12a
0610
(K12a
0610
)
A knot diagram
1
Linearized knot diagam
3 7 9 12 11 2 10 4 1 6 5 8
Solving Sequence
2,6
7 3
1,11
5 12 4 10 8 9
c
6
c
2
c
1
c
5
c
11
c
4
c
10
c
7
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.93763 × 10
105
u
84
+ 6.40033 × 10
105
u
83
+ ··· + 5.22721 × 10
105
b − 5.47893 × 10
106
,
− 1.05688 × 10
107
u
84
+ 1.58154 × 10
107
u
83
+ ··· + 9.93169 × 10
106
a + 6.22411 × 10
108
,
u
85
− 2u
84
+ ··· − 29u + 19i
I
u
2
= h−u
16
− u
15
+ ··· + b − 3,
− u
14
− u
13
+ 3u
12
+ 2u
11
− 8u
10
− 4u
9
+ 12u
8
+ 3u
7
− 15u
6
− 3u
5
+ 12u
4
+ u
3
− 5u
2
+ a + 2,
u
17
+ u
16
+ ··· + u + 1i
* 2 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
= h−1.94 × 10
105
u
84
+ 6.40 × 10
105
u
83
+ · · · + 5.23 × 10
105
b − 5.48 ×
10
106
, −1.06 × 10
107
u
84
+ 1.58 × 10
107
u
83
+ · · · + 9.93 × 10
106
a + 6.22 ×
10
108
, u
85
− 2u
84
+ · · · − 29u + 19i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
11
=
1.06415u
84
− 1.59242u
83
+ ··· − 9.71962u − 62.6691
0.370682u
84
− 1.22443u
83
+ ··· − 53.3393u + 10.4816
a
5
=
−0.366811u
84
− 0.137769u
83
+ ··· − 48.4547u + 21.4022
−0.349390u
84
+ 0.613843u
83
+ ··· + 15.4483u + 13.8709
a
12
=
0.0586430u
84
+ 0.345218u
83
+ ··· − 33.7770u − 4.01764
−0.898344u
84
+ 2.16337u
83
+ ··· + 76.0579u − 28.6076
a
4
=
1.35820u
84
− 1.82953u
83
+ ··· + 44.0089u − 36.4802
−0.879980u
84
+ 1.21621u
83
+ ··· + 13.8302u + 15.4803
a
10
=
1.43484u
84
− 2.81684u
83
+ ··· − 63.0589u − 52.1876
0.370682u
84
− 1.22443u
83
+ ··· − 53.3393u + 10.4816
a
8
=
0.861966u
84
− 1.69287u
83
+ ··· + 24.3927u − 72.7494
−0.0526491u
84
+ 0.252680u
83
+ ··· − 29.5740u + 4.29926
a
9
=
1.28326u
84
− 2.26001u
83
+ ··· − 61.0116u − 45.5381
0.329735u
84
− 1.20748u
83
+ ··· − 42.6117u + 13.5326
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.130039u
84
+ 0.718141u
83
+ ··· + 77.5891u − 93.5890
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
85
+ 30u
84
+ ··· + 17713u + 361
c
2
, c
6
u
85
− 2u
84
+ ··· − 29u + 19
c
3
, c
8
u
85
− u
84
+ ··· + 26u + 19
c
4
, c
5
, c
10
c
11
u
85
+ u
84
+ ··· − 13u + 1
c
7
u
85
− 14u
84
+ ··· − 548721u + 148409
c
9
u
85
+ 4u
84
+ ··· + 15735u + 2737
c
12
u
85
− 2u
84
+ ··· − 405993u + 904999
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
85
+ 58y
84
+ ··· + 17060353y −130321
c
2
, c
6
y
85
− 30y
84
+ ··· + 17713y −361
c
3
, c
8
y
85
+ 77y
84
+ ··· − 5556y −361
c
4
, c
5
, c
10
c
11
y
85
+ 109y
84
+ ··· − 127y −1
c
7
y
85
+ 36y
84
+ ··· − 93911252195y −22025231281
c
9
y
85
+ 20y
84
+ ··· + 4057439y −7491169
c
12
y
85
+ 44y
84
+ ··· − 15920612859961y −819023190001
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.647105 + 0.753959I
a = −0.224133 − 0.420689I
b = 0.824332 − 0.180446I
4.70008 + 2.71758I 0
u = 0.647105 − 0.753959I
a = −0.224133 + 0.420689I
b = 0.824332 + 0.180446I
4.70008 − 2.71758I 0
u = −0.556564 + 0.860766I
a = −0.36210 − 2.15933I
