12a
0897
(K12a
0897
)
A knot diagram
1
Linearized knot diagam
4 6 8 9 12 11 10 1 2 7 3 5
Solving Sequence
6,11 3,7
12 2 5 1 10 8 9 4
c
6
c
11
c
2
c
5
c
12
c
10
c
7
c
9
c
4
c
1
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h57881957452448u
41
+ 869354193740770u
40
+ ··· + 35295682071297b − 13155101208038300,
1.31551 × 10
16
u
41
+ 1.76547 × 10
17
u
40
+ ··· + 1.26711 × 10
16
a − 8.53632 × 10
17
,
u
42
+ 15u
41
+ ··· − 7744u − 359i
I
u
2
= h−1.04951 × 10
13
a
5
u
14
+ 2.29419 × 10
15
a
4
u
14
+ ··· − 1.07487 × 10
15
a − 3.31910 × 10
15
,
− u
14
a
5
+ 3u
14
a
4
+ ··· − 48a − 192,
u
15
− 3u
14
+ 12u
13
− 25u
12
+ 52u
11
− 78u
10
+ 104u
9
− 109u
8
+ 94u
7
− 58u
6
+ 24u
5
+ 2u
4
− 8u
3
+ 4u
2
− 1i
I
u
3
= h23u
22
+ 100u
21
+ ··· + 623b − 207, −207u
22
+ 1058u
21
+ ··· + 623a + 1151,
u
23
− 5u
22
+ ··· − 2u − 1i
I
u
4
= hu
3
+ b + u, u
2
+ a + 1, u
4
− u
3
+ 2u
2
− 2u + 1i
I
v
1
= ha, b
3
+ b
2
− 1, v −1i
* 5 irreducible components of dim
C
= 0, with total 162 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
=
h5.79×10
13
u
41
+8.69×10
14
u
40
+· · ·+3.53×10
13
b−1.32×10
16
, 1.32×10
16
u
41
+
1.77×10
17
u
40
+· · ·+1.27×10
16
a−8.54×10
17
, u
42
+15u
41
+· · ·−7744u−359i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
−1.03819u
41
− 13.9330u
40
+ ··· + 1261.90u + 67.3681
−1.63992u
41
− 24.6306u
40
+ ··· + 7972.40u + 372.711
a
7
=
1
u
2
a
12
=
0.173456u
41
+ 3.15349u
40
+ ··· − 143.162u − 6.32280
−0.551641u
41
− 6.89586u
40
+ ··· − 1335.92u − 62.2709
a
2
=
0.601723u
41
+ 10.6976u
40
+ ··· − 6710.50u − 305.343
−1.63992u
41
− 24.6306u
40
+ ··· + 7972.40u + 372.711
a
5
=
−1.57357u
41
− 21.8016u
40
+ ··· − 1184.91u − 54.6381
−0.423171u
41
− 8.96377u
40
+ ··· + 7907.19u + 366.873
a
1
=
0.557687u
41
+ 4.38234u
40
+ ··· + 10797.2u + 500.615
2.74550u
41
+ 42.6628u
40
+ ··· − 12062.7u − 550.167
a
10
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
0.679616u
41
+ 10.3741u
40
+ ··· − 3056.20u − 144.610
−0.584616u
41
− 8.36449u
40
+ ··· − 555.966u − 34.1050
a
4
=
−0.952487u
41
− 14.7913u
40
+ ··· + 6842.37u + 332.671
0.555898u
41
+ 7.29831u
40
+ ··· − 374.764u − 12.6868
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
56056292405896
11765227357099
u
41
−
807397111618689
11765227357099
u
40
+ ··· +
169436635472717727
11765227357099
u +
8474387662208614
11765227357099
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
42
− 32u
41
+ ··· + 4335u − 359
c
2
, c
11
u
42
− u
41
+ ··· + u − 1
c
3
, c
9
u
42
− 2u
41
+ ··· + 2u − 11
c
4
, c
8
u
42
− 2u
41
+ ··· + 4u
2
− 1
c
5
, c
12
u
42
− 28u
41
+ ··· + 606208u − 32768
c
6
, c
7
, c
10
u
42
− 15u
41
+ ··· + 7744u − 359
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
42
− 6y
41
+ ··· − 5783501y + 128881
c
2
, c
11
y
42
− 13y
41
+ ··· − 75y + 1
c
3
, c
9
y
42
− 16y
41
+ ··· − 730y + 121
c
4
, c
8
y
42
+ 4y
41
+ ··· − 8y + 1
c
5
, c
12
y
42
+ 26y
41
+ ··· − 6174015488y + 1073741824
c
6
, c
7
, c
10
y
42
+ 47y
41
+ ··· − 7312852y + 128881
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.847798 + 0.516810I
a = 0.21167 + 1.44844I
b = 0.92802 + 1.11859I
−7.3624 + 15.0662I 0
u = −0.847798 − 0.516810I
a = 0.21167 − 1.44844I
b = 0.92802 − 1.11859I
−7.3624 − 15.0662I 0
u = −0.561817 + 0.847271I
a = −0.951772 − 0.095818I
b = −0.615905 + 0.752577I
−5.47132 − 2.16930I 0
u = −0.561817 − 0.847271I
a = −0.951772 + 0.095818I
b = −0.615905 − 0.752577I
−5.47132 + 2.16930I 0
u = −0.921261 + 0.448486I
a = −0.465925 − 0.892200I
b = −0.829379 − 0.612988I
−0.78802 + 9.08376I 0
u = −0.921261 − 0.448486I
a = −0.465925 + 0.892200I
b = −0.829379 + 0.612988I
−0.78802 − 9.08376I 0
