12n
0777
(K12n
0777
)
A knot diagram
1
Linearized knot diagam
4 6 9 11 12 10 3 12 7 2 5 9
Solving Sequence
4,11
5 12
6,9
1 3 2 8 7 10
c
4
c
11
c
5
c
12
c
3
c
2
c
8
c
7
c
10
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h4585u
29
− 53373u
28
+ ··· + 32b − 211552, 13955u
29
− 160849u
28
+ ··· + 64a − 593856,
u
30
− 13u
29
+ ··· − 96u + 64i
I
u
2
= h3u
21
− 2u
20
+ ··· + b + 1, 5u
21
− 6u
20
+ ··· + a + 4, u
22
− 12u
20
+ ··· + 2u + 1i
I
u
3
= h−8.71806 × 10
22
a
11
u + 1.90564 × 10
22
a
10
u + ··· + 4.42015 × 10
24
a + 2.07365 × 10
24
,
− a
11
u − 8a
10
u + ··· − 155a + 597, u
2
+ u − 1i
* 3 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
= h4585u
29
− 53373u
28
+ · · · + 32b − 211552, 13955u
29
− 160849u
28
+
· · · + 64a − 593856, u
30
− 13u
29
+ · · · − 96u + 64i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
u
2
a
12
=
−u
−u
3
+ u
a
6
=
−u
2
+ 1
−u
4
+ 2u
2
a
9
=
−218.047u
29
+ 2513.27u
28
+ ··· − 7883.75u + 9279
−143.281u
29
+ 1667.91u
28
+ ··· − 5240.50u + 6611
a
1
=
−12u
29
+
583
4
u
28
+ ··· −
961
2
u +
1409
2
31
4
u
29
−
325
4
u
28
+ ··· +
465
2
u − 112
a
3
=
12u
29
−
583
4
u
28
+ ··· +
959
2
u −
1407
2
−
31
4
u
29
+
325
4
u
28
+ ··· −
463
2
u + 112
a
2
=
−
79
4
u
29
+ 227u
28
+ ··· − 713u +
1633
2
31
4
u
29
−
325
4
u
28
+ ··· +
465
2
u − 112
a
8
=
−412.797u
29
+ 4786.39u
28
+ ··· − 15027.8u + 18449
−282.531u
29
+ 3320.78u
28
+ ··· − 10460.5u + 13993
a
7
=
−
1425
8
u
29
+
32277
16
u
28
+ ··· − 6300u + 6463
−
3901
16
u
29
+
5761
2
u
28
+ ··· − 9090u + 12556
a
10
=
−
77
4
u
29
+
825
4
u
28
+ ··· −
2465
4
u + 368
−90u
29
+
4209
4
u
28
+ ··· − 3335u + 4240
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
3861
4
u
29
+
22479
2
u
28
+ ··· − 35492u + 44366
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
− 14u
29
+ ··· − 1674u + 180
c
2
, c
10
u
30
− u
29
+ ··· − 4u + 1
c
3
, c
8
, c
12
u
30
+ 25u
28
+ ··· + 14u
2
+ 1
c
4
, c
5
, c
11
u
30
− 13u
29
+ ··· − 96u + 64
c
6
, c
9
u
30
+ 9u
29
+ ··· + 58u + 4
c
7
u
30
+ u
29
+ ··· + 134u + 43
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
− 42y
29
+ ··· − 660636y + 32400
c
2
, c
10
y
30
+ 27y
29
+ ··· + 10y + 1
c
3
, c
8
, c
12
y
30
+ 50y
29
+ ··· + 28y + 1
c
4
, c
5
, c
11
y
30
− 27y
29
+ ··· + 7168y + 4096
c
6
, c
9
y
30
+ 21y
29
+ ··· − 204y + 16
c
7
y
30
+ 37y
29
+ ··· − 12796y + 1849
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.712100 + 0.956564I
a = 0.866632 − 0.189288I
b = −0.17533 − 2.06721I
−12.2909 + 9.4994I 0. − 5.67165I
u = −0.712100 − 0.956564I
a = 0.866632 + 0.189288I
b = −0.17533 + 2.06721I
−12.2909 − 9.4994I 0. + 5.67165I
u = 1.076880 + 0.516113I
a = 1.16983 + 0.89905I
b = −0.750113 + 0.531557I
−0.60829 − 5.16519I 7.68800 − 3.17301I
u = 1.076880 − 0.516113I
a = 1.16983 − 0.89905I
b = −0.750113 − 0.531557I
