12n
0826
(K12n
0826
)
A knot diagram
1
Linearized knot diagam
4 6 11 8 2 12 10 4 1 7 3 8
Solving Sequence
7,12 3,6
2 5 11 4 1 10 8 9
c
6
c
2
c
5
c
11
c
3
c
1
c
10
c
7
c
8
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h3.56490 × 10
251
u
63
+ 5.72448 × 10
251
u
62
+ ··· + 5.50146 × 10
254
b + 8.86861 × 10
253
,
− 2.35876 × 10
254
u
63
− 4.13220 × 10
254
u
62
+ ··· + 4.26363 × 10
255
a + 8.91301 × 10
256
,
u
64
+ 2u
63
+ ··· − 735u − 124i
I
u
2
= h284428202u
14
+ 396867456u
13
+ ··· + 506758949b + 426150472,
− 8189375817u
14
− 6846809578u
13
+ ··· + 2533794745a + 27837731986,
u
15
+ u
14
− u
13
+ 6u
12
+ 26u
11
+ 12u
10
− 24u
9
− 24u
8
− 10u
7
− 32u
6
+ 9u
5
+ 51u
4
+ 12u
3
− 17u
2
− 6u − 1i
* 2 irreducible components of dim
C
= 0, with total 79 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
= h3.56 × 10
251
u
63
+ 5.72 × 10
251
u
62
+ · · · + 5.50 × 10
254
b + 8.87 ×
10
253
, −2.36 × 10
254
u
63
− 4.13 × 10
254
u
62
+ · · · + 4.26 × 10
255
a + 8.91 ×
10
256
, u
64
+ 2u
63
+ · · · − 735u − 124i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
0.0553228u
63
+ 0.0969175u
62
+ ··· − 78.2318u − 20.9047
−0.000647992u
63
− 0.00104054u
62
+ ··· − 1.92857u − 0.161205
a
6
=
1
−u
2
a
2
=
0.0567994u
63
+ 0.100527u
62
+ ··· − 83.3905u − 22.7682
−0.000281111u
63
− 0.000325930u
62
+ ··· − 2.59418u − 0.242607
a
5
=
0.0564900u
63
+ 0.0995986u
62
+ ··· − 85.0876u − 19.9751
0.00255943u
63
+ 0.00450226u
62
+ ··· + 0.805611u + 1.02426
a
11
=
−0.165563u
63
− 0.264911u
62
+ ··· + 226.261u + 27.5914
0.00582935u
63
+ 0.00991425u
62
+ ··· − 9.04574u − 1.72680
a
4
=
0.0723938u
63
− 0.000941407u
62
+ ··· − 43.1756u + 139.987
−0.0116628u
63
− 0.0183746u
62
+ ··· + 13.8692u + 1.03110
a
1
=
−2.03665u
63
− 3.81811u
62
+ ··· + 3046.36u + 1071.95
0.0128152u
63
+ 0.0318513u
62
+ ··· − 25.6739u − 16.6834
a
10
=
−0.159734u
63
− 0.254996u
62
+ ··· + 217.215u + 25.8646
0.00582935u
63
+ 0.00991425u
62
+ ··· − 9.04574u − 1.72680
a
8
=
−0.135914u
63
− 0.259560u
62
+ ··· + 202.668u + 78.8031
0.00237433u
63
+ 0.00489477u
62
+ ··· − 1.28540u − 0.718444
a
9
=
2.15886u
63
+ 3.39630u
62
+ ··· − 2926.06u − 284.022
−0.0649284u
63
− 0.111193u
62
+ ··· + 97.1411u + 21.8225
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.208334u
63
+ 0.401745u
62
+ ··· − 321.895u − 123.850
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
64
− 5u
63
+ ··· + 1916u + 23
c
2
, c
5
u
64
+ 2u
63
+ ··· − 9167u − 1601
c
3
, c
11
u
64
− 7u
63
+ ··· + 229u + 41
c
4
, c
8
u
64
− u
63
