12a
0883
(K12a
0883
)
A knot diagram
1
Linearized knot diagam
4 6 7 10 9 11 1 12 5 2 3 8
Solving Sequence
5,9 2,6
3 10 11 7 12 4 1 8
c
5
c
2
c
9
c
10
c
6
c
11
c
4
c
1
c
8
c
3
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h161211550u
26
+ 163067087u
25
+ ··· + 168567233b + 184311963,
− 64532319u
26
− 105037379u
25
+ ··· + 168567233a − 400814896, u
27
+ u
26
+ ··· + 2u − 1i
I
u
2
= h8.05343 × 10
231
u
97
− 2.98534 × 10
231
u
96
+ ··· + 7.84596 × 10
231
b − 9.54856 × 10
232
,
1.36459 × 10
233
u
97
− 1.17790 × 10
233
u
96
+ ··· + 7.84596 × 10
231
a − 1.42631 × 10
234
, u
98
− u
97
+ ··· − 36u + 1i
I
u
3
= hu
4
+ u
3
+ 2u
2
+ b + 2u, −u
6
− 2u
4
− u
3
+ u
2
+ a − u + 1, u
7
+ u
6
+ 4u
5
+ 5u
4
+ 5u
3
+ 6u
2
+ 2u + 1i
I
u
4
= h4u
25
− 11u
24
+ ··· + b − 3, 5u
25
− 13u
24
+ ··· + a + 4, u
26
− 2u
25
+ ··· − 2u + 1i
* 4 irreducible components of dim
C
= 0, with total 158 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
= h1.61 × 10
8
u
26
+ 1.63 × 10
8
u
25
+ · · · + 1.69 × 10
8
b + 1.84 × 10
8
, −6.45 ×
10
7
u
26
− 1.05 × 10
8
u
25
+ · · · + 1.69 × 10
8
a − 4.01 × 10
8
, u
27
+ u
26
+ · · · + 2u − 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
2
=
0.382828u
26
+ 0.623119u
25
+ ··· + 2.47957u + 2.37777
−0.956364u
26
− 0.967371u
25
+ ··· − 0.798674u − 1.09340
a
6
=
1
−u
2
a
3
=
0.110178u
26
+ 0.0591229u
25
+ ··· + 1.58315u + 1.52466
−0.538924u
26
− 0.745833u
25
+ ··· − 1.10871u − 0.802058
a
10
=
u
u
a
11
=
−0.959060u
26
− 1.36051u
25
+ ··· + 0.0254923u − 2.73531
−0.00114729u
26
+ 0.449549u
25
+ ··· + 1.51778u + 0.626626
a
7
=
−u
3
− 2u
0.576586u
26
+ 1.01727u
25
+ ··· + 1.09757u + 0.898510
a
12
=
−1
0.469768u
26
+ 0.828129u
25
+ ··· + 1.88993u + 0.768115
a
4
=
u
2
+ 1
u
2
a
1
=
u
2
+ 1
−0.428742u
26
− 0.646967u
25
+ ··· − 1.64298u − 1.12648
a
8
=
−u
0.358361u
26
+ 0.317336u
25
+ ··· + 0.828580u + 0.469768
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
314978218
168567233
u
26
−
605025497
168567233
u
25
+ ··· −
1917677278
168567233
u +
586286315
168567233
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
27
− 7u
26
+ ··· + 176u − 16
c
2
, c
11
u
27
+ u
26
+ ··· − 3u + 1
c
3
, c
10
u
27
+ u
26
+ ··· + 3u + 1
c
4
, c
5
, c
7
c
8
, c
9
, c
12
u
27
− u
26
+ ··· + 2u + 1
c
6
u
27
− 16u
26
+ ··· + 22u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
27
− 5y
26
+ ··· + 5280y −256
c
2
, c
11
y
27
− 7y
26
+ ··· + 27y −1
c
3
, c
10
y
27
− 7y
26
+ ··· + 17y −1
c
4
, c
5
, c
7
c
8
, c
9
, c
12
y
27
+ 25y
26
+ ··· + 18y −1
c
6
y
27
− 10y
26
+ ··· + 492y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.070166 + 0.997411I
a = 0.050375 + 0.136338I
b = 1.106230 + 0.535575I
−0.70818 + 3.60837I 2.50627 − 4.79457I
u = 0.070166 − 0.997411I
a = 0.050375 − 0.136338I
b = 1.106230 − 0.535575I
−0.70818 − 3.60837I 2.50627 + 4.79457I
u = −0.995972 + 0.202368I
a = −0.0990140 + 0.0471163I
b = 0.473624 + 0.134565I
−0.0498204 + 0.0658137I 13.3792 − 20.3584I
u = −0.995972 − 0.202368I
a = −0.0990140 − 0.0471163I
b = 0.473624 − 0.134565I
−0.0498204 − 0.0658137I 13.3792 + 20.3584I
u = 0.791226 + 0.513863I
a = −0.736086 + 0.718981I
b = −0.141477 − 0.624312I
−1.14567 + 9.89138I 2.32394 − 9.56251I
u = 0.791226 − 0.513863I
a = −0.736086 − 0.718981I
b = −0.141477 + 0.624312I
−1.14567 − 9.89138I 2.32394 + 9.56251I
