12n
0746
(K12n
0746
)
A knot diagram
1
Linearized knot diagam
4 6 7 8 12 10 1 2 7 6 3 5
Solving Sequence
2,6 3,10
7 4 11 12 1 5 9 8
c
2
c
6
c
3
c
10
c
11
c
1
c
5
c
9
c
8
c
4
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, −1.83924 × 10
21
u
27
+ 7.51768 × 10
21
u
26
+ ··· + 3.02460 × 10
21
a − 9.01849 × 10
21
,
u
28
− 2u
27
+ ··· − 2u + 1i
I
u
2
= h−4.38637 × 10
21
u
23
− 6.05223 × 10
21
u
22
+ ··· + 9.74526 × 10
20
b + 2.66742 × 10
23
,
− 1.58823 × 10
23
u
23
− 2.15936 × 10
23
u
22
+ ··· + 2.24141 × 10
22
a + 9.91766 × 10
24
,
u
24
+ u
23
+ ··· − 230u + 23i
I
u
3
= hb + u, −99658301453u
19
+ 22815726133u
18
+ ··· + 73658938123a − 286826314291,
u
20
− u
19
+ ··· − 2u + 1i
I
u
4
= h−3.66729 × 10
26
u
23
+ 3.10786 × 10
26
u
22
+ ··· + 9.53312 × 10
27
b − 4.94358 × 10
28
,
− 7.82120 × 10
27
u
23
+ 8.56311 × 10
27
u
22
+ ··· + 4.09924 × 10
29
a − 2.28465 × 10
30
,
u
24
− 8u
22
+ ··· + 242u + 43i
I
u
5
= hb − u, a, u
3
+ u
2
− 1i
* 5 irreducible components of dim
C
= 0, with total 99 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
= hb − u, −1.84 × 10
21
u
27
+ 7.52 × 10
21
u
26
+ · · · + 3.02 × 10
21
a −
9.02 × 10
21
, u
28
− 2u
27
+ · · · − 2u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
10
=
0.608092u
27
− 2.48551u
26
+ ··· − 16.5137u + 2.98171
u
a
7
=
3.02147u
27
− 5.56752u
26
+ ··· − 8.71227u − 7.54372
0.146622u
27
− 0.672339u
26
+ ··· − 2.14675u + 1.26933
a
4
=
1.25423u
27
− 2.25494u
26
+ ··· + 7.72816u + 4.89956
−0.309280u
27
+ 0.794974u
26
+ ··· + 1.07232u − 0.906326
a
11
=
0.608092u
27
− 2.48551u
26
+ ··· − 16.5137u + 2.98171
−0.146622u
27
+ 0.672339u
26
+ ··· + 4.14675u − 1.26933
a
12
=
0.608092u
27
− 2.48551u
26
+ ··· − 15.5137u + 2.98171
−0.146622u
27
+ 0.672339u
26
+ ··· + 4.14675u − 1.26933
a
1
=
2.64646u
27
− 4.80020u
26
+ ··· + 5.40118u − 0.731153
−0.452414u
27
+ 1.16215u
26
+ ··· + 1.92755u − 0.493859
a
5
=
−3.31472u
27
+ 6.91219u
26
+ ··· + 15.0058u + 5.00506
−0.0676430u
27
+ 0.0431589u
26
+ ··· + 0.266521u − 0.986574
a
9
=
2.27197u
27
− 3.48515u
26
+ ··· + 13.3274u − 0.442136
0.317299u
27
− 0.919860u
26
+ ··· − 4.21736u + 0.793896
a
8
=
2.58927u
27
− 4.40501u
26
+ ··· + 9.11008u + 0.351760
0.317299u
27
− 0.919860u
26
+ ··· − 4.21736u + 0.793896
(ii) Obstruction class = −1
(iii) Cusp Shapes =
582961495882437832970
3024598968157486859593
u
27
−
7584312197379865856979
3024598968157486859593
u
26
+ ··· −
48717383677932330753372
3024598968157486859593
u +
53712721057335359768630
3024598968157486859593
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
28
− 21u
27
+ ··· − 1076u + 85
c
2
, c
11
u
28
− 2u
27
+ ··· − 2u + 1
c
3
, c
8
u
28
+ u
26
+ ··· + 5u + 1
c
4
, c
7
u
28
− u
27
+ ··· − u + 1
c
5
, c
12
u
28
− 16u
27
+ ··· − 3584u + 256
c
6
, c
9
, c
10
u
28
+ 14u
27
+ ··· + 388u + 85
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
+ 5y
27
+ ··· + 88494y + 7225
c
2
, c
11
y
28
− 30y
27
+ ··· − 14y + 1
c
3
, c
8
y
28
+ 2y
27
+ ··· − y + 1
c
4
, c
7
y
28
+ 5y
27
