11a
283
(K11a
283
)
A knot diagram
1
Linearized knot diagam
6 9 1 11 2 10 4 3 5 7 8
Solving Sequence
2,9 3,6
1 4 5 10 8 7 11
c
2
c
1
c
3
c
5
c
9
c
8
c
7
c
11
c
4
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.41985 × 10
252
u
85
+ 4.09833 × 10
252
u
84
+ ··· + 1.22301 × 10
255
b − 6.27945 × 10
254
,
− 1.71138 × 10
256
u
85
+ 1.63229 × 10
256
u
84
+ ··· + 1.02611 × 10
258
a + 4.21212 × 10
259
,
u
86
− u
85
+ ··· − 4313u + 839i
I
u
2
= h6846u
19
− 8204u
18
+ ··· + 20003b − 10945,
− 1034553u
19
− 1458425u
18
+ ··· + 1180177a − 4013026, u
20
+ 8u
18
+ ··· − 3u + 1i
I
u
3
= hu
2
+ b, a − 1, u
7
+ u
5
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 113 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−3.42 × 10
252
u
85
+ 4.10 × 10
252
u
84
+ · · · + 1.22 × 10
255
b − 6.28 ×
10
254
, −1.71 × 10
256
u
85
+ 1.63 × 10
256
u
84
+ · · · + 1.03 × 10
258
a + 4.21 ×
10
259
, u
86
− u
85
+ · · · − 4313u + 839i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
−u
2
a
6
=
0.0166784u
85
− 0.0159077u
84
+ ··· + 114.699u − 41.0496
0.00279626u
85
− 0.00335102u
84
+ ··· + 16.6837u + 0.513442
a
1
=
0.00695378u
85
− 0.000700898u
84
+ ··· + 21.3589u + 9.44845
−0.0173378u
85
+ 0.0147297u
84
+ ··· − 102.814u + 31.6226
a
4
=
−0.00332478u
85
+ 0.000929287u
84
+ ··· − 42.6202u + 8.23376
0.00603896u
85
− 0.00447428u
84
+ ··· + 28.7233u − 4.85824
a
5
=
0.0138821u
85
− 0.0125566u
84
+ ··· + 98.0158u − 41.5631
0.00279626u
85
− 0.00335102u
84
+ ··· + 16.6837u + 0.513442
a
10
=
−0.00463099u
85
− 0.00234483u
84
+ ··· − 22.7331u − 11.9767
0.00886090u
85
− 0.00901715u
84
+ ··· + 82.5953u − 20.3806
a
8
=
−u
u
3
+ u
a
7
=
0.00673940u
85
− 0.00311584u
84
+ ··· + 1.27697u + 5.88708
0.00790831u
85
− 0.0112601u
84
+ ··· + 23.7107u − 8.85273
a
11
=
0.0104754u
85
− 0.00701084u
84
+ ··· + 43.4674u + 6.56795
−0.0169282u
85
+ 0.0130534u
84
+ ··· − 109.942u + 32.1637
a
11
=
0.0104754u
85
− 0.00701084u
84
+ ··· + 43.4674u + 6.56795
−0.0169282u
85
+ 0.0130534u
84
+ ··· − 109.942u + 32.1637
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0966063u
85
+ 0.0534792u
84
+ ··· − 636.168u + 175.613
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
86
− 2u
85
+ ··· + 4061u + 367
c
2
, c
8
u
86
+ u
85
+ ··· + 4313u + 839
c
3
u
86
− 10u
85
+ ··· − 578u + 79
c
4
u
86
− 5u
85
+ ··· + 16u + 1
c
6
, c
10
u
86
+ 6u
85
+ ··· − 2700u + 200
c
7
u
86
+ 4u
85
+ ··· + 379u + 169
c
9
u
86
+ u
85
+ ··· + 760266u + 130321
c
11
u
86
+ 5u
85
+ ··· + 690u + 179
