12n
0652
(K12n
0652
)
A knot diagram
1
Linearized knot diagam
3 8 10 11 1 4 2 11 7 6 8 5
Solving Sequence
3,8
2
1,5
6 7 12 11 9 4 10
c
2
c
1
c
5
c
7
c
12
c
11
c
8
c
4
c
10
c
3
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.95566 × 10
237
u
100
− 6.62307 × 10
237
u
99
+ ··· + 4.78420 × 10
238
b − 4.22616 × 10
240
,
− 5.09303 × 10
240
u
100
− 6.43646 × 10
240
u
99
+ ··· + 1.00947 × 10
241
a − 1.17880 × 10
243
,
u
101
− 29u
99
+ ··· − 366u − 211i
I
u
2
= h−6594748663u
31
+ 11676405243u
30
+ ··· + 304614406b − 9241004294,
9719505347u
31
− 16695825813u
30
+ ··· + 304614406a + 11648772074, u
32
− u
31
+ ··· − 3u + 1i
* 2 irreducible components of dim
C
= 0, with total 133 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−7.96 × 10
237
u
100
− 6.62 × 10
237
u
99
+ · · · + 4.78 × 10
238
b − 4.23 ×
10
240
, −5.09 × 10
240
u
100
− 6.44 × 10
240
u
99
+ · · · + 1.01 × 10
241
a − 1.18 ×
10
243
, u
101
− 29u
99
+ · · · − 366u − 211i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
5
=
0.504526u
100
+ 0.637610u
99
+ ··· + 220.410u + 116.774
0.166290u
100
+ 0.138436u
99
+ ··· + 298.648u + 88.3358
a
6
=
0.719768u
100
+ 0.816275u
99
+ ··· + 396.415u + 177.901
−0.314263u
100
− 0.311027u
99
+ ··· − 78.0601u − 44.1993
a
7
=
u
−u
3
+ u
a
12
=
0.0646741u
100
+ 0.102419u
99
+ ··· − 5.30493u + 10.0598
0.709533u
100
+ 0.284808u
99
+ ··· + 376.424u + 77.2488
a
11
=
0.0646741u
100
+ 0.102419u
99
+ ··· − 5.30493u + 10.0598
0.560079u
100
+ 0.146742u
99
+ ··· + 325.292u + 55.6384
a
9
=
0.574178u
100
+ 0.482635u
99
+ ··· + 367.785u + 130.977
−0.0616652u
100
− 0.285923u
99
+ ··· − 131.623u − 77.5243
a
4
=
1.02386u
100
+ 0.779755u
99
+ ··· + 593.132u + 198.503
−0.120196u
100
− 0.169073u
99
+ ··· − 85.7088u − 33.7270
a
10
=
0.716347u
100
+ 0.710368u
99
+ ··· + 544.466u + 211.942
0.0100619u
100
− 0.152637u
99
+ ··· − 68.2902u − 44.6114
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4.64685u
100
− 3.26032u
99
+ ··· − 3712.21u − 1141.11
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
101
+ 58u
100
+ ··· + 943774u + 44521
c
2
, c
7
u
101
− 29u
99
+ ··· − 366u − 211
c
3
u
101
− 2u
100
+ ··· − 97u + 7
c
4
u
101
+ 23u
99
+ ··· + 750579u + 306659
c
5
, c
12
u
101
− 16u
99
+ ··· − 953u − 133
c
6
u
101
− u
100
+ ··· + 227u − 23
c
8
, c
11
u
101
+ 15u
100
+ ··· + 3501095u + 215671
c
9
u
101
− 7u
100
+ ··· − 1316600u + 92575
c
10
u
101
− 3u
100
+ ··· − 790u − 83
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
101
− 14y
100
+ ··· + 27975815430y −1982119441
c
2
, c
7
y
101
− 58y
100
+ ··· + 943774y −44521
c
3
y
101
− 10y
100
+ ··· + 155y −49
c
4
y
101
+ 46y
100
+ ··· − 3797359557157y −94039742281
c
5
, c
12
y
101
− 32y
100
