12n
0408
(K12n
0408
)
A knot diagram
1
Linearized knot diagam
3 6 8 12 2 9 12 5 1 7 5 10
Solving Sequence
7,12 5,8
9 4 3 6 2 11 10 1
c
7
c
8
c
4
c
3
c
6
c
2
c
11
c
10
c
12
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h3.32134 × 10
359
u
70
− 4.44408 × 10
359
u
69
+ ··· + 2.07193 × 10
364
b − 6.03914 × 10
363
,
− 2.44678 × 10
364
u
70
+ 4.95782 × 10
364
u
69
+ ··· + 1.09626 × 10
368
a + 4.70274 × 10
368
,
u
71
− 2u
70
+ ··· − 50760u + 5291i
I
u
2
= h−1.01666 × 10
17
u
20
− 3.63265 × 10
17
u
19
+ ··· + 1.76908 × 10
18
b − 7.59833 × 10
17
,
− 2.78942 × 10
18
u
20
− 2.28690 × 10
18
u
19
+ ··· + 5.30723 × 10
18
a − 3.58565 × 10
18
, u
21
+ u
20
+ ··· + u + 3i
* 2 irreducible components of dim
C
= 0, with total 92 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
= h3.32 × 10
359
u
70
− 4.44 × 10
359
u
69
+ · · · + 2.07 × 10
364
b − 6.04 ×
10
363
, −2.45 × 10
364
u
70
+ 4.96 × 10
364
u
69
+ · · · + 1.10 × 10
368
a + 4.70 ×
10
368
, u
71
− 2u
70
+ · · · − 50760u + 5291i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
5
=
0.000223193u
70
− 0.000452249u
69
+ ··· + 29.0701u − 4.28980
−0.0000160301u
70
+ 0.0000214489u
69
+ ··· + 1.55560u + 0.291474
a
8
=
1
−u
2
a
9
=
−0.000108414u
70
+ 0.000231215u
69
+ ··· − 26.9057u + 3.05037
0.0000349665u
70
− 0.0000665424u
69
+ ··· − 0.330042u + 0.239270
a
4
=
0.000223193u
70
− 0.000452249u
69
+ ··· + 29.0701u − 4.28980
−4.77057 × 10
−6
u
70
− 4.55792 × 10
−6
u
69
+ ··· + 3.03409u + 0.260456
a
3
=
0.000239223u
70
− 0.000473698u
69
+ ··· + 27.5145u − 4.58128
−4.53515 × 10
−6
u
70
− 5.71553 × 10
−6
u
69
+ ··· + 2.58027u + 0.316601
a
6
=
−0.0000654430u
70
+ 0.000121036u
69
+ ··· + 2.03966u + 1.27408
−0.0000373474u
70
+ 0.0000850284u
69
+ ··· − 4.95248u + 0.211483
a
2
=
0.000128361u
70
− 0.000267216u
69
+ ··· + 30.3146u − 3.65679
−0.0000243416u
70
+ 0.0000407389u
69
+ ··· − 2.19710u + 0.550891
a
11
=
−0.0000513840u
70
+ 0.0000471219u
69
+ ··· + 9.13849u − 0.0700090
−0.0000138702u
70
+ 0.0000242156u
69
+ ··· + 7.00547u − 0.868044
a
10
=
−0.0000375138u
70
+ 0.0000229063u
69
+ ··· + 2.13303u + 0.798035
−0.0000138702u
70
+ 0.0000242156u
69
+ ··· + 7.00547u − 0.868044
a
1
=
−0.000128274u
70
+ 0.000225121u
69
+ ··· + 9.96795u − 1.80594
−0.0000358515u
70
+ 0.0000911766u
69
+ ··· − 9.35995u + 0.946339
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0000814784u
70
− 0.000121110u
69
+ ··· − 8.51691u − 4.14593
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
71
+ 34u
70
+ ··· + 99u + 1
c
2
, c
5
u
71
+ 6u
70
+ ··· + 3u − 1
c
3
u
71
+ 3u
70
+ ··· + 3403u − 821
c
4
, c
11
u
71
+ 2u
70
+ ··· + 8576u − 1849
c
6
u
71
+ 18u
70
+ ··· − 3847u − 341
c
7
u
71
+ 2u
70
+ ··· − 50760u − 5291
c
8
u
71
− 3u
70
+ ··· − 921625u − 136291
