12n
0733
(K12n
0733
)
A knot diagram
1
Linearized knot diagam
4 9 10 1 3 4 11 5 6 8 7 5
Solving Sequence
3,10 4,6
7 5 9 2 1 8 11 12
c
3
c
6
c
5
c
9
c
2
c
1
c
8
c
10
c
12
c
4
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h7.85180 × 10
324
u
84
− 5.53960 × 10
324
u
83
+ ··· + 5.09556 × 10
323
b + 5.72110 × 10
326
,
5.13372 × 10
326
u
84
− 3.22757 × 10
326
u
83
+ ··· + 1.17198 × 10
325
a + 3.19118 × 10
328
,
u
85
− u
84
+ ··· + 171u − 23i
I
u
2
= h5u
19
− 6u
18
+ ··· + 2b − 13, 4u
19
− 5u
18
+ ··· + 2a − 3, u
20
+ 3u
18
+ ··· + 5u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 105 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
= h7.85 × 10
324
u
84
− 5.54 × 10
324
u
83
+ · · · + 5.10 × 10
323
b + 5.72 ×
10
326
, 5.13 × 10
326
u
84
− 3.23 × 10
326
u
83
+ · · · + 1.17 × 10
325
a + 3.19 ×
10
328
, u
85
− u
84
+ · · · + 171u − 23i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
6
=
−43.8039u
84
+ 27.5395u
83
+ ··· + 13107.8u − 2722.90
−15.4091u
84
+ 10.8714u
83
+ ··· + 5055.34u − 1122.76
a
7
=
−53.6006u
84
+ 34.8765u
83
+ ··· + 16389.4u − 3471.58
−15.7706u
84
+ 11.3455u
83
+ ··· + 5250.63u − 1179.34
a
5
=
−59.2130u
84
+ 38.4110u
83
+ ··· + 18163.1u − 3845.66
−15.4091u
84
+ 10.8714u
83
+ ··· + 5055.34u − 1122.76
a
9
=
−100.072u
84
+ 57.1100u
83
+ ··· + 27587.5u − 5300.30
−27.6763u
84
+ 16.6280u
83
+ ··· + 7904.83u − 1574.20
a
2
=
−32.2653u
84
+ 25.7906u
83
+ ··· + 11118.1u − 2655.82
17.9359u
84
− 11.0484u
83
+ ··· − 5175.15u + 1047.54
a
1
=
−14.0239u
84
+ 13.3991u
83
+ ··· + 5577.88u − 1459.36
19.8199u
84
− 12.5011u
83
+ ··· − 5755.92u + 1182.08
a
8
=
−63.1948u
84
+ 34.9424u
83
+ ··· + 17087.5u − 3198.98
−17.6497u
84
+ 7.33319u
83
+ ··· + 4042.64u − 585.929
a
11
=
23.0154u
84
− 12.3805u
83
+ ··· − 5914.82u + 1084.83
−55.2963u
84
+ 33.1820u
83
+ ··· + 15690.5u − 3105.92
a
12
=
−59.0148u
84
+ 37.4295u
83
+ ··· + 17255.2u − 3578.54
43.6488u
84
− 27.5891u
83
+ ··· − 12864.2u + 2648.65
(ii) Obstruction class = −1
(iii) Cusp Shapes = 31.3947u
84
− 16.5057u
83
+ ··· − 10580.4u + 2033.20
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
85
+ 5u
84
+ ··· + 97u + 11
c
2
u
85
− u
84
+ ··· + 301u + 71
c
3
u
85
+ u
84
+ ··· + 171u + 23
c
5
u
85
− 3u
84
+ ··· − 22u + 3
c
6
u
85
− 2u
84
+ ··· + 54441u + 8717
c
7
, c
10
, c
11
u
85
+ 3u
84
+ ··· − 31u + 21
c
8
u
85
− 2u
84
+ ··· − 43138551u + 7230569
c
9
u
85
− 5u
84
+ ··· + 9u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
85
+ 31y
84
+ ··· − 4605y −121
c
2
y
85
+ 25y
