12n
0247
(K12n
0247
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 11 10 12 4 5 6 8 7
Solving Sequence
5,11 3,6
2 1 4 10 7 9 8 12
c
5
c
2
c
1
c
4
c
10
c
6
c
9
c
8
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−3u
17
+ 3u
16
+ ··· + 32b + 11, 29u
17
+ 7u
16
+ ··· + 64a + 79, u
18
+ 13u
16
+ ··· + u − 1i
I
u
2
= h−345563974u
19
− 637671531u
18
+ ··· + 3761745161b + 3368246020,
21843240461u
19
+ 28442594981u
18
+ ··· + 63949667737a − 48916675361,
u
20
+ 2u
19
+ ··· − 4u + 17i
I
u
3
= hb + 1, u
2
+ 2a + u + 3, u
3
+ 2u − 1i
I
u
4
= ha
2
u − 2a
2
− 4au + 5b + 3a − 5, a
3
+ 3a
2
u − 2a
2
− au − a − u − 2, u
2
+ 1i
I
u
5
= hb + 1, u
3
+ u
2
+ a + u + 2, u
4
+ u
3
+ 2u
2
+ 2u + 1i
* 5 irreducible components of dim
C
= 0, with total 51 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−3u
17
+ 3u
16
+ · · · + 32b + 11, 29u
17
+ 7u
16
+ · · · + 64a + 79, u
18
+
13u
16
+ · · · + u − 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
3
=
−0.453125u
17
− 0.109375u
16
+ ··· − 5.84375u − 1.23438
0.0937500u
17
− 0.0937500u
16
+ ··· − 0.812500u − 0.343750
a
6
=
1
u
2
a
2
=
−0.359375u
17
− 0.203125u
16
+ ··· − 6.65625u − 1.57813
0.0937500u
17
− 0.0937500u
16
+ ··· − 0.812500u − 0.343750
a
1
=
−u
3
− 2u
−
1
8
u
16
−
3
2
u
14
+ ··· +
7
8
u +
1
8
a
4
=
−0.640625u
17
− 0.296875u
16
+ ··· − 5.59375u − 1.17188
−0.406250u
17
− 0.0937500u
16
+ ··· − 0.562500u − 0.843750
a
10
=
u
u
3
+ u
a
7
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
u
3
+ 2u
u
3
+ u
a
8
=
−1
1
8
u
17
+
3
2
u
15
+ ··· −
23
8
u
2
−
1
8
u
a
12
=
−u
−
1
8
u
16
−
3
2
u
14
+ ··· +
7
8
u +
1
8
(ii) Obstruction class = −1
(iii) Cusp Shapes =
229
128
u
17
−
33
128
u
16
+ ··· +
427
64
u −
505
128
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
+ 4u
17
+ ··· + 257u + 16
c
2
, c
4
u
18
− 4u
17
+ ··· + 13u − 4
c
3
, c
8
u
18
+ 3u
17
+ ··· + 232u + 32
c
5
, c
6
, c
7
c
10
, c
11
, c
12
u
18
+ 13u
16
+ ··· + u − 1
c
9
u
18
− 6u
17
+ ··· − 256u − 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
+ 24y
17
+ ··· − 22945y + 256
c
2
, c
4
y
18
− 4y
17
+ ··· − 257y + 16
c
3
, c
8
y
18
− 21y
17
+ ··· − 10560y + 1024
c
5
, c
6
, c
7
c
10
, c
11
, c
12
y
18
+ 26y
17
+ ··· − 11y + 1
c
9
y
18
+ 26y
17
+ ··· − 98304y + 65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.513277 + 0.615531I
a = 0.69273 − 1.30024I
b = 0.926284 + 0.896765I
5.03715 − 4.73308I −6.17449 + 6.98654I
