12a
0958
(K12a
0958
)
A knot diagram
1
Linearized knot diagam
4 6 10 9 12 3 11 1 2 7 8 5
Solving Sequence
5,9 1,4
2 10 3 8 12 6 11 7
c
4
c
1
c
9
c
3
c
8
c
12
c
5
c
11
c
7
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3.24811 × 10
815
u
126
− 2.46551 × 10
815
u
125
+ ··· + 9.83532 × 10
817
b + 9.09376 × 10
818
,
− 1.75194 × 10
818
u
126
− 5.25120 × 10
815
u
125
+ ··· + 1.51562 × 10
821
a − 1.08916 × 10
822
,
u
127
− u
126
+ ··· + 17533u + 1541i
I
u
2
= h−1.10098 × 10
15
u
22
+ 8.50756 × 10
14
u
21
+ ··· + 6.63632 × 10
15
b + 1.53110 × 10
16
,
4522732367957282u
22
− 975327261831870u
21
+ ··· + 6636320717064427a + 5366933139683854,
u
23
+ 8u
21
+ ··· − 2u + 1i
I
u
3
= hu
2
+ b + 3u + 1, −u
2
+ a − 4u − 4, u
3
+ 3u
2
+ 2u + 1i
I
u
4
= hb − u, −u
2
+ a + u − 2, u
3
− u
2
+ 2u − 1i
* 4 irreducible components of dim
C
= 0, with total 156 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
= h3.25 × 10
815
u
126
− 2.47 × 10
815
u
125
+ · · · + 9.84 × 10
817
b + 9.09 ×
10
818
, −1.75 × 10
818
u
126
− 5.25 × 10
815
u
125
+ · · · + 1.52 × 10
821
a − 1.09 ×
10
822
, u
127
− u
126
+ · · · + 17533u + 1541i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
0.00115592u
126
+ 3.46471 × 10
−6
u
125
+ ··· + 50.3754u + 7.18625
−0.00330250u
126
+ 0.00250680u
125
+ ··· − 119.213u − 9.24602
a
4
=
1
u
2
a
2
=
0.00477679u
126
− 0.00358681u
125
+ ··· + 147.480u + 14.6457
−0.00393245u
126
+ 0.00319957u
125
+ ··· − 125.329u − 9.29317
a
10
=
−0.00686858u
126
+ 0.0127713u
125
+ ··· + 464.976u + 54.0429
0.000983727u
126
− 0.00205194u
125
+ ··· − 136.835u − 14.3804
a
3
=
0.0156371u
126
− 0.0127997u
125
+ ··· + 573.026u + 44.8327
−0.00738456u
126
+ 0.00721566u
125
+ ··· − 281.515u − 20.3776
a
8
=
−0.00750345u
126
+ 0.0130698u
125
+ ··· + 405.454u + 47.2377
0.00108359u
126
− 0.00196659u
125
+ ··· − 99.6256u − 10.0985
a
12
=
0.00445842u
126
− 0.00250333u
125
+ ··· + 169.589u + 16.4323
−0.00330250u
126
+ 0.00250680u
125
+ ··· − 119.213u − 9.24602
a
6
=
0.0100270u
126
− 0.00862773u
125
+ ··· + 375.684u + 28.8926
−0.00347385u
126
+ 0.00315813u
125
+ ··· − 186.725u − 13.6212
a
11
=
−0.00496870u
126
+ 0.000885001u
125
+ ··· − 378.517u − 36.7701
0.000661809u
126
+ 0.000354500u
125
+ ··· + 63.5886u + 6.17548
a
7
=
−0.00506831u
126
+ 0.00355203u
125
+ ··· − 219.198u − 13.1992
0.00335759u
126
− 0.00443429u
125
+ ··· + 58.2261u + 3.86702
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0123516u
126
− 0.00278997u
125
+ ··· − 1942.80u − 202.679
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
127
− 5u
126
+ ··· − 1344u + 64
c
2
, c
6
u
127
+ 2u
126
+ ··· + 10323u + 2467
c
3
u
127
− 3u
126
+ ··· + 1233985982u − 292939631
c
4
u
127
+ u
126
+ ··· + 17533u − 1541
c
5
, c
12
u
127
+ 3u
126
+ ··· − 39833u + 3461
c
7
, c
10
, c
11
u
127
− 5u
126
+ ··· − 361u + 29
c
8
u
127
+ u
126
+ ··· − 26u − 1
c
9
u
127
− u
126
+ ··· + 3405u + 207
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
127
+ 5y
126
+ ··· + 215040y −4096
c
2
, c
6
y
127
− 82y
126
+ ··· + 357241133y −6086089
c
3
y
127
+ 37y
126
+ ··· − 3665675937186530842y −85813627410416161
c
4
y
127
+ 35y
126
+ ··· + 35832577y −2374681
c
5
, c
12
y
127
+ 61y
126
+ ··· + 1408883241y −11978521
c
7
, c
10
, c
11
y
127
− 141y
126
+ ··· + 115183y −841
c
8
y
127
+ y
126
