12a
0705
(K12a
0705
)
A knot diagram
1
Linearized knot diagam
3 8 6 12 9 10 11 2 4 1 5 7
Solving Sequence
4,12 5,9
6 10 7 1 3 11 8 2
c
4
c
5
c
9
c
6
c
12
c
3
c
11
c
7
c
2
c
1
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.77814 × 10
223
u
84
+ 1.16049 × 10
224
u
83
+ ··· + 5.71791 × 10
224
b − 2.02352 × 10
225
,
6.93165 × 10
224
u
84
+ 8.28583 × 10
225
u
83
+ ··· + 4.57433 × 10
226
a + 1.25867 × 10
228
,
u
85
+ 5u
84
+ ··· + 951u + 160i
I
u
2
= h2.63966 × 10
86
au
58
+ 8.74141 × 10
84
u
58
+ ··· − 5.15249 × 10
85
a − 6.04873 × 10
86
,
5.11511 × 10
86
au
58
+ 5.45554 × 10
85
u
58
+ ··· − 5.67633 × 10
84
a − 9.66817 × 10
86
, u
59
− u
58
+ ··· − 2u + 1i
I
u
3
= h4325521u
21
a − 5569352u
21
+ ··· + 770633a + 20960753,
51468579u
21
a + 49951560u
21
+ ··· − 135794681a − 49237463, u
22
+ 13u
20
+ ··· − 3u + 1i
I
u
4
= h−u
4
− 2u
3
− 2u
2
+ b − 2u, u
4
+ u
3
+ a − u − 2, u
5
+ 2u
4
+ 3u
3
+ 3u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 252 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
= h2.78 × 10
223
u
84
+ 1.16 × 10
224
u
83
+ · · · + 5.72 × 10
224
b − 2.02 ×
10
225
, 6.93 × 10
224
u
84
+ 8.29 × 10
225
u
83
+ · · · + 4.57 × 10
226
a + 1.26 ×
10
228
, u
85
+ 5u
84
+ · · · + 951u + 160i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
9
=
−0.0151534u
84
− 0.181137u
83
+ ··· − 148.935u − 27.5159
−0.0485866u
84
− 0.202956u
83
+ ··· + 5.73116u + 3.53891
a
6
=
0.229002u
84
+ 1.05119u
83
+ ··· − 12.0998u − 14.1719
−0.0683057u
84
− 0.350783u
83
+ ··· − 74.6193u − 11.0319
a
10
=
−0.0637400u
84
− 0.384094u
83
+ ··· − 143.204u − 23.9770
−0.0485866u
84
− 0.202956u
83
+ ··· + 5.73116u + 3.53891
a
7
=
−0.0221182u
84
− 0.159178u
83
+ ··· − 94.1381u − 15.3032
−0.0653935u
84
− 0.272677u
83
+ ··· + 36.6397u + 10.1984
a
1
=
0.00497274u
84
+ 0.114466u
83
+ ··· + 130.312u + 22.5502
0.0447022u
84
+ 0.202464u
83
+ ··· + 16.4799u − 0.834762
a
3
=
−0.104846u
84
− 0.302981u
83
+ ··· + 245.097u + 51.8678
0.0841183u
84
+ 0.400156u
83
+ ··· + 54.2721u + 6.26190
a
11
=
u
u
3
+ u
a
8
=
−0.0189559u
84
− 0.192940u
83
+ ··· − 178.497u − 31.7372
−0.0447255u
84
− 0.208162u
83
+ ··· − 1.08021u + 1.69630
a
2
=
−0.290244u
84
− 1.22579u
83
+ ··· + 55.3401u + 25.6354
0.109881u
84
+ 0.562827u
83
+ ··· + 120.402u + 17.0715
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.514445u
84
− 2.31397u
83
+ ··· − 6.34406u + 23.9114
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
85
+ 45u
84
+ ··· − 58368u − 4096
c
2
, c
8
u
85
+ 3u
84
+ ··· + 288u + 64
c
3
, c
10
u
85
− u
84
+ ··· − 3u + 1
c
4
, c
11
u
85
+ 5u
84
+ ··· + 951u + 160
c
5
, c
7
u
85
+ 2u
84
+ ··· + 54u − 1
c
6
u
85
+ 10u
84
+ ··· − 35445u − 2194
c
9
, c
12
u
85
− 3u
83
+ ··· − 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
85
+ y
84
+ ··· + 204472320y −16777216
c
2
, c
8
y
85
+ 45y
84
+ ··· − 58368y −4096
c
3
, c
10
y
85
− y
84
+ ··· − 53y −1
c
4
, c
11
y
85
+ 37y
84
+ ··· − 57839y −25600
c
5
, c
7
y
85
− 18y
84
+ ··· + 2716y −1
c
6
y
85
+ 2y
84
+ ··· + 255642685y −4813636
c
9
, c
12
y
85
− 6y
84
+ ··· + 46y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.145023 + 0.999078I
a = 1.19262 − 0.94042I
b = −1.219270 + 0.307226I
−0.02146 − 4.72656I 0
u = −0.145023 − 0.999078I
a = 1.19262 + 0.94042I
b = −1.219270 − 0.307226I
−0.02146 + 4.72656I 0
u = −0.414665 + 0.862773I
a = −0.670244 + 0.551943I
b = 0.306642 + 0.570240I
0.16279 + 1.74173I 0
u = −0.414665 − 0.862773I
a = −0.670244 − 0.551943I
b = 0.306642 − 0.570240I
0.16279 − 1.74173I 0
u = 0.467897 + 0.811337I
a = 1.61458 − 0.44871I
b = −0.11055 + 1.71276I
−6.17853 − 1.94386I 0
u = 0.467897 − 0.811337I
a = 1.61458 + 0.44871I
b = −0.11055 − 1.71276I
−6.17853 + 1.94386I 0
u = −0.237851 + 0.903591I
a = −0.351699 + 0.573757I
b = 0.120379 + 0.448116I
0.25713 + 1.76398I 0
u = −0.237851 − 0.903591I
a = −0.351699 − 0.573757I
b = 0.120379 − 0.448116I
0.25713 − 1.76398I 0
u = −0.744454 + 0.553688I
a = −0.574586 + 0.793591I
b = 0.740393 + 0.780188I
0.86628 + 1.67485I 0
u = −0.744454 − 0.553688I
a = −0.574586 − 0.793591I
b = 0.740393 − 0.780188I
0.86628 − 1.67485I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.325831 + 0.857016I
a = −2.17780 + 0.76800I
b = 0.26280 − 1.96854I
−5.20417 − 1.44091I 15.1928 + 0.I
u = 0.325831 − 0.857016I
a = −2.17780 − 0.76800I
b = 0.26280 + 1.96854I
−5.20417 + 1.44091I 15.1928 + 0.I
u = −1.007860 + 0.442367I
a = 0.171364 + 0.089166I
b = 0.97401 − 1.04691I
−6.33527 − 6.47253I 0
u = −1.007860 − 0.442367I
a = 0.171364 − 0.089166I
b = 0.97401 + 1.04691I
−6.33527 + 6.47253I 0
u = −0.387180 + 1.051580I
a = −1.90614 − 0.15376I
b = 0.991243 + 0.329483I
0.34615 + 4.52822I 0
u = −0.387180 − 1.051580I
a = −1.90614 + 0.15376I
b = 0.991243 − 0.329483I
0.34615 − 4.52822I 0
u = 1.134890 + 0.030841I
a = 0.630137 + 0.153086I
b = 0.348898 − 0.070015I
−5.09082 − 3.47004I 0
u = 1.134890 − 0.030841I
a = 0.630137 − 0.153086I
b = 0.348898 + 0.070015I
