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Maass forms of levels 1 to 15 with $0 \leq R\leq 15$

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 5 6 7 8 9 10 11 12 13 14 15 1 3 5 7 9 11 13 15 Level R 13.7797513519 9.53369526135 12.1730083247 14.3585095183 8.92287648699 12.0929948751 14.6850159506 5.41733480684 7.22087197596 8.27366588959 10.7127069007 11.3176797015 12.821988162 13.3101642835 14.0972037339 5.09874190873 8.03886120386 8.77828239355 9.74374939916 10.2310756893 11.3464186204 11.8899755746 12.580463057 13.1351445113 13.9931761916 14.6262358404 4.38805356322 6.12057553309 6.75741527775 7.75813319502 8.19303593168 9.29237932822 10.5076073043 10.9135396775 11.3659037782 11.7145309917 12.6279481097 13.3786205776 13.3954804003 13.5079113404 14.6012532084 14.7873247385 14.9169973013 5.87935415776 8.04247759169 14.4778027317 3.70330780122 6.62042287384 8.52250301688 9.93491995937 10.7647106832 11.972776694 13.228828713 14.1438850658 14.9703130686 4.13240421506 5.43618046142 6.05402838077 6.82352699542 7.98654905098 8.29469778357 8.4800158394 9.27729778527 9.39741755066 10.2463013805 10.6311530866 11.181381958 11.2834406791 11.6923207345 12.0183185174 12.1207735459 12.6360800548 12.8554583746 13.0006638517 13.4689817279 13.6993069852 13.8573264614 14.3530892608 14.5957035794 14.7907011072 14.9562214606 3.02837629307 4.10322180991 4.89723501573 5.70582652719 6.35122321676 6.45847643848 7.32552437933 7.58531840144 8.01848237839 8.2261459726 8.81789729862 8.82074088495 9.83341273669 10.045820825 10.3070268656 10.5004431507 10.983968955 11.0931280005 11.1539349348 11.6005386371 11.87084943 12.3141719404 12.6585068804 12.7159021442 13.0963889192 13.2197860798 13.5751469722 13.6473942985 13.7599489451 14.0342548179 14.2458963378 14.6981676744 14.955192517 14.9867895143 3.84467228501 6.00033540888 6.30636358623 6.87436376055 7.38627450582 7.90114750377 9.65240704243 9.66046617807 10.6298273272 11.3130895989 11.7057493189 12.3544320764 12.8347409661 13.1778468571 13.2545279009 13.9018163092 13.9637989662 14.4676129234 14.8720924008 2.59237977171 3.3088170303 4.54845492142 5.8716820925 7.15749058532 8.66395307858 8.81974775988 9.37443036553 10.1454558365 10.1961201777 10.2048624763 11.5585635397 12.1162222939 12.5299513826 12.6353414748 13.6987468059 14.007064483 14.3794514696 3.45422650357 4.02170481942 4.82800766847 5.58279102848 6.06885693385 6.27191087352 7.33182919217 7.35799566148 7.7010258369 8.15572563068 8.42175366822 8.69750590723 9.04317475934 9.25079724881 9.35463469751 9.66612934925 10.1616724897 10.175062328 10.2719888709 10.6557340712 11.0772643773 11.2287594983 11.3093434777 11.3483973599 11.6600704287 11.7636315651 12.1478256896 12.3739809414 12.53434192 12.6838332458 12.7062239332 13.1209012524 13.3683356647 13.3795867468 13.6053245138 13.9084271212 14.1415558991 14.2644093436 14.3008035903 14.3335466515 14.6660794527 14.6701383491 1.92464430511 3.19085876294 4.11900929292 4.71971646829 5.10146081193 5.44273917126 5.82926875013 6.25758390694 6.33448316434 7.05035422681 7.05407006402 7.4314578005 7.71956232873 8.07161868259 8.25178553271 8.46236495549 8.80251162268 8.94499430391 8.99915977043 9.20407719967 9.98429702517 9.99016407004 10.5312060637 10.5773733824 10.6456998611 10.6716858394 10.6717085945 11.2763113507 11.3084693945 11.4943991008 11.6962468302 12.0215787893 12.1833418195 12.4301522386 12.7126452398 12.7314919646 12.9574195877 13.1285144687 13.1471805638 13.4012029876 13.5838479949 13.6464251756 13.8037862149 13.8587404552 13.8682520057 14.2650692615 14.4303062141 14.6754864014 14.7695313418 14.9500435341 3.24997696354 4.64659164296 5.62812092942 6.58769285315 7.22656906706 7.69684780643 8.21171118246 9.01322849206 9.4700831342 