b = 0.04521 + 1.67260I
11.69870 + 0.50746I 0
u = −0.556564 − 0.860766I
a = −0.36210 + 2.15933I
b = 0.04521 − 1.67260I
11.69870 − 0.50746I 0
u = −0.565073 + 0.787127I
a = −0.40557 + 2.28724I
b = −0.07092 − 1.67258I
11.70450 − 3.80032I 0
u = −0.565073 − 0.787127I
a = −0.40557 − 2.28724I
b = −0.07092 + 1.67258I
11.70450 + 3.80032I 0
u = −0.811348 + 0.652520I
a = −1.95108 − 1.86614I
b = 0.002056 + 0.816600I
5.99934 + 0.54360I 0
u = −0.811348 − 0.652520I
a = −1.95108 + 1.86614I
b = 0.002056 − 0.816600I
5.99934 − 0.54360I 0
u = −1.045990 + 0.023525I
a = 0.675867 + 0.404666I
b = 0.231608 + 0.627961I
−2.16388 − 1.62762I 0
u = −1.045990 − 0.023525I
a = 0.675867 − 0.404666I
b = 0.231608 − 0.627961I
−2.16388 + 1.62762I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.787091 + 0.701132I
a = 0.86089 + 1.51565I
b = 0.741333 − 0.874735I
6.62681 + 2.54168I 0
u = −0.787091 − 0.701132I
a = 0.86089 − 1.51565I
b = 0.741333 + 0.874735I
6.62681 − 2.54168I 0
u = 0.727290 + 0.600758I
a = −0.317175 + 0.570445I
b = 0.240056 − 0.954237I
2.60222 − 1.41006I 0
u = 0.727290 − 0.600758I
a = −0.317175 − 0.570445I
b = 0.240056 + 0.954237I
2.60222 + 1.41006I 0
u = −0.761116 + 0.550447I
a = −0.341801 − 0.103536I
b = −0.523133 − 0.083727I
0.007740 + 0.354268I 0
u = −0.761116 − 0.550447I
a = −0.341801 + 0.103536I
b = −0.523133 + 0.083727I
0.007740 − 0.354268I 0
u = −1.067980 + 0.060235I
a = −0.656023 + 0.333160I
b = −0.638161 − 0.121268I
−1.04027 + 2.23555I 0
u = −1.067980 − 0.060235I
a = −0.656023 − 0.333160I
b = −0.638161 + 0.121268I
−1.04027 − 2.23555I 0
u = 0.826055 + 0.686952I
a = −0.20738 + 3.33992I
b = −0.01217 − 1.69343I
15.0313 − 4.7059I 0
u = 0.826055 − 0.686952I
a = −0.20738 − 3.33992I
b = −0.01217 + 1.69343I
15.0313 + 4.7059I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.609980 + 0.679262I
a = −0.325099 − 1.045890I
b = −0.300819 + 0.858960I
2.83585 + 2.41811I −12.00000 + 0.I
u = 0.609980 − 0.679262I
a = −0.325099 + 1.045890I
b = −0.300819 − 0.858960I
2.83585 − 2.41811I −12.00000 + 0.I
u = −0.612018 + 0.899881I
a = −0.281445 − 1.092780I
b = 0.488638 + 1.001550I
8.33566 − 7.04031I 0
u = −0.612018 − 0.899881I
a = −0.281445 + 1.092780I
b = 0.488638 − 1.001550I
8.33566 + 7.04031I 0
u = 0.897868 + 0.155214I
a = 1.37373 − 0.80599I
b = 0.303749 + 0.272887I
−3.24400 − 0.43047I −16.2817 + 10.9205I
u = 0.897868 − 0.155214I
a = 1.37373 + 0.80599I
b = 0.303749 − 0.272887I
−3.24400 + 0.43047I −16.2817 − 10.9205I
u = −0.813594 + 0.405787I
a = 1.90281 + 1.78662I
b = 0.089790 − 1.372960I
2.17807 + 1.68544I −12.00000 + 0.I
u = −0.813594 − 0.405787I
a = 1.90281 − 1.78662I
b = 0.089790 + 1.372960I
2.17807 − 1.68544I −12.00000 + 0.I
u = −0.892941 + 0.643912I
a = 0.02925 − 2.05496I
b = −0.032718 + 0.920802I
5.74174 + 4.50633I 0
u = −0.892941 − 0.643912I
a = 0.02925 + 2.05496I
b = −0.032718 − 0.920802I
