11a
100
(K11a
100
)
1
Arc Sequences
6 1 10 8 2 3 9 5 11 4 7
Solving Sequence
1,6
2 3 7
5,8
9 4 11 10
c
1
c
2
c
6
c
5
c
8
c
4
c
11
c
10
c
3
, c
7
, c
9
Representation Ideals
I =
3
\
i=1
I
u
i
\
I
v
1
I
u
1
= hu
4
+ 2u
2
+ 2, 2u
3
+ b + 2u + 1, u
3
+ 2u
2
+ 2a 4u + 2i
I
u
2
= ha
46
6a
45
+ ··· + 1474282a + 1911187,
7.60020 × 10
270
u + 3.42359 × 10
264
a
45
+ ··· 2.82514 × 10
271
a 1.50084 × 10
271
,
9.88026 × 10
271
b + 1.16430 × 10
265
a
45
+ ··· 5.05650 × 10
271
a 1.27320 × 10
272
i
I
u
3
= hu
31
3u
30
+ ··· 6u + 2, u
30
+ u
29
+ ··· + 2u
2
+ 2a, u
30
2u
29
+ ··· + b 1i
I
v
1
= hv + 1, b + 1, ai
There are 4 irreducible components with 82 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
4
+ 2u
2
+ 2, 2u
3
+ b + 2u + 1, u
3
+ 2u
2
+ 2a 4u + 2i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
7
=
u
u
3
u
a
5
=
u
u
3
+ u
a
8
=
1
2
u
3
u
2
+ 2u 1
2u
3
2u 1
a
9
=
1
2
u
3
u
2
+ u 1
u
3
u 1
a
4
=
1
2
u
3
u
2
+ u 1
u
3
u 1
a
11
=
u
2
1
u
2
a
10
=
1
2
u
3
2u
2
+ u 2
u
3
+ u
2
u 1
a
10
=
1
2
u
3
2u
2
+ u 2
u
3
+ u
2
u 1
(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 = 0.455090 1.098684I
a = 0.13329 2.87557I
b = 3.19737 + 0.91018I
5.75727 + 3.66386I 16.0000 4.0000I
u = 0.455090 + 1.098684I
a = 0.13329 + 2.87557I
b = 3.19737 0.91018I
5.75727 3.66386I 16.0000 + 4.0000I
u = 0.455090 1.098684I
a = 0.133293 0.875571I
b = 1.19737 + 0.91018I
5.75727 3.66386I 16.0000 + 4.0000I
u = 0.455090 + 1.098684I
a = 0.133293 + 0.875571I
b = 1.19737 0.91018I
5.75727 + 3.66386I 16.0000 4.0000I
3
II. I
u
2
= ha
46
6a
45
+ · · · + 1474282a + 1911187, 7.60 × 10
270
u + 3.42 ×
10
264
a
45
+ · · · 2.83 × 10
271
a 1.50 × 10
271
, 9.88 × 10
271
b + 1.16 ×
10
265
a
45
+ · · · 5.06 × 10
271
a 1.27 × 10
272
i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
4.50461 × 10
7
a
45
+ 2.51008 × 10
6
a
44
+ ··· + 3.71718a + 1.97473
a
2
=
1
1.61052 × 10
7
a
45
+ 9.02720 × 10
7
a
44
+ ··· + 5.10567a + 1.52594
a
3
=
1.61052 × 10
7
a
45
9.02720 × 10
7
a
44
+ ··· 5.10567a 0.525941
1.61052 × 10
7
a
45
+ 9.02720 × 10
7
a
44
+ ··· + 5.10567a + 1.52594
a
7
=
3.52353 × 10
8
a
45
2.80928 × 10
7
a
44
+ ··· 0.132474a + 1.30891
4.59348 × 10
7
a
45
+ 2.57704 × 10
6
a
44
+ ··· + 3.81399a + 0.886189
a
5
=
4.50461 × 10
7
a
45
2.51008 × 10
6
a
44
+ ··· 3.71718a 1.97473
2.63481 × 10
8
a
45
+ 2.13972 × 10
7
a
44
+ ··· + 0.0356687a 0.220368
a
8
=
a
1.17841 × 10
7
a
45
+ 5.92379 × 10
7
a
44
+ ··· + 0.511778a + 1.28863
a
9
=
8.21266 × 10
8
a
45
+ 4.38162 × 10
7
a
44
+ ··· + 2.03883a 0.661799
2.27808 × 10
8
a
45
1.70315 × 10
7
a
44
+ ··· 4.40470a + 0.711005
a
4
=
5.57031 × 10
7
a
45
3.11207 × 10
6
a
44
+ ··· 5.08178a 2.74806
7.82799 × 10
8
a
45
+ 4.70746 × 10
7
a
44
+ ··· + 3.04817a + 0.832794
a
11
=
3.27753 × 10
