12a
0149
(K12a
0149
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 10 11 1 4 8 12 7 6
Solving Sequence
6,11
7 12
1,3
2 8 10 5 4 9
c
6
c
11
c
12
c
1
c
7
c
10
c
5
c
4
c
9
c
2
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
104
− u
103
+ ··· + b − 2u, −u
102
− u
101
+ ··· + a − 1, u
105
+ 2u
104
+ ··· + 3u + 1i
I
u
2
= hb + 1, −u
4
+ u
2
+ a + u, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 111 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
104
−u
103
+· · ·+b−2u, −u
102
−u
101
+· · ·+a−1, u
105
+2u
104
+· · ·+3u+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
12
=
−u
−u
3
+ u
a
1
=
−u
3
−u
3
+ u
a
3
=
u
102
+ u
101
+ ··· − 5u + 1
u
104
+ u
103
+ ··· − 2u
2
+ 2u
a
2
=
−u
104
− u
103
+ ··· + 6u
2
− 5u
u
104
+ u
103
+ ··· − u
2
+ 3u
a
8
=
u
8
− u
6
+ u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
10
=
u
3
u
5
− u
3
+ u
a
5
=
u
8
− u
6
+ u
4
+ 1
u
10
− 2u
8
+ 3u
6
− 2u
4
+ u
2
a
4
=
−2u
104
− 2u
103
+ ··· + 8u
2
− 7u
u
104
+ u
103
+ ··· − 12u
3
+ 3u
a
9
=
−u
21
+ 4u
19
+ ··· + 2u
3
− u
−u
21
+ 5u
19
− 13u
17
+ 20u
15
− 20u
13
+ 13u
11
− 7u
9
+ 4u
7
− u
5
− u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
103
+ 47u
101
+ ··· + 4u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
105
+ 55u
104
+ ··· + 8u + 1
c
2
, c
4
u
105
− 7u
104
+ ··· − 6u + 1
c
3
, c
8
u
105
− u
104
+ ··· + 64u + 64
c
5
, c
7
u
105
− 2u
104
+ ··· + 333u + 9
c
6
, c
11
u
105
+ 2u
104
+ ··· + 3u + 1
c
9
u
105
− 39u
104
+ ··· − 81920u + 4096
c
10
u
105
+ 48u
104
+ ··· + 15u + 1
c
12
u
105
+ 6u
104
+ ··· + 99u + 5
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
105
− 3y
104
+ ··· − 8y −1
c
2
, c
4
y
105
− 55y
104
+ ··· + 8y −1
c
3
, c
8
y
105
+ 39y
104
+ ··· − 81920y −4096
c
5
, c
7
y
105
− 72y
104
+ ··· + 23067y −81
c
6
, c
11
y
105
− 48y
104
+ ··· + 15y −1
c
9
y
105
+ 43y
104
+ ··· + 486539264y −16777216
c
10
y
105
+ 20y
104
+ ··· + 143y −1
c
12
y
105
+ 8y
104
+ ··· − 29y −25
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.871041 + 0.511708I
a = −0.369393 − 0.110166I
b = 0.440206 − 0.618461I
1.88999 − 2.94964I 0
u = 0.871041 − 0.511708I
a = −0.369393 + 0.110166I
b = 0.440206 + 0.618461I
1.88999 + 2.94964I 0
u = 0.922799 + 0.352325I
a = −1.77246 + 0.60448I
b = −1.312370 + 0.212834I
−2.93812 − 1.40462I 0
u = 0.922799 − 0.352325I
a = −1.77246 − 0.60448I
b = −1.312370 − 0.212834I
−2.93812 + 1.40462I 0
u = −0.921835 + 0.433717I
a = −1.18386 − 2.01805I
b = −1.236050 + 0.589796I
−2.05807 + 3.12857I 0
u = −0.921835 − 0.433717I
a = −1.18386 + 2.01805I
b = −1.236050 − 0.589796I
−2.05807 − 3.12857I 0
u = −1.020100 + 0.189153I
a = 0.430373 − 1.257180I
b = −0.437411 − 0.526557I