−5.09082 + 3.47004I 0
u = −1.14821
a = −0.384806
b = −0.488004
−2.55206 0
u = 0.839575 + 0.114772I
a = −0.032887 + 0.714584I
b = −0.806543 + 0.923956I
1.32571 − 6.56605I 1.99732 + 8.56393I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.839575 − 0.114772I
a = −0.032887 − 0.714584I
b = −0.806543 − 0.923956I
1.32571 + 6.56605I 1.99732 − 8.56393I
u = −0.007264 + 0.829533I
a = −1.85140 + 0.83210I
b = 0.746495 + 0.782670I
−0.92279 + 4.99667I −0.32701 − 9.48610I
u = −0.007264 − 0.829533I
a = −1.85140 − 0.83210I
b = 0.746495 − 0.782670I
−0.92279 − 4.99667I −0.32701 + 9.48610I
u = −0.382038 + 1.114950I
a = −1.75536 + 0.63931I
b = 1.017940 + 0.557572I
2.49649 − 0.28839I 0
u = −0.382038 − 1.114950I
a = −1.75536 − 0.63931I
b = 1.017940 − 0.557572I
2.49649 + 0.28839I 0
u = −0.344478 + 1.127640I
a = 1.86709 + 0.14823I
b = −0.90135 − 1.49524I
4.89992 + 4.14078I 0
u = −0.344478 − 1.127640I
a = 1.86709 − 0.14823I
b = −0.90135 + 1.49524I
4.89992 − 4.14078I 0
u = 0.569645 + 1.041430I
a = 0.900230 + 0.832130I
b = −0.622261 + 0.147422I
3.79995 − 2.91202I 0
u = 0.569645 − 1.041430I
a = 0.900230 − 0.832130I
b = −0.622261 − 0.147422I
3.79995 + 2.91202I 0
u = −0.568028 + 1.044380I
a = −1.060440 + 0.880912I
b = 0.948370 − 0.004808I
1.42121 + 7.52668I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.568028 − 1.044380I
a = −1.060440 − 0.880912I
b = 0.948370 + 0.004808I
1.42121 − 7.52668I 0
u = 1.166520 + 0.304583I
a = −0.0068236 − 0.0796588I
b = −0.960647 − 0.983402I
−0.93503 + 9.65311I 0
u = 1.166520 − 0.304583I
a = −0.0068236 + 0.0796588I
b = −0.960647 + 0.983402I
−0.93503 − 9.65311I 0
u = −0.485027 + 1.110170I
a = −2.05258 + 0.14746I
b = 0.930371 + 0.364814I
2.52269 + 11.49970I 0
u = −0.485027 − 1.110170I
a = −2.05258 − 0.14746I
b = 0.930371 − 0.364814I
2.52269 − 11.49970I 0
u = 0.506109 + 1.102090I
a = 0.724641 + 0.937788I
b = −0.353150 + 0.174525I
4.28934 − 0.95475I 0
u = 0.506109 − 1.102090I
a = 0.724641 − 0.937788I
b = −0.353150 − 0.174525I
4.28934 + 0.95475I 0
u = 0.454589 + 1.131320I
a = 1.93379 + 0.18704I
b = −0.950181 + 0.386813I
4.48376 − 6.60665I 0
u = 0.454589 − 1.131320I
a = 1.93379 − 0.18704I
b = −0.950181 − 0.386813I
4.48376 + 6.60665I 0
u = 0.427905 + 1.148690I
a = 1.70847 + 0.45962I
b = −1.001950 + 0.461990I
4.52844 − 4.64681I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.427905 − 1.148690I
a = 1.70847 − 0.45962I
b = −1.001950 − 0.461990I
4.52844 + 4.64681I 0
u = −0.469824 + 1.147620I
a = −0.651852 + 0.990039I
b = 0.279787 + 0.178360I
2.66701 − 3.92013I 0
u = −0.469824 − 1.147620I
a = −0.651852 − 0.990039I
b = 0.279787 − 0.178360I
2.66701 + 3.92013I 0
u = −0.740758 + 0.028690I
a = −0.167876 + 0.743200I
b = −0.388579 − 0.395849I
−2.81486 + 1.35585I −4.32855 − 3.99004I
u = −0.740758 − 0.028690I
a = −0.167876 − 0.743200I
b = −0.388579 + 0.395849I
−2.81486 − 1.35585I −4.32855 + 3.99004I
u = −0.169253 + 0.718680I
a = 1.95614 + 0.75611I
b = −0.700499 + 0.757219I
−1.26329 − 1.91287I 0.12963 + 3.91780I
u = −0.169253 − 0.718680I
a = 1.95614 − 0.75611I
b = −0.700499 − 0.757219I
−1.26329 + 1.91287I 0.12963 − 3.91780I
u = 0.447982 + 1.200670I
a = −1.77308 − 0.06023I
b = 1.04387 − 1.39049I
5.05317 − 10.87710I 0
u = 0.447982 − 1.200670I
a = −1.77308 + 0.06023I
b = 1.04387 + 1.39049I
5.05317 + 10.87710I 0
u = 0.022272 + 0.716797I
a = 1.78274 + 0.99592I
b = −0.087749 − 1.147130I
2.50161 − 2.17329I 6.51599 + 3.54221I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.022272 − 0.716797I
a = 1.78274 − 0.99592I
b = −0.087749 + 1.147130I
2.50161 + 2.17329I 6.51599 − 3.54221I
u = −1.249110 + 0.368300I
a = −0.0645207 − 0.0257805I
b = 0.984331 − 0.975875I
−3.3385 − 15.1009I 0
u = −1.249110 − 0.368300I
a = −0.0645207 + 0.0257805I
b = 0.984331 + 0.975875I
−3.3385 + 15.1009I 0
u = −0.328044 + 0.609728I
a = −1.34132 + 1.32062I
b = 0.036244 − 0.771250I
0.63834 + 7.93490I 2.22123 − 7.11106I
u = −0.328044 − 0.609728I
a = −1.34132 − 1.32062I
b = 0.036244 + 0.771250I
0.63834 − 7.93490I 2.22123 + 7.11106I
u = 0.421773 + 1.268360I
a = −0.710011 − 0.688684I
b = 1.188010 + 0.454540I
5.08186 + 1.66877I 0
u = 0.421773 − 1.268360I
a = −0.710011 + 0.688684I
b = 1.188010 − 0.454540I
5.08186 − 1.66877I 0
u = −0.612698 + 1.191870I
a = 0.484243 − 0.713869I
b = −1.156650 + 0.513704I
2.92851 + 3.88301I 0
u = −0.612698 − 1.191870I
a = 0.484243 + 0.713869I
b = −1.156650 − 0.513704I
2.92851 − 3.88301I 0
u = −0.649982 + 1.178850I
a = 1.68535 − 0.36388I
b = −1.21185 − 1.24863I
−3.97588 + 12.45700I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.649982 − 1.178850I
a = 1.68535 + 0.36388I
b = −1.21185 + 1.24863I
−3.97588 − 12.45700I 0
u = −1.352570 + 0.262899I
a = −0.049030 − 0.153871I
b = −0.749695 + 0.152939I
−2.13033 − 0.64925I 0
u = −1.352570 − 0.262899I
a = −0.049030 + 0.153871I
b = −0.749695 − 0.152939I
−2.13033 + 0.64925I 0
u = −0.645574 + 1.242540I
a = −1.041700 + 0.352813I
b = 0.980190 + 0.450183I