c
9
, c
12
u
71
+ 7u
70
+ ··· − 836u − 53
c
10
u
71
− 4u
70
+ ··· − 12683514u − 12102611
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
71
+ 22y
70
+ ··· + 7631y −1
c
2
, c
5
y
71
− 34y
70
+ ··· + 99y −1
c
3
y
71
+ 107y
70
+ ··· − 25018129y −674041
c
4
, c
11
y
71
− 96y
70
+ ··· + 156138908y −3418801
c
6
y
71
+ 8y
70
+ ··· − 3768041y −116281
c
7
y
71
+ 96y
70
+ ··· − 99726602y −27994681
c
8
y
71
+ 31y
70
+ ··· − 411466202141y −18575236681
c
9
, c
12
y
71
+ 51y
70
+ ··· + 6292y −2809
c
10
y
71
+ 58y
70
+ ··· − 4549217659521294y −146473193017321
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.580765 + 0.835800I
a = −0.292777 − 0.451256I
b = 0.282543 + 0.413279I
−4.96899 + 3.96926I 0. − 7.49324I
u = 0.580765 − 0.835800I
a = −0.292777 + 0.451256I
b = 0.282543 − 0.413279I
−4.96899 − 3.96926I 0. + 7.49324I
u = −0.788689 + 0.650257I
a = 0.878827 − 0.718311I
b = −0.098470 − 0.332871I
1.02161 + 2.87191I 0
u = −0.788689 − 0.650257I
a = 0.878827 + 0.718311I
b = −0.098470 + 0.332871I
1.02161 − 2.87191I 0
u = −1.102090 + 0.196980I
a = −0.565213 − 0.502463I
b = −0.181280 − 0.585679I
1.32872 − 1.06319I 0
u = −1.102090 − 0.196980I
a = −0.565213 + 0.502463I
b = −0.181280 + 0.585679I
1.32872 + 1.06319I 0
u = −0.644955 + 0.431962I
a = −0.131388 − 0.611300I
b = 1.44716 + 0.73868I
−1.87321 + 8.07778I −2.27368 − 4.02394I
u = −0.644955 − 0.431962I
a = −0.131388 + 0.611300I
b = 1.44716 − 0.73868I
−1.87321 − 8.07778I −2.27368 + 4.02394I
u = −1.219390 + 0.158809I
a = 0.605127 − 0.575176I
b = −0.018267 − 0.533663I
0.46636 − 2.54570I 0
u = −1.219390 − 0.158809I
a = 0.605127 + 0.575176I
b = −0.018267 + 0.533663I
0.46636 + 2.54570I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.338847 + 0.652992I
a = 2.05956 + 0.00269I
b = 0.322023 + 0.276626I
−2.65434 − 8.89707I −3.34744 + 5.99725I
u = 0.338847 − 0.652992I
a = 2.05956 − 0.00269I
b = 0.322023 − 0.276626I
−2.65434 + 8.89707I −3.34744 − 5.99725I
u = −0.413420 + 0.603171I
a = −1.19312 + 0.91314I
b = 0.013449 + 0.272129I
2.09910 − 1.55037I 2.13059 + 4.88188I
u = −0.413420 − 0.603171I
a = −1.19312 − 0.91314I
b = 0.013449 − 0.272129I
2.09910 + 1.55037I 2.13059 − 4.88188I
u = −0.206337 + 1.264600I
a = 0.87744 + 1.44981I
b = 0.97694 + 2.04446I
−7.83303 − 3.23562I 0
u = −0.206337 − 1.264600I
a = 0.87744 − 1.44981I
b = 0.97694 − 2.04446I
−7.83303 + 3.23562I 0
u = −0.495470 + 0.518548I
a = −0.309042 + 0.617419I
b = −1.36002 − 0.62813I
0.29797 + 2.50456I 0.701081 − 0.103219I
u = −0.495470 − 0.518548I
a = −0.309042 − 0.617419I
b = −1.36002 + 0.62813I
0.29797 − 2.50456I 0.701081 + 0.103219I
u = 0.659094 + 0.234693I
a = −0.688554 + 0.725722I
b = 0.061050 − 0.639663I
−1.59434 + 1.80020I 0.62667 − 4.98436I
u = 0.659094 − 0.234693I
