12a
0274
(K12a
0274
)
A knot diagram
1
Linearized knot diagam
3 6 8 9 2 10 12 4 5 1 7 11
Solving Sequence
2,5
6
3,10
7 1 11 9 4 8 12
c
5
c
2
c
6
c
1
c
10
c
9
c
4
c
8
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.74822 × 10
78
u
76
− 6.58436 × 10
78
u
75
+ ··· + 3.26649 × 10
78
b − 2.45503 × 10
79
,
3.83245 × 10
80
u
76
+ 1.21540 × 10
81
u
75
+ ··· + 1.50259 × 10
80
a + 7.16663 × 10
81
, u
77
+ 4u
76
+ ··· − 83u + 23i
I
u
2
= hb, a
3
− a
2
+ 2a − 1, u + 1i
I
u
3
= h−58a
5
− 93a
4
+ 166a
3
+ 145a
2
+ 1375b − 1557a − 761, a
6
+ 2a
5
− a
4
− 2a
3
+ 14a
2
+ 16a − 23, u − 1i
* 3 irreducible components of dim
C
= 0, with total 86 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−2.75 × 10
78
u
76
− 6.58 × 10
78
u
75
+ · · · + 3.27 × 10
78
b − 2.46 ×
10
79
, 3.83 × 10
80
u
76
+ 1.22 × 10
81
u
75
+ · · · + 1.50 × 10
80
a + 7.17 ×
10
81
, u
77
+ 4u
76
+ · · · − 83u + 23i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
−2.55057u
76
− 8.08869u
75
+ ··· + 198.750u − 47.6953
0.841338u
76
+ 2.01573u
75
+ ··· − 6.68307u + 7.51581
a
7
=
0.0655842u
76
− 0.348936u
75
+ ··· + 48.3109u − 3.54945
0.0711030u
76
+ 0.423687u
75
+ ··· − 38.3393u + 8.52212
a
1
=
u
3
u
5
− u
3
+ u
a
11
=
−3.33726u
76
− 10.1169u
75
+ ··· + 200.943u − 51.1967
0.855842u
76
+ 2.09894u
75
+ ··· − 11.7733u + 8.37597
a
9
=
−3.39191u
76
− 10.1044u
75
+ ··· + 205.433u − 55.2111
0.841338u
76
+ 2.01573u
75
+ ··· − 6.68307u + 7.51581
a
4
=
0.874063u
76
+ 3.35873u
75
+ ··· − 110.479u + 22.8121
−0.662021u
76
− 2.14455u
75
+ ··· + 63.8417u − 16.9405
a
8
=
3.78999u
76
+ 11.7097u
75
+ ··· − 255.675u + 57.5747
−1.08746u
76
− 2.22875u
75
+ ··· − 36.8047u + 1.34287
a
12
=
0.300634u
76
+ 0.554541u
75
+ ··· + 21.2154u − 0.921596
−0.0330706u
76
+ 0.409257u
75
+ ··· − 65.3295u + 13.9071
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.17395u
76
+ 8.19414u
75
+ ··· − 265.163u + 68.6829
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
77
+ 36u
76
+ ··· + 18067u + 529
c
2
, c
5
u
77
+ 4u
76
+ ··· − 83u + 23
c
3
, c
4
, c
8
c
9
u
77
+ u
76
+ ··· + 40u − 8
c
6
u
77
− 2u
76
+ ··· + 15744u + 1429
c
7
, c
11
u
77
+ 2u
76
+ ··· + 8u + 1
c
10
, c
12
u
77
− 26u
76
+ ··· + 52u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
77
+ 20y
76
+ ··· + 58766823y −279841
c
2
, c
5
y
77
− 36y
76
+ ··· + 18067y −529
c
3
, c
4
, c
8
c
9
y
77
− 91y
76
+ ··· + 1600y −64
c
6
y
77
− 18y
76
+ ··· + 161870600y −2042041
c
7
, c
11
y
77
− 26y
76
+ ··· + 52y −1
c
10
, c
12
y
77
+ 54y
76
+ ··· + 1876y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.909672 + 0.421724I
a = 1.145770 − 0.117310I
b = 1.316650 + 0.146721I
1.44070 + 0.67158I 0
u = 0.909672 − 0.421724I
a = 1.145770 + 0.117310I
b = 1.316650 − 0.146721I
1.44070 − 0.67158I 0
u = 0.958740 + 0.259334I
a = −1.02808 − 1.54394I
b = 0.436907 − 0.282220I
−4.69950 + 2.00322I 0
