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Maass forms of levels 100 to 250 with $0 \leq R\leq 2$

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.

Examples of some ranges with complete data:

Clicking on a dot takes you to the homepage of the Maass form.

1 2 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150 152 154 156 158 160 162 164 166 168 170 172 174 176 178 180 182 184 186 188 190 192 194 196 198 200 202 204 206 208 210 212 214 216 218 220 222 224 226 228 230 232 234 236 238 240 242 244 246 248 250 Level R 0.840090994356 1.84548430295 0.822618972722 1.2560160357 1.33113009011 0.880387550668 1.11450387401 1.13391697604 1.5401895345 1.59484529536 1.66086944888 1.66851301739 1.79290981203 1.95706562633 1.98072032893 0.545603945163 0.605542215453 0.83479174517 1.04641452468 1.19028575135 1.29546919344 1.30721081201 1.43329891341 1.58040202446 1.64961268864 1.79506538095 1.88202163105 1.9729917361 0.814580109612 0.987633245948 1.17640869473 1.17901531946 1.23677665021 1.35049246463 1.61025415503 1.66529584216 1.8040421768 1.81235198608 1.87635006977 0.30117539827 0.46295900475 0.845103502221 0.980674960406 1.08641256334 1.26921921774 1.52858470546 1.55750891533 1.61075108932 1.68959144131 1.78837578087 1.87587473581 1.88016909661 1.94399709606 1.30562582217 1.50499652266 1.61774536143 0.453759246671 0.88198037948 0.953142387968 1.18320717292 1.43848626066 1.56483509767 1.63184189495 1.86255027029 1.90250330058 0.780027271598 0.84975710329 1.21127385834 1.41537369051 1.59768741093 1.60922486016 1.64346214047 1.8363299862 0.546229901257 1.11356288285 1.29517513362 1.40290720484 1.79658161953 1.97518714517 0.904408023977 1.5845953994 1.59904230192 1.66929355624 1.82808610228 1.94542519509 1.04534567017 1.25797759897 1.56009376349 1.63273794919 1.81205410772 0.905224483362 1.02729599977 1.10671767356 1.15510113002 1.43451435495 1.80195794222 0.581678563695 1.65447519155 1.69829902421 1.78597231247 1.98267047629 1.20149246031 1.29410067896 1.54544941412 1.76578731747 1.84674951646 1.8992283835 1.91391803143 1.96662451237 0.284673165521 0.736928841121 0.766740331825 0.776045028256 0.892847896989 1.28503763594 1.3458321648 1.42186651441 1.49365755985 1.50276943648 1.65760880909 1.82715131359 1.84284727507 1.93389755254 0.604111174409 0.773871735297 0.785550827625 0.873587140931 1.10516529274 1.37466798772 1.40234748082 1.48413072184 1.52161981468 1.59536810931 1.75110878973 1.7625438356 1.98858299308 0.839229816277 0.931471539335 1.008823518 1.48142144346 1.56130464614 1.66189287244 1.72896437398 1.90944335322 1.17310986932 1.34761045668 1.3519332208 1.35193322089 1.76543141647 1.88463437665 1.92487910427 1.99030634486 0.365885353336 0.781298963533 0.875001923761 0.971062058453 1.03642582593 1.26553782526 1.36006854674 1.38355327603 1.60091918746 1.76266641903 1.89017577712 1.99506440235 0.413439046641 0.792774123056 0.978113085058 1.14286618239 1.19072672862 1.22139471935 1.35622746053 1.51688712306 1.60806985606 1.84026095135 1.84032328718 1.85891579728 0.635918170892 1.1364370886 1.24385988586 1.39961330851 1.43614249331 1.6966432731 1.80245000876 1.81017824231 0.981700516542 1.0095866503 1.39303372517 1.534436671 1.58241250134 1.66485038925 1.76678437629 1.85736752813 1.99748268353 0.309546539387 0.670477154629 0.775705820262 0.830393780114 1.06066286268 1.10948423686 1.14503610614 1.16222089503 1.16817037835 1.34978261884 1.44510209742 1.50381309789 1.69780241139 1.75643049092 1.87792242135 1.89633251326 1.91618844923 1.98848039253 0.32825578889 0.4050362923 