u = −0.542866 + 0.539927I
a = 0.390658 − 0.702555I
b = −0.0570518 + 0.0874559I
1.32847 − 1.67905I 10.52150 + 4.30869I
u = −0.542866 − 0.539927I
a = 0.390658 + 0.702555I
b = −0.0570518 − 0.0874559I
1.32847 + 1.67905I 10.52150 − 4.30869I
u = −0.122477 + 1.262950I
a = −1.31674 − 1.34075I
b = −1.11217 − 2.28394I
−9.69201 − 3.22381I −6.38040 + 1.87892I
u = −0.122477 − 1.262950I
a = −1.31674 + 1.34075I
b = −1.11217 + 2.28394I
−9.69201 + 3.22381I −6.38040 − 1.87892I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.230598 + 1.267870I
a = −0.39953 + 1.81101I
b = −0.47291 + 2.86023I
−7.30514 + 6.01759I −0.32733 − 7.30981I
u = 0.230598 − 1.267870I
a = −0.39953 − 1.81101I
b = −0.47291 − 2.86023I
−7.30514 − 6.01759I −0.32733 + 7.30981I
u = 0.204690 + 1.330900I
a = −0.26598 + 1.62179I
b = −0.47881 + 1.96936I
−7.82612 + 5.05552I −1.17987 − 2.39455I
u = 0.204690 − 1.330900I
a = −0.26598 − 1.62179I
b = −0.47881 − 1.96936I
−7.82612 − 5.05552I −1.17987 + 2.39455I
u = −0.179338 + 1.344090I
a = −0.04177 − 2.74708I
b = 0.38158 − 3.28794I
−8.31053 − 8.16537I −3.33517 + 11.01444I
u = −0.179338 − 1.344090I
a = −0.04177 + 2.74708I
b = 0.38158 + 3.28794I
−8.31053 + 8.16537I −3.33517 − 11.01444I
u = −0.603103
a = 2.07379
b = 0.171319
0.515822 11.7560
u = 0.01958 + 1.42133I
a = 0.704503 + 0.398347I
b = −0.235482 + 0.318924I
−6.81655 + 2.85614I −2.29662 − 2.94714I
u = 0.01958 − 1.42133I
a = 0.704503 − 0.398347I
b = −0.235482 − 0.318924I
−6.81655 − 2.85614I −2.29662 + 2.94714I
u = −0.473384
a = 1.02334
b = 0.321318
0.921050 10.8530
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.375751 + 0.179645I
a = 0.80850 − 1.25731I
b = 0.727471 + 0.972773I
1.25767 + 3.71987I 13.1792 − 10.4060I
u = 0.375751 − 0.179645I
a = 0.80850 + 1.25731I
b = 0.727471 − 0.972773I
1.25767 − 3.71987I 13.1792 + 10.4060I
u = −0.32805 + 1.55024I
a = 0.08115 + 1.75485I
b = −0.33517 + 2.81280I
−14.5174 − 18.3439I −3.23925 + 8.58445I
u = −0.32805 − 1.55024I
a = 0.08115 − 1.75485I
b = −0.33517 − 2.81280I
−14.5174 + 18.3439I −3.23925 − 8.58445I
u = 0.35424 + 1.56608I
a = 0.129600 − 1.020350I
b = −0.22137 − 1.77783I
−13.3669 + 10.0927I −3.30444 − 7.62979I
u = 0.35424 − 1.56608I
a = 0.129600 + 1.020350I
b = −0.22137 + 1.77783I
−13.3669 − 10.0927I −3.30444 + 7.62979I
u = 0.321408
a = 2.29153
b = −0.761575
−2.01710 −4.30310
7
II. I
u
2
= h8.05 × 10
231
u
97
− 2.99 × 10
231
u
96
+ · · · + 7.85 × 10
231
b − 9.55 ×
10
232
, 1.36 × 10
233
u
97
− 1.18 × 10
233
u
96
+ · · · + 7.85 × 10
231
a − 1.43 ×
10
234
, u
98
− u
97
+ · · · − 36u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
2
=
−17.3923u
97
+ 15.0129u
96
+ ··· − 4433.65u + 181.789
−1.02644u
97
+ 0.380494u
96
+ ··· − 235.466u + 12.1700
a
6
=
1
−u
2
a
3
=
−17.9778u
97
+ 15.8292u
96
+ ··· − 4737.38u + 196.338
−0.273211u
97
+ 0.251929u
96
+ ··· − 244.360u + 12.4008
a
10
=
u
u
a
11
=
−9.95056u
97
+ 8.64388u
96
+ ··· − 2431.59u + 104.303
0.850940u
97
− 0.650011u
96
+ ··· + 280.898u − 11.5019
a
7
=
−4.56522u
97
+ 3.03576u
96
+ ··· − 694.079u + 32.8371
1.99051u
97
− 2.57908u
96
+ ··· + 546.222u − 22.8070
a
12
=
−24.0010u
97
+ 22.2667u
96
+ ··· − 7216.77u + 308.025
−1.43913u
97
+ 1.65677u
96
+ ··· − 365.233u + 18.0341
a
4
=
u
2
+ 1
u
2
a
1
=
−17.4547u
97
+ 15.3237u
96
+ ··· − 4630.14u + 192.443
−0.306071u
97
+ 0.126649u
96
