12n
0441
(K12n
0441
)
A knot diagram
1
Linearized knot diagam
3 6 8 7 2 9 11 1 5 7 8 4
Solving Sequence
3,8 4,11
12 1 9 7 5 6 2 10
c
3
c
11
c
12
c
8
c
7
c
4
c
6
c
2
c
10
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−9309481822991u
25
+ 73829652568183u
24
+ ··· + 260029930933511b + 103914726631843,
469820212829242u
25
− 103914726631843u
24
+ ··· + 260029930933511a + 3878572919965900,
u
26
+ 11u
24
+ ··· + 9u + 1i
I
u
2
= h−2.76733 × 10
64
u
39
− 5.89505 × 10
64
u
38
+ ··· + 1.60944 × 10
63
b + 2.15660 × 10
65
,
1.58706 × 10
65
u
39
+ 3.38445 × 10
65
u
38
+ ··· + 1.60944 × 10
63
a − 1.20443 × 10
66
, u
40
+ 2u
39
+ ··· − 31u + 1i
I
u
3
= h23u
9
+ 7u
8
+ 70u
7
+ 16u
6
+ 102u
5
+ 97u
4
+ 66u
3
+ 55u
2
+ 37b − 37u − 9,
− 56u
9
− 9u
8
− 201u
7
+ 27u
6
− 369u
5
− 56u
4
− 402u
3
+ 72u
2
+ 37a − 37u + 149,
u
10
+ 4u
8
− u
7
+ 8u
6
+ 9u
4
− u
3
+ 2u
2
− 2u − 1i
I
u
4
= h−9u
7
+ 2u
6
− 53u
5
+ 24u
4
− 91u
3
+ 41u
2
+ 13b − 62u + 18,
− u
7
− 6u
5
+ 2u
4
− 10u
3
+ 6u
2
+ a − 7u + 4, u
8
+ 6u
6
− 2u
5
+ 10u
4
− 6u
3
+ 7u
2
− 4u + 1i
I
u
5
= hb − u + 1, a, u
2
− u + 1i
* 5 irreducible components of dim
C
= 0, with total 86 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−9.31 × 10
12
u
25
+ 7.38 × 10
13
u
24
+ · · · + 2.60 × 10
14
b + 1.04 ×
10
14
, 4.70 × 10
14
u
25
− 1.04 × 10
14
u
24
+ · · · + 2.60 × 10
14
a + 3.88 ×
10
15
, u
26
+ 11u
24
+ · · · + 9u + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
11
=
−1.80679u
25
+ 0.399626u
24
+ ··· − 40.3048u − 14.9159
0.0358016u
25
− 0.283928u
24
+ ··· − 0.789841u − 0.399626
a
12
=
−1.80679u
25
+ 0.399626u
24
+ ··· − 40.3048u − 14.9159
0.0716032u
25
− 0.567855u
24
+ ··· − 2.57968u − 0.799252
a
1
=
−1.77099u
25
+ 0.115699u
24
+ ··· − 41.0946u − 15.3155
−0.169902u
25
− 0.371239u
24
+ ··· − 0.0601367u − 0.515325
a
9
=
3.57844u
25
− 0.00928018u
24
+ ··· + 60.7654u + 24.7620
0.339222u
25
− 0.587326u
24
+ ··· − 7.69123u − 0.0242533
a
7
=
−3.14858u
25
− 0.276584u
24
+ ··· − 69.8097u − 24.6725
0.0250668u
25
+ 0.127352u
24
+ ··· + 4.84799u − 0.123042
a
5
=
0.0553456u
25
+ 0.301266u
24
+ ··· − 9.68720u − 7.23255
−0.0310923u
25
+ 0.0379551u
24
+ ··· − 1.69626u − 0.240398
a
6
=
1.98609u
25
− 1.47838u
24
+ ··· + 22.3075u + 16.0739
−0.0620066u
25
+ 0.275777u
24
+ ··· + 9.47790u + 1.77196
a
2
=
−1.60109u
25
+ 0.486937u
24
+ ··· − 41.0345u − 14.8002
−0.169902u
25
− 0.371239u
24
+ ··· − 0.0601367u − 0.515325
a
10
=
3.27718u
25
+ 0.178388u
24
+ ··· + 68.4960u + 24.8174
0.301266u
25
− 0.187668u
24
+ ··· − 7.73066u − 0.0553456
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
2458339353424590
260029930933511
u
25
+
166778339040524
260029930933511
u
24
+ ··· +
28387935709051593
260029930933511
u +
