11a
305
(K11a
305
)
A knot diagram
1
Linearized knot diagam
10 9 1 8 3 2 11 5 6 7 4
Solving Sequence
4,8
5
9,11
1 3 6 2 7 10
c
4
c
8
c
11
c
3
c
5
c
2
c
7
c
10
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h128458353823909u
26
+ 129748020078821u
25
+ ··· + 71455439122482b − 307532868153053,
a − 1, u
27
− 15u
25
+ ··· + 8u + 1i
I
u
2
= h6.23874 × 10
124
u
53
+ 1.39776 × 10
125
u
52
+ ··· + 4.41978 × 10
127
b + 4.69540 × 10
127
,
5.28258 × 10
127
u
53
− 1.64275 × 10
127
u
52
+ ··· + 8.57438 × 10
129
a + 7.90543 × 10
128
,
2u
54
− 3u
53
+ ··· + 95u − 97i
I
u
3
= h2u
7
− 3u
6
− 5u
5
+ 6u
4
+ 10u
3
− 12u
2
+ b − u + 4, a + 1, u
8
− u
7
− 3u
6
+ 2u
5
+ 6u
4
− 4u
3
− 3u
2
+ 2u + 1i
I
u
4
= hu
2
+ b, a + 1, u
3
− u − 1i
I
u
5
= hb + 1, a − 2, 2u − 1i
I
u
6
= hb + 1, 2a − 1, u + 1i
I
u
7
= hb + 1, a + 1, u + 1i
* 7 irreducible components of dim
C
= 0, with total 95 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
= h1.28 × 10
14
u
26
+ 1.30 × 10
14
u
25
+ · · · + 7.15 × 10
13
b − 3.08 ×
10
14
, a − 1, u
27
− 15u
25
+ · · · + 8u + 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
−u
2
a
9
=
u
−u
3
+ u
a
11
=
1
−1.79774u
26
− 1.81579u
25
+ ··· + 35.4655u + 4.30384
a
1
=
1.79774u
26
+ 1.81579u
25
+ ··· − 35.4655u − 3.30384
−1.79774u
26
− 1.81579u
25
+ ··· + 35.4655u + 4.30384
a
3
=
2.79486u
26
+ 3.00477u
25
+ ··· − 62.0548u − 7.92538
−0.997121u
26
− 1.18898u
25
+ ··· + 26.5893u + 4.62154
a
6
=
−3.74472u
26
− 3.04658u
25
+ ··· + 45.3634u + 2.81681
0.625459u
26
+ 1.07598u
25
+ ··· − 25.4593u − 2.82772
a
2
=
1.08283u
26
+ 1.65073u
25
+ ··· − 41.4105u − 5.52428
−1.60344u
26
− 1.67881u
25
+ ··· + 34.6892u + 5.66859
a
7
=
−u
1.81579u
26
+ 1.36688u
25
+ ··· − 17.6858u − 1.79774
a
10
=
−u
2
+ 1
−0.430865u
26
− 0.712953u
25
+ ··· + 19.1414u + 2.48805
a
10
=
−u
2
+ 1
−0.430865u
26
− 0.712953u
25
+ ··· + 19.1414u + 2.48805
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
110984790327346
11909239853747
u
26
+
77302583361155
11909239853747
u
25
+ ··· −
911733716325243
11909239853747
u −
123671657013453
11909239853747
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
27
+ 2u
26
+ ··· + 8u + 2
c
2
, c
6
u
27
+ 7u
25
+ ··· − 3u + 1
c
3
, c
11
u
27
− 10u
26
+ ··· + 172u − 16
c
4
, c
7
, c
8
c
10
u
27
− 15u
25
+ ··· + 8u + 1
c
9
u
27
+ 13u
26
+ ··· − 28u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
27
− 4y
26
+ ··· + 84y −4
c
2
, c
6
y
27
+ 14y
26
+ ··· − 15y −1
c
3
, c
11
y
27
+ 16y
26
+ ··· + 6320y −256
c
4
, c
7
, c
8
c
10
y
27
− 30y
26
+ ··· + 34y −1
c
9
