12a
1151
(K12a
1151
)
A knot diagram
1
Linearized knot diagam
4 8 10 1 9 12 11 3 5 2 7 6
Solving Sequence
6,9
5
1,10
4 2 3 8 12 7 11
c
5
c
9
c
4
c
1
c
3
c
8
c
12
c
6
c
11
c
2
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.84155 × 10
139
u
78
− 5.86060 × 10
140
u
77
+ ··· + 3.54905 × 10
139
b + 7.76498 × 10
140
,
− 3.04871 × 10
140
u
78
− 2.59985 × 10
141
u
77
+ ··· + 3.54905 × 10
139
a − 8.26678 × 10
141
,
u
79
+ 9u
78
+ ··· + 312u + 16i
I
u
2
= h1422881983u
23
− 5915588584u
22
+ ··· + 1616424857b − 14740278204,
629416068u
23
− 2394813871u
22
+ ··· + 1616424857a + 1027469093, u
24
− 2u
23
+ ··· + 12u
2
+ 1i
I
u
3
= ha
5
u − a
5
+ a
4
− 6a
3
u + 5a
3
+ a
2
u − 3a
2
+ 5au + 3b − 6a + 4u − 4,
a
6
− 6a
4
− 3a
3
u + 3a
2
u + 9a
2
+ 9au + 3a + 3u − 2, u
2
− u + 1i
* 3 irreducible components of dim
C
= 0, with total 115 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−7.84 × 10
139
u
78
− 5.86 × 10
140
u
77
+ · · · + 3.55 × 10
139
b + 7.76 ×
10
140
, −3.05 × 10
140
u
78
− 2.60 × 10
141
u
77
+ · · · + 3.55 × 10
139
a − 8.27 ×
10
141
, u
79
+ 9u
78
+ · · · + 312u + 16i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
1
=
8.59020u
78
+ 73.2548u
77
+ ··· + 4369.81u + 232.929
2.20948u
78
+ 16.5132u
77
+ ··· − 304.035u − 21.8790
a
10
=
u
u
3
+ u
a
4
=
4.41608u
78
+ 37.7333u
77
+ ··· + 712.316u + 11.5442
−0.115368u
78
− 0.227832u
77
+ ··· + 445.621u + 24.6192
a
2
=
6.63533u
78
+ 60.0366u
77
+ ··· + 3925.20u + 195.258
0.658120u
78
+ 11.9172u
77
+ ··· + 3859.32u + 218.139
a
3
=
4.24499u
78
+ 36.9550u
77
+ ··· + 1239.11u + 42.1422
−0.673937u
78
− 4.63249u
77
+ ··· + 737.578u + 43.0337
a
8
=
2.82716u
78
+ 25.5853u
77
+ ··· + 1757.24u + 112.506
0.880297u
78
+ 11.7432u
77
+ ··· + 3253.57u + 185.762
a
12
=
10.7997u
78
+ 89.7680u
77
+ ··· + 4065.78u + 211.050
2.20948u
78
+ 16.5132u
77
+ ··· − 304.035u − 21.8790
a
7
=
−1.59360u
78
− 13.0102u
77
+ ··· + 1119.31u + 87.6656
−0.900530u
78
− 8.93749u
77
+ ··· − 1110.00u − 59.2587
a
11
=
−5.22487u
78
− 39.9580u
77
+ ··· + 817.645u + 48.4343
−1.91964u
78
− 11.2753u
77
+ ··· + 1557.11u + 85.8871
(ii) Obstruction class = −1
(iii) Cusp Shapes = 12.0387u
78
+ 103.817u
77
+ ··· + 4299.97u + 226.784
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
79
− 5u
78
+ ··· + 212u − 41
c
2
, c
8
u
79
− u
78
+ ··· + 765u − 241
c
3
u
79
+ 9u
78
+ ··· + 2805u − 271
c
5
, c
9
u
79
− 9u
78
+ ··· + 312u − 16
c
6
, c
7
, c
11
c
12
u
79
+ u
78
+ ··· + 56u − 11
c
10
u
79
− 15u
78
+ ··· − 99261632u + 6792448
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
79
+ 55y
78
+ ··· − 61082y −1681
c
2
, c
8
y
79
− 61y
78
+ ··· + 942387y −58081
c
3
y
79
− 5y
78
+ ··· + 2781355y −73441
c
5
, c
9
y
79
+ 39y
78
+ ··· − 4928y −256
c
6
, c
7
, c
11
c
12
y
79
+ 101y
78
+ ··· − 2100y −121
