12a
1019
(K12a
1019
)
A knot diagram
1
Linearized knot diagam
4 7 6 9 8 11 10 1 12 3 2 5
Solving Sequence
5,9 1,4
2 8 6 12 10 7 3 11
c
4
c
1
c
8
c
5
c
12
c
9
c
7
c
2
c
11
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hb + u, a − 1, u
10
+ 5u
9
+ 12u
8
+ 15u
7
+ 9u
6
− u
5
− 3u
4
+ u
3
+ 4u
2
+ u − 1i
I
u
2
= hb + u, −1.75613 × 10
16
u
21
+ 1.11888 × 10
17
u
20
+ ··· + 2.50431 × 10
13
a + 1.70131 × 10
16
,
5u
22
− 35u
21
+ ··· − 6u + 3i
I
u
3
= h1.10406 × 10
16
u
21
− 7.03969 × 10
16
u
20
+ ··· + 2.50431 × 10
13
b − 1.05368 × 10
16
, a − 1,
5u
22
− 35u
21
+ ··· − 6u + 3i
I
u
4
= h3.63226 × 10
15
u
21
+ 8.27964 × 10
16
u
20
+ ··· + 3.35609 × 10
15
b + 3.49818 × 10
17
,
8.19885 × 10
15
u
21
+ 1.82243 × 10
17
u
20
+ ··· + 1.34244 × 10
16
a + 4.80275 × 10
17
,
3u
22
+ 72u
21
+ ··· + 1792u + 512i
I
u
5
= hb + u, a + 1, u
14
− 5u
13
+ 12u
12
− 16u
11
+ 13u
10
− 8u
9
+ 8u
8
− 9u
7
+ 6u
6
− 3u
5
+ 3u
4
− 3u
3
+ u
2
+ 1i
I
u
6
= h−u
2
+ b − 1, u
3
− u
2
+ a − 1, u
4
− u
3
+ u
2
− u + 1i
I
u
7
= hb + u, −u
3
− 2u
2
+ a − u + 1, u
4
+ 3u
3
+ 4u
2
+ 2u + 1i
I
u
8
= hu
3
+ 3u
2
+ b + 3u + 1, a + 1, u
4
+ 3u
3
+ 4u
2
+ 2u + 1i
I
u
9
= h−2.18056 × 10
72
u
53
+ 2.46832 × 10
73
u
52
+ ··· + 5.29251 × 10
67
b + 9.57025 × 10
72
,
9.57025 × 10
72
au
53
+ 6.77762 × 10
72
u
53
+ ··· − 4.18369 × 10
73
a − 3.12165 × 10
73
,
3u
54
− 36u
53
+ ··· − 72u + 9i
I
u
10
= hb + u, a − 1, u
4
+ 2u
3
+ 2u
2
+ u + 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
= h3u
5
a
3
− 3u
5
a
2
+ ··· + 3a + 3, −4u
5
a
3
+ 4u
5
a
2
+ ··· + b − 9a,
u
5
a
3
+ u
4
a
3
− u
5
a
2
− u
4
a
2
− 2u
3
a
2
− a
2
u
2
+ 2u
3
a + bau + u
2
b − 2bu + 3au + a − 2u + 1,
u
6
a
3
− u
6
a
2
+ ··· + a − u,
u
5
a
4
+ a
4
u
4
− u
5
a
3
− 2u
4
a
3
− 2a
3
u
3
+ u
4
a
2
− a
3
u
2
+ 2u
3
a
2
+ 2a
2
u
2
+ 3a
2
u − u
2
a + a
2
− 3au − a + 1i
* 10 irreducible components of dim
C
= 0, with total 214 representations.
* 1 irreducible components of dim
C
= 1
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
= hb + u, a − 1, u
10
+ 5u
9
+ · · · + u − 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
1
−u
a
4
=
1
u
2
a
2
=
u
2
+ u + 1
u
4
+ u
3
− u
a
8
=
−u
u
2
+ u
a
6
=
−u
3
− u
2
+ 1
u
4
+ 2u
3
+ u
2
a
12
=
u + 1
−u
a
10
=
−u
3
− 2u
2
− u
u
3
+ u
2
+ u
a
7
=
−u
8
− 4u
7
− 7u
6
− 6u
5
− 2u
4
− u
u
8
+ 3u
7
+ 5u
6
+ 4u
5
+ 2u
4
+ u
2
+ u
a
3
=
−u
8
− 3u
7
− 4u
6
− u
5
+ 2u
4
+ 2u
3
+ 1
u
9
+ 4u
8
+ 7u
7
+ 6u
6
+ 2u
5
+ u
2
a
11
=
u
7
+ 3u
6
+ 5u
5
+ 4u
4
+ 2u
3
+ u + 1
u
9
+ 3u
8
+ 4u
7
+ u
6
− 2u
5
− 2u
4
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6u
9
− 30u
8
− 66u
7
− 72u
6
− 33u
5
+ 6u
4
+ 6u
3
− 9u
2
− 15u
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
9
u
10
− 4u
9
+ 9u
8
− 11u
7
+ 8u
6
− 7u
5
+ 10u
4
− 13u
3
+ 3u
2
+ 6u − 1
c
2
, c
6
, c
10
u
10
+ 5u
9
+ 12u
8
+ 15u
7
+ 9u
6
− u
5
− 3u
4
+ u
3
+ 4u
2
+ u − 1
c
3
, c
7
, c
11
u
10
+ 4u
9
+ 9u
8
+ 11u
7
+ 8u
6
+ 7u
5
+ 10u
4
+ 13u
3
+ 3u
2
− 6u − 1
c
4
, c
8
, c
12
u
10
− 5u
9
+ 12u
8
− 15u
7
+ 9u
6
+ u
5
− 3u
4
− u
3
+ 4u
2
− u − 1
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
7
, c
9
, c
11
y
10
+ 2y
9
+ ··· − 42y + 1
c
2
, c
4
, c
6
c
8
, c
10
, c
12
y
10
− y
9
+ 12y
8
− 5y
7
+ 37y
6
− y
5
+ 29y
4
− 41y
3
+ 20y
2
− 9y + 1
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.479749 + 0.993559I
a = 1.00000
b = 0.479749 − 0.993559I
−7.19382 + 6.52036I −6.88308 − 3.27411I
u = −0.479749 − 0.993559I
a = 1.00000
b = 0.479749 + 0.993559I
−7.19382 − 6.52036I −6.88308 + 3.27411I
u = −0.797113
a = 1.00000
b = 0.797113
1.30949 7.15720
u = 0.548565 + 0.400517I
a = 1.00000
b = −0.548565 − 0.400517I
− 3.62072I 0. + 2.45070I
u = 0.548565 − 0.400517I
a = 1.00000
b = −0.548565 + 0.400517I
3.62072I 0. − 2.45070I
u = −1.17617 + 0.93991I
a = 1.00000
b = 1.17617 − 0.93991I
7.19382 − 6.52036I 6.88308 + 3.27411I
u = −1.17617 − 0.93991I
a = 1.00000
b = 1.17617 + 0.93991I
7.19382 + 6.52036I 6.88308 − 3.27411I
u = −1.18492 + 1.08537I
a = 1.00000
b = 1.18492 − 1.08537I
− 23.1517I 0. + 11.68475I
u = −1.18492 − 1.08537I
a = 1.00000
b = 1.18492 + 1.08537I
23.1517I 0. − 11.68475I
u = 0.381661
a = 1.00000
b = −0.381661
−1.30949 −7.15720
6
II. I
u
2
= hb + u, −1.76 × 10
16
u
21
+ 1.12 × 10
17
u
20
+ · · · + 2.50 × 10
13
a +
1.70 × 10
16
, 5u
22
− 35u
21
+ · · · − 6u + 3i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
701.241u
21
− 4467.82u
20
+ ··· + 278.914u − 679.351
−u
a
4
=
1
u
2
a
2
=
976.258u
21
− 6219.70u
20
+ ··· + 388.205u − 943.869
108.799u
21
− 692.854u
20
+ ··· + 41.8787u − 103.945
a
8
=
1700.33u
21
− 10820.3u
20
+ ··· + 771.696u − 1669.95
275.017u
21
− 1751.88u
20
+ ··· + 109.291u − 264.518
a
6
=
61.3336u
21
− 372.520u
20
+ ··· + 149.128u − 102.182
−77.3231u
21
+ 493.468u
20
+ ··· − 24.7045u + 72.4263
a
12
=
701.241u
21
− 4467.82u
20
+ ··· + 279.914u − 679.351
−u
a
10
=
1150.30u
21
− 7316.58u
20
+ ··· + 555.113u − 1140.91
275.017u
21
− 1751.88u
20
+ ··· + 109.291u − 264.518
a
7
=
202.358u
21
− 1275.68u
20
+ ··· + 198.939u − 228.787
−81.7460u
21
+ 519.761u
20
+ ··· − 28.5216u + 74.5041
a
3
=
531.498u
21
− 3324.09u
20
+ ··· + 609.330u − 637.060
19.5456u
21
