12a
0415
(K12a
0415
)
A knot diagram
1
Linearized knot diagam
3 6 9 12 7 2 10 11 5 1 4 8
Solving Sequence
2,6
3
7,10
8 1 11 5 9 12 4
c
2
c
6
c
7
c
1
c
10
c
5
c
9
c
12
c
4
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.22695 × 10
232
u
156
− 2.83942 × 10
233
u
155
+ ··· + 7.03858 × 10
232
b − 6.42788 × 10
232
,
− 2.77552 × 10
233
u
156
− 1.00711 × 10
234
u
155
+ ··· + 7.03858 × 10
232
a − 8.46264 × 10
233
,
u
157
+ 3u
156
+ ··· + 20u − 1i
I
u
2
= h6u
32
− 8u
31
+ ··· + b + 3, u
31
− 4u
30
+ ··· + a + 1, u
33
− 2u
32
+ ··· − 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 190 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−7.23 × 10
232
u
156
− 2.84 × 10
233
u
155
+ · · · + 7.04 × 10
232
b − 6.43 ×
10
232
, −2.78 × 10
233
u
156
− 1.01 × 10
234
u
155
+ · · · + 7.04 × 10
232
a − 8.46 ×
10
233
, u
157
+ 3u
156
+ · · · + 20u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
10
=
3.94330u
156
+ 14.3084u
155
+ ··· − 215.833u + 12.0232
1.02676u
156
+ 4.03408u
155
+ ··· + 7.45787u + 0.913236
a
8
=
−4.91003u
156
− 11.8337u
155
+ ··· + 405.512u − 35.1552
−0.0408320u
156
+ 1.65797u
155
+ ··· + 25.4097u − 1.67370
a
1
=
u
2
+ 1
−u
4
a
11
=
3.72168u
156
+ 14.4412u
155
+ ··· − 240.641u + 14.6185
−0.0679406u
156
+ 0.144116u
155
+ ··· − 22.1587u + 2.44123
a
5
=
u
3
u
3
+ u
a
9
=
3.94427u
156
+ 15.7459u
155
+ ··· − 194.196u + 10.9237
0.675606u
156
+ 3.31577u
155
+ ··· − 6.23214u + 1.75659
a
12
=
0.865828u
156
+ 3.51473u
155
+ ··· + 134.531u − 19.8156
1.78361u
156
+ 6.57450u
155
+ ··· − 9.63089u + 0.852523
a
4
=
−1.38787u
156
− 3.84467u
155
+ ··· + 22.3222u + 11.7347
0.0715685u
156
+ 2.04385u
155
+ ··· + 73.2958u − 4.75087
(ii) Obstruction class = −1
(iii) Cusp Shapes = −7.48606u
156
− 19.1787u
155
+ ··· + 332.793u − 21.7130
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
157
+ 49u
156
+ ··· + 66u − 1
c
2
, c
6
u
157
− 3u
156
+ ··· + 20u + 1
c
3
u
157
+ u
156
+ ··· + 15730067u + 2315629
c
4
, c
11
u
157
+ u
156
+ ··· + 427u + 286
c
7
u
157
− 6u
156
+ ··· − 586611u − 71082
c
8
u
157
+ 7u
156
+ ··· − 141270u − 7225
c
9
u
157
+ u
156
+ ··· − 1890458u − 514883
c
10
u
157
+ 16u
156
+ ··· + 71u + 1
c
12
u
157
+ 8u
156
+ ··· − 61u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
157
+ 125y
156
+ ··· − 3938y −1
c
2
, c
6
y
157
+ 49y
156
+ ··· + 66y −1
c
3
y
157
+ 17y
156
+ ··· − 194381535859813y −5362137665641
c
4
, c
11
y
157
− 93y
156
+ ··· + 2756329y −81796
c
7
y
157
− 34y
156
+ ··· − 162359863767y −5052650724
c
8
y
157
− 29y
156
+ ··· + 11092528050y −52200625
c
9
y
157
− 23y
156
+ ··· − 20454032272420y −265104503689
c
10
y
157
− 20y
156
+ ··· + 353y −1
c
12
y
157
− 14y
156
+ ··· + 135y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.201208 + 0.984879I
a = 0.215267 − 0.186219I
b = 1.176400 + 0.563128I
−1.12356 − 2.75108I 0
u = −0.201208 − 0.984879I
a = 0.215267 + 0.186219I
b = 1.176400 − 0.563128I
−1.12356 + 2.75108I 0
u = 0.073592 + 0.985926I
a = −0.061955 + 1.047270I
b = −0.341724 − 0.280817I
−5.47274 − 1.99235I 0
u = 0.073592 − 0.985926I
a = −0.061955 − 1.047270I
b = −0.341724 + 0.280817I
−5.47274 + 1.99235I 0
u = 0.163978 + 0.973025I
a = −0.547272 − 0.500259I
b = −1.85073 + 0.27586I
−1.97008 + 5.28169I 0
u = 0.163978 − 0.973025I
a = −0.547272 + 0.500259I
