11n
157
(K11n
157
)
1
Arc Sequences
6 7 1 11 8 9 4 2 1 8 7
Solving Sequence
2,7 3,9
6 1 4 8 11 5 10
c
2
c
6
c
1
c
3
c
8
c
11
c
4
c
10
c
5
, c
7
, c
9
Representation Ideals
I =
5
\
i=1
I
u
i
I
u
1
= hu
2
u + 1, a u, b ui
I
u
2
= hu
4
+ 3u
3
+ 5u
2
+ 6u + 4, u
3
+ u
2
+ 2b + u, 3u
3
+ 5u
2
+ 4a + 7u + 6i
I
u
3
= hu
9
u
8
+ 2u
7
2u
6
3u
5
+ 6u
4
9u
3
+ 12u
2
6u + 1, u
6
+ u
5
+ 4u
2
+ b 5u + 2,
2u
8
+ 2u
7
4u
6
+ 4u
5
+ 7u
4
12u
3
+ 18u
2
+ a 24u + 9i
I
u
4
= hu
15
+ 4u
13
u
12
+ 25u
11
2u
10
+ 32u
9
4u
8
17u
7
30u
6
22u
5
74u
4
+ 31u
3
58u
2
+ 21u 7,
705015011496u
14
+ 21480496654932u
13
+ ··· + 1172351061436163a 2457562853095546,
9995435080564u
14
11043230947933u
13
+ ··· + 167478723062309b 13448157975820i
I
u
5
= hu
28
+ 14u
26
+ ··· + 18426u + 5476,
5.01957 × 10
36
u
27
4.04248 × 10
36
u
26
+ ··· + 1.56844 × 10
40
b + 3.94962 × 10
40
,
2.99859 × 10
65
u
27
8.44978 × 10
65
u
26
+ ··· + 3.46519 × 10
69
a 1.04902 × 10
70
i
There are 5 irreducible components with 58 representations.
1
The knot diagram image is adapter from “C. Livingston and A. H. Moore, KnotInfo: Table of Knot
Invariants, http://www.indiana.edu/ knotinfo”
1
I. I
u
1
= hu
2
u + 1, a u, b ui
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u + 1
a
9
=
u
u
a
6
=
1
u 1
a
1
=
u
u
a
4
=
0
u
a
8
=
0
u
a
11
=
u
u 1
a
5
=
1
0
a
10
=
u
u
a
10
=
u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.500000 0.866025I
a = 0.500000 0.866025I
b = 0.500000 0.866025I
2.02988I 3.46410I
u = 0.500000 + 0.866025I
a = 0.500000 + 0.866025I
b = 0.500000 + 0.866025I
2.02988I 3.46410I
3
II. I
u
2
= hu
4
+ 3u
3
+ 5u
2
+ 6u + 4, u
3
+ u
2
+ 2b + u, 3u
3
+ 5u
2
+ 4a + 7u + 6i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
9
=
3
4
u
3
5
4
u
2
7
4
u
3
2
1
2
u
3
1
2
u
2
1
2
u
a
6
=
1
4
u
3
+
1
4
u
2
1
4
u +
1
2
1
2
u
3
+
3
2
u
2
+
5
2
u + 2
a
1
=
1
2
u
3
u
2
u
1
2
1
2
u
3
1
2
u
2
+
1
2
u + 1
a
4
=
1
4
u
3
+
3
4
u
2
+
5
4
u +
3
2
1
2
u
3
+
1
2
u
2
+
3
2
u
a
8
=
1
4
u
3
3
4
u
2
5
4
u
3
2
1
2
u
3
1
2
u
2
1
2
u
a
11
=
1
2
u
3
u
2
u
1
2
1
2
u
3
1
2
u
2
1
2
u 1
a
5
=
1
4
u
3
+
5
4
u
2
+
7
4
u + 2
1
a
10
=
3
4
u
3
5
4
u
2
7
4
u
3
2
1
2
u
3
1
2
u
2
1
2
u
a
10
=
3
4
u
3
5
4
u
2
7
4
u
3
2
1
2
u
3
1
2
u
2
1
2
u
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
4
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.30902 0.53523I
a = 0.154508 + 1.133642I
b = 0.500000 + 0.866025I
1.64493 + 2.02988I 11.00000 3.46410I
u = 1.30902 + 0.53523I
a = 0.154508 1.133642I
b = 0.500000 0.866025I
1.64493 2.02988I 11.00000 + 3.46410I
u = 0.19098 1.40126I
a = 0.404508 0.165396I
b = 0.500000 0.866025I
1.64493 2.02988I 11.00000 + 3.46410I
u = 0.19098 + 1.40126I
a = 0.404508 + 0.165396I
b = 0.500000 + 0.866025I
1.64493 + 2.02988I 11.00000 3.46410I
5
III.