+ ··· + 2985u + 1949
c
6
u
64
+ 2u
63
+ ··· − 735u − 124
c
7
, c
10
u
64
− 8u
63
+ ··· + 355u − 25
c
9
u
64
+ u
63
+ ··· + 8216u − 400
c
12
u
64
+ 31u
63
+ ··· − 13162594u − 3152393
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
64
+ 91y
63
+ ··· − 2472756y + 529
c
2
, c
5
y
64
− 36y
63
+ ··· − 23099829y + 2563201
c
3
, c
11
y
64
+ 41y
63
+ ··· + 48501y + 1681
c
4
, c
8
y
64
− 71y
63
+ ··· − 12929063y + 3798601
c
6
y
64
− 12y
63
+ ··· − 119121y + 15376
c
7
, c
10
y
64
+ 46y
63
+ ··· + 6025y + 625
c
9
y
64
+ 75y
63
+ ··· − 82949056y + 160000
c
12
y
64
− 291y
63
+ ··· + 164152624346502y + 9937581626449
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.633361 + 0.835451I
a = −0.530837 + 1.034980I
b = −1.22852 − 1.74056I
9.22096 + 8.60656I −4.00000 − 6.23706I
u = −0.633361 − 0.835451I
a = −0.530837 − 1.034980I
b = −1.22852 + 1.74056I
9.22096 − 8.60656I −4.00000 + 6.23706I
u = 0.253229 + 0.900252I
a = 0.646605 − 0.735868I
b = 0.197400 − 0.437594I
3.52271 + 1.68170I 3.06688 − 2.85627I
u = 0.253229 − 0.900252I
a = 0.646605 + 0.735868I
b = 0.197400 + 0.437594I
3.52271 − 1.68170I 3.06688 + 2.85627I
u = −0.377573 + 0.852675I
a = 0.896250 − 0.658963I
b = −1.065120 + 0.904713I
3.87587 + 2.56306I −0.62210 − 7.87266I
u = −0.377573 − 0.852675I
a = 0.896250 + 0.658963I
b = −1.065120 − 0.904713I
3.87587 − 2.56306I −0.62210 + 7.87266I
u = 0.968214 + 0.475093I
a = 0.677564 − 0.491270I
b = 0.176332 + 0.400779I
4.21273 − 5.33178I 0
u = 0.968214 − 0.475093I
a = 0.677564 + 0.491270I
b = 0.176332 − 0.400779I
4.21273 + 5.33178I 0
u = 0.773876 + 0.769109I
a = 0.892108 − 0.775301I
b = 0.281562 − 0.440255I
8.67364 − 9.43479I 0
u = 0.773876 − 0.769109I
a = 0.892108 + 0.775301I
b = 0.281562 + 0.440255I
8.67364 + 9.43479I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.859282 + 0.057231I
a = −0.94062 + 1.30856I
b = −0.294118 − 0.799242I
1.356600 − 0.236124I −10.20366 + 0.45727I
u = −0.859282 − 0.057231I
a = −0.94062 − 1.30856I
b = −0.294118 + 0.799242I
1.356600 + 0.236124I −10.20366 − 0.45727I
u = −0.637038 + 0.946755I
a = 0.399510 + 0.471571I
b = 0.408356 + 0.442921I
1.75404 + 3.75138I 0
u = −0.637038 − 0.946755I
a = 0.399510 − 0.471571I
b = 0.408356 − 0.442921I
1.75404 − 3.75138I 0
u = −0.857334
a = 0.655331
b = 0.234820
−2.02039 −2.98300
u = 0.890002 + 0.755372I
a = −0.560431 − 1.010460I
b = −0.14451 + 1.51757I
−5.87560 − 2.84637I 0
u = 0.890002 − 0.755372I
a = −0.560431 + 1.010460I
b = −0.14451 − 1.51757I
−5.87560 + 2.84637I 0
u = −0.905414 + 0.761217I
