12a
0555
(K12a
0555
)
A knot diagram
1
Linearized knot diagam
3 7 9 8 11 2 5 1 12 6 10 4
Solving Sequence
2,6
7 3
1,11
5 8 4 10 12 9
c
6
c
2
c
1
c
5
c
7
c
4
c
10
c
11
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.57592 × 10
318
u
123
− 2.08157 × 10
318
u
122
+ ··· + 2.25880 × 10
319
b − 3.26705 × 10
319
,
3.30221 × 10
318
u
123
− 4.03875 × 10
318
u
122
+ ··· + 2.25880 × 10
319
a − 1.14717 × 10
320
, u
124
− u
123
+ ··· − 13u + 1i
I
u
2
= h7u
27
− 42u
25
+ ··· + 16u
3
+ b, 24u
27
− 13u
26
+ ··· + a + 27, u
28
− 7u
26
+ ··· + u + 1i
* 2 irreducible components of dim
C
= 0, with total 152 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
= h1.58 × 10
318
u
123
− 2.08 × 10
318
u
122
+ · · · + 2.26 × 10
319
b − 3.27 ×
10
319
, 3.30 × 10
318
u
123
− 4.04 × 10
318
u
122
+ · · · + 2.26 × 10
319
a − 1.15 ×
10
320
, u
124
− u
123
+ · · · − 13u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
11
=
−0.146193u
123
+ 0.178800u
122
+ ··· − 13.8891u + 5.07865
−0.0697681u
123
+ 0.0921538u
122
+ ··· − 10.2467u + 1.44636
a
5
=
−0.356991u
123
+ 0.445191u
122
+ ··· − 55.4783u + 6.75271
−0.119813u
123
+ 0.134953u
122
+ ··· − 19.0220u + 1.00634
a
8
=
−0.547390u
123
+ 0.484893u
122
+ ··· − 80.7903u − 2.39707
−0.0369578u
123
+ 0.0165463u
122
+ ··· − 1.32633u − 2.40645
a
4
=
0.547878u
123
− 0.540683u
122
+ ··· + 90.4297u − 9.53174
0.286119u
123
− 0.265471u
122
+ ··· + 37.8431u − 1.66144
a
10
=
−0.0764246u
123
+ 0.0866464u
122
+ ··· − 3.64233u + 3.63229
−0.0697681u
123
+ 0.0921538u
122
+ ··· − 10.2467u + 1.44636
a
12
=
−0.473969u
123
+ 0.562191u
122
+ ··· − 75.5693u + 7.83665
−0.174923u
123
+ 0.183416u
122
+ ··· − 28.4694u + 1.00218
a
9
=
−0.547891u
123
+ 0.484216u
122
+ ··· − 80.7327u − 2.40114
−0.0395895u
123
+ 0.0231613u
122
+ ··· − 1.15575u − 2.46193
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.236486u
123
+ 0.153343u
122
+ ··· + 23.5886u − 7.90116
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
124
+ 45u
123
+ ··· − 65u + 1
c
2
, c
6
u
124
− u
123
+ ··· − 13u + 1
c
3
u
124
− 18u
122
+ ··· + 83060u + 9129
c
4
, c
7
u
124
− 2u
123
+ ··· − 570346u + 135173
c
5
, c
10
u
124
+ u
123
+ ··· + u + 1
c
8
u
124
+ 11u
123
+ ··· + 19900u + 5329
c
9
, c
11
u
124
+ 37u
123
+ ··· + 31u + 1
c
12
u
124
+ 9u
123
+ ··· + 54702u + 6689
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
124
+ 83y
123
+ ··· + 22757y + 1
c
2
, c
6
y
124
− 45y
123
+ ··· + 65y + 1
c
3
y
124
− 36y
123
+ ··· − 3698902198y + 83338641
c
4
, c
7
y
124
+ 108y
123
+ ··· + 105445018624y + 18271739929
c
5
, c
10
y
124
+ 37y
123
+ ··· + 31y + 1
c
8
y
124
− 35y
123
+ ··· − 1554065648y + 28398241
c
9
, c
11
y
124
+ 113y
123
+ ··· − 61y + 1
c
12
y
124
− 39y
123
+ ··· − 869394118y + 44742721
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.653672 + 0.754028I
