12a
1211
(K12a
1211
)
A knot diagram
1
Linearized knot diagam
5 6 7 9 10 11 12 4 1 2 3 8
Solving Sequence
4,8
9
5,12
1 2 10 7 3 11 6
c
8
c
4
c
12
c
1
c
9
c
7
c
3
c
11
c
6
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.75820 × 10
1048
u
163
− 3.15201 × 10
1048
u
162
+ ··· + 7.37813 × 10
1048
b − 3.04580 × 10
1050
,
1.81233 × 10
1053
u
163
− 5.92096 × 10
1054
u
162
+ ··· + 2.02597 × 10
1055
a − 4.42522 × 10
1056
,
u
164
− 2u
163
+ ··· − 3386u + 61i
I
u
2
= h−5.26861 × 10
16
u
25
+ 2.05028 × 10
16
u
24
+ ··· + 3.42865 × 10
15
b − 8.25553 × 10
16
,
4.92095 × 10
16
u
25
− 2.56966 × 10
16
u
24
+ ··· + 3.42865 × 10
15
a + 1.11054 × 10
17
, u
26
− u
25
+ ··· + 23u − 1i
I
u
3
= h−u
3
+ b + u − 1, u
5
+ 4u
4
− u
2
+ 3a + 3u + 2, u
6
− u
4
+ 2u
3
+ u
2
− u + 1i
* 3 irreducible components of dim
C
= 0, with total 196 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
= h2.76 × 10
1048
u
163
− 3.15 × 10
1048
u
162
+ · · · + 7.38 × 10
1048
b − 3.05 ×
10
1050
, 1.81 × 10
1053
u
163
− 5.92 × 10
1054
u
162
+ · · · + 2.03 × 10
1055
a − 4.43 ×
10
1056
, u
164
− 2u
163
+ · · · − 3386u + 61i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
5
=
−u
−u
3
+ u
a
12
=
−0.00894549u
163
+ 0.292253u
162
+ ··· + 398.496u + 21.8424
−0.373834u
163
+ 0.427210u
162
+ ··· − 2124.70u + 41.2815
a
1
=
−0.382780u
163
+ 0.719463u
162
+ ··· − 1726.20u + 63.1239
−0.373834u
163
+ 0.427210u
162
+ ··· − 2124.70u + 41.2815
a
2
=
−0.104186u
163
+ 0.429492u
162
+ ··· − 498.173u + 40.4408
−0.441826u
163
+ 0.511079u
162
+ ··· − 2464.92u + 47.6643
a
10
=
−0.171894u
163
+ 0.144356u
162
+ ··· + 465.124u − 54.8742
0.158864u
163
− 0.326697u
162
+ ··· − 480.252u + 6.26403
a
7
=
0.246697u
163
− 0.380836u
162
+ ··· − 1682.95u + 77.4279
0.100974u
163
− 0.192003u
162
+ ··· + 873.840u − 13.7367
a
3
=
−0.366074u
163
+ 0.741373u
162
+ ··· − 1622.52u + 83.2336
0.283184u
163
− 0.109775u
162
+ ··· + 1197.22u − 18.3804
a
11
=
−0.142442u
163
+ 0.0702581u
162
+ ··· − 583.910u − 17.2748
0.105327u
163
− 0.196052u
162
+ ··· − 774.839u + 12.9511
a
6
=
1.01159u
163
− 2.64363u
162
+ ··· − 2987.89u + 108.144
−0.176189u
163
+ 0.321162u
162
+ ··· + 544.973u − 7.21403
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.183937u
163
+ 1.47453u
162
+ ··· − 1344.67u + 46.8656
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
164
+ 7u
163
+ ··· − 114622u − 349484
c
2
u
164
+ 2u
163
+ ··· − 173301u + 10677
c
3
3(3u
164
+ 30u
163
+ ··· − 23u − 1)
c
4
, c
8
u
164
− 2u
163
+ ··· − 3386u + 61
c
5
3(3u
164
− 14u
162
+ ··· + 3228u + 43)
c
6
3(3u
164
− 14u
162
+ ··· − 3228u + 43)
c
7
, c
12
u
164
+ 2u
163
+ ··· + 3386u + 61
c
9
3(3u
164
− 30u
163
+ ··· + 23u − 1)
c
10
u
164
− 2u
163
+ ··· + 173301u + 10677
c
11
u
164
− 7u
163
+ ··· + 114622u − 349484
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
164
− 41y
163
+ ··· − 4668550960796y + 122139066256
c
2
, c
10
y
164
− 34y
163
+ ··· − 9384110787y + 113998329
c
3
, c
9
9(9y
164
+ 168y
163
+ ··· − 3213y + 1)
c
4
, c
7
, c
8
c
12
y
164
− 110y
163
+ ··· − 5163208y + 3721
c
5
, c
6
9(9y
164
− 84y
163
+ ··· − 1.13525 × 10
7
y + 1849)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.798897 + 0.600859I
a = −1.58652 − 1.10809I
b = 1.043510 − 0.483445I
0.39756 − 4.84593I 0
u = 0.798897 − 0.600859I
a = −1.58652 + 1.10809I
b = 1.043510 + 0.483445I
0.39756 + 4.84593I 0
u = −0.763806 + 0.635007I
a = 1.25065 − 0.72745I
b = −0.763806 − 0.635007I
3.87653I 0
u = −0.763806 − 0.635007I
a = 1.25065 + 0.72745I
b = −0.763806 + 0.635007I
− 3.87653I 0
u = −0.936998 + 0.373525I
