12a
0868
(K12a
0868
)
A knot diagram
1
Linearized knot diagam
4 6 7 9 8 11 10 12 1 3 2 5
Solving Sequence
5,12 1,9
10 4 2 8 6 7 3 11
c
12
c
9
c
4
c
1
c
8
c
5
c
7
c
3
c
11
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.34907 × 10
25
u
25
− 1.80642 × 10
26
u
24
+ ··· + 7.92164 × 10
25
b + 4.11760 × 10
26
,
3.95167 × 10
23
u
25
+ 1.51546 × 10
24
u
24
+ ··· + 2.64055 × 10
25
a − 6.82923 × 10
25
, u
26
+ 3u
25
+ ··· − 15u + 3i
I
u
2
= h2.73334 × 10
2858
u
227
− 1.92123 × 10
2858
u
226
+ ··· + 4.27537 × 10
2861
b + 2.16549 × 10
2863
,
4.43607 × 10
2844
u
227
+ 8.55713 × 10
2844
u
226
+ ··· + 8.30905 × 10
2847
a + 4.47338 × 10
2849
,
u
228
− 2u
227
+ ··· − 120069u + 8487i
I
u
3
= h1.77876 × 10
199
u
59
− 4.11117 × 10
199
u
58
+ ··· + 4.10975 × 10
201
b − 1.03369 × 10
201
,
− 1.12963 × 10
195
u
59
+ 3.04187 × 10
195
u
58
+ ··· + 3.32182 × 10
196
a + 1.29221 × 10
197
,
u
60
− 3u
59
+ ··· − 405u + 81i
I
u
4
= h−u
5
− 3u
4
− 4u
3
− 3u
2
+ b − u − 1, −u
4
− 2u
3
− 3u
2
+ a − 2u − 1, u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 320 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
= h−5.35 × 10
25
u
25
− 1.81 × 10
26
u
24
+ · · · + 7.92 × 10
25
b + 4.12 ×
10
26
, 3.95 × 10
23
u
25
+ 1.52 × 10
24
u
24
+ · · · + 2.64 × 10
25
a − 6.83 ×
10
25
, u
26
+ 3u
25
+ · · · − 15u + 3i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
9
=
−0.0149653u
25
− 0.0573920u
24
+ ··· − 5.13455u + 2.58629
0.675248u
25
+ 2.28036u
24
+ ··· + 14.2808u − 5.19791
a
10
=
−0.632801u
25
− 2.22531u
24
+ ··· − 19.2728u + 7.74671
0.825829u
25
+ 2.74001u
24
+ ··· + 17.1435u − 6.14114
a
4
=
−0.674011u
25
− 2.06149u
24
+ ··· − 0.724059u + 0.371443
0.0748759u
25
+ 0.392514u
24
+ ··· + 2.78632u − 1.21956
a
2
=
−0.757263u
25
− 2.08651u
24
+ ··· − 10.3107u + 2.23996
0.267117u
25
+ 0.978083u
24
+ ··· + 2.56900u − 2.07064
a
8
=
−0.690213u
25
− 2.33776u
24
+ ··· − 19.4154u + 7.78420
0.675248u
25
+ 2.28036u
24
+ ··· + 14.2808u − 5.19791
a
6
=
−0.851189u
25
− 2.96069u
24
+ ··· − 6.06101u + 2.28294
0.102302u
25
+ 0.506686u
24
+ ··· + 4.55063u − 0.691938
a
7
=
−0.424070u
25
− 1.10116u
24
+ ··· − 17.7829u + 3.92612
0.166509u
25
+ 0.680241u
24
+ ··· + 0.997296u + 0.529442
a
3
=
0.815413u
25
+ 2.85812u
24
+ ··· + 23.5628u − 11.7902
−1.40196u
25
− 4.61527u
24
+ ··· − 26.5088u + 11.0509
a
11
=
−0.547726u
25
− 1.21606u
24
+ ··· + 8.21515u − 3.50603
−0.407127u
25
− 1.15717u
24
+ ··· − 10.4849u + 2.55357
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1260977761418218210095504584
237649321085197816953007317
u
25
+
1395857718298382707824957472
79216440361732605651002439
u
24
+
··· +
36059835826067669335416717074
237649321085197816953007317
u −
4085664600030892994473000376
79216440361732605651002439
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
26
− u
25
+ ··· + 21u + 7
c
2
, c
8
3(3u
26
− 3u
25
+ ··· − u + 1)
c
3
, c
9
3(3u
26
+ 3u
25
+ ··· + u + 1)
c
4
, c
10
u
26
+ 3u
25
+ ··· − 15u + 3
c
5
, c
11
u
26
+ u
25
+ ··· − 21u + 7
c
6
, c
12
u
26
− 3u
25
+ ··· + 15u + 3
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
11
y
26
+ 15y
25
+ ··· + 777y + 49
c
2
, c
3
, c
8
c
9
9(9y
26
+ 123y
25
+ ··· − 3y + 1)
c
4
, c
6
, c
10
c
12
y
26
+ 3y
25
+ ··· − 39y + 9
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.845489 + 0.535083I
a = 0.02844 + 1.51551I
b = 0.335856 + 0.179407I
3.75175 + 7.29916I 7.10463 − 6.60908I
u = 0.845489 − 0.535083I
a = 0.02844 − 1.51551I
b = 0.335856 − 0.179407I
3.75175 − 7.29916I 7.10463 + 6.60908I
u = −0.412083 + 0.907598I
a = −1.229110 + 0.268720I
b = −0.327018 − 0.255373I
−1.031450 − 0.731362I −5.81274 + 5.12436I
u = −0.412083 − 0.907598I
a = −1.229110 − 0.268720I
b = −0.327018 + 0.255373I
−1.031450 + 0.731362I −5.81274 − 5.12436I
u = 0.815740 + 0.766504I
a = 0.037856 + 1.304310I
b = 0.95346 + 1.24193I
3.90122 + 10.59870I 3.57222 − 11.00535I
u = 0.815740 − 0.766504I
a = 0.037856 − 1.304310I
b = 0.95346 − 1.24193I
3.90122 − 10.59870I 3.57222 + 11.00535I
u = 0.262607 + 1.226280I
a = −0.776479 + 0.169761I
b = −0.677732 + 0.488296I
1.031450 − 0.731362I 5.81274 + 5.12436I
u = 0.262607 − 1.226280I
a = −0.776479 − 0.169761I
b = −0.677732 − 0.488296I
1.031450 + 0.731362I 5.81274 − 5.12436I
u = 0.483028 + 0.515672I
a = −0.11814 − 2.27233I
b = −0.207260 − 0.904960I
1.45995 + 7.35605I −7.17269 − 6.50998I
u = 0.483028 − 0.515672I
a = −0.11814 + 2.27233I
b = −0.207260 + 0.904960I
1.45995 − 7.35605I −7.17269 + 6.50998I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.167410 + 0.663095I
a = 1.65128 + 2.17905I
b = −0.329021 + 0.860688I
−2.74535 − 5.73210I −12.7377 + 11.1594I
u = −0.167410 − 0.663095I
a = 1.65128 − 2.17905I
b = −0.329021 − 0.860688I
−2.74535 + 5.73210I −12.7377 − 11.1594I
u = −0.291479 + 0.576161I
a = −0.592442 + 0.805613I
b = −0.208461 + 0.489857I
− 1.28045I 0. + 5.59729I
u = −0.291479 − 0.576161I
a = −0.592442 − 0.805613I
b = −0.208461 − 0.489857I
1.28045I 0. − 5.59729I
u = −0.96888 + 1.09299I
a = 0.022234 − 0.766044I
b = 0.67467 − 1.39088I
−3.90122 − 10.59870I −3.57222 + 11.00535I
u = −0.96888 − 1.09299I
a = 0.022234 + 0.766044I
b = 0.67467 + 1.39088I
−3.90122 + 10.59870I −3.57222 − 11.00535I
u = −0.78688 + 1.29657I
a = 0.012380 − 0.659611I
b = 1.023210 − 0.854597I
−3.75175 − 7.29916I −7.10463 + 6.60908I
u = −0.78688 − 1.29657I
a = 0.012380 + 0.659611I
b = 1.023210 + 0.854597I
−3.75175 + 7.29916I −7.10463 − 6.60908I
u = −1.03954 + 1.20307I
a = −0.145069 + 0.989422I
b = −1.26401 + 1.10023I
− 23.4387I 0. + 11.88508I
u = −1.03954 − 1.20307I
