12n
0864
(K12n
0864
)
A knot diagram
1
Linearized knot diagam
4 8 10 1 11 12 3 1 6 4 9 7
Solving Sequence
7,12
1
6,9
10 8 11 5 4 2 3
c
12
c
6
c
9
c
8
c
11
c
5
c
4
c
1
c
3
c
2
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.53286 × 10
291
u
92
− 4.50467 × 10
291
u
91
+ ··· + 3.77692 × 10
291
b + 9.71265 × 10
293
,
1.02824 × 10
294
u
92
− 2.85879 × 10
294
u
91
+ ··· + 2.69294 × 10
294
a + 5.18020 × 10
296
,
u
93
− 4u
92
+ ··· − 4518u − 713i
I
u
2
= h2.96874 × 10
21
u
27
− 7.47427 × 10
21
u
26
+ ··· + 2.70703 × 10
22
b − 6.60332 × 10
22
,
− 2.02325 × 10
23
u
27
+ 3.57824 × 10
23
u
26
+ ··· + 5.14336 × 10
23
a + 2.57084 × 10
24
,
u
28
− 3u
27
+ ··· − 39u + 19i
* 2 irreducible components of dim
C
= 0, with total 121 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
= h1.53 × 10
291
u
92
− 4.50 × 10
291
u
91
+ · · · + 3.78 × 10
291
b + 9.71 ×
10
293
, 1.03 × 10
294
u
92
− 2.86 × 10
294
u
91
+ · · · + 2.69 × 10
294
a + 5.18 ×
10
296
, u
93
− 4u
92
+ · · · − 4518u − 713i
(i) Arc colorings
a
7
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
6
=
u
u
a
9
=
−0.381829u
92
+ 1.06158u
91
+ ··· − 1356.84u − 192.362
−0.405849u
92
+ 1.19268u
91
+ ··· − 1876.85u − 257.158
a
10
=
−0.269383u
92
+ 0.806354u
91
+ ··· − 1215.75u − 167.393
−0.293403u
92
+ 0.937454u
91
+ ··· − 1735.76u − 232.189
a
8
=
−0.198655u
92
+ 0.601956u
91
+ ··· − 857.280u − 117.454
−0.0283513u
92
+ 0.170440u
91
+ ··· − 512.537u − 62.4622
a
11
=
−0.0836198u
92
+ 0.223873u
91
+ ··· − 836.341u − 115.884
0.0332956u
92
− 0.174545u
91
+ ··· − 119.532u − 20.4044
a
5
=
−0.200462u
92
+ 0.633350u
91
+ ··· − 886.658u − 122.121
0.179157u
92
− 0.428392u
91
+ ··· + 718.139u + 105.165
a
4
=
0.166083u
92
− 0.405497u
91
+ ··· + 735.690u + 103.184
0.673488u
92
− 1.84254u
91
+ ··· + 2910.18u + 409.855
a
2
=
−0.118324u
92
+ 0.280389u
91
+ ··· − 580.650u − 81.3422
−1.46243u
92
+ 4.12770u
91
+ ··· − 6543.71u − 913.615
a
3
=
0.153240u
92
− 0.419507u
91
+ ··· + 634.309u + 92.1542
2.16090u
92
− 6.20878u
91
+ ··· + 9792.14u + 1358.75
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.46340u
92
− 4.46296u
91
+ ··· + 8949.13u + 1229.02
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
93
− 7u
92
+ ··· + 24150u − 1231
c
2
, c
7
3(3u
93
− 7u
92
+ ··· + 5337u + 845)
c
3
, c
10
3(3u
93
− 7u
92
+ ··· − 29u − 1)
c
5
u
93
+ u
92
+ ··· − 233909u + 97395
c
6
, c
12
u
93
− 4u
92
+ ··· − 4518u − 713
c
8
u
93
+ 5u
92
+ ··· − 67117955u + 23409813
c
9
u
93
+ 12u
91
+ ··· − 34564u − 1089
c
11
9(9u
93
− 94u
