12n
0764
(K12n
0764
)
A knot diagram
1
Linearized knot diagam
4 7 10 8 12 3 11 1 4 5 7 10
Solving Sequence
7,11
8
5,12
4 10 1 2 3 6 9
c
7
c
11
c
4
c
10
c
12
c
1
c
3
c
6
c
9
c
2
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−521239u
17
− 378608u
16
+ ··· + 1930047b + 369959,
− 4207072u
17
− 369959u
16
+ ··· + 1930047a + 27427427, u
18
+ 9u
16
+ ··· − 7u + 1i
I
u
2
= hu
2
+ b, u
6
− u
5
+ 2u
4
− 4u
3
+ u
2
+ a − 2u + 2, u
7
− u
6
+ 2u
5
− 4u
4
+ u
3
− 2u
2
+ u + 1i
I
u
3
= h−47u
11
− 232u
10
+ ··· + 125b − 849, 3669u
11
+ 13414u
10
+ ··· + 14875a + 13098,
u
12
+ 2u
11
+ 8u
10
+ 12u
9
+ 29u
8
+ 33u
7
+ 54u
6
+ 51u
5
+ 54u
4
+ 43u
3
+ 28u
2
+ 15u + 7i
I
u
4
= h−2931u
11
+ 6882u
10
+ ··· + 36253b − 67921, 20673u
11
− 60690u
10
+ ··· + 471289a − 219170,
u
12
− 2u
11
− 2u
10
+ 4u
9
+ 11u
8
− u
7
− 6u
6
− 7u
5
− 14u
4
− 19u
3
+ 10u
2
+ 25u + 13i
* 4 irreducible components of dim
C
= 0, with total 49 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−5.21 × 10
5
u
17
− 3.79 × 10
5
u
16
+ · · · + 1.93 × 10
6
b + 3.70 × 10
5
, −4.21 ×
10
6
u
17
−3.70×10
5
u
16
+· · · +1.93×10
6
a+2.74×10
7
, u
18
+9u
16
+· · · − 7u +1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u
2
a
5
=
2.17978u
17
+ 0.191684u
16
+ ··· + 26.2071u − 14.2108
0.270065u
17
+ 0.196165u
16
+ ··· − 1.83799u − 0.191684
a
12
=
−u
u
a
4
=
2.17978u
17
+ 0.191684u
16
+ ··· + 25.2071u − 14.2108
0.270065u
17
+ 0.196165u
16
+ ··· − 1.83799u − 0.191684
a
10
=
−2.64153u
17
− 0.657915u
16
+ ··· − 25.4168u + 18.5822
−0.576170u
17
− 0.104194u
16
+ ··· − 0.125886u + 0.849598
a
1
=
7.90979u
17
+ 1.38868u
16
+ ··· + 54.3071u − 42.6181
0.275909u
17
+ 0.141446u
16
+ ··· + 7.93863u − 3.32710
a
2
=
2.85131u
17
+ 0.717915u
16
+ ··· + 18.8121u − 16.5368
0.0775567u
17
− 0.0705465u
16
+ ··· + 6.12764u − 1.93842
a
3
=
−2.77375u
17
− 0.788461u
16
+ ··· − 12.6845u + 14.5983
−0.0775567u
17
+ 0.0705465u
16
+ ··· − 6.12764u + 1.93842
a
6
=
2.06984u
17
+ 0.123529u
16
+ ··· + 25.9420u − 13.8229
0.380005u
17
+ 0.264320u
16
+ ··· − 1.57289u − 0.579533
a
9
=
−5.96916u
17
− 1.48818u
16
+ ··· − 52.2245u + 38.4019
−0.707998u
17
− 0.0464724u
16
+ ··· − 2.87520u + 2.06771
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
464573
91907
u
17
−
454121
643349
u
16
+ ··· −
30228500
643349
u +
10577045
643349
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
+ u
17
+ ··· + 10u + 7
c
2
, c
6
, c
8
u
18
+ u
17
