12a
0089
(K12a
0089
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 10 9 12 4 6 1 7 11
Solving Sequence
5,10 3,6
2 1 11 4 9 7 8 12
c
5
c
2
c
1
c
10
c
4
c
9
c
6
c
8
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.39749 × 10
215
u
99
− 3.64797 × 10
215
u
98
+ ··· + 1.47790 × 10
217
b − 8.18496 × 10
217
,
− 7.22651 × 10
217
u
99
− 1.52650 × 10
218
u
98
+ ··· + 6.20718 × 10
218
a + 5.09074 × 10
219
,
u
100
+ 2u
99
+ ··· − 329u − 49i
I
u
2
= h1878a
5
u − 2600a
4
u + ··· + 23830a − 8647,
a
6
+ 3a
5
u − 4a
5
− 7a
4
u − a
4
+ a
3
u − 3a
3
− 9a
2
u + 5a
2
+ 6au + 2a − u, u
2
+ 1i
I
u
3
= hb + 1, −u
3
− u
2
+ a − 3u − 2, u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1i
* 3 irreducible components of dim
C
= 0, with total 117 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−2.40 × 10
215
u
99
− 3.65 × 10
215
u
98
+ · · · + 1.48 × 10
217
b − 8.18 ×
10
217
, −7.23 × 10
217
u
99
− 1.53 × 10
218
u
98
+ · · · + 6.21 × 10
218
a + 5.09 ×
10
219
, u
100
+ 2u
99
+ · · · − 329u − 49i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
0.116422u
99
+ 0.245925u
98
+ ··· − 89.5951u − 8.20137
0.0162222u
99
+ 0.0246835u
98
+ ··· + 12.6540u + 5.53823
a
6
=
1
−u
2
a
2
=
0.132644u
99
+ 0.270609u
98
+ ··· − 76.9410u − 2.66314
0.0162222u
99
+ 0.0246835u
98
+ ··· + 12.6540u + 5.53823
a
1
=
0.109624u
99
+ 0.205069u
98
+ ··· − 101.450u − 13.1153
0.0556512u
99
+ 0.125051u
98
+ ··· − 32.6639u − 1.40263
a
11
=
0.0962786u
99
+ 0.162953u
98
+ ··· − 42.0923u + 2.63606
−0.0148568u
99
− 0.0180767u
98
+ ··· + 15.1895u + 5.87732
a
4
=
0.0397497u
99
+ 0.138384u
98
+ ··· − 87.1158u − 19.5365
0.0202763u
99
+ 0.0752641u
98
+ ··· − 32.7675u − 4.86979
a
9
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
0.0290553u
99
+ 0.0399308u
98
+ ··· + 26.9108u + 15.1478
−0.0135353u
99
− 0.0340762u
98
+ ··· + 44.4150u + 8.98928
a
12
=
0.109897u
99
+ 0.198612u
98
+ ··· − 42.6716u + 4.91221
−0.0101391u
99
− 0.0246196u
98
+ ··· + 21.3117u + 6.96002
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.216920u
99
+ 0.318284u
98
+ ··· − 68.3104u + 21.0535
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
100
+ 50u
99
+ ··· + 79u + 1
c
2
, c
4
u
100
− 10u
99
+ ··· + 11u − 1
c
3
, c
8
u
100
+ u
99
+ ··· + 224u + 32
c
5
, c
6
, c
9
u
100
+ 2u
99
+ ··· − 329u − 49
c
7
, c
11
u
100
+ 2u
99
+ ··· − 15u − 17
c
10
, c
12
u
100
− 32u
99
+ ··· + 149u + 289
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
100
+ 10y
99
+ ··· − 2487y + 1
c
2
, c
4
y
100
− 50y
99
+ ··· − 79y + 1
c
3
, c
8
y
100
− 45y
99
+ ··· − 52736y + 1024
c
5
, c
6
, c
9
y
100
+ 98y
99
+ ··· + 34251y + 2401
c
7
, c
11
y
100
− 32y
99
+ ··· + 149y + 289
c
10
, c
12
y
100
+ 80y
99
+ ··· − 3531239y + 83521
