12n
0715
(K12n
0715
)
A knot diagram
1
Linearized knot diagam
4 11 7 9 11 2 1 12 2 7 5 8
Solving Sequence
2,11 3,7
4 1 6 5 12 10 9 8
c
2
c
3
c
1
c
6
c
5
c
11
c
10
c
9
c
8
c
4
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h4.60880 × 10
217
u
59
+ 2.22932 × 10
217
u
58
+ ··· + 2.72986 × 10
221
b − 9.04649 × 10
220
,
2.36217 × 10
222
u
59
+ 8.17530 × 10
221
u
58
+ ··· + 8.32334 × 10
224
a + 1.63524 × 10
225
,
u
60
+ 31u
58
+ ··· − 6806u + 3049i
I
u
2
= h30594119u
15
− 54613383u
14
+ ··· + 339075961b + 341724092,
− 312874829u
15
+ 341866737u
14
+ ··· + 339075961a − 448000694,
u
16
− u
15
+ 5u
14
− 3u
13
+ 10u
12
− 7u
11
+ u
10
− 3u
9
+ 10u
8
− u
7
− u
6
− 3u
5
+ 11u
4
+ 3u
3
− 4u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 76 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
= h4.61 × 10
217
u
59
+ 2.23 × 10
217
u
58
+ · · · + 2.73 × 10
221
b − 9.05 ×
10
220
, 2.36 × 10
222
u
59
+ 8.18 × 10
221
u
58
+ · · · + 8.32 × 10
224
a + 1.64 ×
10
225
, u
60
+ 31u
58
+ · · · − 6806u + 3049i
(i) Arc colorings
a
2
=
1
0
a
11
=
0
u
a
3
=
1
u
2
a
7
=
−0.00283801u
59
− 0.000982214u
58
+ ··· − 46.8813u − 1.96465
−0.000168829u
59
− 0.0000816642u
58
+ ··· − 3.57585u + 0.331390
a
4
=
−0.000945087u
59
+ 0.000227941u
58
+ ··· − 22.2070u + 11.7845
−0.000433429u
59
− 0.000247835u
58
+ ··· − 8.68770u − 0.364595
a
1
=
0.000218505u
59
+ 0.000327052u
58
+ ··· + 4.01660u + 3.62050
0.000530540u
59
− 0.0000863422u
58
+ ··· + 10.7434u − 5.55537
a
6
=
−0.00300684u
59
− 0.00106388u
58
+ ··· − 50.4571u − 1.63326
−0.000168829u
59
− 0.0000816642u
58
+ ··· − 3.57585u + 0.331390
a
5
=
−0.00300684u
59
− 0.00106388u
58
+ ··· − 50.4571u − 1.63326
−0.0000163342u
59
+ 0.000121229u
58
+ ··· − 1.64875u + 3.57516
a
12
=
0.000720153u
59
− 0.000752234u
58
+ ··· + 22.6935u − 14.1062
−0.000822043u
59
+ 0.000203348u
58
+ ··· − 15.0493u + 9.22217
a
10
=
−0.00155459u
59
+ 0.00108020u
58
+ ··· − 39.1669u + 27.2099
0.000345116u
59
− 0.000186298u
58
+ ··· + 8.73955u − 6.17511
a
9
=
−0.00120947u
59
+ 0.000893904u
58
+ ··· − 30.4274u + 21.0348
0.000345116u
59
− 0.000186298u
58
+ ··· + 8.73955u − 6.17511
a
8
=
−0.00175525u
59
− 0.000468763u
58
+ ··· − 34.3728u + 3.63194
0.000128794u
59
− 0.000138534u
58
+ ··· + 3.06900u − 1.69755
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00272374u
59
+ 0.00105874u
58
+ ··· + 53.4296u − 4.72817
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
60
− 8u
59
+ ··· − 27u + 1
c
2
u
60
+ 31u
58
+ ··· + 6806u + 3049
c
3
u
60
− 4u
58
+ ··· + 905u + 79
c
4
u
60
+ 3u
59
+ ··· + 6612u + 977
c
5
, c
11
u
