11a
104
(K11a
104
)
A knot diagram
1
Linearized knot diagam
6 1 8 10 2 4 3 7 11 5 9
Solving Sequence
4,8 1,3
2 7 9 6 5 11 10
c
3
c
2
c
7
c
8
c
6
c
5
c
11
c
9
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.98593 × 10
23
u
59
+ 4.69641 × 10
23
u
58
+ ··· + 1.04287 × 10
24
b + 1.61518 × 10
24
,
3.87855 × 10
23
u
59
− 6.98208 × 10
22
u
58
+ ··· + 5.21436 × 10
23
a − 1.87163 × 10
24
, u
60
+ u
59
+ ··· + 2u + 1i
I
u
2
= hb + u, −u
3
+ u
2
+ a + u − 1, u
4
− u
2
+ 1i
I
u
3
= h−u
7
+ u
5
− 2u
3
+ b + u, −u
5
+ a − u, u
10
− 2u
8
+ 3u
6
− u
5
− 2u
4
+ u
3
+ u
2
− u + 1i
I
u
4
= hu
3
+ b − u, u
3
+ u
2
+ a − 1, u
4
− u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 78 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−1.99×10
23
u
59
+4.70×10
23
u
58
+· · ·+1.04×10
24
b+1.62×10
24
, 3.88×
10
23
u
59
−6.98×10
22
u
58
+· · ·+5.21×10
23
a−1.87×10
24
, u
60
+u
59
+· · ·+2u+1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
1
=
−0.743821u
59
+ 0.133901u
58
+ ··· + 0.842070u + 3.58938
0.190429u
59
− 0.450334u
58
+ ··· + 0.891441u − 1.54878
a
3
=
1
u
2
a
2
=
−1.04281u
59
− 0.496774u
58
+ ··· + 2.17071u + 3.63527
1.12830u
59
+ 0.201741u
58
+ ··· + 4.11950u − 0.780593
a
7
=
−u
−u
3
+ u
a
9
=
u
3
u
5
− u
3
+ u
a
6
=
−u
3
−u
3
+ u
a
5
=
−0.108079u
59
− 1.37479u
58
+ ··· + 6.24741u − 2.70886
1.06440u
59
+ 0.333999u
58
+ ··· + 3.85330u − 0.118756
a
11
=
−1.14257u
59
− 0.131348u
58
+ ··· + 0.640675u + 3.85388
1.04542u
59
+ 0.113508u
58
+ ··· + 3.47215u − 0.882378
a
10
=
0.423997u
59
− 1.42113u
58
+ ··· + 4.04661u − 5.47905
0.233872u
59
− 0.446189u
58
+ ··· + 2.50575u + 0.581286
a
10
=
0.423997u
59
− 1.42113u
58
+ ··· + 4.04661u − 5.47905
0.233872u
59
− 0.446189u
58
+ ··· + 2.50575u + 0.581286
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1243755023537317604710317
521436085097447226945316
u
59
−
113387074254912883763919
260718042548723613472658
u
58
+ ··· +
5765858860985229173060379
521436085097447226945316
u −
629576893531561210869417
130359021274361806736329
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
60
+ 4u
59
+ ··· + 20u + 4
c
2
u
60
+ 28u
59
+ ··· + 136u + 16
c
3
, c
7
u
60
− u
59
+ ··· − 2u + 1
c
4
, c
10
u
60
− u
59
+ ··· + 8u + 1
c
6
u
60
− 3u
59
+ ··· − 628u + 261
c
8
u
60
− 31u
59
+ ··· − 6u + 1
c
9
, c
11
u
60
+ 19u
59
+ ··· + 54u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
60
+ 28y
59
+ ··· + 136y + 16
c
2
y
60
+ 12y
59
+ ··· + 13024y + 256
c
3
, c
7
y
60
− 31y
59
+ ··· − 6y + 1
c
4
, c
10
y
60
− 19y
59
+ ··· − 54y + 1
c
6
y
60
+ 29y
59
