12n
0796
(K12n
0796
)
A knot diagram
1
Linearized knot diagam
4 7 10 9 11 2 12 5 1 2 7 8
Solving Sequence
2,7 3,11
12 8 6 5 10 4 1 9
c
2
c
11
c
7
c
6
c
5
c
10
c
3
c
1
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.55932 × 10
237
u
68
+ 4.63994 × 10
237
u
67
+ ··· + 4.94979 × 10
240
b + 1.30744 × 10
242
,
7.84763 × 10
240
u
68
− 1.52555 × 10
241
u
67
+ ··· + 8.51859 × 10
243
a + 7.61648 × 10
244
,
u
69
− 2u
68
+ ··· + 5609u + 1721i
I
u
2
= h−1472105u
20
+ 1018220u
19
+ ··· + 1155956b − 2256995,
969434u
20
− 866657u
19
+ ··· + 1155956a − 2244463, u
21
− u
20
+ ··· + u − 1i
* 2 irreducible components of dim
C
= 0, with total 90 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
= h1.56 × 10
237
u
68
+ 4.64 × 10
237
u
67
+ · · · + 4.95 × 10
240
b + 1.31 ×
10
242
, 7.85 × 10
240
u
68
− 1.53 × 10
241
u
67
+ · · · + 8.52 × 10
243
a + 7.62 ×
10
244
, u
69
− 2u
68
+ · · · + 5609u + 1721i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
11
=
−0.000921236u
68
+ 0.00179085u
67
+ ··· − 43.1069u − 8.94101
−0.000315028u
68
− 0.000937401u
67
+ ··· − 31.1935u − 26.4140
a
12
=
−0.000921236u
68
+ 0.00179085u
67
+ ··· − 43.1069u − 8.94101
−0.000404125u
68
− 0.00110399u
67
+ ··· − 29.3185u − 26.3252
a
8
=
0.000650255u
68
− 0.00261630u
67
+ ··· − 27.0684u − 14.1292
0.00264634u
68
− 0.00616524u
67
+ ··· + 51.9013u − 0.182253
a
6
=
u
u
a
5
=
0.00238017u
68
− 0.00420828u
67
+ ··· + 72.7085u + 11.6824
−0.00160834u
68
+ 0.00384638u
67
+ ··· − 14.9392u + 5.56054
a
10
=
−0.000606208u
68
+ 0.00272825u
67
+ ··· − 11.9134u + 17.4730
−0.000315028u
68
− 0.000937401u
67
+ ··· − 31.1935u − 26.4140
a
4
=
0.00315336u
68
− 0.00460678u
67
+ ··· + 75.7131u + 28.1976
−0.00117961u
68
+ 0.00385784u
67
+ ··· + 8.86048u + 21.3205
a
1
=
−0.00370793u
68
+ 0.00810308u
67
+ ··· − 52.0777u − 5.15730
−0.00114283u
68
+ 0.000233290u
67
+ ··· − 63.0317u − 36.7696
a
9
=
0.00335059u
68
− 0.00924250u
67
+ ··· + 29.6036u − 19.7274
0.00574565u
68
− 0.0116910u
67
+ ··· + 104.318u + 9.12336
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.00547948u
68
+ 0.0175300u
67
+ ··· − 64.8102u + 67.4117
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
69
− 9u
68
+ ··· + 1142u − 73
c
2
, c
6
u
69
− 2u
68
+ ··· + 5609u + 1721
c
3
u
69
− 9u
67
+ ··· + 7145u + 559
c
4
, c
8
u
69
+ 3u
68
+ ··· + 20u + 4
c
5
u
69
+ u
68
+ ··· − 1168u + 437
c
7
, c
11
, c
12
u
69
− 2u
68
+ ··· + 225u + 161
c
9
u
69
+ 6u
68
+ ··· − 59u + 19
c
10
u
69
− 38u
67
+ ··· + 3400u + 644
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
69
+ 25y
68
+ ··· + 523064y −5329
c
2
, c
6
y
69
+ 70y
68
+ ··· − 122107391y −2961841
c
3
y
69
− 18y
68
+ ··· + 16869293y −312481
c
4
, c
8
y
69
+ 43y
68
+ ··· − 4352y −16
c
5
y
69
