12a
0940
(K12a
0940
)
A knot diagram
1
Linearized knot diagam
4 6 9 1 3 12 11 5 2 8 7 10
Solving Sequence
1,5
4
2,9
10 3 6 8 11 7 12
c
4
c
1
c
9
c
3
c
5
c
8
c
10
c
7
c
12
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h5951u
31
+ 29371u
30
+ ··· + 32768b + 13889, 28929u
31
+ 106501u
30
+ ··· + 32768a − 89345,
u
32
+ 4u
31
+ ··· + u + 1i
I
u
2
= h1.48022 × 10
51
u
53
− 9.91042 × 10
51
u
52
+ ··· + 4.83516 × 10
51
b + 9.88707 × 10
50
,
4.13434 × 10
51
u
53
− 4.03971 × 10
52
u
52
+ ··· + 4.83516 × 10
51
a + 1.72588 × 10
52
, u
54
− 9u
53
+ ··· − 2u + 1i
I
u
3
= hb + a, 16a
4
+ 8a
3
+ 4a
2
+ 1, u + 1i
* 3 irreducible components of dim
C
= 0, with total 90 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
= h5951u
31
+ 29371u
30
+ · · · + 32768b + 13889, 28929u
31
+
106501u
30
+ · · · + 32768a − 89345, u
32
+ 4u
31
+ · · · + u + 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
2
=
−u
u
3
+ u
a
9
=
−0.882843u
31
− 3.25015u
30
+ ··· − 0.148376u + 2.72659
−0.181610u
31
− 0.896332u
30
+ ··· − 2.44537u − 0.423859
a
10
=
−0.712952u
31
− 2.65460u
30
+ ··· + 0.0938721u + 2.54498
−0.146393u
31
− 0.853058u
30
+ ··· − 2.60175u − 0.326263
a
3
=
−
1
4
u
31
−
5
4
u
30
+ ··· −
5
2
u −
1
4
u
a
6
=
−
1
4
u
31
−
3
4
u
30
+ ··· +
7
4
u
2
+
5
4
u
2
a
8
=
−0.701233u
31
− 2.35382u
30
+ ··· + 2.29700u + 3.15045
−0.181610u
31
− 0.896332u
30
+ ··· − 2.44537u − 0.423859
a
11
=
0.511902u
31
+ 1.97064u
30
+ ··· + 1.14709u + 0.383606
−0.204498u
31
− 0.925323u
30
+ ··· − 1.20575u + 0.325104
a
7
=
−0.258972u
31
− 0.793884u
30
+ ··· − 1.97913u + 1.25995
0.0112000u
31
+ 0.0545349u
30
+ ··· − 0.0267944u − 0.0126648
a
12
=
−0.250061u
31
− 0.750305u
30
+ ··· − 3.99988u − 0.749939
0.0000915527u
31
+ 0.000457764u
30
+ ··· + 1.99982u − 0.0000915527
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
86015
65536
u
31
−
380923
65536
u
30
+ ··· −
995329
32768
u −
249857
65536
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
5
u
32
+ 4u
31
+ ··· + u + 1
c
3
u
32
+ 3u
31
+ ··· + 896u + 512
c
6
, c
7
, c
10
c
11
u
32
+ 18u
30
+ ··· − u + 4
c
8
, c
9
16(16u
32
− 24u
31
+ ··· − u + 1)
c
12
u
32
+ 8u
31
+ ··· + 8305u + 2848
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
y
32
+ 14y
31
+ ··· + 33y + 1
c
3
y
32
− 9y
31
+ ··· − 2670592y + 262144
c
6
, c
7
, c
10
c
11
y
32
+ 36y
31
+ ··· + 31y + 16
c
8
, c
9
256(256y
32
− 1472y
31
+ ··· + 17y + 1)
c
12
y
32
+ 32y
30
+ ··· + 102863903y + 8111104
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.256599 + 0.986885I
a = −0.10049 − 1.49632I
b = 0.337537 + 0.540320I
3.01027 + 5.04884I 0.30701 − 11.56239I
u = −0.256599 − 0.986885I
a = −0.10049 + 1.49632I
b = 0.337537 − 0.540320I
3.01027 − 5.04884I 0.30701 + 11.56239I
u = 0.345644 + 1.009830I
a = 2.27410 + 0.29415I
b = 0.565585 − 0.855832I
7.16766 − 6.68129I 1.93207 + 9.16461I
u = 0.345644 − 1.009830I
a = 2.27410 − 0.29415I
b = 0.565585 + 0.855832I
7.16766 + 6.68129I 1.93207 − 9.16461I
u = −1.009820 + 0.356535I
a = 0.0303863 + 0.0965767I
b = 0.314094 − 0.529406I
−2.38238 + 1.00937I −8.36774 + 3.96678I
u = −1.009820 − 0.356535I
a = 0.0303863 − 0.0965767I
b = 0.314094 + 0.529406I
