12n
0425
(K12n
0425
)
A knot diagram
1
Linearized knot diagam
3 6 11 7 2 10 3 11 7 1 4 9
Solving Sequence
6,10 3,7
2 1 11 5 4 9 8 12
c
6
c
2
c
1
c
10
c
5
c
4
c
9
c
8
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−3141u
13
− 16485u
12
+ ··· + 48031b − 35243, −17396u
13
+ 34122u
12
+ ··· + 48031a − 53374,
u
14
− 2u
13
+ 2u
12
+ 2u
11
− u
10
+ 5u
9
− u
8
− 3u
7
+ 16u
6
+ 14u
5
− 7u
4
− 4u
3
+ 5u
2
− 1i
I
u
2
= hu
7
+ u
6
+ 2u
5
− u
3
− 3u
2
+ b − u − 1, u
6
+ u
5
+ 2u
4
− u
2
+ a − 2u, u
8
+ 2u
7
+ 3u
6
+ u
5
− 2u
4
− 5u
3
− 3u
2
+ 1i
I
u
3
= h−18446302691u
17
+ 75111115865u
16
+ ··· + 37469236469b + 161494737225,
1420585009695u
17
− 6247662256333u
16
+ ··· + 412161601159a − 27133691702098,
u
18
− 5u
17
+ ··· − 60u + 11i
I
u
4
= h−u
6
− 3u
5
− 6u
4
− 7u
3
− 5u
2
+ b − 2u, u
6
+ 3u
5
+ 7u
4
+ 10u
3
+ 11u
2
+ a + 8u + 3,
u
8
+ 4u
7
+ 10u
6
+ 16u
5
+ 18u
4
+ 14u
3
+ 7u
2
+ 2u + 1i
* 4 irreducible components of dim
C
= 0, with total 48 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
= h−3141u
13
− 16485u
12
+ · · · + 48031b − 35243, −17396u
13
+
34122u
12
+ · · · + 48031a − 53374, u
14
− 2u
13
+ · · · + 5u
2
− 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
0.362183u
13
− 0.710416u
12
+ ··· − 0.735608u + 1.11124
0.0653953u
13
+ 0.343216u
12
+ ··· + 0.546876u + 0.733755
a
7
=
1
−u
2
a
2
=
0.427578u
13
− 0.367200u
12
+ ··· − 0.188732u + 1.84500
0.0653953u
13
+ 0.343216u
12
+ ··· + 0.546876u + 0.733755
a
1
=
1
−1.57877u
13
+ 2.67779u
12
+ ··· − 6.70952u − 2.45421
a
11
=
u
−0.479753u
13
+ 0.602444u
12
+ ··· − 1.45421u − 1.57877
a
5
=
−0.747705u
13
+ 1.28783u
12
+ ··· − 4.39699u − 0.909059
−1.10989u
13
+ 1.99825u
12
+ ··· − 3.66139u − 2.02030
a
4
=
0.552518u
13
− 0.954071u
12
+ ··· + 0.0120964u + 1.31881
−1.43745u
13
+ 2.65352u
12
+ ··· − 4.96161u − 2.37884
a
9
=
−u
u
3
+ u
a
8
=
0.266224u
13
− 0.584622u
12
+ ··· − 0.520247u + 0.357061
−0.967708u
13
+ 1.43022u
12
+ ··· − 3.29920u − 2.00635
a
12
=
0.357061u
13
− 0.447898u
12
+ ··· + 1.57877u + 1.47975
−1.88366u
13
+ 2.89045u
12
+ ··· − 8.64535u − 3.20018
(ii) Obstruction class = −1
(iii) Cusp Shapes =
