11a
169
(K11a
169
)
A knot diagram
1
Linearized knot diagam
6 1 9 11 2 10 5 4 3 7 8
Solving Sequence
6,10
7
2,11
1 3 5 8 4 9
c
6
c
10
c
1
c
2
c
5
c
7
c
4
c
9
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.96166 × 10
185
u
73
+ 1.25507 × 10
186
u
72
+ ··· + 1.38036 × 10
187
b − 2.21942 × 10
187
,
5.60840 × 10
187
u
73
− 1.03180 × 10
188
u
72
+ ··· + 5.10733 × 10
188
a + 2.81879 × 10
189
, u
74
− u
73
+ ··· + 36u + 37i
I
u
2
= h4u
13
+ 7u
12
− 21u
11
− 33u
10
+ 49u
9
+ 71u
8
− 56u
7
− 90u
6
+ 36u
5
+ 66u
4
− 4u
3
− 26u
2
+ b − 3u + 4,
6u
13
+ 10u
12
+ ··· + a + 10,
u
14
+ 2u
13
− 5u
12
− 10u
11
+ 11u
10
+ 23u
9
− 11u
8
− 31u
7
+ 4u
6
+ 25u
5
+ 4u
4
− 11u
3
− 4u
2
+ 2u + 1i
* 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−4.96 × 10
185
u
73
+ 1.26 × 10
186
u
72
+ · · · + 1.38 × 10
187
b − 2.22 ×
10
187
, 5.61 × 10
187
u
73
− 1.03 × 10
188
u
72
+ · · · + 5.11 × 10
188
a + 2.82 ×
10
189
, u
74
− u
73
+ · · · + 36u + 37i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
2
=
−0.109811u
73
+ 0.202024u
72
+ ··· − 3.01507u − 5.51912
0.0359447u
73
− 0.0909234u
72
+ ··· − 0.656044u + 1.60786
a
11
=
−u
−u
3
+ u
a
1
=
−0.145756u
73
+ 0.292948u
72
+ ··· − 2.35903u − 7.12697
0.0359447u
73
− 0.0909234u
72
+ ··· − 0.656044u + 1.60786
a
3
=
0.107346u
73
− 0.195541u
72
+ ··· − 2.58294u + 3.70574
−0.318159u
73
+ 0.662604u
72
+ ··· − 2.83612u − 10.4308
a
5
=
−0.187310u
73
+ 0.380215u
72
+ ··· − 4.71712u − 5.98298
0.0710115u
73
− 0.143579u
72
+ ··· − 2.35575u + 2.65479
a
8
=
−0.168216u
73
+ 0.379034u
72
+ ··· + 3.07123u − 4.69178
−0.0865870u
73
+ 0.159014u
72
+ ··· + 1.12473u − 4.45130
a
4
=
−0.284387u
73
+ 0.587033u
72
+ ··· − 4.79088u − 9.08039
0.0463239u
73
− 0.104793u
72
+ ··· − 2.64081u + 1.69178
a
9
=
0.0959357u
73
− 0.265994u
72
+ ··· + 1.34312u + 0.825831
−0.160387u
73
+ 0.335587u
72
+ ··· + 1.38132u − 5.82341
a
9
=
0.0959357u
73
− 0.265994u
72
+ ··· + 1.34312u + 0.825831
−0.160387u
73
+ 0.335587u
72
+ ··· + 1.38132u − 5.82341
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.581332u
73
+ 1.19718u
72
+ ··· + 15.2381u − 18.9875
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
74
+ 18u
72
+ ··· + 5u + 1
c
2
u
74
+ 36u
73
+ ··· − 17u + 1
c
3
, c
8
, c
9
u
74
− u
73
+ ··· + 22u + 1
c
4
u
74
− 3u
73
+ ··· − 176u + 1003
c
6
, c
10
u
74
− u
73
+ ··· + 36u + 37
c
7
u
74
− 5u
73
+ ··· − 20u + 1
c
11
u
74
− 5u
73
+ ··· + 300u + 125
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
74
+ 36y
73
+ ··· − 17y + 1
c
2
y
74
+ 12y
73
+ ··· − 77y + 1
c
3
, c
8
, c
9
y
74
+ 77y
73
+ ··· − 58y + 1
c
4
y
74
+ 29y
73
+ ··· + 34287672y + 1006009
c
6
, c
10
y
74
− 57y
73
+ ··· − 4034y + 1369
c
7
y
74
− 9y
73
+ ··· + 14y + 1
