12a
1058
(K12a
1058
)
A knot diagram
1
Linearized knot diagam
4 7 9 11 10 3 12 2 1 5 8 6
Solving Sequence
5,11 1,4
2 10 6 9 3 8 12 7
c
4
c
1
c
10
c
5
c
9
c
3
c
8
c
12
c
7
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h6.77987 × 10
529
u
151
− 2.60638 × 10
530
u
150
+ ··· + 2.32236 × 10
530
b − 7.75568 × 10
530
,
4.01232 × 10
530
u
151
− 1.86825 × 10
530
u
150
+ ··· + 6.96708 × 10
530
a − 1.05433 × 10
532
, u
152
− u
151
+ ··· − 61u + 3i
I
u
2
= h23135489547260u
41
− 791878135073u
40
+ ··· + 785779145393b − 1057448627428,
− 61366371188204u
41
− 63826689923786u
40
+ ··· + 3928895726965a − 80218304578144,
u
42
+ 23u
40
+ ··· + 26u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 194 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
= h6.78 × 10
529
u
151
− 2.61 × 10
530
u
150
+ · · · + 2.32 × 10
530
b − 7.76 ×
10
530
, 4.01 × 10
530
u
151
− 1.87 × 10
530
u
150
+ · · · + 6.97 × 10
530
a − 1.05 ×
10
532
, u
152
− u
151
+ · · · − 61u + 3i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
1
=
−0.575897u
151
+ 0.268154u
150
+ ··· − 218.578u + 15.1330
−0.291939u
151
+ 1.12230u
150
+ ··· − 58.3679u + 3.33957
a
4
=
1
u
2
a
2
=
−0.188865u
151
− 0.260558u
150
+ ··· − 177.254u + 12.7167
−0.542871u
151
+ 1.76489u
150
+ ··· − 68.1715u + 3.76461
a
10
=
−u
u
a
6
=
u
2
+ 1
−u
2
a
9
=
−1.96213u
151
+ 0.333521u
150
+ ··· − 400.771u + 20.0410
−0.0536691u
151
+ 2.47127u
150
+ ··· + 3.73527u − 1.95372
a
3
=
7.33103u
151
− 6.16852u
150
+ ··· + 1895.49u − 129.107
−0.954188u
151
+ 0.712754u
150
+ ··· + 40.7323u − 2.82961
a
8
=
0.535983u
151
− 0.784566u
150
+ ··· + 77.8051u − 8.33785
0.0700948u
151
+ 0.756951u
150
+ ··· − 52.3469u + 2.24342
a
12
=
−0.203870u
151
− 0.152271u
150
+ ··· − 182.925u + 12.7787
−0.638054u
151
+ 1.71099u
150
+ ··· − 70.1352u + 3.92211
a
7
=
−0.487296u
151
− 0.705863u
150
+ ··· − 34.0215u − 6.18471
−0.0704317u
151
+ 2.34336u
150
+ ··· − 31.4761u + 0.0244434
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0312083u
151
− 1.55714u
150
+ ··· − 167.321u + 31.3804
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
152
− 11u
151
+ ··· + 18140u + 5351
c
2
, c
6
u
152
− u
151
+ ··· + 4353u + 1651
c
3
u
152
− 2u
151
+ ··· + 87u + 7
c
4
, c
5
, c
10
u
152
+ u
151
+ ··· + 61u + 3
c
7
, c
11
u
152
+ 3u
151
+ ··· + 61152u + 8128
c
8
u
152
− u
151
+ ··· + 57030u + 6997
c
9
u
152
− 5u
151
+ ··· + 176391091u + 46936013
c
12
u
152
+ u
151
+ ··· − 347000939u + 62972897
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
152
− 33y
151
+ ··· − 1604598874y + 28633201
c
2
, c
6
y
152
+ 83y
151
+ ··· + 110545925y + 2725801
c
3
y
152
− 10y
151
+ ··· + 3323y + 49
c
4
, c
5
, c
10
y
152
+ 155y
151
+ ··· + 275y + 9
c
7
, c
11
y
152
+ 87y
151
+ ··· + 2765433856y + 66064384
c
8
y
152
+ 3y
151
+ ··· + 3614155020y + 48958009
c
9
y
152
+ 31y
151
+ ··· + 104404411598711997y + 2202989316336169
c
12
y
152
+ 47y
151
+ ··· + 710392624054179195y + 3965585756572609
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.878179 + 0.495642I
a = −0.564021 − 0.738126I
b = −0.752235 + 0.139735I
−0.7060 + 15.2759I 0
u = 0.878179 − 0.495642I
a = −0.564021 + 0.738126I
b = −0.752235 − 0.139735I
−0.7060 − 15.2759I 0
u = −0.886322 + 0.532057I
a = 0.420058 − 0.788913I
b = 0.644080 + 0.199211I
−3.72811 − 8.56360I 0
u = −0.886322 − 0.532057I
a = 0.420058 + 0.788913I
b = 0.644080 − 0.199211I
−3.72811 + 8.56360I 0
u = 0.116120 + 0.945775I