c
10
y
79
− 39y
78
+ ··· + 546186244640768y −46137349832704
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.023800 + 1.030940I
a = 1.144260 + 0.499043I
b = −0.343277 − 0.203755I
−3.36900 − 0.75920I 0
u = 0.023800 − 1.030940I
a = 1.144260 − 0.499043I
b = −0.343277 + 0.203755I
−3.36900 + 0.75920I 0
u = 0.470758 + 0.927302I
a = 1.398390 + 0.187507I
b = −0.555908 − 0.114573I
−0.31736 + 4.31539I 0
u = 0.470758 − 0.927302I
a = 1.398390 − 0.187507I
b = −0.555908 + 0.114573I
−0.31736 − 4.31539I 0
u = −0.266379 + 0.891409I
a = 1.70242 − 0.50761I
b = −0.195113 − 0.741709I
−1.86223 − 1.13419I 0
u = −0.266379 − 0.891409I
a = 1.70242 + 0.50761I
b = −0.195113 + 0.741709I
−1.86223 + 1.13419I 0
u = 0.354891 + 0.769340I
a = −1.071220 − 0.126911I
b = 0.494709 + 0.343759I
0.261328 − 0.631677I 0
u = 0.354891 − 0.769340I
a = −1.071220 + 0.126911I
b = 0.494709 − 0.343759I
0.261328 + 0.631677I 0
u = 1.151780 + 0.216696I
a = −0.095609 + 0.236404I
b = 0.02984 + 1.68336I
13.60590 − 3.08638I 0
u = 1.151780 − 0.216696I
a = −0.095609 − 0.236404I
b = 0.02984 − 1.68336I
13.60590 + 3.08638I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.630807 + 0.534227I
a = −1.59911 + 1.50283I
b = −0.06854 + 1.63478I
12.76480 + 4.44702I 0
u = −0.630807 − 0.534227I
a = −1.59911 − 1.50283I
b = −0.06854 − 1.63478I
12.76480 − 4.44702I 0
u = 0.143148 + 1.181990I
a = 0.533602 − 1.146280I
b = 0.026851 + 1.281330I
1.08946 + 1.81199I 0
u = 0.143148 − 1.181990I
a = 0.533602 + 1.146280I
b = 0.026851 − 1.281330I
1.08946 − 1.81199I 0
u = 0.467597 + 1.096360I
a = −1.217970 − 0.323265I
b = 0.435028 − 0.947042I
1.99976 + 7.20460I 0
u = 0.467597 − 1.096360I
a = −1.217970 + 0.323265I
b = 0.435028 + 0.947042I
1.99976 − 7.20460I 0
u = 0.009704 + 1.194850I
a = −0.704930 + 0.058295I
b = 0.498721 + 0.561666I
0.178271 + 0.057111I 0
u = 0.009704 − 1.194850I
a = −0.704930 − 0.058295I
b = 0.498721 − 0.561666I
0.178271 − 0.057111I 0
u = −0.772582 + 0.216203I
a = −0.358690 + 0.251842I
b = 0.131224 − 0.951947I
4.36734 + 2.49071I 0
u = −0.772582 − 0.216203I
a = −0.358690 − 0.251842I
b = 0.131224 + 0.951947I
4.36734 − 2.49071I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.291360 + 1.165960I
a = −0.887219 + 0.300056I
b = 0.631464 + 0.106906I
−1.21371 − 3.57365I 0
u = −0.291360 − 1.165960I
a = −0.887219 − 0.300056I
b = 0.631464 − 0.106906I
−1.21371 + 3.57365I 0
u = 0.425835 + 1.139080I
a = −0.433166 + 0.125823I
b = 0.07867 − 1.47146I
6.69360 + 2.18923I 0
u = 0.425835 − 1.139080I
a = −0.433166 − 0.125823I
b = 0.07867 + 1.47146I
6.69360 − 2.18923I 0
u = −0.620307 + 1.046960I
a = −1.41879 + 0.34275I
b = 0.12439 + 1.69908I
11.2380 − 9.4496I 0
u = −0.620307 − 1.046960I
a = −1.41879 − 0.34275I
b = 0.12439 − 1.69908I
11.2380 + 9.4496I 0
