12n
0622
(K12n
0622
)
A knot diagram
1
Linearized knot diagam
3 8 6 10 1 9 12 2 12 5 8 4
Solving Sequence
3,6 4,8
2 9 1 5 12 7 11 10
c
3
c
2
c
8
c
1
c
5
c
12
c
7
c
11
c
10
c
4
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h4.92452 × 10
287
u
78
+ 1.93718 × 10
288
u
77
+ ··· + 2.14374 × 10
288
b + 4.20946 × 10
287
,
1.49187 × 10
288
u
78
+ 4.54831 × 10
288
u
77
+ ··· + 2.14374 × 10
288
a + 3.02836 × 10
288
, u
79
+ 4u
78
+ ··· − 15u − 2i
I
u
2
= h8.86602 × 10
26
u
29
+ 4.96461 × 10
27
u
28
+ ··· + 2.07890 × 10
27
b − 8.46568 × 10
27
,
− 2.14303 × 10
27
u
29
− 1.46624 × 10
28
u
28
+ ··· + 2.07890 × 10
27
a + 2.20584 × 10
27
, u
30
+ 7u
29
+ ··· − 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 109 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
= h4.92 × 10
287
u
78
+ 1.94 × 10
288
u
77
+ · · · + 2.14 × 10
288
b + 4.21 ×
10
287
, 1.49 × 10
288
u
78
+ 4.55 × 10
288
u
77
+ · · · + 2.14 × 10
288
a + 3.03 ×
10
288
, u
79
+ 4u
78
+ · · · − 15u − 2i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
4
=
1
−u
2
a
8
=
−0.695917u
78
− 2.12167u
77
+ ··· + 3.19841u − 1.41265
−0.229716u
78
− 0.903642u
77
+ ··· + 3.41853u − 0.196360
a
2
=
−1.80728u
78
− 6.63665u
77
+ ··· + 33.4230u + 4.46023
0.282833u
78
+ 0.998771u
77
+ ··· + 5.24866u + 1.63785
a
9
=
−1.28126u
78
− 4.73105u
77
+ ··· + 59.6882u + 8.86459
−0.0732110u
78
− 0.146482u
77
+ ··· − 14.5367u − 3.50294
a
1
=
−1.52445u
78
− 5.63788u
77
+ ··· + 38.6717u + 6.09808
0.282833u
78
+ 0.998771u
77
+ ··· + 5.24866u + 1.63785
a
5
=
−0.671308u
78
− 3.15509u
77
+ ··· + 49.0749u + 14.1783
0.212306u
78
+ 0.790438u
77
+ ··· − 8.06833u − 1.68927
a
12
=
−1.73942u
78
− 6.33735u
77
+ ··· + 29.5732u + 3.54039
0.312581u
78
+ 1.11717u
77
+ ··· + 3.27223u + 1.31700
a
7
=
−3.40969u
78
− 12.5097u
77
+ ··· + 117.027u + 16.8820
−0.193655u
78
− 0.656440u
77
+ ··· − 7.35796u − 2.70038
a
11
=
0.593823u
78
+ 1.60440u
77
+ ··· + 10.7553u + 9.93213
0.224564u
78
+ 0.848409u
77
+ ··· − 5.84297u − 1.44066
a
10
=
1.06875u
78
+ 4.43417u
77
+ ··· − 57.8967u − 11.3128
−0.200371u
78
− 0.773026u
77
+ ··· + 6.71504u + 0.666681
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.466124u
78
− 1.35878u
77
+ ··· − 90.0451u − 15.6671
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
79
+ 43u
78
+ ··· − 1004u − 100
c
2
, c
8
u
79
+ 3u
78
+ ··· − 14u − 10
c
3
u
79
+ 4u
78
+ ··· − 15u − 2
c
4
, c
10
u
79
− 2u
78
+ ··· − 120u + 26
c
5
u
79
− 2u
78
+ ··· − 8478u − 3078
c
6
u
79
− 6u
78
+ ··· + 1496873u + 115748
c
7
, c
11
u
79
+ 4u
78
+ ··· + 1193295u − 523514
c
9
u
79
− 5u
78
+ ··· + 16594u − 12214
c
12
u
79
+ 6u
78
+ ··· + 45561u − 4572
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
79
− y
78
+ ··· + 465616y −10000
c
2
, c
8
y
79
+ 43y
78
+ ··· − 1004y −100
c
3
y
79
− 8y
78
+ ··· − 151y −4
c
4
, c
10
y
79
− 60y
78
+ ··· + 42480y −676
c
5
y
79
+ 8y
78
+ ··· − 207913716y −9474084
c
6
y
79
− 116y
78
