11a
332
(K11a
332
)
A knot diagram
1
Linearized knot diagam
5 8 1 10 3 9 2 11 4 7 6
Solving Sequence
3,5 6,8
2 1 7 11 9 10 4
c
5
c
2
c
1
c
7
c
11
c
8
c
10
c
4
c
3
, c
6
, c
9
Ideals for irreducible components
2
of X
par
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).
1
I
u
1
= h−11u
14
− 4u
13
+ ··· + 18b + 5, 10u
14
+ 9u
12
+ ··· + 18a − 18,
u
15
+ 2u
13
+ 2u
12
+ 8u
11
+ 4u
10
+ 16u
9
+ 13u
8
+ 21u
7
+ 12u
6
+ 18u
5
+ 6u
4
+ 6u
3
− 1i
I
u
2
= h−1.37804 × 10
45
u
35
− 1.80053 × 10
44
u
34
+ ··· + 3.99041 × 10
45
b − 1.10674 × 10
46
,
3.65397 × 10
45
u
35
− 4.93039 × 10
45
u
34
+ ··· + 3.99041 × 10
45
a + 1.27280 × 10
45
, u
36
− u
35
+ ··· − 2u + 1i
I
u
3
= h1.73314 × 10
71
u
35
− 1.61154 × 10
72
u
34
+ ··· + 1.23451 × 10
71
b + 2.96287 × 10
71
,
− 2.28749 × 10
71
u
35
+ 1.95052 × 10
72
u
34
+ ··· + 1.23451 × 10
71
a − 2.50099 × 10
72
,
u
36
− 10u
35
+ ··· − 6u − 1i
I
u
4
= h−61u
9
+ 5u
8
− 23u
7
− 223u
6
− 204u
5
+ 3u
4
− 340u
3
− 294u
2
+ 53b + 46u − 34,
24u
9
− 15u
8
+ 16u
7
+ 86u
6
+ 29u
5
− 9u
4
+ 172u
3
+ 34u
2
+ 53a − 32u + 102,
u
10
+ 4u
7
+ 4u
6
− u
5
+ 5u
4
+ 7u
3
− u
2
− u + 1i
I
u
5
= hu
5
− u
3
+ u
2
+ b + u − 1, −u
5
+ u
4
+ u
3
− 2u
2
+ a + 2, u
6
− u
5
+ 2u
3
− u + 1i
I
u
6
= h−u
5
+ 2u
4
+ u
2
+ 2b − 3u + 1, −u
5
+ 3u
4
− 2u
3
+ 2u
2
+ 2a − 8u + 7, u
6
− 2u
5
− 2u
3
+ 5u
2
− 2u − 1i
I
u
7
= h−17597088363u
11
+ 49269694805u
10
+ ··· + 102937123333b − 11160459778,
231997276705u
11
− 468551566961u
10
+ ··· + 102937123333a − 3200274870268,
u
12
− 2u
11
− 22u
10
− 36u
9
− 6u
8
+ 58u
7
+ 35u
6
− 80u
5
− 142u
4
− 120u
3
− 58u
2
− 12u + 1i
I
u
8
= h−3839279u
11
+ 8525704u
10
+ ··· + 9619063b − 14981729,
21714338u
11
− 64033521u
10
+ ··· + 28857189a + 1783311,
u
12
− 3u
11
− 4u
10
+ 8u
9
+ 10u
8
− 12u
7
− 33u
6
+ 50u
5
+ 2u
4
− 44u
3
+ 25u
2
− 3i
I
u
9
= hb − 1, a, u + 1i
I
u
10
= hb − 1, a + u − 3, u
2
− 2u − 1i
I
u
11
= hb, a − 1, u − 1i
I
u
12
= hb − 1, a − 1, u − 1i
I
u
13
= hb + 1, a − 1, u + 1i
I
v
1
= ha, b + 1, v − 1i
* 14 irreducible components of dim
C
= 0, with total 140 representations.
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
2
I. I
u
1
= h−11u
14
− 4u
13
+ · · · + 18b + 5, 10u
14
+ 9u
12
+ · · · + 18a − 18, u
15
+
2u
13
+ · · · + 6u
3
− 1i
(i) Arc colorings
a
3
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
8
=
−
5
9
u
14
−
1
2
u
12
+ ··· +
23
18
u + 1
11
18
u
14
+
2
9
u
13
+ ··· −
11
9
u −
5
18
a
2
=
−
5
18
u
14
−
1
3
u
12
+ ··· −
7
9
u −
2
3
5
18
u
14
+
1
3
u
12
+ ··· +
7
9
u −
1
3
a
1
=
−1
5
18
u
14
+
1
3
u
12
+ ··· +
7
9
u −
1
3
a
7
=
−0.222222u
14
− 0.277778u
13
+ ··· − 0.722222u + 1.55556
5
18
u
14
−
1
9
u
13
+ ··· −
2
9
u −
5
18
a
11
=
−
5
18
u
14
−
1
3
u
12
+ ··· −
7
9
u −
2
3
1
2
u
14
−
1
3
u
13
+ ··· +
1
2
u −
1
3
a
9
=
−0.555556u
14
+ 0.222222u
13
+ ··· + 0.611111u + 0.722222
5
18
u
14
−
5
18
u
13
+ ··· −
14
9
u +
2
9
a
10
=
−0.0555556u
14
− 0.222222u
13
+ ··· − 0.0555556u − 0.722222
11
18
u
13
+ u
11
+ ··· + u −
5
9
a
4
=
−u
−
2
9
u
13
+
1
3
u
12
+ ··· +
2
3
u +
5
18
a
4
=
−u
−
2
9
u
13
+
1
3
u
12
+ ··· +
2
3
u +
5
18
(ii) Obstruction class = −1
(iii) Cusp Shapes =
55
9
u
14
−
8
9
u
13
+
29
3
u
12
+
89
9
u
11
+
385
9
u
10
+
116
9
u
9
+
223
3
u
8
+
484
9
u
7
+
748
9
u
6
+
241
9
u
5
+
511
9
u
4
+
25
9
u
3
+
112
9
u
2
−
47
9
u +
25
9
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
15
+ 9u
14
+ ··· − 32u − 16
c
2
, c
4
, c
7
c
9
u
15
− 4u
13
+ 9u
11
− 2u
10
− 8u
9
+ 7u
8
+ 2u
7
− 12u
6
+ 4u
5
+ 9u
4
− 2u − 2
c
3
, c
5
, c
6
c
8
u
15
+ 2u
13
+ ··· + 6u
3
− 1
c
11
u
15
+ 13u
14
+ ··· − 416u − 64
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
15
− 5y
14
+ ··· + 384y −256
c
2
, c
4
, c
7
c
9
y
15
− 8y
14
+ ··· + 4y −4
c
3
, c
5
, c
6
c
8
y
15
+ 4y
14
+ ··· + 12y
2
− 1
c
11
y
15
− 7y
14
+ ··· + 11264y −4096
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.375965 + 0.932481I
a = −0.022789 − 1.214510I
b = 0.76086 + 2.35797I
5.04027 − 9.43708I 7.9635 + 11.7594I
u = 0.375965 − 0.932481I
a = −0.022789 + 1.214510I
b = 0.76086 − 2.35797I
5.04027 + 9.43708I 7.9635 − 11.7594I
u = −0.770687 + 0.717882I
a = 0.585197 + 0.439087I
b = −0.78233 − 1.39703I
0.48581 + 3.45966I 2.92722 − 6.50047I
u = −0.770687 − 0.717882I
a = 0.585197 − 0.439087I
b = −0.78233 + 1.39703I
0.48581 − 3.45966I 2.92722 + 6.50047I
u = −0.017197 + 0.777026I
a = −0.70943 + 1.35975I
b = −0.32717 − 1.53341I
4.09690 + 5.67488I 5.06867 − 6.10846I
u = −0.017197 − 0.777026I
a = −0.70943 − 1.35975I
b = −0.32717 + 1.53341I
4.09690 − 5.67488I 5.06867 + 6.10846I
u = 0.483358 + 1.164780I
a = 0.793953 − 0.756191I
b = 0.527888 + 1.092680I
5.64308 + 1.61043I 6.76634 + 1.00019I
u = 0.483358 − 1.164780I
a = 0.793953 + 0.756191I
b = 0.527888 − 1.092680I
5.64308 − 1.61043I 6.76634 − 1.00019I
u = −0.442558 + 0.472159I
a = 0.761967 − 0.578478I
b = −0.096613 − 0.396023I
−0.61502 + 1.62852I −1.81112 − 4.54842I
u = −0.442558 − 0.472159I
a = 0.761967 + 0.578478I
b = −0.096613 + 0.396023I
−0.61502 − 1.62852I −1.81112 + 4.54842I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.031270 + 0.943313I
a = −0.670358 + 0.362743I
b = −0.175859 − 0.100257I
−3.28483 + 7.08124I −3.75198 − 5.71793I
u = −1.031270 − 0.943313I
a = −0.670358 − 0.362743I
b = −0.175859 + 0.100257I
−3.28483 − 7.08124I −3.75198 + 5.71793I
u = 0.419879
a = 2.09302
b = −0.477344
1.70444 5.76330
u = 1.19245 + 1.13162I
a = −0.285046 + 0.850536I
b = −0.66810 − 2.22561I
2.5860 − 19.7120I 0.95572 + 10.39733I
u = 1.19245 − 1.13162I
a = −0.285046 − 0.850536I
b = −0.66810 + 2.22561I
2.5860 + 19.7120I 0.95572 − 10.39733I
7
II.
