11a
128
(K11a
128
)
A knot diagram
1
Linearized knot diagam
6 1 7 10 2 8 3 5 11 4 9
Solving Sequence
2,5 6,8
7 9 1 3 11 10 4
c
5
c
6
c
8
c
1
c
2
c
11
c
9
c
4
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
27
+ u
26
+ ··· + 8b + 1, −u
27
+ u
26
+ ··· + 8a − 7, u
28
+ 6u
26
+ ··· − 2u + 1i
I
u
2
= h−1.55682 × 10
17
u
41
+ 7.44166 × 10
16
u
40
+ ··· + 3.93707 × 10
17
b − 4.00955 × 10
17
,
− 3.62508 × 10
17
u
41
+ 5.17336 × 10
17
u
40
+ ··· + 3.93707 × 10
17
a + 8.90477 × 10
17
, u
42
− u
41
+ ··· + 2u + 1i
I
u
3
= hb − a − 1, a
3
− a
2
u + 3a
2
− 2au + a − 1, u
2
+ 1i
* 3 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−u
27
+u
26
+· · ·+8b+1, −u
27
+u
26
+· · ·+8a−7, u
28
+6u
26
+· · ·−2u+1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
8
=
1
8
u
27
−
1
8
u
26
+ ··· +
3
8
u +
7
8
1
8
u
27
−
1
8
u
26
+ ··· +
3
8
u −
1
8
a
7
=
1
8
u
27
−
1
8
u
26
+ ··· +
3
8
u +
7
8
1
8
u
27
−
1
8
u
26
+ ··· +
3
8
u −
1
8
a
9
=
u
4
+ u
2
+ 1
1
8
u
27
−
1
8
u
26
+ ··· +
3
8
u −
1
8
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
11
=
1
8
u
27
+
1
8
u
26
+ ··· −
17
8
u +
1
8
5
8
u
27
+
7
8
u
26
+ ··· −
3
8
u +
9
8
a
10
=
−
3
4
u
27
+
1
4
u
26
+ ··· − 2u +
3
2
−
9
8
u
27
−
5
8
u
26
+ ··· −
19
8
u −
1
8
a
4
=
−
1
8
u
27
−
1
8
u
26
+ ··· +
9
8
u −
1
8
−
1
8
u
27
−
1
8
u
26
+ ··· +
9
8
u −
1
8
a
4
=
−
1
8
u
27
−
1
8
u
26
+ ··· +
9
8
u −
1
8
−
1
8
u
27
−
1
8
u
26
+ ··· +
9
8
u −
1
8
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
9
2
u
27
− 26u
25
+ ··· − 20u +
7
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
7
u
28
+ 6u
26
+ ··· − 2u + 1
c
2
, c
6
u
28
+ 12u
27
+ ··· + 10u + 1
c
4
, c
10
u
28
+ 3u
27
+ ··· + u + 2
c
8
u
28
− 15u
27
+ ··· − 785u + 86
c
9
, c
11
u
28
− 9u
27
+ ··· − 19u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
7
y
28
+ 12y
27
+ ··· + 10y + 1
c
2
, c
6
y
28
+ 16y
27
+ ··· + 30y + 1
c
4
, c
10
y
28
+ 9y
27
+ ··· + 19y + 4
c
8
y
28
− 3y
27
+ ··· + 53715y + 7396
c
9
, c
11
y
28
+ 21y
27
+ ··· + 111y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.759562 + 0.603461I
a = 0.262237 − 0.123439I
b = −0.155404 + 1.183400I
5.48513 − 0.99092I 8.59434 + 2.33645I
u = −0.759562 − 0.603461I
a = 0.262237 + 0.123439I
b = −0.155404 − 1.183400I
5.48513 + 0.99092I 8.59434 − 2.33645I
u = 0.616775 + 0.724242I
a = −0.025809 − 0.273919I
b = −0.104321 − 0.909807I
0.69719 + 2.24985I 1.09419 − 3.47682I
u = 0.616775 − 0.724242I
a = −0.025809 + 0.273919I
b = −0.104321 + 0.909807I
0.69719 − 2.24985I 1.09419 + 3.47682I
u = −0.724810 + 0.770942I
a = −0.188930 − 0.061129I
b = 0.124282 + 0.902212I
2.05272 − 7.06945I 3.67598 + 8.34686I
u = −0.724810 − 0.770942I
a = −0.188930 + 0.061129I
b = 0.124282 − 0.902212I
