12n
0621
(K12n
0621
)
A knot diagram
1
Linearized knot diagam
3 8 6 11 1 9 11 2 12 4 7 4
Solving Sequence
7,11 2,8
3 9 12 1 6 4 5 10
c
7
c
2
c
8
c
11
c
1
c
6
c
3
c
4
c
10
c
5
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.93614 × 10
247
u
74
− 5.74396 × 10
247
u
73
+ ··· + 4.12848 × 10
248
b − 5.70956 × 10
248
,
1.02425 × 10
248
u
74
+ 2.08487 × 10
248
u
73
+ ··· + 8.25697 × 10
248
a + 4.56133 × 10
249
, u
75
+ 2u
74
+ ··· + 14u + 1i
I
u
2
= h−3110107574105u
27
+ 3424303947942u
26
+ ··· + 1161098476808b − 3547833988250,
8831335807959u
27
− 8605065406950u
26
+ ··· + 1161098476808a + 15780292874526,
u
28
− u
27
+ ··· + 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 103 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−2.94 × 10
247
u
74
− 5.74 × 10
247
u
73
+ · · · + 4.13 × 10
248
b − 5.71 ×
10
248
, 1.02 × 10
248
u
74
+ 2.08 × 10
248
u
73
+ · · · + 8.26 × 10
248
a + 4.56 ×
10
249
, u
75
+ 2u
74
+ · · · + 14u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
2
=
−0.124047u
74
− 0.252498u
73
+ ··· − 19.1786u − 5.52422
0.0711190u
74
+ 0.139130u
73
+ ··· + 10.8001u + 1.38297
a
8
=
1
−u
2
a
3
=
−0.0562848u
74
− 0.118506u
73
+ ··· − 8.19273u − 4.13684
0.0684905u
74
+ 0.133802u
73
+ ··· + 10.8464u + 1.38143
a
9
=
0.438977u
74
+ 0.862197u
73
+ ··· + 60.1161u + 7.08484
−0.0864639u
74
− 0.173895u
73
+ ··· − 16.5768u − 0.680945
a
12
=
u
u
a
1
=
−0.525441u
74
− 1.03609u
73
+ ··· − 76.6929u − 7.76579
0.0786284u
74
+ 0.164196u
73
+ ··· + 22.0608u + 0.532563
a
6
=
0.0636480u
74
+ 0.130102u
73
+ ··· + 42.4904u − 4.45507
0.0800330u
74
+ 0.158503u
73
+ ··· + 4.65689u + 2.07918
a
4
=
0.456997u
74
+ 0.856393u
73
+ ··· − 37.0559u + 4.65699
−0.0506077u
74
− 0.0881954u
73
+ ··· + 4.56215u − 0.218959
a
5
=
0.456997u
74
+ 0.856393u
73
+ ··· − 37.0559u + 4.65699
−0.0587013u
74
− 0.106320u
73
+ ··· + 4.21274u − 0.276560
a
10
=
0.436497u
74
+ 0.856775u
73
+ ··· + 59.7977u + 7.09963
−0.0889433u
74
− 0.179317u
73
+ ··· − 16.8952u − 0.666156
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.296278u
74
− 0.494942u
73
+ ··· + 11.7325u + 14.5179
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
75
+ 37u
74
+ ··· − 48u − 16
c
2
, c
8
u
75
+ u
74
+ ··· − 8u − 4
c
3
u
75
+ 9u
74
+ ··· − 284u − 19
c
4
, c
10
u
75
− u
74
+ ··· − 2058072u − 145372
c
5
u
75
− 3u
74
+ ··· + 2493542u − 4382428
c
6
u
75
− 5u
74
+ ··· + 54618u − 5068
c
7
, c
11
u
75
− 2u
74
+ ··· + 14u − 1
c
9
u
75
− 7u
74
+ ··· + 1121u − 691
c
12
u
75
+ 3u
74
+ ··· − 60886u − 6196
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
75
+ 21y
74
+ ··· + 1408y −256
c
2
, c
8
y
75
+ 37y
74
+ ··· − 48y −16
c
3
y
75
− y
74
+ ··· − 9366y −361
c
4
, c
10
y
75
+ 103y
74
