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: \( 2.42924558709 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.036292069\) \(a_{3}=-0.976584354\) \(a_{4}=-0.998682886\) \(a_{5}=+0.352272338\)
\(a_{6}=-0.035442267\) \(a_{7}=-0.143652514\) \(a_{8}=-0.072536337\) \(a_{9}=-0.046282999\) \(a_{10}=+0.012784692\)
\(a_{11}=+0.052058127\) \(a_{12}=+0.975298081\) \(a_{13}=-0.328692559\) \(a_{14}=-0.005213447\) \(a_{15}=-0.344023654\)
\(a_{16}=+0.996050392\) \(a_{17}=-1.576952465\) \(a_{18}=-0.001679706\) \(a_{19}=-0.726580153\) \(a_{20}=-0.351808355\)
\(a_{21}=+0.140288797\) \(a_{22}=+0.001889297\) \(a_{23}=+0.532213322\) \(a_{24}=+0.070837852\) \(a_{25}=-0.875904200\)
\(a_{26}=-0.011928933\) \(a_{27}=+1.021783607\) \(a_{28}=+0.143463307\) \(a_{29}=-0.185695338\) \(a_{30}=-0.012485330\)
\(a_{31}=+1.413750179\) \(a_{32}=+0.108685065\) \(a_{33}=-0.050839152\) \(a_{34}=-0.057230867\) \(a_{35}=-0.050604806\)
\(a_{36}=+0.046222040\) \(a_{37}=+0.615378027\) \(a_{38}=-0.026369100\) \(a_{39}=+0.320996010\) \(a_{40}=-0.025552541\)
\(a_{41}=-1.683498597\) \(a_{42}=+0.005091370\) \(a_{43}=-1.159629206\) \(a_{44}=-0.051989565\) \(a_{45}=-0.016304218\)
\(a_{46}=+0.019315133\) \(a_{47}=+0.983246090\) \(a_{48}=-0.972727217\) \(a_{49}=-0.979363915\) \(a_{50}=-0.031788358\)
\(a_{51}=+1.540027069\) \(a_{52}=+0.328259580\) \(a_{53}=-0.663727632\) \(a_{54}=+0.037082719\) \(a_{55}=+0.018338633\)
\(a_{56}=+0.010420026\) \(a_{57}=+0.709566811\) \(a_{58}=-0.006739271\) \(a_{59}=-1.134926055\) \(a_{60}=+0.343570508\)
\(a_{61}=+0.505356587\) \(a_{62}=+0.051307912\) \(a_{63}=+0.006648705\) \(a_{64}=-0.992106014\) \(a_{65}=-0.115789295\)
\(a_{66}=-0.001845056\) \(a_{67}=+1.003664360\) \(a_{68}=+1.574875447\) \(a_{69}=-0.519751216\) \(a_{70}=-0.001836459\)
\(a_{71}=-0.304279120\) \(a_{72}=+0.003357328\) \(a_{73}=+1.109450784\) \(a_{74}=+0.022333242\) \(a_{75}=+0.855394426\)
\(a_{76}=+0.725623117\) \(a_{77}=-0.007478236\) \(a_{78}=+0.011649693\) \(a_{79}=-0.895196585\) \(a_{80}=+0.350880996\)
\(a_{81}=-0.951574936\) \(a_{82}=-0.061097600\) \(a_{83}=-1.676789636\) \(a_{84}=-0.140103961\) \(a_{85}=-0.555516683\)
\(a_{86}=-0.042085432\) \(a_{87}=+0.181347172\) \(a_{88}=-0.003776207\) \(a_{89}=-0.238105840\) \(a_{90}=-0.000591718\)
\(a_{91}=+0.047217601\) \(a_{92}=-0.531512239\) \(a_{93}=-1.380646300\) \(a_{94}=+0.035684081\) \(a_{95}=-0.255954054\)
\(a_{96}=-0.106140162\) \(a_{97}=+0.932812194\) \(a_{98}=-0.035543231\) \(a_{99}=-0.002409437\) \(a_{100}=+0.874750603\)

Showing 100 of 1500 available coefficients

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