+ ··· + 823621y −17689
c
6
y
101
− 9y
100
+ ··· + 23423y −529
c
8
, c
11
y
101
− 93y
100
+ ··· + 1171525903947y −46513980241
c
9
y
101
− 45y
100
+ ··· + 570114040500y −8570130625
c
10
y
101
+ 11y
100
+ ··· − 196936y −6889
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.820034 + 0.585292I
a = 0.033824 − 0.300405I
b = −0.94355 − 1.29230I
4.33943 + 1.14415I 0
u = 0.820034 − 0.585292I
a = 0.033824 + 0.300405I
b = −0.94355 + 1.29230I
4.33943 − 1.14415I 0
u = 0.985457 + 0.104624I
a = 0.037446 − 0.669943I
b = 0.726416 + 0.509050I
−3.62929 − 2.83489I 0
u = 0.985457 − 0.104624I
a = 0.037446 + 0.669943I
b = 0.726416 − 0.509050I
−3.62929 + 2.83489I 0
u = −0.530981 + 0.810422I
a = 1.61271 − 1.19757I
b = 0.532324 − 0.580869I
−2.63257 + 3.84014I 0
u = −0.530981 − 0.810422I
a = 1.61271 + 1.19757I
b = 0.532324 + 0.580869I
−2.63257 − 3.84014I 0
u = 1.027270 + 0.217643I
a = −0.340119 − 1.308040I
b = 0.243063 − 1.221120I
−7.61850 − 0.65923I 0
u = 1.027270 − 0.217643I
a = −0.340119 + 1.308040I
b = 0.243063 + 1.221120I
−7.61850 + 0.65923I 0
u = −0.112192 + 0.938796I
a = 1.95188 − 0.30689I
b = 0.468388 + 0.284137I
−1.67442 − 1.04305I 0
u = −0.112192 − 0.938796I
a = 1.95188 + 0.30689I
b = 0.468388 − 0.284137I
−1.67442 + 1.04305I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.172731 + 1.067630I
a = 1.47812 − 0.48759I
b = 0.295965 − 0.883833I
−0.38324 + 3.98606I 0
u = 0.172731 − 1.067630I
a = 1.47812 + 0.48759I
b = 0.295965 + 0.883833I
−0.38324 − 3.98606I 0
u = −0.422357 + 0.996136I
a = 1.88932 + 0.35696I
b = 0.689307 + 1.005280I
−2.01850 − 3.05243I 0
u = −0.422357 − 0.996136I
a = 1.88932 − 0.35696I
b = 0.689307 − 1.005280I
−2.01850 + 3.05243I 0
u = −0.832349 + 0.372279I
a = −0.139598 + 1.207060I
b = −0.0679636 − 0.0471394I
1.34976 − 0.66315I 0
u = −0.832349 − 0.372279I
a = −0.139598 − 1.207060I
b = −0.0679636 + 0.0471394I
1.34976 + 0.66315I 0
u = −0.656254 + 0.632742I
a = 0.564801 − 1.036380I
b = 0.962520 − 0.528825I
−0.33221 + 2.15160I 0
u = −0.656254 − 0.632742I
a = 0.564801 + 1.036380I
b = 0.962520 + 0.528825I
−0.33221 − 2.15160I 0
u = −0.421401 + 0.800169I
a = −1.125030 + 0.132865I
b = −0.293273 − 0.851923I
−2.71761 − 1.32653I 0
u = −0.421401 − 0.800169I
a = −1.125030 − 0.132865I
b = −0.293273 + 0.851923I
−2.71761 + 1.32653I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.259609 + 1.067610I
a = −1.72155 + 0.32265I
b = −0.466377 + 0.881217I
−1.92144 + 12.29610I 0
u = 0.259609 − 1.067610I
a = −1.72155 − 0.32265I
b = −0.466377 − 0.881217I
−1.92144 − 12.29610I 0
u = −0.723110 + 0.827949I
a = 0.84434 + 1.80493I
b = −0.38782 + 1.81403I
2.61470 − 2.35298I 0
u = −0.723110 − 0.827949I
a = 0.84434 − 1.80493I
b = −0.38782 − 1.81403I
