12n
0411
(K12n
0411
)
A knot diagram
1
Linearized knot diagam
3 6 7 10 2 11 3 12 6 4 9 8
Solving Sequence
6,11 4,7
3 2 1 5 10 9 12 8
c
6
c
3
c
2
c
1
c
5
c
10
c
9
c
11
c
8
c
4
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= hu
12
− 6u
11
+ 10u
10
− 16u
9
+ 24u
8
− 45u
7
+ 45u
6
− 39u
5
+ 21u
4
− 20u
3
− 3u
2
+ 3b + u − 6,
u
12
− 5u
11
+ 10u
10
− 15u
9
+ 23u
8
− 39u
7
+ 45u
6
− 36u
5
+ 18u
4
− 11u
3
− 2u
2
+ 3a + 4u − 5,
u
13
− 4u
12
+ 10u
11
− 17u
10
+ 28u
9
− 42u
8
+ 57u
7
− 57u
6
+ 45u
5
− 23u
4
+ 8u
3
+ 4u
2
− 4u + 3i
I
u
2
= hu
3
+ 2u
2
+ b + 3u + 2, −u
3
− 3u
2
+ a − 5u − 2, u
4
+ 3u
3
+ 5u
2
+ 3u + 1i
I
u
3
= h−u
3
− u
2
+ b − a − u, a
2
+ au + u
2
, u
4
+ u
3
+ u
2
+ 1i
I
u
4
= h−u
3
+ u
2
+ b − a − u, a
2
+ au − u
2
+ 2u − 2, u
4
− u
3
+ u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 33 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
12
−6u
11
+· · ·+3b−6, u
12
−5u
11
+· · ·+3a−5, u
13
−4u
12
+· · ·−4u+3i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
4
=
−
1
3
u
12
+
5
3
u
11
+ ··· −
4
3
u +
5
3
−
1
3
u
12
+ 2u
11
+ ··· −
1
3
u + 2
a
7
=
1
−u
2
a
3
=
−
4
3
u
12
+
11
3
u
11
+ ··· −
10
3
u +
2
3
5
3
u
12
− 6u
11
+ ··· +
14
3
u − 4
a
2
=
1
3
u
12
−
7
3
u
11
+ ··· +
4
3
u −
10
3
5
3
u
12
− 6u
11
+ ··· +
14
3
u − 4
a
1
=
−
5
3
u
12
+ 6u
11
+ ··· −
14
3
u + 3
4
3
u
12
− 9u
11
+ ··· +
19
3
u − 10
a
5
=
5
3
u
12
−
14
3
u
11
+ ··· +
5
3
u −
5
3
5
3
u
12
− 3u
11
+ ··· + u
2
+
8
3
u
a
10
=
−
4
3
u
11
+ 3u
10
+ ··· −
4
3
u
2
−
4
3
1
3
u
12
− 3u
11
+ ··· +
4
3
u − 3
a
9
=
−
1
3
u
12
+
5
3
u
11
+ ··· −
4
3
u +
5
3
1
3
u
12
− 3u
11
+ ··· +
4
3
u − 3
a
12
=
4
3
u
11
− 3u
10
+ ··· +
4
3
u
2
+
4
3
−2u
12
+ 5u
11
+ ··· − 2u + 2
a
8
=
5
3
u
12
−
14
3
u
11
+ ··· +
5
3
u −
5
3
−2u
12
+ 8u
11
+ ··· − 4u + 5
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −3u
12
+11u
11
−24u
10
+36u
9
−58u
8
+85u
7
−105u
6
+83u
5
−44u
4
+u
3
+16u
2
−21u + 9
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
+ 20u
11
+ ··· + 36u + 1
c
2
, c
5
u
13
+ 2u
12
