12n
0807
(K12n
0807
)
A knot diagram
1
Linearized knot diagam
4 7 12 7 10 3 10 12 6 1 4 8
Solving Sequence
6,10
5
9,12
8 1 7 4 2 3 11
c
5
c
9
c
8
c
12
c
7
c
4
c
1
c
3
c
11
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h12477565171u
19
− 2707721730u
18
+ ··· + 64702086776b + 27595919604,
78169757719u
19
− 30849689152u
18
+ ··· + 129404173552a + 57487393140,
u
20
− u
19
+ ··· − 24u + 4i
I
u
2
= h−2.57900 × 10
40
u
27
+ 3.53622 × 10
40
u
26
+ ··· + 9.02119 × 10
41
b − 2.68374 × 10
42
,
− 1.76496 × 10
42
u
27
+ 2.49630 × 10
42
u
26
+ ··· + 8.57013 × 10
43
a − 4.54812 × 10
44
,
u
28
− u
27
+ ··· + 95u + 25i
I
u
3
= h−u
5
− 2u
4
− 3u
3
+ 2b + u + 1, u
3
+ u
2
+ a + 2u − 1, u
6
+ u
5
+ 3u
4
− u
3
+ u
2
− 2u + 1i
I
u
4
= h6613602u
13
+ 3587729u
12
+ ··· + 4472398b + 51425184,
7928755u
13
+ 5002338u
12
+ ··· + 8944796a + 66385836,
u
14
+ u
12
+ 3u
11
− 7u
10
− u
9
+ 5u
8
− 6u
7
+ u
6
+ u
5
+ u
4
+ 12u
3
− 22u
2
+ 16u − 4i
* 4 irreducible components of dim
C
= 0, with total 68 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
= h1.25 × 10
10
u
19
− 2.71 × 10
9
u
18
+ · · · + 6.47 × 10
10
b + 2.76 × 10
10
, 7.82 ×
10
10
u
19
−3.08×10
10
u
18
+· · ·+1.29×10
11
a+5.75×10
10
, u
20
−u
19
+· · ·−24u+4i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
9
=
u
u
a
12
=
−0.604074u
19
+ 0.238398u
18
+ ··· − 4.76779u − 0.444247
−0.192846u
19
+ 0.0418491u
18
+ ··· + 1.83993u − 0.426507
a
8
=
0.516386u
19
− 0.359863u
18
+ ··· + 5.34580u + 0.660241
0.0583155u
19
− 0.180402u
18
+ ··· + 4.96135u − 0.712465
a
1
=
−0.516386u
19
+ 0.359863u
18
+ ··· − 5.34580u − 0.660241
−0.125103u
19
+ 0.150575u
18
+ ··· − 3.16402u + 0.759990
a
7
=
0.516386u
19
− 0.359863u
18
+ ··· + 5.34580u + 0.660241
0.179296u
19
− 0.251320u
18
+ ··· + 3.27034u − 0.0863736
a
4
=
−0.298481u
19
+ 0.162206u
18
+ ··· − 4.44207u + 1.60482
−0.190429u
19
+ 0.224600u
18
+ ··· − 4.91842u + 0.679023
a
2
=
−0.0233919u
19
+ 0.141504u
18
+ ··· − 0.574180u − 1.17094
0.0994137u
19
− 0.225778u
18
+ ··· + 6.99444u − 0.952482
a
3
=
0.0671954u
19
− 0.268402u
18
+ ··· + 10.5000u − 0.811473
−0.0394315u
19
+ 0.0310711u
18
+ ··· + 0.136398u − 0.0923623
a
11
=
−0.740350u
19
+ 0.510891u
18
+ ··· − 10.3265u + 0.749678
−0.158675u
19
+ 0.234881u
18
+ ··· − 2.05133u + 0.335208
(ii) Obstruction class = −1
(iii) Cusp Shapes =
28600507011
16175521694
u
19
−
9150517238
8087760847
u
18
+ ··· +
468797321056
8087760847
u −
126502436106
8087760847
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
20
− 2u
19
+ ··· − 14u + 1
c
2
, c
6
u
20
+ 5u
19
+ ··· + 28u + 10
c
3
, c
5
, c
9
c
11
u
20
+ u
19
+ ··· + 24u + 4
