12n
0634
(K12n
0634
)
A knot diagram
1
Linearized knot diagam
3 7 9 11 3 10 2 5 12 7 4 6
Solving Sequence
3,7
2 8
1,11
10 6 5 9 4 12
c
2
c
7
c
1
c
10
c
6
c
5
c
8
c
4
c
12
c
3
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.95711 × 10
172
u
51
− 3.47717 × 10
172
u
50
+ ··· + 1.87747 × 10
177
b + 1.65522 × 10
176
,
5.80863 × 10
175
u
51
+ 7.03687 × 10
175
u
50
+ ··· + 8.07312 × 10
178
a + 1.92816 × 10
178
,
u
52
+ u
51
+ ··· − 430u − 1849i
I
u
2
= h7.95354 × 10
18
u
28
− 2.49597 × 10
18
u
27
+ ··· + 1.30438 × 10
19
b + 9.76819 × 10
18
,
− 2.06470 × 10
19
u
28
− 4.89686 × 10
18
u
27
+ ··· + 1.30438 × 10
19
a − 4.59506 × 10
19
,
u
29
+ 16u
27
+ ··· + 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 81 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−1.96 × 10
172
u
51
− 3.48 × 10
172
u
50
+ · · · + 1.88 × 10
177
b + 1.66 ×
10
176
, 5.81 × 10
175
u
51
+ 7.04 × 10
175
u
50
+ · · · + 8.07 × 10
178
a + 1.93 ×
10
178
, u
52
+ u
51
+ · · · − 430u − 1849i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
8
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
11
=
−0.000719502u
51
− 0.000871642u
50
+ ··· − 2.02990u − 0.238837
0.0000104242u
51
+ 0.0000185205u
50
+ ··· − 2.44475u − 0.0881622
a
10
=
−0.000719502u
51
− 0.000871642u
50
+ ··· − 2.02990u − 0.238837
−8.14632 × 10
−7
u
51
− 0.0000812325u
50
+ ··· − 1.04897u + 0.193144
a
6
=
0.000695591u
51
+ 0.000693094u
50
+ ··· + 5.78811u + 1.78101
0.000147181u
51
+ 0.000119151u
50
+ ··· + 2.46237u + 0.340252
a
5
=
0.000548410u
51
+ 0.000573943u
50
+ ··· + 3.32574u + 1.44076
0.000147181u
51
+ 0.000119151u
50
+ ··· + 2.46237u + 0.340252
a
9
=
−0.000562077u
51
− 0.000571100u
50
+ ··· − 6.77593u − 2.97489
−0.000159864u
51
− 0.000179227u
50
+ ··· − 2.17934u − 0.533160
a
4
=
0.000231771u
51
+ 0.000153448u
50
+ ··· + 10.5786u + 4.67788
0.0000301411u
51
+ 0.0000823394u
50
+ ··· + 2.47373u + 0.457419
a
12
=
0.000440440u
51
+ 0.000638660u
50
+ ··· − 4.30838u + 4.57675
0.0000737660u
51
+ 0.0000885300u
50
+ ··· − 0.804093u + 0.949948
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.000209766u
51
+ 0.000739361u
50
+ ··· + 3.85584u − 4.14186
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
52
+ 83u
51
+ ··· − 10239762u + 3418801
c
2
, c
7
u
52
− u
51
+ ··· + 430u − 1849
c
3
u
52
− u
51
+ ··· − 96u + 9
c
4
, c
11
u
52
− 2u
51
+ ··· − 1077u − 89
c
5
u
52
+ 47u
50
+ ··· − 950335u − 289973
c
6
, c
10
u
52
+ 2u
51
+ ··· + 91u − 181
c
8
u
52
+ 5u
51
+ ··· − 38226689u + 7428119
c
9
u
52
− 5u
51
+ ··· + 324u + 356
c
12
u
52
− 2u
51
+ ··· − 81165u + 4259
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
52
− 209y
51
+ ··· + 1284466243376242y + 11688200277601
c
2
, c
7
y