+ ··· + 18u
2
− 1
c
3
, c
7
u
13
− u
12
+ ··· + 3u − 9
c
4
, c
8
, c
10
c
11
, c
12
u
13
+ 7u
11
+ ··· − u − 1
c
6
u
13
+ 4u
12
+ ··· − 4u − 3
c
9
u
13
− 2u
12
+ ··· − 133u − 47
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
13
+ 40y
12
+ ··· + 516y −1
c
2
, c
5
y
13
+ 20y
11
+ ··· + 36y −1
c
3
, c
7
y
13
+ 5y
12
+ ··· + 531y −81
c
4
, c
8
, c
10
c
11
, c
12
y
13
+ 14y
12
+ ··· − 3y −1
c
6
y
13
+ 4y
12
+ ··· − 8y −9
c
9
y
13
+ 2y
12
+ ··· + 7725y −2209
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.112707 + 0.825249I
a = 1.70029 − 0.14926I
b = 2.12147 − 1.28759I
−12.72660 − 0.46866I −5.30984 − 0.31692I
u = −0.112707 − 0.825249I
a = 1.70029 + 0.14926I
b = 2.12147 + 1.28759I
−12.72660 + 0.46866I −5.30984 + 0.31692I
u = 0.406174 + 0.693805I
a = −0.149604 − 0.367477I
b = −0.471527 + 0.893453I
−1.76494 + 1.40421I 0.52711 − 5.14601I
u = 0.406174 − 0.693805I
a = −0.149604 + 0.367477I
b = −0.471527 − 0.893453I
−1.76494 − 1.40421I 0.52711 + 5.14601I
u = 1.024170 + 0.753551I
a = 0.053482 + 1.217710I
b = 0.722949 − 0.068003I
3.48672 − 4.77545I 3.43860 + 2.44766I
u = 1.024170 − 0.753551I
a = 0.053482 − 1.217710I
b = 0.722949 + 0.068003I
3.48672 + 4.77545I 3.43860 − 2.44766I
u = 0.843226 + 1.079170I
a = 1.241480 + 0.154013I
b = 2.48433 − 0.51976I
2.43630 + 11.55640I 2.21919 − 5.92330I
u = 0.843226 − 1.079170I
a = 1.241480 − 0.154013I
b = 2.48433 + 0.51976I
2.43630 − 11.55640I 2.21919 + 5.92330I
u = 0.909975 + 1.063640I
a = −0.583078 − 0.410756I
b = −1.264870 − 0.146138I
−5.92792 + 3.64387I −2.44803 − 4.63149I
u = 0.909975 − 1.063640I
a = −0.583078 + 0.410756I
b = −1.264870 + 0.146138I
−5.92792 − 3.64387I −2.44803 + 4.63149I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.81473 + 1.23874I
a = −0.804503 + 0.414194I
b = −2.15769 − 0.65518I
−8.05335 − 3.89125I −0.817708 + 0.132635I
u = −0.81473 − 1.23874I
a = −0.804503 − 0.414194I
b = −2.15769 + 0.65518I
−8.05335 + 3.89125I −0.817708 − 0.132635I
u = −0.512230
a = 0.750525
b = 0.130679
0.686378 14.7810
6
II.
