12a
1238
(K12a
1238
)
A knot diagram
1
Linearized knot diagam
5 6 9 1 10 11 12 3 4 2 7 8
Solving Sequence
1,4
5
2,9
10 6 11 3 8 12 7
c
4
c
1
c
9
c
5
c
10
c
3
c
8
c
12
c
7
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.62330 × 10
233
u
81
− 1.12307 × 10
233
u
80
+ ··· + 7.45191 × 10
232
b + 8.93587 × 10
234
,
− 1.56282 × 10
234
u
81
− 3.71971 × 10
233
u
80
+ ··· + 3.72595 × 10
233
a − 2.44109 × 10
236
,
u
82
− 29u
80
+ ··· + 580u + 25i
I
u
2
= h−57u
16
+ 139u
15
+ ··· + b + 105, 18u
16
− 43u
15
+ ··· + a − 24, u
17
− 3u
16
+ ··· − 3u + 1i
* 2 irreducible components of dim
C
= 0, with total 99 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
= h1.62 × 10
233
u
81
− 1.12 × 10
233
u
80
+ · · · + 7.45 × 10
232
b + 8.94 ×
10
234
, −1.56 × 10
234
u
81
− 3.72 × 10
233
u
80
+ · · · + 3.73 × 10
233
a − 2.44 ×
10
236
, u
82
− 29u
80
+ · · · + 580u + 25i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
2
=
−u
−u
3
+ u
a
9
=
4.19443u
81
+ 0.998323u
80
+ ··· + 12103.0u + 655.158
−2.17837u
81
+ 1.50709u
80
+ ··· − 2279.85u − 119.914
a
10
=
2.01606u
81
+ 2.50541u
80
+ ··· + 9823.13u + 535.245
−2.17837u
81
+ 1.50709u
80
+ ··· − 2279.85u − 119.914
a
6
=
4.65242u
81
− 1.59030u
80
+ ··· + 8732.87u + 474.826
−2.43795u
81
+ 1.31148u
80
+ ··· − 3819.62u − 208.334
a
11
=
3.51386u
81
+ 1.04832u
80
+ ··· + 10330.4u + 553.673
−2.43681u
81
+ 1.96106u
80
+ ··· − 1979.41u − 101.915
a
3
=
−7.59176u
81
+ 2.77225u
80
+ ··· − 13921.6u − 746.885
0.100451u
81
+ 0.634586u
80
+ ··· + 2030.94u + 123.163
a
8
=
4.09643u
81
− 2.86268u
80
+ ··· + 2668.54u + 89.1960
3.37277u
81
− 1.62221u
80
+ ··· + 4955.44u + 259.192
a
12
=
2.14385u
81
− 0.151279u
80
+ ··· + 4824.36u + 223.253
2.86534u
81
− 0.999373u
80
+ ··· + 5564.66u + 300.621
a
7
=
−4.86395u
81
+ 0.711191u
80
+ ··· − 10254.4u − 525.349
−2.54931u
81
+ 1.00523u
80
+ ··· − 4203.94u − 218.636
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.46764u
81
+ 2.98675u
80
+ ··· + 13265.8u + 747.283
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
82
− 29u
80
+ ··· + 580u + 25
c
2
u
82
− 5u
81
+ ··· + 2079u + 931
c
3
, c
8
, c
9
u
82
− u
81
+ ··· + 181u + 173
c
5
u
82
+ 2u
81
+ ··· + 17u − 1
c
6
, c
7
, c
11
c
12
u
82
− u
81
+ ··· − 79u − 7
c
10
u
82
+ 2u
81
+ ··· − 3884u + 1867
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
82
− 58y
81
+ ··· − 62350y + 625
c
2
y
82
+ 15y
81
+ ··· + 9331805y + 866761
c
3
, c
8
, c
9
y
82
− 77y
81
+ ··· + 235043y + 29929
c
5
y
82
+ 64y
80
+ ··· − 209y + 1
c
6
, c
7
, c
11
c
12
y
82
− 101y
81
+ ··· − 2405y + 49
c
10
y
82
− 34y
81
