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: \( 0.697197476625 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.124276953\) \(a_{3}=-0.140759901\) \(a_{4}=+0.263998673\) \(a_{5}=-0.723687912\)
\(a_{6}=-0.158253115\) \(a_{7}=+0.629849744\) \(a_{8}=-0.827469335\) \(a_{9}=-0.980186656\) \(a_{10}=-0.813625641\)
\(a_{11}=+0.531456101\) \(a_{12}=-0.037160418\) \(a_{13}=+0.156983613\) \(a_{14}=+0.708125550\) \(a_{15}=+0.101866243\)
\(a_{16}=-1.194303381\) \(a_{17}=-0.581581236\) \(a_{18}=-1.102001270\) \(a_{19}=+0.819114151\) \(a_{20}=-0.191052650\)
\(a_{21}=-0.088657590\) \(a_{22}=+0.597503846\) \(a_{23}=+1.136740370\) \(a_{24}=+0.116474511\) \(a_{25}=-0.476275813\)
\(a_{26}=+0.176493059\) \(a_{27}=+0.278730878\) \(a_{28}=+0.166279500\) \(a_{29}=+1.096197359\) \(a_{30}=+0.114525867\)
\(a_{31}=-0.529307296\) \(a_{32}=-0.515258432\) \(a_{33}=-0.074807704\) \(a_{34}=-0.653858384\) \(a_{35}=-0.455814645\)
\(a_{36}=-0.258767974\) \(a_{37}=-0.967345449\) \(a_{38}=+0.920911164\) \(a_{39}=-0.022097003\) \(a_{40}=+0.598829552\)
\(a_{41}=+0.569130466\) \(a_{42}=-0.099675686\) \(a_{43}=+1.657017725\) \(a_{44}=+0.140303713\) \(a_{45}=+0.709349230\)
\(a_{46}=+1.278010991\) \(a_{47}=-0.226578584\) \(a_{48}=+0.168110017\) \(a_{49}=-0.603289309\) \(a_{50}=-0.535465913\)
\(a_{51}=+0.081863325\) \(a_{52}=+0.041443457\) \(a_{53}=+0.903851439\) \(a_{54}=+0.313370705\) \(a_{55}=-0.384608351\)
\(a_{56}=-0.521181326\) \(a_{57}=-0.115298431\) \(a_{58}=+1.232429434\) \(a_{59}=+1.406900642\) \(a_{60}=+0.026892540\)
\(a_{61}=-1.162097097\) \(a_{62}=-0.595088000\) \(a_{63}=-0.617370304\) \(a_{64}=+0.615010196\) \(a_{65}=-0.113607143\)
\(a_{66}=-0.084104582\) \(a_{67}=-1.001577172\) \(a_{68}=-0.153536675\) \(a_{69}=-0.160007466\) \(a_{70}=-0.512461899\)
\(a_{71}=-1.495060159\) \(a_{72}=+0.811074393\) \(a_{73}=+0.071889746\) \(a_{74}=-1.087564197\) \(a_{75}=+0.067040552\)
\(a_{76}=+0.216245042\) \(a_{77}=+0.334737482\) \(a_{78}=-0.024843138\) \(a_{79}=-0.728052102\) \(a_{80}=+0.864302918\)
\(a_{81}=+0.940952523\) \(a_{82}=+0.639860278\) \(a_{83}=+0.182826912\) \(a_{84}=-0.023405490\) \(a_{85}=+0.420883308\)
\(a_{86}=+1.862946858\) \(a_{87}=-0.154300641\) \(a_{88}=-0.439763613\) \(a_{89}=-0.392029933\) \(a_{90}=+0.797504995\)
\(a_{91}=+0.098876092\) \(a_{92}=+0.300097944\) \(a_{93}=+0.074505237\) \(a_{94}=-0.254737088\) \(a_{95}=-0.592783002\)
\(a_{96}=+0.072527715\) \(a_{97}=+0.933294172\) \(a_{98}=-0.678264269\) \(a_{99}=-0.520926164\) \(a_{100}=-0.125736168\)

Showing 100 of 990 available coefficients

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