12a
0577
(K12a
0577
)
A knot diagram
1
Linearized knot diagam
3 7 9 10 11 2 12 1 4 6 5 8
Solving Sequence
1,8 4,9
10 5 3 2 12 7 6 11
c
8
c
9
c
4
c
3
c
1
c
12
c
7
c
6
c
11
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.56312 × 10
33
u
48
+ 2.83092 × 10
33
u
47
+ ··· + 7.56342 × 10
33
b + 4.45246 × 10
32
,
− 1.28759 × 10
35
u
48
+ 2.69158 × 10
35
u
47
+ ··· + 1.21015 × 10
35
a + 9.76615 × 10
34
, u
49
− 2u
48
+ ··· − u + 1i
I
u
2
= h−u
5
+ u
3
+ b − u, u
3
+ a, u
18
− 6u
16
+ ··· − u − 1i
I
u
3
= hb + 1, a
4
− 4a
3
+ 3a
2
+ 2a + 1, u + 1i
I
u
4
= hb − 1, a
4
+ 4a
3
+ 5a
2
+ 2a − 1, u − 1i
I
u
5
= hb + 1, a − 1, u + 1i
* 5 irreducible components of dim
C
= 0, with total 76 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−2.56×10
33
u
48
+2.83×10
33
u
47
+· · ·+7.56×10
33
b+4.45×10
32
, −1.29×
10
35
u
48
+2.69×10
35
u
47
+· · ·+1.21×10
35
a+9.77×10
34
, u
49
−2u
48
+· · ·−u+1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
1.06400u
48
− 2.22417u
47
+ ··· − 66.3671u − 0.807022
0.338884u
48
− 0.374291u
47
+ ··· − 9.12038u − 0.0588683
a
9
=
1
−u
2
a
10
=
0.0728905u
48
+ 0.0869859u
47
+ ··· − 20.9570u − 12.0327
−0.0255946u
48
− 0.118358u
47
+ ··· + 0.625886u − 1.30939
a
5
=
−0.437918u
48
+ 0.654552u
47
+ ··· + 53.0608u + 0.351204
0.194691u
48
− 0.265650u
47
+ ··· + 6.68311u + 0.189616
a
3
=
0.998861u
48
− 2.15004u
47
+ ··· − 56.0865u − 0.844336
0.314692u
48
− 0.206403u
47
+ ··· − 9.12938u − 0.115001
a
2
=
1.24728u
48
− 2.43234u
47
+ ··· − 64.0218u − 0.840988
0.0651347u
48
− 0.0741368u
47
+ ··· − 9.28056u + 0.0373145
a
12
=
−u
u
a
7
=
−u
2
+ 1
u
2
a
6
=
0.0588683u
48
+ 0.221147u
47
+ ··· − 22.4060u − 9.17925
−0.0961828u
48
− 0.0813832u
47
+ ··· + 0.256973u − 1.06400
a
11
=
−0.471607u
48
+ 1.41230u
47
+ ··· − 23.3549u − 5.40971
−0.141421u
48
+ 0.0729172u
47
+ ··· + 2.01016u − 1.08423
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.776631u
48
+ 0.563664u
47
+ ··· + 20.3985u + 3.27444
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
49
+ 16u
48
+ ··· + 51u + 1
c
2
, c
6
u
49
− 2u
48
+ ··· + 3u − 1
c
3
, c
4
, c
9
u
49
+ 2u
48
+ ··· − 24u + 16
c
5
, c
10
, c
11
u
49
− 2u
48
+ ··· − 2u + 2
c
7
, c
8
, c
12
u
49
+ 2u
48
+ ··· − u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
49
+ 44y
48
+ ··· + 1819y −1
c
2
, c
6
y
49
− 16y
48
+ ··· + 51y −1
c
3
, c
4
, c
9
y
49
− 50y
48
+ ··· − 8256y −256
c
5
, c
10
, c
11
y
49
+ 38y
48
+ ··· + 8y −4
c
7
, c
8
, c
12
y
49
− 56y
48
+ ··· + 99y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.506103 + 0.862902I
a = 0.500355 + 1.042960I
b = 0.781459 + 0.968591I
3.13730 − 0.87606I 7.33623 + 1.94038I
u = −0.506103 − 0.862902I
a = 0.500355 − 1.042960I
b = 0.781459 − 0.968591I
3.13730 + 0.87606I 7.33623 − 1.94038I
u = −0.441469 + 0.898603I
a = 0.587546 + 0.830187I
b = 1.30109 + 0.70065I
2.66998 − 10.11010I 6.39603 + 7.85117I
u = −0.441469 − 0.898603I