84
+ ··· − 1039577y −5041
c
3
y
85
− 3y
84
+ ··· + 25423y −529
c
5
y
85
− 5y
84
+ ··· + 454y −9
c
6
y
85
+ 32y
84
+ ··· − 3915581617y −75986089
c
7
, c
10
, c
11
y
85
+ 73y
84
+ ··· + 247y −441
c
8
y
85
− 24y
84
+ ··· + 583651994447037y −52281128063761
c
9
y
85
+ 5y
84
+ ··· + 13y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.831046 + 0.557044I
a = −0.241571 − 0.365025I
b = 0.849319 + 0.261416I
−1.44654 − 0.25256I 0
u = 0.831046 − 0.557044I
a = −0.241571 + 0.365025I
b = 0.849319 − 0.261416I
−1.44654 + 0.25256I 0
u = −0.127487 + 0.957078I
a = 0.638468 − 1.021490I
b = −0.698591 + 1.035080I
6.99156 + 0.55070I 0
u = −0.127487 − 0.957078I
a = 0.638468 + 1.021490I
b = −0.698591 − 1.035080I
6.99156 − 0.55070I 0
u = −0.813260 + 0.513670I
a = 0.488792 + 0.961975I
b = 0.309711 − 0.495129I
1.12817 + 2.01460I 0
u = −0.813260 − 0.513670I
a = 0.488792 − 0.961975I
b = 0.309711 + 0.495129I
1.12817 − 2.01460I 0
u = −0.698511 + 0.631519I
a = −0.566077 − 1.087700I
b = −1.27175 + 0.92234I
5.16779 + 6.57404I 0
u = −0.698511 − 0.631519I
a = −0.566077 + 1.087700I
b = −1.27175 − 0.92234I
5.16779 − 6.57404I 0
u = −0.818146 + 0.459472I
a = 0.31309 + 1.54710I
b = 0.747796 − 0.917953I
0.55790 + 4.56915I 0
u = −0.818146 − 0.459472I
a = 0.31309 − 1.54710I
b = 0.747796 + 0.917953I
0.55790 − 4.56915I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.065336 + 0.910896I
a = 1.115130 + 0.555808I
b = −0.547614 − 0.217318I
−0.64133 − 2.51721I 0
u = 0.065336 − 0.910896I
a = 1.115130 − 0.555808I
b = −0.547614 + 0.217318I
−0.64133 + 2.51721I 0
u = 0.882759 + 0.165692I
a = 0.145743 + 1.002340I
b = 0.85643 − 1.48425I
0.54061 + 5.76543I 0
u = 0.882759 − 0.165692I
a = 0.145743 − 1.002340I
b = 0.85643 + 1.48425I
0.54061 − 5.76543I 0
u = 0.885894
a = 0.163031
b = 0.708021
−1.16186 0
u = 1.034170 + 0.415668I
a = 0.520931 − 1.110500I
b = 1.08674 + 1.06190I
3.59865 − 4.22466I 0
u = 1.034170 − 0.415668I
a = 0.520931 + 1.110500I
b = 1.08674 − 1.06190I
3.59865 + 4.22466I 0
u = −0.742150 + 0.452220I
a = 0.137812 + 0.901496I
b = −0.35871 − 1.48351I
0.464606 + 0.538811I 0
u = −0.742150 − 0.452220I
a = 0.137812 − 0.901496I
b = −0.35871 + 1.48351I
0.464606 − 0.538811I 0
u = 0.533262 + 0.684484I
a = −0.49644 − 1.55374I
b = 0.412791 + 1.193030I
5.66071 − 5.76005I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.533262 − 0.684484I
a = −0.49644 + 1.55374I
b = 0.412791 − 1.193030I
5.66071 + 5.76005I 0
u = −0.857850 + 0.050796I
a = 1.66393 − 1.08609I
b = 0.939994 + 0.127390I