+ ··· + y + 1
c
5
, c
12
y
28
+ 24y
27
+ ··· − 65536y + 65536
c
6
, c
9
, c
10
y
28
+ 14y
27
+ ··· − 10634y + 7225
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.086820 + 0.335626I
a = 0.377913 + 0.742585I
b = −1.086820 + 0.335626I
−2.65449 − 3.26122I 2.78730 + 2.85719I
u = −1.086820 − 0.335626I
a = 0.377913 − 0.742585I
b = −1.086820 − 0.335626I
−2.65449 + 3.26122I 2.78730 − 2.85719I
u = 1.291560 + 0.285093I
a = −0.764348 + 0.803904I
b = 1.291560 + 0.285093I
−1.20504 + 9.37586I 5.06931 − 5.78305I
u = 1.291560 − 0.285093I
a = −0.764348 − 0.803904I
b = 1.291560 − 0.285093I
−1.20504 − 9.37586I 5.06931 + 5.78305I
u = −0.521856 + 0.406646I
a = −1.15897 + 1.81439I
b = −0.521856 + 0.406646I
−8.79310 − 0.90672I 1.94268 + 8.40913I
u = −0.521856 − 0.406646I
a = −1.15897 − 1.81439I
b = −0.521856 − 0.406646I
−8.79310 + 0.90672I 1.94268 − 8.40913I
u = 1.361260 + 0.077580I
a = −0.583212 − 0.841707I
b = 1.361260 + 0.077580I
2.74957 + 4.57356I 4.51737 − 9.50673I
u = 1.361260 − 0.077580I
a = −0.583212 + 0.841707I
b = 1.361260 − 0.077580I
2.74957 − 4.57356I 4.51737 + 9.50673I
u = −1.43638 + 0.07970I
a = 0.790538 − 0.457604I
b = −1.43638 + 0.07970I
5.39731 + 4.50866I 8.58445 − 4.27811I
u = −1.43638 − 0.07970I
a = 0.790538 + 0.457604I
b = −1.43638 − 0.07970I
5.39731 − 4.50866I 8.58445 + 4.27811I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.537196 + 0.036679I
a = −0.23574 + 1.76134I
b = −0.537196 + 0.036679I
−2.45068 − 2.83732I 4.31985 + 3.27002I
u = −0.537196 − 0.036679I
a = −0.23574 − 1.76134I
b = −0.537196 − 0.036679I
−2.45068 + 2.83732I 4.31985 − 3.27002I
u = −0.071489 + 0.529570I
a = 1.14088 − 0.95443I
b = −0.071489 + 0.529570I
−0.26010 + 1.93004I 3.61653 − 5.71528I
u = −0.071489 − 0.529570I
a = 1.14088 + 0.95443I
b = −0.071489 − 0.529570I
−0.26010 − 1.93004I 3.61653 + 5.71528I
u = 1.43308 + 0.34927I
a = −0.591407 − 0.524106I
b = 1.43308 + 0.34927I
1.87639 + 2.56909I −2.67930 + 1.43996I
u = 1.43308 − 0.34927I
a = −0.591407 + 0.524106I
b = 1.43308 − 0.34927I
1.87639 − 2.56909I −2.67930 − 1.43996I
u = 0.282745 + 0.391125I
a = 0.483464 − 0.962937I
b = 0.282745 + 0.391125I
1.155910 + 0.293260I 10.43664 − 2.43272I
u = 0.282745 − 0.391125I
a = 0.483464 + 0.962937I
b = 0.282745 − 0.391125I
1.155910 − 0.293260I 10.43664 + 2.43272I
u = 1.42876 + 0.51566I
a = −0.703819 − 0.195243I
b = 1.42876 + 0.51566I
4.50289 + 1.59330I 8.77713 + 1.98299I
u = 1.42876 − 0.51566I
a = −0.703819 + 0.195243I
b = 1.42876 − 0.51566I
4.50289 − 1.59330I 8.77713 − 1.98299I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50305 + 0.53936I
a = 0.767624 − 0.498981I
b = −1.50305 + 0.53936I
3.99815 − 11.69660I 6.00000 + 8.56335I
u = −1.50305 − 0.53936I
a = 0.767624 + 0.498981I
b = −1.50305 − 0.53936I
3.99815 + 11.69660I 6.00000 − 8.56335I
u = 0.308666 + 0.171864I
a = −2.41196 − 4.47005I
b = 0.308666 + 0.171864I
−11.73900 − 4.61344I 11.46925 − 5.36985I
u = 0.308666 − 0.171864I
a = −2.41196 + 4.47005I
b = 0.308666 − 0.171864I
