12n
0852
(K12n
0852
)
A knot diagram
1
Linearized knot diagam
4 7 9 10 12 3 10 2 1 7 5 6
Solving Sequence
1,4 2,9
10 5 3 8 7 11 6 12
c
1
c
9
c
4
c
3
c
8
c
7
c
10
c
6
c
12
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h3.07370 × 10
309
u
88
+ 7.02933 × 10
309
u
87
+ ··· + 4.88148 × 10
305
b − 4.73335 × 10
310
,
− 5.19770 × 10
310
u
88
− 1.16472 × 10
311
u
87
+ ··· + 9.12837 × 10
307
a + 6.31502 × 10
311
,
u
89
+ 3u
88
+ ··· − 128u − 11i
I
u
2
= h5.39113 × 10
24
u
26
− 2.77278 × 10
25
u
25
+ ··· + 3.88238 × 10
24
b + 3.65850 × 10
25
,
3.40177 × 10
25
u
26
− 1.13953 × 10
26
u
25
+ ··· + 3.88238 × 10
24
a + 4.53762 × 10
25
, u
27
− 4u
26
+ ··· + 7u − 1i
* 2 irreducible components of dim
C
= 0, with total 116 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
= h3.07 × 10
309
u
88
+ 7.03 × 10
309
u
87
+ · · · + 4.88 × 10
305
b − 4.73 ×
10
310
, −5.20 × 10
310
u
88
− 1.16 × 10
311
u
87
+ · · · + 9.13 × 10
307
a + 6.32 ×
10
311
, u
89
+ 3u
88
+ · · · − 128u − 11i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
9
=
569.400u
88
+ 1275.94u
87
+ ··· − 76010.6u − 6918.01
−6296.66u
88
− 14400.0u
87
+ ··· + 992607.u + 96965.4
a
10
=
−5727.26u
88
− 13124.0u
87
+ ··· + 916597.u + 90047.4
−6296.66u
88
− 14400.0u
87
+ ··· + 992607.u + 96965.4
a
5
=
9085.14u
88
+ 21847.1u
87
+ ··· − 1.67677 × 10
6
u − 168656.
3271.85u
88
+ 7597.71u
87
+ ··· − 544620.u − 53820.5
a
3
=
5108.21u
88
+ 12633.7u
87
+ ··· − 1.02025 × 10
6
u − 103895.
705.083u
88
+ 1615.68u
87
+ ··· − 111892.u − 10941.3
a
8
=
−6026.68u
88
− 13826.0u
87
+ ··· + 965663.u + 94802.3
−9614.20u
88
− 22011.9u
87
+ ··· + 1.51990 × 10
6
u + 148515.
a
7
=
−3942.79u
88
− 9158.68u
87
+ ··· + 643604.u + 62940.5
−12173.0u
88
− 28391.4u
87
+ ··· + 2.03504 × 10
6
u + 200771.
a
11
=
−20489.4u
88
− 47720.8u
87
+ ··· + 3.42997 × 10
6
u + 339274.
−9470.05u
88
− 21709.7u
87
+ ··· + 1.49822 × 10
6
u + 146332.
a
6
=
7371.14u
88
+ 18256.7u
87
+ ··· − 1.50139 × 10
6
u − 154005.
−3644.14u
88
− 8508.11u
87
+ ··· + 609864.u + 60134.4
a
12
=
−21862.8u
88
− 52168.9u
87
+ ··· + 3.95274 × 10
6
u + 396541.
