12a
0269
(K12a
0269
)
A knot diagram
1
Linearized knot diagam
3 6 8 7 11 2 4 12 1 5 10 9
Solving Sequence
8,12
9 1
4,10
3 2 7 5 6 11
c
8
c
12
c
9
c
3
c
1
c
7
c
4
c
6
c
11
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−8.62713 × 10
15
u
65
− 2.11985 × 10
16
u
64
+ ··· + 2.49267 × 10
16
b − 1.13014 × 10
15
,
4.31598 × 10
16
u
65
+ 1.40820 × 10
17
u
64
+ ··· + 9.97068 × 10
16
a + 5.56705 × 10
17
, u
66
+ 4u
65
+ ··· + 35u + 4i
I
u
2
= h−83u
7
a
2
− 105u
7
a + ··· − 2a + 166, −2u
7
a
2
+ 8u
7
a + ··· + 18a − 6,
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1i
I
u
3
= h−u
4
a + u
2
a + u
3
− au + b + a − u + 1, u
4
− 2u
2
a + u
3
+ a
2
− 2au − 2u
2
+ 2a + 3,
u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
I
u
4
= h−2a
3
− a
2
+ b − a, 2a
4
+ 3a
3
+ 4a
2
+ 3a + 1, u − 1i
* 4 irreducible components of dim
C
= 0, with total 104 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−8.63 × 10
15
u
65
− 2.12 × 10
16
u
64
+ · · · + 2.49 × 10
16
b − 1.13 ×
10
15
, 4.32 × 10
16
u
65
+ 1.41 × 10
17
u
64
+ · · · + 9.97 × 10
16
a + 5.57 ×
10
17
, u
66
+ 4u
65
+ · · · + 35u + 4i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
u
2
a
1
=
−u
−u
3
+ u
a
4
=
−0.432868u
65
− 1.41234u
64
+ ··· − 25.5775u − 5.58342
0.346100u
65
+ 0.850432u
64
+ ··· + 4.81724u + 0.0453386
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
−0.0867675u
65
− 0.561913u
64
+ ··· − 20.7603u − 5.53808
0.346100u
65
+ 0.850432u
64
+ ··· + 4.81724u + 0.0453386
a
2
=
−0.00547462u
65
+ 0.184155u
64
+ ··· + 13.3969u + 1.98843
−0.0754890u
65
− 0.133427u
64
+ ··· + 1.98495u + 0.305099
a
7
=
−0.132128u
65
− 0.450532u
64
+ ··· − 13.0108u − 0.408261
0.468288u
65
+ 1.18384u
64
+ ··· + 9.40368u + 1.08447
a
5
=
−0.410233u
65
− 1.26602u
64
+ ··· − 24.2954u − 3.94259
0.275978u
65
+ 0.641853u
64
+ ··· + 2.90510u − 0.110199
a
6
=
−0.114697u
65
− 0.539674u
64
+ ··· − 18.9899u − 3.33232
0.265315u
65
+ 0.589033u
64
+ ··· + 2.64364u − 0.213478
a
11
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
22848277210974797
49853400611938144
u
65
−
33245267932303681
49853400611938144
u
64
+···+
1408726762689068359
49853400611938144
u+
18620167407452593
12463350152984536
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
66
+ 24u
65
+ ··· + 5878u + 289
c
2
, c
6
u
66
− 2u
65
+ ··· − 138u + 17
c
3
, c
4
, c
7
u
66
− 2u
65
+ ··· − 186u + 17
c
5
, c
10
u
66
− 2u
65
+ ··· − 16u + 64
c
8
, c
9
, c
12
u
66
− 4u
65
+ ··· − 35u + 4
c
11
u
66
+ 24u
65
+ ··· − 13056u + 4096
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
66
+ 48y
65
+ ··· + 10918642y + 83521
c
2
, c
6
y
66
+ 24y
65
+ ··· + 5878y + 289
c
3
, c
4
, c
7
y
66
+ 72y
65
+ ··· − 9674y + 289
c
5
, c
10
y
66
− 24y
65
+ ··· + 13056y + 4096
c
8
, c
9
, c
12
y
66
− 56y
65
+ ··· − 657y + 16
c
11
y
66
+ 28y
65
+ ··· − 578879488y + 16777216
