 6.85728
−0.00790244u
72
+ 0.00893571u
71
+ ··· + 7.42915u + 1.73646
a
6
=
−0.0675535u
72
+ 0.0804100u
71
+ ··· + 32.6859u + 7.80933
0.00236218u
72
− 0.00404640u
71
+ ··· + 2.31253u − 0.239928
a
5
=
−0.0675535u
72
+ 0.0804100u
71
+ ··· + 32.6859u + 7.80933
1.32859 × 10
−6
u
72
− 0.00128498u
71
+ ··· + 3.38038u + 0.312900
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0794662u
72
− 0.103769u
71
+ ··· − 34.4075u − 13.9361
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
73
+ 6u
72
+ ··· − 63093u − 11592
c
2
u
73
+ 3u
72
+ ··· + 20760218389u + 1628977223
c
3
u
73
+ u
72
+ ··· + 56046u − 10579
c
4
u
73
− 2u
72
+ ··· + 285527u − 23711
c
5
u
73
+ 46u
71
+ ··· + 172232704u − 28909568
c
6
u
73
− 8u
72
+ ··· + 26606u + 4801
c
7
u
73
− 5u
72
+ ··· − 1326094u − 293207
c
8
, c
11
u
73
− u
72
+ ··· − 309u − 43
c
9
u
73
+ 4u
72
+ ··· − 19u − 4
c
10
u
73
− 5u
72
+ ··· + 9u − 1
c
12
u
73
+ 45u
71
+ ··· + 241471u + 54913
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
73
− 88y
72
+ ··· + 7315837785y −134374464
c
2
y
73
− 75y
72
+ ··· + 5.45 × 10
20
y −2.65 × 10
18
c
3
y
73
+ 25y
72
+ ··· − 491484062y −111915241
c
4
y
73
− 82y
72
+ ··· + 5333119705y −562211521
c
5
y
73
+ 92y
72
+ ··· − 5265299779616768y −835763121946624
c
6
y
73
− 52y
72
+ ··· − 10859270y −23049601
c
7
y
73
+ 29y
72
+ ··· − 2637873238424y −85970344849
c
8
, c
11
y
73
+ 65y
72
+ ··· − 4365y −1849
c
9
y
73
+ 4y
72
+ ··· − 343y −16
c
10
y
73
+ 3y
72
+ ··· − 49y −1
c
12
y
73
+ 90y
72
+ ··· + 125937776729y −3015437569
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.127388 + 1.019780I
a = −0.27880 + 2.25156I
b = −0.420810 + 1.154600I
−5.96688 + 0.04720I 0
u = −0.127388 − 1.019780I
a = −0.27880 − 2.25156I
b = −0.420810 − 1.154600I
−5.96688 − 0.04720I 0
u = −0.546347 + 0.885676I
a = −1.43696 − 0.50950I
b = −0.485548 − 1.108380I
−3.59850 − 4.60468I 0
u = −0.546347 − 0.885676I
a = −1.43696 + 0.50950I
b = −0.485548 + 1.108380I
−3.59850 + 4.60468I 0
u = 0.957502
a = 0.139905
b = 0.588088
1.55339 0
u = 0.753002 + 0.520273I
a = 0.432133 + 0.644140I
b = −0.507710 + 0.528497I
0.328053 + 1.143710I 0
u = 0.753002 − 0.520273I
a = 0.432133 − 0.644140I
b = −0.507710 − 0.528497I
0.328053 − 1.143710I 0
u = 0.553850 + 1.039870I
a = 0.808148 − 0.733469I
b = −0.335070 − 0.338007I
−0.05050 + 2.22046I 0
u = 0.553850 − 1.039870I
a = 0.808148 + 0.733469I
b = −0.335070 + 0.338007I
−0.05050 − 2.22046I 0
u = 0.038876 + 1.186330I
a = 0.49937 + 1.40132I
b = 0.297313 + 0.986317I
