12a
0186
(K12a
0186
)
A knot diagram
1
Linearized knot diagam
3 5 9 7 2 10 12 1 11 6 4 8
Solving Sequence
1,8 4,9
3 2 12 7 5 11 10 6
c
8
c
3
c
1
c
12
c
7
c
4
c
11
c
9
c
6
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.83274 × 10
205
u
101
+ 3.91863 × 10
206
u
100
+ ··· + 3.50853 × 10
206
b + 1.57493 × 10
206
,
1.45541 × 10
206
u
101
− 5.81604 × 10
206
u
100
+ ··· + 3.50853 × 10
206
a − 4.94259 × 10
206
,
u
102
− 3u
101
+ ··· + 8u
2
− 1i
I
u
2
= hb + a, −21u
2
a + 49a
2
+ 35au + 10u
2
− 7a − 19u + 22, u
3
− u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 108 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−7.83 × 10
205
u
101
+ 3.92 × 10
206
u
100
+ · · · + 3.51 × 10
206
b + 1.57 ×
10
206
, 1.46 × 10
206
u
101
− 5.82 × 10
206
u
100
+ · · · + 3.51 × 10
206
a − 4.94 ×
10
206
, u
102
− 3u
101
+ · · · + 8u
2
− 1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
−0.414820u
101
+ 1.65768u
100
+ ··· − 2.81202u + 1.40873
0.223249u
101
− 1.11689u
100
+ ··· + 4.14860u − 0.448887
a
9
=
1
−u
2
a
3
=
−0.476650u
101
+ 1.78872u
100
+ ··· − 6.54580u + 1.44440
−0.106382u
101
+ 0.250932u
100
+ ··· + 4.21043u − 0.394429
a
2
=
0.643889u
101
− 1.30576u
100
+ ··· + 0.763924u + 0.781537
−1.78169u
101
+ 3.56162u
100
+ ··· + 1.44173u − 1.38730
a
12
=
−u
u
a
7
=
−u
2
+ 1
u
2
a
5
=
−0.498144u
101
+ 1.88558u
100
+ ··· − 6.66075u + 1.65027
−0.184868u
101
+ 0.302979u
100
+ ··· + 3.65716u − 0.275453
a
11
=
0.649518u
101
− 1.16680u
100
+ ··· + 1.05959u − 0.0364924
−0.379081u
101
+ 0.596176u
100
+ ··· − 0.990884u − 0.301947
a
10
=
−1.00635u
101
+ 1.44490u
100
+ ··· − 0.159676u + 0.574120
1.43698u
101
− 2.29172u
100
+ ··· + 0.720833u + 0.738916
a
6
=
−0.270437u
101
+ 0.570627u
100
+ ··· − 0.0687015u + 0.338440
−0.379081u
101
+ 0.596176u
100
+ ··· − 0.990884u − 0.301947
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.59541u
101
+ 0.803708u
100
+ ··· + 5.97952u + 6.60121
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
102
+ 36u
101
+ ··· − 20973u + 2401
c
2
, c
5
u
102
+ 4u
101
+ ··· − 197u + 49
c
3
49(49u
102
− 70u
101
+ ··· − 5.45423 × 10
8
u − 2.55402 × 10
8
)
c
4
49(49u
102
− 126u
101
+ ··· + 2407086u + 356047)
c
6
, c
10
u
102
− 3u
101
+ ··· + 6u − 1
c
7
, c
8
, c
12
u
102
− 3u
101
+ ··· + 8u
2
− 1
c
9
u
102
+ 43u
101
+ ··· − 16u + 1
c
11
u
102
− 5u
101
+ ··· + 174048u − 21952
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
102
+ 64y
101
+ ··· − 2635965389y + 5764801
c
2
, c
5
y
102
+ 36y
101
+ ··· − 20973y + 2401
c
3
2401(2401y
102
− 211092y
101
+ ··· − 1.97644 × 10
18
y + 6.52300 × 10
16
)
c
4
2401
· (2401y
102
+ 47530y
101
+ ··· − 8262494848850y + 126769466209)
c
6
, c
10
y
102
+ 43y
101
+ ··· − 16y + 1
c
7
, c
8
, c
12
y
102
− 101y
101
+ ··· − 16y + 1
c
9
y
102
+ 35y
101
+ ··· + 372y + 1
c
11
y
102
− 35y
101
