12a
0817
(K12a
0817
)
A knot diagram
1
Linearized knot diagam
4 5 7 2 12 3 10 11 1 8 6 9
Solving Sequence
1,4
2 5
3,9
10 12 6 7 11 8
c
1
c
4
c
2
c
9
c
12
c
5
c
6
c
11
c
8
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
17
− 2u
16
+ ··· + 2b − 5u, u
17
+ 5u
16
+ ··· + 2a + 9, u
18
+ 3u
17
+ ··· + 5u − 1i
I
u
2
= h5.45567 × 10
75
u
73
+ 4.11793 × 10
76
u
72
+ ··· + 1.46489 × 10
74
b − 3.85724 × 10
75
,
− 1.05682 × 10
75
u
73
− 8.04501 × 10
75
u
72
+ ··· + 7.32443 × 10
73
a + 2.11780 × 10
75
,
u
74
+ 9u
73
+ ··· + 25u − 1i
I
u
3
= hb, 3u
7
+ 5u
6
− 7u
5
− 11u
4
+ 5u
3
+ 3u
2
+ a + 7, u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1i
I
u
4
= h−16a
7
+ 37a
6
+ 131a
5
− 231a
4
− 337a
3
+ 380a
2
+ 86b + 82a − 115,
a
8
− 9a
6
− 5a
5
+ 18a
4
+ 9a
3
− 11a
2
− 5a + 1, u − 1i
I
u
5
= hb + u, a + u, u
2
+ u − 1i
I
u
6
= hb − u − 1, a + 2, u
2
+ u − 1i
* 6 irreducible components of dim
C
= 0, with total 112 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−u
17
−2u
16
+· · ·+2b −5u, u
17
+5u
16
+· · ·+2a +9, u
18
+3u
17
+· · ·+5u −1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
a
9
=
−
1
2
u
17
−
5
2
u
16
+ ··· +
9
2
u −
9
2
1
2
u
17
+ u
16
+ ··· − 3u
2
+
5
2
u
a
10
=
−u
17
−
7
2
u
16
+ ··· + 2u −
9
2
1
2
u
17
+ u
16
+ ··· − 3u
2
+
5
2
u
a
12
=
1
2
u
17
+ 2u
16
+ ··· −
3
2
u + 3
u
3
− u
a
6
=
1
2
u
17
−
9
2
u
15
+ ··· +
5
2
u − 2
−
1
2
u
17
−
1
2
u
16
+ ··· −
3
2
u +
1
2
a
7
=
−
1
2
u
16
− u
15
+ ··· + 3u −
5
2
−2u
17
− 3u
16
+ ··· − 10u + 2
a
11
=
u
17
+ 3u
16
+ ··· − 3u + 4
5
2
u
17
+
9
2
u
16
+ ··· +
25
2
u −
5
2
a
8
=
−
1
2
u
17
−
3
2
u
16
+ ··· +
7
2
u −
7
2
−
5
2
u
17
−
9
2
u
16
+ ··· −
25
2
u +
5
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3u
17
+ 4u
16
− 25u
15
− 30u
14
+ 79u
13
+ 59u
12
− 138u
11
+ 24u
10
+
161u
9
− 176u
8
− 68u
7
+ 150u
6
− 100u
5
− 11u
4
+ 62u
3
− 42u
2
+ 33u − 16
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
7
, c
8
, c
10
u
18
− 3u
17
+ ··· − 5u − 1
c
3
, c
6
, c
9
c
12
u
18
+ u
17
+ ··· − 5u − 1
c
5
, c
11
u
18
− 5u
17
+ ··· − 8u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
7
, c
8
, c
10
y
18
− 17y
17
+ ··· − 19y + 1
c
3
, c
6
, c
9
c
12
y
18
− 9y
17
+ ··· − 11y + 1
c
5
, c
11
y
18
+ 5y
17
+ ··· + 96y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.989632 + 0.118366I
a = 4.41550 + 0.71456I
b = 0.386038 − 0.294983I
−2.95901 − 0.54782I −26.1989 − 20.7388I
u = 0.989632 − 0.118366I
a = 4.41550 − 0.71456I
b = 0.386038 + 0.294983I
−2.95901 + 0.54782I −26.1989 + 20.7388I
u = 0.422326 + 0.866115I
a = −0.769480 + 0.797033I
b = −1.218200 − 0.431947I
−1.45893 − 7.65022I −14.1263 + 7.9961I
u = 0.422326 − 0.866115I
a = −0.769480 − 0.797033I
b = −1.218200 + 0.431947I
−1.45893 + 7.65022I −14.1263 − 7.9961I
u = 0.505624 + 0.659339I
a = 0.58411 − 1.48309I
b = 1.039530 + 0.211769I
−2.76095 − 2.16079I −16.8057 + 4.7341I
u = 0.505624 − 0.659339I
a = 0.58411 + 1.48309I
