12a
1224
(K12a
1224
)
A knot diagram
1
Linearized knot diagam
5 6 8 10 2 12 11 4 1 3 7 9
Solving Sequence
1,5
2 6
3,10
4 9 8 12 7 11
c
1
c
5
c
2
c
4
c
9
c
8
c
12
c
6
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.21800 × 10
175
u
86
+ 1.10072 × 10
176
u
85
+ ··· + 5.56542 × 10
175
b + 9.38658 × 10
176
,
− 2.03509 × 10
176
u
86
+ 9.22272 × 10
176
u
85
+ ··· + 5.56542 × 10
175
a + 3.49997 × 10
177
,
u
87
− 5u
86
+ ··· − 31u − 1i
I
u
2
= h3u
20
− 5u
19
+ ··· + b − 2, −3u
20
+ 4u
19
+ ··· + a + 4, u
21
− 14u
19
+ ··· + u − 1i
I
u
3
= hb + 1, −u
5
+ 2u
4
+ 2u
3
− 4u
2
+ a − u + 1, u
6
− 3u
5
+ 6u
3
− 4u
2
+ 1i
I
u
4
= hb + 1, a − 1, u + 1i
* 4 irreducible components of dim
C
= 0, with total 115 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
= h1.22 × 10
175
u
86
+ 1.10 × 10
176
u
85
+ · · · + 5.57 × 10
175
b + 9.39 ×
10
176
, −2.04 × 10
176
u
86
+ 9.22 × 10
176
u
85
+ · · · + 5.57 × 10
175
a + 3.50 ×
10
177
, u
87
− 5u
86
+ · · · − 31u − 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
a
10
=
3.65668u
86
− 16.5715u
85
+ ··· − 1025.07u − 62.8879
−0.218852u
86
− 1.97778u
85
+ ··· − 412.229u − 16.8659
a
4
=
−20.1258u
86
+ 100.004u
85
+ ··· + 3106.06u + 123.163
1.01692u
86
− 6.75872u
85
+ ··· − 461.880u − 22.8410
a
9
=
3.43783u
86
− 18.5492u
85
+ ··· − 1437.30u − 79.7538
−0.218852u
86
− 1.97778u
85
+ ··· − 412.229u − 16.8659
a
8
=
20.7323u
86
− 106.664u
85
+ ··· − 4060.99u − 176.355
−1.96351u
86
+ 8.22272u
85
+ ··· + 158.487u + 9.66986
a
12
=
−21.5377u
86
+ 114.337u
85
+ ··· + 5556.14u + 273.143
1.30331u
86
− 0.885320u
85
+ ··· + 627.672u + 26.9509
a
7
=
−3.73334u
86
+ 32.1426u
85
+ ··· + 2150.24u + 65.7851
8.70129u
86
− 35.1065u
85
+ ··· − 562.970u − 33.7329
a
11
=
3.49067u
86
− 18.8111u
85
+ ··· − 1445.83u − 79.7310
0.510581u
86
− 4.63816u
85
+ ··· − 407.668u − 16.8546
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3.04694u
86
+ 31.0771u
85
+ ··· + 2704.70u + 109.774
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
u
87
+ 5u
86
+ ··· − 31u + 1
c
3
, c
8
u
87
+ 2u
86
+ ··· + 1867u − 1459
c
4
u
87
− u
86
+ ··· − 108842u + 15817
c
6
, c
7
, c
11
u
87
+ 2u
86
+ ··· − 36u + 7
c
9
, c
12
u
87
− 9u
86
+ ··· + 784u − 8
c
10
u
87
+ 3u
86
+ ··· + 619168u + 590297
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
y
87
− 91y
86
+ ··· + 301y −1
c
3
, c
8
y
87
− 64y
86
+ ··· + 35213103y −2128681
c
4
y
87
+ 33y
86
+ ··· + 197455366y −250177489
