12a
1124
(K12a
1124
)
A knot diagram
1
Linearized knot diagam
4 8 6 1 11 3 10 2 12 7 5 9
Solving Sequence
3,7
6
4,11
5 12 10 8 2 1 9
c
6
c
3
c
5
c
11
c
10
c
7
c
2
c
1
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.07302 × 10
16
u
25
+ 3.50154 × 10
16
u
24
+ ··· + 1.30132 × 10
17
b + 3.86213 × 10
16
,
− 3.50638 × 10
16
u
25
− 1.89759 × 10
17
u
24
+ ··· + 2.60265 × 10
17
a − 6.11748 × 10
17
, u
26
+ u
25
+ ··· − 14u + 3i
I
u
2
= h−6.92061 × 10
445
u
111
− 1.24528 × 10
446
u
110
+ ··· + 3.50085 × 10
446
b − 1.06405 × 10
447
,
− 1.84028 × 10
450
u
111
− 2.50015 × 10
451
u
110
+ ··· + 2.82749 × 10
452
a − 3.75263 × 10
453
,
u
112
+ 2u
111
+ ··· + 645u + 123i
I
u
3
= h−8.60666 × 10
28
u
35
+ 2.78547 × 10
29
u
34
+ ··· + 1.04041 × 10
29
b − 4.59118 × 10
29
,
− 2.41162 × 10
30
u
35
+ 3.63435 × 10
31
u
34
+ ··· + 7.01535 × 10
30
a + 6.17284 × 10
31
, u
36
− 5u
35
+ ··· + 3u + 1i
I
u
4
= hb + u − 1, a + 1, u
2
− u + 1i
* 4 irreducible components of dim
C
= 0, with total 176 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
= h1.07×10
16
u
25
+3.50×10
16
u
24
+· · ·+1.30×10
17
b+3.86×10
16
, −3.51×
10
16
u
25
−1.90×10
17
u
24
+· · ·+2.60×10
17
a−6.12×10
17
, u
26
+u
25
+· · ·−14u+3i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
4
=
u
u
3
+ u
a
11
=
0.134724u
25
+ 0.729100u
24
+ ··· − 4.54509u + 2.35048
−0.0824562u
25
− 0.269075u
24
+ ··· + 1.18090u − 0.296785
a
5
=
−0.223395u
25
− 0.761058u
24
+ ··· + 4.15107u − 0.466322
0.363051u
25
+ 0.387123u
24
+ ··· + 2.48399u − 0.167850
a
12
=
−0.517977u
25
+ 0.957739u
24
+ ··· − 18.4642u + 4.40381
−0.483957u
25
− 0.564125u
24
+ ··· − 1.03960u − 0.0706293
a
10
=
0.0522675u
25
+ 0.460025u
24
+ ··· − 3.36419u + 2.05370
−0.0824562u
25
− 0.269075u
24
+ ··· + 1.18090u − 0.296785
a
8
=
−0.0944248u
25
+ 0.107519u
24
+ ··· − 3.24925u + 1.84810
0.0343026u
25
− 0.266952u
24
+ ··· + 4.94697u − 1.34175
a
2
=
0.396266u
25
+ 0.347145u
24
+ ··· − 2.41543u + 0.113900
−0.230814u
25
− 0.152987u
24
+ ··· − 2.28807u + 0.465361
a
1
=
0.582885u
25
+ 0.580597u
24
+ ··· − 0.964263u − 0.133469
−0.0819378u
25
+ 0.0357949u
24
+ ··· − 0.741099u + 0.0774950
a
9
=
−1.42345u
25
− 1.35854u
24
+ ··· − 0.516330u + 0.499768
−0.00228858u
25
− 0.568183u
24
+ ··· + 8.02692u − 1.74866
(ii) Obstruction class = −1
(iii) Cusp Shapes =
−
50626243171306417
43377435355664855
u
25
−
28511993568223339
17350974142265942
u
24
+···−
1992721032938816786
43377435355664855
u+
762069217574817183
86754870711329710
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
26
− u
25
+ ··· + 14u + 3
c
2
, c
8
4(4u
26
− 36u
25
+ ··· − 360u + 52)
c
3
, c
6
, c
9
c
12
u
26
+ u
25
+ ··· − 14u + 3
c
5
, c
11
4(4u
26
+ 36u
25
+ ··· + 360u + 52)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
9
c
10
, c
12
y
26
+ 9y
25
+ ··· + 122y + 9
c
2
, c
5
, c
8
c
11
16(16y
26
+ 8y
25
+ ··· + 19952y + 2704)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.171905 + 1.015710I
a = −1.50278 + 0.45928I
b = 0.635907 − 0.179675I
−3.39880 + 2.53537I −6.23800 − 4.79646I
u = 0.171905 − 1.015710I
a = −1.50278 − 0.45928I
b = 0.635907 + 0.179675I
−3.39880 − 2.53537I −6.23800 + 4.79646I
u = −0.099111 + 0.948892I
a = 3.05682 + 0.16034I
b = −0.099111 − 0.948892I
− 0.788870I 0. − 8.08674I