2.61470 + 2.35298I 0
u = −0.947967 + 0.574342I
a = 0.878995 − 0.261408I
b = 0.142593 + 0.500799I
−1.15276 + 2.52280I 0
u = −0.947967 − 0.574342I
a = 0.878995 + 0.261408I
b = 0.142593 − 0.500799I
−1.15276 − 2.52280I 0
u = −0.825651 + 0.325227I
a = −1.03139 + 1.08118I
b = −1.96412 + 0.68654I
1.46496 + 3.76761I 0
u = −0.825651 − 0.325227I
a = −1.03139 − 1.08118I
b = −1.96412 − 0.68654I
1.46496 − 3.76761I 0
u = 1.037520 + 0.423630I
a = −0.655068 − 0.350769I
b = −0.390864 + 1.168550I
1.02564 − 5.30362I 0
u = 1.037520 − 0.423630I
a = −0.655068 + 0.350769I
b = −0.390864 − 1.168550I
1.02564 + 5.30362I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.091290 + 0.326589I
a = −0.125661 + 0.458687I
b = −0.98139 + 2.35676I
1.78195 + 6.72216I 0
u = −1.091290 − 0.326589I
a = −0.125661 − 0.458687I
b = −0.98139 − 2.35676I
1.78195 − 6.72216I 0
u = 0.715518 + 0.470453I
a = −0.146982 − 0.233324I
b = 1.19859 + 0.91932I
4.69000 − 5.44399I 0
u = 0.715518 − 0.470453I
a = −0.146982 + 0.233324I
b = 1.19859 − 0.91932I
4.69000 + 5.44399I 0
u = 1.105060 + 0.348432I
a = −0.429969 − 1.131870I
b = −0.29685 − 1.62962I
−5.52117 + 1.02862I 0
u = 1.105060 − 0.348432I
a = −0.429969 + 1.131870I
b = −0.29685 + 1.62962I
−5.52117 − 1.02862I 0
u = 0.834281 + 0.073903I
a = −0.085148 − 1.349500I
b = 0.742747 + 0.274742I
−3.70589 − 2.85195I 0
u = 0.834281 − 0.073903I
a = −0.085148 + 1.349500I
b = 0.742747 − 0.274742I
−3.70589 + 2.85195I 0
u = 1.168720 + 0.132657I
a = 0.374634 + 1.230770I
b = 0.446630 + 1.106190I
−8.14969 + 0.29983I 0
u = 1.168720 − 0.132657I
a = 0.374634 − 1.230770I
b = 0.446630 − 1.106190I
−8.14969 − 0.29983I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.057890 + 0.529949I
a = −0.549762 + 0.270888I
b = 0.32388 + 1.47416I
0.69986 − 5.52879I 0
u = 1.057890 − 0.529949I
a = −0.549762 − 0.270888I
b = 0.32388 − 1.47416I
0.69986 + 5.52879I 0
u = 1.133440 + 0.362308I
a = 0.37569 + 1.43089I
b = 2.68251 + 2.44321I
−6.79023 − 6.46863I 0
u = 1.133440 − 0.362308I
a = 0.37569 − 1.43089I
b = 2.68251 − 2.44321I
−6.79023 + 6.46863I 0
u = 0.774969 + 0.908000I
a = 0.847818 − 0.971440I
b = −0.253631 − 1.291530I
4.25675 − 0.06797I 0
u = 0.774969 − 0.908000I
a = 0.847818 + 0.971440I
b = −0.253631 + 1.291530I
4.25675 + 0.06797I 0
u = −1.165960 + 0.275055I
a = 0.456960 + 0.048402I
b = 0.603489 − 0.827587I
−1.65982 + 1.25712I 0
u = −1.165960 − 0.275055I
a = 0.456960 − 0.048402I
b = 0.603489 + 0.827587I
−1.65982 − 1.25712I 0
u = 0.598387 + 0.502597I
a = 0.32061 − 1.55924I
b = −1.45875 − 1.20083I
2.45000 + 1.47696I −2.21815 + 0.I
u = 0.598387 − 0.502597I
a = 0.32061 + 1.55924I
b = −1.45875 + 1.20083I
2.45000 − 1.47696I −2.21815 + 0.I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.781170