I
u
3
= hu
9
u
8
+· · ·6u+1, u
6
+u
5
+4u
2
+b5u+2, 2u
8
+2u
7
+· · ·+a+9i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
9
=
2u
8
2u
7
+ 4u
6
4u
5
7u
4
+ 12u
3
18u
2
+ 24u 9
u
6
u
5
4u
2
+ 5u 2
a
6
=
3u
8
+ 2u
7
6u
6
+ 5u
5
+ 10u
4
15u
3
+ 24u
2
33u + 11
u
5
3u + 2
a
1
=
4u
8
2u
7
+ 7u
6
6u
5
14u
4
+ 17u
3
28u
2
+ 39u 11
u
8
+ u
6
u
5
3u
4
+ 3u
3
3u
2
+ 7u 3
a
4
=
4u
8
+ 2u
7
7u
6
+ 5u
5
+ 14u
4
17u
3
+ 28u
2
36u + 9
2u
8
+ 2u
7
4u
6
+ 3u
5
+ 7u
4
12u
3
+ 17u
2
21u + 6
a
8
=
2u
8
2u
7
+ 3u
6
3u
5
7u
4
+ 12u
3
14u
2
+ 19u 7
u
6
u
5
4u
2
+ 5u 2
a
11
=
4u
8
2u
7
+ 7u
6
6u
5
14u
4
+ 17u
3
28u
2
+ 39u 11
2u
8
2u
7
+ 3u
6
2u
5
7u
4
+ 12u
3
14u
2
+ 15u 5
a
5
=
3u
8
+ u
7
5u
6
+ 4u
5
+ 10u
4
11u
3
+ 19u
2
28u + 9
u
7
u
6
+ u
5
4u
3
+ 5u
2
5u + 2
a
10
=
9u
8
6u
7
+ 15u
6
12u
5
32u
4
+ 43u
3
63u
2
+ 81u 23
3u
8
2u
7
+ 5u
6
4u
5
10u
4
+ 15u
3
21u
2
+ 27u 9
a
10
=
9u
8
6u
7
+ 15u
6
12u
5
32u
4
+ 43u
3
63u
2
+ 81u 23
3u
8
2u
7
+ 5u
6
4u
5
10u
4
+ 15u
3
21u
2
+ 27u 9
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
6
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.49861
a = 0.709255
b = 0.409931
1.40144 6.42529
u = 0.140218 1.394344I
a = 0.408133 + 0.085067I
b = 1.34817 + 0.48943I
7.80162 + 4.26526I 1.95279 3.52841I
u = 0.140218 + 1.394344I
a = 0.408133 0.085067I
b = 1.34817 0.48943I
7.80162 4.26526I 1.95279 + 3.52841I
u = 0.057685 1.384416I
a = 0.575037 0.830974I
b = 0.436892 0.813735I
2.48959 + 5.91665I 4.21171 4.65114I
u = 0.057685 + 1.384416I
a = 0.575037 + 0.830974I
b = 0.436892 + 0.813735I
2.48959 5.91665I 4.21171 + 4.65114I
u = 0.358532 0.101992I
a = 2.16930 1.45078I
b = 0.681483 0.213018I
3.44968 2.27918I 6.79542 + 4.07405I
u = 0.358532 + 0.101992I
a = 2.16930 + 1.45078I
b = 0.681483 + 0.213018I
3.44968 + 2.27918I 6.79542 4.07405I
u = 1.088678 0.297442I
a = 0.507093 + 0.953533I
b = 1.43476 + 0.81752I
3.17057 5.55556I 0.67256 + 7.78739I
u = 1.088678 + 0.297442I
a = 0.507093 0.953533I
b = 1.43476 0.81752I
3.17057 + 5.55556I 0.67256 7.78739I
7
IV. I
u
4
=
hu
15
+4u
13
+· · ·+21u7, 7.05×10
11
u
14
+2.15×10
13
u
13
+· · ·+1.17×10
15
a
2.46 × 10
15
, 1.00× 10
13
u
14
1.10 × 10
13
u
13
+ · · · + 1.67 × 10
14
b 1.34 × 10
13
i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
9
=
0.000601369u
14
0.0183226u
13
+ ··· + 0.363672u + 2.09627
0.0596818u
14
+ 0.0659381u
13
+ ··· + 0.990024u + 0.0802977
