12a
0283
(K12a
0283
)
A knot diagram
1
Linearized knot diagam
3 6 8 9 7 2 1 11 12 5 4 10
Solving Sequence
2,7
6 3 1 8 4
5,10
11 12 9
c
6
c
2
c
1
c
7
c
3
c
5
c
10
c
12
c
9
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.90119 × 10
36
u
112
− 1.11419 × 10
37
u
111
+ ··· + 3.32893 × 10
36
b − 5.90383 × 10
36
,
− 1.73556 × 10
37
u
112
− 1.93532 × 10
37
u
111
+ ··· + 3.32893 × 10
36
a − 1.78658 × 10
37
,
u
113
+ 2u
112
+ ··· + 5u + 1i
I
u
2
= hb + 1, a − 2u + 2, u
2
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 115 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−7.90 × 10
36
u
112
− 1.11 × 10
37
u
111
+ · · · + 3.33 × 10
36
b − 5.90 ×
10
36
, −1.74 × 10
37
u
112
− 1.94 × 10
37
u
111
+ · · · + 3.33 × 10
36
a − 1.79 ×
10
37
, u
113
+ 2u
112
+ · · · + 5u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
8
=
−u
8
− u
6
− u
4
+ 1
−u
10
− 2u
8
− 3u
6
− 2u
4
− u
2
a
4
=
−u
15
− 2u
13
− 4u
11
− 4u
9
− 2u
7
+ 2u
3
+ 2u
−u
17
− 3u
15
− 7u
13
− 10u
11
− 11u
9
− 8u
7
− 4u
5
+ u
a
5
=
u
2
+ 1
u
2
a
10
=
5.21357u
112
+ 5.81366u
111
+ ··· + 18.2825u + 5.36683
2.37349u
112
+ 3.34698u
111
+ ··· + 10.5007u + 1.77349
a
11
=
2.57332u
112
+ 3.57332u
111
+ ··· + 12.2084u + 4.96666
0.133325u
112
+ 0.0666489u
111
+ ··· + 1.69996u − 0.0666762
a
12
=
5.11321u
112
+ 5.91317u
111
+ ··· + 17.5894u + 5.71659
2.47326u
112
+ 3.54651u
111
+ ··· + 11.6496u + 1.87326
a
9
=
−0.233210u
112
− 0.633170u
111
+ ··· − 0.666853u − 1.11658
−0.833251u
112
− 1.66650u
111
+ ··· − 4.04963u − 0.833250
(ii) Obstruction class = −1
(iii) Cusp Shapes = 11.7807u
112
+ 18.4014u
111
+ ··· + 41.3370u + 11.9807
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
113
+ 36u
112
+ ··· − 5u − 1
c
2
, c
6
u
113
− 2u
112
+ ··· + 5u − 1
c
3
u
113
− 34u
111
+ ··· − 426005u − 37025
c
4
u
113
+ 4u
112
+ ··· + u + 1
c
7
u
113
+ 5u
112
+ ··· − 28640u − 6976
c
8
u
113
− 19u
112
+ ··· − 12u + 4
c
9
, c
12
u
113
+ 3u
112
+ ··· + 2u − 1
c
10
u
113
− 2u
112
+ ··· + 459991u + 41101
c
11
u
113
− 4u
112
+ ··· − 58837u + 9439
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
113
+ 84y
112
+ ··· − 257y −1
c
2
, c
6
y
113
+ 36y
112
+ ··· − 5y −1
c
3
y
113
− 68y
112
+ ··· + 209188214975y −1370850625
c
4
y
113
+ 20y
112
+ ··· − 5y −1
c
7
y
113
− 17y
112
+ ··· − 533582720y −48664576
c
8
y
113
+ 15y
112
+ ··· − 280y −16
c
9
, c
12
y
113
− 83y
112
+ ··· + 26y −1
c
10
y
113
− 68y
112
+ ··· − 308333217253y −1689292201
c
11
y
113
− 136y
112
+ ··· + 1552528283y −89094721
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.189604 + 0.989106I
a = 0.732820 + 0.284224I
b = −1.91009 + 0.59078I
2.22230 + 4.51942I 0
u = 0.189604 − 0.989106I
a = 0.732820 − 0.284224I
b = −1.91009 − 0.59078I