8
a
45
1.70021 × 10
7
a
44
+ ··· + 3.76029a + 0.819361
7.43329 × 10
7
a
45
+ 4.14800 × 10
6
a
44
+ ··· + 8.01445a + 3.54707
a
10
=
5.69070 × 10
7
a
45
3.14032 × 10
6
a
44
+ ··· 5.44147a 2.45437
5.69269 × 10
7
a
45
+ 3.23829 × 10
6
a
44
+ ··· + 8.53468a + 3.28118
a
10
=
5.69070 × 10
7
a
45
3.14032 × 10
6
a
44
+ ··· 5.44147a 2.45437
5.69269 × 10
7
a
45
+ 3.23829 × 10
6
a
44
+ ··· + 8.53468a + 3.28118
(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 = 0.764487 + 0.367117I
a = 2.36168 0.52399I
b = 2.27500 0.43511I
2.34965 + 5.52406I 3.72778 3.52157I
u = 0.764487 0.367117I
a = 2.36168 + 0.52399I
b = 2.27500 + 0.43511I
2.34965 5.52406I 3.72778 + 3.52157I
u = 0.678759 0.332917I
a = 2.12318 0.59645I
b = 1.75171 1.12059I
3.06946 + 2.29224I 8.17333 3.81893I
u = 0.678759 + 0.332917I
a = 2.12318 + 0.59645I
b = 1.75171 + 1.12059I
3.06946 2.29224I 8.17333 + 3.81893I
u = 0.289337 + 1.083673I
a = 1.89769 1.45544I
b = 1.67602 + 1.89674I
7.03235 + 0.30335I 15.4115 + 0.4048I
u = 0.289337 1.083673I
a = 1.89769 + 1.45544I
b = 1.67602 1.89674I
7.03235 0.30335I 15.4115 0.4048I
u = 0.578827 + 1.116212I
a = 0.77164 2.38420I
b = 3.10289 + 0.21556I
0.14155 10.59584I 6.96908 + 7.47788I
u = 0.578827 1.116212I
a = 0.77164 + 2.38420I
b = 3.10289 0.21556I
0.14155 + 10.59584I 6.96908 7.47788I
u = 0.578827 1.116212I
a = 0.560517 0.540442I
b = 0.111782 + 0.874193I
0.14155 + 10.59584I 6.96908 7.47788I
u = 0.578827 + 1.116212I
a = 0.560517 + 0.540442I
b = 0.111782 0.874193I
0.14155 10.59584I 6.96908 + 7.47788I
5
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.587297 0.977894I
a = 0.545763 0.299759I
b = 0.353276 0.870310I
2.35134 1.73636I 4.20687 + 2.46590I
u = 0.587297 + 0.977894I
a = 0.545763 + 0.299759I
b = 0.353276 + 0.870310I
2.35134 + 1.73636I 4.20687 2.46590I
u = 0.401368 1.094533I
a = 0.27205 2.03831I
b = 1.94539 + 1.05759I
4.31524 + 3.60580I 10.88555 4.48858I
u = 0.401368 + 1.094533I
a = 0.27205 + 2.03831I
b = 1.94539 1.05759I
4.31524 3.60580I 10.88555 + 4.48858I
u = 0.678518 + 0.591878I
a = 0.212620 0.101472I
b = 0.472558 0.961619I
3.49101 + 3.16234I 2.33540 3.46689I
u = 0.678518 0.591878I
a = 0.212620 + 0.101472I
b = 0.472558 + 0.961619I
3.49101 3.16234I 2.33540 + 3.46689I
u = 0.401368 1.094533I
a = 0.142915 0.795694I
b = 1.022678 + 0.010362I
4.31524 + 3.60580I 10.88555 4.48858I
u = 0.401368 + 1.094533I
a = 0.142915 + 0.795694I
b = 1.022678 0.010362I
4.31524 3.60580I 10.88555 + 4.48858I
u = 0.500260 1.048709I
a = 0.07394 1.93113I
b = 2.47131 + 1.31302I
3.90982 + 3.26242I 8.80376 2.26815I
u = 0.500260 + 1.048709I
a = 0.07394 + 1.93113I
b = 2.47131 1.31302I
3.90982 3.26242I 8.80376 + 2.26815I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.545632 1.104543I
a = 0.04135 2.02261I