+ ··· + 1057720100009y −13397599504
c
7
, c
11
y
79
− 90y
78
+ ··· + 5429126130809y −274066908196
c
9
y
79
− 103y
78
+ ··· + 453343244y −149181796
c
12
y
79
+ 28y
78
+ ··· + 771038217y −20903184
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.816172 + 0.646013I
a = −1.209900 − 0.076500I
b = 0.70666 + 1.38162I
−9.03674 + 7.36246I 0
u = 0.816172 − 0.646013I
a = −1.209900 + 0.076500I
b = 0.70666 − 1.38162I
−9.03674 − 7.36246I 0
u = −0.851565 + 0.604278I
a = −0.096173 + 0.355509I
b = −0.432323 − 0.206165I
−0.59266 − 4.94262I 0
u = −0.851565 − 0.604278I
a = −0.096173 − 0.355509I
b = −0.432323 + 0.206165I
−0.59266 + 4.94262I 0
u = −1.034490 + 0.191822I
a = −0.361792 − 0.581823I
b = −0.241504 + 0.613860I
−0.96739 − 5.14315I 0
u = −1.034490 − 0.191822I
a = −0.361792 + 0.581823I
b = −0.241504 − 0.613860I
−0.96739 + 5.14315I 0
u = 0.013775 + 0.937830I
a = 0.51318 + 1.52869I
b = 0.585484 + 0.360436I
−8.21660 + 2.04904I −8.02716 − 3.74321I
u = 0.013775 − 0.937830I
a = 0.51318 − 1.52869I
b = 0.585484 − 0.360436I
−8.21660 − 2.04904I −8.02716 + 3.74321I
u = 0.700344 + 0.855508I
a = −0.934162 + 0.922785I
b = 0.369105 + 1.037020I
−1.01865 + 3.56912I 0
u = 0.700344 − 0.855508I
a = −0.934162 − 0.922785I
b = 0.369105 − 1.037020I
−1.01865 − 3.56912I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.448324 + 1.013580I
a = 0.752506 − 0.152892I
b = 0.520524 − 1.124140I
−10.49970 − 2.46799I 0
u = 0.448324 − 1.013580I
a = 0.752506 + 0.152892I
b = 0.520524 + 1.124140I
−10.49970 + 2.46799I 0
u = −0.633902 + 0.922767I
a = 1.021790 + 0.912971I
b = −0.461486 + 1.144140I
−3.30115 − 8.89430I 0
u = −0.633902 − 0.922767I
a = 1.021790 − 0.912971I
b = −0.461486 − 1.144140I
−3.30115 + 8.89430I 0
u = −0.660179 + 0.559566I
a = 1.78017 − 0.22112I
b = −0.578067 + 1.168530I
−5.07794 − 5.70686I −7.10807 − 1.44397I
u = −0.660179 − 0.559566I
a = 1.78017 + 0.22112I
b = −0.578067 − 1.168530I
−5.07794 + 5.70686I −7.10807 + 1.44397I
u = 1.085140 + 0.338076I
a = 0.255368 + 1.163830I
b = 0.070726 − 0.734940I
0.773012 + 1.152010I 0
u = 1.085140 − 0.338076I
a = 0.255368 − 1.163830I
b = 0.070726 + 0.734940I
0.773012 − 1.152010I 0
u = −0.937083 + 0.647339I
a = −1.101110 + 0.038652I
b = 0.744421 − 0.366284I
−0.58487 − 4.01785I 0
u = −0.937083 − 0.647339I
a = −1.101110 − 0.038652I
b = 0.744421 + 0.366284I
−0.58487 + 4.01785I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.220511 + 1.146240I
a = −0.436797 − 0.196503I
b = −0.295511 − 1.078110I
−7.37626 + 2.11501I 0
u = −0.220511 − 1.146240I
a = −0.436797 + 0.196503I
b = −0.295511 + 1.078110I
−7.37626 − 2.11501I 0
u = −0.868469 + 0.803966I
a = −0.675181 − 0.843567I
b = 0.772773 + 0.559676I
−0.96281 − 1.45120I 0
u = −0.868469 − 0.803966I
a = −0.675181 + 0.843567I
b = 0.772773 − 0.559676I
−0.96281 + 1.45120I 0
u = −0.574732 + 1.037720I
a = 0.152511 + 0.119525I
b = −0.15417 − 1.51805I
−15.5511 − 5.8296I 0
u = −0.574732 − 1.037720I