a = −0.688554 − 0.725722I
b = 0.061050 + 0.639663I
−1.59434 − 1.80020I 0.62667 + 4.98436I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.184729 + 0.633390I
a = −2.09854 + 0.37802I
b = −0.435861 − 0.070705I
−0.19378 − 3.46779I −1.36386 + 2.69751I
u = 0.184729 − 0.633390I
a = −2.09854 − 0.37802I
b = −0.435861 + 0.070705I
−0.19378 + 3.46779I −1.36386 − 2.69751I
u = 0.155035 + 1.339750I
a = 0.03561 − 1.62777I
b = −0.35185 − 2.24462I
−6.17756 + 4.77517I 0
u = 0.155035 − 1.339750I
a = 0.03561 + 1.62777I
b = −0.35185 + 2.24462I
−6.17756 − 4.77517I 0
u = −0.645433
a = −0.542319
b = −0.377916
1.01771 11.3920
u = 1.270820 + 0.486913I
a = −0.482541 + 0.074369I
b = 0.453419 − 0.446420I
−1.12010 + 3.38645I 0
u = 1.270820 − 0.486913I
a = −0.482541 − 0.074369I
b = 0.453419 + 0.446420I
−1.12010 − 3.38645I 0
u = 1.027510 + 0.932024I
a = 0.338936 + 0.076836I
b = −0.448741 + 0.004535I
−4.73552 + 1.86861I 0
u = 1.027510 − 0.932024I
a = 0.338936 − 0.076836I
b = −0.448741 − 0.004535I
−4.73552 − 1.86861I 0
u = 0.045687 + 0.585291I
a = −0.191858 + 0.636762I
b = 1.130060 − 0.314443I
0.83945 − 5.04601I −0.72754 + 7.42828I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.045687 − 0.585291I
a = −0.191858 − 0.636762I
b = 1.130060 + 0.314443I
0.83945 + 5.04601I −0.72754 − 7.42828I
u = −0.184861 + 0.554459I
a = −0.189001 − 0.545144I
b = −1.084770 + 0.040106I
2.19151 − 0.19769I 2.21273 + 1.68853I
u = −0.184861 − 0.554459I
a = −0.189001 + 0.545144I
b = −1.084770 − 0.040106I
2.19151 + 0.19769I 2.21273 − 1.68853I
u = 0.09305 + 1.45285I
a = −0.277047 + 1.109460I
b = −0.01604 + 1.70541I
−3.73297 − 1.70076I 0
u = 0.09305 − 1.45285I
a = −0.277047 − 1.109460I
b = −0.01604 − 1.70541I
−3.73297 + 1.70076I 0
u = 0.43800 + 1.46752I
a = 0.460286 − 0.948050I
b = −0.05146 − 1.72191I
−5.23559 + 3.76380I 0
u = 0.43800 − 1.46752I
a = 0.460286 + 0.948050I
b = −0.05146 + 1.72191I
−5.23559 − 3.76380I 0
u = 1.44469 + 0.67653I
a = 0.461376 + 0.000212I
b = −0.610829 + 0.359999I
−2.82185 + 8.13246I 0
u = 1.44469 − 0.67653I
a = 0.461376 − 0.000212I
b = −0.610829 − 0.359999I
−2.82185 − 8.13246I 0
u = 0.222485 + 0.329255I
a = −0.22314 − 2.06764I
b = 0.103952 + 0.761599I
−3.63364 − 2.57307I −2.03072 + 1.09466I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.222485 − 0.329255I
a = −0.22314 + 2.06764I
b = 0.103952 − 0.761599I
−3.63364 + 2.57307I −2.03072 − 1.09466I
u = −0.036076 + 0.328318I
a = 2.77493 − 2.15222I
b = 0.956928 + 0.554431I
−6.09160 − 0.21690I −5.79568 − 0.48270I
u = −0.036076 − 0.328318I
a = 2.77493 + 2.15222I
b = 0.956928 − 0.554431I
−6.09160 + 0.21690I −5.79568 + 0.48270I
u = 0.14109 + 1.71542I
a = −0.103585 − 0.983039I
b = 0.41054 − 1.70085I
−8.85568 − 1.19614I 0
u = 0.14109 − 1.71542I