5.74174 − 4.50633I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.830217 + 0.723714I
a = 0.56953 − 2.00230I
b = −0.17837 + 1.75045I
15.7652 + 0.8537I 0
u = 0.830217 − 0.723714I
a = 0.56953 + 2.00230I
b = −0.17837 − 1.75045I
15.7652 − 0.8537I 0
u = 0.562524 + 0.698432I
a = −0.632069 + 0.699105I
b = 0.148063 + 0.105521I
3.91125 − 0.86087I −7.44019 + 3.38376I
u = 0.562524 − 0.698432I
a = −0.632069 − 0.699105I
b = 0.148063 − 0.105521I
3.91125 + 0.86087I −7.44019 − 3.38376I
u = −0.932054 + 0.609477I
a = 0.517583 + 0.527861I
b = 0.576720 + 0.064604I
−0.55714 + 4.33362I 0
u = −0.932054 − 0.609477I
a = 0.517583 − 0.527861I
b = 0.576720 − 0.064604I
−0.55714 − 4.33362I 0
u = 0.893893 + 0.681468I
a = −2.65625 + 2.64884I
b = −0.00283 − 1.67019I
14.8209 − 0.5681I 0
u = 0.893893 − 0.681468I
a = −2.65625 − 2.64884I
b = −0.00283 + 1.67019I
14.8209 + 0.5681I 0
u = 0.954964 + 0.633066I
a = −0.856249 + 0.886381I
b = −0.403009 − 0.741709I
1.88427 − 3.52097I 0
u = 0.954964 − 0.633066I
a = −0.856249 − 0.886381I
b = −0.403009 + 0.741709I
1.88427 + 3.52097I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.898469 + 0.713573I
a = 1.90554 − 1.88784I
b = 0.21178 + 1.71770I
15.5555 − 6.3400I 0
u = 0.898469 − 0.713573I
a = 1.90554 + 1.88784I
b = 0.21178 − 1.71770I
15.5555 + 6.3400I 0
u = −0.926032 + 0.681783I
a = 0.478596 + 0.485534I
b = −0.716859 − 0.982030I
6.19768 + 2.77909I 0
u = −0.926032 − 0.681783I
a = 0.478596 − 0.485534I
b = −0.716859 + 0.982030I
6.19768 − 2.77909I 0
u = −0.446139 + 1.072420I
a = −0.098836 + 0.989967I
b = 0.121122 − 0.860217I
6.78292 + 1.92597I 0
u = −0.446139 − 1.072420I
a = −0.098836 − 0.989967I
b = 0.121122 + 0.860217I
6.78292 − 1.92597I 0
u = 1.168160 + 0.042928I
a = 0.554142 + 0.148794I
b = 0.03344 + 1.61381I
5.64367 − 2.43731I 0
u = 1.168160 − 0.042928I
a = 0.554142 − 0.148794I
b = 0.03344 − 1.61381I
5.64367 + 2.43731I 0
u = 0.629848 + 0.994180I
a = −0.04602 + 2.25812I
b = 0.13524 − 1.71018I
17.7707 + 9.5522I 0
u = 0.629848 − 0.994180I
a = −0.04602 − 2.25812I
b = 0.13524 + 1.71018I
17.7707 − 9.5522I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.005390 + 0.647624I
a = 1.45289 − 1.00573I
b = 0.376561 + 0.808119I
1.68859 − 7.58283I 0
u = 1.005390 − 0.647624I
a = 1.45289 + 1.00573I
b = 0.376561 − 0.808119I
1.68859 + 7.58283I 0
u = −0.802068 + 0.045860I
a = −0.61059 − 1.85147I
b = 0.09331 − 1.61773I
11.34640 + 2.99639I −8.69665 − 2.24681I
u = −0.802068 − 0.045860I
a = −0.61059 + 1.85147I
b = 0.09331 + 1.61773I
11.34640 − 2.99639I −8.69665 + 2.24681I
u = 0.789258 + 0.059653I
a = −1.103960 + 0.847330I
b = −0.328099 − 1.040420I
2.55734 − 1.18348I −8.52720 + 1.71025I
u = 0.789258 − 0.059653I
a = −1.103960 − 0.847330I
b = −0.328099 + 1.040420I
2.55734 + 1.18348I −8.52720 − 1.71025I
u = 1.012580 + 0.685568I
a = −0.181393 + 0.667802I
b = −0.898129 − 0.088432I
3.61303 − 8.20470I 0
u = 1.012580 − 0.685568I
a = −0.181393 − 0.667802I
