12n
0788
(K12n
0788
)
A knot diagram
1
Linearized knot diagam
4 5 11 8 3 12 5 1 12 4 6 9
Solving Sequence
1,8 5,9
4 2 3 7 12 10 6 11
c
8
c
4
c
1
c
2
c
7
c
12
c
9
c
6
c
11
c
3
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.58578 × 10
94
u
73
+ 3.02439 × 10
94
u
72
+ ··· + 7.24165 × 10
94
b − 1.13790 × 10
95
,
6.83460 × 10
94
u
73
+ 2.06996 × 10
95
u
72
+ ··· + 7.24165 × 10
94
a − 1.20278 × 10
96
, u
74
+ 3u
73
+ ··· + 21u + 1i
I
u
2
= h−u
18
+ 3u
17
+ ··· + b − 1, u
19
− u
18
+ ··· + a + 3, u
20
− 2u
19
+ ··· + 11u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 94 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
=
h1.59×10
94
u
73
+3.02×10
94
u
72
+· · ·+7.24×10
94
b−1.14×10
95
, 6.83×10
94
u
73
+
2.07 × 10
95
u
72
+ · · · + 7.24 × 10
94
a − 1.20 × 10
96
, u
74
+ 3u
73
+ · · · + 21u + 1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
5
=
−0.943790u
73
− 2.85841u
72
+ ··· − 200.219u + 16.6092
−0.218980u
73
− 0.417638u
72
+ ··· + 27.3920u + 1.57132
a
9
=
1
u
2
a
4
=
−1.16277u
73
− 3.27605u
72
+ ··· − 172.827u + 18.1805
−0.218980u
73
− 0.417638u
72
+ ··· + 27.3920u + 1.57132
a
2
=
−3.74724u
73
− 11.5498u
72
+ ··· − 1374.87u − 47.8329
−0.289918u
73
− 0.893819u
72
+ ··· − 5.30721u + 1.13701
a
3
=
0.150555u
73
+ 0.0467585u
72
+ ··· − 582.950u − 39.8482
−0.519493u
73
− 1.69333u
72
+ ··· − 12.9835u − 0.00334082
a
7
=
−1.09362u
73
− 3.80737u
72
+ ··· − 462.305u − 29.4024
−0.0433920u
73
+ 0.106412u
72
+ ··· − 6.49614u + 0.217922
a
12
=
u
u
3
+ u
a
10
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
−1.24781u
73
− 4.44356u
72
+ ··· − 463.401u − 29.5039
0.0832740u
73
+ 0.529036u
72
+ ··· − 3.79157u + 0.290107
a
11
=
1.06428u
73
+ 2.50104u
72
+ ··· + 542.210u + 39.2751
−0.0130542u
73
+ 0.238478u
72
+ ··· + 15.1776u + 0.0881159
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.346623u
73
+ 2.28437u
72
+ ··· + 298.542u + 13.6537
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
74
− 12u
73
+ ··· + 512u + 73
c
2
, c
5
u
74
− 22u
72
+ ··· + 12106u + 4059
c
3
, c
10
u
74
− u
73
+ ··· + 18411u + 6049
c
4
, c
7
u
74
− 4u
73
+ ··· − 2438u + 529
c
6
, c
11
u
74
− u
73
+ ··· − 1273u + 2357
c
8
, c
9
, c
12
u
74
− 3u
73
+ ··· − 21u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
74
+ 46y
72
+ ··· + 277034y + 5329
c
2
, c
5
y
74
− 44y
73
+ ··· − 265207924y + 16475481
c
3
, c
10
y
74
+ 47y
73
+ ··· + 954117711y + 36590401
c
4
, c
7
y
74
+ 36y
73
+ ··· + 5248738y + 279841
c
6
, c
11
y
74
− 45y
73
+ ··· − 110160379y + 5555449
c
8
, c
9
, c
12
y
74
+ 69y
73
+ ··· + 273y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.936804 + 0.339968I