u = 1.136680 + 0.439324I
a = 0.090083 + 0.191845I
b = −0.429435 − 0.933174I
8.67853 − 6.47962I 0
u = 1.136680 − 0.439324I
a = 0.090083 − 0.191845I
b = −0.429435 + 0.933174I
8.67853 + 6.47962I 0
u = −0.589457 + 1.073090I
a = −1.244540 + 0.275008I
b = 0.961256 + 0.001853I
3.34417 − 7.71939I 0
u = −0.589457 − 1.073090I
a = −1.244540 − 0.275008I
b = 0.961256 − 0.001853I
3.34417 + 7.71939I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.549505 + 1.110860I
a = −1.83815 − 0.80102I
b = 0.00021 + 1.66667I
15.3513 − 1.9660I 0
u = −0.549505 − 1.110860I
a = −1.83815 + 0.80102I
b = 0.00021 − 1.66667I
15.3513 + 1.9660I 0
u = −0.531675 + 1.124370I
a = 1.60443 + 1.00348I
b = −0.22168 − 1.70090I
15.1502 − 5.8509I 0
u = −0.531675 − 1.124370I
a = 1.60443 − 1.00348I
b = −0.22168 + 1.70090I
15.1502 + 5.8509I 0
u = −0.659458 + 1.055530I
a = −1.084660 + 0.021855I
b = 0.511231 + 0.533981I
0.76357 − 2.89451I 0
u = −0.659458 − 1.055530I
a = −1.084660 − 0.021855I
b = 0.511231 − 0.533981I
0.76357 + 2.89451I 0
u = −0.768976 + 0.991373I
a = 0.538655 − 0.226066I
b = −0.338115 + 0.361457I
1.20575 − 3.22169I 0
u = −0.768976 − 0.991373I
a = 0.538655 + 0.226066I
b = −0.338115 − 0.361457I
1.20575 + 3.22169I 0
u = 0.515057 + 1.166160I
a = 0.335827 + 0.059039I
b = 0.051286 + 0.785007I
0.420526 + 1.222690I 0
u = 0.515057 − 1.166160I
a = 0.335827 − 0.059039I
b = 0.051286 − 0.785007I
0.420526 − 1.222690I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.589468 + 1.138130I
a = 1.40884 + 0.26786I
b = −0.393655 − 0.809318I
1.81506 − 7.57460I 0
u = −0.589468 − 1.138130I
a = 1.40884 − 0.26786I
b = −0.393655 + 0.809318I
1.81506 + 7.57460I 0
u = −0.506572 + 0.508924I
a = −0.051904 + 0.850237I
b = 0.03144 + 1.76394I
17.2962 − 2.4742I 11.19134 + 0.I
u = −0.506572 − 0.508924I
a = −0.051904 − 0.850237I
b = 0.03144 − 1.76394I
17.2962 + 2.4742I 11.19134 + 0.I
u = −0.581550 + 0.398663I
a = 1.14962 − 1.44411I
b = −0.673429 + 0.256729I
5.22564 + 2.91137I 0
u = −0.581550 − 0.398663I
a = 1.14962 + 1.44411I
b = −0.673429 − 0.256729I
5.22564 − 2.91137I 0
u = −0.702104
a = 0.0149403
b = −0.530668
2.36953 2.18680
u = −0.463096 + 0.517128I
a = 0.332312 + 0.276180I
b = 0.12648 − 1.81097I
17.1693 + 1.5821I 9.06677 + 0.I
u = −0.463096 − 0.517128I
a = 0.332312 − 0.276180I
b = 0.12648 + 1.81097I
17.1693 − 1.5821I 9.06677 + 0.I
u = −0.801464 + 1.091750I
a = 0.675727 − 0.239048I
b = 0.00436 − 1.65785I
9.04989 − 1.08392I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.801464 − 1.091750I
a = 0.675727 + 0.239048I
b = 0.00436 + 1.65785I
9.04989 + 1.08392I 0
u = 0.624243 + 0.143897I
a = −0.08781 − 1.43506I
b = −0.356900 − 0.747079I
4.58359 − 3.00778I 6.62264 + 3.57380I
u = 0.624243 − 0.143897I
a = −0.08781 + 1.43506I
b = −0.356900 + 0.747079I
