12n
0858
(K12n
0858
)
A knot diagram
1
Linearized knot diagam
4 7 9 1 9 12 2 11 2 1 6 8
Solving Sequence
2,4
1
5,10
11 9 6 12 3 8 7
c
1
c
4
c
10
c
9
c
5
c
11
c
3
c
8
c
7
c
2
, c
6
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.03636 × 10
222
u
84
− 3.95825 × 10
222
u
83
+ ··· + 1.02307 × 10
222
b − 2.68730 × 10
221
,
− 1.33652 × 10
222
u
84
− 4.40227 × 10
222
u
83
+ ··· + 3.06922 × 10
222
a − 2.90267 × 10
223
,
u
85
+ 4u
84
+ ··· + 2u + 1i
I
u
2
= h−2.67401 × 10
19
u
27
+ 1.56488 × 10
20
u
26
+ ··· + 1.03296 × 10
19
b + 9.72270 × 10
16
,
− 2.83742 × 10
19
u
27
+ 1.86866 × 10
20
u
26
+ ··· + 1.03296 × 10
19
a + 1.15270 × 10
20
, u
28
− 6u
27
+ ··· − 5u + 1i
I
u
3
= hb, a − u + 1, u
2
− u + 1i
* 3 irreducible components of dim
C
= 0, with total 115 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h−1.04 × 10
222
u
84
− 3.96 × 10
222
u
83
+ · · · + 1.02 × 10
222
b − 2.69 ×
10
221
, −1.34 × 10
222
u
84
− 4.40 × 10
222
u
83
+ · · · + 3.07 × 10
222
a − 2.90 ×
10
223
, u
85
+ 4u
84
+ · · · + 2u + 1i
(i) Arc colorings
a
2
=
1
0
a
4
=
0
u
a
1
=
1
−u
2
a
5
=
−u
u
3
+ u
a
10
=
0.435460u
84
+ 1.43433u
83
+ ··· − 57.4184u + 9.45737
1.01299u
84
+ 3.86898u
83
+ ··· + 18.3676u + 0.262670
a
11
=
−0.0186202u
84
− 0.424498u
83
+ ··· − 75.9656u + 8.88719
0.905660u
84
+ 3.44358u
83
+ ··· + 17.8285u + 0.220165
a
9
=
−0.577528u
84
− 2.43465u
83
+ ··· − 75.7860u + 9.19470
1.01299u
84
+ 3.86898u
83
+ ··· + 18.3676u + 0.262670
a
6
=
−0.342675u
84
− 1.51095u
83
+ ··· − 91.5089u − 14.8953
−0.120732u
84
− 0.834502u
83
+ ··· − 5.90626u + 0.893350
a
12
=
0.303518u
84
+ 0.747086u
83
+ ··· + 102.130u + 17.1171
0.499714u
84
+ 1.68173u
83
+ ··· + 5.70936u − 2.24895
a
3
=
0.279580u
84
+ 0.737945u
83
+ ··· − 83.3181u − 17.0118
−0.216374u
84
− 0.998041u
83
+ ··· − 6.67199u + 1.73603
a
8
=
−2.00860u
84
− 8.08594u
83
+ ··· − 109.439u + 4.86586
0.228258u
84
+ 1.23880u
83
+ ··· + 16.5717u + 1.16566
a
7
=
−2.23686u
84
− 9.32474u
83
+ ··· − 126.011u + 3.70020
0.228258u
84
+ 1.23880u
83
+ ··· + 16.5717u + 1.16566
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5.33059u
84
− 22.7759u
83
+ ··· − 48.3401u − 9.30996
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
85
− 4u
84
+ ··· + 2u − 1
c
2
, c
7
u
85
+ 30u
83
+ ··· + 26u − 1
c
3
u
85
+ u
84
+ ··· − 8586859u − 7135679
c
5
u
85
+ 10u
84
+ ··· + 4292211u − 291526
c
6
, c
11
u
85
+ 2u
84
+ ··· − 564u − 172
c
8
u
85
+ u
84
+ ··· + 15u + 1
c
9
u
85
− 3u
84
+ ··· + 5809196u − 707552
c
10
u
85
− 12u
84
+ ··· + 63060030u − 7539289
c
12
u
85
− 3u
84
+ ··· − 35799u − 3454