1.25521 + 7.10290I 0
u = −0.645574 − 1.242540I
a = −1.041700 − 0.352813I
b = 0.980190 − 0.450183I
1.25521 − 7.10290I 0
u = −0.458967 + 0.357277I
a = 1.85016 + 0.00734I
b = −0.641156 + 0.680423I
0.24321 − 7.41159I 1.55361 + 9.94736I
u = −0.458967 − 0.357277I
a = 1.85016 − 0.00734I
b = −0.641156 − 0.680423I
0.24321 + 7.41159I 1.55361 − 9.94736I
u = 0.66404 + 1.27922I
a = −1.58041 − 0.29916I
b = 1.13884 − 1.21294I
2.1680 − 16.1005I 0
u = 0.66404 − 1.27922I
a = −1.58041 + 0.29916I
b = 1.13884 + 1.21294I
2.1680 + 16.1005I 0
u = 0.554829 + 0.040510I
a = −0.436541 + 0.045823I
b = 0.659061 + 0.357831I
1.49082 + 0.81139I 5.16124 − 3.30442I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.554829 − 0.040510I
a = −0.436541 − 0.045823I
b = 0.659061 − 0.357831I
1.49082 − 0.81139I 5.16124 + 3.30442I
u = 0.518360 + 0.164912I
a = −1.285340 − 0.456448I
b = 0.596205 + 0.595908I
1.77682 + 2.60946I 4.38584 − 4.48074I
u = 0.518360 − 0.164912I
a = −1.285340 + 0.456448I
b = 0.596205 − 0.595908I
1.77682 − 2.60946I 4.38584 + 4.48074I
u = −0.71122 + 1.29452I
a = 1.53972 − 0.32682I
b = −1.13897 − 1.18316I
−0.3408 + 21.9635I 0
u = −0.71122 − 1.29452I
a = 1.53972 + 0.32682I
b = −1.13897 + 1.18316I
−0.3408 − 21.9635I 0
u = −0.494608 + 0.093658I
a = 0.199289 − 0.545574I
b = −0.844479 − 0.233581I
−0.63017 − 3.57283I 0.99238 + 2.73815I
u = −0.494608 − 0.093658I
a = 0.199289 + 0.545574I
b = −0.844479 + 0.233581I
−0.63017 + 3.57283I 0.99238 − 2.73815I
u = 0.41775 + 1.45859I
a = 1.075160 + 0.005477I
b = −1.066850 + 0.445652I
2.07936 − 4.29169I 0
u = 0.41775 − 1.45859I
a = 1.075160 − 0.005477I
b = −1.066850 − 0.445652I
2.07936 + 4.29169I 0
u = 0.08042 + 1.56201I
a = −0.891755 − 0.352633I
b = 1.140010 + 0.429042I
6.10542 + 4.62752I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.08042 − 1.56201I
a = −0.891755 + 0.352633I
b = 1.140010 − 0.429042I
6.10542 − 4.62752I 0
u = 1.62763 + 0.16845I
a = −0.0435748 − 0.0623811I
b = 0.853798 + 0.066764I
−3.25627 − 2.89779I 0
u = 1.62763 − 0.16845I
a = −0.0435748 + 0.0623811I
b = 0.853798 − 0.066764I
−3.25627 + 2.89779I 0
u = 0.03257 + 1.67503I
a = 0.881764 − 0.251048I
b = −1.131520 + 0.441094I
4.64394 − 9.72183I 0
u = 0.03257 − 1.67503I
a = 0.881764 + 0.251048I
b = −1.131520 − 0.441094I
4.64394 + 9.72183I 0
13
II.
I
u
2
= h2.64×10
86
au
58
+8.74×10
84
u
58
+· · ·−5.15×10
85
a−6.05×10
86
, 5.12×
10
86
au
58
+5.46×10
85
u
58
+· · ·−5.68×10
84
a−9.67×10
86
, u
59
−u
58
+· · ·−2u+1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
9
=
a
−113.936au
58
− 3.77304u
58
+ ··· + 22.2396a + 261.081
a
6
=
5.63240au
58
+ 435.052u
58
+ ··· + 311.680a − 64.1170
−2.18470au
58
+ 14.9121u
58
+ ··· + 30.4822a + 65.8181
a
10
=
−113.936au
58
− 3.77304u
58
+ ··· + 23.2396a + 261.081
−113.936au
58
− 3.77304u
58
+ ··· + 22.2396a + 261.081
a
7
=
22.2396au
58
+ 227.772u
58
+ ··· + 203.514a + 16.6509
20.1444au
58
− 192.367u
58
+ ··· − 113.936a + 146.586
a
1
=
77.9773au
58
+ 456.902u
58
+ ··· + 88.3564a − 383.094
88.5791au
58
+ 182.326u
58
+ ··· + 1.55254a − 303.914
a
3
=
27.1191au
58
− 373.742u
58
+ ··· − 315.980a − 207.066
27.1425au
58
− 20.7041u
58
+ ··· − 56.2659a − 215.782
a
11
=
u
u
3
+ u
a
8
=
2.09525au
58
+ 402.226u
58
+ ··· + 317.450a + 11.0185
27.1425au
58
− 96.9355u
58
+ ··· − 56.2659a + 88.0119
a
2
=
−168.522au
58
− 227.202u
58
+ ··· − 77.8489a + 429.624
67.4805au
58
− 61.6163u
58
+ ··· − 70.8785a − 232.710
(ii) Obstruction class = −1
(iii) Cusp Shapes = −372.274u
58
+ 267.999u
57
+ ··· − 702.756u + 77.0685
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
59
+ 28u
58
+ ··· + 414u − 81)
2
c
2
(u
59
+ 14u
57
+ ··· + 36u + 9)
2
c
3
u
118
− 30u
117
+ ··· − 1174u + 373
c
4
(u
59
− u
58
+ ··· − 2u + 1)
2
c
5
, c
7
u
118
+ u
117
+ ··· + 4805u + 275
c
6
(u
59
− 5u
58
+ ··· + 1690u − 227)
2
c
8
(u
59
+ 14u
57
+ ··· + 36u − 9)
2
c
9
, c
12
u
118
+ u
117
+ ··· + 13u + 1
c
10
u
118
+ 30u
117
+ ··· + 1174u + 373
c
11
(u
59
+ u
58
+ ··· − 2u − 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
59
+ 4y
58
+ ··· + 1220022y −6561)
2
c
2
, c
8
(y
59
+ 28y
58
+ ··· + 414y −81)
2
c
3
, c
10
y
118
− 72y
117
+ ··· − 14598888y + 139129
c
4
, c
11
(y
59
+ 49y
58
+ ··· − 36y −1)
2
c
5
, c
7
y
118
+ 49y
117
+ ··· − 4205975y + 75625
c
6
(y
59
− 31y
58
+ ··· + 42662y −51529)
2
c
9
, c
12
y
118
+ 49y
117
+ ··· − 85y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.974248
a = −0.422435 + 0.047119I
b = −0.465721 + 0.488306I
−2.45323 0
u = −0.974248
a = −0.422435 − 0.047119I
b = −0.465721 − 0.488306I
−2.45323 0
u = −0.616383 + 0.878313I
a = −0.389792 + 0.484669I
b = −0.299598 + 1.115800I
0.637962 + 1.184170I 0
u = −0.616383 + 0.878313I
a = −0.520375 − 0.252563I
b = 0.208429 + 0.727615I
0.637962 + 1.184170I 0
u = −0.616383 − 0.878313I
a = −0.389792 − 0.484669I
b = −0.299598 − 1.115800I
0.637962 − 1.184170I 0
u = −0.616383 − 0.878313I
a = −0.520375 + 0.252563I
b = 0.208429 − 0.727615I