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.065515 + 0.990541I
a = −0.41447 + 7.77506I
b = −1.024690 − 0.010060I
−3.35320 − 2.04195I 0
u = −0.065515 − 0.990541I
a = −0.41447 − 7.77506I
b = −1.024690 + 0.010060I
−3.35320 + 2.04195I 0
u = −0.969042 + 0.362969I
a = −0.44792 − 1.56289I
b = 1.167800 + 0.578024I
−1.88652 − 12.41730I 0
u = −0.969042 − 0.362969I
a = −0.44792 + 1.56289I
b = 1.167800 − 0.578024I
−1.88652 + 12.41730I 0
u = 0.940871 + 0.436198I
a = −0.35176 + 1.46851I
b = 1.145610 − 0.541902I
−2.76156 + 6.42552I 0
u = 0.940871 − 0.436198I
a = −0.35176 − 1.46851I
b = 1.145610 + 0.541902I
−2.76156 − 6.42552I 0
u = −0.449054 + 0.956643I
a = 0.757248 − 1.013000I
b = 0.254382 + 0.493343I
−1.24139 + 2.42018I 0
u = −0.449054 − 0.956643I
a = 0.757248 + 1.013000I
b = 0.254382 − 0.493343I
−1.24139 − 2.42018I 0
u = −0.246189 + 1.031340I
a = −0.113223 + 0.585328I
b = 0.978093 − 0.719756I
2.20888 + 3.42556I 0
u = −0.246189 − 1.031340I
a = −0.113223 − 0.585328I
b = 0.978093 + 0.719756I
2.20888 − 3.42556I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.843566 + 0.298352I
a = −0.38582 + 1.43354I
b = 0.289367 − 0.846254I
0.73862 − 7.15845I 0
u = −0.843566 − 0.298352I
a = −0.38582 − 1.43354I
b = 0.289367 + 0.846254I
0.73862 + 7.15845I 0
u = −0.299712 + 1.087720I
a = 0.278229 − 1.043020I
b = 0.683576 + 0.775155I
3.05539 − 2.19835I 0
u = −0.299712 − 1.087720I
a = 0.278229 + 1.043020I
b = 0.683576 − 0.775155I
3.05539 + 2.19835I 0
u = 0.764156 + 0.417633I
a = 0.82151 − 2.08873I
b = −1.072760 + 0.478965I
−3.62812 + 6.33519I 0
u = 0.764156 − 0.417633I
a = 0.82151 + 2.08873I
b = −1.072760 − 0.478965I
−3.62812 − 6.33519I 0
u = 0.588441 + 0.632133I
a = 0.860063 + 0.744032I
b = −1.160920 − 0.298625I
−4.41103 − 1.68246I 0
u = 0.588441 − 0.632133I
a = 0.860063 − 0.744032I
b = −1.160920 + 0.298625I
−4.41103 + 1.68246I 0
u = 0.187210 + 1.126150I
a = 1.048240 + 0.603763I
b = −0.668387 − 0.373530I
−1.86846 + 1.01624I 0
u = 0.187210 − 1.126150I
a = 1.048240 − 0.603763I
b = −0.668387 + 0.373530I
−1.86846 − 1.01624I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.680822 + 0.503951I
a = 0.71326 + 2.08961I
b = −1.097340 − 0.410444I
−4.15515 − 0.77241I 0
u = −0.680822 − 0.503951I
a = 0.71326 − 2.08961I
b = −1.097340 + 0.410444I
−4.15515 + 0.77241I 0
u = 0.775959 + 0.333569I
a = −0.247079 − 1.299000I
b = 0.253877 + 0.752651I
−0.16735 + 1.55705I 0
u = 0.775959 − 0.333569I
a = −0.247079 + 1.299000I
b = 0.253877 − 0.752651I
−0.16735 − 1.55705I 0
u = 0.796339 + 0.840767I
a = −0.413671 − 0.190155I
b = 1.063020 + 0.436471I
−3.95267 − 0.55388I 0
u = 0.796339 − 0.840767I
a = −0.413671 + 0.190155I
b = 1.063020 − 0.436471I
−3.95267 + 0.55388I 0
u = −0.670815 + 0.499865I
a = 0.827036 − 0.598048I
