12n
0226
(K12n
0226
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 9 11 3 6 12 8 5 10
Solving Sequence
6,11 3,7
8 9 5 12 2 1 4 10
c
6
c
7
c
8
c
5
c
11
c
2
c
1
c
4
c
10
c
3
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.38993 × 10
213
u
52
− 3.85126 × 10
213
u
51
+ ··· + 8.47410 × 10
215
b + 8.97607 × 10
216
,
2.88140 × 10
215
u
52
− 8.01190 × 10
215
u
51
+ ··· + 4.57601 × 10
217
a + 1.91823 × 10
219
,
u
53
− 2u
52
+ ··· + 22464u + 5184i
I
u
2
= hu
8
+ u
6
+ 2u
4
+ u
2
+ b + u, u
8
+ u
7
+ 3u
6
+ u
5
+ 4u
4
+ u
3
+ 4u
2
+ a + 2,
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1i
I
v
1
= ha, 18315v
5
+ 20514v
4
+ 76517v
3
+ 68962v
2
+ 11867b − 4895v + 9310,
9v
6
+ 3v
5
+ 38v
4
+ 6v
3
+ 7v
2
+ 3v + 1i
* 3 irreducible components of dim
C
= 0, with total 68 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
= h1.39 × 10
213
u
52
− 3.85 × 10
213
u
51
+ · · · + 8.47 × 10
215
b + 8.98 ×
10
216
, 2.88 × 10
215
u
52
− 8.01 × 10
215
u
51
+ · · · + 4.58 × 10
217
a + 1.92 ×
10
219
, u
53
− 2u
52
+ · · · + 22464u + 5184i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
−0.00629675u
52
+ 0.0175085u
51
+ ··· − 128.153u − 41.9191
−0.00164021u
52
+ 0.00454474u
51
+ ··· − 31.1195u − 10.5924
a
7
=
1
u
2
a
8
=
0.00570365u
52
− 0.0158936u
51
+ ··· + 113.481u + 37.6349
0.00300075u
52
− 0.00832795u
51
+ ··· + 62.3538u + 20.6068
a
9
=
0.00870440u
52
− 0.0242216u
51
+ ··· + 175.834u + 58.2417
0.00300075u
52
− 0.00832795u
51
+ ··· + 62.3538u + 20.6068
a
5
=
0.000384770u
52
− 0.000892176u
51
+ ··· + 10.3952u + 5.00364
0.00146358u
52
− 0.00397329u
51
+ ··· + 32.4577u + 10.6141
a
12
=
0.00264793u
52
− 0.00764690u
51
+ ··· + 49.3301u + 15.6401
−0.00203270u
52
+ 0.00553763u
51
+ ··· − 41.9729u − 14.2915
a
2
=
−0.00349732u
52
+ 0.00965215u
51
+ ··· − 71.0018u − 24.3376
−0.000464535u
52
+ 0.00120085u
51
+ ··· − 9.87081u − 3.79816
a
1
=
0.000762957u
52
− 0.00212328u
51
+ ··· + 15.5695u + 6.49566
0.00230398u
52
− 0.00638244u
51
+ ··· + 45.5648u + 14.7106
a
4
=
−0.00418756u
52
+ 0.0117419u
51
+ ··· − 81.5052u − 27.0323
−0.000471548u
52
+ 0.00132482u
51
+ ··· − 7.27553u − 2.56665
a
10
=
0.00778197u
52
− 0.0219456u
51
+ ··· + 153.438u + 50.5587
0.000923497u
52
− 0.00264094u
51
+ ··· + 18.6239u + 5.59256
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0103737u
52
− 0.0284322u
51
+ ··· + 214.510u + 70.9728
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
53
+ 63u
52
+ ··· + 371u + 1
c
2
, c
4
u
53
− 11u
52
+ ··· + 27u − 1
c
3
, c
7
u
53
− 2u
52
+ ··· + 2560u + 512
c
5
, c
8
u
53
+ 3u
52
+ ··· + 3u + 1
c
6
u
53
+ 2u
52
+ ··· + 22464u − 5184
c
9
, c
12
u
53
− 8u
52
+ ··· + 936u − 81
c
10
9(9u
53
− 6u
