12n
0281
(K12n
0281
)
A knot diagram
1
Linearized knot diagam
3 6 7 11 9 2 5 11 1 5 7 10
Solving Sequence
5,7 8,11
9 12 4 3 10 1 2 6
c
7
c
8
c
11
c
4
c
3
c
10
c
12
c
1
c
6
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h1.82494 × 10
252
u
57
+ 1.82764 × 10
251
u
56
+ ··· + 7.78104 × 10
252
b − 1.44190 × 10
253
,
1.60321 × 10
253
u
57
+ 2.56712 × 10
252
u
56
+ ··· + 7.78104 × 10
252
a − 9.32328 × 10
253
,
u
58
+ 51u
56
+ ··· − 13u + 1i
I
u
2
= h−6.06692 × 10
19
u
19
+ 9.41482 × 10
19
u
18
+ ··· + 3.14683 × 10
19
b + 6.57389 × 10
19
,
3.61452 × 10
19
u
19
− 9.01759 × 10
19
u
18
+ ··· + 3.14683 × 10
19
a − 2.09263 × 10
20
, u
20
− u
19
+ ··· + 8u + 1i
* 2 irreducible components of dim
C
= 0, with total 78 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
= h1.82 × 10
252
u
57
+ 1.83 × 10
251
u
56
+ · · · + 7.78 × 10
252
b − 1.44 ×
10
253
, 1.60 × 10
253
u
57
+ 2.57 × 10
252
u
56
+ · · · + 7.78 × 10
252
a − 9.32 ×
10
253
, u
58
+ 51u
56
+ · · · − 13u + 1i
(i) Arc colorings
a
5
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
11
=
−2.06041u
57
− 0.329920u
56
+ ··· − 90.1499u + 11.9821
−0.234536u
57
− 0.0234883u
56
+ ··· − 14.4397u + 1.85309
a
9
=
1.04387u
57
+ 0.167750u
56
+ ··· + 52.9864u − 10.8517
0.0421526u
57
+ 0.0173690u
56
+ ··· − 0.700871u − 1.05817
a
12
=
−2.29494u
57
− 0.353409u
56
+ ··· − 104.590u + 13.8351
−0.234536u
57
− 0.0234883u
56
+ ··· − 14.4397u + 1.85309
a
4
=
−1.79431u
57
− 0.269090u
56
+ ··· − 65.9513u + 8.42012
−0.213324u
57
− 0.0357409u
56
+ ··· − 2.42241u + 1.31296
a
3
=
−2.00763u
57
− 0.304831u
56
+ ··· − 68.3737u + 9.73308
−0.213324u
57
− 0.0357409u
56
+ ··· − 2.42241u + 1.31296
a
10
=
−2.06041u
57
− 0.329920u
56
+ ··· − 90.1499u + 11.9821
−0.208881u
57
− 0.0233171u
56
+ ··· − 12.2111u + 1.52317
a
1
=
−0.509191u
57
− 0.192771u
56
+ ··· − 58.2608u + 2.04977
−0.241169u
57
− 0.0405319u
56
+ ··· − 13.7690u + 1.62656
a
2
=
−0.507749u
57
+ 0.0273770u
56
+ ··· − 44.2370u + 10.1377
0.125301u
57
+ 0.0350847u
56
+ ··· + 1.61989u + 0.441525
a
6
=
1.13600u
57
+ 0.228021u
56
+ ··· + 37.0000u − 3.53009
0.207315u
57
+ 0.0430301u
56
+ ··· + 3.66730u − 1.06964
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.19694u
57
− 0.252356u
56
+ ··· − 49.4008u + 2.76120
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
58
+ 28u
57
+ ··· + 886u + 121
c
2
, c
6
u
58
− 2u
57
+ ··· − 40u + 11
c
3
u
58
+ 2u
57
+ ··· − 2542u + 3839
c
4
, c
10
u
58
− u
57
+ ··· + 10u + 1
c
5
u
58
+ 3u
57
+ ··· + 60u + 88
c
7
u
58
+ 51u
56
+ ··· − 13u + 1
c
8
u
58
+ 3u
57
+ ··· + 12935u + 481
c
9
, c
12
u
58
+ 6u
57
+ ··· + 289u + 41
c
11
u
58