−2.38238 − 1.00937I −8.36774 − 3.96678I
u = 0.192413 + 0.860169I
a = −2.53919 − 0.65062I
b = −0.169632 + 0.678086I
0.86200 − 3.30892I −5.34169 + 10.20096I
u = 0.192413 − 0.860169I
a = −2.53919 + 0.65062I
b = −0.169632 − 0.678086I
0.86200 + 3.30892I −5.34169 − 10.20096I
u = −0.951470 + 0.602157I
a = −0.034445 − 0.220687I
b = −0.231296 + 0.765884I
3.88599 + 2.41937I −3.11602 + 0.15009I
u = −0.951470 − 0.602157I
a = −0.034445 + 0.220687I
b = −0.231296 − 0.765884I
3.88599 − 2.41937I −3.11602 − 0.15009I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.281511 + 1.125070I
a = −0.416521 + 1.283760I
b = −0.516289 − 0.577005I
11.55230 + 7.75949I 4.97482 − 8.49376I
u = −0.281511 − 1.125070I
a = −0.416521 − 1.283760I
b = −0.516289 + 0.577005I
11.55230 − 7.75949I 4.97482 + 8.49376I
u = −1.220860 + 0.244274I
a = 0.0399097 − 0.0594691I
b = −0.566108 + 0.372615I
−1.73949 − 1.91549I 2.47585 + 12.40549I
u = −1.220860 − 0.244274I
a = 0.0399097 + 0.0594691I
b = −0.566108 − 0.372615I
−1.73949 + 1.91549I 2.47585 − 12.40549I
u = −0.094959 + 0.725357I
a = 1.48981 + 1.00716I
b = −0.129239 − 0.554693I
0.025535 + 1.139960I −8.50574 − 4.30443I
u = −0.094959 − 0.725357I
a = 1.48981 − 1.00716I
b = −0.129239 + 0.554693I
0.025535 − 1.139960I −8.50574 + 4.30443I
u = 0.420269 + 1.246540I
a = 1.82639 + 0.12302I
b = 1.14437 − 0.83909I
8.23091 − 6.44551I 4.12576 + 4.32269I
u = 0.420269 − 1.246540I
a = 1.82639 − 0.12302I
b = 1.14437 + 0.83909I
8.23091 + 6.44551I 4.12576 − 4.32269I
u = 0.314298 + 1.327880I
a = −1.72841 + 0.10017I
b = −1.238090 + 0.535901I
17.7364 − 5.5790I 7.02792 + 4.53110I
u = 0.314298 − 1.327880I
a = −1.72841 − 0.10017I
b = −1.238090 − 0.535901I
17.7364 + 5.5790I 7.02792 − 4.53110I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.355850 + 0.236568I
a = −0.0739722 + 0.0539747I
b = 0.760876 − 0.360985I
5.62503 − 3.78657I 5.70330 + 6.74787I
u = −1.355850 − 0.236568I
a = −0.0739722 − 0.0539747I
b = 0.760876 + 0.360985I
5.62503 + 3.78657I 5.70330 − 6.74787I
u = 0.518418 + 1.275920I
a = −1.72300 − 0.24772I
b = −1.29171 + 1.03781I
4.24362 − 9.76929I −1.25839 + 5.39032I
u = 0.518418 − 1.275920I
a = −1.72300 + 0.24772I
b = −1.29171 − 1.03781I
4.24362 + 9.76929I −1.25839 − 5.39032I
u = 0.55321 + 1.32014I
a = 1.64721 + 0.26796I
b = 1.42278 − 1.08044I
5.7810 − 13.9685I 0. + 9.87189I
u = 0.55321 − 1.32014I
a = 1.64721 − 0.26796I
b = 1.42278 + 1.08044I
5.7810 + 13.9685I 0. − 9.87189I
u = 0.57387 + 1.35873I
a = −1.59057 − 0.27419I
b = −1.52973 + 1.09458I
13.6556 − 16.7401I 0. + 8.51609I
u = 0.57387 − 1.35873I
a = −1.59057 + 0.27419I
b = −1.52973 − 1.09458I
13.6556 + 16.7401I 0. − 8.51609I
u = 0.280609 + 0.273796I
a = −2.70544 − 0.09547I
b = 0.602370 + 0.560777I
6.37411 + 2.65460I 3.56626 − 0.84161I
u = 0.280609 − 0.273796I
a = −2.70544 + 0.09547I
b = 0.602370 − 0.560777I
6.37411 − 2.65460I 3.56626 + 0.84161I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.027669 + 0.289263I
a = 1.85423 − 0.48024I
b = −0.225524 − 0.449890I
−0.136971 + 0.967105I −2.67074 − 6.06482I
u = −0.027669 − 0.289263I
a = 1.85423 + 0.48024I
b = −0.225524 + 0.449890I
−0.136971 − 0.967105I −2.67074 + 6.06482I
8
II.
