12n
0613
(K12n
0613
)
A knot diagram
1
Linearized knot diagam
3 8 6 10 9 10 2 1 12 6 4 5
Solving Sequence
5,9 6,12
10 7 1 4 3 8 2 11
c
5
c
9
c
6
c
12
c
4
c
3
c
8
c
2
c
11
c
1
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, 5.43932 × 10
30
u
31
+ 8.12908 × 10
30
u
30
+ ··· + 3.35339 × 10
30
a − 9.00124 × 10
30
,
u
32
+ u
31
+ ··· − 5u + 1i
I
u
2
= hb + u, −2006601310117u
21
− 1475756618264u
20
+ ··· + 214817393669a − 6503947392620,
u
22
+ u
21
+ ··· + 6u + 1i
I
u
3
= h2.83028 × 10
140
u
47
+ 8.71962 × 10
140
u
46
+ ··· + 1.13769 × 10
141
b − 1.39265 × 10
141
,
6.79051 × 10
120
u
47
+ 2.06789 × 10
121
u
46
+ ··· + 6.50621 × 10
120
a − 3.02432 × 10
121
, u
48
+ 3u
47
+ ··· − 14u + 1i
* 3 irreducible components of dim
C
= 0, with total 102 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
= hb − u, 5.44 × 10
30
u
31
+ 8.13 × 10
30
u
30
+ · · · + 3.35 × 10
30
a − 9.00 ×
10
30
, u
32
+ u
31
+ · · · − 5u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
u
2
a
12
=
−1.62204u
31
− 2.42414u
30
+ ··· − 16.2084u + 2.68422
u
a
10
=
−5.53414u
31
− 6.62833u
30
+ ··· − 35.0052u + 20.9674
0.249234u
31
+ 0.273240u
30
+ ··· + 3.38846u − 0.802100
a
7
=
−7.19778u
31
− 9.20184u
30
+ ··· − 52.2087u + 21.0419
0.101749u
31
+ 0.189658u
30
+ ··· + 1.30173u + 0.191010
a
1
=
−1.62204u
31
− 2.42414u
30
+ ··· − 17.2084u + 2.68422
u
a
4
=
0.441611u
31
+ 0.993111u
30
+ ··· + 10.9819u + 4.63637
0.0376695u
31
+ 0.0100421u
30
+ ··· + 1.01416u − 0.742510
a
3
=
0.543360u
31
+ 1.18277u
30
+ ··· + 12.2837u + 4.82738
0.0198247u
31
− 0.00142549u
30
+ ··· + 1.35196u − 0.830419
a
8
=
−6.03260u
31
− 7.17481u
30
+ ··· − 39.7822u + 22.5716
0.249234u
31
+ 0.273240u
30
+ ··· + 3.38846u − 0.802100
a
2
=
−8.35596u
31
− 10.3141u
30
+ ··· − 49.1564u + 32.2862
0.207248u
31
+ 0.365116u
30
+ ··· + 2.95393u − 0.843951
a
11
=
−5.04086u
31
− 6.12139u
30
+ ··· − 31.6800u + 19.0711
0.257866u
31
+ 0.306994u
30
+ ··· + 2.96350u − 0.815763
(ii) Obstruction class = −1
(iii) Cusp Shapes = 7.99213u
31
+ 9.89259u
30
+ ··· + 52.3956u − 21.8422
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
32
+ 16u
31
+ ··· − 384u + 256
c
2
, c
7
u
32
− 8u
31
+ ··· − 128u + 16
c
3
u
32
+ 22u
31
+ ··· + 27648u + 4096
c
4
u
32
− 8u
30
+ ··· + 7u − 6
c
5
, c
12
u
32
+ u
31
+ ··· − 5u + 1
c
6
, c
10
, c
11
u
32
− 23u
30
+ ··· − 9u
2
+ 1
c
8
u
32
− 24u
31
+ ··· − 24064u − 2544
c
9
u
32
− 21u
31
+ ··· − 992u + 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
32
+ 4y
31
+ ··· − 614400y + 65536
c
2
, c
7
y
32
− 16y
31
+ ··· + 384y + 256
c
3
y
32
− 30y
31
+ ··· − 131072000y + 16777216
c
4
y
32
− 16y
31
+ ··· − 661y + 36
