12n
0744
(K12n
0744
)
A knot diagram
1
Linearized knot diagam
4 12 9 10 1 2 12 11 1 2 8 6
Solving Sequence
1,4 2,10
5 6 7 11 9 3 8 12
c
1
c
4
c
5
c
6
c
10
c
9
c
3
c
8
c
12
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−170628010722u
28
− 1866088423702u
27
+ ··· + 214215715127b + 903136739857,
− 903136739857u
28
− 9593248116983u
27
+ ··· + 428431430254a + 3314728870309,
u
29
+ 11u
28
+ ··· − 9u − 2i
I
u
2
= h−u
10
+ 5u
9
− 13u
8
+ 20u
7
− 20u
6
+ 11u
5
− u
4
− 4u
3
− au + u
2
+ b + u − 1, −u
10
a − u
10
+ ··· − a + 3,
u
11
− 5u
10
+ 12u
9
− 15u
8
+ 8u
7
+ 4u
6
− 8u
5
+ 3u
4
+ 3u
3
− 3u
2
+ 1i
I
u
3
= hu
15
− 6u
14
+ ··· + b + 1, −u
16
+ 8u
15
+ ··· + a + 1, u
17
− 8u
16
+ ··· − 5u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 68 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−1.71 × 10
11
u
28
− 1.87 × 10
12
u
27
+ · · · + 2.14 × 10
11
b + 9.03 ×
10
11
, −9.03 × 10
11
u
28
− 9.59 × 10
12
u
27
+ · · · + 4.28 × 10
11
a + 3.31 ×
10
12
, u
29
+ 11u
28
+ · · · − 9u − 2i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
10
=
2.10801u
28
+ 22.3916u
27
+ ··· − 23.6508u − 7.73689
0.796524u
28
+ 8.71126u
27
+ ··· − 11.2352u − 4.21602
a
5
=
0.303942u
28
+ 3.37670u
27
+ ··· − 1.68222u + 0.481415
−0.0333470u
28
− 0.309258u
27
+ ··· − 2.21689u − 0.607883
a
6
=
0.337289u
28
+ 3.68596u
27
+ ··· + 0.534668u + 1.08930
−0.0333470u
28
− 0.309258u
27
+ ··· − 2.21689u − 0.607883
a
7
=
−0.270964u
28
− 2.09093u
27
+ ··· + 3.20823u + 1.64876
−1.00627u
28
− 10.9830u
27
+ ··· + 4.79161u + 1.21989
a
11
=
1.36199u
28
+ 14.4817u
27
+ ··· − 15.3684u − 5.11393
1.06901u
28
+ 10.7545u
27
+ ··· − 10.0600u − 3.62329
a
9
=
1.31148u
28
+ 13.6803u
27
+ ··· − 12.4157u − 3.52088
0.796524u
28
+ 8.71126u
27
+ ··· − 11.2352u − 4.21602
a
3
=
0.313077u
28
+ 2.77803u
27
+ ··· + 5.65956u + 1.76387
0.0242119u
28
+ 0.907930u
27
+ ··· − 3.12489u − 0.674577
a
8
=
0.365788u
28
+ 3.53413u
27
+ ··· + 2.53468u + 1.66264
0.286543u
28
+ 3.52311u
27
+ ··· − 7.55846u − 2.08245
a
12
=
−0.473567u
28
− 5.70993u
27
+ ··· + 3.97518u + 2.84095
0.727878u
28
+ 7.72192u
27
+ ··· − 2.77982u − 0.441928
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
591062458684
214215715127
u
28
+
6286984528582
214215715127
u
27
+ ··· −
7402417712510
214215715127
u −
3687661591178
214215715127
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
29
− 11u
28
+ ··· − 9u + 2
c
2
, c
6
u
29
− u
28
+ ··· − 2u + 1
c
3
, c
10
u
29
+ u
28
+ ··· − 21u + 61
c
4
, c
9
u
29
+ 17u
27
+ ··· + u + 1
c
5
, c
12
u
29
+ 23u
28
+ ··· + 30720u + 2048
c
7
, c
8
, c
11
u
29
− 8u
28
+ ··· − 5u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
29
+ 7y
28
+ ··· + 9y −4
c
2
, c
6
y
29
− 31y
28
+ ··· − 8y −1
c
3
, c
10
y
29
− 33y
28
+ ··· − 3829y −3721
c
4
, c
9
y
29
+ 34y
28
+ ··· + 21y −1
c
5
, c
12
y
29
+ 11y
28
+ ··· + 10485760y −4194304
c
7
, c
8
, c
11
y
29
+ 24y
28
+ ··· + 249y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.098165 + 1.116340I
a = 0.500410 + 0.496116I
b = 0.602958 − 0.509928I
8.55456 − 1.35151I −1.44678 + 5.66145I
u = −0.098165 − 1.116340I
a = 0.500410 − 0.496116I
