11n
75
(K11n
75
)
1
Arc Sequences
4 1 8 2 11 9 4 10 7 1 6
Solving Sequence
1,4 2,8
3
6,7
11 5 10 9
c
1
c
3
c
7
c
11
c
5
c
10
c
9
c
2
, c
4
, c
6
, c
8
Representation Ideals
I =
8
\
i=1
I
u
i
\
I
v
1
1
The knot diagram image is adapter from “C. Livingston and A. H. Mo ore, KnotInfo: Table of Knot
Invariants, http://www.indiana.edu/ knotinfo”
1
I
u
1
= hc, b 1, u 1, da 1i
I
u
2
= ha, c, b 1, d 1, u 1i
I
u
3
= ha, b u, c + u, u
3
u
2
+ 1, u
2
+ d + u 1i
I
u
4
= ha, b u, u
4
u
2
+ c + u 1, u
6
+ u
5
2u
4
+ 2u
2
2u 1, 2u
5
u
4
3u
3
+ 4u
2
+ d u 2i
I
u
5
= hb, c, d 1, u 1, a + 1i
I
u
6
= hb
10
b
9
b
8
+ 3b
7
2b
5
+ b
4
+ 4b
3
3b
2
4b + 4,
4b
9
3b
8
+ 12b
6
+ 3b
5
12b
4
+ b
3
+ 21b
2
+ 19d 2b 7,
49b
9
+ 51b
8
+ 19b
7
109b
6
+ 6b
5
+ 14b
4
17b
3
186b
2
+ 91b + 76a + 62,
37b
9
+ 23b
8
+ 19b
7
73b
6
42b
5
+ 54b
4
33b
3
142b
2
+ 76c + 47b + 98,
21b
9
11b
8
19b
7
+ 25b
6
+ 30b
5
6b
4
47b
3
+ 58b
2
+ 37b + 76u 70i
I
u
7
= h−u
5
+ 2u
3
u
2
+ b + 1, u
4
u
2
+ c + u 1, u
6
+ u
5
2u
4
+ 2u
2
2u 1,
u
5
+ u
4
+ 2u
3
2u
2
+ a + 2u + 2, 2u
5
u
4
3u
3
+ 4u
2
+ d u 2i
I
u
8
= hu
13
+ 2u
12
5u
11
10u
10
+ 9u
9
+ 14u
8
10u
7
+ u
6
+ 14u
5
8u
4
13u
3
3u
2
+ 8u + 4,
153u
12
+ 312u
11
+ ··· + 1228a + 972, 41u
12
+ 204u
11
+ ··· + 1228b + 730,
357u
12
728u
11
+ ··· + 2456c 1654, 503u
12
496u
11
+ ··· + 1228d 2726i
I
v
1
= ha, d, v 1, c + 1, b + 1i
There are 9 irreducible components with 41 representations.
There are 1 irreducible components of dim
C
= 1 for 11n
75
2
I. I
u
1
= hc, b 1, u 1, da 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
8
=
0
d
a
3
=
0
1
a
6
=
a
1
a
7
=
0
d
a
11
=
a + 1
1
a
5
=
1
0
a
10
=
a
1
a
9
=
a
d + 1
a
9
=
a
d + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
3
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = ···
a = ···
b = ···
c = ···
d = ···
1.64493 9.85070 + 0.18976I
4
II. I
u
2
= ha, c, b 1, d 1, u 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
8
=
0
1
a
3
=
0
1
a
6
=
0
1
a
7
=
0
1
a
11
=
1
1
a
5
=
1
0
a
10
=
0
1
a
9
=
0
1
a
9
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
5
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.00000
a = 0
b = 1.00000
c = 0
d = 1.00000
0 0
6
III. I
u
3
= ha, b u, c + u, u
3
u
2
+ 1, u
2
+ d + u 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
8
=
u
u
2
u + 1
a
3
=
u
2
+ 1
u
2
a
6
=
0
u
a
7
=
u
u + 2
a
11
=
1
u
2
a
5
=
u
u
2
+ u + 1
a
10
=
u
2
+ 1
u
2
a
9
=
1
2u
2
2u
a
9
=
1
2u
2
2u
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
7
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.754878
a = 0
b = 0.754878
c = 0.754878
d = 2.32472
1.11345 9.01951
u = 0.877439 0.744862I
a = 0
b = 0.877439 0.744862I
c = 0.877439 + 0.744862I
d = 0.337641 0.562280I
3.02413 2.82812I 2.49024 + 2.97945I
u = 0.877439 + 0.744862I
a = 0
b = 0.877439 + 0.744862I
c = 0.877439 0.744862I
d = 0.337641 + 0.562280I
3.02413 + 2.82812I 2.49024 2.97945I
8
IV.
