12a
0804
(K12a
0804
)
A knot diagram
1
Linearized knot diagam
4 5 6 9 8 11 3 2 12 1 7 10
Solving Sequence
10,12 1,4
2 9 5 3 8 6 7 11
c
12
c
1
c
9
c
4
c
2
c
8
c
5
c
7
c
11
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.46655 × 10
73
u
66
+ 4.19280 × 10
74
u
65
+ ··· + 5.68441 × 10
73
b + 8.22113 × 10
74
,
− 6.82885 × 10
73
u
66
+ 3.74607 × 10
74
u
65
+ ··· + 5.68441 × 10
73
a + 4.88086 × 10
74
,
u
67
− 7u
66
+ ··· + 17u + 16i
I
u
2
= h−4.31286 × 10
18
au
45
+ 7.66921 × 10
18
u
45
+ ··· + 2.80217 × 10
18
a − 5.40388 × 10
18
,
4276100239374611u
45
a + 1318919595635818u
45
+ ··· − 2872520987122649a − 510440857054024,
u
46
− 5u
45
+ ··· + u + 1i
I
u
3
= hu
20
− 8u
19
+ ··· + b − 4u, 3u
20
− 12u
19
+ ··· + a + 3, u
21
− 4u
20
+ ··· − u − 1i
I
u
4
= h4a
3
− 7a
2
+ b + 6a − 3, 4a
4
− 7a
3
+ 7a
2
− 4a + 1, u + 1i
I
u
5
= ha
5
− 5a
4
+ 13a
3
− 16a
2
+ b + 11a − 4, a
6
− 5a
5
+ 13a
4
− 16a
3
+ 12a
2
− 5a + 1, u + 1i
I
u
6
= h−au + b − a − 1, a
2
+ 2au − a − 3u + 6, u
2
− u − 1i
* 6 irreducible components of dim
C
= 0, with total 194 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−7.47 × 10
73
u
66
+ 4.19 × 10
74
u
65
+ · · · + 5.68 × 10
73
b + 8.22 ×
10
74
, −6.83 × 10
73
u
66
+ 3.75 × 10
74
u
65
+ · · · + 5.68 × 10
73
a + 4.88 ×
10
74
, u
67
− 7u
66
+ · · · + 17u + 16i
(i) Arc colorings
a
10
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
1.20133u
66
− 6.59007u
65
+ ··· − 8.38458u − 8.58640
1.31351u
66
− 7.37596u
65
+ ··· − 28.0095u − 14.4626
a
2
=
3.37831u
66
− 18.7956u
65
+ ··· − 63.1226u − 34.2832
1.97158u
66
− 10.8079u
65
+ ··· − 34.5481u − 19.6508
a
9
=
u
u
a
5
=
1.43693u
66
− 7.65419u
65
+ ··· − 6.59990u − 8.59606
1.54912u
66
− 8.44009u
65
+ ··· − 26.2248u − 14.4723
a
3
=
2.78686u
66
− 15.6625u
65
+ ··· − 51.4076u − 30.4248
1.70541u
66
− 9.35021u
65
+ ··· − 30.1704u − 16.9114
a
8
=
−2.88579u
66
+ 16.9817u
65
+ ··· + 66.6836u + 38.9741
−0.883475u
66
+ 5.46866u
65
+ ··· + 30.5641u + 14.4408
a
6
=
−1.59108u
66
+ 8.68445u
65
+ ··· + 35.8380u + 17.6639
−1.23122u
66
+ 6.72157u
65
+ ··· + 18.6619u + 12.2584
a
7
=
2.65000u
66
− 15.0717u
65
+ ··· − 65.4616u − 33.0722
0.963019u
66
− 5.68222u
65
+ ··· − 23.4083u − 13.2523
a
11
=
−u
−u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.97364u
66
+ 17.8037u
65
+ ··· + 63.3507u + 35.1757
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
67
+ 10u
66
+ ··· + 102u − 1
c
2
u
67
+ 37u
66
+ ··· + 52u + 4
c
4
, c
7
u
67
+ 5u
65
+ ··· − 4u + 1
c
5
, c
8
u
67
+ u
66
+ ··· + 5u + 1
c
6
, c
11
u
67
− 5u
66
+ ··· − 736u + 256
c
9
, c
10
, c
12
u
67
− 7u
66
+ ··· + 17u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
67
− 34y
66
+ ··· + 7148y −1
c
2
y
67
− y
66
+ ··· + 1096y −16
c
4
, c
7
y
67
+ 10y
66
+ ··· + 40y −1
c
5
, c
8
y
67
+ 29y
66
+ ··· − 69y −1
c
6
, c
11
y
67
− 27y
66
+ ··· + 947200y −65536
c
9
, c
10
, c
12
y
67
− 59y
66
+ ··· − 10527y −256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.886040 + 0.462607I
a = 0.418801 − 0.553515I
b = 0.941164 + 0.197930I
−3.77727 − 2.29823I 0
u = −0.886040 − 0.462607I
a = 0.418801 + 0.553515I
b = 0.941164 − 0.197930I
−3.77727 + 2.29823I 0
u = −0.506108 + 0.879870I
a = 0.103195 + 0.584858I
b = −0.095104 − 0.358363I
−2.67608 − 0.95592I 0
u = −0.506108 − 0.879870I
a = 0.103195 − 0.584858I
b = −0.095104 + 0.358363I
−2.67608 + 0.95592I 0
u = −0.278352 + 0.927953I
a = 0.381479 + 0.825242I
b = −1.177430 + 0.199299I
−0.2794 + 15.6078I −6.00000 − 9.90214I
u = −0.278352 − 0.927953I
a = 0.381479 − 0.825242I
b = −1.177430 − 0.199299I
−0.2794 − 15.6078I −6.00000 + 9.90214I
u = −0.875010 + 0.359675I
a = 0.086232 − 0.705853I
b = 0.651120 − 0.766803I
−3.78014 + 1.26212I −17.5567 − 2.3807I
u = −0.875010 − 0.359675I
a = 0.086232 + 0.705853I
b = 0.651120 + 0.766803I
−3.78014 − 1.26212I −17.5567 + 2.3807I
u = −0.832278 + 0.744916I
a = 0.307640 + 0.044559I
b = −0.719105 − 0.118462I
−3.66147 + 6.63575I 0
u = −0.832278 − 0.744916I
a = 0.307640 − 0.044559I
b = −0.719105 + 0.118462I
−3.66147 − 6.63575I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.146600 + 0.015974I
a = 0.236410 − 0.731304I
b = −0.179252 + 0.333247I
0.57345 + 7.56399I 0
u = 1.146600 − 0.015974I
a = 0.236410 + 0.731304I
b = −0.179252 − 0.333247I
0.57345 − 7.56399I 0
u = −0.265956 + 0.807155I
a = −0.144674 − 1.268960I
b = 0.774720 − 0.398888I
−1.83450 + 6.83794I −13.0499 − 9.4798I
u = −0.265956 − 0.807155I