a = −0.221936 + 0.365917I
b = 0.863933 + 1.051610I
9.50348 + 3.93899I 0
u = 0.653672 − 0.754028I
a = −0.221936 − 0.365917I
b = 0.863933 − 1.051610I
9.50348 − 3.93899I 0
u = 0.593554 + 0.784926I
a = 0.300113 + 1.131170I
b = 0.421338 + 1.101320I
3.00860 + 6.79683I 0
u = 0.593554 − 0.784926I
a = 0.300113 − 1.131170I
b = 0.421338 − 1.101320I
3.00860 − 6.79683I 0
u = 0.698473 + 0.746424I
a = −0.636687 − 0.050603I
b = 0.847556 − 0.866163I
9.60030 − 2.95359I 0
u = 0.698473 − 0.746424I
a = −0.636687 + 0.050603I
b = 0.847556 + 0.866163I
9.60030 + 2.95359I 0
u = 1.021970 + 0.040581I
a = 0.41698 + 1.93112I
b = −0.700899 + 0.983946I
−0.40305 − 6.21537I 0
u = 1.021970 − 0.040581I
a = 0.41698 − 1.93112I
b = −0.700899 − 0.983946I
−0.40305 + 6.21537I 0
u = −0.666582 + 0.709797I
a = −0.959766 − 0.552903I
b = 0.824752 − 0.937359I
9.38055 − 3.27018I 0
u = −0.666582 − 0.709797I
a = −0.959766 + 0.552903I
b = 0.824752 + 0.937359I
9.38055 + 3.27018I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.674920 + 0.781390I
a = −0.324639 − 0.487747I
b = 0.830949 + 0.788178I
5.51421 − 0.24477I 0
u = 0.674920 − 0.781390I
a = −0.324639 + 0.487747I
b = 0.830949 − 0.788178I
5.51421 + 0.24477I 0
u = −0.848576 + 0.605017I
a = −1.48509 + 2.87938I
b = 0.220178 + 0.887084I
2.23676 + 4.86931I 0
u = −0.848576 − 0.605017I
a = −1.48509 − 2.87938I
b = 0.220178 − 0.887084I
2.23676 − 4.86931I 0
u = −0.956092 + 0.041318I
a = −0.421817 + 0.553059I
b = −0.756039 + 0.700147I
0.446725 + 0.678269I 0
u = −0.956092 − 0.041318I
a = −0.421817 − 0.553059I
b = −0.756039 − 0.700147I
0.446725 − 0.678269I 0
u = −0.719659 + 0.758218I
a = −0.708310 + 0.499013I
b = 0.787875 − 0.928615I
5.06471 − 6.00007I 0
u = −0.719659 − 0.758218I
a = −0.708310 − 0.499013I
b = 0.787875 + 0.928615I
5.06471 + 6.00007I 0
u = 0.763125 + 0.714898I
a = −1.82587 − 0.44160I
b = 0.808628 − 0.851275I
5.30381 + 0.01095I 0
u = 0.763125 − 0.714898I
a = −1.82587 + 0.44160I
b = 0.808628 + 0.851275I
5.30381 − 0.01095I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.043170 + 0.125351I
a = −0.02299 + 2.54445I
b = 0.115043 + 0.998344I
−5.35836 + 0.99192I 0
u = 1.043170 − 0.125351I
a = −0.02299 − 2.54445I
b = 0.115043 − 0.998344I
−5.35836 − 0.99192I 0
u = 1.055390 + 0.065223I
a = −0.77306 − 2.07144I
b = −0.793365 − 0.814158I
4.50475 + 2.60325I 0
u = 1.055390 − 0.065223I
a = −0.77306 + 2.07144I
b = −0.793365 + 0.814158I
4.50475 − 2.60325I 0
u = 0.833543 + 0.655869I
a = −1.09202 − 1.99986I
b = 0.171148 − 1.273080I
1.10782 − 1.42271I 0
u = 0.833543 − 0.655869I
a = −1.09202 + 1.99986I
b = 0.171148 + 1.273080I
1.10782 + 1.42271I 0
u = −0.733187 + 0.769749I
a = −0.579198 + 0.681931I
b = 0.997080 + 0.784039I
10.35130 + 2.83481I 0
u = −0.733187 − 0.769749I
a = −0.579198 − 0.681931I
b = 0.997080 − 0.784039I
10.35130 − 2.83481I 0
