12n
0631
(K12n
0631
)
A knot diagram
1
Linearized knot diagam
3 8 10 12 3 10 11 2 5 1 5 7
Solving Sequence
2,8 3,5
6 9 10 1 11 12 4 7
c
2
c
5
c
8
c
9
c
1
c
10
c
11
c
4
c
7
c
3
, c
6
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.40561 × 10
133
u
75
+ 1.69044 × 10
133
u
74
+ ··· + 6.99960 × 10
133
b − 1.41008 × 10
134
,
− 3.83689 × 10
134
u
75
+ 2.93325 × 10
134
u
74
+ ··· + 1.32992 × 10
135
a − 2.98368 × 10
136
,
u
76
− u
75
+ ··· − 161u + 38i
I
u
2
= h2320203740u
35
+ 625690452u
34
+ ··· + 215633713b − 4438611716,
18527903408u
35
− 1296857930u
34
+ ··· + 1078168565a − 23635723173,
u
36
+ 11u
34
+ ··· + 4u + 5i
* 2 irreducible components of dim
C
= 0, with total 112 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−1.41 × 10
133
u
75
+ 1.69 × 10
133
u
74
+ · · · + 7.00 × 10
133
b − 1.41 ×
10
134
, −3.84 × 10
134
u
75
+ 2.93 × 10
134
u
74
+ · · · + 1.33 × 10
135
a − 2.98 ×
10
136
, u
76
− u
75
+ · · · − 161u + 38i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
−u
2
a
5
=
0.288505u
75
− 0.220558u
74
+ ··· − 67.3037u + 22.4350
0.200813u
75
− 0.241505u
74
+ ··· + 2.79038u + 2.01452
a
6
=
0.343481u
75
− 0.329454u
74
+ ··· − 64.5370u + 21.8675
0.255942u
75
− 0.347843u
74
+ ··· + 13.5607u − 0.0344589
a
9
=
u
u
a
10
=
−0.0370385u
75
− 0.311899u
74
+ ··· + 197.400u − 40.7028
0.000948893u
75
− 0.267585u
74
+ ··· + 110.531u − 21.4633
a
1
=
u
2
+ 1
−u
4
a
11
=
−0.0506671u
75
− 0.184581u
74
+ ··· + 146.321u − 32.9272
0.0132693u
75
− 0.287903u
74
+ ··· + 120.083u − 23.6069
a
12
=
−0.0878875u
75
− 0.0853599u
74
+ ··· + 96.7438u − 15.3384
−0.0715523u
75
− 0.214330u
74
+ ··· + 100.028u − 19.2572
a
4
=
0.813857u
75
− 0.422378u
74
+ ··· − 85.2711u + 45.1346
−0.0140915u
75
+ 0.246118u
74
+ ··· − 38.2220u + 11.8442
a
7
=
0.974728u
75
− 1.25970u
74
+ ··· + 96.9366u − 1.10803
0.131084u
75
− 0.0921550u
74
+ ··· − 48.0650u + 11.8828
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.23257u
75
+ 1.09381u
74
+ ··· − 72.2514u − 13.9195
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
76
+ 31u
75
+ ··· + 56539u + 1444
c
2
, c
8
u
76
+ u
75
+ ··· + 161u + 38
c
3
u
76
+ u
75
+ ··· + 785435u + 192925
c
4
, c
11
u
76
+ u
75
+ ··· + 115u + 42
c
5
u
76
+ 7u
75
+ ··· − 176881u + 193903
c
6
u
76
− u
75
+ ··· − 1137222277u + 654834962
c
7
u
76
− 5u
75
+ ··· + 1855244u + 7111423
c
9
u
76
− 2u
75
+ ··· − 34044488u + 10812743
c
10
u
76
− 3u
75
+ ··· + 56u + 493
c
12
u
76
+ u
