12n
0023
(K12n
0023
)
A knot diagram
1
Linearized knot diagam
3 5 6 7 2 12 4 11 6 7 9 10
Solving Sequence
2,6
5 3
1,10
9 12 7 4 8 11
c
5
c
2
c
1
c
9
c
12
c
6
c
4
c
7
c
11
c
3
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−65383723517u
23
− 453837508340u
22
+ ··· + 211475563064b − 190647925896,
− 283168958672u
23
− 1828538327515u
22
+ ··· + 422951126128a − 1427493398353,
u
24
+ 7u
23
+ ··· + 4u + 1i
I
u
2
= h−u
3
− u
2
+ b − u, −u
3
+ a − u + 1, u
4
+ u
2
− u + 1i
I
u
3
= h85a
4
u − 127a
4
+ 387a
3
u − 586a
3
+ 170a
2
u − 254a
2
− 1331au + 661b + 690a − 639u + 76,
a
5
+ a
4
u + 5a
4
+ 3a
3
u + 4a
3
+ 4a
2
u − 6a
2
+ 4au − 7a + 3u − 1, u
2
− u + 1i
I
u
4
= h−u
5
− u
4
− 2u
3
− u
2
+ b − u − 1, −u
3
− 2u
2
+ a − 2u − 1, u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 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
= h−6.54×10
10
u
23
−4.54×10
11
u
22
+· · ·+2.11×10
11
b−1.91×10
11
, −2.83×
10
11
u
23
−1.83×10
12
u
22
+· · ·+4.23×10
11
a−1.43×10
12
, u
24
+7u
23
+· · ·+4u+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
10
=
0.669508u
23
+ 4.32329u
22
+ ··· − 0.711116u + 3.37508
0.309179u
23
+ 2.14605u
22
+ ··· + 1.09437u + 0.901513
a
9
=
0.360329u
23
+ 2.17723u
22
+ ··· − 1.80549u + 2.47357
0.309179u
23
+ 2.14605u
22
+ ··· + 1.09437u + 0.901513
a
12
=
0.954675u
23
+ 6.60431u
22
+ ··· + 5.13017u + 0.682204
0.103867u
23
+ 0.631846u
22
+ ··· + 1.92070u + 0.466780
a
7
=
−0.379476u
23
− 2.46625u
22
+ ··· − 1.86572u − 1.71578
−0.260086u
23
− 1.75059u
22
+ ··· − 0.202905u − 0.639562
a
4
=
−u
3
u
3
+ u
a
8
=
−0.336233u
23
− 2.26307u
22
+ ··· − 1.85658u − 1.73341
−0.223668u
23
− 1.41378u
22
+ ··· + 0.416575u − 0.352405
a
11
=
0.406427u
23
+ 2.72175u
22
+ ··· − 0.116545u + 1.59093
0.178954u
23
+ 1.12467u
22
+ ··· + 1.69860u + 0.508208
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
372525508513
422951126128
u
23
−
297894180927
52868890766
u
22
+ ··· −
5224084603407
422951126128
u −
308570800851
52868890766
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
, c
11
u
24
− 13u
23
+ ··· − 2u + 1
c
9
u
24
− 2u
23
+ ··· + 2185u + 1831
c
10
u
24
+ 4u
23
+ ··· − 3009503u + 1672193
c
12
u
24
+ u
23
+ ··· − 5120u + 1024
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
, c
11
y
24
− 27y
23
+ ··· − 198y + 1
c
9
y
24
+ 20y
23
+ ··· + 72680737y + 3352561
c
10
y
24
+ 132y
23
+ ··· + 20945455419869y + 2796229429249
c
12
y
24
− 57y
23
+ ··· − 1572864y + 1048576
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.389764 + 0.874669I
a = −2.77917 − 3.58598I
b = 0.772730 + 0.886269I
−2.26240 + 2.45863I −0.58956 − 2.80745I
u = 0.389764 − 0.874669I
a = −2.77917 + 3.58598I
b = 0.772730 − 0.886269I
−2.26240 − 2.45863I −0.58956 + 2.80745I
u = 0.531670 + 0.965706I
a = −1.110060 − 0.431467I
b = 0.161827 − 0.572669I
−0.14272 + 2.78886I 1.24898 − 0.91559I
u = 0.531670 − 0.965706I
a = −1.110060 + 0.431467I
