12n
0031
(K12n
0031
)
A knot diagram
1
Linearized knot diagam
3 5 6 7 2 9 4 11 12 6 7 10
Solving Sequence
5,7
4
8,12
11 9 6 3 2 1 10
c
4
c
7
c
11
c
8
c
6
c
3
c
2
c
1
c
10
c
5
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.28889 × 10
59
u
23
− 1.73916 × 10
59
u
22
+ ··· + 2.88300 × 10
61
b − 2.28440 × 10
62
,
7.35803 × 10
59
u
23
− 1.22890 × 10
60
u
22
+ ··· + 5.76599 × 10
61
a − 1.59769 × 10
63
,
u
24
− 2u
23
+ ··· − 7168u + 1024i
I
u
2
= hu
2
+ b − u + 1, u
2
+ a − u + 1, u
4
+ u
2
+ u + 1i
I
u
3
= h−2u
5
− 3u
3
+ u
2
+ b − 2u + 2, −2u
5
− 3u
3
+ u
2
+ a − 2u + 2, u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
I
v
1
= ha, 1523v
9
+ 2050v
8
+ ··· + 3335b + 8448,
v
10
+ v
9
− 7v
8
+ 2v
7
+ 58v
6
+ 19v
5
− 16v
4
− 7v
3
+ 6v
2
+ 3v + 1i
* 4 irreducible components of dim
C
= 0, with total 44 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
=
h1.29×10
59
u
23
−1.74×10
59
u
22
+· · ·+2.88×10
61
b−2.28×10
62
, 7.36×10
59
u
23
−
1.23×10
60
u
22
+· · ·+5.77×10
61
a−1.60×10
63
, u
24
−2u
23
+· · ·−7168u+1024i
(i) Arc colorings
a
5
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
8
=
u
u
3
+ u
a
12
=
−0.0127611u
23
+ 0.0213129u
22
+ ··· − 146.902u + 27.7088
−0.00447065u
23
+ 0.00603249u
22
+ ··· − 37.8270u + 7.92371
a
11
=
−0.0127611u
23
+ 0.0213129u
22
+ ··· − 146.902u + 27.7088
−0.00460868u
23
+ 0.00759863u
22
+ ··· − 54.9313u + 12.2340
a
9
=
0.0184954u
23
− 0.0271361u
22
+ ··· + 171.538u − 29.5518
0.00880936u
23
− 0.00909508u
22
+ ··· + 38.6739u − 3.95155
a
6
=
0.00328632u
23
− 0.00596273u
22
+ ··· + 41.3269u − 7.17877
−0.00508827u
23
+ 0.00785301u
22
+ ··· − 54.7848u + 10.3149
a
3
=
0.0000553993u
23
+ 0.0000911467u
22
+ ··· + 0.275591u + 0.984609
−0.000298497u
23
+ 0.00144194u
22
+ ··· − 10.6087u + 2.48202
a
2
=
0.000353896u
23
− 0.00135079u
22
+ ··· + 10.8843u − 1.49741
−0.000298497u
23
+ 0.00144194u
22
+ ··· − 10.6087u + 2.48202
a
1
=
0.00774850u
23
− 0.0135211u
22
+ ··· + 97.1183u − 18.1182
0.00446218u
23
− 0.00755839u
22
+ ··· + 55.7915u − 10.9394
a
10
=
−0.00105139u
23
+ 0.00330070u
22
+ ··· − 27.5679u + 6.56444
0.00223494u
23
− 0.00266203u
22
+ ··· + 13.7590u − 0.614331
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0413329u
23
+ 0.0683918u
22
+ ··· − 470.295u + 85.7076
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
+ 3u
23
+ ··· − 8u + 1
c
2
, c
5
u
24
+ 7u
23
+ ··· + 4u + 1
c
3
u
24
− 7u
23
+ ··· + 155372u + 47236
c
4
, c
7
u
24
+ 2u
23
+ ··· + 7168u + 1024
c
6
u
24
− 4u
23
+ ··· − 3u + 1
c
8
u
24
+ u
23
+ ··· − 5120u + 1024
c
9
, c
12
u
24
− 13u
23
+ ··· − 2u + 1
c
10
u
24
+ 4u
23
+ ··· − 3009503u + 1672193
c
11
u
24
− 2u
23
+ ··· + 2185u + 1831
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
+ 43y
23
+ ··· + 60y + 1
c
2
, c
5
y
24
+ 3y
23
+ ··· − 8y + 1
c
3
y
24
+ 107y
23
+ ··· − 359116296y + 2231239696
c
4
, c
7
y
24
− 30y
23
