12n
0762
(K12n
0762
)
A knot diagram
1
Linearized knot diagam
4 6 9 7 12 2 12 3 1 8 6 10
Solving Sequence
2,6
3
7,12
8 9 5 4 1 11 10
c
2
c
6
c
7
c
8
c
5
c
4
c
1
c
11
c
10
c
3
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.39438 × 10
155
u
61
− 1.83142 × 10
156
u
60
+ ··· + 1.27661 × 10
155
b + 4.88446 × 10
156
,
− 4.08969 × 10
156
u
61
− 1.17222 × 10
157
u
60
+ ··· + 1.27661 × 10
155
a + 3.11795 × 10
157
,
u
62
+ 3u
61
+ ··· − 18u − 1i
I
u
2
= h−4390048992u
27
+ 17294455334u
26
+ ··· + 1052877967b − 16499967912,
− 1778777089u
27
+ 10103913125u
26
+ ··· + 1052877967a − 14753500781,
u
28
− 2u
27
+ ··· − 3u − 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
= h−6.39 × 10
155
u
61
− 1.83 × 10
156
u
60
+ · · · + 1.28 × 10
155
b + 4.88 ×
10
156
, −4.09 × 10
156
u
61
− 1.17 × 10
157
u
60
+ · · · + 1.28 × 10
155
a + 3.12 ×
10
157
, u
62
+ 3u
61
+ · · · − 18u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
12
=
32.0357u
61
+ 91.8228u
60
+ ··· − 2497.42u − 244.237
5.00889u
61
+ 14.3460u
60
+ ··· − 387.238u − 38.2613
a
8
=
−5.65842u
61
− 16.2812u
60
+ ··· + 456.306u + 40.1573
3.01761u
61
+ 8.66285u
60
+ ··· − 242.152u − 24.6253
a
9
=
−8.58616u
61
− 24.6845u
60
+ ··· + 691.623u + 64.0885
3.06626u
61
+ 8.80184u
60
+ ··· − 246.062u − 25.0051
a
5
=
1.10750u
61
+ 3.21521u
60
+ ··· − 87.7707u − 3.39247
−4.55092u
61
− 13.0660u
60
+ ··· + 368.535u + 36.7648
a
4
=
1.01763u
61
+ 2.95572u
60
+ ··· − 80.9356u − 2.69839
−4.64079u
61
− 13.3255u
60
+ ··· + 375.370u + 37.4589
a
1
=
14.0757u
61
+ 40.4062u
60
+ ··· − 1167.51u − 118.139
3.44249u
61
+ 9.89638u
60
+ ··· − 294.292u − 28.6685
a
11
=
32.0357u
61
+ 91.8228u
60
+ ··· − 2497.42u − 244.237
4.46323u
61
+ 12.7861u
60
+ ··· − 342.159u − 33.9771
a
10
=
18.5714u
61
+ 53.2721u
60
+ ··· − 1400.80u − 141.560
−0.0553237u
61
− 0.161959u
60
+ ··· + 11.9855u − 0.335246
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5.41881u
61
− 15.7513u
60
+ ··· + 462.106u + 47.0844
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
62
− 8u
61
+ ··· − 14573u − 2354
c
2
, c
6
u
62
− 3u
61
+ ··· + 18u − 1
c
3
, c
8
u
62
− u
61
+ ··· − 1064u + 127
c
4
u
62
− 7u
61
+ ··· + 2345u − 631
c
5
, c
11
u
62
− u
61
+ ··· − 67775u + 24008
c
7
u
62
+ 3u
61
+ ··· − 11203u + 18287
c
9
, c
12
u
62
+ 5u
61
+ ··· + 7u + 1
c
10
u
62
− 13u
61
+ ··· + 690763u − 71359
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
62
− 30y
61
+ ··· + 87051763y + 5541316
c
2
, c
6
y
62
+ 59y
61
+ ··· − 98y + 1
c
3
, c
8
y
62
− 57y
61
+ ··· − 252240y + 16129
c
4
y
62
− 95y
61
+ ··· − 19707883y + 398161
c
5
, c
11
y
62
− 99y
61
+ ··· − 7503268241y + 576384064
c
7
y
62
− 89y
61
+ ··· − 6246385553y + 334414369
c
9
, c
12
y
62
+ 51y