b = 0.602958 + 0.509928I
8.55456 + 1.35151I −1.44678 − 5.66145I
u = 0.548183 + 0.560700I
a = 0.520202 − 0.557055I
b = −0.597507 + 0.013691I
1.15086 − 2.34551I −4.15925 + 5.49477I
u = 0.548183 − 0.560700I
a = 0.520202 + 0.557055I
b = −0.597507 − 0.013691I
1.15086 + 2.34551I −4.15925 − 5.49477I
u = 0.260946 + 1.189770I
a = 0.036619 − 0.297728I
b = −0.363784 + 0.034123I
2.53104 − 2.04396I 1.60323 + 2.96059I
u = 0.260946 − 1.189770I
a = 0.036619 + 0.297728I
b = −0.363784 − 0.034123I
2.53104 + 2.04396I 1.60323 − 2.96059I
u = −0.615626 + 0.456161I
a = −0.08330 + 1.86759I
b = 0.80064 + 1.18774I
6.05487 + 4.19684I −2.11903 + 4.96577I
u = −0.615626 − 0.456161I
a = −0.08330 − 1.86759I
b = 0.80064 − 1.18774I
6.05487 − 4.19684I −2.11903 − 4.96577I
u = 0.694406 + 0.054995I
a = −0.636984 − 0.496719I
b = 0.415008 + 0.379955I
−0.269382 + 0.537269I −7.35658 − 1.73614I
u = 0.694406 − 0.054995I
a = −0.636984 + 0.496719I
b = 0.415008 − 0.379955I
−0.269382 − 0.537269I −7.35658 + 1.73614I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.103300 + 0.861575I
a = 0.376035 − 1.243150I
b = −0.65619 − 1.69554I
−7.90254 + 3.02678I −9.76473 − 1.78042I
u = −1.103300 − 0.861575I
a = 0.376035 + 1.243150I
b = −0.65619 + 1.69554I
−7.90254 − 3.02678I −9.76473 + 1.78042I
u = 0.32044 + 1.44374I
a = −0.257368 + 0.140851I
b = 0.285822 + 0.326437I
4.37255 − 4.79804I −8.00000 + 0.I
u = 0.32044 − 1.44374I
a = −0.257368 − 0.140851I
b = 0.285822 − 0.326437I
4.37255 + 4.79804I −8.00000 + 0.I
u = 0.510259
a = −0.688382
b = 0.351253
−0.807989 −12.5760
u = −0.91528 + 1.17700I
a = −0.862893 + 0.570733I
b = −0.11804 + 1.53800I
−6.84831 + 4.41259I −8.00000 + 0.I
u = −0.91528 − 1.17700I
a = −0.862893 − 0.570733I
b = −0.11804 − 1.53800I
−6.84831 − 4.41259I −8.00000 + 0.I
u = −1.10567 + 1.01770I
a = −0.451102 + 1.142920I
b = 0.66438 + 1.72279I
−12.0141 + 9.0716I −8.00000 + 0.I
u = −1.10567 − 1.01770I
a = −0.451102 − 1.142920I
b = 0.66438 − 1.72279I
−12.0141 − 9.0716I −8.00000 + 0.I
u = −0.472362 + 0.098700I
a = −0.18874 − 2.17189I
b = −0.303518 − 1.007290I
−0.75815 + 1.61312I −5.38396 − 3.22860I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.472362 − 0.098700I
a = −0.18874 + 2.17189I
b = −0.303518 + 1.007290I
−0.75815 − 1.61312I −5.38396 + 3.22860I
u = −1.04583 + 1.12396I
a = 0.524247 − 1.088190I
b = −0.67480 − 1.72730I
−7.6508 + 14.9381I 0
u = −1.04583 − 1.12396I
a = 0.524247 + 1.088190I
b = −0.67480 + 1.72730I
−7.6508 − 14.9381I 0
u = −1.17801 + 0.98698I
a = −0.711549 + 0.760443I
b = −0.08767 + 1.59810I
−8.15639 − 6.90751I 0
u = −1.17801 − 0.98698I
a = −0.711549 − 0.760443I
b = −0.08767 − 1.59810I
−8.15639 + 6.90751I 0
u = −1.06954 + 1.11198I
a = 0.772171 − 0.666300I
b = 0.08496 − 1.57128I
−11.73330 − 1.13215I 0
u = −1.06954 − 1.11198I
a = 0.772171 + 0.666300I
b = 0.08496 + 1.57128I
−11.73330 + 1.13215I 0
u = 0.024689 + 0.424590I
a = 2.55644 − 0.38810I
b = −0.227898 − 1.075860I
0.174514 − 0.084806I −5.47486 − 0.21908I
u = 0.024689 − 0.424590I
a = 2.55644 + 0.38810I
b = −0.227898 + 1.075860I
0.174514 + 0.084806I −5.47486 + 0.21908I
7
II.