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.667544 + 0.679084I
a = 0.86928 − 1.38453I
b = 0.149820 + 1.369760I
1.68392 − 4.80194I −8.00000 + 6.16806I
u = 0.667544 − 0.679084I
a = 0.86928 + 1.38453I
b = 0.149820 − 1.369760I
1.68392 + 4.80194I −8.00000 − 6.16806I
u = 0.189066 + 0.903983I
a = 0.74953 − 2.41334I
b = 0.32275 + 1.48528I
6.85220 − 11.84780I −4.90258 + 7.91039I
u = 0.189066 − 0.903983I
a = 0.74953 + 2.41334I
b = 0.32275 − 1.48528I
6.85220 + 11.84780I −4.90258 − 7.91039I
u = 1.083740 + 0.168606I
a = 1.242980 + 0.094384I
b = 0.111698 + 0.687804I
−1.18380 − 0.83133I 0
u = 1.083740 − 0.168606I
a = 1.242980 − 0.094384I
b = 0.111698 − 0.687804I
−1.18380 + 0.83133I 0
u = 0.514125 + 0.739694I
a = −0.64446 + 1.40518I
b = 0.065420 − 1.343790I
2.12892 − 0.16897I −6.25009 + 0.21372I
u = 0.514125 − 0.739694I
a = −0.64446 − 1.40518I
b = 0.065420 + 1.343790I
2.12892 + 0.16897I −6.25009 − 0.21372I
u = 0.130215 + 0.881989I
a = −0.46791 + 2.65814I
b = −0.21538 − 1.51295I
8.94622 − 5.72427I −2.18443 + 3.66030I
u = 0.130215 − 0.881989I
a = −0.46791 − 2.65814I
b = −0.21538 + 1.51295I
8.94622 + 5.72427I −2.18443 − 3.66030I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.046270 + 0.417779I
a = −0.002021 − 0.327101I
b = 0.730735 − 0.378556I
−1.82882 + 3.10174I 0
u = 1.046270 − 0.417779I
a = −0.002021 + 0.327101I
b = 0.730735 + 0.378556I
−1.82882 − 3.10174I 0
u = 0.173783 + 0.831807I
a = −0.307675 − 0.785989I
b = 0.845661 + 0.377568I
0.84572 − 7.60212I −7.64898 + 8.09357I
u = 0.173783 − 0.831807I
a = −0.307675 + 0.785989I
b = 0.845661 − 0.377568I
0.84572 + 7.60212I −7.64898 − 8.09357I
u = −1.147790 + 0.229735I
a = 0.102586 + 1.241460I
b = −0.19773 − 1.58186I
5.40538 − 2.32156I 0
u = −1.147790 − 0.229735I
a = 0.102586 − 1.241460I
b = −0.19773 + 1.58186I
5.40538 + 2.32156I 0
u = 0.651446 + 0.470027I
a = 0.284563 + 0.188739I
b = 0.505053 + 0.174111I
−3.20898 − 2.48763I −16.3622 + 5.4337I
u = 0.651446 − 0.470027I
a = 0.284563 − 0.188739I
b = 0.505053 − 0.174111I
−3.20898 + 2.48763I −16.3622 − 5.4337I
u = 1.081520 + 0.529987I
a = −0.355349 + 1.221180I
b = 0.27716 − 1.46865I
4.13434 + 6.78830I 0
u = 1.081520 − 0.529987I
a = −0.355349 − 1.221180I
b = 0.27716 + 1.46865I
4.13434 − 6.78830I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.071965 + 0.786913I
a = 0.79882 + 2.76845I
b = 0.13150 − 1.53519I
9.78957 − 0.29681I −0.83343 + 1.63973I
u = −0.071965 − 0.786913I
a = 0.79882 − 2.76845I
b = 0.13150 + 1.53519I
9.78957 + 0.29681I −0.83343 − 1.63973I
u = 1.143660 + 0.471596I
a = 0.69893 − 1.38761I
b = −0.15146 + 1.48688I
5.84968 + 0.90599I 0
u = 1.143660 − 0.471596I
a = 0.69893 + 1.38761I
b = −0.15146 − 1.48688I
5.84968 − 0.90599I 0
u = −1.197360 + 0.317299I
a = −0.50038 − 1.39693I
b = 0.06232 + 1.59267I
6.36342 + 4.30106I 0
u = −1.197360 − 0.317299I
a = −0.50038 + 1.39693I
b = 0.06232 − 1.59267I
