Eigenvalue problems

This script explores how to use Matlab to solve eigenvalue problems. Both the naive and 'proper' way are shown.

The Eig function

The simplest way to compute eigenvalues and eigenvectors in Matlab is to use the built in "eig" function.

```A=rand(10);
tic
EigVal1=eig(A)
toc
```
```EigVal1 =

4.7876 + 0.0000i
-0.7449 + 0.3597i
-0.7449 - 0.3597i
-0.3286 + 0.4946i
-0.3286 - 0.4946i
-0.1755 + 0.5365i
-0.1755 - 0.5365i
0.1586 + 0.1528i
0.1586 - 0.1528i
-0.0319 + 0.0000i

Elapsed time is 0.000291 seconds.
```

This will produce a column vector of the eigenvalues of A. To also get the eigenvectors, return two outputs:

```tic
[EigVec2,EigVal2]=eig(A);
toc
```
```Elapsed time is 0.000281 seconds.
```

This will return the eigenvectors as the columns of EigVec, and the eigenvalues as the entries of the diagonal matrix EigVal.

Root Solving

We can also use Matlab to solve an eigenvalue problem in the direct way one would do it on paper. We can calculate the characteristic polynomial of our matrix and then find the roots. Using the built in functions charpoly and roots, this is:

```tic
EigVal3=roots(charpoly(A))
toc
```
```EigVal3 =

4.7876 + 0.0000i
-0.7449 + 0.3597i
-0.7449 - 0.3597i
-0.3286 + 0.4946i
-0.3286 - 0.4946i
-0.1755 + 0.5365i
-0.1755 - 0.5365i
0.1586 + 0.1528i
0.1586 - 0.1528i
-0.0319 + 0.0000i

Elapsed time is 0.097021 seconds.
```

Large matrices

As you can see in the timings, this method is significantly slower than using the built in function. For large enough matrices, it is not feasible to solve the problem algebraically.

```A=rand(1000);
tic
EigVal4=eig(A)
toc
tic
[EigVec5,EigVal5]=eig(A);
toc
```
```EigVal4 =

1.0e+02 *

5.0013 + 0.0000i
0.0920 + 0.0148i
0.0920 - 0.0148i
0.0935 + 0.0000i
0.0730 + 0.0548i
0.0730 - 0.0548i
0.0786 + 0.0463i
0.0786 - 0.0463i
0.0813 + 0.0393i
0.0813 - 0.0393i
0.0892 + 0.0000i
0.0678 + 0.0598i
0.0678 - 0.0598i
0.0483 + 0.0785i
0.0483 - 0.0785i
0.0854 + 0.0247i
0.0854 - 0.0247i
0.0747 + 0.0480i
0.0747 - 0.0480i
0.0670 + 0.0581i
0.0670 - 0.0581i
0.0610 + 0.0642i
0.0610 - 0.0642i
0.0520 + 0.0722i
0.0520 - 0.0722i
0.0485 + 0.0747i
0.0485 - 0.0747i
0.0725 + 0.0480i
0.0725 - 0.0480i
0.0557 + 0.0672i
0.0557 - 0.0672i
0.0418 + 0.0784i
0.0418 - 0.0784i
0.0334 + 0.0825i
0.0334 - 0.0825i
0.0214 + 0.0870i
0.0214 - 0.0870i
0.0301 + 0.0829i
0.0301 - 0.0829i
-0.0050 + 0.0906i
-0.0050 - 0.0906i
-0.0430 + 0.0817i
-0.0430 - 0.0817i
-0.0340 + 0.0852i
-0.0340 - 0.0852i
0.0086 + 0.0880i
0.0086 - 0.0880i
-0.0301 + 0.0860i
-0.0301 - 0.0860i
-0.0914 + 0.0118i
-0.0914 - 0.0118i
-0.0472 + 0.0774i
-0.0472 - 0.0774i
-0.0646 + 0.0637i
-0.0646 - 0.0637i
-0.0906 + 0.0040i
-0.0906 - 0.0040i
-0.0896 + 0.0000i
-0.0859 + 0.0293i
-0.0859 - 0.0293i
-0.0702 + 0.0570i
-0.0702 - 0.0570i
-0.0498 + 0.0744i
-0.0498 - 0.0744i
-0.0129 + 0.0879i
-0.0129 - 0.0879i
-0.0832 + 0.0346i
-0.0832 - 0.0346i
-0.0772 + 0.0449i
-0.0772 - 0.0449i
-0.0195 + 0.0866i
-0.0195 - 0.0866i
-0.0588 + 0.0657i
-0.0588 - 0.0657i
-0.0806 + 0.0370i
-0.0806 - 0.0370i
-0.0723 + 0.0500i
-0.0723 - 0.0500i
-0.0659 + 0.0570i
-0.0659 - 0.0570i
-0.0425 + 0.0765i
-0.0425 - 0.0765i
-0.0353 + 0.0805i
-0.0353 - 0.0805i
-0.0612 + 0.0611i
-0.0612 - 0.0611i
0.0854 + 0.0201i
0.0854 - 0.0201i
0.0869 + 0.0000i
0.0854 + 0.0111i
0.0854 - 0.0111i
0.0600 + 0.0600i
0.0600 - 0.0600i
0.0502 + 0.0694i
0.0502 - 0.0694i
0.0390 + 0.0776i
0.0390 - 0.0776i
0.0145 + 0.0860i
0.0145 - 0.0860i
-0.0203 + 0.0851i
-0.0203 - 0.0851i
0.0291 + 0.0821i
0.0291 - 0.0821i
-0.0884 + 0.0059i
-0.0884 - 0.0059i
-0.0461 + 0.0721i
-0.0461 - 0.0721i
-0.0717 + 0.0477i
-0.0717 - 0.0477i
-0.0841 + 0.0240i
-0.0841 - 0.0240i
-0.0672 + 0.0531i
-0.0672 - 0.0531i
0.0775 + 0.0354i
0.0775 - 0.0354i
-0.0774 + 0.0378i
-0.0774 - 0.0378i
0.0808 + 0.0263i
0.0808 - 0.0263i
0.0655 + 0.0522i
0.0655 - 0.0522i
0.0602 + 0.0574i
0.0602 - 0.0574i
-0.0582 + 0.0606i
-0.0582 - 0.0606i
-0.0010 + 0.0856i
-0.0010 - 0.0856i
0.0092 + 0.0851i
0.0092 - 0.0851i
-0.0842 + 0.0176i
-0.0842 - 0.0176i
-0.0819 + 0.0262i
-0.0819 - 0.0262i
-0.0252 + 0.0813i
-0.0252 - 0.0813i
-0.0168 + 0.0838i
-0.0168 - 0.0838i
0.0674 + 0.0488i
0.0674 - 0.0488i
0.0833 + 0.0130i
0.0833 - 0.0130i
0.0025 + 0.0848i
0.0025 - 0.0848i
-0.0488 + 0.0670i
-0.0488 - 0.0670i
0.0788 + 0.0296i
0.0788 - 0.0296i
0.0759 + 0.0352i
0.0759 - 0.0352i
0.0811 + 0.0218i
0.0811 - 0.0218i
0.0411 + 0.0718i
0.0411 - 0.0718i
0.0518 + 0.0637i
0.0518 - 0.0637i
-0.0028 + 0.0841i
-0.0028 - 0.0841i
0.0831 + 0.0052i
0.0831 - 0.0052i
0.0448 + 0.0686i
0.0448 - 0.0686i
0.0532 + 0.0618i
0.0532 - 0.0618i
0.0596 + 0.0543i
0.0596 - 0.0543i
-0.0767 + 0.0324i
-0.0767 - 0.0324i
-0.0689 + 0.0455i
-0.0689 - 0.0455i
-0.0642 + 0.0504i
-0.0642 - 0.0504i
-0.0457 + 0.0675i
-0.0457 - 0.0675i
-0.0305 + 0.0773i
-0.0305 - 0.0773i
0.0214 + 0.0808i
0.0214 - 0.0808i
-0.0082 + 0.0825i
-0.0082 - 0.0825i
0.0709 + 0.0399i
0.0709 - 0.0399i
0.0695 + 0.0424i
0.0695 - 0.0424i
0.0805 + 0.0175i
0.0805 - 0.0175i
-0.0839 + 0.0000i
-0.0831 + 0.0106i
-0.0831 - 0.0106i
-0.0647 + 0.0478i
-0.0647 - 0.0478i
-0.0599 + 0.0527i
-0.0599 - 0.0527i
-0.0413 + 0.0703i
-0.0413 - 0.0703i
-0.0464 + 0.0651i
-0.0464 - 0.0651i
-0.0007 + 0.0826i
-0.0007 - 0.0826i
0.0264 + 0.0780i
0.0264 - 0.0780i
0.0391 + 0.0707i
0.0391 - 0.0707i
-0.0506 + 0.0607i
-0.0506 - 0.0607i
0.0181 + 0.0802i
0.0181 - 0.0802i
0.0818 + 0.0026i
0.0818 - 0.0026i
0.0525 + 0.0593i
0.0525 - 0.0593i
0.0604 + 0.0504i
0.0604 - 0.0504i
0.0061 + 0.0819i
0.0061 - 0.0819i
-0.0787 + 0.0227i
-0.0787 - 0.0227i
-0.0810 + 0.0000i
-0.0232 + 0.0785i
-0.0232 - 0.0785i
-0.0489 + 0.0617i
-0.0489 - 0.0617i
0.0602 + 0.0495i
0.0602 - 0.0495i
-0.0820 + 0.0041i
-0.0820 - 0.0041i
-0.0574 + 0.0526i
-0.0574 - 0.0526i
0.0780 + 0.0193i
0.0780 - 0.0193i
0.0766 + 0.0244i
0.0766 - 0.0244i
0.0657 + 0.0427i
0.0657 - 0.0427i
0.0742 + 0.0284i
0.0742 - 0.0284i
0.0184 + 0.0788i
0.0184 - 0.0788i
0.0297 + 0.0741i
0.0297 - 0.0741i
0.0440 + 0.0643i
0.0440 - 0.0643i
-0.0141 + 0.0797i
-0.0141 - 0.0797i
-0.0349 + 0.0720i
-0.0349 - 0.0720i
-0.0197 + 0.0781i
-0.0197 - 0.0781i
-0.0379 + 0.0697i
-0.0379 - 0.0697i
-0.0032 + 0.0800i
-0.0032 - 0.0800i
-0.0688 + 0.0392i
-0.0688 - 0.0392i
-0.0791 + 0.0157i
-0.0791 - 0.0157i
-0.0537 + 0.0550i
-0.0537 - 0.0550i
-0.0747 + 0.0268i
-0.0747 - 0.0268i
-0.0653 + 0.0424i
-0.0653 - 0.0424i
-0.0705 + 0.0350i
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-0.0767 + 0.0215i
-0.0767 - 0.0215i
-0.0670 + 0.0382i
-0.0670 - 0.0382i
-0.0785 + 0.0137i
-0.0785 - 0.0137i
-0.0708 + 0.0330i
-0.0708 - 0.0330i
0.0780 + 0.0127i
0.0780 - 0.0127i
0.0724 + 0.0315i
0.0724 - 0.0315i
-0.0074 + 0.0793i
-0.0074 - 0.0793i
