12a
1250
(K12a
1250
)
A knot diagram
1
Linearized knot diagam
5 7 8 10 2 11 12 4 1 6 3 9
Solving Sequence
7,12 3,8
4 9 2 11 6 5 1 10
c
7
c
3
c
8
c
2
c
11
c
6
c
5
c
1
c
10
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, 7.70010 × 10
31
u
26
− 5.62456 × 10
31
u
25
+ ··· + 2.15871 × 10
31
a + 1.22744 × 10
32
, u
27
− u
26
+ ··· − u − 1i
I
u
2
= h4.84865 × 10
726
u
109
− 7.94449 × 10
726
u
108
+ ··· + 4.71721 × 10
727
b + 2.09824 × 10
728
,
1.16970 × 10
728
u
109
− 2.33622 × 10
728
u
108
+ ··· + 4.71721 × 10
727
a − 5.42261 × 10
729
,
u
110
− 2u
109
+ ··· − 61u + 1i
I
u
3
= hb + u, u
8
+ 56u
7
− 94u
6
+ 123u
5
+ 22u
4
− 254u
3
+ 48u
2
+ 137a + 269u − 286,
u
9
− u
8
+ 2u
7
+ u
6
− 2u
5
− u
4
+ 4u
3
− u
2
− u − 1i
I
u
4
= h−1.58027 × 10
18
u
19
− 6.87073 × 10
17
u
18
+ ··· + 3.87707 × 10
18
b + 3.02858 × 10
18
,
7.97216 × 10
18
u
19
+ 6.43988 × 10
18
u
18
+ ··· + 3.87707 × 10
18
a − 3.92152 × 10
19
, u
20
+ u
19
+ ··· − 7u − 1i
* 4 irreducible components of dim
C
= 0, with total 166 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, 7.70 × 10
31
u
26
− 5.62 × 10
31
u
25
+ · · · + 2.16 × 10
31
a + 1.23 ×
10
32
, u
27
− u
26
+ · · · − u − 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
−3.56698u
26
+ 2.60552u
25
+ ··· − 4.88748u − 5.68596
u
a
8
=
1
u
2
a
4
=
−2.88044u
26
+ 2.25984u
25
+ ··· + 0.640970u − 4.72449
0.177619u
26
− 0.100159u
25
+ ··· + 2.02741u + 0.340863
a
9
=
1.57118u
26
− 0.212597u
25
+ ··· + 20.1688u + 5.62807
−0.688725u
26
+ 0.271933u
25
+ ··· − 3.68073u − 1.38945
a
2
=
−3.56698u
26
+ 2.60552u
25
+ ··· − 3.88748u − 5.68596
u
a
11
=
−3.80911u
26
+ 1.86959u
25
+ ··· − 11.4495u − 13.7172
0.686544u
26
− 0.345680u
25
+ ··· + 5.52845u + 0.961469
a
6
=
−4.77289u
26
+ 1.75400u
25
+ ··· − 33.9661u − 4.39005
1.32981u
26
− 0.626906u
25
+ ··· + 6.61049u + 2.74803
a
5
=
−2.08988u
26
+ 1.15394u
25
+ ··· − 6.43107u − 1.87197
0.688725u
26
− 0.271933u
25
+ ··· + 3.68073u + 1.38945
a
1
=
−3.89150u
26
+ 2.46159u
25
+ ··· − 7.29656u − 6.52772
1.20561u
26
− 0.456383u
25
+ ··· + 7.89661u + 2.30690
a
10
=
1.36591u
26
− 0.755536u
25
+ ··· + 1.30324u − 3.58531
−1.35273u
26
+ 0.596087u
25
+ ··· − 6.04003u − 2.77861
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.380648u
26
− 0.165770u
25
+ ··· + 7.21208u − 2.80163
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
9
c
12
u
27
+ u
26
+ ··· + 7u − 1
c
2
, c
7
u
27
− u
26
+ ··· − u − 1
c
3
, c
6
, c
8
c
10
u
27
− u
26
+ ··· + 2u + 1
c
4
u
27
− 21u
26
+ ··· − 776u + 8
c
11
u
27
− 13u
26
+ ··· − 444u + 72
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
9
c
12
y
27
− 25y
26
+ ··· + 45y − 1
c
2
, c
7
y
27
− 15y
26
+ ··· + 5y − 1
c
3
, c
6
, c
8
c
10
y
27
− 21y
26
+ ··· + 6y − 1
c
4
y
27
− 7y
26
+ ··· + 456672y − 64
c
11
y
27
− 7y
26
+ ··· + 41040y − 5184
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.781819 + 0.631176I
a = 0.929861 + 0.399699I
b = 0.781819 + 0.631176I
−3.28970 − 2.28835I −2.71013 + 3.35068I
u = 0.781819 − 0.631176I
a = 0.929861 − 0.399699I
b = 0.781819 − 0.631176I
−3.28970 + 2.28835I −2.71013 − 3.35068I
u = −0.892407
a = 0.974906
b = −0.892407
10.2498 43.3390
u = 1.16370
a = −0.405849
b = 1.16370
−0.711699 −7.17600
u = −1.149710 + 0.219773I
a = −0.803273 − 0.736758I
b = −1.149710 + 0.219773I
−8.27330 − 1.09335I −7.94541 − 0.68772I
u = −1.149710 − 0.219773I
a = −0.803273 + 0.736758I
b = −1.149710 − 0.219773I
−8.27330 + 1.09335I −7.94541 + 0.68772I
u = 1.091930 + 0.455489I
a = 0.278245 − 0.905101I
b = 1.091930 + 0.455489I
−9.40709 − 6.96260I −7.55252 + 5.81824I
u = 1.091930 − 0.455489I
a = 0.278245 + 0.905101I
b = 1.091930 − 0.455489I
−9.40709 + 6.96260I −7.55252 − 5.81824I
u = 0.710875 + 1.032870I
a = 0.012712 − 1.150810I
