12a
0347
(K12a
0347
)
A knot diagram
1
Linearized knot diagam
3 6 9 7 2 10 12 11 1 5 8 4
Solving Sequence
7,12 5,8
4 1 11 9 3 10 6 2
c
7
c
4
c
12
c
11
c
8
c
3
c
10
c
6
c
2
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.99189 × 10
50
u
63
+ 7.06651 × 10
51
u
62
+ ··· + 5.23150 × 10
51
b + 4.68036 × 10
51
,
3.28198 × 10
51
u
63
− 3.59525 × 10
52
u
62
+ ··· + 1.04630 × 10
52
a + 6.79922 × 10
51
, u
64
− 11u
63
+ ··· − 7u + 2i
I
u
2
= hu
40
a − 23u
40
+ ··· − 2a − 351, u
40
a + u
40
+ ··· + 2a
2
+ 12a, u
41
+ 9u
40
+ ··· − 2u − 2i
I
u
3
= hu
22
+ 8u
21
+ ··· + b + 5, −5u
24
− 40u
23
+ ··· + 3a − 28, u
25
+ 8u
24
+ ··· + 32u + 3i
I
u
4
= hau + 3b − 2a + u + 1, 2a
2
− au + 2a + 5, u
2
+ 2i
I
v
1
= ha, b + v, v
2
− v + 1i
* 5 irreducible components of dim
C
= 0, with total 177 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−6.99 × 10
50
u
63
+ 7.07 × 10
51
u
62
+ · · · + 5.23 × 10
51
b + 4.68 ×
10
51
, 3.28 × 10
51
u
63
− 3.60 × 10
52
u
62
+ · · · + 1.05 × 10
52
a + 6.80 ×
10
51
, u
64
− 11u
63
+ · · · − 7u + 2i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
5
=
−0.313675u
63
+ 3.43616u
62
+ ··· − 0.979049u − 0.649835
0.133650u
63
− 1.35076u
62
+ ··· + 2.88646u − 0.894649
a
8
=
1
−u
2
a
4
=
−0.447325u
63
+ 4.78692u
62
+ ··· − 3.86551u + 0.244814
0.133650u
63
− 1.35076u
62
+ ··· + 2.88646u − 0.894649
a
1
=
1.67303u
63
− 17.6572u
62
+ ··· + 0.940447u − 3.11259
−0.746060u
63
+ 8.24220u
62
+ ··· − 7.59861u + 3.34606
a
11
=
−u
u
3
+ u
a
9
=
u
2
+ 1
−u
4
− 2u
2
a
3
=
−0.113300u
63
+ 1.19153u
62
+ ··· − 2.35850u + 0.200252
0.0119472u
63
− 0.0387449u
62
+ ··· + 0.388066u + 0.0571673
a
10
=
0.313673u
63
− 3.54242u
62
+ ··· − 17.1019u + 2.42950
0.107084u
63
− 1.16286u
62
+ ··· − 2.46244u + 0.413177
a
6
=
−0.321571u
63
+ 3.42748u
62
+ ··· + 30.6898u − 2.41310
0.0791778u
63
− 0.868562u
62
+ ··· + 4.62645u − 0.699356
a
2
=
0.300016u
63
− 3.26751u
62
+ ··· − 28.0092u + 2.98991
−0.0356783u
63
+ 0.359671u
62
+ ··· − 3.75000u + 0.585720
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4.29495u
63
+ 46.7201u
62
+ ··· − 27.3846u − 3.10996
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
64
+ 26u
63
+ ··· + 5617u + 576
c
2
, c
5
u
64
+ 14u
63
+ ··· + 247u + 24
c
3
, c
10
u
64
+ 4u
62
+ ··· − 60u + 8
c
4
, c
12
u
64
+ 4u
63
+ ··· − 8u + 1
c
6
, c
9
u
64
− u
63
+ ··· + 8u + 3
c
7
, c
8
, c
11
u
64
+ 11u
63
+ ··· + 7u + 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
64
+ 26y
63
+ ··· + 2583071y + 331776
c
2
, c
5
y
64
− 26y
63
+ ··· − 5617y + 576
c
3
, c
10
y
64
+ 8y
63
+ ··· − 784y + 64
c
4
, c
12
y
64
+ 52y
63
+ ··· + 84y + 1
c
6
, c
9
y
64
− 21y
63
+ ··· − 406y + 9
c
7
, c
8
, c
11
y
64
+ 61y
63
+ ··· − 101y + 4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.874586 + 0.463761I
a = −0.476193 + 0.497848I
b = 0.78291 + 1.18416I
0.1569 + 15.1946I 0
u = 0.874586 − 0.463761I
a = −0.476193 − 0.497848I
b = 0.78291 − 1.18416I
0.1569 − 15.1946I 0
u = −0.134967 + 0.969394I
a = −0.716869 − 0.325913I
b = −0.493479 + 0.152045I
−0.52369 − 1.36537I 0
u = −0.134967 − 0.969394I
a = −0.716869 + 0.325913I
b = −0.493479 − 0.152045I
−0.52369 + 1.36537I 0
u = 0.850863 + 0.422917I
a = 0.512533 − 0.435812I
b = −0.78408 − 1.19047I
1.85492 + 9.31414I 0
u = 0.850863 − 0.422917I
a = 0.512533 + 0.435812I
b = −0.78408 + 1.19047I
1.85492 − 9.31414I 0
u = 0.709244 + 0.777818I
a = −0.806471 + 0.011283I
b = −0.453682 + 0.916244I
0.81096 − 3.99682I 0
u = 0.709244 − 0.777818I
a = −0.806471 − 0.011283I
b = −0.453682 − 0.916244I
0.81096 + 3.99682I 0
u = −0.735026 + 0.753807I
