11a
217
(K11a
217
)
1
Arc Sequences
7 1 10 8 11 2 4 6 3 5 9
Solving Sequence
1,7
2
3,9
10 4 6 8 11 5
c
1
c
2
c
9
c
3
c
6
c
8
c
11
c
5
c
4
, c
7
, c
10
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
19
+ 6u
17
+ ··· + 2u 1, u
18
+ u
17
+ ··· + b 1, 2u
18
3u
17
+ ··· + a + 7i
I
u
2
= hu
88
+ u
87
+ ··· 15u 9, 1.17366 × 10
130
u
87
2.47035 × 10
130
u
86
+ ··· + 1.30550 × 10
131
b + 1.73562 × 10
131
,
1.20844 × 10
131
u
87
1.95249 × 10
131
u
86
+ ··· + 3.91650 × 10
131
a + 2.77458 × 10
132
i
There are 2 irreducible components with 107 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
19
+6u
17
+· · ·+2u1, u
18
+u
17
+· · ·+b1, 2u
18
3u
17
+· · ·+a+7i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
9
=
2u
18
+ 3u
17
+ ··· + 16u 7
u
18
u
17
+ ··· + 4u
2
+ 1
a
10
=
2u
18
+ 2u
17
+ ··· + 13u 5
u
18
u
17
+ ··· 2u + 2
a
4
=
3u
18
+ 16u
16
+ ··· 5u + 2
u
18
+ u
17
+ ··· u
2
1
a
6
=
u
u
3
+ u
a
8
=
2u
18
+ 3u
17
+ ··· + 13u 6
u
18
+ 5u
16
+ ··· 2u
2
+ 3u
a
11
=
2u
18
+ u
17
+ ··· + 5u 5
u
18
u
17
+ ··· + 5u
2
+ 1
a
5
=
4u
18
+ u
17
+ ··· 4u
2
4
u
18
2u
17
+ ··· 2u + 2
a
5
=
4u
18
+ u
17
+ ··· 4u
2
4
u
18
2u
17
+ ··· 2u + 2
(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 = 0.769769 0.810412I
a = 0.639951 + 0.518424I
b = 0.811253 0.714824I
3.17953 1.36019I 3.92371 + 4.81231I
u = 0.769769 + 0.810412I
a = 0.639951 0.518424I
b = 0.811253 + 0.714824I
3.17953 + 1.36019I 3.92371 4.81231I
u = 0.706602 0.910457I
a = 1.67700 + 0.51030I
b = 0.753084 + 1.044951I
2.86959 + 6.94689I 4.90485 11.31459I
u = 0.706602 + 0.910457I
a = 1.67700 0.51030I
b = 0.753084 1.044951I
2.86959 6.94689I 4.90485 + 11.31459I
u = 0.300339 1.028097I
a = 0.710824 0.912612I
b = 0.164956 + 1.062829I
0.80374 + 5.96566I 2.56814 7.23829I
u = 0.300339 + 1.028097I
a = 0.710824 + 0.912612I
b = 0.164956 1.062829I
0.80374 5.96566I 2.56814 + 7.23829I
u = 0.273008 0.799953I
a = 2.28416 0.16634I
b = 0.142356 1.370337I
0.06532 3.52454I 1.23723 + 4.17495I
u = 0.273008 + 0.799953I
a = 2.28416 + 0.16634I
b = 0.142356 + 1.370337I
0.06532 + 3.52454I 1.23723 4.17495I
u = 0.029408 1.410933I
a = 0.338962 0.132093I
b = 0.319721 + 0.077815I
4.90569 0.94743I 3.91857 6.41242I
u = 0.029408 + 1.410933I
a = 0.338962 + 0.132093I
b = 0.319721 0.077815I
4.90569 + 0.94743I 3.91857 + 6.41242I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.181011 0.621059I
a = 1.96932 1.56059I
b = 0.890170 0.697260I
0.988482 + 0.416067I 1.322447 0.053453I
u = 0.181011 + 0.621059I
a = 1.96932 + 1.56059I
b = 0.890170 + 0.697260I
0.988482 0.416067I 1.322447 + 0.053453I
u = 0.448828 1.089752I