I
u
4
= ha, bu, u
4
u
2
+c +u 1, u
6
+u
5
+· · ·2u 1, 2u
5
u
4
+· · ·+d 2i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
8
=
u
4
+ u
2
u + 1
2u
5
+ u
4
+ 3u
3
4u
2
+ u + 2
a
3
=
u
2
+ 1
u
2
a
6
=
0
u
a
7
=
u
4
+ u
2
u + 1
u
5
+ 2u
3
u
2
u + 1
a
11
=
1
u
2
a
5
=
u
u
3
+ u
a
10
=
u
2
+ 1
u
2
a
9
=
u
5
+ 2u
3
2u
2
u + 2
1
a
9
=
u
5
+ 2u
3
2u
2
u + 2
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
9
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.47043 0.10268I
a = 0
b = 1.47043 0.10268I
c = 0.083785 0.894804I
d = 0.14251 + 2.74752I
3.02413 2.82812I 2.49024 + 2.97945I
u = 1.47043 + 0.10268I
a = 0
b = 1.47043 + 0.10268I
c = 0.083785 + 0.894804I
d = 0.14251 2.74752I
3.02413 + 2.82812I 2.49024 2.97945I
u = 0.379278
a = 0
b = 0.379278
c = 1.50244
d = 0.918028
1.11345 9.01951
u = 0.592989 0.847544I
a = 0
b = 0.592989 0.847544I
c = 0.916215 0.894804I
d = 0.235028 + 0.695513I
3.02413 + 2.82812I 2.49024 2.97945I
u = 0.592989 + 0.847544I
a = 0
b = 0.592989 + 0.847544I
c = 0.916215 + 0.894804I
d = 0.235028 0.695513I
3.02413 2.82812I 2.49024 + 2.97945I
u = 1.13416
a = 0
b = 1.13416
c = 0.502436
d = 0.267010
1.11345 9.01951
10
V. I
u
5
= hb, c, d 1, u 1, a + 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
8
=
0
1
a
3
=
0
1
a
6
=
1
0
a
7
=
0
1
a
11
=
1
0
a
5
=
1
0
a
10
=
1
0
a
9
=
1
1
a
9
=
1
1
(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 = 1.00000
a = 1.00000
b = 0
c = 0
d = 1.00000
0 0
12
VI. I
u
6
= hb
10
b
9
+ · · · 4b + 4, 4b
9
+ 19d + · · · 2b 7, 49b
9
+ 51b
8
+
· · · + 76a + 62, 37b
9
+ 76c + · · · + 47b + 98, 21b
9
+ 76u + · · · + 37b 70i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
0.276316b
9
+ 0.144737b
8
+ ··· 0.486842b + 0.921053
a
2
=
1
0.131579b
9
+ 0.0263158b
8
+ ··· + 0.184211b 0.105263
a
8
=
0.486842b
9
0.302632b
8
+ ··· 0.618421b 1.28947
0.210526b
9
+ 0.157895b
8
+ ··· + 0.105263b + 0.368421
a
3
=
0.131579b
9
0.0263158b
8
+ ··· 0.184211b + 1.10526
0.131579b
9
+ 0.0263158b
8
+ ··· + 0.184211b 0.105263
a
6
=
0.644737b
9
0.671053b
8
+ ··· 1.19737b 0.815789
b
a
7
=
0.486842b
9
0.302632b
8
+ ··· 0.618421b 1.28947
0.276316b
9
+ 0.144737b
8
+ ··· 0.486842b + 0.921053
a
11
=
0.0263158b
9
+ 0.394737b
8
