12n
0136
(K12n
0136
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 11 4 10 12 7 8 5 9
Solving Sequence
7,10
8
4,11
3 6 5 12 2 1 9
c
7
c
10
c
3
c
6
c
5
c
11
c
2
c
1
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−8.90997 × 10
57
u
44
− 6.51627 × 10
58
u
43
+ ··· + 1.48622 × 10
59
b + 7.97191 × 10
58
,
1.29931 × 10
59
u
44
+ 1.18228 × 10
60
u
43
+ ··· + 5.94490 × 10
59
a − 4.97521 × 10
60
, u
45
+ 7u
44
+ ··· + 12u − 1i
I
u
2
= hb, 3u
7
+ 5u
6
− 7u
5
− 11u
4
+ 5u
3
+ 3u
2
+ a + 7, u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1i
I
u
3
= h5a
2
u − 3a
2
+ 12au + b − 7a + 3u − 1, a
3
− a
2
u + a
2
+ 3au + 6a + 3u + 5, u
2
+ u − 1i
I
u
4
= hb + a − 2, a
2
− 3a + 1, u − 1i
* 4 irreducible components of dim
C
= 0, with total 61 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
= h−8.91 × 10
57
u
44
− 6.52 × 10
58
u
43
+ · · · + 1.49 × 10
59
b + 7.97 ×
10
58
, 1.30 × 10
59
u
44
+ 1.18 × 10
60
u
43
+ · · · + 5.94 × 10
59
a − 4.98 ×
10
60
, u
45
+ 7u
44
+ · · · + 12u − 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
8
=
1
u
2
a
4
=
−0.218558u
44
− 1.98872u
43
+ ··· − 84.8505u + 8.36887
0.0599504u
44
+ 0.438445u
43
+ ··· − 0.981685u − 0.536386
a
11
=
−u
−u
3
+ u
a
3
=
−0.158608u
44
− 1.55028u
43
+ ··· − 85.8322u + 7.83248
0.0599504u
44
+ 0.438445u
43
+ ··· − 0.981685u − 0.536386
a
6
=
0.441060u
44
+ 3.11339u
43
+ ··· − 65.1681u + 7.22415
0.0840649u
44
+ 0.554982u
43
+ ··· − 0.887359u − 0.303624
a
5
=
0.519991u
44
+ 3.59140u
43
+ ··· − 64.5950u + 7.21939
0.0844612u
44
+ 0.574806u
43
+ ··· − 0.487423u − 0.373377
a
12
=
−0.131038u
44
− 0.902044u
43
+ ··· + 25.2448u − 3.79525
−0.0152230u
44
− 0.0901999u
43
+ ··· + 2.22280u + 0.131038
a
2
=
−0.365995u
44
− 2.97364u
43
+ ··· − 44.5369u + 4.24425
0.0844612u
44
+ 0.574806u
43
+ ··· − 0.487423u − 0.373377
a
1
=
0.0782668u
44
+ 0.573436u
43
+ ··· − 25.1426u + 3.79639
−0.0375483u
44
− 0.238408u
43
+ ··· − 2.12064u − 0.129900
a
9
=
u
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 10.5915u
44
+ 78.5347u
43
+ ··· − 186.556u + 9.63178
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
45
+ 10u
44
+ ··· + 930u + 1
c
2
, c
4
u
45
− 12u
44
+ ··· − 26u − 1
c
3
, c
6
u
45
− 4u
44
+ ··· − 640u − 256
c
5
, c
11
u
45
− 3u
44
+ ··· + 32u − 64
c
7
, c
9
, c
10
u
45
− 7u
44
+ ··· + 12u + 1
c
8
, c
12
u
45
+ 5u
44
+ ··· − 4u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
45
+ 62y
44
+ ··· + 852778y −1
c
2
, c
4
y
45
− 10y
44
+ ··· + 930y −1
c
3
, c
6
y
45
+ 54y
44
+ ··· + 4571136y −65536
c
5
, c
11
y
45
+ 33y
44
+ ··· + 234496y −4096
c
7
, c
9
, c
10
y
45
− 31y
44
+ ··· − 142y −1
c
8
, c
12
y
45