b = −1.85073 − 0.27586I
−1.97008 − 5.28169I 0
u = 0.978842
a = 0.266508
b = −0.0814898
−2.97828 0
u = 0.559456 + 0.800879I
a = 0.074828 + 0.468716I
b = 0.424074 + 1.306130I
−0.279021 − 0.579349I 0
u = 0.559456 − 0.800879I
a = 0.074828 − 0.468716I
b = 0.424074 − 1.306130I
−0.279021 + 0.579349I 0
u = −0.602309 + 0.828265I
a = −0.448183 + 0.442765I
b = 0.604976 + 0.013917I
−2.42132 − 5.60551I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.602309 − 0.828265I
a = −0.448183 − 0.442765I
b = 0.604976 − 0.013917I
−2.42132 + 5.60551I 0
u = −0.774462 + 0.683397I
a = −0.26860 − 1.67585I
b = 0.722832 − 1.110780I
3.73933 − 1.99675I 0
u = −0.774462 − 0.683397I
a = −0.26860 + 1.67585I
b = 0.722832 + 1.110780I
3.73933 + 1.99675I 0
u = −0.045809 + 1.032020I
a = −0.064751 + 1.026910I
b = −0.348408 + 1.257120I
−5.01032 + 0.14405I 0
u = −0.045809 − 1.032020I
a = −0.064751 − 1.026910I
b = −0.348408 − 1.257120I
−5.01032 − 0.14405I 0
u = −0.394621 + 0.881038I
a = −0.443078 − 0.098640I
b = 0.914861 + 0.004448I
−2.52117 − 5.72463I 0
u = −0.394621 − 0.881038I
a = −0.443078 + 0.098640I
b = 0.914861 − 0.004448I
−2.52117 + 5.72463I 0
u = −0.107571 + 1.029930I
a = 0.0333086 − 0.0080671I
b = 0.435800 + 0.751966I
−1.31814 − 2.17688I 0
u = −0.107571 − 1.029930I
a = 0.0333086 + 0.0080671I
b = 0.435800 − 0.751966I
−1.31814 + 2.17688I 0
u = −0.682088 + 0.653673I
a = −0.033472 + 1.392020I
b = −1.11051 + 1.23927I
−0.14301 − 2.01106I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.682088 − 0.653673I
a = −0.033472 − 1.392020I
b = −1.11051 − 1.23927I
−0.14301 + 2.01106I 0
u = −0.498827 + 0.785060I
a = −0.051337 + 1.128470I
b = −0.671617 + 1.106300I
0.03492 − 1.91028I 0
u = −0.498827 − 0.785060I
a = −0.051337 − 1.128470I
b = −0.671617 − 1.106300I
0.03492 + 1.91028I 0
u = 0.713937 + 0.808691I
a = −2.36514 − 1.46548I
b = −2.33367 − 0.96370I
−1.62637 − 3.86394I 0
u = 0.713937 − 0.808691I
a = −2.36514 + 1.46548I
b = −2.33367 + 0.96370I
−1.62637 + 3.86394I 0
u = 0.709341 + 0.819725I
a = −1.064600 + 0.505493I
b = 0.00550 + 1.60216I
1.58352 − 0.45210I 0
u = 0.709341 − 0.819725I
a = −1.064600 − 0.505493I
b = 0.00550 − 1.60216I
1.58352 + 0.45210I 0
u = 0.648285 + 0.871160I
a = 2.41457 + 1.54681I
b = 2.91933 + 0.15929I
−2.67946 + 6.69375I 0
u = 0.648285 − 0.871160I
a = 2.41457 − 1.54681I
b = 2.91933 − 0.15929I
−2.67946 − 6.69375I 0
u = −0.028975 + 0.913460I
a = 1.11090 − 1.46897I
b = 2.15217 − 1.09553I
−6.22454 − 5.03713I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.028975 − 0.913460I
a = 1.11090 + 1.46897I
b = 2.15217 + 1.09553I
−6.22454 + 5.03713I 0
u = −0.739150 + 0.798583I
a = 1.43082 + 1.34761I
b = −0.30481 + 2.39283I
−0.87274 + 4.34252I 0
u = −0.739150 − 0.798583I
a = 1.43082 − 1.34761I
b = −0.30481 − 2.39283I
−0.87274 − 4.34252I 0
u = −0.033004 + 0.909989I
a = −0.183970 + 1.006050I
b = 0.910284 + 0.357221I
−2.91444 − 1.66395I 0
u = −0.033004 − 0.909989I
a = −0.183970 − 1.006050I
b = 0.910284 − 0.357221I
−2.91444 + 1.66395I 0
u = −0.802189 + 0.743976I
a = 1.78310 − 1.90574I
b = 2.01442 − 0.28552I
4.33661 + 4.41255I 0
u = −0.802189 − 0.743976I
a = 1.78310 + 1.90574I
b = 2.01442 + 0.28552I
4.33661 − 4.41255I 0
u = 0.066685 + 0.897045I
a = 0.303805 + 1.279130I
b = −1.346920 − 0.022914I
−5.91062 + 5.71475I 0
