11a
328
(K11a
328
)
1
Arc Sequences
9 6 1 8 10 2 11 4 3 7 5
Solving Sequence
5,11 1,8
4 9 2 3 7 6 10
c
11
c
4
c
8
c
1
c
3
c
7
c
6
c
10
c
2
, c
5
, c
9
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
13
+ u
12
+ 5u
11
+ 5u
10
+ 15u
9
+ 6u
8
+ 26u
7
3u
6
+ 25u
5
10u
4
+ 13u
3
5u
2
+ 2u 1,
491u
12
351u
11
+ ··· + 2441b + 3926, 4157u
12
+ 5972u
11
+ ··· + 4882a + 3087i
I
u
2
= hu
87
+ 4u
86
+ ··· + 343u 49,
2.23921 × 10
242
u
86
7.92450 × 10
242
u
85
+ ··· + 2.99360 × 10
243
b + 1.15001 × 10
243
,
1.77864 × 10
242
u
86
5.20910 × 10
242
u
85
+ ··· + 5.98721 × 10
243
a 3.75514 × 10
244
i
There are 2 irreducible components with 100 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
13
+ u
12
+ · · · + 2u 1, 491u
12
351u
11
+ · · · + 2441b +
3926, 4157u
12
+ 5972u
11
+ · · · + 4882a + 3087i
(i) Arc colorings
a
5
=
1
0
a
11
=
0.851495u
12
1.22327u
11
+ ··· + 1.65772u 0.632323
0.201147u
12
+ 0.143794u
11
+ ··· + 3.64154u 1.60836
a
1
=
0.650348u
12
1.36706u
11
+ ··· 1.98382u + 0.976034
0.201147u
12
+ 0.143794u
11
+ ··· + 3.64154u 1.60836
a
8
=
0
u
a
4
=
1
u
2
a
9
=
u
u
3
+ u
a
2
=
0.495494u
12
0.779189u
11
+ ··· 0.591766u + 0.104261
0.261368u
12
+ 0.192954u
11
+ ··· + 4.32241u 2.04711
a
3
=
0.880479u
12
+ 1.39349u
11
+ ··· 3.72522u + 0.700635
0.612864u
12
1.03032u
11
+ ··· 0.519869u + 0.820565
a
7
=
0.744879u
12
+ 1.74908u
11
+ ··· + 1.39973u 0.573023
0.798853u
12
+ 1.14379u
11
+ ··· 0.358460u + 0.391643
a
6
=
0.0437321u
12
+ 0.892872u
11
+ ··· + 3.54127u 1.68138
1.35190u
12
+ 1.24334u
11
+ ··· 4.52970u + 0.278165
a
10
=
0.978748u
12
0.0836747u
11
+ ··· + 5.32861u 2.05945
0.196641u
12
+ 0.635395u
11
+ ··· + 3.45023u 0.995903
a
10
=
0.978748u
12
0.0836747u
11
+ ··· + 5.32861u 2.05945
0.196641u
12
+ 0.635395u
11
+ ··· + 3.45023u 0.995903
(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 = 1.29035 1.11018I
a = 0.246183 0.395145I
b = 0.277898 0.180723I
1.05481 + 2.28411I 28.6060 + 9.4367I
u = 1.29035 + 1.11018I
a = 0.246183 + 0.395145I
b = 0.277898 + 0.180723I
1.05481 2.28411I 28.6060 9.4367I
u = 0.325948 1.074868I
a = 0.048824 + 1.076169I
b = 2.08257 + 0.08658I
1.43580 + 8.24449I 11.3041 10.0681I
u = 0.325948 + 1.074868I
a = 0.048824 1.076169I
b = 2.08257 0.08658I
1.43580 8.24449I 11.3041 + 10.0681I
u = 0.097116 0.522146I
a = 0.801452 0.579628I
b = 0.095808 1.315795I
4.14699 1.46163I 8.28713 + 5.07807I
u = 0.097116 + 0.522146I
a = 0.801452 + 0.579628I
b = 0.095808 + 1.315795I
4.14699 + 1.46163I 8.28713 5.07807I
u = 0.089681 1.215233I
a = 0.199486 + 0.973168I
b = 2.05969 + 0.84594I
6.78588 1.52935I 8.62170 + 4.17456I
u = 0.089681 + 1.215233I
