11a
189
(K11a
189
)
A knot diagram
1
Linearized knot diagam
7 1 10 11 9 2 3 4 6 8 5
Solving Sequence
4,11 5,8
9 6 1 10 3 2 7
c
4
c
8
c
5
c
11
c
10
c
3
c
2
c
7
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h6.42009 × 10
257
u
88
− 4.87876 × 10
257
u
87
+ ··· + 2.36068 × 10
257
b + 8.83509 × 10
259
,
6.20222 × 10
258
u
88
+ 4.18516 × 10
258
u
87
+ ··· + 3.09249 × 10
259
a + 2.68994 × 10
260
,
u
89
− 30u
87
+ ··· − 598u + 131i
I
u
2
= h−u
14
+ u
13
+ 5u
12
− 4u
11
− 12u
10
+ 9u
9
+ 17u
8
− 15u
7
− 14u
6
+ 12u
5
+ 6u
4
− 7u
3
− u
2
+ b,
− 7u
14
+ 6u
13
+ ··· + a + 7,
u
15
− u
14
− 6u
13
+ 5u
12
+ 17u
11
− 13u
10
− 29u
9
+ 24u
8
+ 31u
7
− 27u
6
− 20u
5
+ 19u
4
+ 7u
3
− 7u
2
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 104 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
= h6.42 × 10
257
u
88
− 4.88 × 10
257
u
87
+ · · · + 2.36 × 10
257
b + 8.84 ×
10
259
, 6.20 × 10
258
u
88
+ 4.19 × 10
258
u
87
+ · · · + 3.09 × 10
259
a + 2.69 ×
10
260
, u
89
− 30u
87
+ · · · − 598u + 131i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
u
2
a
8
=
−0.200557u
88
− 0.135333u
87
+ ··· + 189.917u − 8.69828
−2.71959u
88
+ 2.06667u
87
+ ··· + 2244.10u − 374.260
a
9
=
−2.92015u
88
+ 1.93134u
87
+ ··· + 2434.01u − 382.958
−2.71959u
88
+ 2.06667u
87
+ ··· + 2244.10u − 374.260
a
6
=
2.84782u
88
− 2.54786u
87
+ ··· − 2839.07u + 510.136
0.594470u
88
− 0.409964u
87
+ ··· − 776.183u + 135.349
a
1
=
−u
−u
3
+ u
a
10
=
−3.69459u
88
+ 2.73242u
87
+ ··· + 2749.91u − 445.177
−0.851550u
88
+ 0.449332u
87
+ ··· + 777.942u − 121.621
a
3
=
−1.70941u
88
+ 1.84202u
87
+ ··· + 1720.23u − 327.215
0.0173264u
88
+ 0.0106093u
87
+ ··· + 245.379u − 48.9621
a
2
=
−1.77307u
88
+ 1.96142u
87
+ ··· + 1963.93u − 375.540
0.0672428u
88
− 0.0641570u
87
+ ··· + 81.4241u − 16.2786
a
7
=
−0.967025u
88
+ 1.19947u
87
+ ··· + 1231.97u − 237.907
−0.376658u
88
+ 0.389535u
87
+ ··· + 428.290u − 81.3056
a
7
=
−0.967025u
88
+ 1.19947u
87
+ ··· + 1231.97u − 237.907
−0.376658u
88
+ 0.389535u
87
+ ··· + 428.290u − 81.3056
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.125878u
88
− 0.576729u
87
+ ··· − 1166.86u + 242.988
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
89
+ u
88
+ ··· + u + 1
c
2
u
89
+ 45u
88
+ ··· − 7u − 1
c
3
u
89
− 3u
88
+ ··· + 27u + 1
c
4
, c
11
u
89
− 30u
87
+ ··· − 598u + 131
c
5
, c
9
u
89
− 27u
87
+ ··· + 2u − 1
c
7
u
89
− u
88
+ ··· − 219u + 3737
c
8
u
89
+ u
88
+ ··· − 11u + 3
c
10
u
89