7983772528255336
260029930933511
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
26
+ 7u
25
+ ··· + 769u + 16
c
2
, c
5
u
26
+ 7u
25
+ ··· − 43u − 4
c
3
, c
9
u
26
+ 11u
24
+ ··· + 9u + 1
c
4
, c
12
u
26
+ 2u
25
+ ··· + 11u + 1
c
6
, c
8
u
26
+ u
25
+ ··· − u − 1
c
7
, c
10
, c
11
u
26
+ 11u
25
+ ··· − 23u − 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
26
+ 17y
25
+ ··· − 418017y + 256
c
2
, c
5
y
26
− 7y
25
+ ··· − 769y + 16
c
3
, c
9
y
26
+ 22y
25
+ ··· − 33y + 1
c
4
, c
12
y
26
− 26y
25
+ ··· − 17y + 1
c
6
, c
8
y
26
− 13y
25
+ ··· − 5y + 1
c
7
, c
10
, c
11
y
26
− 3y
25
+ ··· − 89y + 4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.925328 + 0.204781I
a = 0.576015 − 0.245577I
b = −0.549350 − 0.213489I
−1.185780 − 0.477506I −8.56678 − 2.27892I
u = −0.925328 − 0.204781I
a = 0.576015 + 0.245577I
b = −0.549350 + 0.213489I
−1.185780 + 0.477506I −8.56678 + 2.27892I
u = 0.437987 + 0.957320I
a = −1.273680 − 0.370591I
b = 1.67170 + 0.15777I
4.40116 − 1.97219I −17.1827 − 0.9744I
u = 0.437987 − 0.957320I
a = −1.273680 + 0.370591I
b = 1.67170 − 0.15777I
4.40116 + 1.97219I −17.1827 + 0.9744I
u = 0.248708 + 1.048740I
a = 0.062948 + 0.711511I
b = −0.187797 + 0.343031I
−1.73508 − 1.89801I −8.55455 + 3.04477I
u = 0.248708 − 1.048740I
a = 0.062948 − 0.711511I
b = −0.187797 − 0.343031I
−1.73508 + 1.89801I −8.55455 − 3.04477I
u = 1.033700 + 0.477780I
a = −0.441315 + 0.395879I
b = 0.271845 + 0.374508I
−1.59430 + 2.89984I −9.85116 − 8.11236I
u = 1.033700 − 0.477780I
a = −0.441315 − 0.395879I
b = 0.271845 − 0.374508I
−1.59430 − 2.89984I −9.85116 + 8.11236I
u = 0.152393 + 0.838106I
a = 0.304017 − 0.370147I
b = 0.040457 + 1.167170I
−1.68902 + 1.74396I −6.90590 − 3.41950I
u = 0.152393 − 0.838106I
a = 0.304017 + 0.370147I
b = 0.040457 − 1.167170I
−1.68902 − 1.74396I −6.90590 + 3.41950I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.157882 + 1.174830I
a = 0.147312 + 0.389022I
b = −0.186083 + 0.702237I
−1.75577 − 1.91027I −7.85130 + 3.44778I
u = 0.157882 − 1.174830I
a = 0.147312 − 0.389022I
b = −0.186083 − 0.702237I
−1.75577 + 1.91027I −7.85130 − 3.44778I
u = −0.041568 + 1.314780I
a = −0.962386 + 0.969307I
b = 1.72636 − 0.25395I
8.64541 + 0.35254I −5.05913 − 0.86290I
u = −0.041568 − 1.314780I
a = −0.962386 − 0.969307I
b = 1.72636 + 0.25395I
8.64541 − 0.35254I −5.05913 + 0.86290I
u = 0.091023 + 1.338640I
a = 0.930924 + 0.895385I
b = −1.78763 − 0.03157I
7.58539 − 7.09977I −6.01709 + 4.34352I
u = 0.091023 − 1.338640I
a = 0.930924 − 0.895385I
b = −1.78763 + 0.03157I
7.58539 + 7.09977I −6.01709 − 4.34352I
u = −0.689089 + 1.219170I
a = 0.961669 + 0.093949I
b = −1.50398 − 0.49169I
−0.10698 + 7.65731I −11.70226 − 7.14009I
u = −0.689089 − 1.219170I
