12n
0302
(K12n
0302
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 11 2 1 5 1 4 8 9
Solving Sequence
5,8 1,9
10 4 7 3 12 11 6 2
c
8
c
9
c
4
c
7
c
3
c
12
c
11
c
5
c
2
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
30
− u
29
+ ··· + 64b + 1, u
30
+ u
29
+ ··· + 64a − 65, u
31
+ 4u
29
+ ··· + 2u − 1i
I
u
2
= h1.68907 × 10
23
u
35
− 1.11374 × 10
23
u
34
+ ··· + 9.33256 × 10
23
b + 1.62659 × 10
24
,
− 2.83334 × 10
24
u
35
+ 1.80304 × 10
24
u
34
+ ··· + 1.58653 × 10
25
a + 2.57411 × 10
25
,
u
36
− u
35
+ ··· − 44u + 17i
I
u
3
= hb + a + 1, a
6
+ a
5
u + 6a
5
+ 5a
4
u + 16a
4
+ 12a
3
u + 24a
3
+ 16a
2
u + 21a
2
+ 12au + 10a + 4u + 1, u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 79 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−u
30
−u
29
+· · ·+64b+1, u
30
+u
29
+· · ·+64a−65, u
31
+4u
29
+· · ·+2u−1i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
1
=
−0.0156250u
30
− 0.0156250u
29
+ ··· − 0.0156250u + 1.01563
0.0156250u
30
+ 0.0156250u
29
+ ··· + 0.0156250u − 0.0156250
a
9
=
1
u
2
a
10
=
−0.0156250u
30
− 0.0156250u
29
+ ··· − 0.0156250u + 1.01563
0.0156250u
30
+ 0.0156250u
29
+ ··· + 0.0156250u − 0.0156250
a
4
=
u
u
3
+ u
a
7
=
−0.171875u
30
− 0.203125u
29
+ ··· − 0.265625u + 1.23438
5
32
u
30
+
3
16
u
29
+ ··· +
1
4
u −
7
32
a
3
=
−2.37500u
30
− 0.125000u
29
+ ··· + 7.68750u − 0.625000
1.45313u
30
+ 0.453125u
29
+ ··· − 2.23438u + 0.0468750
a
12
=
−0.0156250u
30
− 0.0156250u
29
+ ··· − 0.0156250u + 1.01563
0.0156250u
30
+ 0.0156250u
29
+ ··· + 0.0156250u − 0.0156250
a
11
=
1
0.0156250u
30
+ 0.0156250u
29
+ ··· + 0.0156250u − 0.0156250
a
6
=
−u
−0.0156250u
30
+ 0.0156250u
29
+ ··· + 1.04688u − 0.0156250
a
2
=
−2.45313u
30
− 1.10938u
29
+ ··· + 6.73438u + 1.04688
1
32
u
30
+
43
32
u
29
+ ··· +
61
16
u −
7
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
15
8
u
30
+
7
2
u
29
+ ··· +
343
16
u −
181
16
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
31
+ 15u
30
+ ··· − 3u − 4
c
2
, c
6
u
31
− 3u
30
+ ··· − 5u + 2
c
3
u
31
+ 3u
30
+ ··· − 13u + 2
c
4
, c
5
, c
8
u
31
+ 4u
29
+ ··· + 2u + 1
c
7
u
31
− 15u
30
+ ··· − 971u + 86
c
9
, c
12
u
31
− 8u
30
+ ··· − 12u + 1
c
10
u
31
− 19u
29
+ ··· + 328u + 73
c
11
u
31
+ 29u
30
+ ··· + 2490368u + 262144
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
31
+ 3y
30
+ ··· + 129y −16
c
2
, c
6
y
31
+ 15y
30
+ ··· − 3y −4
c
3
y
31
− 9y
30
+ ··· − 27y −4
c
4
, c
5
, c
8
y
31
+ 8y
30
+ ··· − 12y −1
c
7
y
31
