12a
0631
(K12a
0631
)
A knot diagram
1
Linearized knot diagam
3 7 10 9 11 2 6 5 12 1 8 4
Solving Sequence
2,6
7 3
8,11
12 1 5 9 4 10
c
6
c
2
c
7
c
11
c
1
c
5
c
8
c
4
c
10
c
3
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.55586 × 10
199
u
136
− 3.48558 × 10
199
u
135
+ ··· + 7.08230 × 10
199
b − 2.19097 × 10
201
,
− 3.62369 × 10
200
u
136
+ 5.95737 × 10
199
u
135
+ ··· + 9.20699 × 10
200
a − 4.72404 × 10
202
,
u
137
− 20u
135
+ ··· + 8u + 13i
I
u
2
= h−2u
24
− 2u
23
+ ··· + b + 3u, 411u
24
+ 715u
23
+ ··· + 29a − 1052, u
25
+ u
24
+ ··· − 9u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 162 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−1.56 × 10
199
u
136
− 3.49 × 10
199
u
135
+ · · · + 7.08 × 10
199
b − 2.19 ×
10
201
, −3.62 × 10
200
u
136
+ 5.96 × 10
199
u
135
+ · · · + 9.21 × 10
200
a − 4.72 ×
10
202
, u
137
− 20u
135
+ · · · + 8u + 13i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
u
2
a
11
=
0.393580u
136
− 0.0647048u
135
+ ··· − 72.5869u + 51.3092
0.219683u
136
+ 0.492153u
135
+ ··· − 16.7611u + 30.9359
a
12
=
0.624416u
136
− 1.58638u
135
+ ··· − 71.2059u + 68.4912
1.42220u
136
+ 0.528391u
135
+ ··· − 23.5112u + 50.2466
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
5.56418u
136
− 4.23778u
135
+ ··· − 98.6052u + 66.8624
3.90303u
136
− 4.04280u
135
+ ··· − 37.9656u + 104.599
a
9
=
−0.540857u
136
+ 1.45019u
135
+ ··· + 13.5778u − 12.5870
−2.27532u
136
− 0.201414u
135
+ ··· + 54.9112u − 22.6952
a
4
=
4.41963u
136
− 3.59377u
135
+ ··· − 71.2216u + 92.7479
4.18373u
136
− 3.47970u
135
+ ··· − 56.9236u + 81.5572
a
10
=
0.208814u
136
− 0.757186u
135
+ ··· − 69.1192u + 57.1447
0.453845u
136
+ 0.907411u
135
+ ··· − 0.585492u + 26.8148
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.68992u
136
+ 6.00496u
135
+ ··· − 46.6040u − 120.851
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
137
+ 40u
136
+ ··· + 4042u + 169
c
2
, c
6
u
137
− 20u
135
+ ··· + 8u + 13
c
3
u
137
+ 2u
136
+ ··· − 31644u + 3869
c
4
, c
8
u
137
+ 6u
136
+ ··· + 60u + 2
c
5
u
137
+ u
136
+ ··· + 11u + 1
c
9
u
137
− 12u
136
+ ··· + 48u + 1
c
10
u
137
+ 9u
136
+ ··· + 32u − 128
c
11
u
137
+ u
136
+ ··· + 760u + 7
c
12
u
137
+ 9u
136
+ ··· + 55158u + 5036
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
137
+ 120y
136
+ ··· + 779962y −28561
c
2
, c
6
y
137
− 40y
136
+ ··· + 4042y −169
c
3
y
137
+ 36y
136
+ ··· − 513688022y −14969161
c
4
, c
8
y
137
+ 100y
136
+ ··· − 848y −4
c
5
y
137
− 3y
136
+ ··· − 191y −1
c
9
y
137
+ 12y
136
+ ··· − 696y −1
c
10
y
137
+ 21y
136
+ ··· + 152576y −16384
c
11
y
137
− 13y
136
+ ··· + 530448y −49
c
12
y
137
+ 35y
136
+ ··· − 1685724212y −25361296
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.950342 + 0.290973I
a = 0.93783 − 1.43485I
b = −0.91390 − 1.41574I
−6.41076 + 4.67038I 0
u = −0.950342 − 0.290973I
a = 0.93783 + 1.43485I
b = −0.91390 + 1.41574I
−6.41076 − 4.67038I 0
u = −1.001520 + 0.114802I