c
11
y
74
+ 15y
73
+ ··· + 308750y + 15625
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.041401 + 1.026520I
a = 0.661998 − 0.676360I
b = −0.590855 − 0.983471I
1.11109 + 6.26090I 0
u = −0.041401 − 1.026520I
a = 0.661998 + 0.676360I
b = −0.590855 + 0.983471I
1.11109 − 6.26090I 0
u = −0.986532 + 0.392792I
a = 0.390575 − 0.412307I
b = −0.201955 − 0.077354I
−1.70214 + 1.37634I 0
u = −0.986532 − 0.392792I
a = 0.390575 + 0.412307I
b = −0.201955 + 0.077354I
−1.70214 − 1.37634I 0
u = −1.064540 + 0.083077I
a = −0.038681 − 0.719869I
b = −1.066260 − 0.903808I
−3.93189 + 3.73813I 0
u = −1.064540 − 0.083077I
a = −0.038681 + 0.719869I
b = −1.066260 + 0.903808I
−3.93189 − 3.73813I 0
u = −0.054647 + 1.089920I
a = −0.798538 + 0.520307I
b = 0.662690 + 0.358460I
−3.49876 − 4.45579I 0
u = −0.054647 − 1.089920I
a = −0.798538 − 0.520307I
b = 0.662690 − 0.358460I
−3.49876 + 4.45579I 0
u = 1.008160 + 0.419741I
a = −1.13208 − 2.49760I
b = 0.086823 − 0.942517I
−5.90718 − 3.61297I 0
u = 1.008160 − 0.419741I
a = −1.13208 + 2.49760I
b = 0.086823 + 0.942517I
−5.90718 + 3.61297I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.164060 + 0.892569I
a = 0.610647 + 0.324648I
b = −0.635278 + 0.581899I
2.28203 + 1.45434I 7.07609 − 2.82697I
u = 0.164060 − 0.892569I
a = 0.610647 − 0.324648I
b = −0.635278 − 0.581899I
2.28203 − 1.45434I 7.07609 + 2.82697I
u = −1.020520 + 0.447604I
a = 0.90579 − 1.99644I
b = −0.56045 − 1.35749I
−7.03134 + 7.38518I 0
u = −1.020520 − 0.447604I
a = 0.90579 + 1.99644I
b = −0.56045 + 1.35749I
−7.03134 − 7.38518I 0
u = −0.706637 + 0.528963I
a = 0.715385 + 0.015552I
b = −0.111730 + 0.682639I
−1.94267 + 1.36984I −1.20938 − 5.61656I
u = −0.706637 − 0.528963I
a = 0.715385 − 0.015552I
b = −0.111730 − 0.682639I
−1.94267 − 1.36984I −1.20938 + 5.61656I
u = −1.118000 + 0.053349I
a = −1.16980 + 2.42638I
b = 0.427319 + 1.057150I
−3.93201 + 1.54935I 0
u = −1.118000 − 0.053349I
a = −1.16980 − 2.42638I
b = 0.427319 − 1.057150I
−3.93201 − 1.54935I 0
u = 1.094100 + 0.269644I
a = −0.50567 − 2.00641I
b = 0.561390 − 1.183450I
−1.87663 − 4.80358I 0
u = 1.094100 − 0.269644I
a = −0.50567 + 2.00641I
b = 0.561390 + 1.183450I
−1.87663 + 4.80358I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.716202 + 0.466840I
a = −0.082574 − 0.910018I
b = −0.902862 − 0.142948I
−2.54067 + 2.00646I 4.56819 − 2.62899I
u = −0.716202 − 0.466840I
a = −0.082574 + 0.910018I
b = −0.902862 + 0.142948I
−2.54067 − 2.00646I 4.56819 + 2.62899I
u = −0.453990 + 0.701764I
a = −0.330021 + 0.379368I
b = −0.539990 + 1.146080I
−5.37822 − 3.01874I −1.04024 + 2.49965I
u = −0.453990 − 0.701764I
a = −0.330021 − 0.379368I
b = −0.539990 − 1.146080I
−5.37822 + 3.01874I −1.04024 − 2.49965I