92
+ ··· + 2774u − 2627)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
93
− 81y
92
+ ··· + 49128530y −1515361
c
2
, c
7
9(9y
93
+ 239y
92
+ ··· − 1.29958 × 10
7
y −714025)
c
3
, c
10
9(9y
93
− 355y
92
+ ··· + 4293y −1)
c
5
y
93
+ 35y
92
+ ··· − 415484901389y −9485786025
c
6
, c
12
y
93
− 64y
92
+ ··· − 3721300y −508369
c
8
y
93
− 61y
92
+ ··· + 33849166602934771y −548019344694969
c
9
y
93
+ 24y
92
+ ··· + 318031630y −1185921
c
11
81(81y
93
− 7702y
92
+ ··· + 2.17902 × 10
8
y −6901129)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.970806 + 0.203578I
a = −1.216500 + 0.303430I
b = −1.087430 − 0.883567I
−4.33926 − 3.64290I 0
u = 0.970806 − 0.203578I
a = −1.216500 − 0.303430I
b = −1.087430 + 0.883567I
−4.33926 + 3.64290I 0
u = 0.966862 + 0.306426I
a = 2.12102 − 0.54952I
b = 1.140770 + 0.801410I
4.07438 − 4.79787I 0
u = 0.966862 − 0.306426I
a = 2.12102 + 0.54952I
b = 1.140770 − 0.801410I
4.07438 + 4.79787I 0
u = −1.01503
a = 8.34900
b = 8.17604
−3.31997 0
u = −1.012850 + 0.093449I
a = −1.87245 + 0.51826I
b = −1.030470 − 0.573297I
−0.912721 + 0.800698I 0
u = −1.012850 − 0.093449I
a = −1.87245 − 0.51826I
b = −1.030470 + 0.573297I
−0.912721 − 0.800698I 0
u = 0.132859 + 1.039890I
a = 0.073148 + 0.240715I
b = 0.752841 − 0.369880I
2.92510 + 3.79910I 0
u = 0.132859 − 1.039890I
a = 0.073148 − 0.240715I
b = 0.752841 + 0.369880I
2.92510 − 3.79910I 0
u = 1.072560 + 0.081654I
a = 1.26700 − 1.92489I
b = 0.668861 + 0.188400I
−7.68862 − 0.49446I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.072560 − 0.081654I
a = 1.26700 + 1.92489I
b = 0.668861 − 0.188400I
−7.68862 + 0.49446I 0
u = −0.377912 + 1.043730I
a = −0.192515 − 0.154482I
b = −0.966009 + 0.593968I
−2.83740 − 0.28747I 0
u = −0.377912 − 1.043730I
a = −0.192515 + 0.154482I
b = −0.966009 − 0.593968I
−2.83740 + 0.28747I 0
u = 0.074277 + 0.874223I
a = −0.175800 + 0.171193I
b = −1.014600 − 0.732602I
−3.04223 − 5.10822I 0
u = 0.074277 − 0.874223I
a = −0.175800 − 0.171193I
b = −1.014600 + 0.732602I
−3.04223 + 5.10822I 0
u = −0.090255 + 1.119050I
a = 0.187340 + 0.249519I
b = 0.922770 + 0.634829I
−3.47535 − 4.38011I 0
u = −0.090255 − 1.119050I
a = 0.187340 − 0.249519I
b = 0.922770 − 0.634829I
−3.47535 + 4.38011I 0
u = −1.113330 + 0.179803I
a = −2.72446 + 1.29296I
b = −0.580050 + 0.122241I
−3.79023 + 7.52581I 0
u = −1.113330 − 0.179803I
a = −2.72446 − 1.29296I
b = −0.580050 − 0.122241I
−3.79023 − 7.52581I 0
u = 0.558600 + 0.649221I
a = −0.330098 − 0.251452I
b = 0.782526 − 0.802658I