+ ··· − 180569463856y −21133018384
c
5
y
75
+ 59y
74
+ ··· + 152134872802076y −19205675175184
c
6
y
75
− 19y
74
+ ··· + 614373132y −25684624
c
7
, c
11
y
75
+ 56y
74
+ ··· − 26y −1
c
9
y
75
− 111y
74
+ ··· + 20483025y −477481
c
12
y
75
+ 105y
74
+ ··· + 337608668y −38390416
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.338490 + 1.014360I
a = −0.083989 + 0.737529I
b = −0.225489 + 0.455556I
−1.59254 − 2.41045I 0
u = −0.338490 − 1.014360I
a = −0.083989 − 0.737529I
b = −0.225489 − 0.455556I
−1.59254 + 2.41045I 0
u = 0.343964 + 0.853499I
a = −1.63427 + 3.28949I
b = 1.11108 + 2.10173I
−5.77417 + 1.98856I 0
u = 0.343964 − 0.853499I
a = −1.63427 − 3.28949I
b = 1.11108 − 2.10173I
−5.77417 − 1.98856I 0
u = 0.812407 + 0.295359I
a = −0.650857 − 0.548434I
b = −0.49354 + 1.63137I
0.50070 − 3.88299I 0
u = 0.812407 − 0.295359I
a = −0.650857 + 0.548434I
b = −0.49354 − 1.63137I
0.50070 + 3.88299I 0
u = 0.211341 + 1.118520I
a = −0.33364 + 1.80730I
b = 0.87362 + 1.28162I
−4.06339 − 1.03839I 0
u = 0.211341 − 1.118520I
a = −0.33364 − 1.80730I
b = 0.87362 − 1.28162I
−4.06339 + 1.03839I 0
u = −0.688873 + 0.501015I
a = −0.700829 − 0.337773I
b = −0.285517 + 0.188871I
1.72423 − 1.07048I 0
u = −0.688873 − 0.501015I
a = −0.700829 + 0.337773I
b = −0.285517 − 0.188871I
1.72423 + 1.07048I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.533903 + 1.016930I
a = 1.58173 − 1.65823I
b = −0.15810 − 1.89823I
−3.86944 + 5.81407I 0
u = 0.533903 − 1.016930I
a = 1.58173 + 1.65823I
b = −0.15810 + 1.89823I
−3.86944 − 5.81407I 0
u = −0.545651 + 1.035230I
a = −0.426292 + 0.404260I
b = 0.052141 + 0.213347I
0.10985 − 3.67304I 0
u = −0.545651 − 1.035230I
a = −0.426292 − 0.404260I
b = 0.052141 − 0.213347I
0.10985 + 3.67304I 0
u = −0.248881 + 0.790036I
a = −0.094181 + 1.033320I
b = −0.328403 + 1.126780I
−1.88152 − 2.41983I 0
u = −0.248881 − 0.790036I
a = −0.094181 − 1.033320I
b = −0.328403 − 1.126780I
−1.88152 + 2.41983I 0
u = 0.097339 + 1.218700I
a = 0.222120 − 0.272580I
b = −0.662838 − 0.164392I
−0.26158 + 2.14205I 0
u = 0.097339 − 1.218700I
a = 0.222120 + 0.272580I
b = −0.662838 + 0.164392I
−0.26158 − 2.14205I 0
u = 1.260860 + 0.012988I
a = −0.813627 + 0.273446I
b = 0.635193 − 0.683649I
−4.57011 − 3.93986I 0
u = 1.260860 − 0.012988I
a = −0.813627 − 0.273446I
b = 0.635193 + 0.683649I
−4.57011 + 3.93986I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.096237 + 1.263760I
a = 0.068326 + 0.488408I
b = −0.901195 − 0.026334I
−6.63701 + 4.14284I 0
u = 0.096237 − 1.263760I
a = 0.068326 − 0.488408I
b = −0.901195 + 0.026334I
−6.63701 − 4.14284I 0
u = −0.244538 + 1.249340I
a = 0.273380 + 0.486740I
b = −0.322007 + 0.572207I
−1.46648 − 2.68040I 0
u = −0.244538 − 1.249340I
