12a
1222
(K12a
1222
)
A knot diagram
1
Linearized knot diagam
5 6 7 1 10 11 4 12 2 3 8 9
Solving Sequence
3,7
4
8,11
12 6 2 10 5 1 9
c
3
c
7
c
11
c
6
c
2
c
10
c
5
c
1
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h8.54050 × 10
28
u
33
− 1.19908 × 10
29
u
32
+ ··· + 2.02956 × 10
29
b − 1.46806 × 10
29
,
2.00324 × 10
28
u
33
− 1.85192 × 10
28
u
32
+ ··· + 1.19386 × 10
28
a − 1.66365 × 10
29
, u
34
− u
33
+ ··· − 14u + 1i
I
u
2
= h−1.00686 × 10
316
u
83
− 2.20932 × 10
316
u
82
+ ··· + 1.65013 × 10
317
b − 2.02613 × 10
318
,
3.54486 × 10
318
u
83
+ 6.01988 × 10
318
u
82
+ ··· + 3.48177 × 10
319
a − 5.74769 × 10
319
,
u
84
+ 3u
83
+ ··· + 1498u + 211i
I
u
3
= hu
11
+ u
10
− 5u
9
− u
8
+ 12u
7
− 3u
6
− 20u
5
+ 9u
4
+ 17u
3
− 12u
2
+ b − 8u + 5,
6u
11
− 3u
10
− 20u
9
+ 15u
8
+ 38u
7
− 43u
6
− 46u
5
+ 59u
4
+ 28u
3
− 49u
2
+ a − 11u + 14,
u
12
− u
11
− 3u
10
+ 4u
9
+ 5u
8
− 10u
7
− 4u
6
+ 13u
5
− 10u
3
+ 2u
2
+ 3u − 1i
I
u
4
= hb − 1, a − 1, u
2
+ u − 1i
I
u
5
= hb − u, a − u − 1, u
2
+ u − 1i
* 5 irreducible components of dim
C
= 0, with total 134 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
= h8.54 × 10
28
u
33
− 1.20 × 10
29
u
32
+ · · · + 2.03 × 10
29
b − 1.47 × 10
29
, 2.00 ×
10
28
u
33
−1.85×10
28
u
32
+· · ·+1.19×10
28
a−1.66×10
29
, u
34
−u
33
+· · ·−14u+1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
8
=
−u
−u
3
+ u
a
11
=
−1.67795u
33
+ 1.55120u
32
+ ··· − 54.4816u + 13.9351
−0.420805u
33
+ 0.590807u
32
+ ··· + 0.214756u + 0.723340
a
12
=
−1.82607u
33
+ 1.79373u
32
+ ··· − 55.2072u + 14.1232
−0.374427u
33
+ 0.626344u
32
+ ··· + 2.41017u + 0.440872
a
6
=
0.0849368u
33
− 0.674220u
32
+ ··· − 22.0169u − 4.53343
0.0652050u
33
− 0.290176u
32
+ ··· − 4.20788u + 0.0290844
a
2
=
1.23819u
33
− 1.28700u
32
+ ··· + 25.7222u + 0.477757
0.429517u
33
− 0.646675u
32
+ ··· − 0.921613u + 0.0488161
a
10
=
−2.09876u
33
+ 2.14201u
32
+ ··· − 54.2669u + 14.6584
−0.420805u
33
+ 0.590807u
32
+ ··· + 0.214756u + 0.723340
a
5
=
1.11813u
33
− 2.58902u
32
+ ··· − 39.5230u + 1.70908
1.06931u
33
− 2.11069u
32
+ ··· − 21.7107u + 1.47090
a
1
=
2.70908u
33
− 3.82721u
32
+ ··· + 8.35933u + 1.59588
1.47090u
33
− 2.54021u
32
+ ··· − 17.3628u + 1.11813
a
9
=
−0.370824u
33
+ 1.27805u
32
+ ··· + 28.8631u + 4.34212
−0.628147u
33
+ 1.22765u
32
+ ··· + 14.1089u − 0.498700
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.52397u
33
− 1.46607u
32
+ ··· + 104.427u − 1.38626
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
7
u
34
− u
33
+ ··· − 14u + 1
c
2
u
34
− 15u
33
+ ··· − 42u + 4
c
5
, c
10
u
34
− u
33
+ ··· + 2u − 1
c
6
, c
9
u
34
− u
33
+ ··· + 8u + 1
c
8
, c
11
, c
12
u
34
− 12u
33
+ ··· + 48u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
y
34
− 29y
33
+ ··· − 146y + 1
c
2
y
34
− 7y
33
+ ··· − 1628y + 16
c
5
, c
10
y
34
− 23y
33
+ ··· − 42y + 1
c
6
, c
9
y
34
− 5y
33
+ ··· − 48y + 1
c
