12a
0945
(K12a
0945
)
A knot diagram
1
Linearized knot diagam
4 6 10 2 9 11 12 3 5 1 8 7
Solving Sequence
2,5
4
1,10
11 3 9 6 7 8 12
c
4
c
1
c
10
c
3
c
9
c
5
c
6
c
8
c
12
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.02739 × 10
332
u
98
− 2.37382 × 10
331
u
97
+ ··· + 3.74964 × 10
331
b − 1.45413 × 10
332
,
− 1.49879 × 10
332
u
98
+ 7.34438 × 10
331
u
97
+ ··· + 3.74964 × 10
331
a + 3.88173 × 10
332
,
u
99
− u
98
+ ··· + 23u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 99 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
= h1.03 × 10
332
u
98
− 2.37 × 10
331
u
97
+ · · · + 3.75 × 10
331
b − 1.45 ×
10
332
, −1.50 × 10
332
u
98
+ 7.34 × 10
331
u
97
+ · · · + 3.75 × 10
331
a + 3.88 ×
10
332
, u
99
− u
98
+ · · · + 23u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
1
=
u
−u
3
+ u
a
10
=
3.99717u
98
− 1.95869u
97
+ ··· + 5.84289u − 10.3523
−2.73998u
98
+ 0.633079u
97
+ ··· + 11.1270u + 3.87805
a
11
=
1.49086u
98
− 1.37385u
97
+ ··· + 10.6124u − 7.30046
−3.56577u
98
+ 0.832592u
97
+ ··· + 13.3902u + 5.00840
a
3
=
1.93055u
98
− 4.68758u
97
+ ··· + 18.1992u + 7.78150
0.155337u
98
− 1.61346u
97
+ ··· − 1.45150u + 2.25046
a
9
=
1.25719u
98
− 1.32561u
97
+ ··· + 16.9699u − 6.47424
−2.73998u
98
+ 0.633079u
97
+ ··· + 11.1270u + 3.87805
a
6
=
1.93654u
98
+ 1.72896u
97
+ ··· − 27.0840u − 7.72022
−4.92304u
98
+ 0.941981u
97
+ ··· + 8.31108u + 5.39610
a
7
=
0.371340u
98
+ 1.23713u
97
+ ··· − 22.3156u − 0.337780
1.37216u
98
− 0.185051u
97
+ ··· − 5.23013u − 2.09610
a
8
=
0.277222u
98
− 0.970149u
97
+ ··· + 24.8608u − 5.43616
−2.32353u
98
+ 0.371790u
97
+ ··· + 10.4207u + 3.83701
a
12
=
0.402554u
98
− 0.156919u
97
+ ··· + 23.0714u − 6.03950
−1.47855u
98
+ 0.456172u
97
+ ··· + 8.63301u + 1.93043
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4.12981u
98
+ 4.34684u
97
+ ··· − 11.0775u − 8.25641
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
99
− u
98
+ ··· + 23u
2
+ 1
c
2
u
99
− 17u
98
+ ··· − 188u + 19
c
3
u
99
− u
98
+ ··· + 140544u + 38593
c
5
, c
9
u
99
+ 3u
98
+ ··· + 4u + 1
c
6
u
99
+ 3u
98
+ ··· + 27558u + 10961
c
7
, c
11
, c
12
u
99
− 3u
98
+ ··· − 5u
2
+ 1
c
8
u
99
+ u
98
+ ··· + 2u + 1
c
10
u
99
+ 17u
98
+ ··· − 745808u − 47873
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
99
− 65y
98
+ ··· − 46y −1
c
2
y
99
+ 167y
98
+ ··· + 15926y −361
c
3
y
99
− 173y
98
+ ··· + 31500556694y −1489419649
c
5
, c
9
y
99
+ 59y
98
+ ··· + 10y −1
c
6
y
99
+ 23y
98
+ ··· − 2411815078y −120143521
c
7
, c
11
, c
12
y
99
+ 91y
98
+ ··· + 10y −1
c
8
y
99
+ 3y
98
+ ··· + 66y −1
c
10
y
99
+ 63y
98
+ ··· + 18472642594y −2291824129
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.994492 + 0.018996I
a = −8.09675 + 8.01488I
b = 0.036500 + 1.030300I
