Singularities of Møller-Plesset series: example "a83"

[n₁, n₂, n₃] approximant is defined as a solution of the quadratic equation
A(z)f² + B(z)f + C(z) = 0
with polynomial coefficients A(z), B(z) and C(z) of degree n₃, n₂ and n₁ respectively.

Square-root singularities are determined as zeroes of the discriminant
D(z) = B²(z) - 4A(z)C(z).
The weight c of the singularity z_c is defined so that
f ~ c(1 - z/z_c)^1/2 at z -> z_c.
The weight is calculated by formula
c = 1/2[-z(D/A²)']^1/2
where r. h. s. of the above equation is evaluated at z = z_c.

Table 1. Singularities with their weights for the quadratic approximant [1, 0, 0]
The most stable singularity is highlighted.

No. z_c c Location in the complex plane

1

2.3493

0.688
Singularities of quadratic [1, 0, 0] approximant

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Table 2. Singularities with their weights for the quadratic approximant [1, 1, 0]
The most stable singularity is highlighted.

No. z_c c Location in the complex plane

1

2.906

1.07

2

230.9003

9.56 i

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Table 3. Singularities with their weights for the quadratic approximant [1, 1, 1]
The most stable singularity is highlighted.

No. z_c c Location in the complex plane

1

2.4929

0.614
Singularities of quadratic [1, 1, 1] approximant

2

16.2961

6.64 i

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Table 4. Singularities with their weights for the quadratic approximant [2, 1, 1]
The most stable singularity is highlighted.

No. z_c c Location in the complex plane

1

1.1712

0.0799
Singularities of quadratic [2, 1, 1] approximant

2

1.3348

0.0874 i

3

4.7728

99.6

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Table 5. Singularities with their weights for the quadratic approximant [2, 2, 1]
The most stable singularity is highlighted.

No. z_c c Location in the complex plane

1

-1.5267 + 0.1032 i

0.0244 + 0.0222 i
Singularities of quadratic [2, 2, 1] approximant

2

-1.5267 - 0.1032 i

0.0244 - 0.0222 i

3

1.9255

0.167

4

15.1405

27.8 i

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Table 6. Singularities with their weights for the quadratic approximant [2, 2, 2]
The most stable singularity is highlighted.

No. z_c c Location in the complex plane

1

-1.9157

0.0284
Singularities of quadratic [2, 2, 2] approximant

2

2.0405 + 1.1131 i

0.133 + 0.0199 i

3

2.0405 - 1.1131 i

0.133 - 0.0199 i

4

-3.3296

0.0378 i

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Table 7. Singularities with their weights for the quadratic approximant [3, 2, 2]
The most stable singularity is highlighted.

No. z_c c Location in the complex plane

1

-2.1878

0.0484
Singularities of quadratic [3, 2, 2] approximant

2

2.7464 + 0.9806 i

0.423 + 0.19 i

3

2.7464 - 0.9806 i

0.423 - 0.19 i

4

-5.1815 + 1.9432 i

0.0276 - 0.0672 i

5

-5.1815 - 1.9432 i

0.0276 + 0.0672 i

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Table 8. Singularities with their weights for the quadratic approximant [3, 3, 2]
The most stable singularity is highlighted.

No. z_c c Location in the complex plane

1

0.7844

0.00101
Singularities of quadratic [3, 3, 2] approximant

2

0.7933

0.00102 i

3

-2.0367 + 0.7328 i

0.0154 + 0.00647 i

4

-2.0367 - 0.7328 i

0.0154 - 0.00647 i

5

2.103 + 1.8386 i

0.0362 - 0.0717 i

6

2.103 - 1.8386 i

0.0362 + 0.0717 i

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Table 9. Singularities with their weights for the quadratic approximant [3, 3, 3]
The most stable singularity is highlighted.

No. z_c c Location in the complex plane

1

-1.7104

0.00828
Singularities of quadratic [3, 3, 3] approximant

2

-1.2378 + 2.61 i

0.00702 + 0.013 i

3

-1.2378 - 2.61 i

0.00702 - 0.013 i

4

1.775 + 2.4598 i

0.00237 - 0.0412 i

5

1.775 - 2.4598 i

0.00237 + 0.0412 i

6

3.7629

0.299

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Table 10. Singularities with their weights for the quadratic approximant [4, 3, 3]
The most stable singularity is highlighted.