a = −0.145069 − 0.989422I
b = −1.26401 − 1.10023I
23.4387I 0. − 11.88508I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.11471 + 1.15852I
a = −0.022818 − 0.438890I
b = −0.928596 − 0.889733I
−1.45995 + 7.35605I 7.17269 − 6.50998I
u = 1.11471 − 1.15852I
a = −0.022818 + 0.438890I
b = −0.928596 + 0.889733I
−1.45995 − 7.35605I 7.17269 + 6.50998I
u = 0.366048 + 0.079011I
a = 0.910967 − 0.412479I
b = −0.07012 + 2.08604I
− 3.95888I 0. + 19.3379I
u = 0.366048 − 0.079011I
a = 0.910967 + 0.412479I
b = −0.07012 − 2.08604I
3.95888I 0. − 19.3379I
u = −1.72136 + 0.73016I
a = 0.220907 − 0.291513I
b = 0.525012 + 0.402973I
2.74535 + 5.73210I 12.7377 − 11.1594I
u = −1.72136 − 0.73016I
a = 0.220907 + 0.291513I
b = 0.525012 − 0.402973I
2.74535 − 5.73210I 12.7377 + 11.1594I
7
II. I
u
2
= h2.73 × 10
2858
u
227
− 1.92 × 10
2858
u
226
+ · · · + 4.28 × 10
2861
b + 2.17 ×
10
2863
, 4.44 × 10
2844
u
227
+ 8.56 × 10
2844
u
226
+ · · · + 8.31 × 10
2847
a + 4.47 ×
10
2849
, u
228
− 2u
227
+ · · · − 120069u + 8487i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
9
=
−0.000533884u
227
− 0.00102986u
226
+ ··· + 509.800u − 53.8374
−0.000639322u
227
+ 0.000449372u
226
+ ··· + 665.496u − 50.6504
a
10
=
0.000973408u
227
− 0.00355423u
226
+ ··· + 91.6330u − 20.9896
−0.000312050u
227
− 0.0000481389u
226
+ ··· + 619.429u − 46.4900
a
4
=
−0.00260219u
227
+ 0.00541797u
226
+ ··· − 591.763u + 39.6752
−0.000294906u
227
− 0.000314458u
226
+ ··· + 350.080u − 26.3569
a
2
=
0.00943454u
227
− 0.0189153u
226
+ ··· + 1354.50u − 84.5624
0.00101777u
227
− 0.00171219u
226
+ ··· − 78.1751u + 8.76891
a
8
=
0.000105438u
227
− 0.00147923u
226
+ ··· − 155.696u − 3.18704
−0.000639322u
227
+ 0.000449372u
226
+ ··· + 665.496u − 50.6504
a
6
=
−0.00317145u
227
+ 0.00769773u
226
+ ··· − 1569.89u + 108.053
0.000864162u
227
− 0.00196531u
226
+ ··· + 630.046u − 42.0209
a
7
=
−0.00844623u
227
+ 0.0132865u
226
+ ··· + 77.7048u − 39.3309
0.000578702u
227
− 0.00216850u
226
+ ··· + 752.583u − 48.3559
a
3
=
0.00876827u
227
− 0.0152721u
226
+ ··· − 650.077u + 79.1653
−0.00279035u
227
+ 0.00568240u
226
+ ··· − 389.402u + 6.90679
a
11
=
0.00684100u
227
− 0.0134311u
226
+ ··· + 611.474u − 13.4745
0.00135278u
227
− 0.00106211u
226
+ ··· − 388.490u + 29.0289
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00480003u
227
− 0.00745917u
226
+ ··· − 106.584u − 13.9909
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
228
+ 8u
227
+ ··· − 11192067647u + 984049733
c
2
, c
8
9(9u
228
− 54u
227
+ ··· − 9395u + 1619)
c
3
, c
9
9(9u
228
+ 54u
227
+ ··· + 9395u + 1619)
c
4
, c
10
u
228
− 2u
227
+ ··· − 120069u + 8487
c
5
, c
11
u
228
− 8u
227
+ ··· + 11192067647u + 984049733
c
6
, c
12
u
228
+ 2u
227
+ ··· + 120069u + 8487
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
11
y
228
+ 20y
227
+ ··· + 4.78 × 10
19
y + 9.68 × 10
17
c
2
, c
3
, c
8
c
9
81(81y
228
+ 2052y
227
+ ··· + 8.92055 × 10
7
y + 2621161)
c
4
, c
6
, c
10
c
12
y
228
+ 12y
227
+ ··· + 6749419149y + 72029169
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.472631 + 0.876801I
a = −0.270968 + 1.060490I
b = 0.104155 + 1.397710I
−0.17902 − 4.15433I 0
u = −0.472631 − 0.876801I
a = −0.270968 − 1.060490I
b = 0.104155 − 1.397710I
−0.17902 + 4.15433I 0
u = 0.700933 + 0.696420I
a = 0.16116 − 1.40722I
b = −1.09140 − 1.19241I
2.61654 + 5.18045I 0
u = 0.700933 − 0.696420I
a = 0.16116 + 1.40722I
b = −1.09140 + 1.19241I
2.61654 − 5.18045I 0
u = −0.887697 + 0.424622I
a = −0.244267 + 0.750770I
b = −1.07432 + 1.25389I
0.71894 − 5.15211I 0
u = −0.887697 − 0.424622I
a = −0.244267 − 0.750770I
b = −1.07432 − 1.25389I
0.71894 + 5.15211I 0
u = 0.614351 + 0.767456I
a = −0.14177 − 1.76236I
b = −0.91137 − 1.10218I
1.72572 + 7.49064I 0
u = 0.614351 − 0.767456I
a = −0.14177 + 1.76236I
b = −0.91137 + 1.10218I
1.72572 − 7.49064I 0
u = 0.405452 + 0.887384I
a = 0.458615 − 0.144400I
b = 1.196280 − 0.210695I
−1.17272 − 3.22672I 0
u = 0.405452 − 0.887384I
a = 0.458615 + 0.144400I
b = 1.196280 + 0.210695I
−1.17272 + 3.22672I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.437652 + 0.926858I
a = −0.111817 − 0.254381I
b = −1.227690 − 0.425841I
−2.15015 − 8.23570I 0
u = −0.437652 − 0.926858I
a = −0.111817 + 0.254381I
b = −1.227690 + 0.425841I
−2.15015 + 8.23570I 0
u = −0.563747 + 0.865746I
a = −0.47100 + 1.56851I
b = −1.12449 + 1.24533I
2.77141 − 2.42490I 0
u = −0.563747 − 0.865746I
a = −0.47100 − 1.56851I
b = −1.12449 − 1.24533I
2.77141 + 2.42490I 0
u = 0.303668 + 0.909247I
a = −0.144875 + 0.536056I
b = 0.974296 + 0.848762I
−4.07623 − 0.75664I 0
u = 0.303668 − 0.909247I
a = −0.144875 − 0.536056I
b = 0.974296 − 0.848762I
−4.07623 + 0.75664I 0
u = 0.808370 + 0.673531I
a = 0.09053 + 1.41138I
b = 1.255900 + 0.646328I
4.14980 − 4.96562I 0
u = 0.808370 − 0.673531I
a = 0.09053 − 1.41138I
b = 1.255900 − 0.646328I
4.14980 + 4.96562I 0
u = −0.025731 + 0.947303I
a = −1.56751 − 0.39571I
b = −0.208138 − 0.172320I
−2.91798 + 1.45918I 0
u = −0.025731 − 0.947303I
a = −1.56751 + 0.39571I
b = −0.208138 + 0.172320I
−2.91798 − 1.45918I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.948463 + 0.456251I
a = −0.176635 − 1.187010I
b = 0.574232 − 0.241509I
4.07623 − 0.75664I 0
u = −0.948463 − 0.456251I
a = −0.176635 + 1.187010I
b = 0.574232 + 0.241509I
4.07623 + 0.75664I 0
u = −0.077732 + 0.942885I
a = −0.966354 + 0.671156I
b = 0.018451 + 0.708666I
−1.53101 − 2.78696I 0
u = −0.077732 − 0.942885I
a = −0.966354 − 0.671156I
b = 0.018451 − 0.708666I
−1.53101 + 2.78696I 0
u = 0.903835 + 0.275047I
a = 0.021923 − 0.746122I