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
86
+ 58y
85
+ ··· − 1366917y + 134689
c
2
, c
8
y
86
+ 73y
85
+ ··· − 7899685y + 703921
c
3
y
86
− 14y
85
+ ··· − 153964y + 6241
c
4
y
86
− 5y
85
+ ··· + 200y + 1
c
6
, c
10
y
86
− 58y
85
+ ··· − 4211600y + 40000
c
7
y
86
+ 14y
85
+ ··· + 1122169y + 28561
c
9
y
86
+ 15y
85
+ ··· + 56388593490y + 16983563041
c
11
y
86
− 19y
85
+ ··· − 1161312y + 32041
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.171045 + 0.950486I
a = 1.09878 + 2.26346I
b = 0.131608 + 0.877201I
1.71658 + 1.70443I 0
u = −0.171045 − 0.950486I
a = 1.09878 − 2.26346I
b = 0.131608 − 0.877201I
1.71658 − 1.70443I 0
u = −0.138042 + 1.039980I
a = 0.718636 + 0.240255I
b = −0.712835 + 0.801059I
1.54553 − 2.70454I 0
u = −0.138042 − 1.039980I
a = 0.718636 − 0.240255I
b = −0.712835 − 0.801059I
1.54553 + 2.70454I 0
u = −0.942410 + 0.113313I
a = 0.158648 + 0.099081I
b = 0.455331 + 1.100300I
2.54751 + 4.69288I 0
u = −0.942410 − 0.113313I
a = 0.158648 − 0.099081I
b = 0.455331 − 1.100300I
2.54751 − 4.69288I 0
u = 1.066980 + 0.013369I
a = 0.510040 − 0.562808I
b = −0.334819 − 1.068070I
−1.17731 + 3.15707I 0
u = 1.066980 − 0.013369I
a = 0.510040 + 0.562808I
b = −0.334819 + 1.068070I
−1.17731 − 3.15707I 0
u = 0.597375 + 0.937187I
a = 0.251462 + 0.325322I
b = 0.177390 − 0.920746I
0.43505 + 5.35734I 0
u = 0.597375 − 0.937187I
a = 0.251462 − 0.325322I
b = 0.177390 + 0.920746I
0.43505 − 5.35734I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.139913 + 1.108380I
a = −0.618464 + 0.196975I
b = −1.38818 + 0.35705I
2.56807 + 2.29900I 0
u = 0.139913 − 1.108380I
a = −0.618464 − 0.196975I
b = −1.38818 − 0.35705I
2.56807 − 2.29900I 0
u = −0.499950 + 1.009240I
a = 0.185257 − 0.499774I
b = 0.305862 + 0.044581I
−0.75390 − 3.34791I 0
u = −0.499950 − 1.009240I
a = 0.185257 + 0.499774I
b = 0.305862 − 0.044581I
−0.75390 + 3.34791I 0
u = −0.821993 + 0.102956I
a = −0.655973 + 0.796214I
b = 0.798776 + 0.329650I
4.82477 − 6.81993I 10.08009 + 4.71115I
u = −0.821993 − 0.102956I
a = −0.655973 − 0.796214I
b = 0.798776 − 0.329650I
4.82477 + 6.81993I 10.08009 − 4.71115I
u = −0.199723 + 1.160210I
a = −0.01752 − 3.29341I
b = 0.083947 − 0.961969I
0.51451 − 6.45826I 0
u = −0.199723 − 1.160210I
a = −0.01752 + 3.29341I
b = 0.083947 + 0.961969I
0.51451 + 6.45826I 0
u = −0.512127 + 0.559479I
a = 1.93509 − 0.19891I
b = −0.484188 − 0.707780I
2.45089 + 3.89737I 6.40177 − 6.57898I
u = −0.512127 − 0.559479I
a = 1.93509 + 0.19891I
b = −0.484188 + 0.707780I
