12a
1105
(K12a
1105
)
A knot diagram
1
Linearized knot diagam
4 7 11 12 8 3 10 1 5 6 2 9
Solving Sequence
3,6 7,10
8 11 4 2 12 1 5 9
c
6
c
7
c
10
c
3
c
2
c
11
c
1
c
5
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= ⟨−1.13930 × 10
21
u
39
− 1.89955 × 10
22
u
38
+ ··· + 1.42950 × 10
21
b + 3.75712 × 10
23
,
− 6.56657 × 10
20
u
39
− 9.62976 × 10
21
u
38
+ ··· + 2.85899 × 10
21
a − 1.48932 × 10
23
,
u
40
+ 17u
39
+ ··· − 2560u − 256⟩
I
u
2
= ⟨989449936519u
27
− 4930796017655u
26
+ ··· + 1798585993788b − 6638482452236,
5649032515717u
27
− 20633683854770u
26
+ ··· + 1798585993788a + 15418713106993,
u
28
− 4u
27
+ ··· + 13u
2
+ 1⟩
I
u
3
= ⟨−160u
59
a − 28504115u
59
+ ··· + 32a + 3787205, 52235u
59
a + 20380u
59
+ ··· + 25702a + 2510,
5u
60
− 50u
59
+ ··· − 3u + 1⟩
I
u
4
= ⟨−u
7
a
3
+ u
7
a
2
+ ··· − a + 3, u
7
a
3
− u
7
a
2
+ ··· + 3a − 1,
u
7
a
2
+ u
6
a
2
− u
7
a + 2u
5
a
2
− u
6
a + u
4
a
2
− u
5
a + u
3
a
2
+ u
4
a + u
3
a − u
4
+ u
2
a + bu + au + 2u
2
+ b + 2u + 1,
u
8
a
2
− u
8
a + ··· + 2u + 1⟩
* 3 irreducible components of dim
C
= 0, with total 188 representations.
* 1 irreducible components of dim
C
= 1
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
= ⟨−1.14 × 10
21
u
39
− 1.90 × 10
22
u
38
+ · · · + 1.43 × 10
21
b + 3.76 ×
10
23
, −6.57 × 10
20
u
39
− 9.63 × 10
21
u
38
+ · · · + 2.86 × 10
21
a − 1.49 ×
10
23
, u
40
+ 17u
39
+ · · · − 2560u − 256⟩
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
10
=
0.229681u
39
+ 3.36823u
38
+ ··· + 427.485u + 52.0925
0.796992u
39
+ 13.2882u
38
+ ··· − 2417.55u − 262.828
a
8
=
−0.0129700u
39
− 0.147174u
38
+ ··· − 7.46661u + 1.06374
−0.382727u
39
− 6.19695u
38
+ ··· + 911.623u + 101.298
a
11
=
1.02667u
39
+ 16.6564u
38
+ ··· − 1990.06u − 210.736
0.796992u
39
+ 13.2882u
38
+ ··· − 2417.55u − 262.828
a
4
=
−0.245169u
39
− 3.87419u
38
+ ··· + 753.796u + 88.9443
−0.293676u
39
− 4.54829u
38
+ ··· + 539.688u + 62.7632
a
2
=
u
u
3
+ u
a
12
=
−0.758262u
39
− 11.1881u
38
+ ··· + 54.0332u + 6.22604
−2.66485u
39
− 43.7900u
38
+ ··· + 5568.03u + 593.976
a
1
=
−0.0107557u
39
+ 0.0107774u
38
+ ··· − 87.9801u − 3.23265
−0.503035u
39
− 8.17030u
38
+ ··· + 910.250u + 100.732
a
5
=
−0.0567806u
39
− 0.898599u
38
+ ··· − 348.002u − 42.0306
0.752668u
39
+ 11.5333u
38
+ ··· − 884.556u − 93.8953
a
9
=
−1.60236u
39
− 25.6296u
38
+ ··· + 1879.61u + 190.846
−1.79529u
39
− 29.3126u
38
+ ··· + 4403.99u + 470.747
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
100081583463789896653
47299541498605875888
u
39
−
168233866403703359237
5255504610956208432
u
38
+ ··· +
6734890128933396237742
2956221343662867243
u +
669015638105036849960
2956221343662867243
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
40
− 3u
39
+ ··· − 135u + 27
c
2
, c
6
u
40
+ 17u
39
+ ··· − 2560u − 256
c
3
, c
10
27(27u
40
− 27u
39
+ ··· + u + 1)
c
4
, c
9
27(27u
40
+ 27u
39
+ ··· − u + 1)
c
7
, c
11
u
40
+ 3u
39
+ ··· + 135u + 27
c
8
, c
12
u
40
− 17u
39
+ ··· + 2560u − 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
11
y
40
− 7y
39
+ ··· + 2673y + 729
c
2
, c
6
, c
8
c
12
y
40
+ 17y
39
+ ··· + 65536y + 65536
c
3
, c
4
, c
9
c
10
729(729y
40
− 16767y
39
+ ··· − 59y + 1)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.14028
a = 0.542779
b = −0.289176
−0.678004 −12.8890
u = −1.139630 + 0.242928I
a = −0.042870 + 0.308351I
b = 1.073230 − 0.724091I
−3.3441 − 15.0894I 0
u = −1.139630 − 0.242928I
a = −0.042870 − 0.308351I
b = 1.073230 + 0.724091I
−3.3441 + 15.0894I 0
u = −0.497516 + 1.077900I
a = 1.41196 − 0.31741I
b = −1.15222 − 0.87143I
0.79692 + 3.49099I 0
u = −0.497516 − 1.077900I
