12n
0751
(K12n
0751
)
A knot diagram
1
Linearized knot diagam
4 6 8 10 2 12 3 12 1 5 6 9
Solving Sequence
1,4 2,10
5 6 9 12 7 8 3 11
c
1
c
4
c
5
c
9
c
12
c
6
c
8
c
3
c
11
c
2
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−898244027u
14
− 391531130u
13
+ ··· + 534701171b + 1119066057,
− 898027536u
14
− 389544550u
13
+ ··· + 534701171a + 1652680736,
u
15
− u
13
− u
12
+ 8u
11
− u
10
− 18u
9
− 2u
7
+ 12u
6
− 21u
5
+ 26u
4
− 14u
3
+ 3u
2
− 2u + 1i
I
u
2
= h3.30670 × 10
41
u
29
+ 5.71881 × 10
41
u
28
+ ··· + 1.78529 × 10
43
b + 3.34070 × 10
43
,
1.36375 × 10
44
u
29
− 4.57521 × 10
43
u
28
+ ··· + 3.92765 × 10
44
a + 3.57143 × 10
45
, u
30
+ 2u
28
+ ··· + 81u + 11i
I
u
3
= hu
3
+ b + 3, u
3
+ a − u + 2, u
4
+ u
3
+ 2u + 1i
I
u
4
= hb, a + u − 2, u
2
− u − 1i
I
u
5
= hu
2
+ b − u − 1, −u
3
+ 2u
2
+ a + u − 1, u
4
− 2u
3
− u
2
+ 2u − 1i
I
u
6
= hb, a − 1, u − 1i
I
u
7
= hb − 1, a
2
− a − 1, u − 1i
* 7 irreducible components of dim
C
= 0, with total 58 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−8.98 × 10
8
u
14
− 3.92 × 10
8
u
13
+ · · · + 5.35 × 10
8
b + 1.12 × 10
9
, −8.98 ×
10
8
u
14
− 3.90× 10
8
u
13
+ · · · + 5.35 × 10
8
a +1.65 × 10
9
, u
15
− u
13
+ · · · − 2u + 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
10
=
1.67949u
14
+ 0.728528u
13
+ ··· + 3.65635u − 3.09085
1.67990u
14
+ 0.732243u
13
+ ··· + 0.801226u − 2.09288
a
5
=
−1.07086u
14
− 0.594830u
13
+ ··· − 2.20938u + 2.32522
−1.79456u
14
− 0.830294u
13
+ ··· − 0.599907u + 2.64579
a
6
=
0.235869u
14
− 0.0456390u
13
+ ··· − 1.72828u + 0.274259
−1.49103u
14
− 0.606558u
13
+ ··· − 0.808252u + 2.09660
a
9
=
−0.000404882u
14
− 0.00371531u
13
+ ··· + 2.85513u − 0.997968
1.67990u
14
+ 0.732243u
13
+ ··· + 0.801226u − 2.09288
a
12
=
−0.000404882u
14
− 0.00371531u
13
+ ··· + 2.85513u − 0.997968
−2.64538u
14
− 1.79085u
13
+ ··· + 0.108289u + 5.68964
a
7
=
u
2
− 1
4.04447u
14
+ 2.08478u
13
+ ··· + 5.22270u − 7.34077
a
8
=
1
−5.94603u
14
− 3.12181u
13
+ ··· − 5.52030u + 10.4626
a
3
=
u
−3.12181u
14
− 1.90156u
13
+ ··· − 0.429474u + 5.94603
a
11
=
0.209193u
14
− 0.0694314u
13
+ ··· + 1.83397u − 0.107940
−0.645989u
14
− 0.381117u
13
+ ··· − 0.616195u + 1.74893
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
9257204513
534701171
u
14
−
6026834044
534701171
u
13
+ ··· −
11292543056
534701171
u +
18370247823
534701171
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
7
u
15
− u
13
+ ··· − 2u − 1
c
2
, c
5
u
15
+ 9u
14
+ ··· − 69u − 9
c
4
, c
10
u
15
− u
14
+ ··· + 5u + 1
c
6
, c
11
u
15
− u
14
+ ··· − 4u − 1
c
8
, c
9
, c
12
u
15
− 6u
14
+ ··· + 6u + 9
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
15
− 2y
14
+ ··· − 2y −1
c
2
, c
5
y