a = 0.961669 − 0.093949I
b = −1.50398 + 0.49169I
−0.10698 − 7.65731I −11.70226 + 7.14009I
u = −0.486762
a = 1.08934
b = −0.228656
−0.765965 −12.9500
u = −0.098078 + 0.439549I
a = −0.77333 − 3.25861I
b = −0.237064 + 1.104460I
−5.10383 + 3.18903I −17.4273 − 3.2712I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.098078 − 0.439549I
a = −0.77333 + 3.25861I
b = −0.237064 − 1.104460I
−5.10383 − 3.18903I −17.4273 + 3.2712I
u = 0.50591 + 1.51762I
a = −0.954886 + 0.422620I
b = 1.81183 − 0.81387I
8.81872 − 9.45700I −5.57202 + 4.82775I
u = 0.50591 − 1.51762I
a = −0.954886 − 0.422620I
b = 1.81183 + 0.81387I
8.81872 + 9.45700I −5.57202 − 4.82775I
u = −0.55589 + 1.59469I
a = 0.878916 + 0.428177I
b = −1.76028 − 0.92013I
7.2466 + 15.9916I −8.00000 − 8.39864I
u = −0.55589 − 1.59469I
a = 0.878916 − 0.428177I
b = −1.76028 + 0.92013I
7.2466 − 15.9916I −8.00000 + 8.39864I
u = −0.148557
a = −11.0018
b = −0.391355
−10.0986 22.3080
7
II. I
u
2
= h−2.77 × 10
64
u
39
− 5.90 × 10
64
u
38
+ · · · + 1.61 × 10
63
b + 2.16 ×
10
65
, 1.59 × 10
65
u
39
+ 3.38 × 10
65
u
38
+ · · · + 1.61 × 10
63
a − 1.20 ×
10
66
, u
40
+ 2u
39
+ · · · − 31u + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
11
=
−98.6099u
39
− 210.287u
38
+ ··· − 17327.2u + 748.357
17.1944u
39
+ 36.6280u
38
+ ··· + 3110.76u − 133.997
a
12
=
−98.6099u
39
− 210.287u
38
+ ··· − 17327.2u + 748.357
15.4838u
39
+ 32.9912u
38
+ ··· + 2804.27u − 120.930
a
1
=
−81.4155u
39
− 173.659u
38
+ ··· − 14216.5u + 614.359
15.7727u
39
+ 33.5976u
38
+ ··· + 2856.50u − 123.169
a
9
=
24.3237u
39
+ 51.8494u
38
+ ··· + 4186.11u − 167.565
1.70809u
39
+ 3.60334u
38
+ ··· + 350.584u − 14.1596
a
7
=
−20.2827u
39
− 43.3042u
38
+ ··· − 3387.05u + 134.967
−2.73705u
39
− 5.80246u
38
+ ··· − 523.421u + 21.6408
a
5
=
13.0361u
39
+ 27.9037u
38
+ ··· + 2358.25u − 112.609
5.85766u
39
+ 12.5132u
38
+ ··· + 1011.37u − 44.6712
a
6
=
57.2063u
39
+ 121.962u
38
+ ··· + 9989.28u − 428.196
−12.1175u
39
− 25.8205u
38
+ ··· − 2184.36u + 94.7544
a
2
=
−97.1883u
39
− 207.257u
38
+ ··· − 17073.0u + 737.528
15.7727u
39
+ 33.5976u
38
+ ··· + 2856.50u − 123.169
a
10
=
−182.374u
39
− 388.925u
38
+ ··· − 32001.5u + 1381.43
34.6744u
39
+ 73.8531u
38
+ ··· + 6269.35u − 270.136
(ii) Obstruction class = −1
(iii) Cusp Shapes = −21.2453u
39
− 45.2764u
38
+ ··· − 3927.04u + 165.006
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
20
+ 8u
19
+ ··· + 67u + 9)
2
c
2
, c
5
(u
20
− 2u
19
+ ··· − 7u + 3)
2
c
3
, c
9
u
40
+ 2u
39
+ ··· − 31u + 1
c
4
, c
12
u
40
+ 4u
39
+ ··· + 37u + 1
c
6
, c
8
u
40
+ u
39
+ ··· − 38u + 19
c
7
, c
10
, c
11
(u
20
− 5u
19
+ ··· − 9u + 2)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
20
+ 12y
19
+ ··· − 223y + 81)
