12a
0295
(K12a
0295
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 12 5 11 4 9 1 7
Solving Sequence
4,9
10 5
1,11
12 8 3 2 7 6
c
9
c
4
c
10
c
11
c
8
c
3
c
1
c
7
c
6
c
2
, c
5
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h3u
45
− 6u
44
+ ··· + b + 3, −7u
45
+ 17u
44
+ ··· + 2a − 14, u
46
− 3u
45
+ ··· + 4u − 2i
I
u
2
= h33684u
32
a − 254577u
32
+ ··· + 7807a − 17533, 2u
32
a − 5u
32
+ ··· − 4a + 3, u
33
+ 2u
32
+ ··· − 2u − 1i
I
u
3
= h−u
2
+ b − u + 1, u
3
+ 2a + u − 2, u
4
− u
2
+ 2i
I
u
4
= hb − 1, a + 1, u + 1i
I
u
5
= hb + 1, a + 1, u − 1i
I
u
6
= hb, a + 1, u − 1i
I
u
7
= hb − 1, a, u − 1i
I
u
8
= h−u
3
− u
2
+ b − 1, u
3
+ u
2
+ a − u, u
4
+ 1i
I
v
1
= ha, b − 1, v + 1i
* 9 irreducible components of dim
C
= 0, with total 125 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
=
h3u
45
−6u
44
+· · ·+b+3, −7u
45
+17u
44
+· · ·+2a−14, u
46
−3u
45
+· · ·+4u−2i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
5
=
−u
−u
3
+ u
a
1
=
7
2
u
45
−
17
2
u
44
+ ··· − 10u + 7
−3u
45
+ 6u
44
+ ··· + 7u − 3
a
11
=
−u
2
+ 1
u
2
a
12
=
−
3
2
u
45
+
7
2
u
44
+ ··· + 4u − 2
u
45
− 2u
44
+ ··· − 3u + 1
a
8
=
u
4
− u
2
+ 1
−u
4
a
3
=
u
9
− 2u
7
+ 3u
5
− 2u
3
+ u
−u
9
+ u
7
− u
5
+ u
a
2
=
3
2
u
45
−
7
2
u
44
+ ··· − 5u + 3
−u
45
+ 2u
44
+ ··· + 2u − 1
a
7
=
−u
8
+ u
6
− u
4
+ 1
−u
10
+ 2u
8
− 3u
6
+ 2u
4
− u
2
a
6
=
3
2
u
45
−
3
2
u
44
+ ··· − 3u − 1
2u
45
− 7u
44
+ ··· − 7u + 7
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
45
− 8u
44
+ ··· − 2u + 4
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
46
+ 19u
45
+ ··· + 19u + 1
c
2
, c
5
, c
6
c
12
u
46
+ u
45
+ ··· − 3u − 1
c
3
u
46
+ 3u
45
+ ··· − 1200u − 194
c
4
, c
9
u
46
− 3u
45
+ ··· + 4u − 2
c
7
u
46
− 21u
45
+ ··· − 27796u + 2962
c
8
, c
10
u
46
+ 15u
45
+ ··· + 24u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
46
+ 29y
45
+ ··· − 83y + 1
c
2
, c
5
, c
6
c
12
y
46
− 19y
45
+ ··· − 19y + 1
c
3
y
46
− 3y
45
+ ··· − 95192y + 37636
c
4
, c
9
y
46
− 15y
45
+ ··· − 24y + 4
c
7
y
46
+ 9y
45
+ ··· − 47342296y + 8773444
c
8
, c
10
y
46
+ 33y
45
+ ··· − 448y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.987506 + 0.181737I
a = 0.353118 − 0.157922I
b = 1.104500 + 0.248593I
−0.01578 + 1.44584I −12.13380 − 1.16212I
u = −0.987506 − 0.181737I
a = 0.353118 + 0.157922I
b = 1.104500 − 0.248593I
−0.01578 − 1.44584I −12.13380 + 1.16212I
u = 0.624787 + 0.751761I
a = 0.501815 − 1.195750I
b = 0.27921 + 1.52890I
−1.03505 − 2.62041I −12.25047 + 5.62134I
u = 0.624787 − 0.751761I
a = 0.501815 + 1.195750I
b = 0.27921 − 1.52890I
−1.03505 + 2.62041I −12.25047 − 5.62134I
u = 0.932010 + 0.249601I
a = −0.114325 − 0.813437I
b = −0.108703 + 0.755311I
0.48280 − 3.89081I −12.3138 + 7.4640I
u = 0.932010 − 0.249601I
a = −0.114325 + 0.813437I
b = −0.108703 − 0.755311I
0.48280 + 3.89081I −12.3138 − 7.4640I
u = 1.03795
a = −0.425099
b = 0.441184
−5.06706 −16.3430
u = −0.656480 + 0.675086I
a = 0.421198 + 0.564603I
