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: \( 22.1003136006 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.441822751\) \(a_{3}=-0.577350269\) \(a_{4}=-0.804792656\) \(a_{5}=-1.739703489\)
\(a_{6}=+0.255086484\) \(a_{7}=+1.156707933\) \(a_{8}=+0.797398457\) \(a_{9}=+0.333333333\) \(a_{10}=+0.768640582\)
\(a_{11}=+0.533507504\) \(a_{12}=+0.464647257\) \(a_{13}=-0.323289830\) \(a_{14}=-0.511059882\) \(a_{15}=+1.004418278\)
\(a_{16}=+0.452483876\) \(a_{17}=+1.037360734\) \(a_{18}=-0.147274250\) \(a_{19}=-1.443483378\) \(a_{20}=+1.400100593\)
\(a_{21}=-0.667825637\) \(a_{22}=-0.235715753\) \(a_{23}=+0.907075311\) \(a_{24}=-0.460378214\) \(a_{25}=+2.026568230\)
\(a_{26}=+0.142836802\) \(a_{27}=-0.192450090\) \(a_{28}=-0.930910050\) \(a_{29}=+0.070016687\) \(a_{30}=-0.443774847\)
\(a_{31}=-0.302971229\) \(a_{32}=-0.997316128\) \(a_{33}=-0.308020701\) \(a_{34}=-0.458329574\) \(a_{35}=-2.012328828\)
\(a_{36}=-0.268264219\) \(a_{37}=-0.350488388\) \(a_{38}=+0.637763798\) \(a_{39}=+0.186651470\) \(a_{40}=-1.387236878\)
\(a_{41}=-0.902332197\) \(a_{42}=+0.295060560\) \(a_{43}=+0.424209862\) \(a_{44}=-0.429362922\) \(a_{45}=-0.579901163\)
\(a_{46}=-0.400766509\) \(a_{47}=+1.458982072\) \(a_{48}=-0.261241688\) \(a_{49}=+0.337973243\) \(a_{50}=-0.895383951\)
\(a_{51}=-0.598920499\) \(a_{52}=+0.260181281\) \(a_{53}=+0.185527101\) \(a_{54}=+0.085028828\) \(a_{55}=-0.928144867\)
\(a_{56}=+0.922357121\) \(a_{57}=+0.833395517\) \(a_{58}=-0.030934965\) \(a_{59}=+0.376696403\) \(a_{60}=-0.808348454\)
\(a_{61}=-1.392063669\) \(a_{62}=+0.133859582\) \(a_{63}=+0.385569311\) \(a_{64}=-0.011846921\) \(a_{65}=+0.562428445\)
\(a_{66}=+0.136090554\) \(a_{67}=+0.990420631\) \(a_{68}=-0.834860301\) \(a_{69}=-0.523700175\) \(a_{70}=+0.889092659\)
\(a_{71}=-0.616454263\) \(a_{72}=+0.265799486\) \(a_{73}=-0.831268793\) \(a_{74}=+0.154853744\) \(a_{75}=-1.170039713\)
\(a_{76}=+1.161704823\) \(a_{77}=+0.617112363\) \(a_{78}=-0.082466866\) \(a_{79}=+0.692396087\) \(a_{80}=-0.787187779\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.398670894\) \(a_{83}=-0.128538114\) \(a_{84}=+0.537461168\) \(a_{85}=-1.804700089\)
\(a_{86}=-0.187425568\) \(a_{87}=-0.040424153\) \(a_{88}=+0.425418061\) \(a_{89}=+0.924357132\) \(a_{90}=+0.256213527\)
\(a_{91}=-0.373951911\) \(a_{92}=-0.730007549\) \(a_{93}=+0.174920521\) \(a_{94}=-0.644611473\) \(a_{95}=+2.511233070\)
\(a_{96}=+0.575800735\) \(a_{97}=-1.575646445\) \(a_{98}=-0.149324268\) \(a_{99}=+0.177835835\) \(a_{100}=-1.630967230\)

Showing 100 of 1228 available coefficients

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