12n
0432
(K12n
0432
)
A knot diagram
1
Linearized knot diagam
3 5 9 11 2 10 3 12 7 5 4 8
Solving Sequence
4,9 3,12
8 1 7 11 5 2 6 10
c
3
c
8
c
12
c
7
c
11
c
4
c
2
c
5
c
10
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h74u
12
− 692u
11
+ ··· + 2529b + 2355, 785u
12
− 3703u
11
+ ··· + 7587a + 387,
u
13
− 5u
12
+ 15u
11
− 29u
10
+ 44u
9
− 54u
8
+ 61u
7
− 62u
6
+ 65u
5
− 67u
4
+ 72u
3
− 57u
2
+ 36u − 9i
I
u
2
= hb + u − 1, u
4
− 4u
3
+ 8u
2
+ a − 7u + 3, u
5
− 4u
4
+ 8u
3
− 7u
2
+ 2u + 1i
I
u
3
= ha
3
− a
2
u − a
2
+ 3au + b + 2u + 3, a
4
− a
3
u + 2a
2
u − a
2
+ 4au + 3a + 2, u
2
+ u + 1i
I
u
4
= h−a
3
− a
2
u − a
2
+ au + b + 2u + 1, a
4
+ a
3
u − 2a
2
u − a
2
− 2au − a + 2u, u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 34 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
= h74u
12
− 692u
11
+ · · · + 2529b + 2355, 785u
12
− 3703u
11
+ · · · +
7587a + 387, u
13
− 5u
12
+ · · · + 36u − 9i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
3
=
1
u
2
a
12
=
−0.103466u
12
+ 0.488072u
11
+ ··· + 2.94108u − 0.0510083
−0.0292606u
12
+ 0.273626u
11
+ ··· + 3.67378u − 0.931198
a
8
=
−0.0726242u
12
+ 0.196652u
11
+ ··· − 1.94029u + 0.651246
−0.166469u
12
+ 0.622776u
11
+ ··· + 4.26572u − 0.653618
a
1
=
0.168051u
12
− 0.640569u
11
+ ··· − 3.47331u + 1.42467
0.0723606u
12
− 0.397390u
11
+ ··· − 4.74733u + 1.77580
a
7
=
−0.115724u
12
+ 0.320417u
11
+ ··· − 0.866746u − 0.193357
−0.148675u
12
+ 1.00593u
11
+ ··· + 7.18031u − 1.47924
a
11
=
−0.0742059u
12
+ 0.214446u
11
+ ··· − 0.732701u + 0.880190
−0.0292606u
12
+ 0.273626u
11
+ ··· + 3.67378u − 0.931198
a
5
=
0.0938447u
12
− 0.426124u
11
+ ··· − 5.20601u + 2.30486
−0.166469u
12
+ 0.622776u
11
+ ··· + 3.26572u − 0.653618
a
2
=
0.319889u
12
− 1.34875u
11
+ ··· − 4.40214u + 1.44603
−0.329775u
12
+ 0.876631u
11
+ ··· − 5.21708u + 2.23488
a
6
=
0.628312u
12
− 2.59628u
11
+ ··· − 11.5492u + 3.46856
−0.758798u
12
+ 2.67537u
11
+ ··· + 5.17556u − 0.747331
a
10
=
−0.00237248u
12
− 0.139976u
11
+ ··· − 2.52195u + 0.843416
0.199684u
12
− 0.774219u
11
+ ··· − 4.62515u + 1.51246
(ii) Obstruction class = −1
(iii) Cusp Shapes =
3325
2529
u
12
−
17666
2529
u
11
+
17227
843
u
10
−
96773
2529
u
9
