12a
0575
(K12a
0575
)
A knot diagram
1
Linearized knot diagam
3 7 9 10 11 2 12 6 5 4 1 8
Solving Sequence
5,9
10 4 11
2,6
7 3 1 8 12
c
9
c
4
c
10
c
5
c
6
c
3
c
1
c
8
c
12
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−2u
37
+ 3u
36
+ ··· + b − 3, −3u
39
+ 9u
38
+ ··· + 2a − 10, u
40
− 3u
39
+ ··· + 6u − 2i
I
u
2
= h5150u
29
a − 9644u
29
+ ··· − 4195a − 8440, 2u
29
a + u
28
+ ··· + a + 2, u
30
+ u
29
+ ··· + u + 1i
I
u
3
= hb − 1, −2u
3
+ 3u
2
+ 3a − 3u + 3, u
4
+ 3u
2
+ 3i
I
u
4
= hb + 1, u
2
+ a − u + 1, u
4
+ u
2
− 1i
I
v
1
= ha, b − 1, v + 1i
* 5 irreducible components of dim
C
= 0, with total 109 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−2u
37
+3u
36
+· · ·+b−3, −3u
39
+9u
38
+· · ·+2a−10, u
40
−3u
39
+· · ·+6u−2i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
4
=
u
u
3
+ u
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
2
=
3
2
u
39
−
9
2
u
38
+ ··· −
17
2
u + 5
2u
37
− 3u
36
+ ··· − 3u + 3
a
6
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
7
=
−
3
2
u
39
+
5
2
u
38
+ ··· +
5
2
u − 2
−u
39
+ 2u
38
+ ··· + 3u − 1
a
3
=
u
3
+ 2u
u
3
+ u
a
1
=
5
2
u
39
−
15
2
u
38
+ ··· −
33
2
u + 9
3u
37
− 5u
36
+ ··· − 6u + 5
a
8
=
−u
12
− 5u
10
− 9u
8
− 6u
6
+ u
2
+ 1
−u
14
− 6u
12
− 13u
10
− 10u
8
+ 2u
6
+ 4u
4
− u
2
a
12
=
−
3
2
u
39
+
9
2
u
38
+ ··· +
21
2
u − 4
−2u
37
+ 3u
36
+ ··· + 4u − 3
(ii) Obstruction class = −1
(iii) Cusp Shapes = 8u
39
− 14u
38
+ ··· − 20u − 8
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
40
+ 17u
39
+ ··· + 19u + 1
c
2
, c
6
, c
7
c
12
u
40
− u
39
+ ··· − u − 1
c
3
, c
5
u
40
− 3u
39
+ ··· + 10u − 2
c
4
, c
9
, c
10
u
40
+ 3u
39
+ ··· − 6u − 2
c
8
u
40
− 21u
39
+ ··· − 6214u + 562
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
40
+ 23y
39
+ ··· − 67y + 1
c
2
, c
6
, c
7
c
12
y
40
− 17y
39
+ ··· − 19y + 1
c
3
, c
5
y
40
− 27y
39
+ ··· + 64y + 4
c
4
, c
9
, c
10
y
40
+ 33y
39
+ ··· − 32y + 4
c
8
y
40
− 3y
39
+ ··· − 5405216y + 315844
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.033946 + 1.113580I
a = −0.443213 + 0.659546I
b = −0.529000 − 0.069966I
2.62973 − 1.45530I −8.41133 + 4.63856I
u = 0.033946 − 1.113580I
a = −0.443213 − 0.659546I
b = −0.529000 + 0.069966I
2.62973 + 1.45530I −8.41133 − 4.63856I
u = 0.833882 + 0.049861I
a = 0.866824 + 0.530873I
b = 0.179877 + 0.772910I
−7.70738 + 2.92668I −18.8392 − 4.9556I
u = 0.833882 − 0.049861I
a = 0.866824 − 0.530873I
b = 0.179877 − 0.772910I
−7.70738 − 2.92668I −18.8392 + 4.9556I
u = 0.366756 + 1.108260I
a = 1.59722 + 0.00494I
b = 1.77944 + 1.15129I
−1.99390 + 8.37642I −14.1780 − 5.1626I
u = 0.366756 − 1.108260I
a = 1.59722 − 0.00494I
b = 1.77944 − 1.15129I
−1.99390 − 8.37642I −14.1780 + 5.1626I
u = 0.817179 + 0.133455I
a = −2.11445 + 2.81732I