−5.85875 + 4.44226I 0
u = −0.994492 − 0.018996I
a = −8.09675 − 8.01488I
b = 0.036500 − 1.030300I
−5.85875 − 4.44226I 0
u = 0.975049 + 0.188085I
a = 1.70227 + 0.71514I
b = −0.86106 − 1.23598I
−0.83712 − 3.39889I 0
u = 0.975049 − 0.188085I
a = 1.70227 − 0.71514I
b = −0.86106 + 1.23598I
−0.83712 + 3.39889I 0
u = −0.983393 + 0.005334I
a = 10.61980 + 0.36470I
b = −0.046544 + 0.996080I
−0.29450 − 1.51441I 0
u = −0.983393 − 0.005334I
a = 10.61980 − 0.36470I
b = −0.046544 − 0.996080I
−0.29450 + 1.51441I 0
u = 0.940357 + 0.256776I
a = 1.52630 − 0.64498I
b = −1.120820 + 0.374656I
−3.47108 − 4.80291I 0
u = 0.940357 − 0.256776I
a = 1.52630 + 0.64498I
b = −1.120820 − 0.374656I
−3.47108 + 4.80291I 0
u = 1.015250 + 0.168887I
a = 0.501708 − 0.911504I
b = −0.40788 + 1.65089I
−5.64603 − 6.02681I 0
u = 1.015250 − 0.168887I
a = 0.501708 + 0.911504I
b = −0.40788 − 1.65089I
−5.64603 + 6.02681I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.372488 + 0.867010I
a = 0.0622155 − 0.1044290I
b = 0.329059 − 1.244270I
5.94439 + 2.18444I 0
u = 0.372488 − 0.867010I
a = 0.0622155 + 0.1044290I
b = 0.329059 + 1.244270I
5.94439 − 2.18444I 0
u = 0.305094 + 1.030890I
a = 0.056979 + 0.202482I
b = −0.357545 + 1.219710I
2.48048 + 5.30165I 0
u = 0.305094 − 1.030890I
a = 0.056979 − 0.202482I
b = −0.357545 − 1.219710I
2.48048 − 5.30165I 0
u = 0.901677 + 0.097789I
a = −0.216939 + 1.082560I
b = 0.20471 − 1.71903I
0.62004 − 2.35166I 0
u = 0.901677 − 0.097789I
a = −0.216939 − 1.082560I
b = 0.20471 + 1.71903I
0.62004 + 2.35166I 0
u = −0.509715 + 0.746888I
a = −0.169108 + 0.504425I
b = 0.533589 + 0.088687I
−7.28561 − 1.78675I 0
u = −0.509715 − 0.746888I
a = −0.169108 − 0.504425I
b = 0.533589 − 0.088687I
−7.28561 + 1.78675I 0
u = −0.222287 + 0.862791I
a = 0.302618 − 0.658490I
b = −0.607223 − 0.026295I
−6.34251 + 7.39460I 0
u = −0.222287 − 0.862791I
a = 0.302618 + 0.658490I
b = −0.607223 + 0.026295I
−6.34251 − 7.39460I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.025930 + 0.444337I
a = 1.71502 + 0.33410I
b = −0.661676 − 1.231940I
0.29849 − 3.48845I 0
u = 1.025930 − 0.444337I
a = 1.71502 − 0.33410I
b = −0.661676 + 1.231940I
0.29849 + 3.48845I 0
u = −1.105620 + 0.182833I
a = −1.53301 + 0.66453I
b = 0.149783 − 0.858878I
−0.893637 + 0.928581I 0
u = −1.105620 − 0.182833I
a = −1.53301 − 0.66453I
b = 0.149783 + 0.858878I
−0.893637 − 0.928581I 0
u = −1.052710 + 0.386949I
a = −0.139428 + 0.138796I
b = 0.348717 + 0.244272I
−4.88550 + 1.29779I 0
u = −1.052710 − 0.386949I
a = −0.139428 − 0.138796I
b = 0.348717 − 0.244272I
−4.88550 − 1.29779I 0
u = 0.490947 + 0.724635I
a = −0.115757 − 0.091258I
b = −0.308124 + 1.285350I
1.98588 − 0.94910I 0
u = 0.490947 − 0.724635I
a = −0.115757 + 0.091258I
b = −0.308124 − 1.285350I
