12a
1032
(K12a
1032
)
A knot diagram
1
Linearized knot diagam
4 7 8 10 11 3 2 12 1 6 5 9
Solving Sequence
3,6
7 2 8 4
1,11
5 12 10 9
c
6
c
2
c
7
c
3
c
1
c
5
c
11
c
10
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.13488 × 10
22
u
77
+ 6.96847 × 10
23
u
76
+ ··· + 1.38959 × 10
24
b + 9.38953 × 10
23
,
1.56764 × 10
24
u
77
+ 2.54331 × 10
24
u
76
+ ··· + 4.16876 × 10
24
a − 1.01501 × 10
25
, u
78
+ 2u
77
+ ··· − 3u − 3i
I
u
2
= hb, −u
2
+ a − 1, u
3
+ u
2
+ 2u + 1i
I
u
3
= hu
2
a − 2au + 3u
2
+ 5b − a − u + 2, −2u
2
a + a
2
+ 9u
2
− 2a − 7u + 18, u
3
− u
2
+ 2u − 1i
* 3 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
= h−5.13×10
22
u
77
+6.97×10
23
u
76
+· · ·+1.39×10
24
b+9.39×10
23
, 1.57×
10
24
u
77
+2.54×10
24
u
76
+· · ·+4.17×10
24
a−1.02×10
25
, u
78
+2u
77
+· · ·−3u−3i
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
2
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
4
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
1
=
u
9
+ 4u
7
+ 5u
5
+ 2u
3
+ u
u
11
+ 5u
9
+ 8u
7
+ 3u
5
− u
3
+ u
a
11
=
−0.376045u
77
− 0.610088u
76
+ ··· + 1.32049u + 2.43481
0.0369526u
77
− 0.501478u
76
+ ··· + 0.585143u − 0.675707
a
5
=
1.26294u
77
+ 2.25066u
76
+ ··· − 2.84986u − 1.41015
−0.307268u
77
− 0.831343u
76
+ ··· + 3.63374u + 0.384719
a
12
=
0.259199u
77
+ 0.274703u
76
+ ··· + 2.57149u − 0.449948
0.0447472u
77
+ 0.572456u
76
+ ··· − 1.87435u + 0.827634
a
10
=
−0.412998u
77
− 0.108610u
76
+ ··· + 0.735348u + 3.11052
0.0369526u
77
− 0.501478u
76
+ ··· + 0.585143u − 0.675707
a
9
=
−0.454996u
77
− 0.635848u
76
+ ··· + 2.02928u + 2.79107
−0.00885144u
77
− 0.531385u
76
+ ··· + 0.546815u − 0.805065
(ii) Obstruction class = −1
(iii) Cusp Shapes =
2155115887218372860035718
694792694815903195651135
u
77
+
4180801602356197336101919
694792694815903195651135
u
76
+ ··· +
9214508540967252021234482
694792694815903195651135
u −
2286501097268875425262962
694792694815903195651135
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
78
− 16u
77
+ ··· − 227379u + 30627
c
2
, c
6
, c
7
u
78
+ 2u
77
+ ··· − 3u − 3
c
3
u
78
− 2u
77
+ ··· − 1479u − 867
c
4
u
78
− u
77
+ ··· + 4032u + 3112
c
5
, c
10
, c
11
u
78
+ u
77
+ ··· − 32u
2
+ 8
c
8
, c
9
, c
12
u
78
− 4u
77
+ ··· − 108u − 17
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
78
+ 32y
77
+ ··· + 2934785691y + 938013129
c
2
, c
6
, c
7
y
78
+ 72y
77
+ ··· − 129y + 9
c
3
y
78
+ 8y
77
+ ··· + 5081487y + 751689
c
4
y
78
− 13y
77
+ ··· − 77550976y + 9684544
c
5
, c
10
, c
11
y
78
+ 71y
77
+ ··· − 512y + 64
c
8
, c
9
, c
12
y
78
− 74y
77
+ ··· + 5540y + 289
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.192957 + 1.111600I
a = 1.19779 + 2.02532I
b = −0.168435 + 1.396140I
−3.81969 − 3.89814I 0
u = 0.192957 − 1.111600I
a = 1.19779 − 2.02532I
b = −0.168435 − 1.396140I
−3.81969 + 3.89814I 0
u = 0.320913 + 1.119940I
a = −0.94949 − 2.09661I
b = 0.262940 − 1.340440I
1.05376 − 7.02286I 0
u = 0.320913 − 1.119940I
