12a
0975
(K12a
0975
)
A knot diagram
1
Linearized knot diagam
4 6 11 7 9 2 10 12 5 1 3 8
Solving Sequence
3,11
4
8,12
9 1 10 7 5 6 2
c
3
c
11
c
8
c
12
c
10
c
7
c
4
c
5
c
2
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
6
+ u
5
− 3u
4
+ 2u
3
− 4u
2
+ b + 4u − 2, −u
6
+ u
5
− 3u
4
+ 2u
3
− 4u
2
+ a + 4u − 1,
u
8
− 2u
7
+ 5u
6
− 6u
5
+ 9u
4
− 10u
3
+ 8u
2
− 4u + 1i
I
u
2
= h4u
14
a − u
14
+ ··· + 8b − 6, 4u
14
a − u
14
+ ··· + 4a + 4, u
15
+ 2u
14
+ ··· − 2u − 2i
I
u
3
= h−1.77260 × 10
28
u
29
+ 1.42417 × 10
29
u
28
+ ··· + 2.16558 × 10
29
b + 4.09260 × 10
29
,
1.02276 × 10
29
u
29
− 4.13857 × 10
29
u
28
+ ··· + 4.65600 × 10
30
a − 8.84106 × 10
30
,
u
30
− 8u
29
+ ··· − 148u + 43i
I
u
4
= h−32051170u
19
+ 10432934u
18
+ ··· + 12423084b − 29249775,
− 32051170u
19
+ 10432934u
18
+ ··· + 12423084a − 16826691, 2u
20
+ 11u
18
+ ··· + 4u + 1i
I
u
5
= h−25516394u
19
+ 1505498u
18
+ ··· + 12423084b − 14885617,
− 32363894u
19
+ 11810374u
18
+ ··· + 6211542a − 28830039, 2u
20
+ 11u
18
+ ··· + 4u + 1i
I
u
6
= h2u
6
a + 3u
5
a + 5u
6
+ 8u
4
a + 6u
5
+ 7u
3
a + 17u
4
+ 12u
2
a + 16u
3
+ 6au + 18u
2
+ 6b − a + 15u + 2,
− u
6
a − u
5
a − 4u
4
a − 3u
3
a + u
4
− 5u
2
a + a
2
− 2au + 2u
2
+ 1, u
7
+ u
6
+ 4u
5
+ 3u
4
+ 5u
3
+ 3u
2
+ u + 1i
I
u
7
= h177u
13
− 1117u
12
+ ··· + 52b − 1064, 296u
13
− 1867u
12
+ ··· + 52a − 1718,
u
14
− 7u
13
+ ··· − 20u + 4i
I
u
8
= hb − a − 1, a
2
+ au − a + u, u
2
+ u + 1i
I
u
9
= h−2u
3
− 4u
2
+ 4b − 3u + 1, 2u
3
+ 2a + u − 3, 2u
4
+ 2u
3
+ 3u
2
+ 1i
I
u
10
= h−2u
3
+ 8u
2
+ 4b + 13u + 7, −2u
3
+ 8u
2
+ 4a + 13u + 11, 2u
4
+ 2u
3
+ 3u
2
+ 1i
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
11
= hu
11
− 2u
10
+ 6u
9
− 7u
8
+ 11u
7
− 7u
6
+ 4u
5
− u
4
− 5u
3
− 2u
2
+ 2b − 2u − 2,
5u
11
− 11u
10
+ 32u
9
− 39u
8
+ 60u
7
− 43u
6
+ 31u
5
− 12u
4
− 16u
3
− 12u
2
+ 4a − 8u − 16,
u
12
− 3u
11
+ 8u
10
− 13u
9
+ 18u
8
− 19u
7
+ 13u
6
− 8u
5
− 2u
4
+ 2u
3
+ 4i
I
u
12
= h973497u
11
a + 1110148u
11
+ ··· + 28861189a − 48376404,
2096423u
11
a + 1944076u
11
+ ··· + 42713350a + 16958187,
u
12
+ 4u
11
+ 14u
10
+ 31u
9
+ 68u
8
+ 107u
7
+ 166u
6
+ 189u
5
+ 205u
4
+ 163u
3
+ 110u
2
+ 52u + 17i
I
u
13
= hu
2
+ b, u
2
+ a + 1, u
4
− u
3
+ 3u
2
− 2u + 1i
I
u
14
= hb − a − u, a
2
+ 2au + a − 2, u
2
+ u + 1i
* 14 irreducible components of dim
C
= 0, with total 192 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−u
6
+ u
5
− 3u
4
+ 2u
3
− 4u
2
+ b + 4u − 2, −u
6
+ u
5
− 3u
4
+ 2u
3
−
4u
2
+ a + 4u − 1, u
8
− 2u
7
+ · · · − 4u + 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
8
=
u
6
− u
5
+ 3u
4
− 2u
3
+ 4u
2
− 4u + 1
u
6
− u
5
+ 3u
4
− 2u
3
+ 4u
2
− 4u + 2
a
12
=
u
u
a
9
=
u
6
− u
5
+ 3u
4
− 2u
3
+ 5u
2
− 4u + 1
u
6
− u
5
+ 3u
4
− 2u
3
+ 5u
2
− 4u + 2
a
1
=
−u
7
+ u
6
− 3u
5
+ 2u
4
− 4u
3
+ 4u
2
−u
7
+ u
6
− 3u
5
+ 2u
4
− 4u
3
+ 4u
2
− u
a
10
=
u
7
+ 2u
5
+ 2u
4
+ 2u
3
+ 2u
2
− 4u + 2
u
7
− u
6
+ 3u
5
− u
4
+ 4u
3
− 2u
2
+ 1
a
7
=
u
7
− 3u
6
+ 6u
5
− 9u
4
+ 11u
3
− 14u
2
+ 11u − 4
u
3
+ u
a
5
=
−u
7
+ 3u
6
− 6u
5
+ 9u
4
− 10u
3
+ 14u
2
− 11u + 4
u
7
− u
6
+ 3u
5
− 2u
4
+ 5u
3
− 4u
2
+ u
a
6
=
−2u
7
+ 4u
6
− 9u
5
+ 11u
4
− 15u
3
+ 18u
2
− 12u + 4
−u
a
2
=
−u
6
+ u
5
− 3u
4
+ 2u
3
− 4u
2
+ 4u − 1
u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −12u
7
+ 24u
6
− 56u
5
+ 68u
4
− 92u
3
+ 108u
2
− 72u + 28
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
8
− 2u
7
− u
6
+ 6u
5
− u
4
− 6u
3
+ 8u
2
− 4u + 1
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
u
8
− 2u
7
+ 5u
6
− 6u
5
+ 9u
4
− 10u
3
+ 8u
2
− 4u + 1
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
8
− 6y
7
+ 23y
6
− 42y
5
+ 43y
4
− 6y
3
+ 14y
2
+ 1
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
y
8
+ 6y
7
+ 19y
6
+ 30y
5
+ 27y
4
+ 6y
3
+ 2y
2
+ 1
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.341045 + 0.670313I
a = −1.14930 − 1.40518I
b = −0.149303 − 1.405180I
−5.74556 + 5.06444I −6.22905 − 4.15704I
u = 0.341045 − 0.670313I
a = −1.14930 + 1.40518I
b = −0.149303 + 1.405180I
−5.74556 − 5.06444I −6.22905 + 4.15704I
u = −0.548152 + 1.211390I
a = 0.942196 − 0.385112I
b = 1.94220 − 0.38511I
−7.41391 − 7.06214I 0.57220 + 4.67413I
u = −0.548152 − 1.211390I
a = 0.942196 + 0.385112I
b = 1.94220 + 0.38511I
−7.41391 + 7.06214I 0.57220 − 4.67413I
u = 0.566503 + 0.259919I
a = −0.452212 + 0.073091I
b = 0.547788 + 0.073091I
1.156280 + 0.316293I 9.01033 − 1.88379I
u = 0.566503 − 0.259919I
a = −0.452212 − 0.073091I
b = 0.547788 − 0.073091I
1.156280 − 0.316293I 9.01033 + 1.88379I
u = 0.64060 + 1.47097I
a = 1.65932 + 0.19565I
b = 2.65932 + 0.19565I
−14.3158 + 20.3233I −3.35347 − 9.42778I
u = 0.64060 − 1.47097I
a = 1.65932 − 0.19565I
b = 2.65932 − 0.19565I
−14.3158 − 20.3233I −3.35347 + 9.42778I
6
II.