+ ··· − 3u − 1
c
3
, c
5
, c
9
u
18
− 16u
16
+ ··· − 20u − 11
c
4
, c
7
, c
11
u
18
+ 9u
16
+ ··· + 7u + 1
c
10
u
18
+ 7u
17
+ ··· − 57u − 7
c
12
u
18
− 4u
17
+ ··· + 24u + 117
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
− 29y
17
+ ··· − 1724y + 49
c
2
, c
6
, c
8
y
18
− 15y
17
+ ··· − 3y + 1
c
3
, c
5
, c
9
y
18
− 32y
17
+ ··· − 1060y + 121
c
4
, c
7
, c
11
y
18
+ 18y
17
+ ··· − 31y + 1
c
10
y
18
+ y
17
+ ··· − 337y + 49
c
12
y
18
− 38y
17
+ ··· − 200412y + 13689
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.017806 + 1.047910I
a = 0.678997 − 0.386228I
b = −0.748794 − 0.598570I
−0.15119 + 2.09745I −12.63201 − 4.12977I
u = 0.017806 − 1.047910I
a = 0.678997 + 0.386228I
b = −0.748794 + 0.598570I
−0.15119 − 2.09745I −12.63201 + 4.12977I
u = −0.346086 + 0.994636I
a = −0.819378 + 0.554280I
b = 1.44016 − 0.91249I
5.46595 − 1.70319I −1.84461 + 1.40793I
u = −0.346086 − 0.994636I
a = −0.819378 − 0.554280I
b = 1.44016 + 0.91249I
5.46595 + 1.70319I −1.84461 − 1.40793I
u = −0.442971 + 1.297020I
a = −0.306761 − 0.349541I
b = 0.497178 − 0.425094I
−0.12898 + 2.98542I −11.42448 − 1.55661I
u = −0.442971 − 1.297020I
a = −0.306761 + 0.349541I
b = 0.497178 + 0.425094I
−0.12898 − 2.98542I −11.42448 + 1.55661I
u = 0.680846 + 1.209390I
a = 0.815864 − 0.142059I
b = −1.262000 + 0.276114I
−0.03662 − 6.82707I −12.5292 + 8.6563I
u = 0.680846 − 1.209390I
a = 0.815864 + 0.142059I
b = −1.262000 − 0.276114I
−0.03662 + 6.82707I −12.5292 − 8.6563I
u = −0.76192 + 1.23703I
a = 0.045171 − 1.091190I
b = −1.337910 − 0.285858I
−13.04820 + 4.46526I −11.23742 − 2.32071I
u = −0.76192 − 1.23703I
a = 0.045171 + 1.091190I
b = −1.337910 + 0.285858I
−13.04820 − 4.46526I −11.23742 + 2.32071I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.24569 + 1.44514I
a = −1.051510 − 0.623676I
b = 1.93533 + 0.56642I
8.63765 + 4.81272I −14.8469 + 6.2266I
u = −0.24569 − 1.44514I
a = −1.051510 + 0.623676I
b = 1.93533 − 0.56642I
8.63765 − 4.81272I −14.8469 − 6.2266I
u = −0.172111 + 0.488659I
a = −1.21271 + 2.12963I
b = 0.783985 − 0.730119I
2.63033 − 2.95805I −12.64066 + 3.45085I
u = −0.172111 − 0.488659I
a = −1.21271 − 2.12963I
b = 0.783985 + 0.730119I
2.63033 + 2.95805I −12.64066 − 3.45085I
u = 0.292901
a = 1.34245
b = −0.177730
−0.535468 −18.6140
u = 0.178761
a = −8.26850
b = −0.442984
−7.55325 4.27620
u = 1.03430 + 1.57774I
a = 0.813344 − 0.058598I
b = −1.99758 + 1.15997I