a = 1.41196 + 0.31741I
b = −1.15222 + 0.87143I
0.79692 − 3.49099I 0
u = −0.104793 + 1.182780I
a = 1.52088 − 0.52726I
b = −1.185540 − 0.504784I
3.39633 + 4.91222I 0
u = −0.104793 − 1.182780I
a = 1.52088 + 0.52726I
b = −1.185540 + 0.504784I
3.39633 − 4.91222I 0
u = −1.180500 + 0.265835I
a = 0.091123 − 0.306079I
b = −1.038500 + 0.606550I
− 8.64429I 0
u = −1.180500 − 0.265835I
a = 0.091123 + 0.306079I
b = −1.038500 − 0.606550I
8.64429I 0
u = 0.069133 + 1.222940I
a = −1.41555 + 0.34686I
b = 1.002750 + 0.449758I
5.49218 − 1.74539I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.069133 − 1.222940I
a = −1.41555 − 0.34686I
b = 1.002750 − 0.449758I
5.49218 + 1.74539I 0
u = −0.660444 + 0.377422I
a = 0.462226 + 0.067787I
b = 0.245974 − 0.655330I
−1.29804 + 0.78862I −7.24318 − 3.09779I
u = −0.660444 − 0.377422I
a = 0.462226 − 0.067787I
b = 0.245974 + 0.655330I
−1.29804 − 0.78862I −7.24318 + 3.09779I
u = −1.230810 + 0.195258I
a = −0.089927 + 0.210729I
b = 0.767209 − 0.550768I
−6.55337 − 3.59470I 0
u = −1.230810 − 0.195258I
a = −0.089927 − 0.210729I
b = 0.767209 + 0.550768I
−6.55337 + 3.59470I 0
u = 1.271280 + 0.274737I
a = −0.327798 + 0.175529I
b = 0.194769 − 0.082155I
−5.62477 − 6.34564I 0
u = 1.271280 − 0.274737I
a = −0.327798 − 0.175529I
b = 0.194769 + 0.082155I
−5.62477 + 6.34564I 0
u = −1.31229
a = 0.170911
b = −0.718197
0.678004 0
u = −1.159260 + 0.636698I
a = 0.044626 − 0.246409I
b = −0.425349 + 0.271549I
−5.49218 + 1.74539I 0
u = −1.159260 − 0.636698I
a = 0.044626 + 0.246409I
b = −0.425349 − 0.271549I
−5.49218 − 1.74539I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.695907 + 1.188770I
a = −0.880382 + 0.211344I
b = 0.869437 + 0.526441I
−3.39633 + 4.91222I 0
u = −0.695907 − 1.188770I
a = −0.880382 − 0.211344I
b = 0.869437 − 0.526441I
−3.39633 − 4.91222I 0
u = −0.16888 + 1.42888I
a = 0.875872 − 0.142263I
b = −0.683854 − 0.359026I
1.73091I 0
u = −0.16888 − 1.42888I
a = 0.875872 + 0.142263I
b = −0.683854 + 0.359026I
− 1.73091I 0
u = −0.63247 + 1.29831I
a = 1.61971 − 0.26786I
b = −1.48376 − 0.94120I
21.3615I 0
u = −0.63247 − 1.29831I
a = 1.61971 + 0.26786I
b = −1.48376 + 0.94120I
− 21.3615I 0
u = −0.64624 + 1.30911I
a = −1.52479 + 0.29337I
b = 1.44031 + 0.84855I
3.3441 + 15.0894I 0
u = −0.64624 − 1.30911I
a = −1.52479 − 0.29337I
b = 1.44031 − 0.84855I
3.3441 − 15.0894I 0
u = −0.62417 + 1.33594I
a = 1.398850 − 0.160563I
b = −1.23726 − 0.84107I
−2.88034 + 10.04620I 0
u = −0.62417 − 1.33594I
a = 1.398850 + 0.160563I
b = −1.23726 + 0.84107I
−2.88034 − 10.04620I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.17851 + 1.47621I
a = −0.946229 + 0.461968I
b = 0.912818 + 0.160424I
6.55337 − 3.59470I 0
u = −0.17851 − 1.47621I
a = −0.946229 − 0.461968I
b = 0.912818 − 0.160424I
6.55337 + 3.59470I 0
u = −0.21634 + 1.47625I
a = 0.836758 − 0.579742I
b = −0.908395 − 0.025097I
2.88034 − 10.04620I 0
u = −0.21634 − 1.47625I
a = 0.836758 + 0.579742I
b = −0.908395 + 0.025097I
2.88034 + 10.04620I 0
u = −0.338539 + 0.326750I
a = 1.24825 + 1.08328I
b = 0.919011 − 0.516162I
−0.79692 + 3.49099I 3.06687 − 1.73251I
u = −0.338539 − 0.326750I
a = 1.24825 − 1.08328I
b = 0.919011 + 0.516162I
−0.79692 − 3.49099I 3.06687 + 1.73251I
u = −0.51178 + 1.44815I
a = −1.163360 + 0.203861I
b = 1.046570 + 0.560106I
5.62477 + 6.34564I 0
u = −0.51178 − 1.44815I
a = −1.163360 − 0.203861I
b = 1.046570 − 0.560106I
5.62477 − 6.34564I 0
u = 0.231374 + 0.240170I
a = 0.27380 − 1.92615I
b = −0.353506 + 0.377468I
1.29804 − 0.78862I 7.24318 + 3.09779I
u = 0.231374 − 0.240170I
a = 0.27380 + 1.92615I
b = −0.353506 − 0.377468I
1.29804 + 0.78862I 7.24318 − 3.09779I