2.05272 + 7.06945I 3.67598 − 8.34686I
u = −0.802758 + 0.434476I
a = 0.573015 − 0.162109I
b = −0.603664 + 1.171140I
1.06471 + 4.87874I 4.05798 − 2.77982I
u = −0.802758 − 0.434476I
a = 0.573015 + 0.162109I
b = −0.603664 − 1.171140I
1.06471 − 4.87874I 4.05798 + 2.77982I
u = 0.416029 + 1.025630I
a = −1.55269 − 1.44392I
b = −1.71795 − 0.79732I
−6.63635 − 0.10967I −3.90050 − 2.81899I
u = 0.416029 − 1.025630I
a = −1.55269 + 1.44392I
b = −1.71795 + 0.79732I
−6.63635 + 0.10967I −3.90050 + 2.81899I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.436495 + 1.052560I
a = −1.72314 + 1.24024I
b = −1.80300 + 0.47325I
−7.02411 − 5.90283I −4.75289 + 7.68964I
u = −0.436495 − 1.052560I
a = −1.72314 − 1.24024I
b = −1.80300 − 0.47325I
−7.02411 + 5.90283I −4.75289 − 7.68964I
u = 0.606810 + 1.011990I
a = −1.232890 − 0.281742I
b = −0.498787 + 0.101237I
0.54803 + 3.32331I 2.18088 − 2.29510I
u = 0.606810 − 1.011990I
a = −1.232890 + 0.281742I
b = −0.498787 − 0.101237I
0.54803 − 3.32331I 2.18088 + 2.29510I
u = 0.715634 + 0.398949I
a = 0.607712 + 0.041457I
b = −0.543805 − 0.932641I
0.030119 + 0.482942I 2.45869 − 2.54239I
u = 0.715634 − 0.398949I
a = 0.607712 − 0.041457I
b = −0.543805 + 0.932641I
0.030119 − 0.482942I 2.45869 + 2.54239I
u = −0.570794 + 1.089040I
a = −1.68154 + 0.34539I
b = −1.015660 − 0.550205I
−1.89491 − 7.14346I −3.37367 + 6.75053I
u = −0.570794 − 1.089040I
a = −1.68154 − 0.34539I
b = −1.015660 + 0.550205I
−1.89491 + 7.14346I −3.37367 − 6.75053I
u = 0.626024 + 1.122830I
a = −1.73728 − 0.00452I
b = −0.646939 + 1.032570I
2.17277 + 9.75277I 3.46320 − 8.11852I
u = 0.626024 − 1.122830I
a = −1.73728 + 0.00452I
b = −0.646939 − 1.032570I
2.17277 − 9.75277I 3.46320 + 8.11852I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.023188 + 0.692895I
a = 2.34879 − 0.20424I
b = 1.59940 − 0.20555I
−4.98395 + 2.93184I 0.79314 − 3.40006I
u = 0.023188 − 0.692895I
a = 2.34879 + 0.20424I
b = 1.59940 + 0.20555I
−4.98395 − 2.93184I 0.79314 + 3.40006I
u = −0.588545 + 1.173310I
a = −2.06199 + 0.06635I
b = −1.18576 − 1.39834I
−4.61324 − 9.81937I −3.57047 + 5.81179I
u = −0.588545 − 1.173310I
a = −2.06199 − 0.06635I
b = −1.18576 + 1.39834I
−4.61324 + 9.81937I −3.57047 − 5.81179I
u = 0.605210 + 1.183850I
a = −2.06950 + 0.03808I
b = −1.05260 + 1.57196I
−3.5733 + 15.6943I −1.82098 − 10.41623I
u = 0.605210 − 1.183850I
a = −2.06950 − 0.03808I
b = −1.05260 − 1.57196I
−3.5733 − 15.6943I −1.82098 + 10.41623I
u = 0.273295 + 0.395938I
a = 0.982020 − 0.270229I
b = 0.104195 − 0.451120I
0.225861 + 1.065080I 3.10010 − 6.65254I
u = 0.273295 − 0.395938I
a = 0.982020 + 0.270229I
b = 0.104195 + 0.451120I
0.225861 − 1.065080I 3.10010 + 6.65254I
7
II.
