12n
0586
(K12n
0586
)
A knot diagram
1
Linearized knot diagam
3 7 9 12 10 2 12 1 6 5 7 4
Solving Sequence
3,9 4,7
2 1 6 10 5 8 12 11
c
3
c
2
c
1
c
6
c
9
c
5
c
8
c
12
c
11
c
4
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h5.84707 × 10
197
u
67
− 2.16837 × 10
197
u
66
+ ··· + 3.92981 × 10
199
b − 1.61157 × 10
200
,
− 5.53238 × 10
199
u
67
− 9.61476 × 10
198
u
66
+ ··· + 1.84701 × 10
201
a + 1.52628 × 10
202
,
u
68
+ u
67
+ ··· − 106u + 47i
I
u
2
= h−209u
17
− 81u
16
+ ··· + 310b + 36, −244u
17
+ 1029u
16
+ ··· + 1550a + 3366,
u
18
+ 8u
16
+ ··· − u + 1i
* 2 irreducible components of dim
C
= 0, with total 86 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
= h5.85 × 10
197
u
67
− 2.17 × 10
197
u
66
+ · · · + 3.93 × 10
199
b − 1.61 ×
10
200
, −5.53 × 10
199
u
67
− 9.61 × 10
198
u
66
+ · · · + 1.85 × 10
201
a + 1.53 ×
10
202
, u
68
+ u
67
+ · · · − 106u + 47i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
7
=
0.0299532u
67
+ 0.00520559u
66
+ ··· + 50.3165u − 8.26352
−0.0148788u
67
+ 0.00551776u
66
+ ··· − 6.75829u + 4.10088
a
2
=
−0.0362808u
67
− 0.0242750u
66
+ ··· − 44.0012u + 7.42020
−0.00689572u
67
− 0.0259460u
66
+ ··· + 10.0543u − 4.06600
a
1
=
−0.0431766u
67
− 0.0502210u
66
+ ··· − 33.9469u + 3.35420
−0.00689572u
67
− 0.0259460u
66
+ ··· + 10.0543u − 4.06600
a
6
=
−0.0624288u
67
− 0.0963950u
66
+ ··· + 15.2630u − 9.17122
−0.00205894u
67
− 0.0212165u
66
+ ··· + 6.50316u − 1.16309
a
10
=
0.0381559u
67
+ 0.0535170u
66
+ ··· − 3.05160u + 8.01004
−0.0347763u
67
− 0.0318760u
66
+ ··· − 6.01436u + 0.490177
a
5
=
−0.0944015u
67
− 0.124449u
66
+ ··· − 6.54416u − 8.59604
−0.00498418u
67
− 0.00962390u
66
+ ··· + 6.80395u − 1.39075
a
8
=
0.103443u
67
+ 0.122227u
66
+ ··· + 44.4358u + 2.42709
−0.0284046u
67
+ 0.00567057u
66
+ ··· − 13.2395u + 4.22413
a
12
=
−0.0320963u
67
− 0.0324433u
66
+ ··· − 45.2838u + 7.08912
0.00120374u
67
− 0.0159271u
66
+ ··· + 9.86516u − 3.75123
a
11
=
−0.0569399u
67
− 0.0655646u
66
+ ··· − 37.3182u − 4.99682
0.0560391u
67
+ 0.0440243u
66
+ ··· + 22.0532u − 5.21740
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.100434u
67
− 0.0117449u
66
+ ··· − 58.9561u + 13.3433
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
68
+ 27u
67
+ ··· + 475766u + 29929
c
2
, c
6
u
68
− u
67
+ ··· + 4u + 173
c
3
u
68
− u
67
+ ··· + 106u + 47
c
4
, c
12
u
68
+ 3u
67
+ ··· + 15u + 1
c
5
, c
9
, c
10
u
68
− u
67
+ ··· + 257u + 49
c
7
, c
11
u
68
+ 27u
66
+ ··· + 1735u + 187
c
8
u
68
+ 3u
67
+ ··· + 4213u + 2417
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
68
+ 25y
67
+ ··· + 3728354922y + 895745041
c
2
, c
6
y
68
− 27y
67
+ ··· − 475766y + 29929
c
3
y
68
+ 25y
67