u = −0.065307 + 1.026930I
a = −0.041167 − 0.595688I
b = −0.614420 + 0.003374I
0.85954 − 2.83040I 0
u = −0.065307 − 1.026930I
a = −0.041167 + 0.595688I
b = −0.614420 − 0.003374I
0.85954 + 2.83040I 0
u = −0.935171 + 0.033001I
a = 0.871306 + 0.314755I
b = 0.825208 + 0.265596I
−0.395611 − 0.511403I 0
u = −0.935171 − 0.033001I
a = 0.871306 − 0.314755I
b = 0.825208 − 0.265596I
−0.395611 + 0.511403I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.863179 + 0.646205I
a = 0.892421 − 0.309548I
b = 0.570288 − 0.843882I
−7.03389 − 9.43826I 0
u = −0.863179 − 0.646205I
a = 0.892421 + 0.309548I
b = 0.570288 + 0.843882I
−7.03389 + 9.43826I 0
u = −0.768224 + 0.348445I
a = −0.48288 − 1.60052I
b = −0.928655 − 1.061300I
−6.91525 + 6.82792I 0
u = −0.768224 − 0.348445I
a = −0.48288 + 1.60052I
b = −0.928655 + 1.061300I
−6.91525 − 6.82792I 0
u = −0.639526 + 1.087610I
a = −0.220347 − 0.414915I
b = −0.592182 − 0.025698I
0.78066 − 3.14670I 0
u = −0.639526 − 1.087610I
a = −0.220347 + 0.414915I
b = −0.592182 + 0.025698I
0.78066 + 3.14670I 0
u = 0.730215
a = 0.328191
b = −0.239650
−1.55834 −6.81850
u = 0.006501 + 1.400220I
a = 0.797704 − 0.863607I
b = −1.21442 − 1.11134I
1.79758 + 2.77962I 0
u = 0.006501 − 1.400220I
a = 0.797704 + 0.863607I
b = −1.21442 + 1.11134I
1.79758 − 2.77962I 0
u = 0.031630 + 1.404990I
a = −0.512139 + 0.747941I
b = 1.067050 + 0.695895I
6.06777 − 0.34397I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.031630 − 1.404990I
a = −0.512139 − 0.747941I
b = 1.067050 − 0.695895I
6.06777 + 0.34397I 0
u = 0.134419 + 1.404270I
a = 0.353300 − 0.370383I
b = −0.567608 − 0.446342I
3.34529 − 2.97285I 0
u = 0.134419 − 1.404270I
a = 0.353300 + 0.370383I
b = −0.567608 + 0.446342I
3.34529 + 2.97285I 0
u = −0.384090 + 0.434645I
a = 0.13898 + 1.76739I
b = 0.821565 + 0.618429I
1.89871 + 1.81111I 6.83265 − 3.65343I
u = −0.384090 − 0.434645I
a = 0.13898 − 1.76739I
b = 0.821565 − 0.618429I
1.89871 − 1.81111I 6.83265 + 3.65343I
u = −0.30684 + 1.39651I
a = −0.240117 + 0.905515I
b = 1.190880 + 0.613178I
4.32849 + 3.75468I 0
u = −0.30684 − 1.39651I
a = −0.240117 − 0.905515I
b = 1.190880 − 0.613178I
4.32849 − 3.75468I 0
u = −0.14396 + 1.47109I
a = −0.555100 + 0.872346I
b = 1.20339 + 0.94219I
8.12729 + 3.81472I 0
u = −0.14396 − 1.47109I
a = −0.555100 − 0.872346I
b = 1.20339 − 0.94219I
8.12729 − 3.81472I 0
u = −0.27835 + 1.45472I
a = 0.617727 − 0.997450I
b = −1.27907 − 1.17626I
−1.10701 + 10.59690I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.27835 − 1.45472I
a = 0.617727 + 0.997450I
b = −1.27907 + 1.17626I
−1.10701 − 10.59690I 0
u = −0.42217 + 1.44605I
a = 0.057955 + 0.677331I
b = 1.003920 + 0.202144I
4.29609 + 5.62948I 0
u = −0.42217 − 1.44605I
a = 0.057955 − 0.677331I
b = 1.003920 − 0.202144I
4.29609 − 5.62948I 0
u = −0.11951 + 1.54052I
a = 0.295400 − 0.652375I
b = −0.969698 − 0.533033I
8.90977 − 1.31796I 0
u = −0.11951 − 1.54052I
a = 0.295400 + 0.652375I
b = −0.969698 + 0.533033I
8.90977 + 1.31796I 0
u = −0.32872 + 1.51631I
a = 0.343559 − 0.879510I
b = −1.22067 − 0.81006I
5.5609 + 13.5743I 0
u = −0.32872 − 1.51631I
a = 0.343559 + 0.879510I
b = −1.22067 + 0.81006I
5.5609 − 13.5743I 0
u = −0.30503 + 1.53263I
a = −0.601860 + 0.946634I
b = 1.26726 + 1.21118I
−0.7235 + 19.2776I 0
u = −0.30503 − 1.53263I
a = −0.601860 − 0.946634I
b = 1.26726 − 1.21118I
−0.7235 − 19.2776I 0
u = −0.127622
a = 5.37111
b = 0.685470
1.12354 8.71010
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.08288 + 1.90741I
a = 0.0065428 + 0.1210950I
b = 0.231520 − 0.002443I
1.31408 − 4.69007I 0
u = −0.08288 − 1.90741I
a = 0.0065428 − 0.1210950I
b = 0.231520 + 0.002443I