I
u
2
= h−1.38×10
45
u
35
−1.80×10
44
u
34
+· · ·+3.99×10
45
b−1.11×10
46
, 3.65×
10
45
u
35
−4.93×10
45
u
34
+· · ·+3.99×10
45
a+1.27×10
45
, u
36
−u
35
+· · ·−2u+1i
(i) Arc colorings
a
3
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
8
=
−0.915688u
35
+ 1.23556u
34
+ ··· − 5.91984u − 0.318965
0.345337u
35
+ 0.0451214u
34
+ ··· − 6.72198u + 2.77349
a
2
=
−3.55283u
35
+ 4.15978u
34
+ ··· − 10.7211u − 1.59357
0.343747u
35
− 0.453576u
34
+ ··· − 3.02752u + 0.528741
a
1
=
−3.20909u
35
+ 3.70621u
34
+ ··· − 13.7486u − 1.06483
0.343747u
35
− 0.453576u
34
+ ··· − 3.02752u + 0.528741
a
7
=
0.262533u
35
+ 0.323253u
34
+ ··· − 10.4090u + 6.48551
−0.282683u
35
+ 0.688828u
34
+ ··· − 7.63695u + 1.19971
a
11
=
−3.09336u
35
+ 3.63567u
34
+ ··· − 6.51773u − 2.09069
0.468774u
35
− 0.540153u
34
+ ··· − 3.05287u + 0.483555
a
9
=
−0.373382u
35
+ 1.27775u
34
+ ··· − 14.1973u + 2.77440
0.273958u
35
− 0.0694172u
34
+ ··· − 5.30088u + 2.30472
a
10
=
−2.31277u
35
+ 2.47738u
34
+ ··· − 18.4300u − 0.137385
0.0179996u
35
− 0.268681u
34
+ ··· + 5.18656u − 1.68120
a
4
=
1.78549u
35
− 1.68467u
34
+ ··· − 7.57950u + 4.97500
1.01596u
35
− 1.06117u
34
+ ··· + 5.42208u + 0.378941
a
4
=
1.78549u
35
− 1.68467u
34
+ ··· − 7.57950u + 4.97500
1.01596u
35
− 1.06117u
34
+ ··· + 5.42208u + 0.378941
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5.15842u
35
+ 3.75096u
34
+ ··· + 33.9670u − 14.9765
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
18
− 4u
17
+ ··· + 4u
2
+ 1)
2
c
2
, c
4
, c
7
c
9
u
36
+ 3u
35
+ ··· + 34u + 13
c
3
, c
5
, c
6
c
8
u
36
− u
35
+ ··· − 2u + 1
c
11
(u
18
− 5u
17
+ ··· − 8u + 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
18
+ 10y
17
+ ··· + 8y + 1)
2
c
2
, c
4
, c
7
c
9
y
36
− 15y
35
+ ··· + 40y + 169
c
3
, c
5
, c
6
c
8
y
36
− y
35
+ ··· + 28y + 1
c
11
(y
18
+ 3y
17
+ ··· − 8y + 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.363120 + 1.008320I
a = 0.026422 + 1.101700I
b = 0.70580 − 1.91504I
2.57204 + 5.31192I 3.36040 − 8.00060I
u = −0.363120 − 1.008320I
a = 0.026422 − 1.101700I
b = 0.70580 + 1.91504I
2.57204 − 5.31192I 3.36040 + 8.00060I
u = 0.649836 + 0.632824I
a = 0.608719 + 0.180629I
b = −0.783167 + 0.542527I
2.57204 − 5.31192I 3.36040 + 8.00060I
u = 0.649836 − 0.632824I
a = 0.608719 − 0.180629I
b = −0.783167 − 0.542527I
2.57204 + 5.31192I 3.36040 − 8.00060I
u = 0.893795 + 0.123771I
a = −0.806277 − 0.142896I
b = −0.470358 − 1.315610I
3.30139 + 5.60580I 4.21097 − 5.33069I
u = 0.893795 − 0.123771I
a = −0.806277 + 0.142896I
b = −0.470358 + 1.315610I
3.30139 − 5.60580I 4.21097 + 5.33069I
u = −0.440875 + 1.024740I
a = 0.025375 + 1.272790I
b = 0.33726 − 1.60649I
3.30139 + 5.60580I 4.21097 − 5.33069I
u = −0.440875 − 1.024740I
a = 0.025375 − 1.272790I
b = 0.33726 + 1.60649I
3.30139 − 5.60580I 4.21097 + 5.33069I
u = 0.517386 + 0.999523I
a = 0.149927 − 1.060780I
b = 0.04630 + 2.23105I
5.05604 − 1.80030I 7.45000 + 3.46748I
u = 0.517386 − 0.999523I
a = 0.149927 + 1.060780I
b = 0.04630 − 2.23105I
5.05604 + 1.80030I 7.45000 − 3.46748I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.850004 + 0.786233I
a = −0.268215 − 0.726745I
b = −0.028148 + 0.754872I
2.75241 − 3.93541I 2.90741 + 5.36629I
u = 0.850004 − 0.786233I
a = −0.268215 + 0.726745I
b = −0.028148 − 0.754872I
2.75241 + 3.93541I 2.90741 − 5.36629I
u = 0.298814 + 0.783563I
a = 0.584126 + 0.283863I
b = −0.179299 − 0.216656I
1.88210 + 1.75570I 3.07518 − 1.06674I
u = 0.298814 − 0.783563I
a = 0.584126 − 0.283863I
b = −0.179299 + 0.216656I
1.88210 − 1.75570I 3.07518 + 1.06674I
u = −0.095278 + 0.825512I
a = 1.87436 + 0.04602I
b = −0.009002 − 0.144399I
−1.19542 − 1.15621I 10.86918 − 2.44420I
u = −0.095278 − 0.825512I
a = 1.87436 − 0.04602I
b = −0.009002 + 0.144399I
−1.19542 + 1.15621I 10.86918 + 2.44420I
u = 0.437518 + 1.136460I
a = 0.512918 − 1.258620I
b = 0.45023 + 1.44725I
7.02166 − 7.49599I 6.57969 + 7.14836I
u = 0.437518 − 1.136460I
a = 0.512918 + 1.258620I
b = 0.45023 − 1.44725I
7.02166 + 7.49599I 6.57969 − 7.14836I
u = −0.371712 + 1.181350I
a = 0.390182 + 0.870496I
b = 0.67521 − 1.35698I
2.75241 + 3.93541I 2.90741 − 5.36629I
u = −0.371712 − 1.181350I
a = 0.390182 − 0.870496I
b = 0.67521 + 1.35698I
2.75241 − 3.93541I 2.90741 + 5.36629I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.972609 + 0.975530I
a = −0.804652 − 0.466962I
b = 0.0875024 + 0.0540753I
−0.55505 − 12.95420I −1.0000 + 8.63684I
