12a
0990
(K12a
0990
)
A knot diagram
1
Linearized knot diagam
4 6 11 12 8 3 10 5 1 7 2 9
Solving Sequence
1,9 5,10
8 6 7 12 4 2 11 3
c
9
c
8
c
5
c
7
c
12
c
4
c
1
c
11
c
3
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.42364 × 10
545
u
129
− 6.71560 × 10
546
u
128
+ ··· + 2.82169 × 10
548
b − 2.11413 × 10
552
,
− 1.02551 × 10
550
u
129
− 9.21321 × 10
550
u
128
+ ··· + 1.46192 × 10
552
a − 2.73974 × 10
556
,
u
130
+ 10u
129
+ ··· + 40002776u + 2811556i
I
u
2
= h−8.19734 × 10
33
u
31
− 4.22264 × 10
34
u
30
+ ··· + 9.32464 × 10
31
b − 8.66565 × 10
34
,
− 1.09826 × 10
34
u
31
− 5.65664 × 10
34
u
30
+ ··· + 9.32464 × 10
31
a − 1.17253 × 10
35
,
u
32
+ 6u
31
+ ··· + 48u + 9i
I
u
3
= h−9a
4
− 16a
3
− 76a
2
+ 13b − 40a − 8, a
5
+ 2a
4
+ 9a
3
+ 6a
2
+ 3a + 1, u − 1i
I
u
4
= hb
5
− 2b
4
a + b
3
a
2
− b
3
+ a
2
b + b + a − 1, u − 1i
I
v
1
= ha, b
5
+ b
3
+ b + 1, v − 1i
I
v
2
= ha, b
2
− b + 1, v − 1i
* 5 irreducible components of dim
C
= 0, with total 174 representations.
* 1 irreducible components of dim
C
= 1
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−7.42 × 10
545
u
129
− 6.72 × 10
546
u
128
+ · · · + 2.82 × 10
548
b − 2.11 ×
10
552
, −1.03 × 10
550
u
129
− 9.21 × 10
550
u
128
+ · · · + 1.46 × 10
552
a − 2.74 ×
10
556
, u
130
+ 10u
129
+ · · · + 40002776u + 2811556i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
0.00701480u
129
+ 0.0630213u
128
+ ··· + 249589.u + 18740.7
0.00263092u
129
+ 0.0237999u
128
+ ··· + 99398.1u + 7492.40
a
10
=
1
u
2
a
8
=
0.00101759u
129
+ 0.00900101u
128
+ ··· + 33569.9u + 2537.03
0.000471567u
129
+ 0.00411483u
128
+ ··· + 11762.5u + 842.151
a
6
=
0.00126397u
129
+ 0.0107887u
128
+ ··· + 28928.9u + 2098.07
−0.000934236u
129
− 0.00863981u
128
+ ··· − 40675.0u − 3104.76
a
7
=
0.000150095u
129
+ 0.00122081u
128
+ ··· + 1195.24u + 75.9623
−0.000473077u
129
− 0.00432755u
128
+ ··· − 21590.6u − 1673.46
a
12
=
u
u
a
4
=
0.00233873u
129
+ 0.0208067u
128
+ ··· + 77208.8u + 5758.85
−0.00204515u
129
− 0.0184147u
128
+ ··· − 72982.4u − 5489.48
a
2
=
0.000274293u
129
+ 0.00247203u
128
+ ··· + 11517.0u + 900.409
0.000908201u
129
+ 0.00823727u
128
+ ··· + 35139.9u + 2659.78
a
11
=
0.000756422u
129
+ 0.00676781u
128
+ ··· + 27485.4u + 2094.49
−0.000620407u
129
− 0.00564869u
128
+ ··· − 24415.3u − 1859.15
a
3
=
−0.00217529u
129
− 0.0186835u
128
+ ··· − 48388.1u − 3437.17
−0.000312213u
129
− 0.00218499u
128
+ ··· + 8773.04u + 748.786
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.00272619u
129
− 0.0236021u
128
+ ··· − 76099.3u − 5729.03
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
16(16u
130
− 216u
129
+ ··· − 134148u + 11877)
c
2
, c
6
u
130
+ 10u
129
+ ··· + 40002776u + 2811556
c
3
48(48u
130
− 144u
129
+ ··· − 1.54523 × 10
9
u + 4.56957 × 10
8
)
c
4
48(48u
130
+ 144u
129
+ ··· + 1.54523 × 10
9
u + 4.56957 × 10
8
)
c
5
, c
8
16(16u
130
+ 72u
129
+ ··· + 6.78136 × 10
7
u + 7939137)
c
7
, c
10
16(16u
130
− 72u
129
+ ··· − 6.78136 × 10
7
u + 7939137)
c
9
, c
12
u
130
− 10u
129
+ ··· − 40002776u + 2811556
c
11
16(16u
130
+ 216u
129
+ ··· + 134148u + 11877)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
256(256y
130
− 4640y
129
+ ··· + 2.95033 × 10
9
y + 1.41063 × 10
8
)
c
2
, c
6
, c
9
c
12
y
130
− 80y
129
+ ··· − 226520781477232y + 7904847141136
c
3
, c
4
2304(2304y
130
− 123744y
129
+ ··· − 5.35364 × 10
18
y + 2.08809 × 10
17
)
c
5
, c
7
, c
8
c
10
256
· (256y
130
+ 23008y
129
+ ··· − 581798760447684y + 63029896304769)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.753714 + 0.678165I
a = −0.429062 − 0.743953I
b = −0.617531 + 0.243011I
2.79527 + 2.32555I 0
u = −0.753714 − 0.678165I
a = −0.429062 + 0.743953I
b = −0.617531 − 0.243011I
2.79527 − 2.32555I 0
u = 0.364736 + 0.913386I
