12n
0887
(K12n
0887
)
A knot diagram
1
Linearized knot diagam
5 6 7 1 11 12 4 12 1 2 3 9
Solving Sequence
2,6 3,11
12 7 5 1 4 8 10 9
c
2
c
11
c
6
c
5
c
1
c
4
c
7
c
10
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
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).
1
I
u
1
= hb + u, −u
4
− 2u
3
− 2u
2
+ a −2, u
5
+ 3u
4
+ 4u
3
+ 2u
2
+ 2u + 1i
I
u
2
= hb + u, −270959u
13
+ 772689u
12
+ ··· + 300046a − 41334,
u
14
− 2u
13
− u
12
+ 2u
11
+ 10u
10
− 9u
9
− 29u
8
+ 46u
7
+ 16u
6
− 61u
5
+ 18u
4
+ 22u
3
− 14u
2
+ 3u − 1i
I
u
3
= h−135792u
13
+ 108799u
12
+ ··· + 300046b + 457605,
− 230771u
13
+ 274896u
12
+ ··· + 300046a − 29087,
u
14
− 2u
13
− u
12
+ 2u
11
+ 10u
10
− 9u
9
− 29u
8
+ 46u
7
+ 16u
6
− 61u
5
+ 18u
4
+ 22u
3
− 14u
2
+ 3u − 1i
I
u
4
= h−104218005u
13
+ 702274247u
12
+ ··· + 190982362b + 773333180,
544231529u
13
− 3353087149u
12
+ ··· + 763929448a − 3082001714, u
14
− 7u
13
+ ··· − 8u + 4i
I
u
5
= h−180047861u
13
+ 1175460277u
12
+ ··· + 381964724b + 1337790626,
158399813u
13
− 1046466799u
12
+ ··· + 381964724a − 2606371288, u
14
− 7u
13
+ ··· − 8u + 4i
I
u
6
= h−103563766675u
13
− 565696363294u
12
+ ··· + 912579422726b + 472806896800,
218496302654u
13
+ 1210683237470u
12
+ ··· + 912579422726a − 6915383452949,
u
14
+ 6u
13
+ ··· − 22u + 4i
I
u
7
= hb + u, u
2
+ a − u + 2, u
3
− 2u
2
+ 3u − 1i
I
u
8
= hb, a + u + 1, u
2
+ u − 1i
I
u
9
= hb, a
2
− a − 1, u − 1i
I
u
10
= hb + u, a + 1, u
2
+ u − 1i
I
v
1
= ha, b + 1, v
2
− v − 1i
I
v
2
= ha, b − v − 1, v
2
+ v − 1i
* 12 irreducible components of dim
C
= 0, with total 88 representations.
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
2
I. I
u
1
= hb + u, −u
4
− 2u
3
− 2u
2
+ a − 2, u
5
+ 3u
4
+ 4u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
11
=
u
4
+ 2u
3
+ 2u
2
+ 2
−u
a
12
=
1
u
4
+ 2u
3
+ u
2
+ 1
a
7
=
u
−u
4
− 3u
3
− 2u
2
− 1
a
5
=
−2u
4
− 5u
3
− 5u
2
− u − 3
−u
4
− 2u
3
− 2u
2
− 1
a
1
=
−2u
4
− 5u
3
− 6u
2
− u − 3
−u
4
− 3u
3
− 3u
2
− u − 2
a
4
=
u
4
+ 2u
3
+ 2u
2
+ u + 2
u
2
+ 1
a
8
=
u
4
+ 3u
3
+ 3u
2
+ u + 2
u
4
+ u
3
+ u
2
+ u + 1
a
10
=
u
4
+ 2u
3
+ 2u
2
+ u + 2
−u
a
9
=
−2u
4
− 5u
3
− 5u
2
− u − 3
−u
4
− 2u
3
− 3u
2
− u − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5u
4
− 10u
3
− 10u
2
+ 5u − 14
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
7
, c
8
c
9
, c
11
, c
12
u
5
+ 2u
4
− 4u
2
− 3u − 1
c
2
, c
6
, c
10
u
5
− 3u
4
+ 4u
3
− 2u
2
+ 2u − 1
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
7
, c
8
c
9
, c
11
, c
12
y
5
− 4y
4
+ 10y
3
− 12y
2
+ y − 1
c
2
, c
6
, c
10
y
5
− y
4
+ 8y
3
+ 6y
2
− 1
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.179794 + 0.731571I
a = 0.612209 − 0.379621I
b = −0.179794 − 0.731571I
−0.867863 − 1.011200I −6.16207 + 5.55596I
u = 0.179794 − 0.731571I
a = 0.612209 + 0.379621I
b = −0.179794 + 0.731571I
−0.867863 + 1.011200I −6.16207 − 5.55596I
u = −0.583195
a = 2.39920
b = 0.583195
−12.9336 −18.9120
u = −1.38820 + 1.04608I
a = −0.311811 − 0.840240I
b = 1.38820 − 1.04608I
−0.8900 − 17.3034I −9.38193 + 9.43159I
u = −1.38820 − 1.04608I
a = −0.311811 + 0.840240I
b = 1.38820 + 1.04608I
−0.8900 + 17.3034I −9.38193 − 9.43159I
6
II. I
u
2
= hb + u, −2.71 × 10
5
u
13
+ 7.73 × 10
5
u
12
+ · · · + 3.00 × 10
5
a − 4.13 ×
10
4
, u
14
− 2u
