12n
0729
(K12n
0729
)
A knot diagram
1
Linearized knot diagam
4 10 9 10 1 3 4 11 7 1 9 6
Solving Sequence
4,10 5,7
8 9 3 2 1 11 6 12
c
4
c
7
c
9
c
3
c
2
c
1
c
10
c
6
c
12
c
5
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h8.98709 × 10
197
u
57
+ 3.28099 × 10
198
u
56
+ ··· + 1.56771 × 10
200
b + 3.12866 × 10
201
,
4.24469 × 10
201
u
57
+ 9.55967 × 10
201
u
56
+ ··· + 1.61004 × 10
203
a + 8.17316 × 10
204
,
u
58
+ u
57
+ ··· + 7117u − 1027i
I
u
2
= h2.79079 × 10
21
u
21
+ 1.76550 × 10
20
u
20
+ ··· + 2.38585 × 10
23
b − 1.48787 × 10
23
,
4.29144 × 10
23
u
21
+ 2.28509 × 10
23
u
20
+ ··· + 2.14726 × 10
24
a − 1.05273 × 10
24
, u
22
− 10u
20
+ ··· + 73u − 9i
* 2 irreducible components of dim
C
= 0, with total 80 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
= h8.99 × 10
197
u
57
+ 3.28 × 10
198
u
56
+ · · · + 1.57 × 10
200
b + 3.13 ×
10
201
, 4.24 × 10
201
u
57
+ 9.56 × 10
201
u
56
+ · · · + 1.61 × 10
203
a + 8.17 ×
10
204
, u
58
+ u
57
+ · · · + 7117u − 1027i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
7
=
−0.0263639u
57
− 0.0593753u
56
+ ··· + 306.471u − 50.7637
−0.00573262u
57
− 0.0209285u
56
+ ··· + 140.907u − 19.9569
a
8
=
−0.0320965u
57
− 0.0803038u
56
+ ··· + 447.378u − 70.7206
−0.00573262u
57
− 0.0209285u
56
+ ··· + 140.907u − 19.9569
a
9
=
−0.0276476u
57
− 0.0285016u
56
+ ··· − 4.44141u − 21.8460
−0.0133010u
57
− 0.0190926u
56
+ ··· + 17.6945u − 4.17250
a
3
=
0.00962893u
57
+ 0.0347661u
56
+ ··· − 153.709u + 17.1775
0.00137276u
57
+ 0.0136626u
56
+ ··· − 118.572u + 17.6094
a
2
=
0.00962893u
57
+ 0.0347661u
56
+ ··· − 153.709u + 17.1775
−0.0130047u
57
− 0.0227497u
56
+ ··· + 50.4397u − 8.20641
a
1
=
−0.00337579u
57
+ 0.0120164u
56
+ ··· − 103.269u + 8.97114
−0.0130047u
57
− 0.0227497u
56
+ ··· + 50.4397u − 8.20641
a
11
=
0.0273854u
57
+ 0.0503706u
56
+ ··· − 200.581u + 48.9873
0.0113327u
57
+ 0.0369171u
56
+ ··· − 227.216u + 32.7951
a
6
=
−0.00894778u
57
− 0.00254877u
56
+ ··· − 150.638u + 30.0737
0.0204778u
57
+ 0.0335185u
56
+ ··· − 83.8092u + 15.3951
a
12
=
−0.0314997u
57
− 0.0527340u
56
+ ··· + 69.4621u − 13.0531
−0.0300231u
57
− 0.0787118u
56
+ ··· + 398.575u − 61.1428
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0373141u
57
− 0.119218u
56
+ ··· + 753.945u − 118.284
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
58
+ 7u
57
+ ··· − 22459u + 1219
c
2
u
58
+ 4u
57
+ ··· + 1084u + 167
c
3
u
58
+ u
57
+ ··· − 283u − 43
c
4
u
58
− u
57
+ ··· − 7117u − 1027
c
5
, c
12
u
58
+ 2u
57
+ ··· + 1960u + 664
c
6
u
58
+ 6u
57
+ ··· + 10u + 1
c
7
u
58
+ 9u
56
+ ··· − 10008u − 584
c
8
, c
11
u
58
+ u
57
+ ··· + 1066u + 97
c
9
u
58
+ u
57
+ ··· + u − 1
c
10