52
+ 83y
51
+ ··· − 10239762y + 3418801
c
3
y
52
− 11y
51
+ ··· − 4590y + 81
c
4
, c
11
y
52
+ 50y
51
+ ··· − 321727y + 7921
c
5
y
52
+ 94y
51
+ ··· − 346734679987y + 84084340729
c
6
, c
10
y
52
− 54y
51
+ ··· + 1011111y + 32761
c
8
y
52
− 73y
51
+ ··· − 308498524989461y + 55176951878161
c
9
y
52
− 25y
51
+ ··· + 789296y + 126736
c
12
y
52
+ 98y
51
+ ··· − 7982256041y + 18139081
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.275825 + 0.932345I
a = −0.380468 − 0.078038I
b = 1.52892 + 1.15015I
−2.42630 + 6.41308I 1.23938 − 7.68294I
u = 0.275825 − 0.932345I
a = −0.380468 + 0.078038I
b = 1.52892 − 1.15015I
−2.42630 − 6.41308I 1.23938 + 7.68294I
u = 0.539271 + 0.935679I
a = −0.287527 + 0.954049I
b = −0.817124 + 0.789515I
−3.75694 + 4.49624I −7.52077 − 6.70808I
u = 0.539271 − 0.935679I
a = −0.287527 − 0.954049I
b = −0.817124 − 0.789515I
−3.75694 − 4.49624I −7.52077 + 6.70808I
u = −0.650501 + 0.863107I
a = 0.691550 − 0.812723I
b = −1.61355 − 1.85935I
0.50603 − 2.57474I 0. + 4.06110I
u = −0.650501 − 0.863107I
a = 0.691550 + 0.812723I
b = −1.61355 + 1.85935I
0.50603 + 2.57474I 0. − 4.06110I
u = 0.202582 + 0.881244I
a = 0.630878 − 0.801031I
b = −0.512799 + 0.454432I
−1.81662 − 1.18879I −5.31113 + 2.20959I
u = 0.202582 − 0.881244I
a = 0.630878 + 0.801031I
b = −0.512799 − 0.454432I
−1.81662 + 1.18879I −5.31113 − 2.20959I
u = 0.351525 + 1.081680I
a = −0.672391 + 1.023130I
b = −0.217102 − 0.172805I
−8.65330 − 1.89169I −8.34506 + 0.93318I
u = 0.351525 − 1.081680I
a = −0.672391 − 1.023130I
b = −0.217102 + 0.172805I
−8.65330 + 1.89169I −8.34506 − 0.93318I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.818940 + 0.160767I
a = −1.69144 + 0.20465I
b = −0.928736 + 0.671508I
−5.38897 + 0.87571I −2.85912 + 2.34335I
u = −0.818940 − 0.160767I
a = −1.69144 − 0.20465I
b = −0.928736 − 0.671508I
−5.38897 − 0.87571I −2.85912 − 2.34335I
u = −0.335509 + 0.751647I
a = 0.538199 − 0.371856I
b = −0.932426 − 0.178983I
−0.27804 − 1.89990I 0.73245 + 4.61007I
u = −0.335509 − 0.751647I
a = 0.538199 + 0.371856I
b = −0.932426 + 0.178983I
−0.27804 + 1.89990I 0.73245 − 4.61007I
u = 0.213597 + 1.222440I
a = −0.743596 − 0.589889I
b = 1.60989 − 1.34032I
1.01333 + 1.02881I 0
u = 0.213597 − 1.222440I
a = −0.743596 + 0.589889I
b = 1.60989 + 1.34032I
1.01333 − 1.02881I 0
u = −0.055615 + 0.755904I
a = 0.49398 − 1.42299I
b = −1.190970 − 0.372066I
−2.79971 − 1.53838I −4.05410 + 0.44087I
u = −0.055615 − 0.755904I
a = 0.49398 + 1.42299I
b = −1.190970 + 0.372066I
−2.79971 + 1.53838I −4.05410 − 0.44087I
u = 0.679978
a = 1.52551
b = 0.501507
−1.67869 −6.69150
u = 0.336439 + 0.585453I
a = −0.443953 − 0.493321I
b = −0.599232 − 0.191514I