I
u
2
= h1.48 × 10
51
u
53
− 9.91 × 10
51
u
52
+ · · · + 4.84 × 10
51
b + 9.89 × 10
50
, 4.13 ×
10
51
u
53
−4.04×10
52
u
52
+· · ·+4.84×10
51
a+1.73×10
52
, u
54
−9u
53
+· · ·−2u+1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
2
=
−u
u
3
+ u
a
9
=
−0.855058u
53
+ 8.35487u
52
+ ··· + 22.7938u − 3.56943
−0.306136u
53
+ 2.04966u
52
+ ··· + 0.686080u − 0.204483
a
10
=
−1.69713u
53
+ 16.4737u
52
+ ··· + 25.0991u − 3.91216
0.325290u
53
− 3.70225u
52
+ ··· − 3.54168u + 0.678390
a
3
=
−u
53
+ 9u
52
+ ··· − 2u + 2
0.680220u
53
− 6.68054u
52
+ ··· − 5.48108u + 1.66012
a
6
=
−1.66012u
53
+ 15.6213u
52
+ ··· + 15.9415u − 1.16085
0.558559u
53
− 4.66115u
52
+ ··· − 3.02055u − 0.319780
a
8
=
−0.548922u
53
+ 6.30521u
52
+ ··· + 22.1077u − 3.36495
−0.306136u
53
+ 2.04966u
52
+ ··· + 0.686080u − 0.204483
a
11
=
−4.24669u
53
+ 40.3428u
52
+ ··· + 47.5723u − 10.7217
1.00050u
53
− 9.85994u
52
+ ··· − 14.3356u + 3.91478
a
7
=
1.09133u
53
− 9.91498u
52
+ ··· − 1.16671u + 2.04731
1.21711u
53
− 11.7466u
52
+ ··· − 13.4328u + 2.67483
a
12
=
−3.66332u
53
+ 34.7291u
52
+ ··· + 35.8008u − 7.42606
1.03810u
53
− 9.90418u
52
+ ··· − 10.8850u + 1.65805
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.617081u
53
+ 4.53776u
52
+ ··· − 18.3869u − 0.980733
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
5
u
54
− 9u
53
+ ··· − 2u + 1
c
3
(u
27
− u
26
+ ··· + u
2
+ 1)
2
c
6
, c
7
, c
10
c
11
(u
27
− u
26
+ ··· + 2u − 1)
2
c
8
, c
9
u
54
− 3u
53
+ ··· − 84818u + 19843
c
12
(u
27
+ 7u
26
+ ··· + 8u + 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
y
54
+ 35y
53
+ ··· − 40y
2
+ 1
c
3
(y
27
− 9y
26
+ ··· − 2y −1)
2
c
6
, c
7
, c
10
c
11
(y
27
+ 31y
26
+ ··· − 2y −1)
2
c
8
, c
9
y
54
− 25y
53
+ ··· − 3824037376y + 393744649
c
12
(y
27
− y
26
+ ··· − 34y −1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.921500 + 0.406968I
a = −0.098143 + 0.354459I
b = −0.651210 + 0.363163I
12.35320 − 1.66777I 0
u = 0.921500 − 0.406968I
a = −0.098143 − 0.354459I
b = −0.651210 − 0.363163I
12.35320 + 1.66777I 0
u = 0.161760 + 0.956165I
a = −1.253050 − 0.064754I
b = −0.432000 + 1.105310I
1.02184 − 2.57835I 0
u = 0.161760 − 0.956165I
a = −1.253050 + 0.064754I
b = −0.432000 − 1.105310I
1.02184 + 2.57835I 0
u = 0.951163 + 0.106722I
a = 0.0322837 + 0.0980914I
b = −0.964619 − 0.798896I
0.61653 + 4.47788I 0
u = 0.951163 − 0.106722I
a = 0.0322837 − 0.0980914I
b = −0.964619 + 0.798896I
0.61653 − 4.47788I 0
u = −0.496329 + 0.944022I
a = −1.41814 + 0.28063I
b = −0.314214 − 0.391944I
5.18145 + 2.85128I 0
u = −0.496329 − 0.944022I
a = −1.41814 − 0.28063I