a = 0.457765 + 0.653681I
b = 0.169583 + 0.417592I
−2.65978 − 0.93404I 0
u = 0.116120 − 0.945775I
a = 0.457765 − 0.653681I
b = 0.169583 − 0.417592I
−2.65978 + 0.93404I 0
u = 0.407000 + 1.005930I
a = −0.437541 + 0.247181I
b = 0.810914 + 0.503999I
−1.70138 − 1.08051I 0
u = 0.407000 − 1.005930I
a = −0.437541 − 0.247181I
b = 0.810914 − 0.503999I
−1.70138 + 1.08051I 0
u = −0.742540 + 0.507978I
a = −0.884196 + 0.627862I
b = −0.601044 − 0.139088I
2.69781 − 8.89406I 0
u = −0.742540 − 0.507978I
a = −0.884196 − 0.627862I
b = −0.601044 + 0.139088I
2.69781 + 8.89406I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.833938 + 0.729054I
a = 0.193277 − 0.443729I
b = −0.445113 − 0.516791I
−1.33475 − 9.55748I 0
u = 0.833938 − 0.729054I
a = 0.193277 + 0.443729I
b = −0.445113 + 0.516791I
−1.33475 + 9.55748I 0
u = 0.788215 + 0.402245I
a = −0.397730 − 0.625511I
b = −0.252690 − 0.409109I
−3.76675 + 2.08728I 0
u = 0.788215 − 0.402245I
a = −0.397730 + 0.625511I
b = −0.252690 + 0.409109I
−3.76675 − 2.08728I 0
u = −0.430313 + 1.040840I
a = 0.505748 + 0.188593I
b = 0.216466 − 0.014818I
−2.69394 − 0.61392I 0
u = −0.430313 − 1.040840I
a = 0.505748 − 0.188593I
b = 0.216466 + 0.014818I
−2.69394 + 0.61392I 0
u = −0.718800 + 0.496615I
a = 0.239945 + 0.250970I
b = −0.306341 + 0.691719I
2.65155 + 4.05569I 0
u = −0.718800 − 0.496615I
a = 0.239945 − 0.250970I
b = −0.306341 − 0.691719I
2.65155 − 4.05569I 0
u = 0.765332 + 0.836222I
a = −0.496086 + 0.021099I
b = −0.410884 − 0.209396I
−3.70871 + 3.30219I 0
u = 0.765332 − 0.836222I
a = −0.496086 − 0.021099I
b = −0.410884 + 0.209396I
−3.70871 − 3.30219I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.866630 + 0.737689I
a = −0.257202 − 0.440095I
b = 0.595072 − 0.290409I
−4.23349 + 2.67967I 0
u = −0.866630 − 0.737689I
a = −0.257202 + 0.440095I
b = 0.595072 + 0.290409I
−4.23349 − 2.67967I 0
u = −0.798518 + 0.321414I
a = −0.403875 + 0.708676I
b = −0.678022 − 0.341985I
3.00753 − 0.46886I 0
u = −0.798518 − 0.321414I
a = −0.403875 − 0.708676I
b = −0.678022 + 0.341985I
3.00753 + 0.46886I 0
u = 0.010639 + 1.150670I
a = −0.122608 − 0.168471I
b = 0.389426 + 1.074840I
−1.53894 − 1.47676I 0
u = 0.010639 − 1.150670I
a = −0.122608 + 0.168471I
b = 0.389426 − 1.074840I
−1.53894 + 1.47676I 0
u = −0.670173 + 0.936099I
a = 0.182741 + 0.438576I
b = −0.168191 + 0.197395I
1.30622 − 4.56377I 0
u = −0.670173 − 0.936099I
a = 0.182741 − 0.438576I
b = −0.168191 − 0.197395I
1.30622 + 4.56377I 0
u = 0.885952 + 0.738183I
a = −0.031977 − 0.485715I
b = −0.452412 + 0.243336I
4.23346 + 3.17237I 0
u = 0.885952 − 0.738183I
a = −0.031977 + 0.485715I
b = −0.452412 − 0.243336I
4.23346 − 3.17237I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.632233 + 0.513263I
a = −0.939088 − 0.272049I
b = −0.621434 − 0.417344I
−4.29681 + 2.42359I 0
u = 0.632233 − 0.513263I
a = −0.939088 + 0.272049I
b = −0.621434 + 0.417344I
−4.29681 − 2.42359I 0
u = −0.205898 + 1.186000I
a = −0.582756 + 0.982859I
b = 0.447247 + 0.094284I
−1.65459 + 3.47179I 0
u = −0.205898 − 1.186000I
a = −0.582756 − 0.982859I
b = 0.447247 − 0.094284I
−1.65459 − 3.47179I 0
u = −1.139650 + 0.433163I
a = 0.116838 − 0.194203I
b = 0.262431 − 0.162027I
0.03737 − 5.44081I 0
u = −1.139650 − 0.433163I
a = 0.116838 + 0.194203I
b = 0.262431 + 0.162027I
0.03737 + 5.44081I 0
u = 0.410672 + 0.652255I
a = −0.293315 − 0.129450I
b = −0.508365 + 0.769709I
4.54413 + 3.63997I 0