a = 0.622927 + 0.688917I
b = 0.710500 − 1.130150I
2.76516 + 11.24560I 0
u = −0.936804 − 0.339968I
a = 0.622927 − 0.688917I
b = 0.710500 + 1.130150I
2.76516 − 11.24560I 0
u = 0.930090 + 0.208950I
a = −0.334369 + 0.260725I
b = −0.663146 − 0.942118I
−0.61830 − 4.53833I 0
u = 0.930090 − 0.208950I
a = −0.334369 − 0.260725I
b = −0.663146 + 0.942118I
−0.61830 + 4.53833I 0
u = −0.319333 + 1.020450I
a = 0.23353 + 1.63070I
b = 0.553683 − 0.674115I
3.67304 − 1.08231I 0
u = −0.319333 − 1.020450I
a = 0.23353 − 1.63070I
b = 0.553683 + 0.674115I
3.67304 + 1.08231I 0
u = −0.069737 + 1.104620I
a = 0.46995 + 1.52306I
b = 0.315493 − 0.757914I
3.55481 − 1.00960I 0
u = −0.069737 − 1.104620I
a = 0.46995 − 1.52306I
b = 0.315493 + 0.757914I
3.55481 + 1.00960I 0
u = −0.064033 + 0.874740I
a = 0.598935 + 0.016465I
b = −0.805267 − 0.384169I
−0.142484 − 0.979938I −4.00000 + 2.35513I
u = −0.064033 − 0.874740I
a = 0.598935 − 0.016465I
b = −0.805267 + 0.384169I
−0.142484 + 0.979938I −4.00000 − 2.35513I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.738642 + 0.887199I
a = −0.557382 − 0.422145I
b = 0.566445 + 0.940150I
4.40806 − 5.59603I 0
u = −0.738642 − 0.887199I
a = −0.557382 + 0.422145I
b = 0.566445 − 0.940150I
4.40806 + 5.59603I 0
u = 0.828888 + 0.091510I
a = 0.737287 − 0.641900I
b = 0.572058 + 1.134930I
−0.10298 − 4.06471I −0.40205 + 4.72845I
u = 0.828888 − 0.091510I
a = 0.737287 + 0.641900I
b = 0.572058 − 1.134930I
−0.10298 + 4.06471I −0.40205 − 4.72845I
u = 0.789984 + 0.155180I
a = 0.697528 − 0.295007I
b = 0.608961 + 0.489624I
−2.13816 − 0.67532I −4.89240 − 0.69754I
u = 0.789984 − 0.155180I
a = 0.697528 + 0.295007I
b = 0.608961 − 0.489624I
−2.13816 + 0.67532I −4.89240 + 0.69754I
u = 0.395613 + 1.128880I
a = −0.468940 + 0.976139I
b = 0.587115 − 0.916327I
3.10666 − 0.34724I 0
u = 0.395613 − 1.128880I
a = −0.468940 − 0.976139I
b = 0.587115 + 0.916327I
3.10666 + 0.34724I 0
u = 0.386320 + 1.141930I
a = −0.257479 − 0.302102I
b = 0.741571 − 0.155531I
0.88149 − 3.55827I 0
u = 0.386320 − 1.141930I
a = −0.257479 + 0.302102I
b = 0.741571 + 0.155531I
0.88149 + 3.55827I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.781957 + 0.127588I
a = 0.468419 − 0.340993I
b = 0.969908 + 0.496154I
0.83489 + 5.14638I −2.92699 − 4.12698I
u = −0.781957 − 0.127588I
a = 0.468419 + 0.340993I
b = 0.969908 − 0.496154I
0.83489 − 5.14638I −2.92699 + 4.12698I
u = −0.690960 + 0.376818I
a = −0.930716 − 0.945879I
b = −0.790965 + 0.838168I
−1.32937 + 4.37262I −1.68695 − 7.55471I
u = −0.690960 − 0.376818I
a = −0.930716 + 0.945879I
b = −0.790965 − 0.838168I
−1.32937 − 4.37262I −1.68695 + 7.55471I
u = 0.208976 + 1.238970I