0.12817 − 6.34062I 0
u = −0.857850 − 0.050796I
a = 1.66393 + 1.08609I
b = 0.939994 − 0.127390I
0.12817 + 6.34062I 0
u = −0.655503 + 0.529519I
a = 1.70492 + 0.55646I
b = 0.482345 − 0.572650I
0.80709 + 3.24268I 0
u = −0.655503 − 0.529519I
a = 1.70492 − 0.55646I
b = 0.482345 + 0.572650I
0.80709 − 3.24268I 0
u = −1.162410 + 0.089791I
a = −0.106902 − 0.116132I
b = 0.897619 + 0.731041I
3.40154 − 2.94778I 0
u = −1.162410 − 0.089791I
a = −0.106902 + 0.116132I
b = 0.897619 − 0.731041I
3.40154 + 2.94778I 0
u = 0.439950 + 0.685441I
a = −0.01004 + 1.48686I
b = −0.983699 − 0.818536I
2.22530 − 3.06319I 0
u = 0.439950 − 0.685441I
a = −0.01004 − 1.48686I
b = −0.983699 + 0.818536I
2.22530 + 3.06319I 0
u = 0.567035 + 0.546622I
a = −2.47306 + 0.15550I
b = −0.473503 − 0.438600I
1.97158 − 8.71574I −6.0000 + 13.5098I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.567035 − 0.546622I
a = −2.47306 − 0.15550I
b = −0.473503 + 0.438600I
1.97158 + 8.71574I −6.0000 − 13.5098I
u = 0.913597 + 0.809553I
a = −0.285654 + 0.490373I
b = −0.86921 − 1.39950I
7.94883 − 3.03290I 0
u = 0.913597 − 0.809553I
a = −0.285654 − 0.490373I
b = −0.86921 + 1.39950I
7.94883 + 3.03290I 0
u = 0.629450 + 0.446816I
a = 0.026130 − 0.904408I
b = −0.99443 + 1.41472I
−2.93325 − 4.48039I −9.85243 + 10.13391I
u = 0.629450 − 0.446816I
a = 0.026130 + 0.904408I
b = −0.99443 − 1.41472I
−2.93325 + 4.48039I −9.85243 − 10.13391I
u = 0.692510 + 0.288611I
a = 2.40204 + 0.20862I
b = 0.646277 + 0.227329I
−3.31554 + 1.59248I −13.85520 + 2.64790I
u = 0.692510 − 0.288611I
a = 2.40204 − 0.20862I
b = 0.646277 − 0.227329I
−3.31554 − 1.59248I −13.85520 − 2.64790I
u = −0.565001 + 0.454183I
a = −0.066232 + 0.868689I
b = −1.48274 − 1.36869I
1.49507 + 8.52247I −6.0000 − 12.9551I
u = −0.565001 − 0.454183I
a = −0.066232 − 0.868689I
b = −1.48274 + 1.36869I
1.49507 − 8.52247I −6.0000 + 12.9551I
u = −0.709761 + 0.020702I
a = 0.646694 − 1.140950I
b = −0.334689 + 0.046125I
0.51104 − 2.01003I −2.20570 + 3.99950I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.709761 − 0.020702I
a = 0.646694 + 1.140950I
b = −0.334689 − 0.046125I
0.51104 + 2.01003I −2.20570 − 3.99950I
u = 1.292070 + 0.003692I
a = 0.408255 + 0.744650I
b = 0.251664 + 0.213807I
2.52430 + 1.99992I 0
u = 1.292070 − 0.003692I
a = 0.408255 − 0.744650I
b = 0.251664 − 0.213807I
2.52430 − 1.99992I 0
u = 0.925904 + 0.944482I
a = 0.215413 − 1.215970I
b = 0.270846 + 0.684713I
8.96391 − 3.46153I 0
u = 0.925904 − 0.944482I
a = 0.215413 + 1.215970I