5.18841 + 1.02843I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.558600 − 0.649221I
a = −0.330098 + 0.251452I
b = 0.782526 + 0.802658I
5.18841 − 1.02843I 0
u = −1.155040 + 0.103129I
a = 1.295920 − 0.012517I
b = 1.056300 − 0.235080I
−2.20603 + 0.06003I 0
u = −1.155040 − 0.103129I
a = 1.295920 + 0.012517I
b = 1.056300 + 0.235080I
−2.20603 − 0.06003I 0
u = 1.131360 + 0.303534I
a = 0.53883 − 1.35038I
b = 0.74902 − 1.89355I
−3.07063 − 9.09969I 0
u = 1.131360 − 0.303534I
a = 0.53883 + 1.35038I
b = 0.74902 + 1.89355I
−3.07063 + 9.09969I 0
u = −0.814899 + 0.094544I
a = −1.27335 + 1.04874I
b = −0.887354 − 0.420932I
−0.268157 + 0.195171I 0
u = −0.814899 − 0.094544I
a = −1.27335 − 1.04874I
b = −0.887354 + 0.420932I
−0.268157 − 0.195171I 0
u = 1.185370 + 0.047408I
a = −1.87899 − 0.66704I
b = −1.003780 − 0.320920I
−5.81196 − 2.66335I 0
u = 1.185370 − 0.047408I
a = −1.87899 + 0.66704I
b = −1.003780 + 0.320920I
−5.81196 + 2.66335I 0
u = 0.057798 + 0.804250I
a = 0.527881 − 0.738120I
b = 0.332873 + 0.542258I
4.07256 + 0.75772I 3.56181 + 0.I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.057798 − 0.804250I
a = 0.527881 + 0.738120I
b = 0.332873 − 0.542258I
4.07256 − 0.75772I 3.56181 + 0.I
u = 1.173730 + 0.250919I
a = 0.660195 + 0.121675I
b = 0.551275 − 0.575312I
0.34438 − 4.50053I 0
u = 1.173730 − 0.250919I
a = 0.660195 − 0.121675I
b = 0.551275 + 0.575312I
0.34438 + 4.50053I 0
u = −0.624810 + 1.034520I
a = 0.155627 − 0.161045I
b = −0.563147 − 0.194196I
1.82620 + 1.45624I 0
u = −0.624810 − 1.034520I
a = 0.155627 + 0.161045I
b = −0.563147 + 0.194196I
1.82620 − 1.45624I 0
u = 1.214470 + 0.092248I
a = −1.98528 − 0.50252I
b = −0.903679 − 0.408944I
−5.79506 − 2.66432I 0
u = 1.214470 − 0.092248I
a = −1.98528 + 0.50252I
b = −0.903679 + 0.408944I
−5.79506 + 2.66432I 0
u = −1.026460 + 0.671637I
a = −0.631280 − 0.516781I
b = −0.823668 + 0.657965I
0.27727 + 4.69627I 0
u = −1.026460 − 0.671637I
a = −0.631280 + 0.516781I
b = −0.823668 − 0.657965I
0.27727 − 4.69627I 0
u = 1.202320 + 0.265022I
a = −1.266800 + 0.066335I
b = −1.024440 − 0.779415I
−4.17035 − 3.28923I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.202320 − 0.265022I
a = −1.266800 − 0.066335I
b = −1.024440 + 0.779415I
−4.17035 + 3.28923I 0
u = 0.428597 + 1.157030I
a = 0.284631 − 0.357098I
b = 0.440196 − 0.656343I
5.51789 − 0.51100I 0
u = 0.428597 − 1.157030I
a = 0.284631 + 0.357098I
b = 0.440196 + 0.656343I
5.51789 + 0.51100I 0
u = −0.034127 + 1.237840I
a = 0.262217 − 0.051286I
b = 0.974512 − 0.741654I