a = −0.144674 + 1.268960I
b = 0.774720 + 0.398888I
−1.83450 − 6.83794I −13.0499 + 9.4798I
u = −0.142952 + 0.833197I
a = 0.393388 − 0.285156I
b = 0.717234 − 0.035393I
−1.24487 + 2.78705I −11.56898 − 3.57731I
u = −0.142952 − 0.833197I
a = 0.393388 + 0.285156I
b = 0.717234 + 0.035393I
−1.24487 − 2.78705I −11.56898 + 3.57731I
u = −1.151610 + 0.247358I
a = 1.093750 + 0.479916I
b = 1.326200 − 0.169578I
−0.874218 + 1.068790I 0
u = −1.151610 − 0.247358I
a = 1.093750 − 0.479916I
b = 1.326200 + 0.169578I
−0.874218 − 1.068790I 0
u = −1.003220 + 0.631301I
a = 0.066674 + 0.801201I
b = −0.139183 − 0.463104I
−2.46151 − 10.19180I 0
u = −1.003220 − 0.631301I
a = 0.066674 − 0.801201I
b = −0.139183 + 0.463104I
−2.46151 + 10.19180I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.868429 + 0.825439I
a = 0.178701 + 0.010283I
b = −0.151600 + 0.224746I
4.21754 − 3.05286I 0
u = 0.868429 − 0.825439I
a = 0.178701 − 0.010283I
b = −0.151600 − 0.224746I
4.21754 + 3.05286I 0
u = −1.226260 + 0.017383I
a = −2.80177 + 1.01170I
b = −3.10614 + 1.95095I
−4.09165 + 0.04865I 0
u = −1.226260 − 0.017383I
a = −2.80177 − 1.01170I
b = −3.10614 − 1.95095I
−4.09165 − 0.04865I 0
u = 0.514220 + 0.564393I
a = −0.277985 − 0.852832I
b = −0.077903 + 0.542054I
1.47490 + 6.03278I −3.03499 − 7.78090I
u = 0.514220 − 0.564393I
a = −0.277985 + 0.852832I
b = −0.077903 − 0.542054I
1.47490 − 6.03278I −3.03499 + 7.78090I
u = 0.317644 + 0.657692I
a = 0.923425 − 0.718468I
b = −0.990234 − 0.352466I
2.11508 − 9.83520I −3.28213 + 7.19382I
u = 0.317644 − 0.657692I
a = 0.923425 + 0.718468I
b = −0.990234 + 0.352466I
2.11508 + 9.83520I −3.28213 − 7.19382I
u = −1.267820 + 0.254906I
a = −0.98278 − 1.28187I
b = −1.23559 − 1.32066I
−4.47405 + 1.01497I 0
u = −1.267820 − 0.254906I
a = −0.98278 + 1.28187I
b = −1.23559 + 1.32066I
−4.47405 − 1.01497I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.122225 + 0.694677I
a = 0.507052 − 0.261280I
b = −0.863507 − 0.202693I
2.18927 + 2.39577I −0.67460 − 3.37107I
u = −0.122225 − 0.694677I
a = 0.507052 + 0.261280I
b = −0.863507 + 0.202693I
2.18927 − 2.39577I −0.67460 + 3.37107I
u = 1.308110 + 0.162425I
a = 0.626403 + 0.525881I
b = 1.097540 − 0.180102I
−4.15383 − 0.16010I 0
u = 1.308110 − 0.162425I
a = 0.626403 − 0.525881I
b = 1.097540 + 0.180102I
−4.15383 + 0.16010I 0
u = −0.650492
a = 0.859311
b = 0.351682
−1.00288 −10.0410
u = −1.334120 + 0.204364I
a = −2.54568 − 0.16258I
b = −3.25877 + 0.06740I
−4.75755 + 4.80110I 0
u = −1.334120 − 0.204364I
a = −2.54568 + 0.16258I
b = −3.25877 − 0.06740I
−4.75755 − 4.80110I 0
u = −0.297590 + 0.569032I
a = −0.388782 + 0.838417I
b = 1.67541 + 0.17339I
−1.93809 + 1.60095I −10.43691 − 4.02924I
u = −0.297590 − 0.569032I
a = −0.388782 − 0.838417I
b = 1.67541 − 0.17339I
−1.93809 − 1.60095I −10.43691 + 4.02924I
u = −0.363048 + 0.527813I
a = 0.67980 − 1.94335I
b = −0.054527 − 0.387963I
−2.13919 + 1.55825I −11.25159 − 5.43160I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.363048 − 0.527813I
a = 0.67980 + 1.94335I
b = −0.054527 + 0.387963I
−2.13919 − 1.55825I −11.25159 + 5.43160I
u = 1.342900 + 0.275476I
a = 0.895399 − 0.647673I
b = 1.231760 + 0.093797I
−2.43663 − 5.90398I 0
u = 1.342900 − 0.275476I
a = 0.895399 + 0.647673I
b = 1.231760 − 0.093797I
−2.43663 + 5.90398I 0
u = 1.41253 + 0.22914I
a = −1.74771 + 0.52569I
b = −2.18934 − 0.54716I
−7.40801 − 4.57388I 0
u = 1.41253 − 0.22914I
a = −1.74771 − 0.52569I
b = −2.18934 + 0.54716I
−7.40801 + 4.57388I 0
u = 1.38655 + 0.37104I
a = −1.078820 + 0.668747I
b = −1.43331 + 0.46079I
−6.09824 − 7.18020I 0
u = 1.38655 − 0.37104I
a = −1.078820 − 0.668747I
b = −1.43331 − 0.46079I
−6.09824 + 7.18020I 0
u = 1.42617 + 0.19546I
a = −0.990215 + 0.549897I
b = −1.49974 + 1.39131I
−7.87593 − 4.21311I 0
u = 1.42617 − 0.19546I
a = −0.990215 − 0.549897I
b = −1.49974 − 1.39131I
−7.87593 + 4.21311I 0
u = −1.42366 + 0.26282I
a = 2.21278 + 0.02414I
b = 3.06613 − 0.66738I
−3.44703 + 13.22340I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42366 − 0.26282I
a = 2.21278 − 0.02414I
b = 3.06613 + 0.66738I
−3.44703 − 13.22340I 0
u = 1.41803 + 0.32540I
a = −2.05092 + 0.35648I
b = −2.83519 + 0.16768I
−7.19836 − 10.93070I 0
u = 1.41803 − 0.32540I
a = −2.05092 − 0.35648I
b = −2.83519 − 0.16768I
−7.19836 + 10.93070I 0
u = 0.077770 + 0.518056I
a = −0.54086 + 1.77842I
b = 0.801606 + 0.510059I
−0.26465 − 2.13116I −8.00844 + 3.42216I
u = 0.077770 − 0.518056I