I
u
2
= h−u
10
+5u
9
+· · ·+b−1, −u
10
a−u
10
+· · ·−a+3, u
11
−5u
10
+· · ·−3u
2
+1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
10
=
a
u
10
− 5u
9
+ 13u
8
− 20u
7
+ 20u
6
− 11u
5
+ u
4
+ 4u
3
+ au − u
2
− u + 1
a
5
=
−u
10
a + u
10
+ ··· − a − 1
−1
a
6
=
−u
10
a + u
10
+ ··· − a − 3u
−1
a
7
=
−2u
10
a + u
10
+ ··· − a + 1
−u
8
a + 3u
7
a − 4u
6
a + u
5
a + 2u
4
a − 2u
3
a − u
3
+ au + u
2
− 1
a
11
=
−u
10
+ 5u
9
+ ··· + a − 1
u
8
− 5u
7
+ 11u
6
+ u
4
a − 12u
5
− u
3
a + 5u
4
+ 2u
3
+ au − 2u
2
+ 1
a
9
=
−u
10
+ 5u
9
+ ··· + a − 1
u
10
− 5u
9
+ 13u
8
− 20u
7
+ 20u
6
− 11u
5
+ u
4
+ 4u
3
+ au − u
2
− u + 1
a
3
=
u
10
− 5u
9
+ ··· − a − 1
−u
10
a + 5u
9
a + ··· − u + 1
a
8
=
u
10
− 5u
9
+ ··· + a + 1
−u
8
a + 3u
7
a − 4u
6
a + u
5
a + 2u
4
a − 2u
3
a + u
4
− 3u
3
+ au + 3u
2
− 1
a
12
=
−u
10
a + u
10
+ ··· − a + 1
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
9
−20u
8
+ 52u
7
−72u
6
+ 48u
5
+ 12u
4
−40u
3
+ 20u
2
+ 12u −26
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
11
+ 5u
10
+ 12u
9
+ 15u
8
+ 8u
7
− 4u
6
− 8u
5
− 3u
4
+ 3u
3
+ 3u
2
− 1)
2
c
2
, c
6
u
22
+ u
21
+ ··· + 124u − 113
c
3
, c
10
u
22
− u
21
+ ··· − 1074u − 361
c
4
, c
9
u
22
− 3u
21
+ ··· − 94u + 31
c
5
, c
12
(u − 1)
22
c
7
, c
8
, c
11
(u
11
+ 3u
10
+ ··· + 2u + 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
11
− y
10
+ ··· + 6y −1)
2
c
2
, c
6
y
22
− 9y
21
+ ··· − 218776y + 12769
c
3
, c
10
y
22
− 29y
21
+ ··· − 1134704y + 130321
c
4
, c
9
y
22
+ 15y
21
+ ··· − 36736y + 961
c
5
, c
12
(y −1)
22
c
7
, c
8
, c
11
(y
11
+ 7y
10
+ ··· − 6y −1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.326966 + 0.916688I
a = −0.529318 − 1.119230I
b = −0.242110 − 1.316380I
1.34086 − 5.00074I −4.15941 + 6.22751I
u = 0.326966 + 0.916688I
a = 1.357520 + 0.220088I
b = −0.852918 + 0.851171I
1.34086 − 5.00074I −4.15941 + 6.22751I
u = 0.326966 − 0.916688I
a = −0.529318 + 1.119230I
b = −0.242110 + 1.316380I
1.34086 + 5.00074I −4.15941 − 6.22751I
u = 0.326966 − 0.916688I
a = 1.357520 − 0.220088I
b = −0.852918 − 0.851171I
1.34086 + 5.00074I −4.15941 − 6.22751I