52
+ ··· + 279223u − 329)
c
11
9(9u
53
− 30u
52
+ ··· − 9820u − 5144)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
53
− 135y
52
+ ··· + 162995y −1
c
2
, c
4
y
53
− 63y
52
+ ··· + 371y −1
c
3
, c
7
y
53
+ 54y
52
+ ··· + 6815744y −262144
c
5
, c
8
y
53
+ 37y
52
+ ··· + 11y −1
c
6
y
53
− 36y
52
+ ··· − 140341248y −26873856
c
9
, c
12
y
53
− 54y
52
+ ··· + 624672y −6561
c
10
81(81y
53
− 4590y
52
+ ··· + 7.81268 × 10
10
y −108241)
c
11
81(81y
53
− 3132y
52
+ ··· + 2.63839 × 10
8
y −2.64607 × 10
7
)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.587478 + 0.786624I
a = 0.240520 − 1.341440I
b = −0.996338 − 0.133497I
−4.36101 − 1.13066I −3.77707 + 1.04050I
u = −0.587478 − 0.786624I
a = 0.240520 + 1.341440I
b = −0.996338 + 0.133497I
−4.36101 + 1.13066I −3.77707 − 1.04050I
u = 0.784719 + 0.727591I
a = −0.014954 + 0.267900I
b = −0.814475 − 0.023459I
−1.03321 − 2.55519I 0. + 3.47308I
u = 0.784719 − 0.727591I
a = −0.014954 − 0.267900I
b = −0.814475 + 0.023459I
−1.03321 + 2.55519I 0. − 3.47308I
u = −0.857688 + 0.043715I
a = 0.82268 − 2.49528I
b = 0.600154 − 0.231146I
−11.54620 + 0.81534I −10.67384 + 3.02586I
u = −0.857688 − 0.043715I
a = 0.82268 + 2.49528I
b = 0.600154 + 0.231146I
−11.54620 − 0.81534I −10.67384 − 3.02586I
u = 0.725133 + 0.331259I
a = 0.42484 + 1.56658I
b = −0.513240 − 0.036488I
−0.90481 − 1.57510I −3.08858 + 5.02134I
u = 0.725133 − 0.331259I
a = 0.42484 − 1.56658I
b = −0.513240 + 0.036488I
−0.90481 + 1.57510I −3.08858 − 5.02134I
u = 0.307246 + 0.727363I
a = −0.0797886 + 0.0873572I
b = 0.789629 + 0.027013I
0.78284 − 1.50580I 1.85337 + 3.47450I
u = 0.307246 − 0.727363I
a = −0.0797886 − 0.0873572I
b = 0.789629 − 0.027013I
0.78284 + 1.50580I 1.85337 − 3.47450I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.831004 + 0.912545I
a = −0.0242547 + 0.0656877I
b = −0.518016 + 0.075260I
−4.72794 + 6.87040I 0
u = −0.831004 − 0.912545I
a = −0.0242547 − 0.0656877I
b = −0.518016 − 0.075260I
−4.72794 − 6.87040I 0
u = −0.761253 + 0.017589I
a = −2.29759 + 1.93041I
b = −1.353470 + 0.374252I
−3.70920 − 0.68240I −10.13112 − 2.63548I
u = −0.761253 − 0.017589I
a = −2.29759 − 1.93041I
b = −1.353470 − 0.374252I
−3.70920 + 0.68240I −10.13112 + 2.63548I
u = −0.347262 + 0.578978I
a = 0.129109 − 0.200519I
b = −1.133590 + 0.745300I
−1.55881 − 5.25423I −4.65004 − 2.98399I
u = −0.347262 − 0.578978I
a = 0.129109 + 0.200519I
b = −1.133590 − 0.745300I
−1.55881 + 5.25423I −4.65004 + 2.98399I
u = 1.324240 + 0.127996I
a = 1.145120 + 0.199282I
b = 2.72490 + 0.99639I
−5.64518 + 2.18249I 0
u = 1.324240 − 0.127996I
a = 1.145120 − 0.199282I
b = 2.72490 − 0.99639I
−5.64518 − 2.18249I 0
u = −0.700095 + 1.162100I