a = 0.024867 − 1.138090I
b = 0.568641 − 0.599752I
7.79727 − 3.48496I 0
u = 0.364736 − 0.913386I
a = 0.024867 + 1.138090I
b = 0.568641 + 0.599752I
7.79727 + 3.48496I 0
u = −0.836988 + 0.515749I
a = 0.170742 − 0.519532I
b = −0.865889 − 0.510137I
2.40493 + 2.37289I 0
u = −0.836988 − 0.515749I
a = 0.170742 + 0.519532I
b = −0.865889 + 0.510137I
2.40493 − 2.37289I 0
u = 0.023345 + 1.032480I
a = 0.370646 + 0.393498I
b = −0.226301 + 1.308480I
−1.03079 − 7.20926I 0
u = 0.023345 − 1.032480I
a = 0.370646 − 0.393498I
b = −0.226301 − 1.308480I
−1.03079 + 7.20926I 0
u = −0.014661 + 0.956748I
a = −0.016413 + 0.251138I
b = −0.346796 + 1.202210I
−1.34210 − 3.05609I 0
u = −0.014661 − 0.956748I
a = −0.016413 − 0.251138I
b = −0.346796 − 1.202210I
−1.34210 + 3.05609I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.035250 + 0.190731I
a = 0.19971 + 3.07796I
b = 0.320853 + 1.071130I
4.01258 + 10.32040I 0
u = −1.035250 − 0.190731I
a = 0.19971 − 3.07796I
b = 0.320853 − 1.071130I
4.01258 − 10.32040I 0
u = −1.035300 + 0.209769I
a = −0.09804 − 2.67630I
b = −0.222571 − 1.175360I
−0.16136 + 5.32813I 0
u = −1.035300 − 0.209769I
a = −0.09804 + 2.67630I
b = −0.222571 + 1.175360I
−0.16136 − 5.32813I 0
u = 0.934913 + 0.047377I
a = −1.05680 + 1.64472I
b = −1.37976 + 0.66931I
−1.085330 − 0.334255I 0
u = 0.934913 − 0.047377I
a = −1.05680 − 1.64472I
b = −1.37976 − 0.66931I
−1.085330 + 0.334255I 0
u = 0.049853 + 0.924522I
a = −0.153356 − 0.036650I
b = 0.542235 − 1.129970I
0.16136 − 5.32813I 0
u = 0.049853 − 0.924522I
a = −0.153356 + 0.036650I
b = 0.542235 + 1.129970I
0.16136 + 5.32813I 0
u = −0.872987 + 0.633017I
a = 0.805377 + 0.601460I
b = 0.607331 − 0.671357I
5.31312 + 6.77397I 0
u = −0.872987 − 0.633017I
a = 0.805377 − 0.601460I
b = 0.607331 + 0.671357I
5.31312 − 6.77397I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.072770 + 0.123948I
a = −0.949991 + 0.241825I
b = −1.55098 + 0.35434I
−0.175289 + 0.755522I 0
u = −1.072770 − 0.123948I
a = −0.949991 − 0.241825I
b = −1.55098 − 0.35434I
−0.175289 − 0.755522I 0
u = −0.494026 + 0.973656I
a = −0.039642 + 0.660869I
b = 0.549748 + 0.349714I
8.28948 − 0.12430I 0
u = −0.494026 − 0.973656I
a = −0.039642 − 0.660869I
b = 0.549748 − 0.349714I
8.28948 + 0.12430I 0
u = −1.075040 + 0.250971I
a = 0.44267 + 2.18430I
b = 0.004035 + 1.026040I
3.31794 + 0.02095I 0
u = −1.075040 − 0.250971I
a = 0.44267 − 2.18430I
b = 0.004035 − 1.026040I
3.31794 − 0.02095I 0
u = 0.456734 + 0.758309I
a = −0.220146 + 1.329500I
b = −0.630414 + 0.185361I
3.18794 + 2.74835I 0
u = 0.456734 − 0.758309I
a = −0.220146 − 1.329500I
b = −0.630414 − 0.185361I
3.18794 − 2.74835I 0
u = 0.057062 + 1.121730I
a = −0.328075 − 0.357135I
b = 0.081204 − 1.173900I
−3.18794 − 2.74835I 0
u = 0.057062 − 1.121730I
a = −0.328075 + 0.357135I
b = 0.081204 + 1.173900I
−3.18794 + 2.74835I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.633723 + 0.930558I
a = −0.264958 + 0.097504I
b = 0.360372 + 1.004290I
4.67166 + 6.43689I 0
u = −0.633723 − 0.930558I
a = −0.264958 − 0.097504I
b = 0.360372 − 1.004290I
4.67166 − 6.43689I 0
u = 1.118160 + 0.200599I
a = −0.260842 + 0.467046I
b = −0.241971 − 0.343939I
0.175289 + 0.755522I 0
u = 1.118160 − 0.200599I
a = −0.260842 − 0.467046I
b = −0.241971 + 0.343939I
0.175289 − 0.755522I 0
u = 1.150880 + 0.096037I
a = 0.68555 − 1.68180I
b = 1.31788 − 1.07852I
1.35285 + 1.35711I 0
u = 1.150880 − 0.096037I
a = 0.68555 + 1.68180I
b = 1.31788 + 1.07852I
1.35285 − 1.35711I 0
u = −0.675377 + 0.458882I
a = −0.774522 + 0.511006I
b = 0.883199 + 0.778031I
5.77095 − 2.23844I 0
u = −0.675377 − 0.458882I
a = −0.774522 − 0.511006I
b = 0.883199 − 0.778031I
5.77095 + 2.23844I 0
u = 1.122600 + 0.414773I
a = 0.586166 − 0.434387I
b = 1.51242 − 0.18112I
