12a
0470
(K12a
0470
)
A knot diagram
1
Linearized knot diagam
3 6 11 8 2 1 12 5 7 4 10 9
Solving Sequence
3,6
2 1
7,9
10 5 8 4 12 11
c
2
c
1
c
6
c
9
c
5
c
8
c
4
c
12
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h4.04726 × 10
246
u
151
− 6.41758 × 10
246
u
150
+ ··· + 5.27327 × 10
246
b + 2.97396 × 10
246
,
7.15742 × 10
246
u
151
− 9.25761 × 10
246
u
150
+ ··· + 5.27327 × 10
246
a − 1.31606 × 10
247
, u
152
− 2u
151
+ ··· + u − 1i
I
u
2
= h8u
28
+ 4u
27
+ ··· + b − 8, 5u
28
+ 6u
27
+ ··· + a − 5, u
29
+ u
28
+ ··· − u − 1i
* 2 irreducible components of dim
C
= 0, with total 181 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
= h4.05 × 10
246
u
151
− 6.42 × 10
246
u
150
+ · · · + 5.27 × 10
246
b + 2.97 ×
10
246
, 7.16 × 10
246
u
151
− 9.26 × 10
246
u
150
+ · · · + 5.27 × 10
246
a − 1.32 ×
10
247
, u
152
− 2u
151
+ · · · + u − 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
7
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
9
=
−1.35730u
151
+ 1.75558u
150
+ ··· − 5.13107u + 2.49572
−0.767505u
151
+ 1.21700u
150
+ ··· − 0.938204u − 0.563969
a
10
=
−1.24710u
151
+ 2.18343u
150
+ ··· − 5.16086u + 3.31368
−1.61120u
151
+ 2.24775u
150
+ ··· − 0.307596u − 1.05852
a
5
=
u
−u
3
+ u
a
8
=
−1.64848u
151
+ 2.79384u
150
+ ··· − 5.42734u + 2.23244
−1.90549u
151
+ 2.80402u
150
+ ··· − 0.487392u − 1.28317
a
4
=
−1.00094u
151
+ 3.31075u
150
+ ··· − 4.77710u − 2.74348
0.190513u
151
− 1.42765u
150
+ ··· − 2.05798u + 1.60425
a
12
=
3.78395u
151
− 7.66715u
150
+ ··· + 9.27456u − 1.33763
0.377582u
151
− 1.13512u
150
+ ··· + 5.43079u − 1.54915
a
11
=
7.65369u
151
− 11.9415u
150
+ ··· − 5.79642u + 3.51479
0.585467u
151
− 0.0463453u
150
+ ··· − 0.251655u + 1.47548
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0982650u
151
− 5.31022u
150
+ ··· + 12.0206u − 0.0299219
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
152
+ 76u
151
+ ··· + 13u + 1
c
2
, c
5
u
152
+ 2u
151
+ ··· − u − 1
c
3
, c
10
u
152
+ 33u
150
+ ··· + 783u + 259
c
4
, c
8
u
152
+ u
151
+ ··· + 6u + 1
c
6
u
152
+ 6u
151
+ ··· − 3317745u − 609725
c
7
u
152
− u
151
+ ··· + 57u − 1
c
9
u
152
− 20u
151
+ ··· + 21337u − 12353
c
11
u
152
− 66u
151
+ ··· − 1636585u + 67081
c
12
u
152
− 14u
151
+ ··· − 30u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
152
+ 4y
151
+ ··· − 105y + 1
c
2
, c
5
y
152
− 76y
151
+ ··· − 13y + 1
c
3
, c
10
y
152
+ 66y
151
+ ··· + 1636585y + 67081
c
4
, c
8
y
152
− 99y
151
+ ··· − 18y + 1
c
6
y
152
+ 68y
151
+ ··· − 27842735435875y + 371764575625
c
7
y
152
+ y
151
+ ··· − 129y + 1
c
9
y
152
− 40y
151
+ ··· − 15266440451y + 152596609
c
11
y
152
+ 54y
151
+ ··· + 6314845277y + 4499860561
c
12
y
152
− 4y
151
+ ··· + 152y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.383777 + 0.919433I
a = 1.078470 − 0.262629I
b = 0.962367 − 0.275916I
1.07545 + 4.53235I 0
u = 0.383777 − 0.919433I
a = 1.078470 + 0.262629I
b = 0.962367 + 0.275916I
1.07545 − 4.53235I 0
u = −0.944741 + 0.285279I
a = 1.35833 + 1.30200I
b = −0.650112 + 0.955026I
−3.08140 + 1.12956I 0
u = −0.944741 − 0.285279I
a = 1.35833 − 1.30200I
b = −0.650112 − 0.955026I
−3.08140 − 1.12956I 0