61
+ ··· − 37y + 1
c
10
y
62
− 81y
61
+ ··· + 2924033206473y + 5092106881
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.333052 + 0.944555I
a = 0.389031 − 0.384339I
b = −0.154212 − 0.620844I
−0.62353 − 1.46430I 0
u = −0.333052 − 0.944555I
a = 0.389031 + 0.384339I
b = −0.154212 + 0.620844I
−0.62353 + 1.46430I 0
u = 0.832713 + 0.485235I
a = −0.254095 + 0.534839I
b = −0.07870 + 1.70723I
0.80228 + 3.34364I 0
u = 0.832713 − 0.485235I
a = −0.254095 − 0.534839I
b = −0.07870 − 1.70723I
0.80228 − 3.34364I 0
u = −0.589027 + 0.853031I
a = 0.727906 + 0.227126I
b = 0.309790 − 0.219659I
−0.90701 − 2.10996I 0
u = −0.589027 − 0.853031I
a = 0.727906 − 0.227126I
b = 0.309790 + 0.219659I
−0.90701 + 2.10996I 0
u = −0.183155 + 1.090710I
a = −0.870044 + 0.673371I
b = −0.590651 + 1.128490I
−4.41723 − 3.27563I 0
u = −0.183155 − 1.090710I
a = −0.870044 − 0.673371I
b = −0.590651 − 1.128490I
−4.41723 + 3.27563I 0
u = −0.958678 + 0.626520I
a = 0.093398 − 0.975017I
b = −0.24619 − 1.53004I
0.14869 − 2.80498I 0
u = −0.958678 − 0.626520I
a = 0.093398 + 0.975017I
b = −0.24619 + 1.53004I
0.14869 + 2.80498I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.807646 + 0.092651I
a = −0.386650 + 0.557445I
b = 0.224777 − 0.223097I
−5.34851 − 2.44220I 0
u = 0.807646 − 0.092651I
a = −0.386650 − 0.557445I
b = 0.224777 + 0.223097I
−5.34851 + 2.44220I 0
u = 0.770858
a = 1.84196
b = −0.196952
−3.55600 0
u = −0.350668 + 1.211440I
a = −0.074129 + 0.331633I
b = 1.006790 + 0.617776I
−3.91833 − 0.86784I 0
u = −0.350668 − 1.211440I
a = −0.074129 − 0.331633I
b = 1.006790 − 0.617776I
−3.91833 + 0.86784I 0
u = 0.066377 + 0.729220I
a = 0.474227 − 0.548295I
b = −0.416502 − 0.022118I
−0.903631 − 1.036690I −6.98552 + 4.12911I
u = 0.066377 − 0.729220I
a = 0.474227 + 0.548295I
b = −0.416502 + 0.022118I
−0.903631 + 1.036690I −6.98552 − 4.12911I
u = 0.454755 + 1.195890I
a = −0.313664 + 0.218835I
b = −0.336580 + 0.566077I
−4.85375 + 4.25052I 0
u = 0.454755 − 1.195890I
a = −0.313664 − 0.218835I
b = −0.336580 − 0.566077I
−4.85375 − 4.25052I 0
u = 0.698392 + 0.177356I
a = −1.92419 + 0.75830I
b = 0.236377 + 0.216993I
−7.74561 + 4.18757I −4.00000 − 3.79519I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.698392 − 0.177356I
a = −1.92419 − 0.75830I
b = 0.236377 − 0.216993I
−7.74561 − 4.18757I −4.00000 + 3.79519I
u = 0.459690 + 1.195230I
a = 0.548483 + 0.114412I
b = 0.911400 − 0.215151I
−8.60885 + 7.03690I 0
u = 0.459690 − 1.195230I
a = 0.548483 − 0.114412I
b = 0.911400 + 0.215151I
−8.60885 − 7.03690I 0
u = 0.435856 + 1.211820I
a = 0.098938 − 0.576576I
b = −0.278422 − 1.000790I
−9.25216 + 1.84332I 0
u = 0.435856 − 1.211820I
a = 0.098938 + 0.576576I
b = −0.278422 + 1.000790I