−3836.25u
88
− 8831.88u
87
+ ··· + 618854.u + 60764.8
(ii) Obstruction class = −1
(iii) Cusp Shapes = 66908.2u
88
+ 158354.u
87
+ ··· − 1.16675 × 10
7
u − 1.15911 × 10
6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
89
− 3u
88
+ ··· − 128u + 11
c
2
, c
6
u
89
− u
88
+ ··· − 2324u + 244
c
3
u
89
+ u
88
+ ··· − 35u + 1
c
4
u
89
− u
88
+ ··· − 24352u + 16832
c
5
, c
11
, c
12
u
89
− 40u
87
+ ··· − 525u − 299
c
7
, c
10
u
89
+ 12u
88
+ ··· − 33668u − 16181
c
8
u
89
− u
88
+ ··· − 126958u − 15503
c
9
u
89
− 5u
88
+ ··· − 25u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
89
− 17y
88
+ ··· + 4372y −121
c
2
, c
6
y
89
+ 37y
88
+ ··· + 79336y −59536
c
3
y
89
− 5y
88
+ ··· + 207y −1
c
4
y
89
+ 33y
88
+ ··· − 15159981568y −283316224
c
5
, c
11
, c
12
y
89
− 80y
88
+ ··· − 4317613y −89401
c
7
, c
10
y
89
− 70y
88
+ ··· + 4270382884y −261824761
c
8
y
89
− 29y
88
+ ··· − 1482160124y −240343009
c
9
y
89
+ 5y
88
+ ··· + 231y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.993067 + 0.127078I
a = 0.200540 + 0.455929I
b = −0.33540 − 1.39904I
3.20078 − 1.20884I 0
u = −0.993067 − 0.127078I
a = 0.200540 − 0.455929I
b = −0.33540 + 1.39904I
3.20078 + 1.20884I 0
u = 0.764241 + 0.676726I
a = −0.947281 − 0.895205I
b = 0.340493 − 0.833126I
−0.57886 − 1.51432I 0
u = 0.764241 − 0.676726I
a = −0.947281 + 0.895205I
b = 0.340493 + 0.833126I
−0.57886 + 1.51432I 0
u = −0.760022 + 0.609380I
a = −1.39086 + 0.41043I
b = 0.928173 + 1.010740I
1.56089 + 4.86458I 0
u = −0.760022 − 0.609380I
a = −1.39086 − 0.41043I
b = 0.928173 − 1.010740I
1.56089 − 4.86458I 0
u = 0.689207 + 0.762844I
a = −0.728813 + 0.323818I
b = 1.097610 − 0.099960I
−0.45328 − 4.13288I 0
u = 0.689207 − 0.762844I
a = −0.728813 − 0.323818I
b = 1.097610 + 0.099960I
−0.45328 + 4.13288I 0
u = 1.005520 + 0.290922I
a = 0.818301 − 0.419258I
b = −0.017694 − 0.228854I
−2.29896 − 0.81375I 0
u = 1.005520 − 0.290922I
a = 0.818301 + 0.419258I
b = −0.017694 + 0.228854I
−2.29896 + 0.81375I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.683719 + 0.823293I
a = −0.798187 + 0.260059I
b = 0.779052 − 0.834217I
0.04254 − 3.77924I 0
u = 0.683719 − 0.823293I
a = −0.798187 − 0.260059I
b = 0.779052 + 0.834217I
0.04254 + 3.77924I 0
u = 0.898322 + 0.057751I
a = −1.47888 − 0.45299I
b = −0.394720 − 0.110803I
4.30044 + 0.66708I 0
u = 0.898322 − 0.057751I
a = −1.47888 + 0.45299I
b = −0.394720 + 0.110803I
4.30044 − 0.66708I 0
u = 0.669022 + 0.568571I
a = 1.55704 − 0.05911I
b = −1.49947 + 0.46973I
5.72482 − 2.22060I 0
u = 0.669022 − 0.568571I
a = 1.55704 + 0.05911I
b = −1.49947 − 0.46973I
5.72482 + 2.22060I 0
u = −0.902065 + 0.669900I
a = 1.382100 − 0.221188I
b = −1.14788 − 0.96298I
5.44061 + 8.85234I 0
u = −0.902065 − 0.669900I
a = 1.382100 + 0.221188I
b = −1.14788 + 0.96298I
5.44061 − 8.85234I 0
