12n
0124
(K12n
0124
)
A knot diagram
1
Linearized knot diagam
3 5 6 2 12 4 11 6 5 8 10 9
Solving Sequence
5,9 3,10
2 1 4 12 6 7 8 11
c
9
c
2
c
1
c
4
c
12
c
5
c
6
c
8
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.08067 × 10
71
u
23
+ 5.26175 × 10
71
u
22
+ ··· + 2.02018 × 10
76
b − 3.78380 × 10
76
,
9.08915 × 10
75
u
23
+ 2.34052 × 10
76
u
22
+ ··· + 3.92744 × 10
80
a − 1.11660 × 10
81
,
u
24
− u
23
+ ··· + 74162u − 19441i
I
u
2
= h−967u
11
− 301u
10
+ ··· + 263b − 1376, −1506u
11
− 552u
10
+ ··· + 263a − 2561,
u
12
+ u
11
− u
10
− 6u
9
− 5u
8
+ u
7
+ 5u
6
+ 9u
5
+ 11u
4
+ 7u
3
+ 4u
2
+ 3u + 1i
I
u
3
= hu
7
− 3u
5
− u
4
+ 4u
3
+ 2u
2
+ b − u − 2, −u
8
− u
7
+ 2u
6
+ 3u
5
− u
4
− 3u
3
− 2u
2
+ a + 1,
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1i
* 3 irreducible components of dim
C
= 0, with total 45 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−2.08 × 10
71
u
23
+ 5.26 × 10
71
u
22
+ · · · + 2.02 × 10
76
b − 3.78 ×
10
76
, 9.09 × 10
75
u
23
+ 2.34 × 10
76
u
22
+ · · · + 3.93 × 10
80
a − 1.12 ×
10
81
, u
24
− u
23
+ · · · + 74162u − 19441i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
3
=
−0.0000231427u
23
− 0.0000595940u
22
+ ··· − 5.73288u + 2.84308
0.0000102994u
23
− 0.0000260459u
22
+ ··· − 3.68024u + 1.87300
a
10
=
1
−u
2
a
2
=
−0.0000231427u
23
− 0.0000595940u
22
+ ··· − 5.73288u + 2.84308
0.0000614617u
23
− 0.0000856774u
22
+ ··· − 9.36624u + 3.48148
a
1
=
−0.000169431u
23
+ 0.0000106683u
22
+ ··· + 8.83572u − 1.35661
0.0000252125u
23
− 0.0000460045u
22
+ ··· − 4.17125u + 1.93008
a
4
=
0.0000635308u
23
− 0.0000949036u
22
+ ··· − 11.6803u + 4.35857
0.0000714189u
23
− 0.0000219756u
22
+ ··· − 6.67895u + 2.17463
a
12
=
−0.000194644u
23
+ 0.0000566729u
22
+ ··· + 13.0070u − 3.28669
0.0000252125u
23
− 0.0000460045u
22
+ ··· − 4.17125u + 1.93008
a
6
=
0.0000728869u
23
+ 0.0000468189u
22
+ ··· − 0.0880205u + 0.0552699
−0.000132323u
23
+ 0.0000178400u
22
+ ··· + 9.20508u − 2.72140
a
7
=
0.000289264u
23
− 0.0000276884u
22
+ ··· − 16.0214u + 4.12000
−0.000164735u
23
+ 0.0000153960u
22
+ ··· + 10.2669u − 3.73292
a
8
=
−0.000179309u
23
+ 0.0000323990u
22
+ ··· + 9.44236u − 2.06987
0.0000244553u
23
− 0.0000672943u
22
+ ··· − 5.21820u + 1.94011
a
11
=
−0.000262366u
23
+ 0.0000264100u
22
+ ··· + 15.2839u − 4.03891
0.000137186u
23
− 0.0000456660u
22
+ ··· − 10.1214u + 3.83499
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0000679815u
23
− 0.000171030u
22
+ ··· − 11.2729u + 1.52274
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
+ 24u
23
+ ··· − 179u + 1
c
2
, c
4
u
24
− 12u
23
+ ··· + 17u − 1
c
3
, c
6
u
24
+ u
23
+ ··· − 2560u + 512
c
5
u
24
+ 4u
23
+ ··· − 3u − 1
c
7
, c
10
u
24
+ 8u
23
+ ··· + 7u + 1
c
8
u
24
− 5u