−9.25216 − 1.84332I 0
u = 0.696310
a = 0.539160
b = −0.210110
−1.50281 −7.64330
u = 0.12810 + 1.44057I
a = 0.39257 + 1.87823I
b = 0.23423 + 2.96746I
−15.6787 + 2.6099I 0
u = 0.12810 − 1.44057I
a = 0.39257 − 1.87823I
b = 0.23423 − 2.96746I
−15.6787 − 2.6099I 0
u = 0.28124 + 1.49021I
a = 0.29340 − 1.43793I
b = 0.35314 − 2.63889I
−12.38030 − 0.46591I 0
u = 0.28124 − 1.49021I
a = 0.29340 + 1.43793I
b = 0.35314 + 2.63889I
−12.38030 + 0.46591I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.14213 + 1.52049I
a = −0.27464 − 1.43449I
b = 0.01746 − 2.61143I
−12.42090 + 1.93692I 0
u = 0.14213 − 1.52049I
a = −0.27464 + 1.43449I
b = 0.01746 + 2.61143I
−12.42090 − 1.93692I 0
u = 0.26991 + 1.53473I
a = −0.180066 + 1.299350I
b = −0.17141 + 2.61130I
−9.12418 + 3.84227I 0
u = 0.26991 − 1.53473I
a = −0.180066 − 1.299350I
b = −0.17141 − 2.61130I
−9.12418 − 3.84227I 0
u = −0.08283 + 1.56880I
a = −1.068300 − 0.728241I
b = −0.589996 − 1.278450I
−9.51760 + 5.08658I 0
u = −0.08283 − 1.56880I
a = −1.068300 + 0.728241I
b = −0.589996 + 1.278450I
−9.51760 − 5.08658I 0
u = 0.27775 + 1.56012I
a = 0.132678 − 1.236370I
b = 0.09558 − 2.68981I
−13.8317 + 7.8929I 0
u = 0.27775 − 1.56012I
a = 0.132678 + 1.236370I
b = 0.09558 + 2.68981I
−13.8317 − 7.8929I 0
u = 0.15046 + 1.60424I
a = 0.160295 + 1.146520I
b = −0.31811 + 2.51871I
−17.6021 + 1.1585I 0
u = 0.15046 − 1.60424I
a = 0.160295 − 1.146520I
b = −0.31811 − 2.51871I
−17.6021 − 1.1585I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.341402 + 0.171738I
a = 4.13096 − 1.61392I
b = 0.675184 − 0.592840I
−11.05090 − 0.90973I −10.78531 − 1.39456I
u = 0.341402 − 0.171738I
a = 4.13096 + 1.61392I
b = 0.675184 + 0.592840I
−11.05090 + 0.90973I −10.78531 + 1.39456I
u = 0.03842 + 1.63568I
a = −0.527691 − 0.462807I
b = 0.451791 − 1.092900I
−10.48550 − 5.71222I 0
u = 0.03842 − 1.63568I
a = −0.527691 + 0.462807I
b = 0.451791 + 1.092900I
−10.48550 + 5.71222I 0
u = 0.359374
a = −4.34971
b = −0.676883
−6.85123 −16.8270
u = −1.63565 + 0.23135I
a = −1.293770 − 0.085038I
b = −0.0375020 + 0.0652272I
−14.1359 − 7.0273I 0
u = −1.63565 − 0.23135I
a = −1.293770 + 0.085038I
b = −0.0375020 − 0.0652272I
−14.1359 + 7.0273I 0
u = −0.02899 + 1.68061I
a = 0.815326 + 0.498354I
b = 0.070018 + 1.005780I
−5.54238 − 0.38545I 0
u = −0.02899 − 1.68061I
a = 0.815326 − 0.498354I
b = 0.070018 − 1.005780I
−5.54238 + 0.38545I 0
u = −0.280510 + 0.151518I
a = −0.50395 − 2.20616I
b = −0.683528 − 0.071725I
−0.97360 − 1.69901I −2.82413 + 3.98750I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.280510 − 0.151518I
a = −0.50395 + 2.20616I
b = −0.683528 + 0.071725I
−0.97360 + 1.69901I −2.82413 − 3.98750I
u = −0.63741 + 1.66286I
a = 0.172192 + 1.286190I