u = −0.069371 + 0.971211I
a = −0.117881 − 0.389121I
b = −0.065256 − 0.129430I
−1.18241 − 2.66699I 0
u = −0.069371 − 0.971211I
a = −0.117881 + 0.389121I
b = −0.065256 + 0.129430I
−1.18241 + 2.66699I 0
u = 0.482267 + 0.836728I
a = 1.079100 − 0.220038I
b = 1.014560 − 0.374126I
1.73768 − 0.27266I 0
u = 0.482267 − 0.836728I
a = 1.079100 + 0.220038I
b = 1.014560 + 0.374126I
1.73768 + 0.27266I 0
u = −0.931775 + 0.458661I
a = −0.517037 + 0.052500I
b = −0.963868 − 0.349871I
1.67907 + 3.50297I 0
u = −0.931775 − 0.458661I
a = −0.517037 − 0.052500I
b = −0.963868 + 0.349871I
1.67907 − 3.50297I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.317637 + 0.901806I
a = −1.042530 − 0.284626I
b = −0.868882 − 0.244756I
0.494522 − 0.387668I 0
u = −0.317637 − 0.901806I
a = −1.042530 + 0.284626I
b = −0.868882 + 0.244756I
0.494522 + 0.387668I 0
u = −0.984716 + 0.353336I
a = −0.44854 + 1.50777I
b = −2.22025 + 0.47865I
0.24721 − 3.77251I 0
u = −0.984716 − 0.353336I
a = −0.44854 − 1.50777I
b = −2.22025 − 0.47865I
0.24721 + 3.77251I 0
u = 0.674828 + 0.650638I
a = −0.800877 − 0.378374I
b = −0.262229 − 0.826627I
8.14764 − 3.66069I 0
u = 0.674828 − 0.650638I
a = −0.800877 + 0.378374I
b = −0.262229 + 0.826627I
8.14764 + 3.66069I 0
u = −0.779228 + 0.724899I
a = −0.668136 + 0.162670I
b = 0.1014870 − 0.0587958I
2.90751 − 0.77875I 0
u = −0.779228 − 0.724899I
a = −0.668136 − 0.162670I
b = 0.1014870 + 0.0587958I
2.90751 + 0.77875I 0
u = −0.802715 + 0.700181I
a = 0.528909 − 0.214658I
b = 0.066369 − 0.571812I
2.83078 + 6.12529I 0
u = −0.802715 − 0.700181I
a = 0.528909 + 0.214658I
b = 0.066369 + 0.571812I
2.83078 − 6.12529I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.931258
a = 0.556220
b = 0.725666
−1.56738 0
u = −1.005300 + 0.383584I
a = −0.971898 + 0.294247I
b = −1.30327 − 0.72079I
1.73788 + 3.49522I 0
u = −1.005300 − 0.383584I
a = −0.971898 − 0.294247I
b = −1.30327 + 0.72079I
1.73788 − 3.49522I 0
u = 0.778317 + 0.756459I
a = −0.598115 − 0.112367I
b = −0.174448 − 0.505818I
4.81350 − 11.43230I 0
u = 0.778317 − 0.756459I
a = −0.598115 + 0.112367I
b = −0.174448 + 0.505818I
4.81350 + 11.43230I 0
u = 0.291795 + 0.863898I
a = −1.83268 + 0.83379I
b = −1.48448 + 1.13373I
1.9610 + 14.4178I 0
u = 0.291795 − 0.863898I
a = −1.83268 − 0.83379I
b = −1.48448 − 1.13373I
1.9610 − 14.4178I 0
u = −0.775590 + 0.473858I
a = 0.847989 − 0.837717I
b = 0.90184 + 1.10640I
0.61723 + 7.01848I 0
u = −0.775590 − 0.473858I
a = 0.847989 + 0.837717I
b = 0.90184 − 1.10640I
0.61723 − 7.01848I 0
u = 1.038360 + 0.345757I
a = 0.191067 + 0.995519I
b = 1.53922 + 0.38333I
−1.98195 − 0.69790I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.038360 − 0.345757I
a = 0.191067 − 0.995519I
b = 1.53922 − 0.38333I
−1.98195 + 0.69790I 0
u = 0.906062 + 0.615460I
a = 0.999545 + 0.441678I
b = −0.059051 − 0.308564I
7.47803 − 1.24652I 0
u = 0.906062 − 0.615460I
a = 0.999545 − 0.441678I
b = −0.059051 + 0.308564I
7.47803 + 1.24652I 0
u = −0.965412 + 0.541538I
a = −0.001851 − 0.395682I
b = −0.544932 − 0.587103I
1.74479 + 4.28503I 0
u = −0.965412 − 0.541538I
a = −0.001851 + 0.395682I
b = −0.544932 + 0.587103I