I
u
2
= h4u
14
a−u
14
+· · ·+8b−6, 4u
14
a−u
14
+· · ·+4a+4, u
15
+2u
14
+· · ·−2u−2i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
8
=
a
−
1
2
u
14
a +
1
8
u
14
+ ··· + 3u +
3
4
a
12
=
u
u
a
9
=
1
2
u
14
a −
3
8
u
14
+ ··· + a −
5
4
−
1
4
u
14
−
1
4
u
13
+ ··· + 2u −
1
2
a
1
=
1
8
u
14
a +
3
8
u
14
+ ··· −
1
4
a −
3
4
1
2
u
14
a −
1
4
u
14
+ ··· + a −
3
2
a
10
=
1
2
u
14
a −
5
8
u
14
+ ··· + a +
1
4
1
2
u
14
a −
5
8
u
14
+ ··· + 2u +
1
4
a
7
=
−
7
8
u
14
a +
9
8
u
14
+ ··· +
7
4
a −
1
4
−
1
2
u
14
a + u
14
+ ··· + a + u
a
5
=
3
4
u
14
+
5
4
u
13
+ ··· −
1
2
u +
3
2
1
2
u
13
a +
3
8
u
14
+ ··· − a −
3
4
a
6
=
1
2
u
13
a −
1
8
u
14
+ ··· − a +
9
4
1
2
u
13
a +
1
8
u
14
+ ··· − a −
1
4
a
2
=
−
1
2
u
14
a +
5
4
u
14
+ ··· −
9
2
u −
1
2
−
3
8
u
14
a +
3
8
u
14
+ ··· +
3
4
a −
3
4
(ii) Obstruction class = −1
(iii) Cusp Shapes =
u
14
+u
13
+7u
12
+3u
11
+13u
10
−11u
9
−14u
8
−58u
7
−71u
6
−81u
5
−66u
4
−26u
3
+2u
2
+16u+14
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
30
− 2u
29
+ ··· + 22u + 1
c
2
, c
6
, c
8
c
12
u
30
− 8u
29
+ ··· − 148u + 43
c
3
, c
5
, c
9
c
11
(u
15
+ 2u
14
+ ··· − 2u − 2)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
30
− 18y
29
+ ··· − 206y + 1
c
2
, c
6
, c
8
c
12
y
30
+ 16y
29
+ ··· + 1144y + 1849
c
3
, c
5
, c
9
c
11
(y
15
+ 16y
14
+ ··· − 32y −4)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.784607 + 0.130638I
a = 0.350326 − 0.122670I
b = −0.439042 − 0.323007I
−1.36431 + 3.70005I 4.97943 − 3.63821I
u = −0.784607 + 0.130638I
a = −0.12761 + 1.99961I
b = −0.455331 + 0.530841I
−1.36431 + 3.70005I 4.97943 − 3.63821I
u = −0.784607 − 0.130638I
a = 0.350326 + 0.122670I
b = −0.439042 + 0.323007I
−1.36431 − 3.70005I 4.97943 + 3.63821I
u = −0.784607 − 0.130638I
a = −0.12761 − 1.99961I
b = −0.455331 − 0.530841I
−1.36431 − 3.70005I 4.97943 + 3.63821I
u = 0.013344 + 1.238380I
a = 0.482542 + 0.420194I
b = 0.083565 − 0.439251I
−9.63722 − 1.22028I −4.95246 + 1.57507I
u = 0.013344 + 1.238380I
a = 1.32269 + 0.59357I
b = 2.47269 + 0.15514I
−9.63722 − 1.22028I −4.95246 + 1.57507I
u = 0.013344 − 1.238380I
a = 0.482542 − 0.420194I
b = 0.083565 + 0.439251I
−9.63722 + 1.22028I −4.95246 − 1.57507I
u = 0.013344 − 1.238380I
a = 1.32269 − 0.59357I
b = 2.47269 − 0.15514I
−9.63722 + 1.22028I −4.95246 − 1.57507I
u = −0.520579 + 1.217160I
a = 0.310968 − 1.284780I
b = 0.120416 − 0.985660I
−9.00480 − 3.51911I −6.70931 + 3.75254I
u = −0.520579 + 1.217160I
a = 1.41643 − 0.01039I
b = 2.34549 − 0.39766I
−9.00480 − 3.51911I −6.70931 + 3.75254I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.520579 − 1.217160I
a = 0.310968 + 1.284780I
b = 0.120416 + 0.985660I
−9.00480 + 3.51911I −6.70931 − 3.75254I
u = −0.520579 − 1.217160I
a = 1.41643 + 0.01039I
b = 2.34549 + 0.39766I
−9.00480 + 3.51911I −6.70931 − 3.75254I
u = 0.261916 + 1.297730I
a = 0.020854 − 0.716031I
b = 0.182845 + 0.396366I
−4.42818 + 0.58231I 0.85328 − 2.04557I
u = 0.261916 + 1.297730I
a = −1.40607 − 0.80438I
b = −2.21703 − 0.91007I
−4.42818 + 0.58231I 0.85328 − 2.04557I
u = 0.261916 − 1.297730I
a = 0.020854 + 0.716031I
b = 0.182845 − 0.396366I
−4.42818 − 0.58231I 0.85328 + 2.04557I
u = 0.261916 − 1.297730I
a = −1.40607 + 0.80438I
b = −2.21703 + 0.91007I
−4.42818 − 0.58231I 0.85328 + 2.04557I
u = 0.585635
a = 0.23172 + 2.31597I
b = 0.989112 + 0.591455I
−3.88049 1.05620
u = 0.585635
a = 0.23172 − 2.31597I
b = 0.989112 − 0.591455I
−3.88049 1.05620
u = −0.43937 + 1.41900I
a = −0.136932 + 0.381950I
b = −0.399054 − 0.558077I
−9.7235 − 13.1451I −2.87381 + 8.00014I
u = −0.43937 + 1.41900I
a = −1.83297 + 0.18088I
b = −2.83221 + 0.11599I
−9.7235 − 13.1451I −2.87381 + 8.00014I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.43937 − 1.41900I
a = −0.136932 − 0.381950I
b = −0.399054 + 0.558077I
−9.7235 + 13.1451I −2.87381 − 8.00014I
u = −0.43937 − 1.41900I
a = −1.83297 − 0.18088I
b = −2.83221 − 0.11599I
−9.7235 + 13.1451I −2.87381 − 8.00014I
u = 0.035691 + 0.462074I
a = −0.047221 − 0.354434I
b = −0.399260 + 1.160460I
0.93924 + 2.34318I 11.9184 + 9.2243I
u = 0.035691 + 0.462074I
a = −1.88888 + 1.66026I
b = −0.014065 + 0.524425I
0.93924 + 2.34318I 11.9184 + 9.2243I
u = 0.035691 − 0.462074I
a = −0.047221 + 0.354434I
b = −0.399260 − 1.160460I
0.93924 − 2.34318I 11.9184 − 9.2243I
u = 0.035691 − 0.462074I
a = −1.88888 − 1.66026I
b = −0.014065 − 0.524425I
0.93924 − 2.34318I 11.9184 − 9.2243I
u = 0.14079 + 1.54845I
a = −1.080100 + 0.342845I
b = −2.23176 − 0.04950I
−15.8339 + 5.3491I −7.74364 − 3.13359I
u = 0.14079 + 1.54845I
a = 1.88425 − 0.16237I
b = 2.79363 − 0.26921I
−15.8339 + 5.3491I −7.74364 − 3.13359I
u = 0.14079 − 1.54845I
a = −1.080100 − 0.342845I
b = −2.23176 + 0.04950I
−15.8339 − 5.3491I −7.74364 + 3.13359I
u = 0.14079 − 1.54845I
a = 1.88425 + 0.16237I
b = 2.79363 + 0.26921I
−15.8339 − 5.3491I −7.74364 + 3.13359I
12
III. I
u
3
= h−1.77 × 10
28
u
29
+ 1.42 × 10
29
u
28
+ · · · + 2.17 × 10
29
b + 4.09 ×
10
29
, 1.02 × 10
29
u
29
− 4.14 × 10
29
u
28
+ · · · + 4.66 × 10
30
a − 8.84 ×
10
30
, u
30
− 8u
29
+ · · · − 148u + 43i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
8
=
−0.0219666u
29
+ 0.0888867u
28
+ ··· + 0.298145u + 1.89885
0.0818533u
29
− 0.657640u
28
+ ··· + 9.92980u − 1.88984
a
12
=
u
u
a
9
=
−0.0321478u
29
+ 0.0808101u
28
+ ··· + 8.27059u − 1.71451
0.0716720u
29
− 0.665717u
28
+ ··· + 17.9022u − 5.50320
a
1
=
−0.0704699u
29
+ 0.550645u
28
+ ··· − 8.18718u + 4.94852
−0.0379149u
29
+ 0.345413u
28
+ ··· − 6.57038u + 2.46631
a
10
=
−0.0366426u
29
+ 0.259362u
28
+ ··· − 6.63127u + 4.11399
0.0300022u
29
− 0.243000u
28
+ ··· + 3.11454u + 0.123136
a
7
=
0.0280214u
29
− 0.381962u
28
+ ··· + 17.7589u − 8.40340
0.154881u
29
− 1.25831u
28
+ ··· + 21.8368u − 8.10010
a
5
=
0.104726u
29
− 0.766133u
28
+ ··· − 0.915910u + 2.40284
−0.0946306u
29
+ 0.749606u
28
+ ··· − 18.9034u + 10.2528
a
6
=
0.0439498u
29
− 0.269745u
28
+ ··· − 6.25999u + 3.42523
−0.0840317u
29