a = −0.660008
b = −2.65405
0.526391 −12.4510
u = 1.165080 + 0.391120I
a = −0.554888 − 1.188060I
b = −2.46665 − 2.02558I
−7.73546 + 1.92109I 0
u = 1.165080 − 0.391120I
a = −0.554888 + 1.188060I
b = −2.46665 + 2.02558I
−7.73546 − 1.92109I 0
u = −1.113090 + 0.539386I
a = 0.412358 − 0.117499I
b = 0.398639 + 0.659751I
0.260818 − 0.400392I 0
u = −1.113090 − 0.539386I
a = 0.412358 + 0.117499I
b = 0.398639 − 0.659751I
0.260818 + 0.400392I 0
u = −0.297259 + 0.702085I
a = −1.71072 + 0.42820I
b = −0.086831 − 0.815638I
−1.72276 − 3.92826I −4.92577 + 8.41157I
u = −0.297259 − 0.702085I
a = −1.71072 − 0.42820I
b = −0.086831 + 0.815638I
−1.72276 + 3.92826I −4.92577 − 8.41157I
u = −1.004280 + 0.734721I
a = −1.49398 − 1.38619I
b = 0.06660 − 2.24573I
1.74154 + 8.20625I 0
u = −1.004280 − 0.734721I
a = −1.49398 + 1.38619I
b = 0.06660 + 2.24573I
1.74154 − 8.20625I 0
u = 0.387915 + 0.646900I
a = 0.341745 − 0.685172I
b = −0.754171 − 0.784952I
2.62272 + 0.97071I 1.85950 − 0.63323I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.387915 − 0.646900I
a = 0.341745 + 0.685172I
b = −0.754171 + 0.784952I
2.62272 − 0.97071I 1.85950 + 0.63323I
u = −1.128540 + 0.535413I
a = −0.315092 + 1.093540I
b = −1.92869 + 1.96354I
−4.14830 + 8.67493I 0
u = −1.128540 − 0.535413I
a = −0.315092 − 1.093540I
b = −1.92869 − 1.96354I
−4.14830 − 8.67493I 0
u = −0.749799
a = 0.510552
b = 0.219990
−1.51667 −5.25440
u = −0.192427 + 0.718269I
a = −2.15738 + 0.48060I
b = −0.342576 + 0.575969I
−4.01739 − 5.53614I −4.00000 + 3.69769I
u = −0.192427 − 0.718269I
a = −2.15738 − 0.48060I
b = −0.342576 − 0.575969I
−4.01739 + 5.53614I −4.00000 − 3.69769I
u = −1.117260 + 0.604980I
a = −0.121036 + 1.042240I
b = −1.67025 + 1.58440I
−4.80170 + 6.61061I 0
u = −1.117260 − 0.604980I
a = −0.121036 − 1.042240I
b = −1.67025 − 1.58440I
−4.80170 − 6.61061I 0
u = −1.165570 + 0.513406I
a = −0.449779 + 1.143800I
b = −0.229696 + 1.391280I
−6.84123 + 10.22070I 0
u = −1.165570 − 0.513406I
a = −0.449779 − 1.143800I
b = −0.229696 − 1.391280I
−6.84123 − 10.22070I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.211150 + 0.458943I
a = −0.156975 + 0.229898I
b = −0.571082 − 0.377330I
−0.47114 − 9.20279I 0
u = 1.211150 − 0.458943I
a = −0.156975 − 0.229898I
b = −0.571082 + 0.377330I
−0.47114 + 9.20279I 0
u = −0.051611 + 0.697056I
a = 0.410927 − 0.410638I
b = 0.784635 + 0.092928I
3.06555 + 4.91909I 0.44965 − 7.59677I
u = −0.051611 − 0.697056I
a = 0.410927 + 0.410638I
b = 0.784635 − 0.092928I
3.06555 − 4.91909I 0.44965 + 7.59677I
u = 1.292030 + 0.181188I
a = 0.157375 + 0.926748I
b = 0.587242 + 1.239310I
−6.11471 − 3.27045I 0
u = 1.292030 − 0.181188I
