12n
0298
(K12n
0298
)
A knot diagram
1
Linearized knot diagam
3 6 7 11 8 2 12 5 7 6 9 10
Solving Sequence
2,6
3 7
4,10
11 1 9 12 8 5
c
2
c
6
c
3
c
10
c
1
c
9
c
12
c
7
c
5
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.39637 × 10
86
u
63
+ 5.43528 × 10
86
u
62
+ ··· + 2.96182 × 10
85
b − 1.86518 × 10
86
,
− 2.24145 × 10
86
u
63
− 9.03174 × 10
86
u
62
+ ··· + 2.96182 × 10
85
a − 2.29298 × 10
85
, u
64
+ 4u
63
+ ··· − 4u + 1i
I
u
2
= h2u
19
+ 7u
17
+ ··· + b − 4u, −2u
19
+ u
18
+ ··· + a − 1, u
20
− u
19
+ ··· − 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 84 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
= h1.40×10
86
u
63
+5.44×10
86
u
62
+· · ·+2.96×10
85
b−1.87×10
86
, −2.24×
10
86
u
63
−9.03×10
86
u
62
+· · ·+2.96×10
85
a−2.29×10
85
, u
64
+4u
63
+· · ·−4u+1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
4
=
u
4
+ u
2
+ 1
u
4
a
10
=
7.56782u
63
+ 30.4939u
62
+ ··· + 24.0222u + 0.774178
−4.71457u
63
− 18.3512u
62
+ ··· − 27.2378u + 6.29741
a
11
=
7.56782u
63
+ 30.4939u
62
+ ··· + 24.0222u + 0.774178
−6.38660u
63
− 24.4128u
62
+ ··· − 33.9152u + 6.07481
a
1
=
u
2
+ 1
−u
4
a
9
=
3.86933u
63
+ 16.0937u
62
+ ··· + 10.6018u + 1.05869
−8.41306u
63
− 32.7513u
62
+ ··· − 40.6582u + 6.58192
a
12
=
6.42367u
63
+ 32.1547u
62
+ ··· − 45.0142u + 17.0072
3.79100u
63
+ 16.1352u
62
+ ··· + 0.840596u + 4.38519
a
8
=
0.562618u
63
+ 2.63121u
62
+ ··· − 36.1172u + 8.44512
4.32626u
63
+ 17.5719u
62
+ ··· + 18.4608u − 1.19617
a
5
=
5.84919u
63
+ 21.5137u
62
+ ··· + 53.4241u − 7.65911
1.92460u
63
+ 7.73661u
62
+ ··· + 10.1183u − 1.34592
(ii) Obstruction class = −1
(iii) Cusp Shapes = 30.7036u
63
+ 141.686u
62
+ ··· − 73.0395u + 38.2307
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
64
+ 14u
63
+ ··· + 30u + 1
c
2
, c
6
u
64
− 4u
63
+ ··· + 4u + 1
c
3
u
64
+ 4u
63
+ ··· − 4232566u + 8381893
c
4
u
64
+ 3u
63
+ ··· − 317686u + 108431
c
5
, c
8
u
64
+ u
63
+ ··· + 8u
2
+ 1
c
7
u
64
+ 3u
63
+ ··· − 14u + 1
c
9
u
64
+ 15u
63
+ ··· + 1193304u + 134569
c
10
u
64
+ 2u
63
+ ··· − 28804u + 319
c
11
u
64
− 13u
63
+ ··· − 516u + 31
c
12
u
64
− 11u
63
+ ··· + 4233776u + 540971
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
64
+ 82y
63
+ ··· + 154y + 1
c
2
, c
6
y
64
+ 14y
63
+ ··· + 30y + 1
c
3
y
64
+ 162y
63
+ ··· + 4185418110089892y + 70256130263449
c
4
y
64
+ 29y
63
+ ··· + 248335976782y + 11757281761
c
5
, c
8
y
64
+ 43y
63
+ ··· + 16y + 1
c
7
y
64
+ 5y
63
+ ··· − 30y + 1
c
9
y
64
− 59y
63
+ ··· − 87140422306y + 18108815761
c
10
y
64
+ 100y
63
+ ··· − 262631966y + 101761
c
11
y
64