−0.60829 + 5.16519I 7.68800 + 3.17301I
u = −1.179430 + 0.197792I
a = −0.198189 + 0.197833I
b = −0.370253 + 0.632453I
−2.67535 + 1.28324I 0
u = −1.179430 − 0.197792I
a = −0.198189 − 0.197833I
b = −0.370253 − 0.632453I
−2.67535 − 1.28324I 0
u = −0.576495 + 1.064220I
a = 0.893792 − 0.009633I
b = −0.22203 − 2.04575I
−11.81400 − 2.89439I 0
u = −0.576495 − 1.064220I
a = 0.893792 + 0.009633I
b = −0.22203 + 2.04575I
−11.81400 + 2.89439I 0
u = −0.695385 + 1.054340I
a = −0.834599 + 0.093305I
b = 0.17902 + 2.11004I
−7.50297 + 3.48252I 0
u = −0.695385 − 1.054340I
a = −0.834599 − 0.093305I
b = 0.17902 − 2.11004I
−7.50297 − 3.48252I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.405900 + 0.604201I
a = −1.206390 − 0.215475I
b = 0.706818 + 0.267801I
1.34273 + 0.69486I 10.73680 − 5.94826I
u = 0.405900 − 0.604201I
a = −1.206390 + 0.215475I
b = 0.706818 − 0.267801I
1.34273 − 0.69486I 10.73680 + 5.94826I
u = −0.349023 + 0.634623I
a = 0.391030 + 0.430038I
b = 0.490044 − 0.392098I
−2.73365 + 3.23503I 0.14526 − 3.30647I
u = −0.349023 − 0.634623I
a = 0.391030 − 0.430038I
b = 0.490044 + 0.392098I
−2.73365 − 3.23503I 0.14526 + 3.30647I
u = −0.473468 + 0.455765I
a = 0.178820 − 0.624865I
b = −0.466864 − 0.464807I
−3.35774 + 0.41602I −0.28518 − 3.29821I
u = −0.473468 − 0.455765I
a = 0.178820 + 0.624865I
b = −0.466864 + 0.464807I
−3.35774 − 0.41602I −0.28518 + 3.29821I
u = −0.241152 + 0.560887I
a = −0.450417 + 0.043597I
b = 0.043133 + 0.373812I
0.155530 + 1.274890I 2.11047 − 6.19395I
u = −0.241152 − 0.560887I
a = −0.450417 − 0.043597I
b = 0.043133 − 0.373812I
0.155530 − 1.274890I 2.11047 + 6.19395I
u = 1.40597 + 0.22506I
a = 0.363023 + 0.409362I
b = 0.021884 + 0.360955I
−5.15833 − 4.20213I 0
u = 1.40597 − 0.22506I
a = 0.363023 − 0.409362I
b = 0.021884 − 0.360955I
−5.15833 + 4.20213I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.42237 + 0.17547I
a = 0.152611 − 0.928981I
b = 0.387688 − 0.480108I
−9.29324 − 2.70234I 0
u = 1.42237 − 0.17547I
a = 0.152611 + 0.928981I
b = 0.387688 + 0.480108I
−9.29324 + 2.70234I 0
u = 1.43366 + 0.23827I
a = −0.798085 + 0.019961I
b = −0.459766 − 0.343812I
−8.45070 − 6.42278I 0
u = 1.43366 − 0.23827I
a = −0.798085 − 0.019961I
b = −0.459766 + 0.343812I
−8.45070 + 6.42278I 0
u = 1.64901 + 0.32277I
a = −0.70265 − 1.71037I
b = 0.58983 − 2.17349I
19.4368 − 14.3151I 0
u = 1.64901 − 0.32277I
a = −0.70265 + 1.71037I
b = 0.58983 + 2.17349I
19.4368 + 14.3151I 0
u = 1.67171 + 0.34503I
a = 0.67299 + 1.59613I
b = −0.61499 + 2.14641I
−15.2886 − 8.7374I 0
u = 1.67171 − 0.34503I
a = 0.67299 − 1.59613I
b = −0.61499 − 2.14641I
−15.2886 + 8.7374I 0
u = 1.66154 + 0.39521I
a = −0.74838 − 1.46675I
b = 0.64093 − 2.07022I
−19.0732 − 2.6309I 0
u = 1.66154 − 0.39521I
a = −0.74838 + 1.46675I
b = 0.64093 + 2.07022I
−19.0732 + 2.6309I 0
7
II.