9.9039777038 10.2659151168 10.6817988431 11.1062703875 11.7819543736 11.8777730802 12.0230258884 12.5844685795 12.9838454746 13.5200506514 13.6349664437 13.9223820714 14.3364791366 14.4102250052 14.7798382665 2.42505682709 4.36801954023 4.94783167713 6.22318082532 6.32531406199 7.48301811751 7.74444773702 8.55288032905 9.00120580965 9.19652685256 9.81001812133 10.2618142525 10.5388080579 11.4110059735 11.4536636942 11.4814591662 12.4023495483 12.4144645265 12.9167943228 12.93885778 13.5881834525 13.6459947778 13.9895535537 14.4492628268 14.8479980699 14.988459734 3.53600209294 5.50405667968 6.64658135561 7.43179917172 8.69834295647 9.0800693497 10.0894530628 10.4711201375 11.1309636349 11.728024516 12.6229848659 12.8574162785 13.0773211701 13.9432420039 14.1179069025 14.7326818427 3.53600209294 5.50405667968 6.64658135561 7.43179917172 8.69834295647 9.08006934969 10.0894530628 10.4711201375 11.1309636349 11.728024516 12.6229848659 12.8574162785 13.0773211701 13.9432420039 14.1179069025 14.7326818427 2.73410555925 3.20437245526 4.58236150313 5.10381155304 5.42416298033 6.37879720849 6.4845713681 6.99327291741 7.41262473822 7.56348983462 7.78033646819 8.45261564535 8.58191066592 9.23048002425 9.78345165027 9.95201540908 10.1994943801 10.2641383944 10.7422023202 11.0484521159 11.1924559787 11.4177272153 11.7496208831 12.153525187 12.4596489912 12.5585779181 12.9582818801 12.9729966293 13.2036691317 13.3121869995 13.5633748047 13.8221167093 14.20455634 14.2889756764 14.3176285454 14.4354503421 14.8197544572 1.4463991334 2.55636946085 3.59362788512 4.18409504645 4.64274919042 5.45975729468 6.01171674499 6.67376039246 6.73532969117 7.34617187347 7.788215329 8.42338862095 8.953063681 9.02977428596 9.30018385212 9.44243727649 9.46193719273 10.0194866131 10.2763012571 10.4363421604 11.0009604498 11.5070658355 11.5198192086 11.9357108569 11.9521606244 12.0150070407 12.3624041926 12.657894507 12.9433745145 13.1075094406 13.5062656949 13.7422588437 13.8721865958 14.1093933296 14.6341180002 14.6481407612 14.712382788 14.7336237927 14.9238928466 2.48359105956 3.28347243518 4.01806918822 4.55526078532 4.71167698681 4.93319801574 5.26506649405 5.76387668292 5.98954264666 6.24170166435 6.50705758439 6.53884437383 6.61367529613 7.16536040403 7.26644184887 7.57048468838 7.73368897344 7.88007383383 8.14202179525 8.27450677876 8.51378467859 8.62006794988 8.678686129 8.99092809561 9.1017282089 9.22640277045 9.34515203413 9.58209996972 9.58661569271 9.67447022103 9.86213636819 9.98570868052 10.1232769352 10.3790777118 10.6430998727 10.6466817416 10.6895930795 10.9372887384 11.1472353004 11.1502516476 11.1780820772 11.4741161917 11.4784159679 11.6836999337 11.7850155261 11.8109636758 11.929306545 12.0381132141 12.0601741852 12.3049680992 12.5345178666 12.6105517277 12.611802821 12.634884788 12.8779804005 12.9273387662 12.9741004803 13.1014471684 13.1911590759 13.3166772852 13.3464693158 13.4637893383 13.6447823609 13.9313207376 13.9973467856 14.012936117 14.1810864258 14.1860327882 14.3114710478 14.4299835021 14.5497393535 14.6195267863 14.6742944064 14.6760838373 14.843562745 2.03309099386 2.96820576382 3.0325128349 3.48188847507 3.67969872505 4.4795039188 4.52889442465 4.73801385946 4.96681056895 5.38428160735 5.6632654884 5.8685322206 6.03361084488 6.06921835946 6.58162198464 6.77549251517 6.839443143 7.02463370062 7.29898901639 7.48914848834 7.51799881467 7.59926619693 7.68091057694 8.04940484094 8.16066289196 8.43825975049 8.55580430793 8.57197307003 8.65213300966 8.92993868924 9.04133195662 9.19975228212 9.46659932794 9.58865618654 9.67408869683 9.70588526622 9.85493309177 10.1617823364 10.1854915198 10.2760011955 10.3386794438 10.5313292208 10.644516414 10.6694194813 10.8165867701 