y
27
− 3y
26
+ ··· + 56y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.106573 + 0.849360I
a = 1.00000
b = 0.489173 − 0.963829I
−0.11341 + 6.75527I 1.42209 − 7.76802I
u = 0.106573 − 0.849360I
a = 1.00000
b = 0.489173 + 0.963829I
−0.11341 − 6.75527I 1.42209 + 7.76802I
u = −0.159654 + 0.781613I
a = 1.00000
b = 0.591660 + 0.371074I
−1.77335 + 2.61294I −2.81593 − 2.10661I
u = −0.159654 − 0.781613I
a = 1.00000
b = 0.591660 − 0.371074I
−1.77335 − 2.61294I −2.81593 + 2.10661I
u = 0.784543
a = 1.00000
b = −0.832565
0.365696 11.8450
u = 0.779651
a = 1.00000
b = 0.197132
1.29249 7.75610
u = 1.221600 + 0.595583I
a = 1.00000
b = 0.114881 − 1.150240I
4.22227 + 1.28214I 0. − 2.91907I
u = 1.221600 − 0.595583I
a = 1.00000
b = 0.114881 + 1.150240I
4.22227 − 1.28214I 0. + 2.91907I
u = 1.356240 + 0.153177I
a = 1.00000
b = 0.57541 − 1.70357I
11.55650 − 2.44905I 8.88456 + 3.60972I
u = 1.356240 − 0.153177I
a = 1.00000
b = 0.57541 + 1.70357I
11.55650 + 2.44905I 8.88456 − 3.60972I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.39961 + 0.22669I
a = 1.00000
b = 1.44138 − 0.06147I
6.25875 + 10.21720I 5.61375 − 6.77548I
u = 1.39961 − 0.22669I
a = 1.00000
b = 1.44138 + 0.06147I
6.25875 − 10.21720I 5.61375 + 6.77548I
u = −1.40289 + 0.20762I
a = 1.00000
b = 1.029610 + 0.112240I
7.68644 − 3.38302I 7.90859 + 3.21661I
u = −1.40289 − 0.20762I
a = 1.00000
b = 1.029610 − 0.112240I
7.68644 + 3.38302I 7.90859 − 3.21661I
u = 0.096377 + 0.573318I
a = 1.00000
b = 0.076636 + 0.947154I
2.31133 + 1.38881I 5.27810 − 4.63773I
u = 0.096377 − 0.573318I
a = 1.00000
b = 0.076636 − 0.947154I
2.31133 − 1.38881I 5.27810 + 4.63773I
u = −1.48387 + 0.14705I
a = 1.00000
b = 0.72466 + 1.31085I
10.94040 − 2.59348I 9.36617 + 2.06057I
u = −1.48387 − 0.14705I
a = 1.00000
b = 0.72466 − 1.31085I
10.94040 + 2.59348I 9.36617 − 2.06057I
u = −1.52352 + 0.28324I
a = 1.00000
b = 0.280011 + 1.186500I
10.59150 − 1.56799I 10.06893 + 0.I
u = −1.52352 − 0.28324I
a = 1.00000
b = 0.280011 − 1.186500I
10.59150 + 1.56799I 10.06893 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.371492
a = 1.00000
b = −0.808679
−1.55906 −7.62210
u = 1.60437 + 0.47781I
a = 1.00000
b = 0.59054 − 1.51467I
11.3568 + 17.2512I 6.49370 − 8.44917I
u = 1.60437 − 0.47781I
a = 1.00000
b = 0.59054 + 1.51467I
11.3568 − 17.2512I 6.49370 + 8.44917I
u = −1.61375 + 0.50385I
a = 1.00000
b = 0.47653 + 1.39767I
12.4277 − 8.7733I 10.26210 + 6.04290I
u = −1.61375 − 0.50385I
a = 1.00000
b = 0.47653 − 1.39767I
12.4277 + 8.7733I 10.26210 − 6.04290I
u = −0.197438 + 0.089181I