−11.6616 − 12.5169I −11.17612 + 5.12731I
u = 1.03430 − 1.57774I
a = 0.813344 + 0.058598I
b = −1.99758 − 1.15997I
−11.6616 + 12.5169I −11.17612 − 5.12731I
6
II. I
u
2
=
hu
2
+b, u
6
−u
5
+2u
4
−4u
3
+u
2
+a−2u+2, u
7
−u
6
+2u
5
−4u
4
+u
3
−2u
2
+u+1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u
2
a
5
=
−u
6
+ u
5
− 2u
4
+ 4u
3
− u
2
+ 2u − 2
−u
2
a
12
=
−u
u
a
4
=
−u
6
+ u
5
− 2u
4
+ 4u
3
− u
2
+ u − 2
−u
3
− u
2
a
10
=
−u
6
+ u
5
− 2u
4
+ 4u
3
− u
2
+ 3u − 3
u
3
− u
2
+ u
a
1
=
u
6
− 2u
5
+ 5u
4
− 9u
3
+ 8u
2
− 10u + 5
u
6
− 2u
5
+ u
4
− 4u
3
+ u
2
+ u + 1
a
2
=
u
6
− u
5
+ 3u
4
− 5u
3
+ 3u
2
− 5u + 2
u
6
− u
5
+ 2u
4
− 3u
3
+ u
2
− u
a
3
=
u
4
− 2u
3
+ 2u
2
− 4u + 2
u
6
− u
5
+ 2u
4
− 3u
3
+ u
2
− u
a
6
=
−u
6
+ u
5
− u
4
+ 4u
3
+ u − 2
−u
4
− 2u
2
+ u
a
9
=
−2u
6
+ 2u
5
− 3u
4
+ 9u
3
− 2u
2
+ 5u − 6
u
6
+ u
5
+ u
4
+ u
3
− 2u
2
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
6
+ 5u
5
− 11u
4
+ 28u
3
− 15u
2
+ 14u − 24
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
7
− 6u
5
− u
4
+ 9u
3
+ u
2
− 4u + 1
c
2
, c
8
u
7
+ 2u
6
− u
5
+ 2u
4
+ u
3
− 2u
2
− u − 1
c
3
, c
5
u
7
+ u
6
− 5u
5
+ 5u
4
− 9u
3
+ 7u
2
− 1
c
4
, c
7
u
7
− u
6
+ 2u
5
− 4u
4
+ u
3
− 2u
2
+ u + 1
c
6
u
7
− 2u
6
− u
5
− 2u
4
+ u
3
+ 2u
2
− u + 1
c
9
u
7
− u
6
− 5u
5
− 5u
4
− 9u
3
− 7u
2
+ 1
c
10
u
7
+ 6u
6
+ 17u
5
+ 26u
4
+ 20u
3
+ 3u
2
− 5u − 1
c
11
u
7
+ u
6
+ 2u
5
+ 4u
4
+ u
3
+ 2u
2
+ u − 1
c
12
u
7
+ 5u
6
+ 6u
5
+ 7u
4
+ 18u
3
+ 5u
2
+ 10u + 7
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
7
− 12y
6
+ 54y
5
− 117y
4
+ 131y
3
− 71y
2
+ 14y −1
c
2
, c
6
, c
8
y
7
− 6y
6
− 5y
5
+ 15y
3
− 2y
2
− 3y −1
c
3
, c
5
, c
9
y
7
− 11y
6
− 3y
5
+ 51y
4
+ 13y
3
− 39y
2
+ 14y −1
c
4
, c
7
, c
11
y
7
+ 3y
6
− 2y
5
− 14y
4
− 9y
3
+ 6y
2
+ 5y −1
c
10
y
7
− 2y
6
+ 17y
5
− 42y
4
+ 86y
3
− 157y
2
+ 31y −1
c
12
y
7
− 13y
6
+ 2y
5
+ 137y
4
+ 304y
3
+ 237y
2
+ 30y −49
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.180603 + 0.994309I
a = −1.17684 − 0.97360I
b = 0.956033 + 0.359151I
3.86399 + 3.81570I −7.59315 − 5.07181I
u = −0.180603 − 0.994309I
a = −1.17684 + 0.97360I
b = 0.956033 − 0.359151I
3.86399 − 3.81570I −7.59315 + 5.07181I
u = 0.799230
a = 0.251205
b = −0.638768
−3.11260 −12.2590
u = 1.42119
a = −0.296362
b = −2.01977
−14.5025 −11.1100
u = −0.22015 + 1.41755I
a = −1.106980 − 0.688829I
b = 1.96097 + 0.62416I
8.82336 + 5.00709I 6.2703 − 15.1192I
u = −0.22015 − 1.41755I
