12a
0098
(K12a
0098
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 10 11 9 4 1 12 6 7
Solving Sequence
7,11
6 12
1,3
2 10 5 4 9 8
c
6
c
11
c
12
c
1
c
10
c
5
c
4
c
9
c
7
c
2
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
99
− 2u
98
+ ··· + b + 1, u
98
− u
97
+ ··· + a + 1, u
100
− 2u
99
+ ··· + 3u − 1i
I
u
2
= hb, u
2
+ a − u + 1, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 105 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
= hu
99
−2u
98
+· · · + b + 1, u
98
−u
97
+· · · + a + 1, u
100
−2u
99
+· · · + 3u − 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
6
=
1
u
2
a
12
=
u
u
3
+ u
a
1
=
−u
3
u
3
+ u
a
3
=
−u
98
+ u
97
+ ··· + 2u − 1
−u
99
+ 2u
98
+ ··· + 2u − 1
a
2
=
−u
95
+ u
94
+ ··· + 4u − 2
−u
52
− 14u
50
+ ··· − 2u
3
+ 2u
2
a
10
=
u
3
u
5
+ u
3
+ u
a
5
=
−u
6
− u
4
+ 1
−u
8
− 2u
6
− 2u
4
a
4
=
u
98
− u
97
+ ··· + 5u − 2
u
99
− 2u
98
+ ··· − 3u + 1
a
9
=
u
11
+ 2u
9
+ 2u
7
+ u
3
−u
11
− 3u
9
− 4u
7
− u
5
+ u
3
+ u
a
8
=
u
22
+ 5u
20
+ 12u
18
+ 15u
16
+ 10u
14
+ 2u
12
− u
8
− u
6
− u
4
+ 1
−u
22
− 6u
20
− 17u
18
− 26u
16
− 20u
14
+ 13u
10
+ 10u
8
+ u
6
− 2u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
99
− 15u
98
+ ··· − 24u + 7
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
100
+ 54u
99
+ ··· + 5u + 1
c
2
, c
4
u
100
− 6u
99
+ ··· + 5u − 1
c
3
, c
8
u
100
+ u
99
+ ··· + 64u + 32
c
5
, c
12
u
100
+ 2u
99
+ ··· − 9u − 1
c
6
, c
11
u
100
− 2u
99
+ ··· + 3u − 1
c
7
u
100
− 33u
99
+ ··· − 23040u + 1024
c
9
u
100
− 14u
99
+ ··· − 5687u + 409
c
10
u
100
+ 54u
99
+ ··· + 5u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
100
− 10y
99
+ ··· + 11y + 1
c
2
, c
4
y
100
− 54y
99
+ ··· − 5y + 1
c
3
, c
8
y
100
− 33y
99
+ ··· − 23040y + 1024
c
5
, c
12
y
100
− 82y
99
+ ··· + 149y + 1
c
6
, c
11
y
100
+ 54y
99
+ ··· + 5y + 1
c
7
y
100
+ 59y
99
+ ··· − 17432576y + 1048576
c
9
y
100
− 22y
99
+ ··· + 9736769y + 167281
c
10
y
100
− 14y
99
+ ··· − 3y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.487101 + 0.887376I
a = −0.64534 + 1.56978I
b = 0.237262 + 0.339303I
−2.85974 − 3.13345I 0
u = −0.487101 − 0.887376I
a = −0.64534 − 1.56978I
b = 0.237262 − 0.339303I
−2.85974 + 3.13345I 0
u = 0.512139 + 0.884085I
a = 0.85983 − 1.96917I
b = 2.12852 + 0.82152I
−2.46262 + 5.68656I 0
u = 0.512139 − 0.884085I
a = 0.85983 + 1.96917I
b = 2.12852 − 0.82152I
−2.46262 − 5.68656I 0
u = −0.535428 + 0.873146I
a = −0.102230 + 0.397660I
b = 0.983013 + 0.192627I
1.71894 − 6.57445I 0
u = −0.535428 − 0.873146I
a = −0.102230 − 0.397660I
b = 0.983013 − 0.192627I
1.71894 + 6.57445I 0
u = 0.061097 + 1.022580I
a = −0.064633 + 0.226670I
b = 0.076689 + 0.466636I
−2.29873 + 2.42299I 0
u = 0.061097 − 1.022580I
a = −0.064633 − 0.226670I
b = 0.076689 − 0.466636I
−2.29873 − 2.42299I 0
u = −0.014877 + 1.027310I
a = −1.90233 + 0.83604I
b = 0.90903 − 1.15393I
−6.01004 − 1.32650I 0
u = −0.014877 − 1.027310I
a = −1.90233 − 0.83604I
b = 0.90903 + 1.15393I
−6.01004 + 1.32650I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.281502 + 0.988175I
a = 1.171170 + 0.536052I
b = −0.644688 − 0.009719I
−0.57782 + 2.38994I 0
