12n
0135
(K12n
0135
)
A knot diagram
1
Linearized knot diagam
3 5 6 2 12 3 10 11 1 8 6 9
Solving Sequence
3,5
2
1,9
10 4 12 6 7 11 8
c
2
c
1
c
9
c
4
c
12
c
5
c
6
c
11
c
8
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h7.50785 × 10
65
u
51
+ 7.16783 × 10
66
u
50
+ ··· + 7.42713 × 10
65
b + 1.96991 × 10
66
,
5.02177 × 10
66
u
51
+ 4.81887 × 10
67
u
50
+ ··· + 1.48543 × 10
66
a + 4.88267 × 10
67
, u
52
+ 10u
51
+ ··· + 42u + 1i
I
u
2
= h3a
7
− a
6
− 4a
5
+ 3a
4
+ 6a
3
− 2a
2
+ b − 3a + 4, a
8
− a
7
− a
6
+ 2a
5
+ a
4
− 2a
3
+ 2a − 1, u − 1i
I
u
3
= h−u
4
− u
3
+ u
2
+ b + 2u + 1, u
5
+ u
4
− u
3
− u
2
+ a + u + 1, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 66 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
=
h7.51×10
65
u
51
+7.17×10
66
u
50
+· · ·+7.43×10
65
b+1.97×10
66
, 5.02×10
66
u
51
+
4.82 × 10
67
u
50
+ · · · + 1.49 × 10
66
a + 4.88 × 10
67
, u
52
+ 10u
51
+ · · · + 42u + 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
9
=
−3.38070u
51
− 32.4410u
50
+ ··· − 334.790u − 32.8705
−1.01087u
51
− 9.65087u
50
+ ··· − 83.4897u − 2.65231
a
10
=
−4.55808u
51
− 43.5756u
50
+ ··· − 423.069u − 35.6566
−0.649601u
51
− 6.17332u
50
+ ··· − 52.5054u − 1.87796
a
4
=
u
−u
3
+ u
a
12
=
−0.0984110u
51
− 0.192798u
50
+ ··· + 107.102u + 18.1612
−0.0523888u
51
− 0.301105u
50
+ ··· + 24.7289u + 0.984872
a
6
=
1.75053u
51
+ 16.1107u
50
+ ··· + 66.9644u − 4.72365
0.445418u
51
+ 4.10330u
50
+ ··· + 21.4257u + 0.355988
a
7
=
2.19594u
51
+ 20.2140u
50
+ ··· + 88.3901u − 4.36766
0.445418u
51
+ 4.10330u
50
+ ··· + 21.4257u + 0.355988
a
11
=
−0.520552u
51
− 4.34536u
50
+ ··· + 41.7074u + 19.0709
−0.0705558u
51
− 0.589302u
50
+ ··· + 8.55893u + 0.631584
a
8
=
0.281350u
51
+ 1.78079u
50
+ ··· − 103.579u − 19.6506
−0.196558u
51
− 1.93868u
50
+ ··· − 21.7903u − 0.947282
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.397552u
51
− 3.22353u
50
+ ··· + 24.0213u + 12.7608
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
52
+ 14u
51
+ ··· + 1402u + 1
c
2
, c
4
u
52
− 10u
51
+ ··· − 42u + 1
c
3
, c
6
u
52
+ 6u
51
+ ··· − 384u + 256
c
5
, c
11
u
52
+ 3u
51
+ ··· + 2u + 1
c
7
, c
8
, c
10
u
52
+ 8u
51
+ ··· + 5u + 1
c
9
, c
12
u
52
− 2u
51
+ ··· − 192u + 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
52
+ 58y
51
+ ··· − 1883250y + 1
c
2
, c
4
y
52
− 14y
51
+ ··· − 1402y + 1
c
3
, c
6
y
52
− 54y
51
+ ··· − 6144000y + 65536
c
5
, c
11
y
52
+ 11y
51
+ ··· − 2y + 1
c
7
, c
8
, c
10
y
52
− 56y
51
+ ··· − 11y + 1
c
9
, c
12
y
52
− 42y
51
+ ··· + 4096y + 4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.936589 + 0.362367I
a = −0.132979 + 0.482589I
b = 0.197306 + 0.774360I
−1.82480 − 1.05655I −2.50386 + 1.55405I
