12n
0376
(K12n
0376
)
A knot diagram
1
Linearized knot diagam
3 6 8 9 2 10 3 12 5 7 9 7
Solving Sequence
6,10 3,7
8 11 2 1 5 9 4 12
c
6
c
7
c
10
c
2
c
1
c
5
c
9
c
4
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.29866 × 10
170
u
65
− 1.30524 × 10
169
u
64
+ ··· + 2.37368 × 10
172
b + 1.61064 × 10
172
,
− 1.42092 × 10
172
u
65
− 6.96969 × 10
171
u
64
+ ··· + 1.40047 × 10
174
a − 5.29249 × 10
174
,
u
66
− u
65
+ ··· − 283u − 59i
I
u
2
= h−547107839u
20
+ 650340830u
19
+ ··· + 16127515b + 671904942,
1292670203u
20
− 1531668600u
19
+ ··· + 16127515a − 1597251904, u
21
− 2u
20
+ ··· − 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 87 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−1.30 × 10
170
u
65
− 1.31 × 10
169
u
64
+ · · · + 2.37 × 10
172
b + 1.61 ×
10
172
, −1.42 × 10
172
u
65
− 6.97 × 10
171
u
64
+ · · · + 1.40 × 10
174
a − 5.29 ×
10
174
, u
66
− u
65
+ · · · − 283u − 59i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
0.0101460u
65
+ 0.00497667u
64
+ ··· − 6.90436u + 3.77907
0.00547109u
65
+ 0.000549881u
64
+ ··· + 0.213003u − 0.678540
a
7
=
1
−u
2
a
8
=
−0.0371999u
65
+ 0.000132037u
64
+ ··· − 10.9635u − 4.32444
0.00558096u
65
− 0.00149963u
64
+ ··· + 2.52802u + 0.980850
a
11
=
u
−u
3
+ u
a
2
=
0.0156171u
65
+ 0.00552655u
64
+ ··· − 6.69135u + 3.10053
0.00547109u
65
+ 0.000549881u
64
+ ··· + 0.213003u − 0.678540
a
1
=
0.0130843u
65
− 0.00173031u
64
+ ··· + 1.28588u + 1.21472
−0.00482668u
65
− 0.00301544u
64
+ ··· + 1.23112u − 0.215116
a
5
=
−0.00412372u
65
+ 0.0123233u
64
+ ··· − 10.8977u + 2.49609
−0.0176584u
65
+ 0.00749844u
64
+ ··· − 8.52232u − 2.06406
a
9
=
0.0252026u
65
+ 0.00297306u
64
+ ··· + 2.79443u + 2.86901
−0.00121735u
65
+ 0.00691108u
64
+ ··· − 4.53204u − 1.11595
a
4
=
−0.0725476u
65
+ 0.0237047u
64
+ ··· − 35.1307u − 2.94708
−0.0312738u
65
+ 0.00209774u
64
+ ··· − 8.36009u − 1.96671
a
12
=
0.0148679u
65
− 0.00641855u
64
+ ··· + 6.50217u + 1.66949
−0.000909781u
65
− 0.00295631u
64
+ ··· + 1.94792u − 0.0437386
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0549937u
65
+ 0.0239803u
64
+ ··· − 1.32112u − 6.19761
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
66
+ 38u
65
+ ··· − 20u + 1
c
2
, c
5
u
66
+ 2u
65
+ ··· + 10u
2
+ 1
c
3
, c
7
u
66
− u
65
+ ··· − 599u − 59
c
4
, c
9
u
66
+ u
65
+ ··· + 1920u − 1088
c
6
, c
10
u
66
− u
65
+ ··· − 283u − 59
c
8
, c
11
u
66
− 2u
65
+ ··· − 13u + 1
c
12
u
66
+ 2u
65
+ ··· + 2893677u + 899893
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
66
− 6y
65
+ ··· + 88y + 1
c
2
, c
5
y
66
− 38y
65
+ ··· + 20y + 1
c
3
, c
7
y
66
− 71y
65
+ ··· − 683301y + 3481
c
4
, c
9
y
66
− 27y
65
+ ··· − 23148544y + 1183744
c
6
