12n
0687
(K12n
0687
)
A knot diagram
1
Linearized knot diagam
4 5 6 8 10 1 12 2 6 5 3 7
Solving Sequence
6,10 2,5
3 4 11 12 1 9 8 7
c
5
c
2
c
3
c
10
c
11
c
1
c
9
c
8
c
7
c
4
, c
6
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h9.93374 × 10
151
u
69
− 5.73011 × 10
151
u
68
+ ··· + 1.25167 × 10
152
b − 1.15684 × 10
152
,
− 2.27978 × 10
152
u
69
+ 7.27815 × 10
151
u
68
+ ··· + 1.25167 × 10
152
a − 1.09032 × 10
153
,
u
70
+ 8u
68
+ ··· + 12u + 1i
I
u
2
= h784u
16
− 1472u
15
+ ··· + 281b − 1616, −u
16
− 4u
14
+ ··· + a − 7, u
17
− u
16
+ ··· − u + 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
= h9.93 × 10
151
u
69
− 5.73 × 10
151
u
68
+ · · · + 1.25 × 10
152
b − 1.16 ×
10
152
, −2.28 × 10
152
u
69
+ 7.28 × 10
151
u
68
+ · · · + 1.25 × 10
152
a − 1.09 ×
10
153
, u
70
+ 8u
68
+ · · · + 12u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
2
=
1.82140u
69
− 0.581477u
68
+ ··· + 39.0109u + 8.71095
−0.793642u
69
+ 0.457798u
68
+ ··· + 1.47985u + 0.924244
a
5
=
1
u
2
a
3
=
1.02178u
69
− 0.283802u
68
+ ··· + 35.3344u + 9.05372
−0.484690u
69
+ 0.265454u
68
+ ··· − 1.29264u + 0.626569
a
4
=
1.50647u
69
− 0.549256u
68
+ ··· + 36.6270u + 8.42715
−0.484690u
69
+ 0.265454u
68
+ ··· − 1.29264u + 0.626569
a
11
=
u
u
3
+ u
a
12
=
−2.10413u
69
+ 0.456635u
68
+ ··· − 57.5910u − 11.5890
0.171585u
69
+ 0.157443u
68
+ ··· − 6.10514u − 1.41447
a
1
=
1.13758u
69
− 0.539841u
68
+ ··· + 39.0714u + 7.72721
0.261369u
69
− 0.0100471u
68
+ ··· − 1.35091u + 0.206159
a
9
=
−u
u
a
8
=
−1.63790u
69
+ 0.361732u
68
+ ··· − 57.8284u − 11.6027
−0.708579u
69
− 0.0963778u
68
+ ··· − 16.6684u − 2.12525
a
7
=
−1.39909u
69
+ 0.856722u
68
+ ··· − 38.1398u − 5.68756
−0.279079u
69
− 0.230487u
68
+ ··· − 17.0325u − 1.58453
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.717657u
69
+ 2.08595u
68
+ ··· + 98.0282u + 17.8328
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
70
− 8u
69
+ ··· + 54u + 9
c
2
u
70
− 7u
69
+ ··· + 9260u − 7239
c
3
u
70
+ 2u
69
+ ··· + 564u + 41
c
4
u
70
− u
69
+ ··· − 22u − 1
c
5
, c
9
, c
10
u
70
+ 8u
68
+ ··· − 12u + 1
c
6
, c
7
, c
12
u
70
+ 34u
68
+ ··· + 17u + 3
c
8
u
70
− 2u
69
+ ··· + 4105u + 2083
c
11
u
70
+ u
69
+ ··· − 329u + 1651
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
70
− 10y
69
+ ··· − 144y + 81
c
2
y
70
− 61y
69
+ ··· − 1022459722y + 52403121
c
3
y
70
+ 12y
69
+ ··· − 24782y + 1681
c
4
y
70
+ 7y
69
+ ··· + 122y + 1
c
5
, c
9
, c
10
y
70
+ 16y
69
+ ··· − 30y + 1
c
6
, c
7
, c
12
y
70
+ 68y
69
+ ··· − 223y + 9
c
8
y
70
+ 12y
69
+ ··· + 246685969y + 4338889
