12n
0540
(K12n
0540
)
A knot diagram
1
Linearized knot diagam
3 5 9 12 2 10 5 11 7 3 4 8
Solving Sequence
4,11
12
5,9
3 2 6 8 1 7 10
c
11
c
4
c
3
c
2
c
5
c
8
c
12
c
7
c
10
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.47946 × 10
114
u
67
+ 5.80911 × 10
114
u
66
+ ··· + 2.34165 × 10
114
b + 9.83922 × 10
115
,
1.83497 × 10
116
u
67
− 3.18289 × 10
116
u
66
+ ··· + 1.63915 × 10
115
a − 6.53773 × 10
117
,
u
68
− 2u
67
+ ··· − 116u + 7i
I
u
2
= h5848837527u
22
+ 13674615497u
21
+ ··· + 52233066871b + 111138789648,
7655480010u
22
+ 231901700034u
21
+ ··· + 679029869323a + 1495389378052,
u
23
− u
22
+ ··· + 7u − 13i
* 2 irreducible components of dim
C
= 0, with total 91 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−3.48 × 10
114
u
67
+ 5.81 × 10
114
u
66
+ · · · + 2.34 × 10
114
b + 9.84 ×
10
115
, 1.83 × 10
116
u
67
− 3.18 × 10
116
u
66
+ · · · + 1.64 × 10
115
a − 6.54 ×
10
117
, u
68
− 2u
67
+ · · · − 116u + 7i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
5
=
−u
−u
3
+ u
a
9
=
−11.1946u
67
+ 19.4179u
66
+ ··· − 4458.06u + 398.848
1.48590u
67
− 2.48078u
66
+ ··· + 478.228u − 42.0184
a
3
=
2.99528u
67
− 8.06816u
66
+ ··· + 2059.11u − 186.296
−2.40290u
67
+ 3.48812u
66
+ ··· − 722.342u + 62.8761
a
2
=
2.86290u
67
− 7.77263u
66
+ ··· + 1979.48u − 179.800
−1.95630u
67
+ 3.03856u
66
+ ··· − 638.210u + 56.1653
a
6
=
6.23282u
67
− 9.22792u
66
+ ··· + 1916.42u − 165.385
0.664956u
67
− 0.0247150u
66
+ ··· − 88.8156u + 11.7141
a
8
=
−9.70871u
67
+ 16.9371u
66
+ ··· − 3979.83u + 356.830
1.48590u
67
− 2.48078u
66
+ ··· + 478.228u − 42.0184
a
1
=
3.04846u
67
− 9.72123u
66
+ ··· + 2742.54u − 254.243
−2.53855u
67
+ 3.80062u
66
+ ··· − 783.316u + 67.5088
a
7
=
−10.5542u
67
+ 17.7616u
66
+ ··· − 3993.89u + 354.809
1.59941u
67
− 2.25196u
66
+ ··· + 397.680u − 33.9317
a
10
=
−2.77331u
67
+ 5.28127u
66
+ ··· − 1350.34u + 125.631
1.09656u
67
− 0.524123u
66
+ ··· − 2.65244u + 2.93062
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3.24479u
67
+ 8.28537u
66
+ ··· − 1873.76u + 165.568
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
68
+ 83u
67
+ ··· + 50717133u + 1247689
c
2
, c
5
u
68
+ 3u
67
+ ··· + 2197u + 1117
c
3
u
68
+ u
67
+ ··· + 3064u + 911
c
4
, c
11
u
68
+ 2u
67
+ ··· + 116u + 7
c
6
, c
9
u
68
+ 4u
67
+ ··· − 34u + 3
c
7
u
68
+ 12u
67
+ ··· + 789947u + 129293
c
8
u
68
− 9u
66
+ ··· − 28u + 88
c
10
u
68
− 2u
67
+ ··· + 1328829u + 2269219
c
12
u
68
+ u
67
+ ··· − 3738678u + 370609
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
68
− 177y
67
+ ··· − 202908028705639y + 1556727840721
c
2
, c
5
y
68
+ 83y
67
+ ··· + 50717133y + 1247689
c
3
y
68
+ 21y
67
+ ··· + 24920164y + 829921
c
4
, c
11
y
68
− 48y
67
+ ··· − 2858y + 49
c
6
, c
9
y
68
+ 8y
67
+ ··· − 220y + 9
c
7
y
68
+ 68y
67
+ ··· + 2855259918707y + 16716679849
c
8