2.45089 − 3.89737I 6.40177 + 6.57898I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.057454 + 1.246560I
a = 0.37475 − 1.69448I
b = −0.60933 − 1.42722I
−7.29903 + 0.31589I 0
u = 0.057454 − 1.246560I
a = 0.37475 + 1.69448I
b = −0.60933 + 1.42722I
−7.29903 − 0.31589I 0
u = 0.412211 + 1.181190I
a = 0.60682 − 1.66020I
b = −0.23005 − 1.40830I
−4.58690 + 2.56469I 0
u = 0.412211 − 1.181190I
a = 0.60682 + 1.66020I
b = −0.23005 + 1.40830I
−4.58690 − 2.56469I 0
u = −0.163970 + 1.241080I
a = −1.07090 − 2.17182I
b = 0.44077 − 1.34783I
−4.48521 − 6.86672I 0
u = −0.163970 − 1.241080I
a = −1.07090 + 2.17182I
b = 0.44077 + 1.34783I
−4.48521 + 6.86672I 0
u = 1.203600 + 0.344486I
a = −0.387817 + 0.567429I
b = 0.500645 + 1.141340I
2.30617 + 11.65450I 0
u = 1.203600 − 0.344486I
a = −0.387817 − 0.567429I
b = 0.500645 − 1.141340I
2.30617 − 11.65450I 0
u = −0.662167 + 0.294205I
a = 0.461786 + 0.309921I
b = −0.610997 + 1.105130I
2.64706 − 4.13307I 10.06650 + 7.67107I
u = −0.662167 − 0.294205I
a = 0.461786 − 0.309921I
b = −0.610997 − 1.105130I
2.64706 + 4.13307I 10.06650 − 7.67107I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.297470 + 1.255920I
a = −0.254293 − 0.144773I
b = −1.077280 − 0.185503I
−3.52274 + 6.07547I 0
u = 0.297470 − 1.255920I
a = −0.254293 + 0.144773I
b = −1.077280 + 0.185503I
−3.52274 − 6.07547I 0
u = 0.689327 + 0.123250I
a = 0.062912 + 1.059920I
b = 0.395529 + 0.164925I
0.06236 − 2.46466I 6.83396 + 3.77647I
u = 0.689327 − 0.123250I
a = 0.062912 − 1.059920I
b = 0.395529 − 0.164925I
0.06236 + 2.46466I 6.83396 − 3.77647I
u = 0.226747 + 1.282130I
a = −0.093690 − 0.200426I
b = 0.679000 − 0.036087I
−4.40326 + 0.41121I 0
u = 0.226747 − 1.282130I
a = −0.093690 + 0.200426I
b = 0.679000 + 0.036087I
−4.40326 − 0.41121I 0
u = −0.366588 + 1.260050I
a = 0.098420 − 0.273942I
b = 0.880454 + 0.085541I
−2.11426 − 4.00334I 0
u = −0.366588 − 1.260050I
a = 0.098420 + 0.273942I
b = 0.880454 − 0.085541I
−2.11426 + 4.00334I 0
u = −0.099264 + 1.314460I
a = 0.406154 + 0.976917I
b = 0.732172 + 0.382522I
0.50203 + 2.48920I 0
u = −0.099264 − 1.314460I
a = 0.406154 − 0.976917I
b = 0.732172 − 0.382522I
0.50203 − 2.48920I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.173406 + 1.315340I
a = −0.96739 + 1.70783I
b = 0.294787 + 1.239180I
−8.25891 + 3.00812I 0
u = 0.173406 − 1.315340I
a = −0.96739 − 1.70783I
b = 0.294787 − 1.239180I
−8.25891 − 3.00812I 0
u = −0.409443 + 1.263900I
a = 0.49046 + 1.63199I
b = −0.65824 + 1.38913I
−1.10942 − 9.46579I 0
u = −0.409443 − 1.263900I
a = 0.49046 − 1.63199I
