12n
0311
(K12n
0311
)
A knot diagram
1
Linearized knot diagam
3 6 7 11 9 2 10 12 5 7 6 8
Solving Sequence
2,7
6 3
4,11
5 12 1 10 8 9
c
6
c
2
c
3
c
4
c
11
c
1
c
10
c
7
c
9
c
5
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−2044u
16
− 1922u
15
+ ··· + 3101b − 1979, 2044u
16
+ 1922u
15
+ ··· + 3101a + 1979,
u
17
+ u
16
+ ··· + u + 1i
I
u
2
= hu
7
+ u
6
+ 2u
5
+ u
4
+ 2u
3
+ u
2
+ b + 2u, −u
7
− u
6
− 2u
5
− u
4
− 2u
3
− u
2
+ a − u,
u
8
+ u
7
+ 2u
6
+ u
5
+ 2u
4
+ u
3
+ 2u
2
+ 1i
I
u
3
= h−749460642064u
21
− 2228668431607u
20
+ ··· + 2074714652641b + 2531239700657,
940122740255u
21
+ 759005323853u
20
+ ··· + 2074714652641a − 6054928651235,
u
22
+ 2u
21
+ ··· − u + 1i
I
u
4
= hb − u, 2u
5
+ 3u
4
+ 6u
3
+ 4u
2
+ a + 5u + 4, u
6
+ u
5
+ 3u
4
+ u
3
+ 3u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 53 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−2044u
16
− 1922u
15
+ · · · + 3101b − 1979, 2044u
16
+ 1922u
15
+
· · · + 3101a + 1979, u
17
+ u
16
+ · · · + u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
11
=
−0.659142u
16
− 0.619800u
15
+ ··· − 4.68139u − 0.638181
0.659142u
16
+ 0.619800u
15
+ ··· + 3.68139u + 0.638181
a
5
=
−0.815866u
16
− 0.632699u
15
+ ··· − 3.30119u − 0.598839
0.659142u
16
+ 0.619800u
15
+ ··· + 3.68139u + 0.638181
a
12
=
−0.156724u
16
− 0.0128991u
15
+ ··· − 1.61980u + 0.0393421
0.515640u
16
+ 0.419865u
15
+ ··· + 3.07449u + 0.533699
a
1
=
u
3
u
5
+ u
3
+ u
a
10
=
−u
0.659142u
16
+ 0.619800u
15
+ ··· + 3.68139u + 0.638181
a
8
=
0.0393421u
16
+ 0.196066u
15
+ ··· + 0.0209610u + 1.65914
0.533699u
16
+ 0.0180587u
15
+ ··· + 2.06772u − 1.54079
a
9
=
−0.104482u
16
+ 0.0390197u
15
+ ··· − 0.175105u + 1.50242
0.629474u
16
+ 0.279910u
15
+ ··· + 2.04966u − 1.02515
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
7241
3101
u
16
−
194
443
u
15
+ ··· −
1392
443
u +
27045
3101
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
+ 7u
16
+ ··· − 11u − 1
c
2
, c
6
, c
8
c
12
u
17
− u
16
+ ··· + u − 1
c
3
u
17
+ 4u
16
+ ··· − 9u − 2
c
4
u
17
+ 19u
16
+ ··· − 1920u − 256
c
5
, c
9
u
17
− 5u
16
+ ··· + 11u − 4
c
7
, c
10
u
17
+ 12u
15
+ ··· − 2u − 1
c
11
u
17
+ u
16
+ ··· − 7u − 73
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
+ 23y
16
+ ··· + 53y −1
c
2
, c
6
, c
8
c
12
y
17
+ 7y
16
+ ··· − 11y −1
c
3
y
17
+ 30y
16
+ ··· − 71y −4
c
4
y
17
− 35y
16
+ ··· + 409600y −65536
c
5
, c
9
y
17
+ 13y
16
+ ··· + 57y −16