b = 1.039530 − 0.211769I
−2.76095 + 2.16079I −16.8057 − 4.7341I
u = −1.217590 + 0.250614I
a = 0.519633 + 0.144909I
b = 0.799643 − 0.530407I
−4.05098 + 7.39685I −19.0054 − 11.1633I
u = −1.217590 − 0.250614I
a = 0.519633 − 0.144909I
b = 0.799643 + 0.530407I
−4.05098 − 7.39685I −19.0054 + 11.1633I
u = −1.24743
a = −0.0578863
b = −0.832862
−9.19331 −28.9570
u = 1.41940 + 0.07138I
a = 0.323890 − 0.894237I
b = 0.149813 − 1.200420I
−6.53479 − 2.67378I −17.5529 + 2.6003I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41940 − 0.07138I
a = 0.323890 + 0.894237I
b = 0.149813 + 1.200420I
−6.53479 + 2.67378I −17.5529 − 2.6003I
u = −0.072733 + 0.557292I
a = 0.525452 − 0.116898I
b = −0.545385 − 0.661484I
2.91333 − 1.30971I −5.30920 + 2.88857I
u = −0.072733 − 0.557292I
a = 0.525452 + 0.116898I
b = −0.545385 + 0.661484I
2.91333 + 1.30971I −5.30920 − 2.88857I
u = −1.49614 + 0.31846I
a = −1.43529 − 0.90742I
b = −1.35407 + 0.66015I
−15.4055 + 9.6614I −20.3543 − 4.9770I
u = −1.49614 − 0.31846I
a = −1.43529 + 0.90742I
b = −1.35407 − 0.66015I
−15.4055 − 9.6614I −20.3543 + 4.9770I
u = −1.53609 + 0.37024I
a = 1.76834 + 0.71483I
b = 1.43095 − 0.76866I
−14.0740 + 16.8703I −19.0655 − 8.3694I
u = −1.53609 − 0.37024I
a = 1.76834 − 0.71483I
b = 1.43095 + 0.76866I
−14.0740 − 16.8703I −19.0655 + 8.3694I
u = 0.218580
a = −3.80642
b = 0.456220
−0.840991 −10.2070
6
II. I
u
2
= h5.46 × 10
75
u
73
+ 4.12 × 10
76
u
72
+ · · · + 1.46 × 10
74
b − 3.86 ×
10
75
, −1.06 × 10
75
u
73
− 8.05 × 10
75
u
72
+ · · · + 7.32 × 10
73
a + 2.12 ×
10
75
, u
74
+ 9u
73
+ · · · + 25u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
a
9
=
14.4287u
73
+ 109.838u
72
+ ··· + 281.944u − 28.9142
−37.2429u
73
− 281.109u
72
+ ··· − 661.514u + 26.3313
a
10
=
51.6717u
73
+ 390.947u
72
+ ··· + 943.457u − 55.2455
−37.2429u
73
− 281.109u
72
+ ··· − 661.514u + 26.3313
a
12
=
33.4992u
73
+ 261.898u
72
+ ··· + 709.028u − 16.0765
75.6177u
73
+ 583.270u
72
+ ··· + 1498.50u − 58.5028
a
6
=
−30.8792u
73
− 233.688u
72
+ ··· − 554.094u + 16.6614
−48.3000u
73
− 364.699u
72
+ ··· − 849.392u + 33.2488
a
7
=
36.0803u
73
+ 270.250u
72
+ ··· + 606.729u − 28.7422
−25.1044u
73
− 186.311u
72
+ ··· − 406.556u + 16.0348
a
11
=
32.0304u
73
+ 249.765u
72
+ ··· + 672.873u − 12.6030
13.2898u
73
+ 102.925u
72
+ ··· + 269.186u − 10.8565
a
8
=
85.5243u
73
+ 649.125u
72
+ ··· + 1574.12u − 73.7687
−13.2898u
73
− 102.925u
72
+ ··· − 269.186u + 10.8565
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18.3007u
73
− 137.274u
72
+ ··· − 108.453u − 7.83721
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
7
, c
8
, c
10
u
74
− 9u
73
+ ··· − 25u − 1
c
3
, c
6
, c
9
c
12
u
74
+ 3u
73
+ ··· − 384u − 256
c
5
, c
11
(u
37
+ u
36
+ ··· − 9u + 2)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
7
, c
8
, c
10
y
74
− 75y
73
+ ··· − 675y + 1
c
3
, c
6
, c
9
c
12
y
74
− 51y
73
+ ··· − 5160960y + 65536
