12a
0019
(K12a
0019
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 10 11 12 4 1 8 7
Solving Sequence
3,5
2 6
4,10
7 1 11 9 12 8
c
2
c
5
c
3
c
6
c
1
c
10
c
9
c
12
c
8
c
4
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h205u
104
− 998u
103
+ ··· + 16b − 31, 2u
104
− 29u
103
+ ··· + 8a + 71, u
105
− 6u
104
+ ··· − 5u + 1i
I
u
2
= hb
5
− b
4
u − b
4
+ 2b
3
u + b
2
− bu − b + u, a, u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 115 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
= h205u
104
− 998u
103
+ · · · + 16b − 31, 2u
104
− 29u
103
+ · · · + 8a +
71, u
105
− 6u
104
+ · · · − 5u + 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
u
u
3
+ u
a
4
=
u
4
+ u
2
+ 1
u
6
+ 2u
4
+ u
2
a
10
=
−0.250000u
104
+ 3.62500u
103
+ ··· + 23.2500u − 8.87500
−12.8125u
104
+ 62.3750u
103
+ ··· − 10.4375u + 1.93750
a
7
=
u
12
+ 3u
10
+ 5u
8
− 2u
7
+ 4u
6
− 4u
5
+ 2u
4
− 4u
3
+ u
2
+ 1
−0.0625000u
103
+ 0.312500u
102
+ ··· + 0.250000u − 0.0625000
a
1
=
u
2
+ 1
u
2
a
11
=
−19.3125u
104
+ 82.4375u
103
+ ··· + 46.6875u − 19.2500
−
97
2
u
104
+
1993
8
u
103
+ ··· − 68u +
81
8
a
9
=
−15.2500u
104
+ 69.6250u
103
+ ··· + 24.2500u − 11.8750
−37.9375u
104
+ 192.875u
103
+ ··· − 43.8125u + 6.81250
a
12
=
−0.187500u
104
+ 1.12500u
103
+ ··· − 0.937500u + 1.18750
−1.43750u
104
+ 6.93750u
103
+ ··· + 0.0625000u − 0.375000
a
8
=
−0.250000u
104
+ 2.68750u
103
+ ··· − 6.12500u + 1.43750
2.62500u
104
− 12.5625u
103
+ ··· + 0.375000u + 0.812500
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
461
16
u
104
+
3579
16
u
103
+ ··· −
4979
16
u +
163
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
105
+ 52u
104
+ ··· − 5u − 1
c
2
, c
5
u
105
+ 6u
104
+ ··· − 5u − 1
c
3
u
105
− 6u
104
+ ··· + 107353u − 23497
c
4
, c
9
u
105
+ u
104
+ ··· + 1024u − 1024
c
6
u
105
+ 3u
104
+ ··· − 1465582u − 149381
c
7
, c
8
, c
11
u
105
− 3u
104
+ ··· − 2u − 1
c
10
u
105
− 23u
104
+ ··· + 167398u − 8023
c
12
u
105
+ 9u
104
+ ··· + 6u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
105
+ 8y
104
+ ··· − 21y −1
c
2
, c
5
y
105
+ 52y
104
+ ··· − 5y −1
c
3
y
105
− 36y
104
+ ··· + 985651187y −552109009
c
4
, c
9
y
105
+ 55y
104
+ ··· − 25165824y −1048576
c
6
y
105
− 31y
104
+ ··· + 449047075542y −22314683161
c
7
, c
8
, c
11
y
105
− 95y
104
+ ··· + 2y −1
c
10
y
105
+ 29y
104
+ ··· − 2885666658y −64368529
c
12
y
105
− 3y
104
+ ··· + 14y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.238259 + 0.986456I
a = −1.26147 − 0.77818I
b = −0.958466 + 0.563608I
3.17345 − 4.25894I 0
u = −0.238259 − 0.986456I
a = −1.26147 + 0.77818I
b = −0.958466 − 0.563608I
3.17345 + 4.25894I 0
u = −0.713466 + 0.725019I
a = −0.078403 − 0.675734I
b = −0.507694 + 0.558076I
−0.27464 − 5.50436I 0
u = −0.713466 − 0.725019I
a = −0.078403 + 0.675734I
b = −0.507694 − 0.558076I