+ 0.682435u
28
+ ··· − 11.5766u + 4.46425
a
2
=
−0.0573560u
29
+ 0.420933u
28
+ ··· − 2.70616u + 1.91831
−0.0552081u
29
+ 0.398971u
28
+ ··· − 2.33592u + 1.39986
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.444120u
29
+ 3.62226u
28
+ ··· − 75.2699u + 36.1756
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
30
− 2u
29
+ ··· + 22u + 1
c
2
, c
6
, c
8
c
12
(u
15
+ 2u
14
+ ··· − 2u − 2)
2
c
3
, c
5
, c
9
c
11
u
30
− 8u
29
+ ··· − 148u + 43
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
30
− 18y
29
+ ··· − 206y + 1
c
2
, c
6
, c
8
c
12
(y
15
+ 16y
14
+ ··· − 32y −4)
2
c
3
, c
5
, c
9
c
11
y
30
+ 16y
29
+ ··· + 1144y + 1849
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.591752 + 0.825766I
a = −0.404241 + 0.288042I
b = −0.014065 + 0.524425I
0.93924 + 2.34318I 11.9184 + 9.2243I
u = 0.591752 − 0.825766I
a = −0.404241 − 0.288042I
b = −0.014065 − 0.524425I
0.93924 − 2.34318I 11.9184 − 9.2243I
u = −0.075236 + 1.080100I
a = −1.00453 + 1.06811I
b = −2.21703 + 0.91007I
−4.42818 − 0.58231I 0.85328 + 2.04557I
u = −0.075236 − 1.080100I
a = −1.00453 − 1.06811I
b = −2.21703 − 0.91007I
−4.42818 + 0.58231I 0.85328 − 2.04557I
u = 0.443554 + 1.009940I
a = 0.775618 − 0.105347I
b = 0.989112 − 0.591455I
−3.88049 − 61.056179 + 0.10I
u = 0.443554 − 1.009940I
a = 0.775618 + 0.105347I
b = 0.989112 + 0.591455I
−3.88049 − 61.056179 + 0.10I
u = 1.059000 + 0.505555I
a = 0.52794 + 1.39650I
b = 0.083565 + 0.439251I
−9.63722 + 1.22028I −4.95246 − 1.57507I
u = 1.059000 − 0.505555I
a = 0.52794 − 1.39650I
b = 0.083565 − 0.439251I
−9.63722 − 1.22028I −4.95246 + 1.57507I
u = 0.449007 + 1.109600I
a = −0.310623 − 0.117713I
b = −0.455331 + 0.530841I
−1.36431 + 3.70005I 4.97943 − 3.63821I
u = 0.449007 − 1.109600I
a = −0.310623 + 0.117713I
b = −0.455331 − 0.530841I
−1.36431 − 3.70005I 4.97943 + 3.63821I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.712558 + 0.108600I
a = −0.25372 − 1.78675I
b = −0.399260 − 1.160460I
0.93924 − 2.34318I 11.9184 − 9.2243I
u = −0.712558 − 0.108600I
a = −0.25372 + 1.78675I
b = −0.399260 + 1.160460I
0.93924 + 2.34318I 11.9184 + 9.2243I
u = −0.012294 + 1.332420I
a = 1.42848 − 0.77990I
b = 2.34549 − 0.39766I
−9.00480 − 3.51911I −6.70931 + 3.75254I
u = −0.012294 − 1.332420I
a = 1.42848 + 0.77990I
b = 2.34549 + 0.39766I
−9.00480 + 3.51911I −6.70931 − 3.75254I
u = 0.645515 + 0.054065I
a = 0.751134 − 0.625068I
b = −0.439042 − 0.323007I
−1.36431 + 3.70005I 4.97943 − 3.63821I
u = 0.645515 − 0.054065I
a = 0.751134 + 0.625068I
b = −0.439042 + 0.323007I
−1.36431 − 3.70005I 4.97943 + 3.63821I
u = 0.29345 + 1.39308I
a = 1.70894 − 0.39664I
b = 2.79363 − 0.26921I
−15.8339 + 5.3491I −7.74364 − 3.13359I
u = 0.29345 − 1.39308I
a = 1.70894 + 0.39664I
b = 2.79363 + 0.26921I
−15.8339 − 5.3491I −7.74364 + 3.13359I
u = 1.44906 + 0.04107I
a = −0.12382 − 1.54513I
b = −0.399054 − 0.558077I
−9.7235 − 13.1451I −2.87381 + 8.00014I
u = 1.44906 − 0.04107I
a = −0.12382 + 1.54513I
b = −0.399054 + 0.558077I
−9.7235 + 13.1451I −2.87381 − 8.00014I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.53111 + 1.38940I
a = −1.83564 − 0.05128I
b = −2.83221 − 0.11599I
−9.7235 + 13.1451I −2.87381 − 8.00014I
u = 0.53111 − 1.38940I
a = −1.83564 + 0.05128I
b = −2.83221 + 0.11599I
−9.7235 − 13.1451I −2.87381 + 8.00014I
u = −1.40117 + 0.50158I
a = 0.054654 + 1.276660I
b = 0.182845 + 0.396366I
−4.42818 + 0.58231I 0.85328 − 2.04557I
u = −1.40117 − 0.50158I
a = 0.054654 − 1.276660I
b = 0.182845 − 0.396366I
−4.42818 − 0.58231I 0.85328 + 2.04557I
u = 0.55829 + 1.41828I
a = 1.71347 − 0.13431I
b = 2.47269 + 0.15514I
−9.63722 − 1.22028I −4.95246 + 1.57507I
u = 0.55829 − 1.41828I
a = 1.71347 + 0.13431I
b = 2.47269 − 0.15514I
−9.63722 + 1.22028I −4.95246 − 1.57507I
u = −0.264872 + 0.387644I
a = 1.63538 − 1.39243I
b = 0.120416 + 0.985660I
−9.00480 + 3.51911I −6.70931 − 3.75254I
u = −0.264872 − 0.387644I
a = 1.63538 + 1.39243I
b = 0.120416 − 0.985660I
−9.00480 − 3.51911I −6.70931 + 3.75254I
u = 0.44538 + 1.83853I
a = −1.45375 + 0.31455I
b = −2.23176 + 0.04950I
−15.8339 − 5.3491I 0
u = 0.44538 − 1.83853I
a = −1.45375 − 0.31455I
b = −2.23176 − 0.04950I
−15.8339 + 5.3491I 0
18
IV.
I
u
4
= h−3.21 × 10
7
u
19
+ 1.04 × 10
7
u
18
+ · · · + 1.24 × 10
7
b − 2.92 × 10
7
, −3.21 ×
10
7
u
19
+1.04×10
7
u
18
+· · ·+1.24×10
7
a−1.68×10
7
, 2u
20
+11u
18
+· · ·+4u+1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
8
=
2.57997u
19
− 0.839802u
18
+ ··· + 5.83982u + 1.35447
2.57997u
19
− 0.839802u
18
+ ··· + 5.83982u + 2.35447
a
12
=
u
u
a
9
=
2.57997u
19
− 0.839802u
18
+ ··· + 5.83982u + 1.35447
2.57997u
19
− 0.839802u
18
+ ··· + 5.83982u + 2.35447
a
1
=
0.839802u
19
+ 0.560480u
18
+ ··· + 4.80547u + 1.28998
0.839802u
19
+ 0.560480u
18
+ ··· + 3.80547u + 1.28998
a
10
=
−2.75425u
19
+ 1.12237u
18
+ ··· − 0.266870u + 0.439076
−1.80815u
19
+ 2.12100u
18
+ ··· + 2.27399u + 0.719316
a
7
=
0.368104u
19
+ 0.851099u
18
+ ··· + 1.54512u + 0.318890
1.07331u
19
+ 1.27931u
18
+ ··· + 5.66065u + 2.13487
a
5
=
−2.33263u
19
+ 4.14232u
18
+ ··· + 1.61849u − 0.565148
0.0638148u
19
+ 2.08837u
18
+ ··· + 2.36860u − 0.271319
a
6
=
−2.39644u
19
+ 2.05395u
18
+ ··· − 0.750113u − 0.293830
−1.78017u
19
+ 0.847531u
18
+ ··· − 2.86952u − 1.57817
a
2
=
0.946107u
19
+ 0.998631u
18
+ ··· + 2.54086u + 0.280240
1.82394u
19
+ 0.0731794u
18
+ ··· + 4.73492u + 1.50906
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
201044
3105771
u
19
−
4918603
3105771
u
18
+ ··· −
11843897
1035257
u +
24068461
6211542
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
10
+ 2u
9
+ u
8
− 2u
7
− 3u
6
+ 2u
4
+ 2u
3
− 3u
2
− 2u − 2)
2
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
2(2u
20
+ 11u
18
+ ··· + 4u + 1)
c
4
, c
10
4(4u
20
− 28u
19
+ ··· − 448u + 73)
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
10
− 2y
9
+ 3y
8
− 6y
7
− y
6
− 6y
5
+ 10y
4
− 4y
3
+ 9y
2
+ 8y + 4)
2
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