a = 0.38006 1.45167I
b = 1.72088 + 0.46919I
3.15207 3.62872I 4.99993 + 0.96458I
u = 0.448828 + 1.089752I
a = 0.38006 + 1.45167I
b = 1.72088 0.46919I
3.15207 + 3.62872I 4.99993 0.96458I
u = 0.549531
a = 2.17935
b = 1.13686
0.464251 1.57296
u = 0.562434 0.668186I
a = 1.08875 1.00323I
b = 0.926740 0.221997I
6.76547 0.96312I 8.25509 3.80362I
u = 0.562434 + 0.668186I
a = 1.08875 + 1.00323I
b = 0.926740 + 0.221997I
6.76547 + 0.96312I 8.25509 + 3.80362I
u = 0.612086 1.067955I
a = 0.254962 + 1.118405I
b = 0.614195 + 0.372988I
5.42685 3.75788I 2.42054 + 2.81140I
u = 0.612086 + 1.067955I
a = 0.254962 1.118405I
b = 0.614195 0.372988I
5.42685 + 3.75788I 2.42054 2.81140I
4
II. I
u
2
= hu
88
+ u
87
+ · · · 15u 9, 1.17 × 10
130
u
87
2.47 × 10
130
u
86
+
· · · + 1.31 × 10
131
b + 1.74 × 10
131
, 1.21 × 10
131
u
87
1.95 × 10
131
u
86
+ · · · +
3.92 × 10
131
a + 2.77 × 10
132
i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
9
=
0.308550u
87
+ 0.498528u
86
+ ··· + 7.54550u 7.08434
0.0899012u
87
+ 0.189226u
86
+ ··· 2.55127u 1.32947
a
10
=
0.386032u
87
0.283155u
86
+ ··· + 12.0176u 0.729770
0.256563u
87
+ 0.494342u
86
+ ··· 0.570209u 4.79156
a
4
=
0.317057u
87
0.164745u
86
+ ··· 15.3332u + 2.84818
0.127635u
87
+ 0.423062u
86
+ ··· + 4.82042u 0.610035
a
6
=
u
u
3
+ u
a
8
=
0.244942u
87
0.153358u
86
+ ··· + 12.6279u 2.44254
0.265588u
87
+ 0.498825u
86
+ ··· 1.17630u 5.08573
a
11
=
0.728320u
87
0.445892u
86
+ ··· + 23.4775u + 5.97101
0.299986u
87
+ 0.213630u
86
+ ··· 6.17882u 4.63479
a
5
=
0.566401u
87
+ 0.182126u
86
+ ··· + 13.2863u + 1.44734
0.921798u
87
+ 0.106995u
86
+ ··· 9.79027u 4.16570
a
5
=
0.566401u
87
+ 0.182126u
86
+ ··· + 13.2863u + 1.44734
0.921798u
87
+ 0.106995u
86
+ ··· 9.79027u 4.16570
(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 = 0.954150 0.504375I
a = 1.27641 0.78432I
b = 1.41629 + 0.70913I
6.30173 11.20678I 7.14379 + 5.74414I
u = 0.954150 + 0.504375I
a = 1.27641 + 0.78432I
b = 1.41629 0.70913I
6.30173 + 11.20678I 7.14379 5.74414I
u = 0.864107 0.670402I
a = 0.795663 + 0.661817I
b = 1.117808 0.571773I
3.99640 0.52623I 7.63226 0.55265I
u = 0.864107 + 0.670402I
a = 0.795663 0.661817I
b = 1.117808 + 0.571773I
3.99640 + 0.52623I 7.63226 + 0.55265I
u = 0.825409 0.389965I
a = 0.744459 + 0.263975I
b = 1.099570 + 0.053538I
8.37441 + 1.00046I 11.77868 + 0.61417I
u = 0.825409 + 0.389965I
a = 0.744459 0.263975I
b = 1.099570 0.053538I
8.37441 1.00046I 11.77868 0.61417I
u = 0.743273 0.736993I
a = 0.943024 + 0.750996I
b = 1.073517 0.651963I
3.60538 0.57994I 9.28515 2.16318I
u = 0.743273 + 0.736993I
a = 0.943024 0.750996I
