12a
0297
(K12a
0297
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 12 1 4 11 5 9 7
Solving Sequence
4,10 2,5
6 11 9 12 8 3 1 7
c
4
c
5
c
10
c
9
c
11
c
8
c
3
c
1
c
7
c
2
, c
6
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h2u
60
− 3u
59
+ ··· + 4b − 6, −2u
59
+ 19u
57
+ ··· + 4a − 8, u
61
− 2u
60
+ ··· − 4u + 2i
I
u
2
= h−65u
7
a
2
+ 366u
7
a + ··· − 730a + 714, 2u
7
a
2
− 4u
7
a + ··· + 8a − 4,
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1i
I
u
3
= h−u
2
+ b − u + 1, −u
3
+ 2u
2
+ 2a + u, u
4
− u
2
+ 2i
I
u
4
= hb − 1, a + 1, u − 1i
I
u
5
= hb − 1, a, u + 1i
I
u
6
= hb + 1, a − 2, u − 1i
I
u
7
= hb, a − 1, u + 1i
I
u
8
= hu
3
+ u
2
+ b + 1, a − u − 1, u
4
+ 1i
I
v
1
= ha, b + 1, v −1i
* 9 irreducible components of dim
C
= 0, with total 98 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
=
h2u
60
−3u
59
+· · ·+4b−6, −2u
59
+19u
57
+· · ·+4a−8, u
61
−2u
60
+· · ·−4u+2i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
1
2
u
59
−
19
4
u
57
+ ··· −
3
2
u + 2
−
1
2
u
60
+
3
4
u
59
+ ··· −
5
2
u +
3
2
a
5
=
1
−u
2
a
6
=
1
2
u
60
− u
59
+ ··· − 11u
3
−
1
2
u
60
− 10u
58
+ ··· +
3
2
u + 1
a
11
=
u
−u
3
+ u
a
9
=
−u
3
u
5
− u
3
+ u
a
12
=
u
5
+ u
−u
7
+ u
5
− 2u
3
+ u
a
8
=
−u
5
− u
u
5
− u
3
+ u
a
3
=
−u
10
+ u
8
− 2u
6
+ u
4
− u
2
+ 1
u
10
− 2u
8
+ 3u
6
− 2u
4
+ u
2
a
1
=
1
4
u
56
−
9
4
u
54
+ ··· −
3
2
u +
1
2
−
1
4
u
58
+
5
2
u
56
+ ··· + 4u
3
− u
a
7
=
1
4
u
56
−
9
4
u
54
+ ··· −
3
2
u +
1
2
−
1
4
u
56
+
5
2
u
54
+ ··· −
1
2
u
2
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
60
− 4u
59
+ ··· + 16u
2
− 2u
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
61
+ 21u
60
+ ··· + 741u + 225
c
2
, c
5
u
61
+ 3u
60
+ ··· + 21u − 15
c
3
, c
8
u
61
− 2u
60
+ ··· − 10164u − 3866
c
4
, c
10
u
61
+ 2u
60
+ ··· − 4u − 2
c
6
, c
7
, c
12
u
61
− 3u
60
+ ··· − 15u − 17
c
9
, c
11
u
61
− 20u
60
+ ··· + 44u
2
− 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
61
+ 51y
60
+ ··· − 783819y −50625
c
2
, c
5
y
61
− 21y
60
+ ··· + 741y −225
c
3
, c
8
y
61
− 44y
60
+ ··· + 225348784y −14945956
c
4
, c
10
y
61
− 20y
60
+ ··· + 44y
2
− 4
c
6
, c
7
, c
12
y
61
− 69y
60
+ ··· − 14123y −289
c
9
, c
11
y
61
+ 40y
60
+ ··· + 352y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.684026 + 0.730349I
a = 1.009310 − 0.004276I
b = −0.980208 − 0.876387I
−3.51260 − 0.02973I −1.53347 − 0.41407I
u = 0.684026 − 0.730349I
a = 1.009310 + 0.004276I
b = −0.980208 + 0.876387I
−3.51260 + 0.02973I −1.53347 + 0.41407I
u = −0.596675 + 0.818364I
a = −0.780560 − 0.903959I
b = 1.80103 − 1.76065I
5.86684 + 10.52580I 7.47241 − 5.20514I
u = −0.596675 − 0.818364I
a = −0.780560 + 0.903959I
b = 1.80103 + 1.76065I
5.86684 − 10.52580I 7.47241 + 5.20514I
u = 0.980120 + 0.257609I
a = 1.103770 + 0.621483I
b = 0.089020 − 0.363650I
6.96905 + 0.16982I 14.1748 − 0.9961I