I
u
2
= hu
3
+ 2u
2
+ b + 3u + 2 , −u
3
− 3u
2
+ a − 5u − 2, u
4
+ 3u
3
+ 5u
2
+ 3u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
4
=
u
3
+ 3u
2
+ 5u + 2
−u
3
− 2u
2
− 3u − 2
a
7
=
1
−u
2
a
3
=
2u
3
+ 6u
2
+ 9u + 4
−u
2
− 2u − 2
a
2
=
2u
3
+ 5u
2
+ 7u + 2
−u
2
− 2u − 2
a
1
=
−2u
3
− 5u
2
− 7u − 1
2u
3
+ 5u
2
+ 7u + 2
a
5
=
2u
3
+ 5u
2
+ 7u + 2
−u
3
− 3u
2
− 5u − 3
a
10
=
u
3
+ 3u
2
+ 4u + 1
−u − 1
a
9
=
u
3
+ 3u
2
+ 5u + 2
−u − 1
a
12
=
−u
3
− 3u
2
− 4u − 1
u
2
+ 3u + 1
a
8
=
2u
3
+ 5u
2
+ 7u + 2
−u
3
− 4u
2
− 5u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7u
3
− 18u
2
− 19u − 4
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
− 3u
3
+ 5u
2
− 3u + 1
c
2
u
4
− u
3
− u
2
+ u + 1
c
3
(u
2
− u + 1)
2
c
4
, c
8
u
4
+ u
3
+ 2u
2
+ 2u + 1
c
5
u
4
+ u
3
− u
2
− u + 1
c
6
u
4
+ 3u
3
+ 5u
2
+ 3u + 1
c
7
(u
2
+ u + 1)
2
c
9
, c
10
, c
11
c
12
u
4
− u
3
+ 2u
2
− 2u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
4
+ y
3
+ 9y
2
+ y + 1
c
2
, c
5
y
4
− 3y
3
+ 5y
2
− 3y + 1
c
3
, c
7
(y
2
+ y + 1)
2
c
4
, c
8
, c
9
c
10
, c
11
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.378256 + 0.440597I
a = 0.121744 + 1.306620I
b = −0.929304 − 0.758745I
−1.54288 − 0.56550I 2.94255 − 3.09675I
u = −0.378256 − 0.440597I
a = 0.121744 − 1.306620I
b = −0.929304 + 0.758745I
−1.54288 + 0.56550I 2.94255 + 3.09675I
u = −1.12174 + 1.30662I
a = −0.621744 + 0.440597I
b = −2.07070 − 0.75874I
−8.32672 − 4.62527I −4.94255 + 9.02760I
u = −1.12174 − 1.30662I
a = −0.621744 − 0.440597I
b = −2.07070 + 0.75874I
−8.32672 + 4.62527I −4.94255 − 9.02760I
10
III. I
u
3
= h−u
3
− u
2
+ b − a − u, a
2
+ au + u
2
, u
4
+ u
3
+ u
2
+ 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
4
=
a
u
3
+ u
2
+ a + u
a
7
=
1
−u
2
a
3
=
−u
2
a − u
3
− u
2
− u
−u
3
a + u
3
+ u
2
a
2
=
−u
3
a − u
2
a − u
−u
3
a + u
3
+ u
2
a
1
=
u
3
a − 3u
2
a − 2u
3
+ au − 1
−4u
3
a + 2u
3
+ 3u
2
− 3a − 3u + 3
a
5
=
u
2
+ a − u + 1
2u
3
+ 2u
2
+ a + 1
a
10
=
u
2
a + u
3
u
2
a + u
3
+ a + u
a
9
=
−a − u
u
2
a + u
3
+ a + u
a
12
=
u
2
a
u
3
a + a + u
a
8
=
u
2
− a − 2u + 1
2u
3
− u
2
+ a + 2u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
2
− 4u + 1
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
− 13u
7
+ 49u
6
+ 10u
5
− 330u
4
− 13u
3
+ 1300u
2
+ 868u + 169
c
2