u = −0.887233 + 0.592895I
a = 0.55746 + 1.56023I
b = −0.368249 + 0.900767I
2.12043 − 0.13510I 0
u = −0.887233 − 0.592895I
a = 0.55746 − 1.56023I
b = −0.368249 − 0.900767I
2.12043 + 0.13510I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.760149 + 0.757066I
a = −1.56255 + 0.99397I
b = 0.774107 + 0.978985I
4.92525 + 6.25486I 0
u = −0.760149 − 0.757066I
a = −1.56255 − 0.99397I
b = 0.774107 − 0.978985I
4.92525 − 6.25486I 0
u = −1.077120 + 0.018870I
a = −0.95759 + 1.82621I
b = −0.760737 + 0.953348I
4.07402 − 3.25740I 0
u = −1.077120 − 0.018870I
a = −0.95759 − 1.82621I
b = −0.760737 − 0.953348I
4.07402 + 3.25740I 0
u = −0.890283 + 0.241808I
a = 0.366545 − 0.045722I
b = 0.511763 − 0.270563I
−1.61166 + 0.75107I 0
u = −0.890283 − 0.241808I
a = 0.366545 + 0.045722I
b = 0.511763 + 0.270563I
−1.61166 − 0.75107I 0
u = 0.975577 + 0.473549I
a = −0.535924 − 0.486426I
b = 0.446242 + 0.144626I
−0.18171 − 4.53875I 0
u = 0.975577 − 0.473549I
a = −0.535924 + 0.486426I
b = 0.446242 − 0.144626I
−0.18171 + 4.53875I 0
u = 1.037460 + 0.327001I
a = −0.79407 − 2.29881I
b = 0.488824 − 0.944752I
−3.26816 − 4.56010I 0
u = 1.037460 − 0.327001I
a = −0.79407 + 2.29881I
b = 0.488824 + 0.944752I
−3.26816 + 4.56010I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.753662 + 0.784384I
a = −0.044345 + 0.661694I
b = 0.899046 + 0.156547I
6.18301 − 2.23465I 0
u = −0.753662 − 0.784384I
a = −0.044345 − 0.661694I
b = 0.899046 − 0.156547I
6.18301 + 2.23465I 0
u = −0.883843 + 0.168841I
a = 1.48383 − 1.80805I
b = −0.423273 − 1.028020I
−1.84989 + 0.37525I 0
u = −0.883843 − 0.168841I
a = 1.48383 + 1.80805I
b = −0.423273 + 1.028020I
−1.84989 − 0.37525I 0
u = 0.893238 + 0.656245I
a = −0.58558 − 1.59697I
b = −0.264939 − 1.275620I
0.91832 − 3.67720I 0
u = 0.893238 − 0.656245I
a = −0.58558 + 1.59697I
b = −0.264939 + 1.275620I
0.91832 + 3.67720I 0
u = 0.802159 + 0.352006I
a = 3.10936 + 1.84472I
b = −0.037171 + 0.588188I
0.74296 + 1.30500I 0
u = 0.802159 − 0.352006I
a = 3.10936 − 1.84472I
b = −0.037171 − 0.588188I
0.74296 − 1.30500I 0
u = 0.846228 + 0.141439I
a = −0.035362 − 0.686305I
b = −0.584268 + 0.358023I
0.23076 − 3.63401I 0
u = 0.846228 − 0.141439I
a = −0.035362 + 0.686305I
b = −0.584268 − 0.358023I
0.23076 + 3.63401I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.050360 + 0.471664I
a = 0.64484 − 1.30668I
b = 0.331456 − 0.934867I
−2.51161 + 2.06880I 0
u = −1.050360 − 0.471664I
a = 0.64484 + 1.30668I
b = 0.331456 + 0.934867I
−2.51161 − 2.06880I 0
u = −0.391791 + 0.739877I
a = 0.58553 − 1.63119I
b = 0.383432 − 0.761058I
3.22760 + 0.69995I 0
u = −0.391791 − 0.739877I
a = 0.58553 + 1.63119I
b = 0.383432 + 0.761058I
3.22760 − 0.69995I 0
u = 0.871004 + 0.777912I
a = 0.206283 − 0.510731I
b = 0.116298 + 0.296311I
4.12281 − 2.95423I 0
u = 0.871004 − 0.777912I