b = 0.161827 + 0.572669I
−0.14272 − 2.78886I 1.24898 + 0.91559I
u = 0.476195 + 0.627959I
a = −0.327508 + 0.824390I
b = 0.002656 + 0.357569I
0.84077 + 1.37467I 5.35239 − 4.26754I
u = 0.476195 − 0.627959I
a = −0.327508 − 0.824390I
b = 0.002656 − 0.357569I
0.84077 − 1.37467I 5.35239 + 4.26754I
u = −0.686903 + 1.011450I
a = −0.675553 − 0.075442I
b = 0.016958 + 1.263390I
−5.30004 − 7.06597I −3.39619 + 6.37751I
u = −0.686903 − 1.011450I
a = −0.675553 + 0.075442I
b = 0.016958 − 1.263390I
−5.30004 + 7.06597I −3.39619 − 6.37751I
u = −0.539649 + 1.181310I
a = 0.959620 − 0.350796I
b = −1.16629 − 1.15098I
−5.91731 + 1.32680I −4.55064 − 0.68264I
u = −0.539649 − 1.181310I
a = 0.959620 + 0.350796I
b = −1.16629 + 1.15098I
−5.91731 − 1.32680I −4.55064 + 0.68264I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.064580 + 0.846503I
a = −0.62366 − 1.42540I
b = 1.03585 − 3.55889I
0.03963 + 1.93559I 3.24137 − 4.51519I
u = 1.064580 − 0.846503I
a = −0.62366 + 1.42540I
b = 1.03585 + 3.55889I
0.03963 − 1.93559I 3.24137 + 4.51519I
u = −0.89305 + 1.24747I
a = −1.03439 − 1.00571I
b = −1.51651 + 1.14075I
13.6003 − 6.5164I −1.83375 + 2.31506I
u = −0.89305 − 1.24747I
a = −1.03439 + 1.00571I
b = −1.51651 − 1.14075I
13.6003 + 6.5164I −1.83375 − 2.31506I
u = −0.87342 + 1.29253I
a = 1.44913 + 1.22589I
b = 1.70664 − 2.23520I
13.5215 − 14.1664I −1.97832 + 6.01811I
u = −0.87342 − 1.29253I
a = 1.44913 − 1.22589I
b = 1.70664 + 2.23520I
13.5215 + 14.1664I −1.97832 − 6.01811I
u = −1.38451 + 0.86873I
a = −0.750407 − 0.670749I
b = −2.63229 − 0.87469I
15.2941 − 1.5620I −0.87276 + 1.81859I
u = −1.38451 − 0.86873I
a = −0.750407 + 0.670749I
b = −2.63229 + 0.87469I
15.2941 + 1.5620I −0.87276 − 1.81859I
u = −1.48666 + 0.74894I
a = 0.372127 + 0.956988I
b = 2.70664 + 2.90079I
15.6939 + 6.0170I −0.56934 − 2.21062I
u = −1.48666 − 0.74894I
a = 0.372127 − 0.956988I
b = 2.70664 − 2.90079I
15.6939 − 6.0170I −0.56934 + 2.21062I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.166881 + 0.257157I
a = 2.61727 − 2.58686I
b = −0.422595 + 0.308191I
−2.60162 − 0.06406I −5.33602 − 1.30009I
u = 0.166881 − 0.257157I
a = 2.61727 + 2.58686I
b = −0.422595 − 0.308191I
−2.60162 + 0.06406I −5.33602 + 1.30009I
u = −0.264909 + 0.086925I
a = 0.90260 + 2.62839I
b = 0.334375 + 0.643835I
0.00212 + 1.46917I 0.28384 − 4.39333I
u = −0.264909 − 0.086925I
a = 0.90260 − 2.62839I
b = 0.334375 − 0.643835I
0.00212 − 1.46917I 0.28384 + 4.39333I
7
II. I
u
2
= h−u
3
− u
2
+ b − u, −u
3
+ a − u + 1, u
4
+ u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
2
a
10
=
u
3
+ u − 1
u
3
+ u
2
+ u
a
9
=
−u
2
− 1
u
3
+ u
2
+ u
a
12
=
u
3
u
2
a
7
=
−u
3
+ u
2
− u + 1
−u
2
+ u − 1
a
4
=
−u
3
u
3
+ u
a
8
=
−u
3
−u
2
a
11
=
u
3
− u
2
− 1
u
3
+ 2u
2
+ u
(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
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
6
u
4
+ 2u
3
+ 3u
2
+ u + 1
