12n
0429
(K12n
0429
)
A knot diagram
1
Linearized knot diagam
3 5 10 9 2 11 3 5 12 7 4 8
Solving Sequence
9,12 5,10
4 3 2 6 8 1 7 11
c
9
c
4
c
3
c
2
c
5
c
8
c
12
c
7
c
11
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h5.47377 × 10
153
u
62
− 1.31028 × 10
154
u
61
+ ··· + 3.40987 × 10
153
b − 1.11096 × 10
154
,
− 1.23420 × 10
154
u
62
+ 3.17083 × 10
154
u
61
+ ··· + 3.40987 × 10
153
a + 7.52944 × 10
153
,
u
63
− 3u
62
+ ··· − 2u + 1i
I
u
2
= h1.49872 × 10
24
u
27
+ 8.28499 × 10
24
u
26
+ ··· + 1.24369 × 10
24
b + 2.46098 × 10
24
,
4.65953 × 10
23
u
27
+ 2.34056 × 10
24
u
26
+ ··· + 1.24369 × 10
24
a − 2.67968 × 10
24
, u
28
+ 6u
27
+ ··· + 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 91 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
= h5.47 × 10
153
u
62
− 1.31 × 10
154
u
61
+ · · · + 3.41 × 10
153
b − 1.11 ×
10
154
, −1.23 × 10
154
u
62
+ 3.17 × 10
154
u
61
+ · · · + 3.41 × 10
153
a + 7.53 ×
10
153
, u
63
− 3u
62
+ · · · − 2u + 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
5
=
3.61950u
62
− 9.29897u
61
+ ··· − 13.6429u − 2.20813
−1.60527u
62
+ 3.84260u
61
+ ··· + 0.655818u + 3.25806
a
10
=
1
−u
2
a
4
=
2.01423u
62
− 5.45637u
61
+ ··· − 12.9870u + 1.04993
−1.60527u
62
+ 3.84260u
61
+ ··· + 0.655818u + 3.25806
a
3
=
3.54024u
62
− 9.21354u
61
+ ··· − 12.8013u − 1.62182
−2.02759u
62
+ 4.91478u
61
+ ··· + 0.540061u + 4.07895
a
2
=
3.74628u
62
− 11.2722u
61
+ ··· − 3.10623u + 2.72252
−1.51679u
62
+ 3.81152u
61
+ ··· + 1.37033u + 1.85130
a
6
=
2.19593u
62
− 6.52686u
61
+ ··· + 43.5636u − 10.7702
−1.13065u
62
+ 2.95970u
61
+ ··· − 2.68920u + 1.83845
a
8
=
−2.38714u
62
+ 6.56354u
61
+ ··· + 1.89950u − 0.514982
1.03714u
62
− 2.42670u
61
+ ··· − 2.07634u − 1.29115
a
1
=
1.65476u
62
− 5.01519u
61
+ ··· + 39.9437u − 9.20657
−1.68517u
62
+ 4.43717u
61
+ ··· − 3.41249u + 3.07668
a
7
=
−1.57756u
62
+ 3.19097u
61
+ ··· + 25.5743u − 0.805183
0.777466u
62
− 1.73082u
61
+ ··· − 1.37482u − 1.84107
a
11
=
−3.47962u
62
+ 11.2423u
61
+ ··· + 14.4544u − 6.72853
0.0868469u
62
− 0.443124u
61
+ ··· − 4.50613u + 1.35000
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4.27944u
62
+ 11.2388u
61
+ ··· + 21.3904u + 3.08407
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
63
+ 84u
62
+ ··· + 6421262u − 290521
c
2
, c
5
u
63
+ 42u
61
+ ··· + 9624u − 539
c
3
u
63
+ u
62
+ ··· + 41175u − 7877
c
4
, c
8
u
63
+ 3u
62
+ ··· − 596u − 79
c
6
, c
10
u
63
− u
62
+ ··· − 237u − 113
c
7
u
63
+ 2u
62
+ ··· + 3704u − 3077