4.58359 + 3.00778I 6.62264 − 3.57380I
u = 0.979074 + 0.954928I
a = 0.873271 + 0.389712I
b = −0.226664 + 0.654722I
1.98964 + 5.22706I 0
u = 0.979074 − 0.954928I
a = 0.873271 − 0.389712I
b = −0.226664 − 0.654722I
1.98964 − 5.22706I 0
u = −0.170217 + 0.587957I
a = 1.45135 − 1.04929I
b = −0.255308 + 1.266040I
3.88298 − 1.55898I 2.33887 − 0.69081I
u = −0.170217 − 0.587957I
a = 1.45135 + 1.04929I
b = −0.255308 − 1.266040I
3.88298 + 1.55898I 2.33887 + 0.69081I
u = 0.715900 + 1.193850I
a = −1.346340 + 0.033763I
b = 0.639205 − 0.960912I
6.2881 + 12.9738I 0
u = 0.715900 − 1.193850I
a = −1.346340 − 0.033763I
b = 0.639205 + 0.960912I
6.2881 − 12.9738I 0
u = 0.67679 + 1.27080I
a = 1.44713 − 0.52505I
b = −0.10486 + 1.66021I
10.40900 + 9.46041I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.67679 − 1.27080I
a = 1.44713 + 0.52505I
b = −0.10486 − 1.66021I
10.40900 − 9.46041I 0
u = −0.423191 + 0.323713I
a = 3.90741 − 1.30925I
b = −0.13775 − 1.60269I
12.29310 − 4.85069I 9.24802 − 1.64947I
u = −0.423191 − 0.323713I
a = 3.90741 + 1.30925I
b = −0.13775 + 1.60269I
12.29310 + 4.85069I 9.24802 + 1.64947I
u = −1.35319 + 0.57009I
a = −0.031654 + 0.202799I
b = −0.12478 + 1.68712I
17.7750 + 8.6970I 0
u = −1.35319 − 0.57009I
a = −0.031654 − 0.202799I
b = −0.12478 − 1.68712I
17.7750 − 8.6970I 0
u = −1.12186 + 1.01046I
a = 1.081980 − 0.402723I
b = −0.06024 − 1.62586I
9.99812 − 6.26694I 0
u = −1.12186 − 1.01046I
a = 1.081980 + 0.402723I
b = −0.06024 + 1.62586I
9.99812 + 6.26694I 0
u = −0.82772 + 1.26829I
a = −1.386850 − 0.218529I
b = 0.18650 + 1.70350I
15.4171 − 16.2612I 0
u = −0.82772 − 1.26829I
a = −1.386850 + 0.218529I
b = 0.18650 − 1.70350I
15.4171 + 16.2612I 0
u = 0.99647 + 1.17539I
a = −1.077440 − 0.029336I
b = 0.13006 − 1.53156I
7.61147 + 5.15881I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.99647 − 1.17539I
a = −1.077440 + 0.029336I
b = 0.13006 + 1.53156I
7.61147 − 5.15881I 0
u = −0.31946 + 1.54507I
a = −0.290904 − 0.491644I
b = 0.169497 + 0.576494I
−0.45796 − 2.24296I 0
u = −0.31946 − 1.54507I
a = −0.290904 + 0.491644I
b = 0.169497 − 0.576494I
−0.45796 + 2.24296I 0
u = −0.094450 + 0.347629I
a = −1.083060 + 0.027982I
b = 0.238061 + 0.385513I
0.057577 − 0.845749I 1.55782 + 7.91922I
u = −0.094450 − 0.347629I
a = −1.083060 − 0.027982I
b = 0.238061 − 0.385513I
0.057577 + 0.845749I 1.55782 − 7.91922I
u = −0.223590 + 0.185780I
a = −5.03850 + 2.68271I
b = −0.298899 − 0.397572I
4.99353 − 2.88874I 8.80025 + 0.08168I
u = −0.223590 − 0.185780I
a = −5.03850 − 2.68271I
b = −0.298899 + 0.397572I
4.99353 + 2.88874I 8.80025 − 0.08168I
u = 0.31568 + 1.73340I
a = −0.334268 + 0.795016I
b = 0.04940 − 1.61951I
7.34037 + 3.05784I 0
u = 0.31568 − 1.73340I
a = −0.334268 − 0.795016I
b = 0.04940 + 1.61951I
7.34037 − 3.05784I 0
12
II.