a = −0.54086 − 1.77842I
b = 0.801606 − 0.510059I
−0.26465 + 2.13116I −8.00844 − 3.42216I
u = 1.48184 + 0.01796I
a = −1.88623 + 0.56334I
b = −2.49946 + 0.63940I
−11.54390 + 1.53289I 0
u = 1.48184 − 0.01796I
a = −1.88623 − 0.56334I
b = −2.49946 − 0.63940I
−11.54390 − 1.53289I 0
u = −1.48064 + 0.12268I
a = 0.960629 + 0.677197I
b = 1.60297 + 1.04822I
−5.25353 − 3.65413I 0
u = −1.48064 − 0.12268I
a = 0.960629 − 0.677197I
b = 1.60297 − 1.04822I
−5.25353 + 3.65413I 0
u = 1.44769 + 0.37948I
a = 2.01395 − 0.39710I
b = 2.93042 + 0.30305I
−5.7776 − 20.3102I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.44769 − 0.37948I
a = 2.01395 + 0.39710I
b = 2.93042 − 0.30305I
−5.7776 + 20.3102I 0
u = 1.50160 + 0.27397I
a = 0.892084 − 0.367176I
b = 1.66203 − 0.53253I
−9.25323 − 3.05507I 0
u = 1.50160 − 0.27397I
a = 0.892084 + 0.367176I
b = 1.66203 + 0.53253I
−9.25323 + 3.05507I 0
u = 1.57951 + 0.06444I
a = 1.49720 + 0.37848I
b = 2.31797 + 0.90383I
−12.2490 − 9.1394I 0
u = 1.57951 − 0.06444I
a = 1.49720 − 0.37848I
b = 2.31797 − 0.90383I
−12.2490 + 9.1394I 0
u = 0.052527 + 0.206865I
a = 2.37554 + 2.38725I
b = 0.408286 − 0.391016I
−0.97444 + 1.07725I −5.67594 − 4.49690I
u = 0.052527 − 0.206865I
a = 2.37554 − 2.38725I
b = 0.408286 + 0.391016I
−0.97444 − 1.07725I −5.67594 + 4.49690I
11
II.
I
u
2
= h−4.31×10
18
au
45
+7.67×10
18
u
45
+· · ·+2.80×10
18
a−5.40×10
18
, 4.28×
10
15
au
45
+1.32×10
15
u
45
+· · ·−2.87×10
15
a−5.10×10
14
, u
46
−5u
45
+· · ·+u+1i
(i) Arc colorings
a
10
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
a
7.26494au
45
− 12.9187u
45
+ ··· − 4.72021a + 9.10275
a
2
=
10.0594au
45
+ 15.4174u
45
+ ··· − 8.05021a − 12.4526
6.68466au
45
+ 7.33727u
45
+ ··· − 5.87490a − 7.18934
a
9
=
u
u
a
5
=
−15.9507au
45
+ 30.4136u
45
+ ··· + 11.8538a − 20.4155
−8.68580au
45
+ 17.4950u
45
+ ··· + 6.13364a − 11.3128
a
3
=
−17.5185au
45
+ 44.1901u
45
+ ··· + 13.3266a − 31.6617
−5.57001au
45
+ 23.9234u
45
+ ··· + 4.75911a − 17.0092
a
8
=
−8.81370au
45
− 30.2038u
45
+ ··· + 5.57064a + 20.7364
−9.90551au
45
− 24.5364u
45
+ ··· + 5.91698a + 16.1933
a
6
=
16.2495u
45
− 56.2137u
44
+ ··· − 20.5991u − 11.7119
11.5267u
45
− 40.6880u
44
+ ··· − 11.8242u − 7.98688
a
7
=
−26.2810u
45
+ 96.5901u
44
+ ··· + 38.3673u + 20.9461
−9.23423u
45
+ 36.1396u
44
+ ··· + 13.8688u + 8.53396
a
11
=
−u
−u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
3565132764588699
137866554138758
u
45
+
12143571441573331
137866554138758
u
44
+ ··· +
5241235151619549
137866554138758
u +
692954415625718
68933277069379
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
92
− 6u
91
+ ··· + 21848u − 4007
c
2
(u
46
− 22u
45
+ ··· + 6u + 4)
2
c
4
, c
7
u
92
+ 5u
91
+ ··· + 59081u − 15649
c
5
, c
8
u
92
+ 9u
91
+ ··· + 9u + 1
c
6
, c
11
(u
46
+ 2u
45
+ ··· + 12u − 8)
2
c
9
, c
10
, c
12
(u
46
− 5u
45
+ ··· + u + 1)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
92
+ 26y
91
+ ··· − 169276944y + 16056049
c
2
(y
46
− 6y
45
+ ··· − 460y + 16)
2
c
4
, c
7
y
92
− y
91
+ ··· + 7756027461y + 244891201
c
5
, c
8
y
92
− 25y
91
+ ··· + 5y + 1
c
6
, c
11
(y
46
− 24y
45
+ ··· − 464y + 64)
2
c
9
, c
10
, c
12
(y
46
− 43y
45
+ ··· + y + 1)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.301208 + 0.925317I
a = 0.539502 + 0.595975I
b = −1.070430 − 0.078921I
1.27204 + 7.29420I −2.20923 − 9.60817I
u = −0.301208 + 0.925317I
a = −0.235983 − 0.541720I
b = 0.514580 − 0.442022I
1.27204 + 7.29420I −2.20923 − 9.60817I
u = −0.301208 − 0.925317I
a = 0.539502 − 0.595975I
b = −1.070430 + 0.078921I
1.27204 − 7.29420I −2.20923 + 9.60817I
u = −0.301208 − 0.925317I
a = −0.235983 + 0.541720I
b = 0.514580 + 0.442022I
1.27204 − 7.29420I −2.20923 + 9.60817I
u = −0.722332 + 0.600949I
a = 0.547852 − 0.821980I
b = 0.521373 + 0.207530I
−3.35914 − 1.96952I −15.8602 + 4.3814I
u = −0.722332 + 0.600949I
a = 0.628225 − 0.570814I
b = −1.159030 − 0.808305I
−3.35914 − 1.96952I −15.8602 + 4.3814I
u = −0.722332 − 0.600949I
a = 0.547852 + 0.821980I
b = 0.521373 − 0.207530I
−3.35914 + 1.96952I −15.8602 − 4.3814I
u = −0.722332 − 0.600949I
a = 0.628225 + 0.570814I
b = −1.159030 + 0.808305I
−3.35914 + 1.96952I −15.8602 − 4.3814I
u = −1.069300 + 0.154626I
a = −0.028114 + 0.733560I
b = 0.58442 + 1.82190I
−0.54999 − 3.11732I −1.92655 + 7.58795I
u = −1.069300 + 0.154626I
a = 4.41452 − 0.50911I
b = 4.15151 − 0.93227I
