12a
0021
(K12a
0021
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 10 12 4 8 1 7 11
Solving Sequence
7,11
12
4,8
9 5 1 10 6 3 2
c
11
c
7
c
8
c
4
c
12
c
10
c
6
c
3
c
2
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−19u
103
− 49u
102
+ ··· + 2b + 19, −2u
103
+ 5u
102
+ ··· + 2a − 6, u
104
+ 3u
103
+ ··· − u − 1i
I
u
2
= h−u
2
a + b + a, u
2
a + a
2
− au − u + 1, u
3
− u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 110 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−19u
103
− 49u
102
+ · · · + 2b + 19, −2u
103
+ 5u
102
+ · · · + 2a −
6, u
104
+ 3u
103
+ · · · − u − 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
4
=
u
103
−
5
2
u
102
+ ··· −
1
2
u + 3
19
2
u
103
+
49
2
u
102
+ ··· − 4u −
19
2
a
8
=
−u
−u
3
+ u
a
9
=
−u
8
+ u
6
− u
4
+ 1
−u
10
+ 2u
8
− 3u
6
+ 2u
4
− u
2
a
5
=
−2u
103
−
23
2
u
102
+ ··· +
1
2
u + 7
23
2
u
103
+
57
2
u
102
+ ··· − 5u −
23
2
a
1
=
−u
2
+ 1
u
2
a
10
=
u
4
− u
2
+ 1
−u
4
a
6
=
u
9
− 2u
7
+ 3u
5
− 2u
3
+ u
−u
9
+ u
7
− u
5
+ u
a
3
=
−5u
102
−
13
2
u
101
+ ··· −
1
2
u +
9
2
9u
103
+ 23u
102
+ ··· − 3u − 9
a
2
=
−u
102
−
3
2
u
101
+ ··· +
7
2
u +
5
2
u
103
+ 3u
102
+ ··· − u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes =
33
2
u
103
+ 31u
102
+ ··· −
1
2
u −
33
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
104
+ 48u
103
+ ··· − 24u + 1
c
2
, c
5
u
104
+ 4u
103
+ ··· + 8u + 1
c
3
u
104
− 4u
103
+ ··· − 644u + 193
c
4
, c
8
u
104
− u
103
+ ··· − 96u − 64
c
6
u
104
− 3u
103
+ ··· + 14175u − 2425
c
7
, c
11
u
104
+ 3u
103
+ ··· − u − 1
c
9
u
104
+ 35u
103
+ ··· + 82944u + 4096
c
10
, c
12
u
104
+ 33u
103
+ ··· + 11u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
104
+ 20y
103
+ ··· − 556y + 1
c
2
, c
5
y
104
+ 48y
103
+ ··· − 24y + 1
c
3
y
104
− 8y
103
+ ··· − 3334440y + 37249
c
4
, c
8
y
104
− 35y
103
+ ··· − 82944y + 4096
c
6
y
104
+ 19y
103
+ ··· + 127099125y + 5880625
c
7
, c
11
y
104
− 33y
103
+ ··· − 11y + 1
c
9
y
104
+ 57y
103
+ ··· − 571473920y + 16777216
c
10
, c
12
y
104
+ 79y
103
+ ··· + 285y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.995545 + 0.161097I
a = −0.512579 − 0.871788I
b = −0.644479 − 0.792496I
−1.83155 + 5.70406I 0
u = −0.995545 − 0.161097I
a = −0.512579 + 0.871788I
b = −0.644479 + 0.792496I
−1.83155 − 5.70406I 0
u = 0.970059 + 0.180479I
a = 0.99729 − 1.32904I
b = −0.558830 + 0.049258I
−0.10724 − 3.95678I 0
u = 0.970059 − 0.180479I
a = 0.99729 + 1.32904I
b = −0.558830 − 0.049258I
−0.10724 + 3.95678I 0
u = −0.923833 + 0.339721I
a = 0.616132 + 0.482403I
b = 0.806426 + 0.318937I
−0.284227 − 0.543049I 0
u = −0.923833 − 0.339721I