b = −0.65824 − 1.38913I
−1.10942 + 9.46579I 0
u = 0.050986 + 1.328260I
a = 0.22173 + 1.98084I
b = −0.21254 + 1.53110I
−6.21226 + 5.37580I 0
u = 0.050986 − 1.328260I
a = 0.22173 − 1.98084I
b = −0.21254 − 1.53110I
−6.21226 − 5.37580I 0
u = 0.232857 + 1.345360I
a = −0.25117 + 2.15847I
b = 0.313690 + 1.368680I
−5.14196 + 5.75508I 0
u = 0.232857 − 1.345360I
a = −0.25117 − 2.15847I
b = 0.313690 − 1.368680I
−5.14196 − 5.75508I 0
u = −0.500434 + 0.387851I
a = 0.492345 + 0.241918I
b = −0.431811 + 0.295599I
0.948430 − 0.603776I 9.01347 + 4.18465I
u = −0.500434 − 0.387851I
a = 0.492345 − 0.241918I
b = −0.431811 − 0.295599I
0.948430 + 0.603776I 9.01347 − 4.18465I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.042870 + 1.391350I
a = −0.08872 − 1.61352I
b = 0.455918 − 1.278250I
−6.14811 − 0.65193I 0
u = 0.042870 − 1.391350I
a = −0.08872 + 1.61352I
b = 0.455918 + 1.278250I
−6.14811 + 0.65193I 0
u = −0.359631 + 1.348720I
a = −0.470643 + 0.056389I
b = −1.242270 − 0.193872I
0.23737 − 11.07660I 0
u = −0.359631 − 1.348720I
a = −0.470643 − 0.056389I
b = −1.242270 + 0.193872I
0.23737 + 11.07660I 0
u = 0.596230 + 0.035731I
a = 0.684599 + 0.947731I
b = −0.411492 + 0.980008I
−0.80790 − 2.80909I 5.98332 − 0.21201I
u = 0.596230 − 0.035731I
a = 0.684599 − 0.947731I
b = −0.411492 − 0.980008I
−0.80790 + 2.80909I 5.98332 + 0.21201I
u = 0.417303 + 0.405708I
a = 0.14693 + 2.04390I
b = 0.765463 + 0.496537I
4.56662 − 0.11637I 12.84009 − 2.25680I
u = 0.417303 − 0.405708I
a = 0.14693 − 2.04390I
b = 0.765463 − 0.496537I
4.56662 + 0.11637I 12.84009 + 2.25680I
u = −0.26413 + 1.40109I
a = −0.28448 − 1.99461I
b = 0.66711 − 1.46071I
−2.71748 − 7.52821I 0
u = −0.26413 − 1.40109I
a = −0.28448 + 1.99461I
b = 0.66711 + 1.46071I
−2.71748 + 7.52821I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.10686 + 1.50124I
a = −0.245884 + 1.141140I
b = 0.783069 + 1.067070I
−5.72875 + 3.11452I 0
u = 0.10686 − 1.50124I
a = −0.245884 − 1.141140I
b = 0.783069 − 1.067070I
−5.72875 − 3.11452I 0
u = −0.22724 + 1.49618I
a = −0.81530 − 1.31196I
b = −0.020931 − 0.994862I
−3.17742 + 0.08844I 0
u = −0.22724 − 1.49618I
a = −0.81530 + 1.31196I
b = −0.020931 + 0.994862I
−3.17742 − 0.08844I 0
u = 0.54898 + 1.41093I
a = −0.82747 + 1.53406I
b = 0.517955 + 1.251330I
−5.61570 + 9.08985I 0
u = 0.54898 − 1.41093I
a = −0.82747 − 1.53406I
b = 0.517955 − 1.251330I
−5.61570 − 9.08985I 0
u = −1.41382 + 0.54274I
a = −0.150367 − 0.669536I
b = 0.207903 − 1.033730I
−2.09582 − 4.89045I 0
u = −1.41382 − 0.54274I