+ 3y
44
+ ··· + 1256y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.989081
a = 5.39659
b = −0.601818
−2.67208 −212.850
u = 0.952866 + 0.134525I
a = −4.15928 − 0.51646I
b = −0.377187 + 0.281972I
−2.91440 − 0.52040I −28.2057 − 17.3785I
u = 0.952866 − 0.134525I
a = −4.15928 + 0.51646I
b = −0.377187 − 0.281972I
−2.91440 + 0.52040I −28.2057 + 17.3785I
u = −1.04539
a = 0.313771
b = 1.54859
−10.6185 −59.2780
u = −0.367366 + 0.850305I
a = −0.393666 + 0.059604I
b = 1.16026 + 0.81675I
4.19700 − 1.34910I −7.72837 + 1.14036I
u = −0.367366 − 0.850305I
a = −0.393666 − 0.059604I
b = 1.16026 − 0.81675I
4.19700 + 1.34910I −7.72837 − 1.14036I
u = −0.626112 + 0.680342I
a = 1.12492 + 1.02026I
b = 0.00967 − 1.90333I
5.86522 − 1.45260I −9.17004 + 0.17720I
u = −0.626112 − 0.680342I
a = 1.12492 − 1.02026I
b = 0.00967 + 1.90333I
5.86522 + 1.45260I −9.17004 − 0.17720I
u = −0.952838 + 0.522259I
a = 0.132474 + 0.580825I
b = −0.51946 − 1.36700I
−0.90351 + 3.78658I −12.00000 − 4.56976I
u = −0.952838 − 0.522259I
a = 0.132474 − 0.580825I
b = −0.51946 + 1.36700I
−0.90351 − 3.78658I −12.00000 + 4.56976I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.007870 + 0.493819I
a = 0.985859 − 0.555848I
b = 0.560995 + 0.542777I
−0.360727 − 0.771902I −12.00000 + 0.I
u = 1.007870 − 0.493819I
a = 0.985859 + 0.555848I
b = 0.560995 − 0.542777I
−0.360727 + 0.771902I −12.00000 + 0.I
u = −0.973372 + 0.572106I
a = −1.06022 − 0.96272I
b = −0.62624 + 1.82528I
4.81861 + 6.30906I −12.00000 − 5.34980I
u = −0.973372 − 0.572106I
a = −1.06022 + 0.96272I
b = −0.62624 − 1.82528I
4.81861 − 6.30906I −12.00000 + 5.34980I
u = −0.668847 + 0.501935I
a = −1.094700 − 0.761183I
b = −1.200670 + 0.692757I
−0.018874 + 0.450301I −9.70033 − 2.11767I
u = −0.668847 − 0.501935I
a = −1.094700 + 0.761183I
b = −1.200670 − 0.692757I
−0.018874 − 0.450301I −9.70033 + 2.11767I
u = 0.781094 + 0.070241I
a = −0.13334 + 3.27365I
b = −0.197314 − 1.345870I
1.89233 − 2.90725I −43.5907 + 10.5695I
u = 0.781094 − 0.070241I
a = −0.13334 − 3.27365I
b = −0.197314 + 1.345870I
1.89233 + 2.90725I −43.5907 − 10.5695I
u = 0.068357 + 1.251150I
a = −0.00386 − 1.50825I
b = 0.59331 + 1.89133I
12.3107 − 8.8025I 0
u = 0.068357 − 1.251150I
a = −0.00386 + 1.50825I
b = 0.59331 − 1.89133I
12.3107 + 8.8025I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.139719 + 1.259590I
a = 0.22206 + 1.51967I
b = 0.04895 − 2.08421I
13.18790 − 0.68473I 0
u = −0.139719 − 1.259590I
a = 0.22206 − 1.51967I
b = 0.04895 + 2.08421I
13.18790 + 0.68473I 0
u = 0.306575 + 0.653371I
a = 0.163852 + 0.671962I
b = −0.009810 − 0.890868I
1.38833 − 3.58772I −7.79003 + 7.62926I
