# omega total a= 1 L= 2 a= 2 L= 2 a= 3 L= 2 a= 4 L= 2 0.15707963 3.53969976 0.76595526 0.76628011 0.76413761 0.76751249 0.47123890 3.11228517 0.63235144 0.63240275 0.63085231 0.63379596 0.78539816 2.84984762 0.54623502 0.54631652 0.54548078 0.54690395 1.09955743 2.68281034 0.48782333 0.48789210 0.48741431 0.48814294 1.41371669 2.55716691 0.44342499 0.44348135 0.44318596 0.44359414 1.72787596 2.45328523 0.40755505 0.40759748 0.40740319 0.40765533 2.04203522 2.36290081 0.37752386 0.37755774 0.37742409 0.37758941 2.35619449 2.28185688 0.35176733 0.35178603 0.35169133 0.35181390 2.67035376 2.20797180 0.32929897 0.32931346 0.32924529 0.32933367 2.98451302 2.14033989 0.30957236 0.30958273 0.30953332 0.30959913 3.29867229 2.07801049 0.29208801 0.29209365 0.29205794 0.29210908 3.61283155 2.02014447 0.27642795 0.27643058 0.27640512 0.27644465 3.92699082 1.96625663 0.26232212 0.26232264 0.26230499 0.26233544 4.24115008 1.91603621 0.24957889 0.24957831 0.24956671 0.24958950 4.55530935 1.86902221 0.23798624 0.23798510 0.23797821 0.23799464 4.86946861 1.82510851 0.22745734 0.22745498 0.22745186 0.22746394 5.18362788 1.78382122 0.21780753 0.21780484 0.21780469 0.21781266 5.49778714 1.74492924 0.20893722 0.20893373 0.20893596 0.20894118 5.81194641 1.70816186 0.20074123 0.20073746 0.20074162 0.20074422 6.12610567 1.67359978 0.19321848 0.19321448 0.19322022 0.19322066 6.44026494 1.64068528 0.18620130 0.18619695 0.18620400 0.18620281 6.75442421 1.60953964 0.17970144 0.17969681 0.17970491 0.17970242 7.06858347 1.57978350 0.17360976 0.17360512 0.17361410 0.17361028 7.38274274 1.55153268 0.16794482 0.16793979 0.16794950 0.16794501 7.69690200 1.52450352 0.16262069 0.16261556 0.16262586 0.16262058 8.01106127 1.49863372 0.15761749 0.15761236 0.15762318 0.15761714 8.32522053 1.47389919 0.15292192 0.15291661 0.15292785 0.15292137 8.63937980 1.45024960 0.14851317 0.14850778 0.14851936 0.14851245 8.95353906 1.42720263 0.14426786 0.14426238 0.14427426 0.14426701 9.26769833 1.40524512 0.14030379 0.14029825 0.14031037 0.14030283 9.58185759 1.38427655 0.13659070 0.13658507 0.13659737 0.13658965 9.89601686 1.36399558 0.13305203 0.13304633 0.13305877 0.13305094 10.21017612 1.34439028 0.12968114 0.12967542 0.12968797 0.12968001 10.52433539 1.32556111 0.12650145 0.12649570 0.12650835 0.12650028 10.83849465 1.30731787 0.12346308 0.12345731 0.12347002 0.12346189 11.15265392 1.28963275 0.12055818 0.12055241 0.12056515 0.12055698 11.46681319 1.27245661 0.11777381 0.11776802 0.11778081 0.11777259 11.78097245 1.25577731 0.11510505 0.11509932 0.11511212 0.11510381 12.09513172 1.23956705 0.11254453 0.11253878 0.11255158 0.11254329 12.40929098 1.22385426 0.11009830 0.11009253 0.11010533 0.11009705 12.72345025 1.20871368 0.10778399 0.10777822 0.10779100 0.10778275 13.03760951 1.19406302 0.10558002 0.10557429 0.10558703 0.10557879 13.35176878 1.17982643 0.10346758 0.10346185 0.10347454 0.10346636 13.66592804 1.16594076 0.10143069 0.10142500 0.10143763 0.10142948 13.98008731 1.15224976 0.09943099 0.09942533 0.09943790 0.09942980 14.29424657 1.13897746 0.09752273 0.09751708 0.09752958 0.09752155 14.60840584 1.12608836 0.09569709 0.09569143 0.09570387 0.09569592 14.92256510 1.11348216 0.09392913 0.09392349 0.09393585 0.09392797 15.23672437 1.10115938 0.09221880 0.09221320 0.09222549 0.09221766 15.55088364 1.08916883 0.09057793 0.09057239 0.09058459 0.09057681 15.86504290 1.07746006 0.08899395 0.08898845 0.08900056 0.08899286 16.17920217 1.06603221 0.08746674 0.08746123 0.08747326 