a = 0.152511 − 0.119525I
b = −0.15417 + 1.51805I
−15.5511 + 5.8296I 0
u = 0.779928 + 0.219709I
a = −0.0845212 + 0.0646654I
b = 0.448745 + 0.043523I
1.49146 + 0.64236I 4.77435 + 0.42718I
u = 0.779928 − 0.219709I
a = −0.0845212 − 0.0646654I
b = 0.448745 − 0.043523I
1.49146 − 0.64236I 4.77435 − 0.42718I
u = −0.069592 + 1.215010I
a = −0.284409 + 1.131300I
b = −0.153291 + 0.859355I
−6.20670 + 0.35244I 0
u = −0.069592 − 1.215010I
a = −0.284409 − 1.131300I
b = −0.153291 − 0.859355I
−6.20670 − 0.35244I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.381706 + 0.616663I
a = −0.646954 − 0.302471I
b = 0.63548 + 1.31769I
−3.12841 + 1.60812I −9.18560 + 2.80861I
u = −0.381706 − 0.616663I
a = −0.646954 + 0.302471I
b = 0.63548 − 1.31769I
−3.12841 − 1.60812I −9.18560 − 2.80861I
u = −0.588655 + 1.137800I
a = 0.137393 + 0.569291I
b = 0.046183 + 1.104620I
−6.54145 − 0.12000I 0
u = −0.588655 − 1.137800I
a = 0.137393 − 0.569291I
b = 0.046183 − 1.104620I
−6.54145 + 0.12000I 0
u = −0.926132 + 0.904026I
a = −1.89386 − 0.43776I
b = 0.663678 − 1.048350I
−2.40423 − 6.89015I 0
u = −0.926132 − 0.904026I
a = −1.89386 + 0.43776I
b = 0.663678 + 1.048350I
−2.40423 + 6.89015I 0
u = 0.043690 + 0.643510I
a = 1.38661 − 1.02506I
b = −0.652287 − 0.993200I
−2.52587 + 5.75002I −4.75156 − 7.12777I
u = 0.043690 − 0.643510I
a = 1.38661 + 1.02506I
b = −0.652287 + 0.993200I
−2.52587 − 5.75002I −4.75156 + 7.12777I
u = 0.630240
a = −1.27668
b = 1.47192
−5.02482 5.52250
u = −0.328954 + 0.535707I
a = 0.704767 + 0.026780I
b = −0.568775 + 0.504540I
−1.47696 + 0.84526I −4.04601 − 1.22760I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.328954 − 0.535707I
a = 0.704767 − 0.026780I
b = −0.568775 − 0.504540I
−1.47696 − 0.84526I −4.04601 + 1.22760I
u = −0.948643 + 1.013220I
a = 1.25177 + 0.68906I
b = −0.720763 + 0.189367I
−8.97766 + 3.13474I 0
u = −0.948643 − 1.013220I
a = 1.25177 − 0.68906I
b = −0.720763 − 0.189367I
−8.97766 − 3.13474I 0
u = 0.089016 + 0.565790I
a = 0.924897 + 0.743590I
b = −0.094656 + 0.871815I
−1.11180 + 1.12663I −4.25436 − 4.77232I
u = 0.089016 − 0.565790I
a = 0.924897 − 0.743590I
b = −0.094656 − 0.871815I
−1.11180 − 1.12663I −4.25436 + 4.77232I
u = −1.01144 + 1.00979I
a = 1.026240 + 0.432846I
b = −1.103030 − 0.337146I
−8.88395 − 10.49540I 0
u = −1.01144 − 1.00979I
a = 1.026240 − 0.432846I
b = −1.103030 + 0.337146I
−8.88395 + 10.49540I 0
u = 1.14947 + 0.85016I
a = 0.669035 − 0.352609I
b = −0.724647 + 0.698496I
3.57978 + 1.16112I 0
u = 1.14947 − 0.85016I
a = 0.669035 + 0.352609I
b = −0.724647 − 0.698496I
3.57978 − 1.16112I 0
u = 0.414725 + 0.345278I
a = −4.97629 − 2.25758I
b = 0.417806 + 1.104800I
−11.26510 + 5.06614I −9.4830 − 11.2407I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.414725 − 0.345278I
a = −4.97629 + 2.25758I
b = 0.417806 − 1.104800I
−11.26510 − 5.06614I −9.4830 + 11.2407I
u = 1.04842 + 1.01862I
a = −1.203070 + 0.380286I