c
5
, c
11
(y
37
+ 15y
36
+ ··· + 89y − 4)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.987559
a = −5.10237
b = 0.617439
−2.53018 0
u = 0.765958 + 0.687849I
a = −0.769554 + 0.568181I
b = −1.068030 + 0.296505I
−2.53529 + 2.33569I 0
u = 0.765958 − 0.687849I
a = −0.769554 − 0.568181I
b = −1.068030 − 0.296505I
−2.53529 − 2.33569I 0
u = 0.740221 + 0.600682I
a = 0.083801 + 0.201944I
b = −1.50913 + 0.29868I
−10.44390 + 0.43302I 0
u = 0.740221 − 0.600682I
a = 0.083801 − 0.201944I
b = −1.50913 − 0.29868I
−10.44390 − 0.43302I 0
u = 0.642782 + 0.680172I
a = 1.09156 − 1.09879I
b = 0.050970 + 1.083900I
−4.74326 + 0.09745I 0
u = 0.642782 − 0.680172I
a = 1.09156 + 1.09879I
b = 0.050970 − 1.083900I
−4.74326 − 0.09745I 0
u = 0.444752 + 0.973604I
a = 0.528031 − 0.978953I
b = 1.37729 + 0.67188I
−7.6984 − 11.9811I 0
u = 0.444752 − 0.973604I
a = 0.528031 + 0.978953I
b = 1.37729 − 0.67188I
−7.6984 + 11.9811I 0
u = 0.397060 + 0.840047I
a = 0.009139 + 1.344670I
b = −1.37372 − 0.48631I
−9.28734 − 5.43922I 0
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.397060 − 0.840047I
a = 0.009139 − 1.344670I
b = −1.37372 + 0.48631I
−9.28734 + 5.43922I 0
u = 0.458933 + 0.804344I
a = −0.234033 + 0.783748I
b = 0.264672 − 1.252910I
−4.11115 − 5.12689I 0
u = 0.458933 − 0.804344I
a = −0.234033 − 0.783748I
b = 0.264672 + 1.252910I
−4.11115 + 5.12689I 0
u = 1.009020 + 0.377651I
a = −1.061260 + 0.291632I
b = −0.416875 − 0.417140I
−0.560067 − 0.765120I 0
u = 1.009020 − 0.377651I
a = −1.061260 − 0.291632I
b = −0.416875 + 0.417140I
−0.560067 + 0.765120I 0
u = −0.062358 + 0.874395I
a = −0.364737 + 0.159007I
b = 0.962355 + 0.175040I
−0.68340 − 3.31809I 0
u = −0.062358 − 0.874395I
a = −0.364737 − 0.159007I
b = 0.962355 − 0.175040I
−0.68340 + 3.31809I 0
u = 0.454310 + 0.712668I
a = 0.801818 − 0.221496I
b = 1.187720 + 0.083087I
−2.53529 − 2.33569I 0
u = 0.454310 − 0.712668I
a = 0.801818 + 0.221496I
b = 1.187720 − 0.083087I
−2.53529 + 2.33569I 0
u = 0.844818 + 0.836713I
a = 0.304386 − 0.398418I
b = 1.35981 − 0.54134I
−8.87079 + 5.90908I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.844818 − 0.836713I
a = 0.304386 + 0.398418I
b = 1.35981 + 0.54134I
−8.87079 − 5.90908I 0
u = 0.231667 + 0.747835I
a = −0.012518 − 0.445587I
b = −0.193017 + 0.678428I
1.71361 − 3.34095I −7.14073 + 5.07807I
u = 0.231667 − 0.747835I
a = −0.012518 + 0.445587I
b = −0.193017 − 0.678428I
1.71361 + 3.34095I −7.14073 − 5.07807I
u = 0.719088
a = 2.14467
b = −1.58871
−9.95403 −72.0690
u = 1.265280 + 0.210357I
a = −0.126339 + 0.671818I
b = −0.200503 + 0.532779I
−1.19152 − 1.56254I 0
u = 1.265280 − 0.210357I
a = −0.126339 − 0.671818I
b = −0.200503 − 0.532779I
−1.19152 + 1.56254I 0
u = −1.306060 + 0.081958I
a = −0.837235 + 0.046967I
b = −0.818917 + 0.935827I
−0.68340 + 3.31809I 0
u = −1.306060 − 0.081958I
a = −0.837235 − 0.046967I
b = −0.818917 − 0.935827I
−0.68340 − 3.31809I 0