u = −0.099111 − 0.948892I
a = 3.05682 − 0.16034I
b = −0.099111 + 0.948892I
0.788870I 0. + 8.08674I
u = −0.971898 + 0.533345I
a = 0.169703 − 0.026789I
b = −0.185899 + 1.252460I
9.46539 + 0.44983I 9.20690 + 1.23580I
u = −0.971898 − 0.533345I
a = 0.169703 + 0.026789I
b = −0.185899 − 1.252460I
9.46539 − 0.44983I 9.20690 − 1.23580I
u = 0.444034 + 1.042450I
a = 1.32030 + 0.64016I
b = −1.37806 − 0.69705I
−5.26475 + 4.42469I −3.07955 − 6.39392I
u = 0.444034 − 1.042450I
a = 1.32030 − 0.64016I
b = −1.37806 + 0.69705I
−5.26475 − 4.42469I −3.07955 + 6.39392I
u = 0.262934 + 0.820958I
a = −2.45447 − 0.41027I
b = 1.310570 + 0.212605I
−3.02770 + 1.50091I −0.38117 − 3.23499I
u = 0.262934 − 0.820958I
a = −2.45447 + 0.41027I
b = 1.310570 − 0.212605I
−3.02770 − 1.50091I −0.38117 + 3.23499I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.185899 + 1.252460I
a = 0.863382 − 0.637518I
b = −0.971898 + 0.533345I
−9.46539 − 0.44983I −9.20690 − 1.23580I
u = −0.185899 − 1.252460I
a = 0.863382 + 0.637518I
b = −0.971898 − 0.533345I
−9.46539 + 0.44983I −9.20690 + 1.23580I
u = 0.462470 + 1.233400I
a = 1.380000 + 0.282313I
b = −0.568787 + 1.206040I
−4.58845 + 11.84040I −2.55501 − 8.84767I
u = 0.462470 − 1.233400I
a = 1.380000 − 0.282313I
b = −0.568787 − 1.206040I
−4.58845 − 11.84040I −2.55501 + 8.84767I
u = 1.310570 + 0.212605I
a = 0.222492 + 0.720110I
b = 0.262934 + 0.820958I
3.02770 − 1.50091I 0.38117 + 3.23499I
u = 1.310570 − 0.212605I
a = 0.222492 − 0.720110I
b = 0.262934 − 0.820958I
3.02770 + 1.50091I 0.38117 − 3.23499I
u = −0.568787 + 1.206040I
a = −1.61277 − 0.45045I
b = 0.462470 + 1.233400I
4.58845 − 11.84040I 2.55501 + 8.84767I
u = −0.568787 − 1.206040I
a = −1.61277 + 0.45045I
b = 0.462470 − 1.233400I
4.58845 + 11.84040I 2.55501 − 8.84767I
u = 0.635907 + 0.179675I
a = 0.28808 − 1.39043I
b = 0.171905 − 1.015710I
3.39880 + 2.53537I 6.23800 − 4.79646I
u = 0.635907 − 0.179675I
a = 0.28808 + 1.39043I
b = 0.171905 + 1.015710I
3.39880 − 2.53537I 6.23800 + 4.79646I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.74288 + 1.31638I
a = 1.371160 + 0.094012I
b = −0.74288 − 1.31638I
− 19.4256I 0. + 10.05625I
u = −0.74288 − 1.31638I
a = 1.371160 − 0.094012I
b = −0.74288 + 1.31638I
19.4256I 0. − 10.05625I
u = −1.37806 + 0.69705I
a = −0.0055300 + 0.0592273I
b = 0.444034 − 1.042450I
5.26475 + 4.42469I 3.07955 − 6.39392I
u = −1.37806 − 0.69705I
a = −0.0055300 − 0.0592273I
b = 0.444034 + 1.042450I
5.26475 − 4.42469I 3.07955 + 6.39392I
u = 0.158808 + 0.320085I
a = 1.070290 + 0.730453I
b = 0.158808 − 0.320085I
0.894091I 0. − 7.18165I
u = 0.158808 − 0.320085I
a = 1.070290 − 0.730453I
b = 0.158808 + 0.320085I
− 0.894091I 0. + 7.18165I
7
II. I
u
2
= h−6.92 × 10
445
u
111
− 1.25 × 10
446
u
110
+ · · · + 3.50 × 10
446
b − 1.06 ×
10
447
, −1.84 × 10
450
u
111
− 2.50 × 10
451
u
110
+ · · · + 2.83 × 10
452
a − 3.75 ×
10
453
, u
112
+ 2u
111
+ · · · + 645u + 123i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
4
=
u
u
3
+ u
a
11
=
0.00650853u
111
+ 0.0884229u
110
+ ··· + 57.9641u + 13.2719
0.197684u
111
+ 0.355707u
110
+ ··· + 57.5559u + 3.03942
a
5
=
0.101099u
111
+ 0.135504u
110
+ ··· − 53.2054u − 12.7494
−0.115566u
111
− 0.291705u
110
+ ··· − 127.776u − 20.8814
a
12
=
−0.126207u
111
− 0.259103u
110