−0.54999 − 3.11732I −1.92655 + 7.58795I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.069300 − 0.154626I
a = −0.028114 − 0.733560I
b = 0.58442 − 1.82190I
−0.54999 + 3.11732I −1.92655 − 7.58795I
u = −1.069300 − 0.154626I
a = 4.41452 + 0.50911I
b = 4.15151 + 0.93227I
−0.54999 + 3.11732I −1.92655 − 7.58795I
u = −0.371010 + 0.778352I
a = −0.335013 − 0.893259I
b = 0.943969 − 0.589431I
−2.25962 + 6.70622I −12.6754 − 9.2419I
u = −0.371010 + 0.778352I
a = 0.37172 + 1.51058I
b = 0.135168 − 0.591500I
−2.25962 + 6.70622I −12.6754 − 9.2419I
u = −0.371010 − 0.778352I
a = −0.335013 + 0.893259I
b = 0.943969 + 0.589431I
−2.25962 − 6.70622I −12.6754 + 9.2419I
u = −0.371010 − 0.778352I
a = 0.37172 − 1.51058I
b = 0.135168 + 0.591500I
−2.25962 − 6.70622I −12.6754 + 9.2419I
u = −0.968236 + 0.657208I
a = 0.385680 + 0.494198I
b = 0.021923 − 0.727960I
−0.73382 − 1.83088I 0
u = −0.968236 + 0.657208I
a = 0.351392 − 0.367182I
b = 0.216413 + 0.038938I
−0.73382 − 1.83088I 0
u = −0.968236 − 0.657208I
a = 0.385680 − 0.494198I
b = 0.021923 + 0.727960I
−0.73382 + 1.83088I 0
u = −0.968236 − 0.657208I
a = 0.351392 + 0.367182I
b = 0.216413 − 0.038938I
−0.73382 + 1.83088I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.18912
a = 0.381769 + 0.593804I
b = 0.205686 − 0.488546I
2.15622 −11.6170
u = 1.18912
a = 0.381769 − 0.593804I
b = 0.205686 + 0.488546I
2.15622 −11.6170
u = −1.147130 + 0.330381I
a = 0.662485 − 0.140870I
b = 0.941847 − 0.872914I
−1.02869 + 1.23073I 0
u = −1.147130 + 0.330381I
a = 1.45074 + 1.11037I
b = 1.60150 + 0.22264I
−1.02869 + 1.23073I 0
u = −1.147130 − 0.330381I
a = 0.662485 + 0.140870I
b = 0.941847 + 0.872914I
−1.02869 − 1.23073I 0
u = −1.147130 − 0.330381I
a = 1.45074 − 1.11037I
b = 1.60150 − 0.22264I
−1.02869 − 1.23073I 0
u = −1.209740 + 0.143206I
a = −0.20791 + 2.25198I
b = 0.06312 + 1.64377I
−0.98248 + 4.74267I 0
u = −1.209740 + 0.143206I
a = −3.71784 + 0.24484I
b = −4.79294 + 0.94523I
−0.98248 + 4.74267I 0
u = −1.209740 − 0.143206I
a = −0.20791 − 2.25198I
b = 0.06312 − 1.64377I
−0.98248 − 4.74267I 0
u = −1.209740 − 0.143206I
a = −3.71784 − 0.24484I
b = −4.79294 − 0.94523I
−0.98248 − 4.74267I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.227074 + 0.675918I
a = −0.04766 − 1.46821I
b = −1.11495 − 1.22759I
1.69571 + 6.30129I −2.30828 − 10.19820I
u = −0.227074 + 0.675918I
a = −1.29068 − 1.06858I
b = 0.860694 + 0.064321I
1.69571 + 6.30129I −2.30828 − 10.19820I
u = −0.227074 − 0.675918I
a = −0.04766 + 1.46821I
b = −1.11495 + 1.22759I
1.69571 − 6.30129I −2.30828 + 10.19820I
u = −0.227074 − 0.675918I
a = −1.29068 + 1.06858I
b = 0.860694 − 0.064321I
1.69571 − 6.30129I −2.30828 + 10.19820I
u = 0.344671 + 0.595078I
a = 1.103900 − 0.381172I
b = −0.664606 − 0.215065I
3.89027 − 1.72774I 3.38137 + 3.27076I
u = 0.344671 + 0.595078I
a = −0.612797 − 0.019410I
b = 0.279786 + 0.632492I
3.89027 − 1.72774I 3.38137 + 3.27076I
u = 0.344671 − 0.595078I
a = 1.103900 + 0.381172I
b = −0.664606 + 0.215065I
3.89027 + 1.72774I 3.38137 − 3.27076I
u = 0.344671 − 0.595078I
a = −0.612797 + 0.019410I
b = 0.279786 − 0.632492I
3.89027 + 1.72774I 3.38137 − 3.27076I
u = −0.085734 + 0.681652I
a = 0.963556 − 0.446059I
b = −0.619372 − 0.367941I
2.23568 + 2.45642I −0.01179 − 3.81685I
u = −0.085734 + 0.681652I
a = 0.126903 − 0.138439I
b = −1.141800 + 0.059750I
2.23568 + 2.45642I −0.01179 − 3.81685I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.085734 − 0.681652I
a = 0.963556 + 0.446059I
b = −0.619372 + 0.367941I
2.23568 − 2.45642I −0.01179 + 3.81685I
u = −0.085734 − 0.681652I
a = 0.126903 + 0.138439I
b = −1.141800 − 0.059750I
2.23568 − 2.45642I −0.01179 + 3.81685I
u = 1.341210 + 0.248066I
a = 0.352859 − 0.409330I
b = 0.589078 + 0.533839I
−2.27518 − 5.75756I 0
u = 1.341210 + 0.248066I
a = 1.57949 − 0.74710I
b = 1.83012 − 0.27573I
−2.27518 − 5.75756I 0
u = 1.341210 − 0.248066I
a = 0.352859 + 0.409330I
b = 0.589078 − 0.533839I
−2.27518 + 5.75756I 0
u = 1.341210 − 0.248066I
a = 1.57949 + 0.74710I
b = 1.83012 + 0.27573I
−2.27518 + 5.75756I 0
u = 1.352860 + 0.220635I
a = −0.090295 + 0.166667I
b = 0.286702 − 1.050280I
−2.52895 − 0.78794I 0
u = 1.352860 + 0.220635I
a = 2.25611 + 0.05895I
b = 2.47483 + 0.22157I
−2.52895 − 0.78794I 0
u = 1.352860 − 0.220635I
a = −0.090295 − 0.166667I
b = 0.286702 + 1.050280I
−2.52895 + 0.78794I 0
u = 1.352860 − 0.220635I
a = 2.25611 − 0.05895I
b = 2.47483 − 0.22157I
