12a
0525
(K12a
0525
)
A knot diagram
1
Linearized knot diagam
3 7 8 9 12 11 2 10 4 1 6 5
Solving Sequence
5,9
4
1,10
11 8 3 2 7 12 6
c
4
c
9
c
10
c
8
c
3
c
1
c
7
c
12
c
5
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
27
+ u
26
+ ··· + 4b + 1, u
27
− u
26
+ ··· + 4a + 3, u
28
+ 7u
26
+ ··· + u + 1i
I
u
2
= h716399893584u
45
+ 1564714832102u
44
+ ··· + 14311443700915b − 42121557729620,
− 1246408210566u
45
− 1464820132004u
44
+ ··· + 14311443700915a − 50730055068599,
u
46
− u
45
+ ··· − 6u + 5i
I
u
3
= hb + a + 1, a
2
+ au + 2a + u + 2, u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 78 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I.
I
u
1
= h−u
27
+u
26
+· · ·+4b+1, u
27
−u
26
+· · ·+4a+3, u
28
+7u
26
+· · ·+u+1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
1
=
−
1
4
u
27
+
1
4
u
26
+ ··· −
1
2
u
4
−
3
4
1
4
u
27
−
1
4
u
26
+ ··· − u
2
−
1
4
a
10
=
u
u
3
+ u
a
11
=
5
4
u
27
+
3
4
u
26
+ ··· + 3u +
5
4
−u
27
−
1
2
u
26
+ ··· −
3
2
u − 1
a
8
=
u
3
u
5
+ u
3
+ u
a
3
=
−u
6
− u
4
+ 1
−u
8
− 2u
6
− 2u
4
a
2
=
−
1
4
u
27
+
1
4
u
26
+ ··· + u
2
−
3
4
1
4
u
27
−
1
4
u
26
+ ··· − u
2
−
1
4
a
7
=
1
4
u
27
+
1
4
u
26
+ ··· −
1
2
u +
1
4
−
1
4
u
27
−
1
4
u
26
+ ··· +
1
2
u −
1
4
a
12
=
−
1
2
u
27
+
1
2
u
26
+ ··· + u
2
−
1
2
1
4
u
27
−
1
4
u
26
+ ··· − u
2
−
1
4
a
6
=
5
4
u
27
−
5
4
u
26
+ ··· −
5
2
u
4
−
5
4
−
1
2
u
27
+
1
2
u
26
+ ··· −
1
2
u
2
+ 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6u
27
−3u
26
+ 41u
25
−15u
24
+ 144u
23
−42u
22
+ 311u
21
−64u
20
+
447u
19
− 54u
18
+ 417u
17
+ 12u
16
+ 224u
15
+ 72u
14
+ 22u
13
+ 88u
12
− 43u
11
+ 23u
10
−
15u
8
+ 40u
7
− 32u
6
+ 39u
5
− 2u
4
+ 15u
3
+ u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
28
+ 14u
27
+ ··· + 3u + 1
c
2
, c
4
, c
7
c
9
u
28
+ 7u
26
+ ··· − u + 1
c
3
u
28
− 3u
27
+ ··· − 16u + 32
c
5
, c
6
, c
11
c
12
u
28
− 3u
27
+ ··· − 11u + 2
c
10
u
28
− 9u
27
+ ··· − 577u + 88
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
28
+ 6y
27
+ ··· + 7y + 1
c
2
, c
4
, c
7
c
9
y
28
+ 14y
27
+ ··· + 3y + 1
c
3
y
28
− 17y
27
+ ··· + 9472y + 1024
c
5
, c
6
, c
11
c
12
y
28
+ 33y
27
+ ··· − y + 4
c
10
y
28
− 15y
27
+ ··· − 37601y + 7744
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.561145 + 0.801172I
a = 0.789871 + 0.574150I
b = 0.517508 + 0.330068I
1.48439 − 2.80149I 6.48594 + 3.23788I
u = −0.561145 − 0.801172I
a = 0.789871 − 0.574150I
b = 0.517508 − 0.330068I
1.48439 + 2.80149I 6.48594 − 3.23788I
u = 0.579647 + 0.897152I
a = 1.50711 − 0.28805I
b = 0.497793 + 0.554969I
0.84370 + 6.32564I 3.80658 − 10.10200I
u = 0.579647 − 0.897152I
a = 1.50711 + 0.28805I
b = 0.497793 − 0.554969I
0.84370 − 6.32564I 3.80658 + 10.10200I
u = 0.644615 + 0.631322I
a = −0.490860 − 1.215860I
b = 0.02723 − 1.47847I
−4.08922 + 1.25049I 3.66147 − 3.30700I