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
85
+ 18y
84
+ ··· − 228y −1
c
2
, c
7
y
85
+ 60y
84
+ ··· − 140y −1
c
3
y
85
+ 75y
84
+ ··· − 496895527067841y −50917914791041
c
5
y
85
− 38y
84
+ ··· + 7819625711645y −84987408676
c
6
, c
11
y
85
− 50y
84
+ ··· + 783184y −29584
c
8
y
85
− 15y
84
+ ··· − 11y −1
c
9
y
85
+ 77y
84
+ ··· − 9930483397744y −500629832704
c
10
y
85
− 44y
84
+ ··· + 214383869545346y −56840878625521
c
12
y
85
+ 17y
84
+ ··· − 589394319y −11930116
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.998570 + 0.272294I
a = 0.475791 − 0.395407I
b = 0.032394 − 0.448924I
−1.43220 − 2.66932I 0
u = 0.998570 − 0.272294I
a = 0.475791 + 0.395407I
b = 0.032394 + 0.448924I
−1.43220 + 2.66932I 0
u = −0.078052 + 0.926381I
a = 1.92195 + 1.40477I
b = 0.773943 + 0.472131I
−0.217172 − 1.098890I 0
u = −0.078052 − 0.926381I
a = 1.92195 − 1.40477I
b = 0.773943 − 0.472131I
−0.217172 + 1.098890I 0
u = −0.981755 + 0.507072I
a = 0.196732 + 1.354770I
b = 0.04903 + 2.35138I
−3.61008 + 5.45903I 0
u = −0.981755 − 0.507072I
a = 0.196732 − 1.354770I
b = 0.04903 − 2.35138I
−3.61008 − 5.45903I 0
u = 0.476670 + 1.051240I
a = −0.325982 + 0.333193I
b = −0.425103 − 0.302685I
0.96688 − 5.57781I 0
u = 0.476670 − 1.051240I
a = −0.325982 − 0.333193I
b = −0.425103 + 0.302685I
0.96688 + 5.57781I 0
u = 0.668482 + 0.952846I
a = 0.945938 − 0.449100I
b = 0.277270 − 0.487750I
0.47254 − 2.58298I 0
u = 0.668482 − 0.952846I
a = 0.945938 + 0.449100I
b = 0.277270 + 0.487750I
0.47254 + 2.58298I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.191158 + 0.810743I
a = 0.399071 − 0.163081I
b = 1.13355 − 1.50881I
0.59219 + 4.00643I 9.81408 − 1.58250I
u = 0.191158 − 0.810743I
a = 0.399071 + 0.163081I
b = 1.13355 + 1.50881I
0.59219 − 4.00643I 9.81408 + 1.58250I
u = 0.920774 + 0.721880I
a = −1.023550 + 0.281002I
b = −0.67699 + 1.48386I
−4.32440 − 1.41643I 0
u = 0.920774 − 0.721880I
a = −1.023550 − 0.281002I
b = −0.67699 − 1.48386I
−4.32440 + 1.41643I 0
u = −0.114215 + 0.796267I
a = −1.47054 + 0.01938I
b = −0.738208 + 0.689403I
6.75942 − 3.17501I 7.34012 + 8.97310I
u = −0.114215 − 0.796267I
a = −1.47054 − 0.01938I
b = −0.738208 − 0.689403I
6.75942 + 3.17501I 7.34012 − 8.97310I
u = −0.289881 + 0.745166I
a = 1.140080 − 0.820492I
b = 1.57828 + 0.62135I
6.89613 + 1.55029I 8.65169 − 1.88696I
u = −0.289881 − 0.745166I
a = 1.140080 + 0.820492I
b = 1.57828 − 0.62135I
6.89613 − 1.55029I 8.65169 + 1.88696I
u = 0.736997 + 0.309730I
a = −1.003550 − 0.492868I
b = −1.219120 + 0.187207I
−3.36308 − 1.67385I −3.09379 + 4.70980I