a = 0.616132 − 0.482403I
b = 0.806426 − 0.318937I
−0.284227 + 0.543049I 0
u = 0.827173 + 0.596410I
a = −0.79732 + 1.46815I
b = −0.261002 − 1.178970I
−0.064833 + 0.905297I 0
u = 0.827173 − 0.596410I
a = −0.79732 − 1.46815I
b = −0.261002 + 1.178970I
−0.064833 − 0.905297I 0
u = 1.02711
a = −0.774739
b = 1.02521
−5.59162 0
u = −0.953515 + 0.186747I
a = 0.516727 + 0.739793I
b = 0.632602 + 0.622967I
0.020107 + 1.034370I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.953515 − 0.186747I
a = 0.516727 − 0.739793I
b = 0.632602 − 0.622967I
0.020107 − 1.034370I 0
u = −0.963413 + 0.068510I
a = −0.217097 − 0.862505I
b = −0.268461 − 0.816848I
−3.56083 − 0.88582I 0
u = −0.963413 − 0.068510I
a = −0.217097 + 0.862505I
b = −0.268461 + 0.816848I
−3.56083 + 0.88582I 0
u = −0.972667 + 0.372254I
a = −0.705354 − 0.386489I
b = −0.874004 − 0.283310I
−2.41063 − 5.32876I 0
u = −0.972667 − 0.372254I
a = −0.705354 + 0.386489I
b = −0.874004 + 0.283310I
−2.41063 + 5.32876I 0
u = −0.929413 + 0.472446I
a = −0.399519 − 0.237173I
b = −0.832935 − 0.303200I
−4.34073 + 1.98932I 0
u = −0.929413 − 0.472446I
a = −0.399519 + 0.237173I
b = −0.832935 + 0.303200I
−4.34073 − 1.98932I 0
u = 1.044070 + 0.145718I
a = −0.609037 + 1.077920I
b = 0.727801 + 0.244738I
−6.19328 − 3.93028I 0
u = 1.044070 − 0.145718I
a = −0.609037 − 1.077920I
b = 0.727801 − 0.244738I
−6.19328 + 3.93028I 0
u = 1.040560 + 0.185605I
a = 0.63194 − 1.31168I
b = −0.542661 − 0.263709I
−1.35514 − 6.47708I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.040560 − 0.185605I
a = 0.63194 + 1.31168I
b = −0.542661 + 0.263709I
−1.35514 + 6.47708I 0
u = 1.058190 + 0.027517I
a = 0.523585 − 0.218830I
b = −1.070460 − 0.065154I
−8.85013 − 3.97317I 0
u = 1.058190 − 0.027517I
a = 0.523585 + 0.218830I
b = −1.070460 + 0.065154I
−8.85013 + 3.97317I 0
u = 0.754441 + 0.751915I
a = 0.14946 − 1.60978I
b = 0.80789 + 1.57405I
1.81411 − 1.60183I 0
u = 0.754441 − 0.751915I
a = 0.14946 + 1.60978I
b = 0.80789 − 1.57405I
1.81411 + 1.60183I 0
u = −0.696471 + 0.811179I
a = 1.72568 + 1.53879I
b = −0.10925 − 2.61448I
0.25197 − 3.78803I 0
u = −0.696471 − 0.811179I
a = 1.72568 − 1.53879I
b = −0.10925 + 2.61448I
0.25197 + 3.78803I 0
u = 0.917559 + 0.150661I
a = −1.33133 + 1.31447I
b = 0.699472 − 0.238599I
−1.12265 + 1.04672I 0
u = 0.917559 − 0.150661I
a = −1.33133 − 1.31447I
b = 0.699472 + 0.238599I
−1.12265 − 1.04672I 0
u = −0.845342 + 0.657177I
a = −0.60933 + 1.32456I
b = 2.39972 + 0.27164I
1.80047 + 0.06644I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.845342 − 0.657177I
a = −0.60933 − 1.32456I