c
11
y
70
− 65y
69
+ ··· − 76523125y + 2725801
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.182629 + 0.959522I
a = 1.001330 + 0.504116I
b = −0.495567 + 0.539126I
−5.19104 + 2.89870I −1.83556 − 3.69030I
u = 0.182629 − 0.959522I
a = 1.001330 − 0.504116I
b = −0.495567 − 0.539126I
−5.19104 − 2.89870I −1.83556 + 3.69030I
u = 0.889971 + 0.615220I
a = 1.49599 − 0.81473I
b = 0.658738 + 0.726934I
−2.94953 + 6.14576I 0
u = 0.889971 − 0.615220I
a = 1.49599 + 0.81473I
b = 0.658738 − 0.726934I
−2.94953 − 6.14576I 0
u = 0.467157 + 1.015360I
a = 0.469020 − 0.334689I
b = −0.91014 + 1.45911I
−4.76852 − 0.93744I 0
u = 0.467157 − 1.015360I
a = 0.469020 + 0.334689I
b = −0.91014 − 1.45911I
−4.76852 + 0.93744I 0
u = −0.222651 + 0.847009I
a = 1.14984 + 1.14399I
b = −0.0748484 + 0.0360553I
−7.73355 + 3.72028I −2.51438 − 0.93811I
u = −0.222651 − 0.847009I
a = 1.14984 − 1.14399I
b = −0.0748484 − 0.0360553I
−7.73355 − 3.72028I −2.51438 + 0.93811I
u = −0.751668 + 0.837280I
a = −1.72961 − 0.46280I
b = 1.14330 + 1.25142I
−0.30303 − 6.28207I 0
u = −0.751668 − 0.837280I
a = −1.72961 + 0.46280I
b = 1.14330 − 1.25142I
−0.30303 + 6.28207I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.770010 + 0.372544I
a = 0.581630 − 0.055990I
b = 0.144106 + 0.825142I
−4.08900 + 2.25007I 3.53748 − 2.27099I
u = 0.770010 − 0.372544I
a = 0.581630 + 0.055990I
b = 0.144106 − 0.825142I
−4.08900 − 2.25007I 3.53748 + 2.27099I
u = −1.14498
a = 1.73239
b = 1.53512
2.60015 −58.8670
u = −0.268041 + 0.804909I
a = 0.542252 − 0.218224I
b = −0.423247 − 0.869174I
−0.98658 − 2.03464I 3.76283 + 3.73374I
u = −0.268041 − 0.804909I
a = 0.542252 + 0.218224I
b = −0.423247 + 0.869174I
−0.98658 + 2.03464I 3.76283 − 3.73374I
u = −0.656557 + 0.954242I
a = −0.493373 − 1.239310I
b = −0.00110 + 1.66937I
−0.681468 + 0.834270I 0
u = −0.656557 − 0.954242I
a = −0.493373 + 1.239310I
b = −0.00110 − 1.66937I
−0.681468 − 0.834270I 0
u = 0.825164 + 0.845513I
a = −1.40194 + 0.58938I
b = 0.92803 − 1.30897I
4.72221 + 4.24472I 0
u = 0.825164 − 0.845513I
a = −1.40194 − 0.58938I
b = 0.92803 + 1.30897I
4.72221 − 4.24472I 0
u = 1.068270 + 0.572212I
a = −0.776105 + 0.152158I
b = 0.735609 − 0.965380I
0.233976 + 0.759074I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.068270 − 0.572212I
a = −0.776105 − 0.152158I
b = 0.735609 + 0.965380I
0.233976 − 0.759074I 0
u = −0.819050 + 0.902886I
a = −1.25597 − 1.03649I
b = 0.75273 + 1.61897I
1.70243 − 3.06412I 0
u = −0.819050 − 0.902886I
a = −1.25597 + 1.03649I
b = 0.75273 − 1.61897I
1.70243 + 3.06412I 0
u = −0.532408 + 0.562547I