c
7
, c
10
u
20
− u
19
+ ··· + 9u + 1
c
8
, c
12
u
20
− 8u
19
+ ··· + 26u − 14
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
20
− 30y
19
+ ··· + 10y + 1
c
2
, c
6
y
20
+ 7y
19
+ ··· − 744y + 100
c
3
, c
5
, c
9
c
11
y
20
+ 19y
19
+ ··· + 80y + 16
c
7
, c
10
y
20
− 17y
19
+ ··· − 121y + 1
c
8
, c
12
y
20
− 4y
19
+ ··· − 1516y + 196
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.12905
a = −0.359607
b = −1.01716
−8.01665 −11.3930
u = −0.606091 + 1.044440I
a = −0.154877 + 0.090999I
b = 0.246614 + 0.948938I
4.82527 − 0.08424I −5.01924 − 0.20177I
u = −0.606091 − 1.044440I
a = −0.154877 − 0.090999I
b = 0.246614 − 0.948938I
4.82527 + 0.08424I −5.01924 + 0.20177I
u = 0.330639 + 0.692945I
a = 1.36926 + 1.04069I
b = −0.252443 + 1.228440I
−6.44427 + 0.93056I −10.49794 − 0.14511I
u = 0.330639 − 0.692945I
a = 1.36926 − 1.04069I
b = −0.252443 − 1.228440I
−6.44427 − 0.93056I −10.49794 + 0.14511I
u = 0.040542 + 0.738588I
a = 2.28316 − 0.41519I
b = 0.861536 + 0.029448I
1.19115 + 4.34933I −8.67394 + 0.08725I
u = 0.040542 − 0.738588I
a = 2.28316 + 0.41519I
b = 0.861536 − 0.029448I
1.19115 − 4.34933I −8.67394 − 0.08725I
u = −0.461546 + 1.231960I
a = −0.561795 + 0.808913I
b = −0.85919 + 1.83207I
−4.99906 + 5.81831I −7.50691 − 4.95248I
u = −0.461546 − 1.231960I
a = −0.561795 − 0.808913I
b = −0.85919 − 1.83207I
−4.99906 − 5.81831I −7.50691 + 4.95248I
u = 0.332357 + 1.332800I
a = −0.037401 − 1.225500I
b = −0.25149 − 1.62627I
4.23168 − 3.75806I −8.78905 + 3.32796I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.332357 − 1.332800I
a = −0.037401 + 1.225500I
b = −0.25149 + 1.62627I
4.23168 + 3.75806I −8.78905 − 3.32796I
u = 0.267001 + 0.387206I
a = −1.12051 − 1.01732I
b = −0.112063 + 0.500261I
−0.434096 − 1.337960I −3.82072 + 5.86960I
u = 0.267001 − 0.387206I
a = −1.12051 + 1.01732I
b = −0.112063 − 0.500261I
−0.434096 + 1.337960I −3.82072 − 5.86960I
u = 0.379438
a = −0.343267
b = 0.662281
−0.997451 −8.03610
u = −0.53782 + 1.58865I
a = 0.217202 − 0.766665I
b = −0.04599 − 1.77133I
8.99311 + 1.97630I −1.32435 − 3.05879I
u = −0.53782 − 1.58865I
a = 0.217202 + 0.766665I
b = −0.04599 + 1.77133I
8.99311 − 1.97630I −1.32435 + 3.05879I
u = −0.65030 + 1.59655I
a = −1.028920 + 0.531678I
b = 0.066168 + 0.771188I
−2.70292 + 4.75701I −8.90322 − 3.07361I
u = −0.65030 − 1.59655I
a = −1.028920 − 0.531678I
b = 0.066168 − 0.771188I
−2.70292 − 4.75701I −8.90322 + 3.07361I
u = 1.03097 + 1.49136I
a = 0.385322 + 1.112120I
b = 0.52429 + 2.07473I
−1.7987 − 14.4623I −8.25030 + 6.83242I
u = 1.03097 − 1.49136I
a = 0.385322 − 1.112120I
b = 0.52429 − 2.07473I