− 123.605u
20
+ ··· + 22.1415u − 23.6804
a
11
=
−537.954u
21
+ 3428.49u
20
+ ··· − 168.930u + 494.299
−137.858u
21
+ 877.769u
20
+ ··· − 54.1322u + 129.505
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
18316216866445270
37564710667623
u
21
−
115678549605691945
37564710667623
u
20
+ ···+
11105532068647541
37564710667623
u −
1881652730664947
4173856740847
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
22
+ 5u
21
+ ··· + 115u + 55
c
2
3(3u
22
+ 72u
21
+ ··· + 1792u + 512)
c
3
75(75u
22
+ 1875u
21
+ ··· + 3211264u + 262144)
c
4
, c
12
5(5u
22
+ 35u
21
+ ··· + 6u + 3)
c
6
, c
10
5(5u
22
− 35u
21
+ ··· − 6u + 3)
c
7
, c
11
u
22
− 5u
21
+ ··· − 115u + 55
c
8
3(3u
22
− 72u
21
+ ··· − 1792u + 512)
c
9
75(75u
22
− 1875u
21
+ ··· − 3211264u + 262144)
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
11
y
22
+ 11y
21
+ ··· + 20875y + 3025
c
2
, c
8
9(9y
22
− 84y
21
+ ··· + 9371648y + 262144)
c
3
, c
9
5625
· (5625y
22
− 33375y
21
+ ··· − 184683593728y + 68719476736)
c
4
, c
6
, c
10
c
12
25(25y
22
+ 25y
21
+ ··· − 174y + 9)
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.424422 + 0.935543I
a = 1.44492 + 0.96232I
b = 0.424422 − 0.935543I
−3.80225 − 13.36980I −4.78895 + 11.87368I
u = −0.424422 − 0.935543I
a = 1.44492 − 0.96232I
b = 0.424422 + 0.935543I
−3.80225 + 13.36980I −4.78895 − 11.87368I
u = −0.846187 + 0.332900I
a = 1.75108 − 0.39745I
b = 0.846187 − 0.332900I
3.78801 − 0.96344I 9.72237 + 2.09748I
u = −0.846187 − 0.332900I
a = 1.75108 + 0.39745I
b = 0.846187 + 0.332900I
3.78801 + 0.96344I 9.72237 − 2.09748I
u = 0.449611 + 0.993975I
a = −0.272885 − 0.146365I
b = −0.449611 − 0.993975I
−3.78801 − 0.96344I −9.72237 + 2.09748I
u = 0.449611 − 0.993975I
a = −0.272885 + 0.146365I
b = −0.449611 + 0.993975I
−3.78801 + 0.96344I −9.72237 − 2.09748I
u = 0.634038 + 0.993177I
a = −0.819199 − 0.140629I
b = −0.634038 − 0.993177I
−5.93206 + 1.93386I −15.6328 − 1.6122I
u = 0.634038 − 0.993177I
a = −0.819199 + 0.140629I
b = −0.634038 + 0.993177I
−5.93206 − 1.93386I −15.6328 + 1.6122I
u = −0.536047 + 1.061394I
a = 0.127085 − 0.174072I
b = 0.536047 − 1.061394I
−3.40489 − 7.87661I −4.97285 + 6.45494I
u = −0.536047 − 1.061394I
a = 0.127085 + 0.174072I
b = 0.536047 + 1.061394I
−3.40489 + 7.87661I −4.97285 − 6.45494I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.629786 + 0.256221I
a = −1.13406 + 2.82964I
b = −0.629786 − 0.256221I
−0.44414 + 14.02510I 4.9360 − 14.4554I
u = 0.629786 − 0.256221I
a = −1.13406 − 2.82964I
b = −0.629786 + 0.256221I
−0.44414 − 14.02510I 4.9360 + 14.4554I
u = 1.113808 + 0.776539I
a = −1.163157 − 0.177259I
b = −1.113808 − 0.776539I
3.40489 + 7.87661I 4.97285 − 6.45494I
u = 1.113808 − 0.776539I
a = −1.163157 + 0.177259I
b = −1.113808 + 0.776539I
3.40489 − 7.87661I 4.97285 + 6.45494I
u = 0.628680 + 0.002790I
a = −1.93746 + 2.37902I
b = −0.628680 − 0.002790I
5.93206 − 1.93386I 15.6328 + 1.6122I
u = 0.628680 − 0.002790I
a = −1.93746 − 2.37902I
b = −0.628680 + 0.002790I
5.93206 + 1.93386I 15.6328 − 1.6122I
u = 1.12956 + 1.03672I
a = −1.082565 + 0.004380I
b = −1.12956 − 1.03672I
0.44414 + 14.02510I −4.9360 − 14.4554I
u = 1.12956 − 1.03672I
a = −1.082565 − 0.004380I
b = −1.12956 + 1.03672I
0.44414 − 14.02510I −4.9360 + 14.4554I
u = 1.11352 + 1.07627I
a = −0.980300 + 0.178884I
b = −1.11352 − 1.07627I
3.80225 + 13.36980I 4.78895 − 11.87368I
u = 1.11352 − 1.07627I
a = −0.980300 − 0.178884I
b = −1.11352 + 1.07627I
3.80225 − 13.36980I 4.78895 + 11.87368I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.392344 + 0.032218I
a = 6.89988 − 4.45942I
b = 0.392344 − 0.032218I
3.92307I 0. − 11.69335I
u = −0.392344 − 0.032218I
a = 6.89988 + 4.45942I
b = 0.392344 + 0.032218I
− 3.92307I 0. + 11.69335I
12
III. I
u
3
= h1.10 × 10
16
u
21
− 7.04 × 10
16
u
20
+ · · · + 2.50 × 10
13
b − 1.05 ×
10
16
, a − 1, 5u
22
− 35u
21
+ · · · − 6u + 3i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
1
−440.863u
21
+ 2811.02u
20
+ ··· − 162.138u + 420.745
a
4
=
1
u
2
a
2
=
440.863u
21
− 2811.02u
20
+ ··· + 162.138u − 419.745
−267.622u
21
+ 1707.14u
20
+ ··· − 96.6350u + 255.734
a
8
=
−u
275.017u
21
− 1751.88u
20
+ ··· + 109.291u − 264.518
a
6
=
−173.241u
21
+ 1103.89u
20
+ ··· − 65.5030u + 166.010
−77.3231u
21
+ 493.468u
20
+ ··· − 24.7045u + 72.4263
a
12
=
440.863u
21
− 2811.02u
20
+ ··· + 162.138u − 419.745
−440.863u
21
+ 2811.02u
20
+ ··· − 162.138u + 420.745
a
10
=
120.710u
21
− 767.650u
20
+ ··· + 60.5867u − 120.148
−395.728u
21
+ 2519.53u
20
+ ··· − 168.878u + 384.666
a
7
=
−39.4674u
21
+ 256.726u
20
+ ··· + 14.2498u + 25.2194
−35.2420u
21
+ 218.436u
20
+ ··· − 38.3921u + 41.1163
a
3
=
215.842u
21
− 1373.04u
20
+ ··· + 90.6322u − 204.878
106.519u
21
− 678.178u
20
+ ··· + 37.8759u − 99.8725
a
11
=
−124.174u
21
+ 787.469u
20
+ ··· − 60.6488u + 120.487
−110.111u
21
+ 704.990u
20
+ ··· − 26.5354u + 101.718
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
18316216866445270
37564710667623
u
21
−
115678549605691945
37564710667623
u
20
+ ···+
11105532068647541
37564710667623
u −
1881652730664947
4173856740847
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
75(75u
22