a = 0.273380 − 0.486740I
b = −0.322007 − 0.572207I
−1.46648 + 2.68040I 0
u = 0.149500 + 1.265560I
a = −0.23660 + 1.50686I
b = −0.688027 + 1.076700I
−8.24845 + 3.84574I 0
u = 0.149500 − 1.265560I
a = −0.23660 − 1.50686I
b = −0.688027 − 1.076700I
−8.24845 − 3.84574I 0
u = 0.568915 + 1.158220I
a = 1.14020 − 1.97951I
b = −0.84223 − 2.39603I
−2.08797 + 9.01604I 0
u = 0.568915 − 1.158220I
a = 1.14020 + 1.97951I
b = −0.84223 + 2.39603I
−2.08797 − 9.01604I 0
u = 0.105585 + 1.294190I
a = −0.094589 − 0.455966I
b = −1.00362 − 1.24602I
−8.16649 + 0.01465I 0
u = 0.105585 − 1.294190I
a = −0.094589 + 0.455966I
b = −1.00362 + 1.24602I
−8.16649 − 0.01465I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.083185 + 1.303140I
a = −1.44819 + 1.43760I
b = −2.73221 + 1.68154I
−9.82572 + 5.04338I 0
u = 0.083185 − 1.303140I
a = −1.44819 − 1.43760I
b = −2.73221 − 1.68154I
−9.82572 − 5.04338I 0
u = 0.372696 + 1.256320I
a = −0.65580 + 1.84410I
b = 0.68355 + 2.03412I
−5.97939 + 1.25175I 0
u = 0.372696 − 1.256320I
a = −0.65580 − 1.84410I
b = 0.68355 − 2.03412I
−5.97939 − 1.25175I 0
u = 1.333380 + 0.173682I
a = 0.811498 − 0.849545I
b = −1.37253 + 1.88759I
4.21365 + 1.49945I 0
u = 1.333380 − 0.173682I
a = 0.811498 + 0.849545I
b = −1.37253 − 1.88759I
4.21365 − 1.49945I 0
u = −0.289653 + 1.324520I
a = −1.04672 − 1.72698I
b = −0.82792 − 2.61892I
−4.21139 − 0.24470I 0
u = −0.289653 − 1.324520I
a = −1.04672 + 1.72698I
b = −0.82792 + 2.61892I
−4.21139 + 0.24470I 0
u = −1.42651 + 0.03741I
a = 0.570335 + 0.464102I
b = −0.76187 − 1.78511I
3.79263 − 2.20139I 0
u = −1.42651 − 0.03741I
a = 0.570335 − 0.464102I
b = −0.76187 + 1.78511I
3.79263 + 2.20139I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.374818 + 0.350718I
a = −2.80026 + 0.39715I
b = 0.746495 + 0.170227I
−3.55538 − 2.70832I 5.95415 + 0.21604I
u = 0.374818 − 0.350718I
a = −2.80026 − 0.39715I
b = 0.746495 − 0.170227I
−3.55538 + 2.70832I 5.95415 − 0.21604I
u = 0.456613 + 0.215336I
a = −0.763234 − 0.254726I
b = −0.097092 + 1.163740I
−2.17924 − 1.79406I 3.71045 + 3.85861I
u = 0.456613 − 0.215336I
a = −0.763234 + 0.254726I
b = −0.097092 − 1.163740I
−2.17924 + 1.79406I 3.71045 − 3.85861I
u = −0.21547 + 1.48414I
a = −0.38029 − 1.54285I
b = −0.42424 − 2.38866I
−2.97425 − 7.62553I 0
u = −0.21547 − 1.48414I
a = −0.38029 + 1.54285I
b = −0.42424 + 2.38866I
−2.97425 + 7.62553I 0
u = 0.084889 + 0.487616I
a = −4.49287 − 0.57716I
b = −0.733448 − 0.772570I
−6.72101 − 4.29646I −3.76910 + 2.69049I
u = 0.084889 − 0.487616I
a = −4.49287 + 0.57716I
b = −0.733448 + 0.772570I
−6.72101 + 4.29646I −3.76910 − 2.69049I
u = −1.40921 + 0.57774I
a = −0.451526 + 0.502532I
b = −0.41328 − 2.67844I
−8.29796 − 0.94595I 0
