12n
0419
(K12n
0419
)
A knot diagram
1
Linearized knot diagam
3 6 12 9 2 10 3 11 6 4 8 7
Solving Sequence
6,9
10
3,7
2 1 5 4 11 8 12
c
9
c
6
c
2
c
1
c
5
c
4
c
10
c
8
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.66310 × 10
40
u
18
+ 2.05150 × 10
40
u
17
+ ··· + 1.58940 × 10
42
b + 1.51319 × 10
42
,
− 1.49523 × 10
41
u
18
− 1.67879 × 10
41
u
17
+ ··· + 2.70197 × 10
43
a + 4.39022 × 10
43
,
u
19
+ 2u
18
+ ··· + 197u + 34i
I
u
2
= h−6u
11
+ 17u
10
+ 15u
9
− 46u
8
− 27u
7
+ 16u
6
+ 67u
5
+ 36u
4
− 81u
3
− 12u
2
+ 3b + 33u − 13,
− u
11
+ 8u
9
+ 6u
8
− 20u
7
− 23u
6
+ 6u
5
+ 33u
4
+ 24u
3
− 24u
2
+ 3a − 13u + 12,
u
12
− 3u
11
− 2u
10
+ 8u
9
+ 3u
8
− 3u
7
− 10u
6
− 4u
5
+ 14u
4
− 2u
3
− 6u
2
+ 4u − 1i
I
u
3
= h−u
3
b + u
3
+ b
2
+ u
2
− u − 1, u
3
+ a − u, u
4
− u
2
+ 1i
I
u
4
= hb + u − 1, a − u + 1, u
2
− u + 1i
* 4 irreducible components of dim
C
= 0, with total 41 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
= h1.66 × 10
40
u
18
+ 2.05 × 10
40
u
17
+ · · · + 1.59 × 10
42
b + 1.51 ×
10
42
, −1.50 × 10
41
u
18
− 1.68 × 10
41
u
17
+ · · · + 2.70 × 10
43
a + 4.39 ×
10
43
, u
19
+ 2u
18
+ · · · + 197u + 34i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
3
=
0.00553383u
18
+ 0.00621320u
17
+ ··· + 4.05205u − 1.62482
−0.0104638u
18
− 0.0129074u
17
+ ··· − 4.49529u − 0.952055
a
7
=
−u
−u
3
+ u
a
2
=
0.00553383u
18
+ 0.00621320u
17
+ ··· + 4.05205u − 1.62482
−0.0124793u
18
− 0.0173211u
17
+ ··· − 5.26347u − 1.11711
a
1
=
−0.0156043u
18
− 0.0294312u
17
+ ··· − 5.04992u − 3.27835
0.00435103u
18
+ 0.00855543u
17
+ ··· − 2.18420u − 0.489130
a
5
=
0.0196881u
18
+ 0.0324028u
17
+ ··· + 5.22408u + 0.287287
−0.0163849u
18
− 0.0268543u
17
+ ··· − 3.04420u − 0.799678
a
4
=
0.00330322u
18
+ 0.00554852u
17
+ ··· + 2.17988u − 0.512391
−0.0163849u
18
− 0.0268543u
17
+ ··· − 3.04420u − 0.799678
a
11
=
0.0271290u
18
+ 0.0462190u
17
+ ··· + 4.83481u + 2.57786
0.000739414u
18
+ 0.00488659u
17
+ ··· + 0.324280u + 0.739169
a
8
=
−0.00330322u
18
− 0.00554852u
17
+ ··· − 2.17988u + 0.512391
0.0151808u
18
+ 0.0269510u
17
+ ··· + 2.74012u + 0.653062
a
12
=
−0.0134032u
18
− 0.0261459u
17
+ ··· − 5.10567u − 3.36811
0.00236078u
18
+ 0.00585106u
17
+ ··· − 1.98324u − 0.361402
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0105559u
18
+ 0.0127073u
17
+ ··· + 11.9187u − 12.1302