a = −0.103585 + 0.983039I
b = 0.41054 + 1.70085I
−8.85568 + 1.19614I 0
u = 0.50453 + 1.64767I
a = −0.021638 + 1.079040I
b = −0.31773 + 1.57830I
−11.19700 + 2.71939I 0
u = 0.50453 − 1.64767I
a = −0.021638 − 1.079040I
b = −0.31773 − 1.57830I
−11.19700 − 2.71939I 0
u = −0.33964 + 1.69087I
a = −0.270789 − 0.811108I
b = 0.63080 − 1.85770I
−8.42379 − 1.34719I 0
u = −0.33964 − 1.69087I
a = −0.270789 + 0.811108I
b = 0.63080 + 1.85770I
−8.42379 + 1.34719I 0
u = −0.38005 + 1.74334I
a = −0.004059 + 1.047000I
b = −0.14824 + 1.70632I
−4.48823 − 4.63881I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.38005 − 1.74334I
a = −0.004059 − 1.047000I
b = −0.14824 − 1.70632I
−4.48823 + 4.63881I 0
u = 0.144380 + 0.082580I
a = −2.20673 + 2.28717I
b = 0.462774 − 0.516661I
−1.49223 + 0.50005I −5.24006 − 0.19978I
u = 0.144380 − 0.082580I
a = −2.20673 − 2.28717I
b = 0.462774 + 0.516661I
−1.49223 − 0.50005I −5.24006 + 0.19978I
u = 0.20850 + 1.82203I
a = 0.081777 + 1.082370I
b = 0.40590 + 2.02173I
−15.0313 + 6.8617I 0
u = 0.20850 − 1.82203I
a = 0.081777 − 1.082370I
b = 0.40590 − 2.02173I
−15.0313 − 6.8617I 0
u = 0.45176 + 1.83563I
a = 0.042954 − 1.024460I
b = −0.39692 − 2.03294I
−8.94192 + 10.31780I 0
u = 0.45176 − 1.83563I
a = 0.042954 + 1.024460I
b = −0.39692 + 2.03294I
−8.94192 − 10.31780I 0
u = −0.50536 + 1.86907I
a = −0.039033 − 1.008760I
b = 0.17763 − 1.71497I
−6.53854 − 9.81945I 0
u = −0.50536 − 1.86907I
a = −0.039033 + 1.008760I
b = 0.17763 + 1.71497I
−6.53854 + 9.81945I 0
u = −0.09707 + 1.98496I
a = 0.057879 − 0.937148I
b = 0.14717 − 1.77957I
−9.48997 − 2.54176I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.09707 − 1.98496I
a = 0.057879 + 0.937148I
b = 0.14717 + 1.77957I
−9.48997 + 2.54176I 0
u = 0.49330 + 1.95007I
a = −0.031263 + 0.967843I
b = 0.39373 + 2.03998I
−11.4134 + 16.1003I 0
u = 0.49330 − 1.95007I
a = −0.031263 − 0.967843I
b = 0.39373 − 2.03998I
−11.4134 − 16.1003I 0
u = −0.67907 + 1.94610I
a = 0.247969 + 0.639732I
b = −0.72680 + 2.09501I
−10.02920 − 5.17198I 0
u = −0.67907 − 1.94610I
a = 0.247969 − 0.639732I
b = −0.72680 − 2.09501I
−10.02920 + 5.17198I 0
u = 0.34344 + 2.04434I
a = −0.025252 + 0.944078I
b = −0.25012 + 1.70609I
−11.65100 − 4.31172I 0
u = 0.34344 − 2.04434I
a = −0.025252 − 0.944078I
b = −0.25012 − 1.70609I
−11.65100 + 4.31172I 0
u = 0.00982 + 2.14846I
a = 0.009145 − 0.765336I
b = 0.24624 − 1.99478I
−9.17505 − 2.02606I 0
u = 0.00982 − 2.14846I
a = 0.009145 + 0.765336I
b = 0.24624 + 1.99478I
−9.17505 + 2.02606I 0
u = −0.34232 + 2.31471I
a = 0.089041 + 0.645209I
b = −0.43595 + 2.20178I
−10.43290 + 1.02273I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.34232 − 2.31471I
a = 0.089041 − 0.645209I
b = −0.43595 − 2.20178I
−10.43290 − 1.02273I 0
12
II.