I
u
2
= h1.42 × 10
9
u
23
− 5.92 × 10
9
u
22
+ · · · + 1.62 × 10
9
b − 1.47 × 10
10
, 6.29 ×
10
8
u
23
−2.39×10
9
u
22
+· · ·+1.62×10
9
a+1.03×10
9
, u
24
−2u
23
+· · ·+12u
2
+1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
1
=
−0.389388u
23
+ 1.48155u
22
+ ··· − 8.36240u − 0.635643
−0.880265u
23
+ 3.65967u
22
+ ··· − 10.7223u + 9.11906
a
10
=
u
u
3
+ u
a
4
=
1.11029u
23
− 8.99250u
22
+ ··· + 24.0625u − 15.9479
1.70130u
23
− 2.71489u
22
+ ··· + 12.0591u + 6.90850
a
2
=
−0.353192u
23
+ 1.58262u
22
+ ··· − 4.71894u − 6.32017
0.765620u
23
− 5.19111u
22
+ ··· + 18.5226u − 12.7397
a
3
=
1.39273u
23
− 7.92747u
22
+ ··· + 24.2810u − 10.6853
1.90068u
23
− 1.92430u
22
+ ··· + 11.9952u + 10.5412
a
8
=
5.67983u
23
− 11.0065u
22
+ ··· + 26.9581u + 9.71894
9.11906u
23
− 17.3579u
22
+ ··· + 26.2790u + 10.7223
a
12
=
−1.26965u
23
+ 5.14122u
22
+ ··· − 19.0847u + 8.48342
−0.880265u
23
+ 3.65967u
22
+ ··· − 10.7223u + 9.11906
a
7
=
−4.58438u
23
+ 11.7095u
22
+ ··· − 30.7654u + 6.86722
−2.80359u
23
+ 4.69072u
22
+ ··· − 10.2783u − 10.3657
a
11
=
−2.43201u
23
+ 2.14260u
22
+ ··· + 2.81556u − 20.2898
1.88026u
23
− 5.65967u
22
+ ··· + 22.7223u − 9.11906
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
4436334991
1616424857
u
23
+
15330129255
1616424857
u
22
+ ··· +
4498778865
1616424857
u −
12543205522
1616424857
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
− 4u
23
+ ··· − 4u + 1
c
2
u
24
− 8u
22
+ ··· − u + 1
c
3
u
24
+ 2u
22
+ ··· + u + 1
c
4
u
24
+ 4u
23
+ ··· + 4u + 1
c
5
u
24
− 2u
23
+ ··· + 12u
2
+ 1
c
6
, c
7
u
24
+ 17u
22
+ ··· − 4u + 1
c
8
u
24
− 8u
22
+ ··· + u + 1
c
9
u
24
+ 2u
23
+ ··· + 12u
2
+ 1
c
10
u
24
− 4u
23
+ ··· + 4u + 5
c
11
, c
12
u
24
+ 17u
22
+ ··· + 4u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
24
+ 16y
23
+ ··· + 16y + 1
c
2
, c
8
y
24
− 16y
23
+ ··· − 13y + 1
c
3
y
24
+ 4y
23
+ ··· + 19y + 1
c
5
, c
9
y
24
+ 18y
23
+ ··· + 24y + 1
c
6
, c
7
, c
11
c
12
y
24
+ 34y
23
+ ··· + 26y + 1
c
10
y
24
− 6y
23
+ ··· − 346y + 25
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.160272 + 0.928469I
a = −1.48454 + 0.01654I
b = 0.187858 + 0.598400I
−2.18760 − 0.64012I −1.24511 − 1.80764I
u = −0.160272 − 0.928469I
a = −1.48454 − 0.01654I
b = 0.187858 − 0.598400I
−2.18760 + 0.64012I −1.24511 + 1.80764I
u = 0.449040 + 0.963265I
a = −1.374540 − 0.019153I
b = 0.07046 − 1.59657I