2
c
2
, c
5
(y
20
− 8y
19
+ ··· − 67y + 9)
2
c
3
, c
9
y
40
+ 40y
39
+ ··· + 19y + 1
c
4
, c
12
y
40
− 36y
39
+ ··· − 231y + 1
c
6
, c
8
y
40
+ y
39
+ ··· + 5548y + 361
c
7
, c
10
, c
11
(y
20
− y
19
+ ··· + 15y + 4)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.107685 + 0.869000I
a = −0.09684 + 1.48156I
b = −0.316103 + 0.209805I
−1.93389 − 2.53032I −6.19592 + 4.02108I
u = 0.107685 − 0.869000I
a = −0.09684 − 1.48156I
b = −0.316103 − 0.209805I
−1.93389 + 2.53032I −6.19592 − 4.02108I
u = −0.373189 + 1.166640I
a = −0.636181 − 0.287370I
b = 1.69080 + 0.43538I
2.80723 + 3.42080I 0
u = −0.373189 − 1.166640I
a = −0.636181 + 0.287370I
b = 1.69080 − 0.43538I
2.80723 − 3.42080I 0
u = 1.163750 + 0.469682I
a = 0.612522 + 0.298397I
b = −0.004964 − 0.158740I
2.80723 − 3.42080I 0
u = 1.163750 − 0.469682I
a = 0.612522 − 0.298397I
b = −0.004964 + 0.158740I
2.80723 + 3.42080I 0
u = 0.091657 + 1.296970I
a = 0.932233 − 0.746341I
b = −1.73419 − 0.20045I
8.52898 − 1.35152I 0
u = 0.091657 − 1.296970I
a = 0.932233 + 0.746341I
b = −1.73419 + 0.20045I
8.52898 + 1.35152I 0
u = 0.231177 + 0.655143I
a = 0.791547 − 0.146798I
b = −1.64148 + 0.76911I
−2.77919 − 0.72470I −6.99365 + 10.58729I
u = 0.231177 − 0.655143I
a = 0.791547 + 0.146798I
b = −1.64148 − 0.76911I
−2.77919 + 0.72470I −6.99365 − 10.58729I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.615112 + 1.163700I
a = 0.568955 − 0.258845I
b = −1.72547 + 0.43428I
0.70919 − 8.81461I 0
u = 0.615112 − 1.163700I
a = 0.568955 + 0.258845I
b = −1.72547 − 0.43428I
0.70919 + 8.81461I 0
u = −0.110827 + 1.329560I
a = 0.137120 + 0.964756I
b = 0.151293 − 0.864996I
−1.93389 − 2.53032I 0
u = −0.110827 − 1.329560I
a = 0.137120 − 0.964756I
b = 0.151293 + 0.864996I
−1.93389 + 2.53032I 0
u = 0.299939 + 1.358570I
a = −0.641788 − 0.218251I
b = 1.43525 − 0.13921I
4.45736 − 0.35820I 0
u = 0.299939 − 1.358570I
a = −0.641788 + 0.218251I
b = 1.43525 + 0.13921I
4.45736 + 0.35820I 0
u = −0.080772 + 1.395440I
a = −0.824582 − 0.752869I
b = 1.85230 − 0.03442I
8.30234 + 6.78804I 0
u = −0.080772 − 1.395440I
a = −0.824582 + 0.752869I
b = 1.85230 + 0.03442I
8.30234 − 6.78804I 0
u = 0.109439 + 0.536709I
a = 0.04901 + 1.66403I
b = −0.383758 + 1.251790I
−4.22584 + 1.07930I −18.8617 − 0.2582I
u = 0.109439 − 0.536709I
a = 0.04901 − 1.66403I
b = −0.383758 − 1.251790I
−4.22584 − 1.07930I −18.8617 + 0.2582I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.38851 + 0.47418I
a = −0.073304 − 0.374070I
b = −0.386249 + 0.114590I
−2.77919 − 0.72470I 0
u = −1.38851 − 0.47418I
a = −0.073304 + 0.374070I
b = −0.386249 − 0.114590I
−2.77919 + 0.72470I 0
u = 0.48704 + 1.38580I
a = 0.839633 − 0.417130I
b = −1.128480 + 0.324249I
4.71743 − 3.54403I 0
