12a
1253
(K12a
1253
)
A knot diagram
1
Linearized knot diagam
5 7 8 12 10 2 11 4 1 6 3 9
Solving Sequence
2,6
7
3,10
11 8 12 5 1 4 9
c
6
c
2
c
10
c
7
c
11
c
5
c
1
c
4
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.59766 × 10
581
u
124
+ 3.43383 × 10
581
u
123
+ ··· + 2.82859 × 10
581
b + 5.30736 × 10
583
,
2.20394 × 10
582
u
124
− 4.77048 × 10
582
u
123
+ ··· + 4.80860 × 10
582
a − 7.41864 × 10
584
,
u
125
− 3u
124
+ ··· − 1955u + 289i
I
u
2
= h791694037u
18
+ 148281897u
17
+ ··· + 2256529259b + 2264697959,
− 162403155u
18
+ 758589616u
17
+ ··· + 2256529259a + 24533522042,
u
19
− 8u
17
+ ··· − 15u + 1i
I
u
3
= hb + 1, a, u
2
− u − 1i
I
u
4
= hb + 1, a − 1, u + 1i
* 4 irreducible components of dim
C
= 0, with total 147 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−1.60 × 10
581
u
124
+ 3.43 × 10
581
u
123
+ · · · + 2.83 × 10
581
b + 5.31 ×
10
583
, 2.20 × 10
582
u
124
− 4.77 × 10
582
u
123
+ · · · + 4.81 × 10
582
a − 7.42 ×
10
584
, u
125
− 3u
124
+ · · · − 1955u + 289i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
−0.458334u
124
+ 0.992072u
123
+ ··· − 817.690u + 154.278
0.564827u
124
− 1.21397u
123
+ ··· + 1047.83u − 187.633
a
11
=
0.106493u
124
− 0.221902u
123
+ ··· + 230.141u − 33.3541
0.564827u
124
− 1.21397u
123
+ ··· + 1047.83u − 187.633
a
8
=
0.371742u
124
− 0.828981u
123
+ ··· + 745.819u − 139.719
−0.191219u
124
+ 0.426785u
123
+ ··· − 403.224u + 74.5168
a
12
=
−0.321539u
124
+ 0.694405u
123
+ ··· − 558.595u + 107.776
0.666292u
124
− 1.43070u
123
+ ··· + 1241.24u − 222.472
a
5
=
−0.280445u
124
+ 0.624569u
123
+ ··· − 586.063u + 112.854
−0.311341u
124
+ 0.691375u
123
+ ··· − 323.906u + 58.2541
a
1
=
0.843078u
124
− 1.84273u
123
+ ··· + 1707.88u − 304.272
−0.559460u
124
+ 1.23368u
123
+ ··· − 1142.91u + 208.255
a
4
=
−0.650008u
124
+ 1.44187u
123
+ ··· − 1314.29u + 240.546
0.415494u
124
− 0.925040u
123
+ ··· + 859.265u − 156.839
a
9
=
0.733999u
124
− 1.60760u
123
+ ··· + 1479.66u − 262.978
−0.615104u
124
+ 1.36954u
123
+ ··· − 1246.28u + 226.921
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.20245u
124
− 2.27856u
123
+ ··· + 8267.63u − 1316.86
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
125
+ 6u
124
+ ··· − 103752u + 326
c
2
, c
6
u
125
− 3u
124
+ ··· − 1955u + 289
c
3
, c
8
u
125
− 49u
123
+ ··· + 1952u − 64
c
4
u
125
+ 11u
124
+ ··· + 5083935u + 755075
c
5
, c
10
u
125
+ 15u
124
+ ··· + 1470u + 223
c
7
u
125
− 3u
124
+ ··· − 1329u − 1097
c
9
, c
12
u
125
+ 2u
124
+ ··· − 3u + 1
c
11
u
125
+ 11u
124
+ ··· − 19u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
125
+ 26y
124
+ ··· + 11898756036y −106276
c
2
, c
6
y
125
− 85y
124
+ ··· − 9039053y −83521
c
3
, c
8
y
125
− 98y
124
+ ··· + 891904y −4096
c
4
y
125
− 51y
124
+ ··· − 11330459493975y −570138255625
c
5
, c
10
y
125
− 179y
124
