12a
0567
(K12a
0567
)
A knot diagram
1
Linearized knot diagam
3 7 9 10 8 2 11 12 1 5 6 4
Solving Sequence
2,6
7
3,11
8 12 9 1 5 10 4
c
6
c
2
c
7
c
11
c
8
c
1
c
5
c
10
c
4
c
3
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.09131 × 10
58
u
48
+ 1.86986 × 10
59
u
47
+ ··· + 3.40871 × 10
59
b − 2.44132 × 10
59
,
3.95934 × 10
59
u
48
− 1.71738 × 10
60
u
47
+ ··· + 2.72697 × 10
60
a + 4.13840 × 10
60
, u
49
− 4u
48
+ ··· + 23u + 8i
I
u
2
= h5.76602 × 10
36
au
55
− 4.95035 × 10
36
u
55
+ ··· + 4.07129 × 10
37
a − 2.44952 × 10
37
,
− 3.06643 × 10
37
au
55
+ 1.88524 × 10
37
u
55
+ ··· − 2.77446 × 10
38
a + 8.18996 × 10
38
,
u
56
+ 2u
55
+ ··· + 6u − 1i
I
u
3
= h4249u
14
a − 18260u
14
+ ··· + 1889a − 19853, 391u
14
a − 404u
14
+ ··· + 414a − 30,
u
15
+ u
14
− 4u
13
− 6u
12
+ 5u
11
+ 11u
10
− 5u
9
− 15u
8
+ 12u
6
+ 3u
5
− 4u
4
+ 2u
2
− u − 1i
I
u
4
= hb + u, −u
3
+ u
2
+ a + 1, u
4
− u
3
+ 1i
I
u
5
= hu
2
+ b − 1, u
2
+ a − 1, u
3
− u + 1i
* 5 irreducible components of dim
C
= 0, with total 198 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−4.09 × 10
58
u
48
+ 1.87 × 10
59
u
47
+ · · · + 3.41 × 10
59
b − 2.44 ×
10
59
, 3.96 × 10
59
u
48
− 1.72 × 10
60
u
47
+ · · · + 2.73 × 10
60
a + 4.14 ×
10
60
, u
49
− 4u
48
+ · · · + 23u + 8i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
−0.145192u
48
+ 0.629778u
47
+ ··· − 4.54924u − 1.51758
0.120025u
48
− 0.548555u
47
+ ··· + 0.606531u + 0.716200
a
8
=
0.189703u
48
− 0.932656u
47
+ ··· + 2.33137u + 9.48319
−0.186093u
48
+ 0.727299u
47
+ ··· + 1.76881u − 1.97297
a
12
=
−0.265217u
48
+ 1.17833u
47
+ ··· − 5.15578u − 2.23378
0.120025u
48
− 0.548555u
47
+ ··· + 0.606531u + 0.716200
a
9
=
0.206990u
48
− 0.945493u
47
+ ··· + 14.0872u + 3.57428
−0.0567147u
48
+ 0.239211u
47
+ ··· − 2.81883u − 1.18146
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
−0.562435u
48
+ 2.55775u
47
+ ··· − 12.9670u − 8.28467
0.114740u
48
− 0.470163u
47
+ ··· + 4.03582u + 2.02292
a
10
=
0.169778u
48
− 0.780402u
47
+ ··· + 14.4821u + 3.69444
−0.0697919u
48
+ 0.249032u
47
+ ··· − 1.50204u − 0.424318
a
4
=
−0.180310u
48
+ 0.904758u
47
+ ··· − 9.77548u − 7.99759
0.107011u
48
− 0.544666u
47
+ ··· + 2.86335u + 2.67307
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.767693u
48
+ 3.20767u
47
+ ··· − 21.2132u − 8.56327
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
49
+ 16u
48
+ ··· + 1553u + 64
c
2
, c
6
u
49
− 4u
48
+ ··· + 23u + 8
c
3
, c
11
23(23u
49
+ 48u
48
+ ··· + 4u + 1)
c
4
, c
10
23(23u
49
+ 117u
48
+ ··· − 2048u − 256)
c
5
, c
12
u
49
+ 4u
48
+ ··· + 2u − 23
c
7
, c
9
u
49
− 4u
48
+ ··· − 202u + 23
c
8
u
49
− 8u
48
+ ··· + 84571u − 12398
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
49
+ 16y
48
+ ··· − 2527y −4096
c
2
, c
6
y
49
− 16y
48
+ ··· + 1553y −64
c
3
, c
11
529(529y
49
− 4328y
48
+ ··· + 8y −1)
c
4
, c
10
529(529y
49
− 23901y
48
+ ··· − 1048576y −65536)
c
5
, c
12
y
49
− 4y
48
+ ··· − 2480y −529
c
7
, c
9
y
49
+ 16y
48
+ ··· + 5108y −529
c
8
y
49
+ 2y
48
+ ··· + 658603173y −153710404
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.990760 + 0.010241I
a = 1.66046 − 1.49171I
b = 0.575647 − 0.169924I
−0.30315 + 5.10924I −9.01712 − 6.22750I
u = −0.990760 − 0.010241I
a = 1.66046 + 1.49171I
b = 0.575647 + 0.169924I
−0.30315 − 5.10924I −9.01712 + 6.22750I
u = 1.012260 + 0.023476I
a = −1.68942 + 0.80249I
b = −0.727210 + 0.167304I
−4.31448 + 1.69841I −13.26922 − 4.56796I
u = 1.012260 − 0.023476I
a = −1.68942 − 0.80249I
b = −0.727210 − 0.167304I
−4.31448 − 1.69841I −13.26922 + 4.56796I
u = −0.312749 + 0.928676I
a = 0.216831 − 0.264675I
b = −0.577562 + 0.648919I
1.60781 + 4.77505I 0.7752 − 16.7290I
u = −0.312749 − 0.928676I
a = 0.216831 + 0.264675I
b = −0.577562 − 0.648919I
1.60781 − 4.77505I 0.7752 + 16.7290I
u = 0.853950 + 0.601895I
a = 0.91949 − 1.33690I
b = 0.603418 + 0.748102I
3.57906 − 3.77603I 0.68519 + 6.98344I
u = 0.853950 − 0.601895I
a = 0.91949 + 1.33690I
b = 0.603418 − 0.748102I
3.57906 + 3.77603I 0.68519 − 6.98344I
u = 0.751553 + 0.728094I
a = −1.098480 + 0.238897I
b = −0.917649 + 0.653286I
4.63095 + 4.66427I −0.48019 − 6.24279I