a
6
=
0.0583968u
14
0.0286462u
13
+ ··· + 4.32472u 0.103278
0.0183226u
14
+ 0.00104759u
13
+ ··· + 2.10890u 0.00420958
a
1
=
0.138645u
14
+ 0.0313646u
13
+ ··· 4.01607u + 2.70126
0.0286462u
14
+ 0.0483285u
13
+ ··· 1.12306u + 0.408778
a
4
=
0.0230148u
14
0.00959664u
13
+ ··· 3.32322u + 2.57547
0.0746641u
14
0.0216522u
13
+ ··· 2.18976u + 0.583086
a
8
=
0.0602832u
14
0.0842607u
13
+ ··· 0.626352u + 2.01597
0.0596818u
14
+ 0.0659381u
13
+ ··· + 0.990024u + 0.0802977
a
11
=
0.138645u
14
+ 0.0313646u
13
+ ··· 4.01607u + 2.70126
0.0100475u
14
+ 0.00429470u
13
+ ··· 0.811199u + 0.628330
a
5
=
0.0258639u
14
+ 0.0965872u
13
+ ··· 1.04280u 0.318704
0.0842607u
14
0.0679409u
13
+ ··· 3.28192u + 0.421982
a
10
=
0.0410831u
14
0.0133149u
13
+ ··· 2.92428u + 1.95681
0.101151u
14
+ 0.0422182u
13
+ ··· 0.228012u + 0.00499091
a
10
=
0.0410831u
14
0.0133149u
13
+ ··· 2.92428u + 1.95681
0.101151u
14
+ 0.0422182u
13
+ ··· 0.228012u + 0.00499091
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
8
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.31355 1.77057I
a = 0.033661 + 0.718165I
b = 0.93488 + 1.38939I
9.9244 + 14.7471I 1.34191 7.45505I
u = 1.31355 + 1.77057I
a = 0.033661 0.718165I
b = 0.93488 1.38939I
9.9244 14.7471I 1.34191 + 7.45505I
u = 1.059474 0.476881I
a = 0.290050 + 0.928034I
b = 1.30681 + 0.98166I
3.80312 + 4.84275I 6.83327 2.97437I
u = 1.059474 + 0.476881I
a = 0.290050 0.928034I
b = 1.30681 0.98166I
3.80312 4.84275I 6.83327 + 2.97437I
u = 0.160948 1.159518I
a = 0.243839 + 0.501148I
b = 1.78504 + 1.61345I
8.37106 + 3.72407I 11.66592 + 1.71457I
u = 0.160948 + 1.159518I
a = 0.243839 0.501148I
b = 1.78504 1.61345I
8.37106 3.72407I 11.66592 1.71457I
u = 0.120487 1.111451I
a = 0.522638 0.439615I
b = 2.12055 0.94255I
7.32770 + 5.27705I 2.66781 10.56442I
u = 0.120487 + 1.111451I
a = 0.522638 + 0.439615I
b = 2.12055 + 0.94255I
7.32770 5.27705I 2.66781 + 10.56442I
u = 0.230855 0.312445I
a = 2.04624 0.45457I
b = 0.534282 0.103458I
1.29784 0.91531I 6.30482 + 3.51826I
u = 0.230855 + 0.312445I
a = 2.04624 + 0.45457I
b = 0.534282 + 0.103458I
1.29784 + 0.91531I 6.30482 3.51826I
9
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.255970 0.834952I
a = 0.622953 0.924798I
b = 0.498961 0.743813I
0.01045 1.91554I 0.97885 + 4.27627I
u = 0.255970 + 0.834952I
a = 0.622953 + 0.924798I
b = 0.498961 + 0.743813I