15
− 9y
14
+ ··· + 1071y −81
c
4
, c
10
y
15
− 13y
14
+ ··· + 39y −1
c
6
, c
11
y
15
+ 13y
14
+ ··· + 16y −1
c
8
, c
9
, c
12
y
15
− 26y
14
+ ··· − 1494y −81
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.219964 + 0.819481I
a = −1.44756 − 0.16891I
b = 1.355710 − 0.019020I
3.27965 − 1.21970I 1.31129 + 5.66741I
u = 0.219964 − 0.819481I
a = −1.44756 + 0.16891I
b = 1.355710 + 0.019020I
3.27965 + 1.21970I 1.31129 − 5.66741I
u = −0.788509 + 0.905745I
a = −0.457133 − 1.143780I
b = −0.883513 − 0.932651I
5.92156 + 9.44163I 0.20634 − 8.15923I
u = −0.788509 − 0.905745I
a = −0.457133 + 1.143780I
b = −0.883513 + 0.932651I
5.92156 − 9.44163I 0.20634 + 8.15923I
u = 0.623880 + 0.248532I
a = 0.809525 + 0.462868I
b = −0.072998 + 0.253976I
−1.140580 − 0.339277I −8.98924 + 1.73624I
u = 0.623880 − 0.248532I
a = 0.809525 − 0.462868I
b = −0.072998 − 0.253976I
−1.140580 + 0.339277I −8.98924 − 1.73624I
u = 0.565700
a = −2.01244
b = −2.31417
3.82898 27.9490
u = 1.44661
a = −0.971679
b = −1.39008
3.06003 2.95830
u = −1.52296
a = −0.111508
b = −0.699810
−7.76254 −32.3850
u = −0.192664 + 0.382554I
a = 0.23984 + 1.65841I
b = 1.40585 + 0.42820I
2.17147 + 0.68609I 8.04360 − 5.02078I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.192664 − 0.382554I
a = 0.23984 − 1.65841I
b = 1.40585 − 0.42820I
2.17147 − 0.68609I 8.04360 + 5.02078I
u = 1.10259 + 1.29441I
a = 0.497805 − 0.641547I
b = 1.73219 − 0.23886I
14.6227 − 4.7692I 3.20527 + 2.44636I
u = 1.10259 − 1.29441I
a = 0.497805 + 0.641547I
b = 1.73219 + 0.23886I
14.6227 + 4.7692I 3.20527 − 2.44636I
u = −1.20993 + 1.32914I
a = 0.405328 + 0.848334I
b = 1.66478 + 0.29308I
14.2379 + 14.0822I 1.96139 − 6.46819I
u = −1.20993 − 1.32914I
a = 0.405328 − 0.848334I
b = 1.66478 − 0.29308I
14.2379 − 14.0822I 1.96139 + 6.46819I
6
II. I
u
2
=
h3.31×10
41
u
29
+5.72×10
41
u
28
+· · ·+1.79×10
43
b+3.34×10
43
, 1.36×10
44
u
29
−
4.58 × 10
43
u
28
+ · · · + 3.93 × 10
44
a + 3.57 × 10
45
, u
30
+ 2u
28
+ · · · + 81u + 11i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
10
=
−0.347218u
29
+ 0.116487u
28
+ ··· − 51.0446u − 9.09305
−0.0185219u
29
− 0.0320329u
28
+ ··· − 11.9126u − 1.87123
a
5
=
−0.394706u
29
+ 0.210595u
28
+ ··· − 41.4801u − 8.32205
−0.0263285u
29
+ 0.0298042u
28
+ ··· + 6.05343u + 1.54652
a
6
=
−0.467058u
29
+ 0.222944u
28
+ ··· − 60.2499u − 12.1851
−0.0503337u
29
+ 0.0560610u
28
+ ··· + 5.84906u + 1.41068
a
9
=
−0.328697u
29
+ 0.148520u
28
+ ··· − 39.1319u − 7.22182
−0.0185219u
29
− 0.0320329u
28
+ ··· − 11.9126u − 1.87123
a
12
=
−0.196754u
29
+ 0.0387220u
28
+ ··· − 27.9600u − 3.50095
0.0561620u
29
− 0.0650505u
28
+ ··· − 7.03644u − 1.83361
a
7
=
−0.409410u
29
+ 0.0902696u
28
