12n
0771
(K12n
0771
)
A knot diagram
1
Linearized knot diagam
4 5 9 11 3 12 10 3 1 7 5 8
Solving Sequence
4,11
5
9,12
3 6 7 2 1 8 10
c
4
c
11
c
3
c
5
c
6
c
2
c
1
c
8
c
10
c
7
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.43466 × 10
230
u
78
− 1.85125 × 10
230
u
77
+ ··· + 1.68670 × 10
226
b + 1.01353 × 10
231
,
3.16642 × 10
230
u
78
+ 2.47552 × 10
230
u
77
+ ··· + 1.68670 × 10
226
a − 1.45278 × 10
231
, u
79
+ u
78
+ ··· − 23u − 1i
I
u
2
= h30853u
27
+ 13876u
26
+ ··· + 4193b + 6194, −17745u
27
− 2238u
26
+ ··· + 599a − 7171,
u
28
− 9u
26
+ ··· − u + 1i
* 2 irreducible components of dim
C
= 0, with total 107 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−2.43 × 10
230
u
78
− 1.85 × 10
230
u
77
+ · · · + 1.69 × 10
226
b + 1.01 ×
10
231
, 3.17 × 10
230
u
78
+ 2.48 × 10
230
u
77
+ · · · + 1.69 × 10
226
a − 1.45 ×
10
231
, u
79
+ u
78
+ · · · − 23u − 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
9
=
−18772.9u
78
− 14676.7u
77
+ ··· + 1.58492 × 10
6
u + 86131.4
14434.5u
78
+ 10975.6u
77
+ ··· − 1.13259 × 10
6
u − 60089.5
a
12
=
u
−u
3
+ u
a
3
=
39059.0u
78
+ 30576.8u
77
+ ··· − 3.30373 × 10
6
u − 179312.
21479.6u
78
+ 16581.0u
77
+ ··· − 1.75206 × 10
6
u − 94065.2
a
6
=
−56717.2u
78
− 43448.4u
77
+ ··· + 4.52978 × 10
6
u + 241512.
−41302.3u
78
− 31601.6u
77
+ ··· + 3.29433 × 10
6
u + 175706.
a
7
=
−56068.0u
78
− 42943.8u
77
+ ··· + 4.47650 × 10
6
u + 238660.
−40684.3u
78
− 31121.8u
77
+ ··· + 3.24373 × 10
6
u + 172999.
a
2
=
15741.6u
78
+ 12555.8u
77
+ ··· − 1.39564 × 10
6
u − 76764.3
22681.4u
78
+ 17510.4u
77
+ ··· − 1.85056 × 10
6
u − 99361.6
a
1
=
38423.1u
78
+ 30066.2u
77
+ ··· − 3.24620 × 10
6
u − 176126.
22681.4u
78
+ 17510.4u
77
+ ··· − 1.85056 × 10
6
u − 99361.6
a
8
=
52534.4u
78
+ 39819.5u
77
+ ··· − 4.08761 × 10
6
u − 216260.
28302.2u
78
+ 21431.7u
77
+ ··· − 2.19862 × 10
6
u − 116334.
a
10
=
51542.3u
78
+ 39402.9u
77
+ ··· − 4.09266 × 10
6
u − 217740.
27877.0u
78
+ 21157.7u
77
+ ··· − 2.17777 × 10
6
u − 115419.