a = −0.94949 + 2.09661I
b = 0.262940 + 1.340440I
1.05376 + 7.02286I 0
u = −0.473389 + 0.686908I
a = 0.08281 − 1.56208I
b = 0.33298 − 1.38387I
2.38668 − 7.05623I 4.04957 + 2.76916I
u = −0.473389 − 0.686908I
a = 0.08281 + 1.56208I
b = 0.33298 + 1.38387I
2.38668 + 7.05623I 4.04957 − 2.76916I
u = −0.079678 + 1.178770I
a = 0.286269 − 0.635203I
b = −0.475807 − 0.361911I
1.71847 + 1.56145I 0
u = −0.079678 − 1.178770I
a = 0.286269 + 0.635203I
b = −0.475807 + 0.361911I
1.71847 − 1.56145I 0
u = −0.747048 + 0.324353I
a = 1.52805 − 2.73924I
b = −0.33672 − 1.41782I
1.11303 + 11.32630I 1.74011 − 7.84897I
u = −0.747048 − 0.324353I
a = 1.52805 + 2.73924I
b = −0.33672 + 1.41782I
1.11303 − 11.32630I 1.74011 + 7.84897I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.030969 + 1.197970I
a = −1.68028 − 1.82896I
b = 0.12649 − 1.43914I
−1.033450 − 0.444387I 0
u = 0.030969 − 1.197970I
a = −1.68028 + 1.82896I
b = 0.12649 + 1.43914I
−1.033450 + 0.444387I 0
u = 0.717522 + 0.354101I
a = −0.151776 + 1.187950I
b = −0.818337 + 0.262522I
6.45672 − 7.14735I 6.13824 + 6.79892I
u = 0.717522 − 0.354101I
a = −0.151776 − 1.187950I
b = −0.818337 − 0.262522I
6.45672 + 7.14735I 6.13824 − 6.79892I
u = 0.506406 + 0.609564I
a = 0.129930 − 0.090005I
b = 0.805112 + 0.201005I
7.40344 + 2.95162I 8.38298 − 0.93021I
u = 0.506406 − 0.609564I
a = 0.129930 + 0.090005I
b = 0.805112 − 0.201005I
7.40344 − 2.95162I 8.38298 + 0.93021I
u = 0.771376 + 0.082944I
a = −0.44711 − 3.10641I
b = −0.231533 − 1.297700I
−2.11544 + 3.03018I 0.27772 − 2.58777I
u = 0.771376 − 0.082944I
a = −0.44711 + 3.10641I
b = −0.231533 + 1.297700I
−2.11544 − 3.03018I 0.27772 + 2.58777I
u = −0.290042 + 1.206290I
a = 0.139811 + 0.526105I
b = 0.621955 + 0.111558I
5.66191 + 3.76271I 0
u = −0.290042 − 1.206290I
a = 0.139811 − 0.526105I
b = 0.621955 − 0.111558I
5.66191 − 3.76271I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.655866 + 0.382150I
a = −0.807968 + 0.893907I
b = −0.474927 + 0.866530I
4.52645 + 2.56217I 4.50484 − 2.46419I
u = −0.655866 − 0.382150I
a = −0.807968 − 0.893907I
b = −0.474927 − 0.866530I
4.52645 − 2.56217I 4.50484 + 2.46419I
u = −0.693288 + 0.304422I
a = −1.95436 + 2.45062I
b = 0.272595 + 1.371760I
−4.48416 + 7.09115I −2.04061 − 7.55095I
u = −0.693288 − 0.304422I
a = −1.95436 − 2.45062I
b = 0.272595 − 1.371760I
−4.48416 − 7.09115I −2.04061 + 7.55095I
u = −0.550306 + 0.508147I
a = −0.71523 + 1.43481I
b = 0.411750 + 0.974001I
5.00598 + 1.43831I 5.56279 − 3.99254I
u = −0.550306 − 0.508147I
a = −0.71523 − 1.43481I
b = 0.411750 − 0.974001I
5.00598 − 1.43831I 5.56279 + 3.99254I
u = −0.742831
a = −0.898304
b = −0.609293
1.96168 5.99100
u = 0.088144 + 1.269300I
a = −0.813357 + 0.841995I
b = 0.443490 + 0.349624I
4.80145 − 1.58760I 0
u = 0.088144 − 1.269300I
a = −0.813357 − 0.841995I
b = 0.443490 − 0.349624I
4.80145 + 1.58760I 0
u = 0.625985 + 0.307354I
a = −0.280689 − 1.134010I
b = 0.662399 − 0.196150I