a = 1.62158 − 1.27980I
b = 0.085542 − 0.708863I
−5.96822 + 4.40940I 0
u = −1.001520 − 0.114802I
a = 1.62158 + 1.27980I
b = 0.085542 + 0.708863I
−5.96822 − 4.40940I 0
u = −0.909207 + 0.443165I
a = 0.530936 − 0.405342I
b = 0.330665 − 0.334576I
−1.89367 + 1.23105I 0
u = −0.909207 − 0.443165I
a = 0.530936 + 0.405342I
b = 0.330665 + 0.334576I
−1.89367 − 1.23105I 0
u = 0.956317 + 0.220620I
a = −0.931643 − 1.054290I
b = 0.591141 − 0.803215I
−2.78104 − 3.83969I 0
u = 0.956317 − 0.220620I
a = −0.931643 + 1.054290I
b = 0.591141 + 0.803215I
−2.78104 + 3.83969I 0
u = 1.007280 + 0.176412I
a = 0.008920 + 1.172450I
b = −0.75856 + 1.28902I
−6.99924 − 5.78107I 0
u = 1.007280 − 0.176412I
a = 0.008920 − 1.172450I
b = −0.75856 − 1.28902I
−6.99924 + 5.78107I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.935256 + 0.422309I
a = 0.582088 − 0.381280I
b = 0.117649 − 0.808197I
−1.81476 + 1.51215I 0
u = −0.935256 − 0.422309I
a = 0.582088 + 0.381280I
b = 0.117649 + 0.808197I
−1.81476 − 1.51215I 0
u = −0.791307 + 0.549429I
a = 0.446544 − 0.685802I
b = 0.266359 − 0.001806I
−1.92744 + 1.24860I 0
u = −0.791307 − 0.549429I
a = 0.446544 + 0.685802I
b = 0.266359 + 0.001806I
−1.92744 − 1.24860I 0
u = 0.894078 + 0.265913I
a = −1.65379 − 0.07115I
b = −0.283343 − 1.286370I
−6.60071 − 0.53295I 0
u = 0.894078 − 0.265913I
a = −1.65379 + 0.07115I
b = −0.283343 + 1.286370I
−6.60071 + 0.53295I 0
u = 0.794489 + 0.731554I
a = 1.62095 + 0.72026I
b = −1.375230 − 0.223785I
2.71952 − 0.44182I 0
u = 0.794489 − 0.731554I
a = 1.62095 − 0.72026I
b = −1.375230 + 0.223785I
2.71952 + 0.44182I 0
u = 0.782958 + 0.749202I
a = −1.65544 − 0.30724I
b = −0.0336307 + 0.0554863I
−0.37534 + 3.64365I 0
u = 0.782958 − 0.749202I
a = −1.65544 + 0.30724I
b = −0.0336307 − 0.0554863I
−0.37534 − 3.64365I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.768257 + 0.785459I
a = −0.99074 + 1.59719I
b = 1.41503 − 1.30206I
−0.73290 − 4.89341I 0
u = −0.768257 − 0.785459I
a = −0.99074 − 1.59719I
b = 1.41503 + 1.30206I
−0.73290 + 4.89341I 0
u = −1.098210 + 0.039739I
a = 0.000744 + 0.224690I
b = 0.429666 + 0.334160I
−2.38231 − 0.07495I 0
u = −1.098210 − 0.039739I
a = 0.000744 − 0.224690I
b = 0.429666 − 0.334160I
−2.38231 + 0.07495I 0
u = −1.014590 + 0.425663I
a = −1.130760 − 0.526430I
b = −0.263711 + 0.872601I
−5.56798 + 0.31097I 0
u = −1.014590 − 0.425663I
a = −1.130760 + 0.526430I
b = −0.263711 − 0.872601I
−5.56798 − 0.31097I 0
u = 1.084680 + 0.245425I
a = −0.373890 − 1.292780I
b = 0.599391 − 0.872750I
−2.80549 − 5.27118I 0
u = 1.084680 − 0.245425I
a = −0.373890 + 1.292780I
b = 0.599391 + 0.872750I
−2.80549 + 5.27118I 0
u = −0.885377 + 0.676654I
a = −1.39524 − 0.56773I
b = 0.207385 + 0.294997I
−2.12146 + 3.75084I 0
u = −0.885377 − 0.676654I
a = −1.39524 + 0.56773I
b = 0.207385 − 0.294997I
−2.12146 − 3.75084I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.986584 + 0.522645I
a = −0.537739 − 1.149890I