+
137357
2529
u
8
−
17822
281
u
7
+
173059
2529
u
6
−
170021
2529
u
5
+
175199
2529
u
4
−
187657
2529
u
3
+
67681
843
u
2
−
48875
843
u +
9022
281
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
− u
12
+ ··· + 4u − 1
c
2
, c
5
, c
6
c
9
u
13
+ u
12
+ ··· + 2u − 1
c
3
u
13
− 5u
12
+ ··· + 36u − 9
c
4
, c
8
, c
10
c
11
, c
12
u
13
+ 8u
11
+ ··· − u − 1
c
7
u
13
− u
12
+ ··· + 90u − 25
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
13
+ 35y
12
+ ··· + 212y −1
c
2
, c
5
, c
6
c
9
y
13
− y
12
+ ··· + 4y −1
c
3
y
13
+ 5y
12
+ ··· + 270y −81
c
4
, c
8
, c
10
c
11
, c
12
y
13
+ 16y
12
+ ··· − 5y −1
c
7
y
13
− 7y
12
+ ··· + 3150y −625
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.377421 + 0.995561I
a = 1.42395 + 0.27192I
b = 0.26672 + 1.52025I
−13.25130 + 1.59234I −1.196156 − 0.103558I
u = 0.377421 − 0.995561I
a = 1.42395 − 0.27192I
b = 0.26672 − 1.52025I
−13.25130 − 1.59234I −1.196156 + 0.103558I
u = −0.826366 + 0.684268I
a = −0.040776 + 0.277567I
b = −0.156234 − 0.257273I
−1.74296 − 2.47632I 11.79558 + 3.97407I
u = −0.826366 − 0.684268I
a = −0.040776 − 0.277567I
b = −0.156234 + 0.257273I
−1.74296 + 2.47632I 11.79558 − 3.97407I
u = −0.261323 + 1.190470I
a = −0.753030 + 0.372533I
b = −0.246705 − 0.993811I
−5.78672 − 1.79985I 0.24328 + 2.30841I
u = −0.261323 − 1.190470I
a = −0.753030 − 0.372533I
b = −0.246705 + 0.993811I
−5.78672 + 1.79985I 0.24328 − 2.30841I
u = 1.197260 + 0.637614I
a = 0.000701 + 1.040290I
b = −0.662461 + 1.245930I
3.92798 − 4.17113I 7.23672 + 2.38066I
u = 1.197260 − 0.637614I
a = 0.000701 − 1.040290I
b = −0.662461 − 1.245930I
3.92798 + 4.17113I 7.23672 − 2.38066I
u = 0.80433 + 1.22011I
a = 1.250130 + 0.103984I
b = 0.87865 + 1.60894I
1.94166 + 11.33090I 6.29855 − 5.31818I
u = 0.80433 − 1.22011I
a = 1.250130 − 0.103984I
b = 0.87865 − 1.60894I
1.94166 − 11.33090I 6.29855 + 5.31818I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.425591
a = 0.763681
b = 0.325016
0.561978 17.8790
u = 0.99588 + 1.33587I
a = −0.762815 − 0.387161I
b = −0.24248 − 1.40459I
−8.39874 + 4.39673I 4.68261 + 1.52874I
u = 0.99588 − 1.33587I
a = −0.762815 + 0.387161I
b = −0.24248 + 1.40459I
−8.39874 − 4.39673I 4.68261 − 1.52874I
6
II.