+ ··· + 116y −1
c
9
y
127
− 13y
126
+ ··· + 5912703y −42849
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.454897 + 0.911052I
a = 1.236380 + 0.261261I
b = −0.089606 − 0.913498I
0.559126 + 0.625580I 0
u = −0.454897 − 0.911052I
a = 1.236380 − 0.261261I
b = −0.089606 + 0.913498I
0.559126 − 0.625580I 0
u = 0.364851 + 0.905528I
a = 0.903144 − 0.657744I
b = 0.203950 + 1.280870I
−3.19098 + 2.67904I 0
u = 0.364851 − 0.905528I
a = 0.903144 + 0.657744I
b = 0.203950 − 1.280870I
−3.19098 − 2.67904I 0
u = −0.964069
a = 0.535737
b = 0.630821
1.16343 0
u = 0.353449 + 0.888121I
a = 0.940412 − 0.922540I
b = 0.178902 + 1.286600I
−3.18398 + 2.66953I 0
u = 0.353449 − 0.888121I
a = 0.940412 + 0.922540I
b = 0.178902 − 1.286600I
−3.18398 − 2.66953I 0
u = 1.055390 + 0.142832I
a = 0.348792 − 0.167075I
b = 0.240369 − 0.821665I
−0.35427 − 2.07951I 0
u = 1.055390 − 0.142832I
a = 0.348792 + 0.167075I
b = 0.240369 + 0.821665I
−0.35427 + 2.07951I 0
u = −0.304445 + 0.880878I
a = 1.202040 + 0.207316I
b = 0.52487 − 1.33794I
−2.09198 − 6.77319I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.304445 − 0.880878I
a = 1.202040 − 0.207316I
b = 0.52487 + 1.33794I
−2.09198 + 6.77319I 0
u = 0.632797 + 0.650968I
a = 0.724983 + 0.404447I
b = 1.15491 + 0.96814I
7.33318 − 2.03058I 0
u = 0.632797 − 0.650968I
a = 0.724983 − 0.404447I
b = 1.15491 − 0.96814I
7.33318 + 2.03058I 0
u = 0.612874 + 0.663367I
a = −0.587697 − 0.297157I
b = −0.488503 + 0.291381I
−1.15905 + 1.71609I 0
u = 0.612874 − 0.663367I
a = −0.587697 + 0.297157I
b = −0.488503 − 0.291381I
−1.15905 − 1.71609I 0
u = −0.537008 + 0.717718I
a = 1.36776 + 0.49896I
b = 0.934426 + 0.402625I
11.89500 + 0.48258I 0
u = −0.537008 − 0.717718I
a = 1.36776 − 0.49896I
b = 0.934426 − 0.402625I
11.89500 − 0.48258I 0
u = −0.669529 + 0.880014I
a = −0.849664 − 0.146800I
b = −0.758023 − 0.071047I
0.20746 − 4.43767I 0
u = −0.669529 − 0.880014I
a = −0.849664 + 0.146800I
b = −0.758023 + 0.071047I
0.20746 + 4.43767I 0
u = 0.745732 + 0.817700I
a = 1.33611 + 0.83979I
b = −0.181688 + 0.806349I
7.25608 + 6.95311I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.745732 − 0.817700I
a = 1.33611 − 0.83979I
b = −0.181688 − 0.806349I
7.25608 − 6.95311I 0
u = 0.246295 + 0.856716I
a = 1.44391 − 0.09789I
b = 0.78232 + 1.30470I
5.44496 + 9.85386I 0
u = 0.246295 − 0.856716I
a = 1.44391 + 0.09789I
b = 0.78232 − 1.30470I
5.44496 − 9.85386I 0
u = −0.034823 + 0.889992I
a = −0.921638 − 0.430012I
b = −0.136518 + 1.160520I
−3.73206 + 1.61429I 0
u = −0.034823 − 0.889992I
a = −0.921638 + 0.430012I
b = −0.136518 − 1.160520I
−3.73206 − 1.61429I 0
u = −0.724488 + 0.510499I
a = −0.042859 − 0.169584I
b = −0.84523 − 1.18019I
3.13816 + 0.66185I 0
u = −0.724488 − 0.510499I
a = −0.042859 + 0.169584I
b = −0.84523 + 1.18019I
3.13816 − 0.66185I 0
u = −0.309997 + 0.826021I
a = 1.38789 + 1.88410I
b = 0.19953 − 1.47411I
1.64868 − 4.08208I 0
u = −0.309997 − 0.826021I
a = 1.38789 − 1.88410I
b = 0.19953 + 1.47411I
1.64868 + 4.08208I 0
u = −0.242034 + 0.841163I
a = −0.59511 + 1.58495I
b = 0.313244 − 0.932375I
3.30458 − 2.00993I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.242034 − 0.841163I
a = −0.59511 − 1.58495I
b = 0.313244 + 0.932375I
3.30458 + 2.00993I 0
u = 0.926532 + 0.637758I
a = −1.58255 − 0.25843I