I
u
2
= h−1.02×10
17
u
20
−3.63×10
17
u
19
+· · ·+1.77×10
18
b−7.60×10
17
, −2.79×
10
18
u
20
−2.29×10
18
u
19
+· · ·+5.31×10
18
a−3.59×10
18
, u
21
+u
20
+· · ·+u+3i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
5
=
0.525589u
20
+ 0.430902u
19
+ ··· − 3.87934u + 0.675616
0.0574685u
20
+ 0.205341u
19
+ ··· − 0.674948u + 0.429508
a
8
=
1
−u
2
a
9
=
−0.639678u
20
− 0.519629u
19
+ ··· + 3.71273u + 0.974140
−0.198195u
20
− 0.215992u
19
+ ··· + 1.23162u − 0.765561
a
4
=
0.525589u
20
+ 0.430902u
19
+ ··· − 3.87934u + 0.675616
0.0333158u
20
+ 0.195091u
19
+ ··· + 0.807132u + 0.145445
a
3
=
0.468121u
20
+ 0.225560u
19
+ ··· − 3.20440u + 0.246108
0.0242084u
20
+ 0.247013u
19
+ ··· + 0.486854u − 0.298173
a
6
=
0.243288u
20
+ 0.0876454u
19
+ ··· − 1.24949u − 0.505262
0.414187u
20
+ 0.520712u
19
+ ··· − 2.89587u − 0.0634637
a
2
=
0.296423u
20
+ 0.0723191u
19
+ ··· − 1.42924u − 0.964066
0.265495u
20
+ 0.472573u
19
+ ··· − 1.61833u − 0.682384
a
11
=
−0.327392u
20
− 0.257031u
19
+ ··· − 1.30080u − 0.247004
0.0570984u
20
+ 0.205606u
19
+ ··· − 0.525634u − 1.70795
a
10
=
−0.384491u
20
− 0.462637u
19
+ ··· − 0.775171u + 1.46095
0.0570984u
20
+ 0.205606u
19
+ ··· − 0.525634u − 1.70795
a
1
=
0.717824u
20
+ 0.795971u
19
+ ··· − 5.55816u − 2.12761
−0.148508u
20
− 0.169556u
19
+ ··· + 2.76505u + 1.17130
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
2705003835397264499
1769077763043388471
u
20
−
2258477885563098772
1769077763043388471
u
19
+ ··· +
11494347706283494126
1769077763043388471
u +
15960298128399919686
1769077763043388471
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
21
− 11u
20
+ ··· + 88u − 9
c
2
u
21
+ u
20
+ ··· − 4u − 3
c
3
u
21
− 2u
20
+ ··· + 10u + 5
c
4
u
21
− u
20
+ ··· − 3u + 1
c
5
u
21
− u
20
+ ··· − 4u + 3
c
6
u
21
+ u
20
+ ··· + 8u
2
+ 1
c
7
u
21
+ u
20
+ ··· + u + 3
c
8
u
21
+ 2u
20
+ ··· − 8u
2
− 1
c
9
u
21
+ 6u
20
+ ··· + 45u + 5
c
10
u
21
+ 3u
20
+ ··· + 7u − 1
c
11
u
21
+ u
20
+ ··· − 3u − 1
c
12
u
21
− 6u
20
+ ··· + 45u − 5
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
+ 13y
20
+ ··· + 184y −81
c
2
, c
5
y
21
− 11y
20
+ ··· + 88y −9
c
3
y
21
+ 22y
20
+ ··· + 840y −25
c
4
, c
11
y
21