u = 0.513277 − 0.615531I
a = 0.69273 + 1.30024I
b = 0.926284 − 0.896765I
5.03715 + 4.73308I −6.17449 − 6.98654I
u = 0.322723 + 0.641738I
a = −0.511493 + 0.469718I
b = 0.907757 − 0.852129I
5.02936 + 1.72315I −6.30423 + 2.05854I
u = 0.322723 − 0.641738I
a = −0.511493 − 0.469718I
b = 0.907757 + 0.852129I
5.02936 − 1.72315I −6.30423 − 2.05854I
u = 0.20594 + 1.41832I
a = 0.550117 − 0.463999I
b = 0.820288 + 0.298128I
8.20719 − 5.81488I 1.58758 + 8.21476I
u = 0.20594 − 1.41832I
a = 0.550117 + 0.463999I
b = 0.820288 − 0.298128I
8.20719 + 5.81488I 1.58758 − 8.21476I
u = −0.559591
a = 1.08527
b = 0.320915
−1.10260 −8.67790
u = −0.274931 + 0.275799I
a = 0.85438 − 1.34319I
b = −0.518997 + 0.250386I
−0.591534 + 0.915522I −8.76058 − 7.51611I
u = −0.274931 − 0.275799I
a = 0.85438 + 1.34319I
b = −0.518997 − 0.250386I
−0.591534 − 0.915522I −8.76058 + 7.51611I
u = −0.04969 + 1.63263I
a = −0.017613 − 0.874719I
b = −1.39382 + 0.44407I
9.47411 + 1.71565I −2.49915 − 0.68525I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.04969 − 1.63263I
a = −0.017613 + 0.874719I
b = −1.39382 − 0.44407I
9.47411 − 1.71565I −2.49915 + 0.68525I
u = −0.39884 + 1.63329I
a = 0.30757 + 1.53003I
b = 1.25592 − 0.96097I
−19.6148 + 12.8943I −2.00648 − 5.58395I
u = −0.39884 − 1.63329I
a = 0.30757 − 1.53003I
b = 1.25592 + 0.96097I
−19.6148 − 12.8943I −2.00648 + 5.58395I
u = 0.16134 + 1.67469I
a = 0.135382 + 1.232190I
b = −0.453358 − 1.088430I
12.98160 − 4.39049I −1.06537 + 2.81298I
u = 0.16134 − 1.67469I
a = 0.135382 − 1.232190I
b = −0.453358 + 1.088430I
12.98160 + 4.39049I −1.06537 − 2.81298I
u = 0.264194
a = −3.30167
b = −1.07735
−2.03333 1.10900
u = −0.33212 + 1.72012I
a = −0.652868 − 0.820297I
b = 0.83415 + 1.30011I
−18.1326 + 4.7805I −0.86783 − 1.39495I
u = −0.33212 − 1.72012I
a = −0.652868 + 0.820297I
b = 0.83415 − 1.30011I
−18.1326 − 4.7805I −0.86783 + 1.39495I
6
II. I
u
2
=
h−3.46×10
8
u
19
−6.38×10
8
u
18
+· · ·+3.76×10
9
b+3.37×10
9
, 2.18×10
10
u
19
+
2.84 × 10
10
u
18
+ · · · + 6.39 × 10
10
a − 4.89 × 10
10
, u
20
+ 2u
19
+ · · · − 4u + 17i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
3
=
−0.341569u
19
− 0.444765u
18
+ ··· − 6.80195u + 0.764925
0.0918627u
19
+ 0.169515u
18
+ ··· + 1.48236u − 0.895395
a
6
=
1
u
2
a
2
=
−0.249707u
19
− 0.275251u
18
+ ··· − 5.31959u − 0.130470
0.0918627u
19
+ 0.169515u
18
+ ··· + 1.48236u − 0.895395
a
1
=
0.0321030u
19
+ 0.154890u
18