, c
10
y
66
− 29y
65
+ ··· − 212367y + 3481
c
8
, c
11
y
66
+ 18y
65
+ ··· − 11y + 1
c
12
y
66
− 78y
65
+ ··· − 13342381349441y + 809807411449
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.009630 + 0.086875I
a = −0.865155 + 0.695569I
b = 0.646730 − 0.858274I
6.63058 + 2.08531I 4.22354 − 2.28056I
u = −1.009630 − 0.086875I
a = −0.865155 − 0.695569I
b = 0.646730 + 0.858274I
6.63058 − 2.08531I 4.22354 + 2.28056I
u = −0.630698 + 0.819545I
a = −1.08564 + 1.29025I
b = −0.145705 − 0.660230I
−5.32397 − 3.61939I −3.35802 + 3.00391I
u = −0.630698 − 0.819545I
a = −1.08564 − 1.29025I
b = −0.145705 + 0.660230I
−5.32397 + 3.61939I −3.35802 − 3.00391I
u = 0.855944 + 0.373732I
a = 0.776245 + 1.037920I
b = −0.979060 − 0.922126I
3.16003 − 1.29810I −3.61685 − 1.27981I
u = 0.855944 − 0.373732I
a = 0.776245 − 1.037920I
b = −0.979060 + 0.922126I
3.16003 + 1.29810I −3.61685 + 1.27981I
u = 0.919240 + 0.154057I
a = −0.06475 − 2.48944I
b = −0.959746 + 0.202331I
−0.086654 + 0.709749I 14.6199 + 25.0798I
u = 0.919240 − 0.154057I
a = −0.06475 + 2.48944I
b = −0.959746 − 0.202331I
−0.086654 − 0.709749I 14.6199 − 25.0798I
u = 0.916029 + 0.574839I
a = 0.02130 − 1.84018I
b = −0.915687 + 0.841121I
3.26731 + 5.19167I −4.00000 − 5.91453I
u = 0.916029 − 0.574839I
a = 0.02130 + 1.84018I
b = −0.915687 − 0.841121I
3.26731 − 5.19167I −4.00000 + 5.91453I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.173418 + 1.076000I
a = 0.606519 + 0.088557I
b = 0.974893 − 0.350221I
−2.26147 + 3.75022I −5.56446 − 6.85194I
u = −0.173418 − 1.076000I
a = 0.606519 − 0.088557I
b = 0.974893 + 0.350221I
−2.26147 − 3.75022I −5.56446 + 6.85194I
u = −0.519698 + 0.732621I
a = −0.109977 + 0.297576I
b = 1.47718 − 0.21621I
−10.75900 + 2.41313I −9.03127 + 1.73650I
u = −0.519698 − 0.732621I
a = −0.109977 − 0.297576I
b = 1.47718 + 0.21621I
−10.75900 − 2.41313I −9.03127 − 1.73650I
u = −0.749346 + 0.349951I
a = 0.55197 − 1.77976I
b = 1.059490 + 0.777077I
5.42275 − 4.01479I 2.47646 + 2.55070I
u = −0.749346 − 0.349951I
a = 0.55197 + 1.77976I
b = 1.059490 − 0.777077I
5.42275 + 4.01479I 2.47646 − 2.55070I
u = 1.067390 + 0.520714I
a = −0.98150 + 1.66983I
b = 1.164360 − 0.472130I
−8.03045 + 0.12830I 0
u = 1.067390 − 0.520714I
a = −0.98150 − 1.66983I
b = 1.164360 + 0.472130I
−8.03045 − 0.12830I 0
u = −0.969229 + 0.691515I
a = 0.445965 − 1.042750I
b = −0.375558 + 1.052890I
−4.37518 − 1.96161I 0
u = −0.969229 − 0.691515I
a = 0.445965 + 1.042750I
b = −0.375558 − 1.052890I
−4.37518 + 1.96161I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.702254 + 0.396363I
a = −0.370907 − 0.419474I
b = 1.64825 + 0.27071I
−9.41079 + 3.73475I −1.97764 − 7.57060I
u = 0.702254 − 0.396363I