b = −2.01736 + 1.18808I
−4.96679 − 12.67870I −17.0433 + 8.8234I
u = 0.817179 − 0.133455I
a = −2.11445 − 2.81732I
b = −2.01736 − 1.18808I
−4.96679 + 12.67870I −17.0433 − 8.8234I
u = 0.218298 + 1.152810I
a = −0.690017 + 0.431742I
b = −0.822252 − 0.487537I
2.56813 − 1.57777I −7.38729 + 3.27205I
u = 0.218298 − 1.152810I
a = −0.690017 − 0.431742I
b = −0.822252 + 0.487537I
2.56813 + 1.57777I −7.38729 − 3.27205I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.813800
a = −1.17657
b = −0.516311
−5.88324 −14.0450
u = 0.753305 + 0.134603I
a = 1.75806 − 1.14597I
b = 1.39356 − 0.37494I
−0.35694 − 2.08784I −11.36506 + 1.10964I
u = 0.753305 − 0.134603I
a = 1.75806 + 1.14597I
b = 1.39356 + 0.37494I
−0.35694 + 2.08784I −11.36506 − 1.10964I
u = 0.381450 + 1.215900I
a = −0.154097 + 0.151781I
b = −0.323421 + 0.861671I
−4.11653 − 7.29632I −12.0000 + 8.2173I
u = 0.381450 − 1.215900I
a = −0.154097 − 0.151781I
b = −0.323421 − 0.861671I
−4.11653 + 7.29632I −12.0000 − 8.2173I
u = −0.686189 + 0.170880I
a = 0.15715 + 2.12370I
b = 0.432447 + 0.716843I
0.50362 + 4.50911I −12.14030 − 7.25109I
u = −0.686189 − 0.170880I
a = 0.15715 − 2.12370I
b = 0.432447 − 0.716843I
0.50362 − 4.50911I −12.14030 + 7.25109I
u = −0.129451 + 0.688064I
a = −0.409921 + 0.548317I
b = −0.825583 + 0.231072I
2.57797 − 1.26521I −7.12510 + 2.47533I
u = −0.129451 − 0.688064I
a = −0.409921 − 0.548317I
b = −0.825583 − 0.231072I
2.57797 + 1.26521I −7.12510 − 2.47533I
u = −0.361326 + 1.266880I
a = 0.659360 + 0.462083I
b = 0.516491 − 0.026454I
−1.95240 + 4.22783I −12.00000 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.361326 − 1.266880I
a = 0.659360 − 0.462083I
b = 0.516491 + 0.026454I
−1.95240 − 4.22783I −12.00000 + 0.I
u = −0.391716 + 0.557095I
a = 0.438882 + 0.839532I
b = 1.51444 + 0.60899I
−0.63986 + 8.65751I −12.8507 − 9.2010I
u = −0.391716 − 0.557095I
a = 0.438882 − 0.839532I
b = 1.51444 − 0.60899I
−0.63986 − 8.65751I −12.8507 + 9.2010I
u = 0.373696 + 1.301330I
a = −0.998383 + 0.344441I
b = −0.072953 − 0.689963I
−3.49133 − 1.41285I 0
u = 0.373696 − 1.301330I
a = −0.998383 − 0.344441I
b = −0.072953 + 0.689963I
−3.49133 + 1.41285I 0
u = −0.212237 + 1.347650I
a = −0.30613 + 1.72945I
b = 1.070540 + 0.223660I
3.73398 − 2.59581I 0
u = −0.212237 − 1.347650I
a = −0.30613 − 1.72945I
b = 1.070540 − 0.223660I
3.73398 + 2.59581I 0
u = −0.542858 + 0.319373I
a = −1.52946 − 1.40938I
b = −1.067890 + 0.349863I
−1.40399 − 5.26208I −14.5220 + 2.7158I
u = −0.542858 − 0.319373I
a = −1.52946 + 1.40938I
b = −1.067890 − 0.349863I
−1.40399 + 5.26208I −14.5220 − 2.7158I
u = −0.289068 + 1.350620I
a = 0.94267 − 1.37582I
b = −0.525974 − 1.055320I
5.28661 + 8.06862I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.289068 − 1.350620I
