12n
0493
(K12n
0493
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 9 12 5 7 4 8 7
Solving Sequence
2,6 3,9
7 10 1 5 4 8 12 11
c
2
c
6
c
9
c
1
c
5
c
4
c
8
c
12
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.43760 × 10
104
u
68
+ 2.00230 × 10
105
u
67
+ ··· + 1.22634 × 10
105
b − 1.11649 × 10
106
,
4.64010 × 10
105
u
68
− 1.59745 × 10
106
u
67
+ ··· + 1.34897 × 10
106
a + 7.48313 × 10
106
,
u
69
− 4u
68
+ ··· + 56u − 11i
I
u
2
= h10u
22
+ 5u
21
+ ··· + b − 13, 5u
22
+ 2u
21
+ ··· + a − 3, u
23
+ u
22
+ ··· − u − 1i
* 2 irreducible components of dim
C
= 0, with total 92 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
= h−5.44 × 10
104
u
68
+ 2.00 × 10
105
u
67
+ · · · + 1.23 × 10
105
b − 1.12 ×
10
106
, 4.64 × 10
105
u
68
− 1.60 × 10
106
u
67
+ · · · + 1.35 × 10
106
a + 7.48 ×
10
106
, u
69
− 4u
68
+ · · · + 56u − 11i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
−0.343973u
68
+ 1.18420u
67
+ ··· + 17.5685u − 5.54728
0.443401u
68
− 1.63275u
67
+ ··· − 32.3170u + 9.10424
a
7
=
−0.576164u
68
+ 1.77245u
67
+ ··· + 24.1892u − 5.92136
−0.358276u
68
+ 0.999822u
67
+ ··· + 13.4977u − 3.58010
a
10
=
0.494384u
68
− 1.74440u
67
+ ··· − 36.5327u + 8.98958
0.165294u
68
− 0.478041u
67
+ ··· − 7.38945u + 2.38124
a
1
=
−u
2
+ 1
−u
4
a
5
=
u
u
a
4
=
1.10192u
68
− 3.35873u
67
+ ··· − 47.8714u + 14.8013
0.0132321u
68
− 0.00521372u
67
+ ··· + 5.24343u − 0.0882060
a
8
=
−0.311783u
68
+ 1.36760u
67
+ ··· + 27.5302u − 9.20533
0.475591u
68
− 1.44935u
67
+ ··· − 22.3553u + 5.44619
a
12
=
0.842075u
68
− 3.29112u
67
+ ··· − 71.9419u + 20.0300
−0.344233u
68
+ 0.630033u
67
+ ··· − 6.87988u + 4.46895
a
11
=
−0.829938u
68
+ 1.76140u
67
+ ··· − 4.47063u + 5.32558
−1.27286u
68
+ 3.52866u
67
+ ··· + 35.8363u − 4.75348
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.43232u
68
− 10.6390u
67
+ ··· − 136.515u + 28.1198
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
69
+ 36u
68
+ ··· + 474u + 121
c
2
, c
5
u
69
+ 4u
68
+ ··· + 56u + 11
c
3
u
69
+ u
68
+ ··· + 29817u + 6379
c
4
, c
10
u
69
+ 3u
68
+ ··· − 1049u + 701
c
6
, c
9
u
69
− 3u
68
+ ··· + 55u + 193
c
7
, c
11
, c
12
u
69
+ 2u
68
+ ··· + 13u − 1
c
8
u
69
− u
68
+ ··· + 395u − 29
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
69
+ 8y
68
+ ··· − 141470y −14641
c
2
, c
5
y
69
− 36y
68
+ ··· + 474y −121
c
3
y
69
+ 81y
68
+ ··· − 1405779003y −40691641
c
4
, c
10
y
69
+ 77y
68
+ ··· − 18986053y −491401
c
6
, c
9
y
69
− 33y
68
+ ··· + 199499y −37249
c
7
, c
11
, c
12
y
69
+ 20y
68
+ ··· + 9y −1
c
8
y
69
− 23y
68
+ ··· + 200453y −841
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.290552 + 0.976534I