1.74479 − 4.28503I 0
u = −0.264440 + 0.845180I
a = 1.76638 + 0.91924I
b = 1.42141 + 1.17453I
−0.19681 − 8.54250I 0
u = −0.264440 − 0.845180I
a = 1.76638 − 0.91924I
b = 1.42141 − 1.17453I
−0.19681 + 8.54250I 0
u = 1.090970 + 0.273767I
a = −0.239902 + 1.154550I
b = 1.187110 + 0.692719I
−2.48172 − 0.27312I 0
u = 1.090970 − 0.273767I
a = −0.239902 − 1.154550I
b = 1.187110 − 0.692719I
−2.48172 + 0.27312I 0
u = −0.538885 + 0.671846I
a = −1.000540 − 0.049819I
b = −1.043760 − 0.407156I
1.73680 − 2.93232I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.538885 − 0.671846I
a = −1.000540 + 0.049819I
b = −1.043760 + 0.407156I
1.73680 + 2.93232I 0
u = 0.852933 + 0.761343I
a = 0.609064 + 0.330543I
b = −0.0280414 − 0.0735952I
4.61641 + 5.79207I 0
u = 0.852933 − 0.761343I
a = 0.609064 − 0.330543I
b = −0.0280414 + 0.0735952I
4.61641 − 5.79207I 0
u = 1.047030 + 0.467738I
a = −0.58666 + 2.67220I
b = 1.92124 + 1.21869I
0.164504 + 1.182460I 0
u = 1.047030 − 0.467738I
a = −0.58666 − 2.67220I
b = 1.92124 − 1.21869I
0.164504 − 1.182460I 0
u = −1.030410 + 0.508838I
a = 0.17447 − 1.64458I
b = 1.94710 − 0.08979I
0.29119 + 7.48074I 0
u = −1.030410 − 0.508838I
a = 0.17447 + 1.64458I
b = 1.94710 + 0.08979I
0.29119 − 7.48074I 0
u = −0.589867 + 0.610350I
a = −0.700953 − 0.481848I
b = 0.290361 + 0.120067I
2.84618 + 0.28798I 0
u = −0.589867 − 0.610350I
a = −0.700953 + 0.481848I
b = 0.290361 − 0.120067I
2.84618 − 0.28798I 0
u = −1.068240 + 0.431591I
a = −0.184092 − 0.729158I
b = −0.782026 − 0.803453I
2.17032 + 1.56453I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.068240 − 0.431591I
a = −0.184092 + 0.729158I
b = −0.782026 + 0.803453I
2.17032 − 1.56453I 0
u = 1.029510 + 0.545055I
a = 0.268685 − 0.493310I
b = 0.778055 − 0.624997I
2.59941 − 0.54644I 0
u = 1.029510 − 0.545055I
a = 0.268685 + 0.493310I
b = 0.778055 + 0.624997I
2.59941 + 0.54644I 0
u = −1.094080 + 0.400769I
a = −1.00807 − 1.05475I
b = 2.02800 − 0.86472I
−1.71479 − 2.37202I 0
u = −1.094080 − 0.400769I
a = −1.00807 + 1.05475I
b = 2.02800 + 0.86472I
−1.71479 + 2.37202I 0
u = −1.133100 + 0.281064I
a = 0.30345 − 1.45730I
b = 1.85611 + 0.47793I
1.97754 − 2.59355I 0
u = −1.133100 − 0.281064I
a = 0.30345 + 1.45730I
b = 1.85611 − 0.47793I
1.97754 + 2.59355I 0
u = 0.720540 + 0.411747I
a = −0.767789 − 0.319195I
b = −0.330475 + 1.225820I
−1.26910 − 2.31076I 0
u = 0.720540 − 0.411747I
a = −0.767789 + 0.319195I
b = −0.330475 − 1.225820I
−1.26910 + 2.31076I 0
u = −0.814938 + 0.134931I
a = −0.083292 − 0.966694I
b = −0.96051 − 1.15930I
0.36906 + 4.70085I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.814938 − 0.134931I
a = −0.083292 + 0.966694I
b = −0.96051 + 1.15930I
0.36906 − 4.70085I 0
u = 0.289257 + 0.761883I
a = −1.97581 + 1.16549I
b = −1.50924 + 1.35892I
6.30909 + 5.59657I 0. − 5.18818I
u = 0.289257 − 0.761883I
a = −1.97581 − 1.16549I
b = −1.50924 − 1.35892I
6.30909 − 5.59657I 0. + 5.18818I
u = 1.083520 + 0.481995I
a = 0.248195 − 0.676126I
b = 0.804054 − 0.749773I
2.55663 − 5.43707I 0
u = 1.083520 − 0.481995I
a = 0.248195 + 0.676126I
b = 0.804054 + 0.749773I
2.55663 + 5.43707I 0
u = −0.581841 + 0.568659I