2.22230 − 4.51942I 0
u = 0.026076 + 1.011230I
a = −0.862472 − 0.519253I
b = 1.60460 + 0.26158I
−5.26942 − 0.99049I 0
u = 0.026076 − 1.011230I
a = −0.862472 + 0.519253I
b = 1.60460 − 0.26158I
−5.26942 + 0.99049I 0
u = −0.144566 + 1.004840I
a = −0.170892 − 0.681801I
b = 0.398767 + 0.551773I
−1.95648 − 2.79535I 0
u = −0.144566 − 1.004840I
a = −0.170892 + 0.681801I
b = 0.398767 − 0.551773I
−1.95648 + 2.79535I 0
u = −0.161120 + 0.967489I
a = −2.92000 + 2.19375I
b = 3.14464 − 1.06906I
0.16594 − 2.30056I 0
u = −0.161120 − 0.967489I
a = −2.92000 − 2.19375I
b = 3.14464 + 1.06906I
0.16594 + 2.30056I 0
u = −0.675887 + 0.690929I
a = 1.48016 − 0.54011I
b = 0.786677 − 0.431007I
−0.242700 − 0.820844I 0
u = −0.675887 − 0.690929I
a = 1.48016 + 0.54011I
b = 0.786677 + 0.431007I
−0.242700 + 0.820844I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.662797 + 0.797671I
a = 0.33518 + 2.73691I
b = −1.26294 + 1.81134I
3.48900 − 0.36060I 0
u = 0.662797 − 0.797671I
a = 0.33518 − 2.73691I
b = −1.26294 − 1.81134I
3.48900 + 0.36060I 0
u = 0.170034 + 1.023370I
a = 0.576812 − 0.188643I
b = −1.44988 − 0.25305I
−2.23668 + 7.07465I 0
u = 0.170034 − 1.023370I
a = 0.576812 + 0.188643I
b = −1.44988 + 0.25305I
−2.23668 − 7.07465I 0
u = 0.205935 + 0.940229I
a = 0.083619 + 1.367930I
b = −0.599757 + 0.498152I
2.58224 + 0.70114I 0
u = 0.205935 − 0.940229I
a = 0.083619 − 1.367930I
b = −0.599757 − 0.498152I
2.58224 − 0.70114I 0
u = 0.375783 + 0.967245I
a = 0.50682 − 1.95144I
b = 0.852029 + 0.071099I
3.49202 − 6.70621I 0
u = 0.375783 − 0.967245I
a = 0.50682 + 1.95144I
b = 0.852029 − 0.071099I
3.49202 + 6.70621I 0
u = −0.630738 + 0.848947I
a = −1.42954 + 4.92205I
b = 1.23780 + 2.16333I
2.25355 − 2.08148I 0
u = −0.630738 − 0.848947I
a = −1.42954 − 4.92205I
b = 1.23780 − 2.16333I
2.25355 + 2.08148I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.586086 + 0.884873I
a = 0.496140 + 0.240299I
b = 0.0768557 + 0.0195798I
0.18011 − 2.30125I 0
u = −0.586086 − 0.884873I
a = 0.496140 − 0.240299I
b = 0.0768557 − 0.0195798I
0.18011 + 2.30125I 0
u = −0.026671 + 1.069690I
a = 0.529521 + 0.341317I
b = −0.90525 − 1.22531I
−2.88023 − 5.15805I 0
u = −0.026671 − 1.069690I
a = 0.529521 − 0.341317I
b = −0.90525 + 1.22531I
−2.88023 + 5.15805I 0
u = 0.186610 + 1.057550I
a = −1.166760 + 0.054768I
b = 1.97199 − 0.92146I
2.31195 + 12.95770I 0
u = 0.186610 − 1.057550I
a = −1.166760 − 0.054768I
b = 1.97199 + 0.92146I
2.31195 − 12.95770I 0
u = 0.804411 + 0.716895I
a = 0.735745 + 0.907695I
b = 0.33930 + 1.41948I
4.35773 − 2.32723I 0
u = 0.804411 − 0.716895I
a = 0.735745 − 0.907695I
b = 0.33930 − 1.41948I
4.35773 + 2.32723I 0
u = −0.102129 + 0.914705I
a = 1.154070 − 0.332979I
b = −0.843195 + 1.117950I