c
6
, c
7
, c
11
y
87
+ 90y
86
+ ··· + 2206y −49
c
9
, c
12
y
87
− 59y
86
+ ··· + 638432y −64
c
10
y
87
− 25y
86
+ ··· + 7264616979632y −348450548209
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.919570 + 0.341269I
a = −0.230219 − 1.291490I
b = 1.018910 + 0.767688I
4.92914 − 3.18573I 0
u = 0.919570 − 0.341269I
a = −0.230219 + 1.291490I
b = 1.018910 − 0.767688I
4.92914 + 3.18573I 0
u = 0.643376 + 0.795200I
a = −0.443359 − 0.859364I
b = 1.129980 + 0.180708I
−3.41783 − 2.87585I 0
u = 0.643376 − 0.795200I
a = −0.443359 + 0.859364I
b = 1.129980 − 0.180708I
−3.41783 + 2.87585I 0
u = −0.801927 + 0.529130I
a = −1.221220 − 0.403028I
b = −0.518441 + 0.530723I
8.78928 − 2.20079I 0
u = −0.801927 − 0.529130I
a = −1.221220 + 0.403028I
b = −0.518441 − 0.530723I
8.78928 + 2.20079I 0
u = −0.605395 + 0.915337I
a = 0.449296 − 1.181010I
b = −1.230940 + 0.562762I
6.97761 + 12.04090I 0
u = −0.605395 − 0.915337I
a = 0.449296 + 1.181010I
b = −1.230940 − 0.562762I
6.97761 − 12.04090I 0
u = −0.524939 + 0.728503I
a = −0.50181 + 1.52469I
b = 1.221130 − 0.467400I
0.17465 + 8.23740I 0
u = −0.524939 − 0.728503I
a = −0.50181 − 1.52469I
b = 1.221130 + 0.467400I
0.17465 − 8.23740I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.146280 + 0.016740I
a = −0.218153 + 1.254070I
b = 0.883487 − 0.824717I
5.16086 + 3.06951I 0
u = 1.146280 − 0.016740I
a = −0.218153 − 1.254070I
b = 0.883487 + 0.824717I
5.16086 − 3.06951I 0
u = −0.421925 + 0.731310I
a = −0.889218 + 0.084686I
b = 1.110590 + 0.288943I
0.35974 − 3.47491I 0
u = −0.421925 − 0.731310I
a = −0.889218 − 0.084686I
b = 1.110590 − 0.288943I
0.35974 + 3.47491I 0
u = 0.073826 + 0.813368I
a = −1.60062 + 0.49196I
b = 0.899591 − 0.403821I
7.79839 − 0.95510I 0
u = 0.073826 − 0.813368I
a = −1.60062 − 0.49196I
b = 0.899591 + 0.403821I
7.79839 + 0.95510I 0
u = 1.20375
a = 0.466459
b = 0.00998561
−2.53324 0
u = −0.635177 + 1.044370I
a = 0.662353 − 0.064701I
b = −1.059810 − 0.347777I
7.02919 − 5.71442I 0
u = −0.635177 − 1.044370I
a = 0.662353 + 0.064701I
b = −1.059810 + 0.347777I
7.02919 + 5.71442I 0
u = 0.509200 + 1.127410I
a = 0.472655 + 0.551529I
b = −1.195790 − 0.258865I
1.51094 − 5.10157I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.509200 − 1.127410I
a = 0.472655 − 0.551529I
b = −1.195790 + 0.258865I
1.51094 + 5.10157I 0
u = −0.365776 + 0.653749I
a = −0.081284 + 1.401450I
b = −0.287242 − 1.062190I
10.02620 + 6.30984I 0
