11n
115
(K11n
115
)
A knot diagram
1
Linearized knot diagam
7 1 11 10 9 2 10 3 5 8 9
Solving Sequence
3,8 9,10
11 4 5 6 1 2 7
c
8
c
10
c
3
c
4
c
5
c
11
c
2
c
7
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−674u
17
+ 4280u
16
+ ··· + 3857b + 7561, 5911u
17
− 7561u
16
+ ··· + 3857a − 13760,
u
18
+ 2u
16
+ ··· − u + 1i
I
u
2
= h−3.99406 × 10
27
u
29
+ 7.06888 × 10
27
u
28
+ ··· + 4.03786 × 10
28
b + 1.80487 × 10
29
,
4.44913 × 10
33
u
29
− 9.50806 × 10
33
u
28
+ ··· + 2.74816 × 10
34
a − 2.41871 × 10
35
, u
30
− u
29
+ ··· + 4u + 19i
I
u
3
= hu
8
+ 4u
6
+ u
5
+ 4u
4
+ 2u
3
+ 2u
2
+ b + 2, −2u
8
− 9u
6
− 2u
5
− 12u
4
− 5u
3
− 8u
2
+ a − 2u − 5,
u
10
+ 5u
8
+ u
7
+ 8u
6
+ 3u
5
+ 6u
4
+ 2u
3
+ 4u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 58 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−674u
17
+ 4280u
16
+ · · · + 3857b + 7561, 5911u
17
− 7561u
16
+ · · · +
3857a − 13760, u
18
+ 2u
16
+ · · · − u + 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
10
=
−1.53254u
17
+ 1.96033u
16
+ ··· − 7.35364u + 3.56754
0.174747u
17
− 1.10967u
16
+ ··· + 3.49287u − 1.96033
a
11
=
−1.35779u
17
+ 0.850661u
16
+ ··· − 3.86077u + 1.60721
0.174747u
17
− 1.10967u
16
+ ··· + 3.49287u − 1.96033
a
4
=
−0.607208u
17
− 1.35779u
16
+ ··· + 4.77107u − 3.25356
0.850661u
17
+ 0.363754u
16
+ ··· + 0.249417u + 1.35779
a
5
=
−2.56754u
17
− 1.53254u
16
+ ··· + 2.73606u − 4.78610
1.96033u
17
+ 0.174747u
16
+ ··· + 2.03500u + 1.53254
a
6
=
−2.56754u
17
− 1.53254u
16
+ ··· + 1.73606u − 4.78610
1.96033u
17
+ 0.174747u
16
+ ··· + 2.03500u + 1.53254
a
1
=
−1.16878u
17
+ 1.31216u
16
+ ··· − 5.14519u + 2.71688
−0.0674099u
17
− 1.24553u
16
+ ··· + 3.76536u − 2.42183
a
2
=
0.241379u
17
− 1.58621u
16
+ ··· + 6.55172u − 3.72414
−0.710656u
17
+ 0.607726u
16
+ ··· − 2.60824u + 2.05678
a
7
=
−2.19212u
17
+ 0.650246u
16
+ ··· − 5.41872u + 1.14778
0.834327u
17
+ 0.200415u
16
+ ··· + 1.55795u + 0.459424
a
7
=
−2.19212u
17
+ 0.650246u
16
+ ··· − 5.41872u + 1.14778
0.834327u
17
+ 0.200415u
16
+ ··· + 1.55795u + 0.459424
(ii) Obstruction class = −1
(iii) Cusp Shapes =
54335
3857
u
17
+
9431
3857
u
16
+ ··· +
110875
3857
u +
36718
3857
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
18
+ 6u
17
+ ··· + 36u + 8
c
2
u
18
+ 8u
17
+ ··· + 176u + 64
c
3
u
18
+ 2u
17
+ ··· + u + 1
c
4
, c
5
, c
8
c
9
u
18
+ 2u
16
+ ··· + u + 1
c
7
, c
10
u
18
+ 9u
17
+ ··· + 144u + 32
c
11
u
18
− 2u
17