I
u
2
= h3u
21
−2u
20
+· · ·+b+1, 5u
21
−6u
20
+· · ·+a+4, u
22
−12u
20
+· · ·+2u+1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
u
2
a
12
=
−u
−u
3
+ u
a
6
=
−u
2
+ 1
−u
4
+ 2u
2
a
9
=
−5u
21
+ 6u
20
+ ··· − 3u − 4
−3u
21
+ 2u
20
+ ··· − u − 1
a
1
=
−u
21
+ u
20
+ ··· − 6u − 5
−u
19
+ 10u
17
+ ··· − 8u
2
− 3u
a
3
=
−u
21
+ u
20
+ ··· − 5u − 4
−u
19
+ 10u
17
+ ··· − 8u
2
− 4u
a
2
=
−u
21
+ u
20
+ ··· − 3u − 5
−u
19
+ 10u
17
+ ··· − 8u
2
− 3u
a
8
=
−7u
21
+ 10u
20
+ ··· − 8u − 7
−4u
21
+ 4u
20
+ ··· − 2u − 2
a
7
=
−3u
21
+ 5u
20
+ ··· + 6u − 2
−3u
21
+ 5u
20
+ ··· − 3u − 3
a
10
=
u
21
− 14u
19
+ ··· + 3u + 3
3u
20
− 31u
18
+ ··· − 6u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −3u
21
+ 8u
20
+ 26u
19
−80u
18
−95u
17
+ 329u
16
+ 225u
15
−730u
14
−469u
13
+ 949u
12
+
835u
11
−674u
10
−1053u
9
+ 119u
8
+ 859u
7
+ 156u
6
−388u
5
−102u
4
+ 54u
3
+ 43u
2
−18u
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
22
− 19u
21
+ ··· + 33u + 11
c
2
, c
10
u
22
− u
21
+ ··· − 5u
2
− 1
c
3
, c
8
u
22
+ 8u
20
+ ··· + 6u
2
− 1
c
4
, c
5
u
22
− 12u
20
+ ··· + 2u + 1
c
6
u
22
+ 6u
21
+ ··· + 26u + 5
c
7
u
22
− u
21
+ ··· + 6u
2
− 1
c
9
u
22
− 6u
21
+ ··· − 26u + 5
c
11
u
22
− 12u
20
+ ··· − 2u + 1
c
12
u
22
+ 8u
20
+ ··· + 6u
2
− 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
− 31y
21
+ ··· − 19833y + 121
c
2
, c
10
y
22
− 3y
21
+ ··· + 10y + 1
c
3
, c
8
, c
12
y
22
+ 16y
21
+ ··· − 12y + 1
c
4
, c
5
, c
11
y
22
− 24y
21
+ ··· − 16y + 1
c
6
, c
9
y
22
+ 16y
21
+ ··· + 44y + 25
c
7
y
22
+ 15y
21
+ ··· − 12y + 1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.952998 + 0.363147I
a = 0.447217 + 0.580843I
b = 0.16042 + 1.47642I
−5.37181 − 1.39365I −0.44374 + 4.45166I
u = 0.952998 − 0.363147I
a = 0.447217 − 0.580843I
b = 0.16042 − 1.47642I
−5.37181 + 1.39365I −0.44374 − 4.45166I
u = −0.411052 + 0.829761I
a = 0.908472 − 0.306162I
b = −0.800223 + 0.419012I
0.886074 − 0.327914I −1.50287 − 2.30603I
u = −0.411052 − 0.829761I
a = 0.908472 + 0.306162I
b = −0.800223 − 0.419012I
0.886074 + 0.327914I −1.50287 + 2.30603I
u = −0.991893 + 0.557470I
a = −1.33261 + 0.73674I
b = 0.828904 + 0.495963I
−0.76850 + 5.48421I −1.6991 − 16.1374I
u = −0.991893 − 0.557470I
a = −1.33261 − 0.73674I
b = 0.828904 − 0.495963I
−0.76850 − 5.48421I −1.6991 + 16.1374I
u = −1.26981
a = 1.47162
b = 0.504182
−0.523875 1.69110
u = −1.283890 + 0.044119I
a = −1.67687 + 0.65247I
b = −0.562792 + 0.352530I
−4.65589 − 4.05576I −3.08182 + 3.35198I
u = −1.283890 − 0.044119I
a = −1.67687 − 0.65247I
b = −0.562792 − 0.352530I
−4.65589 + 4.05576I −3.08182 − 3.35198I