8
, c
11
, c
12
y
34
− 36y
33
+ ··· + 480y + 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.911688 + 0.363959I
a = −0.171944 + 0.102128I
b = 1.10685 − 1.31639I
2.69872 − 3.21839I 4.59732 + 8.11808I
u = 0.911688 − 0.363959I
a = −0.171944 − 0.102128I
b = 1.10685 + 1.31639I
2.69872 + 3.21839I 4.59732 − 8.11808I
u = −0.927431 + 0.304938I
a = 0.474616 − 0.316310I
b = −0.220232 + 0.174637I
−1.71183 + 0.63600I −2.75071 − 0.30580I
u = −0.927431 − 0.304938I
a = 0.474616 + 0.316310I
b = −0.220232 − 0.174637I
−1.71183 − 0.63600I −2.75071 + 0.30580I
u = 1.038620 + 0.229840I
a = 1.201340 + 0.604971I
b = 1.061670 + 0.056991I
−1.18415 − 2.37587I −5.06552 + 2.01648I
u = 1.038620 − 0.229840I
a = 1.201340 − 0.604971I
b = 1.061670 − 0.056991I
−1.18415 + 2.37587I −5.06552 − 2.01648I
u = −0.912481
a = −1.14310
b = −2.27341
5.13008 −6.34130
u = −0.697714 + 0.835446I
a = −0.870469 + 0.103720I
b = 0.407551 − 0.163879I
3.45848 + 2.06792I 4.43870 − 5.42623I
u = −0.697714 − 0.835446I
a = −0.870469 − 0.103720I
b = 0.407551 + 0.163879I
3.45848 − 2.06792I 4.43870 + 5.42623I
u = 0.010441 + 1.142570I
a = 0.459850 − 0.901524I
b = −0.963785 + 0.761398I
8.90412 + 5.78014I 5.97608 − 5.27414I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.010441 − 1.142570I
a = 0.459850 + 0.901524I
b = −0.963785 − 0.761398I
8.90412 − 5.78014I 5.97608 + 5.27414I
u = −0.811070 + 0.238646I
a = −0.342154 + 1.115500I
b = −0.619559 − 1.163380I
0.28385 + 1.96283I −6.27590 − 2.16134I
u = −0.811070 − 0.238646I
a = −0.342154 − 1.115500I
b = −0.619559 + 1.163380I
0.28385 − 1.96283I −6.27590 + 2.16134I
u = 0.075427 + 0.817878I
a = −0.858351 + 0.792060I
b = 0.847229 − 0.699141I
1.79815 + 4.38530I 3.95396 − 7.22221I
u = 0.075427 − 0.817878I
a = −0.858351 − 0.792060I
b = 0.847229 + 0.699141I
1.79815 − 4.38530I 3.95396 + 7.22221I
u = −1.155780 + 0.243350I
a = 0.698563 + 0.891085I
b = 1.59207 − 0.90588I
−5.44196 + 7.07361I −4.67726 − 6.51707I
u = −1.155780 − 0.243350I
a = 0.698563 − 0.891085I
b = 1.59207 + 0.90588I
−5.44196 − 7.07361I −4.67726 + 6.51707I
u = 1.303250 + 0.103917I
a = −0.497132 + 0.728849I
b = −1.039970 − 0.136864I
−7.94265 − 0.99791I −7.60667 + 0.14420I
u = 1.303250 − 0.103917I
a = −0.497132 − 0.728849I
b = −1.039970 + 0.136864I
−7.94265 + 0.99791I −7.60667 − 0.14420I
u = −1.33934 + 0.45447I
a = −0.547419 − 0.976370I
b = −1.41479 + 0.88408I
−6.3199 + 13.8634I −3.76798 − 9.05726I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.33934 − 0.45447I
a = −0.547419 + 0.976370I
b = −1.41479 − 0.88408I
−6.3199 − 13.8634I −3.76798 + 9.05726I
u = 1.37512 + 0.39242I
a = 0.190547 − 0.874693I
b = 0.915991 + 0.188064I
−8.36073 − 6.05317I −7.48732 + 5.96067I
u = 1.37512 − 0.39242I
a = 0.190547 + 0.874693I
b = 0.915991 − 0.188064I
−8.36073 + 6.05317I −7.48732 − 5.96067I
u = 0.126385 + 0.485333I
a = 1.268100 − 0.215994I
b = −0.579090 + 0.694270I
