# omega total a= 1 L= 2 a= 2 L= 2 a= 3 L= 2 a= 4 L= 2 0.15707963 3.53810356 0.76555212 0.76587609 0.76373527 0.76711126 0.47123890 3.11230697 0.63234801 0.63240719 0.63085492 0.63379111 0.78539816 2.84997013 0.54626884 0.54634902 0.54551153 0.54693834 1.09955743 2.68266711 0.48777271 0.48785786 0.48737963 0.48809282 1.41371669 2.55710318 0.44339966 0.44345890 0.44316342 0.44356912 1.72787596 2.45319635 0.40752562 0.40757044 0.40737607 0.40762608 2.04203522 2.36266506 0.37746291 0.37749477 0.37736102 0.37752889 2.35619449 2.28175043 0.35174257 0.35176745 0.35167273 0.35178917 2.67035376 2.20801606 0.32931915 0.32933446 0.32926632 0.32935390 2.98451302 2.14029201 0.30956910 0.30957911 0.30952978 0.30959590 3.29867229 2.07781780 0.29204252 0.29204953 0.29201391 0.29206354 3.61283155 2.01994095 0.27637825 0.27638217 0.27635678 0.27639497 3.92699082 1.96626028 0.26232862 0.26232991 0.26231233 0.26234192 4.24115008 1.91604312 0.24958290 0.24958279 0.24957125 0.24959348 4.55530935 1.86921268 0.23804025 0.23804000 0.23803316 0.23804862 4.86946861 1.82512512 0.22746401 0.22746222 0.22745911 0.22747060 5.18362788 1.78371924 0.21778021 0.21777762 0.21777747 0.21778537 5.49778714 1.74470496 0.20887856 0.20887538 0.20887762 0.20888253 5.81194641 1.70804309 0.20071286 0.20070914 0.20071331 0.20071584 6.12610567 1.67325469 0.19313301 0.19312890 0.19313468 0.19313519 6.44026494 1.64045905 0.18614705 0.18614290 0.18614998 0.18614856 6.75442421 1.60927317 0.17963708 0.17963264 0.17964075 0.17963806 7.06858347 1.57941766 0.17351896 0.17351437 0.17352335 0.17351950 7.38274274 1.55122992 0.16787024 0.16786548 0.16787520 0.16787041 7.69690200 1.52415104 0.16253557 0.16253067 0.16254099 0.16253545 8.01106127 1.49839048 0.15755985 0.15755483 0.15756564 0.15755949 8.32522053 1.47383556 0.15290893 0.15290379 0.15291500 0.15290839 8.63937980 1.44991415 0.14843292 0.14842760 0.14843916 0.14843223 8.95353906 1.42706704 0.14423701 0.14423154 0.14424338 0.14423619 9.26769833 1.40505882 0.14025997 0.14025433 0.14026641 0.14025906 9.58185759 1.38402841 0.13653296 0.13652723 0.13653952 0.13653198 9.89601686 1.36383154 0.13301469 0.13300894 0.13302138 0.13301363 10.21017612 1.34431402 0.12966530 0.12965959 0.12967214 0.12966419 10.52433539 1.32530413 0.12644044 0.12643470 0.12644734 0.12643930 10.83849465 1.30700916 0.12339003 0.12338425 0.12339695 0.12338886 11.15265392 1.28931987 0.12048463 0.12047878 0.12049154 0.12048344 11.46681319 1.27222274 0.11771942 0.11771353 0.11772632 0.11771821 11.78097245 1.25570217 0.11508983 0.11508397 0.11509677 0.11508861 12.09513172 1.23963453 0.11256407 0.11255821 0.11257101 0.11256283 12.40929098 1.22387554 0.11010634 0.11010050 0.11011328 0.11010510 12.72345025 1.20859890 0.10775798 0.10775216 0.10776492 0.10775675 13.03760951 1.19395028 0.10555438 0.10554864 0.10556136 0.10555314 13.35176878 1.17953518 0.10339837 0.10339268 0.10340535 0.10339715 13.66592804 1.16554597 0.10133653 0.10133078 0.10134341 0.10133532 13.98008731 1.15197358 