4(4y
20
+ 44y
19
+ ··· − 6y + 1)
c
4
, c
10
16(16y
20
− 8y
19
+ ··· + 42678y + 5329)
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.863041 + 0.424455I
a = 0.150300 − 0.336990I
b = 1.150300 − 0.336990I
−1.77310 + 4.32568I 2.37801 − 5.30660I
u = 0.863041 − 0.424455I
a = 0.150300 + 0.336990I
b = 1.150300 + 0.336990I
−1.77310 − 4.32568I 2.37801 + 5.30660I
u = 0.532247 + 0.733699I
a = 0.094270 − 0.781019I
b = 1.094270 − 0.781019I
−3.96232 2.14246 + 0.I
u = 0.532247 − 0.733699I
a = 0.094270 + 0.781019I
b = 1.094270 + 0.781019I
−3.96232 2.14246 + 0.I
u = −0.854424 + 0.268587I
a = 0.208143 − 1.003220I
b = 1.20814 − 1.00322I
−4.52678 − 8.23619I 1.62263 + 8.93292I
u = −0.854424 − 0.268587I
a = 0.208143 + 1.003220I
b = 1.20814 + 1.00322I
−4.52678 + 8.23619I 1.62263 − 8.93292I
u = −0.294566 + 0.835743I
a = −1.091400 + 0.492363I
b = −0.091403 + 0.492363I
−7.15291 −10.64039 + 0.I
u = −0.294566 − 0.835743I
a = −1.091400 − 0.492363I
b = −0.091403 − 0.492363I
−7.15291 −10.64039 + 0.I
u = −0.219333 + 1.144070I
a = 1.97577 + 0.10621I
b = 2.97577 + 0.10621I
−1.77310 − 4.32568I 2.37801 + 5.30660I
u = −0.219333 − 1.144070I
a = 1.97577 − 0.10621I
b = 2.97577 − 0.10621I
−1.77310 + 4.32568I 2.37801 − 5.30660I
22
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.482255 + 0.664266I
a = −0.579450 + 0.348965I
b = 0.420550 + 0.348965I
0.97046 + 1.97408I 9.55166 − 2.43496I
u = 0.482255 − 0.664266I
a = −0.579450 − 0.348965I
b = 0.420550 − 0.348965I
0.97046 − 1.97408I 9.55166 + 2.43496I
u = −0.365634 + 1.127630I
a = 0.27691 − 1.63768I
b = 1.27691 − 1.63768I
−10.4971 − 10.3444I −5.80333 + 10.34256I
u = −0.365634 − 1.127630I
a = 0.27691 + 1.63768I
b = 1.27691 + 1.63768I
−10.4971 + 10.3444I −5.80333 − 10.34256I
u = −0.445937 + 1.170140I
a = 2.03642 − 0.41858I
b = 3.03642 − 0.41858I
−4.52678 − 8.23619I 1.62263 + 8.93292I
u = −0.445937 − 1.170140I
a = 2.03642 + 0.41858I
b = 3.03642 + 0.41858I
−4.52678 + 8.23619I 1.62263 − 8.93292I
u = −0.387590 + 0.116004I
a = −0.92490 + 1.07958I
b = 0.075100 + 1.079580I
0.97046 + 1.97408I 9.55166 − 2.43496I
u = −0.387590 − 0.116004I
a = −0.92490 − 1.07958I
b = 0.075100 − 1.079580I
0.97046 − 1.97408I 9.55166 + 2.43496I
u = 0.68994 + 1.64040I
a = 1.353940 + 0.198723I
b = 2.35394 + 0.19872I
−10.4971 + 10.3444I −5.80333 − 10.34256I
u = 0.68994 − 1.64040I
a = 1.353940 − 0.198723I
b = 2.35394 − 0.19872I
−10.4971 − 10.3444I −5.80333 + 10.34256I
23
V.
I
u
5
= h−2.55 × 10
7
u
19
+ 1.51 × 10
6
u
18
+ · · · + 1.24 × 10
7
b − 1.49 × 10
7
, −3.24 ×
10
7
u
19
+1.18×10
7
u
18
+· · ·+6.21×10
6
a−2.88×10
7
, 2u
20
+11u
18
+· · ·+4u+1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
8
=
5.21028u
19
− 1.90136u
18
+ ··· + 9.08615u + 4.64137
2.05395u
19
− 0.121186u
18
+ ··· + 4.49906u + 1.19822
a
12
=
u
u
a
9
=
4.36275u
19
− 1.87619u
18
+ ··· + 7.10397u + 3.75128
1.20642u
19
− 0.0960206u
18
+ ··· + 2.51688u + 0.308135
a
1
=
−2.01949u
19
− 0.106305u
18
+ ··· − 6.22944u − 1.77437
0.998631u
19
− 1.93025u
18
+ ··· − 1.61197u − 0.473054
a
10
=
2.08425u
19
− 1.02147u
18
+ ··· + 4.71094u + 2.53696
0.428211u
19
− 1.79215u
18
+ ··· + 0.405560u − 0.352605
a
7
=
5.54874u
19
− 2.01949u
18
+ ··· + 11.7767u + 4.86805
u
3
+ u
a
5
=
−2.61627u
19
+ 1.20642u
18
+ ··· − 2.88059u − 2.71566
−0.925452u
19
+ 0.450391u
18
+ ··· − 0.526847u − 0.438917
a
6
=
−4.70894u
19
+ 2.57997u
18
+ ··· − 7.97120u − 3.57806
−u
a
2
=
−2.57997u
19
+ 0.839802u
18
+ ··· − 5.83982u − 1.35447
u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
201044
3105771
u
19
−
4918603
3105771
u
18
+ ··· −
11843897
1035257
u +
24068461
6211542
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
4(4u
20
− 28u
19
+ ··· − 448u + 73)
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
2(2u
20
+ 11u
18
+ ··· + 4u + 1)
c
4
, c
10
(u
10
+ 2u
9
+ u
8
− 2u
7
− 3u
6
+ 2u
4
+ 2u
3
− 3u
2
− 2u − 2)
2
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
16(16y
20
− 8y
19
+ ··· + 42678y + 5329)
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
4(4y
20
+ 44y
19
+ ··· − 6y + 1)
c
4
, c
10
(y
10
− 2y
9
+ 3y
8
− 6y
7
− y
6
− 6y
5
+ 10y
4
− 4y
3
+ 9y
2
+ 8y + 4)
2
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.863041 + 0.424455I
a = 0.485394 + 0.775205I
b = −0.244227 − 0.191588I
−1.77310 + 4.32568I 2.37801 − 5.30660I
u = 0.863041 − 0.424455I
a = 0.485394 − 0.775205I
b = −0.244227 + 0.191588I
−1.77310 − 4.32568I 2.37801 + 5.30660I
u = 0.532247 + 0.733699I
a = 1.44676 + 0.95061I
b = 1.13636
−3.96232 2.14246 + 0.I
u = 0.532247 − 0.733699I
a = 1.44676 − 0.95061I
b = 1.13636
−3.96232 2.14246 + 0.I
u = −0.854424 + 0.268587I
a = −0.30663 + 1.50788I
b = 0.560140 + 0.410838I
−4.52678 − 8.23619I 1.62263 + 8.93292I
u = −0.854424 − 0.268587I
a = −0.30663 − 1.50788I
b = 0.560140 − 0.410838I
−4.52678 + 8.23619I 1.62263 − 8.93292I
u = −0.294566 + 0.835743I
a = −2.23987 − 0.62703I
b = −3.01887
−7.15291 −10.64039 + 0.I
u = −0.294566 − 0.835743I
a = −2.23987 + 0.62703I
b = −3.01887
−7.15291 −10.64039 + 0.I
u = −0.219333 + 1.144070I
a = 0.253117 + 0.850599I
b = −0.244227 + 0.191588I
−1.77310 − 4.32568I 2.37801 + 5.30660I
u = −0.219333 − 1.144070I
a = 0.253117 − 0.850599I
b = −0.244227 − 0.191588I
−1.77310 + 4.32568I 2.37801 − 5.30660I
27
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.482255 + 0.664266I
a = −0.071592 + 0.163124I
b = −0.234632 + 0.628244I
0.97046 + 1.97408I 9.55166 − 2.43496I
u = 0.482255 − 0.664266I
a = −0.071592 − 0.163124I
b = −0.234632 − 0.628244I
0.97046 − 1.97408I 9.55166 + 2.43496I
u = −0.365634 + 1.127630I
a = −1.144170 + 0.105482I
b = −2.64003 − 0.02134I
−10.4971 − 10.3444I −5.80333 + 10.34256I
u = −0.365634 − 1.127630I
a = −1.144170 − 0.105482I
b = −2.64003 + 0.02134I
−10.4971 + 10.3444I −5.80333 − 10.34256I
u = −0.445937 + 1.170140I
a = 0.116733 − 0.150369I
b = 0.560140 + 0.410838I
−4.52678 − 8.23619I 1.62263 + 8.93292I
u = −0.445937 − 1.170140I
a = 0.116733 + 0.150369I