u = 1.150740 + 0.216584I
a = −0.08189 − 2.43504I
b = −0.150667 − 1.122100I
−6.13754 − 3.74072I 0
u = 1.150740 − 0.216584I
a = −0.08189 + 2.43504I
b = −0.150667 + 1.122100I
−6.13754 + 3.74072I 0
u = −1.109710 + 0.388330I
a = 0.698876 − 0.299047I
b = 0.340968 − 0.383433I
−1.55302 + 1.40337I 0
u = −1.109710 − 0.388330I
a = 0.698876 + 0.299047I
b = 0.340968 + 0.383433I
−1.55302 − 1.40337I 0
u = 1.191070 + 0.010518I
a = −0.022094 + 0.440729I
b = −0.772060 − 0.401516I
−7.86764 − 1.80141I 0
u = 1.191070 − 0.010518I
a = −0.022094 − 0.440729I
b = −0.772060 + 0.401516I
−7.86764 + 1.80141I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.189310 + 0.229765I
a = 1.31840 + 1.49765I
b = −0.583679 + 1.119390I
−10.02310 − 6.93733I 0
u = 1.189310 − 0.229765I
a = 1.31840 − 1.49765I
b = −0.583679 − 1.119390I
−10.02310 + 6.93733I 0
u = 0.730409 + 0.234263I
a = 0.002848 − 0.948008I
b = 0.823183 − 0.768347I
0.90646 − 3.01225I 11.02233 + 8.12268I
u = 0.730409 − 0.234263I
a = 0.002848 + 0.948008I
b = 0.823183 + 0.768347I
0.90646 + 3.01225I 11.02233 − 8.12268I
u = 0.645449 + 1.130360I
a = −0.399107 + 0.201377I
b = 0.330428 + 1.061930I
−7.17177 − 2.00704I 0
u = 0.645449 − 1.130360I
a = −0.399107 − 0.201377I
b = 0.330428 − 1.061930I
−7.17177 + 2.00704I 0
u = −0.644097 + 0.246664I
a = −1.22405 + 1.11061I
b = −0.704733 + 0.577546I
−2.89873 − 2.58975I −0.111793 + 1.162954I
u = −0.644097 − 0.246664I
a = −1.22405 − 1.11061I
b = −0.704733 − 0.577546I
−2.89873 + 2.58975I −0.111793 − 1.162954I
u = 1.229030 + 0.471094I
a = −0.391923 + 0.075906I
b = −0.820281 − 0.357667I
−1.05855 − 6.36832I 0
u = 1.229030 − 0.471094I
a = −0.391923 − 0.075906I
b = −0.820281 + 0.357667I
−1.05855 + 6.36832I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.315060 + 0.070834I
a = 0.10565 + 1.58707I
b = −0.461958 + 1.011830I
−3.68119 − 1.72060I 0
u = −1.315060 − 0.070834I
a = 0.10565 − 1.58707I
b = −0.461958 − 1.011830I
−3.68119 + 1.72060I 0
u = −1.353880 + 0.256891I
a = −0.30501 + 2.26816I
b = 0.478617 + 1.068020I
−3.56136 + 5.27681I 0
u = −1.353880 − 0.256891I
a = −0.30501 − 2.26816I
b = 0.478617 − 1.068020I
−3.56136 − 5.27681I 0
u = 0.563652 + 0.233266I
a = 0.719862 − 0.170364I
b = 0.648787 + 0.161529I
1.084040 + 0.054792I 10.18991 + 0.13008I
u = 0.563652 − 0.233266I
a = 0.719862 + 0.170364I
b = 0.648787 − 0.161529I
1.084040 − 0.054792I 10.18991 − 0.13008I
u = −1.40158 + 0.28073I
a = 0.07621 − 1.71088I
b = 0.15964 − 1.41781I
−13.8677 + 6.0588I 0
u = −1.40158 − 0.28073I
a = 0.07621 + 1.71088I
b = 0.15964 + 1.41781I
−13.8677 − 6.0588I 0
u = −0.179516 + 0.523495I
a = −0.414147 − 0.312461I
b = 0.614780 + 0.802645I
1.20853 + 2.22979I 5.58274 − 4.23366I