a = 0.319731 − 0.980710I
b = 1.01703 + 1.40700I
1.05509 + 3.06315I 0
u = −0.905414 − 0.761217I
a = 0.319731 + 0.980710I
b = 1.01703 − 1.40700I
1.05509 − 3.06315I 0
u = 0.629031 + 0.441968I
a = −0.590354 − 1.251080I
b = −1.30236 + 1.41946I
−0.87655 − 3.21386I −5.46121 + 1.99366I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.629031 − 0.441968I
a = −0.590354 + 1.251080I
b = −1.30236 − 1.41946I
−0.87655 + 3.21386I −5.46121 − 1.99366I
u = 0.745958
a = −0.843570
b = −0.794982
−2.75005 2.80630
u = 0.325605 + 1.226800I
a = −0.479590 + 0.579451I
b = 0.135918 + 0.142703I
11.41820 − 3.52473I 0
u = 0.325605 − 1.226800I
a = −0.479590 − 0.579451I
b = 0.135918 − 0.142703I
11.41820 + 3.52473I 0
u = 0.499154 + 0.523034I
a = −0.352111 − 0.051255I
b = 0.811508 − 0.885581I
5.67586 + 1.02167I 0.667278 + 0.621622I
u = 0.499154 − 0.523034I
a = −0.352111 + 0.051255I
b = 0.811508 + 0.885581I
5.67586 − 1.02167I 0.667278 − 0.621622I
u = 1.233920 + 0.559467I
a = 0.154791 + 0.866376I
b = −0.10145 − 1.88879I
−5.32904 − 3.11782I 0
u = 1.233920 − 0.559467I
a = 0.154791 − 0.866376I
b = −0.10145 + 1.88879I
−5.32904 + 3.11782I 0
u = −0.666405 + 1.183570I
a = 0.923395 − 0.459675I
b = 0.647996 + 0.764798I
1.02762 − 2.42841I 0
u = −0.666405 − 1.183570I
a = 0.923395 + 0.459675I
b = 0.647996 − 0.764798I
1.02762 + 2.42841I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.113490 + 0.809533I
a = −0.233838 − 1.094600I
b = −0.77959 + 1.53834I
−2.47783 − 8.59651I 0
u = 1.113490 − 0.809533I
a = −0.233838 + 1.094600I
b = −0.77959 − 1.53834I
−2.47783 + 8.59651I 0
u = −0.604799 + 0.139734I
a = 0.485635 − 1.204360I
b = −0.556677 + 0.966102I
−0.236047 + 0.888762I −5.62676 − 4.10196I
u = −0.604799 − 0.139734I
a = 0.485635 + 1.204360I
b = −0.556677 − 0.966102I
−0.236047 − 0.888762I −5.62676 + 4.10196I
u = 0.607795 + 0.087221I
a = −0.74621 − 1.56542I
b = 0.68831 + 1.51458I
−0.88330 + 3.97137I −1.334301 − 0.429545I
u = 0.607795 − 0.087221I
a = −0.74621 + 1.56542I
b = 0.68831 − 1.51458I
−0.88330 − 3.97137I −1.334301 + 0.429545I
u = 0.329116 + 0.508643I
a = −0.34712 + 2.17987I
b = −0.460457 + 0.282285I
0.391230 − 0.353831I −2.98869 − 0.49409I
u = 0.329116 − 0.508643I
a = −0.34712 − 2.17987I
b = −0.460457 − 0.282285I
0.391230 + 0.353831I −2.98869 + 0.49409I
u = −1.14937 + 0.90634I
a = −0.347312 + 0.828119I
b = −0.076957 − 1.360690I
−6.72812 + 3.57989I 0
u = −1.14937 − 0.90634I
a = −0.347312 − 0.828119I
b = −0.076957 + 1.360690I
−6.72812 − 3.57989I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.02527 + 1.46729I