u = 0.644615 − 0.631322I
a = −0.490860 + 1.215860I
b = 0.02723 + 1.47847I
−4.08922 − 1.25049I 3.66147 + 3.30700I
u = −0.215428 + 0.829791I
a = −0.37664 − 1.75550I
b = 0.01632 + 1.64841I
−11.32300 − 1.08394I −0.67442 + 6.46054I
u = −0.215428 − 0.829791I
a = −0.37664 + 1.75550I
b = 0.01632 − 1.64841I
−11.32300 + 1.08394I −0.67442 − 6.46054I
u = −0.605441 + 0.975082I
a = 2.03396 − 0.23377I
b = 0.12308 − 1.53651I
−6.10857 − 8.52011I 0.08752 + 8.22687I
u = −0.605441 − 0.975082I
a = 2.03396 + 0.23377I
b = 0.12308 + 1.53651I
−6.10857 + 8.52011I 0.08752 − 8.22687I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.810575 + 0.181460I
a = −1.099550 − 0.535592I
b = −0.11876 − 1.60426I
−8.19035 + 4.61598I 1.91466 − 2.19636I
u = −0.810575 − 0.181460I
a = −1.099550 + 0.535592I
b = −0.11876 + 1.60426I
−8.19035 − 4.61598I 1.91466 + 2.19636I
u = 0.300734 + 0.727001I
a = −0.319517 + 0.635052I
b = 0.051371 − 0.848410I
−2.65911 + 1.36971I −0.64034 − 4.77051I
u = 0.300734 − 0.727001I
a = −0.319517 − 0.635052I
b = 0.051371 + 0.848410I
−2.65911 − 1.36971I −0.64034 + 4.77051I
u = −0.472666 + 1.163270I
a = 0.025330 + 0.342893I
b = −0.373723 − 0.874275I
−7.17751 − 5.06879I −3.79171 + 3.11845I
u = −0.472666 − 1.163270I
a = 0.025330 − 0.342893I
b = −0.373723 + 0.874275I
−7.17751 + 5.06879I −3.79171 − 3.11845I
u = 0.434237 + 1.181820I
a = 0.271152 − 1.262610I
b = −0.09543 + 1.65532I
−15.9103 + 3.3004I −5.83767 − 4.22098I
u = 0.434237 − 1.181820I
a = 0.271152 + 1.262610I
b = −0.09543 − 1.65532I
−15.9103 − 3.3004I −5.83767 + 4.22098I
u = 0.711695 + 0.202130I
a = −1.179690 + 0.185635I
b = −0.417783 + 0.681445I
−0.38114 − 2.62748I 4.50546 + 4.03150I
u = 0.711695 − 0.202130I
a = −1.179690 − 0.185635I
b = −0.417783 − 0.681445I
−0.38114 + 2.62748I 4.50546 − 4.03150I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.517461 + 1.173180I
a = −0.528302 + 0.520595I
b = −0.642923 + 0.090809I
−4.19208 + 8.45490I 1.37879 − 5.98873I
u = 0.517461 − 1.173180I
a = −0.528302 − 0.520595I
b = −0.642923 − 0.090809I
−4.19208 − 8.45490I 1.37879 + 5.98873I
u = −0.532917 + 1.201560I
a = −1.37394 − 0.82619I
b = −0.498601 + 0.771418I
−6.21060 − 12.29660I −2.15740 + 10.05358I
u = −0.532917 − 1.201560I
a = −1.37394 + 0.82619I
b = −0.498601 − 0.771418I
−6.21060 + 12.29660I −2.15740 − 10.05358I
u = 0.539110 + 1.224760I
a = −2.19344 + 0.93037I
b = −0.14542 − 1.63022I
−14.3989 + 14.7396I −4.25699 − 8.49623I
u = 0.539110 − 1.224760I
a = −2.19344 − 0.93037I
b = −0.14542 + 1.63022I
−14.3989 − 14.7396I −4.25699 + 8.49623I
u = −0.529327 + 0.333044I
a = −1.065480 + 0.149372I
b = −0.440655 + 0.212109I
1.000800 − 0.418896I 9.51810 + 3.62447I
u = −0.529327 − 0.333044I
a = −1.065480 − 0.149372I
b = −0.440655 − 0.212109I
1.000800 + 0.418896I 9.51810 − 3.62447I
7
II.