−1.85386 + 0.21349I 0
u = −1.020100 − 0.189153I
a = 0.430373 + 1.257180I
b = −0.437411 + 0.526557I
−1.85386 − 0.21349I 0
u = 1.058570 + 0.031241I
a = −0.73900 + 2.50720I
b = −0.281684 + 1.135380I
2.93779 + 2.55382I 0
u = 1.058570 − 0.031241I
a = −0.73900 − 2.50720I
b = −0.281684 − 1.135380I
2.93779 − 2.55382I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.921723 + 0.557628I
a = 1.06654 − 1.37317I
b = 0.838100 + 0.698342I
0.10374 − 7.55958I 0
u = 0.921723 − 0.557628I
a = 1.06654 + 1.37317I
b = 0.838100 − 0.698342I
0.10374 + 7.55958I 0
u = −0.561631 + 0.730673I
a = 0.317415 + 0.482062I
b = 0.44589 + 2.35840I
3.08653 + 9.35903I 0
u = −0.561631 − 0.730673I
a = 0.317415 − 0.482062I
b = 0.44589 − 2.35840I
3.08653 − 9.35903I 0
u = 1.068320 + 0.168089I
a = −1.99637 − 0.28617I
b = −1.55455 − 0.55344I
−4.75936 + 1.13660I 0
u = 1.068320 − 0.168089I
a = −1.99637 + 0.28617I
b = −1.55455 + 0.55344I
−4.75936 − 1.13660I 0
u = −0.541684 + 0.731152I
a = −0.571433 − 0.349082I
b = −0.625316 − 0.742225I
5.63434 + 4.07144I 0
u = −0.541684 − 0.731152I
a = −0.571433 + 0.349082I
b = −0.625316 + 0.742225I
5.63434 − 4.07144I 0
u = −1.082220 + 0.152274I
a = 1.05559 + 3.81169I
b = 1.45512 + 1.53677I
−4.31563 − 3.76778I 0
u = −1.082220 − 0.152274I
a = 1.05559 − 3.81169I
b = 1.45512 − 1.53677I
−4.31563 + 3.76778I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.491163 + 0.760253I
a = −0.303412 + 0.316758I
b = 0.02554 + 2.32363I
8.31059 + 1.25002I 0
u = −0.491163 − 0.760253I
a = −0.303412 − 0.316758I
b = 0.02554 − 2.32363I
8.31059 − 1.25002I 0
u = −0.468964 + 0.768998I
a = −0.234001 − 0.389085I
b = −1.11862 − 1.92816I
8.18758 − 4.15070I 0
u = −0.468964 − 0.768998I
a = −0.234001 + 0.389085I
b = −1.11862 + 1.92816I
8.18758 + 4.15070I 0
u = 1.094480 + 0.131917I
a = −0.02662 − 1.62635I
b = 0.647265 − 0.798129I
−0.04159 + 4.70125I 0
u = 1.094480 − 0.131917I
a = −0.02662 + 1.62635I
b = 0.647265 + 0.798129I
−0.04159 − 4.70125I 0
u = −1.061330 + 0.302887I
a = 0.650283 − 0.216021I
b = 0.161826 − 0.038082I
−2.49722 + 0.52024I 0
u = −1.061330 − 0.302887I
a = 0.650283 + 0.216021I
b = 0.161826 + 0.038082I
−2.49722 − 0.52024I 0
u = 0.535147 + 0.710912I
a = −0.144639 + 0.767528I
b = −0.49756 + 2.66326I
1.20196 − 3.31272I 0. + 4.05275I
u = 0.535147 − 0.710912I
a = −0.144639 − 0.767528I
b = −0.49756 − 2.66326I
1.20196 + 3.31272I 0. − 4.05275I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.407168 + 0.786367I
a = 0.366623 − 0.319641I
b = −0.93186 − 3.09556I
2.24833 − 12.15740I 0. + 7.45112I
u = −0.407168 − 0.786367I
a = 0.366623 + 0.319641I
b = −0.93186 + 3.09556I
2.24833 + 12.15740I 0. − 7.45112I