b = 2.39972 − 0.27164I
1.80047 − 0.06644I 0
u = 1.059270 + 0.187963I
a = −0.52976 + 1.33230I
b = 0.543826 + 0.360359I
−3.56774 − 11.61460I 0
u = 1.059270 − 0.187963I
a = −0.52976 − 1.33230I
b = 0.543826 − 0.360359I
−3.56774 + 11.61460I 0
u = 0.724424 + 0.808314I
a = 0.06007 − 1.91766I
b = 1.10628 + 2.12037I
4.56534 + 5.10375I 0
u = 0.724424 − 0.808314I
a = 0.06007 + 1.91766I
b = 1.10628 − 2.12037I
4.56534 − 5.10375I 0
u = −0.580019 + 0.700208I
a = −1.098130 − 0.872380I
b = −0.018720 + 0.778011I
−3.49153 − 4.75928I 0
u = −0.580019 − 0.700208I
a = −1.098130 + 0.872380I
b = −0.018720 − 0.778011I
−3.49153 + 4.75928I 0
u = −0.749031 + 0.797955I
a = 1.63183 + 2.03735I
b = 0.75933 − 3.15840I
5.02616 + 2.15983I 0
u = −0.749031 − 0.797955I
a = 1.63183 − 2.03735I
b = 0.75933 + 3.15840I
5.02616 − 2.15983I 0
u = −0.736317 + 0.810407I
a = −1.75080 − 1.89744I
b = −0.39215 + 3.15606I
6.34017 − 3.11840I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.736317 − 0.810407I
a = −1.75080 + 1.89744I
b = −0.39215 − 3.15606I
6.34017 + 3.11840I 0
u = −0.712069 + 0.832469I
a = −1.92411 − 1.64609I
b = 0.23828 + 3.07167I
5.42558 − 6.12943I 0
u = −0.712069 − 0.832469I
a = −1.92411 + 1.64609I
b = 0.23828 − 3.07167I
5.42558 + 6.12943I 0
u = −0.705084 + 0.840871I
a = 1.98457 + 1.57228I
b = −0.44329 − 3.05691I
3.32150 − 11.40490I 0
u = −0.705084 − 0.840871I
a = 1.98457 − 1.57228I
b = −0.44329 + 3.05691I
3.32150 + 11.40490I 0
u = 0.863688 + 0.677581I
a = 0.706681 − 1.039710I
b = 0.260899 + 1.104450I
2.19668 − 2.61840I 0
u = 0.863688 − 0.677581I
a = 0.706681 + 1.039710I
b = 0.260899 − 1.104450I
2.19668 + 2.61840I 0
u = 0.742286 + 0.808762I
a = 0.02357 + 1.86766I
b = −1.23942 − 1.96405I
6.44605 + 0.06854I 0
u = 0.742286 − 0.808762I
a = 0.02357 − 1.86766I
b = −1.23942 + 1.96405I
6.44605 − 0.06854I 0
u = −0.886276 + 0.662580I
a = 1.19777 − 0.80402I
b = −2.29133 − 1.30899I
1.66908 + 5.06000I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.886276 − 0.662580I
a = 1.19777 + 0.80402I
b = −2.29133 + 1.30899I
1.66908 − 5.06000I 0
u = 0.919787 + 0.634859I
a = −1.14826 + 1.18703I
b = −0.297211 − 1.298160I
−0.40958 − 5.76100I 0
u = 0.919787 − 0.634859I
a = −1.14826 − 1.18703I
b = −0.297211 + 1.298160I
−0.40958 + 5.76100I 0
u = −0.628192 + 0.614774I
a = 0.802455 + 0.921266I
b = 0.543250 − 0.575702I
−0.763936 − 0.604697I 0
u = −0.628192 − 0.614774I
a = 0.802455 − 0.921266I
b = 0.543250 + 0.575702I
−0.763936 + 0.604697I 0
u = 0.780695 + 0.820092I
a = 0.27330 + 1.78142I
b = −1.61646 − 1.61478I
6.65697 − 2.35527I 0
u = 0.780695 − 0.820092I
a = 0.27330 − 1.78142I