+ 91y
68
+ ··· − 22307192y −190969
c
7
, c
11
, c
12
y
69
− 64y
68
+ ··· − 149015y −25921
c
9
y
69
+ 2y
68
+ ··· − 9629y −361
c
10
y
69
− 76y
68
+ ··· + 45637904y −414736
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.158298 + 0.986188I
a = −0.272064 − 1.303170I
b = −0.115321 − 1.299330I
−5.58857 + 2.81982I −8.00000 + 0.I
u = −0.158298 − 0.986188I
a = −0.272064 + 1.303170I
b = −0.115321 + 1.299330I
−5.58857 − 2.81982I −8.00000 + 0.I
u = 0.083642 + 1.056570I
a = −0.337592 + 1.151720I
b = −0.02643 + 1.67928I
−1.73341 − 7.58301I 0
u = 0.083642 − 1.056570I
a = −0.337592 − 1.151720I
b = −0.02643 − 1.67928I
−1.73341 + 7.58301I 0
u = 0.897841 + 0.622401I
a = −1.013910 + 0.791688I
b = −0.926980 + 0.100178I
−3.24604 − 2.07530I 0
u = 0.897841 − 0.622401I
a = −1.013910 − 0.791688I
b = −0.926980 − 0.100178I
−3.24604 + 2.07530I 0
u = −0.873469 + 0.076955I
a = 0.183288 + 0.285846I
b = −0.406670 − 0.103429I
−1.062540 + 0.145716I −4.45967 + 4.12515I
u = −0.873469 − 0.076955I
a = 0.183288 − 0.285846I
b = −0.406670 + 0.103429I
−1.062540 − 0.145716I −4.45967 − 4.12515I
u = −0.276545 + 1.134330I
a = −0.419440 − 1.000890I
b = −2.15654 − 0.20349I
5.65453 + 1.08327I 0
u = −0.276545 − 1.134330I
a = −0.419440 + 1.000890I
b = −2.15654 + 0.20349I
5.65453 − 1.08327I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.559678 + 0.527322I
a = −1.39441 − 1.42597I
b = 0.168662 + 0.071411I
−7.42057 − 0.68077I −9.11367 − 4.86767I
u = −0.559678 − 0.527322I
a = −1.39441 + 1.42597I
b = 0.168662 − 0.071411I
−7.42057 + 0.68077I −9.11367 + 4.86767I
u = 0.046375 + 0.765714I
a = 0.29507 + 1.43922I
b = −0.475537 + 1.205130I
−2.54675 + 1.17327I −8.71427 − 1.88942I
u = 0.046375 − 0.765714I
a = 0.29507 − 1.43922I
b = −0.475537 − 1.205130I
−2.54675 − 1.17327I −8.71427 + 1.88942I
u = 1.109890 + 0.543098I
a = −0.167780 − 0.533391I
b = −0.226182 − 0.061038I
2.06906 − 4.86203I 0
u = 1.109890 − 0.543098I
a = −0.167780 + 0.533391I
b = −0.226182 + 0.061038I
2.06906 + 4.86203I 0
u = −0.275066 + 0.704105I
a = −0.58805 − 2.16534I
b = −0.790942 − 0.769428I
−4.81193 + 0.89227I −9.11144 + 1.07907I
u = −0.275066 − 0.704105I
a = −0.58805 + 2.16534I
b = −0.790942 + 0.769428I
−4.81193 − 0.89227I −9.11144 − 1.07907I
u = 0.353524 + 0.612098I
a = −1.23670 + 1.80209I
b = −0.822113 + 0.104555I
−3.12815 − 2.49344I −7.27898 + 4.57610I
u = 0.353524 − 0.612098I
a = −1.23670 − 1.80209I
b = −0.822113 − 0.104555I
−3.12815 + 2.49344I −7.27898 − 4.57610I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.287570 + 0.252312I
a = −0.798351 − 0.401734I
b = −0.700910 − 0.154778I
−3.53458 − 1.35311I 0
u = −1.287570 − 0.252312I
a = −0.798351 + 0.401734I
b = −0.700910 + 0.154778I
−3.53458 + 1.35311I 0
u = 0.438476 + 0.526047I