a = −0.491267 + 0.375201I
b = 0.05004 − 1.69837I
−6.45795 − 6.80158I 1.45639 + 9.56884I
u = −0.532408 − 0.562547I
a = −0.491267 − 0.375201I
b = 0.05004 + 1.69837I
−6.45795 + 6.80158I 1.45639 − 9.56884I
u = 0.763532 + 0.981407I
a = −0.747021 + 1.045390I
b = 0.29445 − 1.52258I
4.29081 + 1.75973I 0
u = 0.763532 − 0.981407I
a = −0.747021 − 1.045390I
b = 0.29445 + 1.52258I
4.29081 − 1.75973I 0
u = 0.031790 + 0.748955I
a = 1.337290 + 0.340343I
b = −1.69605 − 0.47490I
−2.07518 − 1.88050I −0.58788 + 2.54582I
u = 0.031790 − 0.748955I
a = 1.337290 − 0.340343I
b = −1.69605 + 0.47490I
−2.07518 + 1.88050I −0.58788 − 2.54582I
u = −1.026810 + 0.770847I
a = −0.931991 − 0.352914I
b = 0.727009 + 1.062520I
4.78970 − 2.73592I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.026810 − 0.770847I
a = −0.931991 + 0.352914I
b = 0.727009 − 1.062520I
4.78970 + 2.73592I 0
u = −0.076174 + 0.691781I
a = 1.76879 − 0.64957I
b = −2.25934 + 0.77220I
−8.05518 + 4.99038I −5.61415 + 0.00335I
u = −0.076174 − 0.691781I
a = 1.76879 + 0.64957I
b = −2.25934 − 0.77220I
−8.05518 − 4.99038I −5.61415 − 0.00335I
u = 0.403606 + 0.564847I
a = −0.472960 + 0.090622I
b = 0.124640 + 1.386760I
−0.86012 + 4.21216I 6.35099 − 11.74346I
u = 0.403606 − 0.564847I
a = −0.472960 − 0.090622I
b = 0.124640 − 1.386760I
−0.86012 − 4.21216I 6.35099 + 11.74346I
u = 0.019991 + 0.681568I
a = 0.664079 − 1.210490I
b = 0.074205 − 0.421986I
−1.57608 − 2.34912I 0.437437 + 0.644148I
u = 0.019991 − 0.681568I
a = 0.664079 + 1.210490I
b = 0.074205 + 0.421986I
−1.57608 + 2.34912I 0.437437 − 0.644148I
u = −0.316585 + 0.590067I
a = −3.02818 + 1.36465I
b = 1.287870 + 0.396140I
−7.54675 − 6.57227I −0.27416 + 11.76800I
u = −0.316585 − 0.590067I
a = −3.02818 − 1.36465I
b = 1.287870 − 0.396140I
−7.54675 + 6.57227I −0.27416 − 11.76800I
u = −1.075700 + 0.803829I
a = 1.005200 + 0.615424I
b = 0.311248 − 1.377500I
4.84131 − 0.55610I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.075700 − 0.803829I
a = 1.005200 − 0.615424I
b = 0.311248 + 1.377500I
4.84131 + 0.55610I 0
u = 0.902166 + 1.001410I
a = 1.057310 − 0.402054I
b = −0.42852 + 1.63869I
−4.61180 + 3.36092I 0
u = 0.902166 − 1.001410I
a = 1.057310 + 0.402054I
b = −0.42852 − 1.63869I
−4.61180 − 3.36092I 0
u = 1.093450 + 0.794950I
a = 0.905104 − 0.704207I
b = 0.255022 + 1.286370I
5.66823 − 4.85184I 0
u = 1.093450 − 0.794950I
a = 0.905104 + 0.704207I
b = 0.255022 − 1.286370I
5.66823 + 4.85184I 0
u = −1.121410 + 0.784623I
a = 0.828517 + 0.738103I
b = 0.236105 − 1.268720I
−0.59567 + 8.98753I 0
u = −1.121410 − 0.784623I