+ 3y
30
+ ··· + 25565y −7396
c
9
, c
12
y
31
+ 44y
30
+ ··· + 4y −1
c
10
y
31
− 38y
30
+ ··· + 121892y −5329
c
11
y
31
− 7y
30
+ ··· + 188978561024y −68719476736
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.428614 + 0.787639I
a = 0.020444 − 1.071240I
b = 0.277691 + 1.156760I
2.11446 − 7.62347I −2.55486 + 10.23287I
u = 0.428614 − 0.787639I
a = 0.020444 + 1.071240I
b = 0.277691 − 1.156760I
2.11446 + 7.62347I −2.55486 − 10.23287I
u = −0.398489 + 0.747920I
a = 0.277025 + 1.072210I
b = 0.127552 − 1.190720I
3.81643 + 2.62838I 0.13136 − 5.27727I
u = −0.398489 − 0.747920I
a = 0.277025 − 1.072210I
b = 0.127552 + 1.190720I
3.81643 − 2.62838I 0.13136 + 5.27727I
u = −0.823498 + 0.113059I
a = 0.851475 − 0.053587I
b = 1.221930 − 0.380414I
−4.06065 + 3.78130I −10.92047 − 4.50880I
u = −0.823498 − 0.113059I
a = 0.851475 + 0.053587I
b = 1.221930 + 0.380414I
−4.06065 − 3.78130I −10.92047 + 4.50880I
u = −0.308639 + 0.692422I
a = 0.807667 + 1.093890I
b = −0.226940 − 1.192890I
3.71218 + 0.23183I −0.44077 − 4.37023I
u = −0.308639 − 0.692422I
a = 0.807667 − 1.093890I
b = −0.226940 + 1.192890I
3.71218 − 0.23183I −0.44077 + 4.37023I
u = 0.737257 + 0.999674I
a = −1.014960 + 0.279964I
b = −0.405856 − 0.149663I
−1.01582 − 3.41753I −1.81646 + 1.83833I
u = 0.737257 − 0.999674I
a = −1.014960 − 0.279964I
b = −0.405856 + 0.149663I
−1.01582 + 3.41753I −1.81646 − 1.83833I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.493312 + 0.567058I
a = 0.507385 − 0.402871I
b = 0.107522 + 0.874845I
−0.97829 − 1.43223I −7.64253 + 4.49429I
u = 0.493312 − 0.567058I
a = 0.507385 + 0.402871I
b = 0.107522 − 0.874845I
−0.97829 + 1.43223I −7.64253 − 4.49429I
u = 0.263305 + 0.688070I
a = 1.04620 − 1.12763I
b = −0.418303 + 1.197120I
1.88939 + 4.73630I −3.89657 − 0.59420I
u = 0.263305 − 0.688070I
a = 1.04620 + 1.12763I
b = −0.418303 − 1.197120I
1.88939 − 4.73630I −3.89657 + 0.59420I
u = 0.896581 + 0.914182I
a = −0.497658 + 0.734722I
b = −1.22042 + 0.80006I
−4.16004 − 2.58701I −4.00000 + 2.53611I
u = 0.896581 − 0.914182I
a = −0.497658 − 0.734722I
b = −1.22042 − 0.80006I
−4.16004 + 2.58701I −4.00000 − 2.53611I
u = −0.747911 + 1.060550I
a = −1.244110 − 0.413683I
b = −0.518247 + 0.621142I
−0.50947 + 8.32474I −0.66671 − 7.63696I
u = −0.747911 − 1.060550I
a = −1.244110 + 0.413683I
b = −0.518247 − 0.621142I
−0.50947 − 8.32474I −0.66671 + 7.63696I
u = −0.946068 + 0.895466I
a = −0.369074 − 0.860893I
b = −1.39985 − 1.14923I
