12n
0231
(K12n
0231
)
A knot diagram
1
Linearized knot diagam
3 5 7 6 2 12 4 11 6 7 9 10
Solving Sequence
2,6
5 3 1
4,10
9 12 7 8 11
c
5
c
2
c
1
c
4
c
9
c
12
c
6
c
7
c
11
c
3
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.18774 × 10
22
u
33
− 2.14694 × 10
23
u
32
+ ··· + 1.21101 × 10
23
b − 1.90029 × 10
23
,
− 3.45182 × 10
23
u
33
− 2.34305 × 10
24
u
32
+ ··· + 2.42202 × 10
23
a − 4.10630 × 10
23
,
u
34
+ 7u
33
+ ··· − 74u
2
+ 1i
I
u
2
= hu
4
+ u
3
+ u
2
+ b + 1, −u
8
− u
7
− 2u
6
− u
5
− 2u
4
+ a + u, u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1i
I
u
3
= h85a
4
u + 42a
4
+ 387a
3
u + 199a
3
+ 170a
2
u + 84a
2
− 1331au + 661b + 641a − 639u + 563,
a
5
− a
4
u + 6a
4
− 3a
3
u + 7a
3
− 4a
2
u − 2a
2
− 4au − 3a − 3u + 2, u
2
− u + 1i
* 3 irreducible components of dim
C
= 0, with total 53 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−3.19 × 10
22
u
33
− 2.15 × 10
23
u
32
+ · · · + 1.21 × 10
23
b − 1.90 ×
10
23
, −3.45 × 10
23
u
33
− 2.34 × 10
24
u
32
+ · · · + 2.42 × 10
23
a − 4.11 ×
10
23
, u
34
+ 7u
33
+ · · · − 74u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
4
=
u
2
+ 1
u
2
a
10
=
1.42518u
33
+ 9.67395u
32
+ ··· − 42.6225u + 1.69541
0.263230u
33
+ 1.77285u
32
+ ··· + 0.525882u + 1.56918
a
9
=
1.68841u
33
+ 11.4468u
32
+ ··· − 42.0967u + 3.26459
0.263230u
33
+ 1.77285u
32
+ ··· + 0.525882u + 1.56918
a
12
=
0.659832u
33
+ 4.48364u
32
+ ··· − 8.51786u + 6.27891
0.167487u
33
+ 1.14300u
32
+ ··· − 7.71333u + 0.854394
a
7
=
−1.00469u
33
− 6.82609u
32
+ ··· + 27.7668u − 2.41301
−0.206738u
33
− 1.42931u
32
+ ··· + 2.41301u − 1.00469
a
8
=
−1.16508u
33
− 7.90987u
32
+ ··· + 29.5857u − 3.25804
−0.163277u
33
− 1.11534u
32
+ ··· + 2.61686u − 1.03391
a
11
=
1.21680u
33
+ 8.24852u
32
+ ··· − 28.4228u + 3.63665
0.229994u
33
+ 1.53559u
32
+ ··· − 1.41536u + 1.36080
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
238664623265196673820757
242201601551334258096944
u
33
−
192207794961190758657281
30275200193916782262118
u
32
+ ··· +
3081960954854359198439141
242201601551334258096944
u −
108096673891086962943351
30275200193916782262118
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
34
+ 23u
33
+ ··· − 148u + 1
c
2
, c
5
u
34
+ 7u
33
+ ··· − 74u
2
+ 1
c
3
, c
7
u
34
+ 2u
33
+ ··· − 3072u + 1024
c
6
u
34
+ 4u
33
+ ··· − 3u − 1
c
8
, c
11
u
34
+ 12u
33
+ ··· − 11u − 1
c
9
u
34
+ 2u
33
+ ··· − 10595u + 25489
c
10
u
34
− 4u
33
+ ··· − 666199u + 339173
c
12
u
34
− 3u
33
+ ··· − 5632u + 512
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
34
− 17y
33
+ ··· − 14096y + 1
c
2
, c
5
y
34
+ 23y
33
+ ··· − 148y + 1
c
3
, c
7
y
34
+ 50y
33
+ ··· + 1048576y + 1048576
c
6
y
34
− 4y
33
+ ··· − 19y + 1
c
8
, c
11
y
34
− 4y
33
+ ··· + 65y + 1
c
9
y
34
− 36y
33
+ ··· + 7287355609y + 649689121
c
10
y
34
+ 60y
33