13
+ · · · + 3u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
11
=
0.903058u
13
− 2.57524u
12
+ ··· − 24.1076u + 0.137759
−u
a
12
=
1.52512u
13
− 3.50280u
12
+ ··· − 26.3180u + 0.906878
−0.0795245u
13
+ 0.200289u
12
+ ··· − 0.672414u − 0.316548
a
7
=
2.15993u
13
− 4.52017u
12
+ ··· − 23.6907u − 9.18261
0.882721u
13
− 0.910147u
12
+ ··· − 2.84412u + 0.797954
a
5
=
3.24733u
13
− 5.66143u
12
+ ··· − 27.2367u − 6.98262
0.622058u
13
− 0.927568u
12
+ ··· − 2.21041u + 0.769119
a
1
=
2.48254u
13
− 4.44656u
12
+ ··· − 20.0427u + 1.25212
−1.00470u
13
+ 1.07172u
12
+ ··· + 2.53232u − 1.63459
a
4
=
4.54266u
13
− 6.82224u
12
+ ··· − 22.7975u − 5.41276
−1.44675u
13
+ 2.26522u
12
+ ··· + 0.459690u − 0.830456
a
8
=
0.842261u
13
− 0.940929u
12
+ ··· − 12.2541u − 1.81451
0.403411u
13
− 0.923072u
12
+ ··· − 1.22177u + 0.811476
a
10
=
0.903058u
13
− 2.57524u
12
+ ··· − 23.1076u + 0.137759
−u
a
9
=
1.43263u
13
− 2.87432u
12
+ ··· − 11.5747u + 2.51098
−1.18195u
13
+ 2.15844u
12
+ ··· + 0.00298621u − 0.593296
(ii) Obstruction class = −1
(iii) Cusp Shapes =
5034313
300046
u
13
−
7498729
300046
u
12
+ ··· −
19035683
300046
u −
5404048
150023
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
11
u
14
− 3u
13
+ ··· + 4u − 1
c
2
, c
10
u
14
+ 2u
13
+ ··· − 3u − 1
c
3
, c
7
, c
8
c
9
, c
12
u
14
− 2u
13
+ ··· + 3u + 1
c
5
u
14
+ 11u
13
+ ··· + 32u + 16
c
6
u
14
+ 7u
13
+ ··· + 8u + 4
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
11
y
14
− 5y
13
+ ··· − 12y + 1
c
2
, c
10
y
14
− 6y
13
+ ··· + 19y + 1
c
3
, c
7
, c
8
c
9
, c
12
y
14
− 6y
13
+ ··· − 29y + 1
c
5
y
14
− 3y
13
+ ··· − 1952y + 256
c
6
y
14
− 3y
13
+ ··· − 200y + 16
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.047510 + 0.114828I
a = −0.341221 − 0.956988I
b = 1.047510 − 0.114828I
4.40804 − 3.15243I −3.06554 + 3.15957I
u = −1.047510 − 0.114828I
a = −0.341221 + 0.956988I
b = 1.047510 + 0.114828I
4.40804 + 3.15243I −3.06554 − 3.15957I
u = −1.12842
a = 0.452479
b = 1.12842
−9.22310 −8.50330
u = 0.798926 + 0.304657I
a = 0.99674 + 1.31288I
b = −0.798926 − 0.304657I
1.89333 + 9.70124I −6.29823 − 7.45288I
u = 0.798926 − 0.304657I
a = 0.99674 − 1.31288I
b = −0.798926 + 0.304657I
1.89333 − 9.70124I −6.29823 + 7.45288I
u = 0.814809
a = −0.638076
b = −0.814809
−2.25467 4.48040
u = 0.952273 + 1.033700I
a = 0.055278 − 1.038740I
b = −0.952273 − 1.033700I
−3.68844 + 7.96253I −13.0881 − 6.5287I
u = 0.952273 − 1.033700I
a = 0.055278 + 1.038740I
b = −0.952273 + 1.033700I
−3.68844 − 7.96253I −13.0881 + 6.5287I
u = 1.48112 + 0.64101I
a = 0.584752 − 0.699870I
b = −1.48112 − 0.64101I
1.71371 + 2.93592I −6.31999 − 3.15013I
u = 1.48112 − 0.64101I
a = 0.584752 + 0.699870I
b = −1.48112 + 0.64101I
1.71371 − 2.93592I −6.31999 + 3.15013I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.033817 + 0.274663I
a = −4.04711 − 6.52748I
b = −0.033817 − 0.274663I
−2.83399 + 0.18487I −71.9536 − 3.7001I
u = 0.033817 − 0.274663I
a = −4.04711 + 6.52748I
b = −0.033817 + 0.274663I
−2.83399 − 0.18487I −71.9536 + 3.7001I
u = −1.06182 + 1.50747I
a = −0.155646 − 0.589873I
b = 1.06182 − 1.50747I
−2.33351 − 1.82562I −14.2631 + 3.2385I
u = −1.06182 − 1.50747I
a = −0.155646 + 0.589873I
b = 1.06182 + 1.50747I
−2.33351 + 1.82562I −14.2631 − 3.2385I
11
III.