b = 0.270846 − 0.684713I
8.96391 + 3.46153I 0
u = −0.670949 + 0.083829I
a = 0.109150 − 1.101600I
b = 1.19113 + 1.28717I
−4.30679 − 2.27536I −16.5563 + 2.4540I
u = −0.670949 − 0.083829I
a = 0.109150 + 1.101600I
b = 1.19113 − 1.28717I
−4.30679 + 2.27536I −16.5563 − 2.4540I
u = −0.839735 + 1.028720I
a = −0.024893 − 0.614603I
b = −0.920321 + 1.054900I
3.83581 + 3.87716I 0
u = −0.839735 − 1.028720I
a = −0.024893 + 0.614603I
b = −0.920321 − 1.054900I
3.83581 − 3.87716I 0
u = 0.612225 + 1.199640I
a = −0.434189 − 0.108543I
b = 1.008350 − 0.099538I
−1.126070 − 0.317400I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.612225 − 1.199640I
a = −0.434189 + 0.108543I
b = 1.008350 + 0.099538I
−1.126070 + 0.317400I 0
u = −0.863786 + 1.085850I
a = 0.586086 − 0.198313I
b = −0.428910 − 0.311916I
−0.35681 − 2.79976I 0
u = −0.863786 − 1.085850I
a = 0.586086 + 0.198313I
b = −0.428910 + 0.311916I
−0.35681 + 2.79976I 0
u = −0.503079 + 0.267304I
a = −3.34209 + 1.22768I
b = −0.549342 + 0.188748I
−3.54083 + 3.55162I −16.4796 − 10.7233I
u = −0.503079 − 0.267304I
a = −3.34209 − 1.22768I
b = −0.549342 − 0.188748I
−3.54083 − 3.55162I −16.4796 + 10.7233I
u = 1.06471 + 0.98078I
a = 0.010866 + 1.078640I
b = −1.018890 − 0.794064I
−1.50860 − 6.81305I 0
u = 1.06471 − 0.98078I
a = 0.010866 − 1.078640I
b = −1.018890 + 0.794064I
−1.50860 + 6.81305I 0
u = −1.09605 + 0.97519I
a = −0.070271 + 0.951473I
b = 1.15125 − 1.11120I
−0.95392 + 10.39970I 0
u = −1.09605 − 0.97519I
a = −0.070271 − 0.951473I
b = 1.15125 + 1.11120I
−0.95392 − 10.39970I 0
u = −1.23789 + 0.80342I
a = 0.066354 + 0.929504I
b = 1.041570 − 0.765298I
−1.47341 + 1.29795I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.23789 − 0.80342I
a = 0.066354 − 0.929504I
b = 1.041570 + 0.765298I
−1.47341 − 1.29795I 0
u = 1.16995 + 0.90072I
a = −0.006807 − 0.942814I
b = 1.12371 + 0.95306I
−5.16019 − 5.88389I 0
u = 1.16995 − 0.90072I
a = −0.006807 + 0.942814I
b = 1.12371 − 0.95306I
−5.16019 + 5.88389I 0
u = 0.70125 + 1.31396I
a = 0.209393 + 0.604652I
b = −1.06478 − 1.01972I
7.55142 − 5.35757I 0
u = 0.70125 − 1.31396I
a = 0.209393 − 0.604652I
b = −1.06478 + 1.01972I
7.55142 + 5.35757I 0
u = −1.18191 + 0.99684I
a = −0.037548 − 1.016460I
b = −1.12549 + 0.95882I
−3.93658 + 12.48330I 0
u = −1.18191 − 0.99684I
a = −0.037548 + 1.016460I
b = −1.12549 − 0.95882I
−3.93658 − 12.48330I 0
u = −0.80028 + 1.33460I
a = 0.188249 − 0.910710I
b = −0.583389 + 0.702703I
8.95846 + 5.01025I 0
u = −0.80028 − 1.33460I
a = 0.188249 + 0.910710I