+ ··· + 82858y + 2209
c
4
, c
12
y
68
+ 19y
67
+ ··· − 7y + 1
c
5
, c
9
, c
10
y
68
+ 55y
67
+ ··· + 9411y + 2401
c
7
, c
11
y
68
+ 54y
67
+ ··· + 2636053y + 34969
c
8
y
68
− 23y
67
+ ··· − 227917187y + 5841889
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.219883 + 1.008080I
a = 0.241469 + 0.085640I
b = 1.49707 + 0.09193I
−6.12896 − 5.89482I −5.75652 + 6.05557I
u = −0.219883 − 1.008080I
a = 0.241469 − 0.085640I
b = 1.49707 − 0.09193I
−6.12896 + 5.89482I −5.75652 − 6.05557I
u = 0.672615 + 0.850472I
a = −0.83876 − 1.21241I
b = −1.100020 + 0.411678I
−1.73558 + 5.05503I 0
u = 0.672615 − 0.850472I
a = −0.83876 + 1.21241I
b = −1.100020 − 0.411678I
−1.73558 − 5.05503I 0
u = −0.697134 + 0.586038I
a = −0.177708 + 1.159770I
b = 0.620030 − 1.084450I
2.62024 − 1.78240I 2.56416 + 3.76388I
u = −0.697134 − 0.586038I
a = −0.177708 − 1.159770I
b = 0.620030 + 1.084450I
2.62024 + 1.78240I 2.56416 − 3.76388I
u = 0.285172 + 1.071980I
a = −0.250112 − 1.333290I
b = −0.774404 + 0.244058I
−3.84364 + 0.87290I 0
u = 0.285172 − 1.071980I
a = −0.250112 + 1.333290I
b = −0.774404 − 0.244058I
−3.84364 − 0.87290I 0
u = 0.862398 + 0.778967I
a = −0.413310 − 1.002620I
b = 0.248323 + 0.742821I
−2.25225 + 2.76690I 0
u = 0.862398 − 0.778967I
a = −0.413310 + 1.002620I
b = 0.248323 − 0.742821I
−2.25225 − 2.76690I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.825035 + 0.118193I
a = −1.265070 − 0.030158I
b = 0.727846 − 0.338916I
−0.34308 + 2.06616I −0.45806 − 4.18693I
u = 0.825035 − 0.118193I
a = −1.265070 + 0.030158I
b = 0.727846 + 0.338916I
−0.34308 − 2.06616I −0.45806 + 4.18693I
u = −0.652354 + 0.456929I
a = 0.416523 − 0.539818I
b = −0.260189 + 0.688100I
1.12611 − 0.90841I 6.23168 + 2.86305I
u = −0.652354 − 0.456929I
a = 0.416523 + 0.539818I
b = −0.260189 − 0.688100I
1.12611 + 0.90841I 6.23168 − 2.86305I
u = 0.547303 + 1.073360I
a = −0.385360 − 1.119290I
b = −1.27680 + 0.71611I
−2.44164 + 6.42080I 0
u = 0.547303 − 1.073360I
a = −0.385360 + 1.119290I
b = −1.27680 − 0.71611I
−2.44164 − 6.42080I 0
u = −0.408196 + 1.150410I
a = −0.035504 − 0.295582I
b = −1.201720 + 0.270622I
−6.60076 + 0.55952I 0
u = −0.408196 − 1.150410I
a = −0.035504 + 0.295582I
b = −1.201720 − 0.270622I
−6.60076 − 0.55952I 0
u = −0.370976 + 1.165800I
a = 0.626431 − 0.837333I
b = 0.950656 + 0.634963I
−1.29490 − 3.01799I 0
u = −0.370976 − 1.165800I
a = 0.626431 + 0.837333I
b = 0.950656 − 0.634963I
−1.29490 + 3.01799I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.092950 + 0.590264I
a = 0.330797 + 0.819225I
b = −0.803251 − 0.823757I
6.26049 − 3.07517I 0
u = 1.092950 − 0.590264I
a = 0.330797 − 0.819225I
b = −0.803251 + 0.823757I
6.26049 + 3.07517I 0
