12a
0629
(K12a
0629
)
A knot diagram
1
Linearized knot diagam
3 7 10 9 8 2 11 12 1 6 5 4
Solving Sequence
2,7 3,11
8 1 6 5 12 10 9 4
c
2
c
7
c
1
c
6
c
5
c
11
c
10
c
9
c
4
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h8556215038u
35
+ 88954311703u
34
+ ··· + 896216536b + 256623421136,
7106105223u
35
+ 72031097023u
34
+ ··· + 1792433072a + 143687532288,
u
36
+ 11u
35
+ ··· + 272u + 32i
I
u
2
= h−11687u
23
+ 18829u
22
+ ··· + 10412b + 20692, −10340u
23
+ 11229u
22
+ ··· + 5206a + 1655,
u
24
− 2u
23
+ ··· − 3u + 1i
I
u
3
= h−8u
67
a − 1512u
67
+ ··· + 8a − 1868, 511u
67
a + 3u
67
+ ··· + 443a + 3488, u
68
− 6u
67
+ ··· − 11u − 1i
* 3 irreducible components of dim
C
= 0, with total 196 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
=
h8.56×10
9
u
35
+8.90×10
10
u
34
+· · · +8.96×10
8
b+2.57×10
11
, 7.11×10
9
u
35
+
7.20 × 10
10
u
34
+ · · · + 1.79 × 10
9
a + 1.44 × 10
11
, u
36
+ 11u
35
+ · · · + 272u + 32i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
11
=
−3.96450u
35
− 40.1862u
34
+ ··· − 651.842u − 80.1634
−9.54704u
35
− 99.2554u
34
+ ··· − 2249.93u − 286.341
a
8
=
−6.08616u
35
− 59.5811u
34
+ ··· − 971.052u − 121.494
−9.21243u
35
− 90.5844u
34
+ ··· − 1619.60u − 203.975
a
1
=
−u
2
+ 1
−u
4
a
6
=
u
u
a
5
=
4.05928u
35
+ 48.5520u
34
+ ··· + 1754.80u + 230.994
3.45731u
35
+ 47.7820u
34
+ ··· + 2476.13u + 333.311
a
12
=
3.69166u
35
+ 29.8903u
34
+ ··· − 157.090u − 25.3283
12.5638u
35
+ 116.784u
34
+ ··· + 1115.12u + 127.351
a
10
=
−6.60941u
35
− 60.5115u
34
+ ··· − 194.344u − 5.32351
−12.1919u
35
− 119.581u
34
+ ··· − 1792.43u − 211.501
a
9
=
7.05419u
35
+ 69.3065u
34
+ ··· + 1216.08u + 157.152
17.2900u
35
+ 178.333u
34
+ ··· + 3753.55u + 479.519
a
4
=
16.4473u
35
+ 145.651u
34
+ ··· − 514.224u − 124.290
35.2687u
35
+ 346.194u
34
+ ··· + 4598.95u + 526.313
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
37524040947
224054134
u
35
−
350685729393
224054134
u
34
+ ··· −
964109017840
112027067
u −
73536479818
112027067
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
36
+ 11u
35
+ ··· − 4352u + 1024
c
2
, c
6
u
36
− 11u
35
+ ··· − 272u + 32
c
3
, c
10
u
36
+ 6u
35
+ ··· + 2u + 2
c
4
, c
11
u
36
+ 6u
35
+ ··· − u + 1
c
5
, c
12
u
36
+ 2u
35
+ ··· + 8u + 1
c
7
, c
9
u
36
+ 2u
35
+ ··· − u + 1
c
8
u
36
+ 26u
35
+ ··· + 131072u + 8192
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
36
+ y
35
+ ··· − 22740992y + 1048576
c
2
, c
6
y
36
− 11y
35
+ ··· + 4352y + 1024
c
3
, c
10
y
36
+ 36y
35
+ ··· + 148y + 4
c
4
, c
11
y
36
+ 42y
35
+ ··· + 9y + 1
c
5
, c
12
y
36
− 4y
35
+ ··· + 4y + 1
c
7
, c
9
y
36
− 2y
35
+ ··· − 5y + 1
c
8
y
36
+ 10y
35
+ ··· − 503316480y + 67108864
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.917123 + 0.173555I
a = −0.083595 + 0.389036I
b = 0.451653 + 1.048310I
−1.67998 − 0.65565I −2.95585 + 0.33945I
u = 0.917123 − 0.173555I
a = −0.083595 − 0.389036I
b = 0.451653 − 1.048310I
−1.67998 + 0.65565I −2.95585 − 0.33945I
u = 1.016890 + 0.362822I
a = −0.726079 + 0.908015I
b = −0.21078 + 2.05277I
−4.79406 − 0.88716I −1.70616 + 0.I
u = 1.016890 − 0.362822I
a = −0.726079 − 0.908015I
b = −0.21078 − 2.05277I
−4.79406 + 0.88716I −1.70616 + 0.I
u = −0.220844 + 1.083620I
a = 0.588519 − 0.803075I
b = 0.172175 − 0.323778I
0.66875 + 9.32529I 0. − 11.11924I
u = −0.220844 − 1.083620I
a = 0.588519 + 0.803075I
b = 0.172175 + 0.323778I
0.66875 − 9.32529I 0. + 11.11924I
u = −1.015240 + 0.447562I
a = 0.918459 − 0.800426I
b = 0.83041 − 1.55499I
−4.24268 + 5.45049I −6.68187 − 9.06588I
u = −1.015240 − 0.447562I
a = 0.918459 + 0.800426I
b = 0.83041 + 1.55499I
−4.24268 − 5.45049I −6.68187 + 9.06588I
u = −0.586727 + 0.959085I