I
u
2
= h7.16×10
11
u
45
+1.56×10
12
u
44
+· · ·+1.43×10
13
b−4.21×10
13
, −1.25×
10
12
u
45
−1.46×10
12
u
44
+· · ·+1.43×10
13
a−5.07×10
13
, u
46
−u
45
+· · ·−6u+5i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
1
=
0.0870917u
45
+ 0.102353u
44
+ ··· + 0.144487u + 3.54472
−0.0500578u
45
− 0.109333u
44
+ ··· + 1.16384u + 2.94321
a
10
=
u
u
3
+ u
a
11
=
−0.326284u
45
+ 0.410432u
44
+ ··· − 4.06775u + 1.72544
0.543037u
45
+ 0.187376u
44
+ ··· − 0.175104u − 4.56461
a
8
=
u
3
u
5
+ u
3
+ u
a
3
=
−u
6
− u
4
+ 1
−u
8
− 2u
6
− 2u
4
a
2
=
0.343127u
45
+ 0.178658u
44
+ ··· − 0.482261u + 2.67882
−0.517669u
45
+ 0.00968254u
44
+ ··· + 1.41813u + 3.82144
a
7
=
−0.804906u
45
+ 1.05487u
44
+ ··· − 5.92981u + 4.66531
0.0268193u
45
− 0.282855u
44
+ ··· − 0.213286u + 0.465832
a
12
=
0.137150u
45
+ 0.211686u
44
+ ··· − 1.01935u + 0.601511
−0.0500578u
45
− 0.109333u
44
+ ··· + 1.16384u + 2.94321
a
6
=
0.159624u
45
+ 0.184010u
44
+ ··· − 0.492668u − 5.14365
−0.0612648u
45
− 0.180573u
44
+ ··· + 1.65763u + 0.574784
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
26464957613496
14311443700915
u
45
+
19226079710712
14311443700915
u
44
+ ··· −
165615168368444
14311443700915
u −
9675043718942
2862288740183
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
46
+ 27u
45
+ ··· + 44u + 25
c
2
, c
4
, c
7
c
9
u
46
+ u
45
+ ··· + 6u + 5
c
3
(u
23
+ u
22
+ ··· + 4u − 5)
2
c
5
, c
6
, c
11
c
12
(u
23
+ u
22
+ ··· − 2u − 1)
2
c
10
(u
23
− 7u
22
+ ··· + 40u − 17)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
46
− 17y
45
+ ··· − 11736y + 625
c
2
, c
4
, c
7
c
9
y
46
+ 27y
45
+ ··· + 44y + 25
c
3
(y
23
− 17y
22
+ ··· − 144y −25)
2
c
5
, c
6
, c
11
c
12
(y
23
+ 27y
22
+ ··· − 4y −1)
2
c
10
(y
23
− 9y
22
+ ··· + 1260y −289)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.594093 + 0.867126I
a = −1.78487 − 0.73898I
b = −0.08584 − 1.50808I
−4.75454 + 3.53591I 2.63493 − 3.24061I
u = 0.594093 − 0.867126I
a = −1.78487 + 0.73898I
b = −0.08584 + 1.50808I
−4.75454 − 3.53591I 2.63493 + 3.24061I
u = −0.560264 + 0.733902I
a = −1.43784 − 0.04229I
b = −0.477903 + 0.451361I
1.67853 − 1.68040I 6.82272 + 4.29991I
u = −0.560264 − 0.733902I
a = −1.43784 + 0.04229I
b = −0.477903 − 0.451361I
1.67853 + 1.68040I 6.82272 − 4.29991I