+ ··· − 8007738368y + 481890304
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.463265 + 0.883839I
a = 0.035861 + 0.629190I
b = −0.374833 + 0.308984I
4.20876 + 2.87950I 0
u = 0.463265 − 0.883839I
a = 0.035861 − 0.629190I
b = −0.374833 − 0.308984I
4.20876 − 2.87950I 0
u = −0.577868 + 0.813521I
a = 0.472549 + 0.598092I
b = 0.909310 − 0.193187I
1.8572 − 14.1354I 0
u = −0.577868 − 0.813521I
a = 0.472549 − 0.598092I
b = 0.909310 + 0.193187I
1.8572 + 14.1354I 0
u = 0.954849 + 0.281344I
a = −0.041980 − 0.257493I
b = 0.307337 − 0.426122I
0.469698 + 0.856662I 0
u = 0.954849 − 0.281344I
a = −0.041980 + 0.257493I
b = 0.307337 + 0.426122I
0.469698 − 0.856662I 0
u = 0.570625 + 0.835524I
a = −0.368172 + 0.608065I
b = −0.798500 − 0.073995I
3.77268 + 8.13531I 0
u = 0.570625 − 0.835524I
a = −0.368172 − 0.608065I
b = −0.798500 + 0.073995I
3.77268 − 8.13531I 0
u = 0.645597 + 0.723769I
a = 0.473710 − 0.425187I
b = 0.771863 − 0.005327I
4.91261 + 2.43397I 0
u = 0.645597 − 0.723769I
a = 0.473710 + 0.425187I
b = 0.771863 + 0.005327I
4.91261 − 2.43397I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.573506 + 0.862250I
a = 0.260008 − 0.666688I
b = −0.325821 − 0.399726I
1.77977 + 8.59624I 0
u = −0.573506 − 0.862250I
a = 0.260008 + 0.666688I
b = −0.325821 + 0.399726I
1.77977 − 8.59624I 0
u = 0.625060 + 0.855119I
a = −0.072253 − 0.595095I
b = 0.424918 − 0.290495I
3.86224 − 2.49227I 0
u = 0.625060 − 0.855119I
a = −0.072253 + 0.595095I
b = 0.424918 + 0.290495I
3.86224 + 2.49227I 0
u = −0.620905 + 0.706635I
a = −0.630977 − 0.363939I
b = −0.865313 + 0.085922I
3.41050 − 8.30399I 0
u = −0.620905 − 0.706635I
a = −0.630977 + 0.363939I
b = −0.865313 − 0.085922I
3.41050 + 8.30399I 0
u = −0.413392 + 0.842069I
a = −0.198359 + 0.651935I
b = 0.204367 + 0.456259I
2.71161 + 3.24755I 0
u = −0.413392 − 0.842069I
a = −0.198359 − 0.651935I
b = 0.204367 − 0.456259I
2.71161 − 3.24755I 0
u = −0.636919 + 0.931863I
a = 0.212442 + 0.374659I
b = 0.398835 − 0.155929I
−3.21005 − 5.48312I 0
u = −0.636919 − 0.931863I
a = 0.212442 − 0.374659I
b = 0.398835 + 0.155929I
−3.21005 + 5.48312I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.007680 + 0.591458I
a = 0.183227 − 0.022455I
b = −0.112994 − 0.513226I
−3.52837 − 4.73810I 0
u = −1.007680 − 0.591458I
a = 0.183227 + 0.022455I
b = −0.112994 + 0.513226I
−3.52837 + 4.73810I 0
u = −0.683434 + 0.363431I
a = 0.298305 − 0.422340I
b = −0.606073 − 0.754369I
−2.25139 + 3.24449I 0
u = −0.683434 − 0.363431I
a = 0.298305 + 0.422340I
b = −0.606073 + 0.754369I
−2.25139 − 3.24449I 0
u = −0.850848 + 0.891750I
a = −0.009513 − 0.251567I
b = −0.350113 + 0.018910I
−2.71812 − 0.96266I 0
u = −0.850848 − 0.891750I
a = −0.009513 + 0.251567I
b = −0.350113 − 0.018910I
−2.71812 + 0.96266I 0
u = −0.248176 + 0.709636I
a = 0.975285 + 0.448105I
b = 0.373511 − 0.188307I