u = 0.751553 − 0.728094I
a = −1.098480 − 0.238897I
b = −0.917649 − 0.653286I
4.63095 − 4.66427I −0.48019 + 6.24279I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.622417 + 0.699695I
a = 0.511387 + 0.269950I
b = 0.813837 + 0.666017I
0.67081 − 2.28505I −5.95751 + 2.10511I
u = −0.622417 − 0.699695I
a = 0.511387 − 0.269950I
b = 0.813837 − 0.666017I
0.67081 + 2.28505I −5.95751 − 2.10511I
u = −0.679488 + 0.852718I
a = 0.367118 − 0.009690I
b = −0.91748 − 1.39279I
3.85833 − 8.18929I 1.17804 + 7.15730I
u = −0.679488 − 0.852718I
a = 0.367118 + 0.009690I
b = −0.91748 + 1.39279I
3.85833 + 8.18929I 1.17804 − 7.15730I
u = 0.969892 + 0.566315I
a = 0.464777 − 0.615118I
b = −0.188565 + 0.396771I
3.35118 − 0.71038I −1.12350 − 1.34429I
u = 0.969892 − 0.566315I
a = 0.464777 + 0.615118I
b = −0.188565 − 0.396771I
3.35118 + 0.71038I −1.12350 + 1.34429I
u = 0.679113 + 0.905010I
a = 0.248678 − 0.766030I
b = 0.349493 − 0.169174I
5.29678 − 4.75824I −1.81791 + 6.68023I
u = 0.679113 − 0.905010I
a = 0.248678 + 0.766030I
b = 0.349493 + 0.169174I
5.29678 + 4.75824I −1.81791 − 6.68023I
u = 1.132310 + 0.186560I
a = 1.68536 + 0.59737I
b = 1.086950 + 0.852635I
−3.21951 − 7.86938I −6.63301 + 8.97427I
u = 1.132310 − 0.186560I
a = 1.68536 − 0.59737I
b = 1.086950 − 0.852635I
−3.21951 + 7.86938I −6.63301 − 8.97427I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.832906
a = 3.68483
b = 2.05274
0.673510 −30.4930
u = −1.151700 + 0.226303I
a = 0.787962 + 0.316767I
b = 0.775756 + 0.006400I
−2.35055 + 0.22485I −5.48316 − 6.06612I
u = −1.151700 − 0.226303I
a = 0.787962 − 0.316767I
b = 0.775756 − 0.006400I
−2.35055 − 0.22485I −5.48316 + 6.06612I
u = 0.963159 + 0.696372I
a = 2.02429 − 0.69272I
b = 1.009660 + 0.509444I
3.98032 − 10.12050I −2.53052 + 11.41214I
u = 0.963159 − 0.696372I
a = 2.02429 + 0.69272I
b = 1.009660 − 0.509444I
3.98032 + 10.12050I −2.53052 − 11.41214I
u = −1.007620 + 0.650126I
a = −1.71961 − 0.69174I
b = −0.983070 + 0.578977I
−0.46730 + 7.50602I −10.62062 − 8.40734I
u = −1.007620 − 0.650126I
a = −1.71961 + 0.69174I
b = −0.983070 − 0.578977I
−0.46730 − 7.50602I −10.62062 + 8.40734I
u = 0.664979 + 1.010740I
a = 0.0490397 − 0.0679405I
b = 0.96811 − 1.21500I
10.7432 + 14.0283I 3.41403 − 6.66068I
u = 0.664979 − 1.010740I
a = 0.0490397 + 0.0679405I
b = 0.96811 + 1.21500I
10.7432 − 14.0283I 3.41403 + 6.66068I
u = −0.940771 + 0.774401I
a = −0.479255 − 0.605762I
b = −0.156878 + 0.437253I
0.22555 + 2.99206I −9.23818 − 4.58020I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.940771 − 0.774401I
a = −0.479255 + 0.605762I
b = −0.156878 − 0.437253I
0.22555 − 2.99206I −9.23818 + 4.58020I
u = 0.921978 + 0.832111I
a = −0.202913 + 0.593928I
b = −1.088090 + 0.407029I
4.88611 − 1.92773I −4.45196 − 2.98835I
u = 0.921978 − 0.832111I
a = −0.202913 − 0.593928I
b = −1.088090 − 0.407029I
4.88611 + 1.92773I −4.45196 + 2.98835I
u = −1.032470 + 0.738931I
a = 1.81198 + 0.70417I
b = 1.10239 − 1.44459I
2.7816 + 14.1245I 0. − 11.47530I
u = −1.032470 − 0.738931I
a = 1.81198 − 0.70417I
b = 1.10239 + 1.44459I
2.7816 − 14.1245I 0. + 11.47530I
u = 0.945419 + 0.920642I
a = 0.610439 − 0.546138I
b = 0.717987 + 0.408108I
4.99471 − 4.54872I 0. + 8.24622I
u = 0.945419 − 0.920642I
a = 0.610439 + 0.546138I
b = 0.717987 − 0.408108I
4.99471 + 4.54872I 0. − 8.24622I
u = 0.110954 + 1.347940I
a = 0.0385506 + 0.0442015I
b = 0.608073 + 0.613858I
7.12930 − 6.91949I 0. + 13.46028I
u = 0.110954 − 1.347940I
a = 0.0385506 − 0.0442015I
b = 0.608073 − 0.613858I
7.12930 + 6.91949I 0. − 13.46028I
u = 1.105590 + 0.788327I
a = −1.72452 + 0.59522I
b = −1.08248 − 1.25928I
9.3385 − 20.5675I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.105590 − 0.788327I
a = −1.72452 − 0.59522I
b = −1.08248 + 1.25928I
9.3385 + 20.5675I 0
u = −1.342990 + 0.314986I
a = −1.355500 + 0.358423I
b = −0.981026 + 0.806984I
1.72502 + 12.43410I 0
u = −1.342990 − 0.314986I
a = −1.355500 − 0.358423I
b = −0.981026 − 0.806984I
1.72502 − 12.43410I 0
u = −0.323280 + 0.360692I
a = 0.615793 − 0.612104I
b = 0.182207 − 0.540934I
−0.355252 + 1.132390I −3.37752 − 6.52476I
u = −0.323280 − 0.360692I