b = 0.128058 − 1.077410I
−3.61378 − 1.44795I 0
u = 0.986584 − 0.522645I
a = −0.537739 + 1.149890I
b = 0.128058 + 1.077410I
−3.61378 + 1.44795I 0
u = 0.048135 + 0.880536I
a = −0.493626 − 0.402684I
b = 0.622431 + 0.305290I
2.56389 + 3.71181I 0
u = 0.048135 − 0.880536I
a = −0.493626 + 0.402684I
b = 0.622431 − 0.305290I
2.56389 − 3.71181I 0
u = 0.709176 + 0.889402I
a = 1.060470 + 0.245934I
b = −0.938472 − 0.032551I
4.44847 + 0.62496I 0
u = 0.709176 − 0.889402I
a = 1.060470 − 0.245934I
b = −0.938472 + 0.032551I
4.44847 − 0.62496I 0
u = −0.804416 + 0.811717I
a = 1.58736 − 0.88904I
b = −0.984549 + 0.325999I
3.76794 − 2.21552I 0
u = −0.804416 − 0.811717I
a = 1.58736 + 0.88904I
b = −0.984549 − 0.325999I
3.76794 + 2.21552I 0
u = −0.738379 + 0.880183I
a = 0.924035 − 0.625755I
b = −0.917993 + 1.004520I
4.78596 − 4.84103I 0
u = −0.738379 − 0.880183I
a = 0.924035 + 0.625755I
b = −0.917993 − 1.004520I
4.78596 + 4.84103I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.101370 + 0.334392I
a = −0.630612 + 1.044650I
b = 0.77479 + 1.20521I
−6.0459 + 13.5824I 0
u = −1.101370 − 0.334392I
a = −0.630612 − 1.044650I
b = 0.77479 − 1.20521I
−6.0459 − 13.5824I 0
u = −0.878380 + 0.744243I
a = 0.802399 − 0.213731I
b = 0.056170 − 1.387260I
−1.91195 + 2.82674I 0
u = −0.878380 − 0.744243I
a = 0.802399 + 0.213731I
b = 0.056170 + 1.387260I
−1.91195 − 2.82674I 0
u = −0.078237 + 0.841438I
a = 0.582772 − 0.819572I
b = −0.762907 + 0.915721I
−2.58279 − 9.55814I 0
u = −0.078237 − 0.841438I
a = 0.582772 + 0.819572I
b = −0.762907 − 0.915721I
−2.58279 + 9.55814I 0
u = 1.139990 + 0.192620I
a = 0.790000 + 0.279063I
b = 0.397059 + 0.882263I
−6.90350 + 6.13066I 0
u = 1.139990 − 0.192620I
a = 0.790000 − 0.279063I
b = 0.397059 − 0.882263I
−6.90350 − 6.13066I 0
u = 1.110150 + 0.335786I
a = 0.356989 + 0.624780I
b = −0.655276 + 0.780506I
−1.03048 − 7.81260I 0
u = 1.110150 − 0.335786I
a = 0.356989 − 0.624780I
b = −0.655276 − 0.780506I
−1.03048 + 7.81260I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.867468 + 0.781275I
a = −2.35155 − 0.02698I
b = 1.10985 − 1.62312I
5.18453 − 1.05366I 0
u = 0.867468 − 0.781275I
a = −2.35155 + 0.02698I
b = 1.10985 + 1.62312I
5.18453 + 1.05366I 0
u = 0.813156 + 0.841912I
a = −1.35305 − 1.68742I
b = 1.49093 + 1.21883I
0.78055 + 2.73858I 0
u = 0.813156 − 0.841912I
a = −1.35305 + 1.68742I
b = 1.49093 − 1.21883I
0.78055 − 2.73858I 0
u = 0.861177 + 0.796914I
a = −1.47855 − 0.64041I
b = 1.093070 + 0.842656I
2.85072 + 2.60130I 0
u = 0.861177 − 0.796914I
a = −1.47855 + 0.64041I
b = 1.093070 − 0.842656I
2.85072 − 2.60130I 0
u = −0.853253 + 0.814086I
a = 2.46708 − 0.94612I
b = −1.97715 − 0.64182I
3.79616 − 3.17397I 0
u = −0.853253 − 0.814086I
a = 2.46708 + 0.94612I
b = −1.97715 + 0.64182I
3.79616 + 3.17397I 0
u = 0.862701 + 0.805862I
a = 1.68281 − 0.06727I
b = −0.872426 + 1.061440I
4.79052 − 1.96597I 0
u = 0.862701 − 0.805862I
a = 1.68281 + 0.06727I
b = −0.872426 − 1.061440I
