12n
0790
(K12n
0790
)
A knot diagram
1
Linearized knot diagam
4 6 10 7 2 12 4 11 3 1 7 9
Solving Sequence
2,6 3,12
7 5 4 8 11 9 1 10
c
2
c
6
c
5
c
4
c
7
c
11
c
8
c
12
c
10
c
1
, c
3
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.14667 × 10
409
u
92
− 5.32523 × 10
410
u
91
+ ··· + 4.98001 × 10
410
b − 3.89130 × 10
412
,
4.70081 × 10
411
u
92
+ 3.48169 × 10
412
u
91
+ ··· + 3.46111 × 10
413
a + 1.89968 × 10
415
,
3u
93
+ 22u
92
+ ··· + 6023u + 695i
I
u
2
= h−5.47528 × 10
24
u
26
− 9.23714 × 10
22
u
25
+ ··· + 2.62202 × 10
24
b − 3.76400 × 10
22
,
− 2.17634 × 10
24
u
26
+ 3.10319 × 10
24
u
25
+ ··· + 2.62202 × 10
24
a − 1.13279 × 10
25
, 3u
27
− u
26
+ ··· − 6u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 120 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−7.15 × 10
409
u
92
− 5.33 × 10
410
u
91
+ · · · + 4.98 × 10
410
b − 3.89 ×
10
412
, 4.70 × 10
411
u
92
+ 3.48 × 10
412
u
91
+ · · · + 3.46 × 10
413
a + 1.90 ×
10
415
, 3u
93
+ 22u
92
+ · · · + 6023u + 695i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
12
=
−0.0135818u
92
− 0.100595u
91
+ ··· − 238.687u − 54.8864
0.143507u
92
+ 1.06932u
91
+ ··· + 568.056u + 78.1384
a
7
=
−0.301700u
92
− 2.00007u
91
+ ··· − 550.015u − 80.7225
−0.295411u
92
− 1.99275u
91
+ ··· − 598.971u − 73.2675
a
5
=
u
u
a
4
=
0.0629549u
92
+ 0.517586u
91
+ ··· + 447.875u + 108.119
−0.0833166u
92
− 0.479335u
91
+ ··· + 1.31628u + 2.37199
a
8
=
−0.185984u
92
− 1.41044u
91
+ ··· − 1066.72u − 289.305
−0.0386972u
92
− 0.308193u
91
+ ··· − 77.2777u − 1.02321
a
11
=
−0.382257u
92
− 2.77588u
91
+ ··· − 1845.24u − 324.691
0.143790u
92
+ 0.957852u
91
+ ··· + 265.817u + 30.9818
a
9
=
0.127751u
92
+ 0.819530u
91
+ ··· + 175.460u − 2.90117
0.152700u
92
+ 1.01579u
91
+ ··· + 335.904u + 44.8910
a
1
=
1.32557u
92
+ 8.92984u
91
+ ··· + 3658.56u + 546.752
0.468972u
92
+ 3.23240u
91
+ ··· + 1446.79u + 205.465
a
10
=
0.0625451u
92
+ 0.381060u
91
+ ··· + 45.4867u − 20.6145
0.141552u
92
+ 0.924644u
91
+ ··· + 271.287u + 35.6916
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.215998u
92
+ 1.15544u
91
+ ··· + 644.040u + 222.694
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
93
+ u
92
+ ··· − 493754u − 46509
c
2
, c
5
3(3u
93
+ 22u
92
+ ··· + 6023u + 695)
c
3
, c
9
u
93
− 4u
92
+ ··· − 435u + 281
c
4
, c
7
u
93
+ 9u
92
+ ··· − 341511u − 15167
c
6
, c
11
3(3u
93
− 5u
92
+ ··· − 24386u − 2531)
c
8
u
93
+ 16u
92
+ ··· + 256813u + 72465
c
10
9(9u
93
+ 71u
92
+ ··· − 6u − 1)
c
12
u