+ ··· − 76.2442u − 9.47282
−0.294134u
111
− 0.552574u
110
+ ··· − 115.549u − 10.3189
a
10
=
0.204192u
111
+ 0.444130u
110
+ ··· + 115.520u + 16.3114
0.197684u
111
+ 0.355707u
110
+ ··· + 57.5559u + 3.03942
a
8
=
0.0135688u
111
+ 0.103593u
110
+ ··· + 88.4866u + 17.2247
0.191731u
111
+ 0.377269u
110
+ ··· + 96.3823u + 10.7157
a
2
=
0.0751224u
111
+ 0.104048u
110
+ ··· − 57.5579u − 15.7583
0.0701494u
111
+ 0.0353507u
110
+ ··· − 80.4689u − 20.2555
a
1
=
0.0859122u
111
+ 0.169795u
110
+ ··· − 5.67199u − 5.36633
0.0636436u
111
+ 0.0485745u
110
+ ··· − 58.3981u − 15.2962
a
9
=
0.0189622u
111
+ 0.0594773u
110
+ ··· − 27.3713u − 5.26515
0.0833554u
111
+ 0.159039u
110
+ ··· + 40.9020u + 4.95769
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.332720u
111
+ 0.853504u
110
+ ··· + 352.835u + 63.0911
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
112
− 2u
111
+ ··· − 645u + 123
c
2
, c
8
81(9u
56
+ 18u
55
+ ··· + 784u + 455)
2
c
3
, c
6
, c
9
c
12
u
112
+ 2u
111
+ ··· + 645u + 123
c
5
, c
11
81(9u
56
− 18u
55
+ ··· − 784u + 455)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
9
c
10
, c
12
y
112
+ 58y
111
+ ··· + 478431y + 15129
c
2
, c
5
, c
8
c
11
6561(81y
56
+ 3366y
55
+ ··· + 2666804y + 207025)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.884165 + 0.446342I
a = 0.105843 − 0.289868I
b = −0.528679 − 0.595350I
−1.47297 + 2.83228I 0
u = 0.884165 − 0.446342I
a = 0.105843 + 0.289868I
b = −0.528679 + 0.595350I
−1.47297 − 2.83228I 0
u = −0.759962 + 0.702616I
a = 0.087653 + 0.516964I
b = 0.47409 − 1.34478I
4.44565 − 1.93679I 0
u = −0.759962 − 0.702616I
a = 0.087653 − 0.516964I
b = 0.47409 + 1.34478I
4.44565 + 1.93679I 0
u = −0.083724 + 0.953094I
a = −1.50640 − 0.24056I
b = 0.632718 + 1.068020I
−1.14303 − 2.47132I 0
u = −0.083724 − 0.953094I
a = −1.50640 + 0.24056I
b = 0.632718 − 1.068020I
−1.14303 + 2.47132I 0
u = 0.953861 + 0.057825I
a = −0.0126888 − 0.0747161I
b = 0.110749 − 1.287230I
4.95021 + 2.36997I 0
u = 0.953861 − 0.057825I
a = −0.0126888 + 0.0747161I
b = 0.110749 + 1.287230I
4.95021 − 2.36997I 0
u = −0.603185 + 0.740197I
a = 1.223860 − 0.582290I
b = −0.631209 + 0.232434I
4.95021 − 2.36997I 0
u = −0.603185 − 0.740197I
a = 1.223860 + 0.582290I
b = −0.631209 − 0.232434I
4.95021 + 2.36997I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.813104 + 0.676150I
a = 0.326904 − 0.584359I
b = −0.651444 + 1.158900I
6.37753 + 0.27406I 0
u = −0.813104 − 0.676150I
a = 0.326904 + 0.584359I
b = −0.651444 − 1.158900I
6.37753 − 0.27406I 0
u = 0.292409 + 1.020680I
a = −1.58954 − 0.29311I
b = 1.51678 + 0.35730I
−3.79390 + 0.81802I 0
u = 0.292409 − 1.020680I
a = −1.58954 + 0.29311I
b = 1.51678 − 0.35730I
−3.79390 − 0.81802I 0
u = 0.505254 + 0.780652I
a = −0.068301 − 0.984122I
b = 0.113786 − 0.316141I
−1.14303 + 2.47132I 0
u = 0.505254 − 0.780652I
a = −0.068301 + 0.984122I
b = 0.113786 + 0.316141I
−1.14303 − 2.47132I 0
u = −0.592492 + 0.892812I
a = −1.53226 + 0.66927I
b = 0.877171 + 0.152656I
0.67163 − 7.34051I 0
u = −0.592492 − 0.892812I
a = −1.53226 − 0.66927I
b = 0.877171 − 0.152656I
0.67163 + 7.34051I 0
u = −0.844071 + 0.315454I
a = −0.206766 − 0.113144I
b = 0.228643 − 1.394900I
7.35971 + 6.55125I 0
u = −0.844071 − 0.315454I
a = −0.206766 + 0.113144I
b = 0.228643 + 1.394900I