a = 0.725780 − 0.430028I
b = −1.33074 + 0.55805I
2.07909 − 2.04945I 0
u = 0.208976 − 1.238970I
a = 0.725780 + 0.430028I
b = −1.33074 − 0.55805I
2.07909 + 2.04945I 0
u = −0.239083 + 1.235520I
a = −0.56305 − 1.99635I
b = −0.653467 + 1.183850I
2.21691 + 4.57437I 0
u = −0.239083 − 1.235520I
a = −0.56305 + 1.99635I
b = −0.653467 − 1.183850I
2.21691 − 4.57437I 0
u = −0.098165 + 1.270860I
a = 0.22331 + 3.15689I
b = −0.02511 − 1.52128I
11.61620 − 0.14821I 0
u = −0.098165 − 1.270860I
a = 0.22331 − 3.15689I
b = −0.02511 + 1.52128I
11.61620 + 0.14821I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.290096 + 1.244670I
a = −1.42838 − 0.42517I
b = −0.079374 + 0.951986I
9.54324 + 4.38718I 0
u = −0.290096 − 1.244670I
a = −1.42838 + 0.42517I
b = −0.079374 − 0.951986I
9.54324 − 4.38718I 0
u = 0.664261 + 1.105320I
a = 0.578989 − 0.326355I
b = −0.309901 + 0.732892I
1.98668 − 0.96963I 0
u = 0.664261 − 1.105320I
a = 0.578989 + 0.326355I
b = −0.309901 − 0.732892I
1.98668 + 0.96963I 0
u = −0.703470 + 0.069064I
a = 0.078771 − 1.020400I
b = 0.318672 − 0.907573I
5.93010 − 0.78432I 1.48301 − 0.85749I
u = −0.703470 − 0.069064I
a = 0.078771 + 1.020400I
b = 0.318672 + 0.907573I
5.93010 + 0.78432I 1.48301 + 0.85749I
u = 0.000271 + 1.298230I
a = −1.73564 + 1.88420I
b = −0.120936 − 0.853354I
9.15293 + 3.49758I 0
u = 0.000271 − 1.298230I
a = −1.73564 − 1.88420I
b = −0.120936 + 0.853354I
9.15293 − 3.49758I 0
u = −0.654738 + 0.139993I
a = −0.365809 − 0.113721I
b = −0.749123 − 0.884451I
−1.17142 − 1.41028I −0.82219 − 1.94292I
u = −0.654738 − 0.139993I
a = −0.365809 + 0.113721I
b = −0.749123 + 0.884451I
−1.17142 + 1.41028I −0.82219 + 1.94292I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.021534 + 1.337130I
a = 0.554741 − 0.978134I
b = 0.795121 + 0.856242I
9.72603 − 3.20768I 0
u = −0.021534 − 1.337130I
a = 0.554741 + 0.978134I
b = 0.795121 − 0.856242I
9.72603 + 3.20768I 0
u = −0.104300 + 1.333230I
a = −0.26774 − 2.22250I
b = 0.24396 + 1.72146I
12.48010 + 3.12382I 0
u = −0.104300 − 1.333230I
a = −0.26774 + 2.22250I
b = 0.24396 − 1.72146I
12.48010 − 3.12382I 0
u = −0.276951 + 1.318390I
a = 0.405659 + 0.960983I
b = 0.727988 − 1.027740I
10.30720 + 2.74116I 0
u = −0.276951 − 1.318390I
a = 0.405659 − 0.960983I
b = 0.727988 + 1.027740I
10.30720 − 2.74116I 0
u = 0.616600 + 0.149646I
a = −0.576417 + 1.181130I
b = −0.763533 − 0.734900I
−1.25932 − 0.85009I −2.93324 − 0.64796I
u = 0.616600 − 0.149646I
a = −0.576417 − 1.181130I
b = −0.763533 + 0.734900I
−1.25932 + 0.85009I −2.93324 + 0.64796I
u = 0.359175 + 1.322210I
a = 0.82697 − 2.18712I
b = 0.498014 + 1.278840I
4.31927 − 8.33215I 0
u = 0.359175 − 1.322210I