+ ··· + 4984526y −49729
c
7
y
125
− 23y
124
+ ··· + 199287673y −1203409
c
9
, c
12
y
125
− 106y
124
+ ··· − 155y −1
c
11
y
125
− 99y
124
+ ··· + 589y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.942487 + 0.335420I
a = −1.31065 − 0.55928I
b = 0.949578 − 0.100314I
1.073150 − 0.413455I 0
u = 0.942487 − 0.335420I
a = −1.31065 + 0.55928I
b = 0.949578 + 0.100314I
1.073150 + 0.413455I 0
u = −0.998836
a = 0.104757
b = −8.54734
−0.00222811 0
u = −0.984421 + 0.123698I
a = 1.85676 − 1.50641I
b = −1.338110 − 0.348323I
2.57285 + 3.74721I 0
u = −0.984421 − 0.123698I
a = 1.85676 + 1.50641I
b = −1.338110 + 0.348323I
2.57285 − 3.74721I 0
u = −1.006450 + 0.082045I
a = −1.41830 + 0.84737I
b = 1.243520 + 0.340332I
−2.02666 + 1.11572I 0
u = −1.006450 − 0.082045I
a = −1.41830 − 0.84737I
b = 1.243520 − 0.340332I
−2.02666 − 1.11572I 0
u = 0.969937 + 0.142867I
a = −0.025056 − 0.679227I
b = −0.92183 − 1.61532I
4.14076 + 0.37848I 0
u = 0.969937 − 0.142867I
a = −0.025056 + 0.679227I
b = −0.92183 + 1.61532I
4.14076 − 0.37848I 0
u = 0.999678 + 0.255939I
a = −0.295500 − 0.549772I
b = 1.33355 − 0.68586I
3.57785 − 0.70217I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.999678 − 0.255939I
a = −0.295500 + 0.549772I
b = 1.33355 + 0.68586I
3.57785 + 0.70217I 0
u = −0.728834 + 0.747827I
a = −1.39852 + 0.79835I
b = 0.993598 + 0.529369I
3.46231 + 3.84978I 0
u = −0.728834 − 0.747827I
a = −1.39852 − 0.79835I
b = 0.993598 − 0.529369I
3.46231 − 3.84978I 0
u = 0.947940
a = 0.411989
b = −3.26607
4.49095 0
u = −0.201015 + 0.900653I
a = −2.01584 − 0.72120I
b = 1.41913 + 0.13506I
11.14340 − 2.83478I 0
u = −0.201015 − 0.900653I
a = −2.01584 + 0.72120I
b = 1.41913 − 0.13506I
11.14340 + 2.83478I 0
u = 0.763397 + 0.778071I
a = 0.764289 − 0.538999I
b = −0.245655 + 0.161369I
5.66067 + 3.97448I 0
u = 0.763397 − 0.778071I
a = 0.764289 + 0.538999I
b = −0.245655 − 0.161369I
5.66067 − 3.97448I 0
u = −0.905059 + 0.026507I
a = 0.028804 + 1.057240I
b = −0.715124 + 0.404762I
−1.42504 + 0.49524I 0
u = −0.905059 − 0.026507I
a = 0.028804 − 1.057240I
b = −0.715124 − 0.404762I
−1.42504 − 0.49524I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.248411 + 0.848307I
a = 1.50680 + 0.58991I
b = −1.346860 − 0.320768I
7.43042 + 3.38208I 0
u = 0.248411 − 0.848307I
a = 1.50680 − 0.58991I
b = −1.346860 + 0.320768I
7.43042 − 3.38208I 0
u = −0.532827 + 0.983917I
a = −1.102080 + 0.654082I
b = 1.365910 − 0.306586I
11.09390 − 4.19413I 0
u = −0.532827 − 0.983917I
a = −1.102080 − 0.654082I
b = 1.365910 + 0.306586I
11.09390 + 4.19413I 0
u = −0.050306 + 0.874311I
a = 1.60362 + 0.34559I
b = −1.328610 + 0.111859I
7.31902 − 2.80449I 0
u = −0.050306 − 0.874311I
a = 1.60362 − 0.34559I
b = −1.328610 − 0.111859I
7.31902 + 2.80449I 0
u = 1.107530 + 0.221187I
a = 1.22998 + 1.17599I
b = −1.102900 + 0.445367I