+ ··· − 446062y + 68121
c
8
y
60
+ y
59
+ ··· + 38y + 1
c
9
, c
11
y
60
+ 49y
59
+ ··· − 562y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.903831 + 0.403972I
a = 1.269250 − 0.398175I
b = 1.057390 + 0.767924I
0.07179 + 4.23224I 2.32754 − 7.48197I
u = 0.903831 − 0.403972I
a = 1.269250 + 0.398175I
b = 1.057390 − 0.767924I
0.07179 − 4.23224I 2.32754 + 7.48197I
u = −0.711823 + 0.747660I
a = −0.406775 − 0.002759I
b = −0.634669 − 0.607886I
−0.59950 − 7.44517I −1.81786 + 8.61499I
u = −0.711823 − 0.747660I
a = −0.406775 + 0.002759I
b = −0.634669 + 0.607886I
−0.59950 + 7.44517I −1.81786 − 8.61499I
u = 0.804581 + 0.489615I
a = 0.265943 − 0.865672I
b = −0.177298 + 0.044040I
−1.74326 + 2.05593I −4.38675 − 3.92763I
u = 0.804581 − 0.489615I
a = 0.265943 + 0.865672I
b = −0.177298 − 0.044040I
−1.74326 − 2.05593I −4.38675 + 3.92763I
u = 0.859520 + 0.676363I
a = 0.964914 − 0.424298I
b = 0.480610 + 0.345118I
0.30698 + 3.25660I 0. − 2.79575I
u = 0.859520 − 0.676363I
a = 0.964914 + 0.424298I
b = 0.480610 − 0.345118I
0.30698 − 3.25660I 0. + 2.79575I
u = −0.311259 + 0.850032I
a = −0.321328 − 0.147611I
b = −0.73288 + 1.72138I
1.72838 + 10.40930I −1.97334 − 6.85461I
u = −0.311259 − 0.850032I
a = −0.321328 + 0.147611I
b = −0.73288 − 1.72138I
1.72838 − 10.40930I −1.97334 + 6.85461I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.865604 + 0.182246I
a = 0.606319 + 0.298940I
b = 0.748686 − 0.118582I
1.47274 − 0.43868I 6.40126 + 0.73626I
u = −0.865604 − 0.182246I
a = 0.606319 − 0.298940I
b = 0.748686 + 0.118582I
1.47274 + 0.43868I 6.40126 − 0.73626I
u = 0.272152 + 0.836204I
a = −0.196628 + 0.183823I
b = −0.68548 − 1.62535I
2.73192 − 4.52059I −0.21234 + 2.21964I
u = 0.272152 − 0.836204I
a = −0.196628 − 0.183823I
b = −0.68548 + 1.62535I
2.73192 + 4.52059I −0.21234 − 2.21964I
u = −0.568756 + 0.644224I
a = −0.676994 + 0.457932I
b = −0.717357 − 0.302413I
−5.04608 − 2.62544I −9.38058 + 3.85437I
u = −0.568756 − 0.644224I
a = −0.676994 − 0.457932I
b = −0.717357 + 0.302413I
−5.04608 + 2.62544I −9.38058 − 3.85437I
u = −0.993886 + 0.578329I
a = 0.955168 + 0.848146I
b = 0.415861 + 0.077795I
−3.79990 − 2.15619I 0
u = −0.993886 − 0.578329I
a = 0.955168 − 0.848146I
b = 0.415861 − 0.077795I
−3.79990 + 2.15619I 0
u = 1.054100 + 0.478696I
a = 1.15838 + 1.04975I
b = 0.14104 + 1.62136I
0.06948 + 4.64990I 0
u = 1.054100 − 0.478696I
a = 1.15838 − 1.04975I
b = 0.14104 − 1.62136I
0.06948 − 4.64990I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.080780 + 0.429889I
a = 0.96586 − 1.23049I
b = 0.319260 − 0.470303I