u = 0.736997 − 0.309730I
a = −1.003550 + 0.492868I
b = −1.219120 − 0.187207I
−3.36308 + 1.67385I −3.09379 − 4.70980I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.784929 + 0.921642I
a = −0.819247 − 1.130810I
b = 0.36426 − 1.68162I
−6.55646 − 2.64119I 0
u = −0.784929 − 0.921642I
a = −0.819247 + 1.130810I
b = 0.36426 + 1.68162I
−6.55646 + 2.64119I 0
u = −1.007190 + 0.675787I
a = −1.327370 + 0.100127I
b = −0.324588 − 1.238780I
−5.94666 + 1.03450I 0
u = −1.007190 − 0.675787I
a = −1.327370 − 0.100127I
b = −0.324588 + 1.238780I
−5.94666 − 1.03450I 0
u = 1.111950 + 0.502144I
a = −0.682297 − 0.061208I
b = −0.457963 + 0.733480I
−3.52529 − 1.34010I 0
u = 1.111950 − 0.502144I
a = −0.682297 + 0.061208I
b = −0.457963 − 0.733480I
−3.52529 + 1.34010I 0
u = −0.840950 + 0.891035I
a = −1.51043 − 0.31627I
b = −1.00700 − 1.77133I
−6.68939 + 8.75504I 0
u = −0.840950 − 0.891035I
a = −1.51043 + 0.31627I
b = −1.00700 + 1.77133I
−6.68939 − 8.75504I 0
u = 0.528662 + 0.545614I
a = 1.47316 − 2.31272I
b = −0.688160 − 0.114075I
−0.66682 − 6.93179I 4.00000 + 11.91492I
u = 0.528662 − 0.545614I
a = 1.47316 + 2.31272I
b = −0.688160 + 0.114075I
−0.66682 + 6.93179I 4.00000 − 11.91492I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.064801 + 1.255050I
a = −0.327089 + 0.427849I
b = 0.094931 + 0.511084I
5.65951 + 1.98333I 0
u = −0.064801 − 1.255050I
a = −0.327089 − 0.427849I
b = 0.094931 − 0.511084I
5.65951 − 1.98333I 0
u = 0.995122 + 0.770188I
a = 0.941647 − 0.500048I
b = 0.14802 − 1.67413I
−2.68266 + 2.97750I 0
u = 0.995122 − 0.770188I
a = 0.941647 + 0.500048I
b = 0.14802 + 1.67413I
−2.68266 − 2.97750I 0
u = −0.117101 + 0.723899I
a = −0.793624 − 0.270354I
b = −1.35991 + 0.87928I
−0.655020 + 1.237870I 10.88550 − 2.57862I
u = −0.117101 − 0.723899I
a = −0.793624 + 0.270354I
b = −1.35991 − 0.87928I
−0.655020 − 1.237870I 10.88550 + 2.57862I
u = −0.443214 + 0.560209I
a = 1.84470 + 0.04018I
b = 0.881631 − 0.377895I
5.65422 + 5.51636I 16.4245 + 6.0413I
u = −0.443214 − 0.560209I
a = 1.84470 − 0.04018I
b = 0.881631 + 0.377895I
5.65422 − 5.51636I 16.4245 − 6.0413I
u = −0.926014 + 0.904807I
a = 1.315410 + 0.385771I
b = 0.51296 + 1.85233I
−8.99774 + 4.10945I 0
u = −0.926014 − 0.904807I
a = 1.315410 − 0.385771I
b = 0.51296 − 1.85233I
−8.99774 − 4.10945I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.016570 + 0.802307I
a = 0.501441 − 0.416278I
b = 0.370374 − 1.209920I
−0.70125 − 3.83022I 0
u = 1.016570 − 0.802307I
a = 0.501441 + 0.416278I
b = 0.370374 + 1.209920I
−0.70125 + 3.83022I 0
u = 0.393407 + 1.253670I
a = 0.816751 − 0.028019I