+ ··· + 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
18
+ 8y
17
+ ··· + 176y + 64
c
2
y
18
+ 4y
17
+ ··· + 15104y + 4096
c
3
y
18
+ 16y
17
+ ··· + 45y + 1
c
4
, c
5
, c
8
c
9
y
18
+ 4y
17
+ ··· + 11y + 1
c
7
, c
10
y
18
− 9y
17
+ ··· + 3328y + 1024
c
11
y
18
− 18y
17
+ ··· + 23y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.727352 + 0.735291I
a = 0.005136 − 0.376666I
b = 0.391222 + 1.079500I
−1.41496 − 2.43414I −0.56962 + 3.23695I
u = 0.727352 − 0.735291I
a = 0.005136 + 0.376666I
b = 0.391222 − 1.079500I
−1.41496 + 2.43414I −0.56962 − 3.23695I
u = −1.000950 + 0.529895I
a = −0.163201 − 0.016901I
b = 0.585493 − 0.899860I
−6.19243 − 0.93127I −5.63625 + 0.73799I
u = −1.000950 − 0.529895I
a = −0.163201 + 0.016901I
b = 0.585493 + 0.899860I
−6.19243 + 0.93127I −5.63625 − 0.73799I
u = 0.889387 + 0.824360I
a = −1.39177 − 0.79525I
b = 1.122460 − 0.663095I
−4.47725 − 4.89257I −2.95225 + 5.04135I
u = 0.889387 − 0.824360I
a = −1.39177 + 0.79525I
b = 1.122460 + 0.663095I
−4.47725 + 4.89257I −2.95225 − 5.04135I
u = −0.815454 + 0.912371I
a = −0.255737 + 0.447363I
b = 0.541043 − 1.182370I
−3.92260 + 7.75219I −2.08036 − 6.66160I
u = −0.815454 − 0.912371I
a = −0.255737 − 0.447363I
b = 0.541043 + 1.182370I
−3.92260 − 7.75219I −2.08036 + 6.66160I
u = 0.022331 + 0.744756I
a = 2.05987 − 0.16817I
b = −1.69007 + 0.19497I
5.20575 − 2.93660I 10.23255 + 0.78681I
u = 0.022331 − 0.744756I
a = 2.05987 + 0.16817I
b = −1.69007 − 0.19497I
5.20575 + 2.93660I 10.23255 − 0.78681I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.170147 + 0.689243I
a = −3.56038 + 0.93433I
b = 1.361340 + 0.183714I
4.99266 + 3.58040I 11.7317 − 10.3370I
u = −0.170147 − 0.689243I
a = −3.56038 − 0.93433I
b = 1.361340 − 0.183714I
4.99266 − 3.58040I 11.7317 + 10.3370I
u = −0.759355 + 1.116940I
a = −1.62765 + 0.48098I
b = 1.23701 + 0.74198I
1.13316 + 8.99334I 2.75713 − 6.03184I
u = −0.759355 − 1.116940I
a = −1.62765 − 0.48098I
b = 1.23701 − 0.74198I
1.13316 − 8.99334I 2.75713 + 6.03184I
u = 0.248460 + 0.469643I
a = 0.948209 − 0.220971I
b = −0.257868 + 0.489761I
−0.097050 − 1.164640I −1.13861 + 6.02305I
u = 0.248460 − 0.469643I
a = 0.948209 + 0.220971I
b = −0.257868 − 0.489761I
−0.097050 + 1.164640I −1.13861 − 6.02305I
u = 0.85837 + 1.24910I
a = −1.51448 − 0.36642I
b = 1.20938 − 0.80152I
−1.8070 − 14.7634I 0.15571 + 8.71478I
u = 0.85837 − 1.24910I
a = −1.51448 + 0.36642I
b = 1.20938 + 0.80152I
−1.8070 + 14.7634I 0.15571 − 8.71478I
6
II.
