12a
0504
(K12a
0504
)
A knot diagram
1
Linearized knot diagam
3 7 8 9 10 12 2 5 4 1 6 11
Solving Sequence
4,9
5 10
1,6
11 8 3 2 7 12
c
4
c
9
c
5
c
10
c
8
c
3
c
1
c
7
c
12
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.83895 × 10
14
u
55
+ 1.45886 × 10
14
u
54
+ ··· + 3.67417 × 10
15
b − 1.23817 × 10
16
,
9.64057 × 10
16
u
55
− 1.02861 × 10
17
u
54
+ ··· + 1.46967 × 10
16
a + 5.86299 × 10
17
, u
56
− u
55
+ ··· + 12u + 1i
I
u
2
= h−u
8
− 2u
6
− 2u
4
+ b, −u
6
− u
4
+ a + 1, u
24
+ 8u
22
+ ··· + 2u − 1i
I
u
3
= hb + 1, a
2
− au − 2a + u, u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 84 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−7.84×10
14
u
55
+1.46×10
14
u
54
+· · ·+3.67×10
15
b−1.24×10
16
, 9.64×
10
16
u
55
−1.03×10
17
u
54
+· · ·+1.47×10
16
a+5.86×10
17
, u
56
−u
55
+· · ·+12u+1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
10
=
−u
u
a
1
=
−6.55969u
55
+ 6.99890u
54
+ ··· − 234.424u − 39.8933
0.213353u
55
− 0.0397057u
54
+ ··· + 14.8733u + 3.36993
a
6
=
−u
4
− u
2
+ 1
u
4
+ 2u
2
a
11
=
−7.30147u
55
+ 8.14558u
54
+ ··· − 237.184u − 48.1301
−0.805092u
55
+ 0.773921u
54
+ ··· − 22.7624u − 4.24178
a
8
=
u
u
3
+ u
a
3
=
−u
4
− u
2
+ 1
−u
6
− 2u
4
− u
2
a
2
=
−6.66140u
55
+ 7.11337u
54
+ ··· − 239.072u − 41.8370
−0.0587147u
55
− 0.0808551u
54
+ ··· + 16.5555u + 3.49674
a
7
=
−2.86544u
55
+ 2.88023u
54
+ ··· − 100.769u − 25.4493
−0.943701u
55
+ 1.04541u
54
+ ··· − 36.4118u − 6.67618
a
12
=
−6.53973u
55
+ 7.49680u
54
+ ··· − 215.901u − 45.3003
−1.08495u
55
+ 0.999699u
54
+ ··· − 25.8687u − 4.36852
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
14833210943177139
3674173150903357
u
55
+
13598122062567921
3674173150903357
u
54
+···−
427855008730402692
3674173150903357
u−
136869864770758331
3674173150903357
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
56
+ 29u
55
+ ··· + 6u + 1
c
2
, c
7
u
56
+ u
55
+ ··· − 2u + 1
c
3
, c
5
u
56
+ 2u
55
+ ··· − 464u + 32
c
4
, c
8
, c
9
u
56
+ u
55
+ ··· − 12u + 1
c
6
, c
11
u
56
− 2u
55
+ ··· − 3u + 2
c
10
, c
12
u
56
+ 20u
55
+ ··· − 19u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
56
+ y
55
+ ··· + 78y + 1
c
2
, c
7
y
56
+ 29y
55
+ ··· + 6y + 1
c
3
, c
5
y
56
− 42y
55
+ ··· − 81664y + 1024
c
4
, c
8
, c
9
y
56
+ 49y
55
+ ··· − 90y + 1
c
6
, c
11
y
56
− 20y
55
+ ··· + 19y + 4
c
10
, c
12
y
56
+ 32y
55
+ ··· − 33y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.889558 + 0.109792I
a = 0.480562 − 0.208021I
b = −1.39404 − 1.26418I
−5.62716 − 11.26020I −12.2899 + 8.2594I
u = 0.889558 − 0.109792I
a = 0.480562 + 0.208021I
b = −1.39404 + 1.26418I
−5.62716 + 11.26020I −12.2899 − 8.2594I
u = 0.185587 + 0.860066I
a = −1.024400 + 0.085895I
b = −0.0405782 + 0.0105793I
1.79150 − 2.20957I −3.12470 + 4.68768I
u = 0.185587 − 0.860066I
a = −1.024400 − 0.085895I
b = −0.0405782 − 0.0105793I
1.79150 + 2.20957I −3.12470 − 4.68768I
u = −0.861042 + 0.114062I
a = 0.614579 + 0.107443I
b = −1.091830 + 0.875986I
−4.20562 + 5.74688I −10.33539 − 3.77278I