u = 0.281502 − 0.988175I
a = 1.171170 − 0.536052I
b = −0.644688 + 0.009719I
−0.57782 − 2.38994I 0
u = −0.544624 + 0.786486I
a = −0.96241 − 1.40714I
b = −1.38076 + 0.76706I
4.62351 − 4.68716I 0
u = −0.544624 − 0.786486I
a = −0.96241 + 1.40714I
b = −1.38076 − 0.76706I
4.62351 + 4.68716I 0
u = −0.549344 + 0.893780I
a = −0.75864 − 1.80248I
b = −2.01660 + 0.64147I
−0.99980 − 11.63300I 0
u = −0.549344 − 0.893780I
a = −0.75864 + 1.80248I
b = −2.01660 − 0.64147I
−0.99980 + 11.63300I 0
u = 0.440563 + 0.839915I
a = 0.601924 + 0.493045I
b = −0.771261 + 0.570745I
−0.05742 + 1.93114I 0
u = 0.440563 − 0.839915I
a = 0.601924 − 0.493045I
b = −0.771261 − 0.570745I
−0.05742 − 1.93114I 0
u = 0.055568 + 1.074490I
a = 1.82687 + 0.75760I
b = −1.10849 − 0.96099I
−5.21910 + 6.98392I 0
u = 0.055568 − 1.074490I
a = 1.82687 − 0.75760I
b = −1.10849 + 0.96099I
−5.21910 − 6.98392I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.544396 + 0.739925I
a = 0.072681 + 1.149840I
b = 1.49172 + 0.43095I
4.75608 + 0.29953I 0
u = −0.544396 − 0.739925I
a = 0.072681 − 1.149840I
b = 1.49172 − 0.43095I
4.75608 − 0.29953I 0
u = 0.481773 + 0.978864I
a = 0.50337 + 1.72394I
b = −0.521962 + 0.138752I
−2.30351 − 1.49233I 0
u = 0.481773 − 0.978864I
a = 0.50337 − 1.72394I
b = −0.521962 − 0.138752I
−2.30351 + 1.49233I 0
u = 0.435072 + 0.741485I
a = 1.233090 − 0.445011I
b = 0.325832 + 1.179420I
0.21908 + 1.78940I 0.70752 − 5.47893I
u = 0.435072 − 0.741485I
a = 1.233090 + 0.445011I
b = 0.325832 − 1.179420I
0.21908 − 1.78940I 0.70752 + 5.47893I
u = 0.824459 + 0.135370I
a = −0.035450 − 1.023230I
b = −2.22486 + 1.32612I
−4.76000 − 12.04300I −3.90865 + 7.83863I
u = 0.824459 − 0.135370I
a = −0.035450 + 1.023230I
b = −2.22486 − 1.32612I
−4.76000 + 12.04300I −3.90865 − 7.83863I
u = −0.825648 + 0.079549I
a = 0.654212 + 0.474789I
b = −0.026542 + 0.835432I
−6.39732 − 2.29666I −5.74508 + 3.83085I
u = −0.825648 − 0.079549I
a = 0.654212 − 0.474789I
b = −0.026542 − 0.835432I
−6.39732 + 2.29666I −5.74508 − 3.83085I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.578115 + 0.594628I
a = 0.66753 + 1.49885I
b = 1.70331 + 0.41644I
−0.16037 + 7.14748I −0.19098 − 4.78426I
u = −0.578115 − 0.594628I
a = 0.66753 − 1.49885I
b = 1.70331 − 0.41644I
−0.16037 − 7.14748I −0.19098 + 4.78426I
u = −0.543322 + 0.623428I
a = −0.500926 − 0.937819I
b = −0.592010 + 0.346478I
2.41952 + 2.21533I 3.55808 − 1.03686I
u = −0.543322 − 0.623428I
a = −0.500926 + 0.937819I
b = −0.592010 − 0.346478I
2.41952 − 2.21533I 3.55808 + 1.03686I
u = 0.808693 + 0.134012I
a = −0.042565 + 0.155136I
b = 1.43091 − 0.46157I
−1.75864 − 6.90513I −0.71442 + 4.85382I
u = 0.808693 − 0.134012I
a = −0.042565 − 0.155136I
b = 1.43091 + 0.46157I
−1.75864 + 6.90513I −0.71442 − 4.85382I
u = −0.808227 + 0.119737I
a = 0.001013 − 1.118540I
b = 2.18276 + 1.75899I
−5.96708 + 5.74079I −5.45196 − 4.06598I
u = −0.808227 − 0.119737I
a = 0.001013 + 1.118540I
b = 2.18276 − 1.75899I
−5.96708 − 5.74079I −5.45196 + 4.06598I
u = 0.432154 + 1.101560I
a = 1.41814 − 0.54319I
b = −0.682213 + 0.652652I
−0.54978 + 2.70789I 0
u = 0.432154 − 1.101560I