a = −0.115505 + 0.397307I
b = 0.024188 + 0.229007I
1.58932 − 0.39154I 0
u = −0.735026 − 0.753807I
a = −0.115505 − 0.397307I
b = 0.024188 − 0.229007I
1.58932 + 0.39154I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.788162 + 0.760204I
a = 0.744165 − 0.029302I
b = 0.455272 − 0.927701I
−0.67770 − 9.59565I 0
u = 0.788162 − 0.760204I
a = 0.744165 + 0.029302I
b = 0.455272 + 0.927701I
−0.67770 + 9.59565I 0
u = −0.440914 + 1.021510I
a = −0.242910 − 0.322440I
b = −0.236295 − 0.093976I
−0.66096 − 1.51732I 0
u = −0.440914 − 1.021510I
a = −0.242910 + 0.322440I
b = −0.236295 + 0.093976I
−0.66096 + 1.51732I 0
u = 0.696005 + 0.540499I
a = 0.702429 + 0.180538I
b = 0.400897 − 0.949464I
−5.18239 − 2.82741I 0
u = 0.696005 − 0.540499I
a = 0.702429 − 0.180538I
b = 0.400897 + 0.949464I
−5.18239 + 2.82741I 0
u = 0.723846 + 0.467849I
a = −0.719138 + 0.533500I
b = 0.79941 + 1.17427I
−4.95307 + 7.52151I 0
u = 0.723846 − 0.467849I
a = −0.719138 − 0.533500I
b = 0.79941 − 1.17427I
−4.95307 − 7.52151I 0
u = −0.739683 + 0.881622I
a = 0.049686 − 0.386731I
b = −0.062673 − 0.221372I
1.22982 − 5.09618I 0
u = −0.739683 − 0.881622I
a = 0.049686 + 0.386731I
b = −0.062673 + 0.221372I
1.22982 + 5.09618I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.722796 + 0.102347I
a = −0.064511 + 0.695991I
b = −0.003282 + 0.295639I
2.14767 − 2.42621I 3.53989 + 3.29368I
u = −0.722796 − 0.102347I
a = −0.064511 − 0.695991I
b = −0.003282 − 0.295639I
2.14767 + 2.42621I 3.53989 − 3.29368I
u = 0.661440 + 0.269912I
a = 0.917801 − 0.108418I
b = −0.89574 − 1.23400I
0.94406 + 4.53969I 0. − 14.5295I
u = 0.661440 − 0.269912I
a = 0.917801 + 0.108418I
b = −0.89574 + 1.23400I
0.94406 − 4.53969I 0. + 14.5295I
u = 0.679870 + 0.076087I
a = 0.093571 + 0.624963I
b = 0.256092 − 1.288630I
−0.92471 + 3.02354I −8.64857 − 7.07719I
u = 0.679870 − 0.076087I
a = 0.093571 − 0.624963I
b = 0.256092 + 1.288630I
−0.92471 − 3.02354I −8.64857 + 7.07719I
u = −0.268005 + 1.298910I
a = 0.302259 + 0.714643I
b = 0.467658 + 0.320477I
−2.20651 − 5.99017I 0
u = −0.268005 − 1.298910I
a = 0.302259 − 0.714643I
b = 0.467658 − 0.320477I
−2.20651 + 5.99017I 0
u = −0.034395 + 1.366090I
a = −0.30955 + 1.70708I
b = 0.593741 + 1.249710I
−6.03768 + 1.44933I 0
u = −0.034395 − 1.366090I
a = −0.30955 − 1.70708I
b = 0.593741 − 1.249710I
−6.03768 − 1.44933I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.157239 + 0.608409I
a = −1.143040 − 0.086657I
b = −0.300221 + 0.624616I
−0.561743 − 1.227990I −3.53833 + 4.98452I
u = 0.157239 − 0.608409I
a = −1.143040 + 0.086657I
b = −0.300221 − 0.624616I
−0.561743 + 1.227990I −3.53833 − 4.98452I
u = 0.241711 + 1.354500I
a = −0.77684 + 1.53237I
b = 0.32898 + 1.48682I
−5.06349 + 0.11632I 0
u = 0.241711 − 1.354500I
a = −0.77684 − 1.53237I
b = 0.32898 − 1.48682I
−5.06349 − 0.11632I 0
u = 0.306940 + 1.366480I
a = 1.14500 − 1.25058I
b = 0.07904 − 1.54786I
−5.55346 + 6.70378I 0
u = 0.306940 − 1.366480I
a = 1.14500 + 1.25058I
b = 0.07904 + 1.54786I
−5.55346 − 6.70378I 0
u = −0.059218 + 1.403030I
a = 0.23543 − 1.74553I
b = −0.637721 − 1.254150I
−6.56627 − 2.85756I 0
u = −0.059218 − 1.403030I
a = 0.23543 + 1.74553I
b = −0.637721 + 1.254150I
−6.56627 + 2.85756I 0
u = 0.144268 + 1.398570I
a = 0.38334 + 2.17822I
b = 1.39453 + 1.28541I
−7.67530 + 1.01817I 0
u = 0.144268 − 1.398570I
a = 0.38334 − 2.17822I
b = 1.39453 − 1.28541I
−7.67530 − 1.01817I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.25341 + 1.41328I
a = 0.28026 − 2.17866I
b = −1.00687 − 1.69702I
−4.44780 + 7.86984I 0
u = 0.25341 − 1.41328I
a = 0.28026 + 2.17866I