75
+ ··· + 4761u + 5283
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
76
+ 47y
75
+ ··· + 79202767y + 2085136
c
2
, c
8
y
76
+ 31y
75
+ ··· + 56539y + 1444
c
3
y
76
+ 115y
75
+ ··· + 1105604974175y + 37220055625
c
4
, c
11
y
76
+ 67y
75
+ ··· − 35821y + 1764
c
5
y
76
− 109y
75
+ ··· − 932607366479y + 37598373409
c
6
y
76
+ 65y
75
+ ··· − 1108270808871508769y + 428808827457541444
c
7
y
76
− 29y
75
+ ··· + 889309315939338y + 50572337084929
c
9
y
76
+ 102y
75
+ ··· − 390748923918910y + 116915411184049
c
10
y
76
+ 9y
75
+ ··· + 7601882y + 243049
c
12
y
76
− 19y
75
+ ··· + 69943869y + 27910089
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.662916 + 0.756274I
a = 1.101880 + 0.248200I
b = 0.229350 + 0.324684I
1.02372 − 2.77677I 0
u = −0.662916 − 0.756274I
a = 1.101880 − 0.248200I
b = 0.229350 − 0.324684I
1.02372 + 2.77677I 0
u = 0.285315 + 1.007480I
a = 0.728498 + 0.040863I
b = 1.107010 − 0.469266I
−3.83979 − 0.17827I 0
u = 0.285315 − 1.007480I
a = 0.728498 − 0.040863I
b = 1.107010 + 0.469266I
−3.83979 + 0.17827I 0
u = −0.071981 + 0.942071I
a = 0.052219 + 0.419552I
b = 1.53394 + 0.19750I
6.94756 − 2.68529I 0
u = −0.071981 − 0.942071I
a = 0.052219 − 0.419552I
b = 1.53394 − 0.19750I
6.94756 + 2.68529I 0
u = −0.801402 + 0.483212I
a = −0.345937 + 0.673423I
b = −0.798367 − 0.407778I
5.31701 + 1.69426I 0
u = −0.801402 − 0.483212I
a = −0.345937 − 0.673423I
b = −0.798367 + 0.407778I
5.31701 − 1.69426I 0
u = 0.454063 + 0.966732I
a = −0.395209 − 1.081370I
b = −0.834241 − 0.233761I
−4.65855 + 2.75852I 0
u = 0.454063 − 0.966732I
a = −0.395209 + 1.081370I
b = −0.834241 + 0.233761I
−4.65855 − 2.75852I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.065746 + 1.066650I
a = 0.553908 − 0.016598I
b = 0.004846 + 0.584532I
−0.0217467 + 0.0606793I 0
u = −0.065746 − 1.066650I
a = 0.553908 + 0.016598I
b = 0.004846 − 0.584532I
−0.0217467 − 0.0606793I 0
u = 0.817443 + 0.712232I
a = −1.65495 + 1.01142I
b = −0.80510 + 2.04740I
7.26372 + 0.80285I 0
u = 0.817443 − 0.712232I
a = −1.65495 − 1.01142I
b = −0.80510 − 2.04740I
7.26372 − 0.80285I 0
u = −0.567079 + 0.930252I
a = 0.286387 + 0.362192I
b = 0.304274 + 0.981241I
0.45994 − 2.05238I 0
u = −0.567079 − 0.930252I
a = 0.286387 − 0.362192I
b = 0.304274 − 0.981241I
0.45994 + 2.05238I 0
u = −0.035983 + 0.897156I
a = 1.98195 + 0.37899I
b = 1.39142 + 1.28975I
−0.86327 − 4.72694I 0. + 5.69238I
u = −0.035983 − 0.897156I
a = 1.98195 − 0.37899I