u = 0.864248 + 0.407709I
a = 0.217689 + 1.032910I
b = 0.03362 + 1.89151I
−3.71387 − 2.24779I −15.6358 + 5.0636I
u = 0.864248 + 0.407709I
a = −0.87635 − 1.77520I
b = 0.232990 − 0.981446I
−3.71387 − 2.24779I −15.6358 + 5.0636I
u = 0.864248 − 0.407709I
a = 0.217689 − 1.032910I
b = 0.03362 − 1.89151I
−3.71387 + 2.24779I −15.6358 − 5.0636I
u = 0.864248 − 0.407709I
a = −0.87635 + 1.77520I
b = 0.232990 + 0.981446I
−3.71387 + 2.24779I −15.6358 − 5.0636I
u = −0.577598 + 0.283449I
a = −0.202380 − 0.311959I
b = −2.12332 − 0.11036I
−1.52964 + 5.92443I −15.1705 − 10.0235I
u = −0.577598 + 0.283449I
a = −2.88708 − 1.60787I
b = −0.205319 − 0.122822I
−1.52964 + 5.92443I −15.1705 − 10.0235I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.577598 − 0.283449I
a = −0.202380 + 0.311959I
b = −2.12332 + 0.11036I
−1.52964 − 5.92443I −15.1705 + 10.0235I
u = −0.577598 − 0.283449I
a = −2.88708 + 1.60787I
b = −0.205319 + 0.122822I
−1.52964 − 5.92443I −15.1705 + 10.0235I
u = 1.110200 + 0.862988I
a = 0.385481 + 0.834174I
b = −0.28166 + 1.74173I
−4.09276 − 2.70441I −15.4676 − 0.0833I
u = 1.110200 + 0.862988I
a = −0.602034 − 1.100870I
b = 0.291922 − 1.258760I
−4.09276 − 2.70441I −15.4676 − 0.0833I
u = 1.110200 − 0.862988I
a = 0.385481 − 0.834174I
b = −0.28166 − 1.74173I
−4.09276 + 2.70441I −15.4676 + 0.0833I
u = 1.110200 − 0.862988I
a = −0.602034 + 1.100870I
b = 0.291922 + 1.258760I
−4.09276 + 2.70441I −15.4676 + 0.0833I
u = −0.566454
a = 0.335833
b = 2.27902
−5.66863 −24.2610
u = −0.566454
a = 4.02330
b = 0.190234
−5.66863 −24.2610
u = 1.05941 + 1.17096I
a = 0.500509 + 0.981987I
b = −0.207452 + 1.345270I
−3.15221 − 5.21629I −12.4360 + 9.0128I
u = 1.05941 + 1.17096I
a = −0.543605 − 0.668985I
b = 0.61962 − 1.62640I
−3.15221 − 5.21629I −12.4360 + 9.0128I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.05941 − 1.17096I
a = 0.500509 − 0.981987I
b = −0.207452 − 1.345270I
−3.15221 + 5.21629I −12.4360 − 9.0128I
u = 1.05941 − 1.17096I
a = −0.543605 + 0.668985I
b = 0.61962 + 1.62640I
−3.15221 + 5.21629I −12.4360 − 9.0128I
13
III.