− 3u
57
+ ··· − 790066u + 205619
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
58
+ 12y
57
+ ··· + 130490y + 14641
c
2
, c
6
y
58
+ 28y
57
+ ··· + 886y + 121
c
3
y
58
− 4y
57
+ ··· − 237147274y + 14737921
c
4
, c
10
y
58
+ 75y
57
+ ··· − 50y + 1
c
5
y
58
− 21y
57
+ ··· − 103568y + 7744
c
7
y
58
+ 102y
57
+ ··· − 15y + 1
c
8
y
58
− 81y
57
+ ··· + 2622113y + 231361
c
9
, c
12
y
58
+ 22y
57
+ ··· + 63341y + 1681
c
11
y
58
− 77y
57
+ ··· + 288375606396y + 42279173161
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.605403 + 0.770255I
a = 0.476324 − 1.234450I
b = −0.836696 − 0.528282I
−3.29534 − 3.17863I 0
u = −0.605403 − 0.770255I
a = 0.476324 + 1.234450I
b = −0.836696 + 0.528282I
−3.29534 + 3.17863I 0
u = 0.785984 + 0.673927I
a = 0.503071 + 1.150720I
b = −0.611023 + 1.176480I
−3.08132 + 0.18394I 0
u = 0.785984 − 0.673927I
a = 0.503071 − 1.150720I
b = −0.611023 − 1.176480I
−3.08132 − 0.18394I 0
u = −0.933105 + 0.463612I
a = 0.616969 − 0.636242I
b = 0.49017 − 1.36421I
−0.163561 − 0.229805I 0
u = −0.933105 − 0.463612I
a = 0.616969 + 0.636242I
b = 0.49017 + 1.36421I
−0.163561 + 0.229805I 0
u = −1.027790 + 0.224558I
a = 0.284389 − 0.917517I
b = −0.586774 + 0.431083I
−2.33014 − 6.26866I 0
u = −1.027790 − 0.224558I
a = 0.284389 + 0.917517I
b = −0.586774 − 0.431083I
−2.33014 + 6.26866I 0
u = 0.927914 + 0.522270I
a = 0.693785 + 0.874215I
b = 0.21260 + 1.64706I
−1.22894 + 5.19635I 0
u = 0.927914 − 0.522270I
a = 0.693785 − 0.874215I
b = 0.21260 − 1.64706I
−1.22894 − 5.19635I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.202202 + 0.855913I
a = 0.634237 − 1.070540I
b = −0.589135 + 0.465773I
−2.01656 + 2.69465I 0
u = −0.202202 − 0.855913I
a = 0.634237 + 1.070540I
b = −0.589135 − 0.465773I
−2.01656 − 2.69465I 0
u = −0.706681 + 0.907609I
a = 0.680830 − 0.663324I
b = −0.702951 + 0.508789I
−2.73261 + 2.20022I 0
u = −0.706681 − 0.907609I
a = 0.680830 + 0.663324I
b = −0.702951 − 0.508789I
−2.73261 − 2.20022I 0
u = 1.163070 + 0.118652I
a = −0.147695 + 0.083721I
b = 0.503768 + 0.861204I
−6.57959 + 2.03147I 0
u = 1.163070 − 0.118652I
a = −0.147695 − 0.083721I
b = 0.503768 − 0.861204I
−6.57959 − 2.03147I 0
u = −1.132900 + 0.423824I
a = 0.1080040 − 0.0408760I
b = 0.502102 − 0.864389I
−2.52083 + 1.44860I 0
u = −1.132900 − 0.423824I
a = 0.1080040 + 0.0408760I
b = 0.502102 + 0.864389I
−2.52083 − 1.44860I 0
u = 0.613710 + 0.275012I
a = 0.577920 + 1.169060I
b = −0.605409 − 0.442067I
0.68088 + 1.79356I 3.58716 − 3.49376I
u = 0.613710 − 0.275012I
a = 0.577920 − 1.169060I
b = −0.605409 + 0.442067I
0.68088 − 1.79356I 3.58716 + 3.49376I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.112698 + 0.641118I