u = 0.306575 − 0.653371I
a = 0.163852 − 0.671962I
b = −0.009810 + 0.890868I
1.38833 + 3.58772I −7.79003 − 7.62926I
u = −1.141470 + 0.620472I
a = 0.459135 + 0.678243I
b = 1.58964 − 0.23048I
1.89448 + 6.79376I 0
u = −1.141470 − 0.620472I
a = 0.459135 − 0.678243I
b = 1.58964 + 0.23048I
1.89448 − 6.79376I 0
u = 1.300200 + 0.172788I
a = 0.174045 − 0.780639I
b = 0.189316 − 0.701955I
−1.23770 − 1.72442I 0
u = 1.300200 − 0.172788I
a = 0.174045 + 0.780639I
b = 0.189316 + 0.701955I
−1.23770 + 1.72442I 0
u = −1.353400 + 0.275389I
a = −0.297373 + 0.170909I
b = −0.179271 + 0.620523I
−3.67456 + 6.89597I 0
u = −1.353400 − 0.275389I
a = −0.297373 − 0.170909I
b = −0.179271 − 0.620523I
−3.67456 − 6.89597I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.532389
a = 10.6740
b = 0.157357
−2.53079 −190.200
u = −1.52798 + 0.15122I
a = 0.328835 + 0.021672I
b = −0.203375 − 1.016320I
−6.72932 + 1.63796I 0
u = −1.52798 − 0.15122I
a = 0.328835 − 0.021672I
b = −0.203375 + 1.016320I
−6.72932 − 1.63796I 0
u = −1.36799 + 0.70186I
a = −0.945282 − 0.712027I
b = −0.35731 + 1.99808I
9.42541 + 7.53688I 0
u = −1.36799 − 0.70186I
a = −0.945282 + 0.712027I
b = −0.35731 − 1.99808I
9.42541 − 7.53688I 0
u = −1.45214 + 0.59473I
a = 1.17477 + 0.82015I
b = 0.78255 − 1.69623I
7.5666 + 15.2974I 0
u = −1.45214 − 0.59473I
a = 1.17477 − 0.82015I
b = 0.78255 + 1.69623I
7.5666 − 15.2974I 0
u = 0.409223
a = 1.48110
b = −0.181306
−0.821501 −11.8740
u = 1.43589 + 0.72409I
a = −0.688447 + 0.406430I
b = 0.24206 − 1.91261I
8.18611 + 1.85592I 0
u = 1.43589 − 0.72409I
a = −0.688447 − 0.406430I
b = 0.24206 + 1.91261I
8.18611 − 1.85592I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.60934
a = 2.38137
b = 0.531548
−10.0523 0
u = 1.54148 + 0.58637I
a = 1.031150 − 0.470774I
b = 0.40058 + 1.86705I
7.92332 − 5.93163I 0
u = 1.54148 − 0.58637I
a = 1.031150 + 0.470774I
b = 0.40058 − 1.86705I
7.92332 + 5.93163I 0
u = 0.0389335 + 0.0746678I
a = 5.35565 − 7.42873I
b = −0.633876 + 0.017196I
−0.943845 + 0.013085I −9.49805 + 0.60913I
u = 0.0389335 − 0.0746678I
a = 5.35565 + 7.42873I
b = −0.633876 − 0.017196I
−0.943845 − 0.013085I −9.49805 − 0.60913I
9
II. I
u
2
=
hb, 3u
7
+5u
6
−7u
5
−11u
4
+5u
3
+3u
2
+a+7, u
8
+u
7
−3u
6
−2u
5
+3u
4
+2u−1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
8
=
1
u
2
a
4
=
−3u
7
− 5u
6
+ 7u
5
+ 11u
4
− 5u
3
− 3u
2
− 7
0
a
11
=
−u
−u
3
+ u
a
3
=
−3u
7
− 5u
6
+ 7u
5
+ 11u
4
− 5u
3
− 3u
2
− 7
0
a
6
=
1
0
a
5
=
−u
4
+ u
2
+ 1
−u
6
+ 2u
4
− u
2
a
12
=
−u
7
+ 2u
5
− 2u
−u
7
+ u
6
+ 2u
5
− 3u
4
+ 2u
2
− 2u + 1
a
2
=
−3u
7
− 5u
6
+ 7u
5
+ 12u
4
− 5u
3
− 4u
2
− 8
u
6
− 2u
4
+ u
2
a
1
=
u
4
− u
2
− 1
u
6