a = −0.603836 + 0.026259I
b = 0.038716 + 0.193115I
0.33931 + 2.46518I 0
u = −0.02527 − 1.46729I
a = −0.603836 − 0.026259I
b = 0.038716 − 0.193115I
0.33931 − 2.46518I 0
u = −1.15018 + 0.95185I
a = 0.338925 − 0.857634I
b = 0.21681 + 1.86662I
−0.23323 + 9.95941I 0
u = −1.15018 − 0.95185I
a = 0.338925 + 0.857634I
b = 0.21681 − 1.86662I
−0.23323 − 9.95941I 0
u = −0.373052 + 0.273303I
a = 0.467221 − 1.081940I
b = −0.213074 + 0.512505I
−0.286450 + 0.969073I −5.20156 − 6.74642I
u = −0.373052 − 0.273303I
a = 0.467221 + 1.081940I
b = −0.213074 − 0.512505I
−0.286450 − 0.969073I −5.20156 + 6.74642I
u = −0.064752 + 0.327363I
a = −2.26682 + 0.73356I
b = 0.76192 − 1.90756I
5.41696 + 1.08390I 7.59845 − 2.56360I
u = −0.064752 − 0.327363I
a = −2.26682 − 0.73356I
b = 0.76192 + 1.90756I
5.41696 − 1.08390I 7.59845 + 2.56360I
u = −0.264144 + 0.158619I
a = −2.22385 − 11.81440I
b = 0.174020 + 0.255284I
1.84425 − 0.21555I −54.1683 − 39.7304I
u = −0.264144 − 0.158619I
a = −2.22385 + 11.81440I
b = 0.174020 − 0.255284I
1.84425 + 0.21555I −54.1683 + 39.7304I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.51312 + 1.02719I
a = −0.147229 + 0.787597I
b = −0.85869 − 1.71762I
−4.27079 + 6.80776I 0
u = −1.51312 − 1.02719I
a = −0.147229 − 0.787597I
b = −0.85869 + 1.71762I
−4.27079 − 6.80776I 0
u = −1.42579 + 1.18878I
a = 0.215991 − 0.781332I
b = 1.04536 + 1.90254I
4.6282 + 16.0012I 0
u = −1.42579 − 1.18878I
a = 0.215991 + 0.781332I
b = 1.04536 − 1.90254I
4.6282 − 16.0012I 0
u = 1.89889 + 0.04609I
a = 0.259481 + 0.412233I
b = 0.01829 − 2.23354I
6.42656 + 2.16286I 0
u = 1.89889 − 0.04609I
a = 0.259481 − 0.412233I
b = 0.01829 + 2.23354I
6.42656 − 2.16286I 0
u = 1.64927 + 1.03875I
a = 0.137830 + 0.664791I
b = 1.06970 − 2.10818I
−1.72416 − 8.22153I 0
u = 1.64927 − 1.03875I
a = 0.137830 − 0.664791I
b = 1.06970 + 2.10818I
−1.72416 + 8.22153I 0
u = 1.71347 + 1.01637I
a = 0.168962 + 0.420273I
b = 2.00584 − 2.12827I
6.48830 + 3.36563I 0
u = 1.71347 − 1.01637I
a = 0.168962 − 0.420273I
b = 2.00584 + 2.12827I
6.48830 − 3.36563I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.85043 + 0.96309I
a = −0.431038 + 0.249730I
b = −0.75543 − 1.82108I
6.12807 − 2.09855I 0
u = −1.85043 − 0.96309I
a = −0.431038 − 0.249730I
b = −0.75543 + 1.82108I
6.12807 + 2.09855I 0
u = −1.32939 + 2.57903I
a = 0.318575 − 0.116709I
b = 1.42196 + 1.34450I
6.24532 − 4.56303I 0
u = −1.32939 − 2.57903I
a = 0.318575 + 0.116709I
b = 1.42196 − 1.34450I
6.24532 + 4.56303I 0
11
II.