a = 1.00000
b = −0.668438 + 0.903987I
−0.67003 + 2.58307I −5.46112 + 2.85660I
u = −0.197438 − 0.089181I
a = 1.00000
b = −0.668438 − 0.903987I
−0.67003 − 2.58307I −5.46112 − 2.85660I
7
II. I
u
2
= h6.24 × 10
124
u
53
+ 1.40 × 10
125
u
52
+ · · · + 4.42 × 10
127
b + 4.70 ×
10
127
, 5.28 × 10
127
u
53
− 1.64 × 10
127
u
52
+ · · · + 8.57 × 10
129
a + 7.91 ×
10
128
, 2u
54
− 3u
53
+ · · · + 95u − 97i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
−u
2
a
9
=
u
−u
3
+ u
a
11
=
−0.00616088u
53
+ 0.00191588u
52
+ ··· − 2.54802u − 0.0921982
−0.00141155u
53
− 0.00316251u
52
+ ··· + 0.798062u − 1.06236
a
1
=
−0.00474933u
53
+ 0.00507839u
52
+ ··· − 3.34608u + 0.970161
−0.00141155u
53
− 0.00316251u
52
+ ··· + 0.798062u − 1.06236
a
3
=
0.00820072u
53
+ 0.0152695u
52
+ ··· − 2.12375u + 1.68293
−0.0310592u
53
+ 0.0117199u
52
+ ··· + 2.01862u − 1.67137
a
6
=
0.0459316u
53
− 0.0258658u
52
+ ··· − 2.27013u + 4.10710
−0.0103985u
53
− 0.000118880u
52
+ ··· + 0.840301u − 0.133245
a
2
=
−0.00436349u
53
+ 0.0140384u
52
+ ··· − 1.70376u + 1.04810
−0.0229988u
53
+ 0.0141891u
52
+ ··· + 2.09429u − 1.33244
a
7
=
−0.0461208u
53
+ 0.0321142u
52
+ ··· − 2.68247u − 3.34457
−0.00729829u
53
+ 0.00864020u
52
+ ··· + 1.09734u − 1.10864
a
10
=
−0.0553985u
53
+ 0.0605537u
52
+ ··· − 2.42681u − 3.14804
−0.00141547u
53
+ 0.00304333u
52
+ ··· + 1.29536u − 0.247003
a
10
=
−0.0553985u
53
+ 0.0605537u
52
+ ··· − 2.42681u − 3.14804
−0.00141547u
53
+ 0.00304333u
52
+ ··· + 1.29536u − 0.247003
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0491216u
53
− 0.0253069u
52
+ ··· + 8.86509u − 1.04494
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
2(2u
54
+ 15u
53
+ ··· + 95u + 8)
c
2
, c
6
u
54
+ 2u
53
+ ··· + 59u − 58
c
3
, c
11
(u
27
+ 7u
26
+ ··· − 9u + 1)
2
c
4
, c
7
, c
8
c
10
2(2u
54
− 3u
53
+ ··· + 95u − 97)
c
9
4(2u
27
− 15u
26
+ ··· + 13u
2
− 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
4(4y
54
− 45y
53
+ ··· − 3041y + 64)
c
2
, c
6
y
54
− 2y
53
+ ··· + 49299y + 3364
c
3
, c
11
(y
27
+ 21y
26
+ ··· + 79y −1)
2
c
4
, c
7
, c
8
c
10
4(4y
54
− 169y
53
+ ··· − 117277y + 9409)
c
9
16(4y
27
− 9y
26
+ ··· + 26y −1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.191553 + 1.007580I
a = 0.197325 − 1.352280I
b = −0.254804 − 1.313870I
4.62049 − 3.14366I 4.20111 + 7.48213I
u = 0.191553 − 1.007580I
a = 0.197325 + 1.352280I
b = −0.254804 + 1.313870I
4.62049 + 3.14366I 4.20111 − 7.48213I
u = 0.386921 + 0.863120I
a = −0.593875 + 1.093790I
b = −0.336359 + 1.256870I