a = −1.251040 − 0.590338I
b = 0.127432 − 0.327224I
2.6827 − 15.0492I 0. + 7.70054I
u = −0.586727 − 0.959085I
a = −1.251040 + 0.590338I
b = 0.127432 + 0.327224I
2.6827 + 15.0492I 0. − 7.70054I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.540156 + 0.986227I
a = 1.107750 + 0.608530I
b = 0.000323 + 0.280248I
5.32041 − 6.73104I 5.99890 + 5.64253I
u = −0.540156 − 0.986227I
a = 1.107750 − 0.608530I
b = 0.000323 − 0.280248I
5.32041 + 6.73104I 5.99890 − 5.64253I
u = −0.669576 + 0.946052I
a = 0.478928 + 0.494294I
b = −0.273375 + 0.172093I
6.09668 + 0.13115I 8.49502 + 0.I
u = −0.669576 − 0.946052I
a = 0.478928 − 0.494294I
b = −0.273375 − 0.172093I
6.09668 − 0.13115I 8.49502 + 0.I
u = −0.890692 + 0.747997I
a = −0.059904 − 0.192189I
b = 0.77408 − 4.24786I
1.37552 + 2.85385I 12.812 + 161.062I
u = −0.890692 − 0.747997I
a = −0.059904 + 0.192189I
b = 0.77408 + 4.24786I
1.37552 − 2.85385I 12.812 − 161.062I
u = −1.112050 + 0.514367I
a = 0.015186 − 1.076150I
b = −0.29518 − 1.69743I
−0.65310 + 4.94429I 0
u = −1.112050 − 0.514367I
a = 0.015186 + 1.076150I
b = −0.29518 + 1.69743I
−0.65310 − 4.94429I 0
u = −1.216240 + 0.371675I
a = −0.517817 + 0.720739I
b = −0.584631 + 1.037250I
−3.26684 − 3.99030I 0
u = −1.216240 − 0.371675I
a = −0.517817 − 0.720739I
b = −0.584631 − 1.037250I
−3.26684 + 3.99030I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.268260 + 0.156911I
a = 0.706035 − 0.924357I
b = 0.98202 − 1.83484I
−4.9583 − 13.2608I 0
u = 1.268260 − 0.156911I
a = 0.706035 + 0.924357I
b = 0.98202 + 1.83484I
−4.9583 + 13.2608I 0
u = −1.060410 + 0.751628I
a = 0.367953 + 0.546420I
b = 0.55402 + 1.44324I
4.85132 + 6.07493I 0
u = −1.060410 − 0.751628I
a = 0.367953 − 0.546420I
b = 0.55402 − 1.44324I
4.85132 − 6.07493I 0
u = −0.388492 + 0.565688I
a = −1.133240 − 0.428031I
b = −0.305857 + 0.275432I
1.49079 − 0.59945I 4.04927 + 1.08778I
u = −0.388492 − 0.565688I
a = −1.133240 + 0.428031I
b = −0.305857 − 0.275432I
1.49079 + 0.59945I 4.04927 − 1.08778I
u = −1.110850 + 0.731998I
a = −0.493770 − 1.155180I
b = −0.61517 − 2.47736I
1.0454 + 21.2340I 0
u = −1.110850 − 0.731998I
a = −0.493770 + 1.155180I
b = −0.61517 + 2.47736I
1.0454 − 21.2340I 0
u = −0.001988 + 1.332010I
a = −0.522658 + 0.118069I
b = −0.277634 + 0.117341I
3.58239 − 0.69751I 0
u = −0.001988 − 1.332010I
a = −0.522658 − 0.118069I
b = −0.277634 − 0.117341I
3.58239 + 0.69751I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.134270 + 0.722619I
a = 0.486117 + 1.083920I
b = 0.63427 + 2.19811I
3.46949 + 12.94040I 0
u = −1.134270 − 0.722619I
a = 0.486117 − 1.083920I
b = 0.63427 − 2.19811I
3.46949 − 12.94040I 0
u = 1.341160 + 0.144697I
a = −0.452211 + 0.835333I
b = −0.58485 + 1.49371I
−2.36708 − 4.28180I 0
u = 1.341160 − 0.144697I
a = −0.452211 − 0.835333I
b = −0.58485 − 1.49371I
−2.36708 + 4.28180I 0
u = −0.095893 + 0.460209I
a = −1.42864 + 1.29930I
b = 0.121094 + 0.611898I
−2.04162 − 1.95837I −1.88152 + 1.81563I
u = −0.095893 − 0.460209I
a = −1.42864 − 1.29930I
b = 0.121094 − 0.611898I
−2.04162 + 1.95837I −1.88152 − 1.81563I
8
II. I
u
2
= h−11687u
23
+ 18829u
22
+ · · · + 10412b + 20692, −10340u
23
+
11229u
22
+ · · · + 5206a + 1655, u
24
− 2u
23
+ · · · − 3u + 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
11
=
1.98617u
23
− 2.15693u
22
+ ··· + 6.85133u − 0.317902
1.12245u
23
− 1.80839u
22
+ ··· + 5.12889u − 1.98732
a
8
=
5.18402u
23
− 6.75912u
22
+ ··· + 13.2282u − 5.25624
2.97484u
23
− 4.94526u
22
+ ··· + 9.60449u − 4.75202
a
1
=
−u
2
+ 1
−u
4
a
6
=
u
u
a
5
=
−8.20515u
23
+ 10.2555u
22
+ ··· − 17.7053u + 8.70111
−7.73108u
23
+ 10.7737u
22
+ ··· − 20.1091u + 10.7925
a
12
=
0.837591u
23
+ 0.660584u
22