−1.7987 + 14.4623I −8.25030 − 6.83242I
6
II. I
u
2
= h−2.58 × 10
40
u
27
+ 3.54 × 10
40
u
26
+ · · · + 9.02 × 10
41
b − 2.68 ×
10
42
, −1.76 × 10
42
u
27
+ 2.50 × 10
42
u
26
+ · · · + 8.57 × 10
43
a − 4.55 ×
10
44
, u
28
− u
27
+ · · · + 95u + 25i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
9
=
u
u
a
12
=
0.0205943u
27
− 0.0291279u
26
+ ··· − 2.74979u + 5.30694
0.0285882u
27
− 0.0391990u
26
+ ··· − 3.07837u + 2.97493
a
8
=
0.0295456u
27
− 0.0540163u
26
+ ··· − 6.36659u + 1.04698
0.0322136u
27
− 0.0409569u
26
+ ··· + 0.376791u + 1.67777
a
1
=
0.0771412u
27
− 0.0790894u
26
+ ··· + 3.05691u + 7.47630
0.0384494u
27
− 0.0482680u
26
+ ··· − 0.878749u + 4.68521
a
7
=
0.0295456u
27
− 0.0540163u
26
+ ··· − 6.36659u + 1.04698
0.0347077u
27
− 0.0471353u
26
+ ··· − 1.20929u + 1.06600
a
4
=
−0.0575867u
27
+ 0.0693145u
26
+ ··· − 2.27382u − 8.21914
−0.0238237u
27
+ 0.0350049u
26
+ ··· + 2.95822u − 4.74941
a
2
=
−0.0752950u
27
+ 0.0687026u
26
+ ··· − 5.09400u − 7.24933
−0.0319712u
27
+ 0.0360560u
26
+ ··· − 0.410280u − 4.02144
a
3
=
0.0886392u
27
− 0.0807706u
26
+ ··· + 10.1105u + 2.87510
0.0241381u
27
− 0.0163375u
26
+ ··· + 4.61411u + 2.08392
a
11
=
0.186332u
27
− 0.250049u
26
+ ··· − 2.97174u + 16.2242
0.125465u
27
− 0.136882u
26
+ ··· + 3.15967u + 12.8085
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.153961u
27
− 0.244058u
26
+ ··· − 14.1573u + 5.74251
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
28
− 2u
27
+ ··· + 5356u − 619
c
2
, c
6
(u
14
− u
13
+ ··· + 3u − 5)
2
c
3
, c
5
, c
9
c
11
u
28
+ u
27
+ ··· − 95u + 25
c
7
, c
10
u
28
+ 2u
27
+ ··· + 170u − 53
c
8
, c
12
(u
14
+ 3u
13
+ ··· + u + 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
28
− 32y
27
+ ··· − 2525320y + 383161
c
2
, c
6
(y
14
+ 9y
13
+ ··· + 271y + 25)
2
c
3
, c
5
, c
9
c
11
y
28
+ y
27
+ ··· − 2075y + 625
c
7
, c
10
y
28
− 30y
27
+ ··· − 14166y + 2809
c
8
, c
12
(y
14
− 3y
13
+ ··· − 9y + 1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.382569 + 0.961679I
a = 0.84193 + 1.31313I
b = 0.74021 + 1.62534I
−1.05651 + 1.71922I −3.54630 + 3.88789I
u = −0.382569 − 0.961679I
a = 0.84193 − 1.31313I
b = 0.74021 − 1.62534I
−1.05651 − 1.71922I −3.54630 − 3.88789I
u = −0.659980 + 0.684862I
a = −0.614643 + 0.241881I
b = 0.22392 + 1.79952I
5.74683 + 3.41396I −10.73005 − 1.32661I
u = −0.659980 − 0.684862I
a = −0.614643 − 0.241881I
b = 0.22392 − 1.79952I
5.74683 − 3.41396I −10.73005 + 1.32661I
u = −0.228826 + 0.744696I
a = 1.72758 − 0.31252I
b = −0.160568 − 0.530138I
−7.37370 − 3.17606I −3.96370 + 3.07132I
u = −0.228826 − 0.744696I
a = 1.72758 + 0.31252I