b = 0.710875 + 1.032870I
3.58219 − 4.38995I 4.84018 + 4.14000I
u = 0.710875 − 1.032870I
a = 0.012712 + 1.150810I
b = 0.710875 − 1.032870I
3.58219 + 4.38995I 4.84018 − 4.14000I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.644156 + 0.368503I
a = −1.11178 + 1.61261I
b = −0.644156 + 0.368503I
−3.67889 + 11.52960I −3.14313 − 8.69788I
u = −0.644156 − 0.368503I
a = −1.11178 − 1.61261I
b = −0.644156 − 0.368503I
−3.67889 − 11.52960I −3.14313 + 8.69788I
u = 0.603990
a = −2.03134
b = 0.603990
3.10146 2.60470
u = −0.285348 + 0.511101I
a = 0.308003 − 1.070990I
b = −0.285348 + 0.511101I
0.056105 + 1.042570I 1.04906 − 6.21655I
u = −0.285348 − 0.511101I
a = 0.308003 + 1.070990I
b = −0.285348 − 0.511101I
0.056105 − 1.042570I 1.04906 + 6.21655I
u = 0.515570 + 0.073824I
a = −1.12863 + 1.53832I
b = 0.515570 + 0.073824I
2.12465 − 0.60492I 3.40248 − 0.28266I
u = 0.515570 − 0.073824I
a = −1.12863 − 1.53832I
b = 0.515570 − 0.073824I
2.12465 + 0.60492I 3.40248 + 0.28266I
u = −1.13528 + 0.95643I
a = −0.461555 − 1.048120I
b = −1.13528 + 0.95643I
8.36830 + 7.25793I 6.59980 − 4.89800I
u = −1.13528 − 0.95643I
a = −0.461555 + 1.048120I
b = −1.13528 − 0.95643I
8.36830 − 7.25793I 6.59980 + 4.89800I
u = −0.167835 + 0.252267I
a = −2.61305 + 4.57834I
b = −0.167835 + 0.252267I
−0.84726 − 3.06637I −5.24785 − 2.81435I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.167835 − 0.252267I
a = −2.61305 − 4.57834I
b = −0.167835 − 0.252267I
−0.84726 + 3.06637I −5.24785 + 2.81435I
u = 1.30742 + 1.18234I
a = 0.274985 − 0.859641I
b = 1.30742 + 1.18234I
−0.0304 − 19.1903I 0. + 9.60894I
u = 1.30742 − 1.18234I
a = 0.274985 + 0.859641I
b = 1.30742 − 1.18234I
−0.0304 + 19.1903I 0. − 9.60894I
u = −1.11928 + 1.55419I
a = −0.061254 − 0.676810I
b = −1.11928 + 1.55419I
−1.31722 + 8.02915I −2.07270 − 6.52162I
u = −1.11928 − 1.55419I
a = −0.061254 + 0.676810I
b = −1.11928 − 1.55419I
−1.31722 − 8.02915I −2.07270 + 6.52162I
u = −1.95578
a = −0.414695
b = −1.95578
−8.01906 −12.6810
u = 2.26848
a = 0.628451
b = 2.26848
−5.51420 0
7
II. I
u
2
= h4.85 × 10
726
u
109
− 7.94 × 10
726
u
108
+ · · · + 4.72 × 10
727
b + 2.10 ×
10
728
, 1.17 × 10
728
u
109
− 2.34 × 10
728
u
108
+ · · · + 4.72 × 10
727
a − 5.42 ×
10
729
, u
110
− 2u
109
+ · · · − 61u + 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
−2.47964u
109
+ 4.95256u
108
+ ··· − 3207.39u + 114.954
−0.102786u
109
+ 0.168415u
108
+ ··· + 104.323u − 4.44806
a
8
=
1
u
2
a
4
=
−2.57837u
109
+ 5.11495u
108
+ ··· − 3105.13u + 110.499
−0.109476u
109
+ 0.179933u
108
+ ··· + 102.283u − 4.41300
a
9
=
−9.61748u
109
+ 18.8705u
108
+ ··· − 8470.02u + 238.697
1.30572u
109
− 2.51884u
108
+ ··· + 785.576u − 17.1918
a
2
=
−2.58243u
109
+ 5.12097u
108
+ ··· − 3103.06u + 110.506
−0.102786u
109
+ 0.168415u
108
+ ··· + 104.323u − 4.44806
a
11
=
6.11025u
109
− 12.0451u
108
+ ··· + 6254.55u − 195.782
−0.430403u
109
+ 0.856393u
108
+ ··· − 406.059u + 10.7574
a
6
=
13.7340u
109
− 26.8864u
108
+ ··· + 12163.2u − 371.524
−0.153525u
109
+ 0.289259u
108
+ ··· − 155.930u + 7.46005
a
5
=
21.7236u
109
− 42.5002u
108
+ ··· + 18797.6u − 552.054
−1.19225u
109
+ 2.28448u
108
+ ··· − 714.350u + 19.3249
a
1
=
10.1698u
109
− 19.9510u
108
+ ··· + 9792.89u − 324.122
0.780072u
109
− 1.47552u
108
+ ··· + 241.270u + 0.659459
a
10
=
−18.6242u
109
+ 36.7385u
108
+ ··· − 17618.2u + 537.624
1.04694u
109
− 2.02223u
108
+ ··· + 826.486u − 22.9158
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.39827u
109
+ 2.80537u
108
+ ··· − 1473.20u + 34.2235
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
9
c
12
u
110
− 37u
108
+ ··· − 596u + 229
c
2
, c
7
u
110
− 2u
109
+ ··· − 61u + 1
c
3
, c
6
, c
8
c
10
u
110
+ u
109
+ ··· + 2947u + 199
c
4