I
u
2
= hb + u − 1, u
4
− 4u
3
+ 8u
2
+ a − 7u + 3, u
5
− 4u
4
+ 8u
3
− 7u
2
+ 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
3
=
1
u
2
a
12
=
−u
4
+ 4u
3
− 8u
2
+ 7u − 3
−u + 1
a
8
=
u
4
− 4u
3
+ 8u
2
− 8u + 4
−u
2
+ 3u − 1
a
1
=
−2u
4
+ 8u
3
− 17u
2
+ 17u − 8
−u
3
+ 4u
2
− 5u + 2
a
7
=
u
4
− 5u
3
+ 11u
2
− 12u + 5
−u
4
+ 4u
3
− 7u
2
+ 5u
a
11
=
−u
4
+ 4u
3
− 8u
2
+ 8u − 4
−u + 1
a
5
=
u
4
− 4u
3
+ 9u
2
− 10u + 6
−u
2
+ 2u − 1
a
2
=
−3u
4
+ 12u
3
− 25u
2
+ 24u − 10
−u
3
+ 4u
2
− 4u + 2
a
6
=
6u
4
− 26u
3
+ 56u
2
− 58u + 27
−2u
4
+ 8u
3
− 15u
2
+ 13u − 4
a
10
=
−2u
4
+ 9u
3
− 20u
2
+ 22u − 11
−u
3
+ 3u
2
− 4u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
4
− 3u
3
+ 4u
2
− 8u + 5
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
+ 2u
4
− 7u
3
+ 8u
2
− 4u + 1
c
2
, c
6
u
5
+ 2u
4
+ u
3
+ 2u
2
+ 1
c
3
u
5
− 4u
4
+ 8u
3
− 7u
2
+ 2u + 1
c
4
, c
12
u
5
− u
4
+ 2u
3
− 3u
2
+ u − 1
c
5
, c
9
u
5
− 2u
4
+ u
3
− 2u
2
− 1
c
7
u
5
− 2u
3
− 3u
2
− 4u − 3
c
8
, c
10
, c
11
u
5
+ u
4
+ 2u
3
+ 3u
2
+ u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
5
− 18y
4
+ 9y
3
− 12y
2
− 1
c
2
, c
5
, c
6
c
9
y
5
− 2y
4
− 7y
3
− 8y
2
− 4y −1
c
3
y
5
+ 12y
3
− 9y
2
+ 18y −1
c
4
, c
8
, c
10
c
11
, c
12
y
5
+ 3y
4
− 7y
2
− 5y −1
c
7
y
5
− 4y
4
− 4y
3
+ 7y
2
− 2y −9
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.917062 + 0.638199I
a = −0.265352 − 0.511254I
b = 0.082938 − 0.638199I
−2.41512 + 2.46056I −0.73583 − 3.45885I
u = 0.917062 − 0.638199I
a = −0.265352 + 0.511254I
b = 0.082938 + 0.638199I
−2.41512 − 2.46056I −0.73583 + 3.45885I
u = −0.238871
a = −5.18635
b = 1.23887
5.64999 7.18340
u = 1.20237 + 1.38128I
a = −0.641472 − 0.411875I
b = −0.202374 − 1.381280I
−8.63454 + 4.90423I −1.85585 − 10.90056I
u = 1.20237 − 1.38128I
a = −0.641472 + 0.411875I
b = −0.202374 + 1.381280I
−8.63454 − 4.90423I −1.85585 + 10.90056I
10
III. I
u
3
=
ha
3
−a
2
u−a
2
+3au+b+2u+3, a
4
−a
3
u+2a
2
u−a
2
+4au+3a+2, u
2
+u+1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
3
=
1
−u − 1
a
12
=
a
−a
3
+ a
2
u + a
2
− 3au − 2u − 3
a
8
=
−a
2
u
−a
3
u − a
2
+ 2au + 2a − u
a
1
=
−a
3
u − a
3
+ a
a
3
u − au − 2a − 1
a
7
=
a
3
u − a
2
u − 2au − 2a + u
−a
3
u + a
3
− a
2
+ 4au + 2a − u + 1
a
11
=
a
3
− a
2
u − a
2
+ 3au + a + 2u + 3
−a
3
+ a
2
u + a
2
− 3au − 2u − 3
a
5
=
−a
