11a
279
(K11a
279
)
A knot diagram
1
Linearized knot diagam
6 9 1 10 2 4 11 3 5 7 8
Solving Sequence
7,11
8
1,4
3 6 2 10 5 9
c
7
c
11
c
3
c
6
c
1
c
10
c
4
c
9
c
2
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−207u
22
+ 1583u
21
+ ··· + 4b − 1196, −703u
22
+ 5325u
21
+ ··· + 8a − 3908,
u
23
− 9u
22
+ ··· − 16u − 8i
I
u
2
= h−67075021335a
5
u
5
− 139677423007u
5
a
4
+ ··· + 70899952257a − 101012825507,
a
5
u
5
− 8u
5
a
4
+ ··· − 56a + 146, u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1i
I
u
3
= hu
13
+ u
12
− 6u
11
− 6u
10
+ 13u
9
+ 12u
8
− 15u
7
− 10u
6
+ 14u
5
+ 5u
4
− 8u
3
− u
2
+ b + 2u,
u
11
− 6u
9
+ 13u
7
− u
6
− 14u
5
+ 4u
4
+ 10u
3
− 5u
2
+ a − 3u + 2,
u
14
+ 2u
13
− 6u
12
− 13u
11
+ 13u
10
+ 31u
9
− 15u
8
− 36u
7
+ 15u
6
+ 26u
5
− 11u
4
− 12u
3
+ 3u
2
+ 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 73 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−207u
22
+ 1583u
21
+ · · · + 4b − 1196, −703u
22
+ 5325u
21
+ · · · +
8a − 3908, u
23
− 9u
22
+ · · · − 16u − 8i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u
2
a
1
=
−u
−u
3
+ u
a
4
=
87.8750u
22
− 665.625u
21
+ ··· + 1316.50u + 488.500
207
4
u
22
−
1583
4
u
21
+ ··· +
1625
2
u + 299
a
3
=
17.8750u
22
− 127.625u
21
+ ··· + 189.500u + 74.5000
23
4
u
22
−
107
4
u
21
+ ··· −
185
2
u − 23
a
6
=
−27u
22
+ 202u
21
+ ··· −
737
2
u −
279
2
−
41
2
u
22
+ 155u
21
+ ··· −
599
2
u − 112
a
2
=
−
89
2
u
22
+
1365
4
u
21
+ ··· −
2899
4
u − 264
−
127
4
u
22
+
973
4
u
21
+ ··· − 523u − 190
a
10
=
u
u
a
5
=
2.87500u
22
− 31.6250u
21
+ ··· + 143.500u + 46.5000
−
133
4
u
22
+
953
4
u
21
+ ··· −
721
2
u − 143
a
9
=
−14u
22
+ 106u
21
+ ··· −
403
2
u −
151
2
−20u
22
+
305
2
u
21
+ ··· −
599
2
u − 112
a
9
=
−14u
22
+ 106u
21
+ ··· −
403
2
u −
151
2
−20u
22
+
305
2
u
21
+ ··· −
599
2
u − 112
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 170u
22
− 1286u
21
+ 3085u
20
− 847u
19
− 4606u
18
− 3555u
17
+ 14615u
16
+ 14163u
15
−
31843u
14
− 26814u
13
+ 25733u
12
+ 61934u
11
− 11560u
10
− 75044u
9
− 12076u
8
+
43840u
7
+ 41946u
6
− 26305u
5
− 16870u
4
− 1708u
3
+ 3903u
2
+ 2554u + 954
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
23
− 14u
22
+ ··· + 608u − 64
c
2
, c
4
, c
8
c
9
u
23
+ 12u
21
+ ··· + 2u + 1
c
3
, c
6
u
23
− 2u
22
+ ··· − 10u − 1
c
7
, c
10
, c
11
u
23
+ 9u
22
+ ··· − 16u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
23
+ 12y
22
+ ··· − 3072y −4096
c
2
, c
4
, c
8
c
9
y
23
+ 24y
22
+ ··· + 2y −1
c
3
, c
6
y
23
− 16y
22
+ ··· + 58y −1
c
7
, c
10
, c
11
y
23
− 23y
22
+ ··· − 32y −64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.967745 + 0.381665I
a = 0.201884 + 0.414286I
b = −0.183628 − 0.001198I
−1.61771 − 1.40406I −4.39049 − 3.86592I
u = 0.967745 − 0.381665I
a = 0.201884 − 0.414286I
b = −0.183628 + 0.001198I