−0.27464 + 5.50436I 0
u = −0.736153 + 0.712752I
a = 0.194353 + 0.806457I
b = 0.794010 − 0.666918I
5.05878 − 8.91753I 0
u = −0.736153 − 0.712752I
a = 0.194353 − 0.806457I
b = 0.794010 + 0.666918I
5.05878 + 8.91753I 0
u = −0.671892 + 0.802497I
a = −0.092701 + 0.249210I
b = −0.325633 − 0.405265I
1.28850 − 2.57717I 0
u = −0.671892 − 0.802497I
a = −0.092701 − 0.249210I
b = −0.325633 + 0.405265I
1.28850 + 2.57717I 0
u = −0.638895 + 0.706476I
a = −0.318007 + 0.601750I
b = 0.235155 + 0.010258I
1.04013 − 2.17525I 0
u = −0.638895 − 0.706476I
a = −0.318007 − 0.601750I
b = 0.235155 − 0.010258I
1.04013 + 2.17525I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.689517 + 0.630908I
a = 0.364134 − 1.084130I
b = −0.817093 − 0.314730I
6.79137 − 0.46918I 0
u = −0.689517 − 0.630908I
a = 0.364134 + 1.084130I
b = −0.817093 + 0.314730I
6.79137 + 0.46918I 0
u = −0.574800 + 0.919200I
a = −0.397771 + 0.333368I
b = −0.310416 + 0.660624I
0.42904 − 2.56514I 0
u = −0.574800 − 0.919200I
a = −0.397771 − 0.333368I
b = −0.310416 − 0.660624I
0.42904 + 2.56514I 0
u = 0.840312 + 0.309790I
a = −2.27824 − 0.15338I
b = −1.68105 − 1.17690I
2.76203 − 11.75360I 0
u = 0.840312 − 0.309790I
a = −2.27824 + 0.15338I
b = −1.68105 + 1.17690I
2.76203 + 11.75360I 0
u = −0.665816 + 0.883086I
a = 0.305710 + 0.000397I
b = 1.015970 − 0.021122I
−0.741803 + 0.253440I 0
u = −0.665816 − 0.883086I
a = 0.305710 − 0.000397I
b = 1.015970 + 0.021122I
−0.741803 − 0.253440I 0
u = 0.831615 + 0.295643I
a = 2.15583 + 0.06101I
b = 1.63171 + 0.91797I
−2.67355 − 8.10755I 0
u = 0.831615 − 0.295643I
a = 2.15583 − 0.06101I
b = 1.63171 − 0.91797I
−2.67355 + 8.10755I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.452334 + 1.030860I
a = −0.183842 − 0.270970I
b = −1.360810 − 0.270591I
4.93430 − 1.63016I 0
u = 0.452334 − 1.030860I
a = −0.183842 + 0.270970I
b = −1.360810 + 0.270591I
4.93430 + 1.63016I 0
u = −0.217271 + 0.841985I
a = 1.089980 + 0.405677I
b = 0.655102 − 0.510945I
−1.45249 − 1.72915I 0
u = −0.217271 − 0.841985I
a = 1.089980 − 0.405677I
b = 0.655102 + 0.510945I
−1.45249 + 1.72915I 0
u = −0.681527 + 0.905951I
a = −0.382548 − 0.129469I
b = −1.384110 + 0.114120I
4.48814 + 3.55358I 0
u = −0.681527 − 0.905951I
a = −0.382548 + 0.129469I
b = −1.384110 − 0.114120I
4.48814 − 3.55358I 0
u = −0.623618 + 0.962160I
a = 0.721379 − 0.227987I
b = 0.86546 − 1.18166I
5.81874 − 4.58356I 0
u = −0.623618 − 0.962160I
a = 0.721379 + 0.227987I
b = 0.86546 + 1.18166I
5.81874 + 4.58356I 0
u = 0.803505 + 0.279635I
a = −1.88136 − 0.03883I
b = −1.32765 − 0.58750I
−1.22209 − 4.21071I 0
u = 0.803505 − 0.279635I
a = −1.88136 + 0.03883I
b = −1.32765 + 0.58750I
−1.22209 + 4.21071I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.452689 + 1.056720I
a = 0.074853 + 0.313378I
b = 1.017450 + 0.224839I
−0.99128 + 1.45005I 0