7.35971 − 6.55125I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877171 + 0.152656I
a = 0.588923 + 1.119460I
b = −0.592492 + 0.892812I
−0.67163 + 7.34051I 0
u = 0.877171 − 0.152656I
a = 0.588923 − 1.119460I
b = −0.592492 − 0.892812I
−0.67163 − 7.34051I 0
u = 0.867572 + 0.075937I
a = 0.500076 + 0.274476I
b = 0.191909 + 1.225350I
3.62547 − 2.48438I 0
u = 0.867572 − 0.075937I
a = 0.500076 − 0.274476I
b = 0.191909 − 1.225350I
3.62547 + 2.48438I 0
u = 0.382832 + 0.766047I
a = −1.97355 + 0.24792I
b = 0.025588 − 0.334898I
−3.62547 + 2.48438I 0
u = 0.382832 − 0.766047I
a = −1.97355 − 0.24792I
b = 0.025588 + 0.334898I
−3.62547 − 2.48438I 0
u = −0.301465 + 1.117770I
a = −1.140040 + 0.061054I
b = 0.542791 + 1.207620I
−1.47297 − 2.83228I 0
u = −0.301465 − 1.117770I
a = −1.140040 − 0.061054I
b = 0.542791 − 1.207620I
−1.47297 + 2.83228I 0
u = 1.122590 + 0.283421I
a = −0.068402 + 0.143669I
b = −0.485724 − 1.193430I
− 5.88229I 0
u = 1.122590 − 0.283421I
a = −0.068402 − 0.143669I
b = −0.485724 + 1.193430I
5.88229I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.420227 + 1.088870I
a = 1.27405 + 1.05522I
b = −0.394596 − 1.264030I
3.52423 + 3.40169I 0
u = −0.420227 − 1.088870I
a = 1.27405 − 1.05522I
b = −0.394596 + 1.264030I
3.52423 − 3.40169I 0
u = −0.637995 + 0.990357I
a = −1.68006 − 0.10686I
b = 0.75424 + 1.21771I
3.52423 − 3.40169I 0
u = −0.637995 − 0.990357I
a = −1.68006 + 0.10686I
b = 0.75424 − 1.21771I
3.52423 + 3.40169I 0
u = −0.354197 + 1.136970I
a = −1.32575 − 1.08797I
b = 0.585869 + 1.043190I
4.44565 − 1.93679I 0
u = −0.354197 − 1.136970I
a = −1.32575 + 1.08797I
b = 0.585869 − 1.043190I
4.44565 + 1.93679I 0
u = −0.462140 + 1.099560I
a = 1.42581 − 0.30656I
b = −0.685238 − 1.173630I
−7.35971 − 6.55125I 0
u = −0.462140 − 1.099560I
a = 1.42581 + 0.30656I
b = −0.685238 + 1.173630I
−7.35971 + 6.55125I 0
u = 0.585869 + 1.043190I
a = 0.473389 + 0.565880I
b = −0.354197 + 1.136970I
−4.44565 + 1.93679I 0
u = 0.585869 − 1.043190I
a = 0.473389 − 0.565880I
b = −0.354197 − 1.136970I
−4.44565 − 1.93679I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.194380 + 0.109868I
a = −0.052951 + 1.071920I
b = 0.387030 + 0.624603I
3.79390 + 0.81802I 0
u = −1.194380 − 0.109868I
a = −0.052951 − 1.071920I
b = 0.387030 − 0.624603I
3.79390 − 0.81802I 0
u = −0.528679 + 0.595350I
a = −0.894547 + 0.830069I
b = 0.884165 − 0.446342I
1.47297 + 2.83228I 0
u = −0.528679 − 0.595350I
a = −0.894547 − 0.830069I
b = 0.884165 + 0.446342I
1.47297 − 2.83228I 0
u = −0.714680 + 1.010660I
a = 1.71981 − 0.07841I
b = −0.907798 − 0.937963I
5.36521 − 6.00891I 0
u = −0.714680 − 1.010660I
a = 1.71981 + 0.07841I
b = −0.907798 + 0.937963I
5.36521 + 6.00891I 0
u = 0.191909 + 1.225350I
a = −1.139030 + 0.218604I
b = 0.867572 + 0.075937I
−3.62547 + 2.48438I 0
u = 0.191909 − 1.225350I
a = −1.139030 − 0.218604I
b = 0.867572 − 0.075937I
−3.62547 − 2.48438I 0
u = 0.632718 + 1.068020I
a = 0.918916 − 0.125547I
b = −0.083724 + 0.953094I
1.14303 + 2.47132I 0
u = 0.632718 − 1.068020I
a = 0.918916 + 0.125547I
b = −0.083724 − 0.953094I
1.14303 − 2.47132I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.387030 + 0.624603I
a = 2.72128 + 0.74896I
b = −1.194380 + 0.109868I
−3.79390 − 0.81802I −3.81901 + 0.78619I