u = 0.972609 − 0.975530I
a = −0.804652 + 0.466962I
b = 0.0875024 − 0.0540753I
−0.55505 + 12.95420I −1.0000 − 8.63684I
u = −1.375460 + 0.143710I
a = 0.532601 + 0.386317I
b = 0.755723 − 0.967094I
−2.74089 + 1.92073I −7.73857 − 5.49648I
u = −1.375460 − 0.143710I
a = 0.532601 − 0.386317I
b = 0.755723 + 0.967094I
−2.74089 − 1.92073I −7.73857 + 5.49648I
u = 0.338423 + 0.447370I
a = 0.36194 − 1.95892I
b = −0.396182 + 1.120630I
1.88210 − 1.75570I 3.07518 + 1.06674I
u = 0.338423 − 0.447370I
a = 0.36194 + 1.95892I
b = −0.396182 − 1.120630I
1.88210 + 1.75570I 3.07518 − 1.06674I
u = −0.092953 + 0.387873I
a = 2.70253 − 0.69095I
b = 0.598829 − 0.213056I
−2.74089 + 1.92073I −7.73857 − 5.49648I
u = −0.092953 − 0.387873I
a = 2.70253 + 0.69095I
b = 0.598829 + 0.213056I
−2.74089 − 1.92073I −7.73857 + 5.49648I
u = −0.164240 + 0.304020I
a = 0.30937 + 3.57193I
b = −0.77904 − 1.26752I
5.05604 − 1.80030I 7.45000 + 3.46748I
u = −0.164240 − 0.304020I
a = 0.30937 − 3.57193I
b = −0.77904 + 1.26752I
5.05604 + 1.80030I 7.45000 − 3.46748I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.40474 + 0.96008I
a = −0.456383 + 0.579963I
b = −0.73214 − 2.09422I
7.02166 − 7.49599I 0
u = 1.40474 − 0.96008I
a = −0.456383 − 0.579963I
b = −0.73214 + 2.09422I
7.02166 + 7.49599I 0
u = −1.26242 + 1.17225I
a = −0.270237 − 0.743976I
b = −0.67214 + 2.21899I
−0.55505 + 12.95420I 0
u = −1.26242 − 1.17225I
a = −0.270237 + 0.743976I
b = −0.67214 − 2.21899I
−0.55505 − 12.95420I 0
u = −1.69707 + 0.32713I
a = −0.472709 − 0.238795I
b = −1.10737 + 1.60482I
−1.19542 + 1.15621I 0
u = −1.69707 − 0.32713I
a = −0.472709 + 0.238795I
b = −1.10737 − 1.60482I
−1.19542 − 1.15621I 0
14
III. I
u
3
= h1.73 × 10
71
u
35
− 1.61 × 10
72
u
34
+ · · · + 1.23 × 10
71
b + 2.96 ×
10
71
, −2.29 × 10
71
u
35
+ 1.95 × 10
72
u
34
+ · · · + 1.23 × 10
71
a − 2.50 ×
10
72
, u
36
− 10u
35
+ · · · − 6u − 1i
(i) Arc colorings
a
3
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
8
=
1.85295u
35
− 15.7999u
34
+ ··· + 13.9344u + 20.2589
−1.40390u
35
+ 13.0541u
34
+ ··· − 19.0944u − 2.40003
a
2
=
−1.02308u
35
+ 12.5666u
34
+ ··· − 17.7060u + 40.2995
−1.98793u
35
+ 18.5611u
34
+ ··· − 21.0095u − 2.60561
a
1
=
−3.01101u
35
+ 31.1278u
34
+ ··· − 38.7154u + 37.6939
−1.98793u
35
+ 18.5611u
34
+ ··· − 21.0095u − 2.60561
a
7
=
12.7714u
35
− 126.136u
34
+ ··· + 173.374u − 58.1830
0.117701u
35
− 1.17964u
34
+ ··· + 0.298887u − 0.237165
a
11
=
−1.01828u
35
+ 12.4254u
34
+ ··· − 14.6110u + 41.3172
−1.24273u
35
+ 11.5677u
34
+ ··· − 11.6668u − 1.38062
a
9
=
9.38240u
35
− 94.2192u
34
+ ··· + 135.032u − 61.6432
0.456694u
35
− 4.47246u
34
+ ··· + 6.95760u + 0.699328
a
10
=
−26.5737u
35
+ 270.228u
34
+ ··· − 395.140u + 223.633
−0.323427u
35
+ 3.24528u
34
+ ··· − 7.68584u − 0.142044
a
4
=
−23.0908u
35
+ 234.477u
34
+ ··· − 344.610u + 187.947
0.952036u
35
− 8.90987u
34
+ ··· + 13.6977u + 2.55897
a
4
=
−23.0908u
35
+ 234.477u
34
+ ··· − 344.610u + 187.947
0.952036u
35
− 8.90987u
34
+ ··· + 13.6977u + 2.55897
(ii) Obstruction class = −1
(iii) Cusp Shapes = 31.0394u
35
− 320.627u
34
+ ··· + 444.568u − 347.305
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
18
− u
17
+ ··· + 8u − 1)
2
c
2
, c
4
, c
7
c
9
(u
18
− 8u
16
+ ··· + 2u − 1)
2
c
3
, c
5
, c
6
c
8
u
36
− 10u
35
+ ··· − 6u − 1
c
11
(u
9
− u
8
+ 3u
7
+ u
6
+ u
5
− u
4
+ 2u
3
+ u + 1)
4
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
18
− 7y
17
+ ··· − 32y + 1)
2
c
2
, c
4
, c
7
c
9
(y
18
− 16y
17
+ ··· − 18y + 1)
2
c
3
, c
5
, c
6
c
8
y
36
− 42y
35
+ ··· − 66y + 1
c
11
(y
9
+ 5y
8
+ 13y
7
+ 7y
6
+ 17y
5
+ 11y
4
+ 4y
3
+ 6y
2
+ y −1)
4
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.03358
a = −0.814532
b = 2.17328
−0.410667 −404.090
u = −0.974908 + 0.644375I
a = 0.649195 − 0.319150I
b = 0.464754 − 0.305283I
−2.62213 + 1.09146I 0. − 5.89503I
u = −0.974908 − 0.644375I
a = 0.649195 + 0.319150I
b = 0.464754 + 0.305283I
−2.62213 − 1.09146I 0. + 5.89503I
u = −1.210830 + 0.190950I
a = 0.379075 + 0.256363I
b = 0.329763 − 0.186088I
−2.62213 + 1.09146I 0. − 5.89503I
u = −1.210830 − 0.190950I
a = 0.379075 − 0.256363I
b = 0.329763 + 0.186088I
−2.62213 − 1.09146I 0. + 5.89503I
u = 0.972906 + 0.767071I
a = −0.541205 + 0.879014I
b = −0.93294 − 2.13800I
2.94139 − 10.34380I 0. + 12.71172I
u = 0.972906 − 0.767071I
a = −0.541205 − 0.879014I
b = −0.93294 + 2.13800I