93
+ 3u
91
+ ··· + 17755u + 2097
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
93
+ 7y
92
+ ··· − 70016139986y −2163087081
c
2
, c
5
9(9y
93
− 298y
92
+ ··· + 1.07075 × 10
7
y −483025)
c
3
, c
9
y
93
− 62y
92
+ ··· + 1260959y −78961
c
4
, c
7
y
93
− 81y
92
+ ··· − 1602188993y −230037889
c
6
, c
11
9(9y
93
+ 395y
92
+ ··· − 7.45852 × 10
7
y −6405961)
c
8
y
93
− 42y
92
+ ··· + 228494230849y −5251176225
c
10
81(81y
93
− 1621y
92
+ ··· − 20y −1)
c
12
y
93
+ 6y
92
+ ··· + 66493885y −4397409
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.674954 + 0.732172I
a = 1.215980 − 0.268347I
b = 0.139557 + 0.583522I
2.81000 + 0.59876I 0
u = 0.674954 − 0.732172I
a = 1.215980 + 0.268347I
b = 0.139557 − 0.583522I
2.81000 − 0.59876I 0
u = 0.686494 + 0.697906I
a = −0.001348 − 1.067160I
b = 1.10088 − 2.50838I
2.54150 − 7.26629I 0
u = 0.686494 − 0.697906I
a = −0.001348 + 1.067160I
b = 1.10088 + 2.50838I
2.54150 + 7.26629I 0
u = −0.691333 + 0.690971I
a = 0.346050 − 1.118080I
b = 0.103808 − 0.667560I
−1.23938 + 3.77370I 0
u = −0.691333 − 0.690971I
a = 0.346050 + 1.118080I
b = 0.103808 + 0.667560I
−1.23938 − 3.77370I 0
u = −0.937905 + 0.192409I
a = 0.198382 + 0.296203I
b = −0.638617 + 0.629199I
−1.61133 + 0.24005I 0
u = −0.937905 − 0.192409I
a = 0.198382 − 0.296203I
b = −0.638617 − 0.629199I
−1.61133 − 0.24005I 0
u = −0.948386 + 0.462059I
a = −0.133432 + 0.734649I
b = −0.660912 + 0.952450I
−2.50321 + 0.81346I 0
u = −0.948386 − 0.462059I
a = −0.133432 − 0.734649I
b = −0.660912 − 0.952450I
−2.50321 − 0.81346I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.095269 + 0.938474I
a = 0.473851 + 0.415001I
b = 0.512383 − 0.773209I
2.00771 − 3.44099I 0
u = 0.095269 − 0.938474I
a = 0.473851 − 0.415001I
b = 0.512383 + 0.773209I
2.00771 + 3.44099I 0
u = 0.823460 + 0.375542I
a = −0.119724 − 1.144210I
b = −1.03275 − 1.35723I
−6.20249 − 5.22443I 0
u = 0.823460 − 0.375542I
a = −0.119724 + 1.144210I
b = −1.03275 + 1.35723I
−6.20249 + 5.22443I 0
u = 0.854498 + 0.689956I
a = 0.093394 + 0.958920I
b = −1.15625 + 1.81104I
4.75042 − 0.26422I 0
u = 0.854498 − 0.689956I
a = 0.093394 − 0.958920I
b = −1.15625 − 1.81104I
4.75042 + 0.26422I 0
u = 0.918476 + 0.606358I
a = −0.434023 − 0.634737I
b = −0.903200 − 0.654198I
−5.81791 + 4.00342I 0
u = 0.918476 − 0.606358I
a = −0.434023 + 0.634737I
b = −0.903200 + 0.654198I
−5.81791 − 4.00342I 0
u = 0.872877 + 0.109712I
a = −0.52784 + 1.37760I
b = 0.564876 + 0.849824I
−6.64115 + 3.23471I −7.67162 + 0.I