0.799952 + 0.856311I 0
u = 1.080780 − 0.429889I
a = 0.96586 + 1.23049I
b = 0.319260 + 0.470303I
0.799952 − 0.856311I 0
u = 0.210101 + 0.809324I
a = 0.740667 − 0.015178I
b = 0.105661 + 1.028970I
3.79462 − 4.80277I 0.86247 + 2.90071I
u = 0.210101 − 0.809324I
a = 0.740667 + 0.015178I
b = 0.105661 − 1.028970I
3.79462 + 4.80277I 0.86247 − 2.90071I
u = −1.116060 + 0.386772I
a = 1.21794 − 1.49474I
b = 0.00600 − 1.76185I
3.40701 − 1.33155I 0
u = −1.116060 − 0.386772I
a = 1.21794 + 1.49474I
b = 0.00600 + 1.76185I
3.40701 + 1.33155I 0
u = −0.144728 + 0.798733I
a = 0.670793 + 0.046459I
b = 0.000564 − 1.065940I
4.37725 − 1.04056I 1.90122 + 2.49141I
u = −0.144728 − 0.798733I
a = 0.670793 − 0.046459I
b = 0.000564 + 1.065940I
4.37725 + 1.04056I 1.90122 − 2.49141I
u = −1.094520 + 0.479352I
a = 1.03063 + 1.15150I
b = 0.414981 + 0.408719I
0.42302 − 6.32152I 0
u = −1.094520 − 0.479352I
a = 1.03063 − 1.15150I
b = 0.414981 − 0.408719I
0.42302 + 6.32152I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339818 + 0.708730I
a = −0.355808 − 0.663857I
b = −1.06664 + 1.47014I
−4.04431 + 4.50698I −7.28201 − 4.72365I
u = −0.339818 − 0.708730I
a = −0.355808 + 0.663857I
b = −1.06664 − 1.47014I
−4.04431 − 4.50698I −7.28201 + 4.72365I
u = 1.128850 + 0.492143I
a = −0.52081 − 2.12283I
b = 1.32820 − 1.57388I
2.66218 + 6.38495I 0
u = 1.128850 − 0.492143I
a = −0.52081 + 2.12283I
b = 1.32820 + 1.57388I
2.66218 − 6.38495I 0
u = 1.216210 + 0.225171I
a = 1.10465 + 1.80874I
b = −0.02516 + 1.64383I
6.74362 − 7.16149I 0
u = 1.216210 − 0.225171I
a = 1.10465 − 1.80874I
b = −0.02516 − 1.64383I
6.74362 + 7.16149I 0
u = −1.112300 + 0.548551I
a = −0.84176 + 2.42145I
b = 1.34785 + 2.08020I
−1.78746 − 9.32372I 0
u = −1.112300 − 0.548551I
a = −0.84176 − 2.42145I
b = 1.34785 − 2.08020I
−1.78746 + 9.32372I 0
u = −1.212780 + 0.262306I
a = 1.10372 − 1.77604I
b = −0.02790 − 1.67922I
7.49647 + 1.10876I 0
u = −1.212780 − 0.262306I
a = 1.10372 + 1.77604I
b = −0.02790 + 1.67922I
7.49647 − 1.10876I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.207080 + 0.312500I
a = −0.432975 + 1.070400I
b = 0.694965 + 0.705252I
8.19036 + 1.16781I 0
u = −1.207080 − 0.312500I
a = −0.432975 − 1.070400I
b = 0.694965 − 0.705252I
8.19036 − 1.16781I 0
u = 1.207510 + 0.352417I
a = −0.476722 − 1.234610I
b = 0.746612 − 0.850988I
8.50343 + 4.91869I 0
u = 1.207510 − 0.352417I
a = −0.476722 + 1.234610I
b = 0.746612 + 0.850988I
8.50343 − 4.91869I 0
u = −1.179680 + 0.510060I
a = 0.83860 − 1.38186I
b = −0.05723 − 1.67219I
7.41896 − 3.74798I 0
u = −1.179680 − 0.510060I