8
II. I
u
2
=
⟨9.89×10
11
u
27
−4.93×10
12
u
26
+· · ·+1.80×10
12
b−6.64×10
12
, 5.65×10
12
u
27
−
2.06 × 10
13
u
26
+ · · · + 1.80 × 10
12
a + 1.54 × 10
13
, u
28
− 4u
27
+ · · · + 13u
2
+ 1⟩
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
10
=
−3.14082u
27
+ 11.4722u
26
+ ··· − 7.75888u − 8.57269
−0.550127u
27
+ 2.74148u
26
+ ··· − 4.88174u + 3.69095
a
8
=
0.791533u
27
− 3.02387u
26
+ ··· − 2.73997u − 2.68930
−0.481655u
27
+ 1.30270u
26
+ ··· − 3.99918u − 0.309878
a
11
=
−3.69095u
27
+ 14.2137u
26
+ ··· − 12.6406u − 4.88174
−0.550127u
27
+ 2.74148u
26
+ ··· − 4.88174u + 3.69095
a
4
=
0.500393u
27
− 0.727935u
26
+ ··· + 12.0120u + 4.77242
1.27364u
27
− 4.63118u
26
+ ··· + 5.77242u − 0.500393
a
2
=
u
u
3
+ u
a
12
=
−4.28175u
27
+ 16.4743u
26
+ ··· − 15.2405u − 5.85271
−0.881453u
27
+ 4.04850u
26
+ ··· − 6.89077u + 2.82253
a
1
=
0.805857u
27
− 5.11783u
26
+ ··· + 1.87723u − 8.50015
−1.27048u
27
+ 4.47409u
26
+ ··· − 7.19028u − 1.28751
a
5
=
−2.62974u
27
+ 10.9428u
26
+ ··· − 10.3722u + 4.79910
0.582475u
27
− 1.68360u
26
+ ··· + 5.31824u + 1.68675
a
9
=
4.47203u
27
− 14.7420u
26
+ ··· + 8.00604u + 10.7851
1.97526u
27
− 9.60197u
26
+ ··· + 9.33245u − 3.01553
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
3953985943693
1798585993788
u
27
−
20451602633597
1798585993788
u
26
+ ··· −
24752853561361
1798585993788
u −
3067689954026
449646498447
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
28
− 3u
27
+ ··· − 48u + 36
c
2
, c
12
u
28
+ 4u
27
+ ··· + 13u
2
+ 1
c
3
, c
10
4(4u
28
+ 4u
27
+ ··· + 3u + 1)
c
4
, c
9
4(4u
28
− 4u
27
+ ··· − 3u + 1)
c
6
, c
8
u
28
− 4u
27
+ ··· + 13u
2
+ 1
c
7
, c
11
u
28
+ 3u
27
+ ··· + 48u + 36
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
11
y
28
+ 7y
27
+ ··· + 6192y + 1296
c
2
, c
6
, c
8
c
12
y
28
+ 14y
27
+ ··· + 26y + 1
c
3
, c
4
, c
9
c
10
16(16y
28
− 144y
27
+ ··· + 13y + 1)
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.136648 + 0.946331I
a = 1.76583 + 0.81451I
b = −1.200650 + 0.372627I
1.17094I − 70.10 − 0.0853212I
u = −0.136648 − 0.946331I
a = 1.76583 − 0.81451I
b = −1.200650 − 0.372627I
− 1.17094I − 70.10 + 0.0853212I
u = 0.177807 + 0.938169I
a = 1.51071 + 0.88729I
b = −1.247460 + 0.492279I
4.15816 − 3.28640I 5.68449 + 2.42731I
u = 0.177807 − 0.938169I
a = 1.51071 − 0.88729I
b = −1.247460 − 0.492279I
4.15816 + 3.28640I 5.68449 − 2.42731I
u = 0.873788 + 0.210879I
a = −0.272534 + 0.199714I
b = −0.994243 − 0.733917I
1.08386 + 4.88595I −0.88479 − 6.08182I
u = 0.873788 − 0.210879I
a = −0.272534 − 0.199714I
b = −0.994243 + 0.733917I
1.08386 − 4.88595I −0.88479 + 6.08182I
u = −0.634034 + 0.950647I
a = −0.745266 − 0.027755I
b = 0.411893 − 0.183179I
−4.15816 + 3.28640I −5.68449 − 2.42731I
u = −0.634034 − 0.950647I
a = −0.745266 + 0.027755I
b = 0.411893 + 0.183179I
−4.15816 − 3.28640I −5.68449 + 2.42731I
u = −1.028830 + 0.552365I
a = 0.250126 − 0.345287I
b = −0.092210 + 0.218091I
−5.62841 + 2.09236I −7.49506 − 8.83052I
u = −1.028830 − 0.552365I
a = 0.250126 + 0.345287I
b = −0.092210 − 0.218091I
−5.62841 − 2.09236I −7.49506 + 8.83052I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.006272 + 1.212530I
a = −1.33659 − 0.47696I
b = 1.027810 − 0.369099I
5.62841 + 2.09236I 7.49506 − 8.83052I
u = −0.006272 − 1.212530I
a = −1.33659 + 0.47696I
b = 1.027810 + 0.369099I
5.62841 − 2.09236I 7.49506 + 8.83052I
u = −0.339230 + 0.707931I
a = 1.52784 − 0.63710I
b = −0.439616 + 0.736626I
−5.44803 + 1.13999I −6.37606 − 0.43186I
u = −0.339230 − 0.707931I
a = 1.52784 + 0.63710I
b = −0.439616 − 0.736626I
−5.44803 − 1.13999I −6.37606 + 0.43186I