5.23752 − 12.70220I 0
u = 1.122600 − 0.414773I
a = 0.586166 + 0.434387I
b = 1.51242 + 0.18112I
5.23752 + 12.70220I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.117290 + 0.436159I
a = −0.245386 + 0.250409I
b = −1.214300 + 0.189708I
1.03079 − 7.20926I 0
u = 1.117290 − 0.436159I
a = −0.245386 − 0.250409I
b = −1.214300 − 0.189708I
1.03079 + 7.20926I 0
u = 0.358828 + 0.705709I
a = 0.12414 − 1.52453I
b = 0.919060 − 0.181247I
7.61957 + 8.46626I 0
u = 0.358828 − 0.705709I
a = 0.12414 + 1.52453I
b = 0.919060 + 0.181247I
7.61957 − 8.46626I 0
u = −1.194170 + 0.216526I
a = −0.1010310 + 0.0972354I
b = 0.805770 − 0.072117I
−3.83451 + 4.09650I 0
u = −1.194170 − 0.216526I
a = −0.1010310 − 0.0972354I
b = 0.805770 + 0.072117I
−3.83451 − 4.09650I 0
u = −1.044780 + 0.622507I
a = 0.273966 + 0.169597I
b = 0.782603 + 0.048483I
6.48180 + 5.76489I 0
u = −1.044780 − 0.622507I
a = 0.273966 − 0.169597I
b = 0.782603 − 0.048483I
6.48180 − 5.76489I 0
u = 0.329683 + 0.686949I
a = −0.190985 + 0.512753I
b = −0.197167 − 1.139410I
−2.79527 + 2.32555I 0
u = 0.329683 − 0.686949I
a = −0.190985 − 0.512753I
b = −0.197167 + 1.139410I
−2.79527 − 2.32555I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.109786 + 0.751675I
a = −0.176464 − 0.176646I
b = −0.078798 + 1.232700I
−2.40493 − 2.37289I 0. + 3.45498I
u = 0.109786 − 0.751675I
a = −0.176464 + 0.176646I
b = −0.078798 − 1.232700I
−2.40493 + 2.37289I 0. − 3.45498I
u = 0.666778 + 0.352330I
a = −0.221707 − 0.045968I
b = 0.009186 + 0.579580I
−1.40153 − 1.05154I −7.86277 + 4.17147I
u = 0.666778 − 0.352330I
a = −0.221707 + 0.045968I
b = 0.009186 − 0.579580I
−1.40153 + 1.05154I −7.86277 − 4.17147I
u = 1.156020 + 0.469066I
a = 0.96710 + 1.33519I
b = −0.57209 + 1.34004I
−5.31312 − 6.77397I 0
u = 1.156020 − 0.469066I
a = 0.96710 − 1.33519I
b = −0.57209 − 1.34004I
−5.31312 + 6.77397I 0
u = −0.017517 + 0.748826I
a = 0.531992 − 0.438086I
b = −0.676766 + 0.244339I
3.83451 − 4.09650I 7.00500 + 5.47978I
u = −0.017517 − 0.748826I
a = 0.531992 + 0.438086I
b = −0.676766 − 0.244339I
3.83451 + 4.09650I 7.00500 − 5.47978I
u = 1.180970 + 0.449771I
a = 0.390815 + 0.387101I
b = 1.036510 + 0.294546I
5.16636 − 1.35319I 0
u = 1.180970 − 0.449771I
a = 0.390815 − 0.387101I
b = 1.036510 − 0.294546I
5.16636 + 1.35319I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.239640 + 0.260824I
a = 0.48842 − 1.83678I
b = −0.42902 − 1.54205I
−6.48180 + 5.76489I 0
u = −1.239640 − 0.260824I
a = 0.48842 + 1.83678I
b = −0.42902 + 1.54205I
−6.48180 − 5.76489I 0
u = 1.241470 + 0.269723I
a = 1.30830 + 1.83546I
b = −0.197651 + 1.025220I
−1.35285 − 1.35711I 0
u = 1.241470 − 0.269723I
a = 1.30830 − 1.83546I
b = −0.197651 − 1.025220I
−1.35285 + 1.35711I 0
u = 0.093917 + 1.269940I
a = 0.072961 + 0.421937I
b = 0.446580 + 1.263970I
4.13372 + 13.33210I 0
u = 0.093917 − 1.269940I
a = 0.072961 − 0.421937I
b = 0.446580 − 1.263970I
4.13372 − 13.33210I 0
u = −1.243180 + 0.320864I
a = 0.081592 − 0.683870I
b = −0.845275 − 0.346847I
8.02284I 0
u = −1.243180 − 0.320864I
a = 0.081592 + 0.683870I
b = −0.845275 + 0.346847I
− 8.02284I 0
u = 0.666795 + 0.141044I
a = −0.66167 + 2.42044I
b = 0.008754 − 0.627883I
1.085330 − 0.334255I 9.57088 + 1.14801I
u = 0.666795 − 0.141044I
a = −0.66167 − 2.42044I
b = 0.008754 + 0.627883I
1.085330 + 0.334255I 9.57088 − 1.14801I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.008160 + 0.854564I
a = −0.760383 + 1.106950I
b = −0.05437 + 1.53688I
−3.73555 − 0.16975I 0
u = −1.008160 − 0.854564I
a = −0.760383 − 1.106950I
b = −0.05437 − 1.53688I
−3.73555 + 0.16975I 0
u = 1.237590 + 0.474696I
a = −1.02448 − 1.34428I
b = 0.288525 − 1.360860I
−5.77095 − 2.23844I 0
u = 1.237590 − 0.474696I
a = −1.02448 + 1.34428I
b = 0.288525 + 1.360860I