b = −0.483025 − 1.252390I
9.65313 + 9.05864I 0
u = 0.926532 − 0.637758I
a = −1.58255 + 0.25843I
b = −0.483025 + 1.252390I
9.65313 − 9.05864I 0
u = −0.765524 + 0.403805I
a = −1.56302 − 0.22468I
b = −0.872536 − 0.167249I
13.05490 − 4.10370I 0
u = −0.765524 − 0.403805I
a = −1.56302 + 0.22468I
b = −0.872536 + 0.167249I
13.05490 + 4.10370I 0
u = 0.842786 + 0.760771I
a = 0.872088 − 0.638158I
b = 0.914725 + 0.316028I
7.85544 + 0.11358I 0
u = 0.842786 − 0.760771I
a = 0.872088 + 0.638158I
b = 0.914725 − 0.316028I
7.85544 − 0.11358I 0
u = 0.841248 + 0.047036I
a = −1.084480 − 0.673211I
b = −0.588181 + 0.238816I
4.87440 + 0.69256I 0
u = 0.841248 − 0.047036I
a = −1.084480 + 0.673211I
b = −0.588181 − 0.238816I
4.87440 − 0.69256I 0
u = −0.944043 + 0.688858I
a = 0.529722 − 0.529388I
b = 0.1209810 − 0.0073066I
2.75448 − 4.67938I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.944043 − 0.688858I
a = 0.529722 + 0.529388I
b = 0.1209810 + 0.0073066I
2.75448 + 4.67938I 0
u = −0.654357 + 0.484227I
a = 0.821743 + 0.225535I
b = 0.391190 − 0.102487I
1.076060 − 0.369429I 0
u = −0.654357 − 0.484227I
a = 0.821743 − 0.225535I
b = 0.391190 + 0.102487I
1.076060 + 0.369429I 0
u = 0.762044 + 0.916108I
a = −0.004572 + 0.615664I
b = −0.360453 + 1.027130I
9.20578 + 0.95990I 0
u = 0.762044 − 0.916108I
a = −0.004572 − 0.615664I
b = −0.360453 − 1.027130I
9.20578 − 0.95990I 0
u = −1.100180 + 0.460924I
a = 0.349419 + 0.461107I
b = 0.546703 + 1.099350I
5.42405 + 5.10393I 0
u = −1.100180 − 0.460924I
a = 0.349419 − 0.461107I
b = 0.546703 − 1.099350I
5.42405 − 5.10393I 0
u = −0.828021 + 0.862047I
a = 1.278050 − 0.252875I
b = 0.462587 − 0.860582I
3.00752 − 5.37604I 0
u = −0.828021 − 0.862047I
a = 1.278050 + 0.252875I
b = 0.462587 + 0.860582I
3.00752 + 5.37604I 0
u = 0.803669 + 0.893064I
a = 1.59245 + 0.06065I
b = 0.560675 + 1.197540I
9.28090 + 4.98514I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.803669 − 0.893064I
a = 1.59245 − 0.06065I
b = 0.560675 − 1.197540I
9.28090 − 4.98514I 0
u = 0.755494 + 0.938460I
a = −0.881408 + 0.391019I
b = −1.145520 + 0.049576I
7.29999 + 5.77567I 0
u = 0.755494 − 0.938460I
a = −0.881408 − 0.391019I
b = −1.145520 − 0.049576I
7.29999 − 5.77567I 0
u = 0.182060 + 0.773412I
a = −1.59807 − 0.01138I
b = −0.387588 − 1.135120I
−4.73202 + 1.17378I 0
u = 0.182060 − 0.773412I
a = −1.59807 + 0.01138I
b = −0.387588 + 1.135120I
−4.73202 − 1.17378I 0
u = −0.314902 + 0.722477I
a = −2.90582 + 0.44698I
b = 0.154572 + 0.948395I
1.41058 + 0.66806I 0
u = −0.314902 − 0.722477I
a = −2.90582 − 0.44698I
b = 0.154572 − 0.948395I
1.41058 − 0.66806I 0
u = −0.231689 + 0.741214I
a = −1.73699 + 0.50596I
b = −0.721990 + 1.036050I
1.32567 − 2.90614I 0
u = −0.231689 − 0.741214I
a = −1.73699 − 0.50596I
b = −0.721990 − 1.036050I
1.32567 + 2.90614I 0
u = −0.896987 + 0.860662I
a = 0.843915 + 0.201618I
b = 1.401600 + 0.112990I
11.6518 − 11.7658I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.896987 − 0.860662I
a = 0.843915 − 0.201618I
b = 1.401600 − 0.112990I
11.6518 + 11.7658I 0
u = 0.916351 + 0.859472I
a = 0.829089 − 0.033001I
b = 1.049720 + 0.101056I
4.38768 + 8.69266I 0
u = 0.916351 − 0.859472I
a = 0.829089 + 0.033001I
b = 1.049720 − 0.101056I
4.38768 − 8.69266I 0
u = 0.257071 + 0.670014I
a = −2.73889 + 0.10092I