(u
55
+ 10u
54
+ ··· + 8u − 1)
2
c
11
(u
55
+ 6u
54
+ ··· + 262u + 67)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
9
c
12
y
110
− 74y
109
+ ··· − 2941542y + 52441
c
2
, c
7
y
110
+ 8y
109
+ ··· − 995y + 1
c
3
, c
6
, c
8
c
10
y
110
− 71y
109
+ ··· − 1508869y + 39601
c
4
(y
55
+ 12y
54
+ ··· + 236y − 1)
2
c
11
(y
55
− 20y
54
+ ··· + 72932y − 4489)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.998893
a = −0.886698
b = −1.97821
−5.09057 0
u = −0.612762 + 0.750100I
a = 0.116640 − 1.014820I
b = 0.310391 + 0.813099I
0.43264 + 4.10654I 0
u = −0.612762 − 0.750100I
a = 0.116640 + 1.014820I
b = 0.310391 − 0.813099I
0.43264 − 4.10654I 0
u = −0.919737 + 0.556530I
a = −0.418031 − 1.172860I
b = −1.31673 + 1.11908I
−4.79048 + 12.57190I 0
u = −0.919737 − 0.556530I
a = −0.418031 + 1.172860I
b = −1.31673 − 1.11908I
−4.79048 − 12.57190I 0
u = 0.750183 + 0.770595I
a = −0.312632 + 0.823794I
b = −1.28027 − 1.36796I
−2.93335 − 2.67192I 0
u = 0.750183 − 0.770595I
a = −0.312632 − 0.823794I
b = −1.28027 + 1.36796I
−2.93335 + 2.67192I 0
u = 0.865133 + 0.669573I
a = 0.33802 − 1.57490I
b = 0.659251 + 0.966888I
2.74486 − 4.81034I 0
u = 0.865133 − 0.669573I
a = 0.33802 + 1.57490I
b = 0.659251 − 0.966888I
2.74486 + 4.81034I 0
u = 1.095580 + 0.042016I
a = 0.726760 + 1.014680I
b = 0.299331 + 0.204670I
−5.73179 − 5.61364I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.095580 − 0.042016I
a = 0.726760 − 1.014680I
b = 0.299331 − 0.204670I
−5.73179 + 5.61364I 0
u = 0.403309 + 0.807250I
a = −0.18776 − 1.50293I
b = 0.768789 + 0.929711I
3.55445 − 4.03607I 0
u = 0.403309 − 0.807250I
a = −0.18776 + 1.50293I
b = 0.768789 − 0.929711I
3.55445 + 4.03607I 0
u = 0.800426 + 0.358042I
a = −0.778741 + 1.108750I
b = 0.116547 − 0.222950I
2.22016 − 0.68767I 0
u = 0.800426 − 0.358042I
a = −0.778741 − 1.108750I
b = 0.116547 + 0.222950I
2.22016 + 0.68767I 0
u = 0.310391 + 0.813099I
a = 1.044060 − 0.449729I
b = −0.612762 + 0.750100I
0.43264 + 4.10654I 0
u = 0.310391 − 0.813099I
a = 1.044060 + 0.449729I
b = −0.612762 − 0.750100I
0.43264 − 4.10654I 0
u = 0.778176 + 0.373657I
a = −0.222898 + 0.908749I
b = −0.734460 − 0.894698I
−3.57918 − 3.06316I 0
u = 0.778176 − 0.373657I
a = −0.222898 − 0.908749I
b = −0.734460 + 0.894698I
−3.57918 + 3.06316I 0
u = 0.476407 + 1.045930I
a = 0.272044 − 0.568787I
b = −1.14858 + 1.39599I
5.29292 − 4.11535I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.476407 − 1.045930I
a = 0.272044 + 0.568787I
b = −1.14858 − 1.39599I
5.29292 + 4.11535I 0
u = 0.685571 + 0.923676I
a = −0.012161 + 1.122410I
b = −1.09417 − 1.14531I
0.28959 − 9.04527I 0
u = 0.685571 − 0.923676I
a = −0.012161 − 1.122410I
b = −1.09417 + 1.14531I
0.28959 + 9.04527I 0
u = −1.128550 + 0.253990I
a = 0.425568 + 0.390150I
b = 0.720258 − 0.243099I
−2.84990 + 0.29345I 0
u = −1.128550 − 0.253990I
a = 0.425568 − 0.390150I
b = 0.720258 + 0.243099I
−2.84990 − 0.29345I 0
u = −0.734460 + 0.894698I
a = −0.135378 + 0.684525I
b = 0.778176 − 0.373657I
−3.57918 + 3.06316I 0
u = −0.734460 − 0.894698I
a = −0.135378 − 0.684525I
b = 0.778176 + 0.373657I
−3.57918 − 3.06316I 0
u = 0.659251 + 0.966888I
a = −0.15376 − 1.49791I
b = 0.865133 + 0.669573I
2.74486 − 4.81034I 0
u = 0.659251 − 0.966888I
a = −0.15376 + 1.49791I
b = 0.865133 − 0.669573I
2.74486 + 4.81034I 0
u = −0.736806 + 0.367349I
a = 0.35529 + 1.54642I
b = 0.88136 − 1.24598I
0.51004 + 5.45734I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.736806 − 0.367349I
a = 0.35529 − 1.54642I
b = 0.88136 + 1.24598I
0.51004 − 5.45734I 0
u = −1.19982
a = 0.983271
b = 0.755437
−2.52587 0
u = 1.031690 + 0.617279I
a = −1.00449 + 1.18519I
b = −1.185780 − 0.516929I
2.64974 − 1.27843I 0
u = 1.031690 − 0.617279I
