12n
0401
(K12n
0401
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 9 2 11 1 11 5 8 4
Solving Sequence
4,10
5
8,11
12 1 3 7 9 6 2
c
4
c
10
c
11
c
12
c
3
c
7
c
9
c
5
c
2
c
1
, c
6
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h9.38926 × 10
46
u
60
− 4.46475 × 10
46
u
59
+ ··· + 4.27875 × 10
46
b − 7.71448 × 10
47
,
− 5.92525 × 10
47
u
60
+ 3.42901 × 10
47
u
59
+ ··· + 2.99512 × 10
47
a + 4.84559 × 10
48
, u
61
− u
60
+ ··· − 4u + 7i
I
u
2
= hu
17
− 4u
15
+ 9u
13
− 11u
11
+ u
10
+ 9u
9
− 3u
8
− 2u
7
+ 4u
6
− 2u
5
− 2u
4
+ 4u
3
+ b − u,
− 2u
17
+ u
16
+ 8u
15
− 4u
14
− 17u
13
+ 8u
12
+ 19u
11
− 10u
10
− 11u
9
+ 10u
8
− 4u
7
− 6u
6
+ 9u
5
− 5u
3
+ 3u
2
+ a,
u
18
− 5u
16
+ 13u
14
− 20u
12
+ u
11
+ 20u
10
− 4u
9
− 11u
8
+ 7u
7
+ u
6
− 6u
5
+ 4u
4
+ 2u
3
− 3u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 79 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
= h9.39×10
46
u
60
−4.46×10
46
u
59
+· · ·+4.28×10
46
b−7.71×10
47
, −5.93×
10
47
u
60
+3.43×10
47
u
59
+· · ·+3.00×10
47
a+4.85×10
48
, u
61
−u
60
+· · ·−4u+7i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
8
=
1.97830u
60
− 1.14487u
59
+ ··· − 9.80742u − 16.1783
−2.19440u
60
+ 1.04347u
59
+ ··· + 9.97369u + 18.0298
a
11
=
−u
−u
3
+ u
a
12
=
2.02259u
60
− 1.64099u
59
+ ··· − 13.4590u − 21.6582
−0.378227u
60
+ 0.935730u
59
+ ··· + 11.4450u + 10.1138
a
1
=
1.64436u
60
− 0.705262u
59
+ ··· − 2.01406u − 11.5444
−0.378227u
60
+ 0.935730u
59
+ ··· + 11.4450u + 10.1138
a
3
=
−0.129915u
60
+ 0.492637u
59
+ ··· + 13.1288u + 10.6244
−0.000539469u
60
+ 0.281363u
59
+ ··· + 2.40949u + 4.06086
a
7
=
2.95189u
60
− 1.23072u
59
+ ··· − 6.85929u − 18.3643
−2.29268u
60
+ 0.793366u
59
+ ··· + 3.76139u + 14.0016
a
9
=
u
3
u
5
− u
3
+ u
a
6
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
2
=
0.888507u
60
+ 0.465150u
59
+ ··· + 15.6860u + 5.85422
0.416055u
60
− 0.229418u
59
+ ··· − 3.73540u − 1.33752
(ii) Obstruction class = −1
(iii) Cusp Shapes = 8.30801u
60
+ 0.834443u
59
+ ··· + 12.8461u − 49.4860
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
61
+ 22u
60
+ ··· − 10584u − 841
c
2
, c
6
u
61
− 2u
60
+ ··· − 28u + 29
c
3
u
61
− u
60
+ ··· + 4065u + 1393
c
4
, c
10
u
61
− u
60
+ ··· − 4u + 7
c
5
u
61
− 3u
60
+ ··· − 11403u + 4312
c
7
, c
11
u
61
+ 36u
59
+ ··· + 207224u + 19571
c
8
u
61
+ 3u
60
+ ··· + 7u + 2
c
9
u
61
+ 27u
60
+ ··· + 324u + 49
c
12
u
61
+ 7u
60
+ ··· + 119062u + 4921
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
61
+ 58y
60
+ ··· + 53870952y −707281