0.02966 + 1.58034I 0.69900 − 2.53490I
u = 0.126385 − 0.485333I
a = 1.268100 + 0.215994I
b = −0.579090 − 0.694270I
0.02966 − 1.58034I 0.69900 + 2.53490I
u = −1.51144
a = −0.475265
b = 0.265815
1.70861 12.4980
u = 1.36903 + 0.65356I
a = 0.004644 + 0.922982I
b = −0.833672 − 0.184412I
−1.91527 − 10.05270I 0. + 6.54721I
u = 1.36903 − 0.65356I
a = 0.004644 − 0.922982I
b = −0.833672 + 0.184412I
−1.91527 + 10.05270I 0. − 6.54721I
u = 1.54476
a = −0.725617
b = −1.27210
−8.61022 −10.8990
u = −1.43017 + 0.65600I
a = 0.456870 + 0.988687I
b = 1.35012 − 0.87487I
0.1342 + 18.8943I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.43017 − 0.65600I
a = 0.456870 − 0.988687I
b = 1.35012 + 0.87487I
0.1342 − 18.8943I 0
u = 0.270000
a = −5.98277
b = −0.799253
10.5619 31.5940
u = 1.82431
a = 0.862150
b = 1.29581
−5.34464 0
u = 0.0879429
a = 8.53047
b = 0.562384
1.37388 8.39650
8
II. I
u
2
= h−1.01 × 10
316
u
83
− 2.21 × 10
316
u
82
+ · · · + 1.65 × 10
317
b − 2.03 ×
10
318
, 3.54 × 10
318
u
83
+ 6.02 × 10
318
u
82
+ · · · + 3.48 × 10
319
a − 5.75 ×
10
319
, u
84
+ 3u
83
+ · · · + 1498u + 211i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
8
=
−u
−u
3
+ u
a
11
=
−0.101812u
83
− 0.172897u
82
+ ··· − 58.5822u + 1.65079
0.0610170u
83
+ 0.133888u
82
+ ··· + 66.2351u + 12.2786
a
12
=
−0.0229371u
83
− 0.00119685u
82
+ ··· + 45.7496u + 20.0368
0.0387176u
83
+ 0.0855631u
82
+ ··· + 42.5175u + 7.59174
a
6
=
−1.06633u
83
− 2.23318u
82
+ ··· − 1358.51u − 231.319
−0.186757u
83
− 0.369562u
82
+ ··· − 202.390u − 32.6268
a
2
=
−1.08627u
83
− 2.33161u
82
+ ··· − 1675.76u − 278.019
−0.694699u
83
− 1.42478u
82
+ ··· − 999.724u − 167.008
a
10
=
−0.0407949u
83
− 0.0390090u
82
+ ··· + 7.65289u + 13.9294
0.0610170u
83
+ 0.133888u
82
+ ··· + 66.2351u + 12.2786
a
5
=
−0.907194u
83
− 1.88671u
82
+ ··· − 1221.77u − 219.358
−0.115687u
83
− 0.206886u
82
+ ··· − 176.440u − 33.4054
a
1
=
0.153580u
83
+ 0.345053u
82
+ ··· + 226.286u + 53.6228
−0.0896750u
83
− 0.193681u
82
+ ··· − 140.887u − 22.8274
a
9
=
0.285021u
83
+ 0.581129u
82
+ ··· + 272.195u + 48.3765
−0.0732276u
83
− 0.172596u
82
+ ··· − 66.0729u − 15.3657
(ii) Obstruction class = −1
(iii) Cusp Shapes = 5.90715u
83
+ 11.8390u
82
+ ··· + 8273.11u + 1370.31
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
7
u
84
+ 3u
83
+ ··· + 1498u + 211
c
2
(u
42
+ 10u
41
+ ··· − 21u
2
+ 4)
2
c
5
, c
10
u
84
− 2u
83
+ ··· − 1077u − 171
c
6
, c
9
u
84
− 2u
83
+ ··· + 19u + 1
c
8
, c
11
, c
12
(u
42
+ 4u
41
+ ··· + 6u + 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
y
84
− 47y
83
+ ··· − 2568522y + 44521
c
2
(y
42
− 6y
41
+ ··· − 168y + 16)
2
c
5
, c
10
y
84
− 18y
83
+ ··· − 1451997y + 29241
c
6
, c
9
y
84
− 2y
83
+ ··· − 153y + 1
c
8
, c
11
, c
12
(y
42
− 40y
41
+ ··· + 10y + 1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.261682 + 0.947043I
a = 0.496591 + 0.945052I