u = −1.40921 − 0.57774I
a = −0.451526 − 0.502532I
b = −0.41328 + 2.67844I
−8.29796 + 0.94595I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.57774 + 1.46690I
a = −0.136989 − 0.135245I
b = 0.523608 − 0.380389I
−9.27086 + 10.48060I 0
u = 0.57774 − 1.46690I
a = −0.136989 + 0.135245I
b = 0.523608 + 0.380389I
−9.27086 − 10.48060I 0
u = 0.275445 + 0.320660I
a = −2.91158 − 0.02172I
b = 0.501597 − 0.568378I
−5.04243 − 2.17825I 3.70428 + 5.60941I
u = 0.275445 − 0.320660I
a = −2.91158 + 0.02172I
b = 0.501597 + 0.568378I
−5.04243 + 2.17825I 3.70428 − 5.60941I
u = 0.16408 + 1.56901I
a = −0.28564 + 1.78527I
b = −0.26882 + 3.41347I
−3.58764 + 6.75970I 0
u = 0.16408 − 1.56901I
a = −0.28564 − 1.78527I
b = −0.26882 − 3.41347I
−3.58764 − 6.75970I 0
u = 0.63107 + 1.45962I
a = 0.238033 − 0.112386I
b = 0.982552 − 0.988516I
−9.04107 + 2.56417I 0
u = 0.63107 − 1.45962I
a = 0.238033 + 0.112386I
b = 0.982552 + 0.988516I
−9.04107 − 2.56417I 0
u = 0.04084 + 1.60964I
a = 0.75777 − 1.77433I
b = 1.43111 − 3.73653I
−12.12460 − 1.13507I 0
u = 0.04084 − 1.60964I
a = 0.75777 + 1.77433I
b = 1.43111 + 3.73653I
−12.12460 + 1.13507I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.34679 + 1.57824I
a = −0.09367 − 1.58863I
b = 1.63442 − 2.48460I
−15.6106 − 6.7181I 0
u = −0.34679 − 1.57824I
a = −0.09367 + 1.58863I
b = 1.63442 + 2.48460I
−15.6106 + 6.7181I 0
u = −1.63199 + 0.04625I
a = −0.551410 + 0.644182I
b = 0.84326 − 2.91872I
−6.99114 + 8.56653I 0
u = −1.63199 − 0.04625I
a = −0.551410 − 0.644182I
b = 0.84326 + 2.91872I
−6.99114 − 8.56653I 0
u = −0.68541 + 1.54649I
a = 0.83167 + 1.45807I
b = −0.83970 + 3.36363I
−11.8545 − 16.4570I 0
u = −0.68541 − 1.54649I
a = 0.83167 − 1.45807I
b = −0.83970 − 3.36363I
−11.8545 + 16.4570I 0
u = −0.289488
a = −0.732575
b = −0.350214
0.735693 13.9000
u = −0.87530 + 1.54498I
a = 0.88420 + 1.17471I
b = −1.16957 + 3.16272I
−11.35710 − 7.66415I 0
u = −0.87530 − 1.54498I
a = 0.88420 − 1.17471I
b = −1.16957 − 3.16272I
−11.35710 + 7.66415I 0
u = 0.0114997 + 0.0911495I
a = −3.59923 − 1.96297I
b = 0.742740 + 0.718710I
3.67870 − 0.89897I 14.8156 + 6.9184I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.0114997 − 0.0911495I
a = −3.59923 + 1.96297I
b = 0.742740 − 0.718710I
3.67870 + 0.89897I 14.8156 − 6.9184I
u = −0.0699362 + 0.0330813I
a = −4.95235 − 0.65070I
b = 0.732305 + 0.963089I
2.89321 + 6.53096I 16.6016 − 9.8113I
u = −0.0699362 − 0.0330813I
a = −4.95235 + 0.65070I
b = 0.732305 − 0.963089I
2.89321 − 6.53096I 16.6016 + 9.8113I
u = −0.42486 + 1.87987I
a = 0.125652 − 1.290110I
b = 2.73307 − 3.01298I
−13.57810 + 0.08080I 0
u = −0.42486 − 1.87987I
a = 0.125652 + 1.290110I
b = 2.73307 + 3.01298I
−13.57810 − 0.08080I 0
12
II.
