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Maass forms of levels 10 to 100 with $0 \leq R\leq 4$

The horizontal axis is the spectral parameter $R$ with the Laplace eigenvalue satisying $\lambda=1/4+R^2$. The vertical axis is the level $N$. Each point corresponds to a Maass form of weight 0 and trivial character on $\Gamma_0(N)$ with the color showing whether the symmetry is even or odd. For $N>100$ there are only results for prime level.

In the plot below each dot is linked to the homepage of the corresponding Maass forms.

1 2 3 4 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 Level R 2.73410555925 3.20437245526 1.4463991334 2.55636946085 3.59362788512 2.48359105956 3.28347243518 2.03309099386 2.96820576382 3.0325128349 3.48188847507 3.67969872505 2.74421107125 1.69106559844 2.0252843957 2.81634482766 3.33220121006 3.70162757524 0.970815416958 2.42669715561 2.53641204627 2.83080665145 3.75060456267 3.8128927243 3.96466554946 2.29012783647 2.84665998673 3.62819352869 1.79416536046 2.94495321818 3.01504959328 3.71654847808 3.93985827196 1.82147632892 2.91653733402 3.22026652843 3.49290270259 3.92775246896 1.51842933602 2.23047412065 2.36133422204 3.10450058521 3.61330792232 3.85551540683 1.84968790603 2.73170134934 2.99170924628 3.16938238009 3.6190644248 3.8979328254 1.44142854502 1.96798635964 1.97928209991 2.70287894394 1.9678447101 1.9678447101 1.32979889047 2.22001009054 2.81665576076 3.03719602046 3.10538415095 3.64245616518 1.09199155992 1.86922836527 2.29700635907 2.61034478629 2.9956190494 3.19257888594 3.26790747396 3.42597313676 3.77688712054 3.84044805112 2.20427188131 3.44478653588 3.92397086259 2.00967417707 2.00967417707 2.81540778099 1.27404261148 2.04509705725 2.61592856746 2.77837816936 2.9302569376 3.73514871954 0.924007217602 1.92464430482 2.08530975931 2.4385055061 2.65932874893 3.25120755726 3.27272100042 3.36432553144 3.62224302475 3.87100130387 1.72969651767 2.27226262876 2.61952660281 3.07010414741 3.60653766124 3.83392687084 3.85927173808 1.04598060261 1.36941174922 2.16502408584 2.40345084102 3.03564960868 3.67969872473 3.7113634789 3.88512912209 1.57958924015 2.46433387048 2.53213432953 2.61095996203 3.01662095343 3.23574197248 3.52025624378 3.81675523629 3.84003520889 3.91221753176 1.39333714148 1.5061266371 1.93525049265 2.43077741663 2.49362378677 2.73627771325 2.8079149467 3.3723339187 3.52454363828 3.5882850865 3.70627053908 3.8189248762 1.91464670089 2.12237798559 3.2413987165 1.30086635839 2.88439837461 3.40189451957 3.6881408371 3.9787535254 2.63642618632 3.67602901944 2.04374462257 3.98444316588 1.37694606445 2.19080795918 2.81162916951 2.87969244571 3.37938274387 3.60676534504 3.94478854738 1.74983899964 1.9732685967 2.05268848351 3.04384496707 3.20185402946 3.23449524434 3.48445972243 3.72299493743 1.45034943837 2.2456545638 2.47697015662 2.7376477992 1.45034943833 2.2456545646 2.47697015662 2.73764779916 1.69299215834 2.31822472077 3.08496615734 3.77619856172 0.816781268055 2.51495878964 2.57074818487 3.79276348512 1.0172665508 1.79784901838 2.13307606241 2.35848525401 2.86747483412 3.44202285986 3.69016053909 3.89920716121 1.21206072001 1.37929245765 2.21489389918 2.34983686267 2.42924558709 2.94296771268 3.05374848446 3.26711234695 3.41047735769 3.79555144725 3.92021463299 2.0463589284 2.3130351166 2.70328077524 3.61957681704 3.8307211971 0.94690379979 2.0125813397 3.2114071006 3.5367120263 3.88567591945 0.78935617774 1.7546428498 1.83128343514 2.3681029381 2.39253774613 2.6238542673 2.98780843925 3.23123939014 3.3253059439 3.3914645439 3.57095767326 3.61960533228 3.74519506768 