0.558529053468 0.68832569855 0.884399546206 1.01662040797 1.16452085626 1.19474018311 1.34144128594 1.34897047406 1.38753147093 1.61237151672 1.62185193044 1.62703110772 1.69044889654 1.6929251195 1.74677978574 1.83735796525 1.97439667448 0.975096776913 1.04008155353 1.17543071203 1.22279455921 1.57726391717 1.65724227556 1.81236161383 1.82103717124 1.87123383989 1.90079901927 1.91124318187 1.92133180185 0.922914144227 1.1136713316 1.50508738869 1.54053920875 1.78156508623 1.79790948183 1.85204904955 0.455724176035 0.85152487687 0.898900764569 1.11222438629 1.21120931006 1.29890138402 1.31727802226 1.60900015256 1.69168925051 1.69539320761 1.78631391766 1.81263465267 1.91846462945 0.433985036762 0.636626192003 0.69300494876 0.948718960267 1.0620981087 1.08422167696 1.0958168774 1.5265552634 1.56761533124 1.59409564365 1.67460010946 1.73159523163 1.75922324702 1.79081555069 0.737203151602 1.18801105851 1.1922169907 1.30201336219 1.4662250484 1.55956613196 1.69649697653 1.84062255326 1.33855307661 1.55265241979 1.93310307084 0.519274345618 0.68573069321 0.804034803987 1.22610605699 1.23546457734 1.33478341213 1.48486732784 1.57732854532 1.85402699304 1.94266911926 0.423654573886 0.503494760807 0.810515413263 1.14948940239 1.20200435084 1.38435732749 1.40722942581 1.70791338456 1.75903103631 1.76890029431 1.78901322381 1.09063336373 1.41778132917 1.51203362665 1.72645386279 0.582497617145 1.09690348539 1.1486217062 1.35765469019 1.42556231723 1.43214295907 1.6225868017 1.68668312411 1.75819682561 1.76519423035 1.94264392209 1.95139277512 1.96648349521 0.647493219089 0.705035795491 0.746210114647 1.00033423064 1.16081610333 1.193908596 1.26360481822 1.31600348973 1.36579556374 1.51384159931 1.64232481491 1.70008653539 1.72309512238 1.7932630163 0.60948117165 0.611161185678 0.816205370903 0.943135100952 1.0164250245 1.14658748357 1.1796902709 1.4711560076 1.50969940986 1.53333864069 1.5494187767 1.57042953872 1.82405949614 1.87259347188 1.87416996885 1.8848225412 1.94827790581 1.98116252015 0.579838392085 0.674818444774 0.900526293801 1.16112730362 1.17407269382 1.31989816547 1.40204986756 1.52800144428 1.55696815606 1.68645694975 1.70627707075 1.82495599837 1.9551428267 1.00015082645 1.40465778772 1.55742116877 1.76913644959 1.81046562633 1.95515977444 0.373385114902 0.939534113071 1.01132955015 1.08512829276 1.1611202739 1.1834363056 1.47207206595 1.68973252996 1.79272202991 1.88744334359 1.97391908573 0.450881856951 0.889913252411 0.914358149316 1.06946447128 1.2890352727 1.32459446721 1.48654300316 1.66454839356 1.86912865109 1.8926200866 1.96546314695 0.568891385272 1.26018743079 1.26193846403 1.48146307847 1.5129309018 1.65169511561 1.86231269575 1.91426499692 1.07935363631 1.0999346021 1.60447605186 1.62360453581 1.73060851783 1.7982218623 1.94373567561 0.685338417164 0.728202980815 0.930499451534 1.1123413249 1.13904656263 1.42531038416 1.48133313028 1.48527396849 1.54136950575 1.79007645664 0.392996762702 0.743083364307 0.895228912752 1.12874932754 1.16284400562 1.31040629609 1.49348552429 1.63485272474 1.70085577693 1.7253736221 1.7515122511 1.90060839103 0.799948259899 0.840946038925 1.41735853335 1.45077969976 1.5223325969 1.74332392811 1.74513736685 1.8081302198 1.00410100278 1.1790283986 1.30501270117 1.50627163196 1.6021999774 1.72287009703 1.77956755862 1.8932504399 1.91327054141 1.9668680661 0.359083582614 0.519589894961 0.822246565469 0.893729935256 1.0171986525 1.04652691394 1.16235072999 1.29373937847 1.42802538655 1.6280223395 1.66554014963 1.70776758439 1.75888638689 1.78334803998 