u = 0.387030 − 0.624603I
a = 2.72128 − 0.74896I
b = −1.194380 − 0.109868I
−3.79390 + 0.81802I −3.81901 − 0.78619I
u = −0.491811 + 1.165850I
a = 1.255800 − 0.397372I
b = −1.327960 + 0.393036I
−3.01787 − 12.23000I 0
u = −0.491811 − 1.165850I
a = 1.255800 + 0.397372I
b = −1.327960 − 0.393036I
−3.01787 + 12.23000I 0
u = −0.150119 + 0.718590I
a = −0.060211 − 0.683044I
b = −0.03391 + 1.85674I
5.36521 − 6.00891I −5.23529 + 9.39142I
u = −0.150119 − 0.718590I
a = −0.060211 + 0.683044I
b = −0.03391 − 1.85674I
5.36521 + 6.00891I −5.23529 − 9.39142I
u = −0.136237 + 0.713086I
a = −0.687415 + 0.337443I
b = 0.32677 − 1.66929I
6.37753 − 0.27406I −3.16621 + 0.74603I
u = −0.136237 − 0.713086I
a = −0.687415 − 0.337443I
b = 0.32677 + 1.66929I
6.37753 + 0.27406I −3.16621 − 0.74603I
u = −0.485724 + 1.193430I
a = −1.054970 + 0.157438I
b = 1.122590 − 0.283421I
− 5.88229I 0
u = −0.485724 − 1.193430I
a = −1.054970 − 0.157438I
b = 1.122590 + 0.283421I
5.88229I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.130420 + 0.698189I
a = 1.49124 + 0.08272I
b = −0.130420 − 0.698189I
0.727774I 0. − 4.02174I
u = −0.130420 − 0.698189I
a = 1.49124 − 0.08272I
b = −0.130420 + 0.698189I
− 0.727774I 0. + 4.02174I
u = 0.110749 + 1.287230I
a = −1.008870 + 0.047046I
b = 0.953861 − 0.057825I
−4.95021 + 2.36997I 0
u = 0.110749 − 1.287230I
a = −1.008870 − 0.047046I
b = 0.953861 + 0.057825I
−4.95021 − 2.36997I 0
u = −0.907798 + 0.937963I
a = 1.089720 − 0.578246I
b = −0.714680 − 1.010660I
−5.36521 − 6.00891I 0
u = −0.907798 − 0.937963I
a = 1.089720 + 0.578246I
b = −0.714680 + 1.010660I
−5.36521 + 6.00891I 0
u = 0.542791 + 1.207620I
a = 1.106730 − 0.527739I
b = −0.301465 + 1.117770I
1.47297 + 2.83228I 0
u = 0.542791 − 1.207620I
a = 1.106730 + 0.527739I
b = −0.301465 − 1.117770I
1.47297 − 2.83228I 0
u = −0.394596 + 1.264030I
a = 0.721570 − 0.337747I
b = −0.420227 − 1.088870I
−3.52423 + 3.40169I 0
u = −0.394596 − 1.264030I
a = 0.721570 + 0.337747I
b = −0.420227 + 1.088870I
−3.52423 − 3.40169I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.631209 + 0.232434I
a = −0.471205 + 0.855786I
b = −0.603185 + 0.740197I
−4.95021 + 2.36997I −5.26771 − 3.02633I
u = −0.631209 − 0.232434I
a = −0.471205 − 0.855786I
b = −0.603185 − 0.740197I
−4.95021 − 2.36997I −5.26771 + 3.02633I
u = −0.651444 + 1.158900I
a = 0.404280 − 0.334762I
b = −0.813104 + 0.676150I
−6.37753 − 0.27406I 0
u = −0.651444 − 1.158900I
a = 0.404280 + 0.334762I
b = −0.813104 − 0.676150I
−6.37753 + 0.27406I 0
u = 0.549092 + 1.229860I
a = −0.926899 − 0.049173I
b = 0.456838 − 1.292490I
−0.67163 + 7.34051I 0
u = 0.549092 − 1.229860I
a = −0.926899 + 0.049173I
b = 0.456838 + 1.292490I
−0.67163 − 7.34051I 0
u = −0.685238 + 1.173630I
a = 1.42898 + 0.26083I
b = −0.462140 − 1.099560I
7.35971 − 6.55125I 0
u = −0.685238 − 1.173630I
a = 1.42898 − 0.26083I
b = −0.462140 + 1.099560I
7.35971 + 6.55125I 0
u = −0.594063 + 0.232845I
a = −1.27489 + 2.45384I
b = −0.331498 + 0.096194I
0.02827 − 8.03523I 1.79105 + 2.67120I
u = −0.594063 − 0.232845I
a = −1.27489 − 2.45384I
b = −0.331498 − 0.096194I
0.02827 + 8.03523I 1.79105 − 2.67120I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.456838 + 1.292490I
a = −1.242670 + 0.637725I
b = 0.549092 − 1.229860I
0.67163 + 7.34051I 0