u = 0.980120 − 0.257609I
a = 1.103770 − 0.621483I
b = 0.089020 + 0.363650I
6.96905 − 0.16982I 14.1748 + 0.9961I
u = 0.570037 + 0.804645I
a = 0.113760 − 0.379871I
b = 0.174544 − 1.221640I
7.95075 − 4.31712I 9.88882 + 1.03046I
u = 0.570037 − 0.804645I
a = 0.113760 + 0.379871I
b = 0.174544 + 1.221640I
7.95075 + 4.31712I 9.88882 − 1.03046I
u = 0.594682 + 0.783135I
a = −0.477300 + 1.212940I
b = 2.02601 + 1.39309I
−0.22057 − 6.22999I 4.63185 + 5.17897I
u = 0.594682 − 0.783135I
a = −0.477300 − 1.212940I
b = 2.02601 − 1.39309I
−0.22057 + 6.22999I 4.63185 − 5.17897I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.971831 + 0.354476I
a = −0.11982 + 1.97303I
b = −0.327701 − 0.963726I
6.46298 − 5.79381I 12.8562 + 6.6036I
u = −0.971831 − 0.354476I
a = −0.11982 − 1.97303I
b = −0.327701 + 0.963726I
6.46298 + 5.79381I 12.8562 − 6.6036I
u = −0.693342 + 0.628373I
a = 1.030350 − 0.373254I
b = 0.509008 + 0.609720I
0.288787 + 0.262438I 10.25017 − 1.54244I
u = −0.693342 − 0.628373I
a = 1.030350 + 0.373254I
b = 0.509008 − 0.609720I
0.288787 − 0.262438I 10.25017 + 1.54244I
u = −0.741367 + 0.781988I
a = 0.968528 + 0.095329I
b = −0.766103 + 0.579735I
0.550417 − 1.022540I 7.58092 + 2.83590I
u = −0.741367 − 0.781988I
a = 0.968528 − 0.095329I
b = −0.766103 − 0.579735I
0.550417 + 1.022540I 7.58092 − 2.83590I
u = −0.813495 + 0.728217I
a = 1.226460 − 0.093979I
b = −1.10886 + 1.83090I
−5.14522 + 0.66407I 0
u = −0.813495 − 0.728217I
a = 1.226460 + 0.093979I
b = −1.10886 − 1.83090I
−5.14522 − 0.66407I 0
u = −1.105450 + 0.040560I
a = −1.17835 − 2.39972I
b = 0.67943 + 2.15568I
5.68265 − 5.26500I 11.79822 + 5.52257I
u = −1.105450 − 0.040560I
a = −1.17835 + 2.39972I
b = 0.67943 − 2.15568I
5.68265 + 5.26500I 11.79822 − 5.52257I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.798828 + 0.780694I
a = 1.072690 + 0.319738I
b = −0.61454 − 1.92988I
−0.34087 − 3.55037I 6.00000 + 0.I
u = 0.798828 − 0.780694I
a = 1.072690 − 0.319738I
b = −0.61454 + 1.92988I
−0.34087 + 3.55037I 6.00000 + 0.I
u = 0.456914 + 0.747552I
a = 0.187992 + 0.418041I
b = 0.929221 + 0.981503I
8.62819 + 1.29175I 10.29853 − 0.71245I
u = 0.456914 − 0.747552I
a = 0.187992 − 0.418041I
b = 0.929221 − 0.981503I
8.62819 − 1.29175I 10.29853 + 0.71245I
u = 1.128770 + 0.065228I
a = −0.96345 + 2.31373I
b = 0.41291 − 2.04529I
12.1138 + 9.4985I 14.0807 − 5.6869I
u = 1.128770 − 0.065228I
a = −0.96345 − 2.31373I
b = 0.41291 + 2.04529I
12.1138 − 9.4985I 14.0807 + 5.6869I
u = −1.133370 + 0.039127I
a = −1.07901 + 1.94352I
b = 0.67010 − 1.57030I
13.9993 − 3.0917I 16.1356 + 0.I
u = −1.133370 − 0.039127I
a = −1.07901 − 1.94352I
b = 0.67010 + 1.57030I
13.9993 + 3.0917I 16.1356 + 0.I
u = 0.789581 + 0.332833I
a = 0.29668 − 2.08794I
b = −0.413297 + 0.458976I
0.18640 + 3.40430I 8.29784 − 8.43367I
u = 0.789581 − 0.332833I
a = 0.29668 + 2.08794I