−2.73445 + 2.20929I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.038876 − 1.186330I
a = 0.49937 − 1.40132I
b = 0.297313 − 0.986317I
−2.73445 − 2.20929I 0
u = 0.157164 + 1.238850I
a = 0.211536 + 1.345470I
b = 0.198177 + 1.356360I
−2.86036 + 2.78323I 0
u = 0.157164 − 1.238850I
a = 0.211536 − 1.345470I
b = 0.198177 − 1.356360I
−2.86036 − 2.78323I 0
u = 1.242360 + 0.227658I
a = 0.176398 − 0.372203I
b = 0.181626 − 0.479125I
1.11769 + 1.51817I 0
u = 1.242360 − 0.227658I
a = 0.176398 + 0.372203I
b = 0.181626 + 0.479125I
1.11769 − 1.51817I 0
u = −0.565862 + 0.457593I
a = 0.370741 − 0.432657I
b = 1.178140 + 0.731701I
3.28841 + 2.32761I 7.74126 + 0.64227I
u = −0.565862 − 0.457593I
a = 0.370741 + 0.432657I
b = 1.178140 − 0.731701I
3.28841 − 2.32761I 7.74126 − 0.64227I
u = −0.564181 + 1.141560I
a = −0.27712 − 1.76386I
b = 1.32972 − 1.19569I
1.21585 − 6.81490I 0
u = −0.564181 − 1.141560I
a = −0.27712 + 1.76386I
b = 1.32972 + 1.19569I
1.21585 + 6.81490I 0
u = 0.163845 + 1.294260I
a = −0.383545 + 1.220500I
b = −0.755460 + 1.149210I
−4.96510 + 3.26137I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.163845 − 1.294260I
a = −0.383545 − 1.220500I
b = −0.755460 − 1.149210I
−4.96510 − 3.26137I 0
u = −1.295820 + 0.293548I
a = −0.220803 + 0.150460I
b = 0.579096 − 0.311435I
4.49917 − 3.40407I 0
u = −1.295820 − 0.293548I
a = −0.220803 − 0.150460I
b = 0.579096 + 0.311435I
4.49917 + 3.40407I 0
u = −0.648670 + 0.020454I
a = 0.496880 − 0.830329I
b = −0.727089 − 0.500170I
−2.50658 + 2.13672I −1.93005 − 4.19239I
u = −0.648670 − 0.020454I
a = 0.496880 + 0.830329I
b = −0.727089 + 0.500170I
−2.50658 − 2.13672I −1.93005 + 4.19239I
u = 0.742224 + 1.151680I
a = 0.58786 − 1.48452I
b = −0.331175 − 1.062620I
−1.56569 + 4.54226I 0
u = 0.742224 − 1.151680I
a = 0.58786 + 1.48452I
b = −0.331175 + 1.062620I
−1.56569 − 4.54226I 0
u = 0.483926 + 0.292748I
a = 0.759333 − 0.826900I
b = −1.191780 − 0.427247I
2.42747 + 4.75419I 3.78296 − 9.66597I
u = 0.483926 − 0.292748I
a = 0.759333 + 0.826900I
b = −1.191780 + 0.427247I
2.42747 − 4.75419I 3.78296 + 9.66597I
u = −0.26191 + 1.41055I
a = −0.18485 + 1.48467I
b = −0.273685 + 1.126610I
−7.12738 − 5.48865I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.26191 − 1.41055I
a = −0.18485 − 1.48467I
b = −0.273685 − 1.126610I
−7.12738 + 5.48865I 0
u = 0.221452 + 0.469740I
a = 1.224290 + 0.370875I
b = −0.055965 + 0.315212I
0.11148 + 1.50224I 0.98056 − 4.43574I
u = 0.221452 − 0.469740I
a = 1.224290 − 0.370875I