− 11u
88
+ ··· + 2752u − 593
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
89
+ 45y
88
+ ··· − 7y −1
c
2
y
89
+ y
88
+ ··· − 39y −1
c
3
y
89
+ 3y
88
+ ··· + 143y −1
c
4
, c
11
y
89
− 60y
88
+ ··· + 397166y −17161
c
5
, c
9
y
89
− 54y
88
+ ··· + 32y −1
c
7
y
89
− 43y
88
+ ··· − 186682455y −13965169
c
8
y
89
+ 5y
88
+ ··· + 181y −9
c
10
y
89
− 27y
88
+ ··· + 8974170y −351649
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.889747 + 0.452384I
a = −0.53880 + 1.76232I
b = 0.477239 + 0.302395I
−0.63006 + 8.68382I 0
u = −0.889747 − 0.452384I
a = −0.53880 − 1.76232I
b = 0.477239 − 0.302395I
−0.63006 − 8.68382I 0
u = 0.910671 + 0.398320I
a = 0.19557 + 1.62064I
b = −0.403492 + 0.311347I
1.47236 − 3.97526I 0
u = 0.910671 − 0.398320I
a = 0.19557 − 1.62064I
b = −0.403492 − 0.311347I
1.47236 + 3.97526I 0
u = −1.016600 + 0.137245I
a = −0.576279 − 0.124219I
b = 1.28500 − 1.71908I
−0.83265 + 2.51437I 0
u = −1.016600 − 0.137245I
a = −0.576279 + 0.124219I
b = 1.28500 + 1.71908I
−0.83265 − 2.51437I 0
u = −0.954288 + 0.091707I
a = 1.90084 + 0.00472I
b = −1.231680 + 0.032158I
0.74745 + 3.52422I 0
u = −0.954288 − 0.091707I
a = 1.90084 − 0.00472I
b = −1.231680 − 0.032158I
0.74745 − 3.52422I 0
u = 0.912318 + 0.259542I
a = −0.65851 + 1.37947I
b = −0.259979 + 0.234024I
2.10633 − 2.24661I 0
u = 0.912318 − 0.259542I
a = −0.65851 − 1.37947I
b = −0.259979 − 0.234024I
2.10633 + 2.24661I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.250513 + 0.909541I
a = 0.558779 + 0.800837I
b = −1.012260 − 0.599113I
5.28492 + 4.09985I 0
u = 0.250513 − 0.909541I
a = 0.558779 − 0.800837I
b = −1.012260 + 0.599113I
5.28492 − 4.09985I 0
u = 1.061570 + 0.193566I
a = 0.646957 + 0.005889I
b = −1.34806 − 1.48412I
−3.38961 − 8.10177I 0
u = 1.061570 − 0.193566I
a = 0.646957 − 0.005889I
b = −1.34806 + 1.48412I
−3.38961 + 8.10177I 0
u = −0.896503 + 0.169355I
a = 1.19590 + 1.09495I
b = 0.204472 + 0.156620I
0.70886 − 2.35289I 0
u = −0.896503 − 0.169355I
a = 1.19590 − 1.09495I
b = 0.204472 − 0.156620I
0.70886 + 2.35289I 0
u = 1.096800 + 0.024032I
a = 0.843907 − 0.225610I
b = −0.97444 − 1.43273I
−6.30667 + 0.58881I 0
u = 1.096800 − 0.024032I
a = 0.843907 + 0.225610I
b = −0.97444 + 1.43273I
−6.30667 − 0.58881I 0
u = −0.593963 + 0.659935I
a = 0.857622 + 0.233636I
b = −0.639884 − 0.077817I
−0.74312 + 2.38513I 0
u = −0.593963 − 0.659935I
a = 0.857622 − 0.233636I
b = −0.639884 + 0.077817I