u = 0.958740 − 0.259334I
a = −1.02808 + 1.54394I
b = 0.436907 + 0.282220I
−4.69950 − 2.00322I 0
u = −0.406477 + 0.928601I
a = 0.445300 + 0.285962I
b = −1.61605 + 0.12297I
7.99937 − 3.55322I 0
u = −0.406477 − 0.928601I
a = 0.445300 − 0.285962I
b = −1.61605 − 0.12297I
7.99937 + 3.55322I 0
u = −0.836156 + 0.510128I
a = 1.39187 − 1.92431I
b = −1.54628 − 0.04973I
2.10806 − 0.97873I 0
u = −0.836156 − 0.510128I
a = 1.39187 + 1.92431I
b = −1.54628 + 0.04973I
2.10806 + 0.97873I 0
u = −0.846089 + 0.570762I
a = 0.455833 − 1.127310I
b = 0.119346 − 0.679087I
2.27118 + 2.27901I 0
u = −0.846089 − 0.570762I
a = 0.455833 + 1.127310I
b = 0.119346 + 0.679087I
2.27118 − 2.27901I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.597501 + 0.832618I
a = 0.671200 − 0.276505I
b = −1.62202 + 0.04903I
9.40242 − 0.58348I 0
u = −0.597501 − 0.832618I
a = 0.671200 + 0.276505I
b = −1.62202 − 0.04903I
9.40242 + 0.58348I 0
u = 0.802252 + 0.545356I
a = −0.874362 + 0.161172I
b = −1.201920 − 0.173318I
2.10589 − 4.47726I 0
u = 0.802252 − 0.545356I
a = −0.874362 − 0.161172I
b = −1.201920 + 0.173318I
2.10589 + 4.47726I 0
u = −0.890705 + 0.520123I
a = −1.08169 + 2.10827I
b = 1.54943 + 0.06669I
1.91630 + 5.14719I 0
u = −0.890705 − 0.520123I
a = −1.08169 − 2.10827I
b = 1.54943 − 0.06669I
1.91630 − 5.14719I 0
u = 0.991337 + 0.301788I
a = 0.82004 + 1.60677I
b = −0.462524 + 0.336790I
−4.95823 − 3.85716I 0
u = 0.991337 − 0.301788I
a = 0.82004 − 1.60677I
b = −0.462524 − 0.336790I
−4.95823 + 3.85716I 0
u = 0.836998 + 0.614038I
a = −0.041166 − 1.187280I
b = 0.857804 − 0.340914I
1.92653 − 0.25220I 0
u = 0.836998 − 0.614038I
a = −0.041166 + 1.187280I
b = 0.857804 + 0.340914I
1.92653 + 0.25220I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.890297 + 0.288879I
a = −0.425721 + 0.887659I
b = −0.165105 + 0.473169I
−1.49628 + 1.00710I 0
u = −0.890297 − 0.288879I
a = −0.425721 − 0.887659I
b = −0.165105 − 0.473169I
−1.49628 − 1.00710I 0
u = −0.400975 + 0.987005I
a = −0.303931 − 0.289012I
b = 1.63234 − 0.13703I
9.29601 − 9.22325I 0
u = −0.400975 − 0.987005I
a = −0.303931 + 0.289012I
b = 1.63234 + 0.13703I
9.29601 + 9.22325I 0
u = 1.06557
a = 1.39720
b = 1.43866
3.34047 0
u = 0.418780 + 0.816135I
a = −0.148801 − 0.514697I
b = −0.782315 − 0.480447I
1.05052 + 6.88705I 9.76091 − 6.50910I
u = 0.418780 − 0.816135I
a = −0.148801 + 0.514697I
b = −0.782315 + 0.480447I
1.05052 − 6.88705I 9.76091 + 6.50910I
u = 0.573921 + 0.715342I
a = −0.261874 − 0.208626I
b = −0.895579 − 0.336201I
5.54189 + 1.10408I 15.4148 − 1.4693I
u = 0.573921 − 0.715342I
a = −0.261874 + 0.208626I
b = −0.895579 + 0.336201I
5.54189 − 1.10408I 15.4148 + 1.4693I
u = −0.540901 + 0.962764I
a = −0.345496 + 0.047931I
b = 1.65287 − 0.08862I
14.3060 − 2.7130I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.540901 − 0.962764I
a = −0.345496 − 0.047931I