0.637962 − 1.184170I 0
u = 0.160104 + 0.887211I
a = −0.606374 + 1.223140I
b = −0.181398 − 0.098838I
0.32511 + 2.19300I 0
u = 0.160104 + 0.887211I
a = −0.357456 − 0.267890I
b = 0.549568 + 1.119360I
0.32511 + 2.19300I 0
u = 0.160104 − 0.887211I
a = −0.606374 − 1.223140I
b = −0.181398 + 0.098838I
0.32511 − 2.19300I 0
u = 0.160104 − 0.887211I
a = −0.357456 + 0.267890I
b = 0.549568 − 1.119360I
0.32511 − 2.19300I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.346628 + 1.050780I
a = 1.52218 + 0.15604I
b = −1.43515 + 0.76855I
−1.105040 + 0.369460I 0
u = 0.346628 + 1.050780I
a = −1.91998 + 0.29232I
b = 0.362038 − 0.410182I
−1.105040 + 0.369460I 0
u = 0.346628 − 1.050780I
a = 1.52218 − 0.15604I
b = −1.43515 − 0.76855I
−1.105040 − 0.369460I 0
u = 0.346628 − 1.050780I
a = −1.91998 − 0.29232I
b = 0.362038 + 0.410182I
−1.105040 − 0.369460I 0
u = 0.307731 + 0.818133I
a = −1.48167 + 0.02104I
b = −0.09579 − 1.55964I
−5.27758 − 1.46200I 8.4003 + 23.0224I
u = 0.307731 + 0.818133I
a = −3.53563 + 0.52168I
b = 1.41990 − 1.97215I
−5.27758 − 1.46200I 8.4003 + 23.0224I
u = 0.307731 − 0.818133I
a = −1.48167 − 0.02104I
b = −0.09579 + 1.55964I
−5.27758 + 1.46200I 8.4003 − 23.0224I
u = 0.307731 − 0.818133I
a = −3.53563 − 0.52168I
b = 1.41990 + 1.97215I
−5.27758 + 1.46200I 8.4003 − 23.0224I
u = 0.373129 + 1.082460I
a = −0.186146 − 1.267850I
b = 0.177502 − 0.831850I
0.92231 − 6.36053I 0
u = 0.373129 + 1.082460I
a = 2.12050 − 0.15788I
b = −1.26159 + 0.99596I
0.92231 − 6.36053I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.373129 − 1.082460I
a = −0.186146 + 1.267850I
b = 0.177502 + 0.831850I
0.92231 + 6.36053I 0
u = 0.373129 − 1.082460I
a = 2.12050 + 0.15788I
b = −1.26159 − 0.99596I
0.92231 + 6.36053I 0
u = 0.643282 + 0.491700I
a = 0.197149 − 0.882984I
b = 0.607614 + 1.072220I
−4.47069 + 2.29186I −8.70845 − 5.66101I
u = 0.643282 + 0.491700I
a = 0.350461 − 1.306890I
b = −0.087102 − 0.691288I
−4.47069 + 2.29186I −8.70845 − 5.66101I
u = 0.643282 − 0.491700I
a = 0.197149 + 0.882984I
b = 0.607614 − 1.072220I
−4.47069 − 2.29186I −8.70845 + 5.66101I
u = 0.643282 − 0.491700I
a = 0.350461 + 1.306890I
b = −0.087102 + 0.691288I
−4.47069 − 2.29186I −8.70845 + 5.66101I
u = −0.642861 + 0.480334I
a = −0.170528 − 0.288510I
b = −0.465980 − 0.912841I
−4.19902 + 7.99685I −7.28681 − 11.66535I
u = −0.642861 + 0.480334I
a = −2.32051 + 1.78880I
b = 1.004950 + 0.686191I
−4.19902 + 7.99685I −7.28681 − 11.66535I
u = −0.642861 − 0.480334I
a = −0.170528 + 0.288510I
b = −0.465980 + 0.912841I
−4.19902 − 7.99685I −7.28681 + 11.66535I
u = −0.642861 − 0.480334I
a = −2.32051 − 1.78880I
b = 1.004950 − 0.686191I
−4.19902 − 7.99685I −7.28681 + 11.66535I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.566388 + 1.060870I
a = −1.25800 − 0.81911I
b = 0.254299 − 0.570666I
−2.76182 − 7.05009I 0
u = 0.566388 + 1.060870I
a = 1.70251 + 0.18296I
b = −1.29022 + 0.96132I
−2.76182 − 7.05009I 0
u = 0.566388 − 1.060870I
a = −1.25800 + 0.81911I
b = 0.254299 + 0.570666I
−2.76182 + 7.05009I 0
u = 0.566388 − 1.060870I
a = 1.70251 − 0.18296I
b = −1.29022 − 0.96132I
−2.76182 + 7.05009I 0
u = −0.374436 + 1.152900I
a = −0.80326 + 1.45454I
b = 1.87559 − 1.61777I
2.64835 + 6.33789I 0
u = −0.374436 + 1.152900I
a = 1.93886 + 0.24033I
b = −0.674816 − 0.976812I
2.64835 + 6.33789I 0
u = −0.374436 − 1.152900I
a = −0.80326 − 1.45454I
b = 1.87559 + 1.61777I
2.64835 − 6.33789I 0
u = −0.374436 − 1.152900I
a = 1.93886 − 0.24033I
b = −0.674816 + 0.976812I
2.64835 − 6.33789I 0
u = −0.556368 + 1.084320I
a = 0.611322 − 1.254560I
b = −0.181879 − 0.709545I
−2.68379 + 5.13285I 0
u = −0.556368 + 1.084320I
a = −1.88751 + 0.10443I
b = 1.23031 + 0.95333I
−2.68379 + 5.13285I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.556368 − 1.084320I
a = 0.611322 + 1.254560I
b = −0.181879 + 0.709545I
−2.68379 − 5.13285I 0
u = −0.556368 − 1.084320I
a = −1.88751 − 0.10443I
b = 1.23031 − 0.95333I
−2.68379 − 5.13285I 0
u = −0.424810 + 1.157070I
a = 0.266105 − 1.361470I
b = −0.145167 − 0.806235I
−0.65433 + 11.22720I 0
u = −0.424810 + 1.157070I
a = −1.95747 − 0.12629I
b = 1.22661 + 0.99336I
−0.65433 + 11.22720I 0
u = −0.424810 − 1.157070I
a = 0.266105 + 1.361470I
b = −0.145167 + 0.806235I
−0.65433 − 11.22720I 0
u = −0.424810 − 1.157070I
a = −1.95747 + 0.12629I
b = 1.22661 − 0.99336I
−0.65433 − 11.22720I 0
u = 0.148012 + 0.729341I
a = 0.11862 − 1.94126I
b = −0.046545 − 0.912670I
−2.60977 − 2.74850I −9.61755 + 8.55100I
u = 0.148012 + 0.729341I
a = −0.54007 − 2.42336I
b = 0.55160 + 1.75103I
−2.60977 − 2.74850I −9.61755 + 8.55100I
u = 0.148012 − 0.729341I
a = 0.11862 + 1.94126I
b = −0.046545 + 0.912670I
−2.60977 + 2.74850I −9.61755 − 8.55100I
u = 0.148012 − 0.729341I
a = −0.54007 + 2.42336I
b = 0.55160 − 1.75103I
−2.60977 + 2.74850I −9.61755 − 8.55100I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.136361 + 0.723393I
a = 0.460703 − 1.122880I