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
+ 97u
18
+ ··· − 1941683u + 162409
c
2
, c
5
u
19
+ 3u
18
+ ··· − 721u − 403
c
3
u
19
− 5u
18
+ ··· − 24u + 11
c
4
u
19
− 5u
18
+ ··· + 270503u + 65171
c
6
, c
9
u
19
+ 2u
18
+ ··· + 197u + 34
c
7
u
19
− 5u
18
+ ··· + 94u − 421
c
8
, c
11
u
19
+ 4u
18
+ ··· + 111u + 9
c
10
u
19
+ u
18
+ ··· + 706u + 167
c
12
u
19
+ 4u
18
+ ··· − 13967u − 14044
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
− 3221y
18
+ ··· + 5217004770233y −26376683281
c
2
, c
5
y
19
− 97y
18
+ ··· − 1941683y −162409
c
3
y
19
− 9y
18
+ ··· + 1588y −121
c
4
y
19
− 193y
18
+ ··· + 27615258537y −4247259241
c
6
, c
9
y
19
− 54y
18
+ ··· + 33165y −1156
c
7
y
19
− 55y
18
+ ··· + 783476y −177241
c
8
, c
11
y
19
+ 8y
18
+ ··· + 4023y −81
c
10
y
19
+ y
18
+ ··· + 293694y −27889
c
12
y
19
− 210y
18
+ ··· + 15988001y −197233936
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.461221 + 0.540098I
a = −0.329642 + 0.316078I
b = −0.029910 + 0.572548I
−1.03982 + 1.81601I −6.18544 − 3.90826I
u = −0.461221 − 0.540098I
a = −0.329642 − 0.316078I
b = −0.029910 − 0.572548I
−1.03982 − 1.81601I −6.18544 + 3.90826I
u = −1.088290 + 0.702970I
a = −0.517058 − 0.653979I
b = −1.259640 − 0.053971I
−1.72336 + 1.68833I −7.61757 − 1.84714I
u = −1.088290 − 0.702970I
a = −0.517058 + 0.653979I
b = −1.259640 + 0.053971I
−1.72336 − 1.68833I −7.61757 + 1.84714I
u = 1.36853 + 0.50280I
a = −0.383197 + 0.779759I
b = −1.84064 + 0.23118I
−8.13748 − 4.76151I −14.1488 + 2.3927I
u = 1.36853 − 0.50280I
a = −0.383197 − 0.779759I
b = −1.84064 − 0.23118I
−8.13748 + 4.76151I −14.1488 − 2.3927I
u = −0.347878 + 0.247156I
a = −2.26272 − 0.83175I
b = 0.56233 + 1.35367I
−3.68506 + 0.25072I −15.1444 − 0.1476I
u = −0.347878 − 0.247156I
a = −2.26272 + 0.83175I
b = 0.56233 − 1.35367I
−3.68506 − 0.25072I −15.1444 + 0.1476I
u = 0.310858 + 0.201294I
a = 0.06485 + 2.00660I
b = −2.14079 + 0.42046I
−3.21447 + 6.05819I −7.22138 − 2.86734I
u = 0.310858 − 0.201294I
a = 0.06485 − 2.00660I
b = −2.14079 − 0.42046I
−3.21447 − 6.05819I −7.22138 + 2.86734I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.21322 + 1.62429I
a = −0.704489 + 0.702997I
b = 2.62979 − 2.27449I
1.70124 + 2.03414I −9.92889 − 4.28864I
u = 0.21322 − 1.62429I
a = −0.704489 − 0.702997I
b = 2.62979 + 2.27449I