c
2
, c
6
y
61
+ 22y
60
+ ··· − 10584y −841
c
3
y
61
+ 73y
60
+ ··· − 72881301y −1940449
c
4
, c
10
y
61
− 27y
60
+ ··· + 324y −49
c
5
y
61
− 15y
60
+ ··· + 131313385y −18593344
c
7
, c
11
y
61
+ 72y
60
+ ··· + 1955728272y −383024041
c
8
y
61
− 7y
60
+ ··· − 103y −4
c
9
y
61
+ 21y
60
+ ··· + 6192y −2401
c
12
y
61
− 73y
60
+ ··· + 2203035738y −24216241
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.544084 + 0.851164I
a = −0.22388 − 1.93031I
b = 0.31996 + 1.63955I
10.17730 − 2.63661I − 60.10 + 0.555426I
u = −0.544084 − 0.851164I
a = −0.22388 + 1.93031I
b = 0.31996 − 1.63955I
10.17730 + 2.63661I − 60.10 − 0.555426I
u = −0.445650 + 0.880720I
a = −0.00876 + 1.94137I
b = 0.04581 − 1.68414I
9.55356 − 1.38109I −0.535194 + 0.791730I
u = −0.445650 − 0.880720I
a = −0.00876 − 1.94137I
b = 0.04581 + 1.68414I
9.55356 + 1.38109I −0.535194 − 0.791730I
u = −0.857683 + 0.546154I
a = 1.75197 + 2.08794I
b = 0.12804 − 1.85121I
3.18673 + 2.19097I −4.00000 − 2.72424I
u = −0.857683 − 0.546154I
a = 1.75197 − 2.08794I
b = 0.12804 + 1.85121I
3.18673 − 2.19097I −4.00000 + 2.72424I
u = 0.463945 + 0.927138I
a = 0.17894 − 1.78063I
b = −0.37576 + 1.74010I
8.91602 + 9.59094I −1.61071 − 4.50441I
u = 0.463945 − 0.927138I
a = 0.17894 + 1.78063I
b = −0.37576 − 1.74010I
8.91602 − 9.59094I −1.61071 + 4.50441I
u = −0.761332 + 0.580831I
a = −1.49622 − 0.76431I
b = −0.367406 + 0.509362I
−0.006825 − 0.820615I −2.91463 − 0.80498I
u = −0.761332 − 0.580831I
a = −1.49622 + 0.76431I
b = −0.367406 − 0.509362I
−0.006825 + 0.820615I −2.91463 + 0.80498I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.937561 + 0.135130I
a = 0.78806 − 1.55480I
b = 0.864887 − 0.122377I
−3.52138 + 2.97859I −11.18161 − 4.01114I
u = 0.937561 − 0.135130I
a = 0.78806 + 1.55480I
b = 0.864887 + 0.122377I
−3.52138 − 2.97859I −11.18161 + 4.01114I
u = −0.905464 + 0.577132I
a = 0.426084 − 1.101300I
b = 0.231182 + 0.850599I
−0.44348 + 5.44090I 0. − 6.18247I
u = −0.905464 − 0.577132I
a = 0.426084 + 1.101300I
b = 0.231182 − 0.850599I
−0.44348 − 5.44090I 0. + 6.18247I
u = 0.725272 + 0.560786I
a = −0.721026 + 0.356999I
b = 0.552183 − 0.919955I
2.29564 − 1.22082I 0.17143 + 2.41236I
u = 0.725272 − 0.560786I
a = −0.721026 − 0.356999I
b = 0.552183 + 0.919955I
2.29564 + 1.22082I 0.17143 − 2.41236I
u = 0.570512 + 0.922531I
a = −0.20594 + 1.76543I
b = −0.02877 − 1.73498I
9.58894 − 4.78598I 0
u = 0.570512 − 0.922531I
a = −0.20594 − 1.76543I
b = −0.02877 + 1.73498I
9.58894 + 4.78598I 0
u = −0.612012 + 0.676924I