0.08746565 16.49336143 1.05482294 0.08598087 0.08597538 0.08598734 0.08597979 16.80752070 1.04388289 0.08454853 0.08454306 0.08455494 0.08454746 17.12167996 1.03320959 0.08316900 0.08316361 0.08317539 0.08316794 17.43583923 1.02279078 0.08183947 0.08183415 0.08184583 0.08183844 17.74999849 1.01254820 0.08054088 0.08053560 0.08054720 0.08053987 18.06415776 1.00256259 0.07929278 0.07928753 0.07929905 0.07929178 18.37831702 0.99279282 0.07808517 0.07807994 0.07809136 0.07808418 18.69247629 0.98320172 0.07690905 0.07690387 0.07691519 0.07690808 19.00663555 0.97369728 0.07574234 0.07573723 0.07574844 0.07574139 19.32079482 0.96428691 0.07458692 0.07458184 0.07459295 0.07458598 19.63495408 0.95510216 0.07347451 0.07346945 0.07348047 0.07347358 19.94911335 0.94609093 0.07239259 0.07238757 0.07239850 0.07239167 20.26327262 0.93736581 0.07136839 0.07136342 0.07137426 0.07136748 20.57743188 0.92892220 0.07040085 0.07039592 0.07040668 0.07039996 20.89159115 0.92066261 0.06946650 0.06946161 0.06947228 0.06946561 21.20575041 0.91254832 0.06855606 0.06855121 0.06856179 0.06855519 21.51990968 0.90457255 0.06766799 0.06766317 0.06767367 0.06766713 21.83406894 0.89673165 0.06680149 0.06679671 0.06680712 0.06680064 22.14822821 0.88902214 0.06595581 0.06595108 0.06596140 0.06595498 22.46238747 0.88144068 0.06513026 0.06512556 0.06513579 0.06512943 22.77654674 0.87398406 0.06432414 0.06431948 0.06432962 0.06432332 23.09070600 0.86664917 0.06353680 0.06353218 0.06354224 0.06353600 23.40486527 0.85943301 0.06276763 0.06276305 0.06277302 0.06276683 23.71902453 0.85233269 0.06201603 0.06201148 0.06202137 0.06201524 24.03318380 0.84534542 0.06128142 0.06127691 0.06128671 0.06128064 24.34734307 0.83846851 0.06056326 0.06055879 0.06056851 0.06056249 24.66150233 0.83169934 0.05986103 0.05985659 0.05986624 0.05986027 24.97566160 0.82503541 0.05917423 0.05916983 0.05917939 0.05917348 25.28982086 0.81847427 0.05850237 0.05849801 0.05850749 0.05850163 25.60398013 0.81201356 0.05784500 0.05784067 0.05785007 0.05784427 25.91813939 0.80565101 0.05720166 0.05719737 0.05720669 0.05720094 26.23229866 0.79938440 0.05657194 0.05656768 0.05657693 0.05657123 26.54645792 0.79321160 0.05595543 0.05595120 0.05596037 0.05595472 26.86061719 0.78713052 0.05535173 0.05534753 0.05535663 0.05535103 27.17477645 0.78113916 0.05476046 0.05475630 0.05476532 0.05475976 27.48893572 0.77523555 0.05418126 0.05417713 0.05418608 0.05418057 27.80309498 0.76941778 0.05361377 0.05360968 0.05361855 0.05361309 28.11725425 0.76368400 0.05305766 0.05305360 0.05306240 0.05305699 28.43141351 0.75803239 0.05251259 0.05250856 0.05251729 0.05251193 28.74557278 0.75246120 0.05197825 0.05197425 0.05198291 0.05197759 29.05973205 0.74696874 0.05145432 0.05145036 0.05145895 0.05145367 29.37389131 0.74155335 0.05094053 0.05093659 0.05094511 0.05093988 29.68805058 0.73621342 0.05043657 0.05043267 0.05044112 0.05043594 30.00220984 0.73094740 0.04994219 0.04993832 0.04994670 0.04994156 30.31636911 0.72575378 0.04945712 0.04945327 0.04946159 0.04945650 30.63052837 0.72063107 0.04898110 0.04897728 0.04898554 0.04898048 30.94468764 0.71557785 0.04851389 0.04851010 0.04851829 0.04851328 31.25884690 0.71059273 0.04805526 0.04805150 0.04805962 0.04805465 31.57300617 0.70567436 0.04760497 0.04760124 0.04760930 0.04760437 31.88716543 0.70082141 0.04716281 0.04715911 0.04716711 0.04716222 32.20132470 0.69603260 0.04672857 0.04672489 0.04673283 0.04672798 32.51548396 0.69130668 0.04630203 0.04629839 0.04630627 0.04630145 