u = −0.595869 + 0.339811I
a = 1.37457 + 0.51483I
b = 1.135850 − 0.588468I
−3.44427 + 7.05663I −11.58513 − 7.17023I
u = −0.595869 − 0.339811I
a = 1.37457 − 0.51483I
b = 1.135850 + 0.588468I
−3.44427 − 7.05663I −11.58513 + 7.17023I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.364200 + 0.024112I
a = 2.71573 + 0.41433I
b = 1.128650 − 0.067233I
−4.74326 − 0.09745I 0
u = 1.364200 − 0.024112I
a = 2.71573 − 0.41433I
b = 1.128650 + 0.067233I
−4.74326 + 0.09745I 0
u = −1.366460 + 0.029279I
a = 1.223220 + 0.076417I
b = 1.033360 + 0.936789I
−4.82697 + 1.65745I 0
u = −1.366460 − 0.029279I
a = 1.223220 − 0.076417I
b = 1.033360 − 0.936789I
−4.82697 − 1.65745I 0
u = 1.290050 + 0.520157I
a = 0.614962 − 0.662756I
b = 1.088720 + 0.061864I
−4.82697 − 1.65745I 0
u = 1.290050 − 0.520157I
a = 0.614962 + 0.662756I
b = 1.088720 − 0.061864I
−4.82697 + 1.65745I 0
u = 1.40953 + 0.12805I
a = −2.21461 + 0.77406I
b = −1.45817 − 0.42165I
−11.93780 − 3.04537I 0
u = 1.40953 − 0.12805I
a = −2.21461 − 0.77406I
b = −1.45817 + 0.42165I
−11.93780 + 3.04537I 0
u = −1.38711 + 0.28497I
a = 0.264716 − 0.296527I
b = −0.011117 − 0.768662I
−3.44427 + 7.05663I 0
u = −1.38711 − 0.28497I
a = 0.264716 + 0.296527I
b = −0.011117 + 0.768662I
−3.44427 − 7.05663I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.43299 + 0.09516I
a = −0.1258650 − 0.0186642I
b = 0.305601 + 0.680349I
−6.60087 + 1.06308I 0
u = −1.43299 − 0.09516I
a = −0.1258650 + 0.0186642I
b = 0.305601 − 0.680349I
−6.60087 − 1.06308I 0
u = 1.44440 + 0.12650I
a = −2.42296 + 0.13068I
b = −1.172300 − 0.348245I
−4.11115 − 5.12689I 0
u = 1.44440 − 0.12650I
a = −2.42296 − 0.13068I
b = −1.172300 + 0.348245I
−4.11115 + 5.12689I 0
u = 0.530694
a = −10.8001
b = −0.156268
−2.53018 −192.020
u = −0.251570 + 0.421107I
a = −0.26379 − 2.00340I
b = −1.229010 + 0.199425I
−6.60087 + 1.06308I −15.5655 − 0.4982I
u = −0.251570 − 0.421107I
a = −0.26379 + 2.00340I
b = −1.229010 − 0.199425I
−6.60087 − 1.06308I −15.5655 + 0.4982I
u = −0.342720 + 0.342406I
a = −2.05882 − 0.92201I
b = −0.953270 + 0.548459I
1.71361 + 3.34095I −7.14073 − 5.07807I
u = −0.342720 − 0.342406I
a = −2.05882 + 0.92201I
b = −0.953270 − 0.548459I
1.71361 − 3.34095I −7.14073 + 5.07807I
u = −1.49740 + 0.26016I
a = 1.99549 + 0.47867I
b = 1.42581 − 0.12941I
−8.87079 + 5.90908I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.49740 − 0.26016I
a = 1.99549 − 0.47867I
b = 1.42581 + 0.12941I
−8.87079 − 5.90908I 0
u = −1.50364 + 0.23324I
a = 1.62278 + 0.88393I
b = 1.170740 − 0.442254I
−9.28734 + 5.43922I 0
u = −1.50364 − 0.23324I
a = 1.62278 − 0.88393I
b = 1.170740 + 0.442254I
−9.28734 − 5.43922I 0
u = −1.51258 + 0.29195I
a = −0.276538 + 0.634948I
b = 0.32567 + 1.44514I
−10.51240 + 9.13078I 0
u = −1.51258 − 0.29195I
a = −0.276538 − 0.634948I
b = 0.32567 − 1.44514I
−10.51240 − 9.13078I 0
u = −1.53328 + 0.16361I
a = −1.83362 − 0.39801I
b = −1.80406 − 0.33054I