b = −1.054210 − 0.744065I
4.18899 + 2.61263I 0
u = 0.903835 − 0.275047I
a = 0.021923 + 0.746122I
b = −1.054210 + 0.744065I
4.18899 − 2.61263I 0
u = 0.308872 + 0.865220I
a = −0.889294 + 0.058440I
b = −0.991086 + 0.494295I
1.17272 − 3.22672I 0
u = 0.308872 − 0.865220I
a = −0.889294 − 0.058440I
b = −0.991086 − 0.494295I
1.17272 + 3.22672I 0
u = 0.626212 + 0.671141I
a = 1.298530 + 0.548758I
b = −0.051458 − 0.690948I
−2.61654 + 5.18045I 0
u = 0.626212 − 0.671141I
a = 1.298530 − 0.548758I
b = −0.051458 + 0.690948I
−2.61654 − 5.18045I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.801773 + 0.738807I
a = −0.226171 + 0.885169I
b = −1.13088 + 1.04390I
0.17902 − 4.15433I 0
u = −0.801773 − 0.738807I
a = −0.226171 − 0.885169I
b = −1.13088 − 1.04390I
0.17902 + 4.15433I 0
u = −0.698841 + 0.580141I
a = −0.083419 − 1.356350I
b = 0.402780 − 1.316530I
3.12185 0
u = −0.698841 − 0.580141I
a = −0.083419 + 1.356350I
b = 0.402780 + 1.316530I
3.12185 0
u = 0.819062 + 0.385256I
a = 0.147418 + 0.730746I
b = 1.32930 + 1.44019I
1.35038 + 13.87800I 0
u = 0.819062 − 0.385256I
a = 0.147418 − 0.730746I
b = 1.32930 − 1.44019I
1.35038 − 13.87800I 0
u = 0.803943 + 0.408919I
a = −0.073299 − 0.595618I
b = −1.33268 − 1.32831I
2.04342 + 5.79434I 0
u = 0.803943 − 0.408919I
a = −0.073299 + 0.595618I
b = −1.33268 + 1.32831I
2.04342 − 5.79434I 0
u = −0.557707 + 0.963331I
a = −0.698086 + 0.484838I
b = −0.970114 + 0.257695I
1.53101 − 2.78696I 0
u = −0.557707 − 0.963331I
a = −0.698086 − 0.484838I
b = −0.970114 − 0.257695I
1.53101 + 2.78696I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.108000 + 0.112943I
a = −1.153980 + 0.300686I
b = 0.618423 − 0.131290I
2.60879 + 0.44068I 0
u = −1.108000 − 0.112943I
a = −1.153980 − 0.300686I
b = 0.618423 + 0.131290I
2.60879 − 0.44068I 0
u = −0.746845 + 0.835267I
a = −0.314149 + 1.255640I
b = −1.055150 + 0.906055I
1.87947 − 2.48342I 0
u = −0.746845 − 0.835267I
a = −0.314149 − 1.255640I
b = −1.055150 − 0.906055I
1.87947 + 2.48342I 0
u = 0.518135 + 0.704618I
a = 0.78564 − 1.43143I
b = −0.739334 − 1.016840I
−0.60074 + 2.45623I 0
u = 0.518135 − 0.704618I
a = 0.78564 + 1.43143I
b = −0.739334 + 1.016840I
−0.60074 − 2.45623I 0
u = 0.834142 + 0.776731I
a = −0.05376 − 1.42955I
b = −1.42961 − 0.52630I
4.82565 + 3.73868I 0
u = 0.834142 − 0.776731I
a = −0.05376 + 1.42955I
b = −1.42961 + 0.52630I
4.82565 − 3.73868I 0
u = −0.067870 + 1.141420I
a = 1.093080 − 0.538926I
b = 0.257586 − 0.486612I
−2.38963 − 10.26740I 0
u = −0.067870 − 1.141420I
a = 1.093080 + 0.538926I
b = 0.257586 + 0.486612I
−2.38963 + 10.26740I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.968849 + 0.621161I
a = 0.233354 − 1.368620I
b = −1.235180 − 0.223540I
4.85343 + 3.93548I 0
u = 0.968849 − 0.621161I
a = 0.233354 + 1.368620I
b = −1.235180 + 0.223540I
4.85343 − 3.93548I 0
u = 0.058371 + 1.151600I
a = −0.994776 − 0.435515I
b = −1.350760 − 0.323809I
2.60879 − 0.44068I 0
u = 0.058371 − 1.151600I
a = −0.994776 + 0.435515I
b = −1.350760 + 0.323809I
2.60879 + 0.44068I 0
u = −1.041020 + 0.520143I
a = 0.46904 + 1.34296I
b = −0.997382 + 0.195084I
3.12392 − 13.47560I 0
u = −1.041020 − 0.520143I
a = 0.46904 − 1.34296I
b = −0.997382 − 0.195084I
3.12392 + 13.47560I 0
u = −0.228041 + 0.804162I
a = 0.49599 + 1.58544I
b = −0.742664 + 0.931101I
0.00371 − 6.56432I 0
u = −0.228041 − 0.804162I
a = 0.49599 − 1.58544I
b = −0.742664 − 0.931101I
0.00371 + 6.56432I 0
u = −0.325241 + 0.751385I
a = −1.119650 + 0.073578I
b = 0.441430 − 0.019191I
−1.17272 − 3.22672I 0
u = −0.325241 − 0.751385I
a = −1.119650 − 0.073578I
b = 0.441430 + 0.019191I
−1.17272 + 3.22672I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.651445 + 0.464860I
a = −0.23568 + 2.32218I
b = 0.545026 + 0.283692I
0.00371 + 6.56432I 0
u = 0.651445 − 0.464860I
a = −0.23568 − 2.32218I
b = 0.545026 − 0.283692I
0.00371 − 6.56432I 0
u = 0.345017 + 0.721530I
a = 0.000148 − 0.490667I
b = 1.068660 − 0.225560I
−3.83972 − 0.00597I 0
u = 0.345017 − 0.721530I
a = 0.000148 + 0.490667I
b = 1.068660 + 0.225560I
−3.83972 + 0.00597I 0
u = 0.256364 + 0.746911I
a = 0.11222 + 1.81000I
b = 0.161700 + 0.852665I
−3.83972 + 0.00597I 0
u = 0.256364 − 0.746911I
a = 0.11222 − 1.81000I
b = 0.161700 − 0.852665I
−3.83972 − 0.00597I 0
u = 1.212950 + 0.055932I
a = 0.108097 + 0.606132I
b = 0.545998 + 0.782799I
5.53095 − 4.51811I 0
u = 1.212950 − 0.055932I
a = 0.108097 − 0.606132I
b = 0.545998 − 0.782799I
5.53095 + 4.51811I 0
u = −0.101959 + 0.770178I
a = −0.391879 + 1.204470I
b = 0.65678 + 1.89428I
−0.71894 − 5.15211I 0
u = −0.101959 − 0.770178I
a = −0.391879 − 1.204470I
b = 0.65678 − 1.89428I
−0.71894 + 5.15211I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.310814 + 0.708120I
a = −1.85423 − 1.06698I
b = 0.261803 − 0.692954I
−2.04342 − 5.79434I 0
u = −0.310814 − 0.708120I
a = −1.85423 + 1.06698I
b = 0.261803 + 0.692954I
−2.04342 + 5.79434I 0
u = 0.845172 + 0.899480I
a = −0.045173 + 0.734493I
b = 0.70969 + 1.45480I
−3.12185 0
u = 0.845172 − 0.899480I
a = −0.045173 − 0.734493I
b = 0.70969 − 1.45480I
−3.12185 0
u = 0.063660 + 0.759691I
a = 0.69239 − 2.18408I
b = −0.12076 − 1.51380I
−5.33805 + 4.64735I 0
u = 0.063660 − 0.759691I
a = 0.69239 + 2.18408I
b = −0.12076 + 1.51380I
−5.33805 − 4.64735I 0
u = 0.443471 + 1.171000I
a = −0.843565 − 0.369314I
b = −0.0236436 + 0.1185380I
−2.60879 − 0.44068I 0
u = 0.443471 − 1.171000I
a = −0.843565 + 0.369314I
b = −0.0236436 − 0.1185380I
−2.60879 + 0.44068I 0
u = 0.097214 + 0.741255I
a = 0.28515 − 1.59895I
b = −0.62245 − 1.68734I
