12a
0266
(K12a
0266
)
A knot diagram
1
Linearized knot diagam
3 6 8 7 2 10 11 12 1 5 4 9
Solving Sequence
2,5
6
3,10
7 11 8 1 4 9 12
c
5
c
2
c
6
c
10
c
7
c
1
c
4
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.65100 × 10
376
u
138
− 1.59780 × 10
377
u
137
+ ··· + 1.07658 × 10
378
b − 5.53322 × 10
378
,
1.04283 × 10
379
u
138
+ 2.43820 × 10
379
u
137
+ ··· + 5.92116 × 10
379
a − 1.92434 × 10
381
,
u
139
+ 4u
138
+ ··· + 472u − 55i
I
u
2
= h10u
18
− 3u
17
+ ··· + b − 10, 9u
18
− u
17
+ ··· + a − 7, u
19
− u
18
+ ··· − 3u + 1i
I
u
3
= h−u
2
a + au − u
2
+ b + u − 1, u
2
a + a
2
− 3au + 3u
2
+ 2a − 3u + 2, u
3
− u
2
+ 1i
I
u
4
= h−3a
3
+ 2a
2
+ 31b − 8a + 6, a
4
− a
3
− 4a
2
+ 4a + 11, u + 1i
* 4 irreducible components of dim
C
= 0, with total 168 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−5.65 × 10
376
u
138
− 1.60 × 10
377
u
137
+ · · · + 1.08 × 10
378
b − 5.53 ×
10
378
, 1.04 × 10
379
u
138
+ 2.44 × 10
379
u
137
+ · · · + 5.92 × 10
379
a − 1.92 ×
10
381
, u
139
+ 4u
138
+ · · · + 472u − 55i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
−0.176119u
138
− 0.411777u
137
+ ··· − 182.170u + 32.4994
0.0524905u
138
+ 0.148415u
137
+ ··· − 54.4052u + 5.13965
a
7
=
−0.00182425u
138
− 0.00973214u
137
+ ··· − 175.493u + 13.5208
0.144407u
138
+ 0.352288u
137
+ ··· + 58.8870u − 6.47093
a
11
=
−0.228609u
138
− 0.560192u
137
+ ··· − 127.765u + 27.3597
0.0524905u
138
+ 0.148415u
137
+ ··· − 54.4052u + 5.13965
a
8
=
−0.586546u
138
− 1.77386u
137
+ ··· − 408.709u + 48.7522
0.508633u
138
+ 1.39800u
137
+ ··· + 106.194u − 12.7124
a
1
=
u
3
u
5
− u
3
+ u
a
4
=
0.125067u
138
+ 0.930157u
137
+ ··· − 129.743u + 15.4604
−0.100367u
138
− 0.428049u
137
+ ··· − 80.1730u + 9.18097
a
9
=
−0.226178u
138
− 0.541512u
137
+ ··· − 136.597u + 27.7184
0.0388748u
138
+ 0.0924747u
137
+ ··· − 31.6327u + 2.65267
a
12
=
−0.607158u
138
− 2.10441u
137
+ ··· − 159.069u + 30.0427
0.206637u
138
+ 0.507832u
137
+ ··· + 37.1120u − 5.50176
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0201009u
138
− 0.638391u
137
+ ··· − 384.484u + 31.1094
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
139
+ 62u
138
+ ··· + 388114u + 3025
c
2
, c
5
u
139
+ 4u
138
+ ··· + 472u − 55
c
3
u
139
+ 5u
138
+ ··· + 4330u + 1331
c
4
u
139
+ 13u
138
+ ··· + 1376u + 64
c
6
u
139
+ 2u
138
+ ··· − 62783u + 13079
c
7
u
139
+ 7u
138
+ ··· + 472u + 80
c
8
, c
9
, c
12
u
139
+ 5u
138
+ ··· − 23u + 1
c
10
u
139
+ 2u
138
+ ··· − 2000u + 55
c
11
u
139
− 2u
138
+ ··· − 18072u + 112685
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
139
+ 34y
138
+ ··· + 100560976946y −9150625
c
2
, c
5
y
139
− 62y
138
+ ··· + 388114y −3025
c
3
y
139
− 21y
138
+ ··· + 280322344y −1771561
c
4
y
139
+ 23y
138
+ ··· − 1334272y −4096
c
6
y
139
− 18y
138
+ ··· + 16255714379y −171060241
c
7
y
139
− 29y
138
+ ··· + 253504y −6400
c
8
, c
9
, c
12
y
139
− 149y
138
+ ··· + 11y −1
c
10
y
139
+ 34y
138
+ ··· + 7730100y −3025
c
11
y
139
+ 38y
138
+ ··· − 869428969396y −12697909225
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.518078 + 0.849429I
a = −0.121879 − 0.241704I
b = 0.83527 + 1.24208I
2.15020 − 9.13760I 0
u = −0.518078 − 0.849429I
a = −0.121879 + 0.241704I
b = 0.83527 − 1.24208I
2.15020 + 9.13760I 0
u = −0.903632 + 0.398748I
a = −2.38251 + 0.30931I
b = −0.29379 + 2.08108I
−7.96514 + 1.62416I 0
u = −0.903632 − 0.398748I
a = −2.38251 − 0.30931I
b = −0.29379 − 2.08108I
−7.96514 − 1.62416I 0