u = 0.390685 + 1.185710I
a = −0.840034 − 0.831890I
b = 1.107050 − 0.013789I
5.44803 + 1.13999I 6.37606 − 0.43186I
u = 0.390685 − 1.185710I
a = −0.840034 + 0.831890I
b = 1.107050 + 0.013789I
5.44803 − 1.13999I 6.37606 + 0.43186I
u = 0.549899 + 1.210700I
a = −1.71288 − 0.31897I
b = 1.48225 − 1.01007I
4.10977 − 10.09610I 1.16490 + 8.56371I
u = 0.549899 − 1.210700I
a = −1.71288 + 0.31897I
b = 1.48225 + 1.01007I
4.10977 + 10.09610I 1.16490 − 8.56371I
u = 0.421389 + 1.322980I
a = 1.42666 − 0.08889I
b = −0.974358 + 0.969439I
− 12.1531I 0. + 9.97979I
u = 0.421389 − 1.322980I
a = 1.42666 + 0.08889I
b = −0.974358 − 0.969439I
12.1531I 0. − 9.97979I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.401670 + 0.143744I
a = −0.179789 + 0.033183I
b = 0.550372 − 0.248416I
−5.41627 − 6.67339I 4.1940 + 14.0424I
u = 1.401670 − 0.143744I
a = −0.179789 − 0.033183I
b = 0.550372 + 0.248416I
−5.41627 + 6.67339I 4.1940 − 14.0424I
u = −0.012372 + 0.517408I
a = 2.45831 − 1.35804I
b = 0.010640 + 1.278440I
−4.10977 + 10.09610I −1.16490 − 8.56371I
u = −0.012372 − 0.517408I
a = 2.45831 + 1.35804I
b = 0.010640 − 1.278440I
−4.10977 − 10.09610I −1.16490 + 8.56371I
u = 0.47228 + 1.48270I
a = −1.165310 − 0.144959I
b = 1.003810 − 0.583498I
5.41627 − 6.67339I −4.1940 + 14.0424I
u = 0.47228 − 1.48270I
a = −1.165310 + 0.144959I
b = 1.003810 + 0.583498I
5.41627 + 6.67339I −4.1940 − 14.0424I
u = −0.130132 + 0.342927I
a = −2.18708 + 2.27887I
b = −0.145284 − 0.970139I
−1.08386 + 4.88595I 0.88479 − 6.08182I
u = −0.130132 − 0.342927I
a = −2.18708 − 2.27887I
b = −0.145284 + 0.970139I
−1.08386 − 4.88595I 0.88479 + 6.08182I
14
III. I
u
3
= ⟨−160au
59
− 2.85 × 10
7
u
59
+ · · · + 32a + 3.79 × 10
6
, 52235u
59
a +
20380u
59
+ · · · + 25702a + 2510, 5u
60
− 50u
59
+ · · · − 3u + 1⟩
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
10
=
a
0.00673854au
59
+ 1200.48u
59
+ ··· − 0.00134771a − 159.502
a
8
=
−657.727au
59
+ 128.283u
59
+ ··· + 230.545a − 15.2191
676.391au
59
+ 101.012u
59
+ ··· + 9.54999a − 0.233701
a
11
=
0.00673854au
59
+ 1200.48u
59
+ ··· + 0.998652a − 159.502
0.00673854au
59
+ 1200.48u
59
+ ··· − 0.00134771a − 159.502
a
4
=
−1200.48au
59
+ 50.4671u
59
+ ··· + 159.502a + 72.3128
101.641u
59
− 975.234u
58
+ ··· + 32.5156u − 1.60938
a
2
=
u
u
3
+ u
a
12
=
27545
64
u
59
−
21845
4
u
58
+ ··· + a −
18627
64
−0.00673854au
59
+ 525.539u
59
+ ··· + 0.00134771a − 63.3109
a
1
=
30.5585au
59
+ 25.4406u
59
+ ··· − 94.1117a − 64.7600
−551.703au
59
− 131.794u
59
+ ··· + 60.2781a + 6.54620
a
5
=
420u
59
a +
5445
32
u
59
+ ··· +
1049
8
a +
203
8
−146.867au
59
− 181.153u
59
+ ··· − 51.7203a − 27.6287
a
9
=
293.697au
59
+ 509.814u
59
+ ··· − 55.1769a + 131.475
−192.985au
59
+ 861.219u
59
+ ··· − 28.0905a − 24.3376
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1265
8
u
59
+
14965
4
u
58
+ ··· −
8543
8
u +
759
2
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
11
400u
120
− 5480u
119
+ ··· − 472919040u + 28339200
c
2
, c
8
, c
12
(5u
60
− 50u
59
+ ··· − 3u + 1)
2
c
3
, c
9
64u
120
+ 192u
119
+ ··· + 426240000u + 2733137920
c
4
, c
10
64u
120
− 192u
119
+ ··· − 426240000u + 2733137920
c
6
(5u
60
+ 50u
59
+ ··· + 3u + 1)
2
c
7
400u
120
+ 5480u
119
+ ··· + 472919040u + 28339200
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
11
1.60 × 10
5
y
120
− 7200y
119
+ ··· + 3.42 × 10
16
y + 8.03 × 10
14
c
2
, c
6
, c
8
c
12
(25y
60
+ 930y
59
+ ··· + 15y + 1)
2
c
3
, c
4
, c
9
c
10
4096y
120
+ 1.08 × 10
4
y
119
+ ··· + 2.60 × 10
19
y + 7.47 × 10
18
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.321907 + 0.943564I
a = −0.211148 + 1.105250I