u = 0.995812 + 0.570446I
a = −0.155902 + 0.043006I
b = 0.301459 + 0.908339I
−1.22561 − 3.72621I 0
u = 0.995812 − 0.570446I
a = −0.155902 − 0.043006I
b = 0.301459 − 0.908339I
−1.22561 + 3.72621I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.705441 + 0.470348I
a = 0.980226 − 0.082282I
b = −0.273554 + 0.437450I
−1.23728 − 0.76406I 0
u = 0.705441 − 0.470348I
a = 0.980226 + 0.082282I
b = −0.273554 − 0.437450I
−1.23728 + 0.76406I 0
u = 0.684498 + 0.448987I
a = −0.19969 + 2.02237I
b = −0.360630 + 0.502464I
−3.27660 − 4.26157I 0
u = 0.684498 − 0.448987I
a = −0.19969 − 2.02237I
b = −0.360630 − 0.502464I
−3.27660 + 4.26157I 0
u = −0.552981 + 1.083490I
a = −1.42961 − 0.56881I
b = 0.560860 + 0.860648I
6.74974 + 6.19688I 0
u = −0.552981 − 1.083490I
a = −1.42961 + 0.56881I
b = 0.560860 − 0.860648I
6.74974 − 6.19688I 0
u = −0.450193 + 0.633301I
a = −0.478689 + 0.401501I
b = 0.734409 + 0.456658I
1.29822 + 1.05454I 0
u = −0.450193 − 0.633301I
a = −0.478689 − 0.401501I
b = 0.734409 − 0.456658I
1.29822 − 1.05454I 0
u = −0.743607 + 0.209729I
a = 0.31095 + 2.56899I
b = 0.236058 + 0.953099I
1.43846 − 5.32495I 0
u = −0.743607 − 0.209729I
a = 0.31095 − 2.56899I
b = 0.236058 − 0.953099I
1.43846 + 5.32495I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.501394 + 0.585172I
a = 2.05602 − 0.82578I
b = −0.736196 − 0.962460I
6.03500 + 1.36427I 0
u = −0.501394 − 0.585172I
a = 2.05602 + 0.82578I
b = −0.736196 + 0.962460I
6.03500 − 1.36427I 0
u = 0.670311 + 0.380079I
a = 0.999831 − 0.186322I
b = −1.63239 − 0.59106I
−3.33787 + 1.07323I 0
u = 0.670311 − 0.380079I
a = 0.999831 + 0.186322I
b = −1.63239 + 0.59106I
−3.33787 − 1.07323I 0
u = −0.767264
a = −1.97006
b = 0.928015
−4.39996 0
u = −0.572087 + 0.457673I
a = −0.839051 + 0.284723I
b = 1.69990 − 1.54093I
2.29718 + 7.94648I 0
u = −0.572087 − 0.457673I
a = −0.839051 − 0.284723I
b = 1.69990 + 1.54093I
2.29718 − 7.94648I 0
u = −0.932679 + 0.881057I
a = −1.105010 + 0.476206I
b = 0.968417 + 0.207288I
9.26732 + 3.26395I 0
u = −0.932679 − 0.881057I
a = −1.105010 − 0.476206I
b = 0.968417 − 0.207288I
9.26732 − 3.26395I 0
u = 0.708618 + 0.099564I
a = −1.371210 + 0.072508I
b = 1.76000 + 0.96153I
1.07016 + 5.85705I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.708618 − 0.099564I
a = −1.371210 − 0.072508I
b = 1.76000 − 0.96153I
1.07016 − 5.85705I 0
u = 0.604944 + 1.134220I
a = 0.701078 − 0.313258I
b = −1.25751 + 1.36163I
8.06380 − 5.92574I 0
u = 0.604944 − 1.134220I
a = 0.701078 + 0.313258I
b = −1.25751 − 1.36163I
8.06380 + 5.92574I 0
u = −0.803682 + 1.013040I
a = 1.159370 + 0.058891I
b = −0.659826 − 0.594923I
3.75873 + 4.16261I 0
u = −0.803682 − 1.013040I
a = 1.159370 − 0.058891I
b = −0.659826 + 0.594923I
3.75873 − 4.16261I 0
u = −0.680676 + 0.139986I
a = −1.03899 − 1.91698I
b = 0.055904 − 0.875204I