b = 0.249953 − 1.012360I
−0.54273 − 4.18418I −0.7207 + 16.6205I
u = 0.136361 + 0.723393I
a = 3.89862 − 0.46274I
b = −1.71652 + 0.69565I
−0.54273 − 4.18418I −0.7207 + 16.6205I
u = 0.136361 − 0.723393I
a = 0.460703 + 1.122880I
b = 0.249953 + 1.012360I
−0.54273 + 4.18418I −0.7207 − 16.6205I
u = 0.136361 − 0.723393I
a = 3.89862 + 0.46274I
b = −1.71652 − 0.69565I
−0.54273 + 4.18418I −0.7207 − 16.6205I
u = 0.477859 + 1.182000I
a = 0.562616 + 1.051710I
b = −1.46102 − 1.46311I
−0.16797 − 12.64270I 0
u = 0.477859 + 1.182000I
a = −1.84319 + 0.03471I
b = 0.786338 − 1.003220I
−0.16797 − 12.64270I 0
u = 0.477859 − 1.182000I
a = 0.562616 − 1.051710I
b = −1.46102 + 1.46311I
−0.16797 + 12.64270I 0
u = 0.477859 − 1.182000I
a = −1.84319 − 0.03471I
b = 0.786338 + 1.003220I
−0.16797 + 12.64270I 0
u = 0.788076 + 1.019980I
a = −0.501591 − 0.364281I
b = 0.424807 − 0.685140I
−2.50740 − 6.17991I 0
u = 0.788076 + 1.019980I
a = 1.65059 + 0.64202I
b = −1.11612 + 1.03002I
−2.50740 − 6.17991I 0
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.788076 − 1.019980I
a = −0.501591 + 0.364281I
b = 0.424807 + 0.685140I
−2.50740 + 6.17991I 0
u = 0.788076 − 1.019980I
a = 1.65059 − 0.64202I
b = −1.11612 − 1.03002I
−2.50740 + 6.17991I 0
u = −0.429800 + 1.216710I
a = 1.249470 + 0.131662I
b = −0.366186 − 0.510344I
1.50803 + 4.57483I 0
u = −0.429800 + 1.216710I
a = −1.55564 + 0.14036I
b = 1.54852 + 1.10815I
1.50803 + 4.57483I 0
u = −0.429800 − 1.216710I
a = 1.249470 − 0.131662I
b = −0.366186 + 0.510344I
1.50803 − 4.57483I 0
u = −0.429800 − 1.216710I
a = −1.55564 − 0.14036I
b = 1.54852 − 1.10815I
1.50803 − 4.57483I 0
u = −0.633524 + 0.312344I
a = −0.099044 − 0.577222I
b = −0.640592 + 1.061830I
−4.78069 − 0.45328I −8.62280 + 1.56790I
u = −0.633524 + 0.312344I
a = 0.55636 − 2.17187I
b = 0.423500 − 0.458593I
−4.78069 − 0.45328I −8.62280 + 1.56790I
u = −0.633524 − 0.312344I
a = −0.099044 + 0.577222I
b = −0.640592 − 1.061830I
−4.78069 + 0.45328I −8.62280 − 1.56790I
u = −0.633524 − 0.312344I
a = 0.55636 + 2.17187I
b = 0.423500 + 0.458593I
−4.78069 + 0.45328I −8.62280 − 1.56790I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.699228 + 1.121130I
a = 0.136902 + 0.470317I
b = 0.353588 + 1.260610I
−0.59586 + 3.55518I 0
u = 0.699228 + 1.121130I
a = 0.401777 − 0.243100I
b = −0.262030 + 0.601936I
−0.59586 + 3.55518I 0
u = 0.699228 − 1.121130I
a = 0.136902 − 0.470317I
b = 0.353588 − 1.260610I
−0.59586 − 3.55518I 0
u = 0.699228 − 1.121130I
a = 0.401777 + 0.243100I
b = −0.262030 − 0.601936I
−0.59586 − 3.55518I 0
u = −0.051363 + 1.336090I
a = −1.293320 + 0.524250I
b = 1.196380 − 0.535448I
7.86174 + 2.79901I 0
u = −0.051363 + 1.336090I
a = 1.34720 + 0.47819I
b = −1.035230 − 0.566468I
7.86174 + 2.79901I 0
u = −0.051363 − 1.336090I
a = −1.293320 − 0.524250I
b = 1.196380 + 0.535448I
7.86174 − 2.79901I 0
u = −0.051363 − 1.336090I
a = 1.34720 − 0.47819I
b = −1.035230 + 0.566468I
7.86174 − 2.79901I 0
u = 0.626015 + 0.015955I
a = 0.548454 + 0.198254I
b = −0.469338 + 1.089150I
−3.38442 − 8.35809I −7.00708 + 7.27114I
u = 0.626015 + 0.015955I
a = −0.26648 + 3.06750I
b = 0.773216 + 0.747951I
−3.38442 − 8.35809I −7.00708 + 7.27114I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.626015 − 0.015955I
a = 0.548454 − 0.198254I
b = −0.469338 − 1.089150I
−3.38442 + 8.35809I −7.00708 − 7.27114I
u = 0.626015 − 0.015955I
a = −0.26648 − 3.06750I
b = 0.773216 − 0.747951I
−3.38442 + 8.35809I −7.00708 − 7.27114I
u = −0.190249 + 1.399080I
a = −0.024830 + 0.534345I
b = 0.138671 − 0.227105I
−0.18748 + 2.52042I 0
u = −0.190249 + 1.399080I
a = 0.300172 − 0.366177I
b = −0.59533 + 1.79660I
−0.18748 + 2.52042I 0
u = −0.190249 − 1.399080I
a = −0.024830 − 0.534345I
b = 0.138671 + 0.227105I
−0.18748 − 2.52042I 0
u = −0.190249 − 1.399080I
a = 0.300172 + 0.366177I
b = −0.59533 − 1.79660I
−0.18748 − 2.52042I 0
u = −0.488881 + 0.303856I
a = −0.737878 − 0.060779I
b = 0.354514 + 1.076950I
−0.85444 + 3.23679I −3.13111 − 5.47740I
u = −0.488881 + 0.303856I
a = −1.77604 + 2.28587I
b = −0.537600 + 0.678188I
−0.85444 + 3.23679I −3.13111 − 5.47740I
u = −0.488881 − 0.303856I
a = −0.737878 + 0.060779I
b = 0.354514 − 1.076950I
−0.85444 − 3.23679I −3.13111 + 5.47740I
u = −0.488881 − 0.303856I
a = −1.77604 − 2.28587I
b = −0.537600 − 0.678188I
−0.85444 − 3.23679I −3.13111 + 5.47740I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.203007 + 0.451248I
a = −0.324282 − 0.908451I
b = 0.639423 + 1.195230I
−1.09124 + 3.38818I −5.28744 − 0.35006I
u = 0.203007 + 0.451248I
a = −4.43029 − 0.21841I
b = −0.357474 − 0.112457I
−1.09124 + 3.38818I −5.28744 − 0.35006I
u = 0.203007 − 0.451248I
a = −0.324282 + 0.908451I
b = 0.639423 − 1.195230I
−1.09124 − 3.38818I −5.28744 + 0.35006I
u = 0.203007 − 0.451248I
a = −4.43029 + 0.21841I
b = −0.357474 + 0.112457I
−1.09124 − 3.38818I −5.28744 + 0.35006I
u = −0.73608 + 1.32878I
a = 0.706150 − 0.077875I
b = −0.442880 − 0.554410I
2.16805 + 7.38733I 0