+ ··· − 81.9335u − 16.7607
0.0570621u
29
+ 0.0581006u
28
+ ··· + 19.7385u + 2.64502
a
8
=
−0.217120u
29
+ 0.141042u
28
+ ··· − 12.8730u − 3.08396
−0.0595359u
29
+ 0.0111266u
28
+ ··· − 9.03611u − 0.551467
a
3
=
−0.562677u
29
+ 0.183364u
28
+ ··· − 77.5261u − 13.9939
0.105143u
29
− 0.0492747u
28
+ ··· + 6.83973u + 0.371317
a
11
=
0.209727u
29
− 0.119739u
28
+ ··· + 27.3054u + 6.97658
−0.0548665u
29
− 0.0623507u
28
+ ··· − 18.5446u − 2.63799
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.347221u
29
− 0.0667960u
28
+ ··· + 55.5079u + 14.9386
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
7
u
30
+ 2u
28
+ ··· − 81u + 11
c
2
, c
5
(u
15
− 4u
14
+ ··· − 5u + 2)
2
c
4
, c
10
u
30
− u
29
+ ··· − 24u + 1
c
6
, c
11
u
30
+ 2u
29
+ ··· + 31u + 1
c
8
, c
9
, c
12
(u
15
+ 2u
14
+ ··· − 2u + 2)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
30
+ 4y
29
+ ··· + 105y + 121
c
2
, c
5
(y
15
+ 8y
13
+ ··· − 3y −4)
2
c
4
, c
10
y
30
− 33y
29
+ ··· − 56y + 1
c
6
, c
11
y
30
+ 26y
29
+ ··· − 177y + 1
c
8
, c
9
, c
12
(y
15
− 18y
14
+ ··· + 68y −4)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.975339
a = 2.03736
b = 1.13495
−0.455497 −13.6410
u = 0.962045 + 0.405621I
a = −0.920194 + 0.526296I
b = −1.53636
3.54960 2.31783 + 0.I
u = 0.962045 − 0.405621I
a = −0.920194 − 0.526296I
b = −1.53636
3.54960 2.31783 + 0.I
u = −0.605280 + 0.637023I
a = 0.47688 − 1.78582I
b = −1.47359 − 0.25718I
6.96654 + 7.44645I −1.97655 − 7.47153I
u = −0.605280 − 0.637023I
a = 0.47688 + 1.78582I
b = −1.47359 + 0.25718I
6.96654 − 7.44645I −1.97655 + 7.47153I
u = 0.518757 + 0.995170I
a = 0.188630 − 0.965072I
b = 0.398627 − 0.770277I
0.92420 − 3.75884I −2.83571 + 8.62550I
u = 0.518757 − 0.995170I
a = 0.188630 + 0.965072I
b = 0.398627 + 0.770277I
0.92420 + 3.75884I −2.83571 − 8.62550I
u = 0.508270 + 1.021130I
a = −0.311123 + 1.376970I
b = −0.566489 + 0.063512I
6.65494 − 3.78113I 2.84579 + 3.30508I
u = 0.508270 − 1.021130I
a = −0.311123 − 1.376970I
b = −0.566489 − 0.063512I
6.65494 + 3.78113I 2.84579 − 3.30508I
u = −0.069702 + 1.177270I
a = 0.0457627 + 0.0466319I
b = −1.61515 + 0.17952I
9.74746 − 4.20828I 3.86853 + 1.95225I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.069702 − 1.177270I
a = 0.0457627 − 0.0466319I
b = −1.61515 − 0.17952I
9.74746 + 4.20828I 3.86853 − 1.95225I
u = −0.541567 + 1.093190I
a = −0.672453 − 0.922756I
b = −0.566489 + 0.063512I
6.65494 − 3.78113I 2.84579 + 3.30508I
u = −0.541567 − 1.093190I
a = −0.672453 + 0.922756I
b = −0.566489 − 0.063512I
6.65494 + 3.78113I 2.84579 − 3.30508I
u = −0.661146 + 0.389686I
a = −0.48702 + 1.46762I
b = 0.398627 + 0.770277I
0.92420 + 3.75884I −2.83571 − 8.62550I
u = −0.661146 − 0.389686I