u = −0.861042 − 0.114062I
a = 0.614579 − 0.107443I
b = −1.091830 − 0.875986I
−4.20562 − 5.74688I −10.33539 + 3.77278I
u = 0.860629 + 0.049985I
a = 0.413499 + 0.208652I
b = −1.88213 − 0.20431I
−10.13050 − 4.55338I −16.9525 + 3.5771I
u = 0.860629 − 0.049985I
a = 0.413499 − 0.208652I
b = −1.88213 + 0.20431I
−10.13050 + 4.55338I −16.9525 − 3.5771I
u = 0.805415 + 0.008477I
a = 0.690320 − 0.645957I
b = −1.58304 − 0.97985I
−6.37248 − 2.26636I −13.85594 + 1.85600I
u = 0.805415 − 0.008477I
a = 0.690320 + 0.645957I
b = −1.58304 + 0.97985I
−6.37248 + 2.26636I −13.85594 − 1.85600I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.348712 + 1.145540I
a = −1.46239 + 0.70535I
b = 0.639092 + 0.118002I
0.79022 − 2.20219I 0
u = −0.348712 − 1.145540I
a = −1.46239 − 0.70535I
b = 0.639092 − 0.118002I
0.79022 + 2.20219I 0
u = −0.787481 + 0.037354I
a = 0.799208 − 0.381112I
b = −1.144440 − 0.535672I
−4.76193 + 2.90653I −11.38592 − 3.37449I
u = −0.787481 − 0.037354I
a = 0.799208 + 0.381112I
b = −1.144440 + 0.535672I
−4.76193 − 2.90653I −11.38592 + 3.37449I
u = −0.020700 + 1.221230I
a = −0.733753 + 1.108360I
b = 0.060419 − 0.425354I
1.78925 − 1.40742I 0
u = −0.020700 − 1.221230I
a = −0.733753 − 1.108360I
b = 0.060419 + 0.425354I
1.78925 + 1.40742I 0
u = −0.638508 + 0.407850I
a = 0.739741 − 0.354164I
b = 0.589927 − 0.778722I
1.25611 + 6.62961I −7.45851 − 9.59429I
u = −0.638508 − 0.407850I
a = 0.739741 + 0.354164I
b = 0.589927 + 0.778722I
1.25611 − 6.62961I −7.45851 + 9.59429I
u = 0.273524 + 1.225730I
a = −0.725644 − 0.884759I
b = 0.356539 + 0.597946I
2.31046 − 2.56681I 0
u = 0.273524 − 1.225730I
a = −0.725644 + 0.884759I
b = 0.356539 − 0.597946I
2.31046 + 2.56681I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.577497 + 0.456433I
a = 0.431719 + 0.400148I
b = 0.359836 + 0.827641I
1.72923 − 1.31419I −5.78155 + 3.99484I
u = 0.577497 − 0.456433I
a = 0.431719 − 0.400148I
b = 0.359836 − 0.827641I
1.72923 + 1.31419I −5.78155 − 3.99484I
u = −0.142801 + 1.272040I
a = 0.036090 + 1.373970I
b = 0.474215 − 0.667513I
0.98358 + 4.96048I 0
u = −0.142801 − 1.272040I
a = 0.036090 − 1.373970I
b = 0.474215 + 0.667513I
0.98358 − 4.96048I 0
u = 0.354849 + 1.262830I
a = 1.64828 + 0.90921I
b = −0.868433 − 0.073319I
−2.48382 − 1.91013I 0
u = 0.354849 − 1.262830I
a = 1.64828 − 0.90921I
b = −0.868433 + 0.073319I
−2.48382 + 1.91013I 0
u = 0.058481 + 1.310540I
a = −0.153203 − 1.271200I
b = 0.086213 + 0.977970I
4.34759 − 2.11198I 0
u = 0.058481 − 1.310540I
a = −0.153203 + 1.271200I
b = 0.086213 − 0.977970I
4.34759 + 2.11198I 0
u = −0.366060 + 1.267250I
a = −1.13826 + 1.74843I
b = 1.48110 − 0.89517I
−2.57041 + 4.26504I 0
u = −0.366060 − 1.267250I
a = −1.13826 − 1.74843I
b = 1.48110 + 0.89517I
−2.57041 − 4.26504I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.346195 + 1.296780I
a = 0.98892 − 1.05718I
b = −0.612467 + 0.642893I
−0.59522 + 6.99644I 0
u = −0.346195 − 1.296780I
a = 0.98892 + 1.05718I
b = −0.612467 − 0.642893I
−0.59522 − 6.99644I 0