b = −0.982172 − 0.898519I
−1.57098 − 8.97815I 0
u = 0.261682 − 0.947043I
a = 0.496591 − 0.945052I
b = −0.982172 + 0.898519I
−1.57098 + 8.97815I 0
u = −0.963946 + 0.051725I
a = 1.90320 − 2.85570I
b = 1.044480 + 0.188443I
1.70116 + 0.22078I 0
u = −0.963946 − 0.051725I
a = 1.90320 + 2.85570I
b = 1.044480 − 0.188443I
1.70116 − 0.22078I 0
u = 0.089013 + 1.048540I
a = −0.475100 + 1.029690I
b = 0.471537 − 0.871365I
7.08036 + 5.12233I 0
u = 0.089013 − 1.048540I
a = −0.475100 − 1.029690I
b = 0.471537 + 0.871365I
7.08036 − 5.12233I 0
u = −0.844891 + 0.364928I
a = 0.436922 + 0.177443I
b = 0.19300 − 1.49154I
−2.19538 + 5.56633I 0
u = −0.844891 − 0.364928I
a = 0.436922 − 0.177443I
b = 0.19300 + 1.49154I
−2.19538 − 5.56633I 0
u = −1.08532
a = −2.29473
b = 0.843743
1.48229 0
u = 1.074060 + 0.188077I
a = −0.92340 − 1.46590I
b = −0.773246 − 0.035442I
−1.63855 − 9.41269I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.074060 − 0.188077I
a = −0.92340 + 1.46590I
b = −0.773246 + 0.035442I
−1.63855 + 9.41269I 0
u = −1.072080 + 0.206881I
a = −0.08182 − 1.67349I
b = −0.780522 + 0.178469I
−2.86626 + 0.79727I 0
u = −1.072080 − 0.206881I
a = −0.08182 + 1.67349I
b = −0.780522 − 0.178469I
−2.86626 − 0.79727I 0
u = 0.231743 + 0.864034I
a = −0.18036 + 1.40382I
b = −0.703444 − 0.783632I
9.57206 0
u = 0.231743 − 0.864034I
a = −0.18036 − 1.40382I
b = −0.703444 + 0.783632I
9.57206 0
u = −0.867762 + 0.124423I
a = −2.09750 + 1.35331I
b = −0.413691 − 0.104225I
0.507064 + 0.220193I 0
u = −0.867762 − 0.124423I
a = −2.09750 − 1.35331I
b = −0.413691 + 0.104225I
0.507064 − 0.220193I 0
u = −1.134230 + 0.225687I
a = 0.783102 + 1.167270I
b = 0.591631 − 0.669511I
−1.21239 + 1.65323I 0
u = −1.134230 − 0.225687I
a = 0.783102 − 1.167270I
b = 0.591631 + 0.669511I
−1.21239 − 1.65323I 0
u = 0.806169 + 0.198254I
a = 0.752898 − 0.789249I
b = 1.28888 + 0.72301I
0.987868 − 0.521667I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.806169 − 0.198254I
a = 0.752898 + 0.789249I
b = 1.28888 − 0.72301I
0.987868 + 0.521667I 0
u = 0.770426 + 0.275262I
a = −0.353303 + 0.266737I
b = 0.317608 − 1.175300I
0.91619 − 2.04302I 0
u = 0.770426 − 0.275262I
a = −0.353303 − 0.266737I
b = 0.317608 + 1.175300I
0.91619 + 2.04302I 0
u = 1.127580 + 0.401456I
a = −0.499514 + 0.956746I
b = −1.30281 − 0.92417I
−2.69923 − 5.20353I 0
u = 1.127580 − 0.401456I
a = −0.499514 − 0.956746I
b = −1.30281 + 0.92417I
−2.69923 + 5.20353I 0
u = −0.486546 + 0.627534I
a = −0.389167 − 0.809092I
b = −0.87588 + 1.27934I
−1.21239 − 1.65323I 0
u = −0.486546 − 0.627534I
a = −0.389167 + 0.809092I
b = −0.87588 − 1.27934I
−1.21239 + 1.65323I 0
u = 1.152910 + 0.365386I
a = −0.483421 + 0.947859I
b = −1.00729 − 1.11116I
−2.19538 − 5.56633I 0
u = 1.152910 − 0.365386I
a = −0.483421 − 0.947859I
b = −1.00729 + 1.11116I
−2.19538 + 5.56633I 0
u = −1.021970 + 0.681032I
a = −0.276396 − 0.464069I
b = 0.28049 + 1.52247I