a = 0.199486 0.973168I
b = 2.05969 0.84594I
6.78588 + 1.52935I 8.62170 4.17456I
u = 0.360305 0.702792I
a = 0.50592 2.21262I
b = 0.270408 0.367997I
0.852875 + 0.473363I 10.87019 + 3.13875I
u = 0.360305 + 0.702792I
a = 0.50592 + 2.21262I
b = 0.270408 + 0.367997I
0.852875 0.473363I 10.87019 3.13875I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.420998
a = 2.58594
b = 1.13723
3.49272 9.11075
u = 0.55292 1.47705I
a = 0.151914 + 0.865849I
b = 1.17981 + 0.80934I
7.07568 6.46295I 10.78671 + 4.43761I
u = 0.55292 + 1.47705I
a = 0.151914 0.865849I
b = 1.17981 0.80934I
7.07568 + 6.46295I 10.78671 4.43761I
4
II. I
u
2
= hu
87
+ 4u
86
+ · · · + 343u 49, 2.24 × 10
242
u
86
7.92 ×
10
242
u
85
+ · · · + 2.99 × 10
243
b + 1.15 × 10
243
, 1.78 × 10
242
u
86
5.21 ×
10
242
u
85
+ · · · + 5.99 × 10
243
a 3.76 × 10
244
i
(i) Arc colorings
a
5
=
1
0
a
11
=
0.0297073u
86
+ 0.0870039u
85
+ ··· 18.3975u + 6.27193
0.0747999u
86
+ 0.264715u
85
+ ··· 0.552281u 0.384156
a
1
=
0.0450926u
86
0.177711u
85
+ ··· 17.8452u + 6.65609
0.0747999u
86
+ 0.264715u
85
+ ··· 0.552281u 0.384156
a
8
=
0
u
a
4
=
1
u
2
a
9
=
u
u
3
+ u
a
2
=
0.0402372u
86
+ 0.122380u
85
+ ··· 33.7223u + 8.81924
0.0372983u
86
+ 0.116784u
85
+ ··· + 1.89332u 0.241227
a
3
=
0.0493242u
86
0.246384u
85
+ ··· 11.7605u 0.960720
0.0348186u
86
+ 0.139522u
85
+ ··· 21.6142u + 4.39832
a
7
=
0.0601123u
86
+ 0.192499u
85
+ ··· 42.5585u + 12.4589
0.0878581u
86
0.355305u
85
+ ··· + 15.9562u 1.44904
a
6
=
0.0993724u
86
+ 0.357805u
85
+ ··· 25.6649u + 5.15445
0.0206546u
86
+ 0.131560u
85
+ ··· + 0.640094u + 1.53755
a
10
=
0.106056u
86
0.436946u
85
+ ··· + 36.4451u 8.52379
0.0235474u
86
0.0851142u
85
+ ··· + 9.34856u 2.37135
a
10
=
0.106056u
86
0.436946u
85
+ ··· + 36.4451u 8.52379
0.0235474u
86
0.0851142u
85
+ ··· + 9.34856u 2.37135
(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 = 1.88839 0.16543I
a = 0.501270 0.160160I
b = 0.473251 0.100354I
1.16868 + 2.46445I 38.9094 0.7492I
u = 1.88839 + 0.16543I
a = 0.501270 + 0.160160I
b = 0.473251 + 0.100354I
1.16868 2.46445I 38.9094 + 0.7492I
u = 1.210730 0.265007I
a = 0.925319 + 0.591284I
b = 0.811339 + 0.684971I
1.28183 + 11.73515I 6.05190 9.28087I
u = 1.210730 + 0.265007I
a = 0.925319 0.591284I
b = 0.811339 0.684971I
1.28183 11.73515I 6.05190 + 9.28087I
u = 0.834059 0.034209I
a = 1.047805 0.447304I
b = 0.822239 0.737364I
3.93560 2.19338I 1.92699 + 3.84180I
u = 0.834059 + 0.034209I
a = 1.047805 + 0.447304I
b = 0.822239 + 0.737364I
3.93560 + 2.19338I 1.92699 3.84180I
u = 0.776879 0.541054I
a = 1.215044 0.529800I
b = 1.026508 + 0.627724I
1.01962 3.49300I 2.61462 + 4.04484I