u = 0.452689 − 1.056720I
a = 0.074853 − 0.313378I
b = 1.017450 − 0.224839I
−0.99128 − 1.45005I 0
u = 0.249719 + 1.127130I
a = −0.337353 + 0.825247I
b = −1.172070 + 0.570226I
0.735634 + 0.034464I 0
u = 0.249719 − 1.127130I
a = −0.337353 − 0.825247I
b = −1.172070 − 0.570226I
0.735634 − 0.034464I 0
u = −0.359634 + 1.100080I
a = 0.93545 + 1.83419I
b = 1.95166 − 0.28636I
1.89142 + 2.96005I 0
u = −0.359634 − 1.100080I
a = 0.93545 − 1.83419I
b = 1.95166 + 0.28636I
1.89142 − 2.96005I 0
u = −0.389409 + 1.089920I
a = −0.63466 − 1.82375I
b = −1.96185 − 0.06207I
−3.13580 − 0.41934I 0
u = −0.389409 − 1.089920I
a = −0.63466 + 1.82375I
b = −1.96185 + 0.06207I
−3.13580 + 0.41934I 0
u = 0.807528 + 0.227271I
a = −1.67463 + 0.33114I
b = −1.45547 + 0.03303I
−1.76859 − 4.38470I 0
u = 0.807528 − 0.227271I
a = −1.67463 − 0.33114I
b = −1.45547 − 0.03303I
−1.76859 + 4.38470I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772794 + 0.325455I
a = 1.79242 + 0.44030I
b = 0.757606 + 0.919693I
5.25845 − 2.77553I 0
u = 0.772794 − 0.325455I
a = 1.79242 − 0.44030I
b = 0.757606 − 0.919693I
5.25845 + 2.77553I 0
u = 0.502800 + 1.057210I
a = 0.216151 + 0.559139I
b = 0.777715 + 0.999350I
5.38886 + 8.04809I 0
u = 0.502800 − 1.057210I
a = 0.216151 − 0.559139I
b = 0.777715 − 0.999350I
5.38886 − 8.04809I 0
u = 0.481039 + 1.072010I
a = −0.058829 − 0.497848I
b = −0.663625 − 0.543924I
−0.74038 + 5.32830I 0
u = 0.481039 − 1.072010I
a = −0.058829 + 0.497848I
b = −0.663625 + 0.543924I
−0.74038 − 5.32830I 0
u = −0.476095 + 1.075970I
a = −0.23047 + 1.70037I
b = 1.74561 + 1.18904I
−0.79779 − 3.44805I 0
u = −0.476095 − 1.075970I
a = −0.23047 − 1.70037I
b = 1.74561 − 1.18904I
−0.79779 + 3.44805I 0
u = −0.442891 + 1.094540I
a = 0.10056 + 1.92739I
b = 2.09472 + 0.74492I
−0.86758 − 3.63979I 0
u = −0.442891 − 1.094540I
a = 0.10056 − 1.92739I
b = 2.09472 − 0.74492I
−0.86758 + 3.63979I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.537994 + 1.060310I
a = 0.79040 − 1.33454I
b = −1.04542 − 1.96500I
5.06634 − 2.14002I 0
u = −0.537994 − 1.060310I
a = 0.79040 + 1.33454I
b = −1.04542 + 1.96500I
5.06634 + 2.14002I 0
u = 0.791185 + 0.177363I
a = 1.300070 − 0.513805I
b = 1.187640 − 0.524337I
−4.51741 − 0.87205I 0
u = 0.791185 − 0.177363I
a = 1.300070 + 0.513805I
b = 1.187640 + 0.524337I
−4.51741 + 0.87205I 0
u = 0.789318 + 0.130913I
a = −0.990302 + 0.696881I
b = −0.968136 + 0.899123I
0.11479 + 2.61520I 0
u = 0.789318 − 0.130913I
a = −0.990302 − 0.696881I
b = −0.968136 − 0.899123I
0.11479 − 2.61520I 0
u = −0.497296 + 1.109830I
a = 0.54471 − 2.03133I
b = −2.21310 − 1.70139I
−2.35810 − 6.97390I 0
u = −0.497296 − 1.109830I
a = 0.54471 + 2.03133I
b = −2.21310 + 1.70139I
−2.35810 + 6.97390I 0
u = 0.268185 + 1.187910I
a = −0.028682 − 1.225910I
b = 1.40267 − 0.59674I
−5.82532 − 0.95127I 0