a = −0.150367 + 0.669536I
b = 0.207903 + 1.033730I
−2.09582 + 4.89045I 0
u = −0.68545 + 1.36638I
a = 0.30951 + 1.38848I
b = −0.088050 + 0.737680I
1.18894 + 2.12493I 0
u = −0.68545 − 1.36638I
a = 0.30951 − 1.38848I
b = −0.088050 − 0.737680I
1.18894 − 2.12493I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.48985 + 1.50866I
a = 0.52759 − 1.65020I
b = −0.63184 − 1.35216I
−3.4892 + 17.6295I 0
u = 0.48985 − 1.50866I
a = 0.52759 + 1.65020I
b = −0.63184 + 1.35216I
−3.4892 − 17.6295I 0
u = 0.386003 + 0.111568I
a = 0.72617 − 1.21676I
b = −1.015930 − 0.376348I
4.95207 + 1.65937I 17.2147 − 3.6067I
u = 0.386003 − 0.111568I
a = 0.72617 + 1.21676I
b = −1.015930 + 0.376348I
4.95207 − 1.65937I 17.2147 + 3.6067I
u = −0.48750 + 1.53880I
a = 0.43487 + 1.58941I
b = −0.44392 + 1.36956I
−8.42324 − 11.27470I 0
u = −0.48750 − 1.53880I
a = 0.43487 − 1.58941I
b = −0.44392 − 1.36956I
−8.42324 + 11.27470I 0
u = 1.29645 + 0.97439I
a = −0.150528 + 0.680017I
b = −0.180507 + 0.936717I
0.43071 − 3.88005I 0
u = 1.29645 − 0.97439I
a = −0.150528 − 0.680017I
b = −0.180507 − 0.936717I
0.43071 + 3.88005I 0
u = 0.360463 + 0.104511I
a = 1.71701 + 1.38281I
b = 0.099604 − 1.152090I
−3.81257 + 0.89485I −2.25949 − 1.18834I
u = 0.360463 − 0.104511I
a = 1.71701 − 1.38281I
b = 0.099604 + 1.152090I
−3.81257 − 0.89485I −2.25949 + 1.18834I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.67498 + 1.51204I
a = 0.37015 − 1.38509I
b = −0.106244 − 1.278550I
−5.01653 + 3.29033I 0
u = 0.67498 − 1.51204I
a = 0.37015 + 1.38509I
b = −0.106244 + 1.278550I
−5.01653 − 3.29033I 0
u = −0.46654 + 1.63346I
a = −0.45448 − 1.42613I
b = 0.380524 − 1.198130I
−7.86731 − 4.29450I 0
u = −0.46654 − 1.63346I
a = −0.45448 + 1.42613I
b = 0.380524 + 1.198130I
−7.86731 + 4.29450I 0
u = −0.176850 + 0.211457I
a = −0.89004 + 2.77259I
b = −0.176063 − 1.280020I
−1.21164 + 5.29604I 2.45054 − 8.48280I
u = −0.176850 − 0.211457I
a = −0.89004 − 2.77259I
b = −0.176063 + 1.280020I
−1.21164 − 5.29604I 2.45054 + 8.48280I
13
II. I
u
2
= h6846u
19
− 8204u
18
+ · · · + 20003b − 10945, −1.03 × 10
6
u
19
− 1.46 ×
10
6
u
18
+ · · · + 1.18 × 10
6
a − 4.01 × 10
6
, u
20
+ 8u
18
+ · · · − 3u + 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
−u
2
a
6
=
0.876608u
19
+ 1.23577u
18
+ ··· + 8.53335u + 3.40036
−0.342249u
19
+ 0.410138u
18
+ ··· − 6.46158u + 0.547168
a
1
=
−1.40383u
19
− 0.0923734u
18
+ ··· − 20.8719u + 3.90800
0.167425u
19
− 0.0554417u
18
+ ··· + 6.79533u − 1.60261
a
4
=
1.36417u
19
+ 0.513748u
18
+ ··· + 15.8727u + 4.11256
