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There exist weight 0 Maass cusp forms on Hecke congruence groups $\Gamma_0(N)$ with even character $\chi$. The L-function \(L(s,f) = \sum a_n n^{-s} \) associated to the Maass cusp form $f$ has an Euler product of the form \[ L(s,f)= \prod_{p\mid N} \left(1 - a_p p^{-s} \right)^{-1}\prod_{p\nmid N} \left(1 - a_p p^{-s} + \chi(p)p^{-2s} \right)^{-1} \] and satisfies a functional equation of the form \[\begin{aligned} \Lambda(s,f) = N^{s/2} \Gamma_{\R} \left(s + \delta + iR \right) \Gamma_{\R} \left(s + \delta - iR \right) \cdot L(s, f) = \varepsilon \Lambda(1-s,f), \end{aligned}\] where $N$ is the level, $R$ the eigenvalue of the Maass cusp form, $\varepsilon$ is the sign, and $\delta$ is 1 (or 0) when $f$ is odd (or even).

The dots in the plot correspond to L-functions with trivial character and $(R, N)$ as in the functional equation. The color shows whether the functional equation has sign +1 or sign -1. These have been found by a computer search. Click on any of the dots for details about the L-function.

1 2 3 4 5 6 7 8 9 10 1 3 5 7 9 Level R 16.1380731715 2.73410555925 4.58236150313 5.10381155304 6.37879720849 6.99327291741 7.78033646819 8.58191066592 9.23048002425 6.73532969117 9.02977428596 9.30018385212 8.92287648699 10.9203920029 14.6850159506 12.0929948751 7.22087197596 11.3176797015 13.3101642835 5.41733480684 10.7127069007 12.821988162 14.0972037339 5.09874190873 14.9169973013 5.87935415776 8.04247759169 9.85989616224 11.4930044149 12.8776165641 3.70330780122 6.62042287384 8.52250301688 9.93491995937 10.7647106832 11.972776694 13.228828713 14.1438850658 14.9703130686 4.13240421506 6.05402838077 6.82352699542 8.29469778357 8.4800158394 10.2463013805 11.181381958 11.6923207345 12.1207735459 12.8554583746 13.0006638517 13.4689817279 14.3530892608 14.5957035794 5.43618046142 7.98654905098 9.27729778527 9.39741755066 10.6311530866 11.2834406791 12.0183185174 12.6360800548 13.6993069852 13.8573264614 14.7907011072 14.9562214606 4.89723501573 6.35122321676 7.32552437933 8.2261459726 8.81789729862 10.983968955 11.1539349348 11.87084943 12.6585068804 13.6473942985 14.6981676744 14.955192517 3.02837629307 4.10322180991 5.70582652719 6.45847643848 7.58531840144 8.01848237839 10.045820825 10.5004431507 11.0931280005 11.6005386371 12.3141719404 12.7159021442 13.0963889192 13.7599489451 14.0342548179 14.2458963378 9.65240704243 12.3544320764 13.9018163092 3.84467228501 7.90114750377 9.66046617807 11.3130895989 14.8720924008 6.87436376055 13.1778468571 14.4676129234 11.7057493189 13.2545279009 4.54845492142 8.66395307858 10.2048624763 12.5299513826 14.3794514696 10.1454558365 14.007064483 3.3088170303 9.37443036553 11.5585635397 12.6353414748 2.59237977171 8.81974775988 12.1162222939 13.6987468059 5.62812092942 7.22656906706 9.01322849206 11.7819543736 11.8777730802 13.5200506514 4.64659164296 6.58769285315 9.4700831342 9.9039777038 11.1062703875 6.22318082532 11.4814591662 12.4144645265 12.93885778 2.42505682709 6.32531406199 8.55288032905 10.2618142525 11.4110059735 12.9167943228 13.9895535537 7.48301811751 9.4700831342 9.9039777038 3.53600209294 5.50405667968 7.43179917172 9.0800693497 3.53600209294 5.50405667968 6.64658135561 7.43179917172 9.08006934969 8.69834295647 8.03886120386 9.74374939916 8.77828239355 6.12057553309 8.19303593168 4.38805356322 6.75741527775 7.75813319502 9.29237932822 22.1020557995 25.5947866217 25.6508724359 26.4600305542 26.7558383271 26.9534009039 27.7278486137 28.0292141354 28.7922124978 28.9870182837 29.7156119371 29.9772968453 30.2286779791 31.0052017569 31.1424021542 31.7936112213 