c
7
, c
10
y
17
+ 24y
16
+ ··· + 14y −1
c
11
y
17
− y
16
+ ··· − 1119y −5329
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.315205 + 1.046030I
a = 0.082055 − 0.721069I
b = −0.397259 − 0.324959I
−7.22031 + 4.62107I −4.34829 − 2.68112I
u = 0.315205 − 1.046030I
a = 0.082055 + 0.721069I
b = −0.397259 + 0.324959I
−7.22031 − 4.62107I −4.34829 + 2.68112I
u = −0.174342 + 1.095890I
a = 0.69443 − 2.33356I
b = −0.520091 + 1.237680I
−3.36776 + 0.12095I −1.97931 + 0.42212I
u = −0.174342 − 1.095890I
a = 0.69443 + 2.33356I
b = −0.520091 − 1.237680I
−3.36776 − 0.12095I −1.97931 − 0.42212I
u = −0.104664 + 0.862714I
a = −0.258038 − 1.063400I
b = 0.362702 + 0.200685I
−1.97872 − 1.38925I −1.78976 + 4.99153I
u = −0.104664 − 0.862714I
a = −0.258038 + 1.063400I
b = 0.362702 − 0.200685I
−1.97872 + 1.38925I −1.78976 − 4.99153I
u = 0.738518 + 0.422689I
a = −1.34345 − 0.54001I
b = 0.604930 + 0.117324I
−2.97240 + 2.41748I 1.62401 − 1.63968I
u = 0.738518 − 0.422689I
a = −1.34345 + 0.54001I
b = 0.604930 − 0.117324I
−2.97240 − 2.41748I 1.62401 + 1.63968I
u = −0.584000
a = 1.03858
b = −0.454582
1.00795 10.1490
u = −0.92539 + 1.07797I
a = 0.807371 + 0.662951I
b = 0.11801 − 1.74092I
8.59690 − 1.56188I 3.90595 + 1.56397I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.92539 − 1.07797I
a = 0.807371 − 0.662951I
b = 0.11801 + 1.74092I
8.59690 + 1.56188I 3.90595 − 1.56397I
u = 0.97683 + 1.11228I
a = −1.17199 + 0.82087I
b = 0.19516 − 1.93315I
12.7535 + 7.6085I 6.24645 − 4.20129I
u = 0.97683 − 1.11228I
a = −1.17199 − 0.82087I
b = 0.19516 + 1.93315I
12.7535 − 7.6085I 6.24645 + 4.20129I
u = −0.99123 + 1.15222I
a = 1.50875 + 0.73748I
b = −0.51753 − 1.88970I
8.3449 − 13.5034I 3.39007 + 6.77550I
u = −0.99123 − 1.15222I
a = 1.50875 − 0.73748I
b = −0.51753 + 1.88970I
8.3449 + 13.5034I 3.39007 − 6.77550I
u = −0.042937 + 0.454619I
a = −0.33843 − 1.66461I
b = 0.381363 + 1.209990I
0.96686 − 2.33424I 5.87632 − 0.70126I
u = −0.042937 − 0.454619I
a = −0.33843 + 1.66461I
b = 0.381363 − 1.209990I
0.96686 + 2.33424I 5.87632 + 0.70126I
6
II. I
u
2
= hu
7
+ u
6
+ 2u
5
+ u
4
+ 2u
3
+ u
2
+ b + 2u, −u
7
− u
6
− 2u
5
− u
4
−
2u
3
− u
2
+ a − u, u
8
+ u
7
+ 2u
6
+ u
5
+ 2u
4
+ u
3
+ 2u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
11
=
u
7
+ u
6
+ 2u
5
+ u
4
+ 2u
3
+ u
2
+ u
−u
7
− u
6
− 2u
5
− u
4
− 2u
3
− u
2
− 2u
a
5
=
−u
7
− u
6
− u
5
− u
4
− u
3
− u
2
u
7
+ u
6
+ 2u
5
+ u
4
+ 2u
3
+ u
2
+ 2u