c
5
, c
12
y
32
+ 3y
31
+ ··· − 11y + 1
c
6
, c
10
, c
11
y
32
− 46y
31
+ ··· − 18y + 1
c
8
y
32
+ 14y
31
+ ··· − 3117275776y + 6471936
c
9
y
32
+ 9y
31
+ ··· + 39936y + 4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.390564 + 0.967977I
a = −1.60621 − 0.49572I
b = −0.390564 + 0.967977I
9.63313 + 1.78314I 5.24416 − 2.15129I
u = −0.390564 − 0.967977I
a = −1.60621 + 0.49572I
b = −0.390564 − 0.967977I
9.63313 − 1.78314I 5.24416 + 2.15129I
u = −0.859015 + 0.595187I
a = −0.70225 − 1.35017I
b = −0.859015 + 0.595187I
3.11013 + 9.06642I −0.91274 − 7.85173I
u = −0.859015 − 0.595187I
a = −0.70225 + 1.35017I
b = −0.859015 − 0.595187I
3.11013 − 9.06642I −0.91274 + 7.85173I
u = −0.519398 + 0.932460I
a = −0.647989 − 0.004890I
b = −0.519398 + 0.932460I
1.88830 + 3.18747I 4.96056 − 5.55794I
u = −0.519398 − 0.932460I
a = −0.647989 + 0.004890I
b = −0.519398 − 0.932460I
1.88830 − 3.18747I 4.96056 + 5.55794I
u = 0.275358 + 0.858528I
a = 0.738399 − 0.042001I
b = 0.275358 + 0.858528I
2.15595 + 1.03231I 4.92013 − 2.65648I
u = 0.275358 − 0.858528I
a = 0.738399 + 0.042001I
b = 0.275358 − 0.858528I
2.15595 − 1.03231I 4.92013 + 2.65648I
u = 0.657277 + 0.519284I
a = 0.91075 − 1.90121I
b = 0.657277 + 0.519284I
5.54728 − 3.21063I 1.80460 + 6.59174I
u = 0.657277 − 0.519284I
a = 0.91075 + 1.90121I
b = 0.657277 − 0.519284I
5.54728 + 3.21063I 1.80460 − 6.59174I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.791811
a = −1.98040
b = −0.791811
−1.01617 −9.04870
u = −0.755035
a = −0.694813
b = −0.755035
−1.77548 −4.53550
u = 0.621825 + 1.097920I
a = 1.294920 − 0.198954I
b = 0.621825 + 1.097920I
9.99995 − 7.71025I 4.49240 + 6.45370I
u = 0.621825 − 1.097920I
a = 1.294920 + 0.198954I
b = 0.621825 − 1.097920I
9.99995 + 7.71025I 4.49240 − 6.45370I
u = 0.313313 + 0.638057I
a = −1.166610 − 0.622327I
b = 0.313313 + 0.638057I
−2.47132 − 5.60513I −2.05099 + 8.20859I
u = 0.313313 − 0.638057I
a = −1.166610 + 0.622327I
b = 0.313313 − 0.638057I
−2.47132 + 5.60513I −2.05099 − 8.20859I
u = −0.956018 + 0.923610I
a = −0.573225 + 0.070285I
b = −0.956018 + 0.923610I
−0.91090 + 3.64926I 4.33113 − 1.37429I
u = −0.956018 − 0.923610I
a = −0.573225 − 0.070285I
b = −0.956018 − 0.923610I
−0.91090 − 3.64926I 4.33113 + 1.37429I
u = 1.086610 + 0.795029I
a = 0.574623 + 0.109929I
b = 1.086610 + 0.795029I
−4.85287 + 0.14998I −1.49645 − 3.04413I
u = 1.086610 − 0.795029I
a = 0.574623 − 0.109929I
b = 1.086610 − 0.795029I
−4.85287 − 0.14998I −1.49645 + 3.04413I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.06617 + 0.94422I
a = −1.051680 + 0.248881I
b = −1.06617 + 0.94422I
1.89136 + 7.99794I −1.89042 − 4.55066I