+ y
63
+ ··· + 5676y + 961
c
12
y
64
− 91y
63
+ ··· − 7005093425444y + 292649622841
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.939075 + 0.271602I
a = 0.482093 − 0.464401I
b = −0.755445 − 0.284336I
−0.44441 − 3.98622I 0
u = 0.939075 − 0.271602I
a = 0.482093 + 0.464401I
b = −0.755445 + 0.284336I
−0.44441 + 3.98622I 0
u = −0.722916 + 0.601079I
a = 0.123478 − 0.330623I
b = 1.32766 − 0.80295I
−1.03187 − 6.00979I 0. + 8.60089I
u = −0.722916 − 0.601079I
a = 0.123478 + 0.330623I
b = 1.32766 + 0.80295I
−1.03187 + 6.00979I 0. − 8.60089I
u = −0.432677 + 0.976451I
a = 0.843388 − 0.347446I
b = 0.197103 + 0.398413I
−2.46162 + 1.46729I 0
u = −0.432677 − 0.976451I
a = 0.843388 + 0.347446I
b = 0.197103 − 0.398413I
−2.46162 − 1.46729I 0
u = 0.194061 + 1.056770I
a = 0.586720 + 0.232918I
b = 0.052356 − 0.350919I
−1.71226 + 0.14587I 0
u = 0.194061 − 1.056770I
a = 0.586720 − 0.232918I
b = 0.052356 + 0.350919I
−1.71226 − 0.14587I 0
u = −0.475448 + 0.789845I
a = 0.290628 − 0.808412I
b = 0.868055 − 0.780912I
0.01302 − 1.90453I 0. + 2.57583I
u = −0.475448 − 0.789845I
a = 0.290628 + 0.808412I
b = 0.868055 + 0.780912I
0.01302 + 1.90453I 0. − 2.57583I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.791240 + 0.428776I
a = 0.912391 + 1.040550I
b = −0.676221 + 0.565206I
2.49559 − 1.05555I 7.00649 + 1.32061I
u = −0.791240 − 0.428776I
a = 0.912391 − 1.040550I
b = −0.676221 − 0.565206I
2.49559 + 1.05555I 7.00649 − 1.32061I
u = 0.400359 + 0.788642I
a = −0.069876 + 1.329720I
b = 1.035650 + 0.916049I
−0.52477 + 4.45766I −3.10979 − 9.91982I
u = 0.400359 − 0.788642I
a = −0.069876 − 1.329720I
b = 1.035650 − 0.916049I
−0.52477 − 4.45766I −3.10979 + 9.91982I
u = 0.299647 + 0.825342I
a = −0.912074 + 0.700445I
b = −1.95342 + 1.10428I
−3.49922 − 2.68192I −5.19582 + 0.87569I
u = 0.299647 − 0.825342I
a = −0.912074 − 0.700445I
b = −1.95342 − 1.10428I
−3.49922 + 2.68192I −5.19582 − 0.87569I
u = 0.589193 + 0.551154I
a = 0.85587 − 2.43022I
b = −0.536571 − 0.801267I
−2.27399 + 6.14015I 2.22329 − 10.33949I
u = 0.589193 − 0.551154I
a = 0.85587 + 2.43022I
b = −0.536571 + 0.801267I
−2.27399 − 6.14015I 2.22329 + 10.33949I
u = 0.274975 + 1.168590I
a = −0.0110651 + 0.0113996I
b = −0.306856 + 0.642395I
−5.23856 − 0.57022I 0
u = 0.274975 − 1.168590I
a = −0.0110651 − 0.0113996I
b = −0.306856 − 0.642395I
−5.23856 + 0.57022I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.457124 + 1.152150I
a = −0.645292 − 0.183503I
b = −1.24538 − 1.10620I
−0.02531 − 3.74403I 0
u = −0.457124 − 1.152150I
a = −0.645292 + 0.183503I
b = −1.24538 + 1.10620I