I
u
3
= h−1.36 × 10
5
u
13
+ 1.09 × 10
5
u
12
+ · · · + 3.00 × 10
5
b + 4.58 × 10
5
, −2.31 ×
10
5
u
13
+2.75×10
5
u
12
+· · ·+3.00×10
5
a−2.91×10
4
, u
14
−2u
13
+· · ·+3u −1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
11
=
0.769119u
13
− 0.916180u
12
+ ··· + 2.57142u + 0.0969418
0.452571u
13
− 0.362608u
12
+ ··· + 3.66847u − 1.52512
a
12
=
1
0.769119u
13
− 0.916180u
12
+ ··· + 2.57142u − 0.903058
a
7
=
u
0.622058u
13
− 0.927568u
12
+ ··· − 2.21041u + 0.769119
a
5
=
1.63459u
13
− 2.26449u
12
+ ··· − 4.67318u + 2.37146
0.0748585u
13
+ 0.195667u
12
+ ··· − 0.0832706u + 0.597648
a
1
=
0.593296u
13
− 0.00463929u
12
+ ··· − 1.94010u + 1.77690
0.00904861u
13
− 0.187515u
12
+ ··· + 1.78692u − 1.43263
a
4
=
0.316548u
13
− 0.553572u
12
+ ··· − 1.09706u + 1.62206
1.04594u
13
− 1.11069u
12
+ ··· − 2.61029u + 1.55507
a
8
=
−1.55973u
13
+ 2.46016u
12
+ ··· + 4.58991u − 1.77381
−0.849263u
13
+ 0.915503u
12
+ ··· + 0.0414870u − 0.171144
a
10
=
0.316548u
13
− 0.553572u
12
+ ··· − 1.09706u + 1.62206
0.452571u
13
− 0.362608u
12
+ ··· + 3.66847u − 1.52512
a
9
=
1.63459u
13
− 2.26449u
12
+ ··· − 4.67318u + 2.37146
−0.518507u
13
+ 0.943745u
12
+ ··· + 6.19549u − 2.48254
(ii) Obstruction class = −1
(iii) Cusp Shapes =
5034313
300046
u
13
−
7498729
300046
u
12
+ ··· −
19035683
300046
u −
5404048
150023
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
8
c
9
, c
12
u
14
− 2u
13
+ ··· + 3u + 1
c
2
, c
6
u
14
+ 2u
13
+ ··· − 3u − 1
c
3
, c
5
, c
7
u
14
− 3u
13
+ ··· + 4u − 1
c
10
u
14
+ 7u
13
+ ··· + 8u + 4
c
11
u
14
+ 11u
13
+ ··· + 32u + 16
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
8
c
9
, c
12
y
14
− 6y
13
+ ··· − 29y + 1
c
2
, c
6
y
14
− 6y
13
+ ··· + 19y + 1
c
3
, c
5
, c
7
y
14
− 5y
13
+ ··· − 12y + 1
c
10
y
14
− 3y
13
+ ··· − 200y + 16
c
11
y
14
− 3y
13
+ ··· − 1952y + 256
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.047510 + 0.114828I
a = 0.532678 − 0.963275I
b = −0.813064 + 0.209153I
4.40804 − 3.15243I −3.06554 + 3.15957I
u = −1.047510 − 0.114828I
a = 0.532678 + 0.963275I
b = −0.813064 − 0.209153I
4.40804 + 3.15243I −3.06554 − 3.15957I
u = −1.12842
a = 1.51059
b = −1.41289
−9.22310 −8.50330
u = 0.798926 + 0.304657I
a = 0.60365 − 1.35256I
b = −1.38404 − 0.90864I
1.89333 + 9.70124I −6.29823 − 7.45288I
u = 0.798926 − 0.304657I
a = 0.60365 + 1.35256I
b = −1.38404 + 0.90864I
1.89333 − 9.70124I −6.29823 + 7.45288I
u = 0.814809
a = 1.51991
b = −0.489180
−2.25467 4.48040
u = 0.952273 + 1.033700I
a = −0.126389 + 0.932027I
b = 0.68808 + 1.33157I
−3.68844 + 7.96253I −13.0881 − 6.5287I
u = 0.952273 − 1.033700I
a = −0.126389 − 0.932027I
b = 0.68808 − 1.33157I
−3.68844 − 7.96253I −13.0881 + 6.5287I
u = 1.48112 + 0.64101I
a = −0.314710 + 0.661762I
b = 0.502930 + 0.079531I
1.71371 + 2.93592I −6.31999 − 3.15013I
u = 1.48112 − 0.64101I
a = −0.314710 − 0.661762I
b = 0.502930 − 0.079531I
1.71371 − 2.93592I −6.31999 + 3.15013I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.033817 + 0.274663I
a = −0.65600 + 1.33233I
b = −1.67998 + 1.44350I
−2.83399 + 0.18487I −71.9536 − 3.7001I
u = 0.033817 − 0.274663I
a = −0.65600 − 1.33233I
b = −1.67998 − 1.44350I
−2.83399 − 0.18487I −71.9536 + 3.7001I
u = −1.06182 + 1.50747I
a = −0.054484 − 0.391707I
b = 0.137112 − 1.014640I
−2.33351 − 1.82562I −14.2631 + 3.2385I
u = −1.06182 − 1.50747I
a = −0.054484 + 0.391707I
b = 0.137112 + 1.014640I
−2.33351 + 1.82562I −14.2631 − 3.2385I
16
IV.