a = 0.157375 − 0.926748I
b = 0.587242 − 1.239310I
−6.11471 + 3.27045I 0
u = 1.264860 + 0.336878I
a = 0.299011 + 1.080750I
b = 0.47582 + 1.36586I
−6.25089 − 3.34515I 0
u = 1.264860 − 0.336878I
a = 0.299011 − 1.080750I
b = 0.47582 − 1.36586I
−6.25089 + 3.34515I 0
u = 0.985067 + 0.899162I
a = −0.449526 + 1.155670I
b = 0.42203 + 1.54482I
3.65832 − 6.49471I 0
u = 0.985067 − 0.899162I
a = −0.449526 − 1.155670I
b = 0.42203 − 1.54482I
3.65832 + 6.49471I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.237570 + 0.506251I
a = 0.660880 − 1.087730I
b = 1.90594 − 1.83014I
−5.17592 + 6.17586I 0
u = −1.237570 − 0.506251I
a = 0.660880 + 1.087730I
b = 1.90594 + 1.83014I
−5.17592 − 6.17586I 0
u = 0.649004 + 0.074296I
a = 0.51392 + 2.77828I
b = 0.27129 − 2.39289I
−4.46140 + 4.15869I 3.67911 − 0.78240I
u = 0.649004 − 0.074296I
a = 0.51392 − 2.77828I
b = 0.27129 + 2.39289I
−4.46140 − 4.15869I 3.67911 + 0.78240I
u = −1.196790 + 0.651190I
a = 0.19788 − 1.58630I
b = 1.65935 − 2.17229I
−4.47841 + 9.04243I 0
u = −1.196790 − 0.651190I
a = 0.19788 + 1.58630I
b = 1.65935 + 2.17229I
−4.47841 − 9.04243I 0
u = −1.243550 + 0.563865I
a = 0.742729 − 0.977181I
b = 0.526850 − 1.039350I
−5.08145 + 1.93675I 0
u = −1.243550 − 0.563865I
a = 0.742729 + 0.977181I
b = 0.526850 + 1.039350I
−5.08145 − 1.93675I 0
u = −0.603686 + 0.144992I
a = −0.391023 + 0.681439I
b = 1.84033 − 1.17193I
3.67321 − 4.24686I 1.03729 + 9.76117I
u = −0.603686 − 0.144992I
a = −0.391023 − 0.681439I
b = 1.84033 + 1.17193I
3.67321 + 4.24686I 1.03729 − 9.76117I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.263010 + 0.635306I
a = −0.158476 − 1.375500I
b = −1.49608 − 2.22872I
−5.0342 − 18.3765I 0
u = 1.263010 − 0.635306I
a = −0.158476 + 1.375500I
b = −1.49608 + 2.22872I
−5.0342 + 18.3765I 0
u = 1.28903 + 0.61186I
a = 0.076027 + 1.225230I
b = 1.29368 + 2.17190I
−3.81427 − 9.96932I 0
u = 1.28903 − 0.61186I
a = 0.076027 − 1.225230I
b = 1.29368 − 2.17190I
−3.81427 + 9.96932I 0
u = −1.46564 + 0.28112I
a = −0.667596 + 0.882497I
b = −0.603595 + 1.080470I
−7.80114 − 7.45975I 0
u = −1.46564 − 0.28112I
a = −0.667596 − 0.882497I
b = −0.603595 − 1.080470I
−7.80114 + 7.45975I 0
u = −0.212450 + 0.420159I
a = 0.821744 − 0.425029I
b = 0.006894 − 0.395737I
−0.141485 + 1.223150I −1.92517 − 5.09911I
u = −0.212450 − 0.420159I
a = 0.821744 + 0.425029I
b = 0.006894 + 0.395737I
−0.141485 − 1.223150I −1.92517 + 5.09911I
u = −1.50432 + 0.37318I
a = 0.638007 − 0.597793I
b = 0.311741 − 0.809139I
−5.75356 + 1.43008I 0
u = −1.50432 − 0.37318I
a = 0.638007 + 0.597793I
b = 0.311741 + 0.809139I
−5.75356 − 1.43008I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.66200
a = 0.389300
b = 0.523560
−9.93168 0
15
II.