b = 0.29163 + 2.50361I
19.3723 − 14.9543I 0
u = −0.63741 − 1.66286I
a = 0.172192 − 1.286190I
b = 0.29163 − 2.50361I
19.3723 + 14.9543I 0
u = −1.82775
a = 1.25873
b = 0.0527036
−9.14724 0
u = −0.1296520 + 0.0012514I
a = −0.05922 − 4.98520I
b = 1.113010 − 0.819545I
1.23431 − 1.93321I 3.80958 + 0.69705I
u = −0.1296520 − 0.0012514I
a = −0.05922 + 4.98520I
b = 1.113010 + 0.819545I
1.23431 + 1.93321I 3.80958 − 0.69705I
u = −0.0707850 + 0.0951134I
a = −3.35295 + 6.50987I
b = −1.65303 + 0.74429I
−3.99047 − 6.24706I −0.93942 + 7.90678I
u = −0.0707850 − 0.0951134I
a = −3.35295 − 6.50987I
b = −1.65303 − 0.74429I
−3.99047 + 6.24706I −0.93942 − 7.90678I
u = −0.70822 + 1.75594I
a = −0.122804 − 1.218420I
b = −0.26978 − 2.37851I
−14.8352 − 9.0166I 0
u = −0.70822 − 1.75594I
a = −0.122804 + 1.218420I
b = −0.26978 + 2.37851I
−14.8352 + 9.0166I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.89562 + 1.71883I
a = 0.131696 + 1.125940I
b = 0.34909 + 2.24166I
−18.4977 − 2.0999I 0
u = −0.89562 − 1.71883I
a = 0.131696 − 1.125940I
b = 0.34909 − 2.24166I
−18.4977 + 2.0999I 0
11
II.
I
u
2
= h−4.39×10
9
u
27
+1.73×10
10
u
26
+· · ·+1.05×10
9
b−1.65×10
10
, −1.78×
10
9
u
27
+1.01×10
10
u
26
+· · ·+1.05×10
9
a−1.48×10
10
, u
28
−2u
27
+· · ·−3u−1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
12
=
1.68944u
27
− 9.59647u
26
+ ··· + 24.1792u + 14.0125
4.16957u
27
− 16.4259u
26
+ ··· + 32.1745u + 15.6713
a
8
=
−2.24104u
27
+ 7.12886u
26
+ ··· − 3.77423u − 5.73930
2.94974u
27
− 7.15613u
26
+ ··· − 15.1617u − 2.88782
a
9
=
−4.88782u
27
+ 13.7254u
26
+ ··· + 5.68818u − 5.49827
2.90344u
27
− 6.26923u
26
+ ··· − 16.4238u − 4.19078
a
5
=
−0.706864u
27
+ 0.0240004u
26
+ ··· + 5.39279u + 5.52854
−2.94790u
27
+ 7.15286u
26
+ ··· + 1.61856u − 0.210764
a
4
=
−1.00982u
27
+ 0.583605u
26
+ ··· + 11.0921u + 8.17533
−3.25085u
27
+ 7.71247u
26
+ ··· + 7.31789u + 2.43602
a
1
=
−0.0543874u
27
+ 4.91254u
26
+ ··· − 27.6210u − 16.4249
−0.355447u
27
− 3.74364u
26
+ ··· + 2.08328u − 0.417512
a
11
=
1.68944u
27
− 9.59647u
26
+ ··· + 24.1792u + 14.0125
2.50358u
27
− 14.8480u
26
+ ··· + 49.1378u + 21.8889
a
10
=
6.69021u
27
− 18.1519u
26
+ ··· − 16.4160u − 3.40215
0.584244u
27
− 13.8628u
26
+ ··· + 64.1728u + 26.2558
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
2679606931
1052877967
u
27
−
15977495031
1052877967
u
26
+ ···+
130752365383
1052877967
u +
40877254048
1052877967
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
28
− 3u
27
+ ··· − 23u − 1
c
2
u
28
− 2u
27
+ ··· − 3u − 1
c
3
u
28
− 11u
26
+ ··· − 3u + 9
c
4
u
28
− 12u
27
+ ··· − 334u + 61
c
5
u
28
− 12u
26
+ ··· − 15u − 9
c
6
u
28
+ 2u
27
+ ··· + 3u − 1
c
7
u
28
+ 2u
27
+ ··· − 2u − 1
c