u = −1.06617 − 0.94422I
a = −1.051680 − 0.248881I
b = −1.06617 − 0.94422I
1.89136 − 7.99794I −1.89042 + 4.55066I
u = −0.075680 + 0.568202I
a = 1.265330 − 0.049232I
b = −0.075680 + 0.568202I
0.51553 + 1.38561I 2.36633 − 4.82018I
u = −0.075680 − 0.568202I
a = 1.265330 + 0.049232I
b = −0.075680 − 0.568202I
0.51553 − 1.38561I 2.36633 + 4.82018I
u = 1.03468 + 1.01787I
a = 0.546848 + 0.069159I
b = 1.03468 + 1.01787I
−3.90029 − 8.39051I 2.20035 + 3.96164I
u = 1.03468 − 1.01787I
a = 0.546848 − 0.069159I
b = 1.03468 − 1.01787I
−3.90029 + 8.39051I 2.20035 − 3.96164I
u = 1.09517 + 1.16567I
a = 0.950401 + 0.099835I
b = 1.09517 + 1.16567I
7.31268 − 11.42420I 0
u = 1.09517 − 1.16567I
a = 0.950401 − 0.099835I
b = 1.09517 − 1.16567I
7.31268 + 11.42420I 0
u = −1.21195 + 1.18977I
a = −0.876418 + 0.125795I
b = −1.21195 + 1.18977I
4.7481 + 16.9486I 0
u = −1.21195 − 1.18977I
a = −0.876418 − 0.125795I
b = −1.21195 − 1.18977I
4.7481 − 16.9486I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.267983 + 0.096022I
a = −3.81929 − 5.94198I
b = 0.267983 + 0.096022I
−2.01749 + 2.84138I −3.8195 + 16.5875I
u = 0.267983 − 0.096022I
a = −3.81929 + 5.94198I
b = 0.267983 − 0.096022I
−2.01749 − 2.84138I −3.8195 − 16.5875I
8
II. I
u
2
= hb + u, −2.01 × 10
12
u
21
− 1.48 × 10
12
u
20
+ · · · + 2.15 × 10
11
a −
6.50 × 10
12
, u
22
+ u
21
+ · · · + 6u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
u
2
a
12
=
9.34096u
21
+ 6.86982u
20
+ ··· + 89.6739u + 30.2766
−u
a
10
=
14.5794u
21
+ 8.87809u
20
+ ··· + 142.535u + 28.7075
0.590428u
21
+ 0.491225u
20
+ ··· + 6.48590u + 2.47114
a
7
=
−30.2766u
21
− 20.9357u
20
+ ··· − 297.306u − 90.9859
−0.439803u
21
− 0.428977u
20
+ ··· − 4.50594u − 2.28936
a
1
=
9.34096u
21
+ 6.86982u
20
+ ··· + 90.6739u + 30.2766
−u
a
4
=
−8.47114u
21
− 6.88072u
20
+ ··· − 81.7691u − 36.3410
0.340599u
21
+ 0.259687u
20
+ ··· + 3.43451u + 0.698927
a
3
=
−8.91095u
21
− 7.30969u
20
+ ··· − 86.2751u − 38.6303
0.499053u
21
+ 0.260079u
20
+ ··· + 3.80936u + 0.688101
a
8
=
13.3986u
21
+ 7.89564u
20
+ ··· + 131.564u + 23.7653
0.590428u
21
+ 0.491225u
20
+ ··· + 6.48590u + 2.47114
a
2
=
20.5604u
21
+ 11.9205u
20
+ ··· + 201.038u + 37.4919
1.44804u
21
+ 0.929665u
20
+ ··· + 12.8961u + 4.26770
a
11
=
13.2901u
21
+ 8.02853u
20
+ ··· + 129.393u + 25.4774
0.579602u
21
+ 0.321944u
20
+ ··· + 5.13644u + 2.03134
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
8090826551153
214817393669
u
21
−
5909957309789
214817393669
u
20
+ ··· −
76582895018229
214817393669
u −
30531044823813
214817393669
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
22
− 13u
21
+ ··· − 8u + 1