−11.73900 + 4.61344I 11.46925 + 5.36985I
u = −1.43159 + 0.87843I
a = 0.704219 − 0.264488I
b = −1.43159 + 0.87843I
−3.41771 − 8.95629I 0. + 7.40222I
u = −1.43159 − 0.87843I
a = 0.704219 + 0.264488I
b = −1.43159 − 0.87843I
−3.41771 + 8.95629I 0. − 7.40222I
u = 1.48231 + 0.90624I
a = −0.815172 − 0.278277I
b = 1.48231 + 0.90624I
−2.3195 + 17.0944I 6.00000 − 8.92147I
u = 1.48231 − 0.90624I
a = −0.815172 + 0.278277I
b = 1.48231 − 0.90624I
−2.3195 − 17.0944I 6.00000 + 8.92147I
7
II. I
u
2
= h−4.39 × 10
21
u
23
− 6.05 × 10
21
u
22
+ · · · + 9.75 × 10
20
b + 2.67 ×
10
23
, −1.59 × 10
23
u
23
− 2.16 × 10
23
u
22
+ · · · + 2.24 × 10
22
a + 9.92 ×
10
24
, u
24
+ u
23
+ · · · − 230u + 23i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
10
=
7.08586u
23
+ 9.63395u
22
+ ··· + 3246.32u − 442.474
4.50103u
23
+ 6.21044u
22
+ ··· + 2010.44u − 273.715
a
7
=
−6.11064u
23
− 8.32729u
22
+ ··· − 2798.51u + 378.851
−0.415380u
23
− 0.860716u
22
+ ··· + 46.1813u − 25.3055
a
4
=
3.27955u
23
+ 4.32985u
22
+ ··· + 1628.19u − 235.525
5.50322u
23
+ 7.44656u
22
+ ··· + 2558.40u − 349.287
a
11
=
7.08586u
23
+ 9.63395u
22
+ ··· + 3246.32u − 442.474
3.60153u
23
+ 5.01071u
22
+ ··· + 1587.36u − 215.109
a
12
=
11.5869u
23
+ 15.8444u
22
+ ··· + 5256.76u − 716.189
2.94846u
23
+ 4.11075u
22
+ ··· + 1297.72u − 175.792
a
1
=
−8.69992u
23
− 11.2039u
22
+ ··· − 4497.49u + 658.430
−10.2679u
23
− 13.8814u
22
+ ··· − 4772.27u + 653.807
a
5
=
2.84349u
23
+ 4.59701u
22
+ ··· + 726.192u − 47.7595
−4.55216u
23
− 5.85791u
22
+ ··· − 2364.05u + 346.117
a
9
=
9.11922u
23
+ 12.4058u
22
+ ··· + 4166.18u − 565.621
3.66715u
23
+ 5.27000u
22
+ ··· + 1460.26u − 183.205
a
8
=
12.7864u
23
+ 17.6758u
22
+ ··· + 5626.44u − 748.827
3.66715u
23
+ 5.27000u
22
+ ··· + 1460.26u − 183.205
(ii) Obstruction class = −1
(iii) Cusp Shapes =
5311543016724665509336
88593237130145253275
u
23
+
7107141086263947951916
88593237130145253275
u
22
+ ··· +
506145016549541819876372
17718647426029050655
u −
351874446634871455526646
88593237130145253275
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
+ u
3
+ u
2
− u + 1)
6
c
2
, c
11
u
24
+ u
23
+ ··· − 230u + 23
c
3
, c
8
u
24
− 2u
23
+ ··· + 222u + 59
c
4
, c
7
u
24
− u
23
+ ··· + 30u + 25
c
5
, c
12
(u
3
+ u
2
+ 2u + 1)
8
c
6
, c
9
, c
10
(u
4
− u
3
+ u
2
+ u + 1)
6
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
9
c
10
(y
4
+ y
3
+ 5y
2
+ y + 1)
6
c
2
, c
11
y
24
− 5y
23
+ ··· − 17894y + 529
c
3
, c
8
y
24
− 4y
23
+ ··· + 71902y + 3481
c
4
, c
7
y
24
+ 7y
23
+ ··· + 8450y + 625
c
5
, c
12
(y
3
+ 3y
2
+ 2y −1)
8
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.871397 + 0.215536I
a = 0.70645 − 1.47436I
b = −1.288690 + 0.118319I
−0.78305 − 1.85791I 3.78084 + 7.29993I
u = 0.871397 − 0.215536I
a = 0.70645 + 1.47436I
b = −1.288690 − 0.118319I
−0.78305 + 1.85791I 3.78084 − 7.29993I
u = −0.481220 + 1.117750I
a = 0.537698 + 0.156233I
b = −1.45439 + 0.43085I
−5.26521 − 1.85791I 1.19965 + 7.29993I
u = −0.481220 − 1.117750I
a = 0.537698 − 0.156233I