u = 0.390452 + 1.308290I
a = 1.15405 + 1.99315I
b = −1.52261 − 1.10872I
−5.88872 − 9.04102I 0
u = 0.390452 − 1.308290I
a = 1.15405 − 1.99315I
b = −1.52261 + 1.10872I
−5.88872 + 9.04102I 0
u = 0.335008 + 1.329430I
a = −0.32616 − 2.08418I
b = 1.05385 + 2.07205I
3.44326 − 5.11122I 0
u = 0.335008 − 1.329430I
a = −0.32616 + 2.08418I
b = 1.05385 − 2.07205I
3.44326 + 5.11122I 0
u = −0.359700 + 1.337340I
a = −0.49062 + 2.42131I
b = 1.59665 − 2.26221I
2.15359 + 10.68620I 0
u = −0.359700 − 1.337340I
a = −0.49062 − 2.42131I
b = 1.59665 + 2.26221I
2.15359 − 10.68620I 0
u = 0.102530 + 1.394500I
a = 0.964979 + 0.507457I
b = −1.93891 − 0.37473I
8.29178 − 4.25641I 0
u = 0.102530 − 1.394500I
a = 0.964979 − 0.507457I
b = −1.93891 + 0.37473I
8.29178 + 4.25641I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.066007 + 1.396890I
a = 0.810504 − 0.885178I
b = −1.69144 + 0.97965I
8.59831 − 1.41502I 0
u = −0.066007 − 1.396890I
a = 0.810504 + 0.885178I
b = −1.69144 − 0.97965I
8.59831 + 1.41502I 0
u = −0.381595 + 1.347340I
a = 0.25782 − 2.13685I
b = −0.98568 + 2.09120I
0.38459 + 10.21060I 0
u = −0.381595 − 1.347340I
a = 0.25782 + 2.13685I
b = −0.98568 − 2.09120I
0.38459 − 10.21060I 0
u = 0.149156 + 1.399160I
a = −0.56575 − 1.37488I
b = 1.40497 + 1.43686I
7.66294 − 3.69333I 0
u = 0.149156 − 1.399160I
a = −0.56575 + 1.37488I
b = 1.40497 − 1.43686I
7.66294 + 3.69333I 0
u = 0.397706 + 1.350820I
a = 0.30333 + 2.52636I
b = −1.42412 − 2.37758I
−1.0399 − 15.8746I 0
u = 0.397706 − 1.350820I
a = 0.30333 − 2.52636I
b = −1.42412 + 2.37758I
−1.0399 + 15.8746I 0
u = −0.181217 + 1.400850I
a = −0.752908 + 1.133180I
b = 1.76932 − 0.99764I
7.06490 + 9.40242I 0
u = −0.181217 − 1.400850I
a = −0.752908 − 1.133180I
b = 1.76932 + 0.99764I
7.06490 − 9.40242I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.502604 + 0.150960I
a = 1.119810 + 0.498449I
b = 0.406755 − 0.670085I
−3.33096 + 2.74558I −16.7867 − 5.9807I
u = −0.502604 − 0.150960I
a = 1.119810 − 0.498449I
b = 0.406755 + 0.670085I
−3.33096 − 2.74558I −16.7867 + 5.9807I
u = 0.268159 + 0.343396I
a = −0.410785 − 0.686556I
b = 0.387300 + 0.356715I
−0.578536 − 1.108330I −7.65763 + 5.69104I
u = 0.268159 − 0.343396I
a = −0.410785 + 0.686556I
b = 0.387300 − 0.356715I
−0.578536 + 1.108330I −7.65763 − 5.69104I
u = −0.145927 + 0.017514I
a = 3.33046 − 6.22037I
b = 1.013530 + 0.299730I
−1.72221 + 2.04047I −15.8987 − 3.0752I
u = −0.145927 − 0.017514I
a = 3.33046 + 6.22037I
b = 1.013530 − 0.299730I
−1.72221 − 2.04047I −15.8987 + 3.0752I
10
II. I
u
2
= h−u
8
− 2u
6
− 2u
4
+ b, −u
6
− u
4
+ a + 1, u
24
+ 8u
22
+ · · · + 2u − 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
10
=
−u
u
a
1
=
u
6
+ u
4
− 1
u
8
+ 2u
6
+ 2u
4
a
6
=
−u
4
− u
2
+ 1
u
4
+ 2u
2
a
11
=
−u
15
− 4u
13
− 6u
11
− 2u
9
+ 4u
7
+ 4u
5
− 2u
−u
17
− 5u
15
− 11u
13
− 12u
11
− 5u
9
+ 2u
7
+ 2u
5
+ u
a
8
=
u
u
3
+ u
a
3
=
−u
4
− u
2
+ 1
−u
6
− 2u
4
− u
2
a
2
=
u
2
− 1
u
4
a
7
=
u
3
u
5
+ u
3
+ u
a
12
=
−u
22
− u
21
+ ··· − 2u
2
− 2u
−u
