# omega total a= 1 L= 2 a= 2 L= 2 a= 3 L= 2 a= 4 L= 2 0.15707963 3.53896725 0.76576841 0.76599866 0.76384892 0.76733238 0.47123890 3.11271950 0.63245146 0.63248930 0.63093800 0.63389578 0.78539816 2.85027603 0.54633916 0.54641848 0.54558193 0.54700902 1.09955743 2.68288749 0.48783893 0.48790716 0.48742888 0.48815877 1.41371669 2.55733004 0.44345940 0.44351617 0.44322051 0.44362895 1.72787596 2.45339750 0.40757722 0.40761836 0.40742399 0.40767773 2.04203522 2.36297437 0.37754263 0.37757399 0.37744029 0.37760838 2.35619449 2.28191207 0.35177902 0.35180170 0.35170695 0.35182567 2.67035376 2.20819285 0.32936356 0.32937910 0.32931089 0.32939834 2.98451302 2.14031724 0.30957579 0.30958589 0.30953648 0.30960259 3.29867229 2.07790370 0.29206956 0.29207657 0.29204089 0.29209061 3.61283155 2.02020708 0.27645286 0.27645671 0.27643129 0.27646957 3.92699082 1.96644814 0.26238064 0.26238301 0.26236538 0.26239391 4.24115008 1.91637033 0.24967153 0.24967190 0.24966026 0.24968214 4.55530935 1.86943579 0.23810211 0.23810118 0.23809430 0.23811051 4.86946861 1.82537458 0.22752705 0.22752548 0.22752233 0.22753367 5.18362788 1.78406856 0.21787283 0.21787050 0.21787033 0.21787798 5.49778714 1.74520503 0.20900684 0.20900378 0.20900599 0.20901081 5.81194641 1.70854110 0.20084031 0.20083633 0.20084047 0.20084331 6.12610567 1.67359578 0.19321794 0.19321381 0.19321955 0.19322013 6.44026494 1.64073696 0.18621725 0.18621286 0.18621992 0.18621878 6.75442421 1.60965384 0.17973374 0.17972905 0.17973715 0.17973473 7.06858347 1.57984849 0.17362859 0.17362370 0.17363267 0.17362914 7.38274274 1.55161549 0.16796653 0.16796150 0.16797119 0.16796672 7.69690200 1.52452413 0.16262804 0.16262284 0.16263315 0.16262792 8.01106127 1.49876469 0.15765167 0.15764647 0.15765728 0.15765130 8.32522053 1.47386719 0.15291540 0.15291005 0.15292126 0.15291486 8.63937980 1.45014170 0.14848969 0.14848429 0.14849586 0.14848898 8.95353906 1.42736951 0.14431271 0.14430734 0.14431918 0.14431189 9.26769833 1.40547024 0.14036337 0.14035797 0.14037005 0.14036245 9.58185759 1.38439466 0.13662344 0.13661790 0.13663016 0.13662245 9.89601686 1.36404215 0.13306557 0.13305987 0.13307228 0.13306452 10.21017612 1.34431583 0.12966514 0.12965941 0.12967195 0.12966403 10.52433539 1.32555831 0.12650359 0.12649785 0.12651050 0.12650245 10.83849465 1.30732925 0.12346895 0.12346315 0.12347587 0.12346777 11.15265392 1.28958740 0.12055011 0.12054437 0.12055714 0.12054890 11.46681319 1.27250128 0.11778716 0.11778145 0.11779423 0.11778593 11.78097245 1.25584870 0.11512508 0.11511933 0.11513213 0.11512384 12.09513172 1.23967439 0.11257351 0.11256771 0.11258050 0.11257229 12.40929098 1.22396219 0.11012688 0.11012110 0.11013388 0.11012564 12.72345025 1.20886834 0.10782351 0.10781785 0.10783060 0.10782227 13.03760951 1.19413981 0.10560056 0.10559491 0.10560763 0.10559934 13.35176878 1.17981427 0.10346645 0.10346082 0.10347349 0.10346525 13.66592804 1.16590112 0.10142281 0.10141719 0.10142981 0.10142162 13.98008731 1.15228739 0.09944180 0.09943616 0.09944871 0.09944063 14.29424657 1.13902429 0.09753562 0.09752996 0.09754246 0.09753445 14.60840584 1.12615168 0.09571404 0.09570842 0.09572085 0.09571287 14.92256510 1.11347891 0.09392982 0.09392427 0.09393663 0.09392867 15.23672437 1.10111928 0.09221066 0.09220516 0.09221745 0.09220953 15.55088364 1.08911749 0.09056704 0.09056157 0.09057378 0.09056592 15.86504290 1.07738593 0.08897764 0.08897225 0.08898437 0.08897654 16.17920217 1.06600814 0.08746250 0.08745713 0.08746917 