a = 0.615793 + 0.612104I
b = 0.182207 + 0.540934I
−0.355252 − 1.132390I −3.37752 + 6.52476I
u = 0.390090
a = 0.833908
b = −0.714999
3.47781 −0.345410
u = −0.345538 + 0.146876I
a = 2.21115 − 2.51791I
b = −0.450186 + 0.783323I
2.32562 + 5.47653I 5.17929 − 7.75033I
u = −0.345538 − 0.146876I
a = 2.21115 + 2.51791I
b = −0.450186 − 0.783323I
2.32562 − 5.47653I 5.17929 + 7.75033I
u = 1.72004
a = −0.518361
b = −0.697464
0.634491 0
9
II. I
u
2
= h5.77 × 10
36
au
55
− 4.95 × 10
36
u
55
+ · · · + 4.07 × 10
37
a − 2.45 ×
10
37
, −3.07 × 10
37
au
55
+ 1.89 × 10
37
u
55
+ · · · − 2.77 × 10
38
a + 8.19 ×
10
38
, u
56
+ 2u
55
+ · · · + 6u − 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
a
−0.263852au
55
+ 0.226528u
55
+ ··· − 1.86302a + 1.12090
a
8
=
−1.13311au
55
+ 3.97767u
55
+ ··· − 1.44837a + 3.96049
0.346941au
55
+ 0.263235u
55
+ ··· + 0.0411106a − 1.88298
a
12
=
0.263852au
55
− 0.226528u
55
+ ··· + 2.86302a − 1.12090
−0.263852au
55
+ 0.226528u
55
+ ··· − 1.86302a + 1.12090
a
9
=
−1.48785au
55
+ 3.09205u
55
+ ··· − 1.35678a + 2.63162
1.15377au
55
+ 1.14886u
55
+ ··· − 1.37061a − 0.554114
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
0.142306au
55
− 3.09075u
55
+ ··· + 3.95964a − 3.40186
−0.296599au
55
+ 0.0319163u
55
+ ··· − 0.758939a + 0.440740
a
10
=
−0.334078au
55
+ 4.35457u
55
+ ··· − 2.72739a + 1.39494
−0.296599au
55
+ 0.675780u
55
+ ··· − 0.758939a + 2.05880
a
4
=
−0.0113552au
55
+ 0.787260u
55
+ ··· + 2.03843a − 5.29814
−0.166899au
55
+ 0.565160u
55
+ ··· − 1.50228a + 4.66470
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.564168u
55
− 0.320433u
54
+ ··· + 1.27052u − 7.10051
10
(iv) u-Polynomials at the component
11
Crossings u-Polynomials at each crossing
c
1
(u
56
+ 22u
55
+ ··· − 30u + 1)
2
c
2
(u
56
+ 2u
55
+ ··· + 6u − 1)
2
c
3
u
112
− u
111
+ ··· − 45277u + 4693
c
4
(u
56
− u
55
+ ··· + 215u − 71)
2
c
5
u
112
+ 11u
111
+ ··· + 179619u + 54371
c
6
(u
56
− 2u
55
+ ··· − 6u − 1)
2
c
7
u
112
+ 7u
111
+ ··· − 864296u − 57901
c
8
(u
56
+ 9u
55
+ ··· + 3202u − 5311)
2
c
9
− u
112
+ 7u
111
+ ··· − 864296u + 57901
c
10
(u
56
+ u
55
+ ··· − 215u − 71)
2
c
11
u
112
+ u
111
+ ··· + 45277u + 4693
c
12
u
112
− 11u
111
+ ··· − 179619u + 54371
12
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
56
+ 34y
55
+ ··· + 290y + 1)
2
c
2
, c
6
(y
56
− 22y
55
+ ··· + 30y + 1)
2
c
3
, c
11
y
112
+ 49y
111
+ ··· − 2487957489y + 22024249
c
4
, c
10
(y
56
− 49y
55
+ ··· − 29043y + 5041)
2
c
5
, c
12
y
112
− 55y
111
+ ··· − 150031984807y + 2956205641
c
7
, c
9
y
112
+ 37y
111
+ ··· − 781066217638y + 3352525801
c
8
(y
56
− 49y
55
+ ··· − 1194117192y + 28206721)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.671053 + 0.735319I
a = 0.034452 + 0.413041I
b = −1.00065 + 1.35060I
8.15930 + 4.91971I 12.2797 − 8.5675I
u = 0.671053 + 0.735319I
a = −1.26603 + 2.27586I
b = 0.098678 − 0.462847I
8.15930 + 4.91971I 12.2797 − 8.5675I
u = 0.671053 − 0.735319I
a = 0.034452 − 0.413041I
b = −1.00065 − 1.35060I
8.15930 − 4.91971I 12.2797 + 8.5675I
u = 0.671053 − 0.735319I
a = −1.26603 − 2.27586I
b = 0.098678 + 0.462847I
8.15930 − 4.91971I 12.2797 + 8.5675I
u = −0.655268 + 0.731518I
a = −0.398273 + 0.154608I
b = 0.019812 + 1.334000I
8.20794 + 4.66184I 11.91846 − 7.01691I
u = −0.655268 + 0.731518I
a = −1.92896 − 1.98521I
b = −0.091543 + 0.686724I
8.20794 + 4.66184I 11.91846 − 7.01691I
u = −0.655268 − 0.731518I
a = −0.398273 − 0.154608I
b = 0.019812 − 1.334000I
8.20794 − 4.66184I 11.91846 + 7.01691I
u = −0.655268 − 0.731518I
a = −1.92896 + 1.98521I
b = −0.091543 − 0.686724I
8.20794 − 4.66184I 11.91846 + 7.01691I
u = 1.051480 + 0.111605I
a = −0.970862 + 0.318740I
b = −0.59009 + 1.32672I
3.39610 − 5.69525I 1.93131 + 6.67173I
u = 1.051480 + 0.111605I
a = 1.47223 + 1.23810I
b = 0.514661 + 0.883305I
3.39610 − 5.69525I 1.93131 + 6.67173I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.051480 − 0.111605I
a = −0.970862 − 0.318740I
b = −0.59009 − 1.32672I
3.39610 + 5.69525I 1.93131 − 6.67173I
u = 1.051480 − 0.111605I
a = 1.47223 − 1.23810I
b = 0.514661 − 0.883305I
3.39610 + 5.69525I 1.93131 − 6.67173I
u = 0.647956 + 0.835756I
