12n
0633
(K12n
0633
)
A knot diagram
1
Linearized knot diagam
3 7 11 9 3 12 2 5 7 6 4 10
Solving Sequence
4,11 6,12
7 3 2 5 10 1 9 8
c
11
c
6
c
3
c
2
c
5
c
10
c
12
c
9
c
8
c
1
, c
4
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.85653 × 10
96
u
67
+ 6.21801 × 10
96
u
66
+ ··· + 1.94852 × 10
96
b − 2.56391 × 10
97
,
− 1.98079 × 10
97
u
67
+ 7.40641 × 10
96
u
66
+ ··· + 3.89704 × 10
96
a − 1.25871 × 10
98
,
u
68
− 21u
66
+ ··· − 22u + 4i
I
u
2
= h34763u
19
− 7407u
18
+ ··· + 3686b − 174428, −171203u
19
+ 58379u
18
+ ··· + 7372a + 755094,
u
20
− u
19
+ ··· − 2u + 4i
* 2 irreducible components of dim
C
= 0, with total 88 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−6.86 × 10
96
u
67
+ 6.22 × 10
96
u
66
+ · · · + 1.95 × 10
96
b − 2.56 ×
10
97
, −1.98 × 10
97
u
67
+ 7.41 × 10
96
u
66
+ · · · + 3.90 × 10
96
a − 1.26 ×
10
98
, u
68
− 21u
66
+ · · · − 22u + 4i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
6
=
5.08280u
67
− 1.90052u
66
+ ··· − 261.858u + 32.2991
3.51883u
67
− 3.19114u
66
+ ··· − 67.4259u + 13.1583
a
12
=
1
−u
2
a
7
=
0.913294u
67
+ 1.61910u
66
+ ··· − 132.289u + 11.5387
6.79407u
67
− 5.84784u
66
+ ··· − 161.535u + 27.2367
a
3
=
−u
u
a
2
=
16.8822u
67
− 10.5665u
66
+ ··· − 538.941u + 75.0706
−9.25794u
67
+ 6.53626u
66
+ ··· + 329.727u − 48.4229
a
5
=
1.71831u
67
− 0.0689445u
66
+ ··· − 115.435u + 11.9324
6.88332u
67
− 5.02272u
66
+ ··· − 213.849u + 33.5249
a
10
=
25.1621u
67
− 18.4497u
66
+ ··· − 888.032u + 134.487
−17.8873u
67
+ 13.8599u
66
+ ··· + 648.982u − 96.7041
a
1
=
19.3375u
67
− 11.7232u
66
+ ··· − 658.103u + 91.1915
−11.7133u
67
+ 7.69295u
66
+ ··· + 448.888u − 64.5438
a
9
=
−4.85415u
67
+ 4.02937u
66
+ ··· + 67.1858u − 6.11337
28.8964u
67
− 27.6860u
66
+ ··· − 747.269u + 114.575
a
8
=
8.95388u
67
− 5.32862u
66
+ ··· − 419.793u + 66.1754
22.8262u
67
− 22.4977u
66
+ ··· − 524.537u + 80.1631
(ii) Obstruction class = −1
(iii) Cusp Shapes = 292.431u
67
− 245.607u
66
+ ··· − 9342.95u + 1389.56
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
68
+ 74u
67
+ ··· + 5731546u + 418609
c
2
, c
7
u
68
+ 37u
66
+ ··· − 3274u + 647
c
3
, c
11
u
68
− 21u
66
+ ··· + 22u + 4
c
4
, c
8
u
68
− u
67
+ ··· − 11u + 1
c
5
u
68
+ 15u
66
+ ··· + 135093u + 1093
c
6
u
68
+ u
67
+ ··· − 16u
2
+ 1
c
9
u
68
+ 5u
67
+ ··· + 52344u + 5441
c
10
u
68
+ 2u
67
+ ··· − 82u + 23
c
12
u
68
− 10u
67
+ ··· − 74106u + 4643
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
68
− 138y
67
+ ··· + 15388310151698y + 175233494881
c
2
, c
7
y
68
+ 74y
67
+ ··· + 5731546y + 418609
c
3
, c
11
y
68
− 42y
67
+ ··· − 428y + 16
c
4
, c
8
y
68
+ 9y
67
+ ··· − 13y + 1
c
5
y
68
+ 30y
67
+ ··· − 20226072467y + 1194649
c
