12n
0400
(K12n
0400
)
A knot diagram
1
Linearized knot diagam
3 5 7 10 2 12 1 5 4 9 6 4
Solving Sequence
3,7 4,10
5 2 1 9 11 8 12 6
c
3
c
4
c
2
c
1
c
9
c
10
c
8
c
12
c
6
c
5
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h8.20503 × 10
120
u
66
− 4.37537 × 10
120
u
65
+ ··· + 4.05645 × 10
120
b + 2.44731 × 10
122
,
− 2.09871 × 10
122
u
66
+ 3.37585 × 10
122
u
65
+ ··· + 1.09524 × 10
122
a + 8.19876 × 10
123
,
u
67
− u
66
+ ··· − 36u + 27i
I
u
2
= h−162u
19
− 529u
18
+ ··· + 67b − 916, −569u
19
+ 427u
18
+ ··· + 67a + 270,
u
20
+ 6u
18
+ ··· + 9u
2
+ 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
= h8.21 × 10
120
u
66
− 4.38 × 10
120
u
65
+ · · · + 4.06 × 10
120
b + 2.45 ×
10
122
, −2.10 × 10
122
u
66
+ 3.38 × 10
122
u
65
+ · · · + 1.10 × 10
122
a + 8.20 ×
10
123
, u
67
− u
66
+ · · · − 36u + 27i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
10
=
1.91621u
66
− 3.08229u
65
+ ··· + 218.618u − 74.8581
−2.02271u
66
+ 1.07862u
65
+ ··· − 11.8138u − 60.3314
a
5
=
2.42380u
66
− 3.06485u
65
+ ··· + 134.055u − 39.4259
0.382036u
66
− 0.247634u
65
+ ··· + 12.7110u + 12.3558
a
2
=
1.16559u
66
− 0.322858u
65
+ ··· + 43.2405u + 26.4451
−0.679935u
66
+ 1.62318u
65
+ ··· − 157.928u + 68.3586
a
1
=
0.485654u
66
+ 1.30032u
65
+ ··· − 114.687u + 94.8037
−0.679935u
66
+ 1.62318u
65
+ ··· − 157.928u + 68.3586
a
9
=
2.96238u
66
− 2.76939u
65
+ ··· + 136.716u + 16.9575
−2.60117u
66
+ 1.16210u
65
+ ··· + 8.86605u − 97.0263
a
11
=
0.246704u
66
+ 0.254410u
65
+ ··· − 47.6286u + 20.0839
1.49519u
66
− 4.45234u
65
+ ··· + 359.216u − 165.126
a
8
=
7.22609u
66
− 7.67941u
65
+ ··· + 408.413u − 6.27588
2.34500u
66
− 1.98279u
65
+ ··· + 82.0421u + 45.1621
a
12
=
0.806636u
66
− 0.800130u
65
+ ··· + 94.4230u − 21.7763
−0.623210u
66
+ 2.28266u
65
+ ··· − 230.655u + 116.404
a
6
=
3.29459u
66
− 3.09314u
65
+ ··· + 140.386u + 20.3916
−3.12335u
66
+ 2.48303u
65
+ ··· − 105.141u − 65.0291
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5.74045u
66
+ 2.90861u
65
+ ··· + 127.771u − 271.376
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
67
+ 42u
66
+ ··· − 24651u − 1849
c
2
, c
5
u
67
+ 21u
65
+ ··· + 17u − 43
c
3
u
67
+ u
66
+ ··· − 36u − 27
c
4
, c
9
u
67
+ u
66
+ ··· − 20u − 19
c
6
, c
11
u
67
− u
66
+ ··· − 20u − 1
c
7
u
67
− 7u
66
+ ··· + 1902976u − 712609
c
8
u
67
+ 6u
66
+ ··· + 57128562u − 63140553
c
10
u
67
− 19u
66
+ ··· + 5796u − 361
c
12
u
67
+ 10u
66
+ ··· + 65390u + 26317
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
67
− 22y
66
+ ··· + 45805077y −3418801
c
2
, c
5
y
67
+ 42y
66
+ ··· − 24651y −1849
c
3
y
67
+ 23y
66
+ ··· − 28350y −729
c
4
, c
9
y
67
− 19y
66
+ ··· + 5796y −361
c
6
, c
11
y
67
− 15y
66
+ ··· + 72y −1
c
7
