11a
312
(K11a
312
)
A knot diagram
1
Linearized knot diagam
7 9 1 11 10 2 4 3 5 6 8
Solving Sequence
5,9
10 6
3,11
2 4 8 1 7
c
9
c
5
c
10
c
2
c
4
c
8
c
11
c
7
c
1
, c
3
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= h73u
22
+ 403u
21
+ ··· + 4b − 388, 13u
22
+ 105u
21
+ ··· + 8a − 196, u
23
+ 7u
22
+ ··· + 20u − 8i
I
u
2
= h−23118805228540u
7
a
5
+ 8120163058708u
7
a
4
+ ··· + 167668012322500a + 126864012582143,
− 2u
7
a
5
− 3u
7
a
4
+ ··· + 54a + 10, u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1i
I
u
3
= hu
11
− 5u
9
+ 8u
7
+ u
6
− 2u
5
− 3u
4
− 4u
3
+ 2u
2
+ b + u,
− u
10
− u
9
+ 4u
8
+ 4u
7
− 4u
6
− 5u
5
− 3u
4
+ 4u
2
+ a + 3u + 2,
u
12
− 6u
10
+ 13u
8
+ u
7
− 10u
6
− 4u
5
− 2u
4
+ 5u
3
+ 4u
2
− 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 83 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
= h73u
22
+ 403u
21
+ · · · + 4b − 388, 13u
22
+ 105u
21
+ · · · + 8a −
196, u
23
+ 7u
22
+ · · · + 20u − 8i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
6
=
u
−u
3
+ u
a
3
=
−1.62500u
22
− 13.1250u
21
+ ··· − 88.7500u + 24.5000
−
73
4
u
22
−
403
4
u
21
+ ··· − 303u + 97
a
11
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
16.6250u
22
+ 87.6250u
21
+ ··· + 214.250u − 72.5000
−
73
4
u
22
−
403
4
u
21
+ ··· − 303u + 97
a
4
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
8
=
−
93
8
u
22
−
517
8
u
21
+ ··· −
769
4
u + 62
37
4
u
22
+
213
4
u
21
+ ··· +
389
2
u − 59
a
1
=
−
13
8
u
22
−
67
8
u
21
+ ··· − 21u + 8
−
19
2
u
22
− 55u
21
+ ··· −
383
2
u + 59
a
7
=
167
8
u
22
+
943
8
u
21
+ ··· +
1551
4
u − 120
−
37
4
u
22
−
213
4
u
21
+ ··· −
387
2
u + 59
a
7
=
167
8
u
22
+
943
8
u
21
+ ··· +
1551
4
u − 120
−
37
4
u
22
−
213
4
u
21
+ ··· −
387
2
u + 59
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 3u
22
+17u
21
+24u
20
−24u
19
−51u
18
+70u
17
+81u
16
−139u
15
+10u
14
+241u
13
−226u
12
−
212u
11
+ 397u
10
−84u
9
−335u
8
+ 295u
7
−62u
6
−302u
5
+ 136u
4
−15u
3
−78u
2
+ 40u −2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
8
u
23
+ 10u
21
+ ··· + 3u − 1
c
3
u
23
− 24u
22
+ ··· + 3840u − 256
c
4
u
23
− 21u
22
+ ··· − 11268u + 1192
c
5
, c
9
, c
10
u
23
+ 7u
22
+ ··· + 20u − 8
c
7
, c
11
u
23
+ u
22
+ ··· + 3u
2
− 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
23
+ 20y
22
+ ··· + 13y −1
c
3
y
23
− 4y
22
+ ··· + 131072y −65536
c
4
y
23
+ 9y
22
+ ··· + 19115664y −1420864
c
5
, c
9
, c
10
y
23
− 19y
22
+ ··· + 144y −64
c
7
, c
11
y
23
− 3y
22
+ ··· + 6y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.293135 + 1.025030I
a = 0.46656 − 1.57304I
b = −0.147192 − 1.229000I