+ ··· − 1.55839u + 2.59672
2.96984u
23
− 2.43248u
22
+ ··· + 5.80081u − 1.26959
a
10
=
3.36621u
23
− 4.22993u
22
+ ··· + 10.1243u − 1.69679
2.50250u
23
− 3.88139u
22
+ ··· + 8.40184u − 3.36621
a
9
=
1.62265u
23
− 2.29927u
22
+ ··· + 6.00595u − 0.823185
1.77891u
23
− 3.00182u
22
+ ··· + 6.99827u − 2.92230
a
4
=
−3.17979u
23
+ 2.95985u
22
+ ··· − 6.68277u + 2.11727
−3.39973u
23
+ 4.01277u
22
+ ··· − 8.42211u + 3.17979
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
37151
2603
u
23
+
6867
274
u
22
+ ··· −
384495
10412
u +
390481
10412
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
− 8u
23
+ ··· − 5u + 1
c
2
u
24
− 2u
23
+ ··· − 3u + 1
c
3
, c
10
8(8u
24
+ 24u
22
+ ··· − 6u + 2)
c
4
, c
11
8(8u
24
+ 48u
22
+ ··· − 3u + 1)
c
5
, c
12
u
24
+ 2u
23
+ ··· + 16u + 8
c
6
u
24
+ 2u
23
+ ··· + 3u + 1
c
7
, c
9
u
24
+ 4u
23
+ ··· − 16u + 8
c
8
u
24
+ 7u
23
+ ··· − 16u + 2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
− 12y
22
+ ··· + 7y + 1
c
2
, c
6
y
24
− 8y
23
+ ··· − 5y + 1
c
3
, c
10
64(64y
24
+ 384y
23
+ ··· + 56y + 4)
c
4
, c
11
64(64y
24
+ 768y
23
+ ··· + 35y + 1)
c
5
, c
12
y
24
+ 6y
23
+ ··· + 512y + 64
c
7
, c
9
y
24
− 12y
23
+ ··· + 704y + 64
c
8
y
24
+ 5y
23
+ ··· − 204y + 4
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.860065 + 0.565709I
a = −1.34241 − 0.99239I
b = −0.38539 − 2.12630I
0.44061 + 2.25492I 1.75964 − 3.06662I
u = −0.860065 − 0.565709I
a = −1.34241 + 0.99239I
b = −0.38539 + 2.12630I
0.44061 − 2.25492I 1.75964 + 3.06662I
u = −0.883469 + 0.377040I
a = 0.957994 + 0.730874I
b = 0.23436 + 2.09805I
−5.42486 + 1.58176I −6.29167 − 6.08937I
u = −0.883469 − 0.377040I
a = 0.957994 − 0.730874I
b = 0.23436 − 2.09805I
−5.42486 − 1.58176I −6.29167 + 6.08937I
u = 0.815109 + 0.377010I
a = 1.39131 − 0.38326I
b = 1.33421 + 0.51019I
−0.60000 − 1.52156I 3.37855 + 4.24608I
u = 0.815109 − 0.377010I
a = 1.39131 + 0.38326I
b = 1.33421 − 0.51019I
−0.60000 + 1.52156I 3.37855 − 4.24608I
u = 0.540524 + 0.667194I
a = −1.43542 + 0.23924I
b = −0.019679 − 0.531376I
2.05081 + 8.00632I 2.81129 − 7.21454I
u = 0.540524 − 0.667194I
a = −1.43542 − 0.23924I
b = −0.019679 + 0.531376I
2.05081 − 8.00632I 2.81129 + 7.21454I
u = 0.925587 + 0.670732I
a = −0.240368 − 0.117171I
b = −0.519293 − 0.863337I
−3.62915 − 2.67044I −7.90181 + 5.61446I
u = 0.925587 − 0.670732I
a = −0.240368 + 0.117171I
b = −0.519293 + 0.863337I
−3.62915 + 2.67044I −7.90181 − 5.61446I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.875479 + 0.770703I
a = −0.764629 − 0.719022I
b = −0.223407 − 1.116630I
6.02038 + 2.90528I 8.41742 − 2.65430I
u = −0.875479 − 0.770703I
a = −0.764629 + 0.719022I
b = −0.223407 + 1.116630I
6.02038 − 2.90528I 8.41742 + 2.65430I
u = 1.066150 + 0.645953I
a = −0.229528 + 1.092320I
b = −0.69690 + 2.25633I
0.48213 − 13.21490I 0.16852 + 11.73368I
u = 1.066150 − 0.645953I
a = −0.229528 − 1.092320I
b = −0.69690 − 2.25633I
0.48213 + 13.21490I 0.16852 − 11.73368I
u = 1.172970 + 0.510194I
a = 0.118804 − 1.128680I
b = 0.37669 − 1.70359I
−0.35177 − 4.64835I 10.29109 − 0.46131I
u = 1.172970 − 0.510194I
a = 0.118804 + 1.128680I
b = 0.37669 + 1.70359I
−0.35177 + 4.64835I 10.29109 + 0.46131I
u = 0.078763 + 1.315650I
a = 0.551983 − 0.131397I
b = 0.301322 − 0.031826I
3.62833 − 0.58201I 10.5704 − 27.1081I
u = 0.078763 − 1.315650I
a = 0.551983 + 0.131397I
b = 0.301322 + 0.031826I
3.62833 + 0.58201I 10.5704 + 27.1081I
u = −1.337980 + 0.020898I
a = 0.306593 − 0.778635I
b = 0.55628 − 1.33934I
−3.35094 − 5.24005I −6.46504 + 10.35614I
u = −1.337980 − 0.020898I
a = 0.306593 + 0.778635I
b = 0.55628 + 1.33934I
−3.35094 + 5.24005I −6.46504 − 10.35614I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.588050 + 0.216276I