−0.74312 − 2.38513I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.018630 + 0.485863I
a = −0.760663 + 0.983882I
b = 0.506841 + 0.529809I
−2.24793 + 1.87180I 0
u = −1.018630 − 0.485863I
a = −0.760663 − 0.983882I
b = 0.506841 − 0.529809I
−2.24793 − 1.87180I 0
u = 0.398710 + 0.771706I
a = 1.354100 − 0.383086I
b = −0.449816 + 0.871067I
−2.27469 − 6.43119I 0
u = 0.398710 − 0.771706I
a = 1.354100 + 0.383086I
b = −0.449816 − 0.871067I
−2.27469 + 6.43119I 0
u = −0.651535 + 0.565177I
a = 1.57091 + 0.04849I
b = −1.016120 + 0.181206I
0.03725 − 4.55071I 0
u = −0.651535 − 0.565177I
a = 1.57091 − 0.04849I
b = −1.016120 − 0.181206I
0.03725 + 4.55071I 0
u = 1.080740 + 0.451595I
a = 1.089600 + 0.543941I
b = −0.652720 + 0.801813I
−1.82833 − 5.02044I 0
u = 1.080740 − 0.451595I
a = 1.089600 − 0.543941I
b = −0.652720 − 0.801813I
−1.82833 + 5.02044I 0
u = 0.825079 + 0.852973I
a = 1.013710 − 0.231765I
b = −0.404411 + 0.990807I
−2.85121 + 0.37716I 0
u = 0.825079 − 0.852973I
a = 1.013710 + 0.231765I
b = −0.404411 − 0.990807I
−2.85121 − 0.37716I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.799407 + 0.019558I
a = −0.815403 − 0.950050I
b = 0.20638 − 1.47781I
0.082135 − 1.402700I 1.000000 + 0.911438I
u = −0.799407 − 0.019558I
a = −0.815403 + 0.950050I
b = 0.20638 + 1.47781I
0.082135 + 1.402700I 1.000000 − 0.911438I
u = 0.127992 + 1.209710I
a = 0.551795 + 0.738924I
b = −0.807284 − 0.641410I
2.99214 + 5.76178I 0
u = 0.127992 − 1.209710I
a = 0.551795 − 0.738924I
b = −0.807284 + 0.641410I
2.99214 − 5.76178I 0
u = 0.758651 + 0.141414I
a = −1.92316 + 0.06017I
b = 1.166660 + 0.036708I
2.87128 + 0.16130I 2.26530 + 3.31981I
u = 0.758651 − 0.141414I
a = −1.92316 − 0.06017I
b = 1.166660 − 0.036708I
2.87128 − 0.16130I 2.26530 − 3.31981I
u = 0.049165 + 1.230130I
a = −0.559202 + 0.688042I
b = 0.736512 − 0.561358I
−1.33196 − 2.44177I 0
u = 0.049165 − 1.230130I
a = −0.559202 − 0.688042I
b = 0.736512 + 0.561358I
−1.33196 + 2.44177I 0
u = −0.305027 + 0.698562I
a = −0.476739 + 0.863083I
b = 1.162640 − 0.546817I
4.93245 + 0.64307I 7.39513 − 2.13919I
u = −0.305027 − 0.698562I
a = −0.476739 − 0.863083I
b = 1.162640 + 0.546817I
4.93245 − 0.64307I 7.39513 + 2.13919I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.439575 + 0.615498I
a = 1.149600 − 0.115471I
b = −0.698187 + 0.241172I
−0.66030 + 2.49036I 1.19350 − 2.71078I
u = −0.439575 − 0.615498I
a = 1.149600 + 0.115471I
b = −0.698187 − 0.241172I
−0.66030 − 2.49036I 1.19350 + 2.71078I
u = −1.178450 + 0.416595I