0.48579 − 3.66760I 3.12377 + 7.79182I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.625985 − 0.307354I
a = −0.280689 + 1.134010I
b = 0.662399 + 0.196150I
0.48579 + 3.66760I 3.12377 − 7.79182I
u = −0.374022 + 0.584619I
a = 0.281584 + 1.126590I
b = −0.229914 + 1.337150I
−3.29505 − 3.31684I 0.37580 + 2.22795I
u = −0.374022 − 0.584619I
a = 0.281584 − 1.126590I
b = −0.229914 − 1.337150I
−3.29505 + 3.31684I 0.37580 − 2.22795I
u = 0.671062 + 0.114541I
a = 0.46437 + 3.46215I
b = 0.109881 + 1.399800I
−6.76019 + 0.61306I −7.17730 + 0.24747I
u = 0.671062 − 0.114541I
a = 0.46437 − 3.46215I
b = 0.109881 − 1.399800I
−6.76019 − 0.61306I −7.17730 − 0.24747I
u = −0.607811 + 0.306243I
a = 2.18924 − 1.51724I
b = −0.195606 − 1.287310I
−2.60345 + 2.27614I 0.75235 − 3.81852I
u = −0.607811 − 0.306243I
a = 2.18924 + 1.51724I
b = −0.195606 + 1.287310I
−2.60345 − 2.27614I 0.75235 + 3.81852I
u = 0.321608 + 1.293240I
a = 0.86084 + 1.56808I
b = 0.198523 + 1.256840I
2.16962 − 0.91182I 0
u = 0.321608 − 1.293240I
a = 0.86084 − 1.56808I
b = 0.198523 − 1.256840I
2.16962 + 0.91182I 0
u = 0.251582 + 1.328590I
a = −0.98352 − 1.56576I
b = −0.07092 − 1.41475I
−2.23585 − 2.71517I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.251582 − 1.328590I
a = −0.98352 + 1.56576I
b = −0.07092 + 1.41475I
−2.23585 + 2.71517I 0
u = −0.202356 + 1.364250I
a = −0.368264 − 0.065956I
b = −0.067803 + 0.563459I
3.79199 + 3.49836I 0
u = −0.202356 − 1.364250I
a = −0.368264 + 0.065956I
b = −0.067803 − 0.563459I
3.79199 − 3.49836I 0
u = 0.546679 + 0.273991I
a = −1.04542 − 3.63991I
b = −0.04558 − 1.51756I
−3.36178 − 1.38887I 2.35610 + 5.10659I
u = 0.546679 − 0.273991I
a = −1.04542 + 3.63991I
b = −0.04558 + 1.51756I
−3.36178 + 1.38887I 2.35610 − 5.10659I
u = −0.435351 + 0.389359I
a = 0.491782 − 0.204328I
b = 0.084335 − 1.208670I
−2.01640 + 0.97897I 2.34600 − 4.48200I
u = −0.435351 − 0.389359I
a = 0.491782 + 0.204328I
b = 0.084335 + 1.208670I
−2.01640 − 0.97897I 2.34600 + 4.48200I
u = −0.18432 + 1.40986I
a = −0.225592 − 0.553357I
b = −0.152154 + 1.055850I
3.63556 + 3.32279I 0
u = −0.18432 − 1.40986I
a = −0.225592 + 0.553357I
b = −0.152154 − 1.055850I
3.63556 − 3.32279I 0
u = 0.21945 + 1.40861I
a = 0.96270 + 1.46545I
b = 0.04850 + 1.56203I
2.03927 − 4.24747I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.21945 − 1.40861I
a = 0.96270 − 1.46545I
b = 0.04850 − 1.56203I
2.03927 + 4.24747I 0
u = −0.548507 + 0.166008I
a = 0.530033 − 0.629098I
b = 0.218693 − 0.435531I
−1.097180 + 0.763622I −4.24671 − 2.11774I
u = −0.548507 − 0.166008I
a = 0.530033 + 0.629098I
b = 0.218693 + 0.435531I
−1.097180 − 0.763622I −4.24671 + 2.11774I
u = 0.18767 + 1.41646I
a = −1.098180 − 0.416185I
b = 0.692130 + 0.004260I
6.83413 − 1.96589I 0
u = 0.18767 − 1.41646I
a = −1.098180 + 0.416185I
b = 0.692130 − 0.004260I
6.83413 + 1.96589I 0
u = −0.13742 + 1.42992I
a = −0.531214 + 0.250911I
b = 0.273097 − 1.263130I
2.91353 − 1.53997I 0