a = −0.976198 + 0.126169I
b = 1.122560 − 0.323129I
−12.33890 − 1.47775I 0
u = −0.700095 − 1.162100I
a = −0.976198 − 0.126169I
b = 1.122560 + 0.323129I
−12.33890 + 1.47775I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.043959 + 0.630873I
a = 0.008106 + 0.322090I
b = 0.678672 − 0.502775I
1.01456 − 1.24993I 3.91266 + 3.38096I
u = −0.043959 − 0.630873I
a = 0.008106 − 0.322090I
b = 0.678672 + 0.502775I
1.01456 + 1.24993I 3.91266 − 3.38096I
u = −1.358620 + 0.308671I
a = 0.169926 − 1.179720I
b = −0.423412 − 0.390473I
−6.83584 + 3.76717I 0
u = −1.358620 − 0.308671I
a = 0.169926 + 1.179720I
b = −0.423412 + 0.390473I
−6.83584 − 3.76717I 0
u = −0.604410
a = −1.65322
b = −1.20764
−2.44483 1.00720
u = 1.45892
a = 0.101323
b = −1.70701
−9.31076 0
u = −0.269477 + 0.439684I
a = 4.18219 − 1.38429I
b = −0.672684 − 0.197132I
−3.14584 − 0.60875I −6.43020 − 7.79756I
u = −0.269477 − 0.439684I
a = 4.18219 + 1.38429I
b = −0.672684 + 0.197132I
−3.14584 + 0.60875I −6.43020 + 7.79756I
u = 0.460236
a = 1.51100
b = 0.0968051
−1.26040 −8.84480
u = 1.52986 + 0.22695I
a = −0.093190 + 1.107430I
b = −1.34206 + 0.70739I
−11.21080 − 2.39200I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.52986 − 0.22695I
a = −0.093190 − 1.107430I
b = −1.34206 − 0.70739I
−11.21080 + 2.39200I 0
u = 1.52455 + 0.46520I
a = 0.339028 + 0.930463I
b = 0.342173 + 0.677015I
−18.7129 − 3.6964I 0
u = 1.52455 − 0.46520I
a = 0.339028 − 0.930463I
b = 0.342173 − 0.677015I
−18.7129 + 3.6964I 0
u = 1.38129 + 0.81789I
a = −0.478490 − 0.971616I
b = 1.264090 − 0.596385I
−8.77075 − 4.08365I 0
u = 1.38129 − 0.81789I
a = −0.478490 + 0.971616I
b = 1.264090 + 0.596385I
−8.77075 + 4.08365I 0
u = −0.044332 + 0.385912I
a = −0.50758 − 2.65542I
b = −0.469624 + 0.982343I
−2.07856 + 0.90512I −5.97042 + 0.60054I
u = −0.044332 − 0.385912I
a = −0.50758 + 2.65542I
b = −0.469624 − 0.982343I
−2.07856 − 0.90512I −5.97042 − 0.60054I
u = −1.60969 + 0.39785I
a = 0.271528 + 1.346120I
b = 2.46563 + 1.85991I
−4.33713 + 4.43867I 0
u = −1.60969 − 0.39785I
a = 0.271528 − 1.346120I
b = 2.46563 − 1.85991I
−4.33713 − 4.43867I 0
u = 0.39044 + 1.61625I
a = −1.33817 − 0.73379I
b = 3.75376 + 0.88972I
−7.18708 + 1.12498I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.39044 − 1.61625I
a = −1.33817 + 0.73379I
b = 3.75376 − 0.88972I
−7.18708 − 1.12498I 0
u = −1.43936 + 0.92831I
a = −0.465711 + 0.991202I
b = 1.205920 + 0.655448I
−14.6527 + 9.7412I 0
u = −1.43936 − 0.92831I
a = −0.465711 − 0.991202I
b = 1.205920 − 0.655448I
−14.6527 − 9.7412I 0
u = −1.65766 + 0.50774I
a = −0.0133733 − 0.1179740I
b = 1.62509 − 0.20497I
−13.7945 + 6.0358I 0
u = −1.65766 − 0.50774I
a = −0.0133733 + 0.1179740I