+ ··· − 1.20856u + 1.30329
0.0116403u
19
+ 0.0303223u
18
+ ··· − 0.600017u + 0.446055
a
4
=
−0.274136u
19
− 0.394973u
18
+ ··· − 4.73485u − 0.948502
0.105172u
19
+ 0.211195u
18
+ ··· + 1.77125u − 1.07336
a
10
=
u
u
3
+ u
a
7
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
u
3
+ 2u
u
3
+ u
a
8
=
0.0540994u
19
+ 0.0710831u
18
+ ··· + 0.210536u + 1.58028
−0.0628232u
19
− 0.0347199u
18
+ ··· − 1.06815u + 1.63097
a
12
=
−0.0217078u
19
+ 0.0194076u
18
+ ··· − 3.38491u + 1.15498
−0.0538109u
19
− 0.135483u
18
+ ··· − 0.176349u − 0.148305
(ii) Obstruction class = −1
(iii) Cusp Shapes =
687646779
3761745161
u
19
+
3390901343
3761745161
u
18
+ ··· +
12009014830
3761745161
u −
7942008906
3761745161
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
10
+ u
9
+ 10u
8
+ 11u
7
+ 26u
6
+ 30u
5
+ u
4
− 14u
3
+ 3u
2
− 2u + 1)
2
c
2
, c
4
(u
10
− 3u
9
+ 4u
8
+ u
7
− 6u
6
+ 6u
5
+ u
4
− 2u
3
+ 3u
2
− 2u + 1)
2
c
3
, c
8
(u
10
− u
9
− 7u
8
+ 8u
7
+ 13u
6
− 14u
5
− 2u
4
− 2u
3
+ 13u
2
− 12u + 4)
2
c
5
, c
6
, c
7
c
10
, c
11
, c
12
u
20
+ 2u
19
+ ··· − 4u + 17
c
9
(u
10
+ 2u
9
+ ··· − 21u + 17)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
10
+ 19y
9
+ ··· + 2y + 1)
2
c
2
, c
4
(y
10
− y
9
+ 10y
8
− 11y
7
+ 26y
6
− 30y
5
+ y
4
+ 14y
3
+ 3y
2
+ 2y + 1)
2
c
3
, c
8
(y
10
− 15y
9
+ ··· − 40y + 16)
2
c
5
, c
6
, c
7
c
10
, c
11
, c
12
y
20
+ 18y
19
+ ··· + 1480y + 289
c
9
(y
10
+ 26y
9
+ ··· + 2925y + 289)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.598226 + 0.786865I
a = 0.005030 + 0.155416I
b = −0.076965 − 0.657059I
4.43566 − 1.46073I −1.34069 + 3.28644I
u = 0.598226 − 0.786865I
a = 0.005030 − 0.155416I
b = −0.076965 + 0.657059I
4.43566 + 1.46073I −1.34069 − 3.28644I
u = −0.014778 + 1.179270I
a = 0.90480 + 1.65650I
b = −1.016000 − 0.211624I
1.39065 − 0.79591I −8.77960 − 0.81155I
u = −0.014778 − 1.179270I
a = 0.90480 − 1.65650I
b = −1.016000 + 0.211624I
1.39065 + 0.79591I −8.77960 + 0.81155I
u = −1.077400 + 0.591320I
a = 0.927031 + 0.754940I
b = 1.12142 − 1.03617I
12.6890 + 7.4068I −3.25674 − 4.41038I
u = −1.077400 − 0.591320I
a = 0.927031 − 0.754940I
b = 1.12142 + 1.03617I
12.6890 − 7.4068I −3.25674 + 4.41038I
u = −1.033740 + 0.754404I
a = −0.0441939 − 0.0300635I
b = 0.98889 + 1.13481I
13.15130 − 0.50253I −2.50299 − 0.08773I
u = −1.033740 − 0.754404I
a = −0.0441939 + 0.0300635I
b = 0.98889 − 1.13481I
13.15130 + 0.50253I −2.50299 + 0.08773I