a = −1.00449 − 1.18519I
b = −1.185780 + 0.516929I
2.64974 + 1.27843I 0
u = 0.768789 + 0.929711I
a = 0.116846 − 1.126900I
b = 0.403309 + 0.807250I
3.55445 − 4.03607I 0
u = 0.768789 − 0.929711I
a = 0.116846 + 1.126900I
b = 0.403309 − 0.807250I
3.55445 + 4.03607I 0
u = −0.235929 + 0.757530I
a = 0.242037 − 1.144280I
b = −0.71885 + 1.37533I
1.135820 − 0.205465I 0
u = −0.235929 − 0.757530I
a = 0.242037 + 1.144280I
b = −0.71885 − 1.37533I
1.135820 + 0.205465I 0
u = −0.399940 + 1.157640I
a = −0.189094 − 0.717679I
b = 0.91748 + 1.35195I
6.13336 + 4.50289I 0
u = −0.399940 − 1.157640I
a = −0.189094 + 0.717679I
b = 0.91748 − 1.35195I
6.13336 − 4.50289I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.598936 + 0.485246I
a = −1.10106 + 0.89206I
b = 0.598936 − 0.485246I
3.02407 0
u = 0.598936 − 0.485246I
a = −1.10106 − 0.89206I
b = 0.598936 + 0.485246I
3.02407 0
u = 0.720258 + 0.243099I
a = −0.582371 + 0.657801I
b = −1.128550 − 0.253990I
−2.84990 − 0.29345I 0
u = 0.720258 − 0.243099I
a = −0.582371 − 0.657801I
b = −1.128550 + 0.253990I
−2.84990 + 0.29345I 0
u = 0.755437
a = −1.56167
b = −1.19982
−2.52587 −18.3860
u = 0.958529 + 0.798223I
a = 0.367727 − 0.784409I
b = 1.72624 + 1.25070I
−3.70148 − 2.64555I 0
u = 0.958529 − 0.798223I
a = 0.367727 + 0.784409I
b = 1.72624 − 1.25070I
−3.70148 + 2.64555I 0
u = −0.777794 + 1.015010I
a = 0.395951 + 0.516708I
b = −0.777794 − 1.015010I
9.31937 0
u = −0.777794 − 1.015010I
a = 0.395951 − 0.516708I
b = −0.777794 + 1.015010I
9.31937 0
u = −0.651259 + 0.284105I
a = 0.56779 − 2.19424I
b = 0.311295 − 0.145457I
0.80420 + 4.80655I 0. − 9.09767I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.651259 − 0.284105I
a = 0.56779 + 2.19424I
b = 0.311295 + 0.145457I
0.80420 − 4.80655I 0. + 9.09767I
u = −1.185780 + 0.516929I
a = 1.06665 + 0.97326I
b = 1.031690 − 0.617279I
2.64974 + 1.27843I 0
u = −1.185780 − 0.516929I
a = 1.06665 − 0.97326I
b = 1.031690 + 0.617279I
2.64974 − 1.27843I 0
u = −0.186211 + 0.650498I
a = 1.139500 + 0.549929I
b = 0.050931 − 1.383410I
−1.67519 + 3.37319I 0. − 1.85055I
u = −0.186211 − 0.650498I
a = 1.139500 − 0.549929I
b = 0.050931 + 1.383410I
−1.67519 − 3.37319I 0. + 1.85055I
u = −0.334305 + 0.582293I
a = −0.068999 + 1.362830I
b = 1.34936 − 1.20783I
1.22183 + 3.59271I 4.52275 − 8.70901I
u = −0.334305 − 0.582293I
a = −0.068999 − 1.362830I
b = 1.34936 + 1.20783I
1.22183 − 3.59271I 4.52275 + 8.70901I
u = −1.35619
a = −1.03010
b = 0.0351718
3.28865 0
u = −0.621797 + 0.148820I
a = 1.26656 − 1.44413I
b = 0.233671 − 0.407335I
−1.08485 + 2.66555I −6.08010 − 4.56372I
u = −0.621797 − 0.148820I
a = 1.26656 + 1.44413I
b = 0.233671 + 0.407335I
−1.08485 − 2.66555I −6.08010 + 4.56372I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.050931 + 1.383410I
a = −0.476306 + 0.394428I
b = −0.186211 − 0.650498I
−1.67519 − 3.37319I 0
u = 0.050931 − 1.383410I
a = −0.476306 − 0.394428I
b = −0.186211 + 0.650498I
−1.67519 + 3.37319I 0
u = −1.369060 + 0.309100I
a = −0.079909 − 0.455040I
b = −0.457160 − 0.144522I
−5.63317 + 1.03399I 0
u = −1.369060 − 0.309100I
a = −0.079909 + 0.455040I
b = −0.457160 + 0.144522I
−5.63317 − 1.03399I 0
u = −0.457160 + 0.144522I
a = −0.873399 + 1.032580I
b = −1.369060 − 0.309100I
−5.63317 − 1.03399I −11.65387 + 4.39006I
u = −0.457160 − 0.144522I
a = −0.873399 − 1.032580I
b = −1.369060 + 0.309100I
−5.63317 + 1.03399I −11.65387 − 4.39006I
u = 0.88136 + 1.24598I
a = 0.225679 + 0.825663I
b = −0.736806 − 0.367349I
0.51004 − 5.45734I 0
u = 0.88136 − 1.24598I
a = 0.225679 − 0.825663I
b = −0.736806 + 0.367349I
0.51004 + 5.45734I 0
u = 0.233671 + 0.407335I
a = −2.61356 − 0.09350I
b = −0.621797 − 0.148820I
−1.08485 − 2.66555I −6.08010 + 4.56372I
u = 0.233671 − 0.407335I