−0.02531 + 3.74403I 0
u = −0.879640 + 0.881204I
a = −0.79455 + 1.61194I
b = −1.45624 + 0.94426I
6.66965 − 5.86737I 0
u = −0.879640 − 0.881204I
a = −0.79455 − 1.61194I
b = −1.45624 − 0.94426I
6.66965 + 5.86737I 0
u = −0.838867 + 0.958647I
a = −1.35935 + 0.86354I
b = −1.99957 + 0.33680I
6.41424 − 0.52117I 0
u = −0.838867 − 0.958647I
a = −1.35935 − 0.86354I
b = −1.99957 − 0.33680I
6.41424 + 0.52117I 0
u = 0.897037 + 0.932073I
a = −1.13339 − 1.29721I
b = −1.76535 − 0.72437I
8.51868 + 3.30961I 0
u = 0.897037 − 0.932073I
a = −1.13339 + 1.29721I
b = −1.76535 + 0.72437I
8.51868 − 3.30961I 0
u = 0.530563 + 0.465648I
a = −0.472852 + 0.171059I
b = 1.121760 + 0.641421I
0.55435 + 2.88435I 4.59418 − 0.12217I
u = 0.530563 − 0.465648I
a = −0.472852 − 0.171059I
b = 1.121760 − 0.641421I
0.55435 − 2.88435I 4.59418 + 0.12217I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.385835 + 0.588474I
a = 0.836666 − 0.736399I
b = 0.811989 − 0.180829I
0.38260 − 1.61712I 2.69865 + 4.73413I
u = −0.385835 − 0.588474I
a = 0.836666 + 0.736399I
b = 0.811989 + 0.180829I
0.38260 + 1.61712I 2.69865 − 4.73413I
u = −1.026810 + 0.827404I
a = −0.507979 + 1.128420I
b = −1.29031 + 0.58664I
7.40053 − 0.12600I 0
u = −1.026810 − 0.827404I
a = −0.507979 − 1.128420I
b = −1.29031 − 0.58664I
7.40053 + 0.12600I 0
u = 0.488940 + 1.231620I
a = −0.531491 − 0.111009I
b = −1.041740 + 0.612916I
−3.67677 + 9.30666I 0
u = 0.488940 − 1.231620I
a = −0.531491 + 0.111009I
b = −1.041740 − 0.612916I
−3.67677 − 9.30666I 0
u = −0.063841 + 0.650559I
a = 0.415319 − 0.941017I
b = −0.556116 − 1.216000I
−1.14528 − 1.52727I −4.52889 + 4.44249I
u = −0.063841 − 0.650559I
a = 0.415319 + 0.941017I
b = −0.556116 + 1.216000I
−1.14528 + 1.52727I −4.52889 − 4.44249I
u = −1.037000 + 0.860981I
a = 1.10948 − 1.12589I
b = 1.60768 + 0.28265I
7.61657 + 8.96188I 0
u = −1.037000 − 0.860981I
a = 1.10948 + 1.12589I
b = 1.60768 − 0.28265I
7.61657 − 8.96188I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.026730 + 0.876368I
a = 1.16571 + 1.14718I
b = 1.66461 − 0.43980I
11.07350 − 2.80334I 0
u = 1.026730 − 0.876368I
a = 1.16571 − 1.14718I
b = 1.66461 + 0.43980I
11.07350 + 2.80334I 0
u = 0.931671 + 0.980831I
a = −0.964496 − 1.016020I
b = −1.62384 − 0.47553I
8.77138 + 3.50074I 0
u = 0.931671 − 0.980831I
a = −0.964496 + 1.016020I
b = −1.62384 + 0.47553I
8.77138 − 3.50074I 0
u = 0.987503 + 0.947834I
a = −0.788697 − 1.062230I
b = −1.48014 − 0.52580I
8.90447 + 3.52447I 0
u = 0.987503 − 0.947834I
a = −0.788697 + 1.062230I
b = −1.48014 + 0.52580I
8.90447 − 3.52447I 0
u = −0.045837 + 0.617197I