60
+ 19u
58
+ ··· + 1808u + 136
c
6
u
60
+ 3u
59
+ ··· + 5062u + 484
c
7
, c
8
, c
12
u
60
− 2u
59
+ ··· + 12u + 1
c
9
u
60
− 4u
59
+ ··· + 232u + 8
c
10
u
60
+ 3u
59
+ ··· + 1069u + 541
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
60
+ 2y
59
+ ··· − 233y + 1
c
2
y
60
+ 62y
59
+ ··· + 271621986y + 9296401
c
3
y
60
− 8y
59
+ ··· − 193345y + 6241
c
4
y
60
+ 21y
59
+ ··· + 18369806y + 954529
c
5
, c
11
y
60
+ 38y
59
+ ··· − 152832y + 18496
c
6
y
60
+ 63y
59
+ ··· + 4369636y + 234256
c
7
, c
8
, c
12
y
60
+ 64y
59
+ ··· − 6y + 1
c
9
y
60
+ 14y
59
+ ··· + 2240y + 64
c
10
y
60
− 75y
59
+ ··· − 4777199y + 292681
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.643501 + 0.773438I
a = 0.477987 − 0.525534I
b = −0.480857 + 0.417860I
−1.32280 − 2.56367I 5.00187 + 5.20719I
u = 0.643501 − 0.773438I
a = 0.477987 + 0.525534I
b = −0.480857 − 0.417860I
−1.32280 + 2.56367I 5.00187 − 5.20719I
u = 0.926449 + 0.415748I
a = 0.352525 + 0.205719I
b = 0.272409 + 0.505392I
−1.76277 − 1.27508I 3.66951 + 0.I
u = 0.926449 − 0.415748I
a = 0.352525 − 0.205719I
b = 0.272409 − 0.505392I
−1.76277 + 1.27508I 3.66951 + 0.I
u = 0.053170 + 0.925086I
a = 0.623976 − 0.343376I
b = −1.53558 + 0.06817I
−1.87416 − 3.34982I −1.36055 + 8.15563I
u = 0.053170 − 0.925086I
a = 0.623976 + 0.343376I
b = −1.53558 − 0.06817I
−1.87416 + 3.34982I −1.36055 − 8.15563I
u = −0.500509 + 0.765670I
a = −1.83740 − 0.54894I
b = 0.75841 + 1.43263I
−4.99862 + 3.16468I −14.6216 − 8.5416I
u = −0.500509 − 0.765670I
a = −1.83740 + 0.54894I
b = 0.75841 − 1.43263I
−4.99862 − 3.16468I −14.6216 + 8.5416I
u = 0.034645 + 0.884579I
a = 0.286455 + 0.321976I
b = −1.59579 + 0.20592I
−9.60436 + 7.44720I −1.12455 − 5.22316I
u = 0.034645 − 0.884579I
a = 0.286455 − 0.321976I
b = −1.59579 − 0.20592I
−9.60436 − 7.44720I −1.12455 + 5.22316I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.544528 + 1.008840I
a = 0.813613 − 0.130165I
b = 0.488628 − 0.533810I
−6.88275 + 2.17208I 0
u = −0.544528 − 1.008840I
a = 0.813613 + 0.130165I
b = 0.488628 + 0.533810I
−6.88275 − 2.17208I 0
u = −0.318234 + 1.129480I
a = −0.32972 − 1.56989I
b = −0.46348 + 1.86984I
−3.89674 + 0.34222I 0
u = −0.318234 − 1.129480I
a = −0.32972 + 1.56989I
b = −0.46348 − 1.86984I
−3.89674 − 0.34222I 0
u = −0.378871 + 0.636122I
a = −2.18887 + 0.97531I
b = 0.262076 − 0.282529I
−10.56020 − 6.42506I 0.29601 + 1.69572I
u = −0.378871 − 0.636122I
a = −2.18887 − 0.97531I
b = 0.262076 + 0.282529I
−10.56020 + 6.42506I 0.29601 − 1.69572I
u = 0.596985 + 0.415802I
a = 0.630468 + 0.640731I
b = 0.421600 + 0.581478I