a = 0.206283 + 0.510731I
b = 0.116298 − 0.296311I
4.12281 + 2.95423I 0
u = 0.950379 + 0.693123I
a = 0.098369 + 0.687118I
b = −0.852088 − 0.816566I
4.72897 − 5.41685I 0
u = 0.950379 − 0.693123I
a = 0.098369 − 0.687118I
b = −0.852088 + 0.816566I
4.72897 + 5.41685I 0
u = 0.912205 + 0.761221I
a = 0.216369 − 0.079053I
b = −0.370394 + 0.185676I
3.99901 − 2.89538I 0
u = 0.912205 − 0.761221I
a = 0.216369 + 0.079053I
b = −0.370394 − 0.185676I
3.99901 + 2.89538I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.043050 + 0.574371I
a = −1.44284 + 1.64925I
b = 0.293245 + 0.952720I
−2.59632 + 7.39711I 0
u = −1.043050 − 0.574371I
a = −1.44284 − 1.64925I
b = 0.293245 − 0.952720I
−2.59632 − 7.39711I 0
u = −0.464593 + 0.660693I
a = 0.653230 + 0.495283I
b = −0.227972 + 0.873123I
−0.91891 − 2.58208I 0
u = −0.464593 − 0.660693I
a = 0.653230 − 0.495283I
b = −0.227972 − 0.873123I
−0.91891 + 2.58208I 0
u = 0.604766 + 1.033010I
a = 0.521083 − 0.515330I
b = −0.822070 − 1.015320I
11.2961 + 12.0792I 0
u = 0.604766 − 1.033010I
a = 0.521083 + 0.515330I
b = −0.822070 + 1.015320I
11.2961 − 12.0792I 0
u = −0.951867 + 0.730677I
a = 0.0858137 − 0.0438546I
b = −0.801256 + 0.912454I
4.34524 − 0.60821I 0
u = −0.951867 − 0.730677I
a = 0.0858137 + 0.0438546I
b = −0.801256 − 0.912454I
4.34524 + 0.60821I 0
u = −0.645211 + 1.011900I
a = 0.608093 − 0.431790I
b = −0.922887 − 0.793624I
12.00020 − 5.64780I 0
u = −0.645211 − 1.011900I
a = 0.608093 + 0.431790I
b = −0.922887 + 0.793624I
12.00020 + 5.64780I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.006860 + 0.668567I
a = 1.63118 − 2.10655I
b = −0.785826 − 0.946557I
8.34978 + 8.59728I 0
u = −1.006860 − 0.668567I
a = 1.63118 + 2.10655I
b = −0.785826 + 0.946557I
8.34978 − 8.59728I 0
u = −0.986126 + 0.704274I
a = 1.73583 − 1.14409I
b = −0.798178 − 0.969579I
4.25182 + 11.56620I 0
u = −0.986126 − 0.704274I
a = 1.73583 + 1.14409I
b = −0.798178 + 0.969579I
4.25182 − 11.56620I 0
u = −0.967998 + 0.729531I
a = −0.187675 − 0.511154I
b = −0.941554 + 0.046265I
5.52884 + 7.95039I 0
u = −0.967998 − 0.729531I
a = −0.187675 + 0.511154I
b = −0.941554 − 0.046265I
5.52884 − 7.95039I 0
u = −1.213820 + 0.047286I
a = −0.50274 − 2.16777I
b = −0.198147 − 0.950056I
−3.15186 + 5.37506I 0
u = −1.213820 − 0.047286I
a = −0.50274 + 2.16777I
b = −0.198147 + 0.950056I
−3.15186 − 5.37506I 0
u = 0.995430 + 0.701514I
a = −0.804785 + 0.560936I
b = −0.821313 − 0.831824I
8.70655 − 2.57771I 0
u = 0.995430 − 0.701514I
a = −0.804785 − 0.560936I
b = −0.821313 + 0.831824I
8.70655 + 2.57771I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.980256 + 0.722792I
a = −0.636460 − 0.364214I
b = −0.995123 + 0.706512I
9.60423 + 2.82442I 0
u = −0.980256 − 0.722792I
a = −0.636460 + 0.364214I
b = −0.995123 − 0.706512I
9.60423 − 2.82442I 0
u = 1.020710 + 0.687002I