I
u
4
= h−1.04 × 10
8
u
13
+ 7.02 × 10
8
u
12
+ · · · + 1.91 × 10
8
b + 7.73 × 10
8
, 5.44 ×
10
8
u
13
−3.35×10
9
u
12
+· · ·+7.64×10
8
a−3.08×10
9
, u
14
−7u
13
+· · ·−8u +4i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
11
=
−0.712411u
13
+ 4.38926u
12
+ ··· − 2.59669u + 4.03441
0.545694u
13
− 3.67717u
12
+ ··· − 1.57476u − 4.04924
a
12
=
−0.875598u
13
+ 5.65781u
12
+ ··· + 0.909320u + 5.69320
0.385393u
13
− 2.75155u
12
+ ··· − 3.23742u − 3.54428
a
7
=
0.0219389u
13
− 0.215291u
12
+ ··· + 1.15937u + 1.25670
0.633512u
13
− 3.93870u
12
+ ··· + 0.183271u − 2.97735
a
5
=
0.755674u
13
− 4.78868u
12
+ ··· − 1.91812u − 0.628287
−0.597612u
13
+ 3.80078u
12
+ ··· − 1.66488u + 2.84964
a
1
=
−0.260975u
13
+ 2.16396u
12
+ ··· + 9.73485u − 0.384135
−0.501039u
13
+ 2.86343u
12
+ ··· − 5.41711u + 3.02270
a
4
=
0.704558u
13
− 4.30612u
12
+ ··· + 8.29987u − 4.60248
−0.260478u
13
+ 1.67796u
12
+ ··· − 5.13681u + 3.89354
a
8
=
−0.335015u
13
+ 1.43202u
12
+ ··· − 15.3126u + 7.02714
1.42679u
13
− 8.60180u
12
+ ··· + 12.2718u − 9.63626
a
10
=
−1.25811u
13
+ 8.06643u
12
+ ··· − 1.02194u + 8.08364
0.545694u
13
− 3.67717u
12
+ ··· − 1.57476u − 4.04924
a
9
=
−0.347603u
13
+ 2.65881u
12
+ ··· + 8.17214u − 0.167960
−0.100728u
13
+ 0.305485u
12
+ ··· − 5.18215u + 0.0153700
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
107270862
95491181
u
13
+
727704385
95491181
u
12
+ ··· +
409479316
95491181
u +
1040923639
95491181
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
u
14
− 2u
13
+ ··· + 3u + 1
c
2
u
14
+ 7u
13
+ ··· + 8u + 4
c
3
, c
7
u
14
+ 11u
13
+ ··· + 32u + 16
c
6
u
14
+ 2u
13
+ ··· − 3u − 1
c
8
, c
9
, c
11
c
12
u
14
− 3u
13
+ ··· + 4u − 1
c
10
u
14
− 6u
13
+ ··· + 22u + 4
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
y
14
− 6y
13
+ ··· − 29y + 1
c
2
y
14
− 3y
13
+ ··· − 200y + 16
c
3
, c
7
y
14
− 3y
13
+ ··· − 1952y + 256
c
6
y
14
− 6y
13
+ ··· + 19y + 1
c
8
, c
9
, c
11
c
12
y
14
− 5y
13
+ ··· − 12y + 1
c
10
y
14
− 2y
13
+ ··· − 1404y + 16
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.137112 + 1.014640I
a = 0.949623 + 0.496773I
b = 0.173211 + 0.432516I
−2.33351 − 1.82562I −14.2631 + 3.2385I
u = −0.137112 − 1.014640I
a = 0.949623 − 0.496773I
b = 0.173211 − 0.432516I
−2.33351 + 1.82562I −14.2631 − 3.2385I
u = 0.813064 + 0.209153I
a = −0.79509 + 1.24859I
b = 1.36286 + 0.56983I
4.40804 + 3.15243I −3.06554 − 3.15957I
u = 0.813064 − 0.209153I
a = −0.79509 − 1.24859I
b = 1.36286 − 0.56983I
4.40804 − 3.15243I −3.06554 + 3.15957I
u = 1.41289
a = 0.905913
b = −0.103858
−9.22310 −8.50330
u = −0.502930 + 0.079531I
a = −2.17945 + 1.56752I
b = 1.302400 + 0.217496I
1.71371 − 2.93592I −6.31999 + 3.15013I
u = −0.502930 − 0.079531I
a = −2.17945 − 1.56752I
b = 1.302400 − 0.217496I
1.71371 + 2.93592I −6.31999 − 3.15013I
u = −0.68808 + 1.33157I
a = 0.179430 + 0.509070I
b = 0.38414 + 1.74730I
−3.68844 − 7.96253I −13.0881 + 6.5287I
u = −0.68808 − 1.33157I
a = 0.179430 − 0.509070I
b = 0.38414 − 1.74730I
−3.68844 + 7.96253I −13.0881 − 6.5287I
u = 0.489180
a = 0.427228
b = −1.34067
−2.25467 4.48040
20
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.38404 + 0.90864I
a = −0.389974 + 0.785688I
b = 1.50686 + 1.02119I
1.89333 + 9.70124I −6.29823 − 7.45288I
u = 1.38404 − 0.90864I
a = −0.389974 − 0.785688I
b = 1.50686 − 1.02119I
1.89333 − 9.70124I −6.29823 + 7.45288I
u = 1.67998 + 1.44350I
a = 0.318890 − 0.239126I
b = −1.00721 − 1.50515I
−2.83399 − 0.18487I −71.9536 + 3.7001I
u = 1.67998 − 1.44350I
a = 0.318890 + 0.239126I
b = −1.00721 + 1.50515I
−2.83399 + 0.18487I −71.9536 − 3.7001I
21
V.