a = 0.83860 + 1.38186I
b = −0.05723 + 1.67219I
7.41896 + 3.74798I 0
u = 1.173440 + 0.538194I
a = 0.77481 + 1.33580I
b = −0.07894 + 1.64826I
6.63935 + 9.77588I 0
u = 1.173440 − 0.538194I
a = 0.77481 − 1.33580I
b = −0.07894 − 1.64826I
6.63935 − 9.77588I 0
u = 1.169570 + 0.567517I
a = −1.03891 − 2.10766I
b = 0.89396 − 2.01477I
5.40914 + 9.70793I 0
u = 1.169570 − 0.567517I
a = −1.03891 + 2.10766I
b = 0.89396 + 2.01477I
5.40914 − 9.70793I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.163930 + 0.586363I
a = −1.12390 + 2.15224I
b = 0.86334 + 2.13698I
4.2834 − 15.7183I 0
u = −1.163930 − 0.586363I
a = −1.12390 − 2.15224I
b = 0.86334 − 2.13698I
4.2834 + 15.7183I 0
u = 0.429148 + 0.530188I
a = 0.903246 − 0.132373I
b = 0.249666 + 0.565526I
−1.72663 − 0.52634I −4.33031 + 0.44248I
u = 0.429148 − 0.530188I
a = 0.903246 + 0.132373I
b = 0.249666 − 0.565526I
−1.72663 + 0.52634I −4.33031 − 0.44248I
u = 0.637665 + 0.183912I
a = −0.11399 − 1.94899I
b = −0.738126 − 0.352707I
−1.24161 + 2.23775I −0.61490 − 2.94515I
u = 0.637665 − 0.183912I
a = −0.11399 + 1.94899I
b = −0.738126 + 0.352707I
−1.24161 − 2.23775I −0.61490 + 2.94515I
u = −0.362759 + 0.416974I
a = 0.17781 − 1.91746I
b = −1.45310 + 0.56258I
−2.02553 − 1.88873I −4.74604 + 1.07620I
u = −0.362759 − 0.416974I
a = 0.17781 + 1.91746I
b = −1.45310 − 0.56258I
−2.02553 + 1.88873I −4.74604 − 1.07620I
u = −0.262460 + 0.449731I
a = −1.74210 + 0.98505I
b = −0.919872 − 0.033488I
−1.87789 + 2.29756I −4.03068 − 3.27403I
u = −0.262460 − 0.449731I
a = −1.74210 − 0.98505I
b = −0.919872 + 0.033488I
−1.87789 − 2.29756I −4.03068 + 3.27403I
10
II. I
u
2
= hb + u, −u
3
+ u
2
+ a + u − 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
1
=
u
3
− u
2
− u + 1
−u
a
3
=
1
u
2
a
2
=
u
3
− u
2
− u + 2
u
2
− u
a
7
=
−u
−u
3
+ u
a
9
=
u
3
0
a
6
=
−u
3
−u
3
+ u
a
5
=
−u
2
+ u
−u
2
+ 1
a
11
=
u
3
− u
2
+ 1
−u
a
10
=
u
3
− u
2
+ u
u
3
− u
a
10
=
u
3
− u
2
+ u
u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u
2
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
2
+ 1)
2
c
2
(u + 1)
4
c
3
, c
4
, c
6
c
7
, c
10
u
4
− u
2
+ 1
c
8
, c
9
(u
2
− u + 1)
2
c
11
(u
2
+ u + 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y + 1)
4
c
2
(y −1)
4
c
3
, c
4
, c
6
c
7
, c
10
(y
2
− y + 1)
2
c
8
, c
9
, c
11
(y
2
+ y + 1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = −0.366025 − 0.366025I
b = −0.866025 − 0.500000I
−1.64493 + 4.05977I −4.00000 − 6.92820I
u = 0.866025 − 0.500000I
a = −0.366025 + 0.366025I
b = −0.866025 + 0.500000I
−1.64493 − 4.05977I −4.00000 + 6.92820I