b = 1.073517 + 0.651963I
3.60538 + 0.57994I 9.28515 + 2.16318I
u = 0.737322
a = 2.19967
b = 1.48738
0.805893 8.65374
u = 0.699704 1.136127I
a = 1.52044 0.94432I
b = 1.47465 0.92567I
4.3565 + 17.2462I 4.80393 9.55844I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.699704 + 1.136127I
a = 1.52044 + 0.94432I
b = 1.47465 + 0.92567I
4.3565 17.2462I 4.80393 + 9.55844I
u = 0.699347 0.964380I
a = 1.65613 + 0.72307I
b = 1.011393 + 0.874674I
2.91455 + 6.08125I 5.36639 3.03339I
u = 0.699347 + 0.964380I
a = 1.65613 0.72307I
b = 1.011393 0.874674I
2.91455 6.08125I 5.36639 + 3.03339I
u = 0.697556 1.017656I
a = 1.40280 + 0.71129I
b = 1.08357 + 0.92479I
2.90972 + 6.30768I 5.19224 4.92036I
u = 0.697556 + 1.017656I
a = 1.40280 0.71129I
b = 1.08357 0.92479I
2.90972 6.30768I 5.19224 + 4.92036I
u = 0.672994 0.730216I
a = 1.10735 + 1.07414I
b = 0.991137 0.532051I
3.40131 0.63657I 8.39886 0.08397I
u = 0.672994 + 0.730216I
a = 1.10735 1.07414I
b = 0.991137 + 0.532051I
3.40131 + 0.63657I 8.39886 + 0.08397I
u = 0.652582 0.904482I
a = 1.87179 + 0.49715I
b = 1.140727 + 0.831300I
2.89016 + 5.77549I 7.27706 5.57456I
u = 0.652582 + 0.904482I
a = 1.87179 0.49715I
b = 1.140727 0.831300I
2.89016 5.77549I 7.27706 + 5.57456I
u = 0.628107 0.256489I
a = 1.34336 0.46833I
b = 0.423109 + 0.347668I
2.03705 1.14331I 0.66173 + 1.29864I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.628107 + 0.256489I
a = 1.34336 + 0.46833I
b = 0.423109 0.347668I
2.03705 + 1.14331I 0.66173 1.29864I
u = 0.619798 1.190133I
a = 0.321227 0.830580I
b = 0.831881 0.388008I
5.93694 + 4.42882I 8.31773 8.85486I
u = 0.619798 + 1.190133I
a = 0.321227 + 0.830580I
b = 0.831881 + 0.388008I
5.93694 4.42882I 8.31773 + 8.85486I
u = 0.570950 0.920505I
a = 0.35854 1.78146I
b = 0.648133 0.346156I
6.17225 + 2.81909I 7.78995 0.82921I
u = 0.570950 + 0.920505I
a = 0.35854 + 1.78146I
b = 0.648133 + 0.346156I
6.17225 2.81909I 7.78995 + 0.82921I
u = 0.558781 0.949859I
a = 1.159031 0.427247I
b = 0.19983 + 2.03307I
0.64622 + 7.81246I 3.25330 9.91253I
u = 0.558781 + 0.949859I
a = 1.159031 + 0.427247I
b = 0.19983 2.03307I
0.64622 7.81246I 3.25330 + 9.91253I
u = 0.550712 1.074732I
a = 1.29204 0.62612I
b = 0.877930 0.444608I
4.17850 + 5.69977I 2.78773 5.64838I
u = 0.550712 + 1.074732I
a = 1.29204 + 0.62612I
b = 0.877930 + 0.444608I
4.17850 5.69977I 2.78773 + 5.64838I
u = 0.532741 0.803423I
a = 1.41185 + 0.72781I
b = 0.993775 + 0.272407I
6.59048 + 1.60100I 5.07994 6.99877I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.532741 + 0.803423I
a = 1.41185 0.72781I
b = 0.993775 0.272407I
6.59048 1.60100I 5.07994 + 6.99877I