− 2u
4
+ u
2
a
9
=
u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 21u
7
+ 30u
6
− 48u
5
− 61u
4
+ 31u
3
+ 11u
2
+ 11u + 30
10
(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
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
8
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
9
, 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
11
(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
9
, c
10
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
c
8
, c
12
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.180120 + 0.268597I
a = 1.194470 + 0.635084I
b = 0
−2.68559 − 1.13123I −14.0862 + 1.5750I
u = 1.180120 − 0.268597I
a = 1.194470 − 0.635084I
b = 0
−2.68559 + 1.13123I −14.0862 − 1.5750I
u = 0.108090 + 0.747508I
a = 0.637416 + 0.344390I
b = 0
0.51448 − 2.57849I −10.94521 + 2.41352I
u = 0.108090 − 0.747508I
a = 0.637416 − 0.344390I
b = 0
0.51448 + 2.57849I −10.94521 − 2.41352I
u = −1.37100
a = −0.687555
b = 0
−8.14766 −19.2760
u = −1.334530 + 0.318930I
a = 0.286111 − 0.344558I
b = 0
−4.02461 + 6.44354I −18.3815 − 0.5907I
u = −1.334530 − 0.318930I
a = 0.286111 + 0.344558I
b = 0
−4.02461 − 6.44354I −18.3815 + 0.5907I
u = 0.463640
a = −7.54843
b = 0
−2.48997 37.1020
13
III. I
u
3
=
h5a
2
u−3a
2
+12au+b−7a+3u−1, a
3
−a
2
u+a
2
+3au+6a+3u+5, u
2
+u−1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
8
=
1
−u + 1
a
4
=
a
−5a
2
u + 3a
2
− 12au + 7a − 3u + 1
a
11
=
−u
−u + 1
a
3
=
−5a
2
u + 3a
2
− 12au + 8a − 3u + 1
−5a
2
u + 3a
2
− 12au + 7a − 3u + 1
a
6
=
−a
2
u + a
2
− 3au + 2a − u + 1
−2a
2
u + a
2
− 5au + 3a − 2u + 1
a
5
=
−a
2
u + a
2
− 3au + 2a − u + 1
−2a
2
u + a
2
− 5au + 3a − 2u + 1
a
12
=
−u
−u + 1
a
2
=
−3a
2
u + 2a
2
− 8au + 5a − 3u
−2a
2
u + a
2
− 5au + 3a − 2u + 1
a
1
=
−1
0
a
9
=
u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7a
2
u − 7a
2
+ 32au − 22a + 5u − 22
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
4
(u
3
− u
2
+ 1)
2
c
5
, c
11
u
6
c
6
(u
3
+ u
2
+ 2u + 1)
2
c
7
, c
8
(u
2
+ u − 1)
3
c
9
, c
10
, c
12
(u
2
− u − 1)
3
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
(y
3
− y
2
+ 2y −1)
2
c
5
, c
11
y
6
c
7
, c
8
, c
9
c
10
, c
12
(y
2
− 3y + 1)
3
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −0.832857
b = −0.569840
−2.10041 −18.9130
u = 0.618034
a = 0.22545 + 2.85986I
b = −0.215080 − 1.307140I
2.03717 − 2.82812I 2.32130 − 9.80499I
u = 0.618034
a = 0.22545 − 2.85986I
b = −0.215080 + 1.307140I
2.03717 + 2.82812I 2.32130 + 9.80499I
u = −1.61803
a = −0.255488 + 0.062996I
b = −0.215080 + 1.307140I
−5.85852 + 2.82812I −12.36452 − 4.05775I
u = −1.61803
a = −0.255488 − 0.062996I