a = 0.587546 − 0.830187I
b = 1.30109 − 0.70065I
2.66998 + 10.11010I 6.39603 − 7.85117I
u = 0.473125 + 0.885514I
a = −0.561307 + 0.937339I
b = −1.076850 + 0.869299I
6.86021 + 5.51403I 10.47160 − 5.14621I
u = 0.473125 − 0.885514I
a = −0.561307 − 0.937339I
b = −1.076850 − 0.869299I
6.86021 − 5.51403I 10.47160 + 5.14621I
u = 1.06485
a = 1.21417
b = −0.142650
5.55834 16.5270
u = −1.080520 + 0.079944I
a = −1.207880 + 0.284396I
b = 0.160341 − 0.198571I
1.65369 − 3.96617I 11.77753 + 3.57951I
u = −1.080520 − 0.079944I
a = −1.207880 − 0.284396I
b = 0.160341 + 0.198571I
1.65369 + 3.96617I 11.77753 − 3.57951I
u = 0.272859 + 0.717075I
a = 0.097380 + 0.638899I
b = −0.442768 − 0.568471I
−4.96406 + 6.00920I 0.78370 − 7.92298I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.272859 − 0.717075I
a = 0.097380 − 0.638899I
b = −0.442768 + 0.568471I
−4.96406 − 6.00920I 0.78370 + 7.92298I
u = 0.635672 + 0.423399I
a = 0.152656 + 0.981747I
b = 0.481748 − 0.043197I
−1.98468 + 1.46890I 7.38226 − 4.62534I
u = 0.635672 − 0.423399I
a = 0.152656 − 0.981747I
b = 0.481748 + 0.043197I
−1.98468 − 1.46890I 7.38226 + 4.62534I
u = −0.377239 + 0.635400I
a = −0.042557 + 0.925611I
b = 0.106013 − 0.171567I
−0.22370 − 3.57957I 7.57049 + 8.69582I
u = −0.377239 − 0.635400I
a = −0.042557 − 0.925611I
b = 0.106013 + 0.171567I
−0.22370 + 3.57957I 7.57049 − 8.69582I
u = −0.629729
a = 0.0259489
b = −0.419260
0.715837 14.7920
u = 1.367690 + 0.118584I
a = −0.083488 − 0.457258I
b = 0.151194 − 0.356963I
−1.71441 + 2.34609I 0
u = 1.367690 − 0.118584I
a = −0.083488 + 0.457258I
b = 0.151194 + 0.356963I
−1.71441 − 2.34609I 0
u = −1.370000 + 0.090098I
a = −1.174840 + 0.183507I
b = 1.076130 + 0.107236I
2.02971 − 4.19323I 0
u = −1.370000 − 0.090098I
a = −1.174840 − 0.183507I
b = 1.076130 − 0.107236I
2.02971 + 4.19323I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.45161 + 0.04249I
a = 0.952579 − 0.218245I
b = −1.17797 + 0.84568I
6.85291 + 0.94088I 0
u = 1.45161 − 0.04249I
a = 0.952579 + 0.218245I
b = −1.17797 − 0.84568I
6.85291 − 0.94088I 0
u = −1.43096 + 0.24886I
a = 1.232470 + 0.036520I
b = −1.54657 − 0.17959I
0.52977 − 9.47056I 0
u = −1.43096 − 0.24886I
a = 1.232470 − 0.036520I
b = −1.54657 + 0.17959I
0.52977 + 9.47056I 0
u = −1.46839 + 0.13155I
a = 0.244748 + 0.347671I
b = −0.535951 − 1.225870I
4.54898 − 2.99003I 0
u = −1.46839 − 0.13155I
a = 0.244748 − 0.347671I
b = −0.535951 + 1.225870I
4.54898 + 2.99003I 0
u = −1.48327 + 0.04934I
a = −0.376466 + 0.449946I
b = 0.38527 − 1.44906I
4.87290 − 2.72445I 0
u = −1.48327 − 0.04934I
a = −0.376466 − 0.449946I
b = 0.38527 + 1.44906I
4.87290 + 2.72445I 0
u = 1.47136 + 0.20824I
a = −0.878047 + 0.378522I
b = 1.42808 − 0.90342I
5.80687 + 6.61465I 0
u = 1.47136 − 0.20824I
a = −0.878047 − 0.378522I
b = 1.42808 + 0.90342I
5.80687 − 6.61465I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.315421 + 0.397601I
a = 0.039889 + 1.284920I