u = 0.410672 − 0.652255I
a = −0.293315 + 0.129450I
b = −0.508365 − 0.769709I
4.54413 − 3.63997I 0
u = 0.652917 + 0.400077I
a = 0.875931 + 0.919214I
b = 0.587310 − 0.280434I
−0.37881 + 4.59426I 0
u = 0.652917 − 0.400077I
a = 0.875931 − 0.919214I
b = 0.587310 + 0.280434I
−0.37881 − 4.59426I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.129057 + 0.740489I
a = −0.559667 + 0.791209I
b = 1.23420 − 0.86120I
−3.38245 − 1.15411I 0
u = 0.129057 − 0.740489I
a = −0.559667 − 0.791209I
b = 1.23420 + 0.86120I
−3.38245 + 1.15411I 0
u = 0.154921 + 1.244210I
a = 1.49381 + 0.02502I
b = −1.42953 − 0.41635I
−3.34546 + 5.16441I 0
u = 0.154921 − 1.244210I
a = 1.49381 − 0.02502I
b = −1.42953 + 0.41635I
−3.34546 − 5.16441I 0
u = 0.731029 + 0.077477I
a = −0.292731 − 0.205590I
b = 0.480046 + 0.669669I
0.06364 − 2.09801I 0
u = 0.731029 − 0.077477I
a = −0.292731 + 0.205590I
b = 0.480046 − 0.669669I
0.06364 + 2.09801I 0
u = −0.698365 + 0.208979I
a = −0.248960 − 1.215250I
b = −0.079980 − 0.434451I
−1.64281 + 2.39766I 0
u = −0.698365 − 0.208979I
a = −0.248960 + 1.215250I
b = −0.079980 + 0.434451I
−1.64281 − 2.39766I 0
u = 0.070858 + 1.275140I
a = 2.26182 + 0.52413I
b = −3.71114 − 0.78285I
−1.83616 + 7.02854I 0
u = 0.070858 − 1.275140I
a = 2.26182 − 0.52413I
b = −3.71114 + 0.78285I
−1.83616 − 7.02854I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.410942 + 0.550754I
a = 0.774903 − 1.136430I
b = 0.112360 − 0.223213I
4.73178 − 0.42762I 0
u = 0.410942 − 0.550754I
a = 0.774903 + 1.136430I
b = 0.112360 + 0.223213I
4.73178 + 0.42762I 0
u = −0.115670 + 1.319870I
a = −1.36451 + 0.88061I
b = 2.23719 − 0.43979I
−4.80210 − 4.79919I 0
u = −0.115670 − 1.319870I
a = −1.36451 − 0.88061I
b = 2.23719 + 0.43979I
−4.80210 + 4.79919I 0
u = 0.208472 + 1.310300I
a = 0.89939 + 1.17267I
b = −1.58138 − 1.27280I
−6.08306 + 0.50528I 0
u = 0.208472 − 1.310300I
a = 0.89939 − 1.17267I
b = −1.58138 + 1.27280I
−6.08306 − 0.50528I 0
u = −0.508578 + 0.431740I
a = 1.248810 + 0.056768I
b = 1.009340 − 0.226090I
−2.52055 − 5.73891I 0
u = −0.508578 − 0.431740I
a = 1.248810 − 0.056768I
b = 1.009340 + 0.226090I
−2.52055 + 5.73891I 0
u = −0.133462 + 1.331980I
a = −2.90036 − 0.13099I
b = 3.26439 + 0.50437I
−2.23942 − 8.63079I 0
u = −0.133462 − 1.331980I
a = −2.90036 + 0.13099I
b = 3.26439 − 0.50437I
−2.23942 + 8.63079I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.033696 + 1.350720I
a = 1.70640 − 0.85038I
b = −2.82792 + 1.64885I
−0.265313 − 0.091703I 0
u = 0.033696 − 1.350720I
a = 1.70640 + 0.85038I
b = −2.82792 − 1.64885I
−0.265313 + 0.091703I 0
u = 0.606994 + 0.220097I
a = 0.89141 + 1.16253I
b = 0.933696 − 0.308841I
−0.49470 + 3.84426I 0
u = 0.606994 − 0.220097I
a = 0.89141 − 1.16253I
b = 0.933696 + 0.308841I
−0.49470 − 3.84426I 0
u = 0.642477 + 0.029689I
a = 0.48324 − 2.08567I
b = 0.310626 + 0.240849I
1.51598 − 4.61783I 7.58913 + 6.56112I
u = 0.642477 − 0.029689I
a = 0.48324 + 2.08567I
b = 0.310626 − 0.240849I
1.51598 + 4.61783I 7.58913 − 6.56112I
u = −0.115573 + 1.361180I
a = −1.58752 + 0.07873I
b = 2.50751 + 0.05649I
−3.72991 − 2.68509I 0
u = −0.115573 − 1.361180I
a = −1.58752 − 0.07873I
b = 2.50751 − 0.05649I
−3.72991 + 2.68509I 0
u = 0.001948 + 1.367560I
a = −0.634661 − 1.006570I
b = 0.565920 + 0.136836I
−0.09493 − 3.07336I 0
u = 0.001948 − 1.367560I
a = −0.634661 + 1.006570I
b = 0.565920 − 0.136836I