c
9
u
63
+ 3u
62
+ ··· − 2u − 1
c
11
u
63
− 5u
62
+ ··· − 6392u − 811
c
12
u
63
− u
62
+ ··· + 39596508u − 17977599
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
63
− 188y
62
+ ··· + 31966757369702y −84402451441
c
2
, c
5
y
63
+ 84y
62
+ ··· + 6421262y −290521
c
3
y
63
+ 27y
62
+ ··· − 719912377y −62047129
c
4
, c
8
y
63
+ 27y
62
+ ··· + 125010y −6241
c
6
, c
10
y
63
+ 49y
62
+ ··· − 228139y −12769
c
7
y
63
+ 94y
62
+ ··· − 340978482y −9467929
c
9
y
63
− 7y
62
+ ··· + 2y −1
c
11
y
63
+ 3y
62
+ ··· + 494194y −657721
c
12
y
63
+ 111y
62
+ ··· − 5213792993463072y −323194065804801
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.854897 + 0.532929I
a = −0.100050 − 1.334720I
b = 1.29417 + 1.60493I
−10.02610 − 5.81545I 3.97856 + 5.33947I
u = −0.854897 − 0.532929I
a = −0.100050 + 1.334720I
b = 1.29417 − 1.60493I
−10.02610 + 5.81545I 3.97856 − 5.33947I
u = 0.718348 + 0.648111I
a = 0.449487 + 1.049550I
b = −0.87436 − 1.40145I
−3.35191 + 2.65403I 2.16615 − 3.99621I
u = 0.718348 − 0.648111I
a = 0.449487 − 1.049550I
b = −0.87436 + 1.40145I
−3.35191 − 2.65403I 2.16615 + 3.99621I
u = −0.577833 + 0.736890I
a = 0.459738 + 0.125771I
b = 0.646165 + 0.254111I
−1.42068 − 2.29477I 3.60284 + 3.89630I
u = −0.577833 − 0.736890I
a = 0.459738 − 0.125771I
b = 0.646165 − 0.254111I
−1.42068 + 2.29477I 3.60284 − 3.89630I
u = −0.384316 + 1.017510I
a = −0.775849 − 0.891790I
b = 0.619662 − 1.136280I
−11.98870 + 1.15184I 0
u = −0.384316 − 1.017510I
a = −0.775849 + 0.891790I
b = 0.619662 + 1.136280I
−11.98870 − 1.15184I 0
u = 0.012682 + 1.109030I
a = −0.273611 + 0.515935I
b = −0.344619 + 0.593299I
−4.43543 − 0.90885I 0
u = 0.012682 − 1.109030I
a = −0.273611 − 0.515935I
b = −0.344619 − 0.593299I
−4.43543 + 0.90885I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.695265 + 0.873390I
a = −0.668200 − 0.224791I
b = 1.78864 + 0.50256I
−16.4493 + 6.5283I 0
u = 0.695265 − 0.873390I
a = −0.668200 + 0.224791I
b = 1.78864 − 0.50256I
−16.4493 − 6.5283I 0
u = 0.711162 + 0.860779I
a = −0.608050 − 0.358721I
b = −0.773545 + 0.642592I
−3.49757 + 7.28817I 0
u = 0.711162 − 0.860779I
a = −0.608050 + 0.358721I
b = −0.773545 − 0.642592I
−3.49757 − 7.28817I 0
u = 0.152045 + 1.129920I
a = 0.543142 − 0.504864I
b = −0.517588 − 0.574682I
−8.52986 − 1.24389I 0
u = 0.152045 − 1.129920I
a = 0.543142 + 0.504864I
b = −0.517588 + 0.574682I
−8.52986 + 1.24389I 0
u = 0.927854 + 0.686316I
a = 0.129275 + 0.765769I
b = 0.790898 − 0.247331I
−2.96009 + 2.72627I 0