a = −0.48702 − 1.46762I
b = 0.398627 − 0.770277I
0.92420 − 3.75884I −2.83571 + 8.62550I
u = −0.307321 + 0.642721I
a = 0.30958 + 1.50914I
b = 0.709925 + 0.664105I
1.88098 + 1.11902I 2.92830 + 0.60819I
u = −0.307321 − 0.642721I
a = 0.30958 − 1.50914I
b = 0.709925 − 0.664105I
1.88098 − 1.11902I 2.92830 − 0.60819I
u = 1.36054
a = −0.316147
b = 1.13495
−0.455497 −13.6410
u = −0.429729
a = −3.56723
b = 0.336879
−3.04205 11.2360
u = −0.236133 + 0.340530I
a = 1.077030 − 0.148667I
b = 0.709925 − 0.664105I
1.88098 − 1.11902I 2.92830 − 0.60819I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.236133 − 0.340530I
a = 1.077030 + 0.148667I
b = 0.709925 + 0.664105I
1.88098 + 1.11902I 2.92830 + 0.60819I
u = −1.10466 + 1.15958I
a = −0.505916 − 0.815295I
b = −1.61515 − 0.17952I
9.74746 + 4.20828I 3.86853 − 1.95225I
u = −1.10466 − 1.15958I
a = −0.505916 + 0.815295I
b = −1.61515 + 0.17952I
9.74746 − 4.20828I 3.86853 + 1.95225I
u = 1.63208
a = 0.419875
b = 0.336879
−3.04205 11.2360
u = 0.81585 + 1.45626I
a = −0.089554 + 0.856120I
b = −1.47359 + 0.25718I
6.96654 − 7.44645I −2.00000 + 7.47153I
u = 0.81585 − 1.45626I
a = −0.089554 − 0.856120I
b = −1.47359 − 0.25718I
6.96654 + 7.44645I −2.00000 − 7.47153I
u = 1.25585 + 1.17832I
a = 0.577677 − 0.845480I
b = 1.57894 − 0.03518I
14.1007 − 4.2306I 2.71313 + 2.44322I
u = 1.25585 − 1.17832I
a = 0.577677 + 0.845480I
b = 1.57894 + 0.03518I
14.1007 + 4.2306I 2.71313 − 2.44322I
u = −1.32874 + 1.42818I
a = 0.478313 + 0.498197I
b = 1.57894 − 0.03518I
14.1007 − 4.2306I 0
u = −1.32874 − 1.42818I
a = 0.478313 − 0.498197I
b = 1.57894 + 0.03518I
14.1007 + 4.2306I 0
12
III. I
u
3
= hu
3
+ b + 3, u
3
+ a − u + 2, u
4
+ u
3
+ 2u + 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
10
=
−u
3
+ u − 2
−u
3
− 3
a
5
=
−u
3
− u
2
− u − 3
−2u
3
− 2u
2
+ u − 3
a
6
=
−u
−2u
3
− u
2
− 3
a
9
=
u + 1
−u
3
− 3
a
12
=
−u − 1
3u
3
+ u
2
− u + 8
a
7
=
u
2
− 1
7u
3
+ 3u
2
− 4u + 15
a
8
=
−1
9u
3
+ 4u
2
− 3u + 20
a
3
=
u
5u
3
+ 3u
2
− u + 9
a
11
=
u
3
+ u
2
− u
−u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −50u
3
− 21u
2
+ 13u − 97
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
4
+ u
3
+ 2u + 1
c
2
u
4
+ 6u
3
+ 12u
2
+ 11u + 5
c
4
u
4
− 2u
3
+ 3u − 1
c
5
u
4
− 6u
3
+ 12u
2
− 11u + 5
c
6
u
4
− 2u
3
+ u
2
− 4u − 1
c
7
u
4
− u
3
− 2u + 1
c
8
, c
9
u
4
− 5u
3
+ 6u
2
+ 2u − 5
c
10
u
4
+ 2u
3
− 3u − 1
c
11
u
4
+ 2u
3
+ u
2
+ 4u − 1
c
12
u
4
+ 5u
3
+ 6u
2
− 2u − 5
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
4
− y
3
− 2y
2
− 4y + 1
c
2
, c
5
y
4
− 12y
3
+ 22y
2
− y + 25
c
4
, c
10
y
4
− 4y
3
+ 10y
2
− 9y + 1
c
6
, c
11
y
4
− 2y
3
− 17y
2
− 18y + 1
c
8
, c
9
, c
12
y
4
− 13y
3
+ 46y
2
− 64y + 25