u = 0.268185 − 1.187910I
a = −0.028682 + 1.225910I
b = 1.40267 + 0.59674I
−5.82532 + 0.95127I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.243554 + 1.203910I
a = −0.14026 + 1.48236I
b = −1.46102 + 0.43158I
−7.51174 − 4.84738I 0
u = 0.243554 − 1.203910I
a = −0.14026 − 1.48236I
b = −1.46102 − 0.43158I
−7.51174 + 4.84738I 0
u = −0.510942 + 1.117850I
a = −0.74030 + 2.08914I
b = 2.29397 + 2.01991I
2.94950 − 10.49200I 0
u = −0.510942 − 1.117850I
a = −0.74030 − 2.08914I
b = 2.29397 − 2.01991I
2.94950 + 10.49200I 0
u = 0.227624 + 1.207990I
a = 0.29337 − 1.57666I
b = 1.43638 − 0.32576I
−2.19295 − 8.54270I 0
u = 0.227624 − 1.207990I
a = 0.29337 + 1.57666I
b = 1.43638 + 0.32576I
−2.19295 + 8.54270I 0
u = 0.301168 + 1.197690I
a = −0.373349 − 1.125900I
b = 1.43290 − 0.80406I
−6.20384 − 0.85870I 0
u = 0.301168 − 1.197690I
a = −0.373349 + 1.125900I
b = 1.43290 + 0.80406I
−6.20384 + 0.85870I 0
u = 0.333757 + 1.198830I
a = 0.644673 + 0.891724I
b = −1.31591 + 1.01915I
−8.71997 + 2.83880I 0
u = 0.333757 − 1.198830I
a = 0.644673 − 0.891724I
b = −1.31591 − 1.01915I
−8.71997 − 2.83880I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.356711 + 1.200770I
a = −0.824331 − 0.700922I
b = 1.17320 − 1.17227I
−3.93501 + 6.49394I 0
u = 0.356711 − 1.200770I
a = −0.824331 + 0.700922I
b = 1.17320 + 1.17227I
−3.93501 − 6.49394I 0
u = −0.622708 + 0.404742I
a = 1.71545 − 1.16576I
b = 0.23776 − 1.48997I
6.94859 − 2.43790I 11.62543 + 0.I
u = −0.622708 − 0.404742I
a = 1.71545 + 1.16576I
b = 0.23776 + 1.48997I
6.94859 + 2.43790I 11.62543 + 0.I
u = 0.566388 + 1.134480I
a = 0.07140 + 1.51630I
b = −1.59727 + 1.44583I
2.86970 + 7.81430I 0
u = 0.566388 − 1.134480I
a = 0.07140 − 1.51630I
b = −1.59727 − 1.44583I
2.86970 − 7.81430I 0
u = 0.501549 + 1.174570I
a = 0.796476 − 1.026530I
b = 1.015150 + 0.567854I
−2.94328 + 2.09281I 0
u = 0.501549 − 1.174570I
a = 0.796476 + 1.026530I
b = 1.015150 − 0.567854I
−2.94328 − 2.09281I 0
u = 0.521351 + 1.171550I
a = −0.67242 + 1.26699I
b = −1.41472 − 0.23732I
−7.43391 + 5.70780I 0
u = 0.521351 − 1.171550I
a = −0.67242 − 1.26699I
b = −1.41472 + 0.23732I
−7.43391 − 5.70780I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.562673 + 1.156350I
a = 0.19763 − 1.67071I
b = 2.05844 − 0.91159I
−3.81483 + 9.29793I 0
u = 0.562673 − 1.156350I
a = 0.19763 + 1.67071I
b = 2.05844 + 0.91159I
−3.81483 − 9.29793I 0
u = 0.542343 + 1.169450I
a = 0.51864 − 1.52373I
b = 1.86918 − 0.17093I
−4.55606 + 9.37865I 0
u = 0.542343 − 1.169450I
a = 0.51864 + 1.52373I
b = 1.86918 + 0.17093I
−4.55606 − 9.37865I 0
u = 0.550239 + 0.446862I
a = 0.913043 + 0.920010I
b = −0.626335 − 0.207161I
7.18932 − 3.77486I 10.71298 + 4.55097I
u = 0.550239 − 0.446862I
a = 0.913043 − 0.920010I
b = −0.626335 + 0.207161I
7.18932 + 3.77486I 10.71298 − 4.55097I
u = 0.018185 + 0.705737I