−3.82874 − 0.83282I −6.69897 − 1.25074I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.336439 − 0.585453I
a = −0.443953 + 0.493321I
b = −0.599232 + 0.191514I
−3.82874 + 0.83282I −6.69897 + 1.25074I
u = 0.521240 + 0.365317I
a = 0.555831 + 0.734286I
b = −1.084070 + 0.405815I
−1.16726 − 3.02767I 1.89586 + 2.76037I
u = 0.521240 − 0.365317I
a = 0.555831 − 0.734286I
b = −1.084070 − 0.405815I
−1.16726 + 3.02767I 1.89586 − 2.76037I
u = −0.898610 + 1.083740I
a = −0.832366 − 0.553360I
b = −0.203830 + 0.717311I
−7.83351 + 4.08846I 0
u = −0.898610 − 1.083740I
a = −0.832366 + 0.553360I
b = −0.203830 − 0.717311I
−7.83351 − 4.08846I 0
u = 1.02788 + 1.21603I
a = 0.666350 − 1.075790I
b = 2.88476 + 0.58421I
−9.81716 − 1.76389I 0
u = 1.02788 − 1.21603I
a = 0.666350 + 1.075790I
b = 2.88476 − 0.58421I
−9.81716 + 1.76389I 0
u = −0.08564 + 1.59213I
a = −0.412998 + 0.094265I
b = 0.692278 + 0.084135I
−8.51191 − 3.22667I 0
u = −0.08564 − 1.59213I
a = −0.412998 − 0.094265I
b = 0.692278 − 0.084135I
−8.51191 + 3.22667I 0
u = −0.330077 + 0.195063I
a = 0.625921 + 0.929420I
b = 0.680678 − 0.511018I
1.12780 − 0.87427I 7.10299 + 3.37562I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.330077 − 0.195063I
a = 0.625921 − 0.929420I
b = 0.680678 + 0.511018I
1.12780 + 0.87427I 7.10299 − 3.37562I
u = 0.255114 + 0.232956I
a = −3.71521 + 1.79997I
b = −0.880754 − 0.179713I
−5.75128 − 6.56432I −4.11138 + 4.05271I
u = 0.255114 − 0.232956I
a = −3.71521 − 1.79997I
b = −0.880754 + 0.179713I
−5.75128 + 6.56432I −4.11138 − 4.05271I
u = −0.337796
a = 3.69732
b = 1.37016
−0.727216 −13.1080
u = 0.03672 + 1.74560I
a = −0.251249 + 0.023127I
b = 1.289730 + 0.212055I
−12.39400 + 0.81454I 0
u = 0.03672 − 1.74560I
a = −0.251249 − 0.023127I
b = 1.289730 − 0.212055I
−12.39400 − 0.81454I 0
u = −1.15761 + 1.51843I
a = 0.586482 + 0.796448I
b = 2.30536 − 1.24673I
−10.15170 − 6.43419I 0
u = −1.15761 − 1.51843I
a = 0.586482 − 0.796448I
b = 2.30536 + 1.24673I
−10.15170 + 6.43419I 0
u = 0.32226 + 1.90220I
a = 0.014803 − 0.900992I
b = 1.44976 + 0.57133I
−19.1346 + 2.1490I 0
u = 0.32226 − 1.90220I
a = 0.014803 + 0.900992I
b = 1.44976 − 0.57133I
−19.1346 − 2.1490I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.07800 + 1.98796I
a = −0.109017 − 0.866405I
b = 0.805068 + 0.656452I
−15.4556 + 6.9522I 0
u = 0.07800 − 1.98796I
a = −0.109017 + 0.866405I
b = 0.805068 − 0.656452I
−15.4556 − 6.9522I 0
u = −0.02112 + 2.09350I
a = −0.144533 + 0.825946I
b = 0.865609 − 1.012250I
−14.6985 − 0.9884I 0
u = −0.02112 − 2.09350I
a = −0.144533 − 0.825946I
b = 0.865609 + 1.012250I
−14.6985 + 0.9884I 0
u = 0.53139 + 2.03050I
a = 0.245255 + 0.983595I
b = −3.40407 − 0.93661I
19.4506 + 5.7616I 0
u = 0.53139 − 2.03050I