u = −1.208810 + 0.326750I
a = 1.227870 − 0.540184I
b = −0.888058 + 0.281420I
−0.63925 − 3.06252I 0
u = −1.208810 − 0.326750I
a = 1.227870 + 0.540184I
b = −0.888058 − 0.281420I
−0.63925 + 3.06252I 0
u = 0.982954 + 0.811230I
a = 0.647738 + 1.181950I
b = 0.686495 − 0.648752I
2.50618 − 3.05539I 0
u = 0.982954 − 0.811230I
a = 0.647738 − 1.181950I
b = 0.686495 + 0.648752I
2.50618 + 3.05539I 0
u = 0.058122 + 0.694950I
a = 0.497793 + 0.157791I
b = 0.277847 + 0.724175I
0.07404 − 1.89460I 0.12200 + 5.75647I
u = 0.058122 − 0.694950I
a = 0.497793 − 0.157791I
b = 0.277847 − 0.724175I
0.07404 + 1.89460I 0.12200 − 5.75647I
u = −0.250739 + 0.644457I
a = 0.359250 − 0.769410I
b = −0.216911 + 1.356100I
1.036920 + 0.367328I 0.04414 + 3.61743I
u = −0.250739 − 0.644457I
a = 0.359250 + 0.769410I
b = −0.216911 − 1.356100I
1.036920 − 0.367328I 0.04414 − 3.61743I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.272972 + 0.634333I
a = −1.06513 − 2.33502I
b = −1.243240 + 0.447834I
−4.27261 + 6.00177I −7.74759 − 4.23615I
u = 0.272972 − 0.634333I
a = −1.06513 + 2.33502I
b = −1.243240 − 0.447834I
−4.27261 − 6.00177I −7.74759 + 4.23615I
u = −0.002617 + 0.674324I
a = 1.32887 − 0.85280I
b = 1.049360 + 0.436998I
−1.81410 − 2.04263I 0.563270 − 0.027667I
u = −0.002617 − 0.674324I
a = 1.32887 + 0.85280I
b = 1.049360 − 0.436998I
−1.81410 + 2.04263I 0.563270 + 0.027667I
u = 0.953638 + 0.930205I
a = −0.061568 + 1.227830I
b = 1.134930 − 0.766088I
0.91776 + 8.39173I 0
u = 0.953638 − 0.930205I
a = −0.061568 − 1.227830I
b = 1.134930 + 0.766088I
0.91776 − 8.39173I 0
u = 0.831876 + 1.042200I
a = 0.301219 + 0.859411I
b = −0.464635 − 1.087020I
1.73649 + 9.68261I 0
u = 0.831876 − 1.042200I
a = 0.301219 − 0.859411I
b = −0.464635 + 1.087020I
1.73649 − 9.68261I 0
u = 0.603553 + 0.282503I
a = −0.778437 + 0.160505I
b = 0.690703 + 0.550708I
−0.35366 − 1.81069I 0.78941 + 4.64201I
u = 0.603553 − 0.282503I
a = −0.778437 − 0.160505I
b = 0.690703 − 0.550708I
−0.35366 + 1.81069I 0.78941 − 4.64201I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.999379 + 0.885451I
a = −0.229036 + 1.255670I
b = −0.929485 − 0.752340I
5.84722 − 2.80393I 0
u = −0.999379 − 0.885451I
a = −0.229036 − 1.255670I
b = −0.929485 + 0.752340I
5.84722 + 2.80393I 0
u = −0.245626 + 1.337940I
a = −0.097385 − 1.229590I
b = 0.926966 + 0.720129I
−5.22159 − 2.81789I 0
u = −0.245626 − 1.337940I
a = −0.097385 + 1.229590I
b = 0.926966 − 0.720129I
−5.22159 + 2.81789I 0
u = −0.590766 + 1.231350I
a = −1.050480 + 0.810433I
b = −0.881595 − 0.567034I
0.52888 − 3.31346I 0
u = −0.590766 − 1.231350I
a = −1.050480 − 0.810433I
b = −0.881595 + 0.567034I
0.52888 + 3.31346I 0
u = −0.942984 + 1.008420I
