Properties

Level $23$
Weight $0$
Character 23.1
Symmetry odd
Fricke sign $+1$

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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

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