u = 1.281110 + 0.143729I
a = −0.023735 − 0.409037I
b = 0.140554 − 1.199050I
−11.14630 − 3.12297I −7.71456 + 3.43607I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.281110 − 0.143729I
a = −0.023735 + 0.409037I
b = 0.140554 + 1.199050I
−11.14630 + 3.12297I −7.71456 − 3.43607I
u = −0.542807
a = 2.74234
b = −0.680559
2.28404 18.6410
u = 1.44169 + 0.27299I
a = 0.190001 + 0.084721I
b = 0.564861 + 0.493339I
−5.07635 − 3.48825I −0.374917 − 1.318569I
u = 1.44169 − 0.27299I
a = 0.190001 − 0.084721I
b = 0.564861 − 0.493339I
−5.07635 + 3.48825I −0.374917 + 1.318569I
u = 1.46316 + 0.17821I
a = −0.211286 + 0.093946I
b = −0.820499 + 0.187762I
−7.43021 − 6.90057I 0.73795 + 6.43274I
u = 1.46316 − 0.17821I
a = −0.211286 − 0.093946I
b = −0.820499 − 0.187762I
−7.43021 + 6.90057I 0.73795 − 6.43274I
u = 0.392750 + 0.252362I
a = −1.72917 − 1.60391I
b = −0.11303 − 1.55435I
−8.04498 + 1.60371I 2.68984 + 0.68205I
u = 0.392750 − 0.252362I
a = −1.72917 + 1.60391I
b = −0.11303 + 1.55435I
−8.04498 − 1.60371I 2.68984 − 0.68205I
u = −0.322581 + 0.260655I
a = −1.85686 − 1.81617I
b = 0.699900 + 0.348525I
−1.38244 + 4.88830I 7.02230 − 6.99712I
u = −0.322581 − 0.260655I
a = −1.85686 + 1.81617I
b = 0.699900 − 0.348525I
−1.38244 − 4.88830I 7.02230 + 6.99712I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.61599 + 0.03920I
a = 0.17786 − 2.13380I
b = −0.00990 − 2.13633I
−15.4624 − 0.5787I −3.29897 − 0.02802I
u = −1.61599 − 0.03920I
a = 0.17786 + 2.13380I
b = −0.00990 + 2.13633I
−15.4624 + 0.5787I −3.29897 + 0.02802I
13
III. I
u
3
= h−8.72 × 10
22
a
11
u + 1.91 × 10
22
a
10
u + · · · + 4.42 × 10
24
a + 2.07 ×
10
24
, −a
11
u − 8a
10
u + · · · − 155a + 597, u
2
+ u − 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u + 1
a
12
=
−u
−u + 1
a
6
=
u
u
a
9
=
a
0.0214307a
11
u − 0.00468444a
10
u + ··· − 1.08656a − 0.509744
a
1
=
−0.00917669a
11
u + 0.0325719a
10
u + ··· − 0.675635a − 3.24372
−0.00286472a
11
u + 0.00833889a
10
u + ··· + 0.562457a − 0.832737
a
3
=
0.00602071a
11
u − 0.0204554a
10
u + ··· + 0.0565892a + 1.03823
0.00946796a
11
u − 0.0363495a
10
u + ··· + 1.85714a + 2.61648
a
2
=
−0.00631197a
11
u + 0.0242330a
10
u + ··· − 1.23809a − 2.41098
−0.00286472a
11
u + 0.00833889a
10
u + ··· + 0.562457a − 0.832737
a
8
=
−0.0535869a
11
u + 0.00623328a
10
u + ··· + 5.66354a − 0.143400
−0.0643124a
11
u + 0.00309767a
10
u + ··· + 7.15396a − 1.30629
a
7
=
−0.0183450a
11
u + 0.214734a
10
u + ··· + 1.71015a − 3.10299
−0.00922299a
11
u + 0.168170a
10
u + ··· + 1.41669a − 2.28054
a
10
=
0.107560a
11
u − 0.0410873a
10
u + ··· − 1.69236a − 2.46606
0.0907209a
11
u − 0.0394227a
10