b = −1.224950 + 0.246355I
−4.17026 − 3.77857I 0
u = −0.670815 − 0.499865I
a = 0.827036 + 0.598048I
b = −1.224950 − 0.246355I
−4.17026 + 3.77857I 0
u = 0.471451 + 1.064550I
a = 0.468004 + 0.750338I
b = 0.586409 − 0.261443I
−2.12923 + 2.75082I 0
u = 0.471451 − 1.064550I
a = 0.468004 − 0.750338I
b = 0.586409 + 0.261443I
−2.12923 − 2.75082I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.748764 + 0.934617I
a = −0.435746 + 0.254991I
b = 1.101640 − 0.489464I
−3.58978 + 6.56550I 0
u = −0.748764 − 0.934617I
a = −0.435746 − 0.254991I
b = 1.101640 + 0.489464I
−3.58978 − 6.56550I 0
u = 0.545121 + 0.587251I
a = 0.377482 + 1.297890I
b = 0.940217 − 0.555672I
0.74183 + 4.19177I 0. − 6.66805I
u = 0.545121 − 0.587251I
a = 0.377482 − 1.297890I
b = 0.940217 + 0.555672I
0.74183 − 4.19177I 0. + 6.66805I
u = −0.681505 + 0.289527I
a = 0.03851 − 1.94789I
b = 1.043400 + 0.637281I
4.27099 − 6.89948I 11.43396 + 7.69737I
u = −0.681505 − 0.289527I
a = 0.03851 + 1.94789I
b = 1.043400 − 0.637281I
4.27099 + 6.89948I 11.43396 − 7.69737I
u = −0.721641 + 0.152687I
a = −0.844995 + 1.089000I
b = 0.516426 − 0.779174I
5.82753 − 1.57926I 14.4879 + 1.7882I
u = −0.721641 − 0.152687I
a = −0.844995 − 1.089000I
b = 0.516426 + 0.779174I
5.82753 + 1.57926I 14.4879 − 1.7882I
u = −0.082557 + 1.272520I
a = −1.88035 − 0.05417I
b = −1.159760 + 0.213440I
−3.77500 − 2.20981I 0
u = −0.082557 − 1.272520I
a = −1.88035 + 0.05417I
b = −1.159760 − 0.213440I
−3.77500 + 2.20981I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.210143 + 1.259280I
a = 0.208298 − 0.400854I
b = 0.395459 − 0.440267I
−0.98799 + 1.90733I 0
u = −0.210143 − 1.259280I
a = 0.208298 + 0.400854I
b = 0.395459 + 0.440267I
−0.98799 − 1.90733I 0
u = −0.000512 + 1.327390I
a = −0.130531 + 0.995414I
b = 0.925020 − 0.921002I
−0.781932 + 0.661024I 0
u = −0.000512 − 1.327390I
a = −0.130531 − 0.995414I
b = 0.925020 + 0.921002I
−0.781932 − 0.661024I 0
u = 0.609534 + 0.272478I
a = −0.584068 − 0.350171I
b = 0.636787 + 0.561311I
1.64920 − 0.29233I 8.03329 − 0.15871I
u = 0.609534 − 0.272478I
a = −0.584068 + 0.350171I
b = 0.636787 − 0.561311I
1.64920 + 0.29233I 8.03329 + 0.15871I
u = −0.092924 + 1.331590I
a = −0.065930 − 1.068640I
b = 0.866501 + 0.946140I
−0.60519 − 6.07717I 0
u = −0.092924 − 1.331590I
a = −0.065930 + 1.068640I
b = 0.866501 − 0.946140I
−0.60519 + 6.07717I 0
u = 0.171260 + 1.324520I
a = −1.05185 − 1.79678I
b = −1.035660 + 0.449155I
−3.23240 + 4.53436I 0
u = 0.171260 − 1.324520I
a = −1.05185 + 1.79678I
b = −1.035660 − 0.449155I
−3.23240 − 4.53436I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.158952 + 1.352890I
a = 0.057726 − 0.217470I
b = 0.119895 + 0.688596I
−3.26940 + 2.41579I 0
u = 0.158952 − 1.352890I
a = 0.057726 + 0.217470I