u = 0.456838 − 1.292490I
a = −1.242670 − 0.637725I
b = 0.549092 + 1.229860I
0.67163 − 7.34051I 0
u = −1.327960 + 0.393036I
a = 0.0448775 − 0.0484661I
b = −0.491811 + 1.165850I
3.01787 + 12.23000I 0
u = −1.327960 − 0.393036I
a = 0.0448775 + 0.0484661I
b = −0.491811 − 1.165850I
3.01787 − 12.23000I 0
u = 0.228643 + 1.394900I
a = 0.841152 + 0.465681I
b = −0.844071 − 0.315454I
−7.35971 + 6.55125I 0
u = 0.228643 − 1.394900I
a = 0.841152 − 0.465681I
b = −0.844071 + 0.315454I
−7.35971 − 6.55125I 0
u = 0.47409 + 1.34478I
a = 0.641073 + 0.341067I
b = −0.759962 − 0.702616I
−4.44565 − 1.93679I 0
u = 0.47409 − 1.34478I
a = 0.641073 − 0.341067I
b = −0.759962 + 0.702616I
−4.44565 + 1.93679I 0
u = 0.60329 + 1.29581I
a = −1.204750 + 0.272854I
b = 0.62598 − 1.34876I
−0.02827 + 8.03523I 0
u = 0.60329 − 1.29581I
a = −1.204750 − 0.272854I
b = 0.62598 + 1.34876I
−0.02827 − 8.03523I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.67222 + 1.26173I
a = 1.46091 − 0.17983I
b = −0.82966 + 1.29407I
−3.01787 + 12.23000I 0
u = 0.67222 − 1.26173I
a = 1.46091 + 0.17983I
b = −0.82966 − 1.29407I
−3.01787 − 12.23000I 0
u = 0.75424 + 1.21771I
a = 1.152110 + 0.295229I
b = −0.637995 + 0.990357I
−3.52423 + 3.40169I 0
u = 0.75424 − 1.21771I
a = 1.152110 − 0.295229I
b = −0.637995 − 0.990357I
−3.52423 − 3.40169I 0
u = 0.62598 + 1.34876I
a = −1.149320 + 0.241382I
b = 0.60329 − 1.29581I
0.02827 + 8.03523I 0
u = 0.62598 − 1.34876I
a = −1.149320 − 0.241382I
b = 0.60329 + 1.29581I
0.02827 − 8.03523I 0
u = 0.407749 + 0.238643I
a = 0.256790 + 0.906420I
b = 0.407749 − 0.238643I
0.727774I 0. − 4.02174I
u = 0.407749 − 0.238643I
a = 0.256790 − 0.906420I
b = 0.407749 + 0.238643I
− 0.727774I 0. + 4.02174I
u = −0.82966 + 1.29407I
a = −1.191020 + 0.005097I
b = 0.67222 + 1.26173I
3.01787 − 12.23000I 0
u = −0.82966 − 1.29407I
a = −1.191020 − 0.005097I
b = 0.67222 − 1.26173I
3.01787 + 12.23000I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.51678 + 0.35730I
a = 0.0623760 + 0.0218971I
b = 0.292409 + 1.020680I
3.79390 − 0.81802I 0
u = 1.51678 − 0.35730I
a = 0.0623760 − 0.0218971I
b = 0.292409 − 1.020680I
3.79390 + 0.81802I 0
u = −0.331498 + 0.096194I
a = 2.52818 − 4.96451I
b = −0.594063 + 0.232845I
−0.02827 + 8.03523I −1.79105 − 2.67120I
u = −0.331498 − 0.096194I
a = 2.52818 + 4.96451I
b = −0.594063 − 0.232845I
−0.02827 − 8.03523I −1.79105 + 2.67120I
u = 0.113786 + 0.316141I
a = −2.78656 + 2.28051I
b = 0.505254 − 0.780652I
1.14303 + 2.47132I 5.07801 − 4.40819I
u = 0.113786 − 0.316141I
a = −2.78656 − 2.28051I
b = 0.505254 + 0.780652I
1.14303 − 2.47132I 5.07801 + 4.40819I
u = 0.025588 + 0.334898I
a = −4.37473 − 2.36208I
b = 0.382832 − 0.766047I
3.62547 + 2.48438I 2.78870 − 4.88253I
u = 0.025588 − 0.334898I
a = −4.37473 + 2.36208I
b = 0.382832 + 0.766047I
3.62547 − 2.48438I 2.78870 + 4.88253I
u = 0.32677 + 1.66929I
a = −0.156499 + 0.567736I
b = −0.136237 − 0.713086I
−6.37753 − 0.27406I 0
u = 0.32677 − 1.66929I
a = −0.156499 − 0.567736I
b = −0.136237 + 0.713086I
−6.37753 + 0.27406I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.03391 + 1.85674I
a = 0.123122 − 0.448880I
b = −0.150119 + 0.718590I
−5.36521 + 6.00891I 0
u = −0.03391 − 1.85674I
a = 0.123122 + 0.448880I
b = −0.150119 − 0.718590I
−5.36521 − 6.00891I 0
22
III.