a = 0.762585 + 0.066634I
b = −1.25032 − 0.72018I
0.78856 − 3.53503I −0.67914 + 4.86526I
u = −0.612012 − 0.676924I
a = 0.762585 − 0.066634I
b = −1.25032 + 0.72018I
0.78856 + 3.53503I −0.67914 − 4.86526I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.972064 + 0.490213I
a = 2.15529 − 1.24439I
b = 0.639824 + 0.937890I
−2.42306 − 5.32854I 0
u = 0.972064 − 0.490213I
a = 2.15529 + 1.24439I
b = 0.639824 − 0.937890I
−2.42306 + 5.32854I 0
u = 0.912071 + 0.595227I
a = −0.550710 + 1.169500I
b = −0.814075 − 0.611211I
1.74431 − 3.44432I 0
u = 0.912071 − 0.595227I
a = −0.550710 − 1.169500I
b = −0.814075 + 0.611211I
1.74431 + 3.44432I 0
u = −1.027670 + 0.371040I
a = 0.144719 + 1.175400I
b = 0.518266 + 0.746154I
−3.01798 + 0.68032I 0
u = −1.027670 − 0.371040I
a = 0.144719 − 1.175400I
b = 0.518266 − 0.746154I
−3.01798 − 0.68032I 0
u = 0.794773 + 0.421843I
a = −0.03391 − 2.24073I
b = −0.398950 + 1.014180I
−1.69691 + 1.58278I −7.41386 − 0.48848I
u = 0.794773 − 0.421843I
a = −0.03391 + 2.24073I
b = −0.398950 − 1.014180I
−1.69691 − 1.58278I −7.41386 + 0.48848I
u = −1.060130 + 0.302950I
a = −0.104274 + 0.806163I
b = −0.063620 + 0.561834I
−2.67023 + 0.50890I 0
u = −1.060130 − 0.302950I
a = −0.104274 − 0.806163I
b = −0.063620 − 0.561834I
−2.67023 − 0.50890I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.778473 + 0.334352I
a = −0.994984 + 0.158157I
b = 0.123871 − 1.246270I
2.28478 − 1.44807I 0.58146 + 5.23010I
u = 0.778473 − 0.334352I
a = −0.994984 − 0.158157I
b = 0.123871 + 1.246270I
2.28478 + 1.44807I 0.58146 − 5.23010I
u = 0.875823 + 0.776386I
a = −1.08505 + 1.49485I
b = −0.17216 − 1.84671I
4.39723 − 2.92101I 0
u = 0.875823 − 0.776386I
a = −1.08505 − 1.49485I
b = −0.17216 + 1.84671I
4.39723 + 2.92101I 0
u = −1.009640 + 0.624975I
a = 0.47990 + 1.40571I
b = 1.42139 − 0.52111I
−0.40012 + 8.60462I 0
u = −1.009640 − 0.624975I
a = 0.47990 − 1.40571I
b = 1.42139 + 0.52111I
−0.40012 − 8.60462I 0
u = 1.198250 + 0.079684I
a = −0.330295 − 0.216625I
b = −0.12225 − 1.49577I
3.68795 − 1.11069I 0
u = 1.198250 − 0.079684I
a = −0.330295 + 0.216625I
b = −0.12225 + 1.49577I
3.68795 + 1.11069I 0
u = 1.086940 + 0.529361I
a = 1.111350 + 0.319218I
b = 0.067792 + 0.629900I
−1.14743 − 6.56312I 0
u = 1.086940 − 0.529361I
a = 1.111350 − 0.319218I
b = 0.067792 − 0.629900I
−1.14743 + 6.56312I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.136885 + 0.767965I
a = −0.557019 − 0.912726I
b = −0.121244 + 0.476633I
−2.55621 + 0.33359I −6.44684 + 0.49435I
u = −0.136885 − 0.767965I