b = 0.119895 − 0.688596I
−3.26940 − 2.41579I 0
u = −0.270114 + 1.346370I
a = −0.440781 + 0.149707I
b = 0.326391 − 0.819413I
1.09915 − 5.14819I 0
u = −0.270114 − 1.346370I
a = −0.440781 − 0.149707I
b = 0.326391 + 0.819413I
1.09915 + 5.14819I 0
u = 0.359092 + 0.487765I
a = 1.79802 + 1.38487I
b = −0.343192 − 0.347888I
−1.57085 + 2.44408I 6.62536 − 3.00383I
u = 0.359092 − 0.487765I
a = 1.79802 − 1.38487I
b = −0.343192 + 0.347888I
−1.57085 − 2.44408I 6.62536 + 3.00383I
u = −0.039784 + 1.394580I
a = −1.10221 + 0.98947I
b = −1.170370 − 0.381652I
−6.92039 − 1.32032I 0
u = −0.039784 − 1.394580I
a = −1.10221 − 0.98947I
b = −1.170370 + 0.381652I
−6.92039 + 1.32032I 0
u = 0.060535 + 0.600233I
a = 2.03401 − 0.69858I
b = −0.267096 + 0.124271I
−1.59835 + 2.35283I 6.98886 − 5.08882I
u = 0.060535 − 0.600233I
a = 2.03401 + 0.69858I
b = −0.267096 − 0.124271I
−1.59835 − 2.35283I 6.98886 + 5.08882I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.583705 + 0.093529I
a = 1.08030 − 2.39263I
b = −0.837645 + 0.440777I
1.17772 + 1.85934I 10.62955 − 4.30757I
u = 0.583705 − 0.093529I
a = 1.08030 + 2.39263I
b = −0.837645 − 0.440777I
1.17772 − 1.85934I 10.62955 + 4.30757I
u = −0.10232 + 1.46119I
a = 1.233410 − 0.510771I
b = 1.064130 + 0.480659I
−2.93294 − 2.08208I 0
u = −0.10232 − 1.46119I
a = 1.233410 + 0.510771I
b = 1.064130 − 0.480659I
−2.93294 + 2.08208I 0
u = −0.26298 + 1.44481I
a = 1.06935 − 1.24629I
b = 1.148140 + 0.579376I
−1.35388 − 10.35240I 0
u = −0.26298 − 1.44481I
a = 1.06935 + 1.24629I
b = 1.148140 − 0.579376I
−1.35388 + 10.35240I 0
u = −0.530564
a = 0.408996
b = −1.19118
−0.0949506 15.0060
u = 0.17399 + 1.46493I
a = 0.589969 + 0.807489I
b = −0.470039 − 0.824556I
−7.81095 + 4.69129I 0
u = 0.17399 − 1.46493I
a = 0.589969 − 0.807489I
b = −0.470039 + 0.824556I
−7.81095 − 4.69129I 0
u = −0.11054 + 1.47556I
a = 0.500820 − 0.770357I
b = −0.381208 + 0.834378I
−8.30671 + 1.25779I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.11054 − 1.47556I
a = 0.500820 + 0.770357I
b = −0.381208 − 0.834378I
−8.30671 − 1.25779I 0
u = 0.29268 + 1.46125I
a = −0.402718 − 0.591662I
b = 0.224404 + 0.986853I
−5.97166 + 5.43704I 0
u = 0.29268 − 1.46125I
a = −0.402718 + 0.591662I
b = 0.224404 − 0.986853I
−5.97166 − 5.43704I 0
u = −0.33248 + 1.45296I
a = −0.522607 + 0.612576I
b = 0.276570 − 1.013290I
−4.88626 − 11.41650I 0
u = −0.33248 − 1.45296I
a = −0.522607 − 0.612576I
b = 0.276570 + 1.013290I
−4.88626 + 11.41650I 0
u = −0.23283 + 1.49322I
a = −0.434106 + 0.048242I
b = −1.39371 + 0.24719I
−10.62360 − 7.05864I 0
u = −0.23283 − 1.49322I
a = −0.434106 − 0.048242I
b = −1.39371 − 0.24719I
−10.62360 + 7.05864I 0
u = 0.27946 + 1.48522I
a = −0.35493 − 1.59998I
b = −1.116750 + 0.624358I
−9.78659 + 10.13180I 0