No. z_c c Location in the complex plane

1

-1.8115 + 0.322 i

0.00614 + 0.00803 i
Singularities of quadratic [4, 3, 3] approximant

2

-1.8115 - 0.322 i

0.00614 - 0.00803 i

3

2.5281

0.873

4

-2.7489

0.0136

5

-0.9185 + 3.8385 i

0.098 - 0.021 i

6

-0.9185 - 3.8385 i

0.098 + 0.021 i

7

4.5356

1.44 i

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Table 11. Singularities with their weights for the quadratic approximant [4, 4, 3]
The most stable singularity is highlighted.

No. z_c c Location in the complex plane

1

1.1683 + 1.0809 i

0.0025 - 0.00101 i
Singularities of quadratic [4, 4, 3] approximant

2

1.1683 - 1.0809 i

0.0025 + 0.00101 i

3

1.2397 + 1.0335 i

0.0013 + 0.00256 i

4

1.2397 - 1.0335 i

0.0013 - 0.00256 i

5

-1.679

0.00619

6

-0.6793 + 2.912 i

0.0154 - 0.000603 i

7

-0.6793 - 2.912 i

0.0154 + 0.000603 i

8

-289.8786

2.41 i

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Table 12. Singularities with their weights for the quadratic approximant [4, 4, 4]
The most stable singularity is highlighted.

No. z_c c Location in the complex plane

1

-1.5887

0.00311
Singularities of quadratic [4, 4, 4] approximant

2

0.0913 + 1.669 i

0.000481 + 0.000603 i

3

0.0913 - 1.669 i

0.000481 - 0.000603 i

4

-0.0184 + 1.8631 i

0.000561 - 0.000587 i

5

-0.0184 - 1.8631 i

0.000561 + 0.000587 i

6

0.3441 + 1.9746 i

0.00136 + 0.0000108 i

7

0.3441 - 1.9746 i

0.00136 - 0.0000108 i

8

-3.224

0.0584 i

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Table 13. Singularities with their weights for the quadratic approximant [5, 4, 4]
The most stable singularity is highlighted.

No. z_c c Location in the complex plane

1

-1.5315

0.00209
Singularities of quadratic [5, 4, 4] approximant

2

0.0987 + 1.7337 i

0.000413 + 0.000744 i

3

0.0987 - 1.7337 i

0.000413 - 0.000744 i

4

-0.2402 + 1.8719 i

0.00101 - 0.000416 i

5

-0.2402 - 1.8719 i

0.00101 + 0.000416 i

6

0.4543 + 1.8409 i

0.00136 - 0.000716 i

7

0.4543 - 1.8409 i

0.00136 + 0.000716 i

8

-2.298

0.00838 i

9

-7.0949

0.0211

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Table 14. Singularities with their weights for the quadratic approximant [5, 5, 4]
The most stable singularity is highlighted.

No. z_c c Location in the complex plane

1

-1.2074 + 0.0054 i

0.000249 + 0.000251 i
Singularities of quadratic [5, 5, 4] approximant

2

-1.2074 - 0.0054 i

0.000249 - 0.000251 i

3

-1.5984

0.00241

4

2.3929 + 0.571 i

0.0534 - 0.227 i

5

2.3929 - 0.571 i

0.0534 + 0.227 i

6

2.9661 + 1.5259 i

0.0201 - 0.184 i

7

2.9661 - 1.5259 i

0.0201 + 0.184 i

8

0.2311 + 3.5339 i

0.0288 - 0.0444 i

9

0.2311 - 3.5339 i

0.0288 + 0.0444 i

10

-11.6853

0.355 i

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Table 15. Singularities with their weights for the quadratic approximant [5, 5, 5]
The most stable singularity is highlighted.

No. z_c c Location in the complex plane

1

-1.0329 + 0.0013 i

0.0000954 + 0.0000955 i
Singularities of quadratic [5, 5, 5] approximant

2

-1.0329 - 0.0013 i

0.0000954 - 0.0000955 i

3

-1.5887

0.00251

4

2.0245 + 1.1174 i

0.0287 + 0.00901 i

5

2.0245 - 1.1174 i

0.0287 - 0.00901 i

6

1.8545 + 1.3967 i

0.0106 - 0.0195 i

7

1.8545 - 1.3967 i

0.0106 + 0.0195 i

8

0.0901 + 3.0406 i

0.00895 - 0.0192 i

9

0.0901 - 3.0406 i

0.00895 + 0.0192 i

10

-5.314

8.76 i

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Table 16. Singularities with their weights for the quadratic approximant [6, 5, 5]
The most stable singularity is highlighted.