I
u
2
= h−1.56×10
17
u
41
+7.44×10
16
u
40
+· · ·+3.94×10
17
b−4.01×10
17
, −3.63×
10
17
u
41
+5.17×10
17
u
40
+· · ·+3.94×10
17
a+8.90×10
17
, u
42
−u
41
+· · ·+2u+1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
8
=
0.920756u
41
− 1.31402u
40
+ ··· − 0.678222u − 2.26178
0.395427u
41
− 0.189015u
40
+ ··· + 0.318945u + 1.01841
a
7
=
0.525329u
41
− 1.12500u
40
+ ··· − 0.997167u − 2.28019
0.154289u
41
− 0.155024u
40
+ ··· + 0.0143489u + 1.24208
a
9
=
0.525329u
41
− 1.12500u
40
+ ··· − 0.997167u − 3.28019
0.395427u
41
− 0.189015u
40
+ ··· + 0.318945u + 1.01841
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
11
=
−1.16179u
41
+ 1.49863u
40
+ ··· − 7.64525u − 3.07967
−0.0610512u
41
+ 0.300717u
40
+ ··· + 4.24243u + 0.892006
a
10
=
−1.05647u
41
− 0.115032u
40
+ ··· + 1.79735u + 2.62565
0.333742u
41
− 0.317542u
40
+ ··· − 2.13420u − 1.49818
a
4
=
1.61808u
41
− 1.69040u
40
+ ··· + 4.35493u + 2.24321
−0.222935u
41
+ 0.0950704u
40
+ ··· − 2.85741u − 0.597649
a
4
=
1.61808u
41
− 1.69040u
40
+ ··· + 4.35493u + 2.24321
−0.222935u
41
+ 0.0950704u
40
+ ··· − 2.85741u − 0.597649
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
750018447371229972
393706681309071797
u
41
+
1326377308854531456
393706681309071797
u
40
+ ··· +
3939201724436401700
393706681309071797
u +
974136661643821530
393706681309071797
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
7
u
42
− u
41
+ ··· + 2u + 1
c
2
, c
6
u
42
+ 23u
41
+ ··· + 22u
2
+ 1
c
4
, c
10
(u
21
− u
20
+ ··· + u − 1)
2
c
8
(u
21
+ 5u
20
+ ··· − 11u − 3)
2
c
9
, c
11
(u
21
− 7u
20
+ ··· + 3u + 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
7
y
42
+ 23y
41
+ ··· + 22y
2
+ 1
c
2
, c
6
y
42
− 9y
41
+ ··· + 44y + 1
c
4
, c
10
(y
21
+ 7y
20
+ ··· + 3y −1)
2
c
8
(y
21
+ 3y
20
+ ··· − 41y −9)
2
c
9
, c
11
(y
21
+ 15y
20
+ ··· + 27y −1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.384983 + 0.893506I
a = −1.61437 − 0.96323I
b = −0.207726 + 0.818105I
−1.26832 + 1.59690I 3.13274 − 4.73829I
u = 0.384983 − 0.893506I
a = −1.61437 + 0.96323I
b = −0.207726 − 0.818105I
−1.26832 − 1.59690I 3.13274 + 4.73829I
u = 0.900670 + 0.302277I
a = −0.0782845 − 0.0466257I
b = 0.86562 + 1.42640I
−0.91901 − 10.18330I 1.25382 + 7.21296I
u = 0.900670 − 0.302277I
a = −0.0782845 + 0.0466257I
b = 0.86562 − 1.42640I
−0.91901 + 10.18330I 1.25382 − 7.21296I
u = −0.656782 + 0.830369I