u = −0.73608 + 1.32878I
a = −1.355480 + 0.388578I
b = 1.17883 + 1.23108I
2.16805 + 7.38733I 0
u = −0.73608 − 1.32878I
a = 0.706150 + 0.077875I
b = −0.442880 + 0.554410I
2.16805 − 7.38733I 0
u = −0.73608 − 1.32878I
a = −1.355480 − 0.388578I
b = 1.17883 − 1.23108I
2.16805 − 7.38733I 0
u = 0.144988 + 0.455917I
a = 0.543645 − 0.637738I
b = −0.231791 + 1.315070I
−5.23264 − 0.18537I −5.10684 + 9.45911I
u = 0.144988 + 0.455917I
a = 4.73234 − 2.07071I
b = 0.230392 + 0.397665I
−5.23264 − 0.18537I −5.10684 + 9.45911I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.144988 − 0.455917I
a = 0.543645 + 0.637738I
b = −0.231791 − 1.315070I
−5.23264 + 0.18537I −5.10684 − 9.45911I
u = 0.144988 − 0.455917I
a = 4.73234 + 2.07071I
b = 0.230392 − 0.397665I
−5.23264 + 0.18537I −5.10684 − 9.45911I
u = 0.84710 + 1.33446I
a = −0.618994 − 0.084260I
b = 0.477567 − 0.568731I
0.45379 − 12.54640I 0
u = 0.84710 + 1.33446I
a = 1.307490 + 0.483428I
b = −1.10800 + 1.22373I
0.45379 − 12.54640I 0
u = 0.84710 − 1.33446I
a = −0.618994 + 0.084260I
b = 0.477567 + 0.568731I
0.45379 + 12.54640I 0
u = 0.84710 − 1.33446I
a = 1.307490 − 0.483428I
b = −1.10800 − 1.22373I
0.45379 + 12.54640I 0
u = −0.037123 + 0.401056I
a = 0.636805 − 1.099910I
b = −0.59849 + 1.30912I
−3.56442 − 8.10409I −17.0460 + 4.5293I
u = −0.037123 + 0.401056I
a = 8.14813 + 0.91511I
b = 0.337519 + 0.027910I
−3.56442 − 8.10409I −17.0460 + 4.5293I
u = −0.037123 − 0.401056I
a = 0.636805 + 1.099910I
b = −0.59849 − 1.30912I
−3.56442 + 8.10409I −17.0460 − 4.5293I
u = −0.037123 − 0.401056I
a = 8.14813 − 0.91511I
b = 0.337519 − 0.027910I
−3.56442 + 8.10409I −17.0460 − 4.5293I
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.34530 + 1.64339I
a = −0.029382 + 0.257545I
b = 0.23692 + 1.59759I
−2.02916 − 1.62533I 0
u = 0.34530 + 1.64339I
a = 0.146412 − 0.208006I
b = −0.139978 + 0.354900I
−2.02916 − 1.62533I 0
u = 0.34530 − 1.64339I
a = −0.029382 − 0.257545I
b = 0.23692 − 1.59759I
−2.02916 + 1.62533I 0
u = 0.34530 − 1.64339I
a = 0.146412 + 0.208006I
b = −0.139978 − 0.354900I
−2.02916 + 1.62533I 0
u = −0.64420 + 2.25311I
a = 0.1019810 + 0.0566033I
b = −0.71768 + 2.18101I
−1.96431 − 1.71276I 0
u = −0.64420 + 2.25311I
a = −0.0498684 + 0.0094625I
b = 0.1086660 + 0.0456200I
−1.96431 − 1.71276I 0
u = −0.64420 − 2.25311I
a = 0.1019810 − 0.0566033I
b = −0.71768 − 2.18101I
−1.96431 + 1.71276I 0
u = −0.64420 − 2.25311I
a = −0.0498684 − 0.0094625I
b = 0.1086660 − 0.0456200I
−1.96431 + 1.71276I 0
28
III.
I
u
3
= h4.33 × 10
6
au
21
− 5.57 × 10
6
u
21
+ · · · + 7.71 × 10
5
a + 2.10 × 10
7
, 5.15 ×
10
7
au
21
+5.00×10
7
u
21
+· · ·−1.36×10
8
a−4.92×10
7
, u
22
+13u
20
+· · ·−3u+1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
9
=
a
−1.71831au
21
+ 2.21242u
21
+ ··· − 0.306133a − 8.32664
a
6
=
3.26754au
21
+ 0.994732u
21
+ ··· − 12.1468a − 5.94072
0.397380au
21
+ 9.07632u
21
+ ··· − 1.71831a + 6.78609
a
10
=
−1.71831au
21
+ 2.21242u
21
+ ··· + 0.693867a − 8.32664
−1.71831au
21
+ 2.21242u
21
+ ··· − 0.306133a − 8.32664
a
7
=
−0.306133au
21
+ 9.39187u
21
+ ··· + 2.46799a + 4.68568
0.397380au
21
+ 17.4735u
21
+ ··· − 1.71831a + 17.4125
a
1
=
5.78354au
21
− 0.832759u
21
+ ··· + 3.33949a − 1.66232
2.01279au
21
+ 0.435494u
21
+ ··· + 0.815041a + 3.41229
a
3
=
−2.11053au
21
− 14.1733u
21
+ ··· + 7.37956a + 1.79136
0.227978au
21
− 14.1807u
21
+ ··· − 0.845863a − 15.9659
a
11
=
u
u
3
+ u
a
8
=
−0.703514au
21
+ 4.89251u
21
+ ··· + 4.18630a + 1.41814
0.227978au
21
+ 14.7190u
21
+ ··· − 0.845863a + 14.9625
a
2
=
−3.69975au
21
− 8.88729u
21
+ ··· − 3.72407a + 4.99331
0.825793au
21
+ 4.96517u
21
+ ··· − 3.10305a − 30.5982
(ii) Obstruction class = 1
(iii) Cusp Shapes =
220311408
2517311
u
21
+
43573144
2517311
u
20
+ ··· +
724321844
2517311
u −
26958998
2517311
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
22
− 16u
21
+ ··· − 51u + 13)
2
c
2
, c
8
u
44
+ 16u
42
+ ··· + 51u
2
+ 13
c
3
, c
10
u
44
+ 11u
43
+ ··· − 16u + 1
c
4
(u
22
+ 13u
20
+ ··· − 3u + 1)
2
c
5
, c
7
u
44
− 2u
43
+ ··· − 19u + 1
c
6
(u
22
+ 3u
21
+ ··· − 4u + 1)
2
c
9
, c
12
u
44
+ 2u
43
+ ··· + 15u + 1
c
11
(u
22
+ 13u
20
+ ··· + 3u + 1)
2
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
22
− 12y
21
+ ··· − 1977y + 169)
2
c
2
, c
8
(y
22
+ 16y
21
+ ··· + 51y + 13)
2
c
3
, c
10
y
44
− 59y
43
+ ··· − 2y + 1
c
4
, c
11
(y
22
+ 26y
21
+ ··· + 25y + 1)
2
c
5
, c
7
y
44
+ 36y
43
+ ··· − 73y + 1
c
6
(y
22
− 11y
21
+ ··· − 12y + 1)
2
c
9
, c
12
y
44
+ 40y
43
+ ··· + 135y + 1
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.201771 + 1.057170I
a = 0.627916 + 0.573243I
b = −0.256241 + 1.016760I
−1.76921 − 1.89270I −4.21340 + 3.50057I
u = −0.201771 + 1.057170I
a = −0.436160 − 0.556434I
b = 0.396621 + 0.698733I
−1.76921 − 1.89270I −4.21340 + 3.50057I
u = −0.201771 − 1.057170I
a = 0.627916 − 0.573243I
b = −0.256241 − 1.016760I
−1.76921 + 1.89270I −4.21340 − 3.50057I
u = −0.201771 − 1.057170I