(ii) Obstruction class = −1
(iii) Cusp Shapes = −293314.u
78
−224420.u
77
+ ···+ 2.33906 ×10
7
u + 1.24743 × 10
6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
79
− 6u
78
+ ··· − 4390196u + 145732
c
2
, c
5
u
79
+ 6u
78
+ ··· − 318766u + 63403
c
3
, c
8
u
79
+ u
78
+ ··· − 6u − 1
c
4
, c
11
u
79
+ u
78
+ ··· − 23u − 1
c
6
u
79
− u
78
+ ··· − 3836986393u + 691687687
c
7
, c
10
u
79
+ 3u
78
+ ··· + 4u + 4
c
9
u
79
+ u
78
+ ··· − 56386u + 5447
c
12
u
79
+ u
78
+ ··· − 74772u + 31151
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
79
− 82y
78
+ ··· + 5209547957600y −21237815824
c
2
, c
5
y
79
+ 82y
78
+ ··· + 185670572514y −4019940409
c
3
, c
8
y
79
− 59y
78
+ ··· + 140y −1
c
4
, c
11
y
79
− 19y
78
+ ··· + 101y −1
c
6
y
79
+ 83y
78
+ ··· − 1.11 × 10
19
y −4.78 × 10
17
c
7
, c
10
y
79
+ 59y
78
+ ··· + 1152y −16
c
9
y
79
+ 27y
78
+ ··· + 2658310082y −29669809
c
12
y
79
+ 27y
78
+ ··· − 24342580030y −970384801
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.876343 + 0.418237I
a = −0.98814 + 1.09797I
b = −1.086020 − 0.390878I
−3.99440 − 3.41625I 0
u = −0.876343 − 0.418237I
a = −0.98814 − 1.09797I
b = −1.086020 + 0.390878I
−3.99440 + 3.41625I 0
u = 0.107309 + 1.030380I
a = 1.62128 − 0.02467I
b = 1.288120 − 0.276909I
−7.18782 − 0.25504I 0
u = 0.107309 − 1.030380I
a = 1.62128 + 0.02467I
b = 1.288120 + 0.276909I
−7.18782 + 0.25504I 0
u = 1.031440 + 0.237452I
a = 0.70026 − 1.45707I
b = −1.194000 + 0.073259I
−3.76520 − 3.47263I 0
u = 1.031440 − 0.237452I
a = 0.70026 + 1.45707I
b = −1.194000 − 0.073259I
−3.76520 + 3.47263I 0
u = −0.710505 + 0.791863I
a = −0.351388 + 0.386497I
b = 0.070718 + 0.224537I
−6.38277 − 1.11124I 0
u = −0.710505 − 0.791863I
a = −0.351388 − 0.386497I
b = 0.070718 − 0.224537I
−6.38277 + 1.11124I 0
u = −0.893200 + 0.104272I
a = 0.508013 − 0.510710I
b = 1.115270 + 0.582110I
−3.07398 − 5.47491I 0
u = −0.893200 − 0.104272I
a = 0.508013 + 0.510710I
b = 1.115270 − 0.582110I
−3.07398 + 5.47491I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.898671
a = −0.570936
b = 0.677206
1.34236 0
u = −0.881127 + 0.684545I
a = −0.122129 − 0.303526I
b = −0.1263670 − 0.0356777I
−2.33613 − 2.65326I 0
u = −0.881127 − 0.684545I
a = −0.122129 + 0.303526I
b = −0.1263670 + 0.0356777I
−2.33613 + 2.65326I 0
u = 0.834574 + 0.197888I
a = 0.143773 + 0.431583I
b = 0.177668 − 0.801514I
−0.355058 − 0.356466I 0
u = 0.834574 − 0.197888I
a = 0.143773 − 0.431583I
b = 0.177668 + 0.801514I
−0.355058 + 0.356466I 0
u = 0.509087 + 0.677360I
a = 1.87014 + 0.09189I
b = 1.49340 − 0.27656I
−5.90433 + 7.16462I 0
u = 0.509087 − 0.677360I
a = 1.87014 − 0.09189I
b = 1.49340 + 0.27656I
−5.90433 − 7.16462I 0