b = 1.62509 + 0.20497I
−13.7945 − 6.0358I 0
u = 1.58393 + 0.77592I
a = −0.256700 − 1.138260I
b = 2.08530 − 1.06037I
−11.4354 − 9.7069I 0
u = 1.58393 − 0.77592I
a = −0.256700 + 1.138260I
b = 2.08530 + 1.06037I
−11.4354 + 9.7069I 0
u = 1.61919 + 1.26886I
a = 0.552254 + 0.933688I
b = −2.43008 + 1.46142I
−19.2132 − 15.4269I 0
u = 1.61919 − 1.26886I
a = 0.552254 − 0.933688I
b = −2.43008 − 1.46142I
−19.2132 + 15.4269I 0
u = −2.31619 + 1.30414I
a = 0.253148 − 0.797202I
b = −3.48820 − 2.65877I
−12.9006 + 7.5876I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −2.31619 − 1.30414I
a = 0.253148 + 0.797202I
b = −3.48820 + 2.65877I
−12.9006 − 7.5876I 0
u = 1.99609 + 2.43775I
a = 0.166870 + 0.527301I
b = −5.59376 − 1.35007I
−17.5158 + 2.8823I 0
u = 1.99609 − 2.43775I
a = 0.166870 − 0.527301I
b = −5.59376 + 1.35007I
−17.5158 − 2.8823I 0
10
II. I
u
2
= hu
8
+ u
6
+ 2u
4
+ u
2
+ b + u, u
8
+ u
7
+ 3u
6
+ u
5
+ 4u
4
+ u
3
+ 4u
2
+
a + 2, u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
−u
8
− u
7
− 3u
6
− u
5
− 4u
4
− u
3
− 4u
2
− 2
−u
8
− u
6
− 2u
4
− u
2
− u
a
7
=
1
u
2
a
8
=
1
u
2
a
9
=
u
2
+ 1
u
2
a
5
=
u
4
+ u
2
+ 1
u
4
a
12
=
u
8
+ u
6
+ u
4
− 1
u
8
+ u
7
+ u
6
+ 2u
5
+ u
4
+ 2u
3
+ 2u − 1
a
2
=
−u
8
− u
7
− 3u
6
− u
5
− 5u
4
− u
3
− 5u
2
− 3
−u
8
− u
6
− 3u
4
− u
2
− u
a
1
=
−u
4
− u
2
− 1
−u
4
a
4
=
−u
8
− u
7
− 3u
6
− u
5
− 4u
4
− u
3
− 4u
2
− 2
−u
8
− u
6
− 2u
4
− u
2
− u
a
10
=
u
u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
8
− 8u
7
− 13u
6
− 9u
5
− 17u
4
− 16u
3
− 13u
2
− 4u − 16
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
7
u
9
c
4
(u + 1)
9
c
5
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
6
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
8
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
9
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
10
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
11
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
12
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
7
y
9
c
5
, c
8
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
6
, c
10
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
9
, c
12
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
11
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.140343 + 0.966856I
a = 0.483566 + 0.305056I
b = −0.525305 − 0.147929I
0.13850 − 2.09337I −4.94317 + 6.62869I
u = 0.140343 − 0.966856I
a = 0.483566 − 0.305056I
b = −0.525305 + 0.147929I
0.13850 + 2.09337I −4.94317 − 6.62869I
u = 0.628449 + 0.875112I
a = −1.022450 + 0.246780I
b = 0.107759 − 1.216140I
−2.26187 − 2.45442I −8.11682 + 3.00529I
u = 0.628449 − 0.875112I
a = −1.022450 − 0.246780I
b = 0.107759 + 1.216140I