c
8
(u − 1)
4
c
9
, c
10
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
11
(u + 1)
4
c
12
u
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
, c
11
(y −1)
4
c
9
, c
10
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
12
y
4
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.547424 + 0.585652I
a = −0.851808 + 0.911292I
b = 0.10488 + 1.55249I
−0.66484 + 1.39709I −6.04449 − 2.35025I
u = 0.547424 − 0.585652I
a = −0.851808 − 0.911292I
b = 0.10488 − 1.55249I
−0.66484 − 1.39709I −6.04449 + 2.35025I
u = −0.547424 + 1.120870I
a = 0.351808 + 0.720342I
b = 0.395123 − 0.506844I
−4.26996 − 7.64338I −0.45551 + 9.20433I
u = −0.547424 − 1.120870I
a = 0.351808 − 0.720342I
b = 0.395123 + 0.506844I
−4.26996 + 7.64338I −0.45551 − 9.20433I
11
III.
I
u
3
= h85a
4
u + 387a
3
u + · · · + 690a + 76, a
4
u + 3a
3
u + · · · − 7a − 1, u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u − 1
a
3
=
u
u − 1
a
1
=
−1
0
a
10
=
a
−0.128593a
4
u − 0.585477a
3
u + ··· − 1.04387a − 0.114977
a
9
=
0.128593a
4
u + 0.585477a
3
u + ··· + 2.04387a + 0.114977
−0.128593a
4
u − 0.585477a
3
u + ··· − 1.04387a − 0.114977
a
12
=
0.00605144a
4
u − 0.0665658a
3
u + ··· − 0.715582a − 0.806354
0.337368a
4
u + 1.28896a
3
u + ··· + 0.856278a − 0.204236
a
7
=
−0.0862330a
4
u − 0.0514372a
3
u + ··· − 4.05295a + 0.240545
0.611195a
4
u + 2.27685a
3
u + ··· + 2.72617a − 1.44175
a
4
=
1
u − 1
a
8
=
−0.0862330a
4
u − 0.0514372a
3
u + ··· − 4.05295a + 0.240545
0.611195a
4
u + 2.27685a
3
u + ··· + 2.72617a − 1.44175
a
11
=
−0.0226929a
4
u + 0.249622a
3
u + ··· − 5.06657a − 0.726172
0.611195a
4
u + 2.27685a
3
u + ··· + 2.72617a − 1.44175
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
1400
661
a
4
u−
2675
661
a
4
+
3769
661
a
3
u−
11557
661
a
3
−
4471
661
a
2
u−
723
661
a
2
−
11463
661
au+
10937
661
a−
4148
661
u−
3453
661
12
(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
, c
12
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
10
, c
11
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
13
(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
10
, c
11
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
9
, c
12
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.953786 − 0.485650I
b = 0.455697 + 1.200150I
−5.87256 + 6.43072I −9.93110 − 1.72471I
u = 0.500000 + 0.866025I
a = −1.124940 − 0.303641I
b = 0.455697 − 1.200150I
−5.87256 − 2.37095I −6.85700 + 6.98324I
u = 0.500000 + 0.866025I
a = −1.42401 + 0.21550I
b = −0.339110 − 0.822375I
−0.32910 + 3.56046I −2.01870 − 9.75023I
u = 0.500000 + 0.866025I
a = 0.000387 + 0.371855I
b = −0.339110 + 0.822375I
−0.329100 + 0.499304I −1.95395 − 0.91636I
u = 0.500000 + 0.866025I
a = −3.90523 − 0.66409I
b = 0.766826
−2.40108 + 2.02988I 2.76075 + 3.67600I
u = 0.500000 − 0.866025I
a = 0.953786 + 0.485650I
b = 0.455697 − 1.200150I
−5.87256 − 6.43072I −9.93110 + 1.72471I
u = 0.500000 − 0.866025I