a = 1.211820 − 0.034605I
b = 0.128800 + 0.461641I
1.85425 + 1.80763I 4.25907 − 2.73625I
u = −0.656782 − 0.830369I
a = 1.211820 + 0.034605I
b = 0.128800 − 0.461641I
1.85425 − 1.80763I 4.25907 + 2.73625I
u = 0.843980 + 0.412000I
a = 0.264230 − 0.021493I
b = 0.433674 + 1.104090I
4.29768 − 4.29720I 6.75143 + 3.93304I
u = 0.843980 − 0.412000I
a = 0.264230 + 0.021493I
b = 0.433674 − 1.104090I
4.29768 + 4.29720I 6.75143 − 3.93304I
u = 0.742093 + 0.573520I
a = 0.729163 + 0.038018I
b = 0.128800 + 0.461641I
1.85425 + 1.80763I 4.25907 − 2.73625I
u = 0.742093 − 0.573520I
a = 0.729163 − 0.038018I
b = 0.128800 − 0.461641I
1.85425 − 1.80763I 4.25907 + 2.73625I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.528906 + 0.927109I
a = 1.321410 + 0.194864I
b = 0.641247 − 0.630310I
0.10785 + 2.26276I −0.12423 − 3.11409I
u = 0.528906 − 0.927109I
a = 1.321410 − 0.194864I
b = 0.641247 + 0.630310I
0.10785 − 2.26276I −0.12423 + 3.11409I
u = −0.860486 + 0.285796I
a = −0.0772165 − 0.0782315I
b = 0.93790 − 1.24922I
−1.96895 + 4.48385I −0.56586 − 2.47352I
u = −0.860486 − 0.285796I
a = −0.0772165 + 0.0782315I
b = 0.93790 + 1.24922I
−1.96895 − 4.48385I −0.56586 + 2.47352I
u = −0.239332 + 1.082520I
a = −1.021360 + 0.939730I
b = −0.510732
−4.11368 −8.21539 + 0.I
u = −0.239332 − 1.082520I
a = −1.021360 − 0.939730I
b = −0.510732
−4.11368 −8.21539 + 0.I
u = 0.125880 + 1.108300I
a = 0.910717 + 0.374635I
b = 1.127110 + 0.099375I
−4.65974 + 2.68588I −1.85070 − 3.67518I
u = 0.125880 − 1.108300I
a = 0.910717 − 0.374635I
b = 1.127110 − 0.099375I
−4.65974 − 2.68588I −1.85070 + 3.67518I
u = 0.478722 + 1.037960I
a = −1.54549 − 1.29421I
b = −0.98839 + 1.06606I
−6.19421 + 6.51836I −3.49661 − 6.69162I
u = 0.478722 − 1.037960I
a = −1.54549 + 1.29421I
b = −0.98839 − 1.06606I
−6.19421 − 6.51836I −3.49661 + 6.69162I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.444142 + 1.066230I
a = −1.44535 + 1.30052I
b = −1.065450 − 0.815532I
−6.94955 − 0.90110I −5.44354 + 1.25880I
u = −0.444142 − 1.066230I
a = −1.44535 − 1.30052I
b = −1.065450 + 0.815532I
−6.94955 + 0.90110I −5.44354 − 1.25880I
u = −0.638288 + 0.999696I
a = 1.45241 − 0.09124I
b = 0.433674 + 1.104090I
4.29768 − 4.29720I 6.75143 + 3.93304I
u = −0.638288 − 0.999696I
a = 1.45241 + 0.09124I
b = 0.433674 − 1.104090I
4.29768 + 4.29720I 6.75143 − 3.93304I
u = −0.046915 + 1.192480I