6.36342 − 4.30106I 0
u = −0.152582 + 0.737995I
a = −1.22497 − 2.53094I
b = −0.25990 + 1.50993I
8.27559 + 5.90450I −2.31324 − 3.36207I
u = −0.152582 − 0.737995I
a = −1.22497 + 2.53094I
b = −0.25990 − 1.50993I
8.27559 − 5.90450I −2.31324 + 3.36207I
u = 0.320231 + 0.651017I
a = −0.024784 − 0.974380I
b = 0.294810 − 0.021528I
−2.21379 − 1.44886I −14.1875 + 3.2190I
u = 0.320231 − 0.651017I
a = −0.024784 + 0.974380I
b = 0.294810 + 0.021528I
−2.21379 + 1.44886I −14.1875 − 3.2190I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.293670 + 0.097432I
a = −0.83619 + 1.14357I
b = −0.411001 + 0.084755I
−4.64203 + 0.39162I 0
u = 1.293670 − 0.097432I
a = −0.83619 − 1.14357I
b = −0.411001 − 0.084755I
−4.64203 − 0.39162I 0
u = −1.273160 + 0.262278I
a = −0.0679407 + 0.0552696I
b = −0.767866 − 0.639955I
−2.07313 + 1.16836I 0
u = −1.273160 − 0.262278I
a = −0.0679407 − 0.0552696I
b = −0.767866 + 0.639955I
−2.07313 − 1.16836I 0
u = −0.029929 + 0.683021I
a = 0.122246 − 1.180170I
b = −0.752881 + 0.483067I
1.78075 + 2.22287I −4.94550 − 3.02923I
u = −0.029929 − 0.683021I
a = 0.122246 + 1.180170I
b = −0.752881 − 0.483067I
1.78075 − 2.22287I −4.94550 + 3.02923I
u = 1.298880 + 0.280433I
a = −1.102570 + 0.814558I
b = −0.797418 − 0.354964I
−2.38438 − 5.71634I 0
u = 1.298880 − 0.280433I
a = −1.102570 − 0.814558I
b = −0.797418 + 0.354964I
−2.38438 + 5.71634I 0
u = −1.336040 + 0.139935I
a = −0.719400 − 0.528286I
b = −0.412382 + 1.037160I
−3.31894 + 4.09533I 0
u = −1.336040 − 0.139935I
a = −0.719400 + 0.528286I
b = −0.412382 − 1.037160I
−3.31894 − 4.09533I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.310840 + 0.346233I
a = 1.76278 − 1.08503I
b = 0.19081 + 1.48545I
5.46398 − 3.79450I 0
u = 1.310840 − 0.346233I
a = 1.76278 + 1.08503I
b = 0.19081 − 1.48545I
5.46398 + 3.79450I 0
u = 1.359560 + 0.312582I
a = −1.95538 + 0.79171I
b = −0.30460 − 1.46865I
3.49484 − 9.72291I 0
u = 1.359560 − 0.312582I
a = −1.95538 − 0.79171I
b = −0.30460 + 1.46865I
3.49484 + 9.72291I 0
u = 1.406180 + 0.050908I
a = 0.029210 + 0.760234I
b = −0.112046 + 1.346250I
−0.11958 + 2.24868I 0
u = 1.406180 − 0.050908I
a = 0.029210 − 0.760234I
b = −0.112046 − 1.346250I
−0.11958 − 2.24868I 0
u = −1.359320 + 0.386811I
a = −1.45863 − 1.35802I
b = −0.26962 + 1.52010I
4.25937 + 10.27340I 0
u = −1.359320 − 0.386811I
a = −1.45863 + 1.35802I
b = −0.26962 − 1.52010I
4.25937 − 10.27340I 0
u = −1.37498 + 0.35472I
a = 0.660231 + 0.823973I
b = 0.913737 − 0.350179I
−4.04528 + 11.87690I 0
u = −1.37498 − 0.35472I
a = 0.660231 − 0.823973I
b = 0.913737 + 0.350179I
−4.04528 − 11.87690I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.40590 + 0.25321I
a = 0.369639 + 0.895908I
b = 0.325622 − 0.180271I
−7.67732 + 4.73918I 0
u = −1.40590 − 0.25321I
a = 0.369639 − 0.895908I
b = 0.325622 + 0.180271I
−7.67732 − 4.73918I 0
u = −1.44306 + 0.07283I