a = −2.61356 + 0.09350I
b = −0.621797 + 0.148820I
−1.08485 + 2.66555I −6.08010 − 4.56372I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.71885 + 1.37533I
a = 0.017188 − 0.597731I
b = −0.235929 + 0.757530I
1.135820 − 0.205465I 0
u = −0.71885 − 1.37533I
a = 0.017188 + 0.597731I
b = −0.235929 − 0.757530I
1.135820 + 0.205465I 0
u = 0.40372 + 1.51303I
a = −0.118661 + 0.535099I
b = 0.89017 − 1.87925I
1.42772 − 9.18102I 0
u = 0.40372 − 1.51303I
a = −0.118661 − 0.535099I
b = 0.89017 + 1.87925I
1.42772 + 9.18102I 0
u = 1.19083 + 1.04289I
a = −0.325712 + 0.983158I
b = −1.11259 − 1.13543I
5.13513 − 12.91180I 0
u = 1.19083 − 1.04289I
a = −0.325712 − 0.983158I
b = −1.11259 + 1.13543I
5.13513 + 12.91180I 0
u = −1.09417 + 1.14531I
a = 0.109630 + 0.807747I
b = 0.685571 − 0.923676I
0.28959 + 9.04527I 0
u = −1.09417 − 1.14531I
a = 0.109630 − 0.807747I
b = 0.685571 + 0.923676I
0.28959 − 9.04527I 0
u = −1.11259 + 1.13543I
a = 0.248773 + 1.000870I
b = 1.19083 − 1.04289I
5.13513 + 12.91180I 0
u = −1.11259 − 1.13543I
a = 0.248773 − 1.000870I
b = 1.19083 + 1.04289I
5.13513 − 12.91180I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.91748 + 1.35195I
a = 0.346032 − 0.435642I
b = −0.399940 + 1.157640I
6.13336 + 4.50289I 0
u = 0.91748 − 1.35195I
a = 0.346032 + 0.435642I
b = −0.399940 − 1.157640I
6.13336 − 4.50289I 0
u = 0.299331 + 0.204670I
a = 3.49343 + 1.42719I
b = 1.095580 + 0.042016I
−5.73179 − 5.61364I −4.53556 + 5.12202I
u = 0.299331 − 0.204670I
a = 3.49343 − 1.42719I
b = 1.095580 − 0.042016I
−5.73179 + 5.61364I −4.53556 − 5.12202I
u = −0.85657 + 1.41626I
a = 0.013688 + 0.755530I
b = 0.57663 − 1.59776I
−0.05548 + 8.46629I 0
u = −0.85657 − 1.41626I
a = 0.013688 − 0.755530I
b = 0.57663 + 1.59776I
−0.05548 − 8.46629I 0
u = 0.311295 + 0.145457I
a = −1.29063 − 4.50569I
b = −0.651259 − 0.284105I
0.80420 − 4.80655I −1.31755 + 9.09767I
u = 0.311295 − 0.145457I
a = −1.29063 + 4.50569I
b = −0.651259 + 0.284105I
0.80420 + 4.80655I −1.31755 − 9.09767I
u = 0.57663 + 1.59776I
a = 0.131446 + 0.724481I
b = −0.85657 − 1.41626I
−0.05548 − 8.46629I 0
u = 0.57663 − 1.59776I
a = 0.131446 − 0.724481I
b = −0.85657 + 1.41626I
−0.05548 + 8.46629I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.31673 + 1.11908I
a = −0.140282 − 0.761785I
b = −0.919737 + 0.556530I
−4.79048 + 12.57190I 0
u = −1.31673 − 1.11908I
a = −0.140282 + 0.761785I
b = −0.919737 − 0.556530I
−4.79048 − 12.57190I 0
u = 0.116547 + 0.222950I
a = −4.02294 + 2.47338I
b = 0.800426 − 0.358042I
2.22016 + 0.68767I 3.24172 + 1.08060I
u = 0.116547 − 0.222950I
a = −4.02294 − 2.47338I
b = 0.800426 + 0.358042I
2.22016 − 0.68767I 3.24172 − 1.08060I
u = −1.14858 + 1.39599I
a = −0.248844 − 0.314256I
b = 0.476407 + 1.045930I
5.29292 − 4.11535I 0
u = −1.14858 − 1.39599I
a = −0.248844 + 0.314256I
b = 0.476407 − 1.045930I
5.29292 + 4.11535I 0
u = 1.34936 + 1.20783I
a = −0.134425 + 0.487742I
b = −0.334305 − 0.582293I
1.22183 − 3.59271I 0
u = 1.34936 − 1.20783I
a = −0.134425 − 0.487742I
b = −0.334305 + 0.582293I
1.22183 + 3.59271I 0
u = −1.28027 + 1.36796I
a = 0.170112 + 0.476297I
b = 0.750183 − 0.770595I
−2.93335 + 2.67192I 0
u = −1.28027 − 1.36796I
a = 0.170112 − 0.476297I
b = 0.750183 + 0.770595I
−2.93335 − 2.67192I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.0767307 + 0.0358246I
a = 1.43169 − 8.47092I
b = 1.32363 + 1.40196I
−1.41309 − 4.17051I −10.11255 + 0.98560I
u = 0.0767307 − 0.0358246I
a = 1.43169 + 8.47092I
b = 1.32363 − 1.40196I
−1.41309 + 4.17051I −10.11255 − 0.98560I
u = 1.32363 + 1.40196I
a = −0.078616 − 0.369041I
b = 0.0767307 + 0.0358246I
−1.41309 − 4.17051I 0
u = 1.32363 − 1.40196I
a = −0.078616 + 0.369041I
b = 0.0767307 − 0.0358246I
−1.41309 + 4.17051I 0
u = 0.0351718