u = −0.179516 − 0.523495I
a = −0.414147 + 0.312461I
b = 0.614780 − 0.802645I
1.20853 − 2.22979I 5.58274 + 4.23366I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.03616 + 1.44649I
a = −0.485282 − 0.593135I
b = 0.540574 − 1.099130I
−5.65481 − 9.14282I 0
u = 0.03616 − 1.44649I
a = −0.485282 + 0.593135I
b = 0.540574 + 1.099130I
−5.65481 + 9.14282I 0
u = −1.29046 + 0.66405I
a = 0.98402 − 1.42129I
b = −0.450482 − 1.038080I
−3.68654 + 4.65688I 0
u = −1.29046 − 0.66405I
a = 0.98402 + 1.42129I
b = −0.450482 + 1.038080I
−3.68654 − 4.65688I 0
u = −1.35471 + 0.52687I
a = 0.231505 + 0.110886I
b = 1.018660 − 0.327910I
−7.66023 + 10.17330I 0
u = −1.35471 − 0.52687I
a = 0.231505 − 0.110886I
b = 1.018660 + 0.327910I
−7.66023 − 10.17330I 0
u = 1.37570 + 0.47899I
a = 0.73388 + 1.86660I
b = −0.588470 + 1.135700I
−3.38565 − 11.61060I 0
u = 1.37570 − 0.47899I
a = 0.73388 − 1.86660I
b = −0.588470 − 1.135700I
−3.38565 + 11.61060I 0
u = 1.36071 + 0.58544I
a = −0.320853 − 0.015899I
b = 0.748042 + 0.449545I
−7.59610 − 0.90779I 0
u = 1.36071 − 0.58544I
a = −0.320853 + 0.015899I
b = 0.748042 − 0.449545I
−7.59610 + 0.90779I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.440113 + 0.253274I
a = 1.56735 + 0.12834I
b = 0.086114 + 0.816280I
−1.99873 + 1.35242I −1.92328 − 4.74045I
u = −0.440113 − 0.253274I
a = 1.56735 − 0.12834I
b = 0.086114 − 0.816280I
−1.99873 − 1.35242I −1.92328 + 4.74045I
u = 0.356198 + 0.290587I
a = −1.41914 + 2.35526I
b = −0.297912 − 1.078840I
−7.27061 + 4.64233I −5.17242 − 2.62174I
u = 0.356198 − 0.290587I
a = −1.41914 − 2.35526I
b = −0.297912 + 1.078840I
−7.27061 − 4.64233I −5.17242 + 2.62174I
u = 1.56557 + 0.07115I
a = −0.42153 − 1.61275I
b = −0.245943 − 1.066820I
−12.38830 + 0.44974I 0
u = 1.56557 − 0.07115I
a = −0.42153 + 1.61275I
b = −0.245943 + 1.066820I
−12.38830 − 0.44974I 0
u = −1.46364 + 0.61572I
a = −0.75390 + 1.56481I
b = 0.642261 + 1.218140I
−10.4170 + 16.1443I 0
u = −1.46364 − 0.61572I
a = −0.75390 − 1.56481I
b = 0.642261 − 1.218140I
−10.4170 − 16.1443I 0
u = 1.50472 + 0.85046I
a = −0.856898 − 1.096980I
b = 0.587862 − 1.094480I
−9.53471 − 6.00121I 0
u = 1.50472 − 0.85046I
a = −0.856898 + 1.096980I
b = 0.587862 + 1.094480I
−9.53471 + 6.00121I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.086041 + 0.247920I
a = −1.29730 − 2.26020I
b = 0.664169 − 0.876441I
1.04830 − 2.74313I 6.44828 + 0.65245I
u = 0.086041 − 0.247920I
a = −1.29730 + 2.26020I
b = 0.664169 + 0.876441I
1.04830 + 2.74313I 6.44828 − 0.65245I
u = 1.96415 + 0.32367I
a = −0.137388 + 1.240990I
b = 0.263248 + 1.008130I
−11.91390 + 0.82740I 0
u = 1.96415 − 0.32367I
a = −0.137388 − 1.240990I
b = 0.263248 − 1.008130I
−11.91390 − 0.82740I 0
12
II.