a = −1.124940 + 0.303641I
b = 0.455697 + 1.200150I
−5.87256 + 2.37095I −6.85700 − 6.98324I
u = 0.500000 − 0.866025I
a = −1.42401 − 0.21550I
b = −0.339110 + 0.822375I
−0.32910 − 3.56046I −2.01870 + 9.75023I
u = 0.500000 − 0.866025I
a = 0.000387 − 0.371855I
b = −0.339110 − 0.822375I
−0.329100 − 0.499304I −1.95395 + 0.91636I
u = 0.500000 − 0.866025I
a = −3.90523 + 0.66409I
b = 0.766826
−2.40108 − 2.02988I 2.76075 − 3.67600I
15
IV. I
u
4
= h−u
5
− u
4
− 2u
3
− u
2
+ b − u − 1, −u
3
− 2u
2
+ a − 2u − 1, u
6
+
u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
10
=
u
3
+ 2u
2
+ 2u + 1
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
a
9
=
−u
5
− u
4
− u
3
+ u
2
+ u
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
a
12
=
u
3
u
5
+ u
3
+ u
a
7
=
u
4
+ u
2
+ u + 1
−2u
5
− u
4
− 3u
3
− 2u
2
− 3u − 2
a
4
=
−u
3
u
3
+ u
a
8
=
−u
3
−u
5
− u
3
− u
a
11
=
−u
5
− u
4
+ u
2
+ u
2u
5
+ u
4
+ 3u
3
+ u
2
+ 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
5
− u
4
− 8u
3
− 2u
2
− 5u − 4
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
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
6
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
8
(u − 1)
6
c
9
, c
10
u
6
+ 2u
3
+ 4u
2
+ 3u + 1
c
11
(u + 1)
6
c
12
u
6
17
(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
, c
11
(y −1)
6
c
9
, c
10
y
6
+ 8y
4
− 2y
3
+ 4y
2
− y + 1
c
12
y
6
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.498832 + 1.001300I
a = −0.88615 + 3.74409I
b = −1.14366 − 1.20015I
−1.91067 + 2.82812I 5.15973 − 2.26538I
u = 0.498832 − 1.001300I
a = −0.88615 − 3.74409I
b = −1.14366 + 1.20015I
−1.91067 − 2.82812I 5.15973 + 2.26538I
u = −0.284920 + 1.115140I
a = −0.854760 − 0.155763I
b = 0.662359 + 0.362106I
−6.04826 −7.59911 + 2.50363I
u = −0.284920 − 1.115140I
a = −0.854760 + 0.155763I
b = 0.662359 − 0.362106I
−6.04826 −7.59911 − 2.50363I
u = −0.713912 + 0.305839I
a = 0.240915 + 0.177333I
b = 0.481306 + 0.637866I
−1.91067 + 2.82812I −0.06063 − 4.05868I
u = −0.713912 − 0.305839I
a = 0.240915 − 0.177333I
b = 0.481306 − 0.637866I
−1.91067 − 2.82812I −0.06063 + 4.05868I
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 − 1)
10
)(u
5
+ u
4
+ ··· + u − 1)
2
(u
24
− 13u
23
+ ··· − 2u + 1)
c
9
(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
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 + 1)
10
)(u
5
− u
4
+ ··· + u + 1)
2
(u
24
− 13u
23
+ ··· − 2u + 1)
c
12
u
10
(u
5
+ u
4
+ ··· + u + 1)
2
(u
24
+ u
23
+ ··· − 5120u + 1024)
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
, c
11
(y −1)
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
· (y
24
− 27y
23
+ ··· − 198y + 1)
c
9
(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)
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
12
y
10
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
· (y
24
− 57y
23
+ ··· − 1572864y + 1048576)
21