y
68
− 18y
67
+ ··· + 160432y + 7744
c
10
y
68
+ 52y
67
+ ··· + 220850551819415y + 5149354869961
c
12
y
68
− 45y
67
+ ··· − 1916711732460y + 137351030881
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.947765 + 0.357665I
a = 0.040563 + 1.213920I
b = −0.628775 − 0.554793I
−1.10242 − 1.88768I 0
u = 0.947765 − 0.357665I
a = 0.040563 − 1.213920I
b = −0.628775 + 0.554793I
−1.10242 + 1.88768I 0
u = −0.206261 + 1.007020I
a = 0.906803 − 0.883651I
b = −1.166080 + 0.709081I
−9.04368 + 2.56194I 0
u = −0.206261 − 1.007020I
a = 0.906803 + 0.883651I
b = −1.166080 − 0.709081I
−9.04368 − 2.56194I 0
u = −0.952275 + 0.015155I
a = −0.389347 + 1.110760I
b = −1.51867 − 0.44627I
−6.56999 + 0.14060I −5.76756 + 0.I
u = −0.952275 − 0.015155I
a = −0.389347 − 1.110760I
b = −1.51867 + 0.44627I
−6.56999 − 0.14060I −5.76756 + 0.I
u = 0.119156 + 1.120550I
a = 0.632936 + 0.272438I
b = −0.526423 + 0.033002I
0.601823 − 0.891457I 0
u = 0.119156 − 1.120550I
a = 0.632936 − 0.272438I
b = −0.526423 − 0.033002I
0.601823 + 0.891457I 0
u = 1.131540 + 0.066351I
a = −1.34290 − 1.03710I
b = −0.842012 + 0.236969I
−3.61434 − 1.69153I 0
u = 1.131540 − 0.066351I
a = −1.34290 + 1.03710I
b = −0.842012 − 0.236969I
−3.61434 + 1.69153I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.125430 + 0.171124I
a = −0.153836 + 0.563315I
b = 1.11877 − 2.59647I
−10.13300 − 5.69758I 0
u = 1.125430 − 0.171124I
a = −0.153836 − 0.563315I
b = 1.11877 + 2.59647I
−10.13300 + 5.69758I 0
u = 0.175099 + 0.838478I
a = 0.638073 + 0.706860I
b = −0.333831 − 0.671397I
0.31102 − 1.89447I −2.64082 + 6.58964I
u = 0.175099 − 0.838478I
a = 0.638073 − 0.706860I
b = −0.333831 + 0.671397I
0.31102 + 1.89447I −2.64082 − 6.58964I
u = −1.088590 + 0.350394I
a = 0.578583 + 0.954503I
b = 1.31358 − 0.94934I
1.42621 + 5.22038I 0
u = −1.088590 − 0.350394I
a = 0.578583 − 0.954503I
b = 1.31358 + 0.94934I
1.42621 − 5.22038I 0
u = 1.141830 + 0.179993I
a = 0.82568 − 1.37936I
b = 0.908474 + 0.921235I
−0.61521 − 4.20240I 0
u = 1.141830 − 0.179993I
a = 0.82568 + 1.37936I
b = 0.908474 − 0.921235I
−0.61521 + 4.20240I 0
u = −0.043094 + 1.162240I
a = −0.911498 + 0.621527I
b = 1.098450 − 0.740956I
−8.72944 + 10.14780I 0
u = −0.043094 − 1.162240I
a = −0.911498 − 0.621527I
b = 1.098450 + 0.740956I
−8.72944 − 10.14780I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.730243 + 0.911092I
a = 0.436558 − 0.057088I
b = −0.035935 + 0.195728I
−0.33349 − 2.89073I 0
u = 0.730243 − 0.911092I
a = 0.436558 + 0.057088I
b = −0.035935 − 0.195728I
−0.33349 + 2.89073I 0
u = −1.180250 + 0.039699I
a = −0.322263 − 0.642592I
b = −1.36957 + 0.98710I
−4.90609 + 1.45309I 0
u = −1.180250 − 0.039699I
a = −0.322263 + 0.642592I
b = −1.36957 − 0.98710I
−4.90609 − 1.45309I 0
u = −1.176600 + 0.191135I
a = −1.93965 + 0.51920I
b = −0.695306 + 0.367890I
−10.52210 + 6.41640I 0