u = 0.529919 + 0.829440I
a = −0.241841 − 0.146508I
b = −0.057048 + 0.842750I
4.01767 + 1.61831I 0
u = 0.529919 − 0.829440I
a = −0.241841 + 0.146508I
b = −0.057048 − 0.842750I
4.01767 − 1.61831I 0
u = 0.321719 + 0.964111I
a = 0.401303 − 0.061655I
b = 0.011976 − 0.757600I
−2.03450 + 4.35648I 0
u = 0.321719 − 0.964111I
a = 0.401303 + 0.061655I
b = 0.011976 + 0.757600I
−2.03450 − 4.35648I 0
u = −0.503973 + 0.844551I
a = 0.402615 − 0.230848I
b = 0.811807 + 0.685570I
−6.58796 − 5.00116I 0
u = −0.503973 − 0.844551I
a = 0.402615 + 0.230848I
b = 0.811807 − 0.685570I
−6.58796 + 5.00116I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.733246 + 0.708001I
a = −0.147313 + 0.297625I
b = 0.051814 − 0.970327I
3.40281 − 2.04784I 0
u = 0.733246 − 0.708001I
a = −0.147313 − 0.297625I
b = 0.051814 + 0.970327I
3.40281 + 2.04784I 0
u = 0.890456 + 0.407068I
a = −2.23689 + 1.04535I
b = −0.169447 − 1.257180I
−9.52383 − 1.67989I 0
u = 0.890456 − 0.407068I
a = −2.23689 − 1.04535I
b = −0.169447 + 1.257180I
−9.52383 + 1.67989I 0
u = 0.929520 + 0.430078I
a = 0.742660 + 0.613640I
b = 0.504193 − 1.039700I
−4.80822 + 3.72203I 0
u = 0.929520 − 0.430078I
a = 0.742660 − 0.613640I
b = 0.504193 + 1.039700I
−4.80822 − 3.72203I 0
u = −0.907164 + 0.355967I
a = 0.71826 + 1.35959I
b = 0.777868 + 0.880844I
−1.88897 + 1.69399I 0
u = −0.907164 − 0.355967I
a = 0.71826 − 1.35959I
b = 0.777868 − 0.880844I
−1.88897 − 1.69399I 0
u = −0.834450 + 0.604586I
a = −1.85162 − 0.45829I
b = −0.039995 + 0.449436I
2.12387 − 1.25259I 0
u = −0.834450 − 0.604586I
a = −1.85162 + 0.45829I
b = −0.039995 − 0.449436I
2.12387 + 1.25259I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.948446 + 0.180026I
a = 1.69385 − 1.15565I
b = 0.965800 + 0.048534I
−4.24387 + 0.18160I 0
u = 0.948446 − 0.180026I
a = 1.69385 + 1.15565I
b = 0.965800 − 0.048534I
−4.24387 − 0.18160I 0
u = 0.471493 + 0.841619I
a = −0.285061 + 0.229037I
b = 0.696487 − 1.156910I
3.67001 + 2.09092I 0
u = 0.471493 − 0.841619I
a = −0.285061 − 0.229037I
b = 0.696487 + 1.156910I
3.67001 − 2.09092I 0
u = −0.955165 + 0.401924I
a = 0.396434 + 0.614106I
b = 0.87232 + 1.22907I
−3.55379 + 2.24799I 0
u = −0.955165 − 0.401924I
a = 0.396434 − 0.614106I
b = 0.87232 − 1.22907I
−3.55379 − 2.24799I 0
u = −0.991267 + 0.351517I
a = −2.25608 − 0.28666I
b = −1.36258 + 1.01519I
−3.26735 + 0.35606I 0
u = −0.991267 − 0.351517I
a = −2.25608 + 0.28666I
b = −1.36258 − 1.01519I
−3.26735 − 0.35606I 0
u = −0.848516 + 0.622237I
a = 0.559231 − 0.936522I
b = −0.053638 + 0.727288I
2.08931 + 6.08106I 0
u = −0.848516 − 0.622237I
a = 0.559231 + 0.936522I
b = −0.053638 − 0.727288I
2.08931 − 6.08106I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.368090 + 0.991975I
a = −0.089353 + 0.210330I
b = 0.542713 − 0.655345I
1.43820 + 4.87898I 0
u = −0.368090 − 0.991975I
a = −0.089353 − 0.210330I
b = 0.542713 + 0.655345I
1.43820 − 4.87898I 0
u = 0.659318 + 0.666217I
a = 0.918035 − 0.482740I
b = −0.44035 + 1.47663I
0.75819 − 1.58915I 0
u = 0.659318 − 0.666217I
a = 0.918035 + 0.482740I
b = −0.44035 − 1.47663I
0.75819 + 1.58915I 0
u = 0.881320 + 0.274701I
a = 0.94855 − 1.98464I
b = 1.33307 − 0.72765I
−1.35292 + 3.00511I 0
u = 0.881320 − 0.274701I
a = 0.94855 + 1.98464I
b = 1.33307 + 0.72765I
−1.35292 − 3.00511I 0
u = 0.459781 + 0.798318I
a = 0.668492 + 0.368732I
b = 0.607211 − 0.957006I
−5.49109 + 3.15305I 0
u = 0.459781 − 0.798318I
a = 0.668492 − 0.368732I
b = 0.607211 + 0.957006I