a = 0.94267 + 1.37582I
b = −0.525974 + 1.055320I
5.28661 − 8.06862I 0
u = 0.322258 + 1.346450I
a = −0.02734 + 1.57117I
b = −1.65332 + 0.31762I
4.30721 − 5.98911I 0
u = 0.322258 − 1.346450I
a = −0.02734 − 1.57117I
b = −1.65332 − 0.31762I
4.30721 + 5.98911I 0
u = −0.018698 + 1.394080I
a = −0.777700 − 0.023034I
b = 1.34120 − 0.55017I
8.78475 − 0.92619I 0
u = −0.018698 − 1.394080I
a = −0.777700 + 0.023034I
b = 1.34120 + 0.55017I
8.78475 + 0.92619I 0
u = 0.353485 + 1.352330I
a = −0.60310 − 2.64696I
b = 2.18251 − 1.17429I
−0.2892 − 16.8986I 0
u = 0.353485 − 1.352330I
a = −0.60310 + 2.64696I
b = 2.18251 + 1.17429I
−0.2892 + 16.8986I 0
u = −0.075124 + 1.399150I
a = 1.270610 − 0.109417I
b = −1.96624 − 0.40727I
5.50017 + 10.01410I 0
u = −0.075124 − 1.399150I
a = 1.270610 + 0.109417I
b = −1.96624 + 0.40727I
5.50017 − 10.01410I 0
u = 0.318625
a = 0.902652
b = 0.303261
−0.549970 −17.8990
8
II. I
u
2
= h5150u
29
a − 9644u
29
+ · · · − 4195a − 8440, 2u
29
a + u
28
+ · · · + a +
2, u
30
+ u
29
+ · · · + u + 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
4
=
u
u
3
+ u
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
2
=
a
−0.524066au
29
+ 0.981378u
29
+ ··· + 0.426885a + 0.858858
a
6
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
7
=
−0.524066au
29
+ 0.981378u
29
+ ··· − 0.573115a + 0.858858
−0.153658au
29
− 0.0850717u
29
+ ··· + 0.387300a + 0.950850
a
3
=
u
3
+ 2u
u
3
+ u
a
1
=
0.223873au
29
+ 0.289508u
29
+ ··· + 0.866185a + 0.429226
−0.701537au
29
+ 1.67915u
29
+ ··· + 0.223873a + 1.28951
a
8
=
−u
12
− 5u
10
− 9u
8
− 6u
6
+ u
2
+ 1
−u
14
− 6u
12
− 13u
10
− 10u
8
+ 2u
6
+ 4u
4
− u
2
a
12
=
−0.00142465au
29
+ 0.311794u
29
+ ··· + 0.896306a + 1.12272
−0.0934161au
29
+ 1.30192u
29
+ ··· − 0.0850717a + 1.18999
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
29
− 4u
28
− 48u
27
− 44u
26
− 248u
25
− 208u
24
− 700u
23
− 536u
22
− 1096u
21
−
768u
20
− 712u
19
− 480u
18
+ 464u
17
+ 180u
16
+ 1092u
15
+ 464u
14
+ 380u
13
+ 196u
12
−
444u
11
− 40u
10
− 308u
9
− 48u
8
+ 80u
7
− 44u
6
+ 76u
5
− 20u
4
− 8u
3
+ 12u
2
− 8u − 14
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
60
+ 33u
59
+ ··· + 4u + 1
c
2
, c
6
, c
7
c
12
u
60
− u
59
+ ··· − 2u
2
+ 1
c
3
, c
5
(u
30
+ u
29
+ ··· + 5u + 5)
2
c
4
, c
9
, c
10
(u
30
− u
29
+ ··· − u + 1)
2
c
8
(u
30
+ 7u
29
+ ··· + 39u + 7)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
60
− 13y
59
+ ··· + 28y + 1
c
2
, c
6
, c
7
c
12
y
60
− 33y
59
+ ··· − 4y + 1
c
3
, c
5
(y
30
− 19y
29
+ ··· + 115y + 25)
2
c
4
, c
9
, c
10
(y
30
+ 25y
29
+ ··· + 3y + 1)
2
c
8
(y
30
+ 5y
29
+ ··· + 383y + 49)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.325991 + 1.102660I
a = 0.808944 + 0.617632I
b = 1.110360 − 0.539869I