32.82964323 0.68664244 0.04588301 0.04587939 0.04588721 0.04588244 33.14380250 0.68203870 0.04547131 0.04546772 0.04547548 0.04547074 33.45796176 0.67749429 0.04506675 0.04506319 0.04507089 0.04506619 33.77212103 0.67300810 0.04466915 0.04466561 0.04467325 0.04466859 34.08628029 0.66857904 0.04427833 0.04427481 0.04428240 0.04427777 34.40043956 0.66420602 0.04389413 0.04389064 0.04389817 0.04389358 34.71459882 0.65988801 0.04351638 0.04351292 0.04352039 0.04351583 35.02875809 0.65562400 0.04314493 0.04314149 0.04314891 0.04314439 35.34291735 0.65141299 0.04277963 0.04277622 0.04278358 0.04277910 35.65707662 0.64725401 0.04242033 0.04241694 0.04242425 0.04241980 35.97123588 0.64314612 0.04206689 0.04206352 0.04207078 0.04206636 36.28539515 0.63908839 0.04171916 0.04171582 0.04172303 0.04171864 36.59955441 0.63507992 0.04137701 0.04137370 0.04138085 0.04137650 36.91371368 0.63111981 0.04104032 0.04103702 0.04104413 0.04103980 37.22787295 0.62720721 0.04070895 0.04070567 0.04071273 0.04070844 37.54203221 0.62334128 0.04038277 0.04037952 0.04038653 0.04038227 37.85619148 0.61952119 0.04006168 0.04005845 0.04006541 0.04006118 38.17035074 0.61574615 0.03974555 0.03974235 0.03974926 0.03974506 38.48451001 0.61201536 0.03943428 0.03943110 0.03943796 0.03943379 38.79866927 0.60832806 0.03912775 0.03912459 0.03913140 0.03912726 39.11282854 0.60468351 0.03882585 0.03882271 0.03882948 0.03882537 39.42698780 0.60108097 0.03852850 0.03852538 0.03853210 0.03852802 39.74114707 0.59751973 0.03823557 0.03823248 0.03823915 0.03823510 40.05530633 0.59399908 0.03794699 0.03794391 0.03795054 0.03794652 40.36946560 0.59051835 0.03766265 0.03765959 0.03766618 0.03766218 40.68362486 0.58707688 0.03738246 0.03737943 0.03738597 0.03738200 40.99778413 0.58367399 0.03710634 0.03710332 0.03710982 0.03710588 41.31194339 0.58030907 0.03683420 0.03683120 0.03683765 0.03683374 41.62610266 0.57698147 0.03656595 0.03656297 0.03656938 0.03656549 41.94026193 0.57369060 0.03630151 0.03629855 0.03630492 0.03630106 42.25442119 0.57043585 0.03604081 0.03603787 0.03604420 0.03604036 42.56858046 0.56721664 0.03578376 0.03578084 0.03578713 0.03578332 42.88273972 0.56403240 0.03553029 0.03552739 0.03553364 0.03552985 43.19689899 0.56088257 0.03528034 0.03527745 0.03528366 0.03527990 43.51105825 0.55776659 0.03503382 0.03503095 0.03503712 0.03503338 43.82521752 0.55468394 0.03479066 0.03478782 0.03479395 0.03479023 44.13937678 0.55163408 0.03455081 0.03454798 0.03455407 0.03455038 44.45353605 0.54861650 0.03431420 0.03431138 0.03431744 0.03431377 44.76769531 0.54563070 0.03408075 0.03407796 0.03408397 0.03408033 45.08185458 0.54267619 0.03385042 0.03384764 0.03385362 0.03385000 45.39601384 0.53975248 0.03362313 0.03362037 0.03362631 0.03362271 45.71017311 0.53685909 0.03339883 0.03339609 0.03340200 0.03339842 46.02433238 0.53399557 0.03317747 0.03317474 0.03318061 0.03317706 46.33849164 0.53116146 0.03295898 0.03295627 0.03296210 0.03295857 46.65265091 0.52835630 0.03274331 0.03274062 0.03274642 0.03274291 46.96681017 0.52557967 0.03253041 0.03252773 0.03253350 0.03253001 47.28096944 0.52283112 0.03232022 0.03231756 0.03232329 0.03231982 47.59512870 0.52011025 0.03211270 0.03211005 0.03211575 0.03211230 47.90928797 0.51741664 0.03190779 0.03190516 0.03191082 0.03190740 48.22344723 0.51474988 0.03170545 0.03170283 0.03170846 0.03170505 48.53760650 0.51210958 0.03150562 0.03150301 0.03150861 0.03150523 48.85176576 0.50949535 0.03130826 0.03130567 0.03131124 0.03130788 49.16592503 