b = −0.160568 + 0.530138I
−7.37370 + 3.17606I −3.96370 − 3.07132I
u = 0.548168 + 1.129440I
a = −0.528269 − 0.526549I
b = −0.62027 − 1.83839I
−4.37474 − 4.68298I −8.16766 + 3.94230I
u = 0.548168 − 1.129440I
a = −0.528269 + 0.526549I
b = −0.62027 + 1.83839I
−4.37474 + 4.68298I −8.16766 − 3.94230I
u = 0.443597 + 1.210440I
a = −0.78830 − 1.27422I
b = −0.95981 − 2.01969I
3.68681 − 6.62681I −5.84998 + 6.47809I
u = 0.443597 − 1.210440I
a = −0.78830 + 1.27422I
b = −0.95981 + 2.01969I
3.68681 + 6.62681I −5.84998 − 6.47809I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.295300 + 0.052096I
a = 0.615026 − 0.559035I
b = 0.420326 − 0.383474I
−1.05651 − 1.71922I −3.54630 − 3.88789I
u = 1.295300 − 0.052096I
a = 0.615026 + 0.559035I
b = 0.420326 + 0.383474I
−1.05651 + 1.71922I −3.54630 + 3.88789I
u = 0.414876 + 0.547756I
a = 0.384169 + 0.098593I
b = 0.895190 − 0.576100I
−0.830620 −3.28687 + 0.I
u = 0.414876 − 0.547756I
a = 0.384169 − 0.098593I
b = 0.895190 + 0.576100I
−0.830620 −3.28687 + 0.I
u = −1.07957 + 0.93026I
a = 0.136747 − 0.269651I
b = −0.055912 − 0.934276I
3.68681 + 6.62681I −5.84998 − 6.47809I
u = −1.07957 − 0.93026I
a = 0.136747 + 0.269651I
b = −0.055912 + 0.934276I
3.68681 − 6.62681I −5.84998 + 6.47809I
u = 0.65120 + 1.27508I
a = −1.29935 + 0.59748I
b = −0.539193 + 1.025560I
0.06886 − 2.85502I −7.04255 + 3.10308I
u = 0.65120 − 1.27508I
a = −1.29935 − 0.59748I
b = −0.539193 − 1.025560I
0.06886 + 2.85502I −7.04255 − 3.10308I
u = −0.048562 + 0.546580I
a = 2.25353 − 1.01896I
b = −0.003743 − 0.725427I
0.06886 + 2.85502I −7.04255 − 3.10308I
u = −0.048562 − 0.546580I
a = 2.25353 + 1.01896I
b = −0.003743 + 0.725427I
0.06886 − 2.85502I −7.04255 + 3.10308I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.55577 + 0.38232I
a = 0.54476 − 1.59078I
b = 0.38666 − 2.50142I
−7.37370 + 3.17606I −3.96370 − 3.07132I
u = −1.55577 − 0.38232I
a = 0.54476 + 1.59078I
b = 0.38666 + 2.50142I
−7.37370 − 3.17606I −3.96370 + 3.07132I
u = −1.67541
a = 0.252517
b = −0.0936482
−10.6588 16.8870
u = −0.256228
a = 7.59230
b = 5.32881
−10.6588 16.8870
u = 0.25634 + 1.92846I
a = 0.039195 + 0.793027I
b = 0.16064 + 1.64932I
5.74683 − 3.41396I −10.73005 + 1.32661I
u = 0.25634 − 1.92846I
a = 0.039195 − 0.793027I
b = 0.16064 − 1.64932I
5.74683 + 3.41396I −10.73005 − 1.32661I
u = 1.81161 + 0.79415I
a = −0.934769 − 0.342558I
b = −0.105044 − 0.251982I
−4.37474 + 4.68298I −8.00000 − 3.94230I
u = 1.81161 − 0.79415I
a = −0.934769 + 0.342558I
b = −0.105044 + 0.251982I
−4.37474 − 4.68298I −8.00000 + 3.94230I
12
III. I
u
3
=
h−u
5
−2u
4
−3u
3
+2b+u+1, u
3
+u
2
+a+2u−1, u
6