+ ··· + 1.76316b 1.57895
b
2
a
5
=
0.276316b
9
0.144737b
8
+ ··· + 0.486842b 0.921053
b
3
+ b
a
10
=
0.0263158b
9
+ 0.394737b
8
+ ··· + 1.76316b 1.57895
b
2
a
9
=
0.434211b
9
+ 0.486842b
8
+ ··· + 1.90789b 3.44737
1
a
9
=
0.434211b
9
+ 0.486842b
8
+ ··· + 1.90789b 3.44737
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
13
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 0.331409 + 0.386277I
a = 3.38443 0.78229I
b = 1.184729 0.098919I
c = 0.76001 1.23514I
d = 0.014754 + 0.532228I
2.91669 1.13882I 7.28192 + 6.05450I
u = 0.331409 0.386277I
a = 3.38443 + 0.78229I
b = 1.184729 + 0.098919I
c = 0.76001 + 1.23514I
d = 0.014754 0.532228I
2.91669 + 1.13882I 7.28192 6.05450I
u = 1.49784
a = 0.53688 1.32884I
b = 0.748922 0.826228I
c = 0.911163
d = 0.546383
5.22495 1.71424
u = 1.49784
a = 0.53688 + 1.32884I
b = 0.748922 + 0.826228I
c = 0.911163
d = 0.546383
5.22495 1.71424
u = 1.58033 + 0.28256I
a = 0.539372 0.945885I
b = 0.443519 1.107389I
c = 0.195567 1.002697I
d = 0.21205 + 2.53203I
10.17382 + 6.99719I 0.86096 3.54683I
u = 1.58033 0.28256I
a = 0.539372 + 0.945885I
b = 0.443519 + 1.107389I
c = 0.195567 + 1.002697I
d = 0.21205 2.53203I
10.17382 6.99719I 0.86096 + 3.54683I
14
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 0.331409 + 0.386277I
a = 0.397099 1.351198I
b = 0.853320 0.287358I
c = 0.76001 1.23514I
d = 0.014754 + 0.532228I
2.91669 1.13882I 7.28192 + 6.05450I
u = 0.331409 0.386277I
a = 0.397099 + 1.351198I
b = 0.853320 + 0.287358I
c = 0.76001 + 1.23514I
d = 0.014754 0.532228I
2.91669 + 1.13882I 7.28192 6.05450I
u = 1.58033 0.28256I
a = 0.01017 1.44676I
b = 1.136812 0.824833I
c = 0.195567 + 1.002697I
d = 0.21205 2.53203I
10.17382 6.99719I 0.86096 + 3.54683I
u = 1.58033 + 0.28256I
a = 0.01017 + 1.44676I
b = 1.136812 + 0.824833I
c = 0.195567 1.002697I
d = 0.21205 + 2.53203I
10.17382 + 6.99719I 0.86096 3.54683I
15
VII. I
u
7
= h−u
5
+ 2u
3
u
2
+ b + 1, u
4
u
2
+ c + u 1, u
6
+ u
5
+ · · ·
2u 1, u
5
+ u
4
+ · · · + a + 2, 2u
5
u
4
+ · · · + d 2i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
8
=
u
4
+ u
2
u + 1
2u
5
+ u
4
+ 3u
3
4u
2
+ u + 2
a
3
=
u
2
+ 1
u
2
a
6
=
u
5
u
4
2u
3
+ 2u
2
2u 2
u
5
2u
3
+ u
2
1
a
7
=
u
4
+ u
2
u + 1
u
5
+ 2u
3
u