1.31408 + 4.69007I 0
9
II. I
u
2
= h−1.05 × 10
13
a
5
u
14
+ 2.29 × 10
15
a
4
u
14
+ · · · − 1.07 × 10
15
a − 3.32 ×
10
15
, −u
14
a
5
+ 3u
14
a
4
+ · · · − 48a − 192, u
15
− 3u
14
+ · · · + 4u
2
− 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
a
0.00456179a
5
u
14
− 0.997190a
4
u
14
+ ··· + 0.467203a + 1.44268
a
7
=
1
u
2
a
12
=
a
2
u
−0.260599a
5
u
14
+ 0.246071a
4
u
14
+ ··· − 0.281860a + 0.337798
a
2
=
−0.00456179a
5
u
14
+ 0.997190a
4
u
14
+ ··· + 0.532797a − 1.44268
0.00456179a
5
u
14
− 0.997190a
4
u
14
+ ··· + 0.467203a + 1.44268
a
5
=
−0.257142a
5
u
14
− 0.262044a
4
u
14
+ ··· + 0.102646a + 0.158510
−0.0457117a
5
u
14
+ 0.0495339a
4
u
14
+ ··· − 0.248841a − 0.00240832
a
1
=
−0.217390a
5
u
14
+ 0.0754889a
4
u
14
+ ··· − 0.327262a + 0.0327779
0.214887a
5
u
14
− 0.196538a
4
u
14
+ ··· + 0.0330187a + 0.659794
a
10
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
−0.479143a
5
u
14
− 0.504474a
4
u
14
+ ··· + 0.989266a − 0.373754
0.174477a
5
u
14
+ 0.378451a
4
u
14
+ ··· − 0.811595a − 0.355396
a
4
=
−0.0179098a
5
u
14
+ 0.729168a
4
u
14
+ ··· + 0.194326a − 1.28730
−0.107630a
5
u
14
− 0.330844a
4
u
14
+ ··· + 0.688844a + 1.23844
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
395505362197928
460130783040701
u
14
a
5
−
1808659394637108
2300653915203505
u
14
a
4
+ ···+
303858281204832
2300653915203505
a −
16934707989003582
2300653915203505
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
15
+ 7u
14
+ ··· − 4u
2
+ 1)
6
c
2
, c
11
u
90
− u
89
+ ··· + 18u + 1
c
3
, c
9
u
90
+ u
89
+ ··· + 13305908u + 1942847
c
4
, c
8
u
90
+ u
89
+ ··· − 852u + 5809
c
5
, c
12
(u
3
+ u
2
+ 2u + 1)
30
c
6
, c
7
, c
10
(u
15
+ 3u
14
+ ··· − 4u
2
+ 1)
6
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
15
− y
14
+ ··· + 8y − 1)
6
c
2
, c
11
y
90
+ 15y
89
+ ··· + 248y + 1
c
3
, c
9
y
90
− 33y
89
+ ··· − 236967161513892y + 3774654465409
c
4
, c
8
y
90
+ 35y
89
+ ··· + 1669082764y + 33744481
c
5
, c
12
(y
3
+ 3y
2
+ 2y − 1)
30
c
6
, c
7
, c
10
(y
15
+ 15y
14
+ ··· + 8y − 1)
6
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.825834 + 0.538674I
a = 0.728895 + 0.432354I
b = 0.502288 + 1.061940I
−5.79977 + 0.10550I −15.2032 + 5.2409I
u = 0.825834 + 0.538674I
a = −1.015090 − 0.623772I
b = −0.369049 − 0.749690I
−5.79977 + 0.10550I −15.2032 + 5.2409I
u = 0.825834 + 0.538674I
a = 0.102647 − 0.788061I
b = 0.310124 − 0.695084I
−1.66219 − 2.72262I −8.67392 + 8.22039I
u = 0.825834 + 0.538674I
a = 0.121700 + 0.762293I
b = −0.509278 + 0.595515I
−1.66219 − 2.72262I −8.67392 + 8.22039I
u = 0.825834 + 0.538674I
a = −0.039913 − 1.288130I
b = 0.99066 − 1.16606I
−5.79977 − 5.55074I −15.2032 + 11.1998I
u = 0.825834 + 0.538674I
a = −0.19543 + 1.53945I
b = −0.660921 + 1.085280I
−5.79977 − 5.55074I −15.2032 + 11.1998I
u = 0.825834 − 0.538674I
a = 0.728895 − 0.432354I
b = 0.502288 − 1.061940I
−5.79977 − 0.10550I −15.2032 − 5.2409I
u = 0.825834 − 0.538674I
a = −1.015090 + 0.623772I
b = −0.369049 + 0.749690I
−5.79977 − 0.10550I −15.2032 − 5.2409I
u = 0.825834 − 0.538674I
a = 0.102647 + 0.788061I
b = 0.310124 + 0.695084I
−1.66219 + 2.72262I −8.67392 − 8.22039I
u = 0.825834 − 0.538674I
a = 0.121700 − 0.762293I
b = −0.509278 − 0.595515I
−1.66219 + 2.72262I −8.67392 − 8.22039I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.825834 − 0.538674I
a = −0.039913 + 1.288130I
b = 0.99066 + 1.16606I
−5.79977 + 5.55074I −15.2032 − 11.1998I
u = 0.825834 − 0.538674I
a = −0.19543 − 1.53945I
b = −0.660921 − 1.085280I
−5.79977 + 5.55074I −15.2032 − 11.1998I
u = −0.000696 + 1.255430I
a = 0.932334 + 0.293599I
b = −1.115540 − 0.135555I