u = −0.740627 + 0.409243I
a = 0.39635 − 1.67689I
b = 1.013890 + 0.493574I
−0.63566 − 4.72962I 0
u = −0.740627 − 0.409243I
a = 0.39635 + 1.67689I
b = 1.013890 − 0.493574I
−0.63566 + 4.72962I 0
u = −1.18358
a = 1.49313
b = 0.316458
5.25090 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.183450 + 0.177352I
a = −1.239580 − 0.395337I
b = −0.320172 + 0.018633I
1.36097 − 5.26145I 0
u = −1.183450 − 0.177352I
a = −1.239580 + 0.395337I
b = −0.320172 − 0.018633I
1.36097 + 5.26145I 0
u = 0.292091 + 0.747069I
a = −1.74758 − 0.01781I
b = −1.39008 + 0.36679I
−2.83896 + 3.00420I 0
u = 0.292091 − 0.747069I
a = −1.74758 + 0.01781I
b = −1.39008 − 0.36679I
−2.83896 − 3.00420I 0
u = −0.610818 + 0.485146I
a = −0.16218 + 2.43434I
b = −1.031020 − 0.463539I
−4.58288 − 7.29246I 0
u = −0.610818 − 0.485146I
a = −0.16218 − 2.43434I
b = −1.031020 + 0.463539I
−4.58288 + 7.29246I 0
u = 0.861534 + 0.877415I
a = −1.86321 − 0.56614I
b = −1.403680 + 0.103231I
−10.91540 + 5.27509I 0
u = 0.861534 − 0.877415I
a = −1.86321 + 0.56614I
b = −1.403680 − 0.103231I
−10.91540 − 5.27509I 0
u = −0.990925 + 0.780469I
a = 0.401539 + 0.092462I
b = 0.148306 − 0.099772I
−5.60018 − 4.78135I 0
u = −0.990925 − 0.780469I
a = 0.401539 − 0.092462I
b = 0.148306 + 0.099772I
−5.60018 + 4.78135I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.993541 + 0.817452I
a = 1.54937 + 1.15032I
b = 1.324470 − 0.054745I
−10.49360 + 1.06249I 0
u = 0.993541 − 0.817452I
a = 1.54937 − 1.15032I
b = 1.324470 + 0.054745I
−10.49360 − 1.06249I 0
u = 0.809292 + 1.039090I
a = 1.60729 + 0.43751I
b = 1.356460 − 0.150002I
−7.25736 + 3.90884I 0
u = 0.809292 − 1.039090I
a = 1.60729 − 0.43751I
b = 1.356460 + 0.150002I
−7.25736 − 3.90884I 0
u = 1.328100 + 0.137659I
a = −0.201563 + 0.611752I
b = 1.269440 − 0.166800I
1.033330 + 0.782949I 0
u = 1.328100 − 0.137659I
a = −0.201563 − 0.611752I
b = 1.269440 + 0.166800I
1.033330 − 0.782949I 0
u = −1.325470 + 0.228083I
a = 0.36485 − 1.74089I
b = 0.453543 + 1.148540I
4.82710 − 4.04790I 0
u = −1.325470 − 0.228083I
a = 0.36485 + 1.74089I
b = 0.453543 − 1.148540I
4.82710 + 4.04790I 0
u = 0.217070 + 0.610175I
a = 1.066590 − 0.064309I
b = −0.286678 − 0.599720I
−2.62047 + 3.15905I 0
u = 0.217070 − 0.610175I
a = 1.066590 + 0.064309I
b = −0.286678 + 0.599720I
−2.62047 − 3.15905I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.611637 + 0.124694I
a = 0.330543 + 0.344795I
b = −0.957604 − 0.615381I
−0.97782 − 3.18704I 0
u = −0.611637 − 0.124694I
a = 0.330543 − 0.344795I
b = −0.957604 + 0.615381I
−0.97782 + 3.18704I 0
u = 0.983833 + 0.979662I
a = 0.537912 + 0.047191I
b = 0.017508 − 1.337210I
−8.04470 + 9.99314I 0