−1.61771 + 1.40406I −4.39049 + 3.86592I
u = −0.698852 + 0.821638I
a = 0.477872 + 0.534934I
b = 1.29859 − 0.66746I
−10.9998 + 10.3816I −5.93991 − 6.82804I
u = −0.698852 − 0.821638I
a = 0.477872 − 0.534934I
b = 1.29859 + 0.66746I
−10.9998 − 10.3816I −5.93991 + 6.82804I
u = −0.497254 + 0.985536I
a = −0.155208 + 0.547360I
b = 1.111120 + 0.180964I
−10.27160 − 4.44360I −7.21311 + 2.51122I
u = −0.497254 − 0.985536I
a = −0.155208 − 0.547360I
b = 1.111120 − 0.180964I
−10.27160 + 4.44360I −7.21311 − 2.51122I
u = −1.143500 + 0.155903I
a = −0.153289 + 0.400091I
b = −0.166969 + 1.049480I
−2.11154 + 2.89602I −5.87366 − 5.40163I
u = −1.143500 − 0.155903I
a = −0.153289 − 0.400091I
b = −0.166969 − 1.049480I
−2.11154 − 2.89602I −5.87366 + 5.40163I
u = −0.712264 + 0.994425I
a = −0.160694 − 0.410443I
b = −1.026660 + 0.292744I
−5.31535 + 3.36271I −7.37506 − 4.35567I
u = −0.712264 − 0.994425I
a = −0.160694 + 0.410443I
b = −1.026660 − 0.292744I
−5.31535 − 3.36271I −7.37506 + 4.35567I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.42821
a = 1.51970
b = 0.929418
−3.83839 0.512880
u = 1.48911 + 0.05545I
a = −1.87603 − 0.45482I
b = −1.31072 − 0.53567I
−6.91782 − 3.55772I −4.11987 + 3.22917I
u = 1.48911 − 0.05545I
a = −1.87603 + 0.45482I
b = −1.31072 + 0.53567I
−6.91782 + 3.55772I −4.11987 − 3.22917I
u = −0.406359 + 0.227585I
a = −1.54270 + 0.18400I
b = −0.725818 + 0.732059I
−0.62578 + 2.55105I 5.72447 − 4.75724I
u = −0.406359 − 0.227585I
a = −1.54270 − 0.18400I
b = −0.725818 − 0.732059I
−0.62578 − 2.55105I 5.72447 + 4.75724I
u = −0.089013 + 0.421365I
a = 1.053790 + 0.259361I
b = 0.043793 − 0.543989I
0.762182 − 0.859530I 5.83936 + 4.64887I
u = −0.089013 − 0.421365I
a = 1.053790 − 0.259361I
b = 0.043793 + 0.543989I
0.762182 + 0.859530I 5.83936 − 4.64887I
u = 1.60902 + 0.26327I
a = 1.77485 − 0.04465I
b = 1.64226 + 0.99576I
−18.6220 − 14.4160I −7.82251 + 6.36300I
u = 1.60902 − 0.26327I
a = 1.77485 + 0.04465I
b = 1.64226 − 0.99576I
−18.6220 + 14.4160I −7.82251 − 6.36300I
u = 1.62187 + 0.36588I
a = 0.952251 − 0.437186I
b = 1.191870 + 0.399326I
−17.1859 − 0.6728I −9.48576 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.62187 − 0.36588I
a = 0.952251 + 0.437186I
b = 1.191870 − 0.399326I
−17.1859 + 0.6728I −9.48576 + 0.I
u = 1.64539 + 0.28873I
a = −1.332570 + 0.052250I
b = −1.33854 − 0.83024I
−13.1794 − 8.0766I −6.59988 + 4.65013I
u = 1.64539 − 0.28873I
a = −1.332570 − 0.052250I
b = −1.33854 + 0.83024I
−13.1794 + 8.0766I −6.59988 − 4.65013I
7
II. I
u
2
= h−6.71 × 10
10
a
5
u
5
− 1.40 × 10
11
a
4
u
5
+ · · · + 7.09 × 10
10
a − 1.01 ×
10
11
, a
5
u
5
− 8u
5
a
4
+ · · · − 56a + 146, u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u
2
a
1
=
−u
−u
3
+ u
a
4
=
a
0.371284a
5
u
5
+ 0.773165a
4
u
5
+ ··· − 0.392457a + 0.559142
a
3
=
0.170270a
5
u
5
+ 0.0886799a