a = 1.19704 + 1.91362I
b = −0.819185 + 1.090530I
8.39915 − 9.44343I 0
u = 1.020710 − 0.687002I
a = 1.19704 − 1.91362I
b = −0.819185 − 1.090530I
8.39915 + 9.44343I 0
u = 0.787074 + 0.955449I
a = −0.002809 − 0.579455I
b = 0.229015 − 0.498669I
4.14100 − 3.37002I 0
u = 0.787074 − 0.955449I
a = −0.002809 + 0.579455I
b = 0.229015 + 0.498669I
4.14100 + 3.37002I 0
u = 1.158490 + 0.450593I
a = −0.96436 − 1.48450I
b = 0.085295 − 0.506323I
−0.69205 − 4.33660I 0
u = 1.158490 − 0.450593I
a = −0.96436 + 1.48450I
b = 0.085295 + 0.506323I
−0.69205 + 4.33660I 0
u = −0.685173 + 0.317043I
a = 1.79057 − 1.21817I
b = −0.048943 − 0.978647I
−0.91541 + 1.40595I 0
u = −0.685173 − 0.317043I
a = 1.79057 + 1.21817I
b = −0.048943 + 0.978647I
−0.91541 − 1.40595I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.019550 + 0.718152I
a = 1.18723 + 1.02002I
b = −0.814680 + 0.871376I
4.47352 − 5.43867I 0
u = 1.019550 − 0.718152I
a = 1.18723 − 1.02002I
b = −0.814680 − 0.871376I
4.47352 + 5.43867I 0
u = 1.046040 + 0.690874I
a = 0.97455 + 2.00913I
b = −0.354533 + 1.167360I
1.67799 − 12.38850I 0
u = 1.046040 − 0.690874I
a = 0.97455 − 2.00913I
b = −0.354533 − 1.167360I
1.67799 + 12.38850I 0
u = −1.110950 + 0.708410I
a = 0.58130 − 2.03304I
b = −0.216885 − 0.935124I
1.24634 + 4.93011I 0
u = −1.110950 − 0.708410I
a = 0.58130 + 2.03304I
b = −0.216885 + 0.935124I
1.24634 − 4.93011I 0
u = −0.429285 + 1.257950I
a = 0.534786 + 0.523258I
b = −0.815202 + 0.909757I
9.78355 − 1.54381I 0
u = −0.429285 − 1.257950I
a = 0.534786 − 0.523258I
b = −0.815202 − 0.909757I
9.78355 + 1.54381I 0
u = 0.396216 + 0.539236I
a = 0.822039 − 0.202347I
b = −0.435370 − 0.074616I
1.50437 + 0.57239I 5.94469 − 0.24077I
u = 0.396216 − 0.539236I
a = 0.822039 + 0.202347I
b = −0.435370 + 0.074616I
1.50437 − 0.57239I 5.94469 + 0.24077I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.109900 + 0.783654I
a = 0.487496 + 0.278455I
b = 0.942675 − 0.755348I
10.5317 + 12.1645I 0
u = −1.109900 − 0.783654I
a = 0.487496 − 0.278455I
b = 0.942675 + 0.755348I
10.5317 − 12.1645I 0
u = 0.503653 + 1.264530I
a = 0.613804 + 0.532606I
b = −0.822811 + 0.883056I
9.86573 − 4.57266I 0
u = 0.503653 − 1.264530I
a = 0.613804 − 0.532606I
b = −0.822811 − 0.883056I
9.86573 + 4.57266I 0
u = 1.135840 + 0.771590I
a = −1.21683 − 1.72488I
b = 0.810216 − 1.043110I
9.6187 − 18.6094I 0
u = 1.135840 − 0.771590I
a = −1.21683 + 1.72488I
b = 0.810216 + 1.043110I
9.6187 + 18.6094I 0
u = −0.491450 + 0.334915I
a = 1.43190 − 0.29166I
b = −0.036948 − 0.833886I
−0.84720 + 1.41340I −4.24798 − 5.20479I
u = −0.491450 − 0.334915I
a = 1.43190 + 0.29166I
b = −0.036948 + 0.833886I
−0.84720 − 1.41340I −4.24798 + 5.20479I
u = 1.41670 + 0.24907I
a = 0.391736 + 0.998608I
b = 0.809282 + 0.821395I
3.17724 − 3.55761I 0
u = 1.41670 − 0.24907I
a = 0.391736 − 0.998608I