368903
48031
u
13
−
551900
48031
u
12
+ ··· +
897392
48031
u +
1052546
48031
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
+ 7u
13
+ ··· + 128u + 4
c
2
, c
5
u
14
+ 5u
13
+ ··· − 4u + 2
c
3
, c
7
, c
11
u
14
− 2u
13
+ ··· + 3u + 1
c
4
u
14
+ 7u
13
+ ··· − 27u − 1
c
6
, c
9
, c
10
u
14
+ 2u
13
+ ··· + 5u
2
− 1
c
8
u
14
+ 11u
13
+ ··· − 48u − 32
c
12
u
14
− 11u
13
+ ··· + 112u + 26
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
14
− 7y
13
+ ··· − 11904y + 16
c
2
, c
5
y
14
− 7y
13
+ ··· − 128y + 4
c
3
, c
7
, c
11
y
14
− 22y
13
+ ··· − 17y + 1
c
4
y
14
− 69y
13
+ ··· − 481y + 1
c
6
, c
9
, c
10
y
14
+ 10y
12
+ ··· − 10y + 1
c
8
y
14
− 35y
13
+ ··· + 2304y + 1024
c
12
y
14
− 47y
13
+ ··· − 20136y + 676
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.955042 + 0.173183I
a = 0.56818 + 1.84710I
b = −0.847861 − 0.494590I
1.67693 − 2.03514I 12.04529 + 3.68045I
u = −0.955042 − 0.173183I
a = 0.56818 − 1.84710I
b = −0.847861 + 0.494590I
1.67693 + 2.03514I 12.04529 − 3.68045I
u = −0.776212 + 0.543476I
a = 0.165614 + 0.941776I
b = −0.818876 − 1.029970I
1.08798 − 3.87177I 9.94392 + 7.67559I
u = −0.776212 − 0.543476I
a = 0.165614 − 0.941776I
b = −0.818876 + 1.029970I
1.08798 + 3.87177I 9.94392 − 7.67559I
u = 0.391359 + 0.443026I
a = 0.16676 − 2.00716I
b = −0.958890 + 0.494800I
−1.62818 + 1.74525I −0.95153 − 1.16784I
u = 0.391359 − 0.443026I
a = 0.16676 + 2.00716I
b = −0.958890 − 0.494800I
−1.62818 − 1.74525I −0.95153 + 1.16784I
u = −0.13651 + 1.41680I
a = 0.560094 − 0.041919I
b = 0.775471 + 0.132880I
−4.18065 − 3.12026I 9.33417 + 9.86695I
u = −0.13651 − 1.41680I
a = 0.560094 + 0.041919I
b = 0.775471 − 0.132880I
−4.18065 + 3.12026I 9.33417 − 9.86695I
u = 0.503014
a = 0.312373
b = 2.20130
7.91244 48.6950
u = −0.459070
a = 0.839237
b = 0.191558
0.869022 11.1750
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.24791 + 0.91352I
a = 0.223114 + 0.771809I
b = −0.654338 − 1.195730I
18.3099 + 5.1932I 9.79689 − 2.37682I
u = 1.24791 − 0.91352I
a = 0.223114 − 0.771809I
b = −0.654338 + 1.195730I
18.3099 − 5.1932I 9.79689 + 2.37682I
u = 1.20652 + 1.25211I
a = −0.259569 − 1.133580I
