12a
0811
(K12a
0811
)
A knot diagram
1
Linearized knot diagam
4 5 7 2 9 3 11 6 12 1 8 10
Solving Sequence
1,4
2 5
3,10
11 12 9 6 7 8
c
1
c
4
c
2
c
10
c
12
c
9
c
5
c
6
c
8
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hb + u, −2u
17
− 7u
16
+ ··· + 2a − 7, u
18
+ 3u
17
+ ··· + 5u − 1i
I
u
2
= h5.65807 × 10
75
u
73
+ 4.34249 × 10
76
u
72
+ ··· + 1.46489 × 10
74
b − 4.16421 × 10
75
,
1.50543 × 10
75
u
73
+ 1.12371 × 10
76
u
72
+ ··· + 1.46489 × 10
74
a − 3.11479 × 10
75
, u
74
+ 9u
73
+ ··· + 25u − 1i
I
u
3
= hb + 1, −4u
7
− 6u
6
+ 9u
5
+ 12u
4
− 6u
3
− 2u
2
+ a − u − 8, u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1i
I
u
4
= h−1146a
7
+ 3254a
6
+ 13110a
5
− 27698a
4
− 23575a
3
+ 74422a
2
+ 661b − 44359a + 6376,
a
8
− 3a
7
− 11a
6
+ 26a
5
+ 17a
4
− 68a
3
+ 48a
2
− 12a + 1, u − 1i
I
u
5
= hb + u, a − 2, u
2
+ u − 1i
I
u
6
= hb − u − 1, a + u + 1, 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
= hb + u, −2u
17
− 7u
16
+ · · · + 2a − 7, 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
10
=
u
17
+
7
2
u
16
+ ··· − 2u +
7
2
−u
a
11
=
u
17
+
7
2
u
16
+ ··· − u +
7
2
−u
a
12
=
1
2
u
17
+ 2u
16
+ ··· −
3
2
u + 2
−u
2
a
9
=
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
8
=
u
17
+ 3u
16
+ ··· − 3u + 4
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
9
, c
10
, c
12
u
18
− 3u
17
+ ··· − 5u − 1
c
3
, c
6
, c
7
c
11
u
18
+ u
17
+ ··· − 5u − 1
c
5
, c
8
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
9
, c
10
, c
12
y
18
− 17y
17
+ ··· − 19y + 1
c
3
, c
6
, c
7
c
11
y
18
− 9y
17
+ ··· − 11y + 1
c
5
, c
8
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 = −4.73699 + 1.01751I
b = −0.989632 − 0.118366I
−2.95901 − 0.54782I −26.1989 − 20.7388I
u = 0.989632 − 0.118366I
a = −4.73699 − 1.01751I
b = −0.989632 + 0.118366I
−2.95901 + 0.54782I −26.1989 + 20.7388I
u = 0.422326 + 0.866115I
a = −0.292665 + 0.821087I
b = −0.422326 − 0.866115I
−1.45893 − 7.65022I −14.1263 + 7.9961I
u = 0.422326 − 0.866115I
a = −0.292665 − 0.821087I
b = −0.422326 + 0.866115I
−1.45893 + 7.65022I −14.1263 − 7.9961I
u = 0.505624 + 0.659339I
a = −0.37939 + 1.54732I
b = −0.505624 − 0.659339I
−2.76095 − 2.16079I −16.8057 + 4.7341I
u = 0.505624 − 0.659339I
a = −0.37939 − 1.54732I
b = −0.505624 + 0.659339I
−2.76095 + 2.16079I −16.8057 − 4.7341I
u = −1.217590 + 0.250614I
a = 0.999646 + 0.475841I
b = 1.217590 − 0.250614I
−4.05098 + 7.39685I −19.0054 − 11.1633I
u = −1.217590 − 0.250614I
a = 0.999646 − 0.475841I
b = 1.217590 + 0.250614I
−4.05098 − 7.39685I −19.0054 + 11.1633I
u = −1.24743
a = 0.531653
b = 1.24743
−9.19331 −28.9570
u = 1.41940 + 0.07138I
a = −3.39301 + 0.09249I
b = −1.41940 − 0.07138I