a = 1.41814 + 0.54319I
b = −0.682213 − 0.652652I
−0.54978 − 2.70789I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.804661 + 0.108864I
a = −0.773190 + 0.547526I
b = −0.216473 + 0.828174I
−6.30355 − 2.94906I −5.62609 + 3.05585I
u = 0.804661 − 0.108864I
a = −0.773190 − 0.547526I
b = −0.216473 − 0.828174I
−6.30355 + 2.94906I −5.62609 − 3.05585I
u = −0.800011
a = 0.579040
b = −0.453790
−3.31846 3.13170
u = 0.362513 + 1.145170I
a = −1.23658 + 1.82457I
b = 0.406691 − 0.980808I
−1.70065 − 1.90512I 0
u = 0.362513 − 1.145170I
a = −1.23658 − 1.82457I
b = 0.406691 + 0.980808I
−1.70065 + 1.90512I 0
u = −0.789568 + 0.093306I
a = 0.195595 + 0.130891I
b = −1.317430 − 0.428608I
−3.06121 + 1.43669I −2.47302 − 0.11715I
u = −0.789568 − 0.093306I
a = 0.195595 − 0.130891I
b = −1.317430 + 0.428608I
−3.06121 − 1.43669I −2.47302 + 0.11715I
u = 0.498648 + 0.587209I
a = −0.62990 + 1.82971I
b = −1.73628 + 0.37315I
−1.64770 − 1.50599I −1.92217 + 0.80453I
u = 0.498648 − 0.587209I
a = −0.62990 − 1.82971I
b = −1.73628 − 0.37315I
−1.64770 + 1.50599I −1.92217 − 0.80453I
u = −0.435541 + 1.155600I
a = 0.09357 + 3.60800I
b = 1.11804 − 1.66899I
−4.86062 − 2.24576I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.435541 − 1.155600I
a = 0.09357 − 3.60800I
b = 1.11804 + 1.66899I
−4.86062 + 2.24576I 0
u = 0.737955 + 0.179606I
a = −0.253244 − 1.053450I
b = −0.82591 + 1.17880I
2.13680 − 5.42672I 1.72948 + 6.28208I
u = 0.737955 − 0.179606I
a = −0.253244 + 1.053450I
b = −0.82591 − 1.17880I
2.13680 + 5.42672I 1.72948 − 6.28208I
u = 0.495377 + 1.145420I
a = 0.81566 + 2.36176I
b = −1.45498 − 0.50738I
0.07482 + 5.02620I 0
u = 0.495377 − 1.145420I
a = 0.81566 − 2.36176I
b = −1.45498 + 0.50738I
0.07482 − 5.02620I 0
u = 0.453852 + 1.167430I
a = 0.375656 − 0.273528I
b = 0.587582 − 0.060312I
−6.15358 + 4.16473I 0
u = 0.453852 − 1.167430I
a = 0.375656 + 0.273528I
b = 0.587582 + 0.060312I
−6.15358 − 4.16473I 0
u = −0.472406 + 1.164010I
a = −2.77759 − 2.12300I
b = 0.55876 + 2.02590I
−4.58329 − 5.97967I 0
u = −0.472406 − 1.164010I
a = −2.77759 + 2.12300I
b = 0.55876 − 2.02590I
−4.58329 + 5.97967I 0
u = 0.507155 + 1.162800I
a = 0.91044 − 2.82854I
b = 0.76397 + 1.44828I
−0.72084 + 10.09420I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.507155 − 1.162800I
a = 0.91044 + 2.82854I
b = 0.76397 − 1.44828I
−0.72084 − 10.09420I 0
u = 0.381540 + 1.214470I
a = 1.90375 + 0.08418I
b = −1.32632 + 0.72565I
−5.81050 − 2.87951I 0
u = 0.381540 − 1.214470I
a = 1.90375 − 0.08418I
b = −1.32632 − 0.72565I
−5.81050 + 2.87951I 0
u = −0.407140 + 1.208730I
a = −1.92802 + 0.11186I
b = 1.24526 + 0.74300I
−6.90359 − 2.70005I 0
u = −0.407140 − 1.208730I
a = −1.92802 − 0.11186I
b = 1.24526 − 0.74300I
−6.90359 + 2.70005I 0
u = 0.584288 + 0.428222I
a = 0.331398 + 1.168580I
b = 1.042000 + 0.223440I
−0.74199 + 5.73096I −0.46933 − 5.70886I
u = 0.584288 − 0.428222I
a = 0.331398 − 1.168580I
b = 1.042000 − 0.223440I
−0.74199 − 5.73096I −0.46933 + 5.70886I
u = −0.390582 + 1.215960I
a = 3.52756 + 1.57398I
b = −1.95856 − 1.94901I
−9.96791 + 1.65394I 0
u = −0.390582 − 1.215960I
a = 3.52756 − 1.57398I