a = 2.13802 + 0.26864I
b = 0.977455 + 0.640000I
2.36212 + 1.31776I 12.78138 − 4.44329I
u = 0.588050 − 0.216276I
a = 2.13802 − 0.26864I
b = 0.977455 − 0.640000I
2.36212 − 1.31776I 12.78138 + 4.44329I
u = −0.230155 + 0.508581I
a = −0.45235 + 1.78409I
b = −0.935642 + 0.081469I
1.66221 + 8.35232I 3.98025 − 7.75217I
u = −0.230155 − 0.508581I
a = −0.45235 − 1.78409I
b = −0.935642 − 0.081469I
1.66221 − 8.35232I 3.98025 + 7.75217I
14
III. I
u
3
= h−8u
67
a − 1512u
67
+ · · · + 8a − 1868, 511u
67
a + 3u
67
+ · · · +
443a + 3488, u
68
− 6u
67
+ · · · − 11u − 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
11
=
a
1
2
u
67
a +
189
2
u
67
+ ··· −
1
2
a +
467
4
a
8
=
−49.7500au
67
− 11.5000u
67
+ ··· − 31.9375a − 0.187500
−69.9375au
67
+ 22.4375u
67
+ ··· − 110.188a + 15.5625
a
1
=
−u
2
+ 1
−u
4
a
6
=
u
u
a
5
=
−
1615
16
u
67
a +
481
4
u
67
+ ··· −
2435
16
a + 85
−
2747
16
u
67
a + 116u
67
+ ··· −
2783
16
a +
383
4
a
12
=
−82.7500au
67
+ 18.1875u
67
+ ··· − 68.3125a + 25.0625
−113.500au
67
− 6.81250u
67
+ ··· − 130.563a + 32.0625
a
10
=
−
1
2
u
67
a +
337
4
u
67
+ ··· + a −
365
16
178.750u
67
− 877.500u
66
+ ··· − 0.500000a + 93.9375
a
9
=
−
1
2
u
67
a +
553
16
u
67
+ ··· + a − 14
71.0625u
67
− 350.563u
66
+ ··· − 0.500000a + 36.7500
a
4
=
−
365
16
u
67
a +
93
16
u
67
+ ··· −
189
2
a − 10
−22.8125au
67
+ 20.3125u
67
+ ··· − 94.5000a + 2.31250
(ii) Obstruction class = −1
(iii) Cusp Shapes = 57u
67
−
525
2
u
66
+ ··· +
61
4
u +
23
4
15
(iv) u-Polynomials at the component
16
Crossings u-Polynomials at each crossing
c
1
(u
68
+ 26u
67
+ ··· + 205u + 1)
2
c
2
(u
68
+ 6u
67
+ ··· + 11u − 1)
2
c
3
8u
136
+ 8u
135
+ ··· + 4470u + 839
c
4
8u
136
+ 24u
135
+ ··· − 26342u + 6133
c
5
u
136
+ 9u
135
+ ··· + 685520u + 42152
c
6
(u
68
− 6u
67
+ ··· − 11u − 1)
2
c
7
u
136
+ 7u
135
+ ··· + 79519456u + 8899096
c
8
(u
68
− 16u
67
+ ··· − 14u + 1)
2
c
9
u
136
− 7u
135
+ ··· − 79519456u + 8899096
c
10
8u
136
− 8u
135
+ ··· − 4470u + 839
c
11
8u
136
− 24u
135
+ ··· + 26342u + 6133
c
12
u
136
− 9u
135
+ ··· − 685520u + 42152
17
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
68
+ 38y
67
+ ··· − 36005y + 1)
2
c
2
, c
6
(y
68
− 26y
67
+ ··· − 205y + 1)
2
c
3
, c
10
64y
136
− 192y
135
+ ··· + 93218658y + 703921
c
4
, c
11
64y
136
+ 1088y
135
+ ··· + 4629371312y + 37613689
c
5
, c
12
y
136
+ 35y
135
+ ··· + 174484803328y + 1776791104
c
7
, c
9
y
136
− 45y
135
+ ··· − 5223710283802688y + 79193909617216
c
8
(y
68
− 16y
67
+ ··· − 46y + 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.771226 + 0.647144I
a = 0.629168 − 0.566368I
b = 0.55239 − 1.94820I
4.79606 + 0.05468I 0
u = 0.771226 + 0.647144I
a = 1.49131 − 0.53739I
b = 0.241294 − 0.590191I
4.79606 + 0.05468I 0
u = 0.771226 − 0.647144I
a = 0.629168 + 0.566368I
b = 0.55239 + 1.94820I
4.79606 − 0.05468I 0
u = 0.771226 − 0.647144I
a = 1.49131 + 0.53739I
b = 0.241294 + 0.590191I
4.79606 − 0.05468I 0
u = −0.816810 + 0.592425I
a = −0.856749 − 0.266899I
b = 1.146880 + 0.657118I
0.85175 + 1.32895I 0
u = −0.816810 + 0.592425I
a = −0.59934 + 1.41605I
b = −0.08326 + 2.32920I
0.85175 + 1.32895I 0
u = −0.816810 − 0.592425I
a = −0.856749 + 0.266899I
b = 1.146880 − 0.657118I
0.85175 − 1.32895I 0
u = −0.816810 − 0.592425I
a = −0.59934 − 1.41605I
b = −0.08326 − 2.32920I
0.85175 − 1.32895I 0
u = −0.866878 + 0.546435I
a = −0.895805 − 0.645635I
b = 1.11858 − 4.43564I
0.22362 + 2.18520I 0
u = −0.866878 + 0.546435I
a = 3.66906 + 1.80640I
b = 3.28578 + 2.10851I
0.22362 + 2.18520I 0
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.866878 − 0.546435I
a = −0.895805 + 0.645635I
b = 1.11858 + 4.43564I