−6.97286 − 2.17567I −7.38278 + 1.16604I
u = −0.946068 − 0.895466I
a = −0.369074 + 0.860893I
b = −1.39985 + 1.14923I
−6.97286 + 2.17567I −7.38278 − 1.16604I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.918427 + 0.979157I
a = −0.674803 − 0.903235I
b = −1.66201 − 0.48080I
−8.26580 + 6.12965I −8.72219 − 5.26564I
u = −0.918427 − 0.979157I
a = −0.674803 + 0.903235I
b = −1.66201 + 0.48080I
−8.26580 − 6.12965I −8.72219 + 5.26564I
u = 0.654707
a = 0.828573
b = 0.783801
−1.18982 −8.14570
u = −0.789945 + 1.134080I
a = −1.45883 − 0.71380I
b = −0.97512 + 1.29471I
−2.55844 + 10.54750I −1.65094 − 6.34331I
u = −0.789945 − 1.134080I
a = −1.45883 + 0.71380I
b = −0.97512 − 1.29471I
−2.55844 − 10.54750I −1.65094 + 6.34331I
u = 0.831569 + 1.116210I
a = −1.30990 + 0.83774I
b = −1.38338 − 1.03976I
−7.22926 − 7.46449I −7.55894 + 4.20366I
u = 0.831569 − 1.116210I
a = −1.30990 − 0.83774I
b = −1.38338 + 1.03976I
−7.22926 + 7.46449I −7.55894 − 4.20366I
u = 0.796078 + 1.157720I
a = −1.53812 + 0.78506I
b = −1.06685 − 1.54659I
−5.0523 − 15.6504I −4.62054 + 9.85010I
u = 0.796078 − 1.157720I
a = −1.53812 − 0.78506I
b = −1.06685 + 1.54659I
−5.0523 + 15.6504I −4.62054 − 9.85010I
u = 0.158909 + 0.450532I
a = 1.182970 − 0.267894I
b = −0.349614 + 0.360185I
−0.56592 − 1.41483I −5.18401 + 4.52622I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.158909 − 0.450532I
a = 1.182970 + 0.267894I
b = −0.349614 − 0.360185I
−0.56592 + 1.41483I −5.18401 − 4.52622I
8
II. I
u
2
= h1.69 × 10
23
u
35
− 1.11 × 10
23
u
34
+ · · · + 9.33 × 10
23
b + 1.63 ×
10
24
, −2.83 × 10
24
u
35
+ 1.80 × 10
24
u
34
+ · · · + 1.59 × 10
25
a + 2.57 ×
10
25
, u
36
− u
35
+ · · · − 44u + 17i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
1
=
0.178587u
35
− 0.113646u
34
+ ··· − 2.60843u − 1.62248
−0.180987u
35
+ 0.119339u
34
+ ··· − 0.246496u − 1.74292
a
9
=
1
u
2
a
10
=
−0.00240038u
35
+ 0.00569313u
34
+ ··· − 2.85493u − 2.36540
0.0118866u
35
− 0.0147001u
34
+ ··· − 0.196623u − 1.07676
a
4
=
u
u
3
+ u
a
7
=
0.116243u
35
− 0.0798703u
34
+ ··· − 2.42275u − 0.678453
−0.208906u
35
+ 0.154096u
34
+ ··· − 0.572363u − 1.69509
a
3
=
0.0899876u
35
− 0.234769u
34
+ ··· + 6.71425u − 2.77653
0.0464972u
35
− 0.00440409u
34
+ ··· + 2.00161u − 0.344605
a
12
=
0.0509778u
35
− 0.0297385u
34
+ ··· − 2.54053u − 0.983544
−1
a
11
=
0.0509778u
35
− 0.0297385u
34
+ ··· − 2.54053u − 1.98354
−1
a
6
=
−0.0375842u
35
− 0.0900247u
34
+ ··· − 7.79934u + 1.72161
0.0212393u
35