4
u
5
+ ··· + 0.698794a − 0.338523
−0.0269564a
5
u
5
+ 0.359586a
4
u
5
+ ··· − 0.193734a + 0.241379
a
6
=
−0.213956a
5
u
5
− 0.218275a
4
u
5
+ ··· − 0.238216a − 1.06457
−0.561901a
5
u
5
− 0.0721808a
4
u
5
+ ··· + 2.14554a + 0.0866807
a
2
=
0.258733a
5
u
5
+ 0.471591a
4
u
5
+ ··· + 1.67688a − 1.32875
0.378233a
5
u
5
+ 0.298414a
4
u
5
+ ··· − 1.26568a + 2.33162
a
10
=
u
u
a
5
=
0.170270a
5
u
5
+ 0.0886799a
4
u
5
+ ··· + 0.698794a − 0.338523
0.541554a
5
u
5
+ 0.861845a
4
u
5
+ ··· − 0.693662a + 0.220619
a
9
=
0.0275530a
5
u
5
− 0.0220361a
4
u
5
+ ··· − 0.143100a − 1.01359
−0.371225a
5
u
5
− 0.710937a
4
u
5
+ ··· − 0.730561a + 1.33567
a
9
=
0.0275530a
5
u
5
− 0.0220361a
4
u
5
+ ··· − 0.143100a − 1.01359
−0.371225a
5
u
5
− 0.710937a
4
u
5
+ ··· − 0.730561a + 1.33567
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
345052934836
180656766347
a
5
u
5
+
45427860044
180656766347
u
5
a
4
+ ··· +
176923926364
180656766347
a −
1401640745238
180656766347
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
3
+ u
2
+ 2u + 1)
12
c
2
, c
4
, c
8
c
9
u
36
+ u
35
+ ··· − 62u + 59
c
3
, c
6
u
36
− 7u
35
+ ··· − 12064u + 1913
c
7
, c
10
, c
11
(u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
6
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
3
+ 3y
2
+ 2y −1)
12
c
2
, c
4
, c
8
c
9
y
36
+ 35y
35
+ ··· − 69452y + 3481
c
3
, c
6
y
36
− 17y
35
+ ··· − 71361608y + 3659569
c
7
, c
10
, c
11
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
6
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.493180 + 0.575288I
a = 0.740979 − 0.192185I
b = 0.450829 + 0.179718I
−0.86110 − 1.97241I 2.44379 + 3.68478I
u = 0.493180 + 0.575288I
a = 0.278434 − 0.615278I
b = 1.47772 + 0.68516I
−4.99869 − 4.80053I −4.08548 + 6.66423I
u = 0.493180 + 0.575288I
a = −0.091295 + 0.628827I
b = −0.824811 − 0.438466I
−0.86110 − 1.97241I 2.44379 + 3.68478I
u = 0.493180 + 0.575288I
a = −0.30781 − 1.40775I
b = 0.983052 − 0.169478I
−4.99869 + 0.85571I −4.08548 + 0.70533I
u = 0.493180 + 0.575288I
a = −1.46445 + 0.74881I
b = −0.787709 − 0.753418I
−4.99869 − 4.80053I −4.08548 + 6.66423I
u = 0.493180 + 0.575288I
a = −0.016507 + 0.259156I
b = −0.803665 + 0.839255I
−4.99869 + 0.85571I −4.08548 + 0.70533I
u = 0.493180 − 0.575288I
a = 0.740979 + 0.192185I
b = 0.450829 − 0.179718I
−0.86110 + 1.97241I 2.44379 − 3.68478I
u = 0.493180 − 0.575288I
a = 0.278434 + 0.615278I
b = 1.47772 − 0.68516I
−4.99869 + 4.80053I −4.08548 − 6.66423I
u = 0.493180 − 0.575288I
a = −0.091295 − 0.628827I
b = −0.824811 + 0.438466I
−0.86110 + 1.97241I 2.44379 − 3.68478I
u = 0.493180 − 0.575288I
a = −0.30781 + 1.40775I
b = 0.983052 + 0.169478I
−4.99869 − 0.85571I −4.08548 − 0.70533I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.493180 − 0.575288I
a = −1.46445 − 0.74881I
b = −0.787709 + 0.753418I