u = −0.13742 − 1.42992I
a = −0.531214 − 0.250911I
b = 0.273097 + 1.263130I
2.91353 + 1.53997I 0
u = −0.23677 + 1.41753I
a = −2.11985 + 0.25168I
b = 0.258918 + 1.274390I
2.91240 + 5.38467I 0
u = −0.23677 − 1.41753I
a = −2.11985 − 0.25168I
b = 0.258918 − 1.274390I
2.91240 − 5.38467I 0
u = 0.24246 + 1.42058I
a = 0.977967 + 0.877470I
b = −0.728763 + 0.193605I
6.02055 − 6.85421I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.24246 − 1.42058I
a = 0.977967 − 0.877470I
b = −0.728763 − 0.193605I
6.02055 + 6.85421I 0
u = 0.402539 + 0.377206I
a = 0.601844 + 0.257905I
b = −0.569286 − 0.073408I
1.200540 + 0.389375I 7.11392 − 0.40347I
u = 0.402539 − 0.377206I
a = 0.601844 − 0.257905I
b = −0.569286 + 0.073408I
1.200540 − 0.389375I 7.11392 + 0.40347I
u = −0.26934 + 1.42381I
a = 2.25229 − 0.97254I
b = −0.301520 − 1.376090I
1.04570 + 10.59920I 0
u = −0.26934 − 1.42381I
a = 2.25229 + 0.97254I
b = −0.301520 + 1.376090I
1.04570 − 10.59920I 0
u = −0.29110 + 1.43833I
a = −2.01002 + 1.33863I
b = 0.34949 + 1.43466I
6.7579 + 15.1002I 0
u = −0.29110 − 1.43833I
a = −2.01002 − 1.33863I
b = 0.34949 − 1.43466I
6.7579 − 15.1002I 0
u = −0.24762 + 1.44773I
a = 0.282106 + 0.053557I
b = 0.554115 − 0.871299I
10.39850 + 5.86579I 0
u = −0.24762 − 1.44773I
a = 0.282106 − 0.053557I
b = 0.554115 + 0.871299I
10.39850 − 5.86579I 0
u = 0.27412 + 1.44693I
a = −0.699548 − 0.987234I
b = 0.851132 − 0.286592I
12.2378 − 10.7588I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.27412 − 1.44693I
a = −0.699548 + 0.987234I
b = 0.851132 + 0.286592I
12.2378 + 10.7588I 0
u = −0.18060 + 1.46824I
a = 1.035470 − 0.448785I
b = −0.483271 − 1.049450I
11.37490 + 4.05500I 0
u = −0.18060 − 1.46824I
a = 1.035470 + 0.448785I
b = −0.483271 + 1.049450I
11.37490 − 4.05500I 0
u = −0.11112 + 1.47836I
a = 0.465603 + 0.258185I
b = −0.381985 + 1.359540I
9.34604 − 5.22928I 0
u = −0.11112 − 1.47836I
a = 0.465603 − 0.258185I
b = −0.381985 − 1.359540I
9.34604 + 5.22928I 0
u = 0.14455 + 1.47753I
a = 0.674222 + 0.188887I
b = −0.870359 − 0.159641I
14.11730 + 0.73561I 0
u = 0.14455 − 1.47753I
a = 0.674222 − 0.188887I
b = −0.870359 + 0.159641I
14.11730 − 0.73561I 0
u = 0.342782
a = 1.79263
b = −0.341913
1.06094 13.3970
12
II. I
u
2
= hb, −u
2
+ a − 1, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
2
=
u
−u
2
− u − 1
a
8
=
u
2
+ 1
u
2
+ u + 1
a
4
=
1
0
a
1
=
−u
2
− 1
−u
2
− u − 1
a
11
=
u
2
+ 1
0
a
5
=
1
0
a
12
=
u
2
+ 1
0
a
10
=
u
2
+ 1
0
a
9
=
2u
2
+ 2
u
2
+ u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6u
2
− 4u − 4
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
+ u
2
− 1
c
2
u
3
− u
2
+ 2u − 1
c
4
, c
5
, c
10
c
11
u
3
c
6
, c
7
u
3
+ u
2
+ 2u + 1
c
8
, c
9
(u + 1)
3
c
12
(u − 1)
3
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
3
− y
2
+ 2y −1
c
2
, c
6
, c
7
y
3
+ 3y
2
+ 2y −1
c
4
, c
5
, c
10
c
11
y
3
c
8
, c
9
, c
12
(y −1)
3
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = −0.662359 − 0.562280I