− 0.148848u
34
+ ··· + 1.25948u − 0.866623
a
2
=
0.267879u
35
− 0.421650u
34
+ ··· + 20.4123u − 11.1581
0.0138355u
35
+ 0.221537u
34
+ ··· + 0.400166u − 0.936209
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
94459427649077696837288
933255522779965433376737
u
35
+
1669130199746521433848712
933255522779965433376737
u
34
+ ··· −
25170861470598659641440976
933255522779965433376737
u +
1667795781533429661370718
933255522779965433376737
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
18
+ 9u
17
+ ··· + u + 1)
2
c
2
, c
6
(u
18
+ u
17
+ ··· + u + 1)
2
c
3
(u
18
− u
17
+ ··· − u + 5)
2
c
4
, c
5
, c
8
u
36
+ u
35
+ ··· + 44u + 17
c
7
(u
18
+ 5u
17
+ ··· + 13u + 3)
2
c
9
, c
12
u
36
− 15u
35
+ ··· − 3300u + 289
c
10
u
36
+ u
35
+ ··· − 22616u + 236209
c
11
(u − 1)
36
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
18
+ y
17
+ ··· + 9y + 1)
2
c
2
, c
6
(y
18
+ 9y
17
+ ··· + y + 1)
2
c
3
(y
18
− 7y
17
+ ··· − 91y + 25)
2
c
4
, c
5
, c
8
y
36
+ 15y
35
+ ··· + 3300y + 289
c
7
(y
18
− 3y
17
+ ··· + 5y + 9)
2
c
9
, c
12
y
36
+ 11y
35
+ ··· + 3006276y + 83521
c
10
y
36
− 5y
35
+ ··· − 292100155924y + 55794691681
c
11
(y −1)
36
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.320634 + 0.870916I
a = −1.59556 + 0.83474I
b = 0.087095 + 0.616918I
4.20760 + 0.97328I 2.11395 − 4.55184I
u = −0.320634 − 0.870916I
a = −1.59556 − 0.83474I
b = 0.087095 − 0.616918I
4.20760 − 0.97328I 2.11395 + 4.55184I
u = −0.828905 + 0.682944I
a = 0.886516 + 0.217948I
b = 0.420070 + 0.303007I
−1.65768 − 2.36433I −3.03894 + 3.34702I
u = −0.828905 − 0.682944I
a = 0.886516 − 0.217948I
b = 0.420070 − 0.303007I
−1.65768 + 2.36433I −3.03894 − 3.34702I
u = 0.338195 + 1.021420I
a = −1.33297 − 1.04821I
b = 0.609948 − 0.458991I
2.68166 + 3.09151I −0.88507 − 2.77317I
u = 0.338195 − 1.021420I
a = −1.33297 + 1.04821I
b = 0.609948 + 0.458991I
2.68166 − 3.09151I −0.88507 + 2.77317I
u = 0.786288 + 0.800353I
a = 1.137130 − 0.178590I
b = 0.420070 + 0.303007I
−1.65768 − 2.36433I −3.03894 + 3.34702I
u = 0.786288 − 0.800353I
a = 1.137130 + 0.178590I
b = 0.420070 − 0.303007I
−1.65768 + 2.36433I −3.03894 − 3.34702I
u = −0.061644 + 1.184410I
a = 0.586032 − 0.513303I
b = −0.954493 + 0.372508I
−0.299485 − 0.584791I −8.18494 − 0.42463I
u = −0.061644 − 1.184410I
a = 0.586032 + 0.513303I
b = −0.954493 − 0.372508I
−0.299485 + 0.584791I −8.18494 + 0.42463I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.001550 + 0.646267I