−5.53095 + 4.51811I 0
u = 0.097214 − 0.741255I
a = 0.28515 + 1.59895I
b = −0.62245 + 1.68734I
−5.53095 − 4.51811I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.709105 + 1.045240I
a = −0.122648 + 0.824205I
b = 0.575220 + 0.909352I
−4.07623 + 0.75664I 0
u = 0.709105 − 1.045240I
a = −0.122648 − 0.824205I
b = 0.575220 − 0.909352I
−4.07623 − 0.75664I 0
u = 0.181283 + 0.709561I
a = 1.33655 + 1.70911I
b = 0.104052 + 0.466709I
−4.18899 + 2.61263I 0
u = 0.181283 − 0.709561I
a = 1.33655 − 1.70911I
b = 0.104052 − 0.466709I
−4.18899 − 2.61263I 0
u = 0.378988 + 0.611519I
a = 2.06491 − 1.07749I
b = −0.579564 − 0.939308I
6.42431I 0
u = 0.378988 − 0.611519I
a = 2.06491 + 1.07749I
b = −0.579564 + 0.939308I
− 6.42431I 0
u = 0.327824 + 0.629608I
a = −2.24418 + 1.40919I
b = 0.487100 + 0.895188I
−1.1515 + 14.6381I 0
u = 0.327824 − 0.629608I
a = −2.24418 − 1.40919I
b = 0.487100 − 0.895188I
−1.1515 − 14.6381I 0
u = −0.708349 + 0.012911I
a = 0.105577 − 0.805741I
b = 0.77099 − 2.01412I
− 3.40915I 0
u = −0.708349 − 0.012911I
a = 0.105577 + 0.805741I
b = 0.77099 + 2.01412I
3.40915I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.444863 + 1.215140I
a = 0.653408 − 0.276129I
b = 0.588408 − 0.368551I
2.61654 − 5.18045I 0
u = 0.444863 − 1.215140I
a = 0.653408 + 0.276129I
b = 0.588408 + 0.368551I
2.61654 + 5.18045I 0
u = 0.225033 + 0.668341I
a = 0.039346 − 1.339110I
b = 0.66699 − 1.28624I
−4.18899 + 2.61263I 0
u = 0.225033 − 0.668341I
a = 0.039346 + 1.339110I
b = 0.66699 + 1.28624I
−4.18899 − 2.61263I 0
u = −1.099790 + 0.685941I
a = 0.439880 + 0.898056I
b = −0.840026 + 0.161775I
2.94328I 0
u = −1.099790 − 0.685941I
a = 0.439880 − 0.898056I
b = −0.840026 − 0.161775I
− 2.94328I 0
u = −1.017870 + 0.802700I
a = −0.003911 − 1.128620I
b = 1.261700 − 0.468281I
5.53095 − 4.51811I 0
u = −1.017870 − 0.802700I
a = −0.003911 + 1.128620I
b = 1.261700 + 0.468281I
5.53095 + 4.51811I 0
u = 1.079760 + 0.720570I
a = 0.311109 + 0.138789I
b = 0.725983 − 0.258704I
−1.53101 − 2.78696I 0
u = 1.079760 − 0.720570I
a = 0.311109 − 0.138789I
b = 0.725983 + 0.258704I
−1.53101 + 2.78696I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.116331 + 1.311190I
a = 0.187972 + 0.069699I
b = 1.210540 + 0.473338I
0.60074 − 2.45623I 0
u = 0.116331 − 1.311190I
a = 0.187972 − 0.069699I
b = 1.210540 − 0.473338I
0.60074 + 2.45623I 0
u = 0.780577 + 1.063120I
a = 0.278422 + 1.152030I
b = 0.878367 + 1.008520I
−2.15015 + 8.23570I 0
u = 0.780577 − 1.063120I
a = 0.278422 − 1.152030I
b = 0.878367 − 1.008520I
−2.15015 − 8.23570I 0
u = −0.160779 + 0.655320I
a = 0.265273 − 1.314950I
b = −0.94515 − 1.91500I
−1.35038 − 13.87800I 0
u = −0.160779 − 0.655320I
a = 0.265273 + 1.314950I
b = −0.94515 + 1.91500I
−1.35038 + 13.87800I 0
u = 1.244640 + 0.463493I
a = −0.811474 + 0.211442I
b = 0.708285 + 0.522831I
−2.60879 + 0.44068I 0
u = 1.244640 − 0.463493I
a = −0.811474 − 0.211442I
b = 0.708285 − 0.522831I
−2.60879 − 0.44068I 0
u = 0.097447 + 0.653506I
a = −0.68614 + 2.07705I
b = 0.47400 + 1.75742I
−4.85343 − 3.93548I 0
u = 0.097447 − 0.653506I
a = −0.68614 − 2.07705I
b = 0.47400 − 1.75742I
−4.85343 + 3.93548I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.159960 + 0.701632I
a = −0.187181 − 1.052110I
b = 1.199210 − 0.163349I
5.33805 − 4.64735I 0
u = −1.159960 − 0.701632I
a = −0.187181 + 1.052110I
b = 1.199210 + 0.163349I
5.33805 + 4.64735I 0
u = −1.388060 + 0.037314I
a = 0.179732 − 0.574511I
b = 0.456136 + 0.193633I
−0.00371 + 6.56432I 0
u = −1.388060 − 0.037314I
a = 0.179732 + 0.574511I
b = 0.456136 − 0.193633I
−0.00371 − 6.56432I 0
u = 0.540951 + 1.284230I
a = 0.735951 + 0.362851I
b = 1.244970 − 0.043677I
2.38963 + 10.26740I 0
u = 0.540951 − 1.284230I
a = 0.735951 − 0.362851I
b = 1.244970 + 0.043677I
2.38963 − 10.26740I 0
u = 1.092980 + 0.874135I
a = 0.080327 − 0.701422I
b = −0.283472 − 1.043950I
−2.61654 + 5.18045I 0
u = 1.092980 − 0.874135I
a = 0.080327 + 0.701422I
b = −0.283472 + 1.043950I
−2.61654 − 5.18045I 0
u = 0.069902 + 0.594546I
a = −1.68174 + 2.77788I
b = 0.031018 + 1.351510I
−4.82565 − 3.73868I 0
u = 0.069902 − 0.594546I
a = −1.68174 − 2.77788I
b = 0.031018 − 1.351510I
−4.82565 + 3.73868I 0
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.596105 + 0.027599I
a = 2.46432 + 2.26971I
b = −0.206906 − 0.045241I
2.77141 + 2.42490I 0
u = −0.596105 − 0.027599I
a = 2.46432 − 2.26971I
b = −0.206906 + 0.045241I
2.77141 − 2.42490I 0
u = −0.358464 + 0.460113I
a = −3.28279 − 0.91764I
b = 0.281771 − 0.832596I
0.71894 − 5.15211I 0
u = −0.358464 − 0.460113I
a = −3.28279 + 0.91764I
b = 0.281771 + 0.832596I
0.71894 + 5.15211I 0
u = −0.064383 + 0.572109I
a = 0.159877 + 1.220150I
b = −0.80921 + 2.42021I
3.40915I 0
u = −0.064383 − 0.572109I
a = 0.159877 − 1.220150I
b = −0.80921 − 2.42021I
− 3.40915I 0
u = 1.41568 + 0.18810I
a = 0.294665 − 0.536877I
b = −0.126713 − 0.116788I
0.60074 + 2.45623I 0
u = 1.41568 − 0.18810I
a = 0.294665 + 0.536877I
b = −0.126713 + 0.116788I
0.60074 − 2.45623I 0
u = −1.32314 + 0.54784I
a = 0.034124 − 0.550370I
b = 0.586694 − 0.004843I
3.83972 − 0.00597I 0
u = −1.32314 − 0.54784I
a = 0.034124 + 0.550370I
b = 0.586694 + 0.004843I
3.83972 + 0.00597I 0
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.77688 + 1.20866I
a = 0.357204 − 1.071890I
b = 1.24406 − 1.13957I
−3.12392 − 13.47560I 0
u = −0.77688 − 1.20866I
a = 0.357204 + 1.071890I
b = 1.24406 + 1.13957I
−3.12392 + 13.47560I 0
u = 0.108511 + 0.546898I
a = −1.03168 + 2.62206I
b = 0.411387 + 0.469854I
1.87947 − 2.48342I 0
u = 0.108511 − 0.546898I