a = 0.930907 − 0.791991I
b = −1.42614 − 0.93512I
2.66702 + 4.07987I 0
u = −0.936998 − 0.373525I
a = 0.930907 + 0.791991I
b = −1.42614 + 0.93512I
2.66702 − 4.07987I 0
u = −1.011230 + 0.030403I
a = −0.89458 + 2.35109I
b = 1.090610 + 0.363390I
−0.175281 + 0.663751I 0
u = −1.011230 − 0.030403I
a = −0.89458 − 2.35109I
b = 1.090610 − 0.363390I
−0.175281 − 0.663751I 0
u = −0.977792 + 0.007736I
a = 0.51300 − 3.04293I
b = −0.977792 − 0.007736I
− 0.507463I 0
u = −0.977792 − 0.007736I
a = 0.51300 + 3.04293I
b = −0.977792 + 0.007736I
0.507463I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.960617 + 0.124105I
a = 0.235681 − 0.341648I
b = 0.365350 − 0.710425I
−1.70988 + 0.60280I 0
u = −0.960617 − 0.124105I
a = 0.235681 + 0.341648I
b = 0.365350 + 0.710425I
−1.70988 − 0.60280I 0
u = −1.032720 + 0.065105I
a = 0.953281 + 0.485959I
b = −1.46278 + 0.53288I
−2.74159 + 0.88861I 0
u = −1.032720 − 0.065105I
a = 0.953281 − 0.485959I
b = −1.46278 − 0.53288I
−2.74159 − 0.88861I 0
u = 0.963273
a = −1.20577
b = 2.02298
3.88198 0
u = 0.949425 + 0.120762I
a = 0.175869 + 0.128372I
b = 0.07698 + 1.55742I
−0.78508 − 5.40731I 0
u = 0.949425 − 0.120762I
a = 0.175869 − 0.128372I
b = 0.07698 − 1.55742I
−0.78508 + 5.40731I 0
u = −0.006754 + 1.046690I
a = −1.52430 − 0.32954I
b = 1.331860 + 0.369170I
7.13952 + 6.54845I 0
u = −0.006754 − 1.046690I
a = −1.52430 + 0.32954I
b = 1.331860 − 0.369170I
7.13952 − 6.54845I 0
u = 0.086283 + 1.047630I
a = −1.59143 − 0.00241I
b = 1.356670 − 0.282535I
7.20749 − 6.27464I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.086283 − 1.047630I
a = −1.59143 + 0.00241I
b = 1.356670 + 0.282535I
7.20749 + 6.27464I 0
u = 1.074770 + 0.100746I
a = 0.394734 − 0.610938I
b = −0.98104 − 1.33165I
−2.11600 − 5.55049I 0
u = 1.074770 − 0.100746I
a = 0.394734 + 0.610938I
b = −0.98104 + 1.33165I
−2.11600 + 5.55049I 0
u = −0.984874 + 0.458102I
a = −0.0748509 − 0.1043720I
b = 0.554699 − 0.592619I
−1.040880 + 0.811517I 0
u = −0.984874 − 0.458102I
a = −0.0748509 + 0.1043720I
b = 0.554699 + 0.592619I
−1.040880 − 0.811517I 0
u = −1.076700 + 0.166906I
a = 1.56634 − 0.94640I
b = −1.349670 − 0.408498I
−3.03570 + 3.98628I 0
u = −1.076700 − 0.166906I
a = 1.56634 + 0.94640I
b = −1.349670 + 0.408498I
−3.03570 − 3.98628I 0
u = 0.986695 + 0.502565I
a = −0.61025 − 1.29255I
b = 1.149870 − 0.134063I
4.53081 − 4.33380I 0
u = 0.986695 − 0.502565I
a = −0.61025 + 1.29255I
b = 1.149870 + 0.134063I
4.53081 + 4.33380I 0
u = −0.195421 + 1.097560I
a = 1.82772 + 0.41740I
b = −1.345620 − 0.053192I
5.56120 − 5.11329I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.195421 − 1.097560I
a = 1.82772 − 0.41740I
b = −1.345620 + 0.053192I
5.56120 + 5.11329I 0
u = −0.470115 + 0.743651I
a = 0.665886 − 0.437045I
b = 0.091710 + 0.211062I
−1.99149 + 2.63914I 0
u = −0.470115 − 0.743651I
a = 0.665886 + 0.437045I
b = 0.091710 − 0.211062I
−1.99149 − 2.63914I 0
u = −0.856505 + 0.197199I
a = 1.44080 − 0.04041I
b = 0.298357 − 0.180165I
−0.687738 − 0.103671I 0
u = −0.856505 − 0.197199I
a = 1.44080 + 0.04041I
b = 0.298357 + 0.180165I
−0.687738 + 0.103671I 0
u = 0.461785 + 1.023910I
a = −0.520857 + 0.245986I
b = 0.342421 + 0.075790I
0.33309 + 5.06568I 0
u = 0.461785 − 1.023910I
a = −0.520857 − 0.245986I
b = 0.342421 − 0.075790I
0.33309 − 5.06568I 0
u = −0.423919 + 0.764806I
a = −0.203308 + 0.416945I
b = −0.008003 − 0.519204I
−1.68748 + 2.68990I 0
u = −0.423919 − 0.764806I
a = −0.203308 − 0.416945I
b = −0.008003 + 0.519204I
−1.68748 − 2.68990I 0
u = 0.860890 + 0.108703I
a = −0.73831 − 1.48618I
b = 0.993044 − 0.804227I