23
+ ··· − 389242u + 249139
c
9
u
24
+ u
23
+ ··· − 74162u − 19441
c
11
u
24
+ 20u
22
+ ··· + 19u + 1
c
12
u
24
+ 2u
23
+ ··· + 28672u + 4096
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
+ 204y
23
+ ··· − 2901y + 1
c
2
, c
4
y
24
− 24y
23
+ ··· + 179y + 1
c
3
, c
6
y
24
− 63y
23
+ ··· − 3932160y + 262144
c
5
y
24
+ 26y
22
+ ··· − y + 1
c
7
, c
10
y
24
+ 20y
22
+ ··· + 19y + 1
c
8
y
24
+ 111y
23
+ ··· − 469614992544y + 62070241321
c
9
y
24
− 61y
23
+ ··· − 296113128y + 377952481
c
11
y
24
+ 40y
23
+ ··· + 2151y + 1
c
12
y
24
− 90y
23
+ ··· + 67108864y + 16777216
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.001080 + 0.138094I
a = −1.318540 − 0.227339I
b = 0.349925 + 0.133105I
1.03909 − 7.66938I 3.58752 + 6.84907I
u = 1.001080 − 0.138094I
a = −1.318540 + 0.227339I
b = 0.349925 − 0.133105I
1.03909 + 7.66938I 3.58752 − 6.84907I
u = −0.824749 + 0.684019I
a = 0.924018 + 0.059095I
b = −0.397533 + 0.099117I
2.67249 − 0.06243I 6.49122 − 0.13400I
u = −0.824749 − 0.684019I
a = 0.924018 − 0.059095I
b = −0.397533 − 0.099117I
2.67249 + 0.06243I 6.49122 + 0.13400I
u = 0.316783 + 0.857620I
a = 0.0626489 + 0.0577118I
b = −0.019035 + 0.639183I
0.59509 − 2.36713I 1.40991 + 3.67925I
u = 0.316783 − 0.857620I
a = 0.0626489 − 0.0577118I
b = −0.019035 − 0.639183I
0.59509 + 2.36713I 1.40991 − 3.67925I
u = 0.688053 + 0.891806I
a = 0.334387 + 0.540212I
b = 0.461704 + 0.711317I
−1.87950 + 2.72151I 1.13774 − 4.25269I
u = 0.688053 − 0.891806I
a = 0.334387 − 0.540212I
b = 0.461704 − 0.711317I
−1.87950 − 2.72151I 1.13774 + 4.25269I
u = −0.787218
a = 0.180911
b = −0.560374
1.02845 10.2860
u = 0.834451 + 0.915879I
a = 0.352399 − 0.454795I
b = 2.73766 + 0.36092I
−1.38798 + 2.82419I 0.59813 − 2.55909I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.834451 − 0.915879I
a = 0.352399 + 0.454795I
b = 2.73766 − 0.36092I
−1.38798 − 2.82419I 0.59813 + 2.55909I
u = 0.314005 + 0.468028I
a = 0.35394 − 1.75927I
b = 0.255305 − 0.819135I
−1.83062 + 1.07717I −2.53581 − 1.58170I
u = 0.314005 − 0.468028I
a = 0.35394 + 1.75927I
b = 0.255305 + 0.819135I
−1.83062 − 1.07717I −2.53581 + 1.58170I
u = 1.51494
a = 1.23042
b = 0.320247
0.756608 8.01810
u = −1.50875 + 0.34715I
a = −0.824302 − 0.166530I
b = 2.22948 − 1.08324I
−2.60567 + 1.37963I −1.96914 − 4.05392I
u = −1.50875 − 0.34715I
a = −0.824302 + 0.166530I
b = 2.22948 + 1.08324I
−2.60567 − 1.37963I −1.96914 + 4.05392I
u = 1.93298 + 1.06740I
a = −0.453811 + 0.766464I
b = 0.08195 + 1.96919I
18.8685 + 6.6483I 2.16489 − 2.21174I
u = 1.93298 − 1.06740I
a = −0.453811 − 0.766464I
b = 0.08195 − 1.96919I
18.8685 − 6.6483I 2.16489 + 2.21174I
u = −2.70737 + 1.34412I
a = 0.343417 + 0.565612I
b = −0.11926 + 2.26369I
18.7357 − 14.2573I 0. + 5.97304I