2
u + 1
a
11
=
u
5
+ 2u
2
u + 1
u
5
u
3
+ u
2
u
a
5
=
u
u
3
+ u
a
10
=
u
3
+ u
2
+ 1
u
5
u
3
+ u
2
u
a
9
=
u
5
+ 2u
2
u + 1
1
a
9
=
u
5
+ 2u
2
u + 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
16
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
7
1(vol +
1CS) Cusp shape
u = 1.47043 0.10268I
a = 0.43165 1.53698I
b = 0.877439 0.744862I
c = 0.083785 0.894804I
d = 0.14251 + 2.74752I
3.02413 2.82812I 2.49024 + 2.97945I
u = 1.47043 + 0.10268I
a = 0.43165 + 1.53698I
b = 0.877439 + 0.744862I
c = 0.083785 + 0.894804I
d = 0.14251 2.74752I
3.02413 + 2.82812I 2.49024 2.97945I
u = 0.379278
a = 0.873164
b = 0.754878
c = 1.50244
d = 0.918028
1.11345 9.01951
u = 0.592989 0.847544I
a = 0.799335 + 0.697602I
b = 0.877439 + 0.744862I
c = 0.916215 0.894804I
d = 0.235028 + 0.695513I
3.02413 + 2.82812I 2.49024 2.97945I
u = 0.592989 + 0.847544I
a = 0.799335 0.697602I
b = 0.877439 0.744862I
c = 0.916215 + 0.894804I
d = 0.235028 0.695513I
3.02413 2.82812I 2.49024 + 2.97945I
u = 1.13416
a = 4.39147
b = 0.754878
c = 0.502436
d = 0.267010
1.11345 9.01951
17
VIII. I
u
8
= hu
13
+ 2u
12
+ · · · + 8u + 4, 153u
12
+ 312u
11
+ · · · + 1228a +
972, 41u
12
+ 204u
11
+ · · · + 1228b + 730, 357u
12
728u
11
+ · · · + 2456c
1654, 503u
12
496u
11
+ · · · + 1228d 2726i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
8
=
0.145358u
12
+ 0.296417u
11
+ ··· 0.230049u + 0.673453
0.409609u
12
+ 0.403909u
11
+ ··· + 1.54642u + 2.21987
a
3
=
u
2
+ 1
u
2
a
6
=
0.124593u
12
0.254072u
11
+ ··· 1.01710u 0.791531
0.0333876u
12
0.166124u
11
+ ··· + 0.652280u 0.594463
a
7
=
0.145358u
12
+ 0.296417u
11
+ ··· 0.230049u + 0.673453
0.341205u
12
+ 0.587948u
11
+ ··· + 0.919381u + 2.19707
a
11
=
0.153502u
12
+ 0.214984u
11
+ ··· + 0.427932u + 1.34283
0.0993485u
12
+ 0.00651466u
11
+ ··· + 0.327362u + 0.866450
a
5
=
u
u
3
+ u
a
10
=
0.0541531u
12
+ 0.208469u
11
+ ··· + 0.100570u + 0.476384
0.0993485u
12
+ 0.00651466u
11
+ ··· + 0.327362u + 0.866450
a
9
=
0.307003u
12
+ 0.429967u
11
+ ··· + 0.355863u + 1.18567
0.302117u
12
+ 0.478827u
11
+ ··· + 1.06107u + 2.18404
a
9
=
0.307003u
12
+ 0.429967u
11
+ ··· + 0.355863u + 1.18567
0.302117u
12
+ 0.478827u
11
+ ··· + 1.06107u + 2.18404