a = −1.106980 + 0.688829I
b = 1.96097 − 0.62416I
8.82336 − 5.00709I 6.2703 + 15.1192I
u = −0.418901
a = −3.38720
b = −0.175478
−7.75956 −34.9850
10
III. I
u
3
= h−47u
11
− 232u
10
+ · · · + 125b − 849, 3669u
11
+ 13414u
10
+ · · · +
14875a + 13098, u
12
+ 2u
11
+ · · · + 15u + 7i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u
2
a
5
=
−0.246655u
11
− 0.901782u
10
+ ··· − 4.03341u − 0.880538
0.376000u
11
+ 1.85600u
10
+ ··· + 17.0880u + 6.79200
a
12
=
−u
u
a
4
=
−0.154420u
11
− 0.00719328u
10
+ ··· + 5.20094u + 3.05217
0.287059u
11
+ 0.957647u
10
+ ··· + 5.79059u + 1.82118
a
10
=
0.389513u
11
+ 1.18750u
10
+ ··· + 8.03341u + 3.02339
−0.301647u
11
− 0.798118u
10
+ ··· − 5.36847u − 3.08094
a
1
=
0.154420u
11
+ 0.00719328u
10
+ ··· − 5.20094u − 3.05217
−0.187294u
11
− 0.500235u
10
+ ··· − 2.12894u + 0.310118
a
2
=
0.0135126u
11
+ 0.331496u
10
+ ··· + 5.94541u + 2.23139
0.362824u
11
+ 0.871059u
10
+ ··· + 4.34024u + 0.944471
a
3
=
−0.349311u
11
− 0.539563u
10
+ ··· + 1.60518u + 1.28692
0.362824u
11
+ 0.871059u
10
+ ··· + 4.34024u + 0.944471
a
6
=
−0.346420u
11
− 0.359193u
10
+ ··· + 7.30494u + 3.98817
0.475765u
11
+ 1.31341u
10
+ ··· + 5.74965u + 1.92329
a
9
=
0.778958u
11
+ 1.90568u
10
+ ··· + 5.02729u + 1.17002
−0.515765u
11
− 1.55341u
10
+ ··· − 5.26965u − 1.60329
(ii) Obstruction class = 1
(iii) Cusp Shapes =
3466
2125
u
11
+
5146
2125
u
10
+
20662
2125
u
9
+
4013
425
u
8
+
54149
2125
u
7
+
27374
2125
u
6
+
10937
425
u
5
+
7631
2125
u
4
+
2288
2125
u
3
−
3202
425
u
2
−
16867
2125
u −
37678
2125
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
− 3u
2
+ 2u + 1)
4
c
2
, c
8
u
12
− u
11
− u
10
+ u
9
− u
8
+ 2u
7
+ u
6
− 9u
5
+ 15u
4
− 13u
3
+ 9u
2
− 4u + 1
c
3
, c
5
u
12
+ 4u
11
+ ··· + 2u + 1
c
4
, c
7
u
12
+ 2u
11
+ ··· + 15u + 7
c
6
u
12
+ u
11
− u
10
− u
9
− u
8
− 2u
7
+ u
6
+ 9u
5
+ 15u
4
+ 13u
3
+ 9u
2
+ 4u + 1
c
9
u
12
− 4u
11
+ ··· − 2u + 1
c
10
(u
2
− u + 1)
6
c
11
u
12
− 2u
11
+ ··· − 15u + 7
c
12
u
12
− 4u
11
+ ··· + 21u + 7
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
− 5y
2
+ 10y −1)
4
c
2
, c
6
, c
8
y
12
− 3y
11
+ ··· + 2y + 1
c
3
, c
5
, c
9
y
12
− 2y
11
+ ··· + 26y + 1
c
4
, c
7
, c
11
y
12
+ 12y
11
+ ··· + 167y + 49
c
10
(y
2
+ y + 1)
6
c
12
y
12
+ 4y
11
+ ··· + 105y + 49
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.180135 + 0.927755I
a = 0.798712 + 0.694015I
b = −1.29718 + 1.09845I
0.265740 − 0.798239I −10.21508 − 2.15696I