0.22362 − 2.18520I 0
u = −0.866878 − 0.546435I
a = 3.66906 − 1.80640I
b = 3.28578 − 2.10851I
0.22362 − 2.18520I 0
u = 0.781559 + 0.671000I
a = −0.452014 + 0.357104I
b = −1.03850 + 1.91294I
3.73569 + 6.37722I 0
u = 0.781559 + 0.671000I
a = −1.53172 + 0.23469I
b = −0.0956080 + 0.0585280I
3.73569 + 6.37722I 0
u = 0.781559 − 0.671000I
a = −0.452014 − 0.357104I
b = −1.03850 − 1.91294I
3.73569 − 6.37722I 0
u = 0.781559 − 0.671000I
a = −1.53172 − 0.23469I
b = −0.0956080 − 0.0585280I
3.73569 − 6.37722I 0
u = 0.597067 + 0.841668I
a = 1.176330 − 0.086367I
b = −0.185680 + 0.122266I
−0.21257 + 6.72524I 0
u = 0.597067 + 0.841668I
a = −1.200460 + 0.470265I
b = 0.380782 + 0.134623I
−0.21257 + 6.72524I 0
u = 0.597067 − 0.841668I
a = 1.176330 + 0.086367I
b = −0.185680 − 0.122266I
−0.21257 − 6.72524I 0
u = 0.597067 − 0.841668I
a = −1.200460 − 0.470265I
b = 0.380782 − 0.134623I
−0.21257 − 6.72524I 0
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.960987 + 0.099955I
a = 0.612751 − 0.476034I
b = 0.85200 − 1.92449I
−6.38836 + 0.12505I −9.95193 + 0.I
u = −0.960987 + 0.099955I
a = 1.001250 + 0.732056I
b = 0.73872 + 1.99719I
−6.38836 + 0.12505I −9.95193 + 0.I
u = −0.960987 − 0.099955I
a = 0.612751 + 0.476034I
b = 0.85200 + 1.92449I
−6.38836 − 0.12505I −9.95193 + 0.I
u = −0.960987 − 0.099955I
a = 1.001250 − 0.732056I
b = 0.73872 − 1.99719I
−6.38836 − 0.12505I −9.95193 + 0.I
u = 0.892071 + 0.315336I
a = 0.841674 − 0.177264I
b = 2.08526 + 0.69340I
−0.69864 − 2.11200I 0. + 11.57797I
u = 0.892071 + 0.315336I
a = −1.04620 + 1.52727I
b = −0.44186 + 1.49119I
−0.69864 − 2.11200I 0. + 11.57797I
u = 0.892071 − 0.315336I
a = 0.841674 + 0.177264I
b = 2.08526 − 0.69340I
−0.69864 + 2.11200I 0. − 11.57797I
u = 0.892071 − 0.315336I
a = −1.04620 − 1.52727I
b = −0.44186 − 1.49119I
−0.69864 + 2.11200I 0. − 11.57797I
u = −0.883650 + 0.607662I
a = 0.996969 − 0.544762I
b = −0.131833 − 1.004210I
0.63148 + 3.42068I 0
u = −0.883650 + 0.607662I
a = −0.236957 − 0.718877I
b = −1.16814 − 2.17116I
0.63148 + 3.42068I 0
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.883650 − 0.607662I
a = 0.996969 + 0.544762I
b = −0.131833 + 1.004210I
0.63148 − 3.42068I 0
u = −0.883650 − 0.607662I
a = −0.236957 + 0.718877I
b = −1.16814 + 2.17116I
0.63148 − 3.42068I 0
u = −0.808185 + 0.713445I
a = −0.892675 − 0.540085I
b = −0.0087349 − 0.0354248I
5.05562 + 0.30074I 0
u = −0.808185 + 0.713445I
a = 0.423661 + 0.314839I
b = 0.47768 + 1.59358I
5.05562 + 0.30074I 0
u = −0.808185 − 0.713445I
a = −0.892675 + 0.540085I
b = −0.0087349 + 0.0354248I
5.05562 − 0.30074I 0
u = −0.808185 − 0.713445I
a = 0.423661 − 0.314839I
b = 0.47768 − 1.59358I
5.05562 − 0.30074I 0
u = 0.571656 + 0.915375I
a = −0.519660 + 0.628230I
b = 0.427899 − 0.059412I
5.04149 + 6.70792I 0
u = 0.571656 + 0.915375I
a = 1.36463 − 0.58109I
b = 0.134012 − 0.321037I
5.04149 + 6.70792I 0
u = 0.571656 − 0.915375I
a = −0.519660 − 0.628230I
b = 0.427899 + 0.059412I
5.04149 − 6.70792I 0
u = 0.571656 − 0.915375I
a = 1.36463 + 0.58109I
b = 0.134012 + 0.321037I
5.04149 − 6.70792I 0
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.769800 + 0.490237I
a = 0.968177 − 0.475759I
b = −1.98011 + 0.69753I
0.25812 − 1.55035I −8.76425 + 9.95450I
u = 0.769800 + 0.490237I
a = −1.40562 − 2.49578I
b = −1.55177 − 2.59005I
0.25812 − 1.55035I −8.76425 + 9.95450I
u = 0.769800 − 0.490237I
a = 0.968177 + 0.475759I
b = −1.98011 − 0.69753I
0.25812 + 1.55035I −8.76425 − 9.95450I
u = 0.769800 − 0.490237I
a = −1.40562 + 2.49578I
b = −1.55177 + 2.59005I
0.25812 + 1.55035I −8.76425 − 9.95450I
u = 0.916903 + 0.632889I
a = 0.809736 − 0.555766I
b = −0.581118 − 0.629466I
4.34586 − 5.05330I 0