−7.64064 + 1.90172I −11.16155 − 1.95097I
u = 0.293135 − 1.025030I
a = 0.46656 + 1.57304I
b = −0.147192 + 1.229000I
−7.64064 − 1.90172I −11.16155 + 1.95097I
u = 0.202954 + 0.883680I
a = −0.38232 + 2.26017I
b = 0.48719 + 1.49237I
−9.7130 + 11.5082I −0.75618 − 6.89858I
u = 0.202954 − 0.883680I
a = −0.38232 − 2.26017I
b = 0.48719 − 1.49237I
−9.7130 − 11.5082I −0.75618 + 6.89858I
u = 0.881214 + 0.717683I
a = 0.446178 − 1.010460I
b = −0.044762 − 1.270850I
−5.82775 + 3.98753I −2.21274 − 8.17133I
u = 0.881214 − 0.717683I
a = 0.446178 + 1.010460I
b = −0.044762 + 1.270850I
−5.82775 − 3.98753I −2.21274 + 8.17133I
u = 1.14836
a = 0.267977
b = 0.450637
1.73407 6.87040
u = 1.034490 + 0.522098I
a = −0.652102 + 0.902922I
b = −0.37473 + 1.45394I
−7.16797 − 6.55570I 1.22391 + 3.26324I
u = 1.034490 − 0.522098I
a = −0.652102 − 0.902922I
b = −0.37473 − 1.45394I
−7.16797 + 6.55570I 1.22391 − 3.26324I
u = 0.232269 + 0.616489I
a = −0.683421 − 0.586793I
b = −0.575175 + 0.039007I
−0.29865 + 2.39912I 6.29196 − 4.13143I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.232269 − 0.616489I
a = −0.683421 + 0.586793I
b = −0.575175 − 0.039007I
−0.29865 − 2.39912I 6.29196 + 4.13143I
u = −1.372390 + 0.114615I
a = 0.820986 + 0.214490I
b = −0.737153 + 0.407888I
6.36396 − 1.94185I 12.44424 + 2.77963I
u = −1.372390 − 0.114615I
a = 0.820986 − 0.214490I
b = −0.737153 − 0.407888I
6.36396 + 1.94185I 12.44424 − 2.77963I
u = −1.381230 + 0.237993I
a = −0.152679 − 0.704144I
b = 0.670861 − 0.027425I
4.83020 − 5.52175I 12.07498 + 4.89921I
u = −1.381230 − 0.237993I
a = −0.152679 + 0.704144I
b = 0.670861 + 0.027425I
4.83020 + 5.52175I 12.07498 − 4.89921I
u = −1.39795 + 0.37738I
a = 1.40129 + 1.12721I
b = −0.57325 + 1.48723I
−4.6506 − 16.0409I 3.32343 + 8.47375I
u = −1.39795 − 0.37738I
a = 1.40129 − 1.12721I
b = −0.57325 − 1.48723I
−4.6506 + 16.0409I 3.32343 − 8.47375I
u = −1.42052 + 0.45491I
a = −0.968130 − 0.943346I
b = 0.318171 − 1.163070I
−2.31364 − 7.21005I −0.81443 + 11.11700I
u = −1.42052 − 0.45491I
a = −0.968130 + 0.943346I
b = 0.318171 + 1.163070I
−2.31364 + 7.21005I −0.81443 − 11.11700I
u = 0.401495 + 0.274693I
a = −0.290970 + 0.483465I
b = 0.473749 + 0.279232I
0.892504 + 0.454173I 10.11280 − 4.18130I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.401495 − 0.274693I
a = −0.290970 − 0.483465I
b = 0.473749 − 0.279232I
0.892504 − 0.454173I 10.11280 + 4.18130I
u = −1.54765 + 0.11437I
a = −0.389379 + 0.033075I
b = 0.276976 − 1.131580I
2.45199 − 6.58203I 4.53835 + 6.99896I
u = −1.54765 − 0.11437I
a = −0.389379 − 0.033075I
b = 0.276976 + 1.131580I
2.45199 + 6.58203I 4.53835 − 6.99896I