+ ··· − 3145728y + 1048576
c
6
y
24
+ 30y
22
+ ··· + y + 1
c
8
y
24
− 57y
23
+ ··· − 1572864y + 1048576
c
9
, c
12
y
24
− 27y
23
+ ··· − 198y + 1
c
10
y
24
+ 132y
23
+ ··· + 20945455419869y + 2796229429249
c
11
y
24
+ 20y
23
+ ··· + 72680737y + 3352561
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.028680 + 0.626726I
a = −0.533680 − 0.903018I
b = 0.034700 + 0.150384I
−5.30004 + 7.06597I −3.39619 − 6.37751I
u = 1.028680 − 0.626726I
a = −0.533680 + 0.903018I
b = 0.034700 − 0.150384I
−5.30004 − 7.06597I −3.39619 + 6.37751I
u = −0.497474 + 0.507669I
a = −0.361926 + 0.349425I
b = −0.008032 + 0.687395I
0.84077 − 1.37467I 5.35239 + 4.26754I
u = −0.497474 − 0.507669I
a = −0.361926 − 0.349425I
b = −0.008032 − 0.687395I
0.84077 + 1.37467I 5.35239 − 4.26754I
u = 0.551207 + 0.395512I
a = 0.685914 + 0.546768I
b = 0.865249 + 1.020670I
−0.14272 − 2.78886I 1.24898 + 0.91559I
u = 0.551207 − 0.395512I
a = 0.685914 − 0.546768I
b = 0.865249 − 1.020670I
−0.14272 + 2.78886I 1.24898 − 0.91559I
u = 0.534930 + 0.187354I
a = 1.80358 + 1.02511I
b = 2.21805 − 0.06958I
−2.26240 + 2.45863I −0.58956 − 2.80745I
u = 0.534930 − 0.187354I
a = 1.80358 − 1.02511I
b = 2.21805 + 0.06958I
−2.26240 − 2.45863I −0.58956 + 2.80745I
u = −0.53073 + 1.35148I
a = −0.444245 + 1.037430I
b = −0.185137 + 0.065890I
−5.91731 + 1.32680I −4.55064 − 0.68264I
u = −0.53073 − 1.35148I
a = −0.444245 − 1.037430I
b = −0.185137 − 0.065890I
−5.91731 − 1.32680I −4.55064 + 0.68264I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.099117 + 0.535999I
a = −1.273020 − 0.388430I
b = 0.037166 + 0.328529I
0.00212 − 1.46917I 0.28384 + 4.39333I
u = −0.099117 − 0.535999I
a = −1.273020 + 0.388430I
b = 0.037166 − 0.328529I
0.00212 + 1.46917I 0.28384 − 4.39333I
u = 0.465375 + 0.278294I
a = −0.377175 + 0.887793I
b = 1.55399 + 0.43926I
−2.60162 − 0.06406I −5.33602 − 1.30009I
u = 0.465375 − 0.278294I
a = −0.377175 − 0.887793I
b = 1.55399 − 0.43926I
−2.60162 + 0.06406I −5.33602 + 1.30009I
u = −0.48281 + 2.18987I
a = 1.45037 − 0.79279I
b = 2.00018 − 0.40996I
0.03963 − 1.93559I 3.24137 + 4.51519I
u = −0.48281 − 2.18987I
a = 1.45037 + 0.79279I
b = 2.00018 + 0.40996I
0.03963 + 1.93559I 3.24137 − 4.51519I
u = −2.10598 + 1.47278I
a = 0.737984 − 0.025578I
b = 1.81967 − 0.11260I
13.6003 − 6.5164I 0
u = −2.10598 − 1.47278I
a = 0.737984 + 0.025578I
b = 1.81967 + 0.11260I
13.6003 + 6.5164I 0
u = 2.04936 + 1.71103I
a = 1.027290 + 0.232987I
b = 2.09607 + 0.15606I
13.5215 + 14.1664I 0
u = 2.04936 − 1.71103I
a = 1.027290 − 0.232987I
b = 2.09607 − 0.15606I
13.5215 − 14.1664I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 3.44120 + 1.32166I
a = −0.751676 + 0.034514I
b = −1.93632 − 0.01972I
15.2941 − 1.5620I 0
u = 3.44120 − 1.32166I
a = −0.751676 − 0.034514I
b = −1.93632 + 0.01972I
15.2941 + 1.5620I 0
u = −3.35464 + 2.16681I
a = −0.963420 + 0.242424I
b = −1.99558 + 0.06976I