−5.49109 − 3.15305I 0
u = −0.954231 + 0.521077I
a = −0.701801 + 1.021260I
b = −0.009712 − 0.858088I
−4.17893 + 8.80419I 0
u = −0.954231 − 0.521077I
a = −0.701801 − 1.021260I
b = −0.009712 + 0.858088I
−4.17893 − 8.80419I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.975387 + 0.496311I
a = 0.421033 − 0.834158I
b = 0.105808 + 1.032970I
−2.93021 − 3.29605I 0
u = 0.975387 − 0.496311I
a = 0.421033 + 0.834158I
b = 0.105808 − 1.032970I
−2.93021 + 3.29605I 0
u = −0.459258 + 1.002080I
a = −0.043384 + 0.293718I
b = −0.85556 − 1.19146I
−4.58375 − 13.11560I 0
u = −0.459258 − 1.002080I
a = −0.043384 − 0.293718I
b = −0.85556 + 1.19146I
−4.58375 + 13.11560I 0
u = −0.892198 + 0.054746I
a = −2.82485 + 1.20562I
b = −1.76384 + 1.30643I
−2.85597 + 0.13907I 0
u = −0.892198 − 0.054746I
a = −2.82485 − 1.20562I
b = −1.76384 − 1.30643I
−2.85597 − 0.13907I 0
u = −0.509346 + 0.733928I
a = 0.715702 + 0.179651I
b = 0.646144 − 0.550499I
−6.57221 + 1.67196I 0
u = −0.509346 − 0.733928I
a = 0.715702 − 0.179651I
b = 0.646144 + 0.550499I
−6.57221 − 1.67196I 0
u = −0.718936 + 0.511146I
a = 2.90211 − 0.00953I
b = −0.012600 − 0.504221I
−3.41226 − 4.59332I 0
u = −0.718936 − 0.511146I
a = 2.90211 + 0.00953I
b = −0.012600 + 0.504221I
−3.41226 + 4.59332I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.018350 + 0.462157I
a = −1.12350 + 1.36853I
b = −1.65694 + 0.22058I
−2.60610 − 5.91528I 0
u = 1.018350 − 0.462157I
a = −1.12350 − 1.36853I
b = −1.65694 − 0.22058I
−2.60610 + 5.91528I 0
u = 0.912754 + 0.649174I
a = −1.294420 + 0.405595I
b = −0.203435 − 0.835272I
2.85743 − 3.15401I 0
u = 0.912754 − 0.649174I
a = −1.294420 − 0.405595I
b = −0.203435 + 0.835272I
2.85743 + 3.15401I 0
u = 0.301233 + 1.080840I
a = 0.0748882 − 0.0706043I
b = −0.808597 + 0.934476I
−0.72564 + 4.81319I 0
u = 0.301233 − 1.080840I
a = 0.0748882 + 0.0706043I
b = −0.808597 − 0.934476I
−0.72564 − 4.81319I 0
u = 1.120180 + 0.070932I
a = −1.58929 − 0.92264I
b = −1.008550 − 0.842235I
−4.05140 − 7.62984I 0
u = 1.120180 − 0.070932I
a = −1.58929 + 0.92264I
b = −1.008550 + 0.842235I
−4.05140 + 7.62984I 0
u = 0.810128 + 0.335559I
a = −3.04549 − 0.55867I
b = −0.787438 − 0.753727I
−4.31191 − 7.04636I 0
u = 0.810128 − 0.335559I
a = −3.04549 + 0.55867I
b = −0.787438 + 0.753727I
−4.31191 + 7.04636I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.098190 + 0.247781I
a = 0.627114 + 1.189960I
b = 0.515369 + 0.576541I
−3.32878 − 0.58457I 0
u = −1.098190 − 0.247781I
a = 0.627114 − 1.189960I
b = 0.515369 − 0.576541I
−3.32878 + 0.58457I 0
u = 0.866721 + 0.727969I
a = −0.788162 + 0.827515I
b = −0.015964 − 0.988715I
2.99231 − 2.77523I 0
u = 0.866721 − 0.727969I
a = −0.788162 − 0.827515I
b = −0.015964 + 0.988715I
2.99231 + 2.77523I 0
u = 1.005840 + 0.530808I
a = 0.200411 + 1.358880I
b = −1.00788 + 1.44489I
−6.76770 − 3.68595I 0
u = 1.005840 − 0.530808I
a = 0.200411 − 1.358880I
b = −1.00788 − 1.44489I
−6.76770 + 3.68595I 0
u = −0.606352 + 0.611604I
a = 0.546479 + 0.021013I
b = −0.79238 − 1.37477I
1.92028 − 3.63228I 0
u = −0.606352 − 0.611604I
a = 0.546479 − 0.021013I
b = −0.79238 + 1.37477I
1.92028 + 3.63228I 0
u = 0.981328 + 0.590112I
a = 1.89749 − 0.54304I
b = 0.57472 + 1.52482I
−0.22895 − 3.29490I 0
u = 0.981328 − 0.590112I
a = 1.89749 + 0.54304I
b = 0.57472 − 1.52482I
−0.22895 + 3.29490I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.862243 + 0.761524I
a = 0.092919 + 1.076800I
b = 0.112965 − 0.475621I
0.80182 + 2.99396I 0