+u
5
+3u
4
−u
3
+u
2
−2u+1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
9
=
u
u
a
12
=
−u
3
− u
2
− 2u + 1
1
2
u
5
+ u
4
+
3
2
u
3
−
1
2
u −
1
2
a
8
=
−
1
2
u
5
−
1
2
u
3
+ ··· +
1
2
u +
1
2
−
1
2
u
5
− u
4
−
3
2
u
3
+
1
2
u +
1
2
a
1
=
1
2
u
5
+
1
2
u
3
− 2u
2
−
1
2
u −
1
2
u
5
+ 2u
4
+ 3u
3
− 1
a
7
=
−
1
2
u
5
−
1
2
u
3
+ ··· +
1
2
u +
1
2
−u
5
− u
4
− 3u
3
+ u
2
− u + 1
a
4
=
0
u
3
+ u − 1
a
2
=
1
2
u
5
+
1
2
u
3
− 2u
2
−
1
2
u −
1
2
3
2
u
5
+ 2u
4
+
9
2
u
3
+
1
2
u −
3
2
a
3
=
−u
4
− u
3
− 2u
2
+ u
1
2
u
5
+
3
2
u
3
− u
2
+
3
2
u −
3
2
a
11
=
−u
3
− u
2
− 2u + 1
1
2
u
5
+
3
2
u
3
− u
2
+
1
2
u −
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
5
+ 8u
4
+ 13u
3
+ 8u
2
− 4u − 12
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
6
+ 2u
4
− 2u
2
+ 1
c
2
u
6
− 2u
5
+ 4u
4
− 5u
3
+ 5u
2
− 4u + 2
c
3
, c
9
u
6
− u
5
+ 3u
4
+ u
3
+ u
2
+ 2u + 1
c
5
, c
11
u
6
+ u
5
+ 3u
4
− u
3
+ u
2
− 2u + 1
c
6
u
6
+ 2u
5
+ 4u
4
+ 5u
3
+ 5u
2
+ 4u + 2
c
7
, c
10
u
6
− u
5
+ 2u
3
− u + 1
c
8
u
6
+ 5u
5
+ 10u
4
+ 12u
3
+ 11u
2
+ 6u + 2
c
12
u
6
− 5u
5
+ 10u
4
− 12u
3
+ 11u
2
− 6u + 2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
3
+ 2y
2
− 2y + 1)
2
c
2
, c
6
y
6
+ 4y
5
+ 6y
4
+ 3y
3
+ y
2
+ 4y + 4
c
3
, c
5
, c
9
c
11
y
6
+ 5y
5
+ 13y
4
+ 11y
3
+ 3y
2
− 2y + 1
c
7
, c
10
y
6
− y
5
+ 4y
4
− 4y
3
+ 4y
2
− y + 1
c
8
, c
12
y
6
− 5y
5
+ 2y
4
+ 20y
3
+ 17y
2
+ 8y + 4
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.351154 + 0.963944I
a = 1.57262 − 0.71181I
b = 0.710600 − 0.298937I
1.38689 + 5.20040I −6.70776 − 8.14756I
u = −0.351154 − 0.963944I
a = 1.57262 + 0.71181I
b = 0.710600 + 0.298937I
1.38689 − 5.20040I −6.70776 + 8.14756I
u = 0.527759 + 0.238876I
a = −0.333639 − 0.915863I
b = −0.710600 + 0.298937I
−1.44750 − 0.78507I −11.82206 + 4.53910I
u = 0.527759 − 0.238876I
a = −0.333639 + 0.915863I
b = −0.710600 − 0.298937I
−1.44750 + 0.78507I −11.82206 − 4.53910I
u = −0.67660 + 1.54058I
a = −0.238984 + 0.544148I
b = 1.68261I
8.28528 + 1.18132I −6.97019 + 1.68887I
u = −0.67660 − 1.54058I
a = −0.238984 − 0.544148I
b = − 1.68261I
8.28528 − 1.18132I −6.97019 − 1.68887I
16
IV.
I
u
4
= h6.61 × 10
6
u
13
+ 3.59 × 10
6
u
12
+ · · · + 4.47 × 10
6
b + 5.14 × 10
7
, 7.93 ×
10
6
u
13
+5.00×10
6
u
12
+· · · +8.94×10
6
a+6.64×10
7
, u
14
+u
12
+· · · +16u −4i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
9
=
u
u
a
12
=
−0.886410u
13
− 0.559246u
12
+ ··· + 12.0076u − 7.42173
−1.47876u
13
− 0.802194u
12
+ ··· + 22.2687u − 11.4983
a
8
=
0.272987u
13
− 0.137329u
12
+ ··· − 7.73482u + 5.22165
0.394381u
13
+ 0.189086u
12
+ ··· − 6.45287u + 4.53865