u = −2.70737 − 1.34412I
a = 0.343417 − 0.565612I
b = −0.11926 − 2.26369I
18.7357 + 14.2573I 0. − 5.97304I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 3.59990 + 1.47900I
a = −0.314174 + 0.597363I
b = 0.16845 + 2.06886I
−18.5925 + 5.6388I 0
u = 3.59990 − 1.47900I
a = −0.314174 − 0.597363I
b = 0.16845 − 2.06886I
−18.5925 − 5.6388I 0
u = −3.51025 + 2.07425I
a = 0.212826 + 0.620986I
b = −0.12859 + 2.14471I
−18.9745 + 1.9748I 0
u = −3.51025 − 2.07425I
a = 0.212826 − 0.620986I
b = −0.12859 − 2.14471I
−18.9745 − 1.9748I 0
7
II. I
u
2
= h−967u
11
− 301u
10
+ · · · + 263b − 1376, −1506u
11
− 552u
10
+ · · · +
263a − 2561, u
12
+ u
11
+ · · · + 3u + 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
3
=
5.72624u
11
+ 2.09886u
10
+ ··· + 14.5894u + 9.73764
3.67681u
11
+ 1.14449u
10
+ ··· + 9.01521u + 5.23194
a
10
=
1
−u
2
a
2
=
5.72624u
11
+ 2.09886u
10
+ ··· + 14.5894u + 9.73764
1.23954u
11
+ 0.163498u
10
+ ··· + 3.85932u + 1.60456
a
1
=
−7.99620u
11
− 1.69582u
10
+ ··· − 17.4943u − 11.0380
0
a
4
=
−10.4525u
11
− 3.19772u
10
+ ··· − 25.1787u − 16.4753
1.81369u
11
+ 1.09506u
10
+ ··· + 4.22053u + 2.86312
a
12
=
−7.99620u
11
− 1.69582u
10
+ ··· − 17.4943u − 11.0380
0
a
6
=
16.0380u
11
+ 5.04183u
10
+ ··· + 39.0570u + 25.6198
u
a
7
=
7.99620u
11
+ 1.69582u
10
+ ··· + 17.4943u + 11.0380
0
a
8
=
10.9962u
11
+ 3.69582u
10
+ ··· + 22.4943u + 17.0380
−u
2
a
11
=
−12.2662u
11
− 3.29278u
10
+ ··· − 28.3992u − 17.3384
1.83270u
11
+ 0.615970u
10
+ ··· + 3.74905u + 2.67300
(ii) Obstruction class = 1
(iii) Cusp Shapes =
9447
263
u
11
+
3054
263
u
10
−
11456
263
u
9
−
49096
263
u
8
−
14483
263
u
7
+
18808
263
u
6
+
35545
263
u
5
+
63461
263
u
4
+
61950
263
u
3
+
23143
263
u
2
+
19562
263
u +
13360
263
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
c
2
, c
6
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
3
, c
4
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
7
, c
11
(u
2
+ u + 1)
6
c
8
, c
9
u
12
+ u
11
+ ··· + 3u + 1
c
10
(u
2
− u + 1)
6
c
12
u
12
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
2
, c
3
, c
4
c
6
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
c
7
, c
10
, c
11
(y
2
+ y + 1)
6
c
8
, c
9
y
12
− 3y
11
+ ··· − y + 1
c
12
y
12
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.815127 + 0.417821I
a = 0.746988 − 0.432355I
b = −0.167948 − 0.496751I
1.89061 + 1.10558I 3.63443 − 2.52768I
u = −0.815127 − 0.417821I
a = 0.746988 + 0.432355I
b = −0.167948 + 0.496751I
1.89061 − 1.10558I 3.63443 + 2.52768I
u = 0.045720 + 0.914831I
a = −0.747924 + 0.430733I
b = 0.514173 − 0.102928I
1.89061 + 2.95419I 6.39280 − 3.57892I
u = 0.045720 − 0.914831I
a = −0.747924 − 0.430733I
b = 0.514173 + 0.102928I
1.89061 − 2.95419I 6.39280 + 3.57892I