u = −0.220229 + 1.263180I
a = 0.634760 + 0.673705I
b = 0.482659 − 0.410726I
2.87696 + 2.81207I −3.11998 − 4.64391I
u = −0.220229 − 1.263180I
a = 0.634760 − 0.673705I
b = 0.482659 + 0.410726I
2.87696 − 2.81207I −3.11998 + 4.64391I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.661189 + 0.252982I
a = 1.093740 + 0.337893I
b = 0.482659 + 0.410726I
2.87696 − 2.81207I −3.11998 + 4.64391I
u = 0.661189 − 0.252982I
a = 1.093740 − 0.337893I
b = 0.482659 − 0.410726I
2.87696 + 2.81207I −3.11998 − 4.64391I
u = −0.208282 + 0.650238I
a = −3.22497 − 1.66304I
b = −1.016000 + 0.211624I
1.39065 + 0.79591I −8.77960 + 0.81155I
u = −0.208282 − 0.650238I
a = −3.22497 + 1.66304I
b = −1.016000 − 0.211624I
1.39065 − 0.79591I −8.77960 − 0.81155I
u = 0.065595 + 1.361450I
a = 0.719320 − 1.166450I
b = −0.076965 + 0.657059I
4.43566 + 1.46073I −1.34069 − 3.28644I
u = 0.065595 − 1.361450I
a = 0.719320 + 1.166450I
b = −0.076965 − 0.657059I
4.43566 − 1.46073I −1.34069 + 3.28644I
u = 0.17643 + 1.61460I
a = −0.17553 − 1.65533I
b = 1.12142 + 1.03617I
12.6890 − 7.4068I −3.25674 + 4.41038I
u = 0.17643 − 1.61460I
a = −0.17553 + 1.65533I
b = 1.12142 − 1.03617I
12.6890 + 7.4068I −3.25674 − 4.41038I
u = 0.05299 + 1.63807I
a = −0.63412 + 1.33106I
b = 0.98889 − 1.13481I
13.15130 + 0.50253I −2.50299 + 0.08773I
u = 0.05299 − 1.63807I
a = −0.63412 − 1.33106I
b = 0.98889 + 1.13481I
13.15130 − 0.50253I −2.50299 − 0.08773I
11
III. I
u
3
= hb + 1, u
2
+ 2a + u + 3, u
3
+ 2u − 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
3
=
−
1
2
u
2
−
1
2
u −
3
2
−1
a
6
=
1
u
2
a
2
=
−
1
2
u
2
−
1
2
u −
5
2
−1
a
1
=
−1
0
a
4
=
−
1
2
u
2
−
1
2
u −
3
2
−1
a
10
=
u
−u + 1
a
7
=
u
2
+ 1
u
a
9
=
1
−u + 1
a
8
=
1
−u + 1
a
12
=
−u
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
25
4
u
2
−
11
4
u −
71
4
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
8
u
3
c
4
(u + 1)
3
c
5
, c
6
, c
7
u
3
+ 2u − 1
c
9
u
3
+ 3u
2
+ 5u + 2
c
10
, c
11
, c
12
u
3
+ 2u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
3
c
3
, c
8
y
3
c
5
, c
6
, c
7
c
10
, c
11
, c
12
y
3
+ 4y
2
+ 4y −1
c
9
y
3
+ y
2
+ 13y −4
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.22670 + 1.46771I
a = −0.335258 − 0.401127I
b = −1.00000
7.79580 + 5.13794I −3.98417 + 0.12290I
u = −0.22670 − 1.46771I
a = −0.335258 + 0.401127I
b = −1.00000
7.79580 − 5.13794I −3.98417 − 0.12290I
u = 0.453398
a = −1.82948
b = −1.00000
−2.43213 −20.2820
15
IV.