I
u
5
= h−1.80 × 10
8
u
13
+ 1.18 × 10
9
u
12
+ · · · + 3.82 × 10
8
b + 1.34 × 10
9
, 1.58 ×
10
8
u
13
−1.05×10
9
u
12
+· · ·+3.82×10
8
a−2.61×10
9
, u
14
−7u
13
+· · ·−8u +4i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
11
=
−0.414697u
13
+ 2.73969u
12
+ ··· − 3.00966u + 6.82359
0.471373u
13
− 3.07741u
12
+ ··· + 1.31159u − 3.50239
a
12
=
−1.01231u
13
+ 6.54047u
12
+ ··· − 4.67453u + 9.67323
0.740305u
13
− 4.82414u
12
+ ··· + 1.98120u − 5.03242
a
7
=
−1.16635u
13
+ 7.52225u
12
+ ··· + 5.77401u + 5.72657
0.0197023u
13
+ 0.00389654u
12
+ ··· − 1.19294u + 0.280982
a
5
=
−1.71772u
13
+ 11.1301u
12
+ ··· + 1.42987u + 9.42170
0.687501u
13
− 4.38043u
12
+ ··· − 0.398232u − 2.73048
a
1
=
0.00384251u
13
+ 0.0738308u
12
+ ··· − 1.45584u + 5.15141
−0.225586u
13
+ 1.44342u
12
+ ··· + 2.94879u − 1.39041
a
4
=
−1.25811u
13
+ 8.06643u
12
+ ··· − 1.02194u + 8.08364
0.859030u
13
− 5.23410u
12
+ ··· + 6.30713u − 5.98392
a
8
=
−2.51963u
13
+ 16.1117u
12
+ ··· + 5.02726u + 9.20450
1.26962u
13
− 7.85940u
12
+ ··· − 3.00965u − 2.20930
a
10
=
−0.886071u
13
+ 5.81710u
12
+ ··· − 4.32125u + 10.3260
0.471373u
13
− 3.07741u
12
+ ··· + 1.31159u − 3.50239
a
9
=
0.755674u
13
− 4.78868u
12
+ ··· − 1.91812u − 0.628287
−0.337134u
13
+ 2.12282u
12
+ ··· + 2.47194u − 1.04390
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
107270862
95491181
u
13
+
727704385
95491181
u
12
+ ··· +
409479316
95491181
u +
1040923639
95491181
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
14
+ 11u
13
+ ··· + 32u + 16
c
2
u
14
+ 7u
13
+ ··· + 8u + 4
c
3
, c
7
, c
11
u
14
− 2u
13
+ ··· + 3u + 1
c
5
, c
8
, c
9
c
12
u
14
− 3u
13
+ ··· + 4u − 1
c
6
u
14
− 6u
13
+ ··· + 22u + 4
c
10
u
14
+ 2u
13
+ ··· − 3u − 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
14
− 3y
13
+ ··· − 1952y + 256
c
2
y
14
− 3y
13
+ ··· − 200y + 16
c
3
, c
7
, c
11
y
14
− 6y
13
+ ··· − 29y + 1
c
5
, c
8
, c
9
c
12
y
14
− 5y
13
+ ··· − 12y + 1
c
6
y
14
− 2y
13
+ ··· − 1404y + 16
c
10
y
14
− 6y
13
+ ··· + 19y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.137112 + 1.014640I
a = 0.238273 − 0.671186I
b = 1.06182 − 1.50747I
−2.33351 − 1.82562I −14.2631 + 3.2385I
u = −0.137112 − 1.014640I
a = 0.238273 + 0.671186I
b = 1.06182 + 1.50747I
−2.33351 + 1.82562I −14.2631 − 3.2385I
u = 0.813064 + 0.209153I
a = −0.833666 − 1.101810I
b = 1.047510 + 0.114828I
4.40804 + 3.15243I −3.06554 − 3.15957I
u = 0.813064 − 0.209153I
a = −0.833666 + 1.101810I
b = 1.047510 − 0.114828I
4.40804 − 3.15243I −3.06554 + 3.15957I
u = 1.41289
a = −1.20645
b = 1.12842
−9.22310 −8.50330
u = −0.502930 + 0.079531I
a = 1.48829 + 1.78312I
b = −1.48112 + 0.64101I
1.71371 − 2.93592I −6.31999 + 3.15013I
u = −0.502930 − 0.079531I
a = 1.48829 − 1.78312I
b = −1.48112 − 0.64101I
1.71371 + 2.93592I −6.31999 − 3.15013I
u = −0.68808 + 1.33157I
a = −0.116679 + 0.874213I
b = −0.952273 + 1.033700I
−3.68844 − 7.96253I −13.0881 + 6.5287I
u = −0.68808 − 1.33157I
a = −0.116679 − 0.874213I
b = −0.952273 − 1.033700I
−3.68844 + 7.96253I −13.0881 − 6.5287I
u = 0.489180
a = 2.53166
b = −0.814809
−2.25467 4.48040
25
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.38404 + 0.90864I
a = 0.154326 − 0.749194I
b = −0.798926 − 0.304657I