b = 3.06123 + 1.06971I
5.29128 7.02777I 11.56401 + 7.34039I
u = 0.545632 + 1.104543I
a = 0.04135 + 2.02261I
b = 3.06123 1.06971I
5.29128 + 7.02777I 11.56401 7.34039I
u = 0.500260 1.048709I
a = 0.07142 1.44844I
b = 1.044890 0.191819I
3.90982 + 3.26242I 8.80376 2.26815I
u = 0.500260 + 1.048709I
a = 0.07142 + 1.44844I
b = 1.044890 + 0.191819I
3.90982 3.26242I 8.80376 + 2.26815I
u = 0.289337 1.083673I
a = 0.24459 2.49363I
b = 1.63224 + 1.04386I
7.03235 0.30335I 15.4115 0.4048I
u = 0.289337 + 1.083673I
a = 0.24459 + 2.49363I
b = 1.63224 1.04386I
7.03235 + 0.30335I 15.4115 + 0.4048I
u = 0.764487 + 0.367117I
a = 0.403338 0.987217I
b = 0.039410 + 0.541672I
2.34965 + 5.52406I 3.72778 3.52157I
u = 0.764487 0.367117I
a = 0.403338 + 0.987217I
b = 0.039410 0.541672I
2.34965 5.52406I 3.72778 + 3.52157I
u = 0.200891 + 1.110727I
a = 0.415691 0.085865I
b = 0.533177 + 0.554155I
2.33291 + 3.02476I 10.12213 2.21609I
u = 0.200891 1.110727I
a = 0.415691 + 0.085865I
b = 0.533177 0.554155I
2.33291 3.02476I 10.12213 + 2.21609I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.587297 + 0.977894I
a = 0.532388 0.599154I
b = 0.539280 + 0.387094I
2.35134 + 1.73636I 4.20687 2.46590I
u = 0.587297 0.977894I
a = 0.532388 + 0.599154I
b = 0.539280 0.387094I
2.35134 1.73636I 4.20687 + 2.46590I
u = 0.200891 + 1.110727I
a = 0.93605 1.53171I
b = 1.50932 + 0.95081I
2.33291 + 3.02476I 10.12213 2.21609I
u = 0.200891 1.110727I
a = 0.93605 + 1.53171I
b = 1.50932 0.95081I
2.33291 3.02476I 10.12213 + 2.21609I
u = 0.678518 + 0.591878I
a = 0.946089 0.210296I
b = 0.225570 0.176421I
3.49101 + 3.16234I 2.33540 3.46689I
u = 0.678518 0.591878I
a = 0.946089 + 0.210296I
b = 0.225570 + 0.176421I
3.49101 3.16234I 2.33540 + 3.46689I
u = 0.533348 + 0.509445I
a = 1.110225 0.415079I
b = 1.393484 0.052678I
2.27583 0.94673I 5.56367 + 4.33310I
u = 0.533348 0.509445I
a = 1.110225 + 0.415079I
b = 1.393484 + 0.052678I
2.27583 + 0.94673I 5.56367 4.33310I
u = 0.600722
a = 1.36703
b = 1.05024
1.33670 6.47391
u = 0.545632 + 1.104543I
a = 1.66200 2.38549I
b = 3.01631 0.90971I
5.29128 + 7.02777I 11.56401 7.34039I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.545632 1.104543I
a = 1.66200 + 2.38549I
b = 3.01631 + 0.90971I
5.29128 7.02777I 11.56401 + 7.34039I
u = 0.600722
a = 1.67406
b = 1.17363
1.33670 6.47391
u = 0.533348 0.509445I
a = 1.75535 0.51440I
b = 0.81215 1.48197I
2.27583 + 0.94673I 5.56367 4.33310I
u = 0.533348 + 0.509445I
a = 1.75535 + 0.51440I
b = 0.81215 + 1.48197I
2.27583 0.94673I 5.56367 + 4.33310I
u = 0.678759 + 0.332917I
a = 2.32294 1.30214I
b = 2.31067 + 0.65590I
3.06946 2.29224I 8.17333 + 3.81893I
u = 0.678759 0.332917I
a = 2.32294 + 1.30214I
b = 2.31067 0.65590I
3.06946 + 2.29224I 8.17333 3.81893I
9
III.