a = −0.394979 + 0.529136I
b = 0.635572 − 0.849451I
5.46665 − 4.25985I 0
u = −0.942984 − 1.008420I
a = −0.394979 − 0.529136I
b = 0.635572 + 0.849451I
5.46665 + 4.25985I 0
u = −0.280602 + 0.476354I
a = 1.06036 + 1.78747I
b = −0.983679 − 0.799011I
−8.64170 − 3.14980I 7.16331 + 0.66341I
u = −0.280602 − 0.476354I
a = 1.06036 − 1.78747I
b = −0.983679 + 0.799011I
−8.64170 + 3.14980I 7.16331 − 0.66341I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.307300 + 0.457812I
a = −3.78079 + 0.68872I
b = −0.869527 − 0.011159I
−0.58727 + 4.50387I −4.76464 − 6.42986I
u = 0.307300 − 0.457812I
a = −3.78079 − 0.68872I
b = −0.869527 + 0.011159I
−0.58727 − 4.50387I −4.76464 + 6.42986I
u = 1.02698 + 1.04640I
a = 0.458414 + 0.098682I
b = −0.834490 − 0.563961I
0.685407 − 1.197810I 0
u = 1.02698 − 1.04640I
a = 0.458414 − 0.098682I
b = −0.834490 + 0.563961I
0.685407 + 1.197810I 0
u = −0.18944 + 1.46901I
a = 0.488604 − 0.506368I
b = 0.866555 − 0.189018I
−12.42370 + 0.82804I 0
u = −0.18944 − 1.46901I
a = 0.488604 + 0.506368I
b = 0.866555 + 0.189018I
−12.42370 − 0.82804I 0
u = 0.81297 + 1.24271I
a = 0.579912 + 1.211930I
b = 1.045700 − 0.697944I
4.19402 + 10.02790I 0
u = 0.81297 − 1.24271I
a = 0.579912 − 1.211930I
b = 1.045700 + 0.697944I
4.19402 − 10.02790I 0
u = −1.11179 + 1.00012I
a = 0.06005 − 1.45837I
b = 1.138200 + 0.543938I
−4.81124 − 7.61038I 0
u = −1.11179 − 1.00012I
a = 0.06005 + 1.45837I
b = 1.138200 − 0.543938I
−4.81124 + 7.61038I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.43133 + 0.63387I
a = −0.463093 + 0.564401I
b = 0.971703 − 0.612440I
1.63337 + 7.99332I 0
u = −1.43133 − 0.63387I
a = −0.463093 − 0.564401I
b = 0.971703 + 0.612440I
1.63337 − 7.99332I 0
u = −0.91838 + 1.30139I
a = −0.223847 + 1.246210I
b = −1.198190 − 0.719630I
−0.5784 − 16.1377I 0
u = −0.91838 − 1.30139I
a = −0.223847 − 1.246210I
b = −1.198190 + 0.719630I
−0.5784 + 16.1377I 0
u = −0.026899 + 0.339182I
a = 0.73493 + 5.25820I
b = 0.841091 − 0.362306I
−0.643910 + 0.755355I −1.11077 − 3.83651I
u = −0.026899 − 0.339182I
a = 0.73493 − 5.25820I
b = 0.841091 + 0.362306I
−0.643910 − 0.755355I −1.11077 + 3.83651I
u = −0.08792 + 1.93934I
a = −0.317748 − 0.431671I
b = −0.882865 + 0.292259I
−7.83902 + 1.26546I 0
u = −0.08792 − 1.93934I
a = −0.317748 + 0.431671I
b = −0.882865 − 0.292259I
−7.83902 − 1.26546I 0
11
II. I
u
2
= h−209u
17
− 81u
16
+ · · · + 310b + 36, −244u
17
+ 1029u
16
+ · · · +
1550a + 3366, u
18
+ 8u
16
+ · · · − u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
7
=
0.157419u
17
− 0.663871u
16
+ ··· + 0.123871u − 2.17161
0.674194u
17
+ 0.261290u
16
+ ··· + 4.53871u − 0.116129
a
2
=
1.94065u
17
+ 0.110968u
16