I
u
2
= h−6.59 × 10
9
u
31
+ 1.17 × 10
10
u
30
+ · · · + 3.05 × 10
8
b − 9.24 × 10
9
, 9.72 ×
10
9
u
31
−1.67×10
10
u
30
+· · ·+3.05×10
8
a+1.16×10
10
, u
32
−u
31
+· · ·−3u+1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
5
=
−31.9076u
31
+ 54.8097u
30
+ ··· + 185.646u − 38.2410
21.6495u
31
− 38.3318u
30
+ ··· − 140.748u + 30.3367
a
6
=
−33.6655u
31
+ 58.6727u
30
+ ··· + 198.206u − 43.1093
25.7549u
31
− 44.7115u
30
+ ··· − 159.750u + 34.7161
a
7
=
u
−u
3
+ u
a
12
=
−6.37742u
31
+ 9.38738u
30
+ ··· + 37.9502u − 12.0833
−3.23545u
31
+ 0.552598u
30
+ ··· − 1.48578u + 3.98693
a
11
=
−6.37742u
31
+ 9.38738u
30
+ ··· + 37.9502u − 12.0833
−0.0372065u
31
− 3.19741u
30
+ ··· − 16.8931u + 6.99689
a
9
=
9.18508u
31
− 17.8951u
30
+ ··· − 60.9147u + 11.7849
−7.61868u
31
+ 11.8510u
30
+ ··· + 54.3714u − 10.3858
a
4
=
−18.7594u
31
+ 32.8590u
30
+ ··· + 110.242u − 27.5431
10.0143u
31
− 16.9898u
30
+ ··· − 55.6691u + 15.0390
a
10
=
15.5359u
31
− 27.4567u
30
+ ··· − 96.7263u + 19.3080
−4.17918u
31
+ 6.63738u
30
+ ··· + 34.5429u − 6.07334
(ii) Obstruction class = 1
(iii) Cusp Shapes =
26306939827
304614406
u
31
−
45742642605
304614406
u
30
+ ··· −
137351628763
304614406
u +
15592194281
152307203
16
(iv) u-Polynomials at the component
17
Crossings u-Polynomials at each crossing
c
1
u
32
− 21u
31
+ ··· − 35u + 1
c
2
u
32
− u
31
+ ··· − 3u + 1
c
3
u
32
− u
31
+ ··· + 10u
2
+ 1
c
4
u
32
− u
31
+ ··· + 364u + 169
c
5
u
32
+ u
31
+ ··· − 4u − 1
c
6
u
32
+ 4u
31
+ ··· − 6u − 1
c
7
u
32
+ u
31
+ ··· + 3u + 1
c
8
u
32
− 16u
31
+ ··· − 8u + 1
c
9
u
32
+ 4u
31
+ ··· + 205u − 79
c
10
u
32
+ 2u
30
+ ··· − u + 1
c
11
u
32
+ 16u
31
+ ··· + 8u + 1
c
12
u
32
− u
31
+ ··· + 4u − 1
18
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
32
− 5y
31
+ ··· − 395y + 1
c
2
, c
7
y
32
− 21y
31
+ ··· − 35y + 1
c
3
y
32
− 5y
31
+ ··· + 20y + 1
c
4
y
32
+ 11y
31
+ ··· + 378560y + 28561
c
5
, c
12
y
32
− 15y
31
+ ··· − 14y + 1
c
6
y
32
+ 4y
31
+ ··· + 6y
2
+ 1
c
8
, c
11
y
32
− 24y
31
+ ··· + 20y + 1
c
9
y
32
− 16y
31
+ ··· − 52769y + 6241
c
10
y
32
+ 4y
31
+ ··· − 9y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.980268 + 0.194926I
a = 0.34395 + 1.43609I
b = −0.123165 + 1.215990I
−7.36645 − 0.77286I 2.63433 + 11.55591I
u = 0.980268 − 0.194926I
a = 0.34395 − 1.43609I
b = −0.123165 − 1.215990I
−7.36645 + 0.77286I 2.63433 − 11.55591I
u = 0.630734 + 0.750536I
a = 0.42899 − 1.95867I
b = −0.96670 − 1.54528I
3.34075 + 2.07396I 5.65134 − 3.73262I
u = 0.630734 − 0.750536I