u = 0.521304 0.736352I
a = 1.41976 + 0.43169I
b = 0.29104 1.85754I
1.35988 3.41417I 6.68348 + 3.62461I
u = 0.521304 + 0.736352I
a = 1.41976 0.43169I
b = 0.29104 + 1.85754I
1.35988 + 3.41417I 6.68348 3.62461I
u = 0.418001 1.139751I
a = 0.30516 1.43036I
b = 1.74406 + 0.38088I
2.54284 + 4.00372I 5.22023 5.83857I
u = 0.418001 + 1.139751I
a = 0.30516 + 1.43036I
b = 1.74406 0.38088I
2.54284 4.00372I 5.22023 + 5.83857I
u = 0.288083 0.930672I
a = 2.01211 0.27156I
b = 0.75665 1.25554I
0.95666 2.66976I 0.98053 + 1.57732I
u = 0.288083 + 0.930672I
a = 2.01211 + 0.27156I
b = 0.75665 + 1.25554I
0.95666 + 2.66976I 0.98053 1.57732I
u = 0.235896 1.191593I
a = 0.047892 + 0.136256I
b = 0.292908 + 0.768153I
6.26061 + 1.83587I 5.86386 2.18855I
u = 0.235896 + 1.191593I
a = 0.047892 0.136256I
b = 0.292908 0.768153I
6.26061 1.83587I 5.86386 + 2.18855I
u = 0.124814 0.274497I
a = 3.46331 3.55911I
b = 0.199334 + 0.805485I
0.79049 + 4.65679I 5.10183 7.14957I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.124814 + 0.274497I
a = 3.46331 + 3.55911I
b = 0.199334 0.805485I
0.79049 4.65679I 5.10183 + 7.14957I
u = 0.008092 0.764905I
a = 1.14418 1.17371I
b = 0.210534 0.328300I
1.42460 1.54545I 1.14589 + 4.93438I
u = 0.008092 + 0.764905I
a = 1.14418 + 1.17371I
b = 0.210534 + 0.328300I
1.42460 + 1.54545I 1.14589 4.93438I
u = 0.020883 1.113766I
a = 0.786207 + 0.139160I
b = 0.892118 0.756600I
3.07957 + 2.82800I 5.46919 3.00897I
u = 0.020883 + 1.113766I
a = 0.786207 0.139160I
b = 0.892118 + 0.756600I
3.07957 2.82800I 5.46919 + 3.00897I
u = 0.024501 1.333543I
a = 0.231763 + 0.033800I
b = 0.900322 + 0.607173I
0.68113 8.56435I 2.72309 + 7.32318I
u = 0.024501 + 1.333543I
a = 0.231763 0.033800I
b = 0.900322 0.607173I
0.68113 + 8.56435I 2.72309 7.32318I
u = 0.068391 0.882123I
a = 0.289943 0.967539I
b = 0.361809 0.714360I
1.62956 1.49672I 2.18266 + 4.73494I
u = 0.068391 + 0.882123I
a = 0.289943 + 0.967539I
b = 0.361809 + 0.714360I
1.62956 + 1.49672I 2.18266 4.73494I
u = 0.09795 1.48857I
a = 0.198655 0.067322I
b = 0.552268 + 0.131033I
4.69267 + 1.22369I 10.6991 11.5124I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.09795 + 1.48857I
a = 0.198655 + 0.067322I
b = 0.552268 0.131033I
4.69267 1.22369I 10.6991 + 11.5124I
u = 0.157375 1.064389I
a = 0.001733 + 0.538652I
b = 0.730790 + 0.971384I
3.08031 + 3.58796I 1.92784 2.31740I
u = 0.157375 + 1.064389I
a = 0.001733 0.538652I
b = 0.730790 0.971384I
3.08031 3.58796I 1.92784 + 2.31740I
u = 0.396189
a = 0.357439
b = 0.603577
0.888455 11.7577
u = 0.418994 0.851230I
a = 1.92662 0.69990I
b = 1.49127 0.27379I