u = 0.48704 − 1.38580I
a = 0.839633 + 0.417130I
b = −1.128480 − 0.324249I
4.71743 + 3.54403I 0
u = −0.40407 + 1.47756I
a = 0.618122 − 0.115570I
b = −1.342100 − 0.439927I
3.26793 + 6.33523I 0
u = −0.40407 − 1.47756I
a = 0.618122 + 0.115570I
b = −1.342100 + 0.439927I
3.26793 − 6.33523I 0
u = −0.27827 + 1.51128I
a = −0.730955 − 0.518496I
b = 1.66383 + 0.37308I
4.71743 + 3.54403I 0
u = −0.27827 − 1.51128I
a = −0.730955 + 0.518496I
b = 1.66383 − 0.37308I
4.71743 − 3.54403I 0
u = −1.54083 + 0.63283I
a = −0.476317 + 0.130739I
b = −0.0700266 + 0.0232375I
0.70919 + 8.81461I 0
u = −1.54083 − 0.63283I
a = −0.476317 − 0.130739I
b = −0.0700266 − 0.0232375I
0.70919 − 8.81461I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.35133 + 1.67126I
a = −0.780533 − 0.466237I
b = 1.62791 + 0.86433I
8.52898 + 1.35152I 0
u = −0.35133 − 1.67126I
a = −0.780533 + 0.466237I
b = 1.62791 − 0.86433I
8.52898 − 1.35152I 0
u = −0.17475 + 1.70544I
a = 0.173717 + 0.502733I
b = −0.090864 − 1.013700I
−4.22584 + 1.07930I 0
u = −0.17475 − 1.70544I
a = 0.173717 − 0.502733I
b = −0.090864 + 1.013700I
−4.22584 − 1.07930I 0
u = 0.42173 + 1.68142I
a = 0.766594 − 0.472156I
b = −1.44211 + 0.94264I
8.30234 − 6.78804I 0
u = 0.42173 − 1.68142I
a = 0.766594 + 0.472156I
b = −1.44211 − 0.94264I
8.30234 + 6.78804I 0
u = 0.1305640 + 0.0006413I
a = 0.76135 − 7.18315I
b = 0.314121 + 1.236250I
4.45736 − 0.35820I −3.17120 − 1.48913I
u = 0.1305640 − 0.0006413I
a = 0.76135 + 7.18315I
b = 0.314121 − 1.236250I
4.45736 + 0.35820I −3.17120 + 1.48913I
u = 0.0444473 + 0.0647209I
a = 9.50970 + 7.75152I
b = −0.46972 + 1.51512I
3.26793 + 6.33523I −4.73548 − 4.55872I
u = 0.0444473 − 0.0647209I
a = 9.50970 − 7.75152I
b = −0.46972 − 1.51512I
3.26793 − 6.33523I −4.73548 + 4.55872I
14
III. I
u
3
= h23u
9
+ 7u
8
+ · · · + 37b − 9, −56u
9
− 9u
8
+ · · · + 37a + 149, u
10
+
4u
8
− u
7
+ 8u
6
+ 9u
4
− u
3
+ 2u
2
− 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
11
=
56
37
u
9
+
9
37
u
8
+ ··· + u −
149
37
−
23
37
u
9
−
7
37
u
8
+ ··· + u +
9
37
a
12
=
56
37
u
9
+
9
37
u
8
+ ··· + u −
149
37
−1.24324u
9
− 0.378378u
8
+ ··· + 3u + 0.486486
a
1
=
33
37
u
9
+
2
37
u
8
+ ··· + 2u −
140
37
−0.648649u
9
− 0.675676u
8
+ ··· + 2u + 0.297297
a
9
=
−1.89189u
9
− 0.0540541u
8
+ ··· − 5u + 5.78378
1
37
u
9
+
18
37
u
8
+ ··· − 2u −
2
37
a
7
=
2.21622u
9
+ 0.891892u
8
+ ··· + 2u − 6.43243
−0.324324u
9
− 0.837838u
8
+ ··· + 3u + 0.648649
a
5
=
12
37
u
9
−
6
37
u
8
+ ··· − u +
87
37
−
10
37
u
9
+
5
37
u
8
+ ··· − u −
17
37
a
6
=
−0.540541u
9
+ 1.27027u
8
+ ··· − 6u + 3.08108
−
19
37
u
9
−
9
37
u
8
+ ··· + u +
38
37
a
2
=
1.54054u
9
+ 0.729730u
8
+ ··· + 0.162162u
2
− 4.08108
−0.648649u
9
− 0.675676u
8
+ ··· + 2u + 0.297297