−0.09493 + 3.07336I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.314984 + 0.538551I
a = 0.411245 + 0.685565I
b = −1.51127 − 0.96772I
−0.56290 + 7.37137I −3.06670 − 12.47022I
u = 0.314984 − 0.538551I
a = 0.411245 − 0.685565I
b = −1.51127 + 0.96772I
−0.56290 − 7.37137I −3.06670 + 12.47022I
u = −0.184310 + 1.363750I
a = −1.44372 + 0.49130I
b = 2.33228 − 1.00507I
−3.12222 − 3.03364I 0
u = −0.184310 − 1.363750I
a = −1.44372 − 0.49130I
b = 2.33228 + 1.00507I
−3.12222 + 3.03364I 0
u = 0.037332 + 1.388960I
a = −0.202938 − 0.969776I
b = 0.46607 + 2.80907I
−0.46634 + 1.58117I 0
u = 0.037332 − 1.388960I
a = −0.202938 + 0.969776I
b = 0.46607 − 2.80907I
−0.46634 − 1.58117I 0
u = −0.538277 + 0.262771I
a = −0.50775 + 1.86121I
b = −0.204069 − 0.084432I
1.97803 − 0.38146I 5.59987 + 4.41528I
u = −0.538277 − 0.262771I
a = −0.50775 − 1.86121I
b = −0.204069 + 0.084432I
1.97803 + 0.38146I 5.59987 − 4.41528I
u = 0.060103 + 1.402450I
a = −2.24427 + 0.88372I
b = 2.67619 − 1.09906I
−1.05714 + 4.17647I 0
u = 0.060103 − 1.402450I
a = −2.24427 − 0.88372I
b = 2.67619 + 1.09906I
−1.05714 − 4.17647I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.424518 + 0.417116I
a = −0.126083 + 0.185627I
b = −0.994890 + 0.501376I
1.37417 − 2.63932I 1.62166 + 6.27105I
u = −0.424518 − 0.417116I
a = −0.126083 − 0.185627I
b = −0.994890 − 0.501376I
1.37417 + 2.63932I 1.62166 − 6.27105I
u = 0.230894 + 1.392570I
a = 2.28908 + 0.15368I
b = −3.24032 + 0.31085I
−5.66371 + 6.89455I 0
u = 0.230894 − 1.392570I
a = 2.28908 − 0.15368I
b = −3.24032 − 0.31085I
−5.66371 − 6.89455I 0
u = 0.02625 + 1.41853I
a = 1.66091 + 1.08394I
b = −2.30521 − 0.97878I
−6.80026 − 0.18763I 0
u = 0.02625 − 1.41853I
a = 1.66091 − 1.08394I
b = −2.30521 + 0.97878I
−6.80026 + 0.18763I 0
u = 0.08600 + 1.41972I
a = 0.283142 + 0.341148I
b = −0.38647 − 1.70858I
−6.76026 + 4.33959I 0
u = 0.08600 − 1.41972I
a = 0.283142 − 0.341148I
b = −0.38647 + 1.70858I
−6.76026 − 4.33959I 0
u = −0.14412 + 1.42704I
a = −1.50627 + 0.96619I
b = 2.16922 − 0.64576I
−4.51801 − 4.72556I 0
u = −0.14412 − 1.42704I
a = −1.50627 − 0.96619I
b = 2.16922 + 0.64576I
−4.51801 + 4.72556I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.11819 + 1.43236I
a = −0.445663 + 0.854091I
b = 0.91778 − 2.49354I
−4.84175 − 9.29715I 0
u = −0.11819 − 1.43236I
a = −0.445663 − 0.854091I
b = 0.91778 + 2.49354I
−4.84175 + 9.29715I 0
u = −0.552765 + 0.014313I
a = −0.551912 + 0.994139I
b = −1.33289 − 0.60978I
1.92935 − 6.33185I 7.17773 + 7.64906I
u = −0.552765 − 0.014313I
a = −0.551912 − 0.994139I
b = −1.33289 + 0.60978I
1.92935 + 6.33185I 7.17773 − 7.64906I
u = −0.02545 + 1.44803I
a = −0.857855 − 0.915020I
b = 1.379970 + 0.195468I
−7.80468 + 0.57106I 0
u = −0.02545 − 1.44803I
a = −0.857855 + 0.915020I
b = 1.379970 − 0.195468I
−7.80468 − 0.57106I 0
u = 0.265503 + 0.474764I
a = 0.044541 + 0.548942I
b = 0.493979 + 0.594564I
−1.19022 − 1.06033I −1.73863 + 1.28370I
u = 0.265503 − 0.474764I
a = 0.044541 − 0.548942I
b = 0.493979 − 0.594564I
−1.19022 + 1.06033I −1.73863 − 1.28370I
u = 0.08657 + 1.45661I
a = 1.79739 − 0.84767I
b = −2.52447 + 0.59620I
−7.94583 + 5.57874I 0
u = 0.08657 − 1.45661I
a = 1.79739 + 0.84767I
b = −2.52447 − 0.59620I
−7.94583 − 5.57874I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.28382 + 1.43940I
a = −1.78343 + 0.10037I
b = 2.50470 + 0.23320I
−2.63550 − 4.32707I 0
u = −0.28382 − 1.43940I
a = −1.78343 − 0.10037I
b = 2.50470 − 0.23320I