2.31398 + 4.08168I 2.22183 − 6.73318I
u = 0.386921 − 0.863120I
a = −0.593875 − 1.093790I
b = −0.336359 − 1.256870I
2.31398 − 4.08168I 2.22183 + 6.73318I
u = 1.064480 + 0.283281I
a = 0.376709 + 0.499540I
b = 0.1247450 − 0.0513806I
2.28814 + 0.50538I 2.42708 − 2.42335I
u = 1.064480 − 0.283281I
a = 0.376709 − 0.499540I
b = 0.1247450 + 0.0513806I
2.28814 − 0.50538I 2.42708 + 2.42335I
u = −1.173860 + 0.089375I
a = −0.383376 + 0.706097I
b = −0.336359 − 1.256870I
2.31398 − 4.08168I 0. + 6.73318I
u = −1.173860 − 0.089375I
a = −0.383376 − 0.706097I
b = −0.336359 + 1.256870I
2.31398 + 4.08168I 0. − 6.73318I
u = 0.776371 + 0.247739I
a = 0.815173 − 0.579218I
b = −0.614397
0.430797 5.42999 + 0.I
u = 0.776371 − 0.247739I
a = 0.815173 + 0.579218I
b = −0.614397
0.430797 5.42999 + 0.I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.238460 + 0.091746I
a = −0.24657 + 1.71220I
b = −0.030026 − 1.195930I
5.57978 + 0.76639I 0
u = 1.238460 − 0.091746I
a = −0.24657 − 1.71220I
b = −0.030026 + 1.195930I
5.57978 − 0.76639I 0
u = 1.24296
a = −1.09764
b = −1.76258
2.63016 −3.15490
u = −1.145500 + 0.484216I
a = 0.315197 − 0.415169I
b = 0.680724 − 0.185869I
1.17342 − 7.19207I 0
u = −1.145500 − 0.484216I
a = 0.315197 + 0.415169I
b = 0.680724 + 0.185869I
1.17342 + 7.19207I 0
u = −0.670966 + 0.279530I
a = −0.565660 + 0.309098I
b = −0.773490 − 0.664465I
−1.04925 − 2.68015I −5.53151 + 8.74674I
u = −0.670966 − 0.279530I
a = −0.565660 − 0.309098I
b = −0.773490 + 0.664465I
−1.04925 + 2.68015I −5.53151 − 8.74674I
u = 1.280920 + 0.236843I
a = −1.127380 + 0.336604I
b = −0.866120 + 0.477522I
5.60462 + 2.74876I 0
u = 1.280920 − 0.236843I
a = −1.127380 − 0.336604I
b = −0.866120 − 0.477522I
5.60462 − 2.74876I 0
u = 0.259489 + 0.638464I
a = 0.96234 − 1.27613I
b = 0.1247450 − 0.0513806I
2.28814 + 0.50538I 2.42708 − 2.42335I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.259489 − 0.638464I
a = 0.96234 + 1.27613I
b = 0.1247450 + 0.0513806I
2.28814 − 0.50538I 2.42708 + 2.42335I
u = 0.567756 + 0.331092I
a = 2.53793 − 1.74586I
b = 0.166726 − 1.050750I
4.26736 + 0.63431I 12.1339 + 9.7135I
u = 0.567756 − 0.331092I
a = 2.53793 + 1.74586I
b = 0.166726 + 1.050750I
4.26736 − 0.63431I 12.1339 − 9.7135I
u = −0.160026 + 0.628199I
a = 1.16003 + 1.52796I
b = 0.680724 − 0.185869I
1.17342 − 7.19207I 0.11287 + 4.65345I
u = −0.160026 − 0.628199I
a = 1.16003 − 1.52796I
b = 0.680724 + 0.185869I
1.17342 + 7.19207I 0.11287 − 4.65345I
u = −1.36432
a = −0.911050
b = −1.76258
2.63016 0
u = −1.371770 + 0.220283I
a = −1.232130 + 0.224114I