b = −1.19193 + 0.83821I
16.5318 + 12.4168I 7.89590 − 5.61800I
u = 1.20652 − 1.25211I
a = −0.259569 + 1.133580I
b = −1.19193 − 0.83821I
16.5318 − 12.4168I 7.89590 + 5.61800I
6
II. I
u
2
= hu
7
+ u
6
+ 2u
5
− u
3
− 3u
2
+ b − u − 1, u
6
+ u
5
+ 2u
4
− u
2
+ a −
2u, u
8
+ 2u
7
+ 3u
6
+ u
5
− 2u
4
− 5u
3
− 3u
2
+ 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
−u
6
− u
5
− 2u
4
+ u
2
+ 2u
−u
7
− u
6
− 2u
5
+ u
3
+ 3u
2
+ u + 1
a
7
=
1
−u
2
a
2
=
−u
7
− 2u
6
− 3u
5
− 2u
4
+ u
3
+ 4u
2
+ 3u + 1
−u
7
− u
6
− 2u
5
+ u
3
+ 3u
2
+ u + 1
a
1
=
−1
u
7
+ 3u
6
+ 5u
5
+ 4u
4
− u
3
− 6u
2
− 8u − 2
a
11
=
u
−u
7
− 2u
6
− 3u
5
− u
4
+ u
3
+ 5u
2
+ 3u + 1
a
5
=
2u
7
+ 4u
6
+ 6u
5
+ 3u
4
− 3u
3
− 8u
2
− 6u − 1
2u
7
+ 3u
6
+ 5u
5
+ u
4
− 3u
3
− 7u
2
− 4u − 1
a
4
=
0
2u
7
+ 4u
6
+ 6u
5
+ 3u
4
− 3u
3
− 8u
2
− 6u − 1
a
9
=
−u
u
3
+ u
a
8
=
−u
3
− u
2
− 2u
u
7
+ 2u
6
+ 4u
5
+ 2u
4
− 6u
2
− 4u − 2
a
12
=
u
u
7
+ 3u
6
+ 5u
5
+ 4u
4
− 2u
3
− 7u
2
− 9u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 10u
7
+ 21u
6
+ 30u
5
+ 13u
4
− 15u
3
− 43u
2
− 27u + 1
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
− 6u
7
+ 11u
6
− 16u
5
+ 11u
4
− 15u
3
+ 29u
2
− 20u + 4
c
2
u
8
+ 4u
7
+ 5u
6
− 7u
4
− 7u
3
− u
2
+ 4u + 2
c
3
, c
7
u
8
− 6u
6
+ 6u
4
+ u
3
− 6u
2
+ u − 1
c
4
u
8
− 3u
7
− 13u
6
+ 7u
5
+ 23u
4
− 11u
3
− 12u
2
+ 7u − 1
c
5
u
8
− 4u
7
+ 5u
6
− 7u
4
+ 7u
3
− u
2
− 4u + 2
c
6
, c
10
u
8
+ 2u
7
+ 3u
6
+ u
5
− 2u
4
− 5u
3
− 3u
2
+ 1
c
8
u
8
+ 4u
7
+ u
6
− 4u
5
+ 4u
4
+ 7u
3
+ 5u
2
+ 3u + 1
c
9
u
8
− 2u
7
+ 3u
6
− u
5
− 2u
4
+ 5u
3
− 3u
2
+ 1
c
11
u
8
− 6u
6
+ 6u
4
− u
3
− 6u
2
− u − 1
c
12
u
8
+ 8u
7
+ 25u
6
+ 43u
5
+ 48u
4
+ 37u
3
+ 21u
2
+ 8u + 2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
− 14y
7
− 49y
6
− 136y
5
+ 47y
4
− 139y
3
+ 329y
2
− 168y + 16
c
2
, c
5
y
8
− 6y
7
+ 11y
6
− 16y
5
+ 11y
4
− 15y
3
+ 29y
2
− 20y + 4
c
3
, c
7
, c
11
y
8
− 12y
7
+ 48y
6
− 84y
5
+ 106y
4
− 61y
3
+ 22y
2
+ 11y + 1
c
4
y
8
− 35y
7
+ 257y
6
− 737y
5
+ 1035y
4
− 745y
3
+ 252y
2
− 25y + 1
c
6
, c
9
, c
10
y
8
+ 2y
7
+ y
6
+ y
5
− 2y
4
− 7y
3
+ 5y
2
− 6y + 1
c
8
y
8
− 14y
7