, c
5
u
8
+ 3u
7
+ 11u
6
+ 28u
5
+ 48u
4
+ 79u
3
+ 96u
2
+ 58u + 13
c
3
, c
7
u
8
+ u
7
− 5u
6
− 4u
5
+ 15u
4
+ 31u
3
+ 34u
2
+ 32u + 19
c
4
, c
8
, c
10
c
11
, c
12
u
8
+ u
7
− 2u
6
− u
5
+ 6u
4
+ 4u
3
+ u
2
+ 2u + 1
c
6
(u
4
− u
3
+ u
2
+ 1)
2
c
9
u
8
+ u
7
− 4u
6
+ 7u
5
+ 24u
4
− 9u
3
− 9u
2
− 2u + 4
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
− 71y
7
+ ··· − 314024y + 28561
c
2
, c
5
y
8
+ 13y
7
+ 49y
6
− 10y
5
− 330y
4
+ 13y
3
+ 1300y
2
− 868y + 169
c
3
, c
7
y
8
− 11y
7
+ 63y
6
− 160y
5
+ 107y
4
+ 125y
3
− 258y
2
+ 268y + 361
c
4
, c
8
, c
10
c
11
, c
12
y
8
− 5y
7
+ 18y
6
− 31y
5
+ 38y
4
− 4y
3
− 3y
2
− 2y + 1
c
6
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
c
9
y
8
− 9y
7
+ 50y
6
− 241y
5
+ 786y
4
− 517y
3
+ 237y
2
− 76y + 16
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.351808 + 0.720342I
a = 0.447930 − 0.664845I
b = −0.099494 + 0.456028I
−1.85594 + 1.41510I 1.17326 − 4.90874I
u = 0.351808 + 0.720342I
a = −0.799738 − 0.055496I
b = −1.34716 + 1.06538I
−1.85594 + 1.41510I 1.17326 − 4.90874I
u = 0.351808 − 0.720342I
a = 0.447930 + 0.664845I
b = −0.099494 − 0.456028I
−1.85594 − 1.41510I 1.17326 + 4.90874I
u = 0.351808 − 0.720342I
a = −0.799738 + 0.055496I
b = −1.34716 − 1.06538I
−1.85594 − 1.41510I 1.17326 + 4.90874I
u = −0.851808 + 0.911292I
a = −0.363298 − 1.193330I
b = 0.184126 − 0.607681I
5.14581 − 3.16396I 4.82674 + 2.56480I
u = −0.851808 + 0.911292I
a = 1.215110 + 0.282041I
b = 1.76253 + 0.86769I
5.14581 − 3.16396I 4.82674 + 2.56480I
u = −0.851808 − 0.911292I
a = −0.363298 + 1.193330I
b = 0.184126 + 0.607681I
5.14581 + 3.16396I 4.82674 − 2.56480I
u = −0.851808 − 0.911292I
a = 1.215110 − 0.282041I
b = 1.76253 − 0.86769I
5.14581 + 3.16396I 4.82674 − 2.56480I
14
IV. I
u
4
= h−u
3
+ u
2
+ b − a − u, a
2
+ au − u
2
+ 2u − 2, u
4
− u
3
+ u
2
+ 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
4
=
a
u
3
− u
2
+ a + u
a
7
=
1
−u
2
a
3
=
−u
2
a − u
3
+ u
2
− u
u
3
a + u
3
− u
2
a
2
=
u
3
a − u
2
a − u
u
3
a + u
3
− u
2
a
1
=
u
3
a − u
2
a + au − 1
−u
2
− a + u − 1
a
5
=
−u
2
− a + u − 1
−a − 1
a
10
=
u
2
a − u
3
+ 2u
2
− 2u
u
2
a − u
3
+ 2u
2
+ a − u
a
9
=
−a − u
u
2
a − u
3
+ 2u
2
+ a − u
a
12
=
u
2
a + 2u
3
− 2u
2
+ 2u
−u
3
a − 2u
3
+ 2u
2
− a − u
a
8
=
−u
2
+ a + 2u − 1
−u
2
− a