No. z_c c Location in the complex plane

1

-1.4764 + 0.0389 i

0.00079 + 0.00103 i
Singularities of quadratic [6, 5, 5] approximant

2

-1.4764 - 0.0389 i

0.00079 - 0.00103 i

3

-1.6257

0.00181

4

2.4762 + 0.5816 i

0.383 - 0.29 i

5

2.4762 - 0.5816 i

0.383 + 0.29 i

6

3.7381

1.05

7

-0.6092 + 4.3072 i

0.0846 + 0.048 i

8

-0.6092 - 4.3072 i

0.0846 - 0.048 i

9

2.7836 + 3.5692 i

0.313 + 0.513 i

10

2.7836 - 3.5692 i

0.313 - 0.513 i

11

-10.8656

0.103 i

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Table 17. Singularities with their weights for the quadratic approximant [6, 6, 5]
The most stable singularity is highlighted.

No. z_c c Location in the complex plane

1

-1.5355 + 0.0685 i

0.00111 + 0.00159 i
Singularities of quadratic [6, 6, 5] approximant

2

-1.5355 - 0.0685 i

0.00111 - 0.00159 i

3

-1.6973

0.00232

4

2.4282 + 0.6585 i

0.216 - 0.159 i

5

2.4282 - 0.6585 i

0.216 + 0.159 i

6

-2.7463

0.145 i

7

-3.4008

0.0556

8

3.0953 + 1.6365 i

0.109 - 0.234 i

9

3.0953 - 1.6365 i

0.109 + 0.234 i

10

0.3563 + 3.8354 i

0.0524 - 0.0815 i

11

0.3563 - 3.8354 i

0.0524 + 0.0815 i

12

-10.5342

0.573 i

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Table 18. Singularities with their weights for the quadratic approximant [6, 6, 6]
The most stable singularity is highlighted.

No. z_c c Location in the complex plane

1

-1.5164 + 0.0475 i

0.00121 + 0.0017 i
Singularities of quadratic [6, 6, 6] approximant

2

-1.5164 - 0.0475 i

0.00121 - 0.0017 i

3

-1.674

0.00258

4

2.2363 + 0.7676 i

0.0965 - 0.0182 i

5

2.2363 - 0.7676 i

0.0965 + 0.0182 i

6

2.6172 + 1.0304 i

0.00726 - 0.134 i

7

2.6172 - 1.0304 i

0.00726 + 0.134 i

8

1.3993 + 3.5479 i

0.307 - 0.0666 i

9

1.3993 - 3.5479 i

0.307 + 0.0666 i

10

-1.4259 + 4.0714 i

0.0221 + 0.0514 i

11

-1.4259 - 4.0714 i

0.0221 - 0.0514 i

12

16.0583

1.93

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Table 19. Singularities with their weights for the quadratic approximant [7, 6, 6]
The most stable singularity is highlighted.

No. z_c c Location in the complex plane

1

-1.5192 + 0.0463 i

0.00132 + 0.00186 i
Singularities of quadratic [7, 6, 6] approximant

2

-1.5192 - 0.0463 i

0.00132 - 0.00186 i

3

-1.6817

0.00281

4

2.2251 + 0.778 i

0.0869 - 0.00387 i

5

2.2251 - 0.778 i

0.0869 + 0.00387 i

6

2.6538 + 1.0272 i

0.0299 - 0.132 i

7

2.6538 - 1.0272 i

0.0299 + 0.132 i

8

1.4954 + 3.5304 i

0.278 - 0.249 i

9

1.4954 - 3.5304 i

0.278 + 0.249 i

10

-1.301 + 3.9891 i

0.0242 + 0.041 i

11

-1.301 - 3.9891 i

0.0242 - 0.041 i

12

3.1388 + 10.4519 i

0.209 + 0.0475 i

13

3.1388 - 10.4519 i

0.209 - 0.0475 i

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Table 20. Singularities with their weights for the quadratic approximant [7, 7, 6]
The most stable singularity is highlighted.