0.08746142 16.49336143 1.05486950 0.08599370 0.08598834 0.08600029 0.08599263 16.80752070 1.04396352 0.08456962 0.08456430 0.08457616 0.08456857 17.12167996 1.03336198 0.08320752 0.08320224 0.08321401 0.08320649 17.43583923 1.02288555 0.08186398 0.08185871 0.08187037 0.08186297 17.74999849 1.01252032 0.08053565 0.08053040 0.08054198 0.08053465 18.06415776 1.00241895 0.07925949 0.07925427 0.07926577 0.07925849 18.37831702 0.99264541 0.07805102 0.07804586 0.07805727 0.07805003 18.69247629 0.98305202 0.07687444 0.07686936 0.07688067 0.07687349 19.00663555 0.97365857 0.07573454 0.07572948 0.07574069 0.07573361 19.32079482 0.96440506 0.07461689 0.07461185 0.07462297 0.07461597 19.63495408 0.95524558 0.07351050 0.07350549 0.07351651 0.07350959 19.94911335 0.94621877 0.07242479 0.07241981 0.07243074 0.07242389 20.26327262 0.93747432 0.07139590 0.07139095 0.07140179 0.07139501 20.57743188 0.92898080 0.07041628 0.07041136 0.07042211 0.07041540 20.89159115 0.92067341 0.06947036 0.06946547 0.06947614 0.06946949 21.20575041 0.91254314 0.06855604 0.06855119 0.06856177 0.06855518 21.51990968 0.90456608 0.06766763 0.06766282 0.06767331 0.06766678 21.83406894 0.89672538 0.06680116 0.06679638 0.06680679 0.06680032 22.14822821 0.88901609 0.06595552 0.06595078 0.06596110 0.06595469 22.46238747 0.88143485 0.06512999 0.06512529 0.06513552 0.06512917 22.77654674 0.87397842 0.06432389 0.06431923 0.06432938 0.06432308 23.09070600 0.86664372 0.06353658 0.06353196 0.06354202 0.06353578 23.40486527 0.85942774 0.06276743 0.06276285 0.06277282 0.06276664 23.71902453 0.85232759 0.06201585 0.06201130 0.06202119 0.06201507 24.03318380 0.84534048 0.06128126 0.06127675 0.06128656 0.06128049 24.34734307 0.83846372 0.06056312 0.06055864 0.06056837 0.06056236 24.66150233 0.83169470 0.05986091 0.05985647 0.05986611 0.05986015 24.97566160 0.82503091 0.05917412 0.05916972 0.05917928 0.05917337 25.28982086 0.81846990 0.05850228 0.05849791 0.05850739 0.05850154 25.60398013 0.81200932 0.05784492 0.05784058 0.05784999 0.05784419 25.91813939 0.80564689 0.05720159 0.05719730 0.05720662 0.05720087 26.23229866 0.79938040 0.05657188 0.05656762 0.05657687 0.05657117 26.54645792 0.79320771 0.05595538 0.05595115 0.05596032 0.05595467 26.86061719 0.78712673 0.05535169 0.05534749 0.05535659 0.05535099 27.17477645 0.78113547 0.05476043 0.05475626 0.05476529 0.05475974 27.48893572 0.77523196 0.05418123 0.05417711 0.05418605 0.05418055 27.80309498 0.76941429 0.05361376 0.05360966 0.05361853 0.05361308 28.11725425 0.76368060 0.05305765 0.05305359 0.05306239 0.05305698 28.43141351 0.75802908 0.05251259 0.05250856 0.05251729 0.05251193 28.74557278 0.75245797 0.05197825 0.05197425 0.05198291 0.05197760 29.05973205 0.74696559 0.05145433 0.05145036 0.05145895 0.05145369 29.37389131 0.74155028 0.05094054 0.05093660 0.05094513 0.05093990 29.68805058 0.73621043 0.05043659 0.05043269 0.05044114 0.05043596 30.00220984 0.73094448 0.04994222 0.04993834 0.04994673 0.04994159 30.31636911 0.72575092 0.04945715 0.04945330 0.04946162 0.04945653 30.63052837 0.72062829 0.04898113 0.04897732 0.04898557 0.04898052 30.94468764 0.71557513 0.04851393 0.04851014 0.04851833 0.04851332 31.25884690 0.71059008 0.04805530 0.04805154 0.04805966 0.04805469 31.57300617 0.70567176 0.04760501 0.04760128 0.04760935 0.04760442 31.88716543 0.70081887 0.04716286 0.04715916 0.04716716 0.04716227 32.20132470 0.69603012 0.04672862 0.04672494 0.04673288 0.04672803 32.51548396 0.69130426 0.04630209 0.04629844 0.04630632 0.04630151 