# omega total a= 1 L= 2 a= 2 L= 2 a= 3 L= 2 a= 4 L= 2 0.15707963 3.53543631 0.76492186 0.76523407 0.76311890 0.76649791 0.47123890 3.11044116 0.63189944 0.63194559 0.63041917 0.63333758 0.78539816 2.84943712 0.54613622 0.54620630 0.54538142 0.54680430 1.09955743 2.68229967 0.48767915 0.48775067 0.48727837 0.48799964 1.41371669 2.55663463 0.44327103 0.44333230 0.44304029 0.44344122 1.72787596 2.45287974 0.40743402 0.40747777 0.40728557 0.40753529 2.04203522 2.36255688 0.37743549 0.37746406 0.37733182 0.37750192 2.35619449 2.28147106 0.35166464 0.35168637 0.35159277 0.35171170 2.67035376 2.20769441 0.32923235 0.32924656 0.32917921 0.32926739 2.98451302 2.14006377 0.30950325 0.30951473 0.30946592 0.30953027 3.29867229 2.07762259 0.29198877 0.29199658 0.29196129 0.29200993 3.61283155 2.01972101 0.27632601 0.27633108 0.27630599 0.27634274 3.92699082 1.96594367 0.26224971 0.26225226 0.26223488 0.26226301 4.24115008 1.91597547 0.24957102 0.24957149 0.24956005 0.24958160 4.55530935 1.86917745 0.23803678 0.23803534 0.23802855 0.23804517 4.86946861 1.82517578 0.22747994 0.22747809 0.22747500 0.22748654 5.18362788 1.78383308 0.21781564 0.21781267 0.21781253 0.21782077 5.49778714 1.74476533 0.20890209 0.20889836 0.20890061 0.20890603 5.81194641 1.70805589 0.20072376 0.20071974 0.20072391 0.20072672 6.12610567 1.67339293 0.19317224 0.19316810 0.19317382 0.19317440 6.44026494 1.64055500 0.18617610 0.18617160 0.18617860 0.18617760 6.75442421 1.60927291 0.17964294 0.17963814 0.17964621 0.17964389 7.06858347 1.57964291 0.17358384 0.17357899 0.17358795 0.17358433 7.38274274 1.55134561 0.16790474 0.16789967 0.16790932 0.16790487 7.69690200 1.52425772 0.16256805 0.16256270 0.16257296 0.16256788 8.01106127 1.49834551 0.15755416 0.15754865 0.15755940 0.15755376 8.32522053 1.47361498 0.15285901 0.15285346 0.15286464 0.15285841 8.63937980 1.44992654 0.14844176 0.14843606 0.14844757 0.14844099 8.95353906 1.42721673 0.14428181 0.14427607 0.14428787 0.14428090 9.26769833 1.40529757 0.14032693 0.14032137 0.14033342 0.14032592 9.58185759 1.38438212 0.13662684 0.13662133 0.13663356 0.13662574 9.89601686 1.36408297 0.13308212 0.13307653 0.13308888 0.13308097 10.21017612 1.34432581 0.12967368 0.12966798 0.12968046 0.12967249 10.52433539 1.32542052 0.12647580 0.12647003 0.12648260 0.12647458 10.83849465 1.30712624 0.12342536 0.12341953 0.12343218 0.12342410 11.15265392 1.28943819 0.12051946 0.12051373 0.12052641 0.12051817 11.46681319 1.27202235 0.11767542 0.11766971 0.11768241 0.11767413 11.78097245 1.25541390 0.11502441 0.11501864 0.11503136 0.11502310 12.09513172 1.23933985 0.11249776 0.11249201 0.11250474 0.11249644 12.40929098 1.22376110 0.11008469 0.11007896 0.11009168 0.11008338 12.72345025 1.20863925 0.10777434 0.10776867 0.10778136 0.10777304 13.03760951 1.19386940 0.10554098 0.10553532 0.10554796 0.10553970 13.35176878 1.17956371 0.10341173 0.10340606 0.10341866 0.10341046 13.66592804 1.16551415 0.10133506 0.10132936 0.10134192 0.10133379 13.98008731 1.15196791 