2.94139 + 10.34380I 0. − 12.71172I
u = 1.202800 + 0.351550I
a = 0.934184 + 0.310379I
b = −0.368803 − 0.573213I
1.62967 − 1.42694I 0
u = 1.202800 − 0.351550I
a = 0.934184 − 0.310379I
b = −0.368803 + 0.573213I
1.62967 + 1.42694I 0
u = 0.687915 + 0.243994I
a = −1.08739 + 1.22141I
b = 0.64121 − 1.29222I
−0.92113 − 6.20293I −12.02897 + 1.29054I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.687915 − 0.243994I
a = −1.08739 − 1.22141I
b = 0.64121 + 1.29222I
−0.92113 + 6.20293I −12.02897 − 1.29054I
u = −0.556413 + 0.468109I
a = −0.71488 − 2.04959I
b = −0.429966 + 0.930334I
2.94139 + 10.34380I 0.42699 − 12.71172I
u = −0.556413 − 0.468109I
a = −0.71488 + 2.04959I
b = −0.429966 − 0.930334I
2.94139 − 10.34380I 0.42699 + 12.71172I
u = 0.653523 + 0.259178I
a = 0.97344 − 1.45983I
b = 0.555400 + 0.282300I
1.62967 + 1.42694I −3.03389 + 0.96634I
u = 0.653523 − 0.259178I
a = 0.97344 + 1.45983I
b = 0.555400 − 0.282300I
1.62967 − 1.42694I −3.03389 − 0.96634I
u = −0.457113 + 0.422721I
a = −0.99106 − 1.58772I
b = −0.98611 + 1.70538I
1.62967 + 1.42694I −3.03389 + 0.96634I
u = −0.457113 − 0.422721I
a = −0.99106 + 1.58772I
b = −0.98611 − 1.70538I
1.62967 − 1.42694I −3.03389 − 0.96634I
u = −0.528987 + 0.241881I
a = 0.964352 − 0.009017I
b = 1.10558 + 1.36508I
−2.62213 − 1.09146I −4.31933 + 5.89503I
u = −0.528987 − 0.241881I
a = 0.964352 + 0.009017I
b = 1.10558 − 1.36508I
−2.62213 + 1.09146I −4.31933 − 5.89503I
u = 1.27165 + 0.63193I
a = 0.294180 − 0.085640I
b = 0.399780 + 0.320910I
−0.92113 − 6.20293I 0
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.27165 − 0.63193I
a = 0.294180 + 0.085640I
b = 0.399780 − 0.320910I
−0.92113 + 6.20293I 0
u = 0.553048 + 0.027251I
a = −0.83551 − 1.27783I
b = 0.541322 + 0.585100I
−2.62213 − 1.09146I −4.31933 + 5.89503I
u = 0.553048 − 0.027251I
a = −0.83551 + 1.27783I
b = 0.541322 − 0.585100I
−2.62213 + 1.09146I −4.31933 − 5.89503I
u = −0.96035 + 1.23478I
a = 0.120430 + 0.753486I
b = 0.84582 − 2.08861I
−0.92113 + 6.20293I 0
u = −0.96035 − 1.23478I
a = 0.120430 − 0.753486I
b = 0.84582 + 2.08861I
−0.92113 − 6.20293I 0
u = −0.020107 + 0.337379I
a = −0.302784 − 1.251190I
b = −0.97510 − 2.83519I
−0.92113 + 6.20293I −12.02897 − 1.29054I
u = −0.020107 − 0.337379I
a = −0.302784 + 1.251190I
b = −0.97510 + 2.83519I
−0.92113 − 6.20293I −12.02897 + 1.29054I
u = 1.24101 + 1.12995I
a = 0.274705 − 0.899412I
b = 0.45396 + 2.12603I
2.94139 − 10.34380I 0
u = 1.24101 − 1.12995I
a = 0.274705 + 0.899412I
b = 0.45396 − 2.12603I
2.94139 + 10.34380I 0
u = 0.70138 + 1.63277I
a = 0.091048 − 0.649406I
b = 0.21926 + 1.83471I
1.62967 − 1.42694I 0
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.70138 − 1.63277I
a = 0.091048 + 0.649406I
b = 0.21926 − 1.83471I
1.62967 + 1.42694I 0
u = −0.127258
a = 18.2781
b = 0.120902
−0.410667 −404.090
u = 1.41519 + 1.57427I
a = −0.533829 + 0.282886I
b = −1.01282 − 1.31300I
2.94139 + 10.34380I 0
u = 1.41519 − 1.57427I
a = −0.533829 − 0.282886I
b = −1.01282 + 1.31300I
2.94139 − 10.34380I 0
u = −2.25061
a = 1.03351
b = −0.263377
−0.410667 0
u = 5.43001
a = 0.155043
b = 6.26696
−0.410667 0
21
IV. I
u
4
= h−61u
9
+ 5u
8
+ · · · + 53b − 34, 24u
9
− 15u
8
+ · · · + 53a +
102, u
10
+ 4u
7
+ 4u
6
− u
5
+ 5u
4
+ 7u
3
− u
2
− u + 1i
(i) Arc colorings
a
3
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
8
=
−0.452830u
9
+ 0.283019u
8
+ ··· + 0.603774u − 1.92453
1.15094u
9
− 0.0943396u
8
+ ··· − 0.867925u + 0.641509
a
2
=
0.679245u
9
− 0.924528u
8
+ ··· − 3.90566u + 0.886792
−0.679245u
9
+ 0.924528u
8
+ ··· + 3.90566u − 1.88679
a
1
=
−1
−0.679245u
9
+ 0.924528u
8
+ ··· + 3.90566u − 1.88679
a
7
=
1.09434u
9
− 0.433962u
8
+ ··· − 1.79245u − 0.849057
−0.679245u
9
+ 0.924528u
8
+ ··· + 3.90566u − 0.886792
a
11
=
0.679245u
9
− 0.924528u
8
+ ··· − 3.90566u + 0.886792
−0.226415u
9
+ 0.641509u
8
+ ··· + 2.30189u − 0.962264
a
9
=
u
9
+ 4u
6
+ 4u
5
− u
4
+ 5u
3
+ 7u
2
− u − 1
0.433962u
9
− 0.396226u
8
+ ··· − 0.245283u + 1.09434
a
10
=
−0.698113u
9
− 0.188679u
8
+ ··· + 0.264151u + 1.28302
0.283019u
9
− 0.301887u
8
+ ··· − 2.37736u + 0.452830
a
4
=
−u
0.924528u
9
− 0.452830u
8
+ ··· − 1.56604u + 0.679245
a
4
=
−u
0.924528u
9
− 0.452830u
8
+ ··· − 1.56604u + 0.679245
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
199
53
u
9
+
237
53
u
8
−
274
53
u
7
−
691
53
u
6
−
13
53
u
5
+
280
53
u
4
−
1859
53
u
3
+
14
53
u
2
+
548
53
u −
647
53