b = −0.26256 − 1.99549I
−3.67203 − 11.90650I 0
u = 0.321907 + 0.943564I
a = 2.66689 − 0.33653I
b = −0.687502 + 0.733552I
−3.67203 − 11.90650I 0
u = 0.321907 − 0.943564I
a = −0.211148 − 1.105250I
b = −0.26256 + 1.99549I
−3.67203 + 11.90650I 0
u = 0.321907 − 0.943564I
a = 2.66689 + 0.33653I
b = −0.687502 − 0.733552I
−3.67203 + 11.90650I 0
u = 0.290898 + 0.962372I
a = 0.700197 + 0.784048I
b = −0.75843 − 1.46413I
−4.84435 − 2.21317I 0
u = 0.290898 + 0.962372I
a = 2.24984 − 0.55461I
b = −0.637554 + 0.253876I
−4.84435 − 2.21317I 0
u = 0.290898 − 0.962372I
a = 0.700197 − 0.784048I
b = −0.75843 + 1.46413I
−4.84435 + 2.21317I 0
u = 0.290898 − 0.962372I
a = 2.24984 + 0.55461I
b = −0.637554 − 0.253876I
−4.84435 + 2.21317I 0
u = −0.204638 + 0.984696I
a = −1.034140 + 0.554038I
b = −0.071904 + 0.987935I
0.982206 + 0.844454I 0
u = −0.204638 + 0.984696I
a = −2.26834 − 1.27479I
b = 1.29204 + 1.40466I
0.982206 + 0.844454I 0
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.204638 − 0.984696I
a = −1.034140 − 0.554038I
b = −0.071904 − 0.987935I
0.982206 − 0.844454I 0
u = −0.204638 − 0.984696I
a = −2.26834 + 1.27479I
b = 1.29204 − 1.40466I
0.982206 − 0.844454I 0
u = 0.318254 + 0.962466I
a = 0.026549 − 0.690358I
b = 0.24232 + 1.66247I
−0.35565 − 6.64390I 0
u = 0.318254 + 0.962466I
a = −2.48216 + 0.28024I
b = 0.850057 − 0.568151I
−0.35565 − 6.64390I 0
u = 0.318254 − 0.962466I
a = 0.026549 + 0.690358I
b = 0.24232 − 1.66247I
−0.35565 + 6.64390I 0
u = 0.318254 − 0.962466I
a = −2.48216 − 0.28024I
b = 0.850057 + 0.568151I
−0.35565 + 6.64390I 0
u = −0.984855 + 0.363005I
a = −0.655421 + 0.694738I
b = 1.049900 − 0.000916I
−2.65659 + 7.48205I 0
u = −0.984855 + 0.363005I
a = 0.298474 − 0.194999I
b = 0.640368 + 0.540116I
−2.65659 + 7.48205I 0
u = −0.984855 − 0.363005I
a = −0.655421 − 0.694738I
b = 1.049900 + 0.000916I
−2.65659 − 7.48205I 0
u = −0.984855 − 0.363005I
a = 0.298474 + 0.194999I
b = 0.640368 − 0.540116I
−2.65659 − 7.48205I 0
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.304706 + 0.896132I
a = 0.957243 + 0.856438I
b = −0.07957 − 1.50726I
3.23047I 0
u = −0.304706 + 0.896132I
a = 1.79637 + 0.39260I
b = −0.315785 − 0.984822I
3.23047I 0
u = −0.304706 − 0.896132I
a = 0.957243 − 0.856438I
b = −0.07957 + 1.50726I
− 3.23047I 0
u = −0.304706 − 0.896132I
a = 1.79637 − 0.39260I
b = −0.315785 + 0.984822I
− 3.23047I 0
u = −0.159113 + 0.919352I
a = 0.023781 − 0.297620I
b = −0.48301 + 1.39389I
1.29549 + 0.75677I 0
u = −0.159113 + 0.919352I
a = −2.49514 − 0.85194I
b = 0.934786 + 0.596619I
1.29549 + 0.75677I 0
u = −0.159113 − 0.919352I
a = 0.023781 + 0.297620I
b = −0.48301 − 1.39389I
1.29549 − 0.75677I 0
u = −0.159113 − 0.919352I
a = −2.49514 + 0.85194I
b = 0.934786 − 0.596619I
1.29549 − 0.75677I 0
u = −0.563422 + 0.906939I
a = 0.369590 − 0.833889I
b = −0.652128 + 1.007840I
−4.28468 + 5.58928I 0
u = −0.563422 + 0.906939I
a = −1.122690 − 0.374955I
b = −0.001425 + 0.354252I
−4.28468 + 5.58928I 0
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.563422 − 0.906939I
a = 0.369590 + 0.833889I
b = −0.652128 − 1.007840I
−4.28468 − 5.58928I 0
u = −0.563422 − 0.906939I
a = −1.122690 + 0.374955I
b = −0.001425 − 0.354252I
−4.28468 − 5.58928I 0
u = 0.910138 + 0.143266I
a = 0.308329 − 0.280726I
b = 0.947533 + 0.830228I
0.35565 + 6.64390I 0
u = 0.910138 + 0.143266I
a = −0.0917514 − 0.0501821I
b = −1.064280 − 0.680045I
0.35565 + 6.64390I 0
u = 0.910138 − 0.143266I
a = 0.308329 + 0.280726I
b = 0.947533 − 0.830228I
0.35565 − 6.64390I 0
u = 0.910138 − 0.143266I
a = −0.0917514 + 0.0501821I
b = −1.064280 + 0.680045I
0.35565 − 6.64390I 0
u = 0.882774 + 0.181268I