a = 0.828517 − 0.738103I
b = 0.236105 + 1.268720I
−0.59567 − 8.98753I 0
u = 0.436857 + 0.420062I
a = −1.56143 − 2.06163I
b = 1.015010 − 0.438737I
−0.46074 + 3.68809I 9.20342 − 10.39195I
u = 0.436857 − 0.420062I
a = −1.56143 + 2.06163I
b = 1.015010 + 0.438737I
−0.46074 − 3.68809I 9.20342 + 10.39195I
u = −0.89928 + 1.09857I
a = −0.710636 − 0.699922I
b = 0.373865 + 1.162200I
3.77288 − 4.30359I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.89928 − 1.09857I
a = −0.710636 + 0.699922I
b = 0.373865 − 1.162200I
3.77288 + 4.30359I 0
u = −0.08015 + 1.43152I
a = 0.111230 − 0.162640I
b = −0.744088 + 0.291066I
−3.91938 − 2.59263I 0
u = −0.08015 − 1.43152I
a = 0.111230 + 0.162640I
b = −0.744088 − 0.291066I
−3.91938 + 2.59263I 0
u = −0.91292 + 1.10722I
a = 1.054940 + 0.541284I
b = −0.76481 − 1.90183I
3.87345 − 6.65045I 0
u = −0.91292 − 1.10722I
a = 1.054940 − 0.541284I
b = −0.76481 + 1.90183I
3.87345 + 6.65045I 0
u = 0.90704 + 1.11763I
a = 1.107070 − 0.599871I
b = −0.87122 + 1.85913I
4.62505 + 12.08600I 0
u = 0.90704 − 1.11763I
a = 1.107070 + 0.599871I
b = −0.87122 − 1.85913I
4.62505 − 12.08600I 0
u = −0.90562 + 1.12890I
a = 1.159610 + 0.620259I
b = −0.92779 − 1.82023I
−1.7219 − 16.2840I 0
u = −0.90562 − 1.12890I
a = 1.159610 − 0.620259I
b = −0.92779 + 1.82023I
−1.7219 + 16.2840I 0
u = 1.13832 + 0.95435I
a = −0.791876 + 0.485812I
b = 0.603110 − 1.032090I
1.21898 + 4.01853I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.13832 − 0.95435I
a = −0.791876 − 0.485812I
b = 0.603110 + 1.032090I
1.21898 − 4.01853I 0
u = −0.491312 + 0.042330I
a = 0.813900 + 0.845312I
b = 0.487599 + 0.375306I
1.014060 + 0.126536I 10.90445 − 2.01322I
u = −0.491312 − 0.042330I
a = 0.813900 − 0.845312I
b = 0.487599 − 0.375306I
1.014060 − 0.126536I 10.90445 + 2.01322I
u = 0.89008 + 1.25065I
a = −0.591908 + 0.620866I
b = 0.274267 − 1.010060I
−1.81693 + 6.40974I 0
u = 0.89008 − 1.25065I
a = −0.591908 − 0.620866I
b = 0.274267 + 1.010060I
−1.81693 − 6.40974I 0
u = 0.17276 + 1.55205I
a = −0.088754 + 0.194039I
b = −0.414173 − 0.312547I
−10.80100 + 6.09312I 0
u = 0.17276 − 1.55205I
a = −0.088754 − 0.194039I
b = −0.414173 + 0.312547I
−10.80100 − 6.09312I 0
u = −0.165276 + 0.289045I
a = −1.72562 − 2.09252I
b = 0.875139 − 0.770810I
−2.39258 − 2.81193I 4.50166 + 4.86143I
u = −0.165276 − 0.289045I
a = −1.72562 + 2.09252I
b = 0.875139 + 0.770810I
−2.39258 + 2.81193I 4.50166 − 4.86143I
u = −0.137380
a = 6.75871
b = 0.782505
1.05954 8.79670
11
II. I
u
2
= h784u
16
− 1472u
15
+ · · · + 281b − 1616, −u
16
− 4u
14
+ · · · + a −