a = 1.039740 + 0.065197I
b = 0.532056 − 0.185656I
3.24596 − 0.23179I −3.95693 + 3.09799I
u = 0.438476 − 0.526047I
a = 1.039740 − 0.065197I
b = 0.532056 + 0.185656I
3.24596 + 0.23179I −3.95693 − 3.09799I
u = 0.331403 + 0.571115I
a = −0.336557 − 1.133840I
b = −0.333318 + 0.405393I
2.88430 + 3.68981I −3.97105 − 4.01517I
u = 0.331403 − 0.571115I
a = −0.336557 + 1.133840I
b = −0.333318 − 0.405393I
2.88430 − 3.68981I −3.97105 + 4.01517I
u = 0.003294 + 1.405920I
a = 0.424182 − 0.124262I
b = 1.89700 − 0.41536I
8.98523 − 1.65207I 0
u = 0.003294 − 1.405920I
a = 0.424182 + 0.124262I
b = 1.89700 + 0.41536I
8.98523 + 1.65207I 0
u = 1.45256 + 0.09643I
a = 0.882941 + 0.151010I
b = 1.014830 − 0.130294I
−1.63011 − 8.47566I 0
u = 1.45256 − 0.09643I
a = 0.882941 − 0.151010I
b = 1.014830 + 0.130294I
−1.63011 + 8.47566I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.50626 + 1.36552I
a = −0.571385 + 0.832237I
b = −1.55177 + 0.45405I
−0.63369 − 3.48980I 0
u = 0.50626 − 1.36552I
a = −0.571385 − 0.832237I
b = −1.55177 − 0.45405I
−0.63369 + 3.48980I 0
u = 0.304513 + 0.423795I
a = −1.43929 + 2.57107I
b = 0.350883 − 0.574081I
−3.93150 + 6.37374I −6.00431 − 0.55984I
u = 0.304513 − 0.423795I
a = −1.43929 − 2.57107I
b = 0.350883 + 0.574081I
−3.93150 − 6.37374I −6.00431 + 0.55984I
u = −1.45998 + 0.32838I
a = 0.778216 + 0.237416I
b = 1.146240 − 0.151845I
−4.12698 − 1.49086I 0
u = −1.45998 − 0.32838I
a = 0.778216 − 0.237416I
b = 1.146240 + 0.151845I
−4.12698 + 1.49086I 0
u = 0.76152 + 1.29459I
a = 0.565850 − 0.600524I
b = 1.73177 − 0.07649I
6.56829 − 3.06698I 0
u = 0.76152 − 1.29459I
a = 0.565850 + 0.600524I
b = 1.73177 + 0.07649I
6.56829 + 3.06698I 0
u = 0.16311 + 1.51940I
a = −0.278382 + 0.891128I
b = −1.59418 + 1.00854I
3.87490 − 4.93069I 0
u = 0.16311 − 1.51940I
a = −0.278382 − 0.891128I
b = −1.59418 − 1.00854I
3.87490 + 4.93069I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.11712 + 1.52857I
a = 0.503854 − 0.260580I
b = 1.52489 + 0.06927I
5.16690 + 0.91358I 0
u = 0.11712 − 1.52857I
a = 0.503854 + 0.260580I
b = 1.52489 − 0.06927I
5.16690 − 0.91358I 0
u = −0.20757 + 1.56047I
a = −0.180163 − 0.719584I
b = −1.35279 − 0.83587I
3.38686 + 3.48426I 0
u = −0.20757 − 1.56047I
a = −0.180163 + 0.719584I
b = −1.35279 + 0.83587I
3.38686 − 3.48426I 0
u = −0.12399 + 1.59477I
a = 0.681440 + 0.660461I
b = 1.63144 + 0.20640I
8.17838 − 3.00736I 0
u = −0.12399 − 1.59477I
a = 0.681440 − 0.660461I
b = 1.63144 − 0.20640I
8.17838 + 3.00736I 0
u = 0.06103 + 1.60204I
a = 0.782383 − 0.156927I
b = 1.60703 + 0.02690I
5.14159 + 1.38074I 0
u = 0.06103 − 1.60204I
a = 0.782383 + 0.156927I
b = 1.60703 − 0.02690I
5.14159 − 1.38074I 0
u = −0.50160 + 1.56330I
a = −0.605057 − 0.716082I