10.905140061 10.989904792 11.2612425027 11.2733375812 11.3280653248 11.5395912507 11.6712226728 11.7801194448 11.8005163424 11.8348731714 11.9611740135 12.0109888105 12.2747697041 12.3508352281 12.4428495329 12.6217030777 12.735559057 12.8306124018 13.0161442998 13.0390510295 13.0511749815 13.1071273515 13.1552709731 13.2047771281 13.5048664769 13.542173788 13.7227533759 13.7749415755 13.7758633374 13.7880488437 13.8248368262 13.9558494776 13.9736027378 14.2522114277 14.3206812472 14.4220559343 14.5378517272 14.7000772975 14.731131204 14.8103795352 14.8184332563 14.8274044217 14.9043367854 14.9102393782 2.74421107125 4.06617926104 4.9342604018 6.77721877335 7.3417508929 8.28893108415 8.91929514287 9.43936207844 10.3761939522 10.6969521488 10.8658287404 11.4683321275 12.1825187967 12.4574662505 13.4630289211 13.8207204451 14.1970369634 14.5742766808 1.69106559844 4.98315181103 5.35269680215 6.30572613319 7.62347662393 7.68822371255 8.89214384141 9.18273034509 9.95057272015 11.024546463 11.4559859145 11.9780803614 12.1738052763 12.8481421756 12.8912816655 13.7623975926 13.8686943566 14.4214593582 14.8426411807 2.0252843957 2.81634482766 3.33220121006 3.70162757524 4.23019956539 4.46679817957 4.8541487803 5.07311267591 5.08447332119 5.40798563316 5.69430016396 5.89961904796 6.09349565841 6.26632820327 6.56812403596 6.69049934024 7.02357700265 7.2667253274 7.32585783181 7.44755875439 7.70429657275 7.80181234243 7.85507652981 8.16288098035 8.32257722261 8.32672293172 8.63469691495 8.63858381 8.74686205671 8.83126607628 9.01836329954 9.25099668182 9.28155594622 9.32066170464 9.52582083781 9.53738383671 9.77558685478 9.84104766459 9.85601392633 10.0760073189 10.0904073379 10.3174493944 10.4032440533 10.5158166167 10.5221050003 10.8157199068 10.8640225809 10.9710436652 11.0126767304 11.1988184821 11.2083448798 11.4919369702 11.5024933272 11.5318086842 11.6642366671 11.6663574633 11.7519287783 11.961184828 12.0420795438 12.0613012782 12.1393181016 12.2178723261 12.2646912659 12.4727063714 12.5525588285 12.6348148237 12.6439550116 12.7888755111 13.0021596107 13.0184143819 13.1054752895 13.1445892938 13.2236964201 13.405645826 13.4158009597 13.4543890913 13.5164166963 13.610829694 13.6462016637 13.8814284946 13.9647486903 13.9711536111 14.1873963859 14.2138017412 14.2297407058 14.3949315596 14.4339775419 14.4896167576 14.4908655724 14.6718170691 14.8083534801 14.8871157378 0.970815416958 2.42669715561 2.53641204627 2.83080665145 3.75060456267 3.8128927243 3.96466554946 4.38518054954 4.81472029634 4.89514361515 4.89717909208 4.96964302847 5.59109262478 5.77552578547 5.85408357709 5.97548743286 6.17628467046 6.320651643 6.70252321169 6.740246832 6.82830536809 6.93262595947 7.13370465755 7.20820733505 7.2945513252 7.62688614428 7.75262012727 7.78888957422 7.89288900766 7.93496968725 8.16689265709 8.36558181255 8.57895739749 8.63274262957 8.64354031332 8.70919627118 8.81629141635 9.09646793277 9.11965824925 9.16847519035 9.48147888733 9.51361124246 9.74996021691 9.76468995634 9.79800833958 10.1541442748 10.1817974821 10.2672440627 10.3017962586 10.3624939606 10.3651387362 10.5088357522 10.6848366156 10.8857836994 11.0047505292 11.0763942533 11.1541136158 11.1574764474 11.1818394802 11.2248817359 11.4398526025 11.4626443324 11.4792202359 11.640299926 11.8337126876 11.880552271 11.9040550081 11.9634761943 12.1251268084 12.216915973 12.2717682047 12.7038304905 12.7201289012 12.7459072573 12.7835296452 12.8598607555 12.861491372 12.884469058 12.9277629501 13.0572541062 13.0975108772 13.3232958976 13.3582067458 13.4099153485 13.4946762254 13.6112425707 13.6282445067 13.6317924433 13.7647596429 13.9486407549 13.9586118072 13.9901511145 13.9953127695 14.2410737534 14.253253483 14.2696971395 