b = −1.45439 − 0.43085I
−5.26521 + 1.85791I 1.19965 − 7.29993I
u = −1.259050 + 0.270524I
a = −0.893362 + 0.707527I
b = 1.32599 − 0.61457I
3.35454 − 4.68603I 10.3101 + 10.2794I
u = −1.259050 − 0.270524I
a = −0.893362 − 0.707527I
b = 1.32599 + 0.61457I
3.35454 + 4.68603I 10.3101 − 10.2794I
u = −1.288690 + 0.118319I
a = −0.798244 + 0.805500I
b = 0.871397 + 0.215536I
−0.78305 − 1.85791I 3.78084 + 7.29993I
u = −1.288690 − 0.118319I
a = −0.798244 − 0.805500I
b = 0.871397 − 0.215536I
−0.78305 + 1.85791I 3.78084 − 7.29993I
u = 1.32599 + 0.61457I
a = 0.905290 + 0.434484I
b = −1.259050 − 0.270524I
3.35454 + 4.68603I 10.3101 − 10.2794I
u = 1.32599 − 0.61457I
a = 0.905290 − 0.434484I
b = −1.259050 + 0.270524I
3.35454 − 4.68603I 10.3101 + 10.2794I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.03872 + 1.51471I
a = −0.339611 + 0.294797I
b = 0.349222 + 0.081162I
−1.12763 + 4.68603I 7.72892 − 10.27938I
u = −0.03872 − 1.51471I
a = −0.339611 − 0.294797I
b = 0.349222 − 0.081162I
−1.12763 − 4.68603I 7.72892 + 10.27938I
u = −1.45439 + 0.43085I
a = 0.372404 − 0.251224I
b = −0.481220 + 1.117750I
−5.26521 − 1.85791I 1.19965 + 7.29993I
u = −1.45439 − 0.43085I
a = 0.372404 + 0.251224I
b = −0.481220 − 1.117750I
−5.26521 + 1.85791I 1.19965 − 7.29993I
u = 1.49772 + 0.63712I
a = 0.800074 + 0.415791I
b = −1.23605 − 1.10308I
−0.78305 + 7.51416I 3.78084 − 13.25883I
u = 1.49772 − 0.63712I
a = 0.800074 − 0.415791I
b = −1.23605 + 1.10308I
−0.78305 − 7.51416I 3.78084 + 13.25883I
u = 0.349222 + 0.081162I
a = −1.50940 − 1.15491I
b = −0.03872 + 1.51471I
−1.12763 + 4.68603I 7.72892 − 10.27938I
u = 0.349222 − 0.081162I
a = −1.50940 + 1.15491I
b = −0.03872 − 1.51471I
−1.12763 − 4.68603I 7.72892 + 10.27938I
u = 0.352036 + 0.040102I
a = −1.04733 + 1.61298I
b = 0.86175 + 2.12125I
−5.26521 − 7.51416I 1.19965 + 13.25883I
u = 0.352036 − 0.040102I
a = −1.04733 − 1.61298I
b = 0.86175 − 2.12125I
−5.26521 + 7.51416I 1.19965 − 13.25883I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.23605 + 1.10308I
a = −0.875509 + 0.134887I
b = 1.49772 − 0.63712I
−0.78305 − 7.51416I 3.78084 + 13.25883I
u = −1.23605 − 1.10308I
a = −0.875509 − 0.134887I
b = 1.49772 + 0.63712I
−0.78305 + 7.51416I 3.78084 − 13.25883I
u = 0.86175 + 2.12125I
a = 0.141530 + 0.261800I
b = 0.352036 + 0.040102I
−5.26521 − 7.51416I 0
u = 0.86175 − 2.12125I
a = 0.141530 − 0.261800I
b = 0.352036 − 0.040102I
−5.26521 + 7.51416I 0
13
III. I
u
3
= hb + u, −9.97 × 10
10
u
19
+ 2.28 × 10
10
u
18
+ · · · + 7.37 × 10
10
a −
2.87 × 10
11
, u
20
− u
19
+ · · · − 2u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
10
=
1.35297u
19
− 0.309748u
18
+ ··· + 5.01927u + 3.89398
−u
a
7
=
3.05617u
19
− 3.31440u
18
+ ··· + 26.4727u − 6.68081
0.0448430u
19
+ 0.229731u
18
+ ··· + 0.266527u + 1.04322
a
4
=
3.73189u
19
− 2.90830u
18
+ ··· + 22.5207u + 2.75146
−0.0798962u
19
+ 0.122919u
18
+ ··· − 1.56402u + 0.709081
a
11
=
1.35297u
19
− 0.309748u
18
+ ··· + 5.01927u + 3.89398
0.0448430u
19
+ 0.229731u