u = −0.365776 − 0.653749I
a = −0.081284 − 1.401450I
b = −0.287242 + 1.062190I
10.02620 − 6.30984I 0
u = 0.129351 + 0.704209I
a = −0.679190 − 0.828173I
b = 0.103762 + 0.686088I
5.33081 − 1.86604I 0. + 3.90648I
u = 0.129351 − 0.704209I
a = −0.679190 + 0.828173I
b = 0.103762 − 0.686088I
5.33081 + 1.86604I 0. − 3.90648I
u = 1.223970 + 0.401442I
a = −0.462473 − 0.267648I
b = −0.073035 − 0.139352I
2.07456 − 2.27551I 0
u = 1.223970 − 0.401442I
a = −0.462473 + 0.267648I
b = −0.073035 + 0.139352I
2.07456 + 2.27551I 0
u = −1.263230 + 0.374502I
a = −0.746639 + 0.577828I
b = 0.860702 + 0.092884I
3.67205 + 5.24598I 0
u = −1.263230 − 0.374502I
a = −0.746639 − 0.577828I
b = 0.860702 − 0.092884I
3.67205 − 5.24598I 0
u = −0.266580 + 0.588131I
a = 1.35207 − 2.09086I
b = −1.122390 + 0.353863I
0.18453 + 2.81647I −0.56699 − 5.14375I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.266580 − 0.588131I
a = 1.35207 + 2.09086I
b = −1.122390 − 0.353863I
0.18453 − 2.81647I −0.56699 + 5.14375I
u = −0.383725 + 0.510780I
a = −0.35311 − 1.52762I
b = 0.127056 + 0.881304I
3.55177 + 3.39819I 0.84018 − 6.92415I
u = −0.383725 − 0.510780I
a = −0.35311 + 1.52762I
b = 0.127056 − 0.881304I
3.55177 − 3.39819I 0.84018 + 6.92415I
u = −0.631511
a = 0.479038
b = −1.15135
−1.55302 −7.94170
u = 1.382990 + 0.055539I
a = 0.565031 − 0.732391I
b = −0.238430 + 0.708558I
−2.35948 − 0.82108I 0
u = 1.382990 − 0.055539I
a = 0.565031 + 0.732391I
b = −0.238430 − 0.708558I
−2.35948 + 0.82108I 0
u = −1.375540 + 0.190726I
a = 0.047286 + 0.731163I
b = 0.378703 − 1.174100I
0.57233 + 4.93402I 0
u = −1.375540 − 0.190726I
a = 0.047286 − 0.731163I
b = 0.378703 + 1.174100I
0.57233 − 4.93402I 0
u = −1.391300 + 0.009231I
a = 0.421080 + 0.806075I
b = 1.57036 − 0.71094I
−2.89241 + 2.70347I 0
u = −1.391300 − 0.009231I
a = 0.421080 − 0.806075I
b = 1.57036 + 0.71094I
−2.89241 − 2.70347I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.491766 + 0.337151I
a = 1.52671 + 1.10854I
b = 0.131068 − 0.467644I
3.13228 − 0.27068I 1.77490 − 1.85357I
u = −0.491766 − 0.337151I
a = 1.52671 − 1.10854I
b = 0.131068 + 0.467644I
3.13228 + 0.27068I 1.77490 + 1.85357I
u = −1.41338 + 0.09716I
a = 1.63265 − 0.41394I
b = 1.024190 − 0.080144I
3.14701 + 6.03465I 0
u = −1.41338 − 0.09716I
a = 1.63265 + 0.41394I
b = 1.024190 + 0.080144I
3.14701 − 6.03465I 0
u = 1.42796 + 0.02959I
a = 0.701919 + 0.520870I
b = 1.53124 − 0.11552I
−3.60289 − 2.95271I 0