u = 0.872877 − 0.109712I
a = −0.52784 − 1.37760I
b = 0.564876 − 0.849824I
−6.64115 − 3.23471I −7.67162 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.878160 + 0.700675I
a = −1.086750 + 0.245560I
b = −0.028345 − 0.641744I
4.67143 − 5.07155I 0
u = 0.878160 − 0.700675I
a = −1.086750 − 0.245560I
b = −0.028345 + 0.641744I
4.67143 + 5.07155I 0
u = −0.662848 + 0.569436I
a = −0.071156 − 0.971664I
b = −1.63900 − 1.99223I
2.25029 − 5.38425I 0
u = −0.662848 − 0.569436I
a = −0.071156 + 0.971664I
b = −1.63900 + 1.99223I
2.25029 + 5.38425I 0
u = −1.128720 + 0.149564I
a = 0.30651 − 1.52316I
b = 0.02115 − 1.67361I
−8.96468 − 3.92565I 0
u = −1.128720 − 0.149564I
a = 0.30651 + 1.52316I
b = 0.02115 + 1.67361I
−8.96468 + 3.92565I 0
u = 0.398460 + 0.758184I
a = 1.077610 − 0.881690I
b = 0.344671 + 0.364720I
3.37801 + 0.99096I 6.48497 + 0.I
u = 0.398460 − 0.758184I
a = 1.077610 + 0.881690I
b = 0.344671 − 0.364720I
3.37801 − 0.99096I 6.48497 + 0.I
u = 0.933778 + 0.704004I
a = −0.091450 + 1.054630I
b = −0.010874 + 0.746479I
−5.82082 − 9.31118I 0
u = 0.933778 − 0.704004I
a = −0.091450 − 1.054630I
b = −0.010874 − 0.746479I
−5.82082 + 9.31118I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.442517 + 0.688839I
a = 0.176317 + 0.822306I
b = 0.249277 + 0.829583I
−0.81738 + 3.68689I 0. − 7.64746I
u = −0.442517 − 0.688839I
a = 0.176317 − 0.822306I
b = 0.249277 − 0.829583I
−0.81738 − 3.68689I 0. + 7.64746I
u = −0.619214 + 0.521758I
a = 0.742330 + 0.106731I
b = −0.113697 + 0.262021I
−1.67952 + 0.53410I −4.21973 + 0.I
u = −0.619214 − 0.521758I
a = 0.742330 − 0.106731I
b = −0.113697 − 0.262021I
−1.67952 − 0.53410I −4.21973 + 0.I
u = 1.112030 + 0.426697I
a = 0.084200 − 1.167710I
b = −0.10451 − 1.58436I
−5.26330 − 4.96135I 0
u = 1.112030 − 0.426697I
a = 0.084200 + 1.167710I
b = −0.10451 + 1.58436I
−5.26330 + 4.96135I 0
u = −0.623299 + 0.503573I
a = −0.92680 + 1.62860I
b = −0.40002 + 2.17351I
−6.65496 + 6.93046I 0. − 11.05037I
u = −0.623299 − 0.503573I
a = −0.92680 − 1.62860I
b = −0.40002 − 2.17351I
−6.65496 − 6.93046I 0. + 11.05037I
u = −0.692093 + 0.397215I
a = −0.099142 + 0.920873I
b = 1.81566 + 1.93139I
2.87496 + 2.75738I −1.61500 − 5.30010I
u = −0.692093 − 0.397215I
a = −0.099142 − 0.920873I
b = 1.81566 − 1.93139I
2.87496 − 2.75738I −1.61500 + 5.30010I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.044320 + 0.596872I
a = −1.300970 − 0.184765I
b = −0.170854 + 0.517420I
0.96308 + 10.07780I 0
u = −1.044320 − 0.596872I
a = −1.300970 + 0.184765I