1.70124 − 2.03414I −9.92889 + 4.28864I
u = −0.230182
a = −1.93660
b = −0.473485
−0.715844 −14.1990
u = 2.32815
a = −1.06005
b = −3.36761
−18.6560 −21.4300
u = −2.39736 + 1.54309I
a = −1.141170 − 0.008691I
b = −1.78841 + 8.62679I
12.7776 + 11.8645I −10.68698 − 4.25583I
u = −2.39736 − 1.54309I
a = −1.141170 + 0.008691I
b = −1.78841 − 8.62679I
12.7776 − 11.8645I −10.68698 + 4.25583I
u = −2.64357 + 1.95100I
a = 1.147970 + 0.222590I
b = 3.90696 − 11.33980I
13.49670 + 2.32138I −10.59401 + 0.I
u = −2.64357 − 1.95100I
a = 1.147970 − 0.222590I
b = 3.90696 + 11.33980I
13.49670 − 2.32138I −10.59401 + 0.I
u = 5.99343
a = 1.27698
b = 43.7617
17.1155 0
6
II. I
u
2
=
h−6u
11
+ 17u
10
+ · · ·+3b−13, −u
11
+ 8u
9
+ · · ·+3a+12, u
12
−3u
11
+ · · ·+4u−1i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
3
=
1
3
u
11
−
8
3
u
9
+ ··· +
13
3
u − 4
2u
11
−
17
3
u
10
+ ··· − 11u +
13
3
a
7
=
−u
−u
3
+ u
a
2
=
1
3
u
11
−
8
3
u
9
+ ··· +
13
3
u − 4
u
11
− 3u
10
+ ··· −
22
3
u +
10
3
a
1
=
1
3
u
11
−
7
3
u
10
+ ··· − 13u + 7
−
1
3
u
11
+
4
3
u
10
+ ··· +
22
3
u −
1
3
a
5
=
−
2
3
u
11
+
1
3
u
10
+ ··· −
22
3
u + 6
1
3
u
11
−
1
3
u
10
+ ··· +
13
3
u −
4
3
a
4
=
−
1
3
u
11
+
10
3
u
9
+ ··· − 3u +
14
3
1
3
u
11
−
1
3
u
10
+ ··· +
13
3
u −
4
3
a
11
=
−
8
3
u
11
+
22
3
u
10
+ ··· + 15u −
7
3
−
4
3
u
11
+
11
3
u
10
+ ··· +
20
3
u −
10
3
a
8
=
1
3
u
11
−
10
3
u
9
+ ··· + 3u −
14
3
4
3
u
11
− 3u
10
+ ··· −
23
3
u + 2
a
12
=
−
2
3
u
11
+
1
3
u
10
+ ··· −
25
3
u + 6
1
3
u
10
− u
9
+ ··· + 3u +
1
3
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
46
3
u
11
+33u
10
+62u
9
−
247
3
u
8
−114u
7
−
91
3
u
6
+
388
3
u
5
+
526
3
u
4
−
304
3
u
3
−
176
3
u
2
+
181
3
u−
107
3
7
(iv) u-Polynomials at the component
8
Crossings u-Polynomials at each crossing
c
1
u
12
− 10u
11
+ ··· + 2u + 1
c
2
u
12
+ 8u
11
+ ··· − 4u − 1
c
3
u
12
+ 3u
11
+ ··· − 4u − 1
c
4
u
12
− 3u
11
+ ··· − 113u + 61
c
5
u
12
− 8u
11
+ ··· + 4u − 1
c
6
u
12
+ 3u
11
+ ··· − 4u − 1
c
7
u
12
+ 3u
11
+ ··· − 2u − 1
c
8
u
12
+ 3u
11
+ ··· + 6u + 1
c
9
u
12
− 3u
11
+ ··· + 4u − 1
c
10
u
12
+ u
11
+ u
10
− u
9
− 2u
8
− 7u
7
− 3u
6
− 4u
5
+ 4u
4
− u
3
+ 3u
2
+ 1
c
11
u
12
− 3u
11
+ ··· − 6u + 1
c
12
u
12
− 7u
11
+ ··· − 149u + 61
9
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
− 70y
11
+ ··· − 18y + 1
c
2
, c
5
y
12
− 10y
11
+ ··· + 2y + 1