b = 0.871333 − 0.297517I
−3.99736 + 3.71610I 0
u = 1.04842 − 1.01862I
a = −1.203070 − 0.380286I
b = 0.871333 + 0.297517I
−3.99736 − 3.71610I 0
u = 0.99411 + 1.13893I
a = 1.265690 − 0.370176I
b = −0.682775 − 1.000360I
2.66017 + 6.57787I 0
u = 0.99411 − 1.13893I
a = 1.265690 + 0.370176I
b = −0.682775 + 1.000360I
2.66017 − 6.57787I 0
u = −0.313888 + 0.338273I
a = −2.50850 − 0.01377I
b = 0.528219 − 0.898276I
−0.20481 − 2.07908I −2.26565 + 3.54284I
u = −0.313888 − 0.338273I
a = −2.50850 + 0.01377I
b = 0.528219 + 0.898276I
−0.20481 + 2.07908I −2.26565 − 3.54284I
u = −1.23948 + 0.96164I
a = −1.160200 − 0.083777I
b = 0.387636 − 1.191240I
−4.64705 − 7.48016I 0
u = −1.23948 − 0.96164I
a = −1.160200 + 0.083777I
b = 0.387636 + 1.191240I
−4.64705 + 7.48016I 0
u = −1.45045 + 0.60559I
a = 1.51675 − 0.63151I
b = −0.404021 + 1.183230I
−12.70520 − 0.62704I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.45045 − 0.60559I
a = 1.51675 + 0.63151I
b = −0.404021 − 1.183230I
−12.70520 + 0.62704I 0
u = −1.14535 + 1.15657I
a = 1.43220 + 0.07872I
b = −0.67392 + 1.25371I
−11.7549 − 16.8301I 0
u = −1.14535 − 1.15657I
a = 1.43220 − 0.07872I
b = −0.67392 − 1.25371I
−11.7549 + 16.8301I 0
u = −0.273434 + 0.201008I
a = 7.60180 + 6.40532I
b = 0.152256 − 0.562228I
−9.01819 + 2.00460I −0.76875 − 9.29624I
u = −0.273434 − 0.201008I
a = 7.60180 − 6.40532I
b = 0.152256 + 0.562228I
−9.01819 − 2.00460I −0.76875 + 9.29624I
u = 0.66920 + 1.56410I
a = −0.404676 + 0.100855I
b = 0.286627 − 1.202720I
−8.81807 + 0.31313I 0
u = 0.66920 − 1.56410I
a = −0.404676 − 0.100855I
b = 0.286627 + 1.202720I
−8.81807 − 0.31313I 0
u = −0.118942 + 0.240216I
a = 2.08281 + 1.06752I
b = −1.091290 − 0.434988I
−2.41782 − 0.14514I −1.32526 − 13.85499I
u = −0.118942 − 0.240216I
a = 2.08281 − 1.06752I
b = −1.091290 + 0.434988I
−2.41782 + 0.14514I −1.32526 + 13.85499I
u = 0.121981 + 0.177501I
a = 2.08700 − 0.27369I
b = −0.60868 − 1.42128I
−2.62990 − 0.59843I −17.8564 − 15.9399I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.121981 − 0.177501I
a = 2.08700 + 0.27369I
b = −0.60868 + 1.42128I
−2.62990 + 0.59843I −17.8564 + 15.9399I
u = 1.78645 + 0.03549I
a = 1.351430 + 0.373710I
b = −0.605004 − 0.852194I
4.83036 + 2.38662I 0
u = 1.78645 − 0.03549I
a = 1.351430 − 0.373710I
b = −0.605004 + 0.852194I
4.83036 − 2.38662I 0
u = 1.38258 + 1.16195I
a = −1.381930 − 0.144564I
b = 0.583135 + 1.190080I
−6.70689 + 9.09405I 0
u = 1.38258 − 1.16195I
a = −1.381930 + 0.144564I
b = 0.583135 − 1.190080I
−6.70689 − 9.09405I 0
u = −1.22703 + 1.33810I
a = 0.465359 + 0.291972I
b = −0.520857 − 1.179320I
−11.8473 + 7.8938I 0
u = −1.22703 − 1.33810I
a = 0.465359 − 0.291972I
b = −0.520857 + 1.179320I
−11.8473 − 7.8938I 0
u = 1.94618 + 0.21387I
a = 0.868595 + 0.099321I
b = −0.259693 − 0.876278I
2.80268 + 1.18375I 0
u = 1.94618 − 0.21387I
a = 0.868595 − 0.099321I
b = −0.259693 + 0.876278I
2.80268 − 1.18375I 0
12
II.