a = 1.14677 + 1.24755I
b = −0.104986 − 0.459963I
−0.20219 + 1.76036I 2.87139 − 4.54013I
u = 0.112698 − 0.641118I
a = 1.14677 − 1.24755I
b = −0.104986 + 0.459963I
−0.20219 − 1.76036I 2.87139 + 4.54013I
u = 1.34164 + 0.50804I
a = 0.0413867 − 0.0772033I
b = 0.500717 + 0.867698I
−5.31571 − 6.25637I 0
u = 1.34164 − 0.50804I
a = 0.0413867 + 0.0772033I
b = 0.500717 − 0.867698I
−5.31571 + 6.25637I 0
u = −0.215717 + 0.466050I
a = 0.850318 + 0.391504I
b = −0.051763 − 0.414571I
−0.204392 + 1.155360I −2.58460 − 5.42114I
u = −0.215717 − 0.466050I
a = 0.850318 − 0.391504I
b = −0.051763 + 0.414571I
−0.204392 − 1.155360I −2.58460 + 5.42114I
u = −0.316089 + 0.016627I
a = −2.59472 + 1.52273I
b = 0.723432 + 0.374751I
−5.01306 + 2.02127I −6.01042 − 2.94322I
u = −0.316089 − 0.016627I
a = −2.59472 − 1.52273I
b = 0.723432 − 0.374751I
−5.01306 − 2.02127I −6.01042 + 2.94322I
u = 0.139498 + 0.148897I
a = −0.77014 − 3.28112I
b = −0.935346 + 0.418012I
2.35280 − 1.42837I 5.23226 − 0.77346I
u = 0.139498 − 0.148897I
a = −0.77014 + 3.28112I
b = −0.935346 − 0.418012I
2.35280 + 1.42837I 5.23226 + 0.77346I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.072363 + 0.140302I
a = −3.68001 + 2.57740I
b = −1.276320 − 0.323994I
1.40150 − 2.62563I −2.39243 + 7.68960I
u = 0.072363 − 0.140302I
a = −3.68001 − 2.57740I
b = −1.276320 + 0.323994I
1.40150 + 2.62563I −2.39243 − 7.68960I
u = −0.082246 + 0.130921I
a = 7.59312 + 2.53392I
b = 0.915246 − 0.256960I
−0.28851 + 4.07641I 2.15744 − 4.09621I
u = −0.082246 − 0.130921I
a = 7.59312 − 2.53392I
b = 0.915246 + 0.256960I
−0.28851 − 4.07641I 2.15744 + 4.09621I
u = 0.1302840 + 0.0411333I
a = 5.89662 − 7.40372I
b = 1.210170 − 0.117689I
−2.24712 + 9.22197I −1.03586 − 7.84449I
u = 0.1302840 − 0.0411333I
a = 5.89662 + 7.40372I
b = 1.210170 + 0.117689I
−2.24712 − 9.22197I −1.03586 + 7.84449I
u = −0.25501 + 2.08526I
a = −0.853720 + 0.095240I
b = 1.69702 + 0.80685I
8.43308 + 5.72964I 0
u = −0.25501 − 2.08526I
a = −0.853720 − 0.095240I
b = 1.69702 − 0.80685I
8.43308 − 5.72964I 0
u = 0.10045 + 2.09972I
a = 0.851816 + 0.083179I
b = −2.28410 − 0.51852I
9.71957 + 1.80340I 0
u = 0.10045 − 2.09972I
a = 0.851816 − 0.083179I
b = −2.28410 + 0.51852I
9.71957 − 1.80340I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.05252 + 2.17046I
a = −0.740950 + 0.004758I
b = 1.232640 + 0.312711I
5.97993 − 0.81701I 0
u = −0.05252 − 2.17046I
a = −0.740950 − 0.004758I
b = 1.232640 − 0.312711I
5.97993 + 0.81701I 0
u = 0.26686 + 2.16526I
a = −0.800876 − 0.131026I
b = 1.81818 − 0.56412I
10.20810 − 0.71624I 0