−17.8245 + 2.1237I 0
u = −1.53328 − 0.16361I
a = −1.83362 + 0.39801I
b = −1.80406 + 0.33054I
−17.8245 − 2.1237I 0
u = −1.50776 + 0.32383I
a = −1.92923 − 0.67310I
b = −1.36228 + 0.48402I
−7.6984 + 11.9811I 0
u = −1.50776 − 0.32383I
a = −1.92923 + 0.67310I
b = −1.36228 − 0.48402I
−7.6984 − 11.9811I 0
u = 1.53693 + 0.15527I
a = 2.05996 − 0.14354I
b = 1.38923 + 0.60719I
−10.51240 − 9.13078I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.53693 − 0.15527I
a = 2.05996 + 0.14354I
b = 1.38923 − 0.60719I
−10.51240 + 9.13078I 0
u = −1.54388 + 0.20125I
a = 0.376558 − 0.067493I
b = −0.268156 − 1.180450I
−11.93780 + 3.04537I 0
u = −1.54388 − 0.20125I
a = 0.376558 + 0.067493I
b = −0.268156 + 1.180450I
−11.93780 − 3.04537I 0
u = −1.56736 + 0.14197I
a = −1.80095 − 0.55160I
b = −1.068740 + 0.079519I
−10.44390 + 0.43302I 0
u = −1.56736 − 0.14197I
a = −1.80095 + 0.55160I
b = −1.068740 − 0.079519I
−10.44390 − 0.43302I 0
u = 0.401467
a = −1.57968
b = 0.195871
−0.820249 −11.7000
u = −1.60418
a = −2.26280
b = −0.589285
−9.95403 0
u = −0.218129 + 0.234231I
a = −0.130714 + 1.149030I
b = 0.444722 + 0.888915I
−1.19152 + 1.56254I −9.17228 − 1.36855I
u = −0.218129 − 0.234231I
a = −0.130714 − 1.149030I
b = 0.444722 − 0.888915I
−1.19152 − 1.56254I −9.17228 + 1.36855I
u = −0.000170 + 0.316182I
a = 2.28289 + 2.44470I
b = 0.789115 − 0.457450I
−0.560067 − 0.765120I −10.35165 + 1.08474I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.000170 − 0.316182I
a = 2.28289 − 2.44470I
b = 0.789115 + 0.457450I
−0.560067 + 0.765120I −10.35165 − 1.08474I
u = −1.70709 + 0.15451I
a = 1.39938 + 0.39730I
b = 1.43731 + 0.34297I
−17.8245 − 2.1237I 0
u = −1.70709 − 0.15451I
a = 1.39938 − 0.39730I
b = 1.43731 − 0.34297I
−17.8245 + 2.1237I 0
u = 0.0384223
a = −17.9721
b = 0.580310
−0.820249 −11.7000
17
III. I
u
3
=
hb, 3u
7
+5u
6
−7u
5
−11u
4
+5u
3
+3u
2
+a+7, u
8
+u
7
−3u
6
−2u
5
+3u
4
+2u−1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
a
9
=
−3u
7
− 5u
6
+ 7u
5
+ 11u
4
− 5u
3
− 3u
2
− 7
0
a
10
=
−3u
7
− 5u
6
+ 7u
5
+ 11u
4
− 5u
3
− 3u
2
− 7
0
a
12
=
1
0
a
6
=
u
3
− 2u
−u
3
+ u
a
7
=
−u
6
+ 3u
4
− 2u
2
− 1
u
6
− 2u
4
+ u
2
a
11
=
u
6
− 3u
4
+ 2u
2
+ 1
−u
6
+ 2u
4
− u
2
a
8
=
−3u
7
− 6u
6
+ 7u
5
+ 14u
4
− 5u
3
− 5u
2
− 8
u
6
− 2u
4
+ u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 21u
7
+ 30u
6
− 48u
5
− 61u
4
+ 31u
3
+ 11u
2
+ 11u + 30
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
3
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
4
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
c
5
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
6
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1
c
7
, c
8
(u − 1)
8
c
9
, c
12
u
8
c
10
(u + 1)
8
c
11
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
c
3
, c
6
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
c
5
, c
11
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