−2.63550 + 4.32707I 0
u = −0.32556 + 1.43576I
a = 0.786718 − 0.659743I
b = −1.61784 + 0.97399I
−6.90278 − 1.49526I 0
u = −0.32556 − 1.43576I
a = 0.786718 + 0.659743I
b = −1.61784 − 0.97399I
−6.90278 + 1.49526I 0
u = −0.19290 + 1.46908I
a = 1.95452 − 0.08392I
b = −3.03246 − 0.75220I
−8.68740 − 8.37475I 0
u = −0.19290 − 1.46908I
a = 1.95452 + 0.08392I
b = −3.03246 + 0.75220I
−8.68740 + 8.37475I 0
u = −0.492386 + 0.154953I
a = −1.074880 + 0.699992I
b = −0.280796 − 0.145558I
1.040050 − 0.549467I 7.43364 + 2.00474I
u = −0.492386 − 0.154953I
a = −1.074880 − 0.699992I
b = −0.280796 + 0.145558I
1.040050 + 0.549467I 7.43364 − 2.00474I
u = 0.23108 + 1.48576I
a = 1.88952 − 0.11064I
b = −2.90807 + 0.43693I
−6.55064 + 7.81946I 0
u = 0.23108 − 1.48576I
a = 1.88952 + 0.11064I
b = −2.90807 − 0.43693I
−6.55064 − 7.81946I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.22737 + 1.49355I
a = −1.69122 − 0.29947I
b = 3.00950 − 0.23740I
−10.78190 + 5.59014I 0
u = 0.22737 − 1.49355I
a = −1.69122 + 0.29947I
b = 3.00950 + 0.23740I
−10.78190 − 5.59014I 0
u = 0.12929 + 1.51346I
a = −1.47261 − 1.46945I
b = 1.90290 + 1.11091I
−7.32672 + 9.14085I 0
u = 0.12929 − 1.51346I
a = −1.47261 + 1.46945I
b = 1.90290 − 1.11091I
−7.32672 − 9.14085I 0
u = −0.26396 + 1.52000I
a = −1.78890 − 0.10389I
b = 2.87925 + 0.58891I
−3.90420 − 12.58760I 0
u = −0.26396 − 1.52000I
a = −1.78890 + 0.10389I
b = 2.87925 − 0.58891I
−3.90420 + 12.58760I 0
u = 0.30619 + 1.51476I
a = −1.104380 − 0.300115I
b = 2.02876 + 0.09939I
−10.02160 + 6.17791I 0
u = 0.30619 − 1.51476I
a = −1.104380 + 0.300115I
b = 2.02876 − 0.09939I
−10.02160 − 6.17791I 0
u = −0.11442 + 1.55249I
a = 1.63445 + 0.36014I
b = −2.66201 − 0.79590I
−10.77330 − 2.23854I 0
u = −0.11442 − 1.55249I
a = 1.63445 − 0.36014I
b = −2.66201 + 0.79590I
−10.77330 + 2.23854I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.31801 + 1.53267I
a = −1.80409 − 0.05058I
b = 2.84291 − 0.42225I
−7.2738 + 19.6356I 0
u = 0.31801 − 1.53267I
a = −1.80409 + 0.05058I
b = 2.84291 + 0.42225I
−7.2738 − 19.6356I 0
u = −0.340179 + 0.267909I
a = 0.92686 + 4.13715I
b = 0.350396 − 0.479965I
0.73173 − 7.59496I 6.6801 + 14.7598I
u = −0.340179 − 0.267909I
a = 0.92686 − 4.13715I
b = 0.350396 + 0.479965I
0.73173 + 7.59496I 6.6801 − 14.7598I
u = −0.31033 + 1.54831I
a = 1.74043 − 0.02740I
b = −2.71337 − 0.30230I
−10.4891 − 12.9239I 0
u = −0.31033 − 1.54831I
a = 1.74043 + 0.02740I
b = −2.71337 + 0.30230I
−10.4891 + 12.9239I 0
u = 0.18932 + 1.57314I
a = −1.47951 + 0.14267I
b = 2.55432 − 0.66789I
−11.56050 + 6.53889I 0
u = 0.18932 − 1.57314I
a = −1.47951 − 0.14267I
b = 2.55432 + 0.66789I
−11.56050 − 6.53889I 0
u = 0.43712 + 1.52509I
a = 0.431883 + 0.353741I
b = −0.880671 − 0.091812I
−4.61601 + 2.57585I 0
u = 0.43712 − 1.52509I
a = 0.431883 − 0.353741I
b = −0.880671 + 0.091812I
−4.61601 − 2.57585I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.218003 + 0.343210I
a = 1.79163 + 1.71915I
b = 0.294126 − 1.004280I
−2.02235 + 4.35269I −5.29583 − 7.76813I
u = 0.218003 − 0.343210I
a = 1.79163 − 1.71915I
b = 0.294126 + 1.004280I
−2.02235 − 4.35269I −5.29583 + 7.76813I
u = 0.25378 + 1.57679I
a = −1.64001 + 0.07609I
b = 2.32855 − 0.32581I
−3.33192 + 7.07748I 0
u = 0.25378 − 1.57679I
a = −1.64001 − 0.07609I
b = 2.32855 + 0.32581I
−3.33192 − 7.07748I 0
u = −0.36055 + 1.55612I
a = 0.926293 − 0.076577I
b = −1.56139 − 0.28853I
−6.53626 − 10.66010I 0