−5.77095 + 2.23844I 0
u = −0.991826 + 0.911103I
a = 0.573584 − 0.231438I
b = −0.052938 − 0.952608I
3.73555 + 0.16975I 0
u = −0.991826 − 0.911103I
a = 0.573584 + 0.231438I
b = −0.052938 + 0.952608I
3.73555 − 0.16975I 0
u = −0.597839 + 0.258300I
a = −0.753657 − 0.097659I
b = 0.768150 − 0.930723I
5.27647 − 8.28380I 2.01427 + 2.11219I
u = −0.597839 − 0.258300I
a = −0.753657 + 0.097659I
b = 0.768150 + 0.930723I
5.27647 + 8.28380I 2.01427 − 2.11219I
u = −1.357020 + 0.163107I
a = −0.38687 + 1.55697I
b = 0.369656 + 1.349220I
−8.28948 + 0.12430I 0
u = −1.357020 − 0.163107I
a = −0.38687 − 1.55697I
b = 0.369656 − 1.349220I
−8.28948 − 0.12430I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.198050 + 0.689303I
a = 0.72837 − 1.49367I
b = −0.23180 − 1.56792I
−4.67166 + 6.43689I 0
u = −1.198050 − 0.689303I
a = 0.72837 + 1.49367I
b = −0.23180 + 1.56792I
−4.67166 − 6.43689I 0
u = −1.312300 + 0.470220I
a = −0.41812 + 1.71308I
b = 0.79291 + 1.43838I
−4.01258 + 10.32040I 0
u = −1.312300 − 0.470220I
a = −0.41812 − 1.71308I
b = 0.79291 − 1.43838I
−4.01258 − 10.32040I 0
u = −1.300530 + 0.504252I
a = 0.60895 − 1.72558I
b = −0.56564 − 1.50999I
−5.27647 + 8.28380I 0
u = −1.300530 − 0.504252I
a = 0.60895 + 1.72558I
b = −0.56564 + 1.50999I
−5.27647 − 8.28380I 0
u = 1.312370 + 0.479515I
a = −0.87618 − 1.30973I
b = 0.134923 − 1.265220I
−5.43217 − 2.10541I 0
u = 1.312370 − 0.479515I
a = −0.87618 + 1.30973I
b = 0.134923 + 1.265220I
−5.43217 + 2.10541I 0
u = 0.148506 + 1.392590I
a = −0.137908 − 0.474435I
b = −0.325776 − 1.211070I
6.33343I 0
u = 0.148506 − 1.392590I
a = −0.137908 + 0.474435I
b = −0.325776 + 1.211070I
− 6.33343I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.273860 + 0.592135I
a = 0.734001 + 0.890426I
b = 0.051740 + 1.166460I
−3.31794 + 0.02095I 0
u = 1.273860 − 0.592135I
a = 0.734001 − 0.890426I
b = 0.051740 − 1.166460I
−3.31794 − 0.02095I 0
u = −0.495397 + 0.310716I
a = 0.417119 + 0.722502I
b = −0.677998 + 0.911865I
1.34210 − 3.05609I −0.937396 − 0.255279I
u = −0.495397 − 0.310716I
a = 0.417119 − 0.722502I
b = −0.677998 − 0.911865I
1.34210 + 3.05609I −0.937396 + 0.255279I
u = −1.33899 + 0.51718I
a = 0.90186 − 1.60507I
b = −0.42333 − 1.40097I
−5.23752 + 12.70220I 0
u = −1.33899 − 0.51718I
a = 0.90186 + 1.60507I
b = −0.42333 + 1.40097I
−5.23752 − 12.70220I 0
u = 1.41968 + 0.26250I
a = −0.00302 − 1.69865I
b = 0.70256 − 1.50646I
−1.94463 − 10.04110I 0
u = 1.41968 − 0.26250I
a = −0.00302 + 1.69865I
b = 0.70256 + 1.50646I
−1.94463 + 10.04110I 0
u = −1.36539 + 0.52222I
a = −0.78985 + 1.39214I
b = 0.400176 + 1.283150I
−7.61957 + 8.46626I 0
u = −1.36539 − 0.52222I
a = −0.78985 − 1.39214I
b = 0.400176 − 1.283150I
−7.61957 − 8.46626I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.423313 + 0.296983I
a = 0.00550 − 1.68778I
b = −0.724744 − 0.429452I
1.40153 + 1.05154I 7.86277 − 4.17147I
u = −0.423313 − 0.296983I
a = 0.00550 + 1.68778I
b = −0.724744 + 0.429452I
1.40153 − 1.05154I 7.86277 + 4.17147I
u = 0.097755 + 0.491486I
a = −1.236770 + 0.483276I
b = 0.216346 + 0.038687I
− 1.53223I 0. + 5.21422I
u = 0.097755 − 0.491486I
a = −1.236770 − 0.483276I
b = 0.216346 − 0.038687I
1.53223I 0. − 5.21422I
u = 1.38858 + 0.60929I
a = −0.54525 − 1.64395I
b = 0.61138 − 1.50633I
− 19.8680I 0
u = 1.38858 − 0.60929I
a = −0.54525 + 1.64395I
b = 0.61138 + 1.50633I
19.8680I 0
u = −1.40905 + 0.60703I
a = −0.47380 + 1.69536I
b = 0.376799 + 1.360960I
1.94463 + 10.04110I 0
u = −1.40905 − 0.60703I
a = −0.47380 − 1.69536I
b = 0.376799 − 1.360960I
1.94463 − 10.04110I 0
u = 1.43146 + 0.56014I
a = −0.54374 − 1.44918I
b = −0.003348 − 1.376640I
−5.16636 + 1.35319I 0
u = 1.43146 − 0.56014I
a = −0.54374 + 1.44918I
b = −0.003348 + 1.376640I