b = 1.65287 + 0.08862I
14.3060 + 2.7130I 0
u = 0.970781 + 0.539274I
a = 0.23436 + 1.40764I
b = −0.708068 + 0.428688I
0.09329 − 4.18401I 0
u = 0.970781 − 0.539274I
a = 0.23436 − 1.40764I
b = −0.708068 − 0.428688I
0.09329 + 4.18401I 0
u = −0.695841 + 0.894243I
a = −0.401450 + 0.493510I
b = 1.65626 − 0.02689I
11.38460 + 4.14926I 0
u = −0.695841 − 0.894243I
a = −0.401450 − 0.493510I
b = 1.65626 + 0.02689I
11.38460 − 4.14926I 0
u = 0.643060 + 0.568525I
a = −0.462709 + 0.784941I
b = −1.075780 + 0.071760I
2.18683 − 4.44396I 11.04197 + 6.64377I
u = 0.643060 − 0.568525I
a = −0.462709 − 0.784941I
b = −1.075780 − 0.071760I
2.18683 + 4.44396I 11.04197 − 6.64377I
u = −1.15096
a = 0.896231
b = 0.456757
−0.0502180 0
u = −1.024390 + 0.528329I
a = −0.596620 + 1.107350I
b = −0.262025 + 0.677567I
−3.39577 + 2.31723I 0
u = −1.024390 − 0.528329I
a = −0.596620 − 1.107350I
b = −0.262025 − 0.677567I
−3.39577 − 2.31723I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.373401 + 0.749056I
a = 0.027274 + 0.494073I
b = 0.721323 + 0.440410I
0.00960 + 1.45996I 7.97618 − 1.67296I
u = 0.373401 − 0.749056I
a = 0.027274 − 0.494073I
b = 0.721323 − 0.440410I
0.00960 − 1.45996I 7.97618 + 1.67296I
u = −1.017340 + 0.584382I
a = 0.580607 − 1.153790I
b = 0.244773 − 0.720969I
−2.43522 + 7.84920I 0
u = −1.017340 − 0.584382I
a = 0.580607 + 1.153790I
b = 0.244773 + 0.720969I
−2.43522 − 7.84920I 0
u = −0.550357 + 0.611012I
a = 0.327725 − 1.139910I
b = −0.076911 − 0.650916I
−1.07363 − 3.09170I 6.13866 + 1.90820I
u = −0.550357 − 0.611012I
a = 0.327725 + 1.139910I
b = −0.076911 + 0.650916I
−1.07363 + 3.09170I 6.13866 − 1.90820I
u = 1.013480 + 0.645468I
a = −0.05966 − 1.47790I
b = 0.784663 − 0.521607I
4.27243 − 6.32707I 0
u = 1.013480 − 0.645468I
a = −0.05966 + 1.47790I
b = 0.784663 + 0.521607I
4.27243 + 6.32707I 0
u = −1.191670 + 0.202786I
a = −0.937769 + 0.691714I
b = −0.500980 + 0.368243I
−4.82096 + 1.25692I 0
u = −1.191670 − 0.202786I
a = −0.937769 − 0.691714I
b = −0.500980 − 0.368243I
−4.82096 − 1.25692I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.218840 + 0.157900I
a = 1.046590 − 0.605303I
b = 0.556485 − 0.309636I
−4.31085 − 4.23744I 0
u = −1.218840 − 0.157900I
a = 1.046590 + 0.605303I
b = 0.556485 + 0.309636I
−4.31085 + 4.23744I 0
u = 0.590345 + 0.485361I
a = −0.231755 − 0.263888I
b = 0.740376 + 0.068232I
1.195250 − 0.076686I 9.28796 − 0.38114I
u = 0.590345 − 0.485361I
a = −0.231755 + 0.263888I
b = 0.740376 − 0.068232I
1.195250 + 0.076686I 9.28796 + 0.38114I
u = −0.994216 + 0.757099I
a = 0.10861 − 1.43993I
b = −1.63961 − 0.09571I
10.46370 + 1.91251I 0
u = −0.994216 − 0.757099I
a = 0.10861 + 1.43993I
b = −1.63961 + 0.09571I
10.46370 − 1.91251I 0
u = −1.048280 + 0.682578I
a = −0.04252 + 1.74716I
b = 1.61286 + 0.12210I
8.02968 + 6.23821I 0
u = −1.048280 − 0.682578I
a = −0.04252 − 1.74716I