u = 0.066685 − 0.897045I
a = 0.303805 − 1.279130I
b = −1.346920 + 0.022914I
−5.91062 − 5.71475I 0
u = 0.836499 + 0.716446I
a = −0.71149 − 1.55111I
b = −1.342940 − 0.442114I
5.24717 − 1.89423I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.836499 − 0.716446I
a = −0.71149 + 1.55111I
b = −1.342940 + 0.442114I
5.24717 + 1.89423I 0
u = 0.662839 + 0.881717I
a = 1.04288 + 2.88588I
b = 2.51223 + 2.21804I
−2.72596 − 1.60356I 0
u = 0.662839 − 0.881717I
a = 1.04288 − 2.88588I
b = 2.51223 − 2.21804I
−2.72596 + 1.60356I 0
u = −0.666368 + 0.881137I
a = −1.17693 + 1.72791I
b = −1.91037 + 1.09268I
0.44035 − 2.57292I 0
u = −0.666368 − 0.881137I
a = −1.17693 − 1.72791I
b = −1.91037 − 1.09268I
0.44035 + 2.57292I 0
u = 0.824367 + 0.741128I
a = −1.22906 − 1.88243I
b = −1.83057 − 0.40280I
5.56492 − 1.88516I 0
u = 0.824367 − 0.741128I
a = −1.22906 + 1.88243I
b = −1.83057 + 0.40280I
5.56492 + 1.88516I 0
u = 0.244778 + 0.845348I
a = 1.98931 − 0.13370I
b = 2.23901 − 0.62796I
−3.67693 + 6.38209I 0
u = 0.244778 − 0.845348I
a = 1.98931 + 0.13370I
b = 2.23901 + 0.62796I
−3.67693 − 6.38209I 0
u = 0.244159 + 1.093750I
a = 0.244047 + 0.779039I
b = 1.027040 + 0.436203I
−7.46203 + 2.83745I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.244159 − 1.093750I
a = 0.244047 − 0.779039I
b = 1.027040 − 0.436203I
−7.46203 − 2.83745I 0
u = −0.658047 + 0.908619I
a = −0.289438 − 0.016986I
b = −0.994896 + 0.813140I
−2.70986 + 0.61322I 0
u = −0.658047 − 0.908619I
a = −0.289438 + 0.016986I
b = −0.994896 − 0.813140I
−2.70986 − 0.61322I 0
u = −0.751262 + 0.840712I
a = 1.85990 − 1.03677I
b = 2.51953 − 0.49762I
3.83432 + 0.10338I 0
u = −0.751262 − 0.840712I
a = 1.85990 + 1.03677I
b = 2.51953 + 0.49762I
3.83432 − 0.10338I 0
u = −0.886736 + 0.708970I
a = −1.44238 + 1.63955I
b = −1.89383 + 0.19919I
2.2863 + 13.9596I 0
u = −0.886736 − 0.708970I
a = −1.44238 − 1.63955I
b = −1.89383 − 0.19919I
2.2863 − 13.9596I 0
u = 0.885906 + 0.710760I
a = 1.29275 + 1.60248I
b = 1.82115 + 0.35998I
5.87646 − 7.89437I 0
u = 0.885906 − 0.710760I
a = 1.29275 − 1.60248I
b = 1.82115 − 0.35998I
5.87646 + 7.89437I 0
u = −0.873627 + 0.726850I
a = −1.19204 + 1.33245I
b = −1.48137 + 0.42887I
0.03935 + 2.53379I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.873627 − 0.726850I
a = −1.19204 − 1.33245I
b = −1.48137 − 0.42887I
0.03935 − 2.53379I 0
u = 0.733500 + 0.872238I
a = −0.779568 − 0.903612I
b = −1.96498 − 0.89311I
2.93589 + 4.93920I 0
u = 0.733500 − 0.872238I
a = −0.779568 + 0.903612I
b = −1.96498 + 0.89311I
2.93589 − 4.93920I 0
u = 0.730322 + 0.877873I
a = −1.01472 − 1.30634I
b = −0.929917 − 0.077143I
2.91750 + 0.63600I 0
u = 0.730322 − 0.877873I
a = −1.01472 + 1.30634I
b = −0.929917 + 0.077143I
2.91750 − 0.63600I 0
u = 0.238558 + 1.120010I
a = 0.259216 + 0.662635I
b = 1.273900 − 0.095707I
−5.3204 + 13.9634I 0
u = 0.238558 − 1.120010I
a = 0.259216 − 0.662635I
b = 1.273900 + 0.095707I
−5.3204 − 13.9634I 0
u = −0.239835 + 1.121790I
a = −0.225286 + 0.707786I
b = −1.054240 − 0.009339I
−1.73816 − 7.91098I 0
u = −0.239835 − 1.121790I
a = −0.225286 − 0.707786I
b = −1.054240 + 0.009339I
−1.73816 + 7.91098I 0
u = −0.820144 + 0.802641I
a = −0.47769 + 1.91564I
b = −0.610996 + 1.173060I
2.88808 + 4.26724I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.820144 − 0.802641I