1.29235 − 2.53738I 0.57441 + 1.72215I
u = −0.000696 + 1.255430I
a = 0.107483 − 0.888631I
b = 0.369240 − 1.170270I
1.29235 − 2.53738I 0.57441 + 1.72215I
u = −0.000696 + 1.255430I
a = −0.841704 − 0.169778I
b = 2.36969 − 0.27513I
−2.84523 − 5.36551I −5.95486 + 4.70160I
u = −0.000696 + 1.255430I
a = −1.71526 − 0.33087I
b = −0.0044633 + 0.1010780I
−2.84523 + 0.29074I −5.95486 − 1.25729I
u = −0.000696 + 1.255430I
a = 0.22020 + 1.88744I
b = −0.213730 + 1.056580I
−2.84523 − 5.36551I −5.95486 + 4.70160I
u = −0.000696 + 1.255430I
a = −0.0805146 − 0.0035106I
b = −0.41657 + 2.15315I
−2.84523 + 0.29074I −5.95486 − 1.25729I
u = −0.000696 − 1.255430I
a = 0.932334 − 0.293599I
b = −1.115540 + 0.135555I
1.29235 + 2.53738I 0.57441 − 1.72215I
u = −0.000696 − 1.255430I
a = 0.107483 + 0.888631I
b = 0.369240 + 1.170270I
1.29235 + 2.53738I 0.57441 − 1.72215I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.000696 − 1.255430I
a = −0.841704 + 0.169778I
b = 2.36969 + 0.27513I
−2.84523 + 5.36551I −5.95486 − 4.70160I
u = −0.000696 − 1.255430I
a = −1.71526 + 0.33087I
b = −0.0044633 − 0.1010780I
−2.84523 − 0.29074I −5.95486 + 1.25729I
u = −0.000696 − 1.255430I
a = 0.22020 − 1.88744I
b = −0.213730 − 1.056580I
−2.84523 + 5.36551I −5.95486 − 4.70160I
u = −0.000696 − 1.255430I
a = −0.0805146 + 0.0035106I
b = −0.41657 − 2.15315I
−2.84523 − 0.29074I −5.95486 + 1.25729I
u = 0.374558 + 0.641779I
a = 0.794569 − 0.748177I
b = 0.043785 + 0.842537I
−3.35529 − 0.56859I 0.01825 + 5.21728I
u = 0.374558 + 0.641779I
a = −1.008960 − 0.520630I
b = −0.777776 − 0.229702I
−3.35529 − 0.56859I 0.01825 + 5.21728I
u = 0.374558 + 0.641779I
a = 0.122061 − 0.821834I
b = 0.680031 − 0.847450I
0.78229 − 3.39671I 6.54752 + 8.19673I
u = 0.374558 + 0.641779I
a = 0.52368 + 1.36524I
b = −0.573155 + 0.229488I
0.78229 − 3.39671I 6.54752 + 8.19673I
u = 0.374558 + 0.641779I
a = −0.05694 + 1.69423I
b = −0.62312 + 1.42179I
−3.35529 − 6.22484I 0.01825 + 11.17618I
u = 0.374558 + 0.641779I
a = −1.22984 − 1.68868I
b = 1.108650 − 0.598043I
−3.35529 − 6.22484I 0.01825 + 11.17618I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.374558 − 0.641779I
a = 0.794569 + 0.748177I
b = 0.043785 − 0.842537I
−3.35529 + 0.56859I 0.01825 − 5.21728I
u = 0.374558 − 0.641779I
a = −1.008960 + 0.520630I
b = −0.777776 + 0.229702I
−3.35529 + 0.56859I 0.01825 − 5.21728I
u = 0.374558 − 0.641779I
a = 0.122061 + 0.821834I
b = 0.680031 + 0.847450I
0.78229 + 3.39671I 6.54752 − 8.19673I
u = 0.374558 − 0.641779I
a = 0.52368 − 1.36524I
b = −0.573155 − 0.229488I
0.78229 + 3.39671I 6.54752 − 8.19673I
u = 0.374558 − 0.641779I
a = −0.05694 − 1.69423I
b = −0.62312 − 1.42179I
−3.35529 + 6.22484I 0.01825 − 11.17618I
u = 0.374558 − 0.641779I
a = −1.22984 + 1.68868I
b = 1.108650 + 0.598043I
−3.35529 + 6.22484I 0.01825 − 11.17618I
u = 0.678314
a = 0.656234 + 1.097420I
b = 1.01936 + 1.23185I
−5.68548 + 2.82812I −12.78167 − 2.97945I
u = 0.678314
a = 0.656234 − 1.097420I
b = 1.01936 − 1.23185I
−5.68548 − 2.82812I −12.78167 + 2.97945I
u = 0.678314
a = 0.364150 + 0.321172I
b = −0.247008 + 0.217856I
−1.54789 −6.25241 + 0.I
u = 0.678314
a = 0.364150 − 0.321172I
b = −0.247008 − 0.217856I
−1.54789 −6.25241 + 0.I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.678314
a = −1.50278 + 1.81605I
b = −0.445133 + 0.744393I
−5.68548 − 2.82812I −12.78167 + 2.97945I
u = 0.678314
a = −1.50278 − 1.81605I
b = −0.445133 − 0.744393I
−5.68548 + 2.82812I −12.78167 − 2.97945I
u = −0.100337 + 1.375660I
a = 0.879754 − 0.273487I
b = −2.00005 − 0.72017I
−1.34732 + 2.76738I −2.84025 − 4.81401I
u = −0.100337 + 1.375660I
a = −1.326590 − 0.261883I