1.98588 + 0.94910I 0
u = 0.024409 + 1.144880I
a = 0.161084 + 0.384659I
b = −0.368663 + 1.164000I
1.78944 + 4.02340I 0
u = 0.024409 − 1.144880I
a = 0.161084 − 0.384659I
b = −0.368663 − 1.164000I
1.78944 − 4.02340I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.725573 + 0.425618I
a = 1.29629 + 1.12020I
b = −0.236866 + 0.999057I
1.10389 + 2.20019I 0
u = −0.725573 − 0.425618I
a = 1.29629 − 1.12020I
b = −0.236866 − 0.999057I
1.10389 − 2.20019I 0
u = −0.844241 + 0.798032I
a = −0.781444 − 0.619640I
b = 0.326365 − 0.989143I
−3.03348 + 4.34292I 0
u = −0.844241 − 0.798032I
a = −0.781444 + 0.619640I
b = 0.326365 + 0.989143I
−3.03348 − 4.34292I 0
u = −0.814307 + 0.082370I
a = −3.09073 − 1.58258I
b = 0.147889 − 1.005710I
−1.93903 + 0.16998I 0
u = −0.814307 − 0.082370I
a = −3.09073 + 1.58258I
b = 0.147889 + 1.005710I
−1.93903 − 0.16998I 0
u = 0.818015 + 0.013466I
a = −1.83249 + 0.88185I
b = 1.032470 − 0.802275I
1.061010 − 0.905393I 0
u = 0.818015 − 0.013466I
a = −1.83249 − 0.88185I
b = 1.032470 + 0.802275I
1.061010 + 0.905393I 0
u = 1.171430 + 0.160474I
a = −1.35590 − 0.61144I
b = 0.73024 + 1.40259I
−8.18419 − 5.25528I 0
u = 1.171430 − 0.160474I
a = −1.35590 + 0.61144I
b = 0.73024 − 1.40259I
−8.18419 + 5.25528I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.814684
a = −0.0793313
b = −0.268977
−1.15052 −10.1560
u = −0.201959 + 0.761271I
a = −0.248856 + 0.715476I
b = 0.583104 + 0.002888I
−0.70303 + 4.11723I 0
u = −0.201959 − 0.761271I
a = −0.248856 − 0.715476I
b = 0.583104 − 0.002888I
−0.70303 − 4.11723I 0
u = −0.133156 + 1.210760I
a = −0.248294 − 0.438800I
b = 0.378986 − 1.135900I
−4.35827 + 1.78343I 0
u = −0.133156 − 1.210760I
a = −0.248294 + 0.438800I
b = 0.378986 + 1.135900I
−4.35827 − 1.78343I 0
u = 1.113910 + 0.518276I
a = −1.63257 − 0.22728I
b = 0.627590 + 1.260540I
3.60786 − 7.23643I 0
u = 1.113910 − 0.518276I
a = −1.63257 + 0.22728I
b = 0.627590 − 1.260540I
3.60786 + 7.23643I 0
u = 0.091381 + 1.259280I
a = −0.206832 − 0.324273I
b = 0.389645 − 1.173270I
2.61420 + 7.82431I 0
u = 0.091381 − 1.259280I
a = −0.206832 + 0.324273I
b = 0.389645 + 1.173270I
2.61420 − 7.82431I 0
u = 1.270440 + 0.319765I
a = 1.323150 − 0.301719I
b = −1.147510 + 0.129638I
−6.03634 − 3.86723I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.270440 − 0.319765I
a = 1.323150 + 0.301719I
b = −1.147510 − 0.129638I
−6.03634 + 3.86723I 0
u = 1.186390 + 0.567593I
a = 1.57142 + 0.16120I
b = −0.60806 − 1.27771I
−0.32932 − 10.94210I 0
u = 1.186390 − 0.567593I
a = 1.57142 − 0.16120I
b = −0.60806 + 1.27771I
−0.32932 + 10.94210I 0
u = −0.351502 + 0.583602I
a = 0.045268 − 0.641591I
b = −0.505707 − 0.020078I
−1.42824 + 0.58824I −6.32763 + 0.I
u = −0.351502 − 0.583602I
a = 0.045268 + 0.641591I