3.85308028279 3.89638688832 1.06284037124 1.343010459 1.68678370214 1.96542621139 2.23271071476 2.2806857382 2.73466182125 2.74383051118 2.80593495033 2.90917032613 3.29029769112 3.3714667269 3.37678368162 3.47898831142 3.62448924684 3.70593927593 3.76047366069 1.58298402762 1.58298402715 1.29767492872 1.41355464648 2.09079633498 2.17455185368 2.3375835244 2.91533885562 3.08863927445 3.1881464082 3.3337141434 3.6192194385 3.66640524717 3.67574985339 0.673141432593 1.55606576917 1.59599133119 1.82341375434 2.01946112287 2.47009443697 2.7874911756 2.79169797103 2.79855317689 3.24677309037 3.70207783357 3.7635365926 3.80580148624 0.969123650097 1.77324021436 1.88641222669 2.46020834494 2.5810448325 3.12110373215 3.26833247971 3.59526911065 3.64802758318 3.84594741498 0.681987135148 1.43772610252 2.31878442521 2.3891260409 2.51945014895 3.01242186933 3.03671313163 3.19371324389 3.44151236888 3.5338738355 3.61565926071 1.10614037517 1.69515745048 2.03372223026 2.24849963462 2.31198087675 2.44920300935 2.74909857549 2.85386268432 3.04860321178 3.1513437635 3.33462884442 3.41648584604 3.65465234048 3.79209422522 0.95419922138 1.28752900633 1.49319728998 2.10024305499 2.405651738 2.473860342 2.48659618512 2.5495436886 2.99148072164 3.17737109039 3.19738755049 3.5256256815 3.63653301833 3.64836673978 3.81329724629 3.84737205904 3.94033522923 2.95645894 2.9564589412 1.22324304054 1.28068452862 2.01242222483 2.07459336618 2.19429897643 2.2307044784 2.55342145906 2.85373112524 2.8873919912 2.99107796087 3.21582779938 3.3832468962 3.39388746523 3.41236596206 3.57247231927 3.8257891651 3.9129854902 3.94288028632 0.6423059582 0.903734503358 1.58778611761 1.7095550812 2.0009916614 2.23557707722 2.31105388882 2.41405919701 2.48048511582 2.58621468711 2.83763159697 2.94626275346 3.06969494232 3.2889705067 3.34158686112 3.49100447103 3.67309909769 3.6926504722 3.7238949328 3.96133744917 1.62091719511 1.97899241306 2.1880967466 2.39763567756 2.53773621652 3.06936035147 3.1807280699 3.25592207452 3.63924820245 3.72825859859 3.93726583801 3.94853121813 1.16268546048 1.22174953513 1.79524096266 2.17549978279 2.3567382776 2.54046963358 2.9227233499 2.9387997702 3.42294399196 3.66220230255 3.90929361931 0.706744261331 1.53293311693 1.71557556098 2.2241472473 2.36480255311 2.39859492845 2.73749575457 3.1440889886 3.1454790311 3.2368320734 3.527726792 3.55234136034 3.70915503806 3.74588674524 3.99129132616 1.24210145926 1.61677823038 1.74495964014 1.87160388208 2.06339248584 2.40989067867 2.63004565347 2.98226649037 3.08223938181 3.17048923538 3.2467429305 3.253409656 3.37386068199 3.56369050486 3.8013618437 3.8315100807 1.22950519691 1.72976629069 2.15411776731 2.67799302195 2.75213643162 3.51305584417 3.79296743334 3.8130304935 3.97857656643 0.86274827851 1.77503671325 2.04767696 3.09705153025 3.18157965564 3.25711946464 3.5236882862 3.7825351219 0.66572483212 1.4762243008 1.6959287008 1.93420768472 2.0064764673 2.44363909155 2.4641420058 2.4974757343 2.73735838629 2.90945668499 3.04165177247 3.24040706004 3.4908606443 3.49238333272 3.51237166699 3.51589790073 3.52263495658 3.63689192912 3.8900740352 3.9502037603 3.99243620481 0.86739746584 1.20439574249 1.6633712283 1.68939340054 1.8997068997 1.94830897416 2.17248456 2.4436081313 2.44913354769 2.616148676 2.70307903335 2.87729730814 3.1353345742 3.15187453604 3.21378692902 3.2188789561 3.40093860852 3.53515469473 3.56536693508 3.75389527095 3.85816337785 3.87837381639 3.91186428549 3.98292409613 1.421259496 1.78451696812 2.10560838953 2.39261589269 3.07255726908 3.20209314103 3.4250002137 3.44522847332 3.74008791048 1.1125733491 