5.47588 + 1.65777I −0.454623 − 0.548546I
u = 0.449040 − 0.963265I
a = −1.374540 + 0.019153I
b = 0.07046 + 1.59657I
5.47588 − 1.65777I −0.454623 + 0.548546I
u = −0.570467 + 0.684424I
a = 2.89524 − 0.16670I
b = −0.12530 − 1.60732I
12.16410 − 5.54266I 6.98587 + 8.56567I
u = −0.570467 − 0.684424I
a = 2.89524 + 0.16670I
b = −0.12530 + 1.60732I
12.16410 + 5.54266I 6.98587 − 8.56567I
u = 0.479555 + 0.732326I
a = −0.374615 − 0.620422I
b = 0.279898 + 1.199200I
4.19925 + 2.43243I 5.43635 − 6.12529I
u = 0.479555 − 0.732326I
a = −0.374615 + 0.620422I
b = 0.279898 − 1.199200I
4.19925 − 2.43243I 5.43635 + 6.12529I
u = 0.350221 + 0.650854I
a = 3.00312 − 0.00735I
b = −0.448895 + 0.507705I
4.69789 + 3.44732I 2.06092 − 10.54280I
u = 0.350221 − 0.650854I
a = 3.00312 + 0.00735I
b = −0.448895 − 0.507705I
4.69789 − 3.44732I 2.06092 + 10.54280I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.822122 + 0.970775I
a = −0.912075 + 0.262087I
b = 0.275719 + 0.278983I
1.15532 − 4.50171I 2.54279 + 5.83668I
u = −0.822122 − 0.970775I
a = −0.912075 − 0.262087I
b = 0.275719 − 0.278983I
1.15532 + 4.50171I 2.54279 − 5.83668I
u = 0.294306 + 1.281330I
a = 0.416939 − 1.037610I
b = 0.078720 + 1.178880I
1.85656 + 1.20382I 8.09771 + 0.42923I
u = 0.294306 − 1.281330I
a = 0.416939 + 1.037610I
b = 0.078720 − 1.178880I
1.85656 − 1.20382I 8.09771 − 0.42923I
u = −0.105806 + 0.578997I
a = 2.63514 − 0.23656I
b = −0.470964 + 0.978144I
6.19126 − 0.16242I 5.95278 − 0.65654I
u = −0.105806 − 0.578997I
a = 2.63514 + 0.23656I
b = −0.470964 − 0.978144I
6.19126 + 0.16242I 5.95278 + 0.65654I
u = −0.39847 + 1.46021I
a = −0.019571 + 0.179554I
b = 0.103475 + 0.331589I
−0.91882 − 1.89712I −5.02429 − 0.65918I
u = −0.39847 − 1.46021I
a = −0.019571 − 0.179554I
b = 0.103475 − 0.331589I
−0.91882 + 1.89712I −5.02429 + 0.65918I
u = −0.106329 + 0.426026I
a = 1.48004 − 0.33083I
b = −0.07142 − 1.80067I
16.6857 − 2.1538I 0.41567 + 2.69228I
u = −0.106329 − 0.426026I
a = 1.48004 + 0.33083I
b = −0.07142 + 1.80067I
16.6857 + 2.1538I 0.41567 − 2.69228I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.09903 + 1.18765I
a = −0.987243 − 0.118597I
b = 0.08478 − 1.52295I
7.48218 + 5.77748I 3.90381 − 10.03254I
u = 1.09903 − 1.18765I
a = −0.987243 + 0.118597I
b = 0.08478 + 1.52295I
7.48218 − 5.77748I 3.90381 + 10.03254I
u = 0.49131 + 1.56091I
a = −0.277906 + 0.238179I
b = 0.03567 − 1.54322I