b = −1.51304 − 0.58879I
1.18052 + 8.01996I 0
u = −0.50160 − 1.56330I
a = −0.605057 + 0.716082I
b = −1.51304 + 0.58879I
1.18052 − 8.01996I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.108395 + 0.310529I
a = 2.04945 − 0.08178I
b = 0.519163 − 1.201190I
1.60702 − 4.33264I −3.39028 + 0.73355I
u = −0.108395 − 0.310529I
a = 2.04945 + 0.08178I
b = 0.519163 + 1.201190I
1.60702 + 4.33264I −3.39028 − 0.73355I
u = 0.31783 + 1.64373I
a = −0.410181 − 0.179193I
b = −1.56558 − 0.16838I
9.72300 + 0.50483I 0
u = 0.31783 − 1.64373I
a = −0.410181 + 0.179193I
b = −1.56558 + 0.16838I
9.72300 − 0.50483I 0
u = −0.112837 + 0.298176I
a = 1.372770 + 0.307949I
b = 0.223037 + 0.869700I
−0.66690 + 1.42409I −5.32505 − 6.58254I
u = −0.112837 − 0.298176I
a = 1.372770 − 0.307949I
b = 0.223037 − 0.869700I
−0.66690 − 1.42409I −5.32505 + 6.58254I
u = −0.312476
a = 1.51887
b = −0.349862
−0.836204 −10.8240
u = −0.27602 + 1.70711I
a = −0.473587 − 0.096462I
b = −1.57240 − 0.17128I
5.92558 + 5.18269I 0
u = −0.27602 − 1.70711I
a = −0.473587 + 0.096462I
b = −1.57240 + 0.17128I
5.92558 − 5.18269I 0
u = 0.31729 + 1.70235I
a = 0.215927 − 0.598368I
b = 1.142090 − 0.229954I
4.02110 + 1.66857I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.31729 − 1.70235I
a = 0.215927 + 0.598368I
b = 1.142090 + 0.229954I
4.02110 − 1.66857I 0
u = 0.26471 + 1.72015I
a = −0.676450 + 0.114182I
b = −1.78553 + 0.24731I
10.1818 − 10.1391I 0
u = 0.26471 − 1.72015I
a = −0.676450 − 0.114182I
b = −1.78553 − 0.24731I
10.1818 + 10.1391I 0
u = 0.56884 + 1.65411I
a = 0.528673 − 0.738965I
b = 1.73021 − 0.61726I
4.1767 − 15.8025I 0
u = 0.56884 − 1.65411I
a = 0.528673 + 0.738965I
b = 1.73021 + 0.61726I
4.1767 + 15.8025I 0
u = −0.66790 + 1.62331I
a = 0.490922 + 0.682589I
b = 1.64092 + 0.46630I
0.41185 + 9.31633I 0
u = −0.66790 − 1.62331I
a = 0.490922 − 0.682589I
b = 1.64092 − 0.46630I
0.41185 − 9.31633I 0
u = −0.05409 + 1.77796I
a = 0.214954 + 0.777838I
b = 1.230930 + 0.437174I
4.73411 + 4.44269I 0
u = −0.05409 − 1.77796I
a = 0.214954 − 0.777838I
b = 1.230930 − 0.437174I
4.73411 − 4.44269I 0
11
II.
I
u
2
= h−1.47 × 10
6
u
20
+ 1.02 × 10
6
u
19
+ · · · + 1.16 × 10
6
b − 2.26 × 10
6
, 9.69 ×
10
5
u
20
− 8.67 × 10
5
u
19
+ · · · + 1.16 × 10
6
a − 2.24 × 10
6
, u
21
− u
20
+ · · · + u − 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
11
=
−0.838643u
20
+ 0.749732u
19
+ ··· − 0.873164u + 1.94165
1.27350u
20
− 0.880847u
19
+ ··· + 0.587410u + 1.95249
a
12
=
−0.838643u
20
+ 0.749732u
19
+ ··· − 0.873164u + 1.94165
0.936639u
20
− 0.594961u
19
+ ··· − 0.162322u + 1.86358
a
8
=
1.75994u
20
+ 1.25748u
19
+ ··· − 8.26896u + 2.95195
2.45099u
20
− 0.835356u
19
+ ··· − 0.576876u + 3.00745
a
6
=
u
u
a
5
=
−1.13843u