a = −1.26636 − 2.43670I
b = 0.525231 − 0.836008I
−4.46639 − 4.92939I −10.22682 + 5.98582I
u = −0.045837 − 0.617197I
a = −1.26636 + 2.43670I
b = 0.525231 + 0.836008I
−4.46639 + 4.92939I −10.22682 − 5.98582I
u = −1.078850 + 0.866107I
a = 1.51083 − 1.33022I
b = 2.08515 + 1.50091I
5.10332 − 3.48279I 0
u = −1.078850 − 0.866107I
a = 1.51083 + 1.33022I
b = 2.08515 − 1.50091I
5.10332 + 3.48279I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.173180 + 0.577072I
a = 0.03202 + 1.82163I
b = −0.96370 + 2.09264I
−4.26610 + 5.45717I −10.43636 − 7.95059I
u = 0.173180 − 0.577072I
a = 0.03202 − 1.82163I
b = −0.96370 − 2.09264I
−4.26610 − 5.45717I −10.43636 + 7.95059I
u = 0.916042 + 1.056350I
a = 0.83523 + 1.32696I
b = 2.38551 + 1.05444I
10.4719 + 9.8985I 0
u = 0.916042 − 1.056350I
a = 0.83523 − 1.32696I
b = 2.38551 − 1.05444I
10.4719 − 9.8985I 0
u = −0.909045 + 1.065430I
a = 0.88608 − 1.31653I
b = 2.29397 − 1.02161I
6.9320 − 16.0572I 0
u = −0.909045 − 1.065430I
a = 0.88608 + 1.31653I
b = 2.29397 + 1.02161I
6.9320 + 16.0572I 0
u = −0.893030 + 1.085020I
a = −0.944848 + 0.755591I
b = −1.58267 + 0.22697I
6.56784 − 6.89474I 0
u = −0.893030 − 1.085020I
a = −0.944848 − 0.755591I
b = −1.58267 − 0.22697I
6.56784 + 6.89474I 0
u = −0.96327 + 1.05484I
a = 0.81866 − 1.54930I
b = 3.05198 − 0.85138I
4.50809 − 3.90305I 0
u = −0.96327 − 1.05484I
a = 0.81866 + 1.54930I
b = 3.05198 + 0.85138I
4.50809 + 3.90305I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.121840 + 0.455209I
a = 1.85406 − 0.09378I
b = 0.819408 − 0.701563I
0.33452 − 1.86534I 2.56057 + 3.02633I
u = 0.121840 − 0.455209I
a = 1.85406 + 0.09378I
b = 0.819408 + 0.701563I
0.33452 + 1.86534I 2.56057 − 3.02633I
u = 0.230599 + 0.231903I
a = −2.65631 − 1.10766I
b = 0.885454 + 0.326045I
0.41148 + 2.24866I 3.48307 − 5.05352I
u = 0.230599 − 0.231903I
a = −2.65631 + 1.10766I
b = 0.885454 − 0.326045I
0.41148 − 2.24866I 3.48307 + 5.05352I
11
II.
I
u
2
= h2u
19
+7u
17
+· · ·+b−4u, −2u
19
+u
18
+· · ·+a−1, u
20
−u
19
+· · ·−2u+1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
4
=
u
4
+ u
2
+ 1
u
4
a
10
=
2u
19
− u
18
+ ··· + 3u + 1
−2u
19
− 7u
17
+ ··· − 10u
2
+ 4u
a
11
=
2u
19
− u
18
+ ··· + 3u + 1
−2u
19
− 7u
17
+ ··· + 4u − 1
a
1
=
u
2
+ 1
−u
4
a
9
=
u
19
+ 4u
17
+ ··· + 5u − 2
−3u
19
+ u
18
+ ··· + 6u − 3
a
12
=
6u
19
− 3u
18
+ ··· − 4u
2
+ 5u
4u
19
− 3u
18
+ ··· + 9u − 1
a
8
=
−6u
19
+ 3u
18
+ ··· − 9u + 4
−3u
19
− 11u
17
+ ··· + 7u − 3
a
5
=
3u
19
− 2u
18
+ ··· + 3u − 2
5u
19
− 3u
18
+ ··· + 5u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 9u
