Properties

Level $3$
Weight $0$
Character 3.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 28.8252344602 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.480228078\) \(a_{3}=+0.577350269\) \(a_{4}=+1.191075164\) \(a_{5}=+0.974251214\)
\(a_{6}=+0.854610079\) \(a_{7}=+0.546230696\) \(a_{8}=+0.282834822\) \(a_{9}=+0.333333333\) \(a_{10}=+1.442114003\)
\(a_{11}=-0.445757723\) \(a_{12}=+0.687667566\) \(a_{13}=+1.307051848\) \(a_{14}=+0.808546013\) \(a_{15}=+0.562484201\)
\(a_{16}=-0.772415118\) \(a_{17}=+1.384997143\) \(a_{18}=+0.493409359\) \(a_{19}=+0.344597416\) \(a_{20}=+1.160406425\)
\(a_{21}=+0.315366439\) \(a_{22}=-0.659823097\) \(a_{23}=-1.652425890\) \(a_{24}=+0.163294761\) \(a_{25}=-0.050834571\)
\(a_{26}=+1.934734845\) \(a_{27}=+0.192450090\) \(a_{28}=+0.650601815\) \(a_{29}=+1.966699079\) \(a_{30}=+0.832604908\)
\(a_{31}=+0.725334864\) \(a_{32}=-1.426185368\) \(a_{33}=-0.257358341\) \(a_{34}=+2.050111659\) \(a_{35}=+0.532165919\)
\(a_{36}=+0.397025055\) \(a_{37}=-0.144205825\) \(a_{38}=+0.510082770\) \(a_{39}=+0.754626736\) \(a_{40}=+0.275552169\)
\(a_{41}=-1.009300440\) \(a_{42}=+0.466814258\) \(a_{43}=-0.740973150\) \(a_{44}=-0.530930953\) \(a_{45}=+0.324750405\)
\(a_{46}=-2.445967199\) \(a_{47}=+1.551843176\) \(a_{48}=-0.445954076\) \(a_{49}=-0.701632027\) \(a_{50}=-0.075246760\)
\(a_{51}=+0.799628473\) \(a_{52}=+1.556796994\) \(a_{53}=+0.292560359\) \(a_{54}=+0.284870026\) \(a_{55}=-0.434280003\)
\(a_{56}=+0.154493062\) \(a_{57}=+0.198953411\) \(a_{58}=+2.911163198\) \(a_{59}=+0.579165710\) \(a_{60}=+0.669960962\)
\(a_{61}=-0.373008081\) \(a_{62}=+1.073661031\) \(a_{63}=+0.182076899\) \(a_{64}=-1.338664509\) \(a_{65}=+1.273396850\)
\(a_{66}=-0.380949043\) \(a_{67}=+1.248094851\) \(a_{68}=+1.649635699\) \(a_{69}=-0.954028532\) \(a_{70}=+0.787726935\)
\(a_{71}=-0.187260414\) \(a_{72}=+0.094278274\) \(a_{73}=-0.785861071\) \(a_{74}=-0.213457511\) \(a_{75}=-0.029349353\)
\(a_{76}=+0.410441423\) \(a_{77}=-0.243486551\) \(a_{78}=+1.117019683\) \(a_{79}=+1.321846989\) \(a_{80}=-0.752526367\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.493994851\) \(a_{83}=-0.451915338\) \(a_{84}=+0.375625133\) \(a_{85}=+1.349335148\)
\(a_{86}=-1.096809261\) \(a_{87}=+1.135474243\) \(a_{88}=-0.126075806\) \(a_{89}=-1.198966665\) \(a_{90}=+0.480704668\)
\(a_{91}=+0.713951840\) \(a_{92}=-1.968163437\) \(a_{93}=+0.418772279\) \(a_{94}=+2.297081842\) \(a_{95}=+0.335724451\)
\(a_{96}=-0.823408506\) \(a_{97}=-0.034500016\) \(a_{98}=-1.038575427\) \(a_{99}=-0.148585908\) \(a_{100}=-0.060547795\)

Showing 100 of 1228 available coefficients

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