−1.70945 − 1.35880I 2.24467 + 5.29357I
u = 0.596985 − 0.415802I
a = 0.630468 − 0.640731I
b = 0.421600 − 0.581478I
−1.70945 + 1.35880I 2.24467 − 5.29357I
u = −1.295930 + 0.133460I
a = −0.279441 + 0.102123I
b = 0.068794 − 0.818384I
−1.99077 + 4.39001I 0
u = −1.295930 − 0.133460I
a = −0.279441 − 0.102123I
b = 0.068794 + 0.818384I
−1.99077 − 4.39001I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.540732 + 0.427519I
a = 0.760586 + 0.277873I
b = 1.34981 − 0.58688I
−8.08596 + 1.79714I 2.34826 − 0.92148I
u = −0.540732 − 0.427519I
a = 0.760586 − 0.277873I
b = 1.34981 + 0.58688I
−8.08596 − 1.79714I 2.34826 + 0.92148I
u = 0.345641 + 0.471474I
a = 1.388840 − 0.024076I
b = 0.015962 − 0.605849I
−4.31256 + 2.44729I 0.28400 − 3.32996I
u = 0.345641 − 0.471474I
a = 1.388840 + 0.024076I
b = 0.015962 + 0.605849I
−4.31256 − 2.44729I 0.28400 + 3.32996I
u = −1.29147 + 0.58402I
a = 0.565494 − 0.060409I
b = 0.438216 − 0.286617I
−7.55798 + 1.00360I 0
u = −1.29147 − 0.58402I
a = 0.565494 + 0.060409I
b = 0.438216 + 0.286617I
−7.55798 − 1.00360I 0
u = 0.05414 + 1.42407I
a = −0.319172 + 1.234000I
b = −0.01533 − 1.75620I
6.16440 + 0.67247I 0
u = 0.05414 − 1.42407I
a = −0.319172 − 1.234000I
b = −0.01533 + 1.75620I
6.16440 − 0.67247I 0
u = −0.298967 + 0.388601I
a = 1.068600 + 0.374239I
b = −0.238474 + 0.258177I
1.029620 − 0.495284I 8.01687 + 2.31808I
u = −0.298967 − 0.388601I
a = 1.068600 − 0.374239I
b = −0.238474 − 0.258177I
1.029620 + 0.495284I 8.01687 − 2.31808I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.32296 + 1.49533I
a = −0.014077 + 1.294100I
b = −0.62950 − 1.74634I
4.16311 − 5.16210I 0
u = 0.32296 − 1.49533I
a = −0.014077 − 1.294100I
b = −0.62950 + 1.74634I
4.16311 + 5.16210I 0
u = 1.53276 + 0.02218I
a = −0.430876 + 0.228519I
b = 0.008534 − 0.918471I
−8.47818 + 7.22559I 0
u = 1.53276 − 0.02218I
a = −0.430876 − 0.228519I
b = 0.008534 + 0.918471I
−8.47818 − 7.22559I 0
u = 0.160181 + 0.387104I
a = −3.57956 − 1.20981I
b = 0.505995 + 0.337305I
−3.56642 + 2.79917I 3.42811 − 0.46170I
u = 0.160181 − 0.387104I
a = −3.57956 + 1.20981I
b = 0.505995 − 0.337305I
−3.56642 − 2.79917I 3.42811 + 0.46170I
u = 0.206989 + 0.338042I
a = 1.055210 − 0.169889I
b = 0.929185 + 0.315681I
−1.68988 − 0.84367I −1.15133 − 2.48572I
u = 0.206989 − 0.338042I
a = 1.055210 + 0.169889I
b = 0.929185 − 0.315681I
−1.68988 + 0.84367I −1.15133 + 2.48572I
u = −0.53294 + 1.53814I
a = 0.207126 + 0.755558I
b = 0.57668 − 1.68015I
−3.90465 + 5.68518I 0
u = −0.53294 − 1.53814I
a = 0.207126 − 0.755558I
b = 0.57668 + 1.68015I