0.34989 − 4.29120I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.860890 − 0.108703I
a = −0.73831 + 1.48618I
b = 0.993044 + 0.804227I
0.34989 + 4.29120I 0
u = 1.13423
a = 0.110542
b = −1.44475
3.38142 0
u = 1.137900 + 0.144896I
a = 1.23584 + 1.28400I
b = −1.285350 + 0.556809I
−2.07933 − 10.92060I 0
u = 1.137900 − 0.144896I
a = 1.23584 − 1.28400I
b = −1.285350 − 0.556809I
−2.07933 + 10.92060I 0
u = 0.847347 + 0.086135I
a = 0.96361 − 1.68719I
b = −0.646360 − 0.016081I
1.44457 − 2.68465I 0
u = 0.847347 − 0.086135I
a = 0.96361 + 1.68719I
b = −0.646360 + 0.016081I
1.44457 + 2.68465I 0
u = 1.090610 + 0.363390I
a = 0.98490 + 2.18329I
b = −1.011230 + 0.030403I
0.175281 − 0.663751I 0
u = 1.090610 − 0.363390I
a = 0.98490 − 2.18329I
b = −1.011230 − 0.030403I
0.175281 + 0.663751I 0
u = 1.043510 + 0.483445I
a = −0.99622 − 1.06959I
b = 0.798897 − 0.600859I
−0.39756 − 4.84593I 0
u = 1.043510 − 0.483445I
a = −0.99622 + 1.06959I
b = 0.798897 + 0.600859I
−0.39756 + 4.84593I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.149870 + 0.134063I
a = −1.18567 − 0.85008I
b = 0.986695 − 0.502565I
−4.53081 − 4.33380I 0
u = 1.149870 − 0.134063I
a = −1.18567 + 0.85008I
b = 0.986695 + 0.502565I
−4.53081 + 4.33380I 0
u = 0.152711 + 0.817611I
a = −1.46956 − 0.71080I
b = 1.376660 + 0.150410I
7.63231 + 0.40560I 0
u = 0.152711 − 0.817611I
a = −1.46956 + 0.71080I
b = 1.376660 − 0.150410I
7.63231 − 0.40560I 0
u = 0.554699 + 0.592619I
a = 0.944174 + 0.625081I
b = −0.984874 − 0.458102I
1.040880 + 0.811517I 0
u = 0.554699 − 0.592619I
a = 0.944174 − 0.625081I
b = −0.984874 + 0.458102I
1.040880 − 0.811517I 0
u = −1.195730 + 0.036298I
a = −0.752787 + 0.321987I
b = 1.32024 + 0.56199I
−3.50885 − 0.54323I 0
u = −1.195730 − 0.036298I
a = −0.752787 − 0.321987I
b = 1.32024 − 0.56199I
−3.50885 + 0.54323I 0
u = 1.171860 + 0.240590I
a = −0.127633 − 0.562139I
b = −0.041618 − 1.288840I
−1.68961 − 5.60069I 0
u = 1.171860 − 0.240590I
a = −0.127633 + 0.562139I
b = −0.041618 + 1.288840I
−1.68961 + 5.60069I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.365350 + 0.710425I
a = 1.46386 + 0.12391I
b = −0.960617 − 0.124105I
1.70988 + 0.60280I 0
u = 0.365350 − 0.710425I
a = 1.46386 − 0.12391I
b = −0.960617 + 0.124105I
1.70988 − 0.60280I 0
u = −1.191000 + 0.205828I
a = −0.108582 + 0.243410I
b = 0.02588 + 1.63730I
−1.51448 + 4.61341I 0
u = −1.191000 − 0.205828I
a = −0.108582 − 0.243410I
b = 0.02588 − 1.63730I
−1.51448 − 4.61341I 0
u = 0.976181 + 0.729701I
a = −1.82156 − 0.88207I
b = 1.228230 − 0.252391I
0.75099 − 4.04184I 0
u = 0.976181 − 0.729701I
a = −1.82156 + 0.88207I
b = 1.228230 + 0.252391I
0.75099 + 4.04184I 0
u = 1.135540 + 0.459031I
a = 0.933898 + 0.738372I
b = −1.45784 + 0.57451I
4.73064 − 5.03536I 0
u = 1.135540 − 0.459031I
a = 0.933898 − 0.738372I
b = −1.45784 − 0.57451I
4.73064 + 5.03536I 0
u = −0.499041 + 1.144160I
a = 1.156510 − 0.558752I
b = −1.254280 + 0.319827I
5.34717 − 6.30857I 0
u = −0.499041 − 1.144160I
a = 1.156510 + 0.558752I
b = −1.254280 − 0.319827I
5.34717 + 6.30857I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.228230 + 0.252391I
a = −0.441495 − 1.163440I
b = 0.976181 − 0.729701I
−0.75099 − 4.04184I 0
u = 1.228230 − 0.252391I
a = −0.441495 + 1.163440I
b = 0.976181 + 0.729701I
−0.75099 + 4.04184I 0
u = −1.089670 + 0.631278I
a = −1.25503 + 0.72769I
b = 1.39299 + 0.63362I
3.36423 + 12.46140I 0
u = −1.089670 − 0.631278I
a = −1.25503 − 0.72769I
b = 1.39299 − 0.63362I
3.36423 − 12.46140I 0
u = 0.712768 + 0.194411I
a = 0.17258 + 2.03656I
b = 0.712768 − 0.194411I