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
18
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
8
1(vol +
1CS) Cusp shape
u = 1.62942 0.13680I
a = 0.459802 + 1.068801I
b = 0.647958 + 1.070916I
c = 0.092664 1.014196I
d = 0.10115 + 2.58338I
11.70801 0.17366I 0.445368 1.147630I
u = 1.62942 + 0.13680I
a = 0.459802 1.068801I
b = 0.647958 1.070916I
c = 0.092664 + 1.014196I
d = 0.10115 2.58338I
11.70801 + 0.17366I 0.445368 + 1.147630I
u = 1.52223 0.38307I
a = 0.18408 1.52689I
b = 1.23485 0.73165I
c = 0.272209 0.989206I
d = 0.29226 + 2.46933I
7.6949 13.5931I 3.46569 + 7.45820I
u = 1.52223 + 0.38307I
a = 0.18408 + 1.52689I
b = 1.23485 + 0.73165I
c = 0.272209 + 0.989206I
d = 0.29226 2.46933I
7.6949 + 13.5931I 3.46569 7.45820I
u = 0.507731
a = 0.233445
b = 0.644275
c = 1.20906
d = 1.24703
1.13096 8.32650
u = 0.417771 0.584495I
a = 0.735190 + 0.985787I
b = 0.865536 + 0.462701I
c = 1.037440 + 0.827455I
d = 0.560607 1.010537I
1.87851 3.16005I 8.32269 + 6.37622I
19
Solution to I
u
8
1(vol +
1CS) Cusp shape
u = 0.417771 + 0.584495I
a = 0.735190 0.985787I
b = 0.865536 0.462701I
c = 1.037440 0.827455I
d = 0.560607 + 1.010537I
1.87851 + 3.16005I 8.32269 6.37622I
u = 0.394341 0.970918I
a = 0.953053 + 0.652165I
b = 1.083705 + 0.709645I
c = 0.972271 + 0.953967I
d = 0.181829 0.820202I
1.53986 + 8.66555I 5.43123 7.16460I
u = 0.394341 + 0.970918I
a = 0.953053 0.652165I
b = 1.083705 0.709645I
c = 0.972271 0.953967I
d = 0.181829 + 0.820202I
1.53986 8.66555I 5.43123 + 7.16460I
u = 0.927403 0.247855I
a = 0.717635 + 0.462960I
b = 0.218164 + 0.376758I
c = 0.471078 0.548552I
d = 0.194640 + 0.299494I
1.70980 + 0.77307I 3.13297 1.88722I
u = 0.927403 + 0.247855I
a = 0.717635 0.462960I
b = 0.218164 0.376758I
c = 0.471078 + 0.548552I
d = 0.194640 0.299494I
1.70980 0.77307I 3.13297 + 1.88722I
u = 1.50155 0.18625I
a = 0.22350 1.56562I
b = 0.997004 0.758703I
c = 0.930768 + 0.143752I
d = 0.556488 0.114153I
4.46546 + 5.94244I 3.19547 4.81410I
Solution to I
u
8
1(vol +
1CS) Cusp shape
u = 1.50155 + 0.18625I
a = 0.22350 + 1.56562I
b = 0.997004 + 0.758703I
c = 0.930768 0.143752I
d = 0.556488 + 0.114153I
4.46546 5.94244I 3.19547 + 4.81410I
20
IX. I
v
1