u = 1.42796 − 0.02959I
a = 0.701919 − 0.520870I
b = 1.53124 + 0.11552I
−3.60289 + 2.95271I 0
u = −1.43990 + 0.06670I
a = −0.012806 − 0.753944I
b = −0.183222 + 0.885034I
−5.79294 + 2.10750I 0
u = −1.43990 − 0.06670I
a = −0.012806 + 0.753944I
b = −0.183222 − 0.885034I
−5.79294 − 2.10750I 0
u = 1.43586 + 0.20746I
a = −0.41468 + 1.49380I
b = −1.226660 − 0.529473I
−5.35379 − 5.68624I 0
u = 1.43586 − 0.20746I
a = −0.41468 − 1.49380I
b = −1.226660 + 0.529473I
−5.35379 + 5.68624I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.45502 + 0.14563I
a = −0.310433 + 0.637258I
b = 0.052332 − 1.193180I
−2.41136 − 5.70802I 0
u = 1.45502 − 0.14563I
a = −0.310433 − 0.637258I
b = 0.052332 + 1.193180I
−2.41136 + 5.70802I 0
u = 0.427368 + 0.306228I
a = 0.86564 + 1.62484I
b = −1.109570 − 0.540320I
−1.27209 − 2.61374I −8.1476 + 11.5732I
u = 0.427368 − 0.306228I
a = 0.86564 − 1.62484I
b = −1.109570 + 0.540320I
−1.27209 + 2.61374I −8.1476 − 11.5732I
u = 1.47311 + 0.21321I
a = 0.208305 − 0.640823I
b = −0.17007 + 1.45424I
4.02421 − 9.40391I 0
u = 1.47311 − 0.21321I
a = 0.208305 + 0.640823I
b = −0.17007 − 1.45424I
4.02421 + 9.40391I 0
u = 1.49510 + 0.04344I
a = −0.581323 + 0.412900I
b = −1.51105 − 0.29367I
−8.12584 − 0.44534I 0
u = 1.49510 − 0.04344I
a = −0.581323 − 0.412900I
b = −1.51105 + 0.29367I
−8.12584 + 0.44534I 0
u = −0.469577 + 0.132148I
a = 0.607127 + 0.383204I
b = 1.022440 − 0.664659I
2.30869 + 3.10979I 6.28767 + 0.10476I
u = −0.469577 − 0.132148I
a = 0.607127 − 0.383204I
b = 1.022440 + 0.664659I
2.30869 − 3.10979I 6.28767 − 0.10476I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.51638 + 0.07781I
a = −0.311568 − 0.786453I
b = −1.38732 + 0.85466I
−7.83146 + 3.89655I 0
u = −1.51638 − 0.07781I
a = −0.311568 + 0.786453I
b = −1.38732 − 0.85466I
−7.83146 − 3.89655I 0
u = 1.54839 + 0.05770I
a = 0.443126 − 0.341427I
b = 1.47115 + 0.67450I
−4.62587 − 3.85006I 0
u = 1.54839 − 0.05770I
a = 0.443126 + 0.341427I
b = 1.47115 − 0.67450I
−4.62587 + 3.85006I 0
u = 1.52731 + 0.26111I
a = 0.475990 − 1.199960I
b = 1.36229 + 0.58251I
−6.51610 − 11.88980I 0
u = 1.52731 − 0.26111I
a = 0.475990 + 1.199960I
b = 1.36229 − 0.58251I
−6.51610 + 11.88980I 0
u = −1.54118 + 0.17061I
a = −0.318296 − 1.038990I
b = −1.170070 + 0.386041I
−8.66512 + 2.45063I 0
u = −1.54118 − 0.17061I
a = −0.318296 + 1.038990I
b = −1.170070 − 0.386041I
−8.66512 − 2.45063I 0
u = 0.277564 + 0.317493I
a = 0.560535 + 1.041500I