−0.91707 + 11.77280I 0
u = −0.034127 − 1.237840I
a = 0.262217 + 0.051286I
b = 0.974512 + 0.741654I
−0.91707 − 11.77280I 0
u = 1.104130 + 0.633695I
a = 1.61219 − 0.09583I
b = 1.205820 + 0.638774I
3.25583 − 5.58032I 0
u = 1.104130 − 0.633695I
a = 1.61219 + 0.09583I
b = 1.205820 − 0.638774I
3.25583 + 5.58032I 0
u = −1.259240 + 0.270348I
a = 1.305300 + 0.136781I
b = 0.728820 − 1.175300I
1.19424 + 6.48567I 0
u = −1.259240 − 0.270348I
a = 1.305300 − 0.136781I
b = 0.728820 + 1.175300I
1.19424 − 6.48567I 0
u = −1.307360 + 0.038712I
a = 2.30366 − 0.85775I
b = 0.678584 − 0.009011I
−5.16693 − 4.23111I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.307360 − 0.038712I
a = 2.30366 + 0.85775I
b = 0.678584 + 0.009011I
−5.16693 + 4.23111I 0
u = 1.283380 + 0.401547I
a = 0.795514 − 0.879366I
b = 0.870337 + 0.078006I
−8.48265 − 0.61979I 0
u = 1.283380 − 0.401547I
a = 0.795514 + 0.879366I
b = 0.870337 − 0.078006I
−8.48265 + 0.61979I 0
u = 1.284420 + 0.413668I
a = −0.345035 + 0.490889I
b = −0.285715 − 0.573754I
0.11501 − 5.02565I 0
u = 1.284420 − 0.413668I
a = −0.345035 − 0.490889I
b = −0.285715 + 0.573754I
0.11501 + 5.02565I 0
u = −1.36052
a = 1.22117
b = 1.17430
−2.32130 0
u = −1.322400 + 0.448761I
a = −1.81655 − 0.22447I
b = −1.34813 + 0.89270I
−7.33144 + 9.91805I 0
u = −1.322400 − 0.448761I
a = −1.81655 + 0.22447I
b = −1.34813 − 0.89270I
−7.33144 − 9.91805I 0
u = −1.358200 + 0.377781I
a = 1.47648 + 0.38131I
b = 0.722955 − 0.492677I
−0.42204 + 3.52052I 0
u = −1.358200 − 0.377781I
a = 1.47648 − 0.38131I
b = 0.722955 + 0.492677I
−0.42204 − 3.52052I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41210 + 0.09829I
a = −1.52530 − 0.52170I
b = −1.38947 − 1.31051I
−7.64207 − 5.47937I 0
u = 1.41210 − 0.09829I
a = −1.52530 + 0.52170I
b = −1.38947 + 1.31051I
−7.64207 + 5.47937I 0
u = 1.32597 + 0.52524I
a = 1.332630 − 0.457053I
b = 1.007260 + 0.638504I
−0.91883 − 9.40018I 0
u = 1.32597 − 0.52524I
a = 1.332630 + 0.457053I
b = 1.007260 − 0.638504I
−0.91883 + 9.40018I 0
u = 1.24296 + 0.70243I
a = −0.546032 + 0.779638I
b = −0.871214 + 0.248362I
−5.89970 − 0.23874I 0
u = 1.24296 − 0.70243I
a = −0.546032 − 0.779638I
b = −0.871214 − 0.248362I
−5.89970 + 0.23874I 0
u = −0.00838 + 1.43145I
a = 0.123005 − 0.320045I
b = −0.237813 − 0.375436I
5.10663 − 0.60046I 0
u = −0.00838 − 1.43145I
a = 0.123005 + 0.320045I
b = −0.237813 + 0.375436I
5.10663 + 0.60046I 0
u = 0.206452 + 0.525183I
a = 2.42934 − 0.63932I
b = 0.835132 + 0.833288I
−0.36815 + 5.85720I −1.31662 − 3.27309I