a = 0.505321 − 0.535434I
b = 0.882596 − 0.417746I
−4.44976 + 2.73152I −0.80842 − 2.00184I
u = −0.046915 − 1.192480I
a = 0.505321 + 0.535434I
b = 0.882596 + 0.417746I
−4.44976 − 2.73152I −0.80842 + 2.00184I
u = −0.690143 + 0.400372I
a = 0.429900 − 0.357030I
b = 0.641247 − 0.630310I
0.10785 + 2.26276I −0.12423 − 3.11409I
u = −0.690143 − 0.400372I
a = 0.429900 + 0.357030I
b = 0.641247 + 0.630310I
0.10785 − 2.26276I −0.12423 + 3.11409I
u = 0.580018 + 1.088560I
a = 1.53519 + 0.23279I
b = 0.93790 − 1.24922I
−1.96895 + 4.48385I −0.56586 − 2.47352I
u = 0.580018 − 1.088560I
a = 1.53519 − 0.23279I
b = 0.93790 + 1.24922I
−1.96895 − 4.48385I −0.56586 + 2.47352I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.135211 + 1.234020I
a = −0.331836 − 1.074640I
b = −0.207726 − 0.818105I
−1.26832 − 1.59690I 3.13274 + 4.73829I
u = 0.135211 − 1.234020I
a = −0.331836 + 1.074640I
b = −0.207726 + 0.818105I
−1.26832 + 1.59690I 3.13274 − 4.73829I
u = −0.613478 + 1.100460I
a = 1.58130 − 0.19672I
b = 0.86562 + 1.42640I
−0.91901 − 10.18330I 1.00000 + 7.21296I
u = −0.613478 − 1.100460I
a = 1.58130 + 0.19672I
b = 0.86562 − 1.42640I
−0.91901 + 10.18330I 1.00000 − 7.21296I
u = −0.264739 + 1.262700I
a = −0.67780 + 1.45363I
b = −1.065450 + 0.815532I
−6.94955 + 0.90110I −5.44354 − 1.25880I
u = −0.264739 − 1.262700I
a = −0.67780 − 1.45363I
b = −1.065450 − 0.815532I
−6.94955 − 0.90110I −5.44354 + 1.25880I
u = 0.243106 + 1.291400I
a = −0.55702 − 1.49792I
b = −0.98839 − 1.06606I
−6.19421 − 6.51836I −3.49661 + 6.69162I
u = 0.243106 − 1.291400I
a = −0.55702 + 1.49792I
b = −0.98839 + 1.06606I
−6.19421 + 6.51836I −3.49661 − 6.69162I
u = 0.315798 + 0.452715I
a = −2.24033 − 1.05440I
b = 0.882596 + 0.417746I
−4.44976 − 2.73152I −0.80842 + 2.00184I
u = 0.315798 − 0.452715I
a = −2.24033 + 1.05440I
b = 0.882596 − 0.417746I
−4.44976 + 2.73152I −0.80842 − 2.00184I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.325064 + 0.154969I
a = −1.85243 + 2.34864I
b = 1.127110 − 0.099375I
−4.65974 − 2.68588I −1.85070 + 3.67518I
u = −0.325064 − 0.154969I
a = −1.85243 − 2.34864I
b = 1.127110 + 0.099375I
−4.65974 + 2.68588I −1.85070 − 3.67518I
15
III. I
u
3
= hb − a − 1, a
3
− a
2
u + 3a
2
− 2au + a − 1, u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
1
a
8
=
a
a + 1
a
7
=
a + 1
a + 2
a
9
=
−1
a + 1
a
1
=
−u
0
a
3
=
u
u
a
11
=
au
−a
2
u − 2au − u
a
10
=
a
2