3
u + a
2
u + 2au + 2a
a
3
u − a
3
+ a
2
− 4au − 2a − 1
a
2
=
−a
3
u − a
3
+ 2a + 1
a
3
u − 2au − 3a − u − 2
a
6
=
−a
3
u − a
3
+ a
2
u − au + 2a − 2u − 1
2a
3
u + a
3
− a
2
u + a
2
− 3au − 6a + 3u − 1
a
10
=
a
3
u + a
2
− 3au − 3a + 2u − 1
a
3
u + a
3
− 2a
2
u − a
2
+ au − 2a + 2u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u + 9
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
− 7u
7
+ 18u
6
− 20u
5
+ 11u
4
− 5u
3
+ 3u
2
+ 2u + 1
c
2
, c
6
u
8
− u
7
+ 4u
6
− 2u
5
+ 3u
4
− u
3
+ u
2
− 2u + 1
c
3
(u
2
+ u + 1)
4
c
4
, c
12
u
8
+ u
7
+ 6u
6
+ 6u
5
+ 12u
4
+ 13u
3
+ 11u
2
+ 10u + 4
c
5
, c
9
u
8
+ u
7
+ 4u
6
+ 2u
5
+ 3u
4
+ u
3
+ u
2
+ 2u + 1
c
7
u
8
− 5u
7
+ 19u
6
− 45u
5
+ 76u
4
− 100u
3
+ 99u
2
− 60u + 16
c
8
, c
10
, c
11
u
8
− u
7
+ 6u
6
− 6u
5
+ 12u
4
− 13u
3
+ 11u
2
− 10u + 4
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
− 13y
7
+ 66y
6
− 68y
5
+ 59y
4
+ 157y
3
+ 51y
2
+ 2y + 1
c
2
, c
5
, c
6
c
9
y
8
+ 7y
7
+ 18y
6
+ 20y
5
+ 11y
4
+ 5y
3
+ 3y
2
− 2y + 1
c
3
(y
2
+ y + 1)
4
c
4
, c
8
, c
10
c
11
, c
12
y
8
+ 11y
7
+ 48y
6
+ 104y
5
+ 108y
4
+ 23y
3
− 43y
2
− 12y + 16
c
7
y
8
+ 13y
7
+ 63y
6
+ 61y
5
− 30y
4
+ 256y
3
+ 233y
2
− 432y + 256
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −1.008180 + 0.726793I
b = −0.683684 − 0.164757I
−4.27683 − 2.02988I 7.00000 + 3.46410I
u = −0.500000 + 0.866025I
a = −1.271040 + 0.252871I
b = −0.10751 + 1.76242I
−12.17250 − 2.02988I 7.00000 + 3.46410I
u = −0.500000 + 0.866025I
a = 0.199158 + 0.674466I
b = −0.125333 − 1.236500I
−4.27683 − 2.02988I 7.00000 + 3.46410I
u = −0.500000 + 0.866025I
a = 1.58005 − 0.78810I
b = 0.416526 − 1.227190I
−12.17250 − 2.02988I 7.00000 + 3.46410I
u = −0.500000 − 0.866025I
a = −1.008180 − 0.726793I
b = −0.683684 + 0.164757I
−4.27683 + 2.02988I 7.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = −1.271040 − 0.252871I
b = −0.10751 − 1.76242I
−12.17250 + 2.02988I 7.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = 0.199158 − 0.674466I
b = −0.125333 + 1.236500I
−4.27683 + 2.02988I 7.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = 1.58005 + 0.78810I
b = 0.416526 + 1.227190I
−12.17250 + 2.02988I 7.00000 − 3.46410I
14
IV. I
u
4
=
h−a
3
−a
2
u−a
2
+au+b+2u+1, a
4
+a
3
u−2a
2
u−a
2
−2au−a+2u, u
2
+u+1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