0.50690680 0.03111333 0.03111076 0.03111629 0.03111295 49.48008429 0.50434357 0.03092079 0.03091823 0.03092373 0.03092040 49.79424356 0.50180529 0.03073058 0.03072804 0.03073350 0.03073020 50.10840282 0.49929160 0.03054267 0.03054014 0.03054558 0.03054229 50.42256209 0.49680214 0.03035702 0.03035450 0.03035991 0.03035664 50.73672136 0.49433656 0.03017358 0.03017108 0.03017646 0.03017321 51.05088062 0.49189454 0.02999232 0.02998983 0.02999518 0.02999195 51.36503989 0.48947574 0.02981320 0.02981073 0.02981604 0.02981283 51.67919915 0.48707983 0.02963618 0.02963372 0.02963901 0.02963582 51.99335842 0.48470648 0.02946123 0.02945879 0.02946404 0.02946087 52.30751768 0.48235539 0.02928831 0.02928588 0.02929111 0.02928795 52.62167695 0.48002625 0.02911738 0.02911496 0.02912017 0.02911703 52.93583621 0.47771875 0.02894842 0.02894601 0.02895119 0.02894806 53.24999548 0.47543259 0.02878138 0.02877899 0.02878413 0.02878103 53.56415474 0.47316749 0.02861624 0.02861386 0.02861898 0.02861589 53.87831401 0.47092315 0.02845297 0.02845060 0.02845569 0.02845262 54.19247327 0.46869930 0.02829152 0.02828917 0.02829423 0.02829117 54.50663254 0.46649565 0.02813188 0.02812954 0.02813457 0.02813154 54.82079181 0.46431194 0.02797401 0.02797168 0.02797669 0.02797367 55.13495107 0.46214790 0.02781789 0.02781557 0.02782055 0.02781755 55.44911034 0.46000327 0.02766348 0.02766117 0.02766613 0.02766314 55.76326960 0.45787779 0.02751076 0.02750847 0.02751340 0.02751042 56.07742887 0.45577120 0.02735970 0.02735742 0.02736232 0.02735936 56.39158813 0.45368327 0.02721027 0.02720800 0.02721288 0.02720994 56.70574740 0.45161374 0.02706246 0.02706020 0.02706505 0.02706212 57.01990666 0.44956237 0.02691622 0.02691397 0.02691880 0.02691589 57.33406593 0.44752893 0.02677154 0.02676930 0.02677411 0.02677121 57.64822519 0.44551319 0.02662839 0.02662617 0.02663095 0.02662807 57.96238446 0.44351492 0.02648676 0.02648454 0.02648930 0.02648643 58.27654372 0.44153389 0.02634660 0.02634440 0.02634913 0.02634628 58.59070299 0.43956989 0.02620791 0.02620572 0.02621043 0.02620759 58.90486225 0.43762270 0.02607066 0.02606848 0.02607317 0.02607034 59.21902152 0.43569211 0.02593483 0.02593266 0.02593732 0.02593451 59.53318079 0.43377790 0.02580040 0.02579824 0.02580288 0.02580008 59.84734005 0.43187988 0.02566734 0.02566519 0.02566980 0.02566702 60.16149932 0.42999784 0.02553563 0.02553349 0.02553808 0.02553532 60.47565858 0.42813157 0.02540526 0.02540313 0.02540770 0.02540494 60.78981785 0.42628090 0.02527620 0.02527408 0.02527863 0.02527589 61.10397711 0.42444561 0.02514843 0.02514632 0.02515085 0.02514812 61.41813638 0.42262553 0.02502194 0.02501984 0.02502435 0.02502164 61.73229564 0.42082047 0.02489671 0.02489462 0.02489911 0.02489640 62.04645491 0.41903023 0.02477271 0.02477063 0.02477510 0.02477241 62.36061417 0.41725466 0.02464994 0.02464787 0.02465231 0.02464963 62.67477344 0.41549355 0.02452836 0.02452630 0.02453072 0.02452806 62.98893270 0.41374675 0.02440797 0.02440592 0.02441032 0.02440767 63.30309197 0.41201408 0.02428874 0.02428670 0.02429108 0.02428845 63.61725124 0.41029537 0.02417067 0.02416864 0.02417300 0.02417037 63.93141050 0.40859045 0.02405373 0.02405171 0.02405605 0.02405343 64.24556977 0.40689916 0.02393791 0.02393589 0.02394021 0.02393761 64.55972903 0.40522134 0.02382319 0.02382118 0.02382548 0.02382289 64.87388830 0.40355683 0.02370955 0.02370756 0.02371184 0.02370926 65.18804756 0.40190548 0.02359699 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