b = 0.364479 − 0.548670I
−0.056532 − 0.529762I −9.92309 + 2.36241I
u = −0.656480 − 0.675086I
a = 0.421198 − 0.564603I
b = 0.364479 + 0.548670I
−0.056532 + 0.529762I −9.92309 − 2.36241I
u = 0.957126 + 0.460438I
a = −0.173508 + 1.059270I
b = 0.660431 − 0.373019I
−2.47921 + 5.69529I −15.9789 − 3.1429I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.957126 − 0.460438I
a = −0.173508 − 1.059270I
b = 0.660431 + 0.373019I
−2.47921 − 5.69529I −15.9789 + 3.1429I
u = −1.069760 + 0.055455I
a = −0.606557 − 0.782831I
b = 0.110005 − 0.642276I
−6.77795 − 3.22325I −19.8771 + 4.6627I
u = −1.069760 − 0.055455I
a = −0.606557 + 0.782831I
b = 0.110005 + 0.642276I
−6.77795 + 3.22325I −19.8771 − 4.6627I
u = −1.064240 + 0.153207I
a = −0.689961 + 0.702318I
b = −1.50763 − 0.88276I
−4.26259 + 11.90660I −17.9405 − 9.1988I
u = −1.064240 − 0.153207I
a = −0.689961 − 0.702318I
b = −1.50763 + 0.88276I
−4.26259 − 11.90660I −17.9405 + 9.1988I
u = 0.687563 + 0.827125I
a = −3.10547 − 1.38060I
b = 3.34622 − 0.75008I
2.36760 + 11.90970I −10.87368 − 6.80495I
u = 0.687563 − 0.827125I
a = −3.10547 + 1.38060I
b = 3.34622 + 0.75008I
2.36760 − 11.90970I −10.87368 + 6.80495I
u = 0.863194 + 0.660192I
a = 0.498220 − 0.862239I
b = 0.078376 + 0.670779I
1.90782 − 2.56381I −6.43986 + 3.61212I
u = 0.863194 − 0.660192I
a = 0.498220 + 0.862239I
b = 0.078376 − 0.670779I
1.90782 + 2.56381I −6.43986 − 3.61212I
u = 0.726882 + 0.813399I
a = 2.23393 + 0.39337I
b = −2.01663 + 0.93850I
6.48924 + 0.76026I −5.47164 + 1.79704I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.726882 − 0.813399I
a = 2.23393 − 0.39337I
b = −2.01663 − 0.93850I
6.48924 − 0.76026I −5.47164 − 1.79704I
u = −0.761471 + 0.808932I
a = −1.55718 + 1.35768I
b = 2.01414 + 0.41223I
7.06928 − 2.51400I −5.65805 + 2.94720I
u = −0.761471 − 0.808932I
a = −1.55718 − 1.35768I
b = 2.01414 − 0.41223I
7.06928 + 2.51400I −5.65805 − 2.94720I
u = −0.815580 + 0.797638I
a = 2.73888 − 0.86284I
b = −2.59337 − 1.69608I
4.61938 + 8.64883I −8.79522 − 7.48354I
u = −0.815580 − 0.797638I
a = 2.73888 + 0.86284I
b = −2.59337 + 1.69608I
4.61938 − 8.64883I −8.79522 + 7.48354I
u = 0.996141 + 0.593536I
a = −0.527497 + 0.683258I
b = −0.730063 + 0.019372I
−3.55351 − 9.40266I −16.3537 + 9.9962I
u = 0.996141 − 0.593536I
a = −0.527497 − 0.683258I
b = −0.730063 − 0.019372I
−3.55351 + 9.40266I −16.3537 − 9.9962I
u = −0.991896 + 0.659941I
a = 0.425990 + 0.411638I
b = −0.026130 − 0.933046I
−1.04556 + 5.73841I −11.05429 − 7.34426I
u = −0.991896 − 0.659941I
a = 0.425990 − 0.411638I
b = −0.026130 + 0.933046I
−1.04556 − 5.73841I −11.05429 + 7.34426I
u = −0.929854 + 0.761506I
a = −1.21193 + 2.23762I
b = 3.11564 − 0.90437I
4.26620 − 2.79398I −9.33642 + 2.11087I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.929854 − 0.761506I
a = −1.21193 − 2.23762I
b = 3.11564 + 0.90437I
4.26620 + 2.79398I −9.33642 − 2.11087I
u = 1.016200 + 0.678830I
a = 1.28721 − 0.66759I
b = 0.11699 + 1.72866I