+ 41y
6
− 54y
5
+ 60y
4
+ 17y
3
− 9y
2
+ y + 1
c
12
y
8
− 14y
7
+ 33y
6
+ y
5
+ 48y
4
+ 59y
3
+ 41y
2
+ 20y + 4
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.08029
a = −2.45704
b = 0.593006
12.7188 15.1320
u = −0.717708 + 0.491300I
a = −0.421822 + 0.787765I
b = 0.471737 − 0.986547I
2.94742 − 2.05228I 9.34541 + 5.26901I
u = −0.717708 − 0.491300I
a = −0.421822 − 0.787765I
b = 0.471737 + 0.986547I
2.94742 + 2.05228I 9.34541 − 5.26901I
u = −0.817233 + 0.903739I
a = 0.197428 − 1.362760I
b = 1.104120 + 0.718722I
1.10667 − 8.19546I 4.78583 + 8.26595I
u = −0.817233 − 0.903739I
a = 0.197428 + 1.362760I
b = 1.104120 − 0.718722I
1.10667 + 8.19546I 4.78583 − 8.26595I
u = −0.221999 + 1.360760I
a = −0.528351 − 0.011203I
b = −0.891831 + 0.040113I
−4.44049 − 2.73730I −0.23426 − 3.71473I
u = −0.221999 − 1.360760I
a = −0.528351 + 0.011203I
b = −0.891831 − 0.040113I
−4.44049 + 2.73730I −0.23426 + 3.71473I
u = 0.433591
a = 0.962525
b = 2.03893
7.79317 −18.9260
10
III. I
u
3
= h−1.84 × 10
10
u
17
+ 7.51 × 10
10
u
16
+ · · · + 3.75 × 10
10
b + 1.61 ×
10
11
, 1.42 × 10
12
u
17
− 6.25 × 10
12
u
16
+ · · · + 4.12 × 10
11
a − 2.71 ×
10
13
, u
18
− 5u
17
+ · · · − 60u + 11i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
−3.44667u
17
+ 15.1583u
16
+ ··· − 239.602u + 65.8327
0.492305u
17
− 2.00461u
16
+ ··· + 24.0884u − 4.31006
a
7
=
1
−u
2
a
2
=
−2.95436u
17
+ 13.1537u
16
+ ··· − 215.514u + 61.5226
0.492305u
17
− 2.00461u
16
+ ··· + 24.0884u − 4.31006
a
1
=
−2.51715u
17
+ 11.0972u
16
+ ··· − 173.143u + 45.6450
0.836349u
17
− 3.77119u
16
+ ··· + 61.6274u − 15.3746
a
11
=
−0.342094u
17
+ 1.85154u
16
+ ··· − 50.3800u + 20.0714
−1.66048u
17
+ 7.46601u
16
+ ··· − 116.611u + 29.2405
a
5
=
1.68324u
17
− 7.59201u
16
+ ··· + 129.820u − 38.4924
−0.413536u
17
+ 1.54784u
16
+ ··· − 12.4168u + 0.775334
a
4
=
1.67814u
17
− 7.28075u
16
+ ··· + 111.300u − 30.2014
−0.781187u
17
+ 3.02254u
16
+ ··· − 29.6167u + 3.91836
a
9
=
−u
u
3
+ u
a
8
=
6.14612u
17
− 27.5654u
16
+ ··· + 460.756u − 131.949
0.540102u
17
− 2.47677u
16
+ ··· + 45.1613u − 14.0091
a
12
=
−1.68081u
17
+ 7.32598u
16