a = −0.370907 + 0.419474I
b = 1.64825 − 0.27071I
−9.41079 − 3.73475I −1.97764 + 7.57060I
u = 0.189571 + 0.774061I
a = −2.16201 − 0.76177I
b = −0.048717 + 0.448000I
−5.12953 − 3.97226I −2.53620 + 0.67549I
u = 0.189571 − 0.774061I
a = −2.16201 + 0.76177I
b = −0.048717 − 0.448000I
−5.12953 + 3.97226I −2.53620 − 0.67549I
u = −1.199090 + 0.103811I
a = 0.026151 + 0.873772I
b = −1.145820 − 0.448707I
0.701365 + 0.560290I 0
u = −1.199090 − 0.103811I
a = 0.026151 − 0.873772I
b = −1.145820 + 0.448707I
0.701365 − 0.560290I 0
u = −0.855896 + 0.851844I
a = −0.377073 + 0.226573I
b = −1.193960 − 0.293229I
1.14814 − 4.23169I 0
u = −0.855896 − 0.851844I
a = −0.377073 − 0.226573I
b = −1.193960 + 0.293229I
1.14814 + 4.23169I 0
u = −0.588541 + 0.473255I
a = 0.03657 + 2.05711I
b = −0.918831 − 0.419709I
−1.84865 − 1.55160I −9.86951 + 3.77741I
u = −0.588541 − 0.473255I
a = 0.03657 − 2.05711I
b = −0.918831 + 0.419709I
−1.84865 + 1.55160I −9.86951 − 3.77741I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.583231 + 1.105720I
a = 0.365461 + 0.166066I
b = 0.875973 + 0.156748I
−1.25973 + 1.60946I 0
u = 0.583231 − 1.105720I
a = 0.365461 − 0.166066I
b = 0.875973 − 0.156748I
−1.25973 − 1.60946I 0
u = 1.26247
a = 1.73937
b = −0.819691
0.936733 0
u = 0.678975 + 0.254457I
a = −1.38925 − 0.87609I
b = −1.140560 + 0.239727I
−0.962746 + 1.013270I −8.93256 + 2.66135I
u = 0.678975 − 0.254457I
a = −1.38925 + 0.87609I
b = −1.140560 − 0.239727I
−0.962746 − 1.013270I −8.93256 − 2.66135I
u = 1.198670 + 0.480794I
a = −0.123627 − 0.483725I
b = 0.438626 + 0.674148I
3.38567 + 1.03176I 0
u = 1.198670 − 0.480794I
a = −0.123627 + 0.483725I
b = 0.438626 − 0.674148I
3.38567 − 1.03176I 0
u = −1.140890 + 0.605827I
a = −0.62705 − 1.69841I
b = 1.184480 + 0.438695I
−8.77795 − 7.59235I 0
u = −1.140890 − 0.605827I
a = −0.62705 + 1.69841I
b = 1.184480 − 0.438695I
−8.77795 + 7.59235I 0
u = 1.147170 + 0.619204I
a = 0.319998 + 1.132160I
b = −0.308780 − 1.182400I
−2.68437 + 9.27943I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.147170 − 0.619204I
a = 0.319998 − 1.132160I
b = −0.308780 + 1.182400I
−2.68437 − 9.27943I 0
u = 1.297790 + 0.269866I
a = −0.049488 − 0.712548I
b = 0.375452 + 0.619653I
3.28651 + 0.70632I 0
u = 1.297790 − 0.269866I
a = −0.049488 + 0.712548I
b = 0.375452 − 0.619653I
3.28651 − 0.70632I 0
u = −1.306810 + 0.303581I
a = −0.254876 + 0.950359I
b = 0.155440 − 0.803337I
4.37101 − 4.54876I 0
u = −1.306810 − 0.303581I
a = −0.254876 − 0.950359I
b = 0.155440 + 0.803337I
4.37101 + 4.54876I 0
u = −0.792328 + 1.127230I
a = 0.245968 − 0.148562I
b = −1.193740 + 0.508031I
−8.28883 + 1.02130I 0
u = −0.792328 − 1.127230I
a = 0.245968 + 0.148562I
b = −1.193740 − 0.508031I