u = 0.983833 − 0.979662I
a = 0.537912 − 0.047191I
b = 0.017508 + 1.337210I
−8.04470 − 9.99314I 0
u = −0.784345 + 1.145680I
a = 1.002190 − 0.273503I
b = 1.60552 − 0.59569I
−13.07230 − 2.79558I 0
u = −0.784345 − 1.145680I
a = 1.002190 + 0.273503I
b = 1.60552 + 0.59569I
−13.07230 + 2.79558I 0
u = 0.361058 + 0.488552I
a = −0.921454 − 0.696855I
b = −0.669008 + 0.782264I
0.17362 + 2.13315I 0
u = 0.361058 − 0.488552I
a = −0.921454 + 0.696855I
b = −0.669008 − 0.782264I
0.17362 − 2.13315I 0
u = 1.008820 + 0.976571I
a = 0.568830 + 0.028624I
b = −0.277407 − 1.304630I
−7.98302 − 2.79382I 0
u = 1.008820 − 0.976571I
a = 0.568830 − 0.028624I
b = −0.277407 + 1.304630I
−7.98302 + 2.79382I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.531319 + 0.254208I
a = −0.764712 − 0.499735I
b = 0.413560 + 0.543062I
1.055930 + 0.468133I 0
u = 0.531319 − 0.254208I
a = −0.764712 + 0.499735I
b = 0.413560 − 0.543062I
1.055930 − 0.468133I 0
u = 0.99618 + 1.02534I
a = −0.559912 − 0.038895I
b = 0.10002 + 1.47274I
−3.23697 + 3.73023I 0
u = 0.99618 − 1.02534I
a = −0.559912 + 0.038895I
b = 0.10002 − 1.47274I
−3.23697 − 3.73023I 0
u = −0.81627 + 1.20218I
a = −1.047240 + 0.299529I
b = −1.60684 + 0.48551I
−9.14876 + 3.35329I 0
u = −0.81627 − 1.20218I
a = −1.047240 − 0.299529I
b = −1.60684 − 0.48551I
−9.14876 − 3.35329I 0
u = 1.13111 + 0.92779I
a = −1.25926 − 0.81035I
b = −1.306360 + 0.089703I
−6.27013 + 3.29120I 0
u = 1.13111 − 0.92779I
a = −1.25926 + 0.81035I
b = −1.306360 − 0.089703I
−6.27013 − 3.29120I 0
u = −0.85049 + 1.21862I
a = 1.080010 − 0.274442I
b = 1.53645 − 0.46171I
−13.8996 + 8.9563I 0
u = −0.85049 − 1.21862I
a = 1.080010 + 0.274442I
b = 1.53645 + 0.46171I
−13.8996 − 8.9563I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.439096 + 0.241787I
a = −2.48467 − 0.16848I
b = 0.817333 + 0.425600I
−6.30949 − 1.87842I 0. + 3.28089I
u = −0.439096 − 0.241787I
a = −2.48467 + 0.16848I
b = 0.817333 − 0.425600I
−6.30949 + 1.87842I 0. − 3.28089I
u = −1.20607 + 0.92056I
a = −1.08447 + 1.12933I
b = −1.48840 − 0.74155I
−11.71210 − 4.71803I 0
u = −1.20607 − 0.92056I
a = −1.08447 − 1.12933I
b = −1.48840 + 0.74155I
−11.71210 + 4.71803I 0
u = −1.17728 + 0.96277I
a = −1.24134 + 1.03090I
b = −1.46917 − 0.60570I
−12.7672 − 16.7760I 0
u = −1.17728 − 0.96277I
a = −1.24134 − 1.03090I
b = −1.46917 + 0.60570I
−12.7672 + 16.7760I 0
u = −1.18703 + 0.95708I
a = 1.16866 − 1.03328I
b = 1.50856 + 0.63733I
−7.92089 − 11.10750I 0
u = −1.18703 − 0.95708I
a = 1.16866 + 1.03328I
b = 1.50856 − 0.63733I
−7.92089 + 11.10750I 0
u = 1.51003 + 0.36636I
a = −0.299045 − 0.591632I
b = −1.293010 + 0.090598I
−2.23461 + 5.90245I 0
u = 1.51003 − 0.36636I