u = 0.936589 − 0.362367I
a = −0.132979 − 0.482589I
b = 0.197306 − 0.774360I
−1.82480 + 1.05655I −2.50386 − 1.55405I
u = 1.01183
a = −0.483216
b = 5.14944
−0.760272 181.970
u = −0.559950 + 0.773669I
a = −0.737013 + 0.263694I
b = −0.240844 + 0.206423I
2.51889 − 0.64898I 4.15765 − 0.18218I
u = −0.559950 − 0.773669I
a = −0.737013 − 0.263694I
b = −0.240844 − 0.206423I
2.51889 + 0.64898I 4.15765 + 0.18218I
u = 0.559290 + 0.772342I
a = −1.39670 + 1.62328I
b = 0.48402 + 1.50336I
0.23912 − 3.31860I 6.89920 + 8.86972I
u = 0.559290 − 0.772342I
a = −1.39670 − 1.62328I
b = 0.48402 − 1.50336I
0.23912 + 3.31860I 6.89920 − 8.86972I
u = 1.048670 + 0.109728I
a = −1.11061 − 1.03411I
b = −4.91550 + 0.99875I
−0.279878 − 0.575640I 9.6300 − 22.9731I
u = 1.048670 − 0.109728I
a = −1.11061 + 1.03411I
b = −4.91550 − 0.99875I
−0.279878 + 0.575640I 9.6300 + 22.9731I
u = −0.885811 + 0.275583I
a = −0.543684 − 0.920606I
b = −0.464994 − 0.146107I
0.98837 + 7.05447I 10.8678 − 11.9178I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.885811 − 0.275583I
a = −0.543684 + 0.920606I
b = −0.464994 + 0.146107I
0.98837 − 7.05447I 10.8678 + 11.9178I
u = 0.591648 + 0.563249I
a = −1.253030 + 0.325457I
b = 0.97832 + 1.31538I
8.16733 − 1.74753I 11.46085 − 2.28011I
u = 0.591648 − 0.563249I
a = −1.253030 − 0.325457I
b = 0.97832 − 1.31538I
8.16733 + 1.74753I 11.46085 + 2.28011I
u = 1.20718
a = 0.627019
b = −1.27287
6.40671 22.8380
u = −1.038340 + 0.632822I
a = 0.235533 − 0.357978I
b = −0.020097 − 0.228430I
1.02907 + 5.96168I 0
u = −1.038340 − 0.632822I
a = 0.235533 + 0.357978I
b = −0.020097 + 0.228430I
1.02907 − 5.96168I 0
u = 1.267370 + 0.221888I
a = 0.809757 + 0.387823I
b = 1.55628 + 0.73822I
−2.35126 − 1.18530I 0
u = 1.267370 − 0.221888I
a = 0.809757 − 0.387823I
b = 1.55628 − 0.73822I
−2.35126 + 1.18530I 0
u = −0.786110 + 1.048790I
a = −0.21713 − 1.56663I
b = 0.70420 − 1.92030I
14.7382 − 0.7846I 0
u = −0.786110 − 1.048790I
a = −0.21713 + 1.56663I
b = 0.70420 + 1.92030I
14.7382 + 0.7846I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.682528
a = 1.55752
b = 0.428312
5.57235 20.0660
u = −0.930489 + 0.946751I
a = 1.69913 + 0.93383I
b = 0.39846 + 1.91824I
6.81089 + 3.11557I 0
u = −0.930489 − 0.946751I
a = 1.69913 − 0.93383I
b = 0.39846 − 1.91824I
6.81089 − 3.11557I 0
u = −0.638336 + 0.175622I
a = 0.52839 + 1.50233I
b = 0.636738 + 0.330921I
−3.01505 + 2.93991I 8.02854 − 4.94099I
u = −0.638336 − 0.175622I
a = 0.52839 − 1.50233I
b = 0.636738 − 0.330921I
−3.01505 − 2.93991I 8.02854 + 4.94099I
u = −0.770546 + 1.105190I
a = −1.71258 − 1.50608I
b = −0.37064 − 2.04621I
7.28875 − 2.86108I 0
u = −0.770546 − 1.105190I
a = −1.71258 + 1.50608I