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
+ 4u + 1
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
− 7u
7
+ 17u
6
− 14u
5
+ 2u
4
+ u
3
+ 1
c
2
u
8
+ 3u
7
+ u
6
− 4u
5
− 4u
4
− u
3
+ 2u
2
+ 2u + 1
c
3
u
8
+ u
7
+ 5u
6
+ 8u
5
+ 7u
4
+ 11u
3
+ 10u
2
+ 1
c
4
, c
8
u
8
− u
7
+ 6u
6
− 5u
5
+ 12u
4
− 8u
3
+ 9u
2
− 4u + 1
c
5
u
8
− 3u
7
+ u
6
+ 4u
5
− 4u
4
+ u
3
+ 2u
2
− 2u + 1
c
6
(u
4
− u
3
+ u
2
+ 1)
2
c
7
u
8
− u
7
+ 5u
6
− 8u
5
+ 7u
4
− 11u
3
+ 10u
2
+ 1
c
9
u
8
− u
7
+ 8u
6
− 3u
5
− 16u
4
− 15u
3
+ 47u
2
+ 70u + 52
c
10
, c
11
, c
12
u
8
+ u
7
+ 6u
6
+ 5u
5
+ 12u
4
+ 8u
3
+ 9u
2
+ 4u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
− 15y
7
+ 97y
6
− 114y
5
+ 34y
4
+ 33y
3
+ 4y
2
+ 1
c
2
, c
5
y
8
− 7y
7
+ 17y
6
− 14y
5
+ 2y
4
+ y
3
+ 1
c
3
, c
7
y
8
+ 9y
7
+ 23y
6
+ 4y
5
− 25y
4
+ 29y
3
+ 114y
2
+ 20y + 1
c
4
, c
8
, c
10
c
11
, c
12
y
8
+ 11y
7
+ 50y
6
+ 121y
5
+ 166y
4
+ 124y
3
+ 41y
2
+ 2y + 1
c
6
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
c
9
y
8
+ 15y
7
+ ··· − 12y + 2704
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.351808 + 0.720342I
a = −1.44280 + 0.28054I
b = −0.89538 + 1.40141I
−11.72550 − 1.41510I 1.17326 + 4.90874I
u = −0.351808 + 0.720342I
a = 1.79461 − 1.00088I
b = 2.34204 + 0.11999I
−11.72550 − 1.41510I 1.17326 + 4.90874I
u = −0.351808 − 0.720342I
a = −1.44280 − 0.28054I
b = −0.89538 − 1.40141I
−11.72550 + 1.41510I 1.17326 − 4.90874I
u = −0.351808 − 0.720342I
a = 1.79461 + 1.00088I
b = 2.34204 − 0.11999I
−11.72550 + 1.41510I 1.17326 − 4.90874I
u = 0.851808 + 0.911292I
a = −0.855085 − 0.593153I
b = −1.402510 − 0.007501I
−4.72380 + 3.16396I 4.82674 − 2.56480I
u = 0.851808 + 0.911292I
a = 0.003277 − 0.318139I
b = −0.544147 + 0.267512I
−4.72380 + 3.16396I 4.82674 − 2.56480I
u = 0.851808 − 0.911292I
a = −0.855085 + 0.593153I
b = −1.402510 + 0.007501I
−4.72380 − 3.16396I 4.82674 + 2.56480I
u = 0.851808 − 0.911292I
a = 0.003277 + 0.318139I
b = −0.544147 − 0.267512I
−4.72380 − 3.16396I 4.82674 + 2.56480I
18
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
4
− 3u
3
+ 5u
2
− 3u + 1)
· (u
8
− 13u
7
+ 49u
6
+ 10u
5
− 330u
4
− 13u
3
+ 1300u
2
+ 868u + 169)
· (u
8
− 7u
7
+ ··· + u
3
+ 1)(u
13
+ 20u
11
+ ··· + 36u + 1)
c
2
(u
4
− u
3
− u
2
+ u + 1)(u
8
+ 3u
7
+ ··· + 2u + 1)
· (u
8
+ 3u
7