I
u
2
= h−3.11×10
12
u
27
+3.42×10
12
u
26
+· · ·+1.16×10
12
b−3.55×10
12
, 8.83×
10
12
u
27
−8.61×10
12
u
26
+· · ·+1.16×10
12
a+1.58×10
13
, u
28
−u
27
+· · ·+2u+1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
2
=
−7.60602u
27
+ 7.41114u
26
+ ··· − 28.1573u − 13.5908
2.67859u
27
− 2.94919u
26
+ ··· + 12.5728u + 3.05558
a
8
=
1
−u
2
a
3
=
−1.78909u
27
− 0.555285u
26
+ ··· − 7.58876u − 10.3404
3.76486u
27
− 5.95905u
26
+ ··· + 14.0907u + 0.906085
a
9
=
5.11967u
27
− 3.37873u
26
+ ··· + 23.6246u + 13.3115
2.94895u
27
− 4.71299u
26
+ ··· + 11.3071u + 1.62711
a
12
=
u
u
a
1
=
−2.17073u
27
− 1.33426u
26
+ ··· − 12.3175u − 11.6844
5.41544u
27
− 5.71491u
26
+ ··· + 17.5642u + 8.64563
a
6
=
−8.33544u
27
+ 9.42656u
26
+ ··· − 28.3241u − 7.08146
0.216883u
27
+ 2.85982u
26
+ ··· − 3.94102u + 6.19344
a
4
=
0.372892u
27
+ 1.57605u
26
+ ··· − 0.961475u + 1.05287
14.0573u
27
− 15.2791u
26
+ ··· + 37.7260u + 5.10418
a
5
=
0.372892u
27
+ 1.57605u
26
+ ··· − 0.961475u + 1.05287
15.8214u
27
− 16.5557u
26
+ ··· + 41.9968u + 7.05313
a
10
=
2.91230u
27
− 1.44121u
26
+ ··· + 14.4439u + 9.80654
0.741578u
27
− 2.77547u
26
+ ··· + 2.12639u − 1.87788
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
1086730167949
145137309601
u
27
+
1111857372881
145137309601
u
26
+ ··· +
616499354094
145137309601
u −
1697099422906
145137309601
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
28
− 14u
27
+ ··· − 192u + 16
c
2
u
28
+ 7u
26
+ ··· + 4u + 4
c
3
u
28
+ 12u
27
+ ··· − 2u + 1
c
4
u
28
+ 10u
26
+ ··· − 4u + 4
c
5
u
28
+ 2u
27
+ ··· + 17u + 19
c
6
u
28
− 2u
27
+ ··· + 8u + 1
c
7
u
28
− u
27
+ ··· + 2u + 1
c
8
u
28
+ 7u
26
+ ··· − 4u + 4
c
9
u
28
− 12u
27
+ ··· − 915u + 107
c
10
u
28
+ 10u
26
+ ··· + 4u + 4
c
11
u
28
+ u
27
+ ··· − 2u + 1
c
12
u
28
− 2u
27
+ ··· − 18u + 4
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
+ 18y
27
+ ··· + 896y + 256
c
2
, c
8
y
28
+ 14y
27
+ ··· + 192y + 16
c
3
y
28
− 8y
27
+ ··· − 6y + 1
c
4
, c
10
y
28
+ 20y
27
+ ··· − 320y + 16
c
5
y
28
+ 24y
27
+ ··· − 23y + 361
c
6
y
28
+ 6y
27
+ ··· − 18y + 1
c
7
, c
11
y
28
+ 13y
27
+ ··· + 18y + 1
c
9
y
28
− 38y
27
+ ··· − 228181y + 11449
c
12
y
28
+ 18y
27
+ ··· − 188y + 16
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.267770 + 0.909697I
a = 0.280589 − 0.101358I
b = 0.215003 − 0.699264I
−2.54295 − 2.48178I −4.22697 + 3.94108I
u = −0.267770 − 0.909697I
a = 0.280589 + 0.101358I