b = 1.61286 − 0.12210I
8.02968 − 6.23821I 0
u = 1.102630 + 0.596774I
a = 0.11430 + 1.60963I
b = −0.699462 + 0.578264I
−2.08597 − 6.55777I 0
u = 1.102630 − 0.596774I
a = 0.11430 − 1.60963I
b = −0.699462 − 0.578264I
−2.08597 + 6.55777I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.114800 + 0.628614I
a = −0.06903 − 1.61630I
b = 0.722493 − 0.603009I
−1.00381 − 12.28950I 0
u = 1.114800 − 0.628614I
a = −0.06903 + 1.61630I
b = 0.722493 + 0.603009I
−1.00381 + 12.28950I 0
u = 1.306230 + 0.170113I
a = 1.395400 + 0.041474I
b = 1.54130 + 0.08244I
2.08330 + 0.27442I 0
u = 1.306230 − 0.170113I
a = 1.395400 − 0.041474I
b = 1.54130 − 0.08244I
2.08330 − 0.27442I 0
u = −1.119810 + 0.728835I
a = −0.22423 − 1.66256I
b = −1.63651 − 0.15001I
12.5328 + 8.8745I 0
u = −1.119810 − 0.728835I
a = −0.22423 + 1.66256I
b = −1.63651 + 0.15001I
12.5328 − 8.8745I 0
u = −1.164610 + 0.659606I
a = 0.33637 + 1.89170I
b = 1.60778 + 0.17375I
5.70123 + 9.37064I 0
u = −1.164610 − 0.659606I
a = 0.33637 − 1.89170I
b = 1.60778 − 0.17375I
5.70123 − 9.37064I 0
u = −0.376520 + 0.530963I
a = −0.323876 + 1.114950I
b = 0.156016 + 0.563558I
−1.67624 + 1.95624I 4.81633 − 4.78600I
u = −0.376520 − 0.530963I
a = −0.323876 − 1.114950I
b = 0.156016 − 0.563558I
−1.67624 − 1.95624I 4.81633 + 4.78600I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.36189
a = −1.42452
b = −1.57196
7.09596 0
u = −1.188130 + 0.675633I
a = −0.40955 − 1.84238I
b = −1.61626 − 0.18395I
6.8851 + 15.2545I 0
u = −1.188130 − 0.675633I
a = −0.40955 + 1.84238I
b = −1.61626 + 0.18395I
6.8851 − 15.2545I 0
u = 1.370940 + 0.151238I
a = −1.41752 − 0.04527I
b = −1.57417 − 0.07529I
3.00302 + 5.57310I 0
u = 1.370940 − 0.151238I
a = −1.41752 + 0.04527I
b = −1.57417 + 0.07529I
3.00302 − 5.57310I 0
u = 0.510245
a = −2.32566
b = −1.33755
5.64254 18.1120
u = 0.256713
a = −1.32663
b = 0.357915
0.734621 14.2980
12
II. I
u
2
= hb, a
3
− a
2
+ 2a − 1, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
5
=
1
0
a
6
=
1
1
a
3
=
1
0
a
10
=
a
0
a
7
=
a
2
+ 1
1
a
1
=
−1
−1
a
11
=
0
−a
a
9
=
a
0
a
4
=
1
0
a
8
=
a
0
a
12
=
−1
−a
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2a
2
− 2a + 2
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
4
, c
8
c
9
u
3
c
5
(u + 1)
3
c
6
, c
10
u
3
+ u
2
+ 2u + 1
c
7
u
3
− u
2
+ 1
c
11
u
3
+ u
2
− 1
c
12
u
3
− u
2
+ 2u − 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
3
c
3
, c
4
, c
8
c
9
y
3
c
6
, c
10
, c
12
y
3
+ 3y
2
+ 2y −1
c
7
, c
11
y
3
− y
2
+ 2y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.215080 + 1.307140I
b = 0
−4.66906 + 2.82812I 4.89456 − 3.73884I
u = −1.00000
a = 0.215080 − 1.307140I
b = 0
−4.66906 − 2.82812I 4.89456 + 3.73884I
u = −1.00000
a = 0.569840
b = 0
−0.531480 0.210880
16
III. I
u
3
=
h−58a
5
+1375b+· · ·−1557a−761, a
6
+2a
5
−a
4
−2a
3
+14a
2
+16a−23, u−1i