b = 0.560140 − 0.410838I
−4.52678 + 8.23619I 1.62263 − 8.93292I
u = −0.387590 + 0.116004I
a = 0.43654 + 2.54296I
b = −0.234632 + 0.628244I
0.97046 + 1.97408I 9.55166 − 2.43496I
u = −0.387590 − 0.116004I
a = 0.43654 − 2.54296I
b = −0.234632 − 0.628244I
0.97046 − 1.97408I 9.55166 + 2.43496I
u = 0.68994 + 1.64040I
a = −1.97628 + 0.07761I
b = −2.64003 + 0.02134I
−10.4971 + 10.3444I −5.80333 − 10.34256I
u = 0.68994 − 1.64040I
a = −1.97628 − 0.07761I
b = −2.64003 − 0.02134I
−10.4971 − 10.3444I −5.80333 + 10.34256I
28
VI. I
u
6
= h2u
6
a + 5u
6
+ · · · − a + 2, −u
6
a − u
5
a + · · · + a
2
+ 1, u
7
+ u
6
+
4u
5
+ 3u
4
+ 5u
3
+ 3u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
8
=
a
−
1
3
u
6
a −
5
6
u
6
+ ··· +
1
6
a −
1
3
a
12
=
u
u
a
9
=
1
6
u
6
a +
2
3
u
6
+ ··· +
7
6
a +
1
6
−
1
6
u
6
a −
1
6
u
6
+ ··· +
1
3
a −
1
6
a
1
=
−
1
6
u
6
a +
1
3
u
6
+ ··· −
7
6
a +
5
6
1
2
u
6
a + u
6
+ ··· −
1
2
a +
1
2
a
10
=
−u
6
a − u
5
a − 3u
4
a − 2u
3
a − 2u
2
a − au + a
−u
6
a − u
5
a − 3u
4
a − 2u
3
a − 2u
2
a − au
a
7
=
2
3
u
6
a +
1
6
u
6
+ ··· +
13
6
a −
1
3
−
1
2
u
6
a −
1
2
u
6
+ ··· + a −
1
2
a
5
=
−
1
6
u
6
a −
1
6
u
6
+ ··· +
4
3
a +
5
6
−
1
3
u
6
a +
1
6
u
6
+ ··· +
1
6
a −
4
3
a
6
=
1
6
u
6
a −
1
3
u
6
+ ··· +
7
6
a +
1
6
−
1
6
u
6
a −
1
6
u
6
+ ··· +
1
3
a −
7
6
a
2
=
−
1
2
u
6
a −
1
2
u
6
+ ··· − a +
1
2
1
3
u
6
a +
1
3
u
6
+ ··· −
2
3
a +
1
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
6
− 10u
5
− 13u
4
− 32u
3
− 22u
2
− 29u − 16
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
14
− u
13
+ ··· − 6u + 1
c
2
, c
8
u
14
+ 7u
13
+ ··· + 20u + 4
c
3
, c
9
(u
7
+ u
6
+ 4u
5
+ 3u
4
+ 5u
3
+ 3u
2
+ u + 1)
2
c
5
, c
11
(u
7
− u
6
+ 4u
5
− 3u
4
+ 5u
3
− 3u
2
+ u − 1)
2
c
6
, c
12
u
14
− 7u
13
+ ··· − 20u + 4
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
14
+ 7y
13
+ ··· − 6y + 1
c
2
, c
6
, c
8
c
12
y
14
+ 3y
13
+ ··· + 16y + 16
c
3
, c
5
, c
9
c
11
(y
7
+ 7y
6
+ 20y
5
+ 27y
4
+ 13y
3
− 5y
2
− 5y −1)
2
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.727632
a = 0.55098 + 1.42676I
b = 0.190731 − 0.051917I
−1.45874 3.88000
u = −0.727632
a = 0.55098 − 1.42676I
b = 0.190731 + 0.051917I
−1.45874 3.88000
u = 0.181669 + 1.341540I
a = 0.102984 + 0.460514I
b = 0.021966 − 0.804617I
−5.18918 + 0.24371I −8.52695 + 1.31812I
u = 0.181669 + 1.341540I
a = −1.38378 − 1.07006I
b = −2.13249 − 1.12742I
−5.18918 + 0.24371I −8.52695 + 1.31812I
u = 0.181669 − 1.341540I
a = 0.102984 − 0.460514I
b = 0.021966 + 0.804617I
−5.18918 − 0.24371I −8.52695 − 1.31812I
u = 0.181669 − 1.341540I
a = −1.38378 + 1.07006I
b = −2.13249 + 1.12742I
−5.18918 − 0.24371I −8.52695 − 1.31812I
u = 0.111545 + 0.598906I
a = −0.098390 − 0.225904I
b = 0.208665 − 1.320170I
0.76719 + 2.52853I −9.7693 − 13.5452I
u = 0.111545 + 0.598906I
a = −1.31371 + 1.24073I
b = 0.148089 + 0.421187I
0.76719 + 2.52853I −9.7693 − 13.5452I
u = 0.111545 − 0.598906I
a = −0.098390 + 0.225904I
b = 0.208665 + 1.320170I
0.76719 − 2.52853I −9.7693 + 13.5452I
u = 0.111545 − 0.598906I
a = −1.31371 − 1.24073I
b = 0.148089 − 0.421187I
0.76719 − 2.52853I −9.7693 + 13.5452I
32
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.42940 + 1.35504I
a = −1.291350 + 0.284587I
b = −2.47211 + 0.16468I
−9.65304 − 8.50275I −4.64372 + 5.74713I
u = −0.42940 + 1.35504I
a = 0.933270 − 0.968989I
b = 1.53514 − 0.86559I
−9.65304 − 8.50275I −4.64372 + 5.74713I
u = −0.42940 − 1.35504I
a = −1.291350 − 0.284587I
b = −2.47211 − 0.16468I
−9.65304 + 8.50275I −4.64372 − 5.74713I
u = −0.42940 − 1.35504I
a = 0.933270 + 0.968989I
b = 1.53514 + 0.86559I
−9.65304 + 8.50275I −4.64372 − 5.74713I
33
VII. I
u
7
= h177u
13
− 1117u
12
+ · · · + 52b − 1064, 296u
13
− 1867u
12
+ · · · +
52a − 1718, u
14
− 7u
13
+ · · · − 20u + 4i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
8
=
−5.69231u
13
+ 35.9038u
12
+ ··· − 118.846u + 33.0385
−3.40385u
13
+ 21.4808u
12
+ ··· − 73.0385u + 20.4615
a
12
=
u
u
a
9
=
−4.69231u
13
+ 29.5577u
12
+ ··· − 96.0769u + 26.6538
−2.40385u
13
+ 15.1346u
12
+ ··· − 50.2692u + 14.0769
a
1
=
1.21154u
13
− 8.11538u
12
+ ··· + 27u − 7.57692
0.480769u
13
− 3.51923u
12
+ ··· + 14.1923u − 3.38462
a
10
=
−1.13462u
13
+ 7.46154u
12
+ ··· − 25.4231u + 6.19231
−0.173077u
13
+ 1.09615u
12
+ ··· − 10.4231u + 2.61538
a
7
=
−4.75000u
13
+ 29.8846u
12
+ ··· − 99.0769u + 28.0385
−1.01923u
13
+ 6.21154u
12
+ ··· − 18.6538u + 5.53846
a
5
=
−1.67308u
13
+ 10.0769u
12
+ ··· − 25.2692u + 7.03846
−0.403846u
13
+ 2.40385u
12
+ ··· − 1.42308u + 0.153846
a
6
=
−5.11538u
13
+ 32.4038u
12
+ ··· − 105u + 29.2692
−1.59615u
13
+ 10.1731u
12
+ ··· − 33.1923u + 9.15385
a
2
=
0.846154u
13
− 5.44231u
12
+ ··· + 10.3462u − 2.73077
0.519231u
13
− 3.55769u
12
+ ··· + 10.4231u − 2.92308
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
454
13
u
13
+
2870
13
u
12
−
9845
13
u
11
+
23675
13
u
10
−
42801
13
u
9
+
62428
13
u
8
−
76369
13
u
7
+
78835
13
u
6
−
71328
13
u
5
+
55147
13
u
4
−
37555
13
u
3
+
20790
13
u
2
−
9494
13
u +
2552
13
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
14
− u
13
+ ··· − 6u + 1
c
2
, c
8
(u
7
− u
6
+ 4u
5
− 3u
4
+ 5u
3
− 3u
2
+ u − 1)
2
c
3
, c
9
u
14
− 7u
13
+ ··· − 20u + 4
c
5
, c
11
u
14
+ 7u
13
+ ··· + 20u + 4
c
6
, c
12
(u
7
+ u
6
+ 4u
5
+ 3u
4
+ 5u
3
+ 3u
2
+ u + 1)
2
35
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
14
+ 7y
13
+ ··· − 6y + 1
c
2
, c
6
, c
8
c
12
(y
7
+ 7y
6
+ 20y
5
+ 27y
4
+ 13y
3
− 5y
2
− 5y −1)
2
c
3
, c
5
, c
9
c
11
y
14
+ 3y
13
+ ··· + 16y + 16
36
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −0.059064 + 1.014840I
a = −0.80465 + 1.22915I
b = −2.13249 + 1.12742I
−5.18918 − 0.24371I −8.52695 − 1.31812I
u = −0.059064 − 1.014840I
a = −0.80465 − 1.22915I
b = −2.13249 − 1.12742I
−5.18918 + 0.24371I −8.52695 + 1.31812I
u = 0.653886 + 0.784063I
a = −0.372401 + 0.129379I
b = 0.148089 + 0.421187I
0.76719 + 2.52853I −9.7693 − 13.5452I
u = 0.653886 − 0.784063I
a = −0.372401 − 0.129379I