a = 0.662659 + 1.042150I
b = −0.021606 + 0.325176I
3.93320 − 4.10094I 0. + 7.59043I
u = −0.290552 − 0.976534I
a = 0.662659 − 1.042150I
b = −0.021606 − 0.325176I
3.93320 + 4.10094I 0. − 7.59043I
u = 0.170915 + 1.016760I
a = 0.735038 − 0.888007I
b = −0.122632 + 0.149326I
−3.69662 + 2.16087I 0
u = 0.170915 − 1.016760I
a = 0.735038 + 0.888007I
b = −0.122632 − 0.149326I
−3.69662 − 2.16087I 0
u = 0.845794 + 0.445199I
a = 1.042270 − 0.541687I
b = 1.05454 − 1.32366I
1.75302 + 0.23405I 2.64178 + 0.I
u = 0.845794 − 0.445199I
a = 1.042270 + 0.541687I
b = 1.05454 + 1.32366I
1.75302 − 0.23405I 2.64178 + 0.I
u = 0.798359 + 0.685065I
a = 1.103240 − 0.280353I
b = 0.552794 − 0.298714I
2.19476 + 0.59175I 0
u = 0.798359 − 0.685065I
a = 1.103240 + 0.280353I
b = 0.552794 + 0.298714I
2.19476 − 0.59175I 0
u = −0.611426 + 0.705280I
a = 0.834581 + 0.752090I
b = −0.413709 − 0.331884I
6.87382 + 1.62388I 8.32922 − 2.64435I
u = −0.611426 − 0.705280I
a = 0.834581 − 0.752090I
b = −0.413709 + 0.331884I
6.87382 − 1.62388I 8.32922 + 2.64435I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.673306 + 0.638312I
a = −1.45289 − 0.49248I
b = −0.339907 + 0.110846I
2.72164 − 0.99882I 0. − 1.55232I
u = −0.673306 − 0.638312I
a = −1.45289 + 0.49248I
b = −0.339907 − 0.110846I
2.72164 + 0.99882I 0. + 1.55232I
u = 0.828451 + 0.406795I
a = 1.37279 − 0.90899I
b = 0.076668 − 0.891427I
1.87674 − 3.82550I 0. + 7.69744I
u = 0.828451 − 0.406795I
a = 1.37279 + 0.90899I
b = 0.076668 + 0.891427I
1.87674 + 3.82550I 0. − 7.69744I
u = −1.011290 + 0.463825I
a = −0.817036 − 1.011240I
b = −1.21636 − 1.85408I
1.46489 + 5.12150I 0
u = −1.011290 − 0.463825I
a = −0.817036 + 1.011240I
b = −1.21636 + 1.85408I
1.46489 − 5.12150I 0
u = −1.048530 + 0.378591I
a = 0.491834 − 0.900948I
b = 0.00957 − 1.57580I
−2.49072 + 3.79882I 0
u = −1.048530 − 0.378591I
a = 0.491834 + 0.900948I
b = 0.00957 + 1.57580I
−2.49072 − 3.79882I 0
u = 0.398655 + 1.050660I
a = −0.931521 + 0.797871I
b = 0.157270 + 0.032104I
−2.97736 + 9.69199I 0
u = 0.398655 − 1.050660I
a = −0.931521 − 0.797871I
b = 0.157270 − 0.032104I
−2.97736 − 9.69199I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.843195 + 0.221726I
a = −0.93965 + 1.06792I
b = −0.52957 + 1.58476I
−1.18583 − 1.43148I 3.84710 − 6.37744I
u = −0.843195 − 0.221726I
a = −0.93965 − 1.06792I
b = −0.52957 − 1.58476I
−1.18583 + 1.43148I 3.84710 + 6.37744I
u = −0.592910 + 0.619767I
a = −1.42026 − 0.66221I
b = −0.267942 + 0.039618I
2.72523 − 1.00845I 1.13200 − 1.33542I
u = −0.592910 − 0.619767I
a = −1.42026 + 0.66221I
b = −0.267942 − 0.039618I
2.72523 + 1.00845I 1.13200 + 1.33542I