u = −0.36055 − 1.55612I
a = 0.926293 + 0.076577I
b = −1.56139 + 0.28853I
−6.53626 + 10.66010I 0
u = 0.340672 + 0.177792I
a = −2.03903 + 2.59056I
b = −0.069538 − 0.656597I
−1.50489 + 2.93196I 2.99677 − 7.01707I
u = 0.340672 − 0.177792I
a = −2.03903 − 2.59056I
b = −0.069538 + 0.656597I
−1.50489 − 2.93196I 2.99677 + 7.01707I
u = −0.23493 + 1.61887I
a = −0.663396 + 0.127693I
b = 1.227330 + 0.158733I
−4.12564 − 0.03704I 0
u = −0.23493 − 1.61887I
a = −0.663396 − 0.127693I
b = 1.227330 − 0.158733I
−4.12564 + 0.03704I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.01307 + 1.63907I
a = 2.30072 − 0.44773I
b = −2.75483 + 0.37032I
−11.69300 − 0.79290I 0
u = 0.01307 − 1.63907I
a = 2.30072 + 0.44773I
b = −2.75483 − 0.37032I
−11.69300 + 0.79290I 0
u = −0.16494 + 1.63396I
a = 1.346350 − 0.410304I
b = −1.96191 + 0.28987I
−12.55620 − 1.07655I 0
u = −0.16494 − 1.63396I
a = 1.346350 + 0.410304I
b = −1.96191 − 0.28987I
−12.55620 + 1.07655I 0
u = 0.15328 + 1.64996I
a = −1.058120 − 0.378769I
b = 1.73895 + 0.34299I
−9.68133 − 5.83768I 0
u = 0.15328 − 1.64996I
a = −1.058120 + 0.378769I
b = 1.73895 − 0.34299I
−9.68133 + 5.83768I 0
u = 0.119912 + 0.155928I
a = −2.47635 + 1.11465I
b = −0.89605 + 1.13124I
4.12384 + 3.28383I 16.8921 + 6.2759I
u = 0.119912 − 0.155928I
a = −2.47635 − 1.11465I
b = −0.89605 − 1.13124I
4.12384 − 3.28383I 16.8921 − 6.2759I
u = 0.175566 + 0.025621I
a = 9.92478 + 2.46534I
b = 0.199847 − 0.442604I
4.18707 − 0.94466I 27.0614 + 1.9119I
u = 0.175566 − 0.025621I
a = 9.92478 − 2.46534I
b = 0.199847 + 0.442604I
4.18707 + 0.94466I 27.0614 − 1.9119I
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.010212 + 0.164492I
a = −4.26471 + 3.76365I
b = 0.090393 − 1.315380I
−2.25214 + 0.78070I −2.04391 − 5.83531I
u = 0.010212 − 0.164492I
a = −4.26471 − 3.76365I
b = 0.090393 + 1.315380I
−2.25214 − 0.78070I −2.04391 + 5.83531I
20
II. I
u
2
= h2.31 × 10
13
u
41
− 7.92 × 10
11
u
40
+ · · · + 7.86 × 10
11
b − 1.06 ×
10
12
, −6.14 × 10
13
u
41
− 6.38 × 10
13
u
40
+ · · · + 3.93 × 10
12
a − 8.02 ×
10
13
, u
42
+ 23u
40
+ · · · + 26u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
1
=
15.6192u
41
+ 16.2455u
40
+ ··· − 47.7102u + 20.4175
−29.4427u
41
+ 1.00776u
40
+ ··· − 19.6900u + 1.34573
a
4
=
1
u
2
a
2
=
10.9487u
41
− 10.6897u
40
+ ··· − 43.6395u + 2.82633
−21.3908u
41
+ 45.2751u
40
+ ··· − 15.0194u + 28.2809
a
10
=
−u
u
a
6
=
u
2
+ 1
−u
2
a
9
=
1.63053u
41
+ 0.627881u
40
+ ··· + 129.162u + 11.4087
3.66978u
41
+ 13.5200u
40
+ ··· − 5.27254u + 3.61399
a
3
=
−10.3342u
41
− 3.09895u
40
+ ··· − 50.4279u + 43.4124
2.70720u
41
− 16.2755u
40
+ ··· + 11.2746u − 12.3321
a
8
=
7.06947u
41
+ 8.15144u
40
+ ··· + 34.0855u − 0.616606
−47.6337u
41
+ 4.81822u
40
+ ··· − 22.5279u + 5.80141
a
12
=
7.49855u
41
+ 0.306910u
40
+ ··· − 54.5927u + 13.2781
−8.57309u
41
+ 39.9932u
40
+ ··· − 6.94100u + 24.3927
a
7
=
28.0565u
41
− 10.8251u
40
+ ··· + 166.570u − 23.6621
−43.2211u
41
+ 10.6470u
40
+ ··· − 19.2851u + 10.3383
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
384710007573457
3928895726965
u
41
+
356383672834697
3928895726965
u
40
+ ··· −
888254720949903
3928895726965
u +
259826274734503
3928895726965
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
42
− 4u
41
+ ··· − u + 1
c
2
u
42
+ 2u
41
+ ··· − 2u + 1
c
3
u
42
+ 3u
41
+ ··· + 14u
2
+ 1
c
4
, c
5
u
42
+ 23u
40
+ ··· + 26u
2
+ 1
c
6
u
42
− 2u
41
+ ··· + 2u + 1
c