5.70577 + 2.41144I −1.17187 − 2.39550I
u = 0.49131 − 1.56091I
a = −0.277906 − 0.238179I
b = 0.03567 + 1.54322I
5.70577 − 2.41144I −1.17187 + 2.39550I
18
III. I
u
3
= ha
5
u − 6a
3
u + · · · − 6a − 4, −3a
3
u + 3a
2
u + · · · + 3a − 2, u
2
− u + 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
5
=
1
u − 1
a
1
=
a
−
1
3
a
5
u + 2a
3
u + ··· + 2a +
4
3
a
10
=
u
u − 1
a
4
=
1
3
a
3
u −
1
3
a
2
u + ··· +
8
3
a +
4
3
−
1
3
a
2
u −
1
3
a
2
+
2
3
u +
2
3
a
2
=
−
2
3
a
3
u +
7
3
au + ··· −
2
3
a − 1
−
1
3
a
3
u +
5
3
au + ··· −
7
3
a − 1
a
3
=
1
3
a
2
u −
2
3
a
2
−
2
3
u +
4
3
−
1
3
a
5
u +
1
3
a
4
u + ··· +
1
3
a + 2
a
8
=
−
1
3
a
4
+
4
3
a
2
−
4
3
1
3
a
5
u −
2
3
a
4
u + ··· −
1
3
a −
4
3
a
12
=
−
1
3
a
5
u + 2a
3
u + ··· + 3a +
4
3
−
1
3
a
5
u + 2a
3
u + ··· + 2a +
4
3
a
7
=
−
1
3
a
5
u +
1
3
a
4
u + ··· − a
2
+
1
3
a
−
1
3
a
5
u +
1
3
a
4
u + ··· + 3a −
2
3
a
11
=
2
3
a
3
u −
7
3
au + ··· +
2
3
a + 1
1
3
a
3
u −
2
3
a
3
−
5
3
au +
7
3
a + u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u + 10
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
12
+ 4u
10
+ ··· − 10u + 7
c
2
, c
8
u
12
− 4u
10
+ ··· + 20u + 7
c
3
u
12
− 8u
11
+ ··· − 8u
2
+ 1
c
5
, c
9
(u
2
+ u + 1)
6
c
6
, c
7
, c
11
c
12
u
12
+ 8u
10
+ ··· − 6u + 13
c
10
(u + 1)
12
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
12
+ 8y
11
+ ··· + 292y + 49
c
2
, c
8
y
12
− 8y
11
+ ··· − 120y + 49
c
3
y
12
− 8y
11
+ ··· − 16y + 1
c
5
, c
9
(y
2
+ y + 1)
6
c
6
, c
7
, c
11
c
12
y
12
+ 16y
11
+ ··· + 1108y + 169
c
10
(y − 1)
12
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.724321 − 0.650848I
b = 0.719959 + 1.112490I
6.57974 + 2.02988I 8.00000 − 3.46410I
u = 0.500000 + 0.866025I
a = −1.032580 + 0.148538I
b = 0.07514 − 1.53325I
6.57974 + 2.02988I 8.00000 − 3.46410I
u = 0.500000 + 0.866025I
a = −0.110864 − 0.292048I
b = 0.030499 − 1.218920I
6.57974 + 2.02988I 8.00000 − 3.46410I
u = 0.500000 + 0.866025I
a = 1.84992 + 0.64143I
b = −0.04911 + 1.65057I
6.57974 + 2.02988I 8.00000 − 3.46410I
u = 0.500000 + 0.866025I
a = 2.03582 − 0.30303I
b = −0.744942 + 0.795979I
6.57974 + 2.02988I 8.00000 − 3.46410I
u = 0.500000 + 0.866025I
a = −2.01797 + 0.45596I
b = −0.031549 − 0.806876I
6.57974 + 2.02988I 8.00000 − 3.46410I
u = 0.500000 − 0.866025I
a = −0.724321 + 0.650848I
b = 0.719959 − 1.112490I
6.57974 − 2.02988I 8.00000 + 3.46410I