0.0169 + 0.0774i
0.0169 - 0.0774i
0.0288 + 0.0735i
0.0288 - 0.0735i
0.0409 + 0.0644i
0.0409 - 0.0644i
0.0610 + 0.0450i
0.0610 - 0.0450i
0.0553 + 0.0514i
0.0553 - 0.0514i
0.0701 + 0.0343i
0.0701 - 0.0343i
-0.0494 + 0.0559i
-0.0494 - 0.0559i
-0.0722 + 0.0283i
-0.0722 - 0.0283i
0.0077 + 0.0781i
0.0077 - 0.0781i
0.0365 + 0.0683i
0.0365 - 0.0683i
0.0770 + 0.0033i
0.0770 - 0.0033i
-0.0009 + 0.0778i
-0.0009 - 0.0778i
0.0759 + 0.0128i
0.0759 - 0.0128i
-0.0276 + 0.0726i
-0.0276 - 0.0726i
-0.0130 + 0.0762i
-0.0130 - 0.0762i
-0.0614 + 0.0437i
-0.0614 - 0.0437i
-0.0782 + 0.0008i
-0.0782 - 0.0008i
0.0720 + 0.0257i
0.0720 - 0.0257i
-0.0291 + 0.0703i
-0.0291 - 0.0703i
0.0447 + 0.0593i
0.0447 - 0.0593i
-0.0441 + 0.0599i
-0.0441 - 0.0599i
0.0293 + 0.0701i
0.0293 - 0.0701i
-0.0748 + 0.0159i
-0.0748 - 0.0159i
-0.0249 + 0.0720i
-0.0249 - 0.0720i
-0.0756 + 0.0105i
-0.0756 - 0.0105i
0.0143 + 0.0749i
0.0143 - 0.0749i
0.0652 + 0.0358i
0.0652 - 0.0358i
0.0749 + 0.0111i
0.0749 - 0.0111i
-0.0361 + 0.0642i
-0.0361 - 0.0642i
-0.0208 + 0.0730i
-0.0208 - 0.0730i
0.0208 + 0.0726i
0.0208 - 0.0726i
-0.0159 + 0.0742i
-0.0159 - 0.0742i
-0.0491 + 0.0525i
-0.0491 - 0.0525i
0.0518 + 0.0502i
0.0518 - 0.0502i
0.0119 + 0.0742i
0.0119 - 0.0742i
0.0670 + 0.0302i
0.0670 - 0.0302i
0.0686 + 0.0257i
0.0686 - 0.0257i
-0.0302 + 0.0673i
-0.0302 - 0.0673i
0.0015 + 0.0742i
0.0015 - 0.0742i
-0.0713 + 0.0200i
-0.0713 - 0.0200i
0.0649 + 0.0331i
0.0649 - 0.0331i
-0.0362 + 0.0630i
-0.0362 - 0.0630i
0.0462 + 0.0542i
0.0462 - 0.0542i
-0.0713 + 0.0156i
-0.0713 - 0.0156i
-0.0645 + 0.0308i
-0.0645 - 0.0308i
-0.0725 + 0.0040i
-0.0725 - 0.0040i
0.0258 + 0.0690i
0.0258 - 0.0690i
0.0351 + 0.0637i
0.0351 - 0.0637i
-0.0524 + 0.0470i
-0.0524 - 0.0470i
-0.0546 + 0.0440i
-0.0546 - 0.0440i
0.0297 + 0.0657i
0.0297 - 0.0657i
0.0530 + 0.0468i
0.0530 - 0.0468i
-0.0276 + 0.0657i
-0.0276 - 0.0657i
-0.0203 + 0.0684i
-0.0203 - 0.0684i
0.0497 + 0.0494i
0.0497 - 0.0494i
0.0459 + 0.0530i
0.0459 - 0.0530i
0.0211 + 0.0686i
0.0211 - 0.0686i
0.0709 + 0.0098i
0.0709 - 0.0098i
-0.0087 + 0.0709i
-0.0087 - 0.0709i
0.0074 + 0.0708i
0.0074 - 0.0708i
-0.0350 + 0.0611i
-0.0350 - 0.0611i
0.0389 + 0.0580i
0.0389 - 0.0580i
0.0323 + 0.0624i
0.0323 - 0.0624i
0.0718 + 0.0053i
0.0718 - 0.0053i
-0.0709 + 0.0000i
-0.0647 + 0.0278i
-0.0647 - 0.0278i
-0.0603 + 0.0345i
-0.0603 - 0.0345i
-0.0415 + 0.0551i
-0.0415 - 0.0551i
-0.0491 + 0.0470i
-0.0491 - 0.0470i
-0.0561 + 0.0392i
-0.0561 - 0.0392i
-0.0538 + 0.0419i
-0.0538 - 0.0419i
0.0030 + 0.0707i
0.0030 - 0.0707i
0.0135 + 0.0692i
0.0135 - 0.0692i
0.0565 + 0.0379i
0.0565 - 0.0379i
0.0706 + 0.0061i
0.0706 - 0.0061i
0.0679 + 0.0199i
0.0679 - 0.0199i
-0.0659 + 0.0216i
-0.0659 - 0.0216i
-0.0007 + 0.0698i
-0.0007 - 0.0698i
0.0663 + 0.0203i
0.0663 - 0.0203i
0.0356 + 0.0582i
0.0356 - 0.0582i
0.0672 + 0.0153i
0.0672 - 0.0153i
0.0585 + 0.0349i
0.0585 - 0.0349i
0.0229 + 0.0649i
0.0229 - 0.0649i
-0.0667 + 0.0154i
-0.0667 - 0.0154i
0.0541 + 0.0389i
0.0541 - 0.0389i
-0.0676 + 0.0000i
-0.0360 + 0.0564i
-0.0360 - 0.0564i
-0.0443 + 0.0495i
-0.0443 - 0.0495i
-0.0562 + 0.0359i
-0.0562 - 0.0359i
-0.0595 + 0.0309i
-0.0595 - 0.0309i
-0.0628 + 0.0232i
-0.0628 - 0.0232i
0.0666 + 0.0047i
0.0666 - 0.0047i
0.0193 + 0.0645i
0.0193 - 0.0645i
0.0353 + 0.0550i
0.0353 - 0.0550i
-0.0126 + 0.0674i
-0.0126 - 0.0674i
0.0576 + 0.0311i
0.0576 - 0.0311i
-0.0063 + 0.0671i
-0.0063 - 0.0671i
-0.0308 + 0.0588i
-0.0308 - 0.0588i
-0.0406 + 0.0504i
-0.0406 - 0.0504i
-0.0120 + 0.0660i
-0.0120 - 0.0660i
-0.0590 + 0.0285i
-0.0590 - 0.0285i
-0.0238 + 0.0618i
-0.0238 - 0.0618i
-0.0213 + 0.0628i
-0.0213 - 0.0628i
-0.0172 + 0.0640i
-0.0172 - 0.0640i
0.0468 + 0.0438i
0.0468 - 0.0438i
0.0150 + 0.0650i
0.0150 - 0.0650i
-0.0666 + 0.0051i
-0.0666 - 0.0051i
0.0244 + 0.0616i
0.0244 - 0.0616i
-0.0367 + 0.0519i
-0.0367 - 0.0519i
-0.0444 + 0.0453i
-0.0444 - 0.0453i
-0.0660 + 0.0070i
-0.0660 - 0.0070i
-0.0654 + 0.0099i
-0.0654 - 0.0099i
0.0392 + 0.0493i
0.0392 - 0.0493i
0.0628 + 0.0178i
0.0628 - 0.0178i
0.0516 + 0.0357i
0.0516 - 0.0357i
0.0610 + 0.0219i
0.0610 - 0.0219i
-0.0036 + 0.0653i
-0.0036 - 0.0653i
0.0021 + 0.0651i
0.0021 - 0.0651i
-0.0624 + 0.0146i
-0.0624 - 0.0146i
0.0275 + 0.0581i
0.0275 - 0.0581i
0.0583 + 0.0256i
0.0583 - 0.0256i
0.0051 + 0.0645i
0.0051 - 0.0645i
0.0645 + 0.0072i
0.0645 - 0.0072i
0.0532 + 0.0341i
0.0532 - 0.0341i
-0.0531 + 0.0326i
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-0.0167 + 0.0612i
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0.0079 + 0.0629i
0.0079 - 0.0629i
-0.0009 + 0.0634i
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-0.0497 + 0.0353i
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-0.0467 + 0.0389i
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-0.0257 + 0.0556i
-0.0257 - 0.0556i
0.0632 + 0.0035i
0.0632 - 0.0035i
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0.0613 + 0.0124i
0.0613 - 0.0124i
-0.0350 + 0.0488i
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0.0452 + 0.0398i
0.0452 - 0.0398i
0.0350 + 0.0492i
0.0350 - 0.0492i
0.0371 + 0.0473i
0.0371 - 0.0473i
0.0268 + 0.0549i
0.0268 - 0.0549i
-0.0319 + 0.0507i
-0.0319 - 0.0507i
-0.0375 + 0.0462i
-0.0375 - 0.0462i
-0.0591 + 0.0145i
-0.0591 - 0.0145i
0.0234 + 0.0564i
0.0234 - 0.0564i
0.0474 + 0.0353i
0.0474 - 0.0353i
0.0416 + 0.0408i
0.0416 - 0.0408i
-0.0387 + 0.0441i
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-0.0068 + 0.0605i
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-0.0603 + 0.0058i
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0.0347 + 0.0471i
0.0347 - 0.0471i
0.0552 + 0.0239i
0.0552 - 0.0239i
0.0400 + 0.0416i
0.0400 - 0.0416i
0.0607 + 0.0000i
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0.0182 + 0.0566i
0.0182 - 0.0566i
0.0597 + 0.0071i
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-0.0593 + 0.0000i
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0.0125 + 0.0574i
0.0125 - 0.0574i
-0.0527 + 0.0210i
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-0.0035 + 0.0587i
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-0.0452 + 0.0336i
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0.0574 + 0.0139i
0.0574 - 0.0139i
-0.0214 + 0.0529i
-0.0214 - 0.0529i
-0.0399 + 0.0384i
-0.0399 - 0.0384i
0.0071 + 0.0576i
0.0071 - 0.0576i
0.0556 + 0.0178i
0.0556 - 0.0178i
-0.0574 + 0.0000i
0.0475 + 0.0302i
0.0475 - 0.0302i
0.0236 + 0.0519i
0.0236 - 0.0519i
-0.0223 + 0.0506i
-0.0223 - 0.0506i
-0.0140 + 0.0539i
-0.0140 - 0.0539i
0.0179 + 0.0539i
0.0179 - 0.0539i
0.0506 + 0.0247i
0.0506 - 0.0247i
-0.0021 + 0.0564i
-0.0021 - 0.0564i
0.0539 + 0.0181i
0.0539 - 0.0181i
-0.0541 + 0.0131i