b = −0.314214 + 0.391944I
5.18145 − 2.85128I 0
u = −0.104807 + 0.924218I
a = 1.22909 − 2.98282I
b = 1.78798 − 2.72445I
3.33132 − 1.17026I 0
u = −0.104807 − 0.924218I
a = 1.22909 + 2.98282I
b = 1.78798 + 2.72445I
3.33132 + 1.17026I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.065225 + 1.079720I
a = −2.58821 + 1.35436I
b = −3.02330 + 1.65605I
3.33132 + 1.17026I 0
u = −0.065225 − 1.079720I
a = −2.58821 − 1.35436I
b = −3.02330 − 1.65605I
3.33132 − 1.17026I 0
u = 1.078320 + 0.085758I
a = −0.0871196 − 0.0116251I
b = 1.093670 + 0.737998I
1.91204 + 8.19998I 0
u = 1.078320 − 0.085758I
a = −0.0871196 + 0.0116251I
b = 1.093670 − 0.737998I
1.91204 − 8.19998I 0
u = 0.217196 + 1.068080I
a = 1.161920 − 0.060988I
b = 0.58155 − 1.41426I
8.47823 − 4.92710I 0
u = 0.217196 − 1.068080I
a = 1.161920 + 0.060988I
b = 0.58155 + 1.41426I
8.47823 + 4.92710I 0
u = −0.247345 + 0.829128I
a = −0.72161 + 2.41160I
b = −1.71107 + 1.84680I
10.49150 − 2.51533I 0. + 2.69602I
u = −0.247345 − 0.829128I
a = −0.72161 − 2.41160I
b = −1.71107 − 1.84680I
10.49150 + 2.51533I 0. − 2.69602I
u = 1.166100 + 0.065400I
a = 0.1176700 − 0.0348076I
b = −1.188090 − 0.680911I
9.5734 + 10.6398I 0
u = 1.166100 − 0.065400I
a = 0.1176700 + 0.0348076I
b = −1.188090 + 0.680911I
9.5734 − 10.6398I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.079756 + 1.170660I
a = 1.74117 − 0.92940I
b = 2.27864 − 1.57510I
10.49150 + 2.51533I 0
u = −0.079756 − 1.170660I
a = 1.74117 + 0.92940I
b = 2.27864 + 1.57510I
10.49150 − 2.51533I 0
u = −0.073769 + 0.784432I
a = 1.58283 + 0.11155I
b = 0.193099 − 0.493602I
0.014623 + 1.045880I −6.08117 − 3.01333I
u = −0.073769 − 0.784432I
a = 1.58283 − 0.11155I
b = 0.193099 + 0.493602I
0.014623 − 1.045880I −6.08117 + 3.01333I
u = 0.669915 + 0.361204I
a = −0.255426 − 0.498666I
b = 0.703198 + 1.038370I
5.18145 + 2.85128I −1.63883 − 2.96428I
u = 0.669915 − 0.361204I
a = −0.255426 + 0.498666I
b = 0.703198 − 1.038370I
5.18145 − 2.85128I −1.63883 + 2.96428I
u = 0.725355 + 0.171684I
a = 0.393009 − 0.079118I
b = 0.684272 − 0.663809I
4.24468 − 2.34352I 2.62935 + 2.39389I
u = 0.725355 − 0.171684I
a = 0.393009 + 0.079118I
b = 0.684272 + 0.663809I
4.24468 + 2.34352I 2.62935 − 2.39389I
u = −0.283137 + 1.260080I
a = −1.284500 + 0.024403I
b = −1.054780 − 0.274542I
4.24468 + 2.34352I 0
u = −0.283137 − 1.260080I
a = −1.284500 − 0.024403I
b = −1.054780 + 0.274542I
4.24468 − 2.34352I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.409264 + 1.225760I
a = −0.834431 − 0.811290I
b = −1.023220 − 0.245867I
4.95798 0
u = 0.409264 − 1.225760I