0.60611 − 3.12979I −11.08128 + 1.86186I
u = −0.325991 + 1.102660I
a = −1.50190 + 0.34099I
b = −1.38771 + 1.17054I
0.60611 − 3.12979I −11.08128 + 1.86186I
u = −0.325991 − 1.102660I
a = 0.808944 − 0.617632I
b = 1.110360 + 0.539869I
0.60611 + 3.12979I −11.08128 − 1.86186I
u = −0.325991 − 1.102660I
a = −1.50190 − 0.34099I
b = −1.38771 − 1.17054I
0.60611 + 3.12979I −11.08128 − 1.86186I
u = −0.795029 + 0.135105I
a = −1.69100 − 1.06948I
b = −1.45876 − 0.45086I
−2.32727 + 7.24749I −14.0714 − 5.6345I
u = −0.795029 + 0.135105I
a = 1.66235 + 2.98194I
b = 1.66006 + 1.29480I
−2.32727 + 7.24749I −14.0714 − 5.6345I
u = −0.795029 − 0.135105I
a = −1.69100 + 1.06948I
b = −1.45876 + 0.45086I
−2.32727 − 7.24749I −14.0714 + 5.6345I
u = −0.795029 − 0.135105I
a = 1.66235 − 2.98194I
b = 1.66006 − 1.29480I
−2.32727 − 7.24749I −14.0714 + 5.6345I
u = 0.783573 + 0.097897I
a = 0.529648 + 0.504852I
b = −0.375462 + 0.767460I
−7.47443 − 3.64220I −19.1043 + 4.7217I
u = 0.783573 + 0.097897I
a = −1.52847 + 4.09603I
b = −1.54437 + 2.11232I
−7.47443 − 3.64220I −19.1043 + 4.7217I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.783573 − 0.097897I
a = 0.529648 − 0.504852I
b = −0.375462 − 0.767460I
−7.47443 + 3.64220I −19.1043 − 4.7217I
u = 0.783573 − 0.097897I
a = −1.52847 − 4.09603I
b = −1.54437 − 2.11232I
−7.47443 + 3.64220I −19.1043 − 4.7217I
u = 0.319385 + 1.167960I
a = −0.260474 − 0.287792I
b = 0.228296 + 1.005900I
−4.22892 − 0.37332I −16.2067 − 0.5347I
u = 0.319385 + 1.167960I
a = 2.13507 + 0.77166I
b = 1.19273 + 2.00676I
−4.22892 − 0.37332I −16.2067 − 0.5347I
u = 0.319385 − 1.167960I
a = −0.260474 + 0.287792I
b = 0.228296 − 1.005900I
−4.22892 + 0.37332I −16.2067 + 0.5347I
u = 0.319385 − 1.167960I
a = 2.13507 − 0.77166I
b = 1.19273 − 2.00676I
−4.22892 + 0.37332I −16.2067 + 0.5347I
u = −0.754564 + 0.022245I
a = −0.565229 + 0.120861I
b = 0.319648 + 0.177361I
−5.49797 + 0.02948I −16.3720 + 0.4707I
u = −0.754564 + 0.022245I
a = −2.54490 − 0.69654I
b = −1.53986 − 0.33820I
−5.49797 + 0.02948I −16.3720 + 0.4707I
u = −0.754564 − 0.022245I
a = −0.565229 − 0.120861I
b = 0.319648 − 0.177361I
−5.49797 − 0.02948I −16.3720 − 0.4707I
u = −0.754564 − 0.022245I
a = −2.54490 + 0.69654I
b = −1.53986 + 0.33820I
−5.49797 − 0.02948I −16.3720 − 0.4707I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.327133 + 1.241840I
a = 1.081960 + 0.620280I
b = 1.075050 − 0.682255I
−1.72825 + 3.89629I −12.45772 − 4.15365I
u = −0.327133 + 1.241840I
a = 0.564290 + 0.021783I
b = −0.121679 + 0.416377I
−1.72825 + 3.89629I −12.45772 − 4.15365I
u = −0.327133 − 1.241840I
a = 1.081960 − 0.620280I
b = 1.075050 + 0.682255I
−1.72825 − 3.89629I −12.45772 + 4.15365I
u = −0.327133 − 1.241840I
a = 0.564290 − 0.021783I
b = −0.121679 − 0.416377I