b = −0.170854 − 0.517420I
0.96308 − 10.07780I 0
u = −1.083630 + 0.537499I
a = −0.070934 + 1.305290I
b = 0.85778 + 1.95035I
−0.80241 + 7.59723I 0
u = −1.083630 − 0.537499I
a = −0.070934 − 1.305290I
b = 0.85778 − 1.95035I
−0.80241 − 7.59723I 0
u = 0.733455 + 0.252583I
a = −0.30543 − 1.82531I
b = 0.00457 − 2.01689I
−4.01462 − 3.43234I 8.55484 + 7.50603I
u = 0.733455 − 0.252583I
a = −0.30543 + 1.82531I
b = 0.00457 + 2.01689I
−4.01462 + 3.43234I 8.55484 − 7.50603I
u = −1.24771
a = 0.914123
b = −0.758760
0.556605 0
u = 1.089900 + 0.607822I
a = 0.181194 − 1.176140I
b = 0.94657 − 1.94638I
1.36282 − 6.16551I 0
u = 1.089900 − 0.607822I
a = 0.181194 + 1.176140I
b = 0.94657 + 1.94638I
1.36282 + 6.16551I 0
u = 1.264290 + 0.183174I
a = 0.479294 − 0.545939I
b = −0.381207 − 0.859789I
−2.91671 − 0.62225I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.264290 − 0.183174I
a = 0.479294 + 0.545939I
b = −0.381207 + 0.859789I
−2.91671 + 0.62225I 0
u = −0.910304 + 0.900507I
a = 0.522542 − 1.020090I
b = −0.74377 − 1.38645I
−2.57873 + 6.21327I 0
u = −0.910304 − 0.900507I
a = 0.522542 + 1.020090I
b = −0.74377 + 1.38645I
−2.57873 − 6.21327I 0
u = 1.119580 + 0.704429I
a = 0.089214 − 1.066460I
b = 0.79897 − 1.96272I
1.49803 − 6.24365I 0
u = 1.119580 − 0.704429I
a = 0.089214 + 1.066460I
b = 0.79897 + 1.96272I
1.49803 + 6.24365I 0
u = −0.588087 + 0.331536I
a = 1.83719 − 0.13136I
b = 0.125737 − 1.152850I
1.12788 − 3.60271I 1.12062 + 5.92083I
u = −0.588087 − 0.331536I
a = 1.83719 + 0.13136I
b = 0.125737 + 1.152850I
1.12788 + 3.60271I 1.12062 − 5.92083I
u = −1.203700 + 0.590086I
a = −0.347750 + 0.718485I
b = −0.25721 + 1.84323I
−3.96714 + 0.38677I 0
u = −1.203700 − 0.590086I
a = −0.347750 − 0.718485I
b = −0.25721 − 1.84323I
−3.96714 − 0.38677I 0
u = −0.287732 + 1.319090I
a = 0.193631 + 0.189893I
b = 0.192982 − 0.234031I
4.31204 + 3.39765I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.287732 − 1.319090I
a = 0.193631 − 0.189893I
b = 0.192982 + 0.234031I
4.31204 − 3.39765I 0
u = 0.544638 + 0.306845I
a = 0.92896 + 1.85109I
b = 0.519502 + 1.298470I
−2.86298 + 2.13949I 0.67058 − 5.49562I
u = 0.544638 − 0.306845I
a = 0.92896 − 1.85109I
b = 0.519502 − 1.298470I
−2.86298 − 2.13949I 0.67058 + 5.49562I
u = −0.489317 + 1.296330I
a = −0.474834 + 0.068876I
b = 0.355242 + 0.882752I
−0.52324 + 2.36440I 0
u = −0.489317 − 1.296330I
a = −0.474834 − 0.068876I
b = 0.355242 − 0.882752I
−0.52324 − 2.36440I 0
u = −1.297460 + 0.490834I