-0.0541 - 0.0131i
0.0263 + 0.0485i
0.0263 - 0.0485i
0.0302 + 0.0449i
0.0302 - 0.0449i
0.0562 + 0.0000i
0.0410 + 0.0347i
0.0410 - 0.0347i
-0.0111 + 0.0533i
-0.0111 - 0.0533i
-0.0379 + 0.0374i
-0.0379 - 0.0374i
0.0026 + 0.0546i
0.0026 - 0.0546i
-0.0473 + 0.0252i
-0.0473 - 0.0252i
-0.0501 + 0.0191i
-0.0501 - 0.0191i
0.0538 + 0.0000i
0.0423 + 0.0305i
0.0423 - 0.0305i
0.0131 + 0.0530i
0.0131 - 0.0530i
-0.0553 + 0.0026i
-0.0553 - 0.0026i
-0.0219 + 0.0488i
-0.0219 - 0.0488i
0.0057 + 0.0535i
0.0057 - 0.0535i
-0.0229 + 0.0470i
-0.0229 - 0.0470i
-0.0385 + 0.0348i
-0.0385 - 0.0348i
-0.0408 + 0.0320i
-0.0408 - 0.0320i
-0.0275 + 0.0440i
-0.0275 - 0.0440i
0.0525 + 0.0112i
0.0525 - 0.0112i
0.0531 + 0.0068i
0.0531 - 0.0068i
-0.0336 + 0.0379i
-0.0336 - 0.0379i
0.0328 + 0.0383i
0.0328 - 0.0383i
-0.0185 + 0.0494i
-0.0185 - 0.0494i
0.0121 + 0.0517i
0.0121 - 0.0517i
0.0364 + 0.0336i
0.0364 - 0.0336i
0.0404 + 0.0286i
0.0404 - 0.0286i
-0.0042 + 0.0526i
-0.0042 - 0.0526i
-0.0520 + 0.0077i
-0.0520 - 0.0077i
-0.0104 + 0.0506i
-0.0104 - 0.0506i
-0.0083 + 0.0504i
-0.0083 - 0.0504i
0.0022 + 0.0512i
0.0022 - 0.0512i
-0.0465 + 0.0195i
-0.0465 - 0.0195i
0.0080 + 0.0507i
0.0080 - 0.0507i
0.0227 + 0.0454i
0.0227 - 0.0454i
-0.0499 + 0.0077i
-0.0499 - 0.0077i
0.0244 + 0.0441i
0.0244 - 0.0441i
-0.0405 + 0.0276i
-0.0405 - 0.0276i
-0.0292 + 0.0397i
-0.0292 - 0.0397i
0.0483 + 0.0184i
0.0483 - 0.0184i
0.0442 + 0.0246i
0.0442 - 0.0246i
-0.0192 + 0.0452i
-0.0192 - 0.0452i
0.0165 + 0.0465i
0.0165 - 0.0465i
-0.0411 + 0.0244i
-0.0411 - 0.0244i
0.0476 + 0.0153i
0.0476 - 0.0153i
0.0461 + 0.0181i
0.0461 - 0.0181i
0.0497 + 0.0051i
0.0497 - 0.0051i
-0.0309 + 0.0356i
-0.0309 - 0.0356i
-0.0253 + 0.0401i
-0.0253 - 0.0401i
0.0375 + 0.0291i
0.0375 - 0.0291i
0.0407 + 0.0241i
0.0407 - 0.0241i
0.0346 + 0.0310i
0.0346 - 0.0310i
-0.0227 + 0.0403i
-0.0227 - 0.0403i
0.0310 + 0.0336i
0.0310 - 0.0336i
-0.0484 + 0.0000i
0.0322 + 0.0317i
0.0322 - 0.0317i
-0.0466 + 0.0132i
-0.0466 - 0.0132i
-0.0376 + 0.0253i
-0.0376 - 0.0253i
0.0182 + 0.0431i
0.0182 - 0.0431i
0.0148 + 0.0443i
0.0148 - 0.0443i
0.0470 + 0.0037i
0.0470 - 0.0037i
-0.0471 + 0.0072i
-0.0471 - 0.0072i
-0.0442 + 0.0153i
-0.0442 - 0.0153i
-0.0070 + 0.0457i
-0.0070 - 0.0457i
-0.0465 + 0.0029i
-0.0465 - 0.0029i
0.0067 + 0.0458i
0.0067 - 0.0458i
-0.0275 + 0.0351i
-0.0275 - 0.0351i
0.0011 + 0.0450i
0.0011 - 0.0450i
-0.0140 + 0.0421i
-0.0140 - 0.0421i
0.0250 + 0.0372i
0.0250 - 0.0372i
0.0449 + 0.0115i
0.0449 - 0.0115i
-0.0110 + 0.0427i
-0.0110 - 0.0427i
-0.0339 + 0.0275i
-0.0339 - 0.0275i
0.0412 + 0.0168i
0.0412 - 0.0168i
0.0196 + 0.0391i
0.0196 - 0.0391i
0.0436 + 0.0105i
0.0436 - 0.0105i
0.0448 + 0.0058i
0.0448 - 0.0058i
-0.0415 + 0.0140i
-0.0415 - 0.0140i
-0.0217 + 0.0361i
-0.0217 - 0.0361i
0.0045 + 0.0422i
0.0045 - 0.0422i
-0.0432 + 0.0000i
0.0445 + 0.0019i
0.0445 - 0.0019i
0.0211 + 0.0358i
0.0211 - 0.0358i
0.0359 + 0.0192i
0.0359 - 0.0192i
-0.0291 + 0.0286i
-0.0291 - 0.0286i
-0.0378 + 0.0172i
-0.0378 - 0.0172i
0.0274 + 0.0296i
0.0274 - 0.0296i
0.0239 + 0.0322i
0.0239 - 0.0322i
-0.0023 + 0.0419i
-0.0023 - 0.0419i
-0.0360 + 0.0194i
-0.0360 - 0.0194i
0.0373 + 0.0153i
0.0373 - 0.0153i
-0.0093 + 0.0400i
-0.0093 - 0.0400i
0.0316 + 0.0217i
0.0316 - 0.0217i
-0.0418 + 0.0000i
0.0396 + 0.0094i
0.0396 - 0.0094i
0.0137 + 0.0369i
0.0137 - 0.0369i
-0.0322 + 0.0204i
-0.0322 - 0.0204i
0.0286 + 0.0241i
0.0286 - 0.0241i
-0.0135 + 0.0368i
-0.0135 - 0.0368i
-0.0012 + 0.0396i
-0.0012 - 0.0396i
-0.0236 + 0.0275i
-0.0236 - 0.0275i
-0.0394 + 0.0061i
-0.0394 - 0.0061i
0.0391 + 0.0042i
0.0391 - 0.0042i
0.0082 + 0.0376i
0.0082 - 0.0376i
0.0187 + 0.0307i
0.0187 - 0.0307i
0.0273 + 0.0229i
0.0273 - 0.0229i
0.0236 + 0.0260i
0.0236 - 0.0260i
0.0335 + 0.0088i
0.0335 - 0.0088i
0.0035 + 0.0363i
0.0035 - 0.0363i
0.0103 + 0.0339i
0.0103 - 0.0339i
0.0310 + 0.0131i
0.0310 - 0.0131i
-0.0129 + 0.0341i
-0.0129 - 0.0341i
-0.0180 + 0.0309i
-0.0180 - 0.0309i
-0.0357 + 0.0115i
-0.0357 - 0.0115i
-0.0028 + 0.0346i
-0.0028 - 0.0346i
-0.0338 + 0.0143i
-0.0338 - 0.0143i
-0.0276 + 0.0222i
-0.0276 - 0.0222i
-0.0097 + 0.0324i
-0.0097 - 0.0324i
-0.0352 + 0.0080i
-0.0352 - 0.0080i
-0.0185 + 0.0268i
-0.0185 - 0.0268i
-0.0348 + 0.0026i
-0.0348 - 0.0026i
-0.0141 + 0.0287i
-0.0141 - 0.0287i
-0.0285 + 0.0155i
-0.0285 - 0.0155i
-0.0222 + 0.0221i
-0.0222 - 0.0221i
-0.0334 + 0.0010i
-0.0334 - 0.0010i
0.0032 + 0.0323i
0.0032 - 0.0323i
0.0337 + 0.0034i
0.0337 - 0.0034i
0.0145 + 0.0273i
0.0145 - 0.0273i
0.0264 + 0.0159i
0.0264 - 0.0159i
0.0077 + 0.0287i
0.0077 - 0.0287i
-0.0042 + 0.0302i
-0.0042 - 0.0302i
-0.0096 + 0.0277i
-0.0096 - 0.0277i
-0.0246 + 0.0154i
-0.0246 - 0.0154i
-0.0310 + 0.0029i
-0.0310 - 0.0029i
-0.0208 + 0.0195i
-0.0208 - 0.0195i
-0.0176 + 0.0227i
-0.0176 - 0.0227i
-0.0297 + 0.0052i
-0.0297 - 0.0052i
0.0136 + 0.0258i
0.0136 - 0.0258i
0.0236 + 0.0167i
0.0236 - 0.0167i
0.0285 + 0.0089i
0.0285 - 0.0089i
-0.0001 + 0.0292i
-0.0001 - 0.0292i
0.0181 + 0.0204i
0.0181 - 0.0204i
0.0292 + 0.0000i
-0.0119 + 0.0241i
-0.0119 - 0.0241i
-0.0204 + 0.0145i
-0.0204 - 0.0145i
0.0197 + 0.0153i
0.0197 - 0.0153i
0.0258 + 0.0084i
0.0258 - 0.0084i
-0.0029 + 0.0268i
-0.0029 - 0.0268i
0.0289 + 0.0000i
-0.0256 + 0.0059i
-0.0256 - 0.0059i
0.0273 + 0.0020i
0.0273 - 0.0020i
0.0096 + 0.0239i
0.0096 - 0.0239i
-0.0244 + 0.0000i
-0.0237 + 0.0061i
-0.0237 - 0.0061i
0.0173 + 0.0169i
0.0173 - 0.0169i
-0.0234 + 0.0000i
-0.0190 + 0.0119i
-0.0190 - 0.0119i
-0.0113 + 0.0196i
-0.0113 - 0.0196i
-0.0010 + 0.0231i
-0.0010 - 0.0231i
0.0065 + 0.0230i
0.0065 - 0.0230i
0.0206 + 0.0102i
0.0206 - 0.0102i
-0.0049 + 0.0216i
-0.0049 - 0.0216i
-0.0135 + 0.0162i
-0.0135 - 0.0162i
0.0070 + 0.0212i
0.0070 - 0.0212i
0.0113 + 0.0184i
0.0113 - 0.0184i
0.0076 + 0.0205i
0.0076 - 0.0205i
0.0216 + 0.0058i
0.0216 - 0.0058i
-0.0182 + 0.0076i
-0.0182 - 0.0076i
-0.0102 + 0.0155i
-0.0102 - 0.0155i
0.0182 + 0.0074i
0.0182 - 0.0074i
-0.0017 + 0.0170i
-0.0017 - 0.0170i
0.0213 + 0.0000i
0.0194 + 0.0000i
0.0178 + 0.0000i
-0.0131 + 0.0086i
-0.0131 - 0.0086i
-0.0104 + 0.0103i
-0.0104 - 0.0103i
0.0064 + 0.0139i
0.0064 - 0.0139i
0.0086 + 0.0132i
0.0086 - 0.0132i
-0.0138 + 0.0034i
-0.0138 - 0.0034i
-0.0011 + 0.0140i
-0.0011 - 0.0140i
0.0114 + 0.0075i
0.0114 - 0.0075i
-0.0087 + 0.0084i
-0.0087 - 0.0084i
0.0105 + 0.0016i
0.0105 - 0.0016i
-0.0128 + 0.0008i
-0.0128 - 0.0008i
0.0097 + 0.0085i
0.0097 - 0.0085i
-0.0032 + 0.0092i
-0.0032 - 0.0092i
0.0035 + 0.0086i
0.0035 - 0.0086i
0.0090 + 0.0040i
0.0090 - 0.0040i
0.0001 + 0.0085i
0.0001 - 0.0085i
-0.0078 + 0.0015i
-0.0078 - 0.0015i
0.0065 + 0.0000i
-0.0043 + 0.0000i
-0.0004 + 0.0000i
0.0010 + 0.0000i

Elapsed time is 0.845069 seconds.