1.89333 + 9.70124I −6.29823 − 7.45288I
u = 1.38404 − 0.90864I
a = 0.154326 + 0.749194I
b = −0.798926 + 0.304657I
1.89333 − 9.70124I −6.29823 + 7.45288I
u = 1.67998 + 1.44350I
a = −0.093149 + 0.160468I
b = −0.033817 + 0.274663I
−2.83399 − 0.18487I −71.9536 + 3.7001I
u = 1.67998 − 1.44350I
a = −0.093149 − 0.160468I
b = −0.033817 − 0.274663I
−2.83399 + 0.18487I −71.9536 − 3.7001I
26
VI. I
u
6
= h−1.04 × 10
11
u
13
− 5.66 × 10
11
u
12
+ · · · + 9.13 × 10
11
b + 4.73 ×
10
11
, 2.18 × 10
11
u
13
+ 1.21 × 10
12
u
12
+ · · · + 9.13 × 10
11
a − 6.92 ×
10
12
, u
14
+ 6u
13
+ · · · − 22u + 4i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
11
=
−0.239427u
13
− 1.32666u
12
+ ··· + 35.5972u + 7.57784
0.113485u
13
+ 0.619887u
12
+ ··· − 5.68600u − 0.518099
a
12
=
−0.129525u
13
− 0.890634u
12
+ ··· + 37.9076u + 8.53555
−0.170923u
13
− 0.751035u
12
+ ··· − 0.331882u − 1.41165
a
7
=
−0.272337u
13
− 1.64583u
12
+ ··· + 47.2960u + 12.8665
0.0661284u
13
+ 0.355095u
12
+ ··· − 6.57783u − 0.988497
a
5
=
−0.385980u
13
− 2.16522u
12
+ ··· + 38.6580u + 10.3813
0.0370222u
13
+ 0.196920u
12
+ ··· − 5.74828u − 0.941260
a
1
=
−0.533234u
13
− 3.11779u
12
+ ··· + 76.0031u + 17.4936
0.131402u
13
+ 0.701437u
12
+ ··· − 8.56416u − 1.65838
a
4
=
0.557807u
13
+ 3.42037u
12
+ ··· − 89.4565u − 19.4330
−0.136074u
13
− 0.709093u
12
+ ··· + 9.17768u + 1.95251
a
8
=
0.631605u
13
+ 3.86470u
12
+ ··· − 91.9396u − 22.1117
−0.0965292u
13
− 0.519499u
12
+ ··· + 10.0526u + 2.25278
a
10
=
−0.352912u
13
− 1.94655u
12
+ ··· + 41.2832u + 8.09594
0.113485u
13
+ 0.619887u
12
+ ··· − 5.68600u − 0.518099
a
9
=
−0.414595u
13
− 2.61897u
12
+ ··· + 75.0173u + 17.6852
−0.0816170u
13
− 0.301896u
12
+ ··· − 5.76242u − 2.13294
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
171368330863
456289711363
u
13
−
819360607574
456289711363
u
12
+ ··· +
7084810660394
456289711363
u −
5008190287626
456289711363
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
7
u
14
− 3u
13
+ ··· + 4u − 1
c
2
u
14
− 6u
13
+ ··· + 22u + 4
c
5
, c
11
u
14
− 2u
13
+ ··· + 3u + 1
c
6
, c
10
u
14
+ 7u
13
+ ··· + 8u + 4
c
8
, c
9
, c
12
u
14
+ 11u
13
+ ··· + 32u + 16
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
y
14
− 5y
13
+ ··· − 12y + 1
c
2
y
14
− 2y
13
+ ··· − 1404y + 16
c
5
, c
11
y
14
− 6y
13
+ ··· − 29y + 1
c
6
, c
10
y
14
− 3y
13
+ ··· − 200y + 16
c
8
, c
9
, c
12
y
14
− 3y
13
+ ··· − 1952y + 256
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −1.302400 + 0.217496I
a = −0.605686 − 0.839543I
b = 0.502930 + 0.079531I
1.71371 + 2.93592I −6.31999 − 3.15013I
u = −1.302400 − 0.217496I
a = −0.605686 + 0.839543I
b = 0.502930 − 0.079531I
1.71371 − 2.93592I −6.31999 + 3.15013I
u = 1.34067
a = 0.155885
b = −0.489180
−2.25467 4.48040
u = −1.36286 + 0.56983I
a = 0.345177 + 0.767196I
b = −0.813064 + 0.209153I
4.40804 − 3.15243I −3.06554 + 3.15957I
u = −1.36286 − 0.56983I
a = 0.345177 − 0.767196I
b = −0.813064 − 0.209153I
4.40804 + 3.15243I −3.06554 − 3.15957I
u = −0.173211 + 0.432516I
a = −1.27801 + 1.97823I
b = 0.137112 + 1.014640I
−2.33351 + 1.82562I −14.2631 − 3.2385I
u = −0.173211 − 0.432516I
a = −1.27801 − 1.97823I
b = 0.137112 − 1.014640I
−2.33351 − 1.82562I −14.2631 + 3.2385I
u = −0.38414 + 1.74730I
a = 0.156968 + 0.424100I