a
12
=
u
3
−u
7
− u
6
− u
5
− u
4
− u
3
− u
2
− u
a
1
=
u
3
u
5
+ u
3
+ u
a
10
=
−u
−u
7
− u
6
− 2u
5
− u
4
− 2u
3
− u
2
− 2u
a
8
=
0
−u
6
− u
5
− 2u
4
− u
3
− 2u
2
− u − 2
a
9
=
u
4
−u
5
− u
4
− u
3
− u
2
− u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
7
− 9u
6
− 9u
5
− 11u
4
− 8u
3
− 14u
2
− 8u − 7
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
− 3u
7
+ 6u
6
− 9u
5
+ 12u
4
− 11u
3
+ 8u
2
− 4u + 1
c
2
, c
8
u
8
− u
7
+ 2u
6
− u
5
+ 2u
4
− u
3
+ 2u
2
+ 1
c
3
u
8
+ u
7
+ 5u
6
+ 8u
5
+ 7u
4
+ 9u
3
+ 5u
2
+ 1
c
4
u
8
− 2u
7
+ 7u
6
− 12u
5
+ 16u
4
− 15u
3
+ 9u
2
− 4u + 1
c
5
u
8
+ 2u
7
+ 6u
6
+ 8u
5
+ 11u
4
+ 9u
3
+ 7u
2
+ 2u + 1
c
6
, c
12
u
8
+ u
7
+ 2u
6
+ u
5
+ 2u
4
+ u
3
+ 2u
2
+ 1
c
7
u
8
+ 2u
6
+ u
5
+ 2u
4
+ u
3
+ 2u
2
+ u + 1
c
9
u
8
− 2u
7
+ 6u
6
− 8u
5
+ 11u
4
− 9u
3
+ 7u
2
− 2u + 1
c
10
u
8
+ 2u
6
− u
5
+ 2u
4
− u
3
+ 2u
2
− u + 1
c
11
u
8
+ u
7
+ 2u
6
+ 5u
5
+ 9u
4
+ 10u
3
+ 8u
2
+ 4u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
+ 3y
7
+ 6y
6
+ 13y
5
+ 20y
4
+ 11y
3
+ 1
c
2
, c
6
, c
8
c
12
y
8
+ 3y
7
+ 6y
6
+ 9y
5
+ 12y
4
+ 11y
3
+ 8y
2
+ 4y + 1
c
3
y
8
+ 9y
7
+ 23y
6
− 2y
5
− 43y
4
− y
3
+ 39y
2
+ 10y + 1
c
4
y
8
+ 10y
7
+ 33y
6
+ 38y
5
+ 8y
4
− 19y
3
− 7y
2
+ 2y + 1
c
5
, c
9
y
8
+ 8y
7
+ 26y
6
+ 46y
5
+ 55y
4
+ 53y
3
+ 35y
2
+ 10y + 1
c
7
, c
10
y
8
+ 4y
7
+ 8y
6
+ 11y
5
+ 12y
4
+ 9y
3
+ 6y
2
+ 3y + 1
c
11
y
8
+ 3y
7
+ 12y
6
+ 7y
5
+ 7y
4
+ 8y
3
+ 2y
2
+ 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.609994 + 0.714573I
a = −1.301040 + 0.094950I
b = 0.691049 − 0.809524I
0.43885 + 3.70343I 1.67706 − 6.67650I
u = 0.609994 − 0.714573I
a = −1.301040 − 0.094950I
b = 0.691049 + 0.809524I
0.43885 − 3.70343I 1.67706 + 6.67650I
u = −0.894229 + 0.700020I
a = 1.58761 − 0.15723I
b = −0.693376 − 0.542788I
−2.47121 − 3.78237I 2.85720 + 5.66957I
u = −0.894229 − 0.700020I
a = 1.58761 + 0.15723I
b = −0.693376 + 0.542788I
−2.47121 + 3.78237I 2.85720 − 5.66957I
u = −0.388842 + 1.122290I
a = 0.664473 − 0.326753I
b = −0.275631 − 0.795537I
−6.67501 − 5.79166I −1.38166 + 7.29610I
u = −0.388842 − 1.122290I
a = 0.664473 + 0.326753I
b = −0.275631 + 0.795537I
−6.67501 + 5.79166I −1.38166 − 7.29610I
u = 0.173077 + 0.769880I
a = −0.451035 + 0.466536I
b = 0.277959 − 1.236420I
0.48271 + 2.83701I −2.15260 − 6.82394I
u = 0.173077 − 0.769880I
a = −0.451035 − 0.466536I
b = 0.277959 + 1.236420I
0.48271 − 2.83701I −2.15260 + 6.82394I
10
III.