u = −0.862243 − 0.761524I
a = 0.092919 − 1.076800I
b = 0.112965 + 0.475621I
0.80182 − 2.99396I 0
u = −1.000820 + 0.579437I
a = 2.22083 + 0.55037I
b = 1.07625 − 1.48327I
0.72769 + 8.36455I 0
u = −1.000820 − 0.579437I
a = 2.22083 − 0.55037I
b = 1.07625 + 1.48327I
0.72769 − 8.36455I 0
u = −1.013830 + 0.575381I
a = −0.485574 − 1.004790I
b = −0.654459 − 0.747764I
−8.04761 + 3.28161I 0
u = −1.013830 − 0.575381I
a = −0.485574 + 1.004790I
b = −0.654459 + 0.747764I
−8.04761 − 3.28161I 0
u = −0.927701 + 0.711502I
a = 0.912057 + 0.792550I
b = 0.098744 − 0.385414I
0.57585 + 2.66839I 0
u = −0.927701 − 0.711502I
a = 0.912057 − 0.792550I
b = 0.098744 + 0.385414I
0.57585 − 2.66839I 0
u = −1.016740 + 0.578489I
a = 1.84258 + 0.75971I
b = 1.147400 − 0.673024I
−1.83353 + 6.03575I 0
u = −1.016740 − 0.578489I
a = 1.84258 − 0.75971I
b = 1.147400 + 0.673024I
−1.83353 − 6.03575I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.040120 + 0.539538I
a = 2.16829 − 0.23719I
b = 0.732412 + 0.947828I
−1.55374 − 7.40909I 0
u = 1.040120 − 0.539538I
a = 2.16829 + 0.23719I
b = 0.732412 − 0.947828I
−1.55374 + 7.40909I 0
u = −1.163300 + 0.153806I
a = −1.12634 − 1.30599I
b = −0.482739 − 0.780412I
−10.72090 − 0.89969I 0
u = −1.163300 − 0.153806I
a = −1.12634 + 1.30599I
b = −0.482739 + 0.780412I
−10.72090 + 0.89969I 0
u = 0.724908 + 0.388397I
a = 2.39282 − 0.83223I
b = 0.055387 + 0.513550I
−1.96799 − 0.52862I 0
u = 0.724908 − 0.388397I
a = 2.39282 + 0.83223I
b = 0.055387 − 0.513550I
−1.96799 + 0.52862I 0
u = −1.18087
a = 0.107746
b = −0.109489
−2.14969 0
u = 1.182930 + 0.036068I
a = −1.63453 + 0.61137I
b = −0.885401 + 0.429436I
−12.53890 + 3.02692I 0
u = 1.182930 − 0.036068I
a = −1.63453 − 0.61137I
b = −0.885401 − 0.429436I
−12.53890 − 3.02692I 0
u = 0.178997 + 0.794105I
a = 0.066955 + 1.016670I
b = −1.128420 − 0.556413I
−6.47593 + 5.99478I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.178997 − 0.794105I
a = 0.066955 − 1.016670I
b = −1.128420 + 0.556413I
−6.47593 − 5.99478I 0
u = −1.19698
a = −1.28059
b = −1.29312
−2.28585 0
u = −1.143510 + 0.354671I
a = −0.657278 − 0.431659I
b = −0.801048 − 0.085424I
−2.15976 + 0.47143I 0
u = −1.143510 − 0.354671I
a = −0.657278 + 0.431659I
b = −0.801048 + 0.085424I
−2.15976 − 0.47143I 0
u = −0.546539 + 0.584872I
a = −0.326905 − 0.250699I
b = −0.823610 − 0.673732I
−0.46177 − 1.34329I 0
u = −0.546539 − 0.584872I
a = −0.326905 + 0.250699I
b = −0.823610 + 0.673732I
−0.46177 + 1.34329I 0
u = 0.480588 + 0.604530I
a = 1.056010 − 0.903091I
b = 0.718777 + 1.105690I
−5.27965 − 0.75760I 0
u = 0.480588 − 0.604530I
a = 1.056010 + 0.903091I
b = 0.718777 − 1.105690I
−5.27965 + 0.75760I 0
u = 0.892512 + 0.871500I
a = 0.615038 − 1.072300I
b = −0.079001 + 1.044370I
−1.42582 − 3.20188I 0
u = 0.892512 − 0.871500I
a = 0.615038 + 1.072300I
b = −0.079001 − 1.044370I
−1.42582 + 3.20188I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.070190 + 0.662222I
a = 1.279770 − 0.042929I
b = 0.300355 + 0.781437I
2.39451 − 7.18069I 0
u = 1.070190 − 0.662222I
a = 1.279770 + 0.042929I
b = 0.300355 − 0.781437I
2.39451 + 7.18069I 0
u = 1.147560 + 0.534595I
a = 0.875570 − 1.095370I
b = 1.56571 − 0.51458I
−9.2609 − 10.8273I 0
u = 1.147560 − 0.534595I
a = 0.875570 + 1.095370I
b = 1.56571 + 0.51458I
−9.2609 + 10.8273I 0
u = 1.103930 + 0.632263I
a = −2.00172 + 0.43188I
b = −0.684500 − 0.959780I
−7.40721 − 8.54738I 0
u = 1.103930 − 0.632263I
a = −2.00172 − 0.43188I