b = −0.111502 − 1.044230I
−4.25279 + 0.60258I 0. + 7.99103I
u = 0.257071 − 0.670014I
a = −2.73889 − 0.10092I
b = −0.111502 + 1.044230I
−4.25279 − 0.60258I 0. − 7.99103I
u = −0.079891 + 1.294470I
a = 0.112299 − 1.369410I
b = −0.131679 + 0.805279I
10.47890 − 3.07948I 0
u = −0.079891 − 1.294470I
a = 0.112299 + 1.369410I
b = −0.131679 − 0.805279I
10.47890 + 3.07948I 0
u = 0.490618 + 0.493448I
a = 1.136370 − 0.072984I
b = 0.972754 − 0.617116I
3.68376 + 0.15468I 13.04643 − 5.18596I
u = 0.490618 − 0.493448I
a = 1.136370 + 0.072984I
b = 0.972754 + 0.617116I
3.68376 − 0.15468I 13.04643 + 5.18596I
u = −0.442393 + 0.530026I
a = 0.662775 − 0.185174I
b = 1.096030 − 0.379727I
1.67691 + 0.65702I 1.51745 + 4.11768I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.442393 − 0.530026I
a = 0.662775 + 0.185174I
b = 1.096030 + 0.379727I
1.67691 − 0.65702I 1.51745 − 4.11768I
u = −0.777622 + 1.149890I
a = 0.038656 − 0.268231I
b = −0.195483 − 0.459087I
2.45396 − 0.71763I 0
u = −0.777622 − 1.149890I
a = 0.038656 + 0.268231I
b = −0.195483 + 0.459087I
2.45396 + 0.71763I 0
u = −0.005560 + 0.609730I
a = 3.28949 − 1.62600I
b = −0.224196 + 1.006980I
6.49113 − 8.79984I 4.45971 + 5.72952I
u = −0.005560 − 0.609730I
a = 3.28949 + 1.62600I
b = −0.224196 − 1.006980I
6.49113 + 8.79984I 4.45971 − 5.72952I
u = −1.254060 + 0.624367I
a = −0.818721 + 0.391812I
b = −0.357603 + 1.079120I
2.47405 − 4.31871I 0
u = −1.254060 − 0.624367I
a = −0.818721 − 0.391812I
b = −0.357603 − 1.079120I
2.47405 + 4.31871I 0
u = −0.875330 + 1.096280I
a = 0.994591 + 0.148767I
b = 0.69277 − 1.35605I
1.06463 − 7.82295I 0
u = −0.875330 − 1.096280I
a = 0.994591 − 0.148767I
b = 0.69277 + 1.35605I
1.06463 + 7.82295I 0
u = 0.731462 + 1.206850I
a = 0.894000 − 0.269771I
b = 0.393242 + 1.272140I
−3.24017 + 3.59589I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.731462 − 1.206850I
a = 0.894000 + 0.269771I
b = 0.393242 − 1.272140I
−3.24017 − 3.59589I 0
u = −0.88236 + 1.11457I
a = −0.492130 − 0.691183I
b = −0.834998 + 0.681281I
11.01530 + 5.14924I 0
u = −0.88236 − 1.11457I
a = −0.492130 + 0.691183I
b = −0.834998 − 0.681281I
11.01530 − 5.14924I 0
u = 0.571916
a = 0.777170
b = 2.15862
4.54867 34.0560
u = −0.80299 + 1.19060I
a = −1.253900 − 0.293786I
b = −0.59518 + 1.34906I
3.28531 − 11.90180I 0
u = −0.80299 − 1.19060I
a = −1.253900 + 0.293786I
b = −0.59518 − 1.34906I
3.28531 + 11.90180I 0
u = 0.028522 + 0.532814I
a = 2.59823 + 2.19202I
b = −0.092222 − 1.166290I
−0.49895 + 5.51266I 3.87288 − 8.41207I
u = 0.028522 − 0.532814I
a = 2.59823 − 2.19202I
b = −0.092222 + 1.166290I
−0.49895 − 5.51266I 3.87288 + 8.41207I
u = −0.41618 + 1.42484I
a = 0.639655 + 0.556368I
b = 0.114977 − 1.126460I
−0.100427 + 1.151540I 0
u = −0.41618 − 1.42484I
a = 0.639655 − 0.556368I
b = 0.114977 + 1.126460I
−0.100427 − 1.151540I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.191192 + 0.478084I
a = −3.57333 − 1.96870I
b = −0.227655 + 1.258130I
−1.59523 − 2.47874I −1.76895 − 3.57372I
u = −0.191192 − 0.478084I
a = −3.57333 + 1.96870I
b = −0.227655 − 1.258130I
−1.59523 + 2.47874I −1.76895 + 3.57372I
u = 0.81001 + 1.25615I
a = −1.066650 + 0.241770I
b = −0.454020 − 1.234480I
−3.31619 + 8.92992I 0
u = 0.81001 − 1.25615I
a = −1.066650 − 0.241770I
b = −0.454020 + 1.234480I
−3.31619 − 8.92992I 0