−2.26187 + 2.45442I −8.11682 − 3.00529I
u = −0.796005 + 0.733148I
a = 1.23246 + 1.62704I
b = 2.01751 − 1.28212I
−6.01628 − 1.33617I −10.09079 − 3.07774I
u = −0.796005 − 0.733148I
a = 1.23246 − 1.62704I
b = 2.01751 + 1.28212I
−6.01628 + 1.33617I −10.09079 + 3.07774I
u = −0.728966 + 0.986295I
a = −0.411691 + 0.129409I
b = 0.367799 + 0.534872I
−5.24306 + 7.08493I −14.1334 − 8.8789I
u = −0.728966 − 0.986295I
a = −0.411691 − 0.129409I
b = 0.367799 − 0.534872I
−5.24306 − 7.08493I −14.1334 + 8.8789I
u = 0.512358
a = −3.56378
b = −0.935531
−2.84338 −25.4320
14
III. I
v
1
=
ha, 18315v
5
+ 20514 v
4
+· · ·+11867b+9310, 9v
6
+ 3 v
5
+38v
4
+6v
3
+ 7 v
2
+3v+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
v
0
a
3
=
0
−1.54336v
5
− 1.72866v
4
+ ··· + 0.412488v −0.784529
a
7
=
1
0
a
8
=
1
3.02073v
5
+ 0.380467v
4
+ ··· + 3.21968v −0.339176
a
9
=
3.02073v
5
+ 0.380467v
4
+ ··· + 3.21968v + 0.660824
3.02073v
5
+ 0.380467v
4
+ ··· + 3.21968v −0.339176
a
5
=
−3.57437v
5
− 0.956350v
4
+ ··· − 2.47712v −0.821859
−6.59510v
5
− 1.33682v
4
+ ··· − 5.69681v −1.48268
a
12
=
−2.39429v
5
− 0.443920v
4
+ ··· − 0.873599v −0.325187
−3.88228v
5
− 0.314991v
4
+ ··· − 3.93537v −0.393613
a
2
=
−3.02073v
5
− 0.380467v
4
+ ··· − 3.21968v −0.660824
−6.59510v
5
− 1.33682v
4
+ ··· − 5.69681v −1.48268
a
1
=
−3.02073v
5
− 0.380467v
4
+ ··· − 3.21968v −0.660824
−3.02073v
5
− 0.380467v
4
+ ··· − 3.21968v + 0.339176
a
4
=
−1.54336v
5
− 1.72866v
4
+ ··· + 0.412488v −0.784529
−1.54336v
5
− 1.72866v
4
+ ··· + 0.412488v −0.784529
a
10
=
0.626443v
5
− 0.0634533v
4
+ ··· + 2.34609v + 0.335637
−0.861549v
5
+ 0.0654757v
4
+ ··· − 0.715682v −0.732788
(ii) Obstruction class = 1
(iii) Cusp Shapes =
416817
11867
v
5
−
36660
11867
v
4
+
1727641
11867
v
3
−
424337
11867
v
2
+
315169
11867
v −
45696
11867
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
2
, c
7
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
3
, c
4
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
5
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
c
6
u
6
c
9
(u − 1)
6
c
10
9(9u
6
+ 30u
5
+ 41u
4
+ 30u
3
+ 15u
2
+ 5u + 1)
c
11
9(9u
6
− 12u
5
+ 2u
4
+ u
3
+ 4u
2
− 4u + 1)
c
12
(u + 1)
6
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
8
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
2
, c
3
, c
4
c
7
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
6
y
6
c
9
, c
12
(y −1)
6
c
10
81(81y
6
− 162y
5
+ 151y
4
+ 48y
3
+ 7y
2
+ 5y + 1)
c
11
81(81y
6
− 108y
5
+ 100y
4
− 63y
3
+ 28y
2
− 8y + 1)
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.178337 + 0.463585I
a = 0
b = 1.002190 − 0.295542I
0.245672 − 0.924305I −7.47464 − 1.75692I