a = −0.47769 − 1.91564I
b = −0.610996 − 1.173060I
2.88808 − 4.26724I 0
u = −0.816871 + 0.814196I
a = 1.82633 − 1.37311I
b = 2.38233 − 0.01772I
5.33076 + 0.81756I 0
u = −0.816871 − 0.814196I
a = 1.82633 + 1.37311I
b = 2.38233 + 0.01772I
5.33076 − 0.81756I 0
u = 0.704571 + 0.918827I
a = 1.031810 − 0.631118I
b = −0.05049 − 1.60165I
1.27427 + 5.87744I 0
u = 0.704571 − 0.918827I
a = 1.031810 + 0.631118I
b = −0.05049 + 1.60165I
1.27427 − 5.87744I 0
u = 0.647115 + 0.962767I
a = 0.613088 + 0.698427I
b = 0.261570 + 0.594581I
−0.97306 + 5.41264I 0
u = 0.647115 − 0.962767I
a = 0.613088 − 0.698427I
b = 0.261570 − 0.594581I
−0.97306 − 5.41264I 0
u = 0.705485 + 0.925470I
a = −1.39116 − 2.43760I
b = −2.00724 − 2.35969I
−1.98803 + 9.30687I 0
u = 0.705485 − 0.925470I
a = −1.39116 + 2.43760I
b = −2.00724 + 2.35969I
−1.98803 − 9.30687I 0
u = −0.921606 + 0.713066I
a = 0.791175 − 0.677756I
b = 0.880843 + 0.251644I
1.39010 + 4.45714I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.921606 − 0.713066I
a = 0.791175 + 0.677756I
b = 0.880843 − 0.251644I
1.39010 − 4.45714I 0
u = −0.738476 + 0.907353I
a = 1.02500 − 2.23258I
b = 1.57320 − 1.47343I
3.62872 − 5.75784I 0
u = −0.738476 − 0.907353I
a = 1.02500 + 2.23258I
b = 1.57320 + 1.47343I
3.62872 + 5.75784I 0
u = 0.184836 + 0.807635I
a = 0.437704 − 1.146270I
b = −1.101470 − 0.360712I
−0.89775 + 3.22795I 0
u = 0.184836 − 0.807635I
a = 0.437704 + 1.146270I
b = −1.101470 + 0.360712I
−0.89775 − 3.22795I 0
u = 0.861125 + 0.794918I
a = −1.64510 − 1.14081I
b = −1.98990 + 0.36272I
5.09809 − 3.59030I 0
u = 0.861125 − 0.794918I
a = −1.64510 + 1.14081I
b = −1.98990 − 0.36272I
5.09809 + 3.59030I 0
u = 0.321132 + 1.129760I
a = 0.131254 − 0.090547I
b = −0.487912 − 0.201487I
−6.92153 + 4.48026I 0
u = 0.321132 − 1.129760I
a = 0.131254 + 0.090547I
b = −0.487912 + 0.201487I
−6.92153 − 4.48026I 0
u = 0.365755 + 1.119260I
a = 0.608376 − 0.148707I
b = 0.323099 − 0.938107I
−4.57691 − 6.46549I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.365755 − 1.119260I
a = 0.608376 + 0.148707I
b = 0.323099 + 0.938107I
−4.57691 + 6.46549I 0
u = −0.719740 + 0.935038I
a = −1.85704 − 0.85137I
b = −0.72664 − 2.45081I
−1.29110 − 9.90440I 0
u = −0.719740 − 0.935038I
a = −1.85704 + 0.85137I
b = −0.72664 + 2.45081I
−1.29110 + 9.90440I 0
u = −0.674454 + 0.970728I
a = −1.60550 + 0.47572I
b = −1.52755 − 0.63415I
−1.00910 − 3.23420I 0
u = −0.674454 − 0.970728I
a = −1.60550 − 0.47572I
b = −1.52755 + 0.63415I
−1.00910 + 3.23420I 0
u = 0.864216 + 0.814434I
a = 0.57819 + 1.47280I
b = 1.030760 + 0.825089I
7.85686 + 2.08145I 0
u = 0.864216 − 0.814434I
a = 0.57819 − 1.47280I
b = 1.030760 − 0.825089I
7.85686 − 2.08145I 0
u = 0.805639 + 0.091637I
a = −0.618943 − 0.078712I
b = 0.804992 + 0.590652I
−1.23358 + 10.56740I 0
u = 0.805639 − 0.091637I
a = −0.618943 + 0.078712I
b = 0.804992 − 0.590652I
−1.23358 − 10.56740I 0
u = −0.061760 + 0.807895I
a = 0.016424 + 0.466680I
b = 0.709162 + 1.069090I
−1.15874 − 1.91373I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.061760 − 0.807895I
a = 0.016424 − 0.466680I
b = 0.709162 − 1.069090I
−1.15874 + 1.91373I 0
u = −0.803579 + 0.099464I
a = 0.432790 + 0.078868I
b = −0.837023 + 0.490252I
2.36823 − 4.51997I 0
u = −0.803579 − 0.099464I