I
u
3
= hu
15
−6u
14
+· · ·+b+1, −u
16
+8u
15
+· · ·+a+1 , u
17
−8u
16
+· · ·−5u
2
+1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
10
=
u
16
− 8u
15
+ ··· − 4u − 1
−u
15
+ 6u
14
+ ··· − u − 1
a
5
=
−2u
16
+ 15u
15
+ ··· + 3u − 1
−u
16
+ 8u
15
+ ··· − 7u
2
+ 2
a
6
=
−u
16
+ 7u
15
+ ··· + 3u − 3
−u
16
+ 8u
15
+ ··· − 7u
2
+ 2
a
7
=
−u
16
+ 7u
15
+ ··· + 4u − 4
−u
16
+ 8u
15
+ ··· − 8u
2
+ 2
a
11
=
−u
15
+ 7u
14
+ ··· + 13u
2
− 4u
−u
14
+ 6u
13
+ ··· + 10u
3
− 3u
2
a
9
=
u
16
− 7u
15
+ ··· + 14u
2
− 3u
−u
15
+ 6u
14
+ ··· − u − 1
a
3
=
−u
14
+ 7u
13
+ ··· + 7u − 4
−u
16
+ 7u
15
+ ··· − 2u + 1
a
8
=
2u
16
− 13u
15
+ ··· − u − 2
2u
16
− 16u
15
+ ··· − u − 2
a
12
=
−u
16
+ 8u
15
+ ··· − 2u + 6
u
16
− 7u
15
+ ··· + 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 10u
16
− 77u
15
+ 334u
14
− 998u
13
+ 2257u
12
− 3997u
11
+
5638u
10
−6311u
9
+ 5497u
8
−3528u
7
+ 1459u
6
−209u
5
−102u
4
−11u
3
+ 73u
2
−14u −22
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
− 8u
16
+ ··· − 5u
2
+ 1
c
2
, c
6
u
17
+ u
16
+ ··· + 3u + 1
c
3
, c
10
u
17
+ u
16
+ ··· + 4u − 1
c
4
, c
9
u
17
+ 4u
15
+ ··· − 2u − 1
c
5
u
17
+ 6u
15
+ ··· + 7u
2
+ 1
c
7
, c
8
u
17
− 5u
16
+ ··· + 28u − 5
c
11
u
17
+ 5u
16
+ ··· + 28u + 5
c
12
u
17
+ 6u
15
+ ··· − 7u
2
− 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
+ 8y
16
+ ··· + 10y −1
c
2
, c
6
y
17
− 5y
16
+ ··· + 9y −1
c
3
, c
10
y
17
− 15y
16
+ ··· + 8y −1
c
4
, c
9
y
17
+ 8y
16
+ ··· − 10y −1
c
5
, c
12
y
17
+ 12y
16
+ ··· − 14y −1
c
7
, c
8
, c
11
y
17
+ 17y
16
+ ··· − 106y −25
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.893251 + 0.264630I
a = 0.018964 − 1.091470I
b = 0.305775 − 0.969935I
−1.90214 − 2.23369I −11.12752 + 4.61502I
u = 0.893251 − 0.264630I
a = 0.018964 + 1.091470I
b = 0.305775 + 0.969935I
−1.90214 + 2.23369I −11.12752 − 4.61502I
u = 0.684501 + 0.597554I
a = 0.15020 + 1.59282I
b = −0.84898 + 1.18004I
5.93338 − 4.62482I −7.02513 + 11.80589I
u = 0.684501 − 0.597554I
a = 0.15020 − 1.59282I
b = −0.84898 − 1.18004I
5.93338 + 4.62482I −7.02513 − 11.80589I
u = 0.345763 + 1.168970I
a = −0.699467 + 0.234907I
b = −0.516447 − 0.736431I
7.99739 + 0.51870I −7.58791 + 1.24109I
u = 0.345763 − 1.168970I
a = −0.699467 − 0.234907I
b = −0.516447 + 0.736431I
7.99739 − 0.51870I −7.58791 − 1.24109I
u = 0.291791 + 1.326680I
a = 0.365592 + 0.062889I
b = 0.023243 + 0.503375I
1.96562 − 2.04249I −13.40328 + 2.16297I
u = 0.291791 − 1.326680I
a = 0.365592 − 0.062889I
b = 0.023243 − 0.503375I
1.96562 + 2.04249I −13.40328 − 2.16297I
u = 1.085990 + 0.881688I
a = −0.437409 − 0.954977I