−0.91861 − 5.00934I 0
u = 1.107530 − 0.221187I
a = 1.22998 − 1.17599I
b = −1.102900 − 0.445367I
−0.91861 + 5.00934I 0
u = 0.070134 + 0.865185I
a = −1.65106 + 0.14147I
b = 1.47600 − 0.35818I
11.97640 − 2.93586I 0
u = 0.070134 − 0.865185I
a = −1.65106 − 0.14147I
b = 1.47600 + 0.35818I
11.97640 + 2.93586I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.856845 + 0.131608I
a = −0.12179 + 2.20756I
b = 1.030550 − 0.111168I
2.93986 − 2.52030I 0
u = −0.856845 − 0.131608I
a = −0.12179 − 2.20756I
b = 1.030550 + 0.111168I
2.93986 + 2.52030I 0
u = 1.062400 + 0.456633I
a = 0.314056 + 1.059930I
b = −1.209760 − 0.001302I
8.90062 − 1.54659I 0
u = 1.062400 − 0.456633I
a = 0.314056 − 1.059930I
b = −1.209760 + 0.001302I
8.90062 + 1.54659I 0
u = 0.836144
a = −1.81627
b = 1.69790
11.1866 0
u = 1.152110 + 0.191743I
a = −1.00646 − 1.48940I
b = 1.261180 − 0.567330I
4.32440 − 9.08748I 0
u = 1.152110 − 0.191743I
a = −1.00646 + 1.48940I
b = 1.261180 + 0.567330I
4.32440 + 9.08748I 0
u = −0.258052 + 0.789817I
a = 0.140191 − 0.606288I
b = 0.198810 + 0.549299I
1.35239 + 3.40013I 0
u = −0.258052 − 0.789817I
a = 0.140191 + 0.606288I
b = 0.198810 − 0.549299I
1.35239 − 3.40013I 0
u = 0.803999 + 0.190276I
a = −0.05590 + 1.73727I
b = 0.575329 + 0.304263I
1.37533 − 4.04378I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.803999 − 0.190276I
a = −0.05590 − 1.73727I
b = 0.575329 − 0.304263I
1.37533 + 4.04378I 0
u = −1.014540 + 0.603398I
a = 1.19194 − 0.80373I
b = −1.45839 − 0.63741I
9.51821 + 9.86764I 0
u = −1.014540 − 0.603398I
a = 1.19194 + 0.80373I
b = −1.45839 + 0.63741I
9.51821 − 9.86764I 0
u = 1.19033
a = 0.633381
b = −2.57595
5.74232 0
u = 1.008690 + 0.636363I
a = −1.38714 − 1.38113I
b = 1.104040 + 0.048480I
3.42114 − 1.49949I 0
u = 1.008690 − 0.636363I
a = −1.38714 + 1.38113I
b = 1.104040 − 0.048480I
3.42114 + 1.49949I 0
u = −1.20245
a = 1.43195
b = −0.869123
1.87496 0
u = 1.129360 + 0.492218I
a = 1.00124 + 1.02679I
b = −1.078970 + 0.428805I
0.10965 − 4.48168I 0
u = 1.129360 − 0.492218I
a = 1.00124 − 1.02679I
b = −1.078970 − 0.428805I
0.10965 + 4.48168I 0
u = 0.735696 + 0.118101I
a = 0.59129 − 2.40306I
b = −0.850795 + 0.180856I
6.45678 − 8.22259I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.735696 − 0.118101I
a = 0.59129 + 2.40306I
b = −0.850795 − 0.180856I
6.45678 + 8.22259I 0
u = 1.176340 + 0.442144I
a = −1.010910 − 0.975118I
b = 1.40342 − 0.62990I
4.52271 − 8.07392I 0
u = 1.176340 − 0.442144I
a = −1.010910 + 0.975118I
b = 1.40342 + 0.62990I
4.52271 + 8.07392I 0
u = −0.064652 + 1.259870I
a = −1.55286 − 0.19267I
b = 1.38752 + 0.33072I
12.1768 + 12.3422I 0
u = −0.064652 − 1.259870I
a = −1.55286 + 0.19267I
b = 1.38752 − 0.33072I
12.1768 − 12.3422I 0
u = −1.271270 + 0.010472I
a = 0.493530 − 0.645669I
b = 0.372201 − 1.018560I
1.38433 + 3.30057I 0