a = 0.708963 + 0.596743I
b = 1.09501 + 1.09178I
−4.08770 − 3.98828I −3.98066 + 2.30410I
u = −1.001550 − 0.646267I
a = 0.708963 − 0.596743I
b = 1.09501 − 1.09178I
−4.08770 + 3.98828I −3.98066 − 2.30410I
u = 0.216325 + 1.182910I
a = −0.713880 − 1.120330I
b = 0.609948 + 0.458991I
2.68166 − 3.09151I −0.88507 + 2.77317I
u = 0.216325 − 1.182910I
a = −0.713880 + 1.120330I
b = 0.609948 − 0.458991I
2.68166 + 3.09151I −0.88507 − 2.77317I
u = −0.113877 + 1.199280I
a = −0.350242 + 0.891800I
b = 0.087095 − 0.616918I
4.20760 − 0.97328I 2.11395 + 4.55184I
u = −0.113877 − 1.199280I
a = −0.350242 − 0.891800I
b = 0.087095 + 0.616918I
4.20760 + 0.97328I 2.11395 − 4.55184I
u = 1.043630 + 0.630455I
a = 0.645528 − 0.695501I
b = 1.22852 − 1.39513I
−6.71673 + 8.95499I −7.02415 − 5.84784I
u = 1.043630 − 0.630455I
a = 0.645528 + 0.695501I
b = 1.22852 + 1.39513I
−6.71673 − 8.95499I −7.02415 + 5.84784I
u = 0.509916 + 0.585624I
a = −1.93080 − 0.98314I
b = −0.908336 − 0.995159I
1.11805 − 6.64525I −4.64041 + 7.71274I
u = 0.509916 − 0.585624I
a = −1.93080 + 0.98314I
b = −0.908336 + 0.995159I
1.11805 + 6.64525I −4.64041 − 7.71274I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.411107 + 0.639674I
a = −1.94005 + 0.91219I
b = −0.616271 + 0.817602I
3.38528 + 2.06052I −0.97721 − 4.27827I
u = −0.411107 − 0.639674I
a = −1.94005 − 0.91219I
b = −0.616271 − 0.817602I
3.38528 − 2.06052I −0.97721 + 4.27827I
u = 1.021780 + 0.715295I
a = 0.873555 − 0.679781I
b = 1.53845 − 0.79255I
−8.50059 + 0.69909I −9.38255 + 0.31146I
u = 1.021780 − 0.715295I
a = 0.873555 + 0.679781I
b = 1.53845 + 0.79255I
−8.50059 − 0.69909I −9.38255 − 0.31146I
u = −0.006529 + 1.249810I
a = 0.249742 + 0.857549I
b = −0.616271 − 0.817602I
3.38528 − 2.06052I −0.97721 + 4.27827I
u = −0.006529 − 1.249810I
a = 0.249742 − 0.857549I
b = −0.616271 + 0.817602I
3.38528 + 2.06052I −0.97721 − 4.27827I
u = −0.029699 + 1.287060I
a = 0.453155 − 0.982720I
b = −0.908336 + 0.995159I
1.11805 + 6.64525I −4.64041 − 7.71274I
u = −0.029699 − 1.287060I
a = 0.453155 + 0.982720I
b = −0.908336 − 0.995159I
1.11805 − 6.64525I −4.64041 + 7.71274I
u = 0.886065 + 0.936840I
a = 1.41586 − 0.38586I
b = 1.09501 + 1.09178I
−4.08770 − 3.98828I −4.00000 + 2.30410I
u = 0.886065 − 0.936840I
a = 1.41586 + 0.38586I
b = 1.09501 − 1.09178I
−4.08770 + 3.98828I −4.00000 − 2.30410I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.945816 + 0.902689I
a = 1.34476 + 0.52640I
b = 1.53845 − 0.79255I