I
u
2
= h8.87×10
26
u
29
+4.96×10
27
u
28
+· · ·+2.08×10
27
b−8.47×10
27
, −2.14×
10
27
u
29
−1.47×10
28
u
28
+· · ·+2.08×10
27
a+2.21×10
27
, u
30
+7u
29
+· · ·−2u+1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
4
=
1
−u
2
a
8
=
1.03085u
29
+ 7.05295u
28
+ ··· + 12.2937u − 1.06106
−0.426476u
29
− 2.38809u
28
+ ··· − 10.2361u + 4.07219
a
2
=
−1.29736u
29
− 8.81885u
28
+ ··· − 17.3636u + 4.06889
2.19676u
29
+ 14.7075u
28
+ ··· + 28.4474u − 7.43484
a
9
=
0.652770u
29
+ 4.35608u
28
+ ··· + 14.2719u − 2.77345
−1.82323u
29
− 12.2133u
28
+ ··· − 29.2448u + 6.44625
a
1
=
0.899401u
29
+ 5.88861u
28
+ ··· + 11.0838u − 3.36596
2.19676u
29
+ 14.7075u
28
+ ··· + 28.4474u − 7.43484
a
5
=
−0.103982u
29
− 0.503391u
28
+ ··· − 3.73912u + 0.326999
−0.631706u
29
− 4.65881u
28
+ ··· − 1.99763u − 0.427052
a
12
=
−1.11318u
29
− 7.51504u
28
+ ··· − 15.6498u + 3.66170
1.91296u
29
+ 12.7681u
28
+ ··· + 25.0660u − 6.75043
a
7
=
0.584554u
29
+ 3.97113u
28
+ ··· + 14.7136u − 2.86263
−1.71193u
29
− 11.4621u
28
+ ··· − 26.7669u + 6.11442
a
11
=
0.115312u
29
+ 0.750103u
28
+ ··· + 0.568560u + 1.49311
−0.197879u
29
− 1.48329u
28
+ ··· − 1.29316u − 1.23882
a
10
=
0.804684u
29
+ 5.84280u
28
+ ··· + 4.74884u + 1.14498
0.204268u
29
+ 1.47370u
28
+ ··· + 0.799106u + 0.163661
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
16094927794191462172380835339
1039451181930225503654703338
u
29
−
57469821610208664971093176195
519725590965112751827351669
u
28
+ ··· −
62817133116220172602979033368
519725590965112751827351669
u −
17691556347968942647146425724
519725590965112751827351669
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
30
− 16u
29
+ ··· − 68u + 4
c
2
u
30
+ 2u
29
+ ··· + 17u
2
+ 2
c
3
u
30
+ 7u
29
+ ··· − 2u + 1
c
4
u
30
− u
29
+ ··· − 2u + 2
c
5
u
30
+ u
29
+ ··· − 10u + 2
c
6
u
30
− 7u
29
+ ··· − 381u + 29
c
7
u
30
− u
29
+ ··· − 2u + 1
c
8
u
30
− 2u
29
+ ··· + 17u
2
+ 2
c
9
u
30
− 14u
29
+ ··· − 394u + 34
c
10
u
30
+ u
29
+ ··· + 2u + 2
c
11
u
30
+ u
29
+ ··· + 2u + 1
c
12
u
30
− u
29
+ ··· − u + 1
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
+ 8y
29
+ ··· + 184y + 16
c
2
, c
8
y
30
+ 16y
29
+ ··· + 68y + 4
c
3
y
30
− 11y
29
+ ··· + 28y + 1
c
4
, c
10
y
30
− 15y
29
+ ··· − 80y + 4
c
5
y
30
− 7y
29
+ ··· + 64y + 4
c
6
y
30
− 23y
29
+ ··· − 8281y + 841
c
7
, c
11
y
30
− 9y
29
+ ··· + 18y + 1
c
9
y
30
− 34y
29
+ ··· − 35896y + 1156
c
12
y
30
+ y
29
+ ··· + 27y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.982096 + 0.233503I
a = 0.541101 + 0.450562I
b = −0.582901 − 0.646856I