I
u
3
= h−7.49×10
11
u
21
−2.23×10
12
u
20
+· · ·+2.07×10
12
b+2.53×10
12
, 9.40×
10
11
u
21
+7.59×10
11
u
20
+· · ·+2.07×10
12
a−6.05×10
12
, u
22
+2u
21
+· · ·−u+1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
11
=
−0.453134u
21
− 0.365836u
20
+ ··· − 8.73849u + 2.91844
0.361236u
21
+ 1.07420u
20
+ ··· − 1.46154u − 1.22004
a
5
=
1.80823u
21
+ 4.10689u
20
+ ··· − 6.09846u + 5.54053
0.102467u
21
+ 0.504369u
20
+ ··· − 2.52268u − 0.0105824
a
12
=
0.0527569u
21
+ 1.00509u
20
+ ··· − 11.1936u + 2.23883
0.549456u
21
+ 1.48404u
20
+ ··· − 1.60828u − 1.57919
a
1
=
u
3
u
5
+ u
3
+ u
a
10
=
−0.0918980u
21
+ 0.708369u
20
+ ··· − 10.2000u + 1.69840
0.361236u
21
+ 1.07420u
20
+ ··· − 1.46154u − 1.22004
a
8
=
0.0284427u
21
+ 0.181609u
20
+ ··· + 1.05626u − 3.67101
0.386881u
21
+ 0.856405u
20
+ ··· − 0.0832695u − 1.26247
a
9
=
2.17072u
21
+ 3.86720u
20
+ ··· + 12.9324u − 2.07204
0.754654u
21
+ 1.86631u
20
+ ··· − 1.22080u − 0.574813
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
4274991010191
2074714652641
u
21
+
7650116490863
2074714652641
u
20
+ ··· +
37457996269871
2074714652641
u −
2765051938302
2074714652641
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
22
+ 18u
20
+ ··· + u + 1
c
2
, c
6
, c
8
c
12
u
22
− 2u
21
+ ··· + u + 1
c
3
u
22
− 4u
21
+ ··· + 49499u + 24641
c
4
(u
11
− 6u
10
+ ··· − 35u − 17)
2
c
5
, c
9
(u
11
+ 2u
10
+ ··· + 2u + 1)
2
c
7
, c
10
u
22
+ 14u
20
+ ··· − 75u + 37
c
11
u
22
− 4u
21
+ ··· + 7278u + 1669
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
+ 36y
21
+ ··· − 15y + 1
c
2
, c
6
, c
8
c
12
y
22
+ 18y
20
+ ··· + y + 1
c
3
y
22
+ 78y
21
+ ··· + 7715838523y + 607178881
c
4
(y
11
− 18y
10
+ ··· − 1019y −289)
2
c
5
, c
9
(y
11
+ 8y
10
+ ··· − 6y −1)
2
c
7
, c
10
y
22
+ 28y
21
+ ··· + 43881y + 1369
c
11
y
22
− 30y
21
+ ··· + 12275264y + 2785561
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.513561 + 0.876763I
a = −1.74964 + 1.01013I
b = 0.261055 − 1.067110I
−0.28697 + 5.47625I 2.65866 − 8.43971I
u = 0.513561 − 0.876763I
a = −1.74964 − 1.01013I
b = 0.261055 + 1.067110I
−0.28697 − 5.47625I 2.65866 + 8.43971I
u = −0.508636 + 0.767746I
a = −0.123593 − 0.460656I
b = 0.179030 + 0.730958I
1.14459 − 2.07644I 6.88845 + 3.29115I
u = −0.508636 − 0.767746I
a = −0.123593 + 0.460656I
b = 0.179030 − 0.730958I