7, u
17
− u
16
+ · · · − u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
2
=
u
16
+ 4u
14
+ ··· + 2u + 7
−2.79004u
16
+ 5.23843u
15
+ ··· − 14.9786u + 5.75089
a
5
=
1
u
2
a
3
=
−1.79004u
16
+ 5.23843u
15
+ ··· − 12.9786u + 13.7509
−1.61210u
16
+ 3.06762u
15
+ ··· − 9.74021u + 3.30249
a
4
=
−0.177936u
16
+ 2.17082u
15
+ ··· − 3.23843u + 10.4484
−1.61210u
16
+ 3.06762u
15
+ ··· − 9.74021u + 3.30249
a
11
=
u
u
3
+ u
a
12
=
10.3025u
16
− 9.69039u
15
+ ··· + 43.5053u − 2.56228
1.84698u
16
− 0.733096u
15
+ ··· − 1.18505u + 4.82562
a
1
=
−5.93594u
16
+ 10.8185u
15
+ ··· − 36.4342u + 13.3986
1.53381u
16
− 2.51246u
15
+ ··· + 11.7153u − 5.34520
a
9
=
−u
u
a
8
=
9.30249u
16
− 8.69039u
15
+ ··· + 34.5053u − 1.56228
−0.00711744u
16
+ 0.686833u
15
+ ··· − 5.72954u + 2.17794
a
7
=
−2.48754u
16
− 1.45196u
15
+ ··· + 10.5267u − 19.8114
4.92171u
16
− 4.44484u
15
+ ··· + 15.9751u + 0.957295
(ii) Obstruction class = 1
(iii) Cusp Shapes =
2928
281
u
16
−
7172
281
u
15
+ ··· +
18839
281
u −
13628
281
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
− 7u
16
+ ··· + 7u − 1
c
2
u
17
+ 10u
16
+ ··· + 7u + 1
c
3
u
17
− 3u
16
+ ··· + u − 1
c
4
u
17
+ 4u
15
+ ··· + 3u − 1
c
5
u
17
− u
16
+ ··· − u + 1
c
6
, c
7
u
17
+ u
16
+ ··· + 2u + 1
c
8
u
17
+ 3u
16
+ ··· + 4u
2
+ 1
c
9
, c
10
u
17
+ u
16
+ ··· − u − 1
c
11
u
17
− 2u
16
+ ··· − 6u + 1
c
12
u
17
− u
16
+ ··· + 2u − 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
− 5y
16
+ ··· + 17y −1
c
2
y
17
− 8y
16
+ ··· − 9y −1
c
3
y
17
+ 9y
16
+ ··· − 13y −1
c
4
y
17
+ 8y
16
+ ··· + 11y −1
c
5
, c
9
, c
10
y
17
+ 9y
16
+ ··· − 17y −1
c
6
, c
7
, c
12
y
17
+ 17y
16
+ ··· − 24y −1
c
8
y
17
− 11y
16
+ ··· − 8y −1
c
11
y
17
− 8y
16
+ ··· − 14y −1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.09099
a = −1.84015
b = −1.44593
2.66549 64.1610
u = 0.081066 + 0.881798I
a = 0.253907 + 0.232514I
b = 0.351765 − 1.188740I
−3.35095 − 1.89433I 0.39933 + 2.13556I
u = 0.081066 − 0.881798I
a = 0.253907 − 0.232514I
b = 0.351765 + 1.188740I
−3.35095 + 1.89433I 0.39933 − 2.13556I
u = 0.759591 + 0.834731I
a = −0.926163 + 0.781600I
b = −0.031880 − 0.497291I
−2.84481 + 5.18632I 2.68899 − 3.82989I
u = 0.759591 − 0.834731I
a = −0.926163 − 0.781600I
b = −0.031880 + 0.497291I
−2.84481 − 5.18632I 2.68899 + 3.82989I
u = 0.945692 + 0.860913I
a = −1.057260 + 0.608745I
b = 0.856724 − 1.108260I
0.63478 + 3.45959I 1.40689 − 2.05093I
u = 0.945692 − 0.860913I
a = −1.057260 − 0.608745I
b = 0.856724 + 1.108260I
0.63478 − 3.45959I 1.40689 + 2.05093I
u = −0.924682 + 0.905753I