u = 0.503512
a = −0.379845
b = −2.53263
−0.427603 295.740
u = 0.92862 + 1.22137I
a = −0.897664 + 0.088382I
b = −0.85389 − 1.31163I
2.67981 + 9.23774I 0
u = 0.92862 − 1.22137I
a = −0.897664 − 0.088382I
b = −0.85389 + 1.31163I
2.67981 − 9.23774I 0
u = −0.075258 + 0.440919I
a = 0.74661 − 1.95932I
b = 0.00873 + 1.53511I
−0.63644 − 1.38914I 9.64634 − 3.81907I
u = −0.075258 − 0.440919I
a = 0.74661 + 1.95932I
b = 0.00873 − 1.53511I
−0.63644 + 1.38914I 9.64634 + 3.81907I
u = 0.92662 + 1.28415I
a = 1.066380 − 0.217317I
b = 0.67602 + 1.38577I
7.6671 + 18.8250I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.92662 − 1.28415I
a = 1.066380 + 0.217317I
b = 0.67602 − 1.38577I
7.6671 − 18.8250I 0
u = −0.86365 + 1.35509I
a = −0.754931 − 0.232086I
b = −0.617177 + 1.210530I
−2.87015 − 7.04041I 0
u = −0.86365 − 1.35509I
a = −0.754931 + 0.232086I
b = −0.617177 − 1.210530I
−2.87015 + 7.04041I 0
u = 1.52812 + 0.52446I
a = −0.270913 + 0.286614I
b = −0.619035 + 0.982255I
10.0022 − 10.5786I 0
u = 1.52812 − 0.52446I
a = −0.270913 − 0.286614I
b = −0.619035 − 0.982255I
10.0022 + 10.5786I 0
u = −0.80364 + 1.40467I
a = −0.806237 − 0.231371I
b = −0.271442 + 1.012980I
−2.69179 − 4.73591I 0
u = −0.80364 − 1.40467I
a = −0.806237 + 0.231371I
b = −0.271442 − 1.012980I
−2.69179 + 4.73591I 0
u = −0.96341 + 1.34469I
a = 0.926686 + 0.185690I
b = 0.50814 − 1.32598I
0.05392 − 14.09260I 0
u = −0.96341 − 1.34469I
a = 0.926686 − 0.185690I
b = 0.50814 + 1.32598I
0.05392 + 14.09260I 0
u = 1.14186 + 1.21675I
a = −0.395734 + 0.245869I
b = −0.507639 − 0.638127I
3.56550 − 1.64946I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.14186 − 1.21675I
a = −0.395734 − 0.245869I
b = −0.507639 + 0.638127I
3.56550 + 1.64946I 0
u = −1.68050 + 0.09855I
a = −0.209624 − 0.004894I
b = −0.349311 − 0.800477I
3.19565 + 5.32403I 0
u = −1.68050 − 0.09855I
a = −0.209624 + 0.004894I
b = −0.349311 + 0.800477I
3.19565 − 5.32403I 0
u = −0.178580 + 0.249835I
a = −0.525221 + 0.323864I
b = −2.71322 − 2.46711I
5.05784 − 0.07192I −103.3235 + 14.3667I
u = −0.178580 − 0.249835I
a = −0.525221 − 0.323864I
b = −2.71322 + 2.46711I
5.05784 + 0.07192I −103.3235 − 14.3667I
u = 0.60892 + 1.58505I
a = −0.461748 + 0.510598I
b = −0.401564 − 1.122160I
−0.26187 + 3.75347I 0
u = 0.60892 − 1.58505I
a = −0.461748 − 0.510598I
b = −0.401564 + 1.122160I
−0.26187 − 3.75347I 0
u = 1.41449 + 1.10586I
a = −0.218705 − 0.278228I
b = 0.265127 − 0.651380I
4.21071 − 0.79915I 0
u = 1.41449 − 1.10586I
a = −0.218705 + 0.278228I
b = 0.265127 + 0.651380I
4.21071 + 0.79915I 0
u = 1.05729 + 1.52040I
a = 0.674220 − 0.174204I
b = 0.310882 + 1.178710I
−0.61055 + 7.14284I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.05729 − 1.52040I
a = 0.674220 + 0.174204I
b = 0.310882 − 1.178710I
−0.61055 − 7.14284I 0
u = −0.124839
a = 7.53198
b = −0.425097
2.14727 2.32940
u = 1.04219 + 1.57392I
a = 0.0430996 − 0.0774997I
b = 0.248857 − 0.984769I
7.34215 − 2.08826I 0
u = 1.04219 − 1.57392I
a = 0.0430996 + 0.0774997I
b = 0.248857 + 0.984769I
7.34215 + 2.08826I 0
u = −1.97852
a = −0.0986425
b = −0.669676
2.69964 0
u = −0.20582 + 2.15705I
a = 0.061621 + 0.482660I
b = 0.112870 − 0.857557I
8.10694 + 0.46379I 0
u = −0.20582 − 2.15705I
a = 0.061621 − 0.482660I
b = 0.112870 + 0.857557I
8.10694 − 0.46379I 0
17
II.