I
u
2
= h−3.99×10
27
u
29
+7.07×10
27
u
28
+· · ·+4.04×10
28
b+1.80×10
29
, 4.45×
10
33
u
29
−9.51×10
33
u
28
+· · ·+2.75×10
34
a−2.42×10
35
, u
30
−u
29
+· · ·+4u+19i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
10
=
−0.161895u
29
+ 0.345979u
28
+ ··· − 16.7463u + 8.80118
0.0989152u
29
− 0.175065u
28
+ ··· + 3.29797u − 4.46987
a
11
=
−0.0629794u
29
+ 0.170914u
28
+ ··· − 13.4483u + 4.33131
0.0989152u
29
− 0.175065u
28
+ ··· + 3.29797u − 4.46987
a
4
=
−0.316971u
29
+ 0.590127u
28
+ ··· − 27.3471u + 10.7433
0.176327u
29
− 0.254041u
28
+ ··· + 8.35983u − 4.03217
a
5
=
0.00623793u
29
+ 0.145908u
28
+ ··· − 4.22733u + 10.5731
−0.0140293u
29
− 0.0647144u
28
+ ··· − 3.03553u − 3.76001
a
6
=
−0.0130929u
29
+ 0.205656u
28
+ ··· − 1.91890u + 11.4423
−0.00894659u
29
− 0.0916273u
28
+ ··· − 2.82991u − 4.52791
a
1
=
−0.215063u
29
+ 0.358791u
28
+ ··· − 15.9814u + 6.75042
0.193888u
29
− 0.280534u
28
+ ··· + 6.04439u − 5.14994
a
2
=
−0.444660u
29
+ 0.619051u
28
+ ··· − 23.4202u + 6.77557
0.135606u
29
− 0.158420u
28
+ ··· + 2.39399u − 0.503494
a
7
=
0.158988u
29
− 0.0254505u
28
+ ··· + 7.44679u + 5.85736
0.0532312u
29
− 0.0104417u
28
+ ··· + 7.25020u + 3.35135
a
7
=
0.158988u
29
− 0.0254505u
28
+ ··· + 7.44679u + 5.85736
0.0532312u
29
− 0.0104417u
28
+ ··· + 7.25020u + 3.35135
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.436420u
29
− 0.254006u
28
+ ··· + 22.7490u + 12.5484
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
6
c
2
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
6
c
3
u
30
+ 3u
29
+ ··· − 138u + 77
c
4
, c
5
, c
8
c
9
u
30
+ u
29
+ ··· − 4u + 19
c
7
, c
10
(u
3
− u
2
+ 1)
10
c
11
u
30
− 5u
29
+ ··· − 182u + 347
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
6
c
2
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
6
c
3
y
30
− 5y
29
+ ··· + 19456y + 5929
c
4
, c
5
, c
8
c
9
y
30
+ 15y
29
+ ··· + 6520y + 361
c
7
, c
10
(y
3
− y
2
+ 2y −1)
10
c
11
y
30
+ 3y
29
+ ··· + 526240y + 120409
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.097323 + 0.949937I
a = 1.212260 + 0.728023I
b = −0.877439 + 0.744862I
1.58157 − 4.35870I 1.97513 + 7.41010I
u = 0.097323 − 0.949937I
a = 1.212260 − 0.728023I
b = −0.877439 − 0.744862I