− 10.3096I 0
u = 0.712768 − 0.194411I
a = 0.17258 − 2.03656I
b = 0.712768 + 0.194411I
10.3096I 0
u = 0.993044 + 0.804227I
a = −1.24226 − 0.95166I
b = 0.860890 − 0.108703I
−0.34989 − 4.29120I 0
u = 0.993044 − 0.804227I
a = −1.24226 + 0.95166I
b = 0.860890 + 0.108703I
−0.34989 + 4.29120I 0
u = 0.290001 + 0.656433I
a = 1.64742 − 0.02995I
b = −1.48126 + 0.20586I
6.36504 − 0.06325I 0
u = 0.290001 − 0.656433I
a = 1.64742 + 0.02995I
b = −1.48126 − 0.20586I
6.36504 + 0.06325I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.041618 + 1.288840I
a = −1.70660 + 0.24675I
b = 1.171860 − 0.240590I
1.68961 − 5.60069I 0
u = −0.041618 − 1.288840I
a = −1.70660 − 0.24675I
b = 1.171860 + 0.240590I
1.68961 + 5.60069I 0
u = −1.254280 + 0.319827I
a = 0.239759 + 0.067016I
b = −0.499041 + 1.144160I
−5.34717 + 6.30857I 0
u = −1.254280 − 0.319827I
a = 0.239759 − 0.067016I
b = −0.499041 − 1.144160I
−5.34717 − 6.30857I 0
u = −0.498755 + 0.469217I
a = −0.278879 + 1.118990I
b = 1.49497 − 0.31440I
3.83945 − 0.42852I 0
u = −0.498755 − 0.469217I
a = −0.278879 − 1.118990I
b = 1.49497 + 0.31440I
3.83945 + 0.42852I 0
u = 0.586784 + 0.335479I
a = 1.295380 − 0.377074I
b = −0.494252 + 0.014336I
1.58612 + 0.23499I 0
u = 0.586784 − 0.335479I
a = 1.295380 + 0.377074I
b = −0.494252 − 0.014336I
1.58612 − 0.23499I 0
u = 0.407004 + 0.529059I
a = 0.753394 + 1.000670I
b = 0.407004 − 0.529059I
− 10.4288I 0
u = 0.407004 − 0.529059I
a = 0.753394 − 1.000670I
b = 0.407004 + 0.529059I
10.4288I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.155670 + 1.325700I
a = 1.49656 + 0.19172I
b = −1.325370 − 0.337835I
4.9356 + 13.8553I 0
u = −0.155670 − 1.325700I
a = 1.49656 − 0.19172I
b = −1.325370 + 0.337835I
4.9356 − 13.8553I 0
u = −1.345620 + 0.053192I
a = −0.353075 − 0.354293I
b = −0.195421 − 1.097560I
−5.56120 − 5.11329I 0
u = −1.345620 − 0.053192I
a = −0.353075 + 0.354293I
b = −0.195421 + 1.097560I
−5.56120 + 5.11329I 0
u = −0.646360 + 0.016081I
a = 0.58802 + 2.20526I
b = 0.847347 − 0.086135I
−1.44457 − 2.68465I 0
u = −0.646360 − 0.016081I
a = 0.58802 − 2.20526I
b = 0.847347 + 0.086135I
−1.44457 + 2.68465I 0
u = −1.325370 + 0.337835I
a = 0.163443 − 0.146730I
b = −0.155670 − 1.325700I
−4.9356 + 13.8553I 0
u = −1.325370 − 0.337835I
a = 0.163443 + 0.146730I
b = −0.155670 + 1.325700I
−4.9356 − 13.8553I 0
u = 1.331860 + 0.369170I
a = 0.067000 + 0.132865I
b = −0.006754 + 1.046690I
−7.13952 − 6.54845I 0
u = 1.331860 − 0.369170I
a = 0.067000 − 0.132865I
b = −0.006754 − 1.046690I
−7.13952 + 6.54845I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.376660 + 0.150410I
a = −0.306043 + 0.150774I
b = 0.152711 + 0.817611I
−7.63231 − 0.40560I 0
u = 1.376660 − 0.150410I
a = −0.306043 − 0.150774I
b = 0.152711 − 0.817611I
−7.63231 + 0.40560I 0
u = 1.356670 + 0.282535I
a = −0.236381 − 0.150176I
b = 0.086283 − 1.047630I
−7.20749 − 6.27464I 0
u = 1.356670 − 0.282535I
a = −0.236381 + 0.150176I
b = 0.086283 + 1.047630I
−7.20749 + 6.27464I 0
u = −1.360390 + 0.282471I
a = −0.447485 + 0.713209I
b = 1.42211 + 0.85253I
1.34662 + 3.43245I 0
u = −1.360390 − 0.282471I
a = −0.447485 − 0.713209I
b = 1.42211 − 0.85253I
1.34662 − 3.43245I 0
u = −1.285350 + 0.556809I
a = −0.80400 + 1.27577I
b = 1.137900 + 0.144896I
2.07933 + 10.92060I 0
u = −1.285350 − 0.556809I
a = −0.80400 − 1.27577I
b = 1.137900 − 0.144896I
2.07933 − 10.92060I 0
u = −1.349670 + 0.408498I
a = 0.302265 − 1.016180I
b = −1.076700 − 0.166906I
3.03570 + 3.98628I 0
u = −1.349670 − 0.408498I
a = 0.302265 + 1.016180I
b = −1.076700 + 0.166906I