−5.16636 − 1.35319I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41270 + 0.64298I
a = 0.52202 + 1.52720I
b = −0.53044 + 1.45997I
−4.13372 − 13.33210I 0
u = 1.41270 − 0.64298I
a = 0.52202 − 1.52720I
b = −0.53044 − 1.45997I
−4.13372 + 13.33210I 0
u = 1.47977 + 0.48939I
a = 0.38259 + 1.46555I
b = −0.244975 + 1.367290I
−7.79727 − 3.48496I 0
u = 1.47977 − 0.48939I
a = 0.38259 − 1.46555I
b = −0.244975 − 1.367290I
−7.79727 + 3.48496I 0
u = −1.52475 + 0.33245I
a = 0.592449 − 1.130420I
b = −0.217610 − 0.848286I
7.34776I 0
u = −1.52475 − 0.33245I
a = 0.592449 + 1.130420I
b = −0.217610 + 0.848286I
− 7.34776I 0
u = 1.59554 + 0.07582I
a = −0.090742 + 1.368010I
b = −0.652744 + 1.157550I
−6.13156 − 2.73739I 0
u = 1.59554 − 0.07582I
a = −0.090742 − 1.368010I
b = −0.652744 − 1.157550I
−6.13156 + 2.73739I 0
u = −0.35426 + 1.57209I
a = 0.194375 − 0.813301I
b = 0.176423 − 1.150600I
6.13156 − 2.73739I 0
u = −0.35426 − 1.57209I
a = 0.194375 + 0.813301I
b = 0.176423 + 1.150600I
6.13156 + 2.73739I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.49661 + 0.60373I
a = −0.34049 − 1.45850I
b = 0.502340 − 1.293510I
1.74076 − 6.86356I 0
u = 1.49661 − 0.60373I
a = −0.34049 + 1.45850I
b = 0.502340 + 1.293510I
1.74076 + 6.86356I 0
u = 0.10566 + 1.61110I
a = 0.162626 + 0.594949I
b = 0.209513 + 1.047390I
6.69560 − 0.54555I 0
u = 0.10566 − 1.61110I
a = 0.162626 − 0.594949I
b = 0.209513 − 1.047390I
6.69560 + 0.54555I 0
u = −0.339019 + 0.139188I
a = −1.60556 − 1.70786I
b = 0.747329 − 0.756285I
5.43217 + 2.10541I 2.12435 − 2.26526I
u = −0.339019 − 0.139188I
a = −1.60556 + 1.70786I
b = 0.747329 + 0.756285I
5.43217 − 2.10541I 2.12435 + 2.26526I
u = −1.62410 + 0.36256I
a = 0.595319 − 1.218370I
b = 0.034506 − 1.159720I
−1.74076 − 6.86356I 0
u = −1.62410 − 0.36256I
a = 0.595319 + 1.218370I
b = 0.034506 + 1.159720I
−1.74076 + 6.86356I 0
u = −1.72076 + 0.31634I
a = −0.501264 + 1.182190I
b = 0.109340 + 1.061360I
−6.69560 + 0.54555I 0
u = −1.72076 − 0.31634I
a = −0.501264 − 1.182190I
b = 0.109340 − 1.061360I
−6.69560 − 0.54555I 0
17
II. I
u
2
= h−8.20 × 10
33
u
31
− 4.22 × 10
34
u
30
+ · · · + 9.32 × 10
31
b − 8.67 ×
10
34
, −1.10 × 10
34
u
31
− 5.66 × 10
34
u
30
+ · · · + 9.32 × 10
31
a − 1.17 ×
10
35
, u
32
+ 6u
31
+ · · · + 48u + 9i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
117.780u
31
+ 606.634u
30
+ ··· + 5227.65u + 1257.45
87.9105u
31
+ 452.847u
30
+ ··· + 3864.42u + 929.327
a
10
=
1
u
2
a
8
=
384.711u
31
+ 1981.16u
30
+ ··· + 16939.4u + 4078.44
321.464u
31
+ 1655.85u
30
+ ··· + 14166.0u + 3409.21
a
6
=
801.716u
31
+ 4128.38u
30
+ ··· + 35279.6u + 8483.49
652.744u
31
+ 3361.19u
30
+ ··· + 28713.1u + 6905.43
a
7
=
428.301u
31
+ 2206.06u
30
+ ··· + 18866.4u + 4543.65
352.578u
31
+ 1816.29u
30
+ ··· + 15532.2u + 3738.93
a
12
=
u
u
a
4
=
96.7554u
31
+ 498.440u
30
+ ··· + 4275.68u + 1028.55
66.8855u
31
+ 344.654u
30
+ ··· + 2912.45u + 700.428
a
2
=
302.990u
31
+ 1560.23u
30
+ ··· + 13316.1u + 3201.65
246.862u
31
+ 1271.57u
30
+ ··· + 10861.5u + 2614.73
a
11
=
−55.2391u
31
− 284.324u
30
+ ··· − 2423.72u − 584.247
−48.4524u
31
− 250.439u
30
+ ··· − 2119.52u − 515.406
a
3
=
729.244u
31
+ 3754.96u
30
+ ··· + 32086.0u + 7720.11
594.059u
31
+ 3059.45u
30
+ ··· + 26142.9u + 6290.22
(ii) Obstruction class = 1
(iii) Cusp Shapes = −166.444u
31
− 858.041u
30
+ ··· − 7362.62u − 1779.90
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
32
− 9u
31
+ ··· + u + 1
c
2
, c
12
u
32
− 6u
31
+ ··· − 48u + 9
c
3
u
32
− u
31
+ ··· − 5u + 1
c
4
u
32
+ u
31
+ ··· + 5u + 1
c
5
, c
10
u
32
+ 5u
31
+ ··· − 3u + 1
c
6
, c
9
u
32
+ 6u
31
+ ··· + 48u + 9
c
7
, c
8
u
32
− 5u
31
+ ··· + 3u + 1
c
11
u
32
+ 9u
31
+ ··· − u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
32
− 9y
31
+ ··· − 9y + 1
c
2
, c
6
, c
9
c
12
y