a = −1.03168 − 2.62206I
b = 0.411387 − 0.469854I
1.87947 + 2.48342I 0
u = −1.42422 + 0.24599I
a = −0.143396 + 0.434083I
b = −0.495974 + 0.802711I
4.85343 − 3.93548I 0
u = −1.42422 − 0.24599I
a = −0.143396 − 0.434083I
b = −0.495974 − 0.802711I
4.85343 + 3.93548I 0
u = −0.85503 + 1.16703I
a = −0.188598 + 1.032490I
b = −1.21317 + 1.16017I
−4.14980 − 4.96562I 0
u = −0.85503 − 1.16703I
a = −0.188598 − 1.032490I
b = −1.21317 − 1.16017I
−4.14980 + 4.96562I 0
u = 0.95532 + 1.08907I
a = −0.163910 + 0.921310I
b = 0.673038 + 0.756340I
−5.33805 + 4.64735I 0
u = 0.95532 − 1.08907I
a = −0.163910 − 0.921310I
b = 0.673038 − 0.756340I
−5.33805 − 4.64735I 0
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.81417 + 1.20017I
a = −0.187515 + 0.749492I
b = −0.555370 + 1.122340I
−1.87947 − 2.48342I 0
u = −0.81417 − 1.20017I
a = −0.187515 − 0.749492I
b = −0.555370 − 1.122340I
−1.87947 + 2.48342I 0
u = 0.184631 + 0.508816I
a = −0.20353 − 1.65388I
b = 0.97618 − 1.66187I
−2.04342 + 5.79434I 0
u = 0.184631 − 0.508816I
a = −0.20353 + 1.65388I
b = 0.97618 + 1.66187I
−2.04342 − 5.79434I 0
u = 0.68904 + 1.28903I
a = −0.555528 − 0.831498I
b = −1.068190 − 0.685978I
2.94328I 0
u = 0.68904 − 1.28903I
a = −0.555528 + 0.831498I
b = −1.068190 + 0.685978I
− 2.94328I 0
u = 0.90992 + 1.14564I
a = −0.003071 + 0.886030I
b = 0.584092 + 0.904002I
−5.53095 + 4.51811I 0
u = 0.90992 − 1.14564I
a = −0.003071 − 0.886030I
b = 0.584092 − 0.904002I
−5.53095 − 4.51811I 0
u = −0.531402 + 0.031056I
a = −0.46985 − 1.73849I
b = −0.784689 − 0.375017I
4.07623 + 0.75664I 7.36157 + 0.I
u = −0.531402 − 0.031056I
a = −0.46985 + 1.73849I
b = −0.784689 + 0.375017I
4.07623 − 0.75664I 7.36157 + 0.I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.96347 + 1.11269I
a = 0.095107 + 1.050690I
b = 1.22950 + 0.89397I
−2.38963 + 10.26740I 0
u = 0.96347 − 1.11269I
a = 0.095107 − 1.050690I
b = 1.22950 − 0.89397I
−2.38963 − 10.26740I 0
u = −0.87743 + 1.20189I
a = 0.045260 − 0.705623I
b = 0.262897 − 1.026930I
−4.14980 + 4.96562I 0
u = −0.87743 − 1.20189I
a = 0.045260 + 0.705623I
b = 0.262897 + 1.026930I
−4.14980 − 4.96562I 0
u = 1.00515 + 1.11771I
a = −0.101534 − 1.031100I
b = −1.28987 − 1.17149I
1.35038 + 13.87800I 0
u = 1.00515 − 1.11771I
a = −0.101534 + 1.031100I
b = −1.28987 + 1.17149I
1.35038 − 13.87800I 0
u = −1.04370 + 1.10291I
a = −0.171202 + 0.937257I
b = −0.966352 + 0.885152I
4.14980 − 4.96562I 0
u = −1.04370 − 1.10291I
a = −0.171202 − 0.937257I
b = −0.966352 − 0.885152I
4.14980 + 4.96562I 0
u = 0.99001 + 1.16493I
a = 0.179032 + 1.037710I
b = 1.16803 + 1.06035I
−1.1515 + 14.6381I 0
u = 0.99001 − 1.16493I
a = 0.179032 − 1.037710I
b = 1.16803 − 1.06035I
−1.1515 − 14.6381I 0
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.314085 + 0.348420I
a = 1.98381 + 0.62462I
b = −1.014450 − 0.209286I
1.17272 + 3.22672I 6.75579 − 2.71059I
u = 0.314085 − 0.348420I
a = 1.98381 − 0.62462I
b = −1.014450 + 0.209286I
1.17272 − 3.22672I 6.75579 + 2.71059I
u = −0.250133 + 0.395887I
a = −0.530623 + 0.340491I
b = −1.57928 + 2.14816I
0.0421355 9.08507 + 0.I
u = −0.250133 − 0.395887I
a = −0.530623 − 0.340491I
b = −1.57928 − 2.14816I
0.0421355 9.08507 + 0.I
u = 0.41519 + 1.47473I
a = −0.599734 − 0.151400I
b = −1.178190 + 0.258939I
2.91798 + 1.45918I 0
u = 0.41519 − 1.47473I
a = −0.599734 + 0.151400I
b = −1.178190 − 0.258939I
2.91798 − 1.45918I 0
u = −0.185218 + 0.426857I
a = 3.90176 − 1.20430I
b = 0.196243 + 0.404075I
0.17902 + 4.15433I −11.17322 + 2.41881I
u = −0.185218 − 0.426857I
a = 3.90176 + 1.20430I
b = 0.196243 − 0.404075I
0.17902 − 4.15433I −11.17322 − 2.41881I
u = 0.319845 + 0.318752I
a = −1.70345 − 3.32209I
b = 0.433928 − 0.312556I
1.72572 + 7.49064I 7.19657 − 0.61552I
u = 0.319845 − 0.318752I
a = −1.70345 + 3.32209I
b = 0.433928 + 0.312556I
1.72572 − 7.49064I 7.19657 + 0.61552I
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.07746 + 1.11814I
a = 0.085451 − 0.944017I
b = 1.052750 − 0.772378I
2.38963 − 10.26740I 0
u = −1.07746 − 1.11814I
a = 0.085451 + 0.944017I
b = 1.052750 + 0.772378I
2.38963 + 10.26740I 0
u = 1.05041 + 1.14989I
a = −0.094585 − 0.960527I
b = −1.05120 − 1.15324I
−1.35038 + 13.87800I 0
u = 1.05041 − 1.14989I
a = −0.094585 + 0.960527I
b = −1.05120 + 1.15324I
−1.35038 − 13.87800I 0
u = 0.235916 + 0.374034I
a = 2.68079 − 1.19593I
b = −0.711198 − 0.315157I
1.53101 + 2.78696I 3.49090 − 8.15462I
u = 0.235916 − 0.374034I
a = 2.68079 + 1.19593I
b = −0.711198 + 0.315157I
1.53101 − 2.78696I 3.49090 + 8.15462I
u = −1.00742 + 1.19525I
a = 0.198207 − 0.820128I
b = 1.17870 − 0.87048I
2.15015 − 8.23570I 0
u = −1.00742 − 1.19525I
a = 0.198207 + 0.820128I
b = 1.17870 + 0.87048I
2.15015 + 8.23570I 0
u = −1.54595 + 0.27970I
a = −0.129942 + 0.330253I
b = −0.396603 − 0.405971I
−1.87947 − 2.48342I 0
u = −1.54595 − 0.27970I
a = −0.129942 − 0.330253I
b = −0.396603 + 0.405971I
−1.87947 + 2.48342I 0
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.97042 + 1.25819I
a = 0.283924 − 0.363068I
b = 0.964633 − 0.006223I
4.18899 − 2.61263I 0
u = −0.97042 − 1.25819I
a = 0.283924 + 0.363068I
b = 0.964633 + 0.006223I
4.18899 + 2.61263I 0
u = 1.07622 + 1.18104I
a = 0.121061 − 0.710020I
b = −0.541130 − 0.699281I
−4.85343 + 3.93548I 0
u = 1.07622 − 1.18104I
a = 0.121061 + 0.710020I
b = −0.541130 + 0.699281I
−4.85343 − 3.93548I 0
u = −0.094887 + 0.387658I
a = 3.51149 + 3.29191I
b = −0.479660 + 0.671504I
−2.91798 − 1.45918I −13.20482 + 4.97769I
u = −0.094887 − 0.387658I
a = 3.51149 − 3.29191I
b = −0.479660 − 0.671504I