−2.18659 − 2.82834I −14.4909 + 0.I
u = 1.016200 − 0.678830I
a = 1.28721 + 0.66759I
b = 0.11699 − 1.72866I
−2.18659 + 2.82834I −14.4909 + 0.I
u = −0.973166 + 0.747201I
a = 1.45384 − 1.05199I
b = −2.40070 − 0.28498I
6.41991 + 8.35794I −7.07346 − 8.25317I
u = −0.973166 − 0.747201I
a = 1.45384 + 1.05199I
b = −2.40070 + 0.28498I
6.41991 − 8.35794I −7.07346 + 8.25317I
u = 0.994894 + 0.735728I
a = −1.01818 − 2.04408I
b = 2.40436 + 0.51843I
5.66935 − 6.57875I −7.01388 + 3.35805I
u = 0.994894 − 0.735728I
a = −1.01818 + 2.04408I
b = 2.40436 − 0.51843I
5.66935 + 6.57875I −7.01388 − 3.35805I
u = 1.019120 + 0.727882I
a = 2.04434 + 2.70103I
b = −3.96989 − 0.01287I
1.3568 − 17.7372I −12.0000 + 11.5303I
u = 1.019120 − 0.727882I
a = 2.04434 − 2.70103I
b = −3.96989 + 0.01287I
1.3568 + 17.7372I −12.0000 − 11.5303I
u = 0.420136 + 0.618183I
a = 0.091569 + 0.240275I
b = 0.775179 − 0.545225I
−2.09088 + 4.75292I −12.79925 − 4.51898I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.420136 − 0.618183I
a = 0.091569 − 0.240275I
b = 0.775179 + 0.545225I
−2.09088 − 4.75292I −12.79925 + 4.51898I
u = 0.175033 + 0.649364I
a = −0.38522 + 1.64160I
b = 0.405182 + 0.541225I
−0.25533 − 9.46021I −10.70549 + 7.71683I
u = 0.175033 − 0.649364I
a = −0.38522 − 1.64160I
b = 0.405182 − 0.541225I
−0.25533 + 9.46021I −10.70549 − 7.71683I
u = 0.045128 + 0.600618I
a = 0.796115 − 1.095320I
b = −0.290859 − 0.327309I
3.23919 + 1.06884I −5.04128 − 2.43336I
u = 0.045128 − 0.600618I
a = 0.796115 + 1.095320I
b = −0.290859 + 0.327309I
3.23919 − 1.06884I −5.04128 + 2.43336I
u = −0.454468
a = 0.512306
b = 0.297284
−0.646543 −15.2580
9
II. I
u
2
= h33684u
32
a − 254577u
32
+ · · · + 7807a − 17533, 2u
32
a − 5u
32
+ · · · −
4a + 3, u
33
+ 2u
32
+ · · · − 2u − 1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
5
=
−u
−u
3
+ u
a
1
=
a
−0.156182au
32
+ 1.18040u
32
+ ··· − 0.0361987a + 0.0812951
a
11
=
−u
2
+ 1
u
2
a
12
=
−0.0987940au
32
− 0.489797u
32
+ ··· + 0.728290a + 1.20993
0.228199au
32
+ 1.59843u
32
+ ··· − 0.339819a − 0.210575
a
8
=
u
4
− u
2
+ 1
−u
4
a
3
=
u
9
− 2u
7
+ 3u
5
− 2u
3
+ u
−u
9
+ u
7
− u
5
+ u
a
2
=
−0.00898127au
32
− 0.408163u
32
+ ··· + 1.42984a − 0.162734
0.228199au
32
+ 1.59843u
32
+ ··· − 0.339819a − 0.210575
a
7
=
−u
8
+ u
6
− u
4
+ 1
−u
10
+ 2u
8
− 3u
6
+ 2u
4
− u
2
a
6
=
−0.0361987au
32
+ 2.08130u
32
+ ··· + 1.25544a − 0.472103
2u
31
− 10u
29
+ ··· − au − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
32
− 20u
30
− 4u
29
+ 72u
28
+ 16u
27
− 180u
26
− 56u
25
+ 360u
24
+ 128u
23
− 580u
22
−
248u
21
+ 772u
20
+ 384u
19
− 848u
18
− 500u
17
+ 760u
16
+ 548u
15
− 532u
14
− 496u
13
+
264u
12
+ 372u
11
− 52u
10
− 220u
9
− 48u
8
+ 92u
7
+ 56u
6
− 24u
5
− 28u
4
− 4u
3
+ 4u
2
− 10
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
66
+ 36u
65
+ ··· + 492u + 49
c
2
, c
5
, c
6
c
12
u
66
+ 2u
65
+ ··· − 32u − 7
c
3
(u
33
+ u
31
+ ··· − 8u − 1)
2
c
4
, c
9
(u
33
+ 2u
32
+ ··· − 2u − 1)
2
c
7
(u
33
+ 6u
32