b = −0.413297 − 0.458976I
0.18640 − 3.40430I 8.29784 + 8.43367I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.899967 + 0.713782I
a = −1.58036 + 1.59577I
b = −0.51410 − 2.10453I
−4.88256 − 6.15868I 0
u = −0.899967 − 0.713782I
a = −1.58036 − 1.59577I
b = −0.51410 + 2.10453I
−4.88256 + 6.15868I 0
u = −0.963966 + 0.649853I
a = −0.433033 − 0.566210I
b = 0.829635 − 0.624531I
1.09575 − 5.31508I 0
u = −0.963966 − 0.649853I
a = −0.433033 + 0.566210I
b = 0.829635 + 0.624531I
1.09575 + 5.31508I 0
u = −0.401857 + 0.728661I
a = −0.711645 + 1.063690I
b = 0.222763 + 0.716405I
6.99087 − 7.50546I 8.25142 + 5.41277I
u = −0.401857 − 0.728661I
a = −0.711645 − 1.063690I
b = 0.222763 − 0.716405I
6.99087 + 7.50546I 8.25142 − 5.41277I
u = 0.475808 + 0.672313I
a = −0.225590 − 1.386850I
b = −0.018272 − 0.781142I
0.59272 + 3.70509I 5.79703 − 5.82804I
u = 0.475808 − 0.672313I
a = −0.225590 + 1.386850I
b = −0.018272 + 0.781142I
0.59272 − 3.70509I 5.79703 + 5.82804I
u = 0.928616 + 0.747007I
a = −1.66826 − 1.18025I
b = −0.11509 + 2.08092I
0.05447 + 9.30335I 0
u = 0.928616 − 0.747007I
a = −1.66826 + 1.18025I
b = −0.11509 − 2.08092I
0.05447 − 9.30335I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.990835 + 0.679184I
a = −0.347057 − 1.318090I
b = −0.534238 + 1.253020I
−2.58879 + 5.43080I 0
u = 0.990835 − 0.679184I
a = −0.347057 + 1.318090I
b = −0.534238 − 1.253020I
−2.58879 − 5.43080I 0
u = 1.028240 + 0.622031I
a = −1.253520 − 0.573644I
b = −0.78894 + 1.32269I
2.08349 + 1.29638I 0
u = 1.028240 − 0.622031I
a = −1.253520 + 0.573644I
b = −0.78894 − 1.32269I
2.08349 − 1.29638I 0
u = −1.051030 + 0.593594I
a = −1.092970 + 0.306940I
b = −0.664632 − 0.819333I
8.82075 + 2.55632I 0
u = −1.051030 − 0.593594I
a = −1.092970 − 0.306940I
b = −0.664632 + 0.819333I
8.82075 − 2.55632I 0
u = −0.967643 + 0.722048I
a = −0.001148 + 0.746254I
b = −0.390854 − 0.853517I
1.23996 − 4.65549I 0
u = −0.967643 − 0.722048I
a = −0.001148 − 0.746254I
b = −0.390854 + 0.853517I
1.23996 + 4.65549I 0
u = 1.055860 + 0.618891I
a = 0.58117 + 1.82280I
b = 1.34616 − 1.10013I
10.34380 + 3.85829I 0
u = 1.055860 − 0.618891I
a = 0.58117 − 1.82280I
b = 1.34616 + 1.10013I
10.34380 − 3.85829I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.040000 + 0.677333I
a = 0.70242 + 2.72007I
b = 2.36433 − 2.02891I
1.10337 + 11.75260I 0
u = 1.040000 − 0.677333I
a = 0.70242 − 2.72007I
b = 2.36433 + 2.02891I
1.10337 − 11.75260I 0
u = 1.054830 + 0.675605I
a = −1.53601 − 0.38119I
b = −0.01333 + 1.41794I
9.39588 + 9.88209I 0
u = 1.054830 − 0.675605I
a = −1.53601 + 0.38119I
b = −0.01333 − 1.41794I
9.39588 − 9.88209I 0
u = −1.051510 + 0.689969I
a = 1.00404 − 2.59975I
b = 1.96259 + 2.37317I
7.2336 − 16.1846I 0
u = −1.051510 − 0.689969I
a = 1.00404 + 2.59975I
b = 1.96259 − 2.37317I
7.2336 + 16.1846I 0
u = −0.060491 + 0.608567I