b = −0.37076 − 1.49197I
11.82420 − 7.32230I 0
u = −1.371770 − 0.220283I
a = −1.232130 − 0.224114I
b = −0.37076 + 1.49197I
11.82420 + 7.32230I 0
u = 1.332520 + 0.426923I
a = −1.082420 + 0.112700I
b = −0.59674 + 1.64916I
8.39486 + 8.30805I 0
u = 1.332520 − 0.426923I
a = −1.082420 − 0.112700I
b = −0.59674 − 1.64916I
8.39486 − 8.30805I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.400330 + 0.060212I
a = 0.105658 − 0.724076I
b = −0.254804 + 1.313870I
4.62049 + 3.14366I 0
u = 1.400330 − 0.060212I
a = 0.105658 + 0.724076I
b = −0.254804 − 1.313870I
4.62049 − 3.14366I 0
u = −1.374310 + 0.307061I
a = 0.588248 − 0.864299I
b = 0.301099 + 1.258580I
4.62741 − 10.78550I 0
u = −1.374310 − 0.307061I
a = 0.588248 + 0.864299I
b = 0.301099 − 1.258580I
4.62741 + 10.78550I 0
u = −1.39386 + 0.25453I
a = −0.086561 + 0.330904I
b = 0.04157 − 1.44995I
7.17653 − 4.66079I 0
u = −1.39386 − 0.25453I
a = −0.086561 − 0.330904I
b = 0.04157 + 1.44995I
7.17653 + 4.66079I 0
u = −0.54304 + 1.36844I
a = 0.538172 + 0.790723I
b = 0.301099 + 1.258580I
4.62741 − 10.78550I 0
u = −0.54304 − 1.36844I
a = 0.538172 − 0.790723I
b = 0.301099 − 1.258580I
4.62741 + 10.78550I 0
u = 0.036428 + 0.483267I
a = −0.73990 + 2.82847I
b = 0.04157 + 1.44995I
7.17653 + 4.66079I 8.04120 − 5.42805I
u = 0.036428 − 0.483267I
a = −0.73990 − 2.82847I
b = 0.04157 − 1.44995I
7.17653 − 4.66079I 8.04120 + 5.42805I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.49047 + 0.31194I
a = −0.913945 + 0.095159I
b = −0.59674 − 1.64916I
8.39486 − 8.30805I 0
u = −1.49047 − 0.31194I
a = −0.913945 − 0.095159I
b = −0.59674 + 1.64916I
8.39486 + 8.30805I 0
u = 0.293137 + 0.365513I
a = −1.36135 + 0.74389I
b = −0.773490 + 0.664465I
−1.04925 + 2.68015I −5.53151 − 8.74674I
u = 0.293137 − 0.365513I
a = −1.36135 − 0.74389I
b = −0.773490 − 0.664465I
−1.04925 − 2.68015I −5.53151 + 8.74674I
u = −1.52380 + 0.16415I
a = −0.814414 − 0.243162I
b = −0.866120 + 0.477522I
5.60462 + 2.74876I 0
u = −1.52380 − 0.16415I
a = −0.814414 + 0.243162I
b = −0.866120 − 0.477522I
5.60462 − 2.74876I 0
u = −0.367419 + 0.090723I
a = 0.885070 + 0.465459I
b = −0.796175
−1.55865 −7.50405 + 0.I
u = −0.367419 − 0.090723I
a = 0.885070 − 0.465459I
b = −0.796175
−1.55865 −7.50405 + 0.I
u = 1.64083 + 0.57885I
a = −0.785614 + 0.142897I
b = −0.37076 + 1.49197I
11.82420 + 7.32230I 0
u = 1.64083 − 0.57885I
a = −0.785614 − 0.142897I
b = −0.37076 − 1.49197I
11.82420 − 7.32230I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 2.01897 + 0.15093I
a = 0.267457 − 0.183985I
b = 0.166726 + 1.050750I