b = −1.61646 + 1.61478I
6.65697 + 2.35527I 0
u = 0.795951 + 0.829057I
a = −0.41309 − 1.76927I
b = 1.83155 + 1.46562I
4.94995 − 7.32695I 0
u = 0.795951 − 0.829057I
a = −0.41309 + 1.76927I
b = 1.83155 − 1.46562I
4.94995 + 7.32695I 0
u = 0.852838 + 0.784493I
a = −0.518582 − 1.043630I
b = 1.299520 + 0.425878I
2.51710 − 1.46458I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.852838 − 0.784493I
a = −0.518582 + 1.043630I
b = 1.299520 − 0.425878I
2.51710 + 1.46458I 0
u = −0.987793 + 0.609954I
a = −0.282065 − 0.575521I
b = 0.324092 + 1.057970I
−5.36885 + 2.02799I 0
u = −0.987793 − 0.609954I
a = −0.282065 + 0.575521I
b = 0.324092 − 1.057970I
−5.36885 − 2.02799I 0
u = −0.977994 + 0.645453I
a = 0.727268 + 0.700582I
b = −0.32712 − 1.62271I
−1.73240 + 5.61848I 0
u = −0.977994 − 0.645453I
a = 0.727268 − 0.700582I
b = −0.32712 + 1.62271I
−1.73240 − 5.61848I 0
u = 0.903916 + 0.776679I
a = 1.058770 + 0.461633I
b = −1.179650 + 0.645136I
2.36486 − 4.40594I 0
u = 0.903916 − 0.776679I
a = 1.058770 − 0.461633I
b = −1.179650 − 0.645136I
2.36486 + 4.40594I 0
u = −1.004180 + 0.651392I
a = −0.581678 − 1.044430I
b = −0.15909 + 1.56067I
−4.68776 + 9.95104I 0
u = −1.004180 − 0.651392I
a = −0.581678 + 1.044430I
b = −0.15909 − 1.56067I
−4.68776 − 9.95104I 0
u = 0.966141 + 0.711656I
a = 1.60909 − 0.60969I
b = −0.20766 + 1.74080I
1.16387 − 3.97141I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.966141 − 0.711656I
a = 1.60909 + 0.60969I
b = −0.20766 − 1.74080I
1.16387 + 3.97141I 0
u = −0.977928 + 0.735033I
a = 1.85603 + 1.77296I
b = 0.58235 − 3.71912I
4.32467 + 3.61431I 0
u = −0.977928 − 0.735033I
a = 1.85603 − 1.77296I
b = 0.58235 + 3.71912I
4.32467 − 3.61431I 0
u = −0.463429 + 0.618913I
a = −0.886522 − 0.630657I
b = −0.149445 + 0.130543I
−4.04796 + 2.71125I −12.61990 − 3.98241I
u = −0.463429 − 0.618913I
a = −0.886522 + 0.630657I
b = −0.149445 − 0.130543I
−4.04796 − 2.71125I −12.61990 + 3.98241I
u = 0.966506 + 0.761778I
a = −1.80162 + 0.05991I
b = 0.94812 − 1.84887I
6.08454 − 3.56908I 0
u = 0.966506 − 0.761778I
a = −1.80162 − 0.05991I
b = 0.94812 + 1.84887I
6.08454 + 3.56908I 0
u = 0.985337 + 0.739108I
a = −1.90868 + 0.39757I
b = 0.51937 − 2.08817I
5.70138 − 5.88628I 0
u = 0.985337 − 0.739108I
a = −1.90868 − 0.39757I
b = 0.51937 + 2.08817I
5.70138 + 5.88628I 0
u = −0.989286 + 0.737835I
a = −1.70215 − 1.92426I
b = −0.90767 + 3.58230I
5.56561 + 8.93649I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.989286 − 0.737835I
a = −1.70215 + 1.92426I
b = −0.90767 − 3.58230I
5.56561 − 8.93649I 0
u = 0.960435 + 0.775381I
a = 1.79571 + 0.13146I
b = −1.20786 + 1.76111I