− 1875u
21
+ ··· − 3211264u + 262144)
c
2
, c
10
5(5u
22
− 35u
21
+ ··· − 6u + 3)
c
3
, c
11
u
22
− 5u
21
+ ··· − 115u + 55
c
4
, c
8
5(5u
22
+ 35u
21
+ ··· + 6u + 3)
c
5
, c
9
u
22
+ 5u
21
+ ··· + 115u + 55
c
6
3(3u
22
+ 72u
21
+ ··· + 1792u + 512)
c
7
75(75u
22
+ 1875u
21
+ ··· + 3211264u + 262144)
c
12
3(3u
22
− 72u
21
+ ··· − 1792u + 512)
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
5625
· (5625y
22
− 33375y
21
+ ··· − 184683593728y + 68719476736)
c
2
, c
4
, c
8
c
10
25(25y
22
+ 25y
21
+ ··· − 174y + 9)
c
3
, c
5
, c
9
c
11
y
22
+ 11y
21
+ ··· + 20875y + 3025
c
6
, c
12
9(9y
22
− 84y
21
+ ··· + 9371648y + 262144)
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.424422 + 0.935543I
a = 1.00000
b = 1.51354 − 0.94335I
−3.80225 − 13.36980I −4.78895 + 11.87368I
u = −0.424422 − 0.935543I
a = 1.00000
b = 1.51354 + 0.94335I
−3.80225 + 13.36980I −4.78895 − 11.87368I
u = −0.846187 + 0.332900I
a = 1.00000
b = 1.34943 − 0.91925I
3.78801 − 0.96344I 9.72237 + 2.09748I
u = −0.846187 − 0.332900I
a = 1.00000
b = 1.34943 + 0.91925I
3.78801 + 0.96344I 9.72237 − 2.09748I
u = 0.449611 + 0.993975I
a = 1.00000
b = −0.022791 + 0.337049I
−3.78801 − 0.96344I −9.72237 + 2.09748I
u = 0.449611 − 0.993975I
a = 1.00000
b = −0.022791 − 0.337049I
−3.78801 + 0.96344I −9.72237 − 2.09748I
u = 0.634038 + 0.993177I
a = 1.00000
b = 0.379734 + 0.902774I
−5.93206 + 1.93386I −15.6328 − 1.6122I
u = 0.634038 − 0.993177I
a = 1.00000
b = 0.379734 − 0.902774I
−5.93206 − 1.93386I −15.6328 + 1.6122I
u = −0.536047 + 1.061394I
a = 1.00000
b = −0.116635 − 0.228199I
−3.40489 − 7.87661I −4.97285 + 6.45494I
u = −0.536047 − 1.061394I
a = 1.00000
b = −0.116635 + 0.228199I
−3.40489 + 7.87661I −4.97285 − 6.45494I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.629786 + 0.256221I
a = 1.00000
b = 1.43923 − 1.49150I
−0.44414 + 14.02510I 4.9360 − 14.4554I
u = 0.629786 − 0.256221I
a = 1.00000
b = 1.43923 + 1.49150I
−0.44414 − 14.02510I 4.9360 + 14.4554I
u = 1.113808 + 0.776539I
a = 1.00000
b = 1.15789 + 1.10067I
3.40489 + 7.87661I 4.97285 − 6.45494I
u = 1.113808 − 0.776539I
a = 1.00000
b = 1.15789 − 1.10067I
3.40489 − 7.87661I 4.97285 + 6.45494I
u = 0.628680 + 0.002790I
a = 1.00000
b = 1.22468 − 1.49024I
5.93206 − 1.93386I 15.6328 + 1.6122I
u = 0.628680 − 0.002790I
a = 1.00000
b = 1.22468 + 1.49024I
5.93206 + 1.93386I 15.6328 − 1.6122I
u = 1.12956 + 1.03672I
a = 1.00000
b = 1.22736 + 1.11737I
0.44414 + 14.02510I −4.9360 − 14.4554I
u = 1.12956 − 1.03672I
a = 1.00000
b = 1.22736 − 1.11737I
0.44414 − 14.02510I −4.9360 + 14.4554I
u = 1.11352 + 1.07627I
a = 1.00000
b = 1.28411 + 0.85588I
3.80225 + 13.36980I 4.78895 − 11.87368I
u = 1.11352 − 1.07627I
a = 1.00000
b = 1.28411 − 0.85588I
3.80225 − 13.36980I 4.78895 + 11.87368I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.392344 + 0.032218I
a = 1.00000
b = 2.56345 − 1.97192I
3.92307I 0. − 11.69335I
u = −0.392344 − 0.032218I
a = 1.00000
b = 2.56345 + 1.97192I
− 3.92307I 0. + 11.69335I
18
IV. I
u
4
=
h3.63×10
15
u
21
+8.28×10
16
u
20
+· · ·+3.36×10
15
b+3.50×10
17
, 8.20×10
15
u
21
+
1.82×10
17
u
20
+· · ·+1.34×10
16
a+4.80×10
17
, 3u
22
+72u
21
+· · ·+1792u+512i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
−0.610745u
21
− 13.5756u
20
+ ··· − 133.759u − 35.7764
−1.08229u
21
− 24.6705u
20
+ ··· − 329.042u − 104.234
a
4
=
1
u
2
a
2
=
−0.832932u
21
− 19.6028u
20
+ ··· − 346.972u − 116.254
1.37731u
21
+ 29.6426u
20
+ ··· + 123.865u + 14.3337
a
8
=
0.320221u
21
+ 7.51486u
20
+ ··· + 113.953u + 45.4949
0.170429u
21
+ 4.56439u
20
+ ··· + 146.784u + 54.6510
a
6
=
−0.661396u
21
− 14.5522u
20
+ ··· − 140.067u − 42.3997
−0.847192u
21
− 20.2905u
20
+ ··· − 398.826u − 141.965
a
12
=
0.471546u
21
+ 11.0949u
20
+ ··· + 195.283u + 68.4574
−1.08229u
21
− 24.6705u
20
+ ··· − 329.042u − 104.234
a
10
=
−0.494738u
21
− 11.1459u
20
+ ··· − 130.462u − 34.7206
0.644530u
21
+ 14.0964u
20
+ ··· + 99.6319u + 25.5645
a
7
=
−0.846816u
21
− 18.4961u
20
+ ··· − 64.3540u − 11.3598
−0.103089u
21
− 4.25329u
20
+ ··· − 328.016u − 120.337
a
3
=
0.0288036u
21
+ 0.643679u
20
+ ··· − 41.9611u − 8.87420
−0.100826u
21
− 3.30811u
20
+ ··· − 158.801u − 61.2026
a
11
=
−1.01615u
21
− 24.2331u
20
+ ··· − 490.561u − 163.035
1.98464u
21
+ 42.4414u
20
+ ··· + 97.8266u − 16.0462
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
57173920307444841
16780442909704000
u
21
−
25170067340752893
335608858194080
u
20
+···−
160655803191745028
262194420464125
u−
48126678289140558
262194420464125
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
22
+ 5u
21
+ ··· + 115u + 55
c
2
, c
6
5(5u
22
− 35u
21
+ ··· − 6u + 3)
c
3
, c
7
u
22
− 5u
21
+ ··· − 115u + 55
c
4
3(3u
22
− 72u
21
+ ··· − 1792u + 512)
c
5
75(75u
22
− 1875u
21
+ ··· − 3211264u + 262144)
c
8
, c
12
5(5u
22
+ 35u
21
+ ··· + 6u + 3)
c
10
3(3u
22
+ 72u
21
+ ··· + 1792u + 512)
c
11
75(75u
22
+ 1875u
21
+ ··· + 3211264u + 262144)
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
c
9
y
22
+ 11y
21
+ ··· + 20875y + 3025
c
2
, c
6
, c
8
c
12
25(25y
22
+ 25y
21
+ ··· − 174y + 9)
c
4
, c
10
9(9y
22
− 84y
21
+ ··· + 9371648y + 262144)
c
5
, c
11
5625