+ ··· − 111.516u + 29.2703
−0.111180u
17
+ 0.634520u
16
+ ··· − 15.4335u + 5.51612
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
76928705088
37469236469
u
17
−
347641873578
37469236469
u
16
+ ··· +
859374395980
5352748067
u −
1482870335594
37469236469
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
9
+ 3u
8
+ 9u
7
+ 16u
6
+ 24u
5
+ 29u
4
+ 25u
3
+ 20u
2
+ 9u + 1)
2
c
2
, c
5
(u
9
− u
8
− u
7
+ 2u
6
+ 2u
5
− 3u
4
− u
3
+ 4u
2
− u − 1)
2
c
3
, c
7
, c
11
u
18
− u
17
+ ··· + 8u − 1
c
4
u
18
+ u
17
+ ··· − 12208u − 5581
c
6
, c
9
, c
10
u
18
+ 5u
17
+ ··· + 60u + 11
c
8
(u
9
− 7u
8
+ 15u
7
− 11u
6
+ 12u
5
− 12u
4
− 17u
3
− 3u
2
− 11u + 1)
2
c
12
(u
9
+ 5u
8
+ 6u
7
− u
6
− 4u
4
− 14u
3
− u
2
− 9u + 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
9
+ 9y
8
+ 33y
7
+ 52y
6
− 4y
5
− 125y
4
− 135y
3
− 8y
2
+ 41y −1)
2
c
2
, c
5
(y
9
− 3y
8
+ 9y
7
− 16y
6
+ 24y
5
− 29y
4
+ 25y
3
− 20y
2
+ 9y −1)
2
c
3
, c
7
, c
11
y
18
− 37y
17
+ ··· + 38y + 1
c
4
y
18
− 37y
17
+ ··· + 25404472y + 31147561
c
6
, c
9
, c
10
y
18
− y
17
+ ··· − 718y + 121
c
8
(y
9
− 19y
8
+ ··· + 127y −1)
2
c
12
(y
9
− 13y
8
+ ··· + 83y −1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.964780 + 0.260012I
a = −0.442639 + 1.305680I
b = 1.051070 − 0.723457I
1.61768 + 6.30275I 6.85119 − 4.04429I
u = 0.964780 − 0.260012I
a = −0.442639 − 1.305680I
b = 1.051070 + 0.723457I
1.61768 − 6.30275I 6.85119 + 4.04429I
u = −0.053905 + 0.902264I
a = −0.522493 − 0.703476I
b = −1.08132
−3.22594 2.09565 + 0.I
u = −0.053905 − 0.902264I
a = −0.522493 + 0.703476I
b = −1.08132
−3.22594 2.09565 + 0.I
u = −0.596141 + 0.989164I
a = −0.084498 + 1.048500I
b = −0.395865
−0.204218 5.27771 + 0.I
u = −0.596141 − 0.989164I
a = −0.084498 − 1.048500I
b = −0.395865
−0.204218 5.27771 + 0.I
u = −0.960557 + 0.706873I
a = −0.308105 + 0.556474I
b = 0.688981 − 0.846969I
2.75992 − 0.39920I 8.67020 − 0.65321I
u = −0.960557 − 0.706873I
a = −0.308105 − 0.556474I
b = 0.688981 + 0.846969I
2.75992 + 0.39920I 8.67020 + 0.65321I
u = 0.693875 + 0.252032I
a = 0.20218 + 1.57341I
b = 0.688981 − 0.846969I
2.75992 − 0.39920I 8.67020 − 0.65321I