u = −0.866025 + 0.500000I
a = 1.36603 + 1.36603I
b = 0.866025 − 0.500000I
−1.64493 − 4.05977I −4.00000 + 6.92820I
u = −0.866025 − 0.500000I
a = 1.36603 − 1.36603I
b = 0.866025 + 0.500000I
−1.64493 + 4.05977I −4.00000 − 6.92820I
14
III. I
u
3
=
h−u
7
+u
5
−2u
3
+b+u, −u
5
+a−u, u
10
−2u
8
+3u
6
−u
5
−2u
4
+u
3
+u
2
−u+1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
1
=
u
5
+ u
u
7
− u
5
+ 2u
3
− u
a
3
=
1
u
2
a
2
=
u
8
− u
6
+ u
5
+ u
4
− u
3
+ u
u
8
+ u
7
− 2u
6
− u
5
+ 2u
4
+ u
3
− u
2
a
7
=
−u
−u
3
+ u
a
9
=
u
3
u
5
− u
3
+ u
a
6
=
−u
3
−u
3
+ u
a
5
=
1
u
2
a
11
=
u
u
3
− u
a
10
=
0
u
a
10
=
0
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
5
− 4u
3
+ 4u − 2
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
2
− u + 1)
5
c
2
(u
2
+ u + 1)
5
c
3
, c
4
, c
7
c
10
u
10
− 2u
8
+ 3u
6
+ u
5
− 2u
4
− u
3
+ u
2
+ u + 1
c
6
u
10
− 2u
8
+ 2u
7
+ u
6
+ u
5
+ 4u
4
+ 3u
3
+ 9u
2
+ 3u + 3
c
8
u
10
− 4u
9
+ 10u
8
− 16u
7
+ 19u
6
− 15u
5
+ 8u
4
− u
3
− u
2
+ u + 1
c
9
, c
11
u
10
+ 4u
9
+ 10u
8
+ 16u
7
+ 19u
6
+ 15u
5
+ 8u
4
+ u
3
− u
2
− u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y
2
+ y + 1)
5
c
3
, c
4
, c
7
c
10
y
10
− 4y
9
+ 10y
8
− 16y
7
+ 19y
6
− 15y
5
+ 8y
4
− y
3
− y
2
+ y + 1
c
6
y
10
− 4y
9
+ 6y
8
− y
6
− 35y
5
+ 4y
4
+ 63y
3
+ 87y
2
+ 45y + 9
c
8
, c
9
, c
11
y
10
+ 4y
9
+ ··· − 3y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.756352 + 0.712044I
a = −0.217740 − 0.005024I
b = −0.508756 + 0.631168I
2.02988I 0. − 3.46410I
u = 0.756352 − 0.712044I
a = −0.217740 + 0.005024I
b = −0.508756 − 0.631168I
− 2.02988I 0. + 3.46410I
u = 1.053350 + 0.290333I
a = 1.40235 + 1.80795I
b = −0.16807 + 1.84530I
− 2.02988I 0. + 3.46410I
u = 1.053350 − 0.290333I
a = 1.40235 − 1.80795I
b = −0.16807 − 1.84530I
2.02988I 0. − 3.46410I
u = −0.913599 + 0.686557I
a = 1.029360 + 0.529489I
b = 0.538198 − 0.232909I
2.02988I 0. − 3.46410I
u = −0.913599 − 0.686557I
a = 1.029360 − 0.529489I
b = 0.538198 + 0.232909I
− 2.02988I 0. + 3.46410I
u = −1.069540 + 0.472028I
a = −0.00856 + 2.38074I
b = 1.89598 + 1.33554I
− 2.02988I 0. + 3.46410I
u = −1.069540 − 0.472028I
a = −0.00856 − 2.38074I
b = 1.89598 − 1.33554I
2.02988I 0. − 3.46410I
u = 0.173445 + 0.636239I
a = 0.294586 + 0.665896I
b = −0.757353 − 1.050530I
− 2.02988I 0. + 3.46410I
u = 0.173445 − 0.636239I
a = 0.294586 − 0.665896I
b = −0.757353 + 1.050530I
2.02988I 0. − 3.46410I
18
IV. I
u
4
= hu
3
+ b − u, u
3
+ u
2
+ a − 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
1
=
−u
3
− u
2
+ 1
−u
3
+ u
a
3
=
1
u
2
a
2
=
−u
3
− u