−4.99869 + 4.80053I −4.08548 − 6.66423I
u = 0.493180 − 0.575288I
a = −0.016507 − 0.259156I
b = −0.803665 − 0.839255I
−4.99869 − 0.85571I −4.08548 − 0.70533I
u = −0.483672
a = 0.56022 + 1.30558I
b = 1.14384 − 1.41582I
−8.69778 − 2.82812I −12.92653 + 2.97945I
u = −0.483672
a = 0.56022 − 1.30558I
b = 1.14384 + 1.41582I
−8.69778 + 2.82812I −12.92653 − 2.97945I
u = −0.483672
a = −1.14171 + 2.07722I
b = −0.819304 − 0.518752I
−4.56020 −6.39727 + 0.I
u = −0.483672
a = −1.14171 − 2.07722I
b = −0.819304 + 0.518752I
−4.56020 −6.39727 + 0.I
u = −0.483672
a = 2.09393 + 3.55870I
b = 0.760815 + 0.201046I
−8.69778 + 2.82812I −12.92653 − 2.97945I
u = −0.483672
a = 2.09393 − 3.55870I
b = 0.760815 − 0.201046I
−8.69778 − 2.82812I −12.92653 + 2.97945I
u = −1.52087 + 0.16310I
a = 1.132330 + 0.632859I
b = 0.990662 − 0.420388I
−11.65450 + 1.76400I −8.09089 − 0.22537I
u = −1.52087 + 0.16310I
a = 1.46325 + 0.14079I
b = 0.986534 − 0.078657I
−7.51693 + 4.59213I −1.56163 − 3.20482I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.52087 + 0.16310I
a = −1.15205 − 0.98203I
b = −1.29593 − 0.89600I
−11.65450 + 1.76400I −8.09089 − 0.22537I
u = −1.52087 + 0.16310I
a = −1.60159 + 0.04217I
b = −1.39264 + 0.86643I
−7.51693 + 4.59213I −1.56163 − 3.20482I
u = −1.52087 + 0.16310I
a = −1.99126 + 0.06689I
b = −0.995465 + 0.542799I
−11.65450 + 7.42025I −8.09089 − 6.18427I
u = −1.52087 + 0.16310I
a = 2.33259 − 0.14304I
b = 2.24483 − 1.05775I
−11.65450 + 7.42025I −8.09089 − 6.18427I
u = −1.52087 − 0.16310I
a = 1.132330 − 0.632859I
b = 0.990662 + 0.420388I
−11.65450 − 1.76400I −8.09089 + 0.22537I
u = −1.52087 − 0.16310I
a = 1.46325 − 0.14079I
b = 0.986534 + 0.078657I
−7.51693 − 4.59213I −1.56163 + 3.20482I
u = −1.52087 − 0.16310I
a = −1.15205 + 0.98203I
b = −1.29593 + 0.89600I
−11.65450 − 1.76400I −8.09089 + 0.22537I
u = −1.52087 − 0.16310I
a = −1.60159 − 0.04217I
b = −1.39264 − 0.86643I
−7.51693 − 4.59213I −1.56163 + 3.20482I
u = −1.52087 − 0.16310I
a = −1.99126 − 0.06689I
b = −0.995465 − 0.542799I
−11.65450 − 7.42025I −8.09089 + 6.18427I
u = −1.52087 − 0.16310I
a = 2.33259 + 0.14304I
b = 2.24483 + 1.05775I
−11.65450 − 7.42025I −8.09089 + 6.18427I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.53904
a = −1.256830 + 0.322591I
b = −1.04268 + 1.26059I
−11.4814 −5.24999 + 0.I
u = 1.53904
a = −1.256830 − 0.322591I
b = −1.04268 − 1.26059I
−11.4814 −5.24999 + 0.I
u = 1.53904
a = 1.35561 + 0.87104I
b = 0.800589 − 0.413513I
−15.6190 + 2.8281I −11.77925 − 2.97945I
u = 1.53904
a = 1.35561 − 0.87104I
b = 0.800589 + 0.413513I
−15.6190 − 2.8281I −11.77925 + 2.97945I
u = 1.53904
a = 1.56616 + 1.60926I
b = 1.62334 + 2.47120I
−15.6190 + 2.8281I −11.77925 − 2.97945I
u = 1.53904
a = 1.56616 − 1.60926I
b = 1.62334 − 2.47120I
−15.6190 − 2.8281I −11.77925 + 2.97945I
14
III.
