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Maass forms of levels 1 to 10 with $0 \leq R\leq 10$

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 1 3 5 7 9 Level R 9.53369526135 8.92287648699 5.41733480684 7.22087197596 8.27366588959 5.09874190873 8.03886120386 8.77828239355 9.74374939916 4.38805356322 6.12057553309 6.75741527775 7.75813319502 8.19303593168 9.29237932822 5.87935415776 8.04247759169 3.70330780122 6.62042287384 8.52250301688 9.93491995937 4.13240421506 5.43618046142 6.05402838077 6.82352699542 7.98654905098 8.29469778357 8.4800158394 9.27729778527 9.39741755066 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 3.84467228501 6.00033540888 6.30636358623 6.87436376055 7.38627450582 7.90114750377 9.65240704243 9.66046617807 2.59237977171 3.3088170303 4.54845492142 5.8716820925 7.15749058532 8.66395307858 8.81974775988 9.37443036553 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 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 3.24997696354 4.64659164296 5.62812092942 6.58769285315 7.22656906706 7.69684780643 8.21171118246 9.01322849206 9.4700831342 9.9039777038 2.42505682709 4.36801954023 4.94783167713 6.22318082532 6.32531406199 7.48301811751 7.74444773702 8.55288032905 9.00120580965 9.19652685256 9.81001812133 3.53600209294 5.50405667968 6.64658135561 7.43179917172 8.69834295647 9.0800693497 3.53600209294 5.50405667968 6.64658135561 7.43179917172 8.69834295647 9.08006934969 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 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