0.09937076 0.09936509 0.09937759 0.09936950 14.29424657 1.13894751 0.09752405 0.09751840 0.09753084 0.09752281 14.60840584 1.12613234 0.09571619 0.09571055 0.09572292 0.09571496 14.92256510 1.11343527 0.09392593 0.09392037 0.09393265 0.09392472 15.23672437 1.10106360 0.09220372 0.09219821 0.09221042 0.09220253 15.55088364 1.08899310 0.09054334 0.09053787 0.09055000 0.09054216 15.86504290 1.07723831 0.08894809 0.08894264 0.08895469 0.08894691 16.17920217 1.06581288 0.08742130 0.08741588 0.08742786 0.08742013 16.49336143 1.05468645 0.08595555 0.08595017 0.08596206 0.08595439 16.80752070 1.04377090 0.08452920 0.08452386 0.08453566 0.08452806 17.12167996 1.03316249 0.08316543 0.08316012 0.08317184 0.08316430 17.43583923 1.02263779 0.08181017 0.08180489 0.08181652 0.08180906 17.74999849 1.01223539 0.08047291 0.08046765 0.08047919 0.08047180 18.06415776 1.00210720 0.07919030 0.07918510 0.07919655 0.07918921 18.37831702 0.99239229 0.07799593 0.07799078 0.07800214 0.07799487 18.69247629 0.98278087 0.07681493 0.07680982 0.07682109 0.07681387 19.00663555 0.97307159 0.07559875 0.07559367 0.07560484 0.07559771 19.32079482 0.96367021 0.07444550 0.07444045 0.07445153 0.07444447 19.63495408 0.95462840 0.07336763 0.07336262 0.07337361 0.07336661 19.94911335 0.94584480 0.07234064 0.07233569 0.07234659 0.07233964 20.26327262 0.93727383 0.07135361 0.07134870 0.07135951 0.07135263 20.57743188 0.92887100 0.07039586 0.07039099 0.07040171 0.07039489 20.89159115 0.92061560 0.06946246 0.06945762 0.06946825 0.06946150 21.20575041 0.91250235 0.06855221 0.06854742 0.06855796 0.06855126 21.51990968 0.90452751 0.06766431 0.06765955 0.06767000 0.06766337 21.83406894 0.89668748 0.06679796 0.06679324 0.06680361 0.06679703 22.14822821 0.88897880 0.06595243 0.06594775 0.06595803 0.06595152 22.46238747 0.88139813 0.06512701 0.06512237 0.06513256 0.06512611 22.77654674 0.87394226 0.06432102 0.06431641 0.06432651 0.06432012 23.09070600 0.86660808 0.06353380 0.06352923 0.06353925 0.06353291 23.40486527 0.85939259 0.06276474 0.06276020 0.06277014 0.06276386 23.71902453 0.85229292 0.06201323 0.06200874 0.06201859 0.06201237 24.03318380 0.84530627 0.06127872 0.06127426 0.06128403 0.06127787 24.34734307 0.83842995 0.06056066 0.06055624 0.06056592 0.06055982 24.66150233 0.83166134 0.05985852 0.05985413 0.05986373 0.05985768 24.97566160 0.82499795 0.05917179 0.05916744 0.05917697 0.05917097 25.28982086 0.81843733 0.05850001 0.05849570 0.05850514 0.05849920 25.60398013 0.81197712 0.05784271 0.05783843 0.05784779 0.05784190 25.91813939 0.80561504 0.05719944 0.05719519 0.05720448 0.05719865 26.23229866 0.79934889 0.05656978 0.05656557 0.05657478 0.05656900 26.54645792 0.79317653 0.05595333 0.05594915 0.05595828 0.05595255 26.86061719 0.78709588 0.05534968 0.05534554 0.05535460 0.05534892 27.17477645 0.78110493 0.05475847 0.05475436 0.05476334 0.05475771 27.48893572 0.77520171 0.05417932 0.05417524 0.05418415 0.05417857 27.80309498 0.76938433 0.05361188 0.05360784 0.05361667 0.05361114 