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
10
+ 10u
9
+ ··· + 131u + 29
c
2
, c
4
, c
7
c
9
(u
5
− 2u
3
+ u + 1)
2
c
3
, c
5
, c
6
c
8
u
10
+ 4u
7
+ 4u
6
− u
5
+ 5u
4
+ 7u
3
− u
2
− u + 1
c
11
(u
5
+ 5u
4
+ 13u
3
+ 18u
2
+ 16u + 8)
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
10
− 4y
9
+ ··· + 877y + 841
c
2
, c
4
, c
7
c
9
(y
5
− 4y
4
+ 6y
3
− 4y
2
+ y −1)
2
c
3
, c
5
, c
6
c
8
y
10
+ 8y
8
− 6y
7
+ 22y
6
− 15y
5
+ 39y
4
− 53y
3
+ 25y
2
− 3y + 1
c
11
(y
5
+ y
4
+ 21y
3
+ 12y
2
− 32y −64)
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.820200 + 0.152463I
a = −1.25990 − 0.71322I
b = 1.44173 + 0.78416I
1.73183 + 9.10410I −2.74192 − 10.20249I
u = −0.820200 − 0.152463I
a = −1.25990 + 0.71322I
b = 1.44173 − 0.78416I
1.73183 − 9.10410I −2.74192 + 10.20249I
u = 0.583652 + 1.118000I
a = −0.500000 + 0.957760I
b = −0.66223 − 1.77825I
9.67856 7.93446 + 0.I
u = 0.583652 − 1.118000I
a = −0.500000 − 0.957760I
b = −0.66223 + 1.77825I
9.67856 7.93446 + 0.I
u = −1.103430 + 0.668374I
a = 0.522065 − 0.172431I
b = 0.289027 − 0.328931I
−2.45878 + 1.56515I −6.72531 − 0.79694I
u = −1.103430 − 0.668374I
a = 0.522065 + 0.172431I
b = 0.289027 + 0.328931I
−2.45878 − 1.56515I −6.72531 + 0.79694I
u = 0.338542 + 0.315903I
a = −1.52207 − 0.17243I
b = −0.042586 + 1.317710I
−2.45878 − 1.56515I −6.72531 + 0.79694I
u = 0.338542 − 0.315903I
a = −1.52207 + 0.17243I
b = −0.042586 − 1.317710I
−2.45878 + 1.56515I −6.72531 − 0.79694I
u = 1.00143 + 1.23642I
a = 0.259902 − 0.713220I
b = 0.97405 + 2.22028I
1.73183 − 9.10410I −2.74192 + 10.20249I
u = 1.00143 − 1.23642I
a = 0.259902 + 0.713220I
b = 0.97405 − 2.22028I
1.73183 + 9.10410I −2.74192 − 10.20249I
25
V.
I
u
5
= hu
5
−u
3
+u
2
+b+u−1, −u
5
+u
4
+u
3
−2u
2
+a+2, u
6
−u
5
+2u
3
−u+1i
(i) Arc colorings
a
3
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
8
=
u
5
− u
4
− u
3
+ 2u
2
− 2
−u
5
+ u
3
− u
2
− u + 1
a
2
=
−u
4
+ u
2
− u − 2
u
4
− u
2
+ u + 1
a
1
=
−1
u
4
− u
2
+ u + 1
a
7
=
u
5
− u
3
+ 2u
2
+ 2u
−u
5
+ u
3
− u
2
− 2u
a
11
=
−u
4
− u − 2
−u
5
+ u
4
+ u
3
− 2u
2
+ 2
a
9
=
−u
5
+ u
4
− 2u
2
+ 1
u
5
− u
4
+ 2u
2
+ u − 1
a
10
=
u
4
− u
2
+ u + 1
−u
4
− u − 1
a
4
=
−u
u
5
− u
3
+ u
2
+ 2u
a
4
=
−u
u
5
− u
3
+ u
2
+ 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −9u
5
+ 5u
4
+ 4u
3
− 14u
2
− 3u + 5
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
− u
5
− u
4
+ 5u
3
− u
2
− 4u + 2
c
2
, c
4
, c
7
c
9
, c
11
u
6
− 2u
4
+ 2u
2
+ 1
c
3
, c
5
u
6
− u
5
+ 2u
3
− u + 1
c
6
, c
8
u
6
+ u
5
− 2u
3
+ u + 1
c
10
u
6
+ u
5
− u
4
− 5u
3
− u
2
+ 4u + 2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
6
− 3y
5
+ 9y
4
− 27y
3
+ 37y
2
− 20y + 4
c
2
, c
4
, c
7
c
9
, c
11
(y
3
− 2y
2
+ 2y + 1)
2
c
3
, c
5
, c
6
c
8
y
6
− y
5
+ 4y
4
− 4y
3
+ 4y
2
− y + 1
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.915589 + 0.402116I
a = 0.238984 − 0.544148I
b = 0.437621 + 0.402116I
−3.04743 −7.74305 + 0.I
u = −0.915589 − 0.402116I
a = 0.238984 + 0.544148I
b = 0.437621 − 0.402116I
−3.04743 −7.74305 + 0.I
u = 0.510869 + 0.551075I
a = −1.57262 + 0.71181I
b = 0.334264 − 0.651746I
3.16865 + 8.83066I 2.37152 − 6.93552I
u = 0.510869 − 0.551075I
a = −1.57262 − 0.71181I
b = 0.334264 + 0.651746I
3.16865 − 8.83066I 2.37152 + 6.93552I
u = 0.904720 + 0.975923I
a = 0.333639 − 0.915863I
b = 0.72812 + 2.17874I
3.16865 − 8.83066I 2.37152 + 6.93552I
u = 0.904720 − 0.975923I
a = 0.333639 + 0.915863I
b = 0.72812 − 2.17874I
3.16865 + 8.83066I 2.37152 − 6.93552I
29
VI. I
u
6
= h−u
5
+ 2u
4
+ u
2
+ 2b − 3u + 1, −u
5
+ 3u
4
− 2u
3
+ 2u
2
+ 2a − 8u +
7, u
6
− 2u
5
− 2u
3
+ 5u
2
− 2u − 1i
(i) Arc colorings
a
3
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
8
=
1
2
u
5
−
3
2
u
4
+ u
3
− u
2
+ 4u −
7
2
1
2
u
5
− u
4
−
1
2
u
2
+
3
2
u −
1
2
a
2
=
−
3
2
u
5
+ 3u
4
−
1
2
u
3
+
7
2
u
2
− 7u + 4
1
a
1
=
−
3
2
u
5
+ 3u
4
−
1
2
u
3
+
7
2
u
2
− 7u + 5
1
a
7
=
−u
5
+ 2u
4
+ 2u
2
− 5u + 2
u
2
− u
a
11
=
−2u
5
+
7
2
u
4
+
11
2
u
2
−
17
2
u + 4
−
1
2
u
5
+ u
4
+
1
2
u
2
−
3
2
u +
1
2
a
9
=
−u
5
+ 3u
4
− 2u
3
+ 2u
2
− 7u + 7
1
a
10
=
−3u
5
+
11
2
u
4
+
15
2
u
2
−
27
2
u + 6
−
1
2
u
5
+ u
4
+
3
2
u
2
−
5
2
u +
1
2
a
4
=
−2u
5
+
11
2
u
4
+ ··· − 14u +
21
2
1
2
u
4
−
1
2
u
3
−
1
2
u
2
− u +
3
2
a
4
=
−2u
5
+
11
2
u
4
+ ··· − 14u +
21
2
1
2
u
4
−
1
2
u
3
−
1
2
u
2
− u +
3
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −8u
5
+ 14u
4
+ 2u
3
+ 26u
2
− 36u + 8
