12a
0719
(K12a
0719
)
A knot diagram
1
Linearized knot diagam
3 8 9 10 11 12 2 1 5 4 7 6
Solving Sequence
4,11
10 5 6 9
1,3
8 2 12 7
c
10
c
4
c
5
c
9
c
3
c
8
c
2
c
12
c
6
c
1
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
4
+ 2u
2
+ b, u
28
− u
27
+ ··· + 4a − 5, u
29
+ 14u
27
+ ··· + u + 1i
I
u
2
= h−217988152638u
47
+ 1406532927108u
46
+ ··· + 3784892885959b − 5225681996414,
17960627004036u
47
− 14379379524196u
46
+ ··· + 3784892885959a − 93018602061573,
u
48
− u
47
+ ··· − 12u + 1i
I
u
3
= hb − 1, a
2
+ au − 1, u
2
+ 1i
* 3 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
= hu
4
+ 2u
2
+ b, u
28
− u
27
+ · · · + 4a − 5, u
29
+ 14u
27
+ · · · + u + 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
10
=
1
u
2
a
5
=
u
u
3
+ u
a
6
=
u
3
+ 2u
u
3
+ u
a
9
=
u
2
+ 1
u
4
+ 2u
2
a
1
=
−
1
4
u
28
+
1
4
u
27
+ ··· −
11
2
u
2
+
5
4
−u
4
− 2u
2
a
3
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
8
=
−u
27
−
1
2
u
26
+ ··· − u +
1
2
−
1
4
u
28
+
1
4
u
27
+ ··· +
3
2
u
2
+
1
4
a
2
=
−
1
4
u
28
+
1
4
u
27
+ ··· −
13
2
u
2
+
5
4
1
4
u
28
−
1
4
u
27
+ ··· −
1
2
u
2
−
1
4
a
12
=
−
1
4
u
28
+
1
4
u
27
+ ··· −
7
2
u
2
+
5
4
−u
2
a
7
=
1
4
u
28
+
1
4
u
27
+ ··· +
7
2
u +
1
4
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
28
− u
27
+ 27u
26
− 10u
25
+ 159u
24
− 38u
23
+ 522u
22
− 51u
21
+
990u
20
+ 75u
19
+ 912u
18
+ 361u
17
− 172u
16
+ 442u
15
− 1278u
14
− 914u
12
− 460u
11
+
325u
10
− 287u
9
+ 589u
8
+ 114u
7
+ 18u
6
+ 133u
5
− 128u
4
+ 3u
3
+ 18u
2
− 13u + 8
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
29
+ 13u
28
+ ··· + 17u + 4
c
2
, c
7
u
29
+ 3u
28
+ ··· − u − 2
c
3
, c
5
u
29
− 3u
28
+ ··· + 80u − 32
c
4
, c
6
, c
9
c
10
, c
11
, c
12
u
29
+ 14u
27
+ ··· + u − 1
c
8
u
29
+ 9u
28
+ ··· + 95u + 6
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
29
+ 7y
28
+ ··· − 271y −16
c
2
, c
7
y
29
− 13y
28
+ ··· + 17y −4
c
3
, c
5
y
29
− 19y
28
+ ··· − 7424y −1024
c
4
, c
6
, c
9
c
10
, c
11
, c
12
y
29
+ 28y
28
+ ··· + y −1
c
8
y
29
− y
28
+ ··· + 5569y −36
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.837271 + 0.076877I
a = −2.37885 + 0.65426I
b = −1.85683 + 0.43644I
4.96568 − 6.65204I 9.90546 + 5.57516I
u = −0.837271 − 0.076877I
a = −2.37885 − 0.65426I
b = −1.85683 − 0.43644I
4.96568 + 6.65204I 9.90546 − 5.57516I
u = 0.833662 + 0.041563I
a = −2.37643 − 0.35224I
b = −1.86234 − 0.23468I
6.73725 + 1.44483I 12.74743 − 0.59636I
u = 0.833662 − 0.041563I
a = −2.37643 + 0.35224I
b = −1.86234 + 0.23468I
6.73725 − 1.44483I 12.74743 + 0.59636I
u = −0.732519
a = −1.59609
b = −1.36109
1.48106 7.22880
u = 0.028083 + 1.284050I
a = −1.81534 − 0.31795I
b = 0.585292 + 0.093469I
−5.68843 + 2.62043I −0.80670 − 3.52599I
u = 0.028083 − 1.284050I