0.09936607 0.09936032 0.09937290 0.09936488 14.29424657 1.13878201 0.09747769 0.09747197 0.09748448 0.09747652 14.60840584 1.12593398 0.09566196 0.09565627 0.09566873 0.09566079 14.92256510 1.11350408 0.09393711 0.09393146 0.09394385 0.09393595 15.23672437 1.10131317 0.09225891 0.09225328 0.09226558 0.09225776 15.55088364 1.08911067 0.09056625 0.09056064 0.09057286 0.09056512 15.86504290 1.07730210 0.08895798 0.08895238 0.08896452 0.08895685 16.17920217 1.06593454 0.08744535 0.08743980 0.08745186 0.08744423 16.49336143 1.05477217 0.08597072 0.08596523 0.08597720 0.08596962 16.80752070 1.04373847 0.08451554 0.08451010 0.08452199 0.08451445 17.12167996 1.03302146 0.08312547 0.08312012 0.08313192 0.08312440 17.43583923 1.02261898 0.08179993 0.08179464 0.08180634 0.08179890 17.74999849 1.01242794 0.08051385 0.08050858 0.08052018 0.08051284 18.06415776 1.00237866 0.07925028 0.07924501 0.07925652 0.07924928 18.37831702 0.99250661 0.07801791 0.07801268 0.07802410 0.07801692 18.69247629 0.98286130 0.07682876 0.07682358 0.07683490 0.07682778 19.00663555 0.97339877 0.07567226 0.07566711 0.07567834 0.07567128 19.32079482 0.96405770 0.07453361 0.07452852 0.07453966 0.07453265 19.63495408 0.95495946 0.07344205 0.07343700 0.07344805 0.07344111 19.94911335 0.94602857 0.07237942 0.07237440 0.07238535 0.07237849 20.26327262 0.93733712 0.07136328 0.07135830 0.07136916 0.07136236 20.57743188 0.92889997 0.07039725 0.07039231 0.07040308 0.07039635 20.89159115 0.92064184 0.06946321 0.06945831 0.06946899 0.06946232 21.20575041 0.91252861 0.06855298 0.06854812 0.06855872 0.06855210 21.51990968 0.90455383 0.06766511 0.06766029 0.06767079 0.06766424 21.83406894 0.89671384 0.06679879 0.06679401 0.06680442 0.06679793 22.14822821 0.88900519 0.06595329 0.06594854 0.06595887 0.06595244 22.46238747 0.88142453 0.06512789 0.06512318 0.06513343 0.06512706 22.77654674 0.87396866 0.06432192 0.06431725 0.06432740 0.06432109 23.09070600 0.86663447 0.06353472 0.06353009 0.06354015 0.06353390 23.40486527 0.85941897 0.06276567 0.06276108 0.06277106 0.06276487 23.71902453 0.85231928 0.06201418 0.06200963 0.06201953 0.06201339 24.03318380 0.84533259 0.06127969 0.06127517 0.06128498 0.06127890 24.34734307 0.83845623 0.06056163 0.06055715 0.06056688 0.06056086 24.66150233 0.83168758 0.05985950 0.05985505 0.05986470 0.05985873 24.97566160 0.82502414 0.05917278 0.05916838 0.05917794 0.05917203 25.28982086 0.81846346 0.05850101 0.05849664 0.05850612 0.05850026 25.60398013 0.81200318 0.05784371 0.05783937 0.05784878 0.05784297 25.91813939 0.80564104 0.05720045 0.05719615 0.05720548 0.05719972 26.23229866 0.79937482 0.05657080 0.05656653 0.05657578 0.05657007 26.54645792 0.79320239 0.05595434 0.05595011 0.05595929 0.05595363 26.86061719 0.78712166 0.05535070 0.05534650 0.05535560 0.05535000 27.17477645 0.78113063 0.05475949 0.05475532 0.05476435 0.05475879 27.48893572 0.77522733 0.05418034 0.05417621 0.05418516 0.05417965 27.80309498 0.76940986 0.05361290 0.05360880 0.05361768 0.05361222 