b = −0.898129 + 0.088432I
3.61303 + 8.20470I 0
u = 1.037250 + 0.662366I
a = 0.345822 + 0.438701I
b = 0.0335953 − 0.1026880I
2.54217 − 4.42223I 0
u = 1.037250 − 0.662366I
a = 0.345822 − 0.438701I
b = 0.0335953 + 0.1026880I
2.54217 + 4.42223I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.228980 + 0.203243I
a = −0.536826 + 0.200839I
b = −0.420598 − 0.753985I
0.87355 − 5.82145I 0
u = 1.228980 − 0.203243I
a = −0.536826 − 0.200839I
b = −0.420598 + 0.753985I
0.87355 + 5.82145I 0
u = −1.049270 + 0.676448I
a = 2.33788 + 1.53668I
b = 0.09332 − 1.66009I
10.28640 + 9.32446I 0
u = −1.049270 − 0.676448I
a = 2.33788 − 1.53668I
b = 0.09332 + 1.66009I
10.28640 − 9.32446I 0
u = −1.071800 + 0.726814I
a = −1.01750 − 1.29587I
b = −0.566947 + 0.990313I
6.9269 + 13.0405I 0
u = −1.071800 − 0.726814I
a = −1.01750 + 1.29587I
b = −0.566947 − 0.990313I
6.9269 − 13.0405I 0
u = −1.087270 + 0.727678I
a = −1.41199 − 1.55195I
b = −0.10415 + 1.64080I
10.13050 + 5.39662I 0
u = −1.087270 − 0.727678I
a = −1.41199 + 1.55195I
b = −0.10415 − 1.64080I
10.13050 − 5.39662I 0
u = 0.472230 + 1.259750I
a = 0.13075 − 2.11971I
b = 0.02922 + 1.67563I
15.7426 − 2.4908I 0
u = 0.472230 − 1.259750I
a = 0.13075 + 2.11971I
b = 0.02922 − 1.67563I
15.7426 + 2.4908I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.107400 + 0.767076I
a = −1.75743 + 1.77279I
b = −0.16023 − 1.71067I
16.2658 − 15.9591I 0
u = 1.107400 − 0.767076I
a = −1.75743 − 1.77279I
b = −0.16023 + 1.71067I
16.2658 + 15.9591I 0
u = 0.551963 + 0.313389I
a = −0.964569 + 0.755921I
b = −0.066335 − 1.023540I
2.38998 − 1.32990I −6.70793 + 4.87191I
u = 0.551963 − 0.313389I
a = −0.964569 − 0.755921I
b = −0.066335 + 1.023540I
2.38998 + 1.32990I −6.70793 − 4.87191I
u = −1.152350 + 0.798898I
a = 0.770641 + 0.797164I
b = 0.045398 − 0.819870I
4.70193 + 4.76066I 0
u = −1.152350 − 0.798898I
a = 0.770641 − 0.797164I
b = 0.045398 + 0.819870I
4.70193 − 4.76066I 0
u = −1.380490 + 0.277313I
a = −0.656547 − 0.660540I
b = −0.09664 + 1.64151I
9.14952 + 7.66751I 0
u = −1.380490 − 0.277313I
a = −0.656547 + 0.660540I
b = −0.09664 − 1.64151I
9.14952 − 7.66751I 0
u = −0.563721 + 0.067562I
a = −1.40491 + 1.49605I
b = −0.06817 − 1.70836I
12.20380 − 2.58863I −11.77943 + 3.33602I
u = −0.563721 − 0.067562I
a = −1.40491 − 1.49605I
b = −0.06817 + 1.70836I
12.20380 + 2.58863I −11.77943 − 3.33602I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.21378 + 0.87933I
a = 1.10685 − 1.70532I
b = 0.01240 + 1.66995I
13.5267 − 4.9848I 0
u = 1.21378 − 0.87933I
a = 1.10685 + 1.70532I
b = 0.01240 − 1.66995I
13.5267 + 4.9848I 0
u = 0.414901 + 0.112651I
a = −0.19032 + 3.03332I
b = 0.365746 + 0.532815I
3.75166 − 1.38468I −10.94065 + 4.57640I
u = 0.414901 − 0.112651I
a = −0.19032 − 3.03332I
b = 0.365746 − 0.532815I
3.75166 + 1.38468I −10.94065 − 4.57640I
u = −0.310404
a = −0.683642
b = −0.308825
−0.534005 −18.4650
13
II.