b = −0.055965 − 0.315212I
0.11148 − 1.50224I 0.98056 + 4.43574I
u = 0.00759 + 1.48588I
a = −0.485376 + 1.110030I
b = −0.143387 + 1.280090I
−5.38340 − 6.68716I 0
u = 0.00759 − 1.48588I
a = −0.485376 − 1.110030I
b = −0.143387 − 1.280090I
−5.38340 + 6.68716I 0
u = 0.470078 + 0.199325I
a = 0.432686 − 0.286578I
b = 0.819218 + 0.115301I
1.45513 + 0.20645I 6.55614 − 2.36734I
u = 0.470078 − 0.199325I
a = 0.432686 + 0.286578I
b = 0.819218 − 0.115301I
1.45513 − 0.20645I 6.55614 + 2.36734I
u = 0.04776 + 1.50255I
a = 0.848640 + 0.726253I
b = 2.83110 + 0.99905I
−10.85900 − 5.10197I 0
u = 0.04776 − 1.50255I
a = 0.848640 − 0.726253I
b = 2.83110 − 0.99905I
−10.85900 + 5.10197I 0
u = −0.07774 + 1.50686I
a = 0.77000 − 1.29256I
b = 2.47261 − 2.07061I
−11.94820 − 3.97760I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.07774 − 1.50686I
a = 0.77000 + 1.29256I
b = 2.47261 + 2.07061I
−11.94820 + 3.97760I 0
u = −0.36090 + 1.52061I
a = −0.458910 − 0.879495I
b = −0.42844 − 1.43436I
−7.41898 − 1.74650I 0
u = −0.36090 − 1.52061I
a = −0.458910 + 0.879495I
b = −0.42844 + 1.43436I
−7.41898 + 1.74650I 0
u = −0.10399 + 1.58796I
a = 0.466318 + 0.841694I
b = −0.879711 + 0.992820I
−12.64310 + 1.53786I 0
u = −0.10399 − 1.58796I
a = 0.466318 − 0.841694I
b = −0.879711 − 0.992820I
−12.64310 − 1.53786I 0
u = 1.61361 + 0.16148I
a = 0.0185075 − 0.0848877I
b = 0.254782 + 1.357200I
−8.86508 + 0.45729I 0
u = 1.61361 − 0.16148I
a = 0.0185075 + 0.0848877I
b = 0.254782 − 1.357200I
−8.86508 − 0.45729I 0
u = −0.273746 + 0.256270I
a = 0.560662 + 0.836418I
b = −0.458787 + 0.739858I
−2.62991 + 1.32952I 0.695279 − 0.238043I
u = −0.273746 − 0.256270I
a = 0.560662 − 0.836418I
b = −0.458787 − 0.739858I
−2.62991 − 1.32952I 0.695279 + 0.238043I
u = 0.04564 + 1.64650I
a = 0.461842 − 0.869770I
b = −0.826433 − 0.958973I
−12.8260 + 6.0607I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.04564 − 1.64650I
a = 0.461842 + 0.869770I
b = −0.826433 + 0.958973I
−12.8260 − 6.0607I 0
u = 0.13736 + 1.64436I
a = −0.285132 + 0.866905I
b = −0.31077 + 1.58723I
−3.02679 − 1.41120I 0
u = 0.13736 − 1.64436I
a = −0.285132 − 0.866905I
b = −0.31077 − 1.58723I
−3.02679 + 1.41120I 0
u = −0.235061 + 0.209919I
a = 0.633372 − 0.799820I
b = −1.045760 − 0.580762I
−0.88571 + 6.37260I 4.83087 + 2.50059I
u = −0.235061 − 0.209919I
a = 0.633372 + 0.799820I
b = −1.045760 + 0.580762I
−0.88571 − 6.37260I 4.83087 − 2.50059I
u = −1.68184 + 0.13567I
a = 0.0645204 + 0.0399801I
b = 0.189096 − 1.360090I