1.2254146728 1.6341540743 2.3307135722 2.6296044996 3.921825388 3.9238208981 1.10814196343 1.3602107203 1.80282682958 1.8687260657 1.92502282942 2.29523815913 2.33365747269 2.62145844653 2.72251061195 2.8505934452 2.97359402858 3.05103590799 3.09649725186 3.2480265508 3.2527179575 3.40536078149 3.5127513568 3.78479884443 3.8312428031 3.87839736737 3.8828454907 3.88641522087 3.96643855215 0.655452381862 1.3239046204 1.33429136841 1.39820940399 1.7688529369 1.84361969787 2.2728086698 2.32502514096 2.42799539804 2.50389989061 2.6813017464 2.70494977915 2.78619625524 2.85615859854 3.02186250694 3.22708248523 3.38644379606 3.42315589796 3.53033098456 3.56651330433 3.5888363845 3.77108017064 3.8211873563 3.93554758484 3.97203309572 1.05484372709 1.86050010206 2.63281160674 3.23802937487 3.35292838308 3.6485407885 3.76505396915 1.25524213361 2.0662271242 2.4725421493 2.89208074162 3.0854308567 3.69903094932 0.9520288783 2.1189106705 2.56547623931 2.9168145173 3.6316099359 0.9520288783 2.11891067053 2.56547623931 2.9168145173 3.6316099359 0.782058538571 1.43540985512 1.7064589223 1.910080055 2.22242671237 2.33449410277 2.8634525395 2.98540729706 3.30936451822 3.3785486176 3.41932404012 3.54643238888 3.60371844441 0.417338814038 1.2149636536 1.89107798122 1.91367169554 2.20257017251 2.37768022057 2.76763971544 2.883842472 3.0598646253 3.18842827575 3.26803054582 3.29936540609 3.593204051 3.6356404535 1.11157408467 1.2371032283 1.60280120737 1.9998639739 2.00338948889 2.20466725542 2.26750861826 2.43722726343 2.54555268753 2.87652653184 2.8851603588 2.89043767994 2.90967397222 3.05644388657 3.23753800508 3.3257309569 3.57681947632 3.60878782674 3.609113904 3.68170332532 3.70586888077 3.75168582953 3.77775419849 3.86420195112 0.585452143 1.2635566239 1.3345231427 1.7125120984 1.8651389071 1.90995148617 1.92616135436 2.22396805023 2.23318689077 2.45557397194 2.55418810417 2.65156186537 2.67678169402 2.69155380317 2.8276094315 3.11343478615 3.15513163883 3.26955390516 3.31744338099 3.37915586952 3.5371204926 3.56787306816 3.64146205044 3.73396081875 3.82194661521 3.89095551867 3.90183230274 1.5041866 2.34583826 2.53162 2.91732822 3.0539546 3.372511312 3.475933261 3.760281 1.50418661999 2.34583826 2.531619733 2.91732822 3.05395456 3.47593326 3.7074249999 1.53972227888 2.16532306677 3.3177651975 3.724242725 2.61940140558 3.4251186192 3.489580725 0.835743661893 1.07639111582 1.57110616735 1.85512497428 1.94743400007 2.20993583057 2.371097062 2.45279122886 2.50163374451 2.56727259021 2.92860833381 3.104912482 3.1237609224 3.1505701599 3.53928284159 3.58273406161 3.64594761554 3.7323620972 3.82345105932 3.9695730406 0.806534894318 1.0773746475 1.29657787881 1.61189615978 2.100978289 2.11263778015 2.30240498094 2.61848859343 2.69844281788 2.70117698682 2.7907816151 2.96573393343 3.11119547944 3.11757306367 3.27586456683 3.35857801489 3.4662620621 3.53263792914 3.58157256423 3.81509389117 3.82710940564 3.8729430104 3.94503993728 1.16515185623 1.84995779332 2.39177000346 2.7513998587 3.04687614337 3.386997671 3.69847435003 3.7177012025 1.1532811918 1.48517492461 2.06042352995 2.54731683059 3.06368482912 3.08834252984 3.51966161681 1.0158404282 1.38056162259 1.49379571497 1.5360758374 1.89593054753 2.07597101915 2.08151982011 2.24756864757 2.34045977591 2.62862314646 2.70731549048 2.77733239202 2.78993525631 2.96616886316 2.98721988657 3.00192184639 3.02939267074 3.35140004413 3.40008960181 3.45365297628 3.4712986594 3.51311533166 3.59856473522 3.79549625215 3.81318882937 3.81860776643 3.8471796718 3.89485422991 3.96148104155 0.8039894596 1.10150481917 1.128678704 