32.82964323 0.68664007 0.04588307 0.04587945 0.04588727 0.04588249 33.14380250 0.68203638 0.04547137 0.04546778 0.04547554 0.04547080 33.45796176 0.67749203 0.04506681 0.04506324 0.04507094 0.04506625 33.77212103 0.67300589 0.04466921 0.04466567 0.04467331 0.04466865 34.08628029 0.66857686 0.04427839 0.04427487 0.04428246 0.04427783 34.40043956 0.66420389 0.04389419 0.04389070 0.04389823 0.04389364 34.71459882 0.65988593 0.04351644 0.04351298 0.04352045 0.04351590 35.02875809 0.65562196 0.04314500 0.04314156 0.04314898 0.04314446 35.34291735 0.65141099 0.04277970 0.04277629 0.04278365 0.04277916 35.65707662 0.64725206 0.04242040 0.04241701 0.04242432 0.04241987 35.97123588 0.64314421 0.04206696 0.04206359 0.04207085 0.04206643 36.28539515 0.63908652 0.04171923 0.04171589 0.04172310 0.04171871 36.59955441 0.63507808 0.04137708 0.04137377 0.04138092 0.04137657 36.91371368 0.63111801 0.04104039 0.04103709 0.04104420 0.04103988 37.22787295 0.62720545 0.04070902 0.04070575 0.04071280 0.04070851 37.54203221 0.62333955 0.04038285 0.04037960 0.04038660 0.04038234 37.85619148 0.61951950 0.04006175 0.04005853 0.04006548 0.04006125 38.17035074 0.61574448 0.03974563 0.03974242 0.03974933 0.03974513 38.48451001 0.61201373 0.03943435 0.03943117 0.03943803 0.03943386 38.79866927 0.60832646 0.03912782 0.03912466 0.03913147 0.03912734 39.11282854 0.60468194 0.03882593 0.03882279 0.03882956 0.03882545 39.42698780 0.60107943 0.03852857 0.03852545 0.03853217 0.03852809 39.74114707 0.59751822 0.03823565 0.03823255 0.03823923 0.03823517 40.05530633 0.59399760 0.03794707 0.03794399 0.03795062 0.03794659 40.36946560 0.59051690 0.03766273 0.03765967 0.03766625 0.03766226 40.68362486 0.58707545 0.03738254 0.03737950 0.03738604 0.03738207 40.99778413 0.58367259 0.03710642 0.03710340 0.03710990 0.03710596 41.31194339 0.58030769 0.03683427 0.03683128 0.03683773 0.03683382 41.62610266 0.57698012 0.03656602 0.03656305 0.03656946 0.03656557 41.94026193 0.57368927 0.03630159 0.03629863 0.03630500 0.03630114 42.25442119 0.57043455 0.03604088 0.03603794 0.03604427 0.03604044 42.56858046 0.56721536 0.03578384 0.03578091 0.03578720 0.03578339 42.88273972 0.56403114 0.03553037 0.03552747 0.03553372 0.03552993 43.19689899 0.56088133 0.03528041 0.03527753 0.03528374 0.03527998 43.51105825 0.55776538 0.03503389 0.03503103 0.03503720 0.03503346 43.82521752 0.55468274 0.03479074 0.03478789 0.03479402 0.03479031 44.13937678 0.55163291 0.03455089 0.03454806 0.03455415 0.03455046 44.45353605 0.54861535 0.03431427 0.03431146 0.03431751 0.03431385 44.76769531 0.54562957 0.03408083 0.03407803 0.03408405 0.03408041 45.08185458 0.54267508 0.03385049 0.03384771 0.03385369 0.03385007 45.39601384 0.53975139 0.03362321 0.03362045 0.03362639 0.03362279 45.71017311 0.53685802 0.03339891 0.03339616 0.03340207 0.03339850 46.02433238 0.53399452 0.03317755 0.03317482 0.03318069 0.03317713 46.33849164 0.53116042 0.03295906 0.03295634 0.03296218 0.03295865 46.65265091 0.52835528 0.03274339 0.03274069 0.03274649 0.03274298 46.96681017 0.52557866 0.03253049 0.03252781 0.03253357 0.03253008 47.28096944 0.52283014 0.03232030 0.03231763 0.03232336 0.03231990 47.59512870 0.52010928 0.03211277 0.03211013 0.03211582 0.03211238 47.90928797 0.51741568 0.03190786 0.03190523 0.03191089 0.03190747 48.22344723 0.51474894 0.03170552 0.03170290 0.03170853 0.03170513 48.53760650 0.51210866 0.03150569 0.03150309 0.03150869 0.03150530 48.85176576 0.50949444 0.03130834 0.03130575 0.03131131 0.03130795 49.16592503 