7
II. I
u
2
= h−2.31 × 10
13
a
5
u
7
+ 8.12 × 10
12
a
4
u
7
+ · · · + 1.68 × 10
14
a + 1.27 ×
10
14
, −2u
7
a
5
− 3u
7
a
4
+ · · · + 54a + 10, u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
6
=
u
−u
3
+ u
a
3
=
a
0.392427a
5
u
7
− 0.137835a
4
u
7
+ ··· − 2.84606a − 2.15344
a
11
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
−0.392427a
5
u
7
+ 0.137835a
4
u
7
+ ··· + 3.84606a + 2.15344
0.392427a
5
u
7
− 0.137835a
4
u
7
+ ··· − 2.84606a − 2.15344
a
4
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
8
=
0.619590a
5
u
7
+ 0.411741a
4
u
7
+ ··· + 5.96004a + 6.04257
−0.461898a
5
u
7
+ 0.617791a
4
u
7
+ ··· − 2.20681a − 0.962589
a
1
=
0.863277a
5
u
7
+ 0.0511046a
4
u
7
+ ··· − 1.95851a − 2.40659
−1.09603a
5
u
7
− 0.183794a
4
u
7
+ ··· − 3.37057a − 1.13036
a
7
=
0.257408a
5
u
7
− 0.257217a
4
u
7
+ ··· + 8.19095a + 7.33644
−0.388740a
5
u
7
+ 0.461509a
4
u
7
+ ··· − 4.45800a − 2.53941
a
7
=
0.257408a
5
u
7
− 0.257217a
4
u
7
+ ··· + 8.19095a + 7.33644
−0.388740a
5
u
7
+ 0.461509a
4
u
7
+ ··· − 4.45800a − 2.53941
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
17781823578608
58912383397937
u
7
a
5
+
890888304264
58912383397937
u
7
a
4
+ ··· −
483633451308792
58912383397937
a −
241926483811578
58912383397937
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
8
u
48
+ u
47
+ ··· + 160u + 293
c
3
(u
3
+ u
2
− 1)
16
c
4
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
6
c
5
, c
9
, c
10
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
6
c
7
, c
11
u
48
+ 3u
47
+ ··· + 890u + 173
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
48
+ 39y
47
+ ··· − 564720y + 85849
c
3
(y
3
− y
2
+ 2y −1)
16
c
4
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
6
c
5
, c
9
, c
10
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
6
c
7
, c
11
y
48
− 13y
47
+ ··· − 826008y + 29929
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.180120 + 0.268597I
a = −0.896822 − 0.641304I
b = −0.44089 − 1.82899I
−5.00760 − 1.13123I −3.60429 + 0.51079I
u = −1.180120 + 0.268597I
a = −0.989164 − 0.528833I
b = 0.347952 + 0.310629I
−0.87002 − 3.95936I 2.92498 + 3.49024I
u = −1.180120 + 0.268597I
a = 0.141663 + 0.835373I
b = −1.167430 − 0.563919I
−0.87002 + 1.69689I 2.92498 − 2.46866I
u = −1.180120 + 0.268597I
a = −0.123278 + 1.382340I
b = 0.11559 + 1.41262I
−5.00760 − 1.13123I −3.60429 + 0.51079I
u = −1.180120 + 0.268597I
a = −1.09571 − 1.53145I
b = 0.484357 − 1.213990I
−0.87002 − 3.95936I 2.92498 + 3.49024I
u = −1.180120 + 0.268597I
a = 1.17316 + 1.78430I
b = 0.089556 + 1.152970I
−0.87002 + 1.69689I 2.92498 − 2.46866I