2
+ 2
−u
3
+ u
2
+ u
a
7
=
−u
−u
3
+ u
a
9
=
u
3
0
a
6
=
−u
3
−u
3
+ u
a
5
=
u + 1
u
2
a
11
=
−u
2
− u + 1
−u
3
+ u
a
10
=
1
u
a
10
=
1
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
2
+ 1)
2
c
2
(u + 1)
4
c
3
, c
4
, c
6
c
7
, c
10
u
4
− u
2
+ 1
c
8
, c
9
(u
2
− u + 1)
2
c
11
(u
2
+ u + 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y + 1)
4
c
2
(y −1)
4
c
3
, c
4
, c
6
c
7
, c
10
(y
2
− y + 1)
2
c
8
, c
9
, 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 = 0.866025 + 0.500000I
a = 0.50000 − 1.86603I
b = 0.866025 − 0.500000I
−1.64493 −4.00000
u = 0.866025 − 0.500000I
a = 0.50000 + 1.86603I
b = 0.866025 + 0.500000I
−1.64493 −4.00000
u = −0.866025 + 0.500000I
a = 0.500000 − 0.133975I
b = −0.866025 − 0.500000I
−1.64493 −4.00000
u = −0.866025 − 0.500000I
a = 0.500000 + 0.133975I
b = −0.866025 + 0.500000I
−1.64493 −4.00000
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
((u
2
+ 1)
4
)(u
2
− u + 1)
5
(u
60
+ 4u
59
+ ··· + 20u + 4)
c
2
((u + 1)
8
)(u
2
+ u + 1)
5
(u
60
+ 28u
59
+ ··· + 136u + 16)
c
3
, c
7
(u
4
− u
2
+ 1)
2
(u
10
− 2u
8
+ 3u
6
+ u
5
− 2u
4
− u
3
+ u
2
+ u + 1)
· (u
60
− u
59
+ ··· − 2u + 1)
c
4
, c
10
(u
4
− u
2
+ 1)
2
(u
10
− 2u
8
+ 3u
6
+ u
5
− 2u
4
− u
3
+ u
2
+ u + 1)
· (u
60
− u
59
+ ··· + 8u + 1)
c
6
(u
4
− u
2
+ 1)
2
(u
10
− 2u
8
+ 2u
7
+ u
6
+ u
5
+ 4u
4
+ 3u
3
+ 9u
2
+ 3u + 3)
· (u
60
− 3u
59
+ ··· − 628u + 261)
c
8
(u
2
− u + 1)
4
· (u
10
− 4u
9
+ 10u
8
− 16u
7
+ 19u
6
− 15u
5
+ 8u
4
− u
3
− u
2
+ u + 1)
· (u
60
− 31u
59
+ ··· − 6u + 1)
c
9
(u
2
− u + 1)
4
· (u
10
+ 4u
9
+ 10u
8
+ 16u
7
+ 19u
6
+ 15u
5
+ 8u
4
+ u
3
− u
2
− u + 1)
· (u
60
+ 19u
59
+ ··· + 54u + 1)
c
11
(u
2
+ u + 1)
4
· (u
10
+ 4u
9
+ 10u
8
+ 16u
7
+ 19u
6
+ 15u
5
+ 8u
4
+ u
3
− u
2
− u + 1)
· (u
60
+ 19u
59
+ ··· + 54u + 1)
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y + 1)
8
)(y
2
+ y + 1)
5
(y
60
+ 28y
59
+ ··· + 136y + 16)
c
2
((y −1)
8
)(y
2
+ y + 1)
5
(y
60
+ 12y
59
+ ··· + 13024y + 256)
c
3
, c
7
(y
2
− y + 1)
4
· (y
10
− 4y
9
+ 10y
8
− 16y
7
+ 19y
6
− 15y
5
+ 8y
4
− y
3
− y
2
+ y + 1)
· (y
60
− 31y
59
+ ··· − 6y + 1)
c
4
, c
10
(y
2
− y + 1)
4
· (y
10
− 4y
9
+ 10y
8
− 16y
7
+ 19y
6
− 15y
5
+ 8y
4
− y
3
− y
2
+ y + 1)
· (y
60
− 19y
59
+ ··· − 54y + 1)
c
6
(y
2
− y + 1)
4
· (y
10
− 4y
9
+ 6y
8
− y
6
− 35y
5
+ 4y
4
+ 63y
3
+ 87y
2
+ 45y + 9)
· (y
60
+ 29y
59
+ ··· − 446062y + 68121)
c
8
((y
2
+ y + 1)
4
)(y
10
+ 4y
9
+ ··· − 3y + 1)(y
60
+ y
59
+ ··· + 38y + 1)
c
9
, c
11
((y
2
+ y + 1)
4
)(y
10
+ 4y
9
+ ··· − 3y + 1)(y
60
+ 49y
59
+ ··· − 562y + 1)
24