b = −0.583389 − 0.702703I
8.95846 − 5.01025I 0
u = 0.298583 + 0.277764I
a = −1.20840 − 1.79229I
b = −1.026940 − 0.385412I
6.40230 − 2.27863I −0.89056 + 3.31839I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.298583 − 0.277764I
a = −1.20840 + 1.79229I
b = −1.026940 + 0.385412I
6.40230 + 2.27863I −0.89056 − 3.31839I
u = 0.398620 + 0.060755I
a = 0.13074 + 1.54798I
b = 1.74001 − 1.00437I
−1.25022 − 1.15331I −15.9982 + 3.4831I
u = 0.398620 − 0.060755I
a = 0.13074 − 1.54798I
b = 1.74001 + 1.00437I
−1.25022 + 1.15331I −15.9982 − 3.4831I
u = 0.398550 + 0.050882I
a = −2.05034 + 3.97773I
b = −0.672123 − 0.119936I
−1.36735 − 2.11678I −15.1062 + 0.7883I
u = 0.398550 − 0.050882I
a = −2.05034 − 3.97773I
b = −0.672123 + 0.119936I
−1.36735 + 2.11678I −15.1062 − 0.7883I
u = 1.23465 + 1.03140I
a = −0.040428 + 0.975733I
b = −1.14414 − 1.10028I
1.3879 − 17.4955I 0
u = 1.23465 − 1.03140I
a = −0.040428 − 0.975733I
b = −1.14414 + 1.10028I
1.3879 + 17.4955I 0
u = −1.16076 + 1.57900I
a = −0.296277 − 0.026335I
b = 0.553572 + 0.338879I
−2.86751 − 3.88898I 0
u = −1.16076 − 1.57900I
a = −0.296277 + 0.026335I
b = 0.553572 − 0.338879I
−2.86751 + 3.88898I 0
u = 1.16470 + 1.57762I
a = 0.304904 + 0.157476I
b = −0.541884 + 0.107530I
−3.58768 − 2.35741I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.16470 − 1.57762I
a = 0.304904 − 0.157476I
b = −0.541884 − 0.107530I
−3.58768 + 2.35741I 0
u = −1.33827 + 1.50559I
a = 0.216380 − 0.253403I
b = −0.719339 + 0.135725I
0.67050 + 7.44603I 0
u = −1.33827 − 1.50559I
a = 0.216380 + 0.253403I
b = −0.719339 − 0.135725I
0.67050 − 7.44603I 0
u = 1.04952 + 1.76023I
a = −0.334642 + 0.135942I
b = 0.395360 − 0.575779I
2.69608 + 8.47155I 0
u = 1.04952 − 1.76023I
a = −0.334642 − 0.135942I
b = 0.395360 + 0.575779I
2.69608 − 8.47155I 0
13
II. I
u
2
=
h5u
19
−6u
18
+· · ·+2b−13, 4u
19
−5u
18
+· · ·+2a−3, u
20
+3u
18
+· · ·+5u
2
+1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
6
=
−2u
19
+
5
2
u
18
+ ··· −
7
2
u +
3
2
−
5
2
u
19
+ 3u
18
+ ··· − 4u +
13
2
a
7
=
−5u
19
+
15
2
u
18
+ ··· −
19
2
u +
21
2
−
3
2
u
19
− 3u
17
+ ··· − u +
3
2
a
5
=
−
9
2
u
19
+
11
2
u
18
+ ··· −
15
2
u + 8
−
5
2
u
19
+ 3u
18
+ ··· − 4u +
13
2
a
9
=
3
2
u
19
+ 2u
18
+ ··· − 2u +
7
2
u
19
+ 3u
17
+ ··· − u
2
+ 5u
a
2
=
7
2
u
19
−
3
2
u
18
+ ··· +
7
2
u + 3
−u
18
− 3u
16
+ ··· + u − 5
a
1
=
11
2
u
19
− 5u
18
+ ··· + 8u −
7
2
−
1
2
u
19
+ u
18
+ ··· − u −
3
2
a
8
=
11
2
u
19
+
3
2
u
18
+ ··· +
11
2
u
2
+
13
2
u
21
2
u
19
+
3
2
u
18
+ ··· +
45
2
u + 1
a
11