u = 0.927854 − 0.686316I
a = 0.129275 − 0.765769I
b = 0.790898 + 0.247331I
−2.96009 − 2.72627I 0
u = 0.811068 + 0.821995I
a = 1.20206 + 1.10469I
b = 0.385751 − 1.186730I
0.74682 + 6.31225I 0
u = 0.811068 − 0.821995I
a = 1.20206 − 1.10469I
b = 0.385751 + 1.186730I
0.74682 − 6.31225I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.614787 + 0.470038I
a = 1.118150 + 0.859293I
b = 0.237265 − 0.057936I
−1.33985 − 2.52478I 5.87677 + 6.20065I
u = −0.614787 − 0.470038I
a = 1.118150 − 0.859293I
b = 0.237265 + 0.057936I
−1.33985 + 2.52478I 5.87677 − 6.20065I
u = 0.606281 + 0.460474I
a = −0.11967 − 1.89327I
b = −0.80135 + 1.17152I
−6.06901 + 4.19971I 0.46981 + 4.89096I
u = 0.606281 − 0.460474I
a = −0.11967 + 1.89327I
b = −0.80135 − 1.17152I
−6.06901 − 4.19971I 0.46981 − 4.89096I
u = 0.742696 + 0.018030I
a = 0.802844 − 0.672931I
b = 0.123330 − 0.408590I
−2.29683 − 3.13725I 3.03113 + 2.28651I
u = 0.742696 − 0.018030I
a = 0.802844 + 0.672931I
b = 0.123330 + 0.408590I
−2.29683 + 3.13725I 3.03113 − 2.28651I
u = 1.157620 + 0.544016I
a = −0.53473 + 2.17350I
b = 0.888311 − 0.750993I
−14.8647 − 0.9237I 0
u = 1.157620 − 0.544016I
a = −0.53473 − 2.17350I
b = 0.888311 + 0.750993I
−14.8647 + 0.9237I 0
u = −0.679644 + 0.115394I
a = −0.016821 + 0.810279I
b = −1.298680 − 0.546785I
−0.552090 − 1.157580I 8.72526 + 2.52584I
u = −0.679644 − 0.115394I
a = −0.016821 − 0.810279I
b = −1.298680 + 0.546785I
−0.552090 + 1.157580I 8.72526 − 2.52584I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.044930 + 0.812912I
a = −0.75989 − 1.82673I
b = −0.442668 + 1.276840I
−2.69001 + 2.91714I 0
u = 1.044930 − 0.812912I
a = −0.75989 + 1.82673I
b = −0.442668 − 1.276840I
−2.69001 − 2.91714I 0
u = −1.11456 + 0.87594I
a = −0.584881 + 1.062470I
b = −0.301834 − 1.243090I
4.07431 − 2.64903I 0
u = −1.11456 − 0.87594I
a = −0.584881 − 1.062470I
b = −0.301834 + 1.243090I
4.07431 + 2.64903I 0
u = 0.73967 + 1.23237I
a = 0.234778 + 0.158687I
b = −0.732813 − 0.431119I
−5.61316 − 1.82436I 0
u = 0.73967 − 1.23237I
a = 0.234778 − 0.158687I
b = −0.732813 + 0.431119I
−5.61316 + 1.82436I 0
u = 0.489917 + 0.265929I
a = −0.631980 − 1.069290I
b = 0.17708 + 1.44057I
0.77156 − 1.96953I 11.39719 + 1.23723I
u = 0.489917 − 0.265929I
a = −0.631980 + 1.069290I
b = 0.17708 − 1.44057I
0.77156 + 1.96953I 11.39719 − 1.23723I
u = −0.69545 + 1.27793I
a = 0.589761 − 0.467742I
b = −1.013060 + 0.642851I
−10.25240 − 0.58456I 0
u = −0.69545 − 1.27793I
a = 0.589761 + 0.467742I
b = −1.013060 − 0.642851I