I
u
2
= h−1.10×10
15
u
22
+8.51×10
14
u
21
+· · ·+6.64×10
15
b+1.53×10
16
, 4.52×
10
15
u
22
−9.75×10
14
u
21
+· · ·+6.64×10
15
a+5.37×10
15
, u
23
+8u
21
+· · ·−2u+1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
−0.681512u
22
+ 0.146968u
21
+ ··· − 0.923185u − 0.808721
0.165903u
22
− 0.128197u
21
+ ··· + 1.55953u − 2.30715
a
4
=
1
u
2
a
2
=
−0.804788u
22
− 0.0410468u
21
+ ··· − 1.50727u + 1.35146
0.0494357u
22
+ 0.0233899u
21
+ ··· + 1.30678u − 2.11913
a
10
=
1.30715u
22
+ 0.165903u
21
+ ··· − 0.569959u − 1.05476
−0.681155u
22
+ 0.0324941u
21
+ ··· − 1.37312u + 1.91008
a
3
=
−1.85955u
22
− 1.34819u
21
+ ··· + 4.24826u + 5.03093
2.04944u
22
+ 1.02339u
21
+ ··· − 0.693220u − 4.11913
a
8
=
0.265492u
22
+ 0.404260u
21
+ ··· − 7.22799u + 2.45480
−1.08715u
22
+ 0.196252u
21
+ ··· − 3.71722u + 1.02931
a
12
=
−0.847415u
22
+ 0.275165u
21
+ ··· − 2.48272u + 1.49842
0.165903u
22
− 0.128197u
21
+ ··· + 1.55953u − 2.30715
a
6
=
−2.19625u
22
− 1.30761u
21
+ ··· + 3.14499u + 1.91285
1.16694u
22
+ 0.220462u
21
+ ··· + 1.92181u − 3.57145
a
11
=
−2.09717u
22
− 1.20499u
21
+ ··· + 8.43857u − 3.57318
0.995638u
22
− 0.785046u
21
+ ··· + 6.19443u − 2.35145
a
7
=
−0.784171u
22
− 0.751390u
21
+ ··· + 4.05901u − 6.37143
−0.671861u
22
− 1.02224u
21
+ ··· + 5.00174u + 0.688546
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
4521490905524216
6636320717064427
u
22
+
25741386698741685
6636320717064427
u
21
+···+
192580355506969528
6636320717064427
u−
90890914710757047
6636320717064427
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
23
− 12u
22
+ ··· + 303u − 121
c
2
u
23
− 3u
22
+ ··· − 4u + 1
c
3
u
23
− 2u
22
+ ··· + u + 1
c
4
u
23
+ 8u
21
+ ··· − 2u + 1
c
5
u
23
+ 8u
22
+ ··· − 8u + 1
c
6
u
23
+ 3u
22
+ ··· − 4u − 1
c
7
u
23
− 4u
22
+ ··· − 6u + 1
c
8
u
23
+ u
22
+ ··· − 25u − 1
c
9
u
23
− u
22
+ ··· − 10u
2
− 1
c
10
, c
11
u
23
+ 4u
22
+ ··· − 6u − 1
c
12
u
23
− 8u
22
+ ··· − 8u − 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
− 16y
22
+ ··· + 48249y −14641
c
2
, c
6
y
23
− 9y
22
+ ··· + 14y −1
c
3
y
23
− 18y
22
+ ··· − 57y −1
c
4
y
23
+ 16y
22
+ ··· − 2y −1
c
5
, c
12
y
23
− 2y
22
+ ··· + 6y −1
c
7
, c
10
, c
11
y
23
− 32y
22
+ ··· + 70y −1
c
8
y
23
+ 13y
22
+ ··· + 341y −1
c
9
y
23
− y
22
+ ··· − 20y −1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.054122 + 1.044060I
a = −0.036881 + 1.362740I
b = 0.254224 − 0.190898I
11.33820 + 2.54740I 14.7841 − 0.2611I
u = 0.054122 − 1.044060I
a = −0.036881 − 1.362740I
b = 0.254224 + 0.190898I
11.33820 − 2.54740I 14.7841 + 0.2611I
u = −0.335170 + 0.865489I
a = −1.77059 − 0.12287I
b = 0.122291 + 0.940541I
−0.380445 + 0.582794I 0.786758 + 0.621706I
u = −0.335170 − 0.865489I
a = −1.77059 + 0.12287I
b = 0.122291 − 0.940541I
−0.380445 − 0.582794I 0.786758 − 0.621706I
u = −0.031807 + 1.084520I
a = 0.037457 − 0.471825I
b = 0.373542 + 0.101366I
2.82723 − 1.06466I 14.8461 + 0.1978I
u = −0.031807 − 1.084520I
a = 0.037457 + 0.471825I
b = 0.373542 − 0.101366I
2.82723 + 1.06466I 14.8461 − 0.1978I
u = 0.722829 + 0.427606I
a = 1.31265 + 1.51472I
b = 0.500959 + 1.003540I