a = −0.129951 + 0.347717I
b = −1.017010 − 0.715087I
1.39107 + 3.59624I 0
u = 0.882774 + 0.181268I
a = 0.319140 + 0.018071I
b = 0.945911 + 0.532211I
1.39107 + 3.59624I 0
u = 0.882774 − 0.181268I
a = −0.129951 − 0.347717I
b = −1.017010 + 0.715087I
1.39107 − 3.59624I 0
u = 0.882774 − 0.181268I
a = 0.319140 − 0.018071I
b = 0.945911 − 0.532211I
1.39107 − 3.59624I 0
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.519961 + 0.729814I
a = 1.42695 − 0.10017I
b = −0.444188 − 0.465152I
−1.56173 + 2.08294I 0
u = −0.519961 + 0.729814I
a = 0.036719 + 0.306272I
b = 0.098418 − 1.011180I
−1.56173 + 2.08294I 0
u = −0.519961 − 0.729814I
a = 1.42695 + 0.10017I
b = −0.444188 + 0.465152I
−1.56173 − 2.08294I 0
u = −0.519961 − 0.729814I
a = 0.036719 − 0.306272I
b = 0.098418 + 1.011180I
−1.56173 − 2.08294I 0
u = 1.095990 + 0.142402I
a = −0.396890 + 0.128629I
b = −0.280943 − 0.633355I
−6.10739 + 5.95943I 0
u = 1.095990 + 0.142402I
a = −0.345099 − 0.114158I
b = 0.671021 + 0.649697I
−6.10739 + 5.95943I 0
u = 1.095990 − 0.142402I
a = −0.396890 − 0.128629I
b = −0.280943 + 0.633355I
−6.10739 − 5.95943I 0
u = 1.095990 − 0.142402I
a = −0.345099 + 0.114158I
b = 0.671021 − 0.649697I
−6.10739 − 5.95943I 0
u = 0.358153 + 1.115160I
a = 0.843184 + 0.869340I
b = −0.781423 + 0.661689I
4.28468 − 5.58928I 0
u = 0.358153 + 1.115160I
a = −2.01909 − 0.19074I
b = 1.68522 − 0.61722I
4.28468 − 5.58928I 0
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.358153 − 1.115160I
a = 0.843184 − 0.869340I
b = −0.781423 − 0.661689I
4.28468 + 5.58928I 0
u = 0.358153 − 1.115160I
a = −2.01909 + 0.19074I
b = 1.68522 + 0.61722I
4.28468 + 5.58928I 0
u = −0.044759 + 0.769987I
a = 1.78625 + 1.75828I
b = −0.98838 − 2.07654I
−0.982206 − 0.844454I 0
u = −0.044759 + 0.769987I
a = 2.82275 − 0.80695I
b = −0.209346 − 0.628594I
−0.982206 − 0.844454I 0
u = −0.044759 − 0.769987I
a = 1.78625 − 1.75828I
b = −0.98838 + 2.07654I
−0.982206 + 0.844454I 0
u = −0.044759 − 0.769987I
a = 2.82275 + 0.80695I
b = −0.209346 + 0.628594I
−0.982206 + 0.844454I 0
u = 0.330776 + 1.199400I
a = −0.946469 − 0.989763I
b = 0.813263 − 0.304525I
5.39263 − 1.15812I 0
u = 0.330776 + 1.199400I
a = 1.57047 + 0.10732I
b = −1.50830 + 0.58789I
5.39263 − 1.15812I 0
u = 0.330776 − 1.199400I
a = −0.946469 + 0.989763I
b = 0.813263 + 0.304525I
5.39263 + 1.15812I 0
u = 0.330776 − 1.199400I
a = 1.57047 − 0.10732I
b = −1.50830 − 0.58789I
5.39263 + 1.15812I 0
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.369323 + 0.649111I
a = 0.243352 + 0.267315I
b = 0.526307 + 1.292300I
−4.53004 + 8.84379I 0
u = 0.369323 + 0.649111I
a = −2.58061 + 0.83239I
b = 0.728108 − 1.075600I
−4.53004 + 8.84379I 0
u = 0.369323 − 0.649111I
a = 0.243352 − 0.267315I
b = 0.526307 − 1.292300I
−4.53004 − 8.84379I 0
u = 0.369323 − 0.649111I
a = −2.58061 − 0.83239I
b = 0.728108 + 1.075600I
−4.53004 − 8.84379I 0
u = −0.561022 + 0.471335I
a = 0.243530 + 0.297277I
b = 0.243884 + 1.024390I
−5.39263 − 1.15812I 0
u = −0.561022 + 0.471335I
a = −1.54085 + 0.77276I
b = 0.896398 + 0.511751I
−5.39263 − 1.15812I 0
u = −0.561022 − 0.471335I
a = 0.243530 − 0.297277I
b = 0.243884 − 1.024390I
−5.39263 + 1.15812I 0
u = −0.561022 − 0.471335I
a = −1.54085 − 0.77276I
b = 0.896398 − 0.511751I
−5.39263 + 1.15812I 0
u = 0.374728 + 0.600295I
a = 0.1176460 − 0.0657947I
b = −0.587436 − 1.139780I
−1.39107 + 3.59624I 0
u = 0.374728 + 0.600295I
a = 2.35353 − 0.58506I
b = −0.547659 + 0.733776I
−1.39107 + 3.59624I 0
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.374728 − 0.600295I
a = 0.1176460 + 0.0657947I
b = −0.587436 + 1.139780I
−1.39107 − 3.59624I 0