+ 11u
6
+ 28u
5
+ 48u
4
+ 79u
3
+ 96u
2
+ 58u + 13)
· (u
13
+ 2u
12
+ ··· + 18u
2
− 1)
c
3
((u
2
− u + 1)
2
)(u
8
+ u
7
+ ··· + 32u + 19)
· (u
8
+ u
7
+ ··· + 10u
2
+ 1)(u
13
− u
12
+ ··· + 3u − 9)
c
4
, c
8
(u
4
+ u
3
+ 2u
2
+ 2u + 1)
· (u
8
− u
7
+ 6u
6
− 5u
5
+ 12u
4
− 8u
3
+ 9u
2
− 4u + 1)
· (u
8
+ u
7
+ ··· + 2u + 1)(u
13
+ 7u
11
+ ··· − u − 1)
c
5
(u
4
+ u
3
− u
2
− u + 1)(u
8
− 3u
7
+ ··· − 2u + 1)
· (u
8
+ 3u
7
+ 11u
6
+ 28u
5
+ 48u
4
+ 79u
3
+ 96u
2
+ 58u + 13)
· (u
13
+ 2u
12
+ ··· + 18u
2
− 1)
c
6
((u
4
− u
3
+ u
2
+ 1)
4
)(u
4
+ 3u
3
+ ··· + 3u + 1)(u
13
+ 4u
12
+ ··· − 4u − 3)
c
7
(u
2
+ u + 1)
2
(u
8
− u
7
+ 5u
6
− 8u
5
+ 7u
4
− 11u
3
+ 10u
2
+ 1)
· (u
8
+ u
7
− 5u
6
− 4u
5
+ 15u
4
+ 31u
3
+ 34u
2
+ 32u + 19)
· (u
13
− u
12
+ ··· + 3u − 9)
c
9
(u
4
− u
3
+ 2u
2
− 2u + 1)
· (u
8
− u
7
+ 8u
6
− 3u
5
− 16u
4
− 15u
3
+ 47u
2
+ 70u + 52)
· (u
8
+ u
7
− 4u
6
+ 7u
5
+ 24u
4
− 9u
3
− 9u
2
− 2u + 4)
· (u
13
− 2u
12
+ ··· − 133u − 47)
c
10
, c
11
, c
12
(u
4
− u
3
+ 2u
2
− 2u + 1)(u
8
+ u
7
+ ··· + 2u + 1)
· (u
8
+ u
7
+ 6u
6
+ 5u
5
+ 12u
4
+ 8u
3
+ 9u
2
+ 4u + 1)
· (u
13
+ 7u
11
+ ··· − u − 1)
19
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ y
3
+ 9y
2
+ y + 1)(y
8
− 71y
7
+ ··· − 314024y + 28561)
· (y
8
− 15y
7
+ 97y
6
− 114y
5
+ 34y
4
+ 33y
3
+ 4y
2
+ 1)
· (y
13
+ 40y
12
+ ··· + 516y −1)
c
2
, c
5
(y
4
− 3y
3
+ 5y
2
− 3y + 1)(y
8
− 7y
7
+ 17y
6
− 14y
5
+ 2y
4
+ y
3
+ 1)
· (y
8
+ 13y
7
+ 49y
6
− 10y
5
− 330y
4
+ 13y
3
+ 1300y
2
− 868y + 169)
· (y
13
+ 20y
11
+ ··· + 36y −1)
c
3
, c
7
(y
2
+ y + 1)
2
· (y
8
− 11y
7
+ 63y
6
− 160y
5
+ 107y
4
+ 125y
3
− 258y
2
+ 268y + 361)
· (y
8
+ 9y
7
+ 23y
6
+ 4y
5
− 25y
4
+ 29y
3
+ 114y
2
+ 20y + 1)
· (y
13
+ 5y
12
+ ··· + 531y −81)
c
4
, c
8
, c
10
c
11
, c
12
(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
8
− 5y
7
+ 18y
6
− 31y
5
+ 38y
4
− 4y
3
− 3y
2
− 2y + 1)
· (y
8
+ 11y
7
+ 50y
6
+ 121y
5
+ 166y
4
+ 124y
3
+ 41y
2
+ 2y + 1)
· (y
13
+ 14y
12
+ ··· − 3y −1)
c
6
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
4
(y
4
+ y
3
+ 9y
2
+ y + 1)
· (y
13
+ 4y
12
+ ··· − 8y −9)
c
9
(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
8
− 9y
7
+ 50y
6
− 241y
5
+ 786y
4
− 517y
3
+ 237y
2
− 76y + 16)
· (y
8
+ 15y
7
+ ··· − 12y + 2704)(y
13
+ 2y
12
+ ··· + 7725y −2209)
20