+ ··· − 204854804y + 3485689
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.934521 + 0.347459I
a = 0.256869 − 0.427602I
b = 0.366312 − 0.532440I
−1.56095 + 1.32976I 0
u = −0.934521 − 0.347459I
a = 0.256869 + 0.427602I
b = 0.366312 + 0.532440I
−1.56095 − 1.32976I 0
u = −0.985856 + 0.133508I
a = 1.42926 − 1.69263I
b = −1.338240 − 0.226304I
−0.18186 + 2.94088I 0
u = −0.985856 − 0.133508I
a = 1.42926 + 1.69263I
b = −1.338240 + 0.226304I
−0.18186 − 2.94088I 0
u = 0.680966 + 0.774466I
a = −1.285520 − 0.554886I
b = 1.343090 + 0.338900I
−3.26211 + 2.41526I 0
u = 0.680966 − 0.774466I
a = −1.285520 + 0.554886I
b = 1.343090 − 0.338900I
−3.26211 − 2.41526I 0
u = 0.943857
a = 1.46985
b = −1.84151
−0.856208 0
u = 0.000750 + 0.932894I
a = −1.87427 − 0.30470I
b = 1.45322 − 0.06591I
7.14647 − 2.26483I 0
u = 0.000750 − 0.932894I
a = −1.87427 + 0.30470I
b = 1.45322 + 0.06591I
7.14647 + 2.26483I 0
u = −1.066400 + 0.200953I
a = −1.82922 + 1.16741I
b = 1.46675 + 0.30221I
−7.87907 + 6.39586I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.066400 − 0.200953I
a = −1.82922 − 1.16741I
b = 1.46675 − 0.30221I
−7.87907 − 6.39586I 0
u = −0.738427 + 0.486038I
a = −0.819329 + 0.132184I
b = −0.131483 + 0.984194I
−7.99328 + 2.08374I 0
u = −0.738427 − 0.486038I
a = −0.819329 − 0.132184I
b = −0.131483 − 0.984194I
−7.99328 − 2.08374I 0
u = 0.937847 + 0.605715I
a = 1.39663 + 1.28141I
b = −1.35817 + 0.50981I
−4.06787 − 7.61264I 0
u = 0.937847 − 0.605715I
a = 1.39663 − 1.28141I
b = −1.35817 − 0.50981I
−4.06787 + 7.61264I 0
u = −0.164401 + 1.104770I
a = −0.068114 + 0.588364I
b = −0.219137 − 0.621589I
−8.99433 + 5.16744I 0
u = −0.164401 − 1.104770I
a = −0.068114 − 0.588364I
b = −0.219137 + 0.621589I
−8.99433 − 5.16744I 0
u = −1.086900 + 0.269679I
a = 0.334063 + 0.325688I
b = −0.863302 + 0.735990I
−3.51083 + 2.83032I 0
u = −1.086900 − 0.269679I
a = 0.334063 − 0.325688I
b = −0.863302 − 0.735990I
−3.51083 − 2.83032I 0
u = 0.991470 + 0.534374I
a = −1.08848 − 1.20120I
b = 1.362720 − 0.373905I
3.12917 − 5.58769I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.991470 − 0.534374I
a = −1.08848 + 1.20120I
b = 1.362720 + 0.373905I
3.12917 + 5.58769I 0
u = −0.868419 + 0.092461I
a = −0.59650 + 2.11772I
b = 1.190840 + 0.094481I
0.28543 − 1.79070I 0
u = −0.868419 − 0.092461I
a = −0.59650 − 2.11772I
b = 1.190840 − 0.094481I
0.28543 + 1.79070I 0
u = −0.102526 + 0.849065I
a = −0.034516 − 0.292271I
b = 0.351504 + 0.471570I
−0.90967 + 3.66182I 0
u = −0.102526 − 0.849065I
a = −0.034516 + 0.292271I
b = 0.351504 − 0.471570I
−0.90967 − 3.66182I 0