a = 0.245255 − 0.983595I
b = −3.40407 + 0.93661I
19.4506 − 5.7616I 0
u = −0.43024 + 2.08016I
a = 0.185917 − 0.896546I
b = −2.73017 + 0.92922I
17.8356 − 14.3502I 0
u = −0.43024 − 2.08016I
a = 0.185917 + 0.896546I
b = −2.73017 − 0.92922I
17.8356 + 14.3502I 0
u = −0.09944 + 2.16592I
a = 0.924083 + 0.081345I
b = −3.92522 − 0.71460I
−15.4081 + 4.9026I 0
u = −0.09944 − 2.16592I
a = 0.924083 − 0.081345I
b = −3.92522 + 0.71460I
−15.4081 − 4.9026I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.47962 + 2.20629I
a = 0.053614 + 0.744727I
b = 1.49215 − 0.97274I
−18.5854 − 3.5520I 0
u = −0.47962 − 2.20629I
a = 0.053614 − 0.744727I
b = 1.49215 + 0.97274I
−18.5854 + 3.5520I 0
10
II. I
u
2
= h7.95 × 10
18
u
28
− 2.50 × 10
18
u
27
+ · · · + 1.30 × 10
19
b + 9.77 ×
10
18
, −2.06 × 10
19
u
28
− 4.90 × 10
18
u
27
+ · · · + 1.30 × 10
19
a − 4.60 ×
10
19
, u
29
+ 16u
27
+ · · · + 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
8
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
11
=
1.58289u
28
+ 0.375416u
27
+ ··· + 23.0341u + 3.52278
−0.609755u
28
+ 0.191352u
27
+ ··· − 1.62838u − 0.748874
a
10
=
1.58289u
28
+ 0.375416u
27
+ ··· + 23.0341u + 3.52278
−0.646274u
28
+ 0.321379u
27
+ ··· + 0.705339u − 0.373458
a
6
=
−2.19231u
28
− 0.581219u
27
+ ··· − 25.5255u − 3.87277
0.146160u
28
+ 0.168172u
27
+ ··· − 3.05911u + 0.0131335
a
5
=
−2.33847u
28
− 0.749392u
27
+ ··· − 22.4664u − 3.88591
0.146160u
28
+ 0.168172u
27
+ ··· − 3.05911u + 0.0131335
a
9
=
1.23953u
28
+ 0.189431u
27
+ ··· − 8.70535u − 5.08357
0.592887u
28
+ 0.289661u
27
+ ··· + 7.84451u + 1.80937
a
4
=
−3.39570u
28
− 0.362303u
27
+ ··· − 20.3142u + 1.55184
0.716281u
28
+ 0.0775215u
27
+ ··· − 1.88678u − 0.0652422
a
12
=
1.88363u
28
− 0.861725u
27
+ ··· − 12.0156u − 6.82950
−0.288048u
28
+ 0.0864079u
27
+ ··· − 1.05603u − 1.20804
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
37295273734905786033
13043842048949049407
u
28
+
7379073912415012035
13043842048949049407
u
27
+ ··· +
523698604375136567
13043842048949049407
u −
12328496894734939546
13043842048949049407
11
(iv) u-Polynomials at the component
12
Crossings u-Polynomials at each crossing
c
1
u
29
− 32u
28
+ ··· − 30u + 1
c
2
u
29
+ 16u
27
+ ··· + 2u + 1
c
3
u
29
− u
27
+ ··· + 4u + 1
c
4
u
29
+ u
28
+ ··· − u − 13
c
5
u
29
+ u
28
+ ··· − u − 1
c
6
u
29
+ u
28
+ ··· − 3u − 1
c
7
u
29
+ 16u
27
+ ··· + 2u − 1
c
8
u
29
− 6u
27
+ ··· + 5u + 1
c
9
u
29
− 4u
28
+ ··· + 24u − 4
c
10
u
29
− u
28
+ ··· − 3u + 1
c
11
u
29
− u
28
+ ··· − u + 13
c
12
u
29
− u
28
+ ··· + 355u + 187
13
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
29
− 52y
28
+ ··· + 34y −1
c
2
, c
7
y
29
+ 32y
28
+ ··· − 30y −1
c
3
y
29
− 2y
28