a = −0.557019 + 0.912726I
b = −0.121244 − 0.476633I
−2.55621 − 0.33359I −6.44684 − 0.49435I
u = 1.178220 + 0.412066I
a = 0.728261 − 0.428533I
b = −0.188881 + 0.558152I
−6.30273 − 4.26546I 0
u = 1.178220 − 0.412066I
a = 0.728261 + 0.428533I
b = −0.188881 − 0.558152I
−6.30273 + 4.26546I 0
u = −1.077670 + 0.674826I
a = −1.70478 − 1.49229I
b = −0.41657 + 1.59039I
8.56121 + 8.31037I 0
u = −1.077670 − 0.674826I
a = −1.70478 + 1.49229I
b = −0.41657 − 1.59039I
8.56121 − 8.31037I 0
u = −1.283550 + 0.045302I
a = 0.117042 + 0.330596I
b = 0.24808 + 1.56716I
2.50815 − 6.87081I 0
u = −1.283550 − 0.045302I
a = 0.117042 − 0.330596I
b = 0.24808 − 1.56716I
2.50815 + 6.87081I 0
u = 0.310681 + 0.623756I
a = −0.498140 − 0.161924I
b = 0.017763 + 0.701512I
1.02214 + 2.04201I 1.04597 − 2.83641I
u = 0.310681 − 0.623756I
a = −0.498140 + 0.161924I
b = 0.017763 − 0.701512I
1.02214 − 2.04201I 1.04597 + 2.83641I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.203690 + 0.499462I
a = −0.111271 − 0.233894I
b = 0.117954 + 0.733032I
−5.69633 + 4.42131I 0
u = −1.203690 − 0.499462I
a = −0.111271 + 0.233894I
b = 0.117954 − 0.733032I
−5.69633 − 4.42131I 0
u = −1.134950 + 0.650042I
a = 1.64308 + 0.98161I
b = 0.05507 − 1.67770I
7.46478 + 7.04326I 0
u = −1.134950 − 0.650042I
a = 1.64308 − 0.98161I
b = 0.05507 + 1.67770I
7.46478 − 7.04326I 0
u = 1.096100 + 0.730179I
a = −1.46111 + 1.07505I
b = −0.11583 − 1.67692I
7.99251 − 1.27736I 0
u = 1.096100 − 0.730179I
a = −1.46111 − 1.07505I
b = −0.11583 + 1.67692I
7.99251 + 1.27736I 0
u = 1.142240 + 0.674079I
a = 1.67938 − 1.28751I
b = 0.47616 + 1.71273I
6.8432 − 15.4624I 0
u = 1.142240 − 0.674079I
a = 1.67938 + 1.28751I
b = 0.47616 − 1.71273I
6.8432 + 15.4624I 0
u = −0.653934
a = −0.815305
b = −0.427941
−0.989818 −9.99130
u = −0.155534 + 0.460253I
a = −0.400194 − 0.153253I
b = −0.678432 + 0.872645I
−0.59531 + 2.53206I −1.68275 − 3.40674I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.155534 − 0.460253I
a = −0.400194 + 0.153253I
b = −0.678432 − 0.872645I
−0.59531 − 2.53206I −1.68275 + 3.40674I
11
II. I
u
2
=
hu
17
−4u
15
+· · ·+ b −u, −2u
17
+u
16
+· · ·+ 3u
2
+a, u
18
−5u
16
+· · ·− 3u
2
+1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
8
=
2u
17
− u
16
+ ··· + 5u
3
− 3u
2
−u
17
+ 4u
15
+ ··· − 4u
3
+ u
a
11
=
−u
−u
3
+ u
a
12
=
−u
16
− u
15
+ ··· − 4u + 2
−u
16
+ 5u
14
+ ··· + u + 1
a
1
=
−2u
16
− u
15
+ ··· − 3u + 3
−u
16
+ 5u
14
+ ··· + u + 1
a
3
=
−2u
17
+ 9u
15
+ ··· + 2u − 1
−u
16
+ 5u
14
+ ··· − 3u
2
+ 2
a
7
=
2u
17
− 2u
16