32
− 16y
31
+ ··· − 828y + 81
c
3
, c
4
y
32
− 7y
31
+ ··· − 41y + 1
c
5
, c
7
, c
8
c
10
y
32
+ 27y
31
+ ··· + 5y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.067705 + 1.010090I
a = −0.048060 − 0.172045I
b = 0.353850 − 1.166680I
−1.61372 − 4.11514I −0.85266 + 6.11990I
u = −0.067705 − 1.010090I
a = −0.048060 + 0.172045I
b = 0.353850 + 1.166680I
−1.61372 + 4.11514I −0.85266 − 6.11990I
u = −0.943719 + 0.595766I
a = 0.088776 + 0.635826I
b = −0.448591 − 0.100099I
5.35541 + 0.09313I 6.64556 + 0.50727I
u = −0.943719 − 0.595766I
a = 0.088776 − 0.635826I
b = −0.448591 + 0.100099I
5.35541 − 0.09313I 6.64556 − 0.50727I
u = −0.909086 + 0.676337I
a = −0.737129 − 0.415629I
b = −0.177399 + 0.264576I
5.33495 + 4.85201I 2.71864 − 2.25825I
u = −0.909086 − 0.676337I
a = −0.737129 + 0.415629I
b = −0.177399 − 0.264576I
5.33495 − 4.85201I 2.71864 + 2.25825I
u = −0.849383 + 0.001189I
a = 1.96233 + 2.54289I
b = 1.83959 + 1.90523I
−0.523059 + 0.539324I 9.43070 − 3.62826I
u = −0.849383 − 0.001189I
a = 1.96233 − 2.54289I
b = 1.83959 − 1.90523I
−0.523059 − 0.539324I 9.43070 + 3.62826I
u = 1.081470 + 0.446382I
a = −0.87185 − 1.52233I
b = 0.34721 − 1.47661I
−5.33495 − 4.85201I −2.71864 + 2.25825I
u = 1.081470 − 0.446382I
a = −0.87185 + 1.52233I
b = 0.34721 + 1.47661I
−5.33495 + 4.85201I −2.71864 − 2.25825I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.715685 + 0.218279I
a = −1.46034 + 2.45351I
b = 0.093344 − 0.937071I
0.523059 − 0.539324I −9.43070 + 3.62826I
u = 0.715685 − 0.218279I
a = −1.46034 − 2.45351I
b = 0.093344 + 0.937071I
0.523059 + 0.539324I −9.43070 − 3.62826I
u = 0.703772 + 0.206426I
a = −0.14434 − 1.44890I
b = 0.470436 + 0.090968I
− 1.04605I 0. + 6.29952I
u = 0.703772 − 0.206426I
a = −0.14434 + 1.44890I
b = 0.470436 − 0.090968I
1.04605I 0. − 6.29952I
u = −0.093791 + 1.268970I
a = −0.238721 − 0.635122I
b = −0.250820 − 0.812318I
7.26512 − 0.92116I 7.37317 + 3.02039I
u = −0.093791 − 1.268970I
a = −0.238721 + 0.635122I
b = −0.250820 + 0.812318I
7.26512 + 0.92116I 7.37317 − 3.02039I
u = 1.171050 + 0.664348I
a = 0.82723 + 1.15816I
b = 0.026494 + 1.398610I
−5.35541 + 0.09313I 0
u = 1.171050 − 0.664348I
a = 0.82723 − 1.15816I
b = 0.026494 − 1.398610I
−5.35541 − 0.09313I 0
u = −1.291840 + 0.504469I
a = −0.60889 + 1.63176I
b = 0.64554 + 1.43209I
−5.43955 + 9.43203I 0
u = −1.291840 − 0.504469I
a = −0.60889 − 1.63176I
b = 0.64554 − 1.43209I
−5.43955 − 9.43203I 0
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.509836 + 0.230939I
a = −1.20134 + 1.58135I
b = −0.576126 − 0.662311I
5.43955 + 9.43203I 3.26415 − 8.13278I
u = −0.509836 − 0.230939I
a = −1.20134 − 1.58135I
b = −0.576126 + 0.662311I
5.43955 − 9.43203I 3.26415 + 8.13278I
u = −0.229199 + 0.437345I
a = 1.77415 + 0.07651I
b = 0.440725 + 0.723545I
1.61372 + 4.11514I 0.85266 − 6.11990I
u = −0.229199 − 0.437345I
a = 1.77415 − 0.07651I
b = 0.440725 − 0.723545I
1.61372 − 4.11514I 0.85266 + 6.11990I
u = −1.52202 + 0.34957I
a = 0.17516 − 1.62801I
b = −0.485248 − 1.220680I
9.42763I 0
u = −1.52202 − 0.34957I
a = 0.17516 + 1.62801I
b = −0.485248 + 1.220680I
− 9.42763I 0
u = 1.56447 + 0.27140I
a = 0.522596 + 1.253690I
b = −0.190106 + 1.102650I
−7.26512 − 0.92116I 0
u = 1.56447 − 0.27140I
a = 0.522596 − 1.253690I
b = −0.190106 − 1.102650I
−7.26512 + 0.92116I 0
u = −0.18698 + 1.59880I
a = −0.248128 + 0.750877I
b = −0.145927 + 1.131960I
6.00215 − 2.42101I 0
u = −0.18698 − 1.59880I
a = −0.248128 − 0.750877I
b = −0.145927 − 1.131960I
6.00215 + 2.42101I 0
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.63288 + 0.14865I
a = 0.041897 + 1.378680I
b = 0.557035 + 1.203400I
−6.00215 + 2.42101I 0
u = −1.63288 − 0.14865I
a = 0.041897 − 1.378680I
b = 0.557035 − 1.203400I
−6.00215 − 2.42101I 0
24
III.