a = −0.834431 + 0.811290I
b = −1.023220 + 0.245867I
4.95798 0
u = −0.534434 + 1.240260I
a = 1.216300 − 0.185339I
b = 0.813574 + 0.675546I
0.61653 + 4.47788I 0
u = −0.534434 − 1.240260I
a = 1.216300 + 0.185339I
b = 0.813574 − 0.675546I
0.61653 − 4.47788I 0
u = 0.614014 + 1.218040I
a = 0.596564 + 0.709582I
b = 0.715946 − 0.008325I
6.91814 − 2.81912I 0
u = 0.614014 − 1.218040I
a = 0.596564 − 0.709582I
b = 0.715946 + 0.008325I
6.91814 + 2.81912I 0
u = −0.58989 + 1.32429I
a = −1.153210 + 0.187803I
b = −0.919398 − 0.829277I
1.91204 + 8.19998I 0
u = −0.58989 − 1.32429I
a = −1.153210 − 0.187803I
b = −0.919398 + 0.829277I
1.91204 − 8.19998I 0
u = 0.71899 + 1.27750I
a = −0.555253 − 0.611476I
b = −0.668003 + 0.225605I
14.8083 − 4.6242I 0
u = 0.71899 − 1.27750I
a = −0.555253 + 0.611476I
b = −0.668003 − 0.225605I
14.8083 + 4.6242I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.38748 + 1.41670I
a = 0.871541 + 0.567468I
b = 1.235770 − 0.001891I
6.91814 + 2.81912I 0
u = 0.38748 − 1.41670I
a = 0.871541 − 0.567468I
b = 1.235770 + 0.001891I
6.91814 − 2.81912I 0
u = −0.23579 + 1.45379I
a = 1.156770 + 0.055901I
b = 1.358030 + 0.376262I
12.35320 + 1.66777I 0
u = −0.23579 − 1.45379I
a = 1.156770 − 0.055901I
b = 1.358030 − 0.376262I
12.35320 − 1.66777I 0
u = −0.62331 + 1.38795I
a = 1.111630 − 0.185532I
b = 1.007310 + 0.927914I
9.5734 + 10.6398I 0
u = −0.62331 − 1.38795I
a = 1.111630 + 0.185532I
b = 1.007310 − 0.927914I
9.5734 − 10.6398I 0
u = −0.434092 + 0.000491I
a = 2.00424 − 2.44799I
b = −1.037490 − 0.346331I
8.47823 − 4.92710I −0.19733 + 2.17668I
u = −0.434092 − 0.000491I
a = 2.00424 + 2.44799I
b = −1.037490 + 0.346331I
8.47823 + 4.92710I −0.19733 − 2.17668I
u = 0.42273 + 1.51942I
a = −0.823087 − 0.482299I
b = −1.298270 + 0.142651I
14.8083 + 4.6242I 0
u = 0.42273 − 1.51942I
a = −0.823087 + 0.482299I
b = −1.298270 − 0.142651I
14.8083 − 4.6242I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.095617 + 0.346723I
a = 1.93962 + 1.62724I
b = −0.436010 − 0.692684I
0.014623 + 1.045880I −6.08117 − 3.01333I
u = 0.095617 − 0.346723I
a = 1.93962 − 1.62724I
b = −0.436010 + 0.692684I
0.014623 − 1.045880I −6.08117 + 3.01333I
u = −0.271515 + 0.130422I
a = −3.58247 + 1.91151I
b = 0.768628 + 0.413076I
1.02184 − 2.57835I −3.18083 + 3.65038I
u = −0.271515 − 0.130422I
a = −3.58247 − 1.91151I
b = 0.768628 − 0.413076I
1.02184 + 2.57835I −3.18083 − 3.65038I
17
III. I
u
3
= hb + a, 16a
4
+ 8a
3
+ 4a
2
+ 1, u + 1i
(i) Arc colorings
a
1
=
0
−1
a
5
=
1
0
a
4
=
1
−1
a
2
=
1
−2
a
9
=
a
−a
a
10
=
2a
−3a
a
3
=
1
−1
a
6
=
0
1
a
8
=