b = −0.684500 + 0.959780I
−7.40721 + 8.54738I 0
u = −1.089210 + 0.658755I
a = −1.92235 − 0.54409I
b = −0.97782 + 1.35307I
0.4142 + 14.7469I 0
u = −1.089210 − 0.658755I
a = −1.92235 + 0.54409I
b = −0.97782 − 1.35307I
0.4142 − 14.7469I 0
u = 1.102580 + 0.642997I
a = −1.71783 + 0.43351I
b = −0.90728 − 1.34634I
1.77091 − 7.61475I 0
u = 1.102580 − 0.642997I
a = −1.71783 − 0.43351I
b = −0.90728 + 1.34634I
1.77091 + 7.61475I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.244000 + 0.288672I
a = 1.59379 + 0.06668I
b = 1.11976 − 1.18242I
−10.96610 − 2.26870I 0
u = −1.244000 − 0.288672I
a = 1.59379 − 0.06668I
b = 1.11976 + 1.18242I
−10.96610 + 2.26870I 0
u = −1.099600 + 0.661660I
a = −1.67436 − 0.76737I
b = −0.913455 + 0.759311I
−8.38225 + 10.62080I 0
u = −1.099600 − 0.661660I
a = −1.67436 + 0.76737I
b = −0.913455 − 0.759311I
−8.38225 − 10.62080I 0
u = 0.618479 + 0.354846I
a = −0.977460 − 0.497555I
b = −0.529786 + 0.969847I
0.05862 + 3.28480I −12.7291 − 7.0074I
u = 0.618479 − 0.354846I
a = −0.977460 + 0.497555I
b = −0.529786 − 0.969847I
0.05862 − 3.28480I −12.7291 + 7.0074I
u = 1.184930 + 0.643384I
a = −1.244090 − 0.173011I
b = −0.306874 − 0.748914I
−4.62352 − 10.15990I 0
u = 1.184930 − 0.643384I
a = −1.244090 + 0.173011I
b = −0.306874 + 0.748914I
−4.62352 + 10.15990I 0
u = −1.169880 + 0.690427I
a = 1.77420 + 0.48835I
b = 0.93706 − 1.31367I
−6.7965 + 19.2422I 0
u = −1.169880 − 0.690427I
a = 1.77420 − 0.48835I
b = 0.93706 + 1.31367I
−6.7965 − 19.2422I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.505914 + 1.263450I
a = −0.045713 − 0.239155I
b = −0.624033 + 0.485135I
−4.05749 + 6.13939I 0
u = −0.505914 − 1.263450I
a = −0.045713 + 0.239155I
b = −0.624033 − 0.485135I
−4.05749 − 6.13939I 0
u = 1.373060 + 0.015360I
a = 1.176540 + 0.631295I
b = 1.040680 + 0.888333I
−11.6433 − 9.9628I 0
u = 1.373060 − 0.015360I
a = 1.176540 − 0.631295I
b = 1.040680 − 0.888333I
−11.6433 + 9.9628I 0
u = 1.226320 + 0.661413I
a = 1.52899 − 0.30797I
b = 1.03102 + 1.20126I
−3.56276 − 10.96500I 0
u = 1.226320 − 0.661413I
a = 1.52899 + 0.30797I
b = 1.03102 − 1.20126I
−3.56276 + 10.96500I 0
u = −1.32194 + 0.55749I
a = 0.678335 + 0.224414I
b = 0.961004 − 0.138952I
−7.53833 + 0.82289I 0
u = −1.32194 − 0.55749I
a = 0.678335 − 0.224414I
b = 0.961004 + 0.138952I
−7.53833 − 0.82289I 0
u = −1.14010 + 0.89061I
a = −0.374253 − 0.328665I
b = −0.187156 + 0.245428I
−6.72646 + 3.71560I 0
u = −1.14010 − 0.89061I
a = −0.374253 + 0.328665I
b = −0.187156 − 0.245428I
−6.72646 − 3.71560I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.119885 + 0.481859I
a = −0.449528 + 0.346769I
b = −0.535213 + 0.937256I
0.29273 + 3.29427I −8.66948 − 3.26734I
u = 0.119885 − 0.481859I
a = −0.449528 − 0.346769I
b = −0.535213 − 0.937256I
0.29273 − 3.29427I −8.66948 + 3.26734I
u = −1.52353
a = −0.230634
b = 0.0198354
−8.51194 0
u = 0.087210 + 0.467581I
a = −1.11876 − 0.90909I
b = 0.926757 + 0.354839I
−0.46853 + 2.38662I −7.20849 − 3.95616I
u = 0.087210 − 0.467581I
a = −1.11876 + 0.90909I
b = 0.926757 − 0.354839I
−0.46853 − 2.38662I −7.20849 + 3.95616I
u = −1.55730
a = 0.829010
b = 1.14267
−7.79251 0
u = −0.356659 + 0.209440I
a = −1.029550 + 0.446670I
b = −0.426561 + 0.548037I
−0.850285 + 0.820786I −7.15043 − 5.37763I
u = −0.356659 − 0.209440I
a = −1.029550 − 0.446670I
b = −0.426561 − 0.548037I
−0.850285 − 0.820786I −7.15043 + 5.37763I
u = 0.0976189
a = 11.8660
b = −0.539403
−1.94515 −3.57150
18
II.