−0.90049 − 1.52806I 0
u = −0.102129 − 0.914705I
a = 1.154070 + 0.332979I
b = −0.843195 − 1.117950I
−0.90049 + 1.52806I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.819096 + 0.714745I
a = −2.15580 − 0.09456I
b = −1.93234 + 1.04877I
4.33771 + 6.65572I 0
u = −0.819096 − 0.714745I
a = −2.15580 + 0.09456I
b = −1.93234 − 1.04877I
4.33771 − 6.65572I 0
u = 0.804336 + 0.735844I
a = 3.49496 − 0.99406I
b = 3.91616 − 0.62862I
6.48008 − 1.48579I 0
u = 0.804336 − 0.735844I
a = 3.49496 + 0.99406I
b = 3.91616 + 0.62862I
6.48008 + 1.48579I 0
u = 0.789668 + 0.751601I
a = −1.54050 + 0.39634I
b = −1.88394 − 0.46765I
4.99982 − 0.39403I 0
u = 0.789668 − 0.751601I
a = −1.54050 − 0.39634I
b = −1.88394 + 0.46765I
4.99982 + 0.39403I 0
u = −0.401772 + 1.017800I
a = −0.591734 − 0.890779I
b = −0.716621 + 0.195724I
2.46164 − 2.16481I 0
u = −0.401772 − 1.017800I
a = −0.591734 + 0.890779I
b = −0.716621 − 0.195724I
2.46164 + 2.16481I 0
u = −0.198122 + 1.076290I
a = 0.611926 − 0.129141I
b = −1.114960 − 0.661410I
1.26696 − 4.49664I 0
u = −0.198122 − 1.076290I
a = 0.611926 + 0.129141I
b = −1.114960 + 0.661410I
1.26696 + 4.49664I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.839364 + 0.705527I
a = 2.43675 − 1.34274I
b = 1.90827 − 1.96991I
9.1807 + 12.7383I 0
u = −0.839364 − 0.705527I
a = 2.43675 + 1.34274I
b = 1.90827 + 1.96991I
9.1807 − 12.7383I 0
u = −0.817248 + 0.732933I
a = −2.47219 + 1.33611I
b = −1.43792 + 1.92631I
8.80037 + 3.76825I 0
u = −0.817248 − 0.732933I
a = −2.47219 − 1.33611I
b = −1.43792 − 1.92631I
8.80037 − 3.76825I 0
u = 0.701871 + 0.564677I
a = −0.49909 − 1.83088I
b = −0.249255 − 1.199190I
2.51246 − 6.05594I 0
u = 0.701871 − 0.564677I
a = −0.49909 + 1.83088I
b = −0.249255 + 1.199190I
2.51246 + 6.05594I 0
u = 0.849309 + 0.703940I
a = −1.44363 − 1.05383I
b = −1.02819 − 1.27379I
8.30024 − 4.35385I 0
u = 0.849309 − 0.703940I
a = −1.44363 + 1.05383I
b = −1.02819 + 1.27379I
8.30024 + 4.35385I 0
u = 0.686961 + 0.864297I
a = −0.575551 + 0.948996I
b = −1.65465 − 0.21237I
4.86859 + 2.64754I 0
u = 0.686961 − 0.864297I
a = −0.575551 − 0.948996I
b = −1.65465 + 0.21237I
4.86859 − 2.64754I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.812046 + 0.748463I
a = −0.201771 + 0.950170I
b = 0.572463 + 0.018516I
9.08614 − 0.40058I 0
u = −0.812046 − 0.748463I
a = −0.201771 − 0.950170I
b = 0.572463 − 0.018516I
9.08614 + 0.40058I 0
u = −0.644754 + 0.896793I
a = 2.72070 − 3.11928I
b = 0.37701 − 2.38093I
2.08561 − 2.89593I 0
u = −0.644754 − 0.896793I
a = 2.72070 + 3.11928I
b = 0.37701 + 2.38093I
2.08561 + 2.89593I 0
u = −0.799673 + 0.768477I
a = 1.47725 + 0.34620I
b = 1.28181 − 0.95862I
5.32160 − 3.46023I 0
u = −0.799673 − 0.768477I