b = −0.079901 − 0.308666I
−0.183792 − 0.864472I −4.29913 + 7.86972I
u = 0.277564 − 0.317493I
a = 0.560535 − 1.041500I
b = −0.079901 + 0.308666I
−0.183792 + 0.864472I −4.29913 − 7.86972I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.56054 + 0.25243I
a = 0.375410 + 0.928178I
b = 1.353380 − 0.393780I
−10.60940 + 6.66212I 0
u = −1.56054 − 0.25243I
a = 0.375410 − 0.928178I
b = 1.353380 + 0.393780I
−10.60940 − 6.66212I 0
u = −1.55851 + 0.35179I
a = −0.349517 − 0.886182I
b = −1.44084 + 0.41048I
−5.19961 + 10.21640I 0
u = −1.55851 − 0.35179I
a = −0.349517 + 0.886182I
b = −1.44084 − 0.41048I
−5.19961 − 10.21640I 0
u = 1.57773 + 0.32081I
a = −0.413286 + 1.072970I
b = −1.42145 − 0.65571I
−0.1084 − 16.5867I 0
u = 1.57773 − 0.32081I
a = −0.413286 − 1.072970I
b = −1.42145 + 0.65571I
−0.1084 + 16.5867I 0
u = −1.60922 + 0.08030I
a = 0.270773 + 0.717828I
b = 1.37271 − 1.07445I
−3.46237 + 4.60398I 0
u = −1.60922 − 0.08030I
a = 0.270773 − 0.717828I
b = 1.37271 + 1.07445I
−3.46237 − 4.60398I 0
u = 0.125878 + 0.322657I
a = 3.80205 − 2.84036I
b = 0.779351 + 0.457129I
8.28711 − 4.58904I 1.66459 + 8.40382I
u = 0.125878 − 0.322657I
a = 3.80205 + 2.84036I
b = 0.779351 − 0.457129I
8.28711 + 4.58904I 1.66459 − 8.40382I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.55309 + 0.60898I
a = −0.171676 + 0.555702I
b = −1.234490 − 0.047231I
−1.64260 − 2.30540I 0
u = 1.55309 − 0.60898I
a = −0.171676 − 0.555702I
b = −1.234490 + 0.047231I
−1.64260 + 2.30540I 0
u = 1.64697 + 0.30699I
a = 0.307607 − 0.488246I
b = 1.146860 + 0.090509I
−6.04528 − 1.09420I 0
u = 1.64697 − 0.30699I
a = 0.307607 + 0.488246I
b = 1.146860 − 0.090509I
−6.04528 + 1.09420I 0
u = −0.124790
a = 13.9437
b = −0.470722
2.89659 10.5150
u = −0.0876446 + 0.0176727I
a = 2.61863 − 7.91258I
b = 1.41551 − 0.34649I
1.67209 + 2.65200I −6.68294 + 0.54441I
u = −0.0876446 − 0.0176727I
a = 2.61863 + 7.91258I
b = 1.41551 + 0.34649I
1.67209 − 2.65200I −6.68294 − 0.54441I
13
II.
I
u
2
= h3u
20
−5u
19
+· · ·+b−2, −3u
20
+4u
19
+· · ·+a+4, u
21
−14u
19
+· · ·+u−1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
a
10
=
3u
20
− 4u
19
+ ··· + 12u − 4
−3u
20
+ 5u
19
+ ··· − 4u + 2
a
4
=
u
20
− 2u
19
+ ··· − 4u + 3
−4u
20
+ 5u
19
+ ··· − 5u + 2
a
9
=
u
19
− 3u
18
+ ··· + 8u − 2
−3u
20
+ 5u
19
+ ··· − 4u + 2
a
8
=
−3u
20
+ 3u
19
+ ··· − 7u + 5
u
20
− u
19
+ ··· + 2u − 2
a
12
=
2u
20
− 3u
19
+ ··· + 8u − 3
u
19
− u
18