1.58157 + 4.35870I 1.97513 − 7.41010I
u = −0.894293 + 0.564111I
a = 0.362652 − 0.392414I
b = −0.877439 + 0.744862I
−0.49041 − 2.82812I 1.00910 + 2.97945I
u = −0.894293 − 0.564111I
a = 0.362652 + 0.392414I
b = −0.877439 − 0.744862I
−0.49041 + 2.82812I 1.00910 − 2.97945I
u = −0.346958 + 0.849386I
a = −0.65987 + 1.62762I
b = 0.754878
3.64718 7.53837 + 0.I
u = −0.346958 − 0.849386I
a = −0.65987 − 1.62762I
b = 0.754878
3.64718 7.53837 + 0.I
u = −0.882791 + 0.663108I
a = 0.444698 − 0.115781I
b = −0.877439 − 0.744862I
1.58157 + 4.35870I 1.97513 − 7.41010I
u = −0.882791 − 0.663108I
a = 0.444698 + 0.115781I
b = −0.877439 + 0.744862I
1.58157 − 4.35870I 1.97513 + 7.41010I
u = 0.904883 + 0.733963I
a = 0.085071 − 0.822649I
b = 0.754878
0.17569 − 4.40083I 4.27520 + 3.49859I
u = 0.904883 − 0.733963I
a = 0.085071 + 0.822649I
b = 0.754878
0.17569 + 4.40083I 4.27520 − 3.49859I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.585019 + 1.018790I
a = 0.740198 + 0.101986I
b = −0.877439 + 0.744862I
1.58157 − 1.29754I 1.97513 − 1.45120I
u = 0.585019 − 1.018790I
a = 0.740198 − 0.101986I
b = −0.877439 − 0.744862I
1.58157 + 1.29754I 1.97513 + 1.45120I
u = 0.632383 + 1.027640I
a = 1.49597 + 0.29038I
b = −0.877439 + 0.744862I
−0.49041 − 2.82812I 1.00910 + 2.97945I
u = 0.632383 − 1.027640I
a = 1.49597 − 0.29038I
b = −0.877439 − 0.744862I
−0.49041 + 2.82812I 1.00910 − 2.97945I
u = −0.842320 + 0.905421I
a = 1.63420 − 0.29238I
b = −0.877439 − 0.744862I
−3.96189 − 1.57271I −2.25407 + 0.51914I
u = −0.842320 − 0.905421I
a = 1.63420 + 0.29238I
b = −0.877439 + 0.744862I
−3.96189 + 1.57271I −2.25407 − 0.51914I
u = 0.860992 + 0.996268I
a = 0.509484 + 0.372562I
b = −0.877439 − 0.744862I
−3.96189 − 1.57271I −2.25407 + 0.51914I
u = 0.860992 − 0.996268I
a = 0.509484 − 0.372562I
b = −0.877439 + 0.744862I
−3.96189 + 1.57271I −2.25407 − 0.51914I
u = −0.096403 + 0.609074I
a = −2.26622 − 2.93679I
b = 0.754878
0.17569 + 4.40083I 4.27520 − 3.49859I
u = −0.096403 − 0.609074I
a = −2.26622 + 2.93679I
b = 0.754878
0.17569 − 4.40083I 4.27520 + 3.49859I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.70579 + 1.22794I
a = 1.52684 − 0.39422I
b = −0.877439 − 0.744862I
−3.96189 + 7.22895I −2.25407 − 6.47803I