b = 0.806358 + 0.151417I
2.79026 + 5.59550I 3.68902 − 7.79345I
u = −0.100337 + 1.375660I
a = −0.066960 + 0.591047I
b = −0.49337 + 1.79865I
2.79026 + 5.59550I 3.68902 − 7.79345I
u = −0.100337 + 1.375660I
a = 0.41526 − 1.48418I
b = −0.287951 − 1.237680I
−1.34732 + 2.76738I −2.84025 − 4.81401I
u = −0.100337 + 1.375660I
a = 0.0506988 − 0.0596810I
b = 1.63740 − 2.49979I
−1.34732 + 8.42362I −2.84025 − 10.77290I
u = −0.100337 + 1.375660I
a = 1.89390 + 1.05214I
b = −0.0770134 − 0.0757322I
−1.34732 + 8.42362I −2.84025 − 10.77290I
u = −0.100337 − 1.375660I
a = 0.879754 + 0.273487I
b = −2.00005 + 0.72017I
−1.34732 − 2.76738I −2.84025 + 4.81401I
u = −0.100337 − 1.375660I
a = −1.326590 + 0.261883I
b = 0.806358 − 0.151417I
2.79026 − 5.59550I 3.68902 + 7.79345I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.100337 − 1.375660I
a = −0.066960 − 0.591047I
b = −0.49337 − 1.79865I
2.79026 − 5.59550I 3.68902 + 7.79345I
u = −0.100337 − 1.375660I
a = 0.41526 + 1.48418I
b = −0.287951 + 1.237680I
−1.34732 − 2.76738I −2.84025 + 4.81401I
u = −0.100337 − 1.375660I
a = 0.0506988 + 0.0596810I
b = 1.63740 + 2.49979I
−1.34732 − 8.42362I −2.84025 + 10.77290I
u = −0.100337 − 1.375660I
a = 1.89390 − 1.05214I
b = −0.0770134 + 0.0757322I
−1.34732 − 8.42362I −2.84025 + 10.77290I
u = 0.15235 + 1.51729I
a = 0.540617 + 0.954858I
b = −0.727117 + 0.596502I
7.78915 − 5.47678I 11.31764 + 5.38780I
u = 0.15235 + 1.51729I
a = 0.415408 + 0.703417I
b = −1.38278 + 1.79749I
3.65157 − 8.30490I 4.78838 + 8.36725I
u = 0.15235 + 1.51729I
a = 0.088559 − 0.754678I
b = 0.051094 − 0.182246I
3.65157 − 2.64865I 4.78838 + 2.40836I
u = 0.15235 + 1.51729I
a = −0.341574 − 0.513517I
b = 1.36644 − 0.96575I
7.78915 − 5.47678I 11.31764 + 5.38780I
u = 0.15235 + 1.51729I
a = −1.08225 − 1.02001I
b = 1.004000 − 0.737461I
3.65157 − 8.30490I 4.78838 + 8.36725I
u = 0.15235 + 1.51729I
a = 0.1155660 + 0.0452784I
b = −1.158560 − 0.019395I
3.65157 − 2.64865I 4.78838 + 2.40836I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.15235 − 1.51729I
a = 0.540617 − 0.954858I
b = −0.727117 − 0.596502I
7.78915 + 5.47678I 11.31764 − 5.38780I
u = 0.15235 − 1.51729I
a = 0.415408 − 0.703417I
b = −1.38278 − 1.79749I
3.65157 + 8.30490I 4.78838 − 8.36725I
u = 0.15235 − 1.51729I
a = 0.088559 + 0.754678I
b = 0.051094 + 0.182246I
3.65157 + 2.64865I 4.78838 − 2.40836I
u = 0.15235 − 1.51729I
a = −0.341574 + 0.513517I
b = 1.36644 + 0.96575I
7.78915 + 5.47678I 11.31764 − 5.38780I
u = 0.15235 − 1.51729I
a = −1.08225 + 1.02001I
b = 1.004000 + 0.737461I
3.65157 + 8.30490I 4.78838 − 8.36725I
u = 0.15235 − 1.51729I
a = 0.1155660 − 0.0452784I
b = −1.158560 + 0.019395I
3.65157 + 2.64865I 4.78838 − 2.40836I
u = 0.29798 + 1.53037I
a = −0.691431 − 0.746805I
b = 1.41243 − 1.09797I
0.89067 − 9.67569I −4.51522 + 13.25390I
u = 0.29798 + 1.53037I
a = 0.518104 + 1.023810I
b = −0.93686 + 1.28068I
0.89067 − 9.67569I −4.51522 + 13.25390I
u = 0.29798 + 1.53037I
a = 0.488342 + 0.660116I
b = −1.024940 + 0.650833I
5.02825 − 6.84757I 2.01405 + 10.27446I
u = 0.29798 + 1.53037I
a = −0.284102 − 0.725051I
b = 0.864709 − 0.944047I
5.02825 − 6.84757I 2.01405 + 10.27446I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.29798 + 1.53037I
a = −0.409487 − 0.288961I
b = 0.217124 − 0.213845I
0.89067 − 4.01945I −4.51522 + 7.29501I
u = 0.29798 + 1.53037I
a = 0.108014 + 0.162908I
b = −0.320199 + 0.712773I
0.89067 − 4.01945I −4.51522 + 7.29501I
u = 0.29798 − 1.53037I
a = −0.691431 + 0.746805I
b = 1.41243 + 1.09797I
0.89067 + 9.67569I −4.51522 − 13.25390I
u = 0.29798 − 1.53037I
a = 0.518104 − 1.023810I
b = −0.93686 − 1.28068I
0.89067 + 9.67569I −4.51522 − 13.25390I