6
y
68
− 3y
67
+ ··· − 32y + 1
c
9
y
68
+ 97y
67
+ ··· + 2711378272y + 29604481
c
10
y
68
+ 70y
66
+ ··· + 6570y + 529
c
12
y
68
− 38y
67
+ ··· − 545000606y + 21557449
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.949060 + 0.277585I
a = 0.674087 + 0.799939I
b = −1.082240 − 0.511503I
1.62540 + 4.62273I 0
u = 0.949060 − 0.277585I
a = 0.674087 − 0.799939I
b = −1.082240 + 0.511503I
1.62540 − 4.62273I 0
u = 0.477554 + 0.863068I
a = 0.299238 − 0.445376I
b = 0.312922 + 0.155500I
−0.168580 − 1.402730I 0
u = 0.477554 − 0.863068I
a = 0.299238 + 0.445376I
b = 0.312922 − 0.155500I
−0.168580 + 1.402730I 0
u = −0.976594 + 0.352303I
a = −0.09839 + 2.45816I
b = −0.563810 − 0.683484I
1.95040 − 4.90409I 0
u = −0.976594 − 0.352303I
a = −0.09839 − 2.45816I
b = −0.563810 + 0.683484I
1.95040 + 4.90409I 0
u = −0.987338 + 0.336791I
a = 1.31787 − 0.70232I
b = −1.66989 + 1.37122I
−6.65007 + 1.79663I 0
u = −0.987338 − 0.336791I
a = 1.31787 + 0.70232I
b = −1.66989 − 1.37122I
−6.65007 − 1.79663I 0
u = 0.036453 + 0.949205I
a = −0.117308 + 0.268241I
b = −0.933587 − 0.421593I
−2.20089 − 5.01038I 0
u = 0.036453 − 0.949205I
a = −0.117308 − 0.268241I
b = −0.933587 + 0.421593I
−2.20089 + 5.01038I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.562459 + 0.893363I
a = −0.325180 − 0.090948I
b = −0.344858 − 0.579627I
1.89174 − 1.13471I 0
u = −0.562459 − 0.893363I
a = −0.325180 + 0.090948I
b = −0.344858 + 0.579627I
1.89174 + 1.13471I 0
u = −1.033320 + 0.240118I
a = −0.62100 − 2.16741I
b = 0.694803 + 0.385277I
0.70109 − 1.37028I 0
u = −1.033320 − 0.240118I
a = −0.62100 + 2.16741I
b = 0.694803 − 0.385277I
0.70109 + 1.37028I 0
u = 0.900961 + 0.246507I
a = −0.17734 + 1.80879I
b = 0.633695 − 1.091540I
−0.63633 + 2.50561I 0
u = 0.900961 − 0.246507I
a = −0.17734 − 1.80879I
b = 0.633695 + 1.091540I
−0.63633 − 2.50561I 0
u = 0.769050 + 0.512192I
a = −0.458901 + 1.078890I
b = 1.386090 − 0.201350I
−3.53141 + 2.10002I 0
u = 0.769050 − 0.512192I
a = −0.458901 − 1.078890I
b = 1.386090 + 0.201350I
−3.53141 − 2.10002I 0
u = 0.992421 + 0.427912I
a = −1.222460 − 0.492212I
b = −1.026620 + 0.399550I
−7.28832 + 7.29217I 0
u = 0.992421 − 0.427912I
a = −1.222460 + 0.492212I
b = −1.026620 − 0.399550I
−7.28832 − 7.29217I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.024000 + 0.488219I
a = 0.924713 + 0.917552I
b = 1.222870 − 0.449426I
−6.66867 + 0.53139I 0
u = 1.024000 − 0.488219I
a = 0.924713 − 0.917552I
b = 1.222870 + 0.449426I
−6.66867 − 0.53139I 0
u = −0.851677 + 0.071654I
a = 1.98456 − 1.14177I
b = 1.072350 − 0.022127I
−0.468926 − 0.123890I 53.5469 + 43.7479I
u = −0.851677 − 0.071654I
a = 1.98456 + 1.14177I
b = 1.072350 + 0.022127I