−5.59230 + 0.19794I 0
u = −0.248176 − 0.709636I
a = 0.975285 − 0.448105I
b = 0.373511 + 0.188307I
−5.59230 − 0.19794I 0
u = −0.531434 + 0.485622I
a = −0.403276 + 0.205773I
b = −0.499838 + 0.308340I
−2.05892 − 1.75560I 2.99481 + 4.92518I
u = −0.531434 − 0.485622I
a = −0.403276 − 0.205773I
b = −0.499838 − 0.308340I
−2.05892 + 1.75560I 2.99481 − 4.92518I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.302550 + 0.030953I
a = −0.09799 + 1.82910I
b = 0.52176 − 1.51246I
4.38155 − 0.95243I 0
u = 1.302550 − 0.030953I
a = −0.09799 − 1.82910I
b = 0.52176 + 1.51246I
4.38155 + 0.95243I 0
u = −0.331178 + 0.573078I
a = 1.49364 + 1.09467I
b = 0.537434 − 0.209557I
−3.34096 − 6.68172I 1.38828 + 9.11332I
u = −0.331178 − 0.573078I
a = 1.49364 − 1.09467I
b = 0.537434 + 0.209557I
−3.34096 + 6.68172I 1.38828 − 9.11332I
u = −1.356920 + 0.044854I
a = 1.93962 + 2.56034I
b = −2.34234 − 2.36543I
4.60358 − 3.83826I 0
u = −1.356920 − 0.044854I
a = 1.93962 − 2.56034I
b = −2.34234 + 2.36543I
4.60358 + 3.83826I 0
u = 1.392320 + 0.193973I
a = −1.361140 − 0.145231I
b = 2.13438 + 0.72591I
−0.40709 + 2.94965I 0
u = 1.392320 − 0.193973I
a = −1.361140 + 0.145231I
b = 2.13438 − 0.72591I
−0.40709 − 2.94965I 0
u = 0.238337 + 0.527550I
a = −0.88698 + 1.20969I
b = −0.554896 − 0.179442I
−1.56944 + 2.20050I 3.50144 − 4.94016I
u = 0.238337 − 0.527550I
a = −0.88698 − 1.20969I
b = −0.554896 + 0.179442I
−1.56944 − 2.20050I 3.50144 + 4.94016I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.43398 + 0.08205I
a = 2.14168 − 0.02876I
b = −2.86553 − 0.26922I
4.10044 − 3.96620I 0
u = −1.43398 − 0.08205I
a = 2.14168 + 0.02876I
b = −2.86553 + 0.26922I
4.10044 + 3.96620I 0
u = −1.43341 + 0.13902I
a = 2.02100 + 0.05752I
b = −3.17918 + 0.14402I
3.87436 − 4.46338I 0
u = −1.43341 − 0.13902I
a = 2.02100 − 0.05752I
b = −3.17918 − 0.14402I
3.87436 + 4.46338I 0
u = 0.555079 + 0.064471I
a = 2.01633 + 1.39157I
b = 0.267624 − 0.229465I
3.09413 − 0.79742I 15.9448 + 0.0041I
u = 0.555079 − 0.064471I
a = 2.01633 − 1.39157I
b = 0.267624 + 0.229465I
3.09413 + 0.79742I 15.9448 − 0.0041I
u = −0.542802 + 0.100561I
a = −1.78669 + 2.04178I
b = −0.291885 − 0.324437I
2.93517 − 4.09723I 15.0428 + 7.4403I
u = −0.542802 − 0.100561I
a = −1.78669 − 2.04178I
b = −0.291885 + 0.324437I
2.93517 + 4.09723I 15.0428 − 7.4403I
u = −1.45457 + 0.00026I
a = −3.91802 + 2.34344I
b = 4.10714 − 2.07963I
5.01824 − 0.26285I 0
u = −1.45457 − 0.00026I
a = −3.91802 − 2.34344I
b = 4.10714 + 2.07963I
5.01824 + 0.26285I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.44682 + 0.16164I
a = −2.08341 − 0.23008I
b = 3.41637 + 0.72748I
2.41336 + 9.25279I 0
u = 1.44682 − 0.16164I
a = −2.08341 + 0.23008I
b = 3.41637 − 0.72748I
2.41336 − 9.25279I 0
u = 0.438840 + 0.304153I
a = −0.37871 + 3.16877I
b = 0.000805 − 0.274983I