+ ··· + 128u + 23)
2
c
8
, c
10
(u
33
+ 10u
32
+ ··· − 2u + 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
66
− 12y
65
+ ··· − 14116y + 2401
c
2
, c
5
, c
6
c
12
y
66
− 36y
65
+ ··· − 492y + 49
c
3
(y
33
+ 2y
32
+ ··· − 2y −1)
2
c
4
, c
9
(y
33
− 10y
32
+ ··· − 2y −1)
2
c
7
(y
33
+ 14y
32
+ ··· − 2062y −529)
2
c
8
, c
10
(y
33
+ 26y
32
+ ··· + 6y −1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.014300 + 0.118417I
a = −0.526921 + 0.504523I
b = −1.16627 − 1.84224I
−6.89406 + 3.13953I −20.3425 − 5.3611I
u = −1.014300 + 0.118417I
a = −1.16439 − 0.93165I
b = −0.343946 − 0.462272I
−6.89406 + 3.13953I −20.3425 − 5.3611I
u = −1.014300 − 0.118417I
a = −0.526921 − 0.504523I
b = −1.16627 + 1.84224I
−6.89406 − 3.13953I −20.3425 + 5.3611I
u = −1.014300 − 0.118417I
a = −1.16439 + 0.93165I
b = −0.343946 + 0.462272I
−6.89406 − 3.13953I −20.3425 + 5.3611I
u = −0.877024 + 0.414488I
a = 0.264209 + 0.985853I
b = 0.172888 − 0.597335I
−0.262282 − 0.735872I −12.67313 − 0.76984I
u = −0.877024 + 0.414488I
a = −0.147704 − 0.570462I
b = 0.899250 + 0.290937I
−0.262282 − 0.735872I −12.67313 − 0.76984I
u = −0.877024 − 0.414488I
a = 0.264209 − 0.985853I
b = 0.172888 + 0.597335I
−0.262282 + 0.735872I −12.67313 + 0.76984I
u = −0.877024 − 0.414488I
a = −0.147704 + 0.570462I
b = 0.899250 − 0.290937I
−0.262282 + 0.735872I −12.67313 + 0.76984I
u = 1.039060 + 0.162429I
a = −0.574713 − 0.703403I
b = −1.17278 + 1.02414I
−1.75770 − 6.51294I −14.8938 + 5.9887I
u = 1.039060 + 0.162429I
a = 0.456077 + 0.016656I
b = 1.178570 − 0.286332I
−1.75770 − 6.51294I −14.8938 + 5.9887I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.039060 − 0.162429I
a = −0.574713 + 0.703403I
b = −1.17278 − 1.02414I
−1.75770 + 6.51294I −14.8938 − 5.9887I
u = 1.039060 − 0.162429I
a = 0.456077 − 0.016656I
b = 1.178570 + 0.286332I
−1.75770 + 6.51294I −14.8938 − 5.9887I
u = 0.705062 + 0.789522I
a = 0.16155 − 1.51310I
b = 1.09869 + 1.85563I
−0.79038 + 2.85888I −11.96531 − 3.31371I
u = 0.705062 + 0.789522I
a = −2.85859 − 2.52886I
b = 3.42979 + 0.01935I
−0.79038 + 2.85888I −11.96531 − 3.31371I
u = 0.705062 − 0.789522I
a = 0.16155 + 1.51310I
b = 1.09869 − 1.85563I
−0.79038 − 2.85888I −11.96531 + 3.31371I
u = 0.705062 − 0.789522I
a = −2.85859 + 2.52886I
b = 3.42979 − 0.01935I
−0.79038 − 2.85888I −11.96531 + 3.31371I
u = −0.752029 + 0.757937I
a = −0.20561 + 1.43451I
b = 1.55176 − 1.42868I
0.112103 + 0.911954I −9.65130 − 3.13722I
u = −0.752029 + 0.757937I
a = 3.32131 + 0.09950I
b = −1.95320 − 2.11555I
0.112103 + 0.911954I −9.65130 − 3.13722I
u = −0.752029 − 0.757937I
a = −0.20561 − 1.43451I
b = 1.55176 + 1.42868I
0.112103 − 0.911954I −9.65130 + 3.13722I
u = −0.752029 − 0.757937I
a = 3.32131 − 0.09950I
b = −1.95320 + 2.11555I
0.112103 − 0.911954I −9.65130 + 3.13722I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.930115
a = −1.58086
b = −0.257939
−5.02884 −16.7130
u = 0.930115
a = −0.0786238
b = 1.80245
−5.02884 −16.7130