−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 = −3.39301 − 0.09249I
b = −1.41940 + 0.07138I
−6.53479 + 2.67378I −17.5529 − 2.6003I
u = −0.072733 + 0.557292I
a = 1.025250 + 0.580717I
b = 0.072733 − 0.557292I
2.91333 − 1.30971I −5.30920 + 2.88857I
u = −0.072733 − 0.557292I
a = 1.025250 − 0.580717I
b = 0.072733 + 0.557292I
2.91333 + 1.30971I −5.30920 − 2.88857I
u = −1.49614 + 0.31846I
a = 1.58598 + 1.29639I
b = 1.49614 − 0.31846I
−15.4055 + 9.6614I −20.3543 − 4.9770I
u = −1.49614 − 0.31846I
a = 1.58598 − 1.29639I
b = 1.49614 + 0.31846I
−15.4055 − 9.6614I −20.3543 + 4.9770I
u = −1.53609 + 0.37024I
a = 1.87364 + 1.16526I
b = 1.53609 − 0.37024I
−14.0740 + 16.8703I −19.0655 − 8.3694I
u = −1.53609 − 0.37024I
a = 1.87364 − 1.16526I
b = 1.53609 + 0.37024I
−14.0740 − 16.8703I −19.0655 + 8.3694I
u = 0.218580
a = 3.10342
b = −0.218580
−0.840991 −10.2070
6
II. I
u
2
=
h5.66×10
75
u
73
+4.34×10
76
u
72
+· · ·+1.46×10
74
b−4.16×10
75
, 1.51×10
75
u
73
+
1.12 × 10
76
u
72
+ · · · + 1.46 × 10
74
a − 3.11 × 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
10
=
−10.2768u
73
− 76.7095u
72
+ ··· − 183.962u + 21.2630
−38.6246u
73
− 296.439u
72
+ ··· − 742.347u + 28.4268
a
11
=
28.3478u
73
+ 219.729u
72
+ ··· + 558.384u − 7.16380
−38.6246u
73
− 296.439u
72
+ ··· − 742.347u + 28.4268
a
12
=
−55.0611u
73
− 413.482u
72
+ ··· − 963.034u + 44.1715
−100.725u
73
− 764.026u
72
+ ··· − 1830.80u + 71.0456
a
9
=
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
8
=
32.0304u
73
+ 249.765u
72
+ ··· + 672.873u − 12.6030
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
9
, c
10
, c
12
u
74
− 9u
73
+ ··· − 25u − 1
c
3
, c
6
, c
7
c
11
u
74
+ 3u
73
+ ··· − 384u − 256
c
5
, c
8
(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
9
, c
10
, c
12
y
74
− 75y
73
+ ··· − 675y + 1
c
3
, c
6
, c
7
c
11
y
74
− 51y
73
+ ··· − 5160960y + 65536
c
5
, c
8
(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 = 6.51633
b = −0.530694
−2.53018 0
u = 0.765958 + 0.687849I
a = 0.530736 − 0.170061I
b = −0.454310 + 0.712668I
−2.53529 + 2.33569I 0
u = 0.765958 − 0.687849I
a = 0.530736 + 0.170061I
b = −0.454310 − 0.712668I
−2.53529 − 2.33569I 0
u = 0.740221 + 0.600682I
a = 0.324726 − 0.192964I
b = 1.56736 − 0.14197I
−10.44390 + 0.43302I 0
u = 0.740221 − 0.600682I
a = 0.324726 + 0.192964I
b = 1.56736 + 0.14197I
−10.44390 − 0.43302I 0
u = 0.642782 + 0.680172I
a = −1.39299 + 1.23146I
b = −1.364200 + 0.024112I
−4.74326 + 0.09745I 0
u = 0.642782 − 0.680172I
a = −1.39299 − 1.23146I
b = −1.364200 − 0.024112I
−4.74326 − 0.09745I 0
u = 0.444752 + 0.973604I
a = 0.671707 − 1.134520I
b = 1.50776 + 0.32383I
−7.6984 − 11.9811I 0
u = 0.444752 − 0.973604I
a = 0.671707 + 1.134520I