u = −0.418533 + 0.777892I
a = −0.565706 + 0.154413I
b = 0.12298 + 1.64263I
4.96689 − 6.83862I 0. + 4.01071I
u = −0.418533 − 0.777892I
a = −0.565706 − 0.154413I
b = 0.12298 − 1.64263I
4.96689 + 6.83862I 0. − 4.01071I
u = −1.098480 + 0.220916I
a = 1.82717 − 0.51460I
b = 1.28934 − 0.84992I
−4.64089 + 3.53476I 0
u = −1.098480 − 0.220916I
a = 1.82717 + 0.51460I
b = 1.28934 + 0.84992I
−4.64089 − 3.53476I 0
u = 1.114790 + 0.141950I
a = −0.62179 + 3.70068I
b = −1.22790 + 1.88592I
−2.78241 + 9.87820I 0
u = 1.114790 − 0.141950I
a = −0.62179 − 3.70068I
b = −1.22790 − 1.88592I
−2.78241 − 9.87820I 0
u = 0.412854 + 0.764891I
a = −0.329970 − 0.580550I
b = 1.34712 − 3.14233I
0.54594 + 5.90508I −2.83942 − 4.16325I
u = 0.412854 − 0.764891I
a = −0.329970 + 0.580550I
b = 1.34712 + 3.14233I
0.54594 − 5.90508I −2.83942 + 4.16325I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.519162 + 0.696598I
a = 0.639391 + 0.295863I
b = −1.153370 − 0.377703I
0.550091 + 0.784462I −1.20480 − 3.39624I
u = −0.519162 − 0.696598I
a = 0.639391 − 0.295863I
b = −1.153370 + 0.377703I
0.550091 − 0.784462I −1.20480 + 3.39624I
u = 0.616023 + 0.610806I
a = −0.618330 + 0.417161I
b = 0.781913 − 0.579529I
0.97348 + 2.95222I 0. − 2.99817I
u = 0.616023 − 0.610806I
a = −0.618330 − 0.417161I
b = 0.781913 + 0.579529I
0.97348 − 2.95222I 0. + 2.99817I
u = 0.487231 + 0.710886I
a = 0.568469 − 0.441572I
b = 1.46675 − 0.61446I
3.00709 + 0.79659I 0.79816 − 1.47644I
u = 0.487231 − 0.710886I
a = 0.568469 + 0.441572I
b = 1.46675 + 0.61446I
3.00709 − 0.79659I 0.79816 + 1.47644I
u = −0.826365 + 0.242657I
a = 1.77436 + 0.19357I
b = −0.099112 − 0.575729I
−1.346980 + 0.143898I −5.19438 + 1.02775I
u = −0.826365 − 0.242657I
a = 1.77436 − 0.19357I
b = −0.099112 + 0.575729I
−1.346980 − 0.143898I −5.19438 − 1.02775I
u = 0.694568 + 0.503832I
a = 0.426503 − 1.004340I
b = 0.599221 + 0.208369I
2.38068 − 1.26624I 3.02682 + 3.59787I
u = 0.694568 − 0.503832I
a = 0.426503 + 1.004340I
b = 0.599221 − 0.208369I
2.38068 + 1.26624I 3.02682 − 3.59787I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.412674 + 0.751967I
a = 0.608113 − 0.004611I
b = −1.42040 + 0.15308I
−0.02506 − 3.23562I −2.54395 + 3.48237I
u = −0.412674 − 0.751967I
a = 0.608113 + 0.004611I
b = −1.42040 − 0.15308I
−0.02506 + 3.23562I −2.54395 − 3.48237I
u = 0.431391 + 0.735763I
a = 0.600136 + 0.213703I
b = 0.42753 + 1.64026I
2.71628 + 1.63531I − 60.10 + 0.426013I
u = 0.431391 − 0.735763I
a = 0.600136 − 0.213703I
b = 0.42753 − 1.64026I
2.71628 − 1.63531I − 60.10 − 0.426013I
u = −1.085710 + 0.396654I
a = 0.82643 − 1.17997I
b = −0.296620 − 1.185670I
−3.45140 + 1.18279I 0
u = −1.085710 − 0.396654I