−3.90465 − 5.68518I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.34251 + 1.60989I
a = 0.257663 − 1.104060I
b = 0.313142 + 1.134510I
−0.04200 + 2.46645I 0
u = −0.34251 − 1.60989I
a = 0.257663 + 1.104060I
b = 0.313142 − 1.134510I
−0.04200 − 2.46645I 0
u = 0.37318 + 1.63255I
a = 0.196758 − 0.879828I
b = 0.39480 + 1.54627I
2.93179 − 4.03578I 0
u = 0.37318 − 1.63255I
a = 0.196758 + 0.879828I
b = 0.39480 − 1.54627I
2.93179 + 4.03578I 0
u = 0.07899 + 1.69652I
a = −0.205758 − 1.016470I
b = 0.04852 + 1.75392I
7.60928 − 4.45168I 0
u = 0.07899 − 1.69652I
a = −0.205758 + 1.016470I
b = 0.04852 − 1.75392I
7.60928 + 4.45168I 0
u = −0.48846 + 1.64668I
a = −0.076786 − 1.162360I
b = −0.55112 + 1.73815I
4.09640 + 10.99650I 0
u = −0.48846 − 1.64668I
a = −0.076786 + 1.162360I
b = −0.55112 − 1.73815I
4.09640 − 10.99650I 0
u = 0.95133 + 1.45075I
a = 0.334549 − 1.088470I
b = 0.08628 + 1.49845I
−0.33304 − 4.22189I 0
u = 0.95133 − 1.45075I
a = 0.334549 + 1.088470I
b = 0.08628 − 1.49845I
−0.33304 + 4.22189I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.67460 + 1.61393I
a = 0.214492 + 1.072810I
b = 0.09563 − 1.53472I
5.14342 + 3.33363I 0
u = −0.67460 − 1.61393I
a = 0.214492 − 1.072810I
b = 0.09563 + 1.53472I
5.14342 − 3.33363I 0
u = −0.05843 + 1.75203I
a = 0.238224 + 0.996234I
b = 0.301077 − 1.305630I
4.54407 + 0.89244I 0
u = −0.05843 − 1.75203I
a = 0.238224 − 0.996234I
b = 0.301077 + 1.305630I
4.54407 − 0.89244I 0
u = 0.64109 + 1.69574I
a = −0.124519 + 1.104800I
b = −0.52332 − 1.76203I
−2.9040 − 15.1991I 0
u = 0.64109 − 1.69574I
a = −0.124519 − 1.104800I
b = −0.52332 + 1.76203I
−2.9040 + 15.1991I 0
u = −0.18386 + 1.88121I
a = −0.161769 + 0.888934I
b = 0.08443 − 1.80565I
1.96683 + 7.20981I 0
u = −0.18386 − 1.88121I
a = −0.161769 − 0.888934I
b = 0.08443 + 1.80565I
1.96683 − 7.20981I 0
u = 0.52803 + 1.98863I
a = 0.197232 − 0.978791I
b = 0.11327 + 1.46699I
1.77020 − 3.01560I 0
u = 0.52803 − 1.98863I
a = 0.197232 + 0.978791I
b = 0.11327 − 1.46699I
1.77020 + 3.01560I 0
10
II.
I
u
2
= h3.06 × 10
7
u
15
− 5.46 × 10
7
u
14
+ · · · + 3.39 × 10
8
b + 3.42 × 10
8
, −3.13 ×
10
8
u
15
+3.42×10
8
u
14
+· · · +3.39×10
8
a−4.48×10
8
, u
16
−u
15
+· · · −4u
2
+1i
(i) Arc colorings
a
2
=
1
0
a
11
=
0
u
a
3
=
1
u
2
a
7
=
0.922728u
15
− 1.00823u
14
+ ··· + 1.66385u + 1.32124
−0.0902279u
15
+ 0.161065u
14
+ ··· + 0.181578u − 1.00781
a
4
=
−0.832500u
15
+ 0.847165u
14
+ ··· − 1.84543u + 1.68657
0.402236u
15
− 0.549776u
14
+ ··· − 0.832500u + 1.01467
a
1
=
−0.555116u
15
+ 0.977164u
14
+ ··· + 4.61473u − 2.80921
−0.661929u
15
+ 1.03099u
14
+ ··· + 1.18736u − 0.951848
a