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.515596 + 1.045250I
a = 0.068462 + 1.353620I
b = −1.44713 + 0.30837I
8.50524 − 7.16341I 4.70675 + 6.37190I
u = 0.515596 − 1.045250I
a = 0.068462 − 1.353620I
b = −1.44713 − 0.30837I
8.50524 + 7.16341I 4.70675 − 6.37190I
u = −0.472213
a = −2.36692
b = −2.89470
3.76121 −102.560
u = −1.55898
a = 0.229993
b = 0.788973
−7.61222 21.1430
16
IV. I
u
4
= hb, a + u − 2, u
2
− u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u + 1
a
10
=
−u + 2
0
a
5
=
2u − 3
u
a
6
=
2u − 4
−1
a
9
=
−u + 2
0
a
12
=
1
0
a
7
=
2u − 3
−1
a
8
=
−u + 2
0
a
3
=
2u − 3
u
a
11
=
2u − 3
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −22
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
u
2
− u − 1
c
2
, c
6
(u − 1)
2
c
5
, c
11
(u + 1)
2
c
7
, c
10
u
2
+ u − 1
c
8
, c
9
, c
12
u
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
, c
10
y
2
− 3y + 1
c
2
, c
5
, c
6
c
11
(y −1)
2
c
8
, c
9
, c
12
y
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = 2.61803
b = 0
−3.28987 −22.0000
u = 1.61803
a = 0.381966
b = 0
−3.28987 −22.0000
20
V. I
u
5
= hu
2
+ b − u − 1, −u
3
+ 2u
2
+ a + u − 1, u
4
− 2u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
10
=
u
3
− 2u
2
− u + 1
−u
2
+ u + 1
a
5
=
u
3
− 2u
2
u
3
− 2u
2
+ u + 1
a
6
=
u
3
− 2u
2
− 1
u
3
− 3u
2
+ u + 1
a
9
=
u
3
− u
2
− 2u
−u
2
+ u + 1
a
12
=
u
3
− u
2
− 3u + 1
2
a
7
=
−u
2
+ 3u − 2
u
3
− 3u
2
+ u − 1
a
8
=
−u
3
+ 2u
2
+ u − 1
u
2
− u − 1
a
3
=
u
3
− 2u
2
u
3
− 2u
2
+ u + 1
a
11
=
u
2
− 3u + 2
−u
3
+ 3u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
10
u
4
− 2u
3
− u
2
+ 2u − 1
c
2
, c
11
(u − 1)
4
c
4
, c
7
u
4
+ 2u
3
− u
2
− 2u − 1
c
5
, c
6
(u + 1)
4
c
8
, c
9
, c
12
(u
2
− 2)
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
, c
10
y
4
− 6y
3
+ 7y
2
− 2y + 1
c
2
, c
5
, c
6
c
11
(y −1)
4
c
8
, c
9
, c
12
(y −2)
4
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.13224
a = −1.88320
b = −1.41421
1.64493 −4.00000
u = 0.500000 + 0.405233I
a = 0.207107 − 0.978318I
b = 1.41421
1.64493 −4.00000
u = 0.500000 − 0.405233I
a = 0.207107 + 0.978318I
b = 1.41421
1.64493 −4.00000
u = 2.13224
a = −0.531010
b = −1.41421
1.64493 −4.00000
24
VI. I
u
6
= hb, a − 1, u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
10
=
1
0
a
5
=
1
1
a
6
=
1
1
a
9
=
1
0
a
12
=
1
0
a
7
=
0
1
a
8
=
1
0
a
3
=
1
1
a
11
=
0
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
10
c
11
u + 1
c
2
, c
5
, c
8
c
9
, c
12
u
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
10
c
11
y −1
c
2
, c
5
, c
8
c
9
, c
12
y
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000
b = 0
−1.64493 −6.00000
28
VII. I
u
7
= hb − 1, a
2
− a − 1, u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