15.8093206166 13.1720749675 15.7434456453 10.2310756893 20.8820026917 20.6748407007 22.1257147034 19.6990197959 18.3266193296 21.0692394685 22.5317665089 23.4326487652 24.7506671044 22.3339312805 13.9931761916 15.1595355562 14.4778027317 16.0935923774 17.195127212 19.7785769776 23.3156378318 24.354473593 15.3141965842 16.9402609464 20.1399721518 21.6299863738 22.7582184887 23.779963169 25.2639460547 26.5612552725 28.0489249417 29.3375089547 30.332376131 30.7557308668 31.604945484 16.4041087751 17.8780025394 19.1254224082 20.5476038597 22.0890454668 23.4965859557 24.8561990173 25.0524237851 27.1480324512 27.5580690764 28.4123841416 29.5185335504 29.7747483213 30.91248369 8.27366588959 15.4428777438 17.3193334036 18.8501464832 19.2387335253 20.6678761954 21.573637236 23.028056402 23.9305818252 24.7898614149 25.5339642269 26.8083242393 27.2031048477 28.3326105901 28.8086394545 29.9476419195 30.6269936449 31.4604723426 15.2740224848 17.4931127227 18.4370784198 20.5301600346 21.0495260714 22.374933203 24.0285125229 25.1193355839 25.877316768 26.741527413 27.7570459928 28.7211104713 29.6165214395 31.16809096 31.20915801 12.580463057 15.7048957513 17.0740108048 18.4077520222 19.871635671 20.5439502419 23.3165024141 23.5193691394 24.5944725418 25.037005685 25.547914879 26.0905993987 26.8897729312 26.9349648861 27.7036935138 28.053711222 29.0782262249 29.4188261584 29.7063706851 30.193065831 30.5862790482 31.0682993142 31.471753897 31.7175359147 11.3464186204 11.8899755746 13.1351445113 14.6262358404 15.7994939261 16.2709585691 16.7362155908 17.5005568024 18.6474302826 18.9626422396 19.8961039469 20.6649068261 21.4346433457 21.8071264738 22.6592718526 22.8392906713 23.620926593 23.9798500362 24.2982565319 24.9310866374 25.4442636432 26.4520989046 26.7129034756 27.6410466219 27.683289262 27.7011997464 28.4952804949 29.1335076947 29.380289315 29.6543135506 30.0509363683 30.8564751304 31.0095393762 31.1202312685 10.9135396775 11.7145309917 12.6279481097 13.3954804003 14.6012532084 15.7532336885 16.9905650919 17.2883277697 18.0796004487 18.8405820105 19.1759646544 20.018381712 20.7113415288 20.8054689922 21.3531715323 22.3132655923 22.4281719265 23.5369697073 23.9170819774 24.1674291456 24.6012808208 25.3431954147 25.6139927372 26.0780963826 26.4529566231 27.1777919535 27.2724539585 28.0986176195 28.3457877303 28.5688328665 28.8252344602 29.4353295802 30.0124030308 30.5644447508 30.8102571845 31.1496545383 31.7728546691 31.8222975293 10.5076073043 11.3659037782 13.3786205776 13.5079113404 14.7873247385 15.4831618965 16.9653979482 17.8206758792 18.0189772589 19.0267767277 19.566910611 20.4094388903 21.1086958873 21.6126500168 22.1003136006 22.6711177685 23.4601771307 24.2096219473 24.9166573879 24.9526483936 25.4752628288 26.0195962906 26.6494958549 27.2434546598 27.3156558458 28.102435957 28.2155159278 29.0279908058 29.5228489465 29.9680209354 30.0849560775 30.9088896913 31.1067821239 31.4014761773 4.82800766847 6.27191087352 7.33182919217 8.42175366822 8.69750590723 9.66612934925 10.1616724897 10.2719888709 11.0772643773 11.3483973599 11.7636315651 12.53434192 12.7062239332 13.1209012524 13.9084271212 14.1415558991 14.2644093436 14.3335466515 15.0432600354 15.2256370149 15.5640608508 15.8638873119 16.1257956616 16.6298282284 16.751442235 17.1159424365 17.4501903799 17.6812083593 17.835581018 18.0430670243 18.2867069243 18.6846830877 18.6997890901 19.0231432986 19.2014902315 19.7592981735 19.9033408646 20.1708829787 20.3629729386 20.5190992482 21.0123297833 21.0476248855 21.1718200391 21.5159545182 21.5555871518 22.0449800737 22.1583494056 22.1923216667 22.2638475454 22.461011597 23.1135181586 