u = −1.271270 − 0.010472I
a = 0.493530 + 0.645669I
b = 0.372201 + 1.018560I
1.38433 − 3.30057I 0
u = −1.233480 + 0.366840I
a = −0.021203 − 0.182690I
b = 0.188021 − 1.131960I
−2.03657 + 7.38018I 0
u = −1.233480 − 0.366840I
a = −0.021203 + 0.182690I
b = 0.188021 + 1.131960I
−2.03657 − 7.38018I 0
u = 1.291170 + 0.071617I
a = −0.827168 + 0.322335I
b = 0.009115 + 0.461538I
−1.65578 + 0.24540I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.291170 − 0.071617I
a = −0.827168 − 0.322335I
b = 0.009115 − 0.461538I
−1.65578 − 0.24540I 0
u = −1.200070 + 0.510332I
a = 0.497005 + 0.005590I
b = −0.769177 + 0.589646I
1.57951 + 1.76742I 0
u = −1.200070 − 0.510332I
a = 0.497005 − 0.005590I
b = −0.769177 − 0.589646I
1.57951 − 1.76742I 0
u = −1.237890 + 0.416643I
a = −0.403979 + 0.160673I
b = 0.138193 + 0.573082I
−1.49994 + 1.61445I 0
u = −1.237890 − 0.416643I
a = −0.403979 − 0.160673I
b = 0.138193 − 0.573082I
−1.49994 − 1.61445I 0
u = −0.045413 + 1.306590I
a = 1.67730 − 0.20079I
b = −1.301320 + 0.252631I
5.92187 − 6.37567I 0
u = −0.045413 − 1.306590I
a = 1.67730 + 0.20079I
b = −1.301320 − 0.252631I
5.92187 + 6.37567I 0
u = −1.271590 + 0.355578I
a = −0.275443 + 0.222786I
b = 0.243434 + 1.386490I
2.30413 + 12.11600I 0
u = −1.271590 − 0.355578I
a = −0.275443 − 0.222786I
b = 0.243434 − 1.386490I
2.30413 − 12.11600I 0
u = −1.320660 + 0.052173I
a = −0.238135 − 0.284295I
b = −0.292004 − 0.653383I
−3.32174 − 0.72507I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.320660 − 0.052173I
a = −0.238135 + 0.284295I
b = −0.292004 + 0.653383I
−3.32174 + 0.72507I 0
u = 0.419647 + 0.530297I
a = −0.233736 − 0.046973I
b = 0.373441 + 0.584783I
1.99588 + 0.53159I 0
u = 0.419647 − 0.530297I
a = −0.233736 + 0.046973I
b = 0.373441 − 0.584783I
1.99588 − 0.53159I 0
u = 1.307820 + 0.274864I
a = 0.085206 − 0.190905I
b = −0.090114 − 0.900265I
−6.42038 − 3.16549I 0
u = 1.307820 − 0.274864I
a = 0.085206 + 0.190905I
b = −0.090114 + 0.900265I
−6.42038 + 3.16549I 0
u = 1.291080 + 0.349126I
a = 0.306369 + 0.219969I
b = −0.191727 + 1.091060I
−3.29921 − 7.30371I 0
u = 1.291080 − 0.349126I
a = 0.306369 − 0.219969I
b = −0.191727 − 1.091060I
−3.29921 + 7.30371I 0
u = −1.252100 + 0.495718I
a = 0.52941 − 1.50227I
b = −1.121350 − 0.022468I
7.82978 + 7.91392I 0
u = −1.252100 − 0.495718I
a = 0.52941 + 1.50227I
b = −1.121350 + 0.022468I
7.82978 − 7.91392I 0
u = 0.394816 + 1.320890I
a = −1.375450 − 0.027755I
b = 1.140540 − 0.064980I
2.13769 − 1.18631I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.394816 − 1.320890I
a = −1.375450 + 0.027755I
b = 1.140540 + 0.064980I
2.13769 + 1.18631I 0
u = −1.301960 + 0.457122I
a = −0.590109 + 1.091690I
b = 1.156570 + 0.416229I
3.40334 + 7.64879I 0
u = −1.301960 − 0.457122I
a = −0.590109 − 1.091690I
b = 1.156570 − 0.416229I
3.40334 − 7.64879I 0