u = −1.176600 − 0.191135I
a = −1.93965 − 0.51920I
b = −0.695306 − 0.367890I
−10.52210 − 6.41640I 0
u = 0.060621 + 1.190540I
a = −0.571573 − 0.371721I
b = 0.867630 + 0.303277I
−0.46876 − 4.20757I 0
u = 0.060621 − 1.190540I
a = −0.571573 + 0.371721I
b = 0.867630 − 0.303277I
−0.46876 + 4.20757I 0
u = −1.182210 + 0.170919I
a = 0.088084 − 0.589191I
b = 0.714259 + 1.051810I
−2.89595 + 4.08070I 0
u = −1.182210 − 0.170919I
a = 0.088084 + 0.589191I
b = 0.714259 − 1.051810I
−2.89595 − 4.08070I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.404834 + 0.685829I
a = −0.940474 − 0.323677I
b = 0.693348 + 0.865586I
3.55477 − 1.28710I 5.05160 + 1.04556I
u = −0.404834 − 0.685829I
a = −0.940474 + 0.323677I
b = 0.693348 − 0.865586I
3.55477 + 1.28710I 5.05160 − 1.04556I
u = 1.223450 + 0.114208I
a = 0.838650 + 0.592410I
b = 0.466055 − 0.033333I
−3.07031 − 0.92088I 0
u = 1.223450 − 0.114208I
a = 0.838650 − 0.592410I
b = 0.466055 + 0.033333I
−3.07031 + 0.92088I 0
u = 1.242620 + 0.025631I
a = 0.032890 − 0.504754I
b = −1.72206 + 2.06580I
−11.42940 + 2.92629I 0
u = 1.242620 − 0.025631I
a = 0.032890 + 0.504754I
b = −1.72206 − 2.06580I
−11.42940 − 2.92629I 0
u = −1.275810 + 0.008672I
a = 1.30907 + 1.34723I
b = 0.772778 + 0.039008I
−12.42140 + 2.86949I 0
u = −1.275810 − 0.008672I
a = 1.30907 − 1.34723I
b = 0.772778 − 0.039008I
−12.42140 − 2.86949I 0
u = 1.091170 + 0.758270I
a = −0.048055 − 0.621973I
b = 1.388680 + 0.122425I
−5.10581 − 3.43321I 0
u = 1.091170 − 0.758270I
a = −0.048055 + 0.621973I
b = 1.388680 − 0.122425I
−5.10581 + 3.43321I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.269780 + 0.488456I
a = 0.006811 − 1.078700I
b = −0.742033 + 0.701033I
−3.69503 + 6.20269I 0
u = −1.269780 − 0.488456I
a = 0.006811 + 1.078700I
b = −0.742033 − 0.701033I
−3.69503 − 6.20269I 0
u = 0.011349 + 0.622403I
a = 0.565810 + 1.046550I
b = 0.180164 − 0.381969I
0.84600 − 1.53956I 1.33813 + 2.18949I
u = 0.011349 − 0.622403I
a = 0.565810 − 1.046550I
b = 0.180164 + 0.381969I
0.84600 + 1.53956I 1.33813 − 2.18949I
u = 1.38641 + 0.42602I
a = −0.380161 + 1.136250I
b = −1.45552 − 0.92583I
−14.0339 − 7.5741I 0
u = 1.38641 − 0.42602I
a = −0.380161 − 1.136250I
b = −1.45552 + 0.92583I
−14.0339 + 7.5741I 0
u = −1.38018 + 0.44717I
a = −0.180863 − 0.851166I
b = −1.05821 + 1.05211I
−4.53688 + 6.71623I 0
u = −1.38018 − 0.44717I
a = −0.180863 + 0.851166I
b = −1.05821 − 1.05211I
−4.53688 − 6.71623I 0
u = −1.30930 + 0.68061I
a = 0.466558 − 0.599062I
b = −1.119230 − 0.290691I
−12.20000 + 3.56524I 0
u = −1.30930 − 0.68061I
a = 0.466558 + 0.599062I
b = −1.119230 + 0.290691I
−12.20000 − 3.56524I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.39983 + 0.51827I
a = 0.251477 + 0.976417I
b = 1.203380 − 0.632990I
−5.13007 + 10.12020I 0
u = −1.39983 − 0.51827I
a = 0.251477 − 0.976417I