· (5625y
22
− 33375y
21
+ ··· − 184683593728y + 68719476736)
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.379734 + 0.902774I
a = −1.185761 − 0.203556I
b = −0.634038 + 0.993177I
−5.93206 − 1.93386I −15.6328 + 1.6122I
u = −0.379734 − 0.902774I
a = −1.185761 + 0.203556I
b = −0.634038 − 0.993177I
−5.93206 + 1.93386I −15.6328 − 1.6122I
u = −1.28411 + 0.85588I
a = −0.987222 + 0.180147I
b = −1.11352 + 1.07627I
3.80225 − 13.36980I 0. + 11.87368I
u = −1.28411 − 0.85588I
a = −0.987222 − 0.180147I
b = −1.11352 − 1.07627I
3.80225 + 13.36980I 0. − 11.87368I
u = −1.15789 + 1.10067I
a = −0.840216 − 0.128044I
b = −1.113808 + 0.776539I
3.40489 − 7.87661I 0
u = −1.15789 − 1.10067I
a = −0.840216 + 0.128044I
b = −1.113808 − 0.776539I
3.40489 + 7.87661I 0
u = −1.34943 + 0.91925I
a = 0.543096 + 0.123269I
b = 0.846187 − 0.332900I
3.78801 − 0.96344I 0
u = −1.34943 − 0.91925I
a = 0.543096 − 0.123269I
b = 0.846187 + 0.332900I
3.78801 + 0.96344I 0
u = −1.22736 + 1.11737I
a = −0.923717 + 0.003737I
b = −1.12956 + 1.03672I
0.44414 − 14.02510I 0
u = −1.22736 − 1.11737I
a = −0.923717 − 0.003737I
b = −1.12956 − 1.03672I
0.44414 + 14.02510I 0
22
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.022791 + 0.337049I
a = −2.84584 − 1.52640I
b = −0.449611 + 0.993975I
−3.78801 + 0.96344I −9.72237 − 2.09748I
u = 0.022791 − 0.337049I
a = −2.84584 + 1.52640I
b = −0.449611 − 0.993975I
−3.78801 − 0.96344I −9.72237 + 2.09748I
u = 0.116635 + 0.228199I
a = 2.73586 + 3.74737I
b = 0.536047 − 1.061394I
−3.40489 − 7.87661I −4.97285 + 6.45494I
u = 0.116635 − 0.228199I
a = 2.73586 − 3.74737I
b = 0.536047 + 1.061394I
−3.40489 + 7.87661I −4.97285 − 6.45494I
u = −1.51354 + 0.94335I
a = 0.479427 − 0.319300I
b = 0.424422 − 0.935543I
−3.80225 − 13.36980I 0
u = −1.51354 − 0.94335I
a = 0.479427 + 0.319300I
b = 0.424422 + 0.935543I
−3.80225 + 13.36980I 0
u = −1.22468 + 1.49024I
a = −0.205817 − 0.252725I
b = −0.628680 − 0.002790I
5.93206 − 1.93386I 0
u = −1.22468 − 1.49024I
a = −0.205817 + 0.252725I
b = −0.628680 + 0.002790I
5.93206 + 1.93386I 0
u = −1.43923 + 1.49150I
a = −0.122034 − 0.304493I
b = −0.629786 − 0.256221I
−0.44414 + 14.02510I 0
u = −1.43923 − 1.49150I
a = −0.122034 + 0.304493I
b = −0.629786 + 0.256221I
−0.44414 − 14.02510I 0
23
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −2.56345 + 1.97192I
a = 0.1022284 + 0.0660707I
b = 0.392344 − 0.032218I
3.92307I 0
u = −2.56345 − 1.97192I
a = 0.1022284 − 0.0660707I
b = 0.392344 + 0.032218I
− 3.92307I 0
24
V. I
u
5
= hb + u, a + 1, u
14
− 5u
13
+ · · · + u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
−1
−u
a
4
=
1
u
2
a
2
=
−u
2
+ u − 1
−u
4
+ u
3
− u
a
8
=
−u
−u
2
+ u
a
6
=
u
3
− u
2
+ 1
u
4
− 2u
3
+ u
2
a
12
=
u − 1
−u
a
10
=
−u
3
+ 2u
2
− u
u
3
− u
2
+ u
a
7
=
u
8
− 4u
7
+ 7u
6
− 6u
5
+ 2u
4
− u
−u
8
+ 3u
7
− 5u
6
+ 4u
5
− 2u
4
− u
2
+ u
a
3
=
−u
8
+ 3u
7
− 4u
6
+ u
5
+ 2u
4
− 2u
3
+ 1
−u
9
+ 4u
8
− 7u
7
+ 6u
6
− 2u
5
+ u
2
a
11
=
u
7
− 3u
6
+ 5u
5
− 4u
4
+ 2u
3
+ u − 1
u
9
− 3u
8
+ 4u
7
− u
6
− 2u
5
+ 2u
4
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 3u
13
−21u
12
+60u
11
−93u
10
+75u
9
−27u
8
+9u
7
−27u
6
+21u
5
+3u
4
−3u
3
−9u
2
+3u+6
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
9
u
14
− 4u
13
+ ··· − 2u + 1
c
2
, c
6
, c
10
u
14
+ 5u
13
+ ··· + u
2
+ 1
c
3
, c
7
, c
11
u
14
+ 4u
13
+ ··· + 2u + 1
c
4
, c
8
, c
12
u
14
− 5u
13
+ ··· + u
2
+ 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
7
, c
9
, c
11
y
14
+ 4y
13
+ ··· + 24y + 1
c
2
, c
4
, c
6
c
8
, c
10
, c
12
y
14
− y
13
+ ··· + 2y + 1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.582376 + 0.920079I
a = −1.00000
b = −0.582376 − 0.920079I
−4.87762 + 2.24155I −5.71062 − 4.08315I
u = 0.582376 − 0.920079I
a = −1.00000
b = −0.582376 + 0.920079I
−4.87762 − 2.24155I −5.71062 + 4.08315I
u = 1.080860 + 0.257141I
a = −1.00000
b = −1.080860 − 0.257141I
1.97436 + 7.13139I 5.73836 − 7.19904I
u = 1.080860 − 0.257141I
a = −1.00000
b = −1.080860 + 0.257141I
1.97436 − 7.13139I 5.73836 + 7.19904I
u = −0.631419 + 0.425056I
a = −1.00000
b = 0.631419 − 0.425056I
−1.19637 + 13.10040I −1.00584 − 7.21157I
u = −0.631419 − 0.425056I
a = −1.00000
b = 0.631419 + 0.425056I
−1.19637 − 13.10040I −1.00584 + 7.21157I
u = −0.220218 + 0.697336I
a = −1.00000
b = 0.220218 − 0.697336I
− 4.24748I 0. + 7.94314I
u = −0.220218 − 0.697336I
a = −1.00000
b = 0.220218 + 0.697336I
4.24748I 0. − 7.94314I
u = −0.427969 + 0.558421I
a = −1.00000
b = 0.427969 − 0.558421I
4.87762 − 2.24155I 5.71062 + 4.08315I
u = −0.427969 − 0.558421I
a = −1.00000
b = 0.427969 + 0.558421I
4.87762 + 2.24155I 5.71062 − 4.08315I
28
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.958798 + 0.953720I
a = −1.00000
b = −0.958798 − 0.953720I
−1.97436 + 7.13139I −5.73836 − 7.19904I
u = 0.958798 − 0.953720I
a = −1.00000
b = −0.958798 + 0.953720I
−1.97436 − 7.13139I −5.73836 + 7.19904I
u = 1.15757 + 1.04690I
a = −1.00000
b = −1.15757 − 1.04690I
1.19637 + 13.10040I 1.00584 − 7.21157I
u = 1.15757 − 1.04690I
a = −1.00000
b = −1.15757 + 1.04690I
1.19637 − 13.10040I 1.00584 + 7.21157I
29
VI. I
u
6
= h−u
2
+ b − 1, u
3
− u
2
+ a − 1, u