−8.50059 + 0.69909I −9.38255 + 0.31146I
u = −0.945816 − 0.902689I
a = 1.34476 − 0.52640I
b = 1.53845 + 0.79255I
−8.50059 − 0.69909I −9.38255 − 0.31146I
u = −0.904248 + 0.975132I
a = 1.50571 + 0.41815I
b = 1.22852 − 1.39513I
−6.71673 + 8.95499I −7.02415 − 5.84784I
u = −0.904248 − 0.975132I
a = 1.50571 − 0.41815I
b = 1.22852 + 1.39513I
−6.71673 − 8.95499I −7.02415 + 5.84784I
u = 0.321811 + 0.404020I
a = −2.26698 − 1.18927I
b = −0.954493 − 0.372508I
−0.299485 + 0.584791I −8.18494 + 0.42463I
u = 0.321811 − 0.404020I
a = −2.26698 + 1.18927I
b = −0.954493 + 0.372508I
−0.299485 − 0.584791I −8.18494 − 0.42463I
15
III. I
u
3
= hb + a + 1, a
5
u + 5a
4
u + · · · + 10a + 1, u
2
+ 1i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
1
=
a
−a − 1
a
9
=
1
−1
a
10
=
a + 1
−a − 2
a
4
=
u
0
a
7
=
a
2
+ a + 1
−a
2
− 2a − 1
a
3
=
a
4
u + 3a
3
u + 4a
2
u + 3au + 2u
−a
4
u − 4a
3
u − 6a
2
u − 4au − u
a
12
=
a + 1
−a − 2
a
11
=
−1
−a − 2
a
6
=
−u
−au − u
a
2
=
−a
5
u − 4a
4
u − 8a
3
u − 9a
2
u − 6au − u
−a
4
u − 4a
3
u + ··· − 12a − 4
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a
4
− 16a
3
− 28a
2
− 4au − 24a − 4u − 8
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
c
2
, c
6
, c
7
u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1
c
3
u
12
− u
10
+ 5u
8
+ 6u
4
− 3u
2
+ 1
c
4
, c
5
, c
8
(u
2
+ 1)
6
c
9
(u + 1)
12
c
10
u
12
− 2u
11
+ ··· − 56u + 17
c
11
u
12
− 12u
11
+ ··· − 116u + 17
c
12
(u − 1)
12
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
2
, c
6
, c
7
(y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
c
3
(y
6
− y
5
+ 5y
4
+ 6y
2
− 3y + 1)
2
c
4
, c
5
, c
8
(y + 1)
12
c
9
, c
12
(y − 1)
12
c
10
y
12
+ 6y
11
+ ··· − 620y + 289
c
11
y
12
− 6y
11
+ ··· + 620y + 289
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.441248 − 1.073950I
b = −0.558752 + 1.073950I
3.28987 + 5.69302I 2.00000 − 5.51057I
u = 1.000000I
a = −0.704458 + 1.002190I
b = −0.295542 − 1.002190I
5.18047 − 0.92430I 5.71672 + 0.79423I
u = 1.000000I
a = −0.335469 − 0.428243I
b = −0.664531 + 0.428243I
1.39926 − 0.92430I −1.71672 + 0.79423I
u = 1.000000I
a = −1.29554 + 1.00219I
b = 0.295542 − 1.002190I
5.18047 + 0.92430I 5.71672 − 0.79423I
u = 1.000000I
a = −1.66453 − 0.42824I
b = 0.664531 + 0.428243I
1.39926 + 0.92430I −1.71672 − 0.79423I
u = 1.000000I
a = −1.55875 − 1.07395I
b = 0.558752 + 1.073950I
3.28987 − 5.69302I 2.00000 + 5.51057I
u = − 1.000000I
a = −0.441248 + 1.073950I
b = −0.558752 − 1.073950I