a = 0.003892 − 0.554007I
b = 0.313242 + 0.437067I
2.72118 + 0.71702I 0. − 3.61012I
u = −0.581841 − 0.568659I
a = 0.003892 + 0.554007I
b = 0.313242 − 0.437067I
2.72118 − 0.71702I 0. + 3.61012I
u = 1.079460 + 0.493063I
a = 0.99771 − 1.73678I
b = −0.92938 − 2.12480I
2.47693 − 3.26456I 0
u = 1.079460 − 0.493063I
a = 0.99771 + 1.73678I
b = −0.92938 + 2.12480I
2.47693 + 3.26456I 0
u = 1.105180 + 0.442868I
a = 0.39641 − 1.45900I
b = −2.25176 − 0.52753I
−4.30081 − 3.76264I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.105180 − 0.442868I
a = 0.39641 + 1.45900I
b = −2.25176 + 0.52753I
−4.30081 + 3.76264I 0
u = −1.103640 + 0.459878I
a = −0.20205 + 2.37315I
b = −1.77606 + 0.37432I
−4.18487 + 3.65759I 0
u = −1.103640 − 0.459878I
a = −0.20205 − 2.37315I
b = −1.77606 − 0.37432I
−4.18487 − 3.65759I 0
u = 0.490783 + 0.622967I
a = 0.671800 − 1.099070I
b = −0.356204 + 0.144512I
4.17258 − 4.06306I 3.00416 + 6.96901I
u = 0.490783 − 0.622967I
a = 0.671800 + 1.099070I
b = −0.356204 − 0.144512I
4.17258 + 4.06306I 3.00416 − 6.96901I
u = −0.217990 + 0.762289I
a = −1.72701 + 0.46817I
b = −1.32925 − 0.48502I
−1.80194 − 7.82902I −4.00000 + 7.12195I
u = −0.217990 − 0.762289I
a = −1.72701 − 0.46817I
b = −1.32925 + 0.48502I
−1.80194 + 7.82902I −4.00000 − 7.12195I
u = −1.200620 + 0.138247I
a = 0.427924 + 0.370421I
b = −1.115830 + 0.250729I
−4.59892 − 1.62888I 0
u = −1.200620 − 0.138247I
a = 0.427924 − 0.370421I
b = −1.115830 − 0.250729I
−4.59892 + 1.62888I 0
u = −0.055067 + 0.789218I
a = −0.373361 + 0.390003I
b = −0.300683 + 0.596293I
−1.39195 − 2.77336I −6.16101 + 1.36784I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.055067 − 0.789218I
a = −0.373361 − 0.390003I
b = −0.300683 − 0.596293I
−1.39195 + 2.77336I −6.16101 − 1.36784I
u = 1.082950 + 0.540225I
a = 0.30057 − 2.14940I
b = −1.90780 − 1.79160I
1.76357 − 10.40180I 0
u = 1.082950 − 0.540225I
a = 0.30057 + 2.14940I
b = −1.90780 + 1.79160I
1.76357 + 10.40180I 0
u = −0.337682 + 0.710933I
a = −1.66022 − 0.03389I
b = −1.121330 − 0.635122I
1.67787 − 2.33035I 1.15873 + 4.49499I
u = −0.337682 − 0.710933I
a = −1.66022 + 0.03389I
b = −1.121330 + 0.635122I
1.67787 + 2.33035I 1.15873 − 4.49499I
u = −1.160380 + 0.354158I
a = 0.07211 + 1.58299I
b = −1.168230 + 0.639911I
−7.03712 + 0.88475I 0
u = −1.160380 − 0.354158I
a = 0.07211 − 1.58299I
b = −1.168230 − 0.639911I
−7.03712 − 0.88475I 0
u = 1.108930 + 0.493416I
a = 0.87068 + 2.16235I
b = 1.56556 − 0.28063I
−1.04151 − 9.77008I 0
u = 1.108930 − 0.493416I
a = 0.87068 − 2.16235I
b = 1.56556 + 0.28063I
−1.04151 + 9.77008I 0
u = 1.177530 + 0.321781I
a = −0.05443 + 1.47304I
b = 1.117860 + 0.667814I
−5.98061 + 4.36824I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.177530 − 0.321781I
a = −0.05443 − 1.47304I
b = 1.117860 − 0.667814I
−5.98061 − 4.36824I 0
u = 1.205710 + 0.216443I
a = −0.330995 + 0.543381I
b = 1.169470 + 0.369491I
−4.69081 − 2.85034I 0
u = 1.205710 − 0.216443I
a = −0.330995 − 0.543381I
b = 1.169470 − 0.369491I
−4.69081 + 2.85034I 0
u = −1.112930 + 0.525586I
a = −0.36029 − 1.65320I
b = 1.36704 − 1.39558I
−0.63463 + 6.51514I 0
u = −1.112930 − 0.525586I