4.26736 − 0.63431I 0
u = 2.01897 − 0.15093I
a = 0.267457 + 0.183985I
b = 0.166726 − 1.050750I
4.26736 + 0.63431I 0
u = −0.46246 + 2.09787I
a = −0.082399 − 0.572177I
b = −0.030026 − 1.195930I
5.57978 + 0.76639I 0
u = −0.46246 − 2.09787I
a = −0.082399 + 0.572177I
b = −0.030026 + 1.195930I
5.57978 − 0.76639I 0
16
III. I
u
3
= h2u
7
− 3u
6
+ · · · + b + 4, a + 1, u
8
− u
7
+ · · · + 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
−u
2
a
9
=
u
−u
3
+ u
a
11
=
−1
−2u
7
+ 3u
6
+ 5u
5
− 6u
4
− 10u
3
+ 12u
2
+ u − 4
a
1
=
2u
7
− 3u
6
− 5u
5
+ 6u
4
+ 10u
3
− 12u
2
− u + 3
−2u
7
+ 3u
6
+ 5u
5
− 6u
4
− 10u
3
+ 12u
2
+ u − 4
a
3
=
u
7
− u
6
− 2u
5
+ 2u
4
+ 3u
3
− 5u
2
+ u + 2
−3u
7
+ 4u
6
+ 7u
5
− 8u
4
− 13u
3
+ 17u
2
− 5
a
6
=
−u
u
7
− 2u
6
− 2u
5
+ 5u
4
+ 5u
3
− 10u
2
+ 4
a
2
=
0
−3u
7
+ 5u
6
+ 6u
5
− 11u
4
− 12u
3
+ 22u
2
− 2u − 7
a
7
=
−u
u
7
− u
6
− 2u
5
+ 2u
4
+ 4u
3
− 5u
2
+ u + 2
a
10
=
u
2
− 1
−2u
7
+ 2u
6
+ 5u
5
− 4u
4
− 9u
3
+ 8u
2
+ u − 3
a
10
=
u
2
− 1
−2u
7
+ 2u
6
+ 5u
5
− 4u
4
− 9u
3
+ 8u
2
+ u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 16u
7
− 28u
6
− 34u
5
+ 61u
4
+ 69u
3
− 119u
2
+ 4u + 48
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
8
+ u
7
+ 2u
5
+ 3u
4
+ 2u
3
+ 5u
2
+ 6u + 3
c
2
, c
6
u
8
+ u
7
+ u
6
+ 3u
5
+ 4u
4
+ 3u
3
+ 4u
2
+ u + 1
c
3
u
8
+ 2u
7
+ 6u
6
+ 6u
5
+ 8u
4
+ 3u
3
+ 3u
2
− u + 1
c
4
, c
7
u
8
− u
7
− 3u
6
+ 2u
5
+ 6u
4
− 4u
3
− 3u
2
+ 2u + 1
c
8
, c
10
u
8
+ u
7
− 3u
6
− 2u
5
+ 6u
4
+ 4u
3
− 3u
2
− 2u + 1
c
9
u
8
− 5u
7
+ 11u
6
− 11u
5
+ 4u
4
+ 2u
3
+ 1
c
11
u
8
− 2u
7
+ 6u
6
− 6u
5
+ 8u
4
− 3u
3
+ 3u
2
+ u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
8
− y
7
+ 2y
6
+ 2y
5
− 5y
4
+ 2y
3
+ 19y
2
− 6y + 9
c
2
, c
6
y
8
+ y
7
+ 3y
6
+ y
5
+ 6y
4
+ 19y
3
+ 18y
2
+ 7y + 1
c
3
, c
11
y
8
+ 8y
7
+ 28y
6
+ 54y
5
+ 70y
4
+ 63y
3
+ 31y
2
+ 5y + 1
c
4
, c
7
, c
8
c
10
y
8
− 7y
7
+ 25y
6
− 54y
5
+ 76y
4
− 66y
3
+ 37y
2
− 10y + 1
c
9
y
8
− 3y
7
+ 19y
6
− 13y
5
+ 62y
4
+ 18y
3
+ 8y
2
+ 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.830521 + 0.472642I
a = −1.00000
b = 0.278585 − 0.369009I
2.51723 + 7.95538I 6.62650 − 7.10591I
u = 0.830521 − 0.472642I
a = −1.00000
b = 0.278585 + 0.369009I
2.51723 − 7.95538I 6.62650 + 7.10591I
u = −1.22650 + 0.71722I
a = −1.00000
b = −0.111561 − 1.113420I
4.68125 − 1.07313I 14.8263 − 3.4130I
u = −1.22650 − 0.71722I
a = −1.00000
b = −0.111561 + 1.113420I
4.68125 + 1.07313I 14.8263 + 3.4130I
u = 1.39864 + 0.40204I
a = −1.00000
b = −0.43221 + 1.63582I
9.60260 + 7.88243I 8.54857 − 6.07539I