I
u
3
= h−8.61×10
28
u
35
+2.79×10
29
u
34
+· · ·+1.04×10
29
b−4.59×10
29
, −2.41×
10
30
u
35
+3.63×10
31
u
34
+· · ·+7.02×10
30
a+6.17×10
31
, u
36
−5u
35
+· · ·+3u+1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
4
=
u
u
3
+ u
a
11
=
0.343763u
35
− 5.18057u
34
+ ··· − 35.9438u − 8.79905
0.827236u
35
− 2.67728u
34
+ ··· + 19.1420u + 4.41284
a
5
=
−1.97717u
35
+ 9.97818u
34
+ ··· − 3.34201u − 1.59573
−0.413987u
35
+ 1.85894u
34
+ ··· − 1.49699u + 2.12131
a
12
=
2.20740u
35
− 10.8526u
34
+ ··· + 7.07737u + 0.548090
−0.819026u
35
+ 4.38146u
34
+ ··· − 5.54503u − 1.52076
a
10
=
1.17100u
35
− 7.85785u
34
+ ··· − 16.8018u − 4.38620
0.827236u
35
− 2.67728u
34
+ ··· + 19.1420u + 4.41284
a
8
=
0.0970879u
35
+ 0.361789u
34
+ ··· + 10.5563u + 4.13110
0.224099u
35
− 1.20829u
34
+ ··· − 1.18107u − 3.05633
a
2
=
0.258655u
35
− 0.938548u
34
+ ··· − 1.61611u + 0.482228
0.912207u
35
− 4.34155u
34
+ ··· + 9.55551u + 0.0449479
a
1
=
0.389085u
35
− 1.76419u
34
+ ··· − 2.58230u + 0.517489
0.956784u
35
− 4.62078u
34
+ ··· + 8.97936u + 0.253698
a
9
=
−0.429002u
35
+ 2.36713u
34
+ ··· + 1.32597u + 2.11288
1.00044u
35
− 4.55551u
34
+ ··· + 10.9307u − 0.129685
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0.329196u
35
+ 5.91364u
34
+ ··· + 69.4025u + 25.0741
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
c
12
u
36
− 5u
35
+ ··· + 3u + 1
c
2
, c
5
, c
8
c
11
64(64u
36
+ 848u
34
+ ··· + 672u
2
+ 49)
c
3
, c
4
, c
9
c
10
u
36
+ 5u
35
+ ··· − 3u + 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
9
c
10
, c
12
y
36
+ 15y
35
+ ··· + 19y + 1
c
2
, c
5
, c
8
c
11
4096(64y
18
+ 848y
17
+ ··· + 672y + 49)
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.820724 + 0.538227I
a = −0.119632 + 0.530996I
b = 0.473731 − 1.205330I
7.14238 + 0.08114I 7.67724 + 1.23653I
u = −0.820724 − 0.538227I
a = −0.119632 − 0.530996I
b = 0.473731 + 1.205330I
7.14238 − 0.08114I 7.67724 − 1.23653I
u = 0.007256 + 0.938273I
a = −1.72452 − 0.81856I
b = 0.490597 + 0.946124I
− 1.96250I 0. + 2.64993I
u = 0.007256 − 0.938273I
a = −1.72452 + 0.81856I
b = 0.490597 − 0.946124I
1.96250I 0. − 2.64993I
u = 0.490597 + 0.946124I
a = 1.019180 + 0.392510I
b = 0.007256 + 0.938273I
1.96250I 0. − 2.64993I
u = 0.490597 − 0.946124I
a = 1.019180 − 0.392510I
b = 0.007256 − 0.938273I
− 1.96250I 0. + 2.64993I
u = −0.882211 + 0.276225I
a = 1.16611 − 1.41086I
b = 0.151685 − 0.669452I
4.45586 + 1.91497I 9.84662 − 2.65327I
u = −0.882211 − 0.276225I
a = 1.16611 + 1.41086I
b = 0.151685 + 0.669452I
4.45586 − 1.91497I 9.84662 + 2.65327I
u = 0.248696 + 1.128430I
a = −1.51618 − 0.02715I
b = 1.351170 + 0.185322I
−4.45586 + 1.91497I −9.84662 − 2.65327I
u = 0.248696 − 1.128430I
a = −1.51618 + 0.02715I
b = 1.351170 − 0.185322I
−4.45586 − 1.91497I −9.84662 + 2.65327I
26
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.204788 + 0.730230I
a = −2.56341 − 0.14708I
b = 1.303390 + 0.199477I
−2.85825 − 60.341175 + 0.10I
u = 0.204788 − 0.730230I
a = −2.56341 + 0.14708I
b = 1.303390 − 0.199477I
−2.85825 − 60.341175 + 0.10I
u = −0.684168 + 1.040190I
a = −1.66598 − 0.01887I
b = 0.829883 + 0.933923I
5.78137 − 5.67225I 6.40075 + 0.51668I
u = −0.684168 − 1.040190I
a = −1.66598 + 0.01887I
b = 0.829883 − 0.933923I
5.78137 + 5.67225I 6.40075 − 0.51668I
u = 0.829883 + 0.933923I
a = 1.096860 + 0.567991I
b = −0.684168 + 1.040190I
−5.78137 + 5.67225I −6.40075 − 0.51668I
u = 0.829883 − 0.933923I
a = 1.096860 − 0.567991I
b = −0.684168 − 1.040190I
−5.78137 − 5.67225I −6.40075 + 0.51668I
u = 0.473731 + 1.205330I
a = 0.514258 + 0.262124I
b = −0.820724 − 0.538227I
−7.14238 + 0.08114I −7.67724 + 1.23653I
u = 0.473731 − 1.205330I
a = 0.514258 − 0.262124I
b = −0.820724 + 0.538227I
−7.14238 − 0.08114I −7.67724 − 1.23653I
u = 0.151685 + 0.669452I
a = 3.31404 − 0.12734I
b = −0.882211 − 0.276225I