28.11725425 0.76365092 0.05305582 0.05305180 0.05306056 0.05305508 28.43141351 0.75799967 0.05251079 0.05250681 0.05251550 0.05251006 28.74557278 0.75242884 0.05197649 0.05197254 0.05198116 0.05197577 29.05973205 0.74693671 0.05145260 0.05144868 0.05145724 0.05145189 29.37389131 0.74152165 0.05093884 0.05093495 0.05094344 0.05093814 29.68805058 0.73618204 0.05043493 0.05043107 0.05043948 0.05043423 30.00220984 0.73091633 0.04994058 0.04993675 0.04994510 0.04993989 30.31636911 0.72572301 0.04945554 0.04945174 0.04946002 0.04945485 30.63052837 0.72060059 0.04897955 0.04897578 0.04898400 0.04897887 30.94468764 0.71554766 0.04851237 0.04850863 0.04851678 0.04851170 31.25884690 0.71056282 0.04805377 0.04805005 0.04805814 0.04805310 31.57300617 0.70564472 0.04760351 0.04759982 0.04760785 0.04760285 31.88716543 0.70079203 0.04716137 0.04715772 0.04716568 0.04716072 32.20132470 0.69600348 0.04672715 0.04672353 0.04673143 0.04672651 32.51548396 0.69127781 0.04630064 0.04629704 0.04630489 0.04630001 32.82964323 0.68661382 0.04588165 0.04587807 0.04588586 0.04588101 33.14380250 0.68201032 0.04546997 0.04546642 0.04547415 0.04546934 33.45796176 0.67746615 0.04506543 0.04506191 0.04506957 0.04506481 33.77212103 0.67298019 0.04466784 0.04466435 0.04467196 0.04466723 34.08628029 0.66855135 0.04427704 0.04427357 0.04428113 0.04427643 34.40043956 0.66417855 0.04389286 0.04388942 0.04389691 0.04389226 34.71459882 0.65986076 0.04351513 0.04351171 0.04351915 0.04351453 35.02875809 0.65559696 0.04314370 0.04314031 0.04314769 0.04314311 35.34291735 0.65138616 0.04277842 0.04277505 0.04278238 0.04277783 35.65707662 0.64722739 0.04241914 0.04241579 0.04242307 0.04241855 35.97123588 0.64311970 0.04206571 0.04206238 0.04206961 0.04206513 36.28539515 0.63906217 0.04171800 0.04171470 0.04172187 0.04171742 36.59955441 0.63505388 0.04137586 0.04137259 0.04137971 0.04137529 36.91371368 0.63109397 0.04103918 0.04103593 0.04104300 0.04103862 37.22787295 0.62718155 0.04070782 0.04070459 0.04071161 0.04070726 37.54203221 0.62331581 0.04038166 0.04037846 0.04038543 0.04038111 37.85619148 0.61949590 0.04006059 0.04005740 0.04006432 0.04006003 38.17035074 0.61572103 0.03974447 0.03974131 0.03974818 0.03974392 38.48451001 0.61199041 0.03943321 0.03943007 0.03943689 0.03943267 38.79866927 0.60830329 0.03912669 0.03912357 0.03913035 0.03912615 39.11282854 0.60465890 0.03882481 0.03882171 0.03882844 0.03882427 39.42698780 0.60105653 0.03852746 0.03852438 0.03853107 0.03852693 39.74114707 0.59749545 0.03823455 0.03823149 0.03823813 0.03823402 40.05530633 0.59397496 0.03794598 0.03794294 0.03794954 0.03794545 40.36946560 0.59049439 0.03766165 0.03765863 0.03766518 0.03766113 40.68362486 0.58705307 0.03738147 0.03737847 0.03738498 0.03738096 40.99778413 0.58365034 0.03710536 0.03710238 0.03710885 0.03710485 41.31194339 0.58028556 0.03683322 0.03683026 0.03683669 0.03683272 41.62610266 0.57695811 0.03656498 0.03656204 0.03656843 0.03656448 41.94026193 0.57366739 0.03630055 0.03629763 