b = −1.00687 + 1.69702I
−4.44780 − 7.86984I 0
u = −0.01743 + 1.45361I
a = 0.08383 − 1.68567I
b = −0.721594 − 1.179600I
−7.56672 + 1.96899I 0
u = −0.01743 − 1.45361I
a = 0.08383 + 1.68567I
b = −0.721594 + 1.179600I
−7.56672 − 1.96899I 0
u = 0.01724 + 1.45371I
a = −0.142654 + 1.399870I
b = 0.563785 + 1.020420I
−6.78319 − 0.76865I 0
u = 0.01724 − 1.45371I
a = −0.142654 − 1.399870I
b = 0.563785 − 1.020420I
−6.78319 + 0.76865I 0
u = 0.26333 + 1.49598I
a = −0.11458 + 1.96767I
b = 0.97438 + 1.50802I
−11.3104 + 11.1323I 0
u = 0.26333 − 1.49598I
a = −0.11458 − 1.96767I
b = 0.97438 − 1.50802I
−11.3104 − 11.1323I 0
u = 0.335524 + 0.328284I
a = −1.68394 + 0.68354I
b = 0.761604 + 0.863069I
−2.21510 − 0.83970I −11.15859 + 0.95683I
u = 0.335524 − 0.328284I
a = −1.68394 − 0.68354I
b = 0.761604 − 0.863069I
−2.21510 + 0.83970I −11.15859 − 0.95683I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.31619 + 1.49846I
a = 0.16485 − 1.89226I
b = −0.92185 − 1.50636I
−4.3452 + 13.5483I 0
u = 0.31619 − 1.49846I
a = 0.16485 + 1.89226I
b = −0.92185 + 1.50636I
−4.3452 − 13.5483I 0
u = 0.32072 + 1.51879I
a = −0.14001 + 1.87382I
b = 0.92245 + 1.49081I
−6.2511 + 19.5398I 0
u = 0.32072 − 1.51879I
a = −0.14001 − 1.87382I
b = 0.92245 − 1.49081I
−6.2511 − 19.5398I 0
u = 0.21935 + 1.53725I
a = 0.564830 − 1.084320I
b = −0.144261 − 1.091660I
−12.04140 + 0.55096I 0
u = 0.21935 − 1.53725I
a = 0.564830 + 1.084320I
b = −0.144261 + 1.091660I
−12.04140 − 0.55096I 0
u = 0.10218 + 1.55806I
a = −0.358935 + 1.114100I
b = 0.277530 + 0.977718I
−7.36626 − 1.42331I 0
u = 0.10218 − 1.55806I
a = −0.358935 − 1.114100I
b = 0.277530 − 0.977718I
−7.36626 + 1.42331I 0
u = 0.12566 + 1.62075I
a = 0.382955 − 1.012810I
b = −0.199811 − 0.934705I
−9.07622 − 6.32501I 0
u = 0.12566 − 1.62075I
a = 0.382955 + 1.012810I
b = −0.199811 + 0.934705I
−9.07622 + 6.32501I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.014952 + 0.260009I
a = 3.44771 − 1.44981I
b = −0.187548 − 0.937540I
−1.81865 + 2.11391I −8.57768 − 4.29143I
u = 0.014952 − 0.260009I
a = 3.44771 + 1.44981I
b = −0.187548 + 0.937540I
−1.81865 − 2.11391I −8.57768 + 4.29143I
u = −0.150277 + 0.053346I
a = 2.05049 − 7.58298I
b = −0.033361 − 1.087320I
−1.60253 − 2.06668I −7.92019 + 3.31024I
u = −0.150277 − 0.053346I
a = 2.05049 + 7.58298I
b = −0.033361 + 1.087320I
−1.60253 + 2.06668I −7.92019 − 3.31024I
11
II. I
u
2
=
hu
40
a−23u
40
+· · ·−2a −351, u
40
a+u
40
+· · ·+2a
2
+12a, u
41
+9u
40
+· · ·−2u−2i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
5
=
a
−0.00251889au
40
+ 0.0579345u
40
+ ··· + 0.00503778a + 0.884131
a
8
=
1
−u
2
a
4
=
0.00251889au
40
− 0.0579345u
40
+ ··· + 0.994962a − 0.884131
−0.00251889au
40
+ 0.0579345u
40
+ ··· + 0.00503778a + 0.884131
a
1
=
−0.0579345au
40
− 0.167506u
40
+ ··· − 0.884131a + 0.335013
−1
a
11
=
−u
u
3
+ u
a
9
=
u
2
+ 1
−u
4
− 2u
2
a
3
=
0.00755668au
40
+ 0.826196u
40
+ ··· + 0.984887a + 0.347607
−0.0100756au
40
+ 0.231738u
40
+ ··· + 0.0201511a + 0.536524
a
10
=
−0.942065au
40
+ 0.167506u
40
+ ··· + 0.884131a − 1.33501
0.173804au
40
+ 0.00251889u
40
+ ··· + 1.65239a + 0.994962
a
6
=
−0.231738au
40
− 0.170025u
40
+ ··· − 0.536524a + 0.340050
−0.478589au
40
+ 0.00755668u
40
+ ··· + 0.957179a − 1.01511
a
2
=
−0.362720au
40
− 0.157431u
40
+ ··· + 0.725441a + 0.314861
0.0730479au
40
+ 0.319899u
40
+ ··· − 0.146096a − 0.639798
(ii) Obstruction class = −1
(iii) Cusp Shapes = −u
40
− 9u
39
+ ··· + 60u + 10
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
41
+ 18u
40
+ ··· + 8u + 1)
2
c
2
, c
5
(u
41
− 4u
40
+ ··· − 8u + 1)
2
c
3
, c
10
u
82