−2.91798 + 1.45918I −13.20482 − 4.97769I
u = 0.354082 + 0.169181I
a = 0.00062 − 2.03804I
b = −1.312900 − 0.028450I
3.83972 − 0.00597I 10.79982 − 0.35314I
u = 0.354082 − 0.169181I
a = 0.00062 + 2.03804I
b = −1.312900 + 0.028450I
3.83972 + 0.00597I 10.79982 + 0.35314I
u = −1.03161 + 1.23590I
a = 0.161451 − 0.935808I
b = 1.29301 − 1.08215I
1.1515 − 14.6381I 0
u = −1.03161 − 1.23590I
a = 0.161451 + 0.935808I
b = 1.29301 + 1.08215I
1.1515 + 14.6381I 0
29
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.01805 + 1.26448I
a = 0.279820 + 0.839681I
b = 1.075170 + 0.891451I
3.12392 + 13.47560I 0
u = 1.01805 − 1.26448I
a = 0.279820 − 0.839681I
b = 1.075170 − 0.891451I
3.12392 − 13.47560I 0
u = 1.06553 + 1.23421I
a = −0.026271 − 0.698532I
b = −0.417846 − 0.728174I
−4.82565 + 3.73868I 0
u = 1.06553 − 1.23421I
a = −0.026271 + 0.698532I
b = −0.417846 + 0.728174I
−4.82565 − 3.73868I 0
u = 1.33187 + 0.98139I
a = −0.405152 − 0.233137I
b = −0.542779 + 0.555203I
2.04342 − 5.79434I 0
u = 1.33187 − 0.98139I
a = −0.405152 + 0.233137I
b = −0.542779 − 0.555203I
2.04342 + 5.79434I 0
u = −1.18682 + 1.15409I
a = 0.231791 + 0.663668I
b = −0.838412 + 0.779203I
−3.12392 − 13.47560I 0
u = −1.18682 − 1.15409I
a = 0.231791 − 0.663668I
b = −0.838412 − 0.779203I
−3.12392 + 13.47560I 0
u = 1.44148 + 0.85438I
a = 0.380641 + 0.198622I
b = 0.555728 − 0.265983I
− 6.42431I 0
u = 1.44148 − 0.85438I
a = 0.380641 − 0.198622I
b = 0.555728 + 0.265983I
6.42431I 0
30
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.51408 + 1.60553I
a = −0.122216 − 0.238347I
b = −1.110120 − 0.662212I
−1.72572 + 7.49064I 0
u = 0.51408 − 1.60553I
a = −0.122216 + 0.238347I
b = −1.110120 + 0.662212I
−1.72572 − 7.49064I 0
u = −1.09241 + 1.29201I
a = −0.175609 + 0.584815I
b = −0.609899 + 1.027940I
−2.77141 − 2.42490I 0
u = −1.09241 − 1.29201I
a = −0.175609 − 0.584815I
b = −0.609899 − 1.027940I
−2.77141 + 2.42490I 0
u = −0.002070 + 0.295235I
a = −1.33492 + 0.85659I
b = 1.46188 + 2.22119I
−0.0421355 −9.08507 + 0.I
u = −0.002070 − 0.295235I
a = −1.33492 − 0.85659I
b = 1.46188 − 2.22119I
−0.0421355 −9.08507 + 0.I
u = 0.284712 + 0.007691I
a = −1.44817 + 3.29455I
b = 1.359420 + 0.165320I
2.15015 + 8.23570I 4.52846 − 7.12595I
u = 0.284712 − 0.007691I
a = −1.44817 − 3.29455I
b = 1.359420 − 0.165320I
2.15015 − 8.23570I 4.52846 + 7.12595I
u = −0.069521 + 0.254576I
a = 4.67692 − 1.73417I
b = −0.868654 − 0.411797I
−0.60074 + 2.45623I 0.66265 − 6.54800I
u = −0.069521 − 0.254576I
a = 4.67692 + 1.73417I
b = −0.868654 + 0.411797I
−0.60074 − 2.45623I 0.66265 + 6.54800I
31
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.26544 + 1.19151I
a = −0.045352 − 0.563773I
b = −0.780485 − 0.863019I
−1.72572 + 7.49064I 0
u = 1.26544 − 1.19151I
a = −0.045352 + 0.563773I
b = −0.780485 + 0.863019I
−1.72572 − 7.49064I 0
u = 1.70330 + 0.38697I
a = 0.131895 + 0.416047I
b = 0.306306 + 0.195183I
5.33805 − 4.64735I 0
u = 1.70330 − 0.38697I
a = 0.131895 − 0.416047I
b = 0.306306 − 0.195183I
5.33805 + 4.64735I 0
u = −1.23302 + 1.40321I
a = −0.043260 − 0.426240I
b = 0.910516 − 0.624622I
−0.00371 − 6.56432I 0
u = −1.23302 − 1.40321I
a = −0.043260 + 0.426240I
b = 0.910516 + 0.624622I
−0.00371 + 6.56432I 0
u = −1.62293 + 0.95099I
a = −0.319586 + 0.200678I
b = −0.553813 − 0.438381I
1.1515 + 14.6381I 0
u = −1.62293 − 0.95099I
a = −0.319586 − 0.200678I
b = −0.553813 + 0.438381I
1.1515 − 14.6381I 0
u = −0.20861 + 1.88855I
a = 0.234002 + 0.072226I
b = 0.571260 + 0.034766I
−0.17902 − 4.15433I 0
u = −0.20861 − 1.88855I
a = 0.234002 − 0.072226I
b = 0.571260 − 0.034766I
−0.17902 + 4.15433I 0
32
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.60933 + 1.04889I
a = 0.151571 − 0.142094I
b = 0.733566 + 0.051894I
2.91798 + 1.45918I 0
u = −1.60933 − 1.04889I
a = 0.151571 + 0.142094I
b = 0.733566 − 0.051894I
2.91798 − 1.45918I 0
u = −1.76913 + 0.80569I
a = −0.159485 + 0.263434I
b = −0.386375 + 0.243359I
4.82565 − 3.73868I 0
u = −1.76913 − 0.80569I
a = −0.159485 − 0.263434I
b = −0.386375 − 0.243359I
4.82565 + 3.73868I 0
u = 1.59898 + 1.18152I
a = −0.282542 − 0.078979I
b = −0.252226 + 0.326644I
−0.71894 − 5.15211I 0
u = 1.59898 − 1.18152I
a = −0.282542 + 0.078979I
b = −0.252226 − 0.326644I
−0.71894 + 5.15211I 0
u = −1.53164 + 1.28497I
a = 0.219549 + 0.202211I
b = −0.741575 + 0.678467I
−2.77141 + 2.42490I 0
u = −1.53164 − 1.28497I
a = 0.219549 − 0.202211I
b = −0.741575 − 0.678467I
−2.77141 − 2.42490I 0
33
III. I
u
3
= h1.78 × 10
199
u
59
− 4.11 × 10
199
u
58
+ · · · + 4.11 × 10
201
b − 1.03 ×
10
201
, −1.13 × 10
195
u
59
+ 3.04 × 10
195
u
58
+ · · · + 3.32 × 10
196
a + 1.29 ×
10
197
, u
60
− 3u
59
+ · · · − 405u + 81i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
9
=
0.0340064u
59
− 0.0915725u
58
+ ··· + 20.1109u − 3.89008
−0.00432816u
59
+ 0.0100035u
58
+ ··· − 2.01849u + 0.251522
a
10
=
0.0329468u
59
− 0.0870163u
58
+ ··· + 20.6530u − 3.29542
−0.00446432u
59
+ 0.0101269u
58
+ ··· − 2.66223u + 0.363106
a
4
=
0.0380111u
59
− 0.0975197u
58
+ ··· + 26.3422u − 12.2411
−0.00843735u
59
+ 0.0243849u
58
+ ··· − 5.42827u + 2.56305
a
2
=
0.0201182u
59
− 0.0535896u
58
+ ··· + 13.2332u − 0.907135
−0.00666024u
59
+ 0.0168255u
58
+ ··· − 3.93400u + 0.896569
a
8
=
0.0383346u
59
− 0.101576u
58
+ ··· + 22.1294u − 4.14160
−0.00432816u
59
+ 0.0100035u
58
+ ··· − 2.01849u + 0.251522
a
6
=
0.0571166u
59
− 0.152365u
58
+ ··· + 40.0236u − 17.7786
−0.0106682u
59
+ 0.0304602u
58
+ ··· − 6.25318u + 2.97448
a
7
=
0.0419242u
59
− 0.111437u
58
+ ··· + 22.0932u − 8.20065
−0.00486271u
59
+ 0.0142693u
58