0.99489 + 6.60455I 9.1908 − 11.8145I
u = 0.438840 − 0.304153I
a = −0.37871 − 3.16877I
b = 0.000805 + 0.274983I
0.99489 − 6.60455I 9.1908 + 11.8145I
u = 1.47118 + 0.03655I
a = 0.225848 − 0.757857I
b = −0.254049 + 0.004641I
6.45968 + 2.80804I 0
u = 1.47118 − 0.03655I
a = 0.225848 + 0.757857I
b = −0.254049 − 0.004641I
6.45968 − 2.80804I 0
u = −0.445734 + 0.249585I
a = −0.09740 + 3.08006I
b = −0.118542 − 0.379389I
1.62557 − 1.89948I 11.64063 + 5.47837I
u = −0.445734 − 0.249585I
a = −0.09740 − 3.08006I
b = −0.118542 + 0.379389I
1.62557 + 1.89948I 11.64063 − 5.47837I
u = 1.49066 + 0.00722I
a = 1.95997 + 0.26537I
b = −2.32422 − 0.51113I
4.98713 + 2.80685I 0
u = 1.49066 − 0.00722I
a = 1.95997 − 0.26537I
b = −2.32422 + 0.51113I
4.98713 − 2.80685I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48883 + 0.07877I
a = 1.23379 + 0.94819I
b = −2.17835 − 2.35342I
7.34892 − 7.92883I 0
u = −1.48883 − 0.07877I
a = 1.23379 − 0.94819I
b = −2.17835 + 2.35342I
7.34892 + 7.92883I 0
u = 1.49016 + 0.06629I
a = −0.695866 + 0.847577I
b = 1.22694 − 2.31857I
8.00924 + 3.00206I 0
u = 1.49016 − 0.06629I
a = −0.695866 − 0.847577I
b = 1.22694 + 2.31857I
8.00924 − 3.00206I 0
u = −1.49232
a = −1.81358
b = 2.56753
7.18734 0
u = 1.50974 + 0.02638I
a = 1.57497 + 0.79438I
b = −2.75438 − 2.05820I
9.69521 + 4.54334I 0
u = 1.50974 − 0.02638I
a = 1.57497 − 0.79438I
b = −2.75438 + 2.05820I
9.69521 − 4.54334I 0
u = −1.51090 + 0.01774I
a = −1.88274 + 0.55860I
b = 3.30537 − 1.45935I
9.88746 + 0.50387I 0
u = −1.51090 − 0.01774I
a = −1.88274 − 0.55860I
b = 3.30537 + 1.45935I
9.88746 − 0.50387I 0
u = 0.283962 + 0.396183I
a = −0.64955 + 1.95378I
b = −0.490466 − 0.348361I
−1.42104 + 2.40116I 2.87491 − 6.25860I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.283962 − 0.396183I
a = −0.64955 − 1.95378I
b = −0.490466 + 0.348361I
−1.42104 − 2.40116I 2.87491 + 6.25860I
u = 0.457504
a = 0.629904
b = 0.399832
0.720872 13.9880
u = −0.016041 + 0.449349I
a = −0.033429 + 0.542654I
b = −0.287665 + 0.922896I
0.87311 + 2.39546I 3.08710 − 3.61565I
u = −0.016041 − 0.449349I
a = −0.033429 − 0.542654I
b = −0.287665 − 0.922896I
0.87311 − 2.39546I 3.08710 + 3.61565I
u = 0.392748 + 0.215550I
a = −0.469063 − 0.870049I
b = 1.52815 − 0.13896I
−0.880180 − 0.202294I 9.92790 − 3.57486I
u = 0.392748 − 0.215550I
a = −0.469063 + 0.870049I
b = 1.52815 + 0.13896I
−0.880180 + 0.202294I 9.92790 + 3.57486I
u = 1.56060 + 0.23251I
a = 1.87185 + 0.03629I
b = −2.88208 − 0.61189I
10.5879 + 11.7701I 0
u = 1.56060 − 0.23251I
a = 1.87185 − 0.03629I
b = −2.88208 + 0.61189I
10.5879 − 11.7701I 0
u = 1.54397 + 0.34268I
a = −0.788558 + 0.471126I
b = 1.46417 − 0.57180I
9.02348 + 1.22948I 0
u = 1.54397 − 0.34268I
a = −0.788558 − 0.471126I
b = 1.46417 + 0.57180I
9.02348 − 1.22948I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.55874 + 0.27948I