I
u
3
= h−9a
4
− 16a
3
− 76a
2
+ 13b −40a − 8, a
5
+ 2a
4
+ 9a
3
+ 6a
2
+ 3a + 1, u − 1i
(i) Arc colorings
a
1
=
0
1
a
9
=
1
0
a
5
=
a
0.692308a
4
+ 1.23077a
3
+ ··· + 3.07692a + 0.615385
a
10
=
1
1
a
8
=
−0.153846a
4
− 0.384615a
3
+ ··· − 1.46154a + 0.307692
−0.461538a
4
− 1.15385a
3
+ ··· − 4.38462a − 1.07692
a
6
=
0.461538a
4
+ 1.15385a
3
+ ··· + 4.38462a + 1.07692
0.769231a
4
+ 1.92308a
3
+ ··· + 7.30769a + 2.46154
a
7
=
−0.461538a
4
− 1.15385a
3
+ ··· − 4.38462a − 1.07692
−0.769231a
4
− 1.92308a
3
+ ··· − 7.30769a − 2.46154
a
12
=
1
1
a
4
=
0.692308a
4
+ 1.23077a
3
+ ··· + 3.07692a + 0.615385
1.38462a
4
+ 2.46154a
3
+ ··· + 5.15385a + 1.23077
a
2
=
0.461538a
4
+ 1.15385a
3
+ ··· + 4.38462a + 1.07692
0.769231a
4
+ 1.92308a
3
+ ··· + 7.30769a + 2.46154
a
11
=
0.692308a
4
+ 1.23077a
3
+ ··· + 2.07692a + 0.615385
1.38462a
4
+ 2.46154a
3
+ ··· + 5.15385a + 1.23077
a
3
=
0.461538a
4
+ 1.15385a
3
+ ··· + 4.38462a + 1.07692
0.769231a
4
+ 1.92308a
3
+ ··· + 7.30769a + 2.46154
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
+ 2u
4
+ 3u
3
+ 2u
2
+ u − 1
c
2
, c
6
u
5
c
3
, c
7
, c
10
c
11
u
5
+ u
3
+ u + 1
c
4
u
5
+ u
3
− 2u
2
− u + 2
c
5
, c
8
u
5
− 2u
4
+ 3u
3
− 2u
2
+ u + 1
c
9
, c
12
(u + 1)
5
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
8
y
5
+ 2y
4
+ 3y
3
+ 6y
2
+ 5y − 1
c
2
, c
6
y
5
c
3
, c
7
, c
10
c
11
y
5
+ 2y
4
+ 3y
3
+ 2y
2
+ y − 1
c
4
y
5
+ 2y
4
− y
3
− 6y
2
+ 9y − 4
c
9
, c
12
(y − 1)
5
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.104309 + 0.503525I
b = −0.994802 + 0.833601I
−1.64493 −6.00000
u = 1.00000
a = −0.104309 − 0.503525I
b = −0.994802 − 0.833601I
−1.64493 −6.00000
u = 1.00000
a = −0.489595
b = 0.405620
−1.64493 −6.00000
u = 1.00000
a = −0.65089 + 2.70201I
b = −0.208008 + 1.191750I
−1.64493 −6.00000
u = 1.00000
a = −0.65089 − 2.70201I
b = −0.208008 − 1.191750I
−1.64493 −6.00000
28
IV. I
u
4
= hb
5
− 2b
4
a + b
3
a
2
− b
3
+ a
2
b + b + a − 1, u − 1i
(i) Arc colorings
a
1
=
0
1
a
9
=
1
0
a
5
=
a
b
a
10
=
1
1
a
8
=
ba + 1
b
2
a
6
=
b
2
a + b + a
b
3
+ b
a
7
=
b
2
2b
2
− ba − 1
a
12
=
1
1
a
4
=
b
2b − a
a
2
=
−b
2
−2b
2
+ ba + 1
a
11
=
b
4
− b
3
a − b
2
+ 1
2b
4
− 3b
3
a + b
2
a
2
− 3b
2
+ 2ba + 2
a
3
=
b
2
a − b
2
+ b + a
b
3
− 2b
2
+ ba + b + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
(iv) u-Polynomials at the component : It cannot be defined for a positive
dimension component.
(v) Riley Polynomials at the component : It cannot be defined for a positive
dimension component.