− 17y
20
+ ··· − 3y −1
c
6
y
21
− 5y
20
+ ··· − 16y −1
c
7
y
21
+ 19y
20
+ ··· + 115y −9
c
8
y
21
+ 6y
20
+ ··· − 16y −1
c
9
, c
12
y
21
+ 14y
20
+ ··· + 265y −25
c
10
y
21
+ 9y
20
+ ··· + 7y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.017760 + 0.164191I
a = 0.019420 − 0.728210I
b = −0.217020 − 0.758452I
0.01218 − 1.44237I −3.57616 + 0.36303I
u = −1.017760 − 0.164191I
a = 0.019420 + 0.728210I
b = −0.217020 + 0.758452I
0.01218 + 1.44237I −3.57616 − 0.36303I
u = −0.667983 + 0.500875I
a = 0.264507 − 0.993663I
b = −0.740886 − 0.591101I
1.64283 + 4.02770I 3.16447 − 4.97726I
u = −0.667983 − 0.500875I
a = 0.264507 + 0.993663I
b = −0.740886 + 0.591101I
1.64283 − 4.02770I 3.16447 + 4.97726I
u = 0.954936 + 0.692254I
a = 0.072870 − 0.298348I
b = −0.378423 − 0.311339I
−4.60032 + 2.49760I 0.02822 − 6.06015I
u = 0.954936 − 0.692254I
a = 0.072870 + 0.298348I
b = −0.378423 + 0.311339I
−4.60032 − 2.49760I 0.02822 + 6.06015I
u = −0.811685
a = 0.881305
b = 0.180005
0.358951 −3.34010
u = 0.755182 + 0.080789I
a = 0.423871 − 1.018030I
b = −1.089450 − 0.150699I
−0.92163 + 9.19955I 2.77433 − 8.25516I
u = 0.755182 − 0.080789I
a = 0.423871 + 1.018030I
b = −1.089450 + 0.150699I
−0.92163 − 9.19955I 2.77433 + 8.25516I
u = 0.311855 + 1.336120I
a = −0.607669 + 0.987511I
b = −0.69526 + 1.74117I
−7.42230 + 2.81144I −2.33733 + 0.74449I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.311855 − 1.336120I
a = −0.607669 − 0.987511I
b = −0.69526 − 1.74117I
−7.42230 − 2.81144I −2.33733 − 0.74449I
u = −0.271251 + 1.356350I
a = −0.46017 − 1.35418I
b = 0.12651 − 1.96996I
−6.42306 − 4.13848I −5.49167 + 2.04959I
u = −0.271251 − 1.356350I
a = −0.46017 + 1.35418I
b = 0.12651 + 1.96996I
−6.42306 + 4.13848I −5.49167 − 2.04959I
u = −0.468317 + 0.327808I
a = −0.17804 + 1.48507I
b = 0.762786 + 0.342701I
2.92449 − 0.74097I 7.31939 + 1.52438I
u = −0.468317 − 0.327808I
a = −0.17804 − 1.48507I
b = 0.762786 − 0.342701I
2.92449 + 0.74097I 7.31939 − 1.52438I
u = 0.474570 + 0.190158I
a = −0.01766 + 1.77843I
b = 1.076620 + 0.036349I
1.07014 + 3.68507I 5.59024 − 4.51475I
u = 0.474570 − 0.190158I
a = −0.01766 − 1.77843I
b = 1.076620 − 0.036349I
1.07014 − 3.68507I 5.59024 + 4.51475I