a = −0.299045 + 0.591632I
b = −1.293010 − 0.090598I
−2.23461 − 5.90245I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.79204 + 1.35981I
a = −1.40007 − 0.29591I
b = −1.301060 + 0.173804I
−10.67170 + 2.96611I 0
u = 0.79204 − 1.35981I
a = −1.40007 + 0.29591I
b = −1.301060 − 0.173804I
−10.67170 − 2.96611I 0
u = 1.24583 + 1.16094I
a = 1.176150 + 0.530089I
b = 1.286220 − 0.113435I
−9.34277 + 5.87011I 0
u = 1.24583 − 1.16094I
a = 1.176150 − 0.530089I
b = 1.286220 + 0.113435I
−9.34277 − 5.87011I 0
u = −0.271329 + 0.031654I
a = −8.02705 + 3.97881I
b = −0.749966 + 0.052776I
−2.06804 − 3.78913I −2.03961 + 6.55169I
u = −0.271329 − 0.031654I
a = −8.02705 − 3.97881I
b = −0.749966 − 0.052776I
−2.06804 + 3.78913I −2.03961 − 6.55169I
u = −0.234685 + 0.005537I
a = 0.13366 + 1.71141I
b = −0.396879 + 1.158900I
0.89026 + 2.40339I −0.5139 − 16.4120I
u = −0.234685 − 0.005537I
a = 0.13366 − 1.71141I
b = −0.396879 − 1.158900I
0.89026 − 2.40339I −0.5139 + 16.4120I
u = −0.222199
a = 9.15297
b = 0.720846
1.95313 2.25730
12
II. I
u
2
= h30853u
27
+ 13876u
26
+ · · · + 4193b + 6194, −17745u
27
− 2238u
26
+
· · · + 599a − 7171, u
28
− 9u
26
+ · · · − u + 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
9
=
29.6244u
27
+ 3.73623u
26
+ ··· − 69.0184u + 11.9716
−7.35822u
27
− 3.30933u
26
+ ··· + 12.9685u − 1.47722
a
12
=
u
−u
3
+ u
a
3
=
−1.13809u
27
− 18.3236u
26
+ ··· − 50.6220u + 61.0258
−1.73718u
27
+ 5.35345u
26
+ ··· + 29.1855u − 17.3236
a
6
=
42.7021u
27
+ 1.87527u
26
+ ··· − 129.214u − 8.26568
−11.9702u
27
+ 0.798712u
26
+ ··· + 38.8269u − 10.1247
a
7
=
29.7319u
27
+ 1.67398u
26
+ ··· − 88.3871u − 7.39041
−21.0835u
27
+ 0.163606u
26
+ ··· + 66.8848u − 9.45075
a
2
=
−0.138087u
27
− 18.3236u
26
+ ··· − 62.6220u + 60.0258
−1.73718u
27
+ 5.35345u
26
+ ··· + 30.1855u − 17.3236
a
1
=
−1.87527u
27
− 12.9702u
26
+ ··· − 32.4364u + 42.7021
−1.73718u
27
+ 5.35345u
26
+ ··· + 30.1855u − 17.3236
a
8
=
8.52278u
27
+ 11.3582u
26
+ ··· + 4.71572u − 25.4913
8.31600u
27
− 7.33365u
26
+ ··· − 52.6353u + 10.2778
a
10
=
16.5900u
27
+ 17.5521u
26
+ ··· + 20.1171u − 48.1567
−17.1283u
27
+ 3.03434u
26
+ ··· + 38.6172u − 20.0072
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
14948
4193
u
27
−
188690
4193
u
26
+ ··· −
332851
4193
u +
609209
4193
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
28
− 11u
27
+ ··· − 72u − 4
c
2
u
28
+ u
27
+ ··· + 8u
2
− 1
c
3
u
28
− 7u
26
+ ··· + 9u
2
− 1
c
4
u
28
− 9u
26
+ ··· − u + 1
c
5
u
28
− u
27
+ ··· + 8u
2
− 1
c
6
u
28
+ 8u
26
+ ··· + 57u − 107
c
7
u
28
+ 4u
27
+ ··· + 8u + 4
c
8
u
28
− 7u
26
+ ··· + 9u
2
− 1
c
9
u
28
+ 4u
25
+ ··· − 4u − 1
c
10
u
28
− 4u
27
+ ··· − 8u + 4