1.14459 + 2.07644I 6.88845 − 3.29115I
u = −0.666940 + 0.874899I
a = 0.730783 + 0.252461I
b = −0.094389 − 0.234171I
1.04772 − 2.73877I 6.75041 + 0.15171I
u = −0.666940 − 0.874899I
a = 0.730783 − 0.252461I
b = −0.094389 + 0.234171I
1.04772 + 2.73877I 6.75041 − 0.15171I
u = 0.755260 + 0.360527I
a = −1.006180 − 0.143301I
b = 0.75122 − 1.28017I
1.04772 + 2.73877I 6.75041 − 0.15171I
u = 0.755260 − 0.360527I
a = −1.006180 + 0.143301I
b = 0.75122 + 1.28017I
1.04772 − 2.73877I 6.75041 + 0.15171I
u = −1.055500 + 0.632113I
a = 1.66813 + 0.03713I
b = −1.64418 − 0.87598I
−0.28697 − 5.47625I 2.65866 + 8.43971I
u = −1.055500 − 0.632113I
a = 1.66813 − 0.03713I
b = −1.64418 + 0.87598I
−0.28697 + 5.47625I 2.65866 − 8.43971I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.024000 + 0.902635I
a = −1.117000 − 0.234561I
b = 0.36023 + 1.72510I
9.17587 − 5.61734I 4.48506 + 3.30154I
u = −1.024000 − 0.902635I
a = −1.117000 + 0.234561I
b = 0.36023 − 1.72510I
9.17587 + 5.61734I 4.48506 − 3.30154I
u = 1.10872 + 0.93411I
a = 0.845306 − 0.712187I
b = −0.11289 + 1.96334I
13.3784 7.19306 + 0.I
u = 1.10872 − 0.93411I
a = 0.845306 + 0.712187I
b = −0.11289 − 1.96334I
13.3784 7.19306 + 0.I
u = 0.494892 + 0.095903I
a = 0.863812 + 0.114318I
b = 0.075028 + 1.281880I
1.14459 − 2.07644I 6.88845 + 3.29115I
u = 0.494892 − 0.095903I
a = 0.863812 − 0.114318I
b = 0.075028 − 1.281880I
1.14459 + 2.07644I 6.88845 − 3.29115I
u = −1.19422 + 0.92504I
a = −0.398068 − 0.951477I
b = −0.22895 + 2.01375I
9.17587 + 5.61734I 4.48506 − 3.30154I
u = −1.19422 − 0.92504I
a = −0.398068 + 0.951477I
b = −0.22895 − 2.01375I
9.17587 − 5.61734I 4.48506 + 3.30154I
u = 0.73359 + 1.34764I
a = −0.85310 − 1.14643I
b = 0.822086 + 1.042470I
−4.61094 + 3.53079I −0.87911 − 8.44762I
u = 0.73359 − 1.34764I
a = −0.85310 + 1.14643I
b = 0.822086 − 1.042470I
−4.61094 − 3.53079I −0.87911 + 8.44762I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.156708 + 0.376716I
a = 3.63955 − 3.95391I
b = −0.368242 − 0.799335I
−4.61094 − 3.53079I −0.87911 + 8.44762I
u = −0.156708 − 0.376716I
a = 3.63955 + 3.95391I
b = −0.368242 + 0.799335I
−4.61094 + 3.53079I −0.87911 − 8.44762I
16
IV.
I
u
4
= hb−u, 2u
5
+3u
4
+6u
3
+4u
2
+a+5u+4, u
6
+u
5
+3u
4
+u
3
+3u
2
+u+1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
11
=
−2u