u = 1.39864 − 0.40204I
a = −1.00000
b = −0.43221 − 1.63582I
9.60260 − 7.88243I 8.54857 + 6.07539I
u = −0.502656 + 0.059050I
a = −1.00000
b = −0.734811 − 0.874667I
−0.35174 − 2.79718I 11.9986 + 8.3500I
u = −0.502656 − 0.059050I
a = −1.00000
b = −0.734811 + 0.874667I
−0.35174 + 2.79718I 11.9986 − 8.3500I
20
IV. I
u
4
= hu
2
+ b, a + 1, u
3
− u − 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
−u
2
a
9
=
u
−1
a
11
=
−1
−u
2
a
1
=
u
2
− 1
−u
2
a
3
=
u + 1
−u
2
− u
a
6
=
−u
u
a
2
=
0
−u
a
7
=
−u
−1
a
10
=
u
2
− 1
−u
2
+ u
a
10
=
u
2
− 1
−u
2
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)
3
c
2
, c
6
, c
11
u
3
− 2u
2
+ u − 1
c
3
u
3
+ 2u
2
+ u + 1
c
4
, c
7
u
3
− u − 1
c
8
, c
10
u
3
− u + 1
c
9
u
3
− 2u
2
+ 3u − 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y −1)
3
c
2
, c
3
, c
6
c
11
y
3
− 2y
2
− 3y −1
c
4
, c
7
, c
8
c
10
y
3
− 2y
2
+ y −1
c
9
y
3
+ 2y
2
+ 5y −1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.662359 + 0.562280I
a = −1.00000
b = −0.122561 + 0.744862I
3.28987 12.0000
u = −0.662359 − 0.562280I
a = −1.00000
b = −0.122561 − 0.744862I
3.28987 12.0000
u = 1.32472
a = −1.00000
b = −1.75488
3.28987 12.0000
24
V. I
u
5
= hb + 1, a − 2, 2u − 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
0.5
a
5
=
1
−0.25
a
9
=
0.5
0.375
a
11
=
2
−1
a
1
=
3
−1
a
3
=
4
−1
a
6
=
1
−0.25
a
2
=
3
−1.75
a
7
=
−2
1.5
a
10
=
0
0.5
a
10
=
0
0.5
(ii) Obstruction class = 1
(iii) Cusp Shapes = −14.0625
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
2(2u − 3)
c
2
u − 2
c
3
, c
6
, c
7
u + 1
c
4
2(2u − 1)
c
5
u
c
8
, c
9
2(2u + 1)
c
10
, c
11
u − 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
4(4y −9)
c
2
y −4
c
3
, c
6
, c
7
c
10
, c
11
y −1
c
4
, c
8
, c
9
4(4y −1)
c
5
y
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000
a = 2.00000
b = −1.00000
0 −14.0620
28
VI. I
u
6
= hb + 1, 2a − 1, u + 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
−1
a
5
=
1
−1
a
9
=
−1
0
a
11
=
0.5
−1
a
1
=
1.5
−1
a
3
=
2.5
−1
a
6
=
−2.75
0.5
a
2
=
1.5
−1
a
7
=
0.25
−1.5
a
10
=
0.375
−0.25
a
10
=
0.375
−0.25
(ii) Obstruction class = 1
(iii) Cusp Shapes = −14.0625
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
c
2
, c
3
, c
4
u + 1
c
5
2(2u − 3)
c
6
u − 2
c
7
2(2u − 1)
c
8
, c
11
u − 1
c
9
, c
10
2(2u + 1)
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
c
2
, c
3
, c
4
c
8
, c
11
y −1
c
5
4(4y −9)
c
6
y −4
c
7
, c
9
, c
10
4(4y −1)
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.500000
b = −1.00000
0 −14.0620
32
VII. I