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
(u − 1)
6
c
2
, c
4
, c
7
c
9
(u
3
− u − 1)
2
c
3
, c
5
, c
6
c
8
u
6
− 2u
5
− 2u
3
+ 5u
2
− 2u − 1
c
11
(u
3
− 2u
2
+ 3u − 1)
2
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y −1)
6
c
2
, c
4
, c
7
c
9
(y
3
− 2y
2
+ y −1)
2
c
3
, c
5
, c
6
c
8
y
6
− 4y
5
+ 2y
4
− 14y
3
+ 17y
2
− 14y + 1
c
11
(y
3
+ 2y
2
+ 5y −1)
2
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.881088 + 0.396954I
a = −0.385910 + 0.812028I
b = 0.400014 − 0.259730I
−1.71668 − 6.59895I −5.08799 + 11.97592I
u = 0.881088 − 0.396954I
a = −0.385910 − 0.812028I
b = 0.400014 + 0.259730I
−1.71668 + 6.59895I −5.08799 − 11.97592I
u = −0.758527 + 1.141820I
a = −0.074292 + 0.629446I
b = 0.69250 − 2.31173I
−1.71668 + 6.59895I −5.08799 − 11.97592I
u = −0.758527 − 1.141820I
a = −0.074292 − 0.629446I
b = 0.69250 + 2.31173I
−1.71668 − 6.59895I −5.08799 + 11.97592I
u = −0.280032
a = −4.73059
b = −0.966268
1.78843 20.1760
u = 2.03491
a = 0.650996
b = 0.781230
1.78843 20.1760
33
VII. I
u
7
= h−1.76 × 10
10
u
11
+ 4.93 × 10
10
u
10
+ · · · + 1.03 × 10
11
b − 1.12 ×
10
10
, 2.32 × 10
11
u
11
− 4.69 × 10
11
u
10
+ · · · + 1.03 × 10
11
a − 3.20 ×
10
12
, u
12
− 2u
11
+ · · · − 12u + 1i
(i) Arc colorings
a
3
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
8
=
−2.25378u
11
+ 4.55182u
10
+ ··· + 134.798u + 31.0896
0.170950u
11
− 0.478639u
10
+ ··· − 1.76707u + 0.108420
a
2
=
5.33449u
11
− 10.6318u
10
+ ··· − 331.906u − 78.9325
−0.355926u
11
+ 0.917638u
10
+ ··· + 7.76055u − 0.482769
a
1
=
4.97856u
11
− 9.71419u
10
+ ··· − 324.145u − 79.4152
−0.355926u
11
+ 0.917638u
10
+ ··· + 7.76055u − 0.482769
a
7
=
10.4727u
11
− 20.4059u
10
+ ··· − 687.945u − 168.916
−0.0727736u
11
+ 0.157615u
10
+ ··· + 1.99730u + 0.0813584
a
11
=
5.36750u
11
− 10.6628u
10
+ ··· − 333.969u − 79.1754
−0.265808u
11
+ 0.694626u
10
+ ··· + 5.32292u − 0.312044
a
9
=
10.7685u
11
− 21.3803u
10
+ ··· − 679.589u − 161.749
0.351838u
11
− 1.17629u
10
+ ··· − 3.06138u + 0.472073
a
10
=
37.0246u
11
− 71.7730u
10
+ ··· − 2435.33u − 591.123
−0.190524u
11
+ 0.480988u
10
+ ··· + 4.89160u + 0.498647
a
4
=
31.2970u
11
− 60.7573u
10
+ ··· − 2064.36u − 503.536
0.180314u
11
− 0.534039u
10
+ ··· − 2.09965u + 0.898103
a
4
=
31.2970u
11
− 60.7573u
10
+ ··· − 2064.36u − 503.536
0.180314u
11
− 0.534039u
10
+ ··· − 2.09965u + 0.898103
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
120214687040
9357920303
u
11
+
17317169680
9357920303
u
10
+ ··· +
622019165280
322686907
u +
5213231948632
9357920303
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
− 2u
5
− 3u
4
+ 2u
3
− 4u
2
− 10u − 1)
2
c
2
, c
4
, c
7
c
9
u
12
− 9u
10
+ 21u
8
− 30u
6
+ 23u
4
− 8u
2
+ 1
c
3
, c
5
u
12
− 2u
11
+ ··· − 12u + 1
c
6
, c
8
u
12
+ 2u
11
+ ··· + 12u + 1
c
10
(u
6
+ 2u
5
− 3u
4
− 2u
3
− 4u
2
+ 10u − 1)
2
c
11
(u
6
+ 4u
4
+ 11u
2
− 3)
2
35
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
6
− 10y
5
+ 9y
4
− 22y
3
+ 62y
2
− 92y + 1)
2
c
2
, c
4
, c
7
c
9
(y
6
− 9y
5
+ 21y
4
− 30y
3
+ 23y
2
− 8y + 1)
2
c
3
, c
5
, c
6
c
8
y
12
− 48y
11
+ ··· − 260y + 1
c
11
(y
3
+ 4y
2
+ 11y −3)
4
36
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −1.04156
a = 0.818175
b = −2.34015
−0.403335 690.830
u = −0.185343 + 0.681445I
a = 0.199845 + 0.807519I
b = −1.00769 − 3.18429I
−0.62080 + 6.33267I 10.5872 − 10.3937I
u = −0.185343 − 0.681445I
a = 0.199845 − 0.807519I
b = −1.00769 + 3.18429I
−0.62080 − 6.33267I 10.5872 + 10.3937I
u = −0.610652 + 0.293339I
a = −0.93175 − 1.43916I
b = 0.762152 + 1.043440I
−0.62080 + 6.33267I 10.5872 − 10.3937I
u = −0.610652 − 0.293339I
a = −0.93175 + 1.43916I
b = 0.762152 − 1.043440I
−0.62080 − 6.33267I 10.5872 + 10.3937I
u = 1.235890 + 0.607704I
a = 0.378372 − 0.196961I
b = 0.052606 + 0.384202I
−0.62080 − 6.33267I 10.5872 + 10.3937I
u = 1.235890 − 0.607704I
a = 0.378372 + 0.196961I
b = 0.052606 − 0.384202I
−0.62080 + 6.33267I 10.5872 − 10.3937I
u = −0.90547 + 1.21802I
a = 0.069427 + 0.762114I
b = 0.82828 − 2.12111I
−0.62080 + 6.33267I 10.5872 − 10.3937I
u = −0.90547 − 1.21802I
a = 0.069427 − 0.762114I
b = 0.82828 + 2.12111I
−0.62080 − 6.33267I 10.5872 + 10.3937I
u = 0.0621100
a = 40.5810
b = −0.0168748
−0.403335 690.830
37
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −2.43574
a = 1.03479
b = −0.238066
−0.403335 690.830
u = 6.34634
a = 0.134279
b = 7.32440
−0.403335 690.830
38
VIII.