a = 0.147561 − 0.081423I
b = −0.096629 − 0.884005I
8.58456 − 3.25562I 9.50170 + 3.89012I
u = 0.647956 + 0.835756I
a = 1.33719 − 1.38588I
b = 1.29716 + 0.92050I
8.58456 − 3.25562I 9.50170 + 3.89012I
u = 0.647956 − 0.835756I
a = 0.147561 + 0.081423I
b = −0.096629 + 0.884005I
8.58456 + 3.25562I 9.50170 − 3.89012I
u = 0.647956 − 0.835756I
a = 1.33719 + 1.38588I
b = 1.29716 − 0.92050I
8.58456 + 3.25562I 9.50170 − 3.89012I
u = 0.606316 + 0.870830I
a = 0.339911 + 0.114485I
b = −0.83087 + 1.24284I
4.57895 + 2.01945I 5.91153 − 3.01862I
u = 0.606316 + 0.870830I
a = 0.236613 + 0.256096I
b = 0.084853 − 0.779988I
4.57895 + 2.01945I 5.91153 − 3.01862I
u = 0.606316 − 0.870830I
a = 0.339911 − 0.114485I
b = −0.83087 − 1.24284I
4.57895 − 2.01945I 5.91153 + 3.01862I
u = 0.606316 − 0.870830I
a = 0.236613 − 0.256096I
b = 0.084853 + 0.779988I
4.57895 − 2.01945I 5.91153 + 3.01862I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.843962 + 0.643797I
a = 1.42039 − 0.43709I
b = 0.169785 + 0.925363I
3.18492 − 2.51394I 1.39602 + 4.07845I
u = 0.843962 + 0.643797I
a = 0.321321 − 0.313385I
b = −0.099338 + 1.112230I
3.18492 − 2.51394I 1.39602 + 4.07845I
u = 0.843962 − 0.643797I
a = 1.42039 + 0.43709I
b = 0.169785 − 0.925363I
3.18492 + 2.51394I 1.39602 − 4.07845I
u = 0.843962 − 0.643797I
a = 0.321321 + 0.313385I
b = −0.099338 − 1.112230I
3.18492 + 2.51394I 1.39602 − 4.07845I
u = −0.722762 + 0.789161I
a = −0.083301 + 0.139465I
b = −0.72018 − 1.28447I
9.49380 − 5.41487I 7.18004 + 3.12682I
u = −0.722762 + 0.789161I
a = 1.52309 + 1.35169I
b = 1.49182 − 1.13675I
9.49380 − 5.41487I 7.18004 + 3.12682I
u = −0.722762 − 0.789161I
a = −0.083301 − 0.139465I
b = −0.72018 + 1.28447I
9.49380 + 5.41487I 7.18004 − 3.12682I
u = −0.722762 − 0.789161I
a = 1.52309 − 1.35169I
b = 1.49182 + 1.13675I
9.49380 + 5.41487I 7.18004 − 3.12682I
u = −0.784911 + 0.730923I
a = −0.380802 + 0.936687I
b = 1.01727 + 1.42356I
7.84044 + 1.14495I 9.86468 + 0.47121I
u = −0.784911 + 0.730923I
a = −0.738756 + 0.986320I
b = −0.252150 − 0.745357I
7.84044 + 1.14495I 9.86468 + 0.47121I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.784911 − 0.730923I
a = −0.380802 − 0.936687I
b = 1.01727 − 1.42356I
7.84044 − 1.14495I 9.86468 − 0.47121I
u = −0.784911 − 0.730923I
a = −0.738756 − 0.986320I
b = −0.252150 + 0.745357I
7.84044 − 1.14495I 9.86468 − 0.47121I
u = −0.821390 + 0.697737I
a = −0.146388 + 0.503983I
b = 1.02303 + 1.37591I
3.47674 − 1.58032I 2.87158 + 3.23738I
u = −0.821390 + 0.697737I
a = 1.44211 + 0.64984I
b = 0.023723 − 0.545974I
3.47674 − 1.58032I 2.87158 + 3.23738I
u = −0.821390 − 0.697737I
a = −0.146388 − 0.503983I
b = 1.02303 − 1.37591I
3.47674 + 1.58032I 2.87158 − 3.23738I
u = −0.821390 − 0.697737I
a = 1.44211 − 0.64984I
b = 0.023723 + 0.545974I
3.47674 + 1.58032I 2.87158 − 3.23738I
u = 0.903982
a = −0.712165
b = −0.938052
3.16663 2.67970
u = 0.903982
a = 1.55929
b = −0.0837679
3.16663 2.67970
u = −1.100210 + 0.028227I
a = −1.188090 − 0.600760I
b = −0.490366 + 0.894894I
2.64990 + 4.34352I 1.80546 − 6.02172I
u = −1.100210 + 0.028227I
a = 1.24614 − 1.32051I
b = 0.787569 − 0.692463I
2.64990 + 4.34352I 1.80546 − 6.02172I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.100210 − 0.028227I
a = −1.188090 + 0.600760I
b = −0.490366 − 0.894894I
2.64990 − 4.34352I 1.80546 + 6.02172I
u = −1.100210 − 0.028227I
a = 1.24614 + 1.32051I
b = 0.787569 + 0.692463I
2.64990 − 4.34352I 1.80546 + 6.02172I
u = 1.030240 + 0.406172I
a = 0.925326 − 0.997111I
b = 1.052900 − 0.017660I
−2.70052 − 5.63749I −6.44125 + 7.08904I
u = 1.030240 + 0.406172I
a = −2.08321 − 0.05879I
b = −0.851017 − 0.731337I
−2.70052 − 5.63749I −6.44125 + 7.08904I
u = 1.030240 − 0.406172I
a = 0.925326 + 0.997111I
b = 1.052900 + 0.017660I
−2.70052 + 5.63749I −6.44125 − 7.08904I
u = 1.030240 − 0.406172I
a = −2.08321 + 0.05879I
b = −0.851017 + 0.731337I
−2.70052 + 5.63749I −6.44125 − 7.08904I
u = 0.868540 + 0.705776I
a = −0.873366 − 0.293042I
b = 0.77653 − 1.89663I
3.08142 − 2.70536I 1.25594 + 2.81571I
u = 0.868540 + 0.705776I
a = −2.11391 + 0.91929I
b = −0.94598 − 1.72806I
3.08142 − 2.70536I 1.25594 + 2.81571I