−8.28883 − 1.02130I 0
u = −1.269320 + 0.570574I
a = 0.100258 − 1.297270I
b = 1.217640 + 0.524719I
1.20353 − 9.50394I 0
u = −1.269320 − 0.570574I
a = 0.100258 + 1.297270I
b = 1.217640 − 0.524719I
1.20353 + 9.50394I 0
u = 0.98914 + 1.01218I
a = 0.405389 + 0.898557I
b = 1.065930 − 0.564917I
1.55388 + 5.84749I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.98914 − 1.01218I
a = 0.405389 − 0.898557I
b = 1.065930 + 0.564917I
1.55388 − 5.84749I 0
u = −1.14794 + 0.86562I
a = −0.01851 + 1.44202I
b = −1.23555 − 0.69019I
−7.02539 − 8.25526I 0
u = −1.14794 − 0.86562I
a = −0.01851 − 1.44202I
b = −1.23555 + 0.69019I
−7.02539 + 8.25526I 0
u = 0.137966 + 0.528220I
a = 0.796178 − 0.216051I
b = −0.031272 + 0.313358I
−0.101260 + 1.177890I −1.60509 − 5.48121I
u = 0.137966 − 0.528220I
a = 0.796178 + 0.216051I
b = −0.031272 − 0.313358I
−0.101260 − 1.177890I −1.60509 + 5.48121I
u = 0.020560 + 0.528328I
a = −4.29255 − 0.39915I
b = 0.176919 + 0.209119I
−5.14008 − 3.94973I 0.643204 − 0.090602I
u = 0.020560 − 0.528328I
a = −4.29255 + 0.39915I
b = 0.176919 − 0.209119I
−5.14008 + 3.94973I 0.643204 + 0.090602I
u = 1.27921 + 0.73272I
a = 0.076111 + 1.032910I
b = 1.118870 − 0.498354I
1.06224 + 5.14116I 0
u = 1.27921 − 0.73272I
a = 0.076111 − 1.032910I
b = 1.118870 + 0.498354I
1.06224 − 5.14116I 0
u = 0.64925 + 1.38410I
a = 0.118590 + 0.092801I
b = −1.156150 − 0.470421I
−8.02803 − 8.05910I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.64925 − 1.38410I
a = 0.118590 − 0.092801I
b = −1.156150 + 0.470421I
−8.02803 + 8.05910I 0
u = 1.28691 + 0.85432I
a = 0.034457 − 1.326560I
b = −1.29162 + 0.68757I
−5.7819 + 15.8817I 0
u = 1.28691 − 0.85432I
a = 0.034457 + 1.326560I
b = −1.29162 − 0.68757I
−5.7819 − 15.8817I 0
u = −1.63204 + 0.55209I
a = 0.385181 + 0.448101I
b = −0.729629 + 0.000860I
3.55115 − 2.82787I 0
u = −1.63204 − 0.55209I
a = 0.385181 − 0.448101I
b = −0.729629 − 0.000860I
3.55115 + 2.82787I 0
u = −0.131285
a = 4.53665
b = −0.799964
−1.37349 −6.68870
11
II.
I
u
2
= h−5.47 × 10
8
u
20
+ 6.50 × 10
8
u
19
+ · · · + 1.61 × 10
7
b + 6.72 × 10
8
, 1.29 ×
10
9
u
20
−1.53×10
9
u
19
+· · · +1.61×10
7
a−1.60×10
9
, u
21
−2u
20
+· · · − 2u +1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
−80.1531u
20
+ 94.9724u
19
+ ··· − 77.1772u + 99.0389
33.9239u
20
− 40.3249u
19
+ ··· + 33.3984u − 41.6620
a
7
=
1
−u
2
a
8
=
89.2432u
20
− 106.092u
19
+ ··· + 85.7475u − 114.343
−17.4567u
20
+ 21.6317u
19
+ ··· − 15.1161u + 23.6718
a
11
=
u
−u
3
+ u
a
2
=
−46.2292u
20
+ 54.6475u
19
+ ··· − 43.7787u + 57.3769
33.9239u
20
− 40.3249u
19
+ ··· + 33.3984u − 41.6620
a
1
=
26.1717u
20
− 31.1465u
19
+ ··· + 27.5071u − 29.6074
−89.8576u
20