u = 0.906723 + 0.575511I
a = −1.40173 + 0.68737I
b = 1.36348 − 0.94558I
−4.48415 − 2.21654I −18.1634 + 2.4842I
u = 0.906723 + 0.575511I
a = −0.09683 + 1.72632I
b = −1.322680 + 0.118060I
−4.48415 − 2.21654I −18.1634 + 2.4842I
u = 0.906723 − 0.575511I
a = −1.40173 − 0.68737I
b = 1.36348 + 0.94558I
−4.48415 + 2.21654I −18.1634 − 2.4842I
u = 0.906723 − 0.575511I
a = −0.09683 − 1.72632I
b = −1.322680 − 0.118060I
−4.48415 + 2.21654I −18.1634 − 2.4842I
u = −0.703249 + 0.821130I
a = 1.96275 − 0.43057I
b = −1.87462 − 0.57170I
4.82578 − 6.26770I −7.81018 + 3.24511I
u = −0.703249 + 0.821130I
a = −2.82714 + 1.57243I
b = 3.17494 + 0.60153I
4.82578 − 6.26770I −7.81018 + 3.24511I
u = −0.703249 − 0.821130I
a = 1.96275 + 0.43057I
b = −1.87462 + 0.57170I
4.82578 + 6.26770I −7.81018 − 3.24511I
u = −0.703249 − 0.821130I
a = −2.82714 − 1.57243I
b = 3.17494 − 0.60153I
4.82578 + 6.26770I −7.81018 − 3.24511I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.789844 + 0.799846I
a = −1.08493 − 1.02737I
b = 1.39311 − 0.44605I
6.34781 − 3.04389I −6.17382 + 2.90426I
u = 0.789844 + 0.799846I
a = 2.75022 + 0.72353I
b = −2.50757 + 1.57404I
6.34781 − 3.04389I −6.17382 + 2.90426I
u = 0.789844 − 0.799846I
a = −1.08493 + 1.02737I
b = 1.39311 + 0.44605I
6.34781 + 3.04389I −6.17382 − 2.90426I
u = 0.789844 − 0.799846I
a = 2.75022 − 0.72353I
b = −2.50757 − 1.57404I
6.34781 + 3.04389I −6.17382 − 2.90426I
u = −0.963141 + 0.632636I
a = 0.708655 + 1.042530I
b = 0.261323 − 1.067210I
−1.26824 + 5.40417I −13.1681 − 6.2152I
u = −0.963141 + 0.632636I
a = 0.264954 − 0.626134I
b = −0.793319 − 0.573051I
−1.26824 + 5.40417I −13.1681 − 6.2152I
u = −0.963141 − 0.632636I
a = 0.708655 − 1.042530I
b = 0.261323 + 1.067210I
−1.26824 − 5.40417I −13.1681 + 6.2152I
u = −0.963141 − 0.632636I
a = 0.264954 + 0.626134I
b = −0.793319 + 0.573051I
−1.26824 − 5.40417I −13.1681 + 6.2152I
u = −0.600852 + 0.549903I
a = 0.601180 + 0.828746I
b = −0.013590 − 0.731533I
−0.353626 − 0.577287I −10.91131 + 0.00847I
u = −0.600852 + 0.549903I
a = 0.0498087 + 0.0120002I
b = 0.754916 + 0.119020I
−0.353626 − 0.577287I −10.91131 + 0.00847I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.600852 − 0.549903I
a = 0.601180 − 0.828746I
b = −0.013590 + 0.731533I
−0.353626 + 0.577287I −10.91131 − 0.00847I
u = −0.600852 − 0.549903I
a = 0.0498087 − 0.0120002I
b = 0.754916 − 0.119020I
−0.353626 + 0.577287I −10.91131 − 0.00847I
u = −0.965280 + 0.710510I
a = 1.58839 − 0.20834I
b = −0.92369 − 1.80389I
−0.54191 + 4.66940I −11.13674 − 2.61989I
u = −0.965280 + 0.710510I
a = −0.75089 + 2.83490I
b = 2.70961 − 1.66384I
−0.54191 + 4.66940I −11.13674 − 2.61989I
u = −0.965280 − 0.710510I
a = 1.58839 + 0.20834I
b = −0.92369 + 1.80389I
−0.54191 − 4.66940I −11.13674 + 2.61989I
u = −0.965280 − 0.710510I
a = −0.75089 − 2.83490I
b = 2.70961 + 1.66384I
−0.54191 − 4.66940I −11.13674 + 2.61989I
u = 0.950716 + 0.751979I
a = 0.994748 + 0.610801I
b = −1.70633 + 0.12370I