4
− u
3
+ u
2
− u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
−u
3
+ u
2
+ 1
u
2
+ 1
a
4
=
1
u
2
a
2
=
u
u
2
− u + 1
a
8
=
−u
2
− u − 1
−u
3
− u
2
a
6
=
4u
3
− u
2
+ 2u − 2
u
3
− u
2
− 3
a
12
=
−u
3
u
2
+ 1
a
10
=
u
2
u
3
− u
2
+ u − 1
a
7
=
u
3
− u
2
− u − 1
−u
3
− u
2
− 1
a
3
=
3u
3
− 2u
2
+ 2u − 3
−2u − 1
a
11
=
−3u
3
+ u
2
− u + 1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −9u
3
− 7u
2
− 2u + 1
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
10
u
4
+ u
3
+ u
2
+ u + 1
c
2
, c
6
u
4
− 3u
3
+ 4u
2
− 2u + 1
c
3
, c
4
, c
7
u
4
− u
3
+ u
2
− u + 1
c
5
, c
11
u
4
+ 5u
2
+ 5
c
8
, c
12
u
4
+ 3u
3
+ 4u
2
+ 2u + 1
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
, c
9
, c
10
y
4
+ y
3
+ y
2
+ y + 1
c
2
, c
6
, c
8
c
12
y
4
− y
3
+ 6y
2
+ 4y + 1
c
5
, c
11
(y
2
+ 5y + 5)
2
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.309017 + 0.951057I
a = −0.618034
b = 0.190983 − 0.587785I
− 4.25078I 0. + 7.50245I
u = −0.309017 − 0.951057I
a = −0.618034
b = 0.190983 + 0.587785I
4.25078I 0. − 7.50245I
u = 0.809017 + 0.587785I
a = 1.61803
b = 1.30902 + 0.95106I
9.97355I 0. − 16.3925I
u = 0.809017 − 0.587785I
a = 1.61803
b = 1.30902 − 0.95106I
− 9.97355I 0. + 16.3925I
33
VII. I
u
7
= hb + u, −u
3
− 2u
2
+ a − u + 1, u
4
+ 3u
3
+ 4u
2
+ 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
u
3
+ 2u
2
+ u − 1
−u
a
4
=
1
u
2
a
2
=
u
3
+ 3u
2
+ 3u
−u
3
− 3u
2
− 3u − 1
a
8
=
−u
3
− 3u
2
− 4u − 1
u
2
+ 2u + 1
a
6
=
−u
3
− 2u
2
− u + 2
u
3
+ 2u
2
+ 2u
a
12
=
u
3
+ 2u
2
+ 2u − 1
−u
a
10
=
−2u
3
− 5u
2
− 6u − 3
u
3
+ u
2
+ 2u + 1
a
7
=
−3u
3
− 7u
2
− 6u
2u
3
+ 4u
2
+ 4u + 1
a
3
=
2u
3
+ 6u
2
+ 8u + 4
−u
3
− 2u
2
− 3u − 2
a
11
=
−u
2
− 2u − 3
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7u
3
+ 12u
2
+ 19u + 6
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
u
4
+ u
3
+ u
2
+ u + 1
c
3
, c
9
u
4
+ 5u
2
+ 5
c
4
, c
12
u
4
+ 3u
3
+ 4u
2
+ 2u + 1
c
6
, c
10
u
4
− 3u
3
+ 4u
2
− 2u + 1
c
7
, c
8
, c
11
u
4
− u
3
+ u
2
− u + 1
35
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
7
, c
8
, c
11
y
4
+ y
3
+ y
2
+ y + 1
c
3
, c
9
(y
2
+ 5y + 5)
2
c
4
, c
6
, c
10
c
12
y
4
− y
3
+ 6y
2
+ 4y + 1
36
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −0.190983 + 0.587785I
a = −1.61803
b = 0.190983 − 0.587785I
− 4.25078I 0. + 7.50245I
u = −0.190983 − 0.587785I
a = −1.61803
b = 0.190983 + 0.587785I
4.25078I 0. − 7.50245I
u = −1.30902 + 0.95106I
a = 0.618034
b = 1.30902 − 0.95106I
− 9.97355I 0. + 16.3925I
u = −1.30902 − 0.95106I
a = 0.618034
b = 1.30902 + 0.95106I
9.97355I 0. − 16.3925I
37
VIII. I
u
8
= hu
3
+ 3u
2
+ b + 3u + 1, a + 1, u
4
+ 3u
3
+ 4u
2
+ 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
−1
−u
3
− 3u
2
− 3u − 1
a
4
=
1
u
2
a
2
=
u
3
+ 2u
2
+ 3u
u
3
− 2u
a
8
=
−u
u
2
+ 2u + 1
a
6
=
−u
3
− 2u
2
− u + 1
u
3
+ 2u
2
+ 2u
a
12
=
u
3
+ 3u
2
+ 3u
−u
3
− 3u
2
− 3u − 1
a
10
=
−u
2
− 2u − 2
u + 1
a
7
=
−2u
3
− 5u
2
− 6u − 1
2u
2
+ 4u + 1
a
3
=
u
3
+ 3u
2
+ 4u + 2
−2u − 1
a
11
=
u
3
+ u
2
− 2
u
3
+ 2u
2
+ u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7u
3
+ 12u
2
+ 19u + 6
38
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
4
+ 5u
2
+ 5
c
2
, c
10
u
4
− 3u
3
+ 4u
2
− 2u + 1
c
3
, c
11
, c
12
u
4
− u
3
+ u
2
− u + 1
c
4
, c
8
u
4
+ 3u
3
+ 4u
2
+ 2u + 1
c
5
, c
6
, c
9
u
4
+ u
3
+ u
2
+ u + 1
39
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
2
+ 5y + 5)
2
c
2
, c
4
, c
8
c
10
y
4
− y
3
+ 6y
2
+ 4y + 1
c
3
, c
5
, c
6
c
9
, c
11
, c
12
y
4
+ y
3
+ y
2
+ y + 1
40
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = −0.190983 + 0.587785I
a = −1.00000
b = 0.309017 − 0.951057I
− 4.25078I 0. + 7.50245I
u = −0.190983 − 0.587785I
a = −1.00000
b = 0.309017 + 0.951057I
4.25078I 0. − 7.50245I
u = −1.30902 + 0.95106I
a = −1.00000
b = −0.809017 + 0.587785I
− 9.97355I 0. + 16.3925I
u = −1.30902 − 0.95106I
a = −1.00000
b = −0.809017 − 0.587785I
9.97355I 0. − 16.3925I
41
IX. I
u
9
= h−2.18 × 10
72
u
53
+ 2.47 × 10
73
u
52
+ · · · + 5.29 × 10
67
b + 9.57 ×
10
72
, 9.57 × 10
72
au
53
+ 6.78 × 10
72
u
53
+ · · · − 4.18 × 10
73
a − 3.12 ×
10
73
, 3u
54
− 36u
53
+ · · · − 72u + 9i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
a
41200.9u
53
− 466379.u
52
+ ··· + 1.18311 × 10
6
u − 180826.
a
4
=
1
u
2
a
2
=
−41200.9u
53
+ 466379.u
52
+ ··· + a + 180826.
22230.5u
53
− 251496.u
52
+ ··· + 633953.u − 96730.9
a
8
=
41200.9au
53
+ 27950.4u
53
+ ··· − 180826.a − 128061.
18393.7u
53
− 208573.u
52
+ ··· + 542749.u − 83851.1
a
6
=
−30139.1au
53
− 57012.6u
53
+ ··· + 132325.a + 252463.
−26414.5u
53
+ 299009.u
52
+ ··· − 758244.u + 115857.
a
12
=
−41200.9u
53
+ 466379.u
52
+ ··· + a + 180826.
41200.9u
53
− 466379.u
52
+ ··· + 1.18311 × 10
6
u − 180826.
a
10
=
22230.5au
53
+ 22500.6u
53
+ ··· − 96730.9a − 99384.4
18970.5au
53
− 12943.9u
53
+ ··· − 84095.3a + 55174.9
a
7
=
6087.10au
53
+ 3655.90u
53
+ ··· − 27139.9a − 17096.3
5841.57au
53
− 4585.74u
53
+ ··· − 26764.6a + 19417.5
a
3
=
−52.1287au
53
− 32353.2u
53
+ ··· + 1864.50a + 141799.
−3095.10au
53
+ 16497.3u
53
+ ··· + 14696.6a − 70803.7
a
11
=
206.422au
53
+ 32288.3u
53
+ ··· − 2714.92a − 146255.