3.24920 + 10.79950I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.021970 − 0.681032I
a = −0.276396 + 0.464069I
b = 0.28049 − 1.52247I
3.24920 − 10.79950I 0
u = 1.098220 + 0.560900I
a = 0.305597 − 0.466890I
b = −0.434696 + 1.129890I
7.08036 − 5.12233I 0
u = 1.098220 − 0.560900I
a = 0.305597 + 0.466890I
b = −0.434696 − 1.129890I
7.08036 + 5.12233I 0
u = 0.752107 + 0.049257I
a = −0.90125 − 1.83181I
b = −1.070700 + 0.724698I
−0.27560 + 8.13259I 0. − 6.18539I
u = 0.752107 − 0.049257I
a = −0.90125 + 1.83181I
b = −1.070700 − 0.724698I
−0.27560 − 8.13259I 0. + 6.18539I
u = −0.677497 + 1.046410I
a = 0.499516 + 0.752124I
b = 1.02566 − 1.07141I
4.48711 − 4.62327I 0
u = −0.677497 − 1.046410I
a = 0.499516 − 0.752124I
b = 1.02566 + 1.07141I
4.48711 + 4.62327I 0
u = 1.265920 + 0.001741I
a = 0.708745 − 1.102620I
b = 0.680614 − 0.024817I
−7.27997 + 5.36611I 0
u = 1.265920 − 0.001741I
a = 0.708745 + 1.102620I
b = 0.680614 + 0.024817I
−7.27997 − 5.36611I 0
u = −1.208500 + 0.413895I
a = 0.42273 + 1.57398I
b = 0.744344 − 0.370973I
1.34008 + 2.41358I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.208500 − 0.413895I
a = 0.42273 − 1.57398I
b = 0.744344 + 0.370973I
1.34008 − 2.41358I 0
u = 1.202340 + 0.450917I
a = 0.523601 − 1.173700I
b = 1.21578 + 0.78974I
−1.57098 − 8.97815I 0
u = 1.202340 − 0.450917I
a = 0.523601 + 1.173700I
b = 1.21578 − 0.78974I
−1.57098 + 8.97815I 0
u = −1.276910 + 0.228220I
a = −0.888336 − 0.616307I
b = −1.58590 + 0.42462I
−5.60584 + 0.71895I 0
u = −1.276910 − 0.228220I
a = −0.888336 + 0.616307I
b = −1.58590 − 0.42462I
−5.60584 − 0.71895I 0
u = −1.339800 + 0.191596I
a = 0.0909767 + 0.0257604I
b = −1.112800 − 0.283400I
3.89824 + 0.05208I 0
u = −1.339800 − 0.191596I
a = 0.0909767 − 0.0257604I
b = −1.112800 + 0.283400I
3.89824 − 0.05208I 0
u = −1.39164 + 0.28613I
a = 0.218968 + 0.286840I
b = 0.545133 − 0.008653I
−2.39805 + 0.09368I 0
u = −1.39164 − 0.28613I
a = 0.218968 − 0.286840I
b = 0.545133 + 0.008653I
−2.39805 − 0.09368I 0
u = 1.31620 + 0.55010I
a = 0.501394 − 1.024750I
b = 0.859520 + 0.949549I
3.24920 − 10.79950I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.31620 − 0.55010I
a = 0.501394 + 1.024750I
b = 0.859520 − 0.949549I
3.24920 + 10.79950I 0
u = 0.03070 + 1.43339I
a = −0.327596 − 0.653038I
b = 0.930451 + 0.936755I
4.62755 − 11.80560I 0
u = 0.03070 − 1.43339I
a = −0.327596 + 0.653038I
b = 0.930451 − 0.936755I
4.62755 + 11.80560I 0
u = 1.21120 + 0.77433I
a = 0.174602 − 0.980751I
b = 1.14337 + 0.95826I
−0.27560 − 8.13259I 0
u = 1.21120 − 0.77433I
a = 0.174602 + 0.980751I
b = 1.14337 − 0.95826I
−0.27560 + 8.13259I 0
u = 0.050029 + 0.549506I
a = 1.19600 − 1.13071I
b = −0.300770 + 0.829222I
0.91619 + 2.04302I 5.13446 − 5.82498I
u = 0.050029 − 0.549506I
a = 1.19600 + 1.13071I
b = −0.300770 − 0.829222I
0.91619 − 2.04302I 5.13446 + 5.82498I
u = −1.36026 + 0.52579I