a = 0.242981 + 0.811654I
b = 0.74306 + 1.50520I
0.31354 + 2.51804I 0
u = −1.297460 − 0.490834I
a = 0.242981 − 0.811654I
b = 0.74306 − 1.50520I
0.31354 − 2.51804I 0
u = −0.566170
a = 3.10038
b = 0.553177
4.63798 −11.5780
u = 0.48605 + 1.35102I
a = −0.634856 + 0.184510I
b = 0.272403 − 0.519347I
5.10190 + 4.33232I 0
u = 0.48605 − 1.35102I
a = −0.634856 − 0.184510I
b = 0.272403 + 0.519347I
5.10190 − 4.33232I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.401346 + 0.289584I
a = −1.36249 − 1.64357I
b = 0.467604 + 0.316991I
1.39489 + 1.09605I 4.43393 − 5.59913I
u = −0.401346 − 0.289584I
a = −1.36249 + 1.64357I
b = 0.467604 − 0.316991I
1.39489 − 1.09605I 4.43393 + 5.59913I
u = −1.52411 + 0.05080I
a = −0.138758 − 0.528352I
b = −0.11425 − 2.03470I
−3.77465 + 0.88656I 0
u = −1.52411 − 0.05080I
a = −0.138758 + 0.528352I
b = −0.11425 + 2.03470I
−3.77465 − 0.88656I 0
u = 1.29646 + 0.81005I
a = 0.006482 + 0.935911I
b = −0.78276 + 2.01410I
2.45748 − 11.81670I 0
u = 1.29646 − 0.81005I
a = 0.006482 − 0.935911I
b = −0.78276 − 2.01410I
2.45748 + 11.81670I 0
u = −1.32096 + 0.78025I
a = 0.162237 − 0.827746I
b = −0.89132 − 1.79515I
−3.29057 + 5.02576I 0
u = −1.32096 − 0.78025I
a = 0.162237 + 0.827746I
b = −0.89132 + 1.79515I
−3.29057 − 5.02576I 0
u = −0.64910 + 1.41700I
a = −0.793221 − 0.052665I
b = 0.142883 + 0.621132I
0.62586 − 10.14570I 0
u = −0.64910 − 1.41700I
a = −0.793221 + 0.052665I
b = 0.142883 − 0.621132I
0.62586 + 10.14570I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.54061 + 0.31502I
a = −0.232279 + 0.505844I
b = 0.26775 + 2.05575I
−7.67390 − 7.52480I 0
u = 1.54061 − 0.31502I
a = −0.232279 − 0.505844I
b = 0.26775 − 2.05575I
−7.67390 + 7.52480I 0
u = −1.30908 + 0.87953I
a = 0.023926 − 1.014740I
b = −0.69764 − 2.04274I
−1.6681 + 18.1685I 0
u = −1.30908 − 0.87953I
a = 0.023926 + 1.014740I
b = −0.69764 + 2.04274I
−1.6681 − 18.1685I 0
u = −1.33446 + 0.96768I
a = −0.024479 + 0.973454I
b = 0.48958 + 1.98070I
−2.11305 + 8.95351I 0
u = −1.33446 − 0.96768I
a = −0.024479 − 0.973454I
b = 0.48958 − 1.98070I
−2.11305 − 8.95351I 0
u = −0.281062
a = −5.70017
b = 0.206328
3.03653 44.5000
u = 0.107451 + 0.239477I
a = 0.35135 − 2.35992I
b = 0.433352 − 0.347109I
1.228090 − 0.380559I 7.84885 + 1.47754I
u = 0.107451 − 0.239477I
a = 0.35135 + 2.35992I
b = 0.433352 + 0.347109I
1.228090 + 0.380559I 7.84885 − 1.47754I
u = 1.75201 + 0.13606I
a = −0.132922 − 0.636322I
b = 0.11294 − 1.75128I
−9.64128 − 4.45809I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.75201 − 0.13606I