3.28987 − 5.69302I 2.00000 + 5.51057I
u = − 1.000000I
a = −0.704458 − 1.002190I
b = −0.295542 + 1.002190I
5.18047 + 0.92430I 5.71672 − 0.79423I
u = − 1.000000I
a = −0.335469 + 0.428243I
b = −0.664531 − 0.428243I
1.39926 + 0.92430I −1.71672 − 0.79423I
u = − 1.000000I
a = −1.29554 − 1.00219I
b = 0.295542 + 1.002190I
5.18047 − 0.92430I 5.71672 + 0.79423I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = − 1.000000I
a = −1.66453 + 0.42824I
b = 0.664531 − 0.428243I
1.39926 − 0.92430I −1.71672 + 0.79423I
u = − 1.000000I
a = −1.55875 + 1.07395I
b = 0.558752 − 1.073950I
3.28987 + 5.69302I 2.00000 − 5.51057I
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
)(u
18
+ 9u
17
+ ··· + u + 1)
2
· (u
31
+ 15u
30
+ ··· − 3u − 4)
c
2
, c
6
(u
12
+ 3u
10
+ ··· + u
2
+ 1)(u
18
+ u
17
+ ··· + u + 1)
2
· (u
31
− 3u
30
+ ··· − 5u + 2)
c
3
(u
12
− u
10
+ 5u
8
+ 6u
4
− 3u
2
+ 1)(u
18
− u
17
+ ··· − u + 5)
2
· (u
31
+ 3u
30
+ ··· − 13u + 2)
c
4
, c
5
, c
8
((u
2
+ 1)
6
)(u
31
+ 4u
29
+ ··· + 2u + 1)(u
36
+ u
35
+ ··· + 44u + 17)
c
7
(u
12
+ 3u
10
+ ··· + u
2
+ 1)(u
18
+ 5u
17
+ ··· + 13u + 3)
2
· (u
31
− 15u
30
+ ··· − 971u + 86)
c
9
((u + 1)
12
)(u
31
− 8u
30
+ ··· − 12u + 1)
· (u
36
− 15u
35
+ ··· − 3300u + 289)
c
10
(u
12
− 2u
11
+ ··· − 56u + 17)(u
31
− 19u
29
+ ··· + 328u + 73)
· (u
36
+ u
35
+ ··· − 22616u + 236209)
c
11
((u − 1)
36
)(u
12
− 12u
11
+ ··· − 116u + 17)
· (u
31
+ 29u
30
+ ··· + 2490368u + 262144)
c
12
((u − 1)
12
)(u
31
− 8u
30
+ ··· − 12u + 1)
· (u
36
− 15u
35
+ ··· − 3300u + 289)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
)(y
18
+ y
17
+ ··· + 9y + 1)
2
· (y
31
+ 3y
30
+ ··· + 129y − 16)
c
2
, c
6
((y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
)(y
18
+ 9y
17
+ ··· + y + 1)
2
· (y
31
+ 15y
30
+ ··· − 3y − 4)
c
3
((y
6
− y
5
+ 5y
4
+ 6y
2
− 3y + 1)
2
)(y
18
− 7y
17
+ ··· − 91y + 25)
2
· (y
31
− 9y
30
+ ··· − 27y − 4)
c
4
, c
5
, c
8
((y + 1)
12
)(y
31
+ 8y
30
+ ··· − 12y − 1)
· (y
36
+ 15y
35
+ ··· + 3300y + 289)
c
7
((y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
)(y
18
− 3y
17
+ ··· + 5y + 9)
2
· (y
31
+ 3y
30
+ ··· + 25565y − 7396)
c
9
, c
12
((y − 1)
12
)(y
31
+ 44y
30
+ ··· + 4y − 1)
· (y
36
+ 11y
35
+ ··· + 3006276y + 83521)
c
10
(y
12
+ 6y
11
+ ··· − 620y + 289)(y
31
− 38y
30
+ ··· + 121892y − 5329)
· (y
36
− 5y
35
+ ··· − 292100155924y + 55794691681)
c
11
((y − 1)
36
)(y
12
− 6y
11
+ ··· + 620y + 289)
· (y
31
− 7y
30
+ ··· + 188978561024y − 68719476736)
22