a = 0.82697 + 2.18712I
b = 0.498014 − 1.278840I
4.31927 + 8.33215I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.331105 + 1.339680I
a = −0.749942 + 0.054369I
b = 1.238930 + 0.313660I
5.44209 + 9.16208I 0
u = −0.331105 − 1.339680I
a = −0.749942 − 0.054369I
b = 1.238930 − 0.313660I
5.44209 − 9.16208I 0
u = −0.305381 + 1.368770I
a = 0.761541 + 0.467536I
b = −0.853662 − 0.650481I
3.67876 + 2.15533I 0
u = −0.305381 − 1.368770I
a = 0.761541 − 0.467536I
b = −0.853662 + 0.650481I
3.67876 − 2.15533I 0
u = 0.275962 + 1.383250I
a = −0.15950 + 2.10027I
b = −0.462021 − 1.121230I
3.68775 − 4.15450I 0
u = 0.275962 − 1.383250I
a = −0.15950 − 2.10027I
b = −0.462021 + 1.121230I
3.68775 + 4.15450I 0
u = 0.34603 + 1.39240I
a = 0.49266 − 1.38993I
b = 0.540130 + 0.835161I
2.80424 − 4.78161I 0
u = 0.34603 − 1.39240I
a = 0.49266 + 1.38993I
b = 0.540130 − 0.835161I
2.80424 + 4.78161I 0
u = 0.39339 + 1.39442I
a = −0.31063 + 1.63356I
b = −0.77536 − 1.22079I
4.43148 − 9.25628I 0
u = 0.39339 − 1.39442I
a = −0.31063 − 1.63356I
b = −0.77536 + 1.22079I
4.43148 + 9.25628I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.27655 + 1.49326I
a = −0.28891 − 1.91776I
b = −0.713564 + 1.014530I
4.77334 + 7.96569I 0
u = −0.27655 − 1.49326I
a = −0.28891 + 1.91776I
b = −0.713564 − 1.014530I
4.77334 − 7.96569I 0
u = −0.38358 + 1.47124I
a = 0.47036 + 1.92708I
b = 0.72193 − 1.29934I
8.5275 + 16.0127I 0
u = −0.38358 − 1.47124I
a = 0.47036 − 1.92708I
b = 0.72193 + 1.29934I
8.5275 − 16.0127I 0
u = 0.049778 + 0.404950I
a = 1.039240 + 0.230406I
b = −0.504136 − 0.382867I
−0.230831 − 1.075800I −3.86726 + 5.56314I
u = 0.049778 − 0.404950I
a = 1.039240 − 0.230406I
b = −0.504136 + 0.382867I
−0.230831 + 1.075800I −3.86726 − 5.56314I
u = −0.00897 + 1.65353I
a = −0.17869 + 1.83789I
b = 0.212633 − 0.762848I
12.84880 − 0.51128I 0
u = −0.00897 − 1.65353I
a = −0.17869 − 1.83789I
b = 0.212633 + 0.762848I
12.84880 + 0.51128I 0
u = −0.318578 + 0.088858I
a = 1.46832 − 0.71391I
b = 0.12577 + 1.49843I
7.89983 + 1.60233I −5.43520 − 6.25438I
u = −0.318578 − 0.088858I
a = 1.46832 + 0.71391I
b = 0.12577 − 1.49843I
7.89983 − 1.60233I −5.43520 + 6.25438I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10261 + 1.70630I
a = −0.280005 − 1.271740I
b = 0.219435 + 0.960300I
13.66950 − 2.42291I 0
u = −0.10261 − 1.70630I
a = −0.280005 + 1.271740I
b = 0.219435 − 0.960300I
13.66950 + 2.42291I 0
u = −0.0287687 + 0.0617431I
a = 26.4987 − 3.7687I
b = 0.331976 + 0.710871I
5.14104 − 3.45109I 1.82404 + 12.33527I
u = −0.0287687 − 0.0617431I
a = 26.4987 + 3.7687I
b = 0.331976 − 0.710871I
5.14104 + 3.45109I 1.82404 − 12.33527I
12
II.