u = 0.29798 − 1.53037I
a = 0.488342 − 0.660116I
b = −1.024940 − 0.650833I
5.02825 + 6.84757I 2.01405 − 10.27446I
u = 0.29798 − 1.53037I
a = −0.284102 + 0.725051I
b = 0.864709 + 0.944047I
5.02825 + 6.84757I 2.01405 − 10.27446I
u = 0.29798 − 1.53037I
a = −0.409487 + 0.288961I
b = 0.217124 + 0.213845I
0.89067 + 4.01945I −4.51522 − 7.29501I
u = 0.29798 − 1.53037I
a = 0.108014 − 0.162908I
b = −0.320199 − 0.712773I
0.89067 + 4.01945I −4.51522 − 7.29501I
u = −0.388845 + 0.104061I
a = 0.69147 − 1.47342I
b = 1.64496 − 1.23122I
−6.09804 + 6.75772I −13.2254 − 10.9670I
u = −0.388845 + 0.104061I
a = 0.72962 + 1.93595I
b = −0.569102 + 1.008450I
−1.96046 + 3.92960I −6.69617 − 7.98755I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.388845 + 0.104061I
a = −0.23948 − 2.17125I
b = −1.24632 − 1.22239I
−6.09804 + 1.10148I −13.22544 − 5.00810I
u = −0.388845 + 0.104061I
a = −2.01341 + 2.05462I
b = 0.485166 + 0.676861I
−1.96046 + 3.92960I −6.69617 − 7.98755I
u = −0.388845 + 0.104061I
a = −2.20591 − 3.73398I
b = −0.319063 − 0.819358I
−6.09804 + 1.10148I −13.22544 − 5.00810I
u = −0.388845 + 0.104061I
a = 4.73838 − 1.89829I
b = 0.115549 − 0.644888I
−6.09804 + 6.75772I −13.2254 − 10.9670I
u = −0.388845 − 0.104061I
a = 0.69147 + 1.47342I
b = 1.64496 + 1.23122I
−6.09804 − 6.75772I −13.2254 + 10.9670I
u = −0.388845 − 0.104061I
a = 0.72962 − 1.93595I
b = −0.569102 − 1.008450I
−1.96046 − 3.92960I −6.69617 + 7.98755I
u = −0.388845 − 0.104061I
a = −0.23948 + 2.17125I
b = −1.24632 + 1.22239I
−6.09804 − 1.10148I −13.22544 + 5.00810I
u = −0.388845 − 0.104061I
a = −2.01341 − 2.05462I
b = 0.485166 − 0.676861I
−1.96046 − 3.92960I −6.69617 + 7.98755I
u = −0.388845 − 0.104061I
a = −2.20591 + 3.73398I
b = −0.319063 + 0.819358I
−6.09804 − 1.10148I −13.22544 + 5.00810I
u = −0.388845 − 0.104061I
a = 4.73838 + 1.89829I
b = 0.115549 + 0.644888I
−6.09804 − 6.75772I −13.2254 + 10.9670I
21
III. I
u
3
= h23u
22
+ 100u
21
+ · · · + 623b − 207, −207u
22
+ 1058u
21
+ · · · +
623a + 1151, u
23
− 5u
22
+ · · · − 2u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
0.332263u
22
− 1.69823u
21
+ ··· − 9.49599u − 1.84751
−0.0369181u
22
− 0.160514u
21
+ ··· − 1.18299u + 0.332263
a
7
=
1
u
2
a
12
=
−0.179775u
22
+ 0.125201u
21
+ ··· − 5.89727u + 3.18941
−0.773676u
22
+ 3.60514u
21
+ ··· + 3.82986u − 0.179775
a
2
=
0.369181u
22
− 1.53772u
21
+ ··· − 8.31300u − 2.17978
−0.0369181u
22
− 0.160514u
21
+ ··· − 1.18299u + 0.332263
a
5
=
−1.47352u
22
+ 7.81701u
21
+ ··· + 0.311396u + 2.69021
0.186196u
22
− 0.792937u
21
+ ··· − 2.98395u − 2.24719
a
1
=
0.0963082u
22
− 0.301766u
21
+ ··· + 7.49599u − 3.58106
0.581059u
22
− 2.71589u
21
+ ··· − 2.53612u + 1.05618
a
10
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
1.19101u
22
− 5.72231u
21
+ ··· − 15.8234u + 2.13804
−0.290530u
22
+ 0.929374u
21
+ ··· + 5.83949u + 0.900482
a
4
=
0.812199u
22
− 3.18299u
21
+ ··· − 8.68860u − 2.59551
0.0513644u
22
− 1.05618u
21
+ ··· − 0.764045u + 0.252006
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
199
623
u
22
+
223
89
u
21
+ ··· −
189
89
u −
1502
623
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
23
− 8u
22
+ ··· + 2u + 1
c
2
, c
11
u
23
+ 2u
22
+ ··· + u + 1
c
3
, c
9
u
23
− 2u
22
+ ··· + 21u − 5
c
4
, c
8
u
23
+ 3u
22
+ ··· − 2u − 1
c
5
u
23
− 3u
22
+ ··· + 5u − 1
c
6
, c
7
u
23
− 5u
22
+ ··· − 2u − 1
c
10
u
23
+ 5u
22
+ ··· − 2u + 1
c
12
u
23
+ 3u
22
+ ··· + 5u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
− 6y
22
+ ··· + 14y − 1
c
2
, c
11
y
23
+ 2y
22
+ ··· − 19y − 1
c
3
, c
9
y
23
− 8y
22
+ ··· + 131y − 25
c
4
, c
8
y
23
+ 11y
22
+ ··· + 18y − 1