3.03570 − 3.98628I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.32024 + 0.56199I
a = 0.738566 + 0.470619I
b = −1.195730 + 0.036298I
3.50885 + 0.54323I 0
u = 1.32024 − 0.56199I
a = 0.738566 − 0.470619I
b = −1.195730 − 0.036298I
3.50885 − 0.54323I 0
u = −1.44475
a = −1.04745
b = 1.13423
−3.38142 0
u = 1.35508 + 0.51304I
a = 1.012630 + 0.766931I
b = −1.42327 + 0.67155I
2.87526 − 12.08470I 0
u = 1.35508 − 0.51304I
a = 1.012630 − 0.766931I
b = −1.42327 − 0.67155I
2.87526 + 12.08470I 0
u = −1.38671 + 0.50001I
a = 0.918276 − 0.890188I
b = −1.37123 − 0.55799I
2.59907 + 11.77920I 0
u = −1.38671 − 0.50001I
a = 0.918276 + 0.890188I
b = −1.37123 + 0.55799I
2.59907 − 11.77920I 0
u = −1.37123 + 0.55799I
a = 1.29967 − 0.77049I
b = −1.38671 − 0.50001I
−2.59907 + 11.77920I 0
u = −1.37123 − 0.55799I
a = 1.29967 + 0.77049I
b = −1.38671 + 0.50001I
−2.59907 − 11.77920I 0
u = −0.008003 + 0.519204I
a = −0.222744 + 0.326596I
b = −0.423919 − 0.764806I
1.68748 + 2.68990I 7.29861 − 4.99949I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.008003 − 0.519204I
a = −0.222744 − 0.326596I
b = −0.423919 + 0.764806I
1.68748 − 2.68990I 7.29861 + 4.99949I
u = −0.155219 + 0.483254I
a = 1.23021 − 2.08133I
b = 0.057549 + 0.199970I
1.31809 + 3.60191I 8.56739 − 4.52838I
u = −0.155219 − 0.483254I
a = 1.23021 + 2.08133I
b = 0.057549 − 0.199970I
1.31809 − 3.60191I 8.56739 + 4.52838I
u = −1.48126 + 0.20586I
a = −0.0592996 + 0.0998339I
b = 0.290001 + 0.656433I
−6.36504 + 0.06325I 0
u = −1.48126 − 0.20586I
a = −0.0592996 − 0.0998339I
b = 0.290001 − 0.656433I
−6.36504 − 0.06325I 0
u = −0.494252 + 0.014336I
a = 1.193040 + 0.147730I
b = 0.586784 + 0.335479I
−1.58612 − 0.23499I −6.46746 − 1.50521I
u = −0.494252 − 0.014336I
a = 1.193040 − 0.147730I
b = 0.586784 − 0.335479I
−1.58612 + 0.23499I −6.46746 + 1.50521I
u = 1.49497 + 0.31440I
a = 0.653177 − 0.024109I
b = −0.498755 − 0.469217I
−3.83945 − 0.42852I 0
u = 1.49497 − 0.31440I
a = 0.653177 + 0.024109I
b = −0.498755 + 0.469217I
−3.83945 + 0.42852I 0
u = 1.39299 + 0.63362I
a = 0.978354 + 0.557346I
b = −1.089670 + 0.631278I
−3.36423 − 12.46140I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.39299 − 0.63362I
a = 0.978354 − 0.557346I
b = −1.089670 − 0.631278I
−3.36423 + 12.46140I 0
u = −1.46278 + 0.53288I
a = 0.516159 − 0.553946I
b = −1.032720 + 0.065105I
2.74159 − 0.88861I 0
u = −1.46278 − 0.53288I
a = 0.516159 + 0.553946I
b = −1.032720 − 0.065105I
2.74159 + 0.88861I 0
u = 0.07698 + 1.55742I
a = −1.045890 − 0.028272I
b = 0.949425 + 0.120762I
0.78508 + 5.40731I 0
u = 0.07698 − 1.55742I
a = −1.045890 + 0.028272I
b = 0.949425 − 0.120762I
0.78508 − 5.40731I 0
u = 1.56599
a = −0.482884
b = 0.0268950
−8.52468 0
u = −1.45784 + 0.57451I
a = −1.003620 + 0.462150I
b = 1.135540 + 0.459031I
−4.73064 + 5.03536I 0
u = −1.45784 − 0.57451I
a = −1.003620 − 0.462150I
b = 1.135540 − 0.459031I
−4.73064 − 5.03536I 0
u = 1.45165 + 0.59533I
a = −1.132840 − 0.694788I
b = 1.45165 − 0.59533I
− 20.4896I 0
u = 1.45165 − 0.59533I
a = −1.132840 + 0.694788I
b = 1.45165 + 0.59533I
20.4896I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42327 + 0.67155I
a = −1.215300 + 0.648111I
b = 1.35508 + 0.51304I
−2.87526 + 12.08470I 0
u = −1.42327 − 0.67155I
a = −1.215300 − 0.648111I
b = 1.35508 − 0.51304I
−2.87526 − 12.08470I 0
u = 0.388734
a = 1.75056
b = −1.72165
6.81230 −19.9630
u = 1.63044
a = −1.04538
b = 1.68678
−1.46107 0
u = 0.02588 + 1.63730I
a = 1.380900 − 0.154441I
b = −1.191000 + 0.205828I
1.51448 − 4.61341I 0
u = 0.02588 − 1.63730I
a = 1.380900 + 0.154441I