a = 0.430615 + 0.801303I
b = 1.39194 − 0.74929I
−7.27997 + 5.36611I 0
u = −1.36026 − 0.52579I
a = 0.430615 − 0.801303I
b = 1.39194 + 0.74929I
−7.27997 − 5.36611I 0
u = −0.13420 + 1.45685I
a = −0.248480 − 0.121273I
b = 0.488133 + 0.519185I
−2.86626 + 0.79727I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.13420 − 1.45685I
a = −0.248480 + 0.121273I
b = 0.488133 − 0.519185I
−2.86626 − 0.79727I 0
u = −0.408727 + 0.343565I
a = −2.13532 − 0.61742I
b = −0.117649 + 0.517025I
0.987868 + 0.521667I 5.50066 − 8.13511I
u = −0.408727 − 0.343565I
a = −2.13532 + 0.61742I
b = −0.117649 − 0.517025I
0.987868 − 0.521667I 5.50066 + 8.13511I
u = −1.41452 + 0.41919I
a = −0.816772 − 0.885755I
b = −0.836044 + 0.659983I
4.48711 + 4.62327I 0
u = −1.41452 − 0.41919I
a = −0.816772 + 0.885755I
b = −0.836044 − 0.659983I
4.48711 − 4.62327I 0
u = 1.37747 + 0.56787I
a = −0.566296 + 1.126800I
b = −1.23078 − 0.74714I
4.62755 − 11.80560I 0
u = 1.37747 − 0.56787I
a = −0.566296 − 1.126800I
b = −1.23078 + 0.74714I
4.62755 + 11.80560I 0
u = 0.445807 + 0.240650I
a = 1.99187 − 1.36233I
b = 1.55450 + 0.24918I
3.89824 + 0.05208I 2.96308 + 1.55808I
u = 0.445807 − 0.240650I
a = 1.99187 + 1.36233I
b = 1.55450 − 0.24918I
3.89824 − 0.05208I 2.96308 − 1.55808I
u = 0.457836 + 0.210235I
a = 0.336633 + 0.579630I
b = 1.63519 − 1.30874I
0.507064 + 0.220193I −45.7148 − 2.4288I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.457836 − 0.210235I
a = 0.336633 − 0.579630I
b = 1.63519 + 1.30874I
0.507064 − 0.220193I −45.7148 + 2.4288I
u = 0.85356 + 1.25954I
a = 0.175588 + 0.316617I
b = −0.470436 − 0.893443I
1.34008 + 2.41358I 0
u = 0.85356 − 1.25954I
a = 0.175588 − 0.316617I
b = −0.470436 + 0.893443I
1.34008 − 2.41358I 0
u = 1.53419 + 0.16764I
a = −0.598062 + 0.544708I
b = −0.560505 + 0.033219I
−5.60584 + 0.71895I 0
u = 1.53419 − 0.16764I
a = −0.598062 − 0.544708I
b = −0.560505 − 0.033219I
−5.60584 − 0.71895I 0
u = −0.437176 + 0.122731I
a = 1.70371 − 0.40044I
b = −1.024860 − 0.072173I
−2.39805 + 0.09368I −10.6271 + 12.2420I
u = −0.437176 − 0.122731I
a = 1.70371 + 0.40044I
b = −1.024860 + 0.072173I
−2.39805 − 0.09368I −10.6271 − 12.2420I
u = −1.38461 + 0.80608I
a = −0.200188 − 0.822733I
b = −1.20849 + 0.84935I
−1.63855 + 9.41269I 0
u = −1.38461 − 0.80608I
a = −0.200188 + 0.822733I
b = −1.20849 − 0.84935I
−1.63855 − 9.41269I 0
u = −0.243722 + 0.100188I
a = −1.27642 + 2.43808I
b = 0.868378 + 0.853813I
−2.69923 − 5.20353I −2.14266 + 4.41682I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.243722 − 0.100188I
a = −1.27642 − 2.43808I
b = 0.868378 − 0.853813I
−2.69923 + 5.20353I −2.14266 − 4.41682I
u = 1.21685 + 2.64688I
a = −0.0932233 + 0.0359602I
b = 0.199281 − 0.378399I
1.70116 − 0.22078I 0
u = 1.21685 − 2.64688I
a = −0.0932233 − 0.0359602I
b = 0.199281 + 0.378399I
1.70116 + 0.22078I 0
u = −3.22872
a = −0.0656876
b = −0.198217
1.48229 0
20
III.