u = 0.894194 + 0.150322I
a = 1.011220 − 0.336769I
b = 0.13674 − 1.61894I
−11.1611 − 9.5466I −1.28748 + 5.57899I
u = 0.894194 − 0.150322I
a = 1.011220 + 0.336769I
b = 0.13674 + 1.61894I
−11.1611 + 9.5466I −1.28748 − 5.57899I
u = −0.379272 + 0.794858I
a = 2.51473 − 2.40755I
b = 0.03322 − 1.55779I
−10.40710 − 1.68405I −2.35516 + 3.83025I
u = −0.379272 − 0.794858I
a = 2.51473 + 2.40755I
b = 0.03322 + 1.55779I
−10.40710 + 1.68405I −2.35516 − 3.83025I
u = −0.710804 + 0.500232I
a = −0.192902 − 1.103000I
b = −0.08584 − 1.50808I
−4.75454 + 3.53591I 2.63493 − 3.24061I
u = −0.710804 − 0.500232I
a = −0.192902 + 1.103000I
b = −0.08584 + 1.50808I
−4.75454 − 3.53591I 2.63493 + 3.24061I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.846968 + 0.166502I
a = 1.078960 + 0.115479I
b = 0.473302 + 0.738923I
−3.12646 + 7.25342I 0.90266 − 7.25802I
u = −0.846968 − 0.166502I
a = 1.078960 − 0.115479I
b = 0.473302 − 0.738923I
−3.12646 − 7.25342I 0.90266 + 7.25802I
u = 0.052669 + 1.148020I
a = 0.074549 + 0.589699I
b = 0.228067 − 0.467269I
−3.43004 − 0.92592I 1.05751 + 7.44214I
u = 0.052669 − 1.148020I
a = 0.074549 − 0.589699I
b = 0.228067 + 0.467269I
−3.43004 + 0.92592I 1.05751 − 7.44214I
u = 0.599336 + 0.599151I
a = −0.958651 + 0.515545I
b = −0.477903 + 0.451361I
1.67853 − 1.68040I 6.82272 + 4.29991I
u = 0.599336 − 0.599151I
a = −0.958651 − 0.515545I
b = −0.477903 − 0.451361I
1.67853 + 1.68040I 6.82272 − 4.29991I
u = 0.171279 + 0.803495I
a = 2.17027 + 0.98312I
b = 0.228067 + 0.467269I
−3.43004 + 0.92592I 1.05751 − 7.44214I
u = 0.171279 − 0.803495I
a = 2.17027 − 0.98312I
b = 0.228067 − 0.467269I
−3.43004 − 0.92592I 1.05751 + 7.44214I
u = 0.370882 + 1.129040I
a = −0.031596 + 0.407800I
b = 0.324148 − 0.802707I
−4.10703 + 0.74531I −1.080087 + 0.735219I
u = 0.370882 − 1.129040I
a = −0.031596 − 0.407800I
b = 0.324148 + 0.802707I
−4.10703 − 0.74531I −1.080087 − 0.735219I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.471860 + 1.105300I
a = 0.546147 + 0.570157I
b = 0.581337 + 0.108709I
−1.28388 − 3.66457I 4.82434 + 2.67133I
u = −0.471860 − 1.105300I
a = 0.546147 − 0.570157I
b = 0.581337 − 0.108709I
−1.28388 + 3.66457I 4.82434 − 2.67133I
u = 0.770157 + 0.179548I
a = 1.022920 + 0.016288I
b = 0.581337 + 0.108709I
−1.28388 − 3.66457I 4.82434 + 2.67133I