I
u
2
= h4u
13
+7u
12
+· · ·+b+4, 6u
13
+10u
12
+· · ·+a +10, u
14
+2u
13
+· · ·+2u+1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
2
=
−6u
13
− 10u
12
+ ··· − u − 10
−4u
13
− 7u
12
+ ··· + 3u − 4
a
11
=
−u
−u
3
+ u
a
1
=
−2u
13
− 3u
12
+ ··· − 4u − 6
−4u
13
− 7u
12
+ ··· + 3u − 4
a
3
=
−5u
13
− 6u
12
+ ··· − 7u − 10
−10u
13
− 16u
12
+ ··· + 60u
2
− 10
a
5
=
7u
13
+ 9u
12
+ ··· + 6u + 12
4u
13
+ 4u
12
+ ··· + 10u + 10
a
8
=
−u
13
− 2u
12
+ ··· + 3u − 2
−u
13
− u
12
+ ··· − 5u − 5
a
4
=
4u
13
+ 6u
12
+ ··· − 27u
2
+ 5
6u
13
+ 6u
12
+ ··· + 13u + 14
a
9
=
−u
13
− 2u
12
+ ··· + 4u − 3
−u
13
− 2u
12
+ ··· + 19u
2
− 6
a
9
=
−u
13
− 2u
12
+ ··· + 4u − 3
−u
13
− 2u
12
+ ··· + 19u
2
− 6
(ii) Obstruction class = 1
(iii) Cusp Shapes = −15u
13
− 14u
12
+ 99u
11
+ 61u
10
− 276u
9
− 131u
8
+ 403u
7
+
211u
6
− 375u
5
− 194u
4
+ 175u
3
+ 127u
2
− 44u − 33
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
− u
13
+ ··· − u + 1
c
2
u
14
+ 7u
13
+ ··· + 9u + 1
c
3
u
14
+ 8u
12
+ ··· + 4u
2
+ 1
c
4
u
14
+ 4u
12
+ ··· + 3u
2
+ 1
c
5
u
14
+ u
13
+ ··· + u + 1
c
6
u
14
+ 2u
13
+ ··· + 2u + 1
c
7
u
14
+ 2u
13
+ u
12
− 2u
11
− 4u
10
− 2u
9
+ 4u
8
+ 6u
7
+ 2u
6
− 2u
4
− 2u
3
+ 1
c
8
, c
9
u
14
+ 8u
12
+ ··· + 4u
2
+ 1
c
10
u
14
− 2u
13
+ ··· − 2u + 1
c
11
u
14
+ u
12
− 3u
11
− 2u
10
− 2u
9
+ u
8
+ 3u
7
+ 5u
6
+ u
5
+ u
4
− 2u
3
+ 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
14
+ 7y
13
+ ··· + 9y + 1
c
2
y
14
+ 7y
13
+ ··· + 5y + 1
c
3
, c
8
, c
9
y
14
+ 16y
13
+ ··· + 8y + 1
c
4
y
14
+ 8y
13
+ ··· + 6y + 1
c
6
, c
10
y
14
− 14y
13
+ ··· − 12y + 1
c
7
y
14
− 2y
13
+ ··· − 4y
2
+ 1
c
11
y
14
+ 2y
13
+ ··· + 2y
2
+ 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.923995 + 0.558875I
a = 1.48872 − 1.47936I
b = −0.495691 − 1.193760I
−7.49308 + 6.46120I −4.33039 − 4.82668I
u = −0.923995 − 0.558875I
a = 1.48872 + 1.47936I
b = −0.495691 + 1.193760I
−7.49308 − 6.46120I −4.33039 + 4.82668I
u = 0.973601 + 0.510087I
a = 0.180282 − 0.090322I
b = 0.312796 + 0.732458I
−2.09597 − 0.56119I −3.19183 − 3.82330I
u = 0.973601 − 0.510087I
a = 0.180282 + 0.090322I
b = 0.312796 − 0.732458I
−2.09597 + 0.56119I −3.19183 + 3.82330I
u = −0.567641 + 0.492408I
a = 1.95584 − 1.12949I
b = −0.281944 + 0.557057I
−4.89766 + 3.00668I 0.74586 − 1.41093I
u = −0.567641 − 0.492408I
a = 1.95584 + 1.12949I
b = −0.281944 − 0.557057I
−4.89766 − 3.00668I 0.74586 + 1.41093I