u + ··· − 1.61846a − 0.543159
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
133284116432454129908660
4068027487962543539939429
a
11
u +
1093266323961776835486728
4068027487962543539939429
a
10
u +
··· +
9514250227401971513320248
4068027487962543539939429
a −
32385451624456899956132574
4068027487962543539939429
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 5u
5
+ 7u
4
− 2u
2
+ 3u − 1)
4
c
2
, c
10
u
24
− 5u
23
+ ··· − 70u − 359
c
3
, c
8
, c
12
u
24
− u
23
+ ··· − 4244u + 59
c
4
, c
5
, c
11
(u
2
+ u − 1)
12
c
6
, c
9
(u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)
4
c
7
u
24
+ u
23
+ ··· − 34758u − 11549
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
− 11y
5
+ 45y
4
− 60y
3
− 10y
2
− 5y + 1)
4
c
2
, c
10
y
24
− y
23
+ ··· + 306712y + 128881
c
3
, c
8
, c
12
y
24
+ 35y
23
+ ··· − 17208900y + 3481
c
4
, c
5
, c
11
(y
2
− 3y + 1)
12
c
6
, c
9
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1)
4
c
7
y
24
+ 27y
23
+ ··· − 597684620y + 133379401
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −0.449650 + 0.833274I
b = 0.34833 + 1.76411I
−8.88201 + 1.97241I −7.42428 − 3.68478I
u = 0.618034
a = −0.449650 − 0.833274I
b = 0.34833 − 1.76411I
−8.88201 − 1.97241I −7.42428 + 3.68478I
u = 0.618034
a = 1.40776 + 0.25253I
b = −1.053060 + 0.516427I
−2.22618 − 4.59213I −3.41886 + 3.20482I
u = 0.618034
a = 1.40776 − 0.25253I
b = −1.053060 − 0.516427I
−2.22618 + 4.59213I −3.41886 − 3.20482I
u = 0.618034
a = −1.55325
b = 0.936974
1.73832 0.269500
u = 0.618034
a = 0.63314 + 1.45797I
b = −0.14946 + 1.45797I
−5.18291 1.41678 + 0.I
u = 0.618034
a = 0.63314 − 1.45797I
b = −0.14946 − 1.45797I
−5.18291 1.41678 + 0.I
u = 0.618034
a = −2.47602
b = 0.0142072
1.73832 0.269500
u = 0.618034
a = −0.84151 + 2.33940I
b = −0.043531 + 1.408560I
−8.88201 − 1.97241I −7.42428 + 3.68478I
u = 0.618034
a = −0.84151 − 2.33940I
b = −0.043531 − 1.408560I
−8.88201 + 1.97241I −7.42428 − 3.68478I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 2.57392 + 0.67952I
b = 0.113108 + 0.415629I
−2.22618 + 4.59213I −3.41886 − 3.20482I
u = 0.618034
a = 2.57392 − 0.67952I
b = 0.113108 − 0.415629I
−2.22618 − 4.59213I −3.41886 + 3.20482I
u = −1.61803
a = −0.119315 + 0.970364I
b = 0.820632 + 0.869565I
−10.12190 − 4.59213I −3.41886 + 3.20482I
u = −1.61803
a = −0.119315 − 0.970364I
b = 0.820632 − 0.869565I
−10.12190 + 4.59213I −3.41886 − 3.20482I
u = −1.61803
a = −0.293931 + 0.836107I
b = −1.24511 + 0.83611I
−6.15736 − 60.269499 + 0.10I
u = −1.61803
a = −0.293931 − 0.836107I
b = −1.24511 − 0.83611I
−6.15736 − 60.269499 + 0.10I
u = −1.61803
a = 0.700234 + 1.032660I