b = −0.215080 − 1.307140I
−5.85852 − 2.82812I −12.36452 + 4.05775I
u = −1.61803
a = −2.10706
b = −0.569840
−9.99610 44.0000
17
IV. I
u
4
= hb + a − 2, a
2
− 3a + 1, u − 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
1
a
8
=
1
1
a
4
=
a
−a + 2
a
11
=
−1
0
a
3
=
2
−a + 2
a
6
=
a
a − 3
a
5
=
2a − 3
a − 3
a
12
=
3a − 8
3a − 8
a
2
=
a − 2
a − 3
a
1
=
3a − 8
3a − 8
a
9
=
1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 29
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
2
− 3u + 1
c
2
, c
3
u
2
+ u − 1
c
4
, c
6
u
2
− u − 1
c
5
u
2
+ 3u + 1
c
7
(u − 1)
2
c
8
, c
12
u
2
c
9
, c
10
(u + 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
11
y
2
− 7y + 1
c
2
, c
3
, c
4
c
6
y
2
− 3y + 1
c
7
, c
9
, c
10
(y −1)
2
c
8
, c
12
y
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.381966
b = 1.61803
−10.5276 29.0000
u = 1.00000
a = 2.61803
b = −0.618034
−2.63189 29.0000
21
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
8
)(u
2
− 3u + 1)(u
3
− u
2
+ 2u − 1)
2
(u
45
+ 10u
44
+ ··· + 930u + 1)
c
2
((u − 1)
8
)(u
2
+ u − 1)(u
3
+ u
2
− 1)
2
(u
45
− 12u
44
+ ··· − 26u − 1)
c
3
u
8
(u
2
+ u − 1)(u
3
− u
2
+ 2u − 1)
2
(u
45
− 4u
44
+ ··· − 640u − 256)
c
4
((u + 1)
8
)(u
2
− u − 1)(u
3
− u
2
+ 1)
2
(u
45
− 12u
44
+ ··· − 26u − 1)
c
5
u
6
(u
2
+ 3u + 1)(u
8
− 3u
7
+ ··· − 4u + 1)
· (u
45
− 3u
44
+ ··· + 32u − 64)
c
6
u
8
(u
2
− u − 1)(u
3
+ u
2
+ 2u + 1)
2
(u
45
− 4u
44
+ ··· − 640u − 256)
c
7
(u − 1)
2
(u
2
+ u − 1)
3
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
· (u
45
− 7u
44
+ ··· + 12u + 1)
c
8
u
2
(u
2
+ u − 1)
3
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
· (u
45
+ 5u
44
+ ··· − 4u − 4)
c
9
, c
10
(u + 1)
2
(u
2
− u − 1)
3
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
· (u
45
− 7u
44
+ ··· + 12u + 1)
c
11
u
6
(u
2
− 3u + 1)(u
8
+ 3u
7
+ ··· + 4u + 1)
· (u
45
− 3u
44
+ ··· + 32u − 64)
c
12
u
2
(u
2
− u − 1)
3
(u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1)
· (u
45
+ 5u
44
+ ··· − 4u − 4)
22
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
8
(y
2
− 7y + 1)(y
3
+ 3y
2
+ 2y −1)
2
· (y
45
+ 62y
44
+ ··· + 852778y −1)
c
2
, c
4
((y −1)
8
)(y
2
− 3y + 1)(y
3
− y
2
+ 2y −1)
2
(y
45
− 10y
44
+ ··· + 930y −1)
c
3
, c
6
y
8
(y
2
− 3y + 1)(y
3
+ 3y
2
+ 2y −1)
2
· (y
45
+ 54y
44
+ ··· + 4571136y −65536)
c
5
, c
11
y
6
(y
2
− 7y + 1)(y
8
+ 5y
7
+ ··· − 4y + 1)
· (y
45
+ 33y
44
+ ··· + 234496y −4096)
c
7
, c
9
, c
10
(y −1)
2
(y
2
− 3y + 1)
3
· (y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
45
− 31y
44
+ ··· − 142y −1)
c
8
, c
12
y
2
(y
2
− 3y + 1)
3
(y
8
− 3y
7
+ ··· − 4y + 1)
· (y
45
+ 3y
44
+ ··· + 1256y −16)
23