b = 0.215003 + 0.699264I
−2.54295 + 2.48178I −4.22697 − 3.94108I
u = 0.362419 + 0.834030I
a = −1.26402 + 1.33981I
b = 0.585168 + 0.359472I
−5.62897 − 1.61321I −4.30162 + 0.11645I
u = 0.362419 − 0.834030I
a = −1.26402 − 1.33981I
b = 0.585168 − 0.359472I
−5.62897 + 1.61321I −4.30162 − 0.11645I
u = 0.627755 + 0.556467I
a = 2.60329 + 0.16051I
b = 0.350971 − 0.812210I
−6.12012 + 5.18333I 1.32357 − 7.61307I
u = 0.627755 − 0.556467I
a = 2.60329 − 0.16051I
b = 0.350971 + 0.812210I
−6.12012 − 5.18333I 1.32357 + 7.61307I
u = −0.465065 + 1.105660I
a = −0.414926 + 0.141473I
b = 0.279697 + 0.134622I
1.07312 − 3.66281I 10.39366 + 3.77091I
u = −0.465065 − 1.105660I
a = −0.414926 − 0.141473I
b = 0.279697 − 0.134622I
1.07312 + 3.66281I 10.39366 − 3.77091I
u = 0.154178 + 1.190760I
a = 0.12549 + 2.33363I
b = 1.24172 + 2.16205I
−3.93257 + 1.78428I 1.74978 − 2.39317I
u = 0.154178 − 1.190760I
a = 0.12549 − 2.33363I
b = 1.24172 − 2.16205I
−3.93257 − 1.78428I 1.74978 + 2.39317I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.150395 + 1.280860I
a = −0.400844 + 1.298880I
b = −0.99270 + 1.02546I
−7.93382 + 3.89142I 7.52926 − 5.54653I
u = 0.150395 − 1.280860I
a = −0.400844 − 1.298880I
b = −0.99270 − 1.02546I
−7.93382 − 3.89142I 7.52926 + 5.54653I
u = −1.269260 + 0.242314I
a = −0.768342 − 0.629330I
b = 1.11091 + 1.20232I
4.43645 − 1.13982I 13.0180 − 6.8027I
u = −1.269260 − 0.242314I
a = −0.768342 + 0.629330I
b = 1.11091 − 1.20232I
4.43645 + 1.13982I 13.0180 + 6.8027I
u = −0.513572 + 0.422844I
a = 3.33506 + 0.67192I
b = −0.17326 + 2.09327I
−4.94963 − 1.55164I 4.98769 − 1.02506I
u = −0.513572 − 0.422844I
a = 3.33506 − 0.67192I
b = −0.17326 − 2.09327I
−4.94963 + 1.55164I 4.98769 + 1.02506I
u = −0.187112 + 0.634531I
a = −0.503081 − 0.409592I
b = −0.922975 + 0.452604I
3.31096 + 0.53664I 2.87535 + 3.58863I
u = −0.187112 − 0.634531I
a = −0.503081 + 0.409592I
b = −0.922975 − 0.452604I
3.31096 − 0.53664I 2.87535 − 3.58863I
u = 0.504372 + 1.260390I
a = 0.85057 − 1.87567I
b = −0.64684 − 2.46436I
−1.06035 + 9.01292I 7.26243 − 7.29203I
u = 0.504372 − 1.260390I
a = 0.85057 + 1.87567I
b = −0.64684 + 2.46436I
−1.06035 − 9.01292I 7.26243 + 7.29203I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.267072 + 0.558984I
a = −1.13225 + 2.47654I
b = −0.289227 − 0.426768I
−3.73140 − 3.55454I 3.29778 + 9.44776I
u = −0.267072 − 0.558984I
a = −1.13225 − 2.47654I
b = −0.289227 + 0.426768I