u = 0.374728 − 0.600295I
a = 2.35353 + 0.58506I
b = −0.547659 − 0.733776I
−1.39107 − 3.59624I 0
u = 0.367071 + 1.260570I
a = −0.798354 − 0.858019I
b = 0.931039 − 0.107339I
5.87193 − 0.56893I 0
u = 0.367071 + 1.260570I
a = 1.145840 + 0.516614I
b = −1.265610 + 0.187097I
5.87193 − 0.56893I 0
u = 0.367071 − 1.260570I
a = −0.798354 + 0.858019I
b = 0.931039 + 0.107339I
5.87193 + 0.56893I 0
u = 0.367071 − 1.260570I
a = 1.145840 − 0.516614I
b = −1.265610 − 0.187097I
5.87193 + 0.56893I 0
u = 0.295673 + 0.598047I
a = −0.522578 + 0.581146I
b = 0.370410 + 1.047480I
−5.87193 − 0.56893I −5.71165 + 2.62808I
u = 0.295673 + 0.598047I
a = −2.67253 + 0.19240I
b = 1.018990 − 0.390536I
−5.87193 − 0.56893I −5.71165 + 2.62808I
u = 0.295673 − 0.598047I
a = −0.522578 − 0.581146I
b = 0.370410 − 1.047480I
−5.87193 + 0.56893I −5.71165 − 2.62808I
u = 0.295673 − 0.598047I
a = −2.67253 − 0.19240I
b = 1.018990 + 0.390536I
−5.87193 + 0.56893I −5.71165 − 2.62808I
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.382429 + 1.285840I
a = 0.513393 + 0.703587I
b = −0.852984 + 0.063407I
4.84435 + 2.21317I 0
u = 0.382429 + 1.285840I
a = −0.980146 − 0.766268I
b = 1.116100 + 0.143339I
4.84435 + 2.21317I 0
u = 0.382429 − 1.285840I
a = 0.513393 − 0.703587I
b = −0.852984 − 0.063407I
4.84435 − 2.21317I 0
u = 0.382429 − 1.285840I
a = −0.980146 + 0.766268I
b = 1.116100 − 0.143339I
4.84435 − 2.21317I 0
u = 0.551013 + 1.224120I
a = 1.50347 + 0.41968I
b = −1.36326 + 0.91622I
4.53004 − 8.84379I 0
u = 0.551013 + 1.224120I
a = −1.76358 − 0.29845I
b = 1.55805 − 0.90773I
4.53004 − 8.84379I 0
u = 0.551013 − 1.224120I
a = 1.50347 − 0.41968I
b = −1.36326 − 0.91622I
4.53004 + 8.84379I 0
u = 0.551013 − 1.224120I
a = −1.76358 + 0.29845I
b = 1.55805 + 0.90773I
4.53004 + 8.84379I 0
u = 0.542249 + 1.239600I
a = 1.72699 + 0.12373I
b = −1.51023 + 1.09918I
3.67203 − 11.90650I 0
u = 0.542249 + 1.239600I
a = −1.69535 − 0.41640I
b = 1.39839 − 0.93182I
3.67203 − 11.90650I 0
26
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.542249 − 1.239600I
a = 1.72699 − 0.12373I
b = −1.51023 − 1.09918I
3.67203 + 11.90650I 0
u = 0.542249 − 1.239600I
a = −1.69535 + 0.41640I
b = 1.39839 + 0.93182I
3.67203 + 11.90650I 0
u = −0.380832 + 1.323190I
a = 1.19262 − 0.84227I
b = −0.861585 − 0.399905I
2.50586 + 11.87860I 0
u = −0.380832 + 1.323190I
a = 1.62361 + 0.22942I
b = −1.51757 − 0.91108I
2.50586 + 11.87860I 0
u = −0.380832 − 1.323190I
a = 1.19262 + 0.84227I
b = −0.861585 + 0.399905I
2.50586 − 11.87860I 0
u = −0.380832 − 1.323190I
a = 1.62361 − 0.22942I
b = −1.51757 + 0.91108I
2.50586 − 11.87860I 0
u = 0.032535 + 1.376960I
a = −0.067483 + 1.117620I
b = 0.16064 − 1.58335I
0.520516I 0
u = 0.032535 + 1.376960I
a = 1.79080 + 0.25687I
b = −0.644316 − 0.113122I
0.520516I 0
u = 0.032535 − 1.376960I
a = −0.067483 − 1.117620I
b = 0.16064 + 1.58335I
− 0.520516I 0
u = 0.032535 − 1.376960I
a = 1.79080 − 0.25687I
b = −0.644316 + 0.113122I
− 0.520516I 0
27
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.575559 + 0.132100I
a = −0.254659 + 1.029720I
b = −0.899561 − 0.511447I
1.56173 + 2.08294I 1.60950 − 3.67011I
u = 0.575559 + 0.132100I
a = 0.945682 + 0.649198I
b = 0.732785 − 0.145823I
1.56173 + 2.08294I 1.60950 − 3.67011I
u = 0.575559 − 0.132100I
a = −0.254659 − 1.029720I
b = −0.899561 + 0.511447I
1.56173 − 2.08294I 1.60950 + 3.67011I
u = 0.575559 − 0.132100I
a = 0.945682 − 0.649198I
b = 0.732785 + 0.145823I
1.56173 − 2.08294I 1.60950 + 3.67011I
u = 0.67143 + 1.25283I
a = 0.835340 + 0.222425I
b = −0.990351 + 0.766177I
2.65659 − 7.48205I 0
u = 0.67143 + 1.25283I
a = −1.48861 − 0.39915I