u
58
− 4u
57
+ ··· + 129032u − 9829
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
58
− 61y
57
+ ··· − 240710163y + 1485961
c
2
y
58
− 8y
57
+ ··· − 98574y + 27889
c
3
y
58
− 9y
57
+ ··· − 167293y + 1849
c
4
y
58
− 67y
57
+ ··· − 53586855y + 1054729
c
5
, c
12
y
58
+ 36y
57
+ ··· − 6938496y + 440896
c
6
y
58
+ 8y
57
+ ··· − 184y + 1
c
7
y
58
+ 18y
57
+ ··· − 5014784y + 341056
c
8
, c
11
y
58
+ 23y
57
+ ··· + 106020y + 9409
c
9
y
58
− 19y
57
+ ··· − 27y + 1
c
10
y
58
− 52y
57
+ ··· − 2754353568y + 96609241
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.984047 + 0.106547I
a = 0.732984 + 0.485124I
b = −0.71312 + 2.03208I
−5.10938 − 4.31500I 0
u = −0.984047 − 0.106547I
a = 0.732984 − 0.485124I
b = −0.71312 − 2.03208I
−5.10938 + 4.31500I 0
u = 0.951459 + 0.036280I
a = 0.756616 + 0.985473I
b = −0.14380 + 1.51989I
2.83534 − 4.32094I 0
u = 0.951459 − 0.036280I
a = 0.756616 − 0.985473I
b = −0.14380 − 1.51989I
2.83534 + 4.32094I 0
u = 0.889685 + 0.338008I
a = 1.06446 − 1.48155I
b = −0.428769 − 0.679768I
−0.25157 + 3.22294I 0
u = 0.889685 − 0.338008I
a = 1.06446 + 1.48155I
b = −0.428769 + 0.679768I
−0.25157 − 3.22294I 0
u = 0.938379 + 0.011522I
a = −0.161328 − 0.401628I
b = 0.308280 + 0.060433I
−1.102690 − 0.062220I 0
u = 0.938379 − 0.011522I
a = −0.161328 + 0.401628I
b = 0.308280 − 0.060433I
−1.102690 + 0.062220I 0
u = −0.735401 + 0.007028I
a = 1.37029 − 1.13833I
b = −0.71739 − 1.26490I
4.02435 + 6.74078I −6.40897 − 6.18806I
u = −0.735401 − 0.007028I
a = 1.37029 + 1.13833I
b = −0.71739 + 1.26490I
4.02435 − 6.74078I −6.40897 + 6.18806I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.611627 + 0.386837I
a = 1.49854 − 0.36748I
b = −0.269457 + 0.990833I
0.571664 − 1.277470I −8.81085 + 0.40906I
u = 0.611627 − 0.386837I
a = 1.49854 + 0.36748I
b = −0.269457 − 0.990833I
0.571664 + 1.277470I −8.81085 − 0.40906I
u = −0.543172 + 0.422725I
a = 0.719118 + 0.935767I
b = −1.320790 + 0.324187I
4.86373 + 2.09347I −6.47153 − 2.48732I
u = −0.543172 − 0.422725I
a = 0.719118 − 0.935767I
b = −1.320790 − 0.324187I
4.86373 − 2.09347I −6.47153 + 2.48732I
u = 1.208100 + 0.579060I
a = −0.037426 − 0.757251I
b = 0.521975 − 0.291948I
−0.975445 − 0.218387I 0
u = 1.208100 − 0.579060I
a = −0.037426 + 0.757251I
b = 0.521975 + 0.291948I
−0.975445 + 0.218387I 0
u = 0.660076
a = 0.366125
b = 0.323077
−1.09302 −7.08600
u = −0.554976 + 0.140362I
a = 1.75463 − 1.19601I
b = 0.273584 + 0.107138I
4.60137 − 0.26241I −5.57820 + 1.37492I
u = −0.554976 − 0.140362I
a = 1.75463 + 1.19601I
b = 0.273584 − 0.107138I
4.60137 + 0.26241I −5.57820 − 1.37492I
u = 1.34287 + 0.51625I
a = 0.360673 − 0.444881I
b = −0.86318 − 2.71719I