+ ··· − 242.535u + 12.3881
a
8
=
−2.91621u
97
+ 2.48251u
96
+ ··· − 1005.31u + 66.4486
4.29285u
97
− 4.18123u
96
+ ··· + 1267.97u − 52.9233
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6.62974u
97
+ 5.53191u
96
+ ··· − 803.454u + 33.3318
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
49
+ 8u
48
+ ··· − u + 139)
2
c
2
, c
11
u
98
− u
97
+ ··· + 78991u + 5641
c
3
, c
10
u
98
− 12u
96
+ ··· − 2731098u + 1190927
c
4
, c
5
, c
7
c
8
, c
9
, c
12
u
98
+ u
97
+ ··· + 36u + 1
c
6
(u
49
+ 6u
48
+ ··· + 7u + 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
49
− 30y
48
+ ··· − 378913y −19321)
2
c
2
, c
11
y
98
+ 23y
97
+ ··· + 672079733y + 31820881
c
3
, c
10
y
98
− 24y
97
+ ··· − 54241979206882y + 1418307119329
c
4
, c
5
, c
7
c
8
, c
9
, c
12
y
98
+ 101y
97
+ ··· − 326y + 1
c
6
(y
49
− 6y
48
+ ··· + 25y −1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.601265 + 0.799530I
a = 0.371144 + 0.018717I
b = 0.411619 − 0.292634I
0.89188 − 2.50997I 0
u = −0.601265 − 0.799530I
a = 0.371144 − 0.018717I
b = 0.411619 + 0.292634I
0.89188 + 2.50997I 0
u = 0.742965 + 0.599497I
a = −0.341644 − 0.232431I
b = 0.575289 − 0.479550I
−1.41187 − 4.73118I 0
u = 0.742965 − 0.599497I
a = −0.341644 + 0.232431I
b = 0.575289 + 0.479550I
−1.41187 + 4.73118I 0
u = −0.775758 + 0.551464I
a = 0.713884 + 0.158341I
b = 0.345135 − 0.578530I
1.05292 − 2.70150I 0
u = −0.775758 − 0.551464I
a = 0.713884 − 0.158341I
b = 0.345135 + 0.578530I
1.05292 + 2.70150I 0
u = −0.913794 + 0.518684I
a = −0.773466 − 0.493343I
b = −0.107817 + 0.717427I
−7.8103 − 13.8110I 0
u = −0.913794 − 0.518684I
a = −0.773466 + 0.493343I
b = −0.107817 − 0.717427I
−7.8103 + 13.8110I 0
u = 0.838372 + 0.214613I
a = 1.160930 − 0.145018I
b = 0.440949 + 0.575531I
−2.76982 + 1.97446I 0
u = 0.838372 − 0.214613I
a = 1.160930 + 0.145018I
b = 0.440949 − 0.575531I
−2.76982 − 1.97446I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.612109 + 0.604182I
a = −0.362407 − 1.000320I
b = −0.111421 + 0.461219I
−1.41187 − 4.73118I 0
u = −0.612109 − 0.604182I
a = −0.362407 + 1.000320I
b = −0.111421 − 0.461219I
−1.41187 + 4.73118I 0
u = −0.254531 + 1.112700I
a = 0.877864 + 0.438971I
b = −0.251233 + 0.146892I
−7.07475 + 2.20435I 0
u = −0.254531 − 1.112700I
a = 0.877864 − 0.438971I
b = −0.251233 − 0.146892I
−7.07475 − 2.20435I 0
u = 1.049150 + 0.468661I
a = −0.314037 + 0.177739I
b = 0.224808 − 0.342256I
−6.69520 + 5.05617I 0
u = 1.049150 − 0.468661I
a = −0.314037 − 0.177739I
b = 0.224808 + 0.342256I
−6.69520 − 5.05617I 0
u = −0.878034 + 0.748977I
a = −0.428725 + 0.197953I
b = 0.477283 + 0.552534I
−8.41578 + 7.83198I 0
u = −0.878034 − 0.748977I
a = −0.428725 − 0.197953I
b = 0.477283 − 0.552534I
−8.41578 − 7.83198I 0
u = 0.686233 + 0.942381I
a = 0.000271 + 0.415794I
b = 0.175155 − 0.429780I
−8.38703 + 1.13960I 0
u = 0.686233 − 0.942381I
a = 0.000271 − 0.415794I
b = 0.175155 + 0.429780I
−8.38703 − 1.13960I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.766493 + 0.313170I
a = 1.110710 + 0.164116I
b = −0.500160 − 0.031141I
−7.47312 + 0.52726I 0
u = −0.766493 − 0.313170I
a = 1.110710 − 0.164116I
b = −0.500160 + 0.031141I
−7.47312 − 0.52726I 0
u = 0.213501 + 0.776484I
a = −0.843665 + 0.799992I
b = −1.10714 + 1.71994I
−7.12629 + 5.71564I 0
u = 0.213501 − 0.776484I
a = −0.843665 − 0.799992I