b = 1.203380 + 0.632990I
−5.13007 − 10.12020I 0
u = 1.39753 + 0.53362I
a = 0.246829 − 1.107490I
b = 1.48762 + 0.95191I
−13.2811 − 16.0932I 0
u = 1.39753 − 0.53362I
a = 0.246829 + 1.107490I
b = 1.48762 − 0.95191I
−13.2811 + 16.0932I 0
u = 1.40478 + 0.55900I
a = 0.067000 + 0.648345I
b = −1.010050 − 0.582448I
−3.60803 − 5.31106I 0
u = 1.40478 − 0.55900I
a = 0.067000 − 0.648345I
b = −1.010050 + 0.582448I
−3.60803 + 5.31106I 0
u = 1.44778 + 0.50507I
a = 0.107561 − 0.627005I
b = 1.060660 + 0.226591I
−5.13201 − 2.07157I 0
u = 1.44778 − 0.50507I
a = 0.107561 + 0.627005I
b = 1.060660 − 0.226591I
−5.13201 + 2.07157I 0
u = 0.373319 + 0.206165I
a = −2.73778 − 0.45710I
b = 0.508605 − 0.537274I
1.78723 + 2.33202I −4.39316 − 1.89690I
u = 0.373319 − 0.206165I
a = −2.73778 + 0.45710I
b = 0.508605 + 0.537274I
1.78723 − 2.33202I −4.39316 + 1.89690I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.249284 + 0.339745I
a = 2.71001 − 0.73800I
b = 0.947188 + 1.031140I
−7.68973 + 3.58621I −2.25293 − 1.72671I
u = 0.249284 − 0.339745I
a = 2.71001 + 0.73800I
b = 0.947188 − 1.031140I
−7.68973 − 3.58621I −2.25293 + 1.72671I
u = −1.47747 + 0.55770I
a = −0.303874 + 0.589982I
b = 0.961351 + 0.168628I
−13.22700 − 3.78980I 0
u = −1.47747 − 0.55770I
a = −0.303874 − 0.589982I
b = 0.961351 − 0.168628I
−13.22700 + 3.78980I 0
u = −0.097604 + 0.392483I
a = −1.27273 + 2.72091I
b = −0.788066 − 1.085820I
−7.38084 − 4.11631I −1.81227 + 1.53073I
u = −0.097604 − 0.392483I
a = −1.27273 − 2.72091I
b = −0.788066 + 1.085820I
−7.38084 + 4.11631I −1.81227 − 1.53073I
u = 0.184696 + 0.005265I
a = 1.31649 − 3.97124I
b = −0.679221 + 0.376391I
−1.19167 + 1.07394I −6.06832 − 1.82745I
u = 0.184696 − 0.005265I
a = 1.31649 + 3.97124I
b = −0.679221 − 0.376391I
−1.19167 − 1.07394I −6.06832 + 1.82745I
11
II.
I
u
2
= h5.85 × 10
9
u
22
+ 1.37 × 10
10
u
21
+ · · · + 5.22 × 10
10
b + 1.11 × 10
11
, 7.66 ×
10
9
u
22
+2.32×10
11
u
21
+· · ·+6.79×10
11
a+1.50×10
12
, u
23
−u
22
+· · ·+7u−13i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
5
=
−u
−u
3
+ u
a
9
=
−0.0112741u
22
− 0.341519u
21
+ ··· + 2.14006u − 2.20224
−0.111976u
22
− 0.261800u
21
+ ··· − 0.447275u − 2.12775
a
3
=
−0.0163823u
22
− 0.0636141u
21
+ ··· − 0.852866u − 1.60142
−0.148727u
22
+ 0.400493u
21
+ ··· − 3.53623u + 2.19107
a
2
=
0.154088u
22
− 0.430776u
21
+ ··· + 3.46615u − 3.13359
−0.226792u
22
+ 0.342331u
21
+ ··· − 4.26229u + 1.16625
a
6
=
0.0904796u
22
− 0.375433u
21
+ ··· + 3.26034u − 4.38124
0.114745u
22
− 0.0830532u
21
+ ··· − 0.980044u + 1.04095
a
8
=
−0.123250u
22
− 0.603319u
21
+ ··· + 1.69278u − 4.32999
−0.111976u
22
− 0.261800u
21
+ ··· − 0.447275u − 2.12775
a
1
=
0.173695u
22
− 0.175316u
21
+ ··· + 2.07803u − 0.322177
0.170470u
22
− 0.367162u
21
+ ··· + 4.31902u − 2.53217
a
7
=
−0.194704u
22
− 0.406398u
21