=
−
7
2
u
19
−
13
2
u
18
+ ··· −
11
2
u − 9
3u
19
−
13
2
u
18
+ ··· +
5
2
u −
29
2
a
12
=
19
2
u
19
−
21
2
u
18
+ ··· +
27
2
u − 13
7
2
u
19
−
9
2
u
18
+ ··· +
9
2
u − 12
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −36u
19
−
3
2
u
18
−
181
2
u
17
+
55
2
u
16
−
555
2
u
15
+
143
2
u
14
−
641
2
u
13
+
261
2
u
12
− 356u
11
+
244u
10
− 252u
9
+
515
2
u
8
−
217
2
u
7
+ 195u
6
−
377
2
u
5
+
109
2
u
4
−
407
2
u
3
−
51
2
u
2
−
133
2
u −
29
2
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
u
20
− 6u
19
+ ··· − 4u + 1
c
2
u
20
+ 5u
18
+ ··· + 3u
2
+ 1
c
3
u
20
+ 3u
18
+ ··· + 5u
2
+ 1
c
4
u
20
+ 6u
19
+ ··· + 4u + 1
c
5
u
20
+ 2u
19
+ ··· + 5u + 1
c
6
u
20
− 3u
19
+ ··· − 22u + 7
c
7
u
20
− 4u
19
+ ··· − 4u + 1
c
8
u
20
− 3u
19
+ ··· − 8u + 7
c
9
u
20
+ 2u
19
+ ··· + u
3
+ 1
c
10
, c
11
u
20
+ 4u
19
+ ··· + 4u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
20
+ 12y
19
+ ··· + 14y + 1
c
2
y
20
+ 10y
19
+ ··· + 6y + 1
c
3
y
20
+ 6y
19
+ ··· + 10y + 1
c
5
y
20
+ 22y
18
+ ··· + 3y + 1
c
6
y
20
+ 5y
19
+ ··· + 118y + 49
c
7
, c
10
, c
11
y
20
+ 22y
19
+ ··· + 30y + 1
c
8
y
20
+ 9y
19
+ ··· + 188y + 49
c
9
y
20
− 2y
19
+ ··· + 2y
2
+ 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.812253 + 0.473538I
a = 0.40490 + 1.57874I
b = 0.822438 − 0.775505I
0.74373 + 4.05917I −2.82511 − 0.92977I
u = −0.812253 − 0.473538I
a = 0.40490 − 1.57874I
b = 0.822438 + 0.775505I
0.74373 − 4.05917I −2.82511 + 0.92977I
u = 0.906722 + 0.243640I
a = 0.641070 − 1.213010I
b = 1.04129 + 1.08334I
3.46371 − 5.35086I −2.37266 + 7.93016I
u = 0.906722 − 0.243640I
a = 0.641070 + 1.213010I
b = 1.04129 − 1.08334I
3.46371 + 5.35086I −2.37266 − 7.93016I
u = 0.192281 + 0.880278I
a = −0.396919 + 0.625878I
b = −0.498840 + 0.507368I
1.91537 − 7.45410I −2.80666 + 5.14772I
u = 0.192281 − 0.880278I
a = −0.396919 − 0.625878I
b = −0.498840 − 0.507368I
1.91537 + 7.45410I −2.80666 − 5.14772I
u = −0.734190 + 0.823682I
a = −0.029249 − 0.671164I
b = −1.27215 + 1.29437I
7.51988 + 3.71646I −0.19673 − 7.05119I
u = −0.734190 − 0.823682I
a = −0.029249 + 0.671164I
b = −1.27215 − 1.29437I
7.51988 − 3.71646I −0.19673 + 7.05119I
u = −0.061191 + 0.846410I
a = −0.594260 − 0.639400I
b = 0.124196 − 0.469734I
−2.90766 + 2.92514I −7.54786 − 3.63695I
u = −0.061191 − 0.846410I
a = −0.594260 + 0.639400I
b = 0.124196 + 0.469734I
−2.90766 − 2.92514I −7.54786 + 3.63695I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.183312 + 0.749144I
a = −1.08852 + 1.23211I
b = 0.551678 − 0.088695I