a = 0.432790 − 0.078868I
b = −0.837023 − 0.490252I
2.36823 + 4.51997I 0
u = −0.388401 + 1.126610I
a = −0.601116 + 0.104328I
b = −0.470464 − 0.535352I
−0.916145 + 0.340247I 0
u = −0.388401 − 1.126610I
a = −0.601116 − 0.104328I
b = −0.470464 + 0.535352I
−0.916145 − 0.340247I 0
u = 0.043691 + 0.792082I
a = −0.00747 − 2.35008I
b = −0.692674 − 1.055800I
−0.89417 + 2.43900I 0
u = 0.043691 − 0.792082I
a = −0.00747 + 2.35008I
b = −0.692674 + 1.055800I
−0.89417 − 2.43900I 0
u = −0.885820 + 0.826093I
a = −0.377775 + 1.292550I
b = −0.971445 + 0.710462I
4.31412 − 7.83856I 0
u = −0.885820 − 0.826093I
a = −0.377775 − 1.292550I
b = −0.971445 − 0.710462I
4.31412 + 7.83856I 0
u = −0.771170 + 0.949073I
a = 1.04699 − 2.22049I
b = 2.38691 − 1.63496I
4.90963 − 6.76885I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.771170 − 0.949073I
a = 1.04699 + 2.22049I
b = 2.38691 + 1.63496I
4.90963 + 6.76885I 0
u = 0.766267 + 0.104179I
a = −0.049069 − 0.227500I
b = 0.503150 + 0.325295I
−3.54515 − 0.42371I 0
u = 0.766267 − 0.104179I
a = −0.049069 + 0.227500I
b = 0.503150 − 0.325295I
−3.54515 + 0.42371I 0
u = −0.770147 + 0.958219I
a = −1.71648 + 0.47055I
b = −2.37628 + 0.34575I
2.40516 − 10.22520I 0
u = −0.770147 − 0.958219I
a = −1.71648 − 0.47055I
b = −2.37628 − 0.34575I
2.40516 + 10.22520I 0
u = −0.737491 + 0.983617I
a = 1.43135 − 2.04870I
b = 2.91313 − 1.76930I
3.60382 − 10.20860I 0
u = −0.737491 − 0.983617I
a = 1.43135 + 2.04870I
b = 2.91313 + 1.76930I
3.60382 + 10.20860I 0
u = −0.695779 + 1.016150I
a = 1.381670 − 0.246978I
b = 1.80775 + 0.50277I
2.72087 − 3.59006I 0
u = −0.695779 − 1.016150I
a = 1.381670 + 0.246978I
b = 1.80775 − 0.50277I
2.72087 + 3.59006I 0
u = 0.747122 + 0.992790I
a = −1.44605 − 1.66081I
b = −2.81755 − 1.11151I
4.79160 + 7.77443I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.747122 − 0.992790I
a = −1.44605 + 1.66081I
b = −2.81755 + 1.11151I
4.79160 − 7.77443I 0
u = −0.701512 + 0.283712I
a = −0.548781 − 0.592782I
b = 0.131801 + 0.464495I
−0.47725 + 1.87316I 0
u = −0.701512 − 0.283712I
a = −0.548781 + 0.592782I
b = 0.131801 − 0.464495I
−0.47725 − 1.87316I 0
u = 0.802156 + 0.964661I
a = 1.27260 + 0.76602I
b = 1.87417 + 0.41670I
7.38511 + 4.10288I 0
u = 0.802156 − 0.964661I
a = 1.27260 − 0.76602I
b = 1.87417 − 0.41670I
7.38511 − 4.10288I 0
u = 0.788586 + 0.979009I
a = −0.76738 − 2.00914I
b = −2.25690 − 1.67268I
4.51992 + 9.72455I 0
u = 0.788586 − 0.979009I
a = −0.76738 + 2.00914I
b = −2.25690 + 1.67268I
4.51992 − 9.72455I 0
u = 0.743355 + 1.014290I
a = −1.18190 − 1.11018I
b = −2.17273 − 0.59859I
4.33129 + 7.80866I 0
u = 0.743355 − 1.014290I
a = −1.18190 + 1.11018I
b = −2.17273 + 0.59859I
4.33129 − 7.80866I 0
u = 0.867354 + 0.916143I
a = 1.37265 + 1.53380I
b = 1.80047 + 1.10670I
7.90529 + 3.21163I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.867354 − 0.916143I
a = 1.37265 − 1.53380I
b = 1.80047 − 1.10670I
7.90529 − 3.21163I 0
u = 0.587080 + 0.441010I
a = 0.463460 − 0.272370I
b = −0.073387 + 0.600402I
0.000258 − 0.666360I 0
u = 0.587080 − 0.441010I
a = 0.463460 + 0.272370I
b = −0.073387 − 0.600402I
0.000258 + 0.666360I 0
u = −0.830065 + 0.964930I
a = −0.994683 + 0.622151I
b = −1.54883 + 0.18259I
3.88122 + 1.50611I 0
u = −0.830065 − 0.964930I
a = −0.994683 − 0.622151I