−4.56973 − 1.77199I 0
u = −0.680676 − 0.139986I
a = −1.03899 + 1.91698I
b = 0.055904 + 0.875204I
−4.56973 + 1.77199I 0
u = −0.674606 + 0.006235I
a = 0.434040 + 0.302717I
b = 0.358213 − 0.830103I
1.09369 − 1.53017I 0
u = −0.674606 − 0.006235I
a = 0.434040 − 0.302717I
b = 0.358213 + 0.830103I
1.09369 + 1.53017I 0
u = 0.568383 + 0.358844I
a = 1.02786 − 3.41911I
b = 0.469023 − 0.398181I
1.82604 − 7.70258I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.568383 − 0.358844I
a = 1.02786 + 3.41911I
b = 0.469023 + 0.398181I
1.82604 + 7.70258I 0
u = −0.656994 + 0.114545I
a = 0.196690 + 0.824596I
b = −0.02354 + 1.55734I
−3.92764 + 3.06811I 0
u = −0.656994 − 0.114545I
a = 0.196690 − 0.824596I
b = −0.02354 − 1.55734I
−3.92764 − 3.06811I 0
u = −0.959202 + 0.973290I
a = 0.630885 − 0.361979I
b = −1.39767 − 0.66471I
10.28100 + 3.55115I 0
u = −0.959202 − 0.973290I
a = 0.630885 + 0.361979I
b = −1.39767 + 0.66471I
10.28100 − 3.55115I 0
u = 0.354566 + 0.522064I
a = −1.69747 + 0.60020I
b = 1.117580 − 0.802866I
1.79991 − 2.57496I 0
u = 0.354566 − 0.522064I
a = −1.69747 − 0.60020I
b = 1.117580 + 0.802866I
1.79991 + 2.57496I 0
u = −0.579721 + 0.197706I
a = 0.646250 + 0.200700I
b = −0.90475 + 1.75982I
−4.14081 + 3.12659I 0
u = −0.579721 − 0.197706I
a = 0.646250 − 0.200700I
b = −0.90475 − 1.75982I
−4.14081 − 3.12659I 0
u = −0.247717 + 0.536375I
a = 0.69213 − 1.98581I
b = −0.691359 + 0.853223I
6.36140 − 4.27453I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.247717 − 0.536375I
a = 0.69213 + 1.98581I
b = −0.691359 − 0.853223I
6.36140 + 4.27453I 0
u = −0.575286
a = 4.34625
b = −0.0626997
−3.56473 −23.9990
u = −1.17929 + 0.89101I
a = −0.822428 + 0.145424I
b = 1.15916 + 0.99640I
−1.24110 + 5.87258I 0
u = −1.17929 − 0.89101I
a = −0.822428 − 0.145424I
b = 1.15916 − 0.99640I
−1.24110 − 5.87258I 0
u = 0.24869 + 1.46137I
a = −0.453006 − 0.032139I
b = 0.673115 + 0.230690I
1.42043 + 1.69576I 0
u = 0.24869 − 1.46137I
a = −0.453006 + 0.032139I
b = 0.673115 − 0.230690I
1.42043 − 1.69576I 0
u = 1.20458 + 0.89965I
a = −1.003570 − 0.249439I
b = 0.933751 − 0.927723I
−0.82254 − 9.48836I 0
u = 1.20458 − 0.89965I
a = −1.003570 + 0.249439I
b = 0.933751 + 0.927723I
−0.82254 + 9.48836I 0
u = 1.17338 + 0.96189I
a = −0.864496 + 0.237008I
b = 0.61188 − 1.29209I
−2.32543 − 2.20605I 0
u = 1.17338 − 0.96189I
a = −0.864496 − 0.237008I
b = 0.61188 + 1.29209I
−2.32543 + 2.20605I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.19863 + 0.94740I
a = 0.967686 − 0.088945I
b = −1.12242 − 1.12580I
−3.70513 + 12.22050I 0
u = −1.19863 − 0.94740I
a = 0.967686 + 0.088945I
b = −1.12242 + 1.12580I
−3.70513 − 12.22050I 0
u = −1.18143 + 0.97516I
a = −1.098600 + 0.099827I
b = 1.14372 + 1.21653I
1.8734 + 17.6191I 0
u = −1.18143 − 0.97516I
a = −1.098600 − 0.099827I