+ ··· + 6.10903u − 0.927097
0.116129u
17
+ 0.674194u
16
+ ··· − 0.974194u + 3.42258
a
1
=
2.05677u
17
+ 0.785161u
16
+ ··· + 5.13484u + 2.49548
0.116129u
17
+ 0.674194u
16
+ ··· − 0.974194u + 3.42258
a
6
=
−1.25290u
17
− 1.67935u
16
+ ··· − 0.100645u − 4.29806
3.42258u
17
− 0.116129u
16
+ ··· + 14.8161u − 2.44839
a
10
=
0.343871u
17
+ 0.465806u
16
+ ··· + 4.75419u + 1.63742
2.09806u
17
+ 0.447097u
16
+ ··· + 1.23290u + 2.90129
a
5
=
−0.294839u
17
+ 1.00774u
16
+ ··· − 2.88774u + 1.56323
−1.56452u
17
− 1.09677u
16
+ ··· − 1.40323u − 2.29032
a
8
=
−0.363871u
17
+ 0.854194u
16
+ ··· − 6.61419u + 4.64258
−0.552903u
17
+ 0.620645u
16
+ ··· − 4.50065u + 2.40194
a
12
=
2.71290u
17
+ 0.319355u
16
+ ··· + 7.38065u − 0.141935
0.614839u
17
+ 0.872258u
16
+ ··· + 0.147742u + 2.95677
a
11
=
2.67935u
17
− 0.0309677u
16
+ ··· + 11.5510u − 2.25290
2.00774u
17
+ 1.31161u
16
+ ··· + 3.26839u + 5.29484
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1522
775
u
17
+
10921
1550
u
16
+ ··· −
11304
775
u +
20859
1550
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
− 8u
17
+ ··· − 15u + 1
c
2
u
18
− 4u
16
+ ··· − u + 1
c
3
u
18
+ 8u
16
+ ··· − u + 1
c
4
u
18
− 2u
17
+ ··· + 6u
2
+ 1
c
5
u
18
+ 11u
16
+ ··· − 8u + 1
c
6
u
18
− 4u
16
+ ··· + u + 1
c
7
u
18
− u
17
+ ··· + 4u + 1
c
8
u
18
− 2u
16
+ ··· + 2u + 1
c
9
, c
10
u
18
+ 11u
16
+ ··· + 8u + 1
c
11
u
18
+ u
17
+ ··· − 4u + 1
c
12
u
18
+ 2u
17
+ ··· + 6u
2
+ 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
+ 8y
16
+ ··· − 23y + 1
c
2
, c
6
y
18
− 8y
17
+ ··· − 15y + 1
c
3
y
18
+ 16y
17
+ ··· + 13y + 1
c
4
, c
12
y
18
+ 14y
17
+ ··· + 12y + 1
c
5
, c
9
, c
10
y
18
+ 22y
17
+ ··· − 22y + 1
c
7
, c
11
y
18
+ 9y
17
+ ··· − 12y + 1
c
8
y
18
− 4y
17
+ ··· + 28y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.622362 + 0.793944I
a = 0.53839 − 1.59688I
b = 1.283640 + 0.512050I
−3.58496 − 6.70275I −2.03962 + 9.11062I
u = −0.622362 − 0.793944I
a = 0.53839 + 1.59688I
b = 1.283640 − 0.512050I
−3.58496 + 6.70275I −2.03962 − 9.11062I
u = −0.741033 + 0.625230I
a = 1.03638 + 1.09752I
b = −0.635878 + 0.205299I
−0.315342 − 0.434766I −0.66037 + 1.44990I
u = −0.741033 − 0.625230I
a = 1.03638 − 1.09752I
b = −0.635878 − 0.205299I
−0.315342 + 0.434766I −0.66037 − 1.44990I
u = −0.082148 + 1.073030I
a = 0.237276 − 1.230570I
b = 0.922593 + 0.481777I
−3.38851 − 1.96726I −3.41633 + 3.20272I
u = −0.082148 − 1.073030I
a = 0.237276 + 1.230570I
b = 0.922593 − 0.481777I
−3.38851 + 1.96726I −3.41633 − 3.20272I
u = 0.389890 + 1.033720I
a = −1.027160 − 0.646201I
b = −1.082520 + 0.496737I
−2.46815 + 3.75296I −4.41325 − 4.28268I
u = 0.389890 − 1.033720I
a = −1.027160 + 0.646201I