−2.52895 + 0.78794I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.377160 + 0.121934I
a = 1.64144 + 1.05392I
b = 2.76256 + 1.70475I
−4.85206 + 4.48235I 0
u = −1.377160 + 0.121934I
a = −2.38363 + 0.84125I
b = −2.92612 + 1.38254I
−4.85206 + 4.48235I 0
u = −1.377160 − 0.121934I
a = 1.64144 − 1.05392I
b = 2.76256 − 1.70475I
−4.85206 − 4.48235I 0
u = −1.377160 − 0.121934I
a = −2.38363 − 0.84125I
b = −2.92612 − 1.38254I
−4.85206 − 4.48235I 0
u = 1.389940 + 0.148912I
a = 0.349849 + 1.319640I
b = 0.567378 + 0.478581I
−5.20345 + 1.73809I 0
u = 1.389940 + 0.148912I
a = −1.29994 + 1.12545I
b = −2.53703 + 1.65541I
−5.20345 + 1.73809I 0
u = 1.389940 − 0.148912I
a = 0.349849 − 1.319640I
b = 0.567378 − 0.478581I
−5.20345 − 1.73809I 0
u = 1.389940 − 0.148912I
a = −1.29994 − 1.12545I
b = −2.53703 − 1.65541I
−5.20345 − 1.73809I 0
u = −0.126964 + 0.583172I
a = −0.172976 + 0.845888I
b = −0.830353 + 1.056760I
2.17456 − 2.13057I 0.528217 + 0.482801I
u = −0.126964 + 0.583172I
a = −0.71720 + 2.33552I
b = 1.100310 + 0.405651I
2.17456 − 2.13057I 0.528217 + 0.482801I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.126964 − 0.583172I
a = −0.172976 − 0.845888I
b = −0.830353 − 1.056760I
2.17456 + 2.13057I 0.528217 − 0.482801I
u = −0.126964 − 0.583172I
a = −0.71720 − 2.33552I
b = 1.100310 − 0.405651I
2.17456 + 2.13057I 0.528217 − 0.482801I
u = 1.39331 + 0.26832I
a = −0.32148 − 1.52891I
b = −0.221650 − 0.877142I
−3.47417 − 9.74350I 0
u = 1.39331 + 0.26832I
a = −2.17851 + 0.26231I
b = −3.36915 − 0.45804I
−3.47417 − 9.74350I 0
u = 1.39331 − 0.26832I
a = −0.32148 + 1.52891I
b = −0.221650 + 0.877142I
−3.47417 + 9.74350I 0
u = 1.39331 − 0.26832I
a = −2.17851 − 0.26231I
b = −3.36915 + 0.45804I
−3.47417 + 9.74350I 0
u = −1.43606 + 0.24418I
a = −1.135010 + 0.372690I
b = −1.37977 + 0.71731I
−1.82755 + 4.86298I 0
u = −1.43606 + 0.24418I
a = 1.81852 + 0.06882I
b = 2.75506 − 0.57441I
−1.82755 + 4.86298I 0
u = −1.43606 − 0.24418I
a = −1.135010 − 0.372690I
b = −1.37977 − 0.71731I
−1.82755 − 4.86298I 0
u = −1.43606 − 0.24418I
a = 1.81852 − 0.06882I
b = 2.75506 + 0.57441I
−1.82755 − 4.86298I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.45662 + 0.29701I
a = 0.961195 − 0.905782I
b = 2.20336 − 1.56100I
−8.11909 − 10.60200I 0
u = 1.45662 + 0.29701I
a = −2.17260 + 0.01181I
b = −2.84085 − 0.49073I
−8.11909 − 10.60200I 0
u = 1.45662 − 0.29701I
a = 0.961195 + 0.905782I
b = 2.20336 + 1.56100I
−8.11909 + 10.60200I 0
u = 1.45662 − 0.29701I
a = −2.17260 − 0.01181I
b = −2.84085 + 0.49073I
−8.11909 + 10.60200I 0
u = 1.45643 + 0.37392I
a = −1.348470 − 0.086022I
b = −1.77780 − 0.47622I
−4.33358 − 11.97120I 0
u = 1.45643 + 0.37392I
a = 1.74861 − 0.40228I
b = 2.73577 + 0.36563I
−4.33358 − 11.97120I 0
u = 1.45643 − 0.37392I
a = −1.348470 + 0.086022I
b = −1.77780 + 0.47622I
−4.33358 + 11.97120I 0
u = 1.45643 − 0.37392I
a = 1.74861 + 0.40228I
b = 2.73577 − 0.36563I
−4.33358 + 11.97120I 0
u = 1.55105 + 0.09953I
a = −1.130330 + 0.686945I
b = −1.52179 + 0.99310I
−11.04640 − 0.32883I 0
u = 1.55105 + 0.09953I
a = 1.59938 + 0.11962I
b = 2.75969 + 0.96468I
−11.04640 − 0.32883I 0
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.55105 − 0.09953I
a = −1.130330 − 0.686945I
b = −1.52179 − 0.99310I
−11.04640 + 0.32883I 0
u = 1.55105 − 0.09953I
a = 1.59938 − 0.11962I
b = 2.75969 − 0.96468I
−11.04640 + 0.32883I 0
u = −0.327271 + 0.203052I
a = −2.17963 − 1.96372I
b = −0.373911 + 0.659538I
0.12568 − 3.43436I −10.17762 + 5.29029I
u = −0.327271 + 0.203052I
a = 0.68703 + 4.31707I
b = 0.80137 + 1.64583I
0.12568 − 3.43436I −10.17762 + 5.29029I
u = −0.327271 − 0.203052I
a = −2.17963 + 1.96372I
b = −0.373911 − 0.659538I
0.12568 + 3.43436I −10.17762 − 5.29029I
u = −0.327271 − 0.203052I
a = 0.68703 − 4.31707I
b = 0.80137 − 1.64583I
0.12568 + 3.43436I −10.17762 − 5.29029I
u = 1.64968
a = −0.583630
b = −0.721202
−10.4247 0
u = 1.64968
a = 1.43079
b = 2.95527
−10.4247 0
u = 0.163730 + 0.182438I
a = −3.63921 − 0.10567I
b = 0.683249 + 0.865240I
0.07877 − 3.07282I −4.99472 + 4.05780I
u = 0.163730 + 0.182438I
a = 1.39893 − 3.68699I
b = −0.366951 + 0.271171I
0.07877 − 3.07282I −4.99472 + 4.05780I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.163730 − 0.182438I
a = −3.63921 + 0.10567I
b = 0.683249 − 0.865240I
0.07877 + 3.07282I −4.99472 − 4.05780I
u = 0.163730 − 0.182438I
a = 1.39893 + 3.68699I
b = −0.366951 − 0.271171I
0.07877 + 3.07282I −4.99472 − 4.05780I
24
III.