u = −1.333710 + 0.425702I
a = 0.759018 − 0.950054I
b = −1.43023 − 0.69908I
7.61011 + 7.61213I 0
u = −1.333710 − 0.425702I
a = 0.759018 + 0.950054I
b = −1.43023 + 0.69908I
7.61011 − 7.61213I 0
u = 0.218548 + 0.551748I
a = −0.713524 − 0.955013I
b = −0.492758 + 0.692695I
6.57929 − 8.58236I 7.17479 + 7.35116I
u = 0.218548 − 0.551748I
a = −0.713524 + 0.955013I
b = −0.492758 − 0.692695I
6.57929 + 8.58236I 7.17479 − 7.35116I
u = 0.096219 + 1.408040I
a = 1.240840 + 0.138875I
b = −1.138190 − 0.225307I
5.37760 + 6.35842I 0
u = 0.096219 − 1.408040I
a = 1.240840 − 0.138875I
b = −1.138190 + 0.225307I
5.37760 − 6.35842I 0
u = 1.14489 + 0.84151I
a = 1.79580 + 0.56792I
b = −1.39055 + 0.27443I
3.46207 − 4.82583I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.14489 − 0.84151I
a = 1.79580 − 0.56792I
b = −1.39055 − 0.27443I
3.46207 + 4.82583I 0
u = 1.42965
a = 0.686510
b = 0.644590
−5.36152 0
u = −0.478248 + 0.271489I
a = −0.977448 + 0.413736I
b = −0.268229 − 0.088356I
−1.211170 + 0.683772I −5.72849 − 2.30581I
u = −0.478248 − 0.271489I
a = −0.977448 − 0.413736I
b = −0.268229 + 0.088356I
−1.211170 − 0.683772I −5.72849 + 2.30581I
u = 1.11597 + 0.93887I
a = 1.176320 + 0.588254I
b = −0.856393 + 0.342815I
1.70730 − 5.60461I 0
u = 1.11597 − 0.93887I
a = 1.176320 − 0.588254I
b = −0.856393 − 0.342815I
1.70730 + 5.60461I 0
u = −1.36863 + 0.60611I
a = −1.26268 + 0.80568I
b = 1.43156 + 0.48503I
1.78338 + 12.88010I 0
u = −1.36863 − 0.60611I
a = −1.26268 − 0.80568I
b = 1.43156 − 0.48503I
1.78338 − 12.88010I 0
u = 1.38283 + 0.64837I
a = −1.063510 − 0.675951I
b = 1.253970 − 0.571822I
1.32115 − 13.29350I 0
u = 1.38283 − 0.64837I
a = −1.063510 + 0.675951I
b = 1.253970 + 0.571822I
1.32115 + 13.29350I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41640 + 0.59524I
a = 1.116180 + 0.781695I
b = −1.47957 + 0.57235I
7.5925 − 18.7913I 0
u = 1.41640 − 0.59524I
a = 1.116180 − 0.781695I
b = −1.47957 − 0.57235I
7.5925 + 18.7913I 0
u = 1.53727
a = 0.426033
b = −1.46089
8.61324 0
u = −1.40579 + 0.62377I
a = 1.091860 − 0.606808I
b = −1.245940 − 0.466819I
−2.84296 + 8.08154I 0
u = −1.40579 − 0.62377I
a = 1.091860 + 0.606808I
b = −1.245940 + 0.466819I
−2.84296 − 8.08154I 0
u = −0.460679
a = −0.911688
b = −1.22871
0.613536 13.1590
u = −1.54129
a = 0.0352544
b = 0.972874
0.720066 0
u = 0.100125 + 0.404117I
a = 2.12907 − 0.05398I
b = 0.289595 − 0.443502I
1.78277 − 4.00315I 2.74480 + 6.42996I
u = 0.100125 − 0.404117I
a = 2.12907 + 0.05398I
b = 0.289595 + 0.443502I
1.78277 + 4.00315I 2.74480 − 6.42996I
u = −0.198425 + 0.358426I
a = 0.28562 + 3.59401I
b = −0.225943 − 0.133733I
5.65081 + 1.71698I 17.6974 − 1.9857I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.198425 − 0.358426I
a = 0.28562 − 3.59401I
b = −0.225943 + 0.133733I
5.65081 − 1.71698I 17.6974 + 1.9857I
u = 0.225705 + 0.309180I