7
, c
8
, c
10
(y − 1)
8
c
9
, c
12
y
8
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.180120 + 0.268597I
a = 1.194470 + 0.635084I
b = 0
−2.68559 − 1.13123I −14.0862 + 1.5750I
u = 1.180120 − 0.268597I
a = 1.194470 − 0.635084I
b = 0
−2.68559 + 1.13123I −14.0862 − 1.5750I
u = 0.108090 + 0.747508I
a = 0.637416 + 0.344390I
b = 0
0.51448 − 2.57849I −10.94521 + 2.41352I
u = 0.108090 − 0.747508I
a = 0.637416 − 0.344390I
b = 0
0.51448 + 2.57849I −10.94521 − 2.41352I
u = −1.37100
a = −0.687555
b = 0
−8.14766 −19.2760
u = −1.334530 + 0.318930I
a = 0.286111 − 0.344558I
b = 0
−4.02461 + 6.44354I −18.3815 − 0.5907I
u = −1.334530 − 0.318930I
a = 0.286111 + 0.344558I
b = 0
−4.02461 − 6.44354I −18.3815 + 0.5907I
u = 0.463640
a = −7.54843
b = 0
−2.48997 37.1020
21
IV. I
u
4
=
h−16a
7
+86b+· · ·+82a−115, a
8
−9a
6
−5a
5
+18a
4
+9a
3
−11a
2
−5a+1, u−1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
5
=
−1
0
a
3
=
0
1
a
9
=
a
0.186047a
7
− 0.430233a
6
+ ··· − 0.953488a + 1.33721
a
10
=
−0.186047a
7
+ 0.430233a
6
+ ··· + 1.95349a − 1.33721
0.186047a
7
− 0.430233a
6
+ ··· − 0.953488a + 1.33721
a
12
=
0.430233a
7
− 0.151163a
6
+ ··· − 2.26744a + 1.18605
1.20930a
7
− 0.546512a
6
+ ··· − 7.69767a − 0.0581395
a
6
=
0
1.65116a
7
− 0.755814a
6
+ ··· − 12.8372a + 0.430233
a
7
=
0
1.65116a
7
− 0.755814a
6
+ ··· − 12.8372a + 0.430233
a
11
=
0.430233a
7
− 0.151163a
6
+ ··· − 2.26744a + 1.18605
0.918605a
7
− 0.0930233a
6
+ ··· − 9.89535a − 1.61628
a
8
=
0.395349a
7
− 0.476744a
6
+ ··· − 2.65116a + 1.77907
0.918605a
7
− 0.0930233a
6
+ ··· − 9.89535a − 1.61628
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
11
86
a
7
+
6
43
a
6
+
41
43
a
5
−
27
43
a
4
−
57
86
a
3
+
265
43
a
2
+
223
86
a −
1705
86
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
, c
6
u
8
c
4
(u + 1)
8
c
5
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
c
7
, c
8
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
9
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
10
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
c
11
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
12
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
8
c
3
, c
6
y
8
c
5
, c
11
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
7
, c
8
, c
10
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
c
9
, c
12
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.043770 + 0.152194I
b = 0.855237 + 0.665892I
0.51448 − 2.57849I −10.94521 + 2.41352I
u = 1.00000
a = 1.043770 − 0.152194I
b = 0.855237 − 0.665892I
0.51448 + 2.57849I −10.94521 − 2.41352I
u = 1.00000
a = −0.759875 + 0.104398I
b = −1.031810 + 0.655470I
−4.02461 + 6.44354I −18.3815 − 0.5907I
u = 1.00000
a = −0.759875 − 0.104398I
b = −1.031810 − 0.655470I
−4.02461 − 6.44354I −18.3815 + 0.5907I
u = 1.00000
a = −1.80990 + 0.33963I
b = −0.570868 − 0.730671I
−2.68559 + 1.13123I −14.0862 − 1.5750I
u = 1.00000