− 2u
81
+ ··· + 585u − 107
c
4
, c
12
u
82
+ 10u
81
+ ··· + 3081u + 397
c
6
, c
9
u
82
+ 3u
81
+ ··· + 14u − 1
c
7
, c
8
, c
11
(u
41
− 9u
40
+ ··· − 2u + 2)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
41
+ 14y
40
+ ··· − 64y −1)
2
c
2
, c
5
(y
41
− 18y
40
+ ··· + 8y −1)
2
c
3
, c
10
y
82
− 6y
81
+ ··· − 1905495y + 11449
c
4
, c
12
y
82
− 6y
81
+ ··· + 7892863y + 157609
c
6
, c
9
y
82
+ 29y
81
+ ··· + 102y + 1
c
7
, c
8
, c
11
(y
41
+ 41y
40
+ ··· + 68y −4)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.895003 + 0.498727I
a = 0.228170 + 0.653764I
b = −0.364274 + 0.745503I
1.95527 − 0.57118I 6.04148 + 0.I
u = −0.895003 + 0.498727I
a = −0.180264 + 0.084965I
b = 0.484487 − 0.377574I
1.95527 − 0.57118I 6.04148 + 0.I
u = −0.895003 − 0.498727I
a = 0.228170 − 0.653764I
b = −0.364274 − 0.745503I
1.95527 + 0.57118I 6.04148 + 0.I
u = −0.895003 − 0.498727I
a = −0.180264 − 0.084965I
b = 0.484487 + 0.377574I
1.95527 + 0.57118I 6.04148 + 0.I
u = −0.886395 + 0.578180I
a = −0.301896 − 0.711282I
b = 0.362364 − 0.753908I
1.72494 − 5.25730I 0. + 10.31079I
u = −0.886395 + 0.578180I
a = 0.1118320 + 0.0122452I
b = −0.564151 + 0.421846I
1.72494 − 5.25730I 0. + 10.31079I
u = −0.886395 − 0.578180I
a = −0.301896 + 0.711282I
b = 0.362364 + 0.753908I
1.72494 + 5.25730I 0. − 10.31079I
u = −0.886395 − 0.578180I
a = 0.1118320 − 0.0122452I
b = −0.564151 − 0.421846I
1.72494 + 5.25730I 0. − 10.31079I
u = −0.419922 + 0.819685I
a = 0.014090 − 0.384363I
b = 0.885747 − 0.743602I
−0.98956 − 6.71493I −5.68486 + 9.93728I
u = −0.419922 + 0.819685I
a = 1.08553 + 1.35316I
b = −0.071565 + 0.865337I
−0.98956 − 6.71493I −5.68486 + 9.93728I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.419922 − 0.819685I
a = 0.014090 + 0.384363I
b = 0.885747 + 0.743602I
−0.98956 + 6.71493I −5.68486 − 9.93728I
u = −0.419922 − 0.819685I
a = 1.08553 − 1.35316I
b = −0.071565 − 0.865337I
−0.98956 + 6.71493I −5.68486 − 9.93728I
u = −0.611668 + 0.673550I
a = −0.897282 − 0.800935I
b = 0.202337 − 0.749422I
0.11262 − 2.09272I −3.43576 + 6.46528I
u = −0.611668 + 0.673550I
a = 0.051980 + 0.320022I
b = −0.707298 + 0.709139I
0.11262 − 2.09272I −3.43576 + 6.46528I
u = −0.611668 − 0.673550I
a = −0.897282 + 0.800935I
b = 0.202337 + 0.749422I
0.11262 + 2.09272I −3.43576 − 6.46528I
u = −0.611668 − 0.673550I
a = 0.051980 − 0.320022I
b = −0.707298 − 0.709139I
0.11262 + 2.09272I −3.43576 − 6.46528I
u = 0.010846 + 1.176660I
a = 0.220167 − 0.103332I
b = 1.194090 − 0.448882I
−0.81120 − 6.28000I 0
u = 0.010846 + 1.176660I
a = 0.78926 + 2.16046I
b = 0.417158 + 1.142220I
−0.81120 − 6.28000I 0
u = 0.010846 − 1.176660I
a = 0.220167 + 0.103332I
b = 1.194090 + 0.448882I
−0.81120 + 6.28000I 0
u = 0.010846 − 1.176660I
a = 0.78926 − 2.16046I
b = 0.417158 − 1.142220I
−0.81120 + 6.28000I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.818516 + 0.080588I
a = −0.136568 + 0.739988I
b = 0.072690 − 0.231754I
2.05960 − 2.48926I 5.05170 + 3.34988I
u = −0.818516 + 0.080588I
a = 0.022594 + 0.540489I
b = −0.092970 + 0.812250I
2.05960 − 2.48926I 5.05170 + 3.34988I
u = −0.818516 − 0.080588I
a = −0.136568 − 0.739988I
b = 0.072690 + 0.231754I
2.05960 + 2.48926I 5.05170 − 3.34988I
u = −0.818516 − 0.080588I
a = 0.022594 − 0.540489I
b = −0.092970 − 0.812250I
2.05960 + 2.48926I 5.05170 − 3.34988I
u = −0.639274 + 0.516374I
a = −0.896282 − 0.287979I
b = 0.226609 − 0.614971I
0.01587 − 2.19785I −4.62987 + 3.78431I
u = −0.639274 + 0.516374I
a = 0.135764 + 0.379991I
b = −0.548985 + 0.788868I
0.01587 − 2.19785I −4.62987 + 3.78431I
u = −0.639274 − 0.516374I