18
+ ··· − 1.73347u + 1.04322
a
12
=
1.35297u
19
− 0.309748u
18
+ ··· + 4.01927u + 3.89398
0.0448430u
19
+ 0.229731u
18
+ ··· − 1.73347u + 1.04322
a
1
=
−2.24854u
19
+ 0.516651u
18
+ ··· − 4.37312u − 7.02363
−0.0516704u
19
− 0.300485u
18
+ ··· + 2.04578u − 0.397752
a
5
=
−3.14585u
19
+ 2.85493u
18
+ ··· − 25.0058u + 4.59437
−0.124739u
19
− 0.106813u
18
+ ··· − 0.830543u − 1.33414
a
9
=
−2.83500u
19
+ 1.12947u
18
+ ··· − 12.5781u − 7.07266
0.266234u
19
− 0.515357u
18
+ ··· + 3.30610u − 1.30145
a
8
=
−2.56877u
19
+ 0.614111u
18
+ ··· − 9.27198u − 8.37411
0.266234u
19
− 0.515357u
18
+ ··· + 3.30610u − 1.30145
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
456675119914
73658938123
u
19
+
414145420365
73658938123
u
18
+ ··· −
3019589803806
73658938123
u −
62318108709
73658938123
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
− 8u
19
+ ··· + 3u
2
+ 1
c
2
, c
11
u
20
− u
19
+ ··· − 2u + 1
c
3
, c
8
u
20
+ u
19
+ ··· + 3u + 13
c
4
, c
7
u
20
+ 4u
18
+ ··· − u + 1
c
5
u
20
+ 12u
18
+ ··· − u + 3
c
6
u
20
+ 7u
19
+ ··· + 7u
2
+ 1
c
9
, c
10
u
20
− 7u
19
+ ··· + 7u
2
+ 1
c
12
u
20
+ 12u
18
+ ··· + u + 3
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
+ 4y
19
+ ··· + 6y + 1
c
2
, c
11
y
20
− 7y
19
+ ··· + 14y + 1
c
3
, c
8
y
20
+ y
19
+ ··· − 425y + 169
c
4
, c
7
y
20
+ 8y
19
+ ··· + 5y + 1
c
5
, c
12
y
20
+ 24y
19
+ ··· + 5y + 9
c
6
, c
9
, c
10
y
20
+ 13y
19
+ ··· + 14y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.206860 + 0.912738I
a = 0.595089 + 0.399266I
b = −0.206860 − 0.912738I
−1.87110 − 4.11491I −1.55747 + 5.09443I
u = 0.206860 − 0.912738I
a = 0.595089 − 0.399266I
b = −0.206860 + 0.912738I
−1.87110 + 4.11491I −1.55747 − 5.09443I
u = 1.146640 + 0.158956I
a = 0.833442 − 0.963122I
b = −1.146640 − 0.158956I
−0.308612 − 0.887866I 7.01392 + 0.89869I
u = 1.146640 − 0.158956I
a = 0.833442 + 0.963122I
b = −1.146640 + 0.158956I
−0.308612 + 0.887866I 7.01392 − 0.89869I
u = −0.764508 + 1.012020I
a = −0.039227 + 0.271965I
b = 0.764508 − 1.012020I
−5.47737 + 6.62738I −0.42430 − 3.51997I
u = −0.764508 − 1.012020I
a = −0.039227 − 0.271965I
b = 0.764508 + 1.012020I
−5.47737 − 6.62738I −0.42430 + 3.51997I
u = −0.331623 + 0.638727I
a = −1.26938 + 0.62846I
b = 0.331623 − 0.638727I
−3.79735 − 3.38074I −3.18735 + 5.13211I
u = −0.331623 − 0.638727I
a = −1.26938 − 0.62846I
b = 0.331623 + 0.638727I
−3.79735 + 3.38074I −3.18735 − 5.13211I
u = 0.411689 + 0.583746I
a = −1.48118 − 1.12864I
b = −0.411689 − 0.583746I
−9.13088 + 0.23260I −5.20121 + 0.99282I
u = 0.411689 − 0.583746I
a = −1.48118 + 1.12864I
b = −0.411689 + 0.583746I
−9.13088 − 0.23260I −5.20121 − 0.99282I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.277620 + 0.235723I
a = −0.755026 + 0.731922I
b = 1.277620 − 0.235723I
2.53448 − 3.53693I 4.49394 + 2.65444I
u = −1.277620 − 0.235723I
a = −0.755026 − 0.731922I
b = 1.277620 + 0.235723I
2.53448 + 3.53693I 4.49394 − 2.65444I
u = 0.896773 + 0.960875I
a = 0.339283 + 0.184359I
b = −0.896773 − 0.960875I