+ ··· + 26y −1
c
4
, c
11
y
29
+ 23y
28
+ ··· − 2209y −169
c
5
y
29
+ 15y
28
+ ··· + 11y −1
c
6
, c
10
y
29
− 17y
28
+ ··· + 17y −1
c
8
y
29
− 12y
28
+ ··· − 103y −1
c
9
y
29
− 8y
28
+ ··· − 288y −16
c
12
y
29
+ 39y
28
+ ··· + 65437y −34969
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.501818 + 0.833839I
a = 0.467030 + 0.518760I
b = −1.186310 − 0.660678I
−2.46701 + 3.31089I −6.64762 − 4.28533I
u = −0.501818 − 0.833839I
a = 0.467030 − 0.518760I
b = −1.186310 + 0.660678I
−2.46701 − 3.31089I −6.64762 + 4.28533I
u = 0.395046 + 0.881302I
a = 0.193357 − 1.331450I
b = 1.139830 + 0.271865I
−6.12414 + 8.00905I −5.12519 − 8.45010I
u = 0.395046 − 0.881302I
a = 0.193357 + 1.331450I
b = 1.139830 − 0.271865I
−6.12414 − 8.00905I −5.12519 + 8.45010I
u = −0.341041 + 1.028870I
a = −0.194038 − 0.579843I
b = 1.10689 − 1.28067I
−3.12004 − 6.46709I −9.74691 + 8.24915I
u = −0.341041 − 1.028870I
a = −0.194038 + 0.579843I
b = 1.10689 + 1.28067I
−3.12004 + 6.46709I −9.74691 − 8.24915I
u = 0.400082 + 1.085830I
a = 0.741612 + 0.558186I
b = −1.54514 + 1.73471I
1.43870 + 1.55601I 3.91538 − 4.80433I
u = 0.400082 − 1.085830I
a = 0.741612 − 0.558186I
b = −1.54514 − 1.73471I
1.43870 − 1.55601I 3.91538 + 4.80433I
u = −0.377353 + 1.105050I
a = 0.019943 − 0.931023I
b = −1.48812 − 0.50305I
−3.06298 − 3.21483I −6.22465 + 3.26026I
u = −0.377353 − 1.105050I
a = 0.019943 + 0.931023I
b = −1.48812 + 0.50305I
−3.06298 + 3.21483I −6.22465 − 3.26026I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.757913 + 0.894886I
a = −0.934300 + 0.874778I
b = 1.59792 + 2.38337I
−0.51479 − 2.85047I −6.69492 + 4.19394I
u = −0.757913 − 0.894886I
a = −0.934300 − 0.874778I
b = 1.59792 − 2.38337I
−0.51479 + 2.85047I −6.69492 − 4.19394I
u = 0.284256 + 1.182870I
a = 0.333089 − 0.615425I
b = −1.232700 + 0.271698I
−2.12362 + 0.73935I −5.54663 − 2.17801I
u = 0.284256 − 1.182870I
a = 0.333089 + 0.615425I
b = −1.232700 − 0.271698I
−2.12362 − 0.73935I −5.54663 + 2.17801I
u = 0.125391 + 0.740741I
a = 0.072781 + 1.150700I
b = 0.445959 + 0.328062I
−0.218621 + 1.074110I −0.75381 − 2.66974I
u = 0.125391 − 0.740741I
a = 0.072781 − 1.150700I
b = 0.445959 − 0.328062I
−0.218621 − 1.074110I −0.75381 + 2.66974I
u = 0.856142 + 1.047000I
a = −0.906222 + 0.682310I
b = −0.823807 − 0.830433I
−6.75266 − 3.66088I −3.57875 + 1.97522I
u = 0.856142 − 1.047000I
a = −0.906222 − 0.682310I
b = −0.823807 + 0.830433I
−6.75266 + 3.66088I −3.57875 − 1.97522I
u = −0.09611 + 1.48953I
a = 0.207292 − 0.225440I
b = 0.209690 + 0.379206I
−9.07326 − 3.27525I −11.96737 + 3.20156I
u = −0.09611 − 1.48953I
a = 0.207292 + 0.225440I
b = 0.209690 − 0.379206I
−9.07326 + 3.27525I −11.96737 − 3.20156I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.464529