5.85251 − 2.78863I −7.09178 + 2.57820I
u = 0.950716 + 0.751979I
a = −1.20786 − 2.30306I
b = 3.04193 + 0.84808I
5.85251 − 2.78863I −7.09178 + 2.57820I
u = 0.950716 − 0.751979I
a = 0.994748 − 0.610801I
b = −1.70633 − 0.12370I
5.85251 + 2.78863I −7.09178 − 2.57820I
u = 0.950716 − 0.751979I
a = −1.20786 + 2.30306I
b = 3.04193 − 0.84808I
5.85251 + 2.78863I −7.09178 − 2.57820I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.998168 + 0.717071I
a = 1.71463 − 0.23872I
b = −0.48172 + 2.14666I
−1.67944 − 8.54919I −13.8165 + 8.1542I
u = 0.998168 + 0.717071I
a = 3.01380 + 2.02593I
b = −4.03037 + 0.96164I
−1.67944 − 8.54919I −13.8165 + 8.1542I
u = 0.998168 − 0.717071I
a = 1.71463 + 0.23872I
b = −0.48172 − 2.14666I
−1.67944 + 8.54919I −13.8165 − 8.1542I
u = 0.998168 − 0.717071I
a = 3.01380 − 2.02593I
b = −4.03037 − 0.96164I
−1.67944 + 8.54919I −13.8165 − 8.1542I
u = −1.009690 + 0.731074I
a = −1.04859 + 1.84188I
b = 2.16527 − 0.25007I
3.89061 + 12.09090I −9.56427 − 8.11579I
u = −1.009690 + 0.731074I
a = 2.11702 − 2.33765I
b = −3.76945 − 0.18941I
3.89061 + 12.09090I −9.56427 − 8.11579I
u = −1.009690 − 0.731074I
a = −1.04859 − 1.84188I
b = 2.16527 + 0.25007I
3.89061 − 12.09090I −9.56427 + 8.11579I
u = −1.009690 − 0.731074I
a = 2.11702 + 2.33765I
b = −3.76945 + 0.18941I
3.89061 − 12.09090I −9.56427 + 8.11579I
u = −0.129012 + 0.620035I
a = 0.848786 + 0.874401I
b = −0.502349 + 0.193772I
1.97739 + 4.07711I −7.27799 − 3.88410I
u = −0.129012 + 0.620035I
a = 0.01854 − 1.69641I
b = 0.209851 − 0.482305I
1.97739 + 4.07711I −7.27799 − 3.88410I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.129012 − 0.620035I
a = 0.848786 − 0.874401I
b = −0.502349 − 0.193772I
1.97739 − 4.07711I −7.27799 + 3.88410I
u = −0.129012 − 0.620035I
a = 0.01854 + 1.69641I
b = 0.209851 + 0.482305I
1.97739 − 4.07711I −7.27799 + 3.88410I
u = 0.159946 + 0.484229I
a = −0.0999950 + 0.0977691I
b = 1.209480 − 0.222381I
−3.28246 − 1.28200I −12.00329 + 5.16805I
u = 0.159946 + 0.484229I
a = 0.48900 + 2.99039I
b = 0.174771 + 0.129985I
−3.28246 − 1.28200I −12.00329 + 5.16805I
u = 0.159946 − 0.484229I
a = −0.0999950 − 0.0977691I
b = 1.209480 + 0.222381I
−3.28246 + 1.28200I −12.00329 − 5.16805I
u = 0.159946 − 0.484229I
a = 0.48900 − 2.99039I
b = 0.174771 − 0.129985I
−3.28246 + 1.28200I −12.00329 − 5.16805I
19
III. I
u
3
= h−u
2
+ b − u + 1, u
3
+ 2a + u − 2, u
4
− u
2
+ 2i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
5
=
−u
−u
3
+ u
a
1
=
−
1
2
u
3
−
1
2
u + 1
u
2
+ u − 1
a
11
=
−u
2
+ 1
u
2
a
12
=
−
1
2
u
3
− u
2
−
1
2
u + 2
2u
2
+ u − 1
a
8
=
−1
−u
2
+ 2
a
3
=
u
u
3
− u
a
2
=
−
1
2
u
3
+
1
2
u + 1
u
3
+ u
2
− 1
a
7
=
u
2
− 1
−u
2
a
6
=
−
1
2
u
3
−
1
2
u + 1
u
2
+ u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
− 20
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
11
c
12
(u − 1)
4
c
2
, c
6
(u + 1)
4
c
3
, c
4
, c
7
c
9
u
4
− u
2
+ 2
c
8
(u
2
− u + 2)
2
c
10
(u
2
+ u + 2)
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