−0.305317u
19
− 0.405635u
18
+ ··· − 3.25843u − 1.02408
a
5
=
1.21886u
19
+ 0.825630u
18
+ ··· + 14.9949u + 2.85319
−0.342249u
19
+ 0.410138u
18
+ ··· − 6.46158u + 0.547168
a
10
=
0.174699u
19
− 0.367753u
18
+ ··· + 16.3113u − 10.5613
−0.0369317u
19
− 0.184227u
18
+ ··· + 0.796852u + 1.57125
a
8
=
−u
u
3
+ u
a
7
=
1.94985u
19
− 0.957305u
18
+ ··· + 31.9571u − 11.4011
−0.576662u
19
+ 0.967471u
18
+ ··· − 7.65168u + 3.29611
a
11
=
−1.29989u
19
− 0.143133u
18
+ ··· − 20.2101u + 4.10267
−0.0511322u
19
− 0.298609u
18
+ ··· + 6.38976u − 1.84804
a
11
=
−1.29989u
19
− 0.143133u
18
+ ··· − 20.2101u + 4.10267
−0.0511322u
19
− 0.298609u
18
+ ··· + 6.38976u − 1.84804
(ii) Obstruction class = 1
(iii) Cusp Shapes =
296410
1180177
u
19
−
1621082
1180177
u
18
+ ··· −
15966826
1180177
u +
14861551
1180177
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
− u
19
+ ··· + 3u + 1
c
2
u
20
+ 8u
18
+ ··· − 3u + 1
c
3
u
20
+ 3u
19
+ ··· − 2u + 1
c
4
u
20
− 7u
18
+ ··· − 4u + 1
c
5
u
20
+ u
19
+ ··· − 3u + 1
c
6
u
20
− 8u
18
+ ··· + 2u + 3
c
7
u
20
− u
19
+ ··· − 3u + 1
c
8
u
20
+ 8u
18
+ ··· + 3u + 1
c
9
u
20
− 3u
18
+ ··· − 6u + 1
c
10
u
20
− 8u
18
+ ··· − 2u + 3
c
11
u
20
− 4u
17
+ ··· − 2u
2
+ 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
20
+ 9y
19
+ ··· + 15y + 1
c
2
, c
8
y
20
+ 16y
19
+ ··· + 27y + 1
c
3
y
20
− 11y
19
+ ··· + 16y + 1
c
4
y
20
− 14y
19
+ ··· − 4y + 1
c
6
, c
10
y
20
− 16y
19
+ ··· + 62y + 9
c
7
y
20
+ 5y
19
+ ··· + 5y + 1
c
9
y
20
− 6y
19
+ ··· − 26y + 1
c
11
y
20
+ 12y
18
+ ··· − 4y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.946175 + 0.385588I
a = 0.214235 + 0.558661I
b = −0.269177 + 1.077330I
−0.64266 − 3.90221I 3.24651 + 7.37049I
u = 0.946175 − 0.385588I
a = 0.214235 − 0.558661I
b = −0.269177 − 1.077330I
−0.64266 + 3.90221I 3.24651 − 7.37049I
u = −0.310493 + 0.924049I
a = −0.38415 − 1.67139I
b = −0.122898 + 0.479259I
1.71598 − 6.19605I 8.61255 + 6.55788I
u = −0.310493 − 0.924049I
a = −0.38415 + 1.67139I
b = −0.122898 − 0.479259I
1.71598 + 6.19605I 8.61255 − 6.55788I
u = 0.591462 + 0.713970I
a = −0.402644 − 0.443888I
b = −0.208294 − 0.706719I
−1.58446 + 3.70556I −0.94050 − 4.83089I
u = 0.591462 − 0.713970I
a = −0.402644 + 0.443888I
b = −0.208294 + 0.706719I
−1.58446 − 3.70556I −0.94050 + 4.83089I
u = 0.002874 + 1.212570I
a = 0.870653 − 0.229034I
b = 1.42573 + 0.06190I
1.65051 − 1.14565I 6.04640 + 4.20488I
u = 0.002874 − 1.212570I
a = 0.870653 + 0.229034I
b = 1.42573 − 0.06190I
1.65051 + 1.14565I 6.04640 − 4.20488I