b = 1.50776 − 0.32383I
−7.6984 + 11.9811I 0
u = 0.397060 + 0.840047I
a = 0.12647 − 1.41487I
b = 1.50364 + 0.23324I
−9.28734 − 5.43922I 0
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.397060 − 0.840047I
a = 0.12647 + 1.41487I
b = 1.50364 − 0.23324I
−9.28734 + 5.43922I 0
u = 0.458933 + 0.804344I
a = −1.168670 + 0.748598I
b = −1.44440 − 0.12650I
−4.11115 − 5.12689I 0
u = 0.458933 − 0.804344I
a = −1.168670 − 0.748598I
b = −1.44440 + 0.12650I
−4.11115 + 5.12689I 0
u = 1.009020 + 0.377651I
a = 0.396161 − 0.004528I
b = 0.000170 − 0.316182I
−0.560067 − 0.765120I 0
u = 1.009020 − 0.377651I
a = 0.396161 + 0.004528I
b = 0.000170 + 0.316182I
−0.560067 + 0.765120I 0
u = −0.062358 + 0.874395I
a = −0.026642 + 0.252961I
b = 1.306060 + 0.081958I
−0.68340 − 3.31809I 0
u = −0.062358 − 0.874395I
a = −0.026642 − 0.252961I
b = 1.306060 − 0.081958I
−0.68340 + 3.31809I 0
u = 0.454310 + 0.712668I
a = 0.098685 − 0.671650I
b = −0.765958 + 0.687849I
−2.53529 − 2.33569I 0
u = 0.454310 − 0.712668I
a = 0.098685 + 0.671650I
b = −0.765958 − 0.687849I
−2.53529 + 2.33569I 0
u = 0.844818 + 0.836713I
a = 0.790427 − 0.298727I
b = 1.49740 − 0.26016I
−8.87079 + 5.90908I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.844818 − 0.836713I
a = 0.790427 + 0.298727I
b = 1.49740 + 0.26016I
−8.87079 − 5.90908I 0
u = 0.231667 + 0.747835I
a = 0.427670 − 0.319614I
b = 0.342720 + 0.342406I
1.71361 − 3.34095I −7.14073 + 5.07807I
u = 0.231667 − 0.747835I
a = 0.427670 + 0.319614I
b = 0.342720 − 0.342406I
1.71361 + 3.34095I −7.14073 − 5.07807I
u = 0.719088
a = −1.78155
b = 1.60418
−9.95403 −72.0690
u = 1.265280 + 0.210357I
a = 1.098350 + 0.079438I
b = 0.218129 + 0.234231I
−1.19152 − 1.56254I 0
u = 1.265280 − 0.210357I
a = 1.098350 − 0.079438I
b = 0.218129 − 0.234231I
−1.19152 + 1.56254I 0
u = −1.306060 + 0.081958I
a = 0.169294 − 0.019291I
b = 0.062358 + 0.874395I
−0.68340 + 3.31809I 0
u = −1.306060 − 0.081958I
a = 0.169294 + 0.019291I
b = 0.062358 − 0.874395I
−0.68340 − 3.31809I 0
u = −0.595869 + 0.339811I
a = 1.72234 + 1.01149I
b = 1.38711 − 0.28497I
−3.44427 + 7.05663I −11.58513 − 7.17023I
u = −0.595869 − 0.339811I
a = 1.72234 − 1.01149I
b = 1.38711 + 0.28497I
−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 = −1.267920 + 0.136700I
b = −0.642782 + 0.680172I
−4.74326 − 0.09745I 0
u = 1.364200 − 0.024112I
a = −1.267920 − 0.136700I
b = −0.642782 − 0.680172I
−4.74326 + 0.09745I 0
u = −1.366460 + 0.029279I
a = −1.41815 − 0.40189I
b = −1.290050 + 0.520157I
−4.82697 + 1.65745I 0
u = −1.366460 − 0.029279I
a = −1.41815 + 0.40189I
b = −1.290050 − 0.520157I
−4.82697 − 1.65745I 0
u = 1.290050 + 0.520157I
a = 1.16345 − 0.86262I
b = 1.366460 + 0.029279I