4.79052 + 1.96597I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.754607 + 0.910265I
a = −1.068180 + 0.875148I
b = 1.19362 − 0.78063I
7.31766 − 7.24489I 0
u = −0.754607 − 0.910265I
a = −1.068180 − 0.875148I
b = 1.19362 + 0.78063I
7.31766 + 7.24489I 0
u = 0.759250 + 0.912031I
a = 0.97944 + 1.15570I
b = −1.15228 − 1.24083I
2.31414 + 12.93820I 0
u = 0.759250 − 0.912031I
a = 0.97944 − 1.15570I
b = −1.15228 + 1.24083I
2.31414 − 12.93820I 0
u = 0.900770 + 0.772587I
a = 0.33484 + 1.57531I
b = −1.27968 − 1.54211I
5.08111 − 4.80137I 0
u = 0.900770 − 0.772587I
a = 0.33484 − 1.57531I
b = −1.27968 + 1.54211I
5.08111 + 4.80137I 0
u = −0.872344 + 0.804631I
a = 0.916320 − 0.370213I
b = −0.912144 + 0.667956I
7.07442 + 0.97442I 0
u = −0.872344 − 0.804631I
a = 0.916320 + 0.370213I
b = −0.912144 − 0.667956I
7.07442 − 0.97442I 0
u = 0.950395 + 0.716907I
a = −1.67000 − 1.07725I
b = 1.276130 − 0.483192I
2.23344 − 5.09816I 0
u = 0.950395 − 0.716907I
a = −1.67000 + 1.07725I
b = 1.276130 + 0.483192I
2.23344 + 5.09816I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.762758 + 0.244144I
a = 0.028861 − 0.463382I
b = 1.65484 − 0.08751I
−2.43341 − 6.29674I 0
u = 0.762758 − 0.244144I
a = 0.028861 + 0.463382I
b = 1.65484 + 0.08751I
−2.43341 + 6.29674I 0
u = 0.771416 + 0.919326I
a = −0.680630 − 0.581151I
b = 0.860387 + 0.693182I
7.39606 + 0.27229I 0
u = 0.771416 − 0.919326I
a = −0.680630 + 0.581151I
b = 0.860387 − 0.693182I
7.39606 − 0.27229I 0
u = 0.911621 + 0.781692I
a = 2.37631 + 0.99446I
b = −1.005870 + 0.894709I
2.69352 − 8.53175I 0
u = 0.911621 − 0.781692I
a = 2.37631 − 0.99446I
b = −1.005870 − 0.894709I
2.69352 + 8.53175I 0
u = 0.955894 + 0.727386I
a = 1.77188 − 0.02873I
b = −0.109721 + 0.211859I
−0.90606 − 9.26953I 0
u = 0.955894 − 0.727386I
a = 1.77188 + 0.02873I
b = −0.109721 − 0.211859I
−0.90606 + 9.26953I 0
u = −0.906288 + 0.794900I
a = −1.60654 + 0.79600I
b = 0.788727 + 0.745031I
6.96947 + 5.02069I 0
u = −0.906288 − 0.794900I
a = −1.60654 − 0.79600I
b = 0.788727 − 0.745031I
6.96947 − 5.02069I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.791429 + 0.010552I
a = −2.17998 − 1.26884I
b = 0.157896 − 1.009630I
−6.00762 − 0.14286I −9.55958 + 0.I
u = 0.791429 − 0.010552I
a = −2.17998 + 1.26884I
b = 0.157896 + 1.009630I
−6.00762 + 0.14286I −9.55958 + 0.I
u = 0.914397 + 0.794451I
a = −0.392280 − 1.138750I
b = 0.996651 + 0.925423I
4.63337 − 4.03117I 0
u = 0.914397 − 0.794451I
a = −0.392280 + 1.138750I
b = 0.996651 − 0.925423I
4.63337 + 4.03117I 0
u = −0.925023 + 0.790867I
a = −1.63490 + 1.64025I
b = 2.07106 − 0.52305I
3.57237 + 9.18485I 0
u = −0.925023 − 0.790867I
a = −1.63490 − 1.64025I
b = 2.07106 + 0.52305I
3.57237 − 9.18485I 0
u = −0.969972 + 0.744725I
a = 2.42946 − 0.47513I
b = −1.32866 − 1.48883I
−1.34490 + 10.67560I 0
u = −0.969972 − 0.744725I
a = 2.42946 + 0.47513I
b = −1.32866 + 1.48883I
−1.34490 − 10.67560I 0
u = −0.609834 + 1.060780I