−4.45586 + 1.91497I −9.84662 − 2.65327I
u = 0.151685 − 0.669452I
a = 3.31404 + 0.12734I
b = −0.882211 + 0.276225I
−4.45586 − 1.91497I −9.84662 + 2.65327I
27
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.303390 + 0.199477I
a = 0.326461 + 0.647740I
b = 0.204788 + 0.730230I
2.85825 0
u = 1.303390 − 0.199477I
a = 0.326461 − 0.647740I
b = 0.204788 − 0.730230I
2.85825 0
u = −0.483298 + 0.463379I
a = 2.88275 − 2.52294I
b = −0.483298 − 0.463379I
− 8.54028I 0. + 18.8239I
u = −0.483298 − 0.463379I
a = 2.88275 + 2.52294I
b = −0.483298 + 0.463379I
8.54028I 0. − 18.8239I
u = 1.351170 + 0.185322I
a = 0.174105 + 0.084819I
b = 0.248696 + 1.128430I
4.45586 − 1.91497I 9.84662 + 2.65327I
u = 1.351170 − 0.185322I
a = 0.174105 − 0.084819I
b = 0.248696 − 1.128430I
4.45586 + 1.91497I 9.84662 − 2.65327I
u = 0.29330 + 1.41288I
a = 0.283615 − 0.183655I
b = −0.499882 − 0.217642I
−7.14238 − 0.08114I −7.67724 + 0.I
u = 0.29330 − 1.41288I
a = 0.283615 + 0.183655I
b = −0.499882 + 0.217642I
−7.14238 + 0.08114I −7.67724 + 0.I
u = −0.499882 + 0.217642I
a = 0.536918 + 1.080480I
b = 0.29330 − 1.41288I
7.14238 − 0.08114I 7.67724 − 1.23653I
u = −0.499882 − 0.217642I
a = 0.536918 − 1.080480I
b = 0.29330 + 1.41288I
7.14238 + 0.08114I 7.67724 + 1.23653I
28
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.55869 + 1.38511I
a = −1.074710 + 0.371738I
b = 0.55869 − 1.38511I
8.54028I 0. − 18.8239I
u = 0.55869 − 1.38511I
a = −1.074710 − 0.371738I
b = 0.55869 + 1.38511I
− 8.54028I 0. + 18.8239I
u = −0.057431 + 0.371950I
a = 0.46776 − 2.06740I
b = 0.01453 + 1.70811I
5.78137 − 5.67225I 6.40075 + 0.51668I
u = −0.057431 − 0.371950I
a = 0.46776 + 2.06740I
b = 0.01453 − 1.70811I
5.78137 + 5.67225I 6.40075 − 0.51668I
u = 0.01453 + 1.70811I
a = −0.1176210 + 0.0610212I
b = −0.057431 + 0.371950I
−5.78137 + 5.67225I 0
u = 0.01453 − 1.70811I
a = −0.1176210 − 0.0610212I
b = −0.057431 − 0.371950I
−5.78137 − 5.67225I 0
29
IV. I
u
4
= hb + u − 1, a + 1, u
2
− u + 1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
6
=
1
u − 1
a
4
=
u
u − 1
a
11
=
−1
−u + 1
a
5
=
1
u − 1
a
12
=
−1
−u + 1
a
10
=
−u
−u + 1
a
8
=
0
−u
a
2
=
0
u
a
1
=
−1
0
a
9
=
0
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u + 4
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
c
12
u
2
− u + 1
c
2
, c
5
, c
8
c
11
u
2
c
3
, c
4
, c
9
c
10
u
2
+ u + 1
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
9
c
10
, c
12
y
2
+ y + 1
c
2
, c
5
, c
8
c
11
y
2
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −1.00000
b = 0.500000 − 0.866025I
4.05977I 0. − 6.92820I
u = 0.500000 − 0.866025I
a = −1.00000
b = 0.500000 + 0.866025I
− 4.05977I 0. + 6.92820I
33
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
2
− u + 1)(u
26
− u
25
+ ··· + 14u + 3)(u
36
− 5u
35
+ ··· + 3u + 1)
· (u
112
− 2u
111
+ ··· − 645u + 123)
c
2
, c
8
20736u
2
(4u
26
− 36u
25
+ ··· − 360u + 52)
· (64u
36
+ 848u
34
+ ··· + 672u
2
+ 49)
· (9u
56
+ 18u
55
+ ··· + 784u + 455)
2
c
3
, c
9
(u
2
+ u + 1)(u
26
+ u
25
+ ··· − 14u + 3)(u
36
+ 5u
35
+ ··· − 3u + 1)
· (u
112
+ 2u
111
+ ··· + 645u + 123)
c
4
, c
10
(u
2
+ u + 1)(u
26
− u
25
+ ··· + 14u + 3)(u
36
+ 5u
35
+ ··· − 3u + 1)
· (u
112
− 2u
111
+ ··· − 645u + 123)
c
5
, c
11
20736u
2
(4u
26
+ 36u
25
+ ··· + 360u + 52)
· (64u
36
+ 848u
34
+ ··· + 672u
2
+ 49)
· (9u
56
− 18u
55
+ ··· − 784u + 455)
2
c
6
, c
12
(u
2
− u + 1)(u
26
+ u
25
+ ··· − 14u + 3)(u
36
− 5u
35
+ ··· + 3u + 1)
· (u
112
+ 2u
111
+ ··· + 645u + 123)
34
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
9
c
10
, c
12
(y
2
+ y + 1)(y
26
+ 9y
25
+ ··· + 122y + 9)(y
36
+ 15y
35
+ ··· + 19y + 1)
· (y
112
+ 58y
111
+ ··· + 478431y + 15129)
c
2
, c
5
, c
8
c
11
429981696y
2
(64y
18
+ 848y
17
+ ··· + 672y + 49)
2
· (16y
26
+ 8y
25
+ ··· + 19952y + 2704)
· (81y
56
+ 3366y
55
+ ··· + 2666804y + 207025)
2
35