I
u
4
= ha
2
u − 2a
2
− 4au + 5b + 3a − 5, a
3
+ 3a
2
u − 2a
2
− au − a − u − 2, u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
3
=
a
−
1
5
a
2
u +
4
5
au + ··· −
3
5
a + 1
a
6
=
1
−1
a
2
=
−
1
5
a
2
u +
4
5
au + ··· +
2
5
a + 1
−
1
5
a
2
u +
4
5
au + ··· −
3
5
a + 1
a
1
=
−u
−
2
5
a
2
u −
2
5
au + ··· +
4
5
a + 2
a
4
=
3
5
a
2
u −
1
5
a
2
−
7
5
au −
1
5
a
−
1
5
a
2
u −
3
5
a
2
−
6
5
au +
7
5
a
a
10
=
u
0
a
7
=
0
−1
a
9
=
u
0
a
8
=
−1
1
5
a
2
u −
4
5
au + ··· −
2
5
a
2
−
2
5
a
a
12
=
−u
−
2
5
a
2
u −
2
5
au + ··· +
4
5
a + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
4
5
a
2
u +
8
5
a
2
+
16
5
au −
12
5
a
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
3
, c
8
u
6
− 3u
4
+ 2u
2
+ 1
c
4
(u
3
− u
2
+ 1)
2
c
5
, c
6
, c
7
c
10
, c
11
, c
12
(u
2
+ 1)
3
c
9
u
6
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
(y
3
− y
2
+ 2y −1)
2
c
3
, c
8
(y
3
− 3y
2
+ 2y + 1)
2
c
5
, c
6
, c
7
c
10
, c
11
, c
12
(y + 1)
6
c
9
y
6
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.684841 − 1.082500I
b = 0.877439 + 0.744862I
6.31400 − 2.82812I −0.49024 + 2.97945I
u = 1.000000I
a = −0.439718 + 0.407221I
b = 0.877439 − 0.744862I
6.31400 + 2.82812I −0.49024 − 2.97945I
u = 1.000000I
a = 1.75488 − 2.32472I
b = −0.754878
2.17641 −7.01951 + 0.I
u = − 1.000000I
a = 0.684841 + 1.082500I
b = 0.877439 − 0.744862I
6.31400 + 2.82812I −0.49024 − 2.97945I
u = − 1.000000I
a = −0.439718 − 0.407221I
b = 0.877439 + 0.744862I
6.31400 − 2.82812I −0.49024 + 2.97945I
u = − 1.000000I
a = 1.75488 + 2.32472I
b = −0.754878
2.17641 −7.01951 + 0.I
19
V. I
u
5
= hb + 1, u
3
+ u
2
+ a + u + 2, u
4
+ u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
3
=
−u
3
− u
2
− u − 2
−1
a
6
=
1
u
2
a
2
=
−u
3
− u
2
− u − 3
−1
a
1
=
−1
0
a
4
=
−u
3
− u
2
− u − 2
−1
a
10
=
u
u
3
+ u
a
7
=
u
2
+ 1
−u
3
− 2u − 1
a
9
=
u
3
+ 2u
u
3
+ u
a
8
=
u
3
+ 2u
u
3
+ u
a
12
=
−2u
3
− u
2
− 3u − 3
−u
3
− u
2
− u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
3
− 4u − 9
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
8
u
4
c
4
(u + 1)
4
c
5
, c
6
, c
7
u
4
+ u
3
+ 2u
2
+ 2u + 1
c
9
(u
2
− u + 1)
2
c
10
, c
11
, c
12
u
4
− u
3
+ 2u
2
− 2u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
8
y
4
c
5
, c
6
, c
7
c
10
, c
11