a = −1.099490 − 0.347649I
b = −0.495607 + 0.762907I
1.80406 + 0.58240I 2.57608 + 0.I
u = 0.018185 − 0.705737I
a = −1.099490 + 0.347649I
b = −0.495607 − 0.762907I
1.80406 − 0.58240I 2.57608 + 0.I
u = 0.575244 + 1.161420I
a = −0.14081 + 1.86816I
b = −2.47530 + 1.10945I
−5.2550 + 13.3202I 0
u = 0.575244 − 1.161420I
a = −0.14081 − 1.86816I
b = −2.47530 − 1.10945I
−5.2550 − 13.3202I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.429242 + 0.557449I
a = −0.723728 − 0.813562I
b = 0.510392 + 0.973611I
6.41254 + 5.37409I 9.09083 − 0.75897I
u = 0.429242 − 0.557449I
a = −0.723728 + 0.813562I
b = 0.510392 − 0.973611I
6.41254 − 5.37409I 9.09083 + 0.75897I
u = 0.582876 + 1.160370I
a = 0.04995 − 1.94974I
b = 2.62873 − 1.34120I
0.2193 + 17.0224I 0
u = 0.582876 − 1.160370I
a = 0.04995 + 1.94974I
b = 2.62873 + 1.34120I
0.2193 − 17.0224I 0
u = −0.634632 + 0.242992I
a = −2.55479 + 0.96939I
b = −1.30427 + 1.51785I
5.41399 + 6.01907I 9.29127 − 4.00944I
u = −0.634632 − 0.242992I
a = −2.55479 − 0.96939I
b = −1.30427 − 1.51785I
5.41399 − 6.01907I 9.29127 + 4.00944I
u = 0.382893 + 0.502487I
a = 0.804799 + 0.794530I
b = −0.287890 − 0.800421I
0.76766 + 2.22421I 4.53977 − 1.76011I
u = 0.382893 − 0.502487I
a = 0.804799 − 0.794530I
b = −0.287890 + 0.800421I
0.76766 − 2.22421I 4.53977 + 1.76011I
u = −0.577546 + 0.231711I
a = 2.45271 − 0.71226I
b = 1.19514 − 1.16114I
0.07601 + 2.67386I 4.60628 − 4.13106I
u = −0.577546 − 0.231711I
a = 2.45271 + 0.71226I
b = 1.19514 + 1.16114I
0.07601 − 2.67386I 4.60628 + 4.13106I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.482094 + 0.376524I
a = −1.79488 + 0.53486I
b = −0.521056 + 0.936711I
1.225990 − 0.574113I 8.49089 + 2.78120I
u = −0.482094 − 0.376524I
a = −1.79488 − 0.53486I
b = −0.521056 − 0.936711I
1.225990 + 0.574113I 8.49089 − 2.78120I
u = 0.471185 + 0.382816I
a = −0.850445 − 0.822138I
b = 0.283823 + 0.380432I
1.26363 − 1.29419I 6.60572 + 5.01711I
u = 0.471185 − 0.382816I
a = −0.850445 + 0.822138I
b = 0.283823 − 0.380432I
1.26363 + 1.29419I 6.60572 − 5.01711I
u = −0.455100
a = −2.60012
b = −1.23114
1.78041 6.28650
15
II. I
u
2
= hb
5
− b
4
u − b
4
+ 2b
3
u + b
2
− bu − b + u, a, u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
−u − 1
a
6
=
u
u + 1
a
4
=
0
u
a
10
=
0
b
a
7
=
u
b
2
u + u + 1
a
1
=
−u
−u − 1
a
11
=
bu + b
2b
a
9
=
0
b
a
12
=
−b
2
− u
−b
4
+ b
2
u − u − 1
a
8
=
−b
4
u − b
4
+ b
2
+ u
−2b
4
− b
2
u + u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = b
4
u + b
4
+ 4b
3
− 5b
2
u − 5b
2
+ 3bu − b + 4u + 10
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
5
c
2
(u
2
+ u + 1)
5
c
4
, c
9
u
10
c
6
, c
10
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
7
, c
8
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
11
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
12