a = −1.80990 − 0.33963I
b = −0.570868 + 0.730671I
−2.68559 − 1.13123I −14.0862 + 1.5750I
u = 1.00000
a = 0.155540
b = 1.09818
−8.14766 −19.2760
u = 1.00000
a = 2.89645
b = −0.603304
−2.48997 37.1020
25
V. I
u
5
= hb + u, a + u, u
2
+ u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
−u + 1
a
5
=
−u
−u + 1
a
3
=
u
u
a
9
=
−u
−u
a
10
=
0
−u
a
12
=
u
u − 1
a
6
=
−u
−u + 1
a
7
=
−1
0
a
11
=
u
u − 1
a
8
=
−1
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −20
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
u
2
+ u − 1
c
4
, c
6
, c
10
c
12
u
2
− u − 1
c
5
, c
11
u
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
6
, c
7
c
8
, c
9
, c
10
c
12
y
2
− 3y + 1
c
5
, c
11
y
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −0.618034
b = −0.618034
−1.97392 −20.0000
u = −1.61803
a = 1.61803
b = 1.61803
−17.7653 −20.0000
29
VI. I
u
6
= hb − u − 1, a + 2, u
2
+ u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
−u + 1
a
5
=
−u
−u + 1
a
3
=
u
u
a
9
=
−2
u + 1
a
10
=
−u − 3
u + 1
a
12
=
2u + 3
−u − 2
a
6
=
−u
−u + 1
a
7
=
−1
0
a
11
=
2u + 3
−u − 2
a
8
=
3u + 3
−u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 25
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
u
2
+ u − 1
c
4
, c
6
, c
10
c
12
u
2
− u − 1
c
5
, c
11
u
2
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
6
, c
7
c
8
, c
9
, c
10
c
12
y
2
− 3y + 1
c
5
, c
11
y
2
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −2.00000
b = 1.61803
−9.86960 25.0000
u = −1.61803
a = −2.00000
b = −0.618034
−9.86960 25.0000
33
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
(u − 1)
8
(u
2
+ u − 1)
2
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
· (u
18
− 3u
17
+ ··· − 5u − 1)(u
74
− 9u
73
+ ··· − 25u − 1)
c
3
, c
9
u
8
(u
2
+ u − 1)
2
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
· (u
18
+ u
17
+ ··· − 5u − 1)(u
74
+ 3u
73
+ ··· − 384u − 256)
c
4
, c
10
(u + 1)
8
(u
2
− u − 1)
2
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
· (u
18
− 3u
17
+ ··· − 5u − 1)(u
74
− 9u
73
+ ··· − 25u − 1)
c
5
, c
11
u
4
(u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
· (u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
· (u
18
− 5u
17
+ ··· − 8u + 4)(u
37
+ u
36
+ ··· − 9u + 2)
2
c
6
, c
12
u
8
(u
2
− u − 1)
2
(u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1)
· (u
18
+ u
17
+ ··· − 5u − 1)(u
74
+ 3u
73
+ ··· − 384u − 256)
34
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
7
, c
8
, c
10
(y − 1)
8
(y
2
− 3y + 1)
2
· (y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
18
− 17y
17
+ ··· − 19y + 1)(y
74
− 75y
73
+ ··· − 675y + 1)
c
3
, c
6
, c
9
c
12
y
8
(y
2
− 3y + 1)
2
(y
8
− 3y
7
+ ··· − 4y + 1)
· (y
18
− 9y
17
+ ··· − 11y + 1)(y
74
− 51y
73
+ ··· − 5160960y + 65536)
c
5
, c
11
y
4
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
2
· (y
18
+ 5y
17
+ ··· + 96y + 16)(y
37
+ 15y
36
+ ··· + 89y − 4)
2
35