b = −0.37064 + 2.04621I
7.28875 + 2.86108I 0
u = −0.989587 + 0.918401I
a = 0.45156 + 1.89777I
b = −0.78553 + 2.38078I
6.62010 + 3.75962I 0
u = −0.989587 − 0.918401I
a = 0.45156 − 1.89777I
b = −0.78553 − 2.38078I
6.62010 − 3.75962I 0
u = −0.875232 + 1.046570I
a = 1.123190 − 0.374810I
b = 0.481797 − 0.298623I
9.30042 + 0.19617I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.875232 − 1.046570I
a = 1.123190 + 0.374810I
b = 0.481797 + 0.298623I
9.30042 − 0.19617I 0
u = 0.331898 + 0.536708I
a = 1.10257 − 1.85668I
b = −0.014867 − 1.287660I
2.07038 − 1.52953I 7.08674 + 4.40429I
u = 0.331898 − 0.536708I
a = 1.10257 + 1.85668I
b = −0.014867 + 1.287660I
2.07038 + 1.52953I 7.08674 − 4.40429I
u = −1.07831 + 0.92955I
a = −0.621833 + 0.528081I
b = −0.098379 + 0.481486I
8.63174 + 7.01563I 0
u = −1.07831 − 0.92955I
a = −0.621833 − 0.528081I
b = −0.098379 − 0.481486I
8.63174 − 7.01563I 0
u = −1.12261 + 0.87557I
a = −1.29753 − 0.66665I
b = −0.29203 − 1.83559I
13.6500 + 7.8231I 0
u = −1.12261 − 0.87557I
a = −1.29753 + 0.66665I
b = −0.29203 + 1.83559I
13.6500 − 7.8231I 0
u = 0.67896 + 1.25719I
a = 1.47889 − 1.24770I
b = 0.27488 − 1.48136I
7.15465 − 5.75608I 0
u = 0.67896 − 1.25719I
a = 1.47889 + 1.24770I
b = 0.27488 + 1.48136I
7.15465 + 5.75608I 0
u = −1.14863 + 0.89049I
a = −0.81470 − 1.85316I
b = 0.45931 − 2.66963I
6.05959 + 10.09710I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.14863 − 0.89049I
a = −0.81470 + 1.85316I
b = 0.45931 + 2.66963I
6.05959 − 10.09710I 0
u = −0.69380 + 1.36099I
a = 1.30611 + 1.75718I
b = 0.30103 + 2.05635I
15.0358 − 7.1240I 0
u = −0.69380 − 1.36099I
a = 1.30611 − 1.75718I
b = 0.30103 − 2.05635I
15.0358 + 7.1240I 0
u = −0.419666 + 0.131585I
a = −1.25630 + 1.76003I
b = −0.824846 + 0.597324I
0.61020 + 1.37415I 10.26914 − 1.41740I
u = −0.419666 − 0.131585I
a = −1.25630 − 1.76003I
b = −0.824846 − 0.597324I
0.61020 − 1.37415I 10.26914 + 1.41740I
u = −1.28851 + 0.90075I
a = 0.95078 + 1.61316I
b = −0.13690 + 2.61915I
13.0011 + 15.0944I 0
u = −1.28851 − 0.90075I
a = 0.95078 − 1.61316I
b = −0.13690 − 2.61915I
13.0011 − 15.0944I 0
u = 0.413751 + 0.078624I
a = 2.08417 − 1.70106I
b = −1.50990 + 0.03857I
0.524938 + 0.113527I 8.64384 − 0.42173I
u = 0.413751 − 0.078624I
a = 2.08417 + 1.70106I
b = −1.50990 − 0.03857I
0.524938 − 0.113527I 8.64384 + 0.42173I
u = 1.64301 + 0.52942I
a = −0.919697 − 0.977859I
b = −1.16522 − 1.43890I
3.67025 − 2.14792I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.64301 − 0.52942I
a = −0.919697 + 0.977859I
b = −1.16522 + 1.43890I
3.67025 + 2.14792I 0
u = −0.0269946
a = −24.2139
b = −0.570054
0.823260 12.0980
10
II. I
u
2
= h3a
7
− a
6
− 4a
5
+ 3a
4
+ 6a
3
− 2a