b = 0.380543 − 0.236715I
0.87862 − 2.40445I 0
u = 0.393407 − 1.253670I
a = 0.816751 + 0.028019I
b = 0.380543 + 0.236715I
0.87862 + 2.40445I 0
u = −0.873771 + 0.982867I
a = 0.932327 + 0.814540I
b = −0.11560 + 1.83982I
−8.72930 + 2.55502I 0
u = −0.873771 − 0.982867I
a = 0.932327 − 0.814540I
b = −0.11560 − 1.83982I
−8.72930 − 2.55502I 0
u = −0.322301 + 0.597684I
a = −0.98727 + 2.66264I
b = −1.275690 − 0.115283I
6.34439 + 0.92935I 20.3887 − 11.8228I
u = −0.322301 − 0.597684I
a = −0.98727 − 2.66264I
b = −1.275690 + 0.115283I
6.34439 − 0.92935I 20.3887 + 11.8228I
u = 0.012130 + 0.671137I
a = −3.61616 − 1.88171I
b = −1.160720 − 0.362352I
1.07314 + 5.28326I 12.72232 − 3.52720I
u = 0.012130 − 0.671137I
a = −3.61616 + 1.88171I
b = −1.160720 + 0.362352I
1.07314 − 5.28326I 12.72232 + 3.52720I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.320917 + 0.576461I
a = 0.44228 + 2.73702I
b = 0.595528 − 0.251518I
−1.32168 − 2.14852I 5.67361 + 6.10919I
u = 0.320917 − 0.576461I
a = 0.44228 − 2.73702I
b = 0.595528 + 0.251518I
−1.32168 + 2.14852I 5.67361 − 6.10919I
u = 0.792598 + 1.092070I
a = −0.934721 + 0.937326I
b = −0.06898 + 1.54472I
−3.16562 − 4.95912I 0
u = 0.792598 − 1.092070I
a = −0.934721 − 0.937326I
b = −0.06898 − 1.54472I
−3.16562 + 4.95912I 0
u = −1.068700 + 0.849855I
a = −0.730782 − 0.967920I
b = 0.05722 − 1.85054I
−10.13780 − 3.22951I 0
u = −1.068700 − 0.849855I
a = −0.730782 + 0.967920I
b = 0.05722 + 1.85054I
−10.13780 + 3.22951I 0
u = 0.306326 + 0.542199I
a = 1.96796 + 0.29112I
b = 2.60639 − 0.46014I
0.38559 − 6.54347I 7.3888 + 12.6144I
u = 0.306326 − 0.542199I
a = 1.96796 − 0.29112I
b = 2.60639 + 0.46014I
0.38559 + 6.54347I 7.3888 − 12.6144I
u = 0.854442 + 1.081810I
a = 1.21765 − 0.74563I
b = 0.39692 − 1.85331I
−1.70018 − 9.75286I 0
u = 0.854442 − 1.081810I
a = 1.21765 + 0.74563I
b = 0.39692 + 1.85331I
−1.70018 + 9.75286I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.103910 + 0.843065I
a = 0.694324 + 0.843846I
b = −0.27662 + 1.65789I
−6.92146 − 10.17200I 0
u = −1.103910 − 0.843065I
a = 0.694324 − 0.843846I
b = −0.27662 − 1.65789I
−6.92146 + 10.17200I 0
u = 0.892642 + 1.067060I
a = 0.938403 − 0.382310I
b = 0.697204 − 1.065550I
0.08231 − 3.35812I 0
u = 0.892642 − 1.067060I
a = 0.938403 + 0.382310I
b = 0.697204 + 1.065550I
0.08231 + 3.35812I 0
u = −0.343571 + 0.493749I
a = −1.63279 − 0.47457I
b = −0.610765 + 0.376866I
0.27736 + 2.37656I 5.87909 − 3.02757I
u = −0.343571 − 0.493749I
a = −1.63279 + 0.47457I
b = −0.610765 − 0.376866I
0.27736 − 2.37656I 5.87909 + 3.02757I
u = −0.92042 + 1.08713I