−1.72825 − 3.89629I −12.45772 + 4.15365I
u = −0.311870 + 1.296280I
a = 0.908117 + 0.037740I
b = −0.472487 − 0.133427I
−1.37739 + 3.85600I −11.22500 − 2.05029I
u = −0.311870 + 1.296280I
a = 0.61787 + 2.03259I
b = 2.01782 + 0.26010I
−1.37739 + 3.85600I −11.22500 − 2.05029I
u = −0.311870 − 1.296280I
a = 0.908117 − 0.037740I
b = −0.472487 + 0.133427I
−1.37739 − 3.85600I −11.22500 + 2.05029I
u = −0.311870 − 1.296280I
a = 0.61787 − 2.03259I
b = 2.01782 − 0.26010I
−1.37739 − 3.85600I −11.22500 + 2.05029I
u = 0.303367 + 0.581370I
a = −0.455082 + 0.808828I
b = −1.36467 + 0.55806I
1.48330 − 3.51597I −9.20488 + 5.12276I
u = 0.303367 + 0.581370I
a = 0.244487 + 0.473840I
b = 0.651369 + 0.018555I
1.48330 − 3.51597I −9.20488 + 5.12276I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.303367 − 0.581370I
a = −0.455082 − 0.808828I
b = −1.36467 − 0.55806I
1.48330 + 3.51597I −9.20488 − 5.12276I
u = 0.303367 − 0.581370I
a = 0.244487 − 0.473840I
b = 0.651369 − 0.018555I
1.48330 + 3.51597I −9.20488 − 5.12276I
u = −0.035215 + 1.346940I
a = 1.331800 + 0.361268I
b = −2.13172 − 1.05581I
1.86136 + 1.73295I −8.68819 − 4.09879I
u = −0.035215 + 1.346940I
a = −0.08388 + 1.50364I
b = 0.147617 − 0.212500I
1.86136 + 1.73295I −8.68819 − 4.09879I
u = −0.035215 − 1.346940I
a = 1.331800 − 0.361268I
b = −2.13172 + 1.05581I
1.86136 − 1.73295I −8.68819 + 4.09879I
u = −0.035215 − 1.346940I
a = −0.08388 − 1.50364I
b = 0.147617 + 0.212500I
1.86136 − 1.73295I −8.68819 + 4.09879I
u = 0.255107 + 1.342090I
a = −0.772435 − 0.887903I
b = 0.045216 − 0.822216I
5.03529 − 2.69486I −6.58656 + 2.42783I
u = 0.255107 + 1.342090I
a = 0.21904 + 1.80021I
b = −1.358140 + 0.357342I
5.03529 − 2.69486I −6.58656 + 2.42783I
u = 0.255107 − 1.342090I
a = −0.772435 + 0.887903I
b = 0.045216 + 0.822216I
5.03529 + 2.69486I −6.58656 − 2.42783I
u = 0.255107 − 1.342090I
a = 0.21904 − 1.80021I
b = −1.358140 − 0.357342I
5.03529 + 2.69486I −6.58656 − 2.42783I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.337934 + 1.329700I
a = −1.059820 + 0.153001I
b = 0.458705 − 0.598884I
−2.99171 − 7.69168I −14.0304 + 6.9029I
u = 0.337934 + 1.329700I
a = −1.48086 − 2.73805I
b = 1.79750 − 2.17416I
−2.99171 − 7.69168I −14.0304 + 6.9029I
u = 0.337934 − 1.329700I
a = −1.059820 − 0.153001I
b = 0.458705 + 0.598884I
−2.99171 + 7.69168I −14.0304 − 6.9029I
u = 0.337934 − 1.329700I
a = −1.48086 + 2.73805I
b = 1.79750 + 2.17416I
−2.99171 + 7.69168I −14.0304 − 6.9029I
u = 0.575326 + 0.209070I
a = 0.214276 + 1.370120I
b = −0.024140 + 0.286200I
0.241291 + 0.398317I −12.06522 + 1.62643I
u = 0.575326 + 0.209070I
a = 1.63714 − 1.36894I
b = 1.045760 + 0.036819I
0.241291 + 0.398317I −12.06522 + 1.62643I
u = 0.575326 − 0.209070I
a = 0.214276 − 1.370120I