u = 0.693875 − 0.252032I
a = 0.20218 − 1.57341I
b = 0.688981 + 0.846969I
2.75992 + 0.39920I 8.67020 + 0.65321I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.859474 + 1.111270I
a = 0.432850 − 1.182810I
b = 1.051070 + 0.723457I
1.61768 − 6.30275I 6.85119 + 4.04429I
u = −0.859474 − 1.111270I
a = 0.432850 + 1.182810I
b = 1.051070 − 0.723457I
1.61768 + 6.30275I 6.85119 − 4.04429I
u = 1.45749
a = −1.39150
b = 0.812913
11.9229 2.59310
u = 0.496939
a = 6.25056
b = 0.812913
11.9229 2.59310
u = 0.96038 + 1.33439I
a = −0.758555 − 0.968584I
b = −0.907915 + 0.810184I
16.8725 + 3.0439I 8.49539 − 2.64288I
u = 0.96038 − 1.33439I
a = −0.758555 + 0.968584I
b = −0.907915 − 0.810184I
16.8725 − 3.0439I 8.49539 + 2.64288I
u = 1.37383 + 1.22001I
a = 0.279000 + 0.397209I
b = −0.907915 − 0.810184I
16.8725 − 3.0439I 8.49539 + 2.64288I
u = 1.37383 − 1.22001I
a = 0.279000 − 0.397209I
b = −0.907915 + 0.810184I
16.8725 + 3.0439I 8.49539 − 2.64288I
15
IV. I
u
4
= h−u
6
− 3u
5
− 6u
4
− 7u
3
− 5u
2
+ b − 2u, u
6
+ 3u
5
+ 7u
4
+ 10u
3
+
11u
2
+ a + 8u + 3, u
8
+ 4u
7
+ · · · + 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
−u
6
− 3u
5
− 7u
4
− 10u
3
− 11u
2
− 8u − 3
u
6
+ 3u
5
+ 6u
4
+ 7u
3
+ 5u
2
+ 2u
a
7
=
1
−u
2
a
2
=
−u
4
− 3u
3
− 6u
2
− 6u − 3
u
6
+ 3u
5
+ 6u
4
+ 7u
3
+ 5u
2
+ 2u
a
1
=
−u
7
− 4u
6
− 10u
5
− 16u
4
− 18u
3
− 14u
2
− 7u − 1
−u
2
− u − 1
a
11
=
−u
7
− 4u
6
− 10u
5
− 16u
4
− 18u
3
− 14u
2
− 6u
−u
3
− 2u
2
− u − 1
a
5
=
u
7
+ 3u
6
+ 6u
5
+ 7u
4
+ 5u
3
+ u
2
− 2u − 2
u
4
+ 2u
3
+ 3u
2
+ 2u
a
4
=
u
7
+ 2u
6
+ 3u
5
+ u
4
− 2u
3
− 5u
2
− 5u − 3
−u
7
− 4u
6
− 9u
5
− 11u
4
− 9u
3
− 3u
2
− 1
a
9
=
−u
u
3
+ u
a
8
=
u
7
+ 4u
6
+ 10u
5
+ 16u
4
+ 17u
3
+ 11u
2
+ 2u − 1
u
5
+ 3u
4
+ 5u
3
+ 4u
2
+ 3u + 1
a
12
=
−u
7
− 4u
6
− 10u
5
− 16u
4
− 18u
3
− 14u
2
− 8u − 1
u
3
− u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
4
− 8u
3
− 12u
2
− 8u + 4
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
4
c
2
, c
5
, c
8
(u
4
− u
2
+ 1)
2
c
3
, c
7
u
8
− 2u
6
− 2u
5
+ 2u
4
+ 2u
3
+ 3u
2
− 4u + 1
c
4
(u
2
+ 1)
4
c
6
, c
10
u
8
+ 4u
7
+ 10u
6
+ 16u
5
+ 18u
4
+ 14u
3
+ 7u
2
+ 2u + 1
c
9
u