+ ··· − 4.90460u + 1.44464
a
3
=
0.0609340u
59
− 0.171286u
58
+ ··· + 37.9487u − 22.2153
−0.0104278u
59
+ 0.0297725u
58
+ ··· − 6.53554u + 3.97156
a
11
=
−0.0544112u
59
+ 0.147777u
58
+ ··· − 36.0986u + 13.4250
0.00825586u
59
− 0.0230421u
58
+ ··· + 5.45698u − 2.31264
(ii) Obstruction class = 1
(iii) Cusp Shapes = −0.0634322u
59
+ 0.162300u
58
+ ··· − 46.3123u + 18.9761
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
60
− 13u
59
+ ··· + 1249u + 127
c
2
, c
8
81(81u
60
+ 567u
59
+ ··· + 7u + 1)
c
3
, c
9
81(81u
60
− 567u
59
+ ··· − 7u + 1)
c
4
, c
10
u
60
+ 3u
59
+ ··· + 405u + 81
c
5
, c
11
u
60
+ 13u
59
+ ··· − 1249u + 127
c
6
, c
12
u
60
− 3u
59
+ ··· − 405u + 81
35
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
11
y
60
− 3y
59
+ ··· − 2004247y + 16129
c
2
, c
3
, c
8
c
9
6561(6561y
60
+ 88209y
59
+ ··· + 41y + 1)
c
4
, c
6
, c
10
c
12
y
60
− 7y
59
+ ··· − 95499y + 6561
36
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.672996 + 0.644045I
a = 0.202882 − 0.800309I
b = 1.26095 − 1.04967I
0.42397 − 4.54047I 1.41680 + 11.19246I
u = −0.672996 − 0.644045I
a = 0.202882 + 0.800309I
b = 1.26095 + 1.04967I
0.42397 + 4.54047I 1.41680 − 11.19246I
u = −0.612611 + 0.882756I
a = 0.47276 − 1.43991I
b = 1.05726 − 1.11579I
2.68342 − 2.20216I 1.62901 − 11.36162I
u = −0.612611 − 0.882756I
a = 0.47276 + 1.43991I
b = 1.05726 + 1.11579I
2.68342 + 2.20216I 1.62901 + 11.36162I
u = −0.845851 + 0.370106I
a = −0.620036 − 0.480563I
b = 0.733858 − 1.125670I
1.17531 − 5.50379I 2.72483 + 9.97648I
u = −0.845851 − 0.370106I
a = −0.620036 + 0.480563I
b = 0.733858 + 1.125670I
1.17531 + 5.50379I 2.72483 − 9.97648I
u = 0.536122 + 0.718184I
a = 0.08886 + 1.90031I
b = 0.74154 + 1.30092I
1.69146 + 7.79921I 4.9260 − 26.4100I
u = 0.536122 − 0.718184I
a = 0.08886 − 1.90031I
b = 0.74154 − 1.30092I
1.69146 − 7.79921I 4.9260 + 26.4100I
u = −0.067922 + 1.102530I
a = 1.169420 + 0.132080I
b = 0.115783 + 0.179827I
−2.22027 + 1.23412I −2.04804 − 3.92232I
u = −0.067922 − 1.102530I
a = 1.169420 − 0.132080I
b = 0.115783 − 0.179827I
−2.22027 − 1.23412I −2.04804 + 3.92232I
37
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.810603 + 0.123514I
a = −1.36340 + 0.88837I
b = 0.514851 − 0.409112I
−2.22027 − 1.23412I −2.04804 + 3.92232I
u = 0.810603 − 0.123514I
a = −1.36340 − 0.88837I
b = 0.514851 + 0.409112I
−2.22027 + 1.23412I −2.04804 − 3.92232I
u = −0.330497 + 0.711546I
a = −1.61443 − 1.09197I
b = 0.344693 − 0.805106I
−1.17531 − 5.50379I −2.72483 + 9.97648I
u = −0.330497 − 0.711546I
a = −1.61443 + 1.09197I
b = 0.344693 + 0.805106I
−1.17531 + 5.50379I −2.72483 − 9.97648I
u = −0.903585 + 0.816215I
a = 0.052750 − 1.283090I
b = 1.46569 − 0.41316I
4.74340 − 3.56595I 0. − 19.3521I
u = −0.903585 − 0.816215I
a = 0.052750 + 1.283090I
b = 1.46569 + 0.41316I
4.74340 + 3.56595I 0. + 19.3521I
u = −0.775298 + 0.025567I
a = 0.997827 + 0.065882I
b = −0.300870 + 1.154900I
− 13.6095I 0. + 9.25017I
u = −0.775298 − 0.025567I
a = 0.997827 − 0.065882I
b = −0.300870 − 1.154900I
13.6095I 0. − 9.25017I
u = 0.378896 + 0.669270I
a = 0.297632 + 1.174070I
b = −0.574914 + 1.256060I
−0.42397 + 4.54047I −1.41680 − 11.19246I
u = 0.378896 − 0.669270I
a = 0.297632 − 1.174070I
b = −0.574914 − 1.256060I
−0.42397 − 4.54047I −1.41680 + 11.19246I
38
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.702317 + 0.177006I
a = −1.007560 + 0.780914I
b = −0.074291 + 1.015460I
−1.17531 + 5.50379I −2.72483 − 9.97648I
u = 0.702317 − 0.177006I
a = −1.007560 − 0.780914I
b = −0.074291 − 1.015460I
−1.17531 − 5.50379I −2.72483 + 9.97648I
u = −0.225051 + 1.280350I
a = 0.844352 − 0.095365I
b = 1.280560 + 0.155262I
2.22027 − 1.23412I 0
u = −0.225051 − 1.280350I
a = 0.844352 + 0.095365I
b = 1.280560 − 0.155262I
2.22027 + 1.23412I 0
u = −0.099193 + 0.688067I
a = −0.54138 − 2.34954I
b = 0.09895 − 1.92778I
−4.83302 − 4.71436I 3.16224 + 12.50775I
u = −0.099193 − 0.688067I
a = −0.54138 + 2.34954I
b = 0.09895 + 1.92778I
−4.83302 + 4.71436I 3.16224 − 12.50775I
u = −1.214900 + 0.551712I
a = −0.514869 − 0.335480I
b = 0.538095 + 0.111950I
2.22027 + 1.23412I 0
u = −1.214900 − 0.551712I
a = −0.514869 + 0.335480I
b = 0.538095 − 0.111950I
2.22027 − 1.23412I 0
u = 0.347628 + 1.330100I
a = 0.152301 − 0.182658I
b = 0.661726 + 0.088373I
−0.42397 − 4.54047I 0
u = 0.347628 − 1.330100I
a = 0.152301 + 0.182658I
b = 0.661726 − 0.088373I
−0.42397 + 4.54047I 0
39
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.088346 + 0.618364I
a = 1.21677 + 2.81590I
b = 0.08136 + 1.50343I
−4.74340 + 3.56595I 0.1294 + 19.3521I
u = −0.088346 − 0.618364I
a = 1.21677 − 2.81590I
b = 0.08136 − 1.50343I
−4.74340 − 3.56595I 0.1294 − 19.3521I
u = 1.170450 + 0.730983I
a = 0.193385 − 1.055630I
b = −1.346560 − 0.157819I
4.83302 + 4.71436I 0
u = 1.170450 − 0.730983I
a = 0.193385 + 1.055630I
b = −1.346560 + 0.157819I
4.83302 − 4.71436I 0
u = 0.456006 + 0.401313I
a = −0.70412 − 3.25445I
b = −0.173343 − 0.280588I
1.69146 + 7.79921I 4.9260 − 26.4100I
u = 0.456006 − 0.401313I
a = −0.70412 + 3.25445I
b = −0.173343 + 0.280588I
1.69146 − 7.79921I 4.9260 + 26.4100I
u = −0.543305 + 0.112334I
a = 2.44950 + 2.34858I
b = −0.333032 + 0.314810I
2.68342 + 2.20216I 1.62901 + 11.36162I
u = −0.543305 − 0.112334I
a = 2.44950 − 2.34858I
b = −0.333032 − 0.314810I
2.68342 − 2.20216I 1.62901 − 11.36162I
u = 0.99799 + 1.09420I
a = 0.167905 − 0.916544I
b = −0.621393 − 0.709016I
−4.83302 + 4.71436I 0
u = 0.99799 − 1.09420I
a = 0.167905 + 0.916544I
b = −0.621393 + 0.709016I
−4.83302 − 4.71436I 0
40