1.3454264689 1.58019040269 1.773658835 1.819344615 2.06869949437 2.17593531645 2.18589164121 2.46402701549 2.57272881291 2.6910614861 2.71297275229 2.73283718807 2.8304628982 2.84771569119 3.00866291783 3.05378095251 3.10592752857 3.29040977586 3.33798039243 3.41311460063 3.54310007442 3.54509593726 3.57466907108 3.672144167 3.7651956574 3.89457785283 3.92895518347 3.97322882779 1.0850815604 1.71708439906 1.8317806526 2.3048511769 2.96110732556 3.05077635002 3.12073145404 3.29197027079 3.5360586113 3.9584742471 3.97380875392 3.99523485745 1.0850815604 1.71708439906 1.8317806526 2.3048511769 2.9611073255 3.05077635002 3.120731454 3.29197027079 3.53605861133 3.95847424714 3.9738087539 3.9952348574 0.661575152344 1.17519083446 1.40439951677 1.633409688 1.68144381509 1.96506877097 2.07612020831 2.2888123487 2.443976209 2.51703209483 2.60805612989 2.86614556707 2.89705180961 2.9466110626 2.96616327003 3.18494336898 3.22744134333 3.300427267 3.34955628832 3.49595187548 3.54071051737 3.66491651798 3.6981526471 3.70327397173 3.7671596379 3.88339922088 0.887725475999 1.00029094182 1.11537870003 1.58575493394 1.60451714933 1.68207794197 1.77874679978 2.14922397594 2.14942613728 2.33685670635 2.3523003331 2.38634230966 2.70983305794 2.75337037352 2.78727651228 2.8919540853 3.23931335441 3.3436234845 3.38842936182 3.48053157543 3.54334040057 3.5889270764 3.63371894988 3.65762555532 3.83494351339 3.91422309768 0.89568107961 1.5210286376 1.88351246723 2.2981438747 2.44423197756 2.78000163577 2.83785199038 3.2175641845 3.4369570382 3.6148971277 3.91728421927 3.9621427214 1.26201628212 1.33420268344 1.6172114236 2.1601608467 2.74599306682 2.76043534441 3.02214019811 3.30481891434 3.38278649078 3.61207997122 3.636167501 3.8577000162 0.8770038522 1.1941621283 1.67673353646 1.72576830608 1.96355434703 2.09286045954 2.10809373014 2.32130874741 2.52880290037 2.72087101315 2.72994003818 2.73072709669 3.21066697307 3.24723598872 3.34366574106 3.3527577176 3.5003543352 3.53318440291 3.57746445435 3.60996885501 3.72496485074 3.744320943 3.79517889058 3.9101831392 0.48946607452 1.16266914555 1.35907273352 1.72560292218 1.73596057359 1.7477885071 2.15654428034 2.16199075892 2.18552185148 2.37989020464 2.6871593881 2.74071613565 2.81547291599 2.91228317274 2.9745457297 3.0755352729 3.2788307776 3.4482864347 3.54490820553 3.62062759122 3.64863311721 3.79943056848 3.96341726016 3.96898496112 1.19791429819 1.25765110305 1.81280811614 1.97678552648 1.99632496296 2.178318412 2.52043042755 2.6481809479 2.8874500935 3.01041604 3.01200066968 3.24061541108 3.43813961183 3.47169911576 3.62858306898 3.63133614183 3.86547774199 0.56349435606 0.859385049143 1.719437847 1.75130499989 1.77100925114 2.08726596484 2.25696920705 2.3455323865 2.68692812476 2.78151368114 2.84949888878 2.98259255918 3.2194379968 3.28902469545 3.3970823117 3.76351947392 3.86156023754 3.86733283506 3.88616176024 0.59582968816 1.2768121223 1.50919167506 1.6026070832 1.7096938151 1.77418404 2.06116643405 2.1528209134 2.31327401436 2.31538965327 2.38138271924 2.68572206275 2.70391013838 2.7125033238 2.72469041566 2.92239721918 3.07556029248 3.08708280045 3.12731532477 3.2382297617 3.28696703259 3.30133706136 3.42811085908 3.45141007356 3.59724335171 3.76241122031 3.80890115705 3.81944380739 3.87226479669 3.88066051452 3.90705127681 0.5985969867 1.0391204647 1.2992223994 1.3104070581 1.4394717288 1.8584049417 1.89413297345 2.01227818027 2.19666598502 2.25004686447 2.29357600736 2.31717381442 2.44920307372 2.5266265795 2.60825382674 2.7029685972 2.73580667392 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