−1.29465 − 2.40549I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.34287 − 0.51625I
a = 0.360673 + 0.444881I
b = −0.86318 + 2.71719I
−1.29465 + 2.40549I 0
u = −1.09636 + 0.94746I
a = 0.401125 + 0.121349I
b = 0.133549 − 1.228370I
−4.43749 − 1.69406I 0
u = −1.09636 − 0.94746I
a = 0.401125 − 0.121349I
b = 0.133549 + 1.228370I
−4.43749 + 1.69406I 0
u = −0.479931 + 0.256201I
a = 0.80829 + 1.69787I
b = 0.357974 − 0.899794I
4.89868 − 5.92269I −8.28735 + 6.67085I
u = −0.479931 − 0.256201I
a = 0.80829 − 1.69787I
b = 0.357974 + 0.899794I
4.89868 + 5.92269I −8.28735 − 6.67085I
u = −1.45716
a = −0.652587
b = 1.66458
−6.65741 0
u = 1.51660 + 0.17170I
a = −0.397509 − 0.123089I
b = 2.78994 − 1.29874I
−2.05878 − 4.62210I 0
u = 1.51660 − 0.17170I
a = −0.397509 + 0.123089I
b = 2.78994 + 1.29874I
−2.05878 + 4.62210I 0
u = 0.159997 + 0.444223I
a = −0.891005 − 0.942470I
b = −0.215135 + 1.292810I
5.40486 + 3.03261I −1.43535 + 3.06435I
u = 0.159997 − 0.444223I
a = −0.891005 + 0.942470I
b = −0.215135 − 1.292810I
5.40486 − 3.03261I −1.43535 − 3.06435I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.55519 + 0.00032I
a = −0.587461 − 0.437982I
b = 0.67801 − 1.40728I
−6.26258 − 2.81974I 0
u = −1.55519 − 0.00032I
a = −0.587461 + 0.437982I
b = 0.67801 + 1.40728I
−6.26258 + 2.81974I 0
u = 0.127053 + 0.418851I
a = 1.23833 − 1.01400I
b = −0.126610 + 0.836327I
−0.617637 − 1.214780I −6.10791 + 5.67942I
u = 0.127053 − 0.418851I
a = 1.23833 + 1.01400I
b = −0.126610 − 0.836327I
−0.617637 + 1.214780I −6.10791 − 5.67942I
u = −1.63145
a = 0.436826
b = −1.65196
−9.90939 0
u = 1.76333 + 0.03132I
a = −0.750182 + 0.469345I
b = 1.20433 + 1.24812I
−4.94459 + 6.18934I 0
u = 1.76333 − 0.03132I
a = −0.750182 − 0.469345I
b = 1.20433 − 1.24812I
−4.94459 − 6.18934I 0
u = 0.222347 + 0.057423I
a = 4.52994 + 3.59770I
b = −0.062776 − 0.383104I
1.83627 − 4.60135I −3.06433 + 1.23782I
u = 0.222347 − 0.057423I
a = 4.52994 − 3.59770I
b = −0.062776 + 0.383104I
1.83627 + 4.60135I −3.06433 − 1.23782I
u = −0.48982 + 1.70817I
a = 0.647515 + 0.422020I
b = −1.71821 + 0.15561I
6.18677 + 0.35665I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.48982 − 1.70817I
a = 0.647515 − 0.422020I
b = −1.71821 − 0.15561I
6.18677 − 0.35665I 0
u = −1.79356 + 0.11460I
a = −0.715949 + 0.568710I
b = 0.49033 + 1.44237I
−7.85182 + 4.36860I 0
u = −1.79356 − 0.11460I
a = −0.715949 − 0.568710I
b = 0.49033 − 1.44237I
−7.85182 − 4.36860I 0
u = 1.62131 + 0.77787I
a = 0.785352 + 0.143559I
b = −1.54041 + 1.26825I
−2.94636 − 6.95100I 0
u = 1.62131 − 0.77787I
a = 0.785352 − 0.143559I
b = −1.54041 − 1.26825I
−2.94636 + 6.95100I 0
u = −1.75534 + 0.48896I
a = 0.227519 + 0.805258I