u = 0.26686 − 2.16526I
a = −0.800876 + 0.131026I
b = 1.81818 + 0.56412I
10.20810 + 0.71624I 0
u = −0.15055 + 2.20291I
a = 0.825604 − 0.038418I
b = −2.35720 + 0.13376I
10.67330 + 4.49403I 0
u = −0.15055 − 2.20291I
a = 0.825604 + 0.038418I
b = −2.35720 − 0.13376I
10.67330 − 4.49403I 0
u = 0.30268 + 2.31181I
a = 0.721619 + 0.003544I
b = −1.89927 + 0.30757I
2.64098 − 5.70905I 0
u = 0.30268 − 2.31181I
a = 0.721619 − 0.003544I
b = −1.89927 − 0.30757I
2.64098 + 5.70905I 0
u = 0.34239 + 2.31494I
a = −0.684662 − 0.216298I
b = 2.00993 − 0.07441I
9.93307 + 1.69714I 0
u = 0.34239 − 2.31494I
a = −0.684662 + 0.216298I
b = 2.00993 + 0.07441I
9.93307 − 1.69714I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.22218 + 2.35542I
a = 0.755369 + 0.052860I
b = −2.13863 − 0.54775I
8.46254 + 9.07820I 0
u = −0.22218 − 2.35542I
a = 0.755369 − 0.052860I
b = −2.13863 + 0.54775I
8.46254 − 9.07820I 0
u = −0.39552 + 2.35080I
a = −0.640216 + 0.260076I
b = 2.06046 − 0.12425I
7.93450 − 6.76711I 0
u = −0.39552 − 2.35080I
a = −0.640216 − 0.260076I
b = 2.06046 + 0.12425I
7.93450 + 6.76711I 0
u = 0.22078 + 2.39023I
a = 0.737856 − 0.080606I
b = −2.06346 + 0.70700I
5.9812 − 14.7941I 0
u = 0.22078 − 2.39023I
a = 0.737856 + 0.080606I
b = −2.06346 − 0.70700I
5.9812 + 14.7941I 0
u = −0.22242 + 2.48174I
a = −0.583026 + 0.113235I
b = 1.66663 − 0.04894I
5.45632 + 0.40195I 0
u = −0.22242 − 2.48174I
a = −0.583026 − 0.113235I
b = 1.66663 + 0.04894I
5.45632 − 0.40195I 0
10
II.
I
u
2
= h−6.07×10
19
u
19
+9.41×10
19
u
18
+· · ·+3.15×10
19
b+6.57×10
19
, 3.61×
10
19
u
19
−9.02×10
19
u
18
+· · ·+3.15×10
19
a−2.09×10
20
, u
20
−u
19
+· · ·+8u+1i
(i) Arc colorings
a
5
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
11
=
−1.14862u
19
+ 2.86561u
18
+ ··· + 52.5661u + 6.64996
1.92794u
19
− 2.99184u
18
+ ··· − 2.72601u − 2.08905
a
9
=
4.30867u
19
− 5.11776u
18
+ ··· + 67.3450u + 7.63162
−0.169783u
19
− 0.679356u
18
+ ··· − 23.1178u − 2.73782
a
12
=
0.779322u
19
− 0.126232u
18
+ ··· + 49.8401u + 4.56091
1.92794u
19
− 2.99184u
18
+ ··· − 2.72601u − 2.08905
a
4
=
−1.08905u
19
− 0.838895u
18
+ ··· − 59.9916u − 5.98639
1.87298u
19
− 2.05692u
18
+ ··· + 45.3503u + 6.23661
a
3
=
0.783934u
19
− 2.89581u
18
+ ··· − 14.6413u + 0.250227
1.87298u
19
− 2.05692u
18
+ ··· + 45.3503u + 6.23661
a
10
=
−1.14862u
19
+ 2.86561u
18
+ ··· + 52.5661u + 6.64996
1.85691u
19
− 2.41990u
18
+ ··· + 9.86126u − 0.372063
a
1
=
5.08799u
19
− 5.24399u
18
+ ··· + 117.185u + 12.1925
1.91394u
19
− 2.98258u
18
+ ··· − 4.89004u − 1.89814
a
2
=
3.98051u
19
− 5.59567u
18
+ ··· + 17.9946u + 1.21621
0.195657u
19
− 0.183933u
18
