Properties

Level $293$
Weight $0$
Character 293.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 293 \)
Weight: \( 0 \)
Character: 293.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.274912467168 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.228532970\) \(a_{3}=+0.032513601\) \(a_{4}=-0.947772682\) \(a_{5}=+1.093720685\)
\(a_{6}=-0.007430428\) \(a_{7}=-0.404122435\) \(a_{8}=+0.445130277\) \(a_{9}=-0.998942866\) \(a_{10}=-0.249951237\)
\(a_{11}=-1.162114378\) \(a_{12}=-0.030815504\) \(a_{13}=+0.527520626\) \(a_{14}=+0.092355298\) \(a_{15}=+0.035560799\)
\(a_{16}=+0.846045741\) \(a_{17}=+0.404780064\) \(a_{18}=+0.228291380\) \(a_{19}=-0.590758128\) \(a_{20}=-1.036598587\)
\(a_{21}=-0.013139475\) \(a_{22}=+0.265581449\) \(a_{23}=-1.612496620\) \(a_{24}=+0.014472784\) \(a_{25}=+0.196224937\)
\(a_{26}=-0.120555853\) \(a_{27}=-0.064992828\) \(a_{28}=+0.383016198\) \(a_{29}=-0.816417900\) \(a_{30}=-0.008126817\)
\(a_{31}=-0.776992090\) \(a_{32}=-0.638479621\) \(a_{33}=-0.037784521\) \(a_{34}=-0.092505593\) \(a_{35}=-0.441997063\)
\(a_{36}=+0.946770757\) \(a_{37}=+0.770445049\) \(a_{38}=+0.135007712\) \(a_{39}=+0.017151591\) \(a_{40}=+0.486848197\)
\(a_{41}=+0.828368398\) \(a_{42}=+0.003002811\) \(a_{43}=+1.349597579\) \(a_{44}=+1.101420262\) \(a_{45}=-1.092564481\)
\(a_{46}=+0.368508644\) \(a_{47}=+1.529195945\) \(a_{48}=+0.027507991\) \(a_{49}=-0.836685056\) \(a_{50}=-0.044843874\)
\(a_{51}=+0.013160854\) \(a_{52}=-0.499969624\) \(a_{53}=+1.486087593\) \(a_{54}=+0.014853002\) \(a_{55}=-1.271028527\)
\(a_{56}=-0.179887138\) \(a_{57}=-0.019207681\) \(a_{58}=+0.186578409\) \(a_{59}=-0.179195627\) \(a_{60}=-0.033703553\)
\(a_{61}=-0.020355445\) \(a_{62}=+0.177568311\) \(a_{63}=+0.403695223\) \(a_{64}=-0.700132095\) \(a_{65}=+0.576960214\)
\(a_{66}=+0.008635011\) \(a_{67}=+1.722040754\) \(a_{68}=-0.383639479\) \(a_{69}=-0.052428076\) \(a_{70}=+0.101010904\)
\(a_{71}=+0.595636019\) \(a_{72}=-0.444659707\) \(a_{73}=+0.064300477\) \(a_{74}=-0.176072101\) \(a_{75}=+0.006379986\)
\(a_{76}=+0.559904398\) \(a_{77}=+0.469636490\) \(a_{78}=-0.003919706\) \(a_{79}=-1.789355803\) \(a_{80}=+0.925337726\)
\(a_{81}=+0.996829732\) \(a_{82}=-0.189309491\) \(a_{83}=-1.413997460\) \(a_{84}=+0.012453242\) \(a_{85}=+0.442716309\)
\(a_{86}=-0.308427549\) \(a_{87}=-0.026544679\) \(a_{88}=-0.517292306\) \(a_{89}=+0.341744707\) \(a_{90}=+0.249687007\)
\(a_{91}=-0.213182902\) \(a_{92}=+1.528280239\) \(a_{93}=-0.025262804\) \(a_{94}=-0.349471698\) \(a_{95}=-0.646124398\)
\(a_{96}=-0.020759280\) \(a_{97}=-0.862482187\) \(a_{98}=+0.191210136\) \(a_{99}=+1.160885851\) \(a_{100}=-0.185976603\)

Showing 100 of 976 available coefficients

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