b = 0.410897 + 0.818197I
0.70429 + 7.95243I 0
u = −1.75534 − 0.48896I
a = 0.227519 − 0.805258I
b = 0.410897 − 0.818197I
0.70429 − 7.95243I 0
u = −1.80778 + 0.38348I
a = −0.171765 − 0.343297I
b = 0.191963 − 0.552646I
−3.74606 − 2.72375I 0
u = −1.80778 − 0.38348I
a = −0.171765 + 0.343297I
b = 0.191963 + 0.552646I
−3.74606 + 2.72375I 0
u = 1.90742 + 0.23418I
a = −0.392220 − 0.010291I
b = −0.096402 − 0.583283I
−2.82054 + 3.11371I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.90742 − 0.23418I
a = −0.392220 + 0.010291I
b = −0.096402 + 0.583283I
−2.82054 − 3.11371I 0
u = −1.87242 + 0.53585I
a = 0.710787 − 0.294332I
b = −1.36569 − 1.62804I
−0.6525 + 15.7491I 0
u = −1.87242 − 0.53585I
a = 0.710787 + 0.294332I
b = −1.36569 + 1.62804I
−0.6525 − 15.7491I 0
u = −1.96832
a = −1.31909
b = 0.902042
−11.0216 0
u = 0.12762 + 2.16706I
a = −0.451547 + 0.382090I
b = 1.61400 − 0.44696I
6.61103 − 6.39087I 0
u = 0.12762 − 2.16706I
a = −0.451547 − 0.382090I
b = 1.61400 + 0.44696I
6.61103 + 6.39087I 0
u = 1.97864 + 0.91027I
a = 0.389495 + 0.063606I
b = −0.011945 + 1.259660I
−1.21978 − 5.87932I 0
u = 1.97864 − 0.91027I
a = 0.389495 − 0.063606I
b = −0.011945 − 1.259660I
−1.21978 + 5.87932I 0
10
II. I
u
2
=
h2.79×10
21
u
21
+1.77×10
20
u
20
+· · ·+2.39×10
23
b−1.49×10
23
, 4.29×10
23
u
21
+
2.29 × 10
23
u
20
+ · · · + 2.15 × 10
24
a − 1.05 × 10
24
, u
22
− 10u
20
+ · · · + 73u − 9i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
7
=
−0.199856u
21
− 0.106419u
20
+ ··· + 19.6045u + 0.490264
−0.0116973u
21
− 0.000739990u
20
+ ··· − 7.08742u + 0.623622
a
8
=
−0.211553u
21
− 0.107159u
20
+ ··· + 12.5171u + 1.11389
−0.0116973u
21
− 0.000739990u
20
+ ··· − 7.08742u + 0.623622
a
9
=
−0.336127u
21
− 0.0767089u
20
+ ··· + 51.7425u − 6.09472
−0.00505495u
21
+ 0.0250633u
20
+ ··· − 1.05021u + 0.800312
a
3
=
0.324297u
21
+ 0.300057u
20
+ ··· − 20.7701u + 6.75595
0.179573u
21
+ 0.111102u
20
+ ··· − 23.5518u + 3.45052
a
2
=
0.324297u
21
+ 0.300057u
20
+ ··· − 20.7701u + 6.75595
−0.0962234u
21
− 0.138807u
20
+ ··· − 4.56630u + 0.750012
a
1
=
0.228074u
21
+ 0.161250u
20
+ ··· − 25.3364u + 7.50597
−0.0962234u
21
− 0.138807u
20
+ ··· − 4.56630u + 0.750012
a
11
=
0.318413u
21
+ 0.152269u
20
+ ··· − 39.8613u + 2.56934
−0.0745587u
21
− 0.0585677u
20
+ ··· + 12.8859u − 2.38557
a
6
=
0.417332u
21
+ 0.134515u
20
+ ··· − 84.2017u + 11.3295
0.0872425u
21
+ 0.0721007u
20
+ ··· − 7.96511u − 0.936957
a
12
=
−0.196498u
21
− 0.237839u
20
+ ··· + 11.6692u − 7.14808
−0.238971u
21
− 0.175726u
20
+ ··· + 32.6164u − 4.66605
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
457412961431615476330833
238584851591663803618957
u
21
−