b = 1.14372 − 1.21653I
1.8734 − 17.6191I 0
u = 1.22128 + 0.94280I
a = 0.898932 + 0.015878I
b = −0.762082 + 1.059560I
−5.54989 − 5.71430I 0
u = 1.22128 − 0.94280I
a = 0.898932 − 0.015878I
b = −0.762082 − 1.059560I
−5.54989 + 5.71430I 0
u = 1.10608 + 1.18820I
a = 0.588583 − 0.496668I
b = −0.111755 + 1.185780I
−1.62538 − 6.04479I 0
u = 1.10608 − 1.18820I
a = 0.588583 + 0.496668I
b = −0.111755 − 1.185780I
−1.62538 + 6.04479I 0
u = −0.265884 + 0.228074I
a = −0.85791 − 3.46146I
b = −0.516657 + 0.923079I
6.37814 − 4.29762I 3.61480 + 3.37878I
u = −0.265884 − 0.228074I
a = −0.85791 + 3.46146I
b = −0.516657 − 0.923079I
6.37814 + 4.29762I 3.61480 − 3.37878I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.90761 + 1.42077I
a = −0.196182 + 0.526398I
b = 0.771036 − 0.622129I
3.07856 − 9.40229I 0
u = −0.90761 − 1.42077I
a = −0.196182 − 0.526398I
b = 0.771036 + 0.622129I
3.07856 + 9.40229I 0
u = −0.77315 + 1.64287I
a = 0.180370 − 0.341990I
b = −0.608103 + 0.326480I
−2.07969 − 3.93898I 0
u = −0.77315 − 1.64287I
a = 0.180370 + 0.341990I
b = −0.608103 − 0.326480I
−2.07969 + 3.93898I 0
u = 1.35398 + 1.26485I
a = −0.324543 + 0.203787I
b = 0.169257 − 0.795886I
−4.44420 − 3.24591I 0
u = 1.35398 − 1.26485I
a = −0.324543 − 0.203787I
b = 0.169257 + 0.795886I
−4.44420 + 3.24591I 0
u = −1.83965 + 1.07623I
a = 0.225655 − 0.085679I
b = −0.128138 − 0.114270I
1.04604 + 3.20264I 0
u = −1.83965 − 1.07623I
a = 0.225655 + 0.085679I
b = −0.128138 + 0.114270I
1.04604 − 3.20264I 0
u = 2.43404
a = −0.0335479
b = −0.439982
2.94626 0
13
II.
I
u
2
= h5.39 × 10
24
u
26
− 2.77 × 10
25
u
25
+ · · · + 3.88 × 10
24
b + 3.66 × 10
25
, 3.40 ×
10
25
u
26
−1.14×10
26
u
25
+· · ·+3.88×10
24
a+4.54×10
25
, u
27
−4u
26
+· · ·+7u−1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
9
=
−8.76207u
26
+ 29.3514u
25
+ ··· + 73.7899u − 11.6877
−1.38862u
26
+ 7.14196u
25
+ ··· + 42.0599u − 9.42336
a
10
=
−10.1507u
26
+ 36.4934u
25
+ ··· + 115.850u − 21.1111
−1.38862u
26
+ 7.14196u
25
+ ··· + 42.0599u − 9.42336
a
5
=
−12.5325u
26
+ 44.9631u
25
+ ··· + 128.300u − 26.6534
−0.114043u
26
− 0.203824u
25
+ ··· − 3.57314u − 0.593413
a
3
=
−15.7987u
26
+ 56.8992u
25
+ ··· + 160.856u − 29.0392
3.38026u
26
− 11.7322u
25
+ ··· − 26.9829u + 2.97912
a
8
=
−7.21332u
26
+ 25.6911u
25
+ ··· + 84.7338u − 15.4142
0.439720u
26
+ 0.799103u
25
+ ··· + 25.8657u − 6.88864
a
7
=
−3.37998u
26
+ 7.21263u
25
+ ··· − 28.8269u + 11.4562
−7.03919u
26
+ 24.7846u
25
+ ··· + 63.5218u − 10.6411
a
11
=
18.6704u
26
− 62.0850u
25
+ ··· − 124.273u + 15.3936
2.94467u
26
− 9.73923u
25
+ ··· − 19.1662u + 2.85454
a
6
=
11.2303u
26
− 41.4445u
25
+ ··· − 125.663u + 22.5582
−5.24731u
26
+ 17.4835u
25
+ ··· + 40.6679u − 5.38480
a
12
=
15.0114u
26
− 53.8860u
25
+ ··· − 132.594u + 24.3751
−6.43257u
26
+ 22.5753u
25