I
u
2
= h−u
16
− u
15
+ · · · + b − 3, −u
14
− u
13
+ · · · + a + 2, u
17
+ u
16
+ · · · + u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
11
=
u
14
+ u
13
+ ··· + 5u
2
− 2
u
16
+ u
15
+ ··· − 10u
2
+ 3
a
5
=
−u
13
− u
12
+ 2u
11
+ 2u
10
− 5u
9
− 4u
8
+ 4u
7
+ 3u
6
− 5u
5
− 3u
4
+ u
3
+ u
2
−2u
16
− u
15
+ ··· + 6u
2
− 2u
a
12
=
−u
16
− u
15
+ ··· + u − 1
−2u
16
− 2u
15
+ ··· + 2u − 4
a
4
=
u
14
− 3u
12
+ 7u
10
− u
9
− 9u
8
+ u
7
+ 10u
6
− 2u
5
− 7u
4
− u
3
+ 3u
2
+ u − 1
3u
16
+ u
15
+ ··· + 3u + 2
a
10
=
u
16
+ u
15
+ ··· − 5u
2
+ 1
u
16
+ u
15
+ ··· − 10u
2
+ 3
a
8
=
−u
4
+ u
2
− 1
u
16
− u
15
+ ··· + 3u − 1
a
9
=
u
16
− 3u
14
+ ··· + u + 1
u
16
+ u
15
+ ··· − 9u
2
+ 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
16
+ 5u
15
+ 11u
14
− 14u
13
− 28u
12
+ 38u
11
+ 47u
10
− 53u
9
−
58u
8
+ 68u
7
+ 52u
6
− 51u
5
− 40u
4
+ 26u
3
+ 16u
2
− 12u − 11
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
− 7u
16
+ ··· + 7u − 1
c
2
u
17
− u
16
+ ··· + u − 1
c
3
u
17
+ 10u
15
+ ··· + 4u − 3
c
4
, c
5
u
17
+ 12u
15
+ ··· + 7u + 1
c
6
u
17
+ u
16
+ ··· + u + 1
c
7
u
17
+ 3u
16
+ ··· − 3u − 1
c
8
u
17
+ 10u
15
+ ··· + 4u + 3
c
9
u
17
+ 3u
16
+ ··· + u − 1
c
10
, c
11
u
17
+ 12u
15
+ ··· + 7u − 1
c
12
u
17
+ u
16
+ ··· − 3u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
+ 13y
16
+ ··· − 13y −1
c
2
, c
6
y
17
− 7y
16
+ ··· + 7y −1
c
3
, c
8
y
17
+ 20y
16
+ ··· + 10y −9
c
4
, c
5
, c
10
c
11
y
17
+ 24y
16
+ ··· + 35y −1
c
7
y
17
+ 3y
16
+ ··· − y −1
c
9
y
17
− y
16
+ ··· − 3y −1
c
12
y
17
+ 3y
16
+ ··· + y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.720152 + 0.656706I
a = 0.79944 + 1.95784I
b = 0.319931 − 0.860450I
5.06979 + 2.15267I −5.68896 − 4.26478I
u = −0.720152 − 0.656706I
a = 0.79944 − 1.95784I
b = 0.319931 + 0.860450I
5.06979 − 2.15267I −5.68896 + 4.26478I
u = 0.844913 + 0.200306I
a = −1.65011 + 0.63197I
b = −0.092358 − 1.290120I
1.30360 − 0.87814I −15.0870 − 0.5641I
u = 0.844913 − 0.200306I
a = −1.65011 − 0.63197I
b = −0.092358 + 1.290120I
1.30360 + 0.87814I −15.0870 + 0.5641I
u = −0.862236
a = −1.51495
b = −0.147176
−2.99854 −8.51500
u = 0.776801 + 0.839562I
a = 0.78100 − 2.66977I
b = 0.02762 + 1.69581I
14.4535 − 3.1568I −3.79045 + 2.68402I
u = 0.776801 − 0.839562I
a = 0.78100 + 2.66977I
b = 0.02762 − 1.69581I
14.4535 + 3.1568I −3.79045 − 2.68402I
u = −0.942687 + 0.675044I
a = 0.574582 + 0.958429I
b = −0.246755 − 1.006550I
4.37714 + 3.08094I −6.66676 − 2.63554I