0.01045 + 1.91554I 0.97885 4.27627I
u = 1.19992
a = 0.720812
b = 0.387325
1.96166 8.66213
u = 1.32669 1.65838I
a = 0.006735 0.715845I
b = 1.01314 1.39683I
10.07795 6.40199I 2.27236 + 3.45803I
u = 1.32669 + 1.65838I
a = 0.006735 + 0.715845I
b = 1.01314 + 1.39683I
10.07795 + 6.40199I 2.27236 3.45803I
10
V. I
u
5
= hu
28
+ 14u
26
+ · · · + 18426u + 5476, 5.02 × 10
36
u
27
4.04 ×
10
36
u
26
+ · · · + 1.57 × 10
40
b + 3.95 × 10
40
, 3.00 × 10
65
u
27
8.45 ×
10
65
u
26
+ · · · + 3.47 × 10
69
a 1.05 × 10
70
i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
9
=
0.0000865347u
27
+ 0.000243848u
26
+ ··· + 12.9986u + 3.02731
0.000320036u
27
+ 0.000257739u
26
+ ··· 2.49496u 2.51818
a
6
=
0.000552994u
27
0.000211695u
26
+ ··· 19.3860u 3.96800
0.000317668u
27
0.0000988522u
26
+ ··· 9.44894u 2.62095
a
1
=
0.000765206u
27
+ 0.000561938u
26
+ ··· + 22.5005u + 5.61017
0.000119755u
27
+ 0.000543396u
26
+ ··· + 4.95131u 0.787025
a
4
=
0.000485730u
27
+ 0.000255671u
26
+ ··· 7.61338u 1.20376
0.000150061u
27
0.000223125u
26
+ ··· + 4.94912u + 2.49791
a
8
=
0.000406570u
27
0.0000138909u
26
+ ··· + 15.4935u + 5.54549
0.000320036u
27
+ 0.000257739u
26
+ ··· 2.49496u 2.51818
a
11
=
0.000765206u
27
+ 0.000561938u
26
+ ··· + 22.5005u + 5.61017
0.000539649u
27
+ 0.000294340u
26
+ ··· 9.59322u 3.86420
a
5
=
0.000129832u
27
+ 0.000444279u
26
+ ··· + 15.7055u + 5.37316
0.0000138909u
27
0.000324523u
26
+ ··· + 1.94597u + 2.22638
a
10
=
0.00139308u
27
+ 0.000180892u
26
+ ··· + 38.4666u + 11.5704
0.0000245249u
27
+ 0.000618076u
26
+ ··· 5.16046u 7.03883
a
10
=
0.00139308u
27
+ 0.000180892u
26
+ ··· + 38.4666u + 11.5704
0.0000245249u
27
+ 0.000618076u
26
+ ··· 5.16046u 7.03883
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
11
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 1.77266 2.05071I
a = 0.138959 0.331647I
b = 0.500000 0.866025I
8.81923 1.88726I 4.79602 0.46086I
u = 1.77266 + 2.05071I
a = 0.138959 + 0.331647I
b = 0.500000 + 0.866025I
8.81923 + 1.88726I 4.79602 + 0.46086I
u = 0.811855 1.095653I
a = 0.213521 + 0.456424I
b = 0.500000 + 0.866025I
3.77470 + 0.50896I 6.86344 + 1.65325I
u = 0.811855 + 1.095653I
a = 0.213521 0.456424I
b = 0.500000 0.866025I
3.77470 0.50896I 6.86344 1.65325I
u = 0.752580 0.010739I
a = 0.555002 + 0.130336I
b = 0.500000 + 0.866025I
1.98093 + 2.69340I 1.01907 5.70877I
u = 0.752580 + 0.010739I