u = 0.288082 + 0.618530I
a = 0.07779 + 1.77253I
b = −0.483138 + 0.481819I
7.72290I −2.53591 − 7.46338I
u = 0.288082 − 0.618530I
a = 0.07779 − 1.77253I
b = −0.483138 − 0.481819I
− 7.72290I −2.53591 + 7.46338I
u = −0.679704 + 0.059778I
a = 1.49615 + 0.95363I
b = −0.175699 + 0.659319I
− 3.66314I 2.83009 + 6.37777I
u = −0.679704 − 0.059778I
a = 1.49615 − 0.95363I
b = −0.175699 − 0.659319I
3.66314I 2.83009 − 6.37777I
u = −0.93136 + 1.30101I
a = −0.214408 − 0.616830I
b = −2.00856 − 1.94349I
−1.89061 − 2.95419I −7.91752 + 1.81989I
u = −0.93136 − 1.30101I
a = −0.214408 + 0.616830I
b = −2.00856 + 1.94349I
−1.89061 + 2.95419I −7.91752 − 1.81989I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.59239 + 0.15607I
a = 0.641395 + 0.122732I
b = −0.67883 + 2.71121I
−1.89061 + 1.10558I 3.59610 − 6.57635I
u = 1.59239 − 0.15607I
a = 0.641395 − 0.122732I
b = −0.67883 − 2.71121I
−1.89061 − 1.10558I 3.59610 + 6.57635I
12
III. I
u
3
= hu
7
− 3u
5
− u
4
+ 4u
3
+ 2u
2
+ b − u − 2, −u
8
− u
7
+ · · · + a +
1, u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
3
=
u
8
+ u
7
− 2u
6
− 3u
5
+ u
4
+ 3u
3
+ 2u
2
− 1
−u
7
+ 3u
5
+ u
4
− 4u
3
− 2u
2
+ u + 2
a
10
=
1
−u
2
a
2
=
u
8
+ u
7
− 2u
6
− 3u
5
+ u
4
+ 3u
3
+ 2u
2
− 1
−u
7
+ 3u
5
+ u
4
− 4u
3
− 2u
2
+ 2
a
1
=
0
−u
a
4
=
u
8
+ u
7
− 2u
6
− 3u
5
+ u
4
+ 3u
3
+ 2u
2
− 1
−u
7
+ 3u
5
+ u
4
− 4u
3
− 2u
2
+ u + 2
a
12
=
u
−u
a
6
=
u
3
−u
3
+ u
a
7
=
u
3
−u
3
+ u
a
8
=
u
6
− u
4
+ 1
−u
6
+ 2u
4
− u
2
a
11
=
u
3
−u
5
+ u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
8
− u
7
+ 7u
6
+ 6u
5
− 6u
4
− 7u
3
− 5u
2
+ 7u + 1
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
6
u
9
c
4
(u + 1)
9
c
5
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
7
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
8
, c
11
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
9
, c
12
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
10
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
6
y
9
c
5
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
7
, c
10
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
8
, c
11
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
9
, c
12
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.772920 + 0.510351I
a = −0.900982 − 0.594909I
b = 1.126210 − 0.643329I
−3.42837 − 2.09337I −4.41045 + 5.46639I
u = −0.772920 − 0.510351I
a = −0.900982 + 0.594909I
b = 1.126210 + 0.643329I
−3.42837 + 2.09337I −4.41045 − 5.46639I
u = 0.825933
a = 1.21075
b = 0.564116
−0.446489 −0.182090
u = 1.173910 + 0.391555I
a = 0.766570 − 0.255687I
b = −0.466457 − 0.178345I
2.72642 + 1.33617I 8.07941 − 3.55369I
u = 1.173910 − 0.391555I
a = 0.766570 + 0.255687I
b = −0.466457 + 0.178345I
2.72642 − 1.33617I 8.07941 + 3.55369I