(y −1)
4
c
3
, c
4
, c
7
c
9
(y
2
− y + 2)
2
c
8
, c
10
(y
2
+ 3y + 4)
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.978318 + 0.676097I
a = 0.713457 − 1.154170I
b = 0.47832 + 1.99897I
−2.46740 − 5.33349I −18.0000 + 5.2915I
u = 0.978318 − 0.676097I
a = 0.713457 + 1.154170I
b = 0.47832 − 1.99897I
−2.46740 + 5.33349I −18.0000 − 5.2915I
u = −0.978318 + 0.676097I
a = 1.28654 − 1.15417I
b = −1.47832 − 0.64678I
−2.46740 + 5.33349I −18.0000 − 5.2915I
u = −0.978318 − 0.676097I
a = 1.28654 + 1.15417I
b = −1.47832 + 0.64678I
−2.46740 − 5.33349I −18.0000 + 5.2915I
23
IV. I
u
4
= hb − 1, a + 1, u + 1i
(i) Arc colorings
a
4
=
0
−1
a
9
=
1
0
a
10
=
1
1
a
5
=
1
0
a
1
=
−1
1
a
11
=
0
1
a
12
=
−1
2
a
8
=
1
−1
a
3
=
−1
0
a
2
=
−2
1
a
7
=
0
−1
a
6
=
−1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −24
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
7
, c
8
c
11
, c
12
u − 1
c
2
, c
6
, c
9
c
10
u + 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y −1
26
(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
−6.57974 −24.0000
27
V. I
u
5
= hb + 1, a + 1, u − 1i
(i) Arc colorings
a
4
=
0
1
a
9
=
1
0
a
10
=
1
1
a
5
=
−1
0
a
1
=
−1
−1
a
11
=
0
1
a
12
=
−1
0
a
8
=
1
−1
a
3
=
1
0
a
2
=
0
−1
a
7
=
0
−1
a
6
=
−1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −24
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
8
c
9
, c
11
, c
12
u − 1
c
2
, c
3
, c
4
c
6
, c
7
, c
10
u + 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y −1
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = −1.00000
−6.57974 −24.0000
31
VI. I
u
6
= hb, a + 1, u − 1i
(i) Arc colorings
a
4
=
0
1
a
9
=
1
0
a
10
=
1
1
a
5
=
−1
0
a
1
=
−1
0
a
11
=
0
1
a
12
=
−1
1
a
8
=
1
−1
a
3
=
1
0
a
2
=
−1
0
a
7
=
0
−1
a
6
=
−1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
u
c
3
, c
4
, c
6
c
9
, c
12
u − 1
c
7
, c
8
, c
10
c
11
u + 1
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
y
c
3
, c
4
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y − 1
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = 0
−4.93480 −18.0000
35
VII. I
u
7
= hb − 1, a, u − 1i
(i) Arc colorings
a
4
=
0
1
a
9
=
1
0
a
10
=
1
1
a
5
=
−1
0
a
1
=
0
1
a
11
=
0
1
a
12
=
0
1
a
8
=
1
−1
a
3
=
1
0
a
2
=
−1
1
a
7
=
0
−1
a
6
=
0
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
36
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
8
c
10
u + 1
c
2
, c
3
, c
4
c
5
, c
9
u − 1
c
6
, c
11
, c
12
u
37
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
7
c
8
, c
9
, c
10
y − 1
c
6
, c
11
, c
12
y
38
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = 1.00000
−4.93480 −18.0000
39
VIII. I
u
8
= h−u
3
− u
2
+ b − 1, u
3
+ u
2
+ a − u, u
4
+ 1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
5
=
−u
−u
3
+ u
a
1
=
−u
3
− u
2
+ u
u
3
+ u
2
+ 1
a
11
=
−u
2
+ 1
u
2
a
12
=
−u
3
− 2u
2
+ u + 1
u
3
+ 2u
2
+ 1
a
8
=
−u
2
1
a
3
=
−u
−u
3
+ u
a
2
=
−u
3
− u
2
u
2
+ u + 1
a
7
=
−u
2
+ 1
u
2
a
6