−41.2686au
53
+ 620.517u
53
+ ··· − 1017.84a − 1637.48
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −231987.u
53
+ 2.62465 × 10
6
u
52
+ ··· − 6.62939 × 10
6
u + 1.01301 × 10
6
42
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
9
c
11
(3u
54
+ 42u
53
+ ··· + 110u + 11)
2
c
2
, c
6
, c
8
c
12
(3u
54
− 36u
53
+ ··· − 72u + 9)
2
c
3
, c
7
(3u
54
− 42u
53
+ ··· − 110u + 11)
2
c
4
, c
10
(3u
54
+ 36u
53
+ ··· + 72u + 9)
2
43
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
7
, c
9
, c
11
(9y
54
+ 126y
53
+ ··· + 3762y + 121)
2
c
2
, c
4
, c
6
c
8
, c
10
, c
12
(9y
54
− 162y
53
+ ··· − 2754y + 81)
2
44
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = 0.539584 + 0.861312I
a = −1.079029 − 0.089755I
b = −1.26647 − 0.91537I
−3.86284 + 5.00342I 0
u = 0.539584 + 0.861312I
a = 1.42476 − 0.57783I
b = 0.504919 + 0.977810I
−3.86284 + 5.00342I 0
u = 0.539584 − 0.861312I
a = −1.079029 + 0.089755I
b = −1.26647 + 0.91537I
−3.86284 − 5.00342I 0
u = 0.539584 − 0.861312I
a = 1.42476 + 0.57783I
b = 0.504919 − 0.977810I
−3.86284 − 5.00342I 0
u = −0.823135 + 0.507661I
a = 0.520149 + 0.283468I
b = 1.56112 − 0.21438I
0.428605 + 0.663668I 0
u = −0.823135 + 0.507661I
a = 1.49031 + 0.65869I
b = 0.572058 − 0.030727I
0.428605 + 0.663668I 0
u = −0.823135 − 0.507661I
a = 0.520149 − 0.283468I
b = 1.56112 + 0.21438I
0.428605 − 0.663668I 0
u = −0.823135 − 0.507661I
a = 1.49031 − 0.65869I
b = 0.572058 + 0.030727I
0.428605 − 0.663668I 0
u = 0.810036 + 0.694455I
a = 0.248006 − 0.817597I
b = 0.424298 + 0.518741I
−0.92545 + 3.91157I 0
u = 0.810036 + 0.694455I
a = −0.618344 − 0.110278I
b = −0.768678 + 0.490054I
−0.92545 + 3.91157I 0
45
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = 0.810036 − 0.694455I
a = 0.248006 + 0.817597I
b = 0.424298 − 0.518741I
−0.92545 − 3.91157I 0
u = 0.810036 − 0.694455I
a = −0.618344 + 0.110278I
b = −0.768678 − 0.490054I
−0.92545 − 3.91157I 0
u = −0.867525 + 0.293489I
a = −0.696975 − 0.231197I
b = −1.24038 − 1.08864I
3.86284 − 5.00342I 0
u = −0.867525 + 0.293489I
a = −0.90202 − 1.56004I
b = −0.672497 + 0.003985I
3.86284 − 5.00342I 0
u = −0.867525 − 0.293489I
a = −0.696975 + 0.231197I
b = −1.24038 + 1.08864I
3.86284 + 5.00342I 0
u = −0.867525 − 0.293489I
a = −0.90202 + 1.56004I
b = −0.672497 − 0.003985I
3.86284 + 5.00342I 0
u = 0.768678 + 0.490054I
a = 0.339747 − 1.120039I
b = 0.424298 − 0.518741I
−0.92545 − 3.91157I 0
u = 0.768678 + 0.490054I
a = −0.086565 + 0.730036I
b = −0.810036 + 0.694455I
−0.92545 − 3.91157I 0
u = 0.768678 − 0.490054I
a = 0.339747 + 1.120039I
b = 0.424298 + 0.518741I
−0.92545 + 3.91157I 0
u = 0.768678 − 0.490054I
a = −0.086565 − 0.730036I
b = −0.810036 − 0.694455I
−0.92545 + 3.91157I 0
46
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = −0.504919 + 0.977810I
a = −0.920391 − 0.076560I
b = −1.26647 + 0.91537I
−3.86284 − 5.00342I 0
u = −0.504919 + 0.977810I
a = −1.26709 − 0.64091I
b = −0.539584 + 0.861312I
−3.86284 − 5.00342I 0
u = −0.504919 − 0.977810I
a = −0.920391 + 0.076560I
b = −1.26647 − 0.91537I
−3.86284 + 5.00342I 0
u = −0.504919 − 0.977810I
a = −1.26709 + 0.64091I
b = −0.539584 − 0.861312I
−3.86284 + 5.00342I 0
u = 0.854551 + 0.280570I
a = −0.570820 − 0.215971I
b = −1.49575 − 0.85577I
−0.428605 + 0.663668I 0
u = 0.854551 + 0.280570I
a = 1.87681 + 0.38522I
b = 0.427200 + 0.344713I
−0.428605 + 0.663668I 0
u = 0.854551 − 0.280570I
a = −0.570820 + 0.215971I
b = −1.49575 + 0.85577I
−0.428605 − 0.663668I 0
u = 0.854551 − 0.280570I
a = 1.87681 − 0.38522I
b = 0.427200 − 0.344713I
−0.428605 − 0.663668I 0
u = 0.919013 + 0.715336I
a = −1.279558 − 0.156026I
b = −1.24334 − 1.06666I
−0.73009 + 8.94435I 0
u = 0.919013 + 0.715336I
a = 1.405056 + 0.066994I
b = 1.06432 + 1.05870I
−0.73009 + 8.94435I 0
47
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = 0.919013 − 0.715336I
a = −1.279558 + 0.156026I
b = −1.24334 + 1.06666I
−0.73009 − 8.94435I 0
u = 0.919013 − 0.715336I
a = 1.405056 − 0.066994I
b = 1.06432 − 1.05870I
−0.73009 − 8.94435I 0
u = 0.678933 + 0.310643I
a = −1.70402 + 0.37941I
b = −1.15297 − 1.03584I
0.73009 + 8.94435I 0
u = 0.678933 + 0.310643I
a = 1.98147 + 0.61908I
b = 1.274774 + 0.271751I
0.73009 + 8.94435I 0
u = 0.678933 − 0.310643I
a = −1.70402 − 0.37941I
b = −1.15297 + 1.03584I
0.73009 − 8.94435I 0
u = 0.678933 − 0.310643I
a = 1.98147 − 0.61908I
b = 1.274774 − 0.271751I
0.73009 − 8.94435I 0
u = 0.677493 + 0.258191I
a = −0.851798 − 0.189255I
b = −1.22830 + 1.32821I
5.59970I 0
u = 0.677493 + 0.258191I
a = 0.93070 − 2.31517I
b = 0.528224 + 0.348146I
5.59970I 0
u = 0.677493 − 0.258191I
a = −0.851798 + 0.189255I
b = −1.22830 − 1.32821I
− 5.59970I 0
u = 0.677493 − 0.258191I
a = 0.93070 + 2.31517I
b = 0.528224 − 0.348146I
− 5.59970I 0
48
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = −1.274774 + 0.271751I
a = −1.030830 + 0.592823I
b = −0.678933 + 0.310643I
0.73009 − 8.94435I 0
u = −1.274774 + 0.271751I
a = −0.559129 + 0.124492I
b = −1.15297 + 1.03584I
0.73009 − 8.94435I 0
u = −1.274774 − 0.271751I
a = −1.030830 − 0.592823I
b = −0.678933 − 0.310643I
0.73009 + 8.94435I 0
u = −1.274774 − 0.271751I
a = −0.559129 − 0.124492I
b = −1.15297 − 1.03584I
0.73009 + 8.94435I 0
u = 0.672497 + 0.003985I
a = −1.292546 − 0.428757I
b = −1.24038 + 1.08864I
3.86284 + 5.00342I 8.94097 − 8.21473I
u = 0.672497 + 0.003985I
a = 1.83478 − 1.62968I
b = 0.867525 + 0.293489I
3.86284 + 5.00342I 8.94097 − 8.21473I