a = 1.47725 − 0.34620I
b = 1.28181 + 0.95862I
5.32160 + 3.46023I 0
u = 0.676390 + 0.918048I
a = −2.32133 − 1.14228I
b = −0.75684 − 2.25603I
3.11538 + 5.56594I 0
u = 0.676390 − 0.918048I
a = −2.32133 + 1.14228I
b = −0.75684 + 2.25603I
3.11538 − 5.56594I 0
u = −0.825041 + 0.795140I
a = 0.0359918 + 0.0423536I
b = −0.358265 + 0.924552I
10.78520 − 8.74874I 0
u = −0.825041 − 0.795140I
a = 0.0359918 − 0.0423536I
b = −0.358265 − 0.924552I
10.78520 + 8.74874I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.634049 + 0.959454I
a = −0.64721 − 2.33021I
b = 1.34193 − 1.32305I
−1.71577 + 6.42867I 0
u = 0.634049 − 0.959454I
a = −0.64721 + 2.33021I
b = 1.34193 + 1.32305I
−1.71577 − 6.42867I 0
u = 0.477211 + 0.699293I
a = 1.11525 + 0.93560I
b = 0.594232 + 0.916168I
−0.91883 − 1.63359I 0
u = 0.477211 − 0.699293I
a = 1.11525 − 0.93560I
b = 0.594232 − 0.916168I
−0.91883 + 1.63359I 0
u = 0.830935 + 0.807266I
a = −0.460954 − 0.115699I
b = 0.148646 + 0.211422I
10.18150 + 0.03828I 0
u = 0.830935 − 0.807266I
a = −0.460954 + 0.115699I
b = 0.148646 − 0.211422I
10.18150 − 0.03828I 0
u = −0.602752 + 1.009100I
a = −1.27531 − 0.68721I
b = −1.048330 + 0.609756I
0.615565 − 1.062850I 0
u = −0.602752 − 1.009100I
a = −1.27531 + 0.68721I
b = −1.048330 − 0.609756I
0.615565 + 1.062850I 0
u = 0.361501 + 0.737362I
a = 0.848717 + 0.806251I
b = 0.481917 + 0.741929I
−0.91881 − 1.62689I 0. + 2.38205I
u = 0.361501 − 0.737362I
a = 0.848717 − 0.806251I
b = 0.481917 − 0.741929I
−0.91881 + 1.62689I 0. − 2.38205I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.673061 + 0.469584I
a = −0.92029 − 1.20880I
b = −0.743094 − 0.713671I
2.10101 − 3.80196I 6.48289 + 8.14563I
u = −0.673061 − 0.469584I
a = −0.92029 + 1.20880I
b = −0.743094 + 0.713671I
2.10101 + 3.80196I 6.48289 − 8.14563I
u = −0.669832 + 0.975779I
a = 0.34691 + 2.02425I
b = 1.200410 + 0.680396I
−1.08624 − 4.42004I 0
u = −0.669832 − 0.975779I
a = 0.34691 − 2.02425I
b = 1.200410 − 0.680396I
−1.08624 + 4.42004I 0
u = 0.648914 + 1.007590I
a = 1.60848 + 1.60199I
b = −0.25294 + 1.62779I
1.27121 + 11.23550I 0
u = 0.648914 − 1.007590I
a = 1.60848 − 1.60199I
b = −0.25294 − 1.62779I
1.27121 − 11.23550I 0
u = 0.730788 + 0.973951I
a = −0.91332 + 1.98011I
b = −2.18585 + 0.12251I
4.31836 + 6.13109I 0
u = 0.730788 − 0.973951I
a = −0.91332 − 1.98011I
b = −2.18585 − 0.12251I
4.31836 − 6.13109I 0
u = −0.742360 + 0.966006I
a = 0.53593 + 1.31805I
b = 1.68644 + 0.65147I
4.71397 − 2.34203I 0
u = −0.742360 − 0.966006I
a = 0.53593 − 1.31805I
b = 1.68644 − 0.65147I
4.71397 + 2.34203I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.734409 + 0.987664I
a = 3.15400 − 4.10583I
b = 3.98743 + 0.81248I
5.70971 + 7.27585I 0
u = 0.734409 − 0.987664I