b = −1.10714 − 1.71994I
−7.12629 − 5.71564I 0
u = 0.601355 + 1.050520I
a = 0.555692 + 0.226539I
b = −0.022086 + 0.335554I
−5.17927 + 2.97176I 0
u = 0.601355 − 1.050520I
a = 0.555692 − 0.226539I
b = −0.022086 − 0.335554I
−5.17927 − 2.97176I 0
u = 1.000720 + 0.695820I
a = 0.745496 + 0.056805I
b = 0.218609 + 0.616622I
−3.76883 + 3.36908I 0
u = 1.000720 − 0.695820I
a = 0.745496 − 0.056805I
b = 0.218609 − 0.616622I
−3.76883 − 3.36908I 0
u = −0.558069 + 0.522855I
a = −0.122912 + 1.050990I
b = −0.403275 − 0.944836I
−8.37472 − 4.64087I 0
u = −0.558069 − 0.522855I
a = −0.122912 − 1.050990I
b = −0.403275 + 0.944836I
−8.37472 + 4.64087I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.013440 + 1.261000I
a = 0.734942 − 0.472678I
b = −0.179286 − 0.269085I
−1.83648 − 2.54008I 0
u = 0.013440 − 1.261000I
a = 0.734942 + 0.472678I
b = −0.179286 + 0.269085I
−1.83648 + 2.54008I 0
u = −0.093446 + 1.291680I
a = −0.337075 − 0.874524I
b = −1.03246 − 1.19486I
−3.00552 − 2.00178I 0
u = −0.093446 − 1.291680I
a = −0.337075 + 0.874524I
b = −1.03246 + 1.19486I
−3.00552 + 2.00178I 0
u = 0.640464 + 0.266462I
a = 1.066130 + 0.218861I
b = 0.399089 + 0.595313I
−3.00552 + 2.00178I 0
u = 0.640464 − 0.266462I
a = 1.066130 − 0.218861I
b = 0.399089 − 0.595313I
−3.00552 − 2.00178I 0
u = −0.024509 + 1.318700I
a = −0.68071 − 1.58708I
b = −1.29802 − 2.61295I
−2.76982 − 1.97446I 0
u = −0.024509 − 1.318700I
a = −0.68071 + 1.58708I
b = −1.29802 + 2.61295I
−2.76982 + 1.97446I 0
u = −0.327819 + 0.583087I
a = −0.165009 − 0.143366I
b = −0.699085 − 1.112450I
−1.62426 − 2.89139I −1.83614 + 9.00098I
u = −0.327819 − 0.583087I
a = −0.165009 + 0.143366I
b = −0.699085 + 1.112450I
−1.62426 + 2.89139I −1.83614 − 9.00098I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.551909 + 0.314734I
a = 0.89110 − 1.25572I
b = −0.087561 + 0.634422I
−1.62426 + 2.89139I −1.83614 − 9.00098I
u = 0.551909 − 0.314734I
a = 0.89110 + 1.25572I
b = −0.087561 − 0.634422I
−1.62426 − 2.89139I −1.83614 + 9.00098I
u = −0.609151 + 0.069906I
a = 1.100990 + 0.526461I
b = 0.499891 − 1.265130I
−3.88143 − 5.43641I 2.38120 + 7.54528I
u = −0.609151 − 0.069906I
a = 1.100990 − 0.526461I
b = 0.499891 + 1.265130I
−3.88143 + 5.43641I 2.38120 − 7.54528I
u = 0.035210 + 1.406650I
a = 0.952310 − 0.095611I
b = 2.78836 − 0.18377I
−3.76883 + 3.36908I 0
u = 0.035210 − 1.406650I
a = 0.952310 + 0.095611I
b = 2.78836 + 0.18377I
−3.76883 − 3.36908I 0
u = 0.109284 + 1.405400I
a = 0.54725 + 2.33836I
b = 0.80233 + 2.90599I
−3.88143 + 5.43641I 0
u = 0.109284 − 1.405400I
a = 0.54725 − 2.33836I
b = 0.80233 − 2.90599I
−3.88143 − 5.43641I 0
u = 0.24099 + 1.39589I
a = −0.785127 + 1.132930I
b = −0.85392 + 2.05396I
−6.98631 + 2.75445I 0
u = 0.24099 − 1.39589I
a = −0.785127 − 1.132930I
b = −0.85392 − 2.05396I
−6.98631 − 2.75445I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.21579 + 1.40896I
a = −0.23652 + 1.97755I
b = 0.11853 + 3.12136I
−7.12629 + 5.71564I 0
u = 0.21579 − 1.40896I
a = −0.23652 − 1.97755I
b = 0.11853 − 3.12136I
−7.12629 − 5.71564I 0
u = −0.05162 + 1.44380I
a = −0.46405 + 1.39064I
b = −1.01450 + 2.31250I
−5.17927 − 2.97176I 0
u = −0.05162 − 1.44380I
a = −0.46405 − 1.39064I
b = −1.01450 − 2.31250I
−5.17927 + 2.97176I 0
u = 0.01368 + 1.44520I
a = −0.90811 + 1.44980I
b = −0.49977 + 2.20256I
−7.47312 + 0.52726I 0