6
=
0.832500u
15
− 0.847165u
14
+ ··· + 1.84543u + 0.313430
−0.0902279u
15
+ 0.161065u
14
+ ··· + 0.181578u − 1.00781
a
5
=
0.832500u
15
− 0.847165u
14
+ ··· + 1.84543u + 0.313430
0.312008u
15
− 0.388710u
14
+ ··· − 0.650922u − 0.993145
a
12
=
1.94577u
15
− 2.42341u
14
+ ··· − 7.34438u + 0.702070
0.0154462u
15
− 0.545396u
14
+ ··· − 1.25235u + 0.998126
a
10
=
−1.92294u
15
+ 1.59142u
14
+ ··· + 5.80143u + 0.319406
−0.0848705u
15
+ 0.506614u
14
+ ··· + 2.23637u − 0.500984
a
9
=
−2.00781u
15
+ 2.09804u
14
+ ··· + 8.03780u − 0.181578
−0.0848705u
15
+ 0.506614u
14
+ ··· + 2.23637u − 0.500984
a
8
=
−1.32494u
15
+ 2.35544u
14
+ ··· + 3.78101u − 0.969814
0.286898u
15
− 0.131334u
14
+ ··· − 1.86529u + 0.366755
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1384808610
339075961
u
15
−
1263687753
339075961
u
14
+ ··· +
226684056
339075961
u −
2103842549
339075961
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− 7u
15
+ ··· − 3u + 1
c
2
u
16
− u
15
+ ··· − 4u
2
+ 1
c
3
u
16
+ 5u
15
+ ··· + 7u + 1
c
4
u
16
+ 2u
14
+ ··· + 4u + 1
c
5
u
16
− u
15
+ ··· + 8u + 8
c
6
u
16
+ 2u
15
+ ··· + 2u + 4
c
7
, c
8
u
16
− u
15
+ ··· + 2u + 1
c
9
u
16
+ 3u
15
+ ··· − 12u
2
+ 8
c
10
u
16
+ 4u
15
+ ··· + 7u + 1
c
11
u
16
+ u
15
+ ··· − 8u + 8
c
12
u
16
+ u
15
+ ··· − 2u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
+ y
15
+ ··· + 5y + 1
c
2
y
16
+ 9y
15
+ ··· − 8y + 1
c
3
y
16
− 13y
15
+ ··· − 43y + 1
c
4
y
16
+ 4y
15
+ ··· + 4y + 1
c
5
, c
11
y
16
+ 13y
15
+ ··· + 512y + 64
c
6
y
16
+ 6y
15
+ ··· − 92y + 16
c
7
, c
8
, c
12
y
16
+ 19y
15
+ ··· + 20y + 1
c
9
y
16
− 3y
15
+ ··· − 192y + 64
c
10
y
16
− 8y
15
+ ··· − 5y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.589845 + 0.800240I
a = 1.285810 − 0.335799I
b = −0.279376 + 1.265590I
−4.55161 − 2.96740I 1.92397 + 1.31396I
u = 0.589845 − 0.800240I
a = 1.285810 + 0.335799I
b = −0.279376 − 1.265590I
−4.55161 + 2.96740I 1.92397 − 1.31396I
u = −0.792730 + 0.515500I
a = 0.392996 − 0.239529I
b = 0.680353 − 0.403757I
−2.25688 + 1.35793I −13.7316 − 4.6930I
u = −0.792730 − 0.515500I
a = 0.392996 + 0.239529I
b = 0.680353 + 0.403757I
−2.25688 − 1.35793I −13.7316 + 4.6930I
u = 0.981379 + 0.390494I
a = 0.332946 + 0.042006I
b = 1.177310 + 0.586123I
−8.66211 − 1.81322I −12.67811 + 2.30723I
u = 0.981379 − 0.390494I
a = 0.332946 − 0.042006I
b = 1.177310 − 0.586123I
−8.66211 + 1.81322I −12.67811 − 2.30723I
u = −0.466983 + 0.965367I
a = −0.199192 − 0.619672I
b = 0.834189 + 0.461021I
−2.00166 + 2.21071I −4.71974 − 0.56575I
u = −0.466983 − 0.965367I
a = −0.199192 + 0.619672I