a = −1.44989 − 0.76383I
b = −0.72095 − 1.86483I
−9.35077 + 10.45160I 0
u = −0.92042 − 1.08713I
a = −1.44989 + 0.76383I
b = −0.72095 + 1.86483I
−9.35077 − 10.45160I 0
u = −0.99205 + 1.02772I
a = 1.22952 + 1.05529I
b = 0.60550 + 1.78764I
−1.88830 + 3.70194I 0
u = −0.99205 − 1.02772I
a = 1.22952 − 1.05529I
b = 0.60550 − 1.78764I
−1.88830 − 3.70194I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.082020 + 0.555614I
a = 1.56239 + 0.33583I
b = 0.472829 − 0.368700I
0.944298 − 0.816678I 7.73863 + 4.64902I
u = −0.082020 − 0.555614I
a = 1.56239 − 0.33583I
b = 0.472829 + 0.368700I
0.944298 + 0.816678I 7.73863 − 4.64902I
u = −0.92506 + 1.10315I
a = 1.39631 + 0.61370I
b = 0.83273 + 1.89767I
−6.0450 + 17.5019I 0
u = −0.92506 − 1.10315I
a = 1.39631 − 0.61370I
b = 0.83273 − 1.89767I
−6.0450 − 17.5019I 0
u = −0.86980 + 1.18983I
a = −0.546302 − 0.583978I
b = 0.00460 − 1.61732I
−4.35655 + 5.88159I 0
u = −0.86980 − 1.18983I
a = −0.546302 + 0.583978I
b = 0.00460 + 1.61732I
−4.35655 − 5.88159I 0
u = −1.14823 + 0.94306I
a = 0.890564 + 0.131393I
b = 0.15158 + 1.57372I
−7.94495 + 4.03692I 0
u = −1.14823 − 0.94306I
a = 0.890564 − 0.131393I
b = 0.15158 − 1.57372I
−7.94495 − 4.03692I 0
u = −0.503477
a = 1.44168
b = 0.367391
1.50635 7.56670
u = 0.94565 + 1.23775I
a = −0.651844 + 0.326553I
b = −0.437766 + 1.035920I
−1.43053 − 6.16651I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.94565 − 1.23775I
a = −0.651844 − 0.326553I
b = −0.437766 − 1.035920I
−1.43053 + 6.16651I 0
u = 0.38268 + 1.53582I
a = −0.201689 − 0.209453I
b = 0.120638 − 0.218357I
4.55229 − 8.07421I 0
u = 0.38268 − 1.53582I
a = −0.201689 + 0.209453I
b = 0.120638 + 0.218357I
4.55229 + 8.07421I 0
u = 0.0039208 + 0.1000890I
a = 10.56990 − 4.84782I
b = −0.257898 + 1.352100I
−3.13128 + 2.89223I 0.61723 − 2.40153I
u = 0.0039208 − 0.1000890I
a = 10.56990 + 4.84782I
b = −0.257898 − 1.352100I
−3.13128 − 2.89223I 0.61723 + 2.40153I
13
II.
I
u
2
= h−2.67×10
19
u
27
+1.56×10
20
u
26
+· · ·+1.03×10
19
b+9.72×10
16
, −2.84×
10
19
u
27
+1.87×10
20
u
26
+· · ·+1.03×10
19
a+1.15×10
20
, u
28
−6u
27
+· · ·−5u+1i
(i) Arc colorings
a
2
=
1
0
a
4
=
0
u
a
1
=
1
−u
2
a
5
=
−u
u
3
+ u
a
10
=
2.74689u
27
− 18.0903u
26
+ ··· + 70.8440u − 11.1592
2.58870u
27
− 15.1495u
26
+ ··· + 16.1735u − 0.00941249
a
11
=
0.922280u
27
− 7.58964u
26
+ ··· + 65.4625u − 12.7588
2.19598u
27
− 12.9739u
26
+ ··· + 16.5836u − 0.456358
a
9
=
0.158190u
27
− 2.94084u
26
+ ··· + 54.6705u − 11.1498
2.58870u
27
− 15.1495u
26
+ ··· + 16.1735u − 0.00941249
a
6
=
6.62441u
27
− 38.9685u
26