1.87941850237 0.580662847488 0.840374904144 0.952104928204 1.10271048058 1.17931456656 1.25714457741 1.26252248557 1.47297781574 1.52783948978 1.62522296916 1.67265632236 1.81662749737 1.9183276323 1.93600173283 1.93743336914 0.52213132826 0.617943787054 0.962080321973 0.984767228107 1.40647039057 1.45048656454 1.53422325066 1.57233031624 1.62658069113 1.6434957842 1.77876672357 1.85910119828 0.664114925399 1.34492991189 1.38146155468 1.41494730155 1.55584637398 1.64535752068 1.70897808151 1.96257506692 0.768632870549 0.795295813343 0.803452785981 0.827983273907 1.25304501296 1.27390063457 1.43730748477 1.50056327537 1.50331945415 1.66241748399 1.94437060155 1.94828213735 1.96327235725 1.97794829856 0.38151062621 0.555945666178 0.785488235097 0.869561205695 0.991673787983 1.18156795433 1.40044264716 1.45184504292 1.49794363287 1.57273684046 1.60760897568 1.62368679685 1.7520613259 1.80353917745 1.95442799207 0.726719670196 1.063215514 1.12750460996 1.25853290915 1.4437238193 1.67895073334 1.68965359925 1.78367635555 1.93425357162 1.95857195319 0.616976878589 1.17693258727 1.35674493472 1.45230138276 1.47493818304 1.51437562918 1.54197351209 1.92166864473 1.92719091008 0.630727280729 0.758950777742 0.839539364022 0.933954031222 0.944270995623 1.44029939101 1.46470199444 1.57139018328 1.58476216984 1.59179980073 1.63672809113 1.69626384057 1.78667889522 1.92509355027 0.668103392455 0.72606180622 0.851113487853 1.1476297336 1.25595173907 1.35907900982 1.42451468934 1.42743426685 1.49246013172 1.71155386408 1.72944893011 1.76853652422 1.77493820183 0.493192013608 0.577000986458 1.03889992501 1.17073102423 1.20181703997 1.21480913733 1.44980474765 1.57104455286 1.71870215667 1.74631612535 1.85432649812 1.9877588214 1.08153114293 1.57557652159 1.7621560519 1.82692759785 1.89041923352 0.685199772771 0.810627743218 0.914523837866 1.314345178 1.41268258619 1.56919356208 1.61877044941 1.8504179233 1.97667934013 0.56540673692 1.00973864709 1.03750140522 1.2080488963 1.4694852809 1.5813920652 1.69383124087 1.87627571322 1.88550002908 1.92881866214 0.724054488989 1.13071799834 1.39897986155 1.46912833193 1.89213374502 1.92340333123 1.94537194617 1.02609334504 1.32764903809 1.40247917255 1.50009274152 1.5385536252 1.59273550959 1.63343765678 1.81551709597 1.93155372716 0.307664876026 0.397068697475 0.651189263156 0.795689220415 0.907407872302 1.01886594256 1.21005557266 1.23817885806 1.28141111204 1.46754475619 1.53736858447 1.68768459351 1.70698841122 1.70746322469 1.84252369607 1.85879565956 1.87412368782 0.714466712062 0.879710446188 0.992121759831 1.0475110967 1.13467438226 1.30307986833 1.32053009008 1.44643218498 1.55837406909 1.56470874483 1.70771723019 1.72561668393 1.73711865575 1.91290606556 0.289653975869 0.722826095105 0.819657055247 1.04866112991 1.12561981197 1.32863920999 1.43832471394 1.52648355709 1.64061538015 1.69373245165 1.78848873648 1.8176455262 1.86175247187 1.98630738009 1.08372099122 1.34238593196 1.51862027057 1.64003927378 1.75814393184 0.527438597282 0.604110208475 0.828675829521 1.06403367056 1.24175801986 1.35715997708 1.52428656796 1.62347610533 1.68236838172 1.96465961392 1.99887641908 0.710201194977 1.14631038559 1.1965760237 1.26204377796 1.41293833562 1.50272617901 1.53007391301 1.75700103925 1.86698884822 0.261072762333 0.707467193368 1.10171163877 1.29714646179 1.32447772468 1.52708656291 1.72167165897 1.77662502888 1.87947843643 1.91616837529 1.02822771394 1.3897011502 1.47214868945 1.47450017088 1.68459013822 1.76199712759 1.96443891434 1.99279093469 0.431849402694 