b = 1.39142 − 1.28975I
−0.86327 + 4.72694I 0. − 5.69238I
u = −0.776192 + 0.835014I
a = 2.07774 + 1.16141I
b = 0.77380 + 2.17827I
11.69860 − 4.05347I 0
u = −0.776192 − 0.835014I
a = 2.07774 − 1.16141I
b = 0.77380 − 2.17827I
11.69860 + 4.05347I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.685008 + 0.481376I
a = −0.671350 + 0.806633I
b = −0.324604 + 0.807985I
5.03216 − 1.01780I 3.86360 + 0.75310I
u = 0.685008 − 0.481376I
a = −0.671350 − 0.806633I
b = −0.324604 − 0.807985I
5.03216 + 1.01780I 3.86360 − 0.75310I
u = 0.674753 + 0.493249I
a = 0.892957 − 0.164512I
b = −0.0532868 + 0.0446471I
0.03629 − 1.91884I −4.55374 + 4.02239I
u = 0.674753 − 0.493249I
a = 0.892957 + 0.164512I
b = −0.0532868 − 0.0446471I
0.03629 + 1.91884I −4.55374 − 4.02239I
u = 0.125956 + 1.164950I
a = 0.793952 + 0.447911I
b = −0.331670 + 0.408432I
1.57754 + 1.96619I 0
u = 0.125956 − 1.164950I
a = 0.793952 − 0.447911I
b = −0.331670 − 0.408432I
1.57754 − 1.96619I 0
u = −0.905570 + 0.746388I
a = −1.56681 − 0.61842I
b = −0.60049 − 2.22973I
9.01118 + 2.11338I 0
u = −0.905570 − 0.746388I
a = −1.56681 + 0.61842I
b = −0.60049 + 2.22973I
9.01118 − 2.11338I 0
u = 0.857518 + 0.845288I
a = 1.71489 − 1.10425I
b = 0.03590 − 2.23093I
13.33450 − 0.74413I 0
u = 0.857518 − 0.845288I
a = 1.71489 + 1.10425I
b = 0.03590 + 2.23093I
13.33450 + 0.74413I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.808599 + 0.893250I
a = −1.48978 + 0.39296I
b = −0.695470 + 0.566481I
4.03943 + 7.86346I 0
u = 0.808599 − 0.893250I
a = −1.48978 − 0.39296I
b = −0.695470 − 0.566481I
4.03943 − 7.86346I 0
u = −0.755392 + 0.942068I
a = 1.35234 + 1.51692I
b = 0.40854 + 2.69108I
11.36750 − 1.74590I 0
u = −0.755392 − 0.942068I
a = 1.35234 − 1.51692I
b = 0.40854 − 2.69108I
11.36750 + 1.74590I 0
u = 0.586707 + 1.057010I
a = −0.847409 + 0.771102I
b = −0.574387 + 1.013170I
3.36226 + 5.96102I 0
u = 0.586707 − 1.057010I
a = −0.847409 − 0.771102I
b = −0.574387 − 1.013170I
3.36226 − 5.96102I 0
u = −0.891731 + 0.840665I
a = −0.481551 + 0.251785I
b = −1.12694 − 1.25772I
5.26607 − 5.97794I 0
u = −0.891731 − 0.840665I
a = −0.481551 − 0.251785I
b = −1.12694 + 1.25772I
5.26607 + 5.97794I 0
u = 0.586220 + 1.081390I
a = 0.133904 − 0.312139I
b = 0.300788 − 0.900121I
−1.72755 + 6.88426I 0
u = 0.586220 − 1.081390I
a = 0.133904 + 0.312139I
b = 0.300788 + 0.900121I
−1.72755 − 6.88426I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.833867 + 0.931666I