a
10
=
−2.05405u
9
− 0.972973u
8
+ ··· − 2u + 6.10811
6
37
u
9
+
34
37
u
8
+ ··· − 3u −
12
37
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
205
37
u
9
−
84
37
u
8
+
936
37
u
7
−
673
37
u
6
+
2106
37
u
5
−
1127
37
u
4
+
2612
37
u
3
−
1326
37
u
2
+ 23u −
1150
37
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
− 2u
9
+ 5u
8
− 4u
7
+ 4u
6
− 7u
5
+ 22u
4
− 54u
3
+ 40u
2
− 9u + 1
c
2
u
10
+ 4u
9
+ 7u
8
+ 4u
7
− 6u
6
− 15u
5
− 12u
4
+ 8u
2
+ 5u + 1
c
3
, c
9
u
10
+ 4u
8
− u
7
+ 8u
6
+ 9u
4
− u
3
+ 2u
2
− 2u − 1
c
4
, c
12
u
10
+ 2u
9
− 4u
8
− 8u
7
+ 6u
6
+ 8u
5
− 6u
4
+ 3u
3
+ 4u
2
− 6u + 1
c
5
u
10
− 4u
9
+ 7u
8
− 4u
7
− 6u
6
+ 15u
5
− 12u
4
+ 8u
2
− 5u + 1
c
6
, c
8
u
10
+ u
9
− u
8
+ 2u
7
+ u
6
− 2u
5
+ 3u
4
− u
3
− 2u
2
+ 2u − 1
c
7
u
10
+ 8u
9
+ ··· − 2u − 3
c
10
, c
11
u
10
− 8u
9
+ ··· + 2u − 3
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
10
+ 6y
9
+ ··· − y + 1
c
2
, c
5
y
10
− 2y
9
+ 5y
8
− 4y
7
+ 4y
6
− 7y
5
+ 22y
4
− 54y
3
+ 40y
2
− 9y + 1
c
3
, c
9
y
10
+ 8y
9
+ ··· − 8y + 1
c
4
, c
12
y
10
− 12y
9
+ ··· − 28y + 1
c
6
, c
8
y
10
− 3y
9
− y
8
+ 4y
7
+ y
6
+ 4y
5
− 5y
4
− 7y
3
+ 2y
2
+ 1
c
7
, c
10
, c
11
y
10
− 6y
9
+ 5y
8
+ 13y
7
+ 47y
5
− 51y
4
− 237y
3
− 174y
2
− 88y + 9
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.113601 + 0.927431I
a = −0.11490 − 1.98015I
b = −0.206295 + 0.774410I
−4.12954 + 3.49860I −9.01209 − 4.51290I
u = −0.113601 − 0.927431I
a = −0.11490 + 1.98015I
b = −0.206295 − 0.774410I
−4.12954 − 3.49860I −9.01209 + 4.51290I
u = −0.495456 + 0.987445I
a = −1.009770 + 0.387931I
b = 1.61173 − 0.28244I
4.73376 + 2.16483I 1.22717 − 8.71022I
u = −0.495456 − 0.987445I
a = −1.009770 − 0.387931I
b = 1.61173 + 0.28244I
4.73376 − 2.16483I 1.22717 + 8.71022I
u = 0.609357
a = −0.481071
b = −0.787987
−3.04786 −13.9390
u = 0.84505 + 1.13903I
a = 0.589363 + 0.076741I
b = −1.336550 − 0.049223I
2.04346 − 8.28564I −5.35537 + 8.10267I
u = 0.84505 − 1.13903I
a = 0.589363 − 0.076741I
b = −1.336550 + 0.049223I
2.04346 + 8.28564I −5.35537 − 8.10267I
u = −0.37880 + 1.49046I
a = −0.751588 − 0.458927I
b = 1.42239 + 0.31186I
5.62989 + 3.50299I −1.76700 − 2.21802I
u = −0.37880 − 1.49046I
a = −0.751588 + 0.458927I
b = 1.42239 − 0.31186I
5.62989 − 3.50299I −1.76700 + 2.21802I
u = −0.323747
a = −4.94514
b = −0.194564
−10.2174 −45.2470
18
IV. I
u
4
= h−9u
7
+ 2u
6
+ · · · + 13b + 18, −u
7
− 6u
5
+ 2u
4
− 10u
3
+ 6u
2
+ a −
7u + 4, u
8
+ 6u
6
− 2u
5
+ 10u
4
− 6u
3
+ 7u
2
− 4u + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
11
=
u
7
+ 6u
5
− 2u
4
+ 10u
3
− 6u
2
+ 7u − 4
0.692308u
7
− 0.153846u
6
+ ··· + 4.76923u − 1.38462
a
12
=
u
7
+ 6u
5
− 2u
4
+ 10u
3
− 6u
2
+ 7u − 4
0.692308u
7
− 0.153846u
6