a = 0.847236 − 0.127415I
b = −0.534181 + 0.678808I
3.78928 + 2.56985I 6.99731 − 2.63136I
u = −0.060491 − 0.608567I
a = 0.847236 + 0.127415I
b = −0.534181 − 0.678808I
3.78928 − 2.56985I 6.99731 + 2.63136I
u = −0.516262
a = 1.73864
b = 0.0487944
0.822482 12.8010
u = 0.132981 + 0.413625I
a = 0.934359 + 0.065152I
b = −0.756818 − 0.341461I
−1.53288 − 0.93105I −1.52612 + 1.38760I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.132981 − 0.413625I
a = 0.934359 − 0.065152I
b = −0.756818 + 0.341461I
−1.53288 + 0.93105I −1.52612 − 1.38760I
11
II. I
u
2
= h−65u
7
a
2
+ 366u
7
a + · · · − 730a + 714, 2u
7
a
2
− 4u
7
a + · · · + 8a −
4, u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
a
0.631068a
2
u
7
− 3.55340au
7
+ ··· + 7.08738a − 6.93204
a
5
=
1
−u
2
a
6
=
1.32039a
2
u
7
− 5.01942au
7
+ ··· + 9.21359a − 7.61165
−1.66990a
2
u
7
+ 5.49515au
7
+ ··· − 8.44660a + 8.09709
a
11
=
u
−u
3
+ u
a
9
=
−u
3
u
5
− u
3
+ u
a
12
=
u
5
+ u
−u
7
+ u
5
− 2u
3
+ u
a
8
=
−u
5
− u
u
5
− u
3
+ u
a
3
=
−u
5
− u
u
7
− u
5
+ 2u
3
− u
a
1
=
0.834951a
2
u
7
− 1.74757au
7
+ ··· + 4.22330a − 3.04854
0.174757a
2
u
7
− 4.73786au
7
+ ··· + 8.11650a − 7.24272
a
7
=
0.834951a
2
u
7
− 1.74757au
7
+ ··· + 4.22330a − 3.04854
−0.776699a
2
u
7
+ 4.83495au
7
+ ··· − 9.18447a + 9.30097
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
7
+ 8u
5
+ 4u
4
− 8u
3
− 4u
2
+ 4u + 14
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
+ 16u
23
+ ··· + 4u + 1
c
2
, c
5
, c
6
c
7
, c
12
u
24
− 8u
22
+ ··· + 2u − 1
c
3
, c
8
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
3
c
4
, c
10
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
3
c
9
, c
11
(u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
3
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
− 16y
23
+ ··· − 12y + 1
c
2
, c
5
, c
6
c
7
, c
12
y
24
− 16y
23
+ ··· − 4y + 1
c
3
, c
8
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
3
c
4
, c
10
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
3
c
9
, c
11
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
3
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.570868 + 0.730671I
a = 1.043500 − 0.060246I
b = −1.101120 + 0.799785I
1.04066 + 1.13123I 7.41522 − 0.51079I
u = −0.570868 + 0.730671I
a = 0.359671 + 0.817635I
b = −0.016317 + 1.139980I
1.04066 + 1.13123I 7.41522 − 0.51079I
u = −0.570868 + 0.730671I
a = 0.208103 − 1.124120I
b = 1.75850 − 0.67186I
1.04066 + 1.13123I 7.41522 − 0.51079I
u = −0.570868 − 0.730671I
a = 1.043500 + 0.060246I
b = −1.101120 − 0.799785I
1.04066 − 1.13123I 7.41522 + 0.51079I
u = −0.570868 − 0.730671I
a = 0.359671 − 0.817635I
b = −0.016317 − 1.139980I
1.04066 − 1.13123I 7.41522 + 0.51079I
u = −0.570868 − 0.730671I
a = 0.208103 + 1.124120I
b = 1.75850 + 0.67186I
1.04066 − 1.13123I 7.41522 + 0.51079I
u = 0.855237 + 0.665892I
a = 1.278090 − 0.370791I