a = 2.40413
b = 1.14153
−0.233389 4.21310
u = −0.162389 + 0.372510I
a = 1.81490 + 1.30389I
b = −1.027750 + 0.895148I
−4.36963 + 2.21765I −9.43891 − 3.55386I
u = −0.162389 − 0.372510I
a = 1.81490 − 1.30389I
b = −1.027750 − 0.895148I
−4.36963 − 2.21765I −9.43891 + 3.55386I
u = 0.120647 + 0.309845I
a = −2.64004 + 2.81826I
b = 0.376943 + 0.344347I
−5.97746 − 1.81572I −6.79885 + 3.34834I
u = 0.120647 − 0.309845I
a = −2.64004 − 2.81826I
b = 0.376943 − 0.344347I
−5.97746 + 1.81572I −6.79885 − 3.34834I
u = −0.08118 + 1.72162I
a = −0.376707 − 0.332059I
b = 1.30625 + 0.74373I
−12.44300 + 1.68015I −8.40294 + 0.I
u = −0.08118 − 1.72162I
a = −0.376707 + 0.332059I
b = 1.30625 − 0.74373I
−12.44300 − 1.68015I −8.40294 + 0.I
u = 0.36851 + 2.08278I
a = −0.000762 − 0.835761I
b = 1.54959 + 0.95102I
−17.4518 + 2.8402I 0
u = 0.36851 − 2.08278I
a = −0.000762 + 0.835761I
b = 1.54959 − 0.95102I
−17.4518 − 2.8402I 0
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
29
− 32u
28
+ ··· − 30u + 1)
· (u
52
+ 83u
51
+ ··· − 10239762u + 3418801)
c
2
(u
29
+ 16u
27
+ ··· + 2u + 1)(u
52
− u
51
+ ··· + 430u − 1849)
c
3
(u
29
− u
27
+ ··· + 4u + 1)(u
52
− u
51
+ ··· − 96u + 9)
c
4
(u
29
+ u
28
+ ··· − u − 13)(u
52
− 2u
51
+ ··· − 1077u − 89)
c
5
(u
29
+ u
28
+ ··· − u − 1)(u
52
+ 47u
50
+ ··· − 950335u − 289973)
c
6
(u
29
+ u
28
+ ··· − 3u − 1)(u
52
+ 2u
51
+ ··· + 91u − 181)
c
7
(u
29
+ 16u
27
+ ··· + 2u − 1)(u
52
− u
51
+ ··· + 430u − 1849)
c
8
(u
29
− 6u
27
+ ··· + 5u + 1)(u
52
+ 5u
51
+ ··· − 3.82267 × 10
7
u + 7428119)
c
9
(u
29
− 4u
28
+ ··· + 24u − 4)(u
52
− 5u
51
+ ··· + 324u + 356)
c
10
(u
29
− u
28
+ ··· − 3u + 1)(u
52
+ 2u
51
+ ··· + 91u − 181)
c
11
(u
29
− u
28
+ ··· − u + 13)(u
52
− 2u
51
+ ··· − 1077u − 89)
c
12
(u
29
− u
28
+ ··· + 355u + 187)(u
52
− 2u
51
+ ··· − 81165u + 4259)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
29
− 52y
28
+ ··· + 34y −1)
· (y
52
− 209y
51
+ ··· + 1284466243376242y + 11688200277601)
c
2
, c
7
(y
29
+ 32y
28
+ ··· − 30y −1)
· (y
52
+ 83y
51
+ ··· − 10239762y + 3418801)
c
3
(y
29
− 2y
28
+ ··· + 26y −1)(y
52
− 11y
51
+ ··· − 4590y + 81)
c
4
, c
11
(y
29
+ 23y
28
+ ··· − 2209y −169)
· (y
52
+ 50y
51
+ ··· − 321727y + 7921)
c
5
(y
29
+ 15y
28
+ ··· + 11y −1)
· (y
52
+ 94y
51
+ ··· − 346734679987y + 84084340729)
c
6
, c
10
(y
29
− 17y
28
+ ··· + 17y −1)(y
52
− 54y
51
+ ··· + 1011111y + 32761)
c
8
(y
29
− 12y
28
+ ··· − 103y −1)
· (y
52
− 73y
51
+ ··· − 308498524989461y + 55176951878161)
c
9
(y
29
− 8y
28
+ ··· − 288y −16)
· (y
52
− 25y
51
+ ··· + 789296y + 126736)
c
12
(y
29
+ 39y
28
+ ··· + 65437y −34969)
· (y
52
+ 98y
51
+ ··· − 7982256041y + 18139081)
20