a = −1.012340 − 0.596735I
b = 0.607612 + 1.271600I
4.25625 − 3.38186I 8.68961 + 3.41215I
u = −0.924682 − 0.905753I
a = −1.012340 + 0.596735I
b = 0.607612 − 1.271600I
4.25625 + 3.38186I 8.68961 − 3.41215I
u = −0.012323 + 1.348120I
a = −0.449907 − 0.010058I
b = 1.089120 − 0.269541I
−4.38848 − 2.75040I −5.64109 + 6.59552I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.012323 − 1.348120I
a = −0.449907 + 0.010058I
b = 1.089120 + 0.269541I
−4.38848 + 2.75040I −5.64109 − 6.59552I
u = 0.089446 + 0.606473I
a = 1.54762 + 0.76818I
b = −0.646460 + 0.884390I
−1.35598 + 3.18194I 1.32413 − 8.23419I
u = 0.089446 − 0.606473I
a = 1.54762 − 0.76818I
b = −0.646460 − 0.884390I
−1.35598 − 3.18194I 1.32413 + 8.23419I
u = 0.121328 + 1.408910I
a = −0.507302 + 0.085491I
b = 0.851353 + 0.138665I
−11.43630 + 6.17014I −6.02947 − 4.38565I
u = 0.121328 − 1.408910I
a = −0.507302 − 0.085491I
b = 0.851353 − 0.138665I
−11.43630 − 6.17014I −6.02947 + 4.38565I
u = −0.014622 + 0.494941I
a = 3.07152 − 0.24078I
b = −1.35527 − 1.02921I
−7.52130 − 5.63580I 0.08114 + 5.24551I
u = −0.014622 − 0.494941I
a = 3.07152 + 0.24078I
b = −1.35527 + 1.02921I
−7.52130 + 5.63580I 0.08114 − 5.24551I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
17
− 7u
16
+ ··· + 7u − 1)(u
70
− 8u
69
+ ··· + 54u + 9)
c
2
(u
17
+ 10u
16
+ ··· + 7u + 1)(u
70
− 7u
69
+ ··· + 9260u − 7239)
c
3
(u
17
− 3u
16
+ ··· + u − 1)(u
70
+ 2u
69
+ ··· + 564u + 41)
c
4
(u
17
+ 4u
15
+ ··· + 3u − 1)(u
70
− u
69
+ ··· − 22u − 1)
c
5
(u
17
− u
16
+ ··· − u + 1)(u
70
+ 8u
68
+ ··· − 12u + 1)
c
6
, c
7
(u
17
+ u
16
+ ··· + 2u + 1)(u
70
+ 34u
68
+ ··· + 17u + 3)
c
8
(u
17
+ 3u
16
+ ··· + 4u
2
+ 1)(u
70
− 2u
69
+ ··· + 4105u + 2083)
c
9
, c
10
(u
17
+ u
16
+ ··· − u − 1)(u
70
+ 8u
68
+ ··· − 12u + 1)
c
11
(u
17
− 2u
16
+ ··· − 6u + 1)(u
70
+ u
69
+ ··· − 329u + 1651)
c
12
(u
17
− u
16
+ ··· + 2u − 1)(u
70
+ 34u
68
+ ··· + 17u + 3)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
17
− 5y
16
+ ··· + 17y −1)(y
70
− 10y
69
+ ··· − 144y + 81)
c
2
(y
17
− 8y
16
+ ··· − 9y −1)
· (y
70
− 61y
69
+ ··· − 1022459722y + 52403121)
c
3
(y
17
+ 9y
16
+ ··· − 13y −1)(y
70
+ 12y
69
+ ··· − 24782y + 1681)
c
4
(y
17
+ 8y
16
+ ··· + 11y −1)(y
70
+ 7y
69
+ ··· + 122y + 1)
c
5
, c
9
, c
10
(y
17
+ 9y
16
+ ··· − 17y −1)(y
70
+ 16y
69
+ ··· − 30y + 1)
c
6
, c
7
, c
12
(y
17
+ 17y
16
+ ··· − 24y −1)(y
70
+ 68y
69
+ ··· − 223y + 9)
c
8
(y
17
− 11y
16
+ ··· − 8y −1)
· (y
70
+ 12y
69
+ ··· + 246685969y + 4338889)
c
11
(y
17
− 8y
16
+ ··· − 14y −1)
· (y
70
− 65y
69
+ ··· − 76523125y + 2725801)
18