−8.71580 − 8.50495I 0
u = −1.68184 − 0.13567I
a = 0.0645204 − 0.0399801I
b = 0.189096 + 1.360090I
−8.71580 + 8.50495I 0
u = −0.09041 + 1.75091I
a = −0.283240 − 0.909566I
b = −0.29952 − 1.40964I
−8.14219 + 4.14844I 0
u = −0.09041 − 1.75091I
a = −0.283240 + 0.909566I
b = −0.29952 + 1.40964I
−8.14219 − 4.14844I 0
u = 0.29787 + 1.73626I
a = −0.052494 − 1.089090I
b = −0.370146 − 1.246580I
−6.41652 + 7.57448I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.29787 − 1.73626I
a = −0.052494 + 1.089090I
b = −0.370146 + 1.246580I
−6.41652 − 7.57448I 0
u = 0.68655 + 1.63439I
a = −0.223760 + 1.191120I
b = 1.15124 + 1.70140I
−14.4384 + 8.4206I 0
u = 0.68655 − 1.63439I
a = −0.223760 − 1.191120I
b = 1.15124 − 1.70140I
−14.4384 − 8.4206I 0
u = −0.210175 + 0.051229I
a = 6.00130 − 8.92289I
b = 0.486615 + 1.026790I
−6.47634 + 2.96744I −0.62820 − 9.14160I
u = −0.210175 − 0.051229I
a = 6.00130 + 8.92289I
b = 0.486615 − 1.026790I
−6.47634 − 2.96744I −0.62820 + 9.14160I
u = −0.67895 + 1.66488I
a = −0.203231 − 1.168890I
b = 1.05036 − 1.70160I
−14.4011 − 16.7229I 0
u = −0.67895 − 1.66488I
a = −0.203231 + 1.168890I
b = 1.05036 + 1.70160I
−14.4011 + 16.7229I 0
u = 0.075144 + 0.163295I
a = 14.9228 + 5.6279I
b = 0.696111 − 0.896716I
−5.77706 + 5.71802I −7.01640 + 5.74071I
u = 0.075144 − 0.163295I
a = 14.9228 − 5.6279I
b = 0.696111 + 0.896716I
−5.77706 − 5.71802I −7.01640 − 5.74071I
u = 0.80050 + 1.70387I
a = 0.267830 − 0.737442I
b = −0.83131 − 1.25507I
−13.5795 + 8.3759I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.80050 − 1.70387I
a = 0.267830 + 0.737442I
b = −0.83131 + 1.25507I
−13.5795 − 8.3759I 0
u = −0.79456 + 1.72859I
a = 0.282107 + 0.742434I
b = −0.83069 + 1.21010I
−13.64400 − 0.47981I 0
u = −0.79456 − 1.72859I
a = 0.282107 − 0.742434I
b = −0.83069 − 1.21010I
−13.64400 + 0.47981I 0
12
II.
I
u
2
= h1.37 × 10
26
u
32
+ 1.11 × 10
24
u
31
+ · · · + 5.91 × 10
25
b − 2.91 × 10
26
, 6.79 ×
10
26
u
32
+1.41×10
27
u
31
+· · ·+5.91×10
25
a+1.02×10
27
, u
33
+2u
32
+· · ·+u+1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
3
=
−11.4898u
32
− 23.7962u
31
+ ··· − 19.6646u − 17.2920
−2.32135u
32
− 0.0188023u
31
+ ··· − 6.53704u + 4.91763
a
9
=
1
−u
2
a
4
=
−7.62367u
32
− 14.8842u
31
+ ··· − 13.8953u − 11.5579
0.125656u
32
+ 4.04410u
31
+ ··· − 1.49124u + 6.09725
a
12
=
u
u
a
7
=
−15.9081u
32
− 24.5531u
31
+ ··· − 34.9229u − 6.37675
−2.42397u
32
+ 2.28104u
31
+ ··· − 6.80221u + 13.7117
a
10
=
9.16850u
32
+ 23.7774u
31