254429452136571387242067
238584851591663803618957
u
20
+ ··· +
58966595376988644279933534
238584851591663803618957
u −
10233901156098748389216510
238584851591663803618957
11
(iv) u-Polynomials at the component
12
Crossings u-Polynomials at each crossing
c
1
u
22
− 12u
21
+ ··· − 9u + 1
c
2
u
22
− u
21
+ ··· + 72u − 63
c
3
u
22
− u
20
+ ··· − 7u + 1
c
4
u
22
− 10u
20
+ ··· + 73u − 9
c
5
u
22
− u
21
+ ··· + 24u + 8
c
6
u
22
− u
21
+ ··· − 16u − 3
c
7
u
22
+ 3u
21
+ ··· + 8u − 56
c
8
u
22
− 2u
21
+ ··· + 2u + 1
c
9
u
22
+ 6u
21
+ ··· + 5u + 1
c
10
u
22
− 7u
21
+ ··· + 20u − 7
c
11
u
22
+ 2u
21
+ ··· − 2u + 1
c
12
u
22
+ u
21
+ ··· − 24u + 8
13
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
− 22y
21
+ ··· + 83y + 1
c
2
y
22
− 13y
21
+ ··· − 12240y + 3969
c
3
y
22
− 2y
21
+ ··· − 31y + 1
c
4
y
22
− 20y
21
+ ··· + 395y + 81
c
5
, c
12
y
22
+ 7y
21
+ ··· + 64y + 64
c
6
y
22
− 5y
21
+ ··· − 34y + 9
c
7
y
22
+ 5y
21
+ ··· + 39360y + 3136
c
8
, c
11
y
22
+ 6y
21
+ ··· − 2y + 1
c
9
y
22
− 12y
21
+ ··· − 13y + 1
c
10
y
22
− 21y
21
+ ··· + 6y + 49
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.074930 + 0.105891I
a = 1.065490 − 0.834834I
b = −0.116473 − 0.664580I
−0.49759 + 2.56520I −11.45169 − 0.03293I
u = 1.074930 − 0.105891I
a = 1.065490 + 0.834834I
b = −0.116473 + 0.664580I
−0.49759 − 2.56520I −11.45169 + 0.03293I
u = −0.534288 + 0.431482I
a = −0.434617 − 1.025970I
b = −0.157192 + 0.475540I
−1.81004 − 0.52019I −15.0020 + 3.2051I
u = −0.534288 − 0.431482I
a = −0.434617 + 1.025970I
b = −0.157192 − 0.475540I
−1.81004 + 0.52019I −15.0020 − 3.2051I
u = 0.661139 + 0.110313I
a = 1.56420 + 1.41244I
b = −0.229898 + 0.895312I
1.36966 − 5.12657I −11.4526 + 9.5918I
u = 0.661139 − 0.110313I
a = 1.56420 − 1.41244I
b = −0.229898 − 0.895312I
1.36966 + 5.12657I −11.4526 − 9.5918I
u = 1.395400 + 0.151449I
a = −0.635171 + 0.368343I
b = 1.07115 + 1.63083I
−6.51584 + 4.02828I −15.4736 − 6.2870I
u = 1.395400 − 0.151449I
a = −0.635171 − 0.368343I
b = 1.07115 − 1.63083I
−6.51584 − 4.02828I −15.4736 + 6.2870I
u = −0.51433 + 1.35727I
a = 0.844430 + 0.510048I
b = −1.50481 + 0.10273I
6.84628 + 0.34484I 0.584936 + 0.037274I
u = −0.51433 − 1.35727I
a = 0.844430 − 0.510048I
b = −1.50481 − 0.10273I
6.84628 − 0.34484I 0.584936 − 0.037274I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.07066 + 1.58496I
a = −0.581666 + 0.511900I
b = 1.29498 − 0.63093I
7.58470 − 6.19359I −1.94969 + 4.30160I
u = 0.07066 − 1.58496I
a = −0.581666 − 0.511900I
b = 1.29498 + 0.63093I
7.58470 + 6.19359I −1.94969 − 4.30160I
u = 1.62037
a = 0.458428
b = −1.67473
−9.98265 −65.6220
u = 1.38984 + 0.85119I
a = −0.299446 + 0.142790I
b = 0.092686 − 1.119880I