a = 0.42899 + 1.95867I
b = −0.96670 + 1.54528I
3.34075 − 2.07396I 5.65134 + 3.73262I
u = 1.037650 + 0.358363I
a = 0.167211 − 0.000297I
b = −0.48594 − 1.88481I
2.42811 − 6.51399I 2.33326 + 6.81442I
u = 1.037650 − 0.358363I
a = 0.167211 + 0.000297I
b = −0.48594 + 1.88481I
2.42811 + 6.51399I 2.33326 − 6.81442I
u = −0.375099 + 0.816164I
a = 1.75372 − 0.02617I
b = 0.436371 + 0.890345I
−1.61386 − 2.55409I −1.67020 + 1.09385I
u = −0.375099 − 0.816164I
a = 1.75372 + 0.02617I
b = 0.436371 − 0.890345I
−1.61386 + 2.55409I −1.67020 − 1.09385I
u = −0.852551 + 0.705372I
a = −0.348636 − 0.992908I
b = 0.92253 − 1.64631I
5.69538 + 6.55678I 2.56792 − 7.16129I
u = −0.852551 − 0.705372I
a = −0.348636 + 0.992908I
b = 0.92253 + 1.64631I
5.69538 − 6.55678I 2.56792 + 7.16129I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621409 + 0.592076I
a = 1.42985 + 1.30299I
b = 0.320427 + 0.301889I
−2.46201 − 3.44323I −4.82242 + 0.23837I
u = 0.621409 − 0.592076I
a = 1.42985 − 1.30299I
b = 0.320427 − 0.301889I
−2.46201 + 3.44323I −4.82242 − 0.23837I
u = −0.898079 + 0.755548I
a = 0.632834 + 0.698476I
b = −0.39489 + 1.55987I
5.56852 − 1.00520I 3.92655 + 1.26527I
u = −0.898079 − 0.755548I
a = 0.632834 − 0.698476I
b = −0.39489 − 1.55987I
5.56852 + 1.00520I 3.92655 − 1.26527I
u = 0.761896 + 0.319991I
a = 0.055438 + 0.707752I
b = 1.89833 + 1.63743I
3.47370 + 3.63345I −3.55925 + 0.94794I
u = 0.761896 − 0.319991I
a = 0.055438 − 0.707752I
b = 1.89833 − 1.63743I
3.47370 − 3.63345I −3.55925 − 0.94794I
u = −1.090840 + 0.461551I
a = 0.041357 + 0.367261I
b = 0.164825 − 0.197195I
−0.159840 + 0.169610I −6.78432 − 2.26247I
u = −1.090840 − 0.461551I
a = 0.041357 − 0.367261I
b = 0.164825 + 0.197195I
−0.159840 − 0.169610I −6.78432 + 2.26247I
u = −1.226190 + 0.065079I
a = −0.033434 − 1.195280I
b = 0.46043 − 2.53083I
−6.81764 + 4.63942I −9.12510 − 5.17213I
u = −1.226190 − 0.065079I
a = −0.033434 + 1.195280I
b = 0.46043 + 2.53083I
−6.81764 − 4.63942I −9.12510 + 5.17213I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.728651 + 0.020366I
a = 0.12361 − 2.73559I
b = 0.45039 + 1.82542I
−4.78351 − 4.26429I −19.7845 + 8.5177I
u = −0.728651 − 0.020366I
a = 0.12361 + 2.73559I
b = 0.45039 − 1.82542I
−4.78351 + 4.26429I −19.7845 − 8.5177I
u = 1.065580 + 0.712278I
a = −1.23946 + 1.00654I
b = −0.16431 + 1.96766I
2.00750 − 7.68008I 0. + 4.19169I
u = 1.065580 − 0.712278I
a = −1.23946 − 1.00654I
b = −0.16431 − 1.96766I
2.00750 + 7.68008I 0. − 4.19169I
u = −1.164730 + 0.562610I
a = 0.267817 − 1.224490I
b = 1.79705 − 1.96826I