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
c
9
(y
2
+ y + 1)
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621744 + 0.440597I
a = −1.69244 − 0.31815I
b = −1.00000
1.64493 + 2.02988I −7.00000 − 3.46410I
u = −0.621744 − 0.440597I
a = −1.69244 + 0.31815I
b = −1.00000
1.64493 − 2.02988I −7.00000 + 3.46410I
u = 0.121744 + 1.306620I
a = 0.192440 + 0.547877I
b = −1.00000
1.64493 − 2.02988I −7.00000 + 3.46410I
u = 0.121744 − 1.306620I
a = 0.192440 − 0.547877I
b = −1.00000
1.64493 + 2.02988I −7.00000 − 3.46410I
23
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
7
(u
3
− u
2
+ 2u − 1)
2
· (u
10
+ u
9
+ 10u
8
+ 11u
7
+ 26u
6
+ 30u
5
+ u
4
− 14u
3
+ 3u
2
− 2u + 1)
2
· (u
18
+ 4u
17
+ ··· + 257u + 16)
c
2
(u − 1)
7
(u
3
+ u
2
− 1)
2
· (u
10
− 3u
9
+ 4u
8
+ u
7
− 6u
6
+ 6u
5
+ u
4
− 2u
3
+ 3u
2
− 2u + 1)
2
· (u
18
− 4u
17
+ ··· + 13u − 4)
c
3
, c
8
u
7
(u
6
− 3u
4
+ 2u
2
+ 1)
· (u
10
− u
9
− 7u
8
+ 8u
7
+ 13u
6
− 14u
5
− 2u
4
− 2u
3
+ 13u
2
− 12u + 4)
2
· (u
18
+ 3u
17
+ ··· + 232u + 32)
c
4
(u + 1)
7
(u
3
− u
2
+ 1)
2
· (u
10
− 3u
9
+ 4u
8
+ u
7
− 6u
6
+ 6u
5
+ u
4
− 2u
3
+ 3u
2
− 2u + 1)
2
· (u
18
− 4u
17
+ ··· + 13u − 4)
c
5
, c
6
, c
7
((u
2
+ 1)
3
)(u
3
+ 2u − 1)(u
4
+ u
3
+ ··· + 2u + 1)(u
18
+ 13u
16
+ ··· + u − 1)
· (u
20
+ 2u
19
+ ··· − 4u + 17)
c
9
u
6
(u
2
− u + 1)
2
(u
3
+ 3u
2
+ 5u + 2)(u
10
+ 2u
9
+ ··· − 21u + 17)
2
· (u
18
− 6u
17
+ ··· − 256u − 256)
c
10
, c
11
, c
12
((u
2
+ 1)
3
)(u
3
+ 2u + 1)(u
4
− u
3
+ ··· − 2u + 1)(u
18
+ 13u
16
+ ··· + u − 1)
· (u
20
+ 2u
19
+ ··· − 4u + 17)
24
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
7
)(y
3
+ 3y
2
+ 2y −1)
2
(y
10
+ 19y
9
+ ··· + 2y + 1)
2
· (y
18
+ 24y
17
+ ··· − 22945y + 256)
c
2
, c
4
(y −1)
7
(y
3
− y
2
+ 2y −1)
2
· (y
10
− y
9
+ 10y
8
− 11y
7
+ 26y
6
− 30y
5
+ y
4
+ 14y
3
+ 3y
2
+ 2y + 1)
2
· (y
18
− 4y
17
+ ··· − 257y + 16)
c
3
, c
8
y
7
(y
3
− 3y
2
+ 2y + 1)
2
(y
10
− 15y
9
+ ··· − 40y + 16)
2
· (y
18
− 21y
17
+ ··· − 10560y + 1024)
c
5
, c
6
, c
7
c
10
, c
11
, c
12
(y + 1)
6
(y
3
+ 4y
2
+ 4y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
18
+ 26y
17
+ ··· − 11y + 1)(y
20
+ 18y
19
+ ··· + 1480y + 289)
c
9
y
6
(y
2
+ y + 1)
2
(y
3
+ y
2
+ 13y −4)(y
10
+ 26y
9
+ ··· + 2925y + 289)
2
· (y
18
+ 26y
17
+ ··· − 98304y + 65536)
25