a = −0.896282 + 0.287979I
b = 0.226609 + 0.614971I
0.01587 + 2.19785I −4.62987 − 3.78431I
u = −0.639274 − 0.516374I
a = 0.135764 − 0.379991I
b = −0.548985 − 0.788868I
0.01587 + 2.19785I −4.62987 − 3.78431I
u = 0.060616 + 1.245240I
a = −0.478038 − 0.113422I
b = −1.341780 + 0.294249I
0.518741 − 0.467338I 0
u = 0.060616 + 1.245240I
a = −0.74342 − 2.13731I
b = −0.560003 − 1.050850I
0.518741 − 0.467338I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.060616 − 1.245240I
a = −0.478038 + 0.113422I
b = −1.341780 − 0.294249I
0.518741 + 0.467338I 0
u = 0.060616 − 1.245240I
a = −0.74342 + 2.13731I
b = −0.560003 + 1.050850I
0.518741 + 0.467338I 0
u = 0.051790 + 1.355640I
a = 1.67533 + 0.89402I
b = 2.07461 + 0.45198I
−6.82732 + 1.10901I 0
u = 0.051790 + 1.355640I
a = 0.22861 + 2.03380I
b = 0.619918 + 0.518382I
−6.82732 + 1.10901I 0
u = 0.051790 − 1.355640I
a = 1.67533 − 0.89402I
b = 2.07461 − 0.45198I
−6.82732 − 1.10901I 0
u = 0.051790 − 1.355640I
a = 0.22861 − 2.03380I
b = 0.619918 − 0.518382I
−6.82732 − 1.10901I 0
u = 0.113233 + 1.355730I
a = −1.392110 + 0.006299I
b = −1.97238 + 0.29182I
−0.56183 + 4.07949I 0
u = 0.113233 + 1.355730I
a = −0.54589 − 2.21697I
b = −0.452801 − 0.754352I
−0.56183 + 4.07949I 0
u = 0.113233 − 1.355730I
a = −1.392110 − 0.006299I
b = −1.97238 − 0.29182I
−0.56183 − 4.07949I 0
u = 0.113233 − 1.355730I
a = −0.54589 + 2.21697I
b = −0.452801 + 0.754352I
−0.56183 − 4.07949I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.121620 + 1.382840I
a = 1.54321 − 0.21411I
b = 2.09745 − 0.43998I
−2.70065 + 9.94272I 0
u = 0.121620 + 1.382840I
a = 0.56310 + 2.27185I
b = 0.379745 + 0.738954I
−2.70065 + 9.94272I 0
u = 0.121620 − 1.382840I
a = 1.54321 + 0.21411I
b = 2.09745 + 0.43998I
−2.70065 − 9.94272I 0
u = 0.121620 − 1.382840I
a = 0.56310 − 2.27185I
b = 0.379745 − 0.738954I
−2.70065 − 9.94272I 0
u = −0.11243 + 1.47381I
a = 0.94793 + 1.14508I
b = −0.448256 + 0.644032I
−9.88760 − 1.87876I 0
u = −0.11243 + 1.47381I
a = 0.43790 − 2.27062I
b = 0.89542 − 2.00137I
−9.88760 − 1.87876I 0
u = −0.11243 − 1.47381I
a = 0.94793 − 1.14508I
b = −0.448256 − 0.644032I
−9.88760 + 1.87876I 0
u = −0.11243 − 1.47381I
a = 0.43790 + 2.27062I
b = 0.89542 + 2.00137I
−9.88760 + 1.87876I 0
u = −0.19812 + 1.48876I
a = −0.474902 − 1.143990I
b = 0.596565 − 0.804826I
−6.49780 − 5.13988I 0
u = −0.19812 + 1.48876I
a = −0.13362 + 1.85101I
b = −0.71721 + 1.52796I
−6.49780 − 5.13988I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.19812 − 1.48876I
a = −0.474902 + 1.143990I
b = 0.596565 + 0.804826I
−6.49780 + 5.13988I 0
u = −0.19812 − 1.48876I
a = −0.13362 − 1.85101I
b = −0.71721 − 1.52796I
−6.49780 + 5.13988I 0
u = −0.32440 + 1.49994I
a = 0.053639 − 0.997050I
b = 0.898273 − 0.879292I
−4.41110 − 4.99632I 0
u = −0.32440 + 1.49994I
a = 0.23313 + 1.67970I
b = −0.450628 + 1.228700I
−4.41110 − 4.99632I 0
u = −0.32440 − 1.49994I
a = 0.053639 + 0.997050I
b = 0.898273 + 0.879292I
−4.41110 + 4.99632I 0
u = −0.32440 − 1.49994I
a = 0.23313 − 1.67970I
b = −0.450628 − 1.228700I
−4.41110 + 4.99632I 0
u = 0.427131 + 0.126572I
a = −0.850674 − 1.066150I
b = 1.32158 − 0.58582I
2.16617 + 8.04413I 3.23482 − 9.57385I
u = 0.427131 + 0.126572I
a = −1.60367 + 2.58379I
b = 0.867044 + 0.480110I
2.16617 + 8.04413I 3.23482 − 9.57385I
u = 0.427131 − 0.126572I
a = −0.850674 + 1.066150I
b = 1.32158 + 0.58582I
2.16617 − 8.04413I 3.23482 + 9.57385I
u = 0.427131 − 0.126572I
a = −1.60367 − 2.58379I
b = 0.867044 − 0.480110I
2.16617 − 8.04413I 3.23482 + 9.57385I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.219482 + 0.374158I