I
u
3
= hu
13
+ u
12
+ · · · +b + 2u, u
11
− 6u
9
+ · · · +a + 2, u
14
+ 2u
13
+ · · · +2u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u
2
a
1
=
−u
−u
3
+ u
a
4
=
−u
11
+ 6u
9
− 13u
7
+ u
6
+ 14u
5
− 4u
4
− 10u
3
+ 5u
2
+ 3u − 2
−u
13
− u
12
+ ··· + u
2
− 2u
a
3
=
u
13
− 8u
11
+ 25u
9
− 39u
7
+ 2u
6
+ 35u
5
− 7u
4
− 21u
3
+ 6u
2
+ 5u − 1
u
13
− 7u
11
+ ··· − u + 1
a
6
=
−3u
13
− 3u
12
+ ··· + 2u
2
− 8u
−u
13
− u
12
+ ··· − 3u
2
+ 2u
a
2
=
2u
13
+ 2u
12
+ ··· + 9u + 5
u
13
− 8u
11
+ 24u
9
− u
8
− 35u
7
+ 5u
6
+ 29u
5
− 9u
4
− 16u
3
+ 6u
2
+ 3u
a
10
=
u
u
a
5
=
−u
13
− u
12
+ ··· + 2u − 3
−2u
13
− 2u
12
+ ··· − 3u − 1
a
9
=
−u
13
− 2u
12
+ ··· − 10u − 1
u
12
+ u
11
+ ··· + u + 1
a
9
=
−u
13
− 2u
12
+ ··· − 10u − 1
u
12
+ u
11
+ ··· + u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −2u
13
+ 16u
11
− 49u
9
+ 3u
8
+ 74u
7
− 15u
6
− 65u
5
+ 24u
4
+ 37u
3
− 13u
2
− 5u − 5
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
− u
13
+ ··· + 2u + 1
c
2
, c
9
u
14
+ 8u
12
+ ··· + u + 1
c
3
, c
6
u
14
+ 2u
13
+ ··· + 5u + 1
c
4
, c
8
u
14
+ 8u
12
+ ··· − u + 1
c
5
u
14
+ u
13
+ ··· − 2u + 1
c
7
u
14
+ 2u
13
+ ··· + 2u + 1
c
10
, c
11
u
14
− 2u
13
+ ··· − 2u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
14
+ 9y
13
+ ··· + 6y + 1
c
2
, c
4
, c
8
c
9
y
14
+ 16y
13
+ ··· + 25y + 1
c
3
, c
6
y
14
− 4y
13
+ ··· − 7y + 1
c
7
, c
10
, c
11
y
14
− 16y
13
+ ··· + 2y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.914089 + 0.533567I
a = 0.165475 − 0.801291I
b = −0.414186 + 0.217927I
−4.27946 + 2.06111I −5.58371 − 2.18778I
u = −0.914089 − 0.533567I
a = 0.165475 + 0.801291I
b = −0.414186 − 0.217927I
−4.27946 − 2.06111I −5.58371 + 2.18778I
u = 0.639246 + 0.615121I
a = −0.398775 + 0.418812I
b = −0.853967 − 0.278506I
−1.91266 − 2.33379I −7.27584 + 5.70217I
u = 0.639246 − 0.615121I
a = −0.398775 − 0.418812I
b = −0.853967 + 0.278506I
−1.91266 + 2.33379I −7.27584 − 5.70217I
u = 0.878231 + 0.123651I
a = −0.362803 − 0.376792I
b = −0.464478 − 0.739423I
−1.38673 − 2.23365I −1.78196 + 2.13694I
u = 0.878231 − 0.123651I
a = −0.362803 + 0.376792I
b = −0.464478 + 0.739423I
−1.38673 + 2.23365I −1.78196 − 2.13694I
u = −1.41453 + 0.15062I
a = 1.54661 + 1.19373I
b = 1.200660 + 0.246781I