I
u
8
= h−3.84 × 10
6
u
11
+ 8.53 × 10
6
u
10
+ · · · + 9.62 × 10
6
b − 1.50 × 10
7
, 2.17 ×
10
7
u
11
−6.40×10
7
u
10
+· · ·+2.89×10
7
a+1.78×10
6
, u
12
−3u
11
+· · ·+25u
2
−3i
(i) Arc colorings
a
3
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
8
=
−0.752476u
11
+ 2.21898u
10
+ ··· − 14.0569u − 0.0617978
0.399132u
11
− 0.886334u
10
+ ··· + 0.905814u + 1.55750
a
2
=
−1.33055u
11
+ 3.75852u
10
+ ··· − 21.8132u + 1.26455
0.474331u
11
− 1.10281u
10
+ ··· + 0.888146u + 1.98250
a
1
=
−0.856218u
11
+ 2.65571u
10
+ ··· − 20.9251u + 3.24705
0.474331u
11
− 1.10281u
10
+ ··· + 0.888146u + 1.98250
a
7
=
1.27266u
11
− 3.34318u
10
+ ··· + 20.0104u − 5.67212
−0.0952408u
11
+ 0.203920u
10
+ ··· + 1.86972u + 0.223893
a
11
=
−1.26989u
11
+ 3.79571u
10
+ ··· − 24.3819u + 1.52572
0.557626u
11
− 1.21768u
10
+ ··· − 0.352878u + 1.67943
a
9
=
0.481396u
11
− 2.00064u
10
+ ··· + 29.4914u − 5.06785
−0.109216u
11
+ 0.560242u
10
+ ··· − 1.69307u − 1.38466
a
10
=
−1.62779u
11
+ 6.07527u
10
+ ··· − 76.9600u + 20.5954
0.0384477u
11
− 0.150506u
10
+ ··· + 0.0617978u + 1.25743
a
4
=
−2.36787u
11
+ 7.01824u
10
+ ··· − 62.3409u + 15.2970
0.156229u
11
− 0.349463u
10
+ ··· − 1.38815u + 0.476791
a
4
=
−2.36787u
11
+ 7.01824u
10
+ ··· − 62.3409u + 15.2970
0.156229u
11
− 0.349463u
10
+ ··· − 1.38815u + 0.476791
(ii) Obstruction class = −1
(iii) Cusp Shapes =
3743040
9619063
u
11
−
21556320
9619063
u
10
+ ··· +
940282848
9619063
u −
442031262
9619063
39
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
6
+ u
5
− 2u
4
+ 2u
3
− 2u
2
+ 4u − 1)
2
c
2
, c
4
, c
7
c
9
(u
6
+ 3u
5
+ 2u
4
− u
3
− u
2
− 1)
2
c
3
, c
5
, c
6
c
8
u
12
− 3u
11
+ ··· + 25u
2
− 3
c
11
(u
3
+ u + 1)
4
40
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
6
− 5y
5
− 4y
4
− 6y
3
− 8y
2
− 12y + 1)
2
c
2
, c
4
, c
7
c
9
(y
6
− 5y
5
+ 8y
4
− 7y
3
− 3y
2
+ 2y + 1)
2
c
3
, c
5
, c
6
c
8
y
12
− 17y
11
+ ··· − 150y + 9
c
11
(y
3
+ 2y
2
+ y −1)
4
41
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = −0.993657
a = −0.814967
b = 1.77226
−0.403335 −75.8160
u = 0.749156 + 0.689827I
a = 0.512708 + 0.359105I
b = −0.13466 − 1.78906I
−0.62080 + 6.33267I −5.09224 − 6.77700I
u = 0.749156 − 0.689827I
a = 0.512708 − 0.359105I
b = −0.13466 + 1.78906I
−0.62080 − 6.33267I −5.09224 + 6.77700I
u = 1.063990 + 0.437974I
a = −0.096400 − 0.545572I
b = 0.371049 + 0.149196I
−0.62080 − 6.33267I −5.09224 + 6.77700I
u = 1.063990 − 0.437974I
a = −0.096400 + 0.545572I
b = 0.371049 − 0.149196I
−0.62080 + 6.33267I −5.09224 − 6.77700I
u = 0.592462 + 0.353499I
a = −0.95202 + 1.61908I
b = −0.126984 − 1.276200I
−0.62080 − 6.33267I −5.09224 + 6.77700I
u = 0.592462 − 0.353499I
a = −0.95202 − 1.61908I
b = −0.126984 + 1.276200I
−0.62080 + 6.33267I −5.09224 − 6.77700I
u = −1.06445 + 1.26319I
a = 0.155027 + 0.768975I
b = 0.63432 − 2.03002I
−0.62080 + 6.33267I −5.09224 − 6.77700I
u = −1.06445 − 1.26319I
a = 0.155027 − 0.768975I
b = 0.63432 + 2.03002I
−0.62080 − 6.33267I −5.09224 + 6.77700I
u = −0.287025
a = 6.30537
b = 0.313822
−0.403335 −75.8160
42
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = −1.75765
a = 1.02967
b = −0.370859
−0.403335 −75.8160
u = 3.35600
a = 0.241298
b = 3.79733
−0.403335 −75.8160
43
IX. I
u
9
= hb − 1, a, u + 1i
(i) Arc colorings
a
3
=
0
−1
a
5
=
1
0
a
6
=
1
1
a
8
=
0
1
a
2
=
0
−1
a
1
=
−1
−1
a
7
=
0
1
a
11
=
−1
−1
a
9
=
−1
0
a
10
=
−1
0
a
4
=
1
0
a
4
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
44
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
8
u − 1
c
2
, c
4
, c
7
c
9
, c
11
u
c
3
, c
5
, c
10
u + 1
45
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
8
, c
10
y −1
c
2
, c
4
, c
7
c
9
, c
11
y
46
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0
b = 1.00000
−3.28987 −12.0000
47
X. I
u
10
= hb − 1, a + u − 3, u
2
− 2u − 1i
(i) Arc colorings
a
3
=
0
u
a
5
=
1
0
a
6
=
1
2u + 1
a
8
=
−u + 3
1
a
2
=
−2u + 4
1
a
1
=
−2u + 5
1
a
7
=
u − 3
u
a
11
=
−2u + 5
1
a
9
=
4u − 9
u − 1
a
10
=
−3u + 8
−u + 1
a
4
=
−5u + 12
2
a
4
=
−5u + 12
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −36
48
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u + 1)
2
c
2
, c
4
, c
7
c
9
u
2
− 2
c
3
, c
5
u
2
− 2u − 1
c
6
, c
8
u
2
+ 2u − 1
c
10
(u − 1)
2
c
11
u
2
49
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y −1)
2
c
2
, c
4
, c
7
c
9
(y −2)
2
c
3
, c
5
, c
6
c
8
y
2
− 6y + 1
c
11
y
2
50
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = −0.414214
a = 3.41421
b = 1.00000
1.64493 −36.0000
u = 2.41421
a = 0.585786
b = 1.00000
1.64493 −36.0000
51
XI. I
u
11
= hb, a − 1, u − 1i
(i) Arc colorings
a
3
=
0
1
a
5
=
1
0
a
6
=
1
1
a
8
=
1
0
a
2
=
−1
1
a
1
=
0
1
a
7
=
0
1
a
11
=
−1
0
a
9
=
1
0
a
10
=
−1
1
a
4
=
0
1
a
4
=
0
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
52
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
7
c
9
, c
10
, c
11
u − 1
c
3
, c
8
u
53
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
7
c
9
, c
10
, c
11
y −1
c
3
, c
8
y
54
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
11
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000