Elapsed time is 1.303864 seconds.
```

If the matrix you are considering is very large, you may not want all of the eigenvalues, in this case you can use:

```tic
EigVal6=eigs(A);
toc
```
```Elapsed time is 1.893703 seconds.
```

This returns the largest (in magnitude) six eigenvalues of the matrix. The function works the same as the previous one to calculate eigenvectors.

```tic
[EigVec7,EigVal7]=eigs(A)
toc
```
```EigVec7 =

Columns 1 through 4

0.0328 + 0.0000i   0.0276 + 0.0000i  -0.0043 + 0.0225i  -0.0043 - 0.0225i
0.0315 + 0.0000i  -0.0363 + 0.0000i  -0.0451 - 0.0011i  -0.0451 + 0.0011i
0.0329 + 0.0000i  -0.0009 + 0.0000i   0.0071 + 0.0204i   0.0071 - 0.0204i
0.0298 + 0.0000i   0.0055 + 0.0000i  -0.0104 - 0.0227i  -0.0104 + 0.0227i
0.0306 + 0.0000i  -0.0317 + 0.0000i   0.0014 + 0.0340i   0.0014 - 0.0340i
0.0311 + 0.0000i   0.0049 + 0.0000i   0.0071 - 0.0165i   0.0071 + 0.0165i
0.0309 + 0.0000i   0.0796 + 0.0000i   0.0025 - 0.0272i   0.0025 + 0.0272i
0.0321 + 0.0000i  -0.0498 + 0.0000i   0.0381 - 0.0321i   0.0381 + 0.0321i
0.0315 + 0.0000i  -0.0527 + 0.0000i   0.0156 + 0.0025i   0.0156 - 0.0025i
0.0312 + 0.0000i   0.0053 + 0.0000i  -0.0098 + 0.0099i  -0.0098 - 0.0099i
0.0314 + 0.0000i   0.0302 + 0.0000i   0.0427 + 0.0158i   0.0427 - 0.0158i
0.0325 + 0.0000i   0.0309 + 0.0000i   0.0529 + 0.0079i   0.0529 - 0.0079i
0.0319 + 0.0000i   0.0207 + 0.0000i   0.0546 - 0.0217i   0.0546 + 0.0217i
0.0309 + 0.0000i   0.0538 + 0.0000i   0.0053 - 0.0180i   0.0053 + 0.0180i
0.0316 + 0.0000i   0.0096 + 0.0000i  -0.0104 - 0.0117i  -0.0104 + 0.0117i
0.0317 + 0.0000i   0.0001 + 0.0000i   0.0231 + 0.0236i   0.0231 - 0.0236i
0.0318 + 0.0000i  -0.0269 + 0.0000i   0.0091 + 0.0104i   0.0091 - 0.0104i
0.0316 + 0.0000i  -0.0045 + 0.0000i   0.0342 + 0.0007i   0.0342 - 0.0007i
0.0311 + 0.0000i   0.0360 + 0.0000i   0.0524 - 0.0087i   0.0524 + 0.0087i
0.0319 + 0.0000i   0.0312 + 0.0000i   0.0027 + 0.0155i   0.0027 - 0.0155i
0.0318 + 0.0000i  -0.0289 + 0.0000i   0.0020 + 0.0219i   0.0020 - 0.0219i
0.0315 + 0.0000i  -0.0443 + 0.0000i  -0.0338 - 0.0192i  -0.0338 + 0.0192i
0.0332 + 0.0000i   0.0235 + 0.0000i   0.0167 - 0.0124i   0.0167 + 0.0124i
0.0315 + 0.0000i   0.0027 + 0.0000i   0.0243 + 0.0013i   0.0243 - 0.0013i
0.0319 + 0.0000i   0.0175 + 0.0000i  -0.0046 - 0.0309i  -0.0046 + 0.0309i
0.0317 + 0.0000i   0.0557 + 0.0000i  -0.0098 - 0.0014i  -0.0098 + 0.0014i
0.0313 + 0.0000i   0.0212 + 0.0000i  -0.0223 + 0.0191i  -0.0223 - 0.0191i
0.0323 + 0.0000i   0.0356 + 0.0000i  -0.0118 - 0.0105i  -0.0118 + 0.0105i
0.0314 + 0.0000i  -0.0577 + 0.0000i   0.0779 - 0.0041i   0.0779 + 0.0041i
0.0307 + 0.0000i   0.0030 + 0.0000i  -0.0063 - 0.0134i  -0.0063 + 0.0134i
0.0319 + 0.0000i  -0.0039 + 0.0000i  -0.0058 + 0.0129i  -0.0058 - 0.0129i
0.0312 + 0.0000i   0.0347 + 0.0000i  -0.0366 - 0.0442i  -0.0366 + 0.0442i
0.0325 + 0.0000i  -0.0011 + 0.0000i  -0.0280 + 0.0200i  -0.0280 - 0.0200i
0.0312 + 0.0000i  -0.0077 + 0.0000i  -0.0296 - 0.0096i  -0.0296 + 0.0096i
0.0324 + 0.0000i  -0.0425 + 0.0000i  -0.0147 + 0.0382i  -0.0147 - 0.0382i
0.0312 + 0.0000i  -0.0644 + 0.0000i  -0.0261 + 0.0429i  -0.0261 - 0.0429i
0.0312 + 0.0000i   0.0083 + 0.0000i  -0.0057 + 0.0083i  -0.0057 - 0.0083i
0.0319 + 0.0000i   0.0254 + 0.0000i  -0.0134 + 0.0169i  -0.0134 - 0.0169i
0.0314 + 0.0000i   0.0141 + 0.0000i   0.0157 + 0.0252i   0.0157 - 0.0252i
0.0313 + 0.0000i  -0.0214 + 0.0000i   0.0289 - 0.0186i   0.0289 + 0.0186i
0.0307 + 0.0000i  -0.0192 + 0.0000i   0.0094 - 0.0106i   0.0094 + 0.0106i
0.0315 + 0.0000i  -0.0183 + 0.0000i  -0.0162 - 0.0007i  -0.0162 + 0.0007i
0.0326 + 0.0000i  -0.0429 + 0.0000i  -0.0035 - 0.0382i  -0.0035 + 0.0382i
0.0316 + 0.0000i  -0.0508 + 0.0000i   0.0035 + 0.0257i   0.0035 - 0.0257i
0.0309 + 0.0000i   0.0179 + 0.0000i  -0.0078 - 0.0206i  -0.0078 + 0.0206i
0.0319 + 0.0000i   0.0413 + 0.0000i  -0.0022 - 0.0098i  -0.0022 + 0.0098i
0.0310 + 0.0000i  -0.0099 + 0.0000i   0.0210 - 0.0181i   0.0210 + 0.0181i
0.0322 + 0.0000i  -0.0416 + 0.0000i  -0.0270 + 0.0044i  -0.0270 - 0.0044i
0.0315 + 0.0000i  -0.0040 + 0.0000i   0.0018 + 0.0160i   0.0018 - 0.0160i
0.0311 + 0.0000i  -0.0296 + 0.0000i   0.0044 + 0.0024i   0.0044 - 0.0024i
0.0321 + 0.0000i   0.0047 + 0.0000i  -0.0127 + 0.0039i  -0.0127 - 0.0039i
0.0312 + 0.0000i  -0.0428 + 0.0000i  -0.0202 - 0.0059i  -0.0202 + 0.0059i
0.0312 + 0.0000i  -0.0040 + 0.0000i   0.0006 + 0.0437i   0.0006 - 0.0437i
0.0309 + 0.0000i   0.0312 + 0.0000i  -0.0003 + 0.0203i  -0.0003 - 0.0203i
0.0306 + 0.0000i  -0.0211 + 0.0000i   0.0126 + 0.0121i   0.0126 - 0.0121i
0.0321 + 0.0000i  -0.0214 + 0.0000i   0.0225 - 0.0362i   0.0225 + 0.0362i
0.0306 + 0.0000i  -0.0217 + 0.0000i  -0.0557 + 0.0049i  -0.0557 - 0.0049i
0.0313 + 0.0000i  -0.0271 + 0.0000i  -0.0236 - 0.0119i  -0.0236 + 0.0119i
0.0325 + 0.0000i   0.0188 + 0.0000i   0.0378 - 0.0000i   0.0378 + 0.0000i
0.0318 + 0.0000i  -0.0026 + 0.0000i   0.0120 + 0.0013i   0.0120 - 0.0013i
0.0313 + 0.0000i   0.0094 + 0.0000i   0.0259 + 0.0064i   0.0259 - 0.0064i
0.0315 + 0.0000i  -0.0323 + 0.0000i  -0.0341 + 0.0070i  -0.0341 - 0.0070i
0.0313 + 0.0000i   0.0002 + 0.0000i   0.0256 - 0.0071i   0.0256 + 0.0071i
0.0319 + 0.0000i   0.0024 + 0.0000i   0.0023 + 0.0169i   0.0023 - 0.0169i
0.0316 + 0.0000i  -0.0162 + 0.0000i  -0.0115 - 0.0009i  -0.0115 + 0.0009i
0.0316 + 0.0000i  -0.0282 + 0.0000i   0.0066 + 0.0021i   0.0066 - 0.0021i
0.0320 + 0.0000i  -0.0310 + 0.0000i   0.0030 + 0.0011i   0.0030 - 0.0011i
0.0310 + 0.0000i  -0.0273 + 0.0000i  -0.0332 + 0.0253i  -0.0332 - 0.0253i
0.0315 + 0.0000i  -0.0530 + 0.0000i  -0.0072 - 0.0147i  -0.0072 + 0.0147i
0.0319 + 0.0000i  -0.0022 + 0.0000i   0.0388 - 0.0271i   0.0388 + 0.0271i
0.0317 + 0.0000i   0.0035 + 0.0000i  -0.0209 + 0.0085i  -0.0209 - 0.0085i
0.0311 + 0.0000i   0.0482 + 0.0000i   0.0339 - 0.0113i   0.0339 + 0.0113i
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0.0309 + 0.0000i  -0.0239 + 0.0000i   0.0199 + 0.0198i   0.0199 - 0.0198i
0.0310 + 0.0000i  -0.0031 + 0.0000i  -0.0459 - 0.0114i  -0.0459 + 0.0114i
0.0320 + 0.0000i  -0.0142 + 0.0000i  -0.0160 + 0.0093i  -0.0160 - 0.0093i
0.0308 + 0.0000i   0.0561 + 0.0000i  -0.0218 + 0.0063i  -0.0218 - 0.0063i
0.0317 + 0.0000i   0.0089 + 0.0000i  -0.0045 - 0.0064i  -0.0045 + 0.0064i
0.0312 + 0.0000i   0.0023 + 0.0000i   0.0122 - 0.0058i   0.0122 + 0.0058i
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0.0321 + 0.0000i   0.0071 + 0.0000i   0.0253 - 0.0025i   0.0253 + 0.0025i
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0.0304 + 0.0000i   0.0128 + 0.0000i  -0.0077 - 0.0144i  -0.0077 + 0.0144i
0.0316 + 0.0000i   0.0253 + 0.0000i   0.0454 - 0.0219i   0.0454 + 0.0219i
0.0322 + 0.0000i   0.0325 + 0.0000i  -0.0317 - 0.0254i  -0.0317 + 0.0254i
0.0316 + 0.0000i   0.0026 + 0.0000i   0.0089 - 0.0287i   0.0089 + 0.0287i
0.0309 + 0.0000i   0.0290 + 0.0000i   0.0004 + 0.0069i   0.0004 - 0.0069i
0.0312 + 0.0000i   0.0377 + 0.0000i  -0.0136 - 0.0101i  -0.0136 + 0.0101i
0.0304 + 0.0000i  -0.0352 + 0.0000i  -0.0013 - 0.0233i  -0.0013 + 0.0233i
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0.0311 + 0.0000i   0.0371 + 0.0000i  -0.0094 - 0.0077i  -0.0094 + 0.0077i
0.0320 + 0.0000i  -0.0107 + 0.0000i   0.0117 + 0.0068i   0.0117 - 0.0068i