a = −0.36029 + 1.65320I
b = 1.36704 + 1.39558I
−0.63463 − 6.51514I 0
u = 0.389279 + 0.651932I
a = 2.47319 − 0.63631I
b = 1.01971 − 1.20809I
3.78254 + 5.74388I 3.75843 − 8.18320I
u = 0.389279 − 0.651932I
a = 2.47319 + 0.63631I
b = 1.01971 + 1.20809I
3.78254 − 5.74388I 3.75843 + 8.18320I
u = −1.112640 + 0.554702I
a = 0.10133 − 1.62391I
b = 1.88701 − 0.83949I
−0.57472 + 7.17851I 0
u = −1.112640 − 0.554702I
a = 0.10133 + 1.62391I
b = 1.88701 + 0.83949I
−0.57472 − 7.17851I 0
u = −0.088174 + 0.749373I
a = 0.91081 + 1.48634I
b = 0.73142 + 1.51496I
−1.70374 − 3.27624I −8.99219 + 7.85891I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.088174 − 0.749373I
a = 0.91081 − 1.48634I
b = 0.73142 − 1.51496I
−1.70374 + 3.27624I −8.99219 − 7.85891I
u = −0.306550 + 0.678861I
a = −1.72371 − 0.79331I
b = −0.770129 − 0.856932I
1.70576 − 1.87348I −0.42450 + 2.49869I
u = −0.306550 − 0.678861I
a = −1.72371 + 0.79331I
b = −0.770129 + 0.856932I
1.70576 + 1.87348I −0.42450 − 2.49869I
u = 1.187900 + 0.406665I
a = −1.16772 − 0.86560I
b = −1.09338 + 1.34279I
−5.39828 − 0.73516I 0
u = 1.187900 − 0.406665I
a = −1.16772 + 0.86560I
b = −1.09338 − 1.34279I
−5.39828 + 0.73516I 0
u = 1.227390 + 0.266113I
a = −0.333602 − 1.089780I
b = −1.55000 + 0.38750I
−4.99353 + 5.03385I 0
u = 1.227390 − 0.266113I
a = −0.333602 + 1.089780I
b = −1.55000 − 0.38750I
−4.99353 − 5.03385I 0
u = 1.149540 + 0.513252I
a = −0.163868 − 1.302950I
b = −2.15411 − 0.49384I
−5.93528 − 7.25693I 0
u = 1.149540 − 0.513252I
a = −0.163868 + 1.302950I
b = −2.15411 + 0.49384I
−5.93528 + 7.25693I 0
u = 0.185776 + 0.717411I
a = 1.65846 + 0.49340I
b = 1.300110 − 0.457633I
−3.17767 + 2.62041I −6.33336 − 1.66250I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.185776 − 0.717411I
a = 1.65846 − 0.49340I
b = 1.300110 + 0.457633I
−3.17767 − 2.62041I −6.33336 + 1.66250I
u = −1.238700 + 0.235930I
a = 0.259320 − 1.049780I
b = 1.56835 + 0.30870I
−3.07117 − 10.98410I 0
u = −1.238700 − 0.235930I
a = 0.259320 + 1.049780I
b = 1.56835 − 0.30870I
−3.07117 + 10.98410I 0
u = 1.098530 + 0.619511I
a = −0.12705 − 1.41433I
b = −1.40890 − 0.43078I
−0.15592 − 5.14913I 0
u = 1.098530 − 0.619511I
a = −0.12705 + 1.41433I
b = −1.40890 + 0.43078I
−0.15592 + 5.14913I 0
u = 1.141500 + 0.551235I
a = −0.76008 + 2.15876I
b = 1.99570 + 1.66220I
3.80506 − 10.53880I 0
u = 1.141500 − 0.551235I
a = −0.76008 − 2.15876I
b = 1.99570 − 1.66220I
3.80506 + 10.53880I 0
u = 1.187120 + 0.452809I
a = −0.357378 + 0.555827I
b = 0.899507 + 0.695896I
−4.94754 − 1.54657I 0
u = 1.187120 − 0.452809I
a = −0.357378 − 0.555827I
b = 0.899507 − 0.695896I
−4.94754 + 1.54657I 0
u = −1.156470 + 0.532261I
a = 0.274557 − 1.321940I
b = 2.19449 − 0.51983I
−4.53293 + 12.66540I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.156470 − 0.532261I
a = 0.274557 + 1.321940I
b = 2.19449 + 0.51983I
−4.53293 − 12.66540I 0
u = −1.177490 + 0.485615I
a = 1.32633 + 0.93386I
b = −0.89475 + 1.83707I
−4.83960 + 7.81420I 0
u = −1.177490 − 0.485615I
a = 1.32633 − 0.93386I
b = −0.89475 − 1.83707I
−4.83960 − 7.81420I 0
u = −1.202220 + 0.499350I
a = 0.460879 + 0.106966I