b = 0
1.64493 6.00000
55
XII. I
u
12
= hb − 1, a − 1, u − 1i
(i) Arc colorings
a
3
=
0
1
a
5
=
1
0
a
6
=
1
1
a
8
=
1
1
a
2
=
−1
0
a
1
=
−1
0
a
7
=
0
1
a
11
=
−2
−1
a
9
=
−1
0
a
10
=
−2
1
a
4
=
−1
1
a
4
=
−1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
56
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
c
2
, c
9
, c
11
u + 1
c
3
, c
4
, c
5
c
6
, c
7
, c
8
u − 1
c
10
u + 2
57
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
11
y −1
c
10
y −4
58
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
12
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000
b = 1.00000
0 0
59
XIII. I
u
13
= hb + 1, a − 1, u + 1i
(i) Arc colorings
a
3
=
0
−1
a
5
=
1
0
a
6
=
1
1
a
8
=
1
−1
a
2
=
1
−2
a
1
=
−1
−2
a
7
=
0
1
a
11
=
0
−1
a
9
=
1
0
a
10
=
0
−1
a
4
=
1
1
a
4
=
1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
60
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u − 2
c
2
, c
9
, c
11
u − 1
c
3
, c
4
, c
5
c
6
, c
7
, c
8
u + 1
c
10
u
61
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y −4
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
11
y −1
c
10
y
62
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
13
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000
b = −1.00000
0 0
63
XIV. I
v
1
= ha, b + 1, v − 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
1
0
a
6
=
1
0
a
8
=
0
−1
a
2
=
1
1
a
1
=
2
1
a
7
=
1
0
a
11
=
1
1
a
9
=
1
0
a
10
=
2
1
a
4
=
3
1
a
4
=
3
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
64
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
, c
8
c
9
, c
10
, c
11
u − 1
c
5
, c
6
u
65
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
, c
8
c
9
, c
10
, c
11
y −1
c
5
, c
6
y
66
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −1.00000
1.64493 6.00000
67
XV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u − 2)(u − 1)
9
(u + 1)
2
(u
6
− 2u
5
− 3u
4
+ 2u
3
− 4u
2
− 10u − 1)
2
· (u
6
− u
5
− u
4
+ 5u
3
− u
2
− 4u + 2)(u
6
+ u
5
− 2u
4
+ 2u
3
− 2u
2
+ 4u − 1)
2
· (u
10
+ 10u
9
+ ··· + 131u + 29)(u
15
+ 9u
14
+ ··· − 32u − 16)
· ((u
18
− 4u
17
+ ··· + 4u
2
+ 1)
2
)(u
18
− u
17
+ ··· + 8u − 1)
2
c
2
, c
4
, c
7
c
9
u(u − 1)
3
(u + 1)(u
2
− 2)(u
3
− u − 1)
2
(u
5
− 2u
3
+ u + 1)
2
· (u
6
− 2u
4
+ 2u
2
+ 1)(u
6
+ 3u
5
+ 2u
4
− u
3
− u
2
− 1)
2
· (u
12
− 9u
10
+ 21u
8
− 30u
6
+ 23u
4
− 8u
2
+ 1)
· (u
15
− 4u
13
+ 9u
11
− 2u
10
− 8u
9
+ 7u
8
+ 2u
7
− 12u
6
+ 4u
5
+ 9u
4
− 2u − 2)
· ((u
18
− 8u
16
+ ··· + 2u − 1)
2
)(u
36
+ 3u
35
+ ··· + 34u + 13)
c
3
, c
5
u(u − 1)
2
(u + 1)
2
(u
2
− 2u − 1)(u
6
− 2u
5
− 2u
3
+ 5u
2
− 2u − 1)
· (u
6
− u
5
+ 2u
3
− u + 1)(u
10
+ 4u
7
+ ··· − u + 1)
· (u
12
− 3u
11
+ ··· + 25u
2
− 3)(u
12
− 2u
11
+ ··· − 12u + 1)
· (u
15
+ 2u
13
+ ··· + 6u
3
− 1)(u
36
− 10u
35
+ ··· − 6u − 1)
· (u
36
− u
35
+ ··· − 2u + 1)
c
6
, c
8
u(u − 1)
3
(u + 1)(u
2
+ 2u − 1)(u
6
− 2u
5
− 2u
3
+ 5u
2
− 2u − 1)
· (u
6
+ u
5
− 2u
3
+ u + 1)(u
10
+ 4u
7
+ ··· − u + 1)
· (u
12
− 3u
11
+ ··· + 25u
2
− 3)(u
12
+ 2u
11
+ ··· + 12u + 1)
· (u
15
+ 2u
13
+ ··· + 6u
3
− 1)(u
36
− 10u
35
+ ··· − 6u − 1)
· (u
36
− u
35
+ ··· − 2u + 1)
c
10
u(u − 1)
10
(u + 1)(u + 2)(u
6
+ u
5
− 2u
4
+ 2u
3
− 2u
2
+ 4u − 1)
2
· (u
6
+ u
5
− u
4
− 5u
3
− u
2
+ 4u + 2)
· (u
6
+ 2u
5
− 3u
4
− 2u
3
− 4u
2
+ 10u − 1)
2
· (u
10
+ 10u
9
+ ··· + 131u + 29)(u
15
+ 9u
14
+ ··· − 32u − 16)
· ((u
18
− 4u
17
+ ··· + 4u
2
+ 1)
2
)(u
18
− u
17
+ ··· + 8u − 1)
2
c
11
u
3
(u − 1)
3
(u + 1)(u
3
+ u + 1)
4
(u
3
− 2u
2
+ 3u − 1)
2
· (u
5
+ 5u
4
+ 13u
3
+ 18u
2
+ 16u + 8)
2
(u
6
− 2u
4
+ 2u
2
+ 1)
· (u
6
+ 4u
4
+ 11u
2
− 3)
2
(u
9
− u
8
+ 3u
7
+ u
6
+ u
5
− u
4
+ 2u
3
+ u + 1)
4
· (u
15
+ 13u
14
+ ··· − 416u − 64)(u
18
− 5u
17
+ ··· − 8u + 1)
2
68
XVI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
y(y − 4)(y − 1)
11
(y
6
− 10y
5
+ 9y
4
− 22y
3
+ 62y
2
− 92y + 1)
2
· (y
6
− 5y
5
− 4y
4
− 6y
3
− 8y
2
− 12y + 1)
2
· (y
6
− 3y
5
+ 9y
4
− 27y
3
+ 37y
2
− 20y + 4)
· (y
10
− 4y
9
+ ··· + 877y + 841)(y
15
− 5y
14
+ ··· + 384y −256)
· ((y
18
− 7y
17
+ ··· − 32y + 1)
2
)(y
18
+ 10y
17
+ ··· + 8y + 1)
2
c
2
, c
4
, c
7
c
9
y(y − 2)
2
(y −1)
4
(y
3
− 2y
2
+ y −1)
2
(y
3
− 2y
2
+ 2y + 1)
2
· (y
5
− 4y
4
+ 6y
3
− 4y
2
+ y −1)
2
· (y
6
− 9y
5
+ 21y
4
− 30y
3
+ 23y
2
− 8y + 1)
2
· ((y
6
− 5y
5
+ ··· + 2y + 1)
2
)(y
15
− 8y
14
+ ··· + 4y −4)
· ((y
18
− 16y
17
+ ··· − 18y + 1)
2
)(y
36
− 15y
35
+ ··· + 40y + 169)
c
3
, c
5
, c
6
c
8
y(y − 1)
4
(y
2
− 6y + 1)(y
6
− 4y
5
+ 2y
4
− 14y
3
+ 17y
2
− 14y + 1)
· (y
6
− y
5
+ 4y
4
− 4y
3
+ 4y
2
− y + 1)
· (y
10
+ 8y
8
− 6y
7
+ 22y
6
− 15y
5
+ 39y
4
− 53y
3
+ 25y
2
− 3y + 1)
· (y
12
− 48y
11
+ ··· − 260y + 1)(y
12
− 17y
11
+ ··· − 150y + 9)
· (y
15
+ 4y
14
+ ··· + 12y
2
− 1)(y
36
− 42y
35
+ ··· − 66y + 1)
· (y
36
− y
35
+ ··· + 28y + 1)
c
11
y
3
(y −1)
4
(y
3
− 2y
2
+ 2y + 1)
2
(y
3
+ 2y
2
+ y −1)
4
· (y
3
+ 2y
2
+ 5y −1)
2
(y
3
+ 4y
2
+ 11y −3)
4
· (y
5
+ y
4
+ 21y
3
+ 12y
2
− 32y −64)
2
· (y
9
+ 5y
8
+ 13y
7
+ 7y
6
+ 17y
5
+ 11y
4
+ 4y
3
+ 6y
2
+ y −1)
4
· (y
15
− 7y
14
+ ··· + 11264y −4096)(y
18
+ 3y
17
+ ··· − 8y + 1)
2
69