−0.468926 + 0.123890I 53.5469 − 43.7479I
u = −1.101920 + 0.332895I
a = −1.56004 + 1.06712I
b = 1.63485 − 1.88936I
−5.37170 − 6.15935I 0
u = −1.101920 − 0.332895I
a = −1.56004 − 1.06712I
b = 1.63485 + 1.88936I
−5.37170 + 6.15935I 0
u = −0.206713 + 1.141710I
a = 0.0966368 − 0.0568163I
b = 1.10834 − 0.89772I
−9.8473 + 10.2493I 0
u = −0.206713 − 1.141710I
a = 0.0966368 + 0.0568163I
b = 1.10834 + 0.89772I
−9.8473 − 10.2493I 0
u = −1.036630 + 0.527403I
a = −0.563736 + 0.430837I
b = −0.265018 − 0.549706I
1.87759 − 0.90886I 0
u = −1.036630 − 0.527403I
a = −0.563736 − 0.430837I
b = −0.265018 + 0.549706I
1.87759 + 0.90886I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.130330 + 0.383792I
a = −0.58473 + 1.43790I
b = −0.314371 − 0.692494I
3.41676 − 1.44246I 0
u = −1.130330 − 0.383792I
a = −0.58473 − 1.43790I
b = −0.314371 + 0.692494I
3.41676 + 1.44246I 0
u = −0.163217 + 1.186590I
a = −0.0340048 + 0.1210010I
b = −1.047260 + 0.754337I
−10.81970 + 1.95946I 0
u = −0.163217 − 1.186590I
a = −0.0340048 − 0.1210010I
b = −1.047260 − 0.754337I
−10.81970 − 1.95946I 0
u = 1.166730 + 0.482446I
a = 0.21340 + 1.77817I
b = 0.696368 − 1.218600I
1.62803 + 6.96696I 0
u = 1.166730 − 0.482446I
a = 0.21340 − 1.77817I
b = 0.696368 + 1.218600I
1.62803 − 6.96696I 0
u = −0.723291 + 0.103919I
a = 0.19228 + 4.46686I
b = −0.53650 − 2.36375I
−7.96551 − 4.21106I −10.6805 + 9.7958I
u = −0.723291 − 0.103919I
a = 0.19228 − 4.46686I
b = −0.53650 + 2.36375I
−7.96551 + 4.21106I −10.6805 − 9.7958I
u = 1.161530 + 0.541241I
a = 0.38524 + 1.44006I
b = 0.432750 − 0.788611I
2.24420 + 6.51019I 0
u = 1.161530 − 0.541241I
a = 0.38524 − 1.44006I
b = 0.432750 + 0.788611I
2.24420 − 6.51019I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.640613 + 0.315137I
a = −0.998359 − 0.244645I
b = −0.825755 + 0.417032I
0.90027 + 1.87459I 3.46073 − 1.75743I
u = −0.640613 − 0.315137I
a = −0.998359 + 0.244645I
b = −0.825755 − 0.417032I
0.90027 − 1.87459I 3.46073 + 1.75743I
u = 0.148278 + 0.694455I
a = −0.446602 − 0.061714I
b = 0.709628 + 0.749968I
−1.31557 − 2.50850I −5.13435 + 3.12741I
u = 0.148278 − 0.694455I
a = −0.446602 + 0.061714I
b = 0.709628 − 0.749968I
−1.31557 + 2.50850I −5.13435 − 3.12741I
u = 1.272720 + 0.363259I
a = 0.01011 − 1.58994I
b = −1.06776 + 1.36859I
6.88375 + 4.97359I 0
u = 1.272720 − 0.363259I
a = 0.01011 + 1.58994I
b = −1.06776 − 1.36859I
6.88375 − 4.97359I 0
u = 1.261530 + 0.506772I
a = 0.06337 − 1.58271I
b = −0.995510 + 0.749214I
1.52447 + 10.15860I 0
u = 1.261530 − 0.506772I
a = 0.06337 + 1.58271I
b = −0.995510 − 0.749214I
1.52447 − 10.15860I 0
u = −1.380680 + 0.270616I
a = −0.015714 − 0.343875I
b = −0.115547 + 0.236900I
2.41433 − 0.14658I 0
u = −1.380680 − 0.270616I