u = 0.868540 − 0.705776I
a = −0.873366 + 0.293042I
b = 0.77653 + 1.89663I
3.08142 + 2.70536I 1.25594 − 2.81571I
u = 0.868540 − 0.705776I
a = −2.11391 − 0.91929I
b = −0.94598 + 1.72806I
3.08142 + 2.70536I 1.25594 − 2.81571I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.093610 + 0.277348I
a = −0.659902 − 0.916771I
b = −0.486269 − 0.225346I
−3.46638 + 1.04104I −9.55039 − 2.30638I
u = −1.093610 + 0.277348I
a = 1.75845 − 0.05068I
b = 1.194510 − 0.627546I
−3.46638 + 1.04104I −9.55039 − 2.30638I
u = −1.093610 − 0.277348I
a = −0.659902 + 0.916771I
b = −0.486269 + 0.225346I
−3.46638 − 1.04104I −9.55039 + 2.30638I
u = −1.093610 − 0.277348I
a = 1.75845 + 0.05068I
b = 1.194510 + 0.627546I
−3.46638 − 1.04104I −9.55039 + 2.30638I
u = −0.899333 + 0.691537I
a = −0.203718 + 0.844361I
b = 0.056866 − 0.757996I
3.23931 + 6.92218I 2.18653 − 9.52211I
u = −0.899333 + 0.691537I
a = −2.03977 − 0.90936I
b = −1.26485 + 1.23057I
3.23931 + 6.92218I 2.18653 − 9.52211I
u = −0.899333 − 0.691537I
a = −0.203718 − 0.844361I
b = 0.056866 + 0.757996I
3.23931 − 6.92218I 2.18653 + 9.52211I
u = −0.899333 − 0.691537I
a = −2.03977 + 0.90936I
b = −1.26485 − 1.23057I
3.23931 − 6.92218I 2.18653 + 9.52211I
u = −0.940088 + 0.704068I
a = −1.70035 − 0.54160I
b = −1.29908 + 1.26359I
7.36120 + 4.33888I 9.15448 − 6.40900I
u = −0.940088 + 0.704068I
a = 1.91123 + 0.95452I
b = 0.318523 − 0.620422I
7.36120 + 4.33888I 9.15448 − 6.40900I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.940088 − 0.704068I
a = −1.70035 + 0.54160I
b = −1.29908 − 1.26359I
7.36120 − 4.33888I 9.15448 + 6.40900I
u = −0.940088 − 0.704068I
a = 1.91123 − 0.95452I
b = 0.318523 + 0.620422I
7.36120 − 4.33888I 9.15448 + 6.40900I
u = 1.005220 + 0.687044I
a = −0.00656 + 1.67607I
b = −0.054365 − 0.639241I
7.15644 − 10.37530I 10.9783 + 11.7769I
u = 1.005220 + 0.687044I
a = 2.09773 − 0.58903I
b = 1.22251 + 1.21995I
7.15644 − 10.37530I 10.9783 + 11.7769I
u = 1.005220 − 0.687044I
a = −0.00656 − 1.67607I
b = −0.054365 + 0.639241I
7.15644 + 10.37530I 10.9783 − 11.7769I
u = 1.005220 − 0.687044I
a = 2.09773 + 0.58903I
b = 1.22251 − 1.21995I
7.15644 + 10.37530I 10.9783 − 11.7769I
u = −0.992808 + 0.724667I
a = 0.019537 − 1.057320I
b = −1.46147 − 1.42377I
8.67176 + 11.13480I 0
u = −0.992808 + 0.724667I
a = 1.98474 + 0.67247I
b = 0.83751 − 1.21893I
8.67176 + 11.13480I 0
u = −0.992808 − 0.724667I
a = 0.019537 + 1.057320I
b = −1.46147 + 1.42377I
8.67176 − 11.13480I 0
u = −0.992808 − 0.724667I
a = 1.98474 − 0.67247I
b = 0.83751 + 1.21893I
8.67176 − 11.13480I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.762619 + 0.091383I
a = 1.120040 + 0.658603I
b = 0.548557 − 0.901107I
−0.27517 + 3.46206I −4.92312 − 5.23114I
u = 0.762619 + 0.091383I
a = −1.45977 + 2.26715I
b = −1.009500 + 0.467491I
−0.27517 + 3.46206I −4.92312 − 5.23114I
u = 0.762619 − 0.091383I
a = 1.120040 − 0.658603I
b = 0.548557 + 0.901107I
−0.27517 − 3.46206I −4.92312 + 5.23114I
u = 0.762619 − 0.091383I
a = −1.45977 − 2.26715I
b = −1.009500 − 0.467491I
−0.27517 − 3.46206I −4.92312 + 5.23114I
u = −1.030070 + 0.692608I
a = 0.240072 − 0.874574I
b = 0.267916 + 0.932851I
7.07940 + 0.81663I 0
u = −1.030070 + 0.692608I
a = −1.170500 + 0.289772I
b = −0.317845 + 1.099280I
7.07940 + 0.81663I 0
u = −1.030070 − 0.692608I
a = 0.240072 + 0.874574I
b = 0.267916 − 0.932851I
7.07940 − 0.81663I 0
u = −1.030070 − 0.692608I
a = −1.170500 − 0.289772I
b = −0.317845 − 1.099280I
7.07940 − 0.81663I 0
u = −0.731482 + 0.085796I
a = 0.16955 − 1.56338I
b = 0.06539 − 1.55390I
−0.305860 + 0.273475I −5.19778 − 4.40178I
u = −0.731482 + 0.085796I
a = −1.36935 − 2.60328I
b = −0.635165 − 1.033230I
−0.305860 + 0.273475I −5.19778 − 4.40178I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.731482 − 0.085796I
a = 0.16955 + 1.56338I
b = 0.06539 + 1.55390I
−0.305860 − 0.273475I −5.19778 + 4.40178I
u = −0.731482 − 0.085796I
a = −1.36935 + 2.60328I
b = −0.635165 + 1.033230I
−0.305860 − 0.273475I −5.19778 + 4.40178I
u = 1.060640 + 0.726908I
a = −1.146400 + 0.244174I
b = −0.281316 − 0.753506I
3.22224 − 7.94380I 0
u = 1.060640 + 0.726908I