a = 39.7196
b = −1.35619
3.28865 1.98690
u = −1.97821
a = −0.447737
b = −0.998893
−5.09057 0
u = 0.89017 + 1.87925I
a = −0.192398 + 0.365177I
b = 0.40372 − 1.51303I
1.42772 + 9.18102I 0
u = 0.89017 − 1.87925I
a = −0.192398 − 0.365177I
b = 0.40372 + 1.51303I
1.42772 − 9.18102I 0
u = 1.72624 + 1.25070I
a = 0.245604 − 0.443464I
b = 0.958529 + 0.798223I
−3.70148 − 2.64555I 0
u = 1.72624 − 1.25070I
a = 0.245604 + 0.443464I
b = 0.958529 − 0.798223I
−3.70148 + 2.64555I 0
21
III. I
u
3
= hb + u, u
8
+ 56u
7
+ · · · + 137a − 286, u
9
− u
8
+ · · · − u − 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
−0.00729927u
8
− 0.408759u
7
+ ··· − 1.96350u + 2.08759
−u
a
8
=
1
u
2
a
4
=
−0.291971u
8
− 0.350365u
7
+ ··· − 2.54015u + 2.50365
0.102190u
8
− 0.277372u
7
+ ··· − 1.51095u − 0.226277
a
9
=
0.547445u
8
− 0.343066u
7
+ ··· + 0.262774u − 1.56934
−0.372263u
8
+ 0.153285u
7
+ ··· − 0.138686u − 0.532847
a
2
=
−0.00729927u
8
− 0.408759u
7
+ ··· − 2.96350u + 2.08759
−u
a
11
=
1.82482u
8
− 2.81022u
7
+ ··· − 6.12409u − 0.897810
0.284672u
8
− 0.0583942u
7
+ ··· + 0.576642u − 0.416058
a
6
=
−1.09489u
8
+ 1.68613u
7
+ ··· + 4.47445u + 0.138686
0.0218978u
8
+ 0.226277u
7
+ ··· + 0.890511u + 0.737226
a
5
=
−0.160584u
8
+ 0.00729927u
7
+ ··· − 0.197080u + 0.927007
0.372263u
8
− 0.153285u
7
+ ··· + 0.138686u + 0.532847
a
1
=
−0.00729927u
8
− 0.408759u
7
+ ··· − 1.96350u + 1.08759
0
a
10
=
0.927007u
8
− 1.08759u
7
+ ··· − 2.63504u − 1.12409
−0.372263u
8
+ 0.153285u
7
+ ··· − 0.138686u − 0.532847
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
25
137
u
8
−
929
137
u
7
+
664
137
u
6
−
1720
137
u
5
−
1642
137
u
4
+
774
137
u
3
+
926
137
u
2
−
3961
137
u −
848
137
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
9
+ u
8
− 3u
7
− 3u
6
+ 5u
5
+ 4u
4
− 5u
3
− 3u
2
+ 3u + 1
c
2
, c
7
u
9
− u
8
+ 2u
7
+ u
6
− 2u
5
− u
4
+ 4u
3
− u
2
− u − 1
c
3
, c
6
u
9
− u
8
− 3u
7
+ 2u
6
+ 4u
5
− 3u
4
− 2u
3
+ 2u
2
− 1
c
4
u
9
− 6u
8
+ 21u
7
− 47u
6
+ 74u
5
− 92u
4
+ 84u
3
− 58u
2
+ 29u − 7
c
5
, c
12
u
9
− u
8
− 3u
7
+ 3u
6
+ 5u
5
− 4u
4
− 5u
3
+ 3u
2
+ 3u − 1
c
8
, c
10
u
9
+ u
8
− 3u
7
− 2u
6
+ 4u
5
+ 3u
4
− 2u
3
− 2u
2
+ 1
c
11
u
9
− 6u
8
+ 17u
7
− 28u
6
+ 26u
5
− 5u
4
− 16u
3
+ 18u
2
− 7u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
9
c
12
y
9
− 7y
8
+ 25y
7
− 57y
6
+ 91y
5
− 104y
4
+ 85y
3
− 47y
2
+ 15y − 1
c
2
, c
7
y
9
+ 3y
8
+ 2y
7
− 3y
6
+ 18y
5
− 21y
4
+ 20y
3
− 11y
2
− y − 1
c
3
, c
6
, c
8
c
10
y
9
− 7y
8
+ 21y
7
− 38y
6
+ 44y
5
− 35y
4
+ 20y
3
− 10y
2
+ 4y − 1
c
4
y
9
+ 6y
8
+ 25y
7
− 37y
6
− 282y
5
− 350y
4
+ 18y
3
+ 220y
2
+ 29y − 49
c
11
y
9
− 2y
8
+ 5y
7
+ 8y
6
+ 54y
5
− 75y
4
+ 128y
3
− 90y
2
+ 13y − 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.804486 + 0.714091I
a = −0.134158 + 0.291745I
b = −0.804486 − 0.714091I
−4.03408 − 1.66978I −7.37601 + 0.94856I
u = 0.804486 − 0.714091I
a = −0.134158 − 0.291745I
b = −0.804486 + 0.714091I
−4.03408 + 1.66978I −7.37601 − 0.94856I
u = −0.938517 + 0.532432I
a = 0.96482 + 1.38130I
b = 0.938517 − 0.532432I
1.67468 + 2.31760I −1.14876 − 5.35011I
u = −0.938517 − 0.532432I
a = 0.96482 − 1.38130I
b = 0.938517 + 0.532432I
1.67468 − 2.31760I −1.14876 + 5.35011I
u = 0.920540
a = 0.905452
b = −0.920540
10.1540 −40.3310
u = −0.292828 + 0.428229I
a = 2.97786 − 0.66488I
b = 0.292828 − 0.428229I
−0.67048 + 3.43986I 3.2362 − 14.0106I
u = −0.292828 − 0.428229I
a = 2.97786 + 0.66488I
b = 0.292828 + 0.428229I
−0.67048 − 3.43986I 3.2362 + 14.0106I
u = 0.46659 + 1.66685I
a = 0.238757 + 0.590137I
b = −0.46659 − 1.66685I
−0.40218 − 10.64190I −1.04621 + 10.68872I
u = 0.46659 − 1.66685I
a = 0.238757 − 0.590137I
b = −0.46659 + 1.66685I
−0.40218 + 10.64190I −1.04621 − 10.68872I
25
IV.