a = 0.011648 + 0.675666I
b = −0.22419 + 1.43475I
3.94945 − 1.73029I 0
u = 0.833867 − 0.931666I
a = 0.011648 − 0.675666I
b = −0.22419 − 1.43475I
3.94945 + 1.73029I 0
u = −0.620183 + 1.088800I
a = 0.271097 − 0.813299I
b = 1.066280 − 0.583822I
3.47667 − 7.03715I 0
u = −0.620183 − 1.088800I
a = 0.271097 + 0.813299I
b = 1.066280 + 0.583822I
3.47667 + 7.03715I 0
u = 0.812966 + 0.968903I
a = 1.47513 − 1.02155I
b = 0.60131 − 2.65223I
12.9447 + 6.9741I 0
u = 0.812966 − 0.968903I
a = 1.47513 + 1.02155I
b = 0.60131 + 2.65223I
12.9447 − 6.9741I 0
u = 0.417255 + 0.595574I
a = 0.906862 + 1.028830I
b = 1.44318 − 0.59225I
−3.48958 + 0.81926I −1.10723 + 7.17810I
u = 0.417255 − 0.595574I
a = 0.906862 − 1.028830I
b = 1.44318 + 0.59225I
−3.48958 − 0.81926I −1.10723 − 7.17810I
u = 0.755325 + 1.024620I
a = −1.47153 + 1.42806I
b = −0.57159 + 2.27179I
6.31700 + 5.12272I 0
u = 0.755325 − 1.024620I
a = −1.47153 − 1.42806I
b = −0.57159 − 2.27179I
6.31700 − 5.12272I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.122970 + 0.615953I
a = 1.43503 − 0.45100I
b = 0.21012 − 1.85984I
15.5887 − 9.4779I 0
u = 1.122970 − 0.615953I
a = 1.43503 + 0.45100I
b = 0.21012 + 1.85984I
15.5887 + 9.4779I 0
u = −0.097362 + 0.683736I
a = −2.21326 + 0.89923I
b = 0.083644 + 0.547260I
8.06044 + 1.96087I −6.97401 − 6.64687I
u = −0.097362 − 0.683736I
a = −2.21326 − 0.89923I
b = 0.083644 − 0.547260I
8.06044 − 1.96087I −6.97401 + 6.64687I
u = −0.793679 + 1.042660I
a = −1.39866 − 1.40506I
b = −0.07618 − 2.49555I
8.08586 − 8.41406I 0
u = −0.793679 − 1.042660I
a = −1.39866 + 1.40506I
b = −0.07618 + 2.49555I
8.08586 + 8.41406I 0
u = 0.143179 + 0.668479I
a = −2.73389 + 1.26855I
b = −1.91204 + 0.24981I
0.07264 + 5.18640I −2.24311 − 3.02074I
u = 0.143179 − 0.668479I
a = −2.73389 − 1.26855I
b = −1.91204 − 0.24981I
0.07264 − 5.18640I −2.24311 + 3.02074I
u = −0.868591 + 1.008050I
a = −0.612283 − 0.762405I
b = 0.798677 − 0.486252I
4.77438 − 0.52879I 0
u = −0.868591 − 1.008050I
a = −0.612283 + 0.762405I
b = 0.798677 + 0.486252I
4.77438 + 0.52879I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.281600 + 0.509659I
a = 1.165520 + 0.192564I
b = 0.15176 + 1.69413I
14.2247 − 0.6780I 0
u = −1.281600 − 0.509659I
a = 1.165520 − 0.192564I
b = 0.15176 − 1.69413I
14.2247 + 0.6780I 0
u = 0.80610 + 1.17936I
a = 1.10730 − 1.40702I
b = 0.16133 − 2.68309I
13.7755 + 16.3958I 0
u = 0.80610 − 1.17936I
a = 1.10730 + 1.40702I