23.1539772197 23.1917353105 23.3289531491 23.4336062125 23.7806692459 24.1657743425 24.3148087959 24.3594461913 24.6898143331 24.8119483152 24.9020498321 25.0593168202 25.1907498301 25.3873331084 25.5387898396 25.6966150616 26.0841228332 26.315065143 26.490993 26.4910556344 26.49242994 26.6777541971 26.8366282205 27.0884006802 27.2242332907 27.3589423206 27.4506272422 27.5812421356 27.8143056957 28.0025278719 28.1815148181 28.238912424 28.3299734402 28.604527987 28.8084854794 28.9822335023 29.0565438949 29.285321119 29.452479341 29.6015882461 29.8189087496 29.8434261635 29.9056506214 30.1141590927 30.3584827336 30.3716784988 30.4291556764 30.5586154389 30.6594840479 30.9623725964 31.1746666912 31.2084604949 31.3148253378 31.3263543769 31.5346672877 31.995067534 3.45422650357 4.02170481942 5.58279102848 6.06885693385 7.35799566148 7.7010258369 8.15572563068 9.04317475934 9.25079724881 9.35463469751 10.175062328 10.6557340712 11.2287594983 11.3093434777 11.6600704287 12.1478256896 12.3739809414 12.6838332458 13.3683356647 13.3795867468 13.6053245138 14.3008035903 14.6660794527 14.6701383491 15.0086526605 15.2796850577 15.6389761039 15.9346823673 16.1474318373 16.1693715647 16.7118520534 16.9149337674 17.0329772069 17.2781197759 17.3022309802 17.8185309143 18.2697497295 18.2882064017 18.5101631109 18.5780590924 19.0928401251 19.2931417976 19.4820787558 19.6772441617 19.9724866756 20.1572423414 20.16929073 20.4407182443 20.5357685595 20.8399537501 21.2345010443 21.3145205717 21.3367573524 21.7682863763 21.8793442013 22.0094719836 22.5729312972 22.6246828603 22.6525448783 22.7412742535 22.7464449492 23.1283960164 23.4424618798 23.5033525563 23.639166178 23.85855835 24.0465450317 24.1457127562 24.3380802847 24.654316687 24.7321428472 25.040298655 25.0927572348 25.1085920064 25.2975522735 25.4958204016 25.6798988844 25.8399314231 25.8966012935 26.0772448581 26.5755195174 26.6506794442 26.7970962021 26.9258206654 26.9512503395 27.0281785294 27.2699201415 27.6440750167 27.6667531227 27.7596814485 28.0094254838 28.0404311769 28.0498024316 28.2863431447 28.5883588781 28.5993724754 28.7630321783 29.0176602774 29.0432041541 29.1254611454 29.35858679 29.4765268759 29.631354 29.7824669057 29.9477354652 30.1239060224 30.3949093026 30.5038875222 30.6727852103 30.7448694404 30.8005451841 31.0253414573 31.033072476 31.1179375828 31.5089819131 31.7301014263 31.7862225323 31.8448138382 31.8913580351 31.9022369086 31.9632907142 1.92464430511 3.19085876294 4.71971646829 5.44273917126 5.82926875013 6.33448316434 7.05035422681 7.4314578005 8.07161868259 8.80251162268 8.94499430391 8.99915977043 9.98429702517 10.5312060637 10.6716858394 10.6717085945 11.3084693945 11.4943991008 12.0215787893 12.4301522386 12.7314919646 12.9574195877 13.1471805638 13.6464251756 13.8037862149 13.8587404552 14.4303062141 14.6754864014 14.7695313418 15.0867718193 15.323804138 15.4180201868 15.8993221873 16.2523690629 16.3690844264 16.7480735665 17.0001510131 17.1900948369 17.2407467178 17.7542440677 17.9622228895 18.0146274278 18.1016170172 18.490602145 18.5229040194 18.8197579818 18.9670074474 19.26240817 19.59074388 19.6108915604 19.8580043477 20.1806066519 20.3069070161 20.4075310134 20.7326878165 20.9191145233 20.9366132372 21.0140321476 21.3499331014 21.7568901387 21.789259709 22.0902871694 22.1025814331 18.246377892 18.6207750965 22.263446923 22.3624513821 22.634422353 22.7405597567 22.9546879603 23.0908780312 23.4759242354 23.6672961231 23.6961152264 23.9009450257 23.9957408856 24.0992478189 24.4103168039 24.5251654114 24.5846578367 24.7826046209 25.2258613353 25.2349838497 25.3588519787 25.5724599809 