+ ··· − 783443850999y + 115038323929
c
12
y
34
− 51y
33
+ ··· − 3407872y + 262144
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.544020 + 0.828457I
a = −5.20844 + 3.26657I
b = −1.33192 + 0.57161I
2.15188 + 2.20308I −18.1536 + 5.4483I
u = 0.544020 − 0.828457I
a = −5.20844 − 3.26657I
b = −1.33192 − 0.57161I
2.15188 − 2.20308I −18.1536 − 5.4483I
u = 0.257238 + 0.890862I
a = −0.124907 + 0.904670I
b = 0.369797 + 0.819998I
1.56878 + 0.34703I 8.40786 − 0.51532I
u = 0.257238 − 0.890862I
a = −0.124907 − 0.904670I
b = 0.369797 − 0.819998I
1.56878 − 0.34703I 8.40786 + 0.51532I
u = −0.691884 + 0.838034I
a = 0.811010 + 0.201841I
b = 0.622736 − 0.920702I
6.54075 + 2.05806I 13.8961 − 2.8397I
u = −0.691884 − 0.838034I
a = 0.811010 − 0.201841I
b = 0.622736 + 0.920702I
6.54075 − 2.05806I 13.8961 + 2.8397I
u = 0.487947 + 1.003910I
a = −2.08476 + 1.15239I
b = 0.05782 − 1.46259I
0.72250 + 2.82980I 10.05148 − 3.22591I
u = 0.487947 − 1.003910I
a = −2.08476 − 1.15239I
b = 0.05782 + 1.46259I
0.72250 − 2.82980I 10.05148 + 3.22591I
u = 0.657459 + 0.922088I
a = −0.764190 + 0.647851I
b = −0.691749 − 0.367275I
0.62542 + 2.57137I 3.17282 − 2.86214I
u = 0.657459 − 0.922088I
a = −0.764190 − 0.647851I
b = −0.691749 + 0.367275I
0.62542 − 2.57137I 3.17282 + 2.86214I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.175415 + 0.847114I
a = 0.046460 − 1.237630I
b = −0.115474 + 0.349761I
−1.59132 + 1.76956I −2.73476 − 4.21364I
u = 0.175415 − 0.847114I
a = 0.046460 + 1.237630I
b = −0.115474 − 0.349761I
−1.59132 − 1.76956I −2.73476 + 4.21364I
u = −1.132310 + 0.183127I
a = 0.002681 − 0.231147I
b = 1.39864 − 0.29584I
−7.72558 + 0.90268I 5.49060 + 0.21802I
u = −1.132310 − 0.183127I
a = 0.002681 + 0.231147I
b = 1.39864 + 0.29584I
−7.72558 − 0.90268I 5.49060 − 0.21802I
u = −0.623744 + 0.978086I
a = −0.574996 + 0.242105I
b = 0.236214 + 0.979802I
6.07730 − 7.11588I 12.1179 + 9.6630I
u = −0.623744 − 0.978086I
a = −0.574996 − 0.242105I
b = 0.236214 − 0.979802I
6.07730 + 7.11588I 12.1179 − 9.6630I
u = −1.215360 + 0.226914I
a = −0.352940 + 0.538182I
b = −2.06341 + 1.43354I
−7.46169 + 8.00267I 5.84717 − 3.91358I
u = −1.215360 − 0.226914I
a = −0.352940 − 0.538182I
b = −2.06341 − 1.43354I
−7.46169 − 8.00267I 5.84717 + 3.91358I
u = −0.021777 + 1.291760I
a = 1.45710 + 0.36632I
b = −0.94260 − 1.15777I
−2.99715 − 2.34695I 2.86038 + 3.07511I
u = −0.021777 − 1.291760I
a = 1.45710 − 0.36632I
b = −0.94260 + 1.15777I
−2.99715 + 2.34695I 2.86038 − 3.07511I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.649185
a = −0.175240
b = 0.825508
1.38631 7.11490
u = 0.15024 + 1.45013I
a = −1.66300 − 0.69317I
b = 2.33781 + 0.73216I
−3.63061 + 2.77360I 0
u = 0.15024 − 1.45013I
a = −1.66300 + 0.69317I
b = 2.33781 − 0.73216I
−3.63061 − 2.77360I 0
u = −0.65730 + 1.31359I
a = −1.22670 + 0.80696I
b = 1.26804 + 0.74707I