b = 0.405532 − 0.300525I
−1.36715 + 1.10974I 0.89311 − 1.51851I
u = 0.315421 − 0.397601I
a = 0.039889 − 1.284920I
b = 0.405532 + 0.300525I
−1.36715 − 1.10974I 0.89311 + 1.51851I
u = −0.094951 + 0.466215I
a = −0.95838 + 1.34005I
b = −0.572924 − 0.727360I
−6.38447 − 0.32683I −3.51715 + 0.79678I
u = −0.094951 − 0.466215I
a = −0.95838 − 1.34005I
b = −0.572924 + 0.727360I
−6.38447 + 0.32683I −3.51715 − 0.79678I
u = 1.52723 + 0.33642I
a = −1.97469 + 0.88742I
b = 3.60061 − 0.27568I
9.0434 + 14.6216I 0
u = 1.52723 − 0.33642I
a = −1.97469 − 0.88742I
b = 3.60061 + 0.27568I
9.0434 − 14.6216I 0
u = −1.53962 + 0.32307I
a = 1.85586 + 0.99438I
b = −3.59315 − 0.63275I
13.4023 − 9.9407I 0
u = −1.53962 − 0.32307I
a = 1.85586 − 0.99438I
b = −3.59315 + 0.63275I
13.4023 + 9.9407I 0
u = 1.54894 + 0.30323I
a = −1.67927 + 1.07256I
b = 3.42720 − 1.03218I
9.85027 + 5.15212I 0
u = 1.54894 − 0.30323I
a = −1.67927 − 1.07256I
b = 3.42720 + 1.03218I
9.85027 − 5.15212I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.57332 + 0.22114I
a = 2.12554 − 0.50767I
b = −3.82426 − 0.00661I
11.13740 + 8.11094I 0
u = 1.57332 − 0.22114I
a = 2.12554 + 0.50767I
b = −3.82426 + 0.00661I
11.13740 − 8.11094I 0
u = −1.58534 + 0.20019I
a = −2.05798 − 0.63877I
b = 3.85771 + 0.41371I
15.3567 − 3.3643I 0
u = −1.58534 − 0.20019I
a = −2.05798 + 0.63877I
b = 3.85771 − 0.41371I
15.3567 + 3.3643I 0
u = 1.59138 + 0.17411I
a = 1.93614 − 0.75434I
b = −3.71746 + 0.86616I
11.62880 − 1.45194I 0
u = 1.59138 − 0.17411I
a = 1.93614 + 0.75434I
b = −3.71746 − 0.86616I
11.62880 + 1.45194I 0
u = −0.121685 + 0.105182I
a = 6.95371 + 3.79591I
b = 1.189100 − 0.168206I
−1.63772 − 4.11971I 0.12488 + 3.37346I
u = −0.121685 − 0.105182I
a = 6.95371 − 3.79591I
b = 1.189100 + 0.168206I
−1.63772 + 4.11971I 0.12488 − 3.37346I
u = 0.106744
a = −11.6080
b = −1.16523
2.32826 4.47140
9
II. I
u
2
= h−u
5
+ u
3
+ b − u, u
3
+ a, u
18
− 6u
16
+ · · · − u − 1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
−u
3
u
5
− u
3
+ u
a
9
=
1
−u
2
a
10
=
−u
6
+ u
4
+ 1
u
8
− 2u
6
+ 2u
4
− 2u
2
a
5
=
u
9
− 2u
7
+ u
5
− 2u
3
+ u
−u
11
+ 3u
9
− 4u
7
+ 5u
5
− 3u
3
+ u
a
3
=
−u
u
a
2
=
−u
3
u
3
+ u
a
12
=
−u
u
a
7
=
−u
2
+ 1
u
2
a
6
=
u
4
− u
2
+ 1
−u
4
a
11
=
u
16
− 5u
14
+ 11u
12
− 16u
10
+ 17u
8
− 14u
6
+ 8u
4
− 2u
2
+ 1
−u
16
+ 4u
14
− 6u
12
+ 6u
10
− 4u
8
+ 2u
4
− 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
9
+ 12u
7
− 12u
5
+ 12u
3
− 8u + 10
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
+ 12u
17
+ ··· + 5u + 1
c
2
, c
6
, c
7
c
8
, c
12
u
18
− 6u
16
+ ··· + u − 1
c
3
, c
4
, c
9
(u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
3
c
5
, c
10
, c
11
(u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
3
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
− 12y
17
+ ··· + 7y + 1
c
2
, c
6
, c
7
c
8
, c
12
y
18
− 12y
17
+ ··· − 5y + 1
c
3
, c
4
, c
9
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