b = 0
4.66906 + 2.82812I 6.83447 − 1.85489I
u = −0.215080 − 1.307140I
a = −0.662359 + 0.562280I
b = 0
4.66906 − 2.82812I 6.83447 + 1.85489I
u = −0.569840
a = 1.32472
b = 0
0.531480 −3.66890
16
III. I
u
3
=
hu
2
a−2au+3u
2
+5b−a−u+2, −2u
2
a+a
2
+9u
2
−2a−7u+18, u
3
−u
2
+2u−1i
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
2
=
u
u
2
− u + 1
a
8
=
u
2
+ 1
u
2
− u + 1
a
4
=
−1
0
a
1
=
u
2
+ 1
u
2
− u + 1
a
11
=
a
−
1
5
u
2
a −
3
5
u
2
+ ··· +
1
5
a −
2
5
a
5
=
3
5
u
2
a −
11
5
u
2
+ ··· +
2
5
a −
29
5
−2
a
12
=
−
1
5
u
2
a −
3
5
u
2
+ ··· −
4
5
a −
2
5
1
5
u
2
a +
3
5
u
2
+ ··· −
1
5
a +
2
5
a
10
=
1
5
u
2
a +
3
5
u
2
+ ··· +
4
5
a +
2
5
−
1
5
u
2
a −
3
5
u
2
+ ··· +
1
5
a −
2
5
a
9
=
1
5
u
2
a +
8
5
u
2
+ ··· +
4
5
a +
7
5
−
1
5
u
2
a +
2
5
u
2
+ ··· +
1
5
a +
3
5
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
+ 4u − 4
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
− 1)
2
c
2
(u
3
+ u
2
+ 2u + 1)
2
c
3
(u
3
− u
2
+ 1)
2
c
4
, c
5
, c
10
c
11
(u
2
+ 2)
3
c
6
, c
7
(u
3
− u
2
+ 2u − 1)
2
c
8
, c
9
(u − 1)
6
c
12
(u + 1)
6
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y
3
− y
2
+ 2y −1)
2
c
2
, c
6
, c
7
(y
3
+ 3y
2
+ 2y −1)
2
c
4
, c
5
, c
10
c
11
(y + 2)
6
c
8
, c
9
, c
12
(y −1)
6
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −1.71575 − 1.02526I
b = − 1.414210I
−0.26574 − 2.82812I 3.50976 + 2.97945I
u = 0.215080 + 1.307140I
a = 0.39103 + 2.14982I
b = 1.414210I
−0.26574 − 2.82812I 3.50976 + 2.97945I
u = 0.215080 − 1.307140I
a = −1.71575 + 1.02526I
b = 1.414210I
−0.26574 + 2.82812I 3.50976 − 2.97945I
u = 0.215080 − 1.307140I
a = 0.39103 − 2.14982I
b = − 1.414210I
−0.26574 + 2.82812I 3.50976 − 2.97945I
u = 0.569840
a = 1.32472 + 3.89599I
b = 1.414210I
−4.40332 −3.01950
u = 0.569840
a = 1.32472 − 3.89599I
b = − 1.414210I
−4.40332 −3.01950
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
3
+ u
2
− 1)
3
)(u
78
− 16u
77
+ ··· − 227379u + 30627)
c
2
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
2
(u
78
+ 2u
77
+ ··· − 3u − 3)
c
3
((u
3
− u
2
+ 1)
2
)(u
3
+ u
2
− 1)(u
78
− 2u
77
+ ··· − 1479u − 867)
c
4
u
3
(u
2
+ 2)
3
(u
78
− u
77
+ ··· + 4032u + 3112)
c
5
, c
10
, c
11
u
3
(u
2
+ 2)
3
(u
78
+ u
77
+ ··· − 32u
2
+ 8)
c
6
, c
7
((u
3
− u
2
+ 2u − 1)
2
)(u
3
+ u
2
+ 2u + 1)(u
78
+ 2u
77
+ ··· − 3u − 3)
c
8
, c
9
((u − 1)
6
)(u + 1)
3
(u
78
− 4u
77
+ ··· − 108u − 17)
c
12
((u − 1)
3
)(u + 1)
6
(u
78
− 4u
77
+ ··· − 108u − 17)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
3
− y
2
+ 2y −1)
3
· (y
78
+ 32y
77
+ ··· + 2934785691y + 938013129)
c
2
, c
6
, c
7
((y
3
+ 3y
2
+ 2y −1)
3
)(y
78
+ 72y
77
+ ··· − 129y + 9)
c
3
((y
3
− y
2
+ 2y −1)
3
)(y
78
+ 8y
77
+ ··· + 5081487y + 751689)
c
4
y
3
(y + 2)
6
(y
78
− 13y
77
+ ··· − 7.75510 × 10
7
y + 9684544)
c
5
, c
10
, c
11
y
3
(y + 2)
6
(y
78
+ 71y
77
+ ··· − 512y + 64)
c
8
, c
9
, c
12
((y −1)
9
)(y
78
− 74y
77
+ ··· + 5540y + 289)
22