a = 3.15400 + 4.10583I
b = 3.98743 − 0.81248I
5.70971 − 7.27585I 0
u = −0.772019 + 0.958567I
a = 0.801468 − 0.220647I
b = −0.537447 − 0.643819I
10.28110 + 2.77769I 0
u = −0.772019 − 0.958567I
a = 0.801468 + 0.220647I
b = −0.537447 + 0.643819I
10.28110 − 2.77769I 0
u = 0.781509 + 0.952187I
a = −0.510637 + 0.169893I
b = 0.167483 + 0.015866I
9.73329 + 5.97959I 0
u = 0.781509 − 0.952187I
a = −0.510637 − 0.169893I
b = 0.167483 − 0.015866I
9.73329 − 5.97959I 0
u = −0.743165 + 0.983061I
a = 0.203530 − 0.401051I
b = 0.647902 − 0.399445I
8.36627 − 5.43992I 0
u = −0.743165 − 0.983061I
a = 0.203530 + 0.401051I
b = 0.647902 + 0.399445I
8.36627 + 5.43992I 0
u = −0.051258 + 0.765506I
a = 0.751880 − 0.146149I
b = 0.185019 + 0.767687I
−0.78417 − 1.51958I −0.51049 + 4.81030I
u = −0.051258 − 0.765506I
a = 0.751880 + 0.146149I
b = 0.185019 − 0.767687I
−0.78417 + 1.51958I −0.51049 − 4.81030I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.727955 + 0.997623I
a = −0.95083 − 1.14500I
b = 0.64302 − 1.37924I
3.50172 + 8.09550I 0
u = 0.727955 − 0.997623I
a = −0.95083 + 1.14500I
b = 0.64302 + 1.37924I
3.50172 − 8.09550I 0
u = −0.740370 + 0.993682I
a = 0.32291 − 3.06621I
b = −1.86488 − 2.03732I
8.00165 − 9.61390I 0
u = −0.740370 − 0.993682I
a = 0.32291 + 3.06621I
b = −1.86488 + 2.03732I
8.00165 + 9.61390I 0
u = −0.734600 + 1.003670I
a = −0.64261 − 2.29387I
b = −2.34628 − 0.84720I
3.45497 − 12.48640I 0
u = −0.734600 − 1.003670I
a = −0.64261 + 2.29387I
b = −2.34628 + 0.84720I
3.45497 + 12.48640I 0
u = −0.740492 + 1.015850I
a = −0.47297 + 3.32479I
b = 2.25196 + 1.98268I
8.2295 − 18.6443I 0
u = −0.740492 − 1.015850I
a = −0.47297 − 3.32479I
b = 2.25196 − 1.98268I
8.2295 + 18.6443I 0
u = 0.744745 + 1.020400I
a = 0.39036 + 2.07419I
b = −1.24450 + 1.30855I
7.32868 + 10.30150I 0
u = 0.744745 − 1.020400I
a = 0.39036 − 2.07419I
b = −1.24450 − 1.30855I
7.32868 − 10.30150I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.707737 + 0.123386I
a = −1.142620 − 0.447129I
b = −0.658841 − 0.611972I
5.20254 − 1.62878I 14.3386 + 4.2186I
u = −0.707737 − 0.123386I
a = −1.142620 + 0.447129I
b = −0.658841 + 0.611972I
5.20254 + 1.62878I 14.3386 − 4.2186I
u = 0.673521 + 0.113711I
a = 1.67635 − 0.23442I
b = 1.09292 − 0.98112I
6.12000 + 10.24010I 8.20778 − 6.69743I
u = 0.673521 − 0.113711I
a = 1.67635 + 0.23442I
b = 1.09292 + 0.98112I
6.12000 − 10.24010I 8.20778 + 6.69743I
u = 0.601565 + 0.096262I
a = −0.629950 − 1.085550I
b = −0.445017 + 0.310717I
1.31817 + 4.63185I 6.37577 − 6.86199I
u = 0.601565 − 0.096262I
a = −0.629950 + 1.085550I
b = −0.445017 − 0.310717I
1.31817 − 4.63185I 6.37577 + 6.86199I
u = 0.597956 + 0.028270I
a = −1.92039 − 0.38491I
b = −0.810690 + 0.491190I