u = 1.081370 + 0.424377I
a = 0.745037 + 0.932264I
b = −1.384510 + 0.245822I
3.77253 − 2.11296I 0
u = 1.081370 − 0.424377I
a = 0.745037 − 0.932264I
b = −1.384510 − 0.245822I
3.77253 + 2.11296I 0
u = 0.465567 + 0.689784I
a = 1.41558 + 0.55639I
b = −1.43484 − 0.12440I
4.60977 + 0.87355I 0
u = 0.465567 − 0.689784I
a = 1.41558 − 0.55639I
b = −1.43484 + 0.12440I
4.60977 − 0.87355I 0
u = −0.792665 + 0.196482I
a = 0.373105 − 0.661464I
b = 0.071568 − 0.766823I
−1.11360 + 1.22701I 0. − 4.63087I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.792665 − 0.196482I
a = 0.373105 + 0.661464I
b = 0.071568 + 0.766823I
−1.11360 − 1.22701I 0. + 4.63087I
u = 1.19140
a = −0.259535
b = 1.41908
−1.56818 0
u = 0.807827
a = −1.35683
b = 0.556755
−2.84786 1.78860
u = 1.194700 + 0.129051I
a = −0.531258 + 0.795686I
b = 0.095650 + 0.553160I
−4.75226 + 0.05742I 0
u = 1.194700 − 0.129051I
a = −0.531258 − 0.795686I
b = 0.095650 − 0.553160I
−4.75226 − 0.05742I 0
u = 1.166270 + 0.321488I
a = −0.153610 − 0.853500I
b = 0.225832 − 0.623122I
−2.23682 − 4.25562I 0
u = 1.166270 − 0.321488I
a = −0.153610 + 0.853500I
b = 0.225832 + 0.623122I
−2.23682 + 4.25562I 0
u = −1.208780 + 0.276098I
a = −0.584063 − 0.090912I
b = 1.013600 − 0.893633I
−11.84370 + 4.09765I 0
u = −1.208780 − 0.276098I
a = −0.584063 + 0.090912I
b = 1.013600 + 0.893633I
−11.84370 − 4.09765I 0
u = −0.093132 + 1.252800I
a = 1.78653 − 0.00049I
b = −1.41648 + 0.17073I
4.74746 − 6.03651I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.093132 − 1.252800I
a = 1.78653 + 0.00049I
b = −1.41648 − 0.17073I
4.74746 + 6.03651I 0
u = 0.728476
a = −1.20443
b = 1.71906
6.36750 −14.0750
u = 0.887021 + 0.912615I
a = 1.79799 + 1.13995I
b = −1.188290 − 0.136424I
−6.29540 − 2.57592I 0
u = 0.887021 − 0.912615I
a = 1.79799 − 1.13995I
b = −1.188290 + 0.136424I
−6.29540 + 2.57592I 0
u = −0.698988 + 0.129902I
a = −0.18085 − 2.88076I
b = −1.144550 + 0.136710I
−6.50500 − 4.75604I −7.37990 + 2.43004I
u = −0.698988 − 0.129902I
a = −0.18085 + 2.88076I
b = −1.144550 − 0.136710I
−6.50500 + 4.75604I −7.37990 − 2.43004I
u = 1.027950 + 0.833407I
a = −1.64501 − 0.95974I
b = 1.235600 − 0.062510I
0.88385 − 3.01527I 0
u = 1.027950 − 0.833407I
a = −1.64501 + 0.95974I
b = 1.235600 + 0.062510I
0.88385 + 3.01527I 0
u = 1.266880 + 0.432843I
a = 0.403243 + 0.462038I
b = −0.342569 + 0.861570I
−4.98259 − 8.18738I 0
u = 1.266880 − 0.432843I
a = 0.403243 − 0.462038I
b = −0.342569 − 0.861570I
−4.98259 + 8.18738I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.343210 + 0.002023I
a = 0.758946 + 0.291628I
b = −0.377797 + 0.711575I