28.11725425 0.76367636 0.05305684 0.05305277 0.05306157 0.05305616 28.43141351 0.75802502 0.05251181 0.05250777 0.05251651 0.05251114 28.74557278 0.75245410 0.05197751 0.05197350 0.05198217 0.05197685 29.05973205 0.74696188 0.05145362 0.05144965 0.05145824 0.05145297 29.37389131 0.74154672 0.05093986 0.05093592 0.05094444 0.05093921 29.68805058 0.73620702 0.05043594 0.05043203 0.05044049 0.05043530 30.00220984 0.73094121 0.04994159 0.04993771 0.04994610 0.04994096 30.31636911 0.72574779 0.04945655 0.04945270 0.04946102 0.04945592 30.63052837 0.72062528 0.04898056 0.04897674 0.04898499 0.04897994 30.94468764 0.71557225 0.04851337 0.04850958 0.04851778 0.04851276 31.25884690 0.71058730 0.04805476 0.04805100 0.04805913 0.04805416 31.57300617 0.70566910 0.04760450 0.04760077 0.04760883 0.04760390 31.88716543 0.70081631 0.04716236 0.04715866 0.04716666 0.04716177 32.20132470 0.69602766 0.04672814 0.04672447 0.04673241 0.04672755 32.51548396 0.69130189 0.04630163 0.04629798 0.04630586 0.04630104 32.82964323 0.68663780 0.04588263 0.04587900 0.04588682 0.04588205 33.14380250 0.68203419 0.04547094 0.04546735 0.04547511 0.04547037 33.45796176 0.67748992 0.04506640 0.04506283 0.04507053 0.04506583 33.77212103 0.67300386 0.04466881 0.04466527 0.04467291 0.04466825 34.08628029 0.66857491 0.04427800 0.04427449 0.04428208 0.04427745 34.40043956 0.66420201 0.04389382 0.04389033 0.04389786 0.04389327 34.71459882 0.65988412 0.04351608 0.04351262 0.04352010 0.04351554 35.02875809 0.65562022 0.04314465 0.04314121 0.04314863 0.04314411 35.34291735 0.65140931 0.04277936 0.04277595 0.04278331 0.04277883 35.65707662 0.64725044 0.04242007 0.04241668 0.04242400 0.04241954 35.97123588 0.64314265 0.04206664 0.04206327 0.04207053 0.04206611 36.28539515 0.63908501 0.04171892 0.04171558 0.04172279 0.04171840 36.59955441 0.63507663 0.04137679 0.04137347 0.04138062 0.04137627 36.91371368 0.63111661 0.04104010 0.04103680 0.04104391 0.04103959 37.22787295 0.62720410 0.04070874 0.04070546 0.04071252 0.04070823 37.54203221 0.62333825 0.04038257 0.04037932 0.04038633 0.04038207 37.85619148 0.61951824 0.04006149 0.04005826 0.04006522 0.04006099 38.17035074 0.61574327 0.03974537 0.03974216 0.03974907 0.03974487 38.48451001 0.61201256 0.03943410 0.03943092 0.03943778 0.03943361 38.79866927 0.60832533 0.03912758 0.03912442 0.03913123 0.03912709 39.11282854 0.60468085 0.03882569 0.03882255 0.03882932 0.03882521 39.42698780 0.60107838 0.03852834 0.03852522 0.03853194 0.03852786 39.74114707 0.59751720 0.03823542 0.03823232 0.03823900 0.03823495 40.05530633 0.59399662 0.03794684 0.03794377 0.03795040 0.03794637 40.36946560 0.59051595 0.03766251 0.03765945 0.03766604 0.03766204 40.68362486 0.58707453 0.03738233 0.03737929 0.03738583 0.03738186 40.99778413 0.58367170 0.03710621 0.03710319 0.03710969 0.03710575 41.31194339 0.58030683 0.03683407 0.03683107 0.03683753 0.03683361 41.62610266 0.57697929 0.03656583 0.03656285 0.03656926 0.03656537 41.94026193 0.57368847 0.03630139 0.03629844 