v = 0.178337 − 0.463585I
a = 0
b = 1.002190 + 0.295542I
0.245672 + 0.924305I −7.47464 + 1.75692I
v = −0.246749 + 0.226622I
a = 0
b = −1.073950 + 0.558752I
−1.64493 − 5.69302I −7.2342 + 14.2758I
v = −0.246749 − 0.226622I
a = 0
b = −1.073950 − 0.558752I
−1.64493 + 5.69302I −7.2342 − 14.2758I
v = −0.09825 + 2.00069I
a = 0
b = −0.428243 + 0.664531I
−3.53554 + 0.92430I −15.9578 − 1.1630I
v = −0.09825 − 2.00069I
a = 0
b = −0.428243 − 0.664531I
−3.53554 − 0.92430I −15.9578 + 1.1630I
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
9
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
53
+ 63u
52
+ ··· + 371u + 1)
c
2
((u − 1)
9
)(u
6
+ u
5
+ ··· + u + 1)(u
53
− 11u
52
+ ··· + 27u − 1)
c
3
u
9
(u
6
− u
5
+ ··· − u + 1)(u
53
− 2u
52
+ ··· + 2560u + 512)
c
4
((u + 1)
9
)(u
6
− u
5
+ ··· − u + 1)(u
53
− 11u
52
+ ··· + 27u − 1)
c
5
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
53
+ 3u
52
+ ··· + 3u + 1)
c
6
u
6
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
53
+ 2u
52
+ ··· + 22464u − 5184)
c
7
u
9
(u
6
+ u
5
+ ··· + u + 1)(u
53
− 2u
52
+ ··· + 2560u + 512)
c
8
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
53
+ 3u
52
+ ··· + 3u + 1)
c
9
(u − 1)
6
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
53
− 8u
52
+ ··· + 936u − 81)
c
10
81(9u
6
+ 30u
5
+ 41u
4
+ 30u
3
+ 15u
2
+ 5u + 1)
· (u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (9u
53
− 6u
52
+ ··· + 279223u − 329)
c
11
81(9u
6
− 12u
5
+ 2u
4
+ u
3
+ 4u
2
− 4u + 1)
· (u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
· (9u
53
− 30u
52
+ ··· − 9820u − 5144)
c
12
(u + 1)
6
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
53
− 8u
52
+ ··· + 936u − 81)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
9
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
53
− 135y
52
+ ··· + 162995y −1)
c
2
, c
4
(y −1)
9
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
53
− 63y
52
+ ··· + 371y −1)
c
3
, c
7
y
9
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
53
+ 54y
52
+ ··· + 6815744y −262144)
c
5
, c
8
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
53
+ 37y
52
+ ··· + 11y −1)
c
6
y
6
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
53
− 36y
52
+ ··· − 140341248y −26873856)
c
9
, c
12
(y −1)
6
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
53
− 54y
52
+ ··· + 624672y −6561)
c
10
6561(81y
6
− 162y
5
+ 151y
4
+ 48y
3
+ 7y
2
+ 5y + 1)
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (81y
53
− 4590y
52
+ ··· + 78126767425y −108241)
c
11
6561(81y
6
− 108y
5
+ 100y
4
− 63y
3
+ 28y
2
− 8y + 1)
· (y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (81y
53
− 3132y
52
+ ··· + 263838736y −26460736)
20