I
u
4
= h−1.58×10
18
u
19
−6.87×10
17
u
18
+· · ·+3.88×10
18
b+3.03×10
18
, 7.97×
10
18
u
19
+6.44×10
18
u
18
+· · ·+3.88×10
18
a−3.92×10
19
, u
20
+u
19
+· · ·−7u−1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
−2.05623u
19
− 1.66102u
18
+ ··· + 9.06074u + 10.1146
0.407594u
19
+ 0.177214u
18
+ ··· − 0.551302u − 0.781151
a
8
=
1
u
2
a
4
=
−1.65360u
19
− 1.44190u
18
+ ··· + 7.79917u + 8.93827
0.377174u
19
+ 0.175049u
18
+ ··· − 1.43325u − 0.964661
a
9
=
−1.89421u
19
− 1.62742u
18
+ ··· + 10.7070u + 12.6641
−0.0457459u
19
+ 0.0376836u
18
+ ··· − 0.903660u − 1.41322
a
2
=
−1.64864u
19
− 1.48380u
18
+ ··· + 8.50944u + 9.33348
0.407594u
19
+ 0.177214u
18
+ ··· − 0.551302u − 0.781151
a
11
=
−2.48748u
19
− 1.99401u
18
+ ··· + 10.3112u + 16.3692
0.0346744u
19
− 0.105627u
18
+ ··· + 1.97106u − 1.41223
a
6
=
4.63932u
19
+ 3.85064u
18
+ ··· − 19.7840u − 28.6943
−0.407088u
19
− 0.272829u
18
+ ··· − 0.574169u + 2.92888
a
5
=
3.52776u
19
+ 2.76103u
18
+ ··· − 15.5004u − 22.6925
−0.00672773u
19
− 0.122553u
18
+ ··· − 0.928767u + 2.47211
a
1
=
−3.93536u
19
− 3.26600u
18
+ ··· + 19.2514u + 24.5167
0.0941728u
19
+ 0.0232509u
18
+ ··· + 1.09079u − 2.39861
a
10
=
6.10289u
19
+ 5.02301u
18
+ ··· − 29.0368u − 35.9042
−0.650911u
19
− 0.413990u
18
+ ··· − 0.423205u + 3.53449
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
4560398378613783059
3877073948979152066
u
19
−
2098263933845814177
1938536974489576033
u
18
+ ··· +
24166302010425936216
1938536974489576033
u +
25132139406574948537
1938536974489576033
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
20
− u
19
+ ··· − 24u − 1
c
2
, c
7
u
20
+ u
19
+ ··· − 7u − 1
c
3
, c
6
u
20
+ 2u
19
+ ··· − u − 1
c
4
(u
10
+ 3u
9
+ 2u
8
− 7u
6
− 11u
5
− 9u
4
− 3u
3
+ 2u
2
+ 2u + 1)
2
c
5
, c
12
u
20
+ u
19
+ ··· + 24u − 1
c
8
, c
10
u
20
− 2u
19
+ ··· + u − 1
c
11
(u
10
+ u
9
− 2u
8
− 6u
7
− u
6
+ 7u
5
+ 3u
4
− 3u
3
− 2u
2
+ 2u + 1)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
9
c
12
y
20
− 17y
19
+ ··· − 590y + 1
c
2
, c
7
y
20
− 11y
19
+ ··· − 31y + 1
c
3
, c
6
, c
8
c
10
y
20
− 14y
19
+ ··· − 53y + 1
c
4
(y
10
− 5y
9
− 10y
8
+ 20y
7
+ 35y
6
+ 3y
5
− 9y
4
− 15y
3
− 2y
2
+ 1)
2
c
11
(y
10
− 5y
9
+ ··· − 8y + 1)
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00838
a = −1.61933
b = 0.162125
4.36614 12.3040
u = −0.945066
a = −0.462685
b = −1.68952
−5.69952 −11.0360
u = 0.597713 + 0.695835I
a = −0.25137 − 1.68780I
b = 0.461351 + 1.030660I
2.11373 − 5.21014I 1.03646 + 10.01521I
u = 0.597713 − 0.695835I
a = −0.25137 + 1.68780I
b = 0.461351 − 1.030660I
2.11373 + 5.21014I 1.03646 − 10.01521I
u = −0.461351 + 1.030660I
a = 0.586237 − 1.256140I
b = −0.597713 + 0.695835I
2.11373 + 5.21014I 1.03646 − 10.01521I
u = −0.461351 − 1.030660I
a = 0.586237 + 1.256140I
b = −0.597713 − 0.695835I
2.11373 − 5.21014I 1.03646 + 10.01521I
u = 0.761215
a = −1.41887
b = −1.36085
−2.28337 15.8270
u = −0.333546 + 0.601831I
a = −0.172205 + 1.095460I
b = 1.36684 − 1.67888I
−1.02854 + 4.47861I 3.16235 − 10.16462I
u = −0.333546 − 0.601831I
a = −0.172205 − 1.095460I
b = 1.36684 + 1.67888I
−1.02854 − 4.47861I 3.16235 + 10.16462I
u = −0.957947 + 0.934322I
a = −0.017956 − 0.660759I
b = 0.096993 + 0.450900I
0.90404 + 2.83774I 0.093420 + 0.262622I
29