I
u
2
= h−u
18
+3u
17
+· · ·+b−1, u
19
−u
18
+· · ·+a+3, u
20
−2u
19
+· · ·+11u
2
+1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
5
=
−u
19
+ u
18
+ ··· + u − 3
u
18
− 3u
17
+ ··· − 5u + 1
a
9
=
1
u
2
a
4
=
−u
19
+ 2u
18
+ ··· − 4u − 2
u
18
− 3u
17
+ ··· − 5u + 1
a
2
=
2u
19
− 4u
18
+ ··· − 2u + 2
−u
19
+ 2u
18
+ ··· + 2u + 1
a
3
=
3u
19
− 6u
18
+ ··· − 8u + 5
−u
19
+ 2u
18
+ ··· + 7u + 1
a
7
=
−2u
18
+ 2u
17
+ ··· − 11u − 1
−u
19
+ 3u
18
+ ··· + 10u
2
+ 3
a
12
=
u
u
3
+ u
a
10
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
−u
19
− 10u
17
+ ··· − 10u − 1
u
18
− u
17
+ ··· + 2u + 3
a
11
=
u
19
− 4u
18
+ ··· + 14u − 2
−u
19
+ 3u
18
+ ··· + u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −u
19
+ 6u
18
− 19u
17
+ 70u
16
− 134u
15
+ 339u
14
− 478u
13
+ 875u
12
− 956u
11
+
1285u
10
− 1103u
9
+ 1064u
8
− 736u
7
+ 473u
6
− 303u
5
+ 123u
4
− 88u
3
+ 36u
2
− 8u + 12
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
+ 3u
19
+ ··· + 9u + 1
c
2
u
20
+ 5u
19
+ ··· + 5u + 1
c
3
u
20
+ 9u
18
+ ··· + 2u
2
+ 1
c
4
u
20
− 3u
19
+ ··· − 3u + 1
c
5
u
20
− 5u
19
+ ··· − 5u + 1
c
6
u
20
− 7u
18
+ ··· + u
2
+ 1
c
7
u
20
+ 3u
19
+ ··· + 3u + 1
c
8
, c
9
u
20
− 2u
19
+ ··· + 11u
2
+ 1
c
10
u
20
+ 9u
18
+ ··· + 2u
2
+ 1
c
11
u
20
− 7u
18
+ ··· + u
2
+ 1
c
12
u
20
+ 2u
19
+ ··· + 11u
2
+ 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
+ 3y
19
+ ··· + 3y + 1
c
2
, c
5
y
20
− 17y
19
+ ··· − 7y + 1
c
3
, c
10
y
20
+ 18y
19
+ ··· + 4y + 1
c
4
, c
7
y
20
+ 15y
19
+ ··· + 11y + 1
c
6
, c
11
y
20
− 14y
19
+ ··· + 2y + 1
c
8
, c
9
, c
12
y
20
+ 24y
19
+ ··· + 22y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.237849 + 1.138180I
a = 0.595231 − 0.531708I
b = −0.924433 + 0.400435I
1.41358 − 1.18127I −1.009011 + 0.133987I
u = 0.237849 − 1.138180I
a = 0.595231 + 0.531708I
b = −0.924433 − 0.400435I
1.41358 + 1.18127I −1.009011 − 0.133987I
u = 0.458379 + 1.075510I
a = 0.583352 − 0.508557I
b = −0.447997 + 0.445190I
1.38393 − 1.37957I −2.62288 + 2.95794I
u = 0.458379 − 1.075510I
a = 0.583352 + 0.508557I
b = −0.447997 − 0.445190I
1.38393 + 1.37957I −2.62288 − 2.95794I
u = −0.032562 + 1.259960I
a = 0.46714 − 2.85286I
b = 0.19047 + 1.50771I
11.54060 + 1.70476I 5.35646 − 2.70130I
u = −0.032562 − 1.259960I
a = 0.46714 + 2.85286I
b = 0.19047 − 1.50771I
11.54060 − 1.70476I 5.35646 + 2.70130I
u = −0.178451 + 1.257340I
a = 1.210450 + 0.323547I
b = 0.463393 − 0.711840I
8.17331 + 4.87622I 1.33927 − 6.40565I
u = −0.178451 − 1.257340I
a = 1.210450 − 0.323547I
b = 0.463393 + 0.711840I
8.17331 − 4.87622I 1.33927 + 6.40565I
u = 0.707607 + 0.137682I
a = −0.717254 + 0.452751I
b = −0.655863 − 0.894386I
−1.58933 − 2.51677I −3.68440 + 4.44805I