b = −1.93181 − 1.61226I
−2.15941 + 2.57849I 4.27708 − 3.56796I
u = 0.855237 + 0.665892I
a = 0.504800 + 0.137739I
b = 0.0664349 − 0.0459194I
−2.15941 + 2.57849I 4.27708 − 3.56796I
u = 0.855237 + 0.665892I
a = −1.40393 − 2.38771I
b = −1.22880 + 1.98137I
−2.15941 + 2.57849I 4.27708 − 3.56796I
u = 0.855237 − 0.665892I
a = 1.278090 + 0.370791I
b = −1.93181 + 1.61226I
−2.15941 − 2.57849I 4.27708 + 3.56796I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.855237 − 0.665892I
a = 0.504800 − 0.137739I
b = 0.0664349 + 0.0459194I
−2.15941 − 2.57849I 4.27708 + 3.56796I
u = 0.855237 − 0.665892I
a = −1.40393 + 2.38771I
b = −1.22880 − 1.98137I
−2.15941 − 2.57849I 4.27708 + 3.56796I
u = 1.09818
a = 1.32236
b = −0.189255
6.50273 13.8640
u = 1.09818
a = −1.39057 + 2.07577I
b = 0.97427 − 1.80941I
6.50273 13.8640
u = 1.09818
a = −1.39057 − 2.07577I
b = 0.97427 + 1.80941I
6.50273 13.8640
u = −1.031810 + 0.655470I
a = −1.50786 + 0.47222I
b = −0.28319 − 1.61385I
2.37968 − 6.44354I 9.42845 + 5.29417I
u = −1.031810 + 0.655470I
a = −0.13296 + 1.59682I
b = −0.67376 − 1.25902I
2.37968 − 6.44354I 9.42845 + 5.29417I
u = −1.031810 + 0.655470I
a = 0.22313 − 2.40784I
b = 2.31545 + 1.17039I
2.37968 − 6.44354I 9.42845 + 5.29417I
u = −1.031810 − 0.655470I
a = −1.50786 − 0.47222I
b = −0.28319 + 1.61385I
2.37968 + 6.44354I 9.42845 − 5.29417I
u = −1.031810 − 0.655470I
a = −0.13296 − 1.59682I
b = −0.67376 + 1.25902I
2.37968 + 6.44354I 9.42845 − 5.29417I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.031810 − 0.655470I
a = 0.22313 + 2.40784I
b = 2.31545 − 1.17039I
2.37968 + 6.44354I 9.42845 − 5.29417I
u = −0.603304
a = 1.26502
b = −1.64063
0.845036 11.8940
u = −0.603304
a = 1.52434 + 0.84915I
b = 0.0352752 − 0.0977915I
0.845036 11.8940
u = −0.603304
a = 1.52434 − 0.84915I
b = 0.0352752 + 0.0977915I
0.845036 11.8940
17
III. I
u
3
= h−u
2
+ b − u + 1, −u
3
+ 2u
2
+ 2a + u, u
4
− u
2
+ 2i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
1
2
u
3
− u
2
−
1
2
u
u
2
+ u − 1
a
5
=
1
−u
2
a
6
=
1
2
u
3
− u
2
−
1
2
u + 1
u − 1
a
11
=
u
−u
3
+ u
a
9
=
−u
3
−u
a
12
=
u
3
− u
u
a
8
=
−u
3
+ u
−u
a
3
=
−1
u
2
a
1
=
1
2
u
3
− u
2
−
1
2
u + 1
u − 1
a
7
=
−
1
2
u
3
− u
2
+
1
2
u + 1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
+ 8
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
7
(u − 1)
4
c
2
, c
12
(u + 1)
4
c
3
, c
4
, c
8
c
10
u
4
− u
2
+ 2
c
9
(u
2
+ u + 2)
2
c
11
(u
2
− u + 2)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
12
(y − 1)
4
c
3
, c
4
, c
8
c
10
(y
2
− y + 2)
2
c
9
, c
11
(y
2
+ 3y + 4)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.978318 + 0.676097I
a = −1.19178 − 0.84480I
b = 0.47832 + 1.99897I
−0.82247 + 5.33349I 6.00000 − 5.29150I
u = 0.978318 − 0.676097I
a = −1.19178 + 0.84480I
b = 0.47832 − 1.99897I
−0.82247 − 5.33349I 6.00000 + 5.29150I