u = 0.770157 − 0.179548I
a = 1.022920 − 0.016288I
b = 0.581337 − 0.108709I
−1.28388 + 3.66457I 4.82434 − 2.67133I
u = 0.358586 + 1.177180I
a = −0.452320 + 0.592660I
b = −0.546774
−5.29760 0
u = 0.358586 − 1.177180I
a = −0.452320 − 0.592660I
b = −0.546774
−5.29760 0
u = −0.079378 + 1.237910I
a = −0.039508 − 1.412900I
b = 0.03322 + 1.55779I
−10.40710 + 1.68405I −2.35516 − 3.83025I
u = −0.079378 − 1.237910I
a = −0.039508 + 1.412900I
b = 0.03322 − 1.55779I
−10.40710 − 1.68405I −2.35516 + 3.83025I
u = −0.427343 + 1.165780I
a = −1.59551 − 0.97121I
b = −0.413689 + 0.761868I
−7.50172 − 3.22031I −4.22079 + 4.90443I
u = −0.427343 − 1.165780I
a = −1.59551 + 0.97121I
b = −0.413689 − 0.761868I
−7.50172 + 3.22031I −4.22079 − 4.90443I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.342862 + 1.204660I
a = −0.206543 − 1.311020I
b = 0.09185 + 1.62814I
−12.43230 + 0.83337I −2.62647 + 0.I
u = −0.342862 − 1.204660I
a = −0.206543 + 1.311020I
b = 0.09185 − 1.62814I
−12.43230 − 0.83337I −2.62647 + 0.I
u = 0.509144 + 1.151480I
a = 1.48273 − 0.79356I
b = 0.473302 + 0.738923I
−3.12646 + 7.25342I 0. − 7.25802I
u = 0.509144 − 1.151480I
a = 1.48273 + 0.79356I
b = 0.473302 − 0.738923I
−3.12646 − 7.25342I 0. + 7.25802I
u = 0.467885 + 1.180690I
a = −2.63838 + 0.95680I
b = −0.11785 − 1.62483I
−15.6700 + 5.2275I −5.66631 − 3.33432I
u = 0.467885 − 1.180690I
a = −2.63838 − 0.95680I
b = −0.11785 + 1.62483I
−15.6700 − 5.2275I −5.66631 + 3.33432I
u = 0.728113 + 0.045864I
a = 1.54010 − 0.34391I
b = 0.09185 − 1.62814I
−12.43230 − 0.83337I −2.62647 − 0.43888I
u = 0.728113 − 0.045864I
a = 1.54010 + 0.34391I
b = 0.09185 + 1.62814I
−12.43230 + 0.83337I −2.62647 + 0.43888I
u = −0.351491 + 1.244020I
a = −0.034346 + 0.396365I
b = −0.413689 − 0.761868I
−7.50172 + 3.22031I 0. − 4.90443I
u = −0.351491 − 1.244020I
a = −0.034346 − 0.396365I
b = −0.413689 + 0.761868I
−7.50172 − 3.22031I 0. + 4.90443I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.527069 + 1.185450I
a = 2.34188 + 0.80439I
b = 0.13674 − 1.61894I
−11.1611 − 9.5466I 0. + 5.57899I
u = −0.527069 − 1.185450I
a = 2.34188 − 0.80439I
b = 0.13674 + 1.61894I
−11.1611 + 9.5466I 0. − 5.57899I
u = −0.684432 + 0.064859I
a = 1.217270 + 0.099029I
b = 0.324148 − 0.802707I
−4.10703 + 0.74531I −1.080087 + 0.735219I