No. z_c c Location in the complex plane

1

-1.4918 + 0.054 i

0.000593 + 0.000883 i
Singularities of quadratic [7, 7, 6] approximant

2

-1.4918 - 0.054 i

0.000593 - 0.000883 i

3

-1.6066

0.00121

4

1.9657

0.013

5

2.1804 + 0.0947 i

0.00636 + 0.0175 i

6

2.1804 - 0.0947 i

0.00636 - 0.0175 i

7

2.4458 + 0.8194 i

0.0477 - 0.124 i

8

2.4458 - 0.8194 i

0.0477 + 0.124 i

9

1.065 + 3.7595 i

0.0959 + 0.0943 i

10

1.065 - 3.7595 i

0.0959 - 0.0943 i

11

-4.0566

0.0588 i

12

-5.3041 + 4.8052 i

0.335 + 0.0646 i

13

-5.3041 - 4.8052 i

0.335 - 0.0646 i

14

21.7421

1.52 i

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Table 1. Singularities with their weights for the quadratic approximant [1, 0, 0] The most stable singularity is highlighted.
No.	z_c	c	Location in the complex plane
1	2.3493	0.688

Table 2. Singularities with their weights for the quadratic approximant [1, 1, 0] The most stable singularity is highlighted.
No.	z_c	c	Location in the complex plane
1	2.906	1.07
2	230.9003	9.56 i

Table 3. Singularities with their weights for the quadratic approximant [1, 1, 1] The most stable singularity is highlighted.
No.	z_c	c	Location in the complex plane
1	2.4929	0.614
2	16.2961	6.64 i

Table 4. Singularities with their weights for the quadratic approximant [2, 1, 1] The most stable singularity is highlighted.
No.	z_c	c	Location in the complex plane
1	1.1712	0.0799
2	1.3348	0.0874 i
3	4.7728	99.6

Table 5. Singularities with their weights for the quadratic approximant [2, 2, 1] The most stable singularity is highlighted.
No.	z_c	c	Location in the complex plane
1	-1.5267 + 0.1032 i	0.0244 + 0.0222 i
2	-1.5267 - 0.1032 i	0.0244 - 0.0222 i
3	1.9255	0.167
4	15.1405	27.8 i

Table 6. Singularities with their weights for the quadratic approximant [2, 2, 2] The most stable singularity is highlighted.
No.	z_c	c	Location in the complex plane
1	-1.9157	0.0284
2	2.0405 + 1.1131 i	0.133 + 0.0199 i
3	2.0405 - 1.1131 i	0.133 - 0.0199 i
4	-3.3296	0.0378 i

Table 7. Singularities with their weights for the quadratic approximant [3, 2, 2] The most stable singularity is highlighted.
No.	z_c	c	Location in the complex plane
1	-2.1878	0.0484
2	2.7464 + 0.9806 i	0.423 + 0.19 i
3	2.7464 - 0.9806 i	0.423 - 0.19 i
4	-5.1815 + 1.9432 i	0.0276 - 0.0672 i
5	-5.1815 - 1.9432 i	0.0276 + 0.0672 i

Table 8. Singularities with their weights for the quadratic approximant [3, 3, 2] The most stable singularity is highlighted.
No.	z_c	c	Location in the complex plane
1	0.7844	0.00101
2	0.7933	0.00102 i
3	-2.0367 + 0.7328 i	0.0154 + 0.00647 i
4	-2.0367 - 0.7328 i	0.0154 - 0.00647 i
5	2.103 + 1.8386 i	0.0362 - 0.0717 i
6	2.103 - 1.8386 i	0.0362 + 0.0717 i

Table 9. Singularities with their weights for the quadratic approximant [3, 3, 3] The most stable singularity is highlighted.
No.	z_c	c	Location in the complex plane
1	-1.7104	0.00828
2	-1.2378 + 2.61 i	0.00702 + 0.013 i
3	-1.2378 - 2.61 i	0.00702 - 0.013 i
4	1.775 + 2.4598 i	0.00237 - 0.0412 i
5	1.775 - 2.4598 i	0.00237 + 0.0412 i
6	3.7629	0.299

Table 10. Singularities with their weights for the quadratic approximant [4, 3, 3] The most stable singularity is highlighted.
No.	z_c	c	Location in the complex plane
1	-1.8115 + 0.322 i	0.00614 + 0.00803 i
2	-1.8115 - 0.322 i	0.00614 - 0.00803 i
3	2.5281	0.873
4	-2.7489	0.0136
5	-0.9185 + 3.8385 i	0.098 - 0.021 i
6	-0.9185 - 3.8385 i	0.098 + 0.021 i
7	4.5356	1.44 i

