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: \( 25.6139927372 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.588408407\) \(a_{3}=+0.577350269\) \(a_{4}=+1.523041267\) \(a_{5}=+1.577825480\)
\(a_{6}=+0.917068021\) \(a_{7}=+1.300891491\) \(a_{8}=+0.830803146\) \(a_{9}=+0.333333333\) \(a_{10}=+2.506231257\)
\(a_{11}=+0.263850322\) \(a_{12}=+0.879328286\) \(a_{13}=-0.125928147\) \(a_{14}=+2.066346982\) \(a_{15}=+0.910957966\)
\(a_{16}=-0.203386565\) \(a_{17}=-1.622932523\) \(a_{18}=+0.529469469\) \(a_{19}=-0.996461805\) \(a_{20}=+2.403093319\)
\(a_{21}=+0.751070053\) \(a_{22}=+0.419102070\) \(a_{23}=+0.689567259\) \(a_{24}=+0.479664420\) \(a_{25}=+1.489533245\)
\(a_{26}=-0.200025327\) \(a_{27}=+0.192450090\) \(a_{28}=+1.981311426\) \(a_{29}=-0.484255662\) \(a_{30}=+1.446973291\)
\(a_{31}=-0.323715129\) \(a_{32}=-1.153864076\) \(a_{33}=+0.152334055\) \(a_{34}=-2.577879664\) \(a_{35}=+2.052579742\)
\(a_{36}=+0.507680422\) \(a_{37}=-0.973666952\) \(a_{38}=-1.582788308\) \(a_{39}=-0.072704649\) \(a_{40}=+1.310862373\)
\(a_{41}=+1.310313722\) \(a_{42}=+1.193005986\) \(a_{43}=-0.406853884\) \(a_{44}=+0.401854929\) \(a_{45}=+0.525941827\)
\(a_{46}=+1.095314431\) \(a_{47}=+0.465565969\) \(a_{48}=-0.117425288\) \(a_{49}=+0.692318672\) \(a_{50}=+2.365987129\)
\(a_{51}=-0.937000529\) \(a_{52}=-0.191793764\) \(a_{53}=+0.350314873\) \(a_{54}=+0.305689340\) \(a_{55}=+0.416309761\)
\(a_{56}=+1.080784744\) \(a_{57}=-0.575307491\) \(a_{58}=-0.769195765\) \(a_{59}=-1.008277201\) \(a_{60}=+1.387426574\)
\(a_{61}=+1.899253780\) \(a_{62}=-0.514191832\) \(a_{63}=+0.433630497\) \(a_{64}=-1.629420834\) \(a_{65}=-0.198692638\)
\(a_{66}=+0.241968693\) \(a_{67}=+0.947217723\) \(a_{68}=-2.471793207\) \(a_{69}=+0.398121842\) \(a_{70}=+3.260334918\)
\(a_{71}=-1.063150117\) \(a_{72}=+0.276934382\) \(a_{73}=+0.329229740\) \(a_{74}=-1.546580773\) \(a_{75}=+0.859982420\)
\(a_{76}=-1.517652451\) \(a_{77}=+0.343240639\) \(a_{78}=-0.115484676\) \(a_{79}=+0.277193815\) \(a_{80}=-0.320908505\)
\(a_{81}=+0.111111111\) \(a_{82}=+2.081313332\) \(a_{83}=-0.048919589\) \(a_{84}=+1.143910685\) \(a_{85}=-2.560704287\)
\(a_{86}=-0.646250130\) \(a_{87}=-0.279585137\) \(a_{88}=+0.219207678\) \(a_{89}=-0.177367379\) \(a_{90}=+0.835410419\)
\(a_{91}=-0.163818854\) \(a_{92}=+1.050239392\) \(a_{93}=-0.186897017\) \(a_{94}=+0.739508900\) \(a_{95}=-1.572242826\)
\(a_{96}=-0.666183735\) \(a_{97}=-0.215183704\) \(a_{98}=+1.099684800\) \(a_{99}=+0.087950107\) \(a_{100}=+2.268620601\)

Showing 100 of 1228 available coefficients

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