a = 0.782868 − 0.235983I
b = 0.720079 − 0.061282I
−9.98582 + 3.99160I 0
u = −1.44306 − 0.07283I
a = 0.782868 + 0.235983I
b = 0.720079 + 0.061282I
−9.98582 − 3.99160I 0
u = −1.39679 + 0.38869I
a = 1.65483 + 1.20080I
b = 0.35968 − 1.48387I
1.8387 + 16.4870I 0
u = −1.39679 − 0.38869I
a = 1.65483 − 1.20080I
b = 0.35968 + 1.48387I
1.8387 − 16.4870I 0
u = 0.163945 + 0.521690I
a = 0.35960 + 1.64327I
b = −0.163625 − 0.872636I
1.42640 − 1.81968I −0.93847 + 5.51231I
u = 0.163945 − 0.521690I
a = 0.35960 − 1.64327I
b = −0.163625 + 0.872636I
1.42640 + 1.81968I −0.93847 − 5.51231I
u = −0.504824 + 0.128957I
a = 0.362986 − 0.060340I
b = −0.10469 − 1.49108I
5.85879 − 2.92426I 1.08545 + 1.98753I
u = −0.504824 − 0.128957I
a = 0.362986 + 0.060340I
b = −0.10469 + 1.49108I
5.85879 + 2.92426I 1.08545 − 1.98753I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48027 + 0.22599I
a = −0.539486 − 0.091494I
b = 0.035967 + 1.249290I
−4.37053 + 3.52253I 0
u = −1.48027 − 0.22599I
a = −0.539486 + 0.091494I
b = 0.035967 − 1.249290I
−4.37053 − 3.52253I 0
u = −1.51108 + 0.12609I
a = 0.789487 + 0.071213I
b = 0.241287 − 1.319070I
−5.66868 + 7.39507I 0
u = −1.51108 − 0.12609I
a = 0.789487 − 0.071213I
b = 0.241287 + 1.319070I
−5.66868 − 7.39507I 0
u = −0.149615 + 0.078620I
a = −0.80843 − 3.04085I
b = −0.363511 − 0.421563I
−0.423006 − 1.307980I −4.48461 + 4.94953I
u = −0.149615 − 0.078620I
a = −0.80843 + 3.04085I
b = −0.363511 + 0.421563I
−0.423006 + 1.307980I −4.48461 − 4.94953I
11
II. I
u
2
= h−83u
7
a
2
− 105u
7
a + · · · − 2a + 166, −2u
7
a
2
+ 8u
7
a + · · · + 18a −
6, u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
u
2
a
1
=
−u
−u
3
+ u
a
4
=
a
0.167002a
2
u
7
+ 0.211268au
7
+ ··· + 0.00402414a − 0.334004
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
0.167002a
2
u
7
+ 0.211268au
7
+ ··· + 1.00402a − 0.334004
0.167002a
2
u
7
+ 0.211268au
7
+ ··· + 0.00402414a − 0.334004
a
2
=
−a
−0.167002a
2
u
7
− 0.211268au
7
+ ··· − 0.00402414a + 0.334004
a
7
=
−0.513078a
2
u
7
− 0.0965795au
7
+ ··· − 1.44266a + 1.31187
0.197183a
2
u
7
+ 0.0824950au
7
+ ··· + 0.651911a − 0.680080
a
5
=
−u
3
+ 2u
u
3
− u
a
6
=
1
0
a
11
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
6
+ 12u
4
− 4u
3
− 8u
2
+ 8u − 14
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
+ 16u
23
+ ··· − 4u + 1
c
2
, c
3
, c
4
c
6
, c
7
u
24
+ 8u
22
+ ··· + 4u + 1
c
5
, c
10
(u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1)
3
c
8
, c
9
, c
12
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
3
c
11
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
3
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
− 16y
23
+ ··· − 76y + 1
c
2
, c
3
, c
4
c
6
, c
7
y
24
+ 16y
23
+ ··· − 4y + 1
c
5
, c
10
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
3
c
8
, c
9
, c
12
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