y
67
− 23y
66
+ ··· − 3886211988072y −507811586881
c
8
y
67
− 134y
66
+ ··· + 205611754284956160y −3986729433145809
c
10
y
67
+ 69y
66
+ ··· − 1190900y −130321
c
12
y
67
+ 14y
66
+ ··· + 48815900848y −692584489
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.020734 + 0.989112I
a = −2.11448 + 0.88607I
b = 1.102020 + 0.046986I
−2.56036 − 3.61015I 4.00000 + 4.59333I
u = 0.020734 − 0.989112I
a = −2.11448 − 0.88607I
b = 1.102020 − 0.046986I
−2.56036 + 3.61015I 4.00000 − 4.59333I
u = −0.397079 + 0.880420I
a = −0.383090 − 0.299480I
b = −0.722114 + 0.962145I
1.65706 − 1.20024I 8.71578 + 3.20813I
u = −0.397079 − 0.880420I
a = −0.383090 + 0.299480I
b = −0.722114 − 0.962145I
1.65706 + 1.20024I 8.71578 − 3.20813I
u = −0.560483 + 0.777160I
a = 0.828568 + 0.311770I
b = 0.257750 + 0.242820I
−4.00761 + 2.23459I −3.32429 − 2.42501I
u = −0.560483 − 0.777160I
a = 0.828568 − 0.311770I
b = 0.257750 − 0.242820I
−4.00761 − 2.23459I −3.32429 + 2.42501I
u = 0.285894 + 0.913597I
a = −0.003075 − 0.408224I
b = 0.173603 + 0.837678I
0.58721 − 1.40356I 4.00000 + 4.86091I
u = 0.285894 − 0.913597I
a = −0.003075 + 0.408224I
b = 0.173603 − 0.837678I
0.58721 + 1.40356I 4.00000 − 4.86091I
u = 0.569468 + 0.913130I
a = −0.88485 − 1.73481I
b = 1.71439 + 0.31076I
1.09519 − 1.96755I 0
u = 0.569468 − 0.913130I
a = −0.88485 + 1.73481I
b = 1.71439 − 0.31076I
1.09519 + 1.96755I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.830715 + 0.740572I
a = 0.60001 + 1.63780I
b = −1.098950 + 0.108954I
−4.78073 − 2.36169I 0
u = 0.830715 − 0.740572I
a = 0.60001 − 1.63780I
b = −1.098950 − 0.108954I
−4.78073 + 2.36169I 0
u = −0.893443 + 0.696027I
a = −0.391682 + 0.454998I
b = 1.41969 − 0.16929I
−4.31346 − 3.83468I 0
u = −0.893443 − 0.696027I
a = −0.391682 − 0.454998I
b = 1.41969 + 0.16929I
−4.31346 + 3.83468I 0
u = −0.853524 + 0.747440I
a = 1.64500 − 1.97641I
b = −1.43662 − 2.02594I
0.11681 + 6.19592I 0
u = −0.853524 − 0.747440I
a = 1.64500 + 1.97641I
b = −1.43662 + 2.02594I
0.11681 − 6.19592I 0
u = −0.821610 + 0.845291I
a = 0.277124 + 0.508899I
b = 1.66774 − 1.30196I
−8.33360 − 1.96969I 0
u = −0.821610 − 0.845291I
a = 0.277124 − 0.508899I
b = 1.66774 + 1.30196I
−8.33360 + 1.96969I 0
u = 0.931514 + 0.724402I
a = −0.167627 − 0.434622I
b = 1.205880 − 0.088640I
−0.28086 − 3.26362I 0
u = 0.931514 − 0.724402I
a = −0.167627 + 0.434622I
b = 1.205880 + 0.088640I
−0.28086 + 3.26362I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.846645 + 0.822198I
a = 0.487687 + 0.772794I
b = −0.153694 − 0.215450I
−8.55192 − 4.73842I 0
u = 0.846645 − 0.822198I
a = 0.487687 − 0.772794I
b = −0.153694 + 0.215450I
−8.55192 + 4.73842I 0
u = 0.913707 + 0.747374I
a = −0.724192 − 0.211434I
b = −0.484202 − 0.589044I