u = 0.937541 + 0.663875I
a = 0.369232 − 1.125340I
b = 0.23643 − 1.79333I
1.73480 − 5.81339I 0
u = 0.937541 − 0.663875I
a = 0.369232 + 1.125340I
b = 0.23643 + 1.79333I
1.73480 + 5.81339I 0
u = 1.095940 + 0.350670I
a = −0.474582 + 0.632682I
b = −1.72631 + 1.19121I
3.07674 − 3.26894I 0
u = 1.095940 − 0.350670I
a = −0.474582 − 0.632682I
b = −1.72631 − 1.19121I
3.07674 + 3.26894I 0
u = −1.081310 + 0.487072I
a = −0.659733 − 0.708574I
b = 0.62165 − 1.72240I
−7.58609 + 6.42641I 0
u = −1.081310 − 0.487072I
a = −0.659733 + 0.708574I
b = 0.62165 + 1.72240I
−7.58609 − 6.42641I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.105510 + 0.431642I
a = 1.004780 + 0.584794I
b = 0.26453 + 1.61847I
−7.94202 − 0.79088I 0
u = 1.105510 − 0.431642I
a = 1.004780 − 0.584794I
b = 0.26453 − 1.61847I
−7.94202 + 0.79088I 0
u = −1.147280 + 0.304107I
a = 0.550803 + 0.761091I
b = −0.31435 + 1.82784I
−9.68321 − 0.62268I 0
u = −1.147280 − 0.304107I
a = 0.550803 − 0.761091I
b = −0.31435 − 1.82784I
−9.68321 + 0.62268I 0
u = −0.993265 + 0.683955I
a = −0.282845 − 1.144910I
b = −0.76540 − 1.96652I
1.75235 + 6.29447I 0
u = −0.993265 − 0.683955I
a = −0.282845 + 1.144910I
b = −0.76540 + 1.96652I
1.75235 − 6.29447I 0
u = 1.207420 + 0.035311I
a = 0.069551 + 0.357262I
b = 0.526334 + 0.627810I
−2.81273 − 0.16209I 0
u = 1.207420 − 0.035311I
a = 0.069551 − 0.357262I
b = 0.526334 − 0.627810I
−2.81273 + 0.16209I 0
u = −1.033920 + 0.650381I
a = 0.381960 + 0.552392I
b = 1.18877 + 1.43009I
5.59026 + 3.61321I 0
u = −1.033920 − 0.650381I
a = 0.381960 − 0.552392I
b = 1.18877 − 1.43009I
5.59026 − 3.61321I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.117680 + 0.556781I
a = −0.890564 − 0.750983I
b = −0.37281 − 1.65828I
−7.95415 − 8.38570I 0
u = 1.117680 − 0.556781I
a = −0.890564 + 0.750983I
b = −0.37281 + 1.65828I
−7.95415 + 8.38570I 0
u = 1.085710 + 0.625989I
a = −0.503128 + 0.612693I
b = −0.287588 + 1.243300I
−1.07599 − 2.78600I 0
u = 1.085710 − 0.625989I
a = −0.503128 − 0.612693I
b = −0.287588 − 1.243300I
−1.07599 + 2.78600I 0
u = 0.798698 + 0.974655I
a = −0.432695 + 0.595898I
b = −0.166512 + 0.361764I
−0.24985 − 3.26069I 0
u = 0.798698 − 0.974655I
a = −0.432695 − 0.595898I
b = −0.166512 − 0.361764I
−0.24985 + 3.26069I 0
u = 0.319351 + 0.663934I
a = 1.11830 + 1.01941I
b = −0.155956 + 1.246900I
−5.68469 + 3.59684I 0.14375 − 2.17339I
u = 0.319351 − 0.663934I
a = 1.11830 − 1.01941I
b = −0.155956 − 1.246900I
−5.68469 − 3.59684I 0.14375 + 2.17339I
u = 0.961426 + 0.848715I
a = −0.426077 + 0.482317I
b = −0.077045 + 1.197380I
−0.94415 − 3.29961I 0
u = 0.961426 − 0.848715I