a = 0.177931 + 0.161657I
b = −0.302125 − 0.261634I
0.73031 + 4.93195I 0
u = −0.609834 − 1.060780I
a = 0.177931 − 0.161657I
b = −0.302125 + 0.261634I
0.73031 − 4.93195I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.22574
a = −0.0814514
b = 0.224379
−2.40077 0
u = −1.117300 + 0.515290I
a = 0.466977 − 0.272863I
b = −0.052580 − 0.460197I
−1.72491 + 1.17101I 0
u = −1.117300 − 0.515290I
a = 0.466977 + 0.272863I
b = −0.052580 + 0.460197I
−1.72491 − 1.17101I 0
u = −0.959072 + 0.770957I
a = −1.95935 + 0.55083I
b = 1.072950 + 0.489822I
3.29305 + 8.15797I 0
u = −0.959072 − 0.770957I
a = −1.95935 − 0.55083I
b = 1.072950 − 0.489822I
3.29305 − 8.15797I 0
u = −0.747090 + 0.168468I
a = −0.07406 − 3.74823I
b = −0.718374 − 0.537568I
−2.78392 + 5.74159I 0. − 10.59223I
u = −0.747090 − 0.168468I
a = −0.07406 + 3.74823I
b = −0.718374 + 0.537568I
−2.78392 − 5.74159I 0. + 10.59223I
u = −0.902433 + 0.842389I
a = −1.12496 − 1.08347I
b = −0.09084 + 1.94995I
5.11270 + 3.12910I 0
u = −0.902433 − 0.842389I
a = −1.12496 + 1.08347I
b = −0.09084 − 1.94995I
5.11270 − 3.12910I 0
u = −0.754820 + 0.121964I
a = 0.271990 + 0.539948I
b = −1.25951 + 0.76033I
−0.00920 + 1.99741I −4.97461 − 6.58537I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.754820 − 0.121964I
a = 0.271990 − 0.539948I
b = −1.25951 − 0.76033I
−0.00920 − 1.99741I −4.97461 + 6.58537I
u = 0.903929 + 0.852438I
a = −0.042771 + 0.573558I
b = 0.1024700 + 0.0912204I
3.42320 − 3.15870I 0
u = 0.903929 − 0.852438I
a = −0.042771 − 0.573558I
b = 0.1024700 − 0.0912204I
3.42320 + 3.15870I 0
u = 0.965949 + 0.791830I
a = 2.72917 + 0.39462I
b = −1.49793 + 1.37084I
0.30713 − 8.83619I 0
u = 0.965949 − 0.791830I
a = 2.72917 − 0.39462I
b = −1.49793 − 1.37084I
0.30713 + 8.83619I 0
u = 0.689091 + 0.261565I
a = 0.23738 − 2.29046I
b = 0.307364 − 0.189189I
1.11048 − 2.65576I 4.04594 + 9.58056I
u = 0.689091 − 0.261565I
a = 0.23738 + 2.29046I
b = 0.307364 + 0.189189I
1.11048 + 2.65576I 4.04594 − 9.58056I
u = −1.020860 + 0.774765I
a = −1.85604 + 0.67780I
b = 0.875622 + 1.093540I
3.90808 + 10.98490I 0
u = −1.020860 − 0.774765I
a = −1.85604 − 0.67780I
b = 0.875622 − 1.093540I
3.90808 − 10.98490I 0
u = −0.945068 + 0.879974I
a = −0.718309 − 0.709737I
b = 0.122845 + 0.926844I
0.40985 + 3.28937I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.945068 − 0.879974I
a = −0.718309 + 0.709737I
b = 0.122845 − 0.926844I
0.40985 − 3.28937I 0
u = −0.021045 + 0.707004I
a = 0.849935 + 0.171601I
b = −0.701171 − 0.584399I
0.84188 + 2.06256I 6.18345 − 3.30724I
u = −0.021045 − 0.707004I
a = 0.849935 − 0.171601I
b = −0.701171 + 0.584399I
0.84188 − 2.06256I 6.18345 + 3.30724I
u = 0.371008 + 0.597901I
a = −0.719356 − 0.149262I
b = −0.413504 − 1.025830I
−1.91335 − 2.81576I 0.44464 + 3.89047I
u = 0.371008 − 0.597901I
a = −0.719356 + 0.149262I
b = −0.413504 + 1.025830I
−1.91335 + 2.81576I 0.44464 − 3.89047I
u = 1.043550 + 0.771923I
a = −0.946648 − 0.702795I