25.697043857 25.85482 25.8545055 25.9629098002 26.172764478 26.3023854908 26.5764541886 26.6302894554 26.659726411 26.9893359732 27.0965714166 27.3442369982 27.4215044602 27.4334856807 27.5424038642 27.9719974034 28.0107079524 28.0480089398 28.269111804 28.3126193765 28.5580301174 28.7003794041 28.7420104721 28.920544517 29.1827817077 29.2567851538 29.4585027272 29.4703279237 29.656907448 29.8604940752 29.9108811952 30.0212788282 30.1070987261 30.1593944403 30.4500467452 30.6237209859 30.6855821621 30.7922641344 30.9145468508 31.1439284284 31.4301627155 31.4329111807 31.50761424 31.5387460169 31.5832769968 31.5976837563 31.8411905315 4.11900929292 5.10146081193 6.25758390694 7.05407006402 7.71956232873 8.25178553271 8.46236495549 9.20407719967 9.99016407004 10.5773733824 10.6456998611 11.2763113507 11.6962468302 12.1833418195 12.7126452398 13.1285144687 13.4012029876 13.5838479949 13.8682520057 14.2650692615 14.9500435341 15.07573583 15.2943813556 15.6934082186 15.7717239294 15.9149651865 16.1293171928 16.7453956085 17.0004254148 17.4004927583 17.4583335351 17.5896539385 17.7204159046 18.4152950225 18.4348388659 18.6987070382 18.9371850305 19.0457479662 19.4595509732 19.5334802928 19.7482378328 19.8498723847 20.2716653337 20.3387908003 20.8089980299 20.8895804034 20.9591714009 21.0217140627 21.4452095157 21.6229751628 21.6621276015 21.993045165 22.0950312448 22.5177061552 22.6283905717 22.9583461156 23.037291568 23.2186382605 23.3467383587 23.5305997875 23.773426265 23.9421476303 24.2954602802 24.3128742925 24.3807722574 24.4421099852 24.8690917712 24.8979567678 25.1647729072 25.1669214761 25.5123580045 25.5998751528 25.6791237808 25.7801642085 26.2639218072 26.3175436885 26.4848318204 26.7683545091 26.8619381569 26.9122486819 26.9969023158 27.0520080556 27.3978387984 27.5579506943 27.7481300789 27.7800558397 27.9230631064 28.2762454005 28.3683545943 28.8238916508 28.8961103464 28.966352092 29.054148684 29.2838641556 29.5697748412 29.5974259155 29.6216978048 29.8036648597 30.1275802119 30.2876648279 30.3447908207 30.562291709 30.6627956225 30.7279884318 30.8047014341 31.0311304553 31.1428156207 31.1936414789 31.4921046878 31.5323074001 31.5606250592 31.9364936616 31.9738011925 15.505386603 16.0814027887 16.6565506411 16.704640719 17.5496644866 17.5881093469 17.8588406539 18.6758184287 18.7207951201 19.1481237708 19.8102718413 20.2202132686 20.5524152508 20.855891421 21.0407505885 21.4040227916 21.9282574992 22.3136503582 22.3713855521 22.37421795 23.1874097923 23.2343986683 23.5438935716 23.6780530903 24.2332013913 24.7005269979 24.7456176343 24.8202035948 25.2878687094 25.3978622477 25.7212586267 25.9406416457 26.6193144998 26.6337280047 26.9606120514 27.1858223646 27.5695149781 27.6303878586 27.8752553064 28.0269809206 28.149395588 28.8509874185 28.8445 28.8445327877 29.2392047499 29.3891389309 29.438688109 29.8330810576 29.8847604558 29.9061435733 30.3795546372 30.7718094659 30.8357096794 30.9550145054 31.121224741 31.286031795 31.8199280701 15.1510918498 15.7245696084 15.7416308959 16.3026208196 16.7520847209 17.0738778949 17.2811510325 18.1420884687 18.4148079772 18.4531747595 19.0626805047 19.3881310778 19.7037531713 19.9572029658 20.0427344524 20.470941908 20.5643751941 21.0259749533 21.7271219056 22.0199867987 22.0446098707 22.1697410422 22.9509160437 23.0197040761 23.0714709649 23.1944166387 23.8645156001 23.9396104629 24.3724927259 24.4797532762 24.6996606327 25.0277582001 25.4076509626 25.561406868 25.8407697228 26.1585104104 26.4362732229 26.4826765431 26.6003578 27.0461046648 27.2978562063 27.3403884639 27.5093156571 28.0265996438 28.1069020522 28.3657934725 