u = 0.01368 − 1.44520I
a = −0.90811 − 1.44980I
b = −0.49977 − 2.20256I
−7.47312 − 0.52726I 0
u = 0.00842 + 1.44698I
a = 1.00203 − 1.72294I
b = 1.09995 − 2.26368I
−7.07475 − 2.20435I 0
u = 0.00842 − 1.44698I
a = 1.00203 + 1.72294I
b = 1.09995 + 2.26368I
−7.07475 + 2.20435I 0
u = −0.11004 + 1.45882I
a = 0.686718 + 0.373750I
b = 2.28806 + 0.72915I
−11.44370 − 8.12756I 0
u = −0.11004 − 1.45882I
a = 0.686718 − 0.373750I
b = 2.28806 − 0.72915I
−11.44370 + 8.12756I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.06406 + 1.49140I
a = −0.82172 − 1.26604I
b = −0.25457 − 1.95023I
−13.26630 + 3.54268I 0
u = 0.06406 − 1.49140I
a = −0.82172 + 1.26604I
b = −0.25457 + 1.95023I
−13.26630 − 3.54268I 0
u = −0.12213 + 1.49628I
a = −1.02750 − 1.49115I
b = −0.75605 − 2.09017I
−8.37472 − 4.64087I 0
u = −0.12213 − 1.49628I
a = −1.02750 + 1.49115I
b = −0.75605 + 2.09017I
−8.37472 + 4.64087I 0
u = −0.20185 + 1.49925I
a = −0.11825 − 1.81705I
b = 0.71538 − 2.99125I
−14.9424 − 7.4727I 0
u = −0.20185 − 1.49925I
a = −0.11825 + 1.81705I
b = 0.71538 + 2.99125I
−14.9424 + 7.4727I 0
u = −0.32036 + 1.48082I
a = −0.597294 − 0.978220I
b = −0.77820 − 2.01419I
−13.26630 − 3.54268I 0
u = −0.32036 − 1.48082I
a = −0.597294 + 0.978220I
b = −0.77820 + 2.01419I
−13.26630 + 3.54268I 0
u = −0.27276 + 1.51130I
a = −0.00530 − 1.79034I
b = 0.18144 − 2.59266I
−5.57317 − 6.53299I 0
u = −0.27276 − 1.51130I
a = −0.00530 + 1.79034I
b = 0.18144 + 2.59266I
−5.57317 + 6.53299I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.21558 + 1.53803I
a = −0.18613 + 1.73024I
b = −0.63034 + 2.83722I
−8.41578 − 7.83198I 0
u = −0.21558 − 1.53803I
a = −0.18613 − 1.73024I
b = −0.63034 − 2.83722I
−8.41578 + 7.83198I 0
u = −0.320741 + 0.310919I
a = −3.93867 + 0.92331I
b = −0.666263 − 0.313444I
−5.57317 − 6.53299I 2.95283 + 12.42721I
u = −0.320741 − 0.310919I
a = −3.93867 − 0.92331I
b = −0.666263 + 0.313444I
−5.57317 + 6.53299I 2.95283 − 12.42721I
u = 0.27915 + 1.53150I
a = −0.03303 − 1.78922I
b = −0.44692 − 2.87114I
−7.8103 + 13.8110I 0
u = 0.27915 − 1.53150I
a = −0.03303 + 1.78922I
b = −0.44692 + 2.87114I
−7.8103 − 13.8110I 0
u = 0.25714 + 1.55253I
a = 0.502633 − 0.791123I
b = 0.331108 − 1.370570I
−8.38703 − 1.13960I 0
u = 0.25714 − 1.55253I
a = 0.502633 + 0.791123I
b = 0.331108 + 1.370570I
−8.38703 + 1.13960I 0
u = 0.332458 + 0.261172I
a = 1.096740 − 0.884077I
b = −0.701887 + 0.263772I
−1.97135 −3.23135 + 0.I
u = 0.332458 − 0.261172I
a = 1.096740 + 0.884077I
b = −0.701887 − 0.263772I
−1.97135 −3.23135 + 0.I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.13850 + 1.57559I
a = −1.16413 + 1.49269I
b = −0.85316 + 1.98749I
−14.9424 + 7.4727I 0
u = 0.13850 − 1.57559I
a = −1.16413 − 1.49269I
b = −0.85316 − 1.98749I
−14.9424 − 7.4727I 0
u = 0.14088 + 1.60069I
a = −0.23786 − 1.50667I
b = −0.71263 − 2.57130I
−16.8914 + 3.8329I 0
u = 0.14088 − 1.60069I
a = −0.23786 + 1.50667I
b = −0.71263 + 2.57130I
−16.8914 − 3.8329I 0
u = −0.30166 + 1.58225I
a = 0.109516 + 0.838009I
b = −0.23937 + 1.47556I
−6.69520 − 5.05617I 0
u = −0.30166 − 1.58225I
a = 0.109516 − 0.838009I
b = −0.23937 − 1.47556I
−6.69520 + 5.05617I 0
u = 0.106252 + 0.354096I
a = −2.48683 + 2.01384I
b = −1.371860 − 0.053216I
−6.98631 + 2.75445I −5.88485 − 0.42614I
u = 0.106252 − 0.354096I
a = −2.48683 − 2.01384I
b = −1.371860 + 0.053216I