29
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = ···
a = ···
b = ···
0 0
30
V. I
v
1
= ha, b
5
+ b
3
+ b + 1, v − 1i
(i) Arc colorings
a
1
=
1
0
a
9
=
1
0
a
5
=
0
b
a
10
=
1
0
a
8
=
1
b
2
a
6
=
b
b
3
+ b
a
7
=
b
2
+ 1
b
2
a
12
=
1
0
a
4
=
b
b
a
2
=
b
2
+ 1
b
2
a
11
=
b
4
+ b
2
+ 1
b
4
a
3
=
b
2
+ b + 1
b
3
+ b
2
+ b
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
8
u
5
+ u
3
+ u − 1
c
2
, c
6
(u − 1)
5
c
3
u
5
+ u
3
+ 2u
2
− u − 2
c
7
, c
10
u
5
+ 2u
4
+ 3u
3
+ 2u
2
+ u − 1
c
9
, c
12
u
5
c
11
u
5
− 2u
4
+ 3u
3
− 2u
2
+ u + 1
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
8
y
5
+ 2y
4
+ 3y
3
+ 2y
2
+ y − 1
c
2
, c
6
(y − 1)
5
c
3
y
5
+ 2y
4
− y
3
− 6y
2
+ 9y − 4
c
7
, c
10
, c
11
y
5
+ 2y
4
+ 3y
3
+ 6y
2
+ 5y − 1
c
9
, c
12
y
5
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 0.707729 + 0.841955I
1.64493 6.00000
v = 1.00000
a = 0
b = 0.707729 − 0.841955I
1.64493 6.00000
v = 1.00000
a = 0
b = −0.389287 + 1.070680I
1.64493 6.00000
v = 1.00000
a = 0
b = −0.389287 − 1.070680I
1.64493 6.00000
v = 1.00000
a = 0
b = −0.636883
1.64493 6.00000
34
VI. I
v
2
= ha, b
2
− b + 1, v − 1i
(i) Arc colorings
a
1
=
1
0
a
9
=
1
0
a
5
=
0
b
a
10
=
1
0
a
8
=
1
b − 1
a
6
=
b
b − 1
a
7
=
b
b − 1
a
12
=
1
0
a
4
=
b
b
a
2
=
b
b − 1
a
11
=
0
−b
a
3
=
b
b − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
7
c
8
u
2
− u + 1
c
2
, c
6
, c
9
c
12
u
2
c
4
, c
5
, c
10
c
11
u
2
+ u + 1
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
7
, c
8
c
10
, c
11
y
2
+ y + 1
c
2
, c
6
, c
9
c
12
y
2
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 0.500000 + 0.866025I
0 0
v = 1.00000
a = 0
b = 0.500000 − 0.866025I
0 0
38
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
16(u
2
− u + 1)(u
5
+ u
3
+ u − 1)(u
5
+ 2u
4
+ 3u
3
+ 2u
2
+ u − 1)
· (u
32
− 9u
31
+ ··· + u + 1)(16u
130
− 216u
129
+ ··· − 134148u + 11877)
c
2
u
7
(u − 1)
5
(u
32
− 6u
31
+ ··· − 48u + 9)
· (u
130
+ 10u
129
+ ··· + 40002776u + 2811556)
c
3
48(u
2
− u + 1)(u
5
+ u
3
+ u + 1)(u
5
+ u
3
+ 2u
2
− u − 2)
· (u
32
− u
31
+ ··· − 5u + 1)
· (48u
130
− 144u
129
+ ··· − 1545225608u + 456956512)
c
4
48(u
2
+ u + 1)(u
5
+ u
3
+ u − 1)(u
5
+ u
3
− 2u
2
− u + 2)
· (u
32
+ u
31
+ ··· + 5u + 1)
· (48u
130
+ 144u
129
+ ··· + 1545225608u + 456956512)
c
5
16(u
2
+ u + 1)(u
5
+ u
3
+ u − 1)(u
5
− 2u
4
+ 3u
3
− 2u
2
+ u + 1)
· (u
32
+ 5u
31
+ ··· − 3u + 1)
· (16u
130
+ 72u
129
+ ··· + 67813572u + 7939137)
c
6
u
7
(u − 1)
5
(u
32
+ 6u
31
+ ··· + 48u + 9)
· (u
130
+ 10u
129
+ ··· + 40002776u + 2811556)
c
7
16(u
2
− u + 1)(u
5
+ u
3
+ u + 1)(u
5
+ 2u
4
+ 3u
3
+ 2u
2
+ u − 1)
· (u
32
− 5u
31
+ ··· + 3u + 1)
· (16u
130
− 72u
129
+ ··· − 67813572u + 7939137)
c
8
16(u
2
− u + 1)(u
5
+ u
3
+ u − 1)(u
5
− 2u
4
+ 3u
3
− 2u
2
+ u + 1)
· (u
32
− 5u
31
+ ··· + 3u + 1)
· (16u
130
+ 72u
129
+ ··· + 67813572u + 7939137)
c
9
u
7
(u + 1)
5
(u
32
+ 6u
31
+ ··· + 48u + 9)
· (u
130
− 10u
129
+ ··· − 40002776u + 2811556)
c
10
16(u
2
+ u + 1)(u
5
+ u
3
+ u + 1)(u
5
+ 2u
4
+ 3u
3
+ 2u
2
+ u − 1)
· (u
32
+ 5u
31
+ ··· − 3u + 1)
· (16u
130
− 72u
129
+ ··· − 67813572u + 7939137)
c
11
16(u
2
+ u + 1)(u
5
+ u
3
+ u + 1)(u
5
− 2u
4
+ 3u
3
− 2u
2
+ u + 1)
· (u
32
+ 9u
31
+ ··· − u + 1)(16u
130
+ 216u
129
+ ··· + 134148u + 11877)
c
12
u
7
(u + 1)
5
(u
32
− 6u
31
+ ··· − 48u + 9)
· (u
130
− 10u
129
+ ··· − 40002776u + 2811556)
39
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
256(y
2
+ y + 1)(y
5
+ 2y
4
+ 3y
3
+ 2y
2
+ y − 1)
· (y
5
+ 2y
4
+ 3y
3
+ 6y
2
+ 5y − 1)(y
32
− 9y
31
+ ··· − 9y + 1)
· (256y
130
− 4640y
129
+ ··· + 2950330002y + 141063129)
c
2
, c
6
, c
9
c
12
y
7
(y − 1)
5
(y
32
− 16y
31
+ ··· − 828y + 81)
· (y
130
− 80y
129
+ ··· − 226520781477232y + 7904847141136)
c
3
, c
4
2304(y
2
+ y + 1)(y
5
+ 2y
4
− y
3
− 6y
2
+ 9y − 4)
· (y
5
+ 2y
4
+ 3y
3
+ 2y
2
+ y − 1)(y
32
− 7y
31
+ ··· − 41y + 1)
· (2304y
130
− 1.24 × 10
5
y
129
+ ··· − 5.35 × 10
18
y + 2.09 × 10
17
)
c
5
, c
7
, c
8
c
10
256(y
2
+ y + 1)(y
5
+ 2y
4
+ 3y
3
+ 2y
2
+ y − 1)
· (y
5
+ 2y
4
+ 3y
3
+ 6y
2
+ 5y − 1)(y
32
+ 27y
31
+ ··· + 5y + 1)
· (256y
130
+ 23008y
129
+ ··· − 581798760447684y + 63029896304769)
40