a = 0.82643 + 1.17997I
b = −0.296620 + 1.185670I
−3.45140 − 1.18279I 0
u = 1.095630 + 0.417910I
a = −0.02770 + 1.67149I
b = −0.70591 + 1.70291I
−6.99423 − 2.34770I 0
u = 1.095630 − 0.417910I
a = −0.02770 − 1.67149I
b = −0.70591 − 1.70291I
−6.99423 + 2.34770I 0
u = −1.098070 + 0.430864I
a = −1.50322 + 0.79462I
b = 0.50933 + 1.51246I
−6.90518 + 5.01473I 0
u = −1.098070 − 0.430864I
a = −1.50322 − 0.79462I
b = 0.50933 − 1.51246I
−6.90518 − 5.01473I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.116490 + 0.392750I
a = −0.304426 + 1.186820I
b = 0.17668 + 1.56892I
−6.38577 − 3.12199I 0
u = −1.116490 − 0.392750I
a = −0.304426 − 1.186820I
b = 0.17668 − 1.56892I
−6.38577 + 3.12199I 0
u = 0.358533 + 0.732179I
a = −0.473671 − 0.115244I
b = 1.248310 + 0.417986I
−0.180213 − 1.053090I −2.77562 + 3.65050I
u = 0.358533 − 0.732179I
a = −0.473671 + 0.115244I
b = 1.248310 − 0.417986I
−0.180213 + 1.053090I −2.77562 − 3.65050I
u = 1.097470 + 0.449471I
a = −0.57663 − 1.39142I
b = 0.655892 − 1.218070I
−3.08812 − 6.11758I 0
u = 1.097470 − 0.449471I
a = −0.57663 + 1.39142I
b = 0.655892 + 1.218070I
−3.08812 + 6.11758I 0
u = −1.014830 + 0.615237I
a = 3.24068 − 0.49048I
b = 1.02632 − 1.84070I
1.74031 − 4.22648I 0
u = −1.014830 − 0.615237I
a = 3.24068 + 0.49048I
b = 1.02632 + 1.84070I
1.74031 + 4.22648I 0
u = 1.028950 + 0.594658I
a = −3.74068 − 0.70363I
b = −1.39258 − 2.26144I
−0.26335 − 1.69761I 0
u = 1.028950 − 0.594658I
a = −3.74068 + 0.70363I
b = −1.39258 + 2.26144I
−0.26335 + 1.69761I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.038610 + 0.583357I
a = −0.86698 − 1.45055I
b = −1.123260 + 0.479159I
−0.99128 + 4.14969I 0
u = −1.038610 − 0.583357I
a = −0.86698 + 1.45055I
b = −1.123260 − 0.479159I
−0.99128 − 4.14969I 0
u = −1.028780 + 0.610157I
a = −1.38935 − 0.41725I
b = −0.846242 + 0.238296I
4.18740 + 1.04548I 0
u = −1.028780 − 0.610157I
a = −1.38935 + 0.41725I
b = −0.846242 − 0.238296I
4.18740 − 1.04548I 0
u = 1.119170 + 0.448157I
a = 0.916526 + 0.862413I
b = −0.82229 + 1.15840I
−6.01436 − 10.76980I 0
u = 1.119170 − 0.448157I
a = 0.916526 − 0.862413I
b = −0.82229 − 1.15840I
−6.01436 + 10.76980I 0
u = 1.085540 + 0.531264I
a = 0.218413 − 0.818317I
b = 0.272318 − 0.133470I
−0.96342 − 6.54782I 0
u = 1.085540 − 0.531264I
a = 0.218413 + 0.818317I
b = 0.272318 + 0.133470I
−0.96342 + 6.54782I 0
u = 1.056750 + 0.588724I
a = 1.89469 − 1.62052I
b = 1.88122 + 0.04481I
1.32189 − 5.78784I 0
u = 1.056750 − 0.588724I
a = 1.89469 + 1.62052I
b = 1.88122 − 0.04481I
1.32189 + 5.78784I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.064960 + 0.613127I
a = 2.78431 − 1.21297I
b = 0.56806 − 2.38367I
6.60470 + 3.95245I 0