u = 0.180135 − 0.927755I
a = 0.798712 − 0.694015I
b = −1.29718 − 1.09845I
0.265740 + 0.798239I −10.21508 + 2.15696I
u = −0.206453 + 1.188860I
a = −0.636230 + 0.531056I
b = 1.80380 − 0.74655I
4.40332 − 2.02988I −10.56984 + 3.46410I
u = −0.206453 − 1.188860I
a = −0.636230 − 0.531056I
b = 1.80380 + 0.74655I
4.40332 + 2.02988I −10.56984 − 3.46410I
u = 0.300960 + 1.170050I
a = −0.797324 + 0.222244I
b = 1.87013 + 0.59068I
0.26574 − 4.85801I −10.21508 + 4.77124I
u = 0.300960 − 1.170050I
a = −0.797324 − 0.222244I
b = 1.87013 − 0.59068I
0.26574 + 4.85801I −10.21508 − 4.77124I
u = −0.670986 + 0.330909I
a = 0.087396 + 1.333780I
b = 0.828521 − 0.773223I
4.40332 − 2.02988I −10.56984 + 3.46410I
u = −0.670986 − 0.330909I
a = 0.087396 − 1.333780I
b = 0.828521 + 0.773223I
4.40332 + 2.02988I −10.56984 − 3.46410I
u = 0.40365 + 1.40633I
a = −0.663216 + 0.165175I
b = 0.835953 − 0.124983I
0.265740 + 0.798239I −10.21508 + 2.15696I
u = 0.40365 − 1.40633I
a = −0.663216 − 0.165175I
b = 0.835953 + 0.124983I
0.265740 − 0.798239I −10.21508 − 2.15696I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00731 + 1.43634I
a = 0.567805 − 0.050096I
b = −1.041220 − 0.420474I
0.26574 + 4.85801I −10.21508 − 4.77124I
u = −1.00731 − 1.43634I
a = 0.567805 + 0.050096I
b = −1.041220 + 0.420474I
0.26574 − 4.85801I −10.21508 + 4.77124I
15
IV. I
u
4
= h−2931u
11
+ 6882u
10
+ · · · + 36253b − 67921, 20673u
11
−
60690u
10
+ · · · + 471289a − 219170, u
12
− 2u
11
+ · · · + 25u + 13i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u
2
a
5
=
−0.0438648u
11
+ 0.128774u
10
+ ··· − 0.996698u + 0.465044
0.0808485u
11
− 0.189833u
10
+ ··· + 2.60001u + 1.87353
a
12
=
−u
u
a
4
=
0.0941100u
11
− 0.160829u
10
+ ··· + 2.05919u + 2.87215
0.0281356u
11
+ 0.0393623u
10
+ ··· + 1.14768u + 2.05103
a
10
=
0.120788u
11
− 0.282621u
10
+ ··· + 1.76593u + 1.45803
0.0273908u
11
− 0.164621u
10
+ ··· + 0.519405u − 1.22343
a
1
=
−0.0941100u
11
+ 0.160829u
10
+ ··· − 2.05919u − 2.87215
−0.0324939u
11
+ 0.0685461u
10
+ ··· + 0.472016u − 0.826442
a
2
=
−0.133483u
11
+ 0.361165u
10
+ ··· − 2.47857u − 2.33702
−0.190081u
11
+ 0.415166u
10
+ ··· − 2.22379u − 2.79433
a
3
=
−0.0565980u
11
+ 0.0540008u
10
+ ··· + 0.254780u − 0.457318
0.190081u
11
− 0.415166u
10
+ ··· + 2.22379u + 2.79433
a
6
=
0.108895u
11
− 0.270117u
10
+ ··· − 0.193179u + 0.632864
−0.0719113u
11
+ 0.209059u
10
+ ··· + 1.79649u + 1.70571
a