15.6939 − 6.0170I 0
u = −3.35464 − 2.16681I
a = −0.963420 − 0.242424I
b = −1.99558 − 0.06976I
15.6939 + 6.0170I 0
7
II. I
u
2
= hu
2
+ b − u + 1, u
2
+ a − u + 1, u
4
+ u
2
+ u + 1i
(i) Arc colorings
a
5
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
8
=
u
u
3
+ u
a
12
=
−u
2
+ u − 1
−u
2
+ u − 1
a
11
=
−u
2
+ u − 1
u
3
− u
2
+ 2u
a
9
=
u
u
3
+ u
a
6
=
u
3
−u
2
a
3
=
u
3
+ u
2
+ 1
−u
a
2
=
u
3
+ u
2
+ u + 1
−u
a
1
=
−u
−u
3
− u
a
10
=
−u
2
+ 2u − 1
u
3
− u
2
+ 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
3
− 6u
2
− 2u − 7
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
4
− 2u
3
+ 3u
2
− u + 1
c
2
, c
4
u
4
+ u
2
+ u + 1
c
3
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
5
, c
7
u
4
+ u
2
− u + 1
c
8
u
4
c
9
(u − 1)
4
c
10
, c
11
u
4
− u
3
+ 3u
2
− 2u + 1
c
12
(u + 1)
4
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
2
, c
4
, c
5
c
7
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
3
y
4
− y
3
+ 2y
2
+ 7y + 4
c
8
y
4
c
9
, c
12
(y −1)
4
c
10
, c
11
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.547424 + 0.585652I
a = −1.50411 + 1.22685I
b = −1.50411 + 1.22685I
−0.66484 − 1.39709I −6.04449 + 2.35025I
u = −0.547424 − 0.585652I
a = −1.50411 − 1.22685I
b = −1.50411 − 1.22685I
−0.66484 + 1.39709I −6.04449 − 2.35025I
u = 0.547424 + 1.120870I
a = 0.504108 − 0.106312I
b = 0.504108 − 0.106312I
−4.26996 + 7.64338I −0.45551 − 9.20433I
u = 0.547424 − 1.120870I
a = 0.504108 + 0.106312I
b = 0.504108 + 0.106312I
−4.26996 − 7.64338I −0.45551 + 9.20433I
11
III. I
u
3
= h−2u
5
− 3u
3
+ u
2
+ b − 2u + 2, −2u
5
− 3u
3
+ u
2
+ a − 2u + 2, u
6
−
u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
8
=
u
u
3
+ u
a
12
=
2u
5
+ 3u
3
− u
2
+ 2u − 2
2u
5
+ 3u
3
− u
2
+ 2u − 2
a
11
=
2u
5
+ 3u
3
− u
2
+ 2u − 2
3u
5
− u
4
+ 5u
3
− 3u
2
+ 4u − 4
a
9
=
u
u
3
+ u
a
6
=
u
3
u
5
+ u
3
+ u
a
3
=
−u
5
+ u
4
− 2u
3
+ 2u
2
− 2u + 2
−u
5
− 2u
3
+ u
2
− u + 1
a
2
=
u
4
+ u
2
− u + 1
−u
5
− 2u
3
+ u
2
− u + 1
a
1
=
−u
−u
3
− u
a
10
=
2u
5
+ 3u
3
− u
2
+ 3u − 2
2u
5
+ 4u
3
− u
2
+ 3u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
5
+ u
4
+ 4u
2
+ 3u + 1
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
2
, c
4
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
3
(u
3
− u
2
+ 1)
2
c
5
, c
7
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
8
u
6
c
9
(u − 1)
6
c
10
, c
11
u
6
− 2u
3
+ 4u
2
− 3u + 1
c
12
(u + 1)
6
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
2
, c
4
, c
5
c
7
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
3
(y
3
− y
2
+ 2y −1)
2
c
8
y
6
c
9
, c
12
(y −1)
6
c
10
, c
11
y
6
+ 8y
4
− 2y
3
+ 4y
2
− y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.498832 + 1.001300I
a = −0.702221 − 0.130845I
b = −0.702221 − 0.130845I
−1.91067 − 2.82812I −0.06063 + 4.05868I
u = −0.498832 − 1.001300I
a = −0.702221 + 0.130845I
b = −0.702221 + 0.130845I