b = 0.16133 + 2.68309I
13.7755 − 16.3958I 0
u = −0.211361 + 0.486832I
a = 0.397591 − 0.482624I
b = −0.064564 + 0.403505I
−0.073057 − 1.023140I −1.34729 + 6.93509I
u = −0.211361 − 0.486832I
a = 0.397591 + 0.482624I
b = −0.064564 − 0.403505I
−0.073057 + 1.023140I −1.34729 − 6.93509I
u = −0.071583 + 0.511345I
a = −3.10512 − 1.44557I
b = −1.297630 − 0.234701I
−1.77992 + 1.19696I 0.03557 + 2.38161I
u = −0.071583 − 0.511345I
a = −3.10512 + 1.44557I
b = −1.297630 + 0.234701I
−1.77992 − 1.19696I 0.03557 − 2.38161I
u = 0.01963 + 1.54289I
a = 0.20427 − 1.41812I
b = 0.06304 − 2.22995I
−6.31186 − 1.00322I 0
u = 0.01963 − 1.54289I
a = 0.20427 + 1.41812I
b = 0.06304 + 2.22995I
−6.31186 + 1.00322I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.85412 + 1.28528I
a = 0.84162 + 1.24436I
b = −0.09692 + 2.44856I
11.80170 − 6.84042I 0
u = −0.85412 − 1.28528I
a = 0.84162 − 1.24436I
b = −0.09692 − 2.44856I
11.80170 + 6.84042I 0
u = −0.17757 + 1.56950I
a = −0.345899 − 0.007011I
b = 1.013900 − 0.055144I
6.48446 − 6.01294I 0
u = −0.17757 − 1.56950I
a = −0.345899 + 0.007011I
b = 1.013900 + 0.055144I
6.48446 + 6.01294I 0
u = 0.217162 + 0.333065I
a = −0.21882 + 2.01262I
b = −1.295440 + 0.442525I
5.12456 − 0.63054I 2.98724 − 1.55101I
u = 0.217162 − 0.333065I
a = −0.21882 − 2.01262I
b = −1.295440 − 0.442525I
5.12456 + 0.63054I 2.98724 + 1.55101I
12
II. I
u
2
= h2.32 × 10
9
u
35
+ 6.26 × 10
8
u
34
+ · · · + 2.16 × 10
8
b − 4.44 × 10
9
, 1.85 ×
10
10
u
35
−1.30×10
9
u
34
+· · ·+1.08×10
9
a−2.36×10
10
, u
36
+11u
34
+· · ·+4u+5i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
−u
2
a
5
=
−17.1846u
35
+ 1.20283u
34
+ ··· − 75.7116u + 21.9221
−10.7599u
35
− 2.90164u
34
+ ··· − 25.2606u + 20.5840
a
6
=
−16.6658u
35
+ 2.34552u
34
+ ··· − 19.8606u + 36.4920
−14.2879u
35
− 3.75044u
34
+ ··· − 18.0959u + 26.2975
a
9
=
u
u
a
10
=
3.12153u
35
+ 3.61119u
34
+ ··· + 51.1214u + 40.2398
−2.89850u
35
+ 1.59421u
34
+ ··· + 4.90691u − 0.328315
a
1
=
u
2
+ 1
−u
4
a
11
=
1.64216u
35
+ 3.57318u
34
+ ··· + 27.8545u + 41.5188
−5.57167u
35
− 0.0804230u
34
+ ··· − 16.1199u − 6.11863
a
12
=
−1.64253u
35
− 7.92125u
34
+ ··· − 93.3783u + 4.52924
−5.74240u
35
− 12.0937u
34
+ ··· − 135.508u − 86.5034
a
4
=
18.3632u
35
− 6.24544u
34
+ ··· + 113.684u − 33.6728
5.42696u
35
+ 5.48132u
34
+ ··· − 2.11327u + 26.8602
a
7
=
−6.20362u
35
− 12.5212u
34
+ ··· + 8.52928u − 73.1894
−7.13644u
35
− 6.41854u
34
+ ··· − 49.4761u + 11.3475