7
u
42
− 4u
41
+ ··· − 2u + 1
c
8
u
42
− u
40
+ ··· − 69u + 7
c
9
u
42
− 2u
41
+ ··· − 2u + 1
c
10
u
42
+ 23u
40
+ ··· + 26u
2
+ 1
c
11
u
42
+ 4u
41
+ ··· + 2u + 1
c
12
u
42
+ u
40
+ ··· + 178u + 29
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
42
− 22y
41
+ ··· + 3y + 1
c
2
, c
6
y
42
+ 26y
41
+ ··· + 38y + 1
c
3
y
42
− 3y
41
+ ··· + 28y + 1
c
4
, c
5
, c
10
y
42
+ 46y
41
+ ··· + 52y + 1
c
7
, c
11
y
42
+ 22y
41
+ ··· + 40y + 1
c
8
y
42
− 2y
41
+ ··· − 1667y + 49
c
9
y
42
− 10y
41
+ ··· + 10y + 1
c
12
y
42
+ 2y
41
+ ··· − 37136y + 841
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.935015 + 0.465202I
a = 0.115614 + 0.136661I
b = 0.320022 − 0.356603I
0.21293 − 5.19650I 0
u = −0.935015 − 0.465202I
a = 0.115614 − 0.136661I
b = 0.320022 + 0.356603I
0.21293 + 5.19650I 0
u = 0.771341 + 0.782004I
a = −0.026030 + 0.497950I
b = 0.349444 − 0.411143I
4.40215 + 2.91947I 0
u = 0.771341 − 0.782004I
a = −0.026030 − 0.497950I
b = 0.349444 + 0.411143I
4.40215 − 2.91947I 0
u = −0.108321 + 1.107080I
a = −0.090588 + 0.733855I
b = −0.328593 + 0.158640I
−3.15399 + 1.89664I 0
u = −0.108321 − 1.107080I
a = −0.090588 − 0.733855I
b = −0.328593 − 0.158640I
−3.15399 − 1.89664I 0
u = 0.592481 + 0.653798I
a = −0.902488 + 0.113630I
b = −0.482784 − 0.296539I
−3.66950 + 2.80930I 1.88360 − 2.35805I
u = 0.592481 − 0.653798I
a = −0.902488 − 0.113630I
b = −0.482784 + 0.296539I
−3.66950 − 2.80930I 1.88360 + 2.35805I
u = −0.349342 + 0.709873I
a = 0.692030 + 0.789837I
b = −0.854993 + 0.014237I
−2.66470 + 1.94037I −2.85084 − 4.39177I
u = −0.349342 − 0.709873I
a = 0.692030 − 0.789837I
b = −0.854993 − 0.014237I
−2.66470 − 1.94037I −2.85084 + 4.39177I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.115958 + 1.230030I
a = −1.113570 + 0.783199I
b = 1.24627 − 1.59867I
−4.55864 − 3.39138I 0
u = −0.115958 − 1.230030I
a = −1.113570 − 0.783199I
b = 1.24627 + 1.59867I
−4.55864 + 3.39138I 0
u = 0.347078 + 0.660872I
a = 0.319103 + 0.415281I
b = −0.817409 − 1.037710I
−2.66609 + 0.11927I −3.66928 − 0.85360I
u = 0.347078 − 0.660872I
a = 0.319103 − 0.415281I
b = −0.817409 + 1.037710I
−2.66609 − 0.11927I −3.66928 + 0.85360I
u = 0.025342 + 1.283740I
a = 0.82018 + 1.25199I
b = −0.720513 − 0.417969I
0.74966 − 2.90451I 0
u = 0.025342 − 1.283740I
a = 0.82018 − 1.25199I
b = −0.720513 + 0.417969I
0.74966 + 2.90451I 0
u = 0.044937 + 1.298130I
a = 2.40556 + 0.77309I
b = −3.15938 − 1.42777I
−2.75956 + 7.26572I 0
u = 0.044937 − 1.298130I
a = 2.40556 − 0.77309I
b = −3.15938 + 1.42777I
−2.75956 − 7.26572I 0
u = 0.000361 + 1.321850I
a = 0.795975 − 1.125190I
b = −1.20695 + 2.78665I
0.313348 − 0.976815I 0
u = 0.000361 − 1.321850I
a = 0.795975 + 1.125190I
b = −1.20695 − 2.78665I
0.313348 + 0.976815I 0
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.387652 + 1.337110I
a = 0.340284 + 0.622325I
b = −0.928475 − 0.324657I
−4.31023 + 2.76338I 0
u = 0.387652 − 1.337110I
a = 0.340284 − 0.622325I
b = −0.928475 + 0.324657I
−4.31023 − 2.76338I 0
u = −0.210164 + 1.383040I
a = −2.35128 + 0.08957I
b = 3.36733 + 0.32066I
−5.44686 − 7.42912I 0
u = −0.210164 − 1.383040I
a = −2.35128 − 0.08957I
b = 3.36733 − 0.32066I
−5.44686 + 7.42912I 0
u = −0.572535 + 0.163270I
a = −0.92308 + 1.57770I
b = −0.823254 − 0.347001I
−0.47081 − 4.61351I 2.78514 + 10.91680I
u = −0.572535 − 0.163270I
a = −0.92308 − 1.57770I
b = −0.823254 + 0.347001I
−0.47081 + 4.61351I 2.78514 − 10.91680I