+ ··· − 5u
2
− 2u
a
7
=
−3u
20
+ 4u
19
+ ··· − 4u + 3
−u
20
+ 3u
19
+ ··· − u + 1
a
11
=
−2u
20
+ 4u
19
+ ··· − 5u
2
+ 5u
−7u
20
+ 10u
19
+ ··· − 9u + 5
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 7u
20
− 13u
19
− 84u
18
+ 158u
17
+ 425u
16
− 809u
15
− 1168u
14
+ 2256u
13
+ 1870u
12
−
3697u
11
−1742u
10
+3586u
9
+919u
8
−1994u
7
−306u
6
+636u
5
+87u
4
−158u
3
+7u
2
+24u−16
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
21
− 14u
19
+ ··· + u − 1
c
3
u
21
+ u
20
+ ··· − u + 1
c
4
u
21
− 2u
19
+ ··· − 2u − 1
c
5
u
21
− 14u
19
+ ··· + u + 1
c
6
, c
7
u
21
+ u
20
+ ··· − 9u
2
− 1
c
8
u
21
− u
20
+ ··· − u − 1
c
9
u
21
+ 3u
20
+ ··· + 9u
2
− 1
c
10
u
21
+ 3u
19
+ ··· − 8u
2
+ 1
c
11
u
21
− u
20
+ ··· + 9u
2
+ 1
c
12
u
21
− 3u
20
+ ··· − 9u
2
+ 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
y
21
− 28y
20
+ ··· + 9y −1
c
3
, c
8
y
21
− 21y
20
+ ··· + 11y −1
c
4
y
21
− 4y
20
+ ··· − 10y −1
c
6
, c
7
, c
11
y
21
+ 21y
20
+ ··· − 18y −1
c
9
, c
12
y
21
− 17y
20
+ ··· + 18y −1
c
10
y
21
+ 6y
20
+ ··· + 16y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.980123 + 0.287889I
a = −0.202219 − 0.402737I
b = 0.821250 + 0.530110I
1.64253 − 3.32447I −6.73227 + 3.23371I
u = 0.980123 − 0.287889I
a = −0.202219 + 0.402737I
b = 0.821250 − 0.530110I
1.64253 + 3.32447I −6.73227 − 3.23371I
u = 1.12877
a = 0.459570
b = −0.644952
−3.11468 −14.6860
u = −1.23262
a = 1.72801
b = −0.411550
−0.191889 1.35120
u = −1.267400 + 0.189837I
a = −1.145350 + 0.468508I
b = 0.372541 − 0.430174I
5.01252 + 5.95890I 0.38975 − 5.02691I
u = −1.267400 − 0.189837I
a = −1.145350 − 0.468508I
b = 0.372541 + 0.430174I
5.01252 − 5.95890I 0.38975 + 5.02691I
u = 0.513299 + 0.356158I
a = −0.298859 − 0.889580I
b = 1.198820 + 0.616343I
1.84979 − 3.43907I −5.77787 + 8.99517I
u = 0.513299 − 0.356158I
a = −0.298859 + 0.889580I
b = 1.198820 − 0.616343I
1.84979 + 3.43907I −5.77787 − 8.99517I
u = −0.428378 + 0.445644I
a = 0.59208 + 1.78035I
b = 0.635250 + 0.374830I
8.00683 − 3.75384I −1.41538 + 0.52564I
u = −0.428378 − 0.445644I
a = 0.59208 − 1.78035I
b = 0.635250 − 0.374830I
8.00683 + 3.75384I −1.41538 − 0.52564I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50488 + 0.09457I
a = −0.300529 − 0.973392I
b = −1.25356 + 0.73428I
−7.16310 + 3.43030I −3.74353 − 1.15763I
u = −1.50488 − 0.09457I
a = −0.300529 + 0.973392I
b = −1.25356 − 0.73428I
−7.16310 − 3.43030I −3.74353 + 1.15763I
u = −1.54873 + 0.07946I