19
− 4u
18
+ 34u
17
− 7u
16
+ 85u
15
− 23u
14
+ 161u
13
− 51u
12
+
214u
11
− 67u
10
+ 158u
9
− 55u
8
+ 43u
7
− 46u
6
− 26u
5
− 41u
4
− 8u
3
− 22u
2
− u − 16
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
20
− 9u
19
+ ··· − 8u + 1
c
2
u
20
− u
19
+ ··· − 2u + 1
c
3
u
20
+ u
19
+ ··· − 8u + 1
c
4
u
20
+ 4u
19
+ ··· + 2u + 1
c
5
u
20
+ 9u
18
+ ··· + 2u + 1
c
6
u
20
+ u
19
+ ··· + 2u + 1
c
7
u
20
+ 2u
19
+ ··· + 6u + 1
c
8
u
20
+ 9u
18
+ ··· − 2u + 1
c
9
u
20
+ 6u
19
+ ··· + 2u + 1
c
10
u
20
+ u
19
+ ··· − 4u + 1
c
11
u
20
+ 8u
19
+ ··· + 4u + 1
c
12
u
20
− 12u
19
+ ··· − 6u + 1
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
+ 13y
19
+ ··· + 20y + 1
c
2
, c
6
y
20
+ 9y
19
+ ··· + 8y + 1
c
3
y
20
+ 29y
19
+ ··· − 10y + 1
c
4
y
20
+ 4y
19
+ ··· − 12y + 1
c
5
, c
8
y
20
+ 18y
19
+ ··· + 10y + 1
c
7
y
20
+ 2y
18
+ ··· − 20y + 1
c
9
y
20
− 20y
19
+ ··· + 2y
2
+ 1
c
10
y
20
+ 15y
19
+ ··· − 4y + 1
c
11
y
20
− 8y
19
+ ··· + 2y + 1
c
12
y
20
− 12y
19
+ ··· + 10y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.133168 + 1.051170I
a = 0.949802 + 0.057848I
b = 0.467686 + 0.288113I
−1.35651 + 1.16657I 1.05283 − 4.51213I
u = −0.133168 − 1.051170I
a = 0.949802 − 0.057848I
b = 0.467686 − 0.288113I
−1.35651 − 1.16657I 1.05283 + 4.51213I
u = −0.388238 + 1.004590I
a = 0.496532 + 0.200270I
b = 1.47658 + 0.60423I
−0.87995 − 3.76439I −4.04375 + 6.88348I
u = −0.388238 − 1.004590I
a = 0.496532 − 0.200270I
b = 1.47658 − 0.60423I
−0.87995 + 3.76439I −4.04375 − 6.88348I
u = −0.407946 + 0.770783I
a = 0.167116 − 0.458391I
b = −0.406625 + 0.480005I
−0.149706 + 0.500341I 2.17204 + 0.29125I
u = −0.407946 − 0.770783I
a = 0.167116 + 0.458391I
b = −0.406625 − 0.480005I
−0.149706 − 0.500341I 2.17204 − 0.29125I
u = 0.517514 + 1.067790I
a = 0.312393 − 0.547705I
b = 0.860626 − 0.777046I
−4.91212 + 8.66631I −5.37283 − 6.56810I
u = 0.517514 − 1.067790I
a = 0.312393 + 0.547705I
b = 0.860626 + 0.777046I
−4.91212 − 8.66631I −5.37283 + 6.56810I
u = 0.414696 + 1.121450I
a = 0.616873 − 0.475026I
b = 0.685695 − 1.098930I
−5.57840 − 1.56382I −6.00081 + 3.18452I
u = 0.414696 − 1.121450I
a = 0.616873 + 0.475026I
b = 0.685695 + 1.098930I
−5.57840 + 1.56382I −6.00081 − 3.18452I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.393897 + 0.665781I
a = 0.092647 − 0.940148I
b = 1.37333 − 0.87165I
−0.11330 − 3.36458I −3.05713 + 6.74431I
u = −0.393897 − 0.665781I
a = 0.092647 + 0.940148I
b = 1.37333 + 0.87165I
−0.11330 + 3.36458I −3.05713 − 6.74431I
u = 0.493601 + 0.555703I
a = −0.72132 + 1.24890I
b = −0.779779 + 0.032785I