0.0309 + 0.0000i  -0.0481 + 0.0000i  -0.0329 - 0.0152i  -0.0329 + 0.0152i
0.0317 + 0.0000i   0.0111 + 0.0000i   0.0230 - 0.0100i   0.0230 + 0.0100i
0.0319 + 0.0000i  -0.0281 + 0.0000i   0.0366 + 0.0411i   0.0366 - 0.0411i
0.0315 + 0.0000i   0.0138 + 0.0000i   0.0369 + 0.0141i   0.0369 - 0.0141i
0.0310 + 0.0000i   0.0156 + 0.0000i  -0.0009 - 0.0112i  -0.0009 + 0.0112i
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0.0321 + 0.0000i   0.0688 + 0.0000i   0.0464 - 0.0444i   0.0464 + 0.0444i
0.0321 + 0.0000i   0.0049 + 0.0000i  -0.0416 + 0.0094i  -0.0416 - 0.0094i
0.0320 + 0.0000i  -0.0343 + 0.0000i  -0.0373 + 0.0329i  -0.0373 - 0.0329i
0.0318 + 0.0000i   0.0420 + 0.0000i  -0.0299 - 0.0129i  -0.0299 + 0.0129i
0.0322 + 0.0000i   0.0108 + 0.0000i   0.0022 - 0.0370i   0.0022 + 0.0370i
0.0311 + 0.0000i  -0.0204 + 0.0000i  -0.0721 - 0.0051i  -0.0721 + 0.0051i
0.0314 + 0.0000i  -0.0046 + 0.0000i   0.0364 - 0.0177i   0.0364 + 0.0177i
0.0318 + 0.0000i   0.0025 + 0.0000i   0.0580 + 0.0155i   0.0580 - 0.0155i
0.0318 + 0.0000i  -0.0435 + 0.0000i  -0.0216 - 0.0098i  -0.0216 + 0.0098i
0.0320 + 0.0000i  -0.0028 + 0.0000i   0.0264 + 0.0099i   0.0264 - 0.0099i
0.0315 + 0.0000i  -0.0029 + 0.0000i  -0.0038 - 0.0050i  -0.0038 + 0.0050i
0.0313 + 0.0000i   0.0009 + 0.0000i   0.0176 - 0.0005i   0.0176 + 0.0005i
0.0325 + 0.0000i   0.0079 + 0.0000i  -0.0053 - 0.0364i  -0.0053 + 0.0364i
0.0321 + 0.0000i  -0.0386 + 0.0000i   0.0105 - 0.0277i   0.0105 + 0.0277i
0.0321 + 0.0000i  -0.0036 + 0.0000i  -0.0567 + 0.0190i  -0.0567 - 0.0190i
0.0325 + 0.0000i   0.0321 + 0.0000i  -0.0388 + 0.0051i  -0.0388 - 0.0051i
0.0308 + 0.0000i   0.0038 + 0.0000i   0.0072 + 0.0038i   0.0072 - 0.0038i
0.0312 + 0.0000i   0.0231 + 0.0000i   0.0070 - 0.0064i   0.0070 + 0.0064i
0.0314 + 0.0000i  -0.0192 + 0.0000i   0.0075 + 0.0229i   0.0075 - 0.0229i
0.0313 + 0.0000i  -0.0271 + 0.0000i  -0.0162 + 0.0355i  -0.0162 - 0.0355i
0.0318 + 0.0000i  -0.0439 + 0.0000i   0.0382 - 0.0208i   0.0382 + 0.0208i
0.0317 + 0.0000i  -0.0560 + 0.0000i  -0.0620 + 0.0018i  -0.0620 - 0.0018i
0.0312 + 0.0000i   0.0235 + 0.0000i   0.0352 + 0.0084i   0.0352 - 0.0084i
0.0309 + 0.0000i   0.0095 + 0.0000i  -0.0085 + 0.0466i  -0.0085 - 0.0466i
0.0314 + 0.0000i   0.0217 + 0.0000i   0.0294 - 0.0010i   0.0294 + 0.0010i
0.0321 + 0.0000i   0.0261 + 0.0000i  -0.0038 - 0.0029i  -0.0038 + 0.0029i
0.0323 + 0.0000i  -0.0101 + 0.0000i   0.0148 - 0.0153i   0.0148 + 0.0153i
0.0319 + 0.0000i   0.0524 + 0.0000i  -0.0010 + 0.0008i  -0.0010 - 0.0008i
0.0314 + 0.0000i   0.0217 + 0.0000i   0.0615 + 0.0045i   0.0615 - 0.0045i
0.0311 + 0.0000i  -0.0347 + 0.0000i   0.0030 + 0.0154i   0.0030 - 0.0154i
0.0316 + 0.0000i   0.0071 + 0.0000i  -0.0134 - 0.0026i  -0.0134 + 0.0026i
0.0310 + 0.0000i  -0.0270 + 0.0000i   0.0231 + 0.0272i   0.0231 - 0.0272i
0.0313 + 0.0000i  -0.0566 + 0.0000i  -0.0335 - 0.0035i  -0.0335 + 0.0035i
0.0308 + 0.0000i  -0.0190 + 0.0000i   0.0042 - 0.0182i   0.0042 + 0.0182i
0.0322 + 0.0000i  -0.0269 + 0.0000i  -0.0675 + 0.0183i  -0.0675 - 0.0183i
0.0316 + 0.0000i   0.0307 + 0.0000i  -0.0036 + 0.0281i  -0.0036 - 0.0281i
0.0325 + 0.0000i  -0.0303 + 0.0000i   0.0148 + 0.0240i   0.0148 - 0.0240i
0.0316 + 0.0000i   0.0203 + 0.0000i   0.0046 - 0.0126i   0.0046 + 0.0126i
0.0318 + 0.0000i   0.0185 + 0.0000i  -0.0044 - 0.0312i  -0.0044 + 0.0312i
0.0321 + 0.0000i   0.0260 + 0.0000i  -0.0537 - 0.0154i  -0.0537 + 0.0154i
0.0316 + 0.0000i   0.0381 + 0.0000i  -0.0046 - 0.0219i  -0.0046 + 0.0219i
0.0303 + 0.0000i   0.0221 + 0.0000i   0.0421 + 0.0158i   0.0421 - 0.0158i
0.0320 + 0.0000i  -0.0378 + 0.0000i   0.0072 + 0.0048i   0.0072 - 0.0048i
0.0317 + 0.0000i   0.0316 + 0.0000i  -0.0143 - 0.0431i  -0.0143 + 0.0431i
0.0323 + 0.0000i   0.0221 + 0.0000i  -0.0136 - 0.0030i  -0.0136 + 0.0030i
0.0305 + 0.0000i  -0.0483 + 0.0000i  -0.0332 + 0.0177i  -0.0332 - 0.0177i
0.0312 + 0.0000i  -0.0035 + 0.0000i   0.0368 - 0.0014i   0.0368 + 0.0014i
0.0318 + 0.0000i   0.0438 + 0.0000i   0.0162 + 0.0211i   0.0162 - 0.0211i
0.0305 + 0.0000i  -0.0089 + 0.0000i   0.0110 - 0.0012i   0.0110 + 0.0012i
0.0321 + 0.0000i  -0.0578 + 0.0000i  -0.0263 + 0.0336i  -0.0263 - 0.0336i
0.0319 + 0.0000i   0.0062 + 0.0000i   0.0152 + 0.0049i   0.0152 - 0.0049i
0.0321 + 0.0000i   0.0571 + 0.0000i   0.0205 + 0.0169i   0.0205 - 0.0169i
0.0310 + 0.0000i  -0.0053 + 0.0000i   0.0456 + 0.0186i   0.0456 - 0.0186i
0.0306 + 0.0000i  -0.0013 + 0.0000i  -0.0240 - 0.0165i  -0.0240 + 0.0165i
0.0319 + 0.0000i   0.0138 + 0.0000i  -0.0256 - 0.0057i  -0.0256 + 0.0057i
0.0313 + 0.0000i  -0.0016 + 0.0000i   0.0044 - 0.0132i   0.0044 + 0.0132i
0.0316 + 0.0000i   0.0061 + 0.0000i   0.0354 + 0.0109i   0.0354 - 0.0109i
0.0311 + 0.0000i  -0.0498 + 0.0000i  -0.0060 - 0.0263i  -0.0060 + 0.0263i
0.0316 + 0.0000i   0.0702 + 0.0000i   0.0333 - 0.0320i   0.0333 + 0.0320i
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0.0315 + 0.0000i  -0.0124 + 0.0000i   0.0536 - 0.0061i   0.0536 + 0.0061i
0.0329 + 0.0000i  -0.0451 + 0.0000i   0.0032 - 0.0223i   0.0032 + 0.0223i
0.0322 + 0.0000i   0.0629 + 0.0000i   0.0386 + 0.0242i   0.0386 - 0.0242i
0.0315 + 0.0000i  -0.0807 + 0.0000i   0.0125 - 0.0088i   0.0125 + 0.0088i
0.0315 + 0.0000i   0.0004 + 0.0000i   0.0220 + 0.0048i   0.0220 - 0.0048i
0.0319 + 0.0000i   0.0017 + 0.0000i   0.0060 + 0.0089i   0.0060 - 0.0089i
0.0322 + 0.0000i   0.0125 + 0.0000i   0.0212 + 0.0024i   0.0212 - 0.0024i
0.0320 + 0.0000i  -0.0085 + 0.0000i   0.0472 + 0.0027i   0.0472 - 0.0027i
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0.0314 + 0.0000i  -0.0165 + 0.0000i  -0.0224 + 0.0135i  -0.0224 - 0.0135i
0.0311 + 0.0000i  -0.0278 + 0.0000i  -0.0354 + 0.0274i  -0.0354 - 0.0274i
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0.0308 + 0.0000i  -0.0248 + 0.0000i   0.0549 + 0.0033i   0.0549 - 0.0033i
0.0316 + 0.0000i  -0.0120 + 0.0000i  -0.0240 + 0.0127i  -0.0240 - 0.0127i
0.0318 + 0.0000i  -0.0300 + 0.0000i   0.0136 - 0.0154i   0.0136 + 0.0154i
0.0317 + 0.0000i   0.0001 + 0.0000i  -0.0300 - 0.0081i  -0.0300 + 0.0081i
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0.0313 + 0.0000i   0.0034 + 0.0000i  -0.0075 - 0.0218i  -0.0075 + 0.0218i
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0.0305 + 0.0000i  -0.0722 + 0.0000i  -0.0118 - 0.0156i  -0.0118 + 0.0156i
0.0321 + 0.0000i   0.0493 + 0.0000i   0.0594 - 0.0188i   0.0594 + 0.0188i
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0.0320 + 0.0000i  -0.0126 + 0.0000i  -0.0192 + 0.0082i  -0.0192 - 0.0082i
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0.0315 + 0.0000i  -0.0240 + 0.0000i   0.0134 + 0.0156i   0.0134 - 0.0156i
0.0312 + 0.0000i   0.0123 + 0.0000i   0.0165 - 0.0123i   0.0165 + 0.0123i
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0.0307 + 0.0000i   0.0174 + 0.0000i   0.0208 - 0.0173i   0.0208 + 0.0173i
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0.0312 + 0.0000i  -0.0296 + 0.0000i  -0.0154 + 0.0059i  -0.0154 - 0.0059i
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0.0331 + 0.0000i   0.0113 + 0.0000i   0.0278 - 0.0063i   0.0278 + 0.0063i
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0.0320 + 0.0000i  -0.0204 + 0.0000i  -0.0179 - 0.0287i  -0.0179 + 0.0287i
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0.0315 + 0.0000i   0.0009 + 0.0000i   0.0335 + 0.0150i   0.0335 - 0.0150i