u = −1.180120 − 0.268597I
a = −0.896822 + 0.641304I
b = −0.44089 + 1.82899I
−5.00760 + 1.13123I −3.60429 − 0.51079I
u = −1.180120 − 0.268597I
a = −0.989164 + 0.528833I
b = 0.347952 − 0.310629I
−0.87002 + 3.95936I 2.92498 − 3.49024I
u = −1.180120 − 0.268597I
a = 0.141663 − 0.835373I
b = −1.167430 + 0.563919I
−0.87002 − 1.69689I 2.92498 + 2.46866I
u = −1.180120 − 0.268597I
a = −0.123278 − 1.382340I
b = 0.11559 − 1.41262I
−5.00760 + 1.13123I −3.60429 − 0.51079I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.180120 − 0.268597I
a = −1.09571 + 1.53145I
b = 0.484357 + 1.213990I
−0.87002 + 3.95936I 2.92498 − 3.49024I
u = −1.180120 − 0.268597I
a = 1.17316 − 1.78430I
b = 0.089556 − 1.152970I
−0.87002 − 1.69689I 2.92498 + 2.46866I
u = −0.108090 + 0.747508I
a = 1.012830 − 0.490873I
b = 1.294730 − 0.286176I
−4.07009 − 5.40662I −0.21317 + 6.54740I
u = −0.108090 + 0.747508I
a = 0.192080 − 0.476649I
b = −0.465784 − 0.043673I
−4.07009 + 0.24963I −0.213168 + 0.588510I
u = −0.108090 + 0.747508I
a = −0.50426 − 2.37465I
b = −0.220687 − 1.217460I
−4.07009 + 0.24963I −0.213168 + 0.588510I
u = −0.108090 + 0.747508I
a = −0.12907 − 2.65292I
b = 0.66006 − 1.66847I
−8.20767 − 2.57849I −6.74243 + 3.56796I
u = −0.108090 + 0.747508I
a = 1.31751 + 2.32128I
b = −0.172710 + 1.289020I
−8.20767 − 2.57849I −6.74243 + 3.56796I
u = −0.108090 + 0.747508I
a = 0.19648 + 3.09182I
b = −0.240367 + 1.260870I
−4.07009 − 5.40662I −0.21317 + 6.54740I
u = −0.108090 − 0.747508I
a = 1.012830 + 0.490873I
b = 1.294730 + 0.286176I
−4.07009 + 5.40662I −0.21317 − 6.54740I
u = −0.108090 − 0.747508I
a = 0.192080 + 0.476649I
b = −0.465784 + 0.043673I
−4.07009 − 0.24963I −0.213168 − 0.588510I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.108090 − 0.747508I
a = −0.50426 + 2.37465I
b = −0.220687 + 1.217460I
−4.07009 − 0.24963I −0.213168 − 0.588510I
u = −0.108090 − 0.747508I
a = −0.12907 + 2.65292I
b = 0.66006 + 1.66847I
−8.20767 + 2.57849I −6.74243 − 3.56796I
u = −0.108090 − 0.747508I
a = 1.31751 − 2.32128I
b = −0.172710 − 1.289020I
−8.20767 + 2.57849I −6.74243 − 3.56796I
u = −0.108090 − 0.747508I
a = 0.19648 − 3.09182I
b = −0.240367 − 1.260870I
−4.07009 + 5.40662I −0.21317 − 6.54740I
u = 1.37100
a = 0.216638 + 0.976013I
b = 0.312893 − 1.010360I
0.454474 2.84453 + 0.I
u = 1.37100
a = 0.216638 − 0.976013I
b = 0.312893 + 1.010360I
0.454474 2.84453 + 0.I
u = 1.37100
a = −0.567976 + 0.778979I
b = 0.790704 + 0.425774I
4.59206 − 2.82812I 9.37379 + 2.97945I
u = 1.37100
a = −0.567976 − 0.778979I
b = 0.790704 − 0.425774I
4.59206 + 2.82812I 9.37379 − 2.97945I
u = 1.37100