+ ··· + 3.76923u − 1.38462
a
1
=
1.69231u
7
− 0.153846u
6
+ ··· + 11.7692u − 5.38462
0.615385u
7
+ 0.307692u
6
+ ··· + 2.46154u − 1.23077
a
9
=
2.38462u
7
− 0.307692u
6
+ ··· + 17.5385u − 6.76923
0.538462u
7
+ 0.769231u
6
+ ··· + 3.15385u − 1.07692
a
7
=
−u
7
− 6u
5
+ 2u
4
− 10u
3
+ 6u
2
− 7u + 4
−0.692308u
7
+ 0.153846u
6
+ ··· − 3.76923u + 1.38462
a
5
=
1.38462u
7
+ 0.692308u
6
+ ··· + 6.53846u + 0.230769
−0.153846u
7
− 0.0769231u
6
+ ··· + 1.38462u + 0.307692
a
6
=
−0.230769u
7
− 0.615385u
6
+ ··· + 1.07692u + 2.46154
−0.846154u
7
+ 0.0769231u
6
+ ··· − 3.38462u + 1.69231
a
2
=
1.07692u
7
− 0.461538u
6
+ ··· + 9.30769u − 4.15385
0.615385u
7
+ 0.307692u
6
+ ··· + 2.46154u − 1.23077
a
10
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
32
13
u
7
−
16
13
u
6
−
200
13
u
5
−
36
13
u
4
− 24u
3
+
36
13
u
2
−
128
13
u −
144
13
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
4
c
2
, c
5
(u
4
− u
2
+ 1)
2
c
3
, c
9
u
8
+ 6u
6
− 2u
5
+ 10u
4
− 6u
3
+ 7u
2
− 4u + 1
c
4
, c
12
(u
2
+ 1)
4
c
6
, c
8
u
8
− 4u
7
+ 2u
6
+ 8u
5
− 6u
4
− 6u
3
+ 3u
2
+ 2u + 1
c
7
(u − 1)
8
c
10
, c
11
(u + 1)
8
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
4
c
2
, c
5
(y
2
− y + 1)
4
c
3
, c
9
y
8
+ 12y
7
+ 56y
6
+ 130y
5
+ 162y
4
+ 100y
3
+ 21y
2
− 2y + 1
c
4
, c
12
(y + 1)
8
c
6
, c
8
y
8
− 12y
7
+ 56y
6
− 130y
5
+ 162y
4
− 100y
3
+ 21y
2
+ 2y + 1
c
7
, c
10
, c
11
(y − 1)
8
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.170691 + 0.964637I
a = −0.177866 + 1.005190I
b = 1.000000I
−3.28987 − 2.02988I −14.0000 + 3.4641I
u = 0.170691 − 0.964637I
a = −0.177866 − 1.005190I
b = − 1.000000I
−3.28987 + 2.02988I −14.0000 − 3.4641I
u = −0.351035 + 1.212180I
a = 0.220415 + 0.761130I
b = − 1.000000I
−3.28987 − 2.02988I −14.0000 + 3.4641I
u = −0.351035 − 1.212180I
a = 0.220415 − 0.761130I
b = 1.000000I
−3.28987 + 2.02988I −14.0000 − 3.4641I
u = 0.351035 + 0.212180I
a = −2.08644 + 1.26113I
b = 1.000000I
−3.28987 + 2.02988I −14.0000 − 3.4641I
u = 0.351035 − 0.212180I
a = −2.08644 − 1.26113I
b = − 1.000000I
−3.28987 − 2.02988I −14.0000 + 3.4641I
u = −0.17069 + 1.96464I
a = 0.043891 + 0.505187I
b = − 1.000000I
−3.28987 + 2.02988I −14.0000 − 3.4641I
u = −0.17069 − 1.96464I
a = 0.043891 − 0.505187I
b = 1.000000I
−3.28987 − 2.02988I −14.0000 + 3.4641I
22
V. I
u
5
= hb − u + 1, a, u
2
− u + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u − 1
a
11
=
0
u − 1
a
12
=
0
u − 1
a
1
=
u − 1
−1
a
9
=
u − 1
u − 1
a
7
=
0
u
a
5
=
1
0
a
6
=
−u + 1
1
a
2
=
u
−1
a
10
=
0
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −15
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
8
(u − 1)
2
c
3
, c
4
, c
9
c
12
u
2
− u + 1
c
5
(u + 1)
2
c
7
, c
10
, c
11
u