−0.81057 − 5.10480I 0
u = 0.913707 − 0.747374I
a = −0.724192 + 0.211434I
b = −0.484202 + 0.589044I
−0.81057 + 5.10480I 0
u = 0.058759 + 0.809366I
a = 4.53846 − 0.30110I
b = −2.28712 + 0.27809I
4.36128 − 4.16936I 12.4339 + 6.8808I
u = 0.058759 − 0.809366I
a = 4.53846 + 0.30110I
b = −2.28712 − 0.27809I
4.36128 + 4.16936I 12.4339 − 6.8808I
u = −0.209111 + 0.767687I
a = −0.071283 − 1.138760I
b = 0.396327 + 0.485629I
4.86449 + 2.07848I 16.1441 − 2.2028I
u = −0.209111 − 0.767687I
a = −0.071283 + 1.138760I
b = 0.396327 − 0.485629I
4.86449 − 2.07848I 16.1441 + 2.2028I
u = −0.984841 + 0.718671I
a = −1.176210 + 0.239572I
b = −1.14052 + 2.10734I
0.53842 + 1.84717I 0
u = −0.984841 − 0.718671I
a = −1.176210 − 0.239572I
b = −1.14052 − 2.10734I
0.53842 − 1.84717I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.791011 + 0.950672I
a = −1.61662 + 1.62965I
b = 1.96254 + 1.09066I
−8.00368 + 8.01849I 0
u = −0.791011 − 0.950672I
a = −1.61662 − 1.62965I
b = 1.96254 − 1.09066I
−8.00368 − 8.01849I 0
u = 0.749070 + 0.108534I
a = 0.464143 + 0.806483I
b = 1.087010 + 0.830302I
−1.24756 + 2.47949I 1.16218 − 4.53849I
u = 0.749070 − 0.108534I
a = 0.464143 − 0.806483I
b = 1.087010 − 0.830302I
−1.24756 − 2.47949I 1.16218 + 4.53849I
u = −0.458655 + 1.171940I
a = 1.47345 − 0.83047I
b = −1.44496 − 0.40210I
4.31504 + 4.03898I 0
u = −0.458655 − 1.171940I
a = 1.47345 + 0.83047I
b = −1.44496 + 0.40210I
4.31504 − 4.03898I 0
u = 0.746334 + 1.015930I
a = 0.363333 + 0.193804I
b = −1.264550 − 0.463867I
−3.92401 − 3.56783I 0
u = 0.746334 − 1.015930I
a = 0.363333 − 0.193804I
b = −1.264550 + 0.463867I
−3.92401 + 3.56783I 0
u = 0.801818 + 0.982376I
a = 0.433833 − 0.506247I
b = −0.265138 − 0.052591I
−8.05703 − 1.42378I 0
u = 0.801818 − 0.982376I
a = 0.433833 + 0.506247I
b = −0.265138 + 0.052591I
−8.05703 + 1.42378I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.572904 + 1.139750I
a = 0.816949 + 0.121925I
b = −0.49318 + 1.48394I
0.780282 − 0.975175I 0
u = 0.572904 − 1.139750I
a = 0.816949 − 0.121925I
b = −0.49318 − 1.48394I
0.780282 + 0.975175I 0
u = −1.105290 + 0.681901I
a = −0.518893 + 0.695577I
b = −0.068992 + 0.331381I
−9.61789 − 2.23788I 0
u = −1.105290 − 0.681901I
a = −0.518893 − 0.695577I
b = −0.068992 − 0.331381I
−9.61789 + 2.23788I 0
u = 0.529577 + 1.188440I
a = −1.83871 − 0.54447I
b = 1.34592 − 1.37777I
1.79223 − 7.30523I 0
u = 0.529577 − 1.188440I
a = −1.83871 + 0.54447I
b = 1.34592 + 1.37777I
1.79223 + 7.30523I 0
u = −0.777256 + 1.057710I
a = −0.98138 + 1.32398I
b = 1.65665 + 0.10271I
−3.20942 + 10.04150I 0
u = −0.777256 − 1.057710I
a = −0.98138 − 1.32398I
b = 1.65665 − 0.10271I
−3.20942 − 10.04150I 0
u = −0.123671 + 0.652554I
a = 1.108600 − 0.254962I