−0.74515 + 2.10260I −3.47918 + 3.64090I
u = −0.183312 − 0.749144I
a = −1.08852 − 1.23211I
b = 0.551678 + 0.088695I
−0.74515 − 2.10260I −3.47918 − 3.64090I
u = 0.784188 + 0.983742I
a = −0.091190 − 1.352150I
b = 0.410802 + 0.663107I
8.70280 − 3.92804I −1.94399 + 7.70721I
u = 0.784188 − 0.983742I
a = −0.091190 + 1.352150I
b = 0.410802 − 0.663107I
8.70280 + 3.92804I −1.94399 − 7.70721I
u = 0.772112 + 1.011950I
a = −0.058185 + 0.742783I
b = −0.884281 − 1.057570I
4.21490 − 3.96613I 6.63586 + 5.76785I
u = 0.772112 − 1.011950I
a = −0.058185 − 0.742783I
b = −0.884281 + 1.057570I
4.21490 + 3.96613I 6.63586 − 5.76785I
u = 0.024765 + 0.703217I
a = −0.730633 + 0.187577I
b = 1.256050 + 0.516928I
−0.662120 + 1.113620I −1.35328 − 4.61065I
u = 0.024765 − 0.703217I
a = −0.730633 − 0.187577I
b = 1.256050 − 0.516928I
−0.662120 − 1.113620I −1.35328 + 4.61065I
u = −0.88912 + 1.26358I
a = −0.057015 − 0.819735I
b = −0.551188 + 1.009010I
10.65320 + 4.50722I 4.88959 − 4.33286I
u = −0.88912 − 1.26358I
a = −0.057015 + 0.819735I
b = −0.551188 − 1.009010I
10.65320 − 4.50722I 4.88959 + 4.33286I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
12
(u
20
− 6u
19
+ ··· − 4u + 1)(u
85
+ 5u
84
+ ··· + 97u + 11)
c
2
(u
20
+ 5u
18
+ ··· + 3u
2
+ 1)(u
85
− u
84
+ ··· + 301u + 71)
c
3
(u
20
+ 3u
18
+ ··· + 5u
2
+ 1)(u
85
+ u
84
+ ··· + 171u + 23)
c
4
(u
20
+ 6u
19
+ ··· + 4u + 1)(u
85
+ 5u
84
+ ··· + 97u + 11)
c
5
(u
20
+ 2u
19
+ ··· + 5u + 1)(u
85
− 3u
84
+ ··· − 22u + 3)
c
6
(u
20
− 3u
19
+ ··· − 22u + 7)(u
85
− 2u
84
+ ··· + 54441u + 8717)
c
7
(u
20
− 4u
19
+ ··· − 4u + 1)(u
85
+ 3u
84
+ ··· − 31u + 21)
c
8
(u
20
− 3u
19
+ ··· − 8u + 7)(u
85
− 2u
84
+ ··· − 4.31386 × 10
7
u + 7230569)
c
9
(u
20
+ 2u
19
+ ··· + u
3
+ 1)(u
85
− 5u
84
+ ··· + 9u + 1)
c
10
, c
11
(u
20
+ 4u
19
+ ··· + 4u + 1)(u
85
+ 3u
84
+ ··· − 31u + 21)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
(y
20
+ 12y
19
+ ··· + 14y + 1)(y
85
+ 31y
84
+ ··· − 4605y −121)
c
2
(y
20
+ 10y
19
+ ··· + 6y + 1)(y
85
+ 25y
84
+ ··· − 1039577y −5041)
c
3
(y
20
+ 6y
19
+ ··· + 10y + 1)(y
85
− 3y
84
+ ··· + 25423y −529)
c
5
(y
20
+ 22y
18
+ ··· + 3y + 1)(y
85
− 5y
84
+ ··· + 454y −9)
c
6
(y
20
+ 5y
19
+ ··· + 118y + 49)
· (y
85
+ 32y
84
+ ··· − 3915581617y −75986089)
c
7
, c
10
, c
11
(y
20
+ 22y
19
+ ··· + 30y + 1)(y
85
+ 73y
84
+ ··· + 247y −441)
c
8
(y
20
+ 9y
19
+ ··· + 188y + 49)
· (y
85
− 24y
84
+ ··· + 583651994447037y −52281128063761)
c
9
(y
20
− 2y
19
+ ··· + 2y
2
+ 1)(y
85
+ 5y
84
+ ··· + 13y −1)
20