a = −1.91507 + 0.03940I
b = 2.88329 + 0.47808I
8.8410 + 18.1545I 0
u = 1.55874 − 0.27948I
a = −1.91507 − 0.03940I
b = 2.88329 − 0.47808I
8.8410 − 18.1545I 0
u = −1.56710 + 0.23333I
a = −1.75578 − 0.08898I
b = 2.74749 − 0.34774I
12.19110 − 5.95346I 0
u = −1.56710 − 0.23333I
a = −1.75578 + 0.08898I
b = 2.74749 + 0.34774I
12.19110 + 5.95346I 0
u = −1.55962 + 0.28624I
a = 1.75143 + 0.15406I
b = −2.70324 + 0.25575I
10.7337 − 12.2501I 0
u = −1.55962 − 0.28624I
a = 1.75143 − 0.15406I
b = −2.70324 − 0.25575I
10.7337 + 12.2501I 0
u = −1.55677 + 0.31983I
a = 1.101370 + 0.405380I
b = −1.88769 − 0.35195I
10.82960 − 7.34873I 0
u = −1.55677 − 0.31983I
a = 1.101370 − 0.405380I
b = −1.88769 + 0.35195I
10.82960 + 7.34873I 0
u = 1.58135 + 0.20767I
a = 1.368960 + 0.109802I
b = −2.01584 − 0.48289I
5.42779 + 4.37394I 0
u = 1.58135 − 0.20767I
a = 1.368960 − 0.109802I
b = −2.01584 + 0.48289I
5.42779 − 4.37394I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.58119 + 0.29246I
a = −1.357780 − 0.100362I
b = 2.06030 + 0.46043I
4.04057 + 9.87187I 0
u = 1.58119 − 0.29246I
a = −1.357780 + 0.100362I
b = 2.06030 − 0.46043I
4.04057 − 9.87187I 0
u = −1.59811 + 0.24702I
a = −1.224820 − 0.342555I
b = 1.99240 + 0.30445I
11.32910 − 1.56007I 0
u = −1.59811 − 0.24702I
a = −1.224820 + 0.342555I
b = 1.99240 − 0.30445I
11.32910 + 1.56007I 0
u = 1.61200 + 0.27101I
a = 0.953114 − 0.445941I
b = −1.59265 + 0.57540I
9.05980 − 4.29630I 0
u = 1.61200 − 0.27101I
a = 0.953114 + 0.445941I
b = −1.59265 − 0.57540I
9.05980 + 4.29630I 0
u = 0.164335 + 0.323160I
a = −0.721035 − 0.095193I
b = 2.40661 + 0.06716I
0.29109 − 4.52781I −3.87388 − 8.97650I
u = 0.164335 − 0.323160I
a = −0.721035 + 0.095193I
b = 2.40661 − 0.06716I
0.29109 + 4.52781I −3.87388 + 8.97650I
u = −0.082582 + 0.350538I
a = 0.593106 + 0.388987I
b = −2.14141 + 0.19216I
0.587367 + 0.070231I −8.68234 + 3.83864I
u = −0.082582 − 0.350538I
a = 0.593106 − 0.388987I
b = −2.14141 − 0.19216I
0.587367 − 0.070231I −8.68234 − 3.83864I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.333864 + 0.112052I
a = −0.02338 + 2.26835I
b = −0.390438 − 0.889436I
0.44723 − 2.25038I 0.19611 + 5.31591I
u = −0.333864 − 0.112052I
a = −0.02338 − 2.26835I
b = −0.390438 + 0.889436I
0.44723 + 2.25038I 0.19611 − 5.31591I
15
II. I
u
2
= hb + a, −21u
2
a + 10u
2
+ · · · − 7a + 22, u
3
− u
2
+ 1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
a
−a
a
9
=
1
−u
2
a
3
=
−u
2
a + 2a
−au − 2a
a
2
=
−u
2
a − u
2
+ 2a + u
−au +
4
7
u
2
− 2a −
2
7
u −
1
7
a
12
=
−u
u
a
7
=
−u
2
+ 1
u
2
a
5
=
−u
2
a + 2a
u
2
a − a
a
11
=
−u
u
a
10
=
−u
−u
2
+ u + 1
a
6
=
0
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
82
7
u
2
a −
71
7
au +
19
49
u
2
+
17
7
a −
237
49
u +
326
49
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
2
− u + 1)
3
c