+ ··· + 10.8593u + 2.67733
a
6
=
0.627937u
19
− 2.48485u
18
+ ··· − 44.1527u − 4.83777
0.804343u
19
− 0.816067u
18
+ ··· + 28.1407u + 4.32267
(ii) Obstruction class = 1
(iii) Cusp Shapes =
86912471356230966919
31468322960334269681
u
19
−
121955116805407308520
31468322960334269681
u
18
+ ··· −
77257384023725289987
31468322960334269681
u −
180061111953374962015
31468322960334269681
11
(iv) u-Polynomials at the component
12
Crossings u-Polynomials at each crossing
c
1
u
20
− 11u
19
+ ··· − 7u + 1
c
2
u
20
− u
19
+ ··· − u + 1
c
3
u
20
+ u
19
+ ··· + u + 1
c
4
u
20
+ 11u
18
+ ··· + 3u + 1
c
5
u
20
+ 2u
19
+ ··· − 3u + 1
c
6
u
20
+ u
19
+ ··· + u + 1
c
7
u
20
− u
19
+ ··· + 8u + 1
c
8
u
20
+ 6u
19
+ ··· − 2u + 1
c
9
u
20
+ 5u
19
+ ··· − 2u + 1
c
10
u
20
+ 11u
18
+ ··· − 3u + 1
c
11
u
20
+ 2u
19
+ ··· − 5u + 1
c
12
u
20
− 5u
19
+ ··· + 2u + 1
13
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
+ 3y
19
+ ··· − 9y + 1
c
2
, c
6
y
20
+ 11y
19
+ ··· + 7y + 1
c
3
y
20
− 5y
19
+ ··· + 11y + 1
c
4
, c
10
y
20
+ 22y
19
+ ··· + 27y + 1
c
5
y
20
− 14y
19
+ ··· + 9y + 1
c
7
y
20
+ 9y
19
+ ··· + 14y + 1
c
8
y
20
− 14y
19
+ ··· + 10y + 1
c
9
, c
12
y
20
+ 9y
19
+ ··· − 6y + 1
c
11
y
20
− 6y
19
+ ··· + 9y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.654375 + 0.832677I
a = 0.503183 − 0.846050I
b = −0.194792 − 0.729886I
−2.71864 − 1.45971I −0.89646 + 2.17815I
u = −0.654375 − 0.832677I
a = 0.503183 + 0.846050I
b = −0.194792 + 0.729886I
−2.71864 + 1.45971I −0.89646 − 2.17815I
u = −1.326230 + 0.153242I
a = −0.233237 − 0.656743I
b = −0.470432 − 0.684847I
−1.99836 − 2.67759I 0.08880 + 3.61083I
u = −1.326230 − 0.153242I
a = −0.233237 + 0.656743I
b = −0.470432 + 0.684847I
−1.99836 + 2.67759I 0.08880 − 3.61083I
u = −0.283343 + 0.478254I
a = −0.479487 + 0.030100I
b = −0.958183 + 0.057779I
1.50477 + 1.79654I −1.48765 − 0.69459I
u = −0.283343 − 0.478254I
a = −0.479487 − 0.030100I
b = −0.958183 − 0.057779I
1.50477 − 1.79654I −1.48765 + 0.69459I
u = −0.065192 + 0.513948I
a = 2.12487 + 0.49208I
b = −0.029629 + 0.829824I
−4.95539 + 3.67611I −6.05419 − 4.52419I
u = −0.065192 − 0.513948I
a = 2.12487 − 0.49208I
b = −0.029629 − 0.829824I
−4.95539 − 3.67611I −6.05419 + 4.52419I
u = −0.388734 + 0.189482I
a = −2.19950 + 1.65173I
b = −0.172656 + 1.147900I
−1.14234 + 0.98756I −2.34913 − 0.96839I
u = −0.388734 − 0.189482I
a = −2.19950 − 1.65173I
b = −0.172656 − 1.147900I
−1.14234 − 0.98756I −2.34913 + 0.96839I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.093068 + 0.385354I
a = −2.58480 + 1.87857I
b = 0.137373 − 1.131910I
−3.37351 + 4.07065I −4.00523 − 3.92466I
u = −0.093068 − 0.385354I