+ ··· + 13.1275u + 22.2097
11.2913u
32
+ 15.1977u
31
+ ··· + 20.2165u − 1.73829
a
2
=
−10.0196u
32
− 33.1577u
31
+ ··· − 9.74650u − 40.8034
−10.2925u
32
− 20.9387u
31
+ ··· − 11.1974u − 14.2664
a
1
=
−3.85175u
32
− 11.9268u
31
+ ··· + 0.333681u − 13.3131
−5.65414u
32
− 9.63213u
31
+ ··· − 4.44352u − 5.63441
a
6
=
−6.66231u
32
− 8.77963u
31
+ ··· − 12.1623u + 2.66672
−2.59325u
32
+ 1.15214u
31
+ ··· − 3.64255u + 11.7116
a
5
=
−6.66231u
32
− 8.77963u
31
+ ··· − 12.1623u + 2.66672
−2.56789u
32
− 0.602834u
31
+ ··· − 1.52523u + 7.16661
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1061330718895418299219988138
59109744024443719136477737
u
32
+
2552127737284134089230241489
59109744024443719136477737
u
31
+
··· +
13780948593918338218425712
59109744024443719136477737
u +
1228559283459346198238932158
59109744024443719136477737
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
33
− 17u
32
+ ··· + 207u − 11
c
2
u
33
− 4u
31
+ ··· + 233u + 49
c
3
u
33
− 3u
30
+ ··· − 2u + 1
c
4
u
33
+ u
32
+ ··· + 7u + 9
c
5
u
33
+ u
32
+ ··· − 2u + 1
c
6
u
33
+ 11u
32
+ ··· + 10u + 1
c
7
u
33
− 4u
31
+ ··· + 4u + 1
c
8
u
33
+ 2u
32
+ ··· + u + 1
c
9
u
33
− 7u
32
+ ··· − 5u − 1
c
10
u
33
− 8u
32
+ ··· − u + 1
c
11
u
33
− 2u
32
+ ··· + u − 1
c
12
u
33
− 3u
32
+ ··· − 5u + 1
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
33
− 25y
32
+ ··· + 12093y −121
c
2
y
33
− 8y
32
+ ··· − 52335y −2401
c
3
y
33
+ 12y
31
+ ··· − 6y −1
c
4
y
33
− 27y
32
+ ··· + 1705y −81
c
5
y
33
+ 11y
32
+ ··· + 10y −1
c
6
y
33
− 21y
32
+ ··· − 30y −1
c
7
y
33
− 8y
32
+ ··· + 60y −1
c
8
, c
11
y
33
+ 16y
32
+ ··· − 17y −1
c
9
y
33
− 5y
32
+ ··· + 15y −1
c
10
y
33
+ 10y
32
+ ··· − 5y −1
c
12
y
33
+ 29y
32
+ ··· + 13y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.012880 + 0.889456I
a = −0.94758 + 1.84300I
b = −0.648750 + 0.307989I
−4.85180 − 1.92950I −5.97096 + 3.69757I
u = 0.012880 − 0.889456I
a = −0.94758 − 1.84300I
b = −0.648750 − 0.307989I
−4.85180 + 1.92950I −5.97096 − 3.69757I
u = 0.476577 + 0.747168I
a = −0.304791 − 0.528116I
b = −1.54549 + 0.66461I
2.06671 − 3.32759I 0.12323 + 2.24672I
u = 0.476577 − 0.747168I
a = −0.304791 + 0.528116I
b = −1.54549 − 0.66461I
2.06671 + 3.32759I 0.12323 − 2.24672I
u = 0.195546 + 1.153560I
a = −0.609618 + 1.185700I
b = −0.869755 + 0.820750I
−5.56358 + 3.04814I −9.19089 − 2.79673I
u = 0.195546 − 1.153560I
a = −0.609618 − 1.185700I
b = −0.869755 − 0.820750I
−5.56358 − 3.04814I −9.19089 + 2.79673I
u = −0.726465 + 0.932827I
