Maass form of level 23 with the smallest eigenvalue, and also the smallest prime level where the first Maass form has eigenvalue +1 under the Fricke involution.
Maass form invariants
| Level: | \( 23 \) |
| Weight: | \( 0 \) |
| Character: | 23.1 |
| Symmetry: | odd |
| Fricke sign: | $+1$ |
| Spectral parameter: | \( 1.39333714148 \) |
Maass form coefficients
| \(a_{1}=+1.000000000\) | \(a_{2}=-1.632260331\) | \(a_{3}=-1.432812210\) | \(a_{4}=+1.664273789\) | \(a_{5}=-0.018075235\) |
| \(a_{6}=+2.338722532\) | \(a_{7}=-1.089115323\) | \(a_{8}=-1.084267756\) | \(a_{9}=+1.052950829\) | \(a_{10}=+0.029503489\) |
| \(a_{11}=-0.917932960\) | \(a_{12}=-2.384591806\) | \(a_{13}=+0.455515802\) | \(a_{14}=+1.777719739\) | \(a_{15}=+0.025898417\) |
| \(a_{16}=+0.105533457\) | \(a_{17}=-0.604999286\) | \(a_{18}=-1.718689868\) | \(a_{19}=+0.998699642\) | \(a_{20}=-0.030082140\) |
| \(a_{21}=+1.560497733\) | \(a_{22}=+1.498305557\) | \(a_{23}=-0.208514414\) | \(a_{24}=+1.553552079\) | \(a_{25}=-0.999673286\) |
| \(a_{26}=-0.743520374\) | \(a_{27}=-0.075868594\) | \(a_{28}=-1.812586086\) | \(a_{29}=-1.135014620\) | \(a_{30}=-0.042272959\) |
| \(a_{31}=-1.075677403\) | \(a_{32}=+0.912009681\) | \(a_{33}=+1.315225553\) | \(a_{34}=+0.987516335\) | \(a_{35}=+0.019686015\) |
| \(a_{36}=+1.752398466\) | \(a_{37}=-0.151653364\) | \(a_{38}=-1.630137809\) | \(a_{39}=-0.652668603\) | \(a_{40}=+0.019598394\) |
| \(a_{41}=+1.051555904\) | \(a_{42}=-2.547138547\) | \(a_{43}=+1.317634170\) | \(a_{44}=-1.527691765\) | \(a_{45}=-0.019032334\) |
| \(a_{46}=+0.340349807\) | \(a_{47}=-0.691488166\) | \(a_{48}=-0.151209625\) | \(a_{49}=+0.186172188\) | \(a_{50}=+1.631727049\) |
| \(a_{51}=+0.866850364\) | \(a_{52}=+0.758103010\) | \(a_{53}=-0.498097491\) | \(a_{54}=+0.123837296\) | \(a_{55}=+0.016591854\) |
| \(a_{56}=+1.180892627\) | \(a_{57}=-1.430949042\) | \(a_{58}=+1.852639339\) | \(a_{59}=+0.258248845\) | \(a_{60}=+0.043102057\) |
| \(a_{61}=+0.249652429\) | \(a_{62}=+1.755785554\) | \(a_{63}=-1.146784882\) | \(a_{64}=-1.594170680\) | \(a_{65}=-0.008233555\) |
| \(a_{66}=-2.146790496\) | \(a_{67}=-0.333498944\) | \(a_{68}=-1.006884454\) | \(a_{69}=+0.298761998\) | \(a_{70}=-0.032132702\) |
| \(a_{71}=-1.218011574\) | \(a_{72}=-1.141680632\) | \(a_{73}=-1.297050356\) | \(a_{74}=+0.247537770\) | \(a_{75}=+1.432344090\) |
| \(a_{76}=+1.662109638\) | \(a_{77}=+0.999734852\) | \(a_{78}=+1.065325070\) | \(a_{79}=-0.670843746\) | \(a_{80}=-0.001907542\) |
| \(a_{81}=-0.944245381\) | \(a_{82}=-1.716412989\) | \(a_{83}=+0.831844640\) | \(a_{84}=+2.597095476\) | \(a_{85}=+0.010935504\) |
| \(a_{86}=-2.150721987\) | \(a_{87}=+1.626262806\) | \(a_{88}=+0.995285110\) | \(a_{89}=+1.239208773\) | \(a_{90}=+0.031065723\) |
| \(a_{91}=-0.496109240\) | \(a_{92}=-0.347025074\) | \(a_{93}=+1.541243717\) | \(a_{94}=+1.128688703\) | \(a_{95}=-0.018051731\) |
| \(a_{96}=-1.306738606\) | \(a_{97}=+0.720571825\) | \(a_{98}=-0.303881477\) | \(a_{99}=-0.966538271\) | \(a_{100}=-1.663730048\) |
Showing 100 of 546 available coefficients