I
u
3
= hu
11
+u
10
+· · ·+b +5, 6u
11
−3u
10
+· · ·+a +14, u
12
−u
11
+· · ·+3u −1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
8
=
−u
−u
3
+ u
a
11
=
−6u
11
+ 3u
10
+ ··· + 11u − 14
−u
11
− u
10
+ ··· + 8u − 5
a
12
=
−7u
11
+ 3u
10
+ ··· + 17u − 18
−u
10
+ u
9
+ 2u
8
− 3u
7
− 2u
6
+ 7u
5
− 7u
3
+ 3u
2
+ 4u − 2
a
6
=
−7u
11
+ 5u
10
+ ··· + 6u − 16
−u
11
+ u
10
+ 3u
9
− 4u
8
− 5u
7
+ 10u
6
+ 4u
5
− 13u
4
+ 10u
2
− u − 2
a
2
=
7u
11
− 3u
10
+ ··· − 14u + 20
u
11
− 4u
9
+ u
8
+ 9u
7
− 5u
6
− 14u
5
+ 9u
4
+ 13u
3
− 9u
2
− 6u + 4
a
10
=
−7u
11
+ 2u
10
+ ··· + 19u − 19
−u
11
− u
10
+ ··· + 8u − 5
a
5
=
−6u
11
+ 6u
10
+ ··· − 5u − 6
−2u
11
+ 3u
10
+ ··· + 13u
2
− 6u
a
1
=
7u
11
− u
10
+ ··· − 26u + 26
2u
10
− 3u
9
− 4u
8
+ 9u
7
+ 5u
6
− 20u
5
+ 2u
4
+ 20u
3
− 7u
2
− 12u + 6
a
9
=
9u
11
− 8u
10
+ ··· − u + 17
u
11
− 2u
10
− u
9
+ 6u
8
− u
7
− 12u
6
+ 8u
5
+ 10u
4
− 11u
3
− 4u
2
+ 7u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −35u
11
+26u
10
+102u
9
−101u
8
−181u
7
+266u
6
+184u
5
−326u
4
−88u
3
+253u
2
+16u−66
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
12
− u
11
+ ··· + 3u − 1
c
2
u
12
− 10u
11
+ ··· + 41u + 1
c
4
, c
7
u
12
+ u
11
+ ··· − 3u − 1
c
5
, c
10
u
12
− u
11
+ ··· + u + 1
c
6
, c
9
u
12
− u
11
+ u
10
− 2u
9
+ u
8
− 2u
7
− 5u
6
+ u
5
− 4u
4
− 2u
3
− u
2
− u + 1
c
8
u
12
− 3u
11
+ ··· − 4u − 1
c
11
, c
12
u
12
+ 3u
11
+ ··· + 4u − 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
y
12
− 7y
11
+ ··· − 13y + 1
c
2
y
12
− 4y
11
+ ··· − 2031y + 1
c
5
, c
10
y
12
− 9y
11
+ ··· − 13y + 1
c
6
, c
9
y
12
+ y
11
+ ··· − 3y + 1
c
8
, c
11
, c
12
y
12
− 17y
11
+ ··· + 4y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.980426 + 0.359776I
a = 0.315577 + 1.061870I
b = 1.20958 − 1.14556I
−3.49372 + 6.79468I −3.95649 − 8.34398I
u = −0.980426 − 0.359776I
a = 0.315577 − 1.061870I
b = 1.20958 + 1.14556I
−3.49372 − 6.79468I −3.95649 + 8.34398I
u = 0.922366 + 0.567855I
a = 0.507673 + 0.469719I
b = −0.699044 + 0.101088I
−2.48246 − 0.51237I −13.45230 − 1.02564I
u = 0.922366 − 0.567855I
a = 0.507673 − 0.469719I
b = −0.699044 − 0.101088I
−2.48246 + 0.51237I −13.45230 + 1.02564I
u = −0.819983
a = −1.14846
b = −2.35691
5.45924 19.6690
u = 0.844858 + 0.958336I
a = −0.825525 − 0.232337I
b = 0.673751 − 0.164556I
2.99376 − 1.52653I −3.62688 − 2.79584I
u = 0.844858 − 0.958336I
a = −0.825525 + 0.232337I
b = 0.673751 + 0.164556I
2.99376 + 1.52653I −3.62688 + 2.79584I
u = −1.092040 + 0.663905I
a = 0.075491 − 1.097560I
b = −0.802211 + 0.921101I
0.63288 + 10.74750I 0.04011 − 9.58433I
u = −1.092040 − 0.663905I
a = 0.075491 + 1.097560I
b = −0.802211 − 0.921101I
0.63288 − 10.74750I 0.04011 + 9.58433I
u = 0.611943
a = 1.31568
b = 0.787635
0.657166 −4.13140
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.40176
a = −0.316874
b = 0.645260
1.31420 −8.21480
u = 0.416765
a = −3.99678
b = −0.840139
10.4279 −28.3320
25
IV. I
u
4
= hb − 1, a − 1, u