3
c
11
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
3
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.180120 + 0.268597I
a = 1.129310 − 0.679881I
b = 0.526710 + 0.542383I
−1.04066 − 1.13123I −7.41522 + 0.51079I
u = 1.180120 + 0.268597I
a = 0.218627 + 0.497328I
b = −0.474274 + 0.744643I
−1.04066 − 1.13123I −7.41522 + 0.51079I
u = 1.180120 + 0.268597I
a = −1.91067 + 2.43966I
b = −0.052436 − 1.287030I
−1.04066 − 1.13123I −7.41522 + 0.51079I
u = 1.180120 − 0.268597I
a = 1.129310 + 0.679881I
b = 0.526710 − 0.542383I
−1.04066 + 1.13123I −7.41522 − 0.51079I
u = 1.180120 − 0.268597I
a = 0.218627 − 0.497328I
b = −0.474274 − 0.744643I
−1.04066 + 1.13123I −7.41522 − 0.51079I
u = 1.180120 − 0.268597I
a = −1.91067 − 2.43966I
b = −0.052436 + 1.287030I
−1.04066 + 1.13123I −7.41522 − 0.51079I
u = 0.108090 + 0.747508I
a = 0.393429 + 0.915822I
b = −0.659970 − 0.577105I
2.15941 − 2.57849I −4.27708 + 3.56796I
u = 0.108090 + 0.747508I
a = −0.205881 + 1.226480I
b = 0.596595 − 0.782878I
2.15941 − 2.57849I −4.27708 + 3.56796I
u = 0.108090 + 0.747508I
a = 0.22979 − 3.79270I
b = 0.063375 + 1.359980I
2.15941 − 2.57849I −4.27708 + 3.56796I
u = 0.108090 − 0.747508I
a = 0.393429 − 0.915822I
b = −0.659970 + 0.577105I
2.15941 + 2.57849I −4.27708 − 3.56796I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.108090 − 0.747508I
a = −0.205881 − 1.226480I
b = 0.596595 + 0.782878I
2.15941 + 2.57849I −4.27708 − 3.56796I
u = 0.108090 − 0.747508I
a = 0.22979 + 3.79270I
b = 0.063375 − 1.359980I
2.15941 + 2.57849I −4.27708 − 3.56796I
u = −1.37100
a = 1.122450 + 0.593787I
b = 0.381282 − 1.198390I
−6.50273 −13.8640
u = −1.37100
a = 1.122450 − 0.593787I
b = 0.381282 + 1.198390I
−6.50273 −13.8640
u = −1.37100
a = −0.586511
b = −0.762564
−6.50273 −13.8640
u = −1.334530 + 0.318930I
a = −0.635277 − 0.766647I
b = −0.788479 + 0.521654I
−2.37968 + 6.44354I −9.42845 − 5.29417I
u = −1.334530 + 0.318930I
a = −0.1050070 − 0.0244005I
b = 0.661375 + 0.893964I
−2.37968 + 6.44354I −9.42845 − 5.29417I
u = −1.334530 + 0.318930I
a = 1.30906 + 2.00264I
b = 0.12710 − 1.41562I
−2.37968 + 6.44354I −9.42845 − 5.29417I
u = −1.334530 − 0.318930I
a = −0.635277 + 0.766647I
b = −0.788479 − 0.521654I
−2.37968 − 6.44354I −9.42845 + 5.29417I
u = −1.334530 − 0.318930I
a = −0.1050070 + 0.0244005I
b = 0.661375 − 0.893964I
−2.37968 − 6.44354I −9.42845 + 5.29417I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.334530 − 0.318930I
a = 1.30906 − 2.00264I
b = 0.12710 + 1.41562I
−2.37968 − 6.44354I −9.42845 + 5.29417I
u = 0.463640
a = 0.450478
b = −0.328520
−0.845036 −11.8940
u = 0.463640
a = 2.52220 + 3.30247I
b = 0.164260 − 1.039680I
−0.845036 −11.8940
u = 0.463640
a = 2.52220 − 3.30247I
b = 0.164260 + 1.039680I
−0.845036 −11.8940
17
III. I
u
3
= h−u
4
a + u
2
a + u
3
− au + b + a − u + 1, u
4
− 2u
2
a + u