2
+ b − 3a + 4, a
8
− a
7
− a
6
+ 2a
5
+
a
4
− 2a
3
+ 2a − 1, u − 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
1
a
2
=
1
−1
a
1
=
0
−1
a
9
=
a
−3a
7
+ a
6
+ 4a
5
− 3a
4
− 6a
3
+ 2a
2
+ 3a − 4
a
10
=
a
−3a
7
+ a
6
+ 4a
5
− 3a
4
− 6a
3
+ 2a
2
+ 2a − 4
a
4
=
1
0
a
12
=
a
2
−2a
7
+ a
6
+ 3a
5
− 3a
4
− 4a
3
+ 3a
2
+ 2a − 4
a
6
=
a
4
0
a
7
=
a
4
0
a
11
=
a
6
+ a
2
−2a
7
+ a
6
+ 3a
5
− 3a
4
− 4a
3
+ 3a
2
+ 2a − 4
a
8
=
a
6
+ a
2
−2a
7
+ 3a
5
− a
4
− 4a
3
+ 2a − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −36a
7
+ 15a
6
+ 42a
5
− 45a
4
− 62a
3
+ 34a
2
+ 20a − 57
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
, c
6
u
8
c
4
(u + 1)
8
c
5
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
7
, c
8
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
c
9
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1
c
10
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
11
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
c
12
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
8
c
3
, c
6
y
8
c
5
, c
11
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
7
, c
8
, c
10
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
c
9
, c
12
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.570868 + 0.730671I
b = 1.80990 − 0.33963I
−0.604279 − 1.131230I 2.08624 + 1.57496I
u = 1.00000
a = 0.570868 − 0.730671I
b = 1.80990 + 0.33963I
−0.604279 + 1.131230I 2.08624 − 1.57496I
u = 1.00000
a = −0.855237 + 0.665892I
b = −1.043770 + 0.152194I
−3.80435 − 2.57849I −1.05479 + 2.41352I
u = 1.00000
a = −0.855237 − 0.665892I
b = −1.043770 − 0.152194I
−3.80435 + 2.57849I −1.05479 − 2.41352I
u = 1.00000
a = −1.09818
b = −0.155540
4.85780 7.27590
u = 1.00000
a = 1.031810 + 0.655470I
b = 0.759875 + 0.104398I
0.73474 + 6.44354I 6.38151 − 0.59069I
u = 1.00000
a = 1.031810 − 0.655470I
b = 0.759875 − 0.104398I
0.73474 − 6.44354I 6.38151 + 0.59069I
u = 1.00000
a = 0.603304
b = −2.89645
−0.799899 −49.1020
14
III. I
u
3
=
h−u
4
−u
3
+u
2
+b+2u+1, u
5
+u
4
−u
3
−u
2
+a+u+1, u
6
+u
5
−u
4
−2u
3
+u+1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
9
=
−u
5
− u
4
+ u
3
+ u
2
− u − 1
u
4
+ u
3
− u
2
− 2u − 1
a
10
=
−u
5
− u
4
+ u
3
+ u
2
− u − 1
u
4
+ u
3
− u
2
− 2u − 1
a
4
=
u
−u
3
+ u
a
12
=
−u
2
+ 1
−u
2
a
6
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
7
=
2u
5
− 3u
3
+ 2u
u
5
− u
3
+ u
a
11
=
−2u
5
+ 3u
3
− 2u
−u
5
+ u
3
− u
a
8
=
u
5
− u
4
− 2u
3
+ u
2
+ u − 1
u
5
+ u
4
− u
2
− u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
5
+ 7u
4
+ u
3
− 6u
2
− 5u + 11
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
2
, c
6
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
3
, c
4