u = 0.27946 − 1.48522I
a = −0.35493 + 1.59998I
b = −1.116750 − 0.624358I
−9.78659 − 10.13180I 0
u = −0.23041 + 1.49769I
a = −0.41694 + 1.47941I
b = −1.150690 − 0.589914I
−10.65950 − 4.06737I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.23041 − 1.49769I
a = −0.41694 − 1.47941I
b = −1.150690 + 0.589914I
−10.65950 + 4.06737I 0
u = 0.17781 + 1.50580I
a = −0.493571 + 0.136163I
b = −1.372600 − 0.289952I
−11.32570 + 0.98821I 0
u = 0.17781 − 1.50580I
a = −0.493571 − 0.136163I
b = −1.372600 + 0.289952I
−11.32570 − 0.98821I 0
u = 0.18673 + 1.51693I
a = 0.937998 + 0.821389I
b = 1.147980 − 0.495591I
−6.13141 + 6.86398I 0
u = 0.18673 − 1.51693I
a = 0.937998 − 0.821389I
b = 1.147980 + 0.495591I
−6.13141 − 6.86398I 0
u = −0.38259 + 1.49851I
a = 0.59734 − 1.46380I
b = 1.236450 + 0.623365I
−7.8475 − 17.3020I 0
u = −0.38259 − 1.49851I
a = 0.59734 + 1.46380I
b = 1.236450 − 0.623365I
−7.8475 + 17.3020I 0
u = −0.437376 + 0.101038I
a = −1.72342 − 0.02563I
b = 0.743247 − 0.727481I
3.35868 + 4.45930I 11.81530 − 5.58434I
u = −0.437376 − 0.101038I
a = −1.72342 + 0.02563I
b = 0.743247 + 0.727481I
3.35868 − 4.45930I 11.81530 + 5.58434I
u = 0.35136 + 1.52269I
a = 0.61315 + 1.32966I
b = 1.237220 − 0.593339I
−9.0801 + 11.1134I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.35136 − 1.52269I
a = 0.61315 − 1.32966I
b = 1.237220 + 0.593339I
−9.0801 − 11.1134I 0
u = 0.372232
a = 0.631357
b = 0.140150
0.703212 14.5110
u = −0.168382 + 0.282817I
a = −0.07085 + 2.51635I
b = −0.931838 − 0.189422I
−1.65732 − 0.64432I −2.89537 + 1.61582I
u = −0.168382 − 0.282817I
a = −0.07085 − 2.51635I
b = −0.931838 + 0.189422I
−1.65732 + 0.64432I −2.89537 − 1.61582I
u = −0.05157 + 1.68989I
a = 0.526136 + 0.107090I
b = 1.092650 − 0.236274I
−13.14570 + 3.76638I 0
u = −0.05157 − 1.68989I
a = 0.526136 − 0.107090I
b = 1.092650 + 0.236274I
−13.14570 − 3.76638I 0
u = 0.13501 + 1.69283I
a = 0.505949 + 0.016872I
b = 1.038160 + 0.196931I
−12.85800 + 2.90129I 0
u = 0.13501 − 1.69283I
a = 0.505949 − 0.016872I
b = 1.038160 − 0.196931I
−12.85800 − 2.90129I 0
u = −0.146371 + 0.249725I
a = 2.79586 − 1.02647I
b = 0.902300 + 0.690824I
2.91057 − 0.92428I 11.94422 + 0.25513I
u = −0.146371 − 0.249725I
a = 2.79586 + 1.02647I
b = 0.902300 − 0.690824I
2.91057 + 0.92428I 11.94422 − 0.25513I
14
II. I
u
2
=
h1878a
5
u−2600a
4
u+· · ·+23830a−8647, 3a
5
u−7a
4
u+· · ·+5a
2
+2a, u
2
+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
a
−0.313575a
5
u + 0.434129a
4
u + ··· − 3.97896a + 1.44381
a
6
=
1
1
a
2
=
−0.313575a
5
u + 0.434129a
4
u + ··· − 2.97896a + 1.44381
−0.313575a
5
u + 0.434129a
4
u + ··· − 3.97896a + 1.44381
a
1
=
−0.230422a
5
u + 0.782267a
4
u + ··· − 1.18901a + 0.965103
0.165136a
5
u − 0.977292a
4