a
1
=
−1.72801u
13
− 0.995710u
12
+ ··· + 25.1472u − 12.1078
−1.87585u
13
− 0.784387u
12
+ ··· + 30.6478u − 15.8580
a
7
=
0.272987u
13
− 0.137329u
12
+ ··· − 7.73482u + 5.22165
0.598057u
13
+ 0.326361u
12
+ ··· − 9.74208u + 5.08797
a
4
=
−1.15765u
13
− 0.257052u
12
+ ··· + 22.2389u − 12.9234
−1.79179u
13
− 0.902150u
12
+ ··· + 26.9957u − 14.1414
a
2
=
1.28004u
13
+ 0.941848u
12
+ ··· − 14.8390u + 7.56987
1.45644u
13
+ 0.620242u
12
+ ··· − 24.4286u + 12.0920
a
3
=
0.121394u
13
+ 0.326415u
12
+ ··· + 2.28195u − 0.682994
0.482966u
13
+ 0.178873u
12
+ ··· − 8.50155u + 4.01105
a
11
=
−3.14891u
13
− 1.32603u
12
+ ··· + 52.7859u − 29.3838
−4.17554u
13
− 2.22940u
12
+ ··· + 65.1527u − 34.2072
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
13592118
2236199
u
13
−
7846957
2236199
u
12
+ ··· +
200344516
2236199
u −
138314312
2236199
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
14
− 7u
13
+ ··· − 76u − 23
c
2
(u
7
+ 2u
6
+ 2u
5
− u
3
+ u
2
− 2u + 1)
2
c
3
, c
9
u
14
+ u
12
+ ··· − 16u − 4
c
5
, c
11
u
14
+ u
12
+ ··· + 16u − 4
c
6
(u
7
− 2u
6
+ 2u
5
− u
3
− u
2
− 2u − 1)
2
c
7
, c
10
u
14
− 5u
13
+ ··· − 12u + 1
c
8
(u
7
− 3u
6
+ 4u
5
− 3u
4
+ u
3
− u
2
+ u + 1)
2
c
12
(u
7
+ 3u
6
+ 4u
5
+ 3u
4
+ u
3
+ u
2
+ u − 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
14
− 19y
13
+ ··· − 7064y + 529
c
2
, c
6
(y
7
+ 2y
5
− 12y
4
− 11y
3
+ 3y
2
+ 2y −1)
2
c
3
, c
5
, c
9
c
11
y
14
+ 2y
13
+ ··· − 80y + 16
c
7
, c
10
y
14
− 23y
13
+ ··· − 36y + 1
c
8
, c
12
(y
7
− y
6
− 5y
4
+ 9y
3
+ 7y
2
+ 3y −1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.062180 + 0.124907I
a = 0.715657 + 0.799248I
b = 0.350888 + 0.153830I
−1.45870 + 2.15231I −13.6974 − 5.2163I
u = 1.062180 − 0.124907I
a = 0.715657 − 0.799248I
b = 0.350888 − 0.153830I
−1.45870 − 2.15231I −13.6974 + 5.2163I
u = −0.475882 + 0.967579I
a = −0.175035 − 0.754228I
b = −0.47409 − 1.99750I
6.66956 + 3.87774I −3.00763 − 4.44001I
u = −0.475882 − 0.967579I
a = −0.175035 + 0.754228I
b = −0.47409 + 1.99750I
6.66956 − 3.87774I −3.00763 + 4.44001I
u = 0.445391 + 0.989567I
a = −1.16665 + 1.08042I
b = −0.66834 + 1.61478I
−1.45870 − 2.15231I −13.6974 + 5.2163I
u = 0.445391 − 0.989567I
a = −1.16665 − 1.08042I
b = −0.66834 − 1.61478I
−1.45870 + 2.15231I −13.6974 − 5.2163I
u = 0.547747 + 0.489507I
a = −1.41654 − 1.08048I
b = 0.340538 − 0.523367I
−8.03082 + 3.18578I −16.4787 − 3.7094I
u = 0.547747 − 0.489507I
a = −1.41654 + 1.08048I
b = 0.340538 + 0.523367I
−8.03082 − 3.18578I −16.4787 + 3.7094I
u = −1.251080 + 0.458307I
a = 0.76520 − 1.52382I
b = 0.57996 − 2.52308I