c
3
y
12
− 3y
11
+ ··· − 6y + 1
c
4
y
12
− 11y
11
+ ··· + 2725y + 3721
c
6
, c
9
y
12
− 13y
11
+ ··· − 4y + 1
c
7
y
12
− 19y
11
+ ··· − 16y + 1
c
8
, c
11
y
12
+ 3y
11
+ ··· − 20y + 1
c
10
y
12
+ y
11
+ ··· + 6y + 1
c
12
y
12
− 33y
11
+ ··· − 22201y + 3721
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.059480 + 0.154142I
a = 0.819599 − 0.608253I
b = −0.415453 − 0.590193I
1.22664 + 3.11362I −7.04939 − 7.05690I
u = −1.059480 − 0.154142I
a = 0.819599 + 0.608253I
b = −0.415453 + 0.590193I
1.22664 − 3.11362I −7.04939 + 7.05690I
u = −0.457840 + 1.081060I
a = 0.907598 − 0.603898I
b = −3.07960 − 0.50765I
2.31672 + 1.60638I −1.16262 − 0.94623I
u = −0.457840 − 1.081060I
a = 0.907598 + 0.603898I
b = −3.07960 + 0.50765I
2.31672 − 1.60638I −1.16262 + 0.94623I
u = −1.24242
a = −0.422158
b = 0.0575173
−3.40775 −11.1910
u = 0.646031 + 0.179003I
a = −0.948613 − 0.380726I
b = 2.25048 + 0.18881I
−3.62882 − 6.45766I −17.3073 + 12.6531I
u = 0.646031 − 0.179003I
a = −0.948613 + 0.380726I
b = 2.25048 − 0.18881I
−3.62882 + 6.45766I −17.3073 − 12.6531I
u = 1.45298 + 0.05285I
a = −0.107356 − 0.338014I
b = −0.694805 − 0.843286I
−7.20322 − 5.60855I −9.98455 + 5.57082I
u = 1.45298 − 0.05285I
a = −0.107356 + 0.338014I
b = −0.694805 + 0.843286I
−7.20322 + 5.60855I −9.98455 − 5.57082I
u = 0.285356 + 0.363826I
a = −1.91901 + 3.12576I
b = −0.84108 − 1.29227I
−8.23832 − 3.21911I −14.7748 − 0.6369I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.285356 − 0.363826I
a = −1.91901 − 3.12576I
b = −0.84108 + 1.29227I
−8.23832 + 3.21911I −14.7748 + 0.6369I
u = 2.50831
a = −1.08227
b = −4.49661
−18.1761 −4.25130
13
III. I
u
3
= h−u
3
b + u
3
+ b
2
+ u
2
− u − 1, u
3
+ a − u, u
4
− u
2
+ 1i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
3
=
−u
3
+ u
b
a
7
=
−u
−u
3
+ u
a
2
=
−u
3
+ u
b − u
a
1
=
0
−u
a
5
=
−u
3
+ u
b
a
4
=
−u
3
+ b + u
b
a
11
=
−u
3
b − u
3
− u
2
−u
3
a
8
=
u
3
− b − u
−1
a
12
=
−u
3
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
− 16
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
u
8
+ 4u
7
+ 8u
6
+ 10u
5
+ 9u
4
+ 6u
3
− 2u + 1
c
4
u
8
+ 2u
5
+ u
4
+ 6u
3
+ 4u
2
− 2u + 1
c
5
(u + 1)
8
c
6
, c
9
(u
4
− u
2
+ 1)
2
c
7
u
8
+ 2u
7
− u
6
− 4u
5
+ 6u
3
+ 3u
2
− 4u + 1
c
8
, c
11
(u
2
+ 1)
4
c
10
u
8
+ 3u
6
− 2u
5
+ 4u
4
+ 7u
2
+ 2u + 1
c
12
(u
2
+ u + 1)
4