a = −0.077285 − 0.434566I
b = 0.90234 − 1.26494I
−3.72236 − 0.49265I −14.4012 + 8.8169I
u = −0.219482 + 0.374158I
a = 3.66345 + 0.86758I
b = 0.095682 + 0.548786I
−3.72236 − 0.49265I −14.4012 + 8.8169I
u = −0.219482 − 0.374158I
a = −0.077285 + 0.434566I
b = 0.90234 + 1.26494I
−3.72236 + 0.49265I −14.4012 − 8.8169I
u = −0.219482 − 0.374158I
a = 3.66345 − 0.86758I
b = 0.095682 − 0.548786I
−3.72236 + 0.49265I −14.4012 − 8.8169I
u = −0.16366 + 1.55976I
a = 0.57780 + 1.45391I
b = −0.425868 + 0.876727I
−8.69063 − 9.00195I 0
u = −0.16366 + 1.55976I
a = 0.48022 − 1.68275I
b = 1.06453 − 1.47103I
−8.69063 − 9.00195I 0
u = −0.16366 − 1.55976I
a = 0.57780 − 1.45391I
b = −0.425868 − 0.876727I
−8.69063 + 9.00195I 0
u = −0.16366 − 1.55976I
a = 0.48022 + 1.68275I
b = 1.06453 + 1.47103I
−8.69063 + 9.00195I 0
u = 0.423290 + 0.074566I
a = 1.08364 + 1.12062I
b = −1.267640 + 0.504067I
3.99395 + 2.22617I 7.06416 − 3.62614I
u = 0.423290 + 0.074566I
a = 1.75182 − 2.10296I
b = −0.949298 − 0.436305I
3.99395 + 2.22617I 7.06416 − 3.62614I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.423290 − 0.074566I
a = 1.08364 − 1.12062I
b = −1.267640 − 0.504067I
3.99395 − 2.22617I 7.06416 + 3.62614I
u = 0.423290 − 0.074566I
a = 1.75182 + 2.10296I
b = −0.949298 + 0.436305I
3.99395 − 2.22617I 7.06416 + 3.62614I
u = −0.32810 + 1.54346I
a = −0.169998 + 1.063150I
b = −0.956224 + 0.939190I
−5.09204 − 9.73833I 0
u = −0.32810 + 1.54346I
a = −0.25890 − 1.64183I
b = 0.449285 − 1.172840I
−5.09204 − 9.73833I 0
u = −0.32810 − 1.54346I
a = −0.169998 − 1.063150I
b = −0.956224 − 0.939190I
−5.09204 + 9.73833I 0
u = −0.32810 − 1.54346I
a = −0.25890 + 1.64183I
b = 0.449285 + 1.172840I
−5.09204 + 9.73833I 0
u = −0.24479 + 1.56149I
a = −0.22945 + 1.41041I
b = −0.92367 + 1.19156I
−7.15140 − 5.46612I 0
u = −0.24479 + 1.56149I
a = −0.32361 − 1.49103I
b = 0.511679 − 1.030450I
−7.15140 − 5.46612I 0
u = −0.24479 − 1.56149I
a = −0.22945 − 1.41041I
b = −0.92367 − 1.19156I
−7.15140 + 5.46612I 0
u = −0.24479 − 1.56149I
a = −0.32361 + 1.49103I
b = 0.511679 + 1.030450I
−7.15140 + 5.46612I 0
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.306458
a = −1.21310
b = 1.54542
−2.52366 12.9440
u = 0.306458
a = −4.19749
b = 0.845371
−2.52366 12.9440
23
III. I
u
3
=
hu
22
+8u
21
+· · ·+b+5, −5u
24
−40u
23
+· · ·+3a−28, u
25
+8u
24
+· · ·+32u+3i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
5
=
5
3
u
24
+
40
3
u
23
+ ··· + 50u +
28
3
−u
22
− 8u
21
+ ··· − 39u − 5
a
8
=
1
−u
2
a
4
=
5
3
u
24
+
40
3
u
23
+ ··· + 89u +
43
3
−u
22
− 8u
21
+ ··· − 39u − 5
a
1
=
−
1
3
u
24
−
8
3
u
23
+ ··· − 77u −
44
3
−u
23
− 7u
22
+ ··· − 3u + 1
a
11
=
−u
u
3
+ u
a
9
=
u
2
+ 1
−u
4
− 2u
2
a
3
=
5
3
u
24
+
40
3
u
23
+ ··· + 75u +
37
3
−u
23
− 8u
22
+ ··· − 42u − 5
a
10
=
−
1
3
u
24
−
8
3
u
23
+ ··· − 52u −
26
3
u
3
+ u
2
+ 2u + 1
a
6
=
1
3
u
24
+
8
3
u
23
+ ··· + 47u +
23
3
−u
6
− 2u
5
− 5u
4
− 6u
3
− 6u
2
− 4u − 1
a
2
=
1
3
u
24
+
8
3
u
23
+ ··· + 43u +
17
3
u
12
+ 3u
11
+ ··· − 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 3u
24
+ 22u
23
+ 109u
22
+ 388u
21
+ 1105u
20
+ 2575u
19
+ 5015u
18
+ 8151u
17
+ 10861u
16
+
11103u
15
+ 6569u
14
− 4034u
13
− 19705u
12
− 36760u
11
− 50147u
10
− 55645u
9
−
52088u
8
− 41626u
7
− 28506u
6
− 16633u
5
− 8210u
4
− 3352u
3
− 1100u
2
− 264u − 45
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
25
− 11u
24
+ ··· + 181u − 25
c
2
u
25
+ 5u
24
+ ··· − 19u − 5
c
3
, c
10
u
25
− 4u
23
+ ··· + 2u − 1
c
4
, c
12
u
25
− 2u
24
+ ··· − 5u
2
− 1
c
5
u
25
− 5u
24
+ ··· − 19u + 5
c
6
, c
9
u
25
− u
24