+ ··· − 4u
2
+ u
−u
17
+ 4u
15
+ ··· − 2u
2
+ 1
a
9
=
u
3
u
5
− u
3
+ u
a
6
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
2
=
−4u
17
+ 18u
15
+ ··· + 4u − 2
−u
16
+ 5u
14
+ ··· + u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
17
+ 5u
16
+ 21u
15
−24u
14
−48u
13
+ 58u
12
+ 64u
11
−85u
10
−
51u
9
+ 83u
8
− u
7
− 45u
6
+ 41u
5
+ 3u
4
− 37u
3
+ 15u
2
+ 7u − 15
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
18
− 11u
17
+ ··· − 18u + 1
c
2
u
18
− u
17
+ ··· + 9u
2
+ 1
c
3
u
18
+ 9u
16
+ ··· + u + 1
c
4
u
18
− 5u
16
+ ··· − 3u
2
+ 1
c
5
u
18
+ 3u
16
+ ··· − 3u
2
+ 1
c
6
u
18
+ u
17
+ ··· + 9u
2
+ 1
c
7
u
18
+ u
17
+ ··· + 2u + 1
c
8
u
18
+ 2u
17
+ ··· + u + 1
c
9
u
18
− 10u
17
+ ··· − 6u + 1
c
10
u
18
− 5u
16
+ ··· − 3u
2
+ 1
c
11
u
18
− u
17
+ ··· − 2u + 1
c
12
u
18
+ 5u
15
+ ··· + 8u
2
+ 1
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
+ 15y
17
+ ··· − 34y + 1
c
2
, c
6
y
18
+ 11y
17
+ ··· + 18y + 1
c
3
y
18
+ 18y
17
+ ··· + 11y + 1
c
4
, c
10
y
18
− 10y
17
+ ··· − 6y + 1
c
5
y
18
+ 6y
17
+ ··· − 6y + 1
c
7
, c
11
y
18
− 7y
17
+ ··· − 10y + 1
c
8
y
18
− 10y
17
+ ··· − 7y + 1
c
9
y
18
+ 2y
17
+ ··· − 2y + 1
c
12
y
18
− 4y
16
+ ··· + 16y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.904746 + 0.245141I
a = −1.270110 + 0.303445I
b = 0.07442 − 1.44586I
1.62879 − 1.07876I −10.54525 − 0.48529I
u = 0.904746 − 0.245141I
a = −1.270110 − 0.303445I
b = 0.07442 + 1.44586I
1.62879 + 1.07876I −10.54525 + 0.48529I
u = −1.016240 + 0.389137I
a = 0.74048 − 1.68593I
b = −0.332136 − 0.610814I
−3.05100 − 0.53837I −10.07570 + 2.70036I
u = −1.016240 − 0.389137I
a = 0.74048 + 1.68593I
b = −0.332136 + 0.610814I
−3.05100 + 0.53837I −10.07570 − 2.70036I
u = −0.881768 + 0.726056I
a = 1.25651 + 1.55510I
b = 0.14317 − 1.92438I
4.79527 + 2.77083I 5.95842 − 0.39060I
u = −0.881768 − 0.726056I
a = 1.25651 − 1.55510I
b = 0.14317 + 1.92438I
4.79527 − 2.77083I 5.95842 + 0.39060I
u = 1.037690 + 0.534998I
a = −1.356060 − 0.091628I
b = −0.463536 − 0.533807I
−1.99612 − 6.79726I −10.09948 + 9.44320I
u = 1.037690 − 0.534998I
a = −1.356060 + 0.091628I
b = −0.463536 + 0.533807I
−1.99612 + 6.79726I −10.09948 − 9.44320I
u = 0.551142 + 0.552499I
a = 0.792707 + 0.203931I
b = 0.528191 − 0.635299I
−0.49089 + 2.36719I −4.89133 − 3.88006I
u = 0.551142 − 0.552499I
a = 0.792707 − 0.203931I
b = 0.528191 + 0.635299I
−0.49089 − 2.36719I −4.89133 + 3.88006I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.098568 + 0.770121I
a = −0.013002 − 1.254100I
b = 0.425202 + 0.943436I