u = 0.206452 − 0.525183I
a = 2.42934 + 0.63932I
b = 0.835132 − 0.833288I
−0.36815 − 5.85720I −1.31662 + 3.27309I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.33863 + 0.54520I
a = 1.67062 + 0.14858I
b = 1.39883 − 0.85061I
−7.46544 + 10.22760I 0
u = −1.33863 − 0.54520I
a = 1.67062 − 0.14858I
b = 1.39883 + 0.85061I
−7.46544 − 10.22760I 0
u = 1.42171 + 0.34511I
a = −1.65249 − 0.02833I
b = −1.39250 − 0.99250I
−8.59422 − 4.37880I 0
u = 1.42171 − 0.34511I
a = −1.65249 + 0.02833I
b = −1.39250 + 0.99250I
−8.59422 + 4.37880I 0
u = −0.490424 + 0.192252I
a = 2.02573 − 1.32129I
b = 0.775835 − 0.910483I
−2.77711 + 0.92123I −2.40188 − 0.43411I
u = −0.490424 − 0.192252I
a = 2.02573 + 1.32129I
b = 0.775835 + 0.910483I
−2.77711 − 0.92123I −2.40188 + 0.43411I
u = 1.41052 + 0.56464I
a = 1.63990 − 0.17204I
b = 1.32824 + 0.93343I
−5.4749 − 18.0350I 0
u = 1.41052 − 0.56464I
a = 1.63990 + 0.17204I
b = 1.32824 − 0.93343I
−5.4749 + 18.0350I 0
u = −0.373413 + 0.292324I
a = −1.23651 + 2.18723I
b = −0.681200 − 0.818287I
−1.66413 − 5.49946I −1.46246 + 5.05508I
u = −0.373413 − 0.292324I
a = −1.23651 − 2.18723I
b = −0.681200 + 0.818287I
−1.66413 + 5.49946I −1.46246 − 5.05508I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.34540 + 0.73623I
a = −0.598439 − 0.635209I
b = −0.986576 + 0.010327I
−5.63674 + 7.02123I 0
u = −1.34540 − 0.73623I
a = −0.598439 + 0.635209I
b = −0.986576 − 0.010327I
−5.63674 − 7.02123I 0
u = −1.43121 + 0.61007I
a = −1.009230 + 0.287321I
b = −0.948448 + 0.982762I
0.35724 + 7.41586I 0
u = −1.43121 − 0.61007I
a = −1.009230 − 0.287321I
b = −0.948448 − 0.982762I
0.35724 − 7.41586I 0
u = −0.077867 + 0.405146I
a = −2.14768 − 1.36570I
b = 0.551812 + 0.744999I
4.92357 − 3.65063I 1.05797 + 12.64547I
u = −0.077867 − 0.405146I
a = −2.14768 + 1.36570I
b = 0.551812 − 0.744999I
4.92357 + 3.65063I 1.05797 − 12.64547I
u = −0.181026 + 0.342017I
a = 0.500745 − 0.770110I
b = −0.426902 + 0.358041I
−0.200991 + 0.958280I −3.95907 − 6.99416I
u = −0.181026 − 0.342017I
a = 0.500745 + 0.770110I
b = −0.426902 − 0.358041I
−0.200991 − 0.958280I −3.95907 + 6.99416I
u = −0.137092 + 0.322899I
a = −2.24872 − 0.63912I
b = −0.744226 + 1.001560I
−1.96423 + 1.03167I 0.423681 + 0.449105I
u = −0.137092 − 0.322899I
a = −2.24872 + 0.63912I
b = −0.744226 − 1.001560I
−1.96423 − 1.03167I 0.423681 − 0.449105I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.69081
a = 1.34078
b = 0.835244
−10.1731 0
u = −1.63854 + 0.53885I
a = 0.671092 + 0.461091I