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0.0321 + 0.0000i  -0.0209 + 0.0000i  -0.0139 + 0.0275i  -0.0139 - 0.0275i
0.0331 + 0.0000i  -0.0225 + 0.0000i  -0.0448 + 0.0251i  -0.0448 - 0.0251i
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0.0313 + 0.0000i  -0.0360 + 0.0000i  -0.0117 + 0.0346i  -0.0117 - 0.0346i
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0.0324 + 0.0000i   0.0339 + 0.0000i   0.0061 - 0.0093i   0.0061 + 0.0093i
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0.0318 + 0.0000i  -0.0062 + 0.0000i   0.0261 - 0.0096i   0.0261 + 0.0096i
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0.0322 + 0.0000i   0.0008 + 0.0000i  -0.0495 + 0.0106i  -0.0495 - 0.0106i
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0.0328 + 0.0000i  -0.0153 + 0.0000i  -0.0458 + 0.0175i  -0.0458 - 0.0175i
0.0318 + 0.0000i  -0.0204 + 0.0000i   0.0623 + 0.0142i   0.0623 - 0.0142i
0.0314 + 0.0000i   0.0722 + 0.0000i   0.0138 - 0.0351i   0.0138 + 0.0351i
0.0317 + 0.0000i   0.0118 + 0.0000i   0.0321 - 0.0074i   0.0321 + 0.0074i
0.0309 + 0.0000i   0.0021 + 0.0000i  -0.0143 + 0.0017i  -0.0143 - 0.0017i
0.0317 + 0.0000i   0.0180 + 0.0000i   0.0062 - 0.0060i   0.0062 + 0.0060i
0.0314 + 0.0000i  -0.0117 + 0.0000i  -0.0107 + 0.0021i  -0.0107 - 0.0021i
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0.0319 + 0.0000i   0.0171 + 0.0000i  -0.0022 + 0.0130i  -0.0022 - 0.0130i
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0.0314 + 0.0000i   0.0020 + 0.0000i  -0.0102 - 0.0052i  -0.0102 + 0.0052i
0.0316 + 0.0000i  -0.0486 + 0.0000i   0.0241 + 0.0300i   0.0241 - 0.0300i
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0.0311 + 0.0000i  -0.0135 + 0.0000i  -0.0266 + 0.0174i  -0.0266 - 0.0174i
0.0325 + 0.0000i  -0.0293 + 0.0000i  -0.0016 - 0.0419i  -0.0016 + 0.0419i
0.0305 + 0.0000i  -0.0288 + 0.0000i  -0.0381 + 0.0277i  -0.0381 - 0.0277i
0.0313 + 0.0000i  -0.0055 + 0.0000i  -0.0365 + 0.0237i  -0.0365 - 0.0237i
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0.0314 + 0.0000i  -0.0418 + 0.0000i  -0.0149 + 0.0130i  -0.0149 - 0.0130i
0.0321 + 0.0000i  -0.0123 + 0.0000i   0.0065 + 0.0125i   0.0065 - 0.0125i
0.0308 + 0.0000i  -0.0278 + 0.0000i   0.0189 + 0.0054i   0.0189 - 0.0054i
0.0313 + 0.0000i   0.0283 + 0.0000i   0.0188 - 0.0020i   0.0188 + 0.0020i
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0.0306 + 0.0000i  -0.0052 + 0.0000i   0.0153 + 0.0225i   0.0153 - 0.0225i
0.0325 + 0.0000i  -0.0513 + 0.0000i   0.0003 - 0.0180i   0.0003 + 0.0180i
0.0310 + 0.0000i  -0.0058 + 0.0000i   0.0018 - 0.0110i   0.0018 + 0.0110i
0.0321 + 0.0000i  -0.0137 + 0.0000i  -0.0382 + 0.0222i  -0.0382 - 0.0222i
0.0320 + 0.0000i   0.0004 + 0.0000i  -0.0045 - 0.0067i  -0.0045 + 0.0067i
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0.0309 + 0.0000i   0.0080 + 0.0000i   0.0266 + 0.0012i   0.0266 - 0.0012i
0.0313 + 0.0000i  -0.0327 + 0.0000i  -0.0092 - 0.0189i  -0.0092 + 0.0189i
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0.0310 + 0.0000i   0.0061 + 0.0000i   0.0218 - 0.0140i   0.0218 + 0.0140i
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0.0324 + 0.0000i  -0.0215 + 0.0000i  -0.0143 + 0.0292i  -0.0143 - 0.0292i
0.0324 + 0.0000i   0.0005 + 0.0000i   0.0016 + 0.0267i   0.0016 - 0.0267i
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0.0314 + 0.0000i  -0.0131 + 0.0000i  -0.0441 + 0.0026i  -0.0441 - 0.0026i
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0.0325 + 0.0000i  -0.0103 + 0.0000i  -0.0010 + 0.0076i  -0.0010 - 0.0076i
0.0306 + 0.0000i  -0.0006 + 0.0000i  -0.0249 - 0.0074i  -0.0249 + 0.0074i
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0.0314 + 0.0000i   0.0030 + 0.0000i  -0.0402 + 0.0389i  -0.0402 - 0.0389i
0.0315 + 0.0000i  -0.0124 + 0.0000i  -0.0314 - 0.0087i  -0.0314 + 0.0087i
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0.0305 + 0.0000i   0.0111 + 0.0000i  -0.0094 + 0.0008i  -0.0094 - 0.0008i
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0.0322 + 0.0000i  -0.0018 + 0.0000i   0.0325 + 0.0004i   0.0325 - 0.0004i
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0.0312 + 0.0000i  -0.0100 + 0.0000i   0.0019 - 0.0046i   0.0019 + 0.0046i
0.0312 + 0.0000i   0.0543 + 0.0000i   0.0134 - 0.0190i   0.0134 + 0.0190i
0.0317 + 0.0000i   0.0103 + 0.0000i   0.0081 + 0.0325i   0.0081 - 0.0325i

Columns 5 through 6

-0.0344 - 0.0275i  -0.0344 + 0.0275i
0.0001 - 0.0207i   0.0001 + 0.0207i
0.0250 - 0.0228i   0.0250 + 0.0228i
-0.0482 + 0.0209i  -0.0482 - 0.0209i
0.0345 - 0.0173i   0.0345 + 0.0173i
0.0025 - 0.0094i   0.0025 + 0.0094i
0.0087 - 0.0106i   0.0087 + 0.0106i
-0.0034 + 0.0025i  -0.0034 - 0.0025i
-0.0349 + 0.0175i  -0.0349 - 0.0175i
-0.0020 + 0.0079i  -0.0020 - 0.0079i
-0.0087 + 0.0283i  -0.0087 - 0.0283i
0.0308 - 0.0029i   0.0308 + 0.0029i
-0.0202 + 0.0008i  -0.0202 - 0.0008i
0.0050 + 0.0219i   0.0050 - 0.0219i
-0.0187 + 0.0204i  -0.0187 - 0.0204i
0.0124 - 0.0044i   0.0124 + 0.0044i
0.0163 + 0.0191i   0.0163 - 0.0191i
-0.0026 - 0.0221i  -0.0026 + 0.0221i
-0.0186 + 0.0100i  -0.0186 - 0.0100i
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-0.0263 - 0.0019i  -0.0263 + 0.0019i
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0.0288 + 0.0140i   0.0288 - 0.0140i
0.0154 - 0.0122i   0.0154 + 0.0122i
-0.0167 - 0.0347i  -0.0167 + 0.0347i
0.0362 + 0.0326i   0.0362 - 0.0326i
-0.0225 + 0.0508i  -0.0225 - 0.0508i
0.0005 - 0.0021i   0.0005 + 0.0021i
-0.0406 + 0.0095i  -0.0406 - 0.0095i
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0.0106 + 0.0119i   0.0106 - 0.0119i
0.0006 + 0.0152i   0.0006 - 0.0152i
0.0117 - 0.0113i   0.0117 + 0.0113i
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0.0271 - 0.0345i   0.0271 + 0.0345i
0.0246 - 0.0098i   0.0246 + 0.0098i
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-0.0243 - 0.0012i  -0.0243 + 0.0012i
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0.0089 - 0.0271i   0.0089 + 0.0271i
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0.0114 - 0.0365i   0.0114 + 0.0365i
0.0451 - 0.0269i   0.0451 + 0.0269i
-0.0110 - 0.0199i  -0.0110 + 0.0199i
0.0353 - 0.0052i   0.0353 + 0.0052i
-0.0146 + 0.0126i  -0.0146 - 0.0126i
0.0571 - 0.0315i   0.0571 + 0.0315i
0.0215 - 0.0104i   0.0215 + 0.0104i
0.0317 - 0.0210i   0.0317 + 0.0210i
0.0194 + 0.0020i   0.0194 - 0.0020i
-0.0388 + 0.0186i  -0.0388 - 0.0186i
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0.0292 - 0.0306i   0.0292 + 0.0306i
0.0169 - 0.0115i   0.0169 + 0.0115i
-0.0125 - 0.0026i  -0.0125 + 0.0026i
0.0016 + 0.0311i   0.0016 - 0.0311i
0.0332 + 0.0154i   0.0332 - 0.0154i
-0.0061 + 0.0268i  -0.0061 - 0.0268i
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0.0085 - 0.0150i   0.0085 + 0.0150i
0.0159 - 0.0279i   0.0159 + 0.0279i
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0.0104 - 0.0031i   0.0104 + 0.0031i
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0.0046 - 0.0016i   0.0046 + 0.0016i
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0.0375 + 0.0325i   0.0375 - 0.0325i
0.0020 + 0.0048i   0.0020 - 0.0048i
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-0.0182 + 0.0058i  -0.0182 - 0.0058i
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0.0283 - 0.0219i   0.0283 + 0.0219i