a = −1.039030 + 0.416603I
b = −0.391115 − 1.157360I
5.84300 − 2.34407I 12.82711 + 4.41953I
u = 0.225705 − 0.309180I
a = −1.039030 − 0.416603I
b = −0.391115 + 1.157360I
5.84300 + 2.34407I 12.82711 − 4.41953I
u = 0.369506
a = −1.56521
b = 0.633722
0.992586 11.4650
u = 1.63602
a = −0.737016
b = 0.621597
−1.36484 0
u = −1.66203
a = −0.221478
b = 0.162999
−3.11044 0
u = 1.47910 + 0.77322I
a = −1.195450 − 0.390858I
b = 1.258520 − 0.207651I
1.14385 − 1.93389I 0
u = 1.47910 − 0.77322I
a = −1.195450 + 0.390858I
b = 1.258520 + 0.207651I
1.14385 + 1.93389I 0
u = −1.38318 + 0.97054I
a = 0.929310 − 0.600810I
b = −1.152700 + 0.077736I
8.30900 − 4.86994I 0
u = −1.38318 − 0.97054I
a = 0.929310 + 0.600810I
b = −1.152700 − 0.077736I
8.30900 + 4.86994I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.69303
a = 0.0174393
b = −1.05150
2.48679 0
u = −1.53624 + 0.81070I
a = −0.863778 + 0.415887I
b = 1.013210 + 0.197642I
0.20721 + 2.12586I 0
u = −1.53624 − 0.81070I
a = −0.863778 − 0.415887I
b = 1.013210 − 0.197642I
0.20721 − 2.12586I 0
u = −0.0001479 + 0.1236730I
a = 3.31368 + 5.75049I
b = 0.456774 − 0.598825I
1.95643 + 0.05896I 6.47140 + 0.32524I
u = −0.0001479 − 0.1236730I
a = 3.31368 − 5.75049I
b = 0.456774 + 0.598825I
1.95643 − 0.05896I 6.47140 − 0.32524I
17
II.
I
u
2
= h7.92 × 10
8
u
18
+ 1.48 × 10
8
u
17
+ · · · + 2.26 × 10
9
b + 2.26 × 10
9
, −1.62 ×
10
8
u
18
+7.59×10
8
u
17
+· · ·+2.26×10
9
a+2.45×10
10
, u
19
−8u
17
+· · ·−15u+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
0.0719703u
18
− 0.336175u
17
+ ··· + 7.91864u − 10.8722
−0.350846u
18
− 0.0657124u
17
+ ··· − 8.24945u − 1.00362
a
11
=
−0.278876u
18
− 0.401888u
17
+ ··· − 0.330807u − 11.8759
−0.350846u
18
− 0.0657124u
17
+ ··· − 8.24945u − 1.00362
a
8
=
2.06658u
18
+ 0.00280882u
17
+ ··· + 77.8527u − 23.4221
0.471608u
18
+ 0.112728u
17
+ ··· + 19.4581u − 4.07844
a
12
=
−0.0515186u
18
− 0.541545u
17
+ ··· + 6.69380u − 12.3780
−0.722285u
18
− 0.184624u
17
+ ··· − 17.5963u − 0.361828
a
5
=
−0.779187u
18
+ 0.342273u
17
+ ··· − 38.7911u + 20.6169
0.660387u
18
+ 0.793389u
17
+ ··· − 2.30440u + 2.94278
a
1
=
−2.59102u
18
− 0.116156u
17
+ ··· − 92.8719u + 32.0382
−0.698485u
18
+ 0.0443048u
17
+ ··· − 19.1479u + 5.37856
a
4
=
−2.05708u
18
− 0.0504904u
17
+ ··· − 79.1873u + 33.1423
0.195658u
18
+ 0.345667u
17
+ ··· + 2.78270u + 3.86736
a
9
=
−3.86132u
18
− 0.678099u
17
+ ··· − 127.882u + 35.3868
−0.812222u
18
− 0.0812151u
17
+ ··· − 26.5770u + 6.00488
(ii) Obstruction class = 1
(iii) Cusp Shapes =
6831297144
2256529259
u
18
+
11207398997
2256529259
u
17
+ ··· +
41616421755
2256529259
u +
30171201693
2256529259
18
(iv) u-Polynomials at the component
19
Crossings u-Polynomials at each crossing
c
1
u
19
− 2u
18
+ ··· − 4u − 1
c
2
u
19
− 8u
17
+ ··· − 15u − 1
c
3
u
19
+ u
18
+ ··· + 41u − 5