+ a − 1
−a
2
u − 2au − a − 1
a
4
=
−au
−au − u
a
4
=
−au
−au − u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a
2
+ 4au − 8a + 4u − 4
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
7
(u
2
+ 1)
3
c
2
(u + 1)
6
c
4
, c
10
u
6
+ u
4
+ 2u
2
+ 1
c
6
(u − 1)
6
c
8
u
6
− 3u
4
+ 2u
2
+ 1
c
9
(u
3
+ u
2
+ 2u + 1)
2
c
11
(u
3
− u
2
+ 2u − 1)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
7
(y + 1)
6
c
2
, c
6
(y −1)
6
c
4
, c
10
(y
3
+ y
2
+ 2y + 1)
2
c
8
(y
3
− 3y
2
+ 2y + 1)
2
c
9
, c
11
(y
3
+ 3y
2
+ 2y −1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −1.000000 + 0.569840I
b = 0.569840I
−2.17641 −6 − 0.980489 + 0.10I
u = 1.000000I
a = 0.307141 + 0.215080I
b = 1.307140 + 0.215080I
−6.31400 − 2.82812I −7.50976 + 2.97945I
u = 1.000000I
a = −2.30714 + 0.21508I
b = −1.307140 + 0.215080I
−6.31400 + 2.82812I −7.50976 − 2.97945I
u = − 1.000000I
a = −1.000000 − 0.569840I
b = − 0.569840I
−2.17641 −6 − 0.980489 + 0.10I
u = − 1.000000I
a = 0.307141 − 0.215080I
b = 1.307140 − 0.215080I
−6.31400 + 2.82812I −7.50976 − 2.97945I
u = − 1.000000I
a = −2.30714 − 0.21508I
b = −1.307140 − 0.215080I
−6.31400 − 2.82812I −7.50976 + 2.97945I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
7
((u
2
+ 1)
3
)(u
28
+ 6u
26
+ ··· − 2u + 1)(u
42
− u
41
+ ··· + 2u + 1)
c
2
((u + 1)
6
)(u
28
+ 12u
27
+ ··· + 10u + 1)(u
42
+ 23u
41
+ ··· + 22u
2
+ 1)
c
4
, c
10
(u
6
+ u
4
+ 2u
2
+ 1)(u
21
− u
20
+ ··· + u − 1)
2
(u
28
+ 3u
27
+ ··· + u + 2)
c
6
((u − 1)
6
)(u
28
+ 12u
27
+ ··· + 10u + 1)(u
42
+ 23u
41
+ ··· + 22u
2
+ 1)
c
8
(u
6
− 3u
4
+ 2u
2
+ 1)(u
21
+ 5u
20
+ ··· − 11u − 3)
2
· (u
28
− 15u
27
+ ··· − 785u + 86)
c
9
((u
3
+ u
2
+ 2u + 1)
2
)(u
21
− 7u
20
+ ··· + 3u + 1)
2
· (u
28
− 9u
27
+ ··· − 19u + 4)
c
11
((u
3
− u
2
+ 2u − 1)
2
)(u
21
− 7u
20
+ ··· + 3u + 1)
2
· (u
28
− 9u
27
+ ··· − 19u + 4)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
7
((y + 1)
6
)(y
28
+ 12y
27
+ ··· + 10y + 1)(y
42
+ 23y
41
+ ··· + 22y
2
+ 1)
c
2
, c
6
((y −1)
6
)(y
28
+ 16y
27
+ ··· + 30y + 1)(y
42
− 9y
41
+ ··· + 44y + 1)
c
4
, c
10
((y
3
+ y
2
+ 2y + 1)
2
)(y
21
+ 7y
20
+ ··· + 3y −1)
2
· (y
28
+ 9y
27
+ ··· + 19y + 4)
c
8
((y
3
− 3y
2
+ 2y + 1)
2
)(y
21
+ 3y
20
+ ··· − 41y −9)
2
· (y
28
− 3y
27
+ ··· + 53715y + 7396)
c
9
, c
11
((y
3
+ 3y
2
+ 2y −1)
2
)(y
21
+ 15y
20
+ ··· + 27y −1)
2
· (y
28
+ 21y
27
+ ··· + 111y + 16)
21