+ 107.426u
19
+ ··· − 86.4020u + 110.656
a
5
=
−17.4567u
20
+ 20.6317u
19
+ ··· − 17.1161u + 23.6718
80.1961u
20
− 95.9634u
19
+ ··· + 74.8843u − 102.382
a
9
=
−33.2945u
20
+ 41.0318u
19
+ ··· − 30.7499u + 39.7364
62.0383u
20
− 74.4291u
19
+ ··· + 62.2499u − 77.2800
a
4
=
24.4461u
20
− 28.8789u
19
+ ··· + 22.7417u − 29.0227
31.8485u
20
− 37.6738u
19
+ ··· + 32.8621u − 43.6846
a
12
=
−46.8592u
20
+ 56.0635u
19
+ ··· − 42.6727u + 59.8518
−42.9984u
20
+ 51.3621u
19
+ ··· − 41.7293u + 51.8043
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1978262081
16127515
u
20
+
486999773
3225503
u
19
+ ··· −
1665299122
16127515
u +
2329754158
16127515
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
21
− 13u
20
+ ··· + 17u − 1
c
2
u
21
+ 3u
20
+ ··· − 3u − 1
c
3
u
21
− 9u
19
+ ··· − 6u + 1
c
4
u
21
− 7u
19
+ ··· + 9u
2
+ 1
c
5
u
21
− 3u
20
+ ··· − 3u + 1
c
6
u
21
− 2u
20
+ ··· − 2u + 1
c
7
u
21
− 9u
19
+ ··· − 6u − 1
c
8
u
21
− 3u
20
+ ··· − 4u + 1
c
9
u
21
− 7u
19
+ ··· − 9u
2
− 1
c
10
u
21
+ 2u
20
+ ··· − 2u − 1
c
11
u
21
+ 3u
20
+ ··· − 4u − 1
c
12
u
21
− u
20
+ ··· + 12u + 1
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
+ 3y
20
+ ··· + 17y −1
c
2
, c
5
y
21
− 13y
20
+ ··· + 17y −1
c
3
, c
7
y
21
− 18y
20
+ ··· + 22y −1
c
4
, c
9
y
21
− 14y
20
+ ··· − 18y −1
c
6
, c
10
y
21
− 12y
20
+ ··· − 4y −1
c
8
, c
11
y
21
+ 15y
20
+ ··· − 8y −1
c
12
y
21
+ 3y
20
+ ··· + 26y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.497705 + 0.914980I
a = −0.500009 + 0.376999I
b = −0.883156 − 0.078797I
−1.39865 − 2.19121I −5.26683 + 7.34066I
u = −0.497705 − 0.914980I
a = −0.500009 − 0.376999I
b = −0.883156 + 0.078797I
−1.39865 + 2.19121I −5.26683 − 7.34066I
u = −0.906547 + 0.120990I
a = −0.37152 + 1.92475I
b = −1.049690 − 0.261917I
−0.291019 − 0.766881I −12.9784 − 7.1305I
u = −0.906547 − 0.120990I
a = −0.37152 − 1.92475I
b = −1.049690 + 0.261917I
−0.291019 + 0.766881I −12.9784 + 7.1305I
u = −0.952688 + 0.665934I
a = 0.31948 − 1.54539I
b = 0.968691 + 0.804354I
4.83291 − 5.48153I 0.61562 + 6.66233I
u = −0.952688 − 0.665934I
a = 0.31948 + 1.54539I
b = 0.968691 − 0.804354I
4.83291 + 5.48153I 0.61562 − 6.66233I
u = −1.063450 + 0.512232I
a = −0.589209 + 0.637928I
b = 0.810459 − 0.843136I
5.31654 + 0.66491I 0.415399 − 0.133048I
u = −1.063450 − 0.512232I
a = −0.589209 − 0.637928I
b = 0.810459 + 0.843136I
5.31654 − 0.66491I 0.415399 + 0.133048I
u = 0.801649 + 0.001085I
a = 0.07947 − 1.82807I
b = −1.18975 + 0.76944I
3.72958 + 2.65022I −0.33689 − 2.74170I
u = 0.801649 − 0.001085I
a = 0.07947 + 1.82807I
b = −1.18975 − 0.76944I
3.72958 − 2.65022I −0.33689 + 2.74170I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.19930
a = 1.40578
