Properties

Level $449$
Weight $0$
Character 449.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 449 \)
Weight: \( 0 \)
Character: 449.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.52122324113 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.730685762\) \(a_{3}=+0.589103339\) \(a_{4}=+1.995273183\) \(a_{5}=+0.567574369\)
\(a_{6}=-1.019552784\) \(a_{7}=+0.365196049\) \(a_{8}=-1.722505042\) \(a_{9}=-0.652957277\) \(a_{10}=-0.982292867\)
\(a_{11}=+0.957017027\) \(a_{12}=+1.175422127\) \(a_{13}=-1.349480049\) \(a_{14}=-0.632039571\) \(a_{15}=+0.334359984\)
\(a_{16}=+0.985841736\) \(a_{17}=-0.602094221\) \(a_{18}=+1.130063831\) \(a_{19}=-0.043268496\) \(a_{20}=+1.132465933\)
\(a_{21}=+0.215138220\) \(a_{22}=-1.656295767\) \(a_{23}=+1.630310408\) \(a_{24}=-1.014733486\) \(a_{25}=-0.677859353\)
\(a_{26}=+2.335525893\) \(a_{27}=-0.973762699\) \(a_{28}=+0.728665833\) \(a_{29}=+0.617169368\) \(a_{30}=-0.578672043\)
\(a_{31}=+1.443551797\) \(a_{32}=+0.016322778\) \(a_{33}=+0.563781941\) \(a_{34}=+1.042035892\) \(a_{35}=+0.207275922\)
\(a_{36}=-1.302828074\) \(a_{37}=-0.944529341\) \(a_{38}=+0.074884087\) \(a_{39}=-0.794983170\) \(a_{40}=-0.977649720\)
\(a_{41}=-0.565849846\) \(a_{42}=-0.372336601\) \(a_{43}=-1.738505862\) \(a_{44}=+1.909510426\) \(a_{45}=-0.370601775\)
\(a_{46}=-2.821554966\) \(a_{47}=+0.139764175\) \(a_{48}=+0.580762658\) \(a_{49}=-0.866631860\) \(a_{50}=+1.173161476\)
\(a_{51}=-0.354695702\) \(a_{52}=-2.692581306\) \(a_{53}=-0.839692963\) \(a_{54}=+1.685277137\) \(a_{55}=+0.543178353\)
\(a_{56}=-0.629051995\) \(a_{57}=-0.025489611\) \(a_{58}=-1.068126196\) \(a_{59}=-0.090461125\) \(a_{60}=+0.667139446\)
\(a_{61}=+1.435471965\) \(a_{62}=-2.498334503\) \(a_{63}=-0.238457391\) \(a_{64}=-1.014091378\) \(a_{65}=-0.765930310\)
\(a_{66}=-0.975729375\) \(a_{67}=+1.927580911\) \(a_{68}=-1.201342454\) \(a_{69}=+0.960421338\) \(a_{70}=-0.358729492\)
\(a_{71}=-1.201314689\) \(a_{72}=+1.124722192\) \(a_{73}=-1.741309878\) \(a_{74}=+1.634683492\) \(a_{75}=-0.399329199\)
\(a_{76}=-0.086332402\) \(a_{77}=+0.349498854\) \(a_{78}=+1.375866079\) \(a_{79}=-1.215115351\) \(a_{80}=+0.559538528\)
\(a_{81}=+0.079310441\) \(a_{82}=+0.979308148\) \(a_{83}=+0.205899328\) \(a_{84}=+0.429259435\) \(a_{85}=-0.341733195\)
\(a_{86}=+3.008807237\) \(a_{87}=+0.363576572\) \(a_{88}=-1.648466696\) \(a_{89}=+0.977416186\) \(a_{90}=+0.641395279\)
\(a_{91}=-0.492824752\) \(a_{92}=+3.252914455\) \(a_{93}=+0.850401164\) \(a_{94}=-0.241887812\) \(a_{95}=-0.024558038\)
\(a_{96}=+0.009615735\) \(a_{97}=+1.177095884\) \(a_{98}=+1.499867405\) \(a_{99}=-0.624891144\) \(a_{100}=-1.352514596\)

Showing 100 of 1380 available coefficients

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