I
u
3
= hu
20
−8u
19
+· · ·+b−4u, 3u
20
−12u
19
+· · ·+a+3, u
21
−4u
20
+· · ·−u−1i
(i) Arc colorings
a
10
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
−3u
20
+ 12u
19
+ ··· − 6u − 3
−u
20
+ 8u
19
+ ··· + 16u
2
+ 4u
a
2
=
14u
20
− 50u
19
+ ··· − 10u − 2
13u
20
− 44u
19
+ ··· + 13u
2
+ 9u
a
9
=
u
u
a
5
=
−11u
20
+ 35u
19
+ ··· − 12u − 7
−9u
20
+ 31u
19
+ ··· − 2u − 4
a
3
=
−6u
20
+ 20u
19
+ ··· − 11u − 4
−4u
20
+ 16u
19
+ ··· − u − 2
a
8
=
−u
20
+ 5u
19
+ ··· + 15u + 3
2u
20
− 10u
19
+ ··· − u + 2
a
6
=
−10u
20
+ 29u
19
+ ··· − 9u − 9
−7u
20
+ 21u
19
+ ··· − u − 3
a
7
=
−11u
20
+ 33u
19
+ ··· − 12u − 12
−3u
20
+ 11u
19
+ ··· − 11u
2
+ u
a
11
=
−u
−u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
34u
20
−91u
19
−145u
18
+513u
17
+230u
16
−1187u
15
−319u
14
+1629u
13
+670u
12
−1653u
11
−
1075u
10
+ 1056u
9
+ 1354u
8
−121u
7
−1101u
6
−340u
5
+ 255u
4
+ 200u
3
+ 96u
2
+ 20u −5
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
21
− 6u
20
+ ··· + 11u − 1
c
2
u
21
+ 15u
20
+ ··· − 47u − 11
c
4
, c
7
u
21
− 3u
19
+ ··· − 3u − 1
c
5
, c
8
u
21
+ 3u
20
+ ··· + 3u
2
− 1
c
6
u
21
− 2u
20
+ ··· − u + 1
c
9
, c
10
u
21
+ 4u
20
+ ··· − u + 1
c
11
u
21
+ 2u
20
+ ··· − u − 1
c
12
u
21
− 4u
20
+ ··· − u − 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
21
+ 14y
20
+ ··· + 11y −1
c
2
y
21
+ 5y
20
+ ··· + 3331y −121
c
4
, c
7
y
21
− 6y
20
+ ··· + 11y −1
c
5
, c
8
y
21
− 11y
20
+ ··· + 6y −1
c
6
, c
11
y
21
− 6y
20
+ ··· − 7y −1
c
9
, c
10
, c
12
y
21
− 18y
20
+ ··· − 15y −1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.786082 + 0.662342I
a = −0.039577 − 0.206327I
b = 0.377059 + 0.573897I
−1.78905 − 1.86556I −10.45393 + 5.20822I
u = −0.786082 − 0.662342I
a = −0.039577 + 0.206327I
b = 0.377059 − 0.573897I
−1.78905 + 1.86556I −10.45393 − 5.20822I
u = −1.073990 + 0.004776I
a = 4.52653 + 2.65432I
b = 5.18591 + 1.96100I
−0.99148 + 3.67030I 9.64428 − 4.49671I
u = −1.073990 − 0.004776I
a = 4.52653 − 2.65432I
b = 5.18591 − 1.96100I
−0.99148 − 3.67030I 9.64428 + 4.49671I
u = −0.337564 + 0.789732I
a = −0.574936 − 1.042070I
b = 0.448449 − 0.218313I
−0.53843 + 6.73076I −6.35237 − 9.05790I
u = −0.337564 − 0.789732I
a = −0.574936 + 1.042070I
b = 0.448449 + 0.218313I
−0.53843 − 6.73076I −6.35237 + 9.05790I
u = 0.851251 + 0.838826I
a = −0.202834 + 0.042291I
b = 0.157701 − 0.171924I
4.20454 − 3.09844I −32.5936 + 83.7201I
u = 0.851251 − 0.838826I
a = −0.202834 − 0.042291I
b = 0.157701 + 0.171924I
4.20454 + 3.09844I −32.5936 − 83.7201I
u = 1.311130 + 0.227451I
a = 0.691668 − 1.087020I
b = 1.184120 − 0.460768I
−3.03604 − 6.90956I −11.5554 + 10.0692I
u = 1.311130 − 0.227451I
a = 0.691668 + 1.087020I
b = 1.184120 + 0.460768I
−3.03604 + 6.90956I −11.5554 − 10.0692I
28
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.342310 + 0.185206I
a = 1.052450 + 0.424879I
b = 1.60654 − 0.32706I
−3.54626 + 0.58020I −8.86695 − 3.99015I
u = 1.342310 − 0.185206I
a = 1.052450 − 0.424879I
b = 1.60654 + 0.32706I
−3.54626 − 0.58020I −8.86695 + 3.99015I
u = −1.384460 + 0.144996I
a = −1.75860 + 0.39956I
b = −2.46728 + 0.63972I
−3.22992 + 4.52365I −9.21976 − 6.14992I
u = −1.384460 − 0.144996I
a = −1.75860 − 0.39956I
b = −2.46728 − 0.63972I
−3.22992 − 4.52365I −9.21976 + 6.14992I
u = 1.43929 + 0.31387I
a = −1.74095 + 0.11892I
b = −2.57103 − 0.08510I
−6.19647 − 10.73290I −8.91183 + 8.46185I
u = 1.43929 − 0.31387I
a = −1.74095 − 0.11892I
b = −2.57103 + 0.08510I
−6.19647 + 10.73290I −8.91183 − 8.46185I
u = −0.113522 + 0.434272I
a = −0.63865 + 2.97662I
b = 0.518207 + 0.778236I
1.08397 − 2.95386I −2.37662 + 3.52429I
u = −0.113522 − 0.434272I
a = −0.63865 − 2.97662I
b = 0.518207 − 0.778236I
1.08397 + 2.95386I −2.37662 − 3.52429I