3
+ a
2
−
2au − 2u
2
+ 2a + 3, u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
u
2
a
1
=
−u
−u
3
+ u
a
4
=
a
u
4
a − u
2
a − u
3
+ au − a + u − 1
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
u
4
a − u
2
a − u
3
+ au + u − 1
u
4
a − u
2
a − u
3
+ au − a + u − 1
a
2
=
u
4
a − u
2
a − u
3
+ au − 1
u
4
a − u
2
a − 2u
3
+ au − a + 2u − 1
a
7
=
−u
3
a + u
3
+ au + 2u
2
− a
1
a
5
=
−u
4
a + u
2
a + u
3
− au + a − u + 1
0
a
6
=
u
4
a − u
3
a + u
4
− 2u
2
a + 2au − u
2
− a + u
u
4
a + u
4
− 2u
2
a + au − u
2
− a + u − 1
a
11
=
−u
4
+ u
2
+ 1
−u
4
+ 2u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
3
+ 8u − 12
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
10
c
2
, c
3
, c
4
c
6
, c
7
(u
2
+ 1)
5
c
5
, c
10
u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1
c
8
, c
9
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
11
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
c
12
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
10
c
2
, c
3
, c
4
c
6
, c
7
(y + 1)
10
c
5
, c
10
(y
5
− 3y
4
+ 4y
3
− y
2
− y + 1)
2
c
8
, c
9
, c
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
2
c
11
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.21774
a = 1.70062 + 1.07090I
b = 1.000000I
−2.40108 −9.48110
u = 1.21774
a = 1.70062 − 1.07090I
b = − 1.000000I
−2.40108 −9.48110
u = 0.309916 + 0.549911I
a = −0.679539 − 0.876898I
b = 1.000000I
−0.32910 − 1.53058I −8.51511 + 4.43065I
u = 0.309916 + 0.549911I
a = −1.11334 + 2.65842I
b = − 1.000000I
−0.32910 − 1.53058I −8.51511 + 4.43065I
u = 0.309916 − 0.549911I
a = −0.679539 + 0.876898I
b = − 1.000000I
−0.32910 + 1.53058I −8.51511 − 4.43065I
u = 0.309916 − 0.549911I
a = −1.11334 − 2.65842I
b = 1.000000I
−0.32910 + 1.53058I −8.51511 − 4.43065I
u = −1.41878 + 0.21917I
a = −0.925786 − 0.670523I
b = 1.000000I
−5.87256 + 4.40083I −12.74431 − 3.49859I
u = −1.41878 + 0.21917I
a = 0.0180453 − 0.1349390I
b = − 1.000000I
−5.87256 + 4.40083I −12.74431 − 3.49859I
u = −1.41878 − 0.21917I
a = −0.925786 + 0.670523I
b = − 1.000000I
−5.87256 − 4.40083I −12.74431 + 3.49859I
u = −1.41878 − 0.21917I
a = 0.0180453 + 0.1349390I
b = 1.000000I
−5.87256 − 4.40083I −12.74431 + 3.49859I
21
IV. I
u
4
= h−2a
3
− a
2
+ b − a, 2a
4
+ 3a
3
+ 4a
2
+ 3a + 1, u − 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
1
a
9
=
1
1
a
1
=
−1
0
a
4
=
a
2a
3
+ a
2
+ a
a
10
=
0
1
a
3
=
2a
3
+ a
2
+ 2a
2a
3
+ a
2
+ a
a
2
=
2a
3
+ a
2
+ 2a
−2a
2
− a
a
7
=
2a
3
+ 3a
2
+ 3a + 2
−2a
2
− a
a
5
=
0
2a + 1
a
6
=
0
2a + 1
a
11
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −14a
3
− 12a
2
− 14a − 18
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
u
4
− u
3
+ 3u
2
− 2u + 1
c
2
u
4
− u
3
+ u
2
+ 1
c
5
, c
10
, c
11
u
4
c
6
u
4
+ u
3
+ u
2
+ 1
c
7
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
8
, c
9
(u − 1)
4
c
12
(u + 1)
4