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
8
(y − 1)
2
c
3
, c
4
, c
9
c
12
y
2
+ y + 1
c
7
, c
10
, c
11
y
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0
b = −0.500000 + 0.866025I
−3.28987 −15.0000
u = 0.500000 − 0.866025I
a = 0
b = −0.500000 − 0.866025I
−3.28987 −15.0000
26
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
(u
2
− u + 1)
4
· (u
10
− 2u
9
+ 5u
8
− 4u
7
+ 4u
6
− 7u
5
+ 22u
4
− 54u
3
+ 40u
2
− 9u + 1)
· ((u
20
+ 8u
19
+ ··· + 67u + 9)
2
)(u
26
+ 7u
25
+ ··· + 769u + 16)
c
2
(u − 1)
2
(u
4
− u
2
+ 1)
2
· (u
10
+ 4u
9
+ 7u
8
+ 4u
7
− 6u
6
− 15u
5
− 12u
4
+ 8u
2
+ 5u + 1)
· ((u
20
− 2u
19
+ ··· − 7u + 3)
2
)(u
26
+ 7u
25
+ ··· − 43u − 4)
c
3
, c
9
(u
2
− u + 1)(u
8
+ 6u
6
− 2u
5
+ 10u
4
− 6u
3
+ 7u
2
− 4u + 1)
· (u
10
+ 4u
8
− u
7
+ 8u
6
+ 9u
4
− u
3
+ 2u
2
− 2u − 1)
· (u
26
+ 11u
24
+ ··· + 9u + 1)(u
40
+ 2u
39
+ ··· − 31u + 1)
c
4
, c
12
(u
2
+ 1)
4
(u
2
− u + 1)
· (u
10
+ 2u
9
− 4u
8
− 8u
7
+ 6u
6
+ 8u
5
− 6u
4
+ 3u
3
+ 4u
2
− 6u + 1)
· (u
26
+ 2u
25
+ ··· + 11u + 1)(u
40
+ 4u
39
+ ··· + 37u + 1)
c
5
(u + 1)
2
(u
4
− u
2
+ 1)
2
· (u
10
− 4u
9
+ 7u
8
− 4u
7
− 6u
6
+ 15u
5
− 12u
4
+ 8u
2
− 5u + 1)
· ((u
20
− 2u
19
+ ··· − 7u + 3)
2
)(u
26
+ 7u
25
+ ··· − 43u − 4)
c
6
, c
8
(u − 1)
2
(u
8
− 4u
7
+ 2u
6
+ 8u
5
− 6u
4
− 6u
3
+ 3u
2
+ 2u + 1)
· (u
10
+ u
9
− u
8
+ 2u
7
+ u
6
− 2u
5
+ 3u
4
− u
3
− 2u
2
+ 2u − 1)
· (u
26
+ u
25
+ ··· − u − 1)(u
40
+ u
39
+ ··· − 38u + 19)
c
7
u
2
(u − 1)
8
(u
10
+ 8u
9
+ ··· − 2u − 3)(u
20
− 5u
19
+ ··· − 9u + 2)
2
· (u
26
+ 11u
25
+ ··· − 23u − 2)
c
10
, c
11
u
2
(u + 1)
8
(u
10
− 8u
9
+ ··· + 2u − 3)(u
20
− 5u
19
+ ··· − 9u + 2)
2
· (u
26
+ 11u
25
+ ··· − 23u − 2)
27
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
2
)(y
2
+ y + 1)
4
(y
10
+ 6y
9
+ ··· − y + 1)
· (y
20
+ 12y
19
+ ··· − 223y + 81)
2
· (y
26
+ 17y
25
+ ··· − 418017y + 256)
c
2
, c
5
(y − 1)
2
(y
2
− y + 1)
4
· (y
10
− 2y
9
+ 5y
8
− 4y
7
+ 4y
6
− 7y
5
+ 22y
4
− 54y
3
+ 40y
2
− 9y + 1)
· ((y
20
− 8y
19
+ ··· − 67y + 9)
2
)(y
26
− 7y
25
+ ··· − 769y + 16)
c
3
, c
9
(y
2
+ y + 1)
· (y
8
+ 12y
7
+ 56y
6
+ 130y
5
+ 162y
4
+ 100y
3
+ 21y
2
− 2y + 1)
· (y
10
+ 8y
9
+ ··· − 8y + 1)(y
26
+ 22y
25
+ ··· − 33y + 1)
· (y
40
+ 40y
39
+ ··· + 19y + 1)
c
4
, c
12
((y + 1)
8
)(y
2
+ y + 1)(y
10
− 12y
9
+ ··· − 28y + 1)
· (y
26
− 26y
25
+ ··· − 17y + 1)(y
40
− 36y
39
+ ··· − 231y + 1)
c
6
, c
8
((y − 1)
2
)(y
8
− 12y
7
+ ··· + 2y + 1)
· (y
10
− 3y
9
− y
8
+ 4y
7
+ y
6
+ 4y
5
− 5y
4
− 7y
3
+ 2y
2
+ 1)
· (y
26
− 13y
25
+ ··· − 5y + 1)(y
40
+ y
39
+ ··· + 5548y + 361)
c
7
, c
10
, c
11
y
2
(y − 1)
8
· (y
10
− 6y
9
+ 5y
8
+ 13y
7
+ 47y
5
− 51y
4
− 237y
3
− 174y
2
− 88y + 9)
· ((y
20
− y
19
+ ··· + 15y + 4)
2
)(y
26
− 3y
25
+ ··· − 89y + 4)
28