9
=
0.177965u
11
− 0.558920u
10
+ ··· + 2.12679u + 1.81136
0.514054u
11
− 1.53965u
10
+ ··· + 9.23946u + 4.75588
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
3530
36253
u
11
+
19484
36253
u
10
−
23246
36253
u
9
−
11803
36253
u
8
−
17415
36253
u
7
+
113796
36253
u
6
+
5597
36253
u
5
+
68101
36253
u
4
−
58140
36253
u
3
−
1074
36253
u
2
−
209035
36253
u −
58638
5179
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
− u
2
− 2u + 1)
4
c
2
, c
6
, c
8
u
12
+ u
11
+ ··· − 308u + 91
c
3
, c
5
, c
9
u
12
+ 4u
11
+ ··· + 315u
2
+ 189
c
4
, c
7
, c
11
u
12
+ 2u
11
+ ··· − 25u + 13
c
10
(u
2
− u + 1)
6
c
12
u
12
− 18u
10
+ ··· − 525u + 127
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
− 5y
2
+ 6y −1)
4
c
2
, c
6
, c
8
y
12
− 31y
11
+ ··· − 27342y + 8281
c
3
, c
5
, c
9
y
12
− 38y
11
+ ··· + 119070y + 35721
c
4
, c
7
, c
11
y
12
− 8y
11
+ ··· − 365y + 169
c
10
(y
2
+ y + 1)
6
c
12
y
12
− 36y
11
+ ··· − 25943y + 16129
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.935871 + 0.612228I
a = 0.798080 − 0.403281I
b = −1.27562 − 0.98498I
−3.05488 + 2.02988I −11.80194 − 3.46410I
u = −0.935871 − 0.612228I
a = 0.798080 + 0.403281I
b = −1.27562 + 0.98498I
−3.05488 − 2.02988I −11.80194 + 3.46410I
u = 0.267965 + 1.122990I
a = −0.830154 + 0.247151I
b = 1.50749 − 0.36507I
2.58490 − 2.02988I −8.75302 + 3.46410I
u = 0.267965 − 1.122990I
a = −0.830154 − 0.247151I
b = 1.50749 + 0.36507I
2.58490 + 2.02988I −8.75302 − 3.46410I
u = −0.668934 + 0.428490I
a = 1.118010 − 0.578487I
b = −0.304581 + 0.329429I
2.58490 + 2.02988I −8.75302 − 3.46410I
u = −0.668934 − 0.428490I
a = 1.118010 + 0.578487I
b = −0.304581 − 0.329429I
2.58490 − 2.02988I −8.75302 + 3.46410I
u = 1.213350 + 0.131620I
a = −0.483814 − 0.661265I
b = 0.443182 − 0.504374I
−3.05488 − 2.02988I −11.80194 + 3.46410I
u = 1.213350 − 0.131620I
a = −0.483814 + 0.661265I
b = 0.443182 + 0.504374I
−3.05488 + 2.02988I −11.80194 − 3.46410I
u = −0.894944 + 0.895021I
a = 0.763167 − 0.204455I
b = −2.34607 − 2.27347I
−14.3344 + 2.0299I −10.44504 − 3.46410I
u = −0.894944 − 0.895021I
a = 0.763167 + 0.204455I
b = −2.34607 + 2.27347I
−14.3344 − 2.0299I −10.44504 + 3.46410I
19
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 2.01843 + 1.05092I
a = −0.019135 + 0.439021I
b = −1.024400 + 0.327533I
−14.3344 + 2.0299I −10.44504 − 3.46410I
u = 2.01843 − 1.05092I
a = −0.019135 − 0.439021I
b = −1.024400 − 0.327533I
