Properties

Level $29$
Weight $0$
Character 29.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 29 \)
Weight: \( 0 \)
Character: 29.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 2.21489389918 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.292310980\) \(a_{3}=+0.691724278\) \(a_{4}=+0.670067669\) \(a_{5}=-0.866417292\)
\(a_{6}=+0.893922880\) \(a_{7}=+0.937031350\) \(a_{8}=-0.426375173\) \(a_{9}=-0.521517523\) \(a_{10}=-1.119680580\)
\(a_{11}=+0.583815426\) \(a_{12}=+0.463502075\) \(a_{13}=-0.349217940\) \(a_{14}=+1.210935903\) \(a_{15}=-0.599321876\)
\(a_{16}=-1.221076988\) \(a_{17}=+1.101256739\) \(a_{18}=-0.673962821\) \(a_{19}=+0.976694784\) \(a_{20}=-0.580558216\)
\(a_{21}=+0.648167335\) \(a_{22}=+0.754471086\) \(a_{23}=+1.353247908\) \(a_{24}=-0.294934059\) \(a_{25}=-0.249321075\)
\(a_{26}=-0.451298179\) \(a_{27}=-1.052470611\) \(a_{28}=+0.627874414\) \(a_{29}=+0.185695339\) \(a_{30}=-0.774510240\)
\(a_{31}=-1.762134326\) \(a_{32}=-1.151636026\) \(a_{33}=+0.403839303\) \(a_{34}=+1.423166175\) \(a_{35}=-0.811860161\)
\(a_{36}=-0.349452029\) \(a_{37}=+0.131969709\) \(a_{38}=+1.262193389\) \(a_{39}=-0.241562529\) \(a_{40}=+0.369418831\)
\(a_{41}=-1.792582742\) \(a_{42}=+0.837633764\) \(a_{43}=+0.185230832\) \(a_{44}=+0.391195827\) \(a_{45}=+0.451851807\)
\(a_{46}=+1.748817159\) \(a_{47}=+1.386179490\) \(a_{48}=-0.844648578\) \(a_{49}=-0.121972310\) \(a_{50}=-0.322200462\)
\(a_{51}=+0.761766025\) \(a_{52}=-0.233999684\) \(a_{53}=+1.325814771\) \(a_{54}=-1.360119325\) \(a_{55}=-0.505827793\)
\(a_{56}=-0.399526895\) \(a_{57}=+0.675603485\) \(a_{58}=+0.239976155\) \(a_{59}=-0.507588669\) \(a_{60}=-0.401586304\)
\(a_{61}=-1.517140733\) \(a_{62}=-2.277225516\) \(a_{63}=-0.488678281\) \(a_{64}=-0.267194870\) \(a_{65}=+0.302568486\)
\(a_{66}=+0.521885936\) \(a_{67}=-0.043488389\) \(a_{68}=+0.737916537\) \(a_{69}=+0.936074522\) \(a_{70}=-1.049175852\)
\(a_{71}=+1.574605723\) \(a_{72}=+0.222362149\) \(a_{73}=+0.014896131\) \(a_{74}=+0.170545906\) \(a_{75}=-0.172461392\)
\(a_{76}=+0.654451541\) \(a_{77}=+0.547053387\) \(a_{78}=-0.312173873\) \(a_{79}=+0.130283136\) \(a_{80}=+1.057962225\)
\(a_{81}=-0.206501936\) \(a_{82}=-2.316574383\) \(a_{83}=+0.144096543\) \(a_{84}=+0.434315977\) \(a_{85}=-0.954147856\)
\(a_{86}=+0.239375833\) \(a_{87}=+0.128450007\) \(a_{88}=-0.248924422\) \(a_{89}=+0.750902229\) \(a_{90}=+0.583933111\)
\(a_{91}=-0.327228222\) \(a_{92}=+0.906767701\) \(a_{93}=-1.218910993\) \(a_{94}=+1.791374857\) \(a_{95}=-0.846225226\)
\(a_{96}=-0.796614697\) \(a_{97}=+0.489140368\) \(a_{98}=-0.157626069\) \(a_{99}=-0.304470054\) \(a_{100}=-0.167061913\)

Showing 100 of 1500 available coefficients

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