+ ··· + 62.0136u − 3.81446
0.731807u
27
− 3.46192u
26
+ ··· − 15.4905u + 5.80190
a
12
=
−5.07562u
27
+ 29.3393u
26
+ ··· − 31.5420u − 0.554744
0.490281u
27
− 3.23397u
26
+ ··· + 12.0828u − 3.71161
a
3
=
7.45123u
27
− 44.1923u
26
+ ··· + 79.1010u − 8.17538
0.241924u
27
− 0.802233u
26
+ ··· − 10.2116u + 4.87601
a
8
=
2.49779u
27
− 15.0998u
26
+ ··· − 1.12236u + 4.10008
0.0110535u
27
+ 1.02730u
26
+ ··· − 24.9223u + 5.52391
a
7
=
2.48674u
27
− 16.1271u
26
+ ··· + 23.7999u − 1.42383
0.0110535u
27
+ 1.02730u
26
+ ··· − 24.9223u + 5.52391
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
20717020838201378085
10329580082896915583
u
27
+
118843568226093884873
10329580082896915583
u
26
+ ··· −
599585284268000058823
10329580082896915583
u +
187047322357317549099
10329580082896915583
14
(iv) u-Polynomials at the component
15
Crossings u-Polynomials at each crossing
c
1
u
28
− 6u
27
+ ··· − 5u + 1
c
2
u
28
+ 6u
26
+ ··· − 3u + 1
c
3
u
28
+ 2u
27
+ ··· + u + 1
c
4
u
28
+ 6u
27
+ ··· + 5u + 1
c
5
u
28
− 4u
27
+ ··· + 15u + 5
c
6
u
28
+ u
27
+ ··· + 28u + 28
c
7
u
28
+ 6u
26
+ ··· + 3u + 1
c
8
u
28
+ 17u
27
+ ··· + 6u + 1
c
9
u
28
+ 2u
27
+ ··· − 28u + 28
c
10
u
28
+ 4u
27
+ ··· + 3u + 1
c
11
u
28
− u
27
+ ··· − 28u + 28
c
12
u
28
+ 3u
27
+ ··· + 8u + 1
16
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
28
+ 10y
27
+ ··· + 27y + 1
c
2
, c
7
y
28
+ 12y
27
+ ··· + 15y + 1
c
3
y
28
+ 6y
27
+ ··· − 5y + 1
c
5
y
28
− 18y
27
+ ··· + 255y + 25
c
6
, c
11
y
28
− 25y
27
+ ··· − 13272y + 784
c
8
y
28
− 15y
27
+ ··· + 2y + 1
c
9
y
28
+ 2y
27
+ ··· − 7000y + 784
c
10
y
28
− 4y
27
+ ··· − 3y + 1
c
12
y
28
− 11y
27
+ ··· + 180y
2
+ 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.195450 + 1.016640I
a = −0.988655 − 0.103656I
b = −0.633208 − 0.530557I
6.94244 + 2.59962I 10.78801 + 2.45502I
u = 0.195450 − 1.016640I
a = −0.988655 + 0.103656I
b = −0.633208 + 0.530557I
6.94244 − 2.59962I 10.78801 − 2.45502I
u = −0.272084 + 0.912765I
a = −0.922113 + 0.808358I
b = −1.197330 − 0.283008I
7.42228 + 2.16128I 14.1910 − 6.6073I
u = −0.272084 − 0.912765I
a = −0.922113 − 0.808358I
b = −1.197330 + 0.283008I
7.42228 − 2.16128I 14.1910 + 6.6073I
u = 1.003010 + 0.456220I
a = −0.749770 − 0.294796I
b = −0.626372 + 0.815843I
−3.06393 − 0.63831I 2.58541 − 1.90651I
u = 1.003010 − 0.456220I
a = −0.749770 + 0.294796I
b = −0.626372 − 0.815843I
−3.06393 + 0.63831I 2.58541 + 1.90651I
u = −0.828748 + 0.782547I
a = 0.346150 + 0.945765I
b = −0.01787 + 2.00252I
−3.26291 + 4.77226I 4.29602 − 3.74649I
u = −0.828748 − 0.782547I
a = 0.346150 − 0.945765I