c
2
u
22
+ u
21
+ ··· − 4u
2
+ 1
c
3
u
22
+ 15u
21
+ ··· + 132u + 29
c
4
u
22
− 5u
20
+ ··· − 19u + 13
c
5
, c
12
u
22
+ u
21
+ ··· + 6u + 1
c
6
, c
11
u
22
− 2u
21
+ ··· − u + 1
c
7
u
22
− u
21
+ ··· − 4u
2
+ 1
c
8
u
22
− 3u
21
+ ··· − 8u
2
+ 1
c
9
u
22
− 10u
21
+ ··· + 3u
2
+ 1
c
10
u
22
+ 2u
21
+ ··· + u + 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
+ 3y
21
+ ··· − 8y + 1
c
2
, c
7
y
22
− 13y
21
+ ··· − 8y + 1
c
3
y
22
− 23y
21
+ ··· − 7738y + 841
c
4
y
22
− 10y
21
+ ··· + 1017y + 169
c
5
, c
12
y
22
− 7y
21
+ ··· − 20y + 1
c
6
, c
10
, c
11
y
22
− 12y
21
+ ··· + 17y + 1
c
8
y
22
+ 13y
21
+ ··· − 16y + 1
c
9
y
22
+ 8y
21
+ ··· + 6y + 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.858443 + 0.472828I
a = −0.268594 − 0.545737I
b = 0.858443 − 0.472828I
6.63217 − 1.18036I 3.98252 − 0.95830I
u = −0.858443 − 0.472828I
a = −0.268594 + 0.545737I
b = 0.858443 + 0.472828I
6.63217 + 1.18036I 3.98252 + 0.95830I
u = −0.969570 + 0.104792I
a = 0.958370 − 1.015960I
b = 0.969570 − 0.104792I
−4.48502 + 5.07387I −8.63863 − 8.30587I
u = −0.969570 − 0.104792I
a = 0.958370 + 1.015960I
b = 0.969570 + 0.104792I
−4.48502 − 5.07387I −8.63863 + 8.30587I
u = −0.362670 + 0.880683I
a = 0.684664 − 0.540153I
b = 0.362670 − 0.880683I
4.53253 − 2.07273I 8.32895 + 4.83845I
u = −0.362670 − 0.880683I
a = 0.684664 + 0.540153I
b = 0.362670 + 0.880683I
4.53253 + 2.07273I 8.32895 − 4.83845I
u = 0.647068 + 0.985785I
a = −0.320022 − 0.399758I
b = −0.647068 − 0.985785I
3.43411 − 0.50011I 2.53542 + 4.24945I
u = 0.647068 − 0.985785I
a = −0.320022 + 0.399758I
b = −0.647068 + 0.985785I
3.43411 + 0.50011I 2.53542 − 4.24945I
u = 1.153990 + 0.411356I
a = −0.864989 − 0.491617I
b = −1.153990 − 0.411356I
−2.39449 − 2.98768I 1.98501 + 3.10922I
u = 1.153990 − 0.411356I
a = −0.864989 + 0.491617I
b = −1.153990 + 0.411356I
−2.39449 + 2.98768I 1.98501 − 3.10922I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.027480 + 0.719532I
a = 0.048327 − 0.358842I
b = −1.027480 − 0.719532I
4.91059 + 5.90541I 1.71844 − 3.95716I
u = 1.027480 − 0.719532I
a = 0.048327 + 0.358842I
b = −1.027480 + 0.719532I
4.91059 − 5.90541I 1.71844 + 3.95716I
u = 0.470860 + 0.507733I
a = −2.04467 + 0.62131I
b = −0.470860 − 0.507733I
−0.39120 − 2.98356I −1.48889 + 12.19524I
u = 0.470860 − 0.507733I
a = −2.04467 − 0.62131I
b = −0.470860 + 0.507733I
−0.39120 + 2.98356I −1.48889 − 12.19524I
u = 1.015410 + 0.828466I
a = −0.835698 − 0.057216I
b = −1.015410 − 0.828466I
−1.82515 − 4.29426I −2.89416 + 5.12116I
u = 1.015410 − 0.828466I
a = −0.835698 + 0.057216I
b = −1.015410 + 0.828466I
−1.82515 + 4.29426I −2.89416 − 5.12116I