+ ··· − 2u − 1
c
7
, c
8
u
25
+ 8u
24
+ ··· + 32u + 3
c
11
u
25
− 8u
24
+ ··· + 32u − 3
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
25
+ 9y
24
+ ··· − 6839y −625
c
2
, c
5
y
25
− 11y
24
+ ··· + 181y −25
c
3
, c
10
y
25
− 8y
24
+ ··· + 6y −1
c
4
, c
12
y
25
− 4y
24
+ ··· − 10y −1
c
6
, c
9
y
25
+ 19y
24
+ ··· − 4y −1
c
7
, c
8
, c
11
y
25
+ 24y
24
+ ··· + 70y −9
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.576444 + 0.969341I
a = 0.379668 + 0.209239I
b = 0.054711 + 0.458924I
−1.02619 − 1.43748I −16.2333 − 2.9546I
u = −0.576444 − 0.969341I
a = 0.379668 − 0.209239I
b = 0.054711 − 0.458924I
−1.02619 + 1.43748I −16.2333 + 2.9546I
u = −0.931888 + 0.672170I
a = −0.264572 − 0.316082I
b = 0.240368 − 0.658525I
1.25319 − 0.89811I −6.98325 + 4.85594I
u = −0.931888 − 0.672170I
a = −0.264572 + 0.316082I
b = 0.240368 + 0.658525I
1.25319 + 0.89811I −6.98325 − 4.85594I
u = −0.784209 + 0.325897I
a = −0.438102 − 0.122877I
b = 0.442828 − 0.883870I
0.72959 − 3.41642I −1.89603 + 7.39585I
u = −0.784209 − 0.325897I
a = −0.438102 + 0.122877I
b = 0.442828 + 0.883870I
0.72959 + 3.41642I −1.89603 − 7.39585I
u = −0.891055 + 0.802899I
a = 0.267624 + 0.346611I
b = −0.200681 + 0.616389I
0.90295 − 5.48733I −9.1395 + 11.3352I
u = −0.891055 − 0.802899I
a = 0.267624 − 0.346611I
b = −0.200681 − 0.616389I
0.90295 + 5.48733I −9.1395 − 11.3352I
u = 0.009100 + 1.204320I
a = 1.11578 − 1.19339I
b = 1.241870 − 0.161249I
0.55437 + 2.06439I 0.56220 − 5.61553I
u = 0.009100 − 1.204320I
a = 1.11578 + 1.19339I
b = 1.241870 + 0.161249I
0.55437 − 2.06439I 0.56220 + 5.61553I
27
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.077572 + 1.251490I
a = −0.99205 + 1.20898I
b = −1.154850 + 0.276108I
−1.60934 + 8.24258I −3.95853 − 7.30408I
u = 0.077572 − 1.251490I
a = −0.99205 − 1.20898I
b = −1.154850 − 0.276108I
−1.60934 − 8.24258I −3.95853 + 7.30408I
u = −0.024404 + 0.675855I
a = 0.67742 − 1.33114I
b = 0.846931 − 0.084135I
2.57567 − 2.05291I 0.29912 + 2.44445I
u = −0.024404 − 0.675855I
a = 0.67742 + 1.33114I
b = 0.846931 + 0.084135I
2.57567 + 2.05291I 0.29912 − 2.44445I
u = −0.120437 + 1.387100I
a = −0.69250 + 1.93112I
b = −1.45966 + 0.94542I
−7.68290 − 1.31345I −16.2154 + 12.2980I
u = −0.120437 − 1.387100I
a = −0.69250 − 1.93112I
b = −1.45966 − 0.94542I
−7.68290 + 1.31345I −16.2154 − 12.2980I
u = 0.086133 + 0.537197I
a = −0.94595 + 1.72487I
b = −0.877275 + 0.102818I
1.02130 − 7.51968I −3.42239 + 6.83772I
u = 0.086133 − 0.537197I
a = −0.94595 − 1.72487I
b = −0.877275 − 0.102818I
1.02130 + 7.51968I −3.42239 − 6.83772I
u = −0.29046 + 1.43058I
a = −0.48507 − 1.62567I
b = 0.56192 − 1.44547I
−4.88048 − 7.25668I −6.48725 + 7.01686I
u = −0.29046 − 1.43058I
a = −0.48507 + 1.62567I
b = 0.56192 + 1.44547I
−4.88048 + 7.25668I −6.48725 − 7.01686I
28
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.19019 + 1.57688I
a = −0.124245 + 1.364400I
b = −0.776904 + 0.950431I
−7.22545 − 8.96892I −5.89690 + 8.58792I
u = −0.19019 − 1.57688I
a = −0.124245 − 1.364400I
b = −0.776904 − 0.950431I
−7.22545 + 8.96892I −5.89690 − 8.58792I
u = −0.25892 + 1.57684I
a = −0.026557 − 1.314760I
b = 0.662871 − 1.007580I
−6.21776 − 5.03899I −3.59021 + 1.71413I
u = −0.25892 − 1.57684I
a = −0.026557 + 1.314760I
b = 0.662871 + 1.007580I
−6.21776 + 5.03899I −3.59021 − 1.71413I
u = −0.209597
a = 4.39046
b = −1.16425
−2.84804 −18.0770
29
IV. I
u
4
= hau + 3b − 2a + u + 1, 2a
2
− au + 2a + 5, u
2
+ 2i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
5
=
a
−
1
3
au +
2
3
a −
1
3
u −
1
3
a
8
=
1
2
a
4
=
1
3
au +
1
3
a +
1
3
u +
1
3
−
1