3
=
1
−u − 1
a
12
=
a
a
3
+ a
2
u + a
2
− au − 2u − 1
a
8
=
−a
2
u
−a
3
u + a
2
− u − 2
a
1
=
−a
3
u − a
3
+ a
−a
3
u + 2a
2
− au − 2u − 3
a
7
=
a
3
u − a
2
u − 2a
2
+ u + 2
−a
3
u + a
3
+ 2a
2
u + 3a
2
− 3u − 3
a
11
=
−a
3
− a
2
u − a
2
+ au + a + 2u + 1
a
3
+ a
2
u + a
2
− au − 2u − 1
a
5
=
−a
3
u + a
2
u + 2a
2
− 2u − 2
a
3
u − a
3
− 2a
2
u − 3a
2
+ 4u + 3
a
2
=
a
3
u − a
3
− 2a
2
+ 2u + 3
−a
3
u + 2a
3
+ 2a
2
u + 4a
2
+ a − 5u − 4
a
6
=
−3a
3
u + a
3
+ 5a
2
u + 8a
2
− au + 2a − 8u − 7
4a
3
u − 5a
3
− 9a
2
u − 13a
2
+ au − 2a + 15u + 11
a
10
=
a
3
u − 2a
3
− 2a
2
u − 3a
2
+ au + a + 4u + 3
−a
3
u + 3a
3
+ 4a
2
u + 5a
2
− au − 6u − 4
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u + 9
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
− 17u
7
+ 102u
6
− 212u
5
− 177u
4
+ 949u
3
+ 83u
2
− 594u + 361
c
2
, c
5
, c
6
c
9
u
8
+ u
7
− 8u
6
− 12u
5
+ 7u
4
+ 23u
3
+ 45u
2
+ 48u + 19
c
3
(u
2
+ u + 1)
4
c
4
, c
8
, c
10
c
11
, c
12
u
8
− u
7
− 2u
6
+ 4u
4
+ u
3
+ 3u
2
+ 6u + 4
c
7
u
8
− 3u
7
− 3u
6
+ 5u
5
+ 34u
4
− 12u
3
+ 7u
2
− 8u + 4
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
− 85y
7
+ ··· − 292910y + 130321
c
2
, c
5
, c
6
c
9
y
8
− 17y
7
+ 102y
6
− 212y
5
− 177y
4
+ 949y
3
+ 83y
2
− 594y + 361
c
3
(y
2
+ y + 1)
4
c
4
, c
8
, c
10
c
11
, c
12
y
8
− 5y
7
+ 12y
6
− 8y
5
+ 24y
4
+ 7y
3
+ 29y
2
− 12y + 16
c
7
y
8
− 15y
7
+ 107y
6
− 287y
5
+ 1194y
4
+ 388y
3
+ 129y
2
− 8y + 16
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −1.038240 + 0.127249I
b = −0.717935 + 0.427530I
−2.30291 − 2.02988I 7.00000 + 3.46410I
u = −0.500000 + 0.866025I
a = 0.729219 + 0.407985I
b = 0.408918 − 0.962763I
−2.30291 − 2.02988I 7.00000 + 3.46410I
u = −0.500000 + 0.866025I
a = 1.172410 + 0.406591I
b = 1.74734 + 0.58922I
5.59278 − 2.02988I 7.00000 + 3.46410I
u = −0.500000 + 0.866025I
a = −0.36339 − 1.80785I
b = −0.938321 + 0.812037I
5.59278 − 2.02988I 7.00000 + 3.46410I
u = −0.500000 − 0.866025I
a = −1.038240 − 0.127249I
b = −0.717935 − 0.427530I
−2.30291 + 2.02988I 7.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = 0.729219 − 0.407985I
b = 0.408918 + 0.962763I
−2.30291 + 2.02988I 7.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = 1.172410 − 0.406591I
b = 1.74734 − 0.58922I
5.59278 + 2.02988I 7.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = −0.36339 + 1.80785I