a = −1.81534 + 0.31795I
b = 0.585292 − 0.093469I
−5.68843 − 2.62043I −0.80670 + 3.52599I
u = 0.323515 + 1.266490I
a = 0.83700 − 1.78087I
b = 1.42217 + 0.81837I
−2.35148 + 1.67474I 2.52522 − 1.56718I
u = 0.323515 − 1.266490I
a = 0.83700 + 1.78087I
b = 1.42217 − 0.81837I
−2.35148 − 1.67474I 2.52522 + 1.56718I
u = −0.348532 + 1.291470I
a = 1.07285 + 1.53998I
b = 1.51186 − 0.98379I
−1.05837 − 7.04671I 4.61471 + 6.27988I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.348532 − 1.291470I
a = 1.07285 − 1.53998I
b = 1.51186 + 0.98379I
−1.05837 + 7.04671I 4.61471 − 6.27988I
u = 0.133920 + 1.390120I
a = −0.659184 − 0.455120I
b = 0.302303 + 0.681001I
−9.06064 + 3.87312I −0.24533 − 3.24694I
u = 0.133920 − 1.390120I
a = −0.659184 + 0.455120I
b = 0.302303 − 0.681001I
−9.06064 − 3.87312I −0.24533 + 3.24694I
u = −0.380467 + 1.345060I
a = 1.37808 + 1.03819I
b = 1.60610 − 1.36006I
−2.01294 − 10.23390I 4.21079 + 5.73081I
u = −0.380467 − 1.345060I
a = 1.37808 − 1.03819I
b = 1.60610 + 1.36006I
−2.01294 + 10.23390I 4.21079 − 5.73081I
u = 0.338958 + 1.357740I
a = 0.987536 − 0.915157I
b = 1.31640 + 1.34118I
−7.32448 + 7.83990I −2.00524 − 4.89975I
u = 0.338958 − 1.357740I
a = 0.987536 + 0.915157I
b = 1.31640 − 1.34118I
−7.32448 − 7.83990I −2.00524 + 4.89975I
u = 0.39002 + 1.36214I
a = 1.47122 − 0.87684I
b = 1.63429 + 1.49453I
−4.1212 + 15.5713I 1.45377 − 9.68760I
u = 0.39002 − 1.36214I
a = 1.47122 + 0.87684I
b = 1.63429 − 1.49453I
−4.1212 − 15.5713I 1.45377 + 9.68760I
u = −0.08532 + 1.43102I
a = −0.804301 + 0.163541I
b = −0.023082 − 0.508186I
−13.00060 − 0.38893I −5.31626 − 0.21588I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.08532 − 1.43102I
a = −0.804301 − 0.163541I
b = −0.023082 + 0.508186I
−13.00060 + 0.38893I −5.31626 + 0.21588I
u = −0.16556 + 1.42736I
a = −0.411189 + 0.278237I
b = 0.203418 − 0.954656I
−11.9273 − 8.4157I −3.46124 + 6.83368I
u = −0.16556 − 1.42736I
a = −0.411189 − 0.278237I
b = 0.203418 + 0.954656I
−11.9273 + 8.4157I −3.46124 − 6.83368I
u = 0.417850 + 0.314001I
a = 0.589467 − 1.254980I
b = −0.088921 − 0.564710I
−0.65256 + 3.97304I 7.14340 − 9.12328I
u = 0.417850 − 0.314001I
a = 0.589467 + 1.254980I
b = −0.088921 + 0.564710I
−0.65256 − 3.97304I 7.14340 + 9.12328I
u = −0.414438 + 0.109369I
a = 0.217260 + 0.434902I
b = −0.336911 + 0.210279I
0.809813 − 0.139665I 12.95255 + 2.10646I
u = −0.414438 − 0.109369I
a = 0.217260 − 0.434902I
b = −0.336911 − 0.210279I
0.809813 + 0.139665I 12.95255 − 2.10646I
u = 0.131847 + 0.393506I
a = 1.68992 − 0.55774I
b = 0.266797 − 0.179002I
−1.29100 − 1.59593I 3.66703 + 0.23498I
u = 0.131847 − 0.393506I
a = 1.68992 + 0.55774I
b = 0.266797 + 0.179002I
−1.29100 + 1.59593I 3.66703 − 0.23498I
7
II.