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 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)
5
c
4
, c
9
y
10
c
6
, c
10
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
7
, c
8
, c
11
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
12
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0
b = −0.881753 + 0.117510I
0.32910 − 3.56046I 2.53179 + 8.01848I
u = −0.500000 + 0.866025I
a = 0
b = 0.542643 − 0.704866I
0.329100 − 0.499304I 5.04069 − 0.50981I
u = −0.500000 + 0.866025I
a = 0
b = 0.383413 + 0.664091I
2.40108 − 2.02988I 6.62546 + 2.50057I
u = −0.500000 + 0.866025I
a = 0
b = −0.811514 + 0.994721I
5.87256 − 6.43072I 6.60498 + 6.63374I
u = −0.500000 + 0.866025I
a = 0
b = 1.267210 − 0.205431I
5.87256 + 2.37095I 9.19707 − 1.05452I
u = −0.500000 − 0.866025I
a = 0
b = −0.881753 − 0.117510I
0.32910 + 3.56046I 2.53179 − 8.01848I
u = −0.500000 − 0.866025I
a = 0
b = 0.542643 + 0.704866I
0.329100 + 0.499304I 5.04069 + 0.50981I
u = −0.500000 − 0.866025I
a = 0
b = 0.383413 − 0.664091I
2.40108 + 2.02988I 6.62546 − 2.50057I
u = −0.500000 − 0.866025I
a = 0
b = −0.811514 − 0.994721I
5.87256 + 6.43072I 6.60498 − 6.63374I
u = −0.500000 − 0.866025I
a = 0
b = 1.267210 + 0.205431I
5.87256 − 2.37095I 9.19707 + 1.05452I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
5
)(u
105
+ 52u
104
+ ··· − 5u − 1)
c
2
((u
2
+ u + 1)
5
)(u
105
+ 6u
104
+ ··· − 5u − 1)
c
3
((u
2
− u + 1)
5
)(u
105
− 6u
104
+ ··· + 107353u − 23497)
c
4
, c
9
u
10
(u
105
+ u
104
+ ··· + 1024u − 1024)
c
5
((u
2
− u + 1)
5
)(u
105
+ 6u
104
+ ··· − 5u − 1)
c
6
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
· (u
105
+ 3u
104
+ ··· − 1465582u − 149381)
c
7
, c
8
((u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
)(u
105
− 3u
104
+ ··· − 2u − 1)
c
10
((u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
)(u
105
− 23u
104
+ ··· + 167398u − 8023)
c
11
((u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
)(u
105
− 3u
104
+ ··· − 2u − 1)
c
12
((u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
)(u
105
+ 9u
104
+ ··· + 6u + 1)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
5
)(y
105
+ 8y
104
+ ··· − 21y −1)
c
2
, c
5
((y
2
+ y + 1)
5
)(y
105
+ 52y
104
+ ··· − 5y −1)
c
3
((y
2
+ y + 1)
5
)(y
105
− 36y
104
+ ··· + 9.85651 × 10
8
y −5.52109 × 10
8
)
c
4
, c
9
y
10
(y
105
+ 55y
104
+ ··· − 2.51658 × 10
7
y −1048576)
c
6
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
· (y
105
− 31y
104
+ ··· + 449047075542y −22314683161)
c
7
, c
8
, c
11
((y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
)(y
105
− 95y
104
+ ··· + 2y −1)
c
10
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
· (y
105
+ 29y
104
+ ··· − 2885666658y −64368529)
c
12
((y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
)(y
105
− 3y
104
+ ··· + 14y −1)
21