−10.25240 + 0.58456I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.528848
a = −0.754706
b = −0.350552
0.833691 12.5370
u = 1.17530 + 0.94653I
a = −0.099026 − 1.222920I
b = −0.902120 + 0.943721I
−4.22732 + 9.52870I 0
u = 1.17530 − 0.94653I
a = −0.099026 + 1.222920I
b = −0.902120 − 0.943721I
−4.22732 − 9.52870I 0
u = 0.469414 + 0.086831I
a = −0.24275 + 2.14834I
b = 0.304078 − 1.019980I
0.75672 + 1.60252I 5.44397 − 2.96352I
u = 0.469414 − 0.086831I
a = −0.24275 − 2.14834I
b = 0.304078 + 1.019980I
0.75672 − 1.60252I 5.44397 + 2.96352I
u = 1.11667 + 1.07117I
a = 0.32680 + 1.51043I
b = 0.91203 − 1.47375I
−13.1892 + 15.5433I 0
u = 1.11667 − 1.07117I
a = 0.32680 − 1.51043I
b = 0.91203 + 1.47375I
−13.1892 − 15.5433I 0
u = −0.040555 + 0.445575I
a = −2.19312 + 1.06421I
b = −0.162171 − 1.085770I
−2.67022 − 3.59787I 1.26601 + 4.62354I
u = −0.040555 − 0.445575I
a = −2.19312 − 1.06421I
b = −0.162171 + 1.085770I
−2.67022 + 3.59787I 1.26601 − 4.62354I
u = −1.06557 + 1.17893I
a = 0.465568 − 0.962520I
b = 0.214621 + 1.324260I
3.14454 − 5.28865I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.06557 − 1.17893I
a = 0.465568 + 0.962520I
b = 0.214621 − 1.324260I
3.14454 + 5.28865I 0
u = −1.54201 + 0.46506I
a = −0.40850 + 1.52127I
b = −0.000517 − 1.179550I
4.85414 − 2.03164I 0
u = −1.54201 − 0.46506I
a = −0.40850 − 1.52127I
b = −0.000517 + 1.179550I
4.85414 + 2.03164I 0
u = −1.27163 + 0.99225I
a = −0.00808 + 1.62331I
b = −0.84144 − 1.21606I
−8.48368 − 7.48858I 0
u = −1.27163 − 0.99225I
a = −0.00808 − 1.62331I
b = −0.84144 + 1.21606I
−8.48368 + 7.48858I 0
u = −0.160337 + 0.343315I
a = 0.339442 + 0.084802I
b = 0.614423 + 1.266600I
0.79379 − 2.25708I 2.28794 − 4.37801I
u = −0.160337 − 0.343315I
a = 0.339442 − 0.084802I
b = 0.614423 − 1.266600I
0.79379 + 2.25708I 2.28794 + 4.37801I
u = 1.09583 + 1.21738I
a = −0.710263 − 0.627589I
b = 0.779094 + 1.174620I
−13.4744 − 7.2599I 0
u = 1.09583 − 1.21738I
a = −0.710263 + 0.627589I
b = 0.779094 − 1.174620I
−13.4744 + 7.2599I 0
u = −0.234232 + 0.257654I
a = 0.62787 − 9.86711I
b = 0.571174 + 0.777335I
−13.25520 − 3.60698I 0.0981 + 14.8573I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.234232 − 0.257654I
a = 0.62787 + 9.86711I
b = 0.571174 − 0.777335I
−13.25520 + 3.60698I 0.0981 − 14.8573I
u = −1.66651 + 0.55104I
a = −0.176083 − 0.957519I
b = 0.335346 + 0.557889I
2.14723 − 3.04462I 0
u = −1.66651 − 0.55104I
a = −0.176083 + 0.957519I
b = 0.335346 − 0.557889I
2.14723 + 3.04462I 0
11
II.