u = −0.684432 − 0.064859I
a = 1.217270 − 0.099029I
b = 0.324148 + 0.802707I
−4.10703 − 0.74531I −1.080087 − 0.735219I
u = 0.365405 + 1.281630I
a = 0.171683 − 1.256090I
b = −0.11785 + 1.62483I
−15.6700 − 5.2275I 0
u = 0.365405 − 1.281630I
a = 0.171683 + 1.256090I
b = −0.11785 − 1.62483I
−15.6700 + 5.2275I 0
15
III. I
u
3
= hb + a + 1, a
2
+ au + 2a + u + 2, u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
4
=
1
−1
a
1
=
a
−a − 1
a
10
=
u
0
a
11
=
au − a + 3u − 1
a − u + 1
a
8
=
−u
u
a
3
=
1
−1
a
2
=
a + 1
−a − 2
a
7
=
au
−au − u
a
12
=
2a + 1
−a − 1
a
6
=
−2au − a − 2u − 2
au + u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
(u − 1)
4
c
2
, c
4
, c
7
c
9
(u
2
+ 1)
2
c
3
u
4
c
5
, c
6
, c
11
c
12
u
4
+ 3u
2
+ 1
c
10
(u
2
+ u − 1)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y −1)
4
c
2
, c
4
, c
7
c
9
(y + 1)
4
c
3
y
4
c
5
, c
6
, c
11
c
12
(y
2
+ 3y + 1)
2
c
10
(y
2
− 3y + 1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −1.000000 + 0.618034I
b = − 0.618034I
−4.27683 −8.00000
u = 1.000000I
a = −1.00000 − 1.61803I
b = 1.61803I
−12.1725 −8.00000
u = − 1.000000I
a = −1.000000 − 0.618034I
b = 0.618034I
−4.27683 −8.00000
u = − 1.000000I
a = −1.00000 + 1.61803I
b = − 1.61803I
−12.1725 −8.00000
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
((u − 1)
4
)(u
28
+ 14u
27
+ ··· + 3u + 1)(u
46
+ 27u
45
+ ··· + 44u + 25)
c
2
, c
4
, c
7
c
9
((u
2
+ 1)
2
)(u
28
+ 7u
26
+ ··· − u + 1)(u
46
+ u
45
+ ··· + 6u + 5)
c
3
u
4
(u
23
+ u
22
+ ··· + 4u − 5)
2
(u
28
− 3u
27
+ ··· − 16u + 32)
c
5
, c
6
, c
11
c
12
(u
4
+ 3u
2
+ 1)(u
23
+ u
22
+ ··· − 2u − 1)
2
(u
28
− 3u
27
+ ··· − 11u + 2)
c
10
((u
2
+ u − 1)
2
)(u
23
− 7u
22
+ ··· + 40u − 17)
2
· (u
28
− 9u
27
+ ··· − 577u + 88)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
((y −1)
4
)(y
28
+ 6y
27
+ ··· + 7y + 1)(y
46
− 17y
45
+ ··· − 11736y + 625)
c
2
, c
4
, c
7
c
9
((y + 1)
4
)(y
28
+ 14y
27
+ ··· + 3y + 1)(y
46
+ 27y
45
+ ··· + 44y + 25)
c
3
y
4
(y
23
− 17y
22
+ ··· − 144y −25)
2
· (y
28
− 17y
27
+ ··· + 9472y + 1024)
c
5
, c
6
, c
11
c
12
((y
2
+ 3y + 1)
2
)(y
23
+ 27y
22
+ ··· − 4y −1)
2
· (y
28
+ 33y
27
+ ··· − y + 4)
c
10
((y
2
− 3y + 1)
2
)(y
23
− 9y
22
+ ··· + 1260y −289)
2
· (y
28
− 15y
27
+ ··· − 37601y + 7744)
21