u = 0.20693 + 1.47466I
a = 2.00546 − 0.10822I
b = −2.59345 + 0.36187I
−2.60937 + 5.63813I 0
u = 0.20693 − 1.47466I
a = 2.00546 + 0.10822I
b = −2.59345 − 0.36187I
−2.60937 − 5.63813I 0
u = −0.15915 + 1.50804I
a = 1.010670 − 0.397754I
b = −1.39829 − 0.26811I
−6.75553 − 8.30096I 0
u = −0.15915 − 1.50804I
a = 1.010670 + 0.397754I
b = −1.39829 + 0.26811I
−6.75553 + 8.30096I 0
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.21652 + 1.50524I
a = −1.66092 − 0.10940I
b = 2.94978 − 0.49926I
−10.49650 + 5.82710I 0
u = 0.21652 − 1.50524I
a = −1.66092 + 0.10940I
b = 2.94978 + 0.49926I
−10.49650 − 5.82710I 0
u = −0.33537 + 1.50022I
a = −0.573970 + 0.350488I
b = 1.185250 − 0.252318I
−3.84925 − 0.42432I 0
u = −0.33537 − 1.50022I
a = −0.573970 − 0.350488I
b = 1.185250 + 0.252318I
−3.84925 + 0.42432I 0
u = 0.180136 + 0.404802I
a = 0.378500 − 0.058856I
b = 0.844088 − 1.097650I
3.90096 + 3.42102I −9.67445 − 9.04128I
u = 0.180136 − 0.404802I
a = 0.378500 + 0.058856I
b = 0.844088 + 1.097650I
3.90096 − 3.42102I −9.67445 + 9.04128I
u = 0.033288 + 0.418528I
a = −2.27110 + 1.88742I
b = 1.142650 − 0.260930I
0.45843 − 6.85842I 2.68810 + 5.24695I
u = 0.033288 − 0.418528I
a = −2.27110 − 1.88742I
b = 1.142650 + 0.260930I
0.45843 + 6.85842I 2.68810 − 5.24695I
u = −0.01678 + 1.65584I
a = −2.19647 − 0.32527I
b = 2.64227 + 0.24069I
−11.59210 + 0.83440I 0
u = −0.01678 − 1.65584I
a = −2.19647 + 0.32527I
b = 2.64227 − 0.24069I
−11.59210 − 0.83440I 0
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.003438 + 0.292839I
a = −1.77389 − 5.30385I
b = 0.266969 − 0.128098I
3.97276 + 0.97275I −10.60321 − 7.45587I
u = −0.003438 − 0.292839I
a = −1.77389 + 5.30385I
b = 0.266969 + 0.128098I
3.97276 − 0.97275I −10.60321 + 7.45587I
28
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
42
− 4u
41
+ ··· − u + 1)(u
152
− 11u
151
+ ··· + 18140u + 5351)
c
2
(u
42
+ 2u
41
+ ··· − 2u + 1)(u
152
− u
151
+ ··· + 4353u + 1651)
c
3
(u
42
+ 3u
41
+ ··· + 14u
2
+ 1)(u
152
− 2u
151
+ ··· + 87u + 7)
c
4
, c
5
(u
42
+ 23u
40
+ ··· + 26u
2
+ 1)(u
152
+ u
151
+ ··· + 61u + 3)
c
6
(u
42
− 2u
41
+ ··· + 2u + 1)(u
152
− u
151
+ ··· + 4353u + 1651)
c
7
(u
42
− 4u
41
+ ··· − 2u + 1)(u
152
+ 3u
151
+ ··· + 61152u + 8128)
c
8
(u
42
− u
40
+ ··· − 69u + 7)(u
152
− u
151
+ ··· + 57030u + 6997)
c
9
(u
42
− 2u
41
+ ··· − 2u + 1)
· (u
152
− 5u
151
+ ··· + 176391091u + 46936013)
c
10
(u
42
+ 23u
40
+ ··· + 26u
2
+ 1)(u
152
+ u
151
+ ··· + 61u + 3)
c
11
(u
42
+ 4u
41
+ ··· + 2u + 1)(u
152
+ 3u
151
+ ··· + 61152u + 8128)
c
12
(u
42
+ u
40
+ ··· + 178u + 29)
· (u
152
+ u
151
+ ··· − 347000939u + 62972897)
29
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
42
− 22y
41
+ ··· + 3y + 1)
· (y
152
− 33y
151
+ ··· − 1604598874y + 28633201)
c
2
, c
6
(y
42
+ 26y
41
+ ··· + 38y + 1)
· (y
152
+ 83y
151
+ ··· + 110545925y + 2725801)
c
3
(y
42
− 3y
41
+ ··· + 28y + 1)(y
152
− 10y
151
+ ··· + 3323y + 49)
c
4
, c
5
, c
10
(y
42
+ 46y
41
+ ··· + 52y + 1)(y
152
+ 155y
151
+ ··· + 275y + 9)
c
7
, c
11
(y
42
+ 22y
41
+ ··· + 40y + 1)
· (y
152
+ 87y
151
+ ··· + 2765433856y + 66064384)
c
8
(y
42
− 2y
41
+ ··· − 1667y + 49)
· (y
152
+ 3y
151
+ ··· + 3614155020y + 48958009)
c
9
(y
42
− 10y
41
+ ··· + 10y + 1)
· (y
152
+ 31y
151
+ ··· + 104404411598711997y + 2202989316336169)
c
12
(y
42
+ 2y
41
+ ··· − 37136y + 841)
· (y
152
+ 47y
151
+ ··· + 710392624054179195y + 3965585756572609)
30