I
u
2
= h10u
18
−3u
17
+· · ·+b−10, 9u
18
−u
17
+· · ·+a−7, u
19
−u
18
+· · ·−3u+1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
−9u
18
+ u
17
+ ··· − 21u + 7
−10u
18
+ 3u
17
+ ··· − 24u + 10
a
7
=
−2u
18
+ 6u
17
+ ··· − 13u + 13
−u
18
+ 4u
16
+ ··· + 3u
3
− 3u
a
11
=
u
18
− 2u
17
+ ··· + 3u − 3
−10u
18
+ 3u
17
+ ··· − 24u + 10
a
8
=
u
18
+ 6u
17
+ ··· − 4u + 8
7u
18
− u
17
+ ··· + 14u − 6
a
1
=
u
3
u
5
− u
3
+ u
a
4
=
−12u
18
− 2u
17
+ ··· − 22u + 2
7u
18
− u
17
+ ··· + 17u − 7
a
9
=
−5u
18
+ 20u
16
+ ··· − 12u + 2
−6u
18
+ 2u
17
+ ··· − 14u + 6
a
12
=
10u
18
− 8u
17
+ ··· + 34u − 14
−8u
18
+ 3u
17
+ ··· − 19u + 10
(ii) Obstruction class = 1
(iii) Cusp Shapes = −25u
18
+ 15u
17
+ 107u
16
− 81u
15
− 211u
14
+ 112u
13
+ 303u
12
−
70u
11
−312u
10
−86u
9
+ 273u
8
+ 200u
7
−245u
6
−110u
5
+ 55u
4
+ 138u
3
−40u
2
−70u + 36
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
− 9u
18
+ ··· + 5u − 1
c
2
u
19
+ u
18
+ ··· − 3u − 1
c
3
u
19
+ 2u
18
+ ··· − u
2
− 1
c
4
u
19
− u
17
+ ··· + 169u − 19
c
5
u
19
− u
18
+ ··· − 3u + 1
c
6
u
19
+ 2u
18
+ ··· + 2u + 1
c
7
u
19
− 5u
18
+ ··· − 18u + 5
c
8
, c
9
u
19
+ 2u
18
+ ··· + 2u + 1
c
10
u
19
+ 4u
17
+ ··· + 2u
3
+ 1
c
11
u
19
+ 2u
16
+ ··· + 4u
2
+ 1
c
12
u
19
− 2u
18
+ ··· + 2u − 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
− y
18
+ ··· − 15y −1
c
2
, c
5
y
19
− 9y
18
+ ··· + 5y −1
c
3
y
19
− 16y
18
+ ··· − 2y −1
c
4
y
19
− 2y
18
+ ··· + 31221y −361
c
6
y
19
+ 12y
18
+ ··· + 2y −1
c
7
y
19
− 5y
18
+ ··· + 484y −25
c
8
, c
9
, c
12
y
19
− 26y
18
+ ··· − 10y −1
c
10
y
19
+ 8y
18
+ ··· − 4y
2
− 1
c
11
y
19
+ 4y
17
+ ··· − 8y −1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.884875 + 0.416641I
a = 2.27848 + 0.00194I
b = 0.18618 + 1.88904I
−7.71278 − 1.72198I −0.60180 + 7.55176I
u = 0.884875 − 0.416641I
a = 2.27848 − 0.00194I
b = 0.18618 − 1.88904I
−7.71278 + 1.72198I −0.60180 − 7.55176I
u = −0.309564 + 0.904543I
a = 0.681870 + 0.134171I
b = −0.380494 + 0.509090I
−3.24978 + 5.70054I −5.60451 − 5.25885I
u = −0.309564 − 0.904543I
a = 0.681870 − 0.134171I
b = −0.380494 − 0.509090I
−3.24978 − 5.70054I −5.60451 + 5.25885I
u = −0.544749 + 0.743331I
a = −0.212742 + 0.573682I
b = 0.435543 − 0.686831I
1.26041 + 4.35989I −7.53612 − 4.70457I
u = −0.544749 − 0.743331I
a = −0.212742 − 0.573682I
b = 0.435543 + 0.686831I
1.26041 − 4.35989I −7.53612 + 4.70457I
u = 1.014760 + 0.532753I
a = −2.05269 + 0.34384I
b = −0.995678 − 0.891914I
−0.62955 − 7.05446I −6.31432 + 8.24460I
u = 1.014760 − 0.532753I
a = −2.05269 − 0.34384I
b = −0.995678 + 0.891914I
−0.62955 + 7.05446I −6.31432 − 8.24460I
u = 0.672238 + 0.466249I
a = 0.651722 − 0.191858I
b = 0.727860 − 0.990023I
0.57229 + 2.89015I −3.55717 − 0.49519I
u = 0.672238 − 0.466249I
a = 0.651722 + 0.191858I
b = 0.727860 + 0.990023I
0.57229 − 2.89015I −3.55717 + 0.49519I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.812419
a = −2.36743
b = −1.02346
−2.77296 −16.2660
u = −1.19429
a = −0.974950
b = −0.861786
−2.53278 −22.7690
u = −1.023080 + 0.651033I
a = −0.179893 + 0.651598I
b = 0.455452 + 0.967111I
−6.17182 + 2.90306I −8.82043 − 0.05771I
u = −1.023080 − 0.651033I
a = −0.179893 − 0.651598I
b = 0.455452 − 0.967111I
−6.17182 − 2.90306I −8.82043 + 0.05771I
u = 1.129730 + 0.578827I
a = 1.66572 − 0.00286I
b = 0.713842 + 0.637875I
−6.07975 − 10.05750I −11.2886 + 9.0481I
u = 1.129730 − 0.578827I
a = 1.66572 + 0.00286I
b = 0.713842 − 0.637875I
−6.07975 + 10.05750I −11.2886 − 9.0481I
u = 0.471704 + 0.444750I
a = −2.40959 + 0.65367I
b = −0.487396 + 0.698425I
−3.83594 + 5.50297I −9.04721 − 6.95742I
u = 0.471704 − 0.444750I
a = −2.40959 − 0.65367I
b = −0.487396 − 0.698425I
−3.83594 − 5.50297I −9.04721 + 6.95742I
u = −1.58513
a = 0.496613
b = 0.574618
−8.79777 −26.4250
23
III.