a = −0.132922 + 0.636322I
b = 0.11294 + 1.75128I
−9.64128 + 4.45809I 0
u = −0.61216 + 1.97687I
a = 0.972313 − 0.030847I
b = 0.143611 − 0.184027I
−0.0900114 − 0.0409964I 0
u = −0.61216 − 1.97687I
a = 0.972313 + 0.030847I
b = 0.143611 + 0.184027I
−0.0900114 + 0.0409964I 0
14
II. I
u
2
= h−5.48 × 10
24
u
26
− 9.24 × 10
22
u
25
+ · · · + 2.62 × 10
24
b − 3.76 ×
10
22
, −2.18 × 10
24
u
26
+ 3.10 × 10
24
u
25
+ · · · + 2.62 × 10
24
a − 1.13 ×
10
25
, 3u
27
− u
26
+ · · · − 6u
2
+ 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
12
=
0.830026u
26
− 1.18351u
25
+ ··· − 2.18146u + 4.32029
2.08819u
26
+ 0.0352291u
25
+ ··· − 0.969498u + 0.0143553
a
7
=
−9.13895u
26
+ 3.75782u
25
+ ··· + 19.1051u − 0.580350
−1.21146u
26
+ 1.36298u
25
+ ··· + 3.45375u − 0.913452
a
5
=
u
u
a
4
=
19.8999u
26
− 5.44200u
25
+ ··· − 42.0029u − 0.818310
2.13751u
26
− 0.640341u
25
+ ··· − 4.97331u + 0.983879
a
8
=
−53.2973u
26
+ 14.6786u
25
+ ··· + 116.922u + 3.66324
−4.77966u
26
+ 2.89122u
25
+ ··· + 13.8959u − 3.34107
a
11
=
−0.703685u
26
− 7.82470u
25
+ ··· − 4.38591u + 16.7491
1.55379u
26
− 2.01157u
25
+ ··· − 2.08747u + 1.79186
a
9
=
−17.4160u
26
+ 6.20552u
25
+ ··· + 38.6101u − 3.38199
−2.41028u
26
+ 1.11206u
25
+ ··· + 5.03666u − 0.825501
a
1
=
−19.9953u
26
+ 17.9764u
25
+ ··· + 47.8550u − 26.3512
−4.73532u
26
+ 3.06498u
25
+ ··· + 11.6086u − 4.04184
a
10
=
−18.0474u
26
+ 6.17298u
25
+ ··· + 39.3788u − 2.68988
−2.60784u
26
+ 1.19707u
25
+ ··· + 5.24713u − 0.744502
(ii) Obstruction class = 1
(iii) Cusp Shapes =
96546149137055527549848081
2622017778319800888275503
u
26
−
21368440923253031371319385
2622017778319800888275503
u
25
+
··· −
206442519224589606723744388
2622017778319800888275503
u −
13602696470375884795425211
2622017778319800888275503
15
(iv) u-Polynomials at the component
16
Crossings u-Polynomials at each crossing
c
1
u
27
− 6u
26
+ ··· + 41u + 111
c
2
3(3u
27
− u
26
+ ··· − 6u
2
+ 1)
c
3
u
27
− 3u
26
+ ··· − 6u + 1
c
4
u
27
+ 4u
26
+ ··· − 4u + 1
c
5
3(3u
27
+ u
26
+ ··· + 6u
2
− 1)
c
6
3(3u
27
+ 4u
26
+ ··· + u − 1)
c
7
u
27
− 4u
26
+ ··· − 4u − 1
c
8
u
27
− 3u
26
+ ··· − 134u + 123
c
9
u
27
+ 3u
26
+ ··· − 6u − 1
c
10
9(9u
27
+ 52u
26
+ ··· − u + 1)
c
11
3(3u
27
− 4u
26
+ ··· + u + 1)
c
12
u
27
− u
26
+ ··· − 64u + 9
17
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
27
− 6y
26
+ ··· + 125779y −12321
c
2
, c
5
9(9y
27
− 151y
26
+ ··· + 12y −1)
c
3
, c
9
y
27
− 19y
26
+ ··· + 32y −1