−13.80490 − 2.62993I 0
u = 1.343210 − 0.002023I
a = 0.758946 − 0.291628I
b = −0.377797 − 0.711575I
−13.80490 + 2.62993I 0
u = −1.295940 + 0.436278I
a = −0.371872 + 0.202924I
b = 0.182700 + 0.498660I
−4.55328 + 1.51053I 0
u = −1.295940 − 0.436278I
a = −0.371872 − 0.202924I
b = 0.182700 − 0.498660I
−4.55328 − 1.51053I 0
u = 1.43015
a = −0.634353
b = 1.32243
−1.52558 0
u = 1.35007 + 0.48468I
a = −0.467441 − 0.197285I
b = 0.361745 − 1.034720I
−13.6514 − 10.5493I 0
u = 1.35007 − 0.48468I
a = −0.467441 + 0.197285I
b = 0.361745 + 1.034720I
−13.6514 + 10.5493I 0
u = −1.35585 + 0.50291I
a = 0.848857 − 1.108750I
b = −1.387010 − 0.256622I
2.90248 + 7.50413I 0
u = −1.35585 − 0.50291I
a = 0.848857 + 1.108750I
b = −1.387010 + 0.256622I
2.90248 − 7.50413I 0
u = −1.42649 + 0.32907I
a = −0.303670 + 0.877231I
b = 1.281450 + 0.170102I
−1.06903 + 2.42900I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42649 − 0.32907I
a = −0.303670 − 0.877231I
b = 1.281450 − 0.170102I
−1.06903 − 2.42900I 0
u = 0.107130 + 0.515113I
a = 0.478221 − 0.232915I
b = −0.480551 − 0.311322I
0.836840 + 0.981184I 3.21796 − 3.18238I
u = 0.107130 − 0.515113I
a = 0.478221 + 0.232915I
b = −0.480551 + 0.311322I
0.836840 − 0.981184I 3.21796 + 3.18238I
u = 1.21664 + 0.84263I
a = 1.66419 + 0.65205I
b = −1.376890 + 0.199175I
0.44389 − 4.10272I 0
u = 1.21664 − 0.84263I
a = 1.66419 − 0.65205I
b = −1.376890 − 0.199175I
0.44389 + 4.10272I 0
u = −0.18740 + 1.47187I
a = −1.71372 + 0.17580I
b = 1.386330 − 0.259259I
−3.87177 − 8.43053I 0
u = −0.18740 − 1.47187I
a = −1.71372 − 0.17580I
b = 1.386330 + 0.259259I
−3.87177 + 8.43053I 0
u = −1.36890 + 0.61647I
a = −1.17582 + 0.99420I
b = 1.44888 + 0.34016I
0.71934 + 12.51550I 0
u = −1.36890 − 0.61647I
a = −1.17582 − 0.99420I
b = 1.44888 − 0.34016I
0.71934 − 12.51550I 0
u = −1.39571 + 0.69298I
a = 1.36270 − 0.85917I
b = −1.49254 − 0.41405I
−7.7647 + 15.7366I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.39571 − 0.69298I
a = 1.36270 + 0.85917I
b = −1.49254 + 0.41405I
−7.7647 − 15.7366I 0
u = 1.31553 + 0.88818I
a = −1.76649 − 0.51065I
b = 1.47035 − 0.26304I
−7.36965 − 4.81620I 0
u = 1.31553 − 0.88818I
a = −1.76649 + 0.51065I
b = 1.47035 + 0.26304I
−7.36965 + 4.81620I 0
u = −1.53840 + 0.46979I
a = 0.486909 − 0.045020I
b = −0.427428 − 0.623833I
−13.46780 + 1.47338I 0
u = −1.53840 − 0.46979I
a = 0.486909 + 0.045020I
b = −0.427428 + 0.623833I
−13.46780 − 1.47338I 0
u = −0.242978 + 0.057112I
a = −3.75188 − 3.47217I
b = −0.402691 − 0.642389I
−8.57778 − 2.10932I −7.06076 − 4.05023I
u = −0.242978 − 0.057112I