u = 0.672497 − 0.003985I
a = −1.292546 + 0.428757I
b = −1.24038 − 1.08864I
3.86284 − 5.00342I 8.94097 + 8.21473I
u = 0.672497 − 0.003985I
a = 1.83478 + 1.62968I
b = 0.867525 − 0.293489I
3.86284 − 5.00342I 8.94097 + 8.21473I
u = −0.424298 + 0.518741I
a = −0.160173 − 1.350803I
b = −0.810036 + 0.694455I
−0.92545 − 3.91157I 0
u = −0.424298 + 0.518741I
a = −1.56737 − 0.27953I
b = −0.768678 − 0.490054I
−0.92545 − 3.91157I 0
49
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = −0.424298 − 0.518741I
a = −0.160173 + 1.350803I
b = −0.810036 − 0.694455I
−0.92545 + 3.91157I 0
u = −0.424298 − 0.518741I
a = −1.56737 + 0.27953I
b = −0.768678 + 0.490054I
−0.92545 + 3.91157I 0
u = −0.528224 + 0.348146I
a = −1.118759 − 0.248569I
b = −1.22830 − 1.32821I
− 5.59970I 0. + 19.2060I
u = −0.528224 + 0.348146I
a = −0.46575 − 2.82146I
b = −0.677493 + 0.258191I
− 5.59970I 0. + 19.2060I
u = −0.528224 − 0.348146I
a = −1.118759 + 0.248569I
b = −1.22830 + 1.32821I
5.59970I 0. − 19.2060I
u = −0.528224 − 0.348146I
a = −0.46575 + 2.82146I
b = −0.677493 − 0.258191I
5.59970I 0. − 19.2060I
u = 0.604104 + 0.098652I
a = 0.793542 − 0.523402I
b = 0.63555 − 1.44341I
0.92545 − 3.91157I 9.79615 + 4.67347I
u = 0.604104 + 0.098652I
a = −0.64467 + 2.49461I
b = −0.531016 + 0.237905I
0.92545 − 3.91157I 9.79615 + 4.67347I
u = 0.604104 − 0.098652I
a = 0.793542 + 0.523402I
b = 0.63555 + 1.44341I
0.92545 + 3.91157I 9.79615 − 4.67347I
u = 0.604104 − 0.098652I
a = −0.64467 − 2.49461I
b = −0.531016 − 0.237905I
0.92545 + 3.91157I 9.79615 − 4.67347I
50
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = 0.531016 + 0.237905I
a = 0.878144 − 0.579203I
b = 0.63555 + 1.44341I
0.92545 + 3.91157I 9.79615 − 4.67347I
u = 0.531016 + 0.237905I
a = −2.01100 − 1.81723I
b = −0.604104 + 0.098652I
0.92545 + 3.91157I 9.79615 − 4.67347I
u = 0.531016 − 0.237905I
a = 0.878144 + 0.579203I
b = 0.63555 − 1.44341I
0.92545 − 3.91157I 9.79615 + 4.67347I
u = 0.531016 − 0.237905I
a = −2.01100 + 1.81723I
b = −0.604104 − 0.098652I
0.92545 − 3.91157I 9.79615 + 4.67347I
u = −0.572058 + 0.030727I
a = 1.48229 − 0.80781I
b = 1.56112 − 0.21438I
0.428605 + 0.663668I 3.84366 − 7.01212I
u = −0.572058 + 0.030727I
a = 2.74117 − 0.22751I
b = 0.823135 − 0.507661I
0.428605 + 0.663668I 3.84366 − 7.01212I
u = −0.572058 − 0.030727I
a = 1.48229 + 0.80781I
b = 1.56112 + 0.21438I
0.428605 − 0.663668I 3.84366 + 7.01212I
u = −0.572058 − 0.030727I
a = 2.74117 + 0.22751I
b = 0.823135 + 0.507661I
0.428605 − 0.663668I 3.84366 + 7.01212I
u = −0.427200 + 0.344713I
a = −1.53249 − 0.57982I
b = −1.49575 + 0.85577I
−0.428605 − 0.663668I −3.84366 + 7.01212I
u = −0.427200 + 0.344713I
a = −3.09955 − 0.49787I
b = −0.854551 + 0.280570I
−0.428605 − 0.663668I −3.84366 + 7.01212I
51
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = −0.427200 − 0.344713I
a = −1.53249 + 0.57982I
b = −1.49575 − 0.85577I
−0.428605 + 0.663668I −3.84366 − 7.01212I
u = −0.427200 − 0.344713I
a = −3.09955 + 0.49787I
b = −0.854551 − 0.280570I
−0.428605 + 0.663668I −3.84366 − 7.01212I
u = −1.06432 + 1.05870I
a = −1.088282 − 0.080345I
b = −0.919013 + 0.715336I
−0.73009 − 8.94435I 0
u = −1.06432 + 1.05870I
a = −0.770070 − 0.093900I
b = −1.24334 + 1.06666I
−0.73009 − 8.94435I 0
u = −1.06432 − 1.05870I
a = −1.088282 + 0.080345I
b = −0.919013 − 0.715336I
−0.73009 + 8.94435I 0
u = −1.06432 − 1.05870I
a = −0.770070 + 0.093900I
b = −1.24334 − 1.06666I
−0.73009 + 8.94435I 0
u = 1.15297 + 1.03584I
a = −0.728992 + 0.419238I
b = −0.678933 − 0.310643I
0.73009 + 8.94435I 0
u = 1.15297 + 1.03584I
a = 0.459792 − 0.143655I
b = 1.274774 + 0.271751I
0.73009 + 8.94435I 0
u = 1.15297 − 1.03584I
a = −0.728992 − 0.419238I
b = −0.678933 + 0.310643I
0.73009 − 8.94435I 0
u = 1.15297 − 1.03584I
a = 0.459792 + 0.143655I
b = 1.274774 − 0.271751I
0.73009 − 8.94435I 0
52
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = 1.26647 + 0.91537I
a = −0.628427 − 0.317865I
b = −0.539584 − 0.861312I
−3.86284 + 5.00342I 0
u = 1.26647 + 0.91537I
a = 0.602735 + 0.244448I
b = 0.504919 + 0.977810I
−3.86284 + 5.00342I 0
u = 1.26647 − 0.91537I
a = −0.628427 + 0.317865I
b = −0.539584 + 0.861312I
−3.86284 − 5.00342I 0
u = 1.26647 − 0.91537I
a = 0.602735 − 0.244448I
b = 0.504919 − 0.977810I
−3.86284 − 5.00342I 0
u = −1.56112 + 0.21438I
a = 0.561343 − 0.248105I
b = 0.572058 − 0.030727I
0.428605 + 0.663668I 0
u = −1.56112 + 0.21438I
a = 0.362312 + 0.030071I
b = 0.823135 − 0.507661I
0.428605 + 0.663668I 0
u = −1.56112 − 0.21438I
a = 0.561343 + 0.248105I
b = 0.572058 + 0.030727I
0.428605 − 0.663668I 0
u = −1.56112 − 0.21438I
a = 0.362312 − 0.030071I
b = 0.823135 + 0.507661I
0.428605 − 0.663668I 0
u = −0.63555 + 1.44341I
a = −0.097108 − 0.375768I
b = −0.531016 + 0.237905I
0.92545 − 3.91157I 0
u = −0.63555 + 1.44341I
a = −0.273737 − 0.247361I
b = −0.604104 − 0.098652I
0.92545 − 3.91157I 0
53
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = −0.63555 − 1.44341I
a = −0.097108 + 0.375768I
b = −0.531016 − 0.237905I
0.92545 + 3.91157I 0
u = −0.63555 − 1.44341I
a = −0.273737 + 0.247361I
b = −0.604104 + 0.098652I
0.92545 + 3.91157I 0
u = 1.24334 + 1.06666I
a = −0.913898 − 0.067471I
b = −0.919013 − 0.715336I
−0.73009 + 8.94435I 0
u = 1.24334 + 1.06666I
a = 0.710101 − 0.033858I
b = 1.06432 + 1.05870I
−0.73009 + 8.94435I 0
u = 1.24334 − 1.06666I
a = −0.913898 + 0.067471I
b = −0.919013 + 0.715336I
−0.73009 − 8.94435I 0
u = 1.24334 − 1.06666I