u = −1.064960 − 0.613127I
a = 2.78431 + 1.21297I
b = 0.56806 + 2.38367I
6.60470 − 3.95245I 0
u = 1.087140 + 0.587148I
a = −1.72430 − 1.55120I
b = −0.06084 − 2.05367I
0.78044 − 6.68037I 0
u = 1.087140 − 0.587148I
a = −1.72430 + 1.55120I
b = −0.06084 + 2.05367I
0.78044 + 6.68037I 0
u = −1.078250 + 0.611228I
a = −3.10524 − 0.23085I
b = −1.56999 + 1.66367I
6.37670 + 9.36798I 0
u = −1.078250 − 0.611228I
a = −3.10524 + 0.23085I
b = −1.56999 − 1.66367I
6.37670 − 9.36798I 0
u = 1.107430 + 0.568255I
a = 0.32467 − 1.75043I
b = 1.47140 − 0.35337I
−2.36349 − 3.89444I 0
u = 1.107430 − 0.568255I
a = 0.32467 + 1.75043I
b = 1.47140 + 0.35337I
−2.36349 + 3.89444I 0
u = −1.097390 + 0.588994I
a = −0.54573 − 1.77669I
b = −1.57950 − 0.02613I
−2.04553 + 8.32422I 0
u = −1.097390 − 0.588994I
a = −0.54573 + 1.77669I
b = −1.57950 + 0.02613I
−2.04553 − 8.32422I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.100740 + 0.593524I
a = 4.65152 + 0.60219I
b = 2.08615 + 3.31083I
−1.48870 − 11.04220I 0
u = 1.100740 − 0.593524I
a = 4.65152 − 0.60219I
b = 2.08615 − 3.31083I
−1.48870 + 11.04220I 0
u = −1.102420 + 0.599841I
a = 1.90028 − 0.97109I
b = 0.46791 − 1.98595I
2.93810 + 12.03250I 0
u = −1.102420 − 0.599841I
a = 1.90028 + 0.97109I
b = 0.46791 + 1.98595I
2.93810 − 12.03250I 0
u = −1.109180 + 0.599492I
a = −4.19050 + 1.03594I
b = −1.47349 + 3.35952I
0.1644 + 17.3697I 0
u = −1.109180 − 0.599492I
a = −4.19050 − 1.03594I
b = −1.47349 − 3.35952I
0.1644 − 17.3697I 0
u = 0.310775 + 0.617300I
a = 0.224132 + 0.579203I
b = 0.297600 + 0.055669I
1.18758 + 2.03152I 1.33774 − 4.93844I
u = 0.310775 − 0.617300I
a = 0.224132 − 0.579203I
b = 0.297600 − 0.055669I
1.18758 − 2.03152I 1.33774 + 4.93844I
u = 0.068881 + 0.649388I
a = 0.96428 + 1.05711I
b = −0.112211 − 0.913961I
−3.09718 + 6.72998I −5.51837 − 6.26335I
u = 0.068881 − 0.649388I
a = 0.96428 − 1.05711I
b = −0.112211 + 0.913961I
−3.09718 − 6.72998I −5.51837 + 6.26335I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.089393 + 0.585636I
a = −0.065112 − 0.405783I
b = 0.243850 + 0.831568I
−0.37540 + 2.20380I −2.28710 − 3.24292I
u = 0.089393 − 0.585636I
a = −0.065112 + 0.405783I
b = 0.243850 − 0.831568I
−0.37540 − 2.20380I −2.28710 + 3.24292I
u = −0.022104 + 0.581743I
a = −1.05400 + 1.31053I
b = −0.262065 − 1.021320I
−4.04714 − 1.27003I −7.86539 + 0.74571I
u = −0.022104 − 0.581743I
a = −1.05400 − 1.31053I
b = −0.262065 + 1.021320I
−4.04714 + 1.27003I −7.86539 − 0.74571I
u = −0.294464
a = 2.53525
b = −0.625272
−1.19254 −8.33000
15
II. I
u
2
= hb + 1, −u
4
+ u
2
+ a + u, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
12
=
−u
−u
3
+ u
a
1
=
−u
3
−u
3
+ u
a
3
