Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 29.380289315 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.907239476\) \(a_{3}=-0.577350269\) \(a_{4}=+2.637562418\) \(a_{5}=-0.967631673\)
\(a_{6}=+1.101145225\) \(a_{7}=-0.277899588\) \(a_{8}=-3.123223687\) \(a_{9}=+0.333333333\) \(a_{10}=+1.845505325\)
\(a_{11}=-1.333069453\) \(a_{12}=-1.522797372\) \(a_{13}=+0.696222859\) \(a_{14}=+0.530021065\) \(a_{15}=+0.558662407\)
\(a_{16}=+3.319173089\) \(a_{17}=+1.237039354\) \(a_{18}=-0.635746492\) \(a_{19}=+0.216498136\) \(a_{20}=-2.552188936\)
\(a_{21}=+0.160445402\) \(a_{22}=+2.542482685\) \(a_{23}=-1.455612329\) \(a_{24}=+1.803194036\) \(a_{25}=-0.063688945\)
\(a_{26}=-1.327863721\) \(a_{27}=-0.192450090\) \(a_{28}=-0.732977510\) \(a_{29}=-0.666976618\) \(a_{30}=-1.065502996\)
\(a_{31}=-0.660226373\) \(a_{32}=-3.207234256\) \(a_{33}=+0.769648008\) \(a_{34}=-2.359330290\) \(a_{35}=+0.268904444\)
\(a_{36}=+0.879187473\) \(a_{37}=-1.287240622\) \(a_{38}=-0.412913792\) \(a_{39}=-0.401964455\) \(a_{40}=+3.022130162\)
\(a_{41}=-0.327233339\) \(a_{42}=-0.306007805\) \(a_{43}=+0.266614418\) \(a_{44}=-3.516053889\) \(a_{45}=-0.322543891\)
\(a_{46}=+2.776201296\) \(a_{47}=-0.150571235\) \(a_{48}=-1.916325477\) \(a_{49}=-0.922771819\) \(a_{50}=+0.121470069\)
\(a_{51}=-0.714205004\) \(a_{52}=+1.836331247\) \(a_{53}=-0.922475073\) \(a_{54}=+0.367048408\) \(a_{55}=+1.289920226\)
\(a_{56}=+0.867942577\) \(a_{57}=-0.124995257\) \(a_{58}=+1.272084135\) \(a_{59}=-0.657060668\) \(a_{60}=+1.473506969\)
\(a_{61}=-0.187540448\) \(a_{62}=+1.259209802\) \(a_{63}=-0.092633196\) \(a_{64}=+2.797790691\) \(a_{65}=-0.673687290\)
\(a_{66}=-1.467903062\) \(a_{67}=-0.274540823\) \(a_{68}=+3.262768510\) \(a_{69}=+0.840398170\) \(a_{70}=-0.512865170\)
\(a_{71}=-0.368096889\) \(a_{72}=-1.041074562\) \(a_{73}=-1.275445041\) \(a_{74}=+2.455076129\) \(a_{75}=+0.036770829\)
\(a_{76}=+0.571027348\) \(a_{77}=+0.370459452\) \(a_{78}=+0.766642477\) \(a_{79}=+0.755616471\) \(a_{80}=-3.211737011\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.624112341\) \(a_{83}=+0.377297292\) \(a_{84}=+0.423184763\) \(a_{85}=-1.196998461\)
\(a_{86}=-0.508497543\) \(a_{87}=+0.385079130\) \(a_{88}=+4.163474092\) \(a_{89}=-1.686284903\) \(a_{90}=+0.615168442\)
\(a_{91}=-0.193480046\) \(a_{92}=-3.839268374\) \(a_{93}=+0.381181874\) \(a_{94}=+0.287175404\) \(a_{95}=-0.209490454\)
\(a_{96}=+1.851697561\) \(a_{97}=-0.331911574\) \(a_{98}=+1.759946840\) \(a_{99}=-0.444356484\) \(a_{100}=-0.167983567\)

Showing 100 of 1228 available coefficients

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