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.31055 + 0.78785I
a = −0.424986 − 0.287453I
b = −0.472150 + 0.387795I
1.17531 − 5.50379I 0
u = 1.31055 − 0.78785I
a = −0.424986 + 0.287453I
b = −0.472150 − 0.387795I
1.17531 + 5.50379I 0
u = 0.99721 + 1.16715I
a = −0.156069 − 0.987746I
b = −1.17834 − 1.12844I
13.6095I 0
u = 0.99721 − 1.16715I
a = −0.156069 + 0.987746I
b = −1.17834 + 1.12844I
− 13.6095I 0
u = 0.99962 + 1.20244I
a = 0.031987 + 0.778051I
b = 0.418993 + 0.683764I
−4.74340 + 3.56595I 0
u = 0.99962 − 1.20244I
a = 0.031987 − 0.778051I
b = 0.418993 − 0.683764I
−4.74340 − 3.56595I 0
u = 0.98147 + 1.29944I
a = 0.205831 + 0.626907I
b = 0.691083 + 1.045440I
−2.68342 + 2.20216I 0
u = 0.98147 − 1.29944I
a = 0.205831 − 0.626907I
b = 0.691083 − 1.045440I
−2.68342 − 2.20216I 0
u = 0.295898 + 0.139079I
a = 2.69276 + 3.22949I
b = −0.579600 − 0.530295I
0.42397 + 4.54047I 1.41680 − 11.19246I
u = 0.295898 − 0.139079I
a = 2.69276 − 3.22949I
b = −0.579600 + 0.530295I
0.42397 − 4.54047I 1.41680 + 11.19246I
41
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.67034 + 0.13945I
a = −0.093126 − 0.404157I
b = −0.029210 − 0.764645I
4.83302 − 4.71436I 0
u = 1.67034 − 0.13945I
a = −0.093126 + 0.404157I
b = −0.029210 + 0.764645I
4.83302 + 4.71436I 0
u = −1.31713 + 1.08261I
a = 0.024552 − 0.525082I
b = 0.742114 − 0.935385I
−1.69146 − 7.79921I 0
u = −1.31713 − 1.08261I
a = 0.024552 + 0.525082I
b = 0.742114 + 0.935385I
−1.69146 + 7.79921I 0
u = −1.59465 + 1.00083I
a = 0.212707 + 0.203943I
b = −0.645775 + 0.679433I
−2.68342 + 2.20216I 0
u = −1.59465 − 1.00083I
a = 0.212707 − 0.203943I
b = −0.645775 − 0.679433I
−2.68342 − 2.20216I 0
u = −1.84875 + 0.50363I
a = 0.129309 − 0.299252I
b = 0.066736 − 0.315741I
4.74340 − 3.56595I 0
u = −1.84875 − 0.50363I
a = 0.129309 + 0.299252I
b = 0.066736 + 0.315741I
4.74340 + 3.56595I 0
u = 0.98497 + 1.76662I
a = −0.063507 − 0.293531I
b = −0.984779 − 0.690897I
−1.69146 + 7.79921I 0
u = 0.98497 − 1.76662I
a = −0.063507 + 0.293531I
b = −0.984779 + 0.690897I
−1.69146 − 7.79921I 0
42
IV. I
u
4
= h−u
5
− 3u
4
− 4u
3
− 3u
2
+ b − u − 1, −u
4
− 2u
3
− 3u
2
+ a − 2u −
1, u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
9
=
u
4
+ 2u
3
+ 3u
2
+ 2u + 1
u
5
+ 3u
4
+ 4u
3
+ 3u
2
+ u + 1
a
10
=
u
2
+ 2u + 1
u
2
a
4
=
−u
2
− 2u − 1
−u
2
a
2
=
u
5
+ 2u
4
+ 2u
3
− u
−u
5
− 3u
4
− 4u
3
− 3u
2
− u − 1
a
8
=
−u
5
− 2u
4
− 2u
3
+ u
u
5
+ 3u
4
+ 4u
3
+ 3u
2
+ u + 1
a
6
=
−1
0
a
7
=
−1
u
2
a
3
=
−u
4
− 2u
3
− 3u
2
− 2u − 1
−u
5
− 3u
4
− 4u
3
− 3u
2
− u − 1
a
11
=
0
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u
5
+ 24u
4
+ 32u
3
+ 16u
2
+ 4
43
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
7
c
9
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
2
, c
5
, c
8
c
11
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
4
, c
10
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
6
, c
12
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
44
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
7
, c
8
c
9
, c
11
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
4
, c
6
, c
10
c
12
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
45
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.917045 + 0.592379I
a = 0.084211 − 0.566250I
b = 1.002190 − 0.295542I
3.78121 − 1.84861I 7.43343 + 1.58845I
u = −0.917045 − 0.592379I
a = 0.084211 + 0.566250I
b = 1.002190 + 0.295542I
3.78121 + 1.84861I 7.43343 − 1.58845I
u = 0.258209 + 0.569162I
a = 0.25695 + 1.72779I
b = −0.428243 + 0.664531I
−3.78121 + 1.84861I −7.43343 − 1.58845I
u = 0.258209 − 0.569162I
a = 0.25695 − 1.72779I
b = −0.428243 − 0.664531I
−3.78121 − 1.84861I −7.43343 + 1.58845I
u = −0.84116 + 1.20014I
a = −0.341164 + 0.940004I
b = −1.073950 + 0.558752I
− 11.3860I 0. + 11.02114I
u = −0.84116 − 1.20014I
a = −0.341164 − 0.940004I
b = −1.073950 − 0.558752I
11.3860I 0. − 11.02114I
46
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
26
− u
25
+ ··· + 21u + 7)
· (u
60
− 13u
59
+ ··· + 1249u + 127)
· (u
228
+ 8u
227
+ ··· − 11192067647u + 984049733)
c
2
, c
8
2187(u
6
− u
5
+ ··· − u + 1)(3u
26
− 3u
25
+ ··· − u + 1)
· (81u
60
+ 567u
59
+ ··· + 7u + 1)(9u
228
− 54u
227
+ ··· − 9395u + 1619)
c
3
, c
9
2187(u
6
+ u
5
+ ··· + u + 1)(3u
26
+ 3u
25
+ ··· + u + 1)
· (81u
60
− 567u
59
+ ··· − 7u + 1)(9u
228
+ 54u
227
+ ··· + 9395u + 1619)
c
4
, c
10
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)(u
26
+ 3u
25
+ ··· − 15u + 3)
· (u
60
+ 3u
59
+ ··· + 405u + 81)(u
228
− 2u
227
+ ··· − 120069u + 8487)
c
5
, c
11
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
26
+ u
25
+ ··· − 21u + 7)
· (u
60
+ 13u
59
+ ··· − 1249u + 127)
· (u
228
− 8u
227
+ ··· + 11192067647u + 984049733)
c
6
, c
12
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)(u
26
− 3u
25
+ ··· + 15u + 3)
· (u
60
− 3u
59
+ ··· − 405u + 81)(u
228
+ 2u
227
+ ··· + 120069u + 8487)
47
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
11
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
26
+ 15y
25
+ ··· + 777y + 49)
· (y
60
− 3y
59
+ ··· − 2004247y + 16129)
· (y
228
+ 20y
227
+ ··· + 4.78 × 10
19
y + 9.68 × 10
17
)
c
2
, c
3
, c
8
c
9
4782969(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (9y
26
+ 123y
25
+ ··· − 3y + 1)(6561y
60
+ 88209y
59
+ ··· + 41y + 1)
· (81y
228
+ 2052y
227
+ ··· + 89205517y + 2621161)
c
4
, c
6
, c
10
c
12
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)(y
26
+ 3y
25
+ ··· − 39y + 9)
· (y
60
− 7y
59
+ ··· − 95499y + 6561)
· (y
228
+ 12y
227
+ ··· + 6749419149y + 72029169)
48