0.0010 - 0.0242i   0.0010 + 0.0242i
0.0215 - 0.0194i   0.0215 + 0.0194i
0.0362 - 0.0436i   0.0362 + 0.0436i
-0.0200 + 0.0019i  -0.0200 - 0.0019i
0.0437 - 0.0003i   0.0437 + 0.0003i
0.0150 - 0.0036i   0.0150 + 0.0036i
-0.0214 - 0.0043i  -0.0214 + 0.0043i
0.0040 + 0.0142i   0.0040 - 0.0142i
-0.0283 + 0.0016i  -0.0283 - 0.0016i
0.0089 - 0.0198i   0.0089 + 0.0198i
-0.0373 - 0.0368i  -0.0373 + 0.0368i
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0.0415 - 0.0189i   0.0415 + 0.0189i
-0.0003 - 0.0043i  -0.0003 + 0.0043i
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0.0382 - 0.0007i   0.0382 + 0.0007i
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0.0372 - 0.0115i   0.0372 + 0.0115i
0.0027 + 0.0200i   0.0027 - 0.0200i
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0.0213 + 0.0149i   0.0213 - 0.0149i
0.0001 - 0.0214i   0.0001 + 0.0214i
-0.0382 + 0.0129i  -0.0382 - 0.0129i
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0.0212 + 0.0059i   0.0212 - 0.0059i
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0.0172 - 0.0307i   0.0172 + 0.0307i
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0.0460 - 0.0230i   0.0460 + 0.0230i
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0.0468 + 0.0065i   0.0468 - 0.0065i
0.0038 - 0.0137i   0.0038 + 0.0137i
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0.0270 + 0.0496i   0.0270 - 0.0496i
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0.0172 - 0.0480i   0.0172 + 0.0480i
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0.0509 + 0.0291i   0.0509 - 0.0291i
0.0002 + 0.0134i   0.0002 - 0.0134i
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0.0366 + 0.0127i   0.0366 - 0.0127i
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0.0045 + 0.0256i   0.0045 - 0.0256i
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0.0033 + 0.0413i   0.0033 - 0.0413i
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0.0071 - 0.0289i   0.0071 + 0.0289i
0.0168 - 0.0182i   0.0168 + 0.0182i
0.0089 + 0.0057i   0.0089 - 0.0057i
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0.0160 - 0.0406i   0.0160 + 0.0406i
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0.0407 - 0.0045i   0.0407 + 0.0045i
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0.0207 - 0.0023i   0.0207 + 0.0023i
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-0.0042 + 0.0148i  -0.0042 - 0.0148i
0.0117 - 0.0154i   0.0117 + 0.0154i
0.0182 - 0.0221i   0.0182 + 0.0221i
-0.0087 - 0.0074i  -0.0087 + 0.0074i
0.0179 - 0.0283i   0.0179 + 0.0283i
0.0390 + 0.0137i   0.0390 - 0.0137i
0.0168 - 0.0076i   0.0168 + 0.0076i
-0.0156 + 0.0222i  -0.0156 - 0.0222i
-0.0098 + 0.0478i  -0.0098 - 0.0478i
-0.0122 + 0.0148i  -0.0122 - 0.0148i
-0.0072 - 0.0270i  -0.0072 + 0.0270i
0.0305 - 0.0187i   0.0305 + 0.0187i
-0.0076 + 0.0019i  -0.0076 - 0.0019i
-0.0115 + 0.0031i  -0.0115 - 0.0031i
0.0184 - 0.0124i   0.0184 + 0.0124i
0.0161 + 0.0053i   0.0161 - 0.0053i
-0.0051 + 0.0180i  -0.0051 - 0.0180i
-0.0144 + 0.0246i  -0.0144 - 0.0246i
-0.0230 - 0.0288i  -0.0230 + 0.0288i
0.0247 - 0.0456i   0.0247 + 0.0456i
0.0279 + 0.0297i   0.0279 - 0.0297i
-0.0131 + 0.0149i  -0.0131 - 0.0149i
-0.0305 - 0.0373i  -0.0305 + 0.0373i
-0.0221 + 0.0138i  -0.0221 - 0.0138i
0.0344 - 0.0564i   0.0344 + 0.0564i
-0.0647 - 0.0059i  -0.0647 + 0.0059i
0.0431 - 0.0013i   0.0431 + 0.0013i
0.0108 - 0.0037i   0.0108 + 0.0037i
-0.0243 - 0.0426i  -0.0243 + 0.0426i
-0.0057 - 0.0087i  -0.0057 + 0.0087i
-0.0018 + 0.0360i  -0.0018 - 0.0360i
-0.0504 - 0.0076i  -0.0504 + 0.0076i
0.0200 + 0.0271i   0.0200 - 0.0271i
-0.0141 + 0.0226i  -0.0141 - 0.0226i
0.0407 + 0.0323i   0.0407 - 0.0323i
0.0166 + 0.0025i   0.0166 - 0.0025i
0.0242 + 0.0330i   0.0242 - 0.0330i
-0.0098 + 0.0151i  -0.0098 - 0.0151i
-0.0503 - 0.0018i  -0.0503 + 0.0018i
0.0154 + 0.0365i   0.0154 - 0.0365i
-0.0059 + 0.0105i  -0.0059 - 0.0105i
-0.0115 - 0.0050i  -0.0115 + 0.0050i
-0.0081 + 0.0001i  -0.0081 - 0.0001i
0.0203 - 0.0356i   0.0203 + 0.0356i
-0.0202 + 0.0586i  -0.0202 - 0.0586i
0.0280 + 0.0077i   0.0280 - 0.0077i
0.0192 + 0.0143i   0.0192 - 0.0143i
0.0143 + 0.0037i   0.0143 - 0.0037i
-0.0179 + 0.0149i  -0.0179 - 0.0149i
-0.0024 + 0.0210i  -0.0024 - 0.0210i
-0.0124 + 0.0120i  -0.0124 - 0.0120i
0.0071 + 0.0145i   0.0071 - 0.0145i
0.0219 - 0.0380i   0.0219 + 0.0380i
0.0146 - 0.0143i   0.0146 + 0.0143i
0.0471 + 0.0052i   0.0471 - 0.0052i
0.0097 - 0.0071i   0.0097 + 0.0071i
0.0047 + 0.0002i   0.0047 - 0.0002i
-0.0252 + 0.0288i  -0.0252 - 0.0288i
-0.0161 + 0.0291i  -0.0161 - 0.0291i
-0.0131 - 0.0215i  -0.0131 + 0.0215i
0.0318 - 0.0018i   0.0318 + 0.0018i
0.0398 + 0.0052i   0.0398 - 0.0052i
-0.0187 + 0.0165i  -0.0187 - 0.0165i
0.0124 - 0.0059i   0.0124 + 0.0059i
-0.0179 - 0.0074i  -0.0179 + 0.0074i
-0.0438 + 0.0215i  -0.0438 - 0.0215i
-0.0312 - 0.0067i  -0.0312 + 0.0067i
0.0227 - 0.0031i   0.0227 + 0.0031i
0.0224 - 0.0053i   0.0224 + 0.0053i
0.0073 + 0.0134i   0.0073 - 0.0134i
-0.0352 + 0.0087i  -0.0352 - 0.0087i
-0.0057 + 0.0123i  -0.0057 - 0.0123i
-0.0011 + 0.0283i  -0.0011 - 0.0283i
0.0140 - 0.0050i   0.0140 + 0.0050i
0.0012 + 0.0012i   0.0012 - 0.0012i
0.0062 + 0.0191i   0.0062 - 0.0191i
0.0190 + 0.0092i   0.0190 - 0.0092i
0.0054 + 0.0175i   0.0054 - 0.0175i
0.0196 - 0.0149i   0.0196 + 0.0149i
0.0017 + 0.0004i   0.0017 - 0.0004i
0.0094 + 0.0469i   0.0094 - 0.0469i
0.0137 - 0.0337i   0.0137 + 0.0337i
-0.0159 - 0.0201i  -0.0159 + 0.0201i
0.0441 + 0.0084i   0.0441 - 0.0084i
-0.0160 - 0.0250i  -0.0160 + 0.0250i
0.0012 - 0.0026i   0.0012 + 0.0026i
-0.0010 + 0.0239i  -0.0010 - 0.0239i
-0.0124 - 0.0392i  -0.0124 + 0.0392i
0.0059 + 0.0009i   0.0059 - 0.0009i
-0.0107 - 0.0297i  -0.0107 + 0.0297i
-0.0123 - 0.0408i  -0.0123 + 0.0408i
0.0064 - 0.0223i   0.0064 + 0.0223i
-0.0154 + 0.0409i  -0.0154 - 0.0409i
-0.0061 - 0.0349i  -0.0061 + 0.0349i
-0.0192 + 0.0205i  -0.0192 - 0.0205i
0.0125 + 0.0033i   0.0125 - 0.0033i
-0.0430 - 0.0228i  -0.0430 + 0.0228i
-0.0047 + 0.0036i  -0.0047 - 0.0036i
-0.0115 + 0.0082i  -0.0115 - 0.0082i
-0.0127 + 0.0164i  -0.0127 - 0.0164i
-0.0189 + 0.0118i  -0.0189 - 0.0118i
0.0145 + 0.0096i   0.0145 - 0.0096i
-0.0007 - 0.0277i  -0.0007 + 0.0277i
0.0231 + 0.0154i   0.0231 - 0.0154i
0.0018 + 0.0080i   0.0018 - 0.0080i
-0.0105 + 0.0147i  -0.0105 - 0.0147i
0.0105 + 0.0239i   0.0105 - 0.0239i
0.0130 + 0.0351i   0.0130 - 0.0351i
0.0227 - 0.0040i   0.0227 + 0.0040i
-0.0200 - 0.0135i  -0.0200 + 0.0135i
-0.0024 + 0.0231i  -0.0024 - 0.0231i
-0.0156 - 0.0600i  -0.0156 + 0.0600i
-0.0262 - 0.0023i  -0.0262 + 0.0023i
-0.0185 + 0.0196i  -0.0185 - 0.0196i
0.0047 - 0.0598i   0.0047 + 0.0598i
0.0038 - 0.0192i   0.0038 + 0.0192i
0.0114 - 0.0337i   0.0114 + 0.0337i
-0.0024 + 0.0187i  -0.0024 - 0.0187i
-0.0014 + 0.0210i  -0.0014 - 0.0210i
-0.0022 + 0.0204i  -0.0022 - 0.0204i
0.0128 - 0.0115i   0.0128 + 0.0115i
0.0052 + 0.0535i   0.0052 - 0.0535i
-0.0243 + 0.0073i  -0.0243 - 0.0073i
0.0210 - 0.0015i   0.0210 + 0.0015i
0.0031 - 0.0078i   0.0031 + 0.0078i
0.0337 - 0.0023i   0.0337 + 0.0023i
0.0011 + 0.0353i   0.0011 - 0.0353i
0.0261 - 0.0078i   0.0261 + 0.0078i
-0.0297 - 0.0091i  -0.0297 + 0.0091i
0.0108 - 0.0084i   0.0108 + 0.0084i
-0.0135 - 0.0205i  -0.0135 + 0.0205i
0.0354 - 0.0101i   0.0354 + 0.0101i