b = −0.024140 − 0.286200I
0.241291 − 0.398317I −12.06522 − 1.62643I
u = 0.575326 − 0.209070I
a = 1.63714 + 1.36894I
b = 1.045760 − 0.036819I
0.241291 − 0.398317I −12.06522 − 1.62643I
u = −0.341616 + 1.350480I
a = 0.00663 + 1.44057I
b = 1.66219 + 0.34651I
2.35082 + 11.35200I −9.44655 − 7.31316I
u = −0.341616 + 1.350480I
a = 0.83289 − 2.47231I
b = −1.84709 − 1.33663I
2.35082 + 11.35200I −9.44655 − 7.31316I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.341616 − 1.350480I
a = 0.00663 − 1.44057I
b = 1.66219 − 0.34651I
2.35082 − 11.35200I −9.44655 + 7.31316I
u = −0.341616 − 1.350480I
a = 0.83289 + 2.47231I
b = −1.84709 + 1.33663I
2.35082 − 11.35200I −9.44655 + 7.31316I
u = 0.051114 + 1.394540I
a = −1.201200 − 0.037073I
b = 1.89724 − 0.50837I
7.60322 − 4.47665I −4.97371 + 3.57345I
u = 0.051114 + 1.394540I
a = 0.588507 − 0.124880I
b = −1.096760 − 0.435170I
7.60322 − 4.47665I −4.97371 + 3.57345I
u = 0.051114 − 1.394540I
a = −1.201200 + 0.037073I
b = 1.89724 + 0.50837I
7.60322 + 4.47665I −4.97371 − 3.57345I
u = 0.051114 − 1.394540I
a = 0.588507 + 0.124880I
b = −1.096760 + 0.435170I
7.60322 + 4.47665I −4.97371 − 3.57345I
u = −0.234389 + 0.375701I
a = 0.457879 + 0.838104I
b = 1.32986 + 0.99443I
−3.42503 + 0.99510I −14.4861 − 6.8230I
u = −0.234389 + 0.375701I
a = −1.19564 − 2.21012I
b = −0.416589 + 0.588948I
−3.42503 + 0.99510I −14.4861 − 6.8230I
u = −0.234389 − 0.375701I
a = 0.457879 − 0.838104I
b = 1.32986 − 0.99443I
−3.42503 − 0.99510I −14.4861 + 6.8230I
u = −0.234389 − 0.375701I
a = −1.19564 + 2.21012I
b = −0.416589 − 0.588948I
−3.42503 − 0.99510I −14.4861 + 6.8230I
17
III. I
u
3
= hb − 1, −2u
3
+ 3u
2
+ 3a − 3u + 3, u
4
+ 3u
2
+ 3i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
4
=
u
u
3
+ u
a
11
=
u
2
+ 1
−u
2
− 3
a
2
=
2
3
u
3
− u
2
+ u − 1
1
a
6
=
u
3
+ 2u
u
3
+ u
a
7
=
1
3
u
3
+ u
2
+ u + 1
u
3
+ u − 1
a
3
=
u
3
+ 2u
u
3
+ u
a
1
=
−
1
3
u
3
− u
2
− u − 1
−u
3
− u + 1
a
8
=
u
2
+ 1
−u
2
− 3
a
12
=
−
1
3
u
3
− u
−u
3
− u
2
− u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
− 12
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
11
(u − 1)
4
c
3
, c
5
, c
8
u
4
− 3u
2
+ 3
c
4
, c
9
, c
10
u
4
+ 3u
2
+ 3
c
6
, c
12
(u + 1)
4
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
11
, c
12
(y −1)
4
c
3
, c
5
, c
8
(y
2
− 3y + 3)
2
c
4
, c
9
, c
10
(y
2
+ 3y + 3)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.340625 + 1.271230I
a = −0.233945 − 0.669365I
b = 1.00000
−3.28987 − 4.05977I −18.0000 + 3.4641I
u = 0.340625 − 1.271230I
a = −0.233945 + 0.669365I
b = 1.00000
−3.28987 + 4.05977I −18.0000 − 3.4641I
u = −0.340625 + 1.271230I
a = 1.23394 + 1.06269I
b = 1.00000
−3.28987 + 4.05977I −18.0000 − 3.4641I
u = −0.340625 − 1.271230I
a = 1.23394 − 1.06269I
b = 1.00000