u = −0.70579 − 1.22794I
a = 1.52684 + 0.39422I
b = −0.877439 + 0.744862I
−3.96189 − 7.22895I −2.25407 + 6.47803I
u = 1.29743 + 0.57947I
a = 0.408301 + 0.277952I
b = −0.877439 − 0.744862I
−3.96189 + 7.22895I −2.25407 − 6.47803I
u = 1.29743 − 0.57947I
a = 0.408301 − 0.277952I
b = −0.877439 + 0.744862I
−3.96189 − 7.22895I −2.25407 + 6.47803I
u = 0.02684 + 1.44366I
a = −1.83443 + 0.27491I
b = 0.754878
5.71916 − 1.53058I 8.50440 + 4.43065I
u = 0.02684 − 1.44366I
a = −1.83443 − 0.27491I
b = 0.754878
5.71916 + 1.53058I 8.50440 − 4.43065I
u = 0.067135 + 0.495411I
a = 1.17711 − 1.53101I
b = −0.877439 − 0.744862I
1.58157 + 1.29754I 1.97513 + 1.45120I
u = 0.067135 − 0.495411I
a = 1.17711 + 1.53101I
b = −0.877439 + 0.744862I
1.58157 − 1.29754I 1.97513 − 1.45120I
u = −0.20344 + 1.75702I
a = −0.888896 + 0.183201I
b = 0.754878
5.71916 + 1.53058I 8.50440 − 4.43065I
u = −0.20344 − 1.75702I
a = −0.888896 − 0.183201I
b = 0.754878
5.71916 − 1.53058I 8.50440 + 4.43065I
12
III. I
u
3
= hu
8
+ 4u
6
+ u
5
+ 4u
4
+ 2u
3
+ 2u
2
+ b + 2, −2u
8
− 9u
6
+ · · · + a −
5, u
10
+ 5u
8
+ · · · + 4u
2
+ 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
10
=
2u
8
+ 9u
6
+ 2u
5
+ 12u
4
+ 5u
3
+ 8u
2
+ 2u + 5
−u
8
− 4u
6
− u
5
− 4u
4
− 2u
3
− 2u
2
− 2
a
11
=
u
8
+ 5u
6
+ u
5
+ 8u
4
+ 3u
3
+ 6u
2
+ 2u + 3
−u
8
− 4u
6
− u
5
− 4u
4
− 2u
3
− 2u
2
− 2
a
4
=
2u
9
+ 9u
7
+ 2u
6
+ 11u
5
+ 5u
4
+ 4u
3
+ u
2
+ 3u − 2
−u
9
− 5u
7
− u
6
− 8u
5
− 3u
4
− 6u
3
− 2u
2
− 3u
a
5
=
4u
9
+ 18u
7
+ 4u
6
+ 23u
5
+ 10u
4
+ 12u
3
+ 3u
2
+ 8u − 2
−2u
9
− 9u
7
− 2u
6
− 12u
5
− 5u
4
− 8u
3
− 2u
2
− 5u
a
6
=
4u
9
+ 18u
7
+ 4u
6
+ 23u
5
+ 10u
4
+ 12u
3
+ 3u
2
+ 9u − 2
−2u
9
− 9u
7
− 2u
6
− 12u
5
− 5u
4
− 7u
3
− 2u
2
− 5u
a
1
=
2u
8
+ 9u
6
+ 2u
5
+ 12u
4
+ 5u
3
+ 7u
2
+ 2u + 4
−2u
8
− 8u
6
− 2u
5
− 9u
4
− 4u
3
− 5u
2
− 3
a
2
=
3u
9
+ u
8
+ 14u
7
+ 7u
6
+ 20u
5
+ 12u
4
+ 13u
3
+ 4u
2
+ 9u − 1
−2u
9
− 2u
8
− 10u
7
− 10u
6
− 17u
5
− 15u
4
− 13u
3
− 8u
2
− 6u − 2
a
7
=
u
9
− 2u
8
+ 4u
7
− 9u
6
+ 2u
5
− 13u
4
− 4u
3
− 9u
2
− u − 6
−u
9
+ u
8
− 4u
7
+ 4u
6
− 3u
5
+ 5u
4
+ u
3
+ 3u
2
− u + 3
a
7
=
u
9
− 2u
8
+ 4u
7
− 9u
6
+ 2u
5
− 13u
4
− 4u
3
− 9u
2
− u − 6
−u
9
+ u
8
− 4u
7
+ 4u
6
− 3u
5
+ 5u