u = 0.707607 − 0.137682I
a = −0.717254 − 0.452751I
b = −0.655863 + 0.894386I
−1.58933 + 2.51677I −3.68440 − 4.44805I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.30740 + 1.39766I
a = −0.46774 + 1.89500I
b = −0.575858 − 1.113880I
3.36407 − 6.18880I 2.22658 + 5.47050I
u = 0.30740 − 1.39766I
a = −0.46774 − 1.89500I
b = −0.575858 + 1.113880I
3.36407 + 6.18880I 2.22658 − 5.47050I
u = −0.341446 + 0.403300I
a = −3.11005 + 0.22725I
b = 0.254427 + 0.644394I
5.20886 − 2.95060I 4.15959 − 2.66248I
u = −0.341446 − 0.403300I
a = −3.11005 − 0.22725I
b = 0.254427 − 0.644394I
5.20886 + 2.95060I 4.15959 + 2.66248I
u = −0.02478 + 1.56705I
a = −0.30939 + 1.77476I
b = 0.040337 − 1.275460I
15.1260 − 0.9723I 8.34609 + 0.42020I
u = −0.02478 − 1.56705I
a = −0.30939 − 1.77476I
b = 0.040337 + 1.275460I
15.1260 + 0.9723I 8.34609 − 0.42020I
u = −0.06629 + 1.64547I
a = −0.51898 − 1.60081I
b = 0.050399 + 0.710453I
12.82460 − 1.35935I 4.17653 + 4.55797I
u = −0.06629 − 1.64547I
a = −0.51898 + 1.60081I
b = 0.050399 − 0.710453I
12.82460 + 1.35935I 4.17653 − 4.55797I
u = −0.067709 + 0.319554I
a = −2.23275 + 0.53767I
b = 0.105123 − 1.386410I
8.35169 − 1.33697I 8.71177 − 1.53767I
u = −0.067709 − 0.319554I
a = −2.23275 − 0.53767I
b = 0.105123 + 1.386410I
8.35169 + 1.33697I 8.71177 + 1.53767I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
20
+ 3u
19
+ ··· + 9u + 1)(u
74
− 12u
73
+ ··· + 512u + 73)
c
2
(u
20
+ 5u
19
+ ··· + 5u + 1)(u
74
− 22u
72
+ ··· + 12106u + 4059)
c
3
(u
20
+ 9u
18
+ ··· + 2u
2
+ 1)(u
74
− u
73
+ ··· + 18411u + 6049)
c
4
(u
20
− 3u
19
+ ··· − 3u + 1)(u
74
− 4u
73
+ ··· − 2438u + 529)
c
5
(u
20
− 5u
19
+ ··· − 5u + 1)(u
74
− 22u
72
+ ··· + 12106u + 4059)
c
6
(u
20
− 7u
18
+ ··· + u
2
+ 1)(u
74
− u
73
+ ··· − 1273u + 2357)
c
7
(u
20
+ 3u
19
+ ··· + 3u + 1)(u
74
− 4u
73
+ ··· − 2438u + 529)
c
8
, c
9
(u
20
− 2u
19
+ ··· + 11u
2
+ 1)(u
74
− 3u
73
+ ··· − 21u + 1)
c
10
(u
20
+ 9u
18
+ ··· + 2u
2
+ 1)(u
74
− u
73
+ ··· + 18411u + 6049)
c
11
(u
20
− 7u
18
+ ··· + u
2
+ 1)(u
74
− u
73
+ ··· − 1273u + 2357)
c
12
(u
20
+ 2u
19
+ ··· + 11u
2
+ 1)(u
74
− 3u
73
+ ··· − 21u + 1)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
20
+ 3y
19
+ ··· + 3y + 1)(y
74
+ 46y
72
+ ··· + 277034y + 5329)
c
2
, c
5
(y
20
− 17y
19
+ ··· − 7y + 1)
· (y
74
− 44y
73
+ ··· − 265207924y + 16475481)
c
3
, c
10
(y
20
+ 18y
19
+ ··· + 4y + 1)
· (y
74
+ 47y
73
+ ··· + 954117711y + 36590401)
c
4
, c
7
(y
20
+ 15y
19
+ ··· + 11y + 1)
· (y
74
+ 36y
73
+ ··· + 5248738y + 279841)
c
6
, c
11
(y
20
− 14y
19
+ ··· + 2y + 1)
· (y
74
− 45y
73
+ ··· − 110160379y + 5555449)
c
8
, c
9
, c
12
(y
20
+ 24y
19
+ ··· + 22y + 1)(y
74
+ 69y
73
+ ··· + 273y + 1)
19