3
c
5
, c
10
, c
11
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1)
3
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.672231 + 0.755934I
a = −0.848635 − 0.592839I
b = −1.019800 − 0.770263I
3.69558 − 4.59213I 8.58114 + 3.20482I
u = −0.672231 − 0.755934I
a = −0.848635 + 0.592839I
b = −1.019800 + 0.770263I
3.69558 + 4.59213I 8.58114 − 3.20482I
u = 0.945797 + 0.372369I
a = −0.452617 − 0.947657I
b = 0.167799 + 0.459832I
−2.96024 − 1.97241I 4.57572 + 3.68478I
u = 0.945797 − 0.372369I
a = −0.452617 + 0.947657I
b = 0.167799 − 0.459832I
−2.96024 + 1.97241I 4.57572 − 3.68478I
u = 0.719335 + 0.743187I
a = 0.819709 − 0.743187I
b = 0.773023 − 0.902358I
7.66009 12.26950 + 0.I
u = 0.719335 − 0.743187I
a = 0.819709 + 0.743187I
b = 0.773023 + 0.902358I
7.66009 12.26950 + 0.I
u = −0.763761 + 0.724480I
a = −0.757105 − 0.887576I
b = −0.494362 − 0.949066I
3.69558 + 4.59213I 8.58114 − 3.20482I
u = −0.763761 − 0.724480I
a = −0.757105 + 0.887576I
b = −0.494362 + 0.949066I
3.69558 − 4.59213I 8.58114 + 3.20482I
u = 1.18645
a = −1.67012
b = 1.86730
0.738851 13.4170
u = −1.219960 + 0.167385I
a = 1.71314 − 0.74267I
b = −1.70520 + 1.20889I
−2.96024 − 1.97241I 4.57572 + 3.68478I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.219960 − 0.167385I
a = 1.71314 + 0.74267I
b = −1.70520 − 1.20889I
−2.96024 + 1.97241I 4.57572 − 3.68478I
u = −0.593225 + 0.236109I
a = 0.109553 − 0.236109I
b = −0.449977 + 0.100617I
0.738851 13.41678 + 0.I
u = −0.593225 − 0.236109I
a = 0.109553 + 0.236109I
b = −0.449977 − 0.100617I
0.738851 13.41678 + 0.I
u = 0.274166 + 0.539754I
a = 0.219014 + 0.035534I
b = 0.551041 + 0.518149I
−2.96024 + 1.97241I 4.57572 − 3.68478I
u = 0.274166 − 0.539754I
a = 0.219014 − 0.035534I
b = 0.551041 − 0.518149I
−2.96024 − 1.97241I 4.57572 + 3.68478I
u = 1.43599 + 0.03145I
a = −2.95686 − 0.19455I
b = 4.55589 + 0.50499I
3.69558 + 4.59213I 8.58114 − 3.20482I
u = 1.43599 − 0.03145I
a = −2.95686 + 0.19455I
b = 4.55589 − 0.50499I
3.69558 − 4.59213I 8.58114 + 3.20482I
u = −1.43867
a = 2.97771
b = −4.62413
7.66009 12.2690
14
III. I
u
3
= hb + 1, a
4
− 4a
3
+ 3a
2
+ 2a + 1, u + 1i
(i) Arc colorings
a
1
=
0
−1
a
8
=
1
0
a
4
=
a
−1
a
9
=
1
−1
a
10
=
−a
2
+ a + 1
a − 2
a
5
=
−a
3
+ 2a
2
+ a − 1
a
2
− 3a + 1
a
3
=
1
a − 2
a
2
=
1
a − 3
a
12
=
1
−1
a
7
=
0
1
a
6
=
1
a − 2
a
11
=
a
3
− 4a
2
+ 3a + 1
−a
3
+ 5a
2
− 5a − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a
2
+ 8a + 8
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
(u − 1)
4
c
3
, c
4
, c
9
u
4
− 3u
2
+ 3
c
5
, c
10
, c
11
u
4
+ 3u
2
+ 3
c
6
, c
7
, c
8
(u + 1)
4
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
(y −1)
4
c
3
, c
4
, c
9
(y
2
− 3y + 3)
2
c
5
, c
10
, c
11
(y
2
+ 3y + 3)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.271230 + 0.340625I
b = −1.00000
− 4.05977I 6.00000 + 3.46410I
u = −1.00000
a = −0.271230 − 0.340625I
b = −1.00000