0.03630398 0.03630006 42.25442119 0.57041278 0.03603986 0.03603696 0.03604326 0.03603937 42.56858046 0.56719372 0.03578282 0.03577994 0.03578620 0.03578233 42.88273972 0.56400962 0.03552936 0.03552650 0.03553272 0.03552888 43.19689899 0.56085992 0.03527942 0.03527657 0.03528275 0.03527893 43.51105825 0.55774408 0.03503290 0.03503007 0.03503621 0.03503242 43.82521752 0.55466156 0.03478976 0.03478695 0.03479305 0.03478928 44.13937678 0.55161183 0.03454992 0.03454712 0.03455318 0.03454944 44.45353605 0.54859439 0.03431331 0.03431053 0.03431656 0.03431284 44.76769531 0.54560872 0.03407987 0.03407711 0.03408310 0.03407940 45.08185458 0.54265433 0.03384954 0.03384680 0.03385275 0.03384908 45.39601384 0.53973074 0.03362226 0.03361954 0.03362545 0.03362180 45.71017311 0.53683748 0.03339797 0.03339526 0.03340114 0.03339752 46.02433238 0.53397408 0.03317662 0.03317392 0.03317977 0.03317616 46.33849164 0.53114009 0.03295813 0.03295545 0.03296126 0.03295768 46.65265091 0.52833505 0.03274247 0.03273981 0.03274558 0.03274202 46.96681017 0.52555853 0.03252958 0.03252693 0.03253267 0.03252913 47.28096944 0.52281010 0.03231940 0.03231676 0.03232247 0.03231895 47.59512870 0.52008935 0.03211188 0.03210926 0.03211493 0.03211144 47.90928797 0.51739585 0.03190697 0.03190437 0.03191001 0.03190654 48.22344723 0.51472920 0.03170464 0.03170205 0.03170765 0.03170420 48.53760650 0.51208901 0.03150481 0.03150224 0.03150782 0.03150438 48.85176576 0.50947489 0.03130746 0.03130491 0.03131045 0.03130704 49.16592503 0.50688645 0.03111254 0.03111000 0.03111551 0.03111212 49.48008429 0.50432333 0.03092000 0.03091747 0.03092295 0.03091958 49.79424356 0.50178515 0.03072980 0.03072729 0.03073273 0.03072938 50.10840282 0.49927156 0.03054189 0.03053940 0.03054481 0.03054148 50.42256209 0.49678220 0.03035625 0.03035376 0.03035914 0.03035583 50.73672136 0.49431673 0.03017281 0.03017034 0.03017570 0.03017240 51.05088062 0.49187481 0.02999156 0.02998910 0.02999443 0.02999115 51.36503989 0.48945611 0.02981245 0.02981000 0.02981530 0.02981204 51.67919915 0.48706029 0.02963543 0.02963300 0.02963827 0.02963503 51.99335842 0.48468704 0.02946049 0.02945807 0.02946331 0.02946008 52.30751768 0.48233605 0.02928757 0.02928517 0.02929037 0.02928717 52.62167695 0.48000700 0.02911665 0.02911426 0.02911944 0.02911625 52.93583621 0.47769959 0.02894769 0.02894531 0.02895046 0.02894729 53.24999548 0.47541353 0.02878066 0.02877829 0.02878341 0.02878026 53.56415474 0.47314852 0.02861552 0.02861317 0.02861826 0.02861513 53.87831401 0.47090427 0.02845225 0.02844991 0.02845498 0.02845186 54.19247327 0.46868051 0.02829081 0.02828848 0.02829352 0.02829042 54.50663254 0.46647695 0.02813117 0.02812886 0.02813387 0.02813079 54.82079181 0.46429333 0.02797331 0.02797101 0.02797599 0.02797293 55.13495107 0.46212938 0.02781719 0.02781490 0.02781986 0.02781681 55.44911034 0.45998484 0.02766279 0.02766051 0.02766544 0.02766241 55.76326960 0.45785944 0.02751007 0.02750780 0.02751271 0.02750969 56.07742887 0.45575294 0.02735901 