5
− 3u
4
− 6u
3
− 4u
2
− 5u − 4
u
a
5
=
−3u
4
− 2u
3
− 7u
2
+ u − 6
u
5
+ u
4
+ 3u
3
+ u
2
+ 3u + 1
a
12
=
−3u
5
− 4u
4
− 8u
3
− 5u
2
− 7u − 5
u
5
+ u
3
+ 2u
a
1
=
u
3
u
5
+ u
3
+ u
a
10
=
−2u
5
− 3u
4
− 6u
3
− 4u
2
− 4u − 4
u
a
8
=
−u
5
− 2u
3
+ 2u
2
− 2u + 3
u
2
a
9
=
4u
5
+ 2u
4
+ 9u
3
− u
2
+ 8u + 1
u
4
+ 2u
2
+ 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
4
− 3u
3
− 6u
2
− 2
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
− 5u
5
+ 13u
4
− 17u
3
+ 13u
2
− 5u + 1
c
2
, c
8
, c
10
u
6
− u
5
+ 3u
4
− u
3
+ 3u
2
− u + 1
c
3
u
6
+ 4u
5
+ 2u
4
− 3u
3
+ 4u
2
− u + 1
c
4
(u
3
+ 2u
2
+ 3u + 1)
2
c
5
(u
3
− u
2
+ 2u − 1)
2
c
6
, c
7
, c
12
u
6
+ u
5
+ 3u
4
+ u
3
+ 3u
2
+ u + 1
c
9
(u
3
+ u
2
+ 2u + 1)
2
c
11
u
6
+ 3u
5
− u
3
+ 6u
2
− 2u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
+ y
5
+ 25y
4
+ y
3
+ 25y
2
+ y + 1
c
2
, c
6
, c
7
c
8
, c
10
, c
12
y
6
+ 5y
5
+ 13y
4
+ 17y
3
+ 13y
2
+ 5y + 1
c
3
y
6
− 12y
5
+ 36y
4
+ 17y
3
+ 14y
2
+ 7y + 1
c
4
(y
3
+ 2y
2
+ 5y −1)
2
c
5
, c
9
(y
3
+ 3y
2
+ 2y −1)
2
c
11
y
6
− 9y
5
+ 18y
4
+ 13y
3
+ 32y
2
+ 8y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.377439 + 0.926035I
a = 0.53980 − 1.32438I
b = 0.377439 + 0.926035I
−0.531480 4.97415 + 0.I
u = 0.377439 − 0.926035I
a = 0.53980 + 1.32438I
b = 0.377439 − 0.926035I
−0.531480 4.97415 + 0.I
u = −0.273131 + 0.614306I
a = −2.85527 − 1.63609I
b = −0.273131 + 0.614306I
−4.66906 + 2.82812I −0.98708 + 1.68684I
u = −0.273131 − 0.614306I
a = −2.85527 + 1.63609I
b = −0.273131 − 0.614306I
−4.66906 − 2.82812I −0.98708 − 1.68684I
u = −0.60431 + 1.35917I
a = 0.31547 − 1.45351I
b = −0.60431 + 1.35917I
−4.66906 − 2.82812I −0.98708 − 1.68684I
u = −0.60431 − 1.35917I
a = 0.31547 + 1.45351I
b = −0.60431 − 1.35917I
−4.66906 + 2.82812I −0.98708 + 1.68684I
20
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
6
− 5u
5
+ 13u
4
− 17u
3
+ 13u
2
− 5u + 1)
· (u
8
− 3u
7
+ 6u
6
− 9u
5
+ 12u
4
− 11u
3
+ 8u
2
− 4u + 1)
· (u
17
+ 7u
16
+ ··· − 11u − 1)(u
22
+ 18u
20
+ ··· + u + 1)
c
2
, c
8
(u
6
− u
5
+ 3u
4
− u
3
+ 3u
2
− u + 1)(u
8
− u
7
+ ··· + 2u
2
+ 1)
· (u
17
− u
16
+ ··· + u − 1)(u
22
− 2u
21
+ ··· + u + 1)
c
3
(u
6
+ 4u
5
+ 2u
4
− 3u
3
+ 4u
2
− u + 1)
· (u
8
+ u
7
+ ··· + 5u
2
+ 1)(u
17
+ 4u
16
+ ··· − 9u − 2)
· (u
22
− 4u
21
+ ··· + 49499u + 24641)