4.05977I 6.00000 − 3.46410I
u = −1.00000
a = 2.27123 + 0.34063I
b = −1.00000
4.05977I 6.00000 − 3.46410I
u = −1.00000
a = 2.27123 − 0.34063I
b = −1.00000
− 4.05977I 6.00000 + 3.46410I
18
IV. I
u
4
= hb − 1, a
4
+ 4a
3
+ 5a
2
+ 2a − 1, u − 1i
(i) Arc colorings
a
1
=
0
1
a
8
=
1
0
a
4
=
a
1
a
9
=
1
−1
a
10
=
−a
2
− a + 1
−a − 2
a
5
=
−a
3
− 2a
2
+ a + 1
−a
2
− 3a − 1
a
3
=
−1
a + 2
a
2
=
−1
a + 3
a
12
=
−1
1
a
7
=
0
1
a
6
=
1
−a − 2
a
11
=
−a
3
− 4a
2
− 3a + 1
a
3
+ 3a
2
+ a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a
2
+ 8a + 8
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
c
8
(u − 1)
4
c
2
, c
12
(u + 1)
4
c
3
, c
4
, c
9
u
4
− u
2
− 1
c
5
, c
10
, c
11
u
4
+ u
2
− 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
(y −1)
4
c
3
, c
4
, c
9
(y
2
− y −1)
2
c
5
, c
10
, c
11
(y
2
+ y −1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.000000 + 0.786151I
b = 1.00000
−3.94784 1.52786 + 0.I
u = 1.00000
a = −1.000000 − 0.786151I
b = 1.00000
−3.94784 1.52786 + 0.I
u = 1.00000
a = 0.272020
b = 1.00000
3.94784 10.4720
u = 1.00000
a = −2.27202
b = 1.00000
3.94784 10.4720
22
V. I
u
5
= hb + 1, a − 1, u + 1i
(i) Arc colorings
a
1
=
0
−1
a
8
=
1
0
a
4
=
1
−1
a
9
=
1
−1
a
10
=
1
−1
a
5
=
1
−1
a
3
=
1
−1
a
2
=
1
−2
a
12
=
1
−1
a
7
=
0
1
a
6
=
1
−1
a
11
=
1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
u − 1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
c
6
, c
7
, c
8
u + 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
y −1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000
b = −1.00000
0 0
26
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
18
+ 12u
17
+ ··· + 5u + 1)(u
49
+ 16u
48
+ ··· + 51u + 1)
c
2
((u − 1)
5
)(u + 1)
4
(u
18
− 6u
16
+ ··· + u − 1)(u
49
− 2u
48
+ ··· + 3u − 1)
c
3
, c
4
, c
9
u(u
4
− 3u
2
+ 3)(u
4
− u
2
− 1)(u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
3
· (u
49
+ 2u
48
+ ··· − 24u + 16)
c
5
, c
10
, c
11
u(u
4
+ u
2
− 1)(u
4
+ 3u
2
+ 3)(u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
3
· (u
49
− 2u
48
+ ··· − 2u + 2)
c
6
((u − 1)
4
)(u + 1)
5
(u
18
− 6u
16
+ ··· + u − 1)(u
49
− 2u
48
+ ··· + 3u − 1)
c
7
, c
8
((u − 1)
4
)(u + 1)
5
(u
18
− 6u
16
+ ··· + u − 1)(u
49
+ 2u
48
+ ··· − u − 1)
c
12
((u − 1)
5
)(u + 1)
4
(u
18
− 6u
16
+ ··· + u − 1)(u
49
+ 2u
48
+ ··· − u − 1)
27
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
18
− 12y
17
+ ··· + 7y + 1)(y
49
+ 44y
48
+ ··· + 1819y −1)
c
2
, c
6
((y −1)
9
)(y
18
− 12y
17
+ ··· − 5y + 1)(y
49
− 16y
48
+ ··· + 51y −1)
c
3
, c
4
, c
9
y(y
2
− 3y + 3)
2
(y
2
− y −1)
2
· (y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
3
· (y
49
− 50y
48
+ ··· − 8256y −256)
c
5
, c
10
, c
11
y(y
2
+ y −1)
2
(y
2
+ 3y + 3)
2
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1)
3
· (y
49
+ 38y
48
+ ··· + 8y −4)
c
7
, c
8
, c
12
((y −1)
9
)(y
18
− 12y
17
+ ··· − 5y + 1)(y
49
− 56y
48
+ ··· + 99y −1)
28