−3.21796 − 4.42430I −1.43749 + 3.47963I
u = 0.493601 − 0.555703I
a = −0.72132 − 1.24890I
b = −0.779779 − 0.032785I
−3.21796 + 4.42430I −1.43749 − 3.47963I
u = 0.925814 + 0.939172I
a = −0.96685 − 1.16407I
b = −1.53715 − 0.69330I
7.91169 + 3.39538I −5.49582 − 2.79697I
u = 0.925814 − 0.939172I
a = −0.96685 + 1.16407I
b = −1.53715 + 0.69330I
7.91169 − 3.39538I −5.49582 + 2.79697I
u = 0.495885 + 0.454566I
a = −1.23104 + 1.75062I
b = 0.319624 + 1.323120I
−3.23795 + 5.41696I −2.08175 − 6.69309I
u = 0.495885 − 0.454566I
a = −1.23104 − 1.75062I
b = 0.319624 − 1.323120I
−3.23795 − 5.41696I −2.08175 + 6.69309I
u = −1.024260 + 0.937435I
a = −1.21615 + 1.40368I
b = −2.46000 − 0.55113I
4.95446 − 3.69253I 2.76469 + 12.91616I
u = −1.024260 − 0.937435I
a = −1.21615 − 1.40368I
b = −2.46000 + 0.55113I
4.95446 + 3.69253I 2.76469 − 12.91616I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
20
− 9u
19
+ ··· − 8u + 1)(u
64
+ 14u
63
+ ··· + 30u + 1)
c
2
(u
20
− u
19
+ ··· − 2u + 1)(u
64
− 4u
63
+ ··· + 4u + 1)
c
3
(u
20
+ u
19
+ ··· − 8u + 1)(u
64
+ 4u
63
+ ··· − 4232566u + 8381893)
c
4
(u
20
+ 4u
19
+ ··· + 2u + 1)(u
64
+ 3u
63
+ ··· − 317686u + 108431)
c
5
(u
20
+ 9u
18
+ ··· + 2u + 1)(u
64
+ u
63
+ ··· + 8u
2
+ 1)
c
6
(u
20
+ u
19
+ ··· + 2u + 1)(u
64
− 4u
63
+ ··· + 4u + 1)
c
7
(u
20
+ 2u
19
+ ··· + 6u + 1)(u
64
+ 3u
63
+ ··· − 14u + 1)
c
8
(u
20
+ 9u
18
+ ··· − 2u + 1)(u
64
+ u
63
+ ··· + 8u
2
+ 1)
c
9
(u
20
+ 6u
19
+ ··· + 2u + 1)(u
64
+ 15u
63
+ ··· + 1193304u + 134569)
c
10
(u
20
+ u
19
+ ··· − 4u + 1)(u
64
+ 2u
63
+ ··· − 28804u + 319)
c
11
(u
20
+ 8u
19
+ ··· + 4u + 1)(u
64
− 13u
63
+ ··· − 516u + 31)
c
12
(u
20
− 12u
19
+ ··· − 6u + 1)(u
64
− 11u
63
+ ··· + 4233776u + 540971)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
20
+ 13y
19
+ ··· + 20y + 1)(y
64
+ 82y
63
+ ··· + 154y + 1)
c
2
, c
6
(y
20
+ 9y
19
+ ··· + 8y + 1)(y
64
+ 14y
63
+ ··· + 30y + 1)
c
3
(y
20
+ 29y
19
+ ··· − 10y + 1)
· (y
64
+ 162y
63
+ ··· + 4185418110089892y + 70256130263449)
c
4
(y
20
+ 4y
19
+ ··· − 12y + 1)
· (y
64
+ 29y
63
+ ··· + 248335976782y + 11757281761)
c
5
, c
8
(y
20
+ 18y
19
+ ··· + 10y + 1)(y
64
+ 43y
63
+ ··· + 16y + 1)
c
7
(y
20
+ 2y
18
+ ··· − 20y + 1)(y
64
+ 5y
63
+ ··· − 30y + 1)
c
9
(y
20
− 20y
19
+ ··· + 2y
2
+ 1)
· (y
64
− 59y
63
+ ··· − 87140422306y + 18108815761)
c
10
(y
20
+ 15y
19
+ ··· − 4y + 1)
· (y
64
+ 100y
63
+ ··· − 262631966y + 101761)
c
11
(y
20
− 8y
19
+ ··· + 2y + 1)(y
64
+ y
63
+ ··· + 5676y + 961)
c
12
(y
20
− 12y
19
+ ··· + 10y + 1)
· (y
64
− 91y
63
+ ··· − 7005093425444y + 292649622841)
20