−0.28776 + 5.77132I 1.25910 − 9.61525I
u = 0.982096 − 0.233503I
a = 0.541101 − 0.450562I
b = −0.582901 + 0.646856I
−0.28776 − 5.77132I 1.25910 + 9.61525I
u = −0.656086 + 0.809604I
a = 1.48661 + 0.02876I
b = −0.593586 + 1.183260I
−5.04340 − 6.39979I −6.78821 + 9.40377I
u = −0.656086 − 0.809604I
a = 1.48661 − 0.02876I
b = −0.593586 − 1.183260I
−5.04340 + 6.39979I −6.78821 − 9.40377I
u = −0.917272 + 0.197982I
a = −0.307874 + 1.152100I
b = 0.276198 − 0.530692I
1.26278 − 1.69241I 2.26126 + 6.41443I
u = −0.917272 − 0.197982I
a = −0.307874 − 1.152100I
b = 0.276198 + 0.530692I
1.26278 + 1.69241I 2.26126 − 6.41443I
u = 0.918106 + 0.771715I
a = 1.85006 − 0.69444I
b = −0.573366 − 1.005450I
−1.33560 + 8.25410I −2.50174 − 8.51251I
u = 0.918106 − 0.771715I
a = 1.85006 + 0.69444I
b = −0.573366 + 1.005450I
−1.33560 − 8.25410I −2.50174 + 8.51251I
u = 1.065050 + 0.633149I
a = 0.446432 − 1.061380I
b = −0.541817 + 0.704779I
−0.31877 + 3.74358I −2.88615 − 0.98751I
u = 1.065050 − 0.633149I
a = 0.446432 + 1.061380I
b = −0.541817 − 0.704779I
−0.31877 − 3.74358I −2.88615 + 0.98751I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.338353 + 0.587512I
a = −2.38317 + 4.64737I
b = 0.217107 + 0.678621I
−9.24431 − 1.72175I −14.9721 − 7.4712I
u = 0.338353 − 0.587512I
a = −2.38317 − 4.64737I
b = 0.217107 − 0.678621I
−9.24431 + 1.72175I −14.9721 + 7.4712I
u = −0.206345 + 1.320460I
a = −0.045337 − 0.341218I
b = −0.346804 − 1.076280I
−7.20517 + 1.17304I −7.63113 + 0.09572I
u = −0.206345 − 1.320460I
a = −0.045337 + 0.341218I
b = −0.346804 + 1.076280I
−7.20517 − 1.17304I −7.63113 − 0.09572I
u = 0.064745 + 1.339480I
a = −0.158213 + 0.888109I
b = −0.246878 + 0.680207I
−5.60984 − 1.44808I −3.47667 + 5.05288I
u = 0.064745 − 1.339480I
a = −0.158213 − 0.888109I
b = −0.246878 − 0.680207I
−5.60984 + 1.44808I −3.47667 − 5.05288I
u = 0.548914 + 0.356673I
a = 0.05437 + 3.10960I
b = 0.390021 − 1.134390I
−11.21770 − 4.37056I −8.39225 + 0.22548I
u = 0.548914 − 0.356673I
a = 0.05437 − 3.10960I
b = 0.390021 + 1.134390I
−11.21770 + 4.37056I −8.39225 − 0.22548I
u = −1.094150 + 0.837675I
a = −0.594022 − 0.359918I
b = 0.760017 + 0.691233I
3.18674 − 0.90918I −6.11506 − 3.48473I
u = −1.094150 − 0.837675I
a = −0.594022 + 0.359918I
b = 0.760017 − 0.691233I
3.18674 + 0.90918I −6.11506 + 3.48473I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.94229 + 1.13914I
a = −1.232060 − 0.397667I
b = 0.710196 − 1.012440I
2.20945 − 6.51581I −9.66086 + 5.08418I
u = −0.94229 − 1.13914I
a = −1.232060 + 0.397667I
b = 0.710196 + 1.012440I