b = 0.68808 + 1.33157I
−3.68844 + 7.96253I −13.0881 − 6.5287I
u = −0.38414 − 1.74730I
a = 0.156968 − 0.424100I
b = 0.68808 − 1.33157I
−3.68844 − 7.96253I −13.0881 + 6.5287I
u = 1.00721 + 1.50515I
a = 0.297399 − 0.386252I
b = −1.67998 − 1.44350I
−2.83399 − 0.18487I −71.9536 + 3.7001I
30
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00721 − 1.50515I
a = 0.297399 + 0.386252I
b = −1.67998 + 1.44350I
−2.83399 + 0.18487I −71.9536 − 3.7001I
u = −1.50686 + 1.02119I
a = 0.344190 + 0.719748I
b = −1.38404 + 0.90864I
1.89333 − 9.70124I −6.29823 + 7.45288I
u = −1.50686 − 1.02119I
a = 0.344190 − 0.719748I
b = −1.38404 − 0.90864I
1.89333 + 9.70124I −6.29823 − 7.45288I
u = 0.103858
a = 12.3240
b = −1.41289
−9.22310 −8.50330
31
VII. I
u
7
= hb + u, u
2
+ a − u + 2, u
3
− 2u
2
+ 3u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
11
=
−u
2
+ u − 2
−u
a
12
=
−1
u − 1
a
7
=
u
−u
2
+ 2u
a
5
=
u
2
− 2u + 2
u
2
− u + 1
a
1
=
0
u − 1
a
4
=
u
2
− 2u + 2
u
2
− 2u + 1
a
8
=
u − 1
u
a
10
=
−u
2
+ 2u − 2
−u
a
9
=
−u
2
+ 2u − 2
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
2
− 14
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
8
, c
9
, c
11
u
3
+ u
2
− 1
c
2
, c
6
, c
10
u
3
− 2u
2
+ 3u − 1
c
4
, c
7
, c
12
u
3
− u
2
+ 1
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
7
, c
8
c
9
, c
11
, c
12
y
3
− y
2
+ 2y − 1
c
2
, c
6
, c
10
y
3
+ 2y
2
+ 5y − 1
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.78492 + 1.30714I
a = −0.122561 − 0.744862I
b = −0.78492 − 1.30714I
−1.98242 + 9.42707I −8.53741 − 10.26002I
u = 0.78492 − 1.30714I
a = −0.122561 + 0.744862I
b = −0.78492 + 1.30714I
−1.98242 − 9.42707I −8.53741 + 10.26002I
u = 0.430160
a = −1.75488
b = −0.430160
−2.61489 −14.9250
35
VIII. I
u
8
= hb, a + u + 1, u
2
+ u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u − 1
a
11
=
−u − 1
0
a
12
=
−1
−2u + 1
a
7
=
u
−2u + 2
a
5
=
u + 1
u
a
1
=
0
u − 1
a
4
=
u + 1
−u + 1
a
8
=
−1
−u + 1
a
10
=
−u − 1
0
a
9
=
−u − 1
2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −17
36
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
8
, c
9
, c
11
u
2
+ u − 1
c
3
, c
5
(u − 1)
2
c
4
, c
12
u
2
− u − 1
c
7
(u + 1)
2
c
10
u
2
37
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
8
, c
9
c
11
, c
12
y
2
− 3y + 1
c
3
, c
5
, c
7
(y − 1)
2
c
10
y
2
38
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −1.61803
b = 0
−2.63189 −17.0000
u = −1.61803
a = 0.618034
b = 0
−10.5276 −17.0000
39
IX. I
u
9
= hb, a
2
− a − 1, u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
1
a
3
=
1
−1
a
11
=
a
0
a
12
=
0
a
a
7
=
0
1
a
5
=
a + 1
1
a
1
=
−a
−1
a
4
=
1
0
a
8
=
−1
1
a
10
=
a
0
a
9
=
−1
−a
(ii) Obstruction class = 1
(iii) Cusp Shapes = −17
40
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
(u − 1)
2
c
4
, c
7
(u + 1)
2
c
5
, c
8
, c
9
c
11
u
2
+ u − 1
c
6
, c
10
u
2
c
12
u
2
− u − 1
41
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
(y − 1)
2
c
5
, c
8
, c
9
c
11
, c
12
y
2
− 3y + 1
c
6
, c
10
y
2
42
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.618034
b = 0
−2.63189 −17.0000
u = 1.00000
a = 1.61803
b = 0
−10.5276 −17.0000
43
X. I
u
10
= hb + u, a + 1, u
2
+ u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u − 1
a
11