b = −1.137750 − 0.541468I
3.71168 + 4.46923I 9.9645 − 11.0760I
u = −0.123671 − 0.652554I
a = 1.108600 + 0.254962I
b = −1.137750 + 0.541468I
3.71168 − 4.46923I 9.9645 + 11.0760I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.030964 + 0.662671I
a = −3.98163 + 2.37558I
b = 0.85724 − 1.52082I
4.35373 − 1.34213I 11.11045 − 1.66726I
u = 0.030964 − 0.662671I
a = −3.98163 − 2.37558I
b = 0.85724 + 1.52082I
4.35373 + 1.34213I 11.11045 + 1.66726I
u = −0.050606 + 0.651811I
a = 0.902429 + 0.451016I
b = 0.573558 + 0.775451I
−4.00181 + 3.70212I 13.57429 − 0.10210I
u = −0.050606 − 0.651811I
a = 0.902429 − 0.451016I
b = 0.573558 − 0.775451I
−4.00181 − 3.70212I 13.57429 + 0.10210I
u = 1.204890 + 0.695342I
a = −0.432216 + 0.391136I
b = −2.16038 − 1.14469I
−8.45230 + 8.76364I 0
u = 1.204890 − 0.695342I
a = −0.432216 − 0.391136I
b = −2.16038 + 1.14469I
−8.45230 − 8.76364I 0
u = −0.594726
a = −0.215660
b = −0.911050
1.23122 8.43390
u = 0.209731 + 1.392820I
a = −1.31171 − 0.61402I
b = 1.73733 + 0.84785I
3.27062 − 2.27476I 0
u = 0.209731 − 1.392820I
a = −1.31171 + 0.61402I
b = 1.73733 − 0.84785I
3.27062 + 2.27476I 0
u = −0.81844 + 1.15419I
a = −0.273730 − 0.330386I
b = 0.289304 − 0.329456I
−8.05820 + 9.16868I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.81844 − 1.15419I
a = −0.273730 + 0.330386I
b = 0.289304 + 0.329456I
−8.05820 − 9.16868I 0
u = 0.86062 + 1.18663I
a = 1.45137 + 1.13375I
b = −2.16489 + 1.35997I
−6.8030 − 16.0998I 0
u = 0.86062 − 1.18663I
a = 1.45137 − 1.13375I
b = −2.16489 − 1.35997I
−6.8030 + 16.0998I 0
u = −0.60438 + 1.49192I
a = 1.48378 − 0.45493I
b = −2.45741 − 1.34669I
3.02134 + 5.22680I 0
u = −0.60438 − 1.49192I
a = 1.48378 + 0.45493I
b = −2.45741 + 1.34669I
3.02134 − 5.22680I 0
u = 0.083417 + 0.315334I
a = 4.93779 + 3.20489I
b = 0.289054 + 0.647459I
−1.75204 + 2.60727I −2.01169 + 0.16316I
u = 0.083417 − 0.315334I
a = 4.93779 − 3.20489I
b = 0.289054 − 0.647459I
−1.75204 − 2.60727I −2.01169 − 0.16316I
11
II. I
u
2
= h−162u
19
− 529u
18
+ · · · + 67b − 916, −569u
19
+ 427u
18
+ · · · +
67a + 270, u
20
+ 6u
18
+ · · · + 9u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
10
=
8.49254u
19
− 6.37313u
18
+ ··· + 23.1194u − 4.02985
2.41791u
19
+ 7.89552u
18
+ ··· + 15.3134u + 13.6716
a
5
=
−1.79104u
19
+ 20.4478u
18
+ ··· − 1.34328u + 39.8358
−8.91045u
19
− 3.52239u
18
+ ··· − 12.4328u + 2.35821
a
2
=
8.11940u
19
+ 1.97015u
18
+ ··· + 40.0896u + 14.4776
13.3881u
19
+ 4.40299u
18
+ ··· + 28.7910u + 0.552239
a
1
=
21.5075u
19
+ 6.37313u
18
+ ··· + 68.8806u + 15.0299
13.3881u
19
+ 4.40299u
18
+ ··· + 28.7910u + 0.552239
a
9
=
2.41791u
19
− 8.10448u
18
+ ··· − 0.686567u − 11.3284
2.85075u
19
+ 7.53731u
18