−4.82697 − 1.65745I 0
u = 1.290050 − 0.520157I
a = 1.16345 + 0.86262I
b = 1.366460 − 0.029279I
−4.82697 + 1.65745I 0
u = 1.40953 + 0.12805I
a = 2.51596 − 1.15937I
b = 1.54388 + 0.20125I
−11.93780 − 3.04537I 0
u = 1.40953 − 0.12805I
a = 2.51596 + 1.15937I
b = 1.54388 − 0.20125I
−11.93780 + 3.04537I 0
u = −1.38711 + 0.28497I
a = 0.945189 + 0.206760I
b = 0.595869 − 0.339811I
−3.44427 + 7.05663I 0
u = −1.38711 − 0.28497I
a = 0.945189 − 0.206760I
b = 0.595869 + 0.339811I
−3.44427 − 7.05663I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.43299 + 0.09516I
a = 0.755112 + 0.316373I
b = 0.251570 − 0.421107I
−6.60087 + 1.06308I 0
u = −1.43299 − 0.09516I
a = 0.755112 − 0.316373I
b = 0.251570 + 0.421107I
−6.60087 − 1.06308I 0
u = 1.44440 + 0.12650I
a = −0.818084 − 0.341295I
b = −0.458933 − 0.804344I
−4.11115 − 5.12689I 0
u = 1.44440 − 0.12650I
a = −0.818084 + 0.341295I
b = −0.458933 + 0.804344I
−4.11115 + 5.12689I 0
u = 0.530694
a = 12.1261
b = −0.987559
−2.53018 −192.020
u = −0.251570 + 0.421107I
a = 0.49512 + 2.34529I
b = 1.43299 − 0.09516I
−6.60087 + 1.06308I −15.5655 − 0.4982I
u = −0.251570 − 0.421107I
a = 0.49512 − 2.34529I
b = 1.43299 + 0.09516I
−6.60087 − 1.06308I −15.5655 + 0.4982I
u = −0.342720 + 0.342406I
a = −0.852282 − 0.134347I
b = −0.231667 + 0.747835I
1.71361 + 3.34095I −7.14073 − 5.07807I
u = −0.342720 − 0.342406I
a = −0.852282 + 0.134347I
b = −0.231667 − 0.747835I
1.71361 − 3.34095I −7.14073 + 5.07807I
u = −1.49740 + 0.26016I
a = −0.548850 − 0.368493I
b = −0.844818 − 0.836713I
−8.87079 + 5.90908I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.49740 − 0.26016I
a = −0.548850 + 0.368493I
b = −0.844818 + 0.836713I
−8.87079 − 5.90908I 0
u = −1.50364 + 0.23324I
a = −0.758602 − 0.420638I
b = −0.397060 + 0.840047I
−9.28734 + 5.43922I 0
u = −1.50364 − 0.23324I
a = −0.758602 + 0.420638I
b = −0.397060 − 0.840047I
−9.28734 − 5.43922I 0
u = −1.51258 + 0.29195I
a = −2.34120 − 0.86317I
b = −1.53693 + 0.15527I
−10.51240 + 9.13078I 0
u = −1.51258 − 0.29195I
a = −2.34120 + 0.86317I
b = −1.53693 − 0.15527I
−10.51240 − 9.13078I 0
u = −1.53328 + 0.16361I
a = 2.10853 + 0.19378I
b = 1.70709 + 0.15451I
−17.8245 + 2.1237I 0
u = −1.53328 − 0.16361I
a = 2.10853 − 0.19378I
b = 1.70709 − 0.15451I
−17.8245 − 2.1237I 0
u = −1.50776 + 0.32383I
a = −0.910033 − 0.096369I
b = −0.444752 + 0.973604I
−7.6984 + 11.9811I 0
u = −1.50776 − 0.32383I
a = −0.910033 + 0.096369I
b = −0.444752 − 0.973604I
−7.6984 − 11.9811I 0
u = 1.53693 + 0.15527I
a = 2.40267 − 0.64750I
b = 1.51258 + 0.29195I
−10.51240 − 9.13078I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.53693 − 0.15527I
a = 2.40267 + 0.64750I
b = 1.51258 − 0.29195I
−10.51240 + 9.13078I 0