I
u
3
= h−u
2
a+au−u
2
+b+u−1, u
2
a+a
2
−3au+3u
2
+2a−3u+2, u
3
−u
2
+1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
2
+ u + 1
a
10
=
a
u
2
a − au + u
2
− u + 1
a
7
=
−u
2
a + au + 2u − 2
0
a
11
=
−u
2
a + au − u
2
+ a + u − 1
u
2
a − au + u
2
− u + 1
a
8
=
−u
2
+ 1
u
2
a
1
=
u
2
− 1
−u
2
a
4
=
1
0
a
9
=
−u
2
+ a + 1
u
2
a − au + 2u
2
− u + 1
a
12
=
a
u
2
a − au + u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
2
a − 5au + 5u
2
+ 2a − 3u
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
4
u
6
c
5
(u
3
− u
2
+ 1)
2
c
6
, c
7
u
6
− 3u
5
+ 5u
3
− u
2
− 2u + 1
c
8
, c
9
(u − 1)
6
c
10
, c
11
u
6
− 2u
5
+ 4u
4
− 5u
3
+ 4u
2
− 2u + 1
c
12
(u + 1)
6
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
5
(y
3
− y
2
+ 2y −1)
2
c
4
y
6
c
6
, c
7
y
6
− 9y
5
+ 28y
4
− 35y
3
+ 21y
2
− 6y + 1
c
8
, c
9
, c
12
(y −1)
6
c
10
, c
11
y
6
+ 4y
5
+ 4y
4
+ y
3
+ 4y
2
+ 4y + 1
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = 1.021100 − 0.455284I
b = −0.08270 + 1.43799I
1.37919 − 2.82812I −4.06063 + 4.05868I
u = 0.877439 + 0.744862I
a = −0.60387 + 1.38273I
b = −0.039862 − 0.693124I
1.37919 − 2.82812I 1.15973 + 2.26538I
u = 0.877439 − 0.744862I
a = 1.021100 + 0.455284I
b = −0.08270 − 1.43799I
1.37919 + 2.82812I −4.06063 − 4.05868I
u = 0.877439 − 0.744862I
a = −0.60387 − 1.38273I
b = −0.039862 + 0.693124I
1.37919 + 2.82812I 1.15973 − 2.26538I
u = −0.754878
a = −2.41724 + 0.36211I
b = −0.877439 + 0.479689I
−2.75839 −11.59911 + 2.50363I
u = −0.754878
a = −2.41724 − 0.36211I
b = −0.877439 − 0.479689I
−2.75839 −11.59911 − 2.50363I
27
IV. I
u
4
= h−3a
3
+ 2a
2
+ 31b − 8a + 6, a
4
− a
3
− 4a
2
+ 4a + 11, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
5
=
1
0
a
6
=
1
1
a
3
=
1
0
a
10
=
a
0.0967742a
3
− 0.0645161a
2
+ 0.258065a − 0.193548
a
7
=
0.0322581a
3
− 0.354839a
2
− 0.580645a − 0.0645161
−0.0645161a
3
− 0.290323a
2
+ 0.161290a + 1.12903
a
11
=
−0.0967742a
3
+ 0.0645161a
2
+ 0.741935a + 0.193548
0.0967742a
3
− 0.0645161a
2
+ 0.258065a − 0.193548
a
8
=
0.0322581a
3
− 0.354839a
2
− 0.580645a − 0.0645161
−0.0645161a
3
− 0.290323a
2
+ 0.161290a + 1.12903
a
1
=
−1
−1
a
4
=
0.354839a
3
+ 0.0967742a
2
− 1.38710a − 0.709677
0.0322581a
3
− 0.354839a
2
− 0.580645a − 0.0645161
a
9
=
0.0967742a
3
− 0.0645161a
2
+ 0.258065a − 0.193548
0.193548a
3
− 0.129032a
2
− 0.483871a − 0.387097
a
12
=
−0.0645161a
3
− 0.290323a
2
+ 0.161290a − 0.870968
−0.161290a
3
− 0.225806a
2
+ 0.903226a + 0.322581
(ii) Obstruction class = 1
(iii) Cusp Shapes =
5
31
a
3
−
24
31
a
2
−
28
31
a −
351
31
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
4
u
4
− 2u
3
+ 4u
2
− 3u + 1
c
5
(u + 1)
4
c
6
, c
8
, c
9
(u
2
+ u − 1)
2
c
7
u
4
c
10
, c
11
u
4
− u
3
+ u
2
− u + 1
c
12
(u
2
− u − 1)
2
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
4
c
3
, c
4
y
4
+ 4y
3
+ 6y
2
− y + 1
c
6
, c
8
, c
9
c
12
(y
2
− 3y + 1)
2
c
7
y
4
c
10
, c
11
y
4
+ y
3
+ y
2
+ y + 1