a = 1.67828 − 0.54490I
b = 1.10619 + 1.31938I
3.22224 − 7.94380I 0
u = 1.060640 − 0.726908I
a = −1.146400 − 0.244174I
b = −0.281316 + 0.753506I
3.22224 + 7.94380I 0
u = 1.060640 − 0.726908I
a = 1.67828 + 0.54490I
b = 1.10619 − 1.31938I
3.22224 + 7.94380I 0
u = 1.060780 + 0.746153I
a = −0.868087 − 0.231573I
b = −0.098811 − 0.632183I
7.35144 − 2.67401I 0
u = 1.060780 + 0.746153I
a = −0.171399 + 0.728699I
b = −1.29309 + 1.25741I
7.35144 − 2.67401I 0
u = 1.060780 − 0.746153I
a = −0.868087 + 0.231573I
b = −0.098811 + 0.632183I
7.35144 + 2.67401I 0
u = 1.060780 − 0.746153I
a = −0.171399 − 0.728699I
b = −1.29309 − 1.25741I
7.35144 + 2.67401I 0
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.639664 + 1.142700I
a = 0.0907454 + 0.0137080I
b = 0.92323 + 1.10207I
9.64435 − 4.35767I 0
u = −0.639664 + 1.142700I
a = 0.0579156 − 0.0509173I
b = −0.004300 − 0.805991I
9.64435 − 4.35767I 0
u = −0.639664 − 1.142700I
a = 0.0907454 − 0.0137080I
b = 0.92323 − 1.10207I
9.64435 + 4.35767I 0
u = −0.639664 − 1.142700I
a = 0.0579156 + 0.0509173I
b = −0.004300 + 0.805991I
9.64435 + 4.35767I 0
u = −1.39465
a = 0.978333
b = 1.15590
−2.62295 0
u = −1.39465
a = 0.0832108
b = 0.224734
−2.62295 0
u = 0.063466 + 0.584300I
a = 0.651341 + 0.089844I
b = −0.763936 − 0.319395I
−0.10326 + 2.06981I −2.12397 − 3.13917I
u = 0.063466 + 0.584300I
a = 0.298658 − 0.272978I
b = 0.487593 − 0.746997I
−0.10326 + 2.06981I −2.12397 − 3.13917I
u = 0.063466 − 0.584300I
a = 0.651341 − 0.089844I
b = −0.763936 + 0.319395I
−0.10326 − 2.06981I −2.12397 + 3.13917I
u = 0.063466 − 0.584300I
a = 0.298658 + 0.272978I
b = 0.487593 + 0.746997I
−0.10326 − 2.06981I −2.12397 + 3.13917I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.15196 + 0.83596I
a = 0.804054 − 0.064713I
b = 0.275082 − 0.834297I
8.00849 + 11.38970I 0
u = −1.15196 + 0.83596I
a = −1.54003 − 0.57492I
b = −1.01892 + 1.19474I
8.00849 + 11.38970I 0
u = −1.15196 − 0.83596I
a = 0.804054 + 0.064713I
b = 0.275082 + 0.834297I
8.00849 − 11.38970I 0
u = −1.15196 − 0.83596I
a = −1.54003 + 0.57492I
b = −1.01892 − 1.19474I
8.00849 − 11.38970I 0
u = 0.463532
a = 2.74448 + 0.43284I
b = 0.135146 − 1.050140I
4.83953 4.50770
u = 0.463532
a = 2.74448 − 0.43284I
b = 0.135146 + 1.050140I
4.83953 4.50770
u = 1.67030
a = −0.563240 + 0.165349I
b = −0.714634 + 0.222707I
0.625659 0
u = 1.67030
a = −0.563240 − 0.165349I
b = −0.714634 − 0.222707I
0.625659 0
u = 0.069713 + 0.153745I
a = 1.71682 − 1.09990I
b = −0.469761 + 1.259310I
6.94046 + 4.65477I −8.88344 + 1.97207I
u = 0.069713 + 0.153745I
a = 17.3267 + 5.1539I
b = 0.665925 + 0.156361I
6.94046 + 4.65477I −8.88344 + 1.97207I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.069713 − 0.153745I
a = 1.71682 + 1.09990I
b = −0.469761 − 1.259310I
6.94046 − 4.65477I −8.88344 − 1.97207I
u = 0.069713 − 0.153745I
a = 17.3267 − 5.1539I
b = 0.665925 − 0.156361I
6.94046 − 4.65477I −8.88344 − 1.97207I
26
III. I
u
3
= h4249u
14
a − 18260u
14
+ · · · + 1889a − 19853, 391u
14
a − 404u
14
+
· · · + 414a − 30, u
15
+ u
14
+ · · · − u − 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
a
−2.10659au
14
+ 9.05305u
14
+ ··· − 0.936539a + 9.84284
a
8
=
4.94695au
14
− 1.61081u
14
+ ··· + 7.15716a − 4.06891
6.48438au
14
− 4.34804u
14
+ ··· + 7.09767a − 6.10907
a
12
=
2.10659au
14
− 9.05305u
14
+ ··· + 1.93654a − 9.84284
−2.10659au
14
+ 9.05305u
14
+ ··· − 0.936539a + 9.84284
a
9
=
2.14031au
14
+ 1.26971u
14
+ ··· + 4.99554a + 0.471988
1.29103au
14
− 7.22856u
14
+ ··· + 1.25930a − 10.6500
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
15.3733au
14
− 27.8230u
14
+ ··· + 16.9033a − 29.4403
2.33961au
14
+ 2.85424u
14
+ ··· + 2.84432a + 2.24492
a
10
=
3.43133au
14
+ 6.04115u
14
+ ··· + 6.25483a + 3.82201
2.33961au
14
− 3.14576u
14
+ ··· + 2.84432a − 5.75508
a
4
=
7.86019au
14
− 1.50089u
14
+ ··· + 8.25533a − 3.58309
−1.18542au
14
+ 9.85527u
14
+ ··· − 0.824492a + 4.37716
(ii) Obstruction class = 1
(iii) Cusp Shapes = −45u
14
− 79u
13
+ 114u
12
+ 349u
11
+ 57u
10
− 415u
9
− 99u
8
+
555u
7
+ 433u
6
− 148u
5
− 227u
4
− 18u
3
− 17u
2
− 99u − 37
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