b = −0.550979
1.39967 −0.347370
u = 1.194170 + 0.163422I
a = 0.829774 − 1.015350I
b = −0.605623 + 0.779316I
5.50035 + 3.30026I 1.09093 − 4.73816I
u = 1.194170 − 0.163422I
a = 0.829774 + 1.015350I
b = −0.605623 − 0.779316I
5.50035 − 3.30026I 1.09093 + 4.73816I
u = 0.151730 + 0.674872I
a = 3.81452 + 0.99293I
b = 0.512186 − 0.147355I
−5.43869 + 4.12896I −19.9561 − 11.5234I
u = 0.151730 − 0.674872I
a = 3.81452 − 0.99293I
b = 0.512186 + 0.147355I
−5.43869 − 4.12896I −19.9561 + 11.5234I
u = 1.14383 + 1.06714I
a = 0.308798 + 0.748318I
b = 1.099210 − 0.485659I
2.33435 + 5.94594I 3.05578 − 7.68621I
u = 1.14383 − 1.06714I
a = 0.308798 − 0.748318I
b = 1.099210 + 0.485659I
2.33435 − 5.94594I 3.05578 + 7.68621I
u = 0.159929 + 0.360867I
a = −1.98062 + 0.02408I
b = 1.51366 + 0.09512I
−9.61177 + 2.97996I −4.78121 + 1.02692I
u = 0.159929 − 0.360867I
a = −1.98062 − 0.02408I
b = 1.51366 − 0.09512I
−9.61177 − 2.97996I −4.78121 − 1.02692I
u = 1.56873 + 0.63635I
a = −0.113575 − 0.201644I
b = 0.599496 + 0.365497I
4.19616 + 2.23780I 2.81535 − 0.97091I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.56873 − 0.63635I
a = −0.113575 + 0.201644I
b = 0.599496 − 0.365497I
4.19616 − 2.23780I 2.81535 + 0.97091I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
21
− 13u
20
+ ··· + 17u − 1)(u
66
+ 38u
65
+ ··· − 20u + 1)
c
2
(u
21
+ 3u
20
+ ··· − 3u − 1)(u
66
+ 2u
65
+ ··· + 10u
2
+ 1)
c
3
(u
21
− 9u
19
+ ··· − 6u + 1)(u
66
− u
65
+ ··· − 599u − 59)
c
4
(u
21
− 7u
19
+ ··· + 9u
2
+ 1)(u
66
+ u
65
+ ··· + 1920u − 1088)
c
5
(u
21
− 3u
20
+ ··· − 3u + 1)(u
66
+ 2u
65
+ ··· + 10u
2
+ 1)
c
6
(u
21
− 2u
20
+ ··· − 2u + 1)(u
66
− u
65
+ ··· − 283u − 59)
c
7
(u
21
− 9u
19
+ ··· − 6u − 1)(u
66
− u
65
+ ··· − 599u − 59)
c
8
(u
21
− 3u
20
+ ··· − 4u + 1)(u
66
− 2u
65
+ ··· − 13u + 1)
c
9
(u
21
− 7u
19
+ ··· − 9u
2
− 1)(u
66
+ u
65
+ ··· + 1920u − 1088)
c
10
(u
21
+ 2u
20
+ ··· − 2u − 1)(u
66
− u
65
+ ··· − 283u − 59)
c
11
(u
21
+ 3u
20
+ ··· − 4u − 1)(u
66
− 2u
65
+ ··· − 13u + 1)
c
12
(u
21
− u
20
+ ··· + 12u + 1)(u
66
+ 2u
65
+ ··· + 2893677u + 899893)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
21
+ 3y
20
+ ··· + 17y −1)(y
66
− 6y
65
+ ··· + 88y + 1)
c
2
, c
5
(y
21
− 13y
20
+ ··· + 17y −1)(y
66
− 38y
65
+ ··· + 20y + 1)
c
3
, c
7
(y
21
− 18y
20
+ ··· + 22y −1)(y
66
− 71y
65
+ ··· − 683301y + 3481)
c
4
, c
9
(y
21
− 14y
20
+ ··· − 18y −1)
· (y
66
− 27y
65
+ ··· − 23148544y + 1183744)
c
6
, c
10
(y
21
− 12y
20
+ ··· − 4y −1)(y
66
− 29y
65
+ ··· − 212367y + 3481)
c
8
, c
11
(y
21
+ 15y
20
+ ··· − 8y −1)(y
66
+ 18y
65
+ ··· − 11y + 1)
c
12
(y
21
+ 3y
20
+ ··· + 26y −1)
· (y
66
− 78y
65
+ ··· − 13342381349441y + 809807411449)
21