3
au +
2
3
a −
1
3
u −
1
3
a
1
=
−
1
3
au −
1
3
a +
1
6
u +
2
3
1
a
11
=
−u
−u
a
9
=
−1
0
a
3
=
a
−
1
3
au +
2
3
a −
1
3
u −
1
3
a
10
=
1
3
au +
1
3
a −
1
6
u −
5
3
−1
a
6
=
1
3
au +
1
3
a −
1
6
u −
2
3
−1
a
2
=
−
1
3
au +
2
3
a +
1
6
u +
2
3
−
1
3
au +
2
3
a −
1
3
u +
2
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
10
u
4
+ 2u
3
+ 3u
2
+ 2u + 3
c
4
, c
12
u
4
− 2u
3
+ 3u
2
− 2u + 3
c
5
, c
6
, c
9
(u + 1)
4
c
7
, c
8
, c
11
(u
2
+ 2)
2
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
9
(y −1)
4
c
3
, c
4
, c
10
c
12
y
4
+ 2y
3
+ 7y
2
+ 14y + 9
c
7
, c
8
, c
11
(y + 2)
4
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = −0.385607 − 1.191790I
b = −1.15222 − 1.08415I
−8.22467 −12.0000
u = 1.414210I
a = −0.61439 + 1.89890I
b = 0.152220 + 1.084150I
−8.22467 −12.0000
u = − 1.414210I
a = −0.385607 + 1.191790I
b = −1.15222 + 1.08415I
−8.22467 −12.0000
u = − 1.414210I
a = −0.61439 − 1.89890I
b = 0.152220 − 1.084150I
−8.22467 −12.0000
33
V. I
v
1
= ha, b + v, v
2
− v + 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
v
0
a
5
=
0
−v
a
8
=
1
0
a
4
=
v
−v
a
1
=
v − 1
1
a
11
=
v
0
a
9
=
1
0
a
3
=
0
−v
a
10
=
v
1
a
6
=
−v + 1
−1
a
2
=
v − 1
−v + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
9
(u − 1)
2
c
3
, c
4
, c
10
c
12
u
2
− u + 1
c
5
(u + 1)
2
c
7
, c
8
, c
11
u
2
35
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
9
(y − 1)
2
c
3
, c
4
, c
10
c
12
y
2
+ y + 1
c
7
, c
8
, c
11
y
2
36
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = −0.500000 − 0.866025I
−3.28987 −6.00000
v = 0.500000 − 0.866025I
a = 0
b = −0.500000 + 0.866025I
−3.28987 −6.00000
37
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
25
− 11u
24
+ ··· + 181u − 25)
· ((u
41
+ 18u
40
+ ··· + 8u + 1)
2
)(u
64
+ 26u
63
+ ··· + 5617u + 576)
c
2
((u − 1)
6
)(u
25
+ 5u
24
+ ··· − 19u − 5)(u
41
− 4u
40
+ ··· − 8u + 1)
2
· (u
64
+ 14u
63
+ ··· + 247u + 24)
c
3
, c
10
(u
2
− u + 1)(u
4
+ 2u
3
+ ··· + 2u + 3)(u
25
− 4u
23
+ ··· + 2u − 1)
· (u
64
+ 4u
62
+ ··· − 60u + 8)(u
82
− 2u
81
+ ··· + 585u − 107)
c
4
, c
12
(u
2
− u + 1)(u
4
− 2u
3
+ ··· − 2u + 3)(u
25
− 2u
24
+ ··· − 5u
2
− 1)
· (u
64
+ 4u
63
+ ··· − 8u + 1)(u
82
+ 10u
81
+ ··· + 3081u + 397)
c
5
((u + 1)
6
)(u
25
− 5u
24
+ ··· − 19u + 5)(u
41
− 4u
40
+ ··· − 8u + 1)
2
· (u
64
+ 14u
63
+ ··· + 247u + 24)
c
6
, c
9
((u − 1)
2
)(u + 1)
4
(u
25
− u
24
+ ··· − 2u − 1)(u
64
− u
63
+ ··· + 8u + 3)
· (u
82
+ 3u
81
+ ··· + 14u − 1)
c
7
, c
8
u
2
(u
2
+ 2)
2
(u
25
+ 8u
24
+ ··· + 32u + 3)(u
41
− 9u
40
+ ··· − 2u + 2)
2
· (u
64
+ 11u
63
+ ··· + 7u + 2)
c
11
u
2
(u
2
+ 2)
2
(u
25
− 8u
24
+ ··· + 32u − 3)(u
41
− 9u
40
+ ··· − 2u + 2)
2
· (u
64
+ 11u
63
+ ··· + 7u + 2)
38
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
6
)(y
25
+ 9y
24
+ ··· − 6839y − 625)
· (y
41
+ 14y
40
+ ··· − 64y − 1)
2
· (y
64
+ 26y
63
+ ··· + 2583071y + 331776)
c
2
, c
5
((y − 1)
6
)(y
25
− 11y
24
+ ··· + 181y − 25)
· ((y
41
− 18y
40
+ ··· + 8y − 1)
2
)(y
64
− 26y
63
+ ··· − 5617y + 576)
c
3
, c
10
(y
2
+ y + 1)(y
4
+ 2y
3
+ ··· + 14y + 9)(y
25
− 8y
24
+ ··· + 6y − 1)
· (y
64
+ 8y
63
+ ··· − 784y + 64)(y
82
− 6y
81
+ ··· − 1905495y + 11449)
c
4
, c
12
(y
2
+ y + 1)(y
4
+ 2y
3
+ ··· + 14y + 9)(y
25
− 4y
24
+ ··· − 10y − 1)
· (y
64
+ 52y
63
+ ··· + 84y + 1)(y
82
− 6y
81
+ ··· + 7892863y + 157609)
c
6
, c
9
((y − 1)
6
)(y
25
+ 19y
24
+ ··· − 4y − 1)(y
64
− 21y
63
+ ··· − 406y + 9)
· (y
82
+ 29y
81
+ ··· + 102y + 1)
c
7
, c
8
, c
11
y
2
(y + 2)
4
(y
25
+ 24y
24
+ ··· + 70y − 9)
· ((y
41
+ 41y
40
+ ··· + 68y − 4)
2
)(y
64
+ 61y
63
+ ··· − 101y + 4)
39