−11.18750 − 7.23815I 0
u = −0.65730 − 1.31359I
a = −1.22670 − 0.80696I
b = 1.26804 − 0.74707I
−11.18750 + 7.23815I 0
u = −0.69399 + 1.33382I
a = 1.80696 − 0.87095I
b = −1.73482 − 1.78350I
−10.8926 − 14.7212I 0
u = −0.69399 − 1.33382I
a = 1.80696 + 0.87095I
b = −1.73482 + 1.78350I
−10.8926 + 14.7212I 0
u = −0.46062 + 1.48862I
a = −1.34753 + 0.57888I
b = 1.88206 + 0.20245I
−13.09350 − 4.80207I 0
u = −0.46062 − 1.48862I
a = −1.34753 − 0.57888I
b = 1.88206 − 0.20245I
−13.09350 + 4.80207I 0
u = −0.43913 + 1.57970I
a = 1.14509 − 1.20205I
b = −2.89525 + 1.03267I
−13.37580 + 1.94532I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.43913 − 1.57970I
a = 1.14509 + 1.20205I
b = −2.89525 − 1.03267I
−13.37580 − 1.94532I 0
u = −0.207141 + 0.051709I
a = −1.65437 + 3.73289I
b = −0.331665 + 0.940404I
0.61291 + 1.48611I 4.79533 − 4.74523I
u = −0.207141 − 0.051709I
a = −1.65437 − 3.73289I
b = −0.331665 − 0.940404I
0.61291 − 1.48611I 4.79533 + 4.74523I
u = 0.0926838
a = −6.35971
b = 1.04203
2.29528 1.25710
8
II. I
u
2
= hu
4
+ u
3
+ u
2
+ b + 1, −u
8
− u
7
− 2u
6
− u
5
− 2u
4
+ a + u, u
9
+ u
8
+
2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
4
=
u
2
+ 1
u
2
a
10
=
u
8
+ u
7
+ 2u
6
+ u
5
+ 2u
4
− u
−u
4
− u
3
− u
2
− 1
a
9
=
u
8
+ u
7
+ 2u
6
+ u
5
+ u
4
− u
3
− u
2
− u − 1
−u
4
− u
3
− u
2
− 1
a
12
=
u
3
u
5
+ u
3
+ u
a
7
=
−u
8
− u
6
− u
4
+ 1
−u
8
− u
7
− u
6
− 2u
5
− u
4
− 2u
3
− 2u + 1
a
8
=
−u
3
−u
5
− u
3
− u
a
11
=
u
8
+ u
7
+ 2u
6
+ u
5
+ u
4
− u
2
− u − 1
u
5
− u
4
− u
2
+ u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
8
+ 9u
7
+ 12u
6
+ 13u
5
+ 15u
4
+ 15u
3
+ 8u
2
+ 5u + 9
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
2
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
3
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
5
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
6
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
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
8
(u + 1)
9
c
9
, c
10
u
9
− u
8
− 2u
7
+ 4u
6
− u
5
− 9u
4
+ 15u
3
− 12u
2
+ 5u − 1
c
11
(u − 1)
9
c
12
u
9
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
2
, c
5
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
3
, c
7
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
6
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
8
, c
11
(y −1)
9
c
9
, c
10
y
9
− 5y
8
+ 10y
7
− y
5
− 37y
4
+ 7y
3
− 12y
2
+ y −1
c
12
y
9
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.140343 + 0.966856I
a = 0.463951 − 1.179170I
b = −0.457852 + 1.072010I
−0.13850 + 2.09337I 3.38047 − 2.85927I
u = 0.140343 − 0.966856I
a = 0.463951 + 1.179170I
b = −0.457852 − 1.072010I
−0.13850 − 2.09337I 3.38047 + 2.85927I
u = 0.628449 + 0.875112I
a = 1.92263 − 3.37970I
b = 1.63880 − 0.65075I
2.26187 + 2.45442I 6.9022 − 12.4598I
u = 0.628449 − 0.875112I