c
4
, c
7
y
27
− 22y
26
+ ··· − 20y −1
c
6
, c
11
9(9y
27
+ 110y
26
+ ··· + 7y −1)
c
8
y
27
− 15y
26
+ ··· + 270598y −15129
c
10
81(81y
27
+ 14y
26
+ ··· + 9y −1)
c
12
y
27
− 3y
26
+ ··· + 2854y −81
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.075750 + 0.195752I
a = 0.338954 − 0.420995I
b = −0.366566 − 0.722015I
−0.893118 − 0.283770I 4.55411 − 0.56059I
u = 1.075750 − 0.195752I
a = 0.338954 + 0.420995I
b = −0.366566 + 0.722015I
−0.893118 + 0.283770I 4.55411 + 0.56059I
u = 0.889167 + 0.173798I
a = 0.03144 − 1.53477I
b = −0.13313 − 1.99199I
−4.36755 − 3.22896I −8.50125 − 1.58871I
u = 0.889167 − 0.173798I
a = 0.03144 + 1.53477I
b = −0.13313 + 1.99199I
−4.36755 + 3.22896I −8.50125 + 1.58871I
u = −0.745112 + 0.470935I
a = −0.301397 + 1.147620I
b = −0.630277 + 0.476195I
−5.47347 − 3.00815I −1.017488 + 0.600718I
u = −0.745112 − 0.470935I
a = −0.301397 − 1.147620I
b = −0.630277 − 0.476195I
−5.47347 + 3.00815I −1.017488 − 0.600718I
u = −0.987330 + 0.607022I
a = 0.121989 + 1.232100I
b = 0.97162 + 2.08705I
0.91893 + 6.47791I −4.82304 − 9.88552I
u = −0.987330 − 0.607022I
a = 0.121989 − 1.232100I
b = 0.97162 − 2.08705I
0.91893 − 6.47791I −4.82304 + 9.88552I
u = 1.23443
a = 1.05231
b = −0.439230
0.229879 −9.08000
u = −0.665123 + 0.295112I
a = −0.33280 + 1.94387I
b = −0.80748 + 1.86163I
−7.17961 + 6.51507I −9.45653 − 4.65252I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.665123 − 0.295112I
a = −0.33280 − 1.94387I
b = −0.80748 − 1.86163I
−7.17961 − 6.51507I −9.45653 + 4.65252I
u = 0.997412 + 0.825252I
a = −0.395793 − 1.046560I
b = 0.68437 − 1.56270I
−2.71816 − 5.93896I −6.03167 + 0.47266I
u = 0.997412 − 0.825252I
a = −0.395793 + 1.046560I
b = 0.68437 + 1.56270I
−2.71816 + 5.93896I −6.03167 − 0.47266I
u = 0.135489 + 1.313040I
a = 0.183593 + 0.219848I
b = −0.043710 − 0.367398I
4.19524 − 3.66948I −3.32475 + 13.44023I
u = 0.135489 − 1.313040I
a = 0.183593 − 0.219848I
b = −0.043710 + 0.367398I
4.19524 + 3.66948I −3.32475 − 13.44023I
u = 0.293489 + 0.601043I
a = −0.121018 + 0.672950I
b = 1.09153 − 1.28553I
3.46541 − 2.17371I 6.77661 − 0.85419I
u = 0.293489 − 0.601043I
a = −0.121018 − 0.672950I
b = 1.09153 + 1.28553I
3.46541 + 2.17371I 6.77661 + 0.85419I
u = −1.43398 + 0.41435I
a = −0.090956 − 0.588550I
b = 0.50703 − 1.84769I
−8.22496 + 7.18681I −8.49603 − 3.81374I
u = −1.43398 − 0.41435I
a = −0.090956 + 0.588550I
b = 0.50703 + 1.84769I
−8.22496 − 7.18681I −8.49603 + 3.81374I
u = −1.51003 + 0.02788I
a = −0.067211 − 0.943499I