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.957947 − 0.934322I
a = −0.017956 + 0.660759I
b = 0.096993 − 0.450900I
0.90404 − 2.83774I 0.093420 − 0.262622I
u = 1.36085
a = −0.793670
b = −0.761215
−2.28337 15.8270
u = −0.096993 + 0.450900I
a = −1.59549 − 1.06412I
b = 0.957947 + 0.934322I
0.90404 − 2.83774I 0.093420 − 0.262622I
u = −0.096993 − 0.450900I
a = −1.59549 + 1.06412I
b = 0.957947 − 0.934322I
0.90404 + 2.83774I 0.093420 + 0.262622I
u = 1.68952
a = 0.258812
b = 0.945066
−5.69952 −11.0360
u = −1.77382
a = −0.655021
b = −2.29896
−6.94143 −3.68030
u = −0.162125
a = 10.0719
b = −1.00838
4.36614 12.3040
u = −1.36684 + 1.67888I
a = 0.007507 + 0.352366I
b = 0.333546 − 0.601831I
−1.02854 + 4.47861I 3.16235 − 10.16462I
u = −1.36684 − 1.67888I
a = 0.007507 − 0.352366I
b = 0.333546 + 0.601831I
−1.02854 − 4.47861I 3.16235 + 10.16462I
u = 2.29896
a = 0.505398
b = 1.77382
−6.94143 −3.68030
30
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
9
(u
9
+ u
8
− 3u
7
− 3u
6
+ 5u
5
+ 4u
4
− 5u
3
− 3u
2
+ 3u + 1)
· (u
20
− u
19
+ ··· − 24u − 1)(u
27
+ u
26
+ ··· + 7u − 1)
· (u
110
− 37u
108
+ ··· − 596u + 229)
c
2
, c
7
(u
9
− u
8
+ 2u
7
+ u
6
− 2u
5
− u
4
+ 4u
3
− u
2
− u − 1)
· (u
20
+ u
19
+ ··· − 7u − 1)(u
27
− u
26
+ ··· − u − 1)
· (u
110
− 2u
109
+ ··· − 61u + 1)
c
3
, c
6
(u
9
− u
8
− 3u
7
+ 2u
6
+ 4u
5
− 3u
4
− 2u
3
+ 2u
2
− 1)
· (u
20
+ 2u
19
+ ··· − u − 1)(u
27
− u
26
+ ··· + 2u + 1)
· (u
110
+ u
109
+ ··· + 2947u + 199)
c
4
(u
9
− 6u
8
+ 21u
7
− 47u
6
+ 74u
5
− 92u
4
+ 84u
3
− 58u
2
+ 29u − 7)
· (u
10
+ 3u
9
+ 2u
8
− 7u
6
− 11u
5
− 9u
4
− 3u
3
+ 2u
2
+ 2u + 1)
2
· (u
27
− 21u
26
+ ··· − 776u + 8)(u
55
+ 10u
54
+ ··· + 8u − 1)
2
c
5
, c
12
(u
9
− u
8
− 3u
7
+ 3u
6
+ 5u
5
− 4u
4
− 5u
3
+ 3u
2
+ 3u − 1)
· (u
20
+ u
19
+ ··· + 24u − 1)(u
27
+ u
26
+ ··· + 7u − 1)
· (u
110
− 37u
108
+ ··· − 596u + 229)
c
8
, c
10
(u
9
+ u
8
− 3u
7
− 2u
6
+ 4u
5
+ 3u
4
− 2u
3
− 2u
2
+ 1)
· (u
20
− 2u
19
+ ··· + u − 1)(u
27
− u
26
+ ··· + 2u + 1)
· (u
110
+ u
109
+ ··· + 2947u + 199)
c
11
(u
9
− 6u
8
+ 17u
7
− 28u
6
+ 26u
5
− 5u
4
− 16u
3
+ 18u
2
− 7u + 1)
· (u
10
+ u
9
− 2u
8
− 6u
7
− u
6
+ 7u
5
+ 3u
4
− 3u
3
− 2u
2
+ 2u + 1)
2
· (u
27
− 13u
26
+ ··· − 444u + 72)(u
55
+ 6u
54
+ ··· + 262u + 67)
2
31
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
9
c
12
(y
9
− 7y
8
+ 25y
7
− 57y
6
+ 91y
5
− 104y
4
+ 85y
3
− 47y
2
+ 15y − 1)
· (y
20
− 17y
19
+ ··· − 590y + 1)(y
27
− 25y
26
+ ··· + 45y − 1)
· (y
110
− 74y
109
+ ··· − 2941542y + 52441)
c
2
, c
7
(y
9
+ 3y
8
+ 2y
7
− 3y
6
+ 18y
5
− 21y
4
+ 20y
3
− 11y
2
− y − 1)
· (y
20
− 11y
19
+ ··· − 31y + 1)(y
27
− 15y
26
+ ··· + 5y − 1)
· (y
110
+ 8y
109
+ ··· − 995y + 1)
c
3
, c
6
, c
8
c
10
(y
9
− 7y
8
+ 21y
7
− 38y
6
+ 44y
5
− 35y
4
+ 20y
3
− 10y
2
+ 4y − 1)
· (y
20
− 14y
19
+ ··· − 53y + 1)(y
27
− 21y
26
+ ··· + 6y − 1)
· (y
110
− 71y
109
+ ··· − 1508869y + 39601)
c
4
(y
9
+ 6y
8
+ 25y
7
− 37y
6
− 282y
5
− 350y
4
+ 18y
3
+ 220y
2
+ 29y − 49)
· (y
10
− 5y
9
− 10y
8
+ 20y
7
+ 35y
6
+ 3y
5
− 9y
4
− 15y
3
− 2y
2
+ 1)
2
· (y
27
− 7y
26
+ ··· + 456672y − 64)(y
55
+ 12y
54
+ ··· + 236y − 1)
2
c
11
(y
9
− 2y
8
+ 5y
7
+ 8y
6
+ 54y
5
− 75y
4
+ 128y
3
− 90y
2
+ 13y − 1)
· ((y
10
− 5y
9
+ ··· − 8y + 1)
2
)(y
27
− 7y
26
+ ··· + 41040y − 5184)
· (y
55
− 20y
54
+ ··· + 72932y − 4489)
2
32