a = 0.731511 + 0.214900I
b = −0.554508 + 1.009700I
4.59206 − 2.82812I 9.37379 + 2.97945I
u = 1.37100
a = 0.731511 − 0.214900I
b = −0.554508 − 1.009700I
4.59206 + 2.82812I 9.37379 − 2.97945I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.334530 + 0.318930I
a = 0.387884 − 0.883429I
b = −1.407320 − 0.123988I
0.46900 + 9.27166I 4.93820 − 8.27362I
u = 1.334530 + 0.318930I
a = 0.933242 − 0.982503I
b = 0.003311 − 1.250180I
0.46900 + 3.61542I 4.93820 − 2.31472I
u = 1.334530 + 0.318930I
a = −0.314651 − 0.006577I
b = 0.631559 − 0.239514I
0.46900 + 3.61542I 4.93820 − 2.31472I
u = 1.334530 + 0.318930I
a = 1.56880 − 1.06264I
b = −0.82210 − 1.57135I
−3.66858 + 6.44354I −1.59106 − 5.29417I
u = 1.334530 + 0.318930I
a = −1.29077 + 1.62216I
b = 0.328612 + 1.331730I
0.46900 + 9.27166I 4.93820 − 8.27362I
u = 1.334530 + 0.318930I
a = −1.94541 + 0.73100I
b = 0.234132 + 1.197830I
−3.66858 + 6.44354I −1.59106 − 5.29417I
u = 1.334530 − 0.318930I
a = 0.387884 + 0.883429I
b = −1.407320 + 0.123988I
0.46900 − 9.27166I 4.93820 + 8.27362I
u = 1.334530 − 0.318930I
a = 0.933242 + 0.982503I
b = 0.003311 + 1.250180I
0.46900 − 3.61542I 4.93820 + 2.31472I
u = 1.334530 − 0.318930I
a = −0.314651 + 0.006577I
b = 0.631559 + 0.239514I
0.46900 − 3.61542I 4.93820 + 2.31472I
u = 1.334530 − 0.318930I
a = 1.56880 + 1.06264I
b = −0.82210 + 1.57135I
−3.66858 − 6.44354I −1.59106 + 5.29417I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.334530 − 0.318930I
a = −1.29077 − 1.62216I
b = 0.328612 − 1.331730I
0.46900 − 9.27166I 4.93820 + 8.27362I
u = 1.334530 − 0.318930I
a = −1.94541 − 0.73100I
b = 0.234132 − 1.197830I
−3.66858 − 6.44354I −1.59106 + 5.29417I
u = −0.463640
a = −0.863122 + 0.658172I
b = −0.171893 − 1.389680I
−5.20322 − 60.874953 + 0.10I
u = −0.463640
a = −0.863122 − 0.658172I
b = −0.171893 + 1.389680I
−5.20322 − 60.874953 + 0.10I
u = −0.463640
a = −0.53791 + 1.70966I
b = 0.383023 + 0.964868I
−1.06564 + 2.82812I 7.40422 − 2.97945I
u = −0.463640
a = −0.53791 − 1.70966I
b = 0.383023 − 0.964868I
−1.06564 − 2.82812I 7.40422 + 2.97945I
u = −0.463640
a = −0.11364 + 2.25012I
b = −0.512781 − 0.176265I
−1.06564 + 2.82812I 7.40422 − 2.97945I
u = −0.463640
a = −0.11364 − 2.25012I
b = −0.512781 + 0.176265I
−1.06564 − 2.82812I 7.40422 + 2.97945I
15
III.
I
u
3
= hu
11
− 5u
9
+ · · · + b + u, −u
10
− u
9
+ · · · + a + 2, u
12
− 6u
10
+ · · · − 2u + 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
6
=
u
−u
3
+ u
a
3
=
u
10
+ u
9
− 4u
8
− 4u
7
+ 4u
6
+ 5u
5
+ 3u
4
− 4u
2
− 3u − 2
−u
11
+ 5u
9
− 8u
7
− u
6
+ 2u
5
+ 3u
4
+ 4u
3
− 2u
2
− u
a
11