b = −1.95856 + 1.94901I
−9.96791 − 1.65394I 0
u = 0.397348 + 1.215000I
a = −0.153885 + 0.492319I
b = 0.220508 − 1.046930I
−10.25340 + 1.17144I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.397348 − 1.215000I
a = −0.153885 − 0.492319I
b = 0.220508 + 1.046930I
−10.25340 − 1.17144I 0
u = 0.378815 + 1.225050I
a = −3.23541 + 1.04754I
b = 2.06321 − 1.49338I
−8.88797 − 7.96569I 0
u = 0.378815 − 1.225050I
a = −3.23541 − 1.04754I
b = 2.06321 + 1.49338I
−8.88797 + 7.96569I 0
u = 0.680366 + 0.201848I
a = −0.077511 + 0.618875I
b = 1.313020 − 0.208942I
2.79666 − 0.53221I 3.73788 − 0.05845I
u = 0.680366 − 0.201848I
a = −0.077511 − 0.618875I
b = 1.313020 + 0.208942I
2.79666 + 0.53221I 3.73788 + 0.05845I
u = −0.493166 + 1.196550I
a = −1.11383 + 1.86850I
b = 1.57907 − 0.45097I
−6.29130 − 6.13018I 0
u = −0.493166 − 1.196550I
a = −1.11383 − 1.86850I
b = 1.57907 + 0.45097I
−6.29130 + 6.13018I 0
u = −0.413146 + 1.227640I
a = −0.014578 + 0.657209I
b = 0.053942 − 1.014040I
−10.32580 − 6.60037I 0
u = −0.413146 − 1.227640I
a = −0.014578 − 0.657209I
b = 0.053942 + 1.014040I
−10.32580 + 6.60037I 0
u = −0.455587 + 1.212890I
a = −0.917999 + 0.410244I
b = 0.444463 − 0.011374I
−6.88676 − 4.49128I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.455587 − 1.212890I
a = −0.917999 − 0.410244I
b = 0.444463 + 0.011374I
−6.88676 + 4.49128I 0
u = 0.501005 + 1.199870I
a = 1.012660 − 0.468509I
b = 0.376071 + 0.795331I
−9.51720 + 7.72554I 0
u = 0.501005 − 1.199870I
a = 1.012660 + 0.468509I
b = 0.376071 − 0.795331I
−9.51720 − 7.72554I 0
u = 0.511051 + 1.196640I
a = 0.92636 + 1.94812I
b = −1.63284 − 0.49708I
−4.89488 + 11.74760I 0
u = 0.511051 − 1.196640I
a = 0.92636 − 1.94812I
b = −1.63284 + 0.49708I
−4.89488 − 11.74760I 0
u = −0.505714 + 1.199280I
a = 0.27473 − 4.54256I
b = −2.35444 + 1.89934I
−9.15153 − 10.55260I 0
u = −0.505714 − 1.199280I
a = 0.27473 + 4.54256I
b = −2.35444 − 1.89934I
−9.15153 + 10.55260I 0
u = 0.514998 + 1.202160I
a = −0.63872 − 4.05356I
b = 2.37010 + 1.41332I
−7.9226 + 16.9439I 0
u = 0.514998 − 1.202160I
a = −0.63872 + 4.05356I
b = 2.37010 − 1.41332I
−7.9226 − 16.9439I 0
u = −0.492233 + 1.213360I
a = −1.127970 − 0.340973I
b = −0.116806 + 0.827372I
−9.76185 − 2.48344I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.492233 − 1.213360I
a = −1.127970 + 0.340973I
b = −0.116806 − 0.827372I
−9.76185 + 2.48344I 0
u = −0.669706 + 0.085937I
a = 0.594226 − 0.989167I
b = −0.54335 + 1.59916I
−1.54837 + 1.65311I −2.30876 − 3.97340I
u = −0.669706 − 0.085937I
a = 0.594226 + 0.989167I
b = −0.54335 − 1.59916I
−1.54837 − 1.65311I −2.30876 + 3.97340I
u = 0.674398
a = −1.27425
b = −0.524099
−2.93668 0.594550
u = −0.397234 + 0.514555I
a = −0.43988 + 1.63914I
b = −0.698089 + 0.059413I
−1.95778 − 0.78971I −2.64817 − 0.48190I
u = −0.397234 − 0.514555I
a = −0.43988 − 1.63914I
b = −0.698089 − 0.059413I
−1.95778 + 0.78971I −2.64817 + 0.48190I
u = −0.263931 + 0.581955I
a = −0.72627 + 1.86741I
b = −0.564883 − 0.162134I
−1.93880 − 0.78358I −3.76235 − 2.11912I
u = −0.263931 − 0.581955I
a = −0.72627 − 1.86741I
b = −0.564883 + 0.162134I