−6.98631 − 2.75445I −5.88485 + 0.42614I
u = 0.120663 + 0.346842I
a = 3.16037 + 0.38450I
b = −0.296330 + 0.004024I
0.89188 − 2.50997I 5.62365 − 9.86280I
u = 0.120663 − 0.346842I
a = 3.16037 − 0.38450I
b = −0.296330 − 0.004024I
0.89188 + 2.50997I 5.62365 + 9.86280I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.30194 + 1.62391I
a = 0.01529 + 1.62187I
b = 0.15988 + 2.41535I
−11.44370 + 8.12756I 0
u = 0.30194 − 1.62391I
a = 0.01529 − 1.62187I
b = 0.15988 − 2.41535I
−11.44370 − 8.12756I 0
u = −0.17275 + 1.67346I
a = 0.406277 + 1.126200I
b = 0.31705 + 1.83585I
−16.8914 + 3.8329I 0
u = −0.17275 − 1.67346I
a = 0.406277 − 1.126200I
b = 0.31705 − 1.83585I
−16.8914 − 3.8329I 0
u = 0.224421 + 0.014031I
a = −2.33880 − 6.47809I
b = −0.448282 + 0.138536I
1.05292 + 2.70150I 19.0928 − 8.4683I
u = 0.224421 − 0.014031I
a = −2.33880 + 6.47809I
b = −0.448282 − 0.138536I
1.05292 − 2.70150I 19.0928 + 8.4683I
u = 0.0775099 + 0.0095965I
a = −3.08930 − 8.74170I
b = 1.25369 − 0.67794I
−1.83648 − 2.54008I 7.90046 + 0.06865I
u = 0.0775099 − 0.0095965I
a = −3.08930 + 8.74170I
b = 1.25369 + 0.67794I
−1.83648 + 2.54008I 7.90046 − 0.06865I
20
III. I
u
3
= hu
4
+ u
3
+ 2u
2
+ b + 2u, −u
6
− 2u
4
− u
3
+ u
2
+ a − u + 1, u
7
+
u
6
+ 4u
5
+ 5u
4
+ 5u
3
+ 6u
2
+ 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
2
=
u
6
+ 2u
4
+ u
3
− u
2
+ u − 1
−u
4
− u
3
− 2u
2
− 2u
a
6
=
1
−u
2
a
3
=
0
−u
6
− 2u
4
− u
3
+ u
2
− u + 1
a
10
=
u
u
a
11
=
−1
u
3
+ u
2
+ 2u + 1
a
7
=
−u
3
− 2u
u
6
+ u
5
+ 4u
4
+ 4u
3
+ 4u
2
+ 4u + 1
a
12
=
−1
−u
5
− 2u
4
− 2u
3
− 4u
2
− 2u
a
4
=
u
2
+ 1
u
2
a
1
=
−u
2
− 1
−u
6
+ u
5
− u
4
+ u
3
+ 3u
2
+ 1
a
8
=
−u
−u
6
− 2u
5
− 2u
4
− 4u
3
− 2u
2
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
6
+ u
5
− 7u
4
+ 8u
3
− 4u
2
+ 12u + 6
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
7
− 5u
5
+ u
4
+ 14u
3
− 9u
2
+ 2u − 5
c
2
, c
11
u
7
− u
6
− 2u
4
+ 2u
3
+ 4u
2
+ 5u − 1
c
3
, c
10
u
7
+ u
6
+ 2u
5
+ 2u
3
− u
2
+ u − 1
c
4
, c
5
, c
7
c
8
u
7
+ u
6
+ 4u
5
+ 5u
4
+ 5u
3
+ 6u
2
+ 2u + 1
c
6
u
7
− u
6
− 3u
5
+ 10u
4
− 12u
3
+ 8u
2
− 3u + 1
c
9
, c
12
u
7
− u
6
+ 4u
5
− 5u
4
+ 5u
3
− 6u
2
+ 2u − 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
7
− 10y
6
+ 53y
5
− 137y
4
+ 194y
3
− 15y
2
− 86y −25
c
2
, c
11
y
7
− y
6
+ 14y
4
+ 18y
3
+ 33y −1
c
3
, c
10
y
7
+ 3y
6
+ 8y
5
+ 12y
4
+ 10y
3
+ 3y
2
− y −1
c
4
, c
5
, c
7
c
8
, c
9
, c
12
y
7
+ 7y
6
+ 16y
5
+ 7y
4
− 21y
3
− 26y
2
− 8y −1
c
6
y
7
− 7y
6
+ 5y
5
− 18y
4
+ 4y
3
− 12y
2
− 7y −1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.10838
a = 0.174033
b = −0.387834
−0.187807 −39.0540
u = 0.030175 + 1.243640I
a = 1.53616 − 0.67798I
b = 0.787443 − 0.485292I
−4.85229 − 2.21700I 2.43422 + 2.76940I
u = 0.030175 − 1.243640I
a = 1.53616 + 0.67798I
b = 0.787443 + 0.485292I
−4.85229 + 2.21700I 2.43422 − 2.76940I
u = −0.153212 + 0.464251I
a = −0.827817 + 0.635564I
b = 0.578417 − 0.631263I
0.66234 − 3.24612I 5.53982 + 5.24369I
u = −0.153212 − 0.464251I
a = −0.827817 − 0.635564I
b = 0.578417 + 0.631263I
0.66234 + 3.24612I 5.53982 − 5.24369I
u = 0.17723 + 1.55173I
a = −0.295356 + 1.335600I
b = 0.32806 + 2.00086I
−13.8104 + 7.2331I −2.44727 − 4.47528I
u = 0.17723 − 1.55173I
a = −0.295356 − 1.335600I
b = 0.32806 − 2.00086I
−13.8104 − 7.2331I −2.44727 + 4.47528I
24
IV.