b = −1.082520 − 0.496737I
−2.46815 − 3.75296I −4.41325 + 4.28268I
u = 0.826732 + 0.098773I
a = −1.67394 − 1.60575I
b = 0.566394 + 0.034704I
0.25126 + 4.10793I 3.42850 − 4.98379I
u = 0.826732 − 0.098773I
a = −1.67394 + 1.60575I
b = 0.566394 − 0.034704I
0.25126 − 4.10793I 3.42850 + 4.98379I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.233966 + 0.695600I
a = 0.41619 − 1.63599I
b = −1.029600 + 0.818393I
−9.03670 + 3.25723I −12.27411 − 5.61296I
u = 0.233966 − 0.695600I
a = 0.41619 + 1.63599I
b = −1.029600 − 0.818393I
−9.03670 − 3.25723I −12.27411 + 5.61296I
u = 0.16217 + 1.47822I
a = 0.511966 + 0.256356I
b = 0.906631 + 0.321231I
−12.22730 − 1.35209I −2.07336 + 8.23143I
u = 0.16217 − 1.47822I
a = 0.511966 − 0.256356I
b = 0.906631 − 0.321231I
−12.22730 + 1.35209I −2.07336 − 8.23143I
u = −0.001126 + 0.488254I
a = −0.780170 − 0.289026I
b = 0.013305 + 1.244950I
1.11612 + 1.01323I 2.04473 − 6.35072I
u = −0.001126 − 0.488254I
a = −0.780170 + 0.289026I
b = 0.013305 − 1.244950I
1.11612 − 1.01323I 2.04473 + 6.35072I
u = −0.16609 + 1.93105I
a = −0.258913 − 0.545729I
b = −0.944569 + 0.251147I
−8.17988 + 1.03676I −14.5962 + 2.3548I
u = −0.16609 − 1.93105I
a = −0.258913 + 0.545729I
b = −0.944569 − 0.251147I
−8.17988 − 1.03676I −14.5962 − 2.3548I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
18
− 8u
17
+ ··· − 15u + 1)(u
68
+ 27u
67
+ ··· + 475766u + 29929)
c
2
(u
18
− 4u
16
+ ··· − u + 1)(u
68
− u
67
+ ··· + 4u + 173)
c
3
(u
18
+ 8u
16
+ ··· − u + 1)(u
68
− u
67
+ ··· + 106u + 47)
c
4
(u
18
− 2u
17
+ ··· + 6u
2
+ 1)(u
68
+ 3u
67
+ ··· + 15u + 1)
c
5
(u
18
+ 11u
16
+ ··· − 8u + 1)(u
68
− u
67
+ ··· + 257u + 49)
c
6
(u
18
− 4u
16
+ ··· + u + 1)(u
68
− u
67
+ ··· + 4u + 173)
c
7
(u
18
− u
17
+ ··· + 4u + 1)(u
68
+ 27u
66
+ ··· + 1735u + 187)
c
8
(u
18
− 2u
16
+ ··· + 2u + 1)(u
68
+ 3u
67
+ ··· + 4213u + 2417)
c
9
, c
10
(u
18
+ 11u
16
+ ··· + 8u + 1)(u
68
− u
67
+ ··· + 257u + 49)
c
11
(u
18
+ u
17
+ ··· − 4u + 1)(u
68
+ 27u
66
+ ··· + 1735u + 187)
c
12
(u
18
+ 2u
17
+ ··· + 6u
2
+ 1)(u
68
+ 3u
67
+ ··· + 15u + 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
18
+ 8y
16
+ ··· − 23y + 1)
· (y
68
+ 25y
67
+ ··· + 3728354922y + 895745041)
c
2
, c
6
(y
18
− 8y
17
+ ··· − 15y + 1)(y
68
− 27y
67
+ ··· − 475766y + 29929)
c
3
(y
18
+ 16y
17
+ ··· + 13y + 1)(y
68
+ 25y
67
+ ··· + 82858y + 2209)
c
4
, c
12
(y
18
+ 14y
17
+ ··· + 12y + 1)(y
68
+ 19y
67
+ ··· − 7y + 1)
c
5
, c
9
, c
10
(y
18
+ 22y
17
+ ··· − 22y + 1)(y
68
+ 55y
67
+ ··· + 9411y + 2401)
c
7
, c
11
(y
18
+ 9y
17
+ ··· − 12y + 1)(y
68
+ 54y
67
+ ··· + 2636053y + 34969)
c
8
(y
18
− 4y
17
+ ··· + 28y + 1)
· (y
68
− 23y
67
+ ··· − 227917187y + 5841889)
18