-0.0700 - 0.0298i  -0.0700 + 0.0298i
-0.0026 - 0.0042i  -0.0026 + 0.0042i
0.0019 + 0.0162i   0.0019 - 0.0162i
-0.0208 - 0.0075i  -0.0208 + 0.0075i
-0.0140 + 0.0129i  -0.0140 - 0.0129i
-0.0179 + 0.0290i  -0.0179 - 0.0290i
0.0291 + 0.0242i   0.0291 - 0.0242i
-0.0409 + 0.0373i  -0.0409 - 0.0373i
-0.0114 + 0.0378i  -0.0114 - 0.0378i
0.0012 + 0.0031i   0.0012 - 0.0031i
0.0144 - 0.0041i   0.0144 + 0.0041i
-0.0471 + 0.0356i  -0.0471 - 0.0356i
0.0068 + 0.0301i   0.0068 - 0.0301i
0.0114 + 0.0031i   0.0114 - 0.0031i
0.0292 - 0.0293i   0.0292 + 0.0293i
0.0150 - 0.0281i   0.0150 + 0.0281i
0.0282 + 0.0055i   0.0282 - 0.0055i
0.0159 + 0.0416i   0.0159 - 0.0416i
-0.0377 - 0.0174i  -0.0377 + 0.0174i
-0.0110 - 0.0420i  -0.0110 + 0.0420i
0.0080 - 0.0203i   0.0080 + 0.0203i
-0.0016 + 0.0091i  -0.0016 - 0.0091i
-0.0408 - 0.0080i  -0.0408 + 0.0080i
0.0409 + 0.0001i   0.0409 - 0.0001i
0.0043 - 0.0083i   0.0043 + 0.0083i
-0.0135 + 0.0155i  -0.0135 - 0.0155i
0.0008 + 0.0139i   0.0008 - 0.0139i
0.0332 - 0.0053i   0.0332 + 0.0053i
-0.0067 - 0.0391i  -0.0067 + 0.0391i
0.0201 + 0.0174i   0.0201 - 0.0174i
0.0218 + 0.0099i   0.0218 - 0.0099i
0.0030 + 0.0081i   0.0030 - 0.0081i
0.0125 - 0.0222i   0.0125 + 0.0222i
-0.0074 + 0.0283i  -0.0074 - 0.0283i
0.0340 - 0.0078i   0.0340 + 0.0078i
-0.0119 + 0.0033i  -0.0119 - 0.0033i
-0.0118 + 0.0038i  -0.0118 - 0.0038i
-0.0077 - 0.0034i  -0.0077 + 0.0034i
0.0200 + 0.0040i   0.0200 - 0.0040i
-0.0172 - 0.0246i  -0.0172 + 0.0246i
-0.0239 + 0.0012i  -0.0239 - 0.0012i
-0.0002 + 0.0207i  -0.0002 - 0.0207i
0.0206 - 0.0105i   0.0206 + 0.0105i
-0.0144 - 0.0004i  -0.0144 + 0.0004i
0.0156 - 0.0297i   0.0156 + 0.0297i
-0.0095 - 0.0116i  -0.0095 + 0.0116i
0.0227 - 0.0075i   0.0227 + 0.0075i
-0.0079 + 0.0009i  -0.0079 - 0.0009i
0.0113 - 0.0392i   0.0113 + 0.0392i
-0.0144 + 0.0500i  -0.0144 - 0.0500i
0.0009 - 0.0096i   0.0009 + 0.0096i
0.0322 + 0.0068i   0.0322 - 0.0068i
0.0140 - 0.0039i   0.0140 + 0.0039i
0.0108 - 0.0031i   0.0108 + 0.0031i
0.0035 - 0.0309i   0.0035 + 0.0309i
-0.0069 + 0.0282i  -0.0069 - 0.0282i
0.0095 - 0.0354i   0.0095 + 0.0354i
0.0166 + 0.0064i   0.0166 - 0.0064i
-0.0243 + 0.0083i  -0.0243 - 0.0083i
0.0138 - 0.0073i   0.0138 + 0.0073i
-0.0064 + 0.0384i  -0.0064 - 0.0384i
-0.0174 + 0.0060i  -0.0174 - 0.0060i
-0.0210 + 0.0237i  -0.0210 - 0.0237i
-0.0050 - 0.0131i  -0.0050 + 0.0131i
0.0426 + 0.0255i   0.0426 - 0.0255i
0.0258 + 0.0044i   0.0258 - 0.0044i
0.0234 - 0.0597i   0.0234 + 0.0597i
0.0070 + 0.0099i   0.0070 - 0.0099i
-0.0144 + 0.0184i  -0.0144 - 0.0184i
-0.0063 - 0.0156i  -0.0063 + 0.0156i
-0.0020 - 0.0174i  -0.0020 + 0.0174i
-0.0047 - 0.0384i  -0.0047 + 0.0384i
-0.0081 + 0.0047i  -0.0081 - 0.0047i
0.0044 - 0.0323i   0.0044 + 0.0323i
-0.0029 - 0.0252i  -0.0029 + 0.0252i
-0.0179 - 0.0015i  -0.0179 + 0.0015i
0.0178 + 0.0230i   0.0178 - 0.0230i
0.0059 + 0.0048i   0.0059 - 0.0048i
-0.0119 + 0.0276i  -0.0119 - 0.0276i
0.0268 - 0.0274i   0.0268 + 0.0274i
-0.0175 - 0.0198i  -0.0175 + 0.0198i
-0.0005 + 0.0128i  -0.0005 - 0.0128i
-0.0245 + 0.0125i  -0.0245 - 0.0125i
0.0317 + 0.0065i   0.0317 - 0.0065i
0.0012 - 0.0065i   0.0012 + 0.0065i
-0.0039 - 0.0008i  -0.0039 + 0.0008i
-0.0200 - 0.0101i  -0.0200 + 0.0101i
0.0048 + 0.0095i   0.0048 - 0.0095i
0.0268 - 0.0016i   0.0268 + 0.0016i
0.0059 + 0.0059i   0.0059 - 0.0059i
0.0233 + 0.0117i   0.0233 - 0.0117i
0.0014 + 0.0115i   0.0014 - 0.0115i
-0.0302 + 0.0191i  -0.0302 - 0.0191i
0.0497 + 0.0030i   0.0497 - 0.0030i
-0.0002 - 0.0511i  -0.0002 + 0.0511i
0.0023 + 0.0107i   0.0023 - 0.0107i
0.0083 + 0.0294i   0.0083 - 0.0294i
0.0081 - 0.0200i   0.0081 + 0.0200i
-0.0030 - 0.0041i  -0.0030 + 0.0041i
0.0227 - 0.0125i   0.0227 + 0.0125i
-0.0098 - 0.0105i  -0.0098 + 0.0105i
0.0439 + 0.0126i   0.0439 - 0.0126i
-0.0210 - 0.0286i  -0.0210 + 0.0286i
0.0085 - 0.0271i   0.0085 + 0.0271i
0.0175 + 0.0543i   0.0175 - 0.0543i
-0.0327 + 0.0277i  -0.0327 - 0.0277i
0.0006 + 0.0095i   0.0006 - 0.0095i
-0.0135 - 0.0325i  -0.0135 + 0.0325i
-0.0175 + 0.0447i  -0.0175 - 0.0447i
0.0192 + 0.0096i   0.0192 - 0.0096i
0.0039 - 0.0221i   0.0039 + 0.0221i
0.0305 - 0.0007i   0.0305 + 0.0007i
-0.0487 - 0.0324i  -0.0487 + 0.0324i
-0.0262 + 0.0129i  -0.0262 - 0.0129i
-0.0100 + 0.0330i  -0.0100 - 0.0330i
-0.0405 + 0.0353i  -0.0405 - 0.0353i
-0.0185 + 0.0356i  -0.0185 - 0.0356i
-0.0131 - 0.0101i  -0.0131 + 0.0101i
0.0104 - 0.0054i   0.0104 + 0.0054i
-0.0000 - 0.0122i  -0.0000 + 0.0122i
0.0067 - 0.0246i   0.0067 + 0.0246i
0.0220 + 0.0155i   0.0220 - 0.0155i
-0.0279 - 0.0117i  -0.0279 + 0.0117i
0.0098 - 0.0034i   0.0098 + 0.0034i
-0.0112 + 0.0515i  -0.0112 - 0.0515i
-0.0288 - 0.0162i  -0.0288 + 0.0162i
-0.0397 - 0.0070i  -0.0397 + 0.0070i
-0.0314 - 0.0469i  -0.0314 + 0.0469i
0.0094 - 0.0181i   0.0094 + 0.0181i
-0.0290 + 0.0009i  -0.0290 - 0.0009i
-0.0063 + 0.0083i  -0.0063 - 0.0083i
-0.0337 - 0.0354i  -0.0337 + 0.0354i
-0.0027 + 0.0091i  -0.0027 - 0.0091i
0.0289 - 0.0106i   0.0289 + 0.0106i
-0.0460 + 0.0048i  -0.0460 - 0.0048i
-0.0034 + 0.0139i  -0.0034 - 0.0139i
0.0016 - 0.0139i   0.0016 + 0.0139i
-0.0027 + 0.0042i  -0.0027 - 0.0042i
-0.0153 - 0.0099i  -0.0153 + 0.0099i
-0.0248 + 0.0107i  -0.0248 - 0.0107i
-0.0043 - 0.0036i  -0.0043 + 0.0036i
0.0126 - 0.0076i   0.0126 + 0.0076i
-0.0190 + 0.0338i  -0.0190 - 0.0338i
-0.0425 - 0.0128i  -0.0425 + 0.0128i
0.0219 + 0.0171i   0.0219 - 0.0171i
0.0012 + 0.0050i   0.0012 - 0.0050i
0.0037 - 0.0237i   0.0037 + 0.0237i
0.0195 - 0.0400i   0.0195 + 0.0400i
0.0056 + 0.0370i   0.0056 - 0.0370i
-0.0003 - 0.0366i  -0.0003 + 0.0366i
0.0426 + 0.0197i   0.0426 - 0.0197i
-0.0139 - 0.0028i  -0.0139 + 0.0028i
0.0352 + 0.0240i   0.0352 - 0.0240i
-0.0472 - 0.0364i  -0.0472 + 0.0364i
-0.0357 + 0.0350i  -0.0357 - 0.0350i
0.0301 + 0.0626i   0.0301 - 0.0626i
0.0367 - 0.0208i   0.0367 + 0.0208i
-0.0255 - 0.0220i  -0.0255 + 0.0220i
-0.0267 - 0.0158i  -0.0267 + 0.0158i
0.0141 + 0.0288i   0.0141 - 0.0288i
0.0334 - 0.0246i   0.0334 + 0.0246i
0.0016 + 0.0116i   0.0016 - 0.0116i
-0.0003 + 0.0106i  -0.0003 - 0.0106i
-0.0156 - 0.0006i  -0.0156 + 0.0006i
-0.0002 - 0.0070i  -0.0002 + 0.0070i
0.0407 - 0.0040i   0.0407 + 0.0040i
0.0032 + 0.0155i   0.0032 - 0.0155i
0.0727 + 0.0304i   0.0727 - 0.0304i
-0.0134 + 0.0229i  -0.0134 - 0.0229i
0.0029 + 0.0226i   0.0029 - 0.0226i
0.0176 - 0.0073i   0.0176 + 0.0073i
-0.0029 - 0.0032i  -0.0029 + 0.0032i
-0.0272 - 0.0385i  -0.0272 + 0.0385i
-0.0059 + 0.0126i  -0.0059 - 0.0126i

EigVal7 =

1.0e+02 *

Columns 1 through 4

5.0013 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
0.0000 + 0.0000i   0.0935 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
0.0000 + 0.0000i   0.0000 + 0.0000i   0.0920 + 0.0148i   0.0000 + 0.0000i
0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0920 - 0.0148i
0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i

Columns 5 through 6

0.0000 + 0.0000i   0.0000 + 0.0000i
0.0000 + 0.0000i   0.0000 + 0.0000i
0.0000 + 0.0000i   0.0000 + 0.0000i
0.0000 + 0.0000i   0.0000 + 0.0000i
0.0483 + 0.0785i   0.0000 + 0.0000i
0.0000 + 0.0000i   0.0483 - 0.0785i

Elapsed time is 1.047719 seconds.
```

If you specify a number, k, after the matrix, the function will return the largest k eigenvalues.

```tic
EigVal8=eigs(A,1)
toc
```
```EigVal8 =

500.1302

Elapsed time is 0.020651 seconds.
```