+ ··· + 60.6466u − 9.14643
(ii) Obstruction class = 1
(iii) Cusp Shapes =
148831938566104030557876077
3882376926472859185268325
u
26
−
531726001109607055112961716
3882376926472859185268325
u
25
+
··· −
489596660522591318342393429
1294125642157619728422775
u +
269672116835321490369564187
3882376926472859185268325
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
27
− 4u
26
+ ··· + 7u − 1
c
2
u
27
+ 2u
26
+ ··· + 2u − 1
c
3
u
27
− 3u
25
+ ··· + 3u
2
+ 1
c
4
u
27
+ 4u
25
+ ··· − 80u + 100
c
5
u
27
− u
26
+ ··· + 10u − 3
c
6
u
27
− 2u
26
+ ··· + 2u + 1
c
7
u
27
− 13u
26
+ ··· + 7u − 1
c
8
u
27
− 5u
25
+ ··· + 5u − 75
c
9
u
27
− 2u
26
+ ··· − 9u
2
+ 1
c
10
u
27
+ 13u
26
+ ··· + 7u + 1
c
11
, c
12
u
27
+ u
26
+ ··· + 10u + 3
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
27
− 6y
26
+ ··· + 3y −1
c
2
, c
6
y
27
+ 12y
26
+ ··· + 8y
2
− 1
c
3
y
27
− 6y
26
+ ··· − 6y −1
c
4
y
27
+ 8y
26
+ ··· − 119800y −10000
c
5
, c
11
, c
12
y
27
− 29y
26
+ ··· + 94y −9
c
7
, c
10
y
27
− 19y
26
+ ··· − 17y −1
c
8
y
27
− 10y
26
+ ··· + 55075y −5625
c
9
y
27
+ 4y
26
+ ··· + 18y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.547523 + 0.823439I
a = 1.98498 + 0.46447I
b = −0.568114 − 0.792380I
7.35535 + 5.55662I 7.22798 − 4.72119I
u = −0.547523 − 0.823439I
a = 1.98498 − 0.46447I
b = −0.568114 + 0.792380I
7.35535 − 5.55662I 7.22798 + 4.72119I
u = 0.558730 + 0.743089I
a = −0.446274 − 0.447526I
b = −0.272415 − 0.678077I
−3.25720 − 3.00505I −3.64590 + 3.71727I
u = 0.558730 − 0.743089I
a = −0.446274 + 0.447526I
b = −0.272415 + 0.678077I
−3.25720 + 3.00505I −3.64590 − 3.71727I
u = 0.571603 + 0.997750I
a = 0.813411 − 0.295399I
b = −1.33111 + 1.39928I
8.38765 − 5.67920I 10.77839 + 1.13895I
u = 0.571603 − 0.997750I
a = 0.813411 + 0.295399I
b = −1.33111 − 1.39928I
8.38765 + 5.67920I 10.77839 − 1.13895I
u = −0.808508
a = 1.90792
b = −0.430021
−4.92392 −15.5230
u = −0.739109 + 0.990322I
a = −1.220960 − 0.056243I
b = 0.774219 + 0.662020I
4.11233 + 4.35125I 9.30059 − 8.14463I
u = −0.739109 − 0.990322I
a = −1.220960 + 0.056243I
b = 0.774219 − 0.662020I
4.11233 − 4.35125I 9.30059 + 8.14463I
u = 0.517527 + 0.554493I
a = −1.341990 + 0.149845I
b = 1.19968 − 1.00152I
1.62559 − 3.06994I 0.69172 + 10.64768I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.517527 − 0.554493I
a = −1.341990 − 0.149845I
b = 1.19968 + 1.00152I
1.62559 + 3.06994I 0.69172 − 10.64768I
u = 0.586532 + 0.173716I
a = −0.154346 − 0.794401I
b = −0.12170 − 1.70950I
−3.79869 − 3.23469I 12.4388 + 17.0282I
u = 0.586532 − 0.173716I
a = −0.154346 + 0.794401I
b = −0.12170 + 1.70950I
−3.79869 + 3.23469I 12.4388 − 17.0282I
u = −0.940393 + 1.054800I
a = 0.817965 − 0.341623I
b = −1.276650 − 0.517470I
11.41040 + 3.80295I 8.54645 − 3.49194I
u = −0.940393 − 1.054800I
a = 0.817965 + 0.341623I