b = −0.505707 + 0.020078I
−1.42824 − 0.58824I −6.32763 + 0.I
u = 0.080166 + 1.328970I
a = 0.239652 + 0.318158I
b = −0.400675 + 1.169980I
−3.08712 + 11.21620I 0
u = 0.080166 − 1.328970I
a = 0.239652 − 0.318158I
b = −0.400675 − 1.169980I
−3.08712 − 11.21620I 0
u = 1.293750 + 0.385495I
a = −1.268880 + 0.317852I
b = 1.120670 − 0.123023I
−5.16454 − 8.24227I 0
u = 1.293750 − 0.385495I
a = −1.268880 − 0.317852I
b = 1.120670 + 0.123023I
−5.16454 + 8.24227I 0
u = 1.335970 + 0.253610I
a = −1.323960 + 0.222139I
b = 1.164640 − 0.095026I
−12.94020 − 1.45742I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.335970 − 0.253610I
a = −1.323960 − 0.222139I
b = 1.164640 + 0.095026I
−12.94020 + 1.45742I 0
u = 1.332610 + 0.410531I
a = 1.238100 − 0.304781I
b = −1.111890 + 0.110138I
−11.0505 − 11.9189I 0
u = 1.332610 − 0.410531I
a = 1.238100 + 0.304781I
b = −1.111890 − 0.110138I
−11.0505 + 11.9189I 0
u = −1.42681 + 0.24216I
a = 0.712034 − 0.124915I
b = −0.285167 + 0.736373I
−5.40693 + 1.49418I 0
u = −1.42681 − 0.24216I
a = 0.712034 + 0.124915I
b = −0.285167 − 0.736373I
−5.40693 − 1.49418I 0
u = 1.34786 + 0.55727I
a = 1.43150 + 0.12722I
b = −0.59525 − 1.31276I
−2.33740 − 9.95857I 0
u = 1.34786 − 0.55727I
a = 1.43150 − 0.12722I
b = −0.59525 + 1.31276I
−2.33740 + 9.95857I 0
u = 1.38738 + 0.50905I
a = −1.386450 − 0.150028I
b = 0.59836 + 1.32454I
−9.12270 − 7.60585I 0
u = 1.38738 − 0.50905I
a = −1.386450 + 0.150028I
b = 0.59836 − 1.32454I
−9.12270 + 7.60585I 0
u = −1.45704 + 0.27018I
a = 0.329760 − 0.023893I
b = −0.353412 − 0.464496I
−3.73507 + 1.99100I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.45704 − 0.27018I
a = 0.329760 + 0.023893I
b = −0.353412 + 0.464496I
−3.73507 − 1.99100I 0
u = 1.36786 + 0.59962I
a = −1.42831 − 0.09018I
b = 0.58643 + 1.31207I
−1.4502 − 14.2394I 0
u = 1.36786 − 0.59962I
a = −1.42831 + 0.09018I
b = 0.58643 − 1.31207I
−1.4502 + 14.2394I 0
u = 0.137003 + 0.479807I
a = 0.415392 − 1.273760I
b = −0.573266 + 0.183599I
−1.49366 + 1.81906I −1.74281 − 3.69548I
u = 0.137003 − 0.479807I
a = 0.415392 + 1.273760I
b = −0.573266 − 0.183599I
−1.49366 − 1.81906I −1.74281 + 3.69548I
u = −1.33451 + 0.72094I
a = −0.795110 − 0.245516I
b = 0.365795 − 0.879457I
−2.92305 + 1.66150I 0
u = −1.33451 − 0.72094I
a = −0.795110 + 0.245516I
b = 0.365795 + 0.879457I
−2.92305 − 1.66150I 0
u = −1.51217 + 0.15103I
a = −0.384725 − 0.022882I
b = 0.336258 + 0.528779I
−3.83043 − 1.65845I 0
u = −1.51217 − 0.15103I
a = −0.384725 + 0.022882I
b = 0.336258 − 0.528779I
−3.83043 + 1.65845I 0
u = 1.39495 + 0.61409I
a = 1.41261 + 0.07302I
b = −0.58199 − 1.31505I
−7.2935 − 17.8795I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.39495 − 0.61409I
a = 1.41261 − 0.07302I
b = −0.58199 + 1.31505I