b = 0.809282 − 0.821395I
3.17724 + 3.55761I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.43488 + 0.19128I
a = −0.07548 + 1.62220I
b = 0.775054 + 0.949589I
2.78125 + 9.50796I 0
u = −1.43488 − 0.19128I
a = −0.07548 − 1.62220I
b = 0.775054 − 0.949589I
2.78125 − 9.50796I 0
u = −0.086265 + 0.498965I
a = 0.772699 − 0.440926I
b = −0.409913 − 0.799347I
−0.25338 + 1.63604I −2.01455 − 4.40810I
u = −0.086265 − 0.498965I
a = 0.772699 + 0.440926I
b = −0.409913 + 0.799347I
−0.25338 − 1.63604I −2.01455 + 4.40810I
u = 1.21190 + 0.93009I
a = 0.158056 + 0.037351I
b = 0.815383 + 0.814632I
7.74209 − 3.09197I 0
u = 1.21190 − 0.93009I
a = 0.158056 − 0.037351I
b = 0.815383 − 0.814632I
7.74209 + 3.09197I 0
u = −1.25287 + 0.88594I
a = −1.02618 + 1.42812I
b = 0.775781 + 0.954947I
7.30859 + 9.06132I 0
u = −1.25287 − 0.88594I
a = −1.02618 − 1.42812I
b = 0.775781 − 0.954947I
7.30859 − 9.06132I 0
u = −0.238548 + 0.248330I
a = 3.41361 − 2.58485I
b = 0.618216 − 0.722841I
3.23053 + 0.91293I 5.24339 − 2.95455I
u = −0.238548 − 0.248330I
a = 3.41361 + 2.58485I
b = 0.618216 + 0.722841I
3.23053 − 0.91293I 5.24339 + 2.95455I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.248068 + 0.092479I
a = 5.11601 + 1.37161I
b = 0.629717 + 0.947239I
2.54981 + 5.86442I 3.70628 − 9.11728I
u = 0.248068 − 0.092479I
a = 5.11601 − 1.37161I
b = 0.629717 − 0.947239I
2.54981 − 5.86442I 3.70628 + 9.11728I
u = 0.0471368 + 0.0733553I
a = 4.23325 − 1.18357I
b = 0.876687 − 0.917815I
8.01964 − 3.23859I −7.45734 + 4.03366I
u = 0.0471368 − 0.0733553I
a = 4.23325 + 1.18357I
b = 0.876687 + 0.917815I
8.01964 + 3.23859I −7.45734 − 4.03366I
17
II. I
u
2
=
h7u
27
−42u
25
+· · ·+16u
3
+b, 24u
27
−13u
26
+· · ·+a+27, u
28
−7u
26
+· · ·+u+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
11
=
−24u
27
+ 13u
26
+ ··· − 17u − 27
−7u
27
+ 42u
25
+ ··· − 17u
4
− 16u
3
a
5
=
7u
27
− 42u
25
+ ··· − 7u
2
− 6u
6u
27
− 36u
25
+ ··· − u − 1
a
8
=
u
24
− 5u
22
+ ··· − u
3
+ 2
u
27
− 7u
25
+ ··· − 30u
2
+ 6
a
4
=
5u
27
− 29u
25
+ ··· + 6u − 2
u
26
+ 4u
25
+ ··· + 6u − 6
a
10
=
−17u
27
+ 13u
26
+ ··· − 17u − 27
−7u
27
+ 42u
25
+ ··· − 17u
4
− 16u
3
a
12
=
−17u
27
+ u
26
+ ··· + 11u + 1
−7u
27
+ 42u
25
+ ··· + 5u + 5
a
9
=
u
22
− 5u
20
+ ··· − u + 1
u
27
− 7u
25
+ ··· − 31u
2
+ 6
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −17u
27
+ 16u
26
+ 94u
25
− 121u
24
− 302u
23
+ 485u
22
+ 615u
21
− 1288u
20
− 837u
19
+
2486u
18
+ 637u
17
− 3610u
16
+ 27u
15
+ 4051u
14
− 857u
13
− 3549u
12
+ 1316u
11
+
2459u
10
− 1253u
9
− 1354u
8
+ 828u
7
+ 623u
6
− 454u
5
− 212u
4
+ 176u
3
+ 39u
2
− 40u − 2
18
(iv) u-Polynomials at the component
19
Crossings u-Polynomials at each crossing
c
1
u
28
− 14u
27
+ ··· − 15u + 1
c
2
u
28
− 7u
26
+ ··· − u + 1
c
3
u
28
− u
27
+ ··· + 2u + 1
c
4
u
28
− u
27
+ ··· + 10u
2
+ 1