2
(u
2
+ u + 1)
3
c
3
49(49u
6
+ 7u
5
− 6u
4
+ 15u
3
+ 2u
2
− u + 1)
c
4
49(49u
6
− 7u
5
+ 29u
4
+ 18u
3
+ 15u
2
+ 4u + 1)
c
6
(u
3
+ u
2
+ 2u + 1)
2
c
7
, c
8
(u
3
− u
2
+ 1)
2
c
9
(u
3
− 3u
2
+ 2u + 1)
2
c
10
(u
3
− u
2
+ 2u − 1)
2
c
11
u
6
c
12
(u
3
+ u
2
− 1)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y
2
+ y + 1)
3
c
3
2401(2401y
6
− 637y
5
+ 22y
4
− 137y
3
+ 22y
2
+ 3y + 1)
c
4
2401(2401y
6
+ 2793y
5
+ 2563y
4
+ 700y
3
+ 139y
2
+ 14y + 1)
c
6
, c
10
(y
3
+ 3y
2
+ 2y −1)
2
c
7
, c
8
, c
12
(y
3
− y
2
+ 2y −1)
2
c
9
(y
3
− 5y
2
+ 10y −1)
2
c
11
y
6
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = −0.171467 + 0.353309I
b = 0.171467 − 0.353309I
−3.02413 + 0.79824I −2.96264 + 4.86376I
u = 0.877439 + 0.744862I
a = −0.220241 − 0.325149I
b = 0.220241 + 0.325149I
−3.02413 + 4.85801I 12.11332 − 2.35134I
u = 0.877439 − 0.744862I
a = −0.171467 − 0.353309I
b = 0.171467 + 0.353309I
−3.02413 − 0.79824I −2.96264 − 4.86376I
u = 0.877439 − 0.744862I
a = −0.220241 + 0.325149I
b = 0.220241 − 0.325149I
−3.02413 − 4.85801I 12.11332 + 2.35134I
u = −0.754878
a = 0.463136 + 0.802176I
b = −0.463136 − 0.802176I
1.11345 − 2.02988I 12.10442 + 2.73535I
u = −0.754878
a = 0.463136 − 0.802176I
b = −0.463136 + 0.802176I
1.11345 + 2.02988I 12.10442 − 2.73535I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
3
)(u
102
+ 36u
101
+ ··· − 20973u + 2401)
c
2
((u
2
+ u + 1)
3
)(u
102
+ 4u
101
+ ··· − 197u + 49)
c
3
2401(49u
6
+ 7u
5
− 6u
4
+ 15u
3
+ 2u
2
− u + 1)
· (49u
102
− 70u
101
+ ··· − 545422911u − 255401567)
c
4
2401(49u
6
− 7u
5
+ 29u
4
+ 18u
3
+ 15u
2
+ 4u + 1)
· (49u
102
− 126u
101
+ ··· + 2407086u + 356047)
c
5
((u
2
− u + 1)
3
)(u
102
+ 4u
101
+ ··· − 197u + 49)
c
6
((u
3
+ u
2
+ 2u + 1)
2
)(u
102
− 3u
101
+ ··· + 6u − 1)
c
7
, c
8
((u
3
− u
2
+ 1)
2
)(u
102
− 3u
101
+ ··· + 8u
2
− 1)
c
9
((u
3
− 3u
2
+ 2u + 1)
2
)(u
102
+ 43u
101
+ ··· − 16u + 1)
c
10
((u
3
− u
2
+ 2u − 1)
2
)(u
102
− 3u
101
+ ··· + 6u − 1)
c
11
u
6
(u
102
− 5u
101
+ ··· + 174048u − 21952)
c
12
((u
3
+ u
2
− 1)
2
)(u
102
− 3u
101
+ ··· + 8u
2
− 1)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
3
)(y
102
+ 64y
101
+ ··· − 2.63597 × 10
9
y + 5764801)
c
2
, c
5
((y
2
+ y + 1)
3
)(y
102
+ 36y
101
+ ··· − 20973y + 2401)
c
3
5764801(2401y
6
− 637y
5
+ 22y
4
− 137y
3
+ 22y
2
+ 3y + 1)
· (2401y
102
− 2.11 × 10
5
y
101
+ ··· − 1.98 × 10
18
y + 6.52 × 10
16
)
c
4
5764801(2401y
6
+ 2793y
5
+ 2563y
4
+ 700y
3
+ 139y
2
+ 14y + 1)
· (2401y
102
+ 47530y
101
+ ··· − 8262494848850y + 126769466209)
c
6
, c
10
((y
3
+ 3y
2
+ 2y −1)
2
)(y
102
+ 43y
101
+ ··· − 16y + 1)
c
7
, c
8
, c
12
((y
3
− y
2
+ 2y −1)
2
)(y
102
− 101y
101
+ ··· − 16y + 1)
c
9
((y
3
− 5y
2
+ 10y −1)
2
)(y
102
+ 35y
101
+ ··· + 372y + 1)
c
11
y
6
(y
102
− 35y
101
+ ··· − 8.00774 × 10
9
y + 4.81890 × 10
8
)
21