b = 0.916796 − 0.215289I
3.41643 − 6.78870I 0
u = 1.043550 − 0.771923I
a = −0.946648 + 0.702795I
b = 0.916796 + 0.215289I
3.41643 + 6.78870I 0
u = −1.026060 + 0.795755I
a = 1.77087 − 0.63835I
b = −1.19886 − 0.91328I
6.4646 + 13.5453I 0
u = −1.026060 − 0.795755I
a = 1.77087 + 0.63835I
b = −1.19886 + 0.91328I
6.4646 − 13.5453I 0
u = 1.025510 + 0.798343I
a = −2.17818 − 0.44641I
b = 1.14532 − 1.34021I
1.4753 − 19.2542I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.025510 − 0.798343I
a = −2.17818 + 0.44641I
b = 1.14532 + 1.34021I
1.4753 + 19.2542I 0
u = 1.020690 + 0.808844I
a = 1.38714 + 0.43387I
b = −0.826405 + 0.853074I
6.60927 − 6.64188I 0
u = 1.020690 − 0.808844I
a = 1.38714 − 0.43387I
b = −0.826405 − 0.853074I
6.60927 + 6.64188I 0
u = −0.235041 + 0.606361I
a = −0.583250 − 1.254850I
b = 0.697950 + 0.782894I
−3.29450 + 3.57493I −0.71465 − 4.68220I
u = −0.235041 − 0.606361I
a = −0.583250 + 1.254850I
b = 0.697950 − 0.782894I
−3.29450 − 3.57493I −0.71465 + 4.68220I
u = −0.616277 + 0.094778I
a = 0.95146 + 2.29909I
b = 0.376211 + 1.070930I
0.488850 − 0.873464I −0.30635 − 2.99542I
u = −0.616277 − 0.094778I
a = 0.95146 − 2.29909I
b = 0.376211 − 1.070930I
0.488850 + 0.873464I −0.30635 + 2.99542I
u = −0.550352 + 0.231512I
a = −1.70642 + 1.54056I
b = 1.085420 − 0.526133I
−2.22788 − 3.99628I 0. − 2.38605I
u = −0.550352 − 0.231512I
a = −1.70642 − 1.54056I
b = 1.085420 + 0.526133I
−2.22788 + 3.99628I 0. + 2.38605I
u = 0.446303 + 0.353768I
a = −0.22409 + 2.16295I
b = −1.066460 + 0.466635I
−1.53047 + 3.88857I 1.63766 − 0.43600I
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.446303 − 0.353768I
a = −0.22409 − 2.16295I
b = −1.066460 − 0.466635I
−1.53047 − 3.88857I 1.63766 + 0.43600I
u = 0.438822 + 0.314308I
a = 1.44178 − 0.12281I
b = −0.848750 − 0.067338I
1.71356 + 0.21175I 6.32854 + 2.24301I
u = 0.438822 − 0.314308I
a = 1.44178 + 0.12281I
b = −0.848750 + 0.067338I
1.71356 − 0.21175I 6.32854 − 2.24301I
u = −0.099602 + 0.525971I
a = −0.58831 + 1.66889I
b = 0.755169 − 0.982274I
−3.88259 − 1.74357I −2.56304 + 2.88821I
u = −0.099602 − 0.525971I
a = −0.58831 − 1.66889I
b = 0.755169 + 0.982274I
−3.88259 + 1.74357I −2.56304 − 2.88821I
u = −0.087064 + 0.446128I
a = 1.53865 + 0.55613I
b = −0.282786 − 0.627959I
0.12441 + 1.56920I 0.91923 − 3.30401I
u = −0.087064 − 0.446128I
a = 1.53865 − 0.55613I
b = −0.282786 + 0.627959I
0.12441 − 1.56920I 0.91923 + 3.30401I
18
II. I
u
2
= h−2u
24
− 2u
23
+ · · · + b + 3u, 411u
24
+ 715u
23
+ · · · + 29a −
1052, u
25
+ u
24
+ · · · − 9u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
u
2
a
11
=
−14.1724u
24
− 24.6552u
23
+ ··· + 50.2414u + 36.2759
2u
24
+ 2u
23
+ ··· + 31u
3
− 3u
a
12
=
−10.5862u
24
− 18.8276u
23
+ ··· + 40.6207u + 28.1379
3.96552u
24
+ 4.06897u
23
+ ··· − 8.55172u − 2.34483
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
−20.2414u
24
− 29.5172u
23
+ ··· + 73.1379u + 31.5862
3u
23
+ 3u
22
+ ··· + 48u