I
u
4
= h4u
25
−11u
24
+· · ·+b−3, 5u
25
−13u
24
+· · ·+a+4, u
26
−2u
25
+· · ·−2u+1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
2
=
−5u
25
+ 13u
24
+ ··· − 10u − 4
−4u
25
+ 11u
24
+ ··· − 10u + 3
a
6
=
1
−u
2
a
3
=
−3u
25
+ 6u
24
+ ··· − 9u − 4
−u
25
− 9u
23
+ ··· − 8u
2
− 2u
a
10
=
u
u
a
11
=
−5u
25
+ 7u
24
+ ··· − 42u + 5
u
25
− 6u
24
+ ··· + 10u − 2
a
7
=
−3u
25
+ 7u
24
+ ··· − 22u + 15
−7u
25
+ 7u
24
+ ··· + 12u − 7
a
12
=
−2u
25
+ 4u
24
+ ··· − 29u + 1
9u
25
− 18u
24
+ ··· + 3u + 2
a
4
=
u
2
+ 1
u
2
a
1
=
−3u
25
+ 6u
24
+ ··· − 9u − 5
2u
25
− 8u
24
+ ··· + 2u − 1
a
8
=
4u
25
− 8u
24
+ ··· + 25u − 1
−u
25
+ u
24
+ ··· + 11u − 4
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 16u
25
−52u
24
+260u
23
−670u
22
+1842u
21
−3831u
20
+7521u
19
−12817u
18
+19810u
17
−
28104u
16
+ 36014u
15
− 43461u
14
+ 47847u
13
− 50479u
12
+ 48836u
11
− 45762u
10
+
38742u
9
−31570u
8
+ 22476u
7
−15159u
6
+ 8472u
5
−4567u
4
+ 1807u
3
−763u
2
+ 156u −57
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
13
− 6u
12
+ ··· + 5u − 1)
2
c
2
, c
11
u
26
− 4u
25
+ ··· − u + 1
c
3
, c
10
u
26
− u
25
+ ··· + 4u + 1
c
4
, c
5
, c
7
c
8
u
26
− 2u
25
+ ··· − 2u + 1
c
6
(u
13
+ 2u
12
+ ··· + u + 1)
2
c
9
, c
12
u
26
+ 2u
25
+ ··· + 2u + 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
13
+ 4y
11
+ ··· − 3y −1)
2
c
2
, c
11
y
26
+ 4y
25
+ ··· + 5y + 1
c
3
, c
10
y
26
+ 9y
25
+ ··· − 6y + 1
c
4
, c
5
, c
7
c
8
, c
9
, c
12
y
26
+ 26y
25
+ ··· + 34y + 1
c
6
(y
13
− 7y
10
+ ··· − y −1)
2
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.730172 + 0.693234I
a = 0.457696 + 0.118570I
b = 0.236181 − 0.470634I
0.74327 − 2.76180I −9.3941 + 14.0297I
u = −0.730172 − 0.693234I
a = 0.457696 − 0.118570I
b = 0.236181 + 0.470634I
0.74327 + 2.76180I −9.3941 − 14.0297I
u = 0.773462 + 0.552068I
a = 1.026150 + 0.066541I
b = 0.654746 + 0.661477I
−2.74327 + 2.81882I 5.01074 − 8.12348I
u = 0.773462 − 0.552068I
a = 1.026150 − 0.066541I
b = 0.654746 − 0.661477I
−2.74327 − 2.81882I 5.01074 + 8.12348I
u = 0.720017 + 0.607404I
a = −0.275549 − 0.019132I
b = −0.570038 + 0.617491I
−6.28182 + 4.31867I −0.75118 − 2.96077I
u = 0.720017 − 0.607404I
a = −0.275549 + 0.019132I
b = −0.570038 − 0.617491I
−6.28182 − 4.31867I −0.75118 + 2.96077I
u = −0.080666 + 1.268250I
a = −1.08174 − 2.09802I
b = −1.76821 − 2.64796I
−8.68134 − 6.43987I −6.48218 + 7.11485I
u = −0.080666 − 1.268250I
a = −1.08174 + 2.09802I
b = −1.76821 + 2.64796I
−8.68134 + 6.43987I −6.48218 − 7.11485I
u = −0.017263 + 1.283860I
a = 0.198829 + 0.356895I
b = −0.896234 + 0.172667I
−2.39119 + 2.86259I −3.54485 − 5.28321I
u = −0.017263 − 1.283860I
a = 0.198829 − 0.356895I
b = −0.896234 − 0.172667I
−2.39119 − 2.86259I −3.54485 + 5.28321I
28
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.015284 + 1.311700I
a = −1.004590 + 0.763267I
b = −2.46587 + 1.02119I
−2.74327 + 2.81882I 5.01074 − 8.12348I
u = 0.015284 − 1.311700I
a = −1.004590 − 0.763267I
b = −2.46587 − 1.02119I
−2.74327 − 2.81882I 5.01074 + 8.12348I
u = 0.210688 + 0.636307I
a = 0.710237 − 0.090783I
b = 1.30620 + 0.62197I
−2.39119 + 2.86259I −3.54485 − 5.28321I
u = 0.210688 − 0.636307I
a = 0.710237 + 0.090783I
b = 1.30620 − 0.62197I