+ ··· + 21.3881u + 15.4030
a
11
=
22.1045u
19
− 3.77612u
18
+ ··· + 24.3284u − 5.58209
8u
19
+ 11u
18
+ ··· + 43u + 18
a
8
=
28.8955u
19
+ 2.77612u
18
+ ··· + 12.6716u − 25.4179
5.37313u
19
− 4.34328u
18
+ ··· + 7.02985u − 21.5075
a
12
=
3.77612u
19
+ 0.805970u
18
+ ··· + 18.5821u + 8.10448
19.0299u
19
+ 6.49254u
18
+ ··· + 46.5224u + 6.11940
a
6
=
5.32836u
19
+ 1.41791u
18
+ ··· − 13.2537u − 6.68657
−9.10448u
19
− 2.22388u
18
+ ··· − 13.3284u − 1.41791
(ii) Obstruction class = 1
(iii) Cusp Shapes =
2549
67
u
19
+
2495
67
u
18
+ ··· +
11811
67
u +
7516
67
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
20
− 11u
19
+ ··· − 15u + 1
c
2
u
20
+ u
19
+ ··· + u + 1
c
3
u
20
+ 6u
18
+ ··· + 9u
2
+ 1
c
4
u
20
− 5u
18
+ ··· − 6u
2
+ 1
c
5
u
20
− u
19
+ ··· − u + 1
c
6
u
20
+ 2u
19
+ ··· − 4u
2
+ 1
c
7
u
20
+ 2u
19
+ ··· − 2u
2
+ 1
c
8
u
20
− 3u
19
+ ··· − 10u
2
+ 1
c
9
u
20
− 5u
18
+ ··· − 6u
2
+ 1
c
10
u
20
− 10u
19
+ ··· − 12u + 1
c
11
u
20
− 2u
19
+ ··· − 4u
2
+ 1
c
12
u
20
− 3u
19
+ ··· + 4u + 1
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
+ 7y
19
+ ··· − 13y + 1
c
2
, c
5
y
20
+ 11y
19
+ ··· + 15y + 1
c
3
y
20
+ 12y
19
+ ··· + 18y + 1
c
4
, c
9
y
20
− 10y
19
+ ··· − 12y + 1
c
6
, c
11
y
20
− 14y
19
+ ··· − 8y + 1
c
7
y
20
+ 18y
19
+ ··· − 4y + 1
c
8
y
20
− 25y
19
+ ··· − 20y + 1
c
10
y
20
+ 10y
19
+ ··· + 4y + 1
c
12
y
20
− 17y
19
+ ··· + 4y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.355345 + 1.025280I
a = 1.36470 − 1.34565I
b = −1.176260 + 0.757366I
5.09233 + 0.56778I 8.69401 − 1.53858I
u = −0.355345 − 1.025280I
a = 1.36470 + 1.34565I
b = −1.176260 − 0.757366I
5.09233 − 0.56778I 8.69401 + 1.53858I
u = 0.338576 + 1.132500I
a = −2.28130 − 0.58160I
b = 2.06551 − 0.61176I
5.46617 − 6.02563I 11.16031 + 7.36754I
u = 0.338576 − 1.132500I
a = −2.28130 + 0.58160I
b = 2.06551 + 0.61176I
5.46617 + 6.02563I 11.16031 − 7.36754I
u = −0.710578 + 0.966405I
a = −1.52937 − 0.46414I
b = −0.71185 + 2.55057I
1.77651 + 0.66802I 11.11874 + 1.21947I
u = −0.710578 − 0.966405I
a = −1.52937 + 0.46414I
b = −0.71185 − 2.55057I
1.77651 − 0.66802I 11.11874 − 1.21947I
u = −0.317333 + 0.724179I
a = 0.75822 + 1.64326I
b = −0.182533 − 0.634494I
3.96590 + 2.30760I 5.67872 − 4.88992I
u = −0.317333 − 0.724179I
a = 0.75822 − 1.64326I
b = −0.182533 + 0.634494I
3.96590 − 2.30760I 5.67872 + 4.88992I
u = −0.117386 + 0.721837I
a = 3.36707 + 0.83360I
b = −0.704452 − 0.220228I
−1.23001 + 2.92216I 9.81470 − 5.41691I
u = −0.117386 − 0.721837I
a = 3.36707 − 0.83360I
b = −0.704452 + 0.220228I
−1.23001 − 2.92216I 9.81470 + 5.41691I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.098310 + 0.689577I
a = 0.329509 − 0.485063I
b = 1.68283 + 0.28491I
0.16878 − 3.82990I 9.38703 + 7.38381I