c
5
, c
12
y
23
+ 23y
22
+ ··· − 25y − 1
c
6
, c
7
, c
10
y
23
+ 29y
22
+ ··· + 4y − 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.981681
a = 0.779029
b = 0.764758
−0.689716 −2.06440
u = 0.046703 + 0.930712I
a = −0.684416 − 0.366896I
b = 0.309510 − 0.654129I
−0.50604 − 3.37221I −3.10488 + 5.47089I
u = 0.046703 − 0.930712I
a = −0.684416 + 0.366896I
b = 0.309510 + 0.654129I
−0.50604 + 3.37221I −3.10488 − 5.47089I
u = 0.341190 + 0.855994I
a = −0.529435 − 0.592181I
b = 0.326265 − 0.655239I
−0.46996 − 3.38317I −3.76274 + 7.75674I
u = 0.341190 − 0.855994I
a = −0.529435 + 0.592181I
b = 0.326265 + 0.655239I
−0.46996 + 3.38317I −3.76274 − 7.75674I
u = 0.742167 + 0.496463I
a = −0.09108 + 1.53322I
b = −0.828784 + 1.092690I
−5.14269 − 5.20984I −2.27770 + 4.55051I
u = 0.742167 − 0.496463I
a = −0.09108 − 1.53322I
b = −0.828784 − 1.092690I
−5.14269 + 5.20984I −2.27770 − 4.55051I
u = 0.038578 + 1.321770I
a = 0.866874 + 0.821907I
b = −1.05293 + 1.17751I
−1.84794 − 1.28014I −3.86484 + 0.35849I
u = 0.038578 − 1.321770I
a = 0.866874 − 0.821907I
b = −1.05293 − 1.17751I
−1.84794 + 1.28014I −3.86484 − 0.35849I
u = −0.052420 + 1.377800I
a = −0.882813 − 0.778988I
b = 1.11957 − 1.17550I
−1.09614 + 7.15051I −0.40535 − 3.22010I
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.052420 − 1.377800I
a = −0.882813 + 0.778988I
b = 1.11957 + 1.17550I
−1.09614 − 7.15051I −0.40535 + 3.22010I
u = 0.193105 + 0.487515I
a = −1.84547 + 0.45535I
b = −0.578363 − 0.811763I
−5.21658 + 0.59793I −4.49708 − 0.02117I
u = 0.193105 − 0.487515I
a = −1.84547 − 0.45535I
b = −0.578363 + 0.811763I
−5.21658 − 0.59793I −4.49708 + 0.02117I
u = 0.37598 + 1.46502I
a = −0.106547 − 0.671685I
b = 0.943975 − 0.408637I
4.28074 − 4.94018I 1.44473 + 3.42248I
u = 0.37598 − 1.46502I
a = −0.106547 + 0.671685I
b = 0.943975 + 0.408637I
4.28074 + 4.94018I 1.44473 − 3.42248I
u = 0.16604 + 1.50759I
a = −0.538274 − 0.673639I
b = 0.926195 − 0.923344I
6.65222 − 5.57707I 2.37187 + 5.82519I
u = 0.16604 − 1.50759I
a = −0.538274 + 0.673639I
b = 0.926195 + 0.923344I
6.65222 + 5.57707I 2.37187 − 5.82519I
u = 0.26815 + 1.51790I
a = 0.628490 + 0.885531I
b = −1.17562 + 1.19144I
1.41586 − 8.92546I 1.49885 + 4.00660I
u = 0.26815 − 1.51790I
a = 0.628490 − 0.885531I
b = −1.17562 − 1.19144I
1.41586 + 8.92546I 1.49885 − 4.00660I
u = −0.171277 + 0.117996I
a = −0.82086 − 5.18268I
b = 0.752128 + 0.790816I
−5.51473 − 6.41401I −0.58882 + 3.55203I
26
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.171277 − 0.117996I
a = −0.82086 + 5.18268I
b = 0.752128 − 0.790816I
−5.51473 + 6.41401I −0.58882 − 3.55203I
u = 0.06095 + 1.87112I
a = 0.1140130 + 0.0701550I
b = −0.124320 + 0.217608I
1.21038 − 4.74670I −17.7818 + 31.4853I
u = 0.06095 − 1.87112I
a = 0.1140130 − 0.0701550I
b = −0.124320 − 0.217608I
1.21038 + 4.74670I −17.7818 − 31.4853I
27
IV. I
u
4
= hu
3
+ b + u, u
2
+ a + 1, u
4
− u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
−u
2
− 1
−u
3
− u
a
7
=
1
u
2
a
12
=
u
3
+ 2u − 1
u
3
+ 2u − 1
a
2
=
u
3
− u
2
+ u − 1
−u
3
− u
a
5
=
u
3
− u
2
+ u − 1
u
3
− u
2
+ u − 2
a
1
=
u − 1
−u
3
− u
a
10
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
3
+ 2u − 1
a
9
=
1
u
3
+ 2u
a
4
=
−u
2
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
3
− 2u − 3
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
− 3u
3
+ 5u
2
− 3u + 1
c
2
, c
4
, c
8
c
11
(u
2
− u + 1)
2
c
3
, c
9
u
4
+ u
3
− u
2
− u + 1
c
5
, c
10
u
4
+ u
3
+ 2u
2
+ 2u + 1
c
6
, c
7
, c
12
u
4
− u
3
+ 2u
2
− 2u + 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
+ y
3
+ 9y
2
+ y + 1
c
2
, c
4
, c
8
c
11
(y
2
+ y + 1)
2
c
3
, c
9
y
4