2
− 7
a
9
=
−4.68966u
24
− 8.62069u
23
+ ··· + 4.96552u + 13.1034
−8.13793u
24
− 12.7241u
23
+ ··· + 26.7931u + 16.6207
a
4
=
6.68966u
24
+ 14.6207u
23
+ ··· − 20.9655u − 24.1034
u
23
+ u
22
+ ··· − u − 6
a
10
=
−12.6897u
24
− 22.6207u
23
+ ··· + 45.9655u + 34.1034
5.13793u
24
+ 6.72414u
23
+ ··· − 12.7931u − 6.62069
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1161
29
u
24
−
1564
29
u
23
+ ··· +
3435
29
u +
1759
29
19
(iv) u-Polynomials at the component
20
Crossings u-Polynomials at each crossing
c
1
u
25
− 9u
24
+ ··· + 18u − 1
c
2
u
25
− u
24
+ ··· + 9u
2
− 1
c
3
u
25
− u
24
+ ··· + 2u − 1
c
4
u
25
− u
24
+ ··· − 4u − 2
c
5
u
25
− 2u
23
+ ··· + 7u − 1
c
6
u
25
+ u
24
+ ··· − 9u
2
+ 1
c
7
u
25
+ 9u
24
+ ··· + 18u + 1
c
8
u
25
+ u
24
+ ··· − 4u + 2
c
9
u
25
+ 13u
24
+ ··· + 2u + 1
c
10
u
25
− 12u
24
+ ··· + 14u − 2
c
11
u
25
+ 4u
24
+ ··· + 6u − 1
c
12
u
25
− 2u
24
+ ··· + u − 1
21
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
25
+ 19y
24
+ ··· + 26y −1
c
2
, c
6
y
25
− 9y
24
+ ··· + 18y −1
c
3
y
25
+ 7y
24
+ ··· − 10y −1
c
4
, c
8
y
25
+ 19y
24
+ ··· − 92y −4
c
5
y
25
− 4y
24
+ ··· + 17y −1
c
9
y
25
+ 11y
24
+ ··· + 28y −1
c
10
y
25
+ 12y
24
+ ··· − 8y −4
c
11
y
25
− 2y
24
+ ··· + 12y −1
c
12
y
25
+ 10y
24
+ ··· − 7y −1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.853847 + 0.552587I
a = 0.512253 + 1.148570I
b = 0.008849 + 1.124240I
−4.29244 − 2.21126I −7.77753 + 4.59539I
u = 0.853847 − 0.552587I
a = 0.512253 − 1.148570I
b = 0.008849 − 1.124240I
−4.29244 + 2.21126I −7.77753 − 4.59539I
u = 0.956988 + 0.133981I
a = 0.16781 + 1.76193I
b = −0.837945 + 0.690098I
−4.22319 − 5.45739I −7.32513 + 7.71011I
u = 0.956988 − 0.133981I
a = 0.16781 − 1.76193I
b = −0.837945 − 0.690098I
−4.22319 + 5.45739I −7.32513 − 7.71011I
u = 0.763507 + 0.796122I
a = 1.65998 + 0.36519I
b = −1.126830 + 0.115339I
3.51848 + 0.62563I 0.66859 − 1.39194I
u = 0.763507 − 0.796122I
a = 1.65998 − 0.36519I
b = −1.126830 − 0.115339I
3.51848 − 0.62563I 0.66859 + 1.39194I
u = −0.821252 + 0.357299I
a = −1.96111 − 0.57378I
b = 0.112682 + 0.993717I
−5.32296 + 1.50256I −4.89188 − 5.84337I
u = −0.821252 − 0.357299I
a = −1.96111 + 0.57378I
b = 0.112682 − 0.993717I
−5.32296 − 1.50256I −4.89188 + 5.84337I
u = −0.631590 + 0.955154I
a = −0.071440 + 0.175914I
b = 0.361981 + 0.060043I
0.76194 + 4.72903I 2.02160 + 5.84302I
u = −0.631590 − 0.955154I
a = −0.071440 − 0.175914I
b = 0.361981 − 0.060043I
0.76194 − 4.72903I 2.02160 − 5.84302I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.823293 + 0.805651I
a = −1.98055 + 1.20635I
b = 1.48375 − 0.66357I
1.78089 − 3.71135I 0.66058 + 5.26542I
u = −0.823293 − 0.805651I
a = −1.98055 − 1.20635I
b = 1.48375 + 0.66357I
1.78089 + 3.71135I 0.66058 − 5.26542I
u = −1.083320 + 0.476847I
a = −0.278647 + 0.334114I
b = −0.081503 + 0.556369I
−1.65599 + 0.83727I 0.72626 + 9.94888I
u = −1.083320 − 0.476847I
a = −0.278647 − 0.334114I