u = −1.23379 + 0.77502I
a = 0.728855 − 0.197315I
b = 1.23379 − 0.77502I
−5.39649 + 0.76944I −5.69205 − 1.85880I
u = −1.23379 − 0.77502I
a = 0.728855 + 0.197315I
b = 1.23379 + 0.77502I
−5.39649 − 0.76944I −5.69205 + 1.85880I
u = −1.08883 + 0.97192I
a = 0.712895 − 0.033605I
b = 1.08883 − 0.97192I
−4.58982 + 8.86717I −6.46501 − 9.30335I
u = −1.08883 − 0.97192I
a = 0.712895 + 0.033605I
b = 1.08883 + 0.97192I
−4.58982 − 8.86717I −6.46501 + 9.30335I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.301500 + 0.088234I
a = 1.20086 + 7.48943I
b = 0.301500 − 0.088234I
−2.07217 + 2.98695I −23.8716 − 31.2516I
u = −0.301500 − 0.088234I
a = 1.20086 − 7.48943I
b = 0.301500 + 0.088234I
−2.07217 − 2.98695I −23.8716 + 31.2516I
14
III. I
u
3
= h2.83 × 10
140
u
47
+ 8.72 × 10
140
u
46
+ · · · + 1.14 × 10
141
b − 1.39 ×
10
141
, 6.79 × 10
120
u
47
+ 2.07 × 10
121
u
46
+ · · · + 6.51 × 10
120
a − 3.02 ×
10
121
, u
48
+ 3u
47
+ · · · − 14u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
u
2
a
12
=
−1.04370u
47
− 3.17834u
46
+ ··· − 112.473u + 4.64836
−0.248774u
47
− 0.766430u
46
+ ··· − 25.7903u + 1.22410
a
10
=
0.352601u
47
+ 1.15475u
46
+ ··· + 9.77743u + 5.15330
0.0884410u
47
+ 0.277756u
46
+ ··· + 5.39711u + 0.961781
a
7
=
−0.459789u
47
− 1.51384u
46
+ ··· − 18.0243u − 5.98347
−0.181840u
47
− 0.582355u
46
+ ··· − 10.3425u − 1.14025
a
1
=
−0.794923u
47
− 2.41191u
46
+ ··· − 86.6830u + 3.42426
−0.248774u
47
− 0.766430u
46
+ ··· − 25.7903u + 1.22410
a
4
=
0.641629u
47
+ 2.09620u
46
+ ··· + 28.3668u + 7.12371
0.188784u
47
+ 0.597549u
46
+ ··· + 12.0992u + 0.968939
a
3
=
0.459789u
47
+ 1.51384u
46
+ ··· + 18.0243u + 5.98347
0.184999u
47
+ 0.586827u
46
+ ··· + 11.7654u + 1.00577
a
8
=
0.182173u
47
+ 0.616405u
46
+ ··· + 2.12767u + 3.43309
0.0819875u
47
+ 0.260591u
46
+ ··· + 4.25265u + 0.758426
a
2
=
0.182173u
47
+ 0.616405u
46
+ ··· + 2.12767u + 3.43309
0.0524818u
47
+ 0.165721u
46
+ ··· + 2.21890u + 0.634265
a
11
=
0.442236u
47
+ 1.43983u
46
+ ··· + 14.1699u + 6.21203
0.0885446u
47
+ 0.276604u
46
+ ··· + 5.53392u + 0.945606
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.726576u
47
− 2.21182u
46
+ ··· − 75.1418u + 5.51596
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
8
c
2
, c
7
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
8
c
3
(u
4
− 3u
3
+ u
2
+ 2u + 1)
12
c
4
u
48
+ u
47
+ ··· + 30108u + 22357
c
5
, c
12
u
48
+ 3u
47
+ ··· − 14u + 1
c
6
, c
10
, c
11
u
48
+ u
47
+ ··· + 76002u + 31907
c
9
(u
4
+ u
3
+ u
2
+ 1)
12
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
8
c
2
, c
7
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
8
c
3
(y