a = 0.747568 − 0.419084I
b = −1.21853 − 1.36797I
2.16092 + 3.60298I 0
u = −1.178450 − 0.416595I
a = 0.747568 + 0.419084I
b = −1.21853 + 1.36797I
2.16092 − 3.60298I 0
u = −1.216440 + 0.411059I
a = −0.122681 + 0.284283I
b = 0.107118 + 0.672929I
−2.06773 + 2.36101I 0
u = −1.216440 − 0.411059I
a = −0.122681 − 0.284283I
b = 0.107118 − 0.672929I
−2.06773 − 2.36101I 0
u = 1.234760 + 0.357842I
a = 1.253570 + 0.379206I
b = −0.889269 + 0.916124I
−4.17367 − 5.52755I 0
u = 1.234760 − 0.357842I
a = 1.253570 − 0.379206I
b = −0.889269 − 0.916124I
−4.17367 + 5.52755I 0
u = −1.262070 + 0.281444I
a = −1.224250 + 0.302827I
b = 0.931584 + 0.992768I
−8.23912 + 1.98284I 0
u = −1.262070 − 0.281444I
a = −1.224250 − 0.302827I
b = 0.931584 − 0.992768I
−8.23912 − 1.98284I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.036670 + 0.779876I
a = −0.780160 − 0.133305I
b = 0.327917 + 0.979792I
−1.06082 + 3.18631I 0
u = −1.036670 − 0.779876I
a = −0.780160 + 0.133305I
b = 0.327917 − 0.979792I
−1.06082 − 3.18631I 0
u = 0.552589 + 0.430106I
a = −1.64524 + 0.28442I
b = 1.032220 + 0.058574I
2.41961 + 0.34900I 5.67559 + 0.69336I
u = 0.552589 − 0.430106I
a = −1.64524 − 0.28442I
b = 1.032220 − 0.058574I
2.41961 − 0.34900I 5.67559 − 0.69336I
u = −0.148725 + 1.301670I
a = −0.530595 + 0.740434I
b = 0.767567 − 0.682700I
0.33138 − 10.71180I 0
u = −0.148725 − 1.301670I
a = −0.530595 − 0.740434I
b = 0.767567 + 0.682700I
0.33138 + 10.71180I 0
u = 1.220660 + 0.503248I
a = −0.890977 − 0.373556I
b = 1.15837 − 1.27935I
2.20718 − 9.21559I 0
u = 1.220660 − 0.503248I
a = −0.890977 + 0.373556I
b = 1.15837 + 1.27935I
2.20718 + 9.21559I 0
u = −1.32135
a = 0.470030
b = −1.92284
−3.01024 0
u = −1.282490 + 0.377633I
a = −1.306930 + 0.361809I
b = 0.939471 + 0.891330I
−6.96009 + 10.29770I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.282490 − 0.377633I
a = −1.306930 − 0.361809I
b = 0.939471 − 0.891330I
−6.96009 − 10.29770I 0
u = −0.230086 + 0.571128I
a = −1.52959 − 0.58458I
b = 0.360119 + 0.766641I
−0.07957 + 2.04453I 1.68178 − 3.11842I
u = −0.230086 − 0.571128I
a = −1.52959 + 0.58458I
b = 0.360119 − 0.766641I
−0.07957 − 2.04453I 1.68178 + 3.11842I
u = 0.603771 + 0.027652I
a = 1.30220 − 1.60314I
b = −0.026312 − 1.201250I
−1.77198 + 6.54158I −1.95190 − 4.07828I
u = 0.603771 − 0.027652I
a = 1.30220 + 1.60314I
b = −0.026312 + 1.201250I
−1.77198 − 6.54158I −1.95190 + 4.07828I
u = 1.41437 + 0.17024I
a = −0.578378 − 0.040899I