b = 0.148089 − 0.421187I
0.76719 − 2.52853I −9.7693 + 13.5452I
u = 0.262126 + 1.075930I
a = 0.346261 − 0.690308I
b = 0.190731 − 0.051917I
−1.45874 3.87999 + 0.I
u = 0.262126 − 1.075930I
a = 0.346261 + 0.690308I
b = 0.190731 + 0.051917I
−1.45874 3.87999 + 0.I
u = −0.398553 + 0.771164I
a = −0.078706 − 0.588337I
b = 1.53514 − 0.86559I
−9.65304 − 8.50275I −4.64372 + 5.74713I
u = −0.398553 − 0.771164I
a = −0.078706 + 0.588337I
b = 1.53514 + 0.86559I
−9.65304 + 8.50275I −4.64372 − 5.74713I
u = 0.689615 + 0.061837I
a = −0.02905 − 2.16732I
b = 0.208665 − 1.320170I
0.76719 + 2.52853I −9.7693 − 13.5452I
u = 0.689615 − 0.061837I
a = −0.02905 + 2.16732I
b = 0.208665 + 1.320170I
0.76719 − 2.52853I −9.7693 + 13.5452I
37
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.66949 + 1.54849I
a = −1.63384 − 0.07956I
b = −2.47211 − 0.16468I
−9.65304 + 8.50275I −4.64372 − 5.74713I
u = 0.66949 − 1.54849I
a = −1.63384 + 0.07956I
b = −2.47211 + 0.16468I
−9.65304 − 8.50275I −4.64372 + 5.74713I
u = 1.68250 + 0.33852I
a = 0.07238 + 1.59182I
b = 0.021966 + 0.804617I
−5.18918 − 0.24371I −8.52695 − 1.31812I
u = 1.68250 − 0.33852I
a = 0.07238 − 1.59182I
b = 0.021966 − 0.804617I
−5.18918 + 0.24371I −8.52695 + 1.31812I
38
VIII. I
u
8
= hb − a − 1, a
2
+ au − a + u, u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
u + 1
a
8
=
a
a + 1
a
12
=
u
u
a
9
=
a − u − 1
a − u
a
1
=
−au + u
−au
a
10
=
−au − a − u + 1
−au
a
7
=
−a + 2
u + 1
a
5
=
2au + a − 2u − 2
au + 1
a
6
=
au + a − 2u − 3
−u
a
2
=
a + u − 1
−u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 16u + 6
39
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
4
− u
3
− u
2
− 2u + 4
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
(u
2
+ u + 1)
2
40
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
4
− 3y
3
+ 5y
2
− 12y + 16
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
(y
2
+ y + 1)
2
41
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −0.395644 + 0.228425I
b = 0.604356 + 0.228425I
−4.93480 − 8.11953I −2.00000 + 13.85641I
u = −0.500000 + 0.866025I
a = 1.89564 − 1.09445I
b = 2.89564 − 1.09445I
−4.93480 − 8.11953I −2.00000 + 13.85641I
u = −0.500000 − 0.866025I
a = −0.395644 − 0.228425I
b = 0.604356 − 0.228425I
−4.93480 + 8.11953I −2.00000 − 13.85641I
u = −0.500000 − 0.866025I
a = 1.89564 + 1.09445I
b = 2.89564 + 1.09445I
−4.93480 + 8.11953I −2.00000 − 13.85641I
42
IX. I
u
9
= h−2u
3
− 4u
2
+ 4b − 3u + 1 , 2u
3
+ 2a + u − 3 , 2u
4
+ 2u
3
+ 3u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
8
=
−u
3
−
1
2
u +
3
2
1
2
u
3
+ u
2
+
3
4
u −
1
4
a
12
=
u
u
a
9
=
−
3
2
u
3
− u
2
−
5
4
u +
7
4
0
a
1
=
u
3
+ 2u
2
+
7
2
u +
3
2
1
2
u
3
+
3
4
u −
3
4
a
10
=
2u
3
− u − 3
−
1
2
u
3
− u
2
−
3
4
u +
1
4
a
7
=
u
3
+
1
2
u −
7
2
−u
3
− u
a
5
=
4u
3
+ 6u
2
+ 6u − 1
−u
a
6
=
7
2
u
3
+ 4u
2
+
13
4
u −
13
4
−u
a
2
=
−
1
2
u
3
+ 2u
2
+
13
4
u +
11
4
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
3
− 4u
2
− 3u −
5
2
43
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
4(4u
4
− 15u
2
− 2u + 17)
c
2
, c
5
, c
8
c
11
2(2u
4
− 2u
3
+ 3u
2
+ 1)
c
3
, c
6
, c
9
c
12
2(2u
4
+ 2u
3
+ 3u
2
+ 1)
c
4
, c
10
(u
2
− 2u + 2)
2
44
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
16(16y
4
− 120y
3
+ 361y
2
− 514y + 289)
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
4(4y
4
+ 8y
3
+ 13y
2
+ 6y + 1)
c
4
, c
10
(y
2
+ 4)
2
45
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = −0.637550 + 1.056350I
a = −0.056347 − 0.637550I
b = −0.500000 − 0.500000I
−4.93480 − 7.32772I −1.50000 + 2.00000I
u = −0.637550 − 1.056350I
a = −0.056347 + 0.637550I
b = −0.500000 + 0.500000I
−4.93480 + 7.32772I −1.50000 − 2.00000I
u = 0.137550 + 0.556347I
a = 1.55635 − 0.13755I
b = −0.500000 + 0.500000I
−4.93480 + 7.32772I −1.50000 − 2.00000I
u = 0.137550 − 0.556347I
a = 1.55635 + 0.13755I
b = −0.500000 − 0.500000I
−4.93480 − 7.32772I −1.50000 + 2.00000I
46
X.
I
u
10
= h−2u
3
+8u
2
+4b+13u+7, −2u
3
+8u
2
+4a+13u+11, 2u
4
+2u
3
+3u
2
+1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
8
=
1
2
u
3
− 2u
2
−
13
4
u −
11
4
1
2
u
3
− 2u
2
−
13
4
u −
7
4
a
12
=
u
u
a
9
=
1
2
u
3
− u
2
−
13
4
u −
11
4
1
2
u
3
− u
2
−
13
4
u −
7
4
a
1
=
5
2
u
3
+ 4u
2
+
15
4
u +
1
4
5
2
u
3
+ 4u
2
+
11
4
u +
1
4
a
10
=
−
7
2
u
3
−
7
2
u
2
−
23
4
u +
1
2
−2u
3
−
3
2
u
2
−
7
2
u +
5
4
a
7
=
9
4
u
3
+
5
2
u
2
+
31
8
u −
1
8
7
4
u
3
+
3
2
u
2
+
17
8
u −
7
8
a
5
=
−
13
4
u
3
−
11
2
u
2
−
43
8
u −
3
8
−
11
4
u
3
−
9
2
u
2
−
29
8
u +
3
8
a
6
=
1
2
u
3
+ u
2
+
7
4
u +
3
4
1
2
u
3
+ u
2
+
7
4
u +
3
4
a
2
=
3
2
u
3
+ 2u
2
+
9
4
u +
3
4
3
2
u
3
+ 2u
2
+
9
4
u −
1
4
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
3
− 4u
2
− 3u −
5
2
47
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
2
− 2u + 2)
2
c
2
, c
5
, c
8
c
11
2(2u
4
− 2u
3
+ 3u
2
+ 1)
c
3
, c
6
, c
9
c
12
2(2u
4
+ 2u
3
+ 3u
2
+ 1)
c
4
, c
10
4(4u
4
− 15u
2
− 2u + 17)
48
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
2
+ 4)
2
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
4(4y
4
+ 8y
3
+ 13y
2
+ 6y + 1)
c
4
, c
10
16(16y
4
− 120y
3
+ 361y
2
− 514y + 289)
49
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = −0.637550 + 1.056350I
a = 1.67840 − 0.68454I
b = 2.67840 − 0.68454I
−4.93480 − 7.32772I −1.50000 + 2.00000I
u = −0.637550 − 1.056350I
a = 1.67840 + 0.68454I
b = 2.67840 + 0.68454I
−4.93480 + 7.32772I −1.50000 − 2.00000I
u = 0.137550 + 0.556347I
a = −2.67840 − 2.18454I
b = −1.67840 − 2.18454I
−4.93480 + 7.32772I −1.50000 − 2.00000I
u = 0.137550 − 0.556347I
a = −2.67840 + 2.18454I
b = −1.67840 + 2.18454I
−4.93480 − 7.32772I −1.50000 + 2.00000I
50
XI. I
u
11
=
hu
11
−2u
10
+· · ·+2b−2, 5u
11
−11u
10
+· · ·+4a−16, u
12
−3u
11
+· · ·+2u
3
+4i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
8
=
−
5
4
u
11
+
11
4
u
10
+ ··· + 2u + 4
−
1
2
u
11
+ u
10
+ ··· + u + 1
a
12
=
u
u
a
9
=
−
3
4
u
11
+
9
4
u
10
+ ··· − u + 2
1
2
u
10
−
1
2
u
9
+ ··· − 2u − 1
a
1
=
1
2
u
11
− u
10