c
4
u
19
− 3u
18
+ ··· − 6u + 1
c
5
u
19
− 3u
18
+ ··· + u − 1
c
6
u
19
− 8u
17
+ ··· − 15u + 1
c
7
u
19
− 2u
18
+ ··· + 5u − 1
c
8
u
19
− u
18
+ ··· + 41u + 5
c
9
u
19
− 3u
18
+ ··· − 23u + 1
c
10
u
19
+ 3u
18
+ ··· + u + 1
c
11
u
19
− 5u
18
+ ··· + 4u + 1
c
12
u
19
+ 3u
18
+ ··· − 23u − 1
20
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
+ 2y
18
+ ··· + 46y −1
c
2
, c
6
y
19
− 16y
18
+ ··· + 159y −1
c
3
, c
8
y
19
− 17y
18
+ ··· + 1731y −25
c
4
y
19
− 7y
18
+ ··· + 94y −1
c
5
, c
10
y
19
− 31y
18
+ ··· + 27y −1
c
7
y
19
− 6y
18
+ ··· + 9y −1
c
9
, c
12
y
19
− 17y
18
+ ··· + 545y −1
c
11
y
19
− 19y
18
+ ··· + 10y −1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.948882
a = 0.420434
b = −1.51887
−0.0522738 −2.13350
u = 0.948291
a = −0.219082
b = 3.86098
4.55872 88.0720
u = 0.998924 + 0.629882I
a = −1.97905 − 0.90443I
b = 1.343040 − 0.308552I
4.00272 − 4.78550I 10.63922 + 5.01600I
u = 0.998924 − 0.629882I
a = −1.97905 + 0.90443I
b = 1.343040 + 0.308552I
4.00272 + 4.78550I 10.63922 − 5.01600I
u = −0.629570 + 1.040920I
a = −1.49280 + 0.38753I
b = 1.157600 − 0.253486I
7.37353 − 5.84742I 9.30245 + 6.94375I
u = −0.629570 − 1.040920I
a = −1.49280 − 0.38753I
b = 1.157600 + 0.253486I
7.37353 + 5.84742I 9.30245 − 6.94375I
u = −1.168570 + 0.362422I
a = 0.68161 − 1.49743I
b = −1.123780 − 0.641982I
5.52017 + 10.28820I 5.93954 − 9.82069I
u = −1.168570 − 0.362422I
a = 0.68161 + 1.49743I
b = −1.123780 + 0.641982I
5.52017 − 10.28820I 5.93954 + 9.82069I
u = −0.995194 + 0.759827I
a = −1.27070 + 0.94640I
b = 0.856076 + 0.332030I
2.14286 + 5.50598I 11.65232 − 6.69325I
u = −0.995194 − 0.759827I
a = −1.27070 − 0.94640I
b = 0.856076 − 0.332030I
2.14286 − 5.50598I 11.65232 + 6.69325I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.36113
a = 0.643361
b = −0.446430
−0.617884 2.68150
u = 1.40302
a = 0.775709
b = 0.528367
−5.57065 −20.8290
u = 1.50745
a = −0.916677
b = 0.361115
0.709401 −1.47580
u = 0.473561 + 0.057656I
a = −1.57212 + 1.03384I
b = 0.051996 + 0.781955I
5.00025 − 1.76770I 3.74639 + 1.14542I
u = 0.473561 − 0.057656I
a = −1.57212 − 1.03384I
b = 0.051996 − 0.781955I
5.00025 + 1.76770I 3.74639 − 1.14542I
u = 1.32328 + 0.90704I
a = 1.225520 + 0.460064I
b = −1.186300 + 0.176065I
1.45847 − 2.11781I 9.21881 + 9.96997I
u = 1.32328 − 0.90704I
a = 1.225520 − 0.460064I
b = −1.186300 − 0.176065I
1.45847 + 2.11781I 9.21881 − 9.96997I
u = −1.63674
a = 0.0257786
b = −0.374181
−2.95718 25.8480
u = 0.0831383
a = −9.91445
b = −1.60825
12.1515 13.8400
24
III. I
u
3
= hb + 1, a, u
2
− u − 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u + 1
a
3
=
−u
−u − 1
a
10
=
0
−1
a
11
=
−1
−1
a
8
=
u + 1
2u + 1
a
12
=
−u − 1
−u − 2
a
5
=
1
1
a
1
=
u
2u
a
4
=
−u
−u − 1
a
9
=
u + 1
2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −1