I
u
2
= h1.50 × 10
24
u
27
+ 8.28 × 10
24
u
26
+ · · · + 1.24 × 10
24
b + 2.46 × 10
24
, 4.66 ×
10
23
u
27
+2.34×10
24
u
26
+· · ·+1.24×10
24
a−2.68×10
24
, u
28
+6u
27
+· · ·+2u+1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
5
=
−0.374654u
27
− 1.88195u
26
+ ··· + 6.62313u + 2.15462
−1.20506u
27
− 6.66162u
26
+ ··· − 3.47743u − 1.97877
a
10
=
1
−u
2
a
4
=
−1.57971u
27
− 8.54357u
26
+ ··· + 3.14570u + 0.175849
−1.20506u
27
− 6.66162u
26
+ ··· − 3.47743u − 1.97877
a
3
=
−0.347434u
27
− 1.83630u
26
+ ··· + 6.91281u + 3.08931
−1.28412u
27
− 7.15895u
26
+ ··· − 3.61794u − 2.66516
a
2
=
1.99908u
27
+ 12.7360u
26
+ ··· + 6.48433u + 2.16177
−0.842153u
27
− 4.69396u
26
+ ··· − 1.32507u − 0.0688727
a
6
=
2.23949u
27
+ 13.0407u
26
+ ··· − 12.3400u − 5.56425
−0.585524u
27
− 3.13244u
26
+ ··· + 2.42745u + 0.356599
a
8
=
0.260068u
27
+ 1.72336u
26
+ ··· + 5.30274u − 0.950249
0.0297660u
27
+ 0.579857u
26
+ ··· − 1.78144u + 1.63844
a
1
=
2.39626u
27
+ 14.6108u
26
+ ··· − 17.2118u − 6.13078
−0.395076u
27
− 2.09431u
26
+ ··· + 3.82248u + 0.336223
a
7
=
−0.463227u
27
− 3.40262u
26
+ ··· + 8.77999u + 3.35500
−0.00664464u
27
+ 0.175348u
26
+ ··· − 2.87462u + 0.243559
a
11
=
−1.26164u
27
− 8.15989u
26
+ ··· − 12.1726u − 0.310184
0.564215u
27
+ 3.40566u
26
+ ··· + 0.108528u − 0.289834
(ii) Obstruction class = 1
(iii) Cusp Shapes =
14196894526534098056419915
1243689822254210224198313
u
27
+
77156772533747101068768450
1243689822254210224198313
u
26
+
··· +
18009890446390071079402793
1243689822254210224198313
u +
24155927693538196022412912
1243689822254210224198313
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
28
− 29u
27
+ ··· − 336u + 25
c
2
u
28
+ 3u
27
+ ··· + 28u + 5
c
3
u
28
+ 2u
26
+ ··· + u + 1
c
4
u
28
+ 12u
26
+ ··· + 126u
2
+ 13
c
5
u
28
− 3u
27
+ ··· − 28u + 5
c
6
u
28
+ 7u
26
+ ··· + 3u + 1
c
7
u
28
+ u
27
+ ··· − 238u + 79
c
8
u
28
+ 12u
26
+ ··· + 126u
2
+ 13
c
9
u
28
+ 6u
27
+ ··· + 2u + 1
c
10
u
28
+ 7u
26
+ ··· − 3u + 1
c
11
u
28
− 4u
26
+ ··· + 2u + 1
c
12
u
28
+ 6u
26
+ ··· − 6u + 1
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
− 39y
27
+ ··· + 18404y + 625
c
2
, c
5
y
28
+ 29y
27
+ ··· + 336y + 25
c
3
y
28
+ 4y
27
+ ··· + 23y + 1
c
4
, c
8
y
28
+ 24y
27
+ ··· + 3276y + 169
c
6
, c
10
y
28
+ 14y
27
+ ··· + 17y + 1
c
7
y
28
+ 31y
27
+ ··· + 69440y + 6241
c
9
y
28
− 6y
27
+ ··· − 8y + 1
c
11
y
28
− 8y
27
+ ··· + 16y + 1
c
12
y
28
+ 12y
27
+ ··· − 14y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.940292 + 0.413387I