−7.2935 + 17.8795I 0
u = −1.28110 + 0.84155I
a = 0.760307 + 0.307367I
b = −0.379856 + 0.907214I
−2.60113 + 5.38027I 0
u = −1.28110 − 0.84155I
a = 0.760307 − 0.307367I
b = −0.379856 − 0.907214I
−2.60113 − 5.38027I 0
u = −1.51624 + 0.33515I
a = −0.348799 + 0.058863I
b = 0.393435 + 0.465014I
−9.58932 + 4.99478I 0
u = −1.51624 − 0.33515I
a = −0.348799 − 0.058863I
b = 0.393435 − 0.465014I
−9.58932 − 4.99478I 0
u = −1.32704 + 0.90872I
a = −0.723788 − 0.302511I
b = 0.397500 − 0.908490I
−8.44003 + 8.52317I 0
u = −1.32704 − 0.90872I
a = −0.723788 + 0.302511I
b = 0.397500 + 0.908490I
−8.44003 − 8.52317I 0
u = −1.60381 + 0.15830I
a = 0.418149 − 0.011118I
b = −0.375095 − 0.547160I
−9.73725 − 4.53902I 0
u = −1.60381 − 0.15830I
a = 0.418149 + 0.011118I
b = −0.375095 + 0.547160I
−9.73725 + 4.53902I 0
u = −1.44341 + 0.73730I
a = 0.746384 + 0.216819I
b = −0.387157 + 0.863065I
−8.91446 − 1.06218I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.44341 − 0.73730I
a = 0.746384 − 0.216819I
b = −0.387157 − 0.863065I
−8.91446 + 1.06218I 0
u = 0.263548 + 0.166515I
a = 3.54408 + 1.76475I
b = −0.391506 − 0.811020I
−3.86603 + 4.15313I −1.33182 − 1.44818I
u = 0.263548 − 0.166515I
a = 3.54408 − 1.76475I
b = −0.391506 + 0.811020I
−3.86603 − 4.15313I −1.33182 + 1.44818I
u = 0.291799 + 0.090574I
a = −1.56516 + 2.32607I
b = 0.466028 − 0.523896I
1.26906 − 0.95925I 4.32293 + 1.61283I
u = 0.291799 − 0.090574I
a = −1.56516 − 2.32607I
b = 0.466028 + 0.523896I
1.26906 + 0.95925I 4.32293 − 1.61283I
u = −0.168662 + 0.052708I
a = −3.79045 + 6.49188I
b = 0.166465 + 1.024460I
−4.37987 − 4.27329I −3.90810 + 4.27086I
u = −0.168662 − 0.052708I
a = −3.79045 − 6.49188I
b = 0.166465 − 1.024460I
−4.37987 + 4.27329I −3.90810 − 4.27086I
u = −0.0185879 + 0.1145680I
a = −6.90872 + 3.17394I
b = −0.106809 + 1.097290I
1.24428 + 1.65585I 0.29239 − 4.10547I
u = −0.0185879 − 0.1145680I
a = −6.90872 − 3.17394I
b = −0.106809 − 1.097290I
1.24428 − 1.65585I 0.29239 + 4.10547I
14
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
u
99
− u
98
+ ··· + 23u
2
+ 1
c
2
u
99
− 17u
98
+ ··· − 188u + 19
c
3
u
99
− u
98
+ ··· + 140544u + 38593
c
5
, c
9
u
99
+ 3u
98
+ ··· + 4u + 1
c
6
u
99
+ 3u
98
+ ··· + 27558u + 10961
c
7
, c
11
, c
12
u
99
− 3u
98
+ ··· − 5u
2
+ 1
c
8
u
99
+ u
98
+ ··· + 2u + 1
c
10
u
99
+ 17u
98
+ ··· − 745808u − 47873
15
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
99
− 65y
98
+ ··· − 46y −1
c
2
y
99
+ 167y
98
+ ··· + 15926y −361
c
3
y
99
− 173y
98
+ ··· + 31500556694y −1489419649
c
5
, c
9
y
99
+ 59y
98
+ ··· + 10y −1
c
6
y
99
+ 23y
98
+ ··· − 2411815078y −120143521
c
7
, c
11
, c
12
y
99
+ 91y
98
+ ··· + 10y −1
c
8
y
99
+ 3y
98
+ ··· + 66y −1
c
10
y
99
+ 63y
98
+ ··· + 18472642594y −2291824129
16