a = −3.75188 + 3.47217I
b = −0.402691 + 0.642389I
−8.57778 + 2.10932I −7.06076 + 4.05023I
u = −1.75946
a = 0.319097
b = −1.09179
−12.7835 0
u = −0.174156 + 0.108446I
a = 1.11542 + 3.03605I
b = 0.284389 + 0.455864I
−1.125760 − 0.792790I −5.63857 + 0.46918I
u = −0.174156 − 0.108446I
a = 1.11542 − 3.03605I
b = 0.284389 − 0.455864I
−1.125760 + 0.792790I −5.63857 − 0.46918I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.182672
a = 5.86792
b = −1.54836
4.17983 4.89490
u = 2.22736
a = 0.974429
b = −1.18778
−12.0641 0
13
II. I
u
2
= h−57u
16
+ 139u
15
+ · · · + b + 105, 18u
16
− 43u
15
+ · · · + a −
24, u
17
− 3u
16
+ · · · − 3u + 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
2
=
−u
−u
3
+ u
a
9
=
−18u
16
+ 43u
15
+ ··· − 35u + 24
57u
16
− 139u
15
+ ··· + 124u − 105
a
10
=
39u
16
− 96u
15
+ ··· + 89u − 81
57u
16
− 139u
15
+ ··· + 124u − 105
a
6
=
−u
16
+ 10u
14
+ ··· − 4u − 7
u
16
− 2u
15
+ ··· + u − 2
a
11
=
14u
16
− 35u
15
+ ··· + 31u − 33
74u
16
− 180u
15
+ ··· + 165u − 139
a
3
=
−10u
16
+ 28u
15
+ ··· − 12u + 26
−u
16
+ 3u
15
+ ··· + 4u + 4
a
8
=
−33u
16
+ 85u
15
+ ··· − 62u + 68
−105u
16
+ 258u
15
+ ··· − 217u + 191
a
12
=
−62u
16
+ 152u
15
+ ··· − 127u + 120
−26u
16
+ 68u
15
+ ··· − 48u + 67
a
7
=
33u
16
− 85u
15
+ ··· + 62u − 69
18u
16
− 49u
15
+ ··· + 21u − 42
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 279u
16
− 670u
15
− 1521u
14
+ 4682u
13
+ 1978u
12
− 12842u
11
+ 2106u
10
+ 18722u
9
−
9032u
8
− 16445u
7
+ 11324u
6
+ 8791u
5
− 8052u
4
− 3132u
3
+ 2975u
2
+ 642u − 489
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
+ 3u
16
+ ··· − 3u − 1
c
2
u
17
− 3u
14
+ ··· − 2u + 1
c
3
u
17
− 10u
15
+ ··· + 2u − 1
c
4
u
17
− 3u
16
+ ··· − 3u + 1
c
5
u
17
+ u
16
+ ··· + 2u
3
+ 1
c
6
, c
7
u
17
− 12u
15
+ ··· + 2u + 1
c
8
, c
9
u
17
− 10u
15
+ ··· + 2u + 1
c
10
u
17
+ 3u
16
+ ··· − 3u − 1
c
11
, c
12
u
17
− 12u
15
+ ··· + 2u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
17
− 17y
16
+ ··· + 17y −1
c
2
y
17
− 12y
15
+ ··· − 6y −1
c
3
, c
8
, c
9
y
17
− 20y
16
+ ··· + 12y −1
c
5
y
17
− 3y
16
+ ··· + 6y
2
− 1
c
6
, c
7
, c
11
c
12
y
17
− 24y
16
+ ··· + 24y −1
c
10
y
17
− 9y
16
+ ··· + 11y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.671622 + 0.694992I
a = −2.66663 − 0.87339I
b = 1.340170 − 0.277588I
−5.47381 − 6.16611I −4.47218 + 5.21995I
u = 0.671622 − 0.694992I
a = −2.66663 + 0.87339I
b = 1.340170 + 0.277588I
−5.47381 + 6.16611I −4.47218 − 5.21995I
u = −0.820990 + 0.307027I
a = −0.609243 + 0.729341I
b = −0.410410 + 0.486858I
−1.85299 + 1.83764I −10.22921 − 7.07662I