u = 0.727754 + 0.106963I
a = −0.255048 − 0.581565I
b = 0.760930 − 0.850713I
0.39771 − 2.89359I −6.27864 + 3.59976I
u = 0.727754 − 0.106963I
a = −0.255048 + 0.581565I
b = 0.760930 + 0.850713I
0.39771 + 2.89359I −6.27864 − 3.59976I
u = 1.252450 + 0.359700I
a = −0.78037 − 1.99059I
b = 0.410511 − 1.042370I
−3.33539 − 3.64299I −1.75994 + 2.76575I
u = 1.252450 − 0.359700I
a = −0.78037 + 1.99059I
b = 0.410511 + 1.042370I
−3.33539 + 3.64299I −1.75994 − 2.76575I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.623201 + 0.116079I
a = −1.01609 − 1.68081I
b = −0.942798 − 0.813476I
−2.43487 + 3.43645I 5.05060 − 7.06034I
u = −0.623201 − 0.116079I
a = −1.01609 + 1.68081I
b = −0.942798 + 0.813476I
−2.43487 − 3.43645I 5.05060 + 7.06034I
u = −1.83897 + 0.15178I
a = −0.073330 + 1.299140I
b = −0.263802 + 0.940835I
−11.39450 − 1.08865I 1.76433 + 7.16066I
u = −1.83897 − 0.15178I
a = −0.073330 − 1.299140I
b = −0.263802 − 0.940835I
−11.39450 + 1.08865I 1.76433 − 7.16066I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
14
− u
13
+ ··· − u + 1)(u
74
+ 18u
72
+ ··· + 5u + 1)
c
2
(u
14
+ 7u
13
+ ··· + 9u + 1)(u
74
+ 36u
73
+ ··· − 17u + 1)
c
3
(u
14
+ 8u
12
+ ··· + 4u
2
+ 1)(u
74
− u
73
+ ··· + 22u + 1)
c
4
(u
14
+ 4u
12
+ ··· + 3u
2
+ 1)(u
74
− 3u
73
+ ··· − 176u + 1003)
c
5
(u
14
+ u
13
+ ··· + u + 1)(u
74
+ 18u
72
+ ··· + 5u + 1)
c
6
(u
14
+ 2u
13
+ ··· + 2u + 1)(u
74
− u
73
+ ··· + 36u + 37)
c
7
(u
14
+ 2u
13
+ u
12
− 2u
11
− 4u
10
− 2u
9
+ 4u
8
+ 6u
7
+ 2u
6
− 2u
4
− 2u
3
+ 1)
· (u
74
− 5u
73
+ ··· − 20u + 1)
c
8
, c
9
(u
14
+ 8u
12
+ ··· + 4u
2
+ 1)(u
74
− u
73
+ ··· + 22u + 1)
c
10
(u
14
− 2u
13
+ ··· − 2u + 1)(u
74
− u
73
+ ··· + 36u + 37)
c
11
(u
14
+ u
12
− 3u
11
− 2u
10
− 2u
9
+ u
8
+ 3u
7
+ 5u
6
+ u
5
+ u
4
− 2u
3
+ 1)
· (u
74
− 5u
73
+ ··· + 300u + 125)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
14
+ 7y
13
+ ··· + 9y + 1)(y
74
+ 36y
73
+ ··· − 17y + 1)
c
2
(y
14
+ 7y
13
+ ··· + 5y + 1)(y
74
+ 12y
73
+ ··· − 77y + 1)
c
3
, c
8
, c
9
(y
14
+ 16y
13
+ ··· + 8y + 1)(y
74
+ 77y
73
+ ··· − 58y + 1)
c
4
(y
14
+ 8y
13
+ ··· + 6y + 1)
· (y
74
+ 29y
73
+ ··· + 34287672y + 1006009)
c
6
, c
10
(y
14
− 14y
13
+ ··· − 12y + 1)(y
74
− 57y
73
+ ··· − 4034y + 1369)
c
7
(y
14
− 2y
13
+ ··· − 4y
2
+ 1)(y
74
− 9y
73
+ ··· + 14y + 1)
c
11
(y
14
+ 2y
13
+ ··· + 2y
2
+ 1)(y
74
+ 15y
73
+ ··· + 308750y + 15625)
19