u = −0.002126 + 0.708303I
a = −0.640262 + 0.910371I
b = −0.901962 + 0.053941I
3.67242 + 1.15933I 9.29729 − 1.48128I
u = −0.002126 − 0.708303I
a = −0.640262 − 0.910371I
b = −0.901962 − 0.053941I
3.67242 − 1.15933I 9.29729 + 1.48128I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.273746 + 1.297500I
a = −0.66833 + 2.18325I
b = 0.48471 + 1.43675I
−3.70849 + 7.77575I 1.98042 − 8.91503I
u = 0.273746 − 1.297500I
a = −0.66833 − 2.18325I
b = 0.48471 − 1.43675I
−3.70849 − 7.77575I 1.98042 + 8.91503I
u = −0.15872 + 1.40819I
a = −0.46639 − 1.33897I
b = 0.520872 − 1.129990I
−7.04665 − 2.30270I −1.55456 + 0.79605I
u = −0.15872 − 1.40819I
a = −0.46639 + 1.33897I
b = 0.520872 + 1.129990I
−7.04665 + 2.30270I −1.55456 − 0.79605I
u = −0.85387 + 1.18820I
a = 0.71330 + 1.27008I
b = −0.028808 + 0.787340I
0.96215 + 2.51362I 0.64139 − 9.41977I
u = −0.85387 − 1.18820I
a = 0.71330 − 1.27008I
b = −0.028808 − 0.787340I
0.96215 − 2.51362I 0.64139 + 9.41977I
u = −0.56839 + 1.35898I
a = −0.46559 − 1.52661I
b = 0.125964 − 1.327280I
−4.70501 − 3.26631I 10.94198 + 7.13391I
u = −0.56839 − 1.35898I
a = −0.46559 + 1.52661I
b = 0.125964 + 1.327280I
−4.70501 + 3.26631I 10.94198 − 7.13391I
u = 0.079342 + 0.301023I
a = 2.72917 + 2.48490I
b = −0.526131 − 0.810997I
3.10647 + 2.21537I 10.72853 − 2.81043I
u = 0.079342 − 0.301023I
a = 2.72917 − 2.48490I
b = −0.526131 + 0.810997I
3.10647 − 2.21537I 10.72853 + 2.81043I
18
III. I
u
3
= hu
2
+ b, a − 1, u
7
+ u
5
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
−u
2
a
6
=
1
−u
2
a
1
=
−u
2
+ 1
u
4
a
4
=
−u
4
+ u
2
+ 1
u
6
− u
2
a
5
=
u
2
+ 1
−u
2
a
10
=
u
5
+ 2u
3
+ u
−u
5
− u
3
+ u
a
8
=
−u
u
3
+ u
a
7
=
u
5
+ 2u
3
+ u + 1
−u
5
− u
3
− u
2
+ u
a
11
=
1
−u
2
a
11
=
1
−u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
u
7
+ 2u
6
+ u
5
+ 2u
4
+ 2u
3
+ u − 1
c
2
, c
8
, c
11
u
7
+ u
5
+ u − 1
c
4
u
7
+ 2u
6
− 3u
5
− 2u
4
+ 10u
3
− 8u
2
+ u + 1
c
6
, c
10
(u − 1)
7
c
7
, c
9
u
7
+ 3u
5
− 4u
4
+ 4u
3
− 6u
2
+ 3u − 2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
y
7
− 2y
6
− 3y
5
+ 2y
4
+ 10y
3
+ 8y
2
+ y −1
c
2
, c
8
, c
11
y
7
+ 2y
6
+ y
5
+ 2y
4
+ 2y
3
+ y −1
c
4
y
7
− 10y
6
+ 37y
5
− 30y
4
+ 58y
3
− 40y
2
+ 17y −1
c
6
, c
10
(y −1)
7
c
7
, c
9
y
7
+ 6y
6
+ 17y
5
+ 14y
4
− 14y
3
− 28y
2
− 15y −4
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.862570 + 0.551757I
a = 1.00000
b = −0.439591 − 0.951858I
1.64493 6.00000
u = 0.862570 − 0.551757I
a = 1.00000
b = −0.439591 + 0.951858I
1.64493 6.00000