a = 0.337710 + 0.596656I
b = 1.56117 − 0.99590I
−5.11343 + 4.80864I −8.81380 − 6.84118I
u = −1.54873 − 0.07946I
a = 0.337710 − 0.596656I
b = 1.56117 + 0.99590I
−5.11343 − 4.80864I −8.81380 + 6.84118I
u = −0.428907
a = −3.99233
b = −0.611834
2.58386 −16.1200
u = 1.55858 + 0.20556I
a = −0.410534 + 0.603726I
b = −1.123510 − 0.131583I
−5.66515 − 0.90405I −2.75648 − 2.17520I
u = 1.55858 − 0.20556I
a = −0.410534 − 0.603726I
b = −1.123510 + 0.131583I
−5.66515 + 0.90405I −2.75648 + 2.17520I
u = 0.213126 + 0.328797I
a = 2.06155 + 1.99092I
b = −1.118860 − 0.369484I
−1.13219 − 1.99292I −5.58755 − 0.19985I
u = 0.213126 − 0.328797I
a = 2.06155 − 1.99092I
b = −1.118860 + 0.369484I
−1.13219 + 1.99292I −5.58755 + 0.19985I
u = 1.75063 + 0.30855I
a = 0.268529 − 0.284726I
b = 1.241070 + 0.159795I
−2.01124 − 1.49085I −8.33532 + 1.09996I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.75063 − 0.30855I
a = 0.268529 + 0.284726I
b = 1.241070 − 0.159795I
−2.01124 + 1.49085I −8.33532 − 1.09996I
19
III. I
u
3
= hb + 1, −u
5
+ 2u
4
+ 2u
3
− 4u
2
+ a − u + 1, u
6
− 3u
5
+ 6u
3
− 4u
2
+ 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
a
10
=
u
5
− 2u
4
− 2u
3
+ 4u
2
+ u − 1
−1
a
4
=
u
4
− 2u
3
− u
2
+ 2u + 1
u
5
− 2u
4
− 2u
3
+ 5u
2
− 1
a
9
=
u
5
− 2u
4
− 2u
3
+ 4u
2
+ u − 2
−1
a
8
=
−u
3
+ 2u
2
− 2
−u
5
+ 2u
4
+ u
3
− 4u
2
+ u
a
12
=
u
5
− 2u
4
− 2u
3
+ 4u
2
+ u − 1
−1
a
7
=
−u
2
+ 1
−u
4
+ 2u
2
a
11
=
−u
5
+ u
4
+ 2u
3
− 2u
2
+ 2u
−3u
5
+ 4u
4
+ 6u
3
− 7u
2
+ 2u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
u
6
+ 3u
5
− 6u
3
− 4u
2
+ 1
c
3
, c
8
u
6
− 3u
5
+ 6u
3
− 4u
2
+ 1
c
4
u
6
+ u
5
− 2u
4
+ 6u
3
− 4u
2
+ 2u + 1
c
6
, c
7
, c
10
c
11
u
6
− u
5
+ 2u
4
− 2u
3
− 1
c
9
, c
12
(u + 1)
6
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
8
y
6
− 9y
5
+ 28y
4
− 34y
3
+ 16y
2
− 8y + 1
c
4
y
6
− 5y
5
− 16y
4
− 22y
3
− 12y
2
− 12y + 1
c
6
, c
7
, c
10
c
11
y
6
+ 3y
5
− 6y
3
− 4y
2
+ 1
c
9
, c
12
(y −1)
6
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.558227 + 0.461646I
a = 0.64026 + 1.59235I
b = −1.00000
−1.64493 −6.00000
u = 0.558227 − 0.461646I
a = 0.64026 − 1.59235I
b = −1.00000
−1.64493 −6.00000
u = −1.39152
a = −1.97338
b = −1.00000
−1.64493 −6.00000
u = −0.401914
a = −0.688603
b = −1.00000
−1.64493 −6.00000
u = 1.83849 + 0.16576I
a = −0.309272 + 0.392670I
b = −1.00000
−1.64493 −6.00000
u = 1.83849 − 0.16576I
a = −0.309272 − 0.392670I