b = −0.283500 + 0.592956I
−4.72308 + 7.48847I 0
u = −1.202220 − 0.499350I
a = 0.460879 − 0.106966I
b = −0.283500 − 0.592956I
−4.72308 − 7.48847I 0
u = −1.174250 + 0.568288I
a = 0.49497 + 1.87336I
b = −1.87549 + 1.43747I
−2.91281 + 13.75270I 0
u = −1.174250 − 0.568288I
a = 0.49497 − 1.87336I
b = −1.87549 − 1.43747I
−2.91281 − 13.75270I 0
u = 1.173250 + 0.583567I
a = −0.37502 + 1.92947I
b = 1.94210 + 1.38100I
−0.6843 − 19.7445I 0
u = 1.173250 − 0.583567I
a = −0.37502 − 1.92947I
b = 1.94210 − 1.38100I
−0.6843 + 19.7445I 0
u = 0.677018 + 0.122920I
a = −0.090170 + 0.431984I
b = 0.773640 + 0.904200I
−1.39396 − 0.51937I −7.49436 + 3.54433I
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.677018 − 0.122920I
a = −0.090170 − 0.431984I
b = 0.773640 − 0.904200I
−1.39396 + 0.51937I −7.49436 − 3.54433I
u = 1.268380 + 0.338936I
a = 0.258683 − 0.424308I
b = −0.111769 − 0.356158I
−5.73048 − 1.79012I 0
u = 1.268380 − 0.338936I
a = 0.258683 + 0.424308I
b = −0.111769 + 0.356158I
−5.73048 + 1.79012I 0
u = −1.182030 + 0.583698I
a = 0.001713 − 1.285930I
b = 1.176240 − 0.645768I
−2.18165 + 5.82518I 0
u = −1.182030 − 0.583698I
a = 0.001713 + 1.285930I
b = 1.176240 + 0.645768I
−2.18165 − 5.82518I 0
u = −1.259890 + 0.406415I
a = −0.173834 − 0.622203I
b = 0.365866 − 0.414471I
−5.16392 + 7.51600I 0
u = −1.259890 − 0.406415I
a = −0.173834 + 0.622203I
b = 0.365866 + 0.414471I
−5.16392 − 7.51600I 0
u = 1.171820 + 0.620671I
a = −0.076724 − 1.311900I
b = −1.223860 − 0.548169I
−1.36507 − 10.18130I 0
u = 1.171820 − 0.620671I
a = −0.076724 + 1.311900I
b = −1.223860 + 0.548169I
−1.36507 + 10.18130I 0
u = −0.617996 + 0.192261I
a = −2.22103 + 0.11935I
b = 0.786236 + 0.327337I
4.07274 + 1.60672I −3.83245 − 1.97204I
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.617996 − 0.192261I
a = −2.22103 − 0.11935I
b = 0.786236 − 0.327337I
4.07274 − 1.60672I −3.83245 + 1.97204I
u = 0.462574 + 0.416233I
a = −2.96641 + 1.07919I
b = −1.48761 + 0.99410I
1.92061 − 5.04402I 1.03354 + 6.79994I
u = 0.462574 − 0.416233I
a = −2.96641 − 1.07919I
b = −1.48761 − 0.99410I
1.92061 + 5.04402I 1.03354 − 6.79994I
u = 0.229914 + 0.551330I
a = −2.18549 + 0.22408I
b = −1.49300 − 0.68166I
1.38604 + 5.52662I −3.41313 − 7.69772I
u = 0.229914 − 0.551330I
a = −2.18549 − 0.22408I
b = −1.49300 + 0.68166I
1.38604 − 5.52662I −3.41313 + 7.69772I
u = 0.314205 + 0.497227I
a = 2.46177 − 1.97659I
b = 0.328127 − 1.321850I
4.61091 − 0.89127I 3.81617 − 0.08868I
u = 0.314205 − 0.497227I
a = 2.46177 + 1.97659I
b = 0.328127 + 1.321850I
4.61091 + 0.89127I 3.81617 + 0.08868I
u = 0.330308 + 0.437500I
a = 1.56756 − 1.83086I
b = −0.302602 + 0.275810I
4.70777 + 1.42105I 3.12833 − 3.99747I
u = 0.330308 − 0.437500I
a = 1.56756 + 1.83086I
b = −0.302602 − 0.275810I
4.70777 − 1.42105I 3.12833 + 3.99747I
u = −0.009918 + 0.405834I
a = 1.90091 + 1.21729I
b = 1.38844 − 0.26997I
−1.61251 + 0.11334I −7.50597 + 0.03879I
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.009918 − 0.405834I
a = 1.90091 − 1.21729I
b = 1.38844 + 0.26997I
−1.61251 − 0.11334I −7.50597 − 0.03879I
u = −0.345824
a = 3.70752
b = 1.16852
−1.59359 −5.16680
20
II.