c
4
(u
3
+ 2u
2
+ 3u + 1)
2
· (u
8
− 2u
7
+ 7u
6
− 12u
5
+ 16u
4
− 15u
3
+ 9u
2
− 4u + 1)
· ((u
11
− 6u
10
+ ··· − 35u − 17)
2
)(u
17
+ 19u
16
+ ··· − 1920u − 256)
c
5
((u
3
− u
2
+ 2u − 1)
2
)(u
8
+ 2u
7
+ ··· + 2u + 1)
· ((u
11
+ 2u
10
+ ··· + 2u + 1)
2
)(u
17
− 5u
16
+ ··· + 11u − 4)
c
6
, c
12
(u
6
+ u
5
+ 3u
4
+ u
3
+ 3u
2
+ u + 1)(u
8
+ u
7
+ ··· + 2u
2
+ 1)
· (u
17
− u
16
+ ··· + u − 1)(u
22
− 2u
21
+ ··· + u + 1)
c
7
(u
6
+ u
5
+ 3u
4
+ u
3
+ 3u
2
+ u + 1)(u
8
+ 2u
6
+ ··· + u + 1)
· (u
17
+ 12u
15
+ ··· − 2u − 1)(u
22
+ 14u
20
+ ··· − 75u + 37)
c
9
((u
3
+ u
2
+ 2u + 1)
2
)(u
8
− 2u
7
+ ··· − 2u + 1)
· ((u
11
+ 2u
10
+ ··· + 2u + 1)
2
)(u
17
− 5u
16
+ ··· + 11u − 4)
c
10
(u
6
− u
5
+ 3u
4
− u
3
+ 3u
2
− u + 1)(u
8
+ 2u
6
+ ··· − u + 1)
· (u
17
+ 12u
15
+ ··· − 2u − 1)(u
22
+ 14u
20
+ ··· − 75u + 37)
c
11
(u
6
+ 3u
5
− u
3
+ 6u
2
− 2u + 1)
· (u
8
+ u
7
+ 2u
6
+ 5u
5
+ 9u
4
+ 10u
3
+ 8u
2
+ 4u + 1)
· (u
17
+ u
16
+ ··· − 7u − 73)(u
22
− 4u
21
+ ··· + 7278u + 1669)
21
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
6
+ y
5
+ 25y
4
+ y
3
+ 25y
2
+ y + 1)
· (y
8
+ 3y
7
+ ··· + 11y
3
+ 1)(y
17
+ 23y
16
+ ··· + 53y −1)
· (y
22
+ 36y
21
+ ··· − 15y + 1)
c
2
, c
6
, c
8
c
12
(y
6
+ 5y
5
+ 13y
4
+ 17y
3
+ 13y
2
+ 5y + 1)
· (y
8
+ 3y
7
+ 6y
6
+ 9y
5
+ 12y
4
+ 11y
3
+ 8y
2
+ 4y + 1)
· (y
17
+ 7y
16
+ ··· − 11y −1)(y
22
+ 18y
20
+ ··· + y + 1)
c
3
(y
6
− 12y
5
+ 36y
4
+ 17y
3
+ 14y
2
+ 7y + 1)
· (y
8
+ 9y
7
+ 23y
6
− 2y
5
− 43y
4
− y
3
+ 39y
2
+ 10y + 1)
· (y
17
+ 30y
16
+ ··· − 71y −4)
· (y
22
+ 78y
21
+ ··· + 7715838523y + 607178881)
c
4
(y
3
+ 2y
2
+ 5y −1)
2
· (y
8
+ 10y
7
+ 33y
6
+ 38y
5
+ 8y
4
− 19y
3
− 7y
2
+ 2y + 1)
· (y
11
− 18y
10
+ ··· − 1019y −289)
2
· (y
17
− 35y
16
+ ··· + 409600y −65536)
c
5
, c
9
(y
3
+ 3y
2
+ 2y −1)
2
· (y
8
+ 8y
7
+ 26y
6
+ 46y
5
+ 55y
4
+ 53y
3
+ 35y
2
+ 10y + 1)
· ((y
11
+ 8y
10
+ ··· − 6y −1)
2
)(y
17
+ 13y
16
+ ··· + 57y −16)
c
7
, c
10
(y
6
+ 5y
5
+ 13y
4
+ 17y
3
+ 13y
2
+ 5y + 1)
· (y
8
+ 4y
7
+ 8y
6
+ 11y
5
+ 12y
4
+ 9y
3
+ 6y
2
+ 3y + 1)
· (y
17
+ 24y
16
+ ··· + 14y −1)(y
22
+ 28y
21
+ ··· + 43881y + 1369)
c
11
(y
6
− 9y
5
+ 18y
4
+ 13y
3
+ 32y
2
+ 8y + 1)
· (y
8
+ 3y
7
+ 12y
6
+ 7y
5
+ 7y
4
+ 8y
3
+ 2y
2
+ 1)
· (y
17
− y
16
+ ··· − 1119y −5329)
· (y
22
− 30y
21
+ ··· + 12275264y + 2785561)
22