4
+ u
3
+ 3u
2
− u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
9
− 5u
8
+ 3u
7
− 17u
6
− 6u
5
− 13u
4
− 13u
3
− 5u
2
+ u − 4
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
+ u
9
+ 3u
8
+ 2u
7
+ 5u
6
+ 3u
5
+ 6u
4
+ 2u
3
+ 4u
2
+ u + 1
c
2
u
10
+ 5u
9
+ ··· + 7u + 1
c
3
u
10
− u
8
+ 3u
7
− 3u
6
− u
5
+ 4u
4
− 6u
3
+ 5u
2
− 2u + 1
c
4
, c
5
, c
8
u
10
+ 5u
8
+ u
7
+ 8u
6
+ 3u
5
+ 6u
4
+ 2u
3
+ 4u
2
+ 1
c
6
u
10
− u
9
+ 3u
8
− 2u
7
+ 5u
6
− 3u
5
+ 6u
4
− 2u
3
+ 4u
2
− u + 1
c
7
u
10
+ 2u
9
− 2u
8
− 7u
7
− 2u
6
+ 8u
5
+ 7u
4
− 3u
3
− 4u
2
+ 1
c
9
u
10
+ 5u
8
− u
7
+ 8u
6
− 3u
5
+ 6u
4
− 2u
3
+ 4u
2
+ 1
c
10
u
10
− 2u
9
− 2u
8
+ 7u
7
− 2u
6
− 8u
5
+ 7u
4
+ 3u
3
− 4u
2
+ 1
c
11
u
10
− 2u
9
+ 4u
8
− 6u
7
+ 6u
6
− 6u
5
+ 6u
4
− u
3
− 2u
2
+ 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
10
+ 5y
9
+ ··· + 7y + 1
c
2
y
10
+ 5y
9
+ 11y
8
+ 28y
7
+ 69y
6
+ 87y
5
+ 50y
4
+ 32y
3
+ 36y
2
− y + 1
c
3
y
10
− 2y
9
− 5y
8
+ 5y
7
+ 17y
6
+ 3y
5
− 16y
4
− 6y
3
+ 9y
2
+ 6y + 1
c
4
, c
5
, c
8
c
9
y
10
+ 10y
9
+ ··· + 8y + 1
c
7
, c
10
y
10
− 8y
9
+ ··· − 8y + 1
c
11
y
10
+ 4y
9
+ 4y
8
+ 4y
6
+ 10y
5
+ 8y
4
− 13y
3
+ 16y
2
− 4y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.417680 + 0.777889I
a = 0.471406 + 0.198677I
b = −0.762772 + 0.870583I
1.59890 − 2.38428I 1.97609 + 6.43885I
u = 0.417680 − 0.777889I
a = 0.471406 − 0.198677I
b = −0.762772 − 0.870583I
1.59890 + 2.38428I 1.97609 − 6.43885I
u = −0.666811 + 0.558930I
a = −0.614575 − 0.894984I
b = −0.616156 − 0.405644I
−0.77437 + 5.03997I −3.44044 − 8.11191I
u = −0.666811 − 0.558930I
a = −0.614575 + 0.894984I
b = −0.616156 + 0.405644I
−0.77437 − 5.03997I −3.44044 + 8.11191I
u = 0.041017 + 1.338410I
a = −1.68567 − 0.13858I
b = 1.242340 + 0.172736I
7.62836 + 2.65528I 7.48214 − 3.22986I
u = 0.041017 − 1.338410I
a = −1.68567 + 0.13858I
b = 1.242340 − 0.172736I
7.62836 − 2.65528I 7.48214 + 3.22986I
u = 0.102677 + 0.595206I
a = 3.05538 + 0.64412I
b = −1.47267 + 0.27428I
4.57592 − 3.24415I −2.14013 + 2.60549I
u = 0.102677 − 0.595206I
a = 3.05538 − 0.64412I
b = −1.47267 − 0.27428I
4.57592 + 3.24415I −2.14013 − 2.60549I
u = 0.10544 + 1.60602I
a = −1.226540 − 0.081108I
b = 0.609265 + 0.131578I