u = 0.776879 + 0.541054I
a = 1.215044 + 0.529800I
b = 1.026508 0.627724I
1.01962 + 3.49300I 2.61462 4.04484I
u = 0.755476 0.104993I
a = 0.195816 0.886995I
b = 0.223634 0.914975I
1.83703 + 2.21620I 3.51529 3.55324I
u = 0.755476 + 0.104993I
a = 0.195816 + 0.886995I
b = 0.223634 + 0.914975I
1.83703 2.21620I 3.51529 + 3.55324I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.67656 1.24255I
a = 0.036532 0.289307I
b = 0.012280 0.372469I
0.78893 + 2.23324I 0.89499 + 3.76252I
u = 0.67656 + 1.24255I
a = 0.036532 + 0.289307I
b = 0.012280 + 0.372469I
0.78893 2.23324I 0.89499 3.76252I
u = 0.543318 0.090886I
a = 0.345489 + 1.207082I
b = 0.757344 + 0.051881I
2.36842 2.62824I 3.63497 + 2.44788I
u = 0.543318 + 0.090886I
a = 0.345489 1.207082I
b = 0.757344 0.051881I
2.36842 + 2.62824I 3.63497 2.44788I
u = 0.52905 1.51463I
a = 0.167824 + 0.699135I
b = 1.218098 + 0.659542I
6.59608 + 4.70222I 10.43587 1.41159I
u = 0.52905 + 1.51463I
a = 0.167824 0.699135I
b = 1.218098 0.659542I
6.59608 4.70222I 10.43587 + 1.41159I
u = 0.50070 1.46622I
a = 0.012041 1.023534I
b = 1.43093 1.14290I
4.1159 + 17.6919I 8.92390 9.16005I
u = 0.50070 + 1.46622I
a = 0.012041 + 1.023534I
b = 1.43093 + 1.14290I
4.1159 17.6919I 8.92390 + 9.16005I
u = 0.49169 1.48005I
a = 0.060011 + 0.974919I
b = 1.09293 + 0.91892I
6.98154 + 8.93541I 10.75261 8.28401I
u = 0.49169 + 1.48005I
a = 0.060011 0.974919I
b = 1.09293 0.91892I
6.98154 8.93541I 10.75261 + 8.28401I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.388024 1.265103I
a = 0.165127 0.865453I
b = 1.63904 0.82465I
0.10297 + 6.59252I 5.72779 5.82199I
u = 0.388024 + 1.265103I
a = 0.165127 + 0.865453I
b = 1.63904 + 0.82465I
0.10297 6.59252I 5.72779 + 5.82199I
u = 0.374562 1.029911I
a = 0.076659 + 1.218391I
b = 2.04798 + 0.80570I
0.50770 + 7.93768I 3.12459 7.05888I
u = 0.374562 + 1.029911I
a = 0.076659 1.218391I
b = 2.04798 0.80570I
0.50770 7.93768I 3.12459 + 7.05888I
u = 0.370860 1.187911I
a = 0.049379 0.314535I
b = 1.49725 + 0.21594I
0.72894 + 6.29842I 7.75309 6.13790I
u = 0.370860 + 1.187911I
a = 0.049379 + 0.314535I
b = 1.49725 0.21594I
0.72894 6.29842I 7.75309 + 6.13790I
u = 0.328530 1.294477I
a = 0.677640 + 0.243251I
b = 0.815892 + 0.631455I
2.48697 + 6.11850I 9.00903 6.79284I
u = 0.328530 + 1.294477I
a = 0.677640 0.243251I
b = 0.815892 0.631455I
2.48697 6.11850I 9.00903 + 6.79284I
u = 0.220013 1.097369I
a = 0.339303 0.460158I
b = 0.613788 0.509488I
0.94053 + 1.58665I 6.85252 3.45369I
u = 0.220013 + 1.097369I
a = 0.339303 + 0.460158I
b = 0.613788 + 0.509488I
0.94053 1.58665I 6.85252 + 3.45369I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.217099 1.081385I