a = 1.23072 + 2.12971I
b = 0.300613 − 1.070080I
−1.05959 + 4.61100I 6.51158 − 5.52677I
u = 0.940292 − 0.413387I
a = 1.23072 − 2.12971I
b = 0.300613 + 1.070080I
−1.05959 − 4.61100I 6.51158 + 5.52677I
u = 0.806078 + 0.496313I
a = 0.083024 + 0.969496I
b = 0.175391 − 1.342910I
−0.16211 − 1.47199I 4.14534 − 0.40207I
u = 0.806078 − 0.496313I
a = 0.083024 − 0.969496I
b = 0.175391 + 1.342910I
−0.16211 + 1.47199I 4.14534 + 0.40207I
u = −0.653575 + 0.631653I
a = 0.16569 − 1.53605I
b = 0.85490 + 1.21262I
−5.97610 − 4.67435I 3.55527 + 10.86527I
u = −0.653575 − 0.631653I
a = 0.16569 + 1.53605I
b = 0.85490 − 1.21262I
−5.97610 + 4.67435I 3.55527 − 10.86527I
u = 0.217968 + 1.154320I
a = −0.564796 + 0.248293I
b = −0.066810 + 0.479178I
−4.21962 − 1.45210I 5.81625 + 6.66607I
u = 0.217968 − 1.154320I
a = −0.564796 − 0.248293I
b = −0.066810 − 0.479178I
−4.21962 + 1.45210I 5.81625 − 6.66607I
u = −0.216540 + 1.244680I
a = −0.414021 − 0.246811I
b = 0.522371 − 0.713383I
−8.29018 + 0.47114I 3.38775 + 2.13311I
u = −0.216540 − 1.244680I
a = −0.414021 + 0.246811I
b = 0.522371 + 0.713383I
−8.29018 − 0.47114I 3.38775 − 2.13311I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.622908 + 0.349779I
a = −0.216133 + 1.033420I
b = −0.632440 − 1.103600I
−1.58788 + 4.47956I 8.31123 − 10.39210I
u = 0.622908 − 0.349779I
a = −0.216133 − 1.033420I
b = −0.632440 + 1.103600I
−1.58788 − 4.47956I 8.31123 + 10.39210I
u = 0.926454 + 0.990307I
a = −1.014490 − 0.881408I
b = −0.219668 + 1.137670I
−0.67708 + 7.39786I 3.61944 − 6.76047I
u = 0.926454 − 0.990307I
a = −1.014490 + 0.881408I
b = −0.219668 − 1.137670I
−0.67708 − 7.39786I 3.61944 + 6.76047I
u = −1.104760 + 0.873270I
a = −0.517047 + 1.068910I
b = −0.355700 − 1.347290I
3.39497 − 2.92110I 2.45276 + 2.72271I
u = −1.104760 − 0.873270I
a = −0.517047 − 1.068910I
b = −0.355700 + 1.347290I
3.39497 + 2.92110I 2.45276 − 2.72271I
u = −0.354078 + 0.377348I
a = 0.67911 + 1.78144I
b = 0.908649 − 0.411620I
−1.76047 − 1.65206I 2.39742 + 0.15868I
u = −0.354078 − 0.377348I
a = 0.67911 − 1.78144I
b = 0.908649 + 0.411620I
−1.76047 + 1.65206I 2.39742 − 0.15868I
u = −0.462042 + 0.226447I
a = −0.364429 + 1.069470I
b = −0.86212 − 1.27313I
0.99320 − 2.56181I 15.9971 + 14.1165I
u = −0.462042 − 0.226447I
a = −0.364429 − 1.069470I
b = −0.86212 + 1.27313I
0.99320 + 2.56181I 15.9971 − 14.1165I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.377108 + 0.341592I
a = 5.78433 + 1.20797I
b = −0.590667 − 0.703657I
−13.21040 − 3.22197I 2.66915 − 5.24743I