a = −0.426077 − 0.482317I
b = −0.077045 − 1.197380I
−0.94415 + 3.29961I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.687662 + 0.185413I
a = −1.79140 − 0.10939I
b = 0.487312 − 1.099210I
4.79965 + 0.76507I −0.89012 − 1.45079I
u = 0.687662 − 0.185413I
a = −1.79140 + 0.10939I
b = 0.487312 + 1.099210I
4.79965 − 0.76507I −0.89012 + 1.45079I
u = −1.196820 + 0.622088I
a = 0.667975 + 0.833159I
b = 0.97633 + 1.75198I
1.19205 + 9.84022I 0
u = −1.196820 − 0.622088I
a = 0.667975 − 0.833159I
b = 0.97633 − 1.75198I
1.19205 − 9.84022I 0
u = 1.258550 + 0.582507I
a = 0.452188 − 0.889836I
b = 1.10957 − 1.91755I
−7.04483 − 7.85806I 0
u = 1.258550 − 0.582507I
a = 0.452188 + 0.889836I
b = 1.10957 + 1.91755I
−7.04483 + 7.85806I 0
u = 1.213600 + 0.688126I
a = −0.517780 + 0.965581I
b = −1.02405 + 2.11674I
−5.5104 − 15.9437I 0
u = 1.213600 − 0.688126I
a = −0.517780 − 0.965581I
b = −1.02405 − 2.11674I
−5.5104 + 15.9437I 0
u = −0.499390 + 0.340618I
a = −0.919752 − 0.049244I
b = 0.05015 − 2.33868I
−5.61165 − 2.54761I 5.30359 + 0.02313I
u = −0.499390 − 0.340618I
a = −0.919752 + 0.049244I
b = 0.05015 + 2.33868I
−5.61165 + 2.54761I 5.30359 − 0.02313I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43623
a = −0.433547
b = −0.479698
−2.53296 0
u = −1.41770 + 0.37374I
a = −0.534463 + 0.162015I
b = −1.213010 + 0.496378I
−8.86518 + 2.79325I 0
u = −1.41770 − 0.37374I
a = −0.534463 − 0.162015I
b = −1.213010 − 0.496378I
−8.86518 − 2.79325I 0
u = −1.46407 + 0.12048I
a = 0.606194 − 0.353781I
b = 1.12078 − 0.89971I
−9.73214 − 5.62474I 0
u = −1.46407 − 0.12048I
a = 0.606194 + 0.353781I
b = 1.12078 + 0.89971I
−9.73214 + 5.62474I 0
u = 0.262574 + 0.365414I
a = −1.05942 − 1.83282I
b = 0.95586 − 1.50255I
−5.45507 − 2.87217I 0.41122 + 5.66898I
u = 0.262574 − 0.365414I
a = −1.05942 + 1.83282I
b = 0.95586 + 1.50255I
−5.45507 + 2.87217I 0.41122 − 5.66898I
u = 0.093022 + 0.383439I
a = −0.920079 − 0.537348I
b = −0.133968 + 0.391648I
0.152285 − 1.032960I 2.47400 + 6.54310I
u = 0.093022 − 0.383439I
a = −0.920079 + 0.537348I
b = −0.133968 − 0.391648I
0.152285 + 1.032960I 2.47400 − 6.54310I
11
II.
I
u
2
= h10u
22
+5u
21
+· · ·+b−13, 5u
22
+2u
21
+· · ·+a−3, u
23
+u
22
+· · ·−u−1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
−5u
22
− 2u
21
+ ··· + u + 3
−10u
22
− 5u
21
+ ··· − 5u + 13
a
7
=
−2u
22
− 3u
21
+ ··· − 2u + 3
−4u
22
− 3u
21
+ ··· − 6u + 4
a
10
=
−u
22
+ 5u
20
+ ··· − u
2
− 4u
−8u
22
− 2u
21
+ ··· − 4u + 11
a
1
=
−u
2
+ 1
−u
4
a
5
=
u
u
a
4
=
−5u
22
− 3u
21
+ ··· − 6u + 9
−7u
22
− 4u
21
+ ··· − 14u + 16
a
8
=
−5u
22
− u
21
+ ··· + 4u + 1
−10u
22
− 4u
21
+ ··· − 2u + 11
a
12