5.43024 + 1.96351I 13.41312 − 3.71413I
u = 0.597956 − 0.028270I
a = −1.92039 + 0.38491I
b = −0.810690 − 0.491190I
5.43024 − 1.96351I 13.41312 + 3.71413I
u = −0.548711
a = 2.10233
b = 3.19430
3.16762 −20.5050
u = −0.536498 + 0.081266I
a = 0.244010 − 0.063088I
b = −0.344932 + 0.530147I
1.44156 − 0.64172I 6.80204 + 0.19839I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.536498 − 0.081266I
a = 0.244010 + 0.063088I
b = −0.344932 − 0.530147I
1.44156 + 0.64172I 6.80204 − 0.19839I
u = −0.202031 + 0.200826I
a = 2.87891 + 2.43797I
b = −0.407955 + 0.755269I
1.91728 − 0.70497I 4.91663 − 1.79667I
u = −0.202031 − 0.200826I
a = 2.87891 − 2.43797I
b = −0.407955 − 0.755269I
1.91728 + 0.70497I 4.91663 + 1.79667I
16
II. I
u
2
= hb + 1, a − 2u + 2, u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u − 1
a
3
=
u
u − 1
a
1
=
−1
0
a
8
=
1
0
a
4
=
2u − 1
u − 1
a
5
=
u
u − 1
a
10
=
2u − 2
−1
a
11
=
u − 1
0
a
12
=
2u − 3
−1
a
9
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u + 5
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
u
2
− u + 1
c
2
, c
10
, c
11
u
2
+ u + 1
c
7
, c
8
u
2
c
9
(u + 1)
2
c
12
(u − 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
10
, c
11
y
2
+ y + 1
c
7
, c
8
y
2
c
9
, c
12
(y −1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −1.00000 + 1.73205I
b = −1.00000
1.64493 + 2.02988I 3.00000 − 3.46410I
u = 0.500000 − 0.866025I
a = −1.00000 − 1.73205I
b = −1.00000
1.64493 − 2.02988I 3.00000 + 3.46410I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
2
− u + 1)(u
113
+ 36u
112
+ ··· − 5u − 1)
c
2
(u
2
+ u + 1)(u
113
− 2u
112
+ ··· + 5u − 1)
c
3
(u
2
− u + 1)(u
113
− 34u
111
+ ··· − 426005u − 37025)
c
4
(u
2
− u + 1)(u
113
+ 4u
112
+ ··· + u + 1)
c
6
(u
2
− u + 1)(u
113
− 2u
112
+ ··· + 5u − 1)
c
7
u
2
(u
113
+ 5u
112
+ ··· − 28640u − 6976)
c
8
u
2
(u
113
− 19u
112
+ ··· − 12u + 4)
c
9
((u + 1)
2
)(u
113
+ 3u
112
+ ··· + 2u − 1)
c
10
(u
2
+ u + 1)(u
113
− 2u
112
+ ··· + 459991u + 41101)
c
11
(u
2
+ u + 1)(u
113
− 4u
112
+ ··· − 58837u + 9439)
c
12
((u − 1)
2
)(u
113
+ 3u
112
+ ··· + 2u − 1)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
2
+ y + 1)(y
113
+ 84y
112
+ ··· − 257y −1)
c
2
, c
6
(y
2
+ y + 1)(y
113
+ 36y
112
+ ··· − 5y −1)
c
3
(y
2
+ y + 1)(y
113
− 68y
112
+ ··· + 2.09188 × 10
11
y −1.37085 × 10
9
)
c
4
(y
2
+ y + 1)(y
113
+ 20y
112
+ ··· − 5y −1)
c
7
y
2
(y
113
− 17y
112
+ ··· − 5.33583 × 10
8
y −4.86646 × 10
7
)
c
8
y
2
(y
113
+ 15y
112
+ ··· − 280y −16)
c
9
, c
12
((y −1)
2
)(y
113
− 83y
112
+ ··· + 26y −1)
c
10
(y
2
+ y + 1)(y
113
− 68y
112
+ ··· − 3.08333 × 10
11
y −1.68929 × 10
9
)
c
11
(y
2
+ y + 1)(y
113
− 136y
112
+ ··· + 1.55253 × 10
9
y −8.90947 × 10
7
)
22