8
u
28
− 11u
26
+ ··· + 3u + 9
c
9
u
28
+ 6u
27
+ ··· + 40u + 7
c
10
u
28
− 2u
27
+ ··· − 22u − 1
c
11
u
28
− 12u
26
+ ··· + 15u − 9
c
12
u
28
− 6u
27
+ ··· − 40u + 7
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
− 3y
27
+ ··· − 785y + 1
c
2
, c
6
y
28
+ 18y
27
+ ··· + 13y + 1
c
3
, c
8
y
28
− 22y
27
+ ··· − 1017y + 81
c
4
y
28
− 36y
27
+ ··· + 37772y + 3721
c
5
, c
11
y
28
− 24y
27
+ ··· + 1143y + 81
c
7
y
28
− 18y
27
+ ··· + 10y + 1
c
9
, c
12
y
28
+ 22y
27
+ ··· + 206y + 49
c
10
y
28
− 22y
27
+ ··· − 84y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.828405 + 0.452191I
a = 0.028306 − 0.670431I
b = 0.05021 − 1.69084I
1.19357 − 3.29942I 7.01162 + 4.13444I
u = −0.828405 − 0.452191I
a = 0.028306 + 0.670431I
b = 0.05021 + 1.69084I
1.19357 + 3.29942I 7.01162 − 4.13444I
u = −0.244046 + 1.060440I
a = −0.504268 + 0.829036I
b = 0.360086 + 1.027120I
−3.07097 − 2.47420I −8.69591 + 2.72420I
u = −0.244046 − 1.060440I
a = −0.504268 − 0.829036I
b = 0.360086 − 1.027120I
−3.07097 + 2.47420I −8.69591 − 2.72420I
u = 0.440560 + 0.777431I
a = −0.85713 + 1.51445I
b = −0.300793 + 0.409666I
−11.55490 + 2.10708I −14.0670 − 3.9463I
u = 0.440560 − 0.777431I
a = −0.85713 − 1.51445I
b = −0.300793 − 0.409666I
−11.55490 − 2.10708I −14.0670 + 3.9463I
u = −0.181263 + 0.870571I
a = −0.625474 − 0.654885I
b = −1.36669 − 0.40888I
−2.30932 + 0.72869I −9.84041 − 0.97767I
u = −0.181263 − 0.870571I
a = −0.625474 + 0.654885I
b = −1.36669 + 0.40888I
−2.30932 − 0.72869I −9.84041 + 0.97767I
u = 0.868921
a = 2.03119
b = 0.370017
−6.20668 −3.53400
u = −0.464589 + 1.065340I
a = 0.498147 − 0.250055I
b = −0.298592 − 0.642842I
−0.928502 − 0.756039I −7.92403 − 2.74336I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.464589 − 1.065340I
a = 0.498147 + 0.250055I
b = −0.298592 + 0.642842I
−0.928502 + 0.756039I −7.92403 + 2.74336I
u = −0.193282 + 0.717392I
a = 0.726013 − 0.070993I
b = 1.250320 − 0.616788I
0.70335 − 2.38577I −5.36948 + 6.65379I
u = −0.193282 − 0.717392I
a = 0.726013 + 0.070993I
b = 1.250320 + 0.616788I
0.70335 + 2.38577I −5.36948 − 6.65379I
u = 0.311418 + 1.272500I
a = −0.759828 − 0.331562I
b = −0.314202 + 0.008550I
−7.48839 + 7.54015I −7.59672 − 6.45984I
u = 0.311418 − 1.272500I
a = −0.759828 + 0.331562I
b = −0.314202 − 0.008550I
−7.48839 − 7.54015I −7.59672 + 6.45984I
u = 0.003913 + 0.661555I
a = −1.182080 + 0.471507I
b = −1.88693 + 1.20938I
−4.54720 − 6.17336I −15.2173 + 5.6644I
u = 0.003913 − 0.661555I
a = −1.182080 − 0.471507I
b = −1.88693 − 1.20938I
−4.54720 + 6.17336I −15.2173 − 5.6644I
u = 1.325390 + 0.413589I
a = −0.144604 + 0.859044I
b = −0.27440 + 1.56013I
−0.99658 + 3.41956I −11.11044 − 4.64179I
u = 1.325390 − 0.413589I