(ii) Obstruction class = 1
(iii) Cusp Shapes =
4184661271
215633713
u
35
−
680860653
215633713
u
34
+ ··· +
99258781362
215633713
u +
14533752217
215633713
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
36
− 22u
35
+ ··· − 464u + 25
c
2
u
36
+ 11u
34
+ ··· + 4u + 5
c
3
u
36
+ 19u
34
+ ··· − 435u + 493
c
4
u
36
+ 11u
34
+ ··· + 4u + 5
c
5
u
36
− 14u
35
+ ··· − 973u + 73
c
6
u
36
+ 2u
35
+ ··· + 1163u + 175
c
7
u
36
+ 3u
34
+ ··· − 82u + 29
c
8
u
36
+ 11u
34
+ ··· − 4u + 5
c
9
u
36
+ u
35
+ ··· − 2u + 1
c
10
u
36
− 6u
35
+ ··· + 2u + 1
c
11
u
36
+ 11u
34
+ ··· − 4u + 5
c
12
u
36
+ 2u
34
+ ··· − u + 1
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
36
+ 2y
35
+ ··· + 804y + 625
c
2
, c
8
y
36
+ 22y
35
+ ··· + 464y + 25
c
3
y
36
+ 38y
35
+ ··· + 3007387y + 243049
c
4
, c
11
y
36
+ 22y
35
+ ··· + 564y + 25
c
5
y
36
− 38y
35
+ ··· − 246659y + 5329
c
6
y
36
+ 20y
35
+ ··· + 89081y + 30625
c
7
y
36
+ 6y
35
+ ··· + 33006y + 841
c
9
y
36
+ 13y
35
+ ··· − 18y + 1
c
10
y
36
− 8y
35
+ ··· + 30y + 1
c
12
y
36
+ 4y
35
+ ··· − 27y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.346186 + 0.915633I
a = −2.18981 + 0.04924I
b = −2.30967 + 0.67789I
−0.09061 + 6.29545I −2.74141 − 9.81893I
u = 0.346186 − 0.915633I
a = −2.18981 − 0.04924I
b = −2.30967 − 0.67789I
−0.09061 − 6.29545I −2.74141 + 9.81893I
u = 0.358539 + 0.889505I
a = 1.10628 + 1.99818I
b = 1.35666 + 1.39465I
−0.01798 − 3.35229I −0.148269 + 0.744013I
u = 0.358539 − 0.889505I
a = 1.10628 − 1.99818I
b = 1.35666 − 1.39465I
−0.01798 + 3.35229I −0.148269 − 0.744013I
u = 0.793225 + 0.705083I
a = 0.175649 + 0.251827I
b = −0.443614 + 0.878255I
2.93798 − 2.72322I −0.38581 + 3.76403I
u = 0.793225 − 0.705083I
a = 0.175649 − 0.251827I
b = −0.443614 − 0.878255I
2.93798 + 2.72322I −0.38581 − 3.76403I
u = −0.833697 + 0.409348I
a = −0.992290 − 0.210555I
b = −0.204707 + 0.035403I
1.05225 + 1.68422I 3.81700 − 1.49163I
u = −0.833697 − 0.409348I
a = −0.992290 + 0.210555I
b = −0.204707 − 0.035403I
1.05225 − 1.68422I 3.81700 + 1.49163I
u = 0.791352 + 0.733206I
a = −1.47082 + 1.03484I
b = −0.79762 + 2.14988I
7.23477 + 0.01514I 3.93034 + 2.41109I
u = 0.791352 − 0.733206I
a = −1.47082 − 1.03484I
b = −0.79762 − 2.14988I
7.23477 − 0.01514I 3.93034 − 2.41109I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.485657 + 0.963636I
a = −0.330010 + 1.341270I
b = −0.897778 + 0.513044I
−4.27615 − 2.65956I 5.82571 + 1.68378I