−12.27320 + 4.41428I −8.90552 − 3.48503I
u = −1.41453 − 0.15062I
a = 1.54661 − 1.19373I
b = 1.200660 − 0.246781I
−12.27320 − 4.41428I −8.90552 + 3.48503I
u = 1.53841 + 0.05626I
a = 0.092978 + 0.343432I
b = 0.284029 + 1.361390I
−14.1430 + 1.3793I −8.26367 − 0.38542I
u = 1.53841 − 0.05626I
a = 0.092978 − 0.343432I
b = 0.284029 − 1.361390I
−14.1430 − 1.3793I −8.26367 + 0.38542I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.55089 + 0.15006I
a = −1.77076 − 0.02850I
b = −1.48201 + 0.53476I
−9.15749 + 4.88700I −8.41454 − 3.92217I
u = −1.55089 − 0.15006I
a = −1.77076 + 0.02850I
b = −1.48201 − 0.53476I
−9.15749 − 4.88700I −8.41454 + 3.92217I
u = −0.176381 + 0.304536I
a = −3.27272 + 0.24854I
b = 0.729960 − 0.704235I
−7.84036 − 2.64248I −1.77475 + 0.54497I
u = −0.176381 − 0.304536I
a = −3.27272 − 0.24854I
b = 0.729960 + 0.704235I
−7.84036 + 2.64248I −1.77475 − 0.54497I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
3
+ u
2
+ 2u + 1)
12
)(u
14
− u
13
+ ··· + 2u + 1)
· (u
23
− 14u
22
+ ··· + 608u − 64)
c
2
, c
9
(u
14
+ 8u
12
+ ··· + u + 1)(u
23
+ 12u
21
+ ··· + 2u + 1)
· (u
36
+ u
35
+ ··· − 62u + 59)
c
3
, c
6
(u
14
+ 2u
13
+ ··· + 5u + 1)(u
23
− 2u
22
+ ··· − 10u − 1)
· (u
36
− 7u
35
+ ··· − 12064u + 1913)
c
4
, c
8
(u
14
+ 8u
12
+ ··· − u + 1)(u
23
+ 12u
21
+ ··· + 2u + 1)
· (u
36
+ u
35
+ ··· − 62u + 59)
c
5
((u
3
+ u
2
+ 2u + 1)
12
)(u
14
+ u
13
+ ··· − 2u + 1)
· (u
23
− 14u
22
+ ··· + 608u − 64)
c
7
((u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
6
)(u
14
+ 2u
13
+ ··· + 2u + 1)
· (u
23
+ 9u
22
+ ··· − 16u + 8)
c
10
, c
11
((u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
6
)(u
14
− 2u
13
+ ··· − 2u + 1)
· (u
23
+ 9u
22
+ ··· − 16u + 8)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y
3
+ 3y
2
+ 2y −1)
12
)(y
14
+ 9y
13
+ ··· + 6y + 1)
· (y
23
+ 12y
22
+ ··· − 3072y −4096)
c
2
, c
4
, c
8
c
9
(y
14
+ 16y
13
+ ··· + 25y + 1)(y
23
+ 24y
22
+ ··· + 2y −1)
· (y
36
+ 35y
35
+ ··· − 69452y + 3481)
c
3
, c
6
(y
14
− 4y
13
+ ··· − 7y + 1)(y
23
− 16y
22
+ ··· + 58y −1)
· (y
36
− 17y
35
+ ··· − 71361608y + 3659569)
c
7
, c
10
, c
11
((y
6
− 7y
5
+ ··· − 5y + 1)
6
)(y
14
− 16y
13
+ ··· + 2y + 1)
· (y
23
− 23y
22
+ ··· − 32y −64)
21