4.44270 + 1.33279I 0
u = 0.960435 − 0.775381I
a = 1.79571 − 0.13146I
b = −1.20786 − 1.76111I
4.44270 − 1.33279I 0
u = 0.994976 + 0.732633I
a = 1.97881 − 0.50784I
b = −0.37833 + 2.20105I
3.73893 − 10.89850I 0
u = 0.994976 − 0.732633I
a = 1.97881 + 0.50784I
b = −0.37833 − 2.20105I
3.73893 + 10.89850I 0
u = −1.009160 + 0.724746I
a = 1.29694 + 1.92384I
b = 1.13741 − 2.95407I
−0.69811 + 9.56220I 0
u = −1.009160 − 0.724746I
a = 1.29694 − 1.92384I
b = 1.13741 + 2.95407I
−0.69811 − 9.56220I 0
u = −1.010060 + 0.739826I
a = −1.42104 − 2.13601I
b = −1.40773 + 3.26557I
4.51266 + 12.01460I 0
u = −1.010060 − 0.739826I
a = −1.42104 + 2.13601I
b = −1.40773 − 3.26557I
4.51266 − 12.01460I 0
u = −1.016650 + 0.740942I
a = 1.34178 + 2.20727I
b = 1.56778 − 3.17605I
2.3661 + 17.3165I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.016650 − 0.740942I
a = 1.34178 − 2.20727I
b = 1.56778 + 3.17605I
2.3661 − 17.3165I 0
u = −0.112674 + 0.678362I
a = 0.254326 + 0.561225I
b = 0.929761 + 0.461434I
0.24933 + 8.87552I −6.42415 − 7.58828I
u = −0.112674 − 0.678362I
a = 0.254326 − 0.561225I
b = 0.929761 − 0.461434I
0.24933 − 8.87552I −6.42415 + 7.58828I
u = −0.095198 + 0.648369I
a = −0.257752 − 0.658833I
b = −0.939789 − 0.327643I
2.30568 + 3.82799I −3.04052 − 3.48068I
u = −0.095198 − 0.648369I
a = −0.257752 + 0.658833I
b = −0.939789 + 0.327643I
2.30568 − 3.82799I −3.04052 + 3.48068I
u = −0.180364 + 0.604663I
a = 0.495672 + 0.639352I
b = 0.642731 + 0.286163I
−2.31740 + 1.66077I −10.16858 − 2.73214I
u = −0.180364 − 0.604663I
a = 0.495672 − 0.639352I
b = 0.642731 − 0.286163I
−2.31740 − 1.66077I −10.16858 + 2.73214I
u = −0.598144
a = 0.647574
b = 0.367048
−0.843004 −11.7650
u = −0.010244 + 0.579474I
a = −0.197590 − 0.954778I
b = −0.999928 + 0.022692I
2.95584 + 1.48192I −1.41514 − 2.95992I
u = −0.010244 − 0.579474I
a = −0.197590 + 0.954778I
b = −0.999928 − 0.022692I
2.95584 − 1.48192I −1.41514 + 2.95992I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.056043 + 0.556970I
a = 0.110277 + 1.130210I
b = 1.034060 − 0.226304I
1.46285 − 3.40463I −3.80359 + 2.83507I
u = 0.056043 − 0.556970I
a = 0.110277 − 1.130210I
b = 1.034060 + 0.226304I
1.46285 + 3.40463I −3.80359 − 2.83507I
u = 0.213318 + 0.171099I
a = 0.30126 + 2.36442I
b = 0.286313 − 0.575206I
−0.33801 + 1.74815I −2.36854 − 3.15485I
u = 0.213318 − 0.171099I
a = 0.30126 − 2.36442I
b = 0.286313 + 0.575206I
−0.33801 − 1.74815I −2.36854 + 3.15485I
15
II. I
u
2
= h−u
2
a + b + a, u
2
a + a
2
− au − u + 1, u
3
− u
2
+ 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
4
=
a
u
2
a − a
a
8
=
−u
−u
2