u = −0.588920 + 0.721443I
a = 1.00000
b = 0.173654 + 0.849744I
1.64493 6.00000
u = −0.588920 − 0.721443I
a = 1.00000
b = 0.173654 − 0.849744I
1.64493 6.00000
u = 0.084251 + 1.236620I
a = 1.00000
b = 1.52212 − 0.20837I
1.64493 6.00000
u = 0.084251 − 1.236620I
a = 1.00000
b = 1.52212 + 0.20837I
1.64493 6.00000
u = −0.715802
a = 1.00000
b = −0.512372
1.64493 6.00000
22
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
7
+ 2u
6
+ u
5
+ 2u
4
+ 2u
3
+ u − 1)(u
20
− u
19
+ ··· + 3u + 1)
· (u
86
− 2u
85
+ ··· + 4061u + 367)
c
2
(u
7
+ u
5
+ u − 1)(u
20
+ 8u
18
+ ··· − 3u + 1)
· (u
86
+ u
85
+ ··· + 4313u + 839)
c
3
(u
7
+ 2u
6
+ u
5
+ 2u
4
+ 2u
3
+ u − 1)(u
20
+ 3u
19
+ ··· − 2u + 1)
· (u
86
− 10u
85
+ ··· − 578u + 79)
c
4
(u
7
+ 2u
6
+ ··· + u + 1)(u
20
− 7u
18
+ ··· − 4u + 1)
· (u
86
− 5u
85
+ ··· + 16u + 1)
c
5
(u
7
+ 2u
6
+ u
5
+ 2u
4
+ 2u
3
+ u − 1)(u
20
+ u
19
+ ··· − 3u + 1)
· (u
86
− 2u
85
+ ··· + 4061u + 367)
c
6
((u − 1)
7
)(u
20
− 8u
18
+ ··· + 2u + 3)(u
86
+ 6u
85
+ ··· − 2700u + 200)
c
7
(u
7
+ 3u
5
+ ··· + 3u − 2)(u
20
− u
19
+ ··· − 3u + 1)
· (u
86
+ 4u
85
+ ··· + 379u + 169)
c
8
(u
7
+ u
5
+ u − 1)(u
20
+ 8u
18
+ ··· + 3u + 1)
· (u
86
+ u
85
+ ··· + 4313u + 839)
c
9
(u
7
+ 3u
5
+ ··· + 3u − 2)(u
20
− 3u
18
+ ··· − 6u + 1)
· (u
86
+ u
85
+ ··· + 760266u + 130321)
c
10
((u − 1)
7
)(u
20
− 8u
18
+ ··· − 2u + 3)(u
86
+ 6u
85
+ ··· − 2700u + 200)
c
11
(u
7
+ u
5
+ u − 1)(u
20
− 4u
17
+ ··· − 2u
2
+ 1)
· (u
86
+ 5u
85
+ ··· + 690u + 179)
23
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
7
− 2y
6
+ ··· + y −1)(y
20
+ 9y
19
+ ··· + 15y + 1)
· (y
86
+ 58y
85
+ ··· − 1366917y + 134689)
c
2
, c
8
(y
7
+ 2y
6
+ y
5
+ 2y
4
+ 2y
3
+ y −1)(y
20
+ 16y
19
+ ··· + 27y + 1)
· (y
86
+ 73y
85
+ ··· − 7899685y + 703921)
c
3
(y
7
− 2y
6
− 3y
5
+ 2y
4
+ 10y
3
+ 8y
2
+ y −1)
· (y
20
− 11y
19
+ ··· + 16y + 1)(y
86
− 14y
85
+ ··· − 153964y + 6241)
c
4
(y
7
− 10y
6
+ 37y
5
− 30y
4
+ 58y
3
− 40y
2
+ 17y −1)
· (y
20
− 14y
19
+ ··· − 4y + 1)(y
86
− 5y
85
+ ··· + 200y + 1)
c
6
, c
10
((y −1)
7
)(y
20
− 16y
19
+ ··· + 62y + 9)
· (y
86
− 58y
85
+ ··· − 4211600y + 40000)
c
7
(y
7
+ 6y
6
+ 17y
5
+ 14y
4
− 14y
3
− 28y
2
− 15y −4)
· (y
20
+ 5y
19
+ ··· + 5y + 1)(y
86
+ 14y
85
+ ··· + 1122169y + 28561)
c
9
(y
7
+ 6y
6
+ 17y
5
+ 14y
4
− 14y
3
− 28y
2
− 15y −4)
· (y
20
− 6y
19
+ ··· − 26y + 1)
· (y
86
+ 15y
85
+ ··· + 56388593490y + 16983563041)
c
11
(y
7
+ 2y
6
+ y
5
+ 2y
4
+ 2y
3
+ y −1)(y
20
+ 12y
18
+ ··· − 4y + 1)
· (y
86
− 19y
85
+ ··· − 1161312y + 32041)
24