a = 0.555002 0.130336I
b = 0.500000 0.866025I
1.98093 2.69340I 1.01907 + 5.70877I
u = 0.591280 1.032756I
a = 0.229127 1.370694I
b = 0.500000 0.866025I
3.77470 + 4.56872I 6.86344 5.27495I
u = 0.591280 + 1.032756I
a = 0.229127 + 1.370694I
b = 0.500000 + 0.866025I
3.77470 4.56872I 6.86344 + 5.27495I
u = 0.41461 1.65081I
a = 0.391859 + 0.480443I
b = 0.500000 + 0.866025I
3.77470 4.56872I 6.86344 + 5.27495I
u = 0.41461 + 1.65081I
a = 0.391859 0.480443I
b = 0.500000 0.866025I
3.77470 + 4.56872I 6.86344 5.27495I
12
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.237673 1.303805I
a = 1.180832 0.587848I
b = 0.500000 0.866025I
8.81923 1.88726I 4.79602 0.46086I
u = 0.237673 + 1.303805I
a = 1.180832 + 0.587848I
b = 0.500000 + 0.866025I
8.81923 + 1.88726I 4.79602 + 0.46086I
u = 0.226342 0.533560I
a = 0.01127 1.93571I
b = 0.500000 0.866025I
3.77470 0.50896I 6.86344 1.65325I
u = 0.226342 + 0.533560I
a = 0.01127 + 1.93571I
b = 0.500000 + 0.866025I
3.77470 + 0.50896I 6.86344 + 1.65325I
u = 0.036531 0.978489I
a = 1.064376 0.810726I
b = 0.500000 0.866025I
1.98093 + 6.75317I 1.01907 12.63698I
u = 0.036531 + 0.978489I
a = 1.064376 + 0.810726I
b = 0.500000 + 0.866025I
1.98093 6.75317I 1.01907 + 12.63698I
u = 0.05713 1.42849I
a = 1.076850 + 0.777199I
b = 0.500000 + 0.866025I
8.81923 5.94703I 4.79602 + 6.46734I
u = 0.05713 + 1.42849I
a = 1.076850 0.777199I
b = 0.500000 0.866025I
8.81923 + 5.94703I 4.79602 6.46734I
u = 0.322820 0.871129I
a = 0.071954 1.039530I
b = 0.500000 0.866025I
1.98093 2.69340I 1.01907 + 5.70877I
u = 0.322820 + 0.871129I
a = 0.071954 + 1.039530I
b = 0.500000 + 0.866025I
1.98093 + 2.69340I 1.01907 5.70877I
13
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.49371 1.78087I
a = 0.206143 + 0.803367I
b = 0.500000 + 0.866025I
1.98093 6.75317I 1.01907 + 12.63698I
u = 0.49371 + 1.78087I
a = 0.206143 0.803367I
b = 0.500000 0.866025I
1.98093 + 6.75317I 1.01907 12.63698I
u = 0.68290 1.66967I
a = 0.212638 0.163435I
b = 0.500000 0.866025I
1.18584 + 2.02988I 7.71921 3.46410I
u = 0.68290 + 1.66967I
a = 0.212638 + 0.163435I
b = 0.500000 + 0.866025I
1.18584 2.02988I 7.71921 + 3.46410I
u = 1.37110 0.48379I
a = 0.388137 + 1.179404I
b = 0.500000 + 0.866025I
1.18584 2.02988I 7.71921 + 3.46410I
u = 1.37110 + 0.48379I
a = 0.388137 1.179404I
b = 0.500000 0.866025I
1.18584 + 2.02988I 7.71921 3.46410I