−4.14777 + 7.70967I −5.90759 − 5.11382I
u = −1.164730 − 0.562610I
a = 0.267817 + 1.224490I
b = 1.79705 + 1.96826I
−4.14777 − 7.70967I −5.90759 + 5.11382I
u = −0.644594 + 0.276379I
a = −1.02230 + 1.21826I
b = −1.67074 + 0.11441I
1.61620 + 3.09807I −2.35957 − 0.52960I
u = −0.644594 − 0.276379I
a = −1.02230 − 1.21826I
b = −1.67074 − 0.11441I
1.61620 − 3.09807I −2.35957 + 0.52960I
u = 1.43394 + 0.39466I
a = 0.617323 + 0.701200I
b = 0.354730 + 0.873441I
−5.62758 − 1.59349I 0
u = 1.43394 − 0.39466I
a = 0.617323 − 0.701200I
b = 0.354730 − 0.873441I
−5.62758 + 1.59349I 0
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.67414
a = 0.401513
b = 0.486029
−9.89006 91.8550
u = 0.224361
a = 3.16193
b = −1.48470
1.26809 −1.91950
24
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
32
− 21u
31
+ ··· − 35u + 1)(u
101
+ 58u
100
+ ··· + 943774u + 44521)
c
2
(u
32
− u
31
+ ··· − 3u + 1)(u
101
− 29u
99
+ ··· − 366u − 211)
c
3
(u
32
− u
31
+ ··· + 10u
2
+ 1)(u
101
− 2u
100
+ ··· − 97u + 7)
c
4
(u
32
− u
31
+ ··· + 364u + 169)
· (u
101
+ 23u
99
+ ··· + 750579u + 306659)
c
5
(u
32
+ u
31
+ ··· − 4u − 1)(u
101
− 16u
99
+ ··· − 953u − 133)
c
6
(u
32
+ 4u
31
+ ··· − 6u − 1)(u
101
− u
100
+ ··· + 227u − 23)
c
7
(u
32
+ u
31
+ ··· + 3u + 1)(u
101
− 29u
99
+ ··· − 366u − 211)
c
8
(u
32
− 16u
31
+ ··· − 8u + 1)
· (u
101
+ 15u
100
+ ··· + 3501095u + 215671)
c
9
(u
32
+ 4u
31
+ ··· + 205u − 79)
· (u
101
− 7u
100
+ ··· − 1316600u + 92575)
c
10
(u
32
+ 2u
30
+ ··· − u + 1)(u
101
− 3u
100
+ ··· − 790u − 83)
c
11
(u
32
+ 16u
31
+ ··· + 8u + 1)
· (u
101
+ 15u
100
+ ··· + 3501095u + 215671)
c
12
(u
32
− u
31
+ ··· + 4u − 1)(u
101
− 16u
99
+ ··· − 953u − 133)
25
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
32
− 5y
31
+ ··· − 395y + 1)
· (y
101
− 14y
100
+ ··· + 27975815430y −1982119441)
c
2
, c
7
(y
32
− 21y
31
+ ··· − 35y + 1)(y
101
− 58y
100
+ ··· + 943774y −44521)
c
3
(y
32
− 5y
31
+ ··· + 20y + 1)(y
101
− 10y
100
+ ··· + 155y −49)
c
4
(y
32
+ 11y
31
+ ··· + 378560y + 28561)
· (y
101
+ 46y
100
+ ··· − 3797359557157y −94039742281)
c
5
, c
12
(y
32
− 15y
31
+ ··· − 14y + 1)(y
101
− 32y
100
+ ··· + 823621y −17689)
c
6
(y
32
+ 4y
31
+ ··· + 6y
2
+ 1)(y
101
− 9y
100
+ ··· + 23423y −529)
c
8
, c
11
(y
32
− 24y
31
+ ··· + 20y + 1)
· (y
101
− 93y
100
+ ··· + 1171525903947y −46513980241)
c
9
(y
32
− 16y
31
+ ··· − 52769y + 6241)
· (y
101
− 45y
100
+ ··· + 570114040500y −8570130625)
c
10
(y
32
+ 4y
31
+ ··· − 9y + 1)(y
101
+ 11y
100
+ ··· − 196936y −6889)
26