−8.03082 + 3.18578I −16.4787 − 3.7094I
u = −1.251080 − 0.458307I
a = 0.76520 + 1.52382I
b = 0.57996 + 2.52308I
−8.03082 − 3.18578I −16.4787 + 3.7094I
20
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.479131
a = −4.15458
b = −5.10698
−10.8094 −36.6330
u = −1.58531
a = −0.00465607
b = 0.283188
−10.8094 −36.6330
u = 0.22473 + 1.85996I
a = −0.143013 − 0.884457I
b = −0.21707 − 1.61668I
6.66956 − 3.87774I −3.00763 + 4.44001I
u = 0.22473 − 1.85996I
a = −0.143013 + 0.884457I
b = −0.21707 + 1.61668I
6.66956 + 3.87774I −3.00763 − 4.44001I
21
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
6
+ 2u
4
− 2u
2
+ 1)(u
14
− 7u
13
+ ··· − 76u − 23)
· (u
20
− 2u
19
+ ··· − 14u + 1)(u
28
− 2u
27
+ ··· + 5356u − 619)
c
2
(u
6
− 2u
5
+ 4u
4
− 5u
3
+ 5u
2
− 4u + 2)
· ((u
7
+ 2u
6
+ 2u
5
− u
3
+ u
2
− 2u + 1)
2
)(u
14
− u
13
+ ··· + 3u − 5)
2
· (u
20
+ 5u
19
+ ··· + 28u + 10)
c
3
, c
9
(u
6
− u
5
+ 3u
4
+ u
3
+ u
2
+ 2u + 1)(u
14
+ u
12
+ ··· − 16u − 4)
· (u
20
+ u
19
+ ··· + 24u + 4)(u
28
+ u
27
+ ··· − 95u + 25)
c
5
, c
11
(u
6
+ u
5
+ 3u
4
− u
3
+ u
2
− 2u + 1)(u
14
+ u
12
+ ··· + 16u − 4)
· (u
20
+ u
19
+ ··· + 24u + 4)(u
28
+ u
27
+ ··· − 95u + 25)
c
6
(u
6
+ 2u
5
+ 4u
4
+ 5u
3
+ 5u
2
+ 4u + 2)
· ((u
7
− 2u
6
+ 2u
5
− u
3
− u
2
− 2u − 1)
2
)(u
14
− u
13
+ ··· + 3u − 5)
2
· (u
20
+ 5u
19
+ ··· + 28u + 10)
c
7
, c
10
(u
6
− u
5
+ 2u
3
− u + 1)(u
14
− 5u
13
+ ··· − 12u + 1)
· (u
20
− u
19
+ ··· + 9u + 1)(u
28
+ 2u
27
+ ··· + 170u − 53)
c
8
(u
6
+ 5u
5
+ 10u
4
+ 12u
3
+ 11u
2
+ 6u + 2)
· ((u
7
− 3u
6
+ ··· + u + 1)
2
)(u
14
+ 3u
13
+ ··· + u + 1)
2
· (u
20
− 8u
19
+ ··· + 26u − 14)
c
12
(u
6
− 5u
5
+ 10u
4
− 12u
3
+ 11u
2
− 6u + 2)
· ((u
7
+ 3u
6
+ ··· + u − 1)
2
)(u
14
+ 3u
13
+ ··· + u + 1)
2
· (u
20
− 8u
19
+ ··· + 26u − 14)
22
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
3
+ 2y
2
− 2y + 1)
2
)(y
14
− 19y
13
+ ··· − 7064y + 529)
· (y
20
− 30y
19
+ ··· + 10y + 1)
· (y
28
− 32y
27
+ ··· − 2525320y + 383161)
c
2
, c
6
(y
6
+ 4y
5
+ 6y
4
+ 3y
3
+ y
2
+ 4y + 4)
· (y
7
+ 2y
5
− 12y
4
− 11y
3
+ 3y
2
+ 2y −1)
2
· ((y
14
+ 9y
13
+ ··· + 271y + 25)
2
)(y
20
+ 7y
19
+ ··· − 744y + 100)
c
3
, c
5
, c
9
c
11
(y
6
+ 5y
5
+ ··· − 2y + 1)(y
14
+ 2y
13
+ ··· − 80y + 16)
· (y
20
+ 19y
19
+ ··· + 80y + 16)(y
28
+ y
27
+ ··· − 2075y + 625)
c
7
, c
10
(y
6
− y
5
+ 4y
4
− 4y
3
+ 4y
2
− y + 1)(y
14
− 23y
13
+ ··· − 36y + 1)
· (y
20
− 17y
19
+ ··· − 121y + 1)(y
28
− 30y
27
+ ··· − 14166y + 2809)
c
8
, c
12
(y
6
− 5y
5
+ 2y
4
+ 20y
3
+ 17y
2
+ 8y + 4)
· ((y
7
− y
6
− 5y
4
+ 9y
3
+ 7y
2
+ 3y −1)
2
)(y
14
− 3y
13
+ ··· − 9y + 1)
2
· (y
20
− 4y
19
+ ··· − 1516y + 196)
23