I
u
2
= h−2.18×10
11
u
47
+1.41×10
12
u
46
+· · ·+3.78×10
12
b−5.23×10
12
, 1.80×
10
13
u
47
−1.44×10
13
u
46
+· · ·+3.78×10
12
a−9.30×10
13
, u
48
−u
47
+· · ·−12u+1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
10
=
1
u
2
a
5
=
u
u
3
+ u
a
6
=
u
3
+ 2u
u
3
+ u
a
9
=
u
2
+ 1
u
4
+ 2u
2
a
1
=
−4.74535u
47
+ 3.79915u
46
+ ··· − 173.968u + 24.5763
0.0575943u
47
− 0.371618u
46
+ ··· − 3.92085u + 1.38067
a
3
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
8
=
−5.55732u
47
+ 3.55040u
46
+ ··· − 170.824u + 25.8316
−0.158538u
47
− 0.442451u
46
+ ··· + 4.87445u − 0.167244
a
2
=
−3.20292u
47
+ 3.42884u
46
+ ··· − 149.755u + 21.9747
0.847526u
47
− 0.612468u
46
+ ··· + 3.21471u + 1.01524
a
12
=
−3.50861u
47
+ 3.63777u
46
+ ··· − 167.772u + 24.6986
0.647166u
47
− 0.266498u
46
+ ··· + 1.13773u + 1.25150
a
7
=
0.748497u
47
− 0.101330u
46
+ ··· + 20.5778u − 7.84423
−0.251503u
47
+ 0.898670u
46
+ ··· − 27.4222u + 4.15577
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
24601630690532
3784892885959
u
47
+
18604517425224
3784892885959
u
46
+ ··· −
609246536515560
3784892885959
u +
112526788081386
3784892885959
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
24
+ 11u
23
+ ··· − 2u
2
+ 1)
2
c
2
, c
7
(u
24
− u
23
+ ··· − 2u
3
+ 1)
2
c
3
, c
5
(u
24
+ u
23
+ ··· + 10u + 1)
2
c
4
, c
6
, c
9
c
10
, c
11
, c
12
u
48
+ u
47
+ ··· + 12u + 1
c
8
(u
24
− 3u
23
+ ··· − 4u + 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
24
+ 5y
23
+ ··· − 4y + 1)
2
c
2
, c
7
(y
24
− 11y
23
+ ··· − 2y
2
+ 1)
2
c
3
, c
5
(y
24
− 19y
23
+ ··· − 48y + 1)
2
c
4
, c
6
, c
9
c
10
, c
11
, c
12
y
48
+ 35y
47
+ ··· − 48y + 1
c
8
(y
24
+ y
23
+ ··· + 20y + 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.083162 + 1.035970I
a = 0.841864 − 0.321789I
b = −0.0601129 + 0.0367502I
−1.54603 − 2.05721I 8.27298 + 4.01793I
u = −0.083162 − 1.035970I
a = 0.841864 + 0.321789I
b = −0.0601129 − 0.0367502I
−1.54603 + 2.05721I 8.27298 − 4.01793I
u = 0.392939 + 0.971182I
a = −0.309360 − 0.748390I
b = 0.982133 − 0.443510I
−5.03285 + 0.40841I −1.87200 − 0.75563I
u = 0.392939 − 0.971182I
a = −0.309360 + 0.748390I
b = 0.982133 + 0.443510I
−5.03285 − 0.40841I −1.87200 + 0.75563I
u = 0.884347 + 0.132718I
a = 2.11818 + 1.02084I
b = 1.59566 + 1.20269I
0.58237 + 11.00000I 5.31825 − 8.05284I
u = 0.884347 − 0.132718I
a = 2.11818 − 1.02084I
b = 1.59566 − 1.20269I
0.58237 − 11.00000I 5.31825 + 8.05284I
u = −0.859254 + 0.109305I
a = 2.20088 − 0.78527I
b = 1.63876 − 1.06164I
2.55519 − 5.78082I 8.37527 + 3.72629I
u = −0.859254 − 0.109305I
a = 2.20088 + 0.78527I
b = 1.63876 + 1.06164I
2.55519 + 5.78082I 8.37527 − 3.72629I
u = −0.546029 + 0.650274I
a = −0.571077 + 0.256979I
b = 0.470130 − 0.014776I
−6.25412 + 1.34320I −2.02964 − 0.62000I
u = −0.546029 − 0.650274I
a = −0.571077 − 0.256979I
b = 0.470130 + 0.014776I
−6.25412 − 1.34320I −2.02964 + 0.62000I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.649138 + 0.481545I
a = −0.151229 − 0.117560I