−3.73140 + 3.55454I 3.29778 − 9.44776I
u = 0.068068 + 0.588251I
a = −0.684205 − 0.594437I
b = −1.019310 + 0.843066I
2.48894 − 6.40615I −2.05643 + 3.86667I
u = 0.068068 − 0.588251I
a = −0.684205 + 0.594437I
b = −1.019310 − 0.843066I
2.48894 + 6.40615I −2.05643 − 3.86667I
u = 1.52856 + 0.19094I
a = −0.557845 − 0.638107I
b = 0.42693 + 2.77654I
3.46736 − 2.79927I 1.59409 + 8.64873I
u = 1.52856 − 0.19094I
a = −0.557845 + 0.638107I
b = 0.42693 − 2.77654I
3.46736 + 2.79927I 1.59409 − 8.64873I
u = 0.07410 + 1.70425I
a = 0.53052 − 1.55664I
b = 0.83392 − 3.73132I
−11.77570 − 1.30163I 9.05337 + 7.46743I
u = 0.07410 − 1.70425I
a = 0.53052 + 1.55664I
b = 0.83392 + 3.73132I
−11.77570 + 1.30163I 9.05337 − 7.46743I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
28
− 14u
27
+ ··· − 192u + 16)(u
75
+ 37u
74
+ ··· − 48u − 16)
c
2
(u
28
+ 7u
26
+ ··· + 4u + 4)(u
75
+ u
74
+ ··· − 8u − 4)
c
3
(u
28
+ 12u
27
+ ··· − 2u + 1)(u
75
+ 9u
74
+ ··· − 284u − 19)
c
4
(u
28
+ 10u
26
+ ··· − 4u + 4)(u
75
− u
74
+ ··· − 2058072u − 145372)
c
5
(u
28
+ 2u
27
+ ··· + 17u + 19)
· (u
75
− 3u
74
+ ··· + 2493542u − 4382428)
c
6
(u
28
− 2u
27
+ ··· + 8u + 1)(u
75
− 5u
74
+ ··· + 54618u − 5068)
c
7
(u
28
− u
27
+ ··· + 2u + 1)(u
75
− 2u
74
+ ··· + 14u − 1)
c
8
(u
28
+ 7u
26
+ ··· − 4u + 4)(u
75
+ u
74
+ ··· − 8u − 4)
c
9
(u
28
− 12u
27
+ ··· − 915u + 107)(u
75
− 7u
74
+ ··· + 1121u − 691)
c
10
(u
28
+ 10u
26
+ ··· + 4u + 4)(u
75
− u
74
+ ··· − 2058072u − 145372)
c
11
(u
28
+ u
27
+ ··· − 2u + 1)(u
75
− 2u
74
+ ··· + 14u − 1)
c
12
(u
28
− 2u
27
+ ··· − 18u + 4)(u
75
+ 3u
74
+ ··· − 60886u − 6196)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
28
+ 18y
27
+ ··· + 896y + 256)(y
75
+ 21y
74
+ ··· + 1408y −256)
c
2
, c
8
(y
28
+ 14y
27
+ ··· + 192y + 16)(y
75
+ 37y
74
+ ··· − 48y −16)
c
3
(y
28
− 8y
27
+ ··· − 6y + 1)(y
75
− y
74
+ ··· − 9366y −361)
c
4
, c
10
(y
28
+ 20y
27
+ ··· − 320y + 16)
· (y
75
+ 103y
74
+ ··· − 180569463856y −21133018384)
c
5
(y
28
+ 24y
27
+ ··· − 23y + 361)
· (y
75
+ 59y
74
+ ··· + 152134872802076y −19205675175184)
c
6
(y
28
+ 6y
27
+ ··· − 18y + 1)
· (y
75
− 19y
74
+ ··· + 614373132y −25684624)
c
7
, c
11
(y
28
+ 13y
27
+ ··· + 18y + 1)(y
75
+ 56y
74
+ ··· − 26y −1)
c
9
(y
28
− 38y
27
+ ··· − 228181y + 11449)
· (y
75
− 111y
74
+ ··· + 20483025y −477481)
c
12
(y
28
+ 18y
27
+ ··· − 188y + 16)
· (y
75
+ 105y
74
+ ··· + 337608668y −38390416)
22