I
u
2
= h2.84 × 10
8
u
14
+ 3.97 × 10
8
u
13
+ · · · + 5.07 × 10
8
b + 4.26 × 10
8
, −8.19 ×
10
9
u
14
−6.85×10
9
u
13
+· · ·+2.53× 10
9
a+2.78×10
10
, u
15
+u
14
+· · ·−6u − 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
3.23206u
14
+ 2.70220u
13
+ ··· − 61.4746u − 10.9866
−0.561269u
14
− 0.783148u
13
+ ··· − 4.05570u − 0.840933
a
6
=
1
−u
2
a
2
=
2.65780u
14
+ 1.80378u
13
+ ··· − 65.4774u − 12.3574
−0.119451u
14
− 0.0902996u
13
+ ··· − 1.53653u − 0.516781
a
5
=
2.70220u
14
+ 2.15934u
13
+ ··· − 53.0688u − 7.75452
0.0495199u
14
+ 0.0757808u
13
+ ··· + 0.0115506u − 0.198240
a
11
=
−6.42929u
14
− 4.92808u
13
+ ··· + 115.242u + 4.54807
−0.125520u
14
+ 0.0522556u
13
+ ··· + 7.01627u + 1.26673
a
4
=
7.05889u
14
+ 2.95931u
13
+ ··· − 126.691u + 32.5632
0.412693u
14
+ 0.120412u
13
+ ··· − 13.9640u − 1.29863
a
1
=
−16.6301u
14
− 19.6871u
13
+ ··· + 325.929u + 144.504
0.000494896u
14
− 0.495565u
13
+ ··· − 7.85539u + 2.68332
a
10
=
−6.55481u
14
− 4.87583u
13
+ ··· + 122.258u + 5.81480
−0.125520u
14
+ 0.0522556u
13
+ ··· + 7.01627u + 1.26673
a
8
=
4.05411u
14
+ 4.62887u
13
+ ··· − 73.3182u − 29.1773
0.264042u
14
+ 0.287559u
13
+ ··· + 2.00556u − 0.550328
a
9
=
−39.5909u
14
− 29.6382u
13
+ ··· + 741.709u + 48.4775
−1.18765u
14
− 0.793252u
13
+ ··· + 35.0448u + 6.68072
(ii) Obstruction class = 1
(iii) Cusp Shap es = −
6764270976
2533794745
u
14
−
13464586804
2533794745
u
13
+ ··· +
54402764179
2533794745
u +
37139257588
2533794745
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
15
+ 4u
14
+ ··· + 31u − 11
c
2
u
15
+ 5u
14
+ ··· − 12u − 9
c
3
u
15
− 2u
14
+ ··· + 2u + 1
c
4
u
15
+ 4u
14
+ ··· + 5u
2
− 1
c
5
u
15
− 5u
14
+ ··· − 12u + 9
c
6
u
15
+ u
14
+ ··· − 6u − 1
c
7
u
15
− 3u
14
+ ··· + 30u − 7
c
8
u
15
− 4u
14
+ ··· − 5u
2
+ 1
c
9
u
15
+ 6u
13
+ ··· + 3u − 1
c
10
u
15
+ 3u
14
+ ··· + 30u + 7
c
11
u
15
+ 2u
14
+ ··· + 2u − 1
c
12
u
15
+ 10u
14
+ ··· + 21u + 9
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
+ 8y
14
+ ··· − 29y −121
c
2
, c
5
y
15
− 11y
14
+ ··· + 504y −81
c
3
, c
11
y
15
+ 10y
14
+ ··· − 14y −1
c
4
, c
8
y
15
− 6y
14
+ ··· + 10y −1
c
6
y
15
− 3y
14
+ ··· + 2y −1
c
7
, c
10
y
15
+ 11y
14
+ ··· − 10y −49
c
9
y
15
+ 12y
14
+ ··· + 11y −1
c
12
y
15
− 46y
14
+ ··· + 153y −81
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.210934 + 1.069980I
a = 0.349370 + 0.185058I
b = −0.648553 + 0.253657I
1.22966 − 2.43908I −0.15311 + 1.71479I
u = 0.210934 − 1.069980I
a = 0.349370 − 0.185058I
b = −0.648553 − 0.253657I
1.22966 + 2.43908I −0.15311 − 1.71479I
u = 0.884019 + 0.098357I
a = −0.056574 − 0.974530I
b = 1.08511 + 2.03952I
4.78310 − 1.20532I −6.85327 + 1.75712I
u = 0.884019 − 0.098357I
a = −0.056574 + 0.974530I
b = 1.08511 − 2.03952I
4.78310 + 1.20532I −6.85327 − 1.75712I
u = 0.875489
a = −0.596402
b = −0.730423