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
8
c
3
y
8
+ 2y
6
− 4y
5
− 21y
4
+ 20y
3
+ 42y
2
− 4y + 1
c
4
y
8
+ 2y
6
+ 4y
5
− 21y
4
− 20y
3
+ 42y
2
+ 4y + 1
c
6
, c
9
(y
2
− y + 1)
4
c
7
y
8
− 6y
7
+ 17y
6
− 34y
5
+ 60y
4
− 70y
3
+ 57y
2
− 10y + 1
c
8
, c
11
(y + 1)
8
c
10
y
8
+ 6y
7
+ 17y
6
+ 34y
5
+ 60y
4
+ 70y
3
+ 57y
2
+ 10y + 1
c
12
(y
2
+ y + 1)
4
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = 0.866025 − 0.500000I
b = 1.200000 − 0.069179I
−3.28987 − 2.02988I −14.0000 + 3.4641I
u = 0.866025 + 0.500000I
a = 0.866025 − 0.500000I
b = −1.20000 + 1.06918I
−3.28987 − 2.02988I −14.0000 + 3.4641I
u = 0.866025 − 0.500000I
a = 0.866025 + 0.500000I
b = 1.200000 + 0.069179I
−3.28987 + 2.02988I −14.0000 − 3.4641I
u = 0.866025 − 0.500000I
a = 0.866025 + 0.500000I
b = −1.20000 − 1.06918I
−3.28987 + 2.02988I −14.0000 − 3.4641I
u = −0.866025 + 0.500000I
a = −0.866025 − 0.500000I
b = 0.224207 + 1.316270I
−3.28987 + 2.02988I −14.0000 − 3.4641I
u = −0.866025 + 0.500000I
a = −0.866025 − 0.500000I
b = −0.224207 − 0.316268I
−3.28987 + 2.02988I −14.0000 − 3.4641I
u = −0.866025 − 0.500000I
a = −0.866025 + 0.500000I
b = 0.224207 − 1.316270I
−3.28987 − 2.02988I −14.0000 + 3.4641I
u = −0.866025 − 0.500000I
a = −0.866025 + 0.500000I
b = −0.224207 + 0.316268I
−3.28987 − 2.02988I −14.0000 + 3.4641I
17
IV. I
u
4
= hb + u − 1, a − u + 1, u
2
− u + 1i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
u − 1
a
3
=
u − 1
−u + 1
a
7
=
−u
u + 1
a
2
=
u − 1
1
a
1
=
0
u
a
5
=
−u + 1
u − 1
a
4
=
0
u − 1
a
11
=
1
−1
a
8
=
0
1
a
12
=
−1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u − 4
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u + 1)
2
c
2
, c
5
, c
8
c
11
(u − 1)
2
c
3
, c
4
, c
10
u
2
+ u + 1
c
6
, c
7
, c
9
c
12
u
2
− u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
8
, c
11
(y −1)
2
c
3
, c
4
, c
6
c
7
, c
9
, c
10
c
12
y
2
+ y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.500000 + 0.866025I
b = 0.500000 − 0.866025I
1.64493 + 2.02988I −6.00000 − 3.46410I
u = 0.500000 − 0.866025I
a = −0.500000 − 0.866025I
b = 0.500000 + 0.866025I
1.64493 − 2.02988I −6.00000 + 3.46410I
21
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
8
)(u + 1)
2
(u
12
− 10u
11
+ ··· + 2u + 1)
· (u
19
+ 97u
18
+ ··· − 1941683u + 162409)
c
2
((u − 1)
10
)(u
12
+ 8u
11