+ ··· − u − 1
−
1
2
u
7
+ u
6
−
3
2
u
5
+ u
4
−
1
2
u
3
+ u
a
10
=
−
3
4
u
11
+
5
4
u
10
+ ··· + 3u + 3
1
2
u
11
−
3
2
u
10
+ ··· + u − 1
a
7
=
1
2
u
10
−
1
2
u
9
+ ··· − 3u − 1
−
1
2
u
11
+ u
10
+ ··· +
3
2
u
3
− u
a
5
=
−
1
4
u
11
+
3
4
u
10
+ ··· + 3u + 4
1
2
u
10
− 2u
9
+ ··· + 2u + 3
a
6
=
−
1
4
u
11
+
1
4
u
10
+ ··· + u + 1
−
1
2
u
11
+ u
10
+ ··· + 3u + 3
a
2
=
−
1
2
u
6
+ u
5
−
3
2
u
4
+ u
3
−
1
2
u
2
+ 1
1
2
u
11
− u
10
+ ··· − u − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
11
+ 8u
10
− 24u
9
+ 27u
8
− 42u
7
+ 25u
6
− 14u
5
+ u
4
+ 22u
3
+ 6u
2
+ 8u + 10
51
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
(u
6
+ u
5
− 2u
4
− 3u
3
+ 2u
2
+ 3u + 1)
2
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
u
12
− 3u
11
+ 8u
10
− 13u
9
+ 18u
8
− 19u
7
+ 13u
6
− 8u
5
− 2u
4
+ 2u
3
+ 4
52
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
(y
6
− 5y
5
+ 14y
4
− 21y
3
+ 18y
2
− 5y + 1)
2
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
y
12
+ 7y
11
+ ··· − 16y
2
+ 16
53
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
11
√
−1(vol +
√
−1CS) Cusp shape
u = 0.100452 + 1.034960I
a = −0.202900 − 0.823189I
b = −0.530318 − 0.263992I
−2.48820 + 1.50089I −2.33482 − 4.37930I
u = 0.100452 − 1.034960I
a = −0.202900 + 0.823189I
b = −0.530318 + 0.263992I
−2.48820 − 1.50089I −2.33482 + 4.37930I
u = 1.131900 + 0.019003I
a = −0.04695 − 1.79866I
b = 0.247955 − 0.704157I
−5.26528 + 7.27175I −1.11360 − 6.02948I
u = 1.131900 − 0.019003I
a = −0.04695 + 1.79866I
b = 0.247955 + 0.704157I
−5.26528 − 7.27175I −1.11360 + 6.02948I
u = −0.248729 + 1.238530I
a = −1.062330 + 0.867734I
b = −2.21764 + 0.44171I
−11.98570 − 5.80683I −6.55158 + 2.46615I
u = −0.248729 − 1.238530I
a = −1.062330 − 0.867734I
b = −2.21764 − 0.44171I
−11.98570 + 5.80683I −6.55158 − 2.46615I
u = 0.313008 + 1.244470I
a = 0.018436 + 0.147658I
b = 0.247955 − 0.704157I
−5.26528 + 7.27175I −1.11360 − 6.02948I
u = 0.313008 − 1.244470I
a = 0.018436 − 0.147658I
b = 0.247955 + 0.704157I
−5.26528 − 7.27175I −1.11360 + 6.02948I
u = −0.611635 + 0.282691I
a = 0.249427 − 1.067740I
b = −0.530318 + 0.263992I
−2.48820 − 1.50089I −2.33482 + 4.37930I
u = −0.611635 − 0.282691I
a = 0.249427 + 1.067740I
b = −0.530318 − 0.263992I
−2.48820 + 1.50089I −2.33482 − 4.37930I
54
Solutions to I
u
11
√
−1(vol +
√
−1CS) Cusp shape
u = 0.81501 + 1.32491I
a = −1.45568 − 0.16073I
b = −2.21764 − 0.44171I
−11.98570 + 5.80683I −6.55158 − 2.46615I
u = 0.81501 − 1.32491I
a = −1.45568 + 0.16073I
b = −2.21764 + 0.44171I
−11.98570 − 5.80683I −6.55158 + 2.46615I
55
XII.
I
u
12
= h9.73 × 10
5
au
11
+ 1.11 × 10
6
u
11
+ · · · + 2.89 × 10
7
a − 4.84 × 10
7
, 2.10 ×
10
6
au
11
+1.94×10
6
u
11
+· · ·+4.27×10
7
a+1.70×10
7
, u
12
+4u
11
+· · ·+52u+17i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
8
=
a
−0.0499024au
11
− 0.0569073u
11
+ ··· − 1.47945a + 2.47982
a
12
=
u
u
a
9
=
0.0222156au
11
− 0.0306909u
11
+ ··· + 1.34178a − 3.88802
−0.0276868au
11
− 0.0875982u
11
+ ··· − 1.13767a − 1.40820
a
1
=
−0.0255248au
11
+ 0.180008u
11
+ ··· + 2.61958a + 3.43610
−0.0961964au
11
+ 0.157732u
11
+ ··· − 0.610904a + 3.97712
a
10
=
0.240086au
11
− 0.00795682u
11
+ ··· − 7.82112a − 5.40507
0.269684au
11
+ 0.194341u
11
+ ··· − 4.35659a + 3.23725
a
7
=
0.00536180au
11
− 0.0898213u
11
+ ··· − 5.46984a − 5.37452
−0.0396490au
11
− 0.0367192u
11
+ ··· − 3.23173a − 1.66928
a
5
=
−0.117320au
11
− 0.00298672u
11
+ ··· + 2.31111a − 0.617584
−0.257941au
11
− 0.0450108u
11
+ ··· + 1.14812a + 2.23811
a
6
=
−0.0870267au
11
+ 0.233711u
11
+ ··· − 0.177121a − 3.05750
−0.0201047au
11
− 0.0255248u
11
+ ··· + 0.848341a + 2.61958
a
2
=
−0.0359355au
11
− 0.0243270u
11
+ ··· + 3.05350a − 2.36536
−0.147896au
11
+ 0.00387902u
11
+ ··· + 1.20142a + 0.110022
(ii) Obstruction class = −1
(iii) Cusp Shapes =
3584
18491
u
11
+
23252
18491
u
10
+
176
41
u
9
+
208520
18491
u
8
+
424496
18491
u
7
+
769548
18491
u
6
+
1073920
18491
u
5
+
1399512
18491
u
4
+
1275424
18491
u
3
+
1084484
18491
u
2
+
519328
18491
u +
102714
18491
56
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
(u
12
+ 4u
11
+ ··· − 36u + 7)
2
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
(u
12
+ 4u
11
+ ··· + 52u + 17)
2
57
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
(y
12
− 24y
11
+ ··· − 652y + 49)
2
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
(y
12
+ 12y
11
+ ··· + 1036y + 289)
2
58
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
12
√
−1(vol +
√
−1CS) Cusp shape
u = −0.056683 + 0.913161I
a = −0.505160 − 0.428841I
b = −2.00428 + 1.18705I
−4.79131 −9.01951 + 0.I
u = −0.056683 + 0.913161I
a = 4.39644 − 0.12367I
b = 3.40412
−4.79131 −9.01951 + 0.I
u = −0.056683 − 0.913161I
a = −0.505160 + 0.428841I
b = −2.00428 − 1.18705I
−4.79131 −9.01951 + 0.I
u = −0.056683 − 0.913161I
a = 4.39644 + 0.12367I
b = 3.40412
−4.79131 −9.01951 + 0.I
u = −0.603528 + 0.422967I
a = −1.191060 + 0.457673I
b = −0.254482 − 1.035470I
−8.29642 + 6.59895I −2.49024 − 2.97945I
u = −0.603528 + 0.422967I
a = 0.04338 − 1.85087I
b = −0.389899 + 0.085684I
−8.29642 + 6.59895I −2.49024 − 2.97945I
u = −0.603528 − 0.422967I
a = −1.191060 − 0.457673I
b = −0.254482 + 1.035470I
−8.29642 − 6.59895I −2.49024 + 2.97945I
u = −0.603528 − 0.422967I
a = 0.04338 + 1.85087I
b = −0.389899 − 0.085684I
−8.29642 − 6.59895I −2.49024 + 2.97945I
u = 0.066299 + 1.297300I
a = 1.254580 + 0.220823I
b = 2.43003 − 0.13698I
−8.29642 + 6.59895I −2.49024 − 2.97945I
u = 0.066299 + 1.297300I
a = −0.55596 − 1.51610I
b = −0.254482 − 1.035470I
−8.29642 + 6.59895I −2.49024 − 2.97945I
59
Solutions to I
u
12
√
−1(vol +
√
−1CS) Cusp shape
u = 0.066299 − 1.297300I
a = 1.254580 − 0.220823I
b = 2.43003 + 0.13698I
−8.29642 − 6.59895I −2.49024 + 2.97945I
u = 0.066299 − 1.297300I
a = −0.55596 + 1.51610I
b = −0.254482 + 1.035470I
−8.29642 − 6.59895I −2.49024 + 2.97945I
u = −0.55760 + 1.35203I
a = −0.279872 − 0.577449I
b = −0.389899 − 0.085684I