a = −0.436160 + 0.556434I
b = 0.396621 − 0.698733I
−1.76921 + 1.89270I −4.21340 − 3.50057I
u = 0.296107 + 0.837502I
a = 1.96433 + 0.02934I
b = −0.06682 + 1.52563I
−5.37912 − 1.38910I −44.3694 − 13.7052I
u = 0.296107 + 0.837502I
a = −3.41864 + 1.50660I
b = 1.14816 − 2.79572I
−5.37912 − 1.38910I −44.3694 − 13.7052I
u = 0.296107 − 0.837502I
a = 1.96433 − 0.02934I
b = −0.06682 − 1.52563I
−5.37912 + 1.38910I −44.3694 + 13.7052I
u = 0.296107 − 0.837502I
a = −3.41864 − 1.50660I
b = 1.14816 + 2.79572I
−5.37912 + 1.38910I −44.3694 + 13.7052I
u = −0.595144 + 0.962657I
a = 0.659137 − 1.137950I
b = −0.432485 − 0.591297I
−2.25765 + 7.48045I 0.4859 − 14.1943I
u = −0.595144 + 0.962657I
a = −1.92051 + 0.38095I
b = 1.27908 + 0.89560I
−2.25765 + 7.48045I 0.4859 − 14.1943I
32
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.595144 − 0.962657I
a = 0.659137 + 1.137950I
b = −0.432485 + 0.591297I
−2.25765 − 7.48045I 0.4859 + 14.1943I
u = −0.595144 − 0.962657I
a = −1.92051 − 0.38095I
b = 1.27908 − 0.89560I
−2.25765 − 7.48045I 0.4859 + 14.1943I
u = 0.618125 + 1.021360I
a = −0.187871 − 0.945472I
b = 0.170784 − 0.591557I
−2.19248 − 5.12417I 3.58965 + 2.51687I
u = 0.618125 + 1.021360I
a = 1.92298 + 0.31867I
b = −1.16557 + 0.89974I
−2.19248 − 5.12417I 3.58965 + 2.51687I
u = 0.618125 − 1.021360I
a = −0.187871 + 0.945472I
b = 0.170784 + 0.591557I
−2.19248 + 5.12417I 3.58965 − 2.51687I
u = 0.618125 − 1.021360I
a = 1.92298 − 0.31867I
b = −1.16557 − 0.89974I
−2.19248 + 5.12417I 3.58965 − 2.51687I
u = −0.421138 + 1.174640I
a = −0.679434 + 0.402271I
b = 1.012810 − 0.662909I
2.63762 + 5.69978I 2.92422 − 3.43709I
u = −0.421138 + 1.174640I
a = −1.77924 − 0.04634I
b = 0.871174 + 0.880878I
2.63762 + 5.69978I 2.92422 − 3.43709I
u = −0.421138 − 1.174640I
a = −0.679434 − 0.402271I
b = 1.012810 + 0.662909I
2.63762 − 5.69978I 2.92422 + 3.43709I
u = −0.421138 − 1.174640I
a = −1.77924 + 0.04634I
b = 0.871174 − 0.880878I
2.63762 − 5.69978I 2.92422 + 3.43709I
33
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.536596 + 1.174720I
a = 0.450802 − 0.173817I
b = −0.406133 − 0.554925I
0.59983 − 11.01500I 1.07553 + 8.59857I
u = 0.536596 + 1.174720I
a = 1.80600 + 0.18193I
b = −0.995487 + 0.917927I
0.59983 − 11.01500I 1.07553 + 8.59857I
u = 0.536596 − 1.174720I
a = 0.450802 + 0.173817I
b = −0.406133 + 0.554925I
0.59983 + 11.01500I 1.07553 − 8.59857I
u = 0.536596 − 1.174720I
a = 1.80600 − 0.18193I
b = −0.995487 − 0.917927I
0.59983 + 11.01500I 1.07553 − 8.59857I
u = 0.005831 + 0.657923I
a = 0.641547 + 0.850207I
b = −0.486384 + 1.024680I
−0.43220 − 3.66490I 4.41010 + 2.43967I
u = 0.005831 + 0.657923I
a = 3.47837 + 0.40078I
b = −1.025210 + 0.525608I
−0.43220 − 3.66490I 4.41010 + 2.43967I
u = 0.005831 − 0.657923I
a = 0.641547 − 0.850207I
b = −0.486384 − 1.024680I
−0.43220 + 3.66490I 4.41010 − 2.43967I
u = 0.005831 − 0.657923I
a = 3.47837 − 0.40078I
b = −1.025210 − 0.525608I
−0.43220 + 3.66490I 4.41010 − 2.43967I
u = −0.001384 + 0.564588I
a = −0.499426 − 0.235317I
b = 0.57946 + 1.29783I
−3.30245 + 8.15205I 12.8474 − 9.3878I
u = −0.001384 + 0.564588I
a = −6.37715 + 1.41055I
b = 0.652275 + 0.068309I
−3.30245 + 8.15205I 12.8474 − 9.3878I
34
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.001384 − 0.564588I
a = −0.499426 + 0.235317I
b = 0.57946 − 1.29783I
−3.30245 − 8.15205I 12.8474 + 9.3878I
u = −0.001384 − 0.564588I
a = −6.37715 − 1.41055I
b = 0.652275 − 0.068309I
−3.30245 − 8.15205I 12.8474 + 9.3878I
u = 0.01460 + 1.46352I
a = 0.167274 − 0.498034I
b = −0.027733 + 0.357376I
−0.34964 + 2.63420I −23.8140 − 7.7608I
u = 0.01460 + 1.46352I
a = 0.337597 − 0.315688I
b = −0.36501 + 1.98484I
−0.34964 + 2.63420I −23.8140 − 7.7608I
u = 0.01460 − 1.46352I
a = 0.167274 + 0.498034I
b = −0.027733 − 0.357376I
−0.34964 − 2.63420I −23.8140 + 7.7608I
u = 0.01460 − 1.46352I
a = 0.337597 + 0.315688I
b = −0.36501 − 1.98484I
−0.34964 − 2.63420I −23.8140 + 7.7608I
u = 0.201375 + 0.329683I
a = 1.17523 − 0.99657I
b = 0.282712 + 1.277420I
−5.32068 − 0.31973I −9.05297 + 4.67817I
u = 0.201375 + 0.329683I
a = −1.54080 − 4.47948I
b = 0.323637 − 0.757875I
−5.32068 − 0.31973I −9.05297 + 4.67817I
u = 0.201375 − 0.329683I
a = 1.17523 + 0.99657I
b = 0.282712 − 1.277420I
−5.32068 + 0.31973I −9.05297 − 4.67817I
u = 0.201375 − 0.329683I
a = −1.54080 + 4.47948I
b = 0.323637 + 0.757875I
−5.32068 + 0.31973I −9.05297 − 4.67817I
35
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.45320 + 2.24172I
a = 0.0961240 + 0.0785902I
b = −0.53608 + 2.17207I
−1.97323 − 1.71954I −198.883 + 270.228I
u = −0.45320 + 2.24172I
a = 0.01193270 − 0.00475518I
b = 0.0464291 + 0.0694636I
−1.97323 − 1.71954I −198.883 + 270.228I
u = −0.45320 − 2.24172I
a = 0.0961240 − 0.0785902I
b = −0.53608 − 2.17207I
−1.97323 + 1.71954I −198.883 − 270.228I
u = −0.45320 − 2.24172I
a = 0.01193270 + 0.00475518I
b = 0.0464291 − 0.0694636I
−1.97323 + 1.71954I −198.883 − 270.228I
36
IV.