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
u
11
+ u
10
− 4u
9
− 4u
8
+ 4u
7
+ 5u
6
+ 3u
5
− 4u
3
− 2u
2
− 2u − 2
−u
11
+ 5u
9
− 8u
7
− u
6
+ 2u
5
+ 3u
4
+ 4u
3
− 2u
2
− u
a
4
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
8
=
u
11
− 5u
9
+ 9u
7
+ 2u
6
− 5u
5
− 6u
4
− 3u
3
+ 5u
2
+ 4u
−u
10
+ 4u
8
− 4u
6
− u
5
− 2u
4
+ 2u
3
+ 3u
2
a
1
=
u
9
+ u
8
− 4u
7
− 4u
6
+ 5u
5
+ 6u
4
+ u
3
− 3u
2
− 4u
−u
10
+ 5u
8
− u
7
− 8u
6
+ 2u
5
+ 3u
4
+ u
3
+ u
2
− 3u + 1
a
7
=
u
11
+ u
10
− 5u
9
− 4u
8
+ 9u
7
+ 6u
6
− 4u
5
− 4u
4
− 5u
3
+ 2u
2
+ 5u − 1
−u
10
+ 4u
8
− 4u
6
− u
5
− 2u
4
+ u
3
+ 3u
2
+ u
a
7
=
u
11
+ u
10
− 5u
9
− 4u
8
+ 9u
7
+ 6u
6
− 4u
5
− 4u
4
− 5u
3
+ 2u
2
+ 5u − 1
−u
10
+ 4u
8
− 4u
6
− u
5
− 2u
4
+ u
3
+ 3u
2
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
11
−u
10
−u
9
+ 8u
8
−8u
7
−19u
6
+ 16u
5
+ 16u
4
+ 3u
3
−16u + 1
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
12
+ 6u
10
− u
9
+ 14u
8
− 4u
7
+ 17u
6
− 6u
5
+ 12u
4
− 3u
3
+ 5u
2
− u + 1
c
2
, c
6
u
12
+ 6u
10
+ u
9
+ 14u
8
+ 4u
7
+ 17u
6
+ 6u
5
+ 12u
4
+ 3u
3
+ 5u
2
+ u + 1
c
3
u
12
+ 3u
11
+ 3u
10
+ u
9
+ 2u
8
+ 4u
7
+ 3u
6
+ 2u
5
+ 2u
4
− u
3
− 2u
2
+ 1
c
4
u
12
+ 2u
10
+ 3u
9
+ 4u
8
− 4u
7
+ 12u
6
− 7u
5
+ 3u
4
− 4u
3
+ 4u
2
+ 2u + 1
c
5
u
12
− 6u
10
+ 13u
8
− u
7
− 10u
6
+ 4u
5
− 2u
4
− 5u
3
+ 4u
2
+ 2u + 1
c
7
, c
11
u
12
− u
11
− u
10
+ u
9
+ u
8
− u
7
− u
5
+ 2u
4
+ 2u
3
+ 1
c
9
, c
10
u
12
− 6u
10
+ 13u
8
+ u
7
− 10u
6
− 4u
5
− 2u
4
+ 5u
3
+ 4u
2
− 2u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
12
+ 12y
11
+ ··· + 9y + 1
c
3
y
12
− 3y
11
+ 7y
10
− 7y
9
+ 6y
8
+ 6y
7
− 7y
6
+ 14y
5
− 3y
3
+ 8y
2
− 4y + 1
c
4
y
12
+ 4y
11
+ ··· + 4y + 1
c
5
, c
9
, c
10
y
12
− 12y
11
+ ··· + 4y + 1
c
7
, c
11
y
12
− 3y
11
+ 5y
10
− 5y
9
+ 5y
8
+ y
7
+ y
5
+ 10y
4
− 4y
3
+ 4y
2
+ 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215104 + 0.798845I
a = −0.72776 − 1.83625I
b = 0.240699 − 1.306190I
−6.79522 − 1.91915I 0.40771 + 1.45870I
u = −0.215104 − 0.798845I
a = −0.72776 + 1.83625I
b = 0.240699 + 1.306190I
−6.79522 + 1.91915I 0.40771 − 1.45870I
u = −1.181970 + 0.217891I
a = −0.278563 − 0.993678I
b = −0.17391 − 1.59240I
−4.12723 − 1.52744I 6.19652 + 4.95399I
u = −1.181970 − 0.217891I
a = −0.278563 + 0.993678I
b = −0.17391 + 1.59240I
−4.12723 + 1.52744I 6.19652 − 4.95399I
u = 1.286840 + 0.093791I
a = −0.095508 + 1.343010I
b = 0.506197 − 0.617660I
1.54867 − 1.75409I 7.03852 + 3.77129I
u = 1.286840 − 0.093791I
a = −0.095508 − 1.343010I
b = 0.506197 + 0.617660I
1.54867 + 1.75409I 7.03852 − 3.77129I
u = 1.334400 + 0.365970I
a = 1.33435 − 0.96209I
b = −0.445009 − 1.143310I