b = 1.37461 − 0.73147I
−7.33407 − 4.81411I 0
u = 1.41437 − 0.17024I
a = −0.578378 + 0.040899I
b = 1.37461 + 0.73147I
−7.33407 + 4.81411I 0
u = 0.131343 + 0.540464I
a = −1.041380 − 0.558162I
b = 0.427017 + 0.464554I
0.725380 + 1.180740I 4.24551 − 4.64635I
u = 0.131343 − 0.540464I
a = −1.041380 + 0.558162I
b = 0.427017 − 0.464554I
0.725380 − 1.180740I 4.24551 + 4.64635I
u = −1.24203 + 0.75104I
a = −0.513911 − 0.174215I
b = 0.208309 + 0.988394I
−1.64043 + 3.35164I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.24203 − 0.75104I
a = −0.513911 + 0.174215I
b = 0.208309 − 0.988394I
−1.64043 − 3.35164I 0
u = −1.46335 + 0.12164I
a = 0.480507 + 0.020198I
b = −0.528818 − 0.273350I
−3.43024 + 0.04199I 0
u = −1.46335 − 0.12164I
a = 0.480507 − 0.020198I
b = −0.528818 + 0.273350I
−3.43024 − 0.04199I 0
u = 1.34178 + 0.60423I
a = −1.029560 − 0.209600I
b = 1.12935 − 1.20094I
−0.85217 − 12.06680I 0
u = 1.34178 − 0.60423I
a = −1.029560 + 0.209600I
b = 1.12935 + 1.20094I
−0.85217 + 12.06680I 0
u = −1.38287 + 0.55098I
a = 0.963569 − 0.160924I
b = −1.14535 − 1.18423I
−5.82286 + 8.54509I 0
u = −1.38287 − 0.55098I
a = 0.963569 + 0.160924I
b = −1.14535 + 1.18423I
−5.82286 − 8.54509I 0
u = −1.36397 + 0.63423I
a = 1.064370 − 0.179821I
b = −1.12193 − 1.19463I
−3.5526 + 17.3742I 0
u = −1.36397 − 0.63423I
a = 1.064370 + 0.179821I
b = −1.12193 + 1.19463I
−3.5526 − 17.3742I 0
u = 1.51493 + 0.02764I
a = −0.466561 + 0.057922I
b = 0.646933 − 0.507679I
−6.87250 + 4.47387I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.51493 − 0.02764I
a = −0.466561 − 0.057922I
b = 0.646933 + 0.507679I
−6.87250 − 4.47387I 0
u = 1.38354 + 0.69467I
a = 0.327847 − 0.218814I
b = −0.099863 + 0.997213I
−4.70888 + 0.05763I 0
u = 1.38354 − 0.69467I
a = 0.327847 + 0.218814I
b = −0.099863 − 0.997213I
−4.70888 − 0.05763I 0
u = 1.32097 + 0.83036I
a = 0.479237 − 0.302029I
b = −0.183639 + 1.056270I
−4.21471 − 7.50514I 0
u = 1.32097 − 0.83036I
a = 0.479237 + 0.302029I
b = −0.183639 − 1.056270I
−4.21471 + 7.50514I 0
u = 1.64763 + 0.24323I
a = −0.462216 + 0.038991I
b = 0.502599 − 0.125500I
−7.01352 − 4.49963I 0
u = 1.64763 − 0.24323I
a = −0.462216 − 0.038991I
b = 0.502599 + 0.125500I
−7.01352 + 4.49963I 0
u = 0.194550 + 0.184951I
a = 4.04115 − 1.45822I
b = −0.085459 + 0.814007I
−3.77027 + 0.40204I −7.60841 − 1.19387I
u = 0.194550 − 0.184951I
a = 4.04115 + 1.45822I
b = −0.085459 − 0.814007I
−3.77027 − 0.40204I −7.60841 + 1.19387I
13
II.