b = −0.938321 − 0.812037I
5.59278 + 2.02988I 7.00000 − 3.46410I
18
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
5
+ 2u
4
− 7u
3
+ 8u
2
− 4u + 1)
· (u
8
− 17u
7
+ 102u
6
− 212u
5
− 177u
4
+ 949u
3
+ 83u
2
− 594u + 361)
· (u
8
− 7u
7
+ 18u
6
− 20u
5
+ 11u
4
− 5u
3
+ 3u
2
+ 2u + 1)
· (u
13
− u
12
+ ··· + 4u − 1)
c
2
, c
6
(u
5
+ 2u
4
+ u
3
+ 2u
2
+ 1)(u
8
− u
7
+ ··· − 2u + 1)
· (u
8
+ u
7
− 8u
6
− 12u
5
+ 7u
4
+ 23u
3
+ 45u
2
+ 48u + 19)
· (u
13
+ u
12
+ ··· + 2u − 1)
c
3
(u
2
+ u + 1)
8
(u
5
− 4u
4
+ 8u
3
− 7u
2
+ 2u + 1)
· (u
13
− 5u
12
+ ··· + 36u − 9)
c
4
, c
12
(u
5
− u
4
+ 2u
3
− 3u
2
+ u − 1)(u
8
− u
7
+ ··· + 6u + 4)
· (u
8
+ u
7
+ 6u
6
+ 6u
5
+ 12u
4
+ 13u
3
+ 11u
2
+ 10u + 4)
· (u
13
+ 8u
11
+ ··· − u − 1)
c
5
, c
9
(u
5
− 2u
4
+ u
3
− 2u
2
− 1)
· (u
8
+ u
7
− 8u
6
− 12u
5
+ 7u
4
+ 23u
3
+ 45u
2
+ 48u + 19)
· (u
8
+ u
7
+ ··· + 2u + 1)(u
13
+ u
12
+ ··· + 2u − 1)
c
7
(u
5
− 2u
3
− 3u
2
− 4u − 3)
· (u
8
− 5u
7
+ 19u
6
− 45u
5
+ 76u
4
− 100u
3
+ 99u
2
− 60u + 16)
· (u
8
− 3u
7
− 3u
6
+ 5u
5
+ 34u
4
− 12u
3
+ 7u
2
− 8u + 4)
· (u
13
− u
12
+ ··· + 90u − 25)
c
8
, c
10
, c
11
(u
5
+ u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
8
− u
7
+ ··· + 6u + 4)
· (u
8
− u
7
+ 6u
6
− 6u
5
+ 12u
4
− 13u
3
+ 11u
2
− 10u + 4)
· (u
13
+ 8u
11
+ ··· − u − 1)
19
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
5
− 18y
4
+ 9y
3
− 12y
2
− 1)(y
8
− 85y
7
+ ··· − 292910y + 130321)
· (y
8
− 13y
7
+ 66y
6
− 68y
5
+ 59y
4
+ 157y
3
+ 51y
2
+ 2y + 1)
· (y
13
+ 35y
12
+ ··· + 212y −1)
c
2
, c
5
, c
6
c
9
(y
5
− 2y
4
− 7y
3
− 8y
2
− 4y −1)
· (y
8
− 17y
7
+ 102y
6
− 212y
5
− 177y
4
+ 949y
3
+ 83y
2
− 594y + 361)
· (y
8
+ 7y
7
+ 18y
6
+ 20y
5
+ 11y
4
+ 5y
3
+ 3y
2
− 2y + 1)
· (y
13
− y
12
+ ··· + 4y −1)
c
3
((y
2
+ y + 1)
8
)(y
5
+ 12y
3
+ ··· + 18y −1)(y
13
+ 5y
12
+ ··· + 270y −81)
c
4
, c
8
, c
10
c
11
, c
12
(y
5
+ 3y
4
− 7y
2
− 5y −1)
· (y
8
− 5y
7
+ 12y
6
− 8y
5
+ 24y
4
+ 7y
3
+ 29y
2
− 12y + 16)
· (y
8
+ 11y
7
+ 48y
6
+ 104y
5
+ 108y
4
+ 23y
3
− 43y
2
− 12y + 16)
· (y
13
+ 16y
12
+ ··· − 5y −1)
c
7
(y
5
− 4y
4
− 4y
3
+ 7y
2
− 2y −9)
· (y
8
− 15y
7
+ 107y
6
− 287y
5
+ 1194y
4
+ 388y
3
+ 129y
2
− 8y + 16)
· (y
8
+ 13y
7
+ 63y
6
+ 61y
5
− 30y
4
+ 256y
3
+ 233y
2
− 432y + 256)
· (y
13
− 7y
12
+ ··· + 3150y −625)
20