8
− 4u
7
+ 10u
6
− 16u
5
+ 18u
4
− 14u
3
+ 7u
2
− 2u + 1
c
11
u
8
− 2u
6
+ 2u
5
+ 2u
4
− 2u
3
+ 3u
2
+ 4u + 1
c
12
(u − 1)
8
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
4
c
2
, c
5
, c
8
(y
2
− y + 1)
4
c
3
, c
7
, c
11
y
8
− 4y
7
+ 8y
6
− 6y
5
+ 2y
4
− 12y
3
+ 29y
2
− 10y + 1
c
4
(y + 1)
8
c
6
, c
9
, c
10
y
8
+ 4y
7
+ 8y
6
+ 6y
5
+ 2y
4
+ 12y
3
+ 29y
2
+ 10y + 1
c
12
(y −1)
8
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.060940 + 0.445679I
a = 0.390879 + 1.003910I
b = −0.866025 − 0.500000I
− 2.02988I 6.00000 + 3.46410I
u = −1.060940 − 0.445679I
a = 0.390879 − 1.003910I
b = −0.866025 + 0.500000I
2.02988I 6.00000 − 3.46410I
u = −0.305600 + 1.286010I
a = 1.049970 − 0.653467I
b = 0.866025 + 0.500000I
− 2.02988I 6.00000 + 3.46410I
u = −0.305600 − 1.286010I
a = 1.049970 + 0.653467I
b = 0.866025 − 0.500000I
2.02988I 6.00000 − 3.46410I
u = −0.69440 + 1.28601I
a = −0.183947 + 0.114482I
b = 0.866025 − 0.500000I
2.02988I 6.00000 − 3.46410I
u = −0.69440 − 1.28601I
a = −0.183947 − 0.114482I
b = 0.866025 + 0.500000I
− 2.02988I 6.00000 + 3.46410I
u = 0.060942 + 0.445679I
a = −1.25690 − 3.22814I
b = −0.866025 + 0.500000I
2.02988I 6.00000 − 3.46410I
u = 0.060942 − 0.445679I
a = −1.25690 + 3.22814I
b = −0.866025 − 0.500000I
− 2.02988I 6.00000 + 3.46410I
19
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
4
)(u
8
− 6u
7
+ ··· − 20u + 4)
· (u
9
+ 3u
8
+ 9u
7
+ 16u
6
+ 24u
5
+ 29u
4
+ 25u
3
+ 20u
2
+ 9u + 1)
2
· (u
14
+ 7u
13
+ ··· + 128u + 4)
c
2
(u
4
− u
2
+ 1)
2
(u
8
+ 4u
7
+ 5u
6
− 7u
4
− 7u
3
− u
2
+ 4u + 2)
· (u
9
− u
8
− u
7
+ 2u
6
+ 2u
5
− 3u
4
− u
3
+ 4u
2
− u − 1)
2
· (u
14
+ 5u
13
+ ··· − 4u + 2)
c
3
, c
7
(u
8
− 6u
6
+ 6u
4
+ u
3
− 6u
2
+ u − 1)
· (u
8
− 2u
6
+ ··· − 4u + 1)(u
14
− 2u
13
+ ··· + 3u + 1)
· (u
18
− u
17
+ ··· + 8u − 1)
c
4
(u
2
+ 1)
4
(u
8
− 3u
7
− 13u
6
+ 7u
5
+ 23u
4
− 11u
3
− 12u
2
+ 7u − 1)
· (u
14
+ 7u
13
+ ··· − 27u − 1)(u
18
+ u
17
+ ··· − 12208u − 5581)
c
5
(u
4
− u
2
+ 1)
2
(u
8
− 4u
7
+ 5u
6
− 7u
4
+ 7u
3
− u
2
− 4u + 2)
· (u
9
− u
8
− u
7
+ 2u
6
+ 2u
5
− 3u
4
− u
3
+ 4u
2
− u − 1)
2
· (u
14
+ 5u
13
+ ··· − 4u + 2)
c
6