a = −0.015714 + 0.343875I
b = −0.115547 − 0.236900I
2.41433 + 0.14658I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.578179
a = −1.35754
b = 1.34424
−1.69517 −8.62180
u = 0.457759 + 0.331098I
a = −0.95050 − 3.45445I
b = −0.328997 − 0.646374I
−8.83729 − 3.75680I −4.87595 + 0.45083I
u = 0.457759 − 0.331098I
a = −0.95050 + 3.45445I
b = −0.328997 + 0.646374I
−8.83729 + 3.75680I −4.87595 − 0.45083I
u = −1.29321 + 0.62592I
a = 0.14369 − 1.63479I
b = 1.34354 + 1.11783I
−6.4415 − 16.4621I 0
u = −1.29321 − 0.62592I
a = 0.14369 + 1.63479I
b = 1.34354 − 1.11783I
−6.4415 + 16.4621I 0
u = −1.33567 + 0.55610I
a = 0.258977 − 1.031680I
b = 0.70692 + 1.26195I
5.22604 − 5.31158I 0
u = −1.33567 − 0.55610I
a = 0.258977 + 1.031680I
b = 0.70692 − 1.26195I
5.22604 + 5.31158I 0
u = −1.30896 + 0.62516I
a = −0.04918 + 1.49859I
b = −1.32742 − 1.09391I
−7.24233 − 8.26321I 0
u = −1.30896 − 0.62516I
a = −0.04918 − 1.49859I
b = −1.32742 + 1.09391I
−7.24233 + 8.26321I 0
u = 0.298475 + 0.454106I
a = 2.15097 + 2.17240I
b = 0.562565 + 0.849058I
−8.57658 + 3.47140I −3.76489 − 3.57042I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.298475 − 0.454106I
a = 2.15097 − 2.17240I
b = 0.562565 − 0.849058I
−8.57658 − 3.47140I −3.76489 + 3.57042I
u = 0.217791 + 0.460271I
a = −0.420843 − 1.134500I
b = −0.083559 + 0.511003I
0.04096 − 1.67981I 0.32843 + 3.37053I
u = 0.217791 − 0.460271I
a = −0.420843 + 1.134500I
b = −0.083559 − 0.511003I
0.04096 + 1.67981I 0.32843 − 3.37053I
u = 1.45066 + 0.83027I
a = 0.117799 − 0.418638I
b = −0.567734 − 0.021803I
−5.46714 + 5.19884I 0
u = 1.45066 − 0.83027I
a = 0.117799 + 0.418638I
b = −0.567734 + 0.021803I
−5.46714 − 5.19884I 0
u = 0.326449
a = −1.90214
b = 1.12096
−1.71156 −7.01780
u = 1.69533 + 0.19034I
a = −0.308818 − 0.486749I
b = 0.346134 + 0.908029I
−3.50096 − 4.59075I 0
u = 1.69533 − 0.19034I
a = −0.308818 + 0.486749I
b = 0.346134 − 0.908029I
−3.50096 + 4.59075I 0
11
II. I
u
2
= h34763u
19
− 7407u
18
+ · · · + 3686b − 174428, −1.71 × 10
5
u
19
+
5.84 × 10
4
u
18
+ · · · + 7372a + 7.55 × 10
5
, u
20
− u
19
+ · · · − 2u + 4i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
6
=
23.2234u
19
− 7.91902u
18
+ ··· − 102.257u − 102.427
−9.43109u
19
+ 2.00950u
18
+ ··· + 41.0285u + 47.3218
a
12
=
1
−u
2
a
7
=
18.3436u
19
− 4.83356u
18
+ ··· − 81.0007u − 88.5315
−6.01546u
19
− 0.634021u
18
+ ··· + 25.0979u + 40.1443
a
3
=
−u
u
a
2
=
3
4
u
19
+
1
4
u
18
+ ··· +
9
4
u −
5
2
−9.73169u
19
+ 10.5271u
18
+ ··· + 59.5814u − 2.22355
a
5
=
14.5142u
19
− 3.78445u
18
+ ··· − 62.8534u − 70.8961
−0.721921u
19
− 2.12507u
18
+ ··· + 1.62480u + 15.7906
a
10
=
−8.87765u
19
− 2.11503u
18
+ ··· + 22.6549u + 67.2878
8.77998u