=
u
4
− u
2
− u
−1
a
2
=
u
4
− u
3
− u
2
− u
−u
3
+ u − 1
a
8
=
u
3
u
5
− u
3
+ u
a
10
=
u
3
u
5
− u
3
+ u
a
5
=
u
3
u
3
− u
a
4
=
u
4
− u
2
− u
−1
a
9
=
u
3
u
5
− u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
4
− 5u
2
− 5u − 5
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
8
, c
9
u
6
c
4
(u + 1)
6
c
5
, c
7
, c
11
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
6
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
10
, c
12
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
8
, c
9
y
6
c
5
, c
6
, c
7
c
11
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
10
, c
12
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = −1.42918 + 0.19856I
b = −1.00000
−3.53554 − 0.92430I −12.63596 − 0.09369I
u = 1.002190 − 0.295542I
a = −1.42918 − 0.19856I
b = −1.00000
−3.53554 + 0.92430I −12.63596 + 0.09369I
u = −0.428243 + 0.664531I
a = 0.429179 + 0.198557I
b = −1.00000
0.245672 − 0.924305I −2.59683 + 0.69886I
u = −0.428243 − 0.664531I
a = 0.429179 − 0.198557I
b = −1.00000
0.245672 + 0.924305I −2.59683 − 0.69886I
u = −1.073950 + 0.558752I
a = −0.50000 − 1.37764I
b = −1.00000
−1.64493 + 5.69302I −6.76721 − 4.86918I
u = −1.073950 − 0.558752I
a = −0.50000 + 1.37764I
b = −1.00000
−1.64493 − 5.69302I −6.76721 + 4.86918I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
105
+ 55u
104
+ ··· + 8u + 1)
c
2
((u − 1)
6
)(u
105
− 7u
104
+ ··· − 6u + 1)
c
3
, c
8
u
6
(u
105
− u
104
+ ··· + 64u + 64)
c
4
((u + 1)
6
)(u
105
− 7u
104
+ ··· − 6u + 1)
c
5
, c
7
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
105
− 2u
104
+ ··· + 333u + 9)
c
6
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
105
+ 2u
104
+ ··· + 3u + 1)
c
9
u
6
(u
105
− 39u
104
+ ··· − 81920u + 4096)
c
10
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)(u
105
+ 48u
104
+ ··· + 15u + 1)
c
11
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
105
+ 2u
104
+ ··· + 3u + 1)
c
12
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)(u
105
+ 6u
104
+ ··· + 99u + 5)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
6
)(y
105
− 3y
104
+ ··· − 8y −1)
c
2
, c
4
((y −1)
6
)(y
105
− 55y
104
+ ··· + 8y −1)
c
3
, c
8
y
6
(y
105
+ 39y
104
+ ··· − 81920y −4096)
c
5
, c
7
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
105
− 72y
104
+ ··· + 23067y −81)
c
6
, c
11
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
105
− 48y
104
+ ··· + 15y −1)
c
9
y
6
(y
105
+ 43y
104
+ ··· + 4.86539 × 10
8
y −1.67772 × 10
7
)
c
10
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)(y
105
+ 20y
104
+ ··· + 143y −1)
c
12
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)(y
105
+ 8y
104
+ ··· − 29y −25)
21