0.03630481 0.03630094 42.25442119 0.57043378 0.03604070 0.03603775 0.03604409 0.03604025 42.56858046 0.56721462 0.03578365 0.03578073 0.03578702 0.03578321 42.88273972 0.56403042 0.03553019 0.03552729 0.03553354 0.03552975 43.19689899 0.56088064 0.03528024 0.03527735 0.03528356 0.03527980 43.51105825 0.55776471 0.03503372 0.03503085 0.03503702 0.03503328 43.82521752 0.55468210 0.03479057 0.03478772 0.03479385 0.03479014 44.13937678 0.55163228 0.03455072 0.03454789 0.03455398 0.03455029 44.45353605 0.54861475 0.03431411 0.03431130 0.03431735 0.03431368 44.76769531 0.54562899 0.03408067 0.03407787 0.03408389 0.03408025 45.08185458 0.54267451 0.03385034 0.03384756 0.03385354 0.03384992 45.39601384 0.53975084 0.03362305 0.03362029 0.03362623 0.03362264 45.71017311 0.53685749 0.03339876 0.03339601 0.03340192 0.03339834 46.02433238 0.53399400 0.03317740 0.03317467 0.03318054 0.03317699 46.33849164 0.53115992 0.03295891 0.03295620 0.03296203 0.03295850 46.65265091 0.52835480 0.03274324 0.03274055 0.03274635 0.03274284 46.96681017 0.52557820 0.03253034 0.03252766 0.03253343 0.03252994 47.28096944 0.52282969 0.03232016 0.03231749 0.03232323 0.03231976 47.59512870 0.52010885 0.03211264 0.03210999 0.03211569 0.03211224 47.90928797 0.51741527 0.03190773 0.03190510 0.03191076 0.03190733 48.22344723 0.51474854 0.03170539 0.03170277 0.03170840 0.03170499 48.53760650 0.51210827 0.03150556 0.03150296 0.03150856 0.03150517 48.85176576 0.50949407 0.03130821 0.03130562 0.03131118 0.03130782 49.16592503 0.50690555 0.03111328 0.03111071 0.03111624 0.03111290 49.48008429 0.50434235 0.03092074 0.03091818 0.03092368 0.03092035 49.79424356 0.50180409 0.03073053 0.03072798 0.03073345 0.03073015 50.10840282 0.49929042 0.03054262 0.03054009 0.03054553 0.03054224 50.42256209 0.49680098 0.03035697 0.03035445 0.03035986 0.03035659 50.73672136 0.49433544 0.03017353 0.03017103 0.03017641 0.03017316 51.05088062 0.49189344 0.02999228 0.02998979 0.02999514 0.02999191 51.36503989 0.48947466 0.02981316 0.02981068 0.02981600 0.02981279 51.67919915 0.48707877 0.02963614 0.02963368 0.02963897 0.02963578 51.99335842 0.48470545 0.02946119 0.02945874 0.02946400 0.02946083 52.30751768 0.48235438 0.02928827 0.02928584 0.02929107 0.02928791 52.62167695 0.48002525 0.02911735 0.02911493 0.02912013 0.02911699 52.93583621 0.47771777 0.02894838 0.02894598 0.02895115 0.02894803 53.24999548 0.47543164 0.02878135 0.02877895 0.02878410 0.02878099 53.56415474 0.47316655 0.02861621 0.02861383 0.02861894 0.02861585 53.87831401 0.47092223 0.02845293 0.02845056 0.02845565 0.02845258 54.19247327 0.46869840 0.02829149 0.02828913 0.02829420 0.02829114 54.50663254 0.46649477 0.02813185 0.02812951 0.02813454 0.02813150 54.82079181 0.46431108 0.02797398 0.02797165 0.02797666 0.02797364 55.13495107 0.46214706 0.02781786 0.02781554 0.02782052 0.02781752 55.44911034 0.46000244 0.02766345 0.02766114 0.02766610 0.02766311 55.76326960 0.45787698 0.02751073 0.02750844 0.02751337 0.02751039 56.07742887 0.45577041 0.02735967 