u = −0.485657 − 0.963636I
a = −0.330010 − 1.341270I
b = −0.897778 − 0.513044I
−4.27615 + 2.65956I 5.82571 − 1.68378I
u = −0.295770 + 1.046740I
a = −0.668520 − 0.246425I
b = −1.196780 − 0.522064I
−3.40683 − 0.20848I −1.58036 + 4.45786I
u = −0.295770 − 1.046740I
a = −0.668520 + 0.246425I
b = −1.196780 + 0.522064I
−3.40683 + 0.20848I −1.58036 − 4.45786I
u = −0.481168 + 0.730864I
a = 0.943466 − 0.719816I
b = 1.54841 + 0.64568I
−3.47907 − 1.30636I −0.49756 + 8.73623I
u = −0.481168 − 0.730864I
a = 0.943466 + 0.719816I
b = 1.54841 − 0.64568I
−3.47907 + 1.30636I −0.49756 − 8.73623I
u = 0.638782 + 0.989341I
a = −0.602797 + 0.604049I
b = −0.147279 + 0.094498I
2.02425 + 8.10760I −2.00000 − 8.42655I
u = 0.638782 − 0.989341I
a = −0.602797 − 0.604049I
b = −0.147279 − 0.094498I
2.02425 − 8.10760I −2.00000 + 8.42655I
u = 0.387249 + 1.117620I
a = 0.724091 + 0.876891I
b = 0.040960 + 0.770428I
3.07088 + 1.37025I 3.22960 − 2.00825I
u = 0.387249 − 1.117620I
a = 0.724091 − 0.876891I
b = 0.040960 − 0.770428I
3.07088 − 1.37025I 3.22960 + 2.00825I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.837390 + 0.871528I
a = 1.70691 + 1.15090I
b = 0.54310 + 2.35416I
11.77110 − 3.11236I 4.32263 + 1.36336I
u = −0.837390 − 0.871528I
a = 1.70691 − 1.15090I
b = 0.54310 − 2.35416I
11.77110 + 3.11236I 4.32263 − 1.36336I
u = −0.189157 + 0.766784I
a = 1.66961 − 1.22863I
b = 1.021840 − 0.208129I
−2.14208 − 1.85652I −5.61597 + 6.31680I
u = −0.189157 − 0.766784I
a = 1.66961 + 1.22863I
b = 1.021840 + 0.208129I
−2.14208 + 1.85652I −5.61597 − 6.31680I
u = −0.583336 + 1.122560I
a = −0.068672 − 0.608135I
b = −0.208023 − 1.033470I
−1.14083 − 6.93199I 3.42893 + 7.12793I
u = −0.583336 − 1.122560I
a = −0.068672 + 0.608135I
b = −0.208023 + 1.033470I
−1.14083 + 6.93199I 3.42893 − 7.12793I
u = 0.753209 + 1.025770I
a = −1.48035 + 1.37031I
b = −0.50958 + 2.07922I
6.33430 + 5.83706I 2.94405 − 8.41583I
u = 0.753209 − 1.025770I
a = −1.48035 − 1.37031I
b = −0.50958 − 2.07922I
6.33430 − 5.83706I 2.94405 + 8.41583I
u = 0.254814 + 0.679563I
a = −0.729942 + 0.340568I
b = −1.77935 + 0.23036I
4.81487 + 1.44558I −1.16457 − 5.73751I
u = 0.254814 − 0.679563I
a = −0.729942 − 0.340568I
b = −1.77935 − 0.23036I
4.81487 − 1.44558I −1.16457 + 5.73751I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.377590 + 1.241040I
a = −0.163004 − 0.019157I
b = 1.066970 − 0.129596I
5.98759 − 4.35262I 0. + 3.24251I
u = −0.377590 − 1.241040I