−3.25365 −14.4510
u = −0.772671 + 0.267375I
a = 0.109162 − 1.363130I
b = 0.90057 + 1.67261I
−1.41494 + 4.47917I −9.52176 − 8.69041I
u = −0.772671 − 0.267375I
a = 0.109162 + 1.363130I
b = 0.90057 − 1.67261I
−1.41494 − 4.47917I −9.52176 + 8.69041I
u = −1.111680 + 0.803082I
a = −0.366596 + 0.898410I
b = 0.02909 − 1.54137I
−7.54522 + 3.13534I −12.90276 − 1.18531I
u = −1.111680 − 0.803082I
a = −0.366596 − 0.898410I
b = 0.02909 + 1.54137I
−7.54522 − 3.13534I −12.90276 + 1.18531I
u = −1.50791 + 0.90732I
a = −0.118198 + 0.835276I
b = −0.80441 − 1.75992I
−4.71766 + 7.82049I −7.90270 − 7.21830I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50791 − 0.90732I
a = −0.118198 − 0.835276I
b = −0.80441 + 1.75992I
−4.71766 − 7.82049I −7.90270 + 7.21830I
u = −0.157840 + 0.171948I
a = 0.10064 − 10.05960I
b = −0.272890 − 0.178968I
1.94655 − 0.28740I 10.27253 + 8.40570I
u = −0.157840 − 0.171948I
a = 0.10064 + 10.05960I
b = −0.272890 + 0.178968I
1.94655 + 0.28740I 10.27253 − 8.40570I
u = 1.51740 + 1.84920I
a = 0.280397 + 0.100742I
b = 1.57630 − 1.96372I
7.34533 + 4.44406I 3.28670 − 5.71136I
u = 1.51740 − 1.84920I
a = 0.280397 − 0.100742I
b = 1.57630 + 1.96372I
7.34533 − 4.44406I 3.28670 + 5.71136I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
15
+ 4u
14
+ ··· + 31u − 11)(u
64
− 5u
63
+ ··· + 1916u + 23)
c
2
(u
15
+ 5u
14
+ ··· − 12u − 9)(u
64
+ 2u
63
+ ··· − 9167u − 1601)
c
3
(u
15
− 2u
14
+ ··· + 2u + 1)(u
64
− 7u
63
+ ··· + 229u + 41)
c
4
(u
15
+ 4u
14
+ ··· + 5u
2
− 1)(u
64
− u
63
+ ··· + 2985u + 1949)
c
5
(u
15
− 5u
14
+ ··· − 12u + 9)(u
64
+ 2u
63
+ ··· − 9167u − 1601)
c
6
(u
15
+ u
14
+ ··· − 6u − 1)(u
64
+ 2u
63
+ ··· − 735u − 124)
c
7
(u
15
− 3u
14
+ ··· + 30u − 7)(u
64
− 8u
63
+ ··· + 355u − 25)
c
8
(u
15
− 4u
14
+ ··· − 5u
2
+ 1)(u
64
− u
63
+ ··· + 2985u + 1949)
c
9
(u
15
+ 6u
13
+ ··· + 3u − 1)(u
64
+ u
63
+ ··· + 8216u − 400)
c
10
(u
15
+ 3u
14
+ ··· + 30u + 7)(u
64
− 8u
63
+ ··· + 355u − 25)
c
11
(u
15
+ 2u
14
+ ··· + 2u − 1)(u
64
− 7u
63
+ ··· + 229u + 41)
c
12
(u
15
+ 10u
14
+ ··· + 21u + 9)
· (u
64
+ 31u
63
+ ··· − 13162594u − 3152393)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
15
+ 8y
14
+ ··· − 29y −121)(y
64
+ 91y
63
+ ··· − 2472756y + 529)
c
2
, c
5
(y
15
− 11y
14
+ ··· + 504y −81)
· (y
64
− 36y
63
+ ··· − 23099829y + 2563201)
c
3
, c
11
(y
15
+ 10y
14
+ ··· − 14y −1)(y
64
+ 41y
63
+ ··· + 48501y + 1681)
c
4
, c
8
(y
15
− 6y
14
+ ··· + 10y −1)
· (y
64
− 71y
63
+ ··· − 12929063y + 3798601)
c
6
(y
15
− 3y
14
+ ··· + 2y −1)(y
64
− 12y
63
+ ··· − 119121y + 15376)
c
7
, c
10
(y
15
+ 11y
14
+ ··· − 10y −49)(y
64
+ 46y
63
+ ··· + 6025y + 625)
c
9
(y
15
+ 12y
14
+ ··· + 11y −1)
· (y
64
+ 75y
63
+ ··· − 82949056y + 160000)
c
12
(y
15
− 46y
14
+ ··· + 153y −81)
· (y
64
− 291y
63
+ ··· + 164152624346502y + 9937581626449)
20