=
3u
22
+ u
21
+ ··· − u − 7
4u
22
+ 2u
21
+ ··· + 5u − 9
a
11
=
−2u
22
− 2u
21
+ ··· + 9u
2
− 3u
5u
22
+ u
21
+ ··· + u − 7
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 10u
21
+ 6u
20
−52u
19
−29u
18
+ 158u
17
+ 88u
16
−345u
15
−211u
14
+ 537u
13
+ 359u
12
−
638u
11
− 465u
10
+ 558u
9
+ 395u
8
− 397u
7
− 259u
6
+ 220u
5
+ 99u
4
− 84u
3
− 22u
2
+ 29u
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
23
− 13u
22
+ ··· + 13u − 1
c
2
u
23
+ u
22
+ ··· − u − 1
c
3
u
23
+ 2u
21
+ ··· + 2u − 1
c
4
u
23
+ 12u
21
+ ··· + 19u
2
+ 1
c
5
u
23
− u
22
+ ··· − u + 1
c
6
u
23
+ 4u
22
+ ··· + 4u + 1
c
7
u
23
+ u
22
+ ··· − 6u
2
− 1
c
8
u
23
− 8u
21
+ ··· + 8u
2
+ 1
c
9
u
23
− 4u
22
+ ··· + 4u − 1
c
10
u
23
+ 12u
21
+ ··· − 19u
2
− 1
c
11
, c
12
u
23
− u
22
+ ··· + 6u
2
+ 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
+ 7y
22
+ ··· − 7y −1
c
2
, c
5
y
23
− 13y
22
+ ··· + 13y −1
c
3
y
23
+ 4y
22
+ ··· − 28y −1
c
4
, c
10
y
23
+ 24y
22
+ ··· − 38y −1
c
6
, c
9
y
23
− 14y
22
+ ··· − 2y −1
c
7
, c
11
, c
12
y
23
+ 19y
22
+ ··· − 12y −1
c
8
y
23
− 16y
22
+ ··· − 16y −1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.727530 + 0.675450I
a = −1.56715 − 0.40087I
b = −0.658564 + 0.037949I
3.36055 − 1.47768I 8.91324 + 4.94896I
u = −0.727530 − 0.675450I
a = −1.56715 + 0.40087I
b = −0.658564 − 0.037949I
3.36055 + 1.47768I 8.91324 − 4.94896I
u = −0.714405 + 0.569856I
a = 1.342420 + 0.352259I
b = −0.106804 − 0.755904I
5.87840 − 0.07399I 4.63766 − 1.08939I
u = −0.714405 − 0.569856I
a = 1.342420 − 0.352259I
b = −0.106804 + 0.755904I
5.87840 + 0.07399I 4.63766 + 1.08939I
u = 0.873281 + 0.058843I
a = 0.641877 + 1.056520I
b = 0.66167 + 1.39799I
−1.38657 + 1.89044I −3.01798 − 8.02298I
u = 0.873281 − 0.058843I
a = 0.641877 − 1.056520I
b = 0.66167 − 1.39799I
−1.38657 − 1.89044I −3.01798 + 8.02298I
u = 0.682792 + 0.510727I
a = −1.015220 + 0.899830I
b = 0.801359 + 0.100013I
5.58168 − 2.30519I 2.87757 + 4.60257I
u = 0.682792 − 0.510727I
a = −1.015220 − 0.899830I
b = 0.801359 − 0.100013I
5.58168 + 2.30519I 2.87757 − 4.60257I
u = −1.013700 + 0.592894I
a = 0.385259 + 0.861396I
b = 1.35384 + 1.59496I
4.88003 + 4.72768I 2.32962 − 6.66073I
u = −1.013700 − 0.592894I
a = 0.385259 − 0.861396I
b = 1.35384 − 1.59496I
4.88003 − 4.72768I 2.32962 + 6.66073I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.966870 + 0.667630I
a = −0.395637 − 1.302340I
b = −0.71928 − 2.04019I
2.61955 + 6.69998I 6.96792 − 9.85887I
u = −0.966870 − 0.667630I
a = −0.395637 + 1.302340I
b = −0.71928 + 2.04019I
2.61955 − 6.69998I 6.96792 + 9.85887I
u = 1.075530 + 0.534802I
a = −0.628727 + 0.324551I