u = −0.978318 + 0.676097I
a = 0.19178 + 1.80095I
b = −1.47832 − 0.64678I
−0.82247 − 5.33349I 6.00000 + 5.29150I
u = −0.978318 − 0.676097I
a = 0.19178 − 1.80095I
b = −1.47832 + 0.64678I
−0.82247 + 5.33349I 6.00000 − 5.29150I
21
IV. I
u
4
= hb − 1, a + 1, u − 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
1
a
2
=
−1
1
a
5
=
1
−1
a
6
=
1
−1
a
11
=
1
0
a
9
=
−1
1
a
12
=
2
−1
a
8
=
−2
1
a
3
=
−1
1
a
1
=
−1
1
a
7
=
−1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = 18
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
u
c
3
, c
4
, c
6
c
7
, c
8
, c
10
c
12
u + 1
c
9
, c
11
u − 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
y
c
3
, c
4
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y − 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = 1.00000
4.93480 18.0000
25
V. I
u
5
= hb − 1, a, u + 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
−1
a
2
=
0
1
a
5
=
1
−1
a
6
=
1
0
a
11
=
−1
0
a
9
=
1
−1
a
12
=
−2
1
a
8
=
2
−1
a
3
=
−1
1
a
1
=
1
0
a
7
=
3
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
7
, c
8
, c
10
c
11
u − 1
c
2
, c
3
, c
4
c
9
, c
12
u + 1
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y − 1
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0
b = 1.00000
3.28987 12.0000
29
VI. I
u
6
= hb + 1, a − 2, u − 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
1
a
2
=
2
−1
a
5
=
1
−1
a
6
=
3
−2
a
11
=
1
0
a
9
=
−1
1
a
12
=
2
−1
a
8
=
−2
1
a
3
=
−1
1
a
1
=
3
−2
a
7
=
1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
7
c
11
u − 1
c
2
, c
8
, c
9
c
10
, c
12
u + 1
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y − 1
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 2.00000
b = −1.00000
3.28987 12.0000
33
VII. I
u
7
= hb, a − 1, u + 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
−1
a
2
=
1
0
a
5
=
1
−1
a
6
=
2
−1
a
11
=
−1
0
a
9
=
1
−1
a
12
=
−2
1
a
8
=
2
−1
a
3
=
−1
1
a
1
=
2
−1
a
7
=
2
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u + 1
c
2
, c
3
, c
4
c
5
, c
8
, c
9
c
10
, c
11
u − 1
c
6
, c
7
, c
12
u
35
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
8
c
9
, c
10
, c
11
y − 1
c
6
, c
7
, c
12
y
36
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000
b = 0
1.64493 6.00000
37
VIII. I
u
8
= hu
3
+ u
2
+ b + 1, a − u − 1, u
4
+ 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
u + 1
−u
3
− u
2
− 1
a
5
=
1
−u
2
a
6
=
−u
u
3
+ 1
a
11
=
u
−u
3
+ u
a
9
=
−u
3
−u
3
a
12
=
0
−u
3
a
8
=
0
−u
3
a
3
=
1
−u
2
a
1
=
u
−u
3
− 1
a
7
=
−u
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4
38
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
(u − 1)
4
c
3
, c
4
, c
8
c
10
u
4
+ 1
c
5
, c
6
, c
7
(u + 1)
4
c
9
, c
11
(u
2
+ 1)
2
39
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
12
(y − 1)
4
c
3
, c
4
, c
8
c
10
(y
2
+ 1)
2
c
9
, c
11
(y + 1)
4
40