−8.29642 − 6.59895I −2.49024 + 2.97945I
u = −0.55760 + 1.35203I
a = −1.48032 + 0.17170I
b = −2.57057 + 0.22037I
−8.29642 − 6.59895I −2.49024 + 2.97945I
u = −0.55760 − 1.35203I
a = −0.279872 + 0.577449I
b = −0.389899 + 0.085684I
−8.29642 + 6.59895I −2.49024 − 2.97945I
u = −0.55760 − 1.35203I
a = −1.48032 − 0.17170I
b = −2.57057 − 0.22037I
−8.29642 + 6.59895I −2.49024 − 2.97945I
u = 0.54211 + 1.50118I
a = −1.65517 − 0.26125I
b = −2.57057 − 0.22037I
−8.29642 + 6.59895I −2.49024 − 2.97945I
u = 0.54211 + 1.50118I
a = 1.65143 − 0.37398I
b = 2.43003 − 0.13698I
−8.29642 + 6.59895I −2.49024 − 2.97945I
u = 0.54211 − 1.50118I
a = −1.65517 + 0.26125I
b = −2.57057 + 0.22037I
−8.29642 − 6.59895I −2.49024 + 2.97945I
u = 0.54211 − 1.50118I
a = 1.65143 + 0.37398I
b = 2.43003 + 0.13698I
−8.29642 − 6.59895I −2.49024 + 2.97945I
60
Solutions to I
u
12
√
−1(vol +
√
−1CS) Cusp shape
u = −1.39060 + 1.46053I
a = 0.223311 − 0.998797I
b = 0.174283
−4.79131 −9.01951 + 0.I
u = −1.39060 + 1.46053I
a = −1.69572 − 1.51965I
b = −2.00428 − 1.18705I
−4.79131 −9.01951 + 0.I
u = −1.39060 − 1.46053I
a = 0.223311 + 0.998797I
b = 0.174283
−4.79131 −9.01951 + 0.I
u = −1.39060 − 1.46053I
a = −1.69572 + 1.51965I
b = −2.00428 + 1.18705I
−4.79131 −9.01951 + 0.I
61
XIII. I
u
13
= hu
2
+ b, u
2
+ a + 1, u
4
− u
3
+ 3u
2
− 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
8
=
−u
2
− 1
−u
2
a
12
=
u
u
a
9
=
−1
0
a
1
=
u
3
+ 2u
u
3
+ u
a
10
=
−1
u
2
a
7
=
−u
3
− 2u
−u
3
− u
a
5
=
0
−u
a
6
=
−u
−u
a
2
=
u
2
+ 1
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u
3
+ 8u
2
− 24u + 12
62
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
4
+ u
3
+ u
2
+ 1
c
2
, c
5
, c
8
c
11
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
3
, c
6
, c
9
c
12
u
4
− u
3
+ 3u
2
− 2u + 1
63
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
64
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
13
√
−1(vol +
√
−1CS) Cusp shape
u = 0.395123 + 0.506844I
a = −0.899232 − 0.400532I
b = 0.100768 − 0.400532I
0.42201 + 2.83021I 3.65348 − 9.81749I
u = 0.395123 − 0.506844I
a = −0.899232 + 0.400532I
b = 0.100768 + 0.400532I
0.42201 − 2.83021I 3.65348 + 9.81749I
u = 0.10488 + 1.55249I
a = 1.39923 − 0.32564I
b = 2.39923 − 0.32564I
−13.5815 + 6.3279I −3.65348 − 5.12960I
u = 0.10488 − 1.55249I
a = 1.39923 + 0.32564I
b = 2.39923 + 0.32564I
−13.5815 − 6.3279I −3.65348 + 5.12960I
65
XIV. I
u
14
= hb − a − u, a
2
+ 2au + a − 2, u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
u + 1
a
8
=
a
a + u
a
12
=
u
u
a
9
=
a + 1
a + u + 1
a
1
=
au + a + u
au + a + u − 1
a
10
=
−au − a − 2u − 1
−au
a
7
=
−au − u
−u
a
5
=
2au + a + 2u
au + u
a
6
=
au + a + u
u + 1
a
2
=
au
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2
66
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
(u
2
+ u − 1)
2
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
(u
2
+ u + 1)
2
67
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
(y
2
− 3y + 1)
2
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
(y
2
+ y + 1)
2
68
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
14
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 1.118030 − 0.866030I
b = 0.618034
−4.93480 −2.00000
u = −0.500000 + 0.866025I
a = −1.118030 − 0.866030I
b = −1.61803
−4.93480 −2.00000
u = −0.500000 − 0.866025I
a = 1.118030 + 0.866030I
b = 0.618034
−4.93480 −2.00000
u = −0.500000 − 0.866025I
a = −1.118030 + 0.866030I
b = −1.61803
−4.93480 −2.00000
69
XV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
16(u
2
− 2u + 2)
2
(u
2
+ u − 1)
2
(u
4
− u
3
+ ··· − 2u + 4)(u
4
+ u
3
+ u
2
+ 1)
· (4u
4
− 15u
2
− 2u + 17)(u
6
+ u
5
− 2u
4
− 3u
3
+ 2u
2
+ 3u + 1)
2
· (u
8
− 2u
7
− u
6
+ 6u
5
− u
4
− 6u
3
+ 8u
2
− 4u + 1)
· (u
10
+ 2u
9
+ u
8
− 2u
7
− 3u
6
+ 2u
4
+ 2u
3
− 3u
2
− 2u − 2)
2
· ((u
12
+ 4u
11
+ ··· − 36u + 7)
2
)(u
14
− u
13
+ ··· − 6u + 1)
2
· (4u
20
− 28u
19
+ ··· − 448u + 73)(u
30
− 2u
29
+ ··· + 22u + 1)
2
c
2
, c
5
, c
8
c
11
16(u
2
+ u + 1)
4
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(2u
4
− 2u
3
+ 3u
2
+ 1)
2
· (u
7
− u
6
+ 4u
5
− 3u
4
+ 5u
3
− 3u
2
+ u − 1)
2
· (u
8
− 2u
7
+ 5u
6
− 6u
5
+ 9u
4
− 10u
3
+ 8u
2
− 4u + 1)
· (u
12
− 3u
11
+ 8u
10
− 13u
9
+ 18u
8
− 19u
7
+ 13u
6
− 8u
5
− 2u
4
+ 2u
3
+ 4)
· ((u
12
+ 4u
11
+ ··· + 52u + 17)
2
)(u
14
+ 7u
13
+ ··· + 20u + 4)
· ((u
15
+ 2u
14
+ ··· − 2u − 2)
2
)(2u
20
+ 11u
18
+ ··· + 4u + 1)
2
· (u
30
− 8u
29
+ ··· − 148u + 43)
c
3
, c
6
, c
9
c
12
16(u
2
+ u + 1)
4
(u
4
− u
3
+ 3u
2
− 2u + 1)(2u
4
+ 2u
3
+ 3u
2
+ 1)
2
· (u
7
+ u
6
+ 4u
5
+ 3u
4
+ 5u
3
+ 3u
2
+ u + 1)
2
· (u
8
− 2u
7
+ 5u
6
− 6u
5
+ 9u
4
− 10u
3
+ 8u
2
− 4u + 1)
· (u
12
− 3u
11
+ 8u
10
− 13u
9
+ 18u
8
− 19u
7
+ 13u
6
− 8u
5
− 2u
4
+ 2u
3
+ 4)
· ((u
12
+ 4u
11
+ ··· + 52u + 17)
2
)(u
14
− 7u
13
+ ··· − 20u + 4)
· ((u
15
+ 2u
14
+ ··· − 2u − 2)
2
)(2u
20
+ 11u
18
+ ··· + 4u + 1)
2
· (u
30
− 8u
29
+ ··· − 148u + 43)
70
XVI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
256(y
2
+ 4)
2
(y
2
− 3y + 1)
2
(y
4
− 3y
3
+ 5y
2
− 12y + 16)
· (y
4
+ y
3
+ 3y
2
+ 2y + 1)(16y
4
− 120y
3
+ 361y
2
− 514y + 289)
· (y
6
− 5y
5
+ 14y
4
− 21y
3
+ 18y
2
− 5y + 1)
2
· (y
8
− 6y
7
+ 23y
6
− 42y
5
+ 43y
4
− 6y
3
+ 14y
2
+ 1)
· (y
10
− 2y
9
+ 3y
8
− 6y
7
− y
6
− 6y
5
+ 10y
4
− 4y
3
+ 9y
2
+ 8y + 4)
2
· ((y
12
− 24y
11
+ ··· − 652y + 49)
2
)(y
14
+ 7y
13
+ ··· − 6y + 1)
2
· (16y
20
− 8y
19
+ ··· + 42678y + 5329)
· (y
30
− 18y
29
+ ··· − 206y + 1)
2
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
256(y
2
+ y + 1)
4
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
· (4y
4
+ 8y
3
+ 13y
2
+ 6y + 1)
2
· (y
7
+ 7y
6
+ 20y
5
+ 27y
4
+ 13y
3
− 5y
2
− 5y −1)
2
· (y
8
+ 6y
7
+ 19y
6
+ 30y
5
+ 27y
4
+ 6y
3
+ 2y
2
+ 1)
· (y
12
+ 7y
11
+ ··· − 16y
2
+ 16)(y
12
+ 12y
11
+ ··· + 1036y + 289)
2
· (y
14
+ 3y
13
+ ··· + 16y + 16)(y
15
+ 16y
14
+ ··· − 32y −4)
2
· ((4y
20
+ 44y
19
+ ··· − 6y + 1)
2
)(y
30
+ 16y
29
+ ··· + 1144y + 1849)
71