−14.3344 − 2.0299I −10.44504 + 3.46410I
20
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
3
− 3u
2
+ 2u + 1)
4
(u
3
− u
2
− 2u + 1)
4
· (u
7
− 6u
5
− u
4
+ 9u
3
+ u
2
− 4u + 1)(u
18
+ u
17
+ ··· + 10u + 7)
c
2
, c
8
(u
7
+ 2u
6
− u
5
+ 2u
4
+ u
3
− 2u
2
− u − 1)
· (u
12
− u
11
− u
10
+ u
9
− u
8
+ 2u
7
+ u
6
− 9u
5
+ 15u
4
− 13u
3
+ 9u
2
− 4u + 1)
· (u
12
+ u
11
+ ··· − 308u + 91)(u
18
+ u
17
+ ··· − 3u − 1)
c
3
, c
5
(u
7
+ u
6
+ ··· + 7u
2
− 1)(u
12
+ 4u
11
+ ··· + 315u
2
+ 189)
· (u
12
+ 4u
11
+ ··· + 2u + 1)(u
18
− 16u
16
+ ··· − 20u − 11)
c
4
, c
7
(u
7
− u
6
+ ··· + u + 1)(u
12
+ 2u
11
+ ··· − 25u + 13)
· (u
12
+ 2u
11
+ ··· + 15u + 7)(u
18
+ 9u
16
+ ··· + 7u + 1)
c
6
(u
7
− 2u
6
+ ··· − u + 1)(u
12
+ u
11
+ ··· − 308u + 91)
· (u
12
+ u
11
− u
10
− u
9
− u
8
− 2u
7
+ u
6
+ 9u
5
+ 15u
4
+ 13u
3
+ 9u
2
+ 4u + 1)
· (u
18
+ u
17
+ ··· − 3u − 1)
c
9
(u
7
− u
6
+ ··· − 7u
2
+ 1)(u
12
− 4u
11
+ ··· − 2u + 1)
· (u
12
+ 4u
11
+ ··· + 315u
2
+ 189)(u
18
− 16u
16
+ ··· − 20u − 11)
c
10
(u
2
− u + 1)
12
(u
7
+ 6u
6
+ 17u
5
+ 26u
4
+ 20u
3
+ 3u
2
− 5u − 1)
· (u
18
+ 7u
17
+ ··· − 57u − 7)
c
11
(u
7
+ u
6
+ ··· + u − 1)(u
12
− 2u
11
+ ··· − 15u + 7)
· (u
12
+ 2u
11
+ ··· − 25u + 13)(u
18
+ 9u
16
+ ··· + 7u + 1)
c
12
(u
7
+ 5u
6
+ 6u
5
+ 7u
4
+ 18u
3
+ 5u
2
+ 10u + 7)
· (u
12
− 18u
10
+ ··· − 525u + 127)(u
12
− 4u
11
+ ··· + 21u + 7)
· (u
18
− 4u
17
+ ··· + 24u + 117)
21
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
3
− 5y
2
+ 6y −1)
4
(y
3
− 5y
2
+ 10y −1)
4
· (y
7
− 12y
6
+ 54y
5
− 117y
4
+ 131y
3
− 71y
2
+ 14y −1)
· (y
18
− 29y
17
+ ··· − 1724y + 49)
c
2
, c
6
, c
8
(y
7
− 6y
6
− 5y
5
+ 15y
3
− 2y
2
− 3y −1)
· (y
12
− 31y
11
+ ··· − 27342y + 8281)(y
12
− 3y
11
+ ··· + 2y + 1)
· (y
18
− 15y
17
+ ··· − 3y + 1)
c
3
, c
5
, c
9
(y
7
− 11y
6
− 3y
5
+ 51y
4
+ 13y
3
− 39y
2
+ 14y −1)
· (y
12
− 38y
11
+ ··· + 119070y + 35721)(y
12
− 2y
11
+ ··· + 26y + 1)
· (y
18
− 32y
17
+ ··· − 1060y + 121)
c
4
, c
7
, c
11
(y
7
+ 3y
6
− 2y
5
− 14y
4
− 9y
3
+ 6y
2
+ 5y −1)
· (y
12
− 8y
11
+ ··· − 365y + 169)(y
12
+ 12y
11
+ ··· + 167y + 49)
· (y
18
+ 18y
17
+ ··· − 31y + 1)
c
10
(y
2
+ y + 1)
12
(y
7
− 2y
6
+ 17y
5
− 42y
4
+ 86y
3
− 157y
2
+ 31y −1)
· (y
18
+ y
17
+ ··· − 337y + 49)
c
12
(y
7
− 13y
6
+ 2y
5
+ 137y
4
+ 304y
3
+ 237y
2
+ 30y −49)
· (y
12
− 36y
11
+ ··· − 25943y + 16129)(y
12
+ 4y
11
+ ··· + 105y + 49)
· (y
18
− 38y
17
+ ··· − 200412y + 13689)
22