−2.39119 − 2.86259I −3.54485 + 5.28321I
u = 0.370652 + 1.317530I
a = −0.886501 + 0.298765I
b = −0.838761 + 0.875858I
−8.67622 −8.33663 + 0.I
u = 0.370652 − 1.317530I
a = −0.886501 − 0.298765I
b = −0.838761 − 0.875858I
−8.67622 −8.33663 + 0.I
u = 0.26231 + 1.41381I
a = −0.06979 + 2.20797I
b = 0.09292 + 2.96289I
−8.68134 + 6.43987I −6.48218 − 7.11485I
u = 0.26231 − 1.41381I
a = −0.06979 − 2.20797I
b = 0.09292 − 2.96289I
−8.68134 − 6.43987I −6.48218 + 7.11485I
u = −0.080835 + 0.523611I
a = −1.86091 + 1.66996I
b = −0.450527 + 1.118720I
−5.91635 + 5.69889I −0.17009 − 4.31980I
u = −0.080835 − 0.523611I
a = −1.86091 − 1.66996I
b = −0.450527 − 1.118720I
−5.91635 − 5.69889I −0.17009 + 4.31980I
29
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.21536 + 1.46358I
a = 0.02422 − 1.85633I
b = 0.36067 − 2.69743I
−5.91635 − 5.69889I 0. + 4.31980I
u = −0.21536 − 1.46358I
a = 0.02422 + 1.85633I
b = 0.36067 + 2.69743I
−5.91635 + 5.69889I 0. − 4.31980I
u = −0.20434 + 1.48454I
a = −0.179745 − 1.164140I
b = 0.24017 − 1.99352I
−6.28182 − 4.31867I 0. + 2.96077I
u = −0.20434 − 1.48454I
a = −0.179745 + 1.164140I
b = 0.24017 + 1.99352I
−6.28182 + 4.31867I 0. − 2.96077I
u = −0.023777 + 0.333723I
a = −4.05830 + 0.35369I
b = 0.098759 − 0.281806I
0.74327 − 2.76180I −9.3941 + 14.0297I
u = −0.023777 − 0.333723I
a = −4.05830 − 0.35369I
b = 0.098759 + 0.281806I
0.74327 + 2.76180I −9.3941 − 14.0297I
30
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
7
− 5u
5
+ ··· + 2u − 5)(u
13
− 6u
12
+ ··· + 5u − 1)
2
· (u
27
− 7u
26
+ ··· + 176u − 16)(u
49
+ 8u
48
+ ··· − u + 139)
2
c
2
, c
11
(u
7
− u
6
− 2u
4
+ 2u
3
+ 4u
2
+ 5u − 1)(u
26
− 4u
25
+ ··· − u + 1)
· (u
27
+ u
26
+ ··· − 3u + 1)(u
98
− u
97
+ ··· + 78991u + 5641)
c
3
, c
10
(u
7
+ u
6
+ 2u
5
+ 2u
3
− u
2
+ u − 1)(u
26
− u
25
+ ··· + 4u + 1)
· (u
27
+ u
26
+ ··· + 3u + 1)(u
98
− 12u
96
+ ··· − 2731098u + 1190927)
c
4
, c
5
, c
7
c
8
(u
7
+ u
6
+ ··· + 2u + 1)(u
26
− 2u
25
+ ··· − 2u + 1)
· (u
27
− u
26
+ ··· + 2u + 1)(u
98
+ u
97
+ ··· + 36u + 1)
c
6
(u
7
− u
6
− 3u
5
+ 10u
4
− 12u
3
+ 8u
2
− 3u + 1)
· ((u
13
+ 2u
12
+ ··· + u + 1)
2
)(u
27
− 16u
26
+ ··· + 22u − 4)
· (u
49
+ 6u
48
+ ··· + 7u + 1)
2
c
9
, c
12
(u
7
− u
6
+ ··· + 2u − 1)(u
26
+ 2u
25
+ ··· + 2u + 1)
· (u
27
− u
26
+ ··· + 2u + 1)(u
98
+ u
97
+ ··· + 36u + 1)
31
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
7
− 10y
6
+ 53y
5
− 137y
4
+ 194y
3
− 15y
2
− 86y −25)
· ((y
13
+ 4y
11
+ ··· − 3y −1)
2
)(y
27
− 5y
26
+ ··· + 5280y −256)
· (y
49
− 30y
48
+ ··· − 378913y −19321)
2
c
2
, c
11
(y
7
− y
6
+ 14y
4
+ 18y
3
+ 33y −1)(y
26
+ 4y
25
+ ··· + 5y + 1)
· (y
27
− 7y
26
+ ··· + 27y −1)
· (y
98
+ 23y
97
+ ··· + 672079733y + 31820881)
c
3
, c
10
(y
7
+ 3y
6
+ ··· − y −1)(y
26
+ 9y
25
+ ··· − 6y + 1)
· (y
27
− 7y
26
+ ··· + 17y −1)
· (y
98
− 24y
97
+ ··· − 54241979206882y + 1418307119329)
c
4
, c
5
, c
7
c
8
, c
9
, c
12
(y
7
+ 7y
6
+ 16y
5
+ 7y
4
− 21y
3
− 26y
2
− 8y −1)
· (y
26
+ 26y
25
+ ··· + 34y + 1)(y
27
+ 25y
26
+ ··· + 18y −1)
· (y
98
+ 101y
97
+ ··· − 326y + 1)
c
6
(y
7
− 7y
6
+ 5y
5
− 18y
4
+ 4y
3
− 12y
2
− 7y −1)
· ((y
13
− 7y
10
+ ··· − y −1)
2
)(y
27
− 10y
26
+ ··· + 492y −16)
· (y
49
− 6y
48
+ ··· + 25y −1)
2
32