b = −0.01787 − 2.00252I
−3.26291 − 4.77226I 4.29602 + 3.74649I
u = 0.526156 + 0.620084I
a = 1.56323 + 0.05342I
b = 0.846136 + 0.322593I
5.48166 − 5.74807I −0.1857 + 15.7732I
u = 0.526156 − 0.620084I
a = 1.56323 − 0.05342I
b = 0.846136 − 0.322593I
5.48166 + 5.74807I −0.1857 − 15.7732I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.047610 + 0.605260I
a = 0.053121 − 0.268632I
b = 0.252238 − 0.887116I
−1.63945 − 3.87723I −1.59959 + 7.49893I
u = 1.047610 − 0.605260I
a = 0.053121 + 0.268632I
b = 0.252238 + 0.887116I
−1.63945 + 3.87723I −1.59959 − 7.49893I
u = −0.383656 + 0.566202I
a = 0.73253 − 2.19184I
b = 1.40131 + 0.23846I
6.13703 + 0.75645I −3.60377 + 7.62414I
u = −0.383656 − 0.566202I
a = 0.73253 + 2.19184I
b = 1.40131 − 0.23846I
6.13703 − 0.75645I −3.60377 − 7.62414I
u = 0.386244 + 1.310810I
a = 1.050850 + 0.244714I
b = 0.707859 + 0.035635I
1.08520 − 2.10072I 14.0775 − 6.4865I
u = 0.386244 − 1.310810I
a = 1.050850 − 0.244714I
b = 0.707859 − 0.035635I
1.08520 + 2.10072I 14.0775 + 6.4865I
u = −1.09520 + 0.92992I
a = −0.956782 − 0.137648I
b = −0.18150 − 1.62676I
−7.76232 + 3.90199I 15.7592 + 5.7297I
u = −1.09520 − 0.92992I
a = −0.956782 + 0.137648I
b = −0.18150 + 1.62676I
−7.76232 − 3.90199I 15.7592 − 5.7297I
u = 0.163944 + 0.506934I
a = 0.56996 − 1.48095I
b = −0.967645 + 0.372767I
−1.57751 + 1.02438I 1.56957 + 0.86124I
u = 0.163944 − 0.506934I
a = 0.56996 + 1.48095I
b = −0.967645 − 0.372767I
−1.57751 − 1.02438I 1.56957 − 0.86124I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.35297 + 1.42468I
a = −0.496185 − 0.273136I
b = −0.694607 + 0.009257I
5.06460 − 7.92766I 13.27575 + 4.34960I
u = 0.35297 − 1.42468I
a = −0.496185 + 0.273136I
b = −0.694607 − 0.009257I
5.06460 + 7.92766I 13.27575 − 4.34960I
u = 0.96431 + 1.10865I
a = 0.951698 − 0.597069I
b = 0.643637 − 1.122090I
0.48555 − 3.80339I 13.8920 + 11.0557I
u = 0.96431 − 1.10865I
a = 0.951698 + 0.597069I
b = 0.643637 + 1.122090I
0.48555 + 3.80339I 13.8920 − 11.0557I
u = 0.87973 + 1.24865I
a = −0.605082 + 0.439878I
b = −0.238958 + 1.129250I
−0.74446 − 6.38247I 7.05888 + 9.14358I
u = 0.87973 − 1.24865I
a = −0.605082 − 0.439878I
b = −0.238958 − 1.129250I
−0.74446 + 6.38247I 7.05888 − 9.14358I
u = 0.060253 + 0.342971I
a = 2.95104 + 3.62529I
b = 1.70630 + 0.00056I
0.23623 + 5.69463I 4.39569 − 4.52257I
u = 0.060253 − 0.342971I
a = 2.95104 − 3.62529I
b = 1.70630 − 0.00056I
0.23623 − 5.69463I 4.39569 + 4.52257I
21
III. I
u
3
= hb, a − u + 1, u
2
− u + 1i
(i) Arc colorings
a
2
=
1
0
a
4
=
0
u
a
1
=
1
−u + 1
a
5
=
−u
u − 1
a
10
=