20
− 1.31272u
19
+ ··· + 8.94957u − 2.96191
0.218346u
20
− 0.0130316u
19
+ ··· + 1.52471u + 0.716223
a
10
=
−2.11214u
20
+ 1.63058u
19
+ ··· − 1.46057u − 0.0108412
1.27350u
20
− 0.880847u
19
+ ··· + 0.587410u + 1.95249
a
4
=
−3.37269u
20
+ 2.25418u
19
+ ··· − 0.270532u − 1.59771
0.911568u
20
− 0.205314u
19
+ ··· − 0.283777u + 1.12991
a
1
=
−0.0729249u
20
− 0.544418u
19
+ ··· + 1.15694u − 3.07156
−1.75142u
20
+ 0.273581u
19
+ ··· + 0.0784632u − 0.836167
a
9
=
−1.97499u
20
+ 2.56253u
19
+ ··· + 0.0537434u − 3.30592
0.305597u
20
+ 0.371861u
19
+ ··· − 1.77387u + 2.31582
(ii) Obstruction class = 1
(iii) Cusp Shapes =
3328575
288989
u
20
−
3093691
577978
u
19
+ ··· +
1150671
577978
u +
97487
577978
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
21
− 4u
20
+ ··· + 4u − 1
c
2
u
21
− u
20
+ ··· + u − 1
c
3
u
21
+ u
20
+ ··· + 13u + 9
c
4
u
21
+ 2u
20
+ ··· + 8u + 4
c
5
u
21
+ 7u
19
+ ··· + 30u + 1
c
6
u
21
+ u
20
+ ··· + u + 1
c
7
u
21
− u
20
+ ··· + 5u − 1
c
8
u
21
− 2u
20
+ ··· + 8u − 4
c
9
u
21
+ u
20
+ ··· − 3u − 1
c
10
u
21
− 3u
20
+ ··· + 12u − 4
c
11
, c
12
u
21
+ u
20
+ ··· + 5u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
+ 8y
20
+ ··· − 4y −1
c
2
, c
6
y
21
+ 13y
20
+ ··· + 9y −1
c
3
y
21
− 3y
20
+ ··· − 83y −81
c
4
, c
8
y
21
+ 14y
20
+ ··· − 112y −16
c
5
y
21
+ 14y
20
+ ··· + 864y −1
c
7
, c
11
, c
12
y
21
− 25y
20
+ ··· + 9y −1
c
9
y
21
− 3y
20
+ ··· − y −1
c
10
y
21
− 17y
20
+ ··· − 64y −16
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.561157 + 0.901561I
a = −0.68758 − 1.44240I
b = −0.590397 − 0.678765I
−5.00046 + 1.80387I −12.21784 − 5.60758I
u = −0.561157 − 0.901561I
a = −0.68758 + 1.44240I
b = −0.590397 + 0.678765I
−5.00046 − 1.80387I −12.21784 + 5.60758I
u = 0.807360 + 0.286313I
a = −1.38109 + 0.86594I
b = −0.587723 + 0.592712I
−4.40952 + 1.11701I −14.5809 − 2.0497I
u = 0.807360 − 0.286313I
a = −1.38109 − 0.86594I
b = −0.587723 − 0.592712I
−4.40952 − 1.11701I −14.5809 + 2.0497I
u = 0.743753 + 0.239370I
a = −0.276431 + 0.285848I
b = 0.508126 + 0.521370I
−1.33875 + 0.63912I −11.08801 − 5.90714I
u = 0.743753 − 0.239370I
a = −0.276431 − 0.285848I
b = 0.508126 − 0.521370I
−1.33875 − 0.63912I −11.08801 + 5.90714I
u = −0.645247 + 0.396216I
a = −0.362993 + 0.499905I
b = 0.171757 + 0.896114I
0.95419 + 5.02373I −10.96767 − 6.73427I
u = −0.645247 − 0.396216I
a = −0.362993 − 0.499905I
b = 0.171757 − 0.896114I
0.95419 − 5.02373I −10.96767 + 6.73427I
u = 1.24638
a = −0.985958
b = −1.01348
−4.18100 −9.64630
u = 0.011700 + 1.320960I
a = 0.316294 − 0.431096I
b = 1.72321 − 0.15242I
7.96622 + 0.10384I −4.19566 − 0.46618I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.011700 − 1.320960I
a = 0.316294 + 0.431096I