b = −0.081503 − 0.556369I
−1.65599 − 0.83727I 0.72626 − 9.94888I
u = 0.895140 + 0.818131I
a = −0.937691 + 0.810428I
b = −0.10530 − 1.60239I
6.41867 − 3.05480I 8.71564 + 2.55565I
u = 0.895140 − 0.818131I
a = −0.937691 − 0.810428I
b = −0.10530 + 1.60239I
6.41867 + 3.05480I 8.71564 − 2.55565I
u = −0.948266 + 0.771353I
a = 2.59268 − 0.92005I
b = −1.43814 − 0.81492I
1.39289 + 9.64001I −0.11573 − 10.25305I
u = −0.948266 − 0.771353I
a = 2.59268 + 0.92005I
b = −1.43814 + 0.81492I
1.39289 − 9.64001I −0.11573 + 10.25305I
u = 0.991039 + 0.753305I
a = −1.25838 − 0.87715I
b = 1.073250 − 0.143001I
2.82116 − 6.47784I −2.46367 + 5.33192I
u = 0.991039 − 0.753305I
a = −1.25838 + 0.87715I
b = 1.073250 + 0.143001I
2.82116 + 6.47784I −2.46367 − 5.33192I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.24507
a = 0.0444701
b = 0.363774
−2.31670 54.6010
u = −0.571310 + 0.152655I
a = −0.54893 + 1.84217I
b = −0.749069 + 0.806018I
0.69245 + 1.64476I 4.36644 − 3.46206I
u = −0.571310 − 0.152655I
a = −0.54893 − 1.84217I
b = −0.749069 − 0.806018I
0.69245 − 1.64476I 4.36644 + 3.46206I
u = 0.541047 + 0.028394I
a = 0.08177 − 3.20013I
b = 1.116380 + 0.179913I
−2.37849 + 4.73207I −3.38578 − 6.76282I
u = 0.541047 − 0.028394I
a = 0.08177 + 3.20013I
b = 1.116380 − 0.179913I
−2.37849 − 4.73207I −3.38578 + 6.76282I
26
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
25
− 9u
24
+ ··· + 18u − 1)(u
137
+ 40u
136
+ ··· + 4042u + 169)
c
2
(u
25
− u
24
+ ··· + 9u
2
− 1)(u
137
− 20u
135
+ ··· + 8u + 13)
c
3
(u
25
− u
24
+ ··· + 2u − 1)(u
137
+ 2u
136
+ ··· − 31644u + 3869)
c
4
(u
25
− u
24
+ ··· − 4u − 2)(u
137
+ 6u
136
+ ··· + 60u + 2)
c
5
(u
25
− 2u
23
+ ··· + 7u − 1)(u
137
+ u
136
+ ··· + 11u + 1)
c
6
(u
25
+ u
24
+ ··· − 9u
2
+ 1)(u
137
− 20u
135
+ ··· + 8u + 13)
c
7
(u
25
+ 9u
24
+ ··· + 18u + 1)(u
137
+ 40u
136
+ ··· + 4042u + 169)
c
8
(u
25
+ u
24
+ ··· − 4u + 2)(u
137
+ 6u
136
+ ··· + 60u + 2)
c
9
(u
25
+ 13u
24
+ ··· + 2u + 1)(u
137
− 12u
136
+ ··· + 48u + 1)
c
10
(u
25
− 12u
24
+ ··· + 14u − 2)(u
137
+ 9u
136
+ ··· + 32u − 128)
c
11
(u
25
+ 4u
24
+ ··· + 6u − 1)(u
137
+ u
136
+ ··· + 760u + 7)
c
12
(u
25
− 2u
24
+ ··· + u − 1)(u
137
+ 9u
136
+ ··· + 55158u + 5036)
27
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
25
+ 19y
24
+ ··· + 26y −1)
· (y
137
+ 120y
136
+ ··· + 779962y −28561)
c
2
, c
6
(y
25
− 9y
24
+ ··· + 18y −1)(y
137
− 40y
136
+ ··· + 4042y −169)
c
3
(y
25
+ 7y
24
+ ··· − 10y −1)
· (y
137
+ 36y
136
+ ··· − 513688022y −14969161)
c
4
, c
8
(y
25
+ 19y
24
+ ··· − 92y −4)(y
137
+ 100y
136
+ ··· − 848y −4)
c
5
(y
25
− 4y
24
+ ··· + 17y −1)(y
137
− 3y
136
+ ··· − 191y −1)
c
9
(y
25
+ 11y
24
+ ··· + 28y −1)(y
137
+ 12y
136
+ ··· − 696y −1)
c
10
(y
25
+ 12y
24
+ ··· − 8y −4)(y
137
+ 21y
136
+ ··· + 152576y −16384)
c
11
(y
25
− 2y
24
+ ··· + 12y −1)(y
137
− 13y
136
+ ··· + 530448y −49)
c
12
(y
25
+ 10y
24
+ ··· − 7y −1)
· (y
137
+ 35y
136
+ ··· − 1685724212y −25361296)
28