(i) Arc colorings
a
2
=
0
1
a
5
=
1
0
a
6
=
1
1
a
3
=
−1
0
a
10
=
a
0.0421818a
5
+ 0.0676364a
4
+ ··· + 1.13236a + 0.553455
a
7
=
0.0167273a
5
+ 0.0785455a
4
+ ··· + 0.121455a + 0.0298182
−0.0167273a
5
− 0.0785455a
4
+ ··· − 0.121455a − 0.0298182
a
1
=
1
1
a
11
=
0.0421818a
5
+ 0.0676364a
4
+ ··· + 1.13236a + 0.553455
0.0843636a
5
+ 0.135273a
4
+ ··· + 1.26473a + 1.10691
a
9
=
−0.0421818a
5
− 0.0676364a
4
+ ··· − 0.132364a − 0.553455
0.0421818a
5
+ 0.0676364a
4
+ ··· + 1.13236a + 0.553455
a
4
=
−0.0167273a
5
− 0.0785455a
4
+ ··· − 0.121455a − 0.0298182
2
a
8
=
−a
−0.0421818a
5
− 0.0676364a
4
+ ··· − 1.13236a − 0.553455
a
12
=
0.0167273a
5
+ 0.0785455a
4
+ ··· + 0.121455a + 2.02982
0.0501818a
5
+ 0.235636a
4
+ ··· + 0.364364a + 2.08945
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
48
1375
a
5
+
492
1375
a
4
+
896
1375
a
3
+
24
275
a
2
+
608
1375
a +
13784
1375
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)
6
c
2
(u + 1)
6
c
3
, c
4
, c
8
c
9
(u
2
− 2)
3
c
6
, c
12
(u
3
− u
2
+ 2u − 1)
2
c
7
(u
3
+ u
2
− 1)
2
c
10
(u
3
+ u
2
+ 2u + 1)
2
c
11
(u
3
− u
2
+ 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
6
c
3
, c
4
, c
8
c
9
(y −2)
6
c
6
, c
10
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
c
7
, c
11
(y
3
− y
2
+ 2y −1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.844373
b = 1.41421
4.40332 11.0200
u = 1.00000
a = 1.19913 + 1.30714I
b = 1.41421
0.26574 − 2.82812I 4.49024 + 2.97945I
u = 1.00000
a = 1.19913 − 1.30714I
b = 1.41421
0.26574 + 2.82812I 4.49024 − 2.97945I
u = 1.00000
a = −1.98405
b = −1.41421
4.40332 11.0200
u = 1.00000
a = −1.62929 + 1.30714I
b = −1.41421
0.26574 − 2.82812I 4.49024 + 2.97945I
u = 1.00000
a = −1.62929 − 1.30714I
b = −1.41421
0.26574 + 2.82812I 4.49024 − 2.97945I
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
77
+ 36u
76
+ ··· + 18067u + 529)
c
2
((u − 1)
3
)(u + 1)
6
(u
77
+ 4u
76
+ ··· − 83u + 23)
c
3
, c
4
, c
8
c
9
u
3
(u
2
− 2)
3
(u
77
+ u
76
+ ··· + 40u − 8)
c
5
((u − 1)
6
)(u + 1)
3
(u
77
+ 4u
76
+ ··· − 83u + 23)
c
6
(u
3
− u
2
+ 2u − 1)
2
(u
3
+ u
2
+ 2u + 1)
· (u
77
− 2u
76
+ ··· + 15744u + 1429)
c
7
(u
3
− u
2
+ 1)(u
3
+ u
2
− 1)
2
(u
77
+ 2u
76
+ ··· + 8u + 1)
c
10
((u
3
+ u
2
+ 2u + 1)
3
)(u
77
− 26u
76
+ ··· + 52u − 1)
c
11
((u
3
− u
2
+ 1)
2
)(u
3
+ u
2
− 1)(u
77
+ 2u
76
+ ··· + 8u + 1)
c
12
((u
3
− u
2
+ 2u − 1)
3
)(u
77
− 26u
76
+ ··· + 52u − 1)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
77
+ 20y
76
+ ··· + 5.87668 × 10
7
y −279841)
c
2
, c
5
((y −1)
9
)(y
77
− 36y
76
+ ··· + 18067y −529)
c
3
, c
4
, c
8
c
9
y
3
(y −2)
6
(y
77
− 91y
76
+ ··· + 1600y −64)
c
6
((y
3
+ 3y
2
+ 2y −1)
3
)(y
77
− 18y
76
+ ··· + 1.61871 × 10
8
y −2042041)
c
7
, c
11
((y
3
− y
2
+ 2y −1)
3
)(y
77
− 26y
76
+ ··· + 52y −1)
c
10
, c
12
((y
3
+ 3y
2
+ 2y −1)
3
)(y
77
+ 54y
76
+ ··· + 1876y −1)
22