a = −0.877159 − 0.689248I
b = 0.324689 − 0.171405I
−0.64494 − 2.83060I −2.69137 + 4.70129I
u = −0.726465 − 0.932827I
a = −0.877159 + 0.689248I
b = 0.324689 + 0.171405I
−0.64494 + 2.83060I −2.69137 − 4.70129I
u = −1.154940 + 0.278264I
a = 0.080762 + 0.507548I
b = 0.254745 + 0.422242I
1.35997 − 1.47909I 17.4401 + 1.5741I
u = −1.154940 − 0.278264I
a = 0.080762 − 0.507548I
b = 0.254745 − 0.422242I
1.35997 + 1.47909I 17.4401 − 1.5741I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.597976 + 1.048060I
a = 0.38102 − 1.90037I
b = −1.36345 − 0.91938I
0.85933 + 7.68176I 0.70847 − 11.04624I
u = 0.597976 − 1.048060I
a = 0.38102 + 1.90037I
b = −1.36345 + 0.91938I
0.85933 − 7.68176I 0.70847 + 11.04624I
u = −1.26991
a = 0.344062
b = −0.137574
1.07966 −9.75200
u = −0.321557 + 0.627692I
a = 3.39088 + 0.84530I
b = 0.264134 + 1.157590I
−6.78711 + 2.51090I −8.90550 + 1.68996I
u = −0.321557 − 0.627692I
a = 3.39088 − 0.84530I
b = 0.264134 − 1.157590I
−6.78711 − 2.51090I −8.90550 − 1.68996I
u = −0.293467 + 0.596870I
a = −0.718358 − 0.905723I
b = 1.166720 − 0.499174I
2.29262 − 3.48730I 0.62393 + 2.53091I
u = −0.293467 − 0.596870I
a = −0.718358 + 0.905723I
b = 1.166720 + 0.499174I
2.29262 + 3.48730I 0.62393 − 2.53091I
u = −0.712438 + 1.142320I
a = −0.49774 − 1.34960I
b = 0.296372 − 1.112660I
−1.11209 − 4.44827I 8.64560 + 4.56497I
u = −0.712438 − 1.142320I
a = −0.49774 + 1.34960I
b = 0.296372 + 1.112660I
−1.11209 + 4.44827I 8.64560 − 4.56497I
u = −0.412899 + 0.475589I
a = −0.367973 + 1.100360I
b = 0.806962 + 0.402297I
1.30674 − 0.84646I 4.84555 + 1.89808I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.412899 − 0.475589I
a = −0.367973 − 1.100360I
b = 0.806962 − 0.402297I
1.30674 + 0.84646I 4.84555 − 1.89808I
u = 1.393230 + 0.186307I
a = 0.204507 + 0.031336I
b = −0.577269 − 0.457082I
4.36113 + 3.60822I −4.0185 − 17.0285I
u = 1.393230 − 0.186307I
a = 0.204507 − 0.031336I
b = −0.577269 + 0.457082I
4.36113 − 3.60822I −4.0185 + 17.0285I
u = 0.423933 + 0.393846I
a = 4.21051 + 2.46150I
b = 0.635550 − 0.926209I
−5.67765 + 6.04636I −0.6201 − 16.1410I
u = 0.423933 − 0.393846I
a = 4.21051 − 2.46150I
b = 0.635550 + 0.926209I
−5.67765 − 6.04636I −0.6201 + 16.1410I
u = 0.14108 + 1.47056I
a = 0.158663 + 1.043790I
b = 0.28693 + 1.46617I
−2.08926 + 2.22092I 6.72558 + 0.I
u = 0.14108 − 1.47056I
a = 0.158663 − 1.043790I
b = 0.28693 − 1.46617I
−2.08926 − 2.22092I 6.72558 + 0.I
u = 0.203834 + 0.448064I
a = −0.067561 + 0.746888I
b = −1.012040 − 0.429934I