I
u
3
= hu
31
3u
30
+ · · ·6u+2, u
30
+ u
29
+ · · ·+2u
2
+2a, u
30
2u
29
+ · · ·+b1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
7
=
u
5
2u
3
u
u
5
+ u
3
+ u
a
5
=
u
u
3
+ u
a
8
=
1
2
u
30
1
2
u
29
+ ··· 2u
5
u
2
u
30
+ 2u
29
+ ··· 2u + 1
a
9
=
1
2
u
30
3
2
u
29
+ ··· 3u
2
+ u
u
30
2u
29
+ ··· + 3u 1
a
4
=
5
2
u
30
+
15
2
u
29
+ ··· 15u + 6
2u
29
+ 5u
28
+ ··· + 9u 5
a
11
=
u
10
+ 3u
8
+ 4u
6
+ 3u
4
+ u
2
+ 1
u
10
2u
8
3u
6
2u
4
u
2
a
10
=
1
2
u
30
+
1
2
u
29
+ ··· u + 1
u
30
2u
29
+ ··· + 3u 1
a
10
=
1
2
u
30
+
1
2
u
29
+ ··· u + 1
u
30
2u
29
+ ··· + 3u 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
10
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.702598 0.512877I
a = 1.316110 + 0.358208I
b = 0.741706 + 0.261407I
4.33630 2.18000I 1.38223 + 2.85674I
u = 0.702598 + 0.512877I
a = 1.316110 0.358208I
b = 0.741706 0.261407I
4.33630 + 2.18000I 1.38223 2.85674I
u = 0.680709 0.655777I
a = 0.053487 0.198018I
b = 0.59716 + 1.44604I
1.61779 + 8.62066I 5.39345 7.96064I
u = 0.680709 + 0.655777I
a = 0.053487 + 0.198018I
b = 0.59716 1.44604I
1.61779 8.62066I 5.39345 + 7.96064I
u = 0.605299
a = 1.52798
b = 1.12682
1.33697 6.39555
u = 0.603958 0.919074I
a = 0.843575 0.098346I
b = 0.46144 1.35960I
0.83772 3.66094I 6.42863 + 2.29820I
u = 0.603958 + 0.919074I
a = 0.843575 + 0.098346I
b = 0.46144 + 1.35960I
0.83772 + 3.66094I 6.42863 2.29820I
u = 0.590746 1.033093I
a = 0.674808 + 1.048152I
b = 1.225663 0.326476I
2.80358 + 7.15169I 4.41360 8.13736I
u = 0.590746 + 1.033093I
a = 0.674808 1.048152I
b = 1.225663 + 0.326476I
2.80358 7.15169I 4.41360 + 8.13736I
u = 0.443963 1.132408I
a = 0.28258 1.61327I
b = 1.80440 + 0.67903I
4.34804 + 3.91818I 8.50345 5.07903I
11
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.443963 + 1.132408I
a = 0.28258 + 1.61327I
b = 1.80440 0.67903I
4.34804 3.91818I 8.50345 + 5.07903I
u = 0.057058 0.958804I
a = 0.120049 + 0.361001I
b = 0.454222 0.622148I
0.67493 1.41882I 8.11819 + 4.23209I
u = 0.057058 + 0.958804I
a = 0.120049 0.361001I
b = 0.454222 + 0.622148I
0.67493 + 1.41882I 8.11819 4.23209I
u = 0.218932 1.159935I
a = 0.87876 + 1.99955I
b = 1.93986 0.71799I
4.83518 + 8.17855I 13.0634 5.6311I
u = 0.218932 + 1.159935I
a = 0.87876 1.99955I
b = 1.93986 + 0.71799I
4.83518 8.17855I 13.0634 + 5.6311I
u = 0.275696 0.890316I