b = 0.850672 + 0.119820I
−5.87559 − 4.83598I 0
u = −1.63854 − 0.53885I
a = 0.671092 − 0.461091I
b = 0.850672 − 0.119820I
−5.87559 + 4.83598I 0
14
II. I
u
2
= h2.97 × 10
21
u
27
− 7.47 × 10
21
u
26
+ · · · + 2.71 × 10
22
b − 6.60 ×
10
22
, −2.02 × 10
23
u
27
+ 3.58 × 10
23
u
26
+ · · · + 5.14 × 10
23
a + 2.57 ×
10
24
, u
28
− 3u
27
+ · · · − 39u + 19i
(i) Arc colorings
a
7
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
6
=
u
u
a
9
=
0.393370u
27
− 0.695700u
26
+ ··· + 7.51834u − 4.99835
−0.109668u
27
+ 0.276105u
26
+ ··· − 1.97895u + 2.43932
a
10
=
−0.146103u
27
+ 0.419124u
26
+ ··· − 3.87896u + 5.21050
−0.649141u
27
+ 1.39093u
26
+ ··· − 13.3763u + 12.6482
a
8
=
−0.348178u
27
+ 0.716088u
26
+ ··· − 5.87861u + 6.64478
−0.972474u
27
+ 1.99708u
26
+ ··· − 19.5910u + 17.8836
a
11
=
0.312529u
27
− 0.559950u
26
+ ··· + 8.78283u − 4.64925
0.185894u
27
− 0.266959u
26
+ ··· + 6.09066u − 3.17580
a
5
=
−0.435301u
27
+ 0.840298u
26
+ ··· − 8.78720u + 7.15731
−0.502956u
27
+ 0.904377u
26
+ ··· − 8.48786u + 8.02330
a
4
=
−0.318183u
27
+ 0.702283u
26
+ ··· − 7.38719u + 6.33412
−0.165206u
27
+ 0.439800u
26
+ ··· − 2.39284u + 3.96984
a
2
=
−0.100290u
27
+ 0.134408u
26
+ ··· − 4.69317u − 0.385276
−0.263668u
27
+ 0.256350u
26
+ ··· − 2.86034u + 0.586162
a
3
=
0.361386u
27
− 0.629649u
26
+ ··· + 5.94865u − 5.75225
0.812419u
27
− 1.34489u
26
+ ··· + 16.6198u − 11.1591
(ii) Obstruction class = 1
(iii) Cusp Shapes =
36346825326951087058817
730899156647188975048731
u
27
−
381420569456833601389550
730899156647188975048731
u
26
+ ··· +
3998852031337486870792207
730899156647188975048731
u −
9592325382796608124681696
730899156647188975048731
15
(iv) u-Polynomials at the component
16
Crossings u-Polynomials at each crossing
c
1
u
28
− 4u
27
+ ··· + 3u + 1
c
2
3(3u
28
− 4u
27
+ ··· − 2u − 1)
c
3
3(3u
28
− 4u
27
+ ··· − 4u − 1)
c
4
u
28
+ 4u
27
+ ··· − 3u + 1
c
5
u
28
+ 4u
26
+ ··· + 20u + 183
c
6
u
28
+ 3u
27
+ ··· + 39u + 19
c
7
3(3u
28
+ 4u
27
+ ··· + 2u − 1)
c
8
u
28
+ 4u
27
+ ··· − 550u − 393
c
9
u
28
+ u
27
+ ··· − 91u − 9
c
10
3(3u
28
+ 4u
27
+ ··· + 4u − 1)
c
11
9(9u
28
+ 11u
27
+ ··· − 9u − 1)
c
12
u
28
− 3u
27
+ ··· − 39u + 19
17
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
28
− 20y
27
+ ··· + 19y + 1
c
2
, c
7
9(9y
28
+ 128y
27
+ ··· + 16y + 1)
c
3
, c
10
9(9y
28
− 142y
27
+ ··· − 20y + 1)
c
5
y
28
+ 8y
27
+ ··· + 73898y + 33489
c
6
, c
12
y
28
− 19y
27
+ ··· + 1557y + 361
c
8
y
28
− 20y
27
+ ··· − 1881574y + 154449
c
9
y
28
+ 9y
27
+ ··· − 8281y + 81