10
=
a
1
a
5
=
a + 1
a + 1
a
6
=
a + 1
a + 1
a
9
=
a − 1
1
a
12
=
a
1
a
7
=
0
1
a
8
=
−1
0
a
3
=
1
1
a
11
=
−a − 1
−2a
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
12
(u − 1)
2
c
2
, c
5
u
2
c
4
, c
6
u
2
+ u − 1
c
7
, c
8
, c
9
(u + 1)
2
c
10
, c
11
u
2
− u − 1
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
c
8
, c
9
, c
12
(y −1)
2
c
2
, c
5
y
2
c
4
, c
6
, c
10
c
11
y
2
− 3y + 1
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.618034
b = 1.00000
0 5.00000
u = 1.00000
a = 1.61803
b = 1.00000
0 5.00000
32
VIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
((u − 1)
2
)(u + 1)(u
2
− u − 1)(u
4
− 2u
3
+ ··· + 2u − 1)(u
4
+ u
3
+ 2u + 1)
· (u
15
− u
13
+ ··· − 2u − 1)(u
30
+ 2u
28
+ ··· − 81u + 11)
c
2
u
3
(u − 1)
6
(u
4
+ 6u
3
+ ··· + 11u + 5)(u
15
− 4u
14
+ ··· − 5u + 2)
2
· (u
15
+ 9u
14
+ ··· − 69u − 9)
c
4
(u + 1)(u
2
− u − 1)(u
2
+ u − 1)(u
4
− 2u
3
+ 3u − 1)(u
4
+ 2u
3
+ ··· − 2u − 1)
· (u
15
− u
14
+ ··· + 5u + 1)(u
30
− u
29
+ ··· − 24u + 1)
c
5
u
3
(u + 1)
6
(u
4
− 6u
3
+ ··· − 11u + 5)(u
15
− 4u
14
+ ··· − 5u + 2)
2
· (u
15
+ 9u
14
+ ··· − 69u − 9)
c
6
(u − 1)
2
(u + 1)
5
(u
2
+ u − 1)(u
4
− 2u
3
+ u
2
− 4u − 1)
· (u
15
− u
14
+ ··· − 4u − 1)(u
30
+ 2u
29
+ ··· + 31u + 1)
c
7
(u + 1)
3
(u
2
+ u − 1)(u
4
− u
3
− 2u + 1)(u
4
+ 2u
3
− u
2
− 2u − 1)
· (u
15
− u
13
+ ··· − 2u − 1)(u
30
+ 2u
28
+ ··· − 81u + 11)
c
8
, c
9
u
3
(u + 1)
2
(u
2
− 2)
2
(u
4
− 5u
3
+ ··· + 2u − 5)(u
15
− 6u
14
+ ··· + 6u + 9)
· (u
15
+ 2u
14
+ ··· − 2u + 2)
2
c
10
(u + 1)(u
2
− u − 1)(u
2
+ u − 1)(u
4
− 2u
3
+ ··· + 2u − 1)(u
4
+ 2u
3
− 3u − 1)
· (u
15
− u
14
+ ··· + 5u + 1)(u
30
− u
29
+ ··· − 24u + 1)
c
11
(u − 1)
4
(u + 1)
3
(u
2
− u − 1)(u
4
+ 2u
3
+ u
2
+ 4u − 1)
· (u
15
− u
14
+ ··· − 4u − 1)(u
30
+ 2u
29
+ ··· + 31u + 1)
c
12
u
3
(u − 1)
2
(u
2
− 2)
2
(u
4
+ 5u
3
+ ··· − 2u − 5)(u
15
− 6u
14
+ ··· + 6u + 9)
· (u
15
+ 2u
14
+ ··· − 2u + 2)
2
33
IX. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
((y −1)
3
)(y
2
− 3y + 1)(y
4
− 6y
3
+ ··· − 2y + 1)(y
4
− y
3
+ ··· − 4y + 1)
· (y
15
− 2y
14
+ ··· − 2y −1)(y
30
+ 4y
29
+ ··· + 105y + 121)
c
2
, c
5
y
3
(y −1)
6
(y
4
− 12y
3
+ ··· − y + 25)(y
15
+ 8y
13
+ ··· − 3y −4)
2
· (y
15
− 9y
14
+ ··· + 1071y −81)
c
4
, c
10
(y −1)(y
2
− 3y + 1)
2
(y
4
− 6y
3
+ ··· − 2y + 1)(y
4
− 4y
3
+ ··· − 9y + 1)
· (y
15
− 13y
14
+ ··· + 39y −1)(y
30
− 33y
29
+ ··· − 56y + 1)
c
6
, c
11
(y −1)
7
(y
2
− 3y + 1)(y
4
− 2y
3
− 17y
2
− 18y + 1)
· (y
15
+ 13y
14
+ ··· + 16y −1)(y
30
+ 26y
29
+ ··· − 177y + 1)
c
8
, c
9
, c
12
y
3
(y −2)
4
(y −1)
2
(y
4
− 13y
3
+ 46y
2
− 64y + 25)
· (y
15
− 26y
14
+ ··· − 1494y −81)(y
15
− 18y
14
+ ··· + 68y −4)
2
34