b = 0.508439 − 0.442655I
−5.72979 − 5.71321I −0.10823 + 7.50361I
u = −0.649138 − 0.481545I
a = −0.151229 + 0.117560I
b = 0.508439 + 0.442655I
−5.72979 + 5.71321I −0.10823 − 7.50361I
u = 0.784879 + 0.163524I
a = 1.66447 + 0.46022I
b = 1.33791 + 0.89026I
−2.54173 + 3.77265I 2.10807 − 3.49106I
u = 0.784879 − 0.163524I
a = 1.66447 − 0.46022I
b = 1.33791 − 0.89026I
−2.54173 − 3.77265I 2.10807 + 3.49106I
u = −0.795746 + 0.032611I
a = 2.46879 − 0.15993I
b = 1.74739 − 0.69246I
3.07007 − 2.92383I 9.29020 + 3.29300I
u = −0.795746 − 0.032611I
a = 2.46879 + 0.15993I
b = 1.74739 + 0.69246I
3.07007 + 2.92383I 9.29020 − 3.29300I
u = 0.469574 + 1.138130I
a = −0.062143 − 1.315650I
b = 1.41310 − 0.90321I
−2.49287 − 6.17959I 0
u = 0.469574 − 1.138130I
a = −0.062143 + 1.315650I
b = 1.41310 + 0.90321I
−2.49287 + 6.17959I 0
u = −0.423332 + 1.157340I
a = 0.118454 + 1.197480I
b = 1.54922 + 0.71748I
−0.655501 + 1.182900I 0
u = −0.423332 − 1.157340I
a = 0.118454 − 1.197480I
b = 1.54922 − 0.71748I
−0.655501 − 1.182900I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.763915 + 0.011868I
a = 2.60812 + 0.15719I
b = 1.78089 − 0.50529I
1.53995 + 2.24524I 7.02697 − 1.89383I
u = 0.763915 − 0.011868I
a = 2.60812 − 0.15719I
b = 1.78089 + 0.50529I
1.53995 − 2.24524I 7.02697 + 1.89383I
u = 0.187442 + 1.231110I
a = 0.545130 − 0.408643I
b = 1.53791 + 0.32240I
−5.03285 − 0.40841I 0
u = 0.187442 − 1.231110I
a = 0.545130 + 0.408643I
b = 1.53791 − 0.32240I
−5.03285 + 0.40841I 0
u = −0.387629 + 1.193070I
a = −0.37581 − 1.54631I
b = −1.50691 − 0.05742I
1.53995 + 2.24524I 0
u = −0.387629 − 1.193070I
a = −0.37581 + 1.54631I
b = −1.50691 + 0.05742I
1.53995 − 2.24524I 0
u = −0.087792 + 1.256180I
a = 0.194932 − 0.097149I
b = 0.095700 + 0.946512I
−3.23391 − 1.77225I 0
u = −0.087792 − 1.256180I
a = 0.194932 + 0.097149I
b = 0.095700 − 0.946512I
−3.23391 + 1.77225I 0
u = −0.343517 + 1.240530I
a = 0.574621 + 0.998480I
b = 1.93449 + 0.31400I
−0.655501 − 1.182900I 0
u = −0.343517 − 1.240530I
a = 0.574621 − 0.998480I
b = 1.93449 − 0.31400I
−0.655501 + 1.182900I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.381844 + 1.230540I
a = −0.60470 + 1.40460I
b = −1.66121 − 0.16942I
3.07007 + 2.92383I 0
u = 0.381844 − 1.230540I
a = −0.60470 − 1.40460I
b = −1.66121 + 0.16942I
3.07007 − 2.92383I 0
u = 0.003860 + 1.314540I
a = 0.389563 − 0.108946I
b = 0.73816 − 1.24315I
−6.25412 − 1.34320I 0
u = 0.003860 − 1.314540I
a = 0.389563 + 0.108946I
b = 0.73816 + 1.24315I
−6.25412 + 1.34320I 0
u = −0.312455 + 1.285240I
a = −0.685205 − 0.791335I
b = −1.45997 + 0.81592I
−2.54173 − 3.77265I 0
u = −0.312455 − 1.285240I
a = −0.685205 + 0.791335I
b = −1.45997 − 0.81592I
−2.54173 + 3.77265I 0
u = 0.326858 + 1.282730I
a = 0.777912 − 0.946368I
b = 2.13689 − 0.15998I
−2.49287 + 6.17959I 0
u = 0.326858 − 1.282730I
a = 0.777912 + 0.946368I
b = 2.13689 + 0.15998I
−2.49287 − 6.17959I 0
u = 0.502420 + 0.447701I
a = −0.134106 − 0.384855I
b = 0.723438 + 0.251564I