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
7
, c
8
(u + 1)
6
c
9
, c
12
u
6
c
10
(u − 1)
6
c
11
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
11
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
2
, c
3
, c
4
c
6
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
7
, c
8
, c
10
(y −1)
6
c
9
, c
12
y
6
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = −1.00126 − 1.15863I
b = −2.68739 + 0.76772I
−0.245672 − 0.924305I 5.17126 + 7.13914I
u = 1.002190 − 0.295542I
a = −1.00126 + 1.15863I
b = −2.68739 − 0.76772I
−0.245672 + 0.924305I 5.17126 − 7.13914I
u = −0.428243 + 0.664531I
a = 0.001257 − 1.158630I
b = 0.346225 − 0.393823I
3.53554 − 0.92430I 13.12292 + 1.33143I
u = −0.428243 − 0.664531I
a = 0.001257 + 1.158630I
b = 0.346225 + 0.393823I
3.53554 + 0.92430I 13.12292 − 1.33143I
u = −1.073950 + 0.558752I
a = −0.500000 + 0.260139I
b = −0.658836 − 0.177500I
1.64493 + 5.69302I 11.70582 − 2.69056I
u = −1.073950 − 0.558752I
a = −0.500000 − 0.260139I
b = −0.658836 + 0.177500I
1.64493 − 5.69302I 11.70582 + 2.69056I
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
8
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
52
+ 14u
51
+ ··· + 1402u + 1)
c
2
((u − 1)
8
)(u
6
+ u
5
+ ··· + u + 1)(u
52
− 10u
51
+ ··· − 42u + 1)
c
3
u
8
(u
6
− u
5
+ ··· − u + 1)(u
52
+ 6u
51
+ ··· − 384u + 256)
c
4
((u + 1)
8
)(u
6
− u
5
+ ··· − u + 1)(u
52
− 10u
51
+ ··· − 42u + 1)
c
5
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
· (u
52
+ 3u
51
+ ··· + 2u + 1)
c
6
u
8
(u
6
+ u
5
+ ··· + u + 1)(u
52
+ 6u
51
+ ··· − 384u + 256)
c
7
, c
8
((u + 1)
6
)(u
8
− u
7
+ ··· − 2u − 1)(u
52
+ 8u
51
+ ··· + 5u + 1)
c
9
u
6
(u
8
+ u
7
+ ··· − 2u − 1)(u
52
− 2u
51
+ ··· − 192u + 64)
c
10
((u − 1)
6
)(u
8
+ u
7
+ ··· + 2u − 1)(u
52
+ 8u
51
+ ··· + 5u + 1)
c
11
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
· (u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
· (u
52
+ 3u
51
+ ··· + 2u + 1)
c
12
u
6
(u
8
− u
7
+ ··· + 2u − 1)(u
52
− 2u
51
+ ··· − 192u + 64)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
8
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
52
+ 58y
51
+ ··· − 1883250y + 1)
c
2
, c
4
(y −1)
8
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
52
− 14y
51
+ ··· − 1402y + 1)
c
3
, c
6
y
8
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
52
− 54y
51
+ ··· − 6144000y + 65536)
c
5
, c
11
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
· (y
52
+ 11y
51
+ ··· − 2y + 1)
c
7
, c
8
, c
10
(y −1)
6
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
52
− 56y
51
+ ··· − 11y + 1)
c
9
, c
12
y
6
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
52
− 42y
51
+ ··· + 4096y + 4096)
20