0.50690591 0.03111341 0.03111083 0.03111637 0.03111302 49.48008429 0.50434269 0.03092086 0.03091830 0.03092380 0.03092048 49.79424356 0.50180442 0.03073065 0.03072811 0.03073358 0.03073027 50.10840282 0.49929074 0.03054274 0.03054021 0.03054565 0.03054237 50.42256209 0.49680130 0.03035709 0.03035457 0.03035998 0.03035671 50.73672136 0.49433574 0.03017365 0.03017115 0.03017653 0.03017328 51.05088062 0.49189373 0.02999239 0.02998991 0.02999525 0.02999202 51.36503989 0.48947494 0.02981327 0.02981080 0.02981612 0.02981291 51.67919915 0.48707904 0.02963626 0.02963379 0.02963908 0.02963589 51.99335842 0.48470571 0.02946130 0.02945886 0.02946412 0.02946094 52.30751768 0.48235463 0.02928838 0.02928595 0.02929118 0.02928802 52.62167695 0.48002550 0.02911746 0.02911503 0.02912024 0.02911710 52.93583621 0.47771801 0.02894849 0.02894608 0.02895126 0.02894813 53.24999548 0.47543186 0.02878145 0.02877906 0.02878420 0.02878110 53.56415474 0.47316677 0.02861631 0.02861393 0.02861905 0.02861596 53.87831401 0.47092244 0.02845304 0.02845067 0.02845576 0.02845269 54.19247327 0.46869860 0.02829159 0.02828924 0.02829430 0.02829124 54.50663254 0.46649497 0.02813195 0.02812961 0.02813464 0.02813160 54.82079181 0.46431127 0.02797408 0.02797175 0.02797676 0.02797374 55.13495107 0.46214724 0.02781796 0.02781564 0.02782062 0.02781762 55.44911034 0.46000262 0.02766355 0.02766124 0.02766620 0.02766321 55.76326960 0.45787714 0.02751083 0.02750853 0.02751346 0.02751049 56.07742887 0.45577057 0.02735977 0.02735748 0.02736239 0.02735943 56.39158813 0.45368264 0.02721034 0.02720807 0.02721295 0.02721001 56.70574740 0.45161312 0.02706252 0.02706026 0.02706512 0.02706219 57.01990666 0.44956176 0.02691629 0.02691404 0.02691887 0.02691595 57.33406593 0.44752833 0.02677161 0.02676937 0.02677417 0.02677128 57.64822519 0.44551259 0.02662846 0.02662623 0.02663101 0.02662813 57.96238446 0.44351433 0.02648682 0.02648461 0.02648936 0.02648650 58.27654372 0.44153331 0.02634667 0.02634447 0.02634920 0.02634635 58.59070299 0.43956932 0.02620798 0.02620579 0.02621050 0.02620766 58.90486225 0.43762214 0.02607073 0.02606855 0.02607323 0.02607041 59.21902152 0.43569155 0.02593490 0.02593273 0.02593739 0.02593458 59.53318079 0.43377736 0.02580046 0.02579830 0.02580294 0.02580014 59.84734005 0.43187934 0.02566740 0.02566525 0.02566987 0.02566708 60.16149932 0.42999730 0.02553569 0.02553355 0.02553815 0.02553538 60.47565858 0.42813105 0.02540532 0.02540319 0.02540776 0.02540501 60.78981785 0.42628038 0.02527626 0.02527414 0.02527869 0.02527595 61.10397711 0.42444510 0.02514850 0.02514639 0.02515091 0.02514819 61.41813638 0.42262503 0.02502201 0.02501991 0.02502441 0.02502170 61.73229564 0.42081997 0.02489677 0.02489468 0.02489917 0.02489647 62.04645491 0.41902974 0.02477277 0.02477070 0.02477516 0.02477247 62.36061417 0.41725417 0.02465000 0.02464793 0.02465237 0.02464969 62.67477344 0.41549308 0.02452842 0.02452636 0.02453078 0.02452812 62.98893270 0.41374628 0.02440803 0.02440598 0.02441038 0.02440773 63.30309197 0.41201361 0.02428881 0.02428676 0.02429114 0.02428851 63.61725124 0.41029491 0.02417073 0.02416870 0.02417306 0.02417043 63.93141050 0.40859000 0.02405379 0.02405177 0.02405611 0.02405349 64.24556977 0.40689871 0.02393797 0.02393595 0.02394027 0.02393767 64.55972903 0.40522090 0.02382325 0.02382124 0.02382554 0.02382295 64.87388830 0.40355640 0.02370961 0.02370762 0.02371190 0.02370932 65.18804756 0.40190505 0.02359705 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