0.02735739 0.02736229 0.02735934 56.39158813 0.45368249 0.02721025 0.02720797 0.02721285 0.02720991 56.70574740 0.45161297 0.02706243 0.02706017 0.02706502 0.02706209 57.01990666 0.44956162 0.02691619 0.02691394 0.02691877 0.02691586 57.33406593 0.44752819 0.02677151 0.02676928 0.02677408 0.02677118 57.64822519 0.44551247 0.02662837 0.02662614 0.02663092 0.02662804 57.96238446 0.44351421 0.02648673 0.02648452 0.02648927 0.02648641 58.27654372 0.44153320 0.02634658 0.02634438 0.02634911 0.02634626 58.59070299 0.43956921 0.02620789 0.02620570 0.02621041 0.02620757 58.90486225 0.43762203 0.02607064 0.02606846 0.02607315 0.02607032 59.21902152 0.43569145 0.02593481 0.02593264 0.02593730 0.02593449 59.53318079 0.43377726 0.02580037 0.02579821 0.02580285 0.02580006 59.84734005 0.43187925 0.02566731 0.02566516 0.02566978 0.02566700 60.16149932 0.42999722 0.02553561 0.02553347 0.02553806 0.02553529 60.47565858 0.42813097 0.02540524 0.02540311 0.02540768 0.02540492 60.78981785 0.42628030 0.02527618 0.02527406 0.02527861 0.02527587 61.10397711 0.42444503 0.02514841 0.02514630 0.02515083 0.02514810 61.41813638 0.42262496 0.02502192 0.02501982 0.02502433 0.02502162 61.73229564 0.42081990 0.02489669 0.02489460 0.02489909 0.02489638 62.04645491 0.41902968 0.02477269 0.02477061 0.02477508 0.02477239 62.36061417 0.41725411 0.02464992 0.02464785 0.02465229 0.02464961 62.67477344 0.41549302 0.02452834 0.02452628 0.02453070 0.02452804 62.98893270 0.41374623 0.02440795 0.02440590 0.02441030 0.02440765 63.30309197 0.41201357 0.02428873 0.02428669 0.02429107 0.02428843 63.61725124 0.41029486 0.02417065 0.02416862 0.02417298 0.02417036 63.93141050 0.40858995 0.02405371 0.02405169 0.02405603 0.02405342 64.24556977 0.40689867 0.02393789 0.02393588 0.02394020 0.02393760 64.55972903 0.40522086 0.02382317 0.02382117 0.02382547 0.02382288 64.87388830 0.40355636 0.02370954 0.02370754 0.02371182 0.02370924 65.18804756 0.40190502 0.02359697 0.02359499 0.02359925 0.02359668 65.50220683 0.40026667 0.02348547 0.02348349 0.02348773 0.02348518 65.81636609 0.39864118 0.02337500 0.02337303 0.02337725 0.02337471 66.13052536 0.39702839 0.02326556 0.02326360 0.02326780 0.02326527 66.44468462 0.39542815 0.02315713 0.02315518 0.02315937 0.02315685 66.75884389 0.39384032 0.02304971 0.02304776 0.02305193 0.02304942 67.07300315 0.39226475 0.02294326 0.02294133 0.02294548 0.02294298 67.38716242 0.39070132 0.02283779 0.02283587 0.02284000 0.02283751 67.70132168 0.38914987 0.02273328 0.02273136 0.02273548 0.02273300 68.01548095 0.38761028 0.02262971 0.02262781 0.02263190 0.02262944 68.32964022 0.38608241 0.02252708 0.02252518 0.02252926 0.02252680 68.64379948 0.38456613 0.02242537 0.02242348 0.02242753 0.02242509 68.95795875 0.38306131 0.02232456 0.02232268 0.02232672 0.02232429 69.27211801 0.38156782 0.02222465 0.02222278 0.02222680 0.02222438 69.58627728 0.38008553 0.02212563 0.02212376 0.02212777 0.02212536 69.90043654 0.37861433 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