−2.33749 − 1.65920I −4.80081 + 3.98111I
u = 0.098568 − 0.770121I
a = −0.013002 + 1.254100I
b = 0.425202 − 0.943436I
−2.33749 + 1.65920I −4.80081 − 3.98111I
u = −0.703037 + 0.218633I
a = −1.90319 + 0.73681I
b = 0.332995 − 0.720155I
−1.74343 + 3.40184I −6.62172 − 4.93370I
u = −0.703037 − 0.218633I
a = −1.90319 − 0.73681I
b = 0.332995 + 0.720155I
−1.74343 − 3.40184I −6.62172 + 4.93370I
u = −1.194980 + 0.426737I
a = −0.839889 − 0.604413I
b = −0.331200 + 0.919578I
−6.02412 + 5.77721I −9.54886 − 8.25145I
u = −1.194980 − 0.426737I
a = −0.839889 + 0.604413I
b = −0.331200 − 0.919578I
−6.02412 − 5.77721I −9.54886 + 8.25145I
u = 1.203880 + 0.487334I
a = 0.592561 + 0.052274I
b = −0.377110 + 1.031540I
−5.58543 − 3.01264I −6.87525 − 0.89912I
u = 1.203880 − 0.487334I
a = 0.592561 − 0.052274I
b = −0.377110 − 1.031540I
−5.58543 + 3.01264I −6.87525 + 0.89912I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
18
− 11u
17
+ ··· − 18u + 1)(u
61
+ 22u
60
+ ··· − 10584u − 841)
c
2
(u
18
− u
17
+ ··· + 9u
2
+ 1)(u
61
− 2u
60
+ ··· − 28u + 29)
c
3
(u
18
+ 9u
16
+ ··· + u + 1)(u
61
− u
60
+ ··· + 4065u + 1393)
c
4
(u
18
− 5u
16
+ ··· − 3u
2
+ 1)(u
61
− u
60
+ ··· − 4u + 7)
c
5
(u
18
+ 3u
16
+ ··· − 3u
2
+ 1)(u
61
− 3u
60
+ ··· − 11403u + 4312)
c
6
(u
18
+ u
17
+ ··· + 9u
2
+ 1)(u
61
− 2u
60
+ ··· − 28u + 29)
c
7
(u
18
+ u
17
+ ··· + 2u + 1)(u
61
+ 36u
59
+ ··· + 207224u + 19571)
c
8
(u
18
+ 2u
17
+ ··· + u + 1)(u
61
+ 3u
60
+ ··· + 7u + 2)
c
9
(u
18
− 10u
17
+ ··· − 6u + 1)(u
61
+ 27u
60
+ ··· + 324u + 49)
c
10
(u
18
− 5u
16
+ ··· − 3u
2
+ 1)(u
61
− u
60
+ ··· − 4u + 7)
c
11
(u
18
− u
17
+ ··· − 2u + 1)(u
61
+ 36u
59
+ ··· + 207224u + 19571)
c
12
(u
18
+ 5u
15
+ ··· + 8u
2
+ 1)(u
61
+ 7u
60
+ ··· + 119062u + 4921)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
18
+ 15y
17
+ ··· − 34y + 1)
· (y
61
+ 58y
60
+ ··· + 53870952y −707281)
c
2
, c
6
(y
18
+ 11y
17
+ ··· + 18y + 1)(y
61
+ 22y
60
+ ··· − 10584y −841)
c
3
(y
18
+ 18y
17
+ ··· + 11y + 1)
· (y
61
+ 73y
60
+ ··· − 72881301y −1940449)
c
4
, c
10
(y
18
− 10y
17
+ ··· − 6y + 1)(y
61
− 27y
60
+ ··· + 324y −49)
c
5
(y
18
+ 6y
17
+ ··· − 6y + 1)
· (y
61
− 15y
60
+ ··· + 131313385y −18593344)
c
7
, c
11
(y
18
− 7y
17
+ ··· − 10y + 1)
· (y
61
+ 72y
60
+ ··· + 1955728272y −383024041)
c
8
(y
18
− 10y
17
+ ··· − 7y + 1)(y
61
− 7y
60
+ ··· − 103y −4)
c
9
(y
18
+ 2y
17
+ ··· − 2y + 1)(y
61
+ 21y
60
+ ··· + 6192y −2401)
c
12
(y
18
− 4y
16
+ ··· + 16y + 1)
· (y
61
− 73y
60
+ ··· + 2203035738y −24216241)
20