u = −0.141484 + 0.739668I
a = −0.249476 − 1.304240I
b = 1.50705 + 3.27928I
−1.02799 + 2.45442I −2.24638 + 6.63381I
u = −0.141484 − 0.739668I
a = −0.249476 + 1.304240I
b = 1.50705 − 3.27928I
−1.02799 − 2.45442I −2.24638 − 6.63381I
u = −1.172470 + 0.500383I
a = −0.721488 − 0.307914I
b = 0.551136 − 0.143741I
1.95319 − 7.08493I 8.66846 + 5.33071I
u = −1.172470 − 0.500383I
a = −0.721488 + 0.307914I
b = 0.551136 + 0.143741I
1.95319 + 7.08493I 8.66846 − 5.33071I
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
9
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· (u
24
+ 24u
23
+ ··· − 179u + 1)
c
2
((u − 1)
9
)(u
6
+ u
5
+ ··· + u + 1)
2
(u
24
− 12u
23
+ ··· + 17u − 1)
c
3
u
9
(u
6
− u
5
+ ··· − u + 1)
2
(u
24
+ u
23
+ ··· − 2560u + 512)
c
4
((u + 1)
9
)(u
6
− u
5
+ ··· − u + 1)
2
(u
24
− 12u
23
+ ··· + 17u − 1)
c
5
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· (u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
· (u
24
+ 4u
23
+ ··· − 3u − 1)
c
6
u
9
(u
6
+ u
5
+ ··· + u + 1)
2
(u
24
+ u
23
+ ··· − 2560u + 512)
c
7
(u
2
+ u + 1)
6
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
24
+ 8u
23
+ ··· + 7u + 1)
c
8
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
12
+ u
11
+ ··· + 3u + 1)(u
24
− 5u
23
+ ··· − 389242u + 249139)
c
9
(u
9
+ u
8
+ ··· − u − 1)(u
12
+ u
11
+ ··· + 3u + 1)
· (u
24
+ u
23
+ ··· − 74162u − 19441)
c
10
(u
2
− u + 1)
6
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
24
+ 8u
23
+ ··· + 7u + 1)
c
11
(u
2
+ u + 1)
6
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
24
+ 20u
22
+ ··· + 19u + 1)
c
12
u
12
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
24
+ 2u
23
+ ··· + 28672u + 4096)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
9
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
24
+ 204y
23
+ ··· − 2901y + 1)
c
2
, c
4
(y −1)
9
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
24
− 24y
23
+ ··· + 179y + 1)
c
3
, c
6
y
9
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
24
− 63y
23
+ ··· − 3932160y + 262144)
c
5
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
24
+ 26y
22
+ ··· − y + 1)
c
7
, c
10
(y
2
+ y + 1)
6
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
24
+ 20y
22
+ ··· + 19y + 1)
c
8
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
12
− 3y
11
+ ··· − y + 1)
· (y
24
+ 111y
23
+ ··· − 469614992544y + 62070241321)
c
9
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
12
− 3y
11
+ ··· − y + 1)
· (y
24
− 61y
23
+ ··· − 296113128y + 377952481)
c
11
((y
2
+ y + 1)
6
)(y
9
+ 7y
8
+ ··· + 13y −1)
· (y
24
+ 40y
23
+ ··· + 2151y + 1)
c
12
y
12
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
24
− 90y
23
+ ··· + 67108864y + 16777216)
18