c
11
81(81y
28
− 769y
27
+ ··· − 17y + 1)
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.521754 + 0.880090I
a = 0.382943 − 0.169516I
b = −0.411507 + 0.021686I
2.01994 − 1.83061I 1.50906 + 8.83594I
u = 0.521754 − 0.880090I
a = 0.382943 + 0.169516I
b = −0.411507 − 0.021686I
2.01994 + 1.83061I 1.50906 − 8.83594I
u = 1.004320 + 0.286358I
a = 1.207610 + 0.017108I
b = −0.009872 − 0.775666I
−2.87333 − 7.20168I −3.49158 + 5.74174I
u = 1.004320 − 0.286358I
a = 1.207610 − 0.017108I
b = −0.009872 + 0.775666I
−2.87333 + 7.20168I −3.49158 − 5.74174I
u = −1.070500 + 0.186519I
a = 0.88674 + 1.77203I
b = 0.680259 − 0.192286I
−7.57229 + 0.82853I −2.46578 − 12.32293I
u = −1.070500 − 0.186519I
a = 0.88674 − 1.77203I
b = 0.680259 + 0.192286I
−7.57229 − 0.82853I −2.46578 + 12.32293I
u = 0.562054 + 0.961301I
a = 0.029738 − 0.391667I
b = 0.648409 − 0.815439I
6.74803 + 0.55431I 4.39621 − 1.64176I
u = 0.562054 − 0.961301I
a = 0.029738 + 0.391667I
b = 0.648409 + 0.815439I
6.74803 − 0.55431I 4.39621 + 1.64176I
u = −1.12047
a = 2.69049
b = 2.60517
−3.44038 −18.1190
u = 1.048530 + 0.497158I
a = 1.81281 − 0.12113I
b = 1.14446 + 0.91674I
5.07440 − 5.77041I 2.11038 + 6.19669I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.048530 − 0.497158I
a = 1.81281 + 0.12113I
b = 1.14446 − 0.91674I
5.07440 + 5.77041I 2.11038 − 6.19669I
u = −1.255070 + 0.285789I
a = 1.296300 + 0.417482I
b = 0.676477 − 0.994621I
1.63709 + 6.17925I 3.37825 − 3.29613I
u = −1.255070 − 0.285789I
a = 1.296300 − 0.417482I
b = 0.676477 + 0.994621I
1.63709 − 6.17925I 3.37825 + 3.29613I
u = 1.340010 + 0.147694I
a = −1.43207 + 0.40771I
b = −0.460042 + 0.447927I
−4.26015 + 4.72994I −3.25602 − 6.00078I
u = 1.340010 − 0.147694I
a = −1.43207 − 0.40771I
b = −0.460042 − 0.447927I
−4.26015 − 4.72994I −3.25602 + 6.00078I
u = 1.283280 + 0.418019I
a = −1.129020 + 0.697209I
b = −0.681608 − 0.385401I
−0.85125 − 2.97639I −7.07571 − 0.53480I
u = 1.283280 − 0.418019I
a = −1.129020 − 0.697209I
b = −0.681608 + 0.385401I
−0.85125 + 2.97639I −7.07571 + 0.53480I
u = 1.396940 + 0.174140I
a = −1.63173 − 0.37311I
b = −1.43554 − 1.19718I
−7.54617 − 5.02484I −4.07792 − 1.75277I
u = 1.396940 − 0.174140I
a = −1.63173 + 0.37311I
b = −1.43554 + 1.19718I
−7.54617 + 5.02484I −4.07792 + 1.75277I
u = −0.294127 + 0.476992I
a = −1.81518 − 0.27843I
b = 0.543604 + 0.583954I
4.95221 − 3.15515I 2.16472 − 2.64497I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.294127 − 0.476992I
a = −1.81518 + 0.27843I
b = 0.543604 − 0.583954I