u = −1.54388 + 0.20125I
a = −2.24427 − 1.14235I
b = −1.40953 + 0.12805I
−11.93780 + 3.04537I 0
u = −1.54388 − 0.20125I
a = −2.24427 + 1.14235I
b = −1.40953 − 0.12805I
−11.93780 − 3.04537I 0
u = −1.56736 + 0.14197I
a = −0.222469 − 0.053469I
b = −0.740221 − 0.600682I
−10.44390 + 0.43302I 0
u = −1.56736 − 0.14197I
a = −0.222469 + 0.053469I
b = −0.740221 + 0.600682I
−10.44390 − 0.43302I 0
u = 0.401467
a = 1.34983
b = −0.0384223
−0.820249 −11.7000
u = −1.60418
a = 0.798596
b = −0.719088
−9.95403 0
u = −0.218129 + 0.234231I
a = −3.68157 − 2.43333I
b = −1.265280 + 0.210357I
−1.19152 + 1.56254I −9.17228 − 1.36855I
u = −0.218129 − 0.234231I
a = −3.68157 + 2.43333I
b = −1.265280 − 0.210357I
−1.19152 − 1.56254I −9.17228 + 1.36855I
u = −0.000170 + 0.316182I
a = 0.458043 − 1.269910I
b = −1.009020 − 0.377651I
−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 = 0.458043 + 1.269910I
b = −1.009020 + 0.377651I
−0.560067 + 0.765120I −10.35165 − 1.08474I
u = −1.70709 + 0.15451I
a = 1.89436 + 0.19950I
b = 1.53328 + 0.16361I
−17.8245 − 2.1237I 0
u = −1.70709 − 0.15451I
a = 1.89436 − 0.19950I
b = 1.53328 − 0.16361I
−17.8245 + 2.1237I 0
u = 0.0384223
a = 14.1041
b = −0.401467
−0.820249 −11.7000
17
III. I
u
3
= hb + 1, −4u
7
− 6u
6
+ · · · + a − 8, 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
10
=
4u
7
+ 6u
6
− 9u
5
− 12u
4
+ 6u
3
+ 2u
2
+ u + 8
−1
a
11
=
4u
7
+ 6u
6
− 9u
5
− 12u
4
+ 6u
3
+ 2u
2
+ u + 9
−1
a
12
=
4u
7
+ 6u
6
− 9u
5
− 12u
4
+ 6u
3
+ 2u
2
+ u + 9
−1
a
9
=
−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
8
=
−u
6
+ 3u
4
− 2u
2
− 1
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
11
u
8
c
8
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
9
, c
10
(u − 1)
8
c
12
(u + 1)
8
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
8
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
7
, c
11
y
8
c
9
, c
10
, c
12
(y −1)
8
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.180120 + 0.268597I
a = −1.82964 + 0.62117I
b = −1.00000
−2.68559 − 1.13123I −14.0862 + 1.5750I
u = 1.180120 − 0.268597I
a = −1.82964 − 0.62117I
b = −1.00000
−2.68559 + 1.13123I −14.0862 − 1.5750I
u = 0.108090 + 0.747508I
a = 0.001985 − 0.277604I
b = −1.00000
0.51448 − 2.57849I −10.94521 + 2.41352I
u = 0.108090 − 0.747508I
a = 0.001985 + 0.277604I
b = −1.00000
0.51448 + 2.57849I −10.94521 − 2.41352I
u = −1.37100
a = −0.449265
b = −1.00000
−8.14766 −19.2760
u = −1.334530 + 0.318930I
a = −0.858837 − 0.373191I
b = −1.00000
−4.02461 + 6.44354I −18.3815 − 0.5907I
u = −1.334530 − 0.318930I
a = −0.858837 + 0.373191I
b = −1.00000
−4.02461 − 6.44354I −18.3815 + 0.5907I
u = 0.463640
a = 8.82225
b = −1.00000
−2.48997 37.1020
21
IV.