a = −2.58480 − 1.87857I
b = 0.137373 + 1.131910I
−3.37351 − 4.07065I −4.00523 + 3.92466I
u = 1.51215 + 0.68020I
a = 0.028861 + 0.571314I
b = −0.338355 + 0.609590I
−5.61868 − 0.78543I −3.44115 + 0.39623I
u = 1.51215 − 0.68020I
a = 0.028861 − 0.571314I
b = −0.338355 − 0.609590I
−5.61868 + 0.78543I −3.44115 − 0.39623I
u = 1.69347 + 0.07041I
a = −0.187449 + 0.482061I
b = −0.478407 + 0.564426I
−4.74636 + 7.31948I −2.74412 − 7.73216I
u = 1.69347 − 0.07041I
a = −0.187449 − 0.482061I
b = −0.478407 − 0.564426I
−4.74636 − 7.31948I −2.74412 + 7.73216I
u = −0.00070 + 2.14683I
a = −0.831417 − 0.035871I
b = 2.17981 + 0.27698I
9.85332 + 2.88141I 0.90247 − 3.92917I
u = −0.00070 − 2.14683I
a = −0.831417 + 0.035871I
b = 2.17981 − 0.27698I
9.85332 − 2.88141I 0.90247 + 3.92917I
u = 0.10602 + 2.37201I
a = −0.641018 − 0.047557I
b = 1.325270 + 0.136830I
6.61544 − 1.15788I 6.48667 + 6.36754I
u = 0.10602 − 2.37201I
a = −0.641018 + 0.047557I
b = 1.325270 − 0.136830I
6.61544 + 1.15788I 6.48667 − 6.36754I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
20
− 11u
19
+ ··· − 7u + 1)(u
58
+ 28u
57
+ ··· + 886u + 121)
c
2
(u
20
− u
19
+ ··· − u + 1)(u
58
− 2u
57
+ ··· − 40u + 11)
c
3
(u
20
+ u
19
+ ··· + u + 1)(u
58
+ 2u
57
+ ··· − 2542u + 3839)
c
4
(u
20
+ 11u
18
+ ··· + 3u + 1)(u
58
− u
57
+ ··· + 10u + 1)
c
5
(u
20
+ 2u
19
+ ··· − 3u + 1)(u
58
+ 3u
57
+ ··· + 60u + 88)
c
6
(u
20
+ u
19
+ ··· + u + 1)(u
58
− 2u
57
+ ··· − 40u + 11)
c
7
(u
20
− u
19
+ ··· + 8u + 1)(u
58
+ 51u
56
+ ··· − 13u + 1)
c
8
(u
20
+ 6u
19
+ ··· − 2u + 1)(u
58
+ 3u
57
+ ··· + 12935u + 481)
c
9
(u
20
+ 5u
19
+ ··· − 2u + 1)(u
58
+ 6u
57
+ ··· + 289u + 41)
c
10
(u
20
+ 11u
18
+ ··· − 3u + 1)(u
58
− u
57
+ ··· + 10u + 1)
c
11
(u
20
+ 2u
19
+ ··· − 5u + 1)(u
58
− 3u
57
+ ··· − 790066u + 205619)
c
12
(u
20
− 5u
19
+ ··· + 2u + 1)(u
58
+ 6u
57
+ ··· + 289u + 41)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
20
+ 3y
19
+ ··· − 9y + 1)(y
58
+ 12y
57
+ ··· + 130490y + 14641)
c
2
, c
6
(y
20
+ 11y
19
+ ··· + 7y + 1)(y
58
+ 28y
57
+ ··· + 886y + 121)
c
3
(y
20
− 5y
19
+ ··· + 11y + 1)
· (y
58
− 4y
57
+ ··· − 237147274y + 14737921)
c
4
, c
10
(y
20
+ 22y
19
+ ··· + 27y + 1)(y
58
+ 75y
57
+ ··· − 50y + 1)
c
5
(y
20
− 14y
19
+ ··· + 9y + 1)(y
58
− 21y
57
+ ··· − 103568y + 7744)
c
7
(y
20
+ 9y
19
+ ··· + 14y + 1)(y
58
+ 102y
57
+ ··· − 15y + 1)
c
8
(y
20
− 14y
19
+ ··· + 10y + 1)
· (y
58
− 81y
57
+ ··· + 2622113y + 231361)
c
9
, c
12
(y
20
+ 9y
19
+ ··· − 6y + 1)(y
58
+ 22y
57
+ ··· + 63341y + 1681)
c
11
(y
20
− 6y
19
+ ··· + 9y + 1)
· (y
58
− 77y
57
+ ··· + 288375606396y + 42279173161)
19