, c
10
(u
8
+ 2u
7
+ 3u
6
+ u
5
− 2u
4
− 5u
3
− 3u
2
+ 1)
· (u
8
+ 4u
7
+ 10u
6
+ 16u
5
+ 18u
4
+ 14u
3
+ 7u
2
+ 2u + 1)
· (u
14
+ 2u
13
+ ··· + 5u
2
− 1)(u
18
+ 5u
17
+ ··· + 60u + 11)
c
8
(u
4
− u
2
+ 1)
2
(u
8
+ 4u
7
+ u
6
− 4u
5
+ 4u
4
+ 7u
3
+ 5u
2
+ 3u + 1)
· (u
9
− 7u
8
+ 15u
7
− 11u
6
+ 12u
5
− 12u
4
− 17u
3
− 3u
2
− 11u + 1)
2
· (u
14
+ 11u
13
+ ··· − 48u − 32)
c
9
(u
8
− 4u
7
+ 10u
6
− 16u
5
+ 18u
4
− 14u
3
+ 7u
2
− 2u + 1)
· (u
8
− 2u
7
+ ··· − 3u
2
+ 1)(u
14
+ 2u
13
+ ··· + 5u
2
− 1)
· (u
18
+ 5u
17
+ ··· + 60u + 11)
c
11
(u
8
− 6u
6
+ 6u
4
− u
3
− 6u
2
− u − 1)
· (u
8
− 2u
6
+ ··· + 4u + 1)(u
14
− 2u
13
+ ··· + 3u + 1)
· (u
18
− u
17
+ ··· + 8u − 1)
c
12
(u − 1)
8
(u
8
+ 8u
7
+ 25u
6
+ 43u
5
+ 48u
4
+ 37u
3
+ 21u
2
+ 8u + 2)
· (u
9
+ 5u
8
+ 6u
7
− u
6
− 4u
4
− 14u
3
− u
2
− 9u + 1)
2
· (u
14
− 11u
13
+ ··· + 112u + 26)
20
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
4
· (y
8
− 14y
7
− 49y
6
− 136y
5
+ 47y
4
− 139y
3
+ 329y
2
− 168y + 16)
· (y
9
+ 9y
8
+ 33y
7
+ 52y
6
− 4y
5
− 125y
4
− 135y
3
− 8y
2
+ 41y −1)
2
· (y
14
− 7y
13
+ ··· − 11904y + 16)
c
2
, c
5
((y
2
− y + 1)
4
)(y
8
− 6y
7
+ ··· − 20y + 4)
· (y
9
− 3y
8
+ 9y
7
− 16y
6
+ 24y
5
− 29y
4
+ 25y
3
− 20y
2
+ 9y −1)
2
· (y
14
− 7y
13
+ ··· − 128y + 4)
c
3
, c
7
, c
11
(y
8
− 12y
7
+ 48y
6
− 84y
5
+ 106y
4
− 61y
3
+ 22y
2
+ 11y + 1)
· (y
8
− 4y
7
+ 8y
6
− 6y
5
+ 2y
4
− 12y
3
+ 29y
2
− 10y + 1)
· (y
14
− 22y
13
+ ··· − 17y + 1)(y
18
− 37y
17
+ ··· + 38y + 1)
c
4
(y + 1)
8
· (y
8
− 35y
7
+ 257y
6
− 737y
5
+ 1035y
4
− 745y
3
+ 252y
2
− 25y + 1)
· (y
14
− 69y
13
+ ··· − 481y + 1)
· (y
18
− 37y
17
+ ··· + 25404472y + 31147561)
c
6
, c
9
, c
10
(y
8
+ 2y
7
+ y
6
+ y
5
− 2y
4
− 7y
3
+ 5y
2
− 6y + 1)
· (y
8
+ 4y
7
+ 8y
6
+ 6y
5
+ 2y
4
+ 12y
3
+ 29y
2
+ 10y + 1)
· (y
14
+ 10y
12
+ ··· − 10y + 1)(y
18
− y
17
+ ··· − 718y + 121)
c
8
((y
2
− y + 1)
4
)(y
8
− 14y
7
+ ··· + y + 1)
· ((y
9
− 19y
8
+ ··· + 127y −1)
2
)(y
14
− 35y
13
+ ··· + 2304y + 1024)
c
12
(y −1)
8
(y
8
− 14y
7
+ 33y
6
+ y
5
+ 48y
4
+ 59y
3
+ 41y
2
+ 20y + 4)
· ((y
9
− 13y
8
+ ··· + 83y −1)
2
)(y
14
− 47y
13
+ ··· − 20136y + 676)
21