−1.03642 + 6.77192I −1.6278 − 14.7044I
u = 0.203834 − 0.448064I
a = −0.067561 − 0.746888I
b = −1.012040 + 0.429934I
−1.03642 − 6.77192I −1.6278 + 14.7044I
u = −0.14402 + 1.54527I
a = −0.282865 + 1.214820I
b = −0.220290 + 1.194900I
−6.31528 − 6.22709I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.14402 − 1.54527I
a = −0.282865 − 1.214820I
b = −0.220290 − 1.194900I
−6.31528 + 6.22709I 0
u = −0.04432 + 1.55409I
a = 0.575266 − 0.524667I
b = 2.26972 − 0.85869I
−11.60690 − 4.42704I 0
u = −0.04432 − 1.55409I
a = 0.575266 + 0.524667I
b = 2.26972 + 0.85869I
−11.60690 + 4.42704I 0
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
33
− 17u
32
+ ··· + 207u − 11)(u
73
+ 6u
72
+ ··· − 63093u − 11592)
c
2
(u
33
− 4u
31
+ ··· + 233u + 49)
· (u
73
+ 3u
72
+ ··· + 20760218389u + 1628977223)
c
3
(u
33
− 3u
30
+ ··· − 2u + 1)(u
73
+ u
72
+ ··· + 56046u − 10579)
c
4
(u
33
+ u
32
+ ··· + 7u + 9)(u
73
− 2u
72
+ ··· + 285527u − 23711)
c
5
(u
33
+ u
32
+ ··· − 2u + 1)
· (u
73
+ 46u
71
+ ··· + 172232704u − 28909568)
c
6
(u
33
+ 11u
32
+ ··· + 10u + 1)(u
73
− 8u
72
+ ··· + 26606u + 4801)
c
7
(u
33
− 4u
31
+ ··· + 4u + 1)(u
73
− 5u
72
+ ··· − 1326094u − 293207)
c
8
(u
33
+ 2u
32
+ ··· + u + 1)(u
73
− u
72
+ ··· − 309u − 43)
c
9
(u
33
− 7u
32
+ ··· − 5u − 1)(u
73
+ 4u
72
+ ··· − 19u − 4)
c
10
(u
33
− 8u
32
+ ··· − u + 1)(u
73
− 5u
72
+ ··· + 9u − 1)
c
11
(u
33
− 2u
32
+ ··· + u − 1)(u
73
− u
72
+ ··· − 309u − 43)
c
12
(u
33
− 3u
32
+ ··· − 5u + 1)(u
73
+ 45u
71
+ ··· + 241471u + 54913)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
33
− 25y
32
+ ··· + 12093y −121)
· (y
73
− 88y
72
+ ··· + 7315837785y −134374464)
c
2
(y
33
− 8y
32
+ ··· − 52335y −2401)
· (y
73
− 75y
72
+ ··· + 5.45 × 10
20
y −2.65 × 10
18
)
c
3
(y
33
+ 12y
31
+ ··· − 6y −1)
· (y
73
+ 25y
72
+ ··· − 491484062y −111915241)
c
4
(y
33
− 27y
32
+ ··· + 1705y −81)
· (y
73
− 82y
72
+ ··· + 5333119705y −562211521)
c
5
(y
33
+ 11y
32
+ ··· + 10y −1)
· (y
73
+ 92y
72
+ ··· − 5265299779616768y −835763121946624)
c
6
(y
33
− 21y
32
+ ··· − 30y −1)
· (y
73
− 52y
72
+ ··· − 10859270y −23049601)
c
7
(y
33
− 8y
32
+ ··· + 60y −1)
· (y
73
+ 29y
72
+ ··· − 2637873238424y −85970344849)
c
8
, c
11
(y
33
+ 16y
32
+ ··· − 17y −1)(y
73
+ 65y
72
+ ··· − 4365y −1849)
c
9
(y
33
− 5y
32
+ ··· + 15y −1)(y
73
+ 4y
72
+ ··· − 343y −16)
c
10
(y
33
+ 10y
32
+ ··· − 5y −1)(y
73
+ 3y
72
+ ··· − 49y −1)
c
12
(y
33
+ 29y
32
+ ··· + 13y −1)
· (y
73
+ 90y
72
+ ··· + 125937776729y −3015437569)
23