b = −1.00000
−1.64493 −6.00000
23
IV. I
u
4
= hb + 1, a − 1, u + 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
−1
a
2
=
1
1
a
6
=
1
0
a
3
=
0
1
a
10
=
1
−1
a
4
=
1
−2
a
9
=
0
−1
a
8
=
1
−3
a
12
=
1
−1
a
7
=
0
1
a
11
=
1
−2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
5
u − 1
c
3
, c
6
, c
7
c
8
, c
9
, c
10
c
11
, c
12
u + 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y −1
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000
b = −1.00000
−1.64493 −6.00000
27
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)(u
6
+ 3u
5
+ ··· − 4u
2
+ 1)(u
21
− 14u
19
+ ··· + u − 1)
· (u
87
+ 5u
86
+ ··· − 31u + 1)
c
3
(u + 1)(u
6
− 3u
5
+ ··· − 4u
2
+ 1)(u
21
+ u
20
+ ··· − u + 1)
· (u
87
+ 2u
86
+ ··· + 1867u − 1459)
c
4
(u − 1)(u
6
+ u
5
+ ··· + 2u + 1)(u
21
− 2u
19
+ ··· − 2u − 1)
· (u
87
− u
86
+ ··· − 108842u + 15817)
c
5
(u − 1)(u
6
+ 3u
5
+ ··· − 4u
2
+ 1)(u
21
− 14u
19
+ ··· + u + 1)
· (u
87
+ 5u
86
+ ··· − 31u + 1)
c
6
, c
7
(u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
− 1)(u
21
+ u
20
+ ··· − 9u
2
− 1)
· (u
87
+ 2u
86
+ ··· − 36u + 7)
c
8
(u + 1)(u
6
− 3u
5
+ ··· − 4u
2
+ 1)(u
21
− u
20
+ ··· − u − 1)
· (u
87
+ 2u
86
+ ··· + 1867u − 1459)
c
9
((u + 1)
7
)(u
21
+ 3u
20
+ ··· + 9u
2
− 1)(u
87
− 9u
86
+ ··· + 784u − 8)
c
10
(u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
− 1)(u
21
+ 3u
19
+ ··· − 8u
2
+ 1)
· (u
87
+ 3u
86
+ ··· + 619168u + 590297)
c
11
(u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
− 1)(u
21
− u
20
+ ··· + 9u
2
+ 1)
· (u
87
+ 2u
86
+ ··· − 36u + 7)
c
12
((u + 1)
7
)(u
21
− 3u
20
+ ··· − 9u
2
+ 1)(u
87
− 9u
86
+ ··· + 784u − 8)
28
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)(y
6
− 9y
5
+ 28y
4
− 34y
3
+ 16y
2
− 8y + 1)
· (y
21
− 28y
20
+ ··· + 9y −1)(y
87
− 91y
86
+ ··· + 301y −1)
c
3
, c
8
(y −1)(y
6
− 9y
5
+ 28y
4
− 34y
3
+ 16y
2
− 8y + 1)
· (y
21
− 21y
20
+ ··· + 11y −1)
· (y
87
− 64y
86
+ ··· + 35213103y −2128681)
c
4
(y −1)(y
6
− 5y
5
− 16y
4
− 22y
3
− 12y
2
− 12y + 1)
· (y
21
− 4y
20
+ ··· − 10y −1)
· (y
87
+ 33y
86
+ ··· + 197455366y −250177489)
c
6
, c
7
, c
11
(y −1)(y
6
+ 3y
5
+ ··· − 4y
2
+ 1)(y
21
+ 21y
20
+ ··· − 18y −1)
· (y
87
+ 90y
86
+ ··· + 2206y −49)
c
9
, c
12
((y −1)
7
)(y
21
− 17y
20
+ ··· + 18y −1)
· (y
87
− 59y
86
+ ··· + 638432y −64)
c
10
(y −1)(y
6
+ 3y
5
+ ··· − 4y
2
+ 1)(y
21
+ 6y
20
+ ··· + 16y −1)
· (y
87
− 25y
86
+ ··· + 7264616979632y −348450548209)
29