Table 11. Singularities with their weights for the quadratic approximant [4, 4, 3] The most stable singularity is highlighted.
No.	z_c	c	Location in the complex plane
1	1.1683 + 1.0809 i	0.0025 - 0.00101 i
2	1.1683 - 1.0809 i	0.0025 + 0.00101 i
3	1.2397 + 1.0335 i	0.0013 + 0.00256 i
4	1.2397 - 1.0335 i	0.0013 - 0.00256 i
5	-1.679	0.00619
6	-0.6793 + 2.912 i	0.0154 - 0.000603 i
7	-0.6793 - 2.912 i	0.0154 + 0.000603 i
8	-289.8786	2.41 i

Table 12. Singularities with their weights for the quadratic approximant [4, 4, 4] The most stable singularity is highlighted.
No.	z_c	c	Location in the complex plane
1	-1.5887	0.00311
2	0.0913 + 1.669 i	0.000481 + 0.000603 i
3	0.0913 - 1.669 i	0.000481 - 0.000603 i
4	-0.0184 + 1.8631 i	0.000561 - 0.000587 i
5	-0.0184 - 1.8631 i	0.000561 + 0.000587 i
6	0.3441 + 1.9746 i	0.00136 + 0.0000108 i
7	0.3441 - 1.9746 i	0.00136 - 0.0000108 i
8	-3.224	0.0584 i

Table 13. Singularities with their weights for the quadratic approximant [5, 4, 4] The most stable singularity is highlighted.
No.	z_c	c	Location in the complex plane
1	-1.5315	0.00209
2	0.0987 + 1.7337 i	0.000413 + 0.000744 i
3	0.0987 - 1.7337 i	0.000413 - 0.000744 i
4	-0.2402 + 1.8719 i	0.00101 - 0.000416 i
5	-0.2402 - 1.8719 i	0.00101 + 0.000416 i
6	0.4543 + 1.8409 i	0.00136 - 0.000716 i
7	0.4543 - 1.8409 i	0.00136 + 0.000716 i
8	-2.298	0.00838 i
9	-7.0949	0.0211

Table 14. Singularities with their weights for the quadratic approximant [5, 5, 4] The most stable singularity is highlighted.
No.	z_c	c	Location in the complex plane
1	-1.2074 + 0.0054 i	0.000249 + 0.000251 i
2	-1.2074 - 0.0054 i	0.000249 - 0.000251 i
3	-1.5984	0.00241
4	2.3929 + 0.571 i	0.0534 - 0.227 i
5	2.3929 - 0.571 i	0.0534 + 0.227 i
6	2.9661 + 1.5259 i	0.0201 - 0.184 i
7	2.9661 - 1.5259 i	0.0201 + 0.184 i
8	0.2311 + 3.5339 i	0.0288 - 0.0444 i
9	0.2311 - 3.5339 i	0.0288 + 0.0444 i
10	-11.6853	0.355 i

Table 15. Singularities with their weights for the quadratic approximant [5, 5, 5] The most stable singularity is highlighted.
No.	z_c	c	Location in the complex plane
1	-1.0329 + 0.0013 i	0.0000954 + 0.0000955 i
2	-1.0329 - 0.0013 i	0.0000954 - 0.0000955 i
3	-1.5887	0.00251
4	2.0245 + 1.1174 i	0.0287 + 0.00901 i
5	2.0245 - 1.1174 i	0.0287 - 0.00901 i
6	1.8545 + 1.3967 i	0.0106 - 0.0195 i
7	1.8545 - 1.3967 i	0.0106 + 0.0195 i
8	0.0901 + 3.0406 i	0.00895 - 0.0192 i
9	0.0901 - 3.0406 i	0.00895 + 0.0192 i
10	-5.314	8.76 i

Table 16. Singularities with their weights for the quadratic approximant [6, 5, 5] The most stable singularity is highlighted.
No.	z_c	c	Location in the complex plane
1	-1.4764 + 0.0389 i	0.00079 + 0.00103 i
2	-1.4764 - 0.0389 i	0.00079 - 0.00103 i
3	-1.6257	0.00181
4	2.4762 + 0.5816 i	0.383 - 0.29 i
5	2.4762 - 0.5816 i	0.383 + 0.29 i
6	3.7381	1.05
7	-0.6092 + 4.3072 i	0.0846 + 0.048 i
8	-0.6092 - 4.3072 i	0.0846 - 0.048 i
9	2.7836 + 3.5692 i	0.313 + 0.513 i
10	2.7836 - 3.5692 i	0.313 - 0.513 i
11	-10.8656	0.103 i