4
− 7y
3
+ 15y
2
− 2y + 1)
12
c
4
y
48
− 21y
47
+ ··· − 2279703318y + 499835449
c
5
, c
12
y
48
− 9y
47
+ ··· + 44y + 1
c
6
, c
10
, c
11
y
48
− 45y
47
+ ··· − 3001288400y + 1018056649
c
9
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
12
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.629593 + 0.781806I
a = −1.239320 + 0.091509I
b = −1.12594 − 0.99017I
0.03467 − 4.08827I 3.88998 + 3.35903I
u = 0.629593 − 0.781806I
a = −1.239320 − 0.091509I
b = −1.12594 + 0.99017I
0.03467 + 4.08827I 3.88998 − 3.35903I
u = 0.330707 + 0.926113I
a = 0.810156 − 0.090576I
b = 1.69106 − 0.76622I
7.03641 − 0.49080I 7.54346 + 4.11452I
u = 0.330707 − 0.926113I
a = 0.810156 + 0.090576I
b = 1.69106 + 0.76622I
7.03641 + 0.49080I 7.54346 − 4.11452I
u = −1.069080 + 0.043286I
a = 0.761004 + 0.883218I
b = 1.023650 + 0.361469I
−3.74655 − 4.08827I −3.54346 + 3.35903I
u = −1.069080 − 0.043286I
a = 0.761004 − 0.883218I
b = 1.023650 − 0.361469I
−3.74655 + 4.08827I −3.54346 − 3.35903I
u = 1.023650 + 0.361469I
a = −1.019380 − 0.530277I
b = −1.069080 + 0.043286I
−3.74655 − 4.08827I −3.54346 + 3.35903I
u = 1.023650 − 0.361469I
a = −1.019380 + 0.530277I
b = −1.069080 − 0.043286I
−3.74655 + 4.08827I −3.54346 − 3.35903I
u = −1.091250 + 0.090133I
a = −0.266053 − 0.682083I
b = 0.011750 − 1.180710I
3.25520 − 2.33941I 0.11002 + 5.70297I
u = −1.091250 − 0.090133I
a = −0.266053 + 0.682083I
b = 0.011750 + 1.180710I
3.25520 + 2.33941I 0.11002 − 5.70297I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.542828 + 0.716452I
a = 1.380360 + 0.143081I
b = 0.238962 − 0.272108I
0.03467 + 2.23966I 3.88998 − 1.77057I
u = −0.542828 − 0.716452I
a = 1.380360 − 0.143081I
b = 0.238962 + 0.272108I
0.03467 − 2.23966I 3.88998 + 1.77057I
u = −0.358866 + 1.095930I
a = −0.688574 − 0.095537I
b = −1.90461 − 0.46488I
5.14581 − 4.27792I 3.82674 + 0.60183I
u = −0.358866 − 1.095930I
a = −0.688574 + 0.095537I
b = −1.90461 + 0.46488I
5.14581 + 4.27792I 3.82674 − 0.60183I
u = 0.011750 + 1.180710I
a = −0.607068 − 0.304005I
b = −1.091250 − 0.090133I
3.25520 + 2.33941I 0. − 5.70297I
u = 0.011750 − 1.180710I
a = −0.607068 + 0.304005I
b = −1.091250 + 0.090133I
3.25520 − 2.33941I 0. + 5.70297I
u = −0.755849 + 0.949728I
a = 1.024450 + 0.081577I
b = 1.36656 − 1.07638I
−1.85594 + 8.85698I 0. − 8.07537I
u = −0.755849 − 0.949728I
a = 1.024450 − 0.081577I
b = 1.36656 + 1.07638I
−1.85594 − 8.85698I 0. + 8.07537I
u = −1.030050 + 0.657859I
a = 0.988705 − 0.253254I
b = 1.41741 − 0.53201I
−3.74655 + 2.23966I −3.54346 + 0.I
u = −1.030050 − 0.657859I
a = 0.988705 + 0.253254I
b = 1.41741 + 0.53201I