a = 0.169518 + 0.102319I
b = 0.324907 0.363899I
0.56339 1.34523I 5.39791 + 4.30982I
u = 0.275696 + 0.890316I
a = 0.169518 0.102319I
b = 0.324907 + 0.363899I
0.56339 + 1.34523I 5.39791 4.30982I
u = 0.363760 1.167869I
a = 0.67786 2.20452I
b = 1.92375 + 1.00684I
6.59629 7.25038I 13.7743 + 8.1656I
u = 0.363760 + 1.167869I
a = 0.67786 + 2.20452I
b = 1.92375 1.00684I
6.59629 + 7.25038I 13.7743 8.1656I
u = 0.493202 1.158043I
a = 0.18388 1.84989I
b = 2.71307 + 0.20830I
5.71846 1.00535I 12.20049 2.17594I
12
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.493202 + 1.158043I
a = 0.18388 + 1.84989I
b = 2.71307 0.20830I
5.71846 + 1.00535I 12.20049 + 2.17594I
u = 0.578258 1.084225I
a = 0.293363 0.532216I
b = 0.146507 + 0.424670I
1.98591 5.18766I 4.29263 + 2.87164I
u = 0.578258 + 1.084225I
a = 0.293363 + 0.532216I
b = 0.146507 0.424670I
1.98591 + 5.18766I 4.29263 2.87164I
u = 0.578468 1.135690I
a = 0.57926 + 2.72431I
b = 3.59420 0.40523I
2.4315 16.1755I 10.0749 + 10.7687I
u = 0.578468 + 1.135690I
a = 0.57926 2.72431I
b = 3.59420 + 0.40523I
2.4315 + 16.1755I 10.0749 10.7687I
u = 0.726205 0.425825I
a = 0.346921 + 0.789445I
b = 0.051392 0.158260I
3.92659 + 0.20488I 1.21175 + 1.93479I
u = 0.726205 + 0.425825I
a = 0.346921 0.789445I
b = 0.051392 + 0.158260I
3.92659 0.20488I 1.21175 1.93479I
u = 0.739543 0.134613I
a = 1.97336 0.80432I
b = 1.97880 0.01788I
2.76836 3.54859I 8.60512 + 5.21629I
u = 0.739543 + 0.134613I
a = 1.97336 + 0.80432I
b = 1.97880 + 0.01788I
2.76836 + 3.54859I 8.60512 5.21629I
u = 0.793502 0.334919I
a = 2.65532 + 0.41225I
b = 2.72942 + 0.64754I
0.06269 + 11.03949I 6.94221 7.13356I
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.793502 + 0.334919I
a = 2.65532 0.41225I
b = 2.72942 0.64754I
0.06269 11.03949I 6.94221 + 7.13356I
13
IV. I
v
1
= hv + 1, b + 1, ai
(i) Arc colorings
a
1
=
1
0
a
6
=
1
0
a
2
=
1
0
a
3
=
1
0
a
7
=
1
0
a
5
=
1
0
a
8
=
0
1
a
9
=
1
1
a
4
=
1
1
a
11
=
1
0
a
10
=
2
1
a
10
=
2
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
14
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
1
1(vol +
1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
3.28987 12.0000
15
V. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
5
u(u
4
+ 2u
2
+ 2)
(1 + 2u 2u
2
+ 2u
3
3u
4
+ 6u
5
7u
6
+ 13u
7
13u
8
+ 22u
9
22u
10
+ 32u