23
+ u
22
+ ··· − 2u
3
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
18
− 24u
16
− 60u
14
− 68u
12
− 12u
10
− 4u
9
+ 48u
8
− 12u
7
+
36u
6
− 12u
5
− 4u
4
+ 4u
3
− 8u
2
+ 8u − 14
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
+ 16u
23
+ ··· − 4u + 1
c
2
, c
4
, c
7
c
8
, c
9
u
24
+ 8u
22
+ ··· − 2u − 1
c
3
, c
5
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
3
c
6
, c
11
(u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1)
3
c
10
, c
12
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
3
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
− 16y
23
+ ··· − 44y + 1
c
2
, c
4
, c
7
c
8
, c
9
y
24
+ 16y
23
+ ··· − 4y + 1
c
3
, c
5
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
3
c
6
, c
11
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
3
c
10
, c
12
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
3
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.199878 + 1.058230I
a = −0.692366 − 0.490639I
b = 0.755093 + 0.822738I
−0.845036 −11.89446 + 0.I
u = −0.199878 − 1.058230I
a = −0.692366 + 0.490639I
b = 0.755093 − 0.822738I
−0.845036 −11.89446 + 0.I
u = −0.817018 + 0.106623I
a = −0.377081 − 0.448378I
b = 1.35371 − 1.07975I
−2.37968 + 6.44354I −9.42845 − 5.29417I
u = −0.817018 − 0.106623I
a = −0.377081 + 0.448378I
b = 1.35371 + 1.07975I
−2.37968 − 6.44354I −9.42845 + 5.29417I
u = −0.819879
a = −0.244409
b = 1.71535
−6.50273 −13.8640
u = −0.431691 + 0.692037I
a = −0.983121 + 0.409487I
b = −0.014801 + 0.629205I
2.15941 − 2.57849I −4.27708 + 3.56796I
u = −0.431691 − 0.692037I
a = −0.983121 − 0.409487I
b = −0.014801 − 0.629205I
2.15941 + 2.57849I −4.27708 − 3.56796I
u = −0.427601 + 1.146400I
a = 1.133070 − 0.604082I
b = −0.553659 + 0.206534I
−1.04066 − 1.13123I −7.41522 + 0.51079I
u = −0.427601 − 1.146400I
a = 1.133070 + 0.604082I
b = −0.553659 − 0.206534I
−1.04066 + 1.13123I −7.41522 − 0.51079I
u = 0.761196 + 0.098439I
a = −0.551326 + 0.313328I
b = 0.959472 + 0.729841I
−1.04066 − 1.13123I −7.41522 + 0.51079I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.761196 − 0.098439I
a = −0.551326 − 0.313328I
b = 0.959472 − 0.729841I
−1.04066 + 1.13123I −7.41522 − 0.51079I
u = 0.461944 + 1.169380I
a = 1.66867 + 0.56200I
b = −0.853651 + 0.302978I
−2.37968 + 6.44354I −9.42845 − 5.29417I
u = 0.461944 − 1.169380I
a = 1.66867 − 0.56200I
b = −0.853651 − 0.302978I
−2.37968 − 6.44354I −9.42845 + 5.29417I
u = −0.028576 + 1.262710I
a = −2.48788 − 0.31944I
b = 3.39460 + 0.52702I
2.15941 + 2.57849I −4.27708 − 3.56796I
u = −0.028576 − 1.262710I
a = −2.48788 + 0.31944I
b = 3.39460 − 0.52702I
2.15941 − 2.57849I −4.27708 + 3.56796I
u = 0.460267 + 0.570674I
a = −1.170250 − 0.244142I
b = −0.285631 − 0.425378I
2.15941 − 2.57849I −4.27708 + 3.56796I
u = 0.460267 − 0.570674I
a = −1.170250 + 0.244142I
b = −0.285631 + 0.425378I
2.15941 + 2.57849I −4.27708 − 3.56796I
u = −0.333594 + 1.244840I
a = 0.37985 − 2.19261I
b = −1.04688 + 2.20428I
−1.04066 + 1.13123I −7.41522 − 0.51079I