u = 0.377108 − 0.341592I
a = 5.78433 − 1.20797I
b = −0.590667 + 0.703657I
−13.21040 + 3.22197I 2.66915 + 5.24743I
u = −1.00439 + 1.16349I
a = 0.580992 − 0.879373I
b = 0.199655 + 1.398360I
2.49042 − 4.78963I 2.06444 + 2.28263I
u = −1.00439 − 1.16349I
a = 0.580992 + 0.879373I
b = 0.199655 − 1.398360I
2.49042 + 4.78963I 2.06444 − 2.28263I
u = −1.50088 + 0.54145I
a = 0.102083 + 0.905988I
b = −0.168069 − 0.765823I
2.69983 − 2.89612I 11.31267 + 1.19976I
u = −1.50088 − 0.54145I
a = 0.102083 − 0.905988I
b = −0.168069 + 0.765823I
2.69983 + 2.89612I 11.31267 − 1.19976I
u = −1.59455 + 0.53537I
a = 0.46497 − 1.63820I
b = −0.066099 + 1.175650I
4.33596 − 1.99981I 0
u = −1.59455 − 0.53537I
a = 0.46497 + 1.63820I
b = −0.066099 − 1.175650I
4.33596 + 1.99981I 0
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
28
− 29u
27
+ ··· − 336u + 25)
· (u
63
+ 84u
62
+ ··· + 6421262u − 290521)
c
2
(u
28
+ 3u
27
+ ··· + 28u + 5)(u
63
+ 42u
61
+ ··· + 9624u − 539)
c
3
(u
28
+ 2u
26
+ ··· + u + 1)(u
63
+ u
62
+ ··· + 41175u − 7877)
c
4
(u
28
+ 12u
26
+ ··· + 126u
2
+ 13)(u
63
+ 3u
62
+ ··· − 596u − 79)
c
5
(u
28
− 3u
27
+ ··· − 28u + 5)(u
63
+ 42u
61
+ ··· + 9624u − 539)
c
6
(u
28
+ 7u
26
+ ··· + 3u + 1)(u
63
− u
62
+ ··· − 237u − 113)
c
7
(u
28
+ u
27
+ ··· − 238u + 79)(u
63
+ 2u
62
+ ··· + 3704u − 3077)
c
8
(u
28
+ 12u
26
+ ··· + 126u
2
+ 13)(u
63
+ 3u
62
+ ··· − 596u − 79)
c
9
(u
28
+ 6u
27
+ ··· + 2u + 1)(u
63
+ 3u
62
+ ··· − 2u − 1)
c
10
(u
28
+ 7u
26
+ ··· − 3u + 1)(u
63
− u
62
+ ··· − 237u − 113)
c
11
(u
28
− 4u
26
+ ··· + 2u + 1)(u
63
− 5u
62
+ ··· − 6392u − 811)
c
12
(u
28
+ 6u
26
+ ··· − 6u + 1)(u
63
− u
62
+ ··· + 3.95965 × 10
7
u − 1.79776 × 10
7
)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
28
− 39y
27
+ ··· + 18404y + 625)
· (y
63
− 188y
62
+ ··· + 31966757369702y −84402451441)
c
2
, c
5
(y
28
+ 29y
27
+ ··· + 336y + 25)
· (y
63
+ 84y
62
+ ··· + 6421262y −290521)
c
3
(y
28
+ 4y
27
+ ··· + 23y + 1)
· (y
63
+ 27y
62
+ ··· − 719912377y −62047129)
c
4
, c
8
(y
28
+ 24y
27
+ ··· + 3276y + 169)
· (y
63
+ 27y
62
+ ··· + 125010y −6241)
c
6
, c
10
(y
28
+ 14y
27
+ ··· + 17y + 1)(y
63
+ 49y
62
+ ··· − 228139y −12769)
c
7
(y
28
+ 31y
27
+ ··· + 69440y + 6241)
· (y
63
+ 94y
62
+ ··· − 340978482y −9467929)
c
9
(y
28
− 6y
27
+ ··· − 8y + 1)(y
63
− 7y
62
+ ··· + 2y −1)
c
11
(y
28
− 8y
27
+ ··· + 16y + 1)(y
63
+ 3y
62
+ ··· + 494194y −657721)
c
12
(y
28
+ 12y
27
+ ··· − 14y + 1)
· (y
63
+ 111y
62
+ ··· − 5213792993463072y −323194065804801)
21