b = −1.54883 − 0.18259I
3.88122 − 1.50611I 0
u = −0.766378 + 1.022030I
a = −1.19075 + 1.51847I
b = −2.06503 + 1.23835I
−0.87494 − 8.62802I 0
u = −0.766378 − 1.022030I
a = −1.19075 − 1.51847I
b = −2.06503 − 1.23835I
−0.87494 + 8.62802I 0
u = 0.764418 + 1.033720I
a = 1.38195 + 1.69382I
b = 2.53218 + 1.22111I
4.8753 + 14.0132I 0
u = 0.764418 − 1.033720I
a = 1.38195 − 1.69382I
b = 2.53218 − 1.22111I
4.8753 − 14.0132I 0
u = −0.763576 + 1.034880I
a = −1.36017 + 1.82989I
b = −2.67947 + 1.42561I
1.2754 − 20.0776I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.763576 − 1.034880I
a = −1.36017 − 1.82989I
b = −2.67947 − 1.42561I
1.2754 + 20.0776I 0
u = −0.778791 + 1.045440I
a = 0.443795 − 1.090740I
b = 1.36039 − 1.08340I
0.34784 − 10.72000I 0
u = −0.778791 − 1.045440I
a = 0.443795 + 1.090740I
b = 1.36039 + 1.08340I
0.34784 + 10.72000I 0
u = 0.432431 + 1.235860I
a = 0.0172619 + 0.1357320I
b = −0.0895507 + 0.0686148I
−7.04904 + 4.71955I 0
u = 0.432431 − 1.235860I
a = 0.0172619 − 0.1357320I
b = −0.0895507 − 0.0686148I
−7.04904 − 4.71955I 0
u = −0.343798 + 0.596419I
a = −1.197370 + 0.385855I
b = −1.148110 + 0.105555I
0.38875 − 1.52343I 4.46721 + 3.96792I
u = −0.343798 − 0.596419I
a = −1.197370 − 0.385855I
b = −1.148110 − 0.105555I
0.38875 + 1.52343I 4.46721 − 3.96792I
u = −0.599018 + 0.015655I
a = −1.262380 − 0.258268I
b = 0.534824 + 0.118787I
1.94962 + 0.10775I 7.06611 + 1.55327I
u = −0.599018 − 0.015655I
a = −1.262380 + 0.258268I
b = 0.534824 − 0.118787I
1.94962 − 0.10775I 7.06611 − 1.55327I
u = 0.531611 + 0.205209I
a = −0.40835 + 1.68017I
b = 0.930633 + 0.702502I
−1.77645 − 3.56776I 1.01328 + 4.99121I
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.531611 − 0.205209I
a = −0.40835 − 1.68017I
b = 0.930633 − 0.702502I
−1.77645 + 3.56776I 1.01328 − 4.99121I
u = 0.487349 + 0.022942I
a = 1.55251 + 1.07296I
b = −0.641072 − 0.404865I
1.08085 + 3.11229I 5.22633 − 7.56969I
u = 0.487349 − 0.022942I
a = 1.55251 − 1.07296I
b = −0.641072 + 0.404865I
1.08085 − 3.11229I 5.22633 + 7.56969I
u = 0.129012 + 0.280608I
a = −1.68255 − 0.57776I
b = −0.554269 + 0.797550I
0.08912 − 1.53025I 0.56237 + 3.19733I
u = 0.129012 − 0.280608I
a = −1.68255 + 0.57776I
b = −0.554269 − 0.797550I
0.08912 + 1.53025I 0.56237 − 3.19733I
u = 0.0987358 + 0.0498591I
a = −5.56334 − 8.70425I
b = 0.734384 − 0.716062I
−3.57996 − 4.96648I −0.78961 + 5.61080I
u = 0.0987358 − 0.0498591I
a = −5.56334 + 8.70425I
b = 0.734384 + 0.716062I
−3.57996 + 4.96648I −0.78961 − 5.61080I
20
II.
I
u
2
= h6u
32
−8u
31
+· · ·+b+3, u
31
−4u
30
+· · ·+a+1, u
33
−2u
32
+· · ·−2u−1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
10
=
−u
31
+ 4u
30
+ ··· − 10u − 1
−6u
32
+ 8u
31
+ ··· − 2u − 3
a
8
=
8u
32
− 12u
31
+ ··· + 6u + 4
14u
32
− 18u
31
+ ··· − 8u − 1
a
1
=
u
2
+ 1
−u
4
a
11
=
−u
32
+ 2u
31
+ ··· − 22u − 6
−9u
32
+ 12u
31
+ ··· − 7u − 5
a
5
=
u
3
u
3
+ u
a
9
=
−u
32
+ u
31
+ ··· − 10u − 1
−7u
32
+ 10u
31
+ ··· − 6u − 5
a
12
=
−6u
32
+ 6u
31
+ ··· + 3u + 2
−7u
32
+ 7u
31
+ ··· + 15u + 3
a
4
=
−8u
32
+ 7u
31
+ ··· + 15u + 4
−3u
32
+ 4u
31
+ ··· + 6u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −32u
32
+ 65u
31
− 249u
30
+ 380u
29
− 1023u
28
+ 1430u
27
− 3046u
26
+ 3843u
25
−
6891u
24
+ 8128u
23
− 12636u
22
+ 13937u
21