11
30u
12
+ 42u
13
32u
14
+ 44u
15
25u
16
+ 34u
17
14u
18
+ 18u
19
5u
20
+ 6u
21
u
22
+ u
23
)
2
(u
31
+ 3u
30
+ ··· 6u 2)
c
2
u(u
2
+ 2u + 2)
2
(1 2u
2
+ 2u
3
+ 13u
4
+ 38u
5
+ 97u
6
+ 231u
7
+ 465u
8
+ 820u
9
+ 1308u
10
+ 1912u
11
+ 2564u
12
+ 3160u
13
+ 3548u
14
+ 3548u
15
+ 3067u
16
+ 2228u
17
+ 1326u
18
+ 630u
19
+ 231u
20
+ 62u
21
+ 11u
22
+ u
23
)
2
(u
31
+ 15u
30
+ ··· 4u 4)
c
3
, c
8
(u 1)
4
(u + 1)(u
31
+ u
30
+ ··· + 2u + 1)(u
46
+ u
45
+ ··· + 4u + 1)
c
4
, c
10
(u 1)(u + 1)
4
(u
31
+ u
30
+ ··· + 2u + 1)(u
46
+ u
45
+ ··· + 4u + 1)
c
6
(u)(u
4
2u
2
+ 2)(u
31
+ 3u
30
+ ··· + 34u + 2)(u
46
2u
45
+ ··· 80u + 25)
c
7
(u 1)
5
(u
31
+ 13u
30
+ ··· + 8u + 1)(u
46
+ 25u
45
+ ··· + 4u + 1)
c
9
(u 1)
5
(u
31
+ 13u
30
+ ··· + 8u + 1)(u
46
+ 25u
45
+ ··· + 4u + 1)
c
11
u(u
4
2u
2
+ 2)
(7 + 32u 102u
2
+ 232u
3
413u
4
+ 600u
5
731u
6
+ 781u
7
765u
8
+ 728u
9
672u
10
+ 600u
11
516u
12
+ 440u
13
384u
14
+ 322u
15
247u
16
+ 168u
17
106u
18
+ 64u
19
35u
20
+ 16u
21
5u
22
+ u
23
)
2
(u
31
+ 15u
30
+ ··· 1566u 158)
16
VI. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
y(y
2
+ 2y + 2)
2
(1 2y
2
+ 2y
3
+ 13y
4
+ 38y
5
+ 97y
6
+ 231y
7
+ 465y
8
+ 820y
9
+ 1308y
10
+ 1912y
11
+ 2564y
12
+ 3160y
13
+ 3548y
14
+ 3548y
15
+ 3067y
16
+ 2228y
17
+ 1326y
18
+ 630y
19
+ 231y
20
+ 62y
21
+ 11y
22
+ y
23
)
2
(y
31
+ 15y
30
+ ··· 4y 4)
c
2
y(y
2
+ 4)
2
(1 4y + 22y
2
+ 250y
3
+ 1301y
4
+ 4322y
5
+ 9697y
6
+ 1.65 × 10
4
y
7
+ 2.05 × 10
4
y
8
+ 1.89 × 10
4
y
9
+ 1.65 × 10
4
y
10
+ 1.36 × 10
4
y
11
+ 8844y
12
+ 7152y
13
+ 3492y
14
+ 2840y
15
+ 1087y
16
+ 860y
17
+ 266y
18
+ 182y
19
+ 43y
20
+ 22y
21
+ 3y
22
+ y
23
)
2
(y
31
+ 3y
30
+ ··· + 112y 16)
c
3
, c
4
, c
8
(y 1)
5
(y
31
13y
30
+ ··· + 8y 1)(y
46
25y
45
+ ··· 4y + 1)
c
6
(y)(y
2
2y + 2)
2
(y
31
9y
30
+ ··· + 92y 4)
(y
46
10y
45
+ ··· 13200y + 625)
c
7
(y 1)
5
(y
31
+ 19y
30
+ ··· 4y 1)(y
46
9y
45
+ ··· 104y + 1)
c
9
(y 1)
5
(y
31
+ 19y
30
+ ··· 4y 1)(y
46
9y
45
+ ··· 104y + 1)
c
10
(y 1)
5
(y
31
13y
30
+ ··· + 8y 1)(y
46
25y
45
+ ··· 4y + 1)
c
11
y(y
2
2y + 2)
2
(49 404y 1338y
2
2262y
3
2019y
4
298y
5
+ 2829y
6
+ 5979y
7
+ 6205y
8
+ 3736y
9
+ 720y
10
980y
11
1628y
12
1496y
13
1348y
14
596y
15
89y
16
+ 316y
17
+ 322y
18
+ 226y
19
+ 99y
20
+ 34y
21
+ 7y
22
+ y
23
)
2
(y
31
+ 3y
30
+ ··· 219108y 24964)
17