a = 0.710101 + 0.033858I
b = 1.06432 − 1.05870I
−0.73009 − 8.94435I 0
u = 1.24038 + 1.08864I
a = −0.277770 + 0.480402I
b = −0.672497 + 0.003985I
3.86284 − 5.00342I 0
u = 1.24038 + 1.08864I
a = 0.304666 − 0.270609I
b = 0.867525 − 0.293489I
3.86284 − 5.00342I 0
u = 1.24038 − 1.08864I
a = −0.277770 − 0.480402I
b = −0.672497 − 0.003985I
3.86284 + 5.00342I 0
u = 1.24038 − 1.08864I
a = 0.304666 + 0.270609I
b = 0.867525 + 0.293489I
3.86284 + 5.00342I 0
54
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = 1.49575 + 0.85577I
a = 0.511279 − 0.104941I
b = 0.427200 + 0.344713I
−0.428605 + 0.663668I 0
u = 1.49575 + 0.85577I
a = −0.314512 − 0.050519I
b = −0.854551 − 0.280570I
−0.428605 + 0.663668I 0
u = 1.49575 − 0.85577I
a = 0.511279 + 0.104941I
b = 0.427200 − 0.344713I
−0.428605 − 0.663668I 0
u = 1.49575 − 0.85577I
a = −0.314512 + 0.050519I
b = −0.854551 + 0.280570I
−0.428605 − 0.663668I 0
u = 1.22830 + 1.32821I
a = 0.149481 − 0.371843I
b = 0.528224 − 0.348146I
− 5.59970I 0
u = 1.22830 + 1.32821I
a = −0.056954 + 0.345025I
b = −0.677493 + 0.258191I
− 5.59970I 0
u = 1.22830 − 1.32821I
a = 0.149481 + 0.371843I
b = 0.528224 + 0.348146I
5.59970I 0
u = 1.22830 − 1.32821I
a = −0.056954 − 0.345025I
b = −0.677493 − 0.258191I
5.59970I 0
55
X. I
u
10
= hb + u, a − 1, u
4
+ 2u
3
+ 2u
2
+ u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
1
−u
a
4
=
1
u
2
a
2
=
u
2
+ u + 1
−u
3
− 2u
2
− 2u − 1
a
8
=
−u
u
2
+ u
a
6
=
−u
3
− u
2
+ 1
−u
2
− u − 1
a
12
=
u + 1
−u
a
10
=
−u
3
− 2u
2
− u
u
3
+ u
2
+ u
a
7
=
−u
3
− 2u
2
− 3u − 1
u
2
+ 2u
a
3
=
−u
3
− 2u
2
− 2u + 1
u
2
− 1
a
11
=
u + 2
−2u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6u
3
+ 9u
2
+ 3u
56
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
9
(u
2
− u + 1)
2
c
2
, c
6
, c
10
u
4
+ 2u
3
+ 2u
2
+ u + 1
c
3
, c
7
, c
11
(u
2
+ u + 1)
2
c
4
, c
8
, c
12
u
4
− 2u
3
+ 2u
2
− u + 1
57
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
7
, c
9
, c
11
(y
2
+ y + 1)
2
c
2
, c
4
, c
6
c
8
, c
10
, c
12
y
4
+ 2y
2
+ 3y + 1
58
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = 0.070696 + 0.758745I
a = 1.00000
b = −0.070696 − 0.758745I
−3.39192 − 2.59539I −5.65464 + 0.68919I
u = 0.070696 − 0.758745I
a = 1.00000
b = −0.070696 + 0.758745I
−3.39192 + 2.59539I −5.65464 − 0.68919I
u = −1.070696 + 0.758745I
a = 1.00000
b = 1.070696 − 0.758745I
3.39192 − 2.59539I 5.65464 + 0.68919I
u = −1.070696 − 0.758745I
a = 1.00000
b = 1.070696 + 0.758745I
3.39192 + 2.59539I 5.65464 − 0.68919I
59
XI.
I
u
11
= h3u
5
a
3
− 3u
5
a
2
+ · · · + 3a + 3, −4u
5
a
3
+ 4u
5
a
2
+ · · · + b − 9a, u
5
a
3
−
u
5
a
2
+ · · · + a + 1, u
6
a
3
− u
6
a
2
+ · · · + a − u, u
5
a
4
− u
5
a
3
+ · · · − a + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
a
b
a
4
=
1
u
2
a
2
=
u
2
a − b + a
u
4
a − u
2
b + b
a
8
=
−a
2
u
u
5
a
3
− u
5
a
2
+ ··· + a + 1
a
6
=
5u
5
a
3
− 5u
5
a
2
+ ··· + 7a + 2
2u
5
a
3
− 2u
5
a
2
+ ··· + 2a + 1
a
12
=
−b + a
b
a
10
=
u
5
a
3
− u
5
a
2
+ ··· + a + 1
−2u
5
a
3
+ 2u
5
a
2
+ ··· − 2a − 2
a
7
=
4u
5
a
3
− 4u
5
a
2
+ ··· + 7a + 1
−2u
5
a
3
+ 2u
5
a
2
+ ··· − 3a − 1
a
3
=
−3u
5
a
3
+ 3u
5
a
2
+ ··· − a
2
− 4a
−u
5
a
3
+ u
5
a
2
+ ··· − 2a − 1
a
11
=
−u
5
a
3
+ u
5
a
2
+ ··· − 2a + 1
−u
6
a
3
+ u
6
a
2
+ ··· − 4a − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
(iv) u-Polynomials at the component : It cannot be defined for a positive
dimension component.
(v) Riley Polynomials at the component : It cannot be defined for a positive
dimension component.
60
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
11
√
−1(vol +
√
−1CS) Cusp shape
u = ···
a = ···
b = ···
0 0
61
XII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
9
75(u
2
− u + 1)
2
(u
4
+ 5u
2
+ 5)(u
4
+ u
3
+ u
2
+ u + 1)
2
· (u
10
− 4u
9
+ 9u
8
− 11u
7
+ 8u
6
− 7u
5
+ 10u
4
− 13u
3
+ 3u
2
+ 6u − 1)
· (u
14
− 4u
13
+ ··· − 2u + 1)(u
22
+ 5u
21
+ ··· + 115u + 55)
2
· (75u
22
− 1875u
21
+ ··· − 3211264u + 262144)
c
2
, c
6
, c
10
75(u
4
− 3u
3
+ 4u
2
− 2u + 1)
2
(u
4
+ u
3
+ u
2
+ u + 1)
· (u
4
+ 2u
3
+ 2u
2
+ u + 1)
· (u
10
+ 5u
9
+ 12u
8
+ 15u
7
+ 9u
6
− u
5
− 3u
4
+ u
3
+ 4u
2
+ u − 1)
· (u
14
+ 5u
13
+ ··· + u
2
+ 1)(3u
22
+ 72u
21
+ ··· + 1792u + 512)
· (5u
22
− 35u
21
+ ··· − 6u + 3)
2
c
3
, c
7
, c
11
75(u
2
+ u + 1)
2
(u
4
+ 5u
2
+ 5)(u
4
− u
3
+ u
2
− u + 1)
2
· (u
10
+ 4u
9
+ 9u
8
+ 11u
7
+ 8u
6
+ 7u
5
+ 10u
4
+ 13u
3
+ 3u
2
− 6u − 1)
· (u
14
+ 4u
13
+ ··· + 2u + 1)(u
22
− 5u
21
+ ··· − 115u + 55)
2
· (75u
22
+ 1875u
21
+ ··· + 3211264u + 262144)
c
4
, c
8
, c
12
75(u
4
− 2u
3
+ 2u
2
− u + 1)(u
4
− u
3
+ u
2
− u + 1)
· (u
4
+ 3u
3
+ 4u
2
+ 2u + 1)
2
· (u
10
− 5u
9
+ 12u
8
− 15u
7
+ 9u
6
+ u
5
− 3u
4
− u
3
+ 4u
2
− u − 1)
· (u
14
− 5u
13
+ ··· + u
2
+ 1)(3u
22
− 72u
21
+ ··· − 1792u + 512)
· (5u
22
+ 35u
21
+ ··· + 6u + 3)
2
62
XIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
7
, c
9
, c
11
5625(y
2
+ y + 1)
2
(y
2
+ 5y + 5)
2
(y
4
+ y
3
+ y
2
+ y + 1)
2
· (y
10
+ 2y
9
+ ··· − 42y + 1)(y
14
+ 4y
13
+ ··· + 24y + 1)
· (y
22
+ 11y
21
+ ··· + 20875y + 3025)
2
· (5625y
22
− 33375y
21
+ ··· − 184683593728y + 68719476736)
c
2
, c
4
, c
6
c
8
, c
10
, c
12
5625(y
4
+ 2y
2
+ 3y + 1)(y
4
− y
3
+ ··· + 4y + 1)
2
(y
4
+ y
3
+ ··· + y + 1)
· (y
10
− y
9
+ 12y
8
− 5y
7
+ 37y
6
− y
5
+ 29y
4
− 41y
3
+ 20y
2
− 9y + 1)
· (y
14
− y
13
+ ··· + 2y + 1)(9y
22
− 84y
21
+ ··· + 9371648y + 262144)
· (25y
22
+ 25y
21
+ ··· − 174y + 9)
2
63