1.16615 0.99172I 1.12131 + 4.43962I
u = 0.418994 + 0.851230I
a = 1.92662 + 0.69990I
b = 1.49127 + 0.27379I
1.16615 + 0.99172I 1.12131 4.43962I
u = 0.424583 0.989136I
a = 0.85380 1.41030I
b = 1.229642 0.518489I
1.60218 2.32473I 0.92722 + 2.16726I
u = 0.424583 + 0.989136I
a = 0.85380 + 1.41030I
b = 1.229642 + 0.518489I
1.60218 + 2.32473I 0.92722 2.16726I
u = 0.452174 1.105957I
a = 0.538003 0.865414I
b = 0.776965 + 0.935888I
1.27582 4.49844I 2.70860 + 2.74584I
u = 0.452174 + 1.105957I
a = 0.538003 + 0.865414I
b = 0.776965 0.935888I
1.27582 + 4.49844I 2.70860 2.74584I
11
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.525827 0.813502I
a = 1.17367 0.85281I
b = 0.498338 1.251821I
0.090444 1.045917I 2.78656 + 3.65409I
u = 0.525827 + 0.813502I
a = 1.17367 + 0.85281I
b = 0.498338 + 1.251821I
0.090444 + 1.045917I 2.78656 3.65409I
u = 0.539664 0.896196I
a = 0.042642 0.542138I
b = 1.06395 + 1.25945I
0.37079 3.25945I 2.22481 + 3.20776I
u = 0.539664 + 0.896196I
a = 0.042642 + 0.542138I
b = 1.06395 1.25945I
0.37079 + 3.25945I 2.22481 3.20776I
u = 0.549677 0.855702I
a = 1.280459 + 0.488061I
b = 0.644430 + 0.292848I
0.34598 2.20232I 2.36125 + 3.21360I
u = 0.549677 + 0.855702I
a = 1.280459 0.488061I
b = 0.644430 0.292848I
0.34598 + 2.20232I 2.36125 3.21360I
u = 0.603081 0.191254I
a = 1.061455 + 0.858322I
b = 0.699506 0.668876I
1.312401 + 0.427135I 7.68860 0.03322I
u = 0.603081 + 0.191254I
a = 1.061455 0.858322I
b = 0.699506 + 0.668876I
1.312401 0.427135I 7.68860 + 0.03322I
u = 0.603972 1.028596I
a = 2.00103 0.72468I
b = 1.041578 0.628310I
0.23970 9.99743I 3.22834 + 9.09967I
u = 0.603972 + 1.028596I
a = 2.00103 + 0.72468I
b = 1.041578 + 0.628310I
0.23970 + 9.99743I 3.22834 9.09967I
12
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.617819 0.541637I
a = 1.94871 1.12700I
b = 0.745025 + 0.523421I
1.17276 + 5.12018I 5.98234 4.87453I
u = 0.617819 + 0.541637I
a = 1.94871 + 1.12700I
b = 0.745025 0.523421I
1.17276 5.12018I 5.98234 + 4.87453I
u = 0.655494 1.088189I
a = 1.60130 + 1.13359I
b = 1.73234 + 0.92925I
7.17217 10.01928I 7.20832 + 7.44112I
u = 0.655494 + 1.088189I
a = 1.60130 1.13359I
b = 1.73234 0.92925I
7.17217 + 10.01928I 7.20832 7.44112I
u = 0.702911 1.150829I
a = 1.147343 0.666605I
b = 1.10356 0.88760I
0.29144 10.89834I 2.26604 + 8.03376I
u = 0.702911 + 1.150829I
a = 1.147343 + 0.666605I
b = 1.10356 + 0.88760I
0.29144 + 10.89834I 2.26604 8.03376I
u = 0.711121 0.909996I
a = 1.12820 + 1.52674I
b = 0.681383 + 0.228321I
4.78905 6.64535I 8.75073 + 7.16776I
u = 0.711121 + 0.909996I
a = 1.12820 1.52674I
b = 0.681383 0.228321I
4.78905 + 6.64535I 8.75073 7.16776I