u = −0.820990 − 0.307027I
a = −0.609243 − 0.729341I
b = −0.410410 − 0.486858I
−1.85299 − 1.83764I −10.22921 + 7.07662I
u = −1.111800 + 0.192631I
a = −0.592249 − 0.482310I
b = 0.402589 − 0.187905I
−3.71820 + 0.31253I −7.35969 − 1.39651I
u = −1.111800 − 0.192631I
a = −0.592249 + 0.482310I
b = 0.402589 + 0.187905I
−3.71820 − 0.31253I −7.35969 + 1.39651I
u = 0.973005 + 0.667865I
a = 1.82110 + 1.10902I
b = −1.315980 + 0.182191I
1.52051 − 4.20124I −0.29072 + 6.76546I
u = 0.973005 − 0.667865I
a = 1.82110 − 1.10902I
b = −1.315980 − 0.182191I
1.52051 + 4.20124I −0.29072 − 6.76546I
u = −0.662661 + 0.322036I
a = 1.65111 − 0.63989I
b = 0.454005 − 0.653361I
−8.81272 + 2.78715I −10.84432 − 5.92009I
u = −0.662661 − 0.322036I
a = 1.65111 + 0.63989I
b = 0.454005 + 0.653361I
−8.81272 − 2.78715I −10.84432 + 5.92009I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.663836
a = 2.25446
b = −1.58316
3.65134 −10.8550
u = 0.557324
a = −0.640649
b = 1.67161
6.66575 13.2870
u = 1.39919 + 0.47372I
a = −0.775209 − 0.874913I
b = 1.283880 − 0.084545I
−0.54538 − 1.32796I −3.55104 + 0.18556I
u = 1.39919 − 0.47372I
a = −0.775209 + 0.874913I
b = 1.283880 + 0.084545I
−0.54538 + 1.32796I −3.55104 − 0.18556I
u = 0.496618
a = −0.662890
b = −1.73598
0.265606 1.03910
u = −1.71714
a = 0.620217
b = −0.646248
−13.8143 −13.8510
u = 2.10262
a = 0.771100
b = −1.21474
−11.6411 4.87440
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
17
+ 3u
16
+ ··· − 3u − 1)(u
82
− 29u
80
+ ··· + 580u + 25)
c
2
(u
17
− 3u
14
+ ··· − 2u + 1)(u
82
− 5u
81
+ ··· + 2079u + 931)
c
3
(u
17
− 10u
15
+ ··· + 2u − 1)(u
82
− u
81
+ ··· + 181u + 173)
c
4
(u
17
− 3u
16
+ ··· − 3u + 1)(u
82
− 29u
80
+ ··· + 580u + 25)
c
5
(u
17
+ u
16
+ ··· + 2u
3
+ 1)(u
82
+ 2u
81
+ ··· + 17u − 1)
c
6
, c
7
(u
17
− 12u
15
+ ··· + 2u + 1)(u
82
− u
81
+ ··· − 79u − 7)
c
8
, c
9
(u
17
− 10u
15
+ ··· + 2u + 1)(u
82
− u
81
+ ··· + 181u + 173)
c
10
(u
17
+ 3u
16
+ ··· − 3u − 1)(u
82
+ 2u
81
+ ··· − 3884u + 1867)
c
11
, c
12
(u
17
− 12u
15
+ ··· + 2u − 1)(u
82
− u
81
+ ··· − 79u − 7)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
17
− 17y
16
+ ··· + 17y −1)(y
82
− 58y
81
+ ··· − 62350y + 625)
c
2
(y
17
− 12y
15
+ ··· − 6y −1)(y
82
+ 15y
81
+ ··· + 9331805y + 866761)
c
3
, c
8
, c
9
(y
17
− 20y
16
+ ··· + 12y −1)(y
82
− 77y
81
+ ··· + 235043y + 29929)
c
5
(y
17
− 3y
16
+ ··· + 6y
2
− 1)(y
82
+ 64y
80
+ ··· − 209y + 1)
c
6
, c
7
, c
11
c
12
(y
17
− 24y
16
+ ··· + 24y −1)(y
82
− 101y
81
+ ··· − 2405y + 49)
c
10
(y
17
− 9y
16
+ ··· + 11y −1)
· (y
82
− 34y
81
+ ··· − 204854804y + 3485689)
20