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.42705 + 0.58779I
b = −0.809017 + 0.587785I
−2.63189 −11.57295 + 1.31433I
u = −1.00000
a = −1.42705 − 0.58779I
b = −0.809017 − 0.587785I
−2.63189 −11.57295 − 1.31433I
u = −1.00000
a = 1.92705 + 0.95106I
b = 0.309017 + 0.951057I
−10.5276 −14.9271 − 2.1266I
u = −1.00000
a = 1.92705 − 0.95106I
b = 0.309017 − 0.951057I
−10.5276 −14.9271 + 2.1266I
31
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
3
− u
2
+ 2u − 1)
2
(u
19
− 9u
18
+ ··· + 5u − 1)
· (u
139
+ 62u
138
+ ··· + 388114u + 3025)
c
2
((u − 1)
4
)(u
3
+ u
2
− 1)
2
(u
19
+ u
18
+ ··· − 3u − 1)
· (u
139
+ 4u
138
+ ··· + 472u − 55)
c
3
((u
3
− u
2
+ 2u − 1)
2
)(u
4
− 2u
3
+ ··· − 3u + 1)(u
19
+ 2u
18
+ ··· − u
2
− 1)
· (u
139
+ 5u
138
+ ··· + 4330u + 1331)
c
4
u
6
(u
4
− 2u
3
+ ··· − 3u + 1)(u
19
− u
17
+ ··· + 169u − 19)
· (u
139
+ 13u
138
+ ··· + 1376u + 64)
c
5
((u + 1)
4
)(u
3
− u
2
+ 1)
2
(u
19
− u
18
+ ··· − 3u + 1)
· (u
139
+ 4u
138
+ ··· + 472u − 55)
c
6
((u
2
+ u − 1)
2
)(u
6
− 3u
5
+ ··· − 2u + 1)(u
19
+ 2u
18
+ ··· + 2u + 1)
· (u
139
+ 2u
138
+ ··· − 62783u + 13079)
c
7
u
4
(u
6
− 3u
5
+ ··· − 2u + 1)(u
19
− 5u
18
+ ··· − 18u + 5)
· (u
139
+ 7u
138
+ ··· + 472u + 80)
c
8
, c
9
((u − 1)
6
)(u
2
+ u − 1)
2
(u
19
+ 2u
18
+ ··· + 2u + 1)
· (u
139
+ 5u
138
+ ··· − 23u + 1)
c
10
(u
4
− u
3
+ u
2
− u + 1)(u
6
− 2u
5
+ 4u
4
− 5u
3
+ 4u
2
− 2u + 1)
· (u
19
+ 4u
17
+ ··· + 2u
3
+ 1)(u
139
+ 2u
138
+ ··· − 2000u + 55)
c
11
(u
4
− u
3
+ u
2
− u + 1)(u
6
− 2u
5
+ 4u
4
− 5u
3
+ 4u
2
− 2u + 1)
· (u
19
+ 2u
16
+ ··· + 4u
2
+ 1)(u
139
− 2u
138
+ ··· − 18072u + 112685)
c
12
((u + 1)
6
)(u
2
− u − 1)
2
(u
19
− 2u
18
+ ··· + 2u − 1)
· (u
139
+ 5u
138
+ ··· − 23u + 1)
32
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
4
)(y
3
+ 3y
2
+ 2y −1)
2
(y
19
− y
18
+ ··· − 15y −1)
· (y
139
+ 34y
138
+ ··· + 100560976946y −9150625)
c
2
, c
5
((y −1)
4
)(y
3
− y
2
+ 2y −1)
2
(y
19
− 9y
18
+ ··· + 5y −1)
· (y
139
− 62y
138
+ ··· + 388114y −3025)
c
3
(y
3
+ 3y
2
+ 2y −1)
2
(y
4
+ 4y
3
+ 6y
2
− y + 1)
· (y
19
− 16y
18
+ ··· − 2y −1)
· (y
139
− 21y
138
+ ··· + 280322344y −1771561)
c
4
y
6
(y
4
+ 4y
3
+ 6y
2
− y + 1)(y
19
− 2y
18
+ ··· + 31221y −361)
· (y
139
+ 23y
138
+ ··· − 1334272y −4096)
c
6
(y
2
− 3y + 1)
2
(y
6
− 9y
5
+ 28y
4
− 35y
3
+ 21y
2
− 6y + 1)
· (y
19
+ 12y
18
+ ··· + 2y −1)
· (y
139
− 18y
138
+ ··· + 16255714379y −171060241)
c
7
y
4
(y
6
− 9y
5
+ 28y
4
− 35y
3
+ 21y
2
− 6y + 1)
· (y
19
− 5y
18
+ ··· + 484y −25)(y
139
− 29y
138
+ ··· + 253504y −6400)
c
8
, c
9
, c
12
((y −1)
6
)(y
2
− 3y + 1)
2
(y
19
− 26y
18
+ ··· − 10y −1)
· (y
139
− 149y
138
+ ··· + 11y −1)
c
10
(y
4
+ y
3
+ y
2
+ y + 1)(y
6
+ 4y
5
+ 4y
4
+ y
3
+ 4y
2
+ 4y + 1)
· (y
19
+ 8y
18
+ ··· − 4y
2
− 1)(y
139
+ 34y
138
+ ··· + 7730100y −3025)
c
11
(y
4
+ y
3
+ y
2
+ y + 1)(y
6
+ 4y
5
+ 4y
4
+ y
3
+ 4y
2
+ 4y + 1)
· (y
19
+ 4y
17
+ ··· − 8y −1)
· (y
139
+ 38y
138
+ ··· − 869428969396y −12697909225)
33