a = 1.92263 + 3.37970I
b = 1.63880 + 0.65075I
2.26187 − 2.45442I 6.9022 + 12.4598I
u = −0.796005 + 0.733148I
a = −0.502055 + 0.200019I
b = −0.522253 + 0.392004I
6.01628 + 1.33617I 6.48878 + 2.15019I
u = −0.796005 − 0.733148I
a = −0.502055 − 0.200019I
b = −0.522253 − 0.392004I
6.01628 − 1.33617I 6.48878 − 2.15019I
u = −0.728966 + 0.986295I
a = 0.259988 − 0.648365I
b = −0.425734 − 0.444312I
5.24306 − 7.08493I 2.48514 + 6.49599I
u = −0.728966 − 0.986295I
a = 0.259988 + 0.648365I
b = −0.425734 + 0.444312I
5.24306 + 7.08493I 2.48514 − 6.49599I
u = 0.512358
a = −0.289029
b = −1.46592
2.84338 17.4870
12
III.
I
u
3
= h85a
4
u+387a
3
u+· · ·+641a+563, −a
4
u−3a
3
u+· · ·−3a+2, u
2
−u+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u − 1
a
3
=
u
u − 1
a
1
=
−1
0
a
4
=
u
u − 1
a
10
=
a
−0.128593a
4
u − 0.585477a
3
u + ··· − 0.969743a − 0.851740
a
9
=
−0.128593a
4
u − 0.585477a
3
u + ··· + 0.0302572a − 0.851740
−0.128593a
4
u − 0.585477a
3
u + ··· − 0.969743a − 0.851740
a
12
=
−0.00605144a
4
u + 0.0665658a
3
u + ··· − 0.527988a − 0.487141
0.337368a
4
u + 1.28896a
3
u + ··· + 0.685325a − 0.341906
a
7
=
0.0862330a
4
u + 0.0514372a
3
u + ··· − 2.72617a + 1.44175
0.611195a
4
u + 2.27685a
3
u + ··· + 1.32678a + 1.20121
a
8
=
0.0862330a
4
u + 0.0514372a
3
u + ··· − 2.72617a + 1.44175
0.611195a
4
u + 2.27685a
3
u + ··· + 1.32678a + 1.20121
a
11
=
0.0226929a
4
u − 0.249622a
3
u + ··· − 2.77005a + 1.32678
0.611195a
4
u + 2.27685a
3
u + ··· + 1.32678a + 1.20121
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
1623
661
a
4
u +
522
661
a
4
+
5282
661
a
3
u +
4173
661
a
3
−
2703
661
a
2
u +
3688
661
a
2
−
9177
661
au +
2301
661
a −
2465
661
u +
6714
661
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
(u
2
− u + 1)
5
c
2
(u
2
+ u + 1)
5
c
3
, c
7
u
10
c
6
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
c
8
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
9
, c
12
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
10
, c
11
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
5
c
3
, c
7
y
10
c
6
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
c
8
, c
10
, c
11
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
9
, c
12
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.953786 + 0.485650I
b = −0.455697 + 1.200150I
5.87256 + 6.43072I 6.63163 − 0.01393I
u = 0.500000 + 0.866025I
a = −1.124940 + 0.303641I
b = −0.455697 − 1.200150I
5.87256 − 2.37095I 3.55752 + 5.27247I
u = 0.500000 + 0.866025I
a = −1.42401 − 0.21550I
b = 0.339110 − 0.822375I
0.32910 + 3.56046I 3.07628 − 9.77765I
u = 0.500000 + 0.866025I
a = 0.000387 − 0.371855I
b = 0.339110 + 0.822375I
0.329100 + 0.499304I 3.01153 − 0.88894I
u = 0.500000 + 0.866025I
a = −3.90523 + 0.66409I
b = −0.766826
2.40108 + 2.02988I 9.72304 + 3.67600I
u = 0.500000 − 0.866025I