b = 0.834189 − 0.461021I
−2.00166 − 2.21071I −4.71974 + 0.56575I
u = −0.514231 + 0.162757I
a = −0.45194 + 2.42387I
b = −0.851422 − 0.181708I
−11.46830 − 6.99777I −7.06193 + 5.14068I
u = −0.514231 − 0.162757I
a = −0.45194 − 2.42387I
b = −0.851422 + 0.181708I
−11.46830 + 6.99777I −7.06193 − 5.14068I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.448216 + 0.292274I
a = 1.86115 + 1.85868I
b = −0.755540 + 0.212836I
−4.03868 − 3.30271I −5.15759 + 8.58149I
u = 0.448216 − 0.292274I
a = 1.86115 − 1.85868I
b = −0.755540 − 0.212836I
−4.03868 + 3.30271I −5.15759 − 8.58149I
u = −0.48663 + 1.59176I
a = 0.174458 + 1.123490I
b = 0.16570 − 1.57601I
5.02030 + 2.85883I 1.98205 + 2.55647I
u = −0.48663 − 1.59176I
a = 0.174458 − 1.123490I
b = 0.16570 + 1.57601I
5.02030 − 2.85883I 1.98205 − 2.55647I
u = 0.74113 + 1.80908I
a = 0.103771 − 1.009800I
b = 0.02879 + 1.43665I
1.63996 − 4.08509I 2.94294 + 6.31121I
u = 0.74113 − 1.80908I
a = 0.103771 + 1.009800I
b = 0.02879 − 1.43665I
1.63996 + 4.08509I 2.94294 − 6.31121I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
16
− 7u
15
+ ··· − 3u + 1)(u
60
− 8u
59
+ ··· − 27u + 1)
c
2
(u
16
− u
15
+ ··· − 4u
2
+ 1)(u
60
+ 31u
58
+ ··· + 6806u + 3049)
c
3
(u
16
+ 5u
15
+ ··· + 7u + 1)(u
60
− 4u
58
+ ··· + 905u + 79)
c
4
(u
16
+ 2u
14
+ ··· + 4u + 1)(u
60
+ 3u
59
+ ··· + 6612u + 977)
c
5
(u
16
− u
15
+ ··· + 8u + 8)(u
60
+ 19u
58
+ ··· + 1808u + 136)
c
6
(u
16
+ 2u
15
+ ··· + 2u + 4)(u
60
+ 3u
59
+ ··· + 5062u + 484)
c
7
, c
8
(u
16
− u
15
+ ··· + 2u + 1)(u
60
− 2u
59
+ ··· + 12u + 1)
c
9
(u
16
+ 3u
15
+ ··· − 12u
2
+ 8)(u
60
− 4u
59
+ ··· + 232u + 8)
c
10
(u
16
+ 4u
15
+ ··· + 7u + 1)(u
60
+ 3u
59
+ ··· + 1069u + 541)
c
11
(u
16
+ u
15
+ ··· − 8u + 8)(u
60
+ 19u
58
+ ··· + 1808u + 136)
c
12
(u
16
+ u
15
+ ··· − 2u + 1)(u
60
− 2u
59
+ ··· + 12u + 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
16
+ y
15
+ ··· + 5y + 1)(y
60
+ 2y
59
+ ··· − 233y + 1)
c
2
(y
16
+ 9y
15
+ ··· − 8y + 1)
· (y
60
+ 62y
59
+ ··· + 271621986y + 9296401)
c
3
(y
16
− 13y
15
+ ··· − 43y + 1)(y
60
− 8y
59
+ ··· − 193345y + 6241)
c
4
(y
16
+ 4y
15
+ ··· + 4y + 1)(y
60
+ 21y
59
+ ··· + 1.83698 × 10
7
y + 954529)
c
5
, c
11
(y
16
+ 13y
15
+ ··· + 512y + 64)
· (y
60
+ 38y
59
+ ··· − 152832y + 18496)
c
6
(y
16
+ 6y
15
+ ··· − 92y + 16)
· (y
60
+ 63y
59
+ ··· + 4369636y + 234256)
c
7
, c
8
, c
12
(y
16
+ 19y
15
+ ··· + 20y + 1)(y
60
+ 64y
59
+ ··· − 6y + 1)
c
9
(y
16
− 3y
15
+ ··· − 192y + 64)(y
60
+ 14y
59
+ ··· + 2240y + 64)
c
10
(y
16
− 8y
15
+ ··· − 5y + 1)(y
60
− 75y
59
+ ··· − 4777199y + 292681)
17