a = −0.144604 − 0.859044I
b = −0.27440 − 1.56013I
−0.99658 − 3.41956I −11.11044 + 4.64179I
u = −0.258149 + 0.502688I
a = −0.38944 − 2.12090I
b = 0.930879 + 0.071120I
−8.76882 − 4.01982I −13.72838 + 2.52464I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.258149 − 0.502688I
a = −0.38944 + 2.12090I
b = 0.930879 − 0.071120I
−8.76882 + 4.01982I −13.72838 − 2.52464I
u = 0.56341 + 1.32038I
a = 0.654369 − 0.176621I
b = 0.154007 − 0.126542I
−4.61292 + 3.39320I −8.40856 + 0.I
u = 0.56341 − 1.32038I
a = 0.654369 + 0.176621I
b = 0.154007 + 0.126542I
−4.61292 − 3.39320I −8.40856 + 0.I
u = 0.27803 + 1.44237I
a = −0.07083 − 1.57790I
b = 0.21421 − 2.70805I
−14.3357 + 1.1241I −11.79638 + 0.I
u = 0.27803 − 1.44237I
a = −0.07083 + 1.57790I
b = 0.21421 + 2.70805I
−14.3357 − 1.1241I −11.79638 + 0.I
u = −0.471793
a = 2.53420
b = −0.699654
−4.37150 −10.4710
u = 0.04846 + 1.54491I
a = 0.34412 + 1.45356I
b = 0.14671 + 2.63714I
−13.66150 + 2.95733I −11.75419 − 3.36100I
u = 0.04846 − 1.54491I
a = 0.34412 − 1.45356I
b = 0.14671 − 2.63714I
−13.66150 − 2.95733I −11.75419 + 3.36100I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
28
− 3u
27
+ ··· − 23u − 1)(u
62
− 8u
61
+ ··· − 14573u − 2354)
c
2
(u
28
− 2u
27
+ ··· − 3u − 1)(u
62
− 3u
61
+ ··· + 18u − 1)
c
3
(u
28
− 11u
26
+ ··· − 3u + 9)(u
62
− u
61
+ ··· − 1064u + 127)
c
4
(u
28
− 12u
27
+ ··· − 334u + 61)(u
62
− 7u
61
+ ··· + 2345u − 631)
c
5
(u
28
− 12u
26
+ ··· − 15u − 9)(u
62
− u
61
+ ··· − 67775u + 24008)
c
6
(u
28
+ 2u
27
+ ··· + 3u − 1)(u
62
− 3u
61
+ ··· + 18u − 1)
c
7
(u
28
+ 2u
27
+ ··· − 2u − 1)(u
62
+ 3u
61
+ ··· − 11203u + 18287)
c
8
(u
28
− 11u
26
+ ··· + 3u + 9)(u
62
− u
61
+ ··· − 1064u + 127)
c
9
(u
28
+ 6u
27
+ ··· + 40u + 7)(u
62
+ 5u
61
+ ··· + 7u + 1)
c
10
(u
28
− 2u
27
+ ··· − 22u − 1)(u
62
− 13u
61
+ ··· + 690763u − 71359)
c
11
(u
28
− 12u
26
+ ··· + 15u − 9)(u
62
− u
61
+ ··· − 67775u + 24008)
c
12
(u
28
− 6u
27
+ ··· − 40u + 7)(u
62
+ 5u
61
+ ··· + 7u + 1)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
28
− 3y
27
+ ··· − 785y + 1)
· (y
62
− 30y
61
+ ··· + 87051763y + 5541316)
c
2
, c
6
(y
28
+ 18y
27
+ ··· + 13y + 1)(y
62
+ 59y
61
+ ··· − 98y + 1)
c
3
, c
8
(y
28
− 22y
27
+ ··· − 1017y + 81)
· (y
62
− 57y
61
+ ··· − 252240y + 16129)
c
4
(y
28
− 36y
27
+ ··· + 37772y + 3721)
· (y
62
− 95y
61
+ ··· − 19707883y + 398161)
c
5
, c
11
(y
28
− 24y
27
+ ··· + 1143y + 81)
· (y
62
− 99y
61
+ ··· − 7503268241y + 576384064)
c
7
(y
28
− 18y
27
+ ··· + 10y + 1)
· (y
62
− 89y
61
+ ··· − 6246385553y + 334414369)
c
9
, c
12
(y
28
+ 22y
27
+ ··· + 206y + 49)(y
62
+ 51y
61
+ ··· − 37y + 1)
c
10
(y
28
− 22y
27
+ ··· − 84y + 1)
· (y
62
− 81y
61
+ ··· + 2924033206473y + 5092106881)
21