u − 1
0
a
11
=
2u − 1
1
a
9
=
u − 1
0
a
6
=
−u − 1
u − 1
a
12
=
2u − 1
1
a
3
=
u − 1
u
a
8
=
−2
u − 1
a
7
=
−u − 1
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u + 2
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
c
10
, c
12
u
2
− u + 1
c
2
, c
4
, c
8
u
2
+ u + 1
c
3
(u − 1)
2
c
6
, c
9
, c
11
u
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
7
, c
8
c
10
, c
12
y
2
+ y + 1
c
3
(y −1)
2
c
6
, c
9
, c
11
y
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.500000 + 0.866025I
b = 0
− 4.05977I 6.00000 + 6.92820I
u = 0.500000 − 0.866025I
a = −0.500000 − 0.866025I
b = 0
4.05977I 6.00000 − 6.92820I
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)(u
28
− 6u
27
+ ··· − 5u + 1)(u
85
− 4u
84
+ ··· + 2u − 1)
c
2
(u
2
+ u + 1)(u
28
+ 6u
26
+ ··· − 3u + 1)(u
85
+ 30u
83
+ ··· + 26u − 1)
c
3
((u − 1)
2
)(u
28
+ 2u
27
+ ··· + u + 1)
· (u
85
+ u
84
+ ··· − 8586859u − 7135679)
c
4
(u
2
+ u + 1)(u
28
+ 6u
27
+ ··· + 5u + 1)(u
85
− 4u
84
+ ··· + 2u − 1)
c
5
(u
2
− u + 1)(u
28
− 4u
27
+ ··· + 15u + 5)
· (u
85
+ 10u
84
+ ··· + 4292211u − 291526)
c
6
u
2
(u
28
+ u
27
+ ··· + 28u + 28)(u
85
+ 2u
84
+ ··· − 564u − 172)
c
7
(u
2
− u + 1)(u
28
+ 6u
26
+ ··· + 3u + 1)(u
85
+ 30u
83
+ ··· + 26u − 1)
c
8
(u
2
+ u + 1)(u
28
+ 17u
27
+ ··· + 6u + 1)(u
85
+ u
84
+ ··· + 15u + 1)
c
9
u
2
(u
28
+ 2u
27
+ ··· − 28u + 28)
· (u
85
− 3u
84
+ ··· + 5809196u − 707552)
c
10
(u
2
− u + 1)(u
28
+ 4u
27
+ ··· + 3u + 1)
· (u
85
− 12u
84
+ ··· + 63060030u − 7539289)
c
11
u
2
(u
28
− u
27
+ ··· − 28u + 28)(u
85
+ 2u
84
+ ··· − 564u − 172)
c
12
(u
2
− u + 1)(u
28
+ 3u
27
+ ··· + 8u + 1)
· (u
85
− 3u
84
+ ··· − 35799u − 3454)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
2
+ y + 1)(y
28
+ 10y
27
+ ··· + 27y + 1)(y
85
+ 18y
84
+ ··· − 228y −1)
c
2
, c
7
(y
2
+ y + 1)(y
28
+ 12y
27
+ ··· + 15y + 1)(y
85
+ 60y
84
+ ··· − 140y −1)
c
3
((y −1)
2
)(y
28
+ 6y
27
+ ··· − 5y + 1)
· (y
85
+ 75y
84
+ ··· − 496895527067841y −50917914791041)
c
5
(y
2
+ y + 1)(y
28
− 18y
27
+ ··· + 255y + 25)
· (y
85
− 38y
84
+ ··· + 7819625711645y −84987408676)
c
6
, c
11
y
2
(y
28
− 25y
27
+ ··· − 13272y + 784)
· (y
85
− 50y
84
+ ··· + 783184y −29584)
c
8
(y
2
+ y + 1)(y
28
− 15y
27
+ ··· + 2y + 1)(y
85
− 15y
84
+ ··· − 11y −1)
c
9
y
2
(y
28
+ 2y
27
+ ··· − 7000y + 784)
· (y
85
+ 77y
84
+ ··· − 9930483397744y −500629832704)
c
10
(y
2
+ y + 1)(y
28
− 4y
27
+ ··· − 3y + 1)
· (y
85
− 44y
84
+ ··· + 214383869545346y −56840878625521)
c
12
(y
2
+ y + 1)(y
28
− 11y
27
+ ··· + 180y
2
+ 1)
· (y
85
+ 17y
84
+ ··· − 589394319y −11930116)
27