b = −1.191000 − 0.205828I
1.51448 + 4.61341I 0
u = 0.342421 + 0.075790I
a = 1.167660 − 0.158827I
b = 0.461785 + 1.023910I
−0.33309 − 5.06568I −0.32464 + 10.65498I
u = 0.342421 − 0.075790I
a = 1.167660 + 0.158827I
b = 0.461785 − 1.023910I
−0.33309 + 5.06568I −0.32464 − 10.65498I
u = 0.298357 + 0.180165I
a = 4.34060 − 0.83839I
b = −0.856505 − 0.197199I
0.687738 − 0.103671I 8.44993 + 5.47981I
u = 0.298357 − 0.180165I
a = 4.34060 + 0.83839I
b = −0.856505 + 0.197199I
0.687738 + 0.103671I 8.44993 − 5.47981I
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.98104 + 1.33165I
a = −1.200820 + 0.558416I
b = 1.074770 − 0.100746I
2.11600 − 5.55049I 0
u = −0.98104 − 1.33165I
a = −1.200820 − 0.558416I
b = 1.074770 + 0.100746I
2.11600 + 5.55049I 0
u = 1.42211 + 0.85253I
a = 1.48977 + 0.41110I
b = −1.360390 + 0.282471I
−1.34662 − 3.43245I 0
u = 1.42211 − 0.85253I
a = 1.48977 − 0.41110I
b = −1.360390 − 0.282471I
−1.34662 + 3.43245I 0
u = 1.68678
a = −0.619979
b = 1.63044
1.46107 0
u = −1.42614 + 0.93512I
a = 1.004750 − 0.346221I
b = −0.936998 − 0.373525I
−2.66702 + 4.07987I 0
u = −1.42614 − 0.93512I
a = 1.004750 + 0.346221I
b = −0.936998 + 0.373525I
−2.66702 − 4.07987I 0
u = −1.72165
a = 0.00652916
b = 0.388734
−6.81230 0
u = 0.091710 + 0.211062I
a = −2.34302 − 1.90931I
b = −0.470115 + 0.743651I
1.99149 − 2.63914I 8.08632 + 6.08519I
u = 0.091710 − 0.211062I
a = −2.34302 + 1.90931I
b = −0.470115 − 0.743651I
1.99149 + 2.63914I 8.08632 − 6.08519I
20
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.057549 + 0.199970I
a = −5.16534 + 2.06047I
b = −0.155219 + 0.483254I
−1.31809 − 3.60191I −8.56739 + 4.52838I
u = 0.057549 − 0.199970I
a = −5.16534 − 2.06047I
b = −0.155219 − 0.483254I
−1.31809 + 3.60191I −8.56739 − 4.52838I
u = 0.0268950
a = 26.5504
b = 1.56599
8.52468 13.3390
u = 2.02298
a = −0.389126
b = 0.963273
−3.88198 0
21
II.
I
u
2
= h−5.27×10
16
u
25
+2.05×10
16
u
24
+· · ·+3.43×10
15
b−8.26×10
16
, 4.92×
10
16
u
25
−2.57×10
16
u
24
+· · ·+3.43×10
15
a+1.11×10
17
, u
26
−u
25
+· · ·+23u−1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
5
=
−u
−u
3
+ u
a
12
=
−14.3525u
25
+ 7.49467u
24
+ ··· + 560.191u − 32.3899
15.3665u
25
− 5.97984u
24
+ ··· − 552.598u + 24.0781
a
1
=
1.01399u
25
+ 1.51483u
24
+ ··· + 7.59317u − 8.31185
15.3665u
25
− 5.97984u
24
+ ··· − 552.598u + 24.0781
a
2
=
−5.01455u
25
+ 3.45005u
24
+ ··· + 219.539u − 18.1676
19.1393u
25
− 7.37482u
24
+ ··· − 676.426u + 29.8406
a
10
=
−69.6316u
25
+ 28.6474u
24
+ ··· + 2445.57u − 127.201
5.13718u
25
− 1.68516u
24
+ ··· − 168.083u + 4.68301
a
7
=
43.1205u
25
− 16.5489u
24
+ ··· − 1489.15u + 81.1117
18.0048u
25
− 7.33507u
24
+ ··· − 627.342u + 32.5583
a
3
=
−32.8811u
25
+ 12.8170u
24
+ ··· + 1187.04u − 49.3843
61.6923u
25
− 22.0465u
24
+ ··· − 2075.41u + 98.6091
a
11
=
−91.5019u
25
+ 36.5625u
24
+ ··· + 3207.96u − 151.919
−47.3217u
25
+ 17.4796u
24
+ ··· + 1582.99u − 74.3933
a
6
=
−119.764u
25
+ 48.6106u
24
+ ··· + 4487.30u − 201.516
35.5925u
25
− 15.6666u
24
+ ··· − 1270.94u + 62.1390
(ii) Obstruction class = 1
(iii) Cusp Shapes =
843781875852968090
3428645656387843
u
25
−
333222561187417665
3428645656387843
u
24
+ ··· −
29770331489875929664
3428645656387843
u +
1510384610757036397
3428645656387843
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
26
− u
25
+ ··· + 8u − 1
c
2
u
26
− 2u
25
+ ··· − 13u − 1
c
3
u
26
− 5u
25
+ ··· + 10u + 1
c
4
, c
12
u
26
+ u
25
+ ··· − 23u − 1
c
5
u
26
− 2u
25
+ ··· + 4u − 1
c
6
u
26
+ 2u
25
+ ··· − 4u − 1
c
7
, c
8
u
26
− u
25
+ ··· + 23u − 1
c
9
u
26
+ 5u
25
+ ··· − 10u + 1