u = −0.333594 − 1.244840I
a = 0.37985 + 2.19261I
b = −1.04688 − 2.20428I
−1.04066 − 1.13123I −7.41522 + 0.51079I
u = 0.409939 + 1.226440I
a = 1.44167 + 1.68145I
b = −1.73732 − 0.79694I
−6.50273 −13.86404 + 0.I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.409939 − 1.226440I
a = 1.44167 − 1.68145I
b = −1.73732 + 0.79694I
−6.50273 −13.86404 + 0.I
u = 0.355074 + 1.276000I
a = 0.74615 + 2.66734I
b = −1.85855 − 2.47925I
−2.37968 − 6.44354I −9.42845 + 5.29417I
u = 0.355074 − 1.276000I
a = 0.74615 − 2.66734I
b = −1.85855 + 2.47925I
−2.37968 + 6.44354I −9.42845 − 5.29417I
u = 0.399757
a = −0.970381
b = 0.0598901
−0.845036 −11.8940
16
III. I
u
3
= hb + 1, a
2
− au − 2a + u, u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
−1
a
10
=
−u
u
a
1
=
a
−1
a
6
=
1
−1
a
11
=
−au + a − u − 1
au
a
8
=
u
0
a
3
=
1
0
a
2
=
a + 1
−1
a
7
=
−au
u
a
12
=
−au
au + a − u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4au + 4u − 12
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
4
c
2
, c
4
, c
7
c
8
, c
9
(u
2
+ 1)
2
c
3
, c
5
u
4
c
6
, c
11
u
4
− u
2
+ 1
c
10
(u
2
− u + 1)
2
c
12
(u
2
+ u + 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
4
c
2
, c
4
, c
7
c
8
, c
9
(y + 1)
4
c
3
, c
5
y
4
c
6
, c
11
(y
2
− y + 1)
2
c
10
, c
12
(y
2
+ y + 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.133975 + 0.500000I
b = −1.00000
− 2.02988I −10.00000 + 3.46410I
u = 1.000000I
a = 1.86603 + 0.50000I
b = −1.00000
2.02988I −10.00000 − 3.46410I
u = − 1.000000I
a = 0.133975 − 0.500000I
b = −1.00000
2.02988I −10.00000 − 3.46410I
u = − 1.000000I
a = 1.86603 − 0.50000I
b = −1.00000
− 2.02988I −10.00000 + 3.46410I
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
24
+ 16u
23
+ ··· − 4u + 1)(u
56
+ 29u
55
+ ··· + 6u + 1)
c
2
, c
7
((u
2
+ 1)
2
)(u
24
+ 8u
22
+ ··· − 2u − 1)(u
56
+ u
55
+ ··· − 2u + 1)
c
3
, c
5
u
4
(u
8
− u
7
+ ··· − 2u − 1)
3
(u
56
+ 2u
55
+ ··· − 464u + 32)
c
4
, c
8
, c
9
((u
2
+ 1)
2
)(u
24
+ 8u
22
+ ··· − 2u − 1)(u
56
+ u
55
+ ··· − 12u + 1)
c
6
, c
11
(u
4
− u
2
+ 1)(u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1)
3
· (u
56
− 2u
55
+ ··· − 3u + 2)
c
10
(u
2
− u + 1)
2
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
3
· (u
56
+ 20u
55
+ ··· − 19u + 4)
c
12
(u
2
+ u + 1)
2
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
3
· (u
56
+ 20u
55
+ ··· − 19u + 4)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
4
)(y
24
− 16y
23
+ ··· − 44y + 1)(y
56
+ y
55
+ ··· + 78y + 1)
c
2
, c
7
((y + 1)
4
)(y
24
+ 16y
23
+ ··· − 4y + 1)(y
56
+ 29y
55
+ ··· + 6y + 1)
c
3
, c
5
y
4
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
3
· (y
56
− 42y
55
+ ··· − 81664y + 1024)
c
4
, c
8
, c
9
((y + 1)
4
)(y
24
+ 16y
23
+ ··· − 4y + 1)(y
56
+ 49y
55
+ ··· − 90y + 1)
c
6
, c
11
(y
2
− y + 1)
2
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
3
· (y
56
− 20y
55
+ ··· + 19y + 4)
c
10
, c
12
(y
2
+ y + 1)
2
· (y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
3
· (y
56
+ 32y
55
+ ··· − 33y + 16)
22