−1.99720 + 6.23322I 3.71112 − 3.63849I
u = 1.334400 − 0.365970I
a = 1.33435 + 0.96209I
b = −0.445009 + 1.143310I
−1.99720 − 6.23322I 3.71112 + 3.63849I
u = −1.43060 + 0.17503I
a = 0.132739 − 0.441201I
b = 0.229430 − 0.594825I
3.51165 − 5.19940I 5.87830 + 4.31149I
u = −1.43060 − 0.17503I
a = 0.132739 + 0.441201I
b = 0.229430 + 0.594825I
3.51165 + 5.19940I 5.87830 − 4.31149I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.206431 + 0.331897I
a = −2.36526 − 1.65098I
b = −0.357408 − 0.662175I
−2.01027 + 3.15177I −2.73217 − 5.71624I
u = 0.206431 − 0.331897I
a = −2.36526 + 1.65098I
b = −0.357408 + 0.662175I
−2.01027 − 3.15177I −2.73217 + 5.71624I
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
12
+ 6u
10
− u
9
+ 14u
8
− 4u
7
+ 17u
6
− 6u
5
+ 12u
4
− 3u
3
+ 5u
2
− u + 1)
· (u
23
+ 10u
21
+ ··· + 3u − 1)(u
48
+ u
47
+ ··· + 160u + 293)
c
2
, c
6
(u
12
+ 6u
10
+ u
9
+ 14u
8
+ 4u
7
+ 17u
6
+ 6u
5
+ 12u
4
+ 3u
3
+ 5u
2
+ u + 1)
· (u
23
+ 10u
21
+ ··· + 3u − 1)(u
48
+ u
47
+ ··· + 160u + 293)
c
3
(u
3
+ u
2
− 1)
16
· (u
12
+ 3u
11
+ 3u
10
+ u
9
+ 2u
8
+ 4u
7
+ 3u
6
+ 2u
5
+ 2u
4
− u
3
− 2u
2
+ 1)
· (u
23
− 24u
22
+ ··· + 3840u − 256)
c
4
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
6
· (u
12
+ 2u
10
+ 3u
9
+ 4u
8
− 4u
7
+ 12u
6
− 7u
5
+ 3u
4
− 4u
3
+ 4u
2
+ 2u + 1)
· (u
23
− 21u
22
+ ··· − 11268u + 1192)
c
5
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
6
· (u
12
− 6u
10
+ 13u
8
− u
7
− 10u
6
+ 4u
5
− 2u
4
− 5u
3
+ 4u
2
+ 2u + 1)
· (u
23
+ 7u
22
+ ··· + 20u − 8)
c
7
, c
11
(u
12
− u
11
− u
10
+ u
9
+ u
8
− u
7
− u
5
+ 2u
4
+ 2u
3
+ 1)
· (u
23
+ u
22
+ ··· + 3u
2
− 1)(u
48
+ 3u
47
+ ··· + 890u + 173)
c
9
, c
10
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
6
· (u
12
− 6u
10
+ 13u
8
+ u
7
− 10u
6
− 4u
5
− 2u
4
+ 5u
3
+ 4u
2
− 2u + 1)
· (u
23
+ 7u
22
+ ··· + 20u − 8)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
(y
12
+ 12y
11
+ ··· + 9y + 1)(y
23
+ 20y
22
+ ··· + 13y −1)
· (y
48
+ 39y
47
+ ··· − 564720y + 85849)
c
3
(y
3
− y
2
+ 2y −1)
16
· (y
12
− 3y
11
+ 7y
10
− 7y
9
+ 6y
8
+ 6y
7
− 7y
6
+ 14y
5
− 3y
3
+ 8y
2
− 4y + 1)
· (y
23
− 4y
22
+ ··· + 131072y −65536)
c
4
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
6
· (y
12
+ 4y
11
+ ··· + 4y + 1)(y
23
+ 9y
22
+ ··· + 1.91157 × 10
7
y −1420864)
c
5
, c
9
, c
10
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
6
· (y
12
− 12y
11
+ ··· + 4y + 1)(y
23
− 19y
22
+ ··· + 144y −64)
c
7
, c
11
(y
12
− 3y
11
+ 5y
10
− 5y
9
+ 5y
8
+ y
7
+ y
5
+ 10y
4
− 4y
3
+ 4y
2
+ 1)
· (y
23
− 3y
22
+ ··· + 6y −1)(y
48
− 13y
47
+ ··· − 826008y + 29929)
22