2.20945 + 6.51581I −9.66086 − 5.08418I
u = 0.069092 + 0.362777I
a = −0.320279 − 0.098113I
b = −0.19201 + 1.51694I
−2.71262 + 0.82083I −22.1854 − 5.0074I
u = 0.069092 − 0.362777I
a = −0.320279 + 0.098113I
b = −0.19201 − 1.51694I
−2.71262 − 0.82083I −22.1854 + 5.0074I
u = 0.000325 + 0.338133I
a = 1.39217 + 0.48419I
b = −1.24304 − 0.80655I
−2.56167 − 0.26101I −42.1737 + 0.5963I
u = 0.000325 − 0.338133I
a = 1.39217 − 0.48419I
b = −1.24304 + 0.80655I
−2.56167 + 0.26101I −42.1737 − 0.5963I
u = −1.82600 + 0.01286I
a = −1.44229 + 0.42842I
b = 0.597867 − 0.863795I
4.49936 − 2.35975I 0
u = −1.82600 − 0.01286I
a = −1.44229 − 0.42842I
b = 0.597867 + 0.863795I
4.49936 + 2.35975I 0
u = −1.84455 + 0.03679I
a = −0.787501 + 0.113823I
b = 0.368993 − 0.867157I
3.12478 − 1.56604I 0
u = −1.84455 − 0.03679I
a = −0.787501 − 0.113823I
b = 0.368993 + 0.867157I
3.12478 + 1.56604I 0
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
30
− 16u
29
+ ··· − 68u + 4)(u
79
+ 43u
78
+ ··· − 1004u − 100)
c
2
(u
30
+ 2u
29
+ ··· + 17u
2
+ 2)(u
79
+ 3u
78
+ ··· − 14u − 10)
c
3
(u
30
+ 7u
29
+ ··· − 2u + 1)(u
79
+ 4u
78
+ ··· − 15u − 2)
c
4
(u
30
− u
29
+ ··· − 2u + 2)(u
79
− 2u
78
+ ··· − 120u + 26)
c
5
(u
30
+ u
29
+ ··· − 10u + 2)(u
79
− 2u
78
+ ··· − 8478u − 3078)
c
6
(u
30
− 7u
29
+ ··· − 381u + 29)
· (u
79
− 6u
78
+ ··· + 1496873u + 115748)
c
7
(u
30
− u
29
+ ··· − 2u + 1)(u
79
+ 4u
78
+ ··· + 1193295u − 523514)
c
8
(u
30
− 2u
29
+ ··· + 17u
2
+ 2)(u
79
+ 3u
78
+ ··· − 14u − 10)
c
9
(u
30
− 14u
29
+ ··· − 394u + 34)(u
79
− 5u
78
+ ··· + 16594u − 12214)
c
10
(u
30
+ u
29
+ ··· + 2u + 2)(u
79
− 2u
78
+ ··· − 120u + 26)
c
11
(u
30
+ u
29
+ ··· + 2u + 1)(u
79
+ 4u
78
+ ··· + 1193295u − 523514)
c
12
(u
30
− u
29
+ ··· − u + 1)(u
79
+ 6u
78
+ ··· + 45561u − 4572)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
30
+ 8y
29
+ ··· + 184y + 16)(y
79
− y
78
+ ··· + 465616y −10000)
c
2
, c
8
(y
30
+ 16y
29
+ ··· + 68y + 4)(y
79
+ 43y
78
+ ··· − 1004y −100)
c
3
(y
30
− 11y
29
+ ··· + 28y + 1)(y
79
− 8y
78
+ ··· − 151y −4)
c
4
, c
10
(y
30
− 15y
29
+ ··· − 80y + 4)(y
79
− 60y
78
+ ··· + 42480y −676)
c
5
(y
30
− 7y
29
+ ··· + 64y + 4)
· (y
79
+ 8y
78
+ ··· − 207913716y −9474084)
c
6
(y
30
− 23y
29
+ ··· − 8281y + 841)
· (y
79
− 116y
78
+ ··· + 1057720100009y −13397599504)
c
7
, c
11
(y
30
− 9y
29
+ ··· + 18y + 1)
· (y
79
− 90y
78
+ ··· + 5429126130809y −274066908196)
c
9
(y
30
− 34y
29
+ ··· − 35896y + 1156)
· (y
79
− 103y
78
+ ··· + 453343244y −149181796)
c
12
(y
30
+ y
29
+ ··· + 27y + 1)
· (y
79
+ 28y
78
+ ··· + 771038217y −20903184)
22