−1.91067 + 2.82812I −0.06063 − 4.05868I
u = 0.284920 + 1.115140I
a = 0.447279 − 0.479689I
b = 0.447279 − 0.479689I
−6.04826 −7.59911 + 2.50363I
u = 0.284920 − 1.115140I
a = 0.447279 + 0.479689I
b = 0.447279 + 0.479689I
−6.04826 −7.59911 − 2.50363I
u = 0.713912 + 0.305839I
a = −0.74506 + 2.00027I
b = −0.74506 + 2.00027I
−1.91067 − 2.82812I 5.15973 + 2.26538I
u = 0.713912 − 0.305839I
a = −0.74506 − 2.00027I
b = −0.74506 − 2.00027I
−1.91067 + 2.82812I 5.15973 − 2.26538I
15
IV. I
v
1
= ha, 1523v
9
+ 2050v
8
+ · · · + 3335b + 8448, v
10
+ v
9
+ · · · + 3v + 1i
(i) Arc colorings
a
5
=
1
0
a
7
=
v
0
a
4
=
1
0
a
8
=
v
0
a
12
=
0
−0.456672v
9
− 0.614693v
8
+ ··· − 5.06627v −2.53313
a
11
=
−0.158021v
9
− 0.0569715v
8
+ ··· − 0.930735v −0.158021
−0.456672v
9
− 0.614693v
8
+ ··· − 5.06627v −2.53313
a
9
=
0.117241v
9
+ 0.133433v
8
+ ··· + 1.47736v + 0.117241
0.125637v
9
+ 0.242879v
8
+ ··· + 2.66207v + 1.33103
a
6
=
0.178111v
9
+ 0.133433v
8
+ ··· + 1.94693v + 0.178111
0.286957v
9
+ 0.347826v
8
+ ··· + 2.57391v + 1.28696
a
3
=
−0.0932534v
9
+ 0.700750v
7
+ ··· − 0.700750v + 1.44498
−0.286957v
9
− 0.347826v
8
+ ··· − 2.57391v −0.286957
a
2
=
0.193703v
9
+ 0.347826v
8
+ ··· + 1.87316v + 1.73193
−0.286957v
9
− 0.347826v
8
+ ··· − 2.57391v −0.286957
a
1
=
−0.178111v
9
− 0.133433v
8
+ ··· − 1.94693v −0.178111
−0.286957v
9
− 0.347826v
8
+ ··· − 2.57391v −1.28696
a
10
=
0.117241v
9
+ 0.133433v
8
+ ··· + 1.47736v + 0.117241
−0.286957v
9
− 0.347826v
8
+ ··· − 2.57391v −1.28696
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
6289
3335
v
9
−
14
23
v
8
+
46278
3335
v
7
−
43091
3335
v
6
−
341636
3335
v
5
+
22875
667
v
4
+
72729
3335
v
3
+
5464
3335
v
2
−
48743
3335
v−
1839
3335
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
5
c
2
(u
2
+ u + 1)
5
c
4
, c
7
u
10
c
6
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
c
8
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
9
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
10
, c
12
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
11
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
5
c
4
, c
7
y
10
c
6
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
c
8
, c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
9
, c
10
, c
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.540263 + 0.316514I
a = 0
b = −1.13119 − 0.85946I
−0.329100 − 0.499304I −1.95395 + 0.91636I
v = 0.540263 − 0.316514I
a = 0
b = −1.13119 + 0.85946I
−0.329100 + 0.499304I −1.95395 − 0.91636I
v = −0.544240 + 0.309625I
a = 0
b = −0.17872 + 1.40938I
−0.32910 + 3.56046I −2.01870 − 9.75023I
v = −0.544240 − 0.309625I
a = 0
b = −0.17872 − 1.40938I
−0.32910 − 3.56046I −2.01870 + 9.75023I
v = −0.172885 + 0.299445I
a = 0
b = −1.10887 − 1.92062I
−2.40108 − 2.02988I 2.76075 − 3.67600I
v = −0.172885 − 0.299445I
a = 0
b = −1.10887 + 1.92062I
−2.40108 + 2.02988I 2.76075 + 3.67600I