b = 1.34263 − 0.46958I
2.65659 − 7.48205I 0
u = 0.67143 − 1.25283I
a = 0.835340 − 0.222425I
b = −0.990351 − 0.766177I
2.65659 + 7.48205I 0
u = 0.67143 − 1.25283I
a = −1.48861 + 0.39915I
b = 1.34263 + 0.46958I
2.65659 + 7.48205I 0
u = 0.58417 + 1.29672I
a = −1.071870 + 0.156151I
b = 0.94658 − 1.11184I
−2.50586 − 11.87860I 0
u = 0.58417 + 1.29672I
a = 1.60547 + 0.20718I
b = −1.166070 + 0.720746I
−2.50586 − 11.87860I 0
28
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.58417 − 1.29672I
a = −1.071870 − 0.156151I
b = 0.94658 + 1.11184I
−2.50586 + 11.87860I 0
u = 0.58417 − 1.29672I
a = 1.60547 − 0.20718I
b = −1.166070 − 0.720746I
−2.50586 + 11.87860I 0
u = −0.40259 + 1.37690I
a = −1.059920 + 0.600086I
b = 0.839133 + 0.405350I
6.10739 + 5.95943I 0
u = −0.40259 + 1.37690I
a = −1.402550 − 0.068041I
b = 1.29550 + 0.70878I
6.10739 + 5.95943I 0
u = −0.40259 − 1.37690I
a = −1.059920 − 0.600086I
b = 0.839133 − 0.405350I
6.10739 − 5.95943I 0
u = −0.40259 − 1.37690I
a = −1.402550 + 0.068041I
b = 1.29550 − 0.70878I
6.10739 − 5.95943I 0
u = −0.129167 + 0.122817I
a = 0.78075 − 5.53107I
b = 0.336444 − 1.032790I
−1.29549 − 0.75677I −5.76024 + 1.81125I
u = −0.129167 + 0.122817I
a = 6.02259 − 1.91348I
b = −0.661849 − 0.985048I
−1.29549 − 0.75677I −5.76024 + 1.81125I
u = −0.129167 − 0.122817I
a = 0.78075 + 5.53107I
b = 0.336444 + 1.032790I
−1.29549 + 0.75677I −5.76024 − 1.81125I
u = −0.129167 − 0.122817I
a = 6.02259 + 1.91348I
b = −0.661849 + 0.985048I
−1.29549 + 0.75677I −5.76024 − 1.81125I
29
IV. I
u
4
= ⟨−u
7
a
3
+ u
7
a
2
+ · · · − a + 3, u
7
a
3
− u
7
a
2
+ · · · + 3a − 1, u
7
a
2
−
u
7
a + · · · + b + 1, u
8
a
2
− u
8
a + · · · + 2u + 1⟩
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
10
=
a
b
a
8
=
1
2
u
7
a
3
−
1
2
u
7
a
2
+ ··· +
3
2
a +
1
2
u
6
a
2
− u
6
a + ··· + b + 2
a
11
=
b + a
b
a
4
=
−
1
2
u
7
a
3
+
1
2
u
7
a
2
+ ··· +
1
2
a −
1
2
−u
6
a
2
+ u
6
a − 2u
4
a
2
+ u
4
a − a
2
u
2
− u
3
a + u
3
− au − u
2
a
2
=
u
u
3
+ u
a
12
=
−u
3
a + u
3
− au + a − 1
−u
7
a
2
+ u
7
a + ··· − b − 3
a
1
=
−
1
2
u
7
a
4
+
1
4
u
7
a
3
+ ··· −
1
4
a −
7
4
−u
7
a
2
+ u
7
a + ··· − b − 3
a
5
=
−u
7
a
3
+ u
7
a
2
+ ··· − a − 1
1
2
u
7
a
3
−
3
2
u
7
a
2
+ ··· +
1
2
a −
5
2
a
9
=
−
1
2
u
7
a
4
+
7
4
u
7
a
3
+ ··· +
5
4
a +
3
4
u
4
a − u
4
+ u
2
a − au + u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
(iv) u-Polynomials at the component : It cannot be defined for a positive
dimension component.
(v) Riley Polynomials at the component : It cannot be defined for a positive
dimension component.
30
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = ···
a = ···
b = ···
0 0
31
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
28
− 3u
27
+ ··· − 48u + 36)(u
40
− 3u
39
+ ··· − 135u + 27)
c
2
(u
28
+ 4u
27
+ ··· + 13u
2
+ 1)(u
40
+ 17u
39
+ ··· − 2560u − 256)
c
3
, c
10
108(4u
28
+ 4u
27
+ ··· + 3u + 1)(27u
40
− 27u
39
+ ··· + u + 1)
c
4
, c
9
108(4u
28
− 4u
27
+ ··· − 3u + 1)(27u
40
+ 27u
39
+ ··· − u + 1)
c
6
(u
28
− 4u
27
+ ··· + 13u
2
+ 1)(u
40
+ 17u
39
+ ··· − 2560u − 256)
c
7
, c
11
(u
28
+ 3u
27
+ ··· + 48u + 36)(u
40
+ 3u
39
+ ··· + 135u + 27)
c
8
(u
28
− 4u
27
+ ··· + 13u
2
+ 1)(u
40
− 17u
39
+ ··· + 2560u − 256)
c
12
(u
28
+ 4u
27
+ ··· + 13u
2
+ 1)(u
40
− 17u
39
+ ··· + 2560u − 256)
32
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
11
(y
28
+ 7y
27
+ ··· + 6192y + 1296)(y
40
− 7y
39
+ ··· + 2673y + 729)
c
2
, c
6
, c
8
c
12
(y
28
+ 14y
27
+ ··· + 26y + 1)(y
40
+ 17y
39
+ ··· + 65536y + 65536)
c
3
, c
4
, c
9
c
10
11664(16y
28
− 144y
27
+ ··· + 13y + 1)
· (729y
40
− 16767y
39
+ ··· − 59y + 1)
33