4.95221 + 3.15515I 2.16472 + 2.64497I
u = 0.057545 + 0.467455I
a = 0.646815 + 0.815476I
b = −0.894668 + 0.734654I
−2.82369 + 2.83577I −2.08018 − 2.99142I
u = 0.057545 − 0.467455I
a = 0.646815 − 0.815476I
b = −0.894668 − 0.734654I
−2.82369 − 2.83577I −2.08018 + 2.99142I
u = −0.26281 + 1.52272I
a = −0.052675 − 0.290436I
b = −0.419220 − 0.307941I
4.95254 + 0.16143I −7.70420 + 4.24851I
u = −0.26281 − 1.52272I
a = −0.052675 + 0.290436I
b = −0.419220 + 0.307941I
4.95254 − 0.16143I −7.70420 − 4.24851I
u = −1.41891 + 0.65551I
a = −0.943900 + 0.122189I
b = −0.887039 + 0.838068I
0.74318 + 7.19731I 4.06191 − 4.63819I
u = −1.41891 − 0.65551I
a = −0.943900 − 0.122189I
b = −0.887039 − 0.838068I
0.74318 − 7.19731I 4.06191 + 4.63819I
u = −1.70552
a = −1.32420
b = −0.814815
−10.1201 71.7450
22
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
28
− 4u
27
+ ··· + 3u + 1)(u
93
− 7u
92
+ ··· + 24150u − 1231)
c
2
9(3u
28
− 4u
27
+ ··· − 2u − 1)(3u
93
− 7u
92
+ ··· + 5337u + 845)
c
3
9(3u
28
− 4u
27
+ ··· − 4u − 1)(3u
93
− 7u
92
+ ··· − 29u − 1)
c
4
(u
28
+ 4u
27
+ ··· − 3u + 1)(u
93
− 7u
92
+ ··· + 24150u − 1231)
c
5
(u
28
+ 4u
26
+ ··· + 20u + 183)(u
93
+ u
92
+ ··· − 233909u + 97395)
c
6
(u
28
+ 3u
27
+ ··· + 39u + 19)(u
93
− 4u
92
+ ··· − 4518u − 713)
c
7
9(3u
28
+ 4u
27
+ ··· + 2u − 1)(3u
93
− 7u
92
+ ··· + 5337u + 845)
c
8
(u
28
+ 4u
27
+ ··· − 550u − 393)
· (u
93
+ 5u
92
+ ··· − 67117955u + 23409813)
c
9
(u
28
+ u
27
+ ··· − 91u − 9)(u
93
+ 12u
91
+ ··· − 34564u − 1089)
c
10
9(3u
28
+ 4u
27
+ ··· + 4u − 1)(3u
93
− 7u
92
+ ··· − 29u − 1)
c
11
81(9u
28
+ 11u
27
+ ··· − 9u − 1)(9u
93
− 94u
92
+ ··· + 2774u − 2627)
c
12
(u
28
− 3u
27
+ ··· − 39u + 19)(u
93
− 4u
92
+ ··· − 4518u − 713)
23
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
28
− 20y
27
+ ··· + 19y + 1)
· (y
93
− 81y
92
+ ··· + 49128530y −1515361)
c
2
, c
7
81(9y
28
+ 128y
27
+ ··· + 16y + 1)
· (9y
93
+ 239y
92
+ ··· − 12995791y −714025)
c
3
, c
10
81(9y
28
− 142y
27
+ ··· − 20y + 1)(9y
93
− 355y
92
+ ··· + 4293y −1)
c
5
(y
28
+ 8y
27
+ ··· + 73898y + 33489)
· (y
93
+ 35y
92
+ ··· − 415484901389y −9485786025)
c
6
, c
12
(y
28
− 19y
27
+ ··· + 1557y + 361)
· (y
93
− 64y
92
+ ··· − 3721300y −508369)
c
8
(y
28
− 20y
27
+ ··· − 1881574y + 154449)
· (y
93
− 61y
92
+ ··· + 33849166602934771y −548019344694969)
c
9
(y
28
+ 9y
27
+ ··· − 8281y + 81)
· (y
93
+ 24y
92
+ ··· + 318031630y −1185921)
c
11
6561(81y
28
− 769y
27
+ ··· − 17y + 1)
· (81y
93
− 7702y
92
+ ··· + 217902362y −6901129)
24