0.571256405223 1.02594366496 1.03755638046 1.13873167749 1.16401223817 1.24860759059 1.50270978108 1.52583141806 1.63581524218 1.8305892931 1.85901215879 1.97756767565 0.590570312533 0.786826194668 0.936351135222 1.03935693913 1.19316045958 1.24460589415 1.47533025522 1.63951274852 1.64348978654 1.65215937013 1.75047717333 1.81464989184 0.656038005273 0.851036056296 1.05372685731 1.203165834 1.51319915193 1.59003244758 1.70302568266 1.76354795346 1.97632134179 1.02323101478 1.42402345304 1.70468355257 1.84639532536 1.89366611106 1.96241117307 0.555703841798 0.978308637536 1.0054783397 1.15334686911 1.27232690948 1.3645504457 1.7086930456 1.84679099353 1.88267453463 1.97985987713 1.99907141325 0.462002646377 0.863217767536 0.949319935225 1.33392815874 1.35953632906 1.47437812898 1.51614818419 1.64901900183 1.76112035344 1.97159342938 0.852903915736 1.04845968909 1.40820155781 1.65669719871 1.6827391579 1.7599722799 1.09327350596 1.17328424709 1.44391432653 1.56873445808 1.63840771483 1.79911312527 1.90983816177 1.91868426857 1.93414717996 0.158857173089 0.637691167109 0.73403662716 0.855600693281 0.984409470722 1.065946898 1.0998482928 1.11259657509 1.20346228659 1.34202165242 1.62858026853 1.65644854965 1.67747379582 1.85303572749 1.85331851734 1.91225010028 1.94021958827 1.95136029636 1.99588262171 0.48248118587 0.512703843078 0.566806855973 0.82801583677 0.88372745264 1.16173851703 1.26598866483 1.31841730541 1.41845624629 1.4410138747 1.49607207449 1.55102676347 1.5766900115 1.70676245809 1.73114495109 1.76986909073 1.78394315562 0.887087115557 0.98404955563 1.16202588457 1.21423577877 1.59795237352 1.62710806282 1.69961147435 1.73516771187 1.97543917905 1.97637520374 1.04623795106 1.19907997525 1.20177023732 1.60122115407 1.63682010471 1.65075077992 1.70457226656 1.78484325548 1.82777241744 0.3698833861 0.495832124507 0.588553686459 0.736060666865 0.866776012295 1.06813810963 1.09786760184 1.14452329043 1.28718986584 1.34655103294 1.38485988378 1.57110004104 1.61143999635 1.73887625772 1.7496777153 1.87974382137 1.91477321419 1.92655243987 1.95381062262 1.96416099427 0.602498932338 0.714779679001 0.76487704271 0.801281273973 1.04811667743 1.21817795904 1.22187367936 1.28565823714 1.39570400739 1.47750409078 1.51631879015 1.56151280775 1.69794663632 1.71331776954 1.76563417169 1.85135613084 1.87027783296 1.91988391587 0.5342378472 0.953682816452 1.09415864077 1.1033999677 1.14949571796 1.43286826246 1.45307974776 1.61320166139 1.71998346474 1.77053408429 1.79789906122 1.84094199186 1.07486165615 1.15947055944 1.22740980816 1.47924477179 1.6104116316 1.64195142498 1.67481203806 1.68506522274 1.69891792653 1.73829338727 1.77938200351 1.84266608749 0.2385182601 0.3727632707 0.59028176463 0.83159116841 0.896445751874 1.01942164342 1.04434767382 1.11193975102 1.29449527007 1.33939616402 1.4626601236 1.53774882979 1.61641079028 1.69434003472 1.71160529161 1.72921647799 1.85638247501 1.86077434353 1.86966928031 1.90873423935 0.75083189332 0.84136677627 0.942342557078 1.12301943192 1.24854652679 1.28144182828 1.33385173451 1.54691916805 1.56934022534 1.59224557539 1.66289158445 1.68352381017 1.80336498499 1.84560466471 1.85378899054 1.89667974198 1.91890367069 0.34833537579 0.47910294184 0.66436680754 0.87644537797 1.03621879761 1.35406980568 1.40285515183 1.42806787556 1.46262691775 1.50468982234 1.52562681725 1.55971929963 1.73253449342 1.80112909463 1.93584529475 1.95380950846 0.61936426702 0.83308071316 1.17138524123 1.21813287269 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