= ha, d, v 1, c + 1, b + 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
1
0
a
2
=
1
0
a
8
=
1
0
a
3
=
1
0
a
6
=
0
1
a
7
=
1
0
a
11
=
1
1
a
5
=
1
0
a
10
=
0
1
a
9
=
1
1
a
9
=
1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
21
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
1
1(vol +
1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
c = 1.00000
d = 0
3.28987 12.0000
22
X. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
4
u(u 1)
2
(u
3
u
2
+ 1)(u
5
+ u
4
3u
3
2u
2
+ 2u 1)
2
(1 2u + 2u
2
2u
4
+ u
5
+ u
6
)
2
(u
13
+ 2u
12
+ ··· + 8u + 4)
c
2
u(u + 1)
2
(u
3
+ u
2
+ 2u + 1)(u
5
+ 7u
4
+ 17u
3
+ 14u
2
+ 1)
2
(1 + 8u + 8u
2
+ 6u
3
+ 8u
4
+ 5u
5
+ u
6
)
2
(u
13
+ 14u
12
+ ··· + 88u + 16)
c
3
, c
7
u
3
(u
3
+ u
2
+ 2u + 1)
5
(u
5
3u
4
+ 6u
3
7u
2
+ 4u 2)
2
(u
13
+ 2u
12
+ ··· 4u
2
+ 8)
c
5
u(u 1)(u + 1)(u
3
+ u
2
1)
3
(u
6
u
5
2u
4
+ 2u
2
+ 2u 1)
(u
10
+ u
9
u
8
3u
7
+ 2u
5
+ u
4
4u
3
3u
2
+ 4u + 4)
(u
13
+ 2u
12
4u
10
+ 8u
8
+ 7u
7
7u
6
8u
5
+ 3u
4
+ 9u
3
u
2
u 1)
c
6
, c
11
u(u + 1)
2
(u
3
+ u
2
1)
3
(u
6
u
5
2u
4
+ 2u
2
+ 2u 1)
(u
10
+ u
9
u
8
3u
7
+ 2u
5
+ u
4
4u
3
3u
2
+ 4u + 4)
(u
13
+ 2u
12
4u
10
+ 8u
8
+ 7u
7
7u
6
8u
5
+ 3u
4
+ 9u
3
u
2
u 1)
c
8
, c
10
u(u + 1)
2
(u
3
+ u
2
+ 2u + 1)
3
(u
6
+ 5u
5
+ 8u
4
+ 6u
3
+ 8u
2
+ 8u + 1)
(u
10
+ 3u
9
+ ··· + 40u + 16)(u
13
+ 4u
12
+ ··· u + 1)
c
9
u(u 1)
2
(u
3
+ u
2
1)
3
(u
6
u
5
2u
4
+ 2u
2
+ 2u 1)
(u
10
+ u
9
u
8
3u
7
+ 2u
5
+ u
4
4u
3
3u
2
+ 4u + 4)
(u
13
+ 2u
12
4u
10
+ 8u
8
+ 7u
7
7u
6
8u
5
+ 3u
4
+ 9u
3
u
2
u 1)
23
XI. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
4
y(y 1)
2
(y
3
y
2
+ 2y 1)(y
5
7y
4
+ 17y
3
14y
2
1)
2
(1 8y + 8y
2
6y
3
+ 8y
4
5y
5
+ y
6
)
2
(y
13
14y
12
+ ··· + 88y 16)
c
2
(y)(y 1)
2
(y
3
+ 3y
2
+ 2y 1)(1 28y 210y
2
+ 93y
3
15y
4
+ y
5
)
2
(y
6
9y
5
+ 20y
4
+ 14y
3
16y
2
48y + 1)
2
(y
13
30y
12
+ ··· + 2848y 256)
c
3
, c
7
y
3
(y
3
+ 3y
2
+ 2y 1)
5
(y
5
+ 3y
4
+ 2y
3
13y
2
12y 4)
2
(y
13
+ 6y
12
+ ··· + 64y 64)
c
5
, c
6
, c
9
c
11
y(y 1)
2
(y
3
y
2
+ 2y 1)
3
(y
6
5y
5
+ 8y
4
6y
3
+ 8y
2
8y + 1)
(y
10
3y
9
+ ··· 40y + 16)(y
13
4y
12
+ ··· y 1)
c
8
, c
10
y(y 1)
2
(y
3
+ 3y
2
+ 2y 1)
3
(y
6
9y
5
+ 20y
4
+ 14y
3
16y
2
48y + 1)
(y
10
+ 5y
9
+ ··· 32y + 256)(y
13
+ 16y
12
+ ··· 25y 1)
24