−5.79310 + 1.03199I −4.20712 − 0.39355I
u = 0.896773 − 0.960875I
a = 0.339283 − 0.184359I
b = −0.896773 + 0.960875I
−5.79310 − 1.03199I −4.20712 + 0.39355I
u = −1.259400 + 0.425629I
a = −0.881755 + 0.330751I
b = 1.259400 − 0.425629I
3.54204 − 2.99255I 6.08654 + 3.89052I
u = −1.259400 − 0.425629I
a = −0.881755 − 0.330751I
b = 1.259400 + 0.425629I
3.54204 + 2.99255I 6.08654 − 3.89052I
u = 0.095406 + 0.374240I
a = 4.30822 + 1.24073I
b = −0.095406 − 0.374240I
−11.97380 + 4.82580I −7.61339 − 11.34574I
u = 0.095406 − 0.374240I
a = 4.30822 − 1.24073I
b = −0.095406 + 0.374240I
−11.97380 − 4.82580I −7.61339 + 11.34574I
u = 1.37578 + 0.84536I
a = 0.850537 + 0.232509I
b = −1.37578 − 0.84536I
−0.62299 + 6.60843I 4.59643 − 3.39212I
u = 1.37578 − 0.84536I
a = 0.850537 − 0.232509I
b = −1.37578 + 0.84536I
−0.62299 − 6.60843I 4.59643 + 3.39212I
18
IV. I
u
4
= h−3.67 × 10
26
u
23
+ 3.11 × 10
26
u
22
+ · · · + 9.53 × 10
27
b − 4.94 ×
10
28
, −7.82 × 10
27
u
23
+ 8.56 × 10
27
u
22
+ · · · + 4.10 × 10
29
a − 2.28 ×
10
30
, u
24
− 8u
22
+ · · · + 242u + 43i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
10
=
0.0190796u
23
− 0.0208895u
22
+ ··· + 23.9335u + 5.57336
0.0384689u
23
− 0.0326006u
22
+ ··· + 20.6673u + 5.18569
a
7
=
−0.0308549u
23
− 0.0309852u
22
+ ··· + 13.1028u + 4.24203
0.00630508u
23
+ 0.0121205u
22
+ ··· − 4.93815u + 0.374359
a
4
=
0.00429981u
23
+ 0.00889826u
22
+ ··· + 1.52545u + 4.03528
0.0208895u
23
+ 0.0219619u
22
+ ··· − 0.956087u + 1.82042
a
11
=
0.0190796u
23
− 0.0208895u
22
+ ··· + 23.9335u + 5.57336
0.0604308u
23
− 0.0273914u
22
+ ··· + 16.4324u + 4.28744
a
12
=
0.0575485u
23
− 0.0534901u
22
+ ··· + 44.6007u + 10.7591
0.0568322u
23
− 0.00741976u
22
+ ··· + 10.1972u + 2.88562
a
1
=
−0.0301588u
23
+ 0.0179193u
22
+ ··· − 26.1094u − 9.14299
−0.0107939u
23
− 0.00843626u
22
+ ··· − 9.79673u − 3.96761
a
5
=
0.00413390u
23
− 0.0355708u
22
+ ··· + 10.5611u − 4.01184
−0.0204326u
23
− 0.0402020u
22
+ ··· + 10.2954u − 0.924994
a
9
=
−0.0534723u
23
− 0.0588566u
22
+ ··· + 26.2658u + 4.41066
0.0352500u
23
+ 0.00717673u
22
+ ··· + 2.95256u + 1.45494
a
8
=
−0.0182223u
23
− 0.0516798u
22
+ ··· + 29.2184u + 5.86560
0.0352500u
23
+ 0.00717673u
22
+ ··· + 2.95256u + 1.45494
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
535804160101971736815030556
9533118023002544093158027727
u
23
−
629721383815858353997296608
9533118023002544093158027727
u
22
+
··· +
122994948289871385854632596364
9533118023002544093158027727
u −
47116154343604428037295209270
9533118023002544093158027727
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
+ 2u
3
+ 2u
2
+ u + 1)
6
c
2
, c
11
u
24
− 8u
22
+ ··· + 242u + 43
c
3
, c
8
u
24
+ u
23
+ ··· − 36u + 19
c
4
, c
7
u
24
+ 4u
22
+ ··· + 8u + 7
c
5
, c
12
(u
3
+ u
2
+ 2u + 1)
8
c
6
, c
9
, c
10
(u
4
− 2u
3
+ 2u
2
− u + 1)
6
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
9
c
10
(y
4
+ 2y
2
+ 3y + 1)
6
c
2
, c
11
y
24
− 16y
23
+ ··· − 29238y + 1849
c
3
, c
8
y
24
+ 7y
23