c
10
u
26
+ 2u
25
+ ··· + 13u − 1
c
11
u
26
+ u
25
+ ··· − 8u − 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
26
− 9y
25
+ ··· − 140y + 1
c
2
, c
10
y
26
− 10y
25
+ ··· − 59y + 1
c
3
, c
9
y
26
− 13y
25
+ ··· − 34y + 1
c
4
, c
7
, c
8
c
12
y
26
− 21y
25
+ ··· − 447y + 1
c
5
, c
6
y
26
− 20y
25
+ ··· − 64y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.950090
a = 2.44637
b = 0.587694
−0.395278 25.3270
u = −0.874639 + 0.343517I
a = −0.011752 + 0.390988I
b = −0.812497 + 0.405432I
−1.39544 + 1.46259I −2.91445 − 4.27983I
u = −0.874639 − 0.343517I
a = −0.011752 − 0.390988I
b = −0.812497 − 0.405432I
−1.39544 − 1.46259I −2.91445 + 4.27983I
u = −0.833263 + 0.684908I
a = −1.43208 + 0.78533I
b = 0.642979 + 0.426629I
−1.02397 + 4.64096I −9.48838 − 10.08346I
u = −0.833263 − 0.684908I
a = −1.43208 − 0.78533I
b = 0.642979 − 0.426629I
−1.02397 − 4.64096I −9.48838 + 10.08346I
u = −0.812497 + 0.405432I
a = 0.922555 − 0.745467I
b = −0.874639 + 0.343517I
1.39544 − 1.46259I 2.91445 + 4.27983I
u = −0.812497 − 0.405432I
a = 0.922555 + 0.745467I
b = −0.874639 − 0.343517I
1.39544 + 1.46259I 2.91445 − 4.27983I
u = 1.146090 + 0.156103I
a = −0.040064 − 0.297211I
b = −0.46140 − 1.79971I
−2.18650 − 6.14715I −6.4601 + 15.9769I
u = 1.146090 − 0.156103I
a = −0.040064 + 0.297211I
b = −0.46140 + 1.79971I
−2.18650 + 6.14715I −6.4601 − 15.9769I
u = 0.642979 + 0.426629I
a = 1.29715 + 1.55050I
b = −0.833263 + 0.684908I
1.02397 − 4.64096I 9.48838 + 10.08346I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.642979 − 0.426629I
a = 1.29715 − 1.55050I
b = −0.833263 − 0.684908I
1.02397 + 4.64096I 9.48838 − 10.08346I
u = −1.24533
a = −0.895031
b = 1.73856
−4.38217 −13.4150
u = 0.694360
a = −1.83173
b = 1.63134
7.87830 1.59840
u = −1.199700 + 0.541349I
a = 1.22267 − 1.10957I
b = −1.199700 − 0.541349I
12.9759I 0. − 11.17486I
u = −1.199700 − 0.541349I
a = 1.22267 + 1.10957I
b = −1.199700 + 0.541349I
− 12.9759I 0. + 11.17486I
u = 1.250220 + 0.414382I
a = −1.09614 − 1.21395I
b = 1.250220 − 0.414382I
− 2.58704I − 60.10 + 0.655205I
u = 1.250220 − 0.414382I
a = −1.09614 + 1.21395I
b = 1.250220 + 0.414382I
2.58704I − 60.10 − 0.655205I
u = 0.634835
a = 0.389165
b = 1.91889
4.87227 13.6820
u = 0.587694
a = 4.90500
b = −0.950090
0.395278 −25.3270
u = 1.63134
a = 0.0852918
b = 0.694360
−7.87830 0
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.73856
a = 0.604219
b = −1.24533
4.38217 0
u = −1.77412
a = −0.206211
b = 0.0482735
−6.96801 −33.2740
u = −0.46140 + 1.79971I
a = −1.326880 + 0.202721I
b = 1.146090 − 0.156103I
2.18650 − 6.14715I 0
u = −0.46140 − 1.79971I
a = −1.326880 − 0.202721I
b = 1.146090 + 0.156103I
2.18650 + 6.14715I 0
u = 1.91889
a = −0.763583
b = 0.634835
−4.87227 0
u = 0.0482735
a = −5.80440
b = −1.77412
6.96801 33.2740
27
III.
I
u
3
= h−u
3
+ b + u − 1, u
5
+ 4u
4
− u
2
+ 3a + 3u + 2, u
6
− u
4
+ 2u
3
+ u
2
− u + 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
5
=
−u
−u
3
+ u
a
12
=
−
1
3
u
5
−
4
3
u
4
+
1
3
u
2
− u −
2
3
u
3
− u + 1
a
1
=
−
1
3
u
5
−
4
3
u
4
+ ··· − 2u +
1
3
u
3
− u + 1
a
2
=
−
1
3
u
5
−
4
3
u
4
+ ··· − 2u −
2
3
−u
5
+ 2u
3
− u
2
− u + 2
a
10
=
−
1
3
u
4
+
4
3
u
3
+ ··· −
1
3
u +
5
3
2
3
u
5
−
1
3
u
4
+
4
3
u
2
+
1
3
a
7
=
2
3
u
5
+
2
3
u
4
+
1
3
u
2
+ u +
1
3
−u
4
− u
a
3
=
−
1
3
u
5
−
2
3
u
4
+ ··· +
2
3
u
2
−
1
3
u
2
3
u
5
+
2
3
u
4
+
1
3
u
2
+ u +
1
3
a
11
=
−
1
3
u
4
+
1
3
u
3
+ ··· −
1
3
u −
1
3
−
1
3
u
5
−
1
3
u
4
+ ··· − 2u +
4
3
a
6
=
5
9
u
5
+
5
9
u
4
+ ··· +
1
3
u +
10
9
2
3
u
5
−
4
3
u
3
+ u
2
+
4
3
u −
1