b = 0.21093 − 1.86964I
−10.92740 − 4.73924I −8.61695 + 3.75715I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.51003 − 0.02788I
a = −0.067211 + 0.943499I
b = 0.21093 + 1.86964I
−10.92740 + 4.73924I −8.61695 − 3.75715I
u = 1.46823 + 0.36027I
a = 0.149669 + 0.631063I
b = 0.28488 + 2.02810I
−4.37032 + 0.03506I −13.8697 − 2.9082I
u = 1.46823 − 0.36027I
a = 0.149669 − 0.631063I
b = 0.28488 − 2.02810I
−4.37032 − 0.03506I −13.8697 + 2.9082I
u = 0.009582 + 0.469316I
a = 0.211172 − 1.176120I
b = −0.38048 + 2.31558I
1.94645 + 6.31890I −1.86637 − 6.76418I
u = 0.009582 − 0.469316I
a = 0.211172 + 1.176120I
b = −0.38048 − 2.31558I
1.94645 − 6.31890I −1.86637 + 6.76418I
u = 0.408432
a = 4.00133
b = −0.00254819
2.93401 −34.6170
u = −0.364618
a = 4.49108
b = 0.664354
4.87561 22.7180
22
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
27
− 6u
26
+ ··· + 41u + 111)(u
93
+ u
92
+ ··· − 493754u − 46509)
c
2
9(3u
27
− u
26
+ ··· − 6u
2
+ 1)(3u
93
+ 22u
92
+ ··· + 6023u + 695)
c
3
(u
27
− 3u
26
+ ··· − 6u + 1)(u
93
− 4u
92
+ ··· − 435u + 281)
c
4
(u
27
+ 4u
26
+ ··· − 4u + 1)(u
93
+ 9u
92
+ ··· − 341511u − 15167)
c
5
9(3u
27
+ u
26
+ ··· + 6u
2
− 1)(3u
93
+ 22u
92
+ ··· + 6023u + 695)
c
6
9(3u
27
+ 4u
26
+ ··· + u − 1)(3u
93
− 5u
92
+ ··· − 24386u − 2531)
c
7
(u
27
− 4u
26
+ ··· − 4u − 1)(u
93
+ 9u
92
+ ··· − 341511u − 15167)
c
8
(u
27
− 3u
26
+ ··· − 134u + 123)
· (u
93
+ 16u
92
+ ··· + 256813u + 72465)
c
9
(u
27
+ 3u
26
+ ··· − 6u − 1)(u
93
− 4u
92
+ ··· − 435u + 281)
c
10
81(9u
27
+ 52u
26
+ ··· − u + 1)(9u
93
+ 71u
92
+ ··· − 6u − 1)
c
11
9(3u
27
− 4u
26
+ ··· + u + 1)(3u
93
− 5u
92
+ ··· − 24386u − 2531)
c
12
(u
27
− u
26
+ ··· − 64u + 9)(u
93
+ 3u
91
+ ··· + 17755u + 2097)
23
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
27
− 6y
26
+ ··· + 125779y −12321)
· (y
93
+ 7y
92
+ ··· − 70016139986y −2163087081)
c
2
, c
5
81(9y
27
− 151y
26
+ ··· + 12y −1)
· (9y
93
− 298y
92
+ ··· + 10707479y −483025)
c
3
, c
9
(y
27
− 19y
26
+ ··· + 32y −1)(y
93
− 62y
92
+ ··· + 1260959y −78961)
c
4
, c
7
(y
27
− 22y
26
+ ··· − 20y −1)
· (y
93
− 81y
92
+ ··· − 1602188993y −230037889)
c
6
, c
11
81(9y
27
+ 110y
26
+ ··· + 7y −1)
· (9y
93
+ 395y
92
+ ··· − 74585210y −6405961)
c
8
(y
27
− 15y
26
+ ··· + 270598y −15129)
· (y
93
− 42y
92
+ ··· + 228494230849y −5251176225)
c
10
6561(81y
27
+ 14y
26
+ ··· + 9y −1)(81y
93
− 1621y
92
+ ··· − 20y −1)
c
12
(y
27
− 3y
26
+ ··· + 2854y −81)
· (y
93
+ 6y
92
+ ··· + 66493885y −4397409)
24