I
u
2
= h−u
14
+u
13
+· · ·−u
2
+b, −7u
14
+6u
13
+· · ·+a+7, u
15
−u
14
+· · ·−u+1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
u
2
a
8
=
7u
14
− 6u
13
+ ··· − 23u − 7
u
14
− u
13
+ ··· + 7u
3
+ u
2
a
9
=
8u
14
− 7u
13
+ ··· − 23u − 7
u
14
− u
13
+ ··· + 7u
3
+ u
2
a
6
=
−7u
14
− u
13
+ ··· − 142u
2
+ 31
−u
13
+ u
12
+ ··· − 6u
2
− u
a
1
=
−u
−u
3
+ u
a
10
=
−23u
14
+ 17u
13
+ ··· + 52u + 24
u
14
− u
13
+ ··· − 6u − 1
a
3
=
18u
14
− u
13
+ ··· − 8u − 52
−u
14
+ 7u
12
+ ··· − 25u
2
+ 6
a
2
=
22u
14
− u
13
+ ··· − 9u − 63
−4u
14
+ 27u
12
+ ··· + u + 13
a
7
=
−37u
14
+ 15u
13
+ ··· + 32u + 61
12u
14
− 8u
13
+ ··· − 17u − 12
a
7
=
−37u
14
+ 15u
13
+ ··· + 32u + 61
12u
14
− 8u
13
+ ··· − 17u − 12
(ii) Obstruction class = 1
(iii) Cusp Shapes = −50u
14
+ 49u
13
+ 284u
12
− 223u
11
− 761u
10
+ 533u
9
+ 1213u
8
−
928u
7
− 1180u
6
+ 910u
5
+ 666u
4
− 532u
3
− 178u
2
+ 116u + 19
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
+ 4u
13
+ 8u
11
− u
10
+ 8u
9
− 3u
8
+ 4u
7
− 5u
6
− 5u
4
− 3u
2
− 1
c
2
u
15
+ 8u
14
+ ··· − 6u − 1
c
3
u
15
+ u
13
− u
12
− 2u
11
− 2u
9
+ 4u
8
+ 2u
7
+ u
5
− 4u
4
+ 1
c
4
u
15
− u
14
+ ··· − u + 1
c
5
u
15
− u
14
+ ··· − u + 1
c
6
u
15
+ 4u
13
+ 8u
11
+ u
10
+ 8u
9
+ 3u
8
+ 4u
7
+ 5u
6
+ 5u
4
+ 3u
2
+ 1
c
7
u
15
− 4u
13
+ ··· + 2u + 1
c
8
u
15
− 4u
11
+ u
10
+ 2u
8
+ 4u
7
− 2u
6
− 2u
4
− u
3
+ u
2
+ 1
c
9
u
15
+ u
14
+ ··· − u − 1
c
10
u
15
− 4u
13
+ ··· + 7u + 1
c
11
u
15
+ u
14
+ ··· − u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
15
+ 8y
14
+ ··· − 6y −1
c
2
y
15
+ 16y
13
+ ··· − 2y −1
c
3
y
15
+ 2y
14
+ ··· + 8y
2
− 1
c
4
, c
11
y
15
− 13y
14
+ ··· + 15y −1
c
5
, c
9
y
15
− 15y
14
+ ··· + 13y −1
c
7
y
15
− 8y
14
+ ··· − 10y −1
c
8
y
15
− 8y
13
+ ··· − 2y −1
c
10
y
15
− 8y
14
+ ··· + 7y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.906864 + 0.375829I
a = −0.537067 + 0.586861I
b = −0.058211 + 1.303160I
0.29078 + 2.83345I 2.46812 − 4.57300I
u = −0.906864 − 0.375829I
a = −0.537067 − 0.586861I
b = −0.058211 − 1.303160I
0.29078 − 2.83345I 2.46812 + 4.57300I
u = 0.786429 + 0.437105I
a = 0.904328 + 0.831344I
b = 0.187116 + 0.988050I
−1.62575 − 7.79387I −1.04019 + 8.56161I
u = 0.786429 − 0.437105I
a = 0.904328 − 0.831344I
b = 0.187116 − 0.988050I
−1.62575 + 7.79387I −1.04019 − 8.56161I
u = 0.878542 + 0.674122I
a = 0.998231 + 0.130624I
b = −0.106366 + 0.803002I
−3.32177 − 0.98994I −4.43129 + 2.79552I
u = 0.878542 − 0.674122I
a = 0.998231 − 0.130624I
b = −0.106366 − 0.803002I
−3.32177 + 0.98994I −4.43129 − 2.79552I
u = −1.121450 + 0.726120I