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
u
2
+ u − 1
c
3
, c
8
u
2
c
4
, c
5
(u + 1)
2
c
6
, c
7
, c
9
u
2
− u − 1
c
10
, c
11
(u − 1)
2
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
9
, c
12
y
2
− 3y + 1
c
3
, c
8
y
2
c
4
, c
5
, c
10
c
11
(y −1)
2
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = 0
b = −1.00000
0 −1.00000
u = 1.61803
a = 0
b = −1.00000
0 −1.00000
28
IV. I
u
4
= hb + 1, a − 1, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
6
=
1
0
a
7
=
1
1
a
3
=
1
0
a
10
=
1
−1
a
11
=
0
−1
a
8
=
1
0
a
12
=
1
−1
a
5
=
0
1
a
1
=
0
−1
a
4
=
1
0
a
9
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
8
u
c
2
, c
10
, c
11
c
12
u − 1
c
4
, c
5
, c
6
c
7
, c
9
u + 1
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
8
y
c
2
, c
4
, c
5
c
6
, c
7
, c
9
c
10
, c
11
, c
12
y −1
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000
b = −1.00000
0 0
32
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
2
+ u − 1)(u
19
− 2u
18
+ ··· − 4u − 1)
· (u
125
+ 6u
124
+ ··· − 103752u + 326)
c
2
(u − 1)(u
2
+ u − 1)(u
19
− 8u
17
+ ··· − 15u − 1)
· (u
125
− 3u
124
+ ··· − 1955u + 289)
c
3
u
3
(u
19
+ u
18
+ ··· + 41u − 5)(u
125
− 49u
123
+ ··· + 1952u − 64)
c
4
((u + 1)
3
)(u
19
− 3u
18
+ ··· − 6u + 1)
· (u
125
+ 11u
124
+ ··· + 5083935u + 755075)
c
5
((u + 1)
3
)(u
19
− 3u
18
+ ··· + u − 1)(u
125
+ 15u
124
+ ··· + 1470u + 223)
c
6
(u + 1)(u
2
− u − 1)(u
19
− 8u
17
+ ··· − 15u + 1)
· (u
125
− 3u
124
+ ··· − 1955u + 289)
c
7
(u + 1)(u
2
− u − 1)(u
19
− 2u
18
+ ··· + 5u − 1)
· (u
125
− 3u
124
+ ··· − 1329u − 1097)
c
8
u
3
(u
19
− u
18
+ ··· + 41u + 5)(u
125
− 49u
123
+ ··· + 1952u − 64)
c
9
(u + 1)(u
2
− u − 1)(u
19
− 3u
18
+ ··· − 23u + 1)(u
125
+ 2u
124
+ ··· − 3u + 1)
c
10
((u − 1)
3
)(u
19
+ 3u
18
+ ··· + u + 1)(u
125
+ 15u
124
+ ··· + 1470u + 223)
c
11
((u − 1)
3
)(u
19
− 5u
18
+ ··· + 4u + 1)(u
125
+ 11u
124
+ ··· − 19u + 1)
c
12
(u − 1)(u
2
+ u − 1)(u
19
+ 3u
18
+ ··· − 23u − 1)(u
125
+ 2u
124
+ ··· − 3u + 1)
33
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
2
− 3y + 1)(y
19
+ 2y
18
+ ··· + 46y −1)
· (y
125
+ 26y
124
+ ··· + 11898756036y −106276)
c
2
, c
6
(y −1)(y
2
− 3y + 1)(y
19
− 16y
18
+ ··· + 159y −1)
· (y
125
− 85y
124
+ ··· − 9039053y −83521)
c
3
, c
8
y
3
(y
19
− 17y
18
+ ··· + 1731y −25)
· (y
125
− 98y
124
+ ··· + 891904y −4096)
c
4
((y −1)
3
)(y
19
− 7y
18
+ ··· + 94y −1)
· (y
125
− 51y
124
+ ··· − 11330459493975y −570138255625)
c
5
, c
10
((y −1)
3
)(y
19
− 31y
18
+ ··· + 27y −1)
· (y
125
− 179y
124
+ ··· + 4984526y −49729)
c
7
(y −1)(y
2
− 3y + 1)(y
19
− 6y
18
+ ··· + 9y −1)
· (y
125
− 23y
124
+ ··· + 199287673y −1203409)
c
9
, c
12
(y −1)(y
2
− 3y + 1)(y
19
− 17y
18
+ ··· + 545y −1)
· (y
125
− 106y
124
+ ··· − 155y −1)
c
11
((y −1)
3
)(y
19
− 19y
18
+ ··· + 10y −1)(y
125
− 99y
124
+ ··· + 589y −1)
34