+ ··· + 2.57044u − 5.26720
−0.327036u
22
+ 0.120016u
21
+ ··· − 3.13210u + 0.440540
a
10
=
0.157270u
22
+ 0.341210u
21
+ ··· − 0.873536u + 7.44134
−0.0234918u
22
− 0.0729096u
21
+ ··· + 1.55156u − 0.643684
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
68841542409
52233066871
u
22
−
22063841362
52233066871
u
21
+ ··· +
22905478578
52233066871
u −
1118269147194
52233066871
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
23
− 24u
22
+ ··· + 8u + 1
c
2
u
23
+ 12u
21
+ ··· − 6u − 1
c
3
u
23
+ u
21
+ ··· + u − 1
c
4
u
23
+ u
22
+ ··· + 7u + 13
c
5
u
23
+ 12u
21
+ ··· − 6u + 1
c
6
u
23
− 9u
22
+ ··· + u − 1
c
7
u
23
+ u
22
+ ··· + 34u − 1
c
8
u
23
− u
22
+ ··· + 5u − 1
c
9
u
23
+ 9u
22
+ ··· + u + 1
c
10
u
23
− 3u
22
+ ··· + 64u − 1
c
11
u
23
− u
22
+ ··· + 7u − 13
c
12
u
23
− 2u
21
+ ··· − 3u − 1
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
− 32y
22
+ ··· + 176y −1
c
2
, c
5
y
23
+ 24y
22
+ ··· + 8y −1
c
3
y
23
+ 2y
22
+ ··· − 7y −1
c
4
, c
11
y
23
− 15y
22
+ ··· + 491y −169
c
6
, c
9
y
23
+ 13y
22
+ ··· + y −1
c
7
y
23
+ 9y
22
+ ··· + 942y −1
c
8
y
23
+ 3y
22
+ ··· − 5y −1
c
10
y
23
+ 5y
22
+ ··· + 3818y −1
c
12
y
23
− 4y
22
+ ··· − 3y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.969649 + 0.208739I
a = 0.893035 + 0.002983I
b = 0.41251 + 1.38099I
−9.35694 + 4.88290I −5.47805 − 2.39578I
u = −0.969649 − 0.208739I
a = 0.893035 − 0.002983I
b = 0.41251 − 1.38099I
−9.35694 − 4.88290I −5.47805 + 2.39578I
u = 0.706367 + 0.694290I
a = −0.864887 + 0.128919I
b = 0.755463 − 0.588126I
1.99473 + 0.42434I −2.96732 − 0.54228I
u = 0.706367 − 0.694290I
a = −0.864887 − 0.128919I
b = 0.755463 + 0.588126I
1.99473 − 0.42434I −2.96732 + 0.54228I
u = 1.029520 + 0.311855I
a = 0.87335 − 1.12980I
b = 1.081290 + 0.659632I
0.92294 − 4.26461I −2.79214 + 3.19246I
u = 1.029520 − 0.311855I
a = 0.87335 + 1.12980I
b = 1.081290 − 0.659632I
0.92294 + 4.26461I −2.79214 − 3.19246I
u = 0.085426 + 1.108690I
a = 0.650193 + 0.335735I
b = −0.394580 − 0.446615I
1.04180 − 1.37739I 5.17336 + 4.62822I
u = 0.085426 − 1.108690I
a = 0.650193 − 0.335735I
b = −0.394580 + 0.446615I
1.04180 + 1.37739I 5.17336 − 4.62822I
u = 0.612586 + 0.954643I
a = 0.394296 + 0.065832I
b = −0.526420 − 0.116699I
−0.74547 − 3.07047I −10.34573 + 5.68741I
u = 0.612586 − 0.954643I
a = 0.394296 − 0.065832I
b = −0.526420 + 0.116699I
−0.74547 + 3.07047I −10.34573 − 5.68741I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.182480 + 0.093811I
a = −0.716499 + 0.295092I
b = −0.51191 − 1.36850I
−10.36280 − 3.44481I −6.30851 + 2.84638I
u = −1.182480 − 0.093811I
a = −0.716499 − 0.295092I
b = −0.51191 + 1.36850I
−10.36280 + 3.44481I −6.30851 − 2.84638I
u = 1.187240 + 0.178894I
a = 0.373081 + 1.093460I
b = −0.009372 − 0.431374I
−2.75856 − 2.80899I −6.25715 + 4.22155I
u = 1.187240 − 0.178894I