u = 1.55482
a = −1.32648
b = −2.02550
−10.4277 −15.1730
u = −0.025771 + 0.425646I
a = 1.348130 + 0.324850I
b = −0.426919 − 0.922609I
1.15871 + 4.26686I −3.22739 − 7.39189I
29
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.025771 − 0.425646I
a = 1.348130 − 0.324850I
b = −0.426919 + 0.922609I
1.15871 − 4.26686I −3.22739 + 7.39189I
30
IV. I
u
4
= h4a
3
− 7a
2
+ b + 6a − 3, 4a
4
− 7a
3
+ 7a
2
− 4a + 1, u + 1i
(i) Arc colorings
a
10
=
0
−1
a
12
=
1
0
a
1
=
1
1
a
4
=
a
−4a
3
+ 7a
2
− 6a + 3
a
2
=
−a + 2
−8a
3
+ 10a
2
− 8a + 4
a
9
=
−1
−1
a
5
=
4a
3
− 7a
2
+ 8a − 3
a
a
3
=
4a
2
− 6a + 3
−4a
3
+ 7a
2
− 6a + 3
a
8
=
12a
3
− 13a
2
+ 8a − 3
8a
3
− 10a
2
+ 8a − 3
a
6
=
4a
2
− 3a
0
a
7
=
4a
2
− 3a
0
a
11
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −16a
3
− 7a
2
+ 11a − 13
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
u
4
+ u
2
− u + 1
c
2
u
4
− 3u
3
+ 4u
2
− 3u + 2
c
5
u
4
+ 2u
3
+ 3u
2
+ u + 1
c
6
, c
11
u
4
c
7
u
4
+ u
2
+ u + 1
c
8
u
4
− 2u
3
+ 3u
2
− u + 1
c
9
, c
10
(u − 1)
4
c
12
(u + 1)
4
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
2
y
4
− y
3
+ 2y
2
+ 7y + 4
c
5
, c
8
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
6
, c
11
y
4
c
9
, c
10
, c
12
(y −1)
4
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.309733 + 0.767100I
b = −0.237691 − 0.353773I
0.98010 − 7.64338I 2.12768 + 8.80169I
u = −1.00000
a = 0.309733 − 0.767100I
b = −0.237691 + 0.353773I
0.98010 + 7.64338I 2.12768 − 8.80169I
u = −1.00000
a = 0.565267 + 0.213936I
b = 1.112690 − 0.371716I
−2.62503 + 1.39709I −10.34643 − 2.46427I
u = −1.00000
a = 0.565267 − 0.213936I
b = 1.112690 + 0.371716I
−2.62503 − 1.39709I −10.34643 + 2.46427I
34
V. I
u
5
=
ha
5
−5a
4
+13a
3
−16a
2
+b+11a−4, a
6
−5a
5
+13a
4
−16a
3
+12a
2
−5a+1, u+1 i
(i) Arc colorings
a
10
=
0
−1
a
12
=
1
0
a
1
=
1
1
a
4
=
a
−a
5
+ 5a
4
− 13a
3
+ 16a
2
− 11a + 4
a
2
=
−a + 2
−3a
5
+ 14a
4
− 34a
3
+ 35a
2
− 21a + 6
a
9
=
−1
−1
a
5
=
a
5
− 5a
4
+ 13a
3
− 16a
2
+ 13a − 4
a
a
3
=
4a
5
− 19a
4
+ 46a
3
− 47a
2
+ 25a − 5
−a
5
+ 5a
4
− 13a
3
+ 16a
2
− 11a + 4
a
8
=
5a
5
− 23a
4
+ 55a
3
− 54a
2
+ 29a − 6
a
4
− 4a
3
+ 9a
2
− 7a + 3
a
6
=
a
5
− 6a
4
+ 17a
3
− 24a
2
+ 16a − 4
0
a
7
=
a
5
− 6a
4
+ 17a
3
− 24a
2
+ 16a − 4
0
a
11
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −13a
5
+ 50a
4
− 102a
3
+ 53a
2
− 19a − 9
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
2
(u
3
+ u
2
− 1)
2
c
5
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
6
, c
11
u
6
c
7
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
8
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
9
, c
10
(u − 1)
6
c
12
(u + 1)
6
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
2
(y
3
− y
2
+ 2y −1)
2
c
5
, c
8
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
6
, c
11
y
6
c
9
, c
10
, c
12
(y −1)
6
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.407481 + 0.635452I
b = 0.122561 − 0.479689I
2.75839 2.60886 + 0.I
u = −1.00000
a = 0.407481 − 0.635452I
b = 0.122561 + 0.479689I
2.75839 2.60886 + 0.I
u = −1.00000
a = 0.461306 + 0.308178I
b = 0.960138 − 0.693124I
−1.37919 + 2.82812I −10.80443 − 4.65175I
u = −1.00000
a = 0.461306 − 0.308178I
b = 0.960138 + 0.693124I
−1.37919 − 2.82812I −10.80443 + 4.65175I
u = −1.00000
a = 1.63121 + 1.74382I
b = 0.91730 + 1.43799I
−1.37919 + 2.82812I −10.80443 − 4.65175I
u = −1.00000
a = 1.63121 − 1.74382I
b = 0.91730 − 1.43799I
−1.37919 − 2.82812I −10.80443 + 4.65175I
38
VI. I
u
6
= h−au + b − a − 1, a
2
+ 2au − a − 3u + 6, u
2
− u − 1i
(i) Arc colorings
a
10
=
0
u
a
12
=
1
0
a
1
=
1
u + 1
a
4
=
a
au + a + 1
a
2
=
a + 1
au + a + u + 2
a
9
=
u
u
a
5
=
−2au − u − 1
−au − u
a
3
=
a + 1
au + a + u + 2
a
8
=
a + 3u − 2
2au + 2a + 5u + 1
a
6