+ ··· + 3682y + 361
c
4
, c
7
y
24
+ 8y
23
+ ··· + 902y + 49
c
5
, c
12
(y
3
+ 3y
2
+ 2y −1)
8
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.948525 + 0.024117I
a = 1.107750 − 0.828086I
b = −1.36937 − 0.54334I
0.367792 + 0.232734I 10.02977 − 2.06053I
u = 0.948525 − 0.024117I
a = 1.107750 + 0.828086I
b = −1.36937 + 0.54334I
0.367792 − 0.232734I 10.02977 + 2.06053I
u = 0.372920 + 1.033560I
a = 0.627711 + 0.294886I
b = −0.803726 + 0.192944I
−2.27847 + 2.59539I 1.47999 − 0.91892I
u = 0.372920 − 1.033560I
a = 0.627711 − 0.294886I
b = −0.803726 − 0.192944I
−2.27847 − 2.59539I 1.47999 + 0.91892I
u = −0.141566 + 1.107020I
a = −0.666328 + 0.149071I
b = 1.85255 − 0.10648I
−6.41605 − 5.42351I −5.04928 + 3.89837I
u = −0.141566 − 1.107020I
a = −0.666328 − 0.149071I
b = 1.85255 + 0.10648I
−6.41605 + 5.42351I −5.04928 − 3.89837I
u = −1.112460 + 0.319626I
a = −1.070090 + 0.374592I
b = 1.54326 − 0.23864I
4.50538 − 2.59539I 16.5590 + 0.9189I
u = −1.112460 − 0.319626I
a = −1.070090 − 0.374592I
b = 1.54326 + 0.23864I
4.50538 + 2.59539I 16.5590 − 0.9189I
u = −0.803726 + 0.192944I
a = 0.297446 − 0.872629I
b = 0.372920 + 1.033560I
−2.27847 + 2.59539I 1.47999 − 0.91892I
u = −0.803726 − 0.192944I
a = 0.297446 + 0.872629I
b = 0.372920 − 1.033560I
−2.27847 − 2.59539I 1.47999 + 0.91892I
22
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.103880 + 0.609859I
a = 1.034060 + 0.116061I
b = −1.68454 − 0.94082I
0.36779 + 5.42351I 10.02977 − 3.89837I
u = 1.103880 − 0.609859I
a = 1.034060 − 0.116061I
b = −1.68454 + 0.94082I
0.36779 − 5.42351I 10.02977 + 3.89837I
u = −1.36937 + 0.54334I
a = −0.485592 − 0.746758I
b = 0.948525 − 0.024117I
0.367792 − 0.232734I 10.02977 + 2.06053I
u = −1.36937 − 0.54334I
a = −0.485592 + 0.746758I
b = 0.948525 + 0.024117I
0.367792 + 0.232734I 10.02977 − 2.06053I
u = 1.54326 + 0.23864I
a = 0.751836 + 0.375390I
b = −1.112460 − 0.319626I
4.50538 + 2.59539I 16.5590 − 0.9189I
u = 1.54326 − 0.23864I
a = 0.751836 − 0.375390I
b = −1.112460 + 0.319626I
4.50538 − 2.59539I 16.5590 + 0.9189I
u = −0.284414 + 0.156586I
a = −0.93636 + 2.15223I
b = −0.42506 + 1.69414I
−6.41605 + 0.23273I −5.04928 − 2.06053I
u = −0.284414 − 0.156586I
a = −0.93636 − 2.15223I
b = −0.42506 − 1.69414I
−6.41605 − 0.23273I −5.04928 + 2.06053I
u = −0.42506 + 1.69414I
a = −0.411490 + 0.144974I
b = −0.284414 + 0.156586I
−6.41605 + 0.23273I −5.04928 − 2.06053I
u = −0.42506 − 1.69414I
a = −0.411490 − 0.144974I
b = −0.284414 − 0.156586I
−6.41605 − 0.23273I −5.04928 + 2.06053I
23
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.85255 + 0.10648I
a = −0.014573 + 0.410406I
b = −0.141566 − 1.107020I
−6.41605 + 5.42351I −5.04928 − 3.89837I
u = 1.85255 − 0.10648I
a = −0.014573 − 0.410406I
b = −0.141566 + 1.107020I
−6.41605 − 5.42351I −5.04928 + 3.89837I
u = −1.68454 + 0.94082I
a = −0.676227 + 0.072743I
b = 1.103880 − 0.609859I
0.36779 − 5.42351I 10.02977 + 3.89837I
u = −1.68454 − 0.94082I
a = −0.676227 − 0.072743I
b = 1.103880 + 0.609859I