a = −0.163004 + 0.019157I
b = 1.066970 + 0.129596I
5.98759 + 4.35262I 0. − 3.24251I
u = −0.227050 + 0.642295I
a = −1.68646 + 0.93709I
b = 0.425164 + 0.271262I
8.40082 + 1.74571I 10.72780 + 3.90391I
u = −0.227050 − 0.642295I
a = −1.68646 − 0.93709I
b = 0.425164 − 0.271262I
8.40082 − 1.74571I 10.72780 − 3.90391I
u = −0.01254 + 1.58839I
a = 0.156671 − 1.369420I
b = −0.00870 − 2.20506I
−6.17659 − 0.87363I 0
u = −0.01254 − 1.58839I
a = 0.156671 + 1.369420I
b = −0.00870 + 2.20506I
−6.17659 + 0.87363I 0
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
36
− 22u
35
+ ··· − 464u + 25)(u
76
+ 31u
75
+ ··· + 56539u + 1444)
c
2
(u
36
+ 11u
34
+ ··· + 4u + 5)(u
76
+ u
75
+ ··· + 161u + 38)
c
3
(u
36
+ 19u
34
+ ··· − 435u + 493)
· (u
76
+ u
75
+ ··· + 785435u + 192925)
c
4
(u
36
+ 11u
34
+ ··· + 4u + 5)(u
76
+ u
75
+ ··· + 115u + 42)
c
5
(u
36
− 14u
35
+ ··· − 973u + 73)
· (u
76
+ 7u
75
+ ··· − 176881u + 193903)
c
6
(u
36
+ 2u
35
+ ··· + 1163u + 175)
· (u
76
− u
75
+ ··· − 1137222277u + 654834962)
c
7
(u
36
+ 3u
34
+ ··· − 82u + 29)
· (u
76
− 5u
75
+ ··· + 1855244u + 7111423)
c
8
(u
36
+ 11u
34
+ ··· − 4u + 5)(u
76
+ u
75
+ ··· + 161u + 38)
c
9
(u
36
+ u
35
+ ··· − 2u + 1)(u
76
− 2u
75
+ ··· − 3.40445 × 10
7
u + 1.08127 × 10
7
)
c
10
(u
36
− 6u
35
+ ··· + 2u + 1)(u
76
− 3u
75
+ ··· + 56u + 493)
c
11
(u
36
+ 11u
34
+ ··· − 4u + 5)(u
76
+ u
75
+ ··· + 115u + 42)
c
12
(u
36
+ 2u
34
+ ··· − u + 1)(u
76
+ u
75
+ ··· + 4761u + 5283)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
36
+ 2y
35
+ ··· + 804y + 625)
· (y
76
+ 47y
75
+ ··· + 79202767y + 2085136)
c
2
, c
8
(y
36
+ 22y
35
+ ··· + 464y + 25)(y
76
+ 31y
75
+ ··· + 56539y + 1444)
c
3
(y
36
+ 38y
35
+ ··· + 3007387y + 243049)
· (y
76
+ 115y
75
+ ··· + 1105604974175y + 37220055625)
c
4
, c
11
(y
36
+ 22y
35
+ ··· + 564y + 25)(y
76
+ 67y
75
+ ··· − 35821y + 1764)
c
5
(y
36
− 38y
35
+ ··· − 246659y + 5329)
· (y
76
− 109y
75
+ ··· − 932607366479y + 37598373409)
c
6
(y
36
+ 20y
35
+ ··· + 89081y + 30625)
· (y
76
+ 65y
75
+ ··· − 1108270808871508769y + 428808827457541444)
c
7
(y
36
+ 6y
35
+ ··· + 33006y + 841)
· (y
76
− 29y
75
+ ··· + 889309315939338y + 50572337084929)
c
9
(y
36
+ 13y
35
+ ··· − 18y + 1)
· (y
76
+ 102y
75
+ ··· − 390748923918910y + 116915411184049)
c
10
(y
36
− 8y
35
+ ··· + 30y + 1)(y
76
+ 9y
75
+ ··· + 7601882y + 243049)
c
12
(y
36
+ 4y
35
+ ··· − 27y + 1)
· (y
76
− 19y
75
+ ··· + 69943869y + 27910089)
23