28.7008783409 29.1304705515 29.2270335164 29.5994733266 29.6818908015 30.0471435257 30.0846076947 30.3158390271 30.5080414923 30.6390225888 30.7484846234 31.385852162 31.39826035 31.4494243397 8.82074088495 9.83341273669 14.9867895143 15.2652159069 15.6756386314 16.1208819879 16.2786775059 16.6045429004 17.0714186975 17.5731360131 17.6673755467 18.1087269558 18.471510444 18.5673456643 19.0422207378 19.2046073827 19.8753271247 19.926048832 20.3593370402 20.7347932733 20.8424032107 20.931855033 21.3471118382 21.8164739908 21.9693483584 22.5169323511 22.6253049 22.625322 22.6292513 22.672045208 23.2229974233 23.6936400633 23.7603245412 24.0995850844 24.2804053705 24.3767937839 24.7278576838 25.0892048281 25.1936583014 25.5420503289 25.7558279379 25.9255856174 25.9687019162 26.4442650383 26.6879161878 26.804099911 27.1555642189 27.3332067584 27.8476976092 28.0027209009 28.1463635408 28.465564404 28.622993676 28.7051065898 29.0112351516 29.2991769604 29.412983713 29.5077733187 29.6547596338 30.0208783615 30.0880510051 30.2577475913 30.698678089 30.8033073873 31.011287867 31.2453189591 31.3782289983 31.4515035824 31.7488362323 31.8263187949 10.3070268656 13.2197860798 13.5751469722 15.2903226984 15.4622215037 16.2034023613 17.0680234623 17.1582769256 17.6585504205 17.8250471863 18.1085077447 18.7315843929 18.8048764856 19.2305426957 19.5437812807 19.9844229266 20.2831994384 20.6946034505 20.8088935313 21.0956150091 21.4610203311 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30.5618896544 31.1416973854 31.3012406311 31.8889625537 6.00033540888 12.8347409661 13.9637989662 16.2115601963 17.6349741195 18.9955722649 19.082713922 20.2902860914 21.1438145136 22.1200181208 23.3506079392 24.2555291655 24.5590547488 25.2888650099 26.2954888364 27.5085699443 27.5299217633 28.6652847006 28.8167625752 29.8709673384 30.6215366768 31.5119588309 10.6298273272 16.8886860039 18.2041176543 19.5319505212 20.8803220236 21.9718451063 23.0421733914 24.6597629644 25.8175980104 25.9174841182 27.0930893168 28.2906134425 29.155792059 29.9125663694 31.0127402862 31.9019017305 7.38627450582 15.95460255 17.1404035238 19.3650096517 20.1641607379 21.4831049366 22.8210176635 24.1073514314 25.5223796467 26.1127145897 26.8788225753 28.0136343308 28.9674086632 30.1114631705 30.9931982016 31.9457194813 6.30636358623 15.4461705338 17.6524723777 18.636395078 19.8677246351 21.037632959 22.2757225306 23.3915134959 24.5415346228 25.5890682002 26.5038609841 26.8299321307 28.3228800909 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31.2090888951 31.699682076 4.94783167713 9.19652685256 11.4536636942 12.4023495483 13.5881834525 14.8479980699 15.5802527294 15.8044818401 16.3054348151 16.7055201948 17.1283295512 17.7363684242 18.0862694003 18.6626561571 19.0494570431 19.7508348771 19.7951814168 19.9896648101 20.7240917109 21.2336729152 21.3449447488 21.8598686489 22.0191049961 22.6318060954 22.8165247802 23.0763435862 23.5961484818 23.8832982848 24.255704154 24.686457527 24.7335096233 25.349454674 25.4634912302 25.9736390452 26.2955375425 26.4808499528 26.570980611 27.136859063 27.240003788 27.5101652433 28.0053058321 28.0561816474 28.4542960984 28.8753849229 29.1428286095 29.2626379781 29.7564178487 29.9857484438 30.1734261582 30.6334745577 30.6417512857 30.6542761705 31.015936596 31.5407032923 31.6450514901 4.36801954023 7.74444773702 9.00120580965 9.81001812133 10.5388080579 13.6459947778 14.4492628268 14.988459734 15.0277188445 15.901499929 16.8356334489 16.8641917951 17.5715123325 18.0388681461 18.6218581887 18.9434767847 19.2463688624 19.9078744946 20.12782664 20.7344767011 20.9373525221 21.6143186006 