0.36779 + 5.42351I 10.02977 − 3.89837I
24
V. I
u
5
= hb − u, a, u
3
+ u
2
− 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
10
=
0
u
a
7
=
0
u
a
4
=
1
0
a
11
=
0
u
a
12
=
u
u
2
+ u − 1
a
1
=
1
0
a
5
=
u
2
− 1
u
2
a
9
=
0
u
a
8
=
u
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u + 6
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
9
c
10
u
3
c
2
, c
3
, c
4
c
7
, c
8
, c
11
u
3
+ u
2
− 1
c
5
, c
12
u
3
− u
2
+ 2u − 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
9
c
10
y
3
c
2
, c
3
, c
4
c
7
, c
8
, c
11
y
3
− y
2
+ 2y −1
c
5
, c
12
y
3
+ 3y
2
+ 2y −1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = 0
b = −0.877439 + 0.744862I
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = −0.877439 − 0.744862I
a = 0
b = −0.877439 − 0.744862I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = 0.754878
a = 0
b = 0.754878
1.11345 9.01950
28
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
3
(u
4
+ u
3
+ u
2
− u + 1)
6
(u
4
+ 2u
3
+ 2u
2
+ u + 1)
6
· (u
20
− 8u
19
+ ··· + 3u
2
+ 1)(u
28
− 21u
27
+ ··· − 1076u + 85)
c
2
, c
11
(u
3
+ u
2
− 1)(u
20
− u
19
+ ··· − 2u + 1)(u
24
− 8u
22
+ ··· + 242u + 43)
· (u
24
+ u
23
+ ··· − 230u + 23)(u
28
− 2u
27
+ ··· − 2u + 1)
c
3
, c
8
(u
3
+ u
2
− 1)(u
20
+ u
19
+ ··· + 3u + 13)(u
24
− 2u
23
+ ··· + 222u + 59)
· (u
24
+ u
23
+ ··· − 36u + 19)(u
28
+ u
26
+ ··· + 5u + 1)
c
4
, c
7
(u
3
+ u
2
− 1)(u
20
+ 4u
18
+ ··· − u + 1)(u
24
+ 4u
22
+ ··· + 8u + 7)
· (u
24
− u
23
+ ··· + 30u + 25)(u
28
− u
27
+ ··· − u + 1)
c
5
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
16
(u
20
+ 12u
18
+ ··· − u + 3)
· (u
28
− 16u
27
+ ··· − 3584u + 256)
c
6
u
3
(u
4
− 2u
3
+ 2u
2
− u + 1)
6
(u
4
− u
3
+ u
2
+ u + 1)
6
· (u
20
+ 7u
19
+ ··· + 7u
2
+ 1)(u
28
+ 14u
27
+ ··· + 388u + 85)
c
9
, c
10
u
3
(u
4
− 2u
3
+ 2u
2
− u + 1)
6
(u
4
− u
3
+ u
2
+ u + 1)
6
· (u
20
− 7u
19
+ ··· + 7u
2
+ 1)(u
28
+ 14u
27
+ ··· + 388u + 85)
c
12
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
16
(u
20
+ 12u
18
+ ··· + u + 3)
· (u
28
− 16u
27
+ ··· − 3584u + 256)
29
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
3
(y
4
+ 2y
2
+ 3y + 1)
6
(y
4
+ y
3
+ 5y
2
+ y + 1)
6
· (y
20
+ 4y
19
+ ··· + 6y + 1)(y
28
+ 5y
27
+ ··· + 88494y + 7225)
c
2
, c
11
(y
3
− y
2
+ 2y −1)(y
20
− 7y
19
+ ··· + 14y + 1)
· (y
24
− 16y
23
+ ··· − 29238y + 1849)
· (y
24
− 5y
23
+ ··· − 17894y + 529)(y
28
− 30y
27
+ ··· − 14y + 1)
c
3
, c
8
(y
3
− y
2
+ 2y −1)(y
20
+ y
19
+ ··· − 425y + 169)
· (y
24
− 4y
23
+ ··· + 71902y + 3481)(y
24
+ 7y
23
+ ··· + 3682y + 361)
· (y
28
+ 2y
27
+ ··· − y + 1)
c
4
, c
7
(y
3
− y
2
+ 2y −1)(y
20
+ 8y
19
+ ··· + 5y + 1)
· (y
24
+ 7y
23
+ ··· + 8450y + 625)(y
24
+ 8y
23
+ ··· + 902y + 49)
· (y
28
+ 5y
27
+ ··· + y + 1)
c
5
, c
12
((y
3
+ 3y
2
+ 2y −1)
17
)(y
20
+ 24y
19
+ ··· + 5y + 9)
· (y
28
+ 24y
27
+ ··· − 65536y + 65536)
c
6
, c
9
, c
10
y
3
(y
4
+ 2y
2
+ 3y + 1)
6
(y
4
+ y
3
+ 5y
2
+ y + 1)
6
· (y
20
+ 13y
19
+ ··· + 14y + 1)(y
28
+ 14y
27
+ ··· − 10634y + 7225)
30