c
5
u
28
+ 6u
26
+ ··· + u + 1
c
6
u
28
− 7u
26
+ ··· + u + 1
c
7
u
28
+ u
27
+ ··· + 10u
2
+ 1
c
8
u
28
− 4u
27
+ ··· + 4u + 1
c
9
u
28
− 12u
27
+ ··· − 19u + 1
c
10
u
28
+ 6u
26
+ ··· − u + 1
c
11
u
28
+ 12u
27
+ ··· + 19u + 1
c
12
u
28
− 4u
26
+ ··· + 6u + 1
20
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
+ 14y
27
+ ··· + 5y + 1
c
2
, c
6
y
28
− 14y
27
+ ··· − 15y + 1
c
3
y
28
− 9y
27
+ ··· + 2y + 1
c
4
, c
7
y
28
+ 27y
27
+ ··· + 20y + 1
c
5
, c
10
y
28
+ 12y
27
+ ··· + 19y + 1
c
8
y
28
− 12y
27
+ ··· − 4y + 1
c
9
, c
11
y
28
+ 20y
27
+ ··· − 13y + 1
c
12
y
28
− 8y
27
+ ··· − 2y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.853384 + 0.664222I
a = −0.74588 + 1.96237I
b = −0.055540 + 1.152000I
1.13519 + 2.58168I 0.88409 − 2.94336I
u = −0.853384 − 0.664222I
a = −0.74588 − 1.96237I
b = −0.055540 − 1.152000I
1.13519 − 2.58168I 0.88409 + 2.94336I
u = 0.537923 + 0.717505I
a = −0.551794 − 0.411796I
b = 0.869642 − 0.869300I
8.72159 − 3.57143I 3.18095 + 6.94400I
u = 0.537923 − 0.717505I
a = −0.551794 + 0.411796I
b = 0.869642 + 0.869300I
8.72159 + 3.57143I 3.18095 − 6.94400I
u = 1.031470 + 0.394259I
a = 0.884019 + 1.015720I
b = 0.253524 + 0.965914I
−1.88762 − 2.73582I −2.46197 + 5.39447I
u = 1.031470 − 0.394259I
a = 0.884019 − 1.015720I
b = 0.253524 − 0.965914I
−1.88762 + 2.73582I −2.46197 − 5.39447I
u = 1.090380 + 0.316011I
a = −0.462318 − 1.181840I
b = 0.645164 − 0.927138I
0.60203 − 7.50140I −0.88511 + 8.77591I
u = 1.090380 − 0.316011I
a = −0.462318 + 1.181840I
b = 0.645164 + 0.927138I
0.60203 + 7.50140I −0.88511 − 8.77591I
u = −1.120860 + 0.329178I
a = −0.321036 − 1.144460I
b = 0.655538 − 0.798001I
1.01471 + 2.43520I −1.10146 − 2.81294I
u = −1.120860 − 0.329178I
a = −0.321036 + 1.144460I
b = 0.655538 + 0.798001I
1.01471 − 2.43520I −1.10146 + 2.81294I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.748185 + 0.343846I
a = 2.12661 + 1.39161I
b = −0.238931 + 1.062580I
−0.803404 − 0.370994I −0.048681 − 1.061898I
u = 0.748185 − 0.343846I
a = 2.12661 − 1.39161I
b = −0.238931 − 1.062580I
−0.803404 + 0.370994I −0.048681 + 1.061898I
u = 0.776045 + 0.214980I
a = −1.84062 − 2.07691I
b = −0.643350 − 0.967561I
1.91593 + 5.26603I −3.35797 − 3.30432I
u = 0.776045 − 0.214980I
a = −1.84062 + 2.07691I
b = −0.643350 + 0.967561I
1.91593 − 5.26603I −3.35797 + 3.30432I
u = 0.832341 + 0.859052I
a = −0.0133238 + 0.0602746I
b = −0.069032 + 0.532020I
3.72092 − 3.19291I −9.41688 + 4.51552I
u = 0.832341 − 0.859052I
a = −0.0133238 − 0.0602746I
b = −0.069032 − 0.532020I
3.72092 + 3.19291I −9.41688 − 4.51552I
u = −1.120250 + 0.425286I
a = −0.62017 + 2.45055I
b = 0.269140 + 0.713663I
−0.92549 + 5.05069I −4.03247 − 11.08870I
u = −1.120250 − 0.425286I
a = −0.62017 − 2.45055I
b = 0.269140 − 0.713663I
−0.92549 − 5.05069I −4.03247 + 11.08870I
