# Properties

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

# Related objects

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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