u = −0.23006 + 2.10695I
a = −0.158253 − 0.739024I
b = 0.46119 − 1.91480I
−9.48831 − 0.32291I −3.90057 − 0.91919I
u = −0.23006 − 2.10695I
a = −0.158253 + 0.739024I
b = 0.46119 + 1.91480I
−9.48831 + 0.32291I −3.90057 + 0.91919I
u = 0.06467 + 2.12010I
a = 0.033800 + 0.726331I
b = −0.39606 + 1.95200I
−9.87219 − 3.28291I −3.90087 + 4.45768I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.06467 − 2.12010I
a = 0.033800 − 0.726331I
b = −0.39606 − 1.95200I
−9.87219 + 3.28291I −3.90087 − 4.45768I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
21
− 11u
20
+ ··· + 88u − 9)(u
71
+ 34u
70
+ ··· + 99u + 1)
c
2
(u
21
+ u
20
+ ··· − 4u − 3)(u
71
+ 6u
70
+ ··· + 3u − 1)
c
3
(u
21
− 2u
20
+ ··· + 10u + 5)(u
71
+ 3u
70
+ ··· + 3403u − 821)
c
4
(u
21
− u
20
+ ··· − 3u + 1)(u
71
+ 2u
70
+ ··· + 8576u − 1849)
c
5
(u
21
− u
20
+ ··· − 4u + 3)(u
71
+ 6u
70
+ ··· + 3u − 1)
c
6
(u
21
+ u
20
+ ··· + 8u
2
+ 1)(u
71
+ 18u
70
+ ··· − 3847u − 341)
c
7
(u
21
+ u
20
+ ··· + u + 3)(u
71
+ 2u
70
+ ··· − 50760u − 5291)
c
8
(u
21
+ 2u
20
+ ··· − 8u
2
− 1)(u
71
− 3u
70
+ ··· − 921625u − 136291)
c
9
(u
21
+ 6u
20
+ ··· + 45u + 5)(u
71
+ 7u
70
+ ··· − 836u − 53)
c
10
(u
21
+ 3u
20
+ ··· + 7u − 1)
· (u
71
− 4u
70
+ ··· − 12683514u − 12102611)
c
11
(u
21
+ u
20
+ ··· − 3u − 1)(u
71
+ 2u
70
+ ··· + 8576u − 1849)
c
12
(u
21
− 6u
20
+ ··· + 45u − 5)(u
71
+ 7u
70
+ ··· − 836u − 53)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
21
+ 13y
20
+ ··· + 184y −81)(y
71
+ 22y
70
+ ··· + 7631y −1)
c
2
, c
5
(y
21
− 11y
20
+ ··· + 88y −9)(y
71
− 34y
70
+ ··· + 99y −1)
c
3
(y
21
+ 22y
20
+ ··· + 840y −25)
· (y
71
+ 107y
70
+ ··· − 25018129y −674041)
c
4
, c
11
(y
21
− 17y
20
+ ··· − 3y −1)
· (y
71
− 96y
70
+ ··· + 156138908y −3418801)
c
6
(y
21
− 5y
20
+ ··· − 16y −1)(y
71
+ 8y
70
+ ··· − 3768041y −116281)
c
7
(y
21
+ 19y
20
+ ··· + 115y −9)
· (y
71
+ 96y
70
+ ··· − 99726602y −27994681)
c
8
(y
21
+ 6y
20
+ ··· − 16y −1)
· (y
71
+ 31y
70
+ ··· − 411466202141y −18575236681)
c
9
, c
12
(y
21
+ 14y
20
+ ··· + 265y −25)(y
71
+ 51y
70
+ ··· + 6292y −2809)
c
10
(y
21
+ 9y
20
+ ··· + 7y −1)
· (y
71
+ 58y
70
+ ··· − 4549217659521294y −146473193017321)
22