21.7332641514 22.3101457101 22.6374271493 23.0356136893 23.6484221333 23.6549874649 24.0076355072 24.2184769697 24.6588387049 25.3329647659 25.4179363883 25.5983897063 26.1955636128 26.300518007 26.6797374566 27.0051394074 27.4225086476 27.755324965 28.0523777793 28.3182429399 28.3841623545 28.9970379656 29.0566705939 29.1517569384 29.7434964512 29.8618663393 30.2791108784 30.4741904214 30.7701125382 31.2517011276 31.2820207823 31.5754138313 31.7407530606 16.3341323969 18.0578988282 19.919467815 21.9274683772 22.7469632152 23.9848792251 25.5644301817 26.3916471081 27.9002160678 28.9772525747 29.5457088572 30.4276328473 31.5417520821 7.15749058532 15.1417241517 16.1350656627 17.0365482074 18.2737438488 19.9936148045 20.9490481058 21.7844039928 22.8016534245 23.7813561034 24.5005798973 25.8128403297 26.3141717492 27.4530073963 28.0958978155 28.9665828707 29.6878196399 30.461783852 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2.55636946085 4.18409504645 6.67376039246 7.788215329 9.44243727649 10.0194866131 11.0009604498 11.9357108569 12.9433745145 13.7422588437 14.6481407612 15.5673897311 18.2615112082 19.4246337363 19.7518011761 20.3060013567 20.8248391133 21.5655607109 22.2244552093 22.5374419869 22.6900189031 23.246400292 23.4946353042 24.6159903788 24.6372905679 25.3582309994 25.759928588 26.12318927 26.444565745 26.9871409866 27.6452063226 27.7811733014 28.3439938304 28.9384997445 29.1014092651 29.3175625852 29.9472580173 29.9953210933 30.546564283 31.0251790778 31.0493228289 31.8329099691 31.9875849983 1.4463991334 4.64274919042 5.45975729468 7.34617187347 8.42338862095 9.46193719273 10.4363421604 11.5198192086 12.3624041926 13.1075094406 13.8721865958 14.7336237927 14.9238928466 15.9382784617 18.6257215488 19.1774440783 19.7128261759 19.9265889222 20.3173037027 21.2155846326 21.7875095659 22.106362656 22.9495013485 23.3561291756 23.425167202 23.9165494096 24.7649515125 25.0775787865 25.2524967393 25.8565600192 26.4098588141 26.671211243 27.1088850091 27.5213532352 28.1082072398 28.2148889919 28.7503926305 28.8267168675 29.5841732525 30.0062244986 30.3458704079 30.6130320107 30.6522751725 31.63446345 31.7315288843 31.9163478766 3.59362788512 6.01171674499 10.2763012571 12.0150070407 12.657894507 14.1093933296 14.712382788 15.9608513054 15.9987139994 18.570584434 19.32164295 19.3298732 19.32930345 20.1661566994 21.0684479685 21.6168116132 22.3042312641 22.6952412757 23.0718574707 23.6178443809 24.1201522922 24.3141784195 24.9063465366 25.7447796785 26.2945508064 26.4536952758 27.299702759 27.3228024652 28.1553130021 28.3445409049 28.869142831 29.329937903 29.5726130963 29.868898766 30.3643867787 30.6967542171 30.9231048721 31.4195889828 13.7797513519 17.7385633811 19.4234814708 21.3157959402 22.7859084942 24.1123527298 25.8262437127 26.1520854492 28.5307476929 28.8633943539 31.5265821968 31.5662754118 32.5081177599 32.8911702135 34.0278842001 34.456271533 35.5023497714 36.6775529931 36.8563494959 37.8250722906 38.3032761525 39.1680849679 39.4075318615 39.773622619 40.5433512105 40.6886664449 41.5555776736 41.8830032854 42.6434884147 42.9222277836 43.2671820388 44.0774047617 12.1730083247 45.2874384425 45.3616136021 45.3984695313 46.1014563216 46.4814024123 46.65331836 47.4228958985 47.9265583306 48.0393309051 48.7416663476 48.9983076541 49.6835200753 49.9616962905 16.6442592019 18.1809178345 19.4847138547 20.1066946826 21.4790575447 22.1946739776 23.2013961812 23.2637115379 24.4197154423 25.0508548508 26.0569177607 26.446996418 27.2843840117 27.7759207018 28.5102777031 29.1375875578 29.5463881241 9.53369526135 14.3585095183 27.3327080831 35.8416764326 44.4263481186