c
11
u
28
− 9u
26
+ ··· + u + 1
c
12
u
28
− 2u
26
+ ··· − 12u
2
− 1
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
− 25y
27
+ ··· − 3120y + 16
c
2
, c
5
y
28
+ 11y
27
+ ··· − 16y + 1
c
3
, c
8
y
28
− 14y
27
+ ··· − 18y + 1
c
4
, c
11
y
28
− 18y
27
+ ··· − 27y + 1
c
6
y
28
+ 16y
27
+ ··· − 141921y + 11449
c
7
, c
10
y
28
+ 20y
27
+ ··· + 80y + 16
c
9
y
28
+ 24y
26
+ ··· + 16y + 1
c
12
y
28
− 4y
27
+ ··· + 24y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.852125 + 0.601245I
a = −0.832108 − 0.231328I
b = 0.747853 − 0.466030I
−6.71180 + 0.04614I −0.064629 − 0.987396I
u = −0.852125 − 0.601245I
a = −0.832108 + 0.231328I
b = 0.747853 + 0.466030I
−6.71180 − 0.04614I −0.064629 + 0.987396I
u = −0.854084 + 0.782815I
a = 0.436404 − 0.146646I
b = 0.155074 + 0.739479I
−1.77839 − 2.94686I 9.10140 + 4.88751I
u = −0.854084 − 0.782815I
a = 0.436404 + 0.146646I
b = 0.155074 − 0.739479I
−1.77839 + 2.94686I 9.10140 − 4.88751I
u = −0.971333 + 0.742339I
a = −0.197178 + 0.525278I
b = −0.699311 − 0.194741I
−6.17700 − 5.22730I −3.13585 + 7.30911I
u = −0.971333 − 0.742339I
a = −0.197178 − 0.525278I
b = −0.699311 + 0.194741I
−6.17700 + 5.22730I −3.13585 − 7.30911I
u = 1.22488
a = −1.38709
b = −0.689063
4.80480 3.24890
u = 1.232920 + 0.196608I
a = 1.290190 − 0.099792I
b = 0.741690 + 0.131648I
0.83876 + 4.91408I 1.44350 − 1.61325I
u = 1.232920 − 0.196608I
a = 1.290190 + 0.099792I
b = 0.741690 − 0.131648I
0.83876 − 4.91408I 1.44350 + 1.61325I
u = −0.655111 + 0.359817I
a = 0.659090 − 0.948985I
b = 1.048160 + 0.626210I
−1.19938 − 3.96368I 5.40589 + 6.56623I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.655111 − 0.359817I
a = 0.659090 + 0.948985I
b = 1.048160 − 0.626210I
−1.19938 + 3.96368I 5.40589 − 6.56623I
u = −1.263940 + 0.151253I
a = 0.368613 − 0.364180I
b = −1.236920 + 0.502499I
1.20025 + 1.95116I 6.65433 − 3.75191I
u = −1.263940 − 0.151253I
a = 0.368613 + 0.364180I
b = −1.236920 − 0.502499I
1.20025 − 1.95116I 6.65433 + 3.75191I
u = −1.301720 + 0.177857I
a = −0.033564 − 0.438214I
b = 1.132780 + 0.311775I
−0.95254 − 6.85547I 6.26006 + 7.50495I
u = −1.301720 − 0.177857I
a = −0.033564 + 0.438214I
b = 1.132780 − 0.311775I
−0.95254 + 6.85547I 6.26006 − 7.50495I
u = 0.661543
a = −2.96465
b = 0.557034
2.52967 18.0280
u = 0.632952 + 0.113297I
a = 2.91957 − 3.06599I
b = −0.637106 + 0.134427I
−1.64115 − 3.51490I 12.07415 − 1.40885I
u = 0.632952 − 0.113297I
a = 2.91957 + 3.06599I
b = −0.637106 − 0.134427I
−1.64115 + 3.51490I 12.07415 + 1.40885I
u = 0.905198 + 1.014880I
a = 1.58689 + 0.69818I
b = 1.315490 − 0.237768I
−9.20708 + 3.02208I 0.86618 − 2.28131I
u = 0.905198 − 1.014880I
a = 1.58689 − 0.69818I