u + ··· + 0.0687928a + 1.64168
a
11
=
−0.230422a
5
u + 0.782267a
4
u + ··· − 1.18901a + 0.965103
0.227918a
5
u − 0.654199a
4
u + ··· + 1.66522a + 0.175822
a
4
=
0.183336a
5
u + 0.225413a
4
u + ··· + 3.74169a − 0.115712
0.478711a
5
u − 1.41142a
4
u + ··· + 4.04775a − 0.802137
a
9
=
−u
0
a
7
=
0
1
a
8
=
−0.0719653a
5
u + 0.813157a
4
u + ··· + 0.816330a + 0.315913
−0.231758a
5
u + 0.583904a
4
u + ··· − 0.201703a − 0.493071
a
12
=
−0.230422a
5
u + 0.782267a
4
u + ··· − 1.18901a + 0.965103
0.458340a
5
u − 1.43647a
4
u + ··· + 2.85423a − 0.789280
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
5788
5989
a
5
u −
14428
5989
a
5
−
9080
5989
a
4
u +
73372
5989
a
4
+
59108
5989
a
3
u −
39572
5989
a
3
+
20364
5989
a
2
u +
72864
5989
a
2
+
29264
5989
au −
114876
5989
a −
34044
5989
u +
50976
5989
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
− u
2
+ 2u − 1)
4
c
2
(u
3
+ u
2
− 1)
4
c
3
, c
8
(u
6
− 3u
4
+ 2u
2
+ 1)
2
c
4
(u
3
− u
2
+ 1)
4
c
5
, c
6
, c
9
(u
2
+ 1)
6
c
7
, c
11
(u
4
− u
2
+ 1)
3
c
10
(u
2
+ u + 1)
6
c
12
(u
2
− u + 1)
6
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
+ 3y
2
+ 2y −1)
4
c
2
, c
4
(y
3
− y
2
+ 2y −1)
4
c
3
, c
8
(y
3
− 3y
2
+ 2y + 1)
4
c
5
, c
6
, c
9
(y + 1)
12
c
7
, c
11
(y
2
− y + 1)
6
c
10
, c
12
(y
2
+ y + 1)
6
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.450984 + 1.062990I
b = 0.877439 − 0.744862I
1.37919 + 0.79824I 5.50976 + 0.48465I
u = 1.000000I
a = 0.696107 − 0.426734I
b = 0.877439 + 0.744862I
1.37919 − 0.79824I 5.50976 − 0.48465I
u = 1.000000I
a = −0.258387 − 1.162360I
b = −0.754878
−2.75839 − 2.02988I −1.01951 + 3.46410I
u = 1.000000I
a = 0.111295 − 1.400630I
b = 0.877439 + 0.744862I
1.37919 − 4.85801I 5.50976 + 6.44355I
u = 1.000000I
a = 0.133827 + 0.089093I
b = 0.877439 − 0.744862I
1.37919 + 4.85801I 5.50976 − 6.44355I
u = 1.000000I
a = 3.76814 − 1.16236I
b = −0.754878
−2.75839 + 2.02988I −1.01951 − 3.46410I
u = − 1.000000I
a = −0.450984 − 1.062990I
b = 0.877439 + 0.744862I
1.37919 − 0.79824I 5.50976 − 0.48465I
u = − 1.000000I
a = 0.696107 + 0.426734I
b = 0.877439 − 0.744862I
1.37919 + 0.79824I 5.50976 + 0.48465I
u = − 1.000000I
a = −0.258387 + 1.162360I
b = −0.754878
−2.75839 + 2.02988I −1.01951 − 3.46410I
u = − 1.000000I
a = 0.111295 + 1.400630I
b = 0.877439 − 0.744862I
1.37919 + 4.85801I 5.50976 − 6.44355I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = − 1.000000I
a = 0.133827 − 0.089093I
b = 0.877439 + 0.744862I
1.37919 − 4.85801I 5.50976 + 6.44355I
u = − 1.000000I
a = 3.76814 + 1.16236I
b = −0.754878
−2.75839 − 2.02988I −1.01951 + 3.46410I
19
III. I
u
3
= hb + 1, −u
3
− u
2
+ a − 3u − 2, u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
u
3
+ u
2
+ 3u + 2
−1
a
6
=
1
−u
2
a
2
=
u
3
+ u
2