u = −0.507051 + 0.619888I
a = −0.636091 − 0.478461I
b = 0.854058 − 0.944793I
8.49765 − 2.80858I 2.42221 − 3.15710I
u = −0.507051 − 0.619888I
a = −0.636091 + 0.478461I
b = 0.854058 + 0.944793I
8.49765 + 2.80858I 2.42221 + 3.15710I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.736353 + 0.196912I
a = −0.84434 − 3.01531I
b = −0.656573 − 0.740205I
2.63471 − 0.19022I −0.59998 − 2.55486I
u = −0.736353 − 0.196912I
a = −0.84434 + 3.01531I
b = −0.656573 + 0.740205I
2.63471 + 0.19022I −0.59998 + 2.55486I
u = −0.635766 + 0.271311I
a = 2.65852 + 0.60310I
b = −0.289866 + 0.585639I
1.04277 − 1.99325I 1.45235 + 7.13924I
u = −0.635766 − 0.271311I
a = 2.65852 − 0.60310I
b = −0.289866 − 0.585639I
1.04277 + 1.99325I 1.45235 − 7.13924I
u = 1.047480 + 0.810442I
a = −0.367219 + 0.236642I
b = −0.817347 − 0.793291I
7.18286 − 2.42778I 1.33194 − 0.69515I
u = 1.047480 − 0.810442I
a = −0.367219 − 0.236642I
b = −0.817347 + 0.793291I
7.18286 + 2.42778I 1.33194 + 0.69515I
u = −1.090150 + 0.754545I
a = 1.23365 − 1.68460I
b = −0.776426 − 0.974996I
6.62657 + 8.40990I 0.13298 − 4.95467I
u = −1.090150 − 0.754545I
a = 1.23365 + 1.68460I
b = −0.776426 + 0.974996I
6.62657 − 8.40990I 0.13298 + 4.95467I
25
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
28
− 14u
27
+ ··· − 15u + 1)(u
124
+ 45u
123
+ ··· − 65u + 1)
c
2
(u
28
− 7u
26
+ ··· − u + 1)(u
124
− u
123
+ ··· − 13u + 1)
c
3
(u
28
− u
27
+ ··· + 2u + 1)(u
124
− 18u
122
+ ··· + 83060u + 9129)
c
4
(u
28
− u
27
+ ··· + 10u
2
+ 1)(u
124
− 2u
123
+ ··· − 570346u + 135173)
c
5
(u
28
+ 6u
26
+ ··· + u + 1)(u
124
+ u
123
+ ··· + u + 1)
c
6
(u
28
− 7u
26
+ ··· + u + 1)(u
124
− u
123
+ ··· − 13u + 1)
c
7
(u
28
+ u
27
+ ··· + 10u
2
+ 1)(u
124
− 2u
123
+ ··· − 570346u + 135173)
c
8
(u
28
− 4u
27
+ ··· + 4u + 1)(u
124
+ 11u
123
+ ··· + 19900u + 5329)
c
9
(u
28
− 12u
27
+ ··· − 19u + 1)(u
124
+ 37u
123
+ ··· + 31u + 1)
c
10
(u
28
+ 6u
26
+ ··· − u + 1)(u
124
+ u
123
+ ··· + u + 1)
c
11
(u
28
+ 12u
27
+ ··· + 19u + 1)(u
124
+ 37u
123
+ ··· + 31u + 1)
c
12
(u
28
− 4u
26
+ ··· + 6u + 1)(u
124
+ 9u
123
+ ··· + 54702u + 6689)
26
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
28
+ 14y
27
+ ··· + 5y + 1)(y
124
+ 83y
123
+ ··· + 22757y + 1)
c
2
, c
6
(y
28
− 14y
27
+ ··· − 15y + 1)(y
124
− 45y
123
+ ··· + 65y + 1)
c
3
(y
28
− 9y
27
+ ··· + 2y + 1)
· (y
124
− 36y
123
+ ··· − 3698902198y + 83338641)
c
4
, c
7
(y
28
+ 27y
27
+ ··· + 20y + 1)
· (y
124
+ 108y
123
+ ··· + 105445018624y + 18271739929)
c
5
, c
10
(y
28
+ 12y
27
+ ··· + 19y + 1)(y
124
+ 37y
123
+ ··· + 31y + 1)
c
8
(y
28
− 12y
27
+ ··· − 4y + 1)
· (y
124
− 35y
123
+ ··· − 1554065648y + 28398241)
c
9
, c
11
(y
28
+ 20y
27
+ ··· − 13y + 1)(y
124
+ 113y
123
+ ··· − 61y + 1)
c
12
(y
28
− 8y
27
+ ··· − 2y + 1)
· (y
124
− 39y
123
+ ··· − 869394118y + 44742721)
27