u = 0.916903 + 0.632889I
a = 0.73493 − 1.31435I
b = 0.67841 − 2.38123I
4.34586 − 5.05330I 0
u = 0.916903 − 0.632889I
a = 0.809736 + 0.555766I
b = −0.581118 + 0.629466I
4.34586 + 5.05330I 0
u = 0.916903 − 0.632889I
a = 0.73493 + 1.31435I
b = 0.67841 + 2.38123I
4.34586 + 5.05330I 0
u = 0.990204 + 0.516851I
a = 0.532023 − 0.439380I
b = 1.91145 − 1.73936I
−0.49449 − 2.50857I 0
u = 0.990204 + 0.516851I
a = 1.03049 + 1.81539I
b = 1.07680 + 2.05365I
−0.49449 − 2.50857I 0
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.990204 − 0.516851I
a = 0.532023 + 0.439380I
b = 1.91145 + 1.73936I
−0.49449 + 2.50857I 0
u = 0.990204 − 0.516851I
a = 1.03049 − 1.81539I
b = 1.07680 − 2.05365I
−0.49449 + 2.50857I 0
u = 0.912924 + 0.648788I
a = −0.598553 + 0.445636I
b = 1.079260 − 0.060449I
3.32933 − 11.49430I 0
u = 0.912924 + 0.648788I
a = −0.43410 + 1.43935I
b = −0.67928 + 2.65395I
3.32933 − 11.49430I 0
u = 0.912924 − 0.648788I
a = −0.598553 − 0.445636I
b = 1.079260 + 0.060449I
3.32933 + 11.49430I 0
u = 0.912924 − 0.648788I
a = −0.43410 − 1.43935I
b = −0.67928 − 2.65395I
3.32933 + 11.49430I 0
u = −0.889097 + 0.711209I
a = −0.519438 − 0.727905I
b = −0.82446 − 1.44547I
4.81751 + 5.13561I 0
u = −0.889097 + 0.711209I
a = 0.501624 + 0.502302I
b = −0.732031 + 0.378716I
4.81751 + 5.13561I 0
u = −0.889097 − 0.711209I
a = −0.519438 + 0.727905I
b = −0.82446 + 1.44547I
4.81751 − 5.13561I 0
u = −0.889097 − 0.711209I
a = 0.501624 − 0.502302I
b = −0.732031 − 0.378716I
4.81751 − 5.13561I 0
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.583330 + 0.630270I
a = −1.032240 + 0.198269I
b = 0.615041 + 0.272853I
−1.94777 + 0.65282I −3.40956 − 2.01137I
u = 0.583330 + 0.630270I
a = 0.393238 + 1.174200I
b = 0.078598 + 0.927979I
−1.94777 + 0.65282I −3.40956 − 2.01137I
u = 0.583330 − 0.630270I
a = −1.032240 − 0.198269I
b = 0.615041 − 0.272853I
−1.94777 − 0.65282I −3.40956 + 2.01137I
u = 0.583330 − 0.630270I
a = 0.393238 − 1.174200I
b = 0.078598 − 0.927979I
−1.94777 − 0.65282I −3.40956 + 2.01137I
u = 0.429738 + 1.062260I
a = −1.153260 + 0.601615I
b = −0.448930 + 0.436452I
3.84142 − 1.49131I 0
u = 0.429738 + 1.062260I
a = −0.074079 − 0.577017I
b = −0.280866 + 0.015756I
3.84142 − 1.49131I 0
u = 0.429738 − 1.062260I
a = −1.153260 − 0.601615I
b = −0.448930 − 0.436452I
3.84142 + 1.49131I 0
u = 0.429738 − 1.062260I
a = −0.074079 + 0.577017I
b = −0.280866 − 0.015756I
3.84142 + 1.49131I 0
u = −1.147040 + 0.070859I
a = −0.300263 − 0.938028I
b = −0.65798 − 2.03865I
−6.64772 + 5.59976I 0
u = −1.147040 + 0.070859I
a = 0.727414 + 0.749823I
b = 1.13141 + 1.80597I
−6.64772 + 5.59976I 0
26
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.147040 − 0.070859I
a = −0.300263 + 0.938028I
b = −0.65798 + 2.03865I
−6.64772 − 5.59976I 0
u = −1.147040 − 0.070859I
a = 0.727414 − 0.749823I
b = 1.13141 − 1.80597I
−6.64772 − 5.59976I 0
u = 0.394464 + 0.748684I
a = 0.079109 + 1.149570I
b = −0.089208 + 0.339738I
−1.43552 − 3.46348I −1.95919 + 6.98569I
u = 0.394464 + 0.748684I
a = −0.446135 − 0.636292I
b = 0.193948 + 0.076169I
−1.43552 − 3.46348I −1.95919 + 6.98569I
u = 0.394464 − 0.748684I
a = 0.079109 − 1.149570I
b = −0.089208 − 0.339738I
−1.43552 + 3.46348I −1.95919 − 6.98569I
u = 0.394464 − 0.748684I
a = −0.446135 + 0.636292I
b = 0.193948 − 0.076169I
−1.43552 + 3.46348I −1.95919 − 6.98569I
u = −0.343410 + 0.747420I
a = 1.31165 + 0.87995I
b = −0.270471 + 0.135447I
−0.20924 − 7.51418I −0.91018 + 5.58459I
u = −0.343410 + 0.747420I
a = 1.27162 − 0.95759I
b = 0.606431 − 0.634974I
−0.20924 − 7.51418I −0.91018 + 5.58459I
u = −0.343410 − 0.747420I
a = 1.31165 − 0.87995I
b = −0.270471 − 0.135447I
−0.20924 + 7.51418I −0.91018 − 5.58459I