b = −1.276650 + 0.517470I
11.41040 − 3.80295I 8.54645 + 3.49194I
u = 0.464096 + 0.264301I
a = 2.69553 + 1.05128I
b = −0.910258 + 0.774732I
5.20589 − 0.81907I 0.134746 + 0.467373I
u = 0.464096 − 0.264301I
a = 2.69553 − 1.05128I
b = −0.910258 − 0.774732I
5.20589 + 0.81907I 0.134746 − 0.467373I
u = −0.516394
a = −4.36772
b = 0.479113
−3.37568 19.3460
u = 0.144226 + 0.422073I
a = 1.37408 + 2.14194I
b = 1.001730 + 0.269638I
2.08837 − 6.81853I 0.95108 + 4.03401I
u = 0.144226 − 0.422073I
a = 1.37408 − 2.14194I
b = 1.001730 − 0.269638I
2.08837 + 6.81853I 0.95108 − 4.03401I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.22756 + 1.02470I
a = −0.611307 + 0.188314I
b = 0.513222 − 1.069780I
−2.80088 − 3.33974I 0. + 5.34734I
u = 1.22756 − 1.02470I
a = −0.611307 − 0.188314I
b = 0.513222 + 1.069780I
−2.80088 + 3.33974I 0. − 5.34734I
u = 1.20709 + 1.15678I
a = 0.601483 − 0.280831I
b = −0.249669 + 0.962999I
−2.41421 − 5.37812I 0
u = 1.20709 − 1.15678I
a = 0.601483 + 0.280831I
b = −0.249669 − 0.962999I
−2.41421 + 5.37812I 0
u = −1.52163 + 1.11118I
a = −0.207154 + 0.061149I
b = 0.413538 − 0.209689I
1.12816 + 3.00008I 0
u = −1.52163 − 1.11118I
a = −0.207154 − 0.061149I
b = 0.413538 + 0.209689I
1.12816 − 3.00008I 0
u = 2.26747
a = −0.151019
b = −0.394031
2.85198 0
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
27
− 4u
26
+ ··· + 7u − 1)(u
89
− 3u
88
+ ··· − 128u + 11)
c
2
(u
27
+ 2u
26
+ ··· + 2u − 1)(u
89
− u
88
+ ··· − 2324u + 244)
c
3
(u
27
− 3u
25
+ ··· + 3u
2
+ 1)(u
89
+ u
88
+ ··· − 35u + 1)
c
4
(u
27
+ 4u
25
+ ··· − 80u + 100)(u
89
− u
88
+ ··· − 24352u + 16832)
c
5
(u
27
− u
26
+ ··· + 10u − 3)(u
89
− 40u
87
+ ··· − 525u − 299)
c
6
(u
27
− 2u
26
+ ··· + 2u + 1)(u
89
− u
88
+ ··· − 2324u + 244)
c
7
(u
27
− 13u
26
+ ··· + 7u − 1)(u
89
+ 12u
88
+ ··· − 33668u − 16181)
c
8
(u
27
− 5u
25
+ ··· + 5u − 75)(u
89
− u
88
+ ··· − 126958u − 15503)
c
9
(u
27
− 2u
26
+ ··· − 9u
2
+ 1)(u
89
− 5u
88
+ ··· − 25u − 1)
c
10
(u
27
+ 13u
26
+ ··· + 7u + 1)(u
89
+ 12u
88
+ ··· − 33668u − 16181)
c
11
, c
12
(u
27
+ u
26
+ ··· + 10u + 3)(u
89
− 40u
87
+ ··· − 525u − 299)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
27
− 6y
26
+ ··· + 3y −1)(y
89
− 17y
88
+ ··· + 4372y −121)
c
2
, c
6
(y
27
+ 12y
26
+ ··· + 8y
2
− 1)(y
89
+ 37y
88
+ ··· + 79336y −59536)
c
3
(y
27
− 6y
26
+ ··· − 6y −1)(y
89
− 5y
88
+ ··· + 207y −1)
c
4
(y
27
+ 8y
26
+ ··· − 119800y −10000)
· (y
89
+ 33y
88
+ ··· − 15159981568y −283316224)
c
5
, c
11
, c
12
(y
27
− 29y
26
+ ··· + 94y −9)(y
89
− 80y
88
+ ··· − 4317613y −89401)
c
7
, c
10
(y
27
− 19y
26
+ ··· − 17y −1)
· (y
89
− 70y
88
+ ··· + 4270382884y −261824761)
c
8
(y
27
− 10y
26
+ ··· + 55075y −5625)
· (y
89
− 29y
88
+ ··· − 1482160124y −240343009)
c
9
(y
27
+ 4y
26
+ ··· + 18y −1)(y
89
+ 5y
88
+ ··· + 231y −1)
21