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
6
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
5
, c
10
, c
11
y
4
c
8
, c
9
, c
12
(y − 1)
4
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.173850 + 1.069070I
b = −0.10488 − 1.55249I
5.14581 − 3.16396I −10.48546 + 5.24252I
u = 1.00000
a = −0.173850 − 1.069070I
b = −0.10488 + 1.55249I
5.14581 + 3.16396I −10.48546 − 5.24252I
u = 1.00000
a = −0.576150 + 0.307015I
b = −0.395123 + 0.506844I
−1.85594 + 1.41510I −12.38954 − 3.92814I
u = 1.00000
a = −0.576150 − 0.307015I
b = −0.395123 − 0.506844I
−1.85594 − 1.41510I −12.38954 + 3.92814I
25
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
10
)(u
4
− u
3
+ 3u
2
− 2u + 1)(u
24
+ 16u
23
+ ··· − 4u + 1)
· (u
66
+ 24u
65
+ ··· + 5878u + 289)
c
2
((u
2
+ 1)
5
)(u
4
− u
3
+ u
2
+ 1)(u
24
+ 8u
22
+ ··· + 4u + 1)
· (u
66
− 2u
65
+ ··· − 138u + 17)
c
3
, c
4
((u
2
+ 1)
5
)(u
4
− u
3
+ 3u
2
− 2u + 1)(u
24
+ 8u
22
+ ··· + 4u + 1)
· (u
66
− 2u
65
+ ··· − 186u + 17)
c
5
, c
10
u
4
(u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1)
3
· (u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1)(u
66
− 2u
65
+ ··· − 16u + 64)
c
6
((u
2
+ 1)
5
)(u
4
+ u
3
+ u
2
+ 1)(u
24
+ 8u
22
+ ··· + 4u + 1)
· (u
66
− 2u
65
+ ··· − 138u + 17)
c
7
((u
2
+ 1)
5
)(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
24
+ 8u
22
+ ··· + 4u + 1)
· (u
66
− 2u
65
+ ··· − 186u + 17)
c
8
, c
9
(u − 1)
4
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
· ((u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
3
)(u
66
− 4u
65
+ ··· − 35u + 4)
c
11
u
4
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
· (u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
3
· (u
66
+ 24u
65
+ ··· − 13056u + 4096)
c
12
(u + 1)
4
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
· ((u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
3
)(u
66
− 4u
65
+ ··· − 35u + 4)
26
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
10
)(y
4
+ 5y
3
+ ··· + 2y + 1)(y
24
− 16y
23
+ ··· − 76y + 1)
· (y
66
+ 48y
65
+ ··· + 10918642y + 83521)
c
2
, c
6
((y + 1)
10
)(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
24
+ 16y
23
+ ··· − 4y + 1)
· (y
66
+ 24y
65
+ ··· + 5878y + 289)
c
3
, c
4
, c
7
((y + 1)
10
)(y
4
+ 5y
3
+ ··· + 2y + 1)(y
24
+ 16y
23
+ ··· − 4y + 1)
· (y
66
+ 72y
65
+ ··· − 9674y + 289)
c
5
, c
10
y
4
(y
5
− 3y
4
+ 4y
3
− y
2
− y + 1)
2
· (y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
3
· (y
66
− 24y
65
+ ··· + 13056y + 4096)
c
8
, c
9
, c
12
(y − 1)
4
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
2
· (y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
3
· (y
66
− 56y
65
+ ··· − 657y + 16)
c
11
y
4
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
2
· (y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
3
· (y
66
+ 28y
65
+ ··· − 578879488y + 16777216)
27