7.67963 + 9.32725I 10.28698 − 8.16172I
u = 0.722829 − 0.427606I
a = 1.31265 − 1.51472I
b = 0.500959 − 1.003540I
7.67963 − 9.32725I 10.28698 + 8.16172I
u = 0.238134 + 0.661627I
a = −2.45251 − 0.04553I
b = −0.227445 − 1.055220I
−4.11841 + 0.99614I 8.73936 − 8.33227I
u = 0.238134 − 0.661627I
a = −2.45251 + 0.04553I
b = −0.227445 + 1.055220I
−4.11841 − 0.99614I 8.73936 + 8.33227I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.688172
a = −0.667608
b = −2.32315
3.74789 20.9920
u = −1.149550 + 0.704445I
a = 0.750286 − 0.595212I
b = 0.263925 − 0.957953I
1.69234 − 5.69028I 5.73340 + 8.24756I
u = −1.149550 − 0.704445I
a = 0.750286 + 0.595212I
b = 0.263925 + 0.957953I
1.69234 + 5.69028I 5.73340 − 8.24756I
u = −0.142863 + 0.543643I
a = −2.98650 − 0.05802I
b = −0.520824 + 1.180280I
1.62668 − 2.15833I 7.79328 + 0.00342I
u = −0.142863 − 0.543643I
a = −2.98650 + 0.05802I
b = −0.520824 − 1.180280I
1.62668 + 2.15833I 7.79328 − 0.00342I
u = −0.534873
a = −0.327158
b = −2.34103
−0.443802 −201.950
u = −0.91067 + 1.19883I
a = −0.931195 − 0.159406I
b = −0.75546 + 1.33352I
0.57019 − 8.60034I 5.29980 + 8.62878I
u = −0.91067 − 1.19883I
a = −0.931195 + 0.159406I
b = −0.75546 − 1.33352I
0.57019 + 8.60034I 5.29980 − 8.62878I
u = 0.430844
a = 0.134797
b = −2.44864
5.09316 −12.7030
u = 0.85112 + 1.44858I
a = −0.708139 + 0.276602I
b = −0.425265 − 1.101120I
−2.31590 + 5.71532I 7.32651 − 6.47921I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.85112 − 1.44858I
a = −0.708139 − 0.276602I
b = −0.425265 + 1.101120I
−2.31590 − 5.71532I 7.32651 + 6.47921I
u = 0.41178 + 2.06640I
a = 0.215418 − 0.455394I
b = −0.029533 + 0.835700I
8.13560 − 1.01675I 13.2325 + 7.2503I
u = 0.41178 − 2.06640I
a = 0.215418 + 0.455394I
b = −0.029533 − 0.835700I
8.13560 + 1.01675I 13.2325 − 7.2503I
23
III. I
u
3
= hu
2
+ b + 3u + 1, −u
2
+ a − 4u − 4, u
3
+ 3u
2
+ 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
u
2
+ 4u + 4
−u
2
− 3u − 1
a
4
=
1
u
2
a
2
=
u
2
+ 4u + 4
−u
2
− 3u − 1
a
10
=
3u + 7
−2u
2
− 5u − 3
a
3
=
−3u
2
− 7u + 1
−u − 2
a
8
=
3u + 7
−2u
2
− 5u − 3
a
12
=
2u
2
+ 7u + 5
−u
2
− 3u − 1
a
6
=
3u
2
+ 6u − 1
u + 2
a
11
=
2u
2
+ 10u + 12
−3u
2
− 8u − 4
a
7
=
−2u
2
− 7u − 5
u
2
+ 3u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 32u
2
+ 43u + 30
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
c
2
u
3
− u
2
+ 1
c
3
, c
4
u
3
+ 3u
2
+ 2u + 1
c
5
u
3
− u
2
+ 2u − 1
c
6
u
3
+ u
2
− 1
c
7
(u + 1)
3
c
8
, c
9
u
3
− 4u
2
+ 5u − 1
c
10
, c
11
(u − 1)
3
c
12
u
3
+ u
2
+ 2u + 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
3
c
2
, c
6
y
3
− y
2
+ 2y −1
c
3
, c
4
y
3
− 5y
2
− 2y −1
c
5
, c
12
y
3
+ 3y
2
+ 2y −1
c
7
, c
10
, c
11
(y −1)
3
c
8
, c
9
y
3
− 6y
2
+ 17y −1
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.337641 + 0.562280I
a = 2.44728 + 1.86942I
b = 0.215080 − 1.307140I
−1.37919 − 2.82812I 9.0124 + 12.0277I
u = −0.337641 − 0.562280I
a = 2.44728 − 1.86942I
b = 0.215080 + 1.307140I
−1.37919 + 2.82812I 9.0124 − 12.0277I
u = −2.32472
a = 0.105442
b = 0.569840
2.75839 102.980
27
IV. I
u
4
= hb − u, −u
2