−4.73458 + 2.11091I −18.7205 − 5.4471I
u = 1.38984 − 0.85119I
a = −0.299446 − 0.142790I
b = 0.092686 + 1.119880I
−4.73458 − 2.11091I −18.7205 + 5.4471I
u = −1.67782 + 0.22721I
a = −0.181061 + 0.126576I
b = 1.29986 + 1.32033I
−1.70506 + 4.08011I −6.63396 − 1.41336I
u = −1.67782 − 0.22721I
a = −0.181061 − 0.126576I
b = 1.29986 − 1.32033I
−1.70506 − 4.08011I −6.63396 + 1.41336I
u = 0.124026 + 0.167304I
a = 3.57897 − 0.31377I
b = −0.39813 − 1.50149I
5.23332 − 3.56725I −5.47085 + 9.86595I
u = 0.124026 − 0.167304I
a = 3.57897 + 0.31377I
b = −0.39813 + 1.50149I
5.23332 + 3.56725I −5.47085 − 9.86595I
u = −1.82014 + 0.10403I
a = −0.726378 + 0.567727I
b = 0.55876 + 1.35106I
−8.37280 + 4.49491I −17.7083 − 5.1691I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.82014 − 0.10403I
a = −0.726378 − 0.567727I
b = 0.55876 − 1.35106I
−8.37280 − 4.49491I −17.7083 + 5.1691I
u = −1.95919
a = −1.29238
b = 0.852875
−11.1324 −44.8210
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
22
− 12u
21
+ ··· − 9u + 1)(u
58
+ 7u
57
+ ··· − 22459u + 1219)
c
2
(u
22
− u
21
+ ··· + 72u − 63)(u
58
+ 4u
57
+ ··· + 1084u + 167)
c
3
(u
22
− u
20
+ ··· − 7u + 1)(u
58
+ u
57
+ ··· − 283u − 43)
c
4
(u
22
− 10u
20
+ ··· + 73u − 9)(u
58
− u
57
+ ··· − 7117u − 1027)
c
5
(u
22
− u
21
+ ··· + 24u + 8)(u
58
+ 2u
57
+ ··· + 1960u + 664)
c
6
(u
22
− u
21
+ ··· − 16u − 3)(u
58
+ 6u
57
+ ··· + 10u + 1)
c
7
(u
22
+ 3u
21
+ ··· + 8u − 56)(u
58
+ 9u
56
+ ··· − 10008u − 584)
c
8
(u
22
− 2u
21
+ ··· + 2u + 1)(u
58
+ u
57
+ ··· + 1066u + 97)
c
9
(u
22
+ 6u
21
+ ··· + 5u + 1)(u
58
+ u
57
+ ··· + u − 1)
c
10
(u
22
− 7u
21
+ ··· + 20u − 7)(u
58
− 4u
57
+ ··· + 129032u − 9829)
c
11
(u
22
+ 2u
21
+ ··· − 2u + 1)(u
58
+ u
57
+ ··· + 1066u + 97)
c
12
(u
22
+ u
21
+ ··· − 24u + 8)(u
58
+ 2u
57
+ ··· + 1960u + 664)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
22
− 22y
21
+ ··· + 83y + 1)
· (y
58
− 61y
57
+ ··· − 240710163y + 1485961)
c
2
(y
22
− 13y
21
+ ··· − 12240y + 3969)
· (y
58
− 8y
57
+ ··· − 98574y + 27889)
c
3
(y
22
− 2y
21
+ ··· − 31y + 1)(y
58
− 9y
57
+ ··· − 167293y + 1849)
c
4
(y
22
− 20y
21
+ ··· + 395y + 81)
· (y
58
− 67y
57
+ ··· − 53586855y + 1054729)
c
5
, c
12
(y
22
+ 7y
21
+ ··· + 64y + 64)
· (y
58
+ 36y
57
+ ··· − 6938496y + 440896)
c
6
(y
22
− 5y
21
+ ··· − 34y + 9)(y
58
+ 8y
57
+ ··· − 184y + 1)
c
7
(y
22
+ 5y
21
+ ··· + 39360y + 3136)
· (y
58
+ 18y
57
+ ··· − 5014784y + 341056)
c
8
, c
11
(y
22
+ 6y
21
+ ··· − 2y + 1)(y
58
+ 23y
57
+ ··· + 106020y + 9409)
c
9
(y
22
− 12y
21
+ ··· − 13y + 1)(y
58
− 19y
57
+ ··· − 27y + 1)
c
10
(y
22
− 21y
21
+ ··· + 6y + 49)
· (y
58
− 52y
57
+ ··· − 2754353568y + 96609241)
20