I
u
2
= h8u
28
+4u
27
+· · ·+b −8, 5u
28
+6u
27
+· · ·+a −5, u
29
+u
28
+· · ·−u −1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
7
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
9
=
−5u
28
− 6u
27
+ ··· − 6u + 5
−8u
28
− 4u
27
+ ··· − 4u + 8
a
10
=
−8u
28
− 7u
27
+ ··· − 5u + 8
−7u
28
− 4u
27
+ ··· − 5u + 7
a
5
=
u
−u
3
+ u
a
8
=
−4u
28
− 5u
27
+ ··· − 5u + 4
−7u
28
− 4u
27
+ ··· − 4u + 7
a
4
=
6u
28
+ 6u
27
+ ··· + 6u − 6
5u
28
+ 2u
27
+ ··· + 2u − 5
a
12
=
3u
28
− 25u
26
+ ··· − u − 6
7u
28
− 53u
26
+ ··· − u − 12
a
11
=
−7u
28
− 5u
27
+ ··· − 2u + 11
−5u
28
− 2u
27
+ ··· + u + 4
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 15u
28
−6u
27
−122u
26
+ 28u
25
+ 502u
24
−47u
23
−1290u
22
−66u
21
+ 2257u
20
+ 497u
19
−
2721u
18
− 1268u
17
+ 2194u
16
+ 1986u
15
− 962u
14
− 2159u
13
− 163u
12
+ 1660u
11
+
800u
10
− 937u
9
− 994u
8
+ 397u
7
+ 890u
6
− 159u
5
− 552u
4
+ 55u
3
+ 228u
2
− 21u − 56
21
(iv) u-Polynomials at the component
22
Crossings u-Polynomials at each crossing
c
1
u
29
− 15u
28
+ ··· + 11u − 1
c
2
u
29
+ u
28
+ ··· − u − 1
c
3
u
29
− u
28
+ ··· − u + 1
c
4
u
29
− 2u
28
+ ··· − 2u + 1
c
5
u
29
− u
28
+ ··· − u + 1
c
6
u
29
− 3u
28
+ ··· − u + 1
c
7
u
29
− 2u
28
+ ··· − u − 1
c
8
u
29
+ 2u
28
+ ··· − 2u − 1
c
9
u
29
− u
28
+ ··· + 13u + 1
c
10
u
29
+ u
28
+ ··· − u − 1
c
11
u
29
− 15u
28
+ ··· − 19u + 1
c
12
u
29
− u
28
+ ··· + 2u + 1
23
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
29
+ y
28
+ ··· − 5y −1
c
2
, c
5
y
29
− 15y
28
+ ··· + 11y −1
c
3
, c
10
y
29
+ 15y
28
+ ··· − 19y −1
c
4
, c
8
y
29
− 30y
28
+ ··· + 24y −1
c
6
y
29
+ 13y
28
+ ··· + 17y −1
c
7
y
29
− 2y
28
+ ··· + 3y −1
c
9
y
29
− 15y
28
+ ··· + 13y −1
c
11
y
29
+ 11y
28
+ ··· + 5y −1
c
12
y
29
− 3y
28
+ ··· + 2y −1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.012830 + 0.257666I
a = −1.02127 + 1.12267I
b = 0.964290 + 1.002990I
−3.52317 − 0.78224I −13.57115 − 0.79473I
u = 1.012830 − 0.257666I
a = −1.02127 − 1.12267I
b = 0.964290 − 1.002990I
−3.52317 + 0.78224I −13.57115 + 0.79473I
u = −0.447640 + 0.820964I
a = −1.129020 + 0.024098I
b = −0.916140 − 0.220208I
1.067470 − 0.913618I −2.47813 + 4.14437I
u = −0.447640 − 0.820964I
a = −1.129020 − 0.024098I
b = −0.916140 + 0.220208I
1.067470 + 0.913618I −2.47813 − 4.14437I
u = −0.125860 + 0.908684I
a = −0.385304 − 0.793638I
b = −0.313879 − 0.750734I
−0.82578 − 2.86981I 3.34364 + 6.99484I
u = −0.125860 − 0.908684I
a = −0.385304 + 0.793638I
b = −0.313879 + 0.750734I
−0.82578 + 2.86981I 3.34364 − 6.99484I
u = −1.035630 + 0.376015I
a = 0.55437 + 1.94601I
b = −2.40805 + 0.75033I
−0.49978 − 2.67316I −5.42153 + 3.02884I
u = −1.035630 − 0.376015I
a = 0.55437 − 1.94601I
b = −2.40805 − 0.75033I
−0.49978 + 2.67316I −5.42153 − 3.02884I
u = −1.011100 + 0.465853I
a = −0.641998 − 0.234013I
b = −1.33336 − 1.09971I
3.27409 + 4.23230I 3.03729 − 4.05269I
u = −1.011100 − 0.465853I
a = −0.641998 + 0.234013I
b = −1.33336 + 1.09971I
3.27409 − 4.23230I 3.03729 + 4.05269I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.016900 + 0.483979I
a = 0.438928 − 1.222220I
b = 0.208345 − 1.330300I
3.41025 − 1.82150I 2.98987 + 2.43916I
u = 1.016900 − 0.483979I
a = 0.438928 + 1.222220I
b = 0.208345 + 1.330300I
3.41025 + 1.82150I 2.98987 − 2.43916I
u = 0.490643 + 0.667636I
a = 1.82275 + 0.21847I
b = 1.223770 − 0.185664I
2.63775 + 4.59064I 0.73778 − 4.42435I
u = 0.490643 − 0.667636I
a = 1.82275 − 0.21847I