5.06547 − 1.23703I −4.37766 − 1.21888I
u = 0.10544 − 1.60602I
a = −1.226540 + 0.081108I
b = 0.609265 − 0.131578I
5.06547 + 1.23703I −4.37766 + 1.21888I
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
6
· (u
10
+ u
9
+ 3u
8
+ 2u
7
+ 5u
6
+ 3u
5
+ 6u
4
+ 2u
3
+ 4u
2
+ u + 1)
· (u
18
+ 6u
17
+ ··· + 36u + 8)
c
2
((u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
6
)(u
10
+ 5u
9
+ ··· + 7u + 1)
· (u
18
+ 8u
17
+ ··· + 176u + 64)
c
3
(u
10
− u
8
+ 3u
7
− 3u
6
− u
5
+ 4u
4
− 6u
3
+ 5u
2
− 2u + 1)
· (u
18
+ 2u
17
+ ··· + u + 1)(u
30
+ 3u
29
+ ··· − 138u + 77)
c
4
, c
5
, c
8
(u
10
+ 5u
8
+ u
7
+ 8u
6
+ 3u
5
+ 6u
4
+ 2u
3
+ 4u
2
+ 1)
· (u
18
+ 2u
16
+ ··· + u + 1)(u
30
+ u
29
+ ··· − 4u + 19)
c
6
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
6
· (u
10
− u
9
+ 3u
8
− 2u
7
+ 5u
6
− 3u
5
+ 6u
4
− 2u
3
+ 4u
2
− u + 1)
· (u
18
+ 6u
17
+ ··· + 36u + 8)
c
7
((u
3
− u
2
+ 1)
10
)(u
10
+ 2u
9
+ ··· − 4u
2
+ 1)
· (u
18
+ 9u
17
+ ··· + 144u + 32)
c
9
(u
10
+ 5u
8
− u
7
+ 8u
6
− 3u
5
+ 6u
4
− 2u
3
+ 4u
2
+ 1)
· (u
18
+ 2u
16
+ ··· + u + 1)(u
30
+ u
29
+ ··· − 4u + 19)
c
10
((u
3
− u
2
+ 1)
10
)(u
10
− 2u
9
+ ··· − 4u
2
+ 1)
· (u
18
+ 9u
17
+ ··· + 144u + 32)
c
11
(u
10
− 2u
9
+ 4u
8
− 6u
7
+ 6u
6
− 6u
5
+ 6u
4
− u
3
− 2u
2
+ 1)
· (u
18
− 2u
17
+ ··· + 3u + 1)(u
30
− 5u
29
+ ··· − 182u + 347)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
((y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
6
)(y
10
+ 5y
9
+ ··· + 7y + 1)
· (y
18
+ 8y
17
+ ··· + 176y + 64)
c
2
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
6
· (y
10
+ 5y
9
+ 11y
8
+ 28y
7
+ 69y
6
+ 87y
5
+ 50y
4
+ 32y
3
+ 36y
2
− y + 1)
· (y
18
+ 4y
17
+ ··· + 15104y + 4096)
c
3
(y
10
− 2y
9
− 5y
8
+ 5y
7
+ 17y
6
+ 3y
5
− 16y
4
− 6y
3
+ 9y
2
+ 6y + 1)
· (y
18
+ 16y
17
+ ··· + 45y + 1)(y
30
− 5y
29
+ ··· + 19456y + 5929)
c
4
, c
5
, c
8
c
9
(y
10
+ 10y
9
+ ··· + 8y + 1)(y
18
+ 4y
17
+ ··· + 11y + 1)
· (y
30
+ 15y
29
+ ··· + 6520y + 361)
c
7
, c
10
((y
3
− y
2
+ 2y −1)
10
)(y
10
− 8y
9
+ ··· − 8y + 1)
· (y
18
− 9y
17
+ ··· + 3328y + 1024)
c
11
(y
10
+ 4y
9
+ 4y
8
+ 4y
6
+ 10y
5
+ 8y
4
− 13y
3
+ 16y
2
− 4y + 1)
· (y
18
− 18y
17
+ ··· + 23y + 1)(y
30
+ 3y
29
+ ··· + 526240y + 120409)
18