+ a + u − 2, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
u
2
− u + 2
u
a
4
=
1
u
2
a
2
=
u
2
− u + 2
u
a
10
=
−u
2
+ u − 2
0
a
3
=
2
u
2
a
8
=
−u
2
+ u − 2
0
a
12
=
u
2
− 2u + 2
u
a
6
=
u
2
−u
2
a
11
=
−u
u
a
7
=
−u
2
+ 2u − 2
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7u
2
− 5u + 17
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
c
2
u
3
− u
2
+ 1
c
3
, c
4
, c
5
u
3
− u
2
+ 2u − 1
c
6
u
3
+ u
2
− 1
c
7
, c
8
, c
9
(u + 1)
3
c
10
, c
11
(u − 1)
3
c
12
u
3
+ u
2
+ 2u + 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
3
c
2
, c
6
y
3
− y
2
+ 2y −1
c
3
, c
4
, c
5
c
12
y
3
+ 3y
2
+ 2y −1
c
7
, c
8
, c
9
c
10
, c
11
(y −1)
3
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = 0.122561 − 0.744862I
b = 0.215080 + 1.307140I
−1.37919 + 2.82812I 4.28809 − 2.59975I
u = 0.215080 − 1.307140I
a = 0.122561 + 0.744862I
b = 0.215080 − 1.307140I
−1.37919 − 2.82812I 4.28809 + 2.59975I
u = 0.569840
a = 1.75488
b = 0.569840
2.75839 16.4240
31
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
6
(u
23
− 12u
22
+ ··· + 303u − 121)(u
127
− 5u
126
+ ··· − 1344u + 64)
c
2
((u
3
− u
2
+ 1)
2
)(u
23
− 3u
22
+ ··· − 4u + 1)
· (u
127
+ 2u
126
+ ··· + 10323u + 2467)
c
3
(u
3
− u
2
+ 2u − 1)(u
3
+ 3u
2
+ 2u + 1)(u
23
− 2u
22
+ ··· + u + 1)
· (u
127
− 3u
126
+ ··· + 1233985982u − 292939631)
c
4
(u
3
− u
2
+ 2u − 1)(u
3
+ 3u
2
+ 2u + 1)(u
23
+ 8u
21
+ ··· − 2u + 1)
· (u
127
+ u
126
+ ··· + 17533u − 1541)
c
5
((u
3
− u
2
+ 2u − 1)
2
)(u
23
+ 8u
22
+ ··· − 8u + 1)
· (u
127
+ 3u
126
+ ··· − 39833u + 3461)
c
6
((u
3
+ u
2
− 1)
2
)(u
23
+ 3u
22
+ ··· − 4u − 1)
· (u
127
+ 2u
126
+ ··· + 10323u + 2467)
c
7
((u + 1)
6
)(u
23
− 4u
22
+ ··· − 6u + 1)(u
127
− 5u
126
+ ··· − 361u + 29)
c
8
((u + 1)
3
)(u
3
− 4u
2
+ 5u − 1)(u
23
+ u
22
+ ··· − 25u − 1)
· (u
127
+ u
126
+ ··· − 26u − 1)
c
9
((u + 1)
3
)(u
3
− 4u
2
+ 5u − 1)(u
23
− u
22
+ ··· − 10u
2
− 1)
· (u
127
− u
126
+ ··· + 3405u + 207)
c
10
, c
11
((u − 1)
6
)(u
23
+ 4u
22
+ ··· − 6u − 1)(u
127
− 5u
126
+ ··· − 361u + 29)
c
12
((u
3
+ u
2
+ 2u + 1)
2
)(u
23
− 8u
22
+ ··· − 8u − 1)
· (u
127
+ 3u
126
+ ··· − 39833u + 3461)
32
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
6
(y
23
− 16y
22
+ ··· + 48249y −14641)
· (y
127
+ 5y
126
+ ··· + 215040y −4096)
c
2
, c
6
((y
3
− y
2
+ 2y −1)
2
)(y
23
− 9y
22
+ ··· + 14y −1)
· (y
127
− 82y
126
+ ··· + 357241133y −6086089)
c
3
(y
3
− 5y
2
− 2y −1)(y
3
+ 3y
2
+ 2y −1)(y
23
− 18y
22
+ ··· − 57y −1)
· (y
127
+ 37y
126
+ ··· − 3665675937186530842y −85813627410416161)
c
4
(y
3
− 5y
2
− 2y −1)(y
3
+ 3y
2
+ 2y −1)(y
23
+ 16y
22
+ ··· − 2y −1)
· (y
127
+ 35y
126
+ ··· + 35832577y −2374681)
c
5
, c
12
((y
3
+ 3y
2
+ 2y −1)
2
)(y
23
− 2y
22
+ ··· + 6y −1)
· (y
127
+ 61y
126
+ ··· + 1408883241y −11978521)
c
7
, c
10
, c
11
((y −1)
6
)(y
23
− 32y
22
+ ··· + 70y −1)
· (y
127
− 141y
126
+ ··· + 115183y −841)
c
8
((y −1)
3
)(y
3
− 6y
2
+ 17y −1)(y
23
+ 13y
22
+ ··· + 341y −1)
· (y
127
+ y
126
+ ··· + 116y −1)
c
9
((y −1)
3
)(y
3
− 6y
2
+ 17y −1)(y
23
− y
22
+ ··· − 20y −1)
· (y
127
− 13y
126
+ ··· + 5912703y −42849)
33