+ ··· − 4u − 1)(u
19
+ 3u
18
+ ··· − 721u − 403)
c
3
(u
2
+ u + 1)(u
8
+ 4u
7
+ 8u
6
+ 10u
5
+ 9u
4
+ 6u
3
− 2u + 1)
· (u
12
+ 3u
11
+ ··· − 4u − 1)(u
19
− 5u
18
+ ··· − 24u + 11)
c
4
(u
2
+ u + 1)(u
8
+ 2u
5
+ u
4
+ 6u
3
+ 4u
2
− 2u + 1)
· (u
12
− 3u
11
+ ··· − 113u + 61)(u
19
− 5u
18
+ ··· + 270503u + 65171)
c
5
((u − 1)
2
)(u + 1)
8
(u
12
− 8u
11
+ ··· + 4u − 1)
· (u
19
+ 3u
18
+ ··· − 721u − 403)
c
6
(u
2
− u + 1)(u
4
− u
2
+ 1)
2
(u
12
+ 3u
11
+ ··· − 4u − 1)
· (u
19
+ 2u
18
+ ··· + 197u + 34)
c
7
(u
2
− u + 1)(u
8
+ 2u
7
− u
6
− 4u
5
+ 6u
3
+ 3u
2
− 4u + 1)
· (u
12
+ 3u
11
+ ··· − 2u − 1)(u
19
− 5u
18
+ ··· + 94u − 421)
c
8
((u − 1)
2
)(u
2
+ 1)
4
(u
12
+ 3u
11
+ ··· + 6u + 1)
· (u
19
+ 4u
18
+ ··· + 111u + 9)
c
9
(u
2
− u + 1)(u
4
− u
2
+ 1)
2
(u
12
− 3u
11
+ ··· + 4u − 1)
· (u
19
+ 2u
18
+ ··· + 197u + 34)
c
10
(u
2
+ u + 1)(u
8
+ 3u
6
− 2u
5
+ 4u
4
+ 7u
2
+ 2u + 1)
· (u
12
+ u
11
+ u
10
− u
9
− 2u
8
− 7u
7
− 3u
6
− 4u
5
+ 4u
4
− u
3
+ 3u
2
+ 1)
· (u
19
+ u
18
+ ··· + 706u + 167)
c
11
((u − 1)
2
)(u
2
+ 1)
4
(u
12
− 3u
11
+ ··· − 6u + 1)
· (u
19
+ 4u
18
+ ··· + 111u + 9)
c
12
(u
2
− u + 1)(u
2
+ u + 1)
4
(u
12
− 7u
11
+ ··· − 149u + 61)
· (u
19
+ 4u
18
+ ··· − 13967u − 14044)
22
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
10
)(y
12
− 70y
11
+ ··· − 18y + 1)
· (y
19
− 3221y
18
+ ··· + 5217004770233y −26376683281)
c
2
, c
5
((y −1)
10
)(y
12
− 10y
11
+ ··· + 2y + 1)
· (y
19
− 97y
18
+ ··· − 1941683y −162409)
c
3
(y
2
+ y + 1)(y
8
+ 2y
6
− 4y
5
− 21y
4
+ 20y
3
+ 42y
2
− 4y + 1)
· (y
12
− 3y
11
+ ··· − 6y + 1)(y
19
− 9y
18
+ ··· + 1588y −121)
c
4
(y
2
+ y + 1)(y
8
+ 2y
6
+ 4y
5
− 21y
4
− 20y
3
+ 42y
2
+ 4y + 1)
· (y
12
− 11y
11
+ ··· + 2725y + 3721)
· (y
19
− 193y
18
+ ··· + 27615258537y −4247259241)
c
6
, c
9
((y
2
− y + 1)
4
)(y
2
+ y + 1)(y
12
− 13y
11
+ ··· − 4y + 1)
· (y
19
− 54y
18
+ ··· + 33165y −1156)
c
7
(y
2
+ y + 1)(y
8
− 6y
7
+ ··· − 10y + 1)
· (y
12
− 19y
11
+ ··· − 16y + 1)(y
19
− 55y
18
+ ··· + 783476y −177241)
c
8
, c
11
((y −1)
2
)(y + 1)
8
(y
12
+ 3y
11
+ ··· − 20y + 1)
· (y
19
+ 8y
18
+ ··· + 4023y −81)
c
10
(y
2
+ y + 1)(y
8
+ 6y
7
+ ··· + 10y + 1)
· (y
12
+ y
11
+ ··· + 6y + 1)(y
19
+ y
18
+ ··· + 293694y −27889)
c
12
((y
2
+ y + 1)
5
)(y
12
− 33y
11
+ ··· − 22201y + 3721)
· (y
19
− 210y
18
+ ··· + 15988001y −197233936)
23