− 18955u
20
+ 19836u
19
− 23668u
18
+
23517u
17
− 24409u
16
+ 23264u
15
− 20692u
14
+ 18940u
13
− 13996u
12
+ 12500u
11
−
7358u
10
+ 6428u
9
− 2821u
8
+ 2456u
7
− 776u
6
+ 591u
5
− 212u
4
+ 59u
3
− 77u
2
− 16u − 9
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
33
− 12u
32
+ ··· − 12u + 1
c
2
u
33
− 2u
32
+ ··· − 2u − 1
c
3
u
33
− 4u
31
+ ··· + u − 1
c
4
u
33
− 9u
31
+ ··· − u + 1
c
6
u
33
+ 2u
32
+ ··· − 2u + 1
c
7
u
33
+ 15u
32
+ ··· + 19u + 1
c
8
u
33
− 18u
32
+ ··· + 22u − 1
c
9
u
33
+ 6u
31
+ ··· − 4u − 1
c
10
u
33
+ 3u
32
+ ··· + 7u − 1
c
11
u
33
− 9u
31
+ ··· − u − 1
c
12
u
33
− 7u
32
+ ··· − 3u − 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
33
+ 24y
32
+ ··· − 44y −1
c
2
, c
6
y
33
+ 12y
32
+ ··· − 12y −1
c
3
y
33
− 8y
32
+ ··· − 23y −1
c
4
, c
11
y
33
− 18y
32
+ ··· + 25y −1
c
7
y
33
+ 5y
32
+ ··· + 9y −1
c
8
y
33
+ 2y
32
+ ··· + 24y −1
c
9
y
33
+ 12y
32
+ ··· + 2y −1
c
10
y
33
− 21y
32
+ ··· + 19y −1
c
12
y
33
− 19y
32
+ ··· + 21y −1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.979898
a = 0.181454
b = −0.277506
−2.86032 31.9040
u = −0.619913 + 0.851416I
a = 0.670261 + 0.768954I
b = −0.08494 + 1.69295I
0.618512 − 0.282062I 0.44891 + 2.30063I
u = −0.619913 − 0.851416I
a = 0.670261 − 0.768954I
b = −0.08494 − 1.69295I
0.618512 + 0.282062I 0.44891 − 2.30063I
u = −0.337223 + 0.998197I
a = 0.910239 + 0.007882I
b = 0.655075 + 0.431435I
−1.066640 − 0.389674I −2.12985 + 2.41986I
u = −0.337223 − 0.998197I
a = 0.910239 − 0.007882I
b = 0.655075 − 0.431435I
−1.066640 + 0.389674I −2.12985 − 2.41986I
u = −0.171996 + 0.923345I
a = −0.058594 − 0.592817I
b = 1.375650 + 0.231592I
−1.53889 − 3.89395I −5.51397 + 7.40283I
u = −0.171996 − 0.923345I
a = −0.058594 + 0.592817I
b = 1.375650 − 0.231592I
−1.53889 + 3.89395I −5.51397 − 7.40283I
u = −0.610306 + 0.900694I
a = −1.039110 − 0.240984I
b = −0.208657 − 0.659109I
0.45926 − 4.54162I 1.48411 + 4.51493I
u = −0.610306 − 0.900694I
a = −1.039110 + 0.240984I
b = −0.208657 + 0.659109I
0.45926 + 4.54162I 1.48411 − 4.51493I
u = 0.678405 + 0.857790I
a = 0.63562 + 2.08439I
b = 1.83205 + 2.36975I
−1.88547 − 2.45267I −1.47493 + 2.66569I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.678405 − 0.857790I
a = 0.63562 − 2.08439I
b = 1.83205 − 2.36975I
−1.88547 + 2.45267I −1.47493 − 2.66569I
u = 0.673593 + 0.877297I
a = 2.28584 + 0.93796I
b = 1.87259 − 0.13496I
−1.94769 + 7.67754I −1.28925 − 9.19143I
u = 0.673593 − 0.877297I
a = 2.28584 − 0.93796I
b = 1.87259 + 0.13496I
−1.94769 − 7.67754I −1.28925 + 9.19143I
u = 0.821904 + 0.767664I
a = −1.68950 − 1.61769I
b = −2.14986 − 0.00239I
4.88359 − 2.51953I 0.88595 + 2.08851I
u = 0.821904 − 0.767664I
a = −1.68950 + 1.61769I
b = −2.14986 + 0.00239I
4.88359 + 2.51953I 0.88595 − 2.08851I
u = −0.843843 + 0.777959I
a = 0.938104 − 0.983413I
b = 0.876751 − 0.086257I
2.00647 + 3.47982I 0.81347 − 2.39503I
u = −0.843843 − 0.777959I
a = 0.938104 + 0.983413I
b = 0.876751 + 0.086257I
2.00647 − 3.47982I 0.81347 + 2.39503I
u = 0.214773 + 0.818340I
a = −1.70480 + 0.28674I
b = −0.785589 + 0.087307I
−4.62507 − 4.10477I −5.91447 + 2.44881I
u = 0.214773 − 0.818340I
a = −1.70480 − 0.28674I
b = −0.785589 − 0.087307I
−4.62507 + 4.10477I −5.91447 − 2.44881I
u = 0.163339 + 0.809135I
a = −0.807975 − 0.105350I