I
u
4
= h−u
4
−2u
3
−2u
2
+b−2u, u
4
+u
3
+a−u−2, u
5
+2u
4
+3u
3
+3u
2
+u+1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
9
=
−u
4
− u
3
+ u + 2
u
4
+ 2u
3
+ 2u
2
+ 2u
a
6
=
−2u
4
− 4u
3
− 5u
2
− 5u
u
2
+ u + 1
a
10
=
u
3
+ 2u
2
+ 3u + 2
u
4
+ 2u
3
+ 2u
2
+ 2u
a
7
=
u
3
+ 2u
2
+ 2u + 2
u
4
+ 2u
3
+ 3u
2
+ 2u
a
1
=
u
4
+ 2u
3
+ 2u
2
+ u − 1
−u
4
− 2u
3
− 3u
2
− 2u − 1
a
3
=
u
4
+ 2u
3
+ 2u
2
+ u − 1
−u
4
− 2u
3
− 3u
2
− 2u − 1
a
11
=
u
u
3
+ u
a
8
=
−u
4
− u
3
+ u + 2
u
4
+ 2u
3
+ 2u
2
+ 2u
a
2
=
u
4
+ 2u
3
+ 2u
2
+ u − 1
−u
4
− 2u
3
− 3u
2
− 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5u
4
+ 13u
3
+ 19u
2
+ 13u + 9
37
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
8
u
5
c
3
, c
10
u
5
− u
4
− u
3
+ u
2
− 1
c
4
u
5
+ 2u
4
+ 3u
3
+ 3u
2
+ u + 1
c
5
, c
7
u
5
+ 2u
4
+ 3u
3
+ 3u
2
+ 3u + 1
c
6
u
5
− 3u
4
+ 5u
3
− 4u
2
+ 3u − 1
c
9
, c
12
u
5
− u
3
+ u
2
+ u − 1
c
11
u
5
− 2u
4
+ 3u
3
− 3u
2
+ u − 1
38
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
8
y
5
c
3
, c
10
y
5
− 3y
4
+ 3y
3
− 3y
2
+ 2y −1
c
4
, c
11
y
5
+ 2y
4
− y
3
− 7y
2
− 5y −1
c
5
, c
7
y
5
+ 2y
4
+ 3y
3
+ 5y
2
+ 3y −1
c
6
y
5
+ y
4
+ 7y
3
+ 8y
2
+ y −1
c
9
, c
12
y
5
− 2y
4
+ 3y
3
− 3y
2
+ 3y −1
39
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.372466 + 1.263920I
a = −1.347300 + 0.010044I
b = 1.045750 + 0.405588I
3.01018 + 5.17259I 5.18262 − 7.13326I
u = −0.372466 − 1.263920I
a = −1.347300 − 0.010044I
b = 1.045750 − 0.405588I
3.01018 − 5.17259I 5.18262 + 7.13326I
u = −1.33263
a = −0.119827
b = −0.692872
−2.14584 10.4210
u = 0.038780 + 0.656277I
a = 1.90721 + 0.97967I
b = −0.699311 + 0.811268I
−0.29233 − 3.70382I 1.60688 + 5.64419I
u = 0.038780 − 0.656277I
a = 1.90721 − 0.97967I
b = −0.699311 − 0.811268I
−0.29233 + 3.70382I 1.60688 − 5.64419I
40
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
5
(u
22
− 16u
21
+ ··· − 51u + 13)
2
· (u
85
+ 45u
84
+ ··· − 58368u − 4096)
c
2
, c
8
u
5
(u
44
+ 16u
42
+ ··· + 51u
2
+ 13)(u
85
+ 3u
84
+ ··· + 288u + 64)
c
3
, c
10
(u
5
− u
4
− u
3
+ u
2
− 1)(u
44
+ 11u
43
+ ··· − 16u + 1)
· (u
85
− u
84
+ ··· − 3u + 1)
c
4
(u
5
+ 2u
4
+ 3u
3
+ 3u
2
+ u + 1)(u
22
+ 13u
20
+ ··· − 3u + 1)
2
· (u
85
+ 5u
84
+ ··· + 951u + 160)
c
5
, c
7
(u
5
+ 2u
4
+ 3u
3
+ 3u
2
+ 3u + 1)(u
44
− 2u
43
+ ··· − 19u + 1)
· (u
85
+ 2u
84
+ ··· + 54u − 1)
c
6
(u
5
− 3u
4
+ 5u
3
− 4u
2
+ 3u − 1)(u
22
+ 3u
21
+ ··· − 4u + 1)
2
· (u
85
+ 10u
84
+ ··· − 35445u − 2194)
c
9
, c
12
(u
5
− u
3
+ u
2
+ u − 1)(u
44
+ 2u
43
+ ··· + 15u + 1)
· (u
85
− 3u
83
+ ··· − 4u + 1)
c
11
(u
5
− 2u
4
+ 3u
3
− 3u
2
+ u − 1)(u
22
+ 13u
20
+ ··· + 3u + 1)
2
· (u
85
+ 5u
84
+ ··· + 951u + 160)
41
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
5
(y
22
− 12y
21
+ ··· − 1977y + 169)
2
· (y
85
+ y
84
+ ··· + 204472320y −16777216)
c
2
, c
8
y
5
(y
22
+ 16y
21
+ ··· + 51y + 13)
2
· (y
85
+ 45y
84
+ ··· − 58368y −4096)
c
3
, c
10
(y
5
− 3y
4
+ 3y
3
− 3y
2
+ 2y −1)(y
44
− 59y
43
+ ··· − 2y + 1)
· (y
85
− y
84
+ ··· − 53y −1)
c
4
, c
11
(y
5
+ 2y
4
− y
3
− 7y
2
− 5y −1)(y
22
+ 26y
21
+ ··· + 25y + 1)
2
· (y
85
+ 37y
84
+ ··· − 57839y −25600)
c
5
, c
7
(y
5
+ 2y
4
+ 3y
3
+ 5y
2
+ 3y −1)(y
44
+ 36y
43
+ ··· − 73y + 1)
· (y
85
− 18y
84
+ ··· + 2716y −1)
c
6
(y
5
+ y
4
+ 7y
3
+ 8y
2
+ y −1)(y
22
− 11y
21
+ ··· − 12y + 1)
2
· (y
85
+ 2y
84
+ ··· + 255642685y −4813636)
c
9
, c
12
(y
5
− 2y
4
+ 3y
3
− 3y
2
+ 3y −1)(y
44
+ 40y
43
+ ··· + 135y + 1)
· (y
85
− 6y
84
+ ··· + 46y −1)
42