Table 17. Singularities with their weights for the quadratic approximant [6, 6, 5] The most stable singularity is highlighted.
No.	z_c	c	Location in the complex plane
1	-1.5355 + 0.0685 i	0.00111 + 0.00159 i
2	-1.5355 - 0.0685 i	0.00111 - 0.00159 i
3	-1.6973	0.00232
4	2.4282 + 0.6585 i	0.216 - 0.159 i
5	2.4282 - 0.6585 i	0.216 + 0.159 i
6	-2.7463	0.145 i
7	-3.4008	0.0556
8	3.0953 + 1.6365 i	0.109 - 0.234 i
9	3.0953 - 1.6365 i	0.109 + 0.234 i
10	0.3563 + 3.8354 i	0.0524 - 0.0815 i
11	0.3563 - 3.8354 i	0.0524 + 0.0815 i
12	-10.5342	0.573 i

Table 18. Singularities with their weights for the quadratic approximant [6, 6, 6] The most stable singularity is highlighted.
No.	z_c	c	Location in the complex plane
1	-1.5164 + 0.0475 i	0.00121 + 0.0017 i
2	-1.5164 - 0.0475 i	0.00121 - 0.0017 i
3	-1.674	0.00258
4	2.2363 + 0.7676 i	0.0965 - 0.0182 i
5	2.2363 - 0.7676 i	0.0965 + 0.0182 i
6	2.6172 + 1.0304 i	0.00726 - 0.134 i
7	2.6172 - 1.0304 i	0.00726 + 0.134 i
8	1.3993 + 3.5479 i	0.307 - 0.0666 i
9	1.3993 - 3.5479 i	0.307 + 0.0666 i
10	-1.4259 + 4.0714 i	0.0221 + 0.0514 i
11	-1.4259 - 4.0714 i	0.0221 - 0.0514 i
12	16.0583	1.93

Table 19. Singularities with their weights for the quadratic approximant [7, 6, 6] The most stable singularity is highlighted.
No.	z_c	c	Location in the complex plane
1	-1.5192 + 0.0463 i	0.00132 + 0.00186 i
2	-1.5192 - 0.0463 i	0.00132 - 0.00186 i
3	-1.6817	0.00281
4	2.2251 + 0.778 i	0.0869 - 0.00387 i
5	2.2251 - 0.778 i	0.0869 + 0.00387 i
6	2.6538 + 1.0272 i	0.0299 - 0.132 i
7	2.6538 - 1.0272 i	0.0299 + 0.132 i
8	1.4954 + 3.5304 i	0.278 - 0.249 i
9	1.4954 - 3.5304 i	0.278 + 0.249 i
10	-1.301 + 3.9891 i	0.0242 + 0.041 i
11	-1.301 - 3.9891 i	0.0242 - 0.041 i
12	3.1388 + 10.4519 i	0.209 + 0.0475 i
13	3.1388 - 10.4519 i	0.209 - 0.0475 i

Table 20. Singularities with their weights for the quadratic approximant [7, 7, 6] The most stable singularity is highlighted.
No.	z_c	c	Location in the complex plane
1	-1.4918 + 0.054 i	0.000593 + 0.000883 i
2	-1.4918 - 0.054 i	0.000593 - 0.000883 i
3	-1.6066	0.00121
4	1.9657	0.013
5	2.1804 + 0.0947 i	0.00636 + 0.0175 i
6	2.1804 - 0.0947 i	0.00636 - 0.0175 i
7	2.4458 + 0.8194 i	0.0477 - 0.124 i
8	2.4458 - 0.8194 i	0.0477 + 0.124 i
9	1.065 + 3.7595 i	0.0959 + 0.0943 i
10	1.065 - 3.7595 i	0.0959 - 0.0943 i
11	-4.0566	0.0588 i
12	-5.3041 + 4.8052 i	0.335 + 0.0646 i
13	-5.3041 - 4.8052 i	0.335 - 0.0646 i
14	21.7421	1.52 i