b = −2.09434 − 0.49476I
−4.67990 + 5.77153I −6.74734 − 7.51716I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.163339 − 0.809135I
a = −0.807975 + 0.105350I
b = −2.09434 + 0.49476I
−4.67990 − 5.77153I −6.74734 + 7.51716I
u = 0.753322 + 0.978773I
a = −1.20740 − 2.08607I
b = −2.74510 − 1.61225I
4.22833 + 8.42449I −0.53372 − 8.05694I
u = 0.753322 − 0.978773I
a = −1.20740 + 2.08607I
b = −2.74510 + 1.61225I
4.22833 − 8.42449I −0.53372 + 8.05694I
u = −0.771478 + 0.974682I
a = 0.711704 − 1.162630I
b = 1.62338 − 1.27155I
1.39751 − 9.50083I −0.65261 + 7.77528I
u = −0.771478 − 0.974682I
a = 0.711704 + 1.162630I
b = 1.62338 + 1.27155I
1.39751 + 9.50083I −0.65261 − 7.77528I
u = 0.872415 + 0.916785I
a = −1.33154 − 1.50671I
b = −1.75308 − 1.09286I
7.85160 + 3.22634I −68.9435 − 21.5095I
u = 0.872415 − 0.916785I
a = −1.33154 + 1.50671I
b = −1.75308 + 1.09286I
7.85160 − 3.22634I −68.9435 + 21.5095I
u = 0.419962 + 1.254000I
a = −0.135770 − 0.140448I
b = −0.316653 − 0.002062I
−6.99392 + 4.81300I 18.4313 − 36.2674I
u = 0.419962 − 1.254000I
a = −0.135770 + 0.140448I
b = −0.316653 + 0.002062I
−6.99392 − 4.81300I 18.4313 + 36.2674I
u = −0.374713 + 0.530734I
a = −0.22784 − 1.82794I
b = 0.95791 − 1.30566I
0.53129 − 2.69066I 5.74958 + 9.36935I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.374713 − 0.530734I
a = −0.22784 + 1.82794I
b = 0.95791 + 1.30566I
0.53129 + 2.69066I 5.74958 − 9.36935I
u = −0.358188 + 0.333492I
a = −0.53997 − 1.63158I
b = 0.083571 + 0.622453I
0.54623 + 1.80775I 4.93406 − 2.81800I
u = −0.358188 − 0.333492I
a = −0.53997 + 1.63158I
b = 0.083571 − 0.622453I
0.54623 − 1.80775I 4.93406 + 2.81800I
27
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
33
− 12u
32
+ ··· − 12u + 1)(u
157
+ 49u
156
+ ··· + 66u − 1)
c
2
(u
33
− 2u
32
+ ··· − 2u − 1)(u
157
− 3u
156
+ ··· + 20u + 1)
c
3
(u
33
− 4u
31
+ ··· + u − 1)(u
157
+ u
156
+ ··· + 1.57301 × 10
7
u + 2315629)
c
4
(u
33
− 9u
31
+ ··· − u + 1)(u
157
+ u
156
+ ··· + 427u + 286)
c
6
(u
33
+ 2u
32
+ ··· − 2u + 1)(u
157
− 3u
156
+ ··· + 20u + 1)
c
7
(u
33
+ 15u
32
+ ··· + 19u + 1)(u
157
− 6u
156
+ ··· − 586611u − 71082)
c
8
(u
33
− 18u
32
+ ··· + 22u − 1)(u
157
+ 7u
156
+ ··· − 141270u − 7225)
c
9
(u
33
+ 6u
31
+ ··· − 4u − 1)(u
157
+ u
156
+ ··· − 1890458u − 514883)
c
10
(u
33
+ 3u
32
+ ··· + 7u − 1)(u
157
+ 16u
156
+ ··· + 71u + 1)
c
11
(u
33
− 9u
31
+ ··· − u − 1)(u
157
+ u
156
+ ··· + 427u + 286)
c
12
(u
33
− 7u
32
+ ··· − 3u − 1)(u
157
+ 8u
156
+ ··· − 61u + 1)
28
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
33
+ 24y
32
+ ··· − 44y −1)(y
157
+ 125y
156
+ ··· − 3938y −1)
c
2
, c
6
(y
33
+ 12y
32
+ ··· − 12y −1)(y
157
+ 49y
156
+ ··· + 66y −1)
c
3
(y
33
− 8y
32
+ ··· − 23y −1)
· (y
157
+ 17y
156
+ ··· − 194381535859813y −5362137665641)
c
4
, c
11
(y
33
− 18y
32
+ ··· + 25y −1)
· (y
157
− 93y
156
+ ··· + 2756329y −81796)
c
7
(y
33
+ 5y
32
+ ··· + 9y −1)
· (y
157
− 34y
156
+ ··· − 162359863767y −5052650724)
c
8
(y
33
+ 2y
32
+ ··· + 24y −1)
· (y
157
− 29y
156
+ ··· + 11092528050y −52200625)
c
9
(y
33
+ 12y
32
+ ··· + 2y −1)
· (y
157
− 23y
156
+ ··· − 20454032272420y −265104503689)
c
10
(y
33
− 21y
32
+ ··· + 19y −1)(y
157
− 20y
156
+ ··· + 353y −1)
c
12
(y
33
− 19y
32
+ ··· + 21y −1)(y
157
− 14y
156
+ ··· + 135y −1)
29