a = 1.37946 1.13245I
b = 0.529903 0.247555I
0.703925 + 0.037215I 18.8402 8.8294I
u = 0.217099 + 1.081385I
a = 1.37946 + 1.13245I
b = 0.529903 + 0.247555I
0.703925 0.037215I 18.8402 + 8.8294I
u = 0.206735 0.210541I
a = 1.77794 + 3.92726I
b = 1.264925 0.200555I
0.32476 + 6.96628I 7.63597 5.26059I
u = 0.206735 + 0.210541I
a = 1.77794 3.92726I
b = 1.264925 + 0.200555I
0.32476 6.96628I 7.63597 + 5.26059I
u = 0.14180 1.98107I
a = 0.079427 0.560515I
b = 0.270083 0.903599I
2.44085 2.75616I 2.05789 6.07992I
u = 0.14180 + 1.98107I
a = 0.079427 + 0.560515I
b = 0.270083 + 0.903599I
2.44085 + 2.75616I 2.05789 + 6.07992I
u = 0.138100 1.293416I
a = 0.385701 1.225880I
b = 1.168624 0.682207I
4.91824 + 8.48201I 11.81598 6.96267I
u = 0.138100 + 1.293416I
a = 0.385701 + 1.225880I
b = 1.168624 + 0.682207I
4.91824 8.48201I 11.81598 + 6.96267I
u = 0.12280 1.51626I
a = 0.064790 0.355576I
b = 0.441833 0.292673I
0.68412 + 1.98002I 14.1001 1.1636I
u = 0.12280 + 1.51626I
a = 0.064790 + 0.355576I
b = 0.441833 + 0.292673I
0.68412 1.98002I 14.1001 + 1.1636I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.027487 1.147153I
a = 0.04048 + 1.68829I
b = 0.109168 + 1.084488I
2.95518 + 0.92414I 4.42659 + 2.35779I
u = 0.027487 + 1.147153I
a = 0.04048 1.68829I
b = 0.109168 1.084488I
2.95518 0.92414I 4.42659 2.35779I
u = 0.012517 1.341529I
a = 0.118863 + 0.917923I
b = 0.758450 + 0.797102I
6.25662 2.11272I 12.44570 + 3.57219I
u = 0.012517 + 1.341529I
a = 0.118863 0.917923I
b = 0.758450 0.797102I
6.25662 + 2.11272I 12.44570 3.57219I
u = 0.012862 1.192008I
a = 0.039387 0.986276I
b = 1.94746 1.83329I
3.17906 6.66017I 11.24709 + 7.05347I
u = 0.012862 + 1.192008I
a = 0.039387 + 0.986276I
b = 1.94746 + 1.83329I
3.17906 + 6.66017I 11.24709 7.05347I
u = 0.082178 1.267233I
a = 0.386443 1.020835I
b = 1.43238 0.41505I
7.65344 1.93513I 15.6923 + 5.6493I
u = 0.082178 + 1.267233I
a = 0.386443 + 1.020835I
b = 1.43238 + 0.41505I
7.65344 + 1.93513I 15.6923 5.6493I
u = 0.100175 0.612166I
a = 0.09886 2.76368I
b = 0.273208 0.157111I
1.084893 0.871384I 15.6106 + 3.4978I
u = 0.100175 + 0.612166I
a = 0.09886 + 2.76368I
b = 0.273208 + 0.157111I
1.084893 + 0.871384I 15.6106 3.4978I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.112847 1.223689I
a = 0.033011 0.907012I
b = 2.44222 1.06035I
7.01048 0.84605I 13.9296 4.6584I
u = 0.112847 + 1.223689I
a = 0.033011 + 0.907012I
b = 2.44222 + 1.06035I
7.01048 + 0.84605I 13.9296 + 4.6584I
u = 0.154767 1.267259I
a = 0.039823 + 1.050808I
b = 1.16362 + 1.85704I
6.42084 3.25398I 13.9134 + 5.9290I