−1.93880 + 0.78358I −3.76235 + 2.11912I
u = 0.537250 + 0.344396I
a = −0.064717 − 0.765608I
b = 0.092979 + 0.350954I
1.59701 + 1.17190I 3.67208 − 1.41836I
u = 0.537250 − 0.344396I
a = −0.064717 + 0.765608I
b = 0.092979 − 0.350954I
1.59701 − 1.17190I 3.67208 + 1.41836I
14
II. I
u
2
= hb, u
2
+ a − u + 1, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
6
=
1
u
2
a
12
=
u
u
3
+ u
a
1
=
−u
3
u
3
+ u
a
3
=
−u
2
+ u − 1
0
a
2
=
−u
3
− u
2
+ u − 1
u
3
+ u
a
10
=
u
3
u
4
− u
3
+ u
2
+ 1
a
5
=
u
3
−u
3
− u
a
4
=
−u
2
+ u − 1
0
a
9
=
1
0
a
8
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
4
+ 7u
3
− 8u
2
+ 6u − 12
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
5
c
3
, c
7
, c
8
u
5
c
4
(u + 1)
5
c
5
, c
9
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
6
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
10
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
11
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
12
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
5
c
3
, c
7
, c
8
y
5
c
5
, c
9
, c
12
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
6
, c
11
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
10
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 + 0.822375I
a = −0.77780 + 1.38013I
b = 0
−1.97403 − 1.53058I −5.00899 + 6.23673I
u = −0.339110 − 0.822375I
a = −0.77780 − 1.38013I
b = 0
−1.97403 + 1.53058I −5.00899 − 6.23673I
u = 0.766826
a = −0.821196
b = 0
−4.04602 −9.63840
u = 0.455697 + 1.200150I
a = 0.688402 + 0.106340I
b = 0
−7.51750 + 4.40083I −13.17182 − 3.02310I
u = 0.455697 − 1.200150I
a = 0.688402 − 0.106340I
b = 0
−7.51750 − 4.40083I −13.17182 + 3.02310I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
100
+ 54u
99
+ ··· + 5u + 1)
c
2
((u − 1)
5
)(u
100
− 6u
99
+ ··· + 5u − 1)
c
3
, c
8
u
5
(u
100
+ u
99
+ ··· + 64u + 32)
c
4
((u + 1)
5
)(u
100
− 6u
99
+ ··· + 5u − 1)
c
5
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
100
+ 2u
99
+ ··· − 9u − 1)
c
6
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)(u
100
− 2u
99
+ ··· + 3u − 1)
c
7
u
5
(u
100
− 33u
99
+ ··· − 23040u + 1024)
c
9
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
100
− 14u
99
+ ··· − 5687u + 409)
c
10
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)(u
100
+ 54u
99
+ ··· + 5u + 1)
c
11
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)(u
100
− 2u
99
+ ··· + 3u − 1)
c
12
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
100
+ 2u
99
+ ··· − 9u − 1)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
5
)(y
100
− 10y
99
+ ··· + 11y + 1)
c
2
, c
4
((y −1)
5
)(y
100
− 54y
99
+ ··· − 5y + 1)
c
3
, c
8
y
5
(y
100
− 33y
99
+ ··· − 23040y + 1024)
c
5
, c
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
100
− 82y
99
+ ··· + 149y + 1)
c
6
, c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
100
+ 54y
99
+ ··· + 5y + 1)
c
7
y
5
(y
100
+ 59y
99
+ ··· − 1.74326 × 10
7
y + 1048576)
c
9
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
· (y
100
− 22y
99
+ ··· + 9736769y + 167281)
c
10
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)(y
100
− 14y
99
+ ··· − 3y + 1)
20