u = −0.942687 − 0.675044I
a = 0.574582 − 0.958429I
b = −0.246755 + 1.006550I
4.37714 − 3.08094I −6.66676 + 2.63554I
u = 0.626628 + 0.526088I
a = 0.105161 − 0.770507I
b = 0.374391 − 0.661733I
4.43105 + 0.41822I −4.85621 − 0.33566I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.626628 − 0.526088I
a = 0.105161 + 0.770507I
b = 0.374391 + 0.661733I
4.43105 − 0.41822I −4.85621 + 0.33566I
u = 1.084210 + 0.640691I
a = −0.553437 + 0.314492I
b = −0.309644 − 0.517094I
2.82046 − 5.17696I −5.91305 + 8.94380I
u = 1.084210 − 0.640691I
a = −0.553437 − 0.314492I
b = −0.309644 + 0.517094I
2.82046 + 5.17696I −5.91305 − 8.94380I
u = −0.541603 + 0.427521I
a = −0.051956 − 0.620358I
b = 0.09256 + 1.67798I
12.88990 − 2.20254I −1.59840 − 1.45365I
u = −0.541603 − 0.427521I
a = −0.051956 + 0.620358I
b = 0.09256 − 1.67798I
12.88990 + 2.20254I −1.59840 + 1.45365I
u = −1.196990 + 0.623400I
a = −1.24721 − 0.98437I
b = −0.09216 + 1.61922I
10.43660 + 6.68767I −4.14164 − 6.03567I
u = −1.196990 − 0.623400I
a = −1.24721 + 0.98437I
b = −0.09216 − 1.61922I
10.43660 − 6.68767I −4.14164 + 6.03567I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
17
− 7u
16
+ ··· + 7u − 1)(u
85
+ 30u
84
+ ··· + 17713u + 361)
c
2
(u
17
− u
16
+ ··· + u − 1)(u
85
− 2u
84
+ ··· − 29u + 19)
c
3
(u
17
+ 10u
15
+ ··· + 4u − 3)(u
85
− u
84
+ ··· + 26u + 19)
c
4
, c
5
(u
17
+ 12u
15
+ ··· + 7u + 1)(u
85
+ u
84
+ ··· − 13u + 1)
c
6
(u
17
+ u
16
+ ··· + u + 1)(u
85
− 2u
84
+ ··· − 29u + 19)
c
7
(u
17
+ 3u
16
+ ··· − 3u − 1)(u
85
− 14u
84
+ ··· − 548721u + 148409)
c
8
(u
17
+ 10u
15
+ ··· + 4u + 3)(u
85
− u
84
+ ··· + 26u + 19)
c
9
(u
17
+ 3u
16
+ ··· + u − 1)(u
85
+ 4u
84
+ ··· + 15735u + 2737)
c
10
, c
11
(u
17
+ 12u
15
+ ··· + 7u − 1)(u
85
+ u
84
+ ··· − 13u + 1)
c
12
(u
17
+ u
16
+ ··· − 3u + 1)(u
85
− 2u
84
+ ··· − 405993u + 904999)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
17
+ 13y
16
+ ··· − 13y −1)
· (y
85
+ 58y
84
+ ··· + 17060353y −130321)
c
2
, c
6
(y
17
− 7y
16
+ ··· + 7y −1)(y
85
− 30y
84
+ ··· + 17713y −361)
c
3
, c
8
(y
17
+ 20y
16
+ ··· + 10y −9)(y
85
+ 77y
84
+ ··· − 5556y −361)
c
4
, c
5
, c
10
c
11
(y
17
+ 24y
16
+ ··· + 35y −1)(y
85
+ 109y
84
+ ··· − 127y −1)
c
7
(y
17
+ 3y
16
+ ··· − y −1)
· (y
85
+ 36y
84
+ ··· − 93911252195y −22025231281)
c
9
(y
17
− y
16
+ ··· − 3y −1)(y
85
+ 20y
84
+ ··· + 4057439y −7491169)
c
12
(y
17
+ 3y
16
+ ··· + y −1)
· (y
85
+ 44y
84
+ ··· − 15920612859961y −819023190001)
20