u
7
= hb + 1, a + 1, u + 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
−1
a
5
=
1
−1
a
9
=
−1
0
a
11
=
−1
−1
a
1
=
0
−1
a
3
=
1
−1
a
6
=
1
−1
a
2
=
0
−1
a
7
=
1
0
a
10
=
0
−1
a
10
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
c
2
, c
3
, c
4
c
6
, c
7
u + 1
c
8
, c
9
, c
10
c
11
u − 1
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
c
2
, c
3
, c
4
c
6
, c
7
, c
8
c
9
, c
10
, c
11
y −1
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = −1.00000
0 0
36
VIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
4u
2
(u − 1)
3
(2u − 3)(u
8
+ u
7
+ 2u
5
+ 3u
4
+ 2u
3
+ 5u
2
+ 6u + 3)
· (u
27
+ 2u
26
+ ··· + 8u + 2)(2u
54
+ 15u
53
+ ··· + 95u + 8)
c
2
, c
6
(u − 2)(u + 1)
2
(u
3
− 2u
2
+ u − 1)
· (u
8
+ u
7
+ ··· + u + 1)(u
27
+ 7u
25
+ ··· − 3u + 1)
· (u
54
+ 2u
53
+ ··· + 59u − 58)
c
3
(u + 1)
3
(u
3
+ 2u
2
+ u + 1)
· (u
8
+ 2u
7
+ 6u
6
+ 6u
5
+ 8u
4
+ 3u
3
+ 3u
2
− u + 1)
· (u
27
− 10u
26
+ ··· + 172u − 16)(u
27
+ 7u
26
+ ··· − 9u + 1)
2
c
4
, c
7
4(u + 1)
2
(2u − 1)(u
3
− u − 1)
· (u
8
− u
7
− 3u
6
+ 2u
5
+ 6u
4
− 4u
3
− 3u
2
+ 2u + 1)
· (u
27
− 15u
25
+ ··· + 8u + 1)(2u
54
− 3u
53
+ ··· + 95u − 97)
c
8
, c
10
4(u − 1)
2
(2u + 1)(u
3
− u + 1)
· (u
8
+ u
7
− 3u
6
− 2u
5
+ 6u
4
+ 4u
3
− 3u
2
− 2u + 1)
· (u
27
− 15u
25
+ ··· + 8u + 1)(2u
54
− 3u
53
+ ··· + 95u − 97)
c
9
16(u − 1)(2u + 1)
2
(u
3
− 2u
2
+ 3u − 1)
· (u
8
− 5u
7
+ ··· + 2u
3
+ 1)(u
27
+ 13u
26
+ ··· − 28u − 4)
· (2u
27
− 15u
26
+ ··· + 13u
2
− 1)
2
c
11
(u − 1)
3
(u
3
− 2u
2
+ u − 1)
· (u
8
− 2u
7
+ 6u
6
− 6u
5
+ 8u
4
− 3u
3
+ 3u
2
+ u + 1)
· (u
27
− 10u
26
+ ··· + 172u − 16)(u
27
+ 7u
26
+ ··· − 9u + 1)
2
37
IX. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
16y
2
(y −1)
3
(4y −9)(y
8
− y
7
+ ··· − 6y + 9)
· (y
27
− 4y
26
+ ··· + 84y −4)(4y
54
− 45y
53
+ ··· − 3041y + 64)
c
2
, c
6
(y −4)(y −1)
2
(y
3
− 2y
2
− 3y −1)
· (y
8
+ y
7
+ 3y
6
+ y
5
+ 6y
4
+ 19y
3
+ 18y
2
+ 7y + 1)
· (y
27
+ 14y
26
+ ··· − 15y −1)(y
54
− 2y
53
+ ··· + 49299y + 3364)
c
3
, c
11
(y −1)
3
(y
3
− 2y
2
− 3y −1)
· (y
8
+ 8y
7
+ 28y
6
+ 54y
5
+ 70y
4
+ 63y
3
+ 31y
2
+ 5y + 1)
· (y
27
+ 16y
26
+ ··· + 6320y −256)(y
27
+ 21y
26
+ ··· + 79y −1)
2
c
4
, c
7
, c
8
c
10
16(y −1)
2
(4y −1)(y
3
− 2y
2
+ y −1)
· (y
8
− 7y
7
+ 25y
6
− 54y
5
+ 76y
4
− 66y
3
+ 37y
2
− 10y + 1)
· (y
27
− 30y
26
+ ··· + 34y −1)(4y
54
− 169y
53
+ ··· − 117277y + 9409)
c
9
256(y −1)(4y −1)
2
(y
3
+ 2y
2
+ 5y −1)
· (y
8
− 3y
7
+ 19y
6
− 13y
5
+ 62y
4
+ 18y
3
+ 8y
2
+ 1)
· (y
27
− 3y
26
+ ··· + 56y −16)(4y
27
− 9y
26
+ ··· + 26y −1)
2
38