b = −1.44754 + 1.17940I
4.23211 − 1.97181I 3.03479 + 1.17838I
u = 1.075530 − 0.534802I
a = −0.628727 − 0.324551I
b = −1.44754 − 1.17940I
4.23211 + 1.97181I 3.03479 − 1.17838I
u = −1.303880 + 0.187284I
a = −0.064693 − 0.287125I
b = −0.366099 + 0.386969I
−8.98729 + 3.97495I −2.00222 − 3.71380I
u = −1.303880 − 0.187284I
a = −0.064693 + 0.287125I
b = −0.366099 − 0.386969I
−8.98729 − 3.97495I −2.00222 + 3.71380I
u = 0.490623 + 0.440201I
a = 1.30058 − 1.63355I
b = 0.139386 − 0.970644I
2.16809 − 2.83861I 2.59802 + 1.74039I
u = 0.490623 − 0.440201I
a = 1.30058 + 1.63355I
b = 0.139386 + 0.970644I
2.16809 + 2.83861I 2.59802 − 1.74039I
u = −0.616125 + 0.120813I
a = −0.586870 + 0.956582I
b = −0.61338 + 2.92957I
−6.13496 − 2.58789I −11.43780 + 1.43765I
u = −0.616125 − 0.120813I
a = −0.586870 − 0.956582I
b = −0.61338 − 2.92957I
−6.13496 + 2.58789I −11.43780 − 1.43765I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.012970 + 0.928867I
a = 0.352126 − 0.506370I
b = 0.042965 − 1.016720I
−1.20499 − 3.62050I −8.5555 + 14.1463I
u = 1.012970 − 0.928867I
a = 0.352126 + 0.506370I
b = 0.042965 + 1.016720I
−1.20499 + 3.62050I −8.5555 − 14.1463I
u = 1.41461
a = 0.472066
b = 0.824925
−2.27398 14.3090
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
23
− 13u
22
+ ··· + 13u − 1)(u
69
+ 36u
68
+ ··· + 474u + 121)
c
2
(u
23
+ u
22
+ ··· − u − 1)(u
69
+ 4u
68
+ ··· + 56u + 11)
c
3
(u
23
+ 2u
21
+ ··· + 2u − 1)(u
69
+ u
68
+ ··· + 29817u + 6379)
c
4
(u
23
+ 12u
21
+ ··· + 19u
2
+ 1)(u
69
+ 3u
68
+ ··· − 1049u + 701)
c
5
(u
23
− u
22
+ ··· − u + 1)(u
69
+ 4u
68
+ ··· + 56u + 11)
c
6
(u
23
+ 4u
22
+ ··· + 4u + 1)(u
69
− 3u
68
+ ··· + 55u + 193)
c
7
(u
23
+ u
22
+ ··· − 6u
2
− 1)(u
69
+ 2u
68
+ ··· + 13u − 1)
c
8
(u
23
− 8u
21
+ ··· + 8u
2
+ 1)(u
69
− u
68
+ ··· + 395u − 29)
c
9
(u
23
− 4u
22
+ ··· + 4u − 1)(u
69
− 3u
68
+ ··· + 55u + 193)
c
10
(u
23
+ 12u
21
+ ··· − 19u
2
− 1)(u
69
+ 3u
68
+ ··· − 1049u + 701)
c
11
, c
12
(u
23
− u
22
+ ··· + 6u
2
+ 1)(u
69
+ 2u
68
+ ··· + 13u − 1)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
23
+ 7y
22
+ ··· − 7y −1)(y
69
+ 8y
68
+ ··· − 141470y −14641)
c
2
, c
5
(y
23
− 13y
22
+ ··· + 13y −1)(y
69
− 36y
68
+ ··· + 474y −121)
c
3
(y
23
+ 4y
22
+ ··· − 28y −1)
· (y
69
+ 81y
68
+ ··· − 1405779003y −40691641)
c
4
, c
10
(y
23
+ 24y
22
+ ··· − 38y −1)
· (y
69
+ 77y
68
+ ··· − 18986053y −491401)
c
6
, c
9
(y
23
− 14y
22
+ ··· − 2y −1)(y
69
− 33y
68
+ ··· + 199499y −37249)
c
7
, c
11
, c
12
(y
23
+ 19y
22
+ ··· − 12y −1)(y
69
+ 20y
68
+ ··· + 9y −1)
c
8
(y
23
− 16y
22
+ ··· − 16y −1)(y
69
− 23y
68
+ ··· + 200453y −841)
19