I
u
4
= h−1146a
7
+ 661b + · · · − 44359a + 6376, a
8
− 3a
7
+ · · · − 12a + 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
10
=
a
1.73374a
7
− 4.92284a
6
+ ··· + 67.1089a − 9.64599
a
11
=
−1.73374a
7
+ 4.92284a
6
+ ··· − 66.1089a + 9.64599
1.73374a
7
− 4.92284a
6
+ ··· + 67.1089a − 9.64599
a
12
=
−0.278366a
7
+ 0.762481a
6
+ ··· − 11.1589a + 2.73374
1.14977a
7
− 3.10590a
6
+ ··· + 30.4387a − 3.07413
a
9
=
2.07716a
7
− 5.99395a
6
+ ··· + 78.8321a − 10.7958
3.50530a
7
− 9.86233a
6
+ ··· + 120.430a − 16.6036
a
6
=
0
2.85628a
7
− 7.73676a
6
+ ··· + 84.1952a − 9.61573
a
7
=
0
2.85628a
7
− 7.73676a
6
+ ··· + 84.1952a − 9.61573
a
8
=
2.07716a
7
− 5.99395a
6
+ ··· + 78.8321a − 10.7958
1.55371a
7
− 3.60363a
6
+ ··· + 22.5008a − 1.12254
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
2804
661
a
7
+
8399
661
a
6
+
31167
661
a
5
−
73309
661
a
4
−
51158
661
a
3
+
194340
661
a
2
−
127808
661
a +
11630
661
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
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
8
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
9
, c
10
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
11
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1
c
12
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 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
8
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
7
, c
11
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
c
9
, c
10
, c
12
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
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 = 1.265160 + 0.224125I
b = 1.334530 − 0.318930I
−4.02461 + 6.44354I −18.3815 − 0.5907I
u = 1.00000
a = 1.265160 − 0.224125I
b = 1.334530 + 0.318930I
−4.02461 − 6.44354I −18.3815 + 0.5907I
u = 1.00000
a = 0.615944
b = 1.37100
−8.14766 −19.2760
u = 1.00000
a = 0.207725 + 0.028522I
b = −0.108090 + 0.747508I
0.51448 + 2.57849I −10.94521 − 2.41352I
u = 1.00000
a = 0.207725 − 0.028522I
b = −0.108090 − 0.747508I
0.51448 − 2.57849I −10.94521 + 2.41352I
u = 1.00000
a = −2.32604 + 0.24162I
b = −1.180120 − 0.268597I
−2.68559 − 1.13123I −14.0862 + 1.5750I
u = 1.00000
a = −2.32604 − 0.24162I
b = −1.180120 + 0.268597I
−2.68559 + 1.13123I −14.0862 − 1.5750I
u = 1.00000
a = 4.09035
b = −0.463640
−2.48997 37.1020
25
V. I
u
5
= hb + u, 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
10
=
2
−u
a
11
=
u + 2
−u
a
12
=
2u + 1
u − 1
a
9
=
u
u − 1
a
6
=
−u
−u + 1
a
7
=
−1
0
a
8
=
u
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
9
, c
10
u
2
+ u − 1
c
4
, c
6
, c
11
c
12
u
2
− u − 1
c
5
, c
8
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
9
, c
10
, c
11
c
12
y
2
− 3y + 1
c
5
, c
8
y
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 2.00000
b = −0.618034
−1.97392 −20.0000
u = −1.61803
a = 2.00000
b = 1.61803
−17.7653 −20.0000
29
VI. I
u
6
= hb − u − 1, a + u + 1, 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
10
=
−u − 1
u + 1
a
11
=
−2u − 2
u + 1
a
12
=
u + 3
−u − 2
a
9
=
2u + 3
−u − 2
a
6
=
−u
−u + 1
a
7
=
−1
0
a
8
=
2u + 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
9
, c
10
u
2
+ u − 1
c
4
, c
6
, c
11
c
12
u
2
− u − 1
c
5
, c
8
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
9
, c
10
, c
11
c
12
y
2
− 3y + 1
c
5
, c
8
y
2
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −1.61803
b = 1.61803
−9.86960 25.0000
u = −1.61803
a = 0.618034
b = −0.618034
−9.86960 25.0000
33
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
9
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
3
, c
7
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
12
(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
u
4
(u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
2
· (u
18
− 5u
17
+ ··· − 8u + 4)(u
37
+ u
36
+ ··· − 9u + 2)
2
c
6
, c
11
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
8
u
4
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
2
· (u
18
− 5u
17
+ ··· − 8u + 4)(u
37
+ u
36
+ ··· − 9u + 2)
2
34
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
9
, c
10
, c
12
(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
7
c
11
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
8
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