2
+ u − 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−u + 1
a
8
=
−u
−u + 1
a
11
=
1
1
a
12
=
u + 1
u
a
6
=
−u
0
a
2
=
1
0
a
10
=
2
1
a
5
=
u
u
a
1
=
u
u − 1
a
9
=
1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
2
+ u − 1
c
2
u
2
c
4
, c
5
, c
6
c
7
u
2
− u − 1
c
8
, c
9
, c
10
(u + 1)
2
c
11
, c
12
(u − 1)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
7
y
2
− 3y + 1
c
2
y
2
c
8
, c
9
, c
10
c
11
, c
12
(y −1)
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 1.00000
b = 1.00000
0.657974 −5.00000
u = −1.61803
a = 1.00000
b = 1.00000
−7.23771 −5.00000
29
V. I
u
5
= hb − u, a − u − 1, u
2
+ u − 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−u + 1
a
8
=
−u
−u + 1
a
11
=
u + 1
u
a
12
=
2u + 1
2u − 1
a
6
=
−u − 1
0
a
2
=
1
0
a
10
=
2u + 1
u
a
5
=
u
u
a
1
=
u
u − 1
a
9
=
u + 1
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
2
+ u − 1
c
2
u
2
c
4
, c
7
, c
9
c
10
u
2
− u − 1
c
5
, c
6
, c
8
(u + 1)
2
c
11
, c
12
(u − 1)
2
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
, c
9
, c
10
y
2
− 3y + 1
c
2
y
2
c
5
, c
6
, c
8
c
11
, c
12
(y −1)
2
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 1.61803
b = 0.618034
0.657974 −5.00000
u = −1.61803
a = −0.618034
b = −1.61803
−7.23771 −5.00000
33
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
((u
2
+ u − 1)
2
)(u
12
− u
11
+ ··· + 3u − 1)(u
34
− u
33
+ ··· − 14u + 1)
· (u
84
+ 3u
83
+ ··· + 1498u + 211)
c
2
u
4
(u
12
− 10u
11
+ ··· + 41u + 1)(u
34
− 15u
33
+ ··· − 42u + 4)
· (u
42
+ 10u
41
+ ··· − 21u
2
+ 4)
2
c
4
, c
7
((u
2
− u − 1)
2
)(u
12
+ u
11
+ ··· − 3u − 1)(u
34
− u
33
+ ··· − 14u + 1)
· (u
84
+ 3u
83
+ ··· + 1498u + 211)
c
5
, c
10
((u + 1)
2
)(u
2
− u − 1)(u
12
− u
11
+ ··· + u + 1)(u
34
− u
33
+ ··· + 2u − 1)
· (u
84
− 2u
83
+ ··· − 1077u − 171)
c
6
, c
9
(u + 1)
2
(u
2
− u − 1)
· (u
12
− u
11
+ u
10
− 2u
9
+ u
8
− 2u
7
− 5u
6
+ u
5
− 4u
4
− 2u
3
− u
2
− u + 1)
· (u
34
− u
33
+ ··· + 8u + 1)(u
84
− 2u
83
+ ··· + 19u + 1)
c
8
((u + 1)
4
)(u
12
− 3u
11
+ ··· − 4u − 1)(u
34
− 12u
33
+ ··· + 48u + 16)
· (u
42
+ 4u
41
+ ··· + 6u + 1)
2
c
11
, c
12
((u − 1)
4
)(u
12
+ 3u
11
+ ··· + 4u − 1)(u
34
− 12u
33
+ ··· + 48u + 16)
· (u
42
+ 4u
41
+ ··· + 6u + 1)
2
34
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
((y
2
− 3y + 1)
2
)(y
12
− 7y
11
+ ··· − 13y + 1)
· (y
34
− 29y
33
+ ··· − 146y + 1)
· (y
84
− 47y
83
+ ··· − 2568522y + 44521)
c
2
y
4
(y
12
− 4y
11
+ ··· − 2031y + 1)(y
34
− 7y
33
+ ··· − 1628y + 16)
· (y
42
− 6y
41
+ ··· − 168y + 16)
2
c
5
, c
10
((y −1)
2
)(y
2
− 3y + 1)(y
12
− 9y
11
+ ··· − 13y + 1)
· (y
34
− 23y
33
+ ··· − 42y + 1)(y
84
− 18y
83
+ ··· − 1451997y + 29241)
c
6
, c
9
((y −1)
2
)(y
2
− 3y + 1)(y
12
+ y
11
+ ··· − 3y + 1)
· (y
34
− 5y
33
+ ··· − 48y + 1)(y
84
− 2y
83
+ ··· − 153y + 1)
c
8
, c
11
, c
12
((y −1)
4
)(y
12
− 17y
11
+ ··· + 4y + 1)(y
34
− 36y
33
+ ··· + 480y + 256)
· (y
42
− 40y
41
+ ··· + 10y + 1)
2
35