0.02735676 0.02736164 0.02735864 56.39158813 0.45366508 0.02720959 0.02720735 0.02721220 0.02720922 56.70574740 0.45159563 0.02706178 0.02705954 0.02706438 0.02706141 57.01990666 0.44954435 0.02691554 0.02691332 0.02691813 0.02691518 57.33406593 0.44751099 0.02677087 0.02676866 0.02677344 0.02677050 57.64822519 0.44549533 0.02662772 0.02662553 0.02663029 0.02662736 57.96238446 0.44349714 0.02648609 0.02648390 0.02648864 0.02648573 58.27654372 0.44151619 0.02634594 0.02634377 0.02634848 0.02634558 58.59070299 0.43955227 0.02620726 0.02620509 0.02620978 0.02620690 58.90486225 0.43760516 0.02607001 0.02606786 0.02607252 0.02606966 59.21902152 0.43567464 0.02593418 0.02593204 0.02593668 0.02593383 59.53318079 0.43376051 0.02579975 0.02579762 0.02580224 0.02579940 59.84734005 0.43186256 0.02566669 0.02566457 0.02566917 0.02566634 60.16149932 0.42998059 0.02553499 0.02553288 0.02553745 0.02553464 60.47565858 0.42811440 0.02540462 0.02540252 0.02540707 0.02540427 60.78981785 0.42626380 0.02527556 0.02527347 0.02527800 0.02527522 61.10397711 0.42442859 0.02514780 0.02514572 0.02515023 0.02514746 61.41813638 0.42260858 0.02502132 0.02501924 0.02502373 0.02502098 61.73229564 0.42080358 0.02489609 0.02489402 0.02489849 0.02489575 62.04645491 0.41901342 0.02477209 0.02477004 0.02477448 0.02477176 62.36061417 0.41723791 0.02464932 0.02464727 0.02465170 0.02464898 62.67477344 0.41547688 0.02452775 0.02452571 0.02453011 0.02452741 62.98893270 0.41373015 0.02440736 0.02440533 0.02440971 0.02440703 63.30309197 0.41199754 0.02428814 0.02428612 0.02429048 0.02428781 63.61725124 0.41027890 0.02417006 0.02416806 0.02417240 0.02416974 63.93141050 0.40857405 0.02405313 0.02405113 0.02405545 0.02405280 64.24556977 0.40688282 0.02393731 0.02393532 0.02393962 0.02393698 64.55972903 0.40520507 0.02382259 0.02382061 0.02382489 0.02382227 64.87388830 0.40354063 0.02370896 0.02370699 0.02371125 0.02370864 65.18804756 0.40188934 0.02359640 0.02359444 0.02359868 0.02359608 65.50220683 0.40025105 0.02348489 0.02348294 0.02348716 0.02348457 65.81636609 0.39862561 0.02337443 0.02337249 0.02337669 0.02337411 66.13052536 0.39701287 0.02326499 0.02326306 0.02326724 0.02326468 66.44468462 0.39541268 0.02315657 0.02315464 0.02315881 0.02315625 66.75884389 0.39382491 0.02304914 0.02304723 0.02305137 0.02304883 67.07300315 0.39224940 0.02294270 0.02294079 0.02294492 0.02294239 67.38716242 0.39068602 0.02283723 0.02283533 0.02283945 0.02283692 67.70132168 0.38913463 0.02273272 0.02273083 0.02273493 0.02273242 68.01548095 0.38759509 0.02262916 0.02262728 0.02263135 0.02262885 68.32964022 0.38606727 0.02252653 0.02252465 0.02252871 0.02252622 68.64379948 0.38455104 0.02242482 0.02242295 0.02242699 0.02242451 68.95795875 0.38304627 0.02232402 0.02232216 0.02232618 0.02232371 69.27211801 0.38155283 0.02222411 0.02222226 0.02222626 0.02222381 69.58627728 0.38007060 0.02212509 0.02212324 0.02212723 0.02212479 69.90043654 0.37859944 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