=
−1
−u
a
12
=
0
−1
a
7
=
0
u
a
5
=
u
1
a
1
=
−u + 1
−1
a
4
=
1
0
a
8
=
−u
u
a
10
=
u − 1
−u
a
9
=
−u
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −17
44
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
(u − 1)
2
c
2
, c
3
, c
5
c
8
, c
9
, c
10
u
2
+ u − 1
c
4
(u + 1)
2
c
6
u
2
c
7
, c
12
u
2
− u − 1
45
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
11
(y − 1)
2
c
2
, c
3
, c
5
c
7
, c
8
, c
9
c
10
, c
12
y
2
− 3y + 1
c
6
y
2
46
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −1.00000
b = −0.618034
−2.63189 −17.0000
u = −1.61803
a = −1.00000
b = 1.61803
−10.5276 −17.0000
47
XI. I
v
1
= ha, b + 1, v
2
− v − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
v
0
a
3
=
1
0
a
11
=
0
−1
a
12
=
1
−1
a
7
=
2v
−v
a
5
=
v
−v
a
1
=
v + 2
−v − 1
a
4
=
−2v − 1
v + 1
a
8
=
−v − 2
v + 1
a
10
=
1
−1
a
9
=
−v − 1
v
(ii) Obstruction class = 1
(iii) Cusp Shapes = −17
48
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
6
u
2
+ u − 1
c
2
u
2
c
4
, c
7
u
2
− u − 1
c
8
, c
9
, c
10
c
11
(u − 1)
2
c
12
(u + 1)
2
49
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
7
y
2
− 3y + 1
c
2
y
2
c
8
, c
9
, c
10
c
11
, c
12
(y − 1)
2
50
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.618034
a = 0
b = −1.00000
−2.63189 −17.0000
v = 1.61803
a = 0
b = −1.00000
−10.5276 −17.0000
51
XII. I
v
2
= ha, b − v − 1, v
2
+ v − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
v
0
a
3
=
1
0
a
11
=
0
v + 1
a
12
=
−v − 1
v + 1
a
7
=
2v + 1
−v − 1
a
5
=
v
−v − 1
a
1
=
2
−v − 2
a
4
=
−v − 2
v + 2
a
8
=
−2
v + 2
a
10
=
−v − 1
v + 1
a
9
=
−v − 3
2v + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −17
52
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
10
c
11
u
2
+ u − 1
c
2
u
2
c
4
, c
7
u
2
− u − 1
c
5
, c
6
, c
8
c
9
(u − 1)
2
c
12
(u + 1)
2
53
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
, c
10
, c
11
y
2
− 3y + 1
c
2
y
2
c
5
, c
6
, c
8
c
9
, c
12
(y − 1)
2
54
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 0.618034
a = 0
b = 1.61803
−10.5276 −17.0000
v = −1.61803
a = 0
b = −0.618034
−2.63189 −17.0000
55
XIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
8
, c
9
, c
11
(u − 1)
4
(u
2
+ u − 1)
3
(u
3
+ u
2
− 1)(u
5
+ 2u
4
− 4u
2
− 3u − 1)
· ((u
14
− 3u
13
+ ··· + 4u − 1)
2
)(u
14
− 2u
13
+ ··· + 3u + 1)
2
· (u
14
+ 11u
13
+ ··· + 32u + 16)
c
2
, c
6
, c
10
u
4
(u − 1)
2
(u
2
+ u − 1)
2
(u
3
− 2u
2
+ 3u − 1)
· (u
5
− 3u
4
+ 4u
3
− 2u
2
+ 2u − 1)(u
14
− 6u
13
+ ··· + 22u + 4)
· ((u
14
+ 2u
13
+ ··· − 3u − 1)
2
)(u
14
+ 7u
13
+ ··· + 8u + 4)
2
c
4
, c
7
, c
12
(u + 1)
4
(u
2
− u − 1)
3
(u
3
− u
2
+ 1)(u
5
+ 2u
4
− 4u
2
− 3u − 1)
· ((u
14
− 3u
13
+ ··· + 4u − 1)
2
)(u
14
− 2u
13
+ ··· + 3u + 1)
2
· (u
14
+ 11u
13
+ ··· + 32u + 16)
56
XIV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
7
, c
8
c
9
, c
11
, c
12
(y − 1)
4
(y
2
− 3y + 1)
3
(y
3
− y
2
+ 2y − 1)
· (y
5
− 4y
4
+ 10y
3
− 12y
2
+ y − 1)(y
14
− 6y
13
+ ··· − 29y + 1)
2
· ((y
14
− 5y
13
+ ··· − 12y + 1)
2
)(y
14
− 3y
13
+ ··· − 1952y + 256)
c
2
, c
6
, c
10
y
4
(y − 1)
2
(y
2
− 3y + 1)
2
(y
3
+ 2y
2
+ 5y − 1)(y
5
− y
4
+ ··· + 6y
2
− 1)
· ((y
14
− 6y
13
+ ··· + 19y + 1)
2
)(y
14
− 3y
13
+ ··· − 200y + 16)
2
· (y
14
− 2y
13
+ ··· − 1404y + 16)
57