b = 0.36697 − 1.42275I
−3.08880 − 3.07648I −5.91787 + 2.85067I
u = 1.085990 − 0.881688I
a = −0.437409 + 0.954977I
b = 0.36697 + 1.42275I
−3.08880 + 3.07648I −5.91787 − 2.85067I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.16949 + 1.42715I
a = −0.256405 − 0.318176I
b = 0.410628 − 0.419856I
4.55049 − 5.52863I −2.59452 + 8.92048I
u = 0.16949 − 1.42715I
a = −0.256405 + 0.318176I
b = 0.410628 + 0.419856I
4.55049 + 5.52863I −2.59452 − 8.92048I
u = 0.98406 + 1.15345I
a = 0.582475 + 0.763289I
b = −0.30723 + 1.42298I
−2.24300 − 4.51220I −5.31497 + 2.60777I
u = 0.98406 − 1.15345I
a = 0.582475 − 0.763289I
b = −0.30723 − 1.42298I
−2.24300 + 4.51220I −5.31497 − 2.60777I
u = −0.300698 + 0.295414I
a = −2.03045 − 1.73448I
b = 1.122940 − 0.078268I
−0.82315 + 5.54249I −4.57099 − 3.83728I
u = −0.300698 − 0.295414I
a = −2.03045 + 1.73448I
b = 1.122940 + 0.078268I
−0.82315 − 5.54249I −4.57099 + 3.83728I
u = −0.308277
a = 3.61299
b = −1.11380
−5.04041 −7.91560
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
11
+ 5u
10
+ 12u
9
+ 15u
8
+ 8u
7
− 4u
6
− 8u
5
− 3u
4
+ 3u
3
+ 3u
2
− 1)
2
· (u
17
− 8u
16
+ ··· − 5u
2
+ 1)(u
29
− 11u
28
+ ··· − 9u + 2)
c
2
, c
6
(u
17
+ u
16
+ ··· + 3u + 1)(u
22
+ u
21
+ ··· + 124u − 113)
· (u
29
− u
28
+ ··· − 2u + 1)
c
3
, c
10
(u
17
+ u
16
+ ··· + 4u − 1)(u
22
− u
21
+ ··· − 1074u − 361)
· (u
29
+ u
28
+ ··· − 21u + 61)
c
4
, c
9
(u
17
+ 4u
15
+ ··· − 2u − 1)(u
22
− 3u
21
+ ··· − 94u + 31)
· (u
29
+ 17u
27
+ ··· + u + 1)
c
5
((u − 1)
22
)(u
17
+ 6u
15
+ ··· + 7u
2
+ 1)
· (u
29
+ 23u
28
+ ··· + 30720u + 2048)
c
7
, c
8
((u
11
+ 3u
10
+ ··· + 2u + 1)
2
)(u
17
− 5u
16
+ ··· + 28u − 5)
· (u
29
− 8u
28
+ ··· − 5u + 4)
c
11
((u
11
+ 3u
10
+ ··· + 2u + 1)
2
)(u
17
+ 5u
16
+ ··· + 28u + 5)
· (u
29
− 8u
28
+ ··· − 5u + 4)
c
12
((u − 1)
22
)(u
17
+ 6u
15
+ ··· − 7u
2
− 1)
· (u
29
+ 23u
28
+ ··· + 30720u + 2048)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
11
− y
10
+ ··· + 6y −1)
2
)(y
17
+ 8y
16
+ ··· + 10y −1)
· (y
29
+ 7y
28
+ ··· + 9y −4)
c
2
, c
6
(y
17
− 5y
16
+ ··· + 9y −1)(y
22
− 9y
21
+ ··· − 218776y + 12769)
· (y
29
− 31y
28
+ ··· − 8y −1)
c
3
, c
10
(y
17
− 15y
16
+ ··· + 8y −1)(y
22
− 29y
21
+ ··· − 1134704y + 130321)
· (y
29
− 33y
28
+ ··· − 3829y −3721)
c
4
, c
9
(y
17
+ 8y
16
+ ··· − 10y −1)(y
22
+ 15y
21
+ ··· − 36736y + 961)
· (y
29
+ 34y
28
+ ··· + 21y −1)
c
5
, c
12
((y −1)
22
)(y
17
+ 12y
16
+ ··· − 14y −1)
· (y
29
+ 11y
28
+ ··· + 10485760y −4194304)
c
7
, c
8
, c
11
((y
11
+ 7y
10
+ ··· − 6y −1)
2
)(y
17
+ 17y
16
+ ··· − 106y −25)
· (y
29
+ 24y
28
+ ··· + 249y −16)
20