u = 1.098310 − 0.689577I
a = 0.329509 + 0.485063I
b = 1.68283 − 0.28491I
0.16878 + 3.82990I 9.38703 − 7.38381I
u = 0.147095 + 0.666021I
a = −1.42462 − 0.91452I
b = 1.35466 + 0.66805I
3.44748 + 3.77342I 3.92747 − 0.87310I
u = 0.147095 − 0.666021I
a = −1.42462 + 0.91452I
b = 1.35466 − 0.66805I
3.44748 − 3.77342I 3.92747 + 0.87310I
u = 0.158162 + 0.572450I
a = −1.58765 + 0.59956I
b = −0.532818 + 0.609853I
−4.33471 − 3.83881I −8.13243 + 8.66691I
u = 0.158162 − 0.572450I
a = −1.58765 − 0.59956I
b = −0.532818 − 0.609853I
−4.33471 + 3.83881I −8.13243 − 8.66691I
u = −0.76716 + 1.21117I
a = 1.60777 − 0.74753I
b = −1.63951 − 1.98014I
2.21300 + 5.96268I 6.40503 − 7.23236I
u = −0.76716 − 1.21117I
a = 1.60777 + 0.74753I
b = −1.63951 + 1.98014I
2.21300 − 5.96268I 6.40503 + 7.23236I
u = 0.52566 + 1.39685I
a = −1.104330 − 0.728949I
b = 1.84444 − 0.04869I
3.17377 − 3.27114I 7.44642 + 4.46067I
u = 0.52566 − 1.39685I
a = −1.104330 + 0.728949I
b = 1.84444 + 0.04869I
3.17377 + 3.27114I 7.44642 − 4.46067I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
20
− 11u
19
+ ··· − 15u + 1)(u
67
+ 42u
66
+ ··· − 24651u − 1849)
c
2
(u
20
+ u
19
+ ··· + u + 1)(u
67
+ 21u
65
+ ··· + 17u − 43)
c
3
(u
20
+ 6u
18
+ ··· + 9u
2
+ 1)(u
67
+ u
66
+ ··· − 36u − 27)
c
4
(u
20
− 5u
18
+ ··· − 6u
2
+ 1)(u
67
+ u
66
+ ··· − 20u − 19)
c
5
(u
20
− u
19
+ ··· − u + 1)(u
67
+ 21u
65
+ ··· + 17u − 43)
c
6
(u
20
+ 2u
19
+ ··· − 4u
2
+ 1)(u
67
− u
66
+ ··· − 20u − 1)
c
7
(u
20
+ 2u
19
+ ··· − 2u
2
+ 1)(u
67
− 7u
66
+ ··· + 1902976u − 712609)
c
8
(u
20
− 3u
19
+ ··· − 10u
2
+ 1)
· (u
67
+ 6u
66
+ ··· + 57128562u − 63140553)
c
9
(u
20
− 5u
18
+ ··· − 6u
2
+ 1)(u
67
+ u
66
+ ··· − 20u − 19)
c
10
(u
20
− 10u
19
+ ··· − 12u + 1)(u
67
− 19u
66
+ ··· + 5796u − 361)
c
11
(u
20
− 2u
19
+ ··· − 4u
2
+ 1)(u
67
− u
66
+ ··· − 20u − 1)
c
12
(u
20
− 3u
19
+ ··· + 4u + 1)(u
67
+ 10u
66
+ ··· + 65390u + 26317)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
20
+ 7y
19
+ ··· − 13y + 1)
· (y
67
− 22y
66
+ ··· + 45805077y −3418801)
c
2
, c
5
(y
20
+ 11y
19
+ ··· + 15y + 1)(y
67
+ 42y
66
+ ··· − 24651y −1849)
c
3
(y
20
+ 12y
19
+ ··· + 18y + 1)(y
67
+ 23y
66
+ ··· − 28350y −729)
c
4
, c
9
(y
20
− 10y
19
+ ··· − 12y + 1)(y
67
− 19y
66
+ ··· + 5796y −361)
c
6
, c
11
(y
20
− 14y
19
+ ··· − 8y + 1)(y
67
− 15y
66
+ ··· + 72y −1)
c
7
(y
20
+ 18y
19
+ ··· − 4y + 1)
· (y
67
− 23y
66
+ ··· − 3886211988072y −507811586881)
c
8
(y
20
− 25y
19
+ ··· − 20y + 1)
· (y
67
− 134y
66
+ ··· + 205611754284956160y −3986729433145809)
c
10
(y
20
+ 10y
19
+ ··· + 4y + 1)(y
67
+ 69y
66
+ ··· − 1190900y −130321)
c
12
(y
20
− 17y
19
+ ··· + 4y + 1)
· (y
67
+ 14y
66
+ ··· + 48815900848y −692584489)
20