=
−1
−u − 1
a
7
=
u
u
a
11
=
−u
−u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −9u − 21
39
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u − 1)
4
c
2
u
4
c
4
, c
5
, c
7
c
8
u
4
− 3u
3
+ 3u
2
− 3u + 1
c
6
, c
9
, c
10
(u
2
+ u − 1)
2
c
11
, c
12
(u
2
− u − 1)
2
40
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y −1)
4
c
2
y
4
c
4
, c
5
, c
7
c
8
y
4
− 3y
3
− 7y
2
− 3y + 1
c
6
, c
9
, c
10
c
11
, c
12
(y
2
− 3y + 1)
2
41
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = 1.11803 + 2.56984I
b = 1.42705 + 0.98159I
−2.63189 −15.4380
u = −0.618034
a = 1.11803 − 2.56984I
b = 1.42705 − 0.98159I
−2.63189 −15.4380
u = 1.61803
a = −0.795386
b = −1.08235
−10.5276 −35.5620
u = 1.61803
a = −1.44068
b = −2.77176
−10.5276 −35.5620
42
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
(u − 1)
4
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
21
− 6u
20
+ ··· + 11u − 1)(u
67
+ 10u
66
+ ··· + 102u − 1)
· (u
92
− 6u
91
+ ··· + 21848u − 4007)
c
2
u
4
(u
3
+ u
2
− 1)
2
(u
4
− 3u
3
+ ··· − 3u + 2)(u
21
+ 15u
20
+ ··· − 47u − 11)
· ((u
46
− 22u
45
+ ··· + 6u + 4)
2
)(u
67
+ 37u
66
+ ··· + 52u + 4)
c
4
(u
4
+ u
2
− u + 1)(u
4
− 3u
3
+ 3u
2
− 3u + 1)
· (u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)(u
21
− 3u
19
+ ··· − 3u − 1)
· (u
67
+ 5u
65
+ ··· − 4u + 1)(u
92
+ 5u
91
+ ··· + 59081u − 15649)
c
5
(u
4
− 3u
3
+ 3u
2
− 3u + 1)(u
4
+ 2u
3
+ 3u
2
+ u + 1)
· (u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)(u
21
+ 3u
20
+ ··· + 3u
2
− 1)
· (u
67
+ u
66
+ ··· + 5u + 1)(u
92
+ 9u
91
+ ··· + 9u + 1)
c
6
u
10
(u
2
+ u − 1)
2
(u
21
− 2u
20
+ ··· − u + 1)
· ((u
46
+ 2u
45
+ ··· + 12u − 8)
2
)(u
67
− 5u
66
+ ··· − 736u + 256)
c
7
(u
4
+ u
2
+ u + 1)(u
4
− 3u
3
+ 3u
2
− 3u + 1)
· (u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)(u
21
− 3u
19
+ ··· − 3u − 1)
· (u
67
+ 5u
65
+ ··· − 4u + 1)(u
92
+ 5u
91
+ ··· + 59081u − 15649)
c
8
(u
4
− 3u
3
+ 3u
2
− 3u + 1)(u
4
− 2u
3
+ 3u
2
− u + 1)
· (u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)(u
21
+ 3u
20
+ ··· + 3u
2
− 1)
· (u
67
+ u
66
+ ··· + 5u + 1)(u
92
+ 9u
91
+ ··· + 9u + 1)
c
9
, c
10
((u − 1)
10
)(u
2
+ u − 1)
2
(u
21
+ 4u
20
+ ··· − u + 1)
· ((u
46
− 5u
45
+ ··· + u + 1)
2
)(u
67
− 7u
66
+ ··· + 17u + 16)
c
11
u
10
(u
2
− u − 1)
2
(u
21
+ 2u
20
+ ··· − u − 1)
· ((u
46
+ 2u
45
+ ··· + 12u − 8)
2
)(u
67
− 5u
66
+ ··· − 736u + 256)
c
12
((u + 1)
10
)(u
2
− u − 1)
2
(u
21
− 4u
20
+ ··· − u − 1)
· ((u
46
− 5u
45
+ ··· + u + 1)
2
)(u
67
− 7u
66
+ ··· + 17u + 16)
43
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y −1)
4
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
21
+ 14y
20
+ ··· + 11y −1)(y
67
− 34y
66
+ ··· + 7148y −1)
· (y
92
+ 26y
91
+ ··· − 169276944y + 16056049)
c
2
y
4
(y
3
− y
2
+ 2y −1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
21
+ 5y
20
+ ··· + 3331y −121)(y
46
− 6y
45
+ ··· − 460y + 16)
2
· (y
67
− y
66
+ ··· + 1096y −16)
c
4
, c
7
(y
4
− 3y
3
− 7y
2
− 3y + 1)(y
4
+ 2y
3
+ 3y
2
+ y + 1)
· (y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)(y
21
− 6y
20
+ ··· + 11y −1)
· (y
67
+ 10y
66
+ ··· + 40y −1)
· (y
92
− y
91
+ ··· + 7756027461y + 244891201)
c
5
, c
8
(y
4
− 3y
3
− 7y
2
− 3y + 1)(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
· (y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)(y
21
− 11y
20
+ ··· + 6y −1)
· (y
67
+ 29y
66
+ ··· − 69y −1)(y
92
− 25y
91
+ ··· + 5y + 1)
c
6
, c
11
y
10
(y
2
− 3y + 1)
2
(y
21
− 6y
20
+ ··· − 7y −1)
· (y
46
− 24y
45
+ ··· − 464y + 64)
2
· (y
67
− 27y
66
+ ··· + 947200y −65536)
c
9
, c
10
, c
12
((y −1)
10
)(y
2
− 3y + 1)
2
(y
21
− 18y
20
+ ··· − 15y −1)
· ((y
46
− 43y
45
+ ··· + y + 1)
2
)(y
67
− 59y
66
+ ··· − 10527y −256)
44