a = −0.692219 + 0.007640I
b = 0.323008 + 0.742064I
−2.02887 + 3.34950I −5.67040 − 7.67904I
u = −1.121450 − 0.726120I
a = −0.692219 − 0.007640I
b = 0.323008 − 0.742064I
−2.02887 − 3.34950I −5.67040 + 7.67904I
u = −0.650838 + 0.048933I
a = 1.97813 + 0.68804I
b = −1.101810 + 0.205790I
3.03538 + 0.81175I 4.74302 − 6.70940I
u = −0.650838 − 0.048933I
a = 1.97813 − 0.68804I
b = −1.101810 − 0.205790I
3.03538 − 0.81175I 4.74302 + 6.70940I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.600420 + 0.033463I
a = −2.87415 + 0.67196I
b = 0.930317 + 0.110590I
1.74022 + 3.03027I 6.59174 − 2.91144I
u = 0.600420 − 0.033463I
a = −2.87415 − 0.67196I
b = 0.930317 − 0.110590I
1.74022 − 3.03027I 6.59174 + 2.91144I
u = −1.41375
a = −0.353438
b = 1.41559
−2.66084 10.5800
u = 1.62063 + 0.25048I
a = 0.399460 + 0.007533I
b = −0.881854 + 0.297666I
−6.62917 − 4.72492I 6.04899 + 6.78091I
u = 1.62063 − 0.25048I
a = 0.399460 − 0.007533I
b = −0.881854 − 0.297666I
−6.62917 + 4.72492I 6.04899 − 6.78091I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
15
+ 4u
13
+ 8u
11
− u
10
+ 8u
9
− 3u
8
+ 4u
7
− 5u
6
− 5u
4
− 3u
2
− 1)
· (u
89
+ u
88
+ ··· + u + 1)
c
2
(u
15
+ 8u
14
+ ··· − 6u − 1)(u
89
+ 45u
88
+ ··· − 7u − 1)
c
3
(u
15
+ u
13
− u
12
− 2u
11
− 2u
9
+ 4u
8
+ 2u
7
+ u
5
− 4u
4
+ 1)
· (u
89
− 3u
88
+ ··· + 27u + 1)
c
4
(u
15
− u
14
+ ··· − u + 1)(u
89
− 30u
87
+ ··· − 598u + 131)
c
5
(u
15
− u
14
+ ··· − u + 1)(u
89
− 27u
87
+ ··· + 2u − 1)
c
6
(u
15
+ 4u
13
+ 8u
11
+ u
10
+ 8u
9
+ 3u
8
+ 4u
7
+ 5u
6
+ 5u
4
+ 3u
2
+ 1)
· (u
89
+ u
88
+ ··· + u + 1)
c
7
(u
15
− 4u
13
+ ··· + 2u + 1)(u
89
− u
88
+ ··· − 219u + 3737)
c
8
(u
15
− 4u
11
+ u
10
+ 2u
8
+ 4u
7
− 2u
6
− 2u
4
− u
3
+ u
2
+ 1)
· (u
89
+ u
88
+ ··· − 11u + 3)
c
9
(u
15
+ u
14
+ ··· − u − 1)(u
89
− 27u
87
+ ··· + 2u − 1)
c
10
(u
15
− 4u
13
+ ··· + 7u + 1)(u
89
− 11u
88
+ ··· + 2752u − 593)
c
11
(u
15
+ u
14
+ ··· − u − 1)(u
89
− 30u
87
+ ··· − 598u + 131)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
15
+ 8y
14
+ ··· − 6y −1)(y
89
+ 45y
88
+ ··· − 7y −1)
c
2
(y
15
+ 16y
13
+ ··· − 2y −1)(y
89
+ y
88
+ ··· − 39y −1)
c
3
(y
15
+ 2y
14
+ ··· + 8y
2
− 1)(y
89
+ 3y
88
+ ··· + 143y −1)
c
4
, c
11
(y
15
− 13y
14
+ ··· + 15y −1)(y
89
− 60y
88
+ ··· + 397166y −17161)
c
5
, c
9
(y
15
− 15y
14
+ ··· + 13y −1)(y
89
− 54y
88
+ ··· + 32y −1)
c
7
(y
15
− 8y
14
+ ··· − 10y −1)
· (y
89
− 43y
88
+ ··· − 186682455y −13965169)
c
8
(y
15
− 8y
13
+ ··· − 2y −1)(y
89
+ 5y
88
+ ··· + 181y −9)
c
10
(y
15
− 8y
14
+ ··· + 7y −1)(y
89
− 27y
88
+ ··· + 8974170y −351649)
20