+ 3u + 1
−1
a
1
=
−1
0
a
11
=
u
u
a
4
=
u
3
+ u
2
+ 3u + 2
−1
a
9
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
−u
u
3
+ u
a
12
=
−u
2
− 1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
4
+ 5u
3
+ 12u
2
+ 16u + 8
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
5
c
3
, c
8
u
5
c
4
(u + 1)
5
c
5
, c
6
, c
10
u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1
c
7
u
5
+ u
4
− u
2
+ u + 1
c
9
, c
12
u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1
c
11
u
5
− u
4
+ u
2
+ u − 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
5
c
3
, c
8
y
5
c
5
, c
6
, c
9
c
10
, c
12
y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1
c
7
, c
11
y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.233677 + 0.885557I
a = 1.10636 + 1.69341I
b = −1.00000
−3.46474 − 2.21397I −0.36497 + 8.87119I
u = −0.233677 − 0.885557I
a = 1.10636 − 1.69341I
b = −1.00000
−3.46474 + 2.21397I −0.36497 − 8.87119I
u = −0.416284
a = 0.852303
b = −1.00000
−0.762751 3.17840
u = −0.05818 + 1.69128I
a = −0.532511 + 0.056433I
b = −1.00000
−12.60320 − 3.33174I 7.77577 + 5.09400I
u = −0.05818 − 1.69128I
a = −0.532511 − 0.056433I
b = −1.00000
−12.60320 + 3.33174I 7.77577 − 5.09400I
23
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
3
− u
2
+ 2u − 1)
4
(u
100
+ 50u
99
+ ··· + 79u + 1)
c
2
((u − 1)
5
)(u
3
+ u
2
− 1)
4
(u
100
− 10u
99
+ ··· + 11u − 1)
c
3
, c
8
u
5
(u
6
− 3u
4
+ 2u
2
+ 1)
2
(u
100
+ u
99
+ ··· + 224u + 32)
c
4
((u + 1)
5
)(u
3
− u
2
+ 1)
4
(u
100
− 10u
99
+ ··· + 11u − 1)
c
5
, c
6
((u
2
+ 1)
6
)(u
5
+ u
4
+ ··· + 3u + 1)(u
100
+ 2u
99
+ ··· − 329u − 49)
c
7
((u
4
− u
2
+ 1)
3
)(u
5
+ u
4
− u
2
+ u + 1)(u
100
+ 2u
99
+ ··· − 15u − 17)
c
9
((u
2
+ 1)
6
)(u
5
− u
4
+ ··· + 3u − 1)(u
100
+ 2u
99
+ ··· − 329u − 49)
c
10
(u
2
+ u + 1)
6
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
· (u
100
− 32u
99
+ ··· + 149u + 289)
c
11
((u
4
− u
2
+ 1)
3
)(u
5
− u
4
+ u
2
+ u − 1)(u
100
+ 2u
99
+ ··· − 15u − 17)
c
12
(u
2
− u + 1)
6
(u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1)
· (u
100
− 32u
99
+ ··· + 149u + 289)
24
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
5
)(y
3
+ 3y
2
+ 2y −1)
4
(y
100
+ 10y
99
+ ··· − 2487y + 1)
c
2
, c
4
((y −1)
5
)(y
3
− y
2
+ 2y −1)
4
(y
100
− 50y
99
+ ··· − 79y + 1)
c
3
, c
8
y
5
(y
3
− 3y
2
+ 2y + 1)
4
(y
100
− 45y
99
+ ··· − 52736y + 1024)
c
5
, c
6
, c
9
(y + 1)
12
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
· (y
100
+ 98y
99
+ ··· + 34251y + 2401)
c
7
, c
11
(y
2
− y + 1)
6
(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1)
· (y
100
− 32y
99
+ ··· + 149y + 289)
c
10
, c
12
(y
2
+ y + 1)
6
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
· (y
100
+ 80y
99
+ ··· − 3531239y + 83521)
25