b = 1.72321 + 0.15242I
7.96622 − 0.10384I −4.19566 + 0.46618I
u = −0.435613 + 1.277620I
a = −0.403231 − 0.827190I
b = −1.96724 − 0.36213I
5.47011 + 2.02608I −7.19785 − 3.46074I
u = −0.435613 − 1.277620I
a = −0.403231 + 0.827190I
b = −1.96724 + 0.36213I
5.47011 − 2.02608I −7.19785 + 3.46074I
u = 0.511370 + 0.359085I
a = 1.95727 − 1.44685I
b = −0.377286 − 0.543412I
−7.65043 + 1.27003I −13.8530 − 5.9198I
u = 0.511370 − 0.359085I
a = 1.95727 + 1.44685I
b = −0.377286 + 0.543412I
−7.65043 − 1.27003I −13.8530 + 5.9198I
u = −0.512008 + 0.216126I
a = 2.53508 + 0.79978I
b = 0.013476 − 0.796482I
−4.42994 + 7.07571I −12.1028 − 7.6122I
u = −0.512008 − 0.216126I
a = 2.53508 − 0.79978I
b = 0.013476 + 0.796482I
−4.42994 − 7.07571I −12.1028 + 7.6122I
u = −0.18694 + 1.62746I
a = 0.543871 + 0.241555I
b = 1.41334 − 0.08784I
6.13244 − 1.40053I −1.40328 + 1.79349I
u = −0.18694 − 1.62746I
a = 0.543871 − 0.241555I
b = 1.41334 + 0.08784I
6.13244 + 1.40053I −1.40328 − 1.79349I
u = 0.14359 + 1.63447I
a = −0.248205 + 0.792792I
b = −1.30052 + 0.82918I
2.75172 − 5.22509I −10.06988 + 5.83206I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.14359 − 1.63447I
a = −0.248205 − 0.792792I
b = −1.30052 − 0.82918I
2.75172 + 5.22509I −10.06988 − 5.83206I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
21
− 4u
20
+ ··· + 4u − 1)(u
69
− 9u
68
+ ··· + 1142u − 73)
c
2
(u
21
− u
20
+ ··· + u − 1)(u
69
− 2u
68
+ ··· + 5609u + 1721)
c
3
(u
21
+ u
20
+ ··· + 13u + 9)(u
69
− 9u
67
+ ··· + 7145u + 559)
c
4
(u
21
+ 2u
20
+ ··· + 8u + 4)(u
69
+ 3u
68
+ ··· + 20u + 4)
c
5
(u
21
+ 7u
19
+ ··· + 30u + 1)(u
69
+ u
68
+ ··· − 1168u + 437)
c
6
(u
21
+ u
20
+ ··· + u + 1)(u
69
− 2u
68
+ ··· + 5609u + 1721)
c
7
(u
21
− u
20
+ ··· + 5u − 1)(u
69
− 2u
68
+ ··· + 225u + 161)
c
8
(u
21
− 2u
20
+ ··· + 8u − 4)(u
69
+ 3u
68
+ ··· + 20u + 4)
c
9
(u
21
+ u
20
+ ··· − 3u − 1)(u
69
+ 6u
68
+ ··· − 59u + 19)
c
10
(u
21
− 3u
20
+ ··· + 12u − 4)(u
69
− 38u
67
+ ··· + 3400u + 644)
c
11
, c
12
(u
21
+ u
20
+ ··· + 5u + 1)(u
69
− 2u
68
+ ··· + 225u + 161)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
21
+ 8y
20
+ ··· − 4y −1)(y
69
+ 25y
68
+ ··· + 523064y −5329)
c
2
, c
6
(y
21
+ 13y
20
+ ··· + 9y −1)
· (y
69
+ 70y
68
+ ··· − 122107391y −2961841)
c
3
(y
21
− 3y
20
+ ··· − 83y −81)
· (y
69
− 18y
68
+ ··· + 16869293y −312481)
c
4
, c
8
(y
21
+ 14y
20
+ ··· − 112y −16)(y
69
+ 43y
68
+ ··· − 4352y −16)
c
5
(y
21
+ 14y
20
+ ··· + 864y −1)
· (y
69
+ 91y
68
+ ··· − 22307192y −190969)
c
7
, c
11
, c
12
(y
21
− 25y
20
+ ··· + 9y −1)(y
69
− 64y
68
+ ··· − 149015y −25921)
c
9
(y
21
− 3y
20
+ ··· − y −1)(y
69
+ 2y
68
+ ··· − 9629y −361)
c
10
(y
21
− 17y
20
+ ··· − 64y −16)
· (y
69
− 76y
68
+ ··· + 45637904y −414736)
19