u = 0.154767 + 1.267259I
a = 0.039823 1.050808I
b = 1.16362 1.85704I
6.42084 + 3.25398I 13.9134 5.9290I
u = 0.181300 1.304476I
a = 0.096331 + 1.089102I
b = 0.459339 + 0.988301I
6.35047 2.80896I 13.55752 + 3.05323I
u = 0.181300 + 1.304476I
a = 0.096331 1.089102I
b = 0.459339 0.988301I
6.35047 + 2.80896I 13.55752 3.05323I
u = 0.202235 1.161158I
a = 0.993749 0.254248I
b = 0.802586 + 0.468686I
2.03222 0.78901I 4.72245 + 2.85793I
u = 0.202235 + 1.161158I
a = 0.993749 + 0.254248I
b = 0.802586 0.468686I
2.03222 + 0.78901I 4.72245 2.85793I
u = 0.235984 1.200173I
a = 0.529832 + 0.016416I
b = 0.951440 + 0.148069I
4.06130 2.44977I 13.66998 + 0.62409I
u = 0.235984 + 1.200173I
a = 0.529832 0.016416I
b = 0.951440 0.148069I
4.06130 + 2.44977I 13.66998 0.62409I
11
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.245817 0.897592I
a = 0.866755 0.223147I
b = 0.938277 0.817700I
3.46748 3.58811I 2.27202 + 5.87731I
u = 0.245817 + 0.897592I
a = 0.866755 + 0.223147I
b = 0.938277 + 0.817700I
3.46748 + 3.58811I 2.27202 5.87731I
u = 0.283569 0.325822I
a = 0.64720 2.88040I
b = 0.219477 0.269391I
1.04332 1.10567I 9.46807 3.92768I
u = 0.283569 + 0.325822I
a = 0.64720 + 2.88040I
b = 0.219477 + 0.269391I
1.04332 + 1.10567I 9.46807 + 3.92768I
u = 0.294507 0.068923I
a = 3.24602 + 1.41597I
b = 1.327904 0.309964I
3.55911 0.66256I 6.82987 + 9.28934I
u = 0.294507 + 0.068923I
a = 3.24602 1.41597I
b = 1.327904 + 0.309964I
3.55911 + 0.66256I 6.82987 9.28934I
u = 0.315271 0.626744I
a = 0.363379 0.501761I
b = 0.34862 1.39642I
4.42600 + 0.87222I 1.33257 + 4.60840I
u = 0.315271 + 0.626744I
a = 0.363379 + 0.501761I
b = 0.34862 + 1.39642I
4.42600 0.87222I 1.33257 4.60840I
u = 0.354922
a = 0.746725
b = 0.380191
0.829400 12.4505
u = 0.403739 0.208025I
a = 0.54524 + 1.66909I
b = 0.259208 + 1.215850I
4.93158 1.73284I 1.22516 + 5.83487I
12
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.403739 + 0.208025I
a = 0.54524 1.66909I
b = 0.259208 1.215850I
4.93158 + 1.73284I 1.22516 5.83487I
u = 0.428306 1.245237I
a = 0.867434 + 0.540714I
b = 0.755026 + 0.694879I
1.44453 11.33888I 6.00664 + 9.01277I
u = 0.428306 + 1.245237I
a = 0.867434 0.540714I
b = 0.755026 0.694879I
1.44453 + 11.33888I 6.00664 9.01277I
u = 0.42905 1.44683I
a = 0.028457 0.961650I
b = 1.51558 1.17301I
7.14017 11.20711I 11.07835 + 6.94705I
u = 0.42905 + 1.44683I
a = 0.028457 + 0.961650I
b = 1.51558 + 1.17301I
7.14017 + 11.20711I 11.07835 6.94705I
u = 0.43735 1.45185I
a = 0.064177 + 1.007554I
b = 1.21403 + 0.98521I
7.95756 5.21172I 12.63651 + 0.10792I
u = 0.43735 + 1.45185I
a = 0.064177 1.007554I
b = 1.21403 0.98521I