b = 1.223770 + 0.185664I
2.63775 − 4.59064I 0.73778 + 4.42435I
u = 1.076950 + 0.549716I
a = −0.32785 − 2.09071I
b = −1.91152 − 0.68915I
0.82142 − 9.33880I −2.66312 + 8.92858I
u = 1.076950 − 0.549716I
a = −0.32785 + 2.09071I
b = −1.91152 + 0.68915I
0.82142 + 9.33880I −2.66312 − 8.92858I
u = 0.787229
a = −1.47635
b = −1.19340
−2.37934 −17.8910
u = 0.617194 + 0.455336I
a = 2.10546 − 0.52027I
b = −0.156164 − 0.427777I
4.73074 − 2.12491I 3.90460 + 6.70846I
u = 0.617194 − 0.455336I
a = 2.10546 + 0.52027I
b = −0.156164 + 0.427777I
4.73074 + 2.12491I 3.90460 − 6.70846I
u = −0.644637 + 0.408946I
a = −1.38292 − 1.00681I
b = 1.008830 − 0.163629I
4.53076 − 0.49076I 2.29772 − 2.76161I
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.644637 − 0.408946I
a = −1.38292 + 1.00681I
b = 1.008830 + 0.163629I
4.53076 + 0.49076I 2.29772 + 2.76161I
u = −0.718185 + 0.210952I
a = 1.272540 − 0.007370I
b = 1.55321 + 1.24992I
0.87385 + 5.38852I −4.20699 − 10.26261I
u = −0.718185 − 0.210952I
a = 1.272540 + 0.007370I
b = 1.55321 − 1.24992I
0.87385 − 5.38852I −4.20699 + 10.26261I
u = 1.201740 + 0.364526I
a = 0.545294 + 0.710099I
b = 0.916530 − 0.798971I
−5.13331 − 1.17993I −4.64934 + 3.15889I
u = 1.201740 − 0.364526I
a = 0.545294 − 0.710099I
b = 0.916530 + 0.798971I
−5.13331 + 1.17993I −4.64934 − 3.15889I
u = −1.113040 + 0.592971I
a = 0.27814 − 1.39378I
b = 1.50688 − 0.49438I
−0.99821 + 6.18935I −5.01467 − 4.90175I
u = −1.113040 − 0.592971I
a = 0.27814 + 1.39378I
b = 1.50688 + 0.49438I
−0.99821 − 6.18935I −5.01467 + 4.90175I
u = −1.213780 + 0.489666I
a = −0.890937 − 0.393478I
b = 0.253960 − 1.287140I
−4.24162 + 7.81555I 1.63940 − 9.21259I
u = −1.213780 − 0.489666I
a = −0.890937 + 0.393478I
b = 0.253960 + 1.287140I
−4.24162 − 7.81555I 1.63940 + 9.21259I
28
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
29
− 15u
28
+ ··· + 11u − 1)(u
152
+ 76u
151
+ ··· + 13u + 1)
c
2
(u
29
+ u
28
+ ··· − u − 1)(u
152
+ 2u
151
+ ··· − u − 1)
c
3
(u
29
− u
28
+ ··· − u + 1)(u
152
+ 33u
150
+ ··· + 783u + 259)
c
4
(u
29
− 2u
28
+ ··· − 2u + 1)(u
152
+ u
151
+ ··· + 6u + 1)
c
5
(u
29
− u
28
+ ··· − u + 1)(u
152
+ 2u
151
+ ··· − u − 1)
c
6
(u
29
− 3u
28
+ ··· − u + 1)(u
152
+ 6u
151
+ ··· − 3317745u − 609725)
c
7
(u
29
− 2u
28
+ ··· − u − 1)(u
152
− u
151
+ ··· + 57u − 1)
c
8
(u
29
+ 2u
28
+ ··· − 2u − 1)(u
152
+ u
151
+ ··· + 6u + 1)
c
9
(u
29
− u
28
+ ··· + 13u + 1)(u
152
− 20u
151
+ ··· + 21337u − 12353)
c
10
(u
29
+ u
28
+ ··· − u − 1)(u
152
+ 33u
150
+ ··· + 783u + 259)
c
11
(u
29
− 15u
28
+ ··· − 19u + 1)
· (u
152
− 66u
151
+ ··· − 1636585u + 67081)
c
12
(u
29
− u
28
+ ··· + 2u + 1)(u
152
− 14u
151
+ ··· − 30u + 1)
29
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
29
+ y
28
+ ··· − 5y −1)(y
152
+ 4y
151
+ ··· − 105y + 1)
c
2
, c
5
(y
29
− 15y
28
+ ··· + 11y −1)(y
152
− 76y
151
+ ··· − 13y + 1)
c
3
, c
10
(y
29
+ 15y
28
+ ··· − 19y −1)
· (y
152
+ 66y
151
+ ··· + 1636585y + 67081)
c
4
, c
8
(y
29
− 30y
28
+ ··· + 24y −1)(y
152
− 99y
151
+ ··· − 18y + 1)
c
6
(y
29
+ 13y
28
+ ··· + 17y −1)
· (y
152
+ 68y
151
+ ··· − 27842735435875y + 371764575625)
c
7
(y
29
− 2y
28
+ ··· + 3y −1)(y
152
+ y
151
+ ··· − 129y + 1)
c
9
(y
29
− 15y
28
+ ··· + 13y −1)
· (y
152
− 40y
151
+ ··· − 15266440451y + 152596609)
c
11
(y
29
+ 11y
28
+ ··· + 5y −1)
· (y
152
+ 54y
151
+ ··· + 6314845277y + 4499860561)
c
12
(y
29
− 3y
28
+ ··· + 2y −1)(y
152
− 4y
151
+ ··· + 152y + 1)
30