19
− 1.86300u
18
+ ··· − 32.5890u − 45.9289
a
1
=
−4.68353u
19
+ 7.42254u
18
+ ··· + 41.7676u − 9.68177
−4.29816u
19
+ 3.35458u
18
+ ··· + 20.0638u + 4.95822
a
9
=
−6.01858u
19
+ 0.685431u
18
+ ··· + 21.5563u + 38.1120
14.2770u
19
− 24.2748u
18
+ ··· − 113.824u + 57.3445
a
8
=
−22.6367u
19
+ 3.63077u
18
+ ··· + 84.8923u + 126.802
18.5670u
19
− 22.7526u
18
+ ··· − 123.258u + 20.0412
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
67727
1843
u
19
+
137752
1843
u
18
+ ··· +
656532
1843
u −
448817
1843
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
20
− 13u
19
+ ··· − 10u + 1
c
2
u
20
+ u
19
+ ··· − 4u + 1
c
3
u
20
+ u
19
+ ··· + 2u + 4
c
4
u
20
+ 6u
18
+ ··· − 7u + 1
c
5
u
20
− 3u
19
+ ··· − 83u + 19
c
6
u
20
− 2u
19
+ ··· − 4u + 1
c
7
u
20
− u
19
+ ··· + 4u + 1
c
8
u
20
+ 6u
18
+ ··· + 7u + 1
c
9
u
20
− 8u
19
+ ··· + 10u + 1
c
10
u
20
− u
19
+ ··· + u
2
+ 1
c
11
u
20
− u
19
+ ··· − 2u + 4
c
12
u
20
− u
19
+ ··· − 2u + 1
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
− 31y
19
+ ··· + 58y + 1
c
2
, c
7
y
20
+ 13y
19
+ ··· + 10y + 1
c
3
, c
11
y
20
− 15y
19
+ ··· − 140y + 16
c
4
, c
8
y
20
+ 12y
19
+ ··· + 3y + 1
c
5
y
20
− 3y
19
+ ··· + 825y + 361
c
6
y
20
− 4y
19
+ ··· − 4y + 1
c
9
y
20
+ 8y
19
+ ··· − 88y + 1
c
10
y
20
+ 11y
19
+ ··· + 2y + 1
c
12
y
20
− 7y
19
+ ··· − 2y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.131002 + 1.113250I
a = 0.135762 − 0.247562I
b = −0.211337 − 0.712335I
1.33031 − 1.41660I −0.12221 + 8.09754I
u = −0.131002 − 1.113250I
a = 0.135762 + 0.247562I
b = −0.211337 + 0.712335I
1.33031 + 1.41660I −0.12221 − 8.09754I
u = −0.825439 + 0.292703I
a = −0.38792 + 1.50877I
b = 0.520453 − 0.239703I
1.37870 − 3.71317I 0.62059 + 2.55570I
u = −0.825439 − 0.292703I
a = −0.38792 − 1.50877I
b = 0.520453 + 0.239703I
1.37870 + 3.71317I 0.62059 − 2.55570I
u = −0.791371 + 0.025548I
a = −1.49350 + 0.66671I
b = −1.027350 + 0.007941I
−0.519322 − 0.028360I −0.03473 − 12.86700I
u = −0.791371 − 0.025548I
a = −1.49350 − 0.66671I
b = −1.027350 − 0.007941I
−0.519322 + 0.028360I −0.03473 + 12.86700I
u = 0.773025 + 0.011716I
a = −0.10430 + 4.15418I
b = 0.49721 − 1.78697I
−7.62230 + 3.92786I 4.72796 + 1.10442I
u = 0.773025 − 0.011716I
a = −0.10430 − 4.15418I
b = 0.49721 + 1.78697I
−7.62230 − 3.92786I 4.72796 − 1.10442I
u = 1.136810 + 0.495760I
a = 0.29177 + 1.81673I
b = 0.535350 − 0.990359I
2.47500 + 7.36889I 6.99032 − 11.23662I
u = 1.136810 − 0.495760I
a = 0.29177 − 1.81673I
b = 0.535350 + 0.990359I
2.47500 − 7.36889I 6.99032 + 11.23662I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.323852 + 0.618441I
a = −0.011337 − 0.743359I
b = 0.689251 + 0.623831I
0.00877 − 2.95298I 1.04164 + 6.04571I