7.95756 + 5.21172I 12.63651 0.10792I
u = 0.60050 1.43503I
a = 0.270382 + 0.873346I
b = 1.36060 + 0.72302I
6.65882 7.54335I 8.40472 + 9.14433I
u = 0.60050 + 1.43503I
a = 0.270382 0.873346I
b = 1.36060 0.72302I
6.65882 + 7.54335I 8.40472 9.14433I
u = 0.761682 0.143291I
a = 1.53993 0.43049I
b = 0.563074 0.406965I
1.92081 0.61884I 7.87734 + 1.96780I
13
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.761682 + 0.143291I
a = 1.53993 + 0.43049I
b = 0.563074 + 0.406965I
1.92081 + 0.61884I 7.87734 1.96780I
u = 0.908219 0.099499I
a = 0.025719 + 1.089373I
b = 0.390262 + 0.953575I
5.02660 + 6.57361I 1.89523 6.16023I
u = 0.908219 + 0.099499I
a = 0.025719 1.089373I
b = 0.390262 0.953575I
5.02660 6.57361I 1.89523 + 6.16023I
u = 1.007581 0.327641I
a = 0.973764 + 0.664512I
b = 0.789772 + 0.734118I
1.60864 6.07731I 8.39371 + 6.40011I
u = 1.007581 + 0.327641I
a = 0.973764 0.664512I
b = 0.789772 0.734118I
1.60864 + 6.07731I 8.39371 6.40011I
u = 1.354959 0.065636I
a = 0.909413 0.011420I
b = 0.659999 0.151798I
2.16816 0.86837I 6.77062 + 9.55122I
u = 1.354959 + 0.065636I
a = 0.909413 + 0.011420I
b = 0.659999 + 0.151798I
2.16816 + 0.86837I 6.77062 9.55122I
14
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
13
2u
12
+ ··· + 7u + 1)(u
87
+ 3u
86
+ ··· 5484u + 667)
c
2
(u
13
+ 2u
12
+ ··· + u 1)(u
87
+ u
86
+ ··· 140u + 23)
c
3
(2u
13
+ 5u
12
+ ··· + 7u + 1)(2u
87
+ 17u
86
+ ··· 8u 1)
c
4
(u
13
+ u
12
+ ··· + 2u 1)(u
87
+ 4u
86
+ ··· + 343u 49)
c
5
(u
13
+ 2u
12
+ ··· u 2)(u
87
+ 3u
86
+ ··· + 11633u 2362)
c
6
(u
13
2u
12
+ ··· + u + 1)(u
87
+ u
86
+ ··· 140u + 23)
c
7
(2u
13
+ u
12
+ ··· + 13u 5)(2u
87
+ 5u
86
+ ··· + 9624u + 539)
c
8
(u
13
u
12
+ ··· + 2u + 1)(u
87
+ 4u
86
+ ··· + 343u 49)
c
9
(2u
13
u
12
+ ··· + 6u + 1)(2u
87
+ 5u
86
+ ··· + 1311u 349)
c
10
(2u
13
u
12
+ ··· + 13u + 5)(2u
87
+ 5u
86
+ ··· + 9624u + 539)
c
11
(u
13
+ u
12
+ ··· 5u 2)(u
87
+ 2u
86
+ ··· + 2885u + 538)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
13
+ 2y
12
+ ··· + 25y 1)
(y
87
13y
86
+ ··· + 17748096y 444889)
c
2
, c
6
(y
13
+ 4y
12
+ ··· 11y 1)(y
87
+ 45y
86
+ ··· + 11504y 529)
c
3
(4y
13
y
12
+ ··· + 21y 1)(12y
87
39y
86
+ ··· 12y 3)
c
4
, c
8
(y
13
+ 9y
12
+ ··· 6y 1)(y
87
+ 66y
86
+ ··· + 43561y 2401)
c
5
(y
13
4y
12
+ ··· + 21y 4)
(y
87
+ 9y
86
+ ··· 55400087y 5579044)
c
7
(4y
13
65y
12
+ ··· + 189y 25)
(12y
87
855y
86
+ ··· + 38438172y 871563)
c
9
(4y
13
+ 19y
12
+ ··· + 16y 1)
(4y
87
+ 103y
86
+ ··· 17754781y 121801)
c
10
(4y
13
65y
12
+ ··· + 189y 25)
(4y
87
285y
86
+ ··· + 12812724y 290521)
c
11
(y
13
15y
12
+ ··· + 21y 4)
(y
87
38y
86
+ ··· + 7135321y 289444)
16