b = 1.315490 + 0.237768I
−9.20708 − 3.02208I 0.86618 + 2.28131I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.358480 + 0.221950I
a = −0.29847 − 1.70421I
b = −0.427126 + 1.219380I
4.68108 + 4.11341I −14.1729 − 14.5736I
u = 1.358480 − 0.221950I
a = −0.29847 + 1.70421I
b = −0.427126 − 1.219380I
4.68108 − 4.11341I −14.1729 + 14.5736I
u = −0.565004 + 0.040165I
a = −0.26511 + 2.40588I
b = −1.181360 − 0.443555I
−4.21817 − 6.13927I 2.12135 + 6.27361I
u = −0.565004 − 0.040165I
a = −0.26511 − 2.40588I
b = −1.181360 + 0.443555I
−4.21817 + 6.13927I 2.12135 − 6.27361I
u = 0.93379 + 1.09566I
a = −1.43251 − 0.41148I
b = −1.334820 + 0.045448I
−9.12029 + 4.54261I 0. − 2.64613I
u = 0.93379 − 1.09566I
a = −1.43251 + 0.41148I
b = −1.334820 − 0.045448I
−9.12029 − 4.54261I 0. + 2.64613I
u = 0.456757 + 0.180125I
a = 0.474060 + 0.395975I
b = 0.441601 + 1.138690I
1.00966 − 2.17421I 13.7438 − 10.2319I
u = 0.456757 − 0.180125I
a = 0.474060 − 0.395975I
b = 0.441601 − 1.138690I
1.00966 + 2.17421I 13.7438 + 10.2319I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
28
− 11u
27
+ ··· − 72u − 4)(u
79
− 6u
78
+ ··· − 4390196u + 145732)
c
2
(u
28
+ u
27
+ ··· + 8u
2
− 1)(u
79
+ 6u
78
+ ··· − 318766u + 63403)
c
3
(u
28
− 7u
26
+ ··· + 9u
2
− 1)(u
79
+ u
78
+ ··· − 6u − 1)
c
4
(u
28
− 9u
26
+ ··· − u + 1)(u
79
+ u
78
+ ··· − 23u − 1)
c
5
(u
28
− u
27
+ ··· + 8u
2
− 1)(u
79
+ 6u
78
+ ··· − 318766u + 63403)
c
6
(u
28
+ 8u
26
+ ··· + 57u − 107)
· (u
79
− u
78
+ ··· − 3836986393u + 691687687)
c
7
(u
28
+ 4u
27
+ ··· + 8u + 4)(u
79
+ 3u
78
+ ··· + 4u + 4)
c
8
(u
28
− 7u
26
+ ··· + 9u
2
− 1)(u
79
+ u
78
+ ··· − 6u − 1)
c
9
(u
28
+ 4u
25
+ ··· − 4u − 1)(u
79
+ u
78
+ ··· − 56386u + 5447)
c
10
(u
28
− 4u
27
+ ··· − 8u + 4)(u
79
+ 3u
78
+ ··· + 4u + 4)
c
11
(u
28
− 9u
26
+ ··· + u + 1)(u
79
+ u
78
+ ··· − 23u − 1)
c
12
(u
28
− 2u
26
+ ··· − 12u
2
− 1)(u
79
+ u
78
+ ··· − 74772u + 31151)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
28
− 25y
27
+ ··· − 3120y + 16)
· (y
79
− 82y
78
+ ··· + 5209547957600y −21237815824)
c
2
, c
5
(y
28
+ 11y
27
+ ··· − 16y + 1)
· (y
79
+ 82y
78
+ ··· + 185670572514y −4019940409)
c
3
, c
8
(y
28
− 14y
27
+ ··· − 18y + 1)(y
79
− 59y
78
+ ··· + 140y −1)
c
4
, c
11
(y
28
− 18y
27
+ ··· − 27y + 1)(y
79
− 19y
78
+ ··· + 101y −1)
c
6
(y
28
+ 16y
27
+ ··· − 141921y + 11449)
· (y
79
+ 83y
78
+ ··· − 1.11 × 10
19
y −4.78 × 10
17
)
c
7
, c
10
(y
28
+ 20y
27
+ ··· + 80y + 16)(y
79
+ 59y
78
+ ··· + 1152y −16)
c
9
(y
28
+ 24y
26
+ ··· + 16y + 1)
· (y
79
+ 27y
78
+ ··· + 2658310082y −29669809)
c
12
(y
28
− 4y
27
+ ··· + 24y + 1)
· (y
79
+ 27y
78
+ ··· − 24342580030y −970384801)
22