−3.23391 + 1.77225I 4.01088 − 4.04184I
u = 0.502420 − 0.447701I
a = −0.134106 + 0.384855I
b = 0.723438 − 0.251564I
−3.23391 − 1.77225I 4.01088 + 4.04184I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.109509 + 1.330900I
a = 0.0069009 − 0.1157290I
b = −0.02405 − 1.48729I
−5.72979 + 5.71321I 0
u = 0.109509 − 1.330900I
a = 0.0069009 + 0.1157290I
b = −0.02405 + 1.48729I
−5.72979 − 5.71321I 0
u = 0.373011 + 1.298830I
a = −1.01979 + 1.09705I
b = −1.94507 − 0.64857I
2.55519 + 5.78082I 0
u = 0.373011 − 1.298830I
a = −1.01979 − 1.09705I
b = −1.94507 + 0.64857I
2.55519 − 5.78082I 0
u = −0.372104 + 1.322640I
a = −1.17196 − 0.98411I
b = −2.05820 + 0.82837I
0.58237 − 11.00000I 0
u = −0.372104 − 1.322640I
a = −1.17196 + 0.98411I
b = −2.05820 − 0.82837I
0.58237 + 11.00000I 0
u = 0.179559 + 0.049688I
a = 0.07555 − 5.02709I
b = 1.025290 + 0.022853I
−1.54603 + 2.05721I 8.27298 − 4.01793I
u = 0.179559 − 0.049688I
a = 0.07555 + 5.02709I
b = 1.025290 − 0.022853I
−1.54603 − 2.05721I 8.27298 + 4.01793I
15
III. I
u
3
= hb − 1, a
2
+ au − 1, u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
10
=
1
−1
a
5
=
u
0
a
6
=
u
0
a
9
=
0
−1
a
1
=
a
1
a
3
=
0
u
a
8
=
−au + 1
a − 1
a
2
=
a
−a + 1
a
12
=
a + 1
1
a
7
=
−au
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4au
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
2
c
2
, c
7
, c
8
u
4
− u
2
+ 1
c
3
, c
5
u
4
c
4
, c
6
, c
9
c
10
, c
11
, c
12
(u
2
+ 1)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
2
c
2
, c
7
, c
8
(y
2
− y + 1)
2
c
3
, c
5
y
4
c
4
, c
6
, c
9
c
10
, c
11
, c
12
(y + 1)
4
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.866025 − 0.500000I
b = 1.00000
−3.28987 − 2.02988I 2.00000 + 3.46410I
u = 1.000000I
a = 0.866025 − 0.500000I
b = 1.00000
−3.28987 + 2.02988I 2.00000 − 3.46410I
u = − 1.000000I
a = −0.866025 + 0.500000I
b = 1.00000
−3.28987 + 2.02988I 2.00000 − 3.46410I
u = − 1.000000I
a = 0.866025 + 0.500000I
b = 1.00000
−3.28987 − 2.02988I 2.00000 + 3.46410I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
2
)(u
24
+ 11u
23
+ ··· − 2u
2
+ 1)
2
· (u
29
+ 13u
28
+ ··· + 17u + 4)
c
2
, c
7
(u
4
− u
2
+ 1)(u
24
− u
23
+ ··· − 2u
3
+ 1)
2
(u
29
+ 3u
28
+ ··· − u − 2)
c
3
, c
5
u
4
(u
24
+ u
23
+ ··· + 10u + 1)
2
(u
29
− 3u
28
+ ··· + 80u − 32)
c
4
, c
6
, c
9
c
10
, c
11
, c
12
((u
2
+ 1)
2
)(u
29
+ 14u
27
+ ··· + u − 1)(u
48
+ u
47
+ ··· + 12u + 1)
c
8
(u
4
− u
2
+ 1)(u
24
− 3u
23
+ ··· − 4u + 1)
2
(u
29
+ 9u
28
+ ··· + 95u + 6)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
2
)(y
24
+ 5y
23
+ ··· − 4y + 1)
2
· (y
29
+ 7y
28
+ ··· − 271y −16)
c
2
, c
7
((y
2
− y + 1)
2
)(y
24
− 11y
23
+ ··· − 2y
2
+ 1)
2
· (y
29
− 13y
28
+ ··· + 17y −4)
c
3
, c
5
y
4
(y
24
− 19y
23
+ ··· − 48y + 1)
2
(y
29
− 19y
28
+ ··· − 7424y −1024)
c
4
, c
6
, c
9
c
10
, c
11
, c
12
((y + 1)
4
)(y
29
+ 28y
28
+ ··· + y −1)(y
48
+ 35y
47
+ ··· − 48y + 1)
c
8
((y
2
− y + 1)
2
)(y
24
+ y
23
+ ··· + 20y + 1)
2
· (y
29
− y
28
+ ··· + 5569y −36)
21