−3.74655 − 2.23966I −3.54346 + 0.I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.167396 + 0.661515I
a = −0.98845 + 1.53779I
b = 0.414199 − 0.088722I
−1.85594 + 2.52906I 0.17326 − 2.94577I
u = −0.167396 − 0.661515I
a = −0.98845 − 1.53779I
b = 0.414199 + 0.088722I
−1.85594 − 2.52906I 0.17326 + 2.94577I
u = 0.388273 + 0.497540I
a = 1.242770 + 0.262742I
b = 1.39675 − 1.46025I
7.03641 − 2.33941I 7.54346 + 5.70297I
u = 0.388273 − 0.497540I
a = 1.242770 − 0.262742I
b = 1.39675 + 1.46025I
7.03641 + 2.33941I 7.54346 − 5.70297I
u = −0.490886 + 0.302457I
a = −1.174830 + 0.743568I
b = −1.32499 − 1.79381I
5.14581 + 7.10813I 3.82674 − 10.41931I
u = −0.490886 − 0.302457I
a = −1.174830 − 0.743568I
b = −1.32499 + 1.79381I
5.14581 − 7.10813I 3.82674 + 10.41931I
u = −1.12594 + 0.99017I
a = 0.827967 − 0.081233I
b = 0.629593 − 0.781806I
0.03467 + 4.08827I 0
u = −1.12594 − 0.99017I
a = 0.827967 + 0.081233I
b = 0.629593 + 0.781806I
0.03467 − 4.08827I 0
u = 1.41741 + 0.53201I
a = −0.738267 − 0.365826I
b = −1.030050 − 0.657859I
−3.74655 − 2.23966I 0
u = 1.41741 − 0.53201I
a = −0.738267 + 0.365826I
b = −1.030050 + 0.657859I
−3.74655 + 2.23966I 0
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.414199 + 0.088722I
a = −1.51570 + 2.52480I
b = −0.167396 − 0.661515I
−1.85594 − 2.52906I 0.17326 + 2.94577I
u = 0.414199 − 0.088722I
a = −1.51570 − 2.52480I
b = −0.167396 + 0.661515I
−1.85594 + 2.52906I 0.17326 − 2.94577I
u = 0.238962 + 0.272108I
a = −3.44289 + 0.10691I
b = −0.542828 − 0.716452I
0.03467 − 2.23966I 3.88998 + 1.77057I
u = 0.238962 − 0.272108I
a = −3.44289 − 0.10691I
b = −0.542828 + 0.716452I
0.03467 + 2.23966I 3.88998 − 1.77057I
u = −0.61144 + 1.52100I
a = 0.327664 − 0.363021I
b = 0.0642708 − 0.0873744I
3.25520 − 0.49080I 0
u = −0.61144 − 1.52100I
a = 0.327664 + 0.363021I
b = 0.0642708 + 0.0873744I
3.25520 + 0.49080I 0
u = 1.36656 + 1.07638I
a = −0.708821 − 0.108545I
b = −0.755849 − 0.949728I
−1.85594 − 8.85698I 0
u = 1.36656 − 1.07638I
a = −0.708821 + 0.108545I
b = −0.755849 + 0.949728I
−1.85594 + 8.85698I 0
u = 1.69106 + 0.76622I
a = 0.012472 − 0.431621I
b = 0.330707 − 0.926113I
7.03641 + 0.49080I 0
u = 1.69106 − 0.76622I
a = 0.012472 + 0.431621I
b = 0.330707 + 0.926113I
7.03641 − 0.49080I 0
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.0642708 + 0.0873744I
a = −3.42782 − 6.54788I
b = −0.61144 − 1.52100I
3.25520 + 0.49080I 0.11002 − 4.11452I
u = 0.0642708 − 0.0873744I
a = −3.42782 + 6.54788I
b = −0.61144 + 1.52100I
3.25520 − 0.49080I 0.11002 + 4.11452I
u = −1.90461 + 0.46488I
a = −0.087205 − 0.399494I
b = −0.358866 − 1.095930I
5.14581 + 4.27792I 0
u = −1.90461 − 0.46488I
a = −0.087205 + 0.399494I