u = −0.343410 − 0.747420I
a = 1.27162 + 0.95759I
b = 0.606431 + 0.634974I
−0.20924 + 7.51418I −0.91018 − 5.58459I
27
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002490 + 0.618261I
a = −0.276729 + 0.848168I
b = −0.25866 + 2.35131I
−3.14926 − 5.59368I 0
u = 1.002490 + 0.618261I
a = −0.991688 − 0.494804I
b = −0.866908 − 1.061780I
−3.14926 − 5.59368I 0
u = 1.002490 − 0.618261I
a = −0.276729 − 0.848168I
b = −0.25866 − 2.35131I
−3.14926 + 5.59368I 0
u = 1.002490 − 0.618261I
a = −0.991688 + 0.494804I
b = −0.866908 + 1.061780I
−3.14926 + 5.59368I 0
u = 1.064180 + 0.597265I
a = −0.585862 − 0.191724I
b = −0.695961 − 0.488190I
−3.33657 − 1.55685I 0
u = 1.064180 + 0.597265I
a = 0.154689 + 0.554374I
b = 0.441720 + 1.200230I
−3.33657 − 1.55685I 0
u = 1.064180 − 0.597265I
a = −0.585862 + 0.191724I
b = −0.695961 + 0.488190I
−3.33657 + 1.55685I 0
u = 1.064180 − 0.597265I
a = 0.154689 − 0.554374I
b = 0.441720 − 1.200230I
−3.33657 + 1.55685I 0
u = −1.231370 + 0.133780I
a = −0.550559 − 1.129810I
b = −0.78783 − 1.82293I
−2.14467 + 5.06597I 0
u = −1.231370 + 0.133780I
a = 0.235367 − 0.000609I
b = 0.342219 + 0.496387I
−2.14467 + 5.06597I 0
28
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.231370 − 0.133780I
a = −0.550559 + 1.129810I
b = −0.78783 + 1.82293I
−2.14467 − 5.06597I 0
u = −1.231370 − 0.133780I
a = 0.235367 + 0.000609I
b = 0.342219 − 0.496387I
−2.14467 − 5.06597I 0
u = 1.233890 + 0.109777I
a = −0.720753 − 0.574991I
b = −1.12279 − 1.33656I
−5.43865 + 4.78524I 0
u = 1.233890 + 0.109777I
a = 0.632451 − 1.259020I
b = 0.51621 − 2.07871I
−5.43865 + 4.78524I 0
u = 1.233890 − 0.109777I
a = −0.720753 + 0.574991I
b = −1.12279 + 1.33656I
−5.43865 − 4.78524I 0
u = 1.233890 − 0.109777I
a = 0.632451 + 1.259020I
b = 0.51621 + 2.07871I
−5.43865 − 4.78524I 0
u = −1.083630 + 0.601568I
a = 0.529460 + 1.039990I
b = 0.82598 + 2.46200I
−2.24526 + 12.55640I 0
u = −1.083630 + 0.601568I
a = −0.836228 + 1.101970I
b = −0.81105 + 1.64006I
−2.24526 + 12.55640I 0
u = −1.083630 − 0.601568I
a = 0.529460 − 1.039990I
b = 0.82598 − 2.46200I
−2.24526 − 12.55640I 0
u = −1.083630 − 0.601568I
a = −0.836228 − 1.101970I
b = −0.81105 − 1.64006I
−2.24526 − 12.55640I 0
29
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.134470 + 0.538793I
a = −0.041849 − 0.778026I
b = −0.503712 − 1.291620I
−0.71708 + 4.95220I 0
u = −1.134470 + 0.538793I
a = −0.163471 − 1.332450I
b = −0.30362 − 2.07143I
−0.71708 + 4.95220I 0
u = −1.134470 − 0.538793I
a = −0.041849 + 0.778026I
b = −0.503712 + 1.291620I
−0.71708 − 4.95220I 0
u = −1.134470 − 0.538793I
a = −0.163471 + 1.332450I
b = −0.30362 + 2.07143I
−0.71708 − 4.95220I 0
u = −0.710706 + 0.216866I
a = −1.70985 + 0.16838I
b = −0.235683 + 0.524978I
1.75336 − 1.28214I −3.71827 + 2.93694I
u = −0.710706 + 0.216866I
a = −1.58521 + 0.76141I
b = −1.62422 + 0.97960I
1.75336 − 1.28214I −3.71827 + 2.93694I
u = −0.710706 − 0.216866I
a = −1.70985 − 0.16838I
b = −0.235683 − 0.524978I
1.75336 + 1.28214I −3.71827 − 2.93694I
u = −0.710706 − 0.216866I
a = −1.58521 − 0.76141I
b = −1.62422 − 0.97960I
1.75336 + 1.28214I −3.71827 − 2.93694I
u = 1.062150 + 0.697966I
a = 0.080039 − 1.061900I
b = 0.26392 − 2.34393I
−1.62127 − 12.47790I 0
u = 1.062150 + 0.697966I
a = −0.405031 + 1.029800I
b = −0.63309 + 2.50563I
−1.62127 − 12.47790I 0
30
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.062150 − 0.697966I
a = 0.080039 + 1.061900I
b = 0.26392 + 2.34393I
−1.62127 + 12.47790I 0
u = 1.062150 − 0.697966I
a = −0.405031 − 1.029800I
b = −0.63309 − 2.50563I
−1.62127 + 12.47790I 0
u = −0.685270 + 0.156647I
a = 1.20550 − 1.20300I
b = 2.06900 − 1.20717I