−3.28987 − 4.05977I −18.0000 + 3.4641I
21
IV. I
u
4
= hb + 1, u
2
+ a − u + 1, u
4
+ u
2
− 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
4
=
u
u
3
+ u
a
11
=
u
2
+ 1
u
2
+ 1
a
2
=
−u
2
+ u − 1
−1
a
6
=
−u
3
− 2u
−u
3
− u
a
7
=
−u
3
− u
2
− u − 1
−u
3
− u − 1
a
3
=
u
3
+ 2u
u
3
+ u
a
1
=
−u
3
− u
2
− u − 1
−u
3
− u − 1
a
8
=
−u
2
− 1
−u
2
− 1
a
12
=
−u
3
− u
−u
3
+ u
2
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
− 20
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
11
c
12
(u − 1)
4
c
2
, c
7
(u + 1)
4
c
3
, c
5
, c
8
u
4
− u
2
− 1
c
4
, c
9
, c
10
u
4
+ u
2
− 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
11
, c
12
(y −1)
4
c
3
, c
5
, c
8
(y
2
− y −1)
2
c
4
, c
9
, c
10
(y
2
+ y −1)
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.786151
a = −0.831883
b = −1.00000
−7.23771 −22.4720
u = −0.786151
a = −2.40419
b = −1.00000
−7.23771 −22.4720
u = 1.272020I
a = 0.618030 + 1.272020I
b = −1.00000
0.657974 −13.5280
u = − 1.272020I
a = 0.618030 − 1.272020I
b = −1.00000
0.657974 −13.5280
25
V. I
v
1
= ha, b − 1, v + 1i
(i) Arc colorings
a
5
=
−1
0
a
9
=
1
0
a
10
=
1
0
a
4
=
−1
0
a
11
=
1
0
a
2
=
0
1
a
6
=
−1
0
a
7
=
−1
−1
a
3
=
−1
0
a
1
=
1
1
a
8
=
1
0
a
12
=
2
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
2
, c
7
c
11
u − 1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
c
6
, c
12
u + 1
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
11
, c
12
y − 1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
−3.28987 −12.0000
29
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
((u − 1)
9
)(u
40
+ 17u
39
+ ··· + 19u + 1)(u
60
+ 33u
59
+ ··· + 4u + 1)
c
2
, c
7
((u − 1)
5
)(u + 1)
4
(u
40
− u
39
+ ··· − u − 1)(u
60
− u
59
+ ··· − 2u
2
+ 1)
c
3
, c
5
u(u
4
− 3u
2
+ 3)(u
4
− u
2
− 1)(u
30
+ u
29
+ ··· + 5u + 5)
2
· (u
40
− 3u
39
+ ··· + 10u − 2)
c
4
, c
9
, c
10
u(u
4
+ u
2
− 1)(u
4
+ 3u
2
+ 3)(u
30
− u
29
+ ··· − u + 1)
2
· (u
40
+ 3u
39
+ ··· − 6u − 2)
c
6
, c
12
((u − 1)
4
)(u + 1)
5
(u
40
− u
39
+ ··· − u − 1)(u
60
− u
59
+ ··· − 2u
2
+ 1)
c
8
u(u
4
− 3u
2
+ 3)(u
4
− u
2
− 1)(u
30
+ 7u
29
+ ··· + 39u + 7)
2
· (u
40
− 21u
39
+ ··· − 6214u + 562)
30
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
((y − 1)
9
)(y
40
+ 23y
39
+ ··· − 67y + 1)(y
60
− 13y
59
+ ··· + 28y + 1)
c
2
, c
6
, c
7
c
12
((y − 1)
9
)(y
40
− 17y
39
+ ··· − 19y + 1)(y
60
− 33y
59
+ ··· − 4y + 1)
c
3
, c
5
y(y
2
− 3y + 3)
2
(y
2
− y − 1)
2
(y
30
− 19y
29
+ ··· + 115y + 25)
2
· (y
40
− 27y
39
+ ··· + 64y + 4)
c
4
, c
9
, c
10
y(y
2
+ y − 1)
2
(y
2
+ 3y + 3)
2
(y
30
+ 25y
29
+ ··· + 3y + 1)
2
· (y
40
+ 33y
39
+ ··· − 32y + 4)
c
8
y(y
2
− 3y + 3)
2
(y
2
− y − 1)
2
(y
30
+ 5y
29
+ ··· + 383y + 49)
2
· (y
40
− 3y
39
+ ··· − 5405216y + 315844)
31