15
− 9u
14
+ ··· + 5u − 1)
2
c
2
(u
15
− u
14
+ ··· − u + 1)
2
c
3
, c
11
23(23u
30
+ 147u
28
+ ··· + u + 1)
c
4
, c
10
23(23u
30
− 428u
28
+ ··· − 56074u
2
+ 361)
c
5
, c
12
u
30
− 4u
29
+ ··· + 115u + 23
c
6
(u
15
+ u
14
+ ··· − u − 1)
2
c
7
, c
9
u
30
+ 2u
29
+ ··· + 138u − 23
c
8
(u
15
− 8u
14
+ ··· − 5u − 1)
2
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
15
− 5y
14
+ ··· + y −1)
2
c
2
, c
6
(y
15
− 9y
14
+ ··· + 5y −1)
2
c
3
, c
11
529(529y
30
+ 6762y
29
+ ··· − 45y + 1)
c
4
, c
10
529(23y
15
− 428y
14
+ ··· − 56074y + 361)
2
c
5
, c
12
y
30
− 26y
29
+ ··· − 4347y + 529
c
7
, c
9
y
30
+ 10y
29
+ ··· − 2438y + 529
c
8
(y
15
− 12y
14
+ ··· + 3y −1)
2
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.904032 + 0.500962I
a = 0.400934 + 0.876728I
b = 0.069706 − 1.116930I
4.87056 + 2.00812I 5.72627 − 3.22556I
u = −0.904032 + 0.500962I
a = 1.77208 − 0.00014I
b = 0.052148 − 0.855653I
4.87056 + 2.00812I 5.72627 − 3.22556I
u = −0.904032 − 0.500962I
a = 0.400934 − 0.876728I
b = 0.069706 + 1.116930I
4.87056 − 2.00812I 5.72627 + 3.22556I
u = −0.904032 − 0.500962I
a = 1.77208 + 0.00014I
b = 0.052148 + 0.855653I
4.87056 − 2.00812I 5.72627 + 3.22556I
u = −0.604563 + 0.739867I
a = 0.003512 − 0.169021I
b = −0.82144 − 1.27893I
7.78409 − 4.48024I 2.51653 − 2.10573I
u = −0.604563 + 0.739867I
a = −0.38868 − 2.08222I
b = −0.441933 + 0.363599I
7.78409 − 4.48024I 2.51653 − 2.10573I
u = −0.604563 − 0.739867I
a = 0.003512 + 0.169021I
b = −0.82144 + 1.27893I
7.78409 + 4.48024I 2.51653 + 2.10573I
u = −0.604563 − 0.739867I
a = −0.38868 + 2.08222I
b = −0.441933 − 0.363599I
7.78409 + 4.48024I 2.51653 + 2.10573I
u = 0.877651 + 0.004916I
a = 0.085115 + 0.992994I
b = −0.291346 − 0.853722I
1.07810 − 5.33896I −3.04139 + 7.29844I
u = 0.877651 + 0.004916I
a = 1.79796 + 2.08916I
b = 0.677587 + 0.511986I
1.07810 − 5.33896I −3.04139 + 7.29844I
30
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877651 − 0.004916I
a = 0.085115 − 0.992994I
b = −0.291346 + 0.853722I
1.07810 + 5.33896I −3.04139 − 7.29844I
u = 0.877651 − 0.004916I
a = 1.79796 − 2.08916I
b = 0.677587 − 0.511986I
1.07810 + 5.33896I −3.04139 − 7.29844I
u = 0.924863 + 0.711903I
a = −1.153080 + 0.162248I
b = −0.662154 − 0.614581I
6.24642 − 2.74833I 2.99946 + 3.06733I
u = 0.924863 + 0.711903I
a = 0.378437 − 0.530946I
b = 0.768488 − 0.833987I
6.24642 − 2.74833I 2.99946 + 3.06733I
u = 0.924863 − 0.711903I
a = −1.153080 − 0.162248I
b = −0.662154 + 0.614581I
6.24642 + 2.74833I 2.99946 − 3.06733I
u = 0.924863 − 0.711903I
a = 0.378437 + 0.530946I
b = 0.768488 + 0.833987I
6.24642 + 2.74833I 2.99946 − 3.06733I
u = −1.027220 + 0.711068I
a = 0.082567 − 0.636128I
b = 0.320419 + 0.524398I
6.56063 + 10.08130I −0.80300 − 5.65611I
u = −1.027220 + 0.711068I
a = 1.94852 + 0.58493I
b = 1.07611 − 1.14951I
6.56063 + 10.08130I −0.80300 − 5.65611I
u = −1.027220 − 0.711068I
a = 0.082567 + 0.636128I
b = 0.320419 − 0.524398I
6.56063 − 10.08130I −0.80300 + 5.65611I
u = −1.027220 − 0.711068I
a = 1.94852 − 0.58493I
b = 1.07611 + 1.14951I
6.56063 − 10.08130I −0.80300 + 5.65611I
31
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.33306
a = −0.835812
b = −0.858603
−2.75865 −25.0550
u = −1.33306
a = −0.647491
b = −0.647713
−2.75865 −25.0550
u = 0.318556 + 0.568840I
a = −0.221205 − 0.008661I
b = −0.339670 − 1.161460I
7.22377 − 4.92438I 6.89107 + 11.55615I
u = 0.318556 + 0.568840I
a = 1.50073 + 3.42899I
b = −0.522464 + 0.107351I
7.22377 − 4.92438I 6.89107 + 11.55615I
u = 0.318556 − 0.568840I
a = −0.221205 + 0.008661I
b = −0.339670 + 1.161460I
7.22377 + 4.92438I 6.89107 − 11.55615I
u = 0.318556 − 0.568840I
a = 1.50073 − 3.42899I
b = −0.522464 − 0.107351I
7.22377 + 4.92438I 6.89107 − 11.55615I
u = −0.619936
a = 0.22158 + 3.24295I
b = 0.28092 + 1.70648I
0.189631 9.78680
u = −0.619936
a = 0.22158 − 3.24295I
b = 0.28092 − 1.70648I
0.189631 9.78680
u = 1.78249
a = 0.690052
b = 1.02052
0.839240 24.6900
u = 1.78249
a = −0.0636766
b = 0.153043
0.839240 24.6900
32
IV. I
u
4
= hb + u, −u
3
+ u
2
+ a + 1, u
4
− u
3
+ 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
u
3
− u