=
u
3
+ u
2
− u
−u
3
− u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −16
40
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
11
(u − 1)
4
c
3
, c
4
, c
7
c
9
u
4
+ 1
c
5
, c
12
(u + 1)
4
c
8
, c
10
(u
2
+ 1)
2
41
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
(y − 1)
4
c
3
, c
4
, c
7
c
9
(y
2
+ 1)
2
c
8
, c
10
(y + 1)
4
42
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 0.707107 + 0.707107I
a = 1.41421 − 1.00000I
b = 0.29289 + 1.70711I
−1.64493 −16.0000
u = 0.707107 − 0.707107I
a = 1.41421 + 1.00000I
b = 0.29289 − 1.70711I
−1.64493 −16.0000
u = −0.707107 + 0.707107I
a = −1.41421 + 1.00000I
b = 1.70711 − 0.29289I
−1.64493 −16.0000
u = −0.707107 − 0.707107I
a = −1.41421 − 1.00000I
b = 1.70711 + 0.29289I
−1.64493 −16.0000
43
IX. I
v
1
= ha, b − 1, v + 1i
(i) Arc colorings
a
4
=
−1
0
a
9
=
1
0
a
10
=
1
0
a
5
=
−1
0
a
1
=
0
1
a
11
=
1
0
a
12
=
1
1
a
8
=
1
0
a
3
=
−1
0
a
2
=
−1
1
a
7
=
1
0
a
6
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
44
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
11
u − 1
c
3
, c
4
, c
7
c
8
, c
9
, c
10
u
c
5
, c
12
u + 1
45
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
y − 1
c
3
, c
4
, c
7
c
8
, c
9
, c
10
y
46
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
−3.28987 −12.0000
47
X. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
u(u − 1)
11
(u + 1)(u
46
+ 19u
45
+ ··· + 19u + 1)
· (u
66
+ 36u
65
+ ··· + 492u + 49)
c
2
, c
6
u(u − 1)
6
(u + 1)
6
(u
46
+ u
45
+ ··· − 3u − 1)
· (u
66
+ 2u
65
+ ··· − 32u − 7)
c
3
u(u − 1)
3
(u + 1)(u
4
+ 1)(u
4
− u
2
+ 2)(u
33
+ u
31
+ ··· − 8u − 1)
2
· (u
46
+ 3u
45
+ ··· − 1200u − 194)
c
4
, c
9
u(u − 1)
3
(u + 1)(u
4
+ 1)(u
4
− u
2
+ 2)(u
33
+ 2u
32
+ ··· − 2u − 1)
2
· (u
46
− 3u
45
+ ··· + 4u − 2)
c
5
, c
12
u(u − 1)
7
(u + 1)
5
(u
46
+ u
45
+ ··· − 3u − 1)
· (u
66
+ 2u
65
+ ··· − 32u − 7)
c
7
u(u − 1)(u + 1)
3
(u
4
+ 1)(u
4
− u
2
+ 2)(u
33
+ 6u
32
+ ··· + 128u + 23)
2
· (u
46
− 21u
45
+ ··· − 27796u + 2962)
c
8
u(u − 1)
2
(u + 1)
2
(u
2
+ 1)
2
(u
2
− u + 2)
2
· ((u
33
+ 10u
32
+ ··· − 2u + 1)
2
)(u
46
+ 15u
45
+ ··· + 24u + 4)
c
10
u(u + 1)
4
(u
2
+ 1)
2
(u
2
+ u + 2)
2
(u
33
+ 10u
32
+ ··· − 2u + 1)
2
· (u
46
+ 15u
45
+ ··· + 24u + 4)
48
XI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
y(y − 1)
12
(y
46
+ 29y
45
+ ··· − 83y + 1)
· (y
66
− 12y
65
+ ··· − 14116y + 2401)
c
2
, c
5
, c
6
c
12
y(y − 1)
12
(y
46
− 19y
45
+ ··· − 19y + 1)
· (y
66
− 36y
65
+ ··· − 492y + 49)
c
3
y(y − 1)
4
(y
2
+ 1)
2
(y
2
− y + 2)
2
(y
33
+ 2y
32
+ ··· − 2y − 1)
2
· (y
46
− 3y
45
+ ··· − 95192y + 37636)
c
4
, c
9
y(y − 1)
4
(y
2
+ 1)
2
(y
2
− y + 2)
2
(y
33
− 10y
32
+ ··· − 2y − 1)
2
· (y
46
− 15y
45
+ ··· − 24y + 4)
c
7
y(y − 1)
4
(y
2
+ 1)
2
(y
2
− y + 2)
2
· (y
33
+ 14y
32
+ ··· − 2062y − 529)
2
· (y
46
+ 9y
45
+ ··· − 47342296y + 8773444)
c
8
, c
10
y(y − 1)
4
(y + 1)
4
(y
2
+ 3y + 4)
2
(y
33
+ 26y
32
+ ··· + 6y − 1)
2
· (y
46
+ 33y
45
+ ··· − 448y + 16)
49