0.46654 − 7.92697I −4.45028 + 5.61309I
u = −0.685270 + 0.156647I
a = 1.66843 − 0.37101I
b = −0.588258 − 0.315776I
0.46654 − 7.92697I −4.45028 + 5.61309I
u = −0.685270 − 0.156647I
a = 1.20550 + 1.20300I
b = 2.06900 + 1.20717I
0.46654 + 7.92697I −4.45028 − 5.61309I
u = −0.685270 − 0.156647I
a = 1.66843 + 0.37101I
b = −0.588258 + 0.315776I
0.46654 + 7.92697I −4.45028 − 5.61309I
u = 1.095740 + 0.711506I
a = −0.423788 + 0.539478I
b = −0.93395 + 1.57669I
3.42736 − 12.69380I 0
u = 1.095740 + 0.711506I
a = 0.500288 − 1.274430I
b = 0.59641 − 2.42128I
3.42736 − 12.69380I 0
u = 1.095740 − 0.711506I
a = −0.423788 − 0.539478I
b = −0.93395 − 1.57669I
3.42736 + 12.69380I 0
u = 1.095740 − 0.711506I
a = 0.500288 + 1.274430I
b = 0.59641 + 2.42128I
3.42736 + 12.69380I 0
31
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.874928 + 0.995808I
a = −1.014950 − 0.756816I
b = −0.309139 − 1.293450I
3.17525 + 3.55255I 0
u = −0.874928 + 0.995808I
a = 0.295632 + 0.513642I
b = 0.219712 + 0.388832I
3.17525 + 3.55255I 0
u = −0.874928 − 0.995808I
a = −1.014950 + 0.756816I
b = −0.309139 + 1.293450I
3.17525 − 3.55255I 0
u = −0.874928 − 0.995808I
a = 0.295632 − 0.513642I
b = 0.219712 − 0.388832I
3.17525 − 3.55255I 0
u = 0.654472
a = −0.253177 + 0.679046I
b = 1.184610 + 0.403660I
−1.93924 −9.56870
u = 0.654472
a = −0.253177 − 0.679046I
b = 1.184610 − 0.403660I
−1.93924 −9.56870
u = 1.18098 + 0.78281I
a = −0.697257 + 1.220410I
b = −0.51205 + 2.06727I
1.59157 − 5.13808I 0
u = 1.18098 + 0.78281I
a = 0.274968 − 0.214464I
b = 0.538270 − 0.765139I
1.59157 − 5.13808I 0
u = 1.18098 − 0.78281I
a = −0.697257 − 1.220410I
b = −0.51205 − 2.06727I
1.59157 + 5.13808I 0
u = 1.18098 − 0.78281I
a = 0.274968 + 0.214464I
b = 0.538270 + 0.765139I
1.59157 + 5.13808I 0
32
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.104877 + 0.560446I
a = −0.87505 − 1.45621I
b = −0.127553 + 0.265826I
1.92498 − 0.68275I 2.93828 + 2.96732I
u = −0.104877 + 0.560446I
a = −1.80637 − 0.09699I
b = −0.827049 + 0.186943I
1.92498 − 0.68275I 2.93828 + 2.96732I
u = −0.104877 − 0.560446I
a = −0.87505 + 1.45621I
b = −0.127553 − 0.265826I
1.92498 + 0.68275I 2.93828 − 2.96732I
u = −0.104877 − 0.560446I
a = −1.80637 + 0.09699I
b = −0.827049 − 0.186943I
1.92498 + 0.68275I 2.93828 − 2.96732I
u = −0.0725988
a = −13.5105 + 7.4460I
b = −0.919304 − 0.585980I
−0.191567 −0.848680
u = −0.0725988
a = −13.5105 − 7.4460I
b = −0.919304 + 0.585980I
−0.191567 −0.848680
33
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
24
− 8u
23
+ ··· − 5u + 1)(u
36
+ 11u
35
+ ··· − 4352u + 1024)
c
2
(u
24
− 2u
23
+ ··· − 3u + 1)(u
36
− 11u
35
+ ··· − 272u + 32)
c
3
, c
10
8(8u
24
+ 24u
22
+ ··· − 6u + 2)(u
36
+ 6u
35
+ ··· + 2u + 2)
c
4
, c
11
8(8u
24
+ 48u
22
+ ··· − 3u + 1)(u
36
+ 6u
35
+ ··· − u + 1)
c
5
, c
12
(u
24
+ 2u
23
+ ··· + 16u + 8)(u
36
+ 2u
35
+ ··· + 8u + 1)
c
6
(u
24
+ 2u
23
+ ··· + 3u + 1)(u
36
− 11u
35
+ ··· − 272u + 32)
c
7
, c
9
(u
24
+ 4u
23
+ ··· − 16u + 8)(u
36
+ 2u
35
+ ··· − u + 1)
c
8
(u
24
+ 7u
23
+ ··· − 16u + 2)(u
36
+ 26u
35
+ ··· + 131072u + 8192)
34
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
24
− 12y
22
+ ··· + 7y + 1)(y
36
+ y
35
+ ··· − 2.27410 × 10
7
y + 1048576)
c
2
, c
6
(y
24
− 8y
23
+ ··· − 5y + 1)(y
36
− 11y
35
+ ··· + 4352y + 1024)
c
3
, c
10
64(64y
24
+ 384y
23
+ ··· + 56y + 4)(y
36
+ 36y
35
+ ··· + 148y + 4)
c
4
, c
11
64(64y
24
+ 768y
23
+ ··· + 35y + 1)(y
36
+ 42y
35
+ ··· + 9y + 1)
c
5
, c
12
(y
24
+ 6y
23
+ ··· + 512y + 64)(y
36
− 4y
35
+ ··· + 4y + 1)
c
7
, c
9
(y
24
− 12y
23
+ ··· + 704y + 64)(y
36
− 2y
35
+ ··· − 5y + 1)
c
8
(y
24
+ 5y
23
+ ··· − 204y + 4)
· (y
36
+ 10y
35
+ ··· − 503316480y + 67108864)
35