2
− 1
−u
a
8
=
−u
2
− u + 1
−u
3
+ u
2
a
12
=
u
3
− u
2
+ u − 1
−u
a
9
=
−u
2
+ u
u
2
− u
a
1
=
u
3
−1
a
5
=
−u
3
+ u
2
− u
−u
2
+ u
a
10
=
u
3
− u
2
− 1
−u
a
4
=
−u
3
+ u
2
− u
−u
2
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
3
+ 6u
2
− 2
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
9
u
4
− u
3
+ 2u
2
+ 1
c
2
u
4
+ u
3
+ 1
c
3
, c
6
, c
11
u
4
− u
3
+ 1
c
4
, c
10
u
4
c
5
, c
12
u
4
− u + 1
c
8
u
4
+ 3u
3
+ 5u
2
+ 5u + 3
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
9
y
4
+ 3y
3
+ 6y
2
+ 4y + 1
c
2
, c
3
, c
6
c
11
y
4
− y
3
+ 2y
2
+ 1
c
4
, c
10
y
4
c
5
, c
12
y
4
+ 2y
2
− y + 1
c
8
y
4
+ y
3
+ y
2
+ 5y + 9
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.518913 + 0.666610I
a = −0.272864 + 0.934099I
b = 0.518913 − 0.666610I
1.43949 + 4.22398I −2.49855 − 3.90867I
u = −0.518913 − 0.666610I
a = −0.272864 − 0.934099I
b = 0.518913 + 0.666610I
1.43949 − 4.22398I −2.49855 + 3.90867I
u = 1.018910 + 0.602565I
a = −1.72714 + 0.43001I
b = −1.018910 − 0.602565I
0.20545 − 7.54387I 1.99855 + 9.02548I
u = 1.018910 − 0.602565I
a = −1.72714 − 0.43001I
b = −1.018910 + 0.602565I
0.20545 + 7.54387I 1.99855 − 9.02548I
36
V. I
u
5
= hu
2
+ b − 1, u
2
+ a − 1, u
3
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
1
a
11
=
−u
2
+ 1
−u
2
+ 1
a
8
=
−u
2
− u + 1
−u
a
12
=
0
−u
2
+ 1
a
9
=
−u
2
− u + 1
1
a
1
=
u − 1
−u
2
+ u
a
5
=
u
2
u
2
a
10
=
−u
2
+ 1
−u
2
+ 1
a
4
=
u
2
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −11u
2
+ 4u + 1
37
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
− 2u
2
+ u − 1
c
2
, c
5
, c
12
u
3
− u − 1
c
3
, c
11
u
3
+ u
2
− 1
c
4
, c
10
u
3
c
6
u
3
− u + 1
c
7
, c
9
u
3
− u
2
+ 2u − 1
c
8
u
3
+ 2u
2
+ 3u + 1
38
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
3
− 2y
2
− 3y −1
c
2
, c
5
, c
6
c
12
y
3
− 2y
2
+ y −1
c
3
, c
11
y
3
− y
2
+ 2y −1
c
4
, c
10
y
3
c
7
, c
9
y
3
+ 3y
2
+ 2y −1
c
8
y
3
+ 2y
2
+ 5y −1
39
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.662359 + 0.562280I
a = 0.877439 − 0.744862I
b = 0.877439 − 0.744862I
1.37919 + 2.82812I 2.30126 − 5.94436I
u = 0.662359 − 0.562280I
a = 0.877439 + 0.744862I
b = 0.877439 + 0.744862I
1.37919 − 2.82812I 2.30126 + 5.94436I
u = −1.32472
a = −0.754878
b = −0.754878
−2.75839 −23.6030
40
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
3
− 2u
2
+ u − 1)(u
4
− u
3
+ 2u
2
+ 1)(u
15
− 9u
14
+ ··· + 5u − 1)
2
· (u
49
+ 16u
48
+ ··· + 1553u + 64)
c
2
(u
3
− u − 1)(u
4
+ u
3
+ 1)(u
15
− u
14
+ ··· − u + 1)
2
· (u
49
− 4u
48
+ ··· + 23u + 8)
c
3
, c
11
529(u
3
+ u
2
− 1)(u
4
− u
3
+ 1)(23u
30
+ 147u
28
+ ··· + u + 1)
· (23u
49
+ 48u
48
+ ··· + 4u + 1)
c
4
, c
10
529u
7
(23u
30
− 428u
28
+ ··· − 56074u
2
+ 361)
· (23u
49
+ 117u
48
+ ··· − 2048u − 256)
c
5
, c
12
(u
3
− u − 1)(u
4
− u + 1)(u
30
− 4u
29
+ ··· + 115u + 23)
· (u
49
+ 4u
48
+ ··· + 2u − 23)
c
6
(u
3
− u + 1)(u
4
− u
3
+ 1)(u
15
+ u
14
+ ··· − u − 1)
2
· (u
49
− 4u
48
+ ··· + 23u + 8)
c
7
, c
9
(u
3
− u
2
+ 2u − 1)(u
4
− u
3
+ 2u
2
+ 1)(u
30
+ 2u
29
+ ··· + 138u − 23)
· (u
49
− 4u
48
+ ··· − 202u + 23)
c
8
(u
3
+ 2u
2
+ 3u + 1)(u
4
+ 3u
3
+ 5u
2
+ 5u + 3)
· ((u
15
− 8u
14
+ ··· − 5u − 1)
2
)(u
49
− 8u
48
+ ··· + 84571u − 12398)
41
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
3
− 2y
2
− 3y −1)(y
4
+ 3y
3
+ ··· + 4y + 1)(y
15
− 5y
14
+ ··· + y −1)
2
· (y
49
+ 16y
48
+ ··· − 2527y −4096)
c
2
, c
6
(y
3
− 2y
2
+ y −1)(y
4
− y
3
+ 2y
2
+ 1)(y
15
− 9y
14
+ ··· + 5y −1)
2
· (y
49
− 16y
48
+ ··· + 1553y −64)
c
3
, c
11
279841(y
3
− y
2
+ 2y −1)(y
4
− y
3
+ 2y
2
+ 1)
· (529y
30
+ 6762y
29
+ ··· − 45y + 1)(529y
49
− 4328y
48
+ ··· + 8y −1)
c
4
, c
10
279841y
7
(23y
15
− 428y
14
+ ··· − 56074y + 361)
2
· (529y
49
− 23901y
48
+ ··· − 1048576y −65536)
c
5
, c
12
(y
3
− 2y
2
+ y −1)(y
4
+ 2y
2
− y + 1)(y
30
− 26y
29
+ ··· − 4347y + 529)
· (y
49
− 4y
48
+ ··· − 2480y −529)
c
7
, c
9
(y
3
+ 3y
2
+ 2y −1)(y
4
+ 3y
3
+ 6y
2
+ 4y + 1)
· (y
30
+ 10y
29
+ ··· − 2438y + 529)(y
49
+ 16y
48
+ ··· + 5108y −529)
c
8
(y
3
+ 2y
2
+ 5y −1)(y
4
+ y
3
+ y
2
+ 5y + 9)(y
15
− 12y
14
+ ··· + 3y −1)
2
· (y
49
+ 2y
48
+ ··· + 658603173y −153710404)
42