a = 0.373081 − 1.093460I
b = −0.009372 + 0.431374I
−2.75856 + 2.80899I −6.25715 − 4.22155I
u = 1.22751
a = −1.00654
b = −0.980403
−4.04467 −10.7930
u = −1.201890 + 0.352374I
a = 0.494720 + 1.043980I
b = 0.98036 − 1.32039I
−0.35223 + 6.37887I −3.58506 − 6.94969I
u = −1.201890 − 0.352374I
a = 0.494720 − 1.043980I
b = 0.98036 + 1.32039I
−0.35223 − 6.37887I −3.58506 + 6.94969I
u = −0.213051 + 0.598073I
a = −1.58672 − 0.80580I
b = 0.443024 + 0.901041I
2.77756 − 2.68869I 3.20713 + 4.39726I
u = −0.213051 − 0.598073I
a = −1.58672 + 0.80580I
b = 0.443024 − 0.901041I
2.77756 + 2.68869I 3.20713 − 4.39726I
u = 1.25272 + 0.66973I
a = 0.005234 + 0.556877I
b = −1.356660 − 0.234537I
−5.31688 − 3.17755I −16.2847 − 1.1732I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.25272 − 0.66973I
a = 0.005234 − 0.556877I
b = −1.356660 + 0.234537I
−5.31688 + 3.17755I −16.2847 + 1.1732I
u = −1.42054 + 0.53423I
a = −0.050993 − 0.825192I
b = −0.883498 + 0.890898I
−3.78568 + 7.28747I −1.96558 − 11.65600I
u = −1.42054 − 0.53423I
a = −0.050993 + 0.825192I
b = −0.883498 − 0.890898I
−3.78568 − 7.28747I −1.96558 + 11.65600I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
23
− 24u
22
+ ··· + 8u + 1)
· (u
68
+ 83u
67
+ ··· + 50717133u + 1247689)
c
2
(u
23
+ 12u
21
+ ··· − 6u − 1)(u
68
+ 3u
67
+ ··· + 2197u + 1117)
c
3
(u
23
+ u
21
+ ··· + u − 1)(u
68
+ u
67
+ ··· + 3064u + 911)
c
4
(u
23
+ u
22
+ ··· + 7u + 13)(u
68
+ 2u
67
+ ··· + 116u + 7)
c
5
(u
23
+ 12u
21
+ ··· − 6u + 1)(u
68
+ 3u
67
+ ··· + 2197u + 1117)
c
6
(u
23
− 9u
22
+ ··· + u − 1)(u
68
+ 4u
67
+ ··· − 34u + 3)
c
7
(u
23
+ u
22
+ ··· + 34u − 1)(u
68
+ 12u
67
+ ··· + 789947u + 129293)
c
8
(u
23
− u
22
+ ··· + 5u − 1)(u
68
− 9u
66
+ ··· − 28u + 88)
c
9
(u
23
+ 9u
22
+ ··· + u + 1)(u
68
+ 4u
67
+ ··· − 34u + 3)
c
10
(u
23
− 3u
22
+ ··· + 64u − 1)(u
68
− 2u
67
+ ··· + 1328829u + 2269219)
c
11
(u
23
− u
22
+ ··· + 7u − 13)(u
68
+ 2u
67
+ ··· + 116u + 7)
c
12
(u
23
− 2u
21
+ ··· − 3u − 1)(u
68
+ u
67
+ ··· − 3738678u + 370609)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
23
− 32y
22
+ ··· + 176y −1)
· (y
68
− 177y
67
+ ··· − 202908028705639y + 1556727840721)
c
2
, c
5
(y
23
+ 24y
22
+ ··· + 8y −1)
· (y
68
+ 83y
67
+ ··· + 50717133y + 1247689)
c
3
(y
23
+ 2y
22
+ ··· − 7y −1)(y
68
+ 21y
67
+ ··· + 2.49202 × 10
7
y + 829921)
c
4
, c
11
(y
23
− 15y
22
+ ··· + 491y −169)(y
68
− 48y
67
+ ··· − 2858y + 49)
c
6
, c
9
(y
23
+ 13y
22
+ ··· + y −1)(y
68
+ 8y
67
+ ··· − 220y + 9)
c
7
(y
23
+ 9y
22
+ ··· + 942y −1)
· (y
68
+ 68y
67
+ ··· + 2855259918707y + 16716679849)
c
8
(y
23
+ 3y
22
+ ··· − 5y −1)(y
68
− 18y
67
+ ··· + 160432y + 7744)
c
10
(y
23
+ 5y
22
+ ··· + 3818y −1)
· (y
68
+ 52y
67
+ ··· + 220850551819415y + 5149354869961)
c
12
(y
23
− 4y
22
+ ··· − 3y −1)
· (y
68
− 45y
67
+ ··· − 1916711732460y + 137351030881)
21