u = 0.500000 − 0.866025I
a = −1.032580 − 0.148538I
b = 0.07514 + 1.53325I
6.57974 − 2.02988I 8.00000 + 3.46410I
u = 0.500000 − 0.866025I
a = −0.110864 + 0.292048I
b = 0.030499 + 1.218920I
6.57974 − 2.02988I 8.00000 + 3.46410I
u = 0.500000 − 0.866025I
a = 1.84992 − 0.64143I
b = −0.04911 − 1.65057I
6.57974 − 2.02988I 8.00000 + 3.46410I
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 − 0.866025I
a = 2.03582 + 0.30303I
b = −0.744942 − 0.795979I
6.57974 − 2.02988I 8.00000 + 3.46410I
u = 0.500000 − 0.866025I
a = −2.01797 − 0.45596I
b = −0.031549 + 0.806876I
6.57974 − 2.02988I 8.00000 + 3.46410I
23
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
12
+ 4u
10
+ ··· − 10u + 7)(u
24
− 4u
23
+ ··· − 4u + 1)
· (u
79
− 5u
78
+ ··· + 212u − 41)
c
2
(u
12
− 4u
10
+ ··· + 20u + 7)(u
24
− 8u
22
+ ··· − u + 1)
· (u
79
− u
78
+ ··· + 765u − 241)
c
3
(u
12
− 8u
11
+ ··· − 8u
2
+ 1)(u
24
+ 2u
22
+ ··· + u + 1)
· (u
79
+ 9u
78
+ ··· + 2805u − 271)
c
4
(u
12
+ 4u
10
+ ··· − 10u + 7)(u
24
+ 4u
23
+ ··· + 4u + 1)
· (u
79
− 5u
78
+ ··· + 212u − 41)
c
5
((u
2
+ u + 1)
6
)(u
24
− 2u
23
+ ··· + 12u
2
+ 1)
· (u
79
− 9u
78
+ ··· + 312u − 16)
c
6
, c
7
(u
12
+ 8u
10
+ ··· − 6u + 13)(u
24
+ 17u
22
+ ··· − 4u + 1)
· (u
79
+ u
78
+ ··· + 56u − 11)
c
8
(u
12
− 4u
10
+ ··· + 20u + 7)(u
24
− 8u
22
+ ··· + u + 1)
· (u
79
− u
78
+ ··· + 765u − 241)
c
9
((u
2
+ u + 1)
6
)(u
24
+ 2u
23
+ ··· + 12u
2
+ 1)
· (u
79
− 9u
78
+ ··· + 312u − 16)
c
10
((u + 1)
12
)(u
24
− 4u
23
+ ··· + 4u + 5)
· (u
79
− 15u
78
+ ··· − 99261632u + 6792448)
c
11
, c
12
(u
12
+ 8u
10
+ ··· − 6u + 13)(u
24
+ 17u
22
+ ··· + 4u + 1)
· (u
79
+ u
78
+ ··· + 56u − 11)
24
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
12
+ 8y
11
+ ··· + 292y + 49)(y
24
+ 16y
23
+ ··· + 16y + 1)
· (y
79
+ 55y
78
+ ··· − 61082y − 1681)
c
2
, c
8
(y
12
− 8y
11
+ ··· − 120y + 49)(y
24
− 16y
23
+ ··· − 13y + 1)
· (y
79
− 61y
78
+ ··· + 942387y − 58081)
c
3
(y
12
− 8y
11
+ ··· − 16y + 1)(y
24
+ 4y
23
+ ··· + 19y + 1)
· (y
79
− 5y
78
+ ··· + 2781355y − 73441)
c
5
, c
9
((y
2
+ y + 1)
6
)(y
24
+ 18y
23
+ ··· + 24y + 1)
· (y
79
+ 39y
78
+ ··· − 4928y − 256)
c
6
, c
7
, c
11
c
12
(y
12
+ 16y
11
+ ··· + 1108y + 169)(y
24
+ 34y
23
+ ··· + 26y + 1)
· (y
79
+ 101y
78
+ ··· − 2100y − 121)
c
10
((y − 1)
12
)(y
24
− 6y
23
+ ··· − 346y + 25)
· (y
79
− 39y
78
+ ··· + 546186244640768y − 46137349832704)
25