u = 0.323852 − 0.618441I
a = −0.011337 + 0.743359I
b = 0.689251 − 0.623831I
0.00877 + 2.95298I 1.04164 − 6.04571I
u = −1.324440 + 0.377135I
a = 0.082854 − 1.273180I
b = 0.97990 + 1.07266I
6.29671 − 3.98961I 3.78793 + 0.83717I
u = −1.324440 − 0.377135I
a = 0.082854 + 1.273180I
b = 0.97990 − 1.07266I
6.29671 + 3.98961I 3.78793 − 0.83717I
u = 1.303070 + 0.485356I
a = −0.31452 − 1.41895I
b = −0.64491 + 1.58943I
5.64745 + 6.68901I 3.95560 − 7.72080I
u = 1.303070 − 0.485356I
a = −0.31452 + 1.41895I
b = −0.64491 − 1.58943I
5.64745 − 6.68901I 3.95560 + 7.72080I
u = 1.34758 + 0.43306I
a = 0.282070 + 0.271645I
b = −0.551118 − 0.834660I
−4.80101 + 4.75092I 1.34592 − 3.51891I
u = 1.34758 − 0.43306I
a = 0.282070 − 0.271645I
b = −0.551118 + 0.834660I
−4.80101 − 4.75092I 1.34592 + 3.51891I
u = −1.31208 + 0.53837I
a = −0.230879 + 0.508463I
b = −0.287446 − 0.374984I
2.38542 − 0.59111I 10.18699 + 3.52110I
u = −1.31208 − 0.53837I
a = −0.230879 − 0.508463I
b = −0.287446 + 0.374984I
2.38542 + 0.59111I 10.18699 − 3.52110I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
20
− 13u
19
+ ··· − 10u + 1)
· (u
68
+ 74u
67
+ ··· + 5731546u + 418609)
c
2
(u
20
+ u
19
+ ··· − 4u + 1)(u
68
+ 37u
66
+ ··· − 3274u + 647)
c
3
(u
20
+ u
19
+ ··· + 2u + 4)(u
68
− 21u
66
+ ··· + 22u + 4)
c
4
(u
20
+ 6u
18
+ ··· − 7u + 1)(u
68
− u
67
+ ··· − 11u + 1)
c
5
(u
20
− 3u
19
+ ··· − 83u + 19)(u
68
+ 15u
66
+ ··· + 135093u + 1093)
c
6
(u
20
− 2u
19
+ ··· − 4u + 1)(u
68
+ u
67
+ ··· − 16u
2
+ 1)
c
7
(u
20
− u
19
+ ··· + 4u + 1)(u
68
+ 37u
66
+ ··· − 3274u + 647)
c
8
(u
20
+ 6u
18
+ ··· + 7u + 1)(u
68
− u
67
+ ··· − 11u + 1)
c
9
(u
20
− 8u
19
+ ··· + 10u + 1)(u
68
+ 5u
67
+ ··· + 52344u + 5441)
c
10
(u
20
− u
19
+ ··· + u
2
+ 1)(u
68
+ 2u
67
+ ··· − 82u + 23)
c
11
(u
20
− u
19
+ ··· − 2u + 4)(u
68
− 21u
66
+ ··· + 22u + 4)
c
12
(u
20
− u
19
+ ··· − 2u + 1)(u
68
− 10u
67
+ ··· − 74106u + 4643)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
20
− 31y
19
+ ··· + 58y + 1)
· (y
68
− 138y
67
+ ··· + 15388310151698y + 175233494881)
c
2
, c
7
(y
20
+ 13y
19
+ ··· + 10y + 1)
· (y
68
+ 74y
67
+ ··· + 5731546y + 418609)
c
3
, c
11
(y
20
− 15y
19
+ ··· − 140y + 16)(y
68
− 42y
67
+ ··· − 428y + 16)
c
4
, c
8
(y
20
+ 12y
19
+ ··· + 3y + 1)(y
68
+ 9y
67
+ ··· − 13y + 1)
c
5
(y
20
− 3y
19
+ ··· + 825y + 361)
· (y
68
+ 30y
67
+ ··· − 20226072467y + 1194649)
c
6
(y
20
− 4y
19
+ ··· − 4y + 1)(y
68
− 3y
67
+ ··· − 32y + 1)
c
9
(y
20
+ 8y
19
+ ··· − 88y + 1)
· (y
68
+ 97y
67
+ ··· + 2711378272y + 29604481)
c
10
(y
20
+ 11y
19
+ ··· + 2y + 1)(y
68
+ 70y
66
+ ··· + 6570y + 529)
c
12
(y
20
− 7y
19
+ ··· − 2y + 1)
· (y
68
− 38y
67
+ ··· − 545000606y + 21557449)
20