u = 0.748244 0.800032I
a = 1.42273 0.31582I
b = 0.926866 0.143704I
5.12945 + 1.10437I 8.93126 1.09679I
u = 0.748244 + 0.800032I
a = 1.42273 + 0.31582I
b = 0.926866 + 0.143704I
5.12945 1.10437I 8.93126 + 1.09679I
13
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.782309 1.124415I
a = 0.659480 + 0.750725I
b = 0.859534 + 0.291051I
4.85892 0.75021I 7.24105 0.32913I
u = 0.782309 + 1.124415I
a = 0.659480 0.750725I
b = 0.859534 0.291051I
4.85892 + 0.75021I 7.24105 + 0.32913I
u = 0.828880 0.513872I
a = 1.43498 + 1.02467I
b = 1.62216 0.64715I
8.90367 + 4.46822I 9.93176 2.41041I
u = 0.828880 + 0.513872I
a = 1.43498 1.02467I
b = 1.62216 + 0.64715I
8.90367 4.46822I 9.93176 + 2.41041I
u = 0.987316 0.473726I
a = 0.821517 0.527676I
b = 1.091215 + 0.562324I
2.36912 + 4.77643I 5.52433 4.74023I
u = 0.987316 + 0.473726I
a = 0.821517 + 0.527676I
b = 1.091215 0.562324I
2.36912 4.77643I 5.52433 + 4.74023I
u = 0.999619 0.565212I
a = 0.889970 0.066196I
b = 1.045116 0.006616I
6.55539 5.69360I 8.74582 + 5.57593I
u = 0.999619 + 0.565212I
a = 0.889970 + 0.066196I
b = 1.045116 + 0.006616I
6.55539 + 5.69360I 8.74582 5.57593I
14
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
19
+ 6u
17
+ ··· + 2u 1)(u
88
+ u
87
+ ··· 15u 9)
c
2
(u
19
+ 12u
18
+ ··· 8u 1)(u
88
+ 39u
87
+ ··· + 1917u + 81)
c
3
(u
19
+ u
18
+ ··· u 1)(u
88
+ 2u
87
+ ··· + 1806u 5669)
c
4
(u
19
+ u
18
+ ··· u 1)(u
88
+ 2u
87
+ ··· 4u 1)
c
5
(u
19
6u
17
+ ··· + 2u 1)(u
88
+ u
87
+ ··· + 369u + 73)
c
6
(u
19
+ 6u
17
+ ··· + 2u + 1)(u
88
+ u
87
+ ··· 15u 9)
c
7
(u
19
u
18
+ ··· u + 1)(u
88
+ 2u
87
+ ··· 4u 1)
c
8
(u
19
+ 3u
18
+ ··· 5u + 1)(u
88
+ 2u
87
+ ··· 116u 29)
c
9
(u
19
u
18
+ ··· u + 1)(u
88
+ 2u
87
+ ··· + 1806u 5669)
c
10
(u
19
6u
17
+ ··· + 2u + 1)(u
88
+ u
87
+ ··· + 369u + 73)
c
11
(u
19
7u
18
+ ··· + 7u 1)(u
88
+ 4u
87
+ ··· 84596u 23303)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
6
(y
19
+ 12y
18
+ ··· 8y 1)(y
88
+ 39y
87
+ ··· + 1917y + 81)
c
2
(y
19
12y
17
+ ··· + 12y 1)(y
88
+ 31y
87
+ ··· + 1377y + 6561)
c
3
(y
19
19y
18
+ ··· + 15y 1)
(y
88
68y
87
+ ··· 295181122y + 32137561)
c
4
(y
19
15y
18
+ ··· + 19y 1)(y
88
48y
87
+ ··· 78y + 1)
c
5
(y
19
12y
18
+ ··· + 20y 1)(y
88
57y
87
+ ··· 140103y + 5329)
c
7
(y
19
15y
18
+ ··· + 19y 1)(y
88
48y
87
+ ··· 78y + 1)
c
8
(y
19
3y
18
+ ··· + 21y 1)(y
88
+ 8y
87
+ ··· 160080y + 841)
c
9
(y
19
19y
18
+ ··· + 15y 1)
(y
88
68y
87
+ ··· 295181122y + 32137561)
c
10
(y
19
12y
18
+ ··· + 20y 1)(y
88
57y
87
+ ··· 140103y + 5329)
c
11
(y
19
3y
18
+ ··· + 19y 1)
(y
88
32y
87
+ ··· 13342637414y + 543029809)
16