14.4537783311 14.4583560141 14.4904216802 14.5275594968 14.5291035368 14.6867865799 14.841642863 14.9140919949 14.9896072385 2.29012783647 2.84665998673 3.62819352869 4.52208412029 5.03074918113 5.27487748287 5.47351318578 5.80567178777 6.34752444631 6.7163141939 6.75529844582 6.77498260248 6.96485168305 7.6208081452 7.87382712891 7.8976039924 7.98696108952 8.49946505045 8.56497336757 8.96246431384 9.35406838073 9.47558282076 9.83018076843 9.91827612186 10.0976547098 10.2760924426 10.4816995543 10.5906864615 10.8530971085 10.9447198479 11.3345694115 11.6011268459 11.7438172697 11.7621460638 11.9684600064 12.1834972619 12.3586166636 12.4944877194 12.662467626 12.7623808726 12.970719403 13.0957630027 13.1726198685 13.2243046125 13.3475422609 13.6154148611 13.6367214952 13.7229827042 14.0166937828 14.0495345653 14.1639030753 14.3867243415 14.5613307736 14.7158566308 14.758027284 14.8956878041 1.79416536046 2.94495321818 3.01504959328 3.71654847808 3.93985827196 4.29731218878 4.58940589267 5.24897949499 6.01533951853 6.1871464447 6.49256560744 6.59193983828 7.06523224827 7.22295707842 7.82039168819 7.95845200415 7.96478111463 8.69561426476 8.80707934379 9.01223427143 9.17099173626 9.5264015474 9.56689697161 9.61574104808 9.88446834907 9.91987168063 10.0326050176 10.0964548652 10.4310445764 10.8534201922 11.1134306547 11.1403245634 11.4755882818 11.4823151234 11.6639127006 11.7901647197 11.9952732183 12.1185828133 12.2155399768 12.5894301097 12.6852010801 12.790319348 12.9638100974 13.2271086111 13.2327363052 13.6675637224 13.6803604248 13.7108576364 14.0897505881 14.2608730008 14.3232338726 14.4966286948 14.5676396376 14.5820360004 14.6450423737 14.704375019 1.82147632892 2.91653733402 3.22026652843 3.49290270259 3.92775246896 4.53086807747 4.6113780114 4.75479713395 5.31220835199 5.85950414296 5.98505799392 6.18043116288 6.50436815346 6.54089429079 6.93465180361 6.99752889314 7.19520694815 7.33539452441 7.35890306993 7.56217196142 7.76333046178 7.91310981628 8.39388640634 8.66501125743 8.67808170374 8.90821836792 9.10018366859 9.16197265962 9.17881232885 9.61137343978 9.82417896066 9.88449664132 10.0207163445 10.2927392311 10.3332479126 10.4950859748 10.6997344602 10.7704482094 10.7747112928 10.9791052878 11.0415908115 11.2065951033 11.2911907467 11.5221371451 11.6839515325 11.8739984964 11.9275703295 12.0305386588 12.2816628176 12.3164033346 12.3841246799 12.5225202833 12.6337017811 12.783481981 12.891130019 13.1223210202 13.1824583491 13.3100555736 13.3376605549 13.3515727286 13.4772491398 13.7071453228 13.8783567332 13.9376517876 14.0276462278 14.1674813636 14.2010493839 14.3245075202 14.6351891026 14.6421005765 14.7264095665 14.8310779475 14.9021210943 1.51842933602 2.23047412065 2.36133422204 3.10450058521 3.61330792232 3.85551540683 4.22329657414 5.04639152422 5.11720516411 5.23156860277 5.31945091149 5.59861573204 5.90447347445 6.0764219866 6.71350181149 6.84293956587 7.0596541193 7.19821130417 7.39439295726 7.55882759794 7.78622822282 8.15565536137 8.48543970333 8.51721775113 8.6823412923 8.72098116224 8.92232953917 9.00979095879 9.31426261098 9.34823014743 9.65190399311 9.67050751226 9.71661624187 9.82317475634 9.95830408326 10.2345439612 10.4123667458 10.484131488 10.6884337126 10.7330046427 10.9271780665 11.1586298115 11.315636151 11.496291685 11.5695018492 11.7600983055 11.822524358 11.9119697904 12.1105114325 12.1744371988 12.2254089157 12.3738745822 12.5653426649 12.6398086517 12.7992483012 12.8154234545 12.8261277577 12.9799547569 12.9875853926 13.4115494498 13.4427786529 13.4874424443 13.7853115737 13.8341628368 13.9846574473 14.0874463709 14.1483956487 14.2260209936 14.3430871812 14.3452711976 14.4170963473 14.5007913936 14.7541736403 14.8772261448 14.9457053184