− 3y
3
+ 5y
2
− 3y + 1
c
5
, c
6
, c
7
c
10
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621744 + 0.440597I
a = −1.192440 − 0.547877I
b = −0.500000 − 0.866025I
−5.03685 + 0.56550I −4.36523 − 0.45577I
u = 0.621744 − 0.440597I
a = −1.192440 + 0.547877I
b = −0.500000 + 0.866025I
−5.03685 − 0.56550I −4.36523 + 0.45577I
u = −0.121744 + 1.306620I
a = 0.692440 + 0.318148I
b = −0.500000 + 0.866025I
1.74699 + 4.62527I −2.13477 − 4.78589I
u = −0.121744 − 1.306620I
a = 0.692440 − 0.318148I
b = −0.500000 − 0.866025I
1.74699 − 4.62527I −2.13477 + 4.78589I
31
V. I
v
1
= ha, b
3
+ b
2
− 1, v − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
1
0
a
3
=
0
b
a
7
=
1
0
a
12
=
1
−b
2
a
2
=
−b
b
a
5
=
−b
2
+ 1
b
2
+ b − 1
a
1
=
b
−b
a
10
=
1
0
a
8
=
1
0
a
9
=
b
2
+ 1
−b
2
a
4
=
−b
b
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4b + 6
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
c
10
u
3
c
2
, c
3
, c
4
c
8
, c
9
, c
11
u
3
+ u
2
− 1
c
5
, c
12
u
3
− u
2
+ 2u − 1
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
7
c
10
y
3
c
2
, c
3
, c
4
c
8
, c
9
, c
11
y
3
− y
2
+ 2y − 1
c
5
, c
12
y
3
+ 3y
2
+ 2y − 1
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −0.877439 + 0.744862I
−3.02413 − 2.82812I 2.49024 + 2.97945I
v = 1.00000
a = 0
b = −0.877439 − 0.744862I
−3.02413 + 2.82812I 2.49024 − 2.97945I
v = 1.00000
a = 0
b = 0.754878
1.11345 9.01950
35
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
3
(u
4
− 3u
3
+ ··· − 3u + 1)(u
15
+ 7u
14
+ ··· − 4u
2
+ 1)
6
· (u
23
− 8u
22
+ ··· + 2u + 1)(u
42
− 32u
41
+ ··· + 4335u − 359)
c
2
, c
11
((u
2
− u + 1)
2
)(u
3
+ u
2
− 1)(u
23
+ 2u
22
+ ··· + u + 1)
· (u
42
− u
41
+ ··· + u − 1)(u
90
− u
89
+ ··· + 18u + 1)
c
3
, c
9
(u
3
+ u
2
− 1)(u
4
+ u
3
− u
2
− u + 1)(u
23
− 2u
22
+ ··· + 21u − 5)
· (u
42
− 2u
41
+ ··· + 2u − 11)(u
90
+ u
89
+ ··· + 1.33059 × 10
7
u + 1942847)
c
4
, c
8
((u
2
− u + 1)
2
)(u
3
+ u
2
− 1)(u
23
+ 3u
22
+ ··· − 2u − 1)
· (u
42
− 2u
41
+ ··· + 4u
2
− 1)(u
90
+ u
89
+ ··· − 852u + 5809)
c
5
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
30
(u
4
+ u
3
+ 2u
2
+ 2u + 1)
· (u
23
− 3u
22
+ ··· + 5u − 1)(u
42
− 28u
41
+ ··· + 606208u − 32768)
c
6
, c
7
u
3
(u
4
− u
3
+ 2u
2
− 2u + 1)(u
15
+ 3u
14
+ ··· − 4u
2
+ 1)
6
· (u
23
− 5u
22
+ ··· − 2u − 1)(u
42
− 15u
41
+ ··· + 7744u − 359)
c
10
u
3
(u
4
+ u
3
+ 2u
2
+ 2u + 1)(u
15
+ 3u
14
+ ··· − 4u
2
+ 1)
6
· (u
23
+ 5u
22
+ ··· − 2u + 1)(u
42
− 15u
41
+ ··· + 7744u − 359)
c
12
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
30
(u
4
− u
3
+ 2u
2
− 2u + 1)
· (u
23
+ 3u
22
+ ··· + 5u + 1)(u
42
− 28u
41
+ ··· + 606208u − 32768)
36
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
3
(y
4
+ y
3
+ 9y
2
+ y + 1)(y
15
− y
14
+ ··· + 8y − 1)
6
· (y
23
− 6y
22
+ ··· + 14y − 1)(y
42
− 6y
41
+ ··· − 5783501y + 128881)
c
2
, c
11
((y
2
+ y + 1)
2
)(y
3
− y
2
+ 2y − 1)(y
23
+ 2y
22
+ ··· − 19y − 1)
· (y
42
− 13y
41
+ ··· − 75y + 1)(y
90
+ 15y
89
+ ··· + 248y + 1)
c
3
, c
9
(y
3
− y
2
+ 2y − 1)(y
4
− 3y
3
+ ··· − 3y + 1)(y
23
− 8y
22
+ ··· + 131y − 25)
· (y
42
− 16y
41
+ ··· − 730y + 121)
· (y
90
− 33y
89
+ ··· − 236967161513892y + 3774654465409)
c
4
, c
8
((y
2
+ y + 1)
2
)(y
3
− y
2
+ 2y − 1)(y
23
+ 11y
22
+ ··· + 18y − 1)
· (y
42
+ 4y
41
+ ··· − 8y + 1)
· (y
90
+ 35y
89
+ ··· + 1669082764y + 33744481)
c
5
, c
12
((y
3
+ 3y
2
+ 2y − 1)
31
)(y
4
+ 3y
3
+ 2y
2
+ 1)(y
23
+ 23y
22
+ ··· − 25y − 1)
· (y
42
+ 26y
41
+ ··· − 6174015488y + 1073741824)
c
6
, c
7
, c
10
y
3
(y
4
+ 3y
3
+ 2y
2
+ 1)(y
15
+ 15y
14
+ ··· + 8y − 1)
6
· (y
23
+ 29y
22
+ ··· + 4y − 1)(y
42
+ 47y
41
+ ··· − 7312852y + 128881)
37