u = 1.84280 1.98977I
a = 0.101525 + 0.290435I
b = 0.500000 + 0.866025I
8.81923 5.94703I 4.79602 + 6.46734I
u = 1.84280 + 1.98977I
a = 0.101525 0.290435I
b = 0.500000 0.866025I
8.81923 + 5.94703I 4.79602 6.46734I
14
VI. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
6
(u
2
u + 1)(u
4
+ u
3
+ 2u
2
u + 1)
(u
9
u
8
+ ··· + u
2
+ 1)(u
15
+ 2u
14
+ ··· + 3u + 1)
(u
28
3u
26
+ ··· + 15u + 7)
c
2
, c
5
(u
2
+ u + 1)(u
4
+ 3u
3
+ 5u
2
+ 6u + 4)
(u
9
u
8
+ 2u
7
2u
6
3u
5
+ 6u
4
9u
3
+ 12u
2
6u + 1)
(u
15
+ 4u
13
+ ··· + 21u + 7)(u
28
+ 14u
26
+ ··· 18426u + 5476)
c
3
, c
10
(u
2
+ u + 1)
3
(u
9
+ 4u
8
+ ··· + 2u + 1)
(u
15
u
14
+ ··· + 9u + 1)(u
28
+ 3u
27
+ ··· + 702u + 189)
c
4
, c
11
(u
2
+ u + 1)(u
4
+ u
3
+ 2u
2
u + 1)
(u
9
+ 4u
7
+ ··· + 4u + 1)(u
15
u
14
+ ··· + 3u 1)
(u
28
+ 15u
26
+ ··· + 1651u + 211)
c
7
u
2
(u 1)
4
(u
7
2u
6
+ 2u
5
+ u
4
2u
3
+ 3u
2
2u + 1)
4
(u
9
+ 4u
8
+ 6u
7
+ 2u
6
6u
5
9u
4
9u
3
9u
2
4u 1)
(u
15
+ 9u
14
+ ··· + 89u + 13)
c
8
(u
2
u + 1)
14
(u
2
+ u + 1)
3
(u
9
2u
8
u
7
+ 6u
6
2u
5
6u
4
+ 9u
3
4u
2
u + 1)
(u
15
+ 16u
14
+ ··· 384u 64)
c
9
u
6
(u
7
3u
6
+ 3u
5
+ 2u
4
6u
3
+ 3u
2
+ 3u 2)
4
(u
9
5u
8
+ 7u
7
+ 10u
6
43u
5
+ 40u
4
+ 32u
3
101u
2
+ 85u 25)
(u
15
+ 18u
14
+ ··· + 166u + 13)
15
VII. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
6
(y
2
+ y + 1)(y
4
+ 3y
3
+ 8y
2
+ 3y + 1)
(y
9
3y
8
+ 9y
7
15y
6
+ 19y
5
19y
4
+ 9y
3
+ y
2
2y 1)
(y
15
2y
14
+ ··· + 3y 1)(y
28
6y
27
+ ··· 1233y + 49)
c
2
, c
5
(y
2
+ y + 1)(y
4
+ y
3
3y
2
+ 4y + 16)
(y
9
+ 3y
8
6y
7
22y
6
+ 9y
5
+ 44y
4
23y
3
48y
2
+ 12y 1)
(y
15
+ 8y
14
+ ··· 371y 49)
(y
28
+ 28y
27
+ ··· + 251529108y + 29986576)
c
3
, c
10
(y
2
+ y + 1)
3
(y
9
8y
8
+ 28y
7
55y
6
+ 84y
5
74y
4
+ 43y
3
+ 7y
2
6y 1)
(y
15
23y
14
+ ··· + 143y 1)(y
28
31y
27
+ ··· + 442746y + 35721)
c
4
, c
11
(y
2
+ y + 1)(y
4
+ 3y
3
+ 8y
2
+ 3y + 1)
(y
9
+ 8y
8
+ 32y
7
+ 84y
6
+ 152y
5
+ 176y
4
+ 124y
3
+ 47y
2
+ 6y 1)
(y
15
+ 17y
14
+ ··· 9y 1)(y
28
+ 30y
27
+ ··· 141473y + 44521)
c
7
y
2
(y 1)
4
(y
7
+ 4y
5
y
4
6y
3
3y
2
2y 1)
4
(y
9
4y
8
+ 8y
7
22y
6
+ 28y
5
+ 23y
4
29y
3
27y
2
2y 1)
(y
15
3y
14
+ ··· 633y 169)
c
8
(y
2
+ y + 1)
17
(y
9
6y
8
+ 21y
7
38y
6
+ 40y
5
18y
4
+ 25y
3
22y
2
+ 9y 1)
(y
15
6y
14
+ ··· + 49152y 4096)
c
9
y
6
(y
7
3y
6
+ 9y
5
16y
4
+ 30y
3
37y
2
+ 21y 4)
4
(y
9
11y
8
+ ··· + 2175y 625)(y
15
14y
14
+ ··· + 1972y 169)
16