2a
−a
a
11
=
8a
3
+ 2a
−4a
3
− 3a
a
7
=
8a
3
+ 4a
2
+ 1
−12a
3
− 2a
2
−
1
2
a
12
=
4a
2
−6a
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −a
2
− 2
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
u
4
c
4
, c
5
(u + 1)
4
c
6
, c
7
u
4
− u
3
+ 3u
2
− 2u + 1
c
8
16(16u
4
+ 8u
3
+ 4u
2
+ 1)
c
9
16(16u
4
− 8u
3
+ 4u
2
+ 1)
c
10
, c
11
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
12
u
4
+ u
3
+ u
2
+ 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y −1)
4
c
3
y
4
c
6
, c
7
, c
10
c
11
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
8
, c
9
256(256y
4
+ 64y
3
+ 48y
2
+ 8y + 1)
c
12
y
4
+ y
3
+ 3y
2
+ 2y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.425904 + 0.455646I
b = 0.425904 − 0.455646I
5.14581 − 3.16396I −1.97378 + 0.38812I
u = −1.00000
a = −0.425904 − 0.455646I
b = 0.425904 + 0.455646I
5.14581 + 3.16396I −1.97378 − 0.38812I
u = −1.00000
a = 0.175904 + 0.360171I
b = −0.175904 − 0.360171I
−1.85594 + 1.41510I −1.90122 − 0.12671I
u = −1.00000
a = 0.175904 − 0.360171I
b = −0.175904 + 0.360171I
−1.85594 − 1.41510I −1.90122 + 0.12671I
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
((u − 1)
4
)(u
32
+ 4u
31
+ ··· + u + 1)(u
54
− 9u
53
+ ··· − 2u + 1)
c
3
u
4
(u
27
− u
26
+ ··· + u
2
+ 1)
2
(u
32
+ 3u
31
+ ··· + 896u + 512)
c
4
, c
5
((u + 1)
4
)(u
32
+ 4u
31
+ ··· + u + 1)(u
54
− 9u
53
+ ··· − 2u + 1)
c
6
, c
7
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
27
− u
26
+ ··· + 2u − 1)
2
· (u
32
+ 18u
30
+ ··· − u + 4)
c
8
256(16u
4
+ 8u
3
+ 4u
2
+ 1)(16u
32
− 24u
31
+ ··· − u + 1)
· (u
54
− 3u
53
+ ··· − 84818u + 19843)
c
9
256(16u
4
− 8u
3
+ 4u
2
+ 1)(16u
32
− 24u
31
+ ··· − u + 1)
· (u
54
− 3u
53
+ ··· − 84818u + 19843)
c
10
, c
11
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
27
− u
26
+ ··· + 2u − 1)
2
· (u
32
+ 18u
30
+ ··· − u + 4)
c
12
(u
4
+ u
3
+ u
2
+ 1)(u
27
+ 7u
26
+ ··· + 8u + 1)
2
· (u
32
+ 8u
31
+ ··· + 8305u + 2848)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
((y −1)
4
)(y
32
+ 14y
31
+ ··· + 33y + 1)(y
54
+ 35y
53
+ ··· − 40y
2
+ 1)
c
3
y
4
(y
27
− 9y
26
+ ··· − 2y −1)
2
· (y
32
− 9y
31
+ ··· − 2670592y + 262144)
c
6
, c
7
, c
10
c
11
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
27
+ 31y
26
+ ··· − 2y −1)
2
· (y
32
+ 36y
31
+ ··· + 31y + 16)
c
8
, c
9
65536(256y
4
+ 64y
3
+ 48y
2
+ 8y + 1)
· (256y
32
− 1472y
31
+ ··· + 17y + 1)
· (y
54
− 25y
53
+ ··· − 3824037376y + 393744649)
c
12
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
27
− y
26
+ ··· − 34y −1)
2
· (y
32
+ 32y
30
+ ··· + 102863903y + 8111104)
23