v = 2.17384 + 1.62819I
a = 0
b = 0.399195 + 0.253095I
−5.87256 + 2.37095I −6.85700 − 6.98324I
v = 2.17384 − 1.62819I
a = 0
b = 0.399195 − 0.253095I
−5.87256 − 2.37095I −6.85700 + 6.98324I
v = −2.49698 + 1.06850I
a = 0
b = 0.019589 − 0.472260I
−5.87256 + 6.43072I −9.93110 − 1.72471I
v = −2.49698 − 1.06850I
a = 0
b = 0.019589 + 0.472260I
−5.87256 − 6.43072I −9.93110 + 1.72471I
19
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
5
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
24
+ 3u
23
+ ··· − 8u + 1)
c
2
(u
2
+ u + 1)
5
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
24
+ 7u
23
+ ··· + 4u + 1)
c
3
(u
2
− u + 1)
5
(u
3
− u
2
+ 1)
2
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
· (u
24
− 7u
23
+ ··· + 155372u + 47236)
c
4
u
10
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
24
+ 2u
23
+ ··· + 7168u + 1024)
c
5
(u
2
− u + 1)
5
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
24
+ 7u
23
+ ··· + 4u + 1)
c
6
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
· (u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)(u
24
− 4u
23
+ ··· − 3u + 1)
c
7
u
10
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
24
+ 2u
23
+ ··· + 7168u + 1024)
c
8
u
10
(u
5
− u
4
+ ··· + u − 1)
2
(u
24
+ u
23
+ ··· − 5120u + 1024)
c
9
((u − 1)
10
)(u
5
+ u
4
+ ··· + u − 1)
2
(u
24
− 13u
23
+ ··· − 2u + 1)
c
10
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
· (u
6
− 2u
3
+ 4u
2
− 3u + 1)(u
24
+ 4u
23
+ ··· − 3009503u + 1672193)
c
11
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
· (u
6
− 2u
3
+ 4u
2
− 3u + 1)(u
24
− 2u
23
+ ··· + 2185u + 1831)
c
12
((u + 1)
10
)(u
5
− u
4
+ ··· + u + 1)
2
(u
24
− 13u
23
+ ··· − 2u + 1)
20
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
5
)(y
4
+ 2y
3
+ ··· + 5y + 1)(y
6
− y
5
+ ··· + 8y
2
+ 1)
· (y
24
+ 43y
23
+ ··· + 60y + 1)
c
2
, c
5
(y
2
+ y + 1)
5
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
24
+ 3y
23
+ ··· − 8y + 1)
c
3
(y
2
+ y + 1)
5
(y
3
− y
2
+ 2y −1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
24
+ 107y
23
+ ··· − 359116296y + 2231239696)
c
4
, c
7
y
10
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
24
− 30y
23
+ ··· − 3145728y + 1048576)
c
6
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
· (y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)(y
24
+ 30y
22
+ ··· + y + 1)
c
8
y
10
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
· (y
24
− 57y
23
+ ··· − 1572864y + 1048576)
c
9
, c
12
(y −1)
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
· (y
24
− 27y
23
+ ··· − 198y + 1)
c
10
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
· (y
6
+ 8y
4
− 2y
3
+ 4y
2
− y + 1)
· (y
24
+ 132y
23
+ ··· + 20945455419869y + 2796229429249)
c
11
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
· (y
6
+ 8y
4
− 2y
3
+ 4y
2
− y + 1)
· (y
24
+ 20y
23
+ ··· + 72680737y + 3352561)
21