+ u + 1
a
9
=
−u
−u
2
+ u + 1
a
5
=
a
u
2
a − a
a
1
=
−u
2
+ 1
u
2
a
10
=
−u
−u
2
+ u + 1
a
6
=
u
2
− 1
−u
2
a
3
=
−u
2
a + au + 2a
2u
2
a − 2a
a
2
=
−u
2
a + au + u
2
+ 2a − u
2u
2
a − u
2
− 2a
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
2
a + 6au − u
2
+ 6u − 11
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
3
c
2
(u
2
+ u + 1)
3
c
4
, c
8
, c
9
u
6
c
6
, c
10
(u
3
− u
2
+ 2u − 1)
2
c
7
(u
3
+ u
2
− 1)
2
c
11
(u
3
− u
2
+ 1)
2
c
12
(u
3
+ u
2
+ 2u + 1)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
3
c
4
, c
8
, c
9
y
6
c
6
, c
10
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
c
7
, c
11
(y
3
− y
2
+ 2y −1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = 0.818128 + 0.292480I
b = −1.024480 + 0.839835I
3.02413 − 0.79824I −4.03424 − 1.64667I
u = 0.877439 + 0.744862I
a = −0.155769 − 0.854759I
b = 1.239560 + 0.467306I
3.02413 − 4.85801I −2.74410 + 7.22587I
u = 0.877439 − 0.744862I
a = 0.818128 − 0.292480I
b = −1.024480 − 0.839835I
3.02413 + 0.79824I −4.03424 + 1.64667I
u = 0.877439 − 0.744862I
a = −0.155769 + 0.854759I
b = 1.239560 − 0.467306I
3.02413 + 4.85801I −2.74410 − 7.22587I
u = −0.754878
a = −0.662359 + 1.147240I
b = 0.284920 − 0.493496I
−1.11345 + 2.02988I −12.72167 − 5.84990I
u = −0.754878
a = −0.662359 − 1.147240I
b = 0.284920 + 0.493496I
−1.11345 − 2.02988I −12.72167 + 5.84990I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
3
)(u
104
+ 48u
103
+ ··· − 24u + 1)
c
2
((u
2
+ u + 1)
3
)(u
104
+ 4u
103
+ ··· + 8u + 1)
c
3
((u
2
− u + 1)
3
)(u
104
− 4u
103
+ ··· − 644u + 193)
c
4
, c
8
u
6
(u
104
− u
103
+ ··· − 96u − 64)
c
5
((u
2
− u + 1)
3
)(u
104
+ 4u
103
+ ··· + 8u + 1)
c
6
((u
3
− u
2
+ 2u − 1)
2
)(u
104
− 3u
103
+ ··· + 14175u − 2425)
c
7
((u
3
+ u
2
− 1)
2
)(u
104
+ 3u
103
+ ··· − u − 1)
c
9
u
6
(u
104
+ 35u
103
+ ··· + 82944u + 4096)
c
10
((u
3
− u
2
+ 2u − 1)
2
)(u
104
+ 33u
103
+ ··· + 11u + 1)
c
11
((u
3
− u
2
+ 1)
2
)(u
104
+ 3u
103
+ ··· − u − 1)
c
12
((u
3
+ u
2
+ 2u + 1)
2
)(u
104
+ 33u
103
+ ··· + 11u + 1)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
3
)(y
104
+ 20y
103
+ ··· − 556y + 1)
c
2
, c
5
((y
2
+ y + 1)
3
)(y
104
+ 48y
103
+ ··· − 24y + 1)
c
3
((y
2
+ y + 1)
3
)(y
104
− 8y
103
+ ··· − 3334440y + 37249)
c
4
, c
8
y
6
(y
104
− 35y
103
+ ··· − 82944y + 4096)
c
6
((y
3
+ 3y
2
+ 2y −1)
2
)(y
104
+ 19y
103
+ ··· + 1.27099 × 10
8
y + 5880625)
c
7
, c
11
((y
3
− y
2
+ 2y −1)
2
)(y
104
− 33y
103
+ ··· − 11y + 1)
c
9
y
6
(y
104
+ 57y
103
+ ··· − 5.71474 × 10
8
y + 1.67772 × 10
7
)
c
10
, c
12
((y
3
+ 3y
2
+ 2y −1)
2
)(y
104
+ 79y
103
+ ··· + 285y + 1)
21