a = 0.953786 − 0.485650I
b = −0.455697 − 1.200150I
5.87256 − 6.43072I 6.63163 + 0.01393I
u = 0.500000 − 0.866025I
a = −1.124940 − 0.303641I
b = −0.455697 + 1.200150I
5.87256 + 2.37095I 3.55752 − 5.27247I
u = 0.500000 − 0.866025I
a = −1.42401 + 0.21550I
b = 0.339110 + 0.822375I
0.32910 − 3.56046I 3.07628 + 9.77765I
u = 0.500000 − 0.866025I
a = 0.000387 + 0.371855I
b = 0.339110 − 0.822375I
0.329100 − 0.499304I 3.01153 + 0.88894I
u = 0.500000 − 0.866025I
a = −3.90523 − 0.66409I
b = −0.766826
2.40108 − 2.02988I 9.72304 − 3.67600I
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
2
− u + 1)
5
· (u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
34
+ 23u
33
+ ··· − 148u + 1)
c
2
(u
2
+ u + 1)
5
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
34
+ 7u
33
+ ··· − 74u
2
+ 1)
c
3
u
10
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
34
+ 2u
33
+ ··· − 3072u + 1024)
c
5
(u
2
− u + 1)
5
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
34
+ 7u
33
+ ··· − 74u
2
+ 1)
c
6
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
· (u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
34
+ 4u
33
+ ··· − 3u − 1)
c
7
u
10
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
34
+ 2u
33
+ ··· − 3072u + 1024)
c
8
((u + 1)
9
)(u
5
− u
4
+ ··· + u + 1)
2
(u
34
+ 12u
33
+ ··· − 11u − 1)
c
9
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
· (u
9
− u
8
− 2u
7
+ 4u
6
− u
5
− 9u
4
+ 15u
3
− 12u
2
+ 5u − 1)
· (u
34
+ 2u
33
+ ··· − 10595u + 25489)
c
10
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
· (u
9
− u
8
− 2u
7
+ 4u
6
− u
5
− 9u
4
+ 15u
3
− 12u
2
+ 5u − 1)
· (u
34
− 4u
33
+ ··· − 666199u + 339173)
c
11
((u − 1)
9
)(u
5
+ u
4
+ ··· + u − 1)
2
(u
34
+ 12u
33
+ ··· − 11u − 1)
c
12
u
9
(u
5
− u
4
+ ··· + u − 1)
2
(u
34
− 3u
33
+ ··· − 5632u + 512)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
5
)(y
9
+ 7y
8
+ ··· + 13y −1)
· (y
34
− 17y
33
+ ··· − 14096y + 1)
c
2
, c
5
(y
2
+ y + 1)
5
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
34
+ 23y
33
+ ··· − 148y + 1)
c
3
, c
7
y
10
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
34
+ 50y
33
+ ··· + 1048576y + 1048576)
c
6
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
· (y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
34
− 4y
33
+ ··· − 19y + 1)
c
8
, c
11
((y −1)
9
)(y
5
− 5y
4
+ ··· − y −1)
2
(y
34
− 4y
33
+ ··· + 65y + 1)
c
9
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
· (y
9
− 5y
8
+ 10y
7
− y
5
− 37y
4
+ 7y
3
− 12y
2
+ y −1)
· (y
34
− 36y
33
+ ··· + 7287355609y + 649689121)
c
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
· (y
9
− 5y
8
+ 10y
7
− y
5
− 37y
4
+ 7y
3
− 12y
2
+ y −1)
· (y
34
+ 60y
33
+ ··· − 783443850999y + 115038323929)
c
12
y
9
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
· (y
34
− 51y
33
+ ··· − 3407872y + 262144)
18