b = 1.64018 + 1.13346I
−10.12190 + 4.59213I −3.41886 − 3.20482I
u = −1.61803
a = 0.700234 − 1.032660I
b = 1.64018 − 1.13346I
−10.12190 − 4.59213I −3.41886 + 3.20482I
u = −1.61803
a = 0.09237 + 2.05693I
b = 0.39130 + 2.05693I
−13.0786 1.41678 + 0.I
u = −1.61803
a = 0.09237 − 2.05693I
b = 0.39130 − 2.05693I
−13.0786 1.41678 + 0.I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.61803
a = 0.11987 + 2.08307I
b = −0.18493 + 1.72753I
−16.7777 + 1.9724I −7.42428 − 3.68478I
u = −1.61803
a = 0.11987 − 2.08307I
b = −0.18493 − 1.72753I
−16.7777 − 1.9724I −7.42428 + 3.68478I
u = −1.61803
a = −0.30825 + 2.30281I
b = −0.61305 + 2.65836I
−16.7777 − 1.9724I −7.42428 + 3.68478I
u = −1.61803
a = −0.30825 − 2.30281I
b = −0.61305 − 2.65836I
−16.7777 + 1.9724I −7.42428 − 3.68478I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
6
+ 5u
5
+ 7u
4
− 2u
2
+ 3u − 1)
4
)(u
22
− 19u
21
+ ··· + 33u + 11)
· (u
30
− 14u
29
+ ··· − 1674u + 180)
c
2
, c
10
(u
22
− u
21
+ ··· − 5u
2
− 1)(u
24
− 5u
23
+ ··· − 70u − 359)
· (u
30
− u
29
+ ··· − 4u + 1)
c
3
, c
8
(u
22
+ 8u
20
+ ··· + 6u
2
− 1)(u
24
− u
23
+ ··· − 4244u + 59)
· (u
30
+ 25u
28
+ ··· + 14u
2
+ 1)
c
4
, c
5
((u
2
+ u − 1)
12
)(u
22
− 12u
20
+ ··· + 2u + 1)
· (u
30
− 13u
29
+ ··· − 96u + 64)
c
6
((u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)
4
)(u
22
+ 6u
21
+ ··· + 26u + 5)
· (u
30
+ 9u
29
+ ··· + 58u + 4)
c
7
(u
22
− u
21
+ ··· + 6u
2
− 1)(u
24
+ u
23
+ ··· − 34758u − 11549)
· (u
30
+ u
29
+ ··· + 134u + 43)
c
9
((u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)
4
)(u
22
− 6u
21
+ ··· − 26u + 5)
· (u
30
+ 9u
29
+ ··· + 58u + 4)
c
11
((u
2
+ u − 1)
12
)(u
22
− 12u
20
+ ··· − 2u + 1)
· (u
30
− 13u
29
+ ··· − 96u + 64)
c
12
(u
22
+ 8u
20
+ ··· + 6u
2
− 1)(u
24
− u
23
+ ··· − 4244u + 59)
· (u
30
+ 25u
28
+ ··· + 14u
2
+ 1)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
6
− 11y
5
+ 45y
4
− 60y
3
− 10y
2
− 5y + 1)
4
· (y
22
− 31y
21
+ ··· − 19833y + 121)
· (y
30
− 42y
29
+ ··· − 660636y + 32400)
c
2
, c
10
(y
22
− 3y
21
+ ··· + 10y + 1)(y
24
− y
23
+ ··· + 306712y + 128881)
· (y
30
+ 27y
29
+ ··· + 10y + 1)
c
3
, c
8
, c
12
(y
22
+ 16y
21
+ ··· − 12y + 1)(y
24
+ 35y
23
+ ··· − 17208900y + 3481)
· (y
30
+ 50y
29
+ ··· + 28y + 1)
c
4
, c
5
, c
11
((y
2
− 3y + 1)
12
)(y
22
− 24y
21
+ ··· − 16y + 1)
· (y
30
− 27y
29
+ ··· + 7168y + 4096)
c
6
, c
9
((y
6
+ 5y
5
+ ··· − 5y + 1)
4
)(y
22
+ 16y
21
+ ··· + 44y + 25)
· (y
30
+ 21y
29
+ ··· − 204y + 16)
c
7
(y
22
+ 15y
21
+ ··· − 12y + 1)
· (y
24
+ 27y
23
+ ··· − 597684620y + 133379401)
· (y
30
+ 37y
29
+ ··· − 12796y + 1849)
21