b = −0.358866 + 1.095930I
5.14581 − 4.27792I 0
u = 1.39675 + 1.46025I
a = −0.137267 − 0.372220I
b = 0.388273 − 0.497540I
7.03641 + 2.33941I 0
u = 1.39675 − 1.46025I
a = −0.137267 + 0.372220I
b = 0.388273 + 0.497540I
7.03641 − 2.33941I 0
u = −1.32499 + 1.79381I
a = 0.166087 − 0.318804I
b = −0.490886 − 0.302457I
5.14581 − 7.10813I 0
u = −1.32499 − 1.79381I
a = 0.166087 + 0.318804I
b = −0.490886 + 0.302457I
5.14581 + 7.10813I 0
22
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
8
)(u
22
− 13u
21
+ ··· − 8u + 1)
· (u
32
+ 16u
31
+ ··· − 384u + 256)
c
2
((u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
8
)(u
22
+ u
21
+ ··· − 4u
2
+ 1)
· (u
32
− 8u
31
+ ··· − 128u + 16)
c
3
((u
4
− 3u
3
+ u
2
+ 2u + 1)
12
)(u
22
+ 15u
21
+ ··· + 132u + 29)
· (u
32
+ 22u
31
+ ··· + 27648u + 4096)
c
4
(u
22
− 5u
20
+ ··· − 19u + 13)(u
32
− 8u
30
+ ··· + 7u − 6)
· (u
48
+ u
47
+ ··· + 30108u + 22357)
c
5
, c
12
(u
22
+ u
21
+ ··· + 6u + 1)(u
32
+ u
31
+ ··· − 5u + 1)
· (u
48
+ 3u
47
+ ··· − 14u + 1)
c
6
, c
11
(u
22
− 2u
21
+ ··· − u + 1)(u
32
− 23u
30
+ ··· − 9u
2
+ 1)
· (u
48
+ u
47
+ ··· + 76002u + 31907)
c
7
((u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
8
)(u
22
− u
21
+ ··· − 4u
2
+ 1)
· (u
32
− 8u
31
+ ··· − 128u + 16)
c
8
((u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
8
)(u
22
− 3u
21
+ ··· − 8u
2
+ 1)
· (u
32
− 24u
31
+ ··· − 24064u − 2544)
c
9
((u
4
+ u
3
+ u
2
+ 1)
12
)(u
22
− 10u
21
+ ··· + 3u
2
+ 1)
· (u
32
− 21u
31
+ ··· − 992u + 64)
c
10
(u
22
+ 2u
21
+ ··· + u + 1)(u
32
− 23u
30
+ ··· − 9u
2
+ 1)
· (u
48
+ u
47
+ ··· + 76002u + 31907)
23
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
8
)(y
22
+ 3y
21
+ ··· − 8y + 1)
· (y
32
+ 4y
31
+ ··· − 614400y + 65536)
c
2
, c
7
((y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
8
)(y
22
− 13y
21
+ ··· − 8y + 1)
· (y
32
− 16y
31
+ ··· + 384y + 256)
c
3
((y
4
− 7y
3
+ 15y
2
− 2y + 1)
12
)(y
22
− 23y
21
+ ··· − 7738y + 841)
· (y
32
− 30y
31
+ ··· − 131072000y + 16777216)
c
4
(y
22
− 10y
21
+ ··· + 1017y + 169)(y
32
− 16y
31
+ ··· − 661y + 36)
· (y
48
− 21y
47
+ ··· − 2279703318y + 499835449)
c
5
, c
12
(y
22
− 7y
21
+ ··· − 20y + 1)(y
32
+ 3y
31
+ ··· − 11y + 1)
· (y
48
− 9y
47
+ ··· + 44y + 1)
c
6
, c
10
, c
11
(y
22
− 12y
21
+ ··· + 17y + 1)(y
32
− 46y
31
+ ··· − 18y + 1)
· (y
48
− 45y
47
+ ··· − 3001288400y + 1018056649)
c
8
((y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
8
)(y
22
+ 13y
21
+ ··· − 16y + 1)
· (y
32
+ 14y
31
+ ··· − 3117275776y + 6471936)
c
9
((y
4
+ y
3
+ 3y
2
+ 2y + 1)
12
)(y
22
+ 8y
21
+ ··· + 6y + 1)
· (y
32
+ 9y
31
+ ··· + 39936y + 4096)
24