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
22
9
u
5
+
14
9
u
4
+
13
3
u
3
−
8
9
u
2
−
14
3
u +
28
9
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
3
c
2
u
6
− u
5
+ 2u
4
+ u
3
+ u
2
− 6u + 3
c
3
3(3u
6
− 6u
5
+ 10u
4
− 4u
3
+ 6u
2
− u + 1)
c
4
, c
12
u
6
− u
4
− 2u
3
+ u
2
+ u + 1
c
5
3(3u
6
+ 9u
5
+ 16u
4
+ 18u
3
+ 14u
2
+ 6u + 1)
c
6
3(3u
6
− 9u
5
+ 16u
4
− 18u
3
+ 14u
2
− 6u + 1)
c
7
, c
8
u
6
− u
4
+ 2u
3
+ u
2
− u + 1
c
9
3(3u
6
+ 6u
5
+ 10u
4
+ 4u
3
+ 6u
2
+ u + 1)
c
10
u
6
+ u
5
+ 2u
4
− u
3
+ u
2
+ 6u + 3
c
11
(u
2
+ u + 1)
3
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
(y
2
+ y + 1)
3
c
2
, c
10
y
6
+ 3y
5
+ 8y
4
− 3y
3
+ 25y
2
− 30y + 9
c
3
, c
9
9(9y
6
+ 24y
5
+ 88y
4
+ 98y
3
+ 48y
2
+ 11y + 1)
c
4
, c
7
, c
8
c
12
y
6
− 2y
5
+ 3y
4
− 4y
3
+ 3y
2
+ y + 1
c
5
, c
6
9(9y
6
+ 15y
5
+ 16y
4
+ 22y
3
+ 12y
2
− 8y + 1)
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.176510 + 0.285314I
a = −0.395411 + 1.018660I
b = 0.835342 + 0.876227I
4.05977I 5.93553 − 4.32228I
u = −1.176510 − 0.285314I
a = −0.395411 − 1.018660I
b = 0.835342 − 0.876227I
− 4.05977I 5.93553 + 4.32228I
u = 0.835342 + 0.876227I
a = 1.86098 + 0.56645I
b = −1.176510 + 0.285314I
− 4.05977I −5.93553 + 4.32228I
u = 0.835342 − 0.876227I
a = 1.86098 − 0.56645I
b = −1.176510 − 0.285314I
4.05977I −5.93553 − 4.32228I
u = 0.341164 + 0.590913I
a = −0.965571 − 0.163531I
b = 0.341164 − 0.590913I
4.05977I 0. − 3.09490I
u = 0.341164 − 0.590913I
a = −0.965571 + 0.163531I
b = 0.341164 + 0.590913I
− 4.05977I 0. + 3.09490I
31
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
3
)(u
26
− u
25
+ ··· + 8u − 1)
· (u
164
+ 7u
163
+ ··· − 114622u − 349484)
c
2
(u
6
− u
5
+ 2u
4
+ u
3
+ u
2
− 6u + 3)(u
26
− 2u
25
+ ··· − 13u − 1)
· (u
164
+ 2u
163
+ ··· − 173301u + 10677)
c
3
9(3u
6
− 6u
5
+ ··· − u + 1)(u
26
− 5u
25
+ ··· + 10u + 1)
· (3u
164
+ 30u
163
+ ··· − 23u − 1)
c
4
(u
6
− u
4
− 2u
3
+ u
2
+ u + 1)(u
26
+ u
25
+ ··· − 23u − 1)
· (u
164
− 2u
163
+ ··· − 3386u + 61)
c
5
9(3u
6
+ 9u
5
+ ··· + 6u + 1)(u
26
− 2u
25
+ ··· + 4u − 1)
· (3u
164
− 14u
162
+ ··· + 3228u + 43)
c
6
9(3u
6
− 9u
5
+ ··· − 6u + 1)(u
26
+ 2u
25
+ ··· − 4u − 1)
· (3u
164
− 14u
162
+ ··· − 3228u + 43)
c
7
(u
6
− u
4
+ 2u
3
+ u
2
− u + 1)(u
26
− u
25
+ ··· + 23u − 1)
· (u
164
+ 2u
163
+ ··· + 3386u + 61)
c
8
(u
6
− u
4
+ 2u
3
+ u
2
− u + 1)(u
26
− u
25
+ ··· + 23u − 1)
· (u
164
− 2u
163
+ ··· − 3386u + 61)
c
9
9(3u
6
+ 6u
5
+ ··· + u + 1)(u
26
+ 5u
25
+ ··· − 10u + 1)
· (3u
164
− 30u
163
+ ··· + 23u − 1)
c
10
(u
6
+ u
5
+ 2u
4
− u
3
+ u
2
+ 6u + 3)(u
26
+ 2u
25
+ ··· + 13u − 1)
· (u
164
− 2u
163
+ ··· + 173301u + 10677)
c
11
((u
2
+ u + 1)
3
)(u
26
+ u
25
+ ··· − 8u − 1)
· (u
164
− 7u
163
+ ··· + 114622u − 349484)
c
12
(u
6
− u
4
− 2u
3
+ u
2
+ u + 1)(u
26
+ u
25
+ ··· − 23u − 1)
· (u
164
+ 2u
163
+ ··· + 3386u + 61)
32
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
((y
2
+ y + 1)
3
)(y
26
− 9y
25
+ ··· − 140y + 1)
· (y
164
− 41y
163
+ ··· − 4668550960796y + 122139066256)
c
2
, c
10
(y
6
+ 3y
5
+ ··· − 30y + 9)(y
26
− 10y
25
+ ··· − 59y + 1)
· (y
164
− 34y
163
+ ··· − 9384110787y + 113998329)
c
3
, c
9
81(9y
6
+ 24y
5
+ 88y
4
+ 98y
3
+ 48y
2
+ 11y + 1)
· (y
26
− 13y
25
+ ··· − 34y + 1)(9y
164
+ 168y
163
+ ··· − 3213y + 1)
c
4
, c
7
, c
8
c
12
(y
6
− 2y
5
+ 3y
4
− 4y
3
+ 3y
2
+ y + 1)(y
26
− 21y
25
+ ··· − 447y + 1)
· (y
164
− 110y
163
+ ··· − 5163208y + 3721)
c
5
, c
6
81(9y
6
+ 15y
5
+ 16y
4
+ 22y
3
+ 12y
2
− 8y + 1)
· (y
26
− 20y
25
+ ··· − 64y + 1)
· (9y
164
− 84y
163
+ ··· − 11352482y + 1849)
33