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 0.707107 + 0.707107I
a = 1.70711 + 0.70711I
b = −0.29289 − 1.70711I
−1.64493 4.00000
u = 0.707107 − 0.707107I
a = 1.70711 − 0.70711I
b = −0.29289 + 1.70711I
−1.64493 4.00000
u = −0.707107 + 0.707107I
a = 0.292893 + 0.707107I
b = −1.70711 + 0.29289I
−1.64493 4.00000
u = −0.707107 − 0.707107I
a = 0.292893 − 0.707107I
b = −1.70711 − 0.29289I
−1.64493 4.00000
41
IX. I
v
1
= ha, b + 1, v − 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
1
0
a
2
=
0
−1
a
5
=
1
0
a
6
=
1
1
a
11
=
1
0
a
9
=
1
0
a
12
=
1
0
a
8
=
1
0
a
3
=
1
0
a
1
=
−1
−1
a
7
=
2
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
42
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
u − 1
c
3
, c
4
, c
8
c
9
, c
10
, c
11
u
c
5
, c
6
, c
7
u + 1
43
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
12
y − 1
c
3
, c
4
, c
8
c
9
, c
10
, c
11
y
44
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −1.00000
0 0
45
X. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u − 1)
11
(u + 1)(u
24
+ 16u
23
+ ··· + 4u + 1)
· (u
61
+ 21u
60
+ ··· + 741u + 225)
c
2
u(u − 1)
6
(u + 1)
6
(u
24
− 8u
22
+ ··· + 2u − 1)
· (u
61
+ 3u
60
+ ··· + 21u − 15)
c
3
, c
8
u(u − 1)
2
(u + 1)
2
(u
4
+ 1)(u
4
− u
2
+ 2)
· (u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
3
· (u
61
− 2u
60
+ ··· − 10164u − 3866)
c
4
, c
10
u(u − 1)
2
(u + 1)
2
(u
4
+ 1)(u
4
− u
2
+ 2)
· ((u
8
− u
7
+ ··· + 2u − 1)
3
)(u
61
+ 2u
60
+ ··· − 4u − 2)
c
5
u(u − 1)
7
(u + 1)
5
(u
24
− 8u
22
+ ··· + 2u − 1)
· (u
61
+ 3u
60
+ ··· + 21u − 15)
c
6
, c
7
u(u − 1)
6
(u + 1)
6
(u
24
− 8u
22
+ ··· + 2u − 1)
· (u
61
− 3u
60
+ ··· − 15u − 17)
c
9
u(u − 1)
2
(u + 1)
2
(u
2
+ 1)
2
(u
2
+ u + 2)
2
· (u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
3
· (u
61
− 20u
60
+ ··· + 44u
2
− 4)
c
11
u(u − 1)
4
(u
2
+ 1)
2
(u
2
− u + 2)
2
· (u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
3
· (u
61
− 20u
60
+ ··· + 44u
2
− 4)
c
12
u(u − 1)
5
(u + 1)
7
(u
24
− 8u
22
+ ··· + 2u − 1)
· (u
61
− 3u
60
+ ··· − 15u − 17)
46
XI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y − 1)
12
(y
24
− 16y
23
+ ··· − 12y + 1)
· (y
61
+ 51y
60
+ ··· − 783819y − 50625)
c
2
, c
5
y(y − 1)
12
(y
24
− 16y
23
+ ··· − 4y + 1)
· (y
61
− 21y
60
+ ··· + 741y − 225)
c
3
, c
8
y(y − 1)
4
(y
2
+ 1)
2
(y
2
− y + 2)
2
· (y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
3
· (y
61
− 44y
60
+ ··· + 225348784y − 14945956)
c
4
, c
10
y(y − 1)
4
(y
2
+ 1)
2
(y
2
− y + 2)
2
· (y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
3
· (y
61
− 20y
60
+ ··· + 44y
2
− 4)
c
6
, c
7
, c
12
y(y − 1)
12
(y
24
− 16y
23
+ ··· − 4y + 1)
· (y
61
− 69y
60
+ ··· − 14123y − 289)
c
9
, c
11
y(y − 1)
4
(y + 1)
4
(